id	sid	tid	token	lemma	pos
ejpam-5713	1	1	european	european	PROPN
ejpam-5713	1	2	journal	journal	PROPN
ejpam-5713	1	3	of	of	ADP
ejpam-5713	1	4	pure	pure	ADJ
ejpam-5713	1	5	and	and	CCONJ
ejpam-5713	1	6	applied	applied	ADJ
ejpam-5713	1	7	mathematics	mathematic	NOUN
ejpam-5713	1	8	2025	2025	NUM
ejpam-5713	1	9	,	,	PUNCT
ejpam-5713	1	10	vol	vol	NOUN
ejpam-5713	1	11	.	.	PROPN
ejpam-5713	1	12	18	18	NUM
ejpam-5713	1	13	,	,	PUNCT
ejpam-5713	1	14	issue	issue	NOUN
ejpam-5713	1	15	1	1	NUM
ejpam-5713	1	16	,	,	PUNCT
ejpam-5713	1	17	article	article	NOUN
ejpam-5713	1	18	number	number	NOUN
ejpam-5713	1	19	5713	5713	NUM
ejpam-5713	1	20	issn	issn	PROPN
ejpam-5713	1	21	1307	1307	NUM
ejpam-5713	1	22	-	-	SYM
ejpam-5713	1	23	5543	5543	NUM
ejpam-5713	1	24	–	–	PUNCT
ejpam-5713	1	25	ejpam.com	ejpam.com	X
ejpam-5713	1	26	published	publish	VERB
ejpam-5713	1	27	by	by	ADP
ejpam-5713	1	28	new	new	PROPN
ejpam-5713	1	29	york	york	PROPN
ejpam-5713	1	30	business	business	PROPN
ejpam-5713	1	31	global	global	PROPN
ejpam-5713	1	32	super	super	ADJ
ejpam-5713	1	33	vertex	vertex	NOUN
ejpam-5713	1	34	cover	cover	NOUN
ejpam-5713	1	35	of	of	ADP
ejpam-5713	1	36	a	a	DET
ejpam-5713	1	37	graph	graph	NOUN
ejpam-5713	1	38	sergio	sergio	PROPN
ejpam-5713	1	39	r.	r.	PROPN
ejpam-5713	1	40	canoy	canoy	PROPN
ejpam-5713	1	41	,	,	PUNCT
ejpam-5713	1	42	jr.1,2	jr.1,2	PROPN
ejpam-5713	1	43	,	,	PUNCT
ejpam-5713	1	44	maria	maria	PROPN
ejpam-5713	1	45	andrea	andrea	PROPN
ejpam-5713	1	46	o.	o.	PROPN
ejpam-5713	1	47	bonsocan3	bonsocan3	PROPN
ejpam-5713	1	48	,	,	PUNCT
ejpam-5713	1	49	javier	javier	PROPN
ejpam-5713	1	50	a.	a.	PROPN
ejpam-5713	1	51	hassan4,5,∗	hassan4,5,∗	PROPN
ejpam-5713	1	52	,	,	PUNCT
ejpam-5713	1	53	angelica	angelica	PROPN
ejpam-5713	1	54	mae	mae	PROPN
ejpam-5713	1	55	l.	l.	PROPN
ejpam-5713	1	56	mahistrado3	mahistrado3	PROPN
ejpam-5713	1	57	,	,	PUNCT
ejpam-5713	1	58	vergel	vergel	NOUN
ejpam-5713	1	59	t.	t.	NOUN
ejpam-5713	1	60	bilar3	bilar3	NOUN
ejpam-5713	1	61	1	1	NUM
ejpam-5713	1	62	department	department	NOUN
ejpam-5713	1	63	of	of	ADP
ejpam-5713	1	64	mathematics	mathematic	NOUN
ejpam-5713	1	65	and	and	CCONJ
ejpam-5713	1	66	statistics	statistic	NOUN
ejpam-5713	1	67	,	,	PUNCT
ejpam-5713	1	68	college	college	NOUN
ejpam-5713	1	69	of	of	ADP
ejpam-5713	1	70	science	science	NOUN
ejpam-5713	1	71	and	and	CCONJ
ejpam-5713	1	72	mathematics	mathematic	NOUN
ejpam-5713	1	73	,	,	PUNCT
ejpam-5713	1	74	msu	msu	PROPN
ejpam-5713	1	75	-	-	PUNCT
ejpam-5713	1	76	iligan	iligan	PROPN
ejpam-5713	1	77	institute	institute	PROPN
ejpam-5713	1	78	of	of	ADP
ejpam-5713	1	79	technology	technology	PROPN
ejpam-5713	1	80	,	,	PUNCT
ejpam-5713	1	81	iligan	iligan	PROPN
ejpam-5713	1	82	city	city	PROPN
ejpam-5713	1	83	,	,	PUNCT
ejpam-5713	1	84	philippines	philippine	NOUN
ejpam-5713	1	85	2	2	NUM
ejpam-5713	1	86	center	center	NOUN
ejpam-5713	1	87	of	of	ADP
ejpam-5713	1	88	mathematical	mathematical	ADJ
ejpam-5713	1	89	and	and	CCONJ
ejpam-5713	1	90	theoretical	theoretical	ADJ
ejpam-5713	1	91	physical	physical	ADJ
ejpam-5713	1	92	sciences	science	NOUN
ejpam-5713	1	93	prism	prism	NOUN
ejpam-5713	1	94	,	,	PUNCT
ejpam-5713	1	95	msu	msu	PROPN
ejpam-5713	1	96	-	-	PUNCT
ejpam-5713	1	97	iligan	iligan	PROPN
ejpam-5713	1	98	institute	institute	PROPN
ejpam-5713	1	99	of	of	ADP
ejpam-5713	1	100	technology	technology	PROPN
ejpam-5713	1	101	,	,	PUNCT
ejpam-5713	1	102	iligan	iligan	PROPN
ejpam-5713	1	103	city	city	PROPN
ejpam-5713	1	104	,	,	PUNCT
ejpam-5713	1	105	philippines	philippines	PROPN
ejpam-5713	1	106	3	3	NUM
ejpam-5713	1	107	department	department	NOUN
ejpam-5713	1	108	of	of	ADP
ejpam-5713	1	109	mathematics	mathematic	NOUN
ejpam-5713	1	110	,	,	PUNCT
ejpam-5713	1	111	ateneo	ateneo	X
ejpam-5713	1	112	de	de	PROPN
ejpam-5713	1	113	davao	davao	PROPN
ejpam-5713	1	114	university	university	PROPN
ejpam-5713	1	115	,	,	PUNCT
ejpam-5713	1	116	e.	e.	PROPN
ejpam-5713	1	117	jacinto	jacinto	PROPN
ejpam-5713	1	118	street	street	PROPN
ejpam-5713	1	119	,	,	PUNCT
ejpam-5713	1	120	8016	8016	NUM
ejpam-5713	1	121	davao	davao	PROPN
ejpam-5713	1	122	city	city	NOUN
ejpam-5713	1	123	,	,	PUNCT
ejpam-5713	1	124	philippines	philippine	VERB
ejpam-5713	1	125	4mathematics	4mathematics	NUM
ejpam-5713	1	126	and	and	CCONJ
ejpam-5713	1	127	sciences	sciences	PROPN
ejpam-5713	1	128	department	department	PROPN
ejpam-5713	1	129	,	,	PUNCT
ejpam-5713	1	130	college	college	NOUN
ejpam-5713	1	131	of	of	ADP
ejpam-5713	1	132	arts	art	NOUN
ejpam-5713	1	133	and	and	CCONJ
ejpam-5713	1	134	sciences	science	NOUN
ejpam-5713	1	135	,	,	PUNCT
ejpam-5713	1	136	msu	msu	PROPN
ejpam-5713	1	137	tawi	tawi	PROPN
ejpam-5713	1	138	-	-	PUNCT
ejpam-5713	1	139	tawi	tawi	PROPN
ejpam-5713	1	140	college	college	PROPN
ejpam-5713	1	141	of	of	ADP
ejpam-5713	1	142	technology	technology	NOUN
ejpam-5713	1	143	and	and	CCONJ
ejpam-5713	1	144	oceanography	oceanography	NOUN
ejpam-5713	1	145	,	,	PUNCT
ejpam-5713	1	146	bongao	bongao	NOUN
ejpam-5713	1	147	,	,	PUNCT
ejpam-5713	1	148	tawi	tawi	NOUN
ejpam-5713	1	149	-	-	PUNCT
ejpam-5713	1	150	tawi	tawi	NOUN
ejpam-5713	1	151	,	,	PUNCT
ejpam-5713	1	152	philippines	philippine	NOUN
ejpam-5713	1	153	5department	5department	NUM
ejpam-5713	1	154	of	of	ADP
ejpam-5713	1	155	mathematics	mathematic	NOUN
ejpam-5713	1	156	,	,	PUNCT
ejpam-5713	1	157	college	college	NOUN
ejpam-5713	1	158	of	of	ADP
ejpam-5713	1	159	science	science	PROPN
ejpam-5713	1	160	,	,	PUNCT
ejpam-5713	1	161	korea	korea	PROPN
ejpam-5713	1	162	university	university	PROPN
ejpam-5713	1	163	,	,	PUNCT
ejpam-5713	1	164	seoul	seoul	PROPN
ejpam-5713	1	165	02841	02841	PROPN
ejpam-5713	1	166	,	,	PUNCT
ejpam-5713	1	167	south	south	PROPN
ejpam-5713	1	168	korea	korea	PROPN
ejpam-5713	1	169	abstract	abstract	PROPN
ejpam-5713	1	170	.	.	PUNCT
ejpam-5713	2	1	a	a	DET
ejpam-5713	2	2	set	set	NOUN
ejpam-5713	2	3	s	s	NOUN
ejpam-5713	2	4	⊆	⊆	NUM
ejpam-5713	2	5	v	v	NOUN
ejpam-5713	2	6	(	(	PUNCT
ejpam-5713	2	7	g	g	NOUN
ejpam-5713	2	8	)	)	PUNCT
ejpam-5713	2	9	is	be	AUX
ejpam-5713	2	10	a	a	DET
ejpam-5713	2	11	super	super	ADJ
ejpam-5713	2	12	vertex	vertex	NOUN
ejpam-5713	2	13	cover	cover	NOUN
ejpam-5713	2	14	of	of	ADP
ejpam-5713	2	15	g	g	PROPN
ejpam-5713	2	16	if	if	SCONJ
ejpam-5713	2	17	s	s	VERB
ejpam-5713	2	18	is	be	AUX
ejpam-5713	2	19	a	a	DET
ejpam-5713	2	20	vertex	vertex	NOUN
ejpam-5713	2	21	cover	cover	NOUN
ejpam-5713	2	22	and	and	CCONJ
ejpam-5713	2	23	for	for	ADP
ejpam-5713	2	24	every	every	DET
ejpam-5713	2	25	x	x	SYM
ejpam-5713	2	26	∈	∈	PROPN
ejpam-5713	2	27	v	v	ADP
ejpam-5713	2	28	(	(	PUNCT
ejpam-5713	2	29	g	g	NOUN
ejpam-5713	2	30	)	)	PUNCT
ejpam-5713	2	31	\	\	PROPN
ejpam-5713	3	1	s	s	X
ejpam-5713	3	2	,	,	PUNCT
ejpam-5713	3	3	there	there	PRON
ejpam-5713	3	4	exists	exist	VERB
ejpam-5713	3	5	y	y	PROPN
ejpam-5713	3	6	∈	∈	PROPN
ejpam-5713	3	7	s	s	VERB
ejpam-5713	3	8	such	such	ADJ
ejpam-5713	3	9	that	that	PRON
ejpam-5713	3	10	ng(y	ng(y	NOUN
ejpam-5713	3	11	)	)	PUNCT
ejpam-5713	3	12	∩	∩	NOUN
ejpam-5713	3	13	(	(	PUNCT
ejpam-5713	3	14	v	v	NOUN
ejpam-5713	3	15	(	(	PUNCT
ejpam-5713	3	16	g	g	NOUN
ejpam-5713	3	17	)	)	PUNCT
ejpam-5713	3	18	\	\	PROPN
ejpam-5713	4	1	s	s	X
ejpam-5713	4	2	)	)	PUNCT
ejpam-5713	4	3	=	=	SYM
ejpam-5713	4	4	{	{	PUNCT
ejpam-5713	4	5	x	x	NOUN
ejpam-5713	4	6	}	}	PUNCT
ejpam-5713	4	7	.	.	PUNCT
ejpam-5713	5	1	the	the	DET
ejpam-5713	5	2	super	super	ADJ
ejpam-5713	5	3	vertex	vertex	NOUN
ejpam-5713	5	4	cover	cover	NOUN
ejpam-5713	5	5	number	number	NOUN
ejpam-5713	5	6	of	of	ADP
ejpam-5713	5	7	g	g	NOUN
ejpam-5713	5	8	,	,	PUNCT
ejpam-5713	5	9	denoted	denote	VERB
ejpam-5713	5	10	βs(g	βs(g	PUNCT
ejpam-5713	5	11	)	)	PUNCT
ejpam-5713	5	12	,	,	PUNCT
ejpam-5713	5	13	is	be	AUX
ejpam-5713	5	14	the	the	DET
ejpam-5713	5	15	smallest	small	ADJ
ejpam-5713	5	16	cardinality	cardinality	NOUN
ejpam-5713	5	17	of	of	ADP
ejpam-5713	5	18	a	a	DET
ejpam-5713	5	19	super	super	ADJ
ejpam-5713	5	20	vertex	vertex	NOUN
ejpam-5713	5	21	cover	cover	NOUN
ejpam-5713	5	22	of	of	ADP
ejpam-5713	5	23	g.	g.	PROPN
ejpam-5713	5	24	in	in	ADP
ejpam-5713	5	25	this	this	DET
ejpam-5713	5	26	paper	paper	NOUN
ejpam-5713	5	27	,	,	PUNCT
ejpam-5713	5	28	we	we	PRON
ejpam-5713	5	29	show	show	VERB
ejpam-5713	5	30	that	that	SCONJ
ejpam-5713	5	31	the	the	DET
ejpam-5713	5	32	difference	difference	NOUN
ejpam-5713	5	33	of	of	ADP
ejpam-5713	5	34	the	the	DET
ejpam-5713	5	35	super	super	ADJ
ejpam-5713	5	36	vertex	vertex	NOUN
ejpam-5713	5	37	cover	cover	NOUN
ejpam-5713	5	38	number	number	NOUN
ejpam-5713	5	39	and	and	CCONJ
ejpam-5713	5	40	the	the	DET
ejpam-5713	5	41	vertex	vertex	NOUN
ejpam-5713	5	42	cover	cover	NOUN
ejpam-5713	5	43	number	number	NOUN
ejpam-5713	5	44	can	can	AUX
ejpam-5713	5	45	be	be	AUX
ejpam-5713	5	46	made	make	VERB
ejpam-5713	5	47	arbitrarily	arbitrarily	ADV
ejpam-5713	5	48	large	large	ADJ
ejpam-5713	5	49	.	.	PUNCT
ejpam-5713	6	1	graphs	graph	NOUN
ejpam-5713	6	2	of	of	ADP
ejpam-5713	6	3	small	small	ADJ
ejpam-5713	6	4	values	value	NOUN
ejpam-5713	6	5	of	of	ADP
ejpam-5713	6	6	the	the	DET
ejpam-5713	6	7	parameter	parameter	NOUN
ejpam-5713	6	8	are	be	AUX
ejpam-5713	6	9	characterized	characterize	VERB
ejpam-5713	6	10	.	.	PUNCT
ejpam-5713	7	1	moreover	moreover	ADV
ejpam-5713	7	2	,	,	PUNCT
ejpam-5713	7	3	we	we	PRON
ejpam-5713	7	4	give	give	VERB
ejpam-5713	7	5	necessary	necessary	ADJ
ejpam-5713	7	6	and	and	CCONJ
ejpam-5713	7	7	sufficient	sufficient	ADJ
ejpam-5713	7	8	conditions	condition	NOUN
ejpam-5713	7	9	for	for	ADP
ejpam-5713	7	10	a	a	DET
ejpam-5713	7	11	super	super	ADJ
ejpam-5713	7	12	vertex	vertex	NOUN
ejpam-5713	7	13	cover	cover	NOUN
ejpam-5713	7	14	in	in	ADP
ejpam-5713	7	15	the	the	DET
ejpam-5713	7	16	join	join	NOUN
ejpam-5713	7	17	and	and	CCONJ
ejpam-5713	7	18	the	the	DET
ejpam-5713	7	19	corona	corona	NOUN
ejpam-5713	7	20	of	of	ADP
ejpam-5713	7	21	graphs	graph	NOUN
ejpam-5713	7	22	.	.	PUNCT
ejpam-5713	8	1	corresponding	correspond	VERB
ejpam-5713	8	2	value	value	NOUN
ejpam-5713	8	3	of	of	ADP
ejpam-5713	8	4	the	the	DET
ejpam-5713	8	5	super	super	ADJ
ejpam-5713	8	6	vertex	vertex	NOUN
ejpam-5713	8	7	cover	cover	NOUN
ejpam-5713	8	8	number	number	NOUN
ejpam-5713	8	9	of	of	ADP
ejpam-5713	8	10	each	each	PRON
ejpam-5713	8	11	these	these	DET
ejpam-5713	8	12	graphs	graph	NOUN
ejpam-5713	8	13	is	be	AUX
ejpam-5713	8	14	also	also	ADV
ejpam-5713	8	15	determined	determine	VERB
ejpam-5713	8	16	.	.	PUNCT
ejpam-5713	9	1	2020	2020	NUM
ejpam-5713	9	2	mathematics	mathematic	NOUN
ejpam-5713	9	3	subject	subject	NOUN
ejpam-5713	9	4	classifications	classification	NOUN
ejpam-5713	9	5	:	:	PUNCT
ejpam-5713	9	6	05c69	05c69	X
ejpam-5713	9	7	key	key	ADJ
ejpam-5713	9	8	words	word	NOUN
ejpam-5713	9	9	and	and	CCONJ
ejpam-5713	9	10	phrases	phrase	NOUN
ejpam-5713	9	11	:	:	PUNCT
ejpam-5713	9	12	vertex	vertex	NOUN
ejpam-5713	9	13	cover	cover	NOUN
ejpam-5713	9	14	,	,	PUNCT
ejpam-5713	9	15	super	super	ADJ
ejpam-5713	9	16	vertex	vertex	NOUN
ejpam-5713	9	17	cover	cover	NOUN
ejpam-5713	9	18	,	,	PUNCT
ejpam-5713	9	19	super	super	ADJ
ejpam-5713	9	20	vertex	vertex	NOUN
ejpam-5713	9	21	cover	cover	NOUN
ejpam-5713	9	22	number	number	NOUN
ejpam-5713	9	23	1	1	NUM
ejpam-5713	9	24	.	.	PUNCT
ejpam-5713	10	1	introduction	introduction	NOUN
ejpam-5713	10	2	numerous	numerous	ADJ
ejpam-5713	10	3	studies	study	NOUN
ejpam-5713	10	4	have	have	AUX
ejpam-5713	10	5	been	be	AUX
ejpam-5713	10	6	made	make	VERB
ejpam-5713	10	7	on	on	ADP
ejpam-5713	10	8	the	the	DET
ejpam-5713	10	9	vertex	vertex	NOUN
ejpam-5713	10	10	covering	covering	NOUN
ejpam-5713	10	11	of	of	ADP
ejpam-5713	10	12	a	a	DET
ejpam-5713	10	13	graph	graph	NOUN
ejpam-5713	10	14	(	(	PUNCT
ejpam-5713	10	15	for	for	ADP
ejpam-5713	10	16	some	some	DET
ejpam-5713	10	17	studies	study	NOUN
ejpam-5713	10	18	,	,	PUNCT
ejpam-5713	10	19	see	see	VERB
ejpam-5713	10	20	[	[	X
ejpam-5713	10	21	9	9	NUM
ejpam-5713	10	22	]	]	PUNCT
ejpam-5713	10	23	,	,	PUNCT
ejpam-5713	11	1	[	[	X
ejpam-5713	11	2	10	10	NUM
ejpam-5713	11	3	]	]	PUNCT
ejpam-5713	11	4	,	,	PUNCT
ejpam-5713	11	5	[	[	X
ejpam-5713	11	6	20	20	NUM
ejpam-5713	11	7	]	]	PUNCT
ejpam-5713	11	8	,	,	PUNCT
ejpam-5713	11	9	[	[	X
ejpam-5713	11	10	23	23	NUM
ejpam-5713	11	11	]	]	PUNCT
ejpam-5713	11	12	)	)	PUNCT
ejpam-5713	11	13	since	since	SCONJ
ejpam-5713	11	14	the	the	DET
ejpam-5713	11	15	introduction	introduction	NOUN
ejpam-5713	11	16	of	of	ADP
ejpam-5713	11	17	the	the	DET
ejpam-5713	11	18	concept	concept	NOUN
ejpam-5713	11	19	.	.	PUNCT
ejpam-5713	12	1	as	as	SCONJ
ejpam-5713	12	2	mentioned	mention	VERB
ejpam-5713	12	3	by	by	ADP
ejpam-5713	12	4	angel	angel	NOUN
ejpam-5713	12	5	and	and	CCONJ
ejpam-5713	12	6	amutha	amutha	NOUN
ejpam-5713	12	7	in	in	ADP
ejpam-5713	12	8	[	[	X
ejpam-5713	12	9	1	1	NUM
ejpam-5713	12	10	]	]	PUNCT
ejpam-5713	12	11	,	,	PUNCT
ejpam-5713	12	12	the	the	DET
ejpam-5713	12	13	parameter	parameter	NOUN
ejpam-5713	12	14	can	can	AUX
ejpam-5713	12	15	be	be	AUX
ejpam-5713	12	16	used	use	VERB
ejpam-5713	12	17	for	for	ADP
ejpam-5713	12	18	safety	safety	NOUN
ejpam-5713	12	19	purposes	purpose	NOUN
ejpam-5713	12	20	in	in	ADP
ejpam-5713	12	21	a	a	DET
ejpam-5713	12	22	network	network	NOUN
ejpam-5713	12	23	.	.	PUNCT
ejpam-5713	13	1	in	in	ADP
ejpam-5713	13	2	particular	particular	ADJ
ejpam-5713	13	3	,	,	PUNCT
ejpam-5713	13	4	the	the	DET
ejpam-5713	13	5	paper	paper	NOUN
ejpam-5713	13	6	pointed	point	VERB
ejpam-5713	13	7	out	out	ADP
ejpam-5713	13	8	that	that	SCONJ
ejpam-5713	13	9	in	in	ADP
ejpam-5713	13	10	a	a	DET
ejpam-5713	13	11	computer	computer	NOUN
ejpam-5713	13	12	network	network	NOUN
ejpam-5713	13	13	,	,	PUNCT
ejpam-5713	13	14	the	the	DET
ejpam-5713	13	15	minimum	minimum	ADJ
ejpam-5713	13	16	value	value	NOUN
ejpam-5713	13	17	of	of	ADP
ejpam-5713	13	18	the	the	DET
ejpam-5713	13	19	parameter	parameter	NOUN
ejpam-5713	13	20	offers	offer	VERB
ejpam-5713	13	21	an	an	DET
ejpam-5713	13	22	optimal	optimal	ADJ
ejpam-5713	13	23	solution	solution	NOUN
ejpam-5713	13	24	for	for	ADP
ejpam-5713	13	25	designing	design	VERB
ejpam-5713	13	26	the	the	DET
ejpam-5713	13	27	network	network	NOUN
ejpam-5713	13	28	defense	defense	NOUN
ejpam-5713	13	29	strategy	strategy	NOUN
ejpam-5713	13	30	.	.	PUNCT
ejpam-5713	14	1	according	accord	VERB
ejpam-5713	14	2	to	to	ADP
ejpam-5713	14	3	toregas	toregas	NOUN
ejpam-5713	14	4	∗corresponding	∗corresponding	NOUN
ejpam-5713	14	5	author	author	NOUN
ejpam-5713	14	6	.	.	PUNCT
ejpam-5713	15	1	doi	doi	NOUN
ejpam-5713	15	2	:	:	PUNCT
ejpam-5713	15	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5713	https://doi.org/10.29020/nybg.ejpam.v18i1.5713	NOUN
ejpam-5713	15	4	email	email	NOUN
ejpam-5713	15	5	addresses	address	NOUN
ejpam-5713	15	6	:	:	PUNCT
ejpam-5713	15	7	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-5713	15	8	(	(	PUNCT
ejpam-5713	15	9	s.	s.	PROPN
ejpam-5713	15	10	r.	r.	PROPN
ejpam-5713	15	11	canoy	canoy	PROPN
ejpam-5713	15	12	jr	jr	PROPN
ejpam-5713	15	13	.	.	PROPN
ejpam-5713	15	14	)	)	PUNCT
ejpam-5713	15	15	,	,	PUNCT
ejpam-5713	15	16	maobonsocan@addu.edu.ph	maobonsocan@addu.edu.ph	NOUN
ejpam-5713	15	17	(	(	PUNCT
ejpam-5713	15	18	m.	m.	NOUN
ejpam-5713	15	19	a.	a.	PROPN
ejpam-5713	15	20	bonsocan	bonsocan	PROPN
ejpam-5713	15	21	)	)	PUNCT
ejpam-5713	15	22	,	,	PUNCT
ejpam-5713	15	23	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-5713	15	24	(	(	PUNCT
ejpam-5713	15	25	j.	j.	PROPN
ejpam-5713	15	26	a.	a.	PROPN
ejpam-5713	15	27	hassan	hassan	PROPN
ejpam-5713	15	28	)	)	PUNCT
ejpam-5713	15	29	,	,	PUNCT
ejpam-5713	15	30	amlmahistrado@addu.edu.ph	amlmahistrado@addu.edu.ph	PROPN
ejpam-5713	15	31	(	(	PUNCT
ejpam-5713	15	32	a.	a.	NOUN
ejpam-5713	15	33	m.	m.	NOUN
ejpam-5713	15	34	mahistrado)vtbilar@addu.edu.ph	mahistrado)vtbilar@addu.edu.ph	PROPN
ejpam-5713	15	35	(	(	PUNCT
ejpam-5713	15	36	v.	v.	ADP
ejpam-5713	15	37	t.	t.	PROPN
ejpam-5713	15	38	bilar	bilar	PROPN
ejpam-5713	15	39	)	)	PUNCT
ejpam-5713	15	40	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5713	16	1	1	1	NUM
ejpam-5713	16	2	copyright	copyright	NOUN
ejpam-5713	16	3	:	:	PUNCT
ejpam-5713	16	4	©	©	PROPN
ejpam-5713	16	5	2025	2025	NUM
ejpam-5713	16	6	the	the	DET
ejpam-5713	16	7	author(s	author(s	NOUN
ejpam-5713	16	8	)	)	PUNCT
ejpam-5713	16	9	.	.	PUNCT
ejpam-5713	17	1	(	(	PUNCT
ejpam-5713	17	2	cc	cc	NOUN
ejpam-5713	17	3	by	by	ADP
ejpam-5713	17	4	-	-	PUNCT
ejpam-5713	17	5	nc	nc	PROPN
ejpam-5713	17	6	4.0	4.0	NUM
ejpam-5713	17	7	)	)	PUNCT
ejpam-5713	17	8	s.	s.	PROPN
ejpam-5713	17	9	r.	r.	PROPN
