id	sid	tid	token	lemma	pos
ejpam-4645	1	1	european	european	PROPN
ejpam-4645	1	2	journal	journal	PROPN
ejpam-4645	1	3	of	of	ADP
ejpam-4645	1	4	pure	pure	ADJ
ejpam-4645	1	5	and	and	CCONJ
ejpam-4645	1	6	applied	apply	VERB
ejpam-4645	1	7	mathematics	mathematic	NOUN
ejpam-4645	1	8	vol	vol	NOUN
ejpam-4645	1	9	.	.	PUNCT
ejpam-4645	2	1	16	16	NUM
ejpam-4645	2	2	,	,	PUNCT
ejpam-4645	2	3	no	no	INTJ
ejpam-4645	2	4	.	.	NOUN
ejpam-4645	2	5	1	1	NUM
ejpam-4645	2	6	,	,	PUNCT
ejpam-4645	2	7	2023	2023	NUM
ejpam-4645	2	8	,	,	PUNCT
ejpam-4645	2	9	479	479	NUM
ejpam-4645	2	10	-	-	SYM
ejpam-4645	2	11	490	490	NUM
ejpam-4645	2	12	issn	issn	PROPN
ejpam-4645	2	13	1307	1307	NUM
ejpam-4645	2	14	-	-	SYM
ejpam-4645	2	15	5543	5543	NUM
ejpam-4645	2	16	–	–	PUNCT
ejpam-4645	2	17	ejpam.com	ejpam.com	X
ejpam-4645	2	18	published	publish	VERB
ejpam-4645	2	19	by	by	ADP
ejpam-4645	2	20	new	new	PROPN
ejpam-4645	2	21	york	york	PROPN
ejpam-4645	2	22	business	business	PROPN
ejpam-4645	2	23	global	global	ADJ
ejpam-4645	2	24	stable	stable	ADJ
ejpam-4645	2	25	locating	locating	NOUN
ejpam-4645	2	26	-	-	PUNCT
ejpam-4645	2	27	dominating	dominating	NOUN
ejpam-4645	2	28	sets	set	NOUN
ejpam-4645	2	29	in	in	ADP
ejpam-4645	2	30	the	the	DET
ejpam-4645	2	31	edge	edge	NOUN
ejpam-4645	2	32	corona	corona	NOUN
ejpam-4645	2	33	and	and	CCONJ
ejpam-4645	2	34	lexicographic	lexicographic	ADJ
ejpam-4645	2	35	product	product	NOUN
ejpam-4645	2	36	of	of	ADP
ejpam-4645	2	37	graphs	graph	NOUN
ejpam-4645	2	38	gina	gina	PROPN
ejpam-4645	2	39	a.	a.	PROPN
ejpam-4645	2	40	malacas1,∗	malacas1,∗	PROPN
ejpam-4645	2	41	,	,	PUNCT
ejpam-4645	2	42	sergio	sergio	PROPN
ejpam-4645	2	43	r.	r.	PROPN
ejpam-4645	2	44	canoy	canoy	PROPN
ejpam-4645	2	45	,	,	PUNCT
ejpam-4645	2	46	jr.1	jr.1	NOUN
ejpam-4645	2	47	,	,	PUNCT
ejpam-4645	2	48	emmy	emmy	ADJ
ejpam-4645	2	49	chacon1	chacon1	NOUN
ejpam-4645	2	50	1	1	NUM
ejpam-4645	2	51	department	department	NOUN
ejpam-4645	2	52	of	of	ADP
ejpam-4645	2	53	mathematics	mathematic	NOUN
ejpam-4645	2	54	and	and	CCONJ
ejpam-4645	2	55	statistics	statistic	NOUN
ejpam-4645	2	56	,	,	PUNCT
ejpam-4645	2	57	college	college	NOUN
ejpam-4645	2	58	of	of	ADP
ejpam-4645	2	59	science	science	NOUN
ejpam-4645	2	60	and	and	CCONJ
ejpam-4645	2	61	mathematics	mathematic	NOUN
ejpam-4645	2	62	,	,	PUNCT
ejpam-4645	2	63	center	center	NOUN
ejpam-4645	2	64	for	for	ADP
ejpam-4645	2	65	graph	graph	NOUN
ejpam-4645	2	66	theory	theory	NOUN
ejpam-4645	2	67	,	,	PUNCT
ejpam-4645	2	68	algebra	algebra	NOUN
ejpam-4645	2	69	and	and	CCONJ
ejpam-4645	2	70	analysis	analysis	NOUN
ejpam-4645	2	71	-	-	PUNCT
ejpam-4645	2	72	prism	prism	NOUN
ejpam-4645	2	73	,	,	PUNCT
ejpam-4645	2	74	msu	msu	PROPN
ejpam-4645	2	75	-	-	PUNCT
ejpam-4645	2	76	iligan	iligan	PROPN
ejpam-4645	2	77	institute	institute	PROPN
ejpam-4645	2	78	of	of	ADP
ejpam-4645	2	79	technology	technology	PROPN
ejpam-4645	2	80	,	,	PUNCT
ejpam-4645	2	81	9200	9200	NUM
ejpam-4645	2	82	iligan	iligan	ADJ
ejpam-4645	2	83	city	city	NOUN
ejpam-4645	2	84	,	,	PUNCT
ejpam-4645	2	85	philippines	philippine	NOUN
ejpam-4645	2	86	abstract	abstract	ADJ
ejpam-4645	2	87	.	.	PUNCT
ejpam-4645	3	1	a	a	DET
ejpam-4645	3	2	set	set	NOUN
ejpam-4645	3	3	s	s	NOUN
ejpam-4645	3	4	⊆	⊆	NUM
ejpam-4645	3	5	v	v	NOUN
ejpam-4645	3	6	(	(	PUNCT
ejpam-4645	3	7	g	g	NOUN
ejpam-4645	3	8	)	)	PUNCT
ejpam-4645	3	9	of	of	ADP
ejpam-4645	3	10	an	an	DET
ejpam-4645	3	11	undirected	undirected	ADJ
ejpam-4645	3	12	graph	graph	NOUN
ejpam-4645	3	13	g	g	PROPN
ejpam-4645	3	14	is	be	AUX
ejpam-4645	3	15	a	a	DET
ejpam-4645	3	16	locating	locate	VERB
ejpam-4645	3	17	-	-	PUNCT
ejpam-4645	3	18	dominating	dominate	VERB
ejpam-4645	3	19	set	set	NOUN
ejpam-4645	3	20	of	of	ADP
ejpam-4645	3	21	g	g	PROPN
ejpam-4645	3	22	if	if	SCONJ
ejpam-4645	3	23	for	for	ADP
ejpam-4645	3	24	each	each	PRON
ejpam-4645	3	25	v	v	NUM
ejpam-4645	3	26	∈	∈	PROPN
ejpam-4645	3	27	v	v	NOUN
ejpam-4645	3	28	(	(	PUNCT
ejpam-4645	3	29	g	g	NOUN
ejpam-4645	3	30	)	)	PUNCT
ejpam-4645	3	31	\	\	PROPN
ejpam-4645	4	1	s	s	X
ejpam-4645	4	2	,	,	PUNCT
ejpam-4645	4	3	there	there	PRON
ejpam-4645	4	4	exists	exist	VERB
ejpam-4645	4	5	w	w	PROPN
ejpam-4645	4	6	∈	∈	PROPN
ejpam-4645	4	7	s	s	PART
ejpam-4645	4	8	such	such	ADJ
ejpam-4645	4	9	tha	tha	NOUN
ejpam-4645	4	10	vw	vw	PROPN
ejpam-4645	4	11	∈	∈	PROPN
ejpam-4645	4	12	e(g	e(g	PROPN
ejpam-4645	4	13	)	)	PUNCT
ejpam-4645	4	14	and	and	CCONJ
ejpam-4645	4	15	ng(x	ng(x	NUM
ejpam-4645	4	16	)	)	PUNCT
ejpam-4645	4	17	∩	∩	NOUN
ejpam-4645	4	18	s	s	PART
ejpam-4645	4	19	̸=	̸=	PROPN
ejpam-4645	4	20	ng(y	ng(y	NOUN
ejpam-4645	4	21	)	)	PUNCT
ejpam-4645	4	22	∩	∩	NOUN
ejpam-4645	4	23	s	s	PART
ejpam-4645	4	24	for	for	ADP
ejpam-4645	4	25	any	any	DET
ejpam-4645	4	26	two	two	NUM
ejpam-4645	4	27	distinct	distinct	ADJ
ejpam-4645	4	28	vertices	vertex	NOUN
ejpam-4645	4	29	x	x	PUNCT
ejpam-4645	4	30	and	and	CCONJ
ejpam-4645	4	31	y	y	PROPN
ejpam-4645	4	32	in	in	ADP
ejpam-4645	4	33	v	v	NUM
ejpam-4645	4	34	(	(	PUNCT
ejpam-4645	4	35	g	g	NOUN
ejpam-4645	4	36	)	)	PUNCT
ejpam-4645	4	37	\	\	PUNCT
ejpam-4645	5	1	s.	s.	PROPN
ejpam-4645	5	2	s	s	PART
ejpam-4645	5	3	is	be	AUX
ejpam-4645	5	4	a	a	DET
ejpam-4645	5	5	stable	stable	ADJ
ejpam-4645	5	6	locating	locating	NOUN
ejpam-4645	5	7	-	-	PUNCT
ejpam-4645	5	8	dominating	dominate	VERB
ejpam-4645	5	9	set	set	NOUN
ejpam-4645	5	10	of	of	ADP
ejpam-4645	5	11	g	g	PROPN
ejpam-4645	5	12	if	if	SCONJ
ejpam-4645	5	13	it	it	PRON
ejpam-4645	5	14	is	be	AUX
ejpam-4645	5	15	a	a	DET
ejpam-4645	5	16	locating	locate	VERB
ejpam-4645	5	17	-	-	PUNCT
ejpam-4645	5	18	dominating	dominate	VERB
ejpam-4645	5	19	set	set	NOUN
ejpam-4645	5	20	of	of	ADP
ejpam-4645	5	21	g	g	PROPN
ejpam-4645	5	22	and	and	CCONJ
ejpam-4645	5	23	s	s	PRON
ejpam-4645	5	24	\	\	X
ejpam-4645	5	25	{	{	PUNCT
ejpam-4645	5	26	v	v	NOUN
ejpam-4645	5	27	}	}	PUNCT
ejpam-4645	5	28	is	be	AUX
ejpam-4645	5	29	a	a	DET
ejpam-4645	5	30	locating	locate	VERB
ejpam-4645	5	31	-	-	PUNCT
ejpam-4645	5	32	dominating	dominate	VERB
ejpam-4645	5	33	set	set	NOUN
ejpam-4645	5	34	of	of	ADP
ejpam-4645	5	35	g	g	PROPN
ejpam-4645	5	36	for	for	ADP
ejpam-4645	5	37	each	each	DET
ejpam-4645	5	38	v	v	NOUN
ejpam-4645	5	39	∈	∈	PROPN
ejpam-4645	5	40	s.	s.	PROPN
ejpam-4645	5	41	the	the	DET
ejpam-4645	5	42	minimum	minimum	ADJ
ejpam-4645	5	43	cardinality	cardinality	NOUN
ejpam-4645	5	44	of	of	ADP
ejpam-4645	5	45	a	a	DET
ejpam-4645	5	46	stable	stable	ADJ
ejpam-4645	5	47	locating	locating	NOUN
ejpam-4645	5	48	-	-	PUNCT
ejpam-4645	5	49	dominating	dominate	VERB
ejpam-4645	5	50	set	set	NOUN
ejpam-4645	5	51	of	of	ADP
ejpam-4645	5	52	g	g	NOUN
ejpam-4645	5	53	,	,	PUNCT
ejpam-4645	5	54	denoted	denote	VERB
ejpam-4645	5	55	by	by	ADP
ejpam-4645	5	56	γsld(g	γsld(g	PROPN
ejpam-4645	5	57	)	)	PUNCT
ejpam-4645	5	58	,	,	PUNCT
ejpam-4645	5	59	is	be	AUX
ejpam-4645	5	60	called	call	VERB
ejpam-4645	5	61	the	the	DET
ejpam-4645	5	62	stable	stable	ADJ
ejpam-4645	5	63	locating	locating	NOUN
ejpam-4645	5	64	-	-	PUNCT
ejpam-4645	5	65	domination	domination	NOUN
ejpam-4645	5	66	number	number	NOUN
ejpam-4645	5	67	of	of	ADP
ejpam-4645	5	68	g.	g.	PROPN
ejpam-4645	5	69	in	in	ADP
ejpam-4645	5	70	this	this	DET
ejpam-4645	5	71	paper	paper	NOUN
ejpam-4645	5	72	,	,	PUNCT
ejpam-4645	5	73	we	we	PRON
ejpam-4645	5	74	investigate	investigate	VERB
ejpam-4645	5	75	this	this	DET
ejpam-4645	5	76	concept	concept	NOUN
ejpam-4645	5	77	and	and	CCONJ
ejpam-4645	5	78	the	the	DET
ejpam-4645	5	79	corresponding	corresponding	ADJ
ejpam-4645	5	80	parameter	parameter	NOUN
ejpam-4645	5	81	for	for	ADP
ejpam-4645	5	82	edge	edge	NOUN
ejpam-4645	5	83	corona	corona	NOUN
ejpam-4645	5	84	and	and	CCONJ
ejpam-4645	5	85	lexicographic	lexicographic	ADJ
ejpam-4645	5	86	product	product	NOUN
ejpam-4645	5	87	of	of	ADP
ejpam-4645	5	88	graphs	graph	NOUN
ejpam-4645	5	89	.	.	PUNCT
ejpam-4645	6	1	2020	2020	NUM
ejpam-4645	6	2	mathematics	mathematic	NOUN
ejpam-4645	6	3	subject	subject	NOUN
ejpam-4645	6	4	classifications	classification	NOUN
ejpam-4645	6	5	:	:	PUNCT
ejpam-4645	6	6	05c69	05c69	X
ejpam-4645	6	7	key	key	ADJ
ejpam-4645	6	8	words	word	NOUN
ejpam-4645	6	9	and	and	CCONJ
ejpam-4645	6	10	phrases	phrase	NOUN
ejpam-4645	6	11	:	:	PUNCT
ejpam-4645	6	12	locating	locate	VERB
ejpam-4645	6	13	,	,	PUNCT
ejpam-4645	6	14	stable	stable	ADJ
ejpam-4645	6	15	,	,	PUNCT
ejpam-4645	6	16	domination	domination	NOUN
ejpam-4645	6	17	,	,	PUNCT
ejpam-4645	6	18	edge	edge	NOUN
ejpam-4645	6	19	corona	corona	NOUN
ejpam-4645	6	20	,	,	PUNCT
ejpam-4645	6	21	lexicographic	lexicographic	ADJ
ejpam-4645	6	22	product	product	NOUN
ejpam-4645	6	23	1	1	NUM
ejpam-4645	6	24	.	.	PUNCT
ejpam-4645	7	1	introduction	introduction	NOUN
ejpam-4645	7	2	let	let	VERB
ejpam-4645	7	3	g	g	NOUN
ejpam-4645	7	4	=	=	SYM
ejpam-4645	7	5	(	(	PUNCT
ejpam-4645	7	6	v	v	NOUN
ejpam-4645	7	7	(	(	PUNCT
ejpam-4645	7	8	g	g	NOUN
ejpam-4645	7	9	)	)	PUNCT
ejpam-4645	7	10	,	,	PUNCT
ejpam-4645	7	11	e(g	e(g	PROPN
ejpam-4645	7	12	)	)	PUNCT
ejpam-4645	7	13	)	)	PUNCT
ejpam-4645	7	14	be	be	AUX
ejpam-4645	7	15	an	an	DET
ejpam-4645	7	16	undirected	undirected	ADJ
ejpam-4645	7	17	graph	graph	NOUN
ejpam-4645	7	18	.	.	PUNCT
ejpam-4645	8	1	the	the	DET
ejpam-4645	8	2	distance	distance	NOUN
ejpam-4645	8	3	between	between	ADP
ejpam-4645	8	4	two	two	NUM
ejpam-4645	8	5	vertices	vertex	NOUN
ejpam-4645	8	6	u	u	NOUN
ejpam-4645	8	7	and	and	CCONJ
ejpam-4645	8	8	v	v	NOUN
ejpam-4645	8	9	of	of	ADP
ejpam-4645	8	10	g	g	NOUN
ejpam-4645	8	11	,	,	PUNCT
ejpam-4645	8	12	denoted	denote	VERB
ejpam-4645	8	13	by	by	ADP
ejpam-4645	8	14	dg(u	dg(u	NOUN
ejpam-4645	8	15	,	,	PUNCT
ejpam-4645	8	16	v	v	NOUN
ejpam-4645	8	17	)	)	PUNCT
ejpam-4645	8	18	,	,	PUNCT
ejpam-4645	8	19	is	be	AUX
ejpam-4645	8	20	equal	equal	ADJ
ejpam-4645	8	21	to	to	ADP
ejpam-4645	8	22	the	the	DET
ejpam-4645	8	23	length	length	NOUN
ejpam-4645	8	24	of	of	ADP
ejpam-4645	8	25	a	a	DET
ejpam-4645	8	26	shortest	short	ADJ
ejpam-4645	8	27	path	path	NOUN
ejpam-4645	8	28	connecting	connect	VERB
ejpam-4645	8	29	u	u	NOUN
ejpam-4645	8	30	and	and	CCONJ
ejpam-4645	8	31	v.	v.	ADP
ejpam-4645	8	32	any	any	DET
ejpam-4645	8	33	path	path	NOUN
ejpam-4645	8	34	connecting	connect	VERB
ejpam-4645	8	35	u	u	NOUN
ejpam-4645	8	36	and	and	CCONJ
ejpam-4645	8	37	v	v	NOUN
ejpam-4645	8	38	of	of	ADP
ejpam-4645	8	39	length	length	NOUN
ejpam-4645	8	40	dg(u	dg(u	ADJ
ejpam-4645	8	41	,	,	PUNCT
ejpam-4645	8	42	v	v	NOUN
ejpam-4645	8	43	)	)	PUNCT
ejpam-4645	8	44	is	be	AUX
ejpam-4645	8	45	called	call	VERB
ejpam-4645	8	46	a	a	DET
ejpam-4645	8	47	u	u	NOUN
ejpam-4645	8	48	-	-	NOUN
ejpam-4645	8	49	v	v	ADJ
ejpam-4645	8	50	geodesic.the	geodesic.the	DET
ejpam-4645	8	51	neighborhood	neighborhood	NOUN
ejpam-4645	8	52	of	of	ADP
ejpam-4645	8	53	v	v	NUM
ejpam-4645	8	54	∈	∈	NOUN
ejpam-4645	8	55	v	v	NOUN
ejpam-4645	8	56	(	(	PUNCT
ejpam-4645	8	57	g	g	NOUN
ejpam-4645	8	58	)	)	PUNCT
ejpam-4645	8	59	is	be	AUX
ejpam-4645	8	60	the	the	DET
ejpam-4645	8	61	set	set	ADJ
ejpam-4645	8	62	ng(v)=	ng(v)=	NOUN
ejpam-4645	8	63	{	{	PUNCT
ejpam-4645	8	64	x	x	SYM
ejpam-4645	8	65	∈	∈	PROPN
ejpam-4645	8	66	v	v	NOUN
ejpam-4645	8	67	(	(	PUNCT
ejpam-4645	8	68	g	g	NOUN
ejpam-4645	8	69	)	)	PUNCT
ejpam-4645	8	70	:	:	PUNCT
ejpam-4645	8	71	xv	xv	PROPN
ejpam-4645	8	72	∈	∈	PROPN
ejpam-4645	8	73	e(g	e(g	PROPN
ejpam-4645	8	74	)	)	PUNCT
ejpam-4645	8	75	}	}	PUNCT
ejpam-4645	8	76	.	.	PUNCT
ejpam-4645	9	1	the	the	DET
ejpam-4645	9	2	degree	degree	NOUN
ejpam-4645	9	3	of	of	ADP
ejpam-4645	9	4	v	v	NUM
ejpam-4645	9	5	∈	∈	NOUN
ejpam-4645	9	6	v	v	NOUN
ejpam-4645	9	7	(	(	PUNCT
ejpam-4645	9	8	g	g	NOUN
ejpam-4645	9	9	)	)	PUNCT
ejpam-4645	9	10	,	,	PUNCT
ejpam-4645	9	11	denoted	denote	VERB
ejpam-4645	9	12	by	by	ADP
ejpam-4645	9	13	degg(v	degg(v	PROPN
ejpam-4645	9	14	)	)	PUNCT
ejpam-4645	9	15	,	,	PUNCT
ejpam-4645	9	16	is	be	AUX
ejpam-4645	9	17	equal	equal	ADJ
ejpam-4645	9	18	to	to	ADP
ejpam-4645	9	19	the	the	DET
ejpam-4645	9	20	cardinality	cardinality	NOUN
ejpam-4645	9	21	of	of	ADP
ejpam-4645	9	22	ng(v	ng(v	PUNCT
ejpam-4645	9	23	)	)	PUNCT
ejpam-4645	9	24	and	and	CCONJ
ejpam-4645	9	25	the	the	DET
ejpam-4645	9	26	maximum	maximum	ADJ
ejpam-4645	9	27	degree	degree	NOUN
ejpam-4645	9	28	of	of	ADP
ejpam-4645	9	29	g	g	PROPN
ejpam-4645	9	30	is	be	AUX
ejpam-4645	9	31	∆(g)=	∆(g)=	NOUN
ejpam-4645	9	32	max	max	PROPN
ejpam-4645	9	33	{	{	PUNCT
ejpam-4645	9	34	degg(x	degg(x	NOUN
ejpam-4645	9	35	)	)	PUNCT
ejpam-4645	9	36	:	:	PUNCT
ejpam-4645	9	37	x	x	PUNCT
ejpam-4645	9	38	∈	∈	PROPN
ejpam-4645	9	39	e(g	e(g	PROPN
ejpam-4645	9	40	)	)	PUNCT
ejpam-4645	9	41	}	}	PUNCT
ejpam-4645	9	42	.	.	PUNCT
ejpam-4645	10	1	a	a	DET
ejpam-4645	10	2	vertex	vertex	NOUN
ejpam-4645	10	3	v	v	NOUN
ejpam-4645	10	4	of	of	ADP
ejpam-4645	10	5	g	g	PROPN
ejpam-4645	10	6	is	be	AUX
ejpam-4645	10	7	a	a	DET
ejpam-4645	10	8	leaf	leaf	NOUN
ejpam-4645	10	9	if	if	SCONJ
ejpam-4645	10	10	degg(v	degg(v	VERB
ejpam-4645	10	11	)	)	PUNCT
ejpam-4645	10	12	=	=	SYM
ejpam-4645	10	13	1	1	X
ejpam-4645	10	14	.	.	PUNCT
ejpam-4645	10	15	a	a	DET
ejpam-4645	10	16	vertex	vertex	NOUN
ejpam-4645	10	17	u	u	NOUN
ejpam-4645	10	18	of	of	ADP
ejpam-4645	10	19	g	g	PROPN
ejpam-4645	10	20	is	be	AUX
ejpam-4645	10	21	a	a	DET
ejpam-4645	10	22	support	support	NOUN
ejpam-4645	10	23	if	if	SCONJ
ejpam-4645	10	24	uv	uv	PROPN
ejpam-4645	10	25	∈	∈	PROPN
ejpam-4645	10	26	e(g	e(g	PROPN
ejpam-4645	10	27	)	)	PUNCT
ejpam-4645	10	28	for	for	ADP
ejpam-4645	10	29	some	some	DET
ejpam-4645	10	30	leaf	leaf	NOUN
ejpam-4645	10	31	v	v	NOUN
ejpam-4645	10	32	of	of	ADP
ejpam-4645	10	33	g.	g.	PROPN
ejpam-4645	10	34	a	a	DET
ejpam-4645	10	35	connected	connected	ADJ
ejpam-4645	10	36	graph	graph	NOUN
ejpam-4645	10	37	g	g	NOUN
ejpam-4645	10	38	of	of	ADP
ejpam-4645	10	39	order	order	NOUN
ejpam-4645	10	40	n	n	PRON
ejpam-4645	10	41	≥	≥	NOUN
ejpam-4645	10	42	3	3	NUM
ejpam-4645	10	43	is	be	AUX
ejpam-4645	10	44	point	point	NOUN
ejpam-4645	10	45	distinguishing	distinguish	VERB
ejpam-4645	10	46	if	if	SCONJ
ejpam-4645	10	47	for	for	ADP
ejpam-4645	10	48	any	any	DET
ejpam-4645	10	49	two	two	NUM
ejpam-4645	10	50	distinct	distinct	ADJ
ejpam-4645	10	51	vertices	vertex	NOUN
ejpam-4645	10	52	u	u	NOUN
ejpam-4645	10	53	and	and	CCONJ
ejpam-4645	10	54	v	v	NOUN
ejpam-4645	10	55	of	of	ADP
ejpam-4645	10	56	g	g	NOUN
ejpam-4645	10	57	,	,	PUNCT
ejpam-4645	10	58	ng[u	ng[u	PROPN
ejpam-4645	10	59	]	]	X
ejpam-4645	10	60	̸=	̸=	PROPN
ejpam-4645	10	61	ng[v	ng[v	PROPN
ejpam-4645	10	62	]	]	PUNCT
ejpam-4645	10	63	.	.	PUNCT
ejpam-4645	11	1	it	it	PRON
ejpam-4645	11	2	is	be	AUX
ejpam-4645	11	3	totally	totally	ADV
ejpam-4645	11	4	point	point	NOUN
ejpam-4645	11	5	determining	determine	VERB
ejpam-4645	11	6	if	if	SCONJ
ejpam-4645	11	7	for	for	ADP
ejpam-4645	11	8	any	any	DET
ejpam-4645	11	9	two	two	NUM
ejpam-4645	11	10	distinct	distinct	ADJ
ejpam-4645	11	11	vertices	vertex	NOUN
ejpam-4645	11	12	u	u	NOUN
ejpam-4645	11	13	and	and	CCONJ
ejpam-4645	11	14	v	v	NOUN
ejpam-4645	11	15	of	of	ADP
ejpam-4645	11	16	g	g	NOUN
ejpam-4645	11	17	,	,	PUNCT
ejpam-4645	11	18	ng(u	ng(u	NOUN
ejpam-4645	11	19	)	)	PUNCT
ejpam-4645	11	20	̸=	̸=	PROPN
ejpam-4645	11	21	ng(v	ng(v	PUNCT
ejpam-4645	11	22	)	)	PUNCT
ejpam-4645	11	23	and	and	CCONJ
ejpam-4645	11	24	ng[u	ng[u	PROPN
ejpam-4645	11	25	]	]	X
ejpam-4645	11	26	̸=	̸=	PROPN
ejpam-4645	11	27	ng[v	ng[v	PROPN
ejpam-4645	11	28	]	]	PUNCT
ejpam-4645	11	29	.	.	PUNCT
ejpam-4645	12	1	these	these	DET
ejpam-4645	12	2	concepts	concept	NOUN
ejpam-4645	12	3	are	be	AUX
ejpam-4645	12	4	defined	define	VERB
ejpam-4645	12	5	and	and	CCONJ
ejpam-4645	12	6	studied	study	VERB
ejpam-4645	12	7	in	in	ADP
ejpam-4645	12	8	[	[	X
ejpam-4645	12	9	7	7	NUM
ejpam-4645	12	10	]	]	PUNCT
ejpam-4645	12	11	and	and	CCONJ
ejpam-4645	12	12	[	[	X
ejpam-4645	12	13	21	21	NUM
ejpam-4645	12	14	]	]	PUNCT
ejpam-4645	12	15	.	.	PUNCT
ejpam-4645	13	1	a	a	DET
ejpam-4645	13	2	subset	subset	NOUN
ejpam-4645	13	3	s	s	X
ejpam-4645	13	4	of	of	ADP
ejpam-4645	13	5	v	v	NOUN
ejpam-4645	13	6	(	(	PUNCT
ejpam-4645	13	7	g	g	NOUN
ejpam-4645	13	8	)	)	PUNCT
ejpam-4645	13	9	is	be	AUX
ejpam-4645	13	10	a	a	DET
ejpam-4645	13	11	dominating	dominating	NOUN
ejpam-4645	13	12	set	set	NOUN
ejpam-4645	13	13	of	of	ADP
ejpam-4645	13	14	g	g	PROPN
ejpam-4645	13	15	if	if	SCONJ
ejpam-4645	13	16	for	for	ADP
ejpam-4645	13	17	every	every	PRON
ejpam-4645	13	18	v	v	NUM
ejpam-4645	13	19	∈	∈	NOUN
ejpam-4645	13	20	v	v	NOUN
ejpam-4645	13	21	(	(	PUNCT
ejpam-4645	13	22	g	g	NOUN
ejpam-4645	13	23	)	)	PUNCT
ejpam-4645	13	24	\	\	PROPN
ejpam-4645	14	1	s	s	X
ejpam-4645	14	2	,	,	PUNCT
ejpam-4645	14	3	there	there	PRON
ejpam-4645	14	4	exists	exist	VERB
ejpam-4645	14	5	u	u	PROPN
ejpam-4645	14	6	∈	∈	PROPN
ejpam-4645	14	7	s	s	VERB
ejpam-4645	14	8	such	such	ADJ
ejpam-4645	14	9	that	that	SCONJ
ejpam-4645	14	10	xv	xv	PROPN
ejpam-4645	14	11	∈	∈	PROPN
ejpam-4645	14	12	e(g	e(g	PROPN
ejpam-4645	14	13	)	)	PUNCT
ejpam-4645	14	14	.	.	PUNCT
ejpam-4645	15	1	s	s	PART
ejpam-4645	15	2	is	be	AUX
ejpam-4645	15	3	a	a	DET
ejpam-4645	15	4	locating	locating	NOUN
ejpam-4645	15	5	set	set	VERB
ejpam-4645	15	6	in	in	ADP
ejpam-4645	15	7	g	g	PROPN
ejpam-4645	15	8	if	if	SCONJ
ejpam-4645	15	9	ng(u	ng(u	NOUN
ejpam-4645	15	10	)	)	PUNCT
ejpam-4645	15	11	∩	∩	NOUN
ejpam-4645	15	12	s	s	PART
ejpam-4645	15	13	̸=	̸=	PROPN
ejpam-4645	15	14	ng(v	ng(v	NUM
ejpam-4645	15	15	)	)	PUNCT
ejpam-4645	15	16	∩	∩	NOUN
ejpam-4645	15	17	s	s	PART
ejpam-4645	15	18	for	for	ADP
ejpam-4645	15	19	every	every	DET
ejpam-4645	15	20	∗corresponding	∗corresponde	VERB
ejpam-4645	15	21	author	author	NOUN
ejpam-4645	15	22	.	.	PUNCT
ejpam-4645	16	1	doi	doi	NOUN
ejpam-4645	16	2	:	:	PUNCT
ejpam-4645	16	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4645	https://doi.org/10.29020/nybg.ejpam.v16i1.4645	ADJ
ejpam-4645	16	4	email	email	NOUN
ejpam-4645	16	5	addresses	address	VERB
ejpam-4645	16	6	:	:	PUNCT
ejpam-4645	16	7	gina.malacas@g.msuiit.edu.ph	gina.malacas@g.msuiit.edu.ph	PROPN
ejpam-4645	16	8	(	(	PUNCT
ejpam-4645	16	9	g.	g.	PROPN
ejpam-4645	16	10	malacas	malacas	PROPN
ejpam-4645	16	11	)	)	PUNCT
ejpam-4645	16	12	,	,	PUNCT
ejpam-4645	16	13	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4645	16	14	(	(	PUNCT
ejpam-4645	16	15	s.	s.	PROPN
ejpam-4645	16	16	canoy	canoy	PROPN
ejpam-4645	16	17	,	,	PUNCT
ejpam-4645	16	18	jr	jr	PROPN
ejpam-4645	16	19	.	.	PROPN
ejpam-4645	16	20	)	)	PUNCT
ejpam-4645	16	21	,	,	PUNCT
ejpam-4645	16	22	emmy.chacon@g.msuiit.edu.ph	emmy.chacon@g.msuiit.edu.ph	PROPN
ejpam-4645	16	23	(	(	PUNCT
ejpam-4645	16	24	e.	e.	PROPN
ejpam-4645	16	25	chacon	chacon	PROPN
ejpam-4645	16	26	)	)	PUNCT
ejpam-4645	16	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4645	16	28	479	479	NUM
ejpam-4645	17	1	©	©	ADP
ejpam-4645	17	2	2023	2023	NUM
ejpam-4645	17	3	ejpam	ejpam	NOUN
ejpam-4645	17	4	all	all	DET
ejpam-4645	17	5	rights	right	NOUN
ejpam-4645	17	6	reserved	reserve	VERB
ejpam-4645	17	7	.	.	PUNCT
ejpam-4645	18	1	g.	g.	PROPN
ejpam-4645	18	2	malacas	malacas	PROPN
ejpam-4645	18	3	,	,	PUNCT
ejpam-4645	18	4	s.	s.	PROPN
ejpam-4645	18	5	canoy	canoy	PROPN
ejpam-4645	18	6	,	,	PUNCT
ejpam-4645	18	7	jr	jr	PROPN
ejpam-4645	18	8	.	.	PROPN
ejpam-4645	18	9	,	,	PUNCT
ejpam-4645	18	10	e.	e.	PROPN
ejpam-4645	18	11	chacon	chacon	PROPN
ejpam-4645	18	12	/	/	SYM
ejpam-4645	18	13	eur	eur	PROPN
ejpam-4645	18	14	.	.	PUNCT
ejpam-4645	19	1	j.	j.	PROPN
ejpam-4645	19	2	pure	pure	PROPN
ejpam-4645	19	3	appl	appl	PROPN
ejpam-4645	19	4	.	.	PROPN
ejpam-4645	19	5	math	math	PROPN
ejpam-4645	19	6	,	,	PUNCT
ejpam-4645	19	7	16	16	NUM
ejpam-4645	19	8	(	(	PUNCT
ejpam-4645	19	9	1	1	NUM
ejpam-4645	19	10	)	)	PUNCT
ejpam-4645	19	11	(	(	PUNCT
ejpam-4645	19	12	2023	2023	NUM
ejpam-4645	19	13	)	)	PUNCT
ejpam-4645	19	14	,	,	PUNCT
ejpam-4645	19	15	479	479	NUM
ejpam-4645	19	16	-	-	SYM
ejpam-4645	19	17	490	490	NUM
ejpam-4645	19	18	480	480	NUM
ejpam-4645	19	19	two	two	NUM
ejpam-4645	19	20	distinct	distinct	ADJ
ejpam-4645	19	21	vertices	vertex	NOUN
ejpam-4645	19	22	u	u	NOUN
ejpam-4645	19	23	,	,	PUNCT
ejpam-4645	19	24	v	v	NOUN
ejpam-4645	19	25	∈	∈	PROPN
ejpam-4645	19	26	v	v	NOUN
ejpam-4645	19	27	(	(	PUNCT
ejpam-4645	19	28	g	g	NOUN
ejpam-4645	19	29	)	)	PUNCT
ejpam-4645	19	30	\	\	PUNCT
ejpam-4645	20	1	s.	s.	PROPN
ejpam-4645	20	2	a	a	DET
ejpam-4645	20	3	locating	locate	VERB
ejpam-4645	20	4	set	set	NOUN
ejpam-4645	20	5	s	s	NOUN
ejpam-4645	20	6	is	be	AUX
ejpam-4645	20	7	said	say	VERB
ejpam-4645	20	8	to	to	PART
ejpam-4645	20	9	be	be	AUX
ejpam-4645	20	10	a	a	DET
ejpam-4645	20	11	strictly	strictly	ADV
ejpam-4645	20	12	locating	locate	VERB
ejpam-4645	20	13	set	set	VERB
ejpam-4645	20	14	if	if	SCONJ
ejpam-4645	20	15	ng(u	ng(u	NOUN
ejpam-4645	20	16	)	)	PUNCT
ejpam-4645	20	17	∩	∩	NOUN
ejpam-4645	20	18	s	s	PART
ejpam-4645	20	19	̸=	̸=	PROPN
ejpam-4645	20	20	s	s	PART
ejpam-4645	20	21	for	for	ADP
ejpam-4645	20	22	all	all	DET
ejpam-4645	20	23	u	u	NOUN
ejpam-4645	20	24	∈	∈	PROPN
ejpam-4645	20	25	v	v	NOUN
ejpam-4645	20	26	(	(	PUNCT
ejpam-4645	20	27	g	g	NOUN
ejpam-4645	20	28	)	)	PUNCT
ejpam-4645	20	29	\	\	PUNCT
ejpam-4645	21	1	s.	s.	PROPN
ejpam-4645	21	2	a	a	DET
ejpam-4645	21	3	locating	locate	VERB
ejpam-4645	21	4	set	set	NOUN
ejpam-4645	21	5	(	(	PUNCT
ejpam-4645	21	6	strictly	strictly	ADV
ejpam-4645	21	7	locating	locate	VERB
ejpam-4645	21	8	set	set	NOUN
ejpam-4645	21	9	)	)	PUNCT
ejpam-4645	21	10	s	s	VERB
ejpam-4645	21	11	is	be	AUX
ejpam-4645	21	12	a	a	DET
ejpam-4645	21	13	stable	stable	ADJ
ejpam-4645	21	14	locating	locating	NOUN
ejpam-4645	21	15	set	set	NOUN
ejpam-4645	21	16	(	(	PUNCT
ejpam-4645	21	17	resp	resp	NOUN
ejpam-4645	21	18	.	.	PUNCT
ejpam-4645	22	1	stable	stable	ADJ
ejpam-4645	22	2	strictly	strictly	ADV
ejpam-4645	22	3	locating	locate	VERB
ejpam-4645	22	4	set	set	NOUN
ejpam-4645	22	5	)	)	PUNCT
ejpam-4645	22	6	if	if	SCONJ
ejpam-4645	22	7	s	s	NOUN
ejpam-4645	22	8	\	\	PROPN
ejpam-4645	22	9	{	{	PUNCT
ejpam-4645	22	10	v	v	NOUN
ejpam-4645	22	11	}	}	PUNCT
ejpam-4645	22	12	is	be	AUX
ejpam-4645	22	13	a	a	DET
ejpam-4645	22	14	locating	locating	NOUN
ejpam-4645	22	15	(	(	PUNCT
ejpam-4645	22	16	resp	resp	NOUN
ejpam-4645	22	17	.	.	PUNCT
ejpam-4645	23	1	strictly	strictly	ADV
ejpam-4645	23	2	locating	locate	VERB
ejpam-4645	23	3	)	)	PUNCT
ejpam-4645	23	4	set	set	NOUN
ejpam-4645	23	5	for	for	ADP
ejpam-4645	23	6	each	each	DET
ejpam-4645	23	7	v	v	NOUN
ejpam-4645	23	8	∈	∈	PROPN
ejpam-4645	23	9	s.	s.	PROPN
ejpam-4645	23	10	a	a	DET
ejpam-4645	23	11	locating	locating	NOUN
ejpam-4645	23	12	(	(	PUNCT
ejpam-4645	23	13	resp	resp	NOUN
ejpam-4645	23	14	.	.	PUNCT
ejpam-4645	24	1	strictly	strictly	ADV
ejpam-4645	24	2	locating	locate	VERB
ejpam-4645	24	3	)	)	PUNCT
ejpam-4645	24	4	set	set	VERB
ejpam-4645	24	5	s	s	PROPN
ejpam-4645	24	6	of	of	ADP
ejpam-4645	24	7	v	v	NOUN
ejpam-4645	24	8	(	(	PUNCT
ejpam-4645	24	9	g	g	NOUN
ejpam-4645	24	10	)	)	PUNCT
ejpam-4645	24	11	which	which	PRON
ejpam-4645	24	12	is	be	AUX
ejpam-4645	24	13	also	also	ADV
ejpam-4645	24	14	a	a	DET
ejpam-4645	24	15	dominating	dominating	NOUN
ejpam-4645	24	16	set	set	NOUN
ejpam-4645	24	17	is	be	AUX
ejpam-4645	24	18	called	call	VERB
ejpam-4645	24	19	a	a	DET
ejpam-4645	24	20	locating	locate	VERB
ejpam-4645	24	21	-	-	PUNCT
ejpam-4645	24	22	dominating	dominate	VERB
ejpam-4645	24	23	(	(	PUNCT
ejpam-4645	24	24	resp	resp	NOUN
ejpam-4645	24	25	.	.	PUNCT
ejpam-4645	25	1	strictly	strictly	ADV
ejpam-4645	25	2	locating	locate	VERB
ejpam-4645	25	3	-	-	PUNCT
ejpam-4645	25	4	dominating	dominating	NOUN
ejpam-4645	25	5	)	)	PUNCT
ejpam-4645	25	6	set	set	NOUN
ejpam-4645	25	7	of	of	ADP
ejpam-4645	25	8	g.	g.	PROPN
ejpam-4645	25	9	a	a	DET
ejpam-4645	25	10	locating	locate	VERB
ejpam-4645	25	11	-	-	PUNCT
ejpam-4645	25	12	dominating	dominating	NOUN
ejpam-4645	25	13	(	(	PUNCT
ejpam-4645	25	14	strictly	strictly	ADV
ejpam-4645	25	15	locating	locate	VERB
ejpam-4645	25	16	-	-	PUNCT
ejpam-4645	25	17	dominating	dominating	NOUN
ejpam-4645	25	18	)	)	PUNCT
ejpam-4645	25	19	set	set	NOUN
ejpam-4645	25	20	s	s	PART
ejpam-4645	25	21	is	be	AUX
ejpam-4645	25	22	a	a	DET
ejpam-4645	25	23	stable	stable	ADJ
ejpam-4645	25	24	locatingdominating	locatingdominating	NOUN
ejpam-4645	25	25	(	(	PUNCT
ejpam-4645	25	26	resp	resp	NOUN
ejpam-4645	25	27	.	.	PUNCT
ejpam-4645	26	1	stable	stable	ADJ
ejpam-4645	26	2	strictly	strictly	ADV
ejpam-4645	26	3	locating	locate	VERB
ejpam-4645	26	4	-	-	PUNCT
ejpam-4645	26	5	dominating	dominating	NOUN
ejpam-4645	26	6	)	)	PUNCT
ejpam-4645	26	7	set	set	NOUN
ejpam-4645	26	8	of	of	ADP
ejpam-4645	26	9	g	g	PROPN
ejpam-4645	26	10	if	if	SCONJ
ejpam-4645	26	11	s	s	NOUN
ejpam-4645	26	12	\	\	PROPN
ejpam-4645	26	13	{	{	PUNCT
ejpam-4645	26	14	v	v	NOUN
ejpam-4645	26	15	}	}	PUNCT
ejpam-4645	26	16	is	be	AUX
ejpam-4645	26	17	a	a	DET
ejpam-4645	26	18	locatingdominating	locatingdominating	NOUN
ejpam-4645	26	19	(	(	PUNCT
ejpam-4645	26	20	resp	resp	NOUN
ejpam-4645	26	21	.	.	PUNCT
ejpam-4645	27	1	strictly	strictly	ADV
ejpam-4645	27	2	locating	locate	VERB
ejpam-4645	27	3	-	-	PUNCT
ejpam-4645	27	4	dominating	dominating	NOUN
ejpam-4645	27	5	)	)	PUNCT
ejpam-4645	27	6	set	set	NOUN
ejpam-4645	27	7	of	of	ADP
ejpam-4645	27	8	g	g	NOUN
ejpam-4645	27	9	for	for	ADP
ejpam-4645	27	10	each	each	DET
ejpam-4645	27	11	v	v	NOUN
ejpam-4645	27	12	∈	∈	PROPN
ejpam-4645	27	13	s.	s.	PROPN
ejpam-4645	27	14	the	the	DET
ejpam-4645	27	15	minimum	minimum	ADJ
ejpam-4645	27	16	cardinality	cardinality	NOUN
ejpam-4645	27	17	of	of	ADP
ejpam-4645	27	18	a	a	DET
ejpam-4645	27	19	locating	locating	NOUN
ejpam-4645	27	20	(	(	PUNCT
ejpam-4645	27	21	strictly	strictly	ADV
ejpam-4645	27	22	locating	locate	VERB
ejpam-4645	27	23	,	,	PUNCT
ejpam-4645	27	24	stable	stable	ADJ
ejpam-4645	27	25	locating	locating	NOUN
ejpam-4645	27	26	,	,	PUNCT
ejpam-4645	27	27	stable	stable	ADJ
ejpam-4645	27	28	strictly	strictly	ADV
ejpam-4645	27	29	locating	locate	VERB
ejpam-4645	27	30	)	)	PUNCT
ejpam-4645	27	31	set	set	NOUN
ejpam-4645	27	32	of	of	ADP
ejpam-4645	27	33	g	g	PROPN
ejpam-4645	27	34	is	be	AUX
ejpam-4645	27	35	denoted	denote	VERB
ejpam-4645	27	36	by	by	ADP
ejpam-4645	27	37	ln(g	ln(g	NOUN
ejpam-4645	27	38	)	)	PUNCT
ejpam-4645	27	39	(	(	PUNCT
ejpam-4645	27	40	resp	resp	NOUN
ejpam-4645	27	41	.	.	PUNCT
ejpam-4645	28	1	sln(g	sln(g	PROPN
ejpam-4645	28	2	)	)	PUNCT
ejpam-4645	28	3	,	,	PUNCT
ejpam-4645	28	4	sbln(g	sbln(g	NOUN
ejpam-4645	28	5	)	)	PUNCT
ejpam-4645	28	6	,	,	PUNCT
ejpam-4645	28	7	sbsln(g	sbsln(g	NOUN
ejpam-4645	28	8	)	)	PUNCT
ejpam-4645	28	9	)	)	PUNCT
ejpam-4645	28	10	.	.	PUNCT
ejpam-4645	29	1	any	any	DET
ejpam-4645	29	2	locating	locating	NOUN
ejpam-4645	29	3	(	(	PUNCT
ejpam-4645	29	4	strictly	strictly	ADV
ejpam-4645	29	5	locating	locate	VERB
ejpam-4645	29	6	,	,	PUNCT
ejpam-4645	29	7	stable	stable	ADJ
ejpam-4645	29	8	locating	locating	NOUN
ejpam-4645	29	9	,	,	PUNCT
ejpam-4645	29	10	stable	stable	ADJ
ejpam-4645	29	11	strictly	strictly	ADV
ejpam-4645	29	12	locating	locate	VERB
ejpam-4645	29	13	)	)	PUNCT
ejpam-4645	29	14	set	set	NOUN
ejpam-4645	29	15	of	of	ADP
ejpam-4645	29	16	g	g	NOUN
ejpam-4645	29	17	with	with	ADP
ejpam-4645	29	18	cardinality	cardinality	PROPN
ejpam-4645	29	19	ln(g	ln(g	NUM
ejpam-4645	29	20	)	)	PUNCT
ejpam-4645	29	21	(	(	PUNCT
ejpam-4645	29	22	resp	resp	NOUN
ejpam-4645	29	23	.	.	PUNCT
ejpam-4645	30	1	sln(g	sln(g	PROPN
ejpam-4645	30	2	)	)	PUNCT
ejpam-4645	30	3	,	,	PUNCT
ejpam-4645	30	4	sbln(g	sbln(g	NOUN
ejpam-4645	30	5	)	)	PUNCT
ejpam-4645	30	6	,	,	PUNCT
ejpam-4645	30	7	sbsln(g	sbsln(g	NOUN
ejpam-4645	30	8	)	)	PUNCT
ejpam-4645	30	9	)	)	PUNCT
ejpam-4645	30	10	is	be	AUX
ejpam-4645	30	11	called	call	VERB
ejpam-4645	30	12	an	an	DET
ejpam-4645	30	13	ln	ln	ADV
ejpam-4645	30	14	-	-	PUNCT
ejpam-4645	30	15	set	set	ADJ
ejpam-4645	30	16	(	(	PUNCT
ejpam-4645	30	17	resp	resp	NOUN
ejpam-4645	30	18	.	.	PUNCT
ejpam-4645	31	1	sln	sln	PROPN
ejpam-4645	31	2	-	-	PUNCT
ejpam-4645	31	3	set	set	ADJ
ejpam-4645	31	4	,	,	PUNCT
ejpam-4645	31	5	sbln	sbln	VERB
ejpam-4645	31	6	-	-	PUNCT
ejpam-4645	31	7	set	set	VERB
ejpam-4645	31	8	,	,	PUNCT
ejpam-4645	31	9	sbsln	sbsln	NOUN
ejpam-4645	31	10	-	-	PUNCT
ejpam-4645	31	11	set	set	NOUN
ejpam-4645	31	12	)	)	PUNCT
ejpam-4645	31	13	of	of	ADP
ejpam-4645	31	14	g.	g.	PROPN
ejpam-4645	31	15	the	the	DET
ejpam-4645	31	16	minimum	minimum	ADJ
ejpam-4645	31	17	cardinality	cardinality	NOUN
ejpam-4645	31	18	of	of	ADP
ejpam-4645	31	19	a	a	DET
