id	sid	tid	token	lemma	pos
ejpam-3501	1	1	european	european	PROPN
ejpam-3501	1	2	journal	journal	PROPN
ejpam-3501	1	3	of	of	ADP
ejpam-3501	1	4	pure	pure	ADJ
ejpam-3501	1	5	and	and	CCONJ
ejpam-3501	1	6	applied	apply	VERB
ejpam-3501	1	7	mathematics	mathematic	NOUN
ejpam-3501	1	8	vol	vol	NOUN
ejpam-3501	1	9	.	.	PROPN
ejpam-3501	2	1	12	12	NUM
ejpam-3501	2	2	,	,	PUNCT
ejpam-3501	2	3	no	no	INTJ
ejpam-3501	2	4	.	.	NOUN
ejpam-3501	2	5	4	4	NUM
ejpam-3501	2	6	,	,	PUNCT
ejpam-3501	2	7	2019	2019	NUM
ejpam-3501	2	8	,	,	PUNCT
ejpam-3501	2	9	1410	1410	NUM
ejpam-3501	2	10	-	-	SYM
ejpam-3501	2	11	1425	1425	NUM
ejpam-3501	2	12	issn	issn	PROPN
ejpam-3501	2	13	1307	1307	NUM
ejpam-3501	2	14	-	-	SYM
ejpam-3501	2	15	5543	5543	NUM
ejpam-3501	2	16	–	–	PUNCT
ejpam-3501	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3501	2	18	published	publish	VERB
ejpam-3501	2	19	by	by	ADP
ejpam-3501	2	20	new	new	PROPN
ejpam-3501	2	21	york	york	PROPN
ejpam-3501	2	22	business	business	PROPN
ejpam-3501	2	23	global	global	PROPN
ejpam-3501	2	24	on	on	ADP
ejpam-3501	2	25	semitotal	semitotal	ADJ
ejpam-3501	2	26	domination	domination	NOUN
ejpam-3501	2	27	in	in	ADP
ejpam-3501	2	28	graphs	graph	NOUN
ejpam-3501	2	29	imelda	imelda	PROPN
ejpam-3501	2	30	s.	s.	PROPN
ejpam-3501	2	31	aniversario1,2	aniversario1,2	PROPN
ejpam-3501	2	32	,	,	PUNCT
ejpam-3501	3	1	sergio	sergio	PROPN
ejpam-3501	3	2	r.	r.	PROPN
ejpam-3501	3	3	canoy	canoy	PROPN
ejpam-3501	3	4	jr.1,2	jr.1,2	PROPN
ejpam-3501	3	5	,	,	PUNCT
ejpam-3501	3	6	ferdinand	ferdinand	PROPN
ejpam-3501	3	7	p.	p.	PROPN
ejpam-3501	3	8	jamil1,2,∗	jamil1,2,∗	PROPN
ejpam-3501	4	1	1	1	NUM
ejpam-3501	4	2	department	department	NOUN
ejpam-3501	4	3	of	of	ADP
ejpam-3501	4	4	mathematics	mathematic	NOUN
ejpam-3501	4	5	and	and	CCONJ
ejpam-3501	4	6	statistics	statistic	NOUN
ejpam-3501	4	7	,	,	PUNCT
ejpam-3501	4	8	college	college	NOUN
ejpam-3501	4	9	of	of	ADP
ejpam-3501	4	10	science	science	NOUN
ejpam-3501	4	11	and	and	CCONJ
ejpam-3501	4	12	mathematics	mathematic	NOUN
ejpam-3501	4	13	,	,	PUNCT
ejpam-3501	4	14	mindanao	mindanao	PROPN
ejpam-3501	4	15	state	state	PROPN
ejpam-3501	4	16	university	university	PROPN
ejpam-3501	4	17	-	-	PUNCT
ejpam-3501	4	18	iligan	iligan	PROPN
ejpam-3501	4	19	institute	institute	PROPN
ejpam-3501	4	20	of	of	ADP
ejpam-3501	4	21	technology	technology	PROPN
ejpam-3501	4	22	,	,	PUNCT
ejpam-3501	4	23	9200	9200	NUM
ejpam-3501	4	24	iligan	iligan	ADJ
ejpam-3501	4	25	city	city	NOUN
ejpam-3501	4	26	,	,	PUNCT
ejpam-3501	4	27	philippines	philippine	NOUN
ejpam-3501	4	28	2	2	NUM
ejpam-3501	4	29	center	center	NOUN
ejpam-3501	4	30	for	for	ADP
ejpam-3501	4	31	graph	graph	NOUN
ejpam-3501	4	32	theory	theory	NOUN
ejpam-3501	4	33	,	,	PUNCT
ejpam-3501	4	34	algebra	algebra	NOUN
ejpam-3501	4	35	and	and	CCONJ
ejpam-3501	4	36	analysis	analysis	NOUN
ejpam-3501	4	37	,	,	PUNCT
ejpam-3501	4	38	premier	premier	PROPN
ejpam-3501	4	39	research	research	PROPN
ejpam-3501	4	40	institute	institute	PROPN
ejpam-3501	4	41	of	of	ADP
ejpam-3501	4	42	science	science	NOUN
ejpam-3501	4	43	and	and	CCONJ
ejpam-3501	4	44	mathematics	mathematics	PROPN
ejpam-3501	4	45	(	(	PUNCT
ejpam-3501	4	46	prism	prism	NOUN
ejpam-3501	4	47	)	)	PUNCT
ejpam-3501	4	48	,	,	PUNCT
ejpam-3501	4	49	mindanao	mindanao	PROPN
ejpam-3501	4	50	state	state	PROPN
ejpam-3501	4	51	university	university	PROPN
ejpam-3501	4	52	-	-	PUNCT
ejpam-3501	4	53	iligan	iligan	PROPN
ejpam-3501	4	54	institute	institute	PROPN
ejpam-3501	4	55	of	of	ADP
ejpam-3501	4	56	technology	technology	PROPN
ejpam-3501	4	57	,	,	PUNCT
ejpam-3501	4	58	9200	9200	NUM
ejpam-3501	4	59	iligan	iligan	ADJ
ejpam-3501	4	60	city	city	NOUN
ejpam-3501	4	61	,	,	PUNCT
ejpam-3501	4	62	philippines	philippine	NOUN
ejpam-3501	4	63	abstract	abstract	ADJ
ejpam-3501	4	64	.	.	PUNCT
ejpam-3501	5	1	a	a	DET
ejpam-3501	5	2	set	set	NOUN
ejpam-3501	5	3	s	s	NOUN
ejpam-3501	5	4	of	of	ADP
ejpam-3501	5	5	vertices	vertex	NOUN
ejpam-3501	5	6	of	of	ADP
ejpam-3501	5	7	a	a	DET
ejpam-3501	5	8	connected	connected	ADJ
ejpam-3501	5	9	graph	graph	NOUN
ejpam-3501	5	10	g	g	PROPN
ejpam-3501	5	11	is	be	AUX
ejpam-3501	5	12	a	a	DET
ejpam-3501	5	13	semitotal	semitotal	ADJ
ejpam-3501	5	14	dominating	dominating	NOUN
ejpam-3501	5	15	set	set	NOUN
ejpam-3501	5	16	if	if	SCONJ
ejpam-3501	5	17	every	every	DET
ejpam-3501	5	18	vertex	vertex	NOUN
ejpam-3501	5	19	in	in	ADP
ejpam-3501	5	20	v	v	NOUN
ejpam-3501	5	21	(	(	PUNCT
ejpam-3501	5	22	g)\s	g)\s	NOUN
ejpam-3501	5	23	is	be	AUX
ejpam-3501	5	24	adjacent	adjacent	ADJ
ejpam-3501	5	25	to	to	ADP
ejpam-3501	5	26	a	a	DET
ejpam-3501	5	27	vertex	vertex	NOUN
ejpam-3501	5	28	in	in	ADP
ejpam-3501	5	29	s	s	PROPN
ejpam-3501	5	30	,	,	PUNCT
ejpam-3501	5	31	and	and	CCONJ
ejpam-3501	5	32	every	every	DET
ejpam-3501	5	33	vertex	vertex	NOUN
ejpam-3501	5	34	in	in	ADP
ejpam-3501	5	35	s	s	PROPN
ejpam-3501	5	36	is	be	AUX
ejpam-3501	5	37	of	of	ADP
ejpam-3501	5	38	distance	distance	NOUN
ejpam-3501	5	39	at	at	ADP
ejpam-3501	5	40	most	most	ADV
ejpam-3501	5	41	2	2	NUM
ejpam-3501	5	42	from	from	ADP
ejpam-3501	5	43	another	another	DET
ejpam-3501	5	44	vertex	vertex	NOUN
ejpam-3501	5	45	in	in	ADP
ejpam-3501	5	46	s.	s.	PROPN
ejpam-3501	5	47	a	a	DET
ejpam-3501	5	48	semitotal	semitotal	ADJ
ejpam-3501	5	49	dominating	dominating	NOUN
ejpam-3501	5	50	set	set	NOUN
ejpam-3501	5	51	s	s	NOUN
ejpam-3501	5	52	in	in	ADP
ejpam-3501	5	53	g	g	PROPN
ejpam-3501	5	54	is	be	AUX
ejpam-3501	5	55	a	a	DET
ejpam-3501	5	56	secure	secure	ADJ
ejpam-3501	5	57	semitotal	semitotal	ADJ
ejpam-3501	5	58	dominating	dominating	NOUN
ejpam-3501	5	59	set	set	NOUN
ejpam-3501	5	60	if	if	SCONJ
ejpam-3501	5	61	for	for	ADP
ejpam-3501	5	62	every	every	PRON
ejpam-3501	5	63	v	v	NUM
ejpam-3501	5	64	∈	∈	NOUN
ejpam-3501	5	65	v	v	NOUN
ejpam-3501	5	66	(	(	PUNCT
ejpam-3501	5	67	g	g	NOUN
ejpam-3501	5	68	)	)	PUNCT
ejpam-3501	5	69	\	\	PROPN
ejpam-3501	6	1	s	s	X
ejpam-3501	6	2	,	,	PUNCT
ejpam-3501	6	3	there	there	PRON
ejpam-3501	6	4	is	be	VERB
ejpam-3501	6	5	a	a	DET
ejpam-3501	6	6	vertex	vertex	NOUN
ejpam-3501	6	7	x	x	PUNCT
ejpam-3501	6	8	∈	∈	NOUN
ejpam-3501	6	9	s	s	VERB
ejpam-3501	6	10	such	such	ADJ
ejpam-3501	6	11	that	that	SCONJ
ejpam-3501	6	12	x	x	PRON
ejpam-3501	6	13	is	be	AUX
ejpam-3501	6	14	adjacent	adjacent	ADJ
ejpam-3501	6	15	to	to	ADP
ejpam-3501	6	16	v	v	NOUN
ejpam-3501	6	17	and	and	CCONJ
ejpam-3501	6	18	that	that	SCONJ
ejpam-3501	6	19	(	(	PUNCT
ejpam-3501	6	20	s	s	NOUN
ejpam-3501	6	21	\	\	X
ejpam-3501	6	22	{	{	PUNCT
ejpam-3501	6	23	x	x	NOUN
ejpam-3501	6	24	}	}	PUNCT
ejpam-3501	6	25	)	)	PUNCT
ejpam-3501	6	26	∪	∪	ADP
ejpam-3501	6	27	{	{	PUNCT
ejpam-3501	6	28	v	v	NOUN
ejpam-3501	6	29	}	}	PUNCT
ejpam-3501	6	30	is	be	AUX
ejpam-3501	6	31	a	a	DET
ejpam-3501	6	32	semitotal	semitotal	ADJ
ejpam-3501	6	33	dominating	dominating	NOUN
ejpam-3501	6	34	set	set	VERB
ejpam-3501	6	35	in	in	ADP
ejpam-3501	6	36	g.	g.	PROPN
ejpam-3501	6	37	in	in	ADP
ejpam-3501	6	38	this	this	DET
ejpam-3501	6	39	paper	paper	NOUN
ejpam-3501	6	40	,	,	PUNCT
ejpam-3501	6	41	we	we	PRON
ejpam-3501	6	42	characterize	characterize	VERB
ejpam-3501	6	43	the	the	DET
ejpam-3501	6	44	semitotal	semitotal	ADJ
ejpam-3501	6	45	dominating	dominating	NOUN
ejpam-3501	6	46	sets	set	NOUN
ejpam-3501	6	47	and	and	CCONJ
ejpam-3501	6	48	the	the	DET
ejpam-3501	6	49	secure	secure	ADJ
ejpam-3501	6	50	semitotal	semitotal	ADJ
ejpam-3501	6	51	dominating	dominating	NOUN
ejpam-3501	6	52	sets	set	NOUN
ejpam-3501	6	53	in	in	ADP
ejpam-3501	6	54	the	the	DET
ejpam-3501	6	55	join	join	NOUN
ejpam-3501	6	56	,	,	PUNCT
ejpam-3501	6	57	corona	corona	NOUN
ejpam-3501	6	58	and	and	CCONJ
ejpam-3501	6	59	lexicographic	lexicographic	ADJ
ejpam-3501	6	60	product	product	NOUN
ejpam-3501	6	61	of	of	ADP
ejpam-3501	6	62	graphs	graph	NOUN
ejpam-3501	6	63	and	and	CCONJ
ejpam-3501	6	64	determine	determine	VERB
ejpam-3501	6	65	their	their	PRON
ejpam-3501	6	66	corresponding	correspond	VERB
ejpam-3501	6	67	semitotal	semitotal	ADJ
ejpam-3501	6	68	domination	domination	NOUN
ejpam-3501	6	69	and	and	CCONJ
ejpam-3501	6	70	secure	secure	VERB
ejpam-3501	6	71	semitotal	semitotal	ADJ
ejpam-3501	6	72	domination	domination	NOUN
ejpam-3501	6	73	numbers	number	NOUN
ejpam-3501	6	74	.	.	PUNCT
ejpam-3501	7	1	2010	2010	NUM
ejpam-3501	7	2	mathematics	mathematic	NOUN
ejpam-3501	7	3	subject	subject	NOUN
ejpam-3501	7	4	classifications	classification	NOUN
ejpam-3501	7	5	:	:	PUNCT
ejpam-3501	7	6	05c69	05c69	X
ejpam-3501	7	7	key	key	ADJ
ejpam-3501	7	8	words	word	NOUN
ejpam-3501	7	9	and	and	CCONJ
ejpam-3501	7	10	phrases	phrase	NOUN
ejpam-3501	7	11	:	:	PUNCT
ejpam-3501	7	12	semitotal	semitotal	ADJ
ejpam-3501	7	13	dominating	dominating	NOUN
ejpam-3501	7	14	set	set	NOUN
ejpam-3501	7	15	,	,	PUNCT
ejpam-3501	7	16	secure	secure	ADJ
ejpam-3501	7	17	semitotal	semitotal	ADJ
ejpam-3501	7	18	dominating	dominating	NOUN
ejpam-3501	7	19	set	set	NOUN
ejpam-3501	7	20	,	,	PUNCT
ejpam-3501	7	21	semitotal	semitotal	ADJ
ejpam-3501	7	22	domination	domination	NOUN
ejpam-3501	7	23	number	number	NOUN
ejpam-3501	7	24	,	,	PUNCT
ejpam-3501	7	25	secure	secure	ADJ
ejpam-3501	7	26	semitotal	semitotal	ADJ
ejpam-3501	7	27	domination	domination	NOUN
ejpam-3501	7	28	number	number	NOUN
ejpam-3501	7	29	1	1	NUM
ejpam-3501	7	30	.	.	PUNCT
ejpam-3501	7	31	introduction	introduction	NOUN
ejpam-3501	7	32	the	the	DET
ejpam-3501	7	33	concept	concept	NOUN
ejpam-3501	7	34	of	of	ADP
ejpam-3501	7	35	semitotal	semitotal	ADJ
ejpam-3501	7	36	domination	domination	NOUN
ejpam-3501	7	37	was	be	AUX
ejpam-3501	7	38	introduced	introduce	VERB
ejpam-3501	7	39	by	by	ADP
ejpam-3501	7	40	w.	w.	PROPN
ejpam-3501	7	41	goddard	goddard	PROPN
ejpam-3501	7	42	,	,	PUNCT
ejpam-3501	7	43	m.	m.	NOUN
ejpam-3501	7	44	henning	henning	PROPN
ejpam-3501	7	45	and	and	CCONJ
ejpam-3501	7	46	c.	c.	PROPN
ejpam-3501	7	47	mcpil	mcpil	PROPN
ejpam-3501	7	48	(	(	PUNCT
ejpam-3501	7	49	see	see	VERB
ejpam-3501	7	50	[	[	X
ejpam-3501	7	51	13	13	NUM
ejpam-3501	7	52	]	]	PUNCT
ejpam-3501	7	53	)	)	PUNCT
ejpam-3501	7	54	in	in	ADP
ejpam-3501	7	55	2014	2014	NUM
ejpam-3501	7	56	.	.	PUNCT
ejpam-3501	8	1	it	it	PRON
ejpam-3501	8	2	is	be	AUX
ejpam-3501	8	3	further	far	ADV
ejpam-3501	8	4	studied	study	VERB
ejpam-3501	8	5	by	by	ADP
ejpam-3501	8	6	m.henning	m.henne	VERB
ejpam-3501	8	7	and	and	CCONJ
ejpam-3501	8	8	a.	a.	NOUN
ejpam-3501	8	9	marcon	marcon	PROPN
ejpam-3501	8	10	(	(	PUNCT
ejpam-3501	8	11	see	see	VERB
ejpam-3501	8	12	[	[	X
ejpam-3501	8	13	17	17	NUM
ejpam-3501	8	14	,	,	PUNCT
ejpam-3501	8	15	18	18	NUM
ejpam-3501	8	16	]	]	PUNCT
ejpam-3501	8	17	)	)	PUNCT
ejpam-3501	8	18	in	in	ADP
ejpam-3501	8	19	2014	2014	NUM
ejpam-3501	8	20	and	and	CCONJ
ejpam-3501	8	21	2016	2016	NUM
ejpam-3501	8	22	,	,	PUNCT
ejpam-3501	8	23	and	and	CCONJ
ejpam-3501	8	24	by	by	ADP
ejpam-3501	8	25	g.	g.	PROPN
ejpam-3501	8	26	hao	hao	PROPN
ejpam-3501	8	27	and	and	CCONJ
ejpam-3501	8	28	w.	w.	PROPN
ejpam-3501	8	29	zhuang	zhuang	PROPN
ejpam-3501	8	30	(	(	PUNCT
ejpam-3501	8	31	see	see	VERB
ejpam-3501	8	32	[	[	X
ejpam-3501	8	33	14	14	NUM
ejpam-3501	8	34	]	]	SYM
ejpam-3501	8	35	)	)	PUNCT
ejpam-3501	8	36	in	in	ADP
ejpam-3501	8	37	2018	2018	NUM
ejpam-3501	8	38	.	.	PUNCT
ejpam-3501	9	1	accordingly	accordingly	ADV
ejpam-3501	9	2	,	,	PUNCT
ejpam-3501	9	3	this	this	DET
ejpam-3501	9	4	parameter	parameter	NOUN
ejpam-3501	9	5	is	be	AUX
ejpam-3501	9	6	a	a	DET
ejpam-3501	9	7	strengthening	strengthening	NOUN
ejpam-3501	9	8	of	of	ADP
ejpam-3501	9	9	domination	domination	NOUN
ejpam-3501	9	10	but	but	CCONJ
ejpam-3501	9	11	a	a	DET
ejpam-3501	9	12	relaxation	relaxation	NOUN
ejpam-3501	9	13	of	of	ADP
ejpam-3501	9	14	both	both	DET
ejpam-3501	9	15	total	total	ADJ
ejpam-3501	9	16	domination	domination	NOUN
ejpam-3501	9	17	and	and	CCONJ
ejpam-3501	9	18	weakly	weakly	ADJ
ejpam-3501	9	19	connected	connected	ADJ
ejpam-3501	9	20	domination	domination	NOUN
ejpam-3501	9	21	[	[	X
ejpam-3501	9	22	13	13	NUM
ejpam-3501	9	23	]	]	PUNCT
ejpam-3501	9	24	.	.	PUNCT
ejpam-3501	10	1	in	in	ADP
ejpam-3501	10	2	this	this	DET
ejpam-3501	10	3	paper	paper	NOUN
ejpam-3501	10	4	,	,	PUNCT
ejpam-3501	10	5	we	we	PRON
ejpam-3501	10	6	investigate	investigate	VERB
ejpam-3501	10	7	semitotal	semitotal	ADJ
ejpam-3501	10	8	domination	domination	NOUN
ejpam-3501	10	9	in	in	ADP
ejpam-3501	10	10	the	the	DET
ejpam-3501	10	11	join	join	NOUN
ejpam-3501	10	12	,	,	PUNCT
ejpam-3501	10	13	corona	corona	NOUN
ejpam-3501	10	14	and	and	CCONJ
ejpam-3501	10	15	lexicographic	lexicographic	ADJ
ejpam-3501	10	16	product	product	NOUN
ejpam-3501	10	17	of	of	ADP
ejpam-3501	10	18	graphs	graph	NOUN
ejpam-3501	10	19	.	.	PUNCT
ejpam-3501	11	1	we	we	PRON
ejpam-3501	11	2	also	also	ADV
ejpam-3501	11	3	introduce	introduce	VERB
ejpam-3501	11	4	the	the	DET
ejpam-3501	11	5	secure	secure	ADJ
ejpam-3501	11	6	semitotal	semitotal	ADJ
ejpam-3501	11	7	domination	domination	NOUN
ejpam-3501	11	8	and	and	CCONJ
ejpam-3501	11	9	investigate	investigate	VERB
ejpam-3501	11	10	the	the	DET
ejpam-3501	11	11	concept	concept	NOUN
ejpam-3501	11	12	in	in	ADP
ejpam-3501	11	13	these	these	DET
ejpam-3501	11	14	classes	class	NOUN
ejpam-3501	11	15	of	of	ADP
ejpam-3501	11	16	graphs	graph	NOUN
ejpam-3501	11	17	.	.	PUNCT
ejpam-3501	12	1	all	all	DET
ejpam-3501	12	2	graphs	graph	NOUN
ejpam-3501	12	3	considered	consider	VERB
ejpam-3501	12	4	in	in	ADP
ejpam-3501	12	5	this	this	DET
ejpam-3501	12	6	study	study	NOUN
ejpam-3501	12	7	are	be	AUX
ejpam-3501	12	8	finite	finite	ADJ
ejpam-3501	12	9	and	and	CCONJ
ejpam-3501	12	10	undirected	undirected	ADJ
ejpam-3501	12	11	.	.	PUNCT
ejpam-3501	13	1	we	we	PRON
ejpam-3501	13	2	refer	refer	VERB
ejpam-3501	13	3	to	to	ADP
ejpam-3501	13	4	[	[	X
ejpam-3501	13	5	7	7	X
ejpam-3501	13	6	]	]	PUNCT
ejpam-3501	13	7	for	for	ADP
ejpam-3501	13	8	the	the	DET
ejpam-3501	13	9	basic	basic	ADJ
ejpam-3501	13	10	graph	graph	NOUN
ejpam-3501	13	11	terminologies	terminology	NOUN
ejpam-3501	13	12	used	use	VERB
ejpam-3501	13	13	here	here	ADV
ejpam-3501	13	14	.	.	PUNCT
ejpam-3501	14	1	the	the	DET
ejpam-3501	14	2	symbols	symbol	NOUN
ejpam-3501	14	3	v	v	ADP
ejpam-3501	14	4	(	(	PUNCT
ejpam-3501	14	5	g	g	NOUN
ejpam-3501	14	6	)	)	PUNCT
ejpam-3501	14	7	and	and	CCONJ
ejpam-3501	14	8	e(g	e(g	PROPN
ejpam-3501	14	9	)	)	PUNCT
ejpam-3501	14	10	denote	denote	VERB
ejpam-3501	14	11	the	the	DET
ejpam-3501	14	12	vertex	vertex	NOUN
ejpam-3501	14	13	set	set	NOUN
ejpam-3501	14	14	∗corresponding	∗corresponde	VERB
ejpam-3501	14	15	author	author	NOUN
ejpam-3501	14	16	.	.	PUNCT
ejpam-3501	15	1	doi	doi	NOUN
ejpam-3501	15	2	:	:	PUNCT
ejpam-3501	15	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3501	https://doi.org/10.29020/nybg.ejpam.v12i4.3501	NUM
ejpam-3501	15	4	email	email	NOUN
ejpam-3501	15	5	addresses	address	NOUN
ejpam-3501	15	6	:	:	PUNCT
ejpam-3501	15	7	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-3501	15	8	(	(	PUNCT
ejpam-3501	15	9	i.s	i.s	PROPN
ejpam-3501	15	10	.	.	PROPN
ejpam-3501	15	11	aniversario	aniversario	PROPN
ejpam-3501	15	12	)	)	PUNCT
ejpam-3501	15	13	,	,	PUNCT
ejpam-3501	15	14	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	NOUN
ejpam-3501	15	15	(	(	PUNCT
ejpam-3501	15	16	s.r.jr	s.r.jr	NOUN
ejpam-3501	15	17	.	.	PUNCT
ejpam-3501	16	1	canoy	canoy	ADJ
ejpam-3501	16	2	)	)	PUNCT
ejpam-3501	16	3	,	,	PUNCT
ejpam-3501	16	4	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-3501	16	5	(	(	PUNCT
ejpam-3501	16	6	f.	f.	PROPN
ejpam-3501	16	7	jamil	jamil	PROPN
ejpam-3501	16	8	)	)	PUNCT
ejpam-3501	16	9	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3501	17	1	1410	1410	NUM
ejpam-3501	17	2	c	c	X
ejpam-3501	17	3	©	©	PROPN
ejpam-3501	17	4	2019	2019	NUM
ejpam-3501	17	5	ejpam	ejpam	NOUN
ejpam-3501	17	6	all	all	DET
ejpam-3501	17	7	rights	right	NOUN
ejpam-3501	17	8	reserved	reserve	VERB
ejpam-3501	17	9	.	.	PUNCT
ejpam-3501	18	1	i.	i.	PROPN
ejpam-3501	18	2	s.	s.	PROPN
ejpam-3501	18	3	aniversario	aniversario	PROPN
ejpam-3501	18	4	,	,	PUNCT
ejpam-3501	18	5	s.	s.	PROPN
ejpam-3501	18	6	r.	r.	PROPN
ejpam-3501	18	7	jr	jr	PROPN
ejpam-3501	18	8	.	.	PROPN
ejpam-3501	18	9	canoy	canoy	PROPN
ejpam-3501	18	10	,	,	PUNCT
ejpam-3501	18	11	f.p	f.p	PROPN
ejpam-3501	18	12	.	.	PROPN
ejpam-3501	18	13	jamil	jamil	PROPN
ejpam-3501	18	14	/	/	SYM
ejpam-3501	18	15	eur	eur	PROPN
ejpam-3501	18	16	.	.	PUNCT
ejpam-3501	19	1	j.	j.	PROPN
ejpam-3501	19	2	pure	pure	PROPN
ejpam-3501	19	3	appl	appl	PROPN
ejpam-3501	19	4	.	.	PROPN
ejpam-3501	19	5	math	math	PROPN
ejpam-3501	19	6	,	,	PUNCT
ejpam-3501	19	7	12	12	NUM
ejpam-3501	19	8	(	(	PUNCT
ejpam-3501	19	9	4	4	NUM
ejpam-3501	19	10	)	)	PUNCT
ejpam-3501	19	11	(	(	PUNCT
ejpam-3501	19	12	2019	2019	NUM
ejpam-3501	19	13	)	)	PUNCT
ejpam-3501	19	14	,	,	PUNCT
ejpam-3501	19	15	1410	1410	NUM
ejpam-3501	19	16	-	-	SYM
ejpam-3501	19	17	1425	1425	NUM
ejpam-3501	19	18	1411	1411	NUM
ejpam-3501	19	19	and	and	CCONJ
ejpam-3501	19	20	edge	edge	NOUN
ejpam-3501	19	21	set	set	NOUN
ejpam-3501	19	22	,	,	PUNCT
ejpam-3501	19	23	respectively	respectively	ADV
ejpam-3501	19	24	,	,	PUNCT
ejpam-3501	19	25	of	of	ADP
ejpam-3501	19	26	g.	g.	NOUN
ejpam-3501	19	27	for	for	ADP
ejpam-3501	19	28	s	s	PROPN
ejpam-3501	19	29	⊆	⊆	NUM
ejpam-3501	19	30	v	v	NOUN
ejpam-3501	19	31	(	(	PUNCT
ejpam-3501	19	32	g	g	NOUN
ejpam-3501	19	33	)	)	PUNCT
ejpam-3501	19	34	,	,	PUNCT
ejpam-3501	19	35	|s|	|s|	PROPN
ejpam-3501	19	36	is	be	AUX
ejpam-3501	19	37	the	the	DET
ejpam-3501	19	38	cardinality	cardinality	NOUN
ejpam-3501	19	39	of	of	ADP
ejpam-3501	19	40	s.	s.	PROPN
ejpam-3501	19	41	in	in	ADP
ejpam-3501	19	42	particular	particular	ADJ
ejpam-3501	19	43	,	,	PUNCT
ejpam-3501	19	44	|v	|v	PROPN
ejpam-3501	19	45	(	(	PUNCT
ejpam-3501	19	46	g)|	g)|	PROPN
ejpam-3501	19	47	is	be	AUX
ejpam-3501	19	48	the	the	DET
ejpam-3501	19	49	order	order	NOUN
ejpam-3501	19	50	of	of	ADP
ejpam-3501	19	51	g.	g.	NOUN
ejpam-3501	19	52	given	give	VERB
ejpam-3501	19	53	two	two	NUM
ejpam-3501	19	54	graphs	graph	NOUN
ejpam-3501	19	55	g	g	NOUN
ejpam-3501	19	56	and	and	CCONJ
ejpam-3501	19	57	h	h	NOUN
ejpam-3501	19	58	with	with	ADP
ejpam-3501	19	59	disjoint	disjoint	ADJ
ejpam-3501	19	60	vertex	vertex	NOUN
ejpam-3501	19	61	sets	set	NOUN
ejpam-3501	19	62	,	,	PUNCT
ejpam-3501	19	63	the	the	DET
ejpam-3501	19	64	join	join	NOUN
ejpam-3501	19	65	of	of	ADP
ejpam-3501	19	66	g	g	PROPN
ejpam-3501	19	67	and	and	CCONJ
ejpam-3501	19	68	h	h	NOUN
ejpam-3501	19	69	is	be	AUX
ejpam-3501	19	70	the	the	DET
ejpam-3501	19	71	graph	graph	NOUN
ejpam-3501	19	72	g+h	g+h	PROPN
ejpam-3501	19	73	with	with	ADP
ejpam-3501	19	74	v	v	PROPN
ejpam-3501	19	75	(	(	PUNCT
ejpam-3501	19	76	g+h	g+h	NOUN
ejpam-3501	19	77	)	)	PUNCT
ejpam-3501	20	1	=	=	SYM
ejpam-3501	20	2	v	v	X
ejpam-3501	20	3	(	(	PUNCT
ejpam-3501	20	4	g)∪v	g)∪v	NOUN
ejpam-3501	20	5	(	(	PUNCT
ejpam-3501	20	6	h	h	NOUN
ejpam-3501	20	7	)	)	PUNCT
ejpam-3501	20	8	and	and	CCONJ
ejpam-3501	20	9	e(g+h	e(g+h	NUM
ejpam-3501	20	10	)	)	PUNCT
ejpam-3501	21	1	=	=	PUNCT
ejpam-3501	21	2	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	X
ejpam-3501	21	3	:	:	PUNCT
ejpam-3501	21	4	u	u	PROPN
ejpam-3501	21	5	∈	∈	PROPN
ejpam-3501	21	6	v	v	NOUN
ejpam-3501	21	7	(	(	PUNCT
ejpam-3501	21	8	g	g	NOUN
ejpam-3501	21	9	)	)	PUNCT
ejpam-3501	21	10	,	,	PUNCT
ejpam-3501	21	11	v	v	X
ejpam-3501	21	12	∈	∈	PROPN
ejpam-3501	21	13	v	v	NOUN
ejpam-3501	21	14	(	(	PUNCT
ejpam-3501	21	15	h	h	NOUN
ejpam-3501	21	16	)	)	PUNCT
ejpam-3501	21	17	}	}	PUNCT
ejpam-3501	21	18	.	.	PUNCT
ejpam-3501	22	1	the	the	DET
ejpam-3501	22	2	corona	corona	NOUN
ejpam-3501	22	3	of	of	ADP
ejpam-3501	22	4	g	g	PROPN
ejpam-3501	22	5	and	and	CCONJ
ejpam-3501	22	6	h	h	NOUN
ejpam-3501	22	7	is	be	AUX
ejpam-3501	22	8	the	the	DET
ejpam-3501	22	9	graph	graph	NOUN
ejpam-3501	22	10	g	g	PROPN
ejpam-3501	22	11	◦	◦	NOUN
ejpam-3501	22	12	h	h	NOUN
ejpam-3501	22	13	obtained	obtain	VERB
ejpam-3501	22	14	by	by	ADP
ejpam-3501	22	15	taking	take	VERB
ejpam-3501	22	16	one	one	NUM
ejpam-3501	22	17	copy	copy	NOUN
ejpam-3501	22	18	of	of	ADP
ejpam-3501	22	19	g	g	PROPN
ejpam-3501	22	20	and	and	CCONJ
ejpam-3501	22	21	|v	|v	PROPN
ejpam-3501	22	22	(	(	PUNCT
ejpam-3501	22	23	g)|	g)|	NOUN
ejpam-3501	22	24	copies	copy	NOUN
ejpam-3501	22	25	of	of	ADP
ejpam-3501	22	26	h	h	NOUN
ejpam-3501	22	27	,	,	PUNCT
ejpam-3501	22	28	and	and	CCONJ
ejpam-3501	22	29	then	then	ADV
ejpam-3501	22	30	joining	join	VERB
ejpam-3501	22	31	the	the	DET
ejpam-3501	22	32	ith	ith	PROPN
ejpam-3501	22	33	vertex	vertex	NOUN
ejpam-3501	22	34	of	of	ADP
ejpam-3501	22	35	g	g	NOUN
ejpam-3501	22	36	to	to	ADP
ejpam-3501	22	37	every	every	DET
ejpam-3501	22	38	vertex	vertex	NOUN
ejpam-3501	22	39	in	in	ADP
ejpam-3501	22	40	the	the	DET
ejpam-3501	22	41	ith	ith	PROPN
ejpam-3501	22	42	copy	copy	NOUN
ejpam-3501	22	43	of	of	ADP
ejpam-3501	22	44	h.	h.	PROPN
ejpam-3501	22	45	the	the	DET
ejpam-3501	22	46	lexicographic	lexicographic	ADJ
ejpam-3501	22	47	product	product	NOUN
ejpam-3501	22	48	or	or	CCONJ
ejpam-3501	22	49	composition	composition	NOUN
ejpam-3501	22	50	g[h	g[h	NOUN
ejpam-3501	22	51	]	]	PUNCT
ejpam-3501	22	52	of	of	ADP
ejpam-3501	22	53	g	g	PROPN
ejpam-3501	22	54	and	and	CCONJ
ejpam-3501	22	55	h	h	NOUN
ejpam-3501	22	56	is	be	AUX
ejpam-3501	22	57	the	the	DET
ejpam-3501	22	58	graph	graph	NOUN
ejpam-3501	22	59	with	with	ADP
ejpam-3501	22	60	v	v	NOUN
ejpam-3501	22	61	(	(	PUNCT
ejpam-3501	22	62	g[h	g[h	PROPN
ejpam-3501	22	63	]	]	PUNCT
ejpam-3501	22	64	)	)	PUNCT
ejpam-3501	23	1	=	=	SYM
ejpam-3501	23	2	v	v	X
ejpam-3501	23	3	(	(	PUNCT
ejpam-3501	23	4	g)×	g)×	NOUN
ejpam-3501	23	5	v	v	NOUN
ejpam-3501	23	6	(	(	PUNCT
ejpam-3501	23	7	h	h	NOUN
ejpam-3501	23	8	)	)	PUNCT
ejpam-3501	23	9	and	and	CCONJ
ejpam-3501	23	10	(	(	PUNCT
ejpam-3501	23	11	u	u	NOUN
ejpam-3501	23	12	,	,	PUNCT
ejpam-3501	23	13	v)(u′	v)(u′	NOUN
ejpam-3501	23	14	,	,	PUNCT
ejpam-3501	23	15	v′	v′	NOUN
ejpam-3501	23	16	)	)	PUNCT
ejpam-3501	23	17	∈	∈	NOUN
ejpam-3501	23	18	e(g[h	e(g[h	NOUN
ejpam-3501	23	19	]	]	PUNCT
ejpam-3501	23	20	)	)	PUNCT
ejpam-3501	23	21	if	if	SCONJ
ejpam-3501	23	22	and	and	CCONJ
ejpam-3501	23	23	only	only	ADV
ejpam-3501	23	24	if	if	SCONJ
ejpam-3501	23	25	either	either	CCONJ
ejpam-3501	23	26	uu′	uu′	PROPN
ejpam-3501	23	27	∈	∈	PROPN
ejpam-3501	23	28	e(g	e(g	PROPN
ejpam-3501	23	29	)	)	PUNCT
ejpam-3501	23	30	or	or	CCONJ
ejpam-3501	23	31	u	u	X
ejpam-3501	23	32	=	=	PUNCT
ejpam-3501	23	33	u′	u′	PROPN
ejpam-3501	23	34	and	and	CCONJ
ejpam-3501	23	35	vv′	vv′	NOUN
ejpam-3501	23	36	∈	∈	PROPN
ejpam-3501	23	37	e(h	e(h	PROPN
ejpam-3501	23	38	)	)	PUNCT
ejpam-3501	23	39	.	.	PUNCT
ejpam-3501	24	1	in	in	ADP
ejpam-3501	24	2	any	any	PRON
ejpam-3501	24	3	of	of	ADP
ejpam-3501	24	4	these	these	DET
ejpam-3501	24	5	graphs	graph	NOUN
ejpam-3501	24	6	,	,	PUNCT
ejpam-3501	24	7	g	g	PROPN
ejpam-3501	24	8	and	and	CCONJ
ejpam-3501	24	9	h	h	NOUN
ejpam-3501	24	10	are	be	AUX
ejpam-3501	24	11	referred	refer	VERB
ejpam-3501	24	12	to	to	ADP
ejpam-3501	24	13	as	as	ADP
ejpam-3501	24	14	their	their	PRON
ejpam-3501	24	15	basic	basic	ADJ
ejpam-3501	24	16	component	component	NOUN
ejpam-3501	24	17	graphs	graph	NOUN
ejpam-3501	24	18	.	.	PUNCT
ejpam-3501	25	1	for	for	ADP
ejpam-3501	25	2	v	v	NUM
ejpam-3501	25	3	∈	∈	PROPN
ejpam-3501	25	4	v	v	NOUN
ejpam-3501	25	5	(	(	PUNCT
ejpam-3501	25	6	g	g	NOUN
ejpam-3501	25	7	)	)	PUNCT
ejpam-3501	25	8	,	,	PUNCT
ejpam-3501	25	9	the	the	DET
ejpam-3501	25	10	neighborhood	neighborhood	NOUN
ejpam-3501	25	11	ng(v	ng(v	PUNCT
ejpam-3501	25	12	)	)	PUNCT
ejpam-3501	25	13	of	of	ADP
ejpam-3501	25	14	v	v	NUM
ejpam-3501	25	15	refers	refer	VERB
ejpam-3501	25	16	to	to	ADP
ejpam-3501	25	17	the	the	DET
ejpam-3501	25	18	set	set	NOUN
ejpam-3501	25	19	of	of	ADP
ejpam-3501	25	20	all	all	DET
ejpam-3501	25	21	vertices	vertex	NOUN
ejpam-3501	25	22	of	of	ADP
ejpam-3501	25	23	g	g	PROPN
ejpam-3501	25	24	that	that	PRON
ejpam-3501	25	25	are	be	AUX
ejpam-3501	25	26	adjacent	adjacent	ADJ
ejpam-3501	25	27	to	to	ADP
ejpam-3501	25	28	v.	v.	ADP
ejpam-3501	25	29	the	the	DET
ejpam-3501	25	30	closed	closed	ADJ
ejpam-3501	25	31	neighborhood	neighborhood	NOUN
ejpam-3501	25	32	of	of	ADP
ejpam-3501	25	33	v	v	NOUN
ejpam-3501	25	34	is	be	AUX
ejpam-3501	25	35	the	the	DET
ejpam-3501	25	36	set	set	NOUN
ejpam-3501	25	37	ng[v	ng[v	NOUN
ejpam-3501	25	38	]	]	X
ejpam-3501	25	39	=	=	SYM
ejpam-3501	25	40	ng(v)∪{v	ng(v)∪{v	PROPN
ejpam-3501	25	41	}	}	PUNCT
ejpam-3501	25	42	.	.	PUNCT
ejpam-3501	26	1	for	for	ADP
ejpam-3501	26	2	s	s	PROPN
ejpam-3501	26	3	⊆	⊆	NUM
ejpam-3501	26	4	v	v	NOUN
ejpam-3501	26	5	(	(	PUNCT
ejpam-3501	26	6	g	g	NOUN
ejpam-3501	26	7	)	)	PUNCT
ejpam-3501	26	8	,	,	PUNCT
ejpam-3501	26	9	ng(s	ng(s	NUM
ejpam-3501	26	10	)	)	PUNCT
ejpam-3501	26	11	=	=	SYM
ejpam-3501	26	12	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-3501	26	13	)	)	PUNCT
ejpam-3501	26	14	and	and	CCONJ
ejpam-3501	26	15	ng[s	ng[s	PROPN
ejpam-3501	26	16	]	]	PUNCT
ejpam-3501	26	17	=	=	SYM
ejpam-3501	26	18	s	s	NOUN
ejpam-3501	26	19	∪ng(s	∪ng(s	NOUN
ejpam-3501	26	20	)	)	PUNCT
ejpam-3501	26	21	.	.	PUNCT
ejpam-3501	27	1	a	a	DET
ejpam-3501	27	2	set	set	NOUN
ejpam-3501	27	3	s	s	NOUN
ejpam-3501	27	4	⊆	⊆	NUM
ejpam-3501	27	5	v	v	NOUN
ejpam-3501	27	6	(	(	PUNCT
ejpam-3501	27	7	g	g	NOUN
ejpam-3501	27	8	)	)	PUNCT
ejpam-3501	27	9	is	be	AUX
ejpam-3501	27	10	a	a	DET
ejpam-3501	27	11	dominating	dominating	NOUN
ejpam-3501	27	12	set	set	VERB
ejpam-3501	27	13	in	in	ADP
ejpam-3501	27	14	g	g	PROPN
ejpam-3501	27	15	if	if	SCONJ
ejpam-3501	27	16	ng[s	ng[	NOUN
ejpam-3501	27	17	]	]	PUNCT
ejpam-3501	27	18	=	=	SYM
ejpam-3501	27	19	v	v	NOUN
ejpam-3501	27	20	(	(	PUNCT
ejpam-3501	27	21	g	g	NOUN
ejpam-3501	27	22	)	)	PUNCT
ejpam-3501	27	23	.	.	PUNCT
ejpam-3501	28	1	thus	thus	ADV
ejpam-3501	28	2	,	,	PUNCT
ejpam-3501	28	3	s	s	VERB
ejpam-3501	28	4	is	be	AUX
ejpam-3501	28	5	a	a	DET
ejpam-3501	28	6	dominating	dominating	NOUN
ejpam-3501	28	7	set	set	VERB
ejpam-3501	28	8	in	in	ADP
ejpam-3501	28	9	g	g	PROPN
ejpam-3501	28	10	if	if	SCONJ
ejpam-3501	28	11	and	and	CCONJ
ejpam-3501	28	12	only	only	ADV
ejpam-3501	28	13	if	if	SCONJ
ejpam-3501	28	14	for	for	ADP
ejpam-3501	28	15	each	each	PRON
ejpam-3501	28	16	v	v	NUM
ejpam-3501	28	17	∈	∈	PROPN
ejpam-3501	28	18	v	v	NOUN
ejpam-3501	28	19	(	(	PUNCT
ejpam-3501	28	20	g	g	NOUN
ejpam-3501	28	21	)	)	PUNCT
ejpam-3501	28	22	\	\	PROPN
ejpam-3501	29	1	s	s	VERB
ejpam-3501	30	1	there	there	PRON
ejpam-3501	30	2	exists	exist	VERB
ejpam-3501	30	3	u	u	PROPN
ejpam-3501	30	4	∈	∈	PROPN
ejpam-3501	30	5	s	s	VERB
ejpam-3501	30	6	such	such	ADJ
ejpam-3501	30	7	that	that	DET
ejpam-3501	30	8	uv	uv	PROPN
ejpam-3501	30	9	∈	∈	PROPN
ejpam-3501	30	10	e(g	e(g	PROPN
ejpam-3501	30	11	)	)	PUNCT
ejpam-3501	30	12	.	.	PUNCT
ejpam-3501	31	1	the	the	DET
ejpam-3501	31	2	minimum	minimum	ADJ
ejpam-3501	31	3	cardinality	cardinality	NOUN
ejpam-3501	31	4	of	of	ADP
ejpam-3501	31	5	a	a	DET
ejpam-3501	31	6	dominating	dominating	NOUN
ejpam-3501	31	7	set	set	NOUN
ejpam-3501	31	8	in	in	ADP
ejpam-3501	31	9	g	g	NOUN
ejpam-3501	31	10	,	,	PUNCT
ejpam-3501	31	11	denoted	denote	VERB
ejpam-3501	31	12	by	by	ADP
ejpam-3501	31	13	γ(g	γ(g	PROPN
ejpam-3501	31	14	)	)	PUNCT
ejpam-3501	31	15	,	,	PUNCT
ejpam-3501	31	16	is	be	AUX
ejpam-3501	31	17	the	the	DET
ejpam-3501	31	18	domination	domination	NOUN
ejpam-3501	31	19	number	number	NOUN
ejpam-3501	31	20	of	of	ADP
ejpam-3501	31	21	g.	g.	PROPN
ejpam-3501	31	22	provided	provide	VERB
ejpam-3501	31	23	that	that	SCONJ
ejpam-3501	31	24	g	g	PROPN
ejpam-3501	31	25	has	have	VERB
ejpam-3501	31	26	no	no	DET
ejpam-3501	31	27	isolated	isolated	ADJ
ejpam-3501	31	28	vertices	vertex	NOUN
ejpam-3501	31	29	,	,	PUNCT
ejpam-3501	31	30	a	a	DET
ejpam-3501	31	31	set	set	NOUN
ejpam-3501	31	32	s	s	NOUN
ejpam-3501	31	33	⊆	⊆	NUM
ejpam-3501	31	34	v	v	NOUN
ejpam-3501	31	35	(	(	PUNCT
ejpam-3501	31	36	g	g	NOUN
ejpam-3501	31	37	)	)	PUNCT
ejpam-3501	31	38	is	be	AUX
ejpam-3501	31	39	a	a	DET
ejpam-3501	31	40	total	total	ADJ
ejpam-3501	31	41	dominating	dominating	NOUN
ejpam-3501	31	42	set	set	VERB
ejpam-3501	31	43	in	in	ADP
ejpam-3501	31	44	g	g	PROPN
ejpam-3501	31	45	if	if	SCONJ
ejpam-3501	31	46	for	for	ADP
ejpam-3501	31	47	every	every	DET
ejpam-3501	31	48	v	v	NUM
ejpam-3501	31	49	∈	∈	NOUN
ejpam-3501	31	50	v	v	NOUN
ejpam-3501	31	51	(	(	PUNCT
ejpam-3501	31	52	g	g	NOUN
ejpam-3501	31	53	)	)	PUNCT
ejpam-3501	31	54	there	there	PRON
ejpam-3501	31	55	exists	exist	VERB
ejpam-3501	31	56	u	u	PROPN
ejpam-3501	31	57	∈	∈	PROPN
ejpam-3501	31	58	s	s	VERB
ejpam-3501	31	59	such	such	ADJ
ejpam-3501	31	60	that	that	DET
ejpam-3501	31	61	uv	uv	PROPN
ejpam-3501	31	62	∈	∈	PROPN
ejpam-3501	31	63	e(g	e(g	PROPN
ejpam-3501	31	64	)	)	PUNCT
ejpam-3501	31	65	.	.	PUNCT
ejpam-3501	32	1	the	the	DET
ejpam-3501	32	2	minimum	minimum	ADJ
ejpam-3501	32	3	cardinality	cardinality	NOUN
ejpam-3501	32	4	of	of	ADP
ejpam-3501	32	5	a	a	DET
ejpam-3501	32	6	total	total	ADJ
ejpam-3501	32	7	dominating	dominating	NOUN
ejpam-3501	32	8	set	set	NOUN
ejpam-3501	32	9	in	in	ADP
ejpam-3501	32	10	g	g	NOUN
ejpam-3501	32	11	,	,	PUNCT
ejpam-3501	32	12	denoted	denote	VERB
ejpam-3501	32	13	by	by	ADP
ejpam-3501	32	14	γt(g	γt(g	NOUN
ejpam-3501	32	15	)	)	PUNCT
ejpam-3501	32	16	,	,	PUNCT
ejpam-3501	32	17	is	be	AUX
ejpam-3501	32	18	the	the	DET
ejpam-3501	32	19	total	total	ADJ
ejpam-3501	32	20	domination	domination	NOUN
ejpam-3501	32	21	number	number	NOUN
ejpam-3501	32	22	of	of	ADP
ejpam-3501	32	23	g.	g.	NOUN
ejpam-3501	32	24	we	we	PRON
ejpam-3501	32	25	refer	refer	VERB
ejpam-3501	32	26	to	to	ADP
ejpam-3501	32	27	[	[	X
ejpam-3501	32	28	1–3	1–3	NOUN
ejpam-3501	32	29	,	,	PUNCT
ejpam-3501	32	30	6	6	NUM
ejpam-3501	32	31	,	,	PUNCT
ejpam-3501	32	32	8	8	NUM
ejpam-3501	32	33	,	,	PUNCT
ejpam-3501	32	34	9	9	NUM
ejpam-3501	32	35	,	,	PUNCT
ejpam-3501	32	36	11	11	NUM
ejpam-3501	32	37	,	,	PUNCT
ejpam-3501	32	38	15	15	NUM
ejpam-3501	32	39	,	,	PUNCT
ejpam-3501	32	40	16	16	NUM
ejpam-3501	32	41	]	]	PUNCT
ejpam-3501	32	42	for	for	ADP
ejpam-3501	32	43	the	the	DET
ejpam-3501	32	44	fundamentals	fundamental	NOUN
ejpam-3501	32	45	and	and	CCONJ
ejpam-3501	32	46	recent	recent	ADJ
ejpam-3501	32	47	developments	development	NOUN
ejpam-3501	32	48	and	and	CCONJ
ejpam-3501	32	49	applications	application	NOUN
ejpam-3501	32	50	of	of	ADP
ejpam-3501	32	51	domination	domination	NOUN
ejpam-3501	32	52	theory	theory	NOUN
ejpam-3501	32	53	in	in	ADP
ejpam-3501	32	54	graphs	graph	NOUN
ejpam-3501	32	55	.	.	PUNCT
ejpam-3501	33	1	a	a	DET
ejpam-3501	33	2	set	set	NOUN
ejpam-3501	33	3	s	s	NOUN
ejpam-3501	33	4	⊆	⊆	NUM
ejpam-3501	33	5	v	v	NOUN
ejpam-3501	33	6	(	(	PUNCT
ejpam-3501	33	7	g	g	NOUN
ejpam-3501	33	8	)	)	PUNCT
ejpam-3501	33	9	is	be	AUX
ejpam-3501	33	10	said	say	VERB
ejpam-3501	33	11	to	to	PART
ejpam-3501	33	12	be	be	AUX
ejpam-3501	33	13	nearly	nearly	ADV
ejpam-3501	33	14	dominating	dominate	VERB
ejpam-3501	33	15	in	in	ADP
ejpam-3501	33	16	g	g	PROPN
ejpam-3501	33	17	if	if	SCONJ
ejpam-3501	33	18	for	for	ADP
ejpam-3501	33	19	every	every	PRON
ejpam-3501	33	20	v	v	NUM
ejpam-3501	33	21	∈	∈	NOUN
ejpam-3501	33	22	v	v	NOUN
ejpam-3501	33	23	(	(	PUNCT
ejpam-3501	33	24	g	g	NOUN
ejpam-3501	33	25	)	)	PUNCT
ejpam-3501	33	26	\	\	PUNCT
ejpam-3501	34	1	ng[s	ng[s	PROPN
ejpam-3501	34	2	]	]	PUNCT
ejpam-3501	34	3	,	,	PUNCT
ejpam-3501	34	4	s	s	NOUN
ejpam-3501	34	5	∪	∪	X
ejpam-3501	34	6	{	{	PUNCT
ejpam-3501	34	7	v	v	NOUN
ejpam-3501	34	8	}	}	PUNCT
ejpam-3501	34	9	is	be	AUX
ejpam-3501	34	10	a	a	DET
ejpam-3501	34	11	dominating	dominating	NOUN
ejpam-3501	34	12	set	set	VERB
ejpam-3501	34	13	in	in	ADP
ejpam-3501	34	14	g.	g.	PROPN
ejpam-3501	34	15	the	the	DET
ejpam-3501	34	16	symbol	symbol	NOUN
ejpam-3501	34	17	γη(g	γη(g	NUM
ejpam-3501	34	18	)	)	PUNCT
ejpam-3501	34	19	denotes	denote	VERB
ejpam-3501	34	20	the	the	DET
ejpam-3501	34	21	minimum	minimum	ADJ
ejpam-3501	34	22	cardinality	cardinality	NOUN
ejpam-3501	34	23	of	of	ADP
ejpam-3501	34	24	a	a	DET
ejpam-3501	34	25	nearly	nearly	ADV
ejpam-3501	34	26	dominating	dominating	NOUN
ejpam-3501	34	27	set	set	VERB
ejpam-3501	34	28	in	in	ADP
ejpam-3501	34	29	g.	g.	PROPN
ejpam-3501	34	30	clearly	clearly	ADV
ejpam-3501	34	31	,	,	PUNCT
ejpam-3501	34	32	γη(g	γη(g	NUM
ejpam-3501	34	33	)	)	PUNCT
ejpam-3501	34	34	=	=	SYM
ejpam-3501	35	1	0	0	PUNCT
ejpam-3501	36	1	if	if	SCONJ
ejpam-3501	36	2	and	and	CCONJ
ejpam-3501	36	3	only	only	ADV
ejpam-3501	36	4	if	if	SCONJ
ejpam-3501	36	5	g	g	PROPN
ejpam-3501	36	6	is	be	AUX
ejpam-3501	36	7	a	a	DET
ejpam-3501	36	8	complete	complete	ADJ
ejpam-3501	36	9	graph	graph	NOUN
ejpam-3501	36	10	,	,	PUNCT
ejpam-3501	36	11	and	and	CCONJ
ejpam-3501	36	12	since	since	SCONJ
ejpam-3501	36	13	dominating	dominating	NOUN
ejpam-3501	36	14	sets	set	NOUN
ejpam-3501	36	15	are	be	AUX
ejpam-3501	36	16	nearly	nearly	ADV
ejpam-3501	36	17	dominating	dominating	NOUN
ejpam-3501	36	18	sets	set	NOUN
ejpam-3501	36	19	,	,	PUNCT
ejpam-3501	36	20	γη(g	γη(g	NUM
ejpam-3501	36	21	)	)	PUNCT
ejpam-3501	36	22	≤	≤	PROPN
ejpam-3501	36	23	γ(g	γ(g	PROPN
ejpam-3501	36	24	)	)	PUNCT
ejpam-3501	36	25	.	.	PUNCT
ejpam-3501	37	1	a	a	DET
ejpam-3501	37	2	secure	secure	ADJ
ejpam-3501	37	3	(	(	PUNCT
ejpam-3501	37	4	total	total	ADJ
ejpam-3501	37	5	)	)	PUNCT
ejpam-3501	37	6	dominating	dominating	NOUN
ejpam-3501	37	7	set	set	NOUN
ejpam-3501	37	8	is	be	AUX
ejpam-3501	37	9	a	a	DET
ejpam-3501	37	10	(	(	PUNCT
ejpam-3501	37	11	total	total	ADJ
ejpam-3501	37	12	)	)	PUNCT
ejpam-3501	37	13	dominating	dominating	NOUN
ejpam-3501	37	14	set	set	NOUN
ejpam-3501	37	15	s	s	AUX
ejpam-3501	37	16	having	have	VERB
ejpam-3501	37	17	the	the	DET
ejpam-3501	37	18	property	property	NOUN
ejpam-3501	37	19	that	that	PRON
ejpam-3501	37	20	for	for	ADP
ejpam-3501	37	21	each	each	PRON
ejpam-3501	37	22	v	v	NUM
ejpam-3501	37	23	∈	∈	PROPN
ejpam-3501	37	24	v	v	NOUN
ejpam-3501	37	25	(	(	PUNCT
ejpam-3501	37	26	g	g	NOUN
ejpam-3501	37	27	)	)	PUNCT
ejpam-3501	37	28	\	\	PROPN
ejpam-3501	38	1	s	s	X
ejpam-3501	38	2	,	,	PUNCT
ejpam-3501	38	3	there	there	PRON
ejpam-3501	38	4	exists	exist	VERB
ejpam-3501	38	5	u	u	PROPN
ejpam-3501	38	6	∈	∈	PROPN
ejpam-3501	38	7	s	s	PART
ejpam-3501	38	8	∩	∩	NOUN
ejpam-3501	38	9	ng(v	ng(v	NOUN
ejpam-3501	38	10	)	)	PUNCT
ejpam-3501	38	11	such	such	ADJ
ejpam-3501	38	12	that	that	SCONJ
ejpam-3501	38	13	(	(	PUNCT
ejpam-3501	38	14	s	s	NOUN
ejpam-3501	38	15	\	\	X
ejpam-3501	38	16	{	{	PUNCT
ejpam-3501	38	17	u	u	NOUN
ejpam-3501	38	18	}	}	PUNCT
ejpam-3501	38	19	)	)	PUNCT
ejpam-3501	38	20	∪	∪	ADP
ejpam-3501	38	21	{	{	PUNCT
ejpam-3501	38	22	v	v	NOUN
ejpam-3501	38	23	}	}	PUNCT
ejpam-3501	38	24	is	be	AUX
ejpam-3501	38	25	a	a	DET
ejpam-3501	38	26	(	(	PUNCT
ejpam-3501	38	27	total	total	ADJ
ejpam-3501	38	28	)	)	PUNCT
ejpam-3501	38	29	dominating	dominating	NOUN
ejpam-3501	38	30	set	set	VERB
ejpam-3501	38	31	ing	ing	NOUN
ejpam-3501	38	32	.	.	PUNCT
ejpam-3501	39	1	the	the	DET
ejpam-3501	39	2	minimum	minimum	ADJ
ejpam-3501	39	3	cardinality	cardinality	NOUN
ejpam-3501	39	4	γs(g	γs(g	PUNCT
ejpam-3501	39	5	)	)	PUNCT
ejpam-3501	39	6	(	(	PUNCT
ejpam-3501	39	7	resp	resp	NOUN
ejpam-3501	39	8	.	.	PUNCT
ejpam-3501	40	1	γst(g	γst(g	PROPN
ejpam-3501	40	2	)	)	PUNCT
ejpam-3501	40	3	)	)	PUNCT
ejpam-3501	40	4	of	of	ADP
ejpam-3501	40	5	a	a	DET
ejpam-3501	40	6	secure	secure	ADJ
ejpam-3501	40	7	dominating	dominating	NOUN
ejpam-3501	40	8	set	set	NOUN
ejpam-3501	40	9	(	(	PUNCT
ejpam-3501	40	10	resp	resp	NOUN
ejpam-3501	40	11	.	.	PUNCT
ejpam-3501	41	1	secure	secure	ADJ
ejpam-3501	41	2	total	total	ADJ
ejpam-3501	41	3	dominating	dominating	NOUN
ejpam-3501	41	4	set	set	NOUN
ejpam-3501	41	5	)	)	PUNCT
ejpam-3501	41	6	in	in	ADP
ejpam-3501	41	7	g	g	PROPN
ejpam-3501	41	8	is	be	AUX
ejpam-3501	41	9	the	the	DET
ejpam-3501	41	10	secure	secure	ADJ
ejpam-3501	41	11	domination	domination	NOUN
ejpam-3501	41	12	number	number	NOUN
ejpam-3501	41	13	(	(	PUNCT
ejpam-3501	41	14	resp	resp	NOUN
ejpam-3501	41	15	.	.	PUNCT
ejpam-3501	42	1	secure	secure	ADJ
ejpam-3501	42	2	total	total	ADJ
ejpam-3501	42	3	domination	domination	NOUN
ejpam-3501	42	4	number	number	NOUN
ejpam-3501	42	5	)	)	PUNCT
ejpam-3501	42	6	of	of	ADP
ejpam-3501	42	7	g.	g.	PROPN
ejpam-3501	42	8	a	a	DET
ejpam-3501	42	9	secure	secure	ADJ
ejpam-3501	42	10	dominating	dominating	NOUN
ejpam-3501	42	11	set	set	NOUN
ejpam-3501	42	12	of	of	ADP
ejpam-3501	42	13	cardinality	cardinality	NOUN
ejpam-3501	42	14	γs(g	γs(g	PUNCT
ejpam-3501	42	15	)	)	PUNCT
ejpam-3501	42	16	is	be	AUX
ejpam-3501	42	17	called	call	VERB
ejpam-3501	42	18	a	a	DET
ejpam-3501	42	19	γs	γs	NOUN
ejpam-3501	42	20	-	-	PUNCT
ejpam-3501	42	21	set	set	VERB
ejpam-3501	42	22	.	.	PUNCT
ejpam-3501	43	1	secure	secure	ADJ
ejpam-3501	43	2	domination	domination	NOUN
ejpam-3501	43	3	and	and	CCONJ
ejpam-3501	43	4	secure	secure	VERB
ejpam-3501	43	5	total	total	ADJ
ejpam-3501	43	6	domination	domination	NOUN
ejpam-3501	43	7	in	in	ADP
ejpam-3501	43	8	graphs	graph	NOUN
ejpam-3501	43	9	have	have	AUX
ejpam-3501	43	10	been	be	AUX
ejpam-3501	43	11	studied	study	VERB
ejpam-3501	43	12	in	in	ADP
ejpam-3501	43	13	[	[	X
ejpam-3501	43	14	4	4	NUM
ejpam-3501	43	15	,	,	PUNCT
ejpam-3501	43	16	5	5	NUM
ejpam-3501	43	17	,	,	PUNCT
ejpam-3501	43	18	10	10	NUM
ejpam-3501	43	19	,	,	PUNCT
ejpam-3501	43	20	12	12	NUM
ejpam-3501	43	21	,	,	PUNCT
ejpam-3501	43	22	19	19	NUM
ejpam-3501	43	23	]	]	PUNCT
ejpam-3501	43	24	.	.	PUNCT
ejpam-3501	44	1	let	let	VERB
ejpam-3501	44	2	g	g	PRON
ejpam-3501	44	3	be	be	AUX
ejpam-3501	44	4	a	a	DET
ejpam-3501	44	5	graph	graph	NOUN
ejpam-3501	44	6	without	without	ADP
ejpam-3501	44	7	isolated	isolated	ADJ
ejpam-3501	44	8	vertices	vertex	NOUN
ejpam-3501	44	9	.	.	PUNCT
ejpam-3501	45	1	a	a	DET
ejpam-3501	45	2	set	set	NOUN
ejpam-3501	45	3	s	s	NOUN
ejpam-3501	45	4	⊆	⊆	NUM
ejpam-3501	45	5	v	v	NOUN
ejpam-3501	45	6	(	(	PUNCT
ejpam-3501	45	7	g	g	NOUN
ejpam-3501	45	8	)	)	PUNCT
ejpam-3501	45	9	is	be	AUX
ejpam-3501	45	10	a	a	DET
ejpam-3501	45	11	semitotal	semitotal	ADJ
ejpam-3501	45	12	dominating	dominating	NOUN
ejpam-3501	45	13	set	set	NOUN
ejpam-3501	45	14	in	in	ADP
ejpam-3501	45	15	g	g	PROPN
ejpam-3501	45	16	if	if	SCONJ
ejpam-3501	45	17	s	s	VERB
ejpam-3501	45	18	is	be	AUX
ejpam-3501	45	19	a	a	DET
ejpam-3501	45	20	dominating	dominating	NOUN
ejpam-3501	45	21	set	set	VERB
ejpam-3501	45	22	in	in	ADP
ejpam-3501	45	23	g	g	PROPN
ejpam-3501	45	24	such	such	ADJ
ejpam-3501	45	25	that	that	PRON
ejpam-3501	45	26	for	for	ADP
ejpam-3501	45	27	every	every	DET
ejpam-3501	45	28	x	x	SYM
ejpam-3501	45	29	∈	∈	PROPN
ejpam-3501	45	30	s	s	VERB
ejpam-3501	45	31	there	there	PRON
ejpam-3501	45	32	exists	exist	VERB
ejpam-3501	45	33	y	y	PROPN
ejpam-3501	45	34	∈	∈	PROPN
ejpam-3501	45	35	s\{x	s\{x	PROPN
ejpam-3501	45	36	}	}	PUNCT
ejpam-3501	45	37	such	such	ADJ
ejpam-3501	45	38	that	that	SCONJ
ejpam-3501	45	39	dg(x	dg(x	PROPN
ejpam-3501	45	40	,	,	PUNCT
ejpam-3501	45	41	y	y	NOUN
ejpam-3501	45	42	)	)	PUNCT
ejpam-3501	45	43	≤	≤	NOUN
ejpam-3501	45	44	2	2	NUM
ejpam-3501	45	45	.	.	PUNCT
ejpam-3501	45	46	the	the	DET
ejpam-3501	45	47	smallest	small	ADJ
ejpam-3501	45	48	cardinality	cardinality	NOUN
ejpam-3501	45	49	of	of	ADP
ejpam-3501	45	50	a	a	DET
ejpam-3501	45	51	semitotal	semitotal	ADJ
ejpam-3501	45	52	dominating	dominating	NOUN
ejpam-3501	45	53	set	set	NOUN
ejpam-3501	45	54	in	in	ADP
ejpam-3501	45	55	g	g	NOUN
ejpam-3501	45	56	,	,	PUNCT
ejpam-3501	45	57	denoted	denote	VERB
ejpam-3501	45	58	by	by	ADP
ejpam-3501	45	59	γt2(g	γt2(g	PROPN
ejpam-3501	45	60	)	)	PUNCT
ejpam-3501	45	61	,	,	PUNCT
ejpam-3501	45	62	is	be	AUX
ejpam-3501	45	63	called	call	VERB
ejpam-3501	45	64	the	the	DET
ejpam-3501	45	65	semitotal	semitotal	ADJ
ejpam-3501	45	66	domination	domination	NOUN
ejpam-3501	45	67	number	number	NOUN
ejpam-3501	45	68	of	of	ADP
ejpam-3501	45	69	g.	g.	PROPN
ejpam-3501	45	70	a	a	DET
ejpam-3501	45	71	semitotal	semitotal	ADJ
ejpam-3501	45	72	dominating	dominating	NOUN
ejpam-3501	45	73	set	set	NOUN
ejpam-3501	45	74	in	in	ADP
ejpam-3501	45	75	g	g	NOUN
ejpam-3501	45	76	with	with	ADP
ejpam-3501	45	77	cardinality	cardinality	NOUN
ejpam-3501	45	78	γt2(g	γt2(g	PROPN
ejpam-3501	45	79	)	)	PUNCT
ejpam-3501	45	80	is	be	AUX
ejpam-3501	45	81	called	call	VERB
ejpam-3501	45	82	a	a	DET
ejpam-3501	45	83	γt2	γt2	NOUN
ejpam-3501	45	84	-	-	PUNCT
ejpam-3501	45	85	set	set	NOUN
ejpam-3501	45	86	.	.	PUNCT
ejpam-3501	46	1	it	it	PRON
ejpam-3501	46	2	is	be	AUX
ejpam-3501	46	3	worth	worth	ADJ
ejpam-3501	46	4	noting	note	VERB
ejpam-3501	46	5	that	that	SCONJ
ejpam-3501	46	6	since	since	SCONJ
ejpam-3501	46	7	a	a	DET
ejpam-3501	46	8	semitotal	semitotal	ADJ
ejpam-3501	46	9	dominating	dominating	NOUN
ejpam-3501	46	10	set	set	NOUN
ejpam-3501	46	11	is	be	AUX
ejpam-3501	46	12	a	a	DET
ejpam-3501	46	13	dominating	dominating	NOUN
ejpam-3501	46	14	set	set	NOUN
ejpam-3501	46	15	and	and	CCONJ
ejpam-3501	46	16	total	total	ADJ
ejpam-3501	46	17	dominating	dominating	NOUN
ejpam-3501	46	18	sets	set	NOUN
ejpam-3501	46	19	are	be	AUX
ejpam-3501	46	20	semitotal	semitotal	ADJ
ejpam-3501	46	21	dominating	dominating	NOUN
ejpam-3501	46	22	sets	set	NOUN
ejpam-3501	46	23	,	,	PUNCT
ejpam-3501	46	24	max{2	max{2	PROPN
ejpam-3501	46	25	,	,	PUNCT
ejpam-3501	46	26	γ(g	γ(g	PROPN
ejpam-3501	46	27	)	)	PUNCT
ejpam-3501	46	28	}	}	PUNCT
ejpam-3501	46	29	≤	≤	NUM
ejpam-3501	46	30	γt2(g	γt2(g	NOUN
ejpam-3501	46	31	)	)	PUNCT
ejpam-3501	46	32	≤	≤	NOUN
ejpam-3501	46	33	γt(g	γt(g	PUNCT
ejpam-3501	46	34	)	)	PUNCT
ejpam-3501	46	35	for	for	ADP
ejpam-3501	46	36	graphs	graph	NOUN
ejpam-3501	46	37	g	g	NOUN
ejpam-3501	46	38	without	without	ADP
ejpam-3501	46	39	isolated	isolated	ADJ
ejpam-3501	46	40	vertices	vertex	NOUN
ejpam-3501	46	41	.	.	PUNCT
ejpam-3501	47	1	for	for	ADP
ejpam-3501	47	2	all	all	DET
ejpam-3501	47	3	connected	connected	ADJ
ejpam-3501	47	4	graphs	graph	NOUN
ejpam-3501	47	5	g	g	NOUN
ejpam-3501	47	6	on	on	ADP
ejpam-3501	47	7	n	n	PRON
ejpam-3501	47	8	≥	≥	NUM
ejpam-3501	47	9	4	4	NUM
ejpam-3501	47	10	vertices	vertex	NOUN
ejpam-3501	47	11	,	,	PUNCT
ejpam-3501	47	12	γt2(g	γt2(g	NOUN
ejpam-3501	47	13	)	)	PUNCT
ejpam-3501	47	14	≤	≤	NOUN
ejpam-3501	47	15	n	n	DET
ejpam-3501	47	16	2	2	NUM
ejpam-3501	47	17	[	[	X
ejpam-3501	47	18	13	13	NUM
ejpam-3501	47	19	]	]	PUNCT
ejpam-3501	47	20	.	.	PUNCT
ejpam-3501	48	1	in	in	ADP
ejpam-3501	48	2	the	the	DET
ejpam-3501	48	3	referred	refer	VERB
ejpam-3501	48	4	paper	paper	NOUN
ejpam-3501	48	5	,	,	PUNCT
ejpam-3501	48	6	the	the	DET
ejpam-3501	48	7	authors	author	NOUN
ejpam-3501	48	8	characterized	characterize	VERB
ejpam-3501	48	9	those	those	DET
ejpam-3501	48	10	trees	tree	NOUN
ejpam-3501	48	11	and	and	CCONJ
ejpam-3501	48	12	graphs	graph	NOUN
ejpam-3501	48	13	of	of	ADP
ejpam-3501	48	14	minimum	minimum	NOUN
ejpam-3501	48	15	degree	degree	NOUN
ejpam-3501	48	16	2	2	NUM
ejpam-3501	48	17	achieving	achieve	VERB
ejpam-3501	48	18	this	this	DET
ejpam-3501	48	19	bound	bind	VERB
ejpam-3501	48	20	.	.	PUNCT
ejpam-3501	49	1	other	other	ADJ
ejpam-3501	49	2	excellent	excellent	ADJ
ejpam-3501	49	3	exposition	exposition	NOUN
ejpam-3501	49	4	on	on	ADP
ejpam-3501	49	5	semitotal	semitotal	ADJ
ejpam-3501	49	6	domination	domination	NOUN
ejpam-3501	49	7	are	be	AUX
ejpam-3501	49	8	found	find	VERB
ejpam-3501	49	9	in	in	ADP
ejpam-3501	49	10	[	[	X
ejpam-3501	49	11	17	17	NUM
ejpam-3501	49	12	]	]	PUNCT
ejpam-3501	49	13	and	and	CCONJ
ejpam-3501	49	14	in	in	ADP
ejpam-3501	49	15	[	[	X
ejpam-3501	49	16	18	18	NUM
ejpam-3501	49	17	]	]	PUNCT
ejpam-3501	49	18	.	.	PUNCT
ejpam-3501	50	1	i.	i.	PROPN
ejpam-3501	50	2	s.	s.	PROPN
ejpam-3501	50	3	aniversario	aniversario	PROPN
ejpam-3501	50	4	,	,	PUNCT
ejpam-3501	50	5	s.	s.	PROPN
ejpam-3501	50	6	r.	r.	PROPN
ejpam-3501	50	7	jr	jr	PROPN
ejpam-3501	50	8	.	.	PROPN
ejpam-3501	50	9	canoy	canoy	PROPN
ejpam-3501	50	10	,	,	PUNCT
ejpam-3501	50	11	f.p	f.p	PROPN
ejpam-3501	50	12	.	.	PROPN
ejpam-3501	50	13	jamil	jamil	PROPN
ejpam-3501	50	14	/	/	SYM