ejpam-5713	17	10	canoy	canoy	PROPN
ejpam-5713	17	11	et	et	PROPN
ejpam-5713	17	12	al	al	PROPN
ejpam-5713	17	13	.	.	PUNCT
ejpam-5713	17	14	/	/	SYM
ejpam-5713	17	15	eur	eur	PROPN
ejpam-5713	17	16	.	.	PUNCT
ejpam-5713	18	1	j.	j.	PROPN
ejpam-5713	18	2	pure	pure	PROPN
ejpam-5713	18	3	appl	appl	PROPN
ejpam-5713	18	4	.	.	PROPN
ejpam-5713	18	5	math	math	PROPN
ejpam-5713	18	6	,	,	PUNCT
ejpam-5713	18	7	18	18	NUM
ejpam-5713	18	8	(	(	PUNCT
ejpam-5713	18	9	1	1	NUM
ejpam-5713	18	10	)	)	PUNCT
ejpam-5713	18	11	(	(	PUNCT
ejpam-5713	18	12	2025	2025	NUM
ejpam-5713	18	13	)	)	PUNCT
ejpam-5713	18	14	,	,	PUNCT
ejpam-5713	18	15	5713	5713	NUM
ejpam-5713	18	16	2	2	NUM
ejpam-5713	18	17	of	of	ADP
ejpam-5713	18	18	13	13	NUM
ejpam-5713	18	19	et	et	NOUN
ejpam-5713	18	20	al	al	PROPN
ejpam-5713	18	21	.	.	PUNCT
ejpam-5713	19	1	[	[	X
ejpam-5713	19	2	21	21	NUM
ejpam-5713	19	3	]	]	PUNCT
ejpam-5713	19	4	,	,	PUNCT
ejpam-5713	19	5	problems	problem	NOUN
ejpam-5713	19	6	involving	involve	VERB
ejpam-5713	19	7	this	this	DET
ejpam-5713	19	8	concept	concept	NOUN
ejpam-5713	19	9	is	be	AUX
ejpam-5713	19	10	also	also	ADV
ejpam-5713	19	11	utilized	utilize	VERB
ejpam-5713	19	12	to	to	PART
ejpam-5713	19	13	determine	determine	VERB
ejpam-5713	19	14	emergency	emergency	NOUN
ejpam-5713	19	15	facility	facility	NOUN
ejpam-5713	19	16	location	location	NOUN
ejpam-5713	19	17	in	in	ADP
ejpam-5713	19	18	telecommunication	telecommunication	NOUN
ejpam-5713	19	19	networks	network	NOUN
ejpam-5713	19	20	.	.	PUNCT
ejpam-5713	20	1	however	however	ADV
ejpam-5713	20	2	,	,	PUNCT
ejpam-5713	20	3	the	the	DET
ejpam-5713	20	4	vertex	vertex	NOUN
ejpam-5713	20	5	cover	cover	NOUN
ejpam-5713	20	6	problem	problem	NOUN
ejpam-5713	20	7	is	be	AUX
ejpam-5713	20	8	an	an	DET
ejpam-5713	20	9	nphard	nphard	ADJ
ejpam-5713	20	10	optimization	optimization	NOUN
ejpam-5713	20	11	problem	problem	NOUN
ejpam-5713	20	12	.	.	PUNCT
ejpam-5713	21	1	in	in	ADP
ejpam-5713	21	2	fact	fact	NOUN
ejpam-5713	21	3	,	,	PUNCT
ejpam-5713	21	4	using	use	VERB
ejpam-5713	21	5	the	the	DET
ejpam-5713	21	6	known	know	VERB
ejpam-5713	21	7	result	result	NOUN
ejpam-5713	21	8	that	that	SCONJ
ejpam-5713	21	9	the	the	DET
ejpam-5713	21	10	clique	clique	ADJ
ejpam-5713	21	11	problem	problem	NOUN
ejpam-5713	21	12	is	be	AUX
ejpam-5713	21	13	np	np	ADP
ejpam-5713	21	14	-complete	-complete	ADJ
ejpam-5713	21	15	,	,	PUNCT
ejpam-5713	21	16	karp	karp	NOUN
ejpam-5713	21	17	[	[	X
ejpam-5713	21	18	11	11	NUM
ejpam-5713	21	19	]	]	PUNCT
ejpam-5713	21	20	proved	prove	VERB
ejpam-5713	21	21	that	that	SCONJ
ejpam-5713	21	22	the	the	DET
ejpam-5713	21	23	vertex	vertex	NOUN
ejpam-5713	21	24	cover	cover	NOUN
ejpam-5713	21	25	problem	problem	NOUN
ejpam-5713	21	26	is	be	AUX
ejpam-5713	21	27	also	also	ADV
ejpam-5713	21	28	np	np	ADP
ejpam-5713	21	29	-complete	-complete	ADJ
ejpam-5713	21	30	.	.	PUNCT
ejpam-5713	22	1	it	it	PRON
ejpam-5713	22	2	should	should	AUX
ejpam-5713	22	3	be	be	AUX
ejpam-5713	22	4	noted	note	VERB
ejpam-5713	22	5	that	that	SCONJ
ejpam-5713	22	6	the	the	DET
ejpam-5713	22	7	problem	problem	NOUN
ejpam-5713	22	8	remains	remain	VERB
ejpam-5713	22	9	np	np	INTJ
ejpam-5713	22	10	-complete	-complete	ADJ
ejpam-5713	22	11	in	in	ADP
ejpam-5713	22	12	cubic	cubic	ADJ
ejpam-5713	22	13	graphs	graph	NOUN
ejpam-5713	22	14	and	and	CCONJ
ejpam-5713	22	15	in	in	ADP
ejpam-5713	22	16	planar	planar	ADJ
ejpam-5713	22	17	graphs	graph	NOUN
ejpam-5713	22	18	(	(	PUNCT
ejpam-5713	22	19	see	see	VERB
ejpam-5713	22	20	[	[	X
ejpam-5713	22	21	6	6	NUM
ejpam-5713	22	22	]	]	PUNCT
ejpam-5713	22	23	and	and	CCONJ
ejpam-5713	22	24	[	[	X
ejpam-5713	22	25	7	7	NUM
ejpam-5713	22	26	]	]	NUM
ejpam-5713	22	27	)	)	PUNCT
ejpam-5713	22	28	.	.	PUNCT
ejpam-5713	23	1	studies	study	NOUN
ejpam-5713	23	2	that	that	PRON
ejpam-5713	23	3	dealt	deal	VERB
ejpam-5713	23	4	with	with	ADP
ejpam-5713	23	5	determining	determine	VERB
ejpam-5713	23	6	bounds	bound	NOUN
ejpam-5713	23	7	and	and	CCONJ
ejpam-5713	23	8	exact	exact	ADJ
ejpam-5713	23	9	values	value	NOUN
ejpam-5713	23	10	of	of	ADP
ejpam-5713	23	11	the	the	DET
ejpam-5713	23	12	vertex	vertex	NOUN
ejpam-5713	23	13	cover	cover	NOUN
ejpam-5713	23	14	numbers	number	NOUN
ejpam-5713	23	15	of	of	ADP
ejpam-5713	23	16	some	some	DET
ejpam-5713	23	17	specific	specific	ADJ
ejpam-5713	23	18	graphs	graph	NOUN
ejpam-5713	23	19	can	can	AUX
ejpam-5713	23	20	be	be	AUX
ejpam-5713	23	21	found	find	VERB
ejpam-5713	23	22	in	in	ADP
ejpam-5713	23	23	[	[	X
ejpam-5713	23	24	2	2	NUM
ejpam-5713	23	25	]	]	PUNCT
ejpam-5713	23	26	and	and	CCONJ
ejpam-5713	23	27	[	[	X
ejpam-5713	23	28	22	22	NUM
ejpam-5713	23	29	]	]	PUNCT
ejpam-5713	23	30	.	.	PUNCT
ejpam-5713	24	1	recently	recently	ADV
ejpam-5713	24	2	,	,	PUNCT
ejpam-5713	24	3	a	a	DET
ejpam-5713	24	4	number	number	NOUN
ejpam-5713	24	5	of	of	ADP
ejpam-5713	24	6	variations	variation	NOUN
ejpam-5713	24	7	of	of	ADP
ejpam-5713	24	8	the	the	DET
ejpam-5713	24	9	vertex	vertex	NOUN
ejpam-5713	24	10	cover	cover	NOUN
ejpam-5713	24	11	had	have	AUX
ejpam-5713	24	12	been	be	AUX
ejpam-5713	24	13	introduced	introduce	VERB
ejpam-5713	24	14	and	and	CCONJ
ejpam-5713	24	15	investigated	investigate	VERB
ejpam-5713	24	16	(	(	PUNCT
ejpam-5713	24	17	see	see	VERB
ejpam-5713	24	18	[	[	X
ejpam-5713	24	19	1	1	NUM
ejpam-5713	24	20	]	]	PUNCT
ejpam-5713	24	21	,	,	PUNCT
ejpam-5713	24	22	[	[	X
ejpam-5713	24	23	3	3	NUM
ejpam-5713	24	24	]	]	PUNCT
ejpam-5713	24	25	,	,	PUNCT
ejpam-5713	24	26	[	[	X
ejpam-5713	24	27	8	8	NUM
ejpam-5713	24	28	]	]	PUNCT
ejpam-5713	24	29	,	,	PUNCT
ejpam-5713	24	30	[	[	X
ejpam-5713	24	31	9	9	NUM
ejpam-5713	24	32	]	]	PUNCT
ejpam-5713	24	33	,	,	PUNCT
ejpam-5713	24	34	[	[	X
ejpam-5713	24	35	15	15	NUM
ejpam-5713	24	36	]	]	PUNCT
ejpam-5713	24	37	,	,	PUNCT
ejpam-5713	24	38	[	[	X
ejpam-5713	24	39	18	18	NUM
ejpam-5713	24	40	]	]	PUNCT
ejpam-5713	24	41	,	,	PUNCT
ejpam-5713	24	42	and	and	CCONJ
ejpam-5713	24	43	[	[	X
ejpam-5713	24	44	19	19	NUM
ejpam-5713	24	45	]	]	NUM
ejpam-5713	24	46	)	)	PUNCT
ejpam-5713	24	47	.	.	PUNCT
ejpam-5713	25	1	motivated	motivate	VERB
ejpam-5713	25	2	by	by	ADP
ejpam-5713	25	3	the	the	DET
ejpam-5713	25	4	introduction	introduction	NOUN
ejpam-5713	25	5	of	of	ADP
ejpam-5713	25	6	these	these	DET
ejpam-5713	25	7	several	several	ADJ
ejpam-5713	25	8	variants	variant	NOUN
ejpam-5713	25	9	of	of	ADP
ejpam-5713	25	10	the	the	DET
ejpam-5713	25	11	parameter	parameter	NOUN
ejpam-5713	25	12	,	,	PUNCT
ejpam-5713	25	13	we	we	PRON
ejpam-5713	25	14	introduce	introduce	VERB
ejpam-5713	25	15	and	and	CCONJ
ejpam-5713	25	16	initiate	initiate	VERB
ejpam-5713	25	17	the	the	DET
ejpam-5713	25	18	study	study	NOUN
ejpam-5713	25	19	of	of	ADP
ejpam-5713	25	20	super	super	ADJ
ejpam-5713	25	21	vertex	vertex	NOUN
ejpam-5713	25	22	cover	cover	NOUN
ejpam-5713	25	23	of	of	ADP
ejpam-5713	25	24	a	a	DET
ejpam-5713	25	25	graph	graph	NOUN
ejpam-5713	25	26	.	.	PUNCT
ejpam-5713	26	1	as	as	SCONJ
ejpam-5713	26	2	the	the	DET
ejpam-5713	26	3	concept	concept	NOUN
ejpam-5713	26	4	suggests	suggest	VERB
ejpam-5713	26	5	,	,	PUNCT
ejpam-5713	26	6	this	this	DET
ejpam-5713	26	7	new	new	ADJ
ejpam-5713	26	8	parameter	parameter	NOUN
ejpam-5713	26	9	combines	combine	VERB
ejpam-5713	26	10	two	two	NUM
ejpam-5713	26	11	existing	exist	VERB
ejpam-5713	26	12	concepts	concept	NOUN
ejpam-5713	26	13	,	,	PUNCT
ejpam-5713	26	14	namely	namely	ADV
ejpam-5713	26	15	;	;	PUNCT
ejpam-5713	26	16	vertex	vertex	NOUN
ejpam-5713	26	17	cover	cover	NOUN
ejpam-5713	26	18	and	and	CCONJ
ejpam-5713	26	19	super	super	ADJ
ejpam-5713	26	20	domination	domination	NOUN
ejpam-5713	26	21	.	.	PUNCT
ejpam-5713	27	1	some	some	DET
ejpam-5713	27	2	studies	study	NOUN
ejpam-5713	27	3	on	on	ADP
ejpam-5713	27	4	super	super	ADJ
ejpam-5713	27	5	domination	domination	NOUN
ejpam-5713	27	6	can	can	AUX
ejpam-5713	27	7	be	be	AUX
ejpam-5713	27	8	found	find	VERB
ejpam-5713	27	9	in	in	ADP
ejpam-5713	27	10	[	[	X
ejpam-5713	27	11	5	5	NUM
ejpam-5713	27	12	]	]	PUNCT
ejpam-5713	27	13	,	,	PUNCT
ejpam-5713	28	1	[	[	X
ejpam-5713	28	2	12],[13	12],[13	NOUN
ejpam-5713	28	3	]	]	X
ejpam-5713	28	4	,	,	PUNCT
ejpam-5713	28	5	[	[	X
ejpam-5713	28	6	14	14	NUM
ejpam-5713	28	7	]	]	PUNCT
ejpam-5713	28	8	,	,	PUNCT
ejpam-5713	28	9	[	[	X
ejpam-5713	28	10	16	16	NUM
ejpam-5713	28	11	]	]	PUNCT
ejpam-5713	28	12	,	,	PUNCT
ejpam-5713	29	1	[	[	X
ejpam-5713	29	2	17	17	NUM
ejpam-5713	29	3	]	]	SYM
ejpam-5713	29	4	.	.	PUNCT
ejpam-5713	30	1	2	2	X
ejpam-5713	30	2	.	.	NOUN
ejpam-5713	30	3	terminologies	terminology	NOUN
ejpam-5713	30	4	and	and	CCONJ
ejpam-5713	30	5	notations	notation	NOUN
ejpam-5713	30	6	let	let	VERB
ejpam-5713	30	7	g	g	NOUN
ejpam-5713	30	8	=	=	SYM
ejpam-5713	30	9	(	(	PUNCT
ejpam-5713	30	10	v	v	NOUN
ejpam-5713	30	11	(	(	PUNCT
ejpam-5713	30	12	g	g	NOUN
ejpam-5713	30	13	)	)	PUNCT
ejpam-5713	30	14	,	,	PUNCT
ejpam-5713	30	15	e(g	e(g	PROPN
ejpam-5713	30	16	)	)	PUNCT
ejpam-5713	30	17	)	)	PUNCT
ejpam-5713	30	18	be	be	AUX
ejpam-5713	30	19	a	a	DET
ejpam-5713	30	20	simple	simple	ADJ
ejpam-5713	30	21	undirected	undirected	ADJ
ejpam-5713	30	22	graph	graph	NOUN
ejpam-5713	30	23	.	.	PUNCT
ejpam-5713	31	1	the	the	DET
ejpam-5713	31	2	open	open	ADJ
ejpam-5713	31	3	neighborhood	neighborhood	NOUN
ejpam-5713	31	4	of	of	ADP
ejpam-5713	31	5	a	a	DET
ejpam-5713	31	6	vertex	vertex	NOUN
ejpam-5713	31	7	v	v	NOUN
ejpam-5713	31	8	of	of	ADP
ejpam-5713	31	9	g	g	PROPN
ejpam-5713	31	10	is	be	AUX
ejpam-5713	31	11	the	the	DET
ejpam-5713	31	12	set	set	NOUN
ejpam-5713	31	13	ng(v	ng(v	PUNCT
ejpam-5713	31	14	)	)	PUNCT
ejpam-5713	31	15	=	=	SYM
ejpam-5713	32	1	{	{	PUNCT
ejpam-5713	32	2	u	u	NOUN
ejpam-5713	32	3	∈	∈	PROPN
ejpam-5713	32	4	v	v	NOUN
ejpam-5713	32	5	(	(	PUNCT
ejpam-5713	32	6	g	g	NOUN
ejpam-5713	32	7	)	)	PUNCT
ejpam-5713	32	8	:	:	PUNCT
ejpam-5713	32	9	uv	uv	PROPN
ejpam-5713	32	10	∈	∈	PROPN
ejpam-5713	32	11	e(g	e(g	PROPN
ejpam-5713	32	12	)	)	PUNCT
ejpam-5713	32	13	}	}	PUNCT
ejpam-5713	32	14	,	,	PUNCT
ejpam-5713	32	15	while	while	SCONJ
ejpam-5713	32	16	its	its	PRON
ejpam-5713	32	17	closed	closed	ADJ
ejpam-5713	32	18	neighborhood	neighborhood	NOUN
ejpam-5713	32	19	is	be	AUX
ejpam-5713	32	20	the	the	DET
ejpam-5713	32	21	set	set	NOUN
ejpam-5713	32	22	ng[v	ng[v	NOUN
ejpam-5713	32	23	]	]	X
ejpam-5713	32	24	=	=	SYM
ejpam-5713	32	25	ng(v	ng(v	X
ejpam-5713	32	26	)	)	PUNCT
ejpam-5713	32	27	∪	∪	ADP
ejpam-5713	32	28	{	{	PUNCT
ejpam-5713	32	29	v	v	NOUN
ejpam-5713	32	30	}	}	PUNCT
ejpam-5713	32	31	.	.	PUNCT
ejpam-5713	33	1	the	the	DET
ejpam-5713	33	2	open	open	ADJ
ejpam-5713	33	3	neighborhood	neighborhood	NOUN
ejpam-5713	33	4	of	of	ADP
ejpam-5713	33	5	a	a	DET
ejpam-5713	33	6	set	set	NOUN
ejpam-5713	33	7	s	s	NOUN
ejpam-5713	33	8	⊆	⊆	NUM
ejpam-5713	33	9	v	v	NOUN
ejpam-5713	33	10	(	(	PUNCT
ejpam-5713	33	11	g	g	NOUN
ejpam-5713	33	12	)	)	PUNCT
ejpam-5713	33	13	is	be	AUX
ejpam-5713	33	14	the	the	DET
ejpam-5713	33	15	set	set	NOUN
ejpam-5713	33	16	ng(s	ng(s	NOUN
ejpam-5713	33	17	)	)	PUNCT
ejpam-5713	33	18	=	=	SYM
ejpam-5713	33	19	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-5713	33	20	)	)	PUNCT
ejpam-5713	33	21	and	and	CCONJ
ejpam-5713	33	22	its	its	PRON
ejpam-5713	33	23	closed	closed	ADJ
ejpam-5713	33	24	neighborhood	neighborhood	NOUN
ejpam-5713	33	25	is	be	AUX
ejpam-5713	33	26	the	the	DET
ejpam-5713	33	27	set	set	VERB
ejpam-5713	33	28	ng[s	ng[	NOUN
ejpam-5713	33	29	]	]	PUNCT
ejpam-5713	33	30	=	=	SYM
ejpam-5713	33	31	s	s	X
ejpam-5713	33	32	∪	∪	NOUN
ejpam-5713	33	33	ng(s	ng(s	NUM
ejpam-5713	33	34	)	)	PUNCT
ejpam-5713	33	35	.	.	PUNCT
ejpam-5713	34	1	any	any	DET
ejpam-5713	34	2	v	v	NUM
ejpam-5713	34	3	∈	∈	PROPN
ejpam-5713	34	4	v	v	NOUN
ejpam-5713	34	5	(	(	PUNCT
ejpam-5713	34	6	g	g	NOUN
ejpam-5713	34	7	)	)	PUNCT
ejpam-5713	34	8	with	with	ADP
ejpam-5713	34	9	|ng(v)|	|ng(v)|	NOUN
ejpam-5713	34	10	=	=	SYM
ejpam-5713	34	11	0	0	NUM
ejpam-5713	34	12	is	be	AUX
ejpam-5713	34	13	called	call	VERB
ejpam-5713	34	14	an	an	DET
ejpam-5713	34	15	isolated	isolated	ADJ
ejpam-5713	34	16	vertex	vertex	NOUN
ejpam-5713	34	17	.	.	PUNCT
ejpam-5713	35	1	vertex	vertex	NOUN
ejpam-5713	35	2	v	v	NOUN
ejpam-5713	35	3	is	be	AUX
ejpam-5713	35	4	a	a	DET
ejpam-5713	35	5	leaf	leaf	NOUN
ejpam-5713	35	6	or	or	CCONJ
ejpam-5713	35	7	an	an	DET
ejpam-5713	35	8	endvertex	endvertex	NOUN
ejpam-5713	35	9	if	if	SCONJ
ejpam-5713	35	10	|ng(v)|	|ng(v)|	VERB
ejpam-5713	35	11	=	=	SYM
ejpam-5713	35	12	1	1	X
ejpam-5713	35	13	.	.	PUNCT
ejpam-5713	36	1	a	a	DET
ejpam-5713	36	2	vertex	vertex	NOUN
ejpam-5713	36	3	w	w	NOUN
ejpam-5713	36	4	of	of	ADP
ejpam-5713	36	5	g	g	PROPN
ejpam-5713	36	6	is	be	AUX
ejpam-5713	36	7	a	a	DET
ejpam-5713	36	8	support	support	NOUN
ejpam-5713	36	9	vertex	vertex	NOUN
ejpam-5713	36	10	if	if	SCONJ
ejpam-5713	36	11	wv	wv	PROPN
ejpam-5713	36	12	∈	∈	PROPN
ejpam-5713	36	13	e(g	e(g	PROPN
ejpam-5713	36	14	)	)	PUNCT
ejpam-5713	36	15	for	for	ADP
ejpam-5713	36	16	some	some	DET
ejpam-5713	36	17	leaf	leaf	NOUN
ejpam-5713	36	18	v	v	NOUN
ejpam-5713	36	19	in	in	ADP
ejpam-5713	36	20	g.	g.	PROPN
ejpam-5713	36	21	the	the	DET
ejpam-5713	36	22	sets	set	NOUN
ejpam-5713	36	23	i(g	i(g	ADV
ejpam-5713	36	24	)	)	PUNCT
ejpam-5713	36	25	,	,	PUNCT
ejpam-5713	36	26	l(g	l(g	PROPN
ejpam-5713	36	27	)	)	PUNCT
ejpam-5713	36	28	,	,	PUNCT
ejpam-5713	36	29	and	and	CCONJ
ejpam-5713	36	30	s(g	s(g	PROPN
ejpam-5713	36	31	)	)	PUNCT
ejpam-5713	36	32	will	will	AUX
ejpam-5713	36	33	,	,	PUNCT
ejpam-5713	36	34	respectively	respectively	ADV
ejpam-5713	36	35	,	,	PUNCT
ejpam-5713	36	36	denote	denote	VERB
ejpam-5713	36	37	the	the	DET
ejpam-5713	36	38	sets	set	NOUN
ejpam-5713	36	39	containing	contain	VERB
ejpam-5713	36	40	all	all	DET
ejpam-5713	36	41	the	the	DET
ejpam-5713	36	42	isolated	isolated	ADJ
ejpam-5713	36	43	vertices	vertex	NOUN
ejpam-5713	36	44	,	,	PUNCT
ejpam-5713	36	45	leaves	leave	NOUN
ejpam-5713	36	46	,	,	PUNCT
ejpam-5713	36	47	and	and	CCONJ
ejpam-5713	36	48	support	support	NOUN
ejpam-5713	36	49	vertices	vertex	NOUN
ejpam-5713	36	50	in	in	ADP
ejpam-5713	36	51	g.	g.	PROPN
ejpam-5713	36	52	a	a	DET
ejpam-5713	36	53	subset	subset	VERB
ejpam-5713	36	54	a	a	PRON
ejpam-5713	36	55	of	of	ADP
ejpam-5713	36	56	v	v	NOUN
ejpam-5713	36	57	(	(	PUNCT
ejpam-5713	36	58	g	g	NOUN
ejpam-5713	36	59	)	)	PUNCT
ejpam-5713	36	60	is	be	AUX
ejpam-5713	36	61	an	an	DET
ejpam-5713	36	62	independent	independent	ADJ
ejpam-5713	36	63	set	set	NOUN
ejpam-5713	36	64	if	if	SCONJ
ejpam-5713	36	65	for	for	SCONJ
ejpam-5713	36	66	every	every	DET
ejpam-5713	36	67	pair	pair	NOUN
ejpam-5713	36	68	of	of	ADP
ejpam-5713	36	69	distinct	distinct	ADJ
ejpam-5713	36	70	vertices	vertex	NOUN
ejpam-5713	36	71	in	in	ADP
ejpam-5713	36	72	g	g	PROPN
ejpam-5713	36	73	do	do	AUX
ejpam-5713	36	74	not	not	PART
ejpam-5713	36	75	form	form	VERB
ejpam-5713	36	76	an	an	DET
ejpam-5713	36	77	edge	edge	NOUN
ejpam-5713	36	78	.	.	PUNCT
ejpam-5713	37	1	the	the	DET
ejpam-5713	37	2	maximum	maximum	ADJ
ejpam-5713	37	3	cardinality	cardinality	NOUN
ejpam-5713	37	4	of	of	ADP
ejpam-5713	37	5	an	an	DET
ejpam-5713	37	6	independent	independent	ADJ
ejpam-5713	37	7	set	set	NOUN
ejpam-5713	37	8	in	in	ADP
ejpam-5713	37	9	g	g	NOUN
ejpam-5713	37	10	,	,	PUNCT
ejpam-5713	37	11	denoted	denote	VERB
ejpam-5713	37	12	by	by	ADP
ejpam-5713	37	13	α(g	α(g	NOUN
ejpam-5713	37	14	)	)	PUNCT
ejpam-5713	37	15	,	,	PUNCT
ejpam-5713	37	16	is	be	AUX
ejpam-5713	37	17	called	call	VERB
ejpam-5713	37	18	the	the	DET
ejpam-5713	37	19	independence	independence	NOUN
ejpam-5713	37	20	number	number	NOUN
ejpam-5713	37	21	of	of	ADP
ejpam-5713	37	22	g.	g.	PROPN
ejpam-5713	37	23	any	any	DET
ejpam-5713	37	24	independent	independent	ADJ
ejpam-5713	37	25	set	set	NOUN
ejpam-5713	37	26	with	with	ADP
ejpam-5713	37	27	cardinality	cardinality	NOUN
ejpam-5713	37	28	equal	equal	ADJ
ejpam-5713	37	29	to	to	ADP
ejpam-5713	37	30	α(g	α(g	NUM
ejpam-5713	37	31	)	)	PUNCT
ejpam-5713	37	32	is	be	AUX
ejpam-5713	37	33	called	call	VERB
ejpam-5713	37	34	an	an	DET
ejpam-5713	37	35	α	α	NOUN
ejpam-5713	37	36	-	-	PUNCT
ejpam-5713	37	37	set	set	VERB
ejpam-5713	37	38	in	in	ADP
ejpam-5713	37	39	g.	g.	PROPN
ejpam-5713	37	40	a	a	DET
ejpam-5713	37	41	set	set	NOUN
ejpam-5713	37	42	s	s	PROPN
ejpam-5713	37	43	⊆	⊆	NUM
ejpam-5713	37	44	v	v	NOUN
ejpam-5713	37	45	(	(	PUNCT
ejpam-5713	37	46	g	g	NOUN
ejpam-5713	37	47	)	)	PUNCT
ejpam-5713	37	48	is	be	AUX
ejpam-5713	37	49	a	a	DET
ejpam-5713	37	50	dominating	dominating	NOUN
ejpam-5713	37	51	set	set	VERB
ejpam-5713	37	52	in	in	ADP