ejpam-4645	31	20	locating	locate	VERB
ejpam-4645	31	21	-	-	PUNCT
ejpam-4645	31	22	dominating	dominate	VERB
ejpam-4645	31	23	(	(	PUNCT
ejpam-4645	31	24	resp	resp	NOUN
ejpam-4645	31	25	.	.	PUNCT
ejpam-4645	32	1	strictly	strictly	ADV
ejpam-4645	32	2	locating	locate	VERB
ejpam-4645	32	3	-	-	PUNCT
ejpam-4645	32	4	dominating	dominating	NOUN
ejpam-4645	32	5	,	,	PUNCT
ejpam-4645	32	6	stable	stable	ADJ
ejpam-4645	32	7	locating	locating	NOUN
ejpam-4645	32	8	-	-	PUNCT
ejpam-4645	32	9	dominating	dominating	NOUN
ejpam-4645	32	10	,	,	PUNCT
ejpam-4645	32	11	stable	stable	ADJ
ejpam-4645	32	12	strictly	strictly	ADV
ejpam-4645	32	13	locating	locate	VERB
ejpam-4645	32	14	-	-	PUNCT
ejpam-4645	32	15	dominating	dominating	NOUN
ejpam-4645	32	16	)	)	PUNCT
ejpam-4645	32	17	set	set	NOUN
ejpam-4645	32	18	of	of	ADP
ejpam-4645	32	19	g	g	PROPN
ejpam-4645	32	20	is	be	AUX
ejpam-4645	32	21	denoted	denote	VERB
ejpam-4645	32	22	by	by	ADP
ejpam-4645	32	23	γl(g	γl(g	NUM
ejpam-4645	32	24	)	)	PUNCT
ejpam-4645	32	25	(	(	PUNCT
ejpam-4645	32	26	resp	resp	NOUN
ejpam-4645	32	27	.	.	PUNCT
ejpam-4645	33	1	γsl(g	γsl(g	X
ejpam-4645	33	2	)	)	PUNCT
ejpam-4645	33	3	,	,	PUNCT
ejpam-4645	34	1	γsl(g	γsl(g	PROPN
ejpam-4645	34	2	)	)	PUNCT
ejpam-4645	34	3	,	,	PUNCT
ejpam-4645	34	4	γssl(g	γssl(g	PROPN
ejpam-4645	34	5	)	)	PUNCT
ejpam-4645	34	6	)	)	PUNCT
ejpam-4645	34	7	.	.	PUNCT
ejpam-4645	35	1	any	any	DET
ejpam-4645	35	2	locating	locate	VERB
ejpam-4645	35	3	-	-	PUNCT
ejpam-4645	35	4	dominating	dominating	NOUN
ejpam-4645	35	5	(	(	PUNCT
ejpam-4645	35	6	strictly	strictly	ADV
ejpam-4645	35	7	locating	locate	VERB
ejpam-4645	35	8	-	-	PUNCT
ejpam-4645	35	9	dominating	dominating	NOUN
ejpam-4645	35	10	,	,	PUNCT
ejpam-4645	35	11	stable	stable	ADJ
ejpam-4645	35	12	locating	locating	NOUN
ejpam-4645	35	13	-	-	PUNCT
ejpam-4645	35	14	dominating	dominating	NOUN
ejpam-4645	35	15	,	,	PUNCT
ejpam-4645	35	16	stable	stable	ADJ
ejpam-4645	35	17	strictly	strictly	ADV
ejpam-4645	35	18	locating	locate	VERB
ejpam-4645	35	19	-	-	PUNCT
ejpam-4645	35	20	dominating	dominating	NOUN
ejpam-4645	35	21	)	)	PUNCT
ejpam-4645	35	22	set	set	NOUN
ejpam-4645	35	23	of	of	ADP
ejpam-4645	35	24	g	g	NOUN
ejpam-4645	35	25	with	with	ADP
ejpam-4645	35	26	cardinality	cardinality	NOUN
ejpam-4645	35	27	γl(g	γl(g	NUM
ejpam-4645	35	28	)	)	PUNCT
ejpam-4645	35	29	(	(	PUNCT
ejpam-4645	35	30	resp	resp	NOUN
ejpam-4645	35	31	.	.	PUNCT
ejpam-4645	35	32	γsl(g	γsl(g	X
ejpam-4645	35	33	)	)	PUNCT
ejpam-4645	35	34	,	,	PUNCT
ejpam-4645	35	35	γsl(g	γsl(g	PROPN
ejpam-4645	35	36	)	)	PUNCT
ejpam-4645	35	37	,	,	PUNCT
ejpam-4645	35	38	γssl(g	γssl(g	PROPN
ejpam-4645	35	39	)	)	PUNCT
ejpam-4645	35	40	)	)	PUNCT
ejpam-4645	35	41	is	be	AUX
ejpam-4645	35	42	called	call	VERB
ejpam-4645	35	43	an	an	DET
ejpam-4645	35	44	γl	γl	NOUN
ejpam-4645	35	45	-	-	PUNCT
ejpam-4645	35	46	set	set	VERB
ejpam-4645	35	47	(	(	PUNCT
ejpam-4645	35	48	resp	resp	NOUN
ejpam-4645	35	49	.	.	PUNCT
ejpam-4645	36	1	γsl	γsl	NOUN
ejpam-4645	36	2	-	-	PUNCT
ejpam-4645	36	3	set	set	VERB
ejpam-4645	36	4	,	,	PUNCT
ejpam-4645	36	5	γsl	γsl	NOUN
ejpam-4645	36	6	-	-	PUNCT
ejpam-4645	36	7	set	set	VERB
ejpam-4645	36	8	,	,	PUNCT
ejpam-4645	36	9	γssl	γssl	NOUN
ejpam-4645	36	10	-	-	PUNCT
ejpam-4645	36	11	set	set	NOUN
ejpam-4645	36	12	)	)	PUNCT
ejpam-4645	36	13	of	of	ADP
ejpam-4645	36	14	g.	g.	PROPN
ejpam-4645	36	15	domination	domination	PROPN
ejpam-4645	36	16	and	and	CCONJ
ejpam-4645	36	17	some	some	DET
ejpam-4645	36	18	variations	variation	NOUN
ejpam-4645	36	19	of	of	ADP
ejpam-4645	36	20	the	the	DET
ejpam-4645	36	21	concept	concept	NOUN
ejpam-4645	36	22	are	be	AUX
ejpam-4645	36	23	found	find	VERB
ejpam-4645	36	24	in	in	ADP
ejpam-4645	36	25	the	the	DET
ejpam-4645	36	26	book	book	NOUN
ejpam-4645	36	27	by	by	ADP
ejpam-4645	36	28	haynes	hayne	NOUN
ejpam-4645	36	29	et	et	PROPN
ejpam-4645	36	30	al	al	PROPN
ejpam-4645	36	31	.	.	PUNCT
ejpam-4645	37	1	(	(	PUNCT
ejpam-4645	37	2	see	see	VERB
ejpam-4645	37	3	[	[	X
ejpam-4645	37	4	9	9	NUM
ejpam-4645	37	5	]	]	NUM
ejpam-4645	37	6	)	)	PUNCT
ejpam-4645	37	7	.	.	PUNCT
ejpam-4645	38	1	other	other	ADJ
ejpam-4645	38	2	variations	variation	NOUN
ejpam-4645	38	3	of	of	ADP
ejpam-4645	38	4	domination	domination	NOUN
ejpam-4645	38	5	can	can	AUX
ejpam-4645	38	6	be	be	AUX
ejpam-4645	38	7	found	find	VERB
ejpam-4645	38	8	in	in	ADP
ejpam-4645	38	9	[	[	X
ejpam-4645	38	10	2	2	NUM
ejpam-4645	38	11	]	]	PUNCT
ejpam-4645	38	12	,	,	PUNCT
ejpam-4645	38	13	[	[	X
ejpam-4645	38	14	3	3	NUM
ejpam-4645	38	15	]	]	PUNCT
ejpam-4645	38	16	,	,	PUNCT
ejpam-4645	38	17	[	[	X
ejpam-4645	38	18	4	4	NUM
ejpam-4645	38	19	]	]	PUNCT
ejpam-4645	38	20	,	,	PUNCT
ejpam-4645	38	21	[	[	X
ejpam-4645	38	22	5	5	NUM
ejpam-4645	38	23	]	]	PUNCT
ejpam-4645	38	24	,	,	PUNCT
ejpam-4645	38	25	[	[	X
ejpam-4645	38	26	11	11	NUM
ejpam-4645	38	27	]	]	PUNCT
ejpam-4645	38	28	,	,	PUNCT
ejpam-4645	38	29	[	[	X
ejpam-4645	38	30	12	12	NUM
ejpam-4645	38	31	]	]	PUNCT
ejpam-4645	38	32	,	,	PUNCT
ejpam-4645	38	33	[	[	X
ejpam-4645	38	34	16	16	NUM
ejpam-4645	38	35	]	]	PUNCT
ejpam-4645	38	36	,	,	PUNCT
ejpam-4645	38	37	and	and	CCONJ
ejpam-4645	38	38	[	[	X
ejpam-4645	38	39	18	18	NUM
ejpam-4645	38	40	]	]	PUNCT
ejpam-4645	38	41	.	.	PUNCT
ejpam-4645	39	1	the	the	DET
ejpam-4645	39	2	concepts	concept	NOUN
ejpam-4645	39	3	of	of	ADP
ejpam-4645	39	4	locating	locate	VERB
ejpam-4645	39	5	,	,	PUNCT
ejpam-4645	39	6	stricly	stricly	ADV
ejpam-4645	39	7	locating	locate	VERB
ejpam-4645	39	8	,	,	PUNCT
ejpam-4645	39	9	locating	locate	VERB
ejpam-4645	39	10	-	-	PUNCT
ejpam-4645	39	11	dominating	dominating	NOUN
ejpam-4645	39	12	,	,	PUNCT
ejpam-4645	39	13	and	and	CCONJ
ejpam-4645	39	14	strictly	strictly	ADV
ejpam-4645	39	15	locating	locate	VERB
ejpam-4645	39	16	-	-	PUNCT
ejpam-4645	39	17	dominating	dominating	NOUN
ejpam-4645	39	18	,	,	PUNCT
ejpam-4645	39	19	and	and	CCONJ
ejpam-4645	39	20	the	the	DET
ejpam-4645	39	21	associated	associated	ADJ
ejpam-4645	39	22	parameters	parameter	NOUN
ejpam-4645	39	23	are	be	AUX
ejpam-4645	39	24	studied	study	VERB
ejpam-4645	39	25	in	in	ADP
ejpam-4645	39	26	[	[	X
ejpam-4645	39	27	6	6	NUM
ejpam-4645	39	28	]	]	PUNCT
ejpam-4645	39	29	,	,	PUNCT
ejpam-4645	40	1	[	[	X
ejpam-4645	40	2	8	8	NUM
ejpam-4645	40	3	]	]	PUNCT
ejpam-4645	40	4	,	,	PUNCT
ejpam-4645	40	5	[	[	X
ejpam-4645	40	6	10	10	NUM
ejpam-4645	40	7	]	]	PUNCT
ejpam-4645	40	8	,	,	PUNCT
ejpam-4645	40	9	[	[	X
ejpam-4645	40	10	13	13	NUM
ejpam-4645	40	11	]	]	PUNCT
ejpam-4645	40	12	,	,	PUNCT
ejpam-4645	40	13	[	[	X
ejpam-4645	40	14	14	14	NUM
ejpam-4645	40	15	]	]	PUNCT
ejpam-4645	40	16	,	,	PUNCT
ejpam-4645	40	17	[	[	X
ejpam-4645	40	18	15	15	NUM
ejpam-4645	40	19	]	]	PUNCT
ejpam-4645	40	20	,	,	PUNCT
ejpam-4645	41	1	[	[	X
ejpam-4645	41	2	17	17	NUM
ejpam-4645	41	3	]	]	PUNCT
ejpam-4645	41	4	,	,	PUNCT
ejpam-4645	41	5	[	[	X
ejpam-4645	41	6	19	19	NUM
ejpam-4645	41	7	]	]	PUNCT
ejpam-4645	41	8	,	,	PUNCT
ejpam-4645	41	9	[	[	X
ejpam-4645	41	10	20	20	NUM
ejpam-4645	41	11	]	]	PUNCT
ejpam-4645	41	12	.	.	PUNCT
ejpam-4645	42	1	the	the	DET
ejpam-4645	42	2	concept	concept	NOUN
ejpam-4645	42	3	of	of	ADP
ejpam-4645	42	4	stable	stable	ADJ
ejpam-4645	42	5	locating	locating	NOUN
ejpam-4645	42	6	-	-	PUNCT
ejpam-4645	42	7	dominating	dominate	VERB
ejpam-4645	42	8	and	and	CCONJ
ejpam-4645	42	9	related	related	ADJ
ejpam-4645	42	10	concepts	concept	NOUN
ejpam-4645	42	11	are	be	AUX
ejpam-4645	42	12	studied	study	VERB
ejpam-4645	42	13	in	in	ADP
ejpam-4645	42	14	[	[	X
ejpam-4645	42	15	1	1	NUM
ejpam-4645	42	16	]	]	PUNCT
ejpam-4645	42	17	.	.	PUNCT
ejpam-4645	43	1	let	let	VERB
ejpam-4645	43	2	g	g	NOUN
ejpam-4645	43	3	andh	andh	NOUN
ejpam-4645	43	4	be	be	AUX
ejpam-4645	43	5	any	any	DET
ejpam-4645	43	6	two	two	NUM
ejpam-4645	43	7	graphs	graph	NOUN
ejpam-4645	43	8	.	.	PUNCT
ejpam-4645	44	1	the	the	DET
ejpam-4645	44	2	edge	edge	NOUN
ejpam-4645	44	3	corona	corona	NOUN
ejpam-4645	44	4	g⋄h	g⋄h	X
ejpam-4645	44	5	is	be	AUX
ejpam-4645	44	6	the	the	DET
ejpam-4645	44	7	graph	graph	NOUN
ejpam-4645	44	8	obtained	obtain	VERB
ejpam-4645	44	9	by	by	ADP
ejpam-4645	44	10	taking	take	VERB
ejpam-4645	44	11	one	one	NUM
ejpam-4645	44	12	copy	copy	NOUN
ejpam-4645	44	13	of	of	ADP
ejpam-4645	44	14	g	g	NOUN
ejpam-4645	44	15	and	and	CCONJ
ejpam-4645	44	16	|e(g)|	|e(g)|	ADJ
ejpam-4645	44	17	copiesh	copiesh	NOUN
ejpam-4645	44	18	and	and	CCONJ
ejpam-4645	44	19	joining	join	VERB
ejpam-4645	44	20	each	each	DET
ejpam-4645	44	21	end	end	NOUN
ejpam-4645	44	22	vertices	vertice	VERB
ejpam-4645	44	23	u	u	NOUN
ejpam-4645	44	24	and	and	CCONJ
ejpam-4645	44	25	v	v	NOUN
ejpam-4645	44	26	of	of	ADP
ejpam-4645	44	27	every	every	DET
ejpam-4645	44	28	edge	edge	NOUN
ejpam-4645	44	29	uv	uv	NOUN
ejpam-4645	44	30	to	to	ADP
ejpam-4645	44	31	every	every	DET
ejpam-4645	44	32	vertex	vertex	NOUN
ejpam-4645	44	33	of	of	ADP
ejpam-4645	44	34	the	the	DET
ejpam-4645	44	35	copyhuv	copyhuv	NOUN
ejpam-4645	44	36	ofh	ofh	PROPN
ejpam-4645	44	37	(	(	PUNCT
ejpam-4645	44	38	i.e.	i.e.	X
ejpam-4645	44	39	forming	form	VERB
ejpam-4645	44	40	the	the	DET
ejpam-4645	44	41	join	join	NOUN
ejpam-4645	44	42	⟨{u	⟨{u	PROPN
ejpam-4645	44	43	,	,	PUNCT
ejpam-4645	44	44	v}⟩+huv	v}⟩+huv	NOUN
ejpam-4645	44	45	for	for	ADP
ejpam-4645	44	46	each	each	DET
ejpam-4645	44	47	uv	uv	PROPN
ejpam-4645	44	48	∈	∈	PROPN
ejpam-4645	44	49	e(g	e(g	PROPN
ejpam-4645	44	50	)	)	PUNCT
ejpam-4645	44	51	)	)	PUNCT
ejpam-4645	44	52	.	.	PUNCT
ejpam-4645	45	1	the	the	DET
ejpam-4645	45	2	lexicographic	lexicographic	ADJ
ejpam-4645	45	3	product	product	NOUN
ejpam-4645	45	4	g[h	g[h	PROPN
ejpam-4645	45	5	]	]	PUNCT
ejpam-4645	45	6	is	be	AUX
ejpam-4645	45	7	the	the	DET
ejpam-4645	45	8	graph	graph	NOUN
ejpam-4645	45	9	with	with	ADP
ejpam-4645	45	10	vertex	vertex	NOUN
ejpam-4645	45	11	-	-	PUNCT
ejpam-4645	45	12	set	set	VERB
ejpam-4645	45	13	v	v	NOUN
ejpam-4645	45	14	(	(	PUNCT
ejpam-4645	45	15	g[h	g[h	PROPN
ejpam-4645	45	16	]	]	PUNCT
ejpam-4645	45	17	)	)	PUNCT
ejpam-4645	45	18	=	=	SYM
ejpam-4645	45	19	v	v	X
ejpam-4645	45	20	(	(	PUNCT
ejpam-4645	45	21	g)×v	g)×v	PROPN
ejpam-4645	45	22	(	(	PUNCT
ejpam-4645	45	23	h	h	NOUN
ejpam-4645	45	24	)	)	PUNCT
ejpam-4645	45	25	and	and	CCONJ
ejpam-4645	45	26	edge	edge	NOUN
ejpam-4645	45	27	-	-	PUNCT
ejpam-4645	45	28	set	set	VERB
ejpam-4645	45	29	e(g[h	e(g[h	NOUN
ejpam-4645	45	30	]	]	PUNCT
ejpam-4645	45	31	)	)	PUNCT
ejpam-4645	45	32	satisfying	satisfy	VERB
ejpam-4645	45	33	the	the	DET
ejpam-4645	45	34	following	follow	VERB
ejpam-4645	45	35	conditions	condition	NOUN
ejpam-4645	45	36	:	:	PUNCT
ejpam-4645	45	37	(	(	PUNCT
ejpam-4645	45	38	x	x	X
ejpam-4645	45	39	,	,	PUNCT
ejpam-4645	45	40	u)(y	u)(y	PROPN
ejpam-4645	45	41	,	,	PUNCT
ejpam-4645	45	42	v	v	NOUN
ejpam-4645	45	43	)	)	PUNCT
ejpam-4645	45	44	∈	∈	NOUN
ejpam-4645	45	45	e(g[h	e(g[h	NOUN
ejpam-4645	45	46	]	]	PUNCT
ejpam-4645	45	47	)	)	PUNCT
ejpam-4645	45	48	if	if	SCONJ
ejpam-4645	45	49	and	and	CCONJ
ejpam-4645	45	50	only	only	ADV
ejpam-4645	45	51	if	if	SCONJ
ejpam-4645	45	52	either	either	CCONJ
ejpam-4645	45	53	xy	xy	PROPN
ejpam-4645	45	54	∈	∈	PROPN
ejpam-4645	45	55	e(g	e(g	PROPN
ejpam-4645	45	56	)	)	PUNCT
ejpam-4645	45	57	or	or	CCONJ
ejpam-4645	45	58	x	x	X
ejpam-4645	45	59	=	=	SYM
ejpam-4645	45	60	y	y	PROPN
ejpam-4645	45	61	and	and	CCONJ
ejpam-4645	45	62	uv	uv	PROPN
ejpam-4645	45	63	∈	∈	PROPN
ejpam-4645	45	64	e(h	e(h	PROPN
ejpam-4645	45	65	)	)	PUNCT
ejpam-4645	45	66	.	.	PUNCT
ejpam-4645	46	1	it	it	PRON
ejpam-4645	46	2	is	be	AUX
ejpam-4645	46	3	easily	easily	ADV
ejpam-4645	46	4	observed	observe	VERB
ejpam-4645	46	5	that	that	SCONJ
ejpam-4645	46	6	for	for	ADP
ejpam-4645	46	7	any	any	DET
ejpam-4645	46	8	non	non	ADJ
ejpam-4645	46	9	-	-	ADJ
ejpam-4645	46	10	empty	empty	ADJ
ejpam-4645	46	11	subset	subset	NOUN
ejpam-4645	46	12	c	c	NOUN
ejpam-4645	46	13	of	of	ADP
ejpam-4645	46	14	v	v	PROPN
ejpam-4645	46	15	(	(	PUNCT
ejpam-4645	46	16	g[h	g[h	PROPN
ejpam-4645	46	17	]	]	PUNCT
ejpam-4645	46	18	)	)	PUNCT
ejpam-4645	46	19	=	=	SYM
ejpam-4645	46	20	v	v	X
ejpam-4645	46	21	(	(	PUNCT
ejpam-4645	46	22	g)×	g)×	NOUN
ejpam-4645	46	23	v	v	NOUN
ejpam-4645	46	24	(	(	PUNCT
ejpam-4645	46	25	h	h	NOUN
ejpam-4645	46	26	)	)	PUNCT
ejpam-4645	46	27	,	,	PUNCT
ejpam-4645	46	28	this	this	DET
ejpam-4645	46	29	set	set	NOUN
ejpam-4645	46	30	can	can	AUX
ejpam-4645	46	31	be	be	AUX
ejpam-4645	46	32	expressed	express	VERB
ejpam-4645	46	33	as	as	ADP
ejpam-4645	46	34	c	c	NOUN
ejpam-4645	46	35	=	=	SYM
ejpam-4645	46	36	∪x∈s({x	∪x∈s({x	NOUN
ejpam-4645	46	37	}	}	PUNCT
ejpam-4645	46	38	×	×	PROPN
ejpam-4645	46	39	tx	tx	PROPN
ejpam-4645	46	40	)	)	PUNCT
ejpam-4645	46	41	,	,	PUNCT
ejpam-4645	46	42	where	where	SCONJ
ejpam-4645	46	43	s	s	VERB
ejpam-4645	46	44	⊆	⊆	NUM
ejpam-4645	46	45	v	v	NOUN
ejpam-4645	46	46	(	(	PUNCT
ejpam-4645	46	47	g	g	NOUN
ejpam-4645	46	48	)	)	PUNCT
ejpam-4645	46	49	and	and	CCONJ
ejpam-4645	46	50	tx	tx	VERB
ejpam-4645	46	51	⊆	⊆	NUM
ejpam-4645	46	52	v	v	NOUN
ejpam-4645	46	53	(	(	PUNCT
ejpam-4645	46	54	h	h	NOUN
ejpam-4645	46	55	)	)	PUNCT
ejpam-4645	46	56	for	for	ADP
ejpam-4645	46	57	each	each	DET
ejpam-4645	46	58	x	x	SYM
ejpam-4645	46	59	∈	∈	PROPN
ejpam-4645	46	60	s.	s.	PROPN
ejpam-4645	46	61	set	set	VERB
ejpam-4645	46	62	s	s	PART
ejpam-4645	47	1	=	=	NOUN
ejpam-4645	47	2	cg	cg	NOUN
ejpam-4645	47	3	=	=	SYM
ejpam-4645	47	4	{	{	PUNCT
ejpam-4645	47	5	x	x	PROPN
ejpam-4645	47	6	∈	∈	PROPN
ejpam-4645	47	7	v	v	NOUN
ejpam-4645	47	8	(	(	PUNCT
ejpam-4645	47	9	g	g	NOUN
ejpam-4645	47	10	)	)	PUNCT
ejpam-4645	47	11	:	:	PUNCT
ejpam-4645	47	12	(	(	PUNCT
ejpam-4645	47	13	x	x	X
ejpam-4645	47	14	,	,	PUNCT
ejpam-4645	47	15	a	a	PRON
ejpam-4645	47	16	)	)	PUNCT
ejpam-4645	47	17	∈	∈	PROPN
ejpam-4645	47	18	c	c	NOUN
ejpam-4645	47	19	for	for	ADP
ejpam-4645	47	20	some	some	DET
ejpam-4645	47	21	a	a	DET
ejpam-4645	47	22	∈	∈	PROPN
ejpam-4645	47	23	v	v	NOUN
ejpam-4645	47	24	(	(	PUNCT
ejpam-4645	47	25	h	h	NOUN
ejpam-4645	47	26	)	)	PUNCT
ejpam-4645	47	27	}	}	PUNCT
ejpam-4645	47	28	is	be	AUX
ejpam-4645	47	29	called	call	VERB
ejpam-4645	47	30	the	the	DET
ejpam-4645	47	31	g	g	NOUN
ejpam-4645	47	32	-	-	PUNCT
ejpam-4645	47	33	projection	projection	NOUN
ejpam-4645	47	34	of	of	ADP
ejpam-4645	47	35	c.	c.	PROPN
ejpam-4645	47	36	moreover	moreover	ADV
ejpam-4645	47	37	,	,	PUNCT
ejpam-4645	47	38	for	for	ADP
ejpam-4645	47	39	each	each	DET
ejpam-4645	47	40	x	x	SYM
ejpam-4645	47	41	∈	∈	PROPN
ejpam-4645	47	42	s	s	NOUN
ejpam-4645	47	43	,	,	PUNCT
ejpam-4645	47	44	tx	tx	PROPN
ejpam-4645	47	45	=	=	PUNCT
ejpam-4645	47	46	{	{	PUNCT
ejpam-4645	47	47	a	a	DET
ejpam-4645	47	48	∈	∈	PROPN
ejpam-4645	47	49	v	v	ADP
ejpam-4645	47	50	(	(	PUNCT
ejpam-4645	47	51	h	h	NOUN
ejpam-4645	47	52	)	)	PUNCT
ejpam-4645	47	53	:	:	PUNCT
ejpam-4645	47	54	(	(	PUNCT
ejpam-4645	47	55	x	x	X
ejpam-4645	47	56	,	,	PUNCT
ejpam-4645	47	57	a	a	PRON
ejpam-4645	47	58	)	)	PUNCT
ejpam-4645	47	59	∈	∈	PROPN
ejpam-4645	47	60	c	c	NOUN
ejpam-4645	47	61	}	}	PUNCT
ejpam-4645	47	62	.	.	PUNCT
ejpam-4645	48	1	2	2	X
ejpam-4645	48	2	.	.	X
ejpam-4645	48	3	results	result	NOUN
ejpam-4645	48	4	throughout	throughout	ADP
ejpam-4645	48	5	,	,	PUNCT
ejpam-4645	48	6	we	we	PRON
ejpam-4645	48	7	denote	denote	VERB
ejpam-4645	48	8	by	by	ADP
ejpam-4645	48	9	l(g	l(g	NOUN
ejpam-4645	48	10	)	)	PUNCT
ejpam-4645	48	11	the	the	DET
ejpam-4645	48	12	set	set	NOUN
ejpam-4645	48	13	containing	contain	VERB
ejpam-4645	48	14	all	all	DET
ejpam-4645	48	15	leaves	leave	NOUN
ejpam-4645	48	16	of	of	ADP
ejpam-4645	48	17	a	a	DET
ejpam-4645	48	18	graph	graph	NOUN
ejpam-4645	48	19	g.	g.	NOUN
ejpam-4645	48	20	the	the	DET
ejpam-4645	48	21	first	first	ADJ
ejpam-4645	48	22	result	result	NOUN
ejpam-4645	48	23	is	be	AUX
ejpam-4645	48	24	found	find	VERB
ejpam-4645	48	25	in	in	ADP
ejpam-4645	48	26	[	[	X
ejpam-4645	48	27	1	1	NUM
ejpam-4645	48	28	]	]	PUNCT
ejpam-4645	48	29	.	.	PUNCT
ejpam-4645	49	1	theorem	theorem	NOUN
ejpam-4645	49	2	1	1	X
ejpam-4645	49	3	.	.	PUNCT
ejpam-4645	50	1	let	let	VERB
ejpam-4645	50	2	g	g	NOUN
ejpam-4645	50	3	be	be	AUX
ejpam-4645	50	4	graph	graph	NOUN
ejpam-4645	50	5	without	without	ADP
ejpam-4645	50	6	isolated	isolated	ADJ
ejpam-4645	50	7	vertices	vertex	NOUN
ejpam-4645	50	8	.	.	PUNCT
ejpam-4645	51	1	then	then	ADV
ejpam-4645	51	2	g	g	PROPN
ejpam-4645	51	3	has	have	VERB
ejpam-4645	51	4	a	a	DET
ejpam-4645	51	5	stable	stable	ADJ
ejpam-4645	51	6	strictly	strictly	ADV
ejpam-4645	51	7	locating	locate	VERB
ejpam-4645	51	8	set	set	VERB
ejpam-4645	51	9	if	if	SCONJ
ejpam-4645	51	10	and	and	CCONJ
ejpam-4645	51	11	only	only	ADV
ejpam-4645	51	12	if	if	SCONJ
ejpam-4645	51	13	γ(g	γ(g	NOUN
ejpam-4645	51	14	)	)	PUNCT
ejpam-4645	51	15	̸=	̸=	PROPN
ejpam-4645	51	16	1	1	NUM
ejpam-4645	51	17	.	.	PUNCT
ejpam-4645	52	1	g.	g.	PROPN
ejpam-4645	52	2	malacas	malacas	PROPN
ejpam-4645	52	3	,	,	PUNCT
ejpam-4645	52	4	s.	s.	PROPN
ejpam-4645	52	5	canoy	canoy	PROPN
ejpam-4645	52	6	,	,	PUNCT
ejpam-4645	52	7	jr	jr	PROPN
ejpam-4645	52	8	.	.	PROPN
ejpam-4645	52	9	,	,	PUNCT
ejpam-4645	52	10	e.	e.	PROPN
ejpam-4645	52	11	chacon	chacon	PROPN
ejpam-4645	52	12	/	/	SYM
ejpam-4645	52	13	eur	eur	PROPN
ejpam-4645	52	14	.	.	PUNCT
ejpam-4645	53	1	j.	j.	PROPN
ejpam-4645	53	2	pure	pure	PROPN
ejpam-4645	53	3	appl	appl	PROPN
ejpam-4645	53	4	.	.	PROPN
ejpam-4645	53	5	math	math	PROPN
ejpam-4645	53	6	,	,	PUNCT
ejpam-4645	53	7	16	16	NUM
ejpam-4645	53	8	(	(	PUNCT
ejpam-4645	53	9	1	1	NUM
ejpam-4645	53	10	)	)	PUNCT
ejpam-4645	53	11	(	(	PUNCT
ejpam-4645	53	12	2023	2023	NUM
ejpam-4645	53	13	)	)	PUNCT
ejpam-4645	53	14	,	,	PUNCT
ejpam-4645	53	15	479	479	NUM
ejpam-4645	53	16	-	-	SYM
ejpam-4645	53	17	490	490	NUM
ejpam-4645	53	18	481	481	NUM
ejpam-4645	53	19	theorem	theorem	NOUN
ejpam-4645	53	20	2	2	NUM
ejpam-4645	53	21	.	.	PUNCT
ejpam-4645	54	1	let	let	VERB
ejpam-4645	54	2	g	g	PRON
ejpam-4645	54	3	be	be	AUX
ejpam-4645	54	4	a	a	DET
ejpam-4645	54	5	connected	connected	ADJ
ejpam-4645	54	6	graph	graph	NOUN
ejpam-4645	54	7	of	of	ADP
ejpam-4645	54	8	order	order	NOUN
ejpam-4645	54	9	m	m	VERB
ejpam-4645	54	10	≥	≥	NOUN
ejpam-4645	54	11	3	3	NUM
ejpam-4645	54	12	and	and	CCONJ
ejpam-4645	54	13	let	let	VERB
ejpam-4645	54	14	h	h	NOUN
ejpam-4645	54	15	be	be	AUX
ejpam-4645	54	16	any	any	DET
ejpam-4645	54	17	non	non	ADJ
ejpam-4645	54	18	-	-	ADJ
ejpam-4645	54	19	trivial	trivial	ADJ
ejpam-4645	54	20	connected	connected	ADJ
ejpam-4645	54	21	graph	graph	NOUN
ejpam-4645	54	22	.	.	PUNCT
ejpam-4645	55	1	then	then	ADV
ejpam-4645	55	2	c	c	PROPN
ejpam-4645	55	3	is	be	AUX
ejpam-4645	55	4	a	a	DET
ejpam-4645	55	5	locating	locate	VERB
ejpam-4645	55	6	-	-	PUNCT
ejpam-4645	55	7	dominating	dominate	VERB
ejpam-4645	55	8	set	set	NOUN
ejpam-4645	55	9	of	of	ADP
ejpam-4645	55	10	g	g	PROPN
ejpam-4645	55	11	⋄	⋄	PROPN
ejpam-4645	55	12	h	h	NOUN
ejpam-4645	56	1	if	if	SCONJ
ejpam-4645	56	2	and	and	CCONJ
ejpam-4645	56	3	only	only	ADV
ejpam-4645	56	4	if	if	SCONJ
ejpam-4645	56	5	c	c	X
ejpam-4645	56	6	=	=	PUNCT
ejpam-4645	56	7	a	a	DET
ejpam-4645	56	8	∪	∪	NOUN
ejpam-4645	56	9	[	[	X
ejpam-4645	56	10	∪uv∈e(g)suv	∪uv∈e(g)suv	NOUN
ejpam-4645	56	11	]	]	PUNCT
ejpam-4645	56	12	and	and	CCONJ
ejpam-4645	56	13	satisfies	satisfy	VERB
ejpam-4645	56	14	the	the	DET
ejpam-4645	56	15	following	follow	VERB
ejpam-4645	56	16	conditions	condition	NOUN
ejpam-4645	56	17	:	:	PUNCT
ejpam-4645	56	18	(	(	PUNCT
ejpam-4645	56	19	i	i	NOUN
ejpam-4645	56	20	)	)	PUNCT
ejpam-4645	56	21	a	a	DET
ejpam-4645	56	22	⊆	⊆	NUM
ejpam-4645	56	23	v	v	NOUN
ejpam-4645	56	24	(	(	PUNCT
ejpam-4645	56	25	g	g	NOUN
ejpam-4645	56	26	)	)	PUNCT
ejpam-4645	56	27	.	.	PUNCT
ejpam-4645	57	1	(	(	PUNCT
ejpam-4645	57	2	ii	ii	NOUN
ejpam-4645	57	3	)	)	PUNCT
ejpam-4645	57	4	for	for	ADP
ejpam-4645	57	5	each	each	DET
ejpam-4645	57	6	uv	uv	PROPN
ejpam-4645	57	7	∈	∈	PROPN
ejpam-4645	57	8	e(g	e(g	PROPN
ejpam-4645	57	9	)	)	PUNCT
ejpam-4645	57	10	,	,	PUNCT
ejpam-4645	57	11	(	(	PUNCT
ejpam-4645	57	12	a	a	X
ejpam-4645	57	13	)	)	PUNCT
ejpam-4645	57	14	suv	suv	NOUN
ejpam-4645	57	15	is	be	AUX
ejpam-4645	57	16	a	a	DET
ejpam-4645	57	17	locating	locate	VERB
ejpam-4645	57	18	set	set	NOUN
ejpam-4645	57	19	of	of	ADP
ejpam-4645	57	20	huv	huv	PROPN
ejpam-4645	57	21	;	;	PUNCT
ejpam-4645	57	22	(	(	PUNCT
ejpam-4645	57	23	b	b	X
ejpam-4645	57	24	)	)	PUNCT
ejpam-4645	57	25	suv	suv	PROPN
ejpam-4645	57	26	is	be	AUX
ejpam-4645	57	27	a	a	DET
ejpam-4645	57	28	locating	locate	VERB
ejpam-4645	57	29	-	-	PUNCT
ejpam-4645	57	30	dominating	dominate	VERB
ejpam-4645	57	31	set	set	NOUN
ejpam-4645	57	32	of	of	ADP
ejpam-4645	57	33	huv	huv	PROPN
ejpam-4645	57	34	whenever	whenever	SCONJ
ejpam-4645	57	35	u	u	NOUN
ejpam-4645	57	36	,	,	PUNCT
ejpam-4645	57	37	v	v	NOUN
ejpam-4645	57	38	/∈	/∈	PUNCT
ejpam-4645	57	39	a	a	PRON
ejpam-4645	57	40	;	;	PUNCT
ejpam-4645	57	41	(	(	PUNCT
ejpam-4645	57	42	c	c	X
ejpam-4645	57	43	)	)	PUNCT
ejpam-4645	57	44	suv	suv	PROPN
ejpam-4645	57	45	is	be	AUX
ejpam-4645	57	46	a	a	DET
ejpam-4645	57	47	strictly	strictly	ADV
ejpam-4645	57	48	locating	locate	VERB
ejpam-4645	57	49	set	set	NOUN
ejpam-4645	57	50	of	of	ADP
ejpam-4645	57	51	huv	huv	PROPN
ejpam-4645	57	52	for	for	ADP
ejpam-4645	57	53	each	each	DET
ejpam-4645	57	54	v	v	ADP
ejpam-4645	57	55	∈	∈	PROPN
ejpam-4645	57	56	l(g	l(g	NOUN
ejpam-4645	57	57	)	)	PUNCT
ejpam-4645	57	58	with	with	ADP
ejpam-4645	57	59	v	v	NUM
ejpam-4645	57	60	/∈	/∈	PUNCT
ejpam-4645	57	61	a	a	NOUN
ejpam-4645	57	62	;	;	PUNCT
ejpam-4645	57	63	and	and	CCONJ
ejpam-4645	57	64	(	(	PUNCT
ejpam-4645	57	65	d	d	X
ejpam-4645	57	66	)	)	PUNCT
ejpam-4645	57	67	suv	suv	PROPN
ejpam-4645	57	68	is	be	AUX
ejpam-4645	57	69	a	a	DET
ejpam-4645	57	70	strictly	strictly	ADV
ejpam-4645	57	71	locating	locate	VERB
ejpam-4645	57	72	-	-	PUNCT
ejpam-4645	57	73	dominating	dominate	VERB
ejpam-4645	57	74	set	set	NOUN
ejpam-4645	57	75	of	of	ADP
ejpam-4645	57	76	huv	huv	PROPN
ejpam-4645	57	77	whenever	whenever	SCONJ
ejpam-4645	57	78	u	u	NOUN
ejpam-4645	57	79	,	,	PUNCT
ejpam-4645	57	80	v	v	NOUN
ejpam-4645	57	81	/∈	/∈	PUNCT
ejpam-4645	57	82	a	a	PRON
ejpam-4645	57	83	and	and	CCONJ
ejpam-4645	57	84	{	{	PUNCT
ejpam-4645	57	85	u	u	NOUN
ejpam-4645	57	86	,	,	PUNCT
ejpam-4645	57	87	v}∩	v}∩	PROPN
ejpam-4645	57	88	l(g	l(g	PROPN
ejpam-4645	57	89	)	)	PUNCT
ejpam-4645	57	90	̸=	̸=	PROPN
ejpam-4645	57	91	∅.	∅.	ADP
ejpam-4645	57	92	(	(	PUNCT
ejpam-4645	57	93	iii	iii	NOUN
ejpam-4645	57	94	)	)	PUNCT
ejpam-4645	57	95	for	for	ADP
ejpam-4645	57	96	each	each	DET
ejpam-4645	57	97	uv	uv	PROPN
ejpam-4645	57	98	∈	∈	PROPN
ejpam-4645	57	99	e(g	e(g	PROPN
ejpam-4645	57	100	)	)	PUNCT
ejpam-4645	57	101	with	with	ADP
ejpam-4645	57	102	v	v	NUM
ejpam-4645	57	103	∈	∈	PROPN
ejpam-4645	57	104	a	a	PRON
ejpam-4645	57	105	and	and	CCONJ
ejpam-4645	57	106	u	u	NOUN
ejpam-4645	57	107	/∈	/∈	PROPN
ejpam-4645	58	1	a	a	INTJ
ejpam-4645	58	2	,	,	PUNCT
ejpam-4645	58	3	if	if	SCONJ
ejpam-4645	58	4	x	x	PROPN
ejpam-4645	58	5	∈	∈	PROPN
ejpam-4645	58	6	v	v	NOUN
ejpam-4645	58	7	(	(	PUNCT
ejpam-4645	58	8	huv)\suv	huv)\suv	PROPN
ejpam-4645	58	9	and	and	CCONJ
ejpam-4645	58	10	nhuv(x)∩suv	nhuv(x)∩suv	NOUN
ejpam-4645	58	11	=	=	SYM
ejpam-4645	58	12	∅	∅	NOUN
ejpam-4645	58	13	,	,	PUNCT
ejpam-4645	58	14	then	then	ADV
ejpam-4645	58	15	for	for	ADP
ejpam-4645	58	16	each	each	DET
ejpam-4645	58	17	w	w	PROPN
ejpam-4645	58	18	∈	∈	PROPN
ejpam-4645	58	19	ng(v)\{u	ng(v)\{u	ADV
ejpam-4645	58	20	}	}	PUNCT
ejpam-4645	58	21	and	and	CCONJ
ejpam-4645	58	22	for	for	ADP
ejpam-4645	58	23	each	each	DET
ejpam-4645	58	24	y	y	PROPN
ejpam-4645	58	25	∈	∈	PROPN
ejpam-4645	58	26	v	v	NOUN
ejpam-4645	58	27	(	(	PUNCT
ejpam-4645	58	28	hwv)\swv	hwv)\swv	PROPN
ejpam-4645	58	29	,	,	PUNCT
ejpam-4645	58	30	it	it	PRON
ejpam-4645	58	31	holds	hold	VERB
ejpam-4645	58	32	that	that	SCONJ
ejpam-4645	58	33	w	w	PROPN
ejpam-4645	58	34	∈	∈	PROPN
ejpam-4645	58	35	a	a	DET
ejpam-4645	58	36	or	or	CCONJ
ejpam-4645	58	37	nhwv(y	nhwv(y	NOUN
ejpam-4645	58	38	)	)	PUNCT
ejpam-4645	58	39	∩	∩	PROPN
ejpam-4645	58	40	swv	swv	PROPN
ejpam-4645	58	41	̸=	̸=	PROPN
ejpam-4645	58	42	∅.	∅.	ADP
ejpam-4645	58	43	proof	proof	NOUN
ejpam-4645	58	44	.	.	PUNCT
ejpam-4645	59	1	suppose	suppose	VERB
ejpam-4645	59	2	c	c	NOUN
ejpam-4645	59	3	is	be	AUX
ejpam-4645	59	4	a	a	DET
ejpam-4645	59	5	locating	locate	VERB
ejpam-4645	59	6	-	-	PUNCT
ejpam-4645	59	7	dominating	dominate	VERB
ejpam-4645	59	8	set	set	NOUN
ejpam-4645	59	9	of	of	ADP
ejpam-4645	59	10	g	g	PROPN
ejpam-4645	59	11	⋄	⋄	PROPN
ejpam-4645	59	12	h.	h.	PROPN
ejpam-4645	59	13	let	let	VERB
ejpam-4645	59	14	a	a	DET
ejpam-4645	59	15	=	=	SYM
ejpam-4645	59	16	c	c	NOUN
ejpam-4645	59	17	∩	∩	X
ejpam-4645	59	18	v	v	X
ejpam-4645	59	19	(	(	PUNCT
ejpam-4645	59	20	g	g	NOUN
ejpam-4645	59	21	)	)	PUNCT
ejpam-4645	59	22	and	and	CCONJ
ejpam-4645	59	23	suv	suv	PROPN
ejpam-4645	59	24	=	=	PROPN
ejpam-4645	59	25	c	c	PROPN
ejpam-4645	59	26	∩	∩	X
ejpam-4645	59	27	v	v	X
ejpam-4645	59	28	(	(	PUNCT
ejpam-4645	59	29	huv	huv	PROPN
ejpam-4645	59	30	)	)	PUNCT
ejpam-4645	59	31	for	for	ADP
ejpam-4645	59	32	each	each	DET
ejpam-4645	59	33	uv	uv	PROPN
ejpam-4645	59	34	∈	∈	PROPN
ejpam-4645	59	35	e(g	e(g	PROPN
ejpam-4645	59	36	)	)	PUNCT
ejpam-4645	59	37	.	.	PUNCT
ejpam-4645	60	1	then	then	ADV
ejpam-4645	60	2	c	c	X
ejpam-4645	60	3	=	=	PUNCT
ejpam-4645	60	4	a	a	DET
ejpam-4645	60	5	∪	∪	NOUN
ejpam-4645	60	6	[	[	X
ejpam-4645	60	7	∪uv∈e(g)suv	∪uv∈e(g)suv	NOUN
ejpam-4645	60	8	]	]	PUNCT
ejpam-4645	60	9	and	and	CCONJ
ejpam-4645	60	10	(	(	PUNCT
ejpam-4645	60	11	i	i	NOUN
ejpam-4645	60	12	)	)	PUNCT
ejpam-4645	60	13	holds	hold	VERB
ejpam-4645	60	14	.	.	PUNCT
ejpam-4645	61	1	let	let	VERB
ejpam-4645	61	2	uv	uv	PRON
ejpam-4645	61	3	∈	∈	PROPN
ejpam-4645	61	4	e(g	e(g	PROPN
ejpam-4645	61	5	)	)	PUNCT
ejpam-4645	61	6	.	.	PUNCT
ejpam-4645	62	1	since	since	SCONJ
ejpam-4645	62	2	c	c	PROPN
ejpam-4645	62	3	is	be	AUX
ejpam-4645	62	4	a	a	DET
ejpam-4645	62	5	locating	locating	NOUN
ejpam-4645	62	6	set	set	NOUN
ejpam-4645	62	7	of	of	ADP
ejpam-4645	62	8	g	g	PROPN
ejpam-4645	62	9	⋄	⋄	PROPN
ejpam-4645	62	10	h	h	NOUN
ejpam-4645	62	11	,	,	PUNCT
ejpam-4645	62	12	suv	suv	PROPN
ejpam-4645	62	13	̸=	̸=	PROPN
ejpam-4645	62	14	∅.	∅.	ADV
ejpam-4645	62	15	let	let	VERB
ejpam-4645	62	16	x	x	PRON
ejpam-4645	62	17	,	,	PUNCT
ejpam-4645	62	18	y	y	PROPN
ejpam-4645	62	19	∈	∈	PROPN
ejpam-4645	62	20	v	v	PROPN
ejpam-4645	62	21	(	(	PUNCT
ejpam-4645	62	22	huv	huv	PROPN
ejpam-4645	62	23	)	)	PUNCT
ejpam-4645	62	24	\	\	PROPN
ejpam-4645	62	25	suv	suv	PROPN
ejpam-4645	62	26	with	with	ADP
ejpam-4645	62	27	x	x	PROPN
ejpam-4645	62	28	̸=	̸=	PROPN
ejpam-4645	62	29	y	y	PROPN
ejpam-4645	62	30	and	and	CCONJ
ejpam-4645	62	31	let	let	VERB
ejpam-4645	62	32	s	s	VERB
ejpam-4645	62	33	=	=	PUNCT
ejpam-4645	62	34	a	a	DET
ejpam-4645	62	35	∩	∩	ADJ
ejpam-4645	62	36	{	{	PUNCT
ejpam-4645	62	37	u	u	NOUN
ejpam-4645	62	38	,	,	PUNCT
ejpam-4645	62	39	v	v	NOUN
ejpam-4645	62	40	}	}	PUNCT
ejpam-4645	62	41	.	.	PUNCT
ejpam-4645	63	1	since	since	SCONJ
ejpam-4645	63	2	c	c	PROPN
ejpam-4645	63	3	is	be	AUX
ejpam-4645	63	4	a	a	DET
ejpam-4645	63	5	locating	locating	NOUN
ejpam-4645	63	6	set	set	NOUN
ejpam-4645	63	7	,	,	PUNCT
ejpam-4645	63	8	[	[	X
ejpam-4645	63	9	nhuv(x	nhuv(x	ADJ
ejpam-4645	63	10	)	)	PUNCT
ejpam-4645	63	11	∩	∩	PROPN
ejpam-4645	63	12	suv	suv	NOUN
ejpam-4645	63	13	]	]	PUNCT
ejpam-4645	63	14	∪	∪	ADP
ejpam-4645	63	15	s	s	PART
ejpam-4645	63	16	=	=	SYM
ejpam-4645	63	17	ng⋄h(x	ng⋄h(x	PROPN
ejpam-4645	63	18	)	)	PUNCT
ejpam-4645	63	19	∩	∩	PROPN
ejpam-4645	63	20	c	c	PROPN
ejpam-4645	63	21	̸=	̸=	PROPN
ejpam-4645	63	22	ng⋄h(y	ng⋄h(y	NOUN
ejpam-4645	63	23	)	)	PUNCT
ejpam-4645	63	24	∩	∩	NOUN
ejpam-4645	63	25	c	c	NOUN
ejpam-4645	63	26	=	=	PUNCT
ejpam-4645	64	1	[	[	X
ejpam-4645	64	2	nhuv(y	nhuv(y	NOUN
ejpam-4645	64	3	)	)	PUNCT
ejpam-4645	64	4	∩	∩	PROPN
ejpam-4645	64	5	suv	suv	PROPN
ejpam-4645	64	6	]	]	PUNCT
ejpam-4645	64	7	∪	∪	ADP
ejpam-4645	64	8	s.	s.	PROPN
ejpam-4645	64	9	this	this	PRON
ejpam-4645	64	10	implies	imply	VERB
ejpam-4645	64	11	that	that	SCONJ
ejpam-4645	64	12	nhuv(x	nhuv(x	X
ejpam-4645	64	13	)	)	PUNCT
ejpam-4645	64	14	∩	∩	PROPN
ejpam-4645	64	15	suv	suv	PROPN
ejpam-4645	64	16	̸=	̸=	PROPN
ejpam-4645	64	17	nhuv(y	nhuv(y	PROPN
ejpam-4645	64	18	)	)	PUNCT
ejpam-4645	64	19	∩	∩	PROPN
ejpam-4645	64	20	suv	suv	PROPN
ejpam-4645	64	21	,	,	PUNCT
ejpam-4645	64	22	showing	show	VERB
ejpam-4645	64	23	that	that	SCONJ