ejpam-3501	50	15	eur	eur	PROPN
ejpam-3501	50	16	.	.	PUNCT
ejpam-3501	51	1	j.	j.	PROPN
ejpam-3501	51	2	pure	pure	PROPN
ejpam-3501	51	3	appl	appl	PROPN
ejpam-3501	51	4	.	.	PROPN
ejpam-3501	51	5	math	math	PROPN
ejpam-3501	51	6	,	,	PUNCT
ejpam-3501	51	7	12	12	NUM
ejpam-3501	51	8	(	(	PUNCT
ejpam-3501	51	9	4	4	NUM
ejpam-3501	51	10	)	)	PUNCT
ejpam-3501	51	11	(	(	PUNCT
ejpam-3501	51	12	2019	2019	NUM
ejpam-3501	51	13	)	)	PUNCT
ejpam-3501	51	14	,	,	PUNCT
ejpam-3501	51	15	1410	1410	NUM
ejpam-3501	51	16	-	-	SYM
ejpam-3501	51	17	1425	1425	NUM
ejpam-3501	51	18	1412	1412	NUM
ejpam-3501	51	19	2	2	NUM
ejpam-3501	51	20	.	.	PUNCT
ejpam-3501	52	1	secure	secure	VERB
ejpam-3501	52	2	semitotal	semitotal	ADJ
ejpam-3501	52	3	domination	domination	NOUN
ejpam-3501	52	4	a	a	DET
ejpam-3501	52	5	semitotal	semitotal	ADJ
ejpam-3501	52	6	dominating	dominating	NOUN
ejpam-3501	52	7	set	set	NOUN
ejpam-3501	52	8	s	s	PROPN
ejpam-3501	52	9	⊆	⊆	NUM
ejpam-3501	52	10	v	v	NOUN
ejpam-3501	52	11	(	(	PUNCT
ejpam-3501	52	12	g	g	NOUN
ejpam-3501	52	13	)	)	PUNCT
ejpam-3501	52	14	is	be	AUX
ejpam-3501	52	15	a	a	DET
ejpam-3501	52	16	secure	secure	ADJ
ejpam-3501	52	17	semitotal	semitotal	ADJ
ejpam-3501	52	18	dominating	dominating	NOUN
ejpam-3501	52	19	set	set	NOUN
ejpam-3501	52	20	if	if	SCONJ
ejpam-3501	52	21	for	for	ADP
ejpam-3501	52	22	each	each	DET
ejpam-3501	52	23	u	u	PROPN
ejpam-3501	52	24	∈	∈	PROPN
ejpam-3501	52	25	v	v	ADP
ejpam-3501	52	26	(	(	PUNCT
ejpam-3501	52	27	g	g	NOUN
ejpam-3501	52	28	)	)	PUNCT
ejpam-3501	52	29	\	\	PROPN
ejpam-3501	53	1	s	s	X
ejpam-3501	53	2	,	,	PUNCT
ejpam-3501	53	3	there	there	PRON
ejpam-3501	53	4	exists	exist	VERB
ejpam-3501	53	5	v	v	ADP
ejpam-3501	53	6	∈	∈	PROPN
ejpam-3501	53	7	s	s	PART
ejpam-3501	53	8	∩	∩	NOUN
ejpam-3501	53	9	ng(u	ng(u	NOUN
ejpam-3501	53	10	)	)	PUNCT
ejpam-3501	53	11	such	such	ADJ
ejpam-3501	53	12	that	that	SCONJ
ejpam-3501	53	13	(	(	PUNCT
ejpam-3501	53	14	s	s	NOUN
ejpam-3501	53	15	\	\	X
ejpam-3501	53	16	{	{	PUNCT
ejpam-3501	53	17	v	v	NOUN
ejpam-3501	53	18	}	}	PUNCT
ejpam-3501	53	19	)	)	PUNCT
ejpam-3501	53	20	∪	∪	ADP
ejpam-3501	53	21	{	{	PUNCT
ejpam-3501	53	22	u	u	NOUN
ejpam-3501	53	23	}	}	PUNCT
ejpam-3501	53	24	is	be	AUX
ejpam-3501	53	25	a	a	DET
ejpam-3501	53	26	semitotal	semitotal	ADJ
ejpam-3501	53	27	dominating	dominating	NOUN
ejpam-3501	53	28	set	set	VERB
ejpam-3501	53	29	in	in	ADP
ejpam-3501	53	30	g.	g.	PROPN
ejpam-3501	53	31	the	the	DET
ejpam-3501	53	32	smallest	small	ADJ
ejpam-3501	53	33	cardinality	cardinality	NOUN
ejpam-3501	53	34	of	of	ADP
ejpam-3501	53	35	a	a	DET
ejpam-3501	53	36	secure	secure	ADJ
ejpam-3501	53	37	semitotal	semitotal	ADJ
ejpam-3501	53	38	dominating	dominating	NOUN
ejpam-3501	53	39	set	set	NOUN
ejpam-3501	53	40	in	in	ADP
ejpam-3501	53	41	g	g	PROPN
ejpam-3501	53	42	is	be	AUX
ejpam-3501	53	43	called	call	VERB
ejpam-3501	53	44	the	the	DET
ejpam-3501	53	45	secure	secure	ADJ
ejpam-3501	53	46	semitotal	semitotal	ADJ
ejpam-3501	53	47	domination	domination	NOUN
ejpam-3501	53	48	number	number	NOUN
ejpam-3501	53	49	of	of	ADP
ejpam-3501	53	50	g	g	NOUN
ejpam-3501	53	51	and	and	CCONJ
ejpam-3501	53	52	is	be	AUX
ejpam-3501	53	53	denoted	denote	VERB
ejpam-3501	53	54	by	by	ADP
ejpam-3501	53	55	γst2(g	γst2(g	NOUN
ejpam-3501	53	56	)	)	PUNCT
ejpam-3501	53	57	.	.	PUNCT
ejpam-3501	54	1	a	a	DET
ejpam-3501	54	2	secure	secure	ADJ
ejpam-3501	54	3	semitotal	semitotal	ADJ
ejpam-3501	54	4	dominating	dominating	NOUN
ejpam-3501	54	5	set	set	VERB
ejpam-3501	54	6	with	with	ADP
ejpam-3501	54	7	cardinality	cardinality	NOUN
ejpam-3501	54	8	γst2(g	γst2(g	NUM
ejpam-3501	54	9	)	)	PUNCT
ejpam-3501	54	10	is	be	AUX
ejpam-3501	54	11	called	call	VERB
ejpam-3501	54	12	a	a	DET
ejpam-3501	54	13	γst2	γst2	ADV
ejpam-3501	54	14	-	-	PUNCT
ejpam-3501	54	15	set	set	NOUN
ejpam-3501	54	16	.	.	PUNCT
ejpam-3501	55	1	secure	secure	VERB
ejpam-3501	55	2	semitotal	semitotal	ADJ
ejpam-3501	55	3	dominating	dominating	NOUN
ejpam-3501	55	4	sets	set	NOUN
ejpam-3501	55	5	are	be	AUX
ejpam-3501	55	6	both	both	PRON
ejpam-3501	55	7	semitotal	semitotal	ADJ
ejpam-3501	55	8	dominating	dominating	NOUN
ejpam-3501	55	9	sets	set	NOUN
ejpam-3501	55	10	and	and	CCONJ
ejpam-3501	55	11	secure	secure	VERB
ejpam-3501	55	12	dominating	dominating	NOUN
ejpam-3501	55	13	sets	set	NOUN
ejpam-3501	55	14	.	.	PUNCT
ejpam-3501	56	1	on	on	ADP
ejpam-3501	56	2	the	the	DET
ejpam-3501	56	3	other	other	ADJ
ejpam-3501	56	4	hand	hand	NOUN
ejpam-3501	56	5	,	,	PUNCT
ejpam-3501	56	6	secure	secure	VERB
ejpam-3501	56	7	total	total	ADJ
ejpam-3501	56	8	dominating	dominating	NOUN
ejpam-3501	56	9	sets	set	NOUN
ejpam-3501	56	10	are	be	AUX
ejpam-3501	56	11	secure	secure	ADJ
ejpam-3501	56	12	semitotal	semitotal	ADJ
ejpam-3501	56	13	dominating	dominating	NOUN
ejpam-3501	56	14	sets	set	NOUN
ejpam-3501	56	15	.	.	PUNCT
ejpam-3501	57	1	thus	thus	ADV
ejpam-3501	57	2	,	,	PUNCT
ejpam-3501	57	3	max{γt2(g	max{γt2(g	NOUN
ejpam-3501	57	4	)	)	PUNCT
ejpam-3501	57	5	,	,	PUNCT
ejpam-3501	57	6	γs(g	γs(g	PUNCT
ejpam-3501	57	7	)	)	PUNCT
ejpam-3501	57	8	}	}	PUNCT
ejpam-3501	57	9	≤	≤	NOUN
ejpam-3501	57	10	γst2(g	γst2(g	NOUN
ejpam-3501	57	11	)	)	PUNCT
ejpam-3501	57	12	≤	≤	NUM
ejpam-3501	57	13	γst(g	γst(g	PROPN
ejpam-3501	57	14	)	)	PUNCT
ejpam-3501	57	15	for	for	ADP
ejpam-3501	57	16	all	all	DET
ejpam-3501	57	17	graphs	graph	NOUN
ejpam-3501	57	18	g	g	NOUN
ejpam-3501	57	19	without	without	ADP
ejpam-3501	57	20	isolated	isolated	ADJ
ejpam-3501	57	21	vertices	vertex	NOUN
ejpam-3501	57	22	.	.	PUNCT
ejpam-3501	58	1	example	example	NOUN
ejpam-3501	58	2	1	1	NUM
ejpam-3501	58	3	.	.	PUNCT
ejpam-3501	59	1	(	(	PUNCT
ejpam-3501	59	2	1	1	X
ejpam-3501	59	3	)	)	PUNCT
ejpam-3501	59	4	for	for	ADP
ejpam-3501	59	5	n	n	X
ejpam-3501	59	6	≥	≥	NUM
ejpam-3501	59	7	2	2	NUM
ejpam-3501	59	8	,	,	PUNCT
ejpam-3501	59	9	γst2(pn	γst2(pn	NUM
ejpam-3501	59	10	)	)	PUNCT
ejpam-3501	59	11	=	=	PUNCT
ejpam-3501	60	1			PRON
ejpam-3501	60	2	dn2	dn2	VERB
ejpam-3501	60	3	e	e	NOUN
ejpam-3501	60	4	,	,	PUNCT
ejpam-3501	60	5	if	if	SCONJ
ejpam-3501	60	6	n	n	PROPN
ejpam-3501	60	7	6=	6=	NUM
ejpam-3501	60	8	2	2	NUM
ejpam-3501	60	9	,	,	PUNCT
ejpam-3501	60	10	6	6	NUM
ejpam-3501	60	11	2	2	NUM
ejpam-3501	60	12	,	,	PUNCT
ejpam-3501	60	13	n	n	NOUN
ejpam-3501	60	14	=	=	SYM
ejpam-3501	60	15	2	2	NUM
ejpam-3501	60	16	4	4	NUM
ejpam-3501	60	17	,	,	PUNCT
ejpam-3501	60	18	n	n	NOUN
ejpam-3501	60	19	=	=	SYM
ejpam-3501	60	20	6	6	NUM
ejpam-3501	60	21	.	.	PUNCT
ejpam-3501	61	1	(	(	PUNCT
ejpam-3501	61	2	2	2	NUM
ejpam-3501	61	3	)	)	PUNCT
ejpam-3501	61	4	for	for	ADP
ejpam-3501	61	5	n	n	X
ejpam-3501	61	6	≥	≥	NUM
ejpam-3501	61	7	3	3	NUM
ejpam-3501	61	8	,	,	PUNCT
ejpam-3501	61	9	γst2(cn	γst2(cn	PROPN
ejpam-3501	61	10	)	)	PUNCT
ejpam-3501	61	11	=	=	PUNCT
ejpam-3501	62	1	⌈	⌈	PROPN
ejpam-3501	62	2	n	n	CCONJ
ejpam-3501	62	3	2	2	NUM
ejpam-3501	62	4	⌉	⌉	X
ejpam-3501	62	5	.	.	PUNCT
ejpam-3501	63	1	(	(	PUNCT
ejpam-3501	63	2	3	3	X
ejpam-3501	63	3	)	)	PUNCT
ejpam-3501	63	4	for	for	ADP
ejpam-3501	63	5	m	m	PROPN
ejpam-3501	63	6	,	,	PUNCT
ejpam-3501	63	7	n	n	PRON
ejpam-3501	63	8	≥	≥	NOUN
ejpam-3501	63	9	2	2	NUM
ejpam-3501	63	10	,	,	PUNCT
ejpam-3501	63	11	γst2(km	γst2(km	NOUN
ejpam-3501	63	12	,	,	PUNCT
ejpam-3501	63	13	n	n	CCONJ
ejpam-3501	63	14	)	)	PUNCT
ejpam-3501	63	15	=	=	SYM
ejpam-3501	63	16	min{m	min{m	PROPN
ejpam-3501	63	17	,	,	PUNCT
ejpam-3501	63	18	n	n	CCONJ
ejpam-3501	63	19	,	,	PUNCT
ejpam-3501	63	20	4	4	NUM
ejpam-3501	63	21	}	}	PUNCT
ejpam-3501	63	22	.	.	PUNCT
ejpam-3501	64	1	for	for	ADP
ejpam-3501	64	2	v	v	NUM
ejpam-3501	64	3	∈	∈	PROPN
ejpam-3501	64	4	v	v	NOUN
ejpam-3501	64	5	(	(	PUNCT
ejpam-3501	64	6	g	g	NOUN
ejpam-3501	64	7	)	)	PUNCT
ejpam-3501	64	8	,	,	PUNCT
ejpam-3501	64	9	we	we	PRON
ejpam-3501	64	10	write	write	VERB
ejpam-3501	64	11	n2	n2	ADJ
ejpam-3501	64	12	g(v	g(v	PROPN
ejpam-3501	64	13	)	)	PUNCT
ejpam-3501	64	14	=	=	PRON
ejpam-3501	64	15	{	{	PUNCT
ejpam-3501	64	16	u	u	NOUN
ejpam-3501	64	17	∈	∈	PROPN
ejpam-3501	64	18	v	v	NOUN
ejpam-3501	64	19	(	(	PUNCT
ejpam-3501	64	20	g	g	NOUN
ejpam-3501	64	21	)	)	PUNCT
ejpam-3501	64	22	\	\	NOUN
ejpam-3501	64	23	{	{	PUNCT
ejpam-3501	64	24	v	v	NOUN
ejpam-3501	64	25	}	}	PUNCT
ejpam-3501	64	26	:	:	PUNCT
ejpam-3501	64	27	dg(u	dg(u	X
ejpam-3501	64	28	,	,	PUNCT
ejpam-3501	64	29	v	v	NOUN
ejpam-3501	64	30	)	)	PUNCT
ejpam-3501	64	31	≤	≤	NOUN
ejpam-3501	64	32	2	2	NUM
ejpam-3501	64	33	}	}	PUNCT
ejpam-3501	64	34	,	,	PUNCT
ejpam-3501	64	35	and	and	CCONJ
ejpam-3501	64	36	for	for	ADP
ejpam-3501	64	37	s	s	PROPN
ejpam-3501	64	38	⊆	⊆	NUM
ejpam-3501	64	39	v	v	NOUN
ejpam-3501	64	40	(	(	PUNCT
ejpam-3501	64	41	g	g	NOUN
ejpam-3501	64	42	)	)	PUNCT
ejpam-3501	64	43	,	,	PUNCT
ejpam-3501	64	44	we	we	PRON
ejpam-3501	64	45	write	write	VERB
ejpam-3501	64	46	n2	n2	ADJ
ejpam-3501	64	47	g(s	g(s	PROPN
ejpam-3501	64	48	)	)	PUNCT
ejpam-3501	64	49	=	=	SYM
ejpam-3501	65	1	∪v∈sn2	∪v∈sn2	NUM
ejpam-3501	65	2	g(v	g(v	PROPN
ejpam-3501	65	3	)	)	PUNCT
ejpam-3501	65	4	.	.	PUNCT
ejpam-3501	66	1	precisely	precisely	ADV
ejpam-3501	66	2	,	,	PUNCT
ejpam-3501	66	3	s	s	VERB
ejpam-3501	66	4	is	be	AUX
ejpam-3501	66	5	a	a	DET
ejpam-3501	66	6	semitotal	semitotal	ADJ
ejpam-3501	66	7	dominating	dominating	NOUN
ejpam-3501	66	8	set	set	NOUN
ejpam-3501	66	9	if	if	SCONJ
ejpam-3501	66	10	and	and	CCONJ
ejpam-3501	66	11	only	only	ADV
ejpam-3501	66	12	if	if	SCONJ
ejpam-3501	66	13	v	v	INTJ
ejpam-3501	66	14	(	(	PUNCT
ejpam-3501	66	15	g	g	NOUN
ejpam-3501	66	16	)	)	PUNCT
ejpam-3501	66	17	\	\	PUNCT
ejpam-3501	66	18	s	s	PART
ejpam-3501	66	19	⊆	⊆	NUM
ejpam-3501	66	20	ng(s	ng(s	NUM
ejpam-3501	66	21	)	)	PUNCT
ejpam-3501	66	22	and	and	CCONJ
ejpam-3501	66	23	s	s	VERB
ejpam-3501	66	24	⊆	⊆	NUM
ejpam-3501	66	25	n2	n2	ADJ
ejpam-3501	66	26	g(s	g(s	PROPN
ejpam-3501	66	27	)	)	PUNCT
ejpam-3501	66	28	.	.	PUNCT
ejpam-3501	67	1	theorem	theorem	NOUN
ejpam-3501	67	2	1	1	NUM
ejpam-3501	67	3	.	.	PUNCT
ejpam-3501	68	1	let	let	VERB
ejpam-3501	68	2	g	g	PRON
ejpam-3501	68	3	be	be	AUX
ejpam-3501	68	4	a	a	DET
ejpam-3501	68	5	connected	connected	ADJ
ejpam-3501	68	6	graph	graph	NOUN
ejpam-3501	68	7	of	of	ADP
ejpam-3501	68	8	order	order	NOUN
ejpam-3501	68	9	n	n	PRON
ejpam-3501	68	10	≥	≥	NOUN
ejpam-3501	68	11	2	2	NUM
ejpam-3501	68	12	.	.	PUNCT
ejpam-3501	69	1	then	then	ADV
ejpam-3501	69	2	γst2(g	γst2(g	NUM
ejpam-3501	69	3	)	)	PUNCT
ejpam-3501	69	4	=	=	SYM
ejpam-3501	69	5	2	2	NUM
ejpam-3501	69	6	if	if	SCONJ
ejpam-3501	69	7	and	and	CCONJ
ejpam-3501	69	8	only	only	ADV
ejpam-3501	69	9	if	if	SCONJ
ejpam-3501	69	10	there	there	PRON
ejpam-3501	69	11	exists	exist	VERB
ejpam-3501	69	12	a	a	DET
ejpam-3501	69	13	dominating	dominating	NOUN
ejpam-3501	69	14	set	set	NOUN
ejpam-3501	69	15	{	{	PUNCT
ejpam-3501	69	16	x	x	NOUN
ejpam-3501	69	17	,	,	PUNCT
ejpam-3501	69	18	y	y	NOUN
ejpam-3501	69	19	}	}	PUNCT
ejpam-3501	69	20	in	in	ADP
ejpam-3501	69	21	g	g	NOUN
ejpam-3501	69	22	satisfying	satisfy	VERB
ejpam-3501	69	23	the	the	DET
ejpam-3501	69	24	following	follow	VERB
ejpam-3501	69	25	properties	property	NOUN
ejpam-3501	69	26	:	:	PUNCT
ejpam-3501	69	27	(	(	PUNCT
ejpam-3501	69	28	i	i	NOUN
ejpam-3501	69	29	)	)	PUNCT
ejpam-3501	69	30	dg(x	dg(x	PROPN
ejpam-3501	69	31	,	,	PUNCT
ejpam-3501	69	32	y	y	NOUN
ejpam-3501	69	33	)	)	PUNCT
ejpam-3501	69	34	≤	≤	NOUN
ejpam-3501	69	35	2	2	NUM
ejpam-3501	69	36	;	;	PUNCT
ejpam-3501	69	37	(	(	PUNCT
ejpam-3501	69	38	ii	ii	NOUN
ejpam-3501	69	39	)	)	PUNCT
ejpam-3501	69	40	n2	n2	NOUN
ejpam-3501	69	41	g(x	g(x	NOUN
ejpam-3501	69	42	)	)	PUNCT
ejpam-3501	70	1	=	=	SYM
ejpam-3501	70	2	v	v	X
ejpam-3501	70	3	(	(	PUNCT
ejpam-3501	70	4	g	g	NOUN
ejpam-3501	70	5	)	)	PUNCT
ejpam-3501	70	6	\	\	NOUN
ejpam-3501	70	7	{	{	PUNCT
ejpam-3501	70	8	x	x	NOUN
ejpam-3501	70	9	}	}	PUNCT
ejpam-3501	70	10	and	and	CCONJ
ejpam-3501	70	11	n2	n2	ADJ
ejpam-3501	70	12	g(y	g(y	PROPN
ejpam-3501	70	13	)	)	PUNCT
ejpam-3501	70	14	=	=	SYM
ejpam-3501	70	15	v	v	X
ejpam-3501	70	16	(	(	PUNCT
ejpam-3501	70	17	g	g	NOUN
ejpam-3501	70	18	)	)	PUNCT
ejpam-3501	70	19	\	\	NOUN
ejpam-3501	70	20	{	{	PUNCT
ejpam-3501	70	21	y	y	NOUN
ejpam-3501	70	22	}	}	PUNCT
ejpam-3501	70	23	;	;	PUNCT
ejpam-3501	70	24	and	and	CCONJ
ejpam-3501	70	25	(	(	PUNCT
ejpam-3501	70	26	iii	iii	NOUN
ejpam-3501	70	27	)	)	PUNCT
ejpam-3501	70	28	{	{	PUNCT
ejpam-3501	70	29	x	x	NOUN
ejpam-3501	70	30	,	,	PUNCT
ejpam-3501	70	31	z	z	NOUN
ejpam-3501	70	32	}	}	PUNCT
ejpam-3501	70	33	and	and	CCONJ
ejpam-3501	70	34	{	{	PUNCT
ejpam-3501	70	35	u	u	NOUN
ejpam-3501	70	36	,	,	PUNCT
ejpam-3501	70	37	y	y	NOUN
ejpam-3501	70	38	}	}	PUNCT
ejpam-3501	70	39	are	be	AUX
ejpam-3501	70	40	dominating	dominate	VERB
ejpam-3501	70	41	sets	set	NOUN
ejpam-3501	70	42	in	in	ADP
ejpam-3501	70	43	g	g	NOUN
ejpam-3501	70	44	for	for	ADP
ejpam-3501	70	45	all	all	DET
ejpam-3501	70	46	z	z	NOUN
ejpam-3501	70	47	∈	∈	PROPN
ejpam-3501	70	48	ng(y	ng(y	NOUN
ejpam-3501	70	49	)	)	PUNCT
ejpam-3501	70	50	\	\	NOUN
ejpam-3501	70	51	{	{	PUNCT
ejpam-3501	70	52	x	x	NOUN
ejpam-3501	70	53	}	}	PUNCT
ejpam-3501	70	54	and	and	CCONJ
ejpam-3501	70	55	for	for	ADP
ejpam-3501	70	56	all	all	PRON
ejpam-3501	70	57	u	u	PROPN
ejpam-3501	70	58	∈	∈	PROPN
ejpam-3501	70	59	ng(x	ng(x	NUM
ejpam-3501	70	60	)	)	PUNCT
ejpam-3501	70	61	\	\	NOUN
ejpam-3501	71	1	{	{	PUNCT
ejpam-3501	71	2	y	y	NOUN
ejpam-3501	71	3	}	}	PUNCT
ejpam-3501	71	4	.	.	PUNCT
ejpam-3501	72	1	proof	proof	NOUN
ejpam-3501	72	2	.	.	PUNCT
ejpam-3501	73	1	suppose	suppose	VERB
ejpam-3501	73	2	that	that	SCONJ
ejpam-3501	73	3	γst2(g	γst2(g	NUM
ejpam-3501	73	4	)	)	PUNCT
ejpam-3501	73	5	=	=	SYM
ejpam-3501	73	6	2	2	NUM
ejpam-3501	73	7	,	,	PUNCT
ejpam-3501	73	8	and	and	CCONJ
ejpam-3501	73	9	let	let	VERB
ejpam-3501	73	10	s	s	PRON
ejpam-3501	73	11	=	=	PUNCT
ejpam-3501	73	12	{	{	PUNCT
ejpam-3501	73	13	x	x	PROPN
ejpam-3501	73	14	,	,	PUNCT
ejpam-3501	73	15	y	y	PROPN
ejpam-3501	73	16	}	}	PUNCT
ejpam-3501	73	17	be	be	AUX
ejpam-3501	73	18	a	a	DET
ejpam-3501	73	19	γst2	γst2	ADV
ejpam-3501	73	20	-	-	PUNCT
ejpam-3501	73	21	set	set	NOUN
ejpam-3501	73	22	of	of	ADP
ejpam-3501	73	23	g.	g.	PROPN
ejpam-3501	73	24	then	then	ADV
ejpam-3501	73	25	s	s	VERB
ejpam-3501	73	26	is	be	AUX
ejpam-3501	73	27	a	a	DET
ejpam-3501	73	28	dominating	dominating	NOUN
ejpam-3501	73	29	set	set	NOUN
ejpam-3501	73	30	in	in	ADP
ejpam-3501	73	31	g	g	PROPN
ejpam-3501	73	32	and	and	CCONJ
ejpam-3501	73	33	dg(x	dg(x	NUM
ejpam-3501	73	34	,	,	PUNCT
ejpam-3501	73	35	y	y	NOUN
ejpam-3501	73	36	)	)	PUNCT
ejpam-3501	73	37	≤	≤	NOUN
ejpam-3501	73	38	2	2	NUM
ejpam-3501	73	39	.	.	PUNCT
ejpam-3501	73	40	suppose	suppose	VERB
ejpam-3501	73	41	that	that	SCONJ
ejpam-3501	73	42	,	,	PUNCT
ejpam-3501	73	43	in	in	ADP
ejpam-3501	73	44	the	the	DET
ejpam-3501	73	45	contrary	contrary	NOUN
ejpam-3501	73	46	,	,	PUNCT
ejpam-3501	73	47	n2	n2	ADJ
ejpam-3501	73	48	g(x	g(x	NOUN
ejpam-3501	73	49	)	)	PUNCT
ejpam-3501	73	50	6=	6=	ADP
ejpam-3501	73	51	v	v	X
ejpam-3501	73	52	(	(	PUNCT
ejpam-3501	73	53	g)\{x	g)\{x	PROPN
ejpam-3501	73	54	}	}	PUNCT
ejpam-3501	73	55	,	,	PUNCT
ejpam-3501	73	56	and	and	CCONJ
ejpam-3501	73	57	let	let	VERB
ejpam-3501	73	58	z	z	NOUN
ejpam-3501	73	59	∈	∈	PROPN
ejpam-3501	73	60	v	v	NOUN
ejpam-3501	73	61	(	(	PUNCT
ejpam-3501	73	62	g)\n2	g)\n2	NOUN
ejpam-3501	73	63	g(x	g(x	NOUN
ejpam-3501	73	64	)	)	PUNCT
ejpam-3501	73	65	with	with	ADP
ejpam-3501	73	66	z	z	PROPN
ejpam-3501	73	67	6=	6=	PROPN
ejpam-3501	73	68	x.	x.	NOUN
ejpam-3501	73	69	then	then	ADV
ejpam-3501	73	70	z	z	PROPN
ejpam-3501	73	71	/∈	/∈	PUNCT
ejpam-3501	73	72	s.	s.	PROPN
ejpam-3501	73	73	since	since	SCONJ
ejpam-3501	73	74	s	s	PROPN
ejpam-3501	73	75	is	be	AUX
ejpam-3501	73	76	a	a	DET
ejpam-3501	73	77	secure	secure	ADJ
ejpam-3501	73	78	semitotal	semitotal	ADJ
ejpam-3501	73	79	dominating	dominating	NOUN
ejpam-3501	73	80	set	set	VERB
ejpam-3501	73	81	in	in	ADP
ejpam-3501	73	82	g	g	PROPN
ejpam-3501	73	83	and	and	CCONJ
ejpam-3501	73	84	z	z	NOUN
ejpam-3501	73	85	/∈	/∈	PUNCT
ejpam-3501	73	86	n2	n2	ADJ
ejpam-3501	73	87	g(x	g(x	PROPN
ejpam-3501	73	88	)	)	PUNCT
ejpam-3501	73	89	,	,	PUNCT
ejpam-3501	73	90	y	y	PROPN
ejpam-3501	73	91	∈	∈	PROPN
ejpam-3501	73	92	ng(z	ng(z	PROPN
ejpam-3501	73	93	)	)	PUNCT
ejpam-3501	73	94	and	and	CCONJ
ejpam-3501	73	95	(	(	PUNCT
ejpam-3501	73	96	s	s	NOUN
ejpam-3501	73	97	\	\	X
ejpam-3501	73	98	{	{	PUNCT
ejpam-3501	73	99	y})∪{z	y})∪{z	NOUN
ejpam-3501	73	100	}	}	PUNCT
ejpam-3501	73	101	=	=	SYM
ejpam-3501	73	102	{	{	PUNCT
ejpam-3501	73	103	x	x	NOUN
ejpam-3501	73	104	,	,	PUNCT
ejpam-3501	73	105	z	z	NOUN
ejpam-3501	73	106	}	}	PUNCT
ejpam-3501	73	107	is	be	AUX
ejpam-3501	73	108	a	a	DET
ejpam-3501	73	109	semitotal	semitotal	ADJ
ejpam-3501	73	110	dominating	dominating	NOUN
ejpam-3501	73	111	set	set	NOUN
ejpam-3501	73	112	in	in	ADP
ejpam-3501	73	113	g	g	PROPN
ejpam-3501	73	114	,	,	PUNCT
ejpam-3501	73	115	a	a	DET
ejpam-3501	73	116	contradiction	contradiction	NOUN
ejpam-3501	73	117	since	since	SCONJ
ejpam-3501	73	118	dg(x	dg(x	NUM
ejpam-3501	73	119	,	,	PUNCT
ejpam-3501	73	120	z	z	NOUN
ejpam-3501	73	121	)	)	PUNCT
ejpam-3501	73	122	>	>	X
ejpam-3501	74	1	2	2	X
ejpam-3501	74	2	.	.	PUNCT
ejpam-3501	74	3	thus	thus	ADV
ejpam-3501	74	4	,	,	PUNCT
ejpam-3501	74	5	n2	n2	ADJ
ejpam-3501	74	6	g(x	g(x	NOUN
ejpam-3501	74	7	)	)	PUNCT
ejpam-3501	75	1	=	=	SYM
ejpam-3501	75	2	v	v	X
ejpam-3501	75	3	(	(	PUNCT
ejpam-3501	75	4	g	g	NOUN
ejpam-3501	75	5	)	)	PUNCT
ejpam-3501	75	6	\	\	NOUN
ejpam-3501	75	7	{	{	PUNCT
ejpam-3501	75	8	x	x	NOUN
ejpam-3501	75	9	}	}	PUNCT
ejpam-3501	75	10	.	.	PUNCT
ejpam-3501	76	1	similarly	similarly	ADV
ejpam-3501	76	2	,	,	PUNCT
ejpam-3501	76	3	n2	n2	PROPN
ejpam-3501	76	4	g(y)\{y	g(y)\{y	PROPN
ejpam-3501	76	5	}	}	PUNCT
ejpam-3501	76	6	=	=	SYM
ejpam-3501	76	7	v	v	NOUN
ejpam-3501	76	8	(	(	PUNCT
ejpam-3501	76	9	g)\{y	g)\{y	PROPN
ejpam-3501	76	10	}	}	PUNCT
ejpam-3501	76	11	.	.	PUNCT
ejpam-3501	77	1	now	now	ADV
ejpam-3501	77	2	let	let	VERB
ejpam-3501	77	3	z	z	NOUN
ejpam-3501	77	4	∈	∈	PROPN
ejpam-3501	77	5	v	v	NOUN
ejpam-3501	77	6	(	(	PUNCT
ejpam-3501	77	7	g)\s	g)\s	NOUN
ejpam-3501	77	8	.	.	PUNCT
ejpam-3501	78	1	since	since	SCONJ
ejpam-3501	78	2	s	s	PROPN
ejpam-3501	78	3	is	be	AUX
ejpam-3501	78	4	a	a	DET
ejpam-3501	78	5	secure	secure	ADJ
ejpam-3501	78	6	semitotal	semitotal	ADJ
ejpam-3501	78	7	dominating	dominating	NOUN
ejpam-3501	78	8	set	set	NOUN
ejpam-3501	78	9	,	,	PUNCT
ejpam-3501	78	10	there	there	PRON
ejpam-3501	78	11	exists	exist	VERB
ejpam-3501	78	12	w	w	PROPN
ejpam-3501	78	13	∈	∈	PROPN
ejpam-3501	78	14	s	s	PART
ejpam-3501	78	15	∩ng(z	∩ng(z	PROPN
ejpam-3501	78	16	)	)	PUNCT
ejpam-3501	78	17	such	such	ADJ
ejpam-3501	78	18	that	that	DET
ejpam-3501	78	19	t	t	NOUN
ejpam-3501	78	20	=	=	PUNCT
ejpam-3501	78	21	(	(	PUNCT
ejpam-3501	78	22	s	s	NOUN
ejpam-3501	78	23	\	\	X
ejpam-3501	78	24	{	{	PUNCT
ejpam-3501	78	25	w	w	NOUN
ejpam-3501	78	26	}	}	PUNCT
ejpam-3501	78	27	)	)	PUNCT
ejpam-3501	78	28	∪	∪	ADP
ejpam-3501	78	29	{	{	PUNCT
ejpam-3501	78	30	z	z	NOUN
ejpam-3501	78	31	}	}	PUNCT
ejpam-3501	78	32	is	be	AUX
ejpam-3501	78	33	a	a	DET
ejpam-3501	78	34	semitotal	semitotal	ADJ
ejpam-3501	78	35	dominating	dominating	NOUN
ejpam-3501	78	36	set	set	NOUN
ejpam-3501	78	37	,	,	PUNCT
ejpam-3501	78	38	and	and	CCONJ
ejpam-3501	78	39	hence	hence	ADV
ejpam-3501	78	40	a	a	DET
ejpam-3501	78	41	dominating	dominating	NOUN
ejpam-3501	78	42	set	set	VERB
ejpam-3501	78	43	in	in	ADP
ejpam-3501	78	44	g.	g.	PROPN
ejpam-3501	78	45	if	if	SCONJ
ejpam-3501	78	46	w	w	PROPN
ejpam-3501	78	47	=	=	SYM
ejpam-3501	78	48	y	y	PROPN
ejpam-3501	78	49	,	,	PUNCT
ejpam-3501	78	50	then	then	ADV
ejpam-3501	78	51	t	t	PROPN
ejpam-3501	78	52	=	=	SYM
ejpam-3501	78	53	{	{	PUNCT
ejpam-3501	78	54	x	x	NOUN
ejpam-3501	78	55	,	,	PUNCT
ejpam-3501	78	56	z	z	NOUN
ejpam-3501	78	57	}	}	PUNCT
ejpam-3501	78	58	and	and	CCONJ
ejpam-3501	78	59	if	if	SCONJ
ejpam-3501	78	60	x	x	X
ejpam-3501	78	61	=	=	SYM
ejpam-3501	78	62	w	w	PROPN
ejpam-3501	78	63	,	,	PUNCT
ejpam-3501	78	64	then	then	ADV
ejpam-3501	78	65	t	t	PROPN
ejpam-3501	78	66	=	=	SYM
ejpam-3501	78	67	{	{	PUNCT
ejpam-3501	78	68	y	y	PROPN
ejpam-3501	78	69	,	,	PUNCT
ejpam-3501	78	70	z	z	NOUN
ejpam-3501	78	71	}	}	PUNCT
ejpam-3501	78	72	.	.	PUNCT
ejpam-3501	79	1	conversely	conversely	ADV
ejpam-3501	79	2	,	,	PUNCT
ejpam-3501	79	3	let	let	VERB
ejpam-3501	79	4	s	s	PRON
ejpam-3501	79	5	=	=	PUNCT
ejpam-3501	79	6	{	{	PUNCT
ejpam-3501	79	7	x	x	PROPN
ejpam-3501	79	8	,	,	PUNCT
ejpam-3501	79	9	y	y	PROPN
ejpam-3501	79	10	}	}	PUNCT
ejpam-3501	79	11	be	be	AUX
ejpam-3501	79	12	a	a	DET
ejpam-3501	79	13	dominating	dominating	NOUN
ejpam-3501	79	14	set	set	VERB
ejpam-3501	79	15	in	in	ADP
ejpam-3501	79	16	g	g	NOUN
ejpam-3501	79	17	satisfying	satisfy	VERB
ejpam-3501	79	18	the	the	DET
ejpam-3501	79	19	properties	property	NOUN
ejpam-3501	79	20	(	(	PUNCT
ejpam-3501	79	21	i	i	NOUN
ejpam-3501	79	22	)	)	PUNCT
ejpam-3501	79	23	,	,	PUNCT
ejpam-3501	79	24	(	(	PUNCT
ejpam-3501	79	25	ii	ii	NOUN
ejpam-3501	79	26	)	)	PUNCT
ejpam-3501	79	27	and	and	CCONJ
ejpam-3501	79	28	(	(	PUNCT
ejpam-3501	79	29	iii	iii	NOUN
ejpam-3501	79	30	)	)	PUNCT
ejpam-3501	79	31	.	.	PUNCT
ejpam-3501	80	1	by	by	ADP
ejpam-3501	80	2	property	property	NOUN
ejpam-3501	80	3	(	(	PUNCT
ejpam-3501	80	4	i	i	NOUN
ejpam-3501	80	5	)	)	PUNCT
ejpam-3501	80	6	,	,	PUNCT
ejpam-3501	80	7	s	s	VERB
ejpam-3501	80	8	is	be	AUX
ejpam-3501	80	9	a	a	DET
ejpam-3501	80	10	semitotal	semitotal	ADJ
ejpam-3501	80	11	dominating	dominating	NOUN
ejpam-3501	80	12	set	set	VERB
ejpam-3501	80	13	in	in	ADP
ejpam-3501	80	14	g.	g.	PROPN
ejpam-3501	80	15	let	let	VERB
ejpam-3501	80	16	z	z	PROPN
ejpam-3501	80	17	∈	∈	PROPN
ejpam-3501	80	18	v	v	ADP
ejpam-3501	80	19	(	(	PUNCT
ejpam-3501	80	20	g	g	NOUN
ejpam-3501	80	21	)	)	PUNCT
ejpam-3501	80	22	\	\	PUNCT
ejpam-3501	81	1	s.	s.	PROPN
ejpam-3501	81	2	then	then	ADV
ejpam-3501	81	3	x	x	SYM
ejpam-3501	81	4	∈	∈	PROPN
ejpam-3501	81	5	s	s	PART
ejpam-3501	81	6	∩	∩	NOUN
ejpam-3501	81	7	ng(z	ng(z	NUM
ejpam-3501	81	8	)	)	PUNCT
ejpam-3501	81	9	or	or	CCONJ
ejpam-3501	81	10	y	y	PROPN
ejpam-3501	81	11	∈	∈	PROPN
ejpam-3501	81	12	s	s	PART
ejpam-3501	81	13	∩	∩	NOUN
ejpam-3501	81	14	ng(z	ng(z	NUM
ejpam-3501	81	15	)	)	PUNCT
ejpam-3501	81	16	.	.	PUNCT
ejpam-3501	82	1	assume	assume	VERB
ejpam-3501	82	2	that	that	SCONJ
ejpam-3501	82	3	x	x	PUNCT
ejpam-3501	82	4	∈	∈	NOUN
ejpam-3501	82	5	s	s	PART
ejpam-3501	82	6	∩	∩	NOUN
ejpam-3501	82	7	ng(z	ng(z	NUM
ejpam-3501	82	8	)	)	PUNCT
ejpam-3501	82	9	.	.	PUNCT
ejpam-3501	83	1	note	note	VERB
ejpam-3501	83	2	that	that	SCONJ
ejpam-3501	83	3	,	,	PUNCT
ejpam-3501	83	4	by	by	ADP
ejpam-3501	83	5	properties	property	NOUN
ejpam-3501	83	6	(	(	PUNCT
ejpam-3501	83	7	ii	ii	NOUN
ejpam-3501	83	8	)	)	PUNCT
ejpam-3501	83	9	and	and	CCONJ
ejpam-3501	83	10	(	(	PUNCT
ejpam-3501	83	11	iii	iii	NOUN
ejpam-3501	83	12	)	)	PUNCT
ejpam-3501	83	13	,	,	PUNCT
ejpam-3501	83	14	(	(	PUNCT
ejpam-3501	83	15	s	s	NOUN
ejpam-3501	83	16	\	\	X
ejpam-3501	83	17	{	{	PUNCT
ejpam-3501	83	18	x})∪{z	x})∪{z	NOUN
ejpam-3501	83	19	}	}	PUNCT
ejpam-3501	83	20	=	=	SYM
ejpam-3501	83	21	{	{	PUNCT
ejpam-3501	83	22	y	y	PROPN
ejpam-3501	83	23	,	,	PUNCT
ejpam-3501	83	24	z	z	NOUN
ejpam-3501	83	25	}	}	PUNCT
ejpam-3501	83	26	is	be	AUX
ejpam-3501	83	27	a	a	DET
ejpam-3501	83	28	semitotal	semitotal	ADJ
ejpam-3501	83	29	dominating	dominating	NOUN
ejpam-3501	83	30	set	set	VERB
ejpam-3501	83	31	in	in	ADP
ejpam-3501	83	32	g.	g.	PROPN
ejpam-3501	83	33	thus	thus	ADV
ejpam-3501	83	34	,	,	PUNCT
ejpam-3501	83	35	γst2(g	γst2(g	NUM
ejpam-3501	83	36	)	)	PUNCT
ejpam-3501	83	37	=	=	SYM
ejpam-3501	83	38	|s|	|s|	NOUN
ejpam-3501	83	39	=	=	SYM
ejpam-3501	83	40	2	2	PROPN
ejpam-3501	83	41	.	.	PUNCT
ejpam-3501	83	42	i.	i.	PROPN
ejpam-3501	83	43	s.	s.	PROPN
ejpam-3501	83	44	aniversario	aniversario	PROPN
ejpam-3501	83	45	,	,	PUNCT
ejpam-3501	83	46	s.	s.	PROPN
ejpam-3501	83	47	r.	r.	PROPN
ejpam-3501	83	48	jr	jr	PROPN
ejpam-3501	83	49	.	.	PROPN
ejpam-3501	83	50	canoy	canoy	PROPN
ejpam-3501	83	51	,	,	PUNCT
ejpam-3501	83	52	f.p	f.p	PROPN
ejpam-3501	83	53	.	.	PROPN
ejpam-3501	83	54	jamil	jamil	PROPN
ejpam-3501	83	55	/	/	SYM
ejpam-3501	83	56	eur	eur	PROPN
ejpam-3501	83	57	.	.	PUNCT
ejpam-3501	84	1	j.	j.	PROPN
ejpam-3501	84	2	pure	pure	PROPN
ejpam-3501	84	3	appl	appl	PROPN
ejpam-3501	84	4	.	.	PROPN
ejpam-3501	84	5	math	math	PROPN
ejpam-3501	84	6	,	,	PUNCT
ejpam-3501	84	7	12	12	NUM
ejpam-3501	84	8	(	(	PUNCT
ejpam-3501	84	9	4	4	NUM
ejpam-3501	84	10	)	)	PUNCT
ejpam-3501	84	11	(	(	PUNCT
ejpam-3501	84	12	2019	2019	NUM
ejpam-3501	84	13	)	)	PUNCT
ejpam-3501	84	14	,	,	PUNCT
ejpam-3501	84	15	1410	1410	NUM
ejpam-3501	84	16	-	-	SYM
ejpam-3501	84	17	1425	1425	NUM
ejpam-3501	84	18	1413	1413	NUM
ejpam-3501	84	19	3	3	NUM
ejpam-3501	84	20	.	.	PUNCT
ejpam-3501	85	1	in	in	ADP
ejpam-3501	85	2	the	the	DET
ejpam-3501	85	3	join	join	NOUN
ejpam-3501	85	4	of	of	ADP
ejpam-3501	85	5	graphs	graph	NOUN
ejpam-3501	85	6	for	for	ADP
ejpam-3501	85	7	any	any	DET
ejpam-3501	85	8	graph	graph	NOUN
ejpam-3501	85	9	g	g	NOUN
ejpam-3501	85	10	,	,	PUNCT
ejpam-3501	85	11	γt2(g	γt2(g	PROPN
ejpam-3501	85	12	+	+	NUM
ejpam-3501	85	13	k1	k1	NOUN
ejpam-3501	85	14	)	)	PUNCT
ejpam-3501	85	15	=	=	SYM
ejpam-3501	85	16	2	2	X
ejpam-3501	85	17	.	.	X
ejpam-3501	85	18	more	more	ADV
ejpam-3501	85	19	specifically	specifically	ADV
ejpam-3501	85	20	,	,	PUNCT
ejpam-3501	85	21	a	a	DET
ejpam-3501	85	22	semitotal	semitotal	ADJ
ejpam-3501	85	23	dominating	dominating	NOUN
ejpam-3501	85	24	set	set	NOUN
ejpam-3501	85	25	in	in	ADP
ejpam-3501	85	26	g+k1	g+k1	NOUN
ejpam-3501	85	27	is	be	AUX
ejpam-3501	85	28	either	either	PRON
ejpam-3501	85	29	of	of	ADP
ejpam-3501	85	30	the	the	DET
ejpam-3501	85	31	form	form	NOUN
ejpam-3501	85	32	v	v	NOUN
ejpam-3501	85	33	(	(	PUNCT
ejpam-3501	85	34	k1	k1	NOUN
ejpam-3501	85	35	)	)	PUNCT
ejpam-3501	85	36	∪	∪	ADP
ejpam-3501	85	37	s	s	PRON
ejpam-3501	85	38	for	for	ADP
ejpam-3501	85	39	some	some	DET
ejpam-3501	85	40	nonempty	nonempty	NOUN
ejpam-3501	85	41	s	s	VERB
ejpam-3501	85	42	⊆	⊆	NUM
ejpam-3501	85	43	v	v	NOUN
ejpam-3501	85	44	(	(	PUNCT
ejpam-3501	85	45	g	g	NOUN
ejpam-3501	85	46	)	)	PUNCT
ejpam-3501	85	47	,	,	PUNCT
ejpam-3501	85	48	or	or	CCONJ
ejpam-3501	85	49	a	a	DET
ejpam-3501	85	50	nonsingleton	nonsingleton	NOUN
ejpam-3501	85	51	dominating	dominating	NOUN
ejpam-3501	85	52	set	set	VERB
ejpam-3501	85	53	in	in	ADP
ejpam-3501	85	54	g	g	NOUN
ejpam-3501	85	55	in	in	ADP
ejpam-3501	85	56	case	case	NOUN
ejpam-3501	85	57	g	g	NOUN
ejpam-3501	85	58	is	be	AUX
ejpam-3501	85	59	nontrivial	nontrivial	ADJ
ejpam-3501	85	60	.	.	PUNCT
ejpam-3501	86	1	theorem	theorem	NOUN
ejpam-3501	86	2	2	2	NUM
ejpam-3501	86	3	.	.	PUNCT
ejpam-3501	87	1	let	let	VERB
ejpam-3501	87	2	g	g	NOUN
ejpam-3501	87	3	and	and	CCONJ
ejpam-3501	87	4	h	h	NOUN
ejpam-3501	87	5	be	be	AUX
ejpam-3501	87	6	nontrivial	nontrivial	ADJ
ejpam-3501	87	7	graphs	graph	NOUN
ejpam-3501	87	8	,	,	PUNCT
ejpam-3501	87	9	and	and	CCONJ
ejpam-3501	87	10	s	s	VERB
ejpam-3501	87	11	⊆	⊆	NUM
ejpam-3501	87	12	v	v	NOUN
ejpam-3501	87	13	(	(	PUNCT
ejpam-3501	87	14	g+h	g+h	PROPN
ejpam-3501	87	15	)	)	PUNCT
ejpam-3501	87	16	.	.	PUNCT
ejpam-3501	88	1	then	then	ADV
ejpam-3501	88	2	s	s	VERB
ejpam-3501	88	3	is	be	AUX
ejpam-3501	88	4	a	a	DET
ejpam-3501	88	5	semitotal	semitotal	ADJ
ejpam-3501	88	6	dominating	dominating	NOUN
ejpam-3501	88	7	set	set	VERB
ejpam-3501	88	8	in	in	ADP
ejpam-3501	88	9	g+h	g+h	PROPN
ejpam-3501	89	1	if	if	SCONJ
ejpam-3501	89	2	and	and	CCONJ
ejpam-3501	89	3	only	only	ADV
ejpam-3501	89	4	if	if	SCONJ
ejpam-3501	89	5	one	one	NUM
ejpam-3501	89	6	of	of	ADP
ejpam-3501	89	7	the	the	DET
ejpam-3501	89	8	following	follow	VERB
ejpam-3501	89	9	holds	hold	VERB
ejpam-3501	89	10	:	:	PUNCT
ejpam-3501	89	11	(	(	PUNCT
ejpam-3501	89	12	i	i	NOUN
ejpam-3501	89	13	)	)	PUNCT
ejpam-3501	89	14	s	s	VERB
ejpam-3501	89	15	⊆	⊆	NUM
ejpam-3501	89	16	v	v	NOUN
ejpam-3501	89	17	(	(	PUNCT
ejpam-3501	89	18	g	g	NOUN
ejpam-3501	89	19	)	)	PUNCT
ejpam-3501	89	20	is	be	AUX
ejpam-3501	89	21	a	a	DET
ejpam-3501	89	22	nonsingleton	nonsingleton	NOUN
ejpam-3501	89	23	dominating	dominating	NOUN
ejpam-3501	89	24	set	set	VERB
ejpam-3501	89	25	in	in	ADP
ejpam-3501	89	26	g	g	NOUN
ejpam-3501	89	27	;	;	PUNCT
ejpam-3501	89	28	(	(	PUNCT
ejpam-3501	89	29	ii	ii	NOUN
ejpam-3501	89	30	)	)	PUNCT
ejpam-3501	89	31	s	s	PART
ejpam-3501	89	32	⊆	⊆	NUM
ejpam-3501	89	33	v	v	NOUN
ejpam-3501	89	34	(	(	PUNCT
ejpam-3501	89	35	h	h	NOUN
ejpam-3501	89	36	)	)	PUNCT
ejpam-3501	89	37	is	be	AUX
ejpam-3501	89	38	a	a	DET
ejpam-3501	89	39	nonsingleton	nonsingleton	NOUN
ejpam-3501	89	40	dominating	dominating	NOUN
ejpam-3501	89	41	set	set	VERB
ejpam-3501	89	42	in	in	ADP
ejpam-3501	89	43	h	h	NOUN
ejpam-3501	89	44	;	;	PUNCT
ejpam-3501	89	45	(	(	PUNCT
ejpam-3501	89	46	iii	iii	X
ejpam-3501	89	47	)	)	PUNCT
ejpam-3501	89	48	s	s	PART
ejpam-3501	89	49	∩	∩	ADJ
ejpam-3501	89	50	v	v	X
ejpam-3501	89	51	(	(	PUNCT
ejpam-3501	89	52	g	g	NOUN
ejpam-3501	89	53	)	)	PUNCT
ejpam-3501	89	54	6=	6=	ADP
ejpam-3501	89	55	∅	∅	NOUN
ejpam-3501	89	56	and	and	CCONJ
ejpam-3501	89	57	s	s	X
ejpam-3501	89	58	∩	∩	ADJ
ejpam-3501	89	59	v	v	ADJ
ejpam-3501	89	60	(	(	PUNCT
ejpam-3501	89	61	h	h	NOUN
ejpam-3501	89	62	)	)	PUNCT
ejpam-3501	89	63	6=	6=	ADP
ejpam-3501	89	64	∅.	∅.	PRON
ejpam-3501	89	65	proof	proof	NOUN
ejpam-3501	89	66	.	.	PUNCT
ejpam-3501	90	1	suppose	suppose	VERB
ejpam-3501	90	2	that	that	SCONJ
ejpam-3501	90	3	s	s	VERB
ejpam-3501	90	4	⊆	⊆	NUM
ejpam-3501	90	5	v	v	NOUN
ejpam-3501	90	6	(	(	PUNCT
ejpam-3501	90	7	g	g	NOUN
ejpam-3501	90	8	)	)	PUNCT
ejpam-3501	90	9	is	be	AUX
ejpam-3501	90	10	a	a	DET
ejpam-3501	90	11	nonsingleton	nonsingleton	NOUN
ejpam-3501	90	12	dominating	dominating	NOUN
ejpam-3501	90	13	set	set	VERB
ejpam-3501	90	14	in	in	ADP
ejpam-3501	90	15	g.	g.	PROPN
ejpam-3501	91	1	then	then	ADV
ejpam-3501	91	2	s	s	VERB
ejpam-3501	91	3	is	be	AUX
ejpam-3501	91	4	a	a	DET
ejpam-3501	91	5	dominating	dominating	NOUN
ejpam-3501	91	6	set	set	NOUN
ejpam-3501	91	7	in	in	ADP
ejpam-3501	91	8	g	g	PROPN
ejpam-3501	91	9	+	+	CCONJ
ejpam-3501	91	10	h.	h.	PROPN
ejpam-3501	91	11	let	let	VERB
ejpam-3501	91	12	v	v	ADP
ejpam-3501	91	13	∈	∈	VERB
ejpam-3501	91	14	s.	s.	PROPN
ejpam-3501	91	15	since	since	SCONJ
ejpam-3501	91	16	s	s	PROPN
ejpam-3501	91	17	is	be	AUX
ejpam-3501	91	18	nonsingleton	nonsingleton	ADJ
ejpam-3501	91	19	,	,	PUNCT
ejpam-3501	91	20	we	we	PRON
ejpam-3501	91	21	may	may	AUX
ejpam-3501	91	22	take	take	VERB
ejpam-3501	91	23	u	u	PRON
ejpam-3501	91	24	∈	∈	NOUN
ejpam-3501	91	25	s	s	NOUN
ejpam-3501	91	26	with	with	ADP
ejpam-3501	91	27	u	u	PROPN
ejpam-3501	91	28	6=	6=	PROPN
ejpam-3501	92	1	v.	v.	ADP
ejpam-3501	92	2	note	note	NOUN
ejpam-3501	93	1	that	that	SCONJ
ejpam-3501	93	2	dg+h(u	dg+h(u	PROPN
ejpam-3501	93	3	,	,	PUNCT
ejpam-3501	93	4	v	v	NOUN
ejpam-3501	93	5	)	)	PUNCT
ejpam-3501	93	6	≤	≤	NOUN
ejpam-3501	93	7	2	2	NUM
ejpam-3501	93	8	.	.	PUNCT
ejpam-3501	94	1	since	since	SCONJ
ejpam-3501	94	2	v	v	NOUN
ejpam-3501	94	3	is	be	AUX
ejpam-3501	94	4	arbitrary	arbitrary	ADJ
ejpam-3501	94	5	,	,	PUNCT
ejpam-3501	94	6	s	s	PART
ejpam-3501	94	7	is	be	AUX
ejpam-3501	94	8	a	a	DET
ejpam-3501	94	9	semitotal	semitotal	ADJ
ejpam-3501	94	10	dominating	dominating	NOUN
ejpam-3501	94	11	set	set	VERB
ejpam-3501	94	12	in	in	ADP
ejpam-3501	94	13	g+h	g+h	PROPN
ejpam-3501	94	14	.	.	PUNCT
ejpam-3501	95	1	similarly	similarly	ADV
ejpam-3501	95	2	,	,	PUNCT
ejpam-3501	95	3	if	if	SCONJ
ejpam-3501	95	4	s	s	VERB
ejpam-3501	95	5	⊆	⊆	NUM
ejpam-3501	95	6	v	v	NOUN
ejpam-3501	95	7	(	(	PUNCT
ejpam-3501	95	8	h	h	NOUN
ejpam-3501	95	9	)	)	PUNCT
ejpam-3501	95	10	is	be	AUX
ejpam-3501	95	11	a	a	DET
ejpam-3501	95	12	nonsingleton	nonsingleton	NOUN
ejpam-3501	95	13	dominating	dominating	NOUN
ejpam-3501	95	14	set	set	VERB
ejpam-3501	95	15	in	in	ADP
ejpam-3501	95	16	h	h	NOUN
ejpam-3501	95	17	,	,	PUNCT
ejpam-3501	95	18	then	then	ADV
ejpam-3501	95	19	s	s	VERB
ejpam-3501	95	20	is	be	AUX
ejpam-3501	95	21	a	a	DET
ejpam-3501	95	22	semitotal	semitotal	ADJ
ejpam-3501	95	23	dominating	dominating	NOUN
ejpam-3501	95	24	set	set	VERB
ejpam-3501	95	25	in	in	ADP
ejpam-3501	95	26	g	g	PROPN
ejpam-3501	95	27	+	+	PROPN
ejpam-3501	95	28	h.	h.	PROPN
ejpam-3501	95	29	suppose	suppose	VERB
ejpam-3501	95	30	that	that	SCONJ
ejpam-3501	95	31	s	s	VERB
ejpam-3501	95	32	intersects	intersect	NOUN
ejpam-3501	95	33	both	both	PRON
ejpam-3501	95	34	v	v	NOUN
ejpam-3501	95	35	(	(	PUNCT
ejpam-3501	95	36	g	g	NOUN
ejpam-3501	95	37	)	)	PUNCT
ejpam-3501	95	38	and	and	CCONJ
ejpam-3501	95	39	v	v	NOUN
ejpam-3501	95	40	(	(	PUNCT
ejpam-3501	95	41	h	h	NOUN
ejpam-3501	95	42	)	)	PUNCT
ejpam-3501	95	43	.	.	PUNCT
ejpam-3501	96	1	then	then	ADV
ejpam-3501	96	2	s	s	VERB
ejpam-3501	96	3	is	be	AUX
ejpam-3501	96	4	a	a	DET
ejpam-3501	96	5	total	total	ADJ
ejpam-3501	96	6	dominating	dominating	NOUN
ejpam-3501	96	7	set	set	NOUN
ejpam-3501	96	8	,	,	PUNCT
ejpam-3501	96	9	hence	hence	ADV
ejpam-3501	96	10	a	a	DET
ejpam-3501	96	11	semitotal	semitotal	ADJ
ejpam-3501	96	12	dominating	dominating	NOUN
ejpam-3501	96	13	set	set	NOUN
ejpam-3501	96	14	,	,	PUNCT
ejpam-3501	96	15	in	in	ADP
ejpam-3501	96	16	g+h	g+h	PROPN
ejpam-3501	96	17	.	.	PUNCT
ejpam-3501	97	1	conversely	conversely	ADV
ejpam-3501	97	2	,	,	PUNCT
ejpam-3501	97	3	suppose	suppose	VERB
ejpam-3501	97	4	that	that	SCONJ
ejpam-3501	97	5	s	s	VERB
ejpam-3501	97	6	is	be	AUX
ejpam-3501	97	7	a	a	DET
ejpam-3501	97	8	semitotal	semitotal	ADJ
ejpam-3501	97	9	dominating	dominating	NOUN
ejpam-3501	97	10	set	set	VERB
ejpam-3501	97	11	in	in	ADP
ejpam-3501	97	12	g	g	PROPN
ejpam-3501	97	13	+	+	CCONJ
ejpam-3501	97	14	h.	h.	PROPN
ejpam-3501	97	15	then	then	ADV
ejpam-3501	97	16	s	s	VERB
ejpam-3501	97	17	is	be	AUX
ejpam-3501	97	18	a	a	DET
ejpam-3501	97	19	dominating	dominating	NOUN
ejpam-3501	97	20	set	set	NOUN
ejpam-3501	97	21	in	in	ADP
ejpam-3501	97	22	g+h	g+h	PROPN
ejpam-3501	97	23	and	and	CCONJ
ejpam-3501	97	24	|s|	|s|	PROPN
ejpam-3501	97	25	≥	≥	NOUN
ejpam-3501	97	26	2	2	NUM
ejpam-3501	97	27	.	.	PUNCT
ejpam-3501	98	1	if	if	SCONJ
ejpam-3501	98	2	s	s	VERB
ejpam-3501	98	3	⊆	⊆	NUM
ejpam-3501	98	4	v	v	NOUN
ejpam-3501	98	5	(	(	PUNCT
ejpam-3501	98	6	g	g	NOUN
ejpam-3501	98	7	)	)	PUNCT
ejpam-3501	98	8	(	(	PUNCT
ejpam-3501	98	9	resp	resp	NOUN
ejpam-3501	98	10	.	.	PUNCT
ejpam-3501	99	1	s	s	PART
ejpam-3501	99	2	⊆	⊆	NUM
ejpam-3501	99	3	v	v	NOUN
ejpam-3501	99	4	(	(	PUNCT
ejpam-3501	99	5	h	h	NOUN
ejpam-3501	99	6	)	)	PUNCT
ejpam-3501	99	7	)	)	PUNCT
ejpam-3501	99	8	,	,	PUNCT
ejpam-3501	99	9	then	then	ADV
ejpam-3501	99	10	(	(	PUNCT
ejpam-3501	99	11	i	i	NOUN
ejpam-3501	99	12	)	)	PUNCT
ejpam-3501	99	13	(	(	PUNCT
ejpam-3501	99	14	resp	resp	NOUN
ejpam-3501	99	15	.	.	PUNCT
ejpam-3501	100	1	(	(	PUNCT
ejpam-3501	100	2	ii	ii	NOUN
ejpam-3501	100	3	)	)	PUNCT
ejpam-3501	100	4	)	)	PUNCT
ejpam-3501	100	5	holds	hold	VERB
ejpam-3501	100	6	.	.	PUNCT
ejpam-3501	101	1	otherwise	otherwise	ADV
ejpam-3501	101	2	,	,	PUNCT
ejpam-3501	101	3	property	property	NOUN
ejpam-3501	101	4	(	(	PUNCT
ejpam-3501	101	5	iii	iii	NOUN
ejpam-3501	101	6	)	)	PUNCT
ejpam-3501	101	7	holds	hold	VERB
ejpam-3501	101	8	.	.	PUNCT
ejpam-3501	102	1	corollary	corollary	ADJ
ejpam-3501	102	2	1	1	NUM
ejpam-3501	102	3	.	.	PUNCT
ejpam-3501	103	1	for	for	ADP
ejpam-3501	103	2	all	all	DET
ejpam-3501	103	3	graphs	graph	NOUN
ejpam-3501	103	4	g	g	NOUN
ejpam-3501	103	5	and	and	CCONJ
ejpam-3501	103	6	h	h	NOUN
ejpam-3501	103	7	,	,	PUNCT
ejpam-3501	103	8	γt2(g+h	γt2(g+h	ADJ
ejpam-3501	103	9	)	)	PUNCT
ejpam-3501	103	10	=	=	SYM
ejpam-3501	103	11	2	2	X
ejpam-3501	103	12	.	.	X
ejpam-3501	103	13	let	let	VERB
ejpam-3501	103	14	g	g	NOUN
ejpam-3501	103	15	be	be	AUX
ejpam-3501	103	16	any	any	DET
ejpam-3501	103	17	graph	graph	NOUN
ejpam-3501	103	18	and	and	CCONJ
ejpam-3501	103	19	kp	kp	PRON
ejpam-3501	103	20	the	the	DET
ejpam-3501	103	21	complete	complete	ADJ
ejpam-3501	103	22	graph	graph	NOUN
ejpam-3501	103	23	of	of	ADP
ejpam-3501	103	24	order	order	NOUN
ejpam-3501	103	25	p	p	X
ejpam-3501	103	26	≥	≥	NUM
ejpam-3501	103	27	2	2	NUM
ejpam-3501	103	28	.	.	X
ejpam-3501	103	29	note	note	VERB
ejpam-3501	103	30	that	that	SCONJ
ejpam-3501	103	31	for	for	ADP
ejpam-3501	103	32	any	any	DET
ejpam-3501	103	33	x	x	NOUN
ejpam-3501	103	34	,	,	PUNCT
ejpam-3501	103	35	y	y	PROPN
ejpam-3501	103	36	∈	∈	PROPN
ejpam-3501	103	37	v	v	PROPN
ejpam-3501	103	38	(	(	PUNCT
ejpam-3501	103	39	kp	kp	PROPN
ejpam-3501	103	40	)	)	PUNCT
ejpam-3501	103	41	,	,	PUNCT
ejpam-3501	103	42	{	{	PUNCT
ejpam-3501	103	43	x	x	X
ejpam-3501	103	44	,	,	PUNCT
ejpam-3501	103	45	y	y	PRON
ejpam-3501	103	46	}	}	PUNCT
ejpam-3501	103	47	is	be	AUX
ejpam-3501	103	48	a	a	DET
ejpam-3501	103	49	dominating	dominating	NOUN
ejpam-3501	103	50	set	set	NOUN
ejpam-3501	103	51	in	in	ADP
ejpam-3501	103	52	g	g	PROPN
ejpam-3501	103	53	+	+	CCONJ
ejpam-3501	103	54	kp	kp	X
ejpam-3501	103	55	satisfying	satisfy	VERB
ejpam-3501	103	56	the	the	DET
ejpam-3501	103	57	properties	property	NOUN
ejpam-3501	103	58	(	(	PUNCT
ejpam-3501	103	59	i	i	NOUN
ejpam-3501	103	60	)	)	PUNCT
ejpam-3501	103	61	,	,	PUNCT
ejpam-3501	103	62	(	(	PUNCT
ejpam-3501	103	63	ii	ii	NOUN
ejpam-3501	103	64	)	)	PUNCT
ejpam-3501	103	65	and	and	CCONJ
ejpam-3501	103	66	(	(	PUNCT
ejpam-3501	103	67	iii	iii	NOUN
ejpam-3501	103	68	)	)	PUNCT
ejpam-3501	103	69	of	of	ADP
ejpam-3501	103	70	theorem	theorem	NOUN
ejpam-3501	103	71	1	1	NUM
ejpam-3501	103	72	.	.	PUNCT
ejpam-3501	103	73	thus	thus	ADV
ejpam-3501	103	74	,	,	PUNCT
ejpam-3501	103	75	γst2(g+kp	γst2(g+kp	NOUN
ejpam-3501	103	76	)	)	PUNCT
ejpam-3501	103	77	=	=	SYM
ejpam-3501	103	78	2	2	X
ejpam-3501	103	79	.	.	X
ejpam-3501	103	80	proposition	proposition	NOUN
ejpam-3501	103	81	1	1	NUM
ejpam-3501	103	82	.	.	PUNCT
ejpam-3501	104	1	for	for	ADP
ejpam-3501	104	2	noncomplete	noncomplete	ADJ
ejpam-3501	104	3	graphs	graph	NOUN
ejpam-3501	104	4	g	g	PROPN
ejpam-3501	104	5	and	and	CCONJ
ejpam-3501	104	6	h	h	NOUN
ejpam-3501	104	7	,	,	PUNCT
ejpam-3501	104	8	2	2	NUM
ejpam-3501	104	9	≤	≤	NUM
ejpam-3501	104	10	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	104	11	)	)	PUNCT
ejpam-3501	104	12	≤	≤	NOUN
ejpam-3501	104	13	4	4	NUM
ejpam-3501	104	14	.	.	PUNCT
ejpam-3501	105	1	proof	proof	NOUN
ejpam-3501	105	2	.	.	PUNCT
ejpam-3501	106	1	let	let	VERB
ejpam-3501	106	2	s	s	PRON
ejpam-3501	106	3	=	=	PUNCT
ejpam-3501	106	4	{	{	PUNCT
ejpam-3501	106	5	x	x	PROPN
ejpam-3501	106	6	,	,	PUNCT
ejpam-3501	106	7	y	y	PROPN
ejpam-3501	106	8	,	,	PUNCT
ejpam-3501	106	9	u	u	NOUN
ejpam-3501	106	10	,	,	PUNCT
ejpam-3501	106	11	v	v	NOUN
ejpam-3501	106	12	}	}	PUNCT
ejpam-3501	106	13	,	,	PUNCT
ejpam-3501	106	14	where	where	SCONJ
ejpam-3501	106	15	x	x	X
ejpam-3501	106	16	,	,	PUNCT
ejpam-3501	106	17	y	y	PROPN
ejpam-3501	106	18	∈	∈	PROPN
ejpam-3501	106	19	v	v	ADP
ejpam-3501	106	20	(	(	PUNCT
ejpam-3501	106	21	g	g	NOUN
ejpam-3501	106	22	)	)	PUNCT
ejpam-3501	106	23	and	and	CCONJ
ejpam-3501	106	24	u	u	NOUN
ejpam-3501	106	25	,	,	PUNCT
ejpam-3501	106	26	v	v	PROPN
ejpam-3501	106	27	∈	∈	PROPN
ejpam-3501	106	28	v	v	NOUN
ejpam-3501	106	29	(	(	PUNCT
ejpam-3501	106	30	h	h	NOUN
ejpam-3501	106	31	)	)	PUNCT
ejpam-3501	106	32	.	.	PUNCT
ejpam-3501	107	1	then	then	ADV
ejpam-3501	107	2	s	s	VERB
ejpam-3501	107	3	is	be	AUX
ejpam-3501	107	4	a	a	DET
ejpam-3501	107	5	semitotal	semitotal	ADJ
ejpam-3501	107	6	dominating	dominating	NOUN
ejpam-3501	107	7	set	set	NOUN
ejpam-3501	107	8	in	in	ADP
ejpam-3501	107	9	g+h	g+h	PROPN
ejpam-3501	107	10	by	by	ADP
ejpam-3501	107	11	theorem	theorem	NOUN
ejpam-3501	107	12	2	2	NUM
ejpam-3501	107	13	.	.	X
ejpam-3501	107	14	for	for	ADP
ejpam-3501	107	15	each	each	DET
ejpam-3501	107	16	w	w	PROPN
ejpam-3501	107	17	∈	∈	PROPN
ejpam-3501	107	18	v	v	NOUN
ejpam-3501	107	19	(	(	PUNCT
ejpam-3501	107	20	g)\s	g)\s	NOUN
ejpam-3501	107	21	(	(	PUNCT
ejpam-3501	107	22	resp	resp	NOUN
ejpam-3501	107	23	.	.	PUNCT
ejpam-3501	108	1	each	each	DET
ejpam-3501	108	2	w	w	PROPN
ejpam-3501	108	3	∈	∈	PROPN
ejpam-3501	108	4	v	v	NOUN
ejpam-3501	108	5	(	(	PUNCT
ejpam-3501	108	6	h)\s	h)\s	PROPN
ejpam-3501	108	7	)	)	PUNCT
ejpam-3501	108	8	,	,	PUNCT
ejpam-3501	108	9	wv	wv	PROPN
ejpam-3501	108	10	∈	∈	PROPN
ejpam-3501	108	11	e(g	e(g	PROPN
ejpam-3501	108	12	+	+	CCONJ
ejpam-3501	108	13	h	h	NOUN
ejpam-3501	108	14	)	)	PUNCT
ejpam-3501	108	15	(	(	PUNCT
ejpam-3501	108	16	resp	resp	NOUN
ejpam-3501	108	17	.	.	PUNCT
ejpam-3501	109	1	wx	wx	PROPN
ejpam-3501	109	2	∈	∈	PROPN
ejpam-3501	109	3	e(g	e(g	PROPN
ejpam-3501	109	4	+	+	CCONJ
ejpam-3501	109	5	h	h	NOUN
ejpam-3501	109	6	)	)	PUNCT
ejpam-3501	109	7	)	)	PUNCT
ejpam-3501	110	1	and	and	CCONJ
ejpam-3501	110	2	,	,	PUNCT
ejpam-3501	110	3	by	by	ADP
ejpam-3501	110	4	theorem	theorem	NOUN
ejpam-3501	110	5	2	2	NUM
ejpam-3501	110	6	,	,	PUNCT
ejpam-3501	110	7	(	(	PUNCT
ejpam-3501	110	8	s	s	NOUN
ejpam-3501	110	9	\	\	X
ejpam-3501	110	10	{	{	PUNCT
ejpam-3501	110	11	v	v	NOUN
ejpam-3501	110	12	}	}	PUNCT
ejpam-3501	110	13	)	)	PUNCT
ejpam-3501	110	14	∪	∪	ADP
ejpam-3501	110	15	{	{	PUNCT
ejpam-3501	110	16	w	w	NOUN
ejpam-3501	110	17	}	}	PUNCT
ejpam-3501	110	18	(	(	PUNCT
ejpam-3501	110	19	resp	resp	NOUN
ejpam-3501	110	20	.	.	PUNCT
ejpam-3501	111	1	(	(	PUNCT
ejpam-3501	111	2	s	s	NOUN
ejpam-3501	111	3	\	\	X
ejpam-3501	111	4	{	{	PUNCT
ejpam-3501	111	5	x	x	NOUN
ejpam-3501	111	6	}	}	PUNCT
ejpam-3501	111	7	)	)	PUNCT
ejpam-3501	111	8	∪	∪	ADP
ejpam-3501	111	9	{	{	PUNCT
ejpam-3501	111	10	w	w	NOUN
ejpam-3501	111	11	}	}	PUNCT
ejpam-3501	111	12	)	)	PUNCT
ejpam-3501	111	13	is	be	AUX
ejpam-3501	111	14	a	a	DET
ejpam-3501	111	15	semitotal	semitotal	ADJ
ejpam-3501	111	16	dominating	dominating	NOUN
ejpam-3501	111	17	set	set	VERB
ejpam-3501	111	18	in	in	ADP
ejpam-3501	111	19	g	g	PROPN
ejpam-3501	111	20	+	+	PROPN
ejpam-3501	111	21	h.	h.	PROPN
ejpam-3501	111	22	thus	thus	ADV
ejpam-3501	111	23	,	,	PUNCT
ejpam-3501	111	24	s	s	VERB
ejpam-3501	111	25	is	be	AUX
ejpam-3501	111	26	a	a	DET
ejpam-3501	111	27	secure	secure	ADJ
ejpam-3501	111	28	semitotal	semitotal	ADJ
ejpam-3501	111	29	dominating	dominating	NOUN
ejpam-3501	111	30	set	set	VERB
ejpam-3501	111	31	in	in	ADP
ejpam-3501	111	32	g+h	g+h	PROPN
ejpam-3501	111	33	.	.	PUNCT
ejpam-3501	112	1	consequently	consequently	ADV
ejpam-3501	112	2	,	,	PUNCT
ejpam-3501	112	3	2	2	NUM
ejpam-3501	112	4	≤	≤	NUM
ejpam-3501	112	5	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	112	6	)	)	PUNCT
ejpam-3501	112	7	≤	≤	NUM
ejpam-3501	112	8	|s|	|s|	PROPN
ejpam-3501	112	9	=	=	SYM
ejpam-3501	112	10	4	4	NUM
ejpam-3501	112	11	.	.	PUNCT
ejpam-3501	112	12	corollary	corollary	ADJ
ejpam-3501	112	13	2	2	NUM
ejpam-3501	112	14	.	.	PUNCT
ejpam-3501	112	15	let	let	VERB
ejpam-3501	112	16	g	g	NOUN
ejpam-3501	112	17	and	and	CCONJ
ejpam-3501	112	18	h	h	NOUN
ejpam-3501	112	19	be	be	VERB
ejpam-3501	112	20	noncomplete	noncomplete	ADJ
ejpam-3501	112	21	graphs	graph	NOUN
ejpam-3501	112	22	of	of	ADP
ejpam-3501	112	23	orders	order	NOUN
ejpam-3501	112	24	m	m	VERB
ejpam-3501	112	25	and	and	CCONJ
ejpam-3501	112	26	n	n	CCONJ
ejpam-3501	112	27	,	,	PUNCT
ejpam-3501	112	28	respectively	respectively	ADV
ejpam-3501	112	29	.	.	PUNCT
ejpam-3501	113	1	then	then	ADV
ejpam-3501	113	2	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	113	3	)	)	PUNCT
ejpam-3501	113	4	=	=	SYM
ejpam-3501	113	5	2	2	NUM
ejpam-3501	113	6	if	if	SCONJ
ejpam-3501	113	7	and	and	CCONJ
ejpam-3501	113	8	only	only	ADV
ejpam-3501	113	9	if	if	SCONJ
ejpam-3501	113	10	at	at	ADV
ejpam-3501	113	11	least	least	ADJ
ejpam-3501	113	12	one	one	NUM
ejpam-3501	113	13	of	of	ADP
ejpam-3501	113	14	the	the	DET
ejpam-3501	113	15	following	follow	VERB
ejpam-3501	113	16	is	be	AUX
ejpam-3501	113	17	true	true	ADJ
ejpam-3501	113	18	:	:	PUNCT
ejpam-3501	113	19	(	(	PUNCT
ejpam-3501	113	20	i	i	NOUN
ejpam-3501	113	21	)	)	PUNCT
ejpam-3501	113	22	γs(g	γs(g	PUNCT
ejpam-3501	113	23	)	)	PUNCT
ejpam-3501	113	24	=	=	SYM
ejpam-3501	113	25	2	2	NUM