ejpam-5713	37	53	g	g	PROPN
ejpam-5713	37	54	if	if	SCONJ
ejpam-5713	37	55	ng[s	ng[	NOUN
ejpam-5713	37	56	]	]	PUNCT
ejpam-5713	37	57	=	=	SYM
ejpam-5713	37	58	v	v	NOUN
ejpam-5713	37	59	(	(	PUNCT
ejpam-5713	37	60	g	g	NOUN
ejpam-5713	37	61	)	)	PUNCT
ejpam-5713	37	62	.	.	PUNCT
ejpam-5713	38	1	it	it	PRON
ejpam-5713	38	2	is	be	AUX
ejpam-5713	38	3	a	a	DET
ejpam-5713	38	4	super	super	ADJ
ejpam-5713	38	5	dominating	dominating	NOUN
ejpam-5713	38	6	set	set	NOUN
ejpam-5713	38	7	if	if	SCONJ
ejpam-5713	38	8	for	for	ADP
ejpam-5713	38	9	every	every	PRON
ejpam-5713	38	10	v	v	NUM
ejpam-5713	38	11	∈	∈	NOUN
ejpam-5713	38	12	v	v	NOUN
ejpam-5713	38	13	(	(	PUNCT
ejpam-5713	38	14	g	g	NOUN
ejpam-5713	38	15	)	)	PUNCT
ejpam-5713	38	16	\s	\s	NOUN
ejpam-5713	38	17	there	there	PRON
ejpam-5713	38	18	exists	exist	VERB
ejpam-5713	38	19	w	w	PROPN
ejpam-5713	38	20	∈	∈	PROPN
ejpam-5713	38	21	s	s	VERB
ejpam-5713	38	22	such	such	ADJ
ejpam-5713	38	23	that	that	SCONJ
ejpam-5713	38	24	ng(w)∩	ng(w)∩	PUNCT
ejpam-5713	39	1	[	[	X
ejpam-5713	39	2	v	v	X
ejpam-5713	39	3	(	(	PUNCT
ejpam-5713	39	4	g	g	NOUN
ejpam-5713	39	5	)	)	PUNCT
ejpam-5713	39	6	\s	\s	NOUN
ejpam-5713	39	7	]	]	PUNCT
ejpam-5713	39	8	=	=	PUNCT
ejpam-5713	39	9	{	{	PUNCT
ejpam-5713	39	10	v	v	NOUN
ejpam-5713	39	11	}	}	PUNCT
ejpam-5713	39	12	.	.	PUNCT
ejpam-5713	40	1	the	the	DET
ejpam-5713	40	2	domination	domination	NOUN
ejpam-5713	40	3	number	number	NOUN
ejpam-5713	40	4	(	(	PUNCT
ejpam-5713	40	5	super	super	ADJ
ejpam-5713	40	6	domination	domination	NOUN
ejpam-5713	40	7	number	number	NOUN
ejpam-5713	40	8	)	)	PUNCT
ejpam-5713	40	9	of	of	ADP
ejpam-5713	40	10	g	g	NOUN
ejpam-5713	40	11	,	,	PUNCT
ejpam-5713	40	12	denoted	denote	VERB
ejpam-5713	40	13	γ(g	γ(g	PROPN
ejpam-5713	40	14	)	)	PUNCT
ejpam-5713	40	15	(	(	PUNCT
ejpam-5713	40	16	resp	resp	NOUN
ejpam-5713	40	17	.	.	PUNCT
ejpam-5713	41	1	γsp(g	γsp(g	NOUN
ejpam-5713	41	2	)	)	PUNCT
ejpam-5713	41	3	)	)	PUNCT
ejpam-5713	41	4	is	be	AUX
ejpam-5713	41	5	the	the	DET
ejpam-5713	41	6	minimum	minimum	ADJ
ejpam-5713	41	7	cardinality	cardinality	NOUN
ejpam-5713	41	8	of	of	ADP
ejpam-5713	41	9	a	a	DET
ejpam-5713	41	10	dominating	dominating	NOUN
ejpam-5713	41	11	(	(	PUNCT
ejpam-5713	41	12	resp	resp	NOUN
ejpam-5713	41	13	.	.	PUNCT
ejpam-5713	42	1	super	super	ADJ
ejpam-5713	42	2	dominating	dominating	NOUN
ejpam-5713	42	3	)	)	PUNCT
ejpam-5713	42	4	set	set	VERB
ejpam-5713	42	5	in	in	ADP
ejpam-5713	42	6	g.	g.	PROPN
ejpam-5713	42	7	any	any	DET
ejpam-5713	42	8	dominating	dominating	NOUN
ejpam-5713	42	9	set	set	NOUN
ejpam-5713	42	10	(	(	PUNCT
ejpam-5713	42	11	super	super	ADJ
ejpam-5713	42	12	dominating	dominating	NOUN
ejpam-5713	42	13	set	set	NOUN
ejpam-5713	42	14	)	)	PUNCT
ejpam-5713	42	15	with	with	ADP
ejpam-5713	42	16	cardinality	cardinality	PROPN
ejpam-5713	42	17	γ(g	γ(g	PROPN
ejpam-5713	42	18	)	)	PUNCT
ejpam-5713	42	19	(	(	PUNCT
ejpam-5713	42	20	resp	resp	NOUN
ejpam-5713	42	21	.	.	PUNCT
ejpam-5713	43	1	γsp(g	γsp(g	NOUN
ejpam-5713	43	2	)	)	PUNCT
ejpam-5713	43	3	)	)	PUNCT
ejpam-5713	43	4	is	be	AUX
ejpam-5713	43	5	called	call	VERB
ejpam-5713	43	6	a	a	DET
ejpam-5713	43	7	γ	γ	NOUN
ejpam-5713	43	8	-	-	PUNCT
ejpam-5713	43	9	set	set	ADJ
ejpam-5713	43	10	(	(	PUNCT
ejpam-5713	43	11	resp	resp	NOUN
ejpam-5713	43	12	.	.	PUNCT
ejpam-5713	44	1	γsp	γsp	PROPN
ejpam-5713	44	2	-	-	PUNCT
ejpam-5713	44	3	set	set	NOUN
ejpam-5713	44	4	)	)	PUNCT
ejpam-5713	44	5	.	.	PUNCT
ejpam-5713	45	1	a	a	DET
ejpam-5713	45	2	subset	subset	ADJ
ejpam-5713	45	3	u	u	NOUN
ejpam-5713	45	4	of	of	ADP
ejpam-5713	45	5	vertices	vertex	NOUN
ejpam-5713	45	6	of	of	ADP
ejpam-5713	45	7	a	a	DET
ejpam-5713	45	8	graph	graph	NOUN
ejpam-5713	45	9	g	g	NOUN
ejpam-5713	45	10	is	be	AUX
ejpam-5713	45	11	called	call	VERB
ejpam-5713	45	12	a	a	DET
ejpam-5713	45	13	vertex	vertex	NOUN
ejpam-5713	45	14	cover	cover	NOUN
ejpam-5713	45	15	of	of	ADP
ejpam-5713	45	16	g	g	PROPN
ejpam-5713	45	17	if	if	SCONJ
ejpam-5713	45	18	for	for	ADP
ejpam-5713	45	19	every	every	DET
ejpam-5713	45	20	edge	edge	NOUN
ejpam-5713	45	21	e	e	NOUN
ejpam-5713	45	22	=	=	PUNCT
ejpam-5713	45	23	uv	uv	PROPN
ejpam-5713	45	24	∈	∈	PROPN
ejpam-5713	45	25	e(g	e(g	PROPN
ejpam-5713	45	26	)	)	PUNCT
ejpam-5713	45	27	,	,	PUNCT
ejpam-5713	45	28	u	u	PROPN
ejpam-5713	45	29	∈	∈	PROPN
ejpam-5713	45	30	u	u	NOUN
ejpam-5713	45	31	or	or	CCONJ
ejpam-5713	45	32	v	v	ADP
ejpam-5713	45	33	∈	∈	PROPN
ejpam-5713	45	34	u	u	NOUN
ejpam-5713	45	35	.	.	PUNCT
ejpam-5713	46	1	the	the	DET
ejpam-5713	46	2	minimum	minimum	ADJ
ejpam-5713	46	3	cardinality	cardinality	NOUN
ejpam-5713	46	4	of	of	ADP
ejpam-5713	46	5	vertex	vertex	NOUN
ejpam-5713	46	6	cover	cover	NOUN
ejpam-5713	46	7	of	of	ADP
ejpam-5713	46	8	g	g	PROPN
ejpam-5713	46	9	is	be	AUX
ejpam-5713	46	10	the	the	DET
ejpam-5713	46	11	vertex	vertex	NOUN
ejpam-5713	46	12	cover	cover	NOUN
ejpam-5713	46	13	number	number	NOUN
ejpam-5713	46	14	ofg	ofg	PROPN
ejpam-5713	46	15	and	and	CCONJ
ejpam-5713	46	16	is	be	AUX
ejpam-5713	46	17	denoted	denote	VERB
ejpam-5713	46	18	by	by	ADP
ejpam-5713	46	19	β(g	β(g	PROPN
ejpam-5713	46	20	)	)	PUNCT
ejpam-5713	46	21	and	and	CCONJ
ejpam-5713	46	22	any	any	DET
ejpam-5713	46	23	vertex	vertex	NOUN
ejpam-5713	46	24	cover	cover	NOUN
ejpam-5713	46	25	ofg	ofg	PROPN
ejpam-5713	46	26	with	with	ADP
ejpam-5713	46	27	cardinality	cardinality	PROPN
ejpam-5713	46	28	β(g	β(g	PROPN
ejpam-5713	46	29	)	)	PUNCT
ejpam-5713	46	30	is	be	AUX
ejpam-5713	46	31	called	call	VERB
ejpam-5713	46	32	a	a	DET
ejpam-5713	46	33	β	β	NOUN
ejpam-5713	46	34	-	-	NOUN
ejpam-5713	46	35	set	set	NOUN
ejpam-5713	46	36	.	.	PUNCT
ejpam-5713	47	1	clearly	clearly	ADV
ejpam-5713	47	2	,	,	PUNCT
ejpam-5713	47	3	a	a	DET
ejpam-5713	47	4	vertex	vertex	NOUN
ejpam-5713	47	5	cover	cover	NOUN
ejpam-5713	47	6	is	be	AUX
ejpam-5713	47	7	also	also	ADV
ejpam-5713	47	8	a	a	DET
ejpam-5713	47	9	dominating	dominating	NOUN
ejpam-5713	47	10	set	set	VERB
ejpam-5713	47	11	in	in	ADP
ejpam-5713	47	12	a	a	DET
ejpam-5713	47	13	non	non	ADJ
ejpam-5713	47	14	-	-	ADJ
ejpam-5713	47	15	trivial	trivial	ADJ
ejpam-5713	47	16	connected	connected	ADJ
ejpam-5713	47	17	graph	graph	NOUN
ejpam-5713	47	18	g.	g.	NOUN
ejpam-5713	47	19	a	a	DET
ejpam-5713	47	20	set	set	NOUN
ejpam-5713	47	21	s	s	PROPN
ejpam-5713	47	22	⊆	⊆	NUM
ejpam-5713	47	23	v	v	NOUN
ejpam-5713	47	24	(	(	PUNCT
ejpam-5713	47	25	g	g	NOUN
ejpam-5713	47	26	)	)	PUNCT
ejpam-5713	47	27	is	be	AUX
ejpam-5713	47	28	called	call	VERB
ejpam-5713	47	29	super	super	ADJ
ejpam-5713	47	30	vertex	vertex	NOUN
ejpam-5713	47	31	cover	cover	NOUN
ejpam-5713	47	32	of	of	ADP
ejpam-5713	47	33	g	g	PROPN
ejpam-5713	47	34	if	if	SCONJ
ejpam-5713	47	35	s	s	VERB
ejpam-5713	47	36	is	be	AUX
ejpam-5713	47	37	a	a	DET
ejpam-5713	47	38	vertex	vertex	NOUN
ejpam-5713	47	39	cover	cover	NOUN
ejpam-5713	47	40	and	and	CCONJ
ejpam-5713	47	41	for	for	ADP
ejpam-5713	47	42	every	every	DET
ejpam-5713	47	43	x	x	SYM
ejpam-5713	47	44	∈	∈	PROPN
ejpam-5713	47	45	v	v	NOUN
ejpam-5713	47	46	(	(	PUNCT
ejpam-5713	47	47	g)\s	g)\s	NOUN
ejpam-5713	47	48	,	,	PUNCT
ejpam-5713	47	49	there	there	PRON
ejpam-5713	47	50	exists	exist	VERB
ejpam-5713	47	51	z	z	PROPN
ejpam-5713	47	52	∈	∈	PROPN
ejpam-5713	47	53	s	s	VERB
ejpam-5713	47	54	such	such	ADJ
ejpam-5713	47	55	that	that	DET
ejpam-5713	47	56	ng(z)∩[v	ng(z)∩[v	PROPN
ejpam-5713	47	57	(	(	PUNCT
ejpam-5713	47	58	g)\s	g)\s	NOUN
ejpam-5713	47	59	]	]	PUNCT
ejpam-5713	47	60	=	=	PUNCT
ejpam-5713	47	61	{	{	PUNCT
ejpam-5713	47	62	x	x	NOUN
ejpam-5713	47	63	}	}	PUNCT
ejpam-5713	47	64	.	.	PUNCT
ejpam-5713	48	1	in	in	ADP
ejpam-5713	48	2	other	other	ADJ
ejpam-5713	48	3	words	word	NOUN
ejpam-5713	48	4	,	,	PUNCT
ejpam-5713	48	5	a	a	DET
ejpam-5713	48	6	super	super	ADJ
ejpam-5713	48	7	vertex	vertex	NOUN
ejpam-5713	48	8	cover	cover	NOUN
ejpam-5713	48	9	is	be	AUX
ejpam-5713	48	10	any	any	DET
ejpam-5713	48	11	set	set	NOUN
ejpam-5713	48	12	that	that	PRON
ejpam-5713	48	13	is	be	AUX
ejpam-5713	48	14	both	both	CCONJ
ejpam-5713	48	15	a	a	DET
ejpam-5713	48	16	vertex	vertex	NOUN
ejpam-5713	48	17	cover	cover	NOUN
ejpam-5713	48	18	and	and	CCONJ
ejpam-5713	48	19	super	super	ADJ
ejpam-5713	48	20	dominating	dominating	NOUN
ejpam-5713	48	21	set	set	VERB
ejpam-5713	48	22	in	in	ADP
ejpam-5713	48	23	g.	g.	PROPN
ejpam-5713	48	24	the	the	DET
ejpam-5713	48	25	super	super	ADJ
ejpam-5713	48	26	vertex	vertex	NOUN
ejpam-5713	48	27	cover	cover	NOUN
ejpam-5713	48	28	number	number	NOUN
ejpam-5713	48	29	of	of	ADP
ejpam-5713	48	30	g	g	NOUN
ejpam-5713	48	31	,	,	PUNCT
ejpam-5713	48	32	denoted	denote	VERB
ejpam-5713	48	33	by	by	ADP
ejpam-5713	48	34	βs(g	βs(g	NOUN
ejpam-5713	48	35	)	)	PUNCT
ejpam-5713	48	36	,	,	PUNCT
ejpam-5713	48	37	is	be	AUX
ejpam-5713	48	38	the	the	DET
ejpam-5713	48	39	smallest	small	ADJ
ejpam-5713	48	40	cardinality	cardinality	NOUN
ejpam-5713	48	41	s.	s.	PROPN
ejpam-5713	48	42	r.	r.	PROPN
ejpam-5713	48	43	canoy	canoy	PROPN
ejpam-5713	48	44	et	et	PROPN
ejpam-5713	48	45	al	al	PROPN
ejpam-5713	48	46	.	.	PUNCT
ejpam-5713	48	47	/	/	SYM
ejpam-5713	48	48	eur	eur	PROPN
ejpam-5713	48	49	.	.	PUNCT
ejpam-5713	49	1	j.	j.	PROPN
ejpam-5713	49	2	pure	pure	PROPN
ejpam-5713	49	3	appl	appl	PROPN
ejpam-5713	49	4	.	.	PROPN
ejpam-5713	49	5	math	math	PROPN
ejpam-5713	49	6	,	,	PUNCT
ejpam-5713	49	7	18	18	NUM
ejpam-5713	49	8	(	(	PUNCT
ejpam-5713	49	9	1	1	NUM
ejpam-5713	49	10	)	)	PUNCT
ejpam-5713	49	11	(	(	PUNCT
ejpam-5713	49	12	2025	2025	NUM
ejpam-5713	49	13	)	)	PUNCT
ejpam-5713	49	14	,	,	PUNCT
ejpam-5713	49	15	5713	5713	NUM
ejpam-5713	49	16	3	3	NUM
ejpam-5713	49	17	of	of	ADP
ejpam-5713	49	18	13	13	NUM
ejpam-5713	49	19	of	of	ADP
ejpam-5713	49	20	a	a	DET
ejpam-5713	49	21	super	super	ADJ
ejpam-5713	49	22	vertex	vertex	NOUN
ejpam-5713	49	23	cover	cover	NOUN
ejpam-5713	49	24	of	of	ADP
ejpam-5713	49	25	g.	g.	PROPN
ejpam-5713	49	26	any	any	DET
ejpam-5713	49	27	super	super	ADJ
ejpam-5713	49	28	vertex	vertex	NOUN
ejpam-5713	49	29	cover	cover	NOUN
ejpam-5713	49	30	of	of	ADP
ejpam-5713	49	31	g	g	NOUN
ejpam-5713	49	32	with	with	ADP
ejpam-5713	49	33	cardinality	cardinality	NOUN
ejpam-5713	49	34	βs(g	βs(g	PUNCT
ejpam-5713	49	35	)	)	PUNCT
ejpam-5713	49	36	is	be	AUX
ejpam-5713	49	37	called	call	VERB
ejpam-5713	49	38	a	a	DET
ejpam-5713	49	39	βs	βs	NOUN
ejpam-5713	49	40	-	-	PUNCT
ejpam-5713	49	41	set	set	NOUN
ejpam-5713	49	42	.	.	PUNCT
ejpam-5713	50	1	let	let	VERB
ejpam-5713	50	2	g	g	NOUN
ejpam-5713	50	3	and	and	CCONJ
ejpam-5713	50	4	h	h	NOUN
ejpam-5713	50	5	be	be	VERB
ejpam-5713	50	6	any	any	DET
ejpam-5713	50	7	two	two	NUM
ejpam-5713	50	8	graphs	graph	NOUN
ejpam-5713	50	9	.	.	PUNCT
ejpam-5713	51	1	the	the	DET
ejpam-5713	51	2	join	join	NOUN
ejpam-5713	51	3	g	g	PROPN
ejpam-5713	51	4	+	+	CCONJ
ejpam-5713	51	5	h	h	NOUN
ejpam-5713	51	6	is	be	AUX
ejpam-5713	51	7	the	the	DET
ejpam-5713	51	8	graph	graph	NOUN
ejpam-5713	51	9	with	with	ADP
ejpam-5713	51	10	vertex	vertex	NOUN
ejpam-5713	51	11	set	set	VERB
ejpam-5713	51	12	v	v	NOUN
ejpam-5713	51	13	(	(	PUNCT
ejpam-5713	51	14	g+h	g+h	NOUN
ejpam-5713	51	15	)	)	PUNCT
ejpam-5713	51	16	=	=	SYM
ejpam-5713	51	17	v	v	NOUN
ejpam-5713	51	18	(	(	PUNCT
ejpam-5713	51	19	g)∪	g)∪	VERB
ejpam-5713	51	20	v	v	NUM
ejpam-5713	51	21	(	(	PUNCT
ejpam-5713	51	22	h	h	NOUN
ejpam-5713	51	23	)	)	PUNCT
ejpam-5713	51	24	and	and	CCONJ
ejpam-5713	51	25	edge	edge	NOUN
ejpam-5713	51	26	set	set	VERB
ejpam-5713	51	27	e(g+h	e(g+h	NUM
ejpam-5713	51	28	)	)	PUNCT
ejpam-5713	52	1	=	=	SYM
ejpam-5713	52	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-5713	52	3	{	{	PUNCT
ejpam-5713	52	4	uv	uv	NOUN
ejpam-5713	52	5	:	:	PUNCT
ejpam-5713	52	6	u	u	PROPN
ejpam-5713	52	7	∈	∈	PROPN
ejpam-5713	52	8	v	v	ADP
ejpam-5713	52	9	(	(	PUNCT
ejpam-5713	52	10	g	g	NOUN
ejpam-5713	52	11	)	)	PUNCT
ejpam-5713	52	12	,	,	PUNCT
ejpam-5713	52	13	v	v	X
ejpam-5713	52	14	∈	∈	PROPN
ejpam-5713	52	15	v	v	NOUN
ejpam-5713	52	16	(	(	PUNCT
ejpam-5713	52	17	h	h	NOUN
ejpam-5713	52	18	)	)	PUNCT
ejpam-5713	52	19	}	}	PUNCT
ejpam-5713	52	20	.	.	PUNCT
ejpam-5713	53	1	the	the	DET
ejpam-5713	53	2	corona	corona	NOUN
ejpam-5713	53	3	g	g	PROPN
ejpam-5713	53	4	◦	◦	NOUN
ejpam-5713	53	5	h	h	NOUN
ejpam-5713	53	6	is	be	AUX
ejpam-5713	53	7	the	the	DET
ejpam-5713	53	8	graph	graph	NOUN
ejpam-5713	53	9	obtained	obtain	VERB
ejpam-5713	53	10	by	by	ADP
ejpam-5713	53	11	taking	take	VERB
ejpam-5713	53	12	one	one	NUM
ejpam-5713	53	13	copy	copy	NOUN
ejpam-5713	53	14	of	of	ADP
ejpam-5713	53	15	g	g	PROPN
ejpam-5713	53	16	and	and	CCONJ
ejpam-5713	53	17	|v	|v	PROPN
ejpam-5713	53	18	(	(	PUNCT
ejpam-5713	53	19	g)|	g)|	NOUN
ejpam-5713	53	20	copies	copy	NOUN
ejpam-5713	53	21	of	of	ADP
ejpam-5713	53	22	h	h	NOUN
ejpam-5713	53	23	,	,	PUNCT
ejpam-5713	53	24	and	and	CCONJ
ejpam-5713	53	25	then	then	ADV
ejpam-5713	53	26	joining	join	VERB
ejpam-5713	53	27	the	the	DET
ejpam-5713	53	28	ith	ith	PROPN
ejpam-5713	53	29	vertex	vertex	NOUN
ejpam-5713	53	30	of	of	ADP
ejpam-5713	53	31	g	g	NOUN
ejpam-5713	53	32	to	to	ADP
ejpam-5713	53	33	every	every	DET
ejpam-5713	53	34	vertex	vertex	NOUN
ejpam-5713	53	35	of	of	ADP
ejpam-5713	53	36	the	the	DET
ejpam-5713	53	37	ith	ith	PROPN
ejpam-5713	53	38	copy	copy	NOUN
ejpam-5713	53	39	of	of	ADP
ejpam-5713	53	40	h.	h.	PROPN
ejpam-5713	53	41	we	we	PRON
ejpam-5713	53	42	denote	denote	VERB
ejpam-5713	53	43	by	by	ADP
ejpam-5713	53	44	hv	hv	PROPN
ejpam-5713	54	1	the	the	DET
ejpam-5713	54	2	copy	copy	NOUN
ejpam-5713	54	3	of	of	ADP
ejpam-5713	54	4	h	h	NOUN
ejpam-5713	54	5	in	in	ADP
ejpam-5713	54	6	g	g	PROPN
ejpam-5713	54	7	◦	◦	NOUN
ejpam-5713	54	8	h	h	NOUN
ejpam-5713	54	9	corresponding	correspond	VERB
ejpam-5713	54	10	to	to	ADP
ejpam-5713	54	11	the	the	DET
ejpam-5713	54	12	vertex	vertex	NOUN
ejpam-5713	54	13	v	v	ADP
ejpam-5713	54	14	∈	∈	PROPN
ejpam-5713	54	15	g	g	NOUN
ejpam-5713	54	16	and	and	CCONJ
ejpam-5713	54	17	write	write	VERB
ejpam-5713	54	18	v+hv	v+hv	NOUN
ejpam-5713	54	19	for	for	ADP
ejpam-5713	54	20	⟨{v}⟩	⟨{v}⟩	ADJ
ejpam-5713	54	21	+	+	NOUN
ejpam-5713	54	22	hv	hv	PROPN
ejpam-5713	54	23	.	.	PUNCT
ejpam-5713	55	1	readers	reader	NOUN
ejpam-5713	55	2	are	be	AUX
ejpam-5713	55	3	referred	refer	VERB
ejpam-5713	55	4	to	to	ADP
ejpam-5713	55	5	[	[	X
ejpam-5713	55	6	4	4	X
ejpam-5713	55	7	]	]	PUNCT
ejpam-5713	55	8	for	for	ADP
ejpam-5713	55	9	other	other	ADJ
ejpam-5713	55	10	basic	basic	ADJ
ejpam-5713	55	11	definitions	definition	NOUN
ejpam-5713	55	12	that	that	PRON
ejpam-5713	55	13	are	be	AUX
ejpam-5713	55	14	not	not	PART
ejpam-5713	55	15	given	give	VERB
ejpam-5713	55	16	here	here	ADV
ejpam-5713	55	17	.	.	PUNCT
ejpam-5713	56	1	3	3	X
ejpam-5713	56	2	.	.	X
ejpam-5713	56	3	results	result	NOUN
ejpam-5713	56	4	remark	remark	VERB
ejpam-5713	56	5	1	1	NUM
ejpam-5713	56	6	.	.	PUNCT
ejpam-5713	57	1	let	let	VERB
ejpam-5713	57	2	g	g	PRON
ejpam-5713	57	3	be	be	AUX
ejpam-5713	57	4	a	a	DET
ejpam-5713	57	5	graph	graph	NOUN
ejpam-5713	57	6	and	and	CCONJ
ejpam-5713	57	7	let	let	VERB
ejpam-5713	57	8	s	s	PRON
ejpam-5713	57	9	be	be	AUX
ejpam-5713	57	10	a	a	DET
ejpam-5713	57	11	super	super	ADJ
ejpam-5713	57	12	vertex	vertex	NOUN
ejpam-5713	57	13	cover	cover	NOUN
ejpam-5713	57	14	of	of	ADP
ejpam-5713	57	15	g.	g.	PROPN
ejpam-5713	57	16	then	then	ADV
ejpam-5713	57	17	each	each	PRON
ejpam-5713	57	18	of	of	ADP
ejpam-5713	57	19	the	the	DET
ejpam-5713	57	20	following	follow	VERB
ejpam-5713	57	21	holds	hold	VERB
ejpam-5713	57	22	:	:	PUNCT
ejpam-5713	57	23	(	(	PUNCT
ejpam-5713	57	24	i	i	NOUN
ejpam-5713	57	25	)	)	PUNCT
ejpam-5713	57	26	s	s	VERB
ejpam-5713	57	27	is	be	AUX
ejpam-5713	57	28	a	a	DET
ejpam-5713	57	29	dominating	dominating	NOUN
ejpam-5713	57	30	set	set	VERB
ejpam-5713	57	31	in	in	ADP
ejpam-5713	57	32	g.	g.	PROPN
ejpam-5713	57	33	(	(	PUNCT
ejpam-5713	57	34	ii	ii	PROPN
ejpam-5713	57	35	)	)	PUNCT
ejpam-5713	57	36	i(g	i(g	NOUN
ejpam-5713	57	37	)	)	PUNCT
ejpam-5713	58	1	⊆	⊆	NUM
ejpam-5713	58	2	s	s	VERB
ejpam-5713	58	3	where	where	SCONJ
ejpam-5713	58	4	i(g	i(g	NOUN
ejpam-5713	58	5	)	)	PUNCT
ejpam-5713	58	6	is	be	AUX
ejpam-5713	58	7	the	the	DET
ejpam-5713	58	8	set	set	NOUN
ejpam-5713	58	9	containing	contain	VERB
ejpam-5713	58	10	all	all	DET
ejpam-5713	58	11	the	the	DET
ejpam-5713	58	12	isolated	isolated	ADJ
ejpam-5713	58	13	vertices	vertex	NOUN
ejpam-5713	58	14	of	of	ADP
ejpam-5713	58	15	g.	g.	PROPN
ejpam-5713	58	16	(	(	PUNCT
ejpam-5713	58	17	iii	iii	X
ejpam-5713	58	18	)	)	PUNCT
ejpam-5713	58	19	if	if	SCONJ
ejpam-5713	58	20	v	v	NOUN
ejpam-5713	58	21	is	be	AUX
ejpam-5713	58	22	a	a	DET