ejpam-4645	64	24	suv	suv	PROPN
ejpam-4645	64	25	is	be	AUX
ejpam-4645	64	26	a	a	DET
ejpam-4645	64	27	locating	locate	VERB
ejpam-4645	64	28	set	set	NOUN
ejpam-4645	64	29	of	of	ADP
ejpam-4645	64	30	huv	huv	PROPN
ejpam-4645	64	31	.	.	PUNCT
ejpam-4645	64	32	suppose	suppose	VERB
ejpam-4645	64	33	u	u	NOUN
ejpam-4645	64	34	,	,	PUNCT
ejpam-4645	64	35	v	v	NOUN
ejpam-4645	64	36	/∈	/∈	NOUN
ejpam-4645	64	37	a.	a.	NOUN
ejpam-4645	64	38	since	since	SCONJ
ejpam-4645	64	39	c	c	PROPN
ejpam-4645	64	40	is	be	AUX
ejpam-4645	64	41	a	a	DET
ejpam-4645	64	42	dominating	dominating	NOUN
ejpam-4645	64	43	set	set	NOUN
ejpam-4645	64	44	of	of	ADP
ejpam-4645	64	45	g	g	PROPN
ejpam-4645	64	46	⋄h	⋄h	PROPN
ejpam-4645	64	47	,	,	PUNCT
ejpam-4645	64	48	suv	suv	PROPN
ejpam-4645	64	49	is	be	AUX
ejpam-4645	64	50	a	a	DET
ejpam-4645	64	51	dominating	dominating	NOUN
ejpam-4645	64	52	set	set	NOUN
ejpam-4645	64	53	of	of	ADP
ejpam-4645	64	54	v	v	NOUN
ejpam-4645	64	55	(	(	PUNCT
ejpam-4645	64	56	huv	huv	PROPN
ejpam-4645	64	57	.	.	PUNCT
ejpam-4645	65	1	hence	hence	ADV
ejpam-4645	65	2	,	,	PUNCT
ejpam-4645	65	3	(	(	PUNCT
ejpam-4645	65	4	a	a	X
ejpam-4645	65	5	)	)	PUNCT
ejpam-4645	65	6	and	and	CCONJ
ejpam-4645	65	7	(	(	PUNCT
ejpam-4645	65	8	b	b	NOUN
ejpam-4645	65	9	)	)	PUNCT
ejpam-4645	65	10	hold	hold	NOUN
ejpam-4645	65	11	.	.	PUNCT
ejpam-4645	66	1	next	next	ADV
ejpam-4645	66	2	,	,	PUNCT
ejpam-4645	66	3	suppose	suppose	VERB
ejpam-4645	66	4	that	that	SCONJ
ejpam-4645	66	5	uv	uv	PROPN
ejpam-4645	66	6	∈	∈	PROPN
ejpam-4645	66	7	e(g	e(g	PROPN
ejpam-4645	66	8	)	)	PUNCT
ejpam-4645	66	9	and	and	CCONJ
ejpam-4645	66	10	v	v	ADP
ejpam-4645	66	11	∈	∈	PROPN
ejpam-4645	66	12	l(g	l(g	X
ejpam-4645	66	13	)	)	PUNCT
ejpam-4645	66	14	\	\	PROPN
ejpam-4645	66	15	a.	a.	NOUN
ejpam-4645	66	16	let	let	VERB
ejpam-4645	66	17	s∗	s∗	PROPN
ejpam-4645	66	18	=	=	PUNCT
ejpam-4645	66	19	a	a	DET
ejpam-4645	66	20	∩	∩	ADJ
ejpam-4645	66	21	{	{	PUNCT
ejpam-4645	66	22	u	u	NOUN
ejpam-4645	66	23	}	}	PUNCT
ejpam-4645	66	24	and	and	CCONJ
ejpam-4645	66	25	let	let	VERB
ejpam-4645	66	26	z	z	NOUN
ejpam-4645	66	27	∈	∈	PROPN
ejpam-4645	66	28	v	v	X
ejpam-4645	66	29	(	(	PUNCT
ejpam-4645	66	30	huv	huv	PROPN
ejpam-4645	66	31	)	)	PUNCT
ejpam-4645	66	32	\	\	PROPN
ejpam-4645	66	33	suv	suv	PROPN
ejpam-4645	66	34	.	.	PUNCT
ejpam-4645	66	35	again	again	ADV
ejpam-4645	66	36	,	,	PUNCT
ejpam-4645	66	37	since	since	SCONJ
ejpam-4645	66	38	c	c	NOUN
ejpam-4645	66	39	is	be	AUX
ejpam-4645	66	40	a	a	DET
ejpam-4645	66	41	locating	locating	NOUN
ejpam-4645	66	42	set	set	NOUN
ejpam-4645	66	43	,	,	PUNCT
ejpam-4645	66	44	[	[	X
ejpam-4645	66	45	nhuv(z	nhuv(z	NOUN
ejpam-4645	66	46	)	)	PUNCT
ejpam-4645	66	47	∩	∩	PROPN
ejpam-4645	66	48	suv	suv	PROPN
ejpam-4645	66	49	]	]	PUNCT
ejpam-4645	66	50	∪	∪	ADP
ejpam-4645	66	51	s∗	s∗	PROPN
ejpam-4645	66	52	=	=	SYM
ejpam-4645	66	53	ng⋄h(z	ng⋄h(z	PROPN
ejpam-4645	66	54	)	)	PUNCT
ejpam-4645	66	55	∩	∩	NOUN
ejpam-4645	66	56	c	c	PROPN
ejpam-4645	66	57	̸=	̸=	PROPN
ejpam-4645	66	58	ng⋄h(v	ng⋄h(v	NUM
ejpam-4645	66	59	)	)	PUNCT
ejpam-4645	66	60	∩	∩	NOUN
ejpam-4645	66	61	c	c	NOUN
ejpam-4645	66	62	=	=	SYM
ejpam-4645	66	63	suv	suv	PROPN
ejpam-4645	66	64	∪	∪	PROPN
ejpam-4645	66	65	s∗.	s∗.	VERB
ejpam-4645	66	66	this	this	PRON
ejpam-4645	66	67	implies	imply	VERB
ejpam-4645	66	68	that	that	SCONJ
ejpam-4645	66	69	[	[	X
ejpam-4645	66	70	nhuv(z)∩suv	nhuv(z)∩suv	NOUN
ejpam-4645	66	71	]	]	X
ejpam-4645	66	72	̸=	̸=	PROPN
ejpam-4645	66	73	suv	suv	NOUN
ejpam-4645	66	74	,	,	PUNCT
ejpam-4645	66	75	showing	show	VERB
ejpam-4645	66	76	that	that	SCONJ
ejpam-4645	66	77	suv	suv	PROPN
ejpam-4645	66	78	is	be	AUX
ejpam-4645	66	79	a	a	DET
ejpam-4645	66	80	strictly	strictly	ADV
ejpam-4645	66	81	locating	locate	VERB
ejpam-4645	66	82	set	set	NOUN
ejpam-4645	66	83	of	of	ADP
ejpam-4645	66	84	huv	huv	PROPN
ejpam-4645	66	85	.	.	PUNCT
ejpam-4645	67	1	if	if	SCONJ
ejpam-4645	67	2	s∗	s∗	PROPN
ejpam-4645	67	3	=	=	SYM
ejpam-4645	67	4	∅	∅	NOUN
ejpam-4645	67	5	(	(	PUNCT
ejpam-4645	67	6	that	that	PRON
ejpam-4645	67	7	is	be	AUX
ejpam-4645	67	8	,	,	PUNCT
ejpam-4645	67	9	u	u	NOUN
ejpam-4645	67	10	/∈	/∈	PROPN
ejpam-4645	67	11	a	a	NOUN
ejpam-4645	67	12	)	)	PUNCT
ejpam-4645	67	13	,	,	PUNCT
ejpam-4645	67	14	then	then	ADV
ejpam-4645	67	15	suv	suv	PROPN
ejpam-4645	67	16	is	be	AUX
ejpam-4645	67	17	a	a	DET
ejpam-4645	67	18	dominating	dominating	NOUN
ejpam-4645	67	19	set	set	NOUN
ejpam-4645	67	20	of	of	ADP
ejpam-4645	67	21	v	v	PROPN
ejpam-4645	67	22	(	(	PUNCT
ejpam-4645	67	23	huv	huv	PROPN
ejpam-4645	67	24	)	)	PUNCT
ejpam-4645	67	25	.	.	PUNCT
ejpam-4645	68	1	thus	thus	ADV
ejpam-4645	68	2	,	,	PUNCT
ejpam-4645	68	3	(	(	PUNCT
ejpam-4645	68	4	c	c	X
ejpam-4645	68	5	)	)	PUNCT
ejpam-4645	68	6	and	and	CCONJ
ejpam-4645	68	7	(	(	PUNCT
ejpam-4645	68	8	d	d	X
ejpam-4645	68	9	)	)	PUNCT
ejpam-4645	68	10	hold	hold	NOUN
ejpam-4645	68	11	.	.	PUNCT
ejpam-4645	69	1	finally	finally	ADV
ejpam-4645	69	2	,	,	PUNCT
ejpam-4645	69	3	let	let	VERB
ejpam-4645	69	4	uv	uv	PRON
ejpam-4645	69	5	∈	∈	PROPN
ejpam-4645	69	6	e(g	e(g	PROPN
ejpam-4645	69	7	)	)	PUNCT
ejpam-4645	69	8	with	with	ADP
ejpam-4645	69	9	v	v	NUM
ejpam-4645	69	10	∈	∈	PROPN
ejpam-4645	69	11	a	a	PRON
ejpam-4645	69	12	and	and	CCONJ
ejpam-4645	69	13	u	u	NOUN
ejpam-4645	69	14	/∈	/∈	NOUN
ejpam-4645	69	15	a.	a.	NOUN
ejpam-4645	69	16	suppose	suppose	VERB
ejpam-4645	69	17	x	x	X
ejpam-4645	69	18	∈	∈	PROPN
ejpam-4645	69	19	v	v	X
ejpam-4645	69	20	(	(	PUNCT
ejpam-4645	69	21	huv	huv	PROPN
ejpam-4645	69	22	)	)	PUNCT
ejpam-4645	69	23	\	\	PROPN
ejpam-4645	69	24	suv	suv	PROPN
ejpam-4645	69	25	and	and	CCONJ
ejpam-4645	69	26	nhuv(x	nhuv(x	NOUN
ejpam-4645	69	27	)	)	PUNCT
ejpam-4645	69	28	∩	∩	ADJ
ejpam-4645	69	29	suv	suv	NOUN
ejpam-4645	69	30	=	=	PUNCT
ejpam-4645	69	31	∅.	∅.	PROPN
ejpam-4645	69	32	then	then	ADV
ejpam-4645	69	33	ng⋄h(x	ng⋄h(x	PROPN
ejpam-4645	69	34	)	)	PUNCT
ejpam-4645	69	35	∩	∩	NOUN
ejpam-4645	69	36	c	c	NOUN
ejpam-4645	69	37	=	=	SYM
ejpam-4645	69	38	{	{	PUNCT
ejpam-4645	69	39	v	v	NOUN
ejpam-4645	69	40	}	}	PUNCT
ejpam-4645	69	41	.	.	PUNCT
ejpam-4645	70	1	let	let	VERB
ejpam-4645	70	2	w	w	NOUN
ejpam-4645	70	3	∈	∈	PROPN
ejpam-4645	70	4	ng(v	ng(v	PRON
ejpam-4645	70	5	)	)	PUNCT
ejpam-4645	70	6	\	\	NOUN
ejpam-4645	71	1	{	{	PUNCT
ejpam-4645	71	2	u	u	NOUN
ejpam-4645	71	3	}	}	PUNCT
ejpam-4645	71	4	and	and	CCONJ
ejpam-4645	71	5	let	let	VERB
ejpam-4645	71	6	y	y	PROPN
ejpam-4645	71	7	∈	∈	PROPN
ejpam-4645	71	8	v	v	ADP
ejpam-4645	71	9	(	(	PUNCT
ejpam-4645	71	10	hwv	hwv	PROPN
ejpam-4645	71	11	)	)	PUNCT
ejpam-4645	71	12	\swv	\swv	PROPN
ejpam-4645	71	13	.	.	PUNCT
ejpam-4645	71	14	suppose	suppose	VERB
ejpam-4645	71	15	w	w	NOUN
ejpam-4645	71	16	/∈	/∈	PUNCT
ejpam-4645	71	17	a.	a.	NOUN
ejpam-4645	71	18	then	then	ADV
ejpam-4645	71	19	ng⋄h(y)∩c	ng⋄h(y)∩c	NOUN
ejpam-4645	71	20	=	=	PUNCT
ejpam-4645	72	1	[	[	X
ejpam-4645	72	2	nhwv(y)∩swv]∪{v	nhwv(y)∩swv]∪{v	NOUN
ejpam-4645	72	3	}	}	PUNCT
ejpam-4645	72	4	.	.	PUNCT
ejpam-4645	73	1	since	since	SCONJ
ejpam-4645	73	2	c	c	PROPN
ejpam-4645	73	3	is	be	AUX
ejpam-4645	73	4	a	a	DET
ejpam-4645	73	5	locating	locate	VERB
ejpam-4645	73	6	set	set	NOUN
ejpam-4645	73	7	of	of	ADP
ejpam-4645	73	8	g⋄h	g⋄h	PROPN
ejpam-4645	73	9	,	,	PUNCT
ejpam-4645	73	10	ng⋄h(x)∩c	ng⋄h(x)∩c	PROPN
ejpam-4645	73	11	̸=	̸=	PROPN
ejpam-4645	73	12	ng⋄h(y)∩c	ng⋄h(y)∩c	NOUN
ejpam-4645	73	13	.	.	PUNCT
ejpam-4645	74	1	this	this	PRON
ejpam-4645	74	2	implies	imply	VERB
ejpam-4645	74	3	that	that	SCONJ
ejpam-4645	74	4	nhwv(y)∩swv	nhwv(y)∩swv	NOUN
ejpam-4645	74	5	̸=	̸=	NOUN
ejpam-4645	74	6	∅	∅	NOUN
ejpam-4645	74	7	,	,	PUNCT
ejpam-4645	74	8	showing	show	VERB
ejpam-4645	74	9	that	that	SCONJ
ejpam-4645	74	10	(	(	PUNCT
ejpam-4645	74	11	iii	iii	NOUN
ejpam-4645	74	12	)	)	PUNCT
ejpam-4645	74	13	holds	hold	VERB
ejpam-4645	74	14	.	.	PUNCT
ejpam-4645	75	1	for	for	ADP
ejpam-4645	75	2	the	the	DET
ejpam-4645	75	3	converse	converse	NOUN
ejpam-4645	75	4	,	,	PUNCT
ejpam-4645	75	5	suppose	suppose	VERB
ejpam-4645	75	6	that	that	SCONJ
ejpam-4645	75	7	c	c	PROPN
ejpam-4645	75	8	has	have	VERB
ejpam-4645	75	9	the	the	DET
ejpam-4645	75	10	form	form	NOUN
ejpam-4645	75	11	described	describe	VERB
ejpam-4645	75	12	and	and	CCONJ
ejpam-4645	75	13	satisfies	satisfie	NOUN
ejpam-4645	75	14	(	(	PUNCT
ejpam-4645	75	15	i	i	NOUN
ejpam-4645	75	16	)	)	PUNCT
ejpam-4645	75	17	,	,	PUNCT
ejpam-4645	75	18	(	(	PUNCT
ejpam-4645	75	19	ii	ii	NOUN
ejpam-4645	75	20	)	)	PUNCT
ejpam-4645	75	21	,	,	PUNCT
ejpam-4645	75	22	and	and	CCONJ
ejpam-4645	75	23	(	(	PUNCT
ejpam-4645	75	24	iii	iii	NOUN
ejpam-4645	75	25	)	)	PUNCT
ejpam-4645	75	26	.	.	PUNCT
ejpam-4645	76	1	let	let	VERB
ejpam-4645	76	2	z	z	NOUN
ejpam-4645	76	3	∈	∈	PROPN
ejpam-4645	76	4	v	v	NOUN
ejpam-4645	76	5	(	(	PUNCT
ejpam-4645	76	6	g	g	PROPN
ejpam-4645	76	7	⋄	⋄	PROPN
ejpam-4645	76	8	h	h	PROPN
ejpam-4645	76	9	)	)	PUNCT
ejpam-4645	76	10	\	\	NOUN
ejpam-4645	77	1	c	c	NOUN
ejpam-4645	78	1	and	and	CCONJ
ejpam-4645	78	2	let	let	VERB
ejpam-4645	78	3	uv	uv	PRON
ejpam-4645	78	4	∈	∈	PROPN
ejpam-4645	78	5	e(g	e(g	PROPN
ejpam-4645	78	6	)	)	PUNCT
ejpam-4645	78	7	such	such	ADJ
ejpam-4645	78	8	that	that	SCONJ
ejpam-4645	78	9	z	z	PROPN
ejpam-4645	78	10	∈	∈	PROPN
ejpam-4645	78	11	⟨{u	⟨{u	PROPN
ejpam-4645	78	12	,	,	PUNCT
ejpam-4645	78	13	v}⟩	v}⟩	PROPN
ejpam-4645	78	14	+	+	CCONJ
ejpam-4645	78	15	huv	huv	PROPN
ejpam-4645	78	16	.	.	PUNCT
ejpam-4645	79	1	if	if	SCONJ
ejpam-4645	79	2	z	z	NOUN
ejpam-4645	79	3	=	=	SYM
ejpam-4645	79	4	u	u	NOUN
ejpam-4645	79	5	or	or	CCONJ
ejpam-4645	79	6	z	z	NOUN
ejpam-4645	79	7	=	=	SYM
ejpam-4645	79	8	v	v	NOUN
ejpam-4645	79	9	,	,	PUNCT
ejpam-4645	79	10	then	then	ADV
ejpam-4645	79	11	there	there	PRON
ejpam-4645	79	12	exists	exist	VERB
ejpam-4645	79	13	t	t	PROPN
ejpam-4645	79	14	∈	∈	PROPN
ejpam-4645	79	15	suv	suv	PROPN
ejpam-4645	80	1	⊂	⊂	PROPN
ejpam-4645	80	2	c	c	PROPN
ejpam-4645	80	3	such	such	ADJ
ejpam-4645	80	4	that	that	SCONJ
ejpam-4645	80	5	z	z	PROPN
ejpam-4645	80	6	∈	∈	PROPN
ejpam-4645	80	7	ng⋄h(t	ng⋄h(t	PROPN
ejpam-4645	80	8	)	)	PUNCT
ejpam-4645	80	9	by	by	ADP
ejpam-4645	80	10	(	(	PUNCT
ejpam-4645	80	11	ii)(a	ii)(a	PROPN
ejpam-4645	80	12	)	)	PUNCT
ejpam-4645	80	13	.	.	PUNCT
ejpam-4645	80	14	suppose	suppose	VERB
ejpam-4645	80	15	z	z	X
ejpam-4645	80	16	∈	∈	PROPN
ejpam-4645	80	17	v	v	PROPN
ejpam-4645	80	18	(	(	PUNCT
ejpam-4645	80	19	huv	huv	PROPN
ejpam-4645	80	20	)	)	PUNCT
ejpam-4645	80	21	\	\	PROPN
ejpam-4645	80	22	suv	suv	PROPN
ejpam-4645	80	23	.	.	PUNCT
ejpam-4645	81	1	if	if	SCONJ
ejpam-4645	81	2	u	u	PROPN
ejpam-4645	81	3	∈	∈	VERB
ejpam-4645	81	4	a	a	DET
ejpam-4645	81	5	or	or	CCONJ
ejpam-4645	81	6	v	v	ADP
ejpam-4645	81	7	∈	∈	PROPN
ejpam-4645	81	8	a	a	PRON
ejpam-4645	81	9	,	,	PUNCT
ejpam-4645	81	10	then	then	ADV
ejpam-4645	81	11	uz	uz	PROPN
ejpam-4645	81	12	∈	∈	PROPN
ejpam-4645	81	13	e(g	e(g	PROPN
ejpam-4645	81	14	⋄h	⋄h	PROPN
ejpam-4645	81	15	)	)	PUNCT
ejpam-4645	81	16	or	or	CCONJ
ejpam-4645	81	17	vz	vz	PROPN
ejpam-4645	81	18	∈	∈	PROPN
ejpam-4645	81	19	e(g	e(g	PROPN
ejpam-4645	81	20	⋄h	⋄h	PROPN
ejpam-4645	81	21	)	)	PUNCT
ejpam-4645	81	22	.	.	PUNCT
ejpam-4645	82	1	if	if	SCONJ
ejpam-4645	82	2	u	u	PROPN
ejpam-4645	82	3	,	,	PUNCT
ejpam-4645	82	4	v	v	INTJ
ejpam-4645	82	5	/∈	/∈	PROPN
ejpam-4645	82	6	a	a	PRON
ejpam-4645	82	7	,	,	PUNCT
ejpam-4645	82	8	then	then	ADV
ejpam-4645	82	9	there	there	PRON
ejpam-4645	82	10	exists	exist	VERB
ejpam-4645	82	11	s	s	PROPN
ejpam-4645	82	12	∈	∈	PROPN
ejpam-4645	82	13	suv	suv	PROPN
ejpam-4645	82	14	∩	∩	PROPN
ejpam-4645	82	15	ng⋄h(z	ng⋄h(z	PROPN
ejpam-4645	82	16	)	)	PUNCT
ejpam-4645	82	17	by	by	ADP
ejpam-4645	82	18	(	(	PUNCT
ejpam-4645	82	19	ii)(b	ii)(b	ADJ
ejpam-4645	82	20	)	)	PUNCT
ejpam-4645	82	21	.	.	PUNCT
ejpam-4645	83	1	hence	hence	ADV
ejpam-4645	83	2	,	,	PUNCT
ejpam-4645	83	3	c	c	PROPN
ejpam-4645	83	4	is	be	AUX
ejpam-4645	83	5	a	a	DET
ejpam-4645	83	6	dominating	dominating	NOUN
ejpam-4645	83	7	set	set	NOUN
ejpam-4645	83	8	of	of	ADP
ejpam-4645	83	9	g	g	PROPN
ejpam-4645	83	10	⋄	⋄	PROPN
ejpam-4645	83	11	h.	h.	PROPN
ejpam-4645	83	12	g.	g.	PROPN
ejpam-4645	83	13	malacas	malacas	PROPN
ejpam-4645	83	14	,	,	PUNCT
ejpam-4645	83	15	s.	s.	PROPN
ejpam-4645	83	16	canoy	canoy	PROPN
ejpam-4645	83	17	,	,	PUNCT
ejpam-4645	83	18	jr	jr	PROPN
ejpam-4645	83	19	.	.	PROPN
ejpam-4645	83	20	,	,	PUNCT
ejpam-4645	83	21	e.	e.	PROPN
ejpam-4645	83	22	chacon	chacon	PROPN
ejpam-4645	83	23	/	/	SYM
ejpam-4645	83	24	eur	eur	PROPN
ejpam-4645	83	25	.	.	PUNCT
ejpam-4645	84	1	j.	j.	PROPN
ejpam-4645	84	2	pure	pure	PROPN
ejpam-4645	84	3	appl	appl	PROPN
ejpam-4645	84	4	.	.	PROPN
ejpam-4645	84	5	math	math	PROPN
ejpam-4645	84	6	,	,	PUNCT
ejpam-4645	84	7	16	16	NUM
ejpam-4645	84	8	(	(	PUNCT
ejpam-4645	84	9	1	1	NUM
ejpam-4645	84	10	)	)	PUNCT
ejpam-4645	84	11	(	(	PUNCT
ejpam-4645	84	12	2023	2023	NUM
ejpam-4645	84	13	)	)	PUNCT
ejpam-4645	84	14	,	,	PUNCT
ejpam-4645	84	15	479	479	NUM
ejpam-4645	84	16	-	-	SYM
ejpam-4645	84	17	490	490	NUM
ejpam-4645	84	18	482	482	NUM
ejpam-4645	84	19	next	next	ADV
ejpam-4645	84	20	,	,	PUNCT
ejpam-4645	84	21	let	let	VERB
ejpam-4645	84	22	p	p	PRON
ejpam-4645	84	23	,	,	PUNCT
ejpam-4645	84	24	q	q	PROPN
ejpam-4645	84	25	∈	∈	PROPN
ejpam-4645	84	26	v	v	NOUN
ejpam-4645	84	27	(	(	PUNCT
ejpam-4645	84	28	g⋄h)\c	g⋄h)\c	VERB
ejpam-4645	84	29	with	with	ADP
ejpam-4645	84	30	p	p	NOUN
ejpam-4645	84	31	̸=	̸=	PROPN
ejpam-4645	84	32	q	q	PROPN
ejpam-4645	84	33	and	and	CCONJ
ejpam-4645	84	34	let	let	VERB
ejpam-4645	84	35	uv	uv	INTJ
ejpam-4645	84	36	,	,	PUNCT
ejpam-4645	84	37	xy	xy	PROPN
ejpam-4645	84	38	∈	∈	PROPN
ejpam-4645	84	39	e(g	e(g	PROPN
ejpam-4645	84	40	)	)	PUNCT
ejpam-4645	84	41	such	such	ADJ
ejpam-4645	84	42	that	that	SCONJ
ejpam-4645	84	43	p	p	PROPN
ejpam-4645	84	44	∈	∈	PROPN
ejpam-4645	84	45	⟨{u	⟨{u	PROPN
ejpam-4645	84	46	,	,	PUNCT
ejpam-4645	84	47	v}⟩+huv	v}⟩+huv	NOUN
ejpam-4645	84	48	and	and	CCONJ
ejpam-4645	84	49	q	q	PROPN
ejpam-4645	84	50	∈	∈	PROPN
ejpam-4645	84	51	⟨{x	⟨{x	PROPN
ejpam-4645	84	52	,	,	PUNCT
ejpam-4645	84	53	y}⟩+hxy	y}⟩+hxy	NOUN
ejpam-4645	84	54	.	.	PUNCT
ejpam-4645	84	55	consider	consider	VERB
ejpam-4645	84	56	the	the	DET
ejpam-4645	84	57	following	follow	VERB
ejpam-4645	84	58	cases	case	NOUN
ejpam-4645	84	59	:	:	PUNCT
ejpam-4645	84	60	case	case	NOUN
ejpam-4645	84	61	1	1	NUM
ejpam-4645	84	62	.	.	PUNCT
ejpam-4645	85	1	the	the	DET
ejpam-4645	85	2	edges	edge	NOUN
ejpam-4645	85	3	uv	uv	INTJ
ejpam-4645	85	4	and	and	CCONJ
ejpam-4645	85	5	xy	xy	PROPN
ejpam-4645	85	6	are	be	AUX
ejpam-4645	85	7	non	non	ADJ
ejpam-4645	85	8	-	-	ADJ
ejpam-4645	85	9	adjacent	adjacent	ADJ
ejpam-4645	85	10	(	(	PUNCT
ejpam-4645	85	11	i.e.	i.e.	X
ejpam-4645	85	12	,	,	PUNCT
ejpam-4645	85	13	they	they	PRON
ejpam-4645	85	14	do	do	AUX
ejpam-4645	85	15	not	not	PART
ejpam-4645	85	16	share	share	VERB
ejpam-4645	85	17	a	a	DET
ejpam-4645	85	18	common	common	ADJ
ejpam-4645	85	19	vertex	vertex	NOUN
ejpam-4645	85	20	)	)	PUNCT
ejpam-4645	85	21	.	.	PUNCT
ejpam-4645	86	1	suppose	suppose	VERB
ejpam-4645	86	2	that	that	SCONJ
ejpam-4645	86	3	p	p	PROPN
ejpam-4645	86	4	∈	∈	PROPN
ejpam-4645	86	5	{	{	PUNCT
ejpam-4645	86	6	u	u	NOUN
ejpam-4645	86	7	,	,	PUNCT
ejpam-4645	86	8	v	v	NOUN
ejpam-4645	86	9	}	}	PUNCT
ejpam-4645	86	10	or	or	CCONJ
ejpam-4645	86	11	q	q	ADJ
ejpam-4645	86	12	∈	∈	PROPN
ejpam-4645	86	13	{	{	PUNCT
ejpam-4645	86	14	x	x	NOUN
ejpam-4645	86	15	,	,	PUNCT
ejpam-4645	86	16	y	y	PROPN
ejpam-4645	86	17	}	}	PUNCT
ejpam-4645	86	18	.	.	PUNCT
ejpam-4645	87	1	since	since	SCONJ
ejpam-4645	87	2	suv	suv	PROPN
ejpam-4645	87	3	⊆	⊆	NUM
ejpam-4645	87	4	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	87	5	)	)	PUNCT
ejpam-4645	87	6	and	and	CCONJ
ejpam-4645	87	7	sxy	sxy	PROPN
ejpam-4645	87	8	⊆	⊆	NUM
ejpam-4645	87	9	ng⋄h(q	ng⋄h(q	NUM
ejpam-4645	87	10	)	)	PUNCT
ejpam-4645	87	11	,	,	PUNCT
ejpam-4645	87	12	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	87	13	)	)	PUNCT
ejpam-4645	87	14	∩	∩	NOUN
ejpam-4645	87	15	c	c	PROPN
ejpam-4645	87	16	̸=	̸=	PROPN
ejpam-4645	87	17	ng⋄h(q	ng⋄h(q	ADV
ejpam-4645	87	18	)	)	PUNCT
ejpam-4645	87	19	∩	∩	PROPN
ejpam-4645	87	20	c.	c.	PROPN
ejpam-4645	87	21	suppose	suppose	VERB
ejpam-4645	87	22	that	that	SCONJ
ejpam-4645	87	23	p	p	PROPN
ejpam-4645	87	24	/∈	/∈	PUNCT
ejpam-4645	87	25	{	{	PUNCT
ejpam-4645	87	26	u	u	NOUN
ejpam-4645	87	27	,	,	PUNCT
ejpam-4645	87	28	v	v	NOUN
ejpam-4645	87	29	}	}	PUNCT
ejpam-4645	87	30	and	and	CCONJ
ejpam-4645	87	31	q	q	NOUN
ejpam-4645	87	32	/∈	/∈	PUNCT
ejpam-4645	87	33	{	{	PUNCT
ejpam-4645	87	34	x	x	NOUN
ejpam-4645	87	35	,	,	PUNCT
ejpam-4645	87	36	y	y	PROPN
ejpam-4645	87	37	}	}	PUNCT
ejpam-4645	87	38	.	.	PUNCT
ejpam-4645	88	1	then	then	ADV
ejpam-4645	88	2	p	p	PROPN
ejpam-4645	88	3	∈	∈	PROPN
ejpam-4645	88	4	v	v	X
ejpam-4645	88	5	(	(	PUNCT
ejpam-4645	88	6	huv	huv	PROPN
ejpam-4645	88	7	)	)	PUNCT
ejpam-4645	88	8	\	\	PROPN
ejpam-4645	88	9	suv	suv	PROPN
ejpam-4645	88	10	and	and	CCONJ
ejpam-4645	88	11	q	q	NOUN
ejpam-4645	88	12	∈	∈	PROPN
ejpam-4645	88	13	v	v	ADP
ejpam-4645	88	14	(	(	PUNCT
ejpam-4645	88	15	hxy	hxy	NOUN
ejpam-4645	88	16	)	)	PUNCT
ejpam-4645	88	17	\	\	PROPN
ejpam-4645	89	1	sxy	sxy	PROPN
ejpam-4645	89	2	.	.	PUNCT
ejpam-4645	90	1	since	since	SCONJ
ejpam-4645	90	2	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	90	3	)	)	PUNCT
ejpam-4645	90	4	∩	∩	NOUN
ejpam-4645	90	5	c	c	PROPN
ejpam-4645	90	6	⊆	⊆	NUM
ejpam-4645	90	7	v	v	X
ejpam-4645	90	8	(	(	PUNCT
ejpam-4645	90	9	⟨{u	⟨{u	PROPN
ejpam-4645	90	10	,	,	PUNCT
ejpam-4645	90	11	v}⟩	v}⟩	PROPN
ejpam-4645	90	12	+	+	CCONJ
ejpam-4645	90	13	huv	huv	PROPN
ejpam-4645	90	14	)	)	PUNCT
ejpam-4645	90	15	and	and	CCONJ
ejpam-4645	90	16	ng⋄h(q	ng⋄h(q	ADJ
ejpam-4645	90	17	)	)	PUNCT
ejpam-4645	90	18	∩	∩	PROPN
ejpam-4645	90	19	c	c	PROPN
ejpam-4645	90	20	⊆	⊆	NUM
ejpam-4645	90	21	v	v	X
ejpam-4645	90	22	(	(	PUNCT
ejpam-4645	90	23	⟨{x	⟨{x	PROPN
ejpam-4645	90	24	,	,	PUNCT
ejpam-4645	90	25	y}⟩+hxy	y}⟩+hxy	NOUN
ejpam-4645	90	26	)	)	PUNCT
ejpam-4645	90	27	,	,	PUNCT
ejpam-4645	90	28	it	it	PRON
ejpam-4645	90	29	follows	follow	VERB
ejpam-4645	90	30	that	that	SCONJ
ejpam-4645	90	31	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	90	32	)	)	PUNCT
ejpam-4645	90	33	∩	∩	NOUN
ejpam-4645	90	34	c	c	PROPN
ejpam-4645	90	35	̸=	̸=	PROPN
ejpam-4645	90	36	ng⋄h(q	ng⋄h(q	ADV
ejpam-4645	90	37	)	)	PUNCT
ejpam-4645	90	38	∩	∩	ADJ
ejpam-4645	90	39	c.	c.	NOUN
ejpam-4645	90	40	case	case	NOUN
ejpam-4645	90	41	2	2	X
ejpam-4645	90	42	.	.	PUNCT
ejpam-4645	91	1	the	the	DET
ejpam-4645	91	2	edges	edge	NOUN
ejpam-4645	91	3	uv	uv	INTJ
ejpam-4645	91	4	and	and	CCONJ
ejpam-4645	91	5	xy	xy	PROPN
ejpam-4645	91	6	are	be	AUX
ejpam-4645	91	7	distinct	distinct	ADJ
ejpam-4645	91	8	and	and	CCONJ
ejpam-4645	91	9	adjacent	adjacent	ADJ
ejpam-4645	91	10	.	.	PUNCT
ejpam-4645	92	1	we	we	PRON
ejpam-4645	92	2	may	may	AUX
ejpam-4645	92	3	assume	assume	VERB
ejpam-4645	92	4	that	that	SCONJ
ejpam-4645	92	5	x	x	X
ejpam-4645	92	6	=	=	PUNCT
ejpam-4645	92	7	u.	u.	NOUN
ejpam-4645	92	8	if	if	SCONJ
ejpam-4645	92	9	p	p	X
ejpam-4645	92	10	∈	∈	PROPN
ejpam-4645	92	11	{	{	PUNCT
ejpam-4645	92	12	u	u	NOUN
ejpam-4645	92	13	,	,	PUNCT
ejpam-4645	92	14	v	v	NOUN
ejpam-4645	92	15	}	}	PUNCT
ejpam-4645	92	16	or	or	CCONJ
ejpam-4645	92	17	q	q	ADJ
ejpam-4645	92	18	∈	∈	PROPN
ejpam-4645	92	19	{	{	PUNCT
ejpam-4645	92	20	x	x	NOUN
ejpam-4645	92	21	,	,	PUNCT
ejpam-4645	92	22	y	y	PROPN
ejpam-4645	92	23	}	}	PUNCT
ejpam-4645	92	24	,	,	PUNCT
ejpam-4645	92	25	then	then	ADV
ejpam-4645	92	26	ng⋄h(p)∩c	ng⋄h(p)∩c	NOUN
ejpam-4645	92	27	̸=	̸=	PROPN
ejpam-4645	92	28	ng⋄h(q)∩c	ng⋄h(q)∩c	NOUN
ejpam-4645	92	29	(	(	PUNCT
ejpam-4645	92	30	as	as	ADP
ejpam-4645	92	31	in	in	ADP
ejpam-4645	92	32	case	case	NOUN
ejpam-4645	92	33	1	1	NUM
ejpam-4645	92	34	)	)	PUNCT
ejpam-4645	92	35	.	.	PUNCT
ejpam-4645	93	1	so	so	ADV
ejpam-4645	93	2	suppose	suppose	VERB
ejpam-4645	93	3	that	that	SCONJ
ejpam-4645	93	4	p	p	PROPN
ejpam-4645	93	5	/∈	/∈	PUNCT
ejpam-4645	93	6	{	{	PUNCT
ejpam-4645	93	7	u	u	NOUN
ejpam-4645	93	8	,	,	PUNCT
ejpam-4645	93	9	v	v	NOUN
ejpam-4645	93	10	}	}	PUNCT
ejpam-4645	93	11	and	and	CCONJ
ejpam-4645	93	12	q	q	NOUN
ejpam-4645	93	13	/∈	/∈	PUNCT
ejpam-4645	93	14	{	{	PUNCT
ejpam-4645	93	15	x	x	NOUN
ejpam-4645	93	16	,	,	PUNCT
ejpam-4645	93	17	y	y	PROPN
ejpam-4645	93	18	}	}	PUNCT
ejpam-4645	93	19	.	.	PUNCT
ejpam-4645	94	1	if	if	SCONJ
ejpam-4645	94	2	nhuv(p	nhuv(p	PROPN
ejpam-4645	94	3	)	)	PUNCT
ejpam-4645	94	4	∩	∩	PROPN
ejpam-4645	94	5	suv	suv	PROPN
ejpam-4645	94	6	̸=	̸=	PROPN
ejpam-4645	94	7	∅	∅	NOUN
ejpam-4645	94	8	or	or	CCONJ
ejpam-4645	94	9	nhxy(y	nhxy(y	NOUN
ejpam-4645	94	10	)	)	PUNCT
ejpam-4645	94	11	∩	∩	NOUN
ejpam-4645	94	12	sxy	sxy	PROPN
ejpam-4645	94	13	̸=	̸=	PROPN
ejpam-4645	94	14	∅	∅	NOUN
ejpam-4645	94	15	,	,	PUNCT
ejpam-4645	94	16	then	then	ADV
ejpam-4645	94	17	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	94	18	)	)	PUNCT
ejpam-4645	94	19	∩c	∩c	NOUN
ejpam-4645	95	1	̸=	̸=	PROPN
ejpam-4645	95	2	ng⋄h(q	ng⋄h(q	ADV
ejpam-4645	95	3	)	)	PUNCT
ejpam-4645	95	4	∩c	∩c	PROPN
ejpam-4645	95	5	.	.	PUNCT
ejpam-4645	95	6	suppose	suppose	VERB
ejpam-4645	95	7	that	that	SCONJ
ejpam-4645	95	8	nhuv(p	nhuv(p	PROPN
ejpam-4645	95	9	)	)	PUNCT
ejpam-4645	95	10	∩	∩	ADJ
ejpam-4645	95	11	suv	suv	NOUN
ejpam-4645	95	12	=	=	NOUN
ejpam-4645	95	13	∅	∅	NOUN
ejpam-4645	95	14	or	or	CCONJ
ejpam-4645	95	15	nhxy(y)∩	nhxy(y)∩	NOUN
ejpam-4645	95	16	sxy	sxy	PROPN
ejpam-4645	95	17	=	=	PUNCT
ejpam-4645	95	18	∅.	∅.	VERB
ejpam-4645	95	19	if	if	SCONJ
ejpam-4645	95	20	u	u	PROPN
ejpam-4645	95	21	∈	∈	PROPN
ejpam-4645	95	22	a	a	PRON
ejpam-4645	95	23	,	,	PUNCT
ejpam-4645	95	24	then	then	ADV
ejpam-4645	95	25	y	y	PROPN
ejpam-4645	95	26	∈	∈	PROPN
ejpam-4645	95	27	a	a	DET
ejpam-4645	95	28	or	or	CCONJ
ejpam-4645	95	29	v	v	ADP
ejpam-4645	95	30	∈	∈	PRON
ejpam-4645	95	31	a	a	DET
ejpam-4645	95	32	by	by	ADP
ejpam-4645	95	33	(	(	PUNCT
ejpam-4645	95	34	iii	iii	NOUN
ejpam-4645	95	35	)	)	PUNCT
ejpam-4645	95	36	.	.	PUNCT
ejpam-4645	95	37	suppose	suppose	VERB
ejpam-4645	95	38	that	that	SCONJ
ejpam-4645	95	39	u	u	PROPN
ejpam-4645	95	40	/∈	/∈	NOUN
ejpam-4645	95	41	a.	a.	NOUN
ejpam-4645	95	42	then	then	ADV
ejpam-4645	95	43	by	by	ADP
ejpam-4645	95	44	(	(	PUNCT
ejpam-4645	95	45	ii)(b	ii)(b	PROPN
ejpam-4645	95	46	)	)	PUNCT
ejpam-4645	95	47	,	,	PUNCT
ejpam-4645	95	48	y	y	PROPN
ejpam-4645	95	49	,	,	PUNCT
ejpam-4645	95	50	v	v	NOUN
ejpam-4645	95	51	∈	∈	NOUN
ejpam-4645	95	52	a.	a.	NOUN
ejpam-4645	95	53	since	since	SCONJ
ejpam-4645	95	54	v	v	NUM
ejpam-4645	95	55	∈	∈	PROPN
ejpam-4645	95	56	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	95	57	)	)	PUNCT
ejpam-4645	95	58	∩	∩	ADJ
ejpam-4645	95	59	c	c	X
ejpam-4645	95	60	,	,	PUNCT
ejpam-4645	95	61	y	y	PROPN
ejpam-4645	95	62	∈	∈	PROPN
ejpam-4645	95	63	ng⋄h(y	ng⋄h(y	NOUN
ejpam-4645	95	64	)	)	PUNCT
ejpam-4645	95	65	∩	∩	ADJ
ejpam-4645	95	66	c	c	NOUN
ejpam-4645	95	67	,	,	PUNCT
ejpam-4645	95	68	and	and	CCONJ
ejpam-4645	95	69	y	y	PROPN
ejpam-4645	95	70	̸=	̸=	PROPN
ejpam-4645	95	71	v	v	NOUN
ejpam-4645	95	72	,	,	PUNCT
ejpam-4645	95	73	it	it	PRON
ejpam-4645	95	74	follows	follow	VERB
ejpam-4645	95	75	that	that	SCONJ
ejpam-4645	95	76	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	95	77	)	)	PUNCT
ejpam-4645	95	78	∩	∩	NOUN
ejpam-4645	95	79	c	c	PROPN
ejpam-4645	95	80	̸=	̸=	PROPN
ejpam-4645	95	81	ng⋄h(q	ng⋄h(q	ADV
ejpam-4645	95	82	)	)	PUNCT
ejpam-4645	95	83	∩	∩	ADJ
ejpam-4645	95	84	c.	c.	NOUN
ejpam-4645	95	85	case	case	NOUN
ejpam-4645	95	86	3	3	X
ejpam-4645	95	87	.	.	PUNCT
ejpam-4645	96	1	the	the	DET
ejpam-4645	96	2	edges	edge	NOUN
ejpam-4645	96	3	uv	uv	INTJ
ejpam-4645	96	4	and	and	CCONJ
ejpam-4645	96	5	xy	xy	PROPN
ejpam-4645	96	6	are	be	AUX
ejpam-4645	96	7	the	the	DET
ejpam-4645	96	8	same	same	ADJ
ejpam-4645	96	9	.	.	PUNCT
ejpam-4645	97	1	we	we	PRON
ejpam-4645	97	2	may	may	AUX
ejpam-4645	97	3	assume	assume	VERB
ejpam-4645	97	4	that	that	SCONJ
ejpam-4645	97	5	x	x	NOUN
ejpam-4645	97	6	=	=	PUNCT
ejpam-4645	97	7	u	u	NOUN
ejpam-4645	97	8	and	and	CCONJ
ejpam-4645	97	9	y	y	PROPN
ejpam-4645	97	10	=	=	PUNCT
ejpam-4645	97	11	v.	v.	CCONJ
ejpam-4645	97	12	suppose	suppose	VERB
ejpam-4645	97	13	first	first	ADV
ejpam-4645	97	14	that	that	SCONJ
ejpam-4645	97	15	p	p	X
ejpam-4645	97	16	=	=	PUNCT
ejpam-4645	97	17	u	u	NOUN
ejpam-4645	97	18	and	and	CCONJ
ejpam-4645	97	19	q	q	NOUN
ejpam-4645	98	1	=	=	PUNCT
ejpam-4645	98	2	v.	v.	CCONJ
ejpam-4645	98	3	since	since	SCONJ
ejpam-4645	98	4	g	g	PROPN
ejpam-4645	98	5	is	be	AUX
ejpam-4645	98	6	connected	connect	VERB
ejpam-4645	98	7	and	and	CCONJ
ejpam-4645	98	8	g	g	PROPN
ejpam-4645	98	9	̸=	̸=	PROPN
ejpam-4645	98	10	k2	k2	NOUN
ejpam-4645	98	11	,	,	PUNCT
ejpam-4645	98	12	we	we	PRON
ejpam-4645	98	13	may	may	AUX
ejpam-4645	98	14	assume	assume	VERB
ejpam-4645	98	15	that	that	SCONJ
ejpam-4645	98	16	there	there	PRON
ejpam-4645	98	17	exists	exist	VERB
ejpam-4645	98	18	w	w	PROPN
ejpam-4645	98	19	∈	∈	PROPN
ejpam-4645	98	20	v	v	ADP
ejpam-4645	98	21	(	(	PUNCT
ejpam-4645	98	22	g	g	NOUN
ejpam-4645	98	23	)	)	PUNCT
ejpam-4645	98	24	\	\	NOUN
ejpam-4645	98	25	{	{	PUNCT
ejpam-4645	98	26	u	u	NOUN
ejpam-4645	98	27	,	,	PUNCT
ejpam-4645	98	28	v	v	NOUN
ejpam-4645	98	29	}	}	PUNCT
ejpam-4645	98	30	such	such	ADJ
ejpam-4645	98	31	that	that	SCONJ
ejpam-4645	98	32	vw	vw	PROPN
ejpam-4645	98	33	∈	∈	PROPN
ejpam-4645	98	34	e(g	e(g	PROPN
ejpam-4645	98	35	)	)	PUNCT
ejpam-4645	98	36	.	.	PUNCT
ejpam-4645	99	1	because	because	SCONJ
ejpam-4645	99	2	∅	∅	NOUN
ejpam-4645	99	3	̸=	̸=	PROPN
ejpam-4645	99	4	svw	svw	VERB
ejpam-4645	99	5	⊆	⊆	NUM
ejpam-4645	99	6	(	(	PUNCT
ejpam-4645	99	7	ng⋄h(q	ng⋄h(q	ADV
ejpam-4645	99	8	)	)	PUNCT
ejpam-4645	99	9	∩c	∩c	NOUN
ejpam-4645	99	10	\	\	NOUN
ejpam-4645	100	1	(	(	PUNCT
ejpam-4645	100	2	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	100	3	)	)	PUNCT
ejpam-4645	100	4	∩c	∩c	NOUN
ejpam-4645	100	5	)	)	PUNCT
ejpam-4645	100	6	,	,	PUNCT
ejpam-4645	100	7	we	we	PRON
ejpam-4645	100	8	have	have	VERB
ejpam-4645	100	9	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	100	10	)	)	PUNCT
ejpam-4645	100	11	∩c	∩c	NOUN
ejpam-4645	101	1	̸=	̸=	PROPN
ejpam-4645	101	2	ng⋄h(q)∩c	ng⋄h(q)∩c	NOUN
ejpam-4645	101	3	.	.	PUNCT
ejpam-4645	102	1	suppose	suppose	VERB
ejpam-4645	102	2	that	that	SCONJ
ejpam-4645	102	3	p	p	X
ejpam-4645	102	4	,	,	PUNCT
ejpam-4645	102	5	q	q	PROPN
ejpam-4645	102	6	∈	∈	PROPN
ejpam-4645	102	7	v	v	NOUN
ejpam-4645	102	8	(	(	PUNCT
ejpam-4645	102	9	huv	huv	PROPN
ejpam-4645	102	10	)	)	PUNCT
ejpam-4645	102	11	\suv	\suv	PROPN
ejpam-4645	102	12	.	.	PUNCT
ejpam-4645	103	1	by	by	ADP
ejpam-4645	103	2	(	(	PUNCT
ejpam-4645	103	3	ii)(a	ii)(a	PROPN
ejpam-4645	103	4	)	)	PUNCT
ejpam-4645	103	5	,	,	PUNCT
ejpam-4645	103	6	ng⋄h(p)∩c	ng⋄h(p)∩c	NOUN
ejpam-4645	103	7	̸=	̸=	PROPN
ejpam-4645	103	8	ng⋄h(q)∩c	ng⋄h(q)∩c	NOUN
ejpam-4645	103	9	.	.	PUNCT
ejpam-4645	104	1	finally	finally	ADV
ejpam-4645	104	2	,	,	PUNCT
ejpam-4645	104	3	suppose	suppose	VERB
ejpam-4645	104	4	that	that	SCONJ
ejpam-4645	104	5	p	p	PROPN
ejpam-4645	104	6	∈	∈	PROPN
ejpam-4645	104	7	v	v	X
ejpam-4645	104	8	(	(	PUNCT
ejpam-4645	104	9	huv	huv	PROPN
ejpam-4645	104	10	)	)	PUNCT
ejpam-4645	104	11	\	\	PROPN
ejpam-4645	104	12	suv	suv	PROPN
ejpam-4645	104	13	(	(	PUNCT
ejpam-4645	104	14	or	or	CCONJ
ejpam-4645	104	15	q	q	PROPN
ejpam-4645	104	16	∈	∈	PROPN
ejpam-4645	104	17	v	v	NOUN
ejpam-4645	104	18	(	(	PUNCT
ejpam-4645	104	19	huv	huv	PROPN
ejpam-4645	104	20	)	)	PUNCT
ejpam-4645	104	21	\	\	PROPN
ejpam-4645	104	22	suv	suv	PROPN
ejpam-4645	104	23	)	)	PUNCT
ejpam-4645	104	24	and	and	CCONJ
ejpam-4645	104	25	q	q	ADJ
ejpam-4645	104	26	∈	∈	PROPN
ejpam-4645	104	27	{	{	PUNCT
ejpam-4645	104	28	u	u	NOUN
ejpam-4645	104	29	,	,	PUNCT
ejpam-4645	104	30	v	v	NOUN
ejpam-4645	104	31	}	}	PUNCT
ejpam-4645	104	32	(	(	PUNCT
ejpam-4645	104	33	resp	resp	NOUN
ejpam-4645	104	34	.	.	PUNCT
ejpam-4645	105	1	p	p	X
ejpam-4645	105	2	∈	∈	PROPN
ejpam-4645	105	3	{	{	PUNCT
ejpam-4645	105	4	u	u	NOUN
ejpam-4645	105	5	,	,	PUNCT
ejpam-4645	105	6	v	v	NOUN
ejpam-4645	105	7	}	}	PUNCT
ejpam-4645	105	8	)	)	PUNCT
ejpam-4645	105	9	.	.	PUNCT
ejpam-4645	106	1	we	we	PRON
ejpam-4645	106	2	may	may	AUX
ejpam-4645	106	3	assume	assume	VERB
ejpam-4645	106	4	without	without	ADP
ejpam-4645	106	5	loss	loss	NOUN
ejpam-4645	106	6	of	of	ADP
ejpam-4645	106	7	generality	generality	NOUN
ejpam-4645	106	8	that	that	PRON