ejpam-3501	113	26	;	;	PUNCT
ejpam-3501	113	27	(	(	PUNCT
ejpam-3501	113	28	ii	ii	NOUN
ejpam-3501	113	29	)	)	PUNCT
ejpam-3501	113	30	γs(h	γs(h	PUNCT
ejpam-3501	113	31	)	)	PUNCT
ejpam-3501	113	32	=	=	SYM
ejpam-3501	114	1	2	2	NUM
ejpam-3501	114	2	;	;	PUNCT
ejpam-3501	114	3	i.	i.	PROPN
ejpam-3501	114	4	s.	s.	PROPN
ejpam-3501	114	5	aniversario	aniversario	PROPN
ejpam-3501	114	6	,	,	PUNCT
ejpam-3501	114	7	s.	s.	PROPN
ejpam-3501	114	8	r.	r.	PROPN
ejpam-3501	114	9	jr	jr	PROPN
ejpam-3501	114	10	.	.	PROPN
ejpam-3501	114	11	canoy	canoy	PROPN
ejpam-3501	114	12	,	,	PUNCT
ejpam-3501	114	13	f.p	f.p	PROPN
ejpam-3501	114	14	.	.	PROPN
ejpam-3501	114	15	jamil	jamil	PROPN
ejpam-3501	114	16	/	/	SYM
ejpam-3501	114	17	eur	eur	PROPN
ejpam-3501	114	18	.	.	PUNCT
ejpam-3501	115	1	j.	j.	PROPN
ejpam-3501	115	2	pure	pure	PROPN
ejpam-3501	115	3	appl	appl	PROPN
ejpam-3501	115	4	.	.	PROPN
ejpam-3501	115	5	math	math	PROPN
ejpam-3501	115	6	,	,	PUNCT
ejpam-3501	115	7	12	12	NUM
ejpam-3501	115	8	(	(	PUNCT
ejpam-3501	115	9	4	4	NUM
ejpam-3501	115	10	)	)	PUNCT
ejpam-3501	115	11	(	(	PUNCT
ejpam-3501	115	12	2019	2019	NUM
ejpam-3501	115	13	)	)	PUNCT
ejpam-3501	115	14	,	,	PUNCT
ejpam-3501	115	15	1410	1410	NUM
ejpam-3501	115	16	-	-	SYM
ejpam-3501	115	17	1425	1425	NUM
ejpam-3501	115	18	1414	1414	NUM
ejpam-3501	115	19	(	(	PUNCT
ejpam-3501	115	20	iii	iii	NOUN
ejpam-3501	115	21	)	)	PUNCT
ejpam-3501	115	22	there	there	PRON
ejpam-3501	115	23	exist	exist	VERB
ejpam-3501	115	24	x	x	SYM
ejpam-3501	115	25	∈	∈	PROPN
ejpam-3501	115	26	v	v	ADP
ejpam-3501	115	27	(	(	PUNCT
ejpam-3501	115	28	g	g	NOUN
ejpam-3501	115	29	)	)	PUNCT
ejpam-3501	115	30	and	and	CCONJ
ejpam-3501	115	31	y	y	PROPN
ejpam-3501	115	32	∈	∈	PROPN
ejpam-3501	115	33	v	v	ADP
ejpam-3501	115	34	(	(	PUNCT
ejpam-3501	115	35	h	h	NOUN
ejpam-3501	115	36	)	)	PUNCT
ejpam-3501	115	37	such	such	ADJ
ejpam-3501	115	38	that	that	SCONJ
ejpam-3501	115	39	{	{	PUNCT
ejpam-3501	115	40	x	x	NOUN
ejpam-3501	115	41	}	}	PUNCT
ejpam-3501	115	42	and	and	CCONJ
ejpam-3501	115	43	{	{	PUNCT
ejpam-3501	115	44	y	y	NOUN
ejpam-3501	115	45	}	}	PUNCT
ejpam-3501	115	46	are	be	AUX
ejpam-3501	115	47	nearly	nearly	ADV
ejpam-3501	115	48	dominating	dominate	VERB
ejpam-3501	115	49	sets	set	NOUN
ejpam-3501	115	50	in	in	ADP
ejpam-3501	115	51	g	g	PROPN
ejpam-3501	115	52	and	and	CCONJ
ejpam-3501	115	53	h	h	NOUN
ejpam-3501	115	54	,	,	PUNCT
ejpam-3501	115	55	respectively	respectively	ADV
ejpam-3501	115	56	.	.	PUNCT
ejpam-3501	116	1	proof	proof	NOUN
ejpam-3501	116	2	.	.	PUNCT
ejpam-3501	117	1	suppose	suppose	VERB
ejpam-3501	117	2	that	that	SCONJ
ejpam-3501	117	3	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	117	4	)	)	PUNCT
ejpam-3501	117	5	=	=	SYM
ejpam-3501	117	6	2	2	NUM
ejpam-3501	117	7	,	,	PUNCT
ejpam-3501	117	8	and	and	CCONJ
ejpam-3501	117	9	let	let	VERB
ejpam-3501	117	10	s	s	PRON
ejpam-3501	117	11	=	=	PUNCT
ejpam-3501	117	12	{	{	PUNCT
ejpam-3501	117	13	x	x	PROPN
ejpam-3501	117	14	,	,	PUNCT
ejpam-3501	117	15	y	y	PROPN
ejpam-3501	117	16	}	}	PUNCT
ejpam-3501	117	17	be	be	AUX
ejpam-3501	117	18	a	a	DET
ejpam-3501	117	19	dominating	dominating	NOUN
ejpam-3501	117	20	set	set	NOUN
ejpam-3501	117	21	in	in	ADP
ejpam-3501	117	22	g+h	g+h	PROPN
ejpam-3501	117	23	satisfying	satisfy	VERB
ejpam-3501	117	24	properties	property	NOUN
ejpam-3501	117	25	(	(	PUNCT
ejpam-3501	117	26	i	i	NOUN
ejpam-3501	117	27	)	)	PUNCT
ejpam-3501	117	28	,	,	PUNCT
ejpam-3501	117	29	(	(	PUNCT
ejpam-3501	117	30	ii	ii	NOUN
ejpam-3501	117	31	)	)	PUNCT
ejpam-3501	117	32	and	and	CCONJ
ejpam-3501	117	33	(	(	PUNCT
ejpam-3501	117	34	iii	iii	NOUN
ejpam-3501	117	35	)	)	PUNCT
ejpam-3501	117	36	in	in	ADP
ejpam-3501	117	37	theorem	theorem	NOUN
ejpam-3501	117	38	1	1	NUM
ejpam-3501	117	39	.	.	PUNCT
ejpam-3501	117	40	first	first	ADV
ejpam-3501	117	41	,	,	PUNCT
ejpam-3501	117	42	suppose	suppose	VERB
ejpam-3501	117	43	that	that	SCONJ
ejpam-3501	117	44	s	s	VERB
ejpam-3501	117	45	⊆	⊆	NUM
ejpam-3501	117	46	v	v	NOUN
ejpam-3501	117	47	(	(	PUNCT
ejpam-3501	117	48	g	g	NOUN
ejpam-3501	117	49	)	)	PUNCT
ejpam-3501	117	50	.	.	PUNCT
ejpam-3501	118	1	then	then	ADV
ejpam-3501	118	2	s	s	VERB
ejpam-3501	118	3	is	be	AUX
ejpam-3501	118	4	a	a	DET
ejpam-3501	118	5	dominating	dominating	NOUN
ejpam-3501	118	6	set	set	VERB
ejpam-3501	118	7	in	in	ADP
ejpam-3501	118	8	g.	g.	PROPN
ejpam-3501	118	9	let	let	VERB
ejpam-3501	118	10	z	z	PROPN
ejpam-3501	118	11	∈	∈	PROPN
ejpam-3501	118	12	v	v	ADP
ejpam-3501	118	13	(	(	PUNCT
ejpam-3501	118	14	g	g	NOUN
ejpam-3501	118	15	)	)	PUNCT
ejpam-3501	118	16	\	\	PUNCT
ejpam-3501	119	1	s.	s.	PROPN
ejpam-3501	119	2	assume	assume	VERB
ejpam-3501	119	3	xz	xz	PROPN
ejpam-3501	119	4	∈	∈	PROPN
ejpam-3501	119	5	e(g	e(g	PROPN
ejpam-3501	119	6	)	)	PUNCT
ejpam-3501	119	7	.	.	PUNCT
ejpam-3501	120	1	by	by	ADP
ejpam-3501	120	2	theorem	theorem	NOUN
ejpam-3501	120	3	1(iii	1(iii	NUM
ejpam-3501	120	4	)	)	PUNCT
ejpam-3501	120	5	,	,	PUNCT
ejpam-3501	120	6	{	{	PUNCT
ejpam-3501	120	7	z	z	X
ejpam-3501	120	8	,	,	PUNCT
ejpam-3501	120	9	y	y	PROPN
ejpam-3501	120	10	}	}	PUNCT
ejpam-3501	120	11	=	=	PUNCT
ejpam-3501	120	12	(	(	PUNCT
ejpam-3501	120	13	s	s	NOUN
ejpam-3501	120	14	\	\	X
ejpam-3501	120	15	{	{	PUNCT
ejpam-3501	120	16	x	x	NOUN
ejpam-3501	120	17	}	}	PUNCT
ejpam-3501	120	18	)	)	PUNCT
ejpam-3501	120	19	∪	∪	ADP
ejpam-3501	120	20	{	{	PUNCT
ejpam-3501	120	21	z	z	NOUN
ejpam-3501	120	22	}	}	PUNCT
ejpam-3501	120	23	is	be	AUX
ejpam-3501	120	24	a	a	DET
ejpam-3501	120	25	dominating	dominating	NOUN
ejpam-3501	120	26	set	set	VERB
ejpam-3501	120	27	in	in	ADP
ejpam-3501	120	28	g	g	PROPN
ejpam-3501	120	29	+	+	CCONJ
ejpam-3501	120	30	h	h	NOUN
ejpam-3501	120	31	,	,	PUNCT
ejpam-3501	120	32	hence	hence	ADV
ejpam-3501	120	33	in	in	ADP
ejpam-3501	120	34	g.	g.	PROPN
ejpam-3501	120	35	thus	thus	ADV
ejpam-3501	120	36	,	,	PUNCT
ejpam-3501	120	37	s	s	VERB
ejpam-3501	120	38	is	be	AUX
ejpam-3501	120	39	a	a	DET
ejpam-3501	120	40	secure	secure	ADJ
ejpam-3501	120	41	dominating	dominating	NOUN
ejpam-3501	120	42	set	set	VERB
ejpam-3501	120	43	in	in	ADP
ejpam-3501	120	44	g.	g.	PROPN
ejpam-3501	120	45	since	since	SCONJ
ejpam-3501	120	46	g	g	PROPN
ejpam-3501	120	47	in	in	ADP
ejpam-3501	120	48	not	not	PART
ejpam-3501	120	49	complete	complete	ADJ
ejpam-3501	120	50	,	,	PUNCT
ejpam-3501	120	51	γs(g	γs(g	PUNCT
ejpam-3501	120	52	)	)	PUNCT
ejpam-3501	120	53	=	=	SYM
ejpam-3501	121	1	2	2	X
ejpam-3501	121	2	.	.	X
ejpam-3501	121	3	similarly	similarly	ADV
ejpam-3501	121	4	,	,	PUNCT
ejpam-3501	121	5	if	if	SCONJ
ejpam-3501	121	6	s	s	VERB
ejpam-3501	121	7	⊆	⊆	NUM
ejpam-3501	121	8	v	v	NOUN
ejpam-3501	121	9	(	(	PUNCT
ejpam-3501	121	10	h	h	NOUN
ejpam-3501	121	11	)	)	PUNCT
ejpam-3501	121	12	,	,	PUNCT
ejpam-3501	121	13	then	then	ADV
ejpam-3501	121	14	γs(h	γs(h	PRON
ejpam-3501	121	15	)	)	PUNCT
ejpam-3501	121	16	=	=	SYM
ejpam-3501	121	17	2	2	X
ejpam-3501	121	18	.	.	PUNCT
ejpam-3501	121	19	suppose	suppose	VERB
ejpam-3501	121	20	that	that	SCONJ
ejpam-3501	121	21	x	x	SYM
ejpam-3501	121	22	∈	∈	NOUN
ejpam-3501	121	23	v	v	X
ejpam-3501	121	24	(	(	PUNCT
ejpam-3501	121	25	g	g	NOUN
ejpam-3501	121	26	)	)	PUNCT
ejpam-3501	121	27	and	and	CCONJ
ejpam-3501	121	28	y	y	PROPN
ejpam-3501	121	29	∈	∈	PROPN
ejpam-3501	121	30	v	v	ADP
ejpam-3501	121	31	(	(	PUNCT
ejpam-3501	121	32	h	h	NOUN
ejpam-3501	121	33	)	)	PUNCT
ejpam-3501	121	34	.	.	PUNCT
ejpam-3501	122	1	let	let	VERB
ejpam-3501	122	2	z	z	NOUN
ejpam-3501	122	3	∈	∈	PROPN
ejpam-3501	122	4	v	v	ADP
ejpam-3501	122	5	(	(	PUNCT
ejpam-3501	122	6	g	g	NOUN
ejpam-3501	122	7	)	)	PUNCT
ejpam-3501	122	8	\	\	PUNCT
ejpam-3501	123	1	ng[x	ng[x	PROPN
ejpam-3501	123	2	]	]	PUNCT
ejpam-3501	123	3	.	.	PUNCT
ejpam-3501	124	1	then	then	ADV
ejpam-3501	124	2	z	z	PROPN
ejpam-3501	124	3	∈	∈	PROPN
ejpam-3501	124	4	ng+h(y	ng+h(y	NUM
ejpam-3501	124	5	)	)	PUNCT
ejpam-3501	124	6	\	\	NOUN
ejpam-3501	124	7	{	{	PUNCT
ejpam-3501	124	8	x	x	NOUN
ejpam-3501	124	9	}	}	PUNCT
ejpam-3501	124	10	.	.	PUNCT
ejpam-3501	125	1	by	by	ADP
ejpam-3501	125	2	theorem	theorem	NOUN
ejpam-3501	125	3	1(iii	1(iii	NUM
ejpam-3501	125	4	)	)	PUNCT
ejpam-3501	125	5	,	,	PUNCT
ejpam-3501	125	6	{	{	PUNCT
ejpam-3501	125	7	x	x	NOUN
ejpam-3501	125	8	,	,	PUNCT
ejpam-3501	125	9	z	z	NOUN
ejpam-3501	125	10	}	}	PUNCT
ejpam-3501	125	11	is	be	AUX
ejpam-3501	125	12	a	a	DET
ejpam-3501	125	13	dominating	dominating	NOUN
ejpam-3501	125	14	set	set	VERB
ejpam-3501	125	15	in	in	ADP
ejpam-3501	125	16	g	g	PROPN
ejpam-3501	126	1	+	+	CCONJ
ejpam-3501	126	2	h	h	NOUN
ejpam-3501	126	3	,	,	PUNCT
ejpam-3501	126	4	hence	hence	ADV
ejpam-3501	126	5	a	a	DET
ejpam-3501	126	6	dominating	dominating	NOUN
ejpam-3501	126	7	set	set	VERB
ejpam-3501	126	8	in	in	ADP
ejpam-3501	126	9	g.	g.	PROPN
ejpam-3501	126	10	similarly	similarly	ADV
ejpam-3501	126	11	,	,	PUNCT
ejpam-3501	126	12	{	{	PUNCT
ejpam-3501	126	13	w	w	PROPN
ejpam-3501	126	14	,	,	PUNCT
ejpam-3501	126	15	y	y	NOUN
ejpam-3501	126	16	}	}	PUNCT
ejpam-3501	126	17	is	be	AUX
ejpam-3501	126	18	a	a	DET
ejpam-3501	126	19	dominating	dominating	NOUN
ejpam-3501	126	20	set	set	VERB
ejpam-3501	126	21	in	in	ADP
ejpam-3501	126	22	h	h	NOUN
ejpam-3501	126	23	for	for	ADP
ejpam-3501	126	24	all	all	DET
ejpam-3501	126	25	w	w	PROPN
ejpam-3501	126	26	∈	∈	PROPN
ejpam-3501	126	27	v	v	ADP
ejpam-3501	126	28	(	(	PUNCT
ejpam-3501	126	29	h	h	NOUN
ejpam-3501	126	30	)	)	PUNCT
ejpam-3501	126	31	\ng[y	\ng[y	PROPN
ejpam-3501	126	32	]	]	PUNCT
ejpam-3501	126	33	.	.	PUNCT
ejpam-3501	127	1	conversely	conversely	ADV
ejpam-3501	127	2	,	,	PUNCT
ejpam-3501	127	3	suppose	suppose	VERB
ejpam-3501	127	4	that	that	SCONJ
ejpam-3501	127	5	γs(g	γs(g	SYM
ejpam-3501	127	6	)	)	PUNCT
ejpam-3501	127	7	=	=	SYM
ejpam-3501	127	8	2	2	NUM
ejpam-3501	127	9	,	,	PUNCT
ejpam-3501	127	10	and	and	CCONJ
ejpam-3501	127	11	let	let	VERB
ejpam-3501	127	12	s	s	PRON
ejpam-3501	127	13	=	=	PUNCT
ejpam-3501	127	14	{	{	PUNCT
ejpam-3501	127	15	x	x	PROPN
ejpam-3501	127	16	,	,	PUNCT
ejpam-3501	127	17	y	y	PROPN
ejpam-3501	127	18	}	}	PUNCT
ejpam-3501	127	19	be	be	AUX
ejpam-3501	127	20	a	a	DET
ejpam-3501	127	21	γs	γs	NOUN
ejpam-3501	127	22	-	-	PUNCT
ejpam-3501	127	23	set	set	NOUN
ejpam-3501	127	24	of	of	ADP
ejpam-3501	127	25	g.	g.	PROPN
ejpam-3501	127	26	by	by	ADP
ejpam-3501	127	27	theorem	theorem	NOUN
ejpam-3501	127	28	2	2	NUM
ejpam-3501	127	29	,	,	PUNCT
ejpam-3501	127	30	s	s	VERB
ejpam-3501	127	31	is	be	AUX
ejpam-3501	127	32	a	a	DET
ejpam-3501	127	33	semitotal	semitotal	ADJ
ejpam-3501	127	34	dominating	dominating	NOUN
ejpam-3501	127	35	set	set	VERB
ejpam-3501	127	36	in	in	ADP
ejpam-3501	127	37	g	g	PROPN
ejpam-3501	127	38	+	+	CCONJ
ejpam-3501	127	39	h.	h.	PROPN
ejpam-3501	127	40	let	let	VERB
ejpam-3501	127	41	z	z	PROPN
ejpam-3501	127	42	∈	∈	PROPN
ejpam-3501	127	43	v	v	NOUN
ejpam-3501	127	44	(	(	PUNCT
ejpam-3501	127	45	g	g	PROPN
ejpam-3501	127	46	+	+	NOUN
ejpam-3501	127	47	h	h	NOUN
ejpam-3501	127	48	)	)	PUNCT
ejpam-3501	127	49	\	\	PUNCT
ejpam-3501	128	1	s.	s.	PROPN
ejpam-3501	128	2	suppose	suppose	VERB
ejpam-3501	128	3	that	that	SCONJ
ejpam-3501	128	4	z	z	PROPN
ejpam-3501	128	5	∈	∈	PROPN
ejpam-3501	128	6	v	v	ADP
ejpam-3501	128	7	(	(	PUNCT
ejpam-3501	128	8	h	h	NOUN
ejpam-3501	128	9	)	)	PUNCT
ejpam-3501	128	10	.	.	PUNCT
ejpam-3501	129	1	in	in	ADP
ejpam-3501	129	2	particular	particular	ADJ
ejpam-3501	129	3	,	,	PUNCT
ejpam-3501	129	4	xz	xz	PROPN
ejpam-3501	129	5	∈	∈	PROPN
ejpam-3501	129	6	e(g	e(g	PROPN
ejpam-3501	130	1	+	+	CCONJ
ejpam-3501	130	2	h	h	NOUN
ejpam-3501	130	3	)	)	PUNCT
ejpam-3501	130	4	and	and	CCONJ
ejpam-3501	130	5	(	(	PUNCT
ejpam-3501	130	6	s	s	NOUN
ejpam-3501	130	7	\	\	X
ejpam-3501	130	8	{	{	PUNCT
ejpam-3501	130	9	x	x	NOUN
ejpam-3501	130	10	}	}	PUNCT
ejpam-3501	130	11	)	)	PUNCT
ejpam-3501	130	12	∪	∪	ADP
ejpam-3501	130	13	{	{	PUNCT
ejpam-3501	130	14	z	z	NOUN
ejpam-3501	130	15	}	}	PUNCT
ejpam-3501	130	16	=	=	SYM
ejpam-3501	130	17	{	{	PUNCT
ejpam-3501	130	18	z	z	PROPN
ejpam-3501	130	19	,	,	PUNCT
ejpam-3501	130	20	y	y	PROPN
ejpam-3501	130	21	}	}	PUNCT
ejpam-3501	130	22	,	,	PUNCT
ejpam-3501	130	23	which	which	PRON
ejpam-3501	130	24	is	be	AUX
ejpam-3501	130	25	a	a	DET
ejpam-3501	130	26	semitotal	semitotal	ADJ
ejpam-3501	130	27	dominating	dominating	NOUN
ejpam-3501	130	28	set	set	VERB
ejpam-3501	130	29	in	in	ADP
ejpam-3501	130	30	g	g	PROPN
ejpam-3501	130	31	+	+	CCONJ
ejpam-3501	130	32	h	h	NOUN
ejpam-3501	130	33	by	by	ADP
ejpam-3501	130	34	theorem	theorem	NOUN
ejpam-3501	130	35	2	2	NUM
ejpam-3501	130	36	.	.	PUNCT
ejpam-3501	130	37	suppose	suppose	VERB
ejpam-3501	130	38	that	that	SCONJ
ejpam-3501	130	39	z	z	PROPN
ejpam-3501	130	40	∈	∈	PROPN
ejpam-3501	130	41	v	v	ADP
ejpam-3501	130	42	(	(	PUNCT
ejpam-3501	130	43	g	g	NOUN
ejpam-3501	130	44	)	)	PUNCT
ejpam-3501	130	45	.	.	PUNCT
ejpam-3501	131	1	since	since	SCONJ
ejpam-3501	131	2	s	s	PROPN
ejpam-3501	131	3	is	be	AUX
ejpam-3501	131	4	a	a	DET
ejpam-3501	131	5	secure	secure	ADJ
ejpam-3501	131	6	dominating	dominating	NOUN
ejpam-3501	131	7	set	set	NOUN
ejpam-3501	131	8	,	,	PUNCT
ejpam-3501	131	9	either	either	CCONJ
ejpam-3501	131	10	xz	xz	PROPN
ejpam-3501	131	11	∈	∈	PROPN
ejpam-3501	131	12	e(g	e(g	PROPN
ejpam-3501	131	13	)	)	PUNCT
ejpam-3501	131	14	and	and	CCONJ
ejpam-3501	131	15	{	{	PUNCT
ejpam-3501	131	16	y	y	PROPN
ejpam-3501	131	17	,	,	PUNCT
ejpam-3501	131	18	z	z	NOUN
ejpam-3501	131	19	}	}	PUNCT
ejpam-3501	131	20	is	be	AUX
ejpam-3501	131	21	a	a	DET
ejpam-3501	131	22	dominating	dominating	NOUN
ejpam-3501	131	23	set	set	NOUN
ejpam-3501	131	24	in	in	ADP
ejpam-3501	131	25	g	g	PROPN
ejpam-3501	131	26	or	or	CCONJ
ejpam-3501	131	27	zy	zy	PROPN
ejpam-3501	131	28	∈	∈	PROPN
ejpam-3501	131	29	e(g	e(g	PROPN
ejpam-3501	131	30	)	)	PUNCT
ejpam-3501	131	31	and	and	CCONJ
ejpam-3501	131	32	{	{	PUNCT
ejpam-3501	131	33	x	x	NOUN
ejpam-3501	131	34	,	,	PUNCT
ejpam-3501	131	35	z	z	NOUN
ejpam-3501	131	36	}	}	PUNCT
ejpam-3501	131	37	is	be	AUX
ejpam-3501	131	38	a	a	DET
ejpam-3501	131	39	dominating	dominating	NOUN
ejpam-3501	131	40	set	set	VERB
ejpam-3501	131	41	in	in	ADP
ejpam-3501	131	42	g.	g.	PROPN
ejpam-3501	131	43	in	in	ADP
ejpam-3501	131	44	either	either	DET
ejpam-3501	131	45	case	case	NOUN
ejpam-3501	131	46	,	,	PUNCT
ejpam-3501	131	47	s	s	VERB
ejpam-3501	131	48	is	be	AUX
ejpam-3501	131	49	a	a	DET
ejpam-3501	131	50	secure	secure	ADJ
ejpam-3501	131	51	semitotal	semitotal	ADJ
ejpam-3501	131	52	dominating	dominating	NOUN
ejpam-3501	131	53	set	set	VERB
ejpam-3501	131	54	in	in	ADP
ejpam-3501	131	55	g	g	PROPN
ejpam-3501	131	56	+	+	CCONJ
ejpam-3501	131	57	h	h	NOUN
ejpam-3501	131	58	by	by	ADP
ejpam-3501	131	59	theorem	theorem	NOUN
ejpam-3501	131	60	2	2	NUM
ejpam-3501	131	61	,	,	PUNCT
ejpam-3501	131	62	so	so	SCONJ
ejpam-3501	131	63	that	that	SCONJ
ejpam-3501	131	64	γst2(g	γst2(g	NUM
ejpam-3501	131	65	+	+	CCONJ
ejpam-3501	131	66	h	h	NOUN
ejpam-3501	131	67	)	)	PUNCT
ejpam-3501	131	68	=	=	PUNCT
ejpam-3501	131	69	|s|	|s|	NOUN
ejpam-3501	131	70	=	=	SYM
ejpam-3501	131	71	2	2	NUM
ejpam-3501	131	72	.	.	PUNCT
ejpam-3501	131	73	similarly	similarly	ADV
ejpam-3501	131	74	,	,	PUNCT
ejpam-3501	131	75	if	if	SCONJ
ejpam-3501	131	76	γs(h	γs(h	NOUN
ejpam-3501	131	77	)	)	PUNCT
ejpam-3501	131	78	=	=	SYM
ejpam-3501	131	79	2	2	NUM
ejpam-3501	131	80	,	,	PUNCT
ejpam-3501	131	81	then	then	ADV
ejpam-3501	131	82	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	131	83	)	)	PUNCT
ejpam-3501	131	84	=	=	SYM
ejpam-3501	132	1	2	2	X
ejpam-3501	132	2	.	.	PUNCT
ejpam-3501	132	3	finally	finally	ADV
ejpam-3501	132	4	,	,	PUNCT
ejpam-3501	132	5	suppose	suppose	VERB
ejpam-3501	132	6	that	that	SCONJ
ejpam-3501	132	7	x	x	PROPN
ejpam-3501	132	8	and	and	CCONJ
ejpam-3501	132	9	y	y	PROPN
ejpam-3501	132	10	satisfy	satisfy	VERB
ejpam-3501	132	11	property	property	NOUN
ejpam-3501	132	12	(	(	PUNCT
ejpam-3501	132	13	iii	iii	NOUN
ejpam-3501	132	14	)	)	PUNCT
ejpam-3501	132	15	,	,	PUNCT
ejpam-3501	132	16	and	and	CCONJ
ejpam-3501	132	17	put	put	VERB
ejpam-3501	132	18	s	s	NOUN
ejpam-3501	132	19	=	=	PUNCT
ejpam-3501	132	20	{	{	PUNCT
ejpam-3501	132	21	x	x	PROPN
ejpam-3501	132	22	,	,	PUNCT
ejpam-3501	132	23	y	y	NOUN
ejpam-3501	132	24	}	}	PUNCT
ejpam-3501	132	25	.	.	PUNCT
ejpam-3501	133	1	by	by	ADP
ejpam-3501	133	2	theorem	theorem	NOUN
ejpam-3501	133	3	2	2	NUM
ejpam-3501	133	4	,	,	PUNCT
ejpam-3501	133	5	s	s	VERB
ejpam-3501	133	6	is	be	AUX
ejpam-3501	133	7	a	a	DET
ejpam-3501	133	8	semitotal	semitotal	ADJ
ejpam-3501	133	9	dominating	dominating	NOUN
ejpam-3501	133	10	set	set	VERB
ejpam-3501	133	11	in	in	ADP
ejpam-3501	133	12	g+h	g+h	PROPN
ejpam-3501	133	13	.	.	PUNCT
ejpam-3501	134	1	let	let	VERB
ejpam-3501	134	2	z	z	NOUN
ejpam-3501	134	3	∈	∈	PROPN
ejpam-3501	134	4	v	v	NOUN
ejpam-3501	134	5	(	(	PUNCT
ejpam-3501	134	6	g)\s	g)\s	NOUN
ejpam-3501	134	7	.	.	PUNCT
ejpam-3501	135	1	suppose	suppose	VERB
ejpam-3501	135	2	that	that	SCONJ
ejpam-3501	135	3	xz	xz	PROPN
ejpam-3501	135	4	∈	∈	PROPN
ejpam-3501	135	5	e(g	e(g	PROPN
ejpam-3501	135	6	)	)	PUNCT
ejpam-3501	135	7	.	.	PUNCT
ejpam-3501	136	1	then	then	ADV
ejpam-3501	136	2	x	x	X
ejpam-3501	136	3	∈	∈	PROPN
ejpam-3501	136	4	s	s	PART
ejpam-3501	136	5	∩ng+h(z	∩ng+h(z	NOUN
ejpam-3501	136	6	)	)	PUNCT
ejpam-3501	136	7	and	and	CCONJ
ejpam-3501	136	8	(	(	PUNCT
ejpam-3501	136	9	s	s	X
ejpam-3501	136	10	\	\	X
ejpam-3501	136	11	{	{	PUNCT
ejpam-3501	136	12	x})∪	x})∪	PROPN
ejpam-3501	136	13	{	{	PUNCT
ejpam-3501	136	14	z	z	PROPN
ejpam-3501	136	15	}	}	PUNCT
ejpam-3501	136	16	=	=	SYM
ejpam-3501	136	17	{	{	PUNCT
ejpam-3501	136	18	z	z	PROPN
ejpam-3501	136	19	,	,	PUNCT
ejpam-3501	136	20	y	y	PROPN
ejpam-3501	136	21	}	}	PUNCT
ejpam-3501	136	22	,	,	PUNCT
ejpam-3501	136	23	which	which	PRON
ejpam-3501	136	24	by	by	ADP
ejpam-3501	136	25	theorem	theorem	NOUN
ejpam-3501	136	26	2	2	NUM
ejpam-3501	136	27	,	,	PUNCT
ejpam-3501	136	28	is	be	AUX
ejpam-3501	136	29	a	a	DET
ejpam-3501	136	30	semitotal	semitotal	ADJ
ejpam-3501	136	31	dominating	dominating	NOUN
ejpam-3501	136	32	set	set	VERB
ejpam-3501	136	33	in	in	ADP
ejpam-3501	136	34	g	g	PROPN
ejpam-3501	136	35	+	+	PROPN
ejpam-3501	136	36	h.	h.	PROPN
ejpam-3501	136	37	suppose	suppose	VERB
ejpam-3501	137	1	that	that	SCONJ
ejpam-3501	137	2	z	z	PROPN
ejpam-3501	137	3	/∈	/∈	PUNCT
ejpam-3501	137	4	ng[x	ng[x	PROPN
ejpam-3501	137	5	]	]	PUNCT
ejpam-3501	137	6	.	.	PUNCT
ejpam-3501	138	1	by	by	ADP
ejpam-3501	138	2	property	property	NOUN
ejpam-3501	138	3	(	(	PUNCT
ejpam-3501	138	4	iii	iii	NOUN
ejpam-3501	138	5	)	)	PUNCT
ejpam-3501	138	6	,	,	PUNCT
ejpam-3501	138	7	{	{	PUNCT
ejpam-3501	138	8	x	x	NOUN
ejpam-3501	138	9	,	,	PUNCT
ejpam-3501	138	10	z	z	NOUN
ejpam-3501	138	11	}	}	PUNCT
ejpam-3501	138	12	is	be	AUX
ejpam-3501	138	13	a	a	DET
ejpam-3501	138	14	dominating	dominating	NOUN
ejpam-3501	138	15	set	set	NOUN
ejpam-3501	138	16	in	in	ADP
ejpam-3501	138	17	g	g	NOUN
ejpam-3501	138	18	,	,	PUNCT
ejpam-3501	138	19	and	and	CCONJ
ejpam-3501	138	20	hence	hence	ADV
ejpam-3501	138	21	a	a	DET
ejpam-3501	138	22	semitotal	semitotal	ADJ
ejpam-3501	138	23	dominating	dominating	NOUN
ejpam-3501	138	24	set	set	NOUN
ejpam-3501	138	25	in	in	ADP
ejpam-3501	138	26	g+h	g+h	PROPN
ejpam-3501	138	27	by	by	ADP
ejpam-3501	138	28	theorem	theorem	NOUN
ejpam-3501	138	29	2	2	NUM
ejpam-3501	138	30	.	.	PUNCT
ejpam-3501	139	1	now	now	ADV
ejpam-3501	139	2	,	,	PUNCT
ejpam-3501	139	3	zy	zy	PROPN
ejpam-3501	139	4	∈	∈	PROPN
ejpam-3501	139	5	e(g+h	e(g+h	NUM
ejpam-3501	139	6	)	)	PUNCT
ejpam-3501	139	7	and	and	CCONJ
ejpam-3501	139	8	(	(	PUNCT
ejpam-3501	139	9	s	s	NOUN
ejpam-3501	139	10	\	\	X
ejpam-3501	139	11	{	{	PUNCT
ejpam-3501	139	12	y	y	NOUN
ejpam-3501	139	13	}	}	PUNCT
ejpam-3501	139	14	)	)	PUNCT
ejpam-3501	139	15	∪	∪	ADP
ejpam-3501	139	16	{	{	PUNCT
ejpam-3501	139	17	z	z	NOUN
ejpam-3501	139	18	}	}	PUNCT
ejpam-3501	139	19	=	=	SYM
ejpam-3501	139	20	{	{	PUNCT
ejpam-3501	139	21	x	x	NOUN
ejpam-3501	139	22	,	,	PUNCT
ejpam-3501	139	23	z	z	NOUN
ejpam-3501	139	24	}	}	PUNCT
ejpam-3501	139	25	.	.	PUNCT
ejpam-3501	140	1	similarly	similarly	ADV
ejpam-3501	140	2	,	,	PUNCT
ejpam-3501	140	3	if	if	SCONJ
ejpam-3501	140	4	z	z	PROPN
ejpam-3501	140	5	∈	∈	PROPN
ejpam-3501	140	6	v	v	ADP
ejpam-3501	140	7	(	(	PUNCT
ejpam-3501	140	8	h	h	NOUN
ejpam-3501	140	9	)	)	PUNCT
ejpam-3501	140	10	\	\	PROPN
ejpam-3501	140	11	s	s	X
ejpam-3501	140	12	,	,	PUNCT
ejpam-3501	140	13	then	then	ADV
ejpam-3501	140	14	there	there	PRON
ejpam-3501	140	15	exists	exist	VERB
ejpam-3501	140	16	w	w	PROPN
ejpam-3501	140	17	∈	∈	PROPN
ejpam-3501	140	18	s	s	PART
ejpam-3501	140	19	∩ng+h(z	∩ng+h(z	NOUN
ejpam-3501	140	20	)	)	PUNCT
ejpam-3501	140	21	such	such	ADJ
ejpam-3501	140	22	that	that	SCONJ
ejpam-3501	140	23	(	(	PUNCT
ejpam-3501	140	24	s	s	NOUN
ejpam-3501	140	25	\	\	X
ejpam-3501	140	26	{	{	PUNCT
ejpam-3501	140	27	w})∪{z	w})∪{z	PROPN
ejpam-3501	140	28	}	}	PUNCT
ejpam-3501	140	29	is	be	AUX
ejpam-3501	140	30	a	a	DET
ejpam-3501	140	31	semitotal	semitotal	ADJ
ejpam-3501	140	32	dominating	dominating	NOUN
ejpam-3501	140	33	set	set	VERB
ejpam-3501	140	34	in	in	ADP
ejpam-3501	140	35	g+h	g+h	PROPN
ejpam-3501	140	36	.	.	PUNCT
ejpam-3501	141	1	thus	thus	ADV
ejpam-3501	141	2	,	,	PUNCT
ejpam-3501	141	3	s	s	VERB
ejpam-3501	141	4	is	be	AUX
ejpam-3501	141	5	a	a	DET
ejpam-3501	141	6	secure	secure	ADJ
ejpam-3501	141	7	semitotal	semitotal	ADJ
ejpam-3501	141	8	dominating	dominating	NOUN
ejpam-3501	141	9	set	set	VERB
ejpam-3501	141	10	in	in	ADP
ejpam-3501	141	11	g+h	g+h	PROPN
ejpam-3501	141	12	.	.	PUNCT
ejpam-3501	142	1	therefore	therefore	ADV
ejpam-3501	142	2	,	,	PUNCT
ejpam-3501	142	3	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	142	4	)	)	PUNCT
ejpam-3501	142	5	=	=	SYM
ejpam-3501	142	6	2	2	X
ejpam-3501	142	7	.	.	X
ejpam-3501	143	1	in	in	ADP
ejpam-3501	143	2	view	view	NOUN
ejpam-3501	143	3	of	of	ADP
ejpam-3501	143	4	corollary	corollary	ADJ
ejpam-3501	143	5	2(iii	2(iii	NUM
ejpam-3501	143	6	)	)	PUNCT
ejpam-3501	143	7	,	,	PUNCT
ejpam-3501	143	8	γst2(k1,n	γst2(k1,n	PUNCT
ejpam-3501	143	9	+	+	ADJ
ejpam-3501	143	10	k1,m	k1,m	NOUN
ejpam-3501	143	11	)	)	PUNCT
ejpam-3501	143	12	=	=	SYM
ejpam-3501	143	13	2	2	NUM
ejpam-3501	143	14	=	=	SYM
ejpam-3501	143	15	γst2(c4	γst2(c4	NOUN
ejpam-3501	143	16	+	+	NUM
ejpam-3501	143	17	c4	c4	NOUN
ejpam-3501	143	18	)	)	PUNCT
ejpam-3501	143	19	.	.	PUNCT
ejpam-3501	144	1	corollary	corollary	ADJ
ejpam-3501	144	2	3	3	X
ejpam-3501	144	3	.	.	PUNCT
ejpam-3501	145	1	let	let	VERB
ejpam-3501	145	2	g	g	NOUN
ejpam-3501	146	1	and	and	CCONJ
ejpam-3501	146	2	h	h	NOUN
ejpam-3501	146	3	be	be	VERB
ejpam-3501	146	4	noncomplete	noncomplete	ADJ
ejpam-3501	146	5	graphs	graph	NOUN
ejpam-3501	146	6	of	of	ADP
ejpam-3501	146	7	orders	order	NOUN
ejpam-3501	146	8	m	m	VERB
ejpam-3501	146	9	and	and	CCONJ
ejpam-3501	146	10	n	n	CCONJ
ejpam-3501	146	11	,	,	PUNCT
ejpam-3501	146	12	respectively	respectively	ADV
ejpam-3501	146	13	,	,	PUNCT
ejpam-3501	146	14	and	and	CCONJ
ejpam-3501	146	15	suppose	suppose	VERB
ejpam-3501	146	16	that	that	SCONJ
ejpam-3501	146	17	γst2(g	γst2(g	NUM
ejpam-3501	146	18	+	+	CCONJ
ejpam-3501	146	19	h	h	NOUN
ejpam-3501	146	20	)	)	PUNCT
ejpam-3501	146	21	6=	6=	ADP
ejpam-3501	146	22	2	2	X
ejpam-3501	146	23	.	.	PUNCT
ejpam-3501	146	24	then	then	ADV
ejpam-3501	146	25	γst2(g	γst2(g	NUM
ejpam-3501	146	26	+	+	CCONJ
ejpam-3501	146	27	h	h	NOUN
ejpam-3501	146	28	)	)	PUNCT
ejpam-3501	146	29	=	=	SYM
ejpam-3501	146	30	3	3	NUM
ejpam-3501	146	31	if	if	SCONJ
ejpam-3501	146	32	and	and	CCONJ
ejpam-3501	146	33	only	only	ADV
ejpam-3501	146	34	if	if	SCONJ
ejpam-3501	146	35	at	at	ADV
ejpam-3501	146	36	least	least	ADJ
ejpam-3501	146	37	one	one	NUM
ejpam-3501	146	38	of	of	ADP
ejpam-3501	146	39	the	the	DET
ejpam-3501	146	40	following	follow	VERB
ejpam-3501	146	41	is	be	AUX
ejpam-3501	146	42	true	true	ADJ
ejpam-3501	146	43	:	:	PUNCT
ejpam-3501	146	44	(	(	PUNCT
ejpam-3501	146	45	i	i	NOUN
ejpam-3501	146	46	)	)	PUNCT
ejpam-3501	146	47	γs(g	γs(g	PUNCT
ejpam-3501	146	48	)	)	PUNCT
ejpam-3501	146	49	=	=	SYM
ejpam-3501	147	1	3	3	NUM
ejpam-3501	147	2	;	;	PUNCT
ejpam-3501	147	3	(	(	PUNCT
ejpam-3501	147	4	ii	ii	NOUN
ejpam-3501	147	5	)	)	PUNCT
ejpam-3501	147	6	γs(h	γs(h	PUNCT
ejpam-3501	147	7	)	)	PUNCT
ejpam-3501	147	8	=	=	SYM
ejpam-3501	147	9	3	3	NUM
ejpam-3501	147	10	;	;	PUNCT
ejpam-3501	147	11	(	(	PUNCT
ejpam-3501	147	12	iii	iii	X
ejpam-3501	147	13	)	)	PUNCT
ejpam-3501	147	14	there	there	PRON
ejpam-3501	147	15	exist	exist	VERB
ejpam-3501	147	16	x	x	NOUN
ejpam-3501	147	17	,	,	PUNCT
ejpam-3501	147	18	y	y	PROPN
ejpam-3501	147	19	∈	∈	PROPN
ejpam-3501	147	20	v	v	ADP
ejpam-3501	147	21	(	(	PUNCT
ejpam-3501	147	22	g	g	NOUN
ejpam-3501	147	23	)	)	PUNCT
ejpam-3501	147	24	such	such	ADJ
ejpam-3501	147	25	that	that	SCONJ
ejpam-3501	147	26	{	{	PUNCT
ejpam-3501	147	27	x	x	NOUN
ejpam-3501	147	28	,	,	PUNCT
ejpam-3501	147	29	y	y	PRON
ejpam-3501	147	30	}	}	PUNCT
ejpam-3501	147	31	is	be	AUX
ejpam-3501	147	32	a	a	DET
ejpam-3501	147	33	nearly	nearly	ADV
ejpam-3501	147	34	dominating	dominating	NOUN
ejpam-3501	147	35	set	set	NOUN
ejpam-3501	147	36	in	in	ADP
ejpam-3501	147	37	g	g	NOUN
ejpam-3501	147	38	;	;	PUNCT
ejpam-3501	147	39	(	(	PUNCT
ejpam-3501	147	40	iv	iv	X
ejpam-3501	147	41	)	)	PUNCT
ejpam-3501	147	42	there	there	PRON
ejpam-3501	147	43	exist	exist	VERB
ejpam-3501	147	44	x	x	NOUN
ejpam-3501	147	45	,	,	PUNCT
ejpam-3501	147	46	y	y	PROPN
ejpam-3501	147	47	∈	∈	PROPN
ejpam-3501	147	48	v	v	ADP
ejpam-3501	147	49	(	(	PUNCT
ejpam-3501	147	50	h	h	NOUN
ejpam-3501	147	51	)	)	PUNCT
ejpam-3501	147	52	such	such	ADJ
ejpam-3501	147	53	that	that	SCONJ
ejpam-3501	147	54	{	{	PUNCT
ejpam-3501	147	55	x	x	NOUN
ejpam-3501	147	56	,	,	PUNCT
ejpam-3501	147	57	y	y	PRON
ejpam-3501	147	58	}	}	PUNCT
ejpam-3501	147	59	is	be	AUX
ejpam-3501	147	60	a	a	DET
ejpam-3501	147	61	nearly	nearly	ADV
ejpam-3501	147	62	dominating	dominating	NOUN
ejpam-3501	147	63	set	set	VERB
ejpam-3501	147	64	in	in	ADP
ejpam-3501	147	65	h.	h.	PROPN
ejpam-3501	147	66	proof	proof	NOUN
ejpam-3501	147	67	.	.	PUNCT
ejpam-3501	148	1	suppose	suppose	VERB
ejpam-3501	148	2	that	that	SCONJ
ejpam-3501	148	3	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	148	4	)	)	PUNCT
ejpam-3501	148	5	=	=	SYM
ejpam-3501	148	6	3	3	NUM
ejpam-3501	148	7	,	,	PUNCT
ejpam-3501	148	8	and	and	CCONJ
ejpam-3501	148	9	let	let	VERB
ejpam-3501	148	10	s	s	PRON
ejpam-3501	148	11	⊆	⊆	NUM
ejpam-3501	148	12	v	v	NOUN
ejpam-3501	148	13	(	(	PUNCT
ejpam-3501	148	14	g+h	g+h	NOUN
ejpam-3501	148	15	)	)	PUNCT
ejpam-3501	148	16	be	be	AUX
ejpam-3501	148	17	a	a	DET
ejpam-3501	148	18	γst2	γst2	ADV
ejpam-3501	148	19	-	-	PUNCT
ejpam-3501	148	20	set	set	NOUN
ejpam-3501	148	21	of	of	ADP
ejpam-3501	148	22	g+h	g+h	PROPN
ejpam-3501	148	23	.	.	PUNCT
ejpam-3501	149	1	suppose	suppose	VERB
ejpam-3501	149	2	that	that	SCONJ
ejpam-3501	149	3	s	s	VERB
ejpam-3501	149	4	⊆	⊆	NUM
ejpam-3501	149	5	v	v	NOUN
ejpam-3501	149	6	(	(	PUNCT
ejpam-3501	149	7	g	g	NOUN
ejpam-3501	149	8	)	)	PUNCT
ejpam-3501	149	9	.	.	PUNCT
ejpam-3501	150	1	by	by	ADP
ejpam-3501	150	2	theorem	theorem	NOUN
ejpam-3501	150	3	2	2	NUM
ejpam-3501	150	4	,	,	PUNCT
ejpam-3501	150	5	s	s	VERB
ejpam-3501	150	6	is	be	AUX
ejpam-3501	150	7	a	a	DET
ejpam-3501	150	8	dominating	dominating	NOUN
ejpam-3501	150	9	set	set	VERB
ejpam-3501	150	10	in	in	ADP
ejpam-3501	150	11	g.	g.	PROPN
ejpam-3501	150	12	let	let	VERB
ejpam-3501	150	13	w	w	PROPN
ejpam-3501	150	14	∈	∈	PROPN
ejpam-3501	150	15	v	v	ADP
ejpam-3501	150	16	(	(	PUNCT
ejpam-3501	150	17	g	g	NOUN
ejpam-3501	150	18	)	)	PUNCT
ejpam-3501	150	19	\	\	PUNCT
ejpam-3501	151	1	s.	s.	PROPN
ejpam-3501	151	2	there	there	PRON
ejpam-3501	151	3	exists	exist	VERB
ejpam-3501	151	4	x	x	X
ejpam-3501	151	5	∈	∈	PROPN
ejpam-3501	151	6	s	s	PART
ejpam-3501	151	7	∩ng+h(w	∩ng+h(w	X
ejpam-3501	151	8	)	)	PUNCT
ejpam-3501	151	9	such	such	ADJ
ejpam-3501	151	10	that	that	DET
ejpam-3501	151	11	t	t	NOUN
ejpam-3501	151	12	=	=	PUNCT
ejpam-3501	151	13	(	(	PUNCT
ejpam-3501	151	14	s	s	NOUN
ejpam-3501	151	15	\	\	X
ejpam-3501	151	16	{	{	PUNCT
ejpam-3501	151	17	x	x	NOUN
ejpam-3501	151	18	}	}	PUNCT
ejpam-3501	151	19	)	)	PUNCT
ejpam-3501	151	20	∪	∪	ADP
ejpam-3501	151	21	{	{	PUNCT
ejpam-3501	151	22	w	w	NOUN
ejpam-3501	151	23	}	}	PUNCT
ejpam-3501	151	24	is	be	AUX
ejpam-3501	151	25	a	a	DET
ejpam-3501	151	26	semitotal	semitotal	ADJ
ejpam-3501	151	27	dominating	dominating	NOUN
ejpam-3501	151	28	set	set	VERB
ejpam-3501	151	29	in	in	ADP
ejpam-3501	151	30	g	g	PROPN
ejpam-3501	151	31	+	+	CCONJ
ejpam-3501	151	32	h.	h.	PROPN
ejpam-3501	151	33	since	since	SCONJ
ejpam-3501	151	34	t	t	PROPN
ejpam-3501	151	35	⊆	⊆	NUM
ejpam-3501	151	36	v	v	NOUN
ejpam-3501	151	37	(	(	PUNCT
ejpam-3501	151	38	g	g	NOUN
ejpam-3501	151	39	)	)	PUNCT
ejpam-3501	151	40	,	,	PUNCT
ejpam-3501	151	41	t	t	PROPN
ejpam-3501	151	42	is	be	AUX
ejpam-3501	151	43	a	a	DET
ejpam-3501	151	44	dominating	dominating	NOUN
ejpam-3501	151	45	set	set	VERB
ejpam-3501	151	46	in	in	ADP
ejpam-3501	151	47	g	g	NOUN
ejpam-3501	151	48	by	by	ADP
ejpam-3501	151	49	theorem	theorem	NOUN
ejpam-3501	151	50	2	2	NUM
ejpam-3501	151	51	,	,	PUNCT
ejpam-3501	151	52	showing	show	VERB
ejpam-3501	151	53	that	that	DET
ejpam-3501	151	54	i.	i.	PROPN
ejpam-3501	151	55	s.	s.	PROPN
ejpam-3501	151	56	aniversario	aniversario	PROPN
ejpam-3501	151	57	,	,	PUNCT
ejpam-3501	152	1	s.	s.	PROPN
ejpam-3501	152	2	r.	r.	PROPN
ejpam-3501	152	3	jr	jr	PROPN
ejpam-3501	152	4	.	.	PROPN
ejpam-3501	152	5	canoy	canoy	PROPN
ejpam-3501	152	6	,	,	PUNCT
ejpam-3501	152	7	f.p	f.p	PROPN
ejpam-3501	152	8	.	.	PROPN
ejpam-3501	152	9	jamil	jamil	PROPN
ejpam-3501	152	10	/	/	SYM
ejpam-3501	152	11	eur	eur	PROPN
ejpam-3501	152	12	.	.	PUNCT
ejpam-3501	153	1	j.	j.	PROPN
ejpam-3501	153	2	pure	pure	PROPN
ejpam-3501	153	3	appl	appl	PROPN
ejpam-3501	153	4	.	.	PROPN
ejpam-3501	153	5	math	math	PROPN
ejpam-3501	153	6	,	,	PUNCT
ejpam-3501	153	7	12	12	NUM
ejpam-3501	153	8	(	(	PUNCT
ejpam-3501	153	9	4	4	NUM
ejpam-3501	153	10	)	)	PUNCT
ejpam-3501	153	11	(	(	PUNCT
ejpam-3501	153	12	2019	2019	NUM
ejpam-3501	153	13	)	)	PUNCT
ejpam-3501	153	14	,	,	PUNCT
ejpam-3501	153	15	1410	1410	NUM
ejpam-3501	153	16	-	-	SYM
ejpam-3501	153	17	1425	1425	NUM
ejpam-3501	153	18	1415	1415	NUM
ejpam-3501	153	19	s	s	VERB
ejpam-3501	153	20	is	be	AUX
ejpam-3501	153	21	a	a	DET
ejpam-3501	153	22	secure	secure	ADJ
ejpam-3501	153	23	dominating	dominating	NOUN
ejpam-3501	153	24	set	set	VERB
ejpam-3501	153	25	in	in	ADP
ejpam-3501	153	26	g.	g.	PROPN
ejpam-3501	153	27	hence	hence	ADV
ejpam-3501	153	28	,	,	PUNCT
ejpam-3501	153	29	γs(g	γs(g	PUNCT
ejpam-3501	153	30	)	)	PUNCT
ejpam-3501	153	31	≤	≤	NUM
ejpam-3501	153	32	|s|	|s|	PROPN
ejpam-3501	153	33	=	=	SYM
ejpam-3501	153	34	3	3	X
ejpam-3501	153	35	.	.	PUNCT
ejpam-3501	154	1	in	in	ADP
ejpam-3501	154	2	view	view	NOUN
ejpam-3501	154	3	of	of	ADP
ejpam-3501	154	4	corollary	corollary	ADJ
ejpam-3501	154	5	2	2	NUM
ejpam-3501	154	6	,	,	PUNCT
ejpam-3501	154	7	since	since	SCONJ
ejpam-3501	154	8	γst2(g	γst2(g	NUM
ejpam-3501	154	9	+	+	CCONJ
ejpam-3501	154	10	h	h	NOUN
ejpam-3501	154	11	)	)	PUNCT
ejpam-3501	154	12	6=	6=	ADP
ejpam-3501	154	13	2	2	NUM
ejpam-3501	154	14	,	,	PUNCT
ejpam-3501	154	15	γs(g	γs(g	PUNCT
ejpam-3501	154	16	)	)	PUNCT
ejpam-3501	154	17	=	=	SYM
ejpam-3501	154	18	3	3	X
ejpam-3501	154	19	.	.	X
ejpam-3501	154	20	similarly	similarly	ADV
ejpam-3501	154	21	,	,	PUNCT
ejpam-3501	154	22	if	if	SCONJ
ejpam-3501	154	23	s	s	VERB
ejpam-3501	154	24	⊆	⊆	NUM
ejpam-3501	154	25	v	v	NOUN
ejpam-3501	154	26	(	(	PUNCT
ejpam-3501	154	27	h	h	NOUN
ejpam-3501	154	28	)	)	PUNCT
ejpam-3501	154	29	,	,	PUNCT
ejpam-3501	154	30	then	then	ADV
ejpam-3501	154	31	γs(h	γs(h	PRON
ejpam-3501	154	32	)	)	PUNCT
ejpam-3501	154	33	=	=	SYM
ejpam-3501	155	1	3	3	X
ejpam-3501	155	2	.	.	PUNCT
ejpam-3501	155	3	now	now	ADV
ejpam-3501	155	4	,	,	PUNCT
ejpam-3501	155	5	let	let	VERB
ejpam-3501	155	6	s	s	PRON
ejpam-3501	155	7	=	=	PUNCT
ejpam-3501	155	8	{	{	PUNCT
ejpam-3501	155	9	x	x	PROPN
ejpam-3501	155	10	,	,	PUNCT
ejpam-3501	155	11	y	y	PROPN
ejpam-3501	155	12	,	,	PUNCT
ejpam-3501	155	13	z	z	NOUN
ejpam-3501	155	14	}	}	PUNCT
ejpam-3501	155	15	,	,	PUNCT
ejpam-3501	155	16	and	and	CCONJ
ejpam-3501	155	17	assume	assume	VERB
ejpam-3501	155	18	that	that	SCONJ
ejpam-3501	155	19	t	t	NOUN
ejpam-3501	155	20	=	=	SYM
ejpam-3501	155	21	{	{	PUNCT
ejpam-3501	155	22	x	x	NOUN
ejpam-3501	155	23	,	,	PUNCT
ejpam-3501	155	24	y	y	PROPN
ejpam-3501	155	25	}	}	PUNCT
ejpam-3501	155	26	⊆	⊆	NUM
ejpam-3501	155	27	v	v	NOUN
ejpam-3501	155	28	(	(	PUNCT
ejpam-3501	155	29	g	g	NOUN
ejpam-3501	155	30	)	)	PUNCT
ejpam-3501	155	31	and	and	CCONJ
ejpam-3501	155	32	z	z	NOUN
ejpam-3501	155	33	∈	∈	PROPN
ejpam-3501	155	34	v	v	ADP
ejpam-3501	155	35	(	(	PUNCT
ejpam-3501	155	36	h	h	NOUN
ejpam-3501	155	37	)	)	PUNCT
ejpam-3501	155	38	.	.	PUNCT
ejpam-3501	156	1	if	if	SCONJ
ejpam-3501	156	2	t	t	PROPN
ejpam-3501	156	3	is	be	AUX
ejpam-3501	156	4	a	a	DET
ejpam-3501	156	5	dominating	dominating	NOUN
ejpam-3501	156	6	set	set	NOUN
ejpam-3501	156	7	in	in	ADP
ejpam-3501	156	8	g	g	NOUN
ejpam-3501	156	9	,	,	PUNCT
ejpam-3501	156	10	then	then	ADV
ejpam-3501	156	11	property	property	NOUN
ejpam-3501	156	12	(	(	PUNCT
ejpam-3501	156	13	iii	iii	NOUN
ejpam-3501	156	14	)	)	PUNCT
ejpam-3501	156	15	holds	hold	VERB
ejpam-3501	156	16	.	.	PUNCT
ejpam-3501	157	1	suppose	suppose	VERB
ejpam-3501	157	2	not	not	PART
ejpam-3501	157	3	,	,	PUNCT
ejpam-3501	157	4	and	and	CCONJ
ejpam-3501	157	5	let	let	VERB
ejpam-3501	157	6	u	u	PRON
ejpam-3501	157	7	∈	∈	PROPN
ejpam-3501	157	8	v	v	ADP
ejpam-3501	157	9	(	(	PUNCT
ejpam-3501	157	10	g	g	NOUN
ejpam-3501	157	11	)	)	PUNCT
ejpam-3501	157	12	\	\	PROPN
ejpam-3501	157	13	ng[t	ng[t	PROPN
ejpam-3501	157	14	]	]	PUNCT
ejpam-3501	157	15	.	.	PUNCT
ejpam-3501	158	1	since	since	SCONJ
ejpam-3501	158	2	s	s	PROPN
ejpam-3501	158	3	is	be	AUX
ejpam-3501	158	4	a	a	DET
ejpam-3501	158	5	secure	secure	ADJ
ejpam-3501	158	6	semitotal	semitotal	ADJ
ejpam-3501	158	7	dominating	dominating	NOUN
ejpam-3501	158	8	set	set	VERB
ejpam-3501	158	9	in	in	ADP
ejpam-3501	158	10	g	g	PROPN
ejpam-3501	158	11	+	+	CCONJ
ejpam-3501	158	12	h	h	NOUN
ejpam-3501	158	13	,	,	PUNCT
ejpam-3501	158	14	(	(	PUNCT
ejpam-3501	158	15	s	s	NOUN
ejpam-3501	158	16	\	\	X
ejpam-3501	158	17	{	{	PUNCT
ejpam-3501	158	18	z	z	NOUN
ejpam-3501	158	19	}	}	PUNCT
ejpam-3501	158	20	)	)	PUNCT
ejpam-3501	158	21	∪	∪	ADP
ejpam-3501	158	22	{	{	PUNCT
ejpam-3501	158	23	u	u	NOUN
ejpam-3501	158	24	}	}	PUNCT
ejpam-3501	158	25	=	=	SYM
ejpam-3501	158	26	{	{	PUNCT
ejpam-3501	158	27	x	x	NOUN
ejpam-3501	158	28	,	,	PUNCT
ejpam-3501	158	29	y	y	PROPN
ejpam-3501	158	30	,	,	PUNCT
ejpam-3501	158	31	u	u	NOUN
ejpam-3501	158	32	}	}	PUNCT
ejpam-3501	158	33	is	be	AUX
ejpam-3501	158	34	a	a	DET
ejpam-3501	158	35	semitotal	semitotal	ADJ
ejpam-3501	158	36	dominating	dominating	NOUN
ejpam-3501	158	37	set	set	VERB
ejpam-3501	158	38	in	in	ADP
ejpam-3501	158	39	g	g	PROPN
ejpam-3501	158	40	+	+	PROPN
ejpam-3501	158	41	h.	h.	PROPN
ejpam-3501	159	1	thus	thus	ADV
ejpam-3501	159	2	,	,	PUNCT
ejpam-3501	159	3	{	{	PUNCT
ejpam-3501	159	4	x	x	NOUN
ejpam-3501	159	5	,	,	PUNCT
ejpam-3501	159	6	y	y	PROPN
ejpam-3501	159	7	,	,	PUNCT
ejpam-3501	159	8	u	u	NOUN
ejpam-3501	159	9	}	}	PUNCT
ejpam-3501	159	10	is	be	AUX
ejpam-3501	159	11	a	a	DET
ejpam-3501	159	12	dominating	dominating	NOUN
ejpam-3501	159	13	set	set	VERB
ejpam-3501	159	14	in	in	ADP
ejpam-3501	159	15	g.	g.	PROPN
ejpam-3501	159	16	accordingly	accordingly	ADV
ejpam-3501	159	17	,	,	PUNCT
ejpam-3501	159	18	t	t	PROPN
ejpam-3501	159	19	is	be	AUX
ejpam-3501	159	20	a	a	DET
ejpam-3501	159	21	nearly	nearly	ADV
ejpam-3501	159	22	dominating	dominating	NOUN
ejpam-3501	159	23	set	set	VERB
ejpam-3501	159	24	in	in	ADP
ejpam-3501	159	25	g.	g.	PROPN
ejpam-3501	159	26	property	property	PROPN
ejpam-3501	159	27	(	(	PUNCT
ejpam-3501	159	28	iv	iv	X
ejpam-3501	159	29	)	)	PUNCT
ejpam-3501	159	30	is	be	AUX
ejpam-3501	159	31	proved	prove	VERB
ejpam-3501	159	32	similarly	similarly	ADV
ejpam-3501	159	33	.	.	PUNCT
ejpam-3501	160	1	conversely	conversely	ADV
ejpam-3501	160	2	,	,	PUNCT
ejpam-3501	160	3	suppose	suppose	VERB
ejpam-3501	160	4	that	that	SCONJ
ejpam-3501	160	5	γs(g	γs(g	SYM
ejpam-3501	160	6	)	)	PUNCT
ejpam-3501	160	7	=	=	SYM
ejpam-3501	160	8	3	3	NUM
ejpam-3501	160	9	,	,	PUNCT
ejpam-3501	160	10	and	and	CCONJ
ejpam-3501	160	11	s	s	VERB
ejpam-3501	160	12	=	=	PUNCT
ejpam-3501	160	13	{	{	PUNCT
ejpam-3501	160	14	x	x	PROPN
ejpam-3501	160	15	,	,	PUNCT
ejpam-3501	160	16	y	y	PROPN
ejpam-3501	160	17	,	,	PUNCT
ejpam-3501	160	18	z	z	NOUN
ejpam-3501	160	19	}	}	PUNCT
ejpam-3501	160	20	⊆	⊆	NUM
ejpam-3501	160	21	v	v	NOUN
ejpam-3501	160	22	(	(	PUNCT
ejpam-3501	160	23	g	g	NOUN
ejpam-3501	160	24	)	)	PUNCT
ejpam-3501	160	25	is	be	AUX
ejpam-3501	160	26	a	a	DET
ejpam-3501	160	27	γs	γs	NOUN
ejpam-3501	160	28	-	-	PUNCT
ejpam-3501	160	29	set	set	NOUN
ejpam-3501	160	30	of	of	ADP
ejpam-3501	160	31	g.	g.	PROPN
ejpam-3501	160	32	by	by	ADP
ejpam-3501	160	33	theorem	theorem	NOUN
ejpam-3501	160	34	2	2	NUM
ejpam-3501	160	35	,	,	PUNCT
ejpam-3501	160	36	s	s	VERB
ejpam-3501	160	37	is	be	AUX
ejpam-3501	160	38	a	a	DET
ejpam-3501	160	39	semitotal	semitotal	ADJ
ejpam-3501	160	40	dominating	dominating	NOUN
ejpam-3501	160	41	set	set	VERB
ejpam-3501	160	42	in	in	ADP
ejpam-3501	160	43	g+h	g+h	PROPN
ejpam-3501	160	44	.	.	PUNCT
ejpam-3501	161	1	let	let	VERB
ejpam-3501	161	2	w	w	NOUN
ejpam-3501	161	3	∈	∈	PROPN
ejpam-3501	161	4	v	v	NOUN
ejpam-3501	161	5	(	(	PUNCT
ejpam-3501	161	6	g+h)\s	g+h)\s	VERB
ejpam-3501	161	7	.	.	PUNCT
ejpam-3501	162	1	if	if	SCONJ
ejpam-3501	162	2	w	w	PROPN
ejpam-3501	162	3	∈	∈	PROPN
ejpam-3501	162	4	v	v	ADP
ejpam-3501	162	5	(	(	PUNCT
ejpam-3501	162	6	h	h	NOUN
ejpam-3501	162	7	)	)	PUNCT
ejpam-3501	162	8	,	,	PUNCT
ejpam-3501	162	9	then	then	ADV
ejpam-3501	162	10	in	in	ADP
ejpam-3501	162	11	particular	particular	ADJ
ejpam-3501	162	12	,	,	PUNCT
ejpam-3501	162	13	xw	xw	PROPN
ejpam-3501	162	14	∈	∈	PROPN
ejpam-3501	162	15	e(g+h	e(g+h	PROPN
ejpam-3501	162	16	)	)	PUNCT
ejpam-3501	162	17	and	and	CCONJ
ejpam-3501	162	18	(	(	PUNCT
ejpam-3501	162	19	s	s	NOUN
ejpam-3501	162	20	\	\	X
ejpam-3501	162	21	{	{	PUNCT
ejpam-3501	162	22	x	x	NOUN
ejpam-3501	162	23	}	}	PUNCT
ejpam-3501	162	24	)	)	PUNCT
ejpam-3501	162	25	∪	∪	ADP
ejpam-3501	162	26	{	{	PUNCT
ejpam-3501	162	27	w	w	NOUN
ejpam-3501	162	28	}	}	PUNCT
ejpam-3501	162	29	=	=	SYM
ejpam-3501	162	30	{	{	PUNCT
ejpam-3501	162	31	y	y	PROPN
ejpam-3501	162	32	,	,	PUNCT
ejpam-3501	162	33	z	z	PROPN
ejpam-3501	162	34	,	,	PUNCT
ejpam-3501	162	35	w	w	PROPN
ejpam-3501	162	36	}	}	PUNCT
ejpam-3501	162	37	,	,	PUNCT
ejpam-3501	162	38	which	which	PRON
ejpam-3501	162	39	is	be	AUX
ejpam-3501	162	40	a	a	DET
ejpam-3501	162	41	semitotal	semitotal	ADJ
ejpam-3501	162	42	dominating	dominating	NOUN
ejpam-3501	162	43	set	set	VERB
ejpam-3501	162	44	in	in	ADP
ejpam-3501	162	45	g	g	PROPN
ejpam-3501	162	46	+	+	CCONJ
ejpam-3501	162	47	h	h	NOUN
ejpam-3501	162	48	by	by	ADP
ejpam-3501	162	49	theorem	theorem	NOUN
ejpam-3501	162	50	2	2	NUM
ejpam-3501	162	51	.	.	PUNCT
ejpam-3501	162	52	suppose	suppose	VERB
ejpam-3501	162	53	that	that	SCONJ
ejpam-3501	162	54	w	w	PROPN
ejpam-3501	162	55	∈	∈	PROPN
ejpam-3501	162	56	v	v	ADP
ejpam-3501	162	57	(	(	PUNCT
ejpam-3501	162	58	g	g	NOUN
ejpam-3501	162	59	)	)	PUNCT
ejpam-3501	162	60	.	.	PUNCT
ejpam-3501	163	1	since	since	SCONJ
ejpam-3501	163	2	s	s	PROPN
ejpam-3501	163	3	is	be	AUX
ejpam-3501	163	4	a	a	DET
ejpam-3501	163	5	secure	secure	ADJ
ejpam-3501	163	6	dominating	dominating	NOUN
ejpam-3501	163	7	set	set	NOUN
ejpam-3501	163	8	in	in	ADP
ejpam-3501	163	9	g	g	NOUN
ejpam-3501	163	10	,	,	PUNCT
ejpam-3501	163	11	there	there	PRON
ejpam-3501	163	12	exists	exist	VERB
ejpam-3501	163	13	t	t	PROPN
ejpam-3501	163	14	∈	∈	PROPN
ejpam-3501	163	15	s	s	PART
ejpam-3501	163	16	∩	∩	NOUN
ejpam-3501	163	17	ng(w	ng(w	NOUN
ejpam-3501	163	18	)	)	PUNCT
ejpam-3501	163	19	such	such	ADJ
ejpam-3501	163	20	that	that	DET
ejpam-3501	163	21	t	t	NOUN
ejpam-3501	163	22	=	=	PUNCT
ejpam-3501	163	23	(	(	PUNCT
ejpam-3501	163	24	s	s	NOUN
ejpam-3501	163	25	\	\	X
ejpam-3501	163	26	{	{	PUNCT
ejpam-3501	163	27	t	t	PROPN
ejpam-3501	163	28	}	}	PUNCT
ejpam-3501	163	29	)	)	PUNCT
ejpam-3501	163	30	∪	∪	ADP
ejpam-3501	163	31	{	{	PUNCT
ejpam-3501	163	32	w	w	NOUN
ejpam-3501	163	33	}	}	PUNCT
ejpam-3501	163	34	is	be	AUX
ejpam-3501	163	35	a	a	DET
ejpam-3501	163	36	dominating	dominating	NOUN
ejpam-3501	163	37	set	set	VERB
ejpam-3501	163	38	in	in	ADP
ejpam-3501	163	39	g.	g.	PROPN
ejpam-3501	163	40	hence	hence	PROPN
ejpam-3501	163	41	t	t	PROPN
ejpam-3501	163	42	is	be	AUX
ejpam-3501	163	43	a	a	DET
ejpam-3501	163	44	semitotal	semitotal	ADJ
ejpam-3501	163	45	dominating	dominating	NOUN
ejpam-3501	163	46	in	in	ADP
ejpam-3501	163	47	g	g	PROPN
ejpam-3501	163	48	+	+	PROPN
ejpam-3501	163	49	h.	h.	PROPN
ejpam-3501	163	50	thus	thus	ADV
ejpam-3501	163	51	,	,	PUNCT
ejpam-3501	163	52	s	s	VERB
ejpam-3501	163	53	is	be	AUX
ejpam-3501	163	54	a	a	DET
ejpam-3501	163	55	secure	secure	ADJ
ejpam-3501	163	56	semitotal	semitotal	ADJ
ejpam-3501	163	57	dominating	dominating	NOUN
ejpam-3501	163	58	set	set	VERB
ejpam-3501	163	59	in	in	ADP
ejpam-3501	163	60	g	g	PROPN
ejpam-3501	163	61	+	+	CCONJ
ejpam-3501	163	62	h.	h.	PROPN
ejpam-3501	163	63	since	since	SCONJ
ejpam-3501	163	64	γst2(g	γst2(g	NUM
ejpam-3501	163	65	+	+	CCONJ
ejpam-3501	163	66	h	h	NOUN
ejpam-3501	163	67	)	)	PUNCT
ejpam-3501	163	68	6=	6=	ADP
ejpam-3501	163	69	2	2	NUM
ejpam-3501	163	70	,	,	PUNCT
ejpam-3501	163	71	γst2(g	γst2(g	PUNCT
ejpam-3501	163	72	+	+	CCONJ
ejpam-3501	163	73	h	h	NOUN
ejpam-3501	163	74	)	)	PUNCT
ejpam-3501	163	75	=	=	SYM
ejpam-3501	163	76	3	3	NUM
ejpam-3501	163	77	=	=	SYM
ejpam-3501	163	78	|s|	|s|	PROPN
ejpam-3501	163	79	.	.	PROPN
ejpam-3501	164	1	similarly	similarly	ADV
ejpam-3501	164	2	,	,	PUNCT
ejpam-3501	164	3	if	if	SCONJ
ejpam-3501	164	4	γs(h	γs(h	NOUN
ejpam-3501	164	5	)	)	PUNCT
ejpam-3501	164	6	=	=	SYM
ejpam-3501	164	7	3	3	NUM
ejpam-3501	164	8	,	,	PUNCT
ejpam-3501	164	9	then	then	ADV
ejpam-3501	164	10	γst2(g	γst2(g	NUM
ejpam-3501	164	11	+	+	CCONJ
ejpam-3501	164	12	h	h	NOUN
ejpam-3501	164	13	)	)	PUNCT
ejpam-3501	164	14	=	=	SYM
ejpam-3501	164	15	3	3	X
ejpam-3501	164	16	.	.	PUNCT
ejpam-3501	164	17	suppose	suppose	VERB
ejpam-3501	164	18	that	that	SCONJ
ejpam-3501	164	19	property	property	NOUN
ejpam-3501	164	20	(	(	PUNCT
ejpam-3501	164	21	iii	iii	NOUN
ejpam-3501	164	22	)	)	PUNCT
ejpam-3501	164	23	holds	hold	NOUN
ejpam-3501	164	24	,	,	PUNCT
ejpam-3501	164	25	and	and	CCONJ
ejpam-3501	164	26	let	let	VERB
ejpam-3501	164	27	{	{	PUNCT
ejpam-3501	164	28	x	x	NOUN
ejpam-3501	164	29	,	,	PUNCT
ejpam-3501	164	30	y	y	PROPN
ejpam-3501	164	31	}	}	PUNCT
ejpam-3501	164	32	be	be	AUX
ejpam-3501	164	33	a	a	DET
ejpam-3501	164	34	nearly	nearly	ADV
ejpam-3501	164	35	dominating	dominating	NOUN
ejpam-3501	164	36	set	set	VERB
ejpam-3501	164	37	in	in	ADP
ejpam-3501	164	38	g.	g.	PROPN
ejpam-3501	164	39	pick	pick	VERB
ejpam-3501	164	40	any	any	DET
ejpam-3501	164	41	z	z	NOUN
ejpam-3501	164	42	∈	∈	PROPN
ejpam-3501	164	43	v	v	NOUN
ejpam-3501	164	44	(	(	PUNCT
ejpam-3501	164	45	h	h	NOUN
ejpam-3501	164	46	)	)	PUNCT
ejpam-3501	164	47	,	,	PUNCT
ejpam-3501	164	48	and	and	CCONJ
ejpam-3501	164	49	put	put	VERB
ejpam-3501	164	50	s	s	NOUN
ejpam-3501	164	51	=	=	PUNCT
ejpam-3501	164	52	{	{	PUNCT
ejpam-3501	164	53	x	x	PROPN
ejpam-3501	164	54	,	,	PUNCT
ejpam-3501	164	55	y	y	PROPN
ejpam-3501	164	56	,	,	PUNCT
ejpam-3501	164	57	z	z	NOUN
ejpam-3501	164	58	}	}	PUNCT
ejpam-3501	164	59	.	.	PUNCT
ejpam-3501	165	1	then	then	ADV
ejpam-3501	165	2	s	s	VERB
ejpam-3501	165	3	is	be	AUX
ejpam-3501	165	4	a	a	DET
ejpam-3501	165	5	semitotal	semitotal	ADJ
ejpam-3501	165	6	dominating	dominating	NOUN
ejpam-3501	165	7	set	set	VERB