ejpam-5713	58	23	support	support	NOUN
ejpam-5713	58	24	vertex	vertex	NOUN
ejpam-5713	58	25	in	in	ADP
ejpam-5713	58	26	g	g	NOUN
ejpam-5713	58	27	,	,	PUNCT
ejpam-5713	58	28	then	then	ADV
ejpam-5713	58	29	|(ng[v]∩l(g))∩	|(ng[v]∩l(g))∩	X
ejpam-5713	58	30	(	(	PUNCT
ejpam-5713	58	31	v	v	NOUN
ejpam-5713	58	32	(	(	PUNCT
ejpam-5713	58	33	g	g	NOUN
ejpam-5713	58	34	)	)	PUNCT
ejpam-5713	58	35	\s)|	\s)|	PROPN
ejpam-5713	58	36	≤	≤	ADJ
ejpam-5713	58	37	1	1	NUM
ejpam-5713	58	38	,	,	PUNCT
ejpam-5713	58	39	where	where	SCONJ
ejpam-5713	58	40	l(g	l(g	NOUN
ejpam-5713	58	41	)	)	PUNCT
ejpam-5713	58	42	is	be	AUX
ejpam-5713	58	43	the	the	DET
ejpam-5713	58	44	set	set	NOUN
ejpam-5713	58	45	of	of	ADP
ejpam-5713	58	46	all	all	DET
ejpam-5713	58	47	leaves	leave	NOUN
ejpam-5713	58	48	(	(	PUNCT
ejpam-5713	58	49	end	end	NOUN
ejpam-5713	58	50	vertices	vertex	NOUN
ejpam-5713	58	51	)	)	PUNCT
ejpam-5713	58	52	in	in	ADP
ejpam-5713	58	53	g.	g.	PROPN
ejpam-5713	58	54	proposition	proposition	NOUN
ejpam-5713	58	55	1	1	X
ejpam-5713	58	56	.	.	PUNCT
ejpam-5713	59	1	let	let	VERB
ejpam-5713	59	2	g	g	PRON
ejpam-5713	59	3	be	be	AUX
ejpam-5713	59	4	a	a	DET
ejpam-5713	59	5	graph	graph	NOUN
ejpam-5713	59	6	of	of	ADP
ejpam-5713	59	7	order	order	NOUN
ejpam-5713	59	8	n	n	PRON
ejpam-5713	59	9	such	such	ADJ
ejpam-5713	59	10	that	that	DET
ejpam-5713	59	11	e(g	e(g	NOUN
ejpam-5713	59	12	)	)	PUNCT
ejpam-5713	60	1	̸=	̸=	PROPN
ejpam-5713	60	2	∅.	∅.	VERB
ejpam-5713	60	3	then	then	ADV
ejpam-5713	60	4	max{γsp(g	max{γsp(g	PROPN
ejpam-5713	60	5	)	)	PUNCT
ejpam-5713	60	6	,	,	PUNCT
ejpam-5713	60	7	β(g	β(g	PROPN
ejpam-5713	60	8	)	)	PUNCT
ejpam-5713	60	9	}	}	PUNCT
ejpam-5713	60	10	≤	≤	NOUN
ejpam-5713	60	11	βs(g	βs(g	PUNCT
ejpam-5713	60	12	)	)	PUNCT
ejpam-5713	60	13	≤	≤	NUM
ejpam-5713	60	14	n−	n−	NOUN
ejpam-5713	60	15	1	1	NUM
ejpam-5713	60	16	.	.	PUNCT
ejpam-5713	61	1	proof	proof	NOUN
ejpam-5713	61	2	.	.	PUNCT
ejpam-5713	62	1	since	since	SCONJ
ejpam-5713	62	2	every	every	DET
ejpam-5713	62	3	super	super	ADJ
ejpam-5713	62	4	vertex	vertex	NOUN
ejpam-5713	62	5	cover	cover	NOUN
ejpam-5713	62	6	of	of	ADP
ejpam-5713	62	7	g	g	PROPN
ejpam-5713	62	8	is	be	AUX
ejpam-5713	62	9	both	both	CCONJ
ejpam-5713	62	10	a	a	DET
ejpam-5713	62	11	vertex	vertex	NOUN
ejpam-5713	62	12	cover	cover	NOUN
ejpam-5713	62	13	and	and	CCONJ
ejpam-5713	62	14	a	a	DET
ejpam-5713	62	15	super	super	ADJ
ejpam-5713	62	16	dominating	dominating	NOUN
ejpam-5713	62	17	set	set	NOUN
ejpam-5713	62	18	in	in	ADP
ejpam-5713	62	19	g	g	PROPN
ejpam-5713	62	20	,	,	PUNCT
ejpam-5713	62	21	it	it	PRON
ejpam-5713	62	22	follows	follow	VERB
ejpam-5713	62	23	that	that	SCONJ
ejpam-5713	62	24	max{γsp(g	max{γsp(g	PROPN
ejpam-5713	62	25	)	)	PUNCT
ejpam-5713	62	26	,	,	PUNCT
ejpam-5713	62	27	β(g	β(g	PROPN
ejpam-5713	62	28	)	)	PUNCT
ejpam-5713	62	29	}	}	PUNCT
ejpam-5713	62	30	≤	≤	NOUN
ejpam-5713	62	31	βs(g	βs(g	PUNCT
ejpam-5713	62	32	)	)	PUNCT
ejpam-5713	62	33	.	.	PUNCT
ejpam-5713	63	1	now	now	ADV
ejpam-5713	63	2	let	let	VERB
ejpam-5713	63	3	e	e	NOUN
ejpam-5713	63	4	=	=	VERB
ejpam-5713	63	5	uv	uv	PROPN
ejpam-5713	63	6	∈	∈	PROPN
ejpam-5713	63	7	e(g	e(g	PROPN
ejpam-5713	63	8	)	)	PUNCT
ejpam-5713	63	9	and	and	CCONJ
ejpam-5713	63	10	set	set	VERB
ejpam-5713	63	11	s	s	PART
ejpam-5713	63	12	=	=	X
ejpam-5713	63	13	v	v	ADJ
ejpam-5713	63	14	(	(	PUNCT
ejpam-5713	63	15	g	g	NOUN
ejpam-5713	63	16	)	)	PUNCT
ejpam-5713	63	17	\	\	NOUN
ejpam-5713	63	18	{	{	PUNCT
ejpam-5713	63	19	u	u	NOUN
ejpam-5713	63	20	}	}	PUNCT
ejpam-5713	63	21	.	.	PUNCT
ejpam-5713	64	1	then	then	ADV
ejpam-5713	64	2	clearly	clearly	ADV
ejpam-5713	64	3	,	,	PUNCT
ejpam-5713	64	4	s	s	VERB
ejpam-5713	64	5	is	be	AUX
ejpam-5713	64	6	a	a	DET
ejpam-5713	64	7	super	super	ADJ
ejpam-5713	64	8	vertex	vertex	NOUN
ejpam-5713	64	9	cover	cover	NOUN
ejpam-5713	64	10	of	of	ADP
ejpam-5713	64	11	g.	g.	PROPN
ejpam-5713	64	12	thus	thus	ADV
ejpam-5713	64	13	,	,	PUNCT
ejpam-5713	64	14	βs(g	βs(g	PUNCT
ejpam-5713	64	15	)	)	PUNCT
ejpam-5713	64	16	≤	≤	NUM
ejpam-5713	64	17	|s|	|s|	PROPN
ejpam-5713	64	18	=	=	SYM
ejpam-5713	64	19	n−	n−	PROPN
ejpam-5713	64	20	1	1	NUM
ejpam-5713	64	21	.	.	PUNCT
ejpam-5713	65	1	remark	remark	NOUN
ejpam-5713	65	2	2	2	NUM
ejpam-5713	65	3	.	.	PUNCT
ejpam-5713	66	1	the	the	DET
ejpam-5713	66	2	bounds	bound	NOUN
ejpam-5713	66	3	given	give	VERB
ejpam-5713	66	4	in	in	ADP
ejpam-5713	66	5	proposition	proposition	NOUN
ejpam-5713	66	6	1	1	NUM
ejpam-5713	66	7	are	be	AUX
ejpam-5713	66	8	sharp	sharp	ADJ
ejpam-5713	66	9	.	.	PUNCT
ejpam-5713	67	1	moreover	moreover	ADV
ejpam-5713	67	2	,	,	PUNCT
ejpam-5713	67	3	strict	strict	ADJ
ejpam-5713	67	4	inequality	inequality	NOUN
ejpam-5713	67	5	is	be	AUX
ejpam-5713	67	6	attainable	attainable	ADJ
ejpam-5713	67	7	.	.	PUNCT
ejpam-5713	68	1	to	to	PART
ejpam-5713	68	2	see	see	VERB
ejpam-5713	68	3	this	this	PRON
ejpam-5713	68	4	,	,	PUNCT
ejpam-5713	68	5	consider	consider	VERB
ejpam-5713	68	6	the	the	DET
ejpam-5713	68	7	graphs	graph	NOUN
ejpam-5713	68	8	g1	g1	VERB
ejpam-5713	68	9	=	=	PUNCT
ejpam-5713	68	10	p5	p5	ADJ
ejpam-5713	69	1	=	=	PUNCT
ejpam-5713	70	1	[	[	X
ejpam-5713	70	2	a	a	PRON
ejpam-5713	70	3	,	,	PUNCT
ejpam-5713	70	4	b	b	NOUN
ejpam-5713	70	5	,	,	PUNCT
ejpam-5713	70	6	c	c	NOUN
ejpam-5713	70	7	,	,	PUNCT
ejpam-5713	70	8	d	d	NOUN
ejpam-5713	70	9	,	,	PUNCT
ejpam-5713	70	10	e	e	NOUN
ejpam-5713	70	11	]	]	X
ejpam-5713	70	12	,	,	PUNCT
ejpam-5713	70	13	g2	g2	PROPN
ejpam-5713	70	14	=	=	SYM
ejpam-5713	70	15	c4	c4	NOUN
ejpam-5713	70	16	=	=	PUNCT
ejpam-5713	71	1	[	[	X
ejpam-5713	71	2	x	x	X
ejpam-5713	71	3	,	,	PUNCT
ejpam-5713	71	4	y	y	PROPN
ejpam-5713	71	5	,	,	PUNCT
ejpam-5713	71	6	z	z	PROPN
ejpam-5713	71	7	,	,	PUNCT
ejpam-5713	71	8	w	w	PROPN
ejpam-5713	71	9	,	,	PUNCT
ejpam-5713	71	10	x	x	NOUN
ejpam-5713	71	11	]	]	X
ejpam-5713	71	12	,	,	PUNCT
ejpam-5713	71	13	and	and	CCONJ
ejpam-5713	71	14	the	the	DET
ejpam-5713	71	15	star	star	NOUN
ejpam-5713	71	16	graph	graph	NOUN
ejpam-5713	71	17	g3	g3	PROPN
ejpam-5713	71	18	=	=	PROPN
ejpam-5713	71	19	k1	k1	PROPN
ejpam-5713	71	20	,	,	PUNCT
ejpam-5713	71	21	4	4	NUM
ejpam-5713	71	22	.	.	PUNCT
ejpam-5713	72	1	the	the	DET
ejpam-5713	72	2	set	set	NOUN
ejpam-5713	72	3	t	t	PROPN
ejpam-5713	72	4	=	=	SYM
ejpam-5713	72	5	{	{	PUNCT
ejpam-5713	72	6	b	b	PROPN
ejpam-5713	72	7	,	,	PUNCT
ejpam-5713	72	8	c	c	NOUN
ejpam-5713	72	9	,	,	PUNCT
ejpam-5713	72	10	d	d	X
ejpam-5713	72	11	}	}	PUNCT
ejpam-5713	72	12	is	be	AUX
ejpam-5713	72	13	a	a	DET
ejpam-5713	72	14	β	β	NOUN
ejpam-5713	72	15	-	-	VERB
ejpam-5713	72	16	set	set	ADJ
ejpam-5713	72	17	,	,	PUNCT
ejpam-5713	72	18	γsp	γsp	X
ejpam-5713	72	19	-	-	PUNCT
ejpam-5713	72	20	set	set	NOUN
ejpam-5713	72	21	,	,	PUNCT
ejpam-5713	72	22	and	and	CCONJ
ejpam-5713	72	23	βs	βs	X
ejpam-5713	72	24	-	-	PUNCT
ejpam-5713	72	25	set	set	NOUN
ejpam-5713	72	26	in	in	ADP
ejpam-5713	72	27	g1	g1	NOUN
ejpam-5713	72	28	.	.	PUNCT
ejpam-5713	73	1	hence	hence	ADV
ejpam-5713	73	2	,	,	PUNCT
ejpam-5713	73	3	γsp(g1	γsp(g1	PROPN
ejpam-5713	73	4	)	)	PUNCT
ejpam-5713	73	5	=	=	PUNCT
ejpam-5713	73	6	β(g1	β(g1	X
ejpam-5713	73	7	)	)	PUNCT
ejpam-5713	73	8	=	=	SYM
ejpam-5713	73	9	βs(g1	βs(g1	X
ejpam-5713	73	10	)	)	PUNCT
ejpam-5713	73	11	=	=	SYM
ejpam-5713	73	12	3	3	NUM
ejpam-5713	73	13	<	<	SYM
ejpam-5713	73	14	4	4	NUM
ejpam-5713	73	15	=	=	SYM
ejpam-5713	73	16	|v	|v	X
ejpam-5713	73	17	(	(	PUNCT
ejpam-5713	73	18	g1)|	g1)|	INTJ
ejpam-5713	73	19	−	−	PROPN
ejpam-5713	74	1	1	1	NUM
ejpam-5713	74	2	.	.	PUNCT
ejpam-5713	75	1	on	on	ADP
ejpam-5713	75	2	the	the	DET
ejpam-5713	75	3	other	other	ADJ
ejpam-5713	75	4	hand	hand	NOUN
ejpam-5713	75	5	,	,	PUNCT
ejpam-5713	75	6	sets	set	VERB
ejpam-5713	75	7	s1	s1	NOUN
ejpam-5713	75	8	=	=	PUNCT
ejpam-5713	75	9	{	{	PUNCT
ejpam-5713	75	10	x	x	PROPN
ejpam-5713	75	11	,	,	PUNCT
ejpam-5713	75	12	y	y	NOUN
ejpam-5713	75	13	}	}	PUNCT
ejpam-5713	75	14	,	,	PUNCT
ejpam-5713	75	15	s2	s2	X
ejpam-5713	75	16	=	=	SYM
ejpam-5713	75	17	{	{	PUNCT
ejpam-5713	75	18	x	x	NOUN
ejpam-5713	75	19	,	,	PUNCT
ejpam-5713	75	20	z	z	NOUN
ejpam-5713	75	21	}	}	PUNCT
ejpam-5713	75	22	,	,	PUNCT
ejpam-5713	75	23	and	and	CCONJ
ejpam-5713	75	24	s3	s3	PROPN
ejpam-5713	75	25	=	=	SYM
ejpam-5713	75	26	{	{	PUNCT
ejpam-5713	75	27	x	x	PROPN
ejpam-5713	75	28	,	,	PUNCT
ejpam-5713	75	29	y	y	PROPN
ejpam-5713	75	30	,	,	PUNCT
ejpam-5713	75	31	z	z	NOUN
ejpam-5713	75	32	}	}	PUNCT
ejpam-5713	75	33	are	be	AUX
ejpam-5713	75	34	γsp	γsp	NOUN
ejpam-5713	75	35	-	-	PUNCT
ejpam-5713	75	36	set	set	NOUN
ejpam-5713	75	37	,	,	PUNCT
ejpam-5713	75	38	β	β	NOUN
ejpam-5713	75	39	-	-	PUNCT
ejpam-5713	75	40	set	set	ADJ
ejpam-5713	75	41	,	,	PUNCT
ejpam-5713	75	42	and	and	CCONJ
ejpam-5713	75	43	βs	βs	X
ejpam-5713	75	44	-	-	PUNCT
ejpam-5713	75	45	set	set	NOUN
ejpam-5713	75	46	in	in	ADP
ejpam-5713	75	47	g2	g2	PROPN
ejpam-5713	75	48	,	,	PUNCT
ejpam-5713	75	49	respectively	respectively	ADV
ejpam-5713	75	50	.	.	PUNCT
ejpam-5713	76	1	thus	thus	ADV
ejpam-5713	76	2	,	,	PUNCT
ejpam-5713	76	3	γsp(g2	γsp(g2	NOUN
ejpam-5713	76	4	)	)	PUNCT
ejpam-5713	76	5	=	=	PUNCT
ejpam-5713	76	6	β(g2	β(g2	X
ejpam-5713	76	7	)	)	PUNCT
ejpam-5713	76	8	=	=	SYM
ejpam-5713	76	9	2	2	NUM
ejpam-5713	76	10	<	<	SYM
ejpam-5713	76	11	3	3	NUM
ejpam-5713	76	12	=	=	SYM
ejpam-5713	76	13	βs(g2	βs(g2	X
ejpam-5713	76	14	)	)	PUNCT
ejpam-5713	76	15	=	=	SYM
ejpam-5713	76	16	|v	|v	X
ejpam-5713	76	17	(	(	PUNCT
ejpam-5713	76	18	g2)|	g2)|	NOUN
ejpam-5713	76	19	−	−	NOUN
ejpam-5713	76	20	1	1	NUM
ejpam-5713	76	21	.	.	PUNCT
ejpam-5713	77	1	finally	finally	ADV
ejpam-5713	77	2	,	,	PUNCT
ejpam-5713	77	3	one	one	PRON
ejpam-5713	77	4	can	can	AUX
ejpam-5713	77	5	easily	easily	ADV
ejpam-5713	77	6	see	see	VERB
ejpam-5713	77	7	that	that	DET
ejpam-5713	77	8	β(g3	β(g3	NOUN
ejpam-5713	77	9	)	)	PUNCT
ejpam-5713	77	10	=	=	SYM
ejpam-5713	78	1	1	1	NUM
ejpam-5713	78	2	<	<	SYM
ejpam-5713	78	3	4	4	NUM
ejpam-5713	78	4	=	=	SYM
ejpam-5713	78	5	βs(g3	βs(g3	NOUN
ejpam-5713	78	6	)	)	PUNCT
ejpam-5713	78	7	=	=	SYM
ejpam-5713	78	8	γsp(g3	γsp(g3	NOUN
ejpam-5713	78	9	)	)	PUNCT
ejpam-5713	78	10	=	=	SYM
ejpam-5713	78	11	|v	|v	PROPN
ejpam-5713	78	12	(	(	PUNCT
ejpam-5713	78	13	g3)|	g3)|	NOUN
ejpam-5713	78	14	−	−	PROPN
ejpam-5713	78	15	1	1	NUM
ejpam-5713	78	16	.	.	PUNCT
ejpam-5713	79	1	s.	s.	PROPN
ejpam-5713	79	2	r.	r.	PROPN
ejpam-5713	79	3	canoy	canoy	PROPN
ejpam-5713	79	4	et	et	PROPN
ejpam-5713	79	5	al	al	PROPN
ejpam-5713	79	6	.	.	PUNCT
ejpam-5713	79	7	/	/	SYM
ejpam-5713	79	8	eur	eur	PROPN
ejpam-5713	79	9	.	.	PUNCT
ejpam-5713	80	1	j.	j.	PROPN
ejpam-5713	80	2	pure	pure	PROPN
ejpam-5713	80	3	appl	appl	PROPN
ejpam-5713	80	4	.	.	PROPN
ejpam-5713	80	5	math	math	PROPN
ejpam-5713	80	6	,	,	PUNCT
ejpam-5713	80	7	18	18	NUM
ejpam-5713	80	8	(	(	PUNCT
ejpam-5713	80	9	1	1	NUM
ejpam-5713	80	10	)	)	PUNCT
ejpam-5713	80	11	(	(	PUNCT
ejpam-5713	80	12	2025	2025	NUM
ejpam-5713	80	13	)	)	PUNCT
ejpam-5713	80	14	,	,	PUNCT
ejpam-5713	80	15	5713	5713	NUM
ejpam-5713	80	16	4	4	NUM
ejpam-5713	80	17	of	of	ADP
ejpam-5713	80	18	13	13	NUM
ejpam-5713	80	19	for	for	ADP
ejpam-5713	80	20	strict	strict	ADJ
ejpam-5713	80	21	inequality	inequality	NOUN
ejpam-5713	80	22	,	,	PUNCT
ejpam-5713	80	23	let	let	VERB
ejpam-5713	80	24	g	g	NOUN
ejpam-5713	80	25	be	be	AUX
ejpam-5713	80	26	the	the	DET
ejpam-5713	80	27	graph	graph	NOUN
ejpam-5713	80	28	in	in	ADP
ejpam-5713	80	29	figure	figure	NOUN
ejpam-5713	80	30	1	1	NUM
ejpam-5713	80	31	.	.	PUNCT
ejpam-5713	81	1	set	set	VERB
ejpam-5713	81	2	{	{	PUNCT
ejpam-5713	81	3	d	d	NOUN
ejpam-5713	81	4	,	,	PUNCT
ejpam-5713	81	5	e	e	NOUN
ejpam-5713	81	6	,	,	PUNCT
ejpam-5713	81	7	c	c	NOUN
ejpam-5713	81	8	}	}	PUNCT
ejpam-5713	81	9	is	be	AUX
ejpam-5713	81	10	a	a	DET
ejpam-5713	81	11	β	β	NOUN
ejpam-5713	81	12	-	-	VERB
ejpam-5713	81	13	set	set	ADJ
ejpam-5713	81	14	,	,	PUNCT
ejpam-5713	81	15	{	{	PUNCT
ejpam-5713	81	16	a	a	PRON
ejpam-5713	81	17	,	,	PUNCT
ejpam-5713	81	18	e	e	NOUN
ejpam-5713	81	19	,	,	PUNCT
ejpam-5713	81	20	f	f	X
ejpam-5713	81	21	,	,	PUNCT
ejpam-5713	81	22	g	g	NOUN
ejpam-5713	81	23	}	}	PUNCT
ejpam-5713	81	24	is	be	AUX
ejpam-5713	81	25	a	a	DET
ejpam-5713	81	26	γsp	γsp	NOUN
ejpam-5713	81	27	-	-	PUNCT
ejpam-5713	81	28	set	set	NOUN
ejpam-5713	81	29	,	,	PUNCT
ejpam-5713	81	30	and	and	CCONJ
ejpam-5713	81	31	{	{	PUNCT
ejpam-5713	81	32	a	a	PRON
ejpam-5713	81	33	,	,	PUNCT
ejpam-5713	81	34	b	b	NOUN
ejpam-5713	81	35	,	,	PUNCT
ejpam-5713	81	36	e	e	NOUN
ejpam-5713	81	37	,	,	PUNCT
ejpam-5713	81	38	f	f	X
ejpam-5713	81	39	,	,	PUNCT
ejpam-5713	81	40	g	g	NOUN
ejpam-5713	81	41	}	}	PUNCT
ejpam-5713	81	42	is	be	AUX
ejpam-5713	81	43	a	a	DET
ejpam-5713	81	44	βs	βs	NOUN
ejpam-5713	81	45	-	-	PUNCT
ejpam-5713	81	46	set	set	NOUN
ejpam-5713	81	47	in	in	ADP
ejpam-5713	81	48	g.	g.	PROPN
ejpam-5713	81	49	hence	hence	ADV
ejpam-5713	81	50	,	,	PUNCT
ejpam-5713	81	51	β(g	β(g	PROPN
ejpam-5713	81	52	)	)	PUNCT
ejpam-5713	81	53	=	=	PUNCT
ejpam-5713	81	54	3	3	NUM
ejpam-5713	81	55	<	<	SYM
ejpam-5713	81	56	4	4	NUM
ejpam-5713	81	57	=	=	SYM
ejpam-5713	81	58	γsp(g	γsp(g	NOUN
ejpam-5713	81	59	)	)	PUNCT
ejpam-5713	81	60	<	<	X
ejpam-5713	81	61	5	5	NUM
ejpam-5713	81	62	=	=	PUNCT
ejpam-5713	81	63	βs(g	βs(g	PUNCT
ejpam-5713	81	64	)	)	PUNCT
ejpam-5713	81	65	<	<	X
ejpam-5713	81	66	6	6	NUM
ejpam-5713	81	67	=	=	SYM
ejpam-5713	81	68	|v	|v	X
ejpam-5713	81	69	(	(	PUNCT
ejpam-5713	81	70	g)|	g)|	INTJ
ejpam-5713	81	71	−	−	NOUN
ejpam-5713	81	72	1	1	NUM
ejpam-5713	81	73	.	.	PUNCT
ejpam-5713	82	1	a	a	DET
ejpam-5713	82	2	d	d	X
ejpam-5713	82	3	b	b	PROPN
ejpam-5713	82	4	c	c	NOUN
ejpam-5713	82	5	e	e	X
ejpam-5713	82	6	f	f	PROPN
ejpam-5713	82	7	g	g	PROPN
ejpam-5713	82	8	figure	figure	NOUN
ejpam-5713	82	9	1	1	NUM
ejpam-5713	82	10	:	:	PUNCT
ejpam-5713	82	11	a	a	DET
ejpam-5713	82	12	graph	graph	NOUN
ejpam-5713	82	13	g	g	NOUN
ejpam-5713	82	14	with	with	ADP
ejpam-5713	82	15	βs(g	βs(g	PUNCT
ejpam-5713	82	16	)	)	PUNCT
ejpam-5713	82	17	=	=	SYM
ejpam-5713	82	18	5	5	NUM
ejpam-5713	82	19	theorem	theorem	NOUN
ejpam-5713	82	20	1	1	NUM
ejpam-5713	82	21	.	.	PUNCT
ejpam-5713	83	1	let	let	VERB
ejpam-5713	83	2	g	g	PRON
ejpam-5713	83	3	be	be	AUX
ejpam-5713	83	4	a	a	DET
ejpam-5713	83	5	graph	graph	NOUN
ejpam-5713	83	6	of	of	ADP
ejpam-5713	83	7	order	order	NOUN
ejpam-5713	83	8	n	n	PRON
ejpam-5713	83	9	such	such	ADJ
ejpam-5713	83	10	that	that	DET
ejpam-5713	83	11	e(g	e(g	NOUN
ejpam-5713	83	12	)	)	PUNCT
ejpam-5713	84	1	̸=	̸=	PROPN
ejpam-5713	84	2	∅.	∅.	VERB
ejpam-5713	84	3	then	then	ADV
ejpam-5713	84	4	βs(g	βs(g	PUNCT
ejpam-5713	84	5	)	)	PUNCT
ejpam-5713	84	6	=	=	SYM
ejpam-5713	85	1	n	n	CCONJ
ejpam-5713	85	2	−	−	PROPN
ejpam-5713	85	3	1	1	NUM
ejpam-5713	86	1	if	if	SCONJ
ejpam-5713	86	2	and	and	CCONJ
ejpam-5713	86	3	only	only	ADV
ejpam-5713	86	4	if	if	SCONJ
ejpam-5713	86	5	for	for	SCONJ
ejpam-5713	86	6	every	every	DET
ejpam-5713	86	7	pair	pair	NOUN
ejpam-5713	86	8	of	of	ADP
ejpam-5713	86	9	non	non	ADJ
ejpam-5713	86	10	-	-	ADJ
ejpam-5713	86	11	adjacent	adjacent	ADJ
ejpam-5713	86	12	vertices	vertex	NOUN
ejpam-5713	86	13	v	v	NOUN
ejpam-5713	86	14	and	and	CCONJ
ejpam-5713	86	15	w	w	NOUN
ejpam-5713	86	16	of	of	ADP
ejpam-5713	86	17	g	g	NOUN
ejpam-5713	86	18	,	,	PUNCT
ejpam-5713	86	19	and	and	CCONJ
ejpam-5713	86	20	for	for	ADP
ejpam-5713	86	21	any	any	DET
ejpam-5713	86	22	x	x	SYM
ejpam-5713	86	23	∈	∈	PROPN
ejpam-5713	86	24	v	v	NOUN
ejpam-5713	86	25	(	(	PUNCT
ejpam-5713	86	26	g	g	NOUN
ejpam-5713	86	27	)	)	PUNCT
ejpam-5713	86	28	with	with	ADP
ejpam-5713	86	29	x	x	PROPN
ejpam-5713	86	30	∈	∈	NOUN
ejpam-5713	86	31	ng(v	ng(v	PUNCT
ejpam-5713	86	32	)	)	PUNCT
ejpam-5713	86	33	\ng(w	\ng(w	PUNCT
ejpam-5713	86	34	)	)	PUNCT
ejpam-5713	86	35	(	(	PUNCT
ejpam-5713	86	36	x	x	SYM
ejpam-5713	86	37	∈	∈	NOUN
ejpam-5713	86	38	ng(w	ng(w	NOUN
ejpam-5713	86	39	)	)	PUNCT
ejpam-5713	86	40	\ng(v	\ng(v	NOUN
ejpam-5713	86	41	)	)	PUNCT
ejpam-5713	86	42	)	)	PUNCT
ejpam-5713	86	43	,	,	PUNCT
ejpam-5713	86	44	it	it	PRON
ejpam-5713	86	45	holds	hold	VERB
ejpam-5713	86	46	that	that	SCONJ
ejpam-5713	86	47	ng(w	ng(w	NOUN
ejpam-5713	86	48	)	)	PUNCT
ejpam-5713	86	49	\ng(x	\ng(x	NUM
ejpam-5713	86	50	)	)	PUNCT
ejpam-5713	86	51	=	=	NOUN
ejpam-5713	86	52	∅	∅	NOUN
ejpam-5713	86	53	(	(	PUNCT
ejpam-5713	86	54	resp	resp	NOUN
ejpam-5713	86	55	.	.	PUNCT
ejpam-5713	86	56	ng(v	ng(v	PUNCT
ejpam-5713	86	57	)	)	PUNCT
ejpam-5713	86	58	\ng(x	\ng(x	NUM
ejpam-5713	86	59	)	)	PUNCT
ejpam-5713	86	60	=	=	SYM
ejpam-5713	86	61	∅	∅	NOUN
ejpam-5713	86	62	)	)	PUNCT
ejpam-5713	86	63	.	.	PUNCT
ejpam-5713	87	1	proof	proof	NOUN