ejpam-4645	106	9	q	q	NOUN
ejpam-4645	106	10	=	=	PUNCT
ejpam-4645	106	11	u.	u.	NOUN
ejpam-4645	106	12	consider	consider	VERB
ejpam-4645	106	13	the	the	DET
ejpam-4645	106	14	following	follow	VERB
ejpam-4645	106	15	subcases	subcase	NOUN
ejpam-4645	106	16	:	:	PUNCT
ejpam-4645	106	17	subcase	subcase	NOUN
ejpam-4645	106	18	1	1	NUM
ejpam-4645	106	19	.	.	X
ejpam-4645	107	1	u	u	PROPN
ejpam-4645	107	2	,	,	PUNCT
ejpam-4645	107	3	v	v	NOUN
ejpam-4645	107	4	/∈	/∈	PUNCT
ejpam-4645	107	5	l(g	l(g	NOUN
ejpam-4645	107	6	)	)	PUNCT
ejpam-4645	107	7	.	.	PUNCT
ejpam-4645	108	1	then	then	ADV
ejpam-4645	108	2	there	there	PRON
ejpam-4645	108	3	exist	exist	VERB
ejpam-4645	108	4	a	a	DET
ejpam-4645	108	5	,	,	PUNCT
ejpam-4645	108	6	b	b	PROPN
ejpam-4645	108	7	∈	∈	PROPN
ejpam-4645	108	8	v	v	NOUN
ejpam-4645	108	9	(	(	PUNCT
ejpam-4645	108	10	g	g	NOUN
ejpam-4645	108	11	)	)	PUNCT
ejpam-4645	108	12	such	such	ADJ
ejpam-4645	108	13	that	that	SCONJ
ejpam-4645	108	14	au	au	PROPN
ejpam-4645	108	15	,	,	PUNCT
ejpam-4645	108	16	bv	bv	PROPN
ejpam-4645	108	17	∈	∈	PROPN
ejpam-4645	108	18	e(g	e(g	PROPN
ejpam-4645	108	19	)	)	PUNCT
ejpam-4645	108	20	.	.	PUNCT
ejpam-4645	109	1	since	since	SCONJ
ejpam-4645	109	2	sau	sau	PROPN
ejpam-4645	109	3	⊆	⊆	NUM
ejpam-4645	109	4	ng⋄h(q	ng⋄h(q	NUM
ejpam-4645	109	5	)	)	PUNCT
ejpam-4645	109	6	∩	∩	PROPN
ejpam-4645	109	7	c	c	PROPN
ejpam-4645	109	8	and	and	CCONJ
ejpam-4645	109	9	sau	sau	PROPN
ejpam-4645	109	10	∩ng⋄h(p	∩ng⋄h(p	PROPN
ejpam-4645	109	11	)	)	PUNCT
ejpam-4645	109	12	=	=	SYM
ejpam-4645	109	13	∅	∅	NOUN
ejpam-4645	109	14	,	,	PUNCT
ejpam-4645	109	15	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	109	16	)	)	PUNCT
ejpam-4645	109	17	∩	∩	NOUN
ejpam-4645	109	18	c	c	PROPN
ejpam-4645	109	19	̸=	̸=	PROPN
ejpam-4645	109	20	ng⋄h(q	ng⋄h(q	ADV
ejpam-4645	109	21	)	)	PUNCT
ejpam-4645	109	22	∩	∩	PROPN
ejpam-4645	109	23	c.	c.	PROPN
ejpam-4645	109	24	subcase	subcase	PROPN
ejpam-4645	109	25	2	2	NUM
ejpam-4645	109	26	.	.	X
ejpam-4645	109	27	u	u	PROPN
ejpam-4645	109	28	∈	∈	PROPN
ejpam-4645	109	29	l(g	l(g	PROPN
ejpam-4645	109	30	)	)	PUNCT
ejpam-4645	109	31	or	or	CCONJ
ejpam-4645	109	32	v	v	ADP
ejpam-4645	109	33	∈	∈	PROPN
ejpam-4645	109	34	l(g	l(g	NOUN
ejpam-4645	109	35	)	)	PUNCT
ejpam-4645	109	36	.	.	PUNCT
ejpam-4645	110	1	by	by	ADP
ejpam-4645	110	2	(	(	PUNCT
ejpam-4645	110	3	ii)(c	ii)(c	PROPN
ejpam-4645	110	4	)	)	PUNCT
ejpam-4645	110	5	and	and	CCONJ
ejpam-4645	110	6	(	(	PUNCT
ejpam-4645	110	7	ii)(d	ii)(d	PROPN
ejpam-4645	110	8	)	)	PUNCT
ejpam-4645	110	9	,	,	PUNCT
ejpam-4645	110	10	suv	suv	PROPN
ejpam-4645	110	11	is	be	AUX
ejpam-4645	110	12	a	a	DET
ejpam-4645	110	13	strictly	strictly	ADV
ejpam-4645	110	14	locating	locate	VERB
ejpam-4645	110	15	set	set	NOUN
ejpam-4645	110	16	of	of	ADP
ejpam-4645	110	17	v	v	NOUN
ejpam-4645	110	18	(	(	PUNCT
ejpam-4645	110	19	huv	huv	PROPN
ejpam-4645	110	20	)	)	PUNCT
ejpam-4645	110	21	.	.	PUNCT
ejpam-4645	111	1	it	it	PRON
ejpam-4645	111	2	follows	follow	VERB
ejpam-4645	111	3	that	that	SCONJ
ejpam-4645	111	4	nhuv(p	nhuv(p	PROPN
ejpam-4645	111	5	)	)	PUNCT
ejpam-4645	111	6	∩	∩	PROPN
ejpam-4645	111	7	suv	suv	PROPN
ejpam-4645	111	8	̸=	̸=	PROPN
ejpam-4645	111	9	suv	suv	PROPN
ejpam-4645	111	10	.	.	PUNCT
ejpam-4645	112	1	since	since	SCONJ
ejpam-4645	112	2	suv	suv	PROPN
ejpam-4645	112	3	⊆	⊆	NUM
ejpam-4645	112	4	ng⋄h(q	ng⋄h(q	NOUN
ejpam-4645	112	5	)	)	PUNCT
ejpam-4645	112	6	∩	∩	PROPN
ejpam-4645	112	7	c	c	X
ejpam-4645	112	8	,	,	PUNCT
ejpam-4645	112	9	ng⋄h(p	ng⋄h(p	PROPN
ejpam-4645	112	10	)	)	PUNCT
ejpam-4645	112	11	∩	∩	NOUN
ejpam-4645	112	12	c	c	PROPN
ejpam-4645	112	13	̸=	̸=	PROPN
ejpam-4645	112	14	ng⋄h(q	ng⋄h(q	ADV
ejpam-4645	112	15	)	)	PUNCT
ejpam-4645	112	16	∩	∩	PROPN
ejpam-4645	112	17	c.	c.	PROPN
ejpam-4645	112	18	accordingly	accordingly	ADV
ejpam-4645	112	19	,	,	PUNCT
ejpam-4645	112	20	c	c	PROPN
ejpam-4645	112	21	is	be	AUX
ejpam-4645	112	22	locating	locate	VERB
ejpam-4645	112	23	-	-	PUNCT
ejpam-4645	112	24	dominating	dominate	VERB
ejpam-4645	112	25	set	set	NOUN
ejpam-4645	112	26	of	of	ADP
ejpam-4645	112	27	g	g	PROPN
ejpam-4645	112	28	⋄h	⋄h	PROPN
ejpam-4645	112	29	.	.	PUNCT
ejpam-4645	113	1	a	a	DET
ejpam-4645	113	2	set	set	NOUN
ejpam-4645	113	3	s	s	NOUN
ejpam-4645	113	4	⊆	⊆	NUM
ejpam-4645	113	5	v	v	NOUN
ejpam-4645	113	6	(	(	PUNCT
ejpam-4645	113	7	g	g	NOUN
ejpam-4645	113	8	)	)	PUNCT
ejpam-4645	113	9	is	be	AUX
ejpam-4645	113	10	a	a	DET
ejpam-4645	113	11	vertex	vertex	NOUN
ejpam-4645	113	12	cover	cover	NOUN
ejpam-4645	113	13	of	of	ADP
ejpam-4645	113	14	g	g	PROPN
ejpam-4645	113	15	if	if	SCONJ
ejpam-4645	113	16	for	for	ADP
ejpam-4645	113	17	every	every	DET
ejpam-4645	113	18	uv	uv	PROPN
ejpam-4645	113	19	∈	∈	PROPN
ejpam-4645	113	20	e(g	e(g	PROPN
ejpam-4645	113	21	)	)	PUNCT
ejpam-4645	113	22	,	,	PUNCT
ejpam-4645	113	23	u	u	PROPN
ejpam-4645	113	24	∈	∈	PROPN
ejpam-4645	113	25	s	s	X
ejpam-4645	113	26	or	or	CCONJ
ejpam-4645	113	27	v	v	ADP
ejpam-4645	113	28	∈	∈	PROPN
ejpam-4645	113	29	s.	s.	PROPN
ejpam-4645	113	30	a	a	DET
ejpam-4645	113	31	vertex	vertex	NOUN
ejpam-4645	113	32	cover	cover	NOUN
ejpam-4645	113	33	s	s	NOUN
ejpam-4645	113	34	is	be	AUX
ejpam-4645	113	35	a	a	DET
ejpam-4645	113	36	perfect	perfect	ADJ
ejpam-4645	113	37	vertex	vertex	NOUN
ejpam-4645	113	38	cover	cover	NOUN
ejpam-4645	113	39	of	of	ADP
ejpam-4645	113	40	g	g	PROPN
ejpam-4645	113	41	if	if	SCONJ
ejpam-4645	113	42	for	for	ADP
ejpam-4645	113	43	each	each	DET
ejpam-4645	113	44	v	v	NOUN
ejpam-4645	113	45	∈	∈	PROPN
ejpam-4645	113	46	s	s	NOUN
ejpam-4645	113	47	and	and	CCONJ
ejpam-4645	113	48	for	for	ADP
ejpam-4645	113	49	each	each	DET
ejpam-4645	113	50	pair	pair	NOUN
ejpam-4645	113	51	of	of	ADP
ejpam-4645	113	52	distinct	distinct	ADJ
ejpam-4645	113	53	edges	edge	NOUN
ejpam-4645	113	54	uv	uv	NOUN
ejpam-4645	113	55	and	and	CCONJ
ejpam-4645	113	56	wv	wv	PROPN
ejpam-4645	113	57	of	of	ADP
ejpam-4645	113	58	g	g	PROPN
ejpam-4645	113	59	,	,	PUNCT
ejpam-4645	113	60	u	u	PROPN
ejpam-4645	113	61	∈	∈	PROPN
ejpam-4645	113	62	s	s	X
ejpam-4645	113	63	or	or	CCONJ
ejpam-4645	113	64	w	w	PROPN
ejpam-4645	113	65	∈	∈	PROPN
ejpam-4645	113	66	s.	s.	PROPN
ejpam-4645	113	67	the	the	DET
ejpam-4645	113	68	smallest	small	ADJ
ejpam-4645	113	69	size	size	NOUN
ejpam-4645	113	70	of	of	ADP
ejpam-4645	113	71	a	a	DET
ejpam-4645	113	72	perfect	perfect	ADJ
ejpam-4645	113	73	vertex	vertex	NOUN
ejpam-4645	113	74	cover	cover	NOUN
ejpam-4645	113	75	of	of	ADP
ejpam-4645	113	76	g.	g.	PROPN
ejpam-4645	113	77	malacas	malacas	PROPN
ejpam-4645	113	78	,	,	PUNCT
ejpam-4645	113	79	s.	s.	PROPN
ejpam-4645	113	80	canoy	canoy	PROPN
ejpam-4645	113	81	,	,	PUNCT
ejpam-4645	113	82	jr	jr	PROPN
ejpam-4645	113	83	.	.	PROPN
ejpam-4645	113	84	,	,	PUNCT
ejpam-4645	113	85	e.	e.	PROPN
ejpam-4645	113	86	chacon	chacon	PROPN
ejpam-4645	113	87	/	/	SYM
ejpam-4645	113	88	eur	eur	PROPN
ejpam-4645	113	89	.	.	PUNCT
ejpam-4645	114	1	j.	j.	PROPN
ejpam-4645	114	2	pure	pure	PROPN
ejpam-4645	114	3	appl	appl	PROPN
ejpam-4645	114	4	.	.	PROPN
ejpam-4645	114	5	math	math	PROPN
ejpam-4645	114	6	,	,	PUNCT
ejpam-4645	114	7	16	16	NUM
ejpam-4645	114	8	(	(	PUNCT
ejpam-4645	114	9	1	1	NUM
ejpam-4645	114	10	)	)	PUNCT
ejpam-4645	114	11	(	(	PUNCT
ejpam-4645	114	12	2023	2023	NUM
ejpam-4645	114	13	)	)	PUNCT
ejpam-4645	114	14	,	,	PUNCT
ejpam-4645	114	15	479	479	NUM
ejpam-4645	114	16	-	-	SYM
ejpam-4645	114	17	490	490	NUM
ejpam-4645	114	18	483	483	NUM
ejpam-4645	114	19	g	g	NOUN
ejpam-4645	114	20	,	,	PUNCT
ejpam-4645	114	21	denoted	denote	VERB
ejpam-4645	114	22	by	by	ADP
ejpam-4645	114	23	βp(g	βp(g	NOUN
ejpam-4645	114	24	)	)	PUNCT
ejpam-4645	114	25	,	,	PUNCT
ejpam-4645	114	26	is	be	AUX
ejpam-4645	114	27	called	call	VERB
ejpam-4645	114	28	the	the	DET
ejpam-4645	114	29	the	the	DET
ejpam-4645	114	30	perfect	perfect	ADJ
ejpam-4645	114	31	vertex	vertex	NOUN
ejpam-4645	114	32	covering	cover	VERB
ejpam-4645	114	33	number	number	NOUN
ejpam-4645	114	34	of	of	ADP
ejpam-4645	114	35	g.	g.	PROPN
ejpam-4645	114	36	any	any	DET
ejpam-4645	114	37	perfect	perfect	ADJ
ejpam-4645	114	38	vertex	vertex	NOUN
ejpam-4645	114	39	cover	cover	NOUN
ejpam-4645	114	40	of	of	ADP
ejpam-4645	114	41	g	g	NOUN
ejpam-4645	114	42	of	of	ADP
ejpam-4645	114	43	size	size	NOUN
ejpam-4645	114	44	βp(g	βp(g	PUNCT
ejpam-4645	114	45	)	)	PUNCT
ejpam-4645	114	46	is	be	AUX
ejpam-4645	114	47	called	call	VERB
ejpam-4645	114	48	a	a	DET
ejpam-4645	114	49	βp	βp	NOUN
ejpam-4645	114	50	-	-	PUNCT
ejpam-4645	114	51	set	set	NOUN
ejpam-4645	114	52	or	or	CCONJ
ejpam-4645	114	53	a	a	DET
ejpam-4645	114	54	minimum	minimum	ADJ
ejpam-4645	114	55	perfect	perfect	ADJ
ejpam-4645	114	56	vertex	vertex	NOUN
ejpam-4645	114	57	cover	cover	NOUN
ejpam-4645	114	58	of	of	ADP
ejpam-4645	114	59	g.	g.	PROPN
ejpam-4645	114	60	example	example	NOUN
ejpam-4645	115	1	1	1	NUM
ejpam-4645	115	2	.	.	X
ejpam-4645	115	3	βp(kn	βp(kn	NUM
ejpam-4645	115	4	)	)	PUNCT
ejpam-4645	116	1	=	=	PUNCT
ejpam-4645	116	2	n−	n−	NOUN
ejpam-4645	116	3	1	1	NUM
ejpam-4645	116	4	for	for	ADP
ejpam-4645	116	5	each	each	DET
ejpam-4645	116	6	n	n	PRON
ejpam-4645	116	7	≥	≥	NOUN
ejpam-4645	116	8	2	2	NUM
ejpam-4645	116	9	.	.	PUNCT
ejpam-4645	116	10	corollary	corollary	ADJ
ejpam-4645	116	11	1	1	NUM
ejpam-4645	116	12	.	.	PUNCT
ejpam-4645	117	1	let	let	VERB
ejpam-4645	117	2	g	g	PRON
ejpam-4645	117	3	be	be	AUX
ejpam-4645	117	4	a	a	DET
ejpam-4645	117	5	connected	connected	ADJ
ejpam-4645	117	6	graph	graph	NOUN
ejpam-4645	117	7	of	of	ADP
ejpam-4645	117	8	order	order	NOUN
ejpam-4645	117	9	m	m	VERB
ejpam-4645	117	10	≥	≥	NOUN
ejpam-4645	117	11	3	3	NUM
ejpam-4645	117	12	and	and	CCONJ
ejpam-4645	117	13	let	let	VERB
ejpam-4645	117	14	h	h	NOUN
ejpam-4645	117	15	be	be	AUX
ejpam-4645	117	16	any	any	DET
ejpam-4645	117	17	non	non	ADJ
ejpam-4645	117	18	-	-	ADJ
ejpam-4645	117	19	trivial	trivial	ADJ
ejpam-4645	117	20	connected	connected	ADJ
ejpam-4645	117	21	graph	graph	NOUN
ejpam-4645	117	22	.	.	PUNCT
ejpam-4645	118	1	(	(	PUNCT
ejpam-4645	118	2	i	i	NOUN
ejpam-4645	118	3	)	)	PUNCT
ejpam-4645	118	4	if	if	SCONJ
ejpam-4645	118	5	l(g	l(g	NOUN
ejpam-4645	118	6	)	)	PUNCT
ejpam-4645	118	7	=	=	SYM
ejpam-4645	118	8	∅	∅	NOUN
ejpam-4645	118	9	,	,	PUNCT
ejpam-4645	118	10	then	then	ADV
ejpam-4645	118	11	γl(g	γl(g	NUM
ejpam-4645	118	12	⋄h	⋄h	PROPN
ejpam-4645	118	13	)	)	PUNCT
ejpam-4645	118	14	≤	≤	NUM
ejpam-4645	118	15	min{βp(g	min{βp(g	NOUN
ejpam-4645	118	16	)	)	PUNCT
ejpam-4645	118	17	+	+	NUM
ejpam-4645	118	18	|e(g)|ln(h	|e(g)|ln(h	NUM
ejpam-4645	118	19	)	)	PUNCT
ejpam-4645	118	20	,	,	PUNCT
ejpam-4645	118	21	|e(g)|γl(h	|e(g)|γl(h	PROPN
ejpam-4645	118	22	)	)	PUNCT
ejpam-4645	118	23	}	}	PUNCT
ejpam-4645	118	24	.	.	PUNCT
ejpam-4645	119	1	(	(	PUNCT
ejpam-4645	119	2	ii	ii	NOUN
ejpam-4645	119	3	)	)	PUNCT
ejpam-4645	119	4	if	if	SCONJ
ejpam-4645	119	5	l(g	l(g	NOUN
ejpam-4645	119	6	)	)	PUNCT
ejpam-4645	119	7	̸=	̸=	PROPN
ejpam-4645	119	8	∅	∅	NOUN
ejpam-4645	119	9	,	,	PUNCT
ejpam-4645	119	10	then	then	ADV
ejpam-4645	119	11	γl(g	γl(g	NUM
ejpam-4645	119	12	⋄h	⋄h	PROPN
ejpam-4645	119	13	)	)	PUNCT
ejpam-4645	119	14	≤	≤	NUM
ejpam-4645	119	15	min{βp(g	min{βp(g	NOUN
ejpam-4645	119	16	)	)	PUNCT
ejpam-4645	119	17	+	+	NUM
ejpam-4645	119	18	|e(g)|sln(h	|e(g)|sln(h	NUM
ejpam-4645	119	19	)	)	PUNCT
ejpam-4645	119	20	,	,	PUNCT
ejpam-4645	119	21	|e(g)|γsl(h	|e(g)|γsl(h	PROPN
ejpam-4645	119	22	)	)	PUNCT
ejpam-4645	119	23	}	}	PUNCT
ejpam-4645	119	24	.	.	PUNCT
ejpam-4645	120	1	proof	proof	NOUN
ejpam-4645	120	2	.	.	PUNCT
ejpam-4645	121	1	(	(	PUNCT
ejpam-4645	121	2	i	i	NOUN
ejpam-4645	121	3	)	)	PUNCT
ejpam-4645	121	4	suppose	suppose	VERB
ejpam-4645	121	5	that	that	SCONJ
ejpam-4645	121	6	l(g	l(g	NOUN
ejpam-4645	121	7	)	)	PUNCT
ejpam-4645	121	8	=	=	PUNCT
ejpam-4645	121	9	∅.	∅.	AUX
ejpam-4645	121	10	let	let	VERB
ejpam-4645	121	11	s1	s1	PROPN
ejpam-4645	121	12	be	be	AUX
ejpam-4645	121	13	a	a	DET
ejpam-4645	121	14	βp	βp	NOUN
ejpam-4645	121	15	-	-	PUNCT
ejpam-4645	121	16	set	set	NOUN
ejpam-4645	121	17	of	of	ADP
ejpam-4645	121	18	g	g	NOUN
ejpam-4645	121	19	and	and	CCONJ
ejpam-4645	121	20	let	let	VERB
ejpam-4645	121	21	suv	suv	PROPN
ejpam-4645	121	22	be	be	AUX
ejpam-4645	121	23	a	a	DET
ejpam-4645	121	24	minimum	minimum	ADJ
ejpam-4645	121	25	locating	locating	NOUN
ejpam-4645	121	26	set	set	NOUN
ejpam-4645	121	27	of	of	ADP
ejpam-4645	121	28	huv	huv	PROPN
ejpam-4645	121	29	for	for	ADP
ejpam-4645	121	30	each	each	DET
ejpam-4645	121	31	uv	uv	PROPN
ejpam-4645	121	32	∈	∈	PROPN
ejpam-4645	121	33	e(g	e(g	PROPN
ejpam-4645	121	34	)	)	PUNCT
ejpam-4645	121	35	.	.	PUNCT
ejpam-4645	122	1	then	then	ADV
ejpam-4645	122	2	c1	c1	PROPN
ejpam-4645	122	3	=	=	PROPN
ejpam-4645	122	4	s	s	PART
ejpam-4645	122	5	∪	∪	X
ejpam-4645	122	6	[	[	X
ejpam-4645	122	7	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-4645	122	8	]	]	PUNCT
ejpam-4645	122	9	is	be	AUX
ejpam-4645	122	10	a	a	DET
ejpam-4645	122	11	locating	locate	VERB
ejpam-4645	122	12	dominating	dominating	NOUN
ejpam-4645	122	13	set	set	NOUN
ejpam-4645	122	14	of	of	ADP
ejpam-4645	122	15	g	g	PROPN
ejpam-4645	122	16	⋄h	⋄h	NOUN
ejpam-4645	122	17	by	by	ADP
ejpam-4645	122	18	theorem	theorem	NOUN
ejpam-4645	122	19	2	2	NUM
ejpam-4645	122	20	.	.	PUNCT
ejpam-4645	122	21	hence	hence	ADV
ejpam-4645	122	22	,	,	PUNCT
ejpam-4645	122	23	γl(g	γl(g	PRON
ejpam-4645	122	24	⋄h	⋄h	PROPN
ejpam-4645	122	25	)	)	PUNCT
ejpam-4645	122	26	≤	≤	NOUN
ejpam-4645	122	27	|c1|	|c1|	NOUN
ejpam-4645	122	28	=	=	SYM
ejpam-4645	122	29	βp(g)+	βp(g)+	NUM
ejpam-4645	122	30	|e(g)|ln(h	|e(g)|ln(h	NUM
ejpam-4645	122	31	)	)	PUNCT
ejpam-4645	122	32	.	.	PUNCT
ejpam-4645	123	1	now	now	ADV
ejpam-4645	123	2	,	,	PUNCT
ejpam-4645	123	3	let	let	VERB
ejpam-4645	123	4	luv	luv	PROPN
ejpam-4645	123	5	be	be	AUX
ejpam-4645	123	6	a	a	DET
ejpam-4645	123	7	γl	γl	NOUN
ejpam-4645	123	8	-	-	PUNCT
ejpam-4645	123	9	set	set	NOUN
ejpam-4645	123	10	of	of	ADP
ejpam-4645	123	11	h	h	NOUN
ejpam-4645	123	12	uv	uv	NOUN
ejpam-4645	123	13	for	for	ADP
ejpam-4645	123	14	each	each	DET
ejpam-4645	123	15	uv	uv	PROPN
ejpam-4645	123	16	∈	∈	PROPN
ejpam-4645	123	17	e(g	e(g	PROPN
ejpam-4645	123	18	)	)	PUNCT
ejpam-4645	123	19	.	.	PUNCT
ejpam-4645	124	1	then	then	ADV
ejpam-4645	124	2	c2	c2	PROPN
ejpam-4645	124	3	=	=	PUNCT
ejpam-4645	124	4	∪uv∈e(g)luv	∪uv∈e(g)luv	PROPN
ejpam-4645	124	5	is	be	AUX
ejpam-4645	124	6	a	a	DET
ejpam-4645	124	7	locating	locate	VERB
ejpam-4645	124	8	dominating	dominating	NOUN
ejpam-4645	124	9	set	set	NOUN
ejpam-4645	124	10	of	of	ADP
ejpam-4645	124	11	g⋄h	g⋄h	X
ejpam-4645	124	12	by	by	ADP
ejpam-4645	124	13	theorem	theorem	NOUN
ejpam-4645	124	14	2	2	NUM
ejpam-4645	124	15	.	.	PUNCT
ejpam-4645	125	1	this	this	PRON
ejpam-4645	125	2	implies	imply	VERB
ejpam-4645	125	3	that	that	SCONJ
ejpam-4645	125	4	γl(g⋄h	γl(g⋄h	NOUN
ejpam-4645	125	5	)	)	PUNCT
ejpam-4645	125	6	≤	≤	NUM
ejpam-4645	125	7	|c2|	|c2|	NOUN
ejpam-4645	125	8	=	=	SYM
ejpam-4645	125	9	|e(g)|γl(h	|e(g)|γl(h	PROPN
ejpam-4645	125	10	)	)	PUNCT
ejpam-4645	125	11	.	.	PUNCT
ejpam-4645	126	1	therefore	therefore	ADV
ejpam-4645	126	2	,	,	PUNCT
ejpam-4645	126	3	(	(	PUNCT
ejpam-4645	126	4	i	i	NOUN
ejpam-4645	126	5	)	)	PUNCT
ejpam-4645	126	6	holds	hold	VERB
ejpam-4645	126	7	.	.	PUNCT
ejpam-4645	127	1	(	(	PUNCT
ejpam-4645	127	2	ii	ii	NOUN
ejpam-4645	127	3	)	)	PUNCT
ejpam-4645	127	4	suppose	suppose	VERB
ejpam-4645	127	5	that	that	SCONJ
ejpam-4645	127	6	l(g	l(g	NOUN
ejpam-4645	127	7	)	)	PUNCT
ejpam-4645	127	8	̸=	̸=	PROPN
ejpam-4645	127	9	∅.	∅.	ADV
ejpam-4645	127	10	let	let	VERB
ejpam-4645	127	11	s	s	PRON
ejpam-4645	127	12	be	be	AUX
ejpam-4645	127	13	a	a	DET
ejpam-4645	127	14	βp	βp	NOUN
ejpam-4645	127	15	-	-	PUNCT
ejpam-4645	127	16	set	set	NOUN
ejpam-4645	127	17	of	of	ADP
ejpam-4645	127	18	g	g	NOUN
ejpam-4645	127	19	and	and	CCONJ
ejpam-4645	127	20	let	let	VERB
ejpam-4645	127	21	s′	s′	ADJ
ejpam-4645	127	22	uv	uv	NOUN
ejpam-4645	127	23	be	be	AUX
ejpam-4645	127	24	a	a	DET
ejpam-4645	127	25	minimum	minimum	NOUN
ejpam-4645	127	26	strictly	strictly	ADV
ejpam-4645	127	27	locating	locate	VERB
ejpam-4645	127	28	set	set	NOUN
ejpam-4645	127	29	of	of	ADP
ejpam-4645	127	30	huv	huv	PROPN
ejpam-4645	127	31	for	for	ADP
ejpam-4645	127	32	each	each	DET
ejpam-4645	127	33	uv	uv	PROPN
ejpam-4645	127	34	∈	∈	PROPN
ejpam-4645	127	35	e(g	e(g	PROPN
ejpam-4645	127	36	)	)	PUNCT
ejpam-4645	127	37	.	.	PUNCT
ejpam-4645	128	1	then	then	ADV
ejpam-4645	128	2	c3	c3	PROPN
ejpam-4645	128	3	=	=	X
ejpam-4645	128	4	s	s	PART
ejpam-4645	128	5	∪	∪	X
ejpam-4645	128	6	[	[	X
ejpam-4645	128	7	∪uv∈e(g)s	∪uv∈e(g)s	X
ejpam-4645	128	8	′	′	NOUN
ejpam-4645	128	9	uv	uv	NOUN
ejpam-4645	128	10	is	be	AUX
ejpam-4645	128	11	a	a	DET
ejpam-4645	128	12	locating	locate	VERB
ejpam-4645	128	13	dominating	dominating	NOUN
ejpam-4645	128	14	set	set	NOUN
ejpam-4645	128	15	of	of	ADP
ejpam-4645	128	16	g⋄h	g⋄h	X
ejpam-4645	128	17	by	by	ADP
ejpam-4645	128	18	theorem	theorem	NOUN
ejpam-4645	128	19	2	2	NUM
ejpam-4645	128	20	.	.	PUNCT
ejpam-4645	128	21	hence	hence	ADV
ejpam-4645	128	22	,	,	PUNCT
ejpam-4645	128	23	γl(g⋄h	γl(g⋄h	X
ejpam-4645	128	24	)	)	PUNCT
ejpam-4645	128	25	≤	≤	NUM
ejpam-4645	128	26	|c3|	|c3|	NOUN
ejpam-4645	128	27	=	=	SYM
ejpam-4645	128	28	βp(g)+	βp(g)+	PUNCT
ejpam-4645	128	29	|e(g)|sln(h	|e(g)|sln(h	NUM
ejpam-4645	128	30	)	)	PUNCT
ejpam-4645	128	31	.	.	PUNCT
ejpam-4645	129	1	let	let	VERB
ejpam-4645	129	2	ruv	ruv	PROPN
ejpam-4645	129	3	be	be	AUX
ejpam-4645	129	4	a	a	DET
ejpam-4645	129	5	γsl	γsl	NOUN
ejpam-4645	129	6	-	-	PUNCT
ejpam-4645	129	7	set	set	NOUN
ejpam-4645	129	8	of	of	ADP
ejpam-4645	129	9	h	h	NOUN
ejpam-4645	129	10	uv	uv	NOUN
ejpam-4645	129	11	for	for	ADP
ejpam-4645	129	12	each	each	DET
ejpam-4645	129	13	uv	uv	PROPN
ejpam-4645	129	14	∈	∈	PROPN
ejpam-4645	129	15	e(g	e(g	PROPN
ejpam-4645	129	16	)	)	PUNCT
ejpam-4645	129	17	.	.	PUNCT
ejpam-4645	130	1	then	then	ADV
ejpam-4645	130	2	c4	c4	NOUN
ejpam-4645	130	3	=	=	SYM
ejpam-4645	130	4	∪uv∈e(g)ruv	∪uv∈e(g)ruv	PROPN
ejpam-4645	130	5	is	be	AUX
ejpam-4645	130	6	a	a	DET
ejpam-4645	130	7	locating	locate	VERB
ejpam-4645	130	8	dominating	dominating	NOUN
ejpam-4645	130	9	set	set	NOUN
ejpam-4645	130	10	of	of	ADP
ejpam-4645	130	11	g	g	PROPN
ejpam-4645	130	12	⋄h	⋄h	NOUN
ejpam-4645	130	13	by	by	ADP
ejpam-4645	130	14	theorem	theorem	NOUN
ejpam-4645	130	15	2	2	NUM
ejpam-4645	130	16	.	.	PUNCT
ejpam-4645	131	1	this	this	PRON
ejpam-4645	131	2	implies	imply	VERB
ejpam-4645	131	3	that	that	SCONJ
ejpam-4645	131	4	γl(g	γl(g	NUM
ejpam-4645	131	5	⋄h	⋄h	PROPN
ejpam-4645	131	6	)	)	PUNCT
ejpam-4645	131	7	≤	≤	NOUN
ejpam-4645	131	8	|c4|	|c4|	NOUN
ejpam-4645	131	9	=	=	SYM
ejpam-4645	131	10	|e(g)|γsl(h	|e(g)|γsl(h	PROPN
ejpam-4645	131	11	)	)	PUNCT
ejpam-4645	131	12	,	,	PUNCT
ejpam-4645	131	13	showing	show	VERB
ejpam-4645	131	14	that	that	SCONJ
ejpam-4645	131	15	(	(	PUNCT
ejpam-4645	131	16	ii	ii	NOUN
ejpam-4645	131	17	)	)	PUNCT
ejpam-4645	131	18	holds	hold	VERB
ejpam-4645	131	19	.	.	PUNCT
ejpam-4645	132	1	remark	remark	PROPN
ejpam-4645	132	2	1	1	NUM
ejpam-4645	132	3	.	.	PUNCT
ejpam-4645	133	1	the	the	DET
ejpam-4645	133	2	bounds	bound	NOUN
ejpam-4645	133	3	in	in	ADP
ejpam-4645	133	4	corollary	corollary	ADJ
ejpam-4645	133	5	2	2	NUM
ejpam-4645	133	6	are	be	AUX
ejpam-4645	133	7	sharp	sharp	ADJ
ejpam-4645	133	8	.	.	PUNCT
ejpam-4645	134	1	indeed	indeed	ADV
ejpam-4645	134	2	,	,	PUNCT
ejpam-4645	134	3	it	it	PRON
ejpam-4645	134	4	can	can	AUX
ejpam-4645	134	5	be	be	AUX
ejpam-4645	134	6	verified	verify	VERB
ejpam-4645	134	7	that	that	SCONJ
ejpam-4645	134	8	γl(k3	γl(k3	VERB
ejpam-4645	134	9	⋄	⋄	PROPN
ejpam-4645	134	10	p5	p5	PROPN
ejpam-4645	134	11	)	)	PUNCT
ejpam-4645	134	12	=	=	SYM
ejpam-4645	135	1	|e(k3)|γl(p5	|e(k3)|γl(p5	X
ejpam-4645	135	2	)	)	PUNCT
ejpam-4645	135	3	=	=	SYM
ejpam-4645	136	1	6	6	NUM
ejpam-4645	136	2	<	<	SYM
ejpam-4645	136	3	8	8	NUM
ejpam-4645	136	4	=	=	SYM
ejpam-4645	136	5	βp(k3	βp(k3	NUM
ejpam-4645	136	6	)	)	PUNCT
ejpam-4645	136	7	+	+	CCONJ
ejpam-4645	136	8	|e(k3)|ln(p5	|e(k3)|ln(p5	NOUN
ejpam-4645	136	9	)	)	PUNCT
ejpam-4645	137	1	,	,	PUNCT
ejpam-4645	137	2	γl(k3	γl(k3	VERB
ejpam-4645	137	3	⋄	⋄	PROPN
ejpam-4645	137	4	p3	p3	PROPN
ejpam-4645	137	5	)	)	PUNCT
ejpam-4645	137	6	=	=	PUNCT
ejpam-4645	138	1	βp(k3	βp(k3	X
ejpam-4645	138	2	)	)	PUNCT
ejpam-4645	139	1	+	+	CCONJ
ejpam-4645	139	2	|e(k3)|ln(p3	|e(k3)|ln(p3	X
ejpam-4645	139	3	)	)	PUNCT
ejpam-4645	139	4	=	=	SYM
ejpam-4645	139	5	5	5	NUM
ejpam-4645	139	6	<	<	SYM
ejpam-4645	139	7	6	6	NUM
ejpam-4645	139	8	=	=	SYM
ejpam-4645	139	9	|e(k3)|γl(p3	|e(k3)|γl(p3	NOUN
ejpam-4645	139	10	)	)	PUNCT
ejpam-4645	139	11	,	,	PUNCT
ejpam-4645	139	12	γl(p3	γl(p3	PROPN
ejpam-4645	139	13	⋄	⋄	PROPN
ejpam-4645	139	14	p3	p3	PROPN
ejpam-4645	139	15	)	)	PUNCT
ejpam-4645	140	1	=	=	SYM
ejpam-4645	140	2	|e(p3)|γsl(p3	|e(p3)|γsl(p3	NOUN
ejpam-4645	140	3	)	)	PUNCT
ejpam-4645	140	4	=	=	PUNCT
ejpam-4645	140	5	4	4	NUM
ejpam-4645	140	6	<	<	SYM
ejpam-4645	140	7	6	6	NUM
ejpam-4645	140	8	=	=	SYM
ejpam-4645	140	9	βp(p3	βp(p3	NOUN
ejpam-4645	140	10	)	)	PUNCT
ejpam-4645	141	1	+	+	CCONJ
ejpam-4645	141	2	|e(p3)|sln(p3	|e(p3)|sln(p3	ADJ
ejpam-4645	141	3	)	)	PUNCT
ejpam-4645	141	4	,	,	PUNCT
ejpam-4645	141	5	and	and	CCONJ
ejpam-4645	141	6	γl(p4	γl(p4	ADP
ejpam-4645	141	7	⋄	⋄	PROPN
ejpam-4645	141	8	p5	p5	PROPN
ejpam-4645	141	9	)	)	PUNCT
ejpam-4645	141	10	=	=	SYM
ejpam-4645	141	11	βp(p4	βp(p4	X
ejpam-4645	141	12	)	)	PUNCT
ejpam-4645	142	1	+	+	CCONJ
ejpam-4645	142	2	|e(p4)|sln(p5	|e(p4)|sln(p5	ADJ
ejpam-4645	142	3	)	)	PUNCT
ejpam-4645	142	4	=	=	SYM
ejpam-4645	142	5	8	8	NUM
ejpam-4645	142	6	<	<	SYM
ejpam-4645	142	7	9	9	NUM
ejpam-4645	142	8	=	=	SYM
ejpam-4645	142	9	|e(p4)|γsl(p5	|e(p4)|γsl(p5	NOUN
ejpam-4645	142	10	)	)	PUNCT
ejpam-4645	142	11	.	.	PUNCT
ejpam-4645	143	1	theorem	theorem	NOUN
ejpam-4645	143	2	3	3	X
ejpam-4645	143	3	.	.	PUNCT
ejpam-4645	144	1	let	let	VERB
ejpam-4645	144	2	g	g	PRON
ejpam-4645	144	3	be	be	AUX
ejpam-4645	144	4	a	a	DET
ejpam-4645	144	5	connected	connected	ADJ
ejpam-4645	144	6	graph	graph	NOUN
ejpam-4645	144	7	of	of	ADP
ejpam-4645	144	8	order	order	NOUN
ejpam-4645	144	9	m	m	VERB
ejpam-4645	144	10	≥	≥	NOUN
ejpam-4645	144	11	3	3	NUM
ejpam-4645	144	12	and	and	CCONJ
ejpam-4645	144	13	let	let	VERB
ejpam-4645	144	14	h	h	NOUN
ejpam-4645	144	15	be	be	AUX
ejpam-4645	144	16	any	any	DET
ejpam-4645	144	17	non	non	ADJ
ejpam-4645	144	18	-	-	ADJ
ejpam-4645	144	19	trivial	trivial	ADJ
ejpam-4645	144	20	connected	connected	ADJ
ejpam-4645	144	21	graph	graph	NOUN
ejpam-4645	144	22	.	.	PUNCT
ejpam-4645	145	1	then	then	ADV
ejpam-4645	145	2	c	c	PROPN
ejpam-4645	145	3	is	be	AUX
ejpam-4645	145	4	a	a	DET
ejpam-4645	145	5	stable	stable	ADJ
ejpam-4645	145	6	locating	locating	NOUN
ejpam-4645	145	7	-	-	PUNCT
ejpam-4645	145	8	dominating	dominate	VERB
ejpam-4645	145	9	set	set	NOUN
ejpam-4645	145	10	of	of	ADP
ejpam-4645	145	11	g	g	PROPN
ejpam-4645	145	12	⋄	⋄	PROPN
ejpam-4645	145	13	h	h	NOUN
ejpam-4645	146	1	if	if	SCONJ
ejpam-4645	146	2	and	and	CCONJ
ejpam-4645	146	3	only	only	ADV
ejpam-4645	146	4	if	if	SCONJ
ejpam-4645	146	5	c	c	X
ejpam-4645	146	6	=	=	PUNCT
ejpam-4645	146	7	a	a	DET
ejpam-4645	146	8	∪	∪	NOUN
ejpam-4645	146	9	[	[	X
ejpam-4645	146	10	∪uv∈e(g)suv	∪uv∈e(g)suv	NOUN
ejpam-4645	146	11	]	]	PUNCT
ejpam-4645	146	12	and	and	CCONJ
ejpam-4645	146	13	satisfies	satisfy	VERB
ejpam-4645	146	14	the	the	DET
ejpam-4645	146	15	following	follow	VERB
ejpam-4645	146	16	conditions	condition	NOUN
ejpam-4645	146	17	:	:	PUNCT
ejpam-4645	146	18	(	(	PUNCT
ejpam-4645	146	19	i	i	NOUN
ejpam-4645	146	20	)	)	PUNCT
ejpam-4645	146	21	a	a	DET
ejpam-4645	146	22	⊆	⊆	NUM
ejpam-4645	146	23	v	v	NOUN
ejpam-4645	146	24	(	(	PUNCT
ejpam-4645	146	25	g	g	NOUN
ejpam-4645	146	26	)	)	PUNCT
ejpam-4645	146	27	.	.	PUNCT
ejpam-4645	147	1	g.	g.	PROPN
ejpam-4645	147	2	malacas	malacas	PROPN
ejpam-4645	147	3	,	,	PUNCT
ejpam-4645	147	4	s.	s.	PROPN
ejpam-4645	147	5	canoy	canoy	PROPN
ejpam-4645	147	6	,	,	PUNCT
ejpam-4645	147	7	jr	jr	PROPN
ejpam-4645	147	8	.	.	PROPN
ejpam-4645	147	9	,	,	PUNCT
ejpam-4645	147	10	e.	e.	PROPN
ejpam-4645	147	11	chacon	chacon	PROPN
ejpam-4645	147	12	/	/	SYM
ejpam-4645	147	13	eur	eur	PROPN
ejpam-4645	147	14	.	.	PUNCT
ejpam-4645	148	1	j.	j.	PROPN
ejpam-4645	148	2	pure	pure	PROPN
ejpam-4645	148	3	appl	appl	PROPN
ejpam-4645	148	4	.	.	PROPN
ejpam-4645	148	5	math	math	PROPN
ejpam-4645	148	6	,	,	PUNCT
ejpam-4645	148	7	16	16	NUM
ejpam-4645	148	8	(	(	PUNCT
ejpam-4645	148	9	1	1	NUM
ejpam-4645	148	10	)	)	PUNCT
ejpam-4645	148	11	(	(	PUNCT
ejpam-4645	148	12	2023	2023	NUM
ejpam-4645	148	13	)	)	PUNCT
ejpam-4645	148	14	,	,	PUNCT
ejpam-4645	148	15	479	479	NUM
ejpam-4645	148	16	-	-	SYM
ejpam-4645	148	17	490	490	NUM
ejpam-4645	148	18	484	484	NUM
ejpam-4645	148	19	(	(	PUNCT
ejpam-4645	148	20	ii	ii	NOUN
ejpam-4645	148	21	)	)	PUNCT
ejpam-4645	148	22	for	for	ADP
ejpam-4645	148	23	each	each	DET
ejpam-4645	148	24	uv	uv	PROPN
ejpam-4645	148	25	∈	∈	PROPN
ejpam-4645	148	26	e(g	e(g	PROPN
ejpam-4645	148	27	)	)	PUNCT
ejpam-4645	148	28	,	,	PUNCT
ejpam-4645	148	29	(	(	PUNCT
ejpam-4645	148	30	a	a	X
ejpam-4645	148	31	)	)	PUNCT
ejpam-4645	148	32	suv	suv	NOUN
ejpam-4645	148	33	is	be	AUX
ejpam-4645	148	34	a	a	DET
ejpam-4645	148	35	stable	stable	ADJ
ejpam-4645	148	36	locating	locating	NOUN
ejpam-4645	148	37	set	set	NOUN
ejpam-4645	148	38	of	of	ADP
ejpam-4645	148	39	huv	huv	PROPN
ejpam-4645	148	40	;	;	PUNCT
ejpam-4645	148	41	(	(	PUNCT
ejpam-4645	148	42	b	b	X
ejpam-4645	148	43	)	)	PUNCT
ejpam-4645	148	44	suv	suv	PROPN
ejpam-4645	148	45	is	be	AUX
ejpam-4645	148	46	a	a	DET
ejpam-4645	148	47	stable	stable	ADJ
ejpam-4645	148	48	locating	locating	NOUN
ejpam-4645	148	49	-	-	PUNCT
ejpam-4645	148	50	dominating	dominate	VERB
ejpam-4645	148	51	set	set	NOUN
ejpam-4645	148	52	of	of	ADP
ejpam-4645	148	53	huv	huv	PROPN
ejpam-4645	148	54	whenever	whenever	SCONJ
ejpam-4645	148	55	u	u	NOUN
ejpam-4645	148	56	,	,	PUNCT
ejpam-4645	148	57	v	v	NOUN
ejpam-4645	148	58	/∈	/∈	PUNCT
ejpam-4645	148	59	a	a	PRON
ejpam-4645	148	60	;	;	PUNCT
ejpam-4645	148	61	(	(	PUNCT
ejpam-4645	148	62	c	c	X
ejpam-4645	148	63	)	)	PUNCT
ejpam-4645	148	64	suv	suv	PROPN
ejpam-4645	148	65	is	be	AUX
ejpam-4645	148	66	a	a	DET
ejpam-4645	148	67	stable	stable	ADJ
ejpam-4645	148	68	strictly	strictly	ADV
ejpam-4645	148	69	locating	locate	VERB
ejpam-4645	148	70	set	set	NOUN
ejpam-4645	148	71	of	of	ADP
ejpam-4645	148	72	huv	huv	PROPN
ejpam-4645	148	73	for	for	ADP
ejpam-4645	148	74	each	each	DET
ejpam-4645	148	75	v	v	ADP
ejpam-4645	148	76	∈	∈	PROPN
ejpam-4645	148	77	l(g	l(g	NOUN
ejpam-4645	148	78	)	)	PUNCT
ejpam-4645	148	79	with	with	ADP
ejpam-4645	148	80	v	v	NUM
ejpam-4645	148	81	/∈	/∈	PUNCT
ejpam-4645	148	82	a	a	NOUN
ejpam-4645	148	83	;	;	PUNCT
ejpam-4645	148	84	and	and	CCONJ
ejpam-4645	148	85	(	(	PUNCT
ejpam-4645	148	86	d	d	X
ejpam-4645	148	87	)	)	PUNCT
ejpam-4645	148	88	suv	suv	PROPN
ejpam-4645	148	89	is	be	AUX
ejpam-4645	148	90	a	a	DET
ejpam-4645	148	91	stable	stable	ADJ
ejpam-4645	148	92	strictly	strictly	ADV
ejpam-4645	148	93	locating	locate	VERB
ejpam-4645	148	94	-	-	PUNCT
ejpam-4645	148	95	dominating	dominate	VERB
ejpam-4645	148	96	set	set	NOUN
ejpam-4645	148	97	of	of	ADP
ejpam-4645	148	98	huv	huv	PROPN
ejpam-4645	148	99	whenever	whenever	SCONJ
ejpam-4645	148	100	u	u	NOUN
ejpam-4645	148	101	,	,	PUNCT
ejpam-4645	148	102	v	v	NOUN
ejpam-4645	148	103	/∈	/∈	PUNCT
ejpam-4645	148	104	a	a	DET
ejpam-4645	148	105	and	and	CCONJ
ejpam-4645	148	106	{	{	PUNCT
ejpam-4645	148	107	u	u	NOUN
ejpam-4645	148	108	,	,	PUNCT
ejpam-4645	148	109	v	v	NOUN
ejpam-4645	148	110	}	}	PUNCT
ejpam-4645	148	111	∩	∩	ADJ
ejpam-4645	148	112	l(g	l(g	NOUN
ejpam-4645	148	113	)	)	PUNCT
ejpam-4645	148	114	̸=	̸=	PROPN
ejpam-4645	148	115	∅.	∅.	ADP
ejpam-4645	148	116	(	(	PUNCT
ejpam-4645	148	117	iii	iii	NOUN
ejpam-4645	148	118	)	)	PUNCT
ejpam-4645	148	119	for	for	ADP
ejpam-4645	148	120	each	each	DET
ejpam-4645	148	121	w	w	PROPN
ejpam-4645	148	122	∈	∈	PROPN
ejpam-4645	148	123	a	a	PRON
ejpam-4645	148	124	and	and	CCONJ
ejpam-4645	148	125	for	for	ADP
ejpam-4645	148	126	each	each	DET
ejpam-4645	148	127	z	z	PROPN
ejpam-4645	148	128	∈	∈	PROPN
ejpam-4645	148	129	ng(w	ng(w	NOUN
ejpam-4645	148	130	)	)	PUNCT
ejpam-4645	148	131	,	,	PUNCT
ejpam-4645	148	132	we	we	PRON
ejpam-4645	148	133	have	have	VERB
ejpam-4645	148	134	:	:	PUNCT