ejpam-3501	165	8	in	in	ADP
ejpam-3501	165	9	g	g	PROPN
ejpam-3501	165	10	+	+	CCONJ
ejpam-3501	165	11	h.	h.	PROPN
ejpam-3501	165	12	let	let	VERB
ejpam-3501	165	13	w	w	PROPN
ejpam-3501	165	14	∈	∈	PROPN
ejpam-3501	165	15	v	v	NOUN
ejpam-3501	165	16	(	(	PUNCT
ejpam-3501	165	17	g	g	PROPN
ejpam-3501	165	18	+	+	NOUN
ejpam-3501	165	19	h	h	NOUN
ejpam-3501	165	20	)	)	PUNCT
ejpam-3501	165	21	\	\	PUNCT
ejpam-3501	166	1	s.	s.	PROPN
ejpam-3501	166	2	if	if	SCONJ
ejpam-3501	166	3	w	w	PROPN
ejpam-3501	166	4	∈	∈	PROPN
ejpam-3501	166	5	v	v	ADP
ejpam-3501	166	6	(	(	PUNCT
ejpam-3501	166	7	h	h	NOUN
ejpam-3501	166	8	)	)	PUNCT
ejpam-3501	166	9	,	,	PUNCT
ejpam-3501	166	10	then	then	ADV
ejpam-3501	166	11	wx	wx	PROPN
ejpam-3501	166	12	∈	∈	PROPN
ejpam-3501	166	13	e(g	e(g	PROPN
ejpam-3501	166	14	+	+	CCONJ
ejpam-3501	166	15	h	h	NOUN
ejpam-3501	166	16	)	)	PUNCT
ejpam-3501	166	17	and	and	CCONJ
ejpam-3501	166	18	(	(	PUNCT
ejpam-3501	166	19	s	s	NOUN
ejpam-3501	166	20	\	\	X
ejpam-3501	166	21	{	{	PUNCT
ejpam-3501	166	22	x	x	NOUN
ejpam-3501	166	23	}	}	PUNCT
ejpam-3501	166	24	)	)	PUNCT
ejpam-3501	166	25	∪	∪	ADP
ejpam-3501	166	26	{	{	PUNCT
ejpam-3501	166	27	w	w	NOUN
ejpam-3501	166	28	}	}	PUNCT
ejpam-3501	166	29	=	=	SYM
ejpam-3501	166	30	{	{	PUNCT
ejpam-3501	166	31	y	y	PROPN
ejpam-3501	166	32	,	,	PUNCT
ejpam-3501	166	33	z	z	PROPN
ejpam-3501	166	34	,	,	PUNCT
ejpam-3501	166	35	w	w	NOUN
ejpam-3501	166	36	}	}	PUNCT
ejpam-3501	166	37	is	be	AUX
ejpam-3501	166	38	a	a	DET
ejpam-3501	166	39	semitotal	semitotal	ADJ
ejpam-3501	166	40	dominating	dominating	NOUN
ejpam-3501	166	41	set	set	VERB
ejpam-3501	166	42	in	in	ADP
ejpam-3501	166	43	g	g	PROPN
ejpam-3501	166	44	+	+	CCONJ
ejpam-3501	166	45	h	h	NOUN
ejpam-3501	166	46	by	by	ADP
ejpam-3501	166	47	theorem	theorem	NOUN
ejpam-3501	166	48	2	2	NUM
ejpam-3501	166	49	.	.	PUNCT
ejpam-3501	166	50	suppose	suppose	VERB
ejpam-3501	166	51	that	that	SCONJ
ejpam-3501	166	52	w	w	PROPN
ejpam-3501	166	53	∈	∈	PROPN
ejpam-3501	166	54	v	v	ADP
ejpam-3501	166	55	(	(	PUNCT
ejpam-3501	166	56	g	g	NOUN
ejpam-3501	166	57	)	)	PUNCT
ejpam-3501	166	58	,	,	PUNCT
ejpam-3501	166	59	and	and	CCONJ
ejpam-3501	166	60	suppose	suppose	VERB
ejpam-3501	166	61	that	that	SCONJ
ejpam-3501	166	62	w	w	PROPN
ejpam-3501	166	63	∈	∈	PROPN
ejpam-3501	166	64	ng[{x	ng[{x	PROPN
ejpam-3501	166	65	,	,	PUNCT
ejpam-3501	166	66	y	y	PROPN
ejpam-3501	166	67	}	}	PUNCT
ejpam-3501	166	68	]	]	PUNCT
ejpam-3501	166	69	,	,	PUNCT
ejpam-3501	166	70	say	say	VERB
ejpam-3501	166	71	wx	wx	PROPN
ejpam-3501	166	72	∈	∈	PROPN
ejpam-3501	166	73	e(g	e(g	PROPN
ejpam-3501	166	74	)	)	PUNCT
ejpam-3501	166	75	.	.	PUNCT
ejpam-3501	167	1	then	then	ADV
ejpam-3501	167	2	x	x	PUNCT
ejpam-3501	167	3	∈	∈	PROPN
ejpam-3501	167	4	s	s	PART
ejpam-3501	167	5	∩	∩	NOUN
ejpam-3501	167	6	ng+h(w	ng+h(w	NUM
ejpam-3501	167	7	)	)	PUNCT
ejpam-3501	167	8	and	and	CCONJ
ejpam-3501	167	9	(	(	PUNCT
ejpam-3501	167	10	s	s	NOUN
ejpam-3501	167	11	\	\	X
ejpam-3501	167	12	{	{	PUNCT
ejpam-3501	167	13	x	x	NOUN
ejpam-3501	167	14	}	}	PUNCT
ejpam-3501	167	15	)	)	PUNCT
ejpam-3501	167	16	∪	∪	ADP
ejpam-3501	167	17	{	{	PUNCT
ejpam-3501	167	18	w	w	NOUN
ejpam-3501	167	19	}	}	PUNCT
ejpam-3501	167	20	=	=	SYM
ejpam-3501	167	21	{	{	PUNCT
ejpam-3501	167	22	w	w	PROPN
ejpam-3501	167	23	,	,	PUNCT
ejpam-3501	167	24	y	y	PROPN
ejpam-3501	167	25	,	,	PUNCT
ejpam-3501	167	26	z	z	NOUN
ejpam-3501	167	27	}	}	PUNCT
ejpam-3501	167	28	is	be	AUX
ejpam-3501	167	29	a	a	DET
ejpam-3501	167	30	semitotal	semitotal	ADJ
ejpam-3501	167	31	dominating	dominating	NOUN
ejpam-3501	167	32	set	set	VERB
ejpam-3501	167	33	in	in	ADP
ejpam-3501	167	34	g+h	g+h	PROPN
ejpam-3501	167	35	.	.	PUNCT
ejpam-3501	168	1	suppose	suppose	VERB
ejpam-3501	168	2	that	that	SCONJ
ejpam-3501	168	3	w	w	PROPN
ejpam-3501	168	4	/∈	/∈	PUNCT
ejpam-3501	168	5	ng[{x	ng[{x	ADJ
ejpam-3501	168	6	,	,	PUNCT
ejpam-3501	168	7	y	y	NOUN
ejpam-3501	168	8	}	}	PUNCT
ejpam-3501	168	9	]	]	PUNCT
ejpam-3501	168	10	.	.	PUNCT
ejpam-3501	169	1	here	here	ADV
ejpam-3501	169	2	we	we	PRON
ejpam-3501	169	3	note	note	VERB
ejpam-3501	169	4	that	that	SCONJ
ejpam-3501	169	5	wz	wz	ADP
ejpam-3501	169	6	∈	∈	PRON
ejpam-3501	169	7	e(g+h	e(g+h	NUM
ejpam-3501	169	8	)	)	PUNCT
ejpam-3501	169	9	and	and	CCONJ
ejpam-3501	169	10	(	(	PUNCT
ejpam-3501	169	11	s	s	NOUN
ejpam-3501	169	12	\	\	X
ejpam-3501	169	13	{	{	PUNCT
ejpam-3501	169	14	z	z	NOUN
ejpam-3501	169	15	}	}	PUNCT
ejpam-3501	169	16	)	)	PUNCT
ejpam-3501	169	17	∪	∪	ADP
ejpam-3501	169	18	{	{	PUNCT
ejpam-3501	169	19	w	w	NOUN
ejpam-3501	169	20	}	}	PUNCT
ejpam-3501	169	21	=	=	SYM
ejpam-3501	169	22	{	{	PUNCT
ejpam-3501	169	23	x	x	NOUN
ejpam-3501	169	24	,	,	PUNCT
ejpam-3501	169	25	y	y	PROPN
ejpam-3501	169	26	,	,	PUNCT
ejpam-3501	169	27	w	w	NOUN
ejpam-3501	169	28	}	}	PUNCT
ejpam-3501	169	29	.	.	PUNCT
ejpam-3501	170	1	since	since	SCONJ
ejpam-3501	170	2	{	{	PUNCT
ejpam-3501	170	3	x	x	NOUN
ejpam-3501	170	4	,	,	PUNCT
ejpam-3501	170	5	y	y	PRON
ejpam-3501	170	6	}	}	PUNCT
ejpam-3501	170	7	is	be	AUX
ejpam-3501	170	8	a	a	DET
ejpam-3501	170	9	nearly	nearly	ADV
ejpam-3501	170	10	dominating	dominating	NOUN
ejpam-3501	170	11	set	set	NOUN
ejpam-3501	170	12	,	,	PUNCT
ejpam-3501	170	13	{	{	PUNCT
ejpam-3501	170	14	x	x	NOUN
ejpam-3501	170	15	,	,	PUNCT
ejpam-3501	170	16	y	y	PROPN
ejpam-3501	170	17	,	,	PUNCT
ejpam-3501	170	18	w	w	NOUN
ejpam-3501	170	19	}	}	PUNCT
ejpam-3501	170	20	is	be	AUX
ejpam-3501	170	21	a	a	DET
ejpam-3501	170	22	dominating	dominating	NOUN
ejpam-3501	170	23	set	set	NOUN
ejpam-3501	170	24	in	in	ADP
ejpam-3501	170	25	g	g	NOUN
ejpam-3501	170	26	,	,	PUNCT
ejpam-3501	170	27	and	and	CCONJ
ejpam-3501	170	28	therefore	therefore	ADV
ejpam-3501	170	29	,	,	PUNCT
ejpam-3501	170	30	is	be	AUX
ejpam-3501	170	31	a	a	DET
ejpam-3501	170	32	semitotal	semitotal	ADJ
ejpam-3501	170	33	dominating	dominating	NOUN
ejpam-3501	170	34	set	set	VERB
ejpam-3501	170	35	in	in	ADP
ejpam-3501	170	36	g	g	PROPN
ejpam-3501	170	37	+	+	CCONJ
ejpam-3501	170	38	h	h	NOUN
ejpam-3501	170	39	by	by	ADP
ejpam-3501	170	40	theorem	theorem	NOUN
ejpam-3501	170	41	2	2	NUM
ejpam-3501	170	42	.	.	PUNCT
ejpam-3501	171	1	all	all	DET
ejpam-3501	171	2	these	these	PRON
ejpam-3501	171	3	imply	imply	VERB
ejpam-3501	171	4	that	that	SCONJ
ejpam-3501	171	5	s	s	VERB
ejpam-3501	171	6	is	be	AUX
ejpam-3501	171	7	a	a	DET
ejpam-3501	171	8	secure	secure	ADJ
ejpam-3501	171	9	semitotal	semitotal	ADJ
ejpam-3501	171	10	dominating	dominating	NOUN
ejpam-3501	171	11	set	set	NOUN
ejpam-3501	171	12	,	,	PUNCT
ejpam-3501	171	13	and	and	CCONJ
ejpam-3501	171	14	since	since	SCONJ
ejpam-3501	171	15	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	171	16	)	)	PUNCT
ejpam-3501	171	17	6=	6=	ADP
ejpam-3501	171	18	2	2	NUM
ejpam-3501	171	19	,	,	PUNCT
ejpam-3501	171	20	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	171	21	)	)	PUNCT
ejpam-3501	171	22	=	=	SYM
ejpam-3501	171	23	|s|	|s|	NOUN
ejpam-3501	171	24	=	=	SYM
ejpam-3501	171	25	3	3	X
ejpam-3501	171	26	.	.	PUNCT
ejpam-3501	171	27	similarly	similarly	ADV
ejpam-3501	171	28	,	,	PUNCT
ejpam-3501	171	29	if	if	SCONJ
ejpam-3501	171	30	property	property	NOUN
ejpam-3501	171	31	(	(	PUNCT
ejpam-3501	171	32	iv	iv	X
ejpam-3501	171	33	)	)	PUNCT
ejpam-3501	171	34	holds	hold	NOUN
ejpam-3501	171	35	,	,	PUNCT
ejpam-3501	171	36	then	then	ADV
ejpam-3501	171	37	γst2(g+h	γst2(g+h	PROPN
ejpam-3501	171	38	)	)	PUNCT
ejpam-3501	172	1	=	=	PUNCT
ejpam-3501	173	1	3	3	NUM
ejpam-3501	173	2	.	.	NOUN
ejpam-3501	173	3	4	4	NUM
ejpam-3501	173	4	.	.	X
ejpam-3501	174	1	in	in	ADP
ejpam-3501	174	2	the	the	DET
ejpam-3501	174	3	corona	corona	NOUN
ejpam-3501	174	4	of	of	ADP
ejpam-3501	174	5	graphs	graph	NOUN
ejpam-3501	174	6	the	the	DET
ejpam-3501	174	7	following	follow	VERB
ejpam-3501	174	8	lemma	lemma	PROPN
ejpam-3501	174	9	is	be	AUX
ejpam-3501	174	10	used	use	VERB
ejpam-3501	174	11	in	in	ADP
ejpam-3501	174	12	the	the	DET
ejpam-3501	174	13	succeeding	succeed	VERB
ejpam-3501	174	14	proposition	proposition	NOUN
ejpam-3501	174	15	.	.	PUNCT
ejpam-3501	175	1	lemma	lemma	PROPN
ejpam-3501	175	2	1	1	NUM
ejpam-3501	175	3	.	.	PUNCT
ejpam-3501	176	1	[	[	X
ejpam-3501	176	2	8	8	NUM
ejpam-3501	176	3	]	]	PUNCT
ejpam-3501	176	4	let	let	VERB
ejpam-3501	176	5	g	g	NOUN
ejpam-3501	176	6	be	be	AUX
ejpam-3501	176	7	any	any	DET
ejpam-3501	176	8	connected	connected	ADJ
ejpam-3501	176	9	graph	graph	NOUN
ejpam-3501	176	10	and	and	CCONJ
ejpam-3501	176	11	h	h	NOUN
ejpam-3501	176	12	any	any	DET
ejpam-3501	176	13	graph	graph	NOUN
ejpam-3501	176	14	.	.	PUNCT
ejpam-3501	177	1	then	then	ADV
ejpam-3501	177	2	s	s	VERB
ejpam-3501	177	3	⊆	⊆	NUM
ejpam-3501	177	4	v	v	NOUN
ejpam-3501	177	5	(	(	PUNCT
ejpam-3501	177	6	g	g	PROPN
ejpam-3501	177	7	◦	◦	NOUN
ejpam-3501	177	8	h	h	NOUN
ejpam-3501	177	9	)	)	PUNCT
ejpam-3501	177	10	is	be	AUX
ejpam-3501	177	11	a	a	DET
ejpam-3501	177	12	dominating	dominating	NOUN
ejpam-3501	177	13	set	set	VERB
ejpam-3501	177	14	in	in	ADP
ejpam-3501	177	15	g	g	PROPN
ejpam-3501	177	16	◦	◦	NOUN
ejpam-3501	177	17	h	h	NOUN
ejpam-3501	177	18	if	if	SCONJ
ejpam-3501	178	1	and	and	CCONJ
ejpam-3501	178	2	only	only	ADV
ejpam-3501	178	3	if	if	SCONJ
ejpam-3501	178	4	s	s	ADP
ejpam-3501	178	5	∩	∩	ADJ
ejpam-3501	178	6	v	v	X
ejpam-3501	178	7	(	(	PUNCT
ejpam-3501	178	8	hv	hv	PROPN
ejpam-3501	178	9	+	+	PROPN
ejpam-3501	178	10	v	v	NOUN
ejpam-3501	178	11	)	)	PUNCT
ejpam-3501	178	12	is	be	AUX
ejpam-3501	178	13	a	a	DET
ejpam-3501	178	14	dominating	dominating	NOUN
ejpam-3501	178	15	set	set	VERB
ejpam-3501	178	16	in	in	ADP
ejpam-3501	178	17	hv	hv	PROPN
ejpam-3501	178	18	+	+	X
ejpam-3501	178	19	v	v	NOUN
ejpam-3501	178	20	for	for	ADP
ejpam-3501	178	21	all	all	PRON
ejpam-3501	178	22	v	v	ADP
ejpam-3501	178	23	∈	∈	NUM
ejpam-3501	178	24	v	v	NOUN
ejpam-3501	178	25	(	(	PUNCT
ejpam-3501	178	26	g	g	NOUN
ejpam-3501	178	27	)	)	PUNCT
ejpam-3501	178	28	.	.	PUNCT
ejpam-3501	179	1	proposition	proposition	NOUN
ejpam-3501	179	2	2	2	NUM
ejpam-3501	179	3	.	.	PUNCT
ejpam-3501	180	1	let	let	VERB
ejpam-3501	180	2	g	g	PRON
ejpam-3501	180	3	be	be	AUX
ejpam-3501	180	4	a	a	DET
ejpam-3501	180	5	nontrivial	nontrivial	ADJ
ejpam-3501	180	6	connected	connect	VERB
ejpam-3501	180	7	graph	graph	NOUN
ejpam-3501	180	8	and	and	CCONJ
ejpam-3501	180	9	h	h	NOUN
ejpam-3501	180	10	any	any	DET
ejpam-3501	180	11	nontrivial	nontrivial	ADJ
ejpam-3501	180	12	graph	graph	NOUN
ejpam-3501	180	13	,	,	PUNCT
ejpam-3501	180	14	and	and	CCONJ
ejpam-3501	180	15	s	s	VERB
ejpam-3501	180	16	⊆	⊆	NUM
ejpam-3501	180	17	v	v	NOUN
ejpam-3501	180	18	(	(	PUNCT
ejpam-3501	180	19	g	g	PROPN
ejpam-3501	180	20	◦	◦	NOUN
ejpam-3501	180	21	h	h	NOUN
ejpam-3501	180	22	)	)	PUNCT
ejpam-3501	180	23	.	.	PUNCT
ejpam-3501	181	1	then	then	ADV
ejpam-3501	181	2	s	s	VERB
ejpam-3501	181	3	is	be	AUX
ejpam-3501	181	4	a	a	DET
ejpam-3501	181	5	semitotal	semitotal	ADJ
ejpam-3501	181	6	dominating	dominating	NOUN
ejpam-3501	181	7	set	set	VERB
ejpam-3501	181	8	in	in	ADP
ejpam-3501	181	9	g	g	PROPN
ejpam-3501	181	10	◦	◦	NOUN
ejpam-3501	181	11	h	h	NOUN
ejpam-3501	181	12	if	if	SCONJ
ejpam-3501	182	1	and	and	CCONJ
ejpam-3501	182	2	only	only	ADV
ejpam-3501	182	3	if	if	SCONJ
ejpam-3501	182	4	the	the	DET
ejpam-3501	182	5	following	follow	VERB
ejpam-3501	182	6	hold	hold	NOUN
ejpam-3501	182	7	:	:	PUNCT
ejpam-3501	182	8	(	(	PUNCT
ejpam-3501	182	9	i	i	NOUN
ejpam-3501	182	10	)	)	PUNCT
ejpam-3501	182	11	s	s	PART
ejpam-3501	182	12	∩	∩	ADJ
ejpam-3501	182	13	v	v	X
ejpam-3501	182	14	(	(	PUNCT
ejpam-3501	182	15	hv	hv	PROPN
ejpam-3501	182	16	+	+	PROPN
ejpam-3501	182	17	v	v	NOUN
ejpam-3501	182	18	)	)	PUNCT
ejpam-3501	182	19	is	be	AUX
ejpam-3501	182	20	a	a	DET
ejpam-3501	182	21	dominating	dominating	NOUN
ejpam-3501	182	22	set	set	VERB
ejpam-3501	182	23	in	in	ADP
ejpam-3501	182	24	hv	hv	PROPN
ejpam-3501	182	25	+	+	X
ejpam-3501	182	26	v	v	NOUN
ejpam-3501	182	27	for	for	ADP
ejpam-3501	182	28	all	all	DET
ejpam-3501	182	29	v	v	ADP
ejpam-3501	182	30	∈	∈	NUM
ejpam-3501	182	31	v	v	NOUN
ejpam-3501	182	32	(	(	PUNCT
ejpam-3501	182	33	g	g	NOUN
ejpam-3501	182	34	)	)	PUNCT
ejpam-3501	182	35	;	;	PUNCT
ejpam-3501	182	36	and	and	CCONJ
ejpam-3501	182	37	(	(	PUNCT
ejpam-3501	182	38	ii	ii	PROPN
ejpam-3501	182	39	)	)	PUNCT
ejpam-3501	182	40	|s	|s	PROPN
ejpam-3501	182	41	∩	∩	PROPN
ejpam-3501	182	42	v	v	NOUN
ejpam-3501	182	43	(	(	PUNCT
ejpam-3501	182	44	hv)|	hv)|	X
ejpam-3501	182	45	≥	≥	NOUN
ejpam-3501	182	46	2	2	NUM
ejpam-3501	182	47	for	for	ADP
ejpam-3501	182	48	each	each	PRON
ejpam-3501	182	49	v	v	NUM
ejpam-3501	182	50	∈	∈	PROPN
ejpam-3501	182	51	v	v	NOUN
ejpam-3501	182	52	(	(	PUNCT
ejpam-3501	182	53	g	g	NOUN
ejpam-3501	182	54	)	)	PUNCT
ejpam-3501	182	55	\	\	PROPN
ejpam-3501	183	1	s	s	PART
ejpam-3501	183	2	with	with	ADP
ejpam-3501	183	3	ng(v	ng(v	NOUN
ejpam-3501	183	4	)	)	PUNCT
ejpam-3501	183	5	∩	∩	NOUN
ejpam-3501	183	6	s	s	PART
ejpam-3501	183	7	=	=	SYM
ejpam-3501	183	8	∅	∅	NOUN
ejpam-3501	183	9	;	;	PUNCT
ejpam-3501	183	10	proof	proof	NOUN
ejpam-3501	183	11	.	.	PUNCT
ejpam-3501	184	1	suppose	suppose	VERB
ejpam-3501	184	2	that	that	SCONJ
ejpam-3501	184	3	s	s	VERB
ejpam-3501	184	4	is	be	AUX
ejpam-3501	184	5	a	a	DET
ejpam-3501	184	6	semitotal	semitotal	ADJ
ejpam-3501	184	7	dominating	dominating	NOUN
ejpam-3501	184	8	set	set	VERB
ejpam-3501	184	9	in	in	ADP
ejpam-3501	184	10	g	g	PROPN
ejpam-3501	184	11	◦	◦	NOUN
ejpam-3501	184	12	h.	h.	NOUN
ejpam-3501	184	13	then	then	ADV
ejpam-3501	184	14	s	s	VERB
ejpam-3501	184	15	is	be	AUX
ejpam-3501	184	16	a	a	DET
ejpam-3501	184	17	dominating	dominating	NOUN
ejpam-3501	184	18	set	set	VERB
ejpam-3501	184	19	in	in	ADP
ejpam-3501	184	20	g	g	PROPN
ejpam-3501	184	21	◦	◦	NOUN
ejpam-3501	184	22	h	h	NOUN
ejpam-3501	184	23	so	so	SCONJ
ejpam-3501	184	24	that	that	SCONJ
ejpam-3501	184	25	property	property	NOUN
ejpam-3501	184	26	(	(	PUNCT
ejpam-3501	184	27	i	i	NOUN
ejpam-3501	184	28	)	)	PUNCT
ejpam-3501	184	29	follows	follow	VERB
ejpam-3501	184	30	immediately	immediately	ADV
ejpam-3501	184	31	from	from	ADP
ejpam-3501	184	32	lemma	lemma	PROPN
ejpam-3501	184	33	1	1	NUM
ejpam-3501	184	34	.	.	PUNCT
ejpam-3501	185	1	let	let	VERB
ejpam-3501	185	2	v	v	NUM
ejpam-3501	185	3	∈	∈	PROPN
ejpam-3501	185	4	v	v	NOUN
ejpam-3501	185	5	(	(	PUNCT
ejpam-3501	185	6	g	g	NOUN
ejpam-3501	185	7	)	)	PUNCT
ejpam-3501	185	8	\	\	PROPN
ejpam-3501	186	1	s	s	PART
ejpam-3501	186	2	i.	i.	PROPN
ejpam-3501	186	3	s.	s.	PROPN
ejpam-3501	186	4	aniversario	aniversario	PROPN
ejpam-3501	186	5	,	,	PUNCT
ejpam-3501	186	6	s.	s.	PROPN
ejpam-3501	186	7	r.	r.	PROPN
ejpam-3501	186	8	jr	jr	PROPN
ejpam-3501	186	9	.	.	PROPN
ejpam-3501	186	10	canoy	canoy	PROPN
ejpam-3501	186	11	,	,	PUNCT
ejpam-3501	186	12	f.p	f.p	PROPN
ejpam-3501	186	13	.	.	PROPN
ejpam-3501	186	14	jamil	jamil	PROPN
ejpam-3501	186	15	/	/	SYM
ejpam-3501	186	16	eur	eur	PROPN
ejpam-3501	186	17	.	.	PUNCT
ejpam-3501	187	1	j.	j.	PROPN
ejpam-3501	187	2	pure	pure	PROPN
ejpam-3501	187	3	appl	appl	PROPN
ejpam-3501	187	4	.	.	PROPN
ejpam-3501	187	5	math	math	PROPN
ejpam-3501	187	6	,	,	PUNCT
ejpam-3501	187	7	12	12	NUM
ejpam-3501	187	8	(	(	PUNCT
ejpam-3501	187	9	4	4	NUM
ejpam-3501	187	10	)	)	PUNCT
ejpam-3501	187	11	(	(	PUNCT
ejpam-3501	187	12	2019	2019	NUM
ejpam-3501	187	13	)	)	PUNCT
ejpam-3501	187	14	,	,	PUNCT
ejpam-3501	187	15	1410	1410	NUM
ejpam-3501	187	16	-	-	SYM
ejpam-3501	187	17	1425	1425	NUM
ejpam-3501	187	18	1416	1416	NUM
ejpam-3501	187	19	such	such	ADJ
ejpam-3501	187	20	that	that	SCONJ
ejpam-3501	187	21	ng(v)∩s	ng(v)∩s	PROPN
ejpam-3501	187	22	=	=	PROPN
ejpam-3501	187	23	∅.	∅.	NOUN
ejpam-3501	187	24	then	then	ADV
ejpam-3501	187	25	s	s	AUX
ejpam-3501	187	26	∩v	∩v	NOUN
ejpam-3501	187	27	(	(	PUNCT
ejpam-3501	187	28	hv	hv	PROPN
ejpam-3501	187	29	+	+	NOUN
ejpam-3501	187	30	v	v	NOUN
ejpam-3501	187	31	)	)	PUNCT
ejpam-3501	187	32	=	=	SYM
ejpam-3501	187	33	s	s	PART
ejpam-3501	187	34	∩v	∩v	NOUN
ejpam-3501	187	35	(	(	PUNCT
ejpam-3501	187	36	hv	hv	PROPN
ejpam-3501	187	37	)	)	PUNCT
ejpam-3501	187	38	.	.	PUNCT
ejpam-3501	188	1	by	by	ADP
ejpam-3501	188	2	property	property	NOUN
ejpam-3501	188	3	(	(	PUNCT
ejpam-3501	188	4	i	i	NOUN
ejpam-3501	188	5	)	)	PUNCT
ejpam-3501	188	6	,	,	PUNCT
ejpam-3501	188	7	s	s	PART
ejpam-3501	188	8	∩v	∩v	NOUN
ejpam-3501	188	9	(	(	PUNCT
ejpam-3501	188	10	hv	hv	X
ejpam-3501	188	11	)	)	PUNCT
ejpam-3501	188	12	is	be	AUX
ejpam-3501	188	13	a	a	DET
ejpam-3501	188	14	dominating	dominating	NOUN
ejpam-3501	188	15	set	set	VERB
ejpam-3501	188	16	in	in	ADP
ejpam-3501	188	17	hv	hv	PROPN
ejpam-3501	188	18	+	+	PROPN
ejpam-3501	188	19	v	v	NOUN
ejpam-3501	188	20	,	,	PUNCT
ejpam-3501	188	21	and	and	CCONJ
ejpam-3501	188	22	consequently	consequently	ADV
ejpam-3501	188	23	in	in	ADP
ejpam-3501	188	24	hv	hv	PROPN
ejpam-3501	188	25	.	.	PUNCT
ejpam-3501	189	1	let	let	VERB
ejpam-3501	189	2	u	u	PRON
ejpam-3501	189	3	∈	∈	PROPN
ejpam-3501	189	4	s	s	PART
ejpam-3501	189	5	∩	∩	ADJ
ejpam-3501	189	6	v	v	X
ejpam-3501	189	7	(	(	PUNCT
ejpam-3501	189	8	hv	hv	PROPN
ejpam-3501	189	9	)	)	PUNCT
ejpam-3501	189	10	.	.	PUNCT
ejpam-3501	190	1	since	since	SCONJ
ejpam-3501	190	2	s	s	PROPN
ejpam-3501	190	3	is	be	AUX
ejpam-3501	190	4	a	a	DET
ejpam-3501	190	5	semitotal	semitotal	ADJ
ejpam-3501	190	6	dominating	dominating	NOUN
ejpam-3501	190	7	set	set	VERB
ejpam-3501	190	8	in	in	ADP
ejpam-3501	190	9	g	g	PROPN
ejpam-3501	190	10	◦	◦	NOUN
ejpam-3501	190	11	h	h	NOUN
ejpam-3501	190	12	,	,	PUNCT
ejpam-3501	190	13	there	there	PRON
ejpam-3501	190	14	exists	exist	VERB
ejpam-3501	190	15	w	w	PROPN
ejpam-3501	190	16	∈	∈	PROPN
ejpam-3501	190	17	s	s	PART
ejpam-3501	190	18	\	\	X
ejpam-3501	190	19	{	{	PUNCT
ejpam-3501	190	20	u	u	NOUN
ejpam-3501	190	21	}	}	PUNCT
ejpam-3501	190	22	such	such	ADJ
ejpam-3501	190	23	that	that	SCONJ
ejpam-3501	190	24	dg	dg	PROPN
ejpam-3501	190	25	◦	◦	PROPN
ejpam-3501	190	26	h(u	h(u	PROPN
ejpam-3501	190	27	,	,	PUNCT
ejpam-3501	190	28	w	w	NOUN
ejpam-3501	190	29	)	)	PUNCT
ejpam-3501	190	30	≤	≤	NOUN
ejpam-3501	190	31	2	2	NUM
ejpam-3501	190	32	.	.	PUNCT
ejpam-3501	191	1	since	since	SCONJ
ejpam-3501	191	2	s	s	PART
ejpam-3501	191	3	∩ng[v	∩ng[v	X
ejpam-3501	191	4	]	]	X
ejpam-3501	191	5	=	=	SYM
ejpam-3501	191	6	∅	∅	NOUN
ejpam-3501	191	7	,	,	PUNCT
ejpam-3501	191	8	w	w	PROPN
ejpam-3501	191	9	∈	∈	PROPN
ejpam-3501	191	10	v	v	ADP
ejpam-3501	191	11	(	(	PUNCT
ejpam-3501	191	12	hv	hv	PROPN
ejpam-3501	191	13	)	)	PUNCT
ejpam-3501	191	14	.	.	PUNCT
ejpam-3501	192	1	this	this	PRON
ejpam-3501	192	2	proves	prove	VERB
ejpam-3501	192	3	that	that	SCONJ
ejpam-3501	192	4	property	property	NOUN
ejpam-3501	192	5	(	(	PUNCT
ejpam-3501	192	6	ii	ii	NOUN
ejpam-3501	192	7	)	)	PUNCT
ejpam-3501	192	8	holds	hold	VERB
ejpam-3501	192	9	.	.	PUNCT
ejpam-3501	193	1	conversely	conversely	ADV
ejpam-3501	193	2	,	,	PUNCT
ejpam-3501	193	3	suppose	suppose	VERB
ejpam-3501	193	4	that	that	SCONJ
ejpam-3501	193	5	all	all	DET
ejpam-3501	193	6	properties	property	NOUN
ejpam-3501	193	7	hold	hold	VERB
ejpam-3501	193	8	for	for	ADP
ejpam-3501	193	9	s.	s.	PROPN
ejpam-3501	193	10	by	by	ADP
ejpam-3501	193	11	property	property	NOUN
ejpam-3501	193	12	(	(	PUNCT
ejpam-3501	193	13	i	i	NOUN
ejpam-3501	193	14	)	)	PUNCT
ejpam-3501	193	15	,	,	PUNCT
ejpam-3501	193	16	s	s	VERB
ejpam-3501	193	17	is	be	AUX
ejpam-3501	193	18	a	a	DET
ejpam-3501	193	19	dominating	dominating	NOUN
ejpam-3501	193	20	set	set	VERB
ejpam-3501	193	21	in	in	ADP
ejpam-3501	193	22	g	g	PROPN
ejpam-3501	193	23	◦	◦	PROPN
ejpam-3501	193	24	h.	h.	PROPN
ejpam-3501	193	25	let	let	VERB
ejpam-3501	193	26	u	u	PRON
ejpam-3501	193	27	∈	∈	PROPN
ejpam-3501	193	28	s	s	PART
ejpam-3501	193	29	,	,	PUNCT
ejpam-3501	193	30	and	and	CCONJ
ejpam-3501	193	31	let	let	VERB
ejpam-3501	193	32	v	v	NUM
ejpam-3501	193	33	∈	∈	PROPN
ejpam-3501	193	34	v	v	NOUN
ejpam-3501	193	35	(	(	PUNCT
ejpam-3501	193	36	g	g	NOUN
ejpam-3501	193	37	)	)	PUNCT
ejpam-3501	193	38	such	such	ADJ
ejpam-3501	193	39	that	that	SCONJ
ejpam-3501	193	40	u	u	PROPN
ejpam-3501	193	41	∈	∈	PROPN
ejpam-3501	193	42	v	v	NOUN
ejpam-3501	193	43	(	(	PUNCT
ejpam-3501	193	44	hv	hv	PROPN
ejpam-3501	193	45	+	+	PROPN
ejpam-3501	193	46	v	v	NOUN
ejpam-3501	193	47	)	)	PUNCT
ejpam-3501	193	48	.	.	PUNCT
ejpam-3501	193	49	suppose	suppose	VERB
ejpam-3501	193	50	that	that	SCONJ
ejpam-3501	193	51	u	u	PROPN
ejpam-3501	193	52	∈	∈	PROPN
ejpam-3501	193	53	v	v	ADP
ejpam-3501	193	54	(	(	PUNCT
ejpam-3501	193	55	hv	hv	PROPN
ejpam-3501	193	56	)	)	PUNCT
ejpam-3501	193	57	.	.	PUNCT
ejpam-3501	194	1	if	if	SCONJ
ejpam-3501	194	2	v	v	NUM
ejpam-3501	194	3	∈	∈	PROPN
ejpam-3501	194	4	s	s	NOUN
ejpam-3501	194	5	,	,	PUNCT
ejpam-3501	194	6	then	then	ADV
ejpam-3501	194	7	v	v	NOUN
ejpam-3501	194	8	is	be	AUX
ejpam-3501	194	9	the	the	DET
ejpam-3501	194	10	required	require	VERB
ejpam-3501	194	11	vertex	vertex	NOUN
ejpam-3501	194	12	in	in	ADP
ejpam-3501	194	13	s	s	PRON
ejpam-3501	194	14	for	for	ADP
ejpam-3501	194	15	which	which	PRON
ejpam-3501	194	16	dg	dg	VERB
ejpam-3501	194	17	◦	◦	PROPN
ejpam-3501	194	18	h(u	h(u	PROPN
ejpam-3501	194	19	,	,	PUNCT
ejpam-3501	194	20	v	v	NOUN
ejpam-3501	194	21	)	)	PUNCT
ejpam-3501	194	22	≤	≤	NOUN
ejpam-3501	194	23	2	2	NUM
ejpam-3501	194	24	.	.	PUNCT
ejpam-3501	194	25	suppose	suppose	VERB
ejpam-3501	194	26	that	that	SCONJ
ejpam-3501	194	27	v	v	NOUN
ejpam-3501	194	28	/∈	/∈	PUNCT
ejpam-3501	194	29	s.	s.	PROPN
ejpam-3501	195	1	if	if	SCONJ
ejpam-3501	195	2	ng(v	ng(v	NOUN
ejpam-3501	195	3	)	)	PUNCT
ejpam-3501	195	4	∩	∩	NOUN
ejpam-3501	195	5	s	s	PART
ejpam-3501	195	6	6=	6=	NUM
ejpam-3501	195	7	∅	∅	NOUN
ejpam-3501	195	8	,	,	PUNCT
ejpam-3501	195	9	say	say	VERB
ejpam-3501	195	10	w	w	PROPN
ejpam-3501	195	11	∈	∈	PROPN
ejpam-3501	195	12	ng(v	ng(v	NOUN
ejpam-3501	195	13	)	)	PUNCT
ejpam-3501	195	14	∩	∩	NOUN
ejpam-3501	195	15	s	s	SYM
ejpam-3501	195	16	,	,	PUNCT
ejpam-3501	195	17	then	then	ADV
ejpam-3501	195	18	dg	dg	VERB
ejpam-3501	195	19	◦	◦	NOUN
ejpam-3501	195	20	h(u	h(u	PROPN
ejpam-3501	195	21	,	,	PUNCT
ejpam-3501	195	22	w	w	NOUN
ejpam-3501	195	23	)	)	PUNCT
ejpam-3501	195	24	=	=	SYM
ejpam-3501	195	25	2	2	X
ejpam-3501	195	26	.	.	PUNCT
ejpam-3501	195	27	suppose	suppose	VERB
ejpam-3501	195	28	that	that	SCONJ
ejpam-3501	195	29	ng(v	ng(v	NOUN
ejpam-3501	195	30	)	)	PUNCT
ejpam-3501	195	31	∩	∩	NOUN
ejpam-3501	195	32	s	s	PART
ejpam-3501	195	33	=	=	X
ejpam-3501	195	34	∅.	∅.	NOUN
ejpam-3501	195	35	by	by	ADP
ejpam-3501	195	36	property	property	NOUN
ejpam-3501	195	37	(	(	PUNCT
ejpam-3501	195	38	ii	ii	NOUN
ejpam-3501	195	39	)	)	PUNCT
ejpam-3501	195	40	,	,	PUNCT
ejpam-3501	195	41	we	we	PRON
ejpam-3501	195	42	may	may	AUX
ejpam-3501	195	43	pick	pick	VERB
ejpam-3501	195	44	w	w	PROPN
ejpam-3501	195	45	∈	∈	PROPN
ejpam-3501	195	46	s	s	PART
ejpam-3501	195	47	∩	∩	ADJ
ejpam-3501	195	48	v	v	X
ejpam-3501	195	49	(	(	PUNCT
ejpam-3501	195	50	hv	hv	PROPN
ejpam-3501	195	51	)	)	PUNCT
ejpam-3501	195	52	\	\	NOUN
ejpam-3501	195	53	{	{	PUNCT
ejpam-3501	195	54	u	u	NOUN
ejpam-3501	195	55	}	}	PUNCT
ejpam-3501	195	56	.	.	PUNCT
ejpam-3501	196	1	then	then	ADV
ejpam-3501	196	2	dg	dg	VERB
ejpam-3501	196	3	◦	◦	PROPN
ejpam-3501	196	4	h(u	h(u	PROPN
ejpam-3501	196	5	,	,	PUNCT
ejpam-3501	196	6	w	w	NOUN
ejpam-3501	196	7	)	)	PUNCT
ejpam-3501	196	8	≤	≤	NUM
ejpam-3501	196	9	2	2	NUM
ejpam-3501	196	10	.	.	PUNCT
ejpam-3501	197	1	finally	finally	ADV
ejpam-3501	197	2	,	,	PUNCT
ejpam-3501	197	3	suppose	suppose	VERB
ejpam-3501	197	4	that	that	SCONJ
ejpam-3501	197	5	u	u	PRON
ejpam-3501	198	1	=	=	NOUN
ejpam-3501	198	2	v.	v.	CCONJ
ejpam-3501	198	3	since	since	SCONJ
ejpam-3501	198	4	g	g	PROPN
ejpam-3501	198	5	is	be	AUX
ejpam-3501	198	6	a	a	DET
ejpam-3501	198	7	nontrivial	nontrivial	ADJ
ejpam-3501	198	8	connected	connect	VERB
ejpam-3501	198	9	graph	graph	NOUN
ejpam-3501	198	10	,	,	PUNCT
ejpam-3501	198	11	we	we	PRON
ejpam-3501	198	12	may	may	AUX
ejpam-3501	198	13	pick	pick	VERB
ejpam-3501	198	14	w	w	PROPN
ejpam-3501	198	15	∈	∈	PROPN
ejpam-3501	198	16	v	v	ADP
ejpam-3501	198	17	(	(	PUNCT
ejpam-3501	198	18	g	g	NOUN
ejpam-3501	198	19	)	)	PUNCT
ejpam-3501	198	20	such	such	ADJ
ejpam-3501	198	21	that	that	SCONJ
ejpam-3501	198	22	vw	vw	PROPN
ejpam-3501	198	23	∈	∈	PROPN
ejpam-3501	198	24	e(g	e(g	PROPN
ejpam-3501	198	25	)	)	PUNCT
ejpam-3501	198	26	.	.	PUNCT
ejpam-3501	199	1	since	since	SCONJ
ejpam-3501	199	2	s	s	PROPN
ejpam-3501	199	3	∩	∩	ADJ
ejpam-3501	199	4	v	v	X
ejpam-3501	199	5	(	(	PUNCT
ejpam-3501	199	6	hw	hw	PROPN
ejpam-3501	199	7	+	+	CCONJ
ejpam-3501	199	8	w	w	X
ejpam-3501	199	9	)	)	PUNCT
ejpam-3501	199	10	is	be	AUX
ejpam-3501	199	11	a	a	DET
ejpam-3501	199	12	dominating	dominating	NOUN
ejpam-3501	199	13	set	set	VERB
ejpam-3501	199	14	in	in	ADP
ejpam-3501	199	15	hw	hw	PROPN
ejpam-3501	200	1	+	+	PROPN
ejpam-3501	200	2	w	w	ADJ
ejpam-3501	200	3	,	,	PUNCT
ejpam-3501	200	4	s	s	NOUN
ejpam-3501	200	5	∩	∩	ADJ
ejpam-3501	200	6	v	v	X
ejpam-3501	200	7	(	(	PUNCT
ejpam-3501	200	8	hw	hw	PROPN
ejpam-3501	200	9	+	+	PROPN
ejpam-3501	200	10	w	w	NOUN
ejpam-3501	200	11	)	)	PUNCT
ejpam-3501	201	1	6=	6=	ADP
ejpam-3501	201	2	∅.	∅.	VERB
ejpam-3501	201	3	for	for	ADP
ejpam-3501	201	4	any	any	DET
ejpam-3501	201	5	z	z	NOUN
ejpam-3501	201	6	∈	∈	PROPN
ejpam-3501	201	7	s	s	PART
ejpam-3501	201	8	∩	∩	ADJ
ejpam-3501	201	9	v	v	X
ejpam-3501	201	10	(	(	PUNCT
ejpam-3501	201	11	hw	hw	PROPN
ejpam-3501	201	12	+	+	PROPN
ejpam-3501	201	13	w	w	NOUN
ejpam-3501	201	14	)	)	PUNCT
ejpam-3501	201	15	,	,	PUNCT
ejpam-3501	201	16	dg	dg	AUX
ejpam-3501	201	17	◦	◦	NOUN
ejpam-3501	201	18	h(v	h(v	PROPN
ejpam-3501	201	19	,	,	PUNCT
ejpam-3501	201	20	z	z	NOUN
ejpam-3501	201	21	)	)	PUNCT
ejpam-3501	201	22	≤	≤	NUM
ejpam-3501	201	23	2	2	NUM
ejpam-3501	201	24	.	.	PUNCT
ejpam-3501	201	25	accordingly	accordingly	ADV
ejpam-3501	201	26	,	,	PUNCT
ejpam-3501	201	27	s	s	VERB
ejpam-3501	201	28	is	be	AUX
ejpam-3501	201	29	a	a	DET
ejpam-3501	201	30	semitotal	semitotal	ADJ
ejpam-3501	201	31	dominating	dominating	NOUN
ejpam-3501	201	32	set	set	VERB
ejpam-3501	201	33	in	in	ADP
ejpam-3501	201	34	g	g	PROPN
ejpam-3501	201	35	◦	◦	NOUN
ejpam-3501	201	36	h.	h.	NOUN
ejpam-3501	201	37	corollary	corollary	ADJ
ejpam-3501	201	38	4	4	NUM
ejpam-3501	201	39	.	.	PUNCT
ejpam-3501	202	1	let	let	VERB
ejpam-3501	202	2	g	g	PRON
ejpam-3501	202	3	be	be	AUX
ejpam-3501	202	4	a	a	DET
ejpam-3501	202	5	nontrivial	nontrivial	ADJ
ejpam-3501	202	6	connected	connect	VERB
ejpam-3501	202	7	graph	graph	NOUN
ejpam-3501	202	8	and	and	CCONJ
ejpam-3501	202	9	h	h	NOUN
ejpam-3501	202	10	any	any	DET
ejpam-3501	202	11	nontrivial	nontrivial	ADJ
ejpam-3501	202	12	graph	graph	NOUN
ejpam-3501	202	13	,	,	PUNCT
ejpam-3501	202	14	and	and	CCONJ
ejpam-3501	202	15	s	s	VERB
ejpam-3501	202	16	⊆	⊆	NUM
ejpam-3501	202	17	v	v	NOUN
ejpam-3501	202	18	(	(	PUNCT
ejpam-3501	202	19	g	g	PROPN
ejpam-3501	202	20	◦	◦	NOUN
ejpam-3501	202	21	h	h	NOUN
ejpam-3501	202	22	)	)	PUNCT
ejpam-3501	202	23	.	.	PUNCT
ejpam-3501	203	1	then	then	ADV
ejpam-3501	203	2	s	s	VERB
ejpam-3501	203	3	is	be	AUX
ejpam-3501	203	4	a	a	DET
ejpam-3501	203	5	semitotal	semitotal	ADJ
ejpam-3501	203	6	dominating	dominating	NOUN
ejpam-3501	203	7	set	set	VERB
ejpam-3501	203	8	in	in	ADP
ejpam-3501	203	9	g	g	PROPN
ejpam-3501	203	10	◦	◦	NOUN
ejpam-3501	203	11	h	h	NOUN
ejpam-3501	203	12	if	if	SCONJ
ejpam-3501	204	1	and	and	CCONJ
ejpam-3501	204	2	only	only	ADV
ejpam-3501	204	3	if	if	SCONJ
ejpam-3501	204	4	s	s	VERB
ejpam-3501	204	5	=	=	NOUN
ejpam-3501	204	6	a	a	DET
ejpam-3501	204	7	∪	∪	NOUN
ejpam-3501	204	8	[	[	X
ejpam-3501	204	9	∪v∈asv	∪v∈asv	NOUN
ejpam-3501	204	10	]	]	PUNCT
ejpam-3501	204	11	∪	∪	ADP
ejpam-3501	204	12	[	[	X
ejpam-3501	204	13	∪u∈v	∪u∈v	X
ejpam-3501	204	14	(	(	PUNCT
ejpam-3501	204	15	g)\adu	g)\adu	PROPN
ejpam-3501	204	16	]	]	X
ejpam-3501	204	17	,	,	PUNCT
ejpam-3501	204	18	where	where	SCONJ
ejpam-3501	204	19	(	(	PUNCT
ejpam-3501	204	20	i	i	NOUN
ejpam-3501	204	21	)	)	PUNCT
ejpam-3501	204	22	a	a	DET
ejpam-3501	204	23	⊆	⊆	NUM
ejpam-3501	204	24	v	v	NOUN
ejpam-3501	204	25	(	(	PUNCT
ejpam-3501	204	26	g	g	NOUN
ejpam-3501	204	27	)	)	PUNCT
ejpam-3501	204	28	;	;	PUNCT
ejpam-3501	204	29	(	(	PUNCT
ejpam-3501	204	30	ii	ii	NOUN
ejpam-3501	204	31	)	)	PUNCT
ejpam-3501	204	32	sv	sv	VERB
ejpam-3501	205	1	⊆	⊆	NUM
ejpam-3501	205	2	v	v	X
ejpam-3501	205	3	(	(	PUNCT
ejpam-3501	205	4	hv	hv	PROPN
ejpam-3501	205	5	)	)	PUNCT
ejpam-3501	205	6	for	for	ADP
ejpam-3501	205	7	each	each	PRON
ejpam-3501	205	8	v	v	ADP
ejpam-3501	205	9	∈	∈	PROPN
ejpam-3501	205	10	a	a	PRON
ejpam-3501	205	11	;	;	PUNCT
ejpam-3501	205	12	(	(	PUNCT
ejpam-3501	205	13	iii	iii	X
ejpam-3501	205	14	)	)	PUNCT
ejpam-3501	205	15	du	du	PROPN
ejpam-3501	205	16	is	be	AUX
ejpam-3501	205	17	a	a	DET
ejpam-3501	205	18	dominating	dominating	NOUN
ejpam-3501	205	19	set	set	VERB
ejpam-3501	205	20	in	in	ADP
ejpam-3501	205	21	hu	hu	PROPN
ejpam-3501	205	22	for	for	ADP
ejpam-3501	205	23	each	each	DET
ejpam-3501	205	24	u	u	PROPN
ejpam-3501	205	25	∈	∈	PROPN
ejpam-3501	205	26	v	v	ADP
ejpam-3501	205	27	(	(	PUNCT
ejpam-3501	205	28	g	g	NOUN
ejpam-3501	205	29	)	)	PUNCT
ejpam-3501	205	30	\a	\a	NUM
ejpam-3501	205	31	;	;	PUNCT
ejpam-3501	205	32	and	and	CCONJ
ejpam-3501	205	33	(	(	PUNCT
ejpam-3501	205	34	iv	iv	X
ejpam-3501	205	35	)	)	PUNCT
ejpam-3501	205	36	|du|	|du|	NOUN
ejpam-3501	205	37	≥	≥	NOUN
ejpam-3501	205	38	2	2	NUM
ejpam-3501	205	39	for	for	ADP
ejpam-3501	205	40	each	each	DET
ejpam-3501	205	41	u	u	PROPN
ejpam-3501	205	42	∈	∈	PROPN
ejpam-3501	205	43	v	v	ADP
ejpam-3501	205	44	(	(	PUNCT
ejpam-3501	205	45	g	g	NOUN
ejpam-3501	205	46	)	)	PUNCT
ejpam-3501	205	47	\a	\a	VERB
ejpam-3501	205	48	with	with	ADP
ejpam-3501	205	49	ng(u	ng(u	NOUN
ejpam-3501	205	50	)	)	PUNCT
ejpam-3501	205	51	∩a	∩a	NOUN
ejpam-3501	205	52	=	=	PUNCT
ejpam-3501	205	53	∅.	∅.	PRON
ejpam-3501	205	54	corollary	corollary	ADJ
ejpam-3501	205	55	5	5	NUM
ejpam-3501	205	56	.	.	PUNCT
ejpam-3501	206	1	for	for	ADP
ejpam-3501	206	2	all	all	DET
ejpam-3501	206	3	nontrivial	nontrivial	ADJ
ejpam-3501	206	4	connected	connect	VERB
ejpam-3501	206	5	graphs	graph	NOUN
ejpam-3501	206	6	g	g	NOUN
ejpam-3501	206	7	and	and	CCONJ
ejpam-3501	206	8	any	any	DET
ejpam-3501	206	9	graph	graph	NOUN
ejpam-3501	206	10	h	h	NOUN
ejpam-3501	206	11	,	,	PUNCT
ejpam-3501	206	12	γt2(g	γt2(g	PROPN
ejpam-3501	206	13	◦	◦	NOUN
ejpam-3501	206	14	h	h	NOUN
ejpam-3501	206	15	)	)	PUNCT
ejpam-3501	206	16	=	=	SYM
ejpam-3501	206	17	|v	|v	PROPN
ejpam-3501	206	18	(	(	PUNCT
ejpam-3501	206	19	g)|	g)|	NOUN
ejpam-3501	206	20	.	.	PUNCT
ejpam-3501	207	1	for	for	ADP
ejpam-3501	207	2	nontrivial	nontrivial	ADJ
ejpam-3501	207	3	connected	connect	VERB
ejpam-3501	207	4	graphs	graph	NOUN
ejpam-3501	207	5	g	g	ADP
ejpam-3501	207	6	,	,	PUNCT
ejpam-3501	207	7	v	v	NOUN
ejpam-3501	207	8	(	(	PUNCT
ejpam-3501	207	9	g	g	NOUN
ejpam-3501	207	10	)	)	PUNCT
ejpam-3501	207	11	is	be	AUX
ejpam-3501	207	12	a	a	DET
ejpam-3501	207	13	secure	secure	ADJ
ejpam-3501	207	14	semitotal	semitotal	ADJ
ejpam-3501	207	15	dominating	dominating	NOUN
ejpam-3501	207	16	set	set	NOUN
ejpam-3501	207	17	in	in	ADP
ejpam-3501	207	18	the	the	DET
ejpam-3501	207	19	corona	corona	NOUN
ejpam-3501	207	20	g	g	ADP
ejpam-3501	207	21	◦	◦	NOUN
ejpam-3501	207	22	kp	kp	NOUN
ejpam-3501	207	23	for	for	ADP
ejpam-3501	207	24	any	any	DET
ejpam-3501	207	25	integer	integer	NOUN
ejpam-3501	207	26	p	p	NOUN
ejpam-3501	207	27	≥	≥	NUM
ejpam-3501	207	28	1	1	NUM
ejpam-3501	207	29	.	.	PUNCT
ejpam-3501	208	1	this	this	PRON
ejpam-3501	208	2	,	,	PUNCT
ejpam-3501	208	3	together	together	ADV
ejpam-3501	208	4	with	with	ADP
ejpam-3501	208	5	corollary	corollary	ADJ
ejpam-3501	208	6	5	5	NUM
ejpam-3501	208	7	,	,	PUNCT
ejpam-3501	208	8	yields	yield	NOUN
ejpam-3501	208	9	γst2(g	γst2(g	PART
ejpam-3501	208	10	◦	◦	NOUN
ejpam-3501	208	11	kp	kp	NOUN
ejpam-3501	208	12	)	)	PUNCT
ejpam-3501	208	13	=	=	SYM
ejpam-3501	208	14	|v	|v	PROPN
ejpam-3501	208	15	(	(	PUNCT
ejpam-3501	208	16	g)|	g)|	NOUN
ejpam-3501	208	17	.	.	PUNCT
ejpam-3501	209	1	in	in	ADP
ejpam-3501	209	2	what	what	PRON
ejpam-3501	209	3	follows	follow	VERB
ejpam-3501	209	4	,	,	PUNCT
ejpam-3501	209	5	we	we	PRON
ejpam-3501	209	6	consider	consider	VERB
ejpam-3501	209	7	g	g	NOUN
ejpam-3501	209	8	◦	◦	NOUN
ejpam-3501	209	9	h	h	NOUN
ejpam-3501	209	10	,	,	PUNCT
ejpam-3501	209	11	where	where	SCONJ
ejpam-3501	209	12	h	h	NOUN
ejpam-3501	209	13	is	be	AUX
ejpam-3501	209	14	noncomplete	noncomplete	ADJ
ejpam-3501	209	15	.	.	PUNCT
ejpam-3501	210	1	theorem	theorem	NOUN
ejpam-3501	210	2	3	3	X
ejpam-3501	210	3	.	.	PUNCT
ejpam-3501	211	1	let	let	VERB
ejpam-3501	211	2	g	g	PRON
ejpam-3501	211	3	be	be	AUX
ejpam-3501	211	4	a	a	DET
ejpam-3501	211	5	nontrivial	nontrivial	ADJ
ejpam-3501	211	6	connected	connect	VERB
ejpam-3501	211	7	graph	graph	NOUN
ejpam-3501	211	8	and	and	CCONJ
ejpam-3501	211	9	h	h	NOUN
ejpam-3501	211	10	be	be	AUX
ejpam-3501	211	11	any	any	DET
ejpam-3501	211	12	noncomplete	noncomplete	ADJ
ejpam-3501	211	13	graph	graph	NOUN
ejpam-3501	211	14	without	without	ADP
ejpam-3501	211	15	isolated	isolated	ADJ
ejpam-3501	211	16	vertices	vertex	NOUN
ejpam-3501	211	17	,	,	PUNCT
ejpam-3501	211	18	and	and	CCONJ
ejpam-3501	211	19	let	let	VERB
ejpam-3501	211	20	s	s	PRON
ejpam-3501	211	21	⊆	⊆	NUM
ejpam-3501	211	22	v	v	NOUN
ejpam-3501	211	23	(	(	PUNCT
ejpam-3501	211	24	g	g	PROPN
ejpam-3501	211	25	◦	◦	NOUN
ejpam-3501	211	26	h	h	NOUN
ejpam-3501	211	27	)	)	PUNCT
ejpam-3501	211	28	.	.	PUNCT
ejpam-3501	212	1	then	then	ADV
ejpam-3501	212	2	s	s	VERB
ejpam-3501	212	3	is	be	AUX
ejpam-3501	212	4	a	a	DET
ejpam-3501	212	5	secure	secure	ADJ
ejpam-3501	212	6	semitotal	semitotal	ADJ
ejpam-3501	212	7	dominating	dominating	NOUN
ejpam-3501	212	8	set	set	NOUN
ejpam-3501	212	9	if	if	SCONJ
ejpam-3501	212	10	and	and	CCONJ
ejpam-3501	212	11	only	only	ADV
ejpam-3501	212	12	if	if	SCONJ
ejpam-3501	212	13	s	s	NOUN
ejpam-3501	212	14	is	be	AUX
ejpam-3501	212	15	a	a	DET
ejpam-3501	212	16	semitotal	semitotal	ADJ
ejpam-3501	212	17	dominating	dominating	NOUN
ejpam-3501	212	18	set	set	VERB
ejpam-3501	212	19	in	in	ADP
ejpam-3501	212	20	g	g	ADP
ejpam-3501	212	21	◦	◦	NOUN
ejpam-3501	212	22	h	h	NOUN
ejpam-3501	212	23	satisfying	satisfy	VERB
ejpam-3501	212	24	the	the	DET
ejpam-3501	212	25	following	follow	VERB
ejpam-3501	212	26	properties	property	NOUN
ejpam-3501	212	27	:	:	PUNCT
ejpam-3501	212	28	(	(	PUNCT
ejpam-3501	212	29	i	i	NOUN
ejpam-3501	212	30	)	)	PUNCT
ejpam-3501	212	31	s	s	PART
ejpam-3501	212	32	∩	∩	ADJ
ejpam-3501	212	33	v	v	X
ejpam-3501	212	34	(	(	PUNCT
ejpam-3501	212	35	hv	hv	X
ejpam-3501	212	36	)	)	PUNCT
ejpam-3501	212	37	is	be	AUX
ejpam-3501	212	38	a	a	DET
ejpam-3501	212	39	secure	secure	ADJ
ejpam-3501	212	40	dominating	dominating	NOUN
ejpam-3501	212	41	set	set	VERB
ejpam-3501	212	42	in	in	ADP
ejpam-3501	212	43	hv	hv	PROPN
ejpam-3501	212	44	for	for	ADP
ejpam-3501	212	45	each	each	PRON
ejpam-3501	212	46	v	v	NUM
ejpam-3501	212	47	∈	∈	PROPN
ejpam-3501	212	48	v	v	NOUN
ejpam-3501	212	49	(	(	PUNCT
ejpam-3501	212	50	g	g	NOUN
ejpam-3501	212	51	)	)	PUNCT
ejpam-3501	212	52	\	\	PROPN
ejpam-3501	213	1	s	s	X
ejpam-3501	213	2	;	;	PUNCT
ejpam-3501	213	3	and	and	CCONJ
ejpam-3501	213	4	(	(	PUNCT
ejpam-3501	213	5	ii	ii	NOUN
ejpam-3501	213	6	)	)	PUNCT
ejpam-3501	213	7	s	s	PART
ejpam-3501	213	8	∩	∩	ADJ
ejpam-3501	213	9	v	v	X
ejpam-3501	213	10	(	(	PUNCT
ejpam-3501	213	11	hv	hv	X
ejpam-3501	213	12	)	)	PUNCT
ejpam-3501	213	13	is	be	AUX
ejpam-3501	213	14	a	a	DET
ejpam-3501	213	15	nearly	nearly	ADV
ejpam-3501	213	16	dominating	dominating	NOUN
ejpam-3501	213	17	set	set	VERB
ejpam-3501	213	18	in	in	ADP
ejpam-3501	213	19	hv	hv	PROPN
ejpam-3501	213	20	for	for	ADP
ejpam-3501	213	21	all	all	PRON
ejpam-3501	213	22	v	v	ADP
ejpam-3501	213	23	∈	∈	NOUN
ejpam-3501	213	24	s	s	NOUN
ejpam-3501	213	25	∩	∩	ADJ
ejpam-3501	213	26	v	v	X
ejpam-3501	213	27	(	(	PUNCT
ejpam-3501	213	28	g	g	NOUN
ejpam-3501	213	29	)	)	PUNCT
ejpam-3501	213	30	.	.	PUNCT
ejpam-3501	214	1	i.	i.	PROPN
ejpam-3501	214	2	s.	s.	PROPN
ejpam-3501	214	3	aniversario	aniversario	PROPN
ejpam-3501	214	4	,	,	PUNCT
ejpam-3501	214	5	s.	s.	PROPN
ejpam-3501	214	6	r.	r.	PROPN
ejpam-3501	214	7	jr	jr	PROPN
ejpam-3501	214	8	.	.	PROPN
ejpam-3501	214	9	canoy	canoy	PROPN
ejpam-3501	214	10	,	,	PUNCT
ejpam-3501	214	11	f.p	f.p	PROPN
ejpam-3501	214	12	.	.	PROPN
ejpam-3501	214	13	jamil	jamil	PROPN
ejpam-3501	214	14	/	/	SYM
ejpam-3501	214	15	eur	eur	PROPN
ejpam-3501	214	16	.	.	PUNCT
ejpam-3501	215	1	j.	j.	PROPN
ejpam-3501	215	2	pure	pure	PROPN
ejpam-3501	215	3	appl	appl	PROPN
ejpam-3501	215	4	.	.	PROPN
ejpam-3501	215	5	math	math	PROPN
ejpam-3501	215	6	,	,	PUNCT
ejpam-3501	215	7	12	12	NUM
ejpam-3501	215	8	(	(	PUNCT
ejpam-3501	215	9	4	4	NUM
ejpam-3501	215	10	)	)	PUNCT
ejpam-3501	215	11	(	(	PUNCT
ejpam-3501	215	12	2019	2019	NUM
ejpam-3501	215	13	)	)	PUNCT
ejpam-3501	215	14	,	,	PUNCT
ejpam-3501	215	15	1410	1410	NUM
ejpam-3501	215	16	-	-	SYM
ejpam-3501	215	17	1425	1425	NUM
ejpam-3501	215	18	1417	1417	NUM
ejpam-3501	215	19	proof	proof	NOUN
ejpam-3501	215	20	.	.	PUNCT
ejpam-3501	216	1	for	for	ADP
ejpam-3501	216	2	each	each	DET
ejpam-3501	216	3	v	v	NUM
ejpam-3501	216	4	∈	∈	PROPN
ejpam-3501	216	5	v	v	NOUN
ejpam-3501	216	6	(	(	PUNCT
ejpam-3501	216	7	g	g	NOUN
ejpam-3501	216	8	)	)	PUNCT
ejpam-3501	216	9	,	,	PUNCT
ejpam-3501	216	10	we	we	PRON
ejpam-3501	216	11	write	write	VERB
ejpam-3501	216	12	sv	sv	PROPN
ejpam-3501	216	13	=	=	SYM
ejpam-3501	216	14	s	s	PROPN
ejpam-3501	216	15	∩	∩	ADJ
ejpam-3501	216	16	v	v	X
ejpam-3501	216	17	(	(	PUNCT
ejpam-3501	216	18	hv	hv	PROPN
ejpam-3501	216	19	)	)	PUNCT
ejpam-3501	216	20	.	.	PUNCT
ejpam-3501	217	1	suppose	suppose	VERB
ejpam-3501	217	2	that	that	SCONJ
ejpam-3501	217	3	s	s	VERB
ejpam-3501	217	4	is	be	AUX
ejpam-3501	217	5	a	a	DET
ejpam-3501	217	6	secure	secure	ADJ
ejpam-3501	217	7	semitotal	semitotal	ADJ
ejpam-3501	217	8	dominating	dominating	NOUN
ejpam-3501	217	9	set	set	VERB
ejpam-3501	217	10	in	in	ADP
ejpam-3501	217	11	g	g	PROPN
ejpam-3501	217	12	◦	◦	NOUN
ejpam-3501	217	13	h.	h.	NOUN
ejpam-3501	217	14	then	then	ADV
ejpam-3501	217	15	s	s	VERB
ejpam-3501	217	16	is	be	AUX
ejpam-3501	217	17	a	a	DET
ejpam-3501	217	18	semitotal	semitotal	ADJ
ejpam-3501	217	19	dominating	dominating	NOUN
ejpam-3501	217	20	set	set	VERB
ejpam-3501	217	21	in	in	ADP
ejpam-3501	217	22	g	g	PROPN
ejpam-3501	217	23	◦	◦	NOUN
ejpam-3501	217	24	h.	h.	NOUN
ejpam-3501	217	25	let	let	VERB
ejpam-3501	217	26	v	v	NUM
ejpam-3501	217	27	∈	∈	PROPN
ejpam-3501	217	28	v	v	NOUN
ejpam-3501	217	29	(	(	PUNCT
ejpam-3501	217	30	g	g	NOUN
ejpam-3501	217	31	)	)	PUNCT
ejpam-3501	217	32	\s	\s	NOUN
ejpam-3501	217	33	.	.	PUNCT
ejpam-3501	218	1	by	by	ADP
ejpam-3501	218	2	proposition	proposition	NOUN
ejpam-3501	218	3	2	2	NUM
ejpam-3501	218	4	,	,	PUNCT
ejpam-3501	218	5	sv	sv	PROPN
ejpam-3501	218	6	is	be	AUX
ejpam-3501	218	7	a	a	DET
ejpam-3501	218	8	dominating	dominating	NOUN
ejpam-3501	218	9	set	set	VERB
ejpam-3501	218	10	in	in	ADP
ejpam-3501	218	11	hv	hv	PROPN
ejpam-3501	218	12	.	.	PUNCT
ejpam-3501	219	1	let	let	VERB
ejpam-3501	219	2	x	x	SYM
ejpam-3501	219	3	∈	∈	PROPN
ejpam-3501	219	4	v	v	ADP
ejpam-3501	219	5	(	(	PUNCT
ejpam-3501	219	6	hv	hv	NOUN
ejpam-3501	219	7	)	)	PUNCT
ejpam-3501	219	8	\sv	\sv	PROPN
ejpam-3501	219	9	.	.	PUNCT
ejpam-3501	220	1	since	since	SCONJ
ejpam-3501	220	2	s	s	PROPN
ejpam-3501	220	3	is	be	AUX
ejpam-3501	220	4	a	a	DET
ejpam-3501	220	5	secure	secure	ADJ
ejpam-3501	220	6	semitotal	semitotal	ADJ
ejpam-3501	220	7	dominating	dominating	NOUN
ejpam-3501	220	8	set	set	VERB
ejpam-3501	220	9	in	in	ADP
ejpam-3501	220	10	g	g	PROPN
ejpam-3501	220	11	◦	◦	NOUN
ejpam-3501	220	12	h	h	NOUN
ejpam-3501	220	13	,	,	PUNCT
ejpam-3501	220	14	there	there	PRON
ejpam-3501	220	15	exists	exist	VERB
ejpam-3501	220	16	y	y	PROPN
ejpam-3501	220	17	∈	∈	PROPN
ejpam-3501	220	18	s	s	AUX
ejpam-3501	220	19	∩ng	∩ng	PROPN
ejpam-3501	220	20	◦	◦	NOUN
ejpam-3501	220	21	h(x	h(x	PROPN
ejpam-3501	220	22	)	)	PUNCT
ejpam-3501	220	23	such	such	ADJ
ejpam-3501	220	24	that	that	DET
ejpam-3501	220	25	s∗	s∗	PROPN
ejpam-3501	220	26	=	=	SYM
ejpam-3501	220	27	(	(	PUNCT
ejpam-3501	220	28	s	s	NOUN
ejpam-3501	220	29	\	\	X
ejpam-3501	220	30	{	{	PUNCT
ejpam-3501	220	31	y	y	NOUN
ejpam-3501	220	32	}	}	PUNCT
ejpam-3501	220	33	)	)	PUNCT
ejpam-3501	220	34	∪	∪	ADP
ejpam-3501	220	35	{	{	PUNCT
ejpam-3501	220	36	x	x	NOUN
ejpam-3501	220	37	}	}	PUNCT
ejpam-3501	220	38	is	be	AUX
ejpam-3501	220	39	a	a	DET
ejpam-3501	220	40	semitotal	semitotal	ADJ
ejpam-3501	220	41	dominating	dominating	NOUN
ejpam-3501	220	42	set	set	VERB
ejpam-3501	220	43	in	in	ADP
ejpam-3501	220	44	g	g	PROPN
ejpam-3501	220	45	◦	◦	NOUN
ejpam-3501	220	46	h.	h.	NOUN
ejpam-3501	220	47	clearly	clearly	ADV
ejpam-3501	220	48	,	,	PUNCT
ejpam-3501	220	49	y	y	PROPN
ejpam-3501	220	50	∈	∈	PROPN
ejpam-3501	220	51	sv	sv	PROPN
ejpam-3501	220	52	∩	∩	PROPN
ejpam-3501	220	53	nhv(x	nhv(x	PROPN
ejpam-3501	220	54	)	)	PUNCT
ejpam-3501	220	55	.	.	PUNCT
ejpam-3501	221	1	write	write	VERB
ejpam-3501	221	2	s∗	s∗	PROPN
ejpam-3501	221	3	=	=	PUNCT
ejpam-3501	221	4	(	(	PUNCT
ejpam-3501	221	5	∪u∈v	∪u∈v	PROPN
ejpam-3501	221	6	(	(	PUNCT
ejpam-3501	221	7	g)\{v}s	g)\{v}s	NOUN
ejpam-3501	221	8	∩	∩	ADJ
ejpam-3501	221	9	v	v	X
ejpam-3501	221	10	(	(	PUNCT
ejpam-3501	221	11	hu	hu	PROPN
ejpam-3501	221	12	+	+	CCONJ
ejpam-3501	221	13	u	u	NOUN
ejpam-3501	221	14	)	)	PUNCT
ejpam-3501	221	15	)	)	PUNCT
ejpam-3501	221	16	∪	∪	ADV
ejpam-3501	221	17	(	(	PUNCT
ejpam-3501	221	18	sv	sv	PROPN
ejpam-3501	221	19	\	\	PROPN
ejpam-3501	221	20	{	{	PUNCT
ejpam-3501	221	21	y	y	NOUN
ejpam-3501	221	22	}	}	PUNCT
ejpam-3501	221	23	)	)	PUNCT
ejpam-3501	221	24	∪	∪	ADP
ejpam-3501	221	25	{	{	PUNCT
ejpam-3501	221	26	x	x	NOUN
ejpam-3501	221	27	}	}	PUNCT
ejpam-3501	221	28	.	.	PUNCT
ejpam-3501	222	1	(	(	PUNCT
ejpam-3501	222	2	1	1	X
ejpam-3501	222	3	)	)	PUNCT
ejpam-3501	222	4	since	since	SCONJ
ejpam-3501	222	5	s∗	s∗	PROPN
ejpam-3501	222	6	is	be	AUX
ejpam-3501	222	7	a	a	DET
ejpam-3501	222	8	dominating	dominating	NOUN
ejpam-3501	222	9	set	set	VERB
ejpam-3501	222	10	in	in	ADP
ejpam-3501	222	11	g	g	ADP
ejpam-3501	222	12	◦	◦	NOUN
ejpam-3501	222	13	h	h	NOUN
ejpam-3501	222	14	,	,	PUNCT
ejpam-3501	222	15	(	(	PUNCT
ejpam-3501	222	16	sv	sv	INTJ
ejpam-3501	222	17	\	\	PROPN
ejpam-3501	222	18	{	{	PUNCT
ejpam-3501	222	19	y})∪{x	y})∪{x	PROPN
ejpam-3501	222	20	}	}	PUNCT
ejpam-3501	222	21	is	be	AUX
ejpam-3501	222	22	a	a	DET
ejpam-3501	222	23	dominating	dominating	NOUN
ejpam-3501	222	24	set	set	NOUN
ejpam-3501	222	25	in	in	ADP
ejpam-3501	222	26	hv	hv	PROPN
ejpam-3501	222	27	by	by	ADP
ejpam-3501	222	28	lemma	lemma	PROPN
ejpam-3501	222	29	1	1	NUM
ejpam-3501	222	30	.	.	PUNCT
ejpam-3501	223	1	thus	thus	ADV
ejpam-3501	223	2	,	,	PUNCT
ejpam-3501	223	3	sv	sv	PROPN
ejpam-3501	223	4	is	be	AUX
ejpam-3501	223	5	a	a	DET
ejpam-3501	223	6	secure	secure	ADJ
ejpam-3501	223	7	dominating	dominating	NOUN
ejpam-3501	223	8	set	set	VERB
ejpam-3501	223	9	in	in	ADP
ejpam-3501	223	10	hv	hv	PROPN
ejpam-3501	223	11	.	.	PUNCT
ejpam-3501	224	1	this	this	PRON
ejpam-3501	224	2	proves	prove	VERB
ejpam-3501	224	3	property	property	NOUN
ejpam-3501	224	4	(	(	PUNCT
ejpam-3501	224	5	i	i	NOUN
ejpam-3501	224	6	)	)	PUNCT
ejpam-3501	224	7	.	.	PUNCT
ejpam-3501	225	1	to	to	PART
ejpam-3501	225	2	prove	prove	VERB
ejpam-3501	225	3	(	(	PUNCT
ejpam-3501	225	4	ii	ii	NOUN
ejpam-3501	225	5	)	)	PUNCT
ejpam-3501	225	6	,	,	PUNCT
ejpam-3501	225	7	let	let	VERB
ejpam-3501	225	8	v	v	NUM
ejpam-3501	225	9	∈	∈	NOUN
ejpam-3501	225	10	s	s	PART
ejpam-3501	225	11	∩	∩	ADJ
ejpam-3501	225	12	v	v	X
ejpam-3501	225	13	(	(	PUNCT
ejpam-3501	225	14	g	g	NOUN
ejpam-3501	225	15	)	)	PUNCT
ejpam-3501	225	16	.	.	PUNCT
ejpam-3501	226	1	if	if	SCONJ
ejpam-3501	226	2	sv	sv	PROPN
ejpam-3501	226	3	is	be	AUX
ejpam-3501	226	4	a	a	DET
ejpam-3501	226	5	dominating	dominating	NOUN
ejpam-3501	226	6	set	set	NOUN
ejpam-3501	226	7	in	in	ADP