ejpam-5713	87	2	.	.	PUNCT
ejpam-5713	88	1	suppose	suppose	VERB
ejpam-5713	88	2	βs(g	βs(g	PUNCT
ejpam-5713	88	3	)	)	PUNCT
ejpam-5713	88	4	=	=	SYM
ejpam-5713	88	5	n−1	n−1	PROPN
ejpam-5713	88	6	.	.	PROPN
ejpam-5713	88	7	suppose	suppose	VERB
ejpam-5713	88	8	further	far	ADV
ejpam-5713	88	9	that	that	SCONJ
ejpam-5713	88	10	there	there	PRON
ejpam-5713	88	11	exist	exist	VERB
ejpam-5713	88	12	a	a	DET
ejpam-5713	88	13	pair	pair	NOUN
ejpam-5713	88	14	of	of	ADP
ejpam-5713	88	15	non	non	ADJ
ejpam-5713	88	16	-	-	ADJ
ejpam-5713	88	17	adjacent	adjacent	ADJ
ejpam-5713	88	18	vertices	vertex	NOUN
ejpam-5713	88	19	v	v	NOUN
ejpam-5713	88	20	and	and	CCONJ
ejpam-5713	88	21	w	w	NOUN
ejpam-5713	88	22	and	and	CCONJ
ejpam-5713	88	23	a	a	DET
ejpam-5713	88	24	vertex	vertex	NOUN
ejpam-5713	88	25	x	x	PUNCT
ejpam-5713	88	26	such	such	ADJ
ejpam-5713	88	27	that	that	SCONJ
ejpam-5713	88	28	x	x	SYM
ejpam-5713	88	29	∈	∈	NOUN
ejpam-5713	88	30	ng(v	ng(v	NOUN
ejpam-5713	88	31	)	)	PUNCT
ejpam-5713	88	32	\	\	NOUN
ejpam-5713	88	33	ng(w	ng(w	NOUN
ejpam-5713	88	34	)	)	PUNCT
ejpam-5713	88	35	but	but	CCONJ
ejpam-5713	88	36	ng(w	ng(w	NOUN
ejpam-5713	88	37	)	)	PUNCT
ejpam-5713	88	38	\	\	NOUN
ejpam-5713	88	39	ng(x	ng(x	NUM
ejpam-5713	88	40	)	)	PUNCT
ejpam-5713	88	41	̸=	̸=	PROPN
ejpam-5713	88	42	∅.	∅.	AUX
ejpam-5713	88	43	pick	pick	VERB
ejpam-5713	88	44	any	any	DET
ejpam-5713	88	45	z	z	PROPN
ejpam-5713	88	46	∈	∈	PROPN
ejpam-5713	88	47	ng(w	ng(w	NOUN
ejpam-5713	88	48	)	)	PUNCT
ejpam-5713	88	49	\ng(x	\ng(x	NUM
ejpam-5713	88	50	)	)	PUNCT
ejpam-5713	88	51	and	and	CCONJ
ejpam-5713	88	52	let	let	VERB
ejpam-5713	88	53	s	s	PRON
ejpam-5713	88	54	=	=	VERB
ejpam-5713	88	55	v	v	ADJ
ejpam-5713	88	56	(	(	PUNCT
ejpam-5713	88	57	g	g	NOUN
ejpam-5713	88	58	)	)	PUNCT
ejpam-5713	88	59	\	\	NOUN
ejpam-5713	88	60	{	{	PUNCT
ejpam-5713	88	61	x	x	NOUN
ejpam-5713	88	62	,	,	PUNCT
ejpam-5713	88	63	w	w	NOUN
ejpam-5713	88	64	}	}	PUNCT
ejpam-5713	88	65	.	.	PUNCT
ejpam-5713	89	1	then	then	ADV
ejpam-5713	89	2	s	s	VERB
ejpam-5713	89	3	is	be	AUX
ejpam-5713	89	4	a	a	DET
ejpam-5713	89	5	super	super	ADJ
ejpam-5713	89	6	vertex	vertex	NOUN
ejpam-5713	89	7	cover	cover	NOUN
ejpam-5713	89	8	of	of	ADP
ejpam-5713	89	9	g.	g.	PROPN
ejpam-5713	89	10	hence	hence	ADV
ejpam-5713	89	11	,	,	PUNCT
ejpam-5713	89	12	βs(g	βs(g	PUNCT
ejpam-5713	89	13	)	)	PUNCT
ejpam-5713	89	14	≤	≤	NUM
ejpam-5713	89	15	|s|	|s|	PROPN
ejpam-5713	89	16	=	=	PUNCT
ejpam-5713	89	17	n	n	CCONJ
ejpam-5713	89	18	−	−	PROPN
ejpam-5713	89	19	2	2	NUM
ejpam-5713	89	20	,	,	PUNCT
ejpam-5713	89	21	a	a	DET
ejpam-5713	89	22	contradiction	contradiction	NOUN
ejpam-5713	89	23	.	.	PUNCT
ejpam-5713	90	1	therefore	therefore	ADV
ejpam-5713	90	2	,	,	PUNCT
ejpam-5713	90	3	the	the	DET
ejpam-5713	90	4	condition	condition	NOUN
ejpam-5713	90	5	or	or	CCONJ
ejpam-5713	90	6	property	property	NOUN
ejpam-5713	90	7	holds	hold	NOUN
ejpam-5713	90	8	.	.	PUNCT
ejpam-5713	91	1	for	for	ADP
ejpam-5713	91	2	the	the	DET
ejpam-5713	91	3	converse	converse	NOUN
ejpam-5713	91	4	,	,	PUNCT
ejpam-5713	91	5	suppose	suppose	VERB
ejpam-5713	91	6	that	that	SCONJ
ejpam-5713	91	7	the	the	DET
ejpam-5713	91	8	property	property	NOUN
ejpam-5713	91	9	holds	hold	VERB
ejpam-5713	91	10	.	.	PUNCT
ejpam-5713	92	1	let	let	VERB
ejpam-5713	92	2	s0	s0	PROPN
ejpam-5713	92	3	be	be	AUX
ejpam-5713	92	4	a	a	DET
ejpam-5713	92	5	βs	βs	NOUN
ejpam-5713	92	6	-	-	PUNCT
ejpam-5713	92	7	set	set	NOUN
ejpam-5713	92	8	in	in	ADP
ejpam-5713	92	9	g.	g.	NOUN
ejpam-5713	92	10	by	by	ADP
ejpam-5713	92	11	proposition	proposition	NOUN
ejpam-5713	92	12	1	1	NUM
ejpam-5713	92	13	,	,	PUNCT
ejpam-5713	92	14	βs	β	NOUN
ejpam-5713	92	15	=	=	NUM
ejpam-5713	92	16	|s0|	|s0|	NOUN
ejpam-5713	92	17	≤	≤	NUM
ejpam-5713	92	18	n−	n−	PROPN
ejpam-5713	92	19	1	1	NUM
ejpam-5713	92	20	.	.	PUNCT
ejpam-5713	93	1	suppose	suppose	VERB
ejpam-5713	93	2	|s0|	|s0|	NOUN
ejpam-5713	93	3	<	<	X
ejpam-5713	93	4	n−	n−	PROPN
ejpam-5713	93	5	1	1	NUM
ejpam-5713	93	6	.	.	PUNCT
ejpam-5713	94	1	then	then	ADV
ejpam-5713	94	2	there	there	PRON
ejpam-5713	94	3	exist	exist	VERB
ejpam-5713	94	4	p	p	PRON
ejpam-5713	94	5	,	,	PUNCT
ejpam-5713	94	6	q	q	PROPN
ejpam-5713	94	7	∈	∈	PROPN
ejpam-5713	94	8	v	v	ADP
ejpam-5713	94	9	(	(	PUNCT
ejpam-5713	94	10	g	g	NOUN
ejpam-5713	94	11	)	)	PUNCT
ejpam-5713	94	12	\s0	\s0	NOUN
ejpam-5713	94	13	.	.	PUNCT
ejpam-5713	95	1	since	since	SCONJ
ejpam-5713	95	2	s0	s0	PROPN
ejpam-5713	95	3	is	be	AUX
ejpam-5713	95	4	a	a	DET
ejpam-5713	95	5	vertex	vertex	NOUN
ejpam-5713	95	6	cover	cover	NOUN
ejpam-5713	95	7	of	of	ADP
ejpam-5713	95	8	g	g	PROPN
ejpam-5713	95	9	,	,	PUNCT
ejpam-5713	95	10	pq	pq	PROPN
ejpam-5713	95	11	/∈	/∈	PUNCT
ejpam-5713	95	12	e(g	e(g	PROPN
ejpam-5713	95	13	)	)	PUNCT
ejpam-5713	95	14	.	.	PUNCT
ejpam-5713	96	1	since	since	SCONJ
ejpam-5713	96	2	s	s	PROPN
ejpam-5713	96	3	is	be	AUX
ejpam-5713	96	4	a	a	DET
ejpam-5713	96	5	super	super	ADJ
ejpam-5713	96	6	dominating	dominating	NOUN
ejpam-5713	96	7	set	set	NOUN
ejpam-5713	96	8	in	in	ADP
ejpam-5713	96	9	g	g	NOUN
ejpam-5713	96	10	,	,	PUNCT
ejpam-5713	96	11	there	there	PRON
ejpam-5713	96	12	exist	exist	VERB
ejpam-5713	96	13	vp	vp	NOUN
ejpam-5713	96	14	,	,	PUNCT
ejpam-5713	96	15	vq	vq	PROPN
ejpam-5713	96	16	∈	∈	PROPN
ejpam-5713	96	17	s	s	VERB
ejpam-5713	96	18	such	such	ADJ
ejpam-5713	96	19	that	that	DET
ejpam-5713	96	20	ng(vp	ng(vp	NOUN
ejpam-5713	96	21	)	)	PUNCT
ejpam-5713	97	1	∩	∩	NOUN
ejpam-5713	97	2	[	[	X
ejpam-5713	97	3	v	v	X
ejpam-5713	97	4	(	(	PUNCT
ejpam-5713	97	5	g	g	NOUN
ejpam-5713	97	6	)	)	PUNCT
ejpam-5713	97	7	\	\	NOUN
ejpam-5713	97	8	s0	s0	PROPN
ejpam-5713	97	9	]	]	PUNCT
ejpam-5713	97	10	=	=	X
ejpam-5713	97	11	{	{	PUNCT
ejpam-5713	97	12	p	p	X
ejpam-5713	97	13	}	}	PUNCT
ejpam-5713	97	14	and	and	CCONJ
ejpam-5713	97	15	ng(vq	ng(vq	NOUN
ejpam-5713	97	16	)	)	PUNCT
ejpam-5713	97	17	∩	∩	NOUN
ejpam-5713	98	1	[	[	X
ejpam-5713	98	2	v	v	X
ejpam-5713	98	3	(	(	PUNCT
ejpam-5713	98	4	g	g	NOUN
ejpam-5713	98	5	)	)	PUNCT
ejpam-5713	98	6	\	\	NOUN
ejpam-5713	98	7	s0	s0	PROPN
ejpam-5713	98	8	]	]	PUNCT
ejpam-5713	98	9	=	=	PUNCT
ejpam-5713	98	10	{	{	PUNCT
ejpam-5713	98	11	q	q	X
ejpam-5713	98	12	}	}	PUNCT
ejpam-5713	98	13	.	.	PUNCT
ejpam-5713	99	1	this	this	PRON
ejpam-5713	99	2	implies	imply	VERB
ejpam-5713	99	3	that	that	SCONJ
ejpam-5713	99	4	p	p	PROPN
ejpam-5713	99	5	∈	∈	PROPN
ejpam-5713	99	6	ng(vp	ng(vp	NOUN
ejpam-5713	99	7	)	)	PUNCT
ejpam-5713	99	8	\ng(q	\ng(q	NOUN
ejpam-5713	99	9	)	)	PUNCT
ejpam-5713	99	10	.	.	PUNCT
ejpam-5713	100	1	by	by	ADP
ejpam-5713	100	2	our	our	PRON
ejpam-5713	100	3	assumption	assumption	NOUN
ejpam-5713	100	4	that	that	SCONJ
ejpam-5713	100	5	the	the	DET
ejpam-5713	100	6	given	give	VERB
ejpam-5713	100	7	property	property	NOUN
ejpam-5713	100	8	holds	hold	NOUN
ejpam-5713	100	9	,	,	PUNCT
ejpam-5713	100	10	it	it	PRON
ejpam-5713	100	11	follows	follow	VERB
ejpam-5713	100	12	that	that	SCONJ
ejpam-5713	100	13	ng(q	ng(q	NOUN
ejpam-5713	100	14	)	)	PUNCT
ejpam-5713	100	15	\	\	NOUN
ejpam-5713	100	16	ng(p	ng(p	NOUN
ejpam-5713	100	17	)	)	PUNCT
ejpam-5713	100	18	=	=	PUNCT
ejpam-5713	100	19	∅.	∅.	ADP
ejpam-5713	100	20	this	this	DET
ejpam-5713	100	21	forces	force	NOUN
ejpam-5713	100	22	vq	vq	ADP
ejpam-5713	100	23	∈	∈	PROPN
ejpam-5713	100	24	ng(p	ng(p	NOUN
ejpam-5713	100	25	)	)	PUNCT
ejpam-5713	100	26	because	because	SCONJ
ejpam-5713	100	27	vq	vq	PROPN
ejpam-5713	100	28	∈	∈	PROPN
ejpam-5713	100	29	ng(q	ng(q	NOUN
ejpam-5713	100	30	)	)	PUNCT
ejpam-5713	100	31	.	.	PUNCT
ejpam-5713	101	1	this	this	PRON
ejpam-5713	101	2	contradicts	contradict	VERB
ejpam-5713	101	3	the	the	DET
ejpam-5713	101	4	property	property	NOUN
ejpam-5713	101	5	of	of	ADP
ejpam-5713	101	6	vertex	vertex	NOUN
ejpam-5713	101	7	vq	vq	NOUN
ejpam-5713	101	8	.	.	PUNCT
ejpam-5713	102	1	thus	thus	ADV
ejpam-5713	102	2	,	,	PUNCT
ejpam-5713	102	3	βs	β	NOUN
ejpam-5713	102	4	=	=	NUM
ejpam-5713	102	5	|s0|	|s0|	NOUN
ejpam-5713	102	6	=	=	SYM
ejpam-5713	102	7	n−	n−	NOUN
ejpam-5713	102	8	1	1	NUM
ejpam-5713	102	9	.	.	PUNCT
ejpam-5713	103	1	the	the	DET
ejpam-5713	103	2	next	next	ADJ
ejpam-5713	103	3	result	result	NOUN
ejpam-5713	103	4	is	be	AUX
ejpam-5713	103	5	immediate	immediate	ADJ
ejpam-5713	103	6	from	from	ADP
ejpam-5713	103	7	theorem	theorem	ADJ
ejpam-5713	103	8	1	1	NUM
ejpam-5713	104	1	.	.	PUNCT
ejpam-5713	104	2	corollary	corollary	ADJ
ejpam-5713	104	3	1	1	NUM
ejpam-5713	104	4	.	.	PUNCT
ejpam-5713	105	1	let	let	VERB
ejpam-5713	105	2	n	n	PRON
ejpam-5713	105	3	be	be	AUX
ejpam-5713	105	4	a	a	DET
ejpam-5713	105	5	positive	positive	ADJ
ejpam-5713	105	6	integer	integer	NOUN
ejpam-5713	105	7	.	.	PUNCT
ejpam-5713	106	1	then	then	ADV
ejpam-5713	106	2	each	each	PRON
ejpam-5713	106	3	of	of	ADP
ejpam-5713	106	4	the	the	DET
ejpam-5713	106	5	following	follow	VERB
ejpam-5713	106	6	holds	hold	VERB
ejpam-5713	106	7	:	:	PUNCT
ejpam-5713	106	8	(	(	PUNCT
ejpam-5713	106	9	i	i	NOUN
ejpam-5713	106	10	)	)	PUNCT
ejpam-5713	106	11	βs(kn	βs(kn	NOUN
ejpam-5713	106	12	)	)	PUNCT
ejpam-5713	107	1	=	=	PUNCT
ejpam-5713	107	2	n−	n−	NOUN
ejpam-5713	107	3	1	1	NUM
ejpam-5713	107	4	for	for	ADP
ejpam-5713	107	5	n	n	PRON
ejpam-5713	107	6	≥	≥	NOUN
ejpam-5713	107	7	2	2	NUM
ejpam-5713	107	8	.	.	PUNCT
ejpam-5713	107	9	(	(	PUNCT
ejpam-5713	107	10	ii	ii	NOUN
ejpam-5713	107	11	)	)	PUNCT
ejpam-5713	107	12	βs(k1,n−1	βs(k1,n−1	PUNCT
ejpam-5713	107	13	)	)	PUNCT
ejpam-5713	108	1	=	=	PUNCT
ejpam-5713	108	2	n−	n−	NOUN
ejpam-5713	108	3	1	1	NUM
ejpam-5713	108	4	for	for	ADP
ejpam-5713	108	5	n	n	PRON
ejpam-5713	108	6	≥	≥	NOUN
ejpam-5713	108	7	2	2	NUM
ejpam-5713	108	8	.	.	PUNCT
ejpam-5713	109	1	it	it	PRON
ejpam-5713	109	2	is	be	AUX
ejpam-5713	109	3	well	well	ADV
ejpam-5713	109	4	known	know	VERB
ejpam-5713	109	5	that	that	SCONJ
ejpam-5713	109	6	γsp(g	γsp(g	NOUN
ejpam-5713	109	7	)	)	PUNCT
ejpam-5713	109	8	≥	≥	NOUN
ejpam-5713	109	9	n	n	CCONJ
ejpam-5713	109	10	2	2	NUM
ejpam-5713	109	11	and	and	CCONJ
ejpam-5713	109	12	α(g	α(g	NUM
ejpam-5713	109	13	)	)	PUNCT
ejpam-5713	110	1	+	+	NUM
ejpam-5713	110	2	β(g	β(g	PROPN
ejpam-5713	110	3	)	)	PUNCT
ejpam-5713	110	4	=	=	SYM
ejpam-5713	110	5	n	n	PROPN
ejpam-5713	110	6	for	for	ADP
ejpam-5713	110	7	every	every	DET
ejpam-5713	110	8	graph	graph	NOUN
ejpam-5713	110	9	g	g	NOUN
ejpam-5713	110	10	of	of	ADP
ejpam-5713	110	11	order	order	NOUN
ejpam-5713	110	12	n.	n.	NOUN
ejpam-5713	110	13	the	the	DET
ejpam-5713	110	14	next	next	ADJ
ejpam-5713	110	15	remark	remark	NOUN
ejpam-5713	110	16	follows	follow	VERB
ejpam-5713	110	17	from	from	ADP
ejpam-5713	110	18	these	these	DET
ejpam-5713	110	19	facts	fact	NOUN
ejpam-5713	110	20	and	and	CCONJ
ejpam-5713	110	21	proposition	proposition	NOUN
ejpam-5713	110	22	1	1	NUM
ejpam-5713	110	23	.	.	PUNCT
ejpam-5713	110	24	remark	remark	NOUN
ejpam-5713	110	25	3	3	NUM
ejpam-5713	110	26	.	.	PUNCT
ejpam-5713	111	1	if	if	SCONJ
ejpam-5713	111	2	g	g	PROPN
ejpam-5713	111	3	is	be	AUX
ejpam-5713	111	4	a	a	DET
ejpam-5713	111	5	graph	graph	NOUN
ejpam-5713	111	6	of	of	ADP
ejpam-5713	111	7	order	order	NOUN
ejpam-5713	111	8	n	n	CCONJ
ejpam-5713	111	9	,	,	PUNCT
ejpam-5713	111	10	then	then	ADV
ejpam-5713	111	11	βs(g	βs(g	PUNCT
ejpam-5713	111	12	)	)	PUNCT
ejpam-5713	111	13	≥	≥	NOUN
ejpam-5713	111	14	max{n	max{n	NUM
ejpam-5713	111	15	2	2	NUM
ejpam-5713	111	16	,	,	PUNCT
ejpam-5713	111	17	n−	n−	NOUN
ejpam-5713	111	18	α(g	α(g	NUM
ejpam-5713	111	19	)	)	PUNCT
ejpam-5713	111	20	}	}	PUNCT
ejpam-5713	111	21	.	.	PUNCT
ejpam-5713	112	1	s.	s.	PROPN
ejpam-5713	112	2	r.	r.	PROPN
ejpam-5713	112	3	canoy	canoy	PROPN
ejpam-5713	112	4	et	et	PROPN
ejpam-5713	112	5	al	al	PROPN
ejpam-5713	112	6	.	.	PUNCT
ejpam-5713	112	7	/	/	SYM
ejpam-5713	112	8	eur	eur	PROPN
ejpam-5713	112	9	.	.	PUNCT
ejpam-5713	113	1	j.	j.	PROPN
ejpam-5713	113	2	pure	pure	PROPN
ejpam-5713	113	3	appl	appl	PROPN
ejpam-5713	113	4	.	.	PROPN
ejpam-5713	113	5	math	math	PROPN
ejpam-5713	113	6	,	,	PUNCT
ejpam-5713	113	7	18	18	NUM
ejpam-5713	113	8	(	(	PUNCT
ejpam-5713	113	9	1	1	NUM
ejpam-5713	113	10	)	)	PUNCT
ejpam-5713	113	11	(	(	PUNCT
ejpam-5713	113	12	2025	2025	NUM
ejpam-5713	113	13	)	)	PUNCT
ejpam-5713	113	14	,	,	PUNCT
ejpam-5713	113	15	5713	5713	NUM
ejpam-5713	113	16	5	5	NUM
ejpam-5713	113	17	of	of	ADP
ejpam-5713	113	18	13	13	NUM
ejpam-5713	113	19	proposition	proposition	NOUN
ejpam-5713	113	20	2	2	NUM
ejpam-5713	113	21	.	.	PUNCT
ejpam-5713	114	1	let	let	VERB
ejpam-5713	114	2	g1	g1	PROPN
ejpam-5713	114	3	,	,	PUNCT
ejpam-5713	114	4	g2	g2	PROPN
ejpam-5713	114	5	,	,	PUNCT
ejpam-5713	114	6	.	.	PUNCT
ejpam-5713	114	7	.	.	PUNCT
ejpam-5713	115	1	.	.	PUNCT
ejpam-5713	116	1	,	,	PUNCT
ejpam-5713	116	2	gk	gk	PROPN
ejpam-5713	116	3	be	be	AUX
ejpam-5713	116	4	the	the	DET
ejpam-5713	116	5	components	component	NOUN
ejpam-5713	116	6	of	of	ADP
ejpam-5713	116	7	g.	g.	PROPN
ejpam-5713	116	8	then	then	ADV
ejpam-5713	116	9	βs(g	βs(g	PUNCT
ejpam-5713	116	10	)	)	PUNCT
ejpam-5713	117	1	=	=	SYM
ejpam-5713	117	2	∑k	∑k	PROPN
ejpam-5713	117	3	j=1	j=1	PROPN
ejpam-5713	117	4	βs(gj	βs(gj	PROPN
ejpam-5713	117	5	)	)	PUNCT
ejpam-5713	117	6	.	.	PUNCT
ejpam-5713	118	1	proof	proof	NOUN
ejpam-5713	118	2	.	.	PUNCT
ejpam-5713	119	1	let	let	VERB
ejpam-5713	119	2	s	s	PRON
ejpam-5713	119	3	be	be	AUX
ejpam-5713	119	4	a	a	DET
ejpam-5713	119	5	βs	βs	NOUN
ejpam-5713	119	6	-	-	PUNCT
ejpam-5713	119	7	set	set	NOUN
ejpam-5713	119	8	in	in	ADP
ejpam-5713	119	9	g.	g.	PROPN
ejpam-5713	119	10	for	for	ADP
ejpam-5713	119	11	each	each	DET
ejpam-5713	119	12	j	j	PROPN
ejpam-5713	119	13	∈	∈	PROPN
ejpam-5713	120	1	[	[	X
ejpam-5713	120	2	k	k	X
ejpam-5713	120	3	]	]	X
ejpam-5713	120	4	=	=	X
ejpam-5713	120	5	{	{	PUNCT
ejpam-5713	120	6	1	1	NUM
ejpam-5713	120	7	,	,	PUNCT
ejpam-5713	120	8	2	2	NUM
ejpam-5713	120	9	,	,	PUNCT
ejpam-5713	120	10	·	·	PUNCT
ejpam-5713	120	11	·	·	PUNCT
ejpam-5713	120	12	·	·	PUNCT
ejpam-5713	120	13	,	,	PUNCT
ejpam-5713	120	14	k	k	X
ejpam-5713	120	15	}	}	PUNCT
ejpam-5713	120	16	,	,	PUNCT
ejpam-5713	120	17	let	let	VERB
ejpam-5713	120	18	sj	sj	INTJ
ejpam-5713	120	19	=	=	NOUN
ejpam-5713	120	20	s	s	PART
ejpam-5713	120	21	∩	∩	ADJ
ejpam-5713	120	22	v	v	NOUN
ejpam-5713	120	23	(	(	PUNCT
ejpam-5713	120	24	gj	gj	NOUN
ejpam-5713	120	25	)	)	PUNCT
ejpam-5713	120	26	.	.	PUNCT
ejpam-5713	121	1	then	then	ADV
ejpam-5713	121	2	s	s	VERB
ejpam-5713	121	3	=	=	SYM
ejpam-5713	121	4	∪k	∪k	PROPN
ejpam-5713	121	5	j=1sj	j=1sj	PROPN
ejpam-5713	121	6	.	.	PUNCT
ejpam-5713	122	1	let	let	VERB
ejpam-5713	122	2	j	j	PROPN
ejpam-5713	122	3	∈	∈	PROPN
ejpam-5713	123	1	[	[	X
ejpam-5713	123	2	k	k	X
ejpam-5713	123	3	]	]	X
ejpam-5713	123	4	.	.	PUNCT
ejpam-5713	124	1	since	since	SCONJ
ejpam-5713	124	2	s	s	PROPN
ejpam-5713	124	3	is	be	AUX
ejpam-5713	124	4	a	a	DET
ejpam-5713	124	5	super	super	ADJ
ejpam-5713	124	6	vertex	vertex	NOUN
ejpam-5713	124	7	cover	cover	NOUN
ejpam-5713	124	8	of	of	ADP
ejpam-5713	124	9	g	g	NOUN
ejpam-5713	124	10	,	,	PUNCT
ejpam-5713	124	11	sj	sj	PROPN
ejpam-5713	124	12	is	be	AUX
ejpam-5713	124	13	a	a	DET
ejpam-5713	124	14	vertex	vertex	NOUN
ejpam-5713	124	15	cover	cover	NOUN
ejpam-5713	124	16	of	of	ADP
ejpam-5713	124	17	gj	gj	NOUN
ejpam-5713	124	18	for	for	ADP
ejpam-5713	124	19	each	each	DET
ejpam-5713	124	20	j	j	PROPN
ejpam-5713	124	21	∈	∈	PROPN
ejpam-5713	125	1	[	[	X
ejpam-5713	125	2	k	k	X
ejpam-5713	125	3	]	]	X
ejpam-5713	125	4	.	.	PUNCT
ejpam-5713	126	1	thus	thus	ADV
ejpam-5713	126	2	,	,	PUNCT
ejpam-5713	126	3	βs(g	βs(g	PUNCT
ejpam-5713	126	4	)	)	PUNCT
ejpam-5713	126	5	=	=	SYM
ejpam-5713	126	6	|s|	|s|	PROPN
ejpam-5713	126	7	=	=	SYM
ejpam-5713	127	1	|	|	NOUN
ejpam-5713	127	2	∪k	∪k	NUM
ejpam-5713	127	3	j=1	j=1	NOUN
ejpam-5713	127	4	sj	sj	INTJ
ejpam-5713	127	5	|	|	ADV
ejpam-5713	127	6	=	=	SYM
ejpam-5713	127	7	k∑	k∑	PROPN
ejpam-5713	128	1	j=1	j=1	NOUN
ejpam-5713	128	2	|sj	|sj	X
ejpam-5713	128	3	|	|	ADV
ejpam-5713	128	4	≥	≥	NOUN
ejpam-5713	128	5	k∑	k∑	VERB
ejpam-5713	128	6	j=1	j=1	PROPN
ejpam-5713	128	7	βs(gj	βs(gj	PROPN
ejpam-5713	128	8	)	)	PUNCT
ejpam-5713	128	9	.	.	PUNCT
ejpam-5713	129	1	for	for	ADP
ejpam-5713	129	2	each	each	DET
ejpam-5713	129	3	j	j	PROPN
ejpam-5713	129	4	∈	∈	PROPN
ejpam-5713	129	5	[	[	X
ejpam-5713	129	6	k	k	X
ejpam-5713	129	7	]	]	X
ejpam-5713	129	8	,	,	PUNCT
ejpam-5713	129	9	let	let	VERB
ejpam-5713	129	10	dj	dj	PRON
ejpam-5713	129	11	be	be	AUX
ejpam-5713	129	12	a	a	DET
ejpam-5713	129	13	βs	βs	NOUN
ejpam-5713	129	14	-	-	PUNCT
ejpam-5713	129	15	set	set	NOUN
ejpam-5713	129	16	in	in	ADP
ejpam-5713	129	17	gj	gj	NOUN