ejpam-4645	148	135	(	(	PUNCT
ejpam-4645	148	136	a	a	X
ejpam-4645	148	137	)	)	PUNCT
ejpam-4645	148	138	szw	szw	NOUN
ejpam-4645	148	139	is	be	AUX
ejpam-4645	148	140	a	a	DET
ejpam-4645	148	141	strictly	strictly	ADV
ejpam-4645	148	142	locating	locate	VERB
ejpam-4645	148	143	set	set	NOUN
ejpam-4645	148	144	of	of	ADP
ejpam-4645	148	145	hzw	hzw	NOUN
ejpam-4645	148	146	whenever	whenever	SCONJ
ejpam-4645	148	147	w	w	PROPN
ejpam-4645	148	148	∈	∈	PROPN
ejpam-4645	148	149	l(g	l(g	PROPN
ejpam-4645	148	150	)	)	PUNCT
ejpam-4645	148	151	and	and	CCONJ
ejpam-4645	148	152	(	(	PUNCT
ejpam-4645	148	153	b	b	X
ejpam-4645	148	154	)	)	PUNCT
ejpam-4645	148	155	szw	szw	NOUN
ejpam-4645	148	156	is	be	AUX
ejpam-4645	148	157	a	a	DET
ejpam-4645	148	158	strictly	strictly	ADV
ejpam-4645	148	159	locating	locate	VERB
ejpam-4645	148	160	-	-	PUNCT
ejpam-4645	148	161	dominating	dominate	VERB
ejpam-4645	148	162	set	set	NOUN
ejpam-4645	148	163	of	of	ADP
ejpam-4645	148	164	hzw	hzw	NOUN
ejpam-4645	148	165	whenever	whenever	SCONJ
ejpam-4645	148	166	z	z	NOUN
ejpam-4645	148	167	/∈	/∈	PUNCT
ejpam-4645	149	1	a	a	DET
ejpam-4645	149	2	and	and	CCONJ
ejpam-4645	149	3	{	{	PUNCT
ejpam-4645	149	4	z	z	NOUN
ejpam-4645	149	5	,	,	PUNCT
ejpam-4645	149	6	w	w	NOUN
ejpam-4645	149	7	}	}	PUNCT
ejpam-4645	149	8	∩	∩	ADJ
ejpam-4645	149	9	l(g	l(g	NOUN
ejpam-4645	149	10	)	)	PUNCT
ejpam-4645	149	11	̸=	̸=	PROPN
ejpam-4645	149	12	∅.	∅.	ADP
ejpam-4645	149	13	(	(	PUNCT
ejpam-4645	149	14	iv	iv	NOUN
ejpam-4645	149	15	)	)	PUNCT
ejpam-4645	149	16	for	for	ADP
ejpam-4645	149	17	each	each	DET
ejpam-4645	149	18	zw	zw	PROPN
ejpam-4645	149	19	∈	∈	PROPN
ejpam-4645	149	20	e(g	e(g	PROPN
ejpam-4645	149	21	)	)	PUNCT
ejpam-4645	149	22	with	with	ADP
ejpam-4645	149	23	z	z	PROPN
ejpam-4645	149	24	∈	∈	PROPN
ejpam-4645	149	25	a	a	PRON
ejpam-4645	149	26	and	and	CCONJ
ejpam-4645	149	27	w	w	PROPN
ejpam-4645	149	28	/∈	/∈	PROPN
ejpam-4645	149	29	a	a	INTJ
ejpam-4645	149	30	,	,	PUNCT
ejpam-4645	149	31	if	if	SCONJ
ejpam-4645	149	32	x	x	PROPN
ejpam-4645	149	33	∈	∈	PROPN
ejpam-4645	149	34	v	v	ADP
ejpam-4645	149	35	(	(	PUNCT
ejpam-4645	149	36	hzw	hzw	NOUN
ejpam-4645	149	37	)	)	PUNCT
ejpam-4645	149	38	\	\	PUNCT
ejpam-4645	150	1	[	[	X
ejpam-4645	150	2	szw	szw	VERB
ejpam-4645	150	3	\	\	NOUN
ejpam-4645	150	4	{	{	PUNCT
ejpam-4645	150	5	p	p	X
ejpam-4645	150	6	}	}	PUNCT
ejpam-4645	150	7	]	]	PUNCT
ejpam-4645	150	8	for	for	ADP
ejpam-4645	150	9	p	p	PROPN
ejpam-4645	150	10	∈	∈	PROPN
ejpam-4645	150	11	szw	szw	NOUN
ejpam-4645	150	12	and	and	CCONJ
ejpam-4645	150	13	nhzw(x)∩	nhzw(x)∩	PROPN
ejpam-4645	150	14	(	(	PUNCT
ejpam-4645	150	15	szw	szw	VERB
ejpam-4645	150	16	\	\	NOUN
ejpam-4645	150	17	{	{	PUNCT
ejpam-4645	150	18	p	p	NOUN
ejpam-4645	150	19	}	}	PUNCT
ejpam-4645	150	20	)	)	PUNCT
ejpam-4645	150	21	=	=	SYM
ejpam-4645	150	22	∅	∅	NOUN
ejpam-4645	150	23	,	,	PUNCT
ejpam-4645	150	24	then	then	ADV
ejpam-4645	150	25	for	for	ADP
ejpam-4645	150	26	each	each	DET
ejpam-4645	150	27	y	y	PROPN
ejpam-4645	150	28	∈	∈	PROPN
ejpam-4645	150	29	ng(z	ng(z	PROPN
ejpam-4645	150	30	)	)	PUNCT
ejpam-4645	150	31	\	\	PUNCT
ejpam-4645	150	32	{	{	PUNCT
ejpam-4645	150	33	w	w	NOUN
ejpam-4645	150	34	}	}	PUNCT
ejpam-4645	150	35	and	and	CCONJ
ejpam-4645	150	36	for	for	ADP
ejpam-4645	150	37	each	each	DET
ejpam-4645	150	38	q	q	PROPN
ejpam-4645	150	39	∈	∈	PROPN
ejpam-4645	150	40	v	v	NOUN
ejpam-4645	150	41	(	(	PUNCT
ejpam-4645	150	42	hyz	hyz	PROPN
ejpam-4645	150	43	)	)	PUNCT
ejpam-4645	150	44	\	\	PROPN
ejpam-4645	150	45	syz	syz	PROPN
ejpam-4645	150	46	,	,	PUNCT
ejpam-4645	150	47	it	it	PRON
ejpam-4645	150	48	holds	hold	VERB
ejpam-4645	150	49	that	that	SCONJ
ejpam-4645	150	50	y	y	PROPN
ejpam-4645	150	51	∈	∈	PROPN
ejpam-4645	150	52	a	a	PRON
ejpam-4645	150	53	or	or	CCONJ
ejpam-4645	150	54	nhyz(q	nhyz(q	NUM
ejpam-4645	150	55	)	)	PUNCT
ejpam-4645	150	56	∩	∩	NOUN
ejpam-4645	150	57	syz	syz	VERB
ejpam-4645	150	58	̸=	̸=	PROPN
ejpam-4645	150	59	∅.	∅.	ADP
ejpam-4645	150	60	proof	proof	NOUN
ejpam-4645	150	61	.	.	PUNCT
ejpam-4645	151	1	suppose	suppose	VERB
ejpam-4645	151	2	c	c	NOUN
ejpam-4645	151	3	is	be	AUX
ejpam-4645	151	4	a	a	DET
ejpam-4645	151	5	stable	stable	ADJ
ejpam-4645	151	6	locating	locating	NOUN
ejpam-4645	151	7	-	-	PUNCT
ejpam-4645	151	8	dominating	dominate	VERB
ejpam-4645	151	9	set	set	NOUN
ejpam-4645	151	10	of	of	ADP
ejpam-4645	151	11	g	g	PROPN
ejpam-4645	151	12	⋄	⋄	PROPN
ejpam-4645	151	13	h.	h.	PROPN
ejpam-4645	151	14	let	let	VERB
ejpam-4645	151	15	a	a	DET
ejpam-4645	151	16	=	=	SYM
ejpam-4645	151	17	c	c	NOUN
ejpam-4645	151	18	∩	∩	X
ejpam-4645	151	19	v	v	X
ejpam-4645	151	20	(	(	PUNCT
ejpam-4645	151	21	g	g	NOUN
ejpam-4645	151	22	)	)	PUNCT
ejpam-4645	151	23	and	and	CCONJ
ejpam-4645	151	24	suv	suv	PROPN
ejpam-4645	151	25	=	=	PROPN
ejpam-4645	151	26	c	c	PROPN
ejpam-4645	151	27	∩	∩	X
ejpam-4645	151	28	v	v	X
ejpam-4645	151	29	(	(	PUNCT
ejpam-4645	151	30	huv	huv	PROPN
ejpam-4645	151	31	)	)	PUNCT
ejpam-4645	151	32	for	for	ADP
ejpam-4645	151	33	each	each	DET
ejpam-4645	151	34	uv	uv	PROPN
ejpam-4645	151	35	∈	∈	PROPN
ejpam-4645	151	36	e(g	e(g	PROPN
ejpam-4645	151	37	)	)	PUNCT
ejpam-4645	151	38	.	.	PUNCT
ejpam-4645	152	1	then	then	ADV
ejpam-4645	152	2	c	c	X
ejpam-4645	152	3	=	=	PUNCT
ejpam-4645	152	4	a	a	DET
ejpam-4645	152	5	∪	∪	NOUN
ejpam-4645	152	6	[	[	X
ejpam-4645	152	7	∪uv∈e(g)suv	∪uv∈e(g)suv	NOUN
ejpam-4645	152	8	]	]	PUNCT
ejpam-4645	152	9	and	and	CCONJ
ejpam-4645	152	10	(	(	PUNCT
ejpam-4645	152	11	i	i	NOUN
ejpam-4645	152	12	)	)	PUNCT
ejpam-4645	152	13	holds	hold	VERB
ejpam-4645	152	14	.	.	PUNCT
ejpam-4645	153	1	let	let	VERB
ejpam-4645	153	2	xy	xy	PROPN
ejpam-4645	153	3	∈	∈	PROPN
ejpam-4645	153	4	e(g	e(g	PROPN
ejpam-4645	153	5	)	)	PUNCT
ejpam-4645	153	6	.	.	PUNCT
ejpam-4645	154	1	by	by	ADP
ejpam-4645	154	2	theorem	theorem	NOUN
ejpam-4645	154	3	2(ii)(a	2(ii)(a	NUM
ejpam-4645	154	4	)	)	PUNCT
ejpam-4645	154	5	,	,	PUNCT
ejpam-4645	154	6	sxy	sxy	PROPN
ejpam-4645	154	7	is	be	AUX
ejpam-4645	154	8	a	a	DET
ejpam-4645	154	9	locating	locating	NOUN
ejpam-4645	154	10	set	set	NOUN
ejpam-4645	154	11	of	of	ADP
ejpam-4645	154	12	hxy	hxy	NOUN
ejpam-4645	154	13	.	.	PUNCT
ejpam-4645	155	1	let	let	VERB
ejpam-4645	155	2	p	p	PROPN
ejpam-4645	155	3	∈	∈	PROPN
ejpam-4645	155	4	sxy	sxy	PROPN
ejpam-4645	155	5	.	.	PUNCT
ejpam-4645	156	1	then	then	ADV
ejpam-4645	156	2	by	by	ADP
ejpam-4645	156	3	assumption	assumption	NOUN
ejpam-4645	156	4	,	,	PUNCT
ejpam-4645	156	5	c	c	NOUN
ejpam-4645	156	6	\{p	\{p	NOUN
ejpam-4645	156	7	}	}	PUNCT
ejpam-4645	156	8	=	=	PUNCT
ejpam-4645	156	9	a∪	a∪	NOUN
ejpam-4645	157	1	[	[	X
ejpam-4645	157	2	∪uv∈[e(g)\{xy}]suv]∪	∪uv∈[e(g)\{xy}]suv]∪	NOUN
ejpam-4645	157	3	(	(	PUNCT
ejpam-4645	157	4	sxy	sxy	PROPN
ejpam-4645	157	5	\{p	\{p	PROPN
ejpam-4645	157	6	}	}	PUNCT
ejpam-4645	157	7	)	)	PUNCT
ejpam-4645	157	8	is	be	AUX
ejpam-4645	157	9	a	a	DET
ejpam-4645	157	10	locating	locate	VERB
ejpam-4645	157	11	-	-	PUNCT
ejpam-4645	157	12	dominating	dominate	VERB
ejpam-4645	157	13	set	set	NOUN
ejpam-4645	157	14	of	of	ADP
ejpam-4645	157	15	g⋄h	g⋄h	PROPN
ejpam-4645	157	16	.	.	PUNCT
ejpam-4645	158	1	it	it	PRON
ejpam-4645	158	2	follows	follow	VERB
ejpam-4645	158	3	from	from	ADP
ejpam-4645	158	4	theorem	theorem	NOUN
ejpam-4645	158	5	2(ii)(a	2(ii)(a	NUM
ejpam-4645	158	6	)	)	PUNCT
ejpam-4645	158	7	that	that	SCONJ
ejpam-4645	158	8	sxy	sxy	PROPN
ejpam-4645	158	9	\{p	\{p	PROPN
ejpam-4645	158	10	}	}	PUNCT
ejpam-4645	158	11	is	be	AUX
ejpam-4645	158	12	a	a	DET
ejpam-4645	158	13	locating	locating	NOUN
ejpam-4645	158	14	set	set	NOUN
ejpam-4645	158	15	of	of	ADP
ejpam-4645	158	16	hxy	hxy	NOUN
ejpam-4645	158	17	.	.	PUNCT
ejpam-4645	159	1	if	if	SCONJ
ejpam-4645	159	2	x	x	X
ejpam-4645	159	3	,	,	PUNCT
ejpam-4645	159	4	y	y	PROPN
ejpam-4645	159	5	/∈	/∈	PUNCT
ejpam-4645	160	1	a	a	PRON
ejpam-4645	160	2	,	,	PUNCT
ejpam-4645	160	3	then	then	ADV
ejpam-4645	160	4	sxy	sxy	PROPN
ejpam-4645	160	5	\	\	PROPN
ejpam-4645	161	1	{	{	PUNCT
ejpam-4645	161	2	p	p	X
ejpam-4645	161	3	}	}	PUNCT
ejpam-4645	161	4	is	be	AUX
ejpam-4645	161	5	a	a	DET
ejpam-4645	161	6	locating	locate	VERB
ejpam-4645	161	7	-	-	PUNCT
ejpam-4645	161	8	dominating	dominate	VERB
ejpam-4645	161	9	set	set	NOUN
ejpam-4645	161	10	of	of	ADP
ejpam-4645	161	11	hxy	hxy	NOUN
ejpam-4645	161	12	by	by	ADP
ejpam-4645	161	13	theorem	theorem	NOUN
ejpam-4645	161	14	2(ii)(b	2(ii)(b	NUM
ejpam-4645	161	15	)	)	PUNCT
ejpam-4645	161	16	.	.	PUNCT
ejpam-4645	162	1	if	if	SCONJ
ejpam-4645	162	2	one	one	NUM
ejpam-4645	162	3	of	of	ADP
ejpam-4645	162	4	x	x	X
ejpam-4645	162	5	and	and	CCONJ
ejpam-4645	162	6	y	y	PROPN
ejpam-4645	162	7	,	,	PUNCT
ejpam-4645	162	8	say	say	VERB
ejpam-4645	162	9	x	x	X
ejpam-4645	162	10	∈	∈	PROPN
ejpam-4645	162	11	l(g	l(g	PROPN
ejpam-4645	162	12	)	)	PUNCT
ejpam-4645	162	13	\	\	PROPN
ejpam-4645	163	1	a	a	PRON
ejpam-4645	163	2	,	,	PUNCT
ejpam-4645	163	3	then	then	ADV
ejpam-4645	163	4	sxy	sxy	PROPN
ejpam-4645	163	5	\	\	PROPN
ejpam-4645	163	6	{	{	PUNCT
ejpam-4645	163	7	p	p	X
ejpam-4645	163	8	}	}	PUNCT
ejpam-4645	163	9	is	be	AUX
ejpam-4645	163	10	a	a	DET
ejpam-4645	163	11	strictly	strictly	ADV
ejpam-4645	163	12	locating	locate	VERB
ejpam-4645	163	13	set	set	NOUN
ejpam-4645	163	14	of	of	ADP
ejpam-4645	163	15	hxy	hxy	NOUN
ejpam-4645	163	16	by	by	ADP
ejpam-4645	163	17	theorem	theorem	NOUN
ejpam-4645	163	18	2(ii)(c	2(ii)(c	NUM
ejpam-4645	163	19	)	)	PUNCT
ejpam-4645	163	20	.	.	PUNCT
ejpam-4645	164	1	morover	morover	PROPN
ejpam-4645	164	2	,	,	PUNCT
ejpam-4645	164	3	if	if	SCONJ
ejpam-4645	164	4	x	x	X
ejpam-4645	164	5	,	,	PUNCT
ejpam-4645	164	6	y	y	PROPN
ejpam-4645	164	7	/∈	/∈	PUNCT
ejpam-4645	165	1	a	a	PRON
ejpam-4645	165	2	and	and	CCONJ
ejpam-4645	165	3	x	x	SYM
ejpam-4645	165	4	∈	∈	PROPN
ejpam-4645	165	5	l(g	l(g	PROPN
ejpam-4645	165	6	)	)	PUNCT
ejpam-4645	165	7	or	or	CCONJ
ejpam-4645	165	8	y	y	PROPN
ejpam-4645	165	9	∈	∈	PROPN
ejpam-4645	165	10	l(g	l(g	PROPN
ejpam-4645	165	11	)	)	PUNCT
ejpam-4645	165	12	,	,	PUNCT
ejpam-4645	165	13	then	then	ADV
ejpam-4645	165	14	sxy	sxy	PROPN
ejpam-4645	165	15	is	be	AUX
ejpam-4645	165	16	a	a	DET
ejpam-4645	165	17	strictly	strictly	ADV
ejpam-4645	165	18	locating	locate	VERB
ejpam-4645	165	19	-	-	PUNCT
ejpam-4645	165	20	dominating	dominate	VERB
ejpam-4645	165	21	set	set	NOUN
ejpam-4645	165	22	of	of	ADP
ejpam-4645	165	23	hxy	hxy	NOUN
ejpam-4645	165	24	by	by	ADP
ejpam-4645	165	25	theorem	theorem	NOUN
ejpam-4645	165	26	2(ii)(d	2(ii)(d	NUM
ejpam-4645	165	27	)	)	PUNCT
ejpam-4645	165	28	.	.	PUNCT
ejpam-4645	166	1	therefore	therefore	ADV
ejpam-4645	166	2	,	,	PUNCT
ejpam-4645	166	3	(	(	PUNCT
ejpam-4645	166	4	a	a	X
ejpam-4645	166	5	)	)	PUNCT
ejpam-4645	166	6	,	,	PUNCT
ejpam-4645	166	7	(	(	PUNCT
ejpam-4645	166	8	b	b	NOUN
ejpam-4645	166	9	)	)	PUNCT
ejpam-4645	166	10	,	,	PUNCT
ejpam-4645	166	11	(	(	PUNCT
ejpam-4645	166	12	c	c	NOUN
ejpam-4645	166	13	)	)	PUNCT
ejpam-4645	166	14	,	,	PUNCT
ejpam-4645	166	15	and	and	CCONJ
ejpam-4645	166	16	(	(	PUNCT
ejpam-4645	166	17	d	d	X
ejpam-4645	166	18	)	)	PUNCT
ejpam-4645	166	19	hold	hold	VERB
ejpam-4645	166	20	.	.	PUNCT
ejpam-4645	167	1	next	next	ADV
ejpam-4645	167	2	,	,	PUNCT
ejpam-4645	167	3	let	let	VERB
ejpam-4645	167	4	w	w	PROPN
ejpam-4645	167	5	∈	∈	PROPN
ejpam-4645	167	6	a	a	PRON
ejpam-4645	167	7	and	and	CCONJ
ejpam-4645	167	8	let	let	VERB
ejpam-4645	167	9	z	z	PROPN
ejpam-4645	167	10	∈	∈	PROPN
ejpam-4645	167	11	ng(w	ng(w	NOUN
ejpam-4645	167	12	)	)	PUNCT
ejpam-4645	167	13	.	.	PUNCT
ejpam-4645	168	1	since	since	SCONJ
ejpam-4645	168	2	c	c	PROPN
ejpam-4645	168	3	is	be	AUX
ejpam-4645	168	4	a	a	DET
ejpam-4645	168	5	stable	stable	ADJ
ejpam-4645	168	6	locating	locating	NOUN
ejpam-4645	168	7	-	-	PUNCT
ejpam-4645	168	8	dominating	dominate	VERB
ejpam-4645	168	9	set	set	NOUN
ejpam-4645	168	10	of	of	ADP
ejpam-4645	168	11	g	g	PROPN
ejpam-4645	168	12	⋄h	⋄h	PROPN
ejpam-4645	168	13	,	,	PUNCT
ejpam-4645	168	14	c	c	NOUN
ejpam-4645	168	15	\	\	PROPN
ejpam-4645	168	16	{	{	PUNCT
ejpam-4645	168	17	w	w	NOUN
ejpam-4645	168	18	}	}	PUNCT
ejpam-4645	168	19	=	=	SYM
ejpam-4645	168	20	(	(	PUNCT
ejpam-4645	168	21	a	a	DET
ejpam-4645	168	22	\	\	PROPN
ejpam-4645	168	23	{	{	PUNCT
ejpam-4645	168	24	w	w	NOUN
ejpam-4645	168	25	}	}	PUNCT
ejpam-4645	168	26	)	)	PUNCT
ejpam-4645	168	27	∪	∪	ADP
ejpam-4645	168	28	[	[	X
ejpam-4645	168	29	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-4645	168	30	]	]	PUNCT
ejpam-4645	168	31	is	be	AUX
ejpam-4645	168	32	a	a	DET
ejpam-4645	168	33	locating	locate	VERB
ejpam-4645	168	34	-	-	PUNCT
ejpam-4645	168	35	dominating	dominate	VERB
ejpam-4645	168	36	set	set	NOUN
ejpam-4645	168	37	of	of	ADP
ejpam-4645	168	38	g⋄h	g⋄h	PROPN
ejpam-4645	168	39	.	.	PUNCT
ejpam-4645	169	1	it	it	PRON
ejpam-4645	169	2	follows	follow	VERB
ejpam-4645	169	3	from	from	ADP
ejpam-4645	169	4	(	(	PUNCT
ejpam-4645	169	5	c	c	NOUN
ejpam-4645	169	6	)	)	PUNCT
ejpam-4645	169	7	and	and	CCONJ
ejpam-4645	169	8	(	(	PUNCT
ejpam-4645	169	9	d	d	NOUN
ejpam-4645	169	10	)	)	PUNCT
ejpam-4645	169	11	of	of	ADP
ejpam-4645	169	12	theorem	theorem	NOUN
ejpam-4645	169	13	2	2	NUM
ejpam-4645	169	14	that	that	PRON
ejpam-4645	169	15	szw	szw	VERB
ejpam-4645	169	16	is	be	AUX
ejpam-4645	169	17	a	a	DET
ejpam-4645	169	18	strictly	strictly	ADV
ejpam-4645	169	19	locating	locate	VERB
ejpam-4645	169	20	set	set	NOUN
ejpam-4645	169	21	of	of	ADP
ejpam-4645	169	22	hzw	hzw	NOUN
ejpam-4645	169	23	whenever	whenever	SCONJ
ejpam-4645	169	24	w	w	PROPN
ejpam-4645	169	25	∈	∈	PROPN
ejpam-4645	169	26	l(g	l(g	PROPN
ejpam-4645	169	27	)	)	PUNCT
ejpam-4645	169	28	and	and	CCONJ
ejpam-4645	169	29	szw	szw	NOUN
ejpam-4645	169	30	is	be	AUX
ejpam-4645	169	31	a	a	DET
ejpam-4645	169	32	strictly	strictly	ADV
ejpam-4645	169	33	locating	locate	VERB
ejpam-4645	169	34	-	-	PUNCT
ejpam-4645	169	35	dominating	dominate	VERB
ejpam-4645	169	36	set	set	NOUN
ejpam-4645	169	37	of	of	ADP
ejpam-4645	169	38	hzw	hzw	NOUN
ejpam-4645	169	39	whenever	whenever	SCONJ
ejpam-4645	169	40	z	z	NOUN
ejpam-4645	169	41	/∈	/∈	PUNCT
ejpam-4645	170	1	a	a	DET
ejpam-4645	170	2	(	(	PUNCT
ejpam-4645	170	3	hence	hence	ADV
ejpam-4645	170	4	,	,	PUNCT
ejpam-4645	170	5	z	z	NOUN
ejpam-4645	170	6	/∈	/∈	PUNCT
ejpam-4645	171	1	a	a	DET
ejpam-4645	171	2	\	\	PROPN
ejpam-4645	171	3	{	{	PUNCT
ejpam-4645	171	4	w	w	NOUN
ejpam-4645	171	5	}	}	PUNCT
ejpam-4645	171	6	)	)	PUNCT
ejpam-4645	171	7	and	and	CCONJ
ejpam-4645	171	8	{	{	PUNCT
ejpam-4645	171	9	z	z	NOUN
ejpam-4645	171	10	,	,	PUNCT
ejpam-4645	171	11	w	w	NOUN
ejpam-4645	171	12	}	}	PUNCT
ejpam-4645	171	13	∩l(g	∩l(g	ADJ
ejpam-4645	171	14	)	)	PUNCT
ejpam-4645	171	15	̸=	̸=	PROPN
ejpam-4645	171	16	∅.	∅.	ADP
ejpam-4645	171	17	this	this	DET
ejpam-4645	171	18	shows	show	VERB
ejpam-4645	171	19	that	that	SCONJ
ejpam-4645	171	20	(	(	PUNCT
ejpam-4645	171	21	iii	iii	NOUN
ejpam-4645	171	22	)	)	PUNCT
ejpam-4645	171	23	holds	hold	VERB
ejpam-4645	171	24	.	.	PUNCT
ejpam-4645	172	1	finally	finally	ADV
ejpam-4645	172	2	,	,	PUNCT
ejpam-4645	172	3	let	let	VERB
ejpam-4645	172	4	zw	zw	PROPN
ejpam-4645	172	5	∈	∈	PROPN
ejpam-4645	172	6	e(g	e(g	PROPN
ejpam-4645	172	7	)	)	PUNCT
ejpam-4645	172	8	with	with	ADP
ejpam-4645	172	9	z	z	PROPN
ejpam-4645	172	10	∈	∈	PROPN
ejpam-4645	172	11	a	a	PRON
ejpam-4645	172	12	and	and	CCONJ
ejpam-4645	172	13	w	w	PROPN
ejpam-4645	172	14	/∈	/∈	NOUN
ejpam-4645	172	15	a.	a.	NOUN
ejpam-4645	172	16	let	let	VERB
ejpam-4645	172	17	p	p	X
ejpam-4645	172	18	∈	∈	PROPN
ejpam-4645	172	19	szw	szw	NOUN
ejpam-4645	172	20	.	.	PUNCT
ejpam-4645	173	1	then	then	ADV
ejpam-4645	173	2	,	,	PUNCT
ejpam-4645	173	3	again	again	ADV
ejpam-4645	173	4	,	,	PUNCT
ejpam-4645	173	5	c	c	PROPN
ejpam-4645	173	6	\	\	X
ejpam-4645	173	7	{	{	PUNCT
ejpam-4645	173	8	p	p	X
ejpam-4645	173	9	}	}	PUNCT
ejpam-4645	173	10	=	=	PUNCT
ejpam-4645	173	11	a	a	DET
ejpam-4645	173	12	∪	∪	NOUN
ejpam-4645	173	13	[	[	X
ejpam-4645	173	14	∪uv∈[e(g)\{zw}]suv	∪uv∈[e(g)\{zw}]suv	X
ejpam-4645	173	15	]	]	PUNCT
ejpam-4645	173	16	∪	∪	X
ejpam-4645	173	17	(	(	PUNCT
ejpam-4645	173	18	szw	szw	VERB
ejpam-4645	173	19	\	\	NOUN
ejpam-4645	173	20	{	{	PUNCT
ejpam-4645	173	21	p	p	NOUN
ejpam-4645	173	22	}	}	PUNCT
ejpam-4645	173	23	)	)	PUNCT
ejpam-4645	173	24	is	be	AUX
ejpam-4645	173	25	a	a	DET
ejpam-4645	173	26	locating	locate	VERB
ejpam-4645	173	27	-	-	PUNCT
ejpam-4645	173	28	dominating	dominate	VERB
ejpam-4645	173	29	set	set	NOUN
ejpam-4645	173	30	of	of	ADP
ejpam-4645	173	31	g	g	PROPN
ejpam-4645	173	32	⋄h	⋄h	PROPN
ejpam-4645	173	33	.	.	PUNCT
ejpam-4645	174	1	hence	hence	ADV
ejpam-4645	174	2	,	,	PUNCT
ejpam-4645	174	3	by	by	ADP
ejpam-4645	174	4	theorem	theorem	ADJ
ejpam-4645	174	5	2(iii	2(iii	NUM
ejpam-4645	174	6	)	)	PUNCT
ejpam-4645	174	7	,	,	PUNCT
ejpam-4645	174	8	statement	statement	NOUN
ejpam-4645	174	9	(	(	PUNCT
ejpam-4645	174	10	iv	iv	X
ejpam-4645	174	11	)	)	PUNCT
ejpam-4645	174	12	holds	hold	NOUN
ejpam-4645	174	13	.	.	PUNCT
ejpam-4645	175	1	for	for	ADP
ejpam-4645	175	2	the	the	DET
ejpam-4645	175	3	converse	converse	NOUN
ejpam-4645	175	4	,	,	PUNCT
ejpam-4645	175	5	suppose	suppose	VERB
ejpam-4645	175	6	that	that	SCONJ
ejpam-4645	175	7	c	c	PROPN
ejpam-4645	175	8	has	have	VERB
ejpam-4645	175	9	the	the	DET
ejpam-4645	175	10	given	give	VERB
ejpam-4645	175	11	form	form	NOUN
ejpam-4645	175	12	and	and	CCONJ
ejpam-4645	175	13	satisfies	satisfie	NOUN
ejpam-4645	175	14	(	(	PUNCT
ejpam-4645	175	15	i	i	NOUN
ejpam-4645	175	16	)	)	PUNCT
ejpam-4645	175	17	,	,	PUNCT
ejpam-4645	175	18	(	(	PUNCT
ejpam-4645	175	19	ii	ii	NOUN
ejpam-4645	175	20	)	)	PUNCT
ejpam-4645	175	21	,	,	PUNCT
ejpam-4645	175	22	(	(	PUNCT
ejpam-4645	175	23	iii	iii	NOUN
ejpam-4645	175	24	)	)	PUNCT
ejpam-4645	175	25	and	and	CCONJ
ejpam-4645	175	26	(	(	PUNCT
ejpam-4645	175	27	iv	iv	X
ejpam-4645	175	28	)	)	PUNCT
ejpam-4645	175	29	.	.	PUNCT
ejpam-4645	176	1	by	by	ADP
ejpam-4645	176	2	(	(	PUNCT
ejpam-4645	176	3	i	i	NOUN
ejpam-4645	176	4	)	)	PUNCT
ejpam-4645	176	5	and	and	CCONJ
ejpam-4645	176	6	(	(	PUNCT
ejpam-4645	176	7	ii	ii	NOUN
ejpam-4645	176	8	)	)	PUNCT
ejpam-4645	176	9	,	,	PUNCT
ejpam-4645	176	10	it	it	PRON
ejpam-4645	176	11	follows	follow	VERB
ejpam-4645	176	12	that	that	SCONJ
ejpam-4645	176	13	(	(	PUNCT
ejpam-4645	176	14	i	i	NOUN
ejpam-4645	176	15	)	)	PUNCT
ejpam-4645	176	16	and	and	CCONJ
ejpam-4645	176	17	(	(	PUNCT
ejpam-4645	176	18	ii	ii	NOUN
ejpam-4645	176	19	)	)	PUNCT
ejpam-4645	176	20	of	of	ADP
ejpam-4645	176	21	theorem	theorem	ADJ
ejpam-4645	176	22	2	2	NUM
ejpam-4645	176	23	are	be	AUX
ejpam-4645	176	24	satisfied	satisfied	ADJ
ejpam-4645	176	25	by	by	ADP
ejpam-4645	176	26	c.	c.	NOUN
ejpam-4645	176	27	let	let	VERB
ejpam-4645	176	28	zw	zw	PROPN
ejpam-4645	176	29	∈	∈	PROPN
ejpam-4645	176	30	e(g	e(g	PROPN
ejpam-4645	176	31	)	)	PUNCT
ejpam-4645	176	32	with	with	ADP
ejpam-4645	176	33	z	z	PROPN
ejpam-4645	176	34	∈	∈	PROPN
ejpam-4645	176	35	a	a	PRON
ejpam-4645	176	36	and	and	CCONJ
ejpam-4645	176	37	w	w	PROPN
ejpam-4645	176	38	/∈	/∈	NOUN
ejpam-4645	176	39	a.	a.	NOUN
ejpam-4645	176	40	let	let	VERB
ejpam-4645	176	41	x	x	PUNCT
ejpam-4645	176	42	∈	∈	PROPN
ejpam-4645	176	43	v	v	ADP
ejpam-4645	176	44	(	(	PUNCT
ejpam-4645	176	45	hzw	hzw	NOUN
ejpam-4645	176	46	)	)	PUNCT
ejpam-4645	176	47	\szw	\szw	VERB
ejpam-4645	176	48	.	.	PUNCT
ejpam-4645	177	1	then	then	ADV
ejpam-4645	177	2	x	x	SYM
ejpam-4645	177	3	∈	∈	PROPN
ejpam-4645	177	4	v	v	ADP
ejpam-4645	177	5	(	(	PUNCT
ejpam-4645	177	6	hzw	hzw	NOUN
ejpam-4645	177	7	)	)	PUNCT
ejpam-4645	177	8	\	\	PUNCT
ejpam-4645	178	1	[	[	X
ejpam-4645	178	2	szw	szw	VERB
ejpam-4645	178	3	\	\	NOUN
ejpam-4645	178	4	{	{	PUNCT
ejpam-4645	178	5	p	p	X
ejpam-4645	178	6	}	}	PUNCT
ejpam-4645	178	7	]	]	PUNCT
ejpam-4645	178	8	for	for	ADP
ejpam-4645	178	9	p	p	PROPN
ejpam-4645	178	10	∈	∈	PROPN
ejpam-4645	178	11	szw	szw	NOUN
ejpam-4645	178	12	.	.	PUNCT
ejpam-4645	178	13	suppose	suppose	VERB
ejpam-4645	178	14	nhzw(x	nhzw(x	ADJ
ejpam-4645	178	15	)	)	PUNCT
ejpam-4645	178	16	∩	∩	NOUN
ejpam-4645	178	17	szw	szw	VERB
ejpam-4645	178	18	=	=	PUNCT
ejpam-4645	178	19	∅.	∅.	NOUN
ejpam-4645	178	20	then	then	ADV
ejpam-4645	178	21	nhzw(x	nhzw(x	ADJ
ejpam-4645	178	22	)	)	PUNCT
ejpam-4645	178	23	∩	∩	NOUN
ejpam-4645	178	24	(	(	PUNCT
ejpam-4645	178	25	szw	szw	VERB
ejpam-4645	178	26	\	\	PROPN
ejpam-4645	178	27	{	{	PUNCT
ejpam-4645	178	28	p	p	NOUN
ejpam-4645	178	29	}	}	PUNCT
ejpam-4645	178	30	)	)	PUNCT
ejpam-4645	178	31	=	=	PUNCT
ejpam-4645	178	32	∅.	∅.	VERB
ejpam-4645	178	33	hence	hence	ADV
ejpam-4645	178	34	,	,	PUNCT
ejpam-4645	178	35	by	by	ADP
ejpam-4645	178	36	(	(	PUNCT
ejpam-4645	178	37	iv	iv	NOUN
ejpam-4645	178	38	)	)	PUNCT
ejpam-4645	178	39	,	,	PUNCT
ejpam-4645	178	40	for	for	ADP
ejpam-4645	178	41	each	each	DET
ejpam-4645	178	42	y	y	PROPN
ejpam-4645	178	43	∈	∈	PROPN
ejpam-4645	178	44	ng(z	ng(z	PROPN
ejpam-4645	178	45	)	)	PUNCT
ejpam-4645	178	46	\	\	PUNCT
ejpam-4645	178	47	{	{	PUNCT
ejpam-4645	178	48	w	w	NOUN
ejpam-4645	178	49	}	}	PUNCT
ejpam-4645	178	50	and	and	CCONJ
ejpam-4645	178	51	for	for	ADP
ejpam-4645	178	52	each	each	DET
ejpam-4645	178	53	q	q	PROPN
ejpam-4645	178	54	∈	∈	PROPN
ejpam-4645	178	55	v	v	NOUN
ejpam-4645	178	56	(	(	PUNCT
ejpam-4645	178	57	hyz	hyz	PROPN
ejpam-4645	178	58	)	)	PUNCT
ejpam-4645	178	59	\	\	PROPN
ejpam-4645	178	60	syz	syz	PROPN
ejpam-4645	178	61	,	,	PUNCT
ejpam-4645	178	62	it	it	PRON
ejpam-4645	178	63	holds	hold	VERB
ejpam-4645	178	64	that	that	SCONJ
ejpam-4645	178	65	y	y	PROPN
ejpam-4645	178	66	∈	∈	PROPN
ejpam-4645	178	67	a	a	PRON
ejpam-4645	178	68	or	or	CCONJ
ejpam-4645	178	69	g.	g.	PROPN
ejpam-4645	178	70	malacas	malacas	PROPN
ejpam-4645	178	71	,	,	PUNCT
ejpam-4645	178	72	s.	s.	PROPN
ejpam-4645	178	73	canoy	canoy	PROPN
ejpam-4645	178	74	,	,	PUNCT
ejpam-4645	178	75	jr	jr	PROPN
ejpam-4645	178	76	.	.	PROPN
ejpam-4645	178	77	,	,	PUNCT
ejpam-4645	178	78	e.	e.	PROPN
ejpam-4645	178	79	chacon	chacon	PROPN
ejpam-4645	178	80	/	/	SYM
ejpam-4645	178	81	eur	eur	PROPN
ejpam-4645	178	82	.	.	PUNCT
ejpam-4645	179	1	j.	j.	PROPN
ejpam-4645	179	2	pure	pure	PROPN
ejpam-4645	179	3	appl	appl	PROPN
ejpam-4645	179	4	.	.	PROPN
ejpam-4645	179	5	math	math	PROPN
ejpam-4645	179	6	,	,	PUNCT
ejpam-4645	179	7	16	16	NUM
ejpam-4645	179	8	(	(	PUNCT
ejpam-4645	179	9	1	1	NUM
ejpam-4645	179	10	)	)	PUNCT
ejpam-4645	179	11	(	(	PUNCT
ejpam-4645	179	12	2023	2023	NUM
ejpam-4645	179	13	)	)	PUNCT
ejpam-4645	179	14	,	,	PUNCT
ejpam-4645	179	15	479	479	NUM
ejpam-4645	179	16	-	-	SYM
ejpam-4645	179	17	490	490	NUM
ejpam-4645	179	18	485	485	NUM
ejpam-4645	179	19	nhyz(q	nhyz(q	NUM
ejpam-4645	179	20	)	)	PUNCT
ejpam-4645	179	21	∩	∩	NOUN
ejpam-4645	179	22	syz	syz	VERB
ejpam-4645	179	23	̸=	̸=	PROPN
ejpam-4645	179	24	∅.	∅.	ADV
ejpam-4645	179	25	thus	thus	ADV
ejpam-4645	179	26	,	,	PUNCT
ejpam-4645	179	27	(	(	PUNCT
ejpam-4645	179	28	iii	iii	NOUN
ejpam-4645	179	29	)	)	PUNCT
ejpam-4645	179	30	of	of	ADP
ejpam-4645	179	31	theorem	theorem	NOUN
ejpam-4645	179	32	2	2	NUM
ejpam-4645	179	33	also	also	ADV
ejpam-4645	179	34	holds	hold	VERB
ejpam-4645	179	35	for	for	ADP
ejpam-4645	179	36	c.	c.	NOUN
ejpam-4645	179	37	therefore	therefore	ADV
ejpam-4645	179	38	,	,	PUNCT
ejpam-4645	179	39	c	c	PROPN
ejpam-4645	179	40	is	be	AUX
ejpam-4645	179	41	a	a	DET
ejpam-4645	179	42	locating	locate	VERB
ejpam-4645	179	43	dominating	dominating	NOUN
ejpam-4645	179	44	set	set	NOUN
ejpam-4645	179	45	of	of	ADP
ejpam-4645	179	46	g	g	PROPN
ejpam-4645	179	47	⋄h	⋄h	PROPN
ejpam-4645	179	48	.	.	PUNCT
ejpam-4645	180	1	let	let	VERB
ejpam-4645	180	2	q	q	PROPN
ejpam-4645	180	3	∈	∈	PROPN
ejpam-4645	180	4	c	c	NOUN
ejpam-4645	180	5	and	and	CCONJ
ejpam-4645	180	6	let	let	VERB
ejpam-4645	180	7	uv	uv	PRON
ejpam-4645	180	8	∈	∈	PROPN
ejpam-4645	180	9	e(g	e(g	PROPN
ejpam-4645	180	10	)	)	PUNCT
ejpam-4645	180	11	such	such	ADJ
ejpam-4645	180	12	that	that	DET
ejpam-4645	180	13	q	q	PROPN
ejpam-4645	180	14	∈	∈	PROPN
ejpam-4645	180	15	v	v	NOUN
ejpam-4645	180	16	(	(	PUNCT
ejpam-4645	180	17	⟨{u	⟨{u	PROPN
ejpam-4645	180	18	,	,	PUNCT
ejpam-4645	180	19	v}⟩+huv	v}⟩+huv	PROPN
ejpam-4645	180	20	)	)	PUNCT
ejpam-4645	180	21	.	.	PUNCT
ejpam-4645	181	1	suppose	suppose	VERB
ejpam-4645	181	2	first	first	ADV
ejpam-4645	181	3	that	that	SCONJ
ejpam-4645	181	4	p	p	PROPN
ejpam-4645	181	5	∈	∈	PROPN
ejpam-4645	181	6	{	{	PUNCT
ejpam-4645	181	7	u	u	NOUN
ejpam-4645	181	8	,	,	PUNCT
ejpam-4645	181	9	v	v	NOUN
ejpam-4645	181	10	}	}	PUNCT
ejpam-4645	181	11	.	.	PUNCT
ejpam-4645	182	1	then	then	ADV
ejpam-4645	182	2	c∗	c∗	PROPN
ejpam-4645	182	3	=	=	PUNCT
ejpam-4645	182	4	c	c	NOUN
ejpam-4645	182	5	\	\	PROPN
ejpam-4645	182	6	{	{	PUNCT
ejpam-4645	182	7	p	p	X
ejpam-4645	182	8	}	}	PUNCT
ejpam-4645	182	9	=	=	SYM
ejpam-4645	182	10	(	(	PUNCT
ejpam-4645	182	11	a	a	DET
ejpam-4645	182	12	\	\	X
ejpam-4645	182	13	{	{	PUNCT
ejpam-4645	182	14	p	p	NOUN
ejpam-4645	182	15	}	}	PUNCT
ejpam-4645	182	16	)	)	PUNCT
ejpam-4645	182	17	∪	∪	ADP
ejpam-4645	182	18	[	[	PUNCT
ejpam-4645	182	19	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-4645	182	20	]	]	PUNCT
ejpam-4645	182	21	.	.	PUNCT
ejpam-4645	183	1	accordingly	accordingly	ADV
ejpam-4645	183	2	,	,	PUNCT
ejpam-4645	183	3	c	c	PROPN
ejpam-4645	183	4	is	be	AUX
ejpam-4645	183	5	a	a	DET
ejpam-4645	183	6	stable	stable	ADJ
ejpam-4645	183	7	locating	locating	NOUN
ejpam-4645	183	8	-	-	PUNCT
ejpam-4645	183	9	dominating	dominate	VERB
ejpam-4645	183	10	set	set	NOUN
ejpam-4645	183	11	of	of	ADP
ejpam-4645	183	12	g	g	PROPN
ejpam-4645	183	13	⋄h	⋄h	PROPN
ejpam-4645	183	14	.	.	PUNCT
ejpam-4645	184	1	the	the	DET
ejpam-4645	184	2	next	next	ADJ
ejpam-4645	184	3	two	two	NUM
ejpam-4645	184	4	results	result	NOUN
ejpam-4645	184	5	follow	follow	VERB
ejpam-4645	184	6	from	from	ADP
ejpam-4645	184	7	theorem	theorem	ADJ
ejpam-4645	184	8	3	3	NUM
ejpam-4645	184	9	.	.	PUNCT
ejpam-4645	184	10	corollary	corollary	ADJ
ejpam-4645	184	11	2	2	NUM
ejpam-4645	184	12	.	.	PUNCT
ejpam-4645	185	1	let	let	VERB
ejpam-4645	185	2	g	g	PRON
ejpam-4645	185	3	be	be	AUX
ejpam-4645	185	4	a	a	DET
ejpam-4645	185	5	connected	connected	ADJ
ejpam-4645	185	6	graph	graph	NOUN
ejpam-4645	185	7	of	of	ADP
ejpam-4645	185	8	orderm	orderm	NOUN
ejpam-4645	185	9	≥	≥	NOUN
ejpam-4645	185	10	3	3	NUM
ejpam-4645	185	11	with	with	ADP
ejpam-4645	185	12	l(g	l(g	NOUN
ejpam-4645	185	13	)	)	PUNCT
ejpam-4645	186	1	=	=	SYM
ejpam-4645	186	2	∅	∅	NOUN
ejpam-4645	186	3	and	and	CCONJ
ejpam-4645	186	4	leth	leth	PROPN
ejpam-4645	186	5	be	be	VERB
ejpam-4645	186	6	any	any	DET
ejpam-4645	186	7	non	non	ADJ
ejpam-4645	186	8	-	-	ADJ
ejpam-4645	186	9	trivial	trivial	ADJ
ejpam-4645	186	10	connected	connected	ADJ
ejpam-4645	186	11	graph	graph	NOUN
ejpam-4645	186	12	.	.	PUNCT
ejpam-4645	187	1	if	if	SCONJ
ejpam-4645	187	2	c	c	NOUN
ejpam-4645	187	3	=	=	SYM
ejpam-4645	187	4	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-4645	187	5	and	and	CCONJ
ejpam-4645	187	6	suv	suv	PROPN
ejpam-4645	187	7	is	be	AUX
ejpam-4645	187	8	a	a	DET
ejpam-4645	187	9	stable	stable	ADJ
ejpam-4645	187	10	locating	locating	NOUN
ejpam-4645	187	11	-	-	PUNCT
ejpam-4645	187	12	dominating	dominate	VERB
ejpam-4645	187	13	set	set	NOUN
ejpam-4645	187	14	of	of	ADP
ejpam-4645	187	15	huv	huv	PROPN
ejpam-4645	187	16	for	for	ADP
ejpam-4645	187	17	each	each	DET
ejpam-4645	187	18	uv	uv	PROPN
ejpam-4645	187	19	∈	∈	PROPN
ejpam-4645	187	20	e(g	e(g	PROPN
ejpam-4645	187	21	)	)	PUNCT
ejpam-4645	187	22	,	,	PUNCT
ejpam-4645	187	23	then	then	ADV
ejpam-4645	187	24	c	c	PROPN
ejpam-4645	187	25	is	be	AUX
ejpam-4645	187	26	a	a	DET
ejpam-4645	187	27	stable	stable	ADJ
ejpam-4645	187	28	locating	locating	NOUN
ejpam-4645	187	29	-	-	PUNCT
ejpam-4645	187	30	dominating	dominate	VERB
ejpam-4645	187	31	set	set	NOUN
ejpam-4645	187	32	of	of	ADP
ejpam-4645	187	33	g	g	PROPN
ejpam-4645	187	34	⋄h	⋄h	PROPN
ejpam-4645	187	35	.	.	PUNCT
ejpam-4645	188	1	in	in	ADP
ejpam-4645	188	2	particular	particular	ADJ
ejpam-4645	188	3	,	,	PUNCT
ejpam-4645	188	4	γsl(g	γsl(g	PROPN
ejpam-4645	188	5	⋄h	⋄h	PROPN
ejpam-4645	188	6	)	)	PUNCT
ejpam-4645	188	7	≤	≤	NUM
ejpam-4645	188	8	|e(g)|γsl(h	|e(g)|γsl(h	PROPN
ejpam-4645	188	9	)	)	PUNCT
ejpam-4645	188	10	.	.	PUNCT
ejpam-4645	189	1	proof	proof	NOUN
ejpam-4645	189	2	.	.	PUNCT
ejpam-4645	190	1	since	since	SCONJ
ejpam-4645	190	2	l(g	l(g	NOUN
ejpam-4645	190	3	)	)	PUNCT
ejpam-4645	190	4	=	=	SYM
ejpam-4645	190	5	∅	∅	NOUN
ejpam-4645	190	6	and	and	CCONJ