ejpam-3501	226	8	hv	hv	PROPN
ejpam-3501	226	9	,	,	PUNCT
ejpam-3501	226	10	then	then	ADV
ejpam-3501	226	11	we	we	PRON
ejpam-3501	226	12	are	be	AUX
ejpam-3501	226	13	done	do	VERB
ejpam-3501	226	14	.	.	PUNCT
ejpam-3501	227	1	suppose	suppose	VERB
ejpam-3501	227	2	that	that	SCONJ
ejpam-3501	227	3	sv	sv	PROPN
ejpam-3501	227	4	is	be	AUX
ejpam-3501	227	5	not	not	PART
ejpam-3501	227	6	a	a	DET
ejpam-3501	227	7	dominating	dominating	NOUN
ejpam-3501	227	8	set	set	VERB
ejpam-3501	227	9	in	in	ADP
ejpam-3501	227	10	hv	hv	PROPN
ejpam-3501	227	11	,	,	PUNCT
ejpam-3501	227	12	and	and	CCONJ
ejpam-3501	227	13	let	let	VERB
ejpam-3501	227	14	x	x	SYM
ejpam-3501	227	15	∈	∈	PROPN
ejpam-3501	227	16	v	v	ADP
ejpam-3501	227	17	(	(	PUNCT
ejpam-3501	227	18	hv	hv	PROPN
ejpam-3501	227	19	)	)	PUNCT
ejpam-3501	227	20	\nhv	\nhv	NOUN
ejpam-3501	228	1	[	[	X
ejpam-3501	228	2	sv	sv	X
ejpam-3501	228	3	]	]	X
ejpam-3501	228	4	.	.	PUNCT
ejpam-3501	229	1	since	since	SCONJ
ejpam-3501	229	2	s	s	PROPN
ejpam-3501	229	3	is	be	AUX
ejpam-3501	229	4	a	a	DET
ejpam-3501	229	5	secure	secure	ADJ
ejpam-3501	229	6	semitotal	semitotal	ADJ
ejpam-3501	229	7	dominating	dominating	NOUN
ejpam-3501	229	8	set	set	VERB
ejpam-3501	229	9	in	in	ADP
ejpam-3501	229	10	g	g	PROPN
ejpam-3501	229	11	◦	◦	NOUN
ejpam-3501	229	12	h	h	NOUN
ejpam-3501	229	13	and	and	CCONJ
ejpam-3501	229	14	x	x	PUNCT
ejpam-3501	229	15	∈	∈	PROPN
ejpam-3501	229	16	v	v	NOUN
ejpam-3501	229	17	(	(	PUNCT
ejpam-3501	229	18	g	g	PROPN
ejpam-3501	229	19	◦	◦	NOUN
ejpam-3501	229	20	h	h	NOUN
ejpam-3501	229	21	)	)	PUNCT
ejpam-3501	229	22	\	\	PROPN
ejpam-3501	230	1	s	s	X
ejpam-3501	230	2	,	,	PUNCT
ejpam-3501	230	3	there	there	PRON
ejpam-3501	230	4	exists	exist	VERB
ejpam-3501	230	5	u	u	PROPN
ejpam-3501	230	6	∈	∈	PROPN
ejpam-3501	230	7	s	s	PART
ejpam-3501	230	8	∩ng	∩ng	NOUN
ejpam-3501	230	9	◦	◦	NOUN
ejpam-3501	230	10	h(x	h(x	PROPN
ejpam-3501	230	11	)	)	PUNCT
ejpam-3501	230	12	such	such	ADJ
ejpam-3501	230	13	that	that	SCONJ
ejpam-3501	230	14	(	(	PUNCT
ejpam-3501	230	15	s	s	AUX
ejpam-3501	230	16	\	\	X
ejpam-3501	230	17	{	{	PUNCT
ejpam-3501	230	18	u})∪{x	u})∪{x	NOUN
ejpam-3501	230	19	}	}	PUNCT
ejpam-3501	230	20	is	be	AUX
ejpam-3501	230	21	a	a	DET
ejpam-3501	230	22	semitotal	semitotal	ADJ
ejpam-3501	230	23	dominating	dominating	NOUN
ejpam-3501	230	24	set	set	VERB
ejpam-3501	230	25	in	in	ADP
ejpam-3501	230	26	g	g	PROPN
ejpam-3501	230	27	◦	◦	NOUN
ejpam-3501	230	28	h.	h.	NOUN
ejpam-3501	230	29	necessarily	necessarily	ADV
ejpam-3501	230	30	,	,	PUNCT
ejpam-3501	230	31	u	u	NOUN
ejpam-3501	230	32	=	=	PROPN
ejpam-3501	230	33	v	v	NOUN
ejpam-3501	230	34	so	so	SCONJ
ejpam-3501	230	35	that	that	SCONJ
ejpam-3501	230	36	sv	sv	ADP
ejpam-3501	230	37	∪{x	∪{x	NOUN
ejpam-3501	230	38	}	}	PUNCT
ejpam-3501	230	39	is	be	AUX
ejpam-3501	230	40	a	a	DET
ejpam-3501	230	41	semitotal	semitotal	ADJ
ejpam-3501	230	42	dominating	dominating	NOUN
ejpam-3501	230	43	set	set	VERB
ejpam-3501	230	44	in	in	ADP
ejpam-3501	230	45	hv	hv	PROPN
ejpam-3501	230	46	+	+	CCONJ
ejpam-3501	230	47	v.	v.	CCONJ
ejpam-3501	230	48	by	by	ADP
ejpam-3501	230	49	theorem	theorem	NOUN
ejpam-3501	230	50	2	2	NUM
ejpam-3501	230	51	,	,	PUNCT
ejpam-3501	230	52	sv	sv	INTJ
ejpam-3501	230	53	∪	∪	X
ejpam-3501	230	54	{	{	PUNCT
ejpam-3501	230	55	x	x	NOUN
ejpam-3501	230	56	}	}	PUNCT
ejpam-3501	230	57	is	be	AUX
ejpam-3501	230	58	a	a	DET
ejpam-3501	230	59	dominating	dominating	NOUN
ejpam-3501	230	60	set	set	VERB
ejpam-3501	230	61	in	in	ADP
ejpam-3501	230	62	hv	hv	PROPN
ejpam-3501	230	63	.	.	PUNCT
ejpam-3501	231	1	thus	thus	ADV
ejpam-3501	231	2	,	,	PUNCT
ejpam-3501	231	3	sv	sv	PROPN
ejpam-3501	231	4	is	be	AUX
ejpam-3501	231	5	nearly	nearly	ADV
ejpam-3501	231	6	dominating	dominate	VERB
ejpam-3501	231	7	in	in	ADP
ejpam-3501	231	8	hv	hv	PROPN
ejpam-3501	231	9	.	.	PUNCT
ejpam-3501	232	1	conversely	conversely	ADV
ejpam-3501	232	2	,	,	PUNCT
ejpam-3501	232	3	suppose	suppose	VERB
ejpam-3501	232	4	that	that	SCONJ
ejpam-3501	232	5	all	all	DET
ejpam-3501	232	6	the	the	DET
ejpam-3501	232	7	properties	property	NOUN
ejpam-3501	232	8	hold	hold	VERB
ejpam-3501	232	9	for	for	ADP
ejpam-3501	232	10	a	a	DET
ejpam-3501	232	11	semitotal	semitotal	ADJ
ejpam-3501	232	12	dominating	dominating	NOUN
ejpam-3501	232	13	set	set	NOUN
ejpam-3501	232	14	s	s	VERB
ejpam-3501	232	15	in	in	ADP
ejpam-3501	232	16	g	g	PROPN
ejpam-3501	232	17	◦	◦	NOUN
ejpam-3501	232	18	h.	h.	NOUN
ejpam-3501	232	19	let	let	VERB
ejpam-3501	232	20	x	x	SYM
ejpam-3501	232	21	∈	∈	PROPN
ejpam-3501	232	22	v	v	X
ejpam-3501	232	23	(	(	PUNCT
ejpam-3501	232	24	g	g	PROPN
ejpam-3501	232	25	◦	◦	NOUN
ejpam-3501	232	26	h	h	NOUN
ejpam-3501	232	27	)	)	PUNCT
ejpam-3501	232	28	\	\	PROPN
ejpam-3501	233	1	s	s	PROPN
ejpam-3501	233	2	,	,	PUNCT
ejpam-3501	233	3	and	and	CCONJ
ejpam-3501	233	4	let	let	VERB
ejpam-3501	233	5	v	v	NUM
ejpam-3501	233	6	∈	∈	PROPN
ejpam-3501	233	7	v	v	NOUN
ejpam-3501	233	8	(	(	PUNCT
ejpam-3501	233	9	g	g	NOUN
ejpam-3501	233	10	)	)	PUNCT
ejpam-3501	233	11	such	such	ADJ
ejpam-3501	233	12	that	that	SCONJ
ejpam-3501	233	13	x	x	SYM
ejpam-3501	233	14	∈	∈	NOUN
ejpam-3501	233	15	v	v	X
ejpam-3501	233	16	(	(	PUNCT
ejpam-3501	233	17	hv	hv	PROPN
ejpam-3501	233	18	+	+	PROPN
ejpam-3501	233	19	v	v	NOUN
ejpam-3501	233	20	)	)	PUNCT
ejpam-3501	233	21	.	.	PUNCT
ejpam-3501	234	1	we	we	PRON
ejpam-3501	234	2	consider	consider	VERB
ejpam-3501	234	3	two	two	NUM
ejpam-3501	234	4	cases	case	NOUN
ejpam-3501	234	5	:	:	PUNCT
ejpam-3501	234	6	case	case	NOUN
ejpam-3501	234	7	1	1	NUM
ejpam-3501	234	8	:	:	PUNCT
ejpam-3501	234	9	x	x	PUNCT
ejpam-3501	234	10	=	=	PUNCT
ejpam-3501	234	11	v.	v.	ADP
ejpam-3501	234	12	pick	pick	VERB
ejpam-3501	234	13	any	any	DET
ejpam-3501	234	14	y	y	PROPN
ejpam-3501	234	15	∈	∈	PROPN
ejpam-3501	234	16	sx	sx	PROPN
ejpam-3501	234	17	.	.	PUNCT
ejpam-3501	235	1	since	since	SCONJ
ejpam-3501	235	2	x	x	PROPN
ejpam-3501	235	3	∈	∈	PROPN
ejpam-3501	235	4	v	v	X
ejpam-3501	235	5	(	(	PUNCT
ejpam-3501	235	6	g	g	NOUN
ejpam-3501	235	7	)	)	PUNCT
ejpam-3501	235	8	,	,	PUNCT
ejpam-3501	235	9	(	(	PUNCT
ejpam-3501	235	10	sx	sx	PROPN
ejpam-3501	235	11	\	\	PROPN
ejpam-3501	235	12	{	{	PUNCT
ejpam-3501	235	13	y})∪	y})∪	PROPN
ejpam-3501	235	14	{	{	PUNCT
ejpam-3501	235	15	x	x	NOUN
ejpam-3501	235	16	}	}	PUNCT
ejpam-3501	235	17	is	be	AUX
ejpam-3501	235	18	a	a	DET
ejpam-3501	235	19	dominating	dominating	NOUN
ejpam-3501	235	20	set	set	VERB
ejpam-3501	235	21	in	in	ADP
ejpam-3501	235	22	hx	hx	PROPN
ejpam-3501	235	23	+	+	CCONJ
ejpam-3501	235	24	x.	x.	NOUN
ejpam-3501	235	25	put	put	VERB
ejpam-3501	235	26	s∗	s∗	PROPN
ejpam-3501	235	27	=	=	SYM
ejpam-3501	235	28	(	(	PUNCT
ejpam-3501	235	29	s	s	NOUN
ejpam-3501	235	30	\	\	X
ejpam-3501	235	31	{	{	PUNCT
ejpam-3501	235	32	y	y	NOUN
ejpam-3501	235	33	}	}	PUNCT
ejpam-3501	235	34	)	)	PUNCT
ejpam-3501	235	35	∪	∪	ADP
ejpam-3501	235	36	{	{	PUNCT
ejpam-3501	235	37	x	x	NOUN
ejpam-3501	235	38	}	}	PUNCT
ejpam-3501	235	39	.	.	PUNCT
ejpam-3501	236	1	then	then	ADV
ejpam-3501	236	2	s	s	VERB
ejpam-3501	236	3	∩	∩	ADJ
ejpam-3501	236	4	v	v	NOUN
ejpam-3501	236	5	(	(	PUNCT
ejpam-3501	236	6	hu	hu	PROPN
ejpam-3501	236	7	+	+	CCONJ
ejpam-3501	236	8	u	u	NOUN
ejpam-3501	236	9	)	)	PUNCT
ejpam-3501	236	10	=	=	PUNCT
ejpam-3501	236	11	s∗	s∗	PROPN
ejpam-3501	236	12	∩	∩	X
ejpam-3501	236	13	v	v	X
ejpam-3501	236	14	(	(	PUNCT
ejpam-3501	236	15	hu	hu	PROPN
ejpam-3501	236	16	+	+	CCONJ
ejpam-3501	236	17	u	u	NOUN
ejpam-3501	236	18	)	)	PUNCT
ejpam-3501	236	19	for	for	ADP
ejpam-3501	236	20	all	all	PRON
ejpam-3501	236	21	u	u	PROPN
ejpam-3501	236	22	∈	∈	PROPN
ejpam-3501	236	23	v	v	NOUN
ejpam-3501	236	24	(	(	PUNCT
ejpam-3501	236	25	g	g	NOUN
ejpam-3501	236	26	)	)	PUNCT
ejpam-3501	236	27	\	\	NOUN
ejpam-3501	236	28	{	{	PUNCT
ejpam-3501	236	29	x	x	X
ejpam-3501	236	30	}	}	PUNCT
ejpam-3501	236	31	,	,	PUNCT
ejpam-3501	236	32	and	and	CCONJ
ejpam-3501	236	33	s∗	s∗	PROPN
ejpam-3501	236	34	∩	∩	PROPN
ejpam-3501	236	35	v	v	X
ejpam-3501	236	36	(	(	PUNCT
ejpam-3501	236	37	hx	hx	PROPN
ejpam-3501	236	38	+	+	CCONJ
ejpam-3501	236	39	x	x	X
ejpam-3501	236	40	)	)	PUNCT
ejpam-3501	236	41	=	=	SYM
ejpam-3501	236	42	(	(	PUNCT
ejpam-3501	236	43	sx	sx	PROPN
ejpam-3501	236	44	\	\	PROPN
ejpam-3501	236	45	{	{	PUNCT
ejpam-3501	236	46	y	y	NOUN
ejpam-3501	236	47	}	}	PUNCT
ejpam-3501	236	48	)	)	PUNCT
ejpam-3501	236	49	∪	∪	ADP
ejpam-3501	236	50	{	{	PUNCT
ejpam-3501	236	51	x	x	NOUN
ejpam-3501	236	52	}	}	PUNCT
ejpam-3501	236	53	.	.	PUNCT
ejpam-3501	237	1	thus	thus	ADV
ejpam-3501	237	2	,	,	PUNCT
ejpam-3501	237	3	s∗	s∗	PROPN
ejpam-3501	237	4	satisfies	satisfy	VERB
ejpam-3501	237	5	property	property	NOUN
ejpam-3501	237	6	(	(	PUNCT
ejpam-3501	237	7	i	i	NOUN
ejpam-3501	237	8	)	)	PUNCT
ejpam-3501	237	9	of	of	ADP
ejpam-3501	237	10	proposition	proposition	NOUN
ejpam-3501	237	11	2	2	NUM
ejpam-3501	237	12	.	.	PUNCT
ejpam-3501	237	13	let	let	VERB
ejpam-3501	237	14	u	u	PRON
ejpam-3501	237	15	∈	∈	PROPN
ejpam-3501	237	16	v	v	ADP
ejpam-3501	237	17	(	(	PUNCT
ejpam-3501	237	18	g	g	NOUN
ejpam-3501	237	19	)	)	PUNCT
ejpam-3501	237	20	\	\	PROPN
ejpam-3501	237	21	s∗	s∗	PROPN
ejpam-3501	237	22	with	with	ADP
ejpam-3501	237	23	ng(u	ng(u	NOUN
ejpam-3501	237	24	)	)	PUNCT
ejpam-3501	237	25	∩	∩	NOUN
ejpam-3501	237	26	s∗	s∗	NOUN
ejpam-3501	237	27	=	=	PUNCT
ejpam-3501	237	28	∅.	∅.	NOUN
ejpam-3501	237	29	then	then	ADV
ejpam-3501	237	30	u	u	X
ejpam-3501	237	31	6=	6=	PROPN
ejpam-3501	237	32	x	x	SYM
ejpam-3501	237	33	so	so	SCONJ
ejpam-3501	237	34	that	that	SCONJ
ejpam-3501	237	35	u	u	PROPN
ejpam-3501	237	36	∈	∈	NOUN
ejpam-3501	237	37	v	v	ADP
ejpam-3501	237	38	(	(	PUNCT
ejpam-3501	237	39	g	g	NOUN
ejpam-3501	237	40	)	)	PUNCT
ejpam-3501	237	41	\	\	PROPN
ejpam-3501	237	42	s	s	PROPN
ejpam-3501	237	43	and	and	CCONJ
ejpam-3501	237	44	ng(u)∩s	ng(u)∩s	PROPN
ejpam-3501	237	45	=	=	PUNCT
ejpam-3501	237	46	∅.	∅.	NOUN
ejpam-3501	237	47	since	since	SCONJ
ejpam-3501	237	48	s	s	PRON
ejpam-3501	237	49	is	be	AUX
ejpam-3501	237	50	a	a	DET
ejpam-3501	237	51	semitotal	semitotal	ADJ
ejpam-3501	237	52	dominating	dominating	NOUN
ejpam-3501	237	53	set	set	VERB
ejpam-3501	237	54	in	in	ADP
ejpam-3501	237	55	g	g	ADP
ejpam-3501	237	56	◦	◦	NOUN
ejpam-3501	237	57	h	h	NOUN
ejpam-3501	237	58	,	,	PUNCT
ejpam-3501	237	59	|s∗u|	|s∗u|	PROPN
ejpam-3501	237	60	=	=	PUNCT
ejpam-3501	237	61	|su|	|su|	NOUN
ejpam-3501	237	62	≥	≥	NOUN
ejpam-3501	237	63	2	2	NUM
ejpam-3501	237	64	.	.	PUNCT
ejpam-3501	237	65	since	since	SCONJ
ejpam-3501	237	66	u	u	NOUN
ejpam-3501	237	67	is	be	AUX
ejpam-3501	237	68	arbitrary	arbitrary	ADJ
ejpam-3501	237	69	,	,	PUNCT
ejpam-3501	237	70	property	property	NOUN
ejpam-3501	237	71	(	(	PUNCT
ejpam-3501	237	72	ii	ii	NOUN
ejpam-3501	237	73	)	)	PUNCT
ejpam-3501	237	74	of	of	ADP
ejpam-3501	237	75	proposition	proposition	NOUN
ejpam-3501	237	76	2	2	NUM
ejpam-3501	237	77	holds	hold	VERB
ejpam-3501	237	78	for	for	ADP
ejpam-3501	237	79	s∗.	s∗.	ADJ
ejpam-3501	237	80	thus	thus	ADV
ejpam-3501	237	81	,	,	PUNCT
ejpam-3501	237	82	s∗	s∗	PROPN
ejpam-3501	237	83	is	be	AUX
ejpam-3501	237	84	a	a	DET
ejpam-3501	237	85	semitotal	semitotal	ADJ
ejpam-3501	237	86	dominating	dominating	NOUN
ejpam-3501	237	87	set	set	VERB
ejpam-3501	237	88	in	in	ADP
ejpam-3501	237	89	g	g	PROPN
ejpam-3501	237	90	◦	◦	NOUN
ejpam-3501	237	91	h.	h.	NOUN
ejpam-3501	237	92	case	case	NOUN
ejpam-3501	237	93	2	2	NUM
ejpam-3501	237	94	:	:	PUNCT
ejpam-3501	237	95	x	x	SYM
ejpam-3501	237	96	6=	6=	ADP
ejpam-3501	237	97	v.	v.	ADP
ejpam-3501	237	98	in	in	ADP
ejpam-3501	237	99	this	this	DET
ejpam-3501	237	100	case	case	NOUN
ejpam-3501	237	101	,	,	PUNCT
ejpam-3501	237	102	x	x	SYM
ejpam-3501	237	103	∈	∈	NOUN
ejpam-3501	237	104	v	v	NOUN
ejpam-3501	237	105	(	(	PUNCT
ejpam-3501	237	106	hv)\sv	hv)\sv	PROPN
ejpam-3501	237	107	.	.	PUNCT
ejpam-3501	238	1	first	first	ADV
ejpam-3501	238	2	,	,	PUNCT
ejpam-3501	238	3	suppose	suppose	VERB
ejpam-3501	238	4	that	that	SCONJ
ejpam-3501	238	5	v	v	NOUN
ejpam-3501	238	6	/∈	/∈	PUNCT
ejpam-3501	238	7	s.	s.	PROPN
ejpam-3501	238	8	by	by	ADP
ejpam-3501	238	9	property	property	NOUN
ejpam-3501	238	10	(	(	PUNCT
ejpam-3501	238	11	i	i	NOUN
ejpam-3501	238	12	)	)	PUNCT
ejpam-3501	238	13	,	,	PUNCT
ejpam-3501	238	14	sv	sv	PROPN
ejpam-3501	238	15	is	be	AUX
ejpam-3501	238	16	a	a	DET
ejpam-3501	238	17	secure	secure	ADJ
ejpam-3501	238	18	dominating	dominating	NOUN
ejpam-3501	238	19	set	set	VERB
ejpam-3501	238	20	in	in	ADP
ejpam-3501	238	21	hv	hv	PROPN
ejpam-3501	238	22	.	.	PUNCT
ejpam-3501	239	1	thus	thus	ADV
ejpam-3501	239	2	,	,	PUNCT
ejpam-3501	239	3	there	there	PRON
ejpam-3501	239	4	exists	exist	VERB
ejpam-3501	239	5	y	y	PROPN
ejpam-3501	239	6	∈	∈	PROPN
ejpam-3501	239	7	sv	sv	PROPN
ejpam-3501	239	8	∩	∩	ADJ
ejpam-3501	239	9	nhv(x	nhv(x	PROPN
ejpam-3501	239	10	)	)	PUNCT
ejpam-3501	239	11	for	for	ADP
ejpam-3501	239	12	which	which	PRON
ejpam-3501	239	13	(	(	PUNCT
ejpam-3501	239	14	sv	sv	PROPN
ejpam-3501	239	15	\	\	PROPN
ejpam-3501	239	16	{	{	PUNCT
ejpam-3501	239	17	y	y	NOUN
ejpam-3501	239	18	}	}	PUNCT
ejpam-3501	239	19	)	)	PUNCT
ejpam-3501	239	20	∪	∪	ADP
ejpam-3501	239	21	{	{	PUNCT
ejpam-3501	239	22	x	x	NOUN
ejpam-3501	239	23	}	}	PUNCT
ejpam-3501	239	24	is	be	AUX
ejpam-3501	239	25	a	a	DET
ejpam-3501	239	26	dominating	dominating	NOUN
ejpam-3501	239	27	set	set	VERB
ejpam-3501	239	28	in	in	ADP
ejpam-3501	239	29	hv	hv	PROPN
ejpam-3501	239	30	,	,	PUNCT
ejpam-3501	239	31	and	and	CCONJ
ejpam-3501	239	32	consequently	consequently	ADV
ejpam-3501	239	33	in	in	ADP
ejpam-3501	239	34	hv	hv	PROPN
ejpam-3501	239	35	+	+	NUM
ejpam-3501	239	36	v	v	NOUN
ejpam-3501	239	37	as	as	ADV
ejpam-3501	239	38	well	well	ADV
ejpam-3501	239	39	.	.	PUNCT
ejpam-3501	240	1	put	put	VERB
ejpam-3501	240	2	s∗	s∗	PROPN
ejpam-3501	240	3	=	=	SYM
ejpam-3501	240	4	(	(	PUNCT
ejpam-3501	240	5	s	s	NOUN
ejpam-3501	240	6	\	\	X
ejpam-3501	240	7	{	{	PUNCT
ejpam-3501	240	8	y	y	NOUN
ejpam-3501	240	9	}	}	PUNCT
ejpam-3501	240	10	)	)	PUNCT
ejpam-3501	240	11	∪	∪	ADP
ejpam-3501	240	12	{	{	PUNCT
ejpam-3501	240	13	x	x	NOUN
ejpam-3501	240	14	}	}	PUNCT
ejpam-3501	240	15	.	.	PUNCT
ejpam-3501	241	1	then	then	ADV
ejpam-3501	241	2	s	s	VERB
ejpam-3501	241	3	∩	∩	ADJ
ejpam-3501	241	4	v	v	NOUN
ejpam-3501	241	5	(	(	PUNCT
ejpam-3501	241	6	hu	hu	PROPN
ejpam-3501	241	7	+	+	CCONJ
ejpam-3501	241	8	u	u	NOUN
ejpam-3501	241	9	)	)	PUNCT
ejpam-3501	241	10	=	=	PUNCT
ejpam-3501	241	11	s∗	s∗	PROPN
ejpam-3501	241	12	∩	∩	X
ejpam-3501	241	13	v	v	X
ejpam-3501	241	14	(	(	PUNCT
ejpam-3501	241	15	hu	hu	PROPN
ejpam-3501	241	16	+	+	CCONJ
ejpam-3501	241	17	u	u	NOUN
ejpam-3501	241	18	)	)	PUNCT
ejpam-3501	241	19	for	for	ADP
ejpam-3501	241	20	all	all	PRON
ejpam-3501	241	21	u	u	PROPN
ejpam-3501	241	22	∈	∈	PROPN
ejpam-3501	241	23	v	v	NOUN
ejpam-3501	241	24	(	(	PUNCT
ejpam-3501	241	25	g	g	NOUN
ejpam-3501	241	26	)	)	PUNCT
ejpam-3501	241	27	\	\	NOUN
ejpam-3501	241	28	{	{	PUNCT
ejpam-3501	241	29	v	v	NOUN
ejpam-3501	241	30	}	}	PUNCT
ejpam-3501	241	31	,	,	PUNCT
ejpam-3501	241	32	and	and	CCONJ
ejpam-3501	241	33	s∗	s∗	PROPN
ejpam-3501	241	34	∩	∩	PROPN
ejpam-3501	241	35	v	v	X
ejpam-3501	241	36	(	(	PUNCT
ejpam-3501	241	37	hv	hv	PROPN
ejpam-3501	241	38	+	+	PROPN
ejpam-3501	241	39	v	v	NOUN
ejpam-3501	241	40	)	)	PUNCT
ejpam-3501	241	41	=	=	SYM
ejpam-3501	241	42	(	(	PUNCT
ejpam-3501	241	43	sv	sv	INTJ
ejpam-3501	241	44	\	\	PROPN
ejpam-3501	241	45	{	{	PUNCT
ejpam-3501	241	46	y})∪	y})∪	PROPN
ejpam-3501	241	47	{	{	PUNCT
ejpam-3501	241	48	x	x	NOUN
ejpam-3501	241	49	}	}	PUNCT
ejpam-3501	241	50	.	.	PUNCT
ejpam-3501	242	1	thus	thus	ADV
ejpam-3501	242	2	,	,	PUNCT
ejpam-3501	242	3	s∗	s∗	PROPN
ejpam-3501	242	4	satisfies	satisfy	VERB
ejpam-3501	242	5	property	property	NOUN
ejpam-3501	242	6	(	(	PUNCT
ejpam-3501	242	7	i	i	NOUN
ejpam-3501	242	8	)	)	PUNCT
ejpam-3501	242	9	of	of	ADP
ejpam-3501	242	10	proposition	proposition	NOUN
ejpam-3501	242	11	2	2	NUM
ejpam-3501	242	12	.	.	PUNCT
ejpam-3501	242	13	let	let	VERB
ejpam-3501	242	14	u	u	PRON
ejpam-3501	242	15	∈	∈	PROPN
ejpam-3501	242	16	v	v	ADP
ejpam-3501	242	17	(	(	PUNCT
ejpam-3501	242	18	g	g	NOUN
ejpam-3501	242	19	)	)	PUNCT
ejpam-3501	242	20	\	\	PROPN
ejpam-3501	242	21	s∗	s∗	PROPN
ejpam-3501	242	22	with	with	ADP
ejpam-3501	242	23	ng(u	ng(u	NOUN
ejpam-3501	242	24	)	)	PUNCT
ejpam-3501	242	25	∩	∩	NOUN
ejpam-3501	242	26	s∗	s∗	NOUN
ejpam-3501	242	27	=	=	PUNCT
ejpam-3501	242	28	∅.	∅.	NOUN
ejpam-3501	242	29	since	since	SCONJ
ejpam-3501	242	30	s	s	PRON
ejpam-3501	242	31	and	and	CCONJ
ejpam-3501	242	32	s∗	s∗	PROPN
ejpam-3501	242	33	differ	differ	VERB
ejpam-3501	242	34	only	only	ADV
ejpam-3501	242	35	by	by	ADP
ejpam-3501	242	36	their	their	PRON
ejpam-3501	242	37	respective	respective	ADJ
ejpam-3501	242	38	sv	sv	NOUN
ejpam-3501	242	39	and	and	CCONJ
ejpam-3501	242	40	s∗v	s∗v	NUM
ejpam-3501	242	41	,	,	PUNCT
ejpam-3501	242	42	u	u	NOUN
ejpam-3501	242	43	∈	∈	PROPN
ejpam-3501	242	44	v	v	ADP
ejpam-3501	242	45	(	(	PUNCT
ejpam-3501	242	46	g	g	NOUN
ejpam-3501	242	47	)	)	PUNCT
ejpam-3501	242	48	\	\	PROPN
ejpam-3501	242	49	s	s	PROPN
ejpam-3501	242	50	and	and	CCONJ
ejpam-3501	242	51	ng(u	ng(u	NOUN
ejpam-3501	242	52	)	)	PUNCT
ejpam-3501	242	53	∩	∩	NOUN
ejpam-3501	242	54	s	s	PART
ejpam-3501	242	55	=	=	X
ejpam-3501	242	56	∅.	∅.	VERB
ejpam-3501	242	57	if	if	SCONJ
ejpam-3501	242	58	u	u	PROPN
ejpam-3501	242	59	6=	6=	PROPN
ejpam-3501	242	60	v	v	NOUN
ejpam-3501	242	61	,	,	PUNCT
ejpam-3501	242	62	then	then	ADV
ejpam-3501	242	63	|s∗u|	|s∗u|	PROPN
ejpam-3501	242	64	=	=	PUNCT
ejpam-3501	242	65	|su|	|su|	NOUN
ejpam-3501	242	66	≥	≥	NOUN
ejpam-3501	242	67	2	2	NUM
ejpam-3501	242	68	.	.	PUNCT
ejpam-3501	243	1	if	if	SCONJ
ejpam-3501	243	2	u	u	PROPN
ejpam-3501	243	3	=	=	PROPN
ejpam-3501	243	4	v	v	NOUN
ejpam-3501	243	5	,	,	PUNCT
ejpam-3501	243	6	then	then	ADV
ejpam-3501	243	7	|su	|su	ADP
ejpam-3501	243	8	\	\	X
ejpam-3501	243	9	{	{	PUNCT
ejpam-3501	243	10	y}|	y}|	NOUN
ejpam-3501	243	11	≥	≥	NOUN
ejpam-3501	243	12	1	1	NUM
ejpam-3501	243	13	so	so	SCONJ
ejpam-3501	243	14	that	that	PRON
ejpam-3501	243	15	|s∗u|	|s∗u|	NOUN
ejpam-3501	243	16	=	=	SYM
ejpam-3501	244	1	|	|	NOUN
ejpam-3501	244	2	(	(	PUNCT
ejpam-3501	244	3	su	su	PROPN
ejpam-3501	244	4	\	\	PROPN
ejpam-3501	244	5	{	{	PUNCT
ejpam-3501	244	6	y	y	NOUN
ejpam-3501	244	7	}	}	PUNCT
ejpam-3501	244	8	)	)	PUNCT
ejpam-3501	244	9	∪	∪	ADP
ejpam-3501	244	10	{	{	PUNCT
ejpam-3501	244	11	x}|	x}|	X
ejpam-3501	244	12	≥	≥	NUM
ejpam-3501	244	13	2	2	NUM
ejpam-3501	244	14	.	.	PUNCT
ejpam-3501	245	1	this	this	PRON
ejpam-3501	245	2	shows	show	VERB
ejpam-3501	245	3	that	that	PRON
ejpam-3501	245	4	s∗	s∗	PROPN
ejpam-3501	245	5	satisfies	satisfy	VERB
ejpam-3501	245	6	property	property	NOUN
ejpam-3501	245	7	(	(	PUNCT
ejpam-3501	245	8	ii	ii	NOUN
ejpam-3501	245	9	)	)	PUNCT
ejpam-3501	245	10	of	of	ADP
ejpam-3501	245	11	proposition	proposition	NOUN
ejpam-3501	245	12	2	2	NUM
ejpam-3501	245	13	.	.	PUNCT
ejpam-3501	246	1	thus	thus	ADV
ejpam-3501	246	2	,	,	PUNCT
ejpam-3501	246	3	s∗	s∗	PROPN
ejpam-3501	246	4	is	be	AUX
ejpam-3501	246	5	a	a	DET
ejpam-3501	246	6	semitotal	semitotal	ADJ
ejpam-3501	246	7	dominating	dominating	NOUN
ejpam-3501	246	8	set	set	VERB
ejpam-3501	246	9	in	in	ADP
ejpam-3501	246	10	g	g	PROPN
ejpam-3501	246	11	◦	◦	NOUN
ejpam-3501	246	12	h.	h.	PROPN
ejpam-3501	246	13	next	next	ADV
ejpam-3501	246	14	,	,	PUNCT
ejpam-3501	246	15	suppose	suppose	VERB
ejpam-3501	246	16	that	that	SCONJ
ejpam-3501	246	17	v	v	X
ejpam-3501	246	18	∈	∈	PRON
ejpam-3501	246	19	s.	s.	PROPN
ejpam-3501	246	20	by	by	ADP
ejpam-3501	246	21	property	property	NOUN
ejpam-3501	246	22	(	(	PUNCT
ejpam-3501	246	23	ii	ii	NOUN
ejpam-3501	246	24	)	)	PUNCT
ejpam-3501	246	25	,	,	PUNCT
ejpam-3501	246	26	sv	sv	PROPN
ejpam-3501	246	27	is	be	AUX
ejpam-3501	246	28	a	a	DET
ejpam-3501	246	29	nearly	nearly	ADV
ejpam-3501	246	30	dominating	dominating	NOUN
ejpam-3501	246	31	set	set	NOUN
ejpam-3501	246	32	in	in	ADP
ejpam-3501	246	33	hv	hv	PROPN
ejpam-3501	246	34	.	.	PUNCT
ejpam-3501	246	35	suppose	suppose	VERB
ejpam-3501	246	36	that	that	SCONJ
ejpam-3501	246	37	x	x	SYM
ejpam-3501	246	38	∈	∈	NOUN
ejpam-3501	246	39	nhv	nhv	NOUN
ejpam-3501	247	1	[	[	X
ejpam-3501	247	2	sv	sv	X
ejpam-3501	247	3	]	]	X
ejpam-3501	247	4	,	,	PUNCT
ejpam-3501	247	5	and	and	CCONJ
ejpam-3501	247	6	y	y	PROPN
ejpam-3501	247	7	∈	∈	PROPN
ejpam-3501	247	8	sv	sv	INTJ
ejpam-3501	247	9	for	for	ADP
ejpam-3501	247	10	which	which	PRON
ejpam-3501	247	11	xy	xy	PROPN
ejpam-3501	247	12	∈	∈	PROPN
ejpam-3501	247	13	e(hv	e(hv	PROPN
ejpam-3501	247	14	)	)	PUNCT
ejpam-3501	247	15	.	.	PUNCT
ejpam-3501	248	1	put	put	VERB
ejpam-3501	248	2	s∗	s∗	PROPN
ejpam-3501	248	3	=	=	SYM
ejpam-3501	248	4	(	(	PUNCT
ejpam-3501	248	5	s	s	NOUN
ejpam-3501	248	6	\	\	X
ejpam-3501	248	7	{	{	PUNCT
ejpam-3501	248	8	y	y	NOUN
ejpam-3501	248	9	}	}	PUNCT
ejpam-3501	248	10	)	)	PUNCT
ejpam-3501	248	11	∪	∪	ADP
ejpam-3501	248	12	{	{	PUNCT
ejpam-3501	248	13	x	x	NOUN
ejpam-3501	248	14	}	}	PUNCT
ejpam-3501	248	15	.	.	PUNCT
ejpam-3501	249	1	since	since	SCONJ
ejpam-3501	249	2	v	v	NUM
ejpam-3501	249	3	∈	∈	PROPN
ejpam-3501	249	4	s∗	s∗	PROPN
ejpam-3501	249	5	∩	∩	X
ejpam-3501	249	6	v	v	X
ejpam-3501	249	7	(	(	PUNCT
ejpam-3501	249	8	hv	hv	PROPN
ejpam-3501	249	9	+	+	PROPN
ejpam-3501	249	10	v	v	NOUN
ejpam-3501	249	11	)	)	PUNCT
ejpam-3501	249	12	,	,	PUNCT
ejpam-3501	249	13	s∗	s∗	PROPN
ejpam-3501	249	14	∩	∩	PROPN
ejpam-3501	249	15	v	v	X
ejpam-3501	249	16	(	(	PUNCT
ejpam-3501	249	17	hv	hv	PROPN
ejpam-3501	249	18	+	+	PROPN
ejpam-3501	249	19	v	v	NOUN
ejpam-3501	249	20	)	)	PUNCT
ejpam-3501	249	21	is	be	AUX
ejpam-3501	249	22	a	a	DET
ejpam-3501	249	23	dominating	dominating	NOUN
ejpam-3501	249	24	set	set	VERB
ejpam-3501	249	25	in	in	ADP
ejpam-3501	249	26	hv	hv	PROPN
ejpam-3501	249	27	+	+	PROPN
ejpam-3501	249	28	v	v	NOUN
ejpam-3501	249	29	,	,	PUNCT
ejpam-3501	249	30	and	and	CCONJ
ejpam-3501	249	31	s∗	s∗	PROPN
ejpam-3501	249	32	satisfies	satisfy	VERB
ejpam-3501	249	33	property	property	NOUN
ejpam-3501	249	34	(	(	PUNCT
ejpam-3501	249	35	i	i	NOUN
ejpam-3501	249	36	)	)	PUNCT
ejpam-3501	249	37	of	of	ADP
ejpam-3501	249	38	proposition	proposition	NOUN
ejpam-3501	249	39	2	2	NUM
ejpam-3501	249	40	.	.	PUNCT
ejpam-3501	250	1	let	let	VERB
ejpam-3501	250	2	u	u	PRON
ejpam-3501	250	3	∈	∈	PROPN
ejpam-3501	250	4	v	v	ADP
ejpam-3501	250	5	(	(	PUNCT
ejpam-3501	250	6	g	g	NOUN
ejpam-3501	250	7	)	)	PUNCT
ejpam-3501	250	8	\	\	PROPN
ejpam-3501	250	9	s∗	s∗	PROPN
ejpam-3501	250	10	with	with	ADP
ejpam-3501	250	11	ng(u	ng(u	NOUN
ejpam-3501	250	12	)	)	PUNCT
ejpam-3501	250	13	∩	∩	NOUN
ejpam-3501	250	14	s∗	s∗	PROPN
ejpam-3501	250	15	=	=	SYM
ejpam-3501	250	16	∅.	∅.	NOUN
ejpam-3501	250	17	note	note	NOUN
ejpam-3501	250	18	also	also	ADV
ejpam-3501	250	19	in	in	ADP
ejpam-3501	250	20	here	here	ADV
ejpam-3501	250	21	that	that	PRON
ejpam-3501	250	22	s∗	s∗	VERB
ejpam-3501	250	23	and	and	CCONJ
ejpam-3501	250	24	s	s	PRON
ejpam-3501	250	25	differ	differ	VERB
ejpam-3501	250	26	only	only	ADV
ejpam-3501	250	27	by	by	ADP
ejpam-3501	250	28	their	their	PRON
ejpam-3501	250	29	respective	respective	ADJ
ejpam-3501	250	30	s∗v	s∗v	NOUN
ejpam-3501	250	31	and	and	CCONJ
ejpam-3501	250	32	sv	sv	NOUN
ejpam-3501	250	33	.	.	PUNCT
ejpam-3501	251	1	thus	thus	ADV
ejpam-3501	251	2	u	u	X
ejpam-3501	251	3	∈	∈	PROPN
ejpam-3501	251	4	v	v	ADP
ejpam-3501	251	5	(	(	PUNCT
ejpam-3501	251	6	g	g	NOUN
ejpam-3501	251	7	)	)	PUNCT
ejpam-3501	251	8	\	\	PROPN
ejpam-3501	252	1	s	s	PART
ejpam-3501	252	2	i.	i.	PROPN
ejpam-3501	252	3	s.	s.	PROPN
ejpam-3501	252	4	aniversario	aniversario	PROPN
ejpam-3501	252	5	,	,	PUNCT
ejpam-3501	252	6	s.	s.	PROPN
ejpam-3501	252	7	r.	r.	PROPN
ejpam-3501	252	8	jr	jr	PROPN
ejpam-3501	252	9	.	.	PROPN
ejpam-3501	252	10	canoy	canoy	PROPN
ejpam-3501	252	11	,	,	PUNCT
ejpam-3501	252	12	f.p	f.p	PROPN
ejpam-3501	252	13	.	.	PROPN
ejpam-3501	252	14	jamil	jamil	PROPN
ejpam-3501	252	15	/	/	SYM
ejpam-3501	252	16	eur	eur	PROPN
ejpam-3501	252	17	.	.	PUNCT
ejpam-3501	253	1	j.	j.	PROPN
ejpam-3501	253	2	pure	pure	PROPN
ejpam-3501	253	3	appl	appl	PROPN
ejpam-3501	253	4	.	.	PROPN
ejpam-3501	253	5	math	math	PROPN
ejpam-3501	253	6	,	,	PUNCT
ejpam-3501	253	7	12	12	NUM
ejpam-3501	253	8	(	(	PUNCT
ejpam-3501	253	9	4	4	NUM
ejpam-3501	253	10	)	)	PUNCT
ejpam-3501	253	11	(	(	PUNCT
ejpam-3501	253	12	2019	2019	NUM
ejpam-3501	253	13	)	)	PUNCT
ejpam-3501	253	14	,	,	PUNCT
ejpam-3501	253	15	1410	1410	NUM
ejpam-3501	253	16	-	-	SYM
ejpam-3501	253	17	1425	1425	NUM
ejpam-3501	253	18	1418	1418	NUM
ejpam-3501	253	19	and	and	CCONJ
ejpam-3501	253	20	ng(u	ng(u	NOUN
ejpam-3501	253	21	)	)	PUNCT
ejpam-3501	253	22	∩	∩	NOUN
ejpam-3501	253	23	s	s	PART
ejpam-3501	253	24	=	=	X
ejpam-3501	253	25	∅.	∅.	NOUN
ejpam-3501	253	26	since	since	SCONJ
ejpam-3501	253	27	u	u	PROPN
ejpam-3501	253	28	6=	6=	PROPN
ejpam-3501	253	29	v	v	NOUN
ejpam-3501	253	30	,	,	PUNCT
ejpam-3501	253	31	|s∗u|	|s∗u|	PROPN
ejpam-3501	253	32	=	=	PUNCT
ejpam-3501	253	33	|su|	|su|	NOUN
ejpam-3501	253	34	≥	≥	NOUN
ejpam-3501	253	35	2	2	NUM
ejpam-3501	253	36	,	,	PUNCT
ejpam-3501	253	37	and	and	CCONJ
ejpam-3501	253	38	s∗	s∗	PROPN
ejpam-3501	253	39	satisfies	satisfy	VERB
ejpam-3501	253	40	property	property	NOUN
ejpam-3501	253	41	(	(	PUNCT
ejpam-3501	253	42	ii	ii	NOUN
ejpam-3501	253	43	)	)	PUNCT
ejpam-3501	253	44	of	of	ADP
ejpam-3501	253	45	proposition	proposition	NOUN
ejpam-3501	253	46	2	2	NUM
ejpam-3501	253	47	.	.	PUNCT
ejpam-3501	253	48	accordingly	accordingly	ADV
ejpam-3501	253	49	,	,	PUNCT
ejpam-3501	253	50	s∗	s∗	PROPN
ejpam-3501	253	51	is	be	AUX
ejpam-3501	253	52	a	a	DET
ejpam-3501	253	53	semitotal	semitotal	ADJ
ejpam-3501	253	54	dominating	dominating	NOUN
ejpam-3501	253	55	set	set	VERB
ejpam-3501	253	56	in	in	ADP
ejpam-3501	253	57	g	g	PROPN
ejpam-3501	253	58	◦	◦	NOUN
ejpam-3501	253	59	h.	h.	PROPN
ejpam-3501	253	60	finally	finally	ADV
ejpam-3501	253	61	,	,	PUNCT
ejpam-3501	253	62	suppose	suppose	VERB
ejpam-3501	253	63	that	that	SCONJ
ejpam-3501	253	64	x	x	X
ejpam-3501	253	65	/∈	/∈	PUNCT
ejpam-3501	254	1	nhv	nhv	PROPN
ejpam-3501	255	1	[	[	X
ejpam-3501	255	2	sv	sv	X
ejpam-3501	255	3	]	]	X
ejpam-3501	255	4	.	.	PUNCT
ejpam-3501	256	1	put	put	VERB
ejpam-3501	256	2	s∗	s∗	PROPN
ejpam-3501	256	3	=	=	SYM
ejpam-3501	256	4	(	(	PUNCT
ejpam-3501	256	5	s	s	NOUN
ejpam-3501	256	6	\	\	X
ejpam-3501	256	7	{	{	PUNCT
ejpam-3501	256	8	v})∪{x	v})∪{x	NOUN
ejpam-3501	256	9	}	}	PUNCT
ejpam-3501	256	10	.	.	PUNCT
ejpam-3501	257	1	note	note	VERB
ejpam-3501	257	2	in	in	ADV
ejpam-3501	257	3	here	here	ADV
ejpam-3501	257	4	that	that	SCONJ
ejpam-3501	257	5	s∗∩v	s∗∩v	ADJ
ejpam-3501	257	6	(	(	PUNCT
ejpam-3501	257	7	hv+v	hv+v	PROPN
ejpam-3501	257	8	)	)	PUNCT
ejpam-3501	257	9	=	=	SYM
ejpam-3501	257	10	sv∪{x	sv∪{x	NOUN
ejpam-3501	257	11	}	}	PUNCT
ejpam-3501	257	12	,	,	PUNCT
ejpam-3501	257	13	which	which	PRON
ejpam-3501	257	14	is	be	AUX
ejpam-3501	257	15	a	a	DET
ejpam-3501	257	16	dominating	dominating	NOUN
ejpam-3501	257	17	set	set	VERB
ejpam-3501	257	18	in	in	ADP
ejpam-3501	257	19	hv	hv	PROPN
ejpam-3501	257	20	because	because	SCONJ
ejpam-3501	257	21	sv	sv	PROPN
ejpam-3501	257	22	is	be	AUX
ejpam-3501	257	23	a	a	DET
ejpam-3501	257	24	nearly	nearly	ADV
ejpam-3501	257	25	dominating	dominating	NOUN
ejpam-3501	257	26	set	set	NOUN
ejpam-3501	257	27	in	in	ADP
ejpam-3501	257	28	hv	hv	PROPN
ejpam-3501	257	29	.	.	PUNCT
ejpam-3501	258	1	as	as	SCONJ
ejpam-3501	258	2	argued	argue	VERB
ejpam-3501	258	3	previously	previously	ADV
ejpam-3501	258	4	,	,	PUNCT
ejpam-3501	258	5	s∗	s∗	PROPN
ejpam-3501	258	6	satisfies	satisfy	VERB
ejpam-3501	258	7	property	property	NOUN
ejpam-3501	258	8	(	(	PUNCT
ejpam-3501	258	9	i	i	NOUN
ejpam-3501	258	10	)	)	PUNCT
ejpam-3501	258	11	of	of	ADP
ejpam-3501	258	12	proposition	proposition	NOUN
ejpam-3501	258	13	2	2	NUM
ejpam-3501	258	14	.	.	PUNCT
ejpam-3501	258	15	by	by	ADP
ejpam-3501	258	16	lemma	lemma	PROPN
ejpam-3501	258	17	1	1	NUM
ejpam-3501	258	18	,	,	PUNCT
ejpam-3501	258	19	s∗	s∗	PROPN
ejpam-3501	258	20	is	be	AUX
ejpam-3501	258	21	a	a	DET
ejpam-3501	258	22	dominating	dominating	NOUN
ejpam-3501	258	23	set	set	VERB
ejpam-3501	258	24	in	in	ADP
ejpam-3501	258	25	g	g	PROPN
ejpam-3501	258	26	◦	◦	PROPN
ejpam-3501	258	27	h.	h.	PROPN
ejpam-3501	258	28	since	since	SCONJ
ejpam-3501	258	29	hv	hv	PROPN
ejpam-3501	258	30	is	be	AUX
ejpam-3501	258	31	a	a	DET
ejpam-3501	258	32	noncomplete	noncomplete	ADJ
ejpam-3501	258	33	graph	graph	NOUN
ejpam-3501	258	34	and	and	CCONJ
ejpam-3501	258	35	sv	sv	PROPN
ejpam-3501	258	36	is	be	AUX
ejpam-3501	258	37	a	a	DET
ejpam-3501	258	38	nearly	nearly	ADV
ejpam-3501	258	39	dominating	dominating	NOUN
ejpam-3501	258	40	set	set	NOUN
ejpam-3501	258	41	in	in	ADP
ejpam-3501	258	42	hv	hv	PROPN
ejpam-3501	258	43	,	,	PUNCT
ejpam-3501	258	44	sv	sv	PROPN
ejpam-3501	258	45	6=	6=	PROPN
ejpam-3501	258	46	∅.	∅.	NOUN
ejpam-3501	258	47	clearly	clearly	ADV
ejpam-3501	258	48	,	,	PUNCT
ejpam-3501	258	49	dg	dg	PROPN
ejpam-3501	258	50	◦	◦	NOUN
ejpam-3501	258	51	h(x	h(x	PROPN
ejpam-3501	258	52	,	,	PUNCT
ejpam-3501	258	53	y	y	PROPN
ejpam-3501	258	54	)	)	PUNCT
ejpam-3501	258	55	≤	≤	NUM
ejpam-3501	258	56	2	2	NUM
ejpam-3501	258	57	for	for	ADP
ejpam-3501	258	58	all	all	DET
ejpam-3501	258	59	y	y	PROPN
ejpam-3501	258	60	∈	∈	PROPN
ejpam-3501	258	61	s∗v	s∗v	NUM
ejpam-3501	258	62	\	\	NOUN
ejpam-3501	258	63	{	{	PUNCT
ejpam-3501	258	64	x$.supposethatthereexistsz∈	x$.supposethatthereexistsz∈	NUM
ejpam-3501	258	65	s∗	s∗	PROPN
ejpam-3501	258	66	such	such	ADJ
ejpam-3501	258	67	that	that	SCONJ
ejpam-3501	258	68	dg	dg	AUX
ejpam-3501	258	69	◦	◦	NOUN
ejpam-3501	258	70	h(z	h(z	NOUN
ejpam-3501	258	71	,	,	PUNCT
ejpam-3501	258	72	y	y	NOUN
ejpam-3501	258	73	)	)	PUNCT
ejpam-3501	258	74	>	>	X
ejpam-3501	258	75	2	2	NUM
ejpam-3501	258	76	for	for	ADP
ejpam-3501	258	77	all	all	DET
ejpam-3501	258	78	y	y	PROPN
ejpam-3501	258	79	∈	∈	PROPN
ejpam-3501	258	80	s∗	s∗	PROPN
ejpam-3501	258	81	\	\	X
ejpam-3501	258	82	{	{	PUNCT
ejpam-3501	258	83	z	z	NOUN
ejpam-3501	258	84	}	}	PUNCT
ejpam-3501	258	85	.	.	PUNCT
ejpam-3501	259	1	in	in	ADP
ejpam-3501	259	2	view	view	NOUN
ejpam-3501	259	3	of	of	ADP
ejpam-3501	259	4	the	the	DET
ejpam-3501	259	5	preceding	precede	VERB
ejpam-3501	259	6	arguments	argument	NOUN
ejpam-3501	259	7	,	,	PUNCT
ejpam-3501	259	8	z	z	PROPN
ejpam-3501	259	9	∈	∈	PROPN
ejpam-3501	259	10	s	s	PART
ejpam-3501	259	11	\	\	PROPN
ejpam-3501	259	12	v	v	NOUN
ejpam-3501	259	13	(	(	PUNCT
ejpam-3501	259	14	hv	hv	PROPN
ejpam-3501	259	15	+	+	PROPN
ejpam-3501	259	16	v	v	NOUN
ejpam-3501	259	17	)	)	PUNCT
ejpam-3501	259	18	.	.	PUNCT
ejpam-3501	259	19	suppose	suppose	VERB
ejpam-3501	259	20	that	that	SCONJ
ejpam-3501	259	21	z	z	PROPN
ejpam-3501	259	22	∈	∈	PROPN
ejpam-3501	259	23	v	v	ADP
ejpam-3501	259	24	(	(	PUNCT
ejpam-3501	259	25	g	g	NOUN
ejpam-3501	259	26	)	)	PUNCT
ejpam-3501	259	27	.	.	PUNCT
ejpam-3501	260	1	by	by	ADP
ejpam-3501	260	2	property	property	NOUN
ejpam-3501	260	3	(	(	PUNCT
ejpam-3501	260	4	ii	ii	NOUN
ejpam-3501	260	5	)	)	PUNCT
ejpam-3501	260	6	,	,	PUNCT
ejpam-3501	260	7	sz	sz	PROPN
ejpam-3501	260	8	is	be	AUX
ejpam-3501	260	9	nearly	nearly	ADV
ejpam-3501	260	10	dominating	dominate	VERB
ejpam-3501	260	11	in	in	ADP
ejpam-3501	260	12	hz	hz	PROPN
ejpam-3501	260	13	.	.	PUNCT
ejpam-3501	261	1	but	but	CCONJ
ejpam-3501	261	2	by	by	ADP
ejpam-3501	261	3	the	the	DET
ejpam-3501	261	4	definition	definition	NOUN
ejpam-3501	261	5	of	of	ADP
ejpam-3501	261	6	z	z	PROPN
ejpam-3501	261	7	,	,	PUNCT
ejpam-3501	261	8	sz	sz	NOUN
ejpam-3501	261	9	=	=	SYM
ejpam-3501	261	10	∅	∅	NOUN
ejpam-3501	261	11	,	,	PUNCT
ejpam-3501	261	12	which	which	PRON
ejpam-3501	261	13	is	be	AUX
ejpam-3501	261	14	impossible	impossible	ADJ
ejpam-3501	261	15	.	.	PUNCT
ejpam-3501	262	1	suppose	suppose	VERB
ejpam-3501	262	2	that	that	SCONJ
ejpam-3501	262	3	z	z	PROPN
ejpam-3501	262	4	∈	∈	PROPN
ejpam-3501	262	5	v	v	ADP
ejpam-3501	262	6	(	(	PUNCT
ejpam-3501	262	7	hw	hw	NOUN
ejpam-3501	262	8	)	)	PUNCT
ejpam-3501	262	9	for	for	ADP
ejpam-3501	262	10	some	some	DET
ejpam-3501	262	11	w	w	PROPN
ejpam-3501	262	12	∈	∈	PROPN
ejpam-3501	262	13	v	v	ADP
ejpam-3501	262	14	(	(	PUNCT
ejpam-3501	262	15	g	g	NOUN
ejpam-3501	262	16	)	)	PUNCT
ejpam-3501	262	17	.	.	PUNCT
ejpam-3501	263	1	then	then	ADV
ejpam-3501	263	2	w	w	PROPN
ejpam-3501	263	3	/∈	/∈	PUNCT
ejpam-3501	263	4	s.	s.	PROPN
ejpam-3501	263	5	by	by	ADP
ejpam-3501	263	6	property	property	NOUN
ejpam-3501	263	7	(	(	PUNCT
ejpam-3501	263	8	i	i	NOUN
ejpam-3501	263	9	)	)	PUNCT
ejpam-3501	263	10	,	,	PUNCT
ejpam-3501	263	11	s	s	VERB
ejpam-3501	263	12	∩	∩	ADJ
ejpam-3501	263	13	v	v	X
ejpam-3501	263	14	(	(	PUNCT
ejpam-3501	263	15	hw	hw	NOUN
ejpam-3501	263	16	)	)	PUNCT
ejpam-3501	263	17	is	be	AUX
ejpam-3501	263	18	a	a	DET
ejpam-3501	263	19	secure	secure	ADJ
ejpam-3501	263	20	dominating	dominating	NOUN
ejpam-3501	263	21	set	set	NOUN
ejpam-3501	263	22	.	.	PUNCT
ejpam-3501	264	1	since	since	SCONJ
ejpam-3501	264	2	h	h	NOUN
ejpam-3501	264	3	is	be	AUX
ejpam-3501	264	4	a	a	DET
ejpam-3501	264	5	noncomplete	noncomplete	ADJ
ejpam-3501	264	6	graph	graph	NOUN
ejpam-3501	264	7	,	,	PUNCT
ejpam-3501	264	8	|s	|s	PROPN
ejpam-3501	264	9	∩	∩	ADJ
ejpam-3501	264	10	v	v	X
ejpam-3501	264	11	(	(	PUNCT
ejpam-3501	264	12	hw)|	hw)|	ADJ
ejpam-3501	264	13	≥	≥	NOUN
ejpam-3501	264	14	2	2	NUM
ejpam-3501	264	15	,	,	PUNCT
ejpam-3501	264	16	which	which	PRON
ejpam-3501	264	17	is	be	AUX
ejpam-3501	264	18	impossible	impossible	ADJ
ejpam-3501	264	19	.	.	PUNCT
ejpam-3501	265	1	this	this	PRON
ejpam-3501	265	2	shows	show	VERB
ejpam-3501	265	3	that	that	SCONJ
ejpam-3501	265	4	s∗	s∗	PROPN
ejpam-3501	265	5	is	be	AUX
ejpam-3501	265	6	a	a	DET
ejpam-3501	265	7	semitotal	semitotal	ADJ
ejpam-3501	265	8	dominating	dominating	NOUN
ejpam-3501	265	9	set	set	VERB
ejpam-3501	265	10	in	in	ADP
ejpam-3501	265	11	g	g	PROPN
ejpam-3501	265	12	◦	◦	NOUN
ejpam-3501	265	13	h.	h.	PROPN
ejpam-3501	265	14	therefore	therefore	ADV
ejpam-3501	265	15	,	,	PUNCT
ejpam-3501	265	16	s	s	VERB
ejpam-3501	265	17	is	be	AUX
ejpam-3501	265	18	a	a	DET
ejpam-3501	265	19	secure	secure	ADJ
ejpam-3501	265	20	semitotal	semitotal	ADJ
ejpam-3501	265	21	dominating	dominating	NOUN
ejpam-3501	265	22	set	set	NOUN
ejpam-3501	265	23	.	.	PUNCT
ejpam-3501	266	1	corollary	corollary	ADJ
ejpam-3501	266	2	6	6	NUM
ejpam-3501	266	3	.	.	PUNCT
ejpam-3501	267	1	let	let	VERB
ejpam-3501	267	2	g	g	PRON
ejpam-3501	267	3	be	be	AUX
ejpam-3501	267	4	a	a	DET
ejpam-3501	267	5	nontrivial	nontrivial	ADJ
ejpam-3501	267	6	connected	connect	VERB
ejpam-3501	267	7	graph	graph	NOUN
ejpam-3501	267	8	and	and	CCONJ
ejpam-3501	267	9	h	h	NOUN
ejpam-3501	267	10	be	be	AUX
ejpam-3501	267	11	any	any	DET
ejpam-3501	267	12	noncomplete	noncomplete	ADJ
ejpam-3501	267	13	graph	graph	NOUN
ejpam-3501	267	14	without	without	ADP
ejpam-3501	267	15	isolated	isolated	ADJ
ejpam-3501	267	16	vertices	vertex	NOUN
ejpam-3501	267	17	,	,	PUNCT
ejpam-3501	267	18	and	and	CCONJ
ejpam-3501	267	19	let	let	VERB
ejpam-3501	267	20	s	s	PRON
ejpam-3501	267	21	⊆	⊆	NUM
ejpam-3501	267	22	v	v	NOUN
ejpam-3501	267	23	(	(	PUNCT
ejpam-3501	267	24	g	g	PROPN
ejpam-3501	267	25	◦	◦	NOUN
ejpam-3501	267	26	h	h	NOUN
ejpam-3501	267	27	)	)	PUNCT
ejpam-3501	267	28	.	.	PUNCT
ejpam-3501	268	1	then	then	ADV
ejpam-3501	268	2	s	s	VERB
ejpam-3501	268	3	is	be	AUX
ejpam-3501	268	4	a	a	DET
ejpam-3501	268	5	secure	secure	ADJ
ejpam-3501	268	6	semitotal	semitotal	ADJ
ejpam-3501	268	7	dominating	dominating	NOUN
ejpam-3501	268	8	set	set	NOUN
ejpam-3501	268	9	if	if	SCONJ
ejpam-3501	268	10	and	and	CCONJ
ejpam-3501	268	11	only	only	ADV
ejpam-3501	268	12	if	if	SCONJ
ejpam-3501	268	13	s	s	VERB
ejpam-3501	268	14	=	=	NOUN
ejpam-3501	268	15	a	a	DET
ejpam-3501	268	16	∪	∪	NOUN
ejpam-3501	268	17	[	[	X
ejpam-3501	268	18	∪v∈asv	∪v∈asv	NOUN
ejpam-3501	268	19	]	]	PUNCT
ejpam-3501	268	20	∪	∪	ADP
ejpam-3501	268	21	[	[	X
ejpam-3501	268	22	∪u∈v	∪u∈v	X
ejpam-3501	268	23	(	(	PUNCT
ejpam-3501	268	24	g)\adu	g)\adu	PROPN
ejpam-3501	268	25	]	]	PUNCT
ejpam-3501	268	26	,	,	PUNCT
ejpam-3501	268	27	satisfying	satisfy	VERB
ejpam-3501	268	28	the	the	DET
ejpam-3501	268	29	following	follow	VERB
ejpam-3501	268	30	properties	property	NOUN
ejpam-3501	268	31	:	:	PUNCT
ejpam-3501	268	32	(	(	PUNCT
ejpam-3501	268	33	i	i	NOUN
ejpam-3501	268	34	)	)	PUNCT
ejpam-3501	268	35	a	a	DET
ejpam-3501	268	36	⊆	⊆	NUM
ejpam-3501	268	37	v	v	NOUN
ejpam-3501	268	38	(	(	PUNCT
ejpam-3501	268	39	g	g	NOUN
ejpam-3501	268	40	)	)	PUNCT
ejpam-3501	268	41	;	;	PUNCT
ejpam-3501	268	42	(	(	PUNCT
ejpam-3501	268	43	ii	ii	NOUN
ejpam-3501	268	44	)	)	PUNCT
ejpam-3501	268	45	sv	sv	PROPN
ejpam-3501	268	46	is	be	AUX
ejpam-3501	268	47	a	a	DET
ejpam-3501	268	48	nearly	nearly	ADV
ejpam-3501	268	49	dominating	dominating	NOUN
ejpam-3501	268	50	set	set	VERB
ejpam-3501	268	51	in	in	ADP
ejpam-3501	268	52	hv	hv	PROPN
ejpam-3501	268	53	for	for	ADP
ejpam-3501	268	54	each	each	DET
ejpam-3501	268	55	v	v	ADP
ejpam-3501	268	56	∈	∈	PROPN
ejpam-3501	268	57	a	a	PRON
ejpam-3501	268	58	;	;	PUNCT
ejpam-3501	268	59	(	(	PUNCT
ejpam-3501	268	60	iii	iii	X
ejpam-3501	268	61	du	du	NOUN
ejpam-3501	268	62	is	be	AUX
ejpam-3501	268	63	a	a	DET
ejpam-3501	268	64	secure	secure	ADJ
ejpam-3501	268	65	dominating	dominating	NOUN
ejpam-3501	268	66	set	set	VERB
ejpam-3501	268	67	in	in	ADP
ejpam-3501	268	68	hv	hv	PROPN
ejpam-3501	268	69	for	for	ADP
ejpam-3501	268	70	each	each	DET
ejpam-3501	268	71	u	u	PROPN
ejpam-3501	268	72	∈	∈	PROPN
ejpam-3501	268	73	v	v	ADP
ejpam-3501	268	74	(	(	PUNCT
ejpam-3501	268	75	g	g	NOUN
ejpam-3501	268	76	)	)	PUNCT
ejpam-3501	268	77	\a	\a	NUM
ejpam-3501	268	78	;	;	PUNCT
ejpam-3501	268	79	and	and	CCONJ
ejpam-3501	268	80	(	(	PUNCT
ejpam-3501	268	81	iv	iv	X
ejpam-3501	268	82	)	)	PUNCT
ejpam-3501	268	83	|du|	|du|	NOUN
ejpam-3501	268	84	≥	≥	NOUN
ejpam-3501	268	85	2	2	NUM
ejpam-3501	268	86	for	for	ADP
ejpam-3501	268	87	each	each	DET
ejpam-3501	268	88	u	u	PROPN
ejpam-3501	268	89	∈	∈	PROPN
ejpam-3501	268	90	v	v	ADP
ejpam-3501	268	91	(	(	PUNCT
ejpam-3501	268	92	g	g	NOUN
ejpam-3501	268	93	)	)	PUNCT
ejpam-3501	268	94	\a	\a	VERB
ejpam-3501	268	95	with	with	ADP
ejpam-3501	268	96	ng(u	ng(u	NOUN
ejpam-3501	268	97	)	)	PUNCT
ejpam-3501	268	98	∩a	∩a	NOUN
ejpam-3501	268	99	=	=	PUNCT
ejpam-3501	268	100	∅.	∅.	AUX
ejpam-3501	268	101	corollary	corollary	ADJ
ejpam-3501	268	102	7	7	NUM
ejpam-3501	268	103	.	.	PUNCT
ejpam-3501	269	1	let	let	VERB
ejpam-3501	269	2	g	g	PRON
ejpam-3501	269	3	be	be	AUX
ejpam-3501	269	4	a	a	DET
ejpam-3501	269	5	nontrivial	nontrivial	ADJ
ejpam-3501	269	6	connected	connect	VERB
ejpam-3501	269	7	graph	graph	NOUN
ejpam-3501	269	8	and	and	CCONJ
ejpam-3501	269	9	h	h	NOUN
ejpam-3501	269	10	be	be	AUX
ejpam-3501	269	11	any	any	DET
ejpam-3501	269	12	noncomplete	noncomplete	ADJ
ejpam-3501	269	13	graph	graph	NOUN
ejpam-3501	269	14	without	without	ADP
ejpam-3501	269	15	isolated	isolated	ADJ
ejpam-3501	269	16	vertices	vertex	NOUN
ejpam-3501	269	17	.	.	PUNCT
ejpam-3501	270	1	(	(	PUNCT
ejpam-3501	270	2	i	i	NOUN
ejpam-3501	270	3	)	)	PUNCT
ejpam-3501	270	4	if	if	SCONJ
ejpam-3501	270	5	γη(h	γη(h	PUNCT
ejpam-3501	270	6	)	)	PUNCT
ejpam-3501	270	7	=	=	SYM
ejpam-3501	270	8	γs(h	γs(h	NOUN
ejpam-3501	270	9	)	)	PUNCT
ejpam-3501	270	10	,	,	PUNCT
ejpam-3501	270	11	then	then	ADV
ejpam-3501	270	12	γst2(g	γst2(g	NUM
ejpam-3501	270	13	◦	◦	NOUN
ejpam-3501	270	14	h	h	NOUN
ejpam-3501	270	15	)	)	PUNCT
ejpam-3501	270	16	=	=	SYM
ejpam-3501	270	17	|v	|v	PROPN
ejpam-3501	270	18	(	(	PUNCT
ejpam-3501	270	19	g)|γη(h	g)|γη(h	PROPN
ejpam-3501	270	20	)	)	PUNCT
ejpam-3501	270	21	.	.	PUNCT
ejpam-3501	271	1	(	(	PUNCT
ejpam-3501	271	2	ii	ii	NOUN
ejpam-3501	271	3	)	)	PUNCT
ejpam-3501	271	4	if	if	SCONJ
ejpam-3501	271	5	γη(h	γη(h	PUNCT
ejpam-3501	271	6	)	)	PUNCT
ejpam-3501	271	7	<	<	X
ejpam-3501	271	8	γs(h	γs(h	PROPN
ejpam-3501	271	9	)	)	PUNCT
ejpam-3501	271	10	,	,	PUNCT
ejpam-3501	271	11	then	then	ADV
ejpam-3501	271	12	γst2(g	γst2(g	NUM
ejpam-3501	271	13	◦	◦	NOUN
ejpam-3501	271	14	h	h	NOUN
ejpam-3501	271	15	)	)	PUNCT
ejpam-3501	271	16	=	=	SYM
ejpam-3501	271	17	|v	|v	PROPN
ejpam-3501	271	18	(	(	PUNCT
ejpam-3501	271	19	g)|	g)|	X
ejpam-3501	271	20	(	(	PUNCT
ejpam-3501	271	21	1	1	NUM
ejpam-3501	271	22	+	+	CCONJ
ejpam-3501	271	23	γη(h	γη(h	NOUN
ejpam-3501	271	24	)	)	PUNCT
ejpam-3501	271	25	)	)	PUNCT
ejpam-3501	271	26	.	.	PUNCT
ejpam-3501	272	1	5	5	X
ejpam-3501	272	2	.	.	X
ejpam-3501	272	3	in	in	ADP
ejpam-3501	272	4	the	the	DET
ejpam-3501	272	5	lexicographic	lexicographic	ADJ
ejpam-3501	272	6	product	product	NOUN
ejpam-3501	272	7	of	of	ADP
ejpam-3501	272	8	grahs	grah	NOUN
ejpam-3501	272	9	theorem	theorem	VERB
ejpam-3501	272	10	4	4	NUM
ejpam-3501	272	11	.	.	PUNCT
ejpam-3501	273	1	[	[	X
ejpam-3501	273	2	2	2	X
ejpam-3501	273	3	]	]	PUNCT
ejpam-3501	273	4	let	let	VERB
ejpam-3501	273	5	g	g	NOUN
ejpam-3501	273	6	and	and	CCONJ
ejpam-3501	273	7	h	h	NOUN
ejpam-3501	273	8	be	be	AUX
ejpam-3501	273	9	nontrivial	nontrivial	ADJ
ejpam-3501	273	10	connected	connected	ADJ
ejpam-3501	273	11	graphs	graph	NOUN
ejpam-3501	273	12	.	.	PUNCT
ejpam-3501	274	1	then	then	ADV
ejpam-3501	274	2	c	c	X
ejpam-3501	274	3	=	=	SYM
ejpam-3501	274	4	∪x∈s	∪x∈s	PROPN
ejpam-3501	274	5	(	(	PUNCT
ejpam-3501	274	6	{	{	PUNCT
ejpam-3501	274	7	x	x	NOUN
ejpam-3501	274	8	}	}	PUNCT
ejpam-3501	274	9	×	×	PROPN
ejpam-3501	274	10	tx	tx	PROPN
ejpam-3501	274	11	)	)	PUNCT
ejpam-3501	274	12	is	be	AUX
ejpam-3501	274	13	a	a	DET
ejpam-3501	274	14	dominating	dominating	NOUN
ejpam-3501	274	15	set	set	VERB
ejpam-3501	274	16	if	if	SCONJ
ejpam-3501	274	17	and	and	CCONJ
ejpam-3501	274	18	only	only	ADV
ejpam-3501	274	19	if	if	SCONJ
ejpam-3501	274	20	one	one	NUM
ejpam-3501	274	21	of	of	ADP
ejpam-3501	274	22	the	the	DET
ejpam-3501	274	23	following	follow	VERB
ejpam-3501	274	24	holds	hold	VERB
ejpam-3501	274	25	:	:	PUNCT
ejpam-3501	274	26	(	(	PUNCT
ejpam-3501	274	27	i	i	NOUN
ejpam-3501	274	28	)	)	PUNCT
ejpam-3501	274	29	s	s	VERB
ejpam-3501	274	30	is	be	AUX
ejpam-3501	274	31	a	a	DET
ejpam-3501	274	32	total	total	ADJ
ejpam-3501	274	33	dominating	dominating	NOUN
ejpam-3501	274	34	set	set	NOUN
ejpam-3501	274	35	in	in	ADP
ejpam-3501	274	36	g	g	NOUN
ejpam-3501	274	37	;	;	PUNCT
ejpam-3501	274	38	(	(	PUNCT
ejpam-3501	274	39	ii	ii	NOUN
ejpam-3501	274	40	)	)	PUNCT
ejpam-3501	274	41	s	s	VERB
ejpam-3501	274	42	is	be	AUX
ejpam-3501	274	43	a	a	DET
ejpam-3501	274	44	dominating	dominating	NOUN
ejpam-3501	274	45	set	set	NOUN
ejpam-3501	274	46	in	in	ADP
ejpam-3501	274	47	g	g	PROPN
ejpam-3501	274	48	and	and	CCONJ
ejpam-3501	274	49	for	for	ADP
ejpam-3501	274	50	each	each	DET
ejpam-3501	274	51	x	x	X
ejpam-3501	274	52	∈	∈	PROPN
ejpam-3501	274	53	s	s	PART
ejpam-3501	274	54	\ng(s	\ng(s	NOUN
ejpam-3501	274	55	)	)	PUNCT
ejpam-3501	274	56	,	,	PUNCT
ejpam-3501	274	57	tx	tx	PROPN
ejpam-3501	274	58	is	be	AUX
ejpam-3501	274	59	a	a	DET
ejpam-3501	274	60	dominating	dominating	NOUN
ejpam-3501	274	61	set	set	NOUN
ejpam-3501	274	62	in	in	ADP
ejpam-3501	274	63	h.	h.	PROPN
ejpam-3501	274	64	i.	i.	PROPN
ejpam-3501	274	65	s.	s.	PROPN
ejpam-3501	274	66	aniversario	aniversario	PROPN
ejpam-3501	274	67	,	,	PUNCT
ejpam-3501	274	68	s.	s.	PROPN
ejpam-3501	274	69	r.	r.	PROPN
ejpam-3501	274	70	jr	jr	PROPN
ejpam-3501	274	71	.	.	PROPN
ejpam-3501	274	72	canoy	canoy	PROPN
ejpam-3501	274	73	,	,	PUNCT
ejpam-3501	274	74	f.p	f.p	PROPN
ejpam-3501	274	75	.	.	PROPN
ejpam-3501	274	76	jamil	jamil	PROPN
ejpam-3501	274	77	/	/	SYM
ejpam-3501	274	78	eur	eur	PROPN
ejpam-3501	274	79	.	.	PUNCT
ejpam-3501	275	1	j.	j.	PROPN
ejpam-3501	275	2	pure	pure	PROPN
ejpam-3501	275	3	appl	appl	PROPN
ejpam-3501	275	4	.	.	PROPN
ejpam-3501	275	5	math	math	PROPN
ejpam-3501	275	6	,	,	PUNCT
ejpam-3501	275	7	12	12	NUM
ejpam-3501	275	8	(	(	PUNCT
ejpam-3501	275	9	4	4	NUM
ejpam-3501	275	10	)	)	PUNCT
ejpam-3501	275	11	(	(	PUNCT