ejpam-5713	129	18	.	.	PUNCT
ejpam-5713	130	1	clearly	clearly	ADV
ejpam-5713	130	2	,	,	PUNCT
ejpam-5713	130	3	d	d	PROPN
ejpam-5713	130	4	=	=	PUNCT
ejpam-5713	130	5	∪k	∪k	NUM
ejpam-5713	130	6	j=1dj	j=1dj	X
ejpam-5713	130	7	is	be	AUX
ejpam-5713	130	8	a	a	DET
ejpam-5713	130	9	super	super	ADJ
ejpam-5713	130	10	vertex	vertex	NOUN
ejpam-5713	130	11	cover	cover	NOUN
ejpam-5713	130	12	of	of	ADP
ejpam-5713	130	13	g.	g.	PROPN
ejpam-5713	130	14	hence	hence	ADV
ejpam-5713	130	15	,	,	PUNCT
ejpam-5713	130	16	βs(g	βs(g	PUNCT
ejpam-5713	130	17	)	)	PUNCT
ejpam-5713	130	18	≤	≤	NUM
ejpam-5713	131	1	|d|	|d|	PROPN
ejpam-5713	131	2	=	=	PUNCT
ejpam-5713	132	1	|	|	ADV
ejpam-5713	132	2	∪k	∪k	NUM
ejpam-5713	132	3	j=1	j=1	NOUN
ejpam-5713	132	4	dj	dj	NOUN
ejpam-5713	132	5	|	|	NOUN
ejpam-5713	132	6	=	=	SYM
ejpam-5713	132	7	k∑	k∑	PROPN
ejpam-5713	133	1	j=1	j=1	NOUN
ejpam-5713	133	2	|dj	|dj	PUNCT
ejpam-5713	133	3	|	|	NOUN
ejpam-5713	133	4	=	=	SYM
ejpam-5713	133	5	k∑	k∑	PROPN
ejpam-5713	133	6	j=1	j=1	PROPN
ejpam-5713	133	7	βs(gj	βs(gj	PROPN
ejpam-5713	133	8	)	)	PUNCT
ejpam-5713	133	9	.	.	PUNCT
ejpam-5713	134	1	this	this	PRON
ejpam-5713	134	2	proves	prove	VERB
ejpam-5713	134	3	the	the	DET
ejpam-5713	134	4	assertion	assertion	NOUN
ejpam-5713	134	5	.	.	PUNCT
ejpam-5713	135	1	theorem	theorem	NOUN
ejpam-5713	135	2	2	2	NUM
ejpam-5713	135	3	.	.	PUNCT
ejpam-5713	136	1	let	let	VERB
ejpam-5713	136	2	g	g	NOUN
ejpam-5713	136	3	be	be	AUX
ejpam-5713	136	4	any	any	DET
ejpam-5713	136	5	graph	graph	NOUN
ejpam-5713	136	6	on	on	ADP
ejpam-5713	136	7	n	n	PRON
ejpam-5713	136	8	≥	≥	NUM
ejpam-5713	136	9	1	1	NUM
ejpam-5713	136	10	vertices	vertex	NOUN
ejpam-5713	136	11	.	.	PUNCT
ejpam-5713	137	1	then	then	ADV
ejpam-5713	137	2	each	each	PRON
ejpam-5713	137	3	of	of	ADP
ejpam-5713	137	4	the	the	DET
ejpam-5713	137	5	following	follow	VERB
ejpam-5713	137	6	holds	hold	VERB
ejpam-5713	137	7	:	:	PUNCT
ejpam-5713	137	8	(	(	PUNCT
ejpam-5713	137	9	i	i	NOUN
ejpam-5713	137	10	)	)	PUNCT
ejpam-5713	137	11	βs(g	βs(g	PUNCT
ejpam-5713	137	12	)	)	PUNCT
ejpam-5713	137	13	=	=	SYM
ejpam-5713	137	14	1	1	NUM
ejpam-5713	137	15	if	if	SCONJ
ejpam-5713	137	16	and	and	CCONJ
ejpam-5713	137	17	only	only	ADV
ejpam-5713	137	18	if	if	SCONJ
ejpam-5713	137	19	g	g	PROPN
ejpam-5713	137	20	∈	∈	PROPN
ejpam-5713	137	21	{	{	PUNCT
ejpam-5713	137	22	k1,k2	k1,k2	PROPN
ejpam-5713	137	23	}	}	PUNCT
ejpam-5713	137	24	.	.	PUNCT
ejpam-5713	138	1	(	(	PUNCT
ejpam-5713	138	2	ii	ii	NOUN
ejpam-5713	138	3	)	)	PUNCT
ejpam-5713	138	4	βs(g	βs(g	PUNCT
ejpam-5713	138	5	)	)	PUNCT
ejpam-5713	138	6	=	=	SYM
ejpam-5713	138	7	2	2	NUM
ejpam-5713	138	8	if	if	SCONJ
ejpam-5713	138	9	and	and	CCONJ
ejpam-5713	138	10	only	only	ADV
ejpam-5713	138	11	if	if	SCONJ
ejpam-5713	138	12	g	g	PROPN
ejpam-5713	138	13	∈	∈	PROPN
ejpam-5713	138	14	{	{	PUNCT
ejpam-5713	138	15	k2,k3	k2,k3	PROPN
ejpam-5713	138	16	,	,	PUNCT
ejpam-5713	138	17	p3,k1	p3,k1	PROPN
ejpam-5713	138	18	∪k2	∪k2	NOUN
ejpam-5713	138	19	,	,	PUNCT
ejpam-5713	138	20	p4,k2	p4,k2	PROPN
ejpam-5713	138	21	∪k2	∪k2	PUNCT
ejpam-5713	138	22	}	}	PUNCT
ejpam-5713	138	23	.	.	PUNCT
ejpam-5713	139	1	(	(	PUNCT
ejpam-5713	139	2	iii	iii	NOUN
ejpam-5713	139	3	)	)	PUNCT
ejpam-5713	139	4	βs(g	βs(g	PUNCT
ejpam-5713	139	5	)	)	PUNCT
ejpam-5713	140	1	=	=	SYM
ejpam-5713	140	2	n	n	NOUN
ejpam-5713	140	3	if	if	SCONJ
ejpam-5713	140	4	and	and	CCONJ
ejpam-5713	140	5	only	only	ADV
ejpam-5713	140	6	if	if	SCONJ
ejpam-5713	140	7	g	g	PROPN
ejpam-5713	140	8	=	=	SYM
ejpam-5713	140	9	kn	kn	PROPN
ejpam-5713	140	10	proof	proof	NOUN
ejpam-5713	140	11	.	.	PUNCT
ejpam-5713	141	1	(	(	PUNCT
ejpam-5713	141	2	i	i	NOUN
ejpam-5713	141	3	)	)	PUNCT
ejpam-5713	141	4	suppose	suppose	VERB
ejpam-5713	141	5	βs(g	βs(g	PUNCT
ejpam-5713	141	6	)	)	PUNCT
ejpam-5713	141	7	=	=	SYM
ejpam-5713	142	1	1	1	X
ejpam-5713	142	2	.	.	PUNCT
ejpam-5713	142	3	by	by	ADP
ejpam-5713	142	4	remark	remark	NOUN
ejpam-5713	142	5	3	3	NUM
ejpam-5713	142	6	,	,	PUNCT
ejpam-5713	142	7	n	n	PRON
ejpam-5713	142	8	≤	≤	NOUN
ejpam-5713	142	9	2	2	NUM
ejpam-5713	142	10	.	.	PUNCT
ejpam-5713	143	1	if	if	SCONJ
ejpam-5713	143	2	n	n	NOUN
ejpam-5713	143	3	=	=	SYM
ejpam-5713	143	4	1	1	NUM
ejpam-5713	143	5	,	,	PUNCT
ejpam-5713	143	6	then	then	ADV
ejpam-5713	143	7	g	g	PROPN
ejpam-5713	143	8	=	=	PROPN
ejpam-5713	143	9	k1	k1	PROPN
ejpam-5713	143	10	.	.	PUNCT
ejpam-5713	144	1	if	if	SCONJ
ejpam-5713	144	2	n	n	NOUN
ejpam-5713	144	3	=	=	SYM
ejpam-5713	144	4	2	2	NUM
ejpam-5713	144	5	,	,	PUNCT
ejpam-5713	144	6	then	then	ADV
ejpam-5713	144	7	g	g	PROPN
ejpam-5713	144	8	=	=	SYM
ejpam-5713	144	9	k2	k2	PROPN
ejpam-5713	144	10	.	.	PUNCT
ejpam-5713	145	1	hence	hence	ADV
ejpam-5713	145	2	,	,	PUNCT
ejpam-5713	145	3	g	g	PROPN
ejpam-5713	145	4	∈	∈	PROPN
ejpam-5713	145	5	{	{	PUNCT
ejpam-5713	145	6	k1,k2	k1,k2	PROPN
ejpam-5713	145	7	}	}	PUNCT
ejpam-5713	145	8	.	.	PUNCT
ejpam-5713	146	1	the	the	DET
ejpam-5713	146	2	converse	converse	NOUN
ejpam-5713	146	3	is	be	AUX
ejpam-5713	146	4	clear	clear	ADJ
ejpam-5713	146	5	.	.	PUNCT
ejpam-5713	147	1	(	(	PUNCT
ejpam-5713	147	2	ii	ii	NOUN
ejpam-5713	147	3	)	)	PUNCT
ejpam-5713	147	4	suppose	suppose	VERB
ejpam-5713	147	5	βs(g	βs(g	PUNCT
ejpam-5713	147	6	)	)	PUNCT
ejpam-5713	147	7	=	=	SYM
ejpam-5713	148	1	2	2	X
ejpam-5713	148	2	.	.	PUNCT
ejpam-5713	148	3	by	by	ADP
ejpam-5713	148	4	remark	remark	NOUN
ejpam-5713	148	5	3	3	NUM
ejpam-5713	148	6	and	and	CCONJ
ejpam-5713	148	7	part	part	NOUN
ejpam-5713	148	8	(	(	PUNCT
ejpam-5713	148	9	i	i	NOUN
ejpam-5713	148	10	)	)	PUNCT
ejpam-5713	148	11	,	,	PUNCT
ejpam-5713	148	12	2	2	NUM
ejpam-5713	148	13	≤	≤	NUM
ejpam-5713	148	14	n	n	CCONJ
ejpam-5713	148	15	≤	≤	NOUN
ejpam-5713	148	16	4	4	NUM
ejpam-5713	148	17	.	.	PUNCT
ejpam-5713	149	1	if	if	SCONJ
ejpam-5713	149	2	n	n	NOUN
ejpam-5713	149	3	=	=	SYM
ejpam-5713	149	4	2	2	NUM
ejpam-5713	149	5	,	,	PUNCT
ejpam-5713	149	6	then	then	ADV
ejpam-5713	149	7	g	g	PROPN
ejpam-5713	149	8	=	=	PROPN
ejpam-5713	149	9	k2	k2	PROPN
ejpam-5713	149	10	by	by	ADP
ejpam-5713	149	11	part	part	NOUN
ejpam-5713	149	12	(	(	PUNCT
ejpam-5713	149	13	i	i	NOUN
ejpam-5713	149	14	)	)	PUNCT
ejpam-5713	149	15	and	and	CCONJ
ejpam-5713	149	16	proposition	proposition	NOUN
ejpam-5713	149	17	2	2	NUM
ejpam-5713	149	18	.	.	PUNCT
ejpam-5713	150	1	if	if	SCONJ
ejpam-5713	150	2	n	n	NUM
ejpam-5713	150	3	=	=	SYM
ejpam-5713	150	4	3	3	NUM
ejpam-5713	150	5	and	and	CCONJ
ejpam-5713	150	6	g	g	NOUN
ejpam-5713	150	7	is	be	AUX
ejpam-5713	150	8	connected	connect	VERB
ejpam-5713	150	9	,	,	PUNCT
ejpam-5713	150	10	then	then	ADV
ejpam-5713	150	11	g	g	PROPN
ejpam-5713	150	12	∈	∈	PROPN
ejpam-5713	150	13	{	{	PUNCT
ejpam-5713	150	14	k3	k3	PROPN
ejpam-5713	150	15	,	,	PUNCT
ejpam-5713	150	16	p3	p3	PROPN
ejpam-5713	150	17	}	}	PUNCT
ejpam-5713	150	18	.	.	PUNCT
ejpam-5713	151	1	if	if	SCONJ
ejpam-5713	151	2	g	g	PROPN
ejpam-5713	151	3	is	be	AUX
ejpam-5713	151	4	disconnected	disconnect	VERB
ejpam-5713	151	5	,	,	PUNCT
ejpam-5713	151	6	then	then	ADV
ejpam-5713	151	7	g	g	PROPN
ejpam-5713	151	8	=	=	PROPN
ejpam-5713	151	9	k1	k1	PROPN
ejpam-5713	151	10	∪	∪	X
ejpam-5713	151	11	k2	k2	NOUN
ejpam-5713	151	12	by	by	ADP
ejpam-5713	151	13	part	part	NOUN
ejpam-5713	151	14	(	(	PUNCT
ejpam-5713	151	15	i	i	NOUN
ejpam-5713	151	16	)	)	PUNCT
ejpam-5713	151	17	and	and	CCONJ
ejpam-5713	151	18	proposition	proposition	NOUN
ejpam-5713	151	19	2	2	NUM
ejpam-5713	151	20	.	.	PUNCT
ejpam-5713	151	21	suppose	suppose	VERB
ejpam-5713	151	22	n	n	PROPN
ejpam-5713	151	23	=	=	SYM
ejpam-5713	151	24	4	4	X
ejpam-5713	151	25	.	.	PUNCT
ejpam-5713	152	1	let	let	VERB
ejpam-5713	152	2	s	s	PRON
ejpam-5713	152	3	=	=	X
ejpam-5713	152	4	{	{	PUNCT
ejpam-5713	152	5	a	a	PRON
ejpam-5713	152	6	,	,	PUNCT
ejpam-5713	152	7	b	b	X
ejpam-5713	152	8	}	}	PUNCT
ejpam-5713	152	9	be	be	AUX
ejpam-5713	152	10	a	a	DET
ejpam-5713	152	11	βs	βs	NOUN
ejpam-5713	152	12	-	-	PUNCT
ejpam-5713	152	13	set	set	NOUN
ejpam-5713	152	14	in	in	ADP
ejpam-5713	152	15	g	g	NOUN
ejpam-5713	152	16	and	and	CCONJ
ejpam-5713	152	17	let	let	VERB
ejpam-5713	152	18	x	x	PRON
ejpam-5713	152	19	,	,	PUNCT
ejpam-5713	152	20	y	y	PROPN
ejpam-5713	152	21	∈	∈	PROPN
ejpam-5713	152	22	v	v	ADP
ejpam-5713	152	23	(	(	PUNCT
ejpam-5713	152	24	g	g	NOUN
ejpam-5713	152	25	)	)	PUNCT
ejpam-5713	152	26	\	\	PUNCT
ejpam-5713	153	1	s.	s.	PROPN
ejpam-5713	153	2	since	since	SCONJ
ejpam-5713	153	3	s	s	PROPN
ejpam-5713	153	4	is	be	AUX
ejpam-5713	153	5	a	a	DET
ejpam-5713	153	6	super	super	ADJ
ejpam-5713	153	7	dominating	dominating	NOUN
ejpam-5713	153	8	set	set	NOUN
ejpam-5713	153	9	in	in	ADP
ejpam-5713	153	10	g	g	PROPN
ejpam-5713	153	11	,	,	PUNCT
ejpam-5713	153	12	we	we	PRON
ejpam-5713	153	13	may	may	AUX
ejpam-5713	153	14	assume	assume	VERB
ejpam-5713	153	15	that	that	SCONJ
ejpam-5713	153	16	ng(a	ng(a	NOUN
ejpam-5713	153	17	)	)	PUNCT
ejpam-5713	153	18	∩	∩	NOUN
ejpam-5713	153	19	(	(	PUNCT
ejpam-5713	153	20	v	v	NOUN
ejpam-5713	153	21	(	(	PUNCT
ejpam-5713	153	22	g	g	NOUN
ejpam-5713	153	23	)	)	PUNCT
ejpam-5713	153	24	\	\	PROPN
ejpam-5713	153	25	s	s	X
ejpam-5713	153	26	)	)	PUNCT
ejpam-5713	153	27	=	=	SYM
ejpam-5713	153	28	{	{	PUNCT
ejpam-5713	153	29	x	x	NOUN
ejpam-5713	153	30	}	}	PUNCT
ejpam-5713	153	31	and	and	CCONJ
ejpam-5713	153	32	ng(b	ng(b	NOUN
ejpam-5713	153	33	)	)	PUNCT
ejpam-5713	153	34	∩	∩	NOUN
ejpam-5713	153	35	(	(	PUNCT
ejpam-5713	153	36	v	v	NOUN
ejpam-5713	153	37	(	(	PUNCT
ejpam-5713	153	38	g	g	NOUN
ejpam-5713	153	39	)	)	PUNCT
ejpam-5713	153	40	\	\	PROPN
ejpam-5713	154	1	s	s	X
ejpam-5713	154	2	)	)	PUNCT
ejpam-5713	154	3	=	=	SYM
ejpam-5713	154	4	{	{	PUNCT
ejpam-5713	154	5	y	y	NOUN
ejpam-5713	154	6	}	}	PUNCT
ejpam-5713	154	7	.	.	PUNCT
ejpam-5713	155	1	since	since	SCONJ
ejpam-5713	155	2	s	s	PROPN
ejpam-5713	155	3	is	be	AUX
ejpam-5713	155	4	a	a	DET
ejpam-5713	155	5	vertex	vertex	NOUN
ejpam-5713	155	6	cover	cover	NOUN
ejpam-5713	155	7	and	and	CCONJ
ejpam-5713	155	8	x	x	NOUN
ejpam-5713	155	9	,	,	PUNCT
ejpam-5713	155	10	y	y	PROPN
ejpam-5713	155	11	/∈	/∈	PUNCT
ejpam-5713	156	1	s	s	X
ejpam-5713	156	2	,	,	PUNCT
ejpam-5713	156	3	it	it	PRON
ejpam-5713	156	4	follows	follow	VERB
ejpam-5713	156	5	that	that	PRON
ejpam-5713	156	6	xy	xy	PROPN
ejpam-5713	156	7	/∈	/∈	PUNCT
ejpam-5713	156	8	e(g	e(g	PROPN
ejpam-5713	156	9	)	)	PUNCT
ejpam-5713	156	10	.	.	PUNCT
ejpam-5713	157	1	if	if	SCONJ
ejpam-5713	157	2	ab	ab	PROPN
ejpam-5713	157	3	∈	∈	PROPN
ejpam-5713	157	4	e(g	e(g	PROPN
ejpam-5713	157	5	)	)	PUNCT
ejpam-5713	157	6	,	,	PUNCT
ejpam-5713	157	7	then	then	ADV
ejpam-5713	157	8	g	g	PROPN
ejpam-5713	157	9	=	=	SYM
ejpam-5713	157	10	p4	p4	ADJ
ejpam-5713	157	11	.	.	PUNCT
ejpam-5713	158	1	if	if	SCONJ
ejpam-5713	158	2	ab	ab	PROPN
ejpam-5713	158	3	/∈	/∈	PUNCT
ejpam-5713	158	4	e(g	e(g	PROPN
ejpam-5713	158	5	)	)	PUNCT
ejpam-5713	158	6	,	,	PUNCT
ejpam-5713	158	7	then	then	ADV
ejpam-5713	158	8	g	g	PROPN
ejpam-5713	158	9	=	=	SYM
ejpam-5713	158	10	⟨{a	⟨{a	PROPN
ejpam-5713	158	11	,	,	PUNCT
ejpam-5713	158	12	x}⟩	x}⟩	X
ejpam-5713	158	13	∪	∪	ADP
ejpam-5713	158	14	⟨{b	⟨{b	PROPN
ejpam-5713	158	15	,	,	PUNCT
ejpam-5713	158	16	y}⟩	y}⟩	PROPN
ejpam-5713	158	17	=	=	SYM
ejpam-5713	158	18	k2	k2	PROPN
ejpam-5713	158	19	∪	∪	PROPN
ejpam-5713	158	20	k2	k2	PROPN
ejpam-5713	158	21	.	.	PUNCT
ejpam-5713	159	1	accordingly	accordingly	ADV
ejpam-5713	159	2	,	,	PUNCT
ejpam-5713	159	3	g	g	PROPN
ejpam-5713	159	4	∈	∈	PROPN
ejpam-5713	159	5	{	{	PUNCT
ejpam-5713	159	6	k2,k3	k2,k3	PROPN
ejpam-5713	159	7	,	,	PUNCT
ejpam-5713	159	8	p3,k1	p3,k1	PROPN
ejpam-5713	159	9	∪k2	∪k2	NOUN
ejpam-5713	159	10	,	,	PUNCT
ejpam-5713	159	11	p4,k2	p4,k2	PROPN
ejpam-5713	159	12	∪k2	∪k2	PUNCT
ejpam-5713	159	13	}	}	PUNCT
ejpam-5713	159	14	.	.	PUNCT
ejpam-5713	160	1	the	the	DET
ejpam-5713	160	2	converse	converse	NOUN
ejpam-5713	160	3	is	be	AUX
ejpam-5713	160	4	clear	clear	ADJ
ejpam-5713	160	5	.	.	PUNCT
ejpam-5713	161	1	(	(	PUNCT
ejpam-5713	161	2	iii	iii	X
ejpam-5713	161	3	)	)	PUNCT
ejpam-5713	161	4	suppose	suppose	VERB
ejpam-5713	161	5	βs(g	βs(g	PUNCT
ejpam-5713	161	6	)	)	PUNCT
ejpam-5713	161	7	=	=	SYM
ejpam-5713	161	8	n.	n.	NOUN
ejpam-5713	161	9	suppose	suppose	VERB
ejpam-5713	161	10	g	g	PROPN
ejpam-5713	161	11	̸=	̸=	PROPN
ejpam-5713	161	12	kn	kn	PROPN
ejpam-5713	161	13	.	.	PUNCT
ejpam-5713	162	1	then	then	ADV
ejpam-5713	162	2	e(g	e(g	PROPN
ejpam-5713	162	3	)	)	PUNCT
ejpam-5713	163	1	̸=	̸=	PROPN
ejpam-5713	163	2	∅.	∅.	PRON
ejpam-5713	163	3	by	by	ADP
ejpam-5713	163	4	proposition	proposition	NOUN
ejpam-5713	163	5	1	1	NUM
ejpam-5713	163	6	,	,	PUNCT
ejpam-5713	163	7	we	we	PRON
ejpam-5713	163	8	have	have	VERB
ejpam-5713	163	9	βs(g	βs(g	NOUN
ejpam-5713	163	10	)	)	PUNCT
ejpam-5713	163	11	≤	≤	NUM
ejpam-5713	163	12	n−	n−	NOUN
ejpam-5713	163	13	1	1	NUM
ejpam-5713	163	14	,	,	PUNCT
ejpam-5713	163	15	a	a	DET
ejpam-5713	163	16	contradiction	contradiction	NOUN
ejpam-5713	163	17	.	.	PUNCT
ejpam-5713	164	1	thus	thus	ADV
ejpam-5713	164	2	,	,	PUNCT
ejpam-5713	164	3	g	g	PROPN
ejpam-5713	164	4	=	=	SYM
ejpam-5713	164	5	kn	kn	PROPN
ejpam-5713	164	6	.	.	PROPN
ejpam-5713	165	1	for	for	ADP
ejpam-5713	165	2	the	the	DET
ejpam-5713	165	3	converse	converse	NOUN
ejpam-5713	165	4	,	,	PUNCT
ejpam-5713	165	5	suppose	suppose	VERB
ejpam-5713	165	6	g	g	PROPN
ejpam-5713	165	7	=	=	PROPN
ejpam-5713	165	8	kn	kn	PROPN
ejpam-5713	165	9	.	.	PUNCT
ejpam-5713	166	1	by	by	ADP
ejpam-5713	166	2	(	(	PUNCT
ejpam-5713	166	3	i	i	NOUN
ejpam-5713	166	4	)	)	PUNCT
ejpam-5713	166	5	and	and	CCONJ
ejpam-5713	166	6	proposition	proposition	NOUN
ejpam-5713	166	7	2	2	NUM
ejpam-5713	166	8	,	,	PUNCT
ejpam-5713	166	9	βs(g	βs(g	PUNCT
ejpam-5713	166	10	)	)	PUNCT
ejpam-5713	166	11	=	=	SYM
ejpam-5713	166	12	n.	n.	PROPN
ejpam-5713	166	13	s.	s.	PROPN
ejpam-5713	166	14	r.	r.	PROPN
ejpam-5713	166	15	canoy	canoy	PROPN
ejpam-5713	166	16	et	et	PROPN
ejpam-5713	166	17	al	al	PROPN
ejpam-5713	166	18	.	.	PUNCT
ejpam-5713	166	19	/	/	SYM
ejpam-5713	166	20	eur	eur	PROPN
ejpam-5713	166	21	.	.	PUNCT
ejpam-5713	167	1	j.	j.	PROPN
ejpam-5713	167	2	pure	pure	PROPN
ejpam-5713	167	3	appl	appl	PROPN
ejpam-5713	167	4	.	.	PROPN
ejpam-5713	167	5	math	math	PROPN
ejpam-5713	167	6	,	,	PUNCT
ejpam-5713	167	7	18	18	NUM
ejpam-5713	167	8	(	(	PUNCT
ejpam-5713	167	9	1	1	NUM
ejpam-5713	167	10	)	)	PUNCT
ejpam-5713	167	11	(	(	PUNCT
ejpam-5713	167	12	2025	2025	NUM
ejpam-5713	167	13	)	)	PUNCT
ejpam-5713	167	14	,	,	PUNCT
ejpam-5713	167	15	5713	5713	NUM
ejpam-5713	167	16	6	6	NUM
ejpam-5713	167	17	of	of	ADP
ejpam-5713	167	18	13	13	NUM
ejpam-5713	167	19	proposition	proposition	NOUN
ejpam-5713	167	20	3	3	NUM
ejpam-5713	167	21	.	.	PUNCT
ejpam-5713	168	1	let	let	VERB
ejpam-5713	168	2	n	n	PRON
ejpam-5713	168	3	be	be	AUX
ejpam-5713	168	4	any	any	DET
ejpam-5713	168	5	positive	positive	ADJ
ejpam-5713	168	6	integer	integer	NOUN
ejpam-5713	168	7	.	.	PUNCT
ejpam-5713	169	1	then	then	ADV
ejpam-5713	169	2	βs(pn	βs(pn	NUM
ejpam-5713	169	3	)	)	PUNCT
ejpam-5713	169	4	=	=	PUNCT
ejpam-5713	169	5			NUM
ejpam-5713	169	6	1	1	NUM
ejpam-5713	169	7	if	if	SCONJ
ejpam-5713	169	8	n	n	NOUN
ejpam-5713	169	9	=	=	SYM
ejpam-5713	169	10	1	1	NUM
ejpam-5713	169	11	,	,	PUNCT
ejpam-5713	169	12	2	2	NUM
ejpam-5713	169	13	2	2	NUM
ejpam-5713	169	14	if	if	SCONJ
ejpam-5713	169	15	n	n	NOUN
ejpam-5713	169	16	=	=	SYM
ejpam-5713	169	17	3	3	NUM
ejpam-5713	169	18	,	,	PUNCT
ejpam-5713	169	19	4	4	NUM
ejpam-5713	169	20	3r	3r	NUM
ejpam-5713	169	21	if	if	SCONJ
ejpam-5713	169	22	n	n	NOUN
ejpam-5713	169	23	=	=	NOUN
ejpam-5713	169	24	5r	5r	NUM
ejpam-5713	169	25	3r	3r	NUM
ejpam-5713	169	26	+	+	CCONJ
ejpam-5713	169	27	1	1	NUM
ejpam-5713	169	28	,	,	PUNCT
ejpam-5713	169	29	if	if	SCONJ
ejpam-5713	169	30	n	n	NOUN
ejpam-5713	169	31	=	=	NOUN
ejpam-5713	170	1	5r	5r	NOUN
ejpam-5713	170	2	+	+	CCONJ
ejpam-5713	170	3	1	1	NUM
ejpam-5713	170	4	or	or	CCONJ
ejpam-5713	170	5	n	n	NOUN
ejpam-5713	170	6	=	=	NOUN
ejpam-5713	170	7	5r	5r	NOUN
ejpam-5713	171	1	+	+	CCONJ
ejpam-5713	171	2	2	2	NUM
ejpam-5713	171	3	3r	3r	NUM
ejpam-5713	171	4	+	+	CCONJ
ejpam-5713	171	5	2	2	NUM
ejpam-5713	171	6	,	,	PUNCT
ejpam-5713	171	7	if	if	SCONJ
ejpam-5713	171	8	n	n	NOUN
ejpam-5713	171	9	=	=	NOUN
ejpam-5713	171	10	5r	5r	NOUN
ejpam-5713	171	11	+	+	CCONJ
ejpam-5713	171	12	3	3	NUM
ejpam-5713	171	13	or	or	CCONJ
ejpam-5713	171	14	n	n	NOUN
ejpam-5713	171	15	=	=	NOUN
ejpam-5713	171	16	5r	5r	NOUN
ejpam-5713	171	17	+	+	CCONJ
ejpam-5713	171	18	4	4	X
ejpam-5713	171	19	.	.	X
ejpam-5713	171	20	proof	proof	NOUN
ejpam-5713	171	21	.	.	PUNCT