ejpam-4645	190	7	suv	suv	PROPN
ejpam-4645	190	8	is	be	AUX
ejpam-4645	190	9	a	a	DET
ejpam-4645	190	10	stable	stable	ADJ
ejpam-4645	190	11	locating	locating	NOUN
ejpam-4645	190	12	-	-	PUNCT
ejpam-4645	190	13	dominating	dominate	VERB
ejpam-4645	190	14	set	set	NOUN
ejpam-4645	190	15	of	of	ADP
ejpam-4645	190	16	huv	huv	PROPN
ejpam-4645	190	17	for	for	ADP
ejpam-4645	190	18	each	each	DET
ejpam-4645	190	19	uv	uv	PROPN
ejpam-4645	190	20	∈	∈	PROPN
ejpam-4645	190	21	e(g	e(g	PROPN
ejpam-4645	190	22	)	)	PUNCT
ejpam-4645	190	23	,	,	PUNCT
ejpam-4645	190	24	c	c	NOUN
ejpam-4645	190	25	=	=	PUNCT
ejpam-4645	190	26	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-4645	190	27	satisfies	satisfy	VERB
ejpam-4645	190	28	the	the	DET
ejpam-4645	190	29	conditions	condition	NOUN
ejpam-4645	190	30	in	in	ADP
ejpam-4645	190	31	theorem	theorem	NOUN
ejpam-4645	190	32	3	3	NUM
ejpam-4645	190	33	.	.	PUNCT
ejpam-4645	191	1	thus	thus	ADV
ejpam-4645	191	2	,	,	PUNCT
ejpam-4645	191	3	c	c	PROPN
ejpam-4645	191	4	is	be	AUX
ejpam-4645	191	5	a	a	DET
ejpam-4645	191	6	stable	stable	ADJ
ejpam-4645	191	7	locating	locating	NOUN
ejpam-4645	191	8	-	-	PUNCT
ejpam-4645	191	9	dominating	dominate	VERB
ejpam-4645	191	10	set	set	NOUN
ejpam-4645	191	11	of	of	ADP
ejpam-4645	191	12	g	g	PROPN
ejpam-4645	191	13	⋄h	⋄h	PROPN
ejpam-4645	191	14	and	and	CCONJ
ejpam-4645	191	15	γsl(g	γsl(g	NUM
ejpam-4645	191	16	⋄h	⋄h	PROPN
ejpam-4645	191	17	)	)	PUNCT
ejpam-4645	191	18	≤	≤	PROPN
ejpam-4645	191	19	|c|	|c|	PROPN
ejpam-4645	191	20	=	=	SYM
ejpam-4645	191	21	|e(g)|γsl(h	|e(g)|γsl(h	PROPN
ejpam-4645	191	22	)	)	PUNCT
ejpam-4645	191	23	.	.	PUNCT
ejpam-4645	192	1	corollary	corollary	ADJ
ejpam-4645	192	2	3	3	X
ejpam-4645	192	3	.	.	PUNCT
ejpam-4645	193	1	let	let	VERB
ejpam-4645	193	2	g	g	PRON
ejpam-4645	193	3	be	be	AUX
ejpam-4645	193	4	a	a	DET
ejpam-4645	193	5	connected	connected	ADJ
ejpam-4645	193	6	graph	graph	NOUN
ejpam-4645	193	7	of	of	ADP
ejpam-4645	193	8	order	order	NOUN
ejpam-4645	193	9	m	m	VERB
ejpam-4645	193	10	≥	≥	NOUN
ejpam-4645	193	11	3	3	NUM
ejpam-4645	193	12	with	with	ADP
ejpam-4645	193	13	l(g	l(g	PROPN
ejpam-4645	193	14	)	)	PUNCT
ejpam-4645	193	15	̸=	̸=	PROPN
ejpam-4645	193	16	∅	∅	NOUN
ejpam-4645	193	17	and	and	CCONJ
ejpam-4645	193	18	let	let	VERB
ejpam-4645	193	19	h	h	NOUN
ejpam-4645	193	20	be	be	AUX
ejpam-4645	193	21	any	any	DET
ejpam-4645	193	22	non	non	ADJ
ejpam-4645	193	23	-	-	ADJ
ejpam-4645	193	24	trivial	trivial	ADJ
ejpam-4645	193	25	connected	connected	ADJ
ejpam-4645	193	26	graph	graph	NOUN
ejpam-4645	193	27	with	with	ADP
ejpam-4645	193	28	γ(h	γ(h	NOUN
ejpam-4645	193	29	)	)	PUNCT
ejpam-4645	193	30	̸=	̸=	PROPN
ejpam-4645	193	31	1	1	NUM
ejpam-4645	193	32	.	.	PUNCT
ejpam-4645	194	1	if	if	SCONJ
ejpam-4645	194	2	c	c	NOUN
ejpam-4645	194	3	=	=	SYM
ejpam-4645	194	4	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-4645	194	5	and	and	CCONJ
ejpam-4645	194	6	suv	suv	PROPN
ejpam-4645	194	7	is	be	AUX
ejpam-4645	194	8	a	a	DET
ejpam-4645	194	9	stable	stable	ADJ
ejpam-4645	194	10	strictly	strictly	ADV
ejpam-4645	194	11	locating	locate	VERB
ejpam-4645	194	12	-	-	PUNCT
ejpam-4645	194	13	dominating	dominate	VERB
ejpam-4645	194	14	set	set	NOUN
ejpam-4645	194	15	of	of	ADP
ejpam-4645	194	16	huv	huv	PROPN
ejpam-4645	194	17	for	for	ADP
ejpam-4645	194	18	each	each	DET
ejpam-4645	194	19	uv	uv	PROPN
ejpam-4645	194	20	∈	∈	PROPN
ejpam-4645	194	21	e(g	e(g	PROPN
ejpam-4645	194	22	)	)	PUNCT
ejpam-4645	194	23	,	,	PUNCT
ejpam-4645	194	24	then	then	ADV
ejpam-4645	194	25	c	c	PROPN
ejpam-4645	194	26	is	be	AUX
ejpam-4645	194	27	a	a	DET
ejpam-4645	194	28	stable	stable	ADJ
ejpam-4645	194	29	locating	locating	NOUN
ejpam-4645	194	30	-	-	PUNCT
ejpam-4645	194	31	dominating	dominate	VERB
ejpam-4645	194	32	set	set	NOUN
ejpam-4645	194	33	of	of	ADP
ejpam-4645	194	34	g	g	PROPN
ejpam-4645	194	35	⋄h	⋄h	PROPN
ejpam-4645	194	36	.	.	PUNCT
ejpam-4645	195	1	moreover	moreover	ADV
ejpam-4645	195	2	,	,	PUNCT
ejpam-4645	195	3	γsl(g	γsl(g	PROPN
ejpam-4645	195	4	⋄h	⋄h	PROPN
ejpam-4645	195	5	)	)	PUNCT
ejpam-4645	195	6	≤	≤	PROPN
ejpam-4645	195	7	|c|	|c|	PROPN
ejpam-4645	195	8	=	=	SYM
ejpam-4645	195	9	|e(g)|γssl(h	|e(g)|γssl(h	PROPN
ejpam-4645	195	10	)	)	PUNCT
ejpam-4645	195	11	.	.	PUNCT
ejpam-4645	196	1	proof	proof	NOUN
ejpam-4645	196	2	.	.	PUNCT
ejpam-4645	197	1	by	by	ADP
ejpam-4645	197	2	theorem	theorem	NOUN
ejpam-4645	197	3	1	1	NUM
ejpam-4645	197	4	and	and	CCONJ
ejpam-4645	197	5	the	the	DET
ejpam-4645	197	6	assumption	assumption	NOUN
ejpam-4645	197	7	that	that	SCONJ
ejpam-4645	197	8	γ(h	γ(h	NOUN
ejpam-4645	197	9	)	)	PUNCT
ejpam-4645	197	10	̸=	̸=	PROPN
ejpam-4645	197	11	1	1	NUM
ejpam-4645	197	12	,	,	PUNCT
ejpam-4645	197	13	h	h	NOUN
ejpam-4645	197	14	admits	admit	VERB
ejpam-4645	197	15	a	a	DET
ejpam-4645	197	16	stable	stable	ADJ
ejpam-4645	197	17	strictly	strictly	ADV
ejpam-4645	197	18	locating	locate	VERB
ejpam-4645	197	19	-	-	PUNCT
ejpam-4645	197	20	dominating	dominating	NOUN
ejpam-4645	197	21	set	set	NOUN
ejpam-4645	197	22	.	.	PUNCT
ejpam-4645	198	1	since	since	SCONJ
ejpam-4645	198	2	suv	suv	PROPN
ejpam-4645	198	3	is	be	AUX
ejpam-4645	198	4	a	a	DET
ejpam-4645	198	5	stable	stable	ADJ
ejpam-4645	198	6	strictly	strictly	ADV
ejpam-4645	198	7	locating	locate	VERB
ejpam-4645	198	8	-	-	PUNCT
ejpam-4645	198	9	dominating	dominate	VERB
ejpam-4645	198	10	set	set	NOUN
ejpam-4645	198	11	of	of	ADP
ejpam-4645	198	12	huv	huv	PROPN
ejpam-4645	198	13	for	for	ADP
ejpam-4645	198	14	each	each	DET
ejpam-4645	198	15	uv	uv	PROPN
ejpam-4645	198	16	∈	∈	PROPN
ejpam-4645	198	17	e(g	e(g	PROPN
ejpam-4645	198	18	)	)	PUNCT
ejpam-4645	198	19	and	and	CCONJ
ejpam-4645	198	20	l(g	l(g	PROPN
ejpam-4645	198	21	)	)	PUNCT
ejpam-4645	198	22	̸=	̸=	NOUN
ejpam-4645	198	23	∅	∅	NOUN
ejpam-4645	198	24	,	,	PUNCT
ejpam-4645	198	25	c	c	NOUN
ejpam-4645	198	26	=	=	SYM
ejpam-4645	198	27	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-4645	198	28	satisfies	satisfy	VERB
ejpam-4645	198	29	the	the	DET
ejpam-4645	198	30	conditions	condition	NOUN
ejpam-4645	198	31	in	in	ADP
ejpam-4645	198	32	theorem	theorem	NOUN
ejpam-4645	198	33	3	3	NUM
ejpam-4645	198	34	.	.	PUNCT
ejpam-4645	199	1	hence	hence	ADV
ejpam-4645	199	2	,	,	PUNCT
ejpam-4645	199	3	c	c	PROPN
ejpam-4645	199	4	is	be	AUX
ejpam-4645	199	5	a	a	DET
ejpam-4645	199	6	stable	stable	ADJ
ejpam-4645	199	7	locating	locating	NOUN
ejpam-4645	199	8	-	-	PUNCT
ejpam-4645	199	9	dominating	dominate	VERB
ejpam-4645	199	10	set	set	NOUN
ejpam-4645	199	11	of	of	ADP
ejpam-4645	199	12	g	g	PROPN
ejpam-4645	199	13	⋄	⋄	PROPN
ejpam-4645	199	14	h	h	NOUN
ejpam-4645	199	15	and	and	CCONJ
ejpam-4645	199	16	γsl(g	γsl(g	PROPN
ejpam-4645	199	17	⋄	⋄	PROPN
ejpam-4645	199	18	h	h	NOUN
ejpam-4645	199	19	)	)	PUNCT
ejpam-4645	199	20	≤	≤	NOUN
ejpam-4645	199	21	|c|	|c|	PROPN
ejpam-4645	199	22	=	=	SYM
ejpam-4645	199	23	|e(g)|γssl(h	|e(g)|γssl(h	PROPN
ejpam-4645	199	24	)	)	PUNCT
ejpam-4645	199	25	.	.	PUNCT
ejpam-4645	200	1	the	the	DET
ejpam-4645	200	2	next	next	ADJ
ejpam-4645	200	3	result	result	NOUN
ejpam-4645	200	4	is	be	AUX
ejpam-4645	200	5	found	find	VERB
ejpam-4645	200	6	in	in	ADP
ejpam-4645	200	7	[	[	X
ejpam-4645	200	8	15	15	NUM
ejpam-4645	200	9	]	]	PUNCT
ejpam-4645	200	10	.	.	PUNCT
ejpam-4645	201	1	theorem	theorem	ADJ
ejpam-4645	201	2	4	4	NUM
ejpam-4645	201	3	.	.	PUNCT
ejpam-4645	202	1	let	let	VERB
ejpam-4645	202	2	g	g	NOUN
ejpam-4645	202	3	and	and	CCONJ
ejpam-4645	202	4	h	h	PROPN
ejpam-4645	202	5	be	be	VERB
ejpam-4645	202	6	non	non	ADJ
ejpam-4645	202	7	-	-	ADJ
ejpam-4645	202	8	trivial	trivial	ADJ
ejpam-4645	202	9	connected	connected	ADJ
ejpam-4645	202	10	graphs	graph	NOUN
ejpam-4645	202	11	such	such	ADJ
ejpam-4645	202	12	that	that	DET
ejpam-4645	202	13	∆(h	∆(h	NOUN
ejpam-4645	202	14	)	)	PUNCT
ejpam-4645	202	15	≤	≤	NOUN
ejpam-4645	202	16	|v	|v	X
ejpam-4645	202	17	(	(	PUNCT
ejpam-4645	202	18	h)|−2	h)|−2	PROPN
ejpam-4645	202	19	.	.	PUNCT
ejpam-4645	203	1	then	then	ADV
ejpam-4645	203	2	c	c	X
ejpam-4645	203	3	=	=	PUNCT
ejpam-4645	203	4	⋃	⋃	PROPN
ejpam-4645	203	5	x∈s	x∈s	NOUN
ejpam-4645	203	6	(	(	PUNCT
ejpam-4645	203	7	{	{	PUNCT
ejpam-4645	203	8	x	x	NOUN
ejpam-4645	203	9	}	}	PUNCT
ejpam-4645	203	10	×	×	PROPN
ejpam-4645	203	11	tx	tx	PROPN
ejpam-4645	203	12	)	)	PUNCT
ejpam-4645	203	13	,	,	PUNCT
ejpam-4645	203	14	where	where	SCONJ
ejpam-4645	203	15	s	s	VERB
ejpam-4645	203	16	⊆	⊆	NUM
ejpam-4645	203	17	v	v	NOUN
ejpam-4645	203	18	(	(	PUNCT
ejpam-4645	203	19	g	g	NOUN
ejpam-4645	203	20	)	)	PUNCT
ejpam-4645	203	21	and	and	CCONJ
ejpam-4645	203	22	tx	tx	VERB
ejpam-4645	203	23	⊆	⊆	NUM
ejpam-4645	203	24	v	v	NOUN
ejpam-4645	203	25	(	(	PUNCT
ejpam-4645	203	26	h	h	NOUN
ejpam-4645	203	27	)	)	PUNCT
ejpam-4645	203	28	for	for	ADP
ejpam-4645	203	29	each	each	DET
ejpam-4645	203	30	x	x	SYM
ejpam-4645	203	31	∈	∈	PROPN
ejpam-4645	203	32	s	s	NOUN
ejpam-4645	203	33	,	,	PUNCT
ejpam-4645	203	34	is	be	AUX
ejpam-4645	203	35	a	a	DET
ejpam-4645	203	36	locatingdominating	locatingdominating	NOUN
ejpam-4645	203	37	set	set	NOUN
ejpam-4645	203	38	of	of	ADP
ejpam-4645	203	39	g	g	PROPN
ejpam-4645	204	1	[	[	X
ejpam-4645	204	2	h	h	X
ejpam-4645	204	3	]	]	X
ejpam-4645	204	4	if	if	SCONJ
ejpam-4645	204	5	and	and	CCONJ
ejpam-4645	204	6	only	only	ADV
ejpam-4645	204	7	if	if	SCONJ
ejpam-4645	204	8	the	the	DET
ejpam-4645	204	9	following	follow	VERB
ejpam-4645	204	10	hold	hold	NOUN
ejpam-4645	204	11	.	.	PUNCT
ejpam-4645	205	1	(	(	PUNCT
ejpam-4645	205	2	i	i	NOUN
ejpam-4645	205	3	)	)	PUNCT
ejpam-4645	205	4	s	s	PART
ejpam-4645	205	5	=	=	SYM
ejpam-4645	205	6	v	v	NOUN
ejpam-4645	205	7	(	(	PUNCT
ejpam-4645	205	8	g	g	NOUN
ejpam-4645	205	9	)	)	PUNCT
ejpam-4645	205	10	.	.	PUNCT
ejpam-4645	206	1	(	(	PUNCT
ejpam-4645	206	2	ii	ii	NOUN
ejpam-4645	206	3	)	)	PUNCT
ejpam-4645	206	4	tx	tx	PROPN
ejpam-4645	206	5	is	be	AUX
ejpam-4645	206	6	a	a	DET
ejpam-4645	206	7	locating	locating	NOUN
ejpam-4645	206	8	set	set	VERB
ejpam-4645	206	9	in	in	ADP
ejpam-4645	206	10	h	h	NOUN
ejpam-4645	206	11	for	for	ADP
ejpam-4645	206	12	every	every	DET
ejpam-4645	206	13	x	x	SYM
ejpam-4645	206	14	∈	∈	PROPN
ejpam-4645	206	15	v	v	NOUN
ejpam-4645	206	16	(	(	PUNCT
ejpam-4645	206	17	g	g	NOUN
ejpam-4645	206	18	)	)	PUNCT
ejpam-4645	206	19	.	.	PUNCT
ejpam-4645	207	1	(	(	PUNCT
ejpam-4645	207	2	iii	iii	X
ejpam-4645	207	3	)	)	PUNCT
ejpam-4645	207	4	tx	tx	NOUN
ejpam-4645	207	5	or	or	CCONJ
ejpam-4645	207	6	ty	ty	INTJ
ejpam-4645	207	7	is	be	AUX
ejpam-4645	207	8	strictly	strictly	ADV
ejpam-4645	207	9	locating	locate	VERB
ejpam-4645	207	10	in	in	ADP
ejpam-4645	207	11	h	h	NOUN
ejpam-4645	207	12	whenever	whenever	SCONJ
ejpam-4645	207	13	x	x	PRON
ejpam-4645	207	14	and	and	CCONJ
ejpam-4645	207	15	y	y	PROPN
ejpam-4645	207	16	are	be	AUX
ejpam-4645	207	17	adjacent	adjacent	ADJ
ejpam-4645	207	18	vertices	vertex	NOUN
ejpam-4645	207	19	of	of	ADP
ejpam-4645	207	20	g	g	NOUN
ejpam-4645	207	21	with	with	ADP
ejpam-4645	207	22	ng[x	ng[x	PROPN
ejpam-4645	207	23	]	]	X
ejpam-4645	207	24	=	=	PUNCT
ejpam-4645	207	25	ng[y	ng[y	PROPN
ejpam-4645	207	26	]	]	PUNCT
ejpam-4645	207	27	.	.	PUNCT
ejpam-4645	208	1	g.	g.	PROPN
ejpam-4645	208	2	malacas	malacas	PROPN
ejpam-4645	208	3	,	,	PUNCT
ejpam-4645	208	4	s.	s.	PROPN
ejpam-4645	208	5	canoy	canoy	PROPN
ejpam-4645	208	6	,	,	PUNCT
ejpam-4645	208	7	jr	jr	PROPN
ejpam-4645	208	8	.	.	PROPN
ejpam-4645	208	9	,	,	PUNCT
ejpam-4645	208	10	e.	e.	PROPN
ejpam-4645	208	11	chacon	chacon	PROPN
ejpam-4645	208	12	/	/	SYM
ejpam-4645	208	13	eur	eur	PROPN
ejpam-4645	208	14	.	.	PUNCT
ejpam-4645	209	1	j.	j.	PROPN
ejpam-4645	209	2	pure	pure	PROPN
ejpam-4645	209	3	appl	appl	PROPN
ejpam-4645	209	4	.	.	PROPN
ejpam-4645	209	5	math	math	PROPN
ejpam-4645	209	6	,	,	PUNCT
ejpam-4645	209	7	16	16	NUM
ejpam-4645	209	8	(	(	PUNCT
ejpam-4645	209	9	1	1	NUM
ejpam-4645	209	10	)	)	PUNCT
ejpam-4645	209	11	(	(	PUNCT
ejpam-4645	209	12	2023	2023	NUM
ejpam-4645	209	13	)	)	PUNCT
ejpam-4645	209	14	,	,	PUNCT
ejpam-4645	209	15	479	479	NUM
ejpam-4645	209	16	-	-	SYM
ejpam-4645	209	17	490	490	NUM
ejpam-4645	209	18	486	486	NUM
ejpam-4645	209	19	(	(	PUNCT
ejpam-4645	209	20	iv	iv	X
ejpam-4645	209	21	)	)	PUNCT
ejpam-4645	209	22	tx	tx	NOUN
ejpam-4645	209	23	or	or	CCONJ
ejpam-4645	209	24	ty	ty	INTJ
ejpam-4645	209	25	is	be	AUX
ejpam-4645	209	26	a	a	DET
ejpam-4645	209	27	dominating	dominating	NOUN
ejpam-4645	209	28	set	set	VERB
ejpam-4645	209	29	in	in	ADP
ejpam-4645	209	30	h	h	NOUN
ejpam-4645	209	31	whenever	whenever	SCONJ
ejpam-4645	209	32	x	x	PRON
ejpam-4645	209	33	and	and	CCONJ
ejpam-4645	209	34	y	y	PROPN
ejpam-4645	209	35	are	be	AUX
ejpam-4645	209	36	distinct	distinct	ADJ
ejpam-4645	209	37	non	non	ADJ
ejpam-4645	209	38	-	-	ADJ
ejpam-4645	209	39	adjacent	adjacent	ADJ
ejpam-4645	209	40	vertices	vertex	NOUN
ejpam-4645	209	41	of	of	ADP
ejpam-4645	209	42	g	g	NOUN
ejpam-4645	209	43	with	with	ADP
ejpam-4645	209	44	ng(x	ng(x	NUM
ejpam-4645	209	45	)	)	PUNCT
ejpam-4645	209	46	=	=	PUNCT
ejpam-4645	209	47	ng(y	ng(y	NOUN
ejpam-4645	209	48	)	)	PUNCT
ejpam-4645	209	49	.	.	PUNCT
ejpam-4645	210	1	theorem	theorem	NOUN
ejpam-4645	210	2	5	5	NUM
ejpam-4645	210	3	.	.	PUNCT
ejpam-4645	211	1	let	let	VERB
ejpam-4645	211	2	g	g	NOUN
ejpam-4645	211	3	and	and	CCONJ
ejpam-4645	211	4	h	h	PROPN
ejpam-4645	211	5	be	be	VERB
ejpam-4645	211	6	non	non	ADJ
ejpam-4645	211	7	-	-	ADJ
ejpam-4645	211	8	trivial	trivial	ADJ
ejpam-4645	211	9	connected	connected	ADJ
ejpam-4645	211	10	graphs	graph	NOUN
ejpam-4645	211	11	with	with	ADP
ejpam-4645	211	12	∆(h	∆(h	NOUN
ejpam-4645	211	13	)	)	PUNCT
ejpam-4645	211	14	≤	≤	NOUN
ejpam-4645	211	15	|v	|v	X
ejpam-4645	211	16	(	(	PUNCT
ejpam-4645	211	17	h)|	h)|	NOUN
ejpam-4645	211	18	−	−	PROPN
ejpam-4645	211	19	2	2	NUM
ejpam-4645	211	20	.	.	PUNCT
ejpam-4645	212	1	then	then	ADV
ejpam-4645	212	2	c	c	NOUN
ejpam-4645	212	3	=	=	PUNCT
ejpam-4645	212	4	⋃	⋃	PROPN
ejpam-4645	212	5	x∈s	x∈s	NOUN
ejpam-4645	212	6	(	(	PUNCT
ejpam-4645	212	7	{	{	PUNCT
ejpam-4645	212	8	x	x	NOUN
ejpam-4645	212	9	}	}	PUNCT
ejpam-4645	212	10	×	×	PROPN
ejpam-4645	212	11	tx	tx	PROPN
ejpam-4645	212	12	)	)	PUNCT
ejpam-4645	212	13	,	,	PUNCT
ejpam-4645	212	14	where	where	SCONJ
ejpam-4645	212	15	s	s	VERB
ejpam-4645	212	16	⊆	⊆	NUM
ejpam-4645	212	17	v	v	NOUN
ejpam-4645	212	18	(	(	PUNCT
ejpam-4645	212	19	g	g	NOUN
ejpam-4645	212	20	)	)	PUNCT
ejpam-4645	212	21	and	and	CCONJ
ejpam-4645	212	22	tx	tx	VERB
ejpam-4645	212	23	⊆	⊆	NUM
ejpam-4645	212	24	v	v	NOUN
ejpam-4645	212	25	(	(	PUNCT
ejpam-4645	212	26	h	h	NOUN
ejpam-4645	212	27	)	)	PUNCT
ejpam-4645	212	28	for	for	ADP
ejpam-4645	212	29	each	each	DET
ejpam-4645	212	30	x	x	SYM
ejpam-4645	212	31	∈	∈	PROPN
ejpam-4645	212	32	s	s	NOUN
ejpam-4645	212	33	,	,	PUNCT
ejpam-4645	212	34	is	be	AUX
ejpam-4645	212	35	a	a	DET
ejpam-4645	212	36	stable	stable	ADJ
ejpam-4645	212	37	locating	locating	NOUN
ejpam-4645	212	38	-	-	PUNCT
ejpam-4645	212	39	dominating	dominate	VERB
ejpam-4645	212	40	set	set	NOUN
ejpam-4645	212	41	of	of	ADP
ejpam-4645	212	42	g	g	PROPN
ejpam-4645	213	1	[	[	X
ejpam-4645	213	2	h	h	X
ejpam-4645	213	3	]	]	X
ejpam-4645	213	4	if	if	SCONJ
ejpam-4645	213	5	and	and	CCONJ
ejpam-4645	213	6	only	only	ADV
ejpam-4645	213	7	if	if	SCONJ
ejpam-4645	213	8	each	each	PRON
ejpam-4645	213	9	of	of	ADP
ejpam-4645	213	10	the	the	DET
ejpam-4645	213	11	following	follow	VERB
ejpam-4645	213	12	conditions	condition	NOUN
ejpam-4645	213	13	hold	hold	VERB
ejpam-4645	213	14	.	.	PUNCT
ejpam-4645	214	1	(	(	PUNCT
ejpam-4645	214	2	i	i	NOUN
ejpam-4645	214	3	)	)	PUNCT
ejpam-4645	214	4	s	s	PART
ejpam-4645	214	5	=	=	SYM
ejpam-4645	214	6	v	v	NOUN
ejpam-4645	214	7	(	(	PUNCT
ejpam-4645	214	8	g	g	NOUN
ejpam-4645	214	9	)	)	PUNCT
ejpam-4645	214	10	.	.	PUNCT
ejpam-4645	215	1	(	(	PUNCT
ejpam-4645	215	2	ii	ii	NOUN
ejpam-4645	215	3	)	)	PUNCT
ejpam-4645	215	4	tx	tx	PROPN
ejpam-4645	215	5	is	be	AUX
ejpam-4645	215	6	a	a	DET
ejpam-4645	215	7	stable	stable	ADJ
ejpam-4645	215	8	locating	locating	NOUN
ejpam-4645	215	9	set	set	VERB
ejpam-4645	215	10	in	in	ADP
ejpam-4645	215	11	h	h	NOUN
ejpam-4645	215	12	for	for	ADP
ejpam-4645	215	13	every	every	DET
ejpam-4645	215	14	x	x	SYM
ejpam-4645	215	15	∈	∈	PROPN
ejpam-4645	215	16	v	v	NOUN
ejpam-4645	215	17	(	(	PUNCT
ejpam-4645	215	18	g	g	NOUN
ejpam-4645	215	19	)	)	PUNCT
ejpam-4645	215	20	.	.	PUNCT
ejpam-4645	216	1	(	(	PUNCT
ejpam-4645	216	2	iii	iii	X
ejpam-4645	216	3	)	)	PUNCT
ejpam-4645	216	4	if	if	SCONJ
ejpam-4645	216	5	x	x	PRON
ejpam-4645	216	6	and	and	CCONJ
ejpam-4645	216	7	y	y	PROPN
ejpam-4645	216	8	are	be	AUX
ejpam-4645	216	9	adjacent	adjacent	ADJ
ejpam-4645	216	10	vertices	vertex	NOUN
ejpam-4645	216	11	of	of	ADP
ejpam-4645	216	12	g	g	NOUN
ejpam-4645	216	13	with	with	ADP
ejpam-4645	216	14	ng[x	ng[x	PROPN
ejpam-4645	216	15	]	]	X
ejpam-4645	216	16	=	=	PUNCT
ejpam-4645	216	17	ng[y	ng[y	PROPN
ejpam-4645	216	18	]	]	PUNCT
ejpam-4645	216	19	and	and	CCONJ
ejpam-4645	216	20	one	one	NUM
ejpam-4645	216	21	,	,	PUNCT
ejpam-4645	216	22	say	say	VERB
ejpam-4645	216	23	tx	tx	PROPN
ejpam-4645	216	24	is	be	AUX
ejpam-4645	216	25	not	not	PART
ejpam-4645	216	26	strictly	strictly	ADV
ejpam-4645	216	27	locating	locate	VERB
ejpam-4645	216	28	,	,	PUNCT
ejpam-4645	216	29	then	then	ADV
ejpam-4645	216	30	ty	ty	INTJ
ejpam-4645	216	31	is	be	AUX
ejpam-4645	216	32	a	a	DET
ejpam-4645	216	33	stable	stable	ADJ
ejpam-4645	216	34	strictly	strictly	ADV
ejpam-4645	216	35	locating	locate	VERB
ejpam-4645	216	36	set	set	NOUN
ejpam-4645	216	37	of	of	ADP
ejpam-4645	216	38	h.	h.	PROPN
ejpam-4645	216	39	(	(	PUNCT
ejpam-4645	216	40	iv	iv	X
ejpam-4645	216	41	)	)	PUNCT
ejpam-4645	216	42	if	if	SCONJ
ejpam-4645	216	43	x	x	PRON
ejpam-4645	216	44	and	and	CCONJ
ejpam-4645	216	45	y	y	PROPN
ejpam-4645	216	46	are	be	AUX
ejpam-4645	216	47	distinct	distinct	ADJ
ejpam-4645	216	48	non	non	ADJ
ejpam-4645	216	49	-	-	ADJ
ejpam-4645	216	50	adjacent	adjacent	ADJ
ejpam-4645	216	51	vertices	vertex	NOUN
ejpam-4645	216	52	of	of	ADP
ejpam-4645	216	53	g	g	NOUN
ejpam-4645	216	54	with	with	ADP
ejpam-4645	216	55	ng(x	ng(x	NUM
ejpam-4645	216	56	)	)	PUNCT
ejpam-4645	216	57	=	=	SYM
ejpam-4645	217	1	ng(y	ng(y	X
ejpam-4645	217	2	)	)	PUNCT
ejpam-4645	217	3	and	and	CCONJ
ejpam-4645	217	4	one	one	NUM
ejpam-4645	217	5	,	,	PUNCT
ejpam-4645	217	6	say	say	VERB
ejpam-4645	217	7	tx	tx	PROPN
ejpam-4645	217	8	is	be	AUX
ejpam-4645	217	9	not	not	PART
ejpam-4645	217	10	a	a	DET
ejpam-4645	217	11	dominating	dominating	NOUN
ejpam-4645	217	12	set	set	NOUN
ejpam-4645	217	13	,	,	PUNCT
ejpam-4645	217	14	then	then	ADV
ejpam-4645	217	15	ty	ty	INTJ
ejpam-4645	217	16	is	be	AUX
ejpam-4645	217	17	a	a	DET
ejpam-4645	217	18	stable	stable	ADJ
ejpam-4645	217	19	dominating	dominating	NOUN
ejpam-4645	217	20	set	set	NOUN
ejpam-4645	217	21	of	of	ADP
ejpam-4645	217	22	h.	h.	PROPN
ejpam-4645	217	23	proof	proof	NOUN
ejpam-4645	217	24	.	.	PUNCT
ejpam-4645	218	1	suppose	suppose	VERB
ejpam-4645	218	2	c	c	NOUN
ejpam-4645	218	3	is	be	AUX
ejpam-4645	218	4	a	a	DET
ejpam-4645	218	5	stable	stable	ADJ
ejpam-4645	218	6	locating	locating	NOUN
ejpam-4645	218	7	-	-	PUNCT
ejpam-4645	218	8	dominating	dominate	VERB
ejpam-4645	218	9	set	set	NOUN
ejpam-4645	218	10	of	of	ADP
ejpam-4645	218	11	g	g	PROPN
ejpam-4645	219	1	[	[	X
ejpam-4645	219	2	h	h	X
ejpam-4645	219	3	]	]	X
ejpam-4645	219	4	.	.	PUNCT
ejpam-4645	220	1	by	by	ADP
ejpam-4645	220	2	theorem	theorem	NOUN
ejpam-4645	220	3	4	4	NUM
ejpam-4645	220	4	,	,	PUNCT
ejpam-4645	220	5	s	s	PART
ejpam-4645	220	6	=	=	SYM
ejpam-4645	220	7	v	v	X
ejpam-4645	220	8	(	(	PUNCT
ejpam-4645	220	9	g	g	NOUN
ejpam-4645	220	10	)	)	PUNCT
ejpam-4645	220	11	and	and	CCONJ
ejpam-4645	220	12	tx	tx	PROPN
ejpam-4645	220	13	is	be	AUX
ejpam-4645	220	14	a	a	DET
ejpam-4645	220	15	locating	locating	NOUN
ejpam-4645	220	16	set	set	NOUN
ejpam-4645	220	17	of	of	ADP
ejpam-4645	220	18	h	h	NOUN
ejpam-4645	220	19	for	for	ADP
ejpam-4645	220	20	each	each	DET
ejpam-4645	220	21	x	x	SYM
ejpam-4645	220	22	∈	∈	PROPN
ejpam-4645	220	23	v	v	NOUN
ejpam-4645	220	24	(	(	PUNCT
ejpam-4645	220	25	g	g	NOUN
ejpam-4645	220	26	)	)	PUNCT
ejpam-4645	220	27	.	.	PUNCT
ejpam-4645	221	1	let	let	VERB
ejpam-4645	221	2	z	z	NOUN
ejpam-4645	221	3	∈	∈	PROPN
ejpam-4645	221	4	s	s	PART
ejpam-4645	221	5	and	and	CCONJ
ejpam-4645	221	6	let	let	VERB
ejpam-4645	221	7	a	a	DET
ejpam-4645	221	8	∈	∈	PROPN
ejpam-4645	221	9	tz	tz	NOUN
ejpam-4645	221	10	.	.	PUNCT
ejpam-4645	221	11	by	by	ADP
ejpam-4645	221	12	assumption	assumption	NOUN
ejpam-4645	221	13	,	,	PUNCT
ejpam-4645	221	14	c	c	PROPN
ejpam-4645	221	15	\{(z	\{(z	PROPN
ejpam-4645	221	16	,	,	PUNCT
ejpam-4645	221	17	a	a	NOUN
ejpam-4645	221	18	)	)	PUNCT
ejpam-4645	221	19	}	}	PUNCT
ejpam-4645	222	1	=	=	SYM
ejpam-4645	222	2	[	[	PUNCT
ejpam-4645	222	3	⋃	⋃	PROPN
ejpam-4645	222	4	x∈s\{z	x∈s\{z	NOUN
ejpam-4645	222	5	}	}	PUNCT
ejpam-4645	222	6	(	(	PUNCT
ejpam-4645	222	7	{	{	PUNCT
ejpam-4645	222	8	x}×tx)]∪	x}×tx)]∪	PROPN
ejpam-4645	222	9	[	[	X
ejpam-4645	222	10	{	{	PUNCT
ejpam-4645	222	11	z}×	z}×	X
ejpam-4645	222	12	(	(	PUNCT
ejpam-4645	222	13	tz	tz	PROPN
ejpam-4645	222	14	\{a	\{a	PROPN
ejpam-4645	222	15	}	}	PUNCT
ejpam-4645	222	16	)	)	PUNCT
ejpam-4645	222	17	]	]	PUNCT
ejpam-4645	222	18	is	be	AUX
ejpam-4645	222	19	a	a	DET
ejpam-4645	222	20	locating	locate	VERB
ejpam-4645	222	21	-	-	PUNCT
ejpam-4645	222	22	dominating	dominate	VERB
ejpam-4645	222	23	set	set	NOUN
ejpam-4645	222	24	of	of	ADP
ejpam-4645	222	25	g[h	g[h	NOUN
ejpam-4645	222	26	]	]	PUNCT
ejpam-4645	222	27	.	.	PUNCT
ejpam-4645	223	1	by	by	ADP
ejpam-4645	223	2	theorem	theorem	NOUN
ejpam-4645	223	3	4(ii	4(ii	NUM
ejpam-4645	223	4	)	)	PUNCT
ejpam-4645	223	5	,	,	PUNCT
ejpam-4645	223	6	tz	tz	PROPN
ejpam-4645	223	7	\	\	PROPN
ejpam-4645	223	8	{	{	PUNCT
ejpam-4645	223	9	a	a	PRON
ejpam-4645	223	10	}	}	PUNCT
ejpam-4645	223	11	is	be	AUX
ejpam-4645	223	12	a	a	DET
ejpam-4645	223	13	locating	locate	VERB
ejpam-4645	223	14	set	set	NOUN
ejpam-4645	223	15	of	of	ADP
ejpam-4645	223	16	h.	h.	PROPN
ejpam-4645	223	17	this	this	PRON
ejpam-4645	223	18	implies	imply	VERB
ejpam-4645	223	19	that	that	SCONJ
ejpam-4645	223	20	tz	tz	PROPN
ejpam-4645	223	21	is	be	AUX
ejpam-4645	223	22	a	a	DET
ejpam-4645	223	23	stable	stable	ADJ
ejpam-4645	223	24	locating	locating	NOUN
ejpam-4645	223	25	set	set	NOUN
ejpam-4645	223	26	of	of	ADP
ejpam-4645	223	27	h.	h.	PROPN
ejpam-4645	223	28	thus	thus	ADV
ejpam-4645	223	29	,	,	PUNCT
ejpam-4645	223	30	(	(	PUNCT
ejpam-4645	223	31	ii	ii	NOUN
ejpam-4645	223	32	)	)	PUNCT
ejpam-4645	223	33	holds	hold	VERB
ejpam-4645	223	34	.	.	PUNCT
ejpam-4645	224	1	suppose	suppose	VERB
ejpam-4645	224	2	now	now	ADV
ejpam-4645	224	3	that	that	SCONJ
ejpam-4645	224	4	x	x	PRON
ejpam-4645	224	5	and	and	CCONJ
ejpam-4645	224	6	y	y	PROPN
ejpam-4645	224	7	are	be	AUX
ejpam-4645	224	8	adjacent	adjacent	ADJ
ejpam-4645	224	9	vertices	vertex	NOUN
ejpam-4645	224	10	of	of	ADP
ejpam-4645	224	11	g	g	NOUN
ejpam-4645	224	12	with	with	ADP
ejpam-4645	224	13	ng[x	ng[x	PROPN
ejpam-4645	224	14	]	]	X
ejpam-4645	224	15	=	=	PUNCT
ejpam-4645	224	16	ng[y	ng[y	PROPN
ejpam-4645	224	17	]	]	PUNCT
ejpam-4645	224	18	.	.	PUNCT
ejpam-4645	225	1	suppose	suppose	VERB
ejpam-4645	225	2	that	that	SCONJ
ejpam-4645	225	3	one	one	NUM
ejpam-4645	225	4	,	,	PUNCT
ejpam-4645	225	5	say	say	VERB
ejpam-4645	225	6	tx	tx	PROPN
ejpam-4645	225	7	is	be	AUX
ejpam-4645	225	8	not	not	PART
ejpam-4645	225	9	a	a	DET
ejpam-4645	225	10	strictly	strictly	ADV
ejpam-4645	225	11	locating	locate	VERB
ejpam-4645	225	12	set	set	NOUN
ejpam-4645	225	13	of	of	ADP
ejpam-4645	225	14	h.	h.	NOUN
ejpam-4645	225	15	by	by	ADP
ejpam-4645	225	16	theorem	theorem	ADJ
ejpam-4645	225	17	4(iii	4(iii	NUM
ejpam-4645	225	18	)	)	PUNCT
ejpam-4645	225	19	,	,	PUNCT
ejpam-4645	225	20	ty	ty	INTJ
ejpam-4645	225	21	is	be	AUX
ejpam-4645	225	22	a	a	DET
ejpam-4645	225	23	strictly	strictly	ADV
ejpam-4645	225	24	locating	locate	VERB
ejpam-4645	225	25	set	set	NOUN
ejpam-4645	225	26	of	of	ADP
ejpam-4645	225	27	h.	h.	PROPN
ejpam-4645	225	28	let	let	VERB
ejpam-4645	225	29	p	p	PROPN
ejpam-4645	225	30	∈	∈	PROPN
ejpam-4645	225	31	ty	ty	PRON
ejpam-4645	225	32	.	.	PUNCT
ejpam-4645	226	1	since	since	SCONJ
ejpam-4645	226	2	c	c	PROPN
ejpam-4645	226	3	\	\	PROPN
ejpam-4645	226	4	{	{	PUNCT
ejpam-4645	226	5	(	(	PUNCT
ejpam-4645	226	6	y	y	PROPN
ejpam-4645	226	7	,	,	PUNCT
ejpam-4645	226	8	p	p	NOUN
ejpam-4645	226	9	)	)	PUNCT
ejpam-4645	226	10	}	}	PUNCT
ejpam-4645	226	11	=	=	SYM
ejpam-4645	226	12	[	[	PUNCT
ejpam-4645	226	13	⋃	⋃	NOUN
ejpam-4645	226	14	z∈s\{y	z∈s\{y	NOUN
ejpam-4645	226	15	}	}	PUNCT
ejpam-4645	226	16	(	(	PUNCT
ejpam-4645	226	17	{	{	PUNCT
ejpam-4645	226	18	z	z	NOUN
ejpam-4645	226	19	}	}	PUNCT
ejpam-4645	226	20	×	×	PROPN
ejpam-4645	226	21	tz	tz	NOUN
ejpam-4645	226	22	)	)	PUNCT
ejpam-4645	226	23	]	]	PUNCT
ejpam-4645	226	24	∪	∪	ADP
ejpam-4645	226	25	[	[	X
ejpam-4645	226	26	{	{	PUNCT
ejpam-4645	226	27	y	y	NOUN
ejpam-4645	226	28	}	}	PUNCT
ejpam-4645	226	29	×	×	NOUN
ejpam-4645	226	30	(	(	PUNCT
ejpam-4645	226	31	ty	ty	INTJ
ejpam-4645	226	32	\	\	PROPN
ejpam-4645	226	33	{	{	PUNCT
ejpam-4645	226	34	p	p	NOUN
ejpam-4645	226	35	}	}	PUNCT
ejpam-4645	226	36	)	)	PUNCT
ejpam-4645	226	37	]	]	PUNCT
ejpam-4645	226	38	is	be	AUX
ejpam-4645	226	39	a	a	DET
ejpam-4645	226	40	locating	locate	VERB
ejpam-4645	226	41	-	-	PUNCT
ejpam-4645	226	42	dominating	dominate	VERB
ejpam-4645	226	43	set	set	NOUN
ejpam-4645	226	44	of	of	ADP
ejpam-4645	226	45	g[h	g[h	PROPN
ejpam-4645	226	46	]	]	PUNCT
ejpam-4645	226	47	and	and	CCONJ
ejpam-4645	226	48	tx	tx	PROPN
ejpam-4645	226	49	is	be	AUX
ejpam-4645	226	50	not	not	PART
ejpam-4645	226	51	strictly	strictly	ADV
ejpam-4645	226	52	locating	locate	VERB
ejpam-4645	226	53	,	,	PUNCT
ejpam-4645	226	54	it	it	PRON
ejpam-4645	226	55	follows	follow	VERB
ejpam-4645	226	56	from	from	ADP
ejpam-4645	226	57	theorem	theorem	ADJ
ejpam-4645	226	58	4(iii	4(iii	NUM
ejpam-4645	226	59	)	)	PUNCT
ejpam-4645	226	60	that	that	SCONJ
ejpam-4645	226	61	ty	ty	X
ejpam-4645	226	62	\	\	VERB
ejpam-4645	226	63	{	{	PUNCT
ejpam-4645	226	64	p	p	X
ejpam-4645	226	65	}	}	PUNCT
ejpam-4645	226	66	is	be	AUX
ejpam-4645	226	67	strictly	strictly	ADV
ejpam-4645	226	68	locating	locate	VERB
ejpam-4645	226	69	.	.	PUNCT
ejpam-4645	227	1	therefore	therefore	ADV
ejpam-4645	227	2	,	,	PUNCT
ejpam-4645	227	3	ty	ty	INTJ
ejpam-4645	227	4	is	be	AUX
ejpam-4645	227	5	a	a	DET
ejpam-4645	227	6	stable	stable	ADJ
ejpam-4645	227	7	strictly	strictly	ADV
ejpam-4645	227	8	locating	locate	VERB
ejpam-4645	227	9	set	set	NOUN
ejpam-4645	227	10	of	of	ADP
ejpam-4645	227	11	h	h	NOUN
ejpam-4645	227	12	,	,	PUNCT
ejpam-4645	227	13	showing	show	VERB
ejpam-4645	227	14	that	that	SCONJ
ejpam-4645	227	15	(	(	PUNCT
ejpam-4645	227	16	iii	iii	NOUN
ejpam-4645	227	17	)	)	PUNCT
ejpam-4645	227	18	holds	hold	VERB
ejpam-4645	227	19	.	.	PUNCT
ejpam-4645	228	1	next	next	ADV
ejpam-4645	228	2	,	,	PUNCT
ejpam-4645	228	3	suppose	suppose	VERB
ejpam-4645	228	4	that	that	SCONJ
ejpam-4645	228	5	x	x	PROPN
ejpam-4645	228	6	and	and	CCONJ
ejpam-4645	228	7	y	y	PROPN
ejpam-4645	228	8	are	be	AUX
ejpam-4645	228	9	distinct	distinct	ADJ
ejpam-4645	228	10	non	non	ADJ
ejpam-4645	228	11	-	-	ADJ
ejpam-4645	228	12	adjacent	adjacent	ADJ
ejpam-4645	228	13	vertices	vertex	NOUN
ejpam-4645	228	14	of	of	ADP
ejpam-4645	228	15	g	g	NOUN
ejpam-4645	228	16	with	with	ADP
ejpam-4645	228	17	ng(x	ng(x	NUM
ejpam-4645	228	18	)	)	PUNCT
ejpam-4645	228	19	=	=	PUNCT
ejpam-4645	228	20	ng(y	ng(y	NOUN
ejpam-4645	228	21	)	)	PUNCT
ejpam-4645	228	22	.	.	PUNCT
ejpam-4645	229	1	suppose	suppose	VERB
ejpam-4645	229	2	that	that	SCONJ
ejpam-4645	229	3	one	one	NUM
ejpam-4645	229	4	,	,	PUNCT
ejpam-4645	229	5	say	say	VERB
ejpam-4645	229	6	tx	tx	PROPN
ejpam-4645	229	7	is	be	AUX
ejpam-4645	229	8	not	not	PART
ejpam-4645	229	9	a	a	DET
ejpam-4645	229	10	dominating	dominating	NOUN
ejpam-4645	229	11	set	set	NOUN
ejpam-4645	229	12	of	of	ADP
ejpam-4645	229	13	h.	h.	PROPN
ejpam-4645	229	14	then	then	ADV
ejpam-4645	229	15	ty	ty	INTJ
ejpam-4645	229	16	is	be	AUX
ejpam-4645	229	17	a	a	DET
ejpam-4645	229	18	dominating	dominating	NOUN
ejpam-4645	229	19	set	set	NOUN
ejpam-4645	229	20	of	of	ADP
ejpam-4645	229	21	g	g	NOUN
ejpam-4645	229	22	by	by	ADP
ejpam-4645	229	23	theorem	theorem	ADJ
ejpam-4645	229	24	4(iv	4(iv	NUM
ejpam-4645	229	25	)	)	PUNCT
ejpam-4645	229	26	.	.	PUNCT