ejpam-3501	275	12	2019	2019	NUM
ejpam-3501	275	13	)	)	PUNCT
ejpam-3501	275	14	,	,	PUNCT
ejpam-3501	275	15	1410	1410	NUM
ejpam-3501	275	16	-	-	SYM
ejpam-3501	275	17	1425	1425	NUM
ejpam-3501	275	18	1419	1419	NUM
ejpam-3501	275	19	the	the	DET
ejpam-3501	275	20	next	next	ADJ
ejpam-3501	275	21	theorem	theorem	NOUN
ejpam-3501	275	22	follows	follow	VERB
ejpam-3501	275	23	immediately	immediately	ADV
ejpam-3501	275	24	from	from	ADP
ejpam-3501	275	25	theorem	theorem	ADJ
ejpam-3501	275	26	4	4	NUM
ejpam-3501	275	27	.	.	PUNCT
ejpam-3501	275	28	theorem	theorem	NOUN
ejpam-3501	275	29	5	5	NUM
ejpam-3501	275	30	.	.	PUNCT
ejpam-3501	276	1	[	[	X
ejpam-3501	276	2	3	3	X
ejpam-3501	276	3	]	]	PUNCT
ejpam-3501	276	4	let	let	VERB
ejpam-3501	276	5	g	g	NOUN
ejpam-3501	276	6	and	and	CCONJ
ejpam-3501	276	7	h	h	NOUN
ejpam-3501	276	8	be	be	AUX
ejpam-3501	276	9	nontrivial	nontrivial	ADJ
ejpam-3501	276	10	connected	connected	ADJ
ejpam-3501	276	11	graphs	graph	NOUN
ejpam-3501	276	12	.	.	PUNCT
ejpam-3501	277	1	then	then	ADV
ejpam-3501	277	2	c	c	X
ejpam-3501	277	3	=	=	SYM
ejpam-3501	277	4	∪x∈s	∪x∈s	PROPN
ejpam-3501	277	5	(	(	PUNCT
ejpam-3501	277	6	{	{	PUNCT
ejpam-3501	277	7	x	x	NOUN
ejpam-3501	277	8	}	}	PUNCT
ejpam-3501	277	9	×	×	PROPN
ejpam-3501	277	10	tx	tx	PROPN
ejpam-3501	277	11	)	)	PUNCT
ejpam-3501	277	12	is	be	AUX
ejpam-3501	277	13	a	a	DET
ejpam-3501	277	14	total	total	ADJ
ejpam-3501	277	15	dominating	dominating	NOUN
ejpam-3501	277	16	set	set	NOUN
ejpam-3501	277	17	if	if	SCONJ
ejpam-3501	277	18	and	and	CCONJ
ejpam-3501	277	19	only	only	ADV
ejpam-3501	277	20	if	if	SCONJ
ejpam-3501	277	21	one	one	NUM
ejpam-3501	277	22	of	of	ADP
ejpam-3501	277	23	the	the	DET
ejpam-3501	277	24	following	follow	VERB
ejpam-3501	277	25	holds	hold	VERB
ejpam-3501	277	26	:	:	PUNCT
ejpam-3501	277	27	(	(	PUNCT
ejpam-3501	277	28	i	i	NOUN
ejpam-3501	277	29	)	)	PUNCT
ejpam-3501	277	30	s	s	AUX
ejpam-3501	277	31	is	be	AUX
ejpam-3501	277	32	a	a	DET
ejpam-3501	277	33	total	total	ADJ
ejpam-3501	277	34	dominating	dominating	NOUN
ejpam-3501	277	35	set	set	NOUN
ejpam-3501	277	36	in	in	ADP
ejpam-3501	277	37	g	g	NOUN
ejpam-3501	277	38	;	;	PUNCT
ejpam-3501	277	39	(	(	PUNCT
ejpam-3501	277	40	ii	ii	NOUN
ejpam-3501	277	41	)	)	PUNCT
ejpam-3501	277	42	s	s	VERB
ejpam-3501	277	43	is	be	AUX
ejpam-3501	277	44	a	a	DET
ejpam-3501	277	45	dominating	dominating	NOUN
ejpam-3501	277	46	set	set	NOUN
ejpam-3501	277	47	in	in	ADP
ejpam-3501	277	48	g	g	PROPN
ejpam-3501	277	49	and	and	CCONJ
ejpam-3501	277	50	for	for	ADP
ejpam-3501	277	51	each	each	DET
ejpam-3501	277	52	x	x	X
ejpam-3501	277	53	∈	∈	PROPN
ejpam-3501	277	54	s	s	PART
ejpam-3501	277	55	\ng(s	\ng(s	NOUN
ejpam-3501	277	56	)	)	PUNCT
ejpam-3501	277	57	,	,	PUNCT
ejpam-3501	277	58	tx	tx	PROPN
ejpam-3501	277	59	is	be	AUX
ejpam-3501	277	60	a	a	DET
ejpam-3501	277	61	total	total	ADJ
ejpam-3501	277	62	dominating	dominating	NOUN
ejpam-3501	277	63	set	set	NOUN
ejpam-3501	277	64	in	in	ADP
ejpam-3501	277	65	h.	h.	PROPN
ejpam-3501	277	66	theorem	theorem	PROPN
ejpam-3501	277	67	6	6	NUM
ejpam-3501	277	68	.	.	PUNCT
ejpam-3501	278	1	let	let	VERB
ejpam-3501	278	2	g	g	NOUN
ejpam-3501	278	3	and	and	CCONJ
ejpam-3501	278	4	h	h	NOUN
ejpam-3501	278	5	be	be	AUX
ejpam-3501	278	6	nontrivial	nontrivial	ADJ
ejpam-3501	278	7	connected	connected	ADJ
ejpam-3501	278	8	graphs	graph	NOUN
ejpam-3501	278	9	,	,	PUNCT
ejpam-3501	278	10	and	and	CCONJ
ejpam-3501	278	11	let	let	VERB
ejpam-3501	278	12	c	c	NOUN
ejpam-3501	278	13	=	=	SYM
ejpam-3501	278	14	∪x∈s	∪x∈s	PROPN
ejpam-3501	278	15	(	(	PUNCT
ejpam-3501	278	16	{	{	PUNCT
ejpam-3501	278	17	x	x	NOUN
ejpam-3501	278	18	}	}	PUNCT
ejpam-3501	278	19	×	×	PROPN
ejpam-3501	278	20	tx	tx	PROPN
ejpam-3501	278	21	)	)	PUNCT
ejpam-3501	278	22	⊆	⊆	NUM
ejpam-3501	278	23	v	v	NOUN
ejpam-3501	278	24	(	(	PUNCT
ejpam-3501	278	25	g[h	g[h	PROPN
ejpam-3501	278	26	]	]	PUNCT
ejpam-3501	278	27	)	)	PUNCT
ejpam-3501	278	28	.	.	PUNCT
ejpam-3501	279	1	then	then	ADV
ejpam-3501	279	2	c	c	PROPN
ejpam-3501	279	3	is	be	AUX
ejpam-3501	279	4	a	a	DET
ejpam-3501	279	5	semitotal	semitotal	ADJ
ejpam-3501	279	6	dominating	dominating	NOUN
ejpam-3501	279	7	set	set	VERB
ejpam-3501	279	8	in	in	ADP
ejpam-3501	279	9	g[h	g[h	PROPN
ejpam-3501	279	10	]	]	PUNCT
ejpam-3501	279	11	if	if	SCONJ
ejpam-3501	279	12	and	and	CCONJ
ejpam-3501	279	13	only	only	ADV
ejpam-3501	279	14	if	if	SCONJ
ejpam-3501	279	15	one	one	NUM
ejpam-3501	279	16	of	of	ADP
ejpam-3501	279	17	the	the	DET
ejpam-3501	279	18	following	follow	VERB
ejpam-3501	279	19	holds	hold	VERB
ejpam-3501	279	20	:	:	PUNCT
ejpam-3501	279	21	(	(	PUNCT
ejpam-3501	279	22	i	i	NOUN
ejpam-3501	279	23	)	)	PUNCT
ejpam-3501	279	24	s	s	VERB
ejpam-3501	279	25	is	be	AUX
ejpam-3501	279	26	a	a	DET
ejpam-3501	279	27	total	total	ADJ
ejpam-3501	279	28	dominating	dominating	NOUN
ejpam-3501	279	29	set	set	NOUN
ejpam-3501	279	30	in	in	ADP
ejpam-3501	279	31	g	g	NOUN
ejpam-3501	279	32	;	;	PUNCT
ejpam-3501	279	33	(	(	PUNCT
ejpam-3501	279	34	ii	ii	NOUN
ejpam-3501	279	35	)	)	PUNCT
ejpam-3501	279	36	s	s	VERB
ejpam-3501	279	37	is	be	AUX
ejpam-3501	279	38	semitotal	semitotal	ADJ
ejpam-3501	279	39	dominating	dominating	NOUN
ejpam-3501	279	40	set	set	VERB
ejpam-3501	279	41	in	in	ADP
ejpam-3501	279	42	g	g	PROPN
ejpam-3501	279	43	and	and	CCONJ
ejpam-3501	279	44	for	for	ADP
ejpam-3501	279	45	each	each	DET
ejpam-3501	279	46	x	x	X
ejpam-3501	279	47	∈	∈	PROPN
ejpam-3501	279	48	s	s	PART
ejpam-3501	279	49	\ng(s	\ng(s	NOUN
ejpam-3501	279	50	)	)	PUNCT
ejpam-3501	279	51	,	,	PUNCT
ejpam-3501	279	52	tx	tx	PROPN
ejpam-3501	279	53	is	be	AUX
ejpam-3501	279	54	a	a	DET
ejpam-3501	279	55	dominating	dominating	NOUN
ejpam-3501	279	56	set	set	VERB
ejpam-3501	279	57	in	in	ADP
ejpam-3501	279	58	h	h	NOUN
ejpam-3501	279	59	;	;	PUNCT
ejpam-3501	279	60	(	(	PUNCT
ejpam-3501	279	61	iii	iii	X
ejpam-3501	279	62	)	)	PUNCT
ejpam-3501	279	63	s	s	VERB
ejpam-3501	279	64	is	be	AUX
ejpam-3501	279	65	a	a	DET
ejpam-3501	279	66	dominating	dominating	NOUN
ejpam-3501	279	67	set	set	VERB
ejpam-3501	279	68	in	in	ADP
ejpam-3501	279	69	g	g	PROPN
ejpam-3501	279	70	such	such	ADJ
ejpam-3501	279	71	that	that	SCONJ
ejpam-3501	279	72	tx	tx	PROPN
ejpam-3501	279	73	is	be	AUX
ejpam-3501	279	74	a	a	DET
ejpam-3501	279	75	dominating	dominating	NOUN
ejpam-3501	279	76	set	set	VERB
ejpam-3501	279	77	in	in	ADP
ejpam-3501	279	78	h	h	NOUN
ejpam-3501	279	79	for	for	ADP
ejpam-3501	279	80	each	each	DET
ejpam-3501	279	81	x	x	SYM
ejpam-3501	279	82	∈	∈	PROPN
ejpam-3501	279	83	s	s	PART
ejpam-3501	279	84	\ng(s	\ng(s	NOUN
ejpam-3501	279	85	)	)	PUNCT
ejpam-3501	279	86	,	,	PUNCT
ejpam-3501	279	87	and	and	CCONJ
ejpam-3501	279	88	|tx|	|tx|	NOUN
ejpam-3501	279	89	≥	≥	NUM
ejpam-3501	279	90	2	2	NUM
ejpam-3501	279	91	for	for	ADP
ejpam-3501	279	92	each	each	DET
ejpam-3501	279	93	x	x	SYM
ejpam-3501	279	94	∈	∈	PROPN
ejpam-3501	279	95	s	s	PART
ejpam-3501	279	96	\n2	\n2	ADJ
ejpam-3501	279	97	g(s	g(	NOUN
ejpam-3501	279	98	)	)	PUNCT
ejpam-3501	279	99	.	.	PUNCT
ejpam-3501	280	1	proof	proof	NOUN
ejpam-3501	280	2	.	.	PUNCT
ejpam-3501	281	1	by	by	ADP
ejpam-3501	281	2	theorem	theorem	NOUN
ejpam-3501	281	3	4	4	NUM
ejpam-3501	281	4	,	,	PUNCT
ejpam-3501	281	5	each	each	PRON
ejpam-3501	281	6	of	of	ADP
ejpam-3501	281	7	the	the	DET
ejpam-3501	281	8	conditions	condition	NOUN
ejpam-3501	281	9	(	(	PUNCT
ejpam-3501	281	10	i	i	NOUN
ejpam-3501	281	11	)	)	PUNCT
ejpam-3501	281	12	,	,	PUNCT
ejpam-3501	281	13	(	(	PUNCT
ejpam-3501	281	14	ii	ii	NOUN
ejpam-3501	281	15	)	)	PUNCT
ejpam-3501	281	16	and	and	CCONJ
ejpam-3501	281	17	(	(	PUNCT
ejpam-3501	281	18	iii	iii	NOUN
ejpam-3501	281	19	)	)	PUNCT
ejpam-3501	281	20	implies	imply	VERB
ejpam-3501	281	21	that	that	SCONJ
ejpam-3501	281	22	c	c	PROPN
ejpam-3501	281	23	is	be	AUX
ejpam-3501	281	24	a	a	DET
ejpam-3501	281	25	dominating	dominating	NOUN
ejpam-3501	281	26	set	set	VERB
ejpam-3501	281	27	in	in	ADP
ejpam-3501	281	28	g[h	g[h	NOUN
ejpam-3501	281	29	]	]	PUNCT
ejpam-3501	281	30	.	.	PUNCT
ejpam-3501	282	1	if	if	SCONJ
ejpam-3501	282	2	condition	condition	NOUN
ejpam-3501	282	3	(	(	PUNCT
ejpam-3501	282	4	i	i	NOUN
ejpam-3501	282	5	)	)	PUNCT
ejpam-3501	282	6	holds	hold	VERB
ejpam-3501	282	7	,	,	PUNCT
ejpam-3501	282	8	then	then	ADV
ejpam-3501	282	9	by	by	ADP
ejpam-3501	282	10	theorem	theorem	NOUN
ejpam-3501	282	11	5	5	NUM
ejpam-3501	282	12	,	,	PUNCT
ejpam-3501	282	13	c	c	PROPN
ejpam-3501	282	14	is	be	AUX
ejpam-3501	282	15	a	a	DET
ejpam-3501	282	16	total	total	ADJ
ejpam-3501	282	17	dominating	dominating	NOUN
ejpam-3501	282	18	set	set	NOUN
ejpam-3501	282	19	,	,	PUNCT
ejpam-3501	282	20	hence	hence	ADV
ejpam-3501	282	21	a	a	DET
ejpam-3501	282	22	semitotal	semitotal	ADJ
ejpam-3501	282	23	dominating	dominating	NOUN
ejpam-3501	282	24	set	set	VERB
ejpam-3501	282	25	in	in	ADP
ejpam-3501	282	26	g[h	g[h	PROPN
ejpam-3501	282	27	]	]	PUNCT
ejpam-3501	282	28	.	.	PUNCT
ejpam-3501	283	1	suppose	suppose	VERB
ejpam-3501	283	2	that	that	SCONJ
ejpam-3501	283	3	condition	condition	NOUN
ejpam-3501	283	4	(	(	PUNCT
ejpam-3501	283	5	ii	ii	NOUN
ejpam-3501	283	6	)	)	PUNCT
ejpam-3501	283	7	holds	hold	VERB
ejpam-3501	283	8	,	,	PUNCT
ejpam-3501	283	9	and	and	CCONJ
ejpam-3501	283	10	let	let	VERB
ejpam-3501	283	11	(	(	PUNCT
ejpam-3501	283	12	x	x	NOUN
ejpam-3501	283	13	,	,	PUNCT
ejpam-3501	283	14	y	y	NOUN
ejpam-3501	283	15	)	)	PUNCT
ejpam-3501	283	16	∈	∈	PROPN
ejpam-3501	283	17	c.	c.	NOUN
ejpam-3501	283	18	since	since	SCONJ
ejpam-3501	283	19	s	s	PROPN
ejpam-3501	283	20	is	be	AUX
ejpam-3501	283	21	a	a	DET
ejpam-3501	283	22	semitotal	semitotal	ADJ
ejpam-3501	283	23	dominating	dominating	NOUN
ejpam-3501	283	24	set	set	NOUN
ejpam-3501	283	25	in	in	ADP
ejpam-3501	283	26	g	g	NOUN
ejpam-3501	283	27	,	,	PUNCT
ejpam-3501	283	28	there	there	PRON
ejpam-3501	283	29	exists	exist	VERB
ejpam-3501	283	30	u	u	PROPN
ejpam-3501	283	31	∈	∈	PROPN
ejpam-3501	283	32	s	s	VERB
ejpam-3501	283	33	such	such	ADJ
ejpam-3501	283	34	that	that	SCONJ
ejpam-3501	283	35	1	1	NUM
ejpam-3501	283	36	≤	≤	NOUN
ejpam-3501	283	37	dg(x	dg(x	NUM
ejpam-3501	283	38	,	,	PUNCT
ejpam-3501	283	39	u	u	NOUN
ejpam-3501	283	40	)	)	PUNCT
ejpam-3501	283	41	≤	≤	NUM
ejpam-3501	283	42	2	2	NUM
ejpam-3501	283	43	.	.	X
ejpam-3501	283	44	pick	pick	VERB
ejpam-3501	283	45	v	v	ADP
ejpam-3501	283	46	∈	∈	PROPN
ejpam-3501	283	47	tu	tu	PROPN
ejpam-3501	283	48	.	.	PUNCT
ejpam-3501	284	1	then	then	ADV
ejpam-3501	284	2	(	(	PUNCT
ejpam-3501	284	3	u	u	NOUN
ejpam-3501	284	4	,	,	PUNCT
ejpam-3501	284	5	v	v	NOUN
ejpam-3501	284	6	)	)	PUNCT
ejpam-3501	284	7	∈	∈	PROPN
ejpam-3501	284	8	c	c	NOUN
ejpam-3501	284	9	and	and	CCONJ
ejpam-3501	284	10	1	1	NUM
ejpam-3501	284	11	≤	≤	NUM
ejpam-3501	284	12	dg[h]((x	dg[h]((x	NOUN
ejpam-3501	284	13	,	,	PUNCT
ejpam-3501	284	14	y	y	PROPN
ejpam-3501	284	15	)	)	PUNCT
ejpam-3501	284	16	,	,	PUNCT
ejpam-3501	284	17	(	(	PUNCT
ejpam-3501	284	18	u	u	NOUN
ejpam-3501	284	19	,	,	PUNCT
ejpam-3501	284	20	v	v	NOUN
ejpam-3501	284	21	)	)	PUNCT
ejpam-3501	284	22	)	)	PUNCT
ejpam-3501	285	1	≤	≤	NUM
ejpam-3501	285	2	2	2	NUM
ejpam-3501	285	3	.	.	PUNCT
ejpam-3501	286	1	thus	thus	ADV
ejpam-3501	286	2	,	,	PUNCT
ejpam-3501	286	3	c	c	PROPN
ejpam-3501	286	4	is	be	AUX
ejpam-3501	286	5	a	a	DET
ejpam-3501	286	6	semitotal	semitotal	ADJ
ejpam-3501	286	7	dominating	dominating	NOUN
ejpam-3501	286	8	set	set	VERB
ejpam-3501	286	9	in	in	ADP
ejpam-3501	286	10	g[h	g[h	PROPN
ejpam-3501	286	11	]	]	PUNCT
ejpam-3501	286	12	.	.	PUNCT
ejpam-3501	287	1	suppose	suppose	VERB
ejpam-3501	287	2	that	that	SCONJ
ejpam-3501	287	3	condition	condition	NOUN
ejpam-3501	287	4	(	(	PUNCT
ejpam-3501	287	5	iii	iii	NOUN
ejpam-3501	287	6	)	)	PUNCT
ejpam-3501	287	7	holds	hold	NOUN
ejpam-3501	287	8	,	,	PUNCT
ejpam-3501	287	9	and	and	CCONJ
ejpam-3501	287	10	let	let	VERB
ejpam-3501	287	11	(	(	PUNCT
ejpam-3501	287	12	x	x	NOUN
ejpam-3501	287	13	,	,	PUNCT
ejpam-3501	287	14	y	y	NOUN
ejpam-3501	287	15	)	)	PUNCT
ejpam-3501	287	16	∈	∈	PROPN
ejpam-3501	287	17	c.	c.	NOUN
ejpam-3501	287	18	if	if	SCONJ
ejpam-3501	287	19	x	x	PROPN
ejpam-3501	287	20	∈	∈	PROPN
ejpam-3501	287	21	n2	n2	NOUN
ejpam-3501	287	22	g(s	g(s	PROPN
ejpam-3501	287	23	)	)	PUNCT
ejpam-3501	287	24	,	,	PUNCT
ejpam-3501	287	25	then	then	ADV
ejpam-3501	287	26	there	there	PRON
ejpam-3501	287	27	exists	exist	VERB
ejpam-3501	287	28	u	u	PROPN
ejpam-3501	287	29	∈	∈	PROPN
ejpam-3501	287	30	s	s	VERB
ejpam-3501	287	31	such	such	ADJ
ejpam-3501	287	32	that	that	SCONJ
ejpam-3501	287	33	1	1	NUM
ejpam-3501	287	34	≤	≤	NOUN
ejpam-3501	287	35	dg(x	dg(x	NUM
ejpam-3501	287	36	,	,	PUNCT
ejpam-3501	287	37	u	u	NOUN
ejpam-3501	287	38	)	)	PUNCT
ejpam-3501	287	39	≤	≤	NUM
ejpam-3501	287	40	2	2	NUM
ejpam-3501	287	41	.	.	X
ejpam-3501	287	42	pick	pick	VERB
ejpam-3501	287	43	v	v	ADP
ejpam-3501	287	44	∈	∈	PROPN
ejpam-3501	287	45	tu	tu	PROPN
ejpam-3501	287	46	.	.	PUNCT
ejpam-3501	288	1	then	then	ADV
ejpam-3501	288	2	1	1	NUM
ejpam-3501	288	3	≤	≤	NUM
ejpam-3501	288	4	dg[h]((x	dg[h]((x	NOUN
ejpam-3501	288	5	,	,	PUNCT
ejpam-3501	288	6	y	y	PROPN
ejpam-3501	288	7	)	)	PUNCT
ejpam-3501	288	8	,	,	PUNCT
ejpam-3501	288	9	(	(	PUNCT
ejpam-3501	288	10	u	u	NOUN
ejpam-3501	288	11	,	,	PUNCT
ejpam-3501	288	12	v	v	NOUN
ejpam-3501	288	13	)	)	PUNCT
ejpam-3501	288	14	)	)	PUNCT
ejpam-3501	288	15	≤	≤	NUM
ejpam-3501	288	16	2	2	NUM
ejpam-3501	288	17	.	.	PUNCT
ejpam-3501	288	18	suppose	suppose	VERB
ejpam-3501	288	19	that	that	SCONJ
ejpam-3501	288	20	x	x	PROPN
ejpam-3501	288	21	/∈	/∈	PUNCT
ejpam-3501	288	22	n2	n2	ADJ
ejpam-3501	288	23	g(s	g(s	PROPN
ejpam-3501	288	24	)	)	PUNCT
ejpam-3501	288	25	.	.	PUNCT
ejpam-3501	289	1	pick	pick	VERB
ejpam-3501	289	2	z	z	PROPN
ejpam-3501	289	3	∈	∈	PROPN
ejpam-3501	289	4	tx	tx	PROPN
ejpam-3501	289	5	\	\	PROPN
ejpam-3501	289	6	{	{	PUNCT
ejpam-3501	289	7	y	y	NOUN
ejpam-3501	289	8	}	}	PUNCT
ejpam-3501	289	9	.	.	PUNCT
ejpam-3501	290	1	then	then	ADV
ejpam-3501	290	2	(	(	PUNCT
ejpam-3501	290	3	x	x	X
ejpam-3501	290	4	,	,	PUNCT
ejpam-3501	290	5	z	z	NOUN
ejpam-3501	290	6	)	)	PUNCT
ejpam-3501	290	7	∈	∈	PROPN
ejpam-3501	290	8	c	c	PROPN
ejpam-3501	290	9	and	and	CCONJ
ejpam-3501	290	10	dg[h]((x	dg[h]((x	PROPN
ejpam-3501	290	11	,	,	PUNCT
ejpam-3501	290	12	y	y	PROPN
ejpam-3501	290	13	)	)	PUNCT
ejpam-3501	290	14	,	,	PUNCT
ejpam-3501	290	15	(	(	PUNCT
ejpam-3501	290	16	x	x	X
ejpam-3501	290	17	,	,	PUNCT
ejpam-3501	290	18	z	z	NOUN
ejpam-3501	290	19	)	)	PUNCT
ejpam-3501	290	20	)	)	PUNCT
ejpam-3501	291	1	≤	≤	NUM
ejpam-3501	291	2	2	2	NUM
ejpam-3501	291	3	.	.	PUNCT
ejpam-3501	291	4	suppose	suppose	VERB
ejpam-3501	291	5	that	that	SCONJ
ejpam-3501	291	6	c	c	PROPN
ejpam-3501	291	7	is	be	AUX
ejpam-3501	291	8	a	a	DET
ejpam-3501	291	9	semitotal	semitotal	ADJ
ejpam-3501	291	10	dominating	dominating	NOUN
ejpam-3501	291	11	set	set	VERB
ejpam-3501	291	12	in	in	ADP
ejpam-3501	291	13	g[h	g[h	PROPN
ejpam-3501	291	14	]	]	PUNCT
ejpam-3501	291	15	.	.	PUNCT
ejpam-3501	292	1	then	then	ADV
ejpam-3501	292	2	s	s	VERB
ejpam-3501	292	3	is	be	AUX
ejpam-3501	292	4	a	a	DET
ejpam-3501	292	5	dominating	dominating	NOUN
ejpam-3501	292	6	set	set	VERB
ejpam-3501	292	7	in	in	ADP
ejpam-3501	292	8	g	g	NOUN
ejpam-3501	292	9	by	by	ADP
ejpam-3501	292	10	theorem	theorem	NOUN
ejpam-3501	292	11	4	4	NUM
ejpam-3501	292	12	.	.	PUNCT
ejpam-3501	293	1	if	if	SCONJ
ejpam-3501	293	2	s	s	PROPN
ejpam-3501	293	3	is	be	AUX
ejpam-3501	293	4	a	a	DET
ejpam-3501	293	5	total	total	ADJ
ejpam-3501	293	6	dominating	dominating	NOUN
ejpam-3501	293	7	set	set	NOUN
ejpam-3501	293	8	in	in	ADP
ejpam-3501	293	9	g	g	NOUN
ejpam-3501	293	10	,	,	PUNCT
ejpam-3501	293	11	then	then	ADV
ejpam-3501	293	12	(	(	PUNCT
ejpam-3501	293	13	i	i	NOUN
ejpam-3501	293	14	)	)	PUNCT
ejpam-3501	293	15	holds	hold	VERB
ejpam-3501	293	16	.	.	PUNCT
ejpam-3501	294	1	suppose	suppose	VERB
ejpam-3501	294	2	that	that	SCONJ
ejpam-3501	294	3	s	s	VERB
ejpam-3501	294	4	is	be	AUX
ejpam-3501	294	5	not	not	PART
ejpam-3501	294	6	a	a	DET
ejpam-3501	294	7	total	total	ADJ
ejpam-3501	294	8	dominating	dominating	NOUN
ejpam-3501	294	9	set	set	VERB
ejpam-3501	294	10	in	in	ADP
ejpam-3501	294	11	g.	g.	PROPN
ejpam-3501	294	12	by	by	ADP
ejpam-3501	294	13	theorem	theorem	NOUN
ejpam-3501	294	14	4	4	NUM
ejpam-3501	294	15	,	,	PUNCT
ejpam-3501	294	16	tx	tx	PROPN
ejpam-3501	294	17	is	be	AUX
ejpam-3501	294	18	a	a	DET
ejpam-3501	294	19	dominating	dominating	NOUN
ejpam-3501	294	20	set	set	VERB
ejpam-3501	294	21	in	in	ADP
ejpam-3501	294	22	h	h	NOUN
ejpam-3501	294	23	for	for	ADP
ejpam-3501	294	24	each	each	DET
ejpam-3501	294	25	x	x	SYM
ejpam-3501	294	26	∈	∈	PROPN
ejpam-3501	294	27	s	s	PART
ejpam-3501	294	28	\	\	NOUN
ejpam-3501	294	29	ng(s	ng(s	NUM
ejpam-3501	294	30	)	)	PUNCT
ejpam-3501	294	31	.	.	PUNCT
ejpam-3501	295	1	if	if	SCONJ
ejpam-3501	295	2	s	s	NOUN
ejpam-3501	295	3	is	be	AUX
ejpam-3501	295	4	a	a	DET
ejpam-3501	295	5	semitotal	semitotal	ADJ
ejpam-3501	295	6	dominating	dominating	NOUN
ejpam-3501	295	7	set	set	NOUN
ejpam-3501	295	8	in	in	ADP
ejpam-3501	295	9	g	g	NOUN
ejpam-3501	295	10	,	,	PUNCT
ejpam-3501	295	11	then	then	ADV
ejpam-3501	295	12	(	(	PUNCT
ejpam-3501	295	13	ii	ii	NOUN
ejpam-3501	295	14	)	)	PUNCT
ejpam-3501	295	15	holds	hold	VERB
ejpam-3501	295	16	.	.	PUNCT
ejpam-3501	296	1	suppose	suppose	VERB
ejpam-3501	296	2	that	that	SCONJ
ejpam-3501	296	3	s	s	VERB
ejpam-3501	296	4	is	be	AUX
ejpam-3501	296	5	not	not	PART
ejpam-3501	296	6	a	a	DET
ejpam-3501	296	7	semitotal	semitotal	ADJ
ejpam-3501	296	8	dominating	dominating	NOUN
ejpam-3501	296	9	set	set	VERB
ejpam-3501	296	10	in	in	ADP
ejpam-3501	296	11	g.	g.	PROPN
ejpam-3501	296	12	let	let	VERB
ejpam-3501	296	13	x	x	PUNCT
ejpam-3501	296	14	∈	∈	PROPN
ejpam-3501	296	15	s	s	PART
ejpam-3501	296	16	\	\	PROPN
ejpam-3501	296	17	n2	n2	ADJ
ejpam-3501	296	18	g(s	g(s	PROPN
ejpam-3501	296	19	)	)	PUNCT
ejpam-3501	296	20	,	,	PUNCT
ejpam-3501	296	21	and	and	CCONJ
ejpam-3501	296	22	let	let	VERB
ejpam-3501	296	23	u	u	PRON
ejpam-3501	296	24	∈	∈	PROPN
ejpam-3501	296	25	tx	tx	PROPN
ejpam-3501	296	26	.	.	PUNCT
ejpam-3501	297	1	since	since	SCONJ
ejpam-3501	297	2	c	c	PROPN
ejpam-3501	297	3	is	be	AUX
ejpam-3501	297	4	a	a	DET
ejpam-3501	297	5	semitotal	semitotal	ADJ
ejpam-3501	297	6	dominating	dominating	NOUN
ejpam-3501	297	7	set	set	VERB
ejpam-3501	297	8	in	in	ADP
ejpam-3501	297	9	g[h	g[h	PROPN
ejpam-3501	297	10	]	]	PUNCT
ejpam-3501	297	11	,	,	PUNCT
ejpam-3501	297	12	there	there	PRON
ejpam-3501	297	13	exists	exist	VERB
ejpam-3501	297	14	(	(	PUNCT
ejpam-3501	297	15	a	a	PRON
ejpam-3501	297	16	,	,	PUNCT
ejpam-3501	297	17	b	b	NOUN
ejpam-3501	297	18	)	)	PUNCT
ejpam-3501	297	19	∈	∈	PROPN
ejpam-3501	297	20	c	c	NOUN
ejpam-3501	297	21	such	such	ADJ
ejpam-3501	297	22	such	such	ADJ
ejpam-3501	297	23	that	that	SCONJ
ejpam-3501	297	24	1	1	NUM
ejpam-3501	297	25	≤	≤	NUM
ejpam-3501	297	26	dg[h]((x	dg[h]((x	NOUN
ejpam-3501	297	27	,	,	PUNCT
ejpam-3501	297	28	u	u	NOUN
ejpam-3501	297	29	)	)	PUNCT
ejpam-3501	297	30	,	,	PUNCT
ejpam-3501	297	31	(	(	PUNCT
ejpam-3501	297	32	a	a	DET
ejpam-3501	297	33	,	,	PUNCT
ejpam-3501	297	34	b	b	NOUN
ejpam-3501	297	35	)	)	PUNCT
ejpam-3501	297	36	)	)	PUNCT
ejpam-3501	298	1	≤	≤	NUM
ejpam-3501	298	2	2	2	NUM
ejpam-3501	298	3	.	.	PUNCT
ejpam-3501	299	1	since	since	SCONJ
ejpam-3501	299	2	x	x	PROPN
ejpam-3501	299	3	∈	∈	PROPN
ejpam-3501	299	4	s	s	PART
ejpam-3501	299	5	\n2	\n2	ADJ
ejpam-3501	299	6	g(s	g(	NOUN
ejpam-3501	299	7	)	)	PUNCT
ejpam-3501	299	8	,	,	PUNCT
ejpam-3501	299	9	a	a	DET
ejpam-3501	299	10	=	=	NOUN
ejpam-3501	299	11	x	x	X
ejpam-3501	299	12	and	and	CCONJ
ejpam-3501	299	13	|tx|	|tx|	PROPN
ejpam-3501	299	14	≥	≥	NUM
ejpam-3501	299	15	2	2	NUM
ejpam-3501	299	16	.	.	PUNCT
ejpam-3501	299	17	the	the	DET
ejpam-3501	299	18	following	follow	VERB
ejpam-3501	299	19	well	well	ADV
ejpam-3501	299	20	-	-	PUNCT
ejpam-3501	299	21	known	know	VERB
ejpam-3501	299	22	lemma	lemma	PROPN
ejpam-3501	299	23	is	be	AUX
ejpam-3501	299	24	essential	essential	ADJ
ejpam-3501	299	25	for	for	ADP
ejpam-3501	299	26	the	the	DET
ejpam-3501	299	27	desired	desire	VERB
ejpam-3501	299	28	results	result	NOUN
ejpam-3501	299	29	.	.	PUNCT
ejpam-3501	300	1	lemma	lemma	PROPN
ejpam-3501	300	2	2	2	NUM
ejpam-3501	300	3	.	.	PUNCT
ejpam-3501	301	1	[	[	X
ejpam-3501	301	2	3	3	X
ejpam-3501	301	3	]	]	PUNCT
ejpam-3501	301	4	let	let	VERB
ejpam-3501	301	5	g	g	PRON
ejpam-3501	301	6	be	be	AUX
ejpam-3501	301	7	a	a	DET
ejpam-3501	301	8	nontrivial	nontrivial	ADJ
ejpam-3501	301	9	connected	connect	VERB
ejpam-3501	301	10	graph	graph	NOUN
ejpam-3501	301	11	and	and	CCONJ
ejpam-3501	301	12	s	s	VERB
ejpam-3501	301	13	⊆	⊆	NUM
ejpam-3501	301	14	v	v	NOUN
ejpam-3501	301	15	(	(	PUNCT
ejpam-3501	301	16	g	g	NOUN
ejpam-3501	301	17	)	)	PUNCT
ejpam-3501	301	18	a	a	DET
ejpam-3501	301	19	dominating	dominating	NOUN
ejpam-3501	301	20	set	set	VERB
ejpam-3501	301	21	in	in	ADP
ejpam-3501	301	22	g.	g.	PROPN
ejpam-3501	301	23	then	then	ADV
ejpam-3501	301	24	γt(g	γt(g	PUNCT
ejpam-3501	301	25	)	)	PUNCT
ejpam-3501	301	26	≤	≤	NUM
ejpam-3501	301	27	|s	|s	PROPN
ejpam-3501	301	28	∩ng(s)|+	∩ng(s)|+	PROPN
ejpam-3501	301	29	2|s	2|s	NUM
ejpam-3501	301	30	\ng(s)|	\ng(s)|	NOUN
ejpam-3501	301	31	.	.	PUNCT
ejpam-3501	302	1	following	follow	VERB
ejpam-3501	302	2	the	the	DET
ejpam-3501	302	3	usual	usual	ADJ
ejpam-3501	302	4	proof	proof	NOUN
ejpam-3501	302	5	also	also	ADV
ejpam-3501	302	6	establishes	establish	VERB
ejpam-3501	302	7	the	the	DET
ejpam-3501	302	8	next	next	ADJ
ejpam-3501	302	9	lemma	lemma	PROPN
ejpam-3501	302	10	.	.	PUNCT
ejpam-3501	302	11	i.	i.	PROPN
ejpam-3501	302	12	s.	s.	PROPN
ejpam-3501	302	13	aniversario	aniversario	PROPN
ejpam-3501	302	14	,	,	PUNCT
ejpam-3501	302	15	s.	s.	PROPN
ejpam-3501	302	16	r.	r.	PROPN
ejpam-3501	302	17	jr	jr	PROPN
ejpam-3501	302	18	.	.	PROPN
ejpam-3501	302	19	canoy	canoy	PROPN
ejpam-3501	302	20	,	,	PUNCT
ejpam-3501	302	21	f.p	f.p	PROPN
ejpam-3501	302	22	.	.	PROPN
ejpam-3501	302	23	jamil	jamil	PROPN
ejpam-3501	302	24	/	/	SYM
ejpam-3501	302	25	eur	eur	PROPN
ejpam-3501	302	26	.	.	PUNCT
ejpam-3501	303	1	j.	j.	PROPN
ejpam-3501	303	2	pure	pure	PROPN
ejpam-3501	303	3	appl	appl	PROPN
ejpam-3501	303	4	.	.	PROPN
ejpam-3501	303	5	math	math	PROPN
ejpam-3501	303	6	,	,	PUNCT
ejpam-3501	303	7	12	12	NUM
ejpam-3501	303	8	(	(	PUNCT
ejpam-3501	303	9	4	4	NUM
ejpam-3501	303	10	)	)	PUNCT
ejpam-3501	303	11	(	(	PUNCT
ejpam-3501	303	12	2019	2019	NUM
ejpam-3501	303	13	)	)	PUNCT
ejpam-3501	303	14	,	,	PUNCT
ejpam-3501	303	15	1410	1410	NUM
ejpam-3501	303	16	-	-	SYM
ejpam-3501	303	17	1425	1425	NUM
ejpam-3501	303	18	1420	1420	NUM
ejpam-3501	303	19	lemma	lemma	PROPN
ejpam-3501	303	20	3	3	X
ejpam-3501	303	21	.	.	PUNCT
ejpam-3501	304	1	if	if	SCONJ
ejpam-3501	304	2	g	g	PROPN
ejpam-3501	304	3	is	be	AUX
ejpam-3501	304	4	a	a	DET
ejpam-3501	304	5	nontrival	nontrival	ADJ
ejpam-3501	304	6	connected	connect	VERB
ejpam-3501	304	7	graph	graph	NOUN
ejpam-3501	304	8	and	and	CCONJ
ejpam-3501	304	9	s	s	VERB
ejpam-3501	304	10	⊆	⊆	NUM
ejpam-3501	304	11	v	v	NOUN
ejpam-3501	304	12	(	(	PUNCT
ejpam-3501	304	13	g	g	NOUN
ejpam-3501	304	14	)	)	PUNCT
ejpam-3501	304	15	is	be	AUX
ejpam-3501	304	16	a	a	DET
ejpam-3501	304	17	dominating	dominating	NOUN
ejpam-3501	304	18	set	set	NOUN
ejpam-3501	304	19	in	in	ADP
ejpam-3501	304	20	g	g	PROPN
ejpam-3501	304	21	,	,	PUNCT
ejpam-3501	304	22	then	then	ADV
ejpam-3501	304	23	γt2(g	γt2(g	NUM
ejpam-3501	304	24	)	)	PUNCT
ejpam-3501	304	25	≤	≤	NOUN
ejpam-3501	304	26	2|s	2|s	PUNCT
ejpam-3501	304	27	\n2	\n2	PROPN
ejpam-3501	304	28	g(s)|+	g(s)|+	PROPN
ejpam-3501	304	29	|s	|s	PROPN
ejpam-3501	304	30	∩n2	∩n2	PROPN
ejpam-3501	304	31	g(s)|	g(s)|	PROPN
ejpam-3501	304	32	.	.	PUNCT
ejpam-3501	305	1	corollary	corollary	ADJ
ejpam-3501	305	2	8	8	NUM
ejpam-3501	305	3	.	.	PUNCT
ejpam-3501	306	1	if	if	SCONJ
ejpam-3501	306	2	g	g	PROPN
ejpam-3501	306	3	and	and	CCONJ
ejpam-3501	306	4	h	h	NOUN
ejpam-3501	306	5	are	be	AUX
ejpam-3501	306	6	nontrivial	nontrivial	ADJ
ejpam-3501	306	7	connected	connect	VERB
ejpam-3501	306	8	graphs	graph	NOUN
ejpam-3501	306	9	with	with	ADP
ejpam-3501	306	10	γ(h	γ(h	NOUN
ejpam-3501	306	11	)	)	PUNCT
ejpam-3501	306	12	=	=	SYM
ejpam-3501	306	13	1	1	NUM
ejpam-3501	306	14	,	,	PUNCT
ejpam-3501	306	15	then	then	ADV
ejpam-3501	306	16	γt2(g[h	γt2(g[h	X
ejpam-3501	306	17	]	]	X
ejpam-3501	306	18	)	)	PUNCT
ejpam-3501	306	19	=	=	PUNCT
ejpam-3501	306	20	γt2(g	γt2(g	NOUN
ejpam-3501	306	21	)	)	PUNCT
ejpam-3501	306	22	.	.	PUNCT
ejpam-3501	307	1	proof	proof	NOUN
ejpam-3501	307	2	.	.	PUNCT
ejpam-3501	308	1	let	let	VERB
ejpam-3501	308	2	v	v	NUM
ejpam-3501	308	3	∈	∈	PROPN
ejpam-3501	308	4	v	v	NOUN
ejpam-3501	308	5	(	(	PUNCT
ejpam-3501	308	6	h	h	NOUN
ejpam-3501	308	7	)	)	PUNCT
ejpam-3501	308	8	be	be	VERB
ejpam-3501	308	9	such	such	ADJ
ejpam-3501	308	10	that	that	SCONJ
ejpam-3501	308	11	{	{	PUNCT
ejpam-3501	308	12	v	v	NOUN
ejpam-3501	308	13	}	}	PUNCT
ejpam-3501	308	14	is	be	AUX
ejpam-3501	308	15	a	a	DET
ejpam-3501	308	16	dominating	dominating	NOUN
ejpam-3501	308	17	set	set	NOUN
ejpam-3501	308	18	in	in	ADP
ejpam-3501	308	19	h.	h.	PROPN
ejpam-3501	308	20	let	let	VERB
ejpam-3501	308	21	s	s	PRON
ejpam-3501	308	22	⊆	⊆	NUM
ejpam-3501	308	23	v	v	NOUN
ejpam-3501	308	24	(	(	PUNCT
ejpam-3501	308	25	g	g	NOUN
ejpam-3501	308	26	)	)	PUNCT
ejpam-3501	308	27	be	be	AUX
ejpam-3501	308	28	a	a	DET
ejpam-3501	308	29	semitotal	semitotal	ADJ
ejpam-3501	308	30	dominating	dominating	NOUN
ejpam-3501	308	31	set	set	VERB
ejpam-3501	308	32	in	in	ADP
ejpam-3501	308	33	g.	g.	PROPN
ejpam-3501	308	34	by	by	ADP
ejpam-3501	308	35	theorem	theorem	NOUN
ejpam-3501	308	36	6	6	NUM
ejpam-3501	308	37	,	,	PUNCT
ejpam-3501	308	38	s	s	PART
ejpam-3501	308	39	×	×	NOUN
ejpam-3501	308	40	{	{	PUNCT
ejpam-3501	308	41	v	v	NOUN
ejpam-3501	308	42	}	}	PUNCT
ejpam-3501	308	43	is	be	AUX
ejpam-3501	308	44	a	a	DET
ejpam-3501	308	45	semitotal	semitotal	ADJ
ejpam-3501	308	46	dominating	dominating	NOUN
ejpam-3501	308	47	set	set	VERB
ejpam-3501	308	48	in	in	ADP
ejpam-3501	308	49	g[h	g[h	PROPN
ejpam-3501	308	50	]	]	PUNCT
ejpam-3501	308	51	.	.	PUNCT
ejpam-3501	309	1	thus	thus	ADV
ejpam-3501	309	2	,	,	PUNCT
ejpam-3501	309	3	γt2(g[h	γt2(g[h	PROPN
ejpam-3501	309	4	]	]	X
ejpam-3501	309	5	)	)	PUNCT
ejpam-3501	309	6	≤	≤	NUM
ejpam-3501	309	7	|s|	|s|	PROPN
ejpam-3501	309	8	.	.	PUNCT
ejpam-3501	310	1	since	since	SCONJ
ejpam-3501	310	2	s	s	NOUN
ejpam-3501	310	3	is	be	AUX
ejpam-3501	310	4	arbitrary	arbitrary	ADJ
ejpam-3501	310	5	,	,	PUNCT
ejpam-3501	310	6	γt2(g[h	γt2(g[h	NOUN
ejpam-3501	310	7	]	]	X
ejpam-3501	310	8	)	)	PUNCT
ejpam-3501	310	9	≤	≤	NOUN
ejpam-3501	310	10	γt2(g	γt2(g	NUM
ejpam-3501	310	11	)	)	PUNCT
ejpam-3501	310	12	.	.	PUNCT
ejpam-3501	311	1	let	let	VERB
ejpam-3501	311	2	c	c	NOUN
ejpam-3501	311	3	=	=	SYM
ejpam-3501	311	4	∪x∈s	∪x∈s	PROPN
ejpam-3501	311	5	(	(	PUNCT
ejpam-3501	311	6	{	{	PUNCT
ejpam-3501	311	7	x	x	NOUN
ejpam-3501	311	8	}	}	PUNCT
ejpam-3501	311	9	×	×	PROPN
ejpam-3501	311	10	tx	tx	PROPN
ejpam-3501	311	11	)	)	PUNCT
ejpam-3501	311	12	⊆	⊆	NUM
ejpam-3501	311	13	v	v	NOUN
ejpam-3501	311	14	(	(	PUNCT
ejpam-3501	311	15	g[h	g[h	PROPN
ejpam-3501	311	16	]	]	PUNCT
ejpam-3501	311	17	)	)	PUNCT
ejpam-3501	311	18	be	be	AUX
ejpam-3501	311	19	a	a	DET
ejpam-3501	311	20	semitotal	semitotal	ADJ
ejpam-3501	311	21	dominating	dominating	NOUN
ejpam-3501	311	22	set	set	VERB
ejpam-3501	311	23	in	in	ADP
ejpam-3501	311	24	g[h	g[h	PROPN
ejpam-3501	311	25	]	]	PUNCT
ejpam-3501	311	26	.	.	PUNCT
ejpam-3501	312	1	by	by	ADP
ejpam-3501	312	2	theorem	theorem	NOUN
ejpam-3501	312	3	6	6	NUM
ejpam-3501	312	4	,	,	PUNCT
ejpam-3501	312	5	s	s	VERB
ejpam-3501	312	6	is	be	AUX
ejpam-3501	312	7	a	a	DET
ejpam-3501	312	8	dominating	dominating	NOUN
ejpam-3501	312	9	set	set	VERB
ejpam-3501	312	10	in	in	ADP
ejpam-3501	312	11	g.	g.	PROPN
ejpam-3501	312	12	if	if	SCONJ
ejpam-3501	312	13	s	s	X
ejpam-3501	312	14	satisfies	satisfie	NOUN
ejpam-3501	312	15	(	(	PUNCT
ejpam-3501	312	16	i	i	NOUN
ejpam-3501	312	17	)	)	PUNCT
ejpam-3501	312	18	or	or	CCONJ
ejpam-3501	312	19	(	(	PUNCT
ejpam-3501	312	20	ii	ii	NOUN
ejpam-3501	312	21	)	)	PUNCT
ejpam-3501	312	22	in	in	ADP
ejpam-3501	312	23	theorem	theorem	NOUN
ejpam-3501	312	24	6	6	NUM
ejpam-3501	312	25	,	,	PUNCT
ejpam-3501	312	26	then	then	ADV
ejpam-3501	312	27	s	s	VERB
ejpam-3501	312	28	is	be	AUX
ejpam-3501	312	29	a	a	DET
ejpam-3501	312	30	semitotal	semitotal	ADJ
ejpam-3501	312	31	dominating	dominating	NOUN
ejpam-3501	312	32	set	set	NOUN
ejpam-3501	312	33	in	in	ADP
ejpam-3501	312	34	g	g	NOUN
ejpam-3501	312	35	,	,	PUNCT
ejpam-3501	312	36	and	and	CCONJ
ejpam-3501	312	37	γt2(g	γt2(g	NUM
ejpam-3501	312	38	)	)	PUNCT
ejpam-3501	312	39	≤	≤	NOUN
ejpam-3501	312	40	|s|	|s|	NOUN
ejpam-3501	312	41	≤	≤	PROPN
ejpam-3501	312	42	∑	∑	PUNCT
ejpam-3501	312	43	x∈s	x∈s	PROPN
ejpam-3501	312	44	|tx|	|tx|	PROPN
ejpam-3501	312	45	=	=	PUNCT
ejpam-3501	312	46	|c|	|c|	PROPN
ejpam-3501	312	47	.	.	PUNCT
ejpam-3501	312	48	suppose	suppose	VERB
ejpam-3501	312	49	that	that	SCONJ
ejpam-3501	312	50	s	s	VERB
ejpam-3501	312	51	is	be	AUX
ejpam-3501	312	52	not	not	PART
ejpam-3501	312	53	a	a	DET
ejpam-3501	312	54	semitotal	semitotal	ADJ
ejpam-3501	312	55	dominating	dominating	NOUN
ejpam-3501	312	56	set	set	NOUN
ejpam-3501	312	57	ing	ing	NOUN
ejpam-3501	312	58	.	.	PUNCT
ejpam-3501	313	1	let	let	VERB
ejpam-3501	313	2	s1	s1	PROPN
ejpam-3501	313	3	=	=	SYM
ejpam-3501	313	4	s\n2	s\n2	PROPN
ejpam-3501	313	5	g(s	g(s	PROPN
ejpam-3501	313	6	)	)	PUNCT
ejpam-3501	313	7	,	,	PUNCT
ejpam-3501	313	8	s2	s2	NOUN
ejpam-3501	313	9	=	=	PUNCT
ejpam-3501	313	10	s∩n2	s∩n2	NOUN
ejpam-3501	313	11	g(s	g(s	NOUN
ejpam-3501	313	12	)	)	PUNCT
ejpam-3501	313	13	.	.	PUNCT
ejpam-3501	314	1	by	by	ADP
ejpam-3501	314	2	theorem	theorem	NOUN
ejpam-3501	314	3	6	6	NUM
ejpam-3501	314	4	,	,	PUNCT
ejpam-3501	314	5	c	c	NOUN
ejpam-3501	314	6	=	=	SYM
ejpam-3501	314	7	(	(	PUNCT
ejpam-3501	314	8	∪x∈s1	∪x∈s1	PROPN
ejpam-3501	314	9	(	(	PUNCT
ejpam-3501	314	10	{	{	PUNCT
ejpam-3501	314	11	x	x	NOUN
ejpam-3501	314	12	}	}	PUNCT
ejpam-3501	314	13	×	×	PROPN
ejpam-3501	314	14	tx	tx	PROPN
ejpam-3501	314	15	)	)	PUNCT
ejpam-3501	314	16	)	)	PUNCT
ejpam-3501	314	17	∪	∪	ADV
ejpam-3501	314	18	(	(	PUNCT
ejpam-3501	314	19	∪x∈s2	∪x∈s2	PROPN
ejpam-3501	314	20	(	(	PUNCT
ejpam-3501	314	21	{	{	PUNCT
ejpam-3501	314	22	x	x	NOUN
ejpam-3501	314	23	}	}	PUNCT
ejpam-3501	314	24	×	×	PROPN
ejpam-3501	314	25	tx	tx	PROPN
ejpam-3501	314	26	)	)	PUNCT
ejpam-3501	314	27	)	)	PUNCT
ejpam-3501	314	28	,	,	PUNCT
ejpam-3501	314	29	where	where	SCONJ
ejpam-3501	314	30	|tx|	|tx|	NOUN
ejpam-3501	314	31	≥	≥	NUM
ejpam-3501	314	32	2	2	NUM
ejpam-3501	314	33	for	for	ADP
ejpam-3501	314	34	all	all	DET
ejpam-3501	314	35	x	x	SYM
ejpam-3501	314	36	∈	∈	PROPN
ejpam-3501	314	37	s1	s1	NOUN
ejpam-3501	314	38	.	.	PUNCT
ejpam-3501	315	1	thus	thus	ADV
ejpam-3501	315	2	,	,	PUNCT
ejpam-3501	315	3	|c|	|c|	PROPN
ejpam-3501	315	4	=	=	PUNCT
ejpam-3501	315	5	∑	∑	PUNCT
ejpam-3501	315	6	x∈s1	x∈s1	PROPN
ejpam-3501	315	7	|tx|+	|tx|+	PROPN
ejpam-3501	315	8	∑	∑	PROPN
ejpam-3501	315	9	x∈s2	x∈s2	PROPN
ejpam-3501	315	10	|tx|	|tx|	PROPN
ejpam-3501	315	11	≥	≥	NOUN
ejpam-3501	315	12	2|s1|+	2|s1|+	NUM
ejpam-3501	315	13	|s2|	|s2|	NOUN
ejpam-3501	315	14	=	=	SYM
ejpam-3501	315	15	2|s	2|s	PROPN
ejpam-3501	315	16	\n2	\n2	VERB
ejpam-3501	315	17	g(s)|+	g(s)|+	PROPN
ejpam-3501	315	18	|s	|s	PROPN
ejpam-3501	315	19	∩n2	∩n2	PROPN
ejpam-3501	315	20	g(s)|	g(s)|	PROPN
ejpam-3501	315	21	.	.	PUNCT
ejpam-3501	316	1	by	by	ADP
ejpam-3501	316	2	lemma	lemma	PROPN
ejpam-3501	316	3	3	3	NUM
ejpam-3501	316	4	,	,	PUNCT
ejpam-3501	316	5	γt2(g	γt2(g	NOUN
ejpam-3501	316	6	)	)	PUNCT
ejpam-3501	316	7	≤	≤	NUM
ejpam-3501	316	8	|c|	|c|	PROPN
ejpam-3501	316	9	.	.	PUNCT
ejpam-3501	317	1	since	since	SCONJ
ejpam-3501	317	2	c	c	PROPN
ejpam-3501	317	3	is	be	AUX
ejpam-3501	317	4	arbitrary	arbitrary	ADJ
ejpam-3501	317	5	,	,	PUNCT
ejpam-3501	317	6	γt2(g	γt2(g	NOUN
ejpam-3501	317	7	)	)	PUNCT
ejpam-3501	317	8	≤	≤	NOUN
ejpam-3501	317	9	γt2(g[h	γt2(g[h	NOUN
ejpam-3501	317	10	]	]	PUNCT
ejpam-3501	317	11	)	)	PUNCT
ejpam-3501	317	12	.	.	PUNCT
ejpam-3501	318	1	corollary	corollary	ADJ
ejpam-3501	318	2	9	9	NUM
ejpam-3501	318	3	.	.	PUNCT
ejpam-3501	319	1	let	let	VERB
ejpam-3501	319	2	g	g	NOUN
ejpam-3501	319	3	and	and	CCONJ
ejpam-3501	319	4	h	h	NOUN
ejpam-3501	319	5	be	be	AUX
ejpam-3501	319	6	nontrivial	nontrivial	ADJ
ejpam-3501	319	7	connected	connect	VERB
ejpam-3501	319	8	graphs	graph	NOUN
ejpam-3501	319	9	with	with	ADP
ejpam-3501	319	10	γ(h	γ(h	NOUN
ejpam-3501	319	11	)	)	PUNCT
ejpam-3501	319	12	=	=	SYM
ejpam-3501	319	13	2	2	NUM
ejpam-3501	319	14	,	,	PUNCT
ejpam-3501	319	15	and	and	CCONJ
ejpam-3501	319	16	let	let	VERB
ejpam-3501	319	17	c	c	NOUN
ejpam-3501	319	18	=	=	SYM
ejpam-3501	319	19	∪x∈s	∪x∈s	PROPN
ejpam-3501	319	20	(	(	PUNCT
ejpam-3501	319	21	{	{	PUNCT
ejpam-3501	319	22	x	x	NOUN
ejpam-3501	319	23	}	}	PUNCT
ejpam-3501	319	24	×	×	PROPN
ejpam-3501	319	25	tx	tx	PROPN
ejpam-3501	319	26	)	)	PUNCT
ejpam-3501	319	27	⊆	⊆	NUM
ejpam-3501	319	28	v	v	NOUN
ejpam-3501	319	29	(	(	PUNCT
ejpam-3501	319	30	g[h	g[h	PROPN
ejpam-3501	319	31	]	]	PUNCT
ejpam-3501	319	32	)	)	PUNCT
ejpam-3501	319	33	.	.	PUNCT
ejpam-3501	320	1	then	then	ADV
ejpam-3501	320	2	c	c	PROPN
ejpam-3501	320	3	is	be	AUX
ejpam-3501	320	4	a	a	DET
ejpam-3501	320	5	γt2	γt2	NOUN
ejpam-3501	320	6	-	-	PUNCT
ejpam-3501	320	7	set	set	NOUN
ejpam-3501	320	8	of	of	ADP
ejpam-3501	320	9	g[h	g[h	NOUN
ejpam-3501	320	10	]	]	PUNCT
ejpam-3501	320	11	if	if	SCONJ
ejpam-3501	320	12	and	and	CCONJ
ejpam-3501	320	13	only	only	ADV
ejpam-3501	320	14	if	if	SCONJ
ejpam-3501	320	15	one	one	NUM
ejpam-3501	320	16	of	of	ADP
ejpam-3501	320	17	the	the	DET
ejpam-3501	320	18	following	follow	VERB
ejpam-3501	320	19	holds	hold	VERB
ejpam-3501	320	20	:	:	PUNCT
ejpam-3501	320	21	(	(	PUNCT
ejpam-3501	320	22	i	i	NOUN
ejpam-3501	320	23	)	)	PUNCT
ejpam-3501	320	24	s	s	VERB
ejpam-3501	320	25	is	be	AUX
ejpam-3501	320	26	a	a	DET
ejpam-3501	320	27	γt	γt	NOUN
ejpam-3501	320	28	-	-	NOUN
ejpam-3501	320	29	set	set	NOUN
ejpam-3501	320	30	of	of	ADP
ejpam-3501	320	31	g	g	NOUN
ejpam-3501	320	32	and	and	CCONJ
ejpam-3501	320	33	|tx|	|tx|	NUM
ejpam-3501	320	34	=	=	SYM
ejpam-3501	320	35	1	1	NUM
ejpam-3501	320	36	for	for	ADP
ejpam-3501	320	37	each	each	DET
ejpam-3501	320	38	x	x	SYM
ejpam-3501	320	39	∈	∈	PROPN
ejpam-3501	320	40	s	s	PART
ejpam-3501	320	41	;	;	PUNCT
ejpam-3501	320	42	(	(	PUNCT
ejpam-3501	320	43	ii	ii	NOUN
ejpam-3501	320	44	)	)	PUNCT
ejpam-3501	320	45	s	s	VERB
ejpam-3501	320	46	is	be	AUX
ejpam-3501	320	47	a	a	DET
ejpam-3501	320	48	semitotal	semitotal	ADJ
ejpam-3501	320	49	dominating	dominating	NOUN
ejpam-3501	320	50	set	set	VERB
ejpam-3501	320	51	in	in	ADP
ejpam-3501	320	52	g	g	PROPN
ejpam-3501	320	53	such	such	ADJ
ejpam-3501	320	54	that	that	PRON
ejpam-3501	320	55	γt(g	γt(g	PUNCT
ejpam-3501	320	56	)	)	PUNCT
ejpam-3501	320	57	=	=	SYM
ejpam-3501	321	1	2|s	2|s	NUM
ejpam-3501	321	2	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3501	321	3	|s	|s	PROPN
ejpam-3501	321	4	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	321	5	.	.	PUNCT
ejpam-3501	321	6	further	far	ADV
ejpam-3501	321	7	,	,	PUNCT
ejpam-3501	321	8	|tx|	|tx|	NOUN
ejpam-3501	321	9	=	=	SYM
ejpam-3501	321	10	1	1	NUM
ejpam-3501	321	11	for	for	ADP
ejpam-3501	321	12	each	each	DET
ejpam-3501	321	13	x	x	SYM
ejpam-3501	321	14	∈	∈	PROPN
ejpam-3501	321	15	s	s	PART
ejpam-3501	321	16	∩	∩	NOUN
ejpam-3501	321	17	ng(s	ng(s	NUM
ejpam-3501	321	18	)	)	PUNCT
ejpam-3501	321	19	and	and	CCONJ
ejpam-3501	321	20	tx	tx	PROPN
ejpam-3501	321	21	is	be	AUX
ejpam-3501	321	22	a	a	DET
ejpam-3501	321	23	γ	γ	NOUN
ejpam-3501	321	24	-	-	PUNCT
ejpam-3501	321	25	set	set	NOUN
ejpam-3501	321	26	of	of	ADP
ejpam-3501	321	27	h	h	NOUN
ejpam-3501	321	28	for	for	ADP
ejpam-3501	321	29	each	each	DET
ejpam-3501	321	30	x	x	SYM
ejpam-3501	321	31	∈	∈	PROPN
ejpam-3501	321	32	s	s	PART
ejpam-3501	321	33	\ng(s	\ng(s	NOUN
ejpam-3501	321	34	)	)	PUNCT
ejpam-3501	321	35	;	;	PUNCT
ejpam-3501	321	36	(	(	PUNCT
ejpam-3501	321	37	iii	iii	X
ejpam-3501	321	38	)	)	PUNCT
ejpam-3501	321	39	s	s	VERB
ejpam-3501	321	40	is	be	AUX
ejpam-3501	321	41	a	a	DET
ejpam-3501	321	42	dominating	dominating	NOUN
ejpam-3501	321	43	set	set	VERB
ejpam-3501	321	44	in	in	ADP
ejpam-3501	321	45	g	g	PROPN
ejpam-3501	321	46	such	such	ADJ
ejpam-3501	321	47	that	that	PRON
ejpam-3501	321	48	γt(g	γt(g	PUNCT
ejpam-3501	321	49	)	)	PUNCT
ejpam-3501	321	50	=	=	SYM
ejpam-3501	322	1	2|s	2|s	NUM
ejpam-3501	322	2	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3501	322	3	|s	|s	PROPN
ejpam-3501	322	4	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	322	5	and	and	CCONJ
ejpam-3501	322	6	where	where	SCONJ
ejpam-3501	322	7	|tx|	|tx|	NOUN
ejpam-3501	322	8	=	=	SYM
ejpam-3501	322	9	1	1	NUM
ejpam-3501	322	10	for	for	ADP
ejpam-3501	322	11	each	each	DET
ejpam-3501	322	12	x	x	SYM
ejpam-3501	322	13	∈	∈	PROPN
ejpam-3501	322	14	s	s	PART
ejpam-3501	322	15	∩	∩	NOUN
ejpam-3501	322	16	ng(s	ng(s	NUM
ejpam-3501	322	17	)	)	PUNCT
ejpam-3501	322	18	,	,	PUNCT
ejpam-3501	322	19	tx	tx	PROPN
ejpam-3501	322	20	is	be	AUX
ejpam-3501	322	21	a	a	DET
ejpam-3501	322	22	γ	γ	NOUN
ejpam-3501	322	23	-	-	PUNCT
ejpam-3501	322	24	set	set	NOUN
ejpam-3501	322	25	of	of	ADP
ejpam-3501	322	26	h	h	NOUN
ejpam-3501	322	27	(	(	PUNCT
ejpam-3501	322	28	thus	thus	ADV
ejpam-3501	322	29	,	,	PUNCT
ejpam-3501	322	30	|tx|	|tx|	NOUN
ejpam-3501	322	31	=	=	SYM
ejpam-3501	322	32	2	2	NUM
ejpam-3501	322	33	)	)	PUNCT
ejpam-3501	322	34	for	for	ADP
ejpam-3501	322	35	each	each	DET
ejpam-3501	322	36	x	x	SYM
ejpam-3501	322	37	∈	∈	PROPN
ejpam-3501	322	38	s	s	PART
ejpam-3501	322	39	∩	∩	NOUN
ejpam-3501	322	40	(	(	PUNCT
ejpam-3501	322	41	n2	n2	ADJ
ejpam-3501	322	42	g(s	g(s	PROPN
ejpam-3501	322	43	)	)	PUNCT
ejpam-3501	322	44	\ng(s	\ng(s	NUM
ejpam-3501	322	45	)	)	PUNCT
ejpam-3501	322	46	)	)	PUNCT
ejpam-3501	322	47	,	,	PUNCT
ejpam-3501	322	48	and	and	CCONJ
ejpam-3501	322	49	|tx|	|tx|	X
ejpam-3501	322	50	=	=	SYM
ejpam-3501	322	51	2	2	NUM
ejpam-3501	322	52	for	for	ADP
ejpam-3501	322	53	each	each	DET
ejpam-3501	322	54	x	x	SYM
ejpam-3501	322	55	∈	∈	PROPN
ejpam-3501	322	56	s	s	PART
ejpam-3501	322	57	\n2	\n2	ADJ
ejpam-3501	322	58	g(s	g(	NOUN
ejpam-3501	322	59	)	)	PUNCT
ejpam-3501	322	60	.	.	PUNCT
ejpam-3501	323	1	proof	proof	NOUN
ejpam-3501	323	2	.	.	PUNCT
ejpam-3501	324	1	let	let	VERB
ejpam-3501	324	2	c	c	PRON
ejpam-3501	324	3	be	be	AUX
ejpam-3501	324	4	a	a	DET
ejpam-3501	324	5	γt2	γt2	NOUN
ejpam-3501	324	6	-	-	PUNCT
ejpam-3501	324	7	set	set	NOUN
ejpam-3501	324	8	of	of	ADP
ejpam-3501	324	9	g[h	g[h	NOUN
ejpam-3501	324	10	]	]	PUNCT
ejpam-3501	324	11	.	.	PUNCT
ejpam-3501	325	1	first	first	ADV
ejpam-3501	325	2	,	,	PUNCT
ejpam-3501	325	3	suppose	suppose	VERB
ejpam-3501	325	4	that	that	SCONJ
ejpam-3501	325	5	s	s	VERB
ejpam-3501	325	6	is	be	AUX
ejpam-3501	325	7	a	a	DET
ejpam-3501	325	8	total	total	ADJ
ejpam-3501	325	9	dominating	dominating	NOUN
ejpam-3501	325	10	set	set	VERB
ejpam-3501	325	11	in	in	ADP
ejpam-3501	325	12	g.	g.	PROPN
ejpam-3501	325	13	we	we	PRON
ejpam-3501	325	14	claim	claim	VERB
ejpam-3501	325	15	that	that	SCONJ
ejpam-3501	325	16	|tx|	|tx|	NOUN
ejpam-3501	325	17	=	=	SYM
ejpam-3501	325	18	1	1	NUM
ejpam-3501	325	19	for	for	ADP
ejpam-3501	325	20	each	each	PRON
ejpam-3501	325	21	x	x	SYM
ejpam-3501	325	22	∈	∈	PROPN
ejpam-3501	325	23	s.	s.	PROPN
ejpam-3501	325	24	suppose	suppose	VERB
ejpam-3501	325	25	that	that	SCONJ
ejpam-3501	325	26	|tx|	|tx|	PROPN
ejpam-3501	325	27	≥	≥	NUM
ejpam-3501	325	28	2	2	NUM
ejpam-3501	325	29	for	for	ADP
ejpam-3501	325	30	some	some	DET
ejpam-3501	325	31	x	x	SYM
ejpam-3501	325	32	∈	∈	PROPN
ejpam-3501	325	33	s.	s.	PROPN
ejpam-3501	325	34	let	let	VERB
ejpam-3501	325	35	i.	i.	PROPN
ejpam-3501	325	36	s.	s.	PROPN
ejpam-3501	325	37	aniversario	aniversario	PROPN
ejpam-3501	325	38	,	,	PUNCT
ejpam-3501	325	39	s.	s.	PROPN
ejpam-3501	325	40	r.	r.	PROPN
ejpam-3501	325	41	jr	jr	PROPN
ejpam-3501	325	42	.	.	PROPN
ejpam-3501	325	43	canoy	canoy	PROPN
ejpam-3501	325	44	,	,	PUNCT
ejpam-3501	325	45	f.p	f.p	PROPN
ejpam-3501	325	46	.	.	PROPN
ejpam-3501	325	47	jamil	jamil	PROPN
ejpam-3501	325	48	/	/	SYM
ejpam-3501	325	49	eur	eur	PROPN
ejpam-3501	325	50	.	.	PUNCT
ejpam-3501	326	1	j.	j.	PROPN
ejpam-3501	326	2	pure	pure	PROPN
ejpam-3501	326	3	appl	appl	PROPN
ejpam-3501	326	4	.	.	PROPN
ejpam-3501	326	5	math	math	PROPN
ejpam-3501	326	6	,	,	PUNCT
ejpam-3501	326	7	12	12	NUM
ejpam-3501	326	8	(	(	PUNCT
ejpam-3501	326	9	4	4	NUM
ejpam-3501	326	10	)	)	PUNCT
ejpam-3501	326	11	(	(	PUNCT
ejpam-3501	326	12	2019	2019	NUM
ejpam-3501	326	13	)	)	PUNCT
ejpam-3501	326	14	,	,	PUNCT
ejpam-3501	326	15	1410	1410	NUM
ejpam-3501	326	16	-	-	SYM
ejpam-3501	326	17	1425	1425	NUM
ejpam-3501	326	18	1421	1421	NUM
ejpam-3501	326	19	c∗	c∗	NOUN
ejpam-3501	326	20	=	=	SYM
ejpam-3501	326	21	s	s	PART
ejpam-3501	326	22	×	×	NOUN
ejpam-3501	326	23	{	{	PUNCT
ejpam-3501	326	24	v	v	NOUN
ejpam-3501	326	25	}	}	PUNCT
ejpam-3501	326	26	=	=	SYM
ejpam-3501	326	27	∪x∈s	∪x∈s	PROPN
ejpam-3501	326	28	(	(	PUNCT
ejpam-3501	326	29	{	{	PUNCT
ejpam-3501	326	30	x	x	NOUN
ejpam-3501	326	31	}	}	PUNCT
ejpam-3501	326	32	×	×	PROPN
ejpam-3501	326	33	{	{	PUNCT
ejpam-3501	326	34	v	v	NOUN
ejpam-3501	326	35	}	}	PUNCT
ejpam-3501	326	36	)	)	PUNCT
ejpam-3501	326	37	,	,	PUNCT
ejpam-3501	326	38	where	where	SCONJ
ejpam-3501	326	39	v	v	X
ejpam-3501	326	40	∈	∈	PROPN
ejpam-3501	326	41	v	v	NOUN
ejpam-3501	326	42	(	(	PUNCT
ejpam-3501	326	43	h	h	NOUN
ejpam-3501	326	44	)	)	PUNCT
ejpam-3501	326	45	.	.	PUNCT
ejpam-3501	327	1	then	then	ADV
ejpam-3501	327	2	c∗	c∗	PROPN
ejpam-3501	327	3	is	be	AUX
ejpam-3501	327	4	a	a	DET
ejpam-3501	327	5	semitotal	semitotal	ADJ
ejpam-3501	327	6	dominating	dominating	NOUN
ejpam-3501	327	7	set	set	VERB
ejpam-3501	327	8	in	in	ADP
ejpam-3501	327	9	g[h	g[h	PROPN
ejpam-3501	327	10	]	]	PUNCT
ejpam-3501	327	11	by	by	ADP
ejpam-3501	327	12	theorem	theorem	NOUN
ejpam-3501	327	13	6	6	NUM
ejpam-3501	327	14	,	,	PUNCT
ejpam-3501	327	15	and	and	CCONJ
ejpam-3501	327	16	|c∗|	|c∗|	VERB
ejpam-3501	327	17	=	=	NOUN
ejpam-3501	327	18	|s|	|s|	PROPN
ejpam-3501	327	19	<	<	X
ejpam-3501	327	20	|c|	|c|	PROPN
ejpam-3501	327	21	,	,	PUNCT
ejpam-3501	327	22	which	which	PRON
ejpam-3501	327	23	is	be	AUX
ejpam-3501	327	24	impossible	impossible	ADJ
ejpam-3501	327	25	since	since	SCONJ
ejpam-3501	327	26	c	c	PROPN
ejpam-3501	327	27	is	be	AUX
ejpam-3501	327	28	a	a	DET
ejpam-3501	327	29	γt2	γt2	NOUN
ejpam-3501	327	30	-	-	PUNCT
ejpam-3501	327	31	set	set	NOUN
ejpam-3501	327	32	.	.	PUNCT
ejpam-3501	328	1	necessarily	necessarily	ADV
ejpam-3501	328	2	,	,	PUNCT
ejpam-3501	328	3	s	s	VERB
ejpam-3501	328	4	is	be	AUX
ejpam-3501	328	5	a	a	DET
ejpam-3501	328	6	γt	γt	NOUN
ejpam-3501	328	7	-	-	NOUN
ejpam-3501	328	8	set	set	NOUN
ejpam-3501	328	9	of	of	ADP
ejpam-3501	328	10	g.	g.	PROPN
ejpam-3501	328	11	in	in	ADP
ejpam-3501	328	12	this	this	DET
ejpam-3501	328	13	case	case	NOUN
ejpam-3501	328	14	,	,	PUNCT
ejpam-3501	328	15	(	(	PUNCT
ejpam-3501	328	16	i	i	NOUN
ejpam-3501	328	17	)	)	PUNCT
ejpam-3501	328	18	holds	hold	VERB
ejpam-3501	328	19	.	.	PUNCT
ejpam-3501	329	1	next	next	ADV
ejpam-3501	329	2	,	,	PUNCT
ejpam-3501	329	3	suppose	suppose	VERB
ejpam-3501	329	4	that	that	SCONJ
ejpam-3501	329	5	s	s	VERB
ejpam-3501	329	6	is	be	AUX
ejpam-3501	329	7	a	a	DET
ejpam-3501	329	8	semitotal	semitotal	ADJ
ejpam-3501	329	9	dominating	dominating	NOUN
ejpam-3501	329	10	set	set	NOUN
ejpam-3501	329	11	in	in	ADP
ejpam-3501	329	12	g	g	PROPN
ejpam-3501	329	13	and	and	CCONJ
ejpam-3501	329	14	tx	tx	PROPN
ejpam-3501	329	15	is	be	AUX
ejpam-3501	329	16	a	a	DET
ejpam-3501	329	17	dominating	dominating	NOUN
ejpam-3501	329	18	set	set	NOUN
ejpam-3501	329	19	for	for	ADP
ejpam-3501	329	20	each	each	DET