ejpam-5713	172	1	clearly	clearly	ADV
ejpam-5713	172	2	,	,	PUNCT
ejpam-5713	172	3	βs(p1	βs(p1	NOUN
ejpam-5713	172	4	)	)	PUNCT
ejpam-5713	172	5	=	=	SYM
ejpam-5713	172	6	βs(p2	βs(p2	X
ejpam-5713	172	7	)	)	PUNCT
ejpam-5713	172	8	=	=	SYM
ejpam-5713	172	9	1	1	NUM
ejpam-5713	172	10	and	and	CCONJ
ejpam-5713	172	11	βs(p3	βs(p3	PUNCT
ejpam-5713	172	12	)	)	PUNCT
ejpam-5713	172	13	=	=	SYM
ejpam-5713	172	14	βs(p4	βs(p4	X
ejpam-5713	172	15	)	)	PUNCT
ejpam-5713	172	16	=	=	SYM
ejpam-5713	172	17	2	2	X
ejpam-5713	172	18	.	.	PUNCT
ejpam-5713	173	1	next	next	ADV
ejpam-5713	173	2	,	,	PUNCT
ejpam-5713	173	3	let	let	VERB
ejpam-5713	173	4	n	n	PRON
ejpam-5713	173	5	=	=	NOUN
ejpam-5713	173	6	5r	5r	NOUN
ejpam-5713	173	7	and	and	CCONJ
ejpam-5713	173	8	let	let	VERB
ejpam-5713	173	9	p5r	p5r	PROPN
ejpam-5713	173	10	=	=	PUNCT
ejpam-5713	174	1	[	[	X
ejpam-5713	174	2	v1	v1	NOUN
ejpam-5713	174	3	,	,	PUNCT
ejpam-5713	174	4	v2	v2	PROPN
ejpam-5713	174	5	,	,	PUNCT
ejpam-5713	174	6	v3	v3	PROPN
ejpam-5713	174	7	,	,	PUNCT
ejpam-5713	174	8	v4	v4	PROPN
ejpam-5713	174	9	,	,	PUNCT
ejpam-5713	174	10	v5	v5	PROPN
ejpam-5713	174	11	,	,	PUNCT
ejpam-5713	174	12	·	·	PUNCT
ejpam-5713	174	13	·	·	PUNCT
ejpam-5713	174	14	·	·	PUNCT
ejpam-5713	174	15	,	,	PUNCT
ejpam-5713	174	16	v5r−3	v5r−3	PROPN
ejpam-5713	174	17	,	,	PUNCT
ejpam-5713	174	18	v5r−2	v5r−2	ADJ
ejpam-5713	174	19	,	,	PUNCT
ejpam-5713	174	20	v5r−1	v5r−1	PROPN
ejpam-5713	174	21	,	,	PUNCT
ejpam-5713	174	22	v5r	v5r	NOUN
ejpam-5713	174	23	]	]	PUNCT
ejpam-5713	174	24	.	.	PUNCT
ejpam-5713	175	1	then	then	ADV
ejpam-5713	175	2	s1	s1	PROPN
ejpam-5713	175	3	=	=	PUNCT
ejpam-5713	175	4	{	{	PUNCT
ejpam-5713	175	5	v2	v2	PROPN
ejpam-5713	175	6	,	,	PUNCT
ejpam-5713	175	7	v7	v7	VERB
ejpam-5713	175	8	,	,	PUNCT
ejpam-5713	175	9	·	·	PUNCT
ejpam-5713	175	10	·	·	PUNCT
ejpam-5713	175	11	·	·	PUNCT
ejpam-5713	175	12	,	,	PUNCT
ejpam-5713	175	13	v5r−3	v5r−3	NOUN
ejpam-5713	175	14	}	}	PUNCT
ejpam-5713	175	15	∪	∪	NOUN
ejpam-5713	175	16	{	{	PUNCT
ejpam-5713	175	17	v3	v3	PROPN
ejpam-5713	175	18	,	,	PUNCT
ejpam-5713	175	19	v8	v8	PROPN
ejpam-5713	175	20	,	,	PUNCT
ejpam-5713	175	21	·	·	PUNCT
ejpam-5713	175	22	·	·	PUNCT
ejpam-5713	175	23	·	·	PUNCT
ejpam-5713	175	24	,	,	PUNCT
ejpam-5713	175	25	v5r−2	v5r−2	ADV
ejpam-5713	175	26	}	}	PUNCT
ejpam-5713	175	27	∪	∪	NOUN
ejpam-5713	175	28	{	{	PUNCT
ejpam-5713	175	29	v5	v5	NOUN
ejpam-5713	175	30	,	,	PUNCT
ejpam-5713	175	31	v10	v10	NOUN
ejpam-5713	175	32	,	,	PUNCT
ejpam-5713	175	33	·	·	PUNCT
ejpam-5713	175	34	·	·	PUNCT
ejpam-5713	175	35	·	·	PUNCT
ejpam-5713	175	36	,	,	PUNCT
ejpam-5713	175	37	v5r	v5r	NOUN
ejpam-5713	175	38	}	}	PUNCT
ejpam-5713	175	39	is	be	AUX
ejpam-5713	175	40	a	a	DET
ejpam-5713	175	41	βs	βs	NOUN
ejpam-5713	175	42	-	-	PUNCT
ejpam-5713	175	43	set	set	NOUN
ejpam-5713	175	44	in	in	ADP
ejpam-5713	175	45	p5r	p5r	PROPN
ejpam-5713	175	46	.	.	PUNCT
ejpam-5713	176	1	hence	hence	ADV
ejpam-5713	176	2	,	,	PUNCT
ejpam-5713	176	3	βs(p5r	βs(p5r	PROPN
ejpam-5713	176	4	)	)	PUNCT
ejpam-5713	176	5	=	=	SYM
ejpam-5713	176	6	|s1|	|s1|	NOUN
ejpam-5713	176	7	=	=	NOUN
ejpam-5713	176	8	3r	3r	NUM
ejpam-5713	176	9	.	.	PUNCT
ejpam-5713	177	1	if	if	SCONJ
ejpam-5713	177	2	n	n	NOUN
ejpam-5713	177	3	=	=	NOUN
ejpam-5713	177	4	5r	5r	NOUN
ejpam-5713	177	5	+	+	CCONJ
ejpam-5713	177	6	1	1	NUM
ejpam-5713	177	7	and	and	CCONJ
ejpam-5713	177	8	if	if	SCONJ
ejpam-5713	177	9	p5r+1	p5r+1	PROPN
ejpam-5713	177	10	=	=	PUNCT
ejpam-5713	178	1	[	[	X
ejpam-5713	178	2	v1	v1	NOUN
ejpam-5713	178	3	,	,	PUNCT
ejpam-5713	178	4	v2	v2	PROPN
ejpam-5713	178	5	,	,	PUNCT
ejpam-5713	178	6	v3	v3	PROPN
ejpam-5713	178	7	,	,	PUNCT
ejpam-5713	178	8	v4	v4	PROPN
ejpam-5713	178	9	,	,	PUNCT
ejpam-5713	178	10	v5	v5	PROPN
ejpam-5713	178	11	,	,	PUNCT
ejpam-5713	178	12	·	·	PUNCT
ejpam-5713	178	13	·	·	PUNCT
ejpam-5713	178	14	·	·	PUNCT
ejpam-5713	178	15	,	,	PUNCT
ejpam-5713	178	16	v5r−3	v5r−3	PROPN
ejpam-5713	178	17	,	,	PUNCT
ejpam-5713	178	18	v5r−2	v5r−2	ADJ
ejpam-5713	178	19	,	,	PUNCT
ejpam-5713	178	20	v5r−1	v5r−1	PROPN
ejpam-5713	178	21	,	,	PUNCT
ejpam-5713	178	22	v5r	v5r	NOUN
ejpam-5713	178	23	,	,	PUNCT
ejpam-5713	178	24	v5r+1	v5r+1	PROPN
ejpam-5713	178	25	]	]	X
ejpam-5713	178	26	,	,	PUNCT
ejpam-5713	178	27	then	then	ADV
ejpam-5713	178	28	s2	s2	VERB
ejpam-5713	178	29	=	=	SYM
ejpam-5713	178	30	{	{	PUNCT
ejpam-5713	178	31	v2	v2	PROPN
ejpam-5713	178	32	,	,	PUNCT
ejpam-5713	178	33	v7	v7	VERB
ejpam-5713	178	34	,	,	PUNCT
ejpam-5713	178	35	·	·	PUNCT
ejpam-5713	178	36	·	·	PUNCT
ejpam-5713	178	37	·	·	PUNCT
ejpam-5713	178	38	,	,	PUNCT
ejpam-5713	178	39	v5r−3	v5r−3	NOUN
ejpam-5713	178	40	}	}	PUNCT
ejpam-5713	178	41	∪	∪	NOUN
ejpam-5713	178	42	{	{	PUNCT
ejpam-5713	178	43	v3	v3	PROPN
ejpam-5713	178	44	,	,	PUNCT
ejpam-5713	178	45	v8	v8	PROPN
ejpam-5713	178	46	,	,	PUNCT
ejpam-5713	178	47	·	·	PUNCT
ejpam-5713	178	48	·	·	PUNCT
ejpam-5713	178	49	·	·	PUNCT
ejpam-5713	178	50	,	,	PUNCT
ejpam-5713	178	51	v5r−2	v5r−2	ADV
ejpam-5713	178	52	}	}	PUNCT
ejpam-5713	178	53	∪	∪	NOUN
ejpam-5713	178	54	{	{	PUNCT
ejpam-5713	178	55	v5	v5	NOUN
ejpam-5713	178	56	,	,	PUNCT
ejpam-5713	178	57	v10	v10	NOUN
ejpam-5713	178	58	,	,	PUNCT
ejpam-5713	178	59	·	·	PUNCT
ejpam-5713	178	60	·	·	PUNCT
ejpam-5713	178	61	·	·	PUNCT
ejpam-5713	178	62	,	,	PUNCT
ejpam-5713	178	63	v5r	v5r	NOUN
ejpam-5713	178	64	}	}	PUNCT
ejpam-5713	178	65	∪	∪	ADJ
ejpam-5713	178	66	{	{	PUNCT
ejpam-5713	178	67	v5r+1	v5r+1	NOUN
ejpam-5713	178	68	}	}	PUNCT
ejpam-5713	178	69	is	be	AUX
ejpam-5713	178	70	a	a	DET
ejpam-5713	178	71	βs	βs	NOUN
ejpam-5713	178	72	-	-	PUNCT
ejpam-5713	178	73	set	set	NOUN
ejpam-5713	178	74	in	in	ADP
ejpam-5713	178	75	p5r+1	p5r+1	PROPN
ejpam-5713	178	76	.	.	PUNCT
ejpam-5713	179	1	this	this	PRON
ejpam-5713	179	2	implies	imply	VERB
ejpam-5713	179	3	that	that	SCONJ
ejpam-5713	179	4	βs(p5r+1	βs(p5r+1	PUNCT
ejpam-5713	179	5	)	)	PUNCT
ejpam-5713	180	1	=	=	SYM
ejpam-5713	180	2	|s2|	|s2|	NOUN
ejpam-5713	180	3	=	=	NOUN
ejpam-5713	180	4	3r	3r	NUM
ejpam-5713	180	5	+	+	CCONJ
ejpam-5713	180	6	1	1	X
ejpam-5713	180	7	.	.	X
ejpam-5713	181	1	if	if	SCONJ
ejpam-5713	181	2	n	n	NOUN
ejpam-5713	181	3	=	=	NOUN
ejpam-5713	181	4	5r	5r	NOUN
ejpam-5713	181	5	+	+	CCONJ
ejpam-5713	181	6	2	2	NUM
ejpam-5713	181	7	and	and	CCONJ
ejpam-5713	181	8	if	if	SCONJ
ejpam-5713	181	9	p5r+2	p5r+2	NOUN
ejpam-5713	181	10	=	=	PUNCT
ejpam-5713	182	1	[	[	X
ejpam-5713	182	2	v1	v1	NOUN
ejpam-5713	182	3	,	,	PUNCT
ejpam-5713	182	4	v2	v2	PROPN
ejpam-5713	182	5	,	,	PUNCT
ejpam-5713	182	6	v3	v3	PROPN
ejpam-5713	182	7	,	,	PUNCT
ejpam-5713	182	8	v4	v4	PROPN
ejpam-5713	182	9	,	,	PUNCT
ejpam-5713	182	10	v5	v5	PROPN
ejpam-5713	182	11	,	,	PUNCT
ejpam-5713	182	12	·	·	PUNCT
ejpam-5713	182	13	·	·	PUNCT
ejpam-5713	182	14	·	·	PUNCT
ejpam-5713	182	15	,	,	PUNCT
ejpam-5713	182	16	v5r−3	v5r−3	PROPN
ejpam-5713	182	17	,	,	PUNCT
ejpam-5713	182	18	v5r−2	v5r−2	ADJ
ejpam-5713	182	19	,	,	PUNCT
ejpam-5713	182	20	v5r−1	v5r−1	PROPN
ejpam-5713	182	21	,	,	PUNCT
ejpam-5713	182	22	v5r	v5r	NOUN
ejpam-5713	182	23	,	,	PUNCT
ejpam-5713	182	24	v5r+1	v5r+1	PROPN
ejpam-5713	182	25	,	,	PUNCT
ejpam-5713	182	26	v5r+2	v5r+2	NOUN
ejpam-5713	182	27	]	]	X
ejpam-5713	182	28	,	,	PUNCT
ejpam-5713	182	29	then	then	ADV
ejpam-5713	182	30	s3	s3	PROPN
ejpam-5713	182	31	=	=	SYM
ejpam-5713	182	32	{	{	PUNCT
ejpam-5713	182	33	v2	v2	PROPN
ejpam-5713	182	34	,	,	PUNCT
ejpam-5713	182	35	v7	v7	VERB
ejpam-5713	182	36	,	,	PUNCT
ejpam-5713	182	37	·	·	PUNCT
ejpam-5713	182	38	·	·	PUNCT
ejpam-5713	182	39	·	·	PUNCT
ejpam-5713	182	40	,	,	PUNCT
ejpam-5713	182	41	v5r−3	v5r−3	NOUN
ejpam-5713	182	42	}	}	PUNCT
ejpam-5713	182	43	∪	∪	NOUN
ejpam-5713	182	44	{	{	PUNCT
ejpam-5713	182	45	v3	v3	PROPN
ejpam-5713	182	46	,	,	PUNCT
ejpam-5713	182	47	v8	v8	PROPN
ejpam-5713	182	48	,	,	PUNCT
ejpam-5713	182	49	·	·	PUNCT
ejpam-5713	182	50	·	·	PUNCT
ejpam-5713	182	51	·	·	PUNCT
ejpam-5713	182	52	,	,	PUNCT
ejpam-5713	182	53	v5r−2	v5r−2	ADV
ejpam-5713	182	54	}	}	PUNCT
ejpam-5713	182	55	∪	∪	NOUN
ejpam-5713	182	56	{	{	PUNCT
ejpam-5713	182	57	v5	v5	NOUN
ejpam-5713	182	58	,	,	PUNCT
ejpam-5713	182	59	v10	v10	NOUN
ejpam-5713	182	60	,	,	PUNCT
ejpam-5713	182	61	·	·	PUNCT
ejpam-5713	182	62	·	·	PUNCT
ejpam-5713	182	63	·	·	PUNCT
ejpam-5713	182	64	,	,	PUNCT
ejpam-5713	182	65	v5r	v5r	NOUN
ejpam-5713	182	66	}	}	PUNCT
ejpam-5713	182	67	∪	∪	X
ejpam-5713	182	68	{	{	PUNCT
ejpam-5713	182	69	v5r+2	v5r+2	NOUN
ejpam-5713	182	70	}	}	PUNCT
ejpam-5713	182	71	is	be	AUX
ejpam-5713	182	72	a	a	DET
ejpam-5713	182	73	βs	βs	NOUN
ejpam-5713	182	74	-	-	PUNCT
ejpam-5713	182	75	set	set	NOUN
ejpam-5713	182	76	in	in	ADP
ejpam-5713	182	77	p5r+2	p5r+2	NOUN
ejpam-5713	182	78	.	.	PUNCT
ejpam-5713	183	1	it	it	PRON
ejpam-5713	183	2	follows	follow	VERB
ejpam-5713	183	3	that	that	PRON
ejpam-5713	183	4	βs(p5r+2	βs(p5r+2	PUNCT
ejpam-5713	183	5	)	)	PUNCT
ejpam-5713	183	6	=	=	SYM
ejpam-5713	183	7	|s3|	|s3|	NOUN
ejpam-5713	183	8	=	=	SYM
ejpam-5713	183	9	3r	3r	NUM
ejpam-5713	183	10	+	+	CCONJ
ejpam-5713	183	11	1	1	X
ejpam-5713	183	12	.	.	X
ejpam-5713	184	1	it	it	PRON
ejpam-5713	184	2	is	be	AUX
ejpam-5713	184	3	routine	routine	ADJ
ejpam-5713	184	4	to	to	PART
ejpam-5713	184	5	show	show	VERB
ejpam-5713	184	6	that	that	SCONJ
ejpam-5713	184	7	βs(p5r+3	βs(p5r+3	ADV
ejpam-5713	184	8	)	)	PUNCT
ejpam-5713	184	9	=	=	PUNCT
ejpam-5713	184	10	βs(p5r+4	βs(p5r+4	PUNCT
ejpam-5713	184	11	)	)	PUNCT
ejpam-5713	185	1	=	=	SYM
ejpam-5713	185	2	3r	3r	NUM
ejpam-5713	185	3	+	+	CCONJ
ejpam-5713	185	4	2	2	X
ejpam-5713	185	5	.	.	X
ejpam-5713	185	6	proposition	proposition	NOUN
ejpam-5713	185	7	4	4	NUM
ejpam-5713	185	8	.	.	PUNCT
ejpam-5713	186	1	let	let	VERB
ejpam-5713	186	2	n	n	PRON
ejpam-5713	186	3	be	be	AUX
ejpam-5713	186	4	any	any	DET
ejpam-5713	186	5	positive	positive	ADJ
ejpam-5713	186	6	integer	integer	NOUN
ejpam-5713	186	7	where	where	SCONJ
ejpam-5713	186	8	n	n	NUM
ejpam-5713	186	9	≥	≥	NOUN
ejpam-5713	186	10	3	3	NUM
ejpam-5713	186	11	.	.	PUNCT
ejpam-5713	186	12	then	then	ADV
ejpam-5713	186	13	βs(cn	βs(cn	NOUN
ejpam-5713	186	14	)	)	PUNCT
ejpam-5713	187	1	=	=	PUNCT
ejpam-5713	187	2			NUM
ejpam-5713	187	3	2	2	NUM
ejpam-5713	187	4	if	if	SCONJ
ejpam-5713	187	5	n	n	NOUN
ejpam-5713	187	6	=	=	SYM
ejpam-5713	187	7	3	3	NUM
ejpam-5713	187	8	3	3	NUM
ejpam-5713	187	9	if	if	SCONJ
ejpam-5713	187	10	n	n	NOUN
ejpam-5713	187	11	=	=	SYM
ejpam-5713	187	12	4	4	NUM
ejpam-5713	187	13	3r	3r	NUM
ejpam-5713	187	14	if	if	SCONJ
ejpam-5713	187	15	n	n	NOUN
ejpam-5713	187	16	=	=	NOUN
ejpam-5713	187	17	5r	5r	NUM
ejpam-5713	187	18	3r	3r	NUM
ejpam-5713	187	19	+	+	CCONJ
ejpam-5713	187	20	1	1	NUM
ejpam-5713	187	21	,	,	PUNCT
ejpam-5713	187	22	if	if	SCONJ
ejpam-5713	187	23	n	n	NOUN
ejpam-5713	187	24	=	=	NOUN
ejpam-5713	187	25	5r	5r	NOUN
ejpam-5713	187	26	+	+	CCONJ
ejpam-5713	187	27	1	1	NUM
ejpam-5713	187	28	or	or	CCONJ
ejpam-5713	187	29	n	n	NOUN
ejpam-5713	187	30	=	=	NOUN
ejpam-5713	187	31	5r	5r	NOUN
ejpam-5713	188	1	+	+	CCONJ
ejpam-5713	188	2	2	2	NUM
ejpam-5713	188	3	3r	3r	NUM
ejpam-5713	188	4	+	+	CCONJ
ejpam-5713	188	5	2	2	NUM
ejpam-5713	188	6	,	,	PUNCT
ejpam-5713	188	7	if	if	SCONJ
ejpam-5713	188	8	n	n	NOUN
ejpam-5713	188	9	=	=	NOUN
ejpam-5713	188	10	5r	5r	NOUN
ejpam-5713	188	11	+	+	CCONJ
ejpam-5713	188	12	3	3	NUM
ejpam-5713	188	13	or	or	CCONJ
ejpam-5713	188	14	n	n	NOUN
ejpam-5713	188	15	=	=	NOUN
ejpam-5713	188	16	5r	5r	NOUN
ejpam-5713	188	17	+	+	CCONJ
ejpam-5713	188	18	4	4	X
ejpam-5713	188	19	.	.	X
ejpam-5713	188	20	proof	proof	NOUN
ejpam-5713	188	21	.	.	PUNCT
ejpam-5713	189	1	it	it	PRON
ejpam-5713	189	2	can	can	AUX
ejpam-5713	189	3	be	be	AUX
ejpam-5713	189	4	verified	verify	VERB
ejpam-5713	189	5	easily	easily	ADV
ejpam-5713	189	6	that	that	SCONJ
ejpam-5713	189	7	βs(c3	βs(c3	VERB
ejpam-5713	189	8	)	)	PUNCT
ejpam-5713	189	9	=	=	SYM
ejpam-5713	189	10	2	2	NUM
ejpam-5713	189	11	and	and	CCONJ
ejpam-5713	189	12	βs(c4	βs(c4	NUM
ejpam-5713	189	13	)	)	PUNCT
ejpam-5713	189	14	=	=	SYM
ejpam-5713	190	1	3	3	X
ejpam-5713	190	2	.	.	X
ejpam-5713	190	3	let	let	VERB
ejpam-5713	190	4	n	n	NOUN
ejpam-5713	190	5	=	=	NOUN
ejpam-5713	190	6	5r	5r	NOUN
ejpam-5713	190	7	and	and	CCONJ
ejpam-5713	190	8	let	let	VERB
ejpam-5713	190	9	c5r	c5r	NOUN
ejpam-5713	190	10	=	=	PUNCT
ejpam-5713	190	11	[	[	X
ejpam-5713	190	12	v1	v1	NOUN
ejpam-5713	190	13	,	,	PUNCT
ejpam-5713	190	14	v2	v2	PROPN
ejpam-5713	190	15	,	,	PUNCT
ejpam-5713	190	16	v3	v3	PROPN
ejpam-5713	190	17	,	,	PUNCT
ejpam-5713	190	18	v4	v4	PROPN
ejpam-5713	190	19	,	,	PUNCT
ejpam-5713	190	20	v5	v5	PROPN
ejpam-5713	190	21	,	,	PUNCT
ejpam-5713	190	22	·	·	PUNCT
ejpam-5713	190	23	·	·	PUNCT
ejpam-5713	190	24	·	·	PUNCT
ejpam-5713	190	25	,	,	PUNCT
ejpam-5713	190	26	v5r−3	v5r−3	PROPN
ejpam-5713	190	27	,	,	PUNCT
ejpam-5713	190	28	v5r−2	v5r−2	ADJ
ejpam-5713	190	29	,	,	PUNCT
ejpam-5713	190	30	v5r−1	v5r−1	PROPN
ejpam-5713	190	31	,	,	PUNCT
ejpam-5713	190	32	v5r	v5r	NOUN
ejpam-5713	190	33	,	,	PUNCT
ejpam-5713	190	34	v1	v1	NOUN
ejpam-5713	190	35	]	]	PUNCT
ejpam-5713	190	36	.	.	PUNCT
ejpam-5713	191	1	then	then	ADV
ejpam-5713	191	2	d1	d1	PROPN
ejpam-5713	191	3	=	=	SYM
ejpam-5713	191	4	{	{	PUNCT
ejpam-5713	191	5	v1	v1	PROPN
ejpam-5713	191	6	,	,	PUNCT
ejpam-5713	191	7	v6	v6	NOUN
ejpam-5713	191	8	,	,	PUNCT
ejpam-5713	191	9	·	·	PUNCT
ejpam-5713	191	10	·	·	PUNCT
ejpam-5713	191	11	·	·	PUNCT
ejpam-5713	191	12	,	,	PUNCT
ejpam-5713	191	13	v5r−4	v5r−4	PROPN
ejpam-5713	191	14	}	}	PUNCT
ejpam-5713	191	15	∪	∪	X
ejpam-5713	191	16	{	{	PUNCT
ejpam-5713	191	17	v2	v2	NOUN
ejpam-5713	191	18	,	,	PUNCT
ejpam-5713	191	19	v7	v7	VERB
ejpam-5713	191	20	,	,	PUNCT
ejpam-5713	191	21	·	·	PUNCT
ejpam-5713	191	22	·	·	PUNCT
ejpam-5713	191	23	·	·	PUNCT
ejpam-5713	191	24	,	,	PUNCT
ejpam-5713	191	25	v5r−3	v5r−3	NOUN
ejpam-5713	191	26	}	}	PUNCT
ejpam-5713	191	27	∪	∪	NOUN
ejpam-5713	191	28	{	{	PUNCT
ejpam-5713	191	29	v4	v4	NOUN
ejpam-5713	191	30	,	,	PUNCT
ejpam-5713	191	31	v9	v9	PROPN
ejpam-5713	191	32	,	,	PUNCT
ejpam-5713	191	33	·	·	PUNCT
ejpam-5713	191	34	·	·	PUNCT
ejpam-5713	191	35	·	·	PUNCT
ejpam-5713	191	36	,	,	PUNCT
ejpam-5713	191	37	v5r−1	v5r−1	PROPN
ejpam-5713	191	38	}	}	PUNCT
ejpam-5713	191	39	is	be	AUX
ejpam-5713	191	40	a	a	DET
ejpam-5713	191	41	βs	βs	ADV
ejpam-5713	191	42	-	-	PUNCT
ejpam-5713	191	43	set	set	NOUN
ejpam-5713	191	44	in	in	ADP
ejpam-5713	191	45	c5r	c5r	NOUN
ejpam-5713	191	46	.	.	PUNCT
ejpam-5713	192	1	hence	hence	ADV
ejpam-5713	192	2	,	,	PUNCT
ejpam-5713	192	3	βs(c5r	βs(c5r	PROPN
ejpam-5713	192	4	)	)	PUNCT
ejpam-5713	193	1	=	=	SYM
ejpam-5713	193	2	|d1|	|d1|	NOUN
ejpam-5713	193	3	=	=	NOUN
ejpam-5713	193	4	3r	3r	NUM
ejpam-5713	193	5	.	.	PUNCT
ejpam-5713	194	1	if	if	SCONJ
ejpam-5713	194	2	n	n	NOUN
ejpam-5713	194	3	=	=	NOUN
ejpam-5713	194	4	5r	5r	NOUN
ejpam-5713	194	5	+	+	CCONJ
ejpam-5713	194	6	1	1	NUM
ejpam-5713	194	7	and	and	CCONJ
ejpam-5713	194	8	if	if	SCONJ
ejpam-5713	194	9	c5r+1	c5r+1	PROPN
ejpam-5713	194	10	=	=	PUNCT
ejpam-5713	195	1	[	[	X
ejpam-5713	195	2	v1	v1	NOUN
ejpam-5713	195	3	,	,	PUNCT
ejpam-5713	195	4	v2	v2	PROPN
ejpam-5713	195	5	,	,	PUNCT
ejpam-5713	195	6	v3	v3	PROPN
ejpam-5713	195	7	,	,	PUNCT
ejpam-5713	195	8	v4	v4	PROPN
ejpam-5713	195	9	,	,	PUNCT
ejpam-5713	195	10	v5	v5	PROPN
ejpam-5713	195	11	,	,	PUNCT
ejpam-5713	195	12	·	·	PUNCT
ejpam-5713	195	13	·	·	PUNCT
ejpam-5713	195	14	·	·	PUNCT
ejpam-5713	195	15	,	,	PUNCT
ejpam-5713	195	16	v5r−3	v5r−3	PROPN
ejpam-5713	195	17	,	,	PUNCT
ejpam-5713	195	18	v5r−2	v5r−2	ADJ
ejpam-5713	195	19	,	,	PUNCT
ejpam-5713	195	20	v5r−1	v5r−1	PROPN
ejpam-5713	195	21	,	,	PUNCT
ejpam-5713	195	22	v5r	v5r	NOUN
ejpam-5713	195	23	,	,	PUNCT
ejpam-5713	195	24	v5r+1	v5r+1	PROPN
ejpam-5713	195	25	]	]	X
ejpam-5713	195	26	,	,	PUNCT
ejpam-5713	195	27	then	then	ADV
ejpam-5713	195	28	d2	d2	PROPN
ejpam-5713	195	29	=	=	SYM
ejpam-5713	195	30	{	{	PUNCT
ejpam-5713	195	31	v1	v1	PROPN
ejpam-5713	195	32	,	,	PUNCT
ejpam-5713	195	33	v6	v6	NOUN
ejpam-5713	195	34	,	,	PUNCT
ejpam-5713	195	35	·	·	PUNCT
ejpam-5713	195	36	·	·	PUNCT
ejpam-5713	195	37	·	·	PUNCT
ejpam-5713	195	38	,	,	PUNCT
ejpam-5713	195	39	v5r−4	v5r−4	PROPN
ejpam-5713	195	40	}	}	PUNCT
ejpam-5713	195	41	∪	∪	X
ejpam-5713	195	42	{	{	PUNCT
ejpam-5713	195	43	v2	v2	NOUN
ejpam-5713	195	44	,	,	PUNCT
ejpam-5713	195	45	v7	v7	VERB
ejpam-5713	195	46	,	,	PUNCT
ejpam-5713	195	47	·	·	PUNCT
ejpam-5713	195	48	·	·	PUNCT
ejpam-5713	195	49	·	·	PUNCT
ejpam-5713	195	50	,	,	PUNCT
ejpam-5713	195	51	v5r−3	v5r−3	NOUN
ejpam-5713	195	52	}	}	PUNCT
ejpam-5713	195	53	∪	∪	NOUN
ejpam-5713	195	54	{	{	PUNCT