ejpam-4645	230	1	let	let	VERB
ejpam-4645	230	2	q	q	PROPN
ejpam-4645	230	3	∈	∈	VERB
ejpam-4645	230	4	ty	ty	INTJ
ejpam-4645	230	5	.	.	PUNCT
ejpam-4645	231	1	since	since	SCONJ
ejpam-4645	231	2	c	c	PROPN
ejpam-4645	231	3	\	\	PROPN
ejpam-4645	231	4	{	{	PUNCT
ejpam-4645	231	5	(	(	PUNCT
ejpam-4645	231	6	y	y	PROPN
ejpam-4645	231	7	,	,	PUNCT
ejpam-4645	231	8	q	q	NOUN
ejpam-4645	231	9	)	)	PUNCT
ejpam-4645	231	10	}	}	PUNCT
ejpam-4645	231	11	=	=	SYM
ejpam-4645	231	12	[	[	PUNCT
ejpam-4645	231	13	⋃	⋃	NOUN
ejpam-4645	231	14	z∈s\{y	z∈s\{y	NOUN
ejpam-4645	231	15	}	}	PUNCT
ejpam-4645	231	16	(	(	PUNCT
ejpam-4645	231	17	{	{	PUNCT
ejpam-4645	231	18	z	z	NOUN
ejpam-4645	231	19	}	}	PUNCT
ejpam-4645	231	20	×	×	PROPN
ejpam-4645	231	21	tz	tz	NOUN
ejpam-4645	231	22	)	)	PUNCT
ejpam-4645	231	23	]	]	PUNCT
ejpam-4645	231	24	∪	∪	ADP
ejpam-4645	231	25	[	[	X
ejpam-4645	231	26	{	{	PUNCT
ejpam-4645	231	27	y	y	NOUN
ejpam-4645	231	28	}	}	PUNCT
ejpam-4645	231	29	×	×	NOUN
ejpam-4645	231	30	(	(	PUNCT
ejpam-4645	231	31	ty	ty	INTJ
ejpam-4645	231	32	\	\	PROPN
ejpam-4645	231	33	{	{	PUNCT
ejpam-4645	231	34	q	q	NOUN
ejpam-4645	231	35	}	}	PUNCT
ejpam-4645	231	36	)	)	PUNCT
ejpam-4645	231	37	]	]	PUNCT
ejpam-4645	231	38	is	be	AUX
ejpam-4645	231	39	a	a	DET
ejpam-4645	231	40	locating	locate	VERB
ejpam-4645	231	41	-	-	PUNCT
ejpam-4645	231	42	dominating	dominate	VERB
ejpam-4645	231	43	set	set	NOUN
ejpam-4645	231	44	of	of	ADP
ejpam-4645	231	45	g[h	g[h	PROPN
ejpam-4645	231	46	]	]	PUNCT
ejpam-4645	231	47	and	and	CCONJ
ejpam-4645	231	48	tx	tx	PROPN
ejpam-4645	231	49	is	be	AUX
ejpam-4645	231	50	not	not	PART
ejpam-4645	231	51	a	a	DET
ejpam-4645	231	52	dominating	dominating	NOUN
ejpam-4645	231	53	set	set	NOUN
ejpam-4645	231	54	of	of	ADP
ejpam-4645	231	55	g	g	PROPN
ejpam-4645	231	56	,	,	PUNCT
ejpam-4645	231	57	ty	ty	INTJ
ejpam-4645	231	58	\	\	PROPN
ejpam-4645	231	59	{	{	PUNCT
ejpam-4645	231	60	q	q	NOUN
ejpam-4645	231	61	}	}	PUNCT
ejpam-4645	231	62	is	be	AUX
ejpam-4645	231	63	a	a	DET
ejpam-4645	231	64	dominating	dominating	NOUN
ejpam-4645	231	65	set	set	NOUN
ejpam-4645	231	66	of	of	ADP
ejpam-4645	231	67	h	h	NOUN
ejpam-4645	231	68	by	by	ADP
ejpam-4645	231	69	theorem	theorem	NOUN
ejpam-4645	231	70	4(iv	4(iv	NUM
ejpam-4645	231	71	)	)	PUNCT
ejpam-4645	231	72	.	.	PUNCT
ejpam-4645	232	1	this	this	PRON
ejpam-4645	232	2	shows	show	VERB
ejpam-4645	232	3	that	that	SCONJ
ejpam-4645	232	4	ty	ty	PRON
ejpam-4645	232	5	is	be	AUX
ejpam-4645	232	6	a	a	DET
ejpam-4645	232	7	stable	stable	ADJ
ejpam-4645	232	8	dominating	dominating	NOUN
ejpam-4645	232	9	set	set	NOUN
ejpam-4645	232	10	of	of	ADP
ejpam-4645	232	11	h.	h.	PROPN
ejpam-4645	232	12	thus	thus	ADV
ejpam-4645	232	13	,	,	PUNCT
ejpam-4645	232	14	(	(	PUNCT
ejpam-4645	232	15	iv	iv	X
ejpam-4645	232	16	)	)	PUNCT
ejpam-4645	232	17	holds	hold	NOUN
ejpam-4645	232	18	.	.	PUNCT
ejpam-4645	233	1	for	for	ADP
ejpam-4645	233	2	the	the	DET
ejpam-4645	233	3	converse	converse	NOUN
ejpam-4645	233	4	,	,	PUNCT
ejpam-4645	233	5	suppose	suppose	VERB
ejpam-4645	233	6	that	that	SCONJ
ejpam-4645	233	7	c	c	PROPN
ejpam-4645	233	8	satisfies	satisfy	VERB
ejpam-4645	233	9	(	(	PUNCT
ejpam-4645	233	10	i	i	NOUN
ejpam-4645	233	11	)	)	PUNCT
ejpam-4645	233	12	,	,	PUNCT
ejpam-4645	233	13	(	(	PUNCT
ejpam-4645	233	14	ii	ii	NOUN
ejpam-4645	233	15	)	)	PUNCT
ejpam-4645	233	16	,	,	PUNCT
ejpam-4645	233	17	(	(	PUNCT
ejpam-4645	233	18	iii	iii	NOUN
ejpam-4645	233	19	)	)	PUNCT
ejpam-4645	233	20	and	and	CCONJ
ejpam-4645	233	21	(	(	PUNCT
ejpam-4645	233	22	iv	iv	X
ejpam-4645	233	23	)	)	PUNCT
ejpam-4645	233	24	.	.	PUNCT
ejpam-4645	234	1	then	then	ADV
ejpam-4645	234	2	c	c	PROPN
ejpam-4645	234	3	satisfies	satisfy	VERB
ejpam-4645	234	4	the	the	DET
ejpam-4645	234	5	conditions	condition	NOUN
ejpam-4645	234	6	(	(	PUNCT
ejpam-4645	234	7	i	i	NOUN
ejpam-4645	234	8	)	)	PUNCT
ejpam-4645	234	9	,	,	PUNCT
ejpam-4645	234	10	(	(	PUNCT
ejpam-4645	234	11	ii	ii	NOUN
ejpam-4645	234	12	)	)	PUNCT
ejpam-4645	234	13	,	,	PUNCT
ejpam-4645	234	14	(	(	PUNCT
ejpam-4645	234	15	iii	iii	NOUN
ejpam-4645	234	16	)	)	PUNCT
ejpam-4645	234	17	and	and	CCONJ
ejpam-4645	234	18	(	(	PUNCT
ejpam-4645	234	19	iv	iv	X
ejpam-4645	234	20	)	)	PUNCT
ejpam-4645	234	21	of	of	ADP
ejpam-4645	234	22	theorem	theorem	ADJ
ejpam-4645	234	23	4	4	NUM
ejpam-4645	234	24	.	.	PUNCT
ejpam-4645	235	1	hence	hence	ADV
ejpam-4645	235	2	,	,	PUNCT
ejpam-4645	235	3	c	c	PROPN
ejpam-4645	235	4	is	be	AUX
ejpam-4645	235	5	a	a	DET
ejpam-4645	235	6	locating	locate	VERB
ejpam-4645	235	7	-	-	PUNCT
ejpam-4645	235	8	dominating	dominate	VERB
ejpam-4645	235	9	set	set	NOUN
ejpam-4645	235	10	of	of	ADP
ejpam-4645	235	11	g.	g.	PROPN
ejpam-4645	235	12	malacas	malacas	PROPN
ejpam-4645	235	13	,	,	PUNCT
ejpam-4645	235	14	s.	s.	PROPN
ejpam-4645	235	15	canoy	canoy	PROPN
ejpam-4645	235	16	,	,	PUNCT
ejpam-4645	235	17	jr	jr	PROPN
ejpam-4645	235	18	.	.	PROPN
ejpam-4645	235	19	,	,	PUNCT
ejpam-4645	235	20	e.	e.	PROPN
ejpam-4645	235	21	chacon	chacon	PROPN
ejpam-4645	235	22	/	/	SYM
ejpam-4645	235	23	eur	eur	PROPN
ejpam-4645	235	24	.	.	PUNCT
ejpam-4645	236	1	j.	j.	PROPN
ejpam-4645	236	2	pure	pure	PROPN
ejpam-4645	236	3	appl	appl	PROPN
ejpam-4645	236	4	.	.	PROPN
ejpam-4645	236	5	math	math	PROPN
ejpam-4645	236	6	,	,	PUNCT
ejpam-4645	236	7	16	16	NUM
ejpam-4645	236	8	(	(	PUNCT
ejpam-4645	236	9	1	1	NUM
ejpam-4645	236	10	)	)	PUNCT
ejpam-4645	236	11	(	(	PUNCT
ejpam-4645	236	12	2023	2023	NUM
ejpam-4645	236	13	)	)	PUNCT
ejpam-4645	236	14	,	,	PUNCT
ejpam-4645	236	15	479	479	NUM
ejpam-4645	236	16	-	-	SYM
ejpam-4645	236	17	490	490	NUM
ejpam-4645	236	18	487	487	NUM
ejpam-4645	236	19	g[h	g[h	NOUN
ejpam-4645	236	20	]	]	PUNCT
ejpam-4645	236	21	.	.	PUNCT
ejpam-4645	237	1	let	let	VERB
ejpam-4645	237	2	(	(	PUNCT
ejpam-4645	237	3	y	y	NOUN
ejpam-4645	237	4	,	,	PUNCT
ejpam-4645	237	5	a	a	PRON
ejpam-4645	237	6	)	)	PUNCT
ejpam-4645	237	7	∈	∈	PROPN
ejpam-4645	237	8	c.	c.	NOUN
ejpam-4645	237	9	then	then	ADV
ejpam-4645	237	10	c∗	c∗	PROPN
ejpam-4645	237	11	=	=	PUNCT
ejpam-4645	237	12	c	c	NOUN
ejpam-4645	237	13	\	\	X
ejpam-4645	238	1	{	{	PUNCT
ejpam-4645	238	2	(	(	PUNCT
ejpam-4645	238	3	y	y	PROPN
ejpam-4645	238	4	,	,	PUNCT
ejpam-4645	238	5	a	a	NOUN
ejpam-4645	238	6	)	)	PUNCT
ejpam-4645	238	7	}	}	PUNCT
ejpam-4645	238	8	=	=	SYM
ejpam-4645	238	9	[	[	PUNCT
ejpam-4645	238	10	⋃	⋃	PROPN
ejpam-4645	238	11	x∈s\{y	x∈s\{y	NUM
ejpam-4645	238	12	}	}	PUNCT
ejpam-4645	238	13	(	(	PUNCT
ejpam-4645	238	14	{	{	PUNCT
ejpam-4645	238	15	x	x	NOUN
ejpam-4645	238	16	}	}	PUNCT
ejpam-4645	238	17	×	×	PROPN
ejpam-4645	238	18	tx	tx	PROPN
ejpam-4645	238	19	)	)	PUNCT
ejpam-4645	238	20	]	]	PUNCT
ejpam-4645	238	21	∪	∪	ADP
ejpam-4645	238	22	[	[	X
ejpam-4645	238	23	{	{	PUNCT
ejpam-4645	238	24	y	y	NOUN
ejpam-4645	238	25	}	}	PUNCT
ejpam-4645	238	26	×	×	NOUN
ejpam-4645	238	27	(	(	PUNCT
ejpam-4645	238	28	ty	ty	INTJ
ejpam-4645	238	29	\	\	PROPN
ejpam-4645	238	30	{	{	PUNCT
ejpam-4645	238	31	a	a	NOUN
ejpam-4645	238	32	}	}	PUNCT
ejpam-4645	238	33	)	)	PUNCT
ejpam-4645	238	34	]	]	PUNCT
ejpam-4645	238	35	.	.	PUNCT
ejpam-4645	239	1	by	by	ADP
ejpam-4645	239	2	(	(	PUNCT
ejpam-4645	239	3	ii	ii	NOUN
ejpam-4645	239	4	)	)	PUNCT
ejpam-4645	239	5	,	,	PUNCT
ejpam-4645	239	6	ty	ty	INTJ
ejpam-4645	239	7	\	\	PROPN
ejpam-4645	239	8	{	{	PUNCT
ejpam-4645	239	9	a	a	PRON
ejpam-4645	239	10	}	}	PUNCT
ejpam-4645	239	11	is	be	AUX
ejpam-4645	239	12	a	a	DET
ejpam-4645	239	13	locating	locating	NOUN
ejpam-4645	239	14	set	set	VERB
ejpam-4645	239	15	and	and	CCONJ
ejpam-4645	239	16	tx	tx	PROPN
ejpam-4645	239	17	are	be	AUX
ejpam-4645	239	18	stable	stable	ADJ
ejpam-4645	239	19	locating	locating	NOUN
ejpam-4645	239	20	sets	set	NOUN
ejpam-4645	239	21	of	of	ADP
ejpam-4645	239	22	h	h	NOUN
ejpam-4645	239	23	for	for	ADP
ejpam-4645	239	24	each	each	DET
ejpam-4645	239	25	x	x	SYM
ejpam-4645	239	26	∈	∈	PROPN
ejpam-4645	239	27	s	s	PART
ejpam-4645	239	28	\	\	X
ejpam-4645	239	29	{	{	PUNCT
ejpam-4645	239	30	y	y	NOUN
ejpam-4645	239	31	}	}	PUNCT
ejpam-4645	239	32	.	.	PUNCT
ejpam-4645	240	1	this	this	PRON
ejpam-4645	240	2	would	would	AUX
ejpam-4645	240	3	also	also	ADV
ejpam-4645	240	4	imply	imply	VERB
ejpam-4645	240	5	that	that	DET
ejpam-4645	240	6	c∗	c∗	PROPN
ejpam-4645	240	7	g	g	PROPN
ejpam-4645	240	8	=	=	PUNCT
ejpam-4645	240	9	s∗	s∗	PROPN
ejpam-4645	240	10	=	=	SYM
ejpam-4645	240	11	s	s	NOUN
ejpam-4645	240	12	=	=	SYM
ejpam-4645	240	13	v	v	X
ejpam-4645	240	14	(	(	PUNCT
ejpam-4645	240	15	g	g	NOUN
ejpam-4645	240	16	)	)	PUNCT
ejpam-4645	240	17	.	.	PUNCT
ejpam-4645	241	1	let	let	VERB
ejpam-4645	241	2	x	x	PRON
ejpam-4645	241	3	and	and	CCONJ
ejpam-4645	241	4	z	z	AUX
ejpam-4645	241	5	be	be	AUX
ejpam-4645	241	6	adjacent	adjacent	ADJ
ejpam-4645	241	7	vertices	vertex	NOUN
ejpam-4645	241	8	of	of	ADP
ejpam-4645	241	9	g	g	NOUN
ejpam-4645	241	10	with	with	ADP
ejpam-4645	241	11	ng[x	ng[x	PROPN
ejpam-4645	241	12	]	]	PUNCT
ejpam-4645	242	1	=	=	PUNCT
ejpam-4645	242	2	ng[z	ng[z	PROPN
ejpam-4645	242	3	]	]	PUNCT
ejpam-4645	242	4	.	.	PUNCT
ejpam-4645	243	1	if	if	SCONJ
ejpam-4645	243	2	tx	tx	PROPN
ejpam-4645	243	3	is	be	AUX
ejpam-4645	243	4	strictly	strictly	ADV
ejpam-4645	243	5	locating	locate	VERB
ejpam-4645	243	6	,	,	PUNCT
ejpam-4645	243	7	then	then	ADV
ejpam-4645	243	8	we	we	PRON
ejpam-4645	243	9	are	be	AUX
ejpam-4645	243	10	done	do	VERB
ejpam-4645	243	11	.	.	PUNCT
ejpam-4645	244	1	so	so	ADV
ejpam-4645	244	2	suppose	suppose	VERB
ejpam-4645	244	3	that	that	SCONJ
ejpam-4645	244	4	tx	tx	PROPN
ejpam-4645	244	5	is	be	AUX
ejpam-4645	244	6	not	not	PART
ejpam-4645	244	7	strictly	strictly	ADV
ejpam-4645	244	8	locating	locate	VERB
ejpam-4645	244	9	.	.	PUNCT
ejpam-4645	245	1	then	then	ADV
ejpam-4645	245	2	by	by	ADP
ejpam-4645	245	3	(	(	PUNCT
ejpam-4645	245	4	iii	iii	NOUN
ejpam-4645	245	5	)	)	PUNCT
ejpam-4645	245	6	,	,	PUNCT
ejpam-4645	245	7	tz	tz	PROPN
ejpam-4645	245	8	is	be	AUX
ejpam-4645	245	9	a	a	DET
ejpam-4645	245	10	stable	stable	ADJ
ejpam-4645	245	11	strictly	strictly	ADV
ejpam-4645	245	12	locating	locate	VERB
ejpam-4645	245	13	set	set	NOUN
ejpam-4645	245	14	.	.	PUNCT
ejpam-4645	246	1	hence	hence	ADV
ejpam-4645	246	2	,	,	PUNCT
ejpam-4645	246	3	if	if	SCONJ
ejpam-4645	246	4	z	z	PROPN
ejpam-4645	246	5	̸=	̸=	PROPN
ejpam-4645	246	6	y	y	PROPN
ejpam-4645	246	7	,	,	PUNCT
ejpam-4645	246	8	then	then	ADV
ejpam-4645	246	9	ty	ty	INTJ
ejpam-4645	246	10	is	be	AUX
ejpam-4645	246	11	strictly	strictly	ADV
ejpam-4645	246	12	locating	locate	VERB
ejpam-4645	246	13	and	and	CCONJ
ejpam-4645	246	14	,	,	PUNCT
ejpam-4645	246	15	if	if	SCONJ
ejpam-4645	246	16	z	z	NOUN
ejpam-4645	246	17	=	=	SYM
ejpam-4645	246	18	y	y	PROPN
ejpam-4645	246	19	,	,	PUNCT
ejpam-4645	246	20	then	then	ADV
ejpam-4645	246	21	ty	ty	INTJ
ejpam-4645	246	22	\	\	PROPN
ejpam-4645	246	23	{	{	PUNCT
ejpam-4645	246	24	a	a	PRON
ejpam-4645	246	25	}	}	PUNCT
ejpam-4645	246	26	is	be	AUX
ejpam-4645	246	27	strictly	strictly	ADV
ejpam-4645	246	28	locating	locate	VERB
ejpam-4645	246	29	.	.	PUNCT
ejpam-4645	247	1	finally	finally	ADV
ejpam-4645	247	2	,	,	PUNCT
ejpam-4645	247	3	let	let	VERB
ejpam-4645	247	4	u	u	PRON
ejpam-4645	247	5	and	and	CCONJ
ejpam-4645	247	6	w	w	PROPN
ejpam-4645	247	7	be	be	AUX
ejpam-4645	247	8	distinct	distinct	ADJ
ejpam-4645	247	9	non	non	ADJ
ejpam-4645	247	10	-	-	ADJ
ejpam-4645	247	11	adjacent	adjacent	ADJ
ejpam-4645	247	12	vertices	vertex	NOUN
ejpam-4645	247	13	of	of	ADP
ejpam-4645	247	14	g	g	NOUN
ejpam-4645	247	15	with	with	ADP
ejpam-4645	247	16	ng(u	ng(u	NOUN
ejpam-4645	247	17	)	)	PUNCT
ejpam-4645	247	18	=	=	NOUN
ejpam-4645	247	19	ng(w	ng(w	NOUN
ejpam-4645	247	20	)	)	PUNCT
ejpam-4645	247	21	.	.	PUNCT
ejpam-4645	248	1	if	if	SCONJ
ejpam-4645	248	2	tu	tu	PROPN
ejpam-4645	248	3	is	be	AUX
ejpam-4645	248	4	dominating	dominate	VERB
ejpam-4645	248	5	is	be	AUX
ejpam-4645	248	6	a	a	DET
ejpam-4645	248	7	dominating	dominating	NOUN
ejpam-4645	248	8	set	set	NOUN
ejpam-4645	248	9	,	,	PUNCT
ejpam-4645	248	10	then	then	ADV
ejpam-4645	248	11	we	we	PRON
ejpam-4645	248	12	are	be	AUX
ejpam-4645	248	13	done	do	VERB
ejpam-4645	248	14	.	.	PUNCT
ejpam-4645	249	1	suppose	suppose	VERB
ejpam-4645	249	2	tu	tu	PROPN
ejpam-4645	249	3	is	be	AUX
ejpam-4645	249	4	not	not	PART
ejpam-4645	249	5	a	a	DET
ejpam-4645	249	6	dominating	dominating	NOUN
ejpam-4645	249	7	set	set	NOUN
ejpam-4645	249	8	in	in	ADP
ejpam-4645	249	9	h.	h.	PROPN
ejpam-4645	249	10	then	then	ADV
ejpam-4645	249	11	by	by	ADP
ejpam-4645	249	12	(	(	PUNCT
ejpam-4645	249	13	iv	iv	X
ejpam-4645	249	14	)	)	PUNCT
ejpam-4645	249	15	,	,	PUNCT
ejpam-4645	249	16	tw	tw	PROPN
ejpam-4645	249	17	is	be	AUX
ejpam-4645	249	18	a	a	DET
ejpam-4645	249	19	stable	stable	ADJ
ejpam-4645	249	20	dominating	dominating	NOUN
ejpam-4645	249	21	set	set	NOUN
ejpam-4645	249	22	of	of	ADP
ejpam-4645	249	23	h.	h.	PROPN
ejpam-4645	249	24	this	this	PRON
ejpam-4645	249	25	implies	imply	VERB
ejpam-4645	249	26	that	that	SCONJ
ejpam-4645	249	27	tw	tw	PROPN
ejpam-4645	249	28	is	be	AUX
ejpam-4645	249	29	a	a	DET
ejpam-4645	249	30	dominating	dominating	NOUN
ejpam-4645	249	31	set	set	NOUN
ejpam-4645	249	32	if	if	SCONJ
ejpam-4645	249	33	w	w	PROPN
ejpam-4645	249	34	̸=	̸=	PROPN
ejpam-4645	249	35	y	y	PROPN
ejpam-4645	249	36	and	and	CCONJ
ejpam-4645	249	37	ty	ty	NOUN
ejpam-4645	249	38	\	\	PROPN
ejpam-4645	249	39	{	{	PUNCT
ejpam-4645	249	40	a	a	PRON
ejpam-4645	249	41	}	}	PUNCT
ejpam-4645	249	42	is	be	AUX
ejpam-4645	249	43	a	a	DET
ejpam-4645	249	44	dominating	dominating	NOUN
ejpam-4645	249	45	set	set	NOUN
ejpam-4645	249	46	if	if	SCONJ
ejpam-4645	249	47	w	w	PROPN
ejpam-4645	249	48	=	=	SYM
ejpam-4645	249	49	y.	y.	PROPN
ejpam-4645	249	50	therefore	therefore	ADV
ejpam-4645	249	51	,	,	PUNCT
ejpam-4645	249	52	c∗	c∗	PROPN
ejpam-4645	249	53	is	be	AUX
ejpam-4645	249	54	a	a	DET
ejpam-4645	249	55	locating	locate	VERB
ejpam-4645	249	56	-	-	PUNCT
ejpam-4645	249	57	dominating	dominate	VERB
ejpam-4645	249	58	set	set	NOUN
ejpam-4645	249	59	of	of	ADP
ejpam-4645	249	60	g[h	g[h	PROPN
ejpam-4645	249	61	]	]	PUNCT
ejpam-4645	249	62	.	.	PUNCT
ejpam-4645	250	1	accordingly	accordingly	ADV
ejpam-4645	250	2	,	,	PUNCT
ejpam-4645	250	3	c	c	PROPN
ejpam-4645	250	4	is	be	AUX
ejpam-4645	250	5	a	a	DET
ejpam-4645	250	6	stable	stable	ADJ
ejpam-4645	250	7	locating	locating	NOUN
ejpam-4645	250	8	-	-	PUNCT
ejpam-4645	250	9	dominating	dominate	VERB
ejpam-4645	250	10	set	set	NOUN
ejpam-4645	250	11	of	of	ADP
ejpam-4645	250	12	g[h	g[h	PROPN
ejpam-4645	250	13	]	]	PUNCT
ejpam-4645	250	14	.	.	PUNCT
ejpam-4645	251	1	given	give	VERB
ejpam-4645	251	2	a	a	DET
ejpam-4645	251	3	non	non	ADJ
ejpam-4645	251	4	-	-	ADJ
ejpam-4645	251	5	trivial	trivial	ADJ
ejpam-4645	251	6	connected	connected	ADJ
ejpam-4645	251	7	graph	graph	NOUN
ejpam-4645	251	8	h	h	NOUN
ejpam-4645	251	9	,	,	PUNCT
ejpam-4645	251	10	we	we	PRON
ejpam-4645	251	11	denote	denote	VERB
ejpam-4645	251	12	by	by	ADP
ejpam-4645	251	13	γsl(h	γsl(h	PROPN
ejpam-4645	251	14	)	)	PUNCT
ejpam-4645	251	15	the	the	DET
ejpam-4645	251	16	smallest	small	ADJ
ejpam-4645	251	17	size	size	NOUN
ejpam-4645	251	18	of	of	ADP
ejpam-4645	251	19	a	a	DET
ejpam-4645	251	20	dominating	dominate	VERB
ejpam-4645	251	21	stable	stable	ADJ
ejpam-4645	251	22	locating	locating	NOUN
ejpam-4645	251	23	set	set	NOUN
ejpam-4645	251	24	of	of	ADP
ejpam-4645	251	25	h	h	NOUN
ejpam-4645	251	26	,	,	PUNCT
ejpam-4645	251	27	i.e.	i.e.	X
ejpam-4645	251	28	,	,	PUNCT
ejpam-4645	251	29	γsl(h	γsl(h	PROPN
ejpam-4645	251	30	)	)	PUNCT
ejpam-4645	252	1	=	=	NOUN
ejpam-4645	252	2	min{|s|	min{|s|	NOUN
ejpam-4645	252	3	:	:	PUNCT
ejpam-4645	252	4	s	s	VERB
ejpam-4645	252	5	is	be	AUX
ejpam-4645	252	6	a	a	DET
ejpam-4645	252	7	dominating	dominate	VERB
ejpam-4645	252	8	stable	stable	ADJ
ejpam-4645	252	9	locating	locating	NOUN
ejpam-4645	252	10	set	set	NOUN
ejpam-4645	252	11	of	of	ADP
ejpam-4645	252	12	h	h	NOUN
ejpam-4645	252	13	}	}	PUNCT
ejpam-4645	252	14	.	.	PUNCT
ejpam-4645	253	1	any	any	DET
ejpam-4645	253	2	dominating	dominate	VERB
ejpam-4645	253	3	stable	stable	ADJ
ejpam-4645	253	4	locating	locating	NOUN
ejpam-4645	253	5	set	set	NOUN
ejpam-4645	253	6	of	of	ADP
ejpam-4645	253	7	h	h	NOUN
ejpam-4645	253	8	of	of	ADP
ejpam-4645	253	9	size	size	NOUN
ejpam-4645	253	10	γsl(h	γsl(h	PROPN
ejpam-4645	253	11	)	)	PUNCT
ejpam-4645	253	12	is	be	AUX
ejpam-4645	253	13	called	call	VERB
ejpam-4645	253	14	a	a	DET
ejpam-4645	253	15	γsl	γsl	NOUN
ejpam-4645	253	16	-	-	PUNCT
ejpam-4645	253	17	set	set	NOUN
ejpam-4645	253	18	of	of	ADP
ejpam-4645	253	19	h.	h.	PROPN
ejpam-4645	253	20	note	note	VERB
ejpam-4645	253	21	that	that	SCONJ
ejpam-4645	253	22	since	since	SCONJ
ejpam-4645	253	23	v	v	X
ejpam-4645	253	24	(	(	PUNCT
ejpam-4645	253	25	h	h	NOUN
ejpam-4645	253	26	)	)	PUNCT
ejpam-4645	253	27	is	be	AUX
ejpam-4645	253	28	a	a	DET
ejpam-4645	253	29	dominating	dominate	VERB
ejpam-4645	253	30	stable	stable	ADJ
ejpam-4645	253	31	locating	locating	NOUN
ejpam-4645	253	32	set	set	NOUN
ejpam-4645	253	33	,	,	PUNCT
ejpam-4645	253	34	it	it	PRON
ejpam-4645	253	35	follows	follow	VERB
ejpam-4645	253	36	that	that	SCONJ
ejpam-4645	253	37	h	h	NOUN
ejpam-4645	253	38	admits	admit	VERB
ejpam-4645	253	39	a	a	DET
ejpam-4645	253	40	dominating	dominating	NOUN
ejpam-4645	253	41	stable	stable	ADJ
ejpam-4645	253	42	locating	locating	NOUN
ejpam-4645	253	43	set	set	NOUN
ejpam-4645	253	44	.	.	PUNCT
ejpam-4645	254	1	consider	consider	VERB
ejpam-4645	254	2	the	the	DET
ejpam-4645	254	3	graph	graph	NOUN
ejpam-4645	254	4	h	h	NOUN
ejpam-4645	254	5	in	in	ADP
ejpam-4645	254	6	figure	figure	NOUN
ejpam-4645	254	7	1	1	NUM
ejpam-4645	254	8	below	below	ADV
ejpam-4645	254	9	.	.	PUNCT
ejpam-4645	255	1	clearly	clearly	ADV
ejpam-4645	255	2	,	,	PUNCT
ejpam-4645	255	3	s	s	VERB
ejpam-4645	255	4	=	=	PUNCT
ejpam-4645	255	5	{	{	PUNCT
ejpam-4645	255	6	c	c	NOUN
ejpam-4645	255	7	,	,	PUNCT
ejpam-4645	255	8	d	d	NOUN
ejpam-4645	255	9	,	,	PUNCT
ejpam-4645	255	10	e	e	NOUN
ejpam-4645	255	11	}	}	PUNCT
ejpam-4645	255	12	is	be	AUX
ejpam-4645	255	13	a	a	DET
ejpam-4645	255	14	dominating	dominate	VERB
ejpam-4645	255	15	stable	stable	ADJ
ejpam-4645	255	16	locating	locating	NOUN
ejpam-4645	255	17	set	set	NOUN
ejpam-4645	255	18	of	of	ADP
ejpam-4645	255	19	h	h	NOUN
ejpam-4645	255	20	and	and	CCONJ
ejpam-4645	255	21	γsl(h	γsl(h	PROPN
ejpam-4645	255	22	)	)	PUNCT
ejpam-4645	255	23	=	=	PUNCT
ejpam-4645	255	24	|s|	|s|	NOUN
ejpam-4645	255	25	=	=	SYM
ejpam-4645	255	26	3	3	PROPN
ejpam-4645	255	27	.	.	PUNCT
ejpam-4645	255	28	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-4645	255	29	....................................	....................................	PUNCT
ejpam-4645	256	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-4645	256	2	................................................................................................................................................................................	................................................................................................................................................................................	PUNCT
ejpam-4645	257	1	....................................	....................................	PUNCT
ejpam-4645	257	2	............	............	PUNCT
ejpam-4645	257	3	...........	...........	PUNCT
ejpam-4645	257	4	...........	...........	PUNCT
ejpam-4645	257	5	...........	...........	PUNCT
ejpam-4645	257	6	...........	...........	PUNCT
ejpam-4645	257	7	...........	...........	PUNCT
ejpam-4645	257	8	...........	...........	PUNCT
ejpam-4645	257	9	...........	...........	PUNCT
ejpam-4645	257	10	...........	...........	PUNCT
ejpam-4645	257	11	...........	...........	PUNCT
ejpam-4645	257	12	...........	...........	PUNCT
ejpam-4645	257	13	...........	...........	PUNCT
ejpam-4645	257	14	...........	...........	PUNCT
ejpam-4645	257	15	........	........	PUNCT
ejpam-4645	257	16	....................................	....................................	PUNCT
ejpam-4645	258	1	....................................	....................................	PUNCT
ejpam-4645	258	2	.........	.........	PUNCT
ejpam-4645	258	3	........	........	PUNCT
ejpam-4645	258	4	........	........	PUNCT
ejpam-4645	258	5	........	........	PUNCT
ejpam-4645	258	6	........	........	PUNCT
ejpam-4645	258	7	........	........	PUNCT
ejpam-4645	258	8	........	........	PUNCT
ejpam-4645	258	9	........	........	PUNCT
ejpam-4645	258	10	........	........	PUNCT
ejpam-4645	258	11	........	........	PUNCT
ejpam-4645	258	12	........	........	PUNCT
ejpam-4645	258	13	........	........	PUNCT
ejpam-4645	258	14	.......	.......	PUNCT
ejpam-4645	259	1	....................................	....................................	PUNCT
ejpam-4645	260	1	....................................	....................................	PUNCT
ejpam-4645	261	1	•	•	NUM
ejpam-4645	261	2	•	•	NUM
ejpam-4645	261	3	•	•	NOUN
ejpam-4645	261	4	a	a	DET
ejpam-4645	261	5	b	b	NOUN
ejpam-4645	261	6	c	c	NOUN
ejpam-4645	261	7	d	d	X
ejpam-4645	261	8	e	e	X
ejpam-4645	261	9	figure	figure	VERB
ejpam-4645	261	10	1	1	NUM
ejpam-4645	261	11	corollary	corollary	ADJ
ejpam-4645	261	12	4	4	NUM
ejpam-4645	261	13	.	.	PUNCT
ejpam-4645	262	1	let	let	VERB
ejpam-4645	262	2	g	g	NOUN
ejpam-4645	262	3	and	and	CCONJ
ejpam-4645	262	4	h	h	PROPN
ejpam-4645	262	5	be	be	VERB
ejpam-4645	262	6	non	non	ADJ
ejpam-4645	262	7	-	-	ADJ
ejpam-4645	262	8	trivial	trivial	ADJ
ejpam-4645	262	9	connected	connected	ADJ
ejpam-4645	262	10	graphs	graph	NOUN
ejpam-4645	262	11	.	.	PUNCT
ejpam-4645	263	1	if	if	SCONJ
ejpam-4645	263	2	g	g	PROPN
ejpam-4645	263	3	is	be	AUX
ejpam-4645	263	4	point	point	NOUN
ejpam-4645	263	5	determining	determine	VERB
ejpam-4645	263	6	,	,	PUNCT
ejpam-4645	263	7	then	then	ADV
ejpam-4645	263	8	γsl(g[h	γsl(g[h	NOUN
ejpam-4645	263	9	]	]	X
ejpam-4645	263	10	)	)	PUNCT
ejpam-4645	263	11	≤	≤	NUM
ejpam-4645	263	12	|v	|v	X
ejpam-4645	263	13	(	(	PUNCT
ejpam-4645	263	14	g)|γsl(h	g)|γsl(h	NOUN
ejpam-4645	263	15	)	)	PUNCT
ejpam-4645	263	16	.	.	PUNCT
ejpam-4645	264	1	proof	proof	NOUN
ejpam-4645	264	2	.	.	PUNCT
ejpam-4645	265	1	let	let	VERB
ejpam-4645	265	2	d	d	PRON
ejpam-4645	265	3	be	be	AUX
ejpam-4645	265	4	a	a	DET
ejpam-4645	265	5	γsl	γsl	NOUN
ejpam-4645	265	6	-	-	PUNCT
ejpam-4645	265	7	set	set	NOUN
ejpam-4645	265	8	of	of	ADP
ejpam-4645	265	9	h	h	NOUN
ejpam-4645	265	10	and	and	CCONJ
ejpam-4645	265	11	let	let	VERB
ejpam-4645	265	12	tx	tx	VERB
ejpam-4645	265	13	=	=	PUNCT
ejpam-4645	266	1	d	d	PROPN
ejpam-4645	266	2	for	for	ADP
ejpam-4645	266	3	each	each	DET
ejpam-4645	266	4	x	x	SYM
ejpam-4645	266	5	∈	∈	PROPN
ejpam-4645	266	6	v	v	NOUN
ejpam-4645	266	7	(	(	PUNCT
ejpam-4645	266	8	g	g	NOUN
ejpam-4645	266	9	)	)	PUNCT
ejpam-4645	266	10	.	.	PUNCT
ejpam-4645	267	1	then	then	ADV
ejpam-4645	267	2	c	c	X
ejpam-4645	267	3	=	=	SYM
ejpam-4645	267	4	⋃	⋃	PROPN
ejpam-4645	267	5	x∈v	x∈v	PROPN
ejpam-4645	267	6	(	(	PUNCT
ejpam-4645	267	7	g	g	NOUN
ejpam-4645	267	8	)	)	PUNCT
ejpam-4645	267	9	(	(	PUNCT
ejpam-4645	267	10	{	{	PUNCT
ejpam-4645	267	11	x	x	NOUN
ejpam-4645	267	12	}	}	PUNCT
ejpam-4645	267	13	×	×	PROPN
ejpam-4645	267	14	tx	tx	PROPN
ejpam-4645	267	15	)	)	PUNCT
ejpam-4645	267	16	is	be	AUX
ejpam-4645	267	17	a	a	DET
ejpam-4645	267	18	stable	stable	ADJ
ejpam-4645	267	19	locating	locating	NOUN
ejpam-4645	267	20	-	-	PUNCT
ejpam-4645	267	21	dominating	dominate	VERB
ejpam-4645	267	22	set	set	NOUN
ejpam-4645	267	23	of	of	ADP
ejpam-4645	267	24	g[h	g[h	PROPN
ejpam-4645	267	25	]	]	PUNCT
ejpam-4645	267	26	by	by	ADP
ejpam-4645	267	27	theorem	theorem	NOUN
ejpam-4645	267	28	5	5	NUM
ejpam-4645	267	29	.	.	PUNCT
ejpam-4645	268	1	thus	thus	ADV
ejpam-4645	268	2	,	,	PUNCT
ejpam-4645	268	3	γsl(g[h	γsl(g[h	NOUN
ejpam-4645	268	4	]	]	PUNCT
ejpam-4645	268	5	)	)	PUNCT
ejpam-4645	268	6	≤	≤	PROPN
ejpam-4645	268	7	|c|	|c|	PROPN
ejpam-4645	268	8	=	=	SYM
ejpam-4645	268	9	|v	|v	PROPN
ejpam-4645	268	10	(	(	PUNCT
ejpam-4645	268	11	g)|γsl(h	g)|γsl(h	NOUN
ejpam-4645	268	12	)	)	PUNCT
ejpam-4645	268	13	.	.	PUNCT
ejpam-4645	269	1	references	reference	NOUN
ejpam-4645	269	2	488	488	NUM
ejpam-4645	269	3	note	note	VERB
ejpam-4645	269	4	that	that	SCONJ
ejpam-4645	269	5	the	the	DET
ejpam-4645	269	6	bound	bind	VERB
ejpam-4645	269	7	in	in	ADP
ejpam-4645	269	8	corollary	corollary	ADJ
ejpam-4645	269	9	4	4	NUM
ejpam-4645	269	10	is	be	AUX
ejpam-4645	269	11	tight	tight	ADJ
ejpam-4645	269	12	.	.	PUNCT
ejpam-4645	270	1	to	to	PART
ejpam-4645	270	2	see	see	VERB
ejpam-4645	270	3	this	this	PRON
ejpam-4645	270	4	,	,	PUNCT
ejpam-4645	270	5	consider	consider	VERB
ejpam-4645	270	6	the	the	DET
ejpam-4645	270	7	graph	graph	NOUN
ejpam-4645	270	8	h	h	NOUN
ejpam-4645	270	9	in	in	ADP
ejpam-4645	270	10	figure	figure	NOUN
ejpam-4645	270	11	1	1	NUM
ejpam-4645	270	12	.	.	PUNCT
ejpam-4645	271	1	it	it	PRON
ejpam-4645	271	2	can	can	AUX
ejpam-4645	271	3	easily	easily	ADV
ejpam-4645	271	4	be	be	AUX
ejpam-4645	271	5	verified	verify	VERB
ejpam-4645	271	6	that	that	SCONJ
ejpam-4645	271	7	γsl(p3[h	γsl(p3[h	ADP
ejpam-4645	271	8	]	]	X
ejpam-4645	271	9	)	)	PUNCT
ejpam-4645	271	10	=	=	SYM
ejpam-4645	271	11	9	9	NUM
ejpam-4645	271	12	=	=	SYM
ejpam-4645	271	13	3.3	3.3	NUM
ejpam-4645	271	14	=	=	SYM
ejpam-4645	271	15	|v	|v	PROPN
ejpam-4645	271	16	(	(	PUNCT
ejpam-4645	271	17	p3)|γsl(h	p3)|γsl(h	PROPN
ejpam-4645	271	18	)	)	PUNCT
ejpam-4645	271	19	.	.	PUNCT
ejpam-4645	272	1	the	the	DET
ejpam-4645	272	2	next	next	ADJ
ejpam-4645	272	3	result	result	NOUN
ejpam-4645	272	4	follows	follow	VERB
ejpam-4645	272	5	from	from	ADP
ejpam-4645	272	6	theorem	theorem	ADJ
ejpam-4645	272	7	5	5	NUM
ejpam-4645	272	8	.	.	PUNCT
ejpam-4645	272	9	corollary	corollary	ADJ
ejpam-4645	272	10	5	5	NUM
ejpam-4645	272	11	.	.	PUNCT
ejpam-4645	273	1	let	let	VERB
ejpam-4645	273	2	g	g	PRON
ejpam-4645	273	3	be	be	AUX
ejpam-4645	273	4	a	a	DET
ejpam-4645	273	5	connected	connected	ADJ
ejpam-4645	273	6	totally	totally	ADV
ejpam-4645	273	7	point	point	NOUN
ejpam-4645	273	8	determining	determine	VERB
ejpam-4645	273	9	graph	graph	NOUN
ejpam-4645	273	10	and	and	CCONJ
ejpam-4645	273	11	let	let	VERB
ejpam-4645	273	12	h	h	NOUN
ejpam-4645	273	13	be	be	AUX
ejpam-4645	273	14	any	any	DET
ejpam-4645	273	15	non	non	ADJ
ejpam-4645	273	16	-	-	ADJ
ejpam-4645	273	17	trivial	trivial	ADJ
ejpam-4645	273	18	connected	connected	ADJ
ejpam-4645	273	19	graph	graph	NOUN
ejpam-4645	273	20	.	.	PUNCT
ejpam-4645	274	1	then	then	ADV
ejpam-4645	274	2	c	c	X
ejpam-4645	274	3	=	=	PUNCT
ejpam-4645	274	4	⋃	⋃	PROPN
ejpam-4645	274	5	x∈s	x∈s	NOUN
ejpam-4645	274	6	(	(	PUNCT
ejpam-4645	274	7	{	{	PUNCT
ejpam-4645	274	8	x	x	NOUN
ejpam-4645	274	9	}	}	PUNCT
ejpam-4645	274	10	×	×	PROPN
ejpam-4645	274	11	tx	tx	PROPN
ejpam-4645	274	12	)	)	PUNCT
ejpam-4645	274	13	,	,	PUNCT
ejpam-4645	274	14	where	where	SCONJ
ejpam-4645	274	15	s	s	VERB
ejpam-4645	274	16	⊆	⊆	NUM
ejpam-4645	274	17	v	v	NOUN
ejpam-4645	274	18	(	(	PUNCT
ejpam-4645	274	19	g	g	NOUN
ejpam-4645	274	20	)	)	PUNCT
ejpam-4645	274	21	and	and	CCONJ
ejpam-4645	274	22	tx	tx	VERB
ejpam-4645	274	23	⊆	⊆	NUM
ejpam-4645	274	24	v	v	NOUN
ejpam-4645	274	25	(	(	PUNCT
ejpam-4645	274	26	h	h	NOUN
ejpam-4645	274	27	)	)	PUNCT
ejpam-4645	274	28	for	for	ADP
ejpam-4645	274	29	each	each	DET
ejpam-4645	274	30	x	x	SYM
ejpam-4645	274	31	∈	∈	PROPN
ejpam-4645	274	32	s	s	NOUN
ejpam-4645	274	33	,	,	PUNCT
ejpam-4645	274	34	is	be	AUX
ejpam-4645	274	35	a	a	DET
ejpam-4645	274	36	γsl	γsl	NOUN
ejpam-4645	274	37	-	-	PUNCT
ejpam-4645	274	38	set	set	NOUN
ejpam-4645	274	39	of	of	ADP
ejpam-4645	274	40	g	g	PROPN
ejpam-4645	275	1	[	[	X
ejpam-4645	275	2	h	h	X
ejpam-4645	275	3	]	]	X
ejpam-4645	275	4	if	if	SCONJ
ejpam-4645	275	5	and	and	CCONJ
ejpam-4645	275	6	only	only	ADV
ejpam-4645	275	7	if	if	SCONJ
ejpam-4645	275	8	s	s	VERB
ejpam-4645	275	9	=	=	SYM
ejpam-4645	275	10	v	v	X
ejpam-4645	275	11	(	(	PUNCT
ejpam-4645	275	12	g	g	NOUN
ejpam-4645	275	13	)	)	PUNCT
ejpam-4645	275	14	and	and	CCONJ
ejpam-4645	275	15	tx	tx	PROPN
ejpam-4645	275	16	is	be	AUX
ejpam-4645	275	17	an	an	DET
ejpam-4645	275	18	sbln	sbln	NOUN
ejpam-4645	275	19	-	-	PUNCT
ejpam-4645	275	20	set	set	NOUN
ejpam-4645	275	21	of	of	ADP
ejpam-4645	275	22	h	h	NOUN
ejpam-4645	275	23	for	for	ADP
ejpam-4645	275	24	every	every	DET
ejpam-4645	275	25	x	x	SYM
ejpam-4645	275	26	∈	∈	PROPN
ejpam-4645	275	27	v	v	NOUN