ejpam-3501	329	21	x	x	PUNCT
ejpam-3501	329	22	∈	∈	PROPN
ejpam-3501	329	23	s	s	PART
ejpam-3501	329	24	\ng(s	\ng(s	NOUN
ejpam-3501	329	25	)	)	PUNCT
ejpam-3501	329	26	.	.	PUNCT
ejpam-3501	330	1	invoking	invoke	VERB
ejpam-3501	330	2	lemma	lemma	PROPN
ejpam-3501	330	3	2	2	NUM
ejpam-3501	330	4	,	,	PUNCT
ejpam-3501	330	5	|c|	|c|	PROPN
ejpam-3501	330	6	=	=	SYM
ejpam-3501	330	7	∑	∑	NOUN
ejpam-3501	330	8	x∈s∩ng(s	x∈s∩ng(s	NOUN
ejpam-3501	330	9	)	)	PUNCT
ejpam-3501	330	10	|tx|+	|tx|+	X
ejpam-3501	330	11	∑	∑	PUNCT
ejpam-3501	330	12	x∈s\ng(s	x∈s\ng(s	NUM
ejpam-3501	330	13	)	)	PUNCT
ejpam-3501	330	14	|tx|	|tx|	PROPN
ejpam-3501	330	15	≥	≥	NUM
ejpam-3501	330	16	2|s	2|s	NUM
ejpam-3501	330	17	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3501	330	18	|s	|s	PROPN
ejpam-3501	330	19	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	330	20	≥	≥	NOUN
ejpam-3501	330	21	γt(g	γt(g	NUM
ejpam-3501	330	22	)	)	PUNCT
ejpam-3501	330	23	.	.	PUNCT
ejpam-3501	331	1	suppose	suppose	VERB
ejpam-3501	331	2	that	that	SCONJ
ejpam-3501	331	3	γt(g	γt(g	PUNCT
ejpam-3501	331	4	)	)	PUNCT
ejpam-3501	331	5	<	<	X
ejpam-3501	331	6	2|s	2|s	NUM
ejpam-3501	331	7	\	\	NOUN
ejpam-3501	331	8	ng(s)|	ng(s)|	PUNCT
ejpam-3501	332	1	+	+	NUM
ejpam-3501	332	2	|s	|s	PROPN
ejpam-3501	332	3	∩	∩	NOUN
ejpam-3501	332	4	ng(s)|	ng(s)|	X
ejpam-3501	332	5	.	.	PUNCT
ejpam-3501	332	6	take	take	VERB
ejpam-3501	332	7	a	a	DET
ejpam-3501	332	8	γt	γt	NOUN
ejpam-3501	332	9	-	-	ADJ
ejpam-3501	332	10	set	set	ADJ
ejpam-3501	332	11	s∗	s∗	PROPN
ejpam-3501	332	12	⊆	⊆	NUM
ejpam-3501	332	13	v	v	NOUN
ejpam-3501	332	14	(	(	PUNCT
ejpam-3501	332	15	g	g	NOUN
ejpam-3501	332	16	)	)	PUNCT
ejpam-3501	332	17	of	of	ADP
ejpam-3501	332	18	g	g	NOUN
ejpam-3501	332	19	,	,	PUNCT
ejpam-3501	332	20	and	and	CCONJ
ejpam-3501	332	21	let	let	VERB
ejpam-3501	332	22	u	u	PRON
ejpam-3501	332	23	∈	∈	PROPN
ejpam-3501	332	24	v	v	ADP
ejpam-3501	332	25	(	(	PUNCT
ejpam-3501	332	26	h	h	NOUN
ejpam-3501	332	27	)	)	PUNCT
ejpam-3501	332	28	.	.	PUNCT
ejpam-3501	333	1	then	then	ADV
ejpam-3501	333	2	c∗	c∗	PROPN
ejpam-3501	333	3	=	=	PUNCT
ejpam-3501	333	4	s∗	s∗	PROPN
ejpam-3501	333	5	×	×	NOUN
ejpam-3501	333	6	{	{	PUNCT
ejpam-3501	333	7	u	u	NOUN
ejpam-3501	333	8	}	}	PUNCT
ejpam-3501	333	9	is	be	AUX
ejpam-3501	333	10	a	a	DET
ejpam-3501	333	11	semitotal	semitotal	ADJ
ejpam-3501	333	12	dominating	dominating	NOUN
ejpam-3501	333	13	set	set	VERB
ejpam-3501	333	14	in	in	ADP
ejpam-3501	333	15	g[h	g[h	PROPN
ejpam-3501	333	16	]	]	PUNCT
ejpam-3501	333	17	with	with	ADP
ejpam-3501	333	18	|c∗|	|c∗|	PROPN
ejpam-3501	333	19	=	=	SYM
ejpam-3501	333	20	γt(g	γt(g	X
ejpam-3501	333	21	)	)	PUNCT
ejpam-3501	333	22	<	<	X
ejpam-3501	333	23	|c|	|c|	PROPN
ejpam-3501	333	24	,	,	PUNCT
ejpam-3501	333	25	a	a	DET
ejpam-3501	333	26	contradiction	contradiction	NOUN
ejpam-3501	333	27	.	.	PUNCT
ejpam-3501	334	1	thus	thus	ADV
ejpam-3501	334	2	γt(g	γt(g	PUNCT
ejpam-3501	334	3	)	)	PUNCT
ejpam-3501	334	4	=	=	SYM
ejpam-3501	334	5	2|s	2|s	NUM
ejpam-3501	334	6	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3501	334	7	|s	|s	PROPN
ejpam-3501	334	8	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	334	9	.	.	PROPN
ejpam-3501	334	10	suppose	suppose	VERB
ejpam-3501	334	11	that	that	SCONJ
ejpam-3501	334	12	|tx|	|tx|	PROPN
ejpam-3501	334	13	≥	≥	NUM
ejpam-3501	334	14	2	2	NUM
ejpam-3501	334	15	for	for	ADP
ejpam-3501	334	16	some	some	DET
ejpam-3501	334	17	x	x	SYM
ejpam-3501	334	18	∈	∈	NOUN
ejpam-3501	334	19	s	s	NOUN
ejpam-3501	334	20	∩ng(s	∩ng(s	NOUN
ejpam-3501	334	21	)	)	PUNCT
ejpam-3501	334	22	or	or	CCONJ
ejpam-3501	334	23	|tx|	|tx|	PROPN
ejpam-3501	334	24	≥	≥	NUM
ejpam-3501	334	25	3	3	NUM
ejpam-3501	334	26	for	for	ADP
ejpam-3501	334	27	some	some	DET
ejpam-3501	334	28	x	x	SYM
ejpam-3501	334	29	∈	∈	NOUN
ejpam-3501	334	30	s	s	PART
ejpam-3501	334	31	\ng(s	\ng(s	NOUN
ejpam-3501	334	32	)	)	PUNCT
ejpam-3501	334	33	.	.	PUNCT
ejpam-3501	335	1	let	let	VERB
ejpam-3501	335	2	{	{	PUNCT
ejpam-3501	335	3	u	u	NOUN
ejpam-3501	335	4	,	,	PUNCT
ejpam-3501	335	5	v	v	NOUN
ejpam-3501	335	6	}	}	PUNCT
ejpam-3501	335	7	be	be	AUX
ejpam-3501	335	8	a	a	DET
ejpam-3501	335	9	γ	γ	NOUN
ejpam-3501	335	10	-	-	PUNCT
ejpam-3501	335	11	set	set	NOUN
ejpam-3501	335	12	of	of	ADP
ejpam-3501	335	13	h.	h.	PROPN
ejpam-3501	335	14	by	by	ADP
ejpam-3501	335	15	theorem	theorem	ADJ
ejpam-3501	335	16	6	6	NUM
ejpam-3501	335	17	,	,	PUNCT
ejpam-3501	335	18	c∗	c∗	NOUN
ejpam-3501	335	19	=	=	SYM
ejpam-3501	335	20	(	(	PUNCT
ejpam-3501	335	21	(	(	PUNCT
ejpam-3501	335	22	s	s	X
ejpam-3501	335	23	\ng(s))×	\ng(s))×	X
ejpam-3501	335	24	{	{	PUNCT
ejpam-3501	335	25	u	u	NOUN
ejpam-3501	335	26	,	,	PUNCT
ejpam-3501	335	27	v})∪((s	v})∪((	VERB
ejpam-3501	335	28	∩ng(s))×	∩ng(s))×	PUNCT
ejpam-3501	336	1	{	{	PUNCT
ejpam-3501	336	2	u	u	NOUN
ejpam-3501	336	3	}	}	PUNCT
ejpam-3501	336	4	)	)	PUNCT
ejpam-3501	336	5	is	be	AUX
ejpam-3501	336	6	a	a	DET
ejpam-3501	336	7	semitotal	semitotal	ADJ
ejpam-3501	336	8	dominating	dominating	NOUN
ejpam-3501	336	9	set	set	VERB
ejpam-3501	336	10	in	in	ADP
ejpam-3501	336	11	g[h	g[h	PROPN
ejpam-3501	336	12	]	]	PUNCT
ejpam-3501	336	13	.	.	PUNCT
ejpam-3501	337	1	moreover	moreover	ADV
ejpam-3501	337	2	,	,	PUNCT
ejpam-3501	337	3	|c∗|	|c∗|	PUNCT
ejpam-3501	337	4	=	=	SYM
ejpam-3501	337	5	2|s	2|s	NUM
ejpam-3501	337	6	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3501	337	7	|s	|s	PROPN
ejpam-3501	337	8	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	337	9	<	<	X
ejpam-3501	337	10	∑	∑	NOUN
ejpam-3501	337	11	x∈s\ng(s	x∈s\ng(s	NUM
ejpam-3501	337	12	)	)	PUNCT
ejpam-3501	337	13	|tx|+	|tx|+	NOUN
ejpam-3501	337	14	∑	∑	PUNCT
ejpam-3501	337	15	x∈s∩ng(s	x∈s∩ng(s	NUM
ejpam-3501	337	16	)	)	PUNCT
ejpam-3501	337	17	|tx|	|tx|	NOUN
ejpam-3501	337	18	=	=	SYM
ejpam-3501	337	19	|c|	|c|	PROPN
ejpam-3501	337	20	,	,	PUNCT
ejpam-3501	337	21	a	a	DET
ejpam-3501	337	22	contradiction	contradiction	NOUN
ejpam-3501	337	23	.	.	PUNCT
ejpam-3501	338	1	thus	thus	ADV
ejpam-3501	338	2	,	,	PUNCT
ejpam-3501	338	3	|tx|	|tx|	X
ejpam-3501	338	4	=	=	SYM
ejpam-3501	338	5	1	1	NUM
ejpam-3501	338	6	for	for	ADP
ejpam-3501	338	7	all	all	DET
ejpam-3501	338	8	x	x	SYM
ejpam-3501	338	9	∈	∈	NOUN
ejpam-3501	338	10	s	s	NOUN
ejpam-3501	338	11	∩ng(s	∩ng(s	NOUN
ejpam-3501	338	12	)	)	PUNCT
ejpam-3501	338	13	and	and	CCONJ
ejpam-3501	338	14	|tx|	|tx|	NUM
ejpam-3501	338	15	=	=	SYM
ejpam-3501	338	16	2	2	NUM
ejpam-3501	338	17	,	,	PUNCT
ejpam-3501	338	18	hence	hence	ADV
ejpam-3501	338	19	tx	tx	PROPN
ejpam-3501	338	20	is	be	AUX
ejpam-3501	338	21	a	a	DET
ejpam-3501	338	22	γ	γ	NOUN
ejpam-3501	338	23	-	-	PUNCT
ejpam-3501	338	24	set	set	NOUN
ejpam-3501	338	25	of	of	ADP
ejpam-3501	338	26	h	h	NOUN
ejpam-3501	338	27	,	,	PUNCT
ejpam-3501	338	28	for	for	ADP
ejpam-3501	338	29	all	all	DET
ejpam-3501	338	30	x	x	PART
ejpam-3501	338	31	∈	∈	NOUN
ejpam-3501	338	32	s	s	PART
ejpam-3501	338	33	\ng(s	\ng(s	NOUN
ejpam-3501	338	34	)	)	PUNCT
ejpam-3501	338	35	.	.	PUNCT
ejpam-3501	339	1	in	in	ADP
ejpam-3501	339	2	this	this	DET
ejpam-3501	339	3	case	case	NOUN
ejpam-3501	339	4	,	,	PUNCT
ejpam-3501	339	5	(	(	PUNCT
ejpam-3501	339	6	ii	ii	NOUN
ejpam-3501	339	7	)	)	PUNCT
ejpam-3501	339	8	holds	hold	VERB
ejpam-3501	339	9	.	.	PUNCT
ejpam-3501	340	1	now	now	ADV
ejpam-3501	340	2	,	,	PUNCT
ejpam-3501	340	3	suppose	suppose	VERB
ejpam-3501	340	4	that	that	SCONJ
ejpam-3501	340	5	s	s	VERB
ejpam-3501	340	6	is	be	AUX
ejpam-3501	340	7	not	not	PART
ejpam-3501	340	8	a	a	DET
ejpam-3501	340	9	semitotal	semitotal	ADJ
ejpam-3501	340	10	dominating	dominating	NOUN
ejpam-3501	340	11	set	set	VERB
ejpam-3501	340	12	in	in	ADP
ejpam-3501	340	13	g.	g.	PROPN
ejpam-3501	340	14	by	by	ADP
ejpam-3501	340	15	theorem	theorem	NOUN
ejpam-3501	340	16	6	6	NUM
ejpam-3501	340	17	,	,	PUNCT
ejpam-3501	340	18	s	s	VERB
ejpam-3501	340	19	is	be	AUX
ejpam-3501	340	20	a	a	DET
ejpam-3501	340	21	dominating	dominating	NOUN
ejpam-3501	340	22	set	set	VERB
ejpam-3501	340	23	in	in	ADP
ejpam-3501	340	24	g	g	PROPN
ejpam-3501	340	25	such	such	ADJ
ejpam-3501	340	26	that	that	SCONJ
ejpam-3501	340	27	tx	tx	PROPN
ejpam-3501	340	28	is	be	AUX
ejpam-3501	340	29	a	a	DET
ejpam-3501	340	30	dominating	dominating	NOUN
ejpam-3501	340	31	set	set	VERB
ejpam-3501	340	32	in	in	ADP
ejpam-3501	340	33	h	h	NOUN
ejpam-3501	340	34	for	for	ADP
ejpam-3501	340	35	each	each	DET
ejpam-3501	340	36	x	x	SYM
ejpam-3501	340	37	∈	∈	PROPN
ejpam-3501	340	38	s	s	PART
ejpam-3501	340	39	\	\	NOUN
ejpam-3501	340	40	ng(s	ng(s	NUM
ejpam-3501	340	41	)	)	PUNCT
ejpam-3501	340	42	,	,	PUNCT
ejpam-3501	340	43	and	and	CCONJ
ejpam-3501	340	44	|tx|	|tx|	NOUN
ejpam-3501	340	45	≥	≥	NUM
ejpam-3501	340	46	2	2	NUM
ejpam-3501	340	47	for	for	ADP
ejpam-3501	340	48	each	each	DET
ejpam-3501	340	49	x	x	SYM
ejpam-3501	340	50	∈	∈	PROPN
ejpam-3501	340	51	s	s	PART
ejpam-3501	340	52	\n2	\n2	ADJ
ejpam-3501	340	53	g(s	g(	NOUN
ejpam-3501	340	54	)	)	PUNCT
ejpam-3501	340	55	.	.	PUNCT
ejpam-3501	341	1	invoking	invoke	VERB
ejpam-3501	341	2	lemma	lemma	PROPN
ejpam-3501	341	3	2	2	NUM
ejpam-3501	341	4	and	and	CCONJ
ejpam-3501	341	5	the	the	DET
ejpam-3501	341	6	assumptions	assumption	NOUN
ejpam-3501	341	7	that	that	SCONJ
ejpam-3501	341	8	γ(h	γ(h	NOUN
ejpam-3501	341	9	)	)	PUNCT
ejpam-3501	341	10	=	=	SYM
ejpam-3501	341	11	2	2	NUM
ejpam-3501	341	12	,	,	PUNCT
ejpam-3501	341	13	|c|	|c|	PROPN
ejpam-3501	341	14	=	=	PUNCT
ejpam-3501	341	15	∑	∑	ADV
ejpam-3501	341	16	x∈s\n2	x∈s\n2	ADJ
ejpam-3501	341	17	g(s	g(	NOUN
ejpam-3501	341	18	)	)	PUNCT
ejpam-3501	341	19	|tx|+	|tx|+	PUNCT
ejpam-3501	341	20	∑	∑	PROPN
ejpam-3501	341	21	x∈s∩(n2	x∈s∩(n2	X
ejpam-3501	341	22	g(s)\ng(s	g(s)\ng(s	NOUN
ejpam-3501	341	23	)	)	PUNCT
ejpam-3501	341	24	)	)	PUNCT
ejpam-3501	341	25	|tx|+	|tx|+	VERB
ejpam-3501	341	26	∑	∑	PROPN
ejpam-3501	341	27	x∈s∩ng(s	x∈s∩ng(s	NUM
ejpam-3501	341	28	)	)	PUNCT
ejpam-3501	342	1	|tx|	|tx|	PROPN
ejpam-3501	342	2	≥	≥	NUM
ejpam-3501	342	3	2|s	2|s	NUM
ejpam-3501	342	4	\n2	\n2	ADP
ejpam-3501	342	5	g(s)|+	g(s)|+	PROPN
ejpam-3501	342	6	2|s	2|s	PROPN
ejpam-3501	342	7	∩	∩	NOUN
ejpam-3501	342	8	(	(	PUNCT
ejpam-3501	342	9	n2	n2	ADJ
ejpam-3501	342	10	g(s	g(s	PROPN
ejpam-3501	342	11	)	)	PUNCT
ejpam-3501	342	12	\ng(s	\ng(s	NUM
ejpam-3501	342	13	)	)	PUNCT
ejpam-3501	342	14	)	)	PUNCT
ejpam-3501	342	15	|+	|+	NOUN
ejpam-3501	342	16	|s	|s	PROPN
ejpam-3501	342	17	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	342	18	=	=	SYM
ejpam-3501	342	19	2|s	2|s	NUM
ejpam-3501	342	20	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3501	342	21	|s	|s	PROPN
ejpam-3501	342	22	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	342	23	≥	≥	NOUN
ejpam-3501	342	24	γt(g	γt(g	NUM
ejpam-3501	342	25	)	)	PUNCT
ejpam-3501	342	26	.	.	PUNCT
ejpam-3501	343	1	as	as	SCONJ
ejpam-3501	343	2	done	do	VERB
ejpam-3501	343	3	previously	previously	ADV
ejpam-3501	343	4	,	,	PUNCT
ejpam-3501	343	5	γt(g	γt(g	PUNCT
ejpam-3501	343	6	)	)	PUNCT
ejpam-3501	343	7	=	=	SYM
ejpam-3501	343	8	2|s	2|s	NUM
ejpam-3501	343	9	\	\	NOUN
ejpam-3501	343	10	ng(s)|	ng(s)|	X
ejpam-3501	343	11	+	+	NUM
ejpam-3501	343	12	|s	|s	PROPN
ejpam-3501	343	13	∩	∩	NOUN
ejpam-3501	343	14	ng(s)|	ng(s)|	X
ejpam-3501	343	15	.	.	PUNCT
ejpam-3501	343	16	suppose	suppose	VERB
ejpam-3501	343	17	that	that	SCONJ
ejpam-3501	343	18	|tx|	|tx|	PROPN
ejpam-3501	343	19	≥	≥	NUM
ejpam-3501	343	20	2	2	NUM
ejpam-3501	343	21	for	for	ADP
ejpam-3501	343	22	some	some	DET
ejpam-3501	343	23	x	x	SYM
ejpam-3501	343	24	∈	∈	PROPN
ejpam-3501	343	25	s	s	PART
ejpam-3501	343	26	∩	∩	NOUN
ejpam-3501	343	27	ng(s	ng(s	NUM
ejpam-3501	343	28	)	)	PUNCT
ejpam-3501	343	29	,	,	PUNCT
ejpam-3501	343	30	|tx|	|tx|	NOUN
ejpam-3501	343	31	>	>	X
ejpam-3501	343	32	2	2	NUM
ejpam-3501	343	33	for	for	ADP
ejpam-3501	343	34	some	some	DET
ejpam-3501	343	35	x	x	SYM
ejpam-3501	343	36	∈	∈	PROPN
ejpam-3501	343	37	s	s	PART
ejpam-3501	343	38	∩	∩	NOUN
ejpam-3501	343	39	(	(	PUNCT
ejpam-3501	343	40	n2	n2	ADJ
ejpam-3501	343	41	g(s	g(s	PROPN
ejpam-3501	343	42	)	)	PUNCT
ejpam-3501	343	43	\ng(s	\ng(s	NUM
ejpam-3501	343	44	)	)	PUNCT
ejpam-3501	343	45	)	)	PUNCT
ejpam-3501	343	46	,	,	PUNCT
ejpam-3501	343	47	or	or	CCONJ
ejpam-3501	343	48	|tx|	|tx|	NOUN
ejpam-3501	343	49	>	>	X
ejpam-3501	343	50	2	2	NUM
ejpam-3501	343	51	for	for	ADP
ejpam-3501	343	52	some	some	DET
ejpam-3501	343	53	x	x	SYM
ejpam-3501	343	54	∈	∈	PROPN
ejpam-3501	343	55	s	s	PART
ejpam-3501	343	56	\n2	\n2	ADJ
ejpam-3501	343	57	g(s	g(	NOUN
ejpam-3501	343	58	)	)	PUNCT
ejpam-3501	343	59	.	.	PUNCT
ejpam-3501	344	1	let	let	VERB
ejpam-3501	344	2	t	t	NOUN
ejpam-3501	344	3	=	=	SYM
ejpam-3501	344	4	{	{	PUNCT
ejpam-3501	344	5	u	u	NOUN
ejpam-3501	344	6	,	,	PUNCT
ejpam-3501	344	7	v	v	NOUN
ejpam-3501	344	8	}	}	PUNCT
ejpam-3501	344	9	⊆	⊆	NUM
ejpam-3501	344	10	v	v	NOUN
ejpam-3501	344	11	(	(	PUNCT
ejpam-3501	344	12	h	h	NOUN
ejpam-3501	344	13	)	)	PUNCT
ejpam-3501	344	14	be	be	AUX
ejpam-3501	344	15	a	a	DET
ejpam-3501	344	16	γ	γ	NOUN
ejpam-3501	344	17	-	-	PUNCT
ejpam-3501	344	18	set	set	NOUN
ejpam-3501	344	19	of	of	ADP
ejpam-3501	344	20	h	h	NOUN
ejpam-3501	344	21	,	,	PUNCT
ejpam-3501	344	22	and	and	CCONJ
ejpam-3501	344	23	put	put	VERB
ejpam-3501	344	24	c∗	c∗	NOUN
ejpam-3501	344	25	=	=	SYM
ejpam-3501	344	26	(	(	PUNCT
ejpam-3501	344	27	(	(	PUNCT
ejpam-3501	344	28	s	s	X
ejpam-3501	344	29	\ng(s))×	\ng(s))×	PROPN
ejpam-3501	344	30	t	t	NOUN
ejpam-3501	344	31	)	)	PUNCT
ejpam-3501	344	32	∪	∪	X
ejpam-3501	344	33	(	(	PUNCT
ejpam-3501	344	34	(	(	PUNCT
ejpam-3501	344	35	s	s	X
ejpam-3501	344	36	∩ng(s))×	∩ng(s))×	X
ejpam-3501	344	37	{	{	PUNCT
ejpam-3501	344	38	u	u	NOUN
ejpam-3501	344	39	}	}	PUNCT
ejpam-3501	344	40	)	)	PUNCT
ejpam-3501	344	41	.	.	PUNCT
ejpam-3501	345	1	then	then	ADV
ejpam-3501	345	2	c∗	c∗	PROPN
ejpam-3501	345	3	is	be	AUX
ejpam-3501	345	4	a	a	DET
ejpam-3501	345	5	semitotal	semitotal	ADJ
ejpam-3501	345	6	dominating	dominating	NOUN
ejpam-3501	345	7	set	set	VERB
ejpam-3501	345	8	in	in	ADP
ejpam-3501	345	9	g[h	g[h	PROPN
ejpam-3501	345	10	]	]	PUNCT
ejpam-3501	345	11	by	by	ADP
ejpam-3501	345	12	theorem	theorem	NOUN
ejpam-3501	345	13	6	6	NUM
ejpam-3501	345	14	.	.	PUNCT
ejpam-3501	346	1	however	however	ADV
ejpam-3501	346	2	,	,	PUNCT
ejpam-3501	346	3	|c|	|c|	PROPN
ejpam-3501	346	4	>	>	SYM
ejpam-3501	346	5	|c∗|	|c∗|	PROPN
ejpam-3501	346	6	=	=	SYM
ejpam-3501	346	7	2|s	2|s	NUM
ejpam-3501	346	8	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3501	346	9	|s	|s	PROPN
ejpam-3501	346	10	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	346	11	=	=	PUNCT
ejpam-3501	346	12	γt(g	γt(g	NUM
ejpam-3501	346	13	)	)	PUNCT
ejpam-3501	346	14	,	,	PUNCT
ejpam-3501	346	15	i.	i.	PROPN
ejpam-3501	346	16	s.	s.	PROPN
ejpam-3501	346	17	aniversario	aniversario	PROPN
ejpam-3501	346	18	,	,	PUNCT
ejpam-3501	346	19	s.	s.	PROPN
ejpam-3501	346	20	r.	r.	PROPN
ejpam-3501	346	21	jr	jr	PROPN
ejpam-3501	346	22	.	.	PROPN
ejpam-3501	346	23	canoy	canoy	PROPN
ejpam-3501	346	24	,	,	PUNCT
ejpam-3501	346	25	f.p	f.p	PROPN
ejpam-3501	346	26	.	.	PROPN
ejpam-3501	346	27	jamil	jamil	PROPN
ejpam-3501	346	28	/	/	SYM
ejpam-3501	346	29	eur	eur	PROPN
ejpam-3501	346	30	.	.	PUNCT
ejpam-3501	347	1	j.	j.	PROPN
ejpam-3501	347	2	pure	pure	PROPN
ejpam-3501	347	3	appl	appl	PROPN
ejpam-3501	347	4	.	.	PROPN
ejpam-3501	347	5	math	math	PROPN
ejpam-3501	347	6	,	,	PUNCT
ejpam-3501	347	7	12	12	NUM
ejpam-3501	347	8	(	(	PUNCT
ejpam-3501	347	9	4	4	NUM
ejpam-3501	347	10	)	)	PUNCT
ejpam-3501	347	11	(	(	PUNCT
ejpam-3501	347	12	2019	2019	NUM
ejpam-3501	347	13	)	)	PUNCT
ejpam-3501	347	14	,	,	PUNCT
ejpam-3501	347	15	1410	1410	NUM
ejpam-3501	347	16	-	-	SYM
ejpam-3501	347	17	1425	1425	NUM
ejpam-3501	347	18	1422	1422	NUM
ejpam-3501	347	19	a	a	DET
ejpam-3501	347	20	contradiction	contradiction	NOUN
ejpam-3501	347	21	.	.	PUNCT
ejpam-3501	348	1	in	in	ADP
ejpam-3501	348	2	this	this	DET
ejpam-3501	348	3	case	case	NOUN
ejpam-3501	348	4	,	,	PUNCT
ejpam-3501	348	5	(	(	PUNCT
ejpam-3501	348	6	iii	iii	NOUN
ejpam-3501	348	7	)	)	PUNCT
ejpam-3501	348	8	holds	hold	VERB
ejpam-3501	348	9	.	.	PUNCT
ejpam-3501	349	1	to	to	PART
ejpam-3501	349	2	prove	prove	VERB
ejpam-3501	349	3	the	the	DET
ejpam-3501	349	4	converse	converse	NOUN
ejpam-3501	349	5	,	,	PUNCT
ejpam-3501	349	6	we	we	PRON
ejpam-3501	349	7	only	only	ADV
ejpam-3501	349	8	show	show	VERB
ejpam-3501	349	9	the	the	DET
ejpam-3501	349	10	case	case	NOUN
ejpam-3501	349	11	where	where	SCONJ
ejpam-3501	349	12	s	s	VERB
ejpam-3501	349	13	satisfies	satisfie	NOUN
ejpam-3501	349	14	(	(	PUNCT
ejpam-3501	349	15	i	i	NOUN
ejpam-3501	349	16	)	)	PUNCT
ejpam-3501	349	17	.	.	PUNCT
ejpam-3501	350	1	the	the	DET
ejpam-3501	350	2	other	other	ADJ
ejpam-3501	350	3	two	two	NUM
ejpam-3501	350	4	cases	case	NOUN
ejpam-3501	350	5	may	may	AUX
ejpam-3501	350	6	follow	follow	VERB
ejpam-3501	350	7	similar	similar	ADJ
ejpam-3501	350	8	arguments	argument	NOUN
ejpam-3501	350	9	.	.	PUNCT
ejpam-3501	351	1	by	by	ADP
ejpam-3501	351	2	theorem	theorem	NOUN
ejpam-3501	351	3	6	6	NUM
ejpam-3501	351	4	,	,	PUNCT
ejpam-3501	351	5	c	c	PROPN
ejpam-3501	351	6	is	be	AUX
ejpam-3501	351	7	a	a	DET
ejpam-3501	351	8	semitotal	semitotal	ADJ
ejpam-3501	351	9	dominating	dominating	NOUN
ejpam-3501	351	10	set	set	VERB
ejpam-3501	351	11	in	in	ADP
ejpam-3501	351	12	g[h	g[h	PROPN
ejpam-3501	351	13	]	]	PUNCT
ejpam-3501	351	14	.	.	PUNCT
ejpam-3501	352	1	let	let	VERB
ejpam-3501	352	2	c∗	c∗	PROPN
ejpam-3501	352	3	=	=	SYM
ejpam-3501	352	4	∪x∈s∗	∪x∈s∗	PROPN
ejpam-3501	352	5	(	(	PUNCT
ejpam-3501	352	6	{	{	PUNCT
ejpam-3501	352	7	x	x	NOUN
ejpam-3501	352	8	}	}	PUNCT
ejpam-3501	352	9	×	×	PROPN
ejpam-3501	352	10	tx	tx	PROPN
ejpam-3501	352	11	)	)	PUNCT
ejpam-3501	352	12	⊆	⊆	NUM
ejpam-3501	352	13	v	v	NOUN
ejpam-3501	352	14	(	(	PUNCT
ejpam-3501	352	15	g[h	g[h	PROPN
ejpam-3501	352	16	]	]	PUNCT
ejpam-3501	352	17	)	)	PUNCT
ejpam-3501	352	18	be	be	AUX
ejpam-3501	352	19	a	a	DET
ejpam-3501	352	20	γt2	γt2	NOUN
ejpam-3501	352	21	-	-	PUNCT
ejpam-3501	352	22	set	set	NOUN
ejpam-3501	352	23	of	of	ADP
ejpam-3501	352	24	g[h	g[h	NOUN
ejpam-3501	352	25	]	]	PUNCT
ejpam-3501	352	26	.	.	PUNCT
ejpam-3501	353	1	then	then	ADV
ejpam-3501	353	2	as	as	SCONJ
ejpam-3501	353	3	shown	show	VERB
ejpam-3501	353	4	in	in	ADP
ejpam-3501	353	5	the	the	DET
ejpam-3501	353	6	necessity	necessity	NOUN
ejpam-3501	353	7	part	part	NOUN
ejpam-3501	353	8	of	of	ADP
ejpam-3501	353	9	the	the	DET
ejpam-3501	353	10	proof	proof	NOUN
ejpam-3501	353	11	,	,	PUNCT
ejpam-3501	353	12	2|s∗	2|s∗	PROPN
ejpam-3501	353	13	\ng(s∗)|+	\ng(s∗)|+	PROPN
ejpam-3501	353	14	|s∗	|s∗	PROPN
ejpam-3501	353	15	∩ng(s∗)|	∩ng(s∗)|	NOUN
ejpam-3501	353	16	=	=	PUNCT
ejpam-3501	353	17	γt(g	γt(g	NUM
ejpam-3501	353	18	)	)	PUNCT
ejpam-3501	353	19	.	.	PUNCT
ejpam-3501	354	1	thus	thus	ADV
ejpam-3501	354	2	,	,	PUNCT
ejpam-3501	354	3	|c∗|	|c∗|	VERB
ejpam-3501	354	4	≥	≥	NOUN
ejpam-3501	354	5	γt(g	γt(g	NUM
ejpam-3501	354	6	)	)	PUNCT
ejpam-3501	354	7	=	=	SYM
ejpam-3501	354	8	|s|	|s|	PROPN
ejpam-3501	354	9	=	=	PUNCT
ejpam-3501	354	10	|c|	|c|	PROPN
ejpam-3501	354	11	,	,	PUNCT
ejpam-3501	354	12	and	and	CCONJ
ejpam-3501	354	13	c	c	NOUN
ejpam-3501	354	14	is	be	AUX
ejpam-3501	354	15	a	a	DET
ejpam-3501	354	16	γt2	γt2	NOUN
ejpam-3501	354	17	-	-	PUNCT
ejpam-3501	354	18	set	set	NOUN
ejpam-3501	354	19	of	of	ADP
ejpam-3501	354	20	g[h	g[h	NOUN
ejpam-3501	354	21	]	]	PUNCT
ejpam-3501	354	22	.	.	PUNCT
ejpam-3501	355	1	corollary	corollary	ADJ
ejpam-3501	355	2	10	10	NUM
ejpam-3501	355	3	.	.	PUNCT
ejpam-3501	356	1	let	let	VERB
ejpam-3501	356	2	g	g	NOUN
ejpam-3501	356	3	and	and	CCONJ
ejpam-3501	356	4	h	h	NOUN
ejpam-3501	356	5	be	be	AUX
ejpam-3501	356	6	nontrivial	nontrivial	ADJ
ejpam-3501	356	7	connected	connect	VERB
ejpam-3501	356	8	graphs	graph	NOUN
ejpam-3501	356	9	with	with	ADP
ejpam-3501	356	10	γ(h	γ(h	NOUN
ejpam-3501	356	11	)	)	PUNCT
ejpam-3501	356	12	≥	≥	NOUN
ejpam-3501	356	13	2	2	NUM
ejpam-3501	356	14	,	,	PUNCT
ejpam-3501	356	15	and	and	CCONJ
ejpam-3501	356	16	let	let	VERB
ejpam-3501	356	17	c	c	NOUN
ejpam-3501	356	18	=	=	SYM
ejpam-3501	356	19	∪x∈s	∪x∈s	PROPN
ejpam-3501	356	20	(	(	PUNCT
ejpam-3501	356	21	{	{	PUNCT
ejpam-3501	356	22	x	x	NOUN
ejpam-3501	356	23	}	}	PUNCT
ejpam-3501	356	24	×	×	PROPN
ejpam-3501	356	25	tx	tx	PROPN
ejpam-3501	356	26	)	)	PUNCT
ejpam-3501	356	27	⊆	⊆	NUM
ejpam-3501	356	28	v	v	NOUN
ejpam-3501	356	29	(	(	PUNCT
ejpam-3501	356	30	g[h	g[h	PROPN
ejpam-3501	356	31	]	]	PUNCT
ejpam-3501	356	32	)	)	PUNCT
ejpam-3501	356	33	.	.	PUNCT
ejpam-3501	357	1	then	then	ADV
ejpam-3501	357	2	c	c	PROPN
ejpam-3501	357	3	is	be	AUX
ejpam-3501	357	4	a	a	DET
ejpam-3501	357	5	γt2	γt2	NOUN
ejpam-3501	357	6	-	-	PUNCT
ejpam-3501	357	7	set	set	NOUN
ejpam-3501	357	8	of	of	ADP
ejpam-3501	357	9	g[h	g[h	NOUN
ejpam-3501	357	10	]	]	PUNCT
ejpam-3501	357	11	)	)	PUNCT
ejpam-3501	357	12	if	if	SCONJ
ejpam-3501	357	13	and	and	CCONJ
ejpam-3501	357	14	only	only	ADV
ejpam-3501	357	15	if	if	SCONJ
ejpam-3501	357	16	s	s	NOUN
ejpam-3501	357	17	is	be	AUX
ejpam-3501	357	18	a	a	DET
ejpam-3501	357	19	γt	γt	NOUN
ejpam-3501	357	20	-	-	NOUN
ejpam-3501	357	21	set	set	NOUN
ejpam-3501	357	22	of	of	ADP
ejpam-3501	357	23	g	g	NOUN
ejpam-3501	357	24	and	and	CCONJ
ejpam-3501	357	25	|tx|	|tx|	NUM
ejpam-3501	357	26	=	=	SYM
ejpam-3501	357	27	1	1	NUM
ejpam-3501	357	28	for	for	ADP
ejpam-3501	357	29	all	all	DET
ejpam-3501	357	30	x	x	SYM
ejpam-3501	357	31	∈	∈	PROPN
ejpam-3501	357	32	s.	s.	PROPN
ejpam-3501	357	33	proof	proof	PROPN
ejpam-3501	357	34	.	.	PUNCT
ejpam-3501	358	1	suppose	suppose	VERB
ejpam-3501	358	2	that	that	SCONJ
ejpam-3501	358	3	c	c	PROPN
ejpam-3501	358	4	is	be	AUX
ejpam-3501	358	5	a	a	DET
ejpam-3501	358	6	γt2	γt2	NOUN
ejpam-3501	358	7	-	-	PUNCT
ejpam-3501	358	8	set	set	NOUN
ejpam-3501	358	9	of	of	ADP
ejpam-3501	358	10	g[h	g[h	NOUN
ejpam-3501	358	11	]	]	PUNCT
ejpam-3501	358	12	.	.	PUNCT
ejpam-3501	359	1	suppose	suppose	VERB
ejpam-3501	359	2	that	that	SCONJ
ejpam-3501	359	3	s	s	VERB
ejpam-3501	359	4	is	be	AUX
ejpam-3501	359	5	not	not	PART
ejpam-3501	359	6	a	a	DET
ejpam-3501	359	7	total	total	ADJ
ejpam-3501	359	8	dominating	dominating	NOUN
ejpam-3501	359	9	set	set	VERB
ejpam-3501	359	10	in	in	ADP
ejpam-3501	359	11	g.	g.	PROPN
ejpam-3501	359	12	by	by	ADP
ejpam-3501	359	13	theorem	theorem	NOUN
ejpam-3501	359	14	6	6	NUM
ejpam-3501	359	15	and	and	CCONJ
ejpam-3501	359	16	lemma	lemma	PROPN
ejpam-3501	359	17	2	2	NUM
ejpam-3501	359	18	|c|	|c|	PROPN
ejpam-3501	359	19	≥	≥	NOUN
ejpam-3501	359	20	2|s	2|s	NUM
ejpam-3501	359	21	\n2	\n2	ADP
ejpam-3501	359	22	g(s)|+	g(s)|+	PROPN
ejpam-3501	359	23	γ(h)|s	γ(h)|s	PROPN
ejpam-3501	359	24	∩	∩	NOUN
ejpam-3501	359	25	(	(	PUNCT
ejpam-3501	359	26	n2	n2	ADJ
ejpam-3501	359	27	g(s	g(s	PROPN
ejpam-3501	359	28	)	)	PUNCT
ejpam-3501	359	29	\ng(s	\ng(s	NUM
ejpam-3501	359	30	)	)	PUNCT
ejpam-3501	359	31	)	)	PUNCT
ejpam-3501	359	32	|+	|+	NOUN
ejpam-3501	360	1	|s	|s	PROPN
ejpam-3501	360	2	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	360	3	>	>	X
ejpam-3501	360	4	2|s	2|s	NUM
ejpam-3501	360	5	\ng(s)|+	\ng(s)|+	NOUN
ejpam-3501	360	6	|s	|s	PROPN
ejpam-3501	360	7	∩ng(s)|	∩ng(s)|	PROPN
ejpam-3501	360	8	≥	≥	NOUN
ejpam-3501	360	9	γt(g	γt(g	NUM
ejpam-3501	360	10	)	)	PUNCT
ejpam-3501	360	11	.	.	PUNCT
ejpam-3501	361	1	now	now	ADV
ejpam-3501	361	2	,	,	PUNCT
ejpam-3501	361	3	take	take	VERB
ejpam-3501	361	4	any	any	DET
ejpam-3501	361	5	γt	γt	NOUN
ejpam-3501	361	6	-	-	ADJ
ejpam-3501	361	7	set	set	ADJ
ejpam-3501	361	8	s∗	s∗	PROPN
ejpam-3501	361	9	⊆	⊆	NUM
ejpam-3501	361	10	v	v	NOUN
ejpam-3501	361	11	(	(	PUNCT
ejpam-3501	361	12	g	g	NOUN
ejpam-3501	361	13	)	)	PUNCT
ejpam-3501	361	14	of	of	ADP
ejpam-3501	361	15	g	g	PROPN
ejpam-3501	361	16	and	and	CCONJ
ejpam-3501	361	17	any	any	DET
ejpam-3501	361	18	u	u	NOUN
ejpam-3501	361	19	∈	∈	PROPN
ejpam-3501	361	20	v	v	NOUN
ejpam-3501	361	21	(	(	PUNCT
ejpam-3501	361	22	h	h	NOUN
ejpam-3501	361	23	)	)	PUNCT
ejpam-3501	361	24	.	.	PUNCT
ejpam-3501	362	1	then	then	ADV
ejpam-3501	362	2	c∗	c∗	PROPN
ejpam-3501	362	3	=	=	PUNCT
ejpam-3501	362	4	s∗	s∗	PROPN
ejpam-3501	362	5	×	×	NOUN
ejpam-3501	362	6	{	{	PUNCT
ejpam-3501	362	7	u	u	NOUN
ejpam-3501	362	8	}	}	PUNCT
ejpam-3501	362	9	is	be	AUX
ejpam-3501	362	10	a	a	DET
ejpam-3501	362	11	semitotal	semitotal	ADJ
ejpam-3501	362	12	dominating	dominating	NOUN
ejpam-3501	362	13	set	set	VERB
ejpam-3501	362	14	in	in	ADP
ejpam-3501	362	15	g[h	g[h	PROPN
ejpam-3501	362	16	]	]	PUNCT
ejpam-3501	362	17	by	by	ADP
ejpam-3501	362	18	theorem	theorem	NOUN
ejpam-3501	362	19	6	6	NUM
ejpam-3501	362	20	.	.	PUNCT
ejpam-3501	362	21	further	far	ADV
ejpam-3501	362	22	,	,	PUNCT
ejpam-3501	362	23	|c∗|	|c∗|	PUNCT
ejpam-3501	362	24	=	=	SYM
ejpam-3501	362	25	γt(g	γt(g	X
ejpam-3501	362	26	)	)	PUNCT
ejpam-3501	362	27	<	<	X
ejpam-3501	362	28	|c|	|c|	PROPN
ejpam-3501	362	29	,	,	PUNCT
ejpam-3501	362	30	a	a	DET
ejpam-3501	362	31	contradiction	contradiction	NOUN
ejpam-3501	362	32	.	.	PUNCT
ejpam-3501	363	1	therefore	therefore	ADV
ejpam-3501	363	2	,	,	PUNCT
ejpam-3501	363	3	s	s	VERB
ejpam-3501	363	4	is	be	AUX
ejpam-3501	363	5	a	a	DET
ejpam-3501	363	6	total	total	ADJ
ejpam-3501	363	7	dominating	dominating	NOUN
ejpam-3501	363	8	set	set	VERB
ejpam-3501	363	9	in	in	ADP
ejpam-3501	363	10	g.	g.	PROPN
ejpam-3501	363	11	in	in	ADP
ejpam-3501	363	12	view	view	NOUN
ejpam-3501	363	13	of	of	ADP
ejpam-3501	363	14	theorem	theorem	NOUN
ejpam-3501	363	15	6	6	NUM
ejpam-3501	363	16	,	,	PUNCT
ejpam-3501	363	17	since	since	SCONJ
ejpam-3501	363	18	c	c	PROPN
ejpam-3501	363	19	is	be	AUX
ejpam-3501	363	20	a	a	DET
ejpam-3501	363	21	γt2	γt2	NOUN
ejpam-3501	363	22	-	-	PUNCT
ejpam-3501	363	23	set	set	VERB
ejpam-3501	363	24	,	,	PUNCT
ejpam-3501	363	25	|s|	|s|	PROPN
ejpam-3501	363	26	=	=	SYM
ejpam-3501	363	27	γt(g	γt(g	NUM
ejpam-3501	363	28	)	)	PUNCT
ejpam-3501	363	29	and	and	CCONJ
ejpam-3501	363	30	|tx|	|tx|	NUM
ejpam-3501	363	31	=	=	SYM
ejpam-3501	363	32	1	1	NUM
ejpam-3501	363	33	for	for	ADP
ejpam-3501	363	34	all	all	DET
ejpam-3501	363	35	x	x	SYM
ejpam-3501	363	36	∈	∈	PROPN
ejpam-3501	363	37	s.	s.	PROPN
ejpam-3501	363	38	at	at	ADP
ejpam-3501	363	39	this	this	DET
ejpam-3501	363	40	point	point	NOUN
ejpam-3501	363	41	,	,	PUNCT
ejpam-3501	363	42	the	the	DET
ejpam-3501	363	43	converse	converse	NOUN
ejpam-3501	363	44	is	be	AUX
ejpam-3501	363	45	a	a	DET
ejpam-3501	363	46	routine	routine	NOUN
ejpam-3501	363	47	.	.	PUNCT
ejpam-3501	364	1	combining	combine	VERB
ejpam-3501	364	2	corollary	corollary	ADJ
ejpam-3501	364	3	9	9	NUM
ejpam-3501	364	4	and	and	CCONJ
ejpam-3501	364	5	corollary	corollary	ADJ
ejpam-3501	364	6	10	10	NUM
ejpam-3501	364	7	yields	yield	NOUN
ejpam-3501	364	8	the	the	DET
ejpam-3501	364	9	following	follow	VERB
ejpam-3501	364	10	:	:	PUNCT
ejpam-3501	364	11	corollary	corollary	ADJ
ejpam-3501	364	12	11	11	NUM
ejpam-3501	364	13	.	.	PUNCT
ejpam-3501	365	1	let	let	VERB
ejpam-3501	365	2	g	g	NOUN
ejpam-3501	365	3	and	and	CCONJ
ejpam-3501	365	4	h	h	NOUN
ejpam-3501	365	5	be	be	AUX
ejpam-3501	365	6	nontrivial	nontrivial	ADJ
ejpam-3501	365	7	connected	connect	VERB
ejpam-3501	365	8	graphs	graph	NOUN
ejpam-3501	365	9	with	with	ADP
ejpam-3501	365	10	γ(h	γ(h	NOUN
ejpam-3501	365	11	)	)	PUNCT
ejpam-3501	365	12	≥	≥	NOUN
ejpam-3501	365	13	2	2	NUM
ejpam-3501	365	14	.	.	PUNCT
ejpam-3501	365	15	then	then	ADV
ejpam-3501	365	16	γt2(g[h	γt2(g[h	NOUN
ejpam-3501	365	17	]	]	X
ejpam-3501	365	18	)	)	PUNCT
ejpam-3501	365	19	=	=	SYM
ejpam-3501	365	20	γt(g	γt(g	NUM
ejpam-3501	365	21	)	)	PUNCT
ejpam-3501	365	22	.	.	PUNCT
ejpam-3501	366	1	theorem	theorem	ADJ
ejpam-3501	366	2	7	7	NUM
ejpam-3501	366	3	.	.	PUNCT
ejpam-3501	367	1	let	let	VERB
ejpam-3501	367	2	g	g	PRON
ejpam-3501	367	3	be	be	AUX
ejpam-3501	367	4	a	a	DET
ejpam-3501	367	5	nontrivial	nontrivial	ADJ
ejpam-3501	367	6	connected	connect	VERB
ejpam-3501	367	7	graph	graph	NOUN
ejpam-3501	367	8	,	,	PUNCT
ejpam-3501	367	9	and	and	CCONJ
ejpam-3501	367	10	let	let	VERB
ejpam-3501	367	11	n	n	PRON
ejpam-3501	367	12	≥	≥	NOUN
ejpam-3501	367	13	2	2	NUM
ejpam-3501	367	14	.	.	PUNCT
ejpam-3501	368	1	then	then	ADV
ejpam-3501	368	2	c	c	X
ejpam-3501	368	3	=	=	SYM
ejpam-3501	368	4	∪x∈s({x}×	∪x∈s({x}×	PROPN
ejpam-3501	368	5	tx	tx	VERB
ejpam-3501	368	6	)	)	PUNCT
ejpam-3501	368	7	⊆	⊆	NUM
ejpam-3501	368	8	v	v	NOUN
ejpam-3501	368	9	(	(	PUNCT
ejpam-3501	368	10	g[kn	g[kn	PROPN
ejpam-3501	368	11	]	]	PUNCT
ejpam-3501	368	12	)	)	PUNCT
ejpam-3501	368	13	is	be	AUX
ejpam-3501	368	14	a	a	DET
ejpam-3501	368	15	secure	secure	ADJ
ejpam-3501	368	16	semitotal	semitotal	ADJ
ejpam-3501	368	17	dominating	dominating	NOUN
ejpam-3501	368	18	set	set	VERB
ejpam-3501	368	19	in	in	ADP
ejpam-3501	368	20	g[h	g[h	PROPN
ejpam-3501	368	21	]	]	PUNCT
ejpam-3501	368	22	if	if	SCONJ
ejpam-3501	368	23	and	and	CCONJ
ejpam-3501	368	24	only	only	ADV
ejpam-3501	368	25	if	if	SCONJ
ejpam-3501	368	26	one	one	NUM
ejpam-3501	368	27	of	of	ADP
ejpam-3501	368	28	the	the	DET
ejpam-3501	368	29	following	follow	VERB
ejpam-3501	368	30	holds	hold	VERB
ejpam-3501	368	31	:	:	PUNCT
ejpam-3501	368	32	(	(	PUNCT
ejpam-3501	368	33	i	i	NOUN
ejpam-3501	368	34	)	)	PUNCT
ejpam-3501	368	35	s	s	VERB
ejpam-3501	368	36	is	be	AUX
ejpam-3501	368	37	a	a	DET
ejpam-3501	368	38	secure	secure	ADJ
ejpam-3501	368	39	semitotal	semitotal	ADJ
ejpam-3501	368	40	dominating	dominating	NOUN
ejpam-3501	368	41	set	set	VERB
ejpam-3501	368	42	in	in	ADP
ejpam-3501	368	43	g.	g.	PROPN
ejpam-3501	368	44	(	(	PUNCT
ejpam-3501	368	45	ii	ii	PROPN
ejpam-3501	368	46	)	)	PUNCT
ejpam-3501	369	1	s	s	VERB
ejpam-3501	369	2	is	be	AUX
ejpam-3501	369	3	a	a	DET
ejpam-3501	369	4	semitotal	semitotal	ADJ
ejpam-3501	369	5	dominating	dominating	NOUN
ejpam-3501	369	6	set	set	NOUN
ejpam-3501	369	7	in	in	ADP
ejpam-3501	369	8	g	g	PROPN
ejpam-3501	369	9	or	or	CCONJ
ejpam-3501	369	10	s	s	NOUN
ejpam-3501	369	11	is	be	AUX
ejpam-3501	369	12	a	a	DET
ejpam-3501	369	13	dominating	dominating	NOUN
ejpam-3501	369	14	set	set	NOUN
ejpam-3501	369	15	in	in	ADP
ejpam-3501	369	16	g	g	NOUN
ejpam-3501	369	17	with	with	ADP
ejpam-3501	369	18	|tu|	|tu|	PROPN
ejpam-3501	369	19	≥	≥	NOUN
ejpam-3501	369	20	2	2	NUM
ejpam-3501	369	21	for	for	ADP
ejpam-3501	369	22	all	all	DET
ejpam-3501	369	23	u	u	PROPN
ejpam-3501	369	24	∈	∈	PROPN
ejpam-3501	369	25	s	s	PART
ejpam-3501	369	26	\n2	\n2	ADJ
ejpam-3501	369	27	g(s	g(	NOUN
ejpam-3501	369	28	)	)	PUNCT
ejpam-3501	369	29	.	.	PUNCT
ejpam-3501	370	1	in	in	ADP
ejpam-3501	370	2	any	any	DET
ejpam-3501	370	3	case	case	NOUN
ejpam-3501	370	4	,	,	PUNCT
ejpam-3501	370	5	for	for	ADP
ejpam-3501	370	6	each	each	DET
ejpam-3501	370	7	u	u	PROPN
ejpam-3501	370	8	∈	∈	PROPN
ejpam-3501	370	9	v	v	ADP
ejpam-3501	370	10	(	(	PUNCT
ejpam-3501	370	11	g	g	NOUN
ejpam-3501	370	12	)	)	PUNCT
ejpam-3501	370	13	\	\	PROPN
ejpam-3501	370	14	s	s	X
ejpam-3501	370	15	,	,	PUNCT
ejpam-3501	370	16	there	there	PRON
ejpam-3501	370	17	exists	exist	VERB
ejpam-3501	370	18	x	x	X
ejpam-3501	370	19	∈	∈	PROPN
ejpam-3501	370	20	s	s	PART
ejpam-3501	370	21	∩ng(u	∩ng(u	PROPN
ejpam-3501	370	22	)	)	PUNCT
ejpam-3501	370	23	such	such	ADJ
ejpam-3501	370	24	that	that	SCONJ
ejpam-3501	370	25	either	either	CCONJ
ejpam-3501	370	26	(	(	PUNCT
ejpam-3501	370	27	a	a	X
ejpam-3501	370	28	)	)	PUNCT
ejpam-3501	370	29	|tx|	|tx|	PROPN
ejpam-3501	370	30	≥	≥	NUM
ejpam-3501	370	31	2	2	NUM
ejpam-3501	370	32	or	or	CCONJ
ejpam-3501	370	33	(	(	PUNCT
ejpam-3501	370	34	b	b	NOUN
ejpam-3501	370	35	)	)	PUNCT
ejpam-3501	370	36	|tx|	|tx|	NOUN
ejpam-3501	370	37	=	=	SYM
ejpam-3501	370	38	1	1	NUM
ejpam-3501	370	39	,	,	PUNCT
ejpam-3501	370	40	(	(	PUNCT
ejpam-3501	370	41	s	s	VERB
ejpam-3501	370	42	\{x})∪{u	\{x})∪{u	VERB
ejpam-3501	370	43	}	}	PUNCT
ejpam-3501	370	44	is	be	AUX
ejpam-3501	370	45	a	a	DET
ejpam-3501	370	46	dominating	dominating	NOUN
ejpam-3501	370	47	set	set	NOUN
ejpam-3501	370	48	in	in	ADP
ejpam-3501	370	49	g	g	PROPN
ejpam-3501	370	50	,	,	PUNCT
ejpam-3501	370	51	u	u	PROPN
ejpam-3501	370	52	∈	∈	PROPN
ejpam-3501	370	53	n2	n2	ADJ
ejpam-3501	370	54	g(s	g(s	PROPN
ejpam-3501	370	55	\{x	\{x	NOUN
ejpam-3501	370	56	}	}	PUNCT
ejpam-3501	370	57	)	)	PUNCT
ejpam-3501	370	58	and	and	CCONJ
ejpam-3501	370	59	|tz|	|tz|	VERB
ejpam-3501	370	60	≥	≥	NOUN
ejpam-3501	370	61	2	2	NUM
ejpam-3501	370	62	for	for	ADP
ejpam-3501	370	63	all	all	DET
ejpam-3501	370	64	z	z	NOUN
ejpam-3501	370	65	∈	∈	PROPN
ejpam-3501	370	66	(	(	PUNCT
ejpam-3501	370	67	s	s	NOUN
ejpam-3501	370	68	\	\	X
ejpam-3501	370	69	{	{	PUNCT
ejpam-3501	370	70	x	x	NOUN
ejpam-3501	370	71	}	}	PUNCT
ejpam-3501	370	72	)	)	PUNCT
ejpam-3501	370	73	\n2	\n2	VERB
ejpam-3501	370	74	g(s	g(s	PROPN
ejpam-3501	370	75	\	\	X
ejpam-3501	370	76	{	{	PUNCT
ejpam-3501	370	77	x	x	NOUN
ejpam-3501	370	78	}	}	PUNCT
ejpam-3501	370	79	)	)	PUNCT
ejpam-3501	370	80	∪	∪	ADP
ejpam-3501	370	81	{	{	PUNCT
ejpam-3501	370	82	u	u	NOUN
ejpam-3501	370	83	}	}	PUNCT
ejpam-3501	370	84	)	)	PUNCT
ejpam-3501	370	85	.	.	PUNCT
ejpam-3501	371	1	i.	i.	PROPN
ejpam-3501	371	2	s.	s.	PROPN
ejpam-3501	371	3	aniversario	aniversario	PROPN
ejpam-3501	371	4	,	,	PUNCT
ejpam-3501	371	5	s.	s.	PROPN
ejpam-3501	371	6	r.	r.	PROPN
ejpam-3501	371	7	jr	jr	PROPN
ejpam-3501	371	8	.	.	PROPN
ejpam-3501	371	9	canoy	canoy	PROPN
ejpam-3501	371	10	,	,	PUNCT
ejpam-3501	371	11	f.p	f.p	PROPN
ejpam-3501	371	12	.	.	PROPN
ejpam-3501	371	13	jamil	jamil	PROPN
ejpam-3501	371	14	/	/	SYM
ejpam-3501	371	15	eur	eur	PROPN
ejpam-3501	371	16	.	.	PUNCT
ejpam-3501	372	1	j.	j.	PROPN
ejpam-3501	372	2	pure	pure	PROPN
ejpam-3501	372	3	appl	appl	PROPN
ejpam-3501	372	4	.	.	PROPN
ejpam-3501	372	5	math	math	PROPN
ejpam-3501	372	6	,	,	PUNCT
ejpam-3501	372	7	12	12	NUM
ejpam-3501	372	8	(	(	PUNCT
ejpam-3501	372	9	4	4	NUM
ejpam-3501	372	10	)	)	PUNCT
ejpam-3501	372	11	(	(	PUNCT
ejpam-3501	372	12	2019	2019	NUM
ejpam-3501	372	13	)	)	PUNCT
ejpam-3501	372	14	,	,	PUNCT
ejpam-3501	372	15	1410	1410	NUM
ejpam-3501	372	16	-	-	SYM
ejpam-3501	372	17	1425	1425	NUM
ejpam-3501	372	18	1423	1423	NUM
ejpam-3501	372	19	proof	proof	NOUN
ejpam-3501	372	20	.	.	PUNCT
ejpam-3501	372	21	suppose	suppose	VERB
ejpam-3501	372	22	that	that	SCONJ
ejpam-3501	372	23	c	c	PROPN
ejpam-3501	372	24	is	be	AUX
ejpam-3501	372	25	a	a	DET
ejpam-3501	372	26	secure	secure	ADJ
ejpam-3501	372	27	semitotal	semitotal	ADJ
ejpam-3501	372	28	dominating	dominating	NOUN
ejpam-3501	372	29	set	set	NOUN
ejpam-3501	372	30	in	in	ADP
ejpam-3501	372	31	g[kn	g[kn	PROPN
ejpam-3501	372	32	]	]	PUNCT
ejpam-3501	372	33	.	.	PUNCT
ejpam-3501	373	1	then	then	ADV
ejpam-3501	373	2	c	c	PROPN
ejpam-3501	373	3	is	be	AUX
ejpam-3501	373	4	a	a	DET
ejpam-3501	373	5	semitotal	semitotal	ADJ
ejpam-3501	373	6	dominating	dominating	NOUN
ejpam-3501	373	7	set	set	NOUN
ejpam-3501	373	8	in	in	ADP
ejpam-3501	373	9	g[kn	g[kn	PROPN
ejpam-3501	373	10	]	]	PUNCT
ejpam-3501	373	11	.	.	PUNCT
ejpam-3501	374	1	if	if	SCONJ
ejpam-3501	374	2	s	s	NOUN
ejpam-3501	374	3	is	be	AUX
ejpam-3501	374	4	a	a	DET
ejpam-3501	374	5	secure	secure	ADJ
ejpam-3501	374	6	semitotal	semitotal	ADJ
ejpam-3501	374	7	dominating	dominating	NOUN
ejpam-3501	374	8	set	set	NOUN
ejpam-3501	374	9	in	in	ADP
ejpam-3501	374	10	g	g	NOUN
ejpam-3501	374	11	,	,	PUNCT
ejpam-3501	374	12	then	then	ADV
ejpam-3501	374	13	(	(	PUNCT
ejpam-3501	374	14	i	i	NOUN
ejpam-3501	374	15	)	)	PUNCT
ejpam-3501	374	16	holds	hold	VERB
ejpam-3501	374	17	.	.	PUNCT
ejpam-3501	375	1	suppose	suppose	VERB
ejpam-3501	375	2	that	that	SCONJ
ejpam-3501	375	3	s	s	VERB
ejpam-3501	375	4	is	be	AUX
ejpam-3501	375	5	a	a	DET
ejpam-3501	375	6	not	not	PART
ejpam-3501	375	7	a	a	DET
ejpam-3501	375	8	secure	secure	ADJ
ejpam-3501	375	9	semitotal	semitotal	ADJ
ejpam-3501	375	10	dominating	dominating	NOUN
ejpam-3501	375	11	set	set	VERB
ejpam-3501	375	12	in	in	ADP
ejpam-3501	375	13	g.	g.	PROPN
ejpam-3501	375	14	by	by	ADP
ejpam-3501	375	15	theorem	theorem	NOUN
ejpam-3501	375	16	6	6	NUM
ejpam-3501	375	17	,	,	PUNCT
ejpam-3501	375	18	s	s	VERB
ejpam-3501	375	19	is	be	AUX
ejpam-3501	375	20	a	a	DET
ejpam-3501	375	21	semitotal	semitotal	ADJ
ejpam-3501	375	22	dominating	dominating	NOUN
ejpam-3501	375	23	set	set	NOUN
ejpam-3501	375	24	in	in	ADP
ejpam-3501	375	25	g	g	PROPN
ejpam-3501	375	26	or	or	CCONJ
ejpam-3501	375	27	s	s	NOUN
ejpam-3501	375	28	is	be	AUX
ejpam-3501	375	29	a	a	DET
ejpam-3501	375	30	dominating	dominating	NOUN
ejpam-3501	375	31	set	set	NOUN
ejpam-3501	375	32	in	in	ADP
ejpam-3501	375	33	g	g	NOUN
ejpam-3501	375	34	with	with	ADP
ejpam-3501	375	35	|tu|	|tu|	PROPN
ejpam-3501	375	36	≥	≥	NOUN
ejpam-3501	375	37	2	2	NUM
ejpam-3501	375	38	for	for	ADP
ejpam-3501	375	39	all	all	DET
ejpam-3501	375	40	u	u	PROPN
ejpam-3501	375	41	∈	∈	PROPN
ejpam-3501	375	42	s	s	PART
ejpam-3501	375	43	\n2	\n2	ADJ
ejpam-3501	375	44	g(s	g(	NOUN
ejpam-3501	375	45	)	)	PUNCT
ejpam-3501	375	46	.	.	PUNCT
ejpam-3501	376	1	let	let	VERB
ejpam-3501	376	2	u	u	PRON
ejpam-3501	376	3	∈	∈	PROPN
ejpam-3501	376	4	v	v	ADP
ejpam-3501	376	5	(	(	PUNCT
ejpam-3501	376	6	g	g	NOUN
ejpam-3501	376	7	)	)	PUNCT
ejpam-3501	376	8	\s	\s	NOUN
ejpam-3501	376	9	.	.	PUNCT
ejpam-3501	377	1	pick	pick	VERB
ejpam-3501	377	2	any	any	DET
ejpam-3501	377	3	v	v	NOUN
ejpam-3501	377	4	∈	∈	PROPN
ejpam-3501	377	5	v	v	NOUN
ejpam-3501	377	6	(	(	PUNCT
ejpam-3501	377	7	kn	kn	PROPN
ejpam-3501	377	8	)	)	PUNCT
ejpam-3501	377	9	.	.	PUNCT
ejpam-3501	378	1	then	then	ADV
ejpam-3501	378	2	there	there	PRON
ejpam-3501	378	3	exists	exist	VERB
ejpam-3501	378	4	(	(	PUNCT
ejpam-3501	378	5	x	x	X
ejpam-3501	378	6	,	,	PUNCT
ejpam-3501	378	7	y	y	NOUN
ejpam-3501	378	8	)	)	PUNCT
ejpam-3501	378	9	∈	∈	PROPN
ejpam-3501	378	10	c	c	NOUN
ejpam-3501	378	11	such	such	ADJ
ejpam-3501	378	12	that	that	PRON
ejpam-3501	378	13	(	(	PUNCT
ejpam-3501	378	14	x	x	X
ejpam-3501	378	15	,	,	PUNCT
ejpam-3501	378	16	y)(u	y)(u	ADJ
ejpam-3501	378	17	,	,	PUNCT
ejpam-3501	378	18	v	v	NOUN
ejpam-3501	378	19	)	)	PUNCT
ejpam-3501	378	20	∈	∈	PROPN
ejpam-3501	378	21	e(g[kn	e(g[kn	PROPN
ejpam-3501	378	22	]	]	X
ejpam-3501	378	23	)	)	PUNCT
ejpam-3501	378	24	and	and	CCONJ
ejpam-3501	378	25	c∗	c∗	PROPN
ejpam-3501	378	26	=	=	SYM
ejpam-3501	378	27	(	(	PUNCT
ejpam-3501	378	28	c	c	NOUN
ejpam-3501	378	29	\	\	X
ejpam-3501	378	30	{	{	PUNCT
ejpam-3501	378	31	(	(	PUNCT
ejpam-3501	378	32	x	x	NOUN
ejpam-3501	378	33	,	,	PUNCT
ejpam-3501	378	34	y	y	NOUN
ejpam-3501	378	35	)	)	PUNCT
ejpam-3501	378	36	}	}	PUNCT
ejpam-3501	378	37	)	)	PUNCT
ejpam-3501	378	38	∪	∪	ADP
ejpam-3501	378	39	{	{	PUNCT
ejpam-3501	378	40	(	(	PUNCT
ejpam-3501	378	41	u	u	NOUN
ejpam-3501	378	42	,	,	PUNCT
ejpam-3501	378	43	v	v	NOUN
ejpam-3501	378	44	)	)	PUNCT
ejpam-3501	378	45	}	}	PUNCT
ejpam-3501	378	46	is	be	AUX
ejpam-3501	378	47	a	a	DET
ejpam-3501	378	48	semitotal	semitotal	ADJ
ejpam-3501	378	49	dominating	dominating	NOUN
ejpam-3501	378	50	set	set	NOUN
ejpam-3501	378	51	in	in	ADP
ejpam-3501	378	52	g[kn	g[kn	PROPN
ejpam-3501	378	53	]	]	PUNCT
ejpam-3501	378	54	.	.	PUNCT
ejpam-3501	379	1	write	write	VERB
ejpam-3501	379	2	c∗	c∗	PROPN
ejpam-3501	379	3	=	=	PUNCT
ejpam-3501	379	4	∪a∈s∗({a}×t	∪a∈s∗({a}×t	NOUN
ejpam-3501	379	5	∗a	∗a	PROPN
ejpam-3501	379	6	)	)	PUNCT
ejpam-3501	379	7	.	.	PUNCT
ejpam-3501	380	1	then	then	ADV
ejpam-3501	380	2	s∗	s∗	PROPN
ejpam-3501	380	3	is	be	AUX
ejpam-3501	380	4	a	a	DET
ejpam-3501	380	5	dominating	dominating	NOUN
ejpam-3501	380	6	set	set	VERB
ejpam-3501	380	7	in	in	ADP
ejpam-3501	380	8	g.	g.	PROPN
ejpam-3501	380	9	if	if	SCONJ
ejpam-3501	380	10	|tx|	|tx|	NOUN
ejpam-3501	380	11	≥	≥	NOUN
ejpam-3501	380	12	2	2	NUM
ejpam-3501	380	13	,	,	PUNCT
ejpam-3501	380	14	then	then	ADV
ejpam-3501	380	15	(	(	PUNCT
ejpam-3501	380	16	ii)(a	ii)(a	NOUN
ejpam-3501	380	17	)	)	PUNCT
ejpam-3501	380	18	holds	hold	VERB
ejpam-3501	380	19	.	.	PUNCT
ejpam-3501	381	1	suppose	suppose	VERB
ejpam-3501	381	2	that	that	SCONJ
ejpam-3501	381	3	tx	tx	PROPN
ejpam-3501	381	4	=	=	PUNCT
ejpam-3501	381	5	{	{	PUNCT
ejpam-3501	381	6	y	y	NOUN
ejpam-3501	381	7	}	}	PUNCT
ejpam-3501	381	8	.	.	PUNCT
ejpam-3501	382	1	since	since	SCONJ
ejpam-3501	382	2	c∗	c∗	PROPN
ejpam-3501	382	3	is	be	AUX
ejpam-3501	382	4	a	a	DET
ejpam-3501	382	5	semitotal	semitotal	ADJ
ejpam-3501	382	6	dominating	dominating	NOUN
ejpam-3501	382	7	set	set	NOUN
ejpam-3501	382	8	,	,	PUNCT
ejpam-3501	382	9	s∗	s∗	PROPN
ejpam-3501	382	10	=	=	SYM
ejpam-3501	382	11	(	(	PUNCT
ejpam-3501	382	12	s	s	NOUN
ejpam-3501	382	13	\	\	X
ejpam-3501	382	14	{	{	PUNCT
ejpam-3501	382	15	x	x	NOUN
ejpam-3501	382	16	}	}	PUNCT
ejpam-3501	382	17	)	)	PUNCT
ejpam-3501	382	18	∪	∪	ADP
ejpam-3501	382	19	{	{	PUNCT
ejpam-3501	382	20	u	u	NOUN
ejpam-3501	382	21	}	}	PUNCT
ejpam-3501	382	22	is	be	AUX
ejpam-3501	382	23	a	a	DET
ejpam-3501	382	24	dominating	dominating	NOUN
ejpam-3501	382	25	set	set	NOUN
ejpam-3501	382	26	in	in	ADP
ejpam-3501	382	27	g	g	NOUN
ejpam-3501	382	28	,	,	PUNCT
ejpam-3501	382	29	and	and	CCONJ
ejpam-3501	382	30	since	since	SCONJ
ejpam-3501	382	31	|t	|t	PROPN
ejpam-3501	382	32	∗u	∗u	PROPN
ejpam-3501	382	33	|	|	NOUN
ejpam-3501	382	34	=	=	SYM
ejpam-3501	382	35	1	1	NUM
ejpam-3501	382	36	,	,	PUNCT
ejpam-3501	382	37	u	u	PROPN
ejpam-3501	382	38	∈	∈	PROPN
ejpam-3501	382	39	n2	n2	ADJ
ejpam-3501	382	40	g(s	g(s	PROPN
ejpam-3501	382	41	\	\	X
ejpam-3501	382	42	{	{	PUNCT
ejpam-3501	382	43	x	x	NOUN
ejpam-3501	382	44	}	}	PUNCT
ejpam-3501	382	45	)	)	PUNCT
ejpam-3501	382	46	.	.	PUNCT
ejpam-3501	383	1	let	let	VERB
ejpam-3501	383	2	z	z	NOUN
ejpam-3501	383	3	∈	∈	PROPN
ejpam-3501	383	4	(	(	PUNCT
ejpam-3501	383	5	s\{x})\n2	s\{x})\n2	NOUN
ejpam-3501	383	6	g(s∗	g(s∗	NOUN
ejpam-3501	383	7	)	)	PUNCT
ejpam-3501	383	8	.	.	PUNCT
ejpam-3501	384	1	suppose	suppose	VERB
ejpam-3501	384	2	that	that	SCONJ
ejpam-3501	384	3	|tz|	|tz|	NOUN
ejpam-3501	384	4	=	=	SYM
ejpam-3501	384	5	1	1	NUM
ejpam-3501	384	6	,	,	PUNCT
ejpam-3501	384	7	say	say	VERB
ejpam-3501	384	8	tz	tz	NOUN
ejpam-3501	384	9	=	=	PUNCT
ejpam-3501	384	10	{	{	PUNCT
ejpam-3501	384	11	w	w	NOUN
ejpam-3501	384	12	}	}	PUNCT
ejpam-3501	384	13	.	.	PUNCT
ejpam-3501	385	1	then	then	ADV
ejpam-3501	385	2	dg[kn]((z	dg[kn]((z	VERB
ejpam-3501	385	3	,	,	PUNCT
ejpam-3501	385	4	w	w	NOUN
ejpam-3501	385	5	)	)	PUNCT
ejpam-3501	385	6	,	,	PUNCT
ejpam-3501	385	7	(	(	PUNCT
ejpam-3501	385	8	a	a	DET
ejpam-3501	385	9	,	,	PUNCT
ejpam-3501	385	10	b	b	NOUN
ejpam-3501	385	11	)	)	PUNCT
ejpam-3501	385	12	)	)	PUNCT
ejpam-3501	385	13	>	>	X
ejpam-3501	385	14	2	2	NUM
ejpam-3501	385	15	for	for	ADP
ejpam-3501	385	16	all	all	PRON
ejpam-3501	385	17	(	(	PUNCT
ejpam-3501	385	18	a	a	PRON
ejpam-3501	385	19	,	,	PUNCT
ejpam-3501	385	20	b	b	NOUN
ejpam-3501	385	21	)	)	PUNCT
ejpam-3501	385	22	∈	∈	PROPN
ejpam-3501	385	23	c∗	c∗	PROPN
ejpam-3501	385	24	\	\	PROPN
ejpam-3501	385	25	{	{	PUNCT
ejpam-3501	385	26	(	(	PUNCT
ejpam-3501	385	27	z	z	NOUN
ejpam-3501	385	28	,	,	PUNCT
ejpam-3501	385	29	w	w	NOUN
ejpam-3501	385	30	)	)	PUNCT
ejpam-3501	385	31	}	}	PUNCT
ejpam-3501	385	32	,	,	PUNCT
ejpam-3501	385	33	a	a	DET
ejpam-3501	385	34	contradiction	contradiction	NOUN
ejpam-3501	385	35	.	.	PUNCT
ejpam-3501	386	1	this	this	PRON
ejpam-3501	386	2	shows	show	VERB
ejpam-3501	386	3	that	that	SCONJ
ejpam-3501	386	4	|tz|	|tz|	NOUN
ejpam-3501	386	5	≥	≥	NOUN
ejpam-3501	386	6	2	2	NUM
ejpam-3501	386	7	,	,	PUNCT
ejpam-3501	386	8	and	and	CCONJ
ejpam-3501	386	9	(	(	PUNCT
ejpam-3501	386	10	ii)(b	ii)(b	ADJ
ejpam-3501	386	11	)	)	PUNCT
ejpam-3501	386	12	holds	hold	VERB
ejpam-3501	386	13	.	.	PUNCT
ejpam-3501	387	1	conversely	conversely	ADV
ejpam-3501	387	2	,	,	PUNCT
ejpam-3501	387	3	suppose	suppose	VERB
ejpam-3501	387	4	that	that	SCONJ
ejpam-3501	387	5	(	(	PUNCT
ejpam-3501	387	6	i	i	NOUN
ejpam-3501	387	7	)	)	PUNCT
ejpam-3501	387	8	holds	hold	VERB
ejpam-3501	387	9	.	.	PUNCT
ejpam-3501	388	1	since	since	SCONJ
ejpam-3501	388	2	s	s	PROPN
ejpam-3501	388	3	is	be	AUX
ejpam-3501	388	4	a	a	DET
ejpam-3501	388	5	semitotal	semitotal	ADJ
ejpam-3501	388	6	dominating	dominating	NOUN