ejpam-4645	275	28	(	(	PUNCT
ejpam-4645	275	29	g	g	NOUN
ejpam-4645	275	30	)	)	PUNCT
ejpam-4645	275	31	.	.	PUNCT
ejpam-4645	276	1	in	in	ADP
ejpam-4645	276	2	particular	particular	ADJ
ejpam-4645	276	3	,	,	PUNCT
ejpam-4645	276	4	γsl(g[h	γsl(g[h	NOUN
ejpam-4645	276	5	]	]	X
ejpam-4645	276	6	)	)	PUNCT
ejpam-4645	276	7	=	=	SYM
ejpam-4645	276	8	|v	|v	PROPN
ejpam-4645	276	9	(	(	PUNCT
ejpam-4645	276	10	g)|sbln(h	g)|sbln(h	PROPN
ejpam-4645	276	11	)	)	PUNCT
ejpam-4645	276	12	.	.	PUNCT
ejpam-4645	277	1	proof	proof	NOUN
ejpam-4645	277	2	.	.	PUNCT
ejpam-4645	278	1	by	by	ADP
ejpam-4645	278	2	theorem	theorem	NOUN
ejpam-4645	278	3	5	5	NUM
ejpam-4645	278	4	,	,	PUNCT
ejpam-4645	278	5	c	c	NOUN
ejpam-4645	278	6	=	=	PUNCT
ejpam-4645	278	7	⋃	⋃	PROPN
ejpam-4645	278	8	x∈s	x∈s	NOUN
ejpam-4645	278	9	(	(	PUNCT
ejpam-4645	278	10	{	{	PUNCT
ejpam-4645	278	11	x	x	NOUN
ejpam-4645	278	12	}	}	PUNCT
ejpam-4645	278	13	×	×	PROPN
ejpam-4645	278	14	tx	tx	PROPN
ejpam-4645	278	15	)	)	PUNCT
ejpam-4645	278	16	,	,	PUNCT
ejpam-4645	278	17	where	where	SCONJ
ejpam-4645	278	18	is	be	AUX
ejpam-4645	278	19	a	a	DET
ejpam-4645	278	20	γsl	γsl	NOUN
ejpam-4645	278	21	-	-	PUNCT
ejpam-4645	278	22	set	set	NOUN
ejpam-4645	278	23	of	of	ADP
ejpam-4645	278	24	g	g	PROPN
ejpam-4645	279	1	[	[	X
ejpam-4645	279	2	h	h	X
ejpam-4645	279	3	]	]	X
ejpam-4645	279	4	if	if	SCONJ
ejpam-4645	279	5	and	and	CCONJ
ejpam-4645	279	6	only	only	ADV
ejpam-4645	279	7	if	if	SCONJ
ejpam-4645	279	8	s	s	VERB
ejpam-4645	279	9	=	=	SYM
ejpam-4645	279	10	v	v	X
ejpam-4645	279	11	(	(	PUNCT
ejpam-4645	279	12	g	g	NOUN
ejpam-4645	279	13	)	)	PUNCT
ejpam-4645	279	14	and	and	CCONJ
ejpam-4645	279	15	tx	tx	PROPN
ejpam-4645	279	16	is	be	AUX
ejpam-4645	279	17	an	an	DET
ejpam-4645	279	18	sbln	sbln	NOUN
ejpam-4645	279	19	-	-	PUNCT
ejpam-4645	279	20	set	set	NOUN
ejpam-4645	279	21	of	of	ADP
ejpam-4645	279	22	h	h	NOUN
ejpam-4645	279	23	for	for	ADP
ejpam-4645	279	24	every	every	DET
ejpam-4645	279	25	x	x	SYM
ejpam-4645	279	26	∈	∈	PROPN
ejpam-4645	279	27	v	v	NOUN
ejpam-4645	279	28	(	(	PUNCT
ejpam-4645	279	29	g	g	NOUN
ejpam-4645	279	30	)	)	PUNCT
ejpam-4645	279	31	.	.	PUNCT
ejpam-4645	280	1	now	now	ADV
ejpam-4645	280	2	,	,	PUNCT
ejpam-4645	280	3	let	let	VERB
ejpam-4645	280	4	d	d	PRON
ejpam-4645	280	5	be	be	AUX
ejpam-4645	280	6	an	an	DET
ejpam-4645	280	7	sbln	sbln	NOUN
ejpam-4645	280	8	-	-	PUNCT
ejpam-4645	280	9	set	set	NOUN
ejpam-4645	280	10	of	of	ADP
ejpam-4645	280	11	h	h	NOUN
ejpam-4645	280	12	and	and	CCONJ
ejpam-4645	280	13	let	let	VERB
ejpam-4645	280	14	tx	tx	VERB
ejpam-4645	280	15	=	=	PUNCT
ejpam-4645	281	1	d	d	PROPN
ejpam-4645	281	2	for	for	ADP
ejpam-4645	281	3	each	each	DET
ejpam-4645	281	4	x	x	SYM
ejpam-4645	281	5	∈	∈	PROPN
ejpam-4645	281	6	v	v	NOUN
ejpam-4645	281	7	(	(	PUNCT
ejpam-4645	281	8	g	g	NOUN
ejpam-4645	281	9	)	)	PUNCT
ejpam-4645	281	10	.	.	PUNCT
ejpam-4645	282	1	then	then	ADV
ejpam-4645	282	2	c0	c0	PROPN
ejpam-4645	282	3	=	=	PUNCT
ejpam-4645	282	4	⋃	⋃	PROPN
ejpam-4645	282	5	x∈v	x∈v	PROPN
ejpam-4645	282	6	(	(	PUNCT
ejpam-4645	282	7	g	g	NOUN
ejpam-4645	282	8	)	)	PUNCT
ejpam-4645	282	9	(	(	PUNCT
ejpam-4645	282	10	{	{	PUNCT
ejpam-4645	282	11	x	x	NOUN
ejpam-4645	282	12	}	}	PUNCT
ejpam-4645	282	13	×	×	PROPN
ejpam-4645	282	14	tx	tx	PROPN
ejpam-4645	282	15	)	)	PUNCT
ejpam-4645	282	16	is	be	AUX
ejpam-4645	282	17	a	a	DET
ejpam-4645	282	18	γsl	γsl	NOUN
ejpam-4645	282	19	-	-	PUNCT
ejpam-4645	282	20	set	set	NOUN
ejpam-4645	282	21	of	of	ADP
ejpam-4645	282	22	g	g	PROPN
ejpam-4645	283	1	[	[	X
ejpam-4645	283	2	h	h	X
ejpam-4645	283	3	]	]	X
ejpam-4645	283	4	.	.	PUNCT
ejpam-4645	284	1	therefore	therefore	ADV
ejpam-4645	284	2	,	,	PUNCT
ejpam-4645	284	3	γsl(g[h	γsl(g[h	NOUN
ejpam-4645	284	4	]	]	X
ejpam-4645	284	5	)	)	PUNCT
ejpam-4645	285	1	=	=	SYM
ejpam-4645	285	2	|c|	|c|	PROPN
ejpam-4645	285	3	=	=	SYM
ejpam-4645	285	4	|v	|v	PROPN
ejpam-4645	285	5	(	(	PUNCT
ejpam-4645	285	6	g)|sbln(h	g)|sbln(h	PROPN
ejpam-4645	285	7	)	)	PUNCT
ejpam-4645	285	8	.	.	PUNCT
ejpam-4645	286	1	3	3	X
ejpam-4645	286	2	.	.	X
ejpam-4645	286	3	conclusion	conclusion	NOUN
ejpam-4645	286	4	the	the	DET
ejpam-4645	286	5	locating	locate	VERB
ejpam-4645	286	6	dominating	dominating	NOUN
ejpam-4645	286	7	sets	set	NOUN
ejpam-4645	286	8	in	in	ADP
ejpam-4645	286	9	the	the	DET
ejpam-4645	286	10	edge	edge	NOUN
ejpam-4645	286	11	corona	corona	NOUN
ejpam-4645	286	12	of	of	ADP
ejpam-4645	286	13	graphs	graph	NOUN
ejpam-4645	286	14	were	be	AUX
ejpam-4645	286	15	characterized	characterize	VERB
ejpam-4645	286	16	and	and	CCONJ
ejpam-4645	286	17	bounds	bound	NOUN
ejpam-4645	286	18	for	for	ADP
ejpam-4645	286	19	its	its	PRON
ejpam-4645	286	20	locating	locate	VERB
ejpam-4645	286	21	-	-	PUNCT
ejpam-4645	286	22	domination	domination	NOUN
ejpam-4645	286	23	number	number	NOUN
ejpam-4645	286	24	were	be	AUX
ejpam-4645	286	25	obtained	obtain	VERB
ejpam-4645	286	26	.	.	PUNCT
ejpam-4645	287	1	the	the	DET
ejpam-4645	287	2	stable	stable	ADJ
ejpam-4645	287	3	locating	locating	NOUN
ejpam-4645	287	4	-	-	PUNCT
ejpam-4645	287	5	dominating	dominating	NOUN
ejpam-4645	287	6	sets	set	NOUN
ejpam-4645	287	7	in	in	ADP
ejpam-4645	287	8	the	the	DET
ejpam-4645	287	9	edge	edge	NOUN
ejpam-4645	287	10	corona	corona	NOUN
ejpam-4645	287	11	and	and	CCONJ
ejpam-4645	287	12	lexicographic	lexicographic	ADJ
ejpam-4645	287	13	products	product	NOUN
ejpam-4645	287	14	of	of	ADP
ejpam-4645	287	15	graphs	graph	NOUN
ejpam-4645	287	16	were	be	AUX
ejpam-4645	287	17	also	also	ADV
ejpam-4645	287	18	characterized	characterize	VERB
ejpam-4645	287	19	.	.	PUNCT
ejpam-4645	288	1	tight	tight	ADJ
ejpam-4645	288	2	bounds	bound	NOUN
ejpam-4645	288	3	for	for	ADP
ejpam-4645	288	4	their	their	PRON
ejpam-4645	288	5	stable	stable	ADJ
ejpam-4645	288	6	locating	locating	NOUN
ejpam-4645	288	7	-	-	PUNCT
ejpam-4645	288	8	domination	domination	NOUN
ejpam-4645	288	9	numbers	number	NOUN
ejpam-4645	288	10	were	be	AUX
ejpam-4645	288	11	determined	determine	VERB
ejpam-4645	288	12	.	.	PUNCT
ejpam-4645	289	1	a	a	DET
ejpam-4645	289	2	further	further	ADJ
ejpam-4645	289	3	study	study	NOUN
ejpam-4645	289	4	of	of	ADP
ejpam-4645	289	5	stable	stable	ADJ
ejpam-4645	289	6	locating	locating	NOUN
ejpam-4645	289	7	-	-	PUNCT
ejpam-4645	289	8	domination	domination	NOUN
ejpam-4645	289	9	in	in	ADP
ejpam-4645	289	10	other	other	ADJ
ejpam-4645	289	11	graphs	graph	NOUN
ejpam-4645	289	12	is	be	AUX
ejpam-4645	289	13	highly	highly	ADV
ejpam-4645	289	14	recommended	recommend	VERB
ejpam-4645	289	15	.	.	PUNCT
ejpam-4645	290	1	it	it	PRON
ejpam-4645	290	2	is	be	AUX
ejpam-4645	290	3	not	not	PART
ejpam-4645	290	4	yet	yet	ADV
ejpam-4645	290	5	known	know	VERB
ejpam-4645	290	6	if	if	SCONJ
ejpam-4645	290	7	the	the	DET
ejpam-4645	290	8	stable	stable	ADJ
ejpam-4645	290	9	locating	locate	VERB
ejpam-4645	290	10	dominating	dominating	NOUN
ejpam-4645	290	11	set	set	NOUN
ejpam-4645	290	12	problem	problem	NOUN
ejpam-4645	290	13	is	be	AUX
ejpam-4645	290	14	np	np	NOUN
ejpam-4645	290	15	-	-	PUNCT
ejpam-4645	290	16	complete	complete	ADJ
ejpam-4645	290	17	.	.	PUNCT
ejpam-4645	291	1	acknowledgements	acknowledgement	NOUN
ejpam-4645	291	2	the	the	DET
ejpam-4645	291	3	authors	author	NOUN
ejpam-4645	291	4	would	would	AUX
ejpam-4645	291	5	like	like	VERB
ejpam-4645	291	6	to	to	PART
ejpam-4645	291	7	thank	thank	VERB
ejpam-4645	291	8	the	the	DET
ejpam-4645	291	9	department	department	NOUN
ejpam-4645	291	10	of	of	ADP
ejpam-4645	291	11	science	science	NOUN
ejpam-4645	291	12	and	and	CCONJ
ejpam-4645	291	13	technology	technology	NOUN
ejpam-4645	291	14	accelerated	accelerate	VERB
ejpam-4645	291	15	science	science	NOUN
ejpam-4645	291	16	and	and	CCONJ
ejpam-4645	291	17	technology	technology	NOUN
ejpam-4645	291	18	human	human	ADJ
ejpam-4645	291	19	resource	resource	NOUN
ejpam-4645	291	20	development	development	NOUN
ejpam-4645	291	21	program	program	NOUN
ejpam-4645	291	22	(	(	PUNCT
ejpam-4645	291	23	dost	dost	NOUN
ejpam-4645	291	24	-	-	PUNCT
ejpam-4645	291	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4645	291	26	,	,	PUNCT
ejpam-4645	291	27	and	and	CCONJ
ejpam-4645	291	28	msu	msu	PROPN
ejpam-4645	291	29	-	-	PUNCT
ejpam-4645	291	30	iligan	iligan	PROPN
ejpam-4645	291	31	institute	institute	PROPN
ejpam-4645	291	32	of	of	ADP
ejpam-4645	291	33	technology	technology	NOUN
ejpam-4645	291	34	for	for	ADP
ejpam-4645	291	35	funding	fund	VERB
ejpam-4645	291	36	this	this	DET
ejpam-4645	291	37	research	research	NOUN
ejpam-4645	291	38	.	.	PUNCT
ejpam-4645	292	1	references	reference	NOUN
ejpam-4645	292	2	[	[	X
ejpam-4645	292	3	1	1	NUM
ejpam-4645	292	4	]	]	PUNCT
ejpam-4645	292	5	e.	e.	PROPN
ejpam-4645	292	6	ahmad	ahmad	PROPN
ejpam-4645	292	7	,	,	PUNCT
ejpam-4645	292	8	g.	g.	PROPN
ejpam-4645	292	9	malacas	malacas	PROPN
ejpam-4645	292	10	,	,	PUNCT
ejpam-4645	292	11	and	and	CCONJ
ejpam-4645	292	12	s.	s.	PROPN
ejpam-4645	292	13	canoy	canoy	PROPN
ejpam-4645	292	14	jr	jr	PROPN
ejpam-4645	292	15	.	.	PROPN
ejpam-4645	292	16	stable	stable	ADJ
ejpam-4645	292	17	locating	locating	NOUN
ejpam-4645	292	18	-	-	PUNCT
ejpam-4645	292	19	dominating	dominating	NOUN
ejpam-4645	292	20	sets	set	NOUN
ejpam-4645	292	21	in	in	ADP
ejpam-4645	292	22	graphs	graph	NOUN
ejpam-4645	292	23	.	.	PUNCT
ejpam-4645	293	1	european	european	ADJ
ejpam-4645	293	2	journal	journal	PROPN
ejpam-4645	293	3	of	of	ADP
ejpam-4645	293	4	pure	pure	ADJ
ejpam-4645	293	5	and	and	CCONJ
ejpam-4645	293	6	applied	applied	ADJ
ejpam-4645	293	7	mathematics	mathematic	NOUN
ejpam-4645	293	8	,	,	PUNCT
ejpam-4645	293	9	14(3):638–649	14(3):638–649	NOUN
ejpam-4645	293	10	,	,	PUNCT
ejpam-4645	293	11	2021	2021	NUM
ejpam-4645	293	12	.	.	PUNCT
ejpam-4645	294	1	[	[	X
ejpam-4645	294	2	2	2	X
ejpam-4645	294	3	]	]	X
ejpam-4645	294	4	m.h	m.h	PROPN
ejpam-4645	294	5	.	.	PROPN
ejpam-4645	294	6	akhbari	akhbari	PROPN
ejpam-4645	294	7	,	,	PUNCT
ejpam-4645	294	8	r.	r.	PROPN
ejpam-4645	294	9	hasni	hasni	PROPN
ejpam-4645	294	10	,	,	PUNCT
ejpam-4645	294	11	o.	o.	PROPN
ejpam-4645	294	12	favaron	favaron	PROPN
ejpam-4645	294	13	,	,	PUNCT
ejpam-4645	294	14	h.	h.	PROPN
ejpam-4645	294	15	karami	karami	PROPN
ejpam-4645	294	16	,	,	PUNCT
ejpam-4645	294	17	and	and	CCONJ
ejpam-4645	294	18	s.m	s.m	PROPN
ejpam-4645	294	19	.	.	PROPN
ejpam-4645	294	20	sheikholeslami	sheikholeslami	PROPN
ejpam-4645	294	21	.	.	PUNCT
ejpam-4645	295	1	on	on	ADP
ejpam-4645	295	2	the	the	DET
ejpam-4645	295	3	outer	outer	ADV
ejpam-4645	295	4	-	-	PUNCT
ejpam-4645	295	5	conected	conecte	VERB
ejpam-4645	295	6	domination	domination	NOUN
ejpam-4645	295	7	numbers	number	NOUN
ejpam-4645	295	8	of	of	ADP
ejpam-4645	295	9	graphs	graph	NOUN
ejpam-4645	295	10	.	.	PUNCT
ejpam-4645	296	1	journal	journal	NOUN
ejpam-4645	296	2	of	of	ADP
ejpam-4645	296	3	combinatorial	combinatorial	ADJ
ejpam-4645	296	4	optimization	optimization	NOUN
ejpam-4645	296	5	,	,	PUNCT
ejpam-4645	296	6	26(1):10–18	26(1):10–18	NUM
ejpam-4645	296	7	,	,	PUNCT
ejpam-4645	296	8	2013	2013	NUM
ejpam-4645	296	9	.	.	PUNCT
ejpam-4645	297	1	references	reference	NOUN
ejpam-4645	297	2	489	489	NUM
ejpam-4645	298	1	[	[	X
ejpam-4645	298	2	3	3	NUM
ejpam-4645	298	3	]	]	PUNCT
ejpam-4645	298	4	b.	b.	PROPN
ejpam-4645	298	5	arriola	arriola	PROPN
ejpam-4645	298	6	and	and	CCONJ
ejpam-4645	298	7	s.	s.	PROPN
ejpam-4645	298	8	canoy	canoy	PROPN
ejpam-4645	298	9	jr	jr	PROPN
ejpam-4645	298	10	.	.	PUNCT
ejpam-4645	298	11	secure	secure	VERB
ejpam-4645	298	12	doubly	doubly	ADV
ejpam-4645	298	13	connected	connected	ADJ
ejpam-4645	298	14	domination	domination	NOUN
ejpam-4645	298	15	in	in	ADP
ejpam-4645	298	16	graphs	graph	NOUN
ejpam-4645	298	17	.	.	PUNCT
ejpam-4645	299	1	international	international	ADJ
ejpam-4645	299	2	journal	journal	PROPN
ejpam-4645	299	3	of	of	ADP
ejpam-4645	299	4	mathematical	mathematical	ADJ
ejpam-4645	299	5	analysis	analysis	NOUN
ejpam-4645	299	6	.	.	PUNCT
ejpam-4645	299	7	,	,	PUNCT
ejpam-4645	299	8	8:1571–1580	8:1571–1580	NUM
ejpam-4645	299	9	,	,	PUNCT
ejpam-4645	299	10	2014	2014	NUM
ejpam-4645	299	11	.	.	PUNCT
ejpam-4645	300	1	[	[	X
ejpam-4645	300	2	4	4	X
ejpam-4645	300	3	]	]	PUNCT
ejpam-4645	300	4	j.	j.	PROPN
ejpam-4645	300	5	cyman	cyman	PROPN
ejpam-4645	300	6	.	.	PUNCT
ejpam-4645	301	1	the	the	DET
ejpam-4645	301	2	outer	outer	ADV
ejpam-4645	301	3	-	-	PUNCT
ejpam-4645	301	4	conected	conecte	VERB
ejpam-4645	301	5	domination	domination	NOUN
ejpam-4645	301	6	numbers	number	NOUN
ejpam-4645	301	7	of	of	ADP
ejpam-4645	301	8	graphs	graph	NOUN
ejpam-4645	301	9	.	.	PUNCT
ejpam-4645	302	1	australasian	australasian	ADJ
ejpam-4645	302	2	journal	journal	NOUN
ejpam-4645	302	3	of	of	ADP
ejpam-4645	302	4	combinatorics	combinatoric	NOUN
ejpam-4645	302	5	,	,	PUNCT
ejpam-4645	302	6	38(1):35–46	38(1):35–46	NUM
ejpam-4645	302	7	,	,	PUNCT
ejpam-4645	302	8	2007	2007	NUM
ejpam-4645	302	9	.	.	PUNCT
ejpam-4645	303	1	[	[	X
ejpam-4645	303	2	5	5	X
ejpam-4645	303	3	]	]	PUNCT
ejpam-4645	303	4	s.	s.	PROPN
ejpam-4645	303	5	daniel	daniel	PROPN
ejpam-4645	303	6	and	and	CCONJ
ejpam-4645	303	7	s.	s.	PROPN
ejpam-4645	303	8	canoy	canoy	PROPN
ejpam-4645	303	9	jr	jr	PROPN
ejpam-4645	303	10	.	.	PROPN
ejpam-4645	303	11	clique	clique	PROPN
ejpam-4645	303	12	domination	domination	PROPN
ejpam-4645	303	13	in	in	ADP
ejpam-4645	303	14	graphs	graph	NOUN
ejpam-4645	303	15	.	.	PUNCT
ejpam-4645	304	1	applied	apply	VERB
ejpam-4645	304	2	mathematical	mathematical	ADJ
ejpam-4645	304	3	sciences	science	NOUN
ejpam-4645	304	4	,	,	PUNCT
ejpam-4645	304	5	9(116):5749–5755	9(116):5749–5755	NUM
ejpam-4645	304	6	,	,	PUNCT
ejpam-4645	304	7	2015	2015	NUM
ejpam-4645	304	8	.	.	PUNCT
ejpam-4645	305	1	[	[	X
ejpam-4645	305	2	6	6	NUM
ejpam-4645	305	3	]	]	PUNCT
ejpam-4645	305	4	a.	a.	NOUN
ejpam-4645	305	5	finbow	finbow	NOUN
ejpam-4645	305	6	and	and	CCONJ
ejpam-4645	305	7	b.l	b.l	PROPN
ejpam-4645	305	8	.	.	PROPN
ejpam-4645	305	9	hartnell	hartnell	PROPN
ejpam-4645	305	10	.	.	PUNCT
ejpam-4645	306	1	on	on	ADP
ejpam-4645	306	2	locating	locate	VERB
ejpam-4645	306	3	-	-	PUNCT
ejpam-4645	306	4	dominating	dominating	NOUN
ejpam-4645	306	5	sets	set	NOUN
ejpam-4645	306	6	and	and	CCONJ
ejpam-4645	306	7	well	well	ADV
ejpam-4645	306	8	-	-	PUNCT
ejpam-4645	306	9	covered	cover	VERB
ejpam-4645	306	10	graphs	graph	NOUN
ejpam-4645	306	11	.	.	PUNCT
ejpam-4645	307	1	congr	congr	NOUN
ejpam-4645	307	2	.	.	PUNCT
ejpam-4645	308	1	numer	numer	PROPN
ejpam-4645	308	2	.	.	PROPN
ejpam-4645	308	3	,	,	PUNCT
ejpam-4645	309	1	65:191–200	65:191–200	NUM
ejpam-4645	309	2	,	,	PUNCT
ejpam-4645	309	3	1988	1988	NUM
ejpam-4645	309	4	.	.	PUNCT
ejpam-4645	310	1	[	[	X
ejpam-4645	310	2	7	7	X
ejpam-4645	310	3	]	]	X
ejpam-4645	310	4	d.	d.	PROPN
ejpam-4645	310	5	geoffrey	geoffrey	PROPN
ejpam-4645	310	6	.	.	PUNCT
ejpam-4645	311	1	nuclei	nuclei	PROPN
ejpam-4645	311	2	for	for	ADP
ejpam-4645	311	3	totally	totally	ADV
ejpam-4645	311	4	point	point	NOUN
ejpam-4645	311	5	determining	determine	VERB
ejpam-4645	311	6	graphs	graph	NOUN
ejpam-4645	311	7	.	.	PUNCT
ejpam-4645	312	1	discrete	discrete	ADJ
ejpam-4645	312	2	mathematics	mathematic	NOUN
ejpam-4645	312	3	,	,	PUNCT
ejpam-4645	312	4	21:145–162	21:145–162	PROPN
ejpam-4645	312	5	,	,	PUNCT
ejpam-4645	312	6	1978	1978	NUM
ejpam-4645	312	7	.	.	PUNCT
ejpam-4645	313	1	[	[	X
ejpam-4645	313	2	8	8	X
ejpam-4645	313	3	]	]	X
ejpam-4645	313	4	j.	j.	PROPN
ejpam-4645	313	5	gimbel	gimbel	PROPN
ejpam-4645	313	6	,	,	PUNCT
ejpam-4645	313	7	b.	b.	PROPN
ejpam-4645	313	8	van	van	PROPN
ejpam-4645	313	9	gorden	gorden	PROPN
ejpam-4645	313	10	,	,	PUNCT
ejpam-4645	313	11	m.	m.	NOUN
ejpam-4645	313	12	nicolescu	nicolescu	PROPN
ejpam-4645	313	13	,	,	PUNCT
ejpam-4645	313	14	c.	c.	PROPN
ejpam-4645	313	15	umstead	umstead	PROPN
ejpam-4645	313	16	,	,	PUNCT
ejpam-4645	313	17	and	and	CCONJ
ejpam-4645	313	18	n.	n.	PROPN
ejpam-4645	313	19	vaiana	vaiana	PROPN
ejpam-4645	313	20	.	.	PUNCT
ejpam-4645	314	1	location	location	NOUN
ejpam-4645	314	2	with	with	ADP
ejpam-4645	314	3	dominating	dominating	NOUN
ejpam-4645	314	4	sets	set	NOUN
ejpam-4645	314	5	.	.	PUNCT
ejpam-4645	315	1	congr	congr	NOUN
ejpam-4645	315	2	.	.	PUNCT
ejpam-4645	316	1	numer	numer	PROPN
ejpam-4645	316	2	.	.	PROPN
ejpam-4645	316	3	,	,	PUNCT
ejpam-4645	316	4	151:129–144	151:129–144	NUM
ejpam-4645	316	5	,	,	PUNCT
ejpam-4645	316	6	2001	2001	NUM
ejpam-4645	316	7	.	.	PUNCT
ejpam-4645	317	1	[	[	X
ejpam-4645	317	2	9	9	NUM
ejpam-4645	317	3	]	]	PUNCT
ejpam-4645	317	4	t.	t.	PROPN
ejpam-4645	317	5	w.	w.	PROPN
ejpam-4645	317	6	haynes	haynes	PROPN
ejpam-4645	317	7	,	,	PUNCT
ejpam-4645	317	8	s.t	s.t	PROPN
ejpam-4645	317	9	.	.	PROPN
ejpam-4645	317	10	hedetnieme	hedetnieme	PROPN
ejpam-4645	317	11	,	,	PUNCT
ejpam-4645	317	12	and	and	CCONJ
ejpam-4645	317	13	p.j	p.j	PROPN
ejpam-4645	317	14	.	.	PROPN
ejpam-4645	317	15	slater	slater	PROPN
ejpam-4645	317	16	.	.	PUNCT
ejpam-4645	318	1	fundamentals	fundamental	NOUN
ejpam-4645	318	2	of	of	ADP
ejpam-4645	318	3	domination	domination	NOUN
ejpam-4645	318	4	in	in	ADP
ejpam-4645	318	5	graphs	graph	NOUN
ejpam-4645	318	6	.	.	PUNCT
ejpam-4645	319	1	monographs	monograph	NOUN
ejpam-4645	319	2	and	and	CCONJ
ejpam-4645	319	3	textbooks	textbook	NOUN
ejpam-4645	319	4	in	in	ADP
ejpam-4645	319	5	pure	pure	ADJ
ejpam-4645	319	6	and	and	CCONJ
ejpam-4645	319	7	applied	applied	ADJ
ejpam-4645	319	8	mathematics	mathematic	NOUN
ejpam-4645	319	9	,	,	PUNCT
ejpam-4645	319	10	28	28	NUM
ejpam-4645	319	11	,	,	PUNCT
ejpam-4645	319	12	1998	1998	NUM
ejpam-4645	319	13	.	.	PUNCT
ejpam-4645	320	1	[	[	X
ejpam-4645	320	2	10	10	NUM
ejpam-4645	320	3	]	]	X
ejpam-4645	320	4	t.w	t.w	PROPN
ejpam-4645	320	5	.	.	PROPN
ejpam-4645	320	6	haynes	haynes	PROPN
ejpam-4645	320	7	,	,	PUNCT
ejpam-4645	320	8	m.a	m.a	PROPN
ejpam-4645	320	9	.	.	PROPN
ejpam-4645	320	10	henning	henning	PROPN
ejpam-4645	320	11	,	,	PUNCT
ejpam-4645	320	12	and	and	CCONJ
ejpam-4645	320	13	j.	j.	PROPN
ejpam-4645	320	14	howard	howard	PROPN
ejpam-4645	320	15	.	.	PUNCT
ejpam-4645	321	1	locating	locate	VERB
ejpam-4645	321	2	and	and	CCONJ
ejpam-4645	321	3	total	total	ADJ
ejpam-4645	321	4	dominating	dominating	NOUN
ejpam-4645	321	5	sets	set	NOUN
ejpam-4645	321	6	in	in	ADP
ejpam-4645	321	7	trees	tree	NOUN
ejpam-4645	321	8	.	.	PUNCT
ejpam-4645	322	1	discrete	discrete	ADJ
ejpam-4645	322	2	applied	apply	VERB
ejpam-4645	322	3	mathematics	mathematic	NOUN
ejpam-4645	322	4	,	,	PUNCT
ejpam-4645	322	5	154(8):1293–1300	154(8):1293–1300	NUM
ejpam-4645	322	6	,	,	PUNCT
ejpam-4645	322	7	2006	2006	NUM
ejpam-4645	322	8	.	.	PUNCT
ejpam-4645	323	1	[	[	X
ejpam-4645	323	2	11	11	NUM
ejpam-4645	323	3	]	]	X
ejpam-4645	323	4	r.	r.	PROPN
ejpam-4645	323	5	hinampas	hinampas	PROPN
ejpam-4645	323	6	and	and	CCONJ
ejpam-4645	323	7	s.	s.	PROPN
ejpam-4645	323	8	canoy	canoy	PROPN
ejpam-4645	323	9	jr	jr	PROPN
ejpam-4645	323	10	.	.	PROPN
ejpam-4645	323	11	1	1	NUM
ejpam-4645	323	12	-	-	PUNCT
ejpam-4645	323	13	movable	movable	ADJ
ejpam-4645	323	14	domination	domination	NOUN
ejpam-4645	323	15	in	in	ADP
ejpam-4645	323	16	graphs	graph	NOUN
ejpam-4645	323	17	.	.	PUNCT
ejpam-4645	324	1	applied	apply	VERB
ejpam-4645	324	2	mathematical	mathematical	ADJ
ejpam-4645	324	3	sciences	sciences	PROPN
ejpam-4645	324	4	,	,	PUNCT
ejpam-4645	324	5	8(172):8565–8571	8(172):8565–8571	NUM
ejpam-4645	324	6	,	,	PUNCT
ejpam-4645	324	7	2014	2014	NUM
ejpam-4645	324	8	.	.	PUNCT
ejpam-4645	325	1	[	[	X
ejpam-4645	325	2	12	12	NUM
ejpam-4645	325	3	]	]	PUNCT
ejpam-4645	325	4	h.	h.	PROPN
ejpam-4645	325	5	jiang	jiang	PROPN
ejpam-4645	325	6	and	and	CCONJ
ejpam-4645	325	7	e.	e.	PROPN
ejpam-4645	325	8	shan	shan	PROPN
ejpam-4645	325	9	.	.	PUNCT
ejpam-4645	326	1	outer	outer	ADJ
ejpam-4645	326	2	-	-	PUNCT
ejpam-4645	326	3	conected	conecte	VERB
ejpam-4645	326	4	domination	domination	NOUN
ejpam-4645	326	5	numbers	number	NOUN
ejpam-4645	326	6	of	of	ADP
ejpam-4645	326	7	graphs	graph	NOUN
ejpam-4645	326	8	.	.	PUNCT
ejpam-4645	327	1	american	american	PROPN
ejpam-4645	327	2	mathematical	mathematical	PROPN
ejpam-4645	327	3	society	society	NOUN
ejpam-4645	327	4	,	,	PUNCT
ejpam-4645	327	5	81(1):265–274	81(1):265–274	NOUN
ejpam-4645	327	6	,	,	PUNCT
ejpam-4645	327	7	2010	2010	NUM
ejpam-4645	327	8	.	.	PUNCT
ejpam-4645	328	1	[	[	X
ejpam-4645	328	2	13	13	NUM
ejpam-4645	328	3	]	]	PUNCT
ejpam-4645	328	4	s.	s.	PROPN
ejpam-4645	328	5	canoy	canoy	PROPN
ejpam-4645	328	6	jr	jr	PROPN
ejpam-4645	328	7	.	.	PROPN
ejpam-4645	328	8	and	and	CCONJ
ejpam-4645	328	9	g.	g.	PROPN
ejpam-4645	328	10	malacas	malacas	PROPN
ejpam-4645	328	11	.	.	PUNCT
ejpam-4645	329	1	determining	determine	VERB
ejpam-4645	329	2	the	the	DET
ejpam-4645	329	3	intruder	intruder	NOUN
ejpam-4645	329	4	’s	’s	PART
ejpam-4645	329	5	location	location	NOUN
ejpam-4645	329	6	in	in	ADP
ejpam-4645	329	7	a	a	DET
ejpam-4645	329	8	given	give	VERB
ejpam-4645	329	9	network	network	NOUN
ejpam-4645	329	10	:	:	PUNCT
ejpam-4645	329	11	locating	locate	VERB
ejpam-4645	329	12	-	-	PUNCT
ejpam-4645	329	13	dominating	dominating	NOUN
ejpam-4645	329	14	sets	set	NOUN
ejpam-4645	329	15	in	in	ADP
ejpam-4645	329	16	a	a	DET
ejpam-4645	329	17	graph	graph	NOUN
ejpam-4645	329	18	.	.	PUNCT
ejpam-4645	330	1	nrcp	nrcp	PROPN
ejpam-4645	330	2	research	research	PROPN
ejpam-4645	330	3	journal	journal	PROPN
ejpam-4645	330	4	.	.	PUNCT
ejpam-4645	330	5	,	,	PUNCT
ejpam-4645	330	6	13(1):1–8	13(1):1–8	NUM
ejpam-4645	330	7	,	,	PUNCT
ejpam-4645	330	8	2013	2013	NUM
ejpam-4645	330	9	.	.	PUNCT
ejpam-4645	331	1	[	[	X
ejpam-4645	331	2	14	14	NUM
ejpam-4645	331	3	]	]	X
ejpam-4645	331	4	s.	s.	PROPN
ejpam-4645	331	5	canoy	canoy	PROPN
ejpam-4645	331	6	jr	jr	PROPN
ejpam-4645	331	7	.	.	PROPN
ejpam-4645	331	8	and	and	CCONJ
ejpam-4645	331	9	g.	g.	PROPN
ejpam-4645	331	10	malacas	malacas	PROPN
ejpam-4645	331	11	.	.	PUNCT
ejpam-4645	332	1	differentiating	differentiate	VERB
ejpam-4645	332	2	-	-	PUNCT
ejpam-4645	332	3	dominating	dominating	NOUN
ejpam-4645	332	4	sets	set	NOUN
ejpam-4645	332	5	in	in	ADP
ejpam-4645	332	6	graphs	graph	NOUN
ejpam-4645	332	7	under	under	ADP
ejpam-4645	332	8	binary	binary	ADJ
ejpam-4645	332	9	operations	operation	NOUN
ejpam-4645	332	10	.	.	PUNCT
ejpam-4645	333	1	tamkang	tamkang	PROPN
ejpam-4645	333	2	journal	journal	PROPN
ejpam-4645	333	3	of	of	ADP
ejpam-4645	333	4	mathematics	mathematic	NOUN
ejpam-4645	333	5	,	,	PUNCT
ejpam-4645	333	6	46(1):51–60	46(1):51–60	NOUN
ejpam-4645	333	7	,	,	PUNCT
ejpam-4645	333	8	2015	2015	NUM
ejpam-4645	333	9	.	.	PUNCT
ejpam-4645	334	1	[	[	X
ejpam-4645	334	2	15	15	NUM
ejpam-4645	334	3	]	]	X
ejpam-4645	334	4	s.	s.	PROPN
ejpam-4645	334	5	canoy	canoy	PROPN
ejpam-4645	334	6	jr	jr	PROPN
ejpam-4645	334	7	.	.	PROPN
ejpam-4645	334	8	,	,	PUNCT
ejpam-4645	334	9	g.	g.	PROPN
ejpam-4645	334	10	malacas	malacas	PROPN
ejpam-4645	334	11	,	,	PUNCT
ejpam-4645	334	12	and	and	CCONJ
ejpam-4645	334	13	d.	d.	PROPN
ejpam-4645	334	14	tarepe	tarepe	PROPN
ejpam-4645	334	15	.	.	PUNCT
ejpam-4645	335	1	locating	locate	VERB
ejpam-4645	335	2	-	-	PUNCT
ejpam-4645	335	3	dominating	dominating	NOUN
ejpam-4645	335	4	sets	set	NOUN
ejpam-4645	335	5	in	in	ADP
ejpam-4645	335	6	graphs	graph	NOUN
ejpam-4645	335	7	.	.	PUNCT
ejpam-4645	336	1	applied	apply	VERB
ejpam-4645	336	2	mathematical	mathematical	ADJ
ejpam-4645	336	3	sciences	sciences	PROPN
ejpam-4645	336	4	,	,	PUNCT
ejpam-4645	336	5	8(88):4381–4388	8(88):4381–4388	NUM
ejpam-4645	336	6	,	,	PUNCT
ejpam-4645	336	7	2014	2014	NUM
ejpam-4645	336	8	.	.	PUNCT
ejpam-4645	337	1	[	[	X
ejpam-4645	337	2	16	16	NUM
ejpam-4645	337	3	]	]	PUNCT
ejpam-4645	337	4	m.	m.	NOUN
ejpam-4645	337	5	labendia	labendia	PROPN
ejpam-4645	337	6	and	and	CCONJ
ejpam-4645	337	7	s.	s.	PROPN
ejpam-4645	337	8	canoy	canoy	PROPN
ejpam-4645	337	9	jr	jr	PROPN
ejpam-4645	337	10	.	.	PROPN
ejpam-4645	337	11	convex	convex	PROPN
ejpam-4645	337	12	domination	domination	NOUN
ejpam-4645	337	13	in	in	ADP
ejpam-4645	337	14	composition	composition	NOUN
ejpam-4645	337	15	and	and	CCONJ
ejpam-4645	337	16	cartesian	cartesian	ADJ
ejpam-4645	337	17	product	product	NOUN
ejpam-4645	337	18	of	of	ADP
ejpam-4645	337	19	graphs	graph	NOUN
ejpam-4645	337	20	.	.	PUNCT
ejpam-4645	338	1	czechoslovak	czechoslovak	ADJ
ejpam-4645	338	2	mathematical	mathematical	PROPN
ejpam-4645	338	3	journal	journal	NOUN
ejpam-4645	338	4	,	,	PUNCT
ejpam-4645	338	5	62(4):1003–1009	62(4):1003–1009	NUM
ejpam-4645	338	6	,	,	PUNCT
ejpam-4645	338	7	2012	2012	NUM
ejpam-4645	338	8	.	.	PUNCT
ejpam-4645	339	1	[	[	X
ejpam-4645	339	2	17	17	NUM
ejpam-4645	339	3	]	]	X
ejpam-4645	339	4	s.	s.	PROPN
ejpam-4645	339	5	omega	omega	PROPN
ejpam-4645	339	6	and	and	CCONJ
ejpam-4645	339	7	s.	s.	PROPN
ejpam-4645	339	8	canoy	canoy	PROPN
ejpam-4645	339	9	jr	jr	PROPN
ejpam-4645	339	10	.	.	PUNCT
ejpam-4645	339	11	locating	locate	VERB
ejpam-4645	339	12	sets	set	NOUN
ejpam-4645	339	13	in	in	ADP
ejpam-4645	339	14	a	a	DET
ejpam-4645	339	15	graph	graph	NOUN
ejpam-4645	339	16	.	.	PUNCT
ejpam-4645	340	1	applied	apply	VERB
ejpam-4645	340	2	mathematical	mathematical	ADJ
ejpam-4645	340	3	sciences	science	NOUN
ejpam-4645	340	4	,	,	PUNCT
ejpam-4645	340	5	60:2957–2964	60:2957–2964	NUM
ejpam-4645	340	6	,	,	PUNCT
ejpam-4645	340	7	2015	2015	NUM
ejpam-4645	340	8	.	.	PUNCT
ejpam-4645	341	1	[	[	X
ejpam-4645	341	2	18	18	NUM
ejpam-4645	341	3	]	]	X
ejpam-4645	341	4	e.	e.	PROPN
ejpam-4645	341	5	sandueta	sandueta	PROPN
ejpam-4645	341	6	and	and	CCONJ
ejpam-4645	341	7	s.	s.	PROPN
ejpam-4645	341	8	canoy	canoy	PROPN
ejpam-4645	341	9	jr	jr	PROPN
ejpam-4645	341	10	.	.	PROPN
ejpam-4645	341	11	weakly	weakly	ADJ
ejpam-4645	341	12	connected	connected	ADJ
ejpam-4645	341	13	domination	domination	NOUN
ejpam-4645	341	14	in	in	ADP
ejpam-4645	341	15	graphs	graph	NOUN
ejpam-4645	341	16	resulting	result	VERB
ejpam-4645	341	17	from	from	ADP
ejpam-4645	341	18	some	some	DET
ejpam-4645	341	19	graph	graph	NOUN
ejpam-4645	341	20	operations	operation	NOUN
ejpam-4645	341	21	.	.	PUNCT
ejpam-4645	342	1	international	international	ADJ
ejpam-4645	342	2	mathematical	mathematical	PROPN
ejpam-4645	342	3	forum	forum	PROPN
ejpam-4645	342	4	.	.	PROPN
ejpam-4645	342	5	,	,	PUNCT
ejpam-4645	342	6	6(21):1031–1035	6(21):1031–1035	NUM
ejpam-4645	342	7	,	,	PUNCT
ejpam-4645	342	8	2011	2011	NUM
ejpam-4645	342	9	.	.	PUNCT
ejpam-4645	343	1	[	[	X
ejpam-4645	343	2	19	19	NUM
ejpam-4645	343	3	]	]	X
ejpam-4645	343	4	p.j	p.j	PROPN
ejpam-4645	343	5	.	.	PROPN
ejpam-4645	343	6	slater	slater	PROPN
ejpam-4645	343	7	.	.	PUNCT
ejpam-4645	344	1	dominating	dominating	NOUN
ejpam-4645	344	2	and	and	CCONJ
ejpam-4645	344	3	location	location	NOUN
ejpam-4645	344	4	in	in	ADP
ejpam-4645	344	5	acyclic	acyclic	ADJ
ejpam-4645	344	6	graphs	graph	NOUN
ejpam-4645	344	7	.	.	PUNCT
ejpam-4645	345	1	networks	network	NOUN
ejpam-4645	345	2	,	,	PUNCT
ejpam-4645	345	3	17:55–64	17:55–64	NUM
ejpam-4645	345	4	,	,	PUNCT
ejpam-4645	345	5	1987	1987	NUM
ejpam-4645	345	6	.	.	PUNCT
ejpam-4645	346	1	references	reference	NOUN
ejpam-4645	346	2	490	490	NUM
ejpam-4645	346	3	[	[	SYM
ejpam-4645	346	4	20	20	NUM
ejpam-4645	346	5	]	]	X
ejpam-4645	346	6	p.j	p.j	PROPN
ejpam-4645	346	7	.	.	PROPN
ejpam-4645	346	8	slater	slater	PROPN
ejpam-4645	346	9	.	.	PUNCT
ejpam-4645	347	1	fault	fault	NOUN
ejpam-4645	347	2	-	-	PUNCT
ejpam-4645	347	3	tolerant	tolerant	ADJ
ejpam-4645	347	4	locating	locating	NOUN
ejpam-4645	347	5	-	-	PUNCT
ejpam-4645	347	6	dominating	dominating	NOUN
ejpam-4645	347	7	sets	set	NOUN
ejpam-4645	347	8	.	.	PUNCT
ejpam-4645	348	1	discrete	discrete	ADJ
ejpam-4645	348	2	mathematics	mathematic	NOUN
ejpam-4645	348	3	,	,	PUNCT
ejpam-4645	348	4	249:179	249:179	NOUN
ejpam-4645	348	5	–	–	PUNCT
ejpam-4645	348	6	189	189	NUM
ejpam-4645	348	7	,	,	PUNCT
ejpam-4645	348	8	2002	2002	NUM
ejpam-4645	348	9	.	.	PUNCT
ejpam-4645	349	1	[	[	X
ejpam-4645	349	2	21	21	NUM
ejpam-4645	349	3	]	]	X
ejpam-4645	349	4	d.	d.	PROPN
ejpam-4645	349	5	summer	summer	NOUN
ejpam-4645	349	6	.	.	PUNCT
ejpam-4645	350	1	point	point	NOUN
ejpam-4645	350	2	determination	determination	NOUN
ejpam-4645	350	3	in	in	ADP
ejpam-4645	350	4	graphs	graph	NOUN
ejpam-4645	350	5	.	.	PUNCT
ejpam-4645	351	1	discrete	discrete	ADJ
ejpam-4645	351	2	mathematics	mathematic	NOUN
ejpam-4645	351	3	,	,	PUNCT
ejpam-4645	351	4	5:179–187	5:179–187	NUM
ejpam-4645	351	5	,	,	PUNCT
ejpam-4645	351	6	1973	1973	NUM
ejpam-4645	351	7	.	.	PUNCT