ejpam-3501	388	7	set	set	NOUN
ejpam-3501	388	8	,	,	PUNCT
ejpam-3501	388	9	c	c	PROPN
ejpam-3501	388	10	is	be	AUX
ejpam-3501	388	11	a	a	DET
ejpam-3501	388	12	semitotal	semitotal	ADJ
ejpam-3501	388	13	dominating	dominating	NOUN
ejpam-3501	388	14	set	set	NOUN
ejpam-3501	388	15	in	in	ADP
ejpam-3501	388	16	g[kn	g[kn	PROPN
ejpam-3501	388	17	]	]	PUNCT
ejpam-3501	388	18	by	by	ADP
ejpam-3501	388	19	theorem	theorem	NOUN
ejpam-3501	388	20	6	6	NUM
ejpam-3501	388	21	.	.	PUNCT
ejpam-3501	389	1	let	let	VERB
ejpam-3501	389	2	(	(	PUNCT
ejpam-3501	389	3	u	u	NOUN
ejpam-3501	389	4	,	,	PUNCT
ejpam-3501	389	5	v	v	NOUN
ejpam-3501	389	6	)	)	PUNCT
ejpam-3501	389	7	∈	∈	NOUN
ejpam-3501	389	8	v	v	NOUN
ejpam-3501	389	9	(	(	PUNCT
ejpam-3501	389	10	g[kn])\c	g[kn])\c	PROPN
ejpam-3501	389	11	.	.	PROPN
ejpam-3501	389	12	suppose	suppose	VERB
ejpam-3501	389	13	that	that	SCONJ
ejpam-3501	389	14	u	u	PROPN
ejpam-3501	389	15	∈	∈	PROPN
ejpam-3501	389	16	s.	s.	PROPN
ejpam-3501	389	17	pick	pick	VERB
ejpam-3501	389	18	a	a	DET
ejpam-3501	389	19	∈	∈	PROPN
ejpam-3501	389	20	tu	tu	PROPN
ejpam-3501	389	21	.	.	PUNCT
ejpam-3501	390	1	then	then	ADV
ejpam-3501	390	2	(	(	PUNCT
ejpam-3501	390	3	u	u	NOUN
ejpam-3501	390	4	,	,	PUNCT
ejpam-3501	390	5	a	a	PRON
ejpam-3501	390	6	)	)	PUNCT
ejpam-3501	390	7	∈	∈	PROPN
ejpam-3501	390	8	c	c	NOUN
ejpam-3501	390	9	and	and	CCONJ
ejpam-3501	390	10	(	(	PUNCT
ejpam-3501	390	11	u	u	NOUN
ejpam-3501	390	12	,	,	PUNCT
ejpam-3501	390	13	v)(u	v)(u	PROPN
ejpam-3501	390	14	,	,	PUNCT
ejpam-3501	390	15	a	a	DET
ejpam-3501	390	16	)	)	PUNCT
ejpam-3501	390	17	∈	∈	PROPN
ejpam-3501	390	18	e(g[kn	e(g[kn	PROPN
ejpam-3501	390	19	]	]	NOUN
ejpam-3501	390	20	)	)	PUNCT
ejpam-3501	390	21	.	.	PUNCT
ejpam-3501	391	1	write	write	VERB
ejpam-3501	391	2	(	(	PUNCT
ejpam-3501	391	3	c	c	NOUN
ejpam-3501	391	4	\	\	X
ejpam-3501	391	5	{	{	PUNCT
ejpam-3501	391	6	(	(	PUNCT
ejpam-3501	391	7	u	u	NOUN
ejpam-3501	391	8	,	,	PUNCT
ejpam-3501	391	9	a	a	NOUN
ejpam-3501	391	10	)	)	PUNCT
ejpam-3501	391	11	}	}	PUNCT
ejpam-3501	391	12	)	)	PUNCT
ejpam-3501	391	13	∪	∪	ADP
ejpam-3501	391	14	{	{	PUNCT
ejpam-3501	391	15	(	(	PUNCT
ejpam-3501	391	16	u	u	NOUN
ejpam-3501	391	17	,	,	PUNCT
ejpam-3501	391	18	v	v	NOUN
ejpam-3501	391	19	)	)	PUNCT
ejpam-3501	391	20	}	}	PUNCT
ejpam-3501	391	21	=	=	SYM
ejpam-3501	391	22	∪a∈s∗({a}×t	∪a∈s∗({a}×t	X
ejpam-3501	391	23	∗a	∗a	PROPN
ejpam-3501	391	24	)	)	PUNCT
ejpam-3501	391	25	.	.	PUNCT
ejpam-3501	392	1	then	then	ADV
ejpam-3501	392	2	s∗	s∗	PROPN
ejpam-3501	392	3	=	=	SYM
ejpam-3501	392	4	s	s	PROPN
ejpam-3501	392	5	and	and	CCONJ
ejpam-3501	392	6	,	,	PUNCT
ejpam-3501	392	7	therefore	therefore	ADV
ejpam-3501	392	8	,	,	PUNCT
ejpam-3501	392	9	s∗	s∗	PROPN
ejpam-3501	392	10	is	be	AUX
ejpam-3501	392	11	a	a	DET
ejpam-3501	392	12	semitotal	semitotal	ADJ
ejpam-3501	392	13	dominating	dominating	NOUN
ejpam-3501	392	14	set	set	NOUN
ejpam-3501	392	15	ing	ing	NOUN
ejpam-3501	392	16	.	.	PUNCT
ejpam-3501	393	1	consequently	consequently	ADV
ejpam-3501	393	2	,	,	PUNCT
ejpam-3501	393	3	(	(	PUNCT
ejpam-3501	393	4	c\{(u	c\{(u	PROPN
ejpam-3501	393	5	,	,	PUNCT
ejpam-3501	393	6	a)})∪{(u	a)})∪{(u	PROPN
ejpam-3501	393	7	,	,	PUNCT
ejpam-3501	393	8	v	v	NOUN
ejpam-3501	393	9	)	)	PUNCT
ejpam-3501	393	10	}	}	PUNCT
ejpam-3501	393	11	is	be	AUX
ejpam-3501	393	12	a	a	DET
ejpam-3501	393	13	semitotal	semitotal	ADJ
ejpam-3501	393	14	dominating	dominating	NOUN
ejpam-3501	393	15	set	set	VERB
ejpam-3501	393	16	ing[kn	ing[kn	PROPN
ejpam-3501	393	17	]	]	PUNCT
ejpam-3501	393	18	.	.	PUNCT
ejpam-3501	394	1	suppose	suppose	VERB
ejpam-3501	394	2	that	that	SCONJ
ejpam-3501	394	3	u	u	PROPN
ejpam-3501	394	4	/∈	/∈	PUNCT
ejpam-3501	394	5	s.	s.	PROPN
ejpam-3501	394	6	since	since	SCONJ
ejpam-3501	394	7	s	s	PROPN
ejpam-3501	394	8	is	be	AUX
ejpam-3501	394	9	a	a	DET
ejpam-3501	394	10	secure	secure	ADJ
ejpam-3501	394	11	semitotal	semitotal	ADJ
ejpam-3501	394	12	dominating	dominating	NOUN
ejpam-3501	394	13	set	set	NOUN
ejpam-3501	394	14	,	,	PUNCT
ejpam-3501	394	15	there	there	PRON
ejpam-3501	394	16	exists	exist	VERB
ejpam-3501	394	17	x	x	X
ejpam-3501	394	18	∈	∈	PROPN
ejpam-3501	394	19	s	s	PART
ejpam-3501	394	20	∩ng(u	∩ng(u	PROPN
ejpam-3501	394	21	)	)	PUNCT
ejpam-3501	394	22	such	such	ADJ
ejpam-3501	394	23	that	that	SCONJ
ejpam-3501	394	24	(	(	PUNCT
ejpam-3501	394	25	s	s	NOUN
ejpam-3501	394	26	\	\	X
ejpam-3501	394	27	{	{	PUNCT
ejpam-3501	394	28	x	x	NOUN
ejpam-3501	394	29	}	}	PUNCT
ejpam-3501	394	30	)	)	PUNCT
ejpam-3501	394	31	∪	∪	ADP
ejpam-3501	394	32	{	{	PUNCT
ejpam-3501	394	33	u	u	NOUN
ejpam-3501	394	34	}	}	PUNCT
ejpam-3501	394	35	is	be	AUX
ejpam-3501	394	36	a	a	DET
ejpam-3501	394	37	semitotal	semitotal	ADJ
ejpam-3501	394	38	dominating	dominating	NOUN
ejpam-3501	394	39	set	set	VERB
ejpam-3501	394	40	in	in	ADP
ejpam-3501	394	41	g.	g.	PROPN
ejpam-3501	394	42	pick	pick	VERB
ejpam-3501	394	43	y	y	PROPN
ejpam-3501	394	44	∈	∈	PROPN
ejpam-3501	394	45	tx	tx	PROPN
ejpam-3501	394	46	.	.	PUNCT
ejpam-3501	395	1	then	then	ADV
ejpam-3501	395	2	(	(	PUNCT
ejpam-3501	395	3	x	x	X
ejpam-3501	395	4	,	,	PUNCT
ejpam-3501	395	5	y	y	NOUN
ejpam-3501	395	6	)	)	PUNCT
ejpam-3501	395	7	∈	∈	PROPN
ejpam-3501	395	8	c	c	PROPN
ejpam-3501	395	9	and	and	CCONJ
ejpam-3501	395	10	(	(	PUNCT
ejpam-3501	395	11	x	x	X
ejpam-3501	395	12	,	,	PUNCT
ejpam-3501	395	13	y)(u	y)(u	ADJ
ejpam-3501	395	14	,	,	PUNCT
ejpam-3501	395	15	v	v	NOUN
ejpam-3501	395	16	)	)	PUNCT
ejpam-3501	395	17	∈	∈	PROPN
ejpam-3501	395	18	e(g[kn	e(g[kn	PROPN
ejpam-3501	395	19	]	]	NOUN
ejpam-3501	395	20	)	)	PUNCT
ejpam-3501	395	21	.	.	PUNCT
ejpam-3501	396	1	write	write	VERB
ejpam-3501	396	2	(	(	PUNCT
ejpam-3501	396	3	c	c	NOUN
ejpam-3501	396	4	\	\	X
ejpam-3501	396	5	{	{	PUNCT
ejpam-3501	396	6	(	(	PUNCT
ejpam-3501	396	7	x	x	NOUN
ejpam-3501	396	8	,	,	PUNCT
ejpam-3501	396	9	y	y	NOUN
ejpam-3501	396	10	)	)	PUNCT
ejpam-3501	396	11	}	}	PUNCT
ejpam-3501	396	12	)	)	PUNCT
ejpam-3501	396	13	∪	∪	ADP
ejpam-3501	396	14	{	{	PUNCT
ejpam-3501	396	15	(	(	PUNCT
ejpam-3501	396	16	u	u	NOUN
ejpam-3501	396	17	,	,	PUNCT
ejpam-3501	396	18	v	v	NOUN
ejpam-3501	396	19	)	)	PUNCT
ejpam-3501	396	20	}	}	PUNCT
ejpam-3501	396	21	=	=	SYM
ejpam-3501	396	22	∪a∈s∗({a	∪a∈s∗({a	PROPN
ejpam-3501	396	23	}	}	PUNCT
ejpam-3501	396	24	×	×	PROPN
ejpam-3501	396	25	t	t	NOUN
ejpam-3501	396	26	∗a	∗a	PROPN
ejpam-3501	396	27	)	)	PUNCT
ejpam-3501	396	28	.	.	PUNCT
ejpam-3501	397	1	either	either	CCONJ
ejpam-3501	397	2	s∗	s∗	PROPN
ejpam-3501	397	3	=	=	SYM
ejpam-3501	397	4	s	s	PART
ejpam-3501	397	5	∪	∪	X
ejpam-3501	397	6	{	{	PUNCT
ejpam-3501	397	7	u	u	NOUN
ejpam-3501	397	8	}	}	PUNCT
ejpam-3501	397	9	or	or	CCONJ
ejpam-3501	397	10	s∗	s∗	PROPN
ejpam-3501	397	11	=	=	SYM
ejpam-3501	397	12	(	(	PUNCT
ejpam-3501	397	13	s	s	NOUN
ejpam-3501	397	14	\	\	X
ejpam-3501	397	15	{	{	PUNCT
ejpam-3501	397	16	x	x	NOUN
ejpam-3501	397	17	}	}	PUNCT
ejpam-3501	397	18	)	)	PUNCT
ejpam-3501	397	19	∪	∪	ADP
ejpam-3501	397	20	{	{	PUNCT
ejpam-3501	397	21	u	u	NOUN
ejpam-3501	397	22	}	}	PUNCT
ejpam-3501	397	23	.	.	PUNCT
ejpam-3501	398	1	in	in	ADP
ejpam-3501	398	2	either	either	DET
ejpam-3501	398	3	case	case	NOUN
ejpam-3501	398	4	,	,	PUNCT
ejpam-3501	398	5	s∗	s∗	PROPN
ejpam-3501	398	6	is	be	AUX
ejpam-3501	398	7	a	a	DET
ejpam-3501	398	8	semitotal	semitotal	ADJ
ejpam-3501	398	9	dominating	dominating	NOUN
ejpam-3501	398	10	set	set	VERB
ejpam-3501	398	11	in	in	ADP
ejpam-3501	398	12	g.	g.	PROPN
ejpam-3501	398	13	thus	thus	ADV
ejpam-3501	398	14	,	,	PUNCT
ejpam-3501	398	15	(	(	PUNCT
ejpam-3501	398	16	c	c	NOUN
ejpam-3501	398	17	\	\	X
ejpam-3501	398	18	{	{	PUNCT
ejpam-3501	398	19	(	(	PUNCT
ejpam-3501	398	20	x	x	NOUN
ejpam-3501	398	21	,	,	PUNCT
ejpam-3501	398	22	y	y	NOUN
ejpam-3501	398	23	)	)	PUNCT
ejpam-3501	398	24	}	}	PUNCT
ejpam-3501	398	25	)	)	PUNCT
ejpam-3501	398	26	∪	∪	ADP
ejpam-3501	398	27	{	{	PUNCT
ejpam-3501	398	28	(	(	PUNCT
ejpam-3501	398	29	u	u	NOUN
ejpam-3501	398	30	,	,	PUNCT
ejpam-3501	398	31	v	v	NOUN
ejpam-3501	398	32	)	)	PUNCT
ejpam-3501	398	33	}	}	PUNCT
ejpam-3501	398	34	is	be	AUX
ejpam-3501	398	35	a	a	DET
ejpam-3501	398	36	dominating	dominating	NOUN
ejpam-3501	398	37	set	set	NOUN
ejpam-3501	398	38	in	in	ADP
ejpam-3501	398	39	g[kn	g[kn	PROPN
ejpam-3501	398	40	]	]	PUNCT
ejpam-3501	398	41	.	.	PUNCT
ejpam-3501	399	1	this	this	PRON
ejpam-3501	399	2	shows	show	VERB
ejpam-3501	399	3	that	that	SCONJ
ejpam-3501	399	4	c	c	PROPN
ejpam-3501	399	5	is	be	AUX
ejpam-3501	399	6	a	a	DET
ejpam-3501	399	7	secure	secure	ADJ
ejpam-3501	399	8	semitotal	semitotal	ADJ
ejpam-3501	399	9	dominating	dominating	NOUN
ejpam-3501	399	10	set	set	NOUN
ejpam-3501	399	11	in	in	ADP
ejpam-3501	399	12	g[kn	g[kn	PROPN
ejpam-3501	399	13	]	]	PUNCT
ejpam-3501	399	14	.	.	PUNCT
ejpam-3501	400	1	suppose	suppose	VERB
ejpam-3501	400	2	that	that	SCONJ
ejpam-3501	400	3	(	(	PUNCT
ejpam-3501	400	4	ii	ii	NOUN
ejpam-3501	400	5	)	)	PUNCT
ejpam-3501	400	6	holds	hold	VERB
ejpam-3501	400	7	.	.	PUNCT
ejpam-3501	401	1	by	by	ADP
ejpam-3501	401	2	theorem	theorem	NOUN
ejpam-3501	401	3	6	6	NUM
ejpam-3501	401	4	,	,	PUNCT
ejpam-3501	401	5	c	c	PROPN
ejpam-3501	401	6	is	be	AUX
ejpam-3501	401	7	a	a	DET
ejpam-3501	401	8	semitotal	semitotal	ADJ
ejpam-3501	401	9	dominating	dominating	NOUN
ejpam-3501	401	10	set	set	NOUN
ejpam-3501	401	11	in	in	ADP
ejpam-3501	401	12	g[kn	g[kn	PROPN
ejpam-3501	401	13	]	]	PUNCT
ejpam-3501	401	14	.	.	PUNCT
ejpam-3501	402	1	let	let	VERB
ejpam-3501	402	2	(	(	PUNCT
ejpam-3501	402	3	u	u	NOUN
ejpam-3501	402	4	,	,	PUNCT
ejpam-3501	402	5	v	v	NOUN
ejpam-3501	402	6	)	)	PUNCT
ejpam-3501	402	7	∈	∈	NOUN
ejpam-3501	402	8	v	v	NOUN
ejpam-3501	402	9	(	(	PUNCT
ejpam-3501	402	10	g[kn	g[kn	PROPN
ejpam-3501	402	11	]	]	PUNCT
ejpam-3501	402	12	)	)	PUNCT
ejpam-3501	402	13	\	\	PUNCT
ejpam-3501	403	1	c	c	X
ejpam-3501	403	2	,	,	PUNCT
ejpam-3501	403	3	and	and	CCONJ
ejpam-3501	403	4	let	let	VERB
ejpam-3501	403	5	x	x	PUNCT
ejpam-3501	403	6	∈	∈	NOUN
ejpam-3501	403	7	s	s	PART
ejpam-3501	403	8	∩	∩	NOUN
ejpam-3501	403	9	ng(u	ng(u	NOUN
ejpam-3501	403	10	)	)	PUNCT
ejpam-3501	403	11	be	be	VERB
ejpam-3501	403	12	such	such	ADJ
ejpam-3501	403	13	that	that	SCONJ
ejpam-3501	403	14	|tx|	|tx|	PROPN
ejpam-3501	403	15	≥	≥	NUM
ejpam-3501	403	16	2	2	NUM
ejpam-3501	403	17	.	.	PUNCT
ejpam-3501	403	18	pick	pick	VERB
ejpam-3501	403	19	y	y	PROPN
ejpam-3501	403	20	∈	∈	PROPN
ejpam-3501	403	21	tx	tx	PROPN
ejpam-3501	403	22	.	.	PUNCT
ejpam-3501	404	1	then	then	ADV
ejpam-3501	404	2	(	(	PUNCT
ejpam-3501	404	3	x	x	X
ejpam-3501	404	4	,	,	PUNCT
ejpam-3501	404	5	y	y	NOUN
ejpam-3501	404	6	)	)	PUNCT
ejpam-3501	404	7	∈	∈	PROPN
ejpam-3501	404	8	c	c	PROPN
ejpam-3501	404	9	and	and	CCONJ
ejpam-3501	404	10	(	(	PUNCT
ejpam-3501	404	11	x	x	X
ejpam-3501	404	12	,	,	PUNCT
ejpam-3501	404	13	y)(u	y)(u	ADJ
ejpam-3501	404	14	,	,	PUNCT
ejpam-3501	404	15	v	v	NOUN
ejpam-3501	404	16	)	)	PUNCT
ejpam-3501	404	17	∈	∈	PROPN
ejpam-3501	404	18	e(g[kn	e(g[kn	PROPN
ejpam-3501	404	19	]	]	NOUN
ejpam-3501	404	20	)	)	PUNCT
ejpam-3501	404	21	.	.	PUNCT
ejpam-3501	405	1	write	write	VERB
ejpam-3501	405	2	c∗	c∗	PROPN
ejpam-3501	405	3	=	=	SYM
ejpam-3501	405	4	(	(	PUNCT
ejpam-3501	405	5	c	c	NOUN
ejpam-3501	405	6	\	\	X
ejpam-3501	405	7	{	{	PUNCT
ejpam-3501	405	8	(	(	PUNCT
ejpam-3501	405	9	x	x	NOUN
ejpam-3501	405	10	,	,	PUNCT
ejpam-3501	405	11	y	y	NOUN
ejpam-3501	405	12	)	)	PUNCT
ejpam-3501	405	13	}	}	PUNCT
ejpam-3501	405	14	)	)	PUNCT
ejpam-3501	405	15	∪	∪	ADP
ejpam-3501	405	16	{	{	PUNCT
ejpam-3501	405	17	(	(	PUNCT
ejpam-3501	405	18	u	u	NOUN
ejpam-3501	405	19	,	,	PUNCT
ejpam-3501	405	20	v	v	NOUN
ejpam-3501	405	21	)	)	PUNCT
ejpam-3501	405	22	}	}	PUNCT
ejpam-3501	405	23	=	=	SYM
ejpam-3501	405	24	∪a∈s∗({a	∪a∈s∗({a	PROPN
ejpam-3501	405	25	}	}	PUNCT
ejpam-3501	405	26	×	×	PROPN
ejpam-3501	405	27	t	t	NOUN
ejpam-3501	405	28	∗a	∗a	PROPN
ejpam-3501	405	29	)	)	PUNCT
ejpam-3501	405	30	.	.	PUNCT
ejpam-3501	406	1	then	then	ADV
ejpam-3501	406	2	s∗	s∗	PROPN
ejpam-3501	406	3	=	=	SYM
ejpam-3501	406	4	s	s	PART
ejpam-3501	406	5	∪	∪	X
ejpam-3501	406	6	{	{	PUNCT
ejpam-3501	406	7	u	u	NOUN
ejpam-3501	406	8	}	}	PUNCT
ejpam-3501	406	9	.	.	PUNCT
ejpam-3501	407	1	if	if	SCONJ
ejpam-3501	407	2	s	s	PROPN
ejpam-3501	407	3	is	be	AUX
ejpam-3501	407	4	a	a	DET
ejpam-3501	407	5	semitotal	semitotal	ADJ
ejpam-3501	407	6	dominating	dominating	NOUN
ejpam-3501	407	7	set	set	NOUN
ejpam-3501	407	8	in	in	ADP
ejpam-3501	407	9	g	g	NOUN
ejpam-3501	407	10	,	,	PUNCT
ejpam-3501	407	11	then	then	ADV
ejpam-3501	407	12	so	so	ADV
ejpam-3501	407	13	is	be	AUX
ejpam-3501	407	14	s∗	s∗	PROPN
ejpam-3501	407	15	and	and	CCONJ
ejpam-3501	407	16	consequently	consequently	ADV
ejpam-3501	407	17	,	,	PUNCT
ejpam-3501	407	18	c∗	c∗	PROPN
ejpam-3501	407	19	is	be	AUX
ejpam-3501	407	20	a	a	DET
ejpam-3501	407	21	semitotal	semitotal	ADJ
ejpam-3501	407	22	dominating	dominating	NOUN
ejpam-3501	407	23	set	set	NOUN
ejpam-3501	407	24	in	in	ADP
ejpam-3501	407	25	g[kn	g[kn	PROPN
ejpam-3501	407	26	]	]	PUNCT
ejpam-3501	407	27	.	.	PUNCT
ejpam-3501	408	1	suppose	suppose	VERB
ejpam-3501	408	2	,	,	PUNCT
ejpam-3501	408	3	on	on	ADP
ejpam-3501	408	4	the	the	DET
ejpam-3501	408	5	other	other	ADJ
ejpam-3501	408	6	hand	hand	NOUN
ejpam-3501	408	7	that	that	PRON
ejpam-3501	408	8	s	s	VERB
ejpam-3501	408	9	is	be	AUX
ejpam-3501	408	10	a	a	DET
ejpam-3501	408	11	dominating	dominating	NOUN
ejpam-3501	408	12	set	set	NOUN
ejpam-3501	408	13	in	in	ADP
ejpam-3501	408	14	g	g	NOUN
ejpam-3501	408	15	with	with	ADP
ejpam-3501	408	16	|tz|	|tz|	NOUN
ejpam-3501	408	17	≥	≥	NOUN
ejpam-3501	408	18	2	2	NUM
ejpam-3501	408	19	for	for	ADP
ejpam-3501	408	20	all	all	DET
ejpam-3501	408	21	z	z	NOUN
ejpam-3501	408	22	∈	∈	PROPN
ejpam-3501	408	23	s	s	PART
ejpam-3501	408	24	\	\	PROPN
ejpam-3501	408	25	n2	n2	ADJ
ejpam-3501	408	26	g(s	g(s	PROPN
ejpam-3501	408	27	)	)	PUNCT
ejpam-3501	408	28	.	.	PUNCT
ejpam-3501	409	1	since	since	SCONJ
ejpam-3501	409	2	u	u	PROPN
ejpam-3501	409	3	∈	∈	PROPN
ejpam-3501	409	4	n2	n2	NOUN
ejpam-3501	409	5	g(s∗	g(s∗	PROPN
ejpam-3501	409	6	)	)	PUNCT
ejpam-3501	409	7	and	and	CCONJ
ejpam-3501	409	8	s	s	NOUN
ejpam-3501	409	9	\	\	PROPN
ejpam-3501	409	10	n2	n2	ADJ
ejpam-3501	409	11	g(s∗	g(s∗	NOUN
ejpam-3501	409	12	)	)	PUNCT
ejpam-3501	409	13	⊆	⊆	NUM
ejpam-3501	409	14	s	s	NOUN
ejpam-3501	409	15	\	\	PROPN
ejpam-3501	409	16	n2	n2	ADJ
ejpam-3501	409	17	g(s	g(s	PROPN
ejpam-3501	409	18	)	)	PUNCT
ejpam-3501	409	19	,	,	PUNCT
ejpam-3501	409	20	|t	|t	PROPN
ejpam-3501	409	21	∗z	∗z	PROPN
ejpam-3501	410	1	|	|	INTJ
ejpam-3501	410	2	≥	≥	NOUN
ejpam-3501	410	3	2	2	NUM
ejpam-3501	410	4	for	for	ADP
ejpam-3501	410	5	all	all	DET
ejpam-3501	410	6	z	z	NOUN
ejpam-3501	410	7	∈	∈	PROPN
ejpam-3501	410	8	s∗	s∗	PROPN
ejpam-3501	410	9	\	\	PROPN
ejpam-3501	410	10	n2	n2	ADJ
ejpam-3501	410	11	g(s∗	g(s∗	PROPN
ejpam-3501	410	12	)	)	PUNCT
ejpam-3501	410	13	.	.	PUNCT
ejpam-3501	411	1	thus	thus	ADV
ejpam-3501	411	2	,	,	PUNCT
ejpam-3501	411	3	c∗	c∗	PROPN
ejpam-3501	411	4	is	be	AUX
ejpam-3501	411	5	a	a	DET
ejpam-3501	411	6	semitotal	semitotal	ADJ
ejpam-3501	411	7	dominating	dominating	NOUN
ejpam-3501	411	8	set	set	NOUN
ejpam-3501	411	9	in	in	ADP
ejpam-3501	411	10	g[kn	g[kn	PROPN
ejpam-3501	411	11	]	]	PUNCT
ejpam-3501	411	12	.	.	PUNCT
ejpam-3501	412	1	now	now	ADV
ejpam-3501	412	2	,	,	PUNCT
ejpam-3501	412	3	let	let	VERB
ejpam-3501	412	4	x	x	PUNCT
ejpam-3501	412	5	∈	∈	PROPN
ejpam-3501	412	6	s	s	PART
ejpam-3501	412	7	∩ng(u	∩ng(u	PROPN
ejpam-3501	412	8	)	)	PUNCT
ejpam-3501	412	9	be	be	VERB
ejpam-3501	412	10	such	such	ADJ
ejpam-3501	412	11	that	that	SCONJ
ejpam-3501	412	12	|tx|	|tx|	NOUN
ejpam-3501	412	13	=	=	SYM
ejpam-3501	412	14	1	1	NUM
ejpam-3501	412	15	,	,	PUNCT
ejpam-3501	412	16	s∗	s∗	PROPN
ejpam-3501	412	17	=	=	SYM
ejpam-3501	412	18	(	(	PUNCT
ejpam-3501	412	19	s	s	NOUN
ejpam-3501	412	20	\	\	X
ejpam-3501	412	21	{	{	PUNCT
ejpam-3501	412	22	x	x	NOUN
ejpam-3501	412	23	}	}	PUNCT
ejpam-3501	412	24	)	)	PUNCT
ejpam-3501	412	25	∪	∪	ADP
ejpam-3501	412	26	{	{	PUNCT
ejpam-3501	412	27	u	u	NOUN
ejpam-3501	412	28	}	}	PUNCT
ejpam-3501	412	29	is	be	AUX
ejpam-3501	412	30	a	a	DET
ejpam-3501	412	31	dominating	dominating	NOUN
ejpam-3501	412	32	set	set	NOUN
ejpam-3501	412	33	in	in	ADP
ejpam-3501	412	34	g	g	NOUN
ejpam-3501	412	35	,	,	PUNCT
ejpam-3501	412	36	and	and	CCONJ
ejpam-3501	412	37	|tz|	|tz|	VERB
ejpam-3501	412	38	≥	≥	NOUN
ejpam-3501	412	39	2	2	NUM
ejpam-3501	412	40	for	for	ADP
ejpam-3501	412	41	all	all	DET
ejpam-3501	412	42	z	z	NOUN
ejpam-3501	412	43	∈	∈	PROPN
ejpam-3501	412	44	(	(	PUNCT
ejpam-3501	412	45	s	s	NOUN
ejpam-3501	412	46	\	\	X
ejpam-3501	412	47	{	{	PUNCT
ejpam-3501	412	48	x	x	NOUN
ejpam-3501	412	49	}	}	PUNCT
ejpam-3501	412	50	)	)	PUNCT
ejpam-3501	412	51	\	\	PROPN
ejpam-3501	412	52	n2	n2	ADJ
ejpam-3501	412	53	g(s∗	g(s∗	PROPN
ejpam-3501	412	54	)	)	PUNCT
ejpam-3501	412	55	.	.	PUNCT
ejpam-3501	413	1	pick	pick	VERB
ejpam-3501	413	2	y	y	PROPN
ejpam-3501	413	3	∈	∈	PROPN
ejpam-3501	413	4	tx	tx	PROPN
ejpam-3501	413	5	.	.	PUNCT
ejpam-3501	414	1	then	then	ADV
ejpam-3501	414	2	(	(	PUNCT
ejpam-3501	414	3	x	x	X
ejpam-3501	414	4	,	,	PUNCT
ejpam-3501	414	5	y)(u	y)(u	ADJ
ejpam-3501	414	6	,	,	PUNCT
ejpam-3501	414	7	v	v	NOUN
ejpam-3501	414	8	)	)	PUNCT
ejpam-3501	414	9	∈	∈	PROPN
ejpam-3501	414	10	e(g[kn	e(g[kn	PROPN
ejpam-3501	414	11	]	]	X
ejpam-3501	414	12	)	)	PUNCT
ejpam-3501	414	13	and	and	CCONJ
ejpam-3501	414	14	c∗	c∗	PROPN
ejpam-3501	414	15	=	=	SYM
ejpam-3501	414	16	(	(	PUNCT
ejpam-3501	414	17	c	c	NOUN
ejpam-3501	414	18	\{(x	\{(x	PROPN
ejpam-3501	414	19	,	,	PUNCT
ejpam-3501	414	20	y)}∪{(u	y)}∪{(u	PROPN
ejpam-3501	414	21	,	,	PUNCT
ejpam-3501	414	22	v	v	NOUN
ejpam-3501	414	23	)	)	PUNCT
ejpam-3501	414	24	}	}	PUNCT
ejpam-3501	415	1	=	=	SYM
ejpam-3501	415	2	∪a∈s∗({a}×t	∪a∈s∗({a}×t	X
ejpam-3501	415	3	∗a	∗a	PROPN
ejpam-3501	415	4	)	)	PUNCT
ejpam-3501	415	5	.	.	PUNCT
ejpam-3501	416	1	since	since	SCONJ
ejpam-3501	416	2	|t	|t	PROPN
ejpam-3501	416	3	∗z	∗z	PROPN
ejpam-3501	417	1	|	|	INTJ
ejpam-3501	417	2	≥	≥	NOUN
ejpam-3501	417	3	2	2	NUM
ejpam-3501	417	4	for	for	ADP
ejpam-3501	417	5	all	all	DET
ejpam-3501	417	6	z	z	NOUN
ejpam-3501	417	7	∈	∈	PROPN
ejpam-3501	417	8	s∗	s∗	PROPN
ejpam-3501	417	9	\n2	\n2	VERB
ejpam-3501	417	10	g(s∗	g(s∗	PROPN
ejpam-3501	417	11	)	)	PUNCT
ejpam-3501	417	12	,	,	PUNCT
ejpam-3501	417	13	c∗	c∗	PROPN
ejpam-3501	417	14	is	be	AUX
ejpam-3501	417	15	a	a	DET
ejpam-3501	417	16	dominating	dominating	NOUN
ejpam-3501	417	17	set	set	VERB
ejpam-3501	417	18	by	by	ADP
ejpam-3501	417	19	theorem	theorem	NOUN
ejpam-3501	417	20	6	6	NUM
ejpam-3501	417	21	.	.	PUNCT
ejpam-3501	418	1	let	let	VERB
ejpam-3501	418	2	(	(	PUNCT
ejpam-3501	418	3	z	z	NOUN
ejpam-3501	418	4	,	,	PUNCT
ejpam-3501	418	5	w	w	NOUN
ejpam-3501	418	6	)	)	PUNCT
ejpam-3501	418	7	∈	∈	PROPN
ejpam-3501	418	8	c∗.	c∗.	NOUN
ejpam-3501	418	9	if	if	SCONJ
ejpam-3501	418	10	z	z	PROPN
ejpam-3501	418	11	∈	∈	PROPN
ejpam-3501	418	12	n2	n2	NOUN
ejpam-3501	418	13	g(s∗	g(s∗	PROPN
ejpam-3501	418	14	)	)	PUNCT
ejpam-3501	418	15	,	,	PUNCT
ejpam-3501	418	16	then	then	ADV
ejpam-3501	418	17	pick	pick	VERB
ejpam-3501	418	18	a	a	DET
ejpam-3501	418	19	∈	∈	NOUN
ejpam-3501	418	20	s∗	s∗	PROPN
ejpam-3501	418	21	\	\	X
ejpam-3501	418	22	{	{	PUNCT
ejpam-3501	418	23	z	z	NOUN
ejpam-3501	418	24	}	}	PUNCT
ejpam-3501	418	25	such	such	ADJ
ejpam-3501	418	26	that	that	SCONJ
ejpam-3501	418	27	dg(z	dg(z	NOUN
ejpam-3501	418	28	,	,	PUNCT
ejpam-3501	418	29	a	a	DET
ejpam-3501	418	30	)	)	PUNCT
ejpam-3501	418	31	≤	≤	NUM
ejpam-3501	418	32	2	2	NUM
ejpam-3501	418	33	.	.	X
ejpam-3501	419	1	for	for	ADP
ejpam-3501	419	2	any	any	DET
ejpam-3501	419	3	b	b	PROPN
ejpam-3501	419	4	∈	∈	PROPN
ejpam-3501	419	5	t	t	NOUN
ejpam-3501	419	6	∗a	∗a	PROPN
ejpam-3501	419	7	,	,	PUNCT
ejpam-3501	419	8	(	(	PUNCT
ejpam-3501	419	9	a	a	DET
ejpam-3501	419	10	,	,	PUNCT
ejpam-3501	419	11	b	b	NOUN
ejpam-3501	419	12	)	)	PUNCT
ejpam-3501	419	13	∈	∈	PROPN
ejpam-3501	419	14	c∗	c∗	NOUN
ejpam-3501	419	15	and	and	CCONJ
ejpam-3501	419	16	dg[kn]((z	dg[kn]((z	NOUN
ejpam-3501	419	17	,	,	PUNCT
ejpam-3501	419	18	w	w	NOUN
ejpam-3501	419	19	)	)	PUNCT
ejpam-3501	419	20	,	,	PUNCT
ejpam-3501	419	21	(	(	PUNCT
ejpam-3501	419	22	a	a	DET
ejpam-3501	419	23	,	,	PUNCT
ejpam-3501	419	24	b	b	NOUN
ejpam-3501	419	25	)	)	PUNCT
ejpam-3501	419	26	)	)	PUNCT
ejpam-3501	419	27	≤	≤	NUM
ejpam-3501	419	28	2	2	NUM
ejpam-3501	419	29	.	.	PUNCT
ejpam-3501	419	30	suppose	suppose	VERB
ejpam-3501	419	31	that	that	SCONJ
ejpam-3501	419	32	z	z	NOUN
ejpam-3501	419	33	/∈	/∈	PUNCT
ejpam-3501	419	34	n2	n2	ADJ
ejpam-3501	419	35	g(s∗	g(s∗	PROPN
ejpam-3501	419	36	)	)	PUNCT
ejpam-3501	419	37	.	.	PUNCT
ejpam-3501	420	1	then	then	ADV
ejpam-3501	420	2	z	z	PROPN
ejpam-3501	420	3	6=	6=	NUM
ejpam-3501	420	4	u	u	NOUN
ejpam-3501	420	5	and	and	CCONJ
ejpam-3501	420	6	|tz|	|tz|	VERB
ejpam-3501	420	7	≥	≥	NOUN
ejpam-3501	420	8	2	2	NUM
ejpam-3501	420	9	,	,	PUNCT
ejpam-3501	420	10	say	say	VERB
ejpam-3501	420	11	w	w	PROPN
ejpam-3501	420	12	,	,	PUNCT
ejpam-3501	420	13	t	t	PROPN
ejpam-3501	420	14	∈	∈	PROPN
ejpam-3501	420	15	tz	tz	PROPN
ejpam-3501	420	16	.	.	PUNCT
ejpam-3501	421	1	then	then	ADV
ejpam-3501	421	2	(	(	PUNCT
ejpam-3501	421	3	z	z	NOUN
ejpam-3501	421	4	,	,	PUNCT
ejpam-3501	421	5	t	t	PROPN
ejpam-3501	421	6	)	)	PUNCT
ejpam-3501	421	7	,	,	PUNCT
ejpam-3501	421	8	(	(	PUNCT
ejpam-3501	421	9	z	z	X
ejpam-3501	421	10	,	,	PUNCT
ejpam-3501	421	11	w	w	NOUN
ejpam-3501	421	12	)	)	PUNCT
ejpam-3501	421	13	∈	∈	PROPN
ejpam-3501	421	14	c∗	c∗	NOUN
ejpam-3501	421	15	and	and	CCONJ
ejpam-3501	421	16	dg[kn]((z	dg[kn]((z	NOUN
ejpam-3501	421	17	,	,	PUNCT
ejpam-3501	421	18	w	w	NOUN
ejpam-3501	421	19	)	)	PUNCT
ejpam-3501	421	20	,	,	PUNCT
ejpam-3501	421	21	(	(	PUNCT
ejpam-3501	421	22	z	z	X
ejpam-3501	421	23	,	,	PUNCT
ejpam-3501	421	24	t	t	PROPN
ejpam-3501	421	25	)	)	PUNCT
ejpam-3501	421	26	)	)	PUNCT
ejpam-3501	422	1	≤	≤	NUM
ejpam-3501	422	2	2	2	NUM
ejpam-3501	422	3	.	.	PUNCT
ejpam-3501	422	4	thus	thus	ADV
ejpam-3501	422	5	c∗	c∗	PROPN
ejpam-3501	422	6	is	be	AUX
ejpam-3501	422	7	a	a	DET
ejpam-3501	422	8	semitotal	semitotal	ADJ
ejpam-3501	422	9	dominating	dominating	NOUN
ejpam-3501	422	10	set	set	NOUN
ejpam-3501	422	11	in	in	ADP
ejpam-3501	422	12	g[kn	g[kn	PROPN
ejpam-3501	422	13	]	]	PUNCT
ejpam-3501	422	14	.	.	PUNCT
ejpam-3501	423	1	corollary	corollary	ADJ
ejpam-3501	423	2	12	12	NUM
ejpam-3501	423	3	.	.	PUNCT
ejpam-3501	424	1	let	let	VERB
ejpam-3501	424	2	g	g	PRON
ejpam-3501	424	3	be	be	AUX
ejpam-3501	424	4	a	a	DET
ejpam-3501	424	5	nontrivial	nontrivial	ADJ
ejpam-3501	424	6	connected	connect	VERB
ejpam-3501	424	7	graph	graph	NOUN
ejpam-3501	424	8	,	,	PUNCT
ejpam-3501	424	9	and	and	CCONJ
ejpam-3501	424	10	let	let	VERB
ejpam-3501	424	11	n	n	PRON
ejpam-3501	424	12	≥	≥	NOUN
ejpam-3501	424	13	2	2	NUM
ejpam-3501	424	14	.	.	PUNCT
ejpam-3501	425	1	then	then	ADV
ejpam-3501	425	2	γst2(g[kn	γst2(g[kn	PROPN
ejpam-3501	425	3	]	]	X
ejpam-3501	425	4	)	)	PUNCT
ejpam-3501	425	5	≤	≤	NOUN
ejpam-3501	425	6	min{γst2(g	min{γst2(g	NOUN
ejpam-3501	425	7	)	)	PUNCT
ejpam-3501	425	8	,	,	PUNCT
ejpam-3501	425	9	2γt2(g	2γt2(g	NUM
ejpam-3501	425	10	)	)	PUNCT
ejpam-3501	425	11	}	}	PUNCT
ejpam-3501	425	12	.	.	PUNCT
ejpam-3501	426	1	references	reference	NOUN
ejpam-3501	426	2	1424	1424	NUM
ejpam-3501	426	3	acknowledgements	acknowledgement	NOUN
ejpam-3501	426	4	this	this	DET
ejpam-3501	426	5	research	research	NOUN
ejpam-3501	426	6	is	be	AUX
ejpam-3501	426	7	fully	fully	ADV
ejpam-3501	426	8	supported	support	VERB
ejpam-3501	426	9	by	by	ADP
ejpam-3501	426	10	the	the	DET
ejpam-3501	426	11	office	office	NOUN
ejpam-3501	426	12	of	of	ADP
ejpam-3501	426	13	the	the	DET
ejpam-3501	426	14	vice	vice	NOUN
ejpam-3501	426	15	chancellor	chancellor	NOUN
ejpam-3501	426	16	for	for	ADP
ejpam-3501	426	17	research	research	NOUN
ejpam-3501	426	18	and	and	CCONJ
ejpam-3501	426	19	extension	extension	NOUN
ejpam-3501	426	20	,	,	PUNCT
ejpam-3501	426	21	msu	msu	PROPN
ejpam-3501	426	22	-	-	PUNCT
ejpam-3501	426	23	iigan	iigan	PROPN
ejpam-3501	426	24	institute	institute	PROPN
ejpam-3501	426	25	of	of	ADP
ejpam-3501	426	26	technology	technology	PROPN
ejpam-3501	426	27	,	,	PUNCT
ejpam-3501	426	28	philippines	philippine	NOUN
ejpam-3501	426	29	,	,	PUNCT
ejpam-3501	426	30	through	through	ADP
ejpam-3501	426	31	the	the	DET
ejpam-3501	426	32	premier	premier	PROPN
ejpam-3501	426	33	research	research	PROPN
ejpam-3501	426	34	institute	institute	PROPN
ejpam-3501	426	35	of	of	ADP
ejpam-3501	426	36	science	science	NOUN
ejpam-3501	426	37	and	and	CCONJ
ejpam-3501	426	38	mathematics	mathematics	PROPN
ejpam-3501	426	39	(	(	PUNCT
ejpam-3501	426	40	prism	prism	NOUN
ejpam-3501	426	41	)	)	PUNCT
ejpam-3501	426	42	.	.	PUNCT
ejpam-3501	427	1	references	reference	NOUN
ejpam-3501	427	2	[	[	X
ejpam-3501	427	3	1	1	NUM
ejpam-3501	427	4	]	]	SYM
ejpam-3501	427	5	b	b	NOUN
ejpam-3501	427	6	acharya	acharya	NOUN
ejpam-3501	427	7	,	,	PUNCT
ejpam-3501	427	8	e	e	PROPN
ejpam-3501	427	9	samathkumar	samathkumar	NOUN
ejpam-3501	427	10	and	and	CCONJ
ejpam-3501	427	11	h.	h.	PROPN
ejpam-3501	427	12	walikar	walikar	PROPN
ejpam-3501	427	13	.	.	PUNCT
ejpam-3501	428	1	recent	recent	ADJ
ejpam-3501	428	2	developments	development	NOUN
ejpam-3501	428	3	in	in	ADP
ejpam-3501	428	4	the	the	DET
ejpam-3501	428	5	theory	theory	NOUN
ejpam-3501	428	6	of	of	ADP
ejpam-3501	428	7	domination	domination	NOUN
ejpam-3501	428	8	in	in	ADP
ejpam-3501	428	9	graphs	graph	NOUN
ejpam-3501	428	10	.	.	PUNCT
ejpam-3501	429	1	allahabad	allahabad	PROPN
ejpam-3501	429	2	,	,	PUNCT
ejpam-3501	429	3	1	1	NUM
ejpam-3501	429	4	,	,	PUNCT
ejpam-3501	429	5	1979	1979	NUM
ejpam-3501	429	6	.	.	PUNCT
ejpam-3501	430	1	[	[	X
ejpam-3501	430	2	2	2	NUM
ejpam-3501	430	3	]	]	X
ejpam-3501	430	4	c	c	PROPN
ejpam-3501	430	5	armada	armada	PROPN
ejpam-3501	430	6	,	,	PUNCT
ejpam-3501	430	7	c	c	PRON
ejpam-3501	430	8	go	go	VERB
ejpam-3501	430	9	and	and	CCONJ
ejpam-3501	430	10	s	s	VERB
ejpam-3501	430	11	jr	jr	PROPN
ejpam-3501	430	12	canoy	canoy	NOUN
ejpam-3501	430	13	.	.	PUNCT
ejpam-3501	431	1	forcing	force	VERB
ejpam-3501	431	2	domination	domination	NOUN
ejpam-3501	431	3	numbers	number	NOUN
ejpam-3501	431	4	of	of	ADP
ejpam-3501	431	5	graphs	graph	NOUN
ejpam-3501	431	6	under	under	ADP
ejpam-3501	431	7	some	some	DET
ejpam-3501	431	8	binary	binary	ADJ
ejpam-3501	431	9	operations	operation	NOUN
ejpam-3501	431	10	.	.	PUNCT
ejpam-3501	432	1	advances	advance	NOUN
ejpam-3501	432	2	and	and	CCONJ
ejpam-3501	432	3	applications	application	NOUN
ejpam-3501	432	4	in	in	ADP
ejpam-3501	432	5	discrete	discrete	ADJ
ejpam-3501	432	6	mathematics	mathematic	NOUN
ejpam-3501	432	7	,	,	PUNCT
ejpam-3501	432	8	vol	vol	NOUN
ejpam-3501	432	9	.	.	NOUN
ejpam-3501	432	10	19(3	19(3	NUM
ejpam-3501	432	11	)	)	PUNCT
ejpam-3501	432	12	,	,	PUNCT
ejpam-3501	432	13	213	213	NUM
ejpam-3501	432	14	-	-	SYM
ejpam-3501	432	15	228	228	NUM
ejpam-3501	432	16	,	,	PUNCT
ejpam-3501	432	17	2018	2018	NUM
ejpam-3501	433	1	[	[	X
ejpam-3501	433	2	3	3	NUM
ejpam-3501	433	3	]	]	X
ejpam-3501	433	4	c	c	PROPN
ejpam-3501	433	5	armada	armada	PROPN
ejpam-3501	433	6	,	,	PUNCT
ejpam-3501	433	7	c	c	PRON
ejpam-3501	433	8	go	go	VERB
ejpam-3501	433	9	and	and	CCONJ
ejpam-3501	433	10	s	s	VERB
ejpam-3501	433	11	jr	jr	PROPN
ejpam-3501	433	12	canoy	canoy	NOUN
ejpam-3501	433	13	.	.	PUNCT
ejpam-3501	434	1	forcing	force	VERB
ejpam-3501	434	2	subsets	subset	NOUN
ejpam-3501	434	3	for	for	ADP
ejpam-3501	434	4	γc	γc	NOUN
ejpam-3501	434	5	-	-	PUNCT
ejpam-3501	434	6	sets	set	NOUN
ejpam-3501	434	7	and	and	CCONJ
ejpam-3501	434	8	γt	γt	NOUN
ejpam-3501	434	9	-	-	NOUN
ejpam-3501	434	10	sets	set	NOUN
ejpam-3501	434	11	of	of	ADP
ejpam-3501	434	12	the	the	DET
ejpam-3501	434	13	lexicographic	lexicographic	ADJ
ejpam-3501	434	14	product	product	NOUN
ejpam-3501	434	15	of	of	ADP
ejpam-3501	434	16	graphs	graph	NOUN
ejpam-3501	434	17	.	.	PUNCT
ejpam-3501	435	1	advances	advance	NOUN
ejpam-3501	435	2	and	and	CCONJ
ejpam-3501	435	3	applications	application	NOUN
ejpam-3501	435	4	in	in	ADP
ejpam-3501	435	5	discrete	discrete	ADJ
ejpam-3501	435	6	mathematics	mathematic	NOUN
ejpam-3501	435	7	,	,	PUNCT
ejpam-3501	435	8	submitted	submit	VERB
ejpam-3501	435	9	.	.	PUNCT
ejpam-3501	436	1	[	[	X
ejpam-3501	436	2	4	4	NUM
ejpam-3501	436	3	]	]	X
ejpam-3501	436	4	s	s	VERB
ejpam-3501	436	5	arumugam	arumugam	NOUN
ejpam-3501	436	6	,	,	PUNCT
ejpam-3501	436	7	d	d	PROPN
ejpam-3501	436	8	rashmi	rashmi	PROPN
ejpam-3501	436	9	and	and	CCONJ
ejpam-3501	436	10	a	a	DET
ejpam-3501	436	11	somasundaram	somasundaram	NOUN
ejpam-3501	436	12	.	.	PUNCT
ejpam-3501	437	1	global	global	ADJ
ejpam-3501	437	2	secure	secure	ADJ
ejpam-3501	437	3	domination	domination	NOUN
ejpam-3501	437	4	in	in	ADP
ejpam-3501	437	5	graphs	graph	NOUN
ejpam-3501	437	6	,	,	PUNCT
ejpam-3501	437	7	theoretical	theoretical	ADJ
ejpam-3501	437	8	computer	computer	NOUN
ejpam-3501	437	9	science	science	NOUN
ejpam-3501	437	10	and	and	CCONJ
ejpam-3501	437	11	discrete	discrete	ADJ
ejpam-3501	437	12	mathematics	mathematic	NOUN
ejpam-3501	437	13	.	.	PUNCT
ejpam-3501	438	1	lecture	lecture	NOUN
ejpam-3501	438	2	notes	note	NOUN
ejpam-3501	438	3	in	in	ADP
ejpam-3501	438	4	computer	computer	NOUN
ejpam-3501	438	5	science	science	NOUN
ejpam-3501	438	6	,	,	PUNCT
ejpam-3501	438	7	vol	vol	NOUN
ejpam-3501	438	8	.	.	PROPN
ejpam-3501	438	9	10398	10398	NUM
ejpam-3501	438	10	,	,	PUNCT
ejpam-3501	438	11	50	50	NUM
ejpam-3501	438	12	-	-	SYM
ejpam-3501	438	13	54	54	NUM
ejpam-3501	438	14	,	,	PUNCT
ejpam-3501	438	15	2016	2016	NUM
ejpam-3501	438	16	.	.	PUNCT
ejpam-3501	439	1	[	[	X
ejpam-3501	439	2	5	5	NUM
ejpam-3501	439	3	]	]	PUNCT
ejpam-3501	439	4	s	s	PART
ejpam-3501	439	5	benecke	benecke	NOUN
ejpam-3501	439	6	,	,	PUNCT
ejpam-3501	439	7	ej	ej	PROPN
ejpam-3501	439	8	cockayne	cockayne	PROPN
ejpam-3501	439	9	and	and	CCONJ
ejpam-3501	439	10	cm	cm	NOUN
ejpam-3501	439	11	mynhardt	mynhardt	ADJ
ejpam-3501	439	12	.	.	PUNCT
ejpam-3501	440	1	secure	secure	ADJ
ejpam-3501	440	2	total	total	ADJ
ejpam-3501	440	3	domination	domination	NOUN
ejpam-3501	440	4	in	in	ADP
ejpam-3501	440	5	graphs	graph	NOUN
ejpam-3501	440	6	.	.	PUNCT
ejpam-3501	441	1	utilitas	utilitas	PROPN
ejpam-3501	441	2	mathematica	mathematica	PROPN
ejpam-3501	441	3	,	,	PUNCT
ejpam-3501	441	4	vol	vol	NOUN
ejpam-3501	441	5	.	.	PROPN
ejpam-3501	441	6	74	74	NUM
ejpam-3501	441	7	,	,	PUNCT
ejpam-3501	441	8	247	247	NUM
ejpam-3501	441	9	-	-	SYM
ejpam-3501	441	10	259	259	NUM
ejpam-3501	441	11	,	,	PUNCT
ejpam-3501	441	12	2017	2017	NUM
ejpam-3501	441	13	.	.	PUNCT
ejpam-3501	442	1	[	[	X
ejpam-3501	442	2	6	6	NUM
ejpam-3501	442	3	]	]	X
ejpam-3501	442	4	j	j	PROPN
ejpam-3501	442	5	bondy	bondy	PROPN
ejpam-3501	442	6	and	and	CCONJ
ejpam-3501	442	7	g	g	PROPN
ejpam-3501	442	8	fan	fan	NOUN
ejpam-3501	442	9	.	.	PUNCT
ejpam-3501	443	1	a	a	DET
ejpam-3501	443	2	sufficient	sufficient	ADJ
ejpam-3501	443	3	condition	condition	NOUN
ejpam-3501	443	4	for	for	ADP
ejpam-3501	443	5	dominating	dominating	NOUN
ejpam-3501	443	6	cycles	cycle	NOUN
ejpam-3501	443	7	.	.	PUNCT
ejpam-3501	444	1	discrete	discrete	ADJ
ejpam-3501	444	2	math	math	NOUN
ejpam-3501	444	3	.	.	PUNCT
ejpam-3501	444	4	,	,	PUNCT
ejpam-3501	444	5	67(2	67(2	NUM
ejpam-3501	444	6	)	)	PUNCT
ejpam-3501	444	7	,	,	PUNCT
ejpam-3501	444	8	205	205	NUM
ejpam-3501	444	9	-	-	SYM
ejpam-3501	444	10	208	208	NUM
ejpam-3501	444	11	,	,	PUNCT
ejpam-3501	444	12	1987	1987	NUM
ejpam-3501	444	13	.	.	PUNCT
ejpam-3501	445	1	[	[	X
ejpam-3501	445	2	7	7	NUM
ejpam-3501	445	3	]	]	SYM
ejpam-3501	445	4	f	f	PROPN
ejpam-3501	445	5	buckley	buckley	PROPN
ejpam-3501	445	6	and	and	CCONJ
ejpam-3501	445	7	f	f	PROPN
ejpam-3501	445	8	harary	harary	NOUN
ejpam-3501	445	9	.	.	PUNCT
ejpam-3501	446	1	distance	distance	NOUN
ejpam-3501	446	2	in	in	ADP
ejpam-3501	446	3	graphs	graph	NOUN
ejpam-3501	446	4	.	.	PUNCT
ejpam-3501	447	1	redwood	redwood	NOUN
ejpam-3501	447	2	city	city	NOUN
ejpam-3501	447	3	.	.	PUNCT
ejpam-3501	448	1	ca	can	AUX
ejpam-3501	448	2	:	:	PUNCT
ejpam-3501	448	3	addisonwesley,1990	addisonwesley,1990	NOUN
ejpam-3501	448	4	.	.	PUNCT
ejpam-3501	449	1	[	[	X
ejpam-3501	449	2	8	8	NUM
ejpam-3501	449	3	]	]	SYM
ejpam-3501	449	4	s	s	PART
ejpam-3501	449	5	jr	jr	PROPN
ejpam-3501	449	6	canoy	canoy	PROPN
ejpam-3501	449	7	and	and	CCONJ
ejpam-3501	449	8	c	c	AUX
ejpam-3501	449	9	go	go	VERB
ejpam-3501	449	10	.	.	PUNCT
ejpam-3501	450	1	domination	domination	NOUN
ejpam-3501	450	2	in	in	ADP
ejpam-3501	450	3	the	the	DET
ejpam-3501	450	4	corona	corona	NOUN
ejpam-3501	450	5	and	and	CCONJ
ejpam-3501	450	6	join	join	VERB
ejpam-3501	450	7	of	of	ADP
ejpam-3501	450	8	graphs	graph	NOUN
ejpam-3501	450	9	.	.	PUNCT
ejpam-3501	451	1	international	international	ADJ
ejpam-3501	451	2	mathematical	mathematical	PROPN
ejpam-3501	451	3	forum	forum	PROPN
ejpam-3501	451	4	,	,	PUNCT
ejpam-3501	451	5	vol	vol	NOUN
ejpam-3501	451	6	.	.	PROPN
ejpam-3501	451	7	6(16	6(16	NUM
ejpam-3501	451	8	)	)	PUNCT
ejpam-3501	451	9	,	,	PUNCT
ejpam-3501	451	10	763	763	NUM
ejpam-3501	451	11	771	771	NUM
ejpam-3501	451	12	,	,	PUNCT
ejpam-3501	451	13	2011	2011	NUM
ejpam-3501	451	14	.	.	PUNCT
ejpam-3501	452	1	[	[	X
ejpam-3501	452	2	9	9	NUM
ejpam-3501	452	3	]	]	SYM
ejpam-3501	452	4	s	s	PART
ejpam-3501	452	5	jr	jr	PROPN
ejpam-3501	452	6	canoy	canoy	PROPN
ejpam-3501	452	7	,	,	PUNCT
ejpam-3501	452	8	f	f	PROPN
ejpam-3501	452	9	jamil	jamil	PROPN
ejpam-3501	452	10	and	and	CCONJ
ejpam-3501	452	11	t	t	PROPN
ejpam-3501	452	12	tacbobo	tacbobo	NOUN
ejpam-3501	452	13	.	.	PUNCT
ejpam-3501	453	1	monophonic	monophonic	ADJ
ejpam-3501	453	2	and	and	CCONJ
ejpam-3501	453	3	geodetic	geodetic	ADJ
ejpam-3501	453	4	domination	domination	NOUN
ejpam-3501	453	5	in	in	ADP
ejpam-3501	453	6	the	the	DET
ejpam-3501	453	7	join	join	NOUN
ejpam-3501	453	8	.	.	PUNCT
ejpam-3501	454	1	corona	corona	NOUN
ejpam-3501	454	2	and	and	CCONJ
ejpam-3501	454	3	composition	composition	NOUN
ejpam-3501	454	4	of	of	ADP
ejpam-3501	454	5	graphs	graph	NOUN
ejpam-3501	454	6	.	.	PUNCT
ejpam-3501	455	1	ars	ars	PROPN
ejpam-3501	455	2	combinatoria	combinatoria	PROPN
ejpam-3501	455	3	,	,	PUNCT
ejpam-3501	455	4	vol	vol	NOUN
ejpam-3501	455	5	.	.	PROPN
ejpam-3501	455	6	112	112	NUM
ejpam-3501	455	7	,	,	PUNCT
ejpam-3501	455	8	2013	2013	NUM
ejpam-3501	455	9	.	.	PUNCT
ejpam-3501	456	1	[	[	X
ejpam-3501	456	2	10	10	NUM
ejpam-3501	456	3	]	]	X
ejpam-3501	456	4	m	m	VERB
ejpam-3501	456	5	chellali	chellali	ADJ
ejpam-3501	456	6	and	and	CCONJ
ejpam-3501	456	7	h	h	NOUN
ejpam-3501	456	8	merouane	merouane	NOUN
ejpam-3501	456	9	.	.	PUNCT
ejpam-3501	457	1	on	on	ADP
ejpam-3501	457	2	secure	secure	ADJ
ejpam-3501	457	3	domination	domination	NOUN
ejpam-3501	457	4	in	in	ADP
ejpam-3501	457	5	graphs	graph	NOUN
ejpam-3501	457	6	.	.	PUNCT
ejpam-3501	458	1	information	information	NOUN
ejpam-3501	458	2	processing	processing	NOUN
ejpam-3501	458	3	letters	letter	NOUN
ejpam-3501	458	4	,	,	PUNCT
ejpam-3501	458	5	vol	vol	NOUN
ejpam-3501	458	6	.	.	PROPN
ejpam-3501	458	7	115	115	NUM
ejpam-3501	458	8	,	,	PUNCT
ejpam-3501	458	9	786	786	NUM
ejpam-3501	458	10	-	-	SYM
ejpam-3501	458	11	790	790	NUM
ejpam-3501	458	12	,	,	PUNCT
ejpam-3501	458	13	2015	2015	NUM
ejpam-3501	458	14	.	.	PUNCT
ejpam-3501	459	1	[	[	X
ejpam-3501	459	2	11	11	NUM
ejpam-3501	459	3	]	]	X
ejpam-3501	459	4	e	e	X
ejpam-3501	459	5	cockayne	cockayne	NOUN
ejpam-3501	459	6	and	and	CCONJ
ejpam-3501	459	7	s	s	VERB
ejpam-3501	459	8	hedetniemi	hedetniemi	ADV
ejpam-3501	459	9	.	.	PUNCT
ejpam-3501	460	1	towards	towards	ADP
ejpam-3501	460	2	a	a	DET
ejpam-3501	460	3	theory	theory	NOUN
ejpam-3501	460	4	of	of	ADP
ejpam-3501	460	5	domination	domination	NOUN
ejpam-3501	460	6	in	in	ADP
ejpam-3501	460	7	graphs	graph	NOUN
ejpam-3501	460	8	.	.	PUNCT
ejpam-3501	461	1	networks	network	NOUN
ejpam-3501	461	2	,	,	PUNCT
ejpam-3501	461	3	7(3	7(3	NUM
ejpam-3501	461	4	)	)	PUNCT
ejpam-3501	461	5	,	,	PUNCT
ejpam-3501	461	6	247	247	NUM
ejpam-3501	461	7	-	-	SYM
ejpam-3501	461	8	261	261	NUM
ejpam-3501	461	9	,	,	PUNCT
ejpam-3501	461	10	1977	1977	NUM
ejpam-3501	461	11	.	.	PUNCT
ejpam-3501	462	1	[	[	X
ejpam-3501	462	2	12	12	NUM
ejpam-3501	462	3	]	]	X
ejpam-3501	462	4	o	o	NOUN
ejpam-3501	462	5	duginov	duginov	NOUN
ejpam-3501	462	6	.	.	PUNCT
ejpam-3501	463	1	secure	secure	VERB
ejpam-3501	463	2	total	total	ADJ
ejpam-3501	463	3	domination	domination	NOUN
ejpam-3501	463	4	in	in	ADP
ejpam-3501	463	5	graphs	graph	NOUN
ejpam-3501	463	6	.	.	PUNCT
ejpam-3501	464	1	discrete	discrete	ADJ
ejpam-3501	464	2	applied	apply	VERB
ejpam-3501	464	3	mathematics	mathematic	NOUN
ejpam-3501	464	4	,	,	PUNCT
ejpam-3501	464	5	vol	vol	NOUN
ejpam-3501	464	6	222(c	222(c	NUM
ejpam-3501	464	7	)	)	PUNCT
ejpam-3501	464	8	,	,	PUNCT
ejpam-3501	464	9	97	97	NUM
ejpam-3501	464	10	-	-	SYM
ejpam-3501	464	11	108	108	NUM
ejpam-3501	464	12	.	.	PUNCT
ejpam-3501	465	1	references	reference	NOUN
ejpam-3501	465	2	1425	1425	NUM
ejpam-3501	465	3	[	[	X
ejpam-3501	465	4	13	13	NUM
ejpam-3501	465	5	]	]	SYM
ejpam-3501	465	6	w	w	NOUN
ejpam-3501	465	7	goddard	goddard	PROPN
ejpam-3501	465	8	,	,	PUNCT
ejpam-3501	465	9	m	m	VERB
ejpam-3501	465	10	henning	henning	PROPN
ejpam-3501	465	11	and	and	CCONJ
ejpam-3501	465	12	c	c	PROPN
ejpam-3501	465	13	mcpil	mcpil	PROPN
ejpam-3501	465	14	.	.	PUNCT
ejpam-3501	466	1	semitotal	semitotal	ADJ
ejpam-3501	466	2	domination	domination	NOUN
ejpam-3501	466	3	in	in	ADP
ejpam-3501	466	4	graphs	graph	NOUN
ejpam-3501	466	5	.	.	PUNCT
ejpam-3501	467	1	utilitas	utilitas	PROPN
ejpam-3501	467	2	mathematica	mathematica	PROPN
ejpam-3501	467	3	,	,	PUNCT
ejpam-3501	467	4	vol	vol	NOUN
ejpam-3501	467	5	94	94	NUM
ejpam-3501	467	6	,	,	PUNCT
ejpam-3501	467	7	67	67	NUM
ejpam-3501	467	8	-	-	SYM
ejpam-3501	467	9	81	81	NUM
ejpam-3501	467	10	,	,	PUNCT
ejpam-3501	467	11	2014	2014	NUM
ejpam-3501	467	12	.	.	PUNCT
ejpam-3501	468	1	[	[	X
ejpam-3501	468	2	14	14	NUM
ejpam-3501	468	3	]	]	X
ejpam-3501	468	4	g	g	PROPN
ejpam-3501	468	5	hao	hao	PROPN
ejpam-3501	468	6	and	and	CCONJ
ejpam-3501	468	7	w	w	PROPN
ejpam-3501	468	8	zhuang	zhuang	PROPN
ejpam-3501	468	9	.	.	PROPN
ejpam-3501	469	1	semitota	semitota	PROPN
ejpam-3501	469	2	domination	domination	NOUN
ejpam-3501	469	3	in	in	ADP
ejpam-3501	469	4	trees	tree	NOUN
ejpam-3501	469	5	.	.	PUNCT
ejpam-3501	470	1	discrete	discrete	ADJ
ejpam-3501	470	2	mathematics	mathematic	NOUN
ejpam-3501	470	3	and	and	CCONJ
ejpam-3501	470	4	theoretical	theoretical	ADJ
ejpam-3501	470	5	computer	computer	NOUN
ejpam-3501	470	6	science	science	NOUN
ejpam-3501	470	7	,	,	PUNCT
ejpam-3501	470	8	vol	vol	NOUN
ejpam-3501	470	9	.	.	PUNCT
ejpam-3501	470	10	20(2	20(2	NUM
ejpam-3501	470	11	)	)	PUNCT
ejpam-3501	470	12	,	,	PUNCT
ejpam-3501	470	13	1	1	NUM
ejpam-3501	470	14	-	-	SYM
ejpam-3501	470	15	11	11	NUM
ejpam-3501	470	16	,	,	PUNCT
ejpam-3501	470	17	2018	2018	NUM
ejpam-3501	470	18	.	.	PUNCT
ejpam-3501	471	1	[	[	X
ejpam-3501	471	2	15	15	NUM
ejpam-3501	471	3	]	]	X
ejpam-3501	471	4	t	t	PROPN
ejpam-3501	471	5	haynes	haynes	PROPN
ejpam-3501	471	6	,	,	PUNCT
ejpam-3501	471	7	s	s	VERB
ejpam-3501	471	8	hedetniemi	hedetniemi	ADV
ejpam-3501	471	9	and	and	CCONJ
ejpam-3501	471	10	m	m	PROPN
ejpam-3501	471	11	henning	henning	NOUN
ejpam-3501	471	12	.	.	PUNCT
ejpam-3501	472	1	domination	domination	NOUN
ejpam-3501	472	2	in	in	ADP
ejpam-3501	472	3	graphs	graph	NOUN
ejpam-3501	472	4	applied	apply	VERB
ejpam-3501	472	5	to	to	ADP
ejpam-3501	472	6	electrical	electrical	ADJ
ejpam-3501	472	7	power	power	NOUN
ejpam-3501	472	8	networks	network	NOUN
ejpam-3501	472	9	.	.	PUNCT
ejpam-3501	473	1	j.	j.	PROPN
ejpam-3501	473	2	discrete	discrete	PROPN
ejpam-3501	473	3	math	math	PROPN
ejpam-3501	473	4	.	.	PUNCT
ejpam-3501	473	5	,	,	PUNCT
ejpam-3501	473	6	15(4	15(4	NUM
ejpam-3501	473	7	)	)	PUNCT
ejpam-3501	473	8	,	,	PUNCT
ejpam-3501	473	9	2000	2000	NUM
ejpam-3501	473	10	.	.	PUNCT
ejpam-3501	474	1	[	[	X
ejpam-3501	474	2	16	16	NUM
ejpam-3501	474	3	]	]	PUNCT
ejpam-3501	474	4	t	t	PROPN
ejpam-3501	474	5	haynes	haynes	PROPN
ejpam-3501	474	6	,	,	PUNCT
ejpam-3501	474	7	s	s	VERB
ejpam-3501	474	8	hedetniemi	hedetniemi	ADV
ejpam-3501	474	9	and	and	CCONJ
ejpam-3501	474	10	p	p	X
ejpam-3501	474	11	slater	slater	NOUN
ejpam-3501	474	12	.	.	PUNCT
ejpam-3501	475	1	fundamentals	fundamental	NOUN
ejpam-3501	475	2	of	of	ADP
ejpam-3501	475	3	domination	domination	NOUN
ejpam-3501	475	4	in	in	ADP
ejpam-3501	475	5	graphs	graph	NOUN
ejpam-3501	475	6	.	.	PUNCT
ejpam-3501	476	1	marcel	marcel	PROPN
ejpam-3501	476	2	dekker	dekker	PROPN
ejpam-3501	476	3	,	,	PUNCT
ejpam-3501	476	4	inc	inc	PROPN
ejpam-3501	476	5	.	.	PROPN
ejpam-3501	476	6	new	new	PROPN
ejpam-3501	476	7	york	york	PROPN
ejpam-3501	476	8	,	,	PUNCT
ejpam-3501	476	9	1998	1998	NUM
ejpam-3501	476	10	.	.	PUNCT
ejpam-3501	477	1	[	[	X
ejpam-3501	477	2	17	17	NUM
ejpam-3501	477	3	]	]	X
ejpam-3501	477	4	m	m	AUX
ejpam-3501	477	5	henning	henning	NOUN
ejpam-3501	477	6	and	and	CCONJ
ejpam-3501	477	7	a	a	DET
ejpam-3501	477	8	marcon	marcon	NOUN
ejpam-3501	477	9	.	.	PUNCT
ejpam-3501	478	1	on	on	ADP
ejpam-3501	478	2	matching	match	VERB
ejpam-3501	478	3	and	and	CCONJ
ejpam-3501	478	4	semitotal	semitotal	ADJ
ejpam-3501	478	5	domination	domination	NOUN
ejpam-3501	478	6	in	in	ADP
ejpam-3501	478	7	graphs	graph	NOUN
ejpam-3501	478	8	.	.	PUNCT
ejpam-3501	479	1	discrete	discrete	ADJ
ejpam-3501	479	2	mathematics	mathematic	NOUN
ejpam-3501	479	3	,	,	PUNCT
ejpam-3501	479	4	vol	vol	NOUN
ejpam-3501	479	5	324(6	324(6	NUM
ejpam-3501	479	6	)	)	PUNCT
ejpam-3501	479	7	,	,	PUNCT
ejpam-3501	479	8	13	13	NUM
ejpam-3501	479	9	-	-	SYM
ejpam-3501	479	10	18	18	NUM
ejpam-3501	479	11	,	,	PUNCT
ejpam-3501	479	12	2014	2014	NUM
ejpam-3501	479	13	.	.	PUNCT
ejpam-3501	480	1	[	[	X
ejpam-3501	480	2	18	18	NUM
ejpam-3501	480	3	]	]	X
ejpam-3501	480	4	m	m	AUX
ejpam-3501	480	5	henning	henning	NOUN
ejpam-3501	480	6	and	and	CCONJ
ejpam-3501	480	7	a	a	DET
ejpam-3501	480	8	marcon	marcon	NOUN
ejpam-3501	480	9	.	.	PUNCT
ejpam-3501	481	1	semitotal	semitotal	ADJ
ejpam-3501	481	2	domination	domination	NOUN
ejpam-3501	481	3	in	in	ADP
ejpam-3501	481	4	claw	claw	NOUN
ejpam-3501	481	5	-	-	PUNCT
ejpam-3501	481	6	free	free	ADJ
ejpam-3501	481	7	cubic	cubic	ADJ
ejpam-3501	481	8	graphs	graph	NOUN
ejpam-3501	481	9	.	.	PUNCT
ejpam-3501	482	1	annals	annal	NOUN
ejpam-3501	482	2	of	of	ADP
ejpam-3501	482	3	combinatorics	combinatoric	NOUN
ejpam-3501	482	4	,	,	PUNCT
ejpam-3501	482	5	vol	vol	NOUN
ejpam-3501	482	6	20(4	20(4	NOUN
ejpam-3501	482	7	)	)	PUNCT
ejpam-3501	482	8	,	,	PUNCT
ejpam-3501	482	9	799	799	NUM
ejpam-3501	482	10	-	-	SYM
ejpam-3501	482	11	813	813	NUM
ejpam-3501	482	12	,	,	PUNCT
ejpam-3501	482	13	2016	2016	NUM
ejpam-3501	482	14	.	.	PUNCT
ejpam-3501	483	1	[	[	X
ejpam-3501	483	2	19	19	NUM
ejpam-3501	483	3	]	]	SYM
ejpam-3501	483	4	w	w	NOUN
ejpam-3501	483	5	klostermeyer	klostermeyer	NOUN
ejpam-3501	483	6	and	and	CCONJ
ejpam-3501	483	7	c	c	PROPN
ejpam-3501	483	8	mynhardt	mynhardt	ADJ
ejpam-3501	483	9	.	.	PUNCT
ejpam-3501	484	1	secure	secure	ADJ
ejpam-3501	484	2	domination	domination	NOUN
ejpam-3501	484	3	and	and	CCONJ
ejpam-3501	484	4	secure	secure	VERB
ejpam-3501	484	5	total	total	ADJ
ejpam-3501	484	6	domination	domination	NOUN
ejpam-3501	484	7	in	in	ADP
ejpam-3501	484	8	graphs	graph	NOUN
ejpam-3501	484	9	.	.	PUNCT
ejpam-3501	485	1	discussiones	discussione	NOUN
ejpam-3501	485	2	mathematicae	mathematicae	PROPN
ejpam-3501	485	3	graph	graph	NOUN
ejpam-3501	485	4	theory	theory	NOUN
ejpam-3501	485	5	,	,	PUNCT
ejpam-3501	485	6	vol	vol	NOUN
ejpam-3501	485	7	.	.	PROPN
ejpam-3501	485	8	28	28	NUM
ejpam-3501	485	9	,	,	PUNCT
ejpam-3501	485	10	267	267	NUM
ejpam-3501	485	11	-	-	SYM
ejpam-3501	485	12	284	284	NUM
ejpam-3501	485	13	,	,	PUNCT
ejpam-3501	485	14	2008	2008	NUM
ejpam-3501	485	15	.	.	PUNCT