ejpam-5713	195	55	v4	v4	NOUN
ejpam-5713	195	56	,	,	PUNCT
ejpam-5713	195	57	v9	v9	PROPN
ejpam-5713	195	58	,	,	PUNCT
ejpam-5713	195	59	·	·	PUNCT
ejpam-5713	195	60	·	·	PUNCT
ejpam-5713	195	61	·	·	PUNCT
ejpam-5713	195	62	,	,	PUNCT
ejpam-5713	195	63	v5r−6	v5r−6	X
ejpam-5713	195	64	,	,	PUNCT
ejpam-5713	195	65	v5r−1	v5r−1	PROPN
ejpam-5713	195	66	}	}	PUNCT
ejpam-5713	195	67	is	be	AUX
ejpam-5713	195	68	a	a	DET
ejpam-5713	195	69	βs	βs	NOUN
ejpam-5713	195	70	-	-	PUNCT
ejpam-5713	195	71	set	set	NOUN
ejpam-5713	195	72	in	in	ADP
ejpam-5713	195	73	c5r+1	c5r+1	PROPN
ejpam-5713	195	74	.	.	PUNCT
ejpam-5713	196	1	this	this	PRON
ejpam-5713	196	2	implies	imply	VERB
ejpam-5713	196	3	that	that	PRON
ejpam-5713	196	4	βs(c5r+1	βs(c5r+1	PUNCT
ejpam-5713	196	5	)	)	PUNCT
ejpam-5713	196	6	=	=	SYM
ejpam-5713	196	7	|d2|	|d2|	NOUN
ejpam-5713	197	1	=	=	NOUN
ejpam-5713	197	2	3r	3r	NUM
ejpam-5713	197	3	+	+	CCONJ
ejpam-5713	197	4	1	1	X
ejpam-5713	197	5	.	.	X
ejpam-5713	198	1	if	if	SCONJ
ejpam-5713	198	2	n	n	NOUN
ejpam-5713	198	3	=	=	NOUN
ejpam-5713	198	4	5r	5r	NOUN
ejpam-5713	198	5	+	+	CCONJ
ejpam-5713	198	6	2	2	NUM
ejpam-5713	198	7	and	and	CCONJ
ejpam-5713	198	8	if	if	SCONJ
ejpam-5713	198	9	c5r+2	c5r+2	PUNCT
ejpam-5713	198	10	=	=	PUNCT
ejpam-5713	198	11	[	[	X
ejpam-5713	198	12	v1	v1	NOUN
ejpam-5713	198	13	,	,	PUNCT
ejpam-5713	198	14	v2	v2	PROPN
ejpam-5713	198	15	,	,	PUNCT
ejpam-5713	198	16	v3	v3	PROPN
ejpam-5713	198	17	,	,	PUNCT
ejpam-5713	198	18	v4	v4	PROPN
ejpam-5713	198	19	,	,	PUNCT
ejpam-5713	198	20	v5	v5	PROPN
ejpam-5713	198	21	,	,	PUNCT
ejpam-5713	198	22	·	·	PUNCT
ejpam-5713	198	23	·	·	PUNCT
ejpam-5713	198	24	·	·	PUNCT
ejpam-5713	198	25	,	,	PUNCT
ejpam-5713	199	1	v5r−4	v5r−4	PROPN
ejpam-5713	199	2	,	,	PUNCT
ejpam-5713	199	3	v5r−3	v5r−3	PROPN
ejpam-5713	199	4	,	,	PUNCT
ejpam-5713	199	5	v5r−2	v5r−2	ADJ
ejpam-5713	199	6	,	,	PUNCT
ejpam-5713	199	7	v5r−1	v5r−1	PROPN
ejpam-5713	199	8	,	,	PUNCT
ejpam-5713	199	9	v5r	v5r	NOUN
ejpam-5713	199	10	,	,	PUNCT
ejpam-5713	199	11	v5r+1	v5r+1	PROPN
ejpam-5713	199	12	,	,	PUNCT
ejpam-5713	199	13	v5r+2	v5r+2	NOUN
ejpam-5713	199	14	]	]	X
ejpam-5713	199	15	,	,	PUNCT
ejpam-5713	199	16	then	then	ADV
ejpam-5713	199	17	d3	d3	PROPN
ejpam-5713	199	18	=	=	SYM
ejpam-5713	199	19	{	{	PUNCT
ejpam-5713	199	20	v1	v1	PROPN
ejpam-5713	199	21	,	,	PUNCT
ejpam-5713	199	22	v6	v6	NOUN
ejpam-5713	199	23	,	,	PUNCT
ejpam-5713	199	24	·	·	PUNCT
ejpam-5713	199	25	·	·	PUNCT
ejpam-5713	199	26	·	·	PUNCT
ejpam-5713	199	27	,	,	PUNCT
ejpam-5713	199	28	v5r−4	v5r−4	PROPN
ejpam-5713	199	29	}	}	PUNCT
ejpam-5713	199	30	∪	∪	X
ejpam-5713	199	31	{	{	PUNCT
ejpam-5713	199	32	v2	v2	NOUN
ejpam-5713	199	33	,	,	PUNCT
ejpam-5713	199	34	v7	v7	VERB
ejpam-5713	199	35	,	,	PUNCT
ejpam-5713	199	36	·	·	PUNCT
ejpam-5713	199	37	·	·	PUNCT
ejpam-5713	199	38	·	·	PUNCT
ejpam-5713	199	39	,	,	PUNCT
ejpam-5713	199	40	v5r−3	v5r−3	NOUN
ejpam-5713	199	41	}	}	PUNCT
ejpam-5713	199	42	∪	∪	NOUN
ejpam-5713	199	43	{	{	PUNCT
ejpam-5713	199	44	v4	v4	NOUN
ejpam-5713	199	45	,	,	PUNCT
ejpam-5713	199	46	v9	v9	PROPN
ejpam-5713	199	47	,	,	PUNCT
ejpam-5713	199	48	·	·	PUNCT
ejpam-5713	199	49	·	·	PUNCT
ejpam-5713	199	50	·	·	PUNCT
ejpam-5713	199	51	,	,	PUNCT
ejpam-5713	199	52	v5r−1	v5r−1	PROPN
ejpam-5713	199	53	}	}	PUNCT
ejpam-5713	199	54	∪	∪	NOUN
ejpam-5713	199	55	{	{	PUNCT
ejpam-5713	199	56	v5r	v5r	NOUN
ejpam-5713	199	57	}	}	PUNCT
ejpam-5713	199	58	is	be	AUX
ejpam-5713	199	59	a	a	DET
ejpam-5713	199	60	βs	βs	NOUN
ejpam-5713	199	61	-	-	PUNCT
ejpam-5713	199	62	set	set	NOUN
ejpam-5713	199	63	in	in	ADP
ejpam-5713	199	64	c5r+2	c5r+2	NOUN
ejpam-5713	199	65	.	.	PUNCT
ejpam-5713	200	1	it	it	PRON
ejpam-5713	200	2	follows	follow	VERB
ejpam-5713	200	3	that	that	PRON
ejpam-5713	200	4	βs(c5r+2	βs(c5r+2	ADV
ejpam-5713	200	5	)	)	PUNCT
ejpam-5713	200	6	=	=	SYM
ejpam-5713	201	1	|d3|	|d3|	NOUN
ejpam-5713	201	2	=	=	SYM
ejpam-5713	201	3	3r	3r	NUM
ejpam-5713	201	4	+	+	CCONJ
ejpam-5713	201	5	1	1	NUM
ejpam-5713	201	6	.	.	X
ejpam-5713	201	7	that	that	PRON
ejpam-5713	201	8	βs(c5r+3	βs(c5r+3	NOUN
ejpam-5713	201	9	)	)	PUNCT
ejpam-5713	201	10	=	=	SYM
ejpam-5713	201	11	βs(c5r+4	βs(c5r+4	PUNCT
ejpam-5713	201	12	)	)	PUNCT
ejpam-5713	202	1	=	=	SYM
ejpam-5713	202	2	3r	3r	NUM
ejpam-5713	202	3	+	+	CCONJ
ejpam-5713	202	4	2	2	NUM
ejpam-5713	202	5	can	can	AUX
ejpam-5713	202	6	be	be	AUX
ejpam-5713	202	7	shown	show	VERB
ejpam-5713	202	8	easily	easily	ADV
ejpam-5713	202	9	.	.	PUNCT
ejpam-5713	203	1	theorem	theorem	VERB
ejpam-5713	203	2	3	3	X
ejpam-5713	203	3	.	.	PUNCT
ejpam-5713	204	1	let	let	VERB
ejpam-5713	204	2	a	a	PRON
ejpam-5713	204	3	and	and	CCONJ
ejpam-5713	204	4	b	b	NOUN
ejpam-5713	204	5	be	be	AUX
ejpam-5713	204	6	positive	positive	ADJ
ejpam-5713	204	7	integers	integer	NOUN
ejpam-5713	204	8	such	such	ADJ
ejpam-5713	204	9	that	that	SCONJ
ejpam-5713	204	10	1	1	NUM
ejpam-5713	204	11	≤	≤	NUM
ejpam-5713	204	12	a	a	DET
ejpam-5713	204	13	≤	≤	PROPN
ejpam-5713	204	14	b.	b.	NOUN
ejpam-5713	205	1	then	then	ADV
ejpam-5713	205	2	there	there	PRON
ejpam-5713	205	3	exists	exist	VERB
ejpam-5713	205	4	a	a	DET
ejpam-5713	205	5	connected	connected	ADJ
ejpam-5713	205	6	graph	graph	NOUN
ejpam-5713	205	7	g	g	ADP
ejpam-5713	205	8	such	such	ADJ
ejpam-5713	205	9	that	that	PRON
ejpam-5713	205	10	β(g	β(g	PROPN
ejpam-5713	205	11	)	)	PUNCT
ejpam-5713	205	12	=	=	SYM
ejpam-5713	205	13	a	a	PRON
ejpam-5713	205	14	and	and	CCONJ
ejpam-5713	205	15	βs(g	βs(g	PUNCT
ejpam-5713	205	16	)	)	PUNCT
ejpam-5713	205	17	=	=	SYM
ejpam-5713	205	18	b.	b.	PROPN
ejpam-5713	205	19	s.	s.	PROPN
ejpam-5713	205	20	r.	r.	PROPN
ejpam-5713	205	21	canoy	canoy	PROPN
ejpam-5713	205	22	et	et	PROPN
ejpam-5713	205	23	al	al	PROPN
ejpam-5713	205	24	.	.	PUNCT
ejpam-5713	205	25	/	/	SYM
ejpam-5713	205	26	eur	eur	PROPN
ejpam-5713	205	27	.	.	PUNCT
ejpam-5713	206	1	j.	j.	PROPN
ejpam-5713	206	2	pure	pure	PROPN
ejpam-5713	206	3	appl	appl	PROPN
ejpam-5713	206	4	.	.	PROPN
ejpam-5713	206	5	math	math	PROPN
ejpam-5713	206	6	,	,	PUNCT
ejpam-5713	206	7	18	18	NUM
ejpam-5713	206	8	(	(	PUNCT
ejpam-5713	206	9	1	1	NUM
ejpam-5713	206	10	)	)	PUNCT
ejpam-5713	206	11	(	(	PUNCT
ejpam-5713	206	12	2025	2025	NUM
ejpam-5713	206	13	)	)	PUNCT
ejpam-5713	206	14	,	,	PUNCT
ejpam-5713	206	15	5713	5713	NUM
ejpam-5713	206	16	7	7	NUM
ejpam-5713	206	17	of	of	ADP
ejpam-5713	206	18	13	13	NUM
ejpam-5713	206	19	proof	proof	NOUN
ejpam-5713	206	20	.	.	PUNCT
ejpam-5713	207	1	if	if	SCONJ
ejpam-5713	207	2	a	a	DET
ejpam-5713	207	3	=	=	SYM
ejpam-5713	207	4	b	b	NOUN
ejpam-5713	207	5	,	,	PUNCT
ejpam-5713	207	6	then	then	ADV
ejpam-5713	207	7	considerg	considerg	PROPN
ejpam-5713	207	8	=	=	SYM
ejpam-5713	207	9	ka+1	ka+1	PROPN
ejpam-5713	207	10	.	.	PUNCT
ejpam-5713	207	11	clearly	clearly	ADV
ejpam-5713	207	12	,	,	PUNCT
ejpam-5713	207	13	β(g	β(g	PROPN
ejpam-5713	207	14	)	)	PUNCT
ejpam-5713	207	15	=	=	PUNCT
ejpam-5713	208	1	a.	a.	NOUN
ejpam-5713	208	2	by	by	ADP
ejpam-5713	208	3	theorem	theorem	NOUN
ejpam-5713	208	4	1	1	NUM
ejpam-5713	208	5	,	,	PUNCT
ejpam-5713	208	6	βs(g	βs(g	PUNCT
ejpam-5713	208	7	)	)	PUNCT
ejpam-5713	208	8	=	=	PUNCT
ejpam-5713	208	9	a.	a.	NOUN
ejpam-5713	208	10	next	next	ADV
ejpam-5713	208	11	,	,	PUNCT
ejpam-5713	208	12	suppose	suppose	VERB
ejpam-5713	208	13	a	a	DET
ejpam-5713	208	14	<	<	X
ejpam-5713	208	15	b	b	NOUN
ejpam-5713	208	16	and	and	CCONJ
ejpam-5713	208	17	let	let	VERB
ejpam-5713	208	18	m	m	PROPN
ejpam-5713	208	19	=	=	VERB
ejpam-5713	208	20	b−a	b−a	NOUN
ejpam-5713	208	21	.	.	PUNCT
ejpam-5713	209	1	let	let	VERB
ejpam-5713	209	2	g	g	NOUN
ejpam-5713	209	3	be	be	AUX
ejpam-5713	209	4	the	the	DET
ejpam-5713	209	5	graph	graph	NOUN
ejpam-5713	209	6	obtained	obtain	VERB
ejpam-5713	209	7	from	from	ADP
ejpam-5713	209	8	ka+1	ka+1	PROPN
ejpam-5713	209	9	by	by	ADP
ejpam-5713	209	10	adding	add	VERB
ejpam-5713	209	11	m	m	PRON
ejpam-5713	209	12	pendant	pendant	ADJ
ejpam-5713	209	13	edges	edge	NOUN
ejpam-5713	209	14	v1x1	v1x1	NOUN
ejpam-5713	209	15	,	,	PUNCT
ejpam-5713	209	16	v1x2	v1x2	NOUN
ejpam-5713	209	17	,	,	PUNCT
ejpam-5713	209	18	.	.	PUNCT
ejpam-5713	209	19	.	.	PUNCT
ejpam-5713	210	1	.	.	PUNCT
ejpam-5713	211	1	,	,	PUNCT
ejpam-5713	211	2	v1xm	v1xm	PROPN
ejpam-5713	211	3	,	,	PUNCT
ejpam-5713	211	4	where	where	SCONJ
ejpam-5713	211	5	v	v	X
ejpam-5713	211	6	(	(	PUNCT
ejpam-5713	211	7	ka+1	ka+1	PROPN
ejpam-5713	211	8	)	)	PUNCT
ejpam-5713	211	9	=	=	NOUN
ejpam-5713	211	10	{	{	PUNCT
ejpam-5713	211	11	v1	v1	PROPN
ejpam-5713	211	12	,	,	PUNCT
ejpam-5713	211	13	v2	v2	PROPN
ejpam-5713	211	14	,	,	PUNCT
ejpam-5713	211	15	·	·	PUNCT
ejpam-5713	211	16	·	·	PUNCT
ejpam-5713	211	17	·	·	PUNCT
ejpam-5713	211	18	,	,	PUNCT
ejpam-5713	211	19	va	va	NOUN
ejpam-5713	211	20	,	,	PUNCT
ejpam-5713	211	21	va+1	va+1	ADJ
ejpam-5713	211	22	}	}	PUNCT
ejpam-5713	211	23	(	(	PUNCT
ejpam-5713	211	24	see	see	VERB
ejpam-5713	211	25	figure	figure	NOUN
ejpam-5713	211	26	2	2	NUM
ejpam-5713	211	27	)	)	PUNCT
ejpam-5713	211	28	.	.	PUNCT
ejpam-5713	212	1	clearly	clearly	ADV
ejpam-5713	212	2	,	,	PUNCT
ejpam-5713	212	3	s1	s1	PROPN
ejpam-5713	212	4	=	=	PUNCT
ejpam-5713	212	5	{	{	PUNCT
ejpam-5713	212	6	v1	v1	PROPN
ejpam-5713	212	7	,	,	PUNCT
ejpam-5713	212	8	v2	v2	PROPN
ejpam-5713	212	9	,	,	PUNCT
ejpam-5713	212	10	·	·	PUNCT
ejpam-5713	212	11	·	·	PUNCT
ejpam-5713	212	12	·	·	PUNCT
ejpam-5713	212	13	,	,	PUNCT
ejpam-5713	212	14	va	va	NOUN
ejpam-5713	212	15	}	}	PUNCT
ejpam-5713	212	16	is	be	AUX
ejpam-5713	212	17	a	a	DET
ejpam-5713	212	18	vertex	vertex	NOUN
ejpam-5713	212	19	cover	cover	NOUN
ejpam-5713	212	20	of	of	ADP
ejpam-5713	212	21	g.	g.	PROPN
ejpam-5713	212	22	hence	hence	ADV
ejpam-5713	212	23	,	,	PUNCT
ejpam-5713	212	24	β(g	β(g	PROPN
ejpam-5713	212	25	)	)	PUNCT
ejpam-5713	212	26	≤	≤	NUM
ejpam-5713	212	27	|s1|	|s1|	NOUN
ejpam-5713	212	28	=	=	PUNCT
ejpam-5713	212	29	a.	a.	NOUN
ejpam-5713	212	30	let	let	VERB
ejpam-5713	212	31	s	s	PRON
ejpam-5713	212	32	be	be	AUX
ejpam-5713	212	33	a	a	DET
ejpam-5713	212	34	β	β	NOUN
ejpam-5713	212	35	-	-	VERB
ejpam-5713	212	36	set	set	VERB
ejpam-5713	212	37	in	in	ADP
ejpam-5713	212	38	g.	g.	PROPN
ejpam-5713	212	39	if	if	SCONJ
ejpam-5713	212	40	v1	v1	PROPN
ejpam-5713	212	41	/∈	/∈	PUNCT
ejpam-5713	213	1	s	s	X
ejpam-5713	213	2	,	,	PUNCT
ejpam-5713	213	3	then	then	ADV
ejpam-5713	213	4	{	{	PUNCT
ejpam-5713	213	5	v2	v2	PROPN
ejpam-5713	213	6	,	,	PUNCT
ejpam-5713	213	7	v3	v3	PROPN
ejpam-5713	213	8	,	,	PUNCT
ejpam-5713	213	9	·	·	PUNCT
ejpam-5713	213	10	·	·	PUNCT
ejpam-5713	213	11	·	·	PUNCT
ejpam-5713	213	12	,	,	PUNCT
ejpam-5713	213	13	va+1	va+1	X
ejpam-5713	213	14	}	}	PUNCT
ejpam-5713	213	15	⊆	⊆	NUM
ejpam-5713	213	16	s	s	NOUN
ejpam-5713	213	17	since	since	SCONJ
ejpam-5713	213	18	s	s	NOUN
ejpam-5713	213	19	is	be	AUX
ejpam-5713	213	20	a	a	DET
ejpam-5713	213	21	vertex	vertex	NOUN
ejpam-5713	213	22	cover	cover	NOUN
ejpam-5713	213	23	of	of	ADP
ejpam-5713	213	24	g.	g.	PROPN
ejpam-5713	213	25	again	again	ADV
ejpam-5713	213	26	,	,	PUNCT
ejpam-5713	213	27	since	since	SCONJ
ejpam-5713	213	28	s	s	NOUN
ejpam-5713	213	29	is	be	AUX
ejpam-5713	213	30	a	a	DET
ejpam-5713	213	31	vertex	vertex	NOUN
ejpam-5713	213	32	cover	cover	NOUN
ejpam-5713	213	33	of	of	ADP
ejpam-5713	213	34	g	g	NOUN
ejpam-5713	213	35	,	,	PUNCT
ejpam-5713	213	36	it	it	PRON
ejpam-5713	213	37	follows	follow	VERB
ejpam-5713	213	38	that	that	SCONJ
ejpam-5713	213	39	{	{	PUNCT
ejpam-5713	213	40	x1	x1	ADJ
ejpam-5713	213	41	,	,	PUNCT
ejpam-5713	213	42	x2	x2	PROPN
ejpam-5713	213	43	,	,	PUNCT
ejpam-5713	213	44	·	·	PUNCT
ejpam-5713	213	45	·	·	PUNCT
ejpam-5713	213	46	·	·	PUNCT
ejpam-5713	213	47	,	,	PUNCT
ejpam-5713	213	48	xm	xm	X
ejpam-5713	213	49	}	}	PUNCT
ejpam-5713	213	50	⊆	⊆	NUM
ejpam-5713	213	51	s.	s.	PROPN
ejpam-5713	213	52	thus	thus	ADV
ejpam-5713	213	53	,	,	PUNCT
ejpam-5713	213	54	s	s	VERB
ejpam-5713	213	55	=	=	PUNCT
ejpam-5713	213	56	{	{	PUNCT
ejpam-5713	213	57	x1	x1	PROPN
ejpam-5713	213	58	,	,	PUNCT
ejpam-5713	213	59	x2	x2	PROPN
ejpam-5713	213	60	,	,	PUNCT
ejpam-5713	213	61	·	·	PUNCT
ejpam-5713	213	62	·	·	PUNCT
ejpam-5713	213	63	·	·	PUNCT
ejpam-5713	213	64	,	,	PUNCT
ejpam-5713	213	65	xm	xm	PROPN
ejpam-5713	213	66	,	,	PUNCT
ejpam-5713	213	67	v2	v2	PROPN
ejpam-5713	213	68	,	,	PUNCT
ejpam-5713	213	69	v3	v3	PROPN
ejpam-5713	213	70	,	,	PUNCT
ejpam-5713	213	71	·	·	PUNCT
ejpam-5713	213	72	·	·	PUNCT
ejpam-5713	213	73	·	·	PUNCT
ejpam-5713	213	74	,	,	PUNCT
ejpam-5713	213	75	va+1	va+1	ADJ
ejpam-5713	213	76	}	}	PUNCT
ejpam-5713	213	77	.	.	PUNCT
ejpam-5713	214	1	consequently	consequently	ADV
ejpam-5713	214	2	,	,	PUNCT
ejpam-5713	214	3	β(g	β(g	PROPN
ejpam-5713	214	4	)	)	PUNCT
ejpam-5713	214	5	=	=	SYM
ejpam-5713	214	6	|s|	|s|	PROPN
ejpam-5713	214	7	=	=	SYM
ejpam-5713	214	8	m+	m+	NUM
ejpam-5713	214	9	a	a	DET
ejpam-5713	214	10	=	=	NOUN
ejpam-5713	214	11	b−	b−	PROPN
ejpam-5713	214	12	a+	a+	PUNCT
ejpam-5713	214	13	a	a	PRON
ejpam-5713	214	14	=	=	SYM
ejpam-5713	214	15	b	b	PROPN
ejpam-5713	214	16	,	,	PUNCT
ejpam-5713	214	17	which	which	PRON
ejpam-5713	214	18	is	be	AUX
ejpam-5713	214	19	not	not	PART
ejpam-5713	214	20	possible	possible	ADJ
ejpam-5713	214	21	.	.	PUNCT
ejpam-5713	215	1	thus	thus	ADV
ejpam-5713	215	2	,	,	PUNCT
ejpam-5713	215	3	v1	v1	PROPN
ejpam-5713	215	4	∈	∈	PROPN
ejpam-5713	215	5	s.	s.	PROPN
ejpam-5713	215	6	suppose	suppose	VERB
ejpam-5713	215	7	|(v	|(v	PROPN
ejpam-5713	215	8	(	(	PUNCT
ejpam-5713	215	9	ka+1	ka+1	PROPN
ejpam-5713	215	10	)	)	PUNCT
ejpam-5713	215	11	\	\	NOUN
ejpam-5713	215	12	{	{	PUNCT
ejpam-5713	215	13	v1	v1	NOUN
ejpam-5713	215	14	}	}	PUNCT
ejpam-5713	215	15	)	)	PUNCT
ejpam-5713	215	16	∩	∩	NOUN
ejpam-5713	215	17	s|	s|	VERB
ejpam-5713	215	18	<	<	X
ejpam-5713	215	19	a	a	DET
ejpam-5713	215	20	−	−	PROPN
ejpam-5713	215	21	1	1	NUM
ejpam-5713	215	22	.	.	PUNCT
ejpam-5713	216	1	then	then	ADV
ejpam-5713	216	2	there	there	PRON
ejpam-5713	216	3	exist	exist	VERB
ejpam-5713	216	4	r	r	NOUN
ejpam-5713	216	5	,	,	PUNCT
ejpam-5713	216	6	t	t	PROPN
ejpam-5713	216	7	∈	∈	PROPN
ejpam-5713	216	8	{	{	PUNCT
ejpam-5713	216	9	2	2	NUM
ejpam-5713	216	10	,	,	PUNCT
ejpam-5713	216	11	3	3	NUM
ejpam-5713	216	12	,	,	PUNCT
ejpam-5713	216	13	·	·	PUNCT
ejpam-5713	216	14	·	·	PUNCT
ejpam-5713	216	15	·	·	PUNCT
ejpam-5713	216	16	,	,	PUNCT
ejpam-5713	216	17	a	a	DET
ejpam-5713	216	18	+	+	NOUN
ejpam-5713	216	19	1	1	NUM
ejpam-5713	216	20	}	}	PUNCT
ejpam-5713	216	21	such	such	ADJ
ejpam-5713	216	22	that	that	SCONJ
ejpam-5713	216	23	vr	vr	PROPN
ejpam-5713	216	24	,	,	PUNCT
ejpam-5713	216	25	vt	vt	PROPN
ejpam-5713	216	26	/∈	/∈	PUNCT
ejpam-5713	216	27	s.	s.	PROPN
ejpam-5713	217	1	this	this	PRON
ejpam-5713	217	2	,	,	PUNCT
ejpam-5713	217	3	however	however	ADV
ejpam-5713	217	4	,	,	PUNCT
ejpam-5713	217	5	is	be	AUX
ejpam-5713	217	6	not	not	PART
ejpam-5713	217	7	possible	possible	ADJ
ejpam-5713	217	8	because	because	SCONJ
ejpam-5713	217	9	vrvt	vrvt	PROPN
ejpam-5713	217	10	∈	∈	PROPN
ejpam-5713	217	11	e(g	e(g	PROPN
ejpam-5713	217	12	)	)	PUNCT
ejpam-5713	217	13	and	and	CCONJ
ejpam-5713	217	14	s	s	VERB
ejpam-5713	217	15	is	be	AUX
ejpam-5713	217	16	a	a	DET
ejpam-5713	217	17	vertex	vertex	NOUN
ejpam-5713	217	18	cover	cover	NOUN
ejpam-5713	217	19	.	.	PUNCT
ejpam-5713	218	1	therefore	therefore	ADV
ejpam-5713	218	2	,	,	PUNCT
ejpam-5713	218	3	|(v	|(v	PROPN
ejpam-5713	218	4	(	(	PUNCT
ejpam-5713	218	5	ka+1	ka+1	PROPN
ejpam-5713	218	6	)	)	PUNCT
ejpam-5713	218	7	\	\	NOUN
ejpam-5713	218	8	{	{	PUNCT
ejpam-5713	218	9	v1	v1	NOUN
ejpam-5713	218	10	}	}	PUNCT
ejpam-5713	218	11	)	)	PUNCT
ejpam-5713	218	12	∩	∩	NOUN
ejpam-5713	218	13	s|	s|	NOUN
ejpam-5713	218	14	=	=	SYM
ejpam-5713	218	15	a−	a−	PROPN
ejpam-5713	218	16	1	1	NUM
ejpam-5713	218	17	.	.	PUNCT
ejpam-5713	219	1	therefore	therefore	ADV
ejpam-5713	219	2	,	,	PUNCT
ejpam-5713	219	3	since	since	SCONJ
ejpam-5713	219	4	s	s	NOUN
ejpam-5713	219	5	is	be	AUX
ejpam-5713	219	6	a	a	DET
ejpam-5713	219	7	β	β	NOUN
ejpam-5713	219	8	-	-	VERB
ejpam-5713	219	9	set	set	VERB
ejpam-5713	219	10	in	in	ADP
ejpam-5713	219	11	g	g	NOUN
ejpam-5713	219	12	,	,	PUNCT
ejpam-5713	219	13	β(g	β(g	PROPN
ejpam-5713	219	14	)	)	PUNCT
ejpam-5713	220	1	=	=	SYM
ejpam-5713	220	2	|s|	|s|	NOUN
ejpam-5713	220	3	=	=	NOUN
ejpam-5713	220	4	a.	a.	NOUN
ejpam-5713	220	5	now	now	ADV
ejpam-5713	220	6	if	if	SCONJ
ejpam-5713	220	7	m	m	VERB
ejpam-5713	220	8	=	=	NOUN
ejpam-5713	220	9	1	1	NUM
ejpam-5713	220	10	,	,	PUNCT
ejpam-5713	220	11	then	then	ADV
ejpam-5713	220	12	clearly	clearly	ADV
ejpam-5713	220	13	,	,	PUNCT
ejpam-5713	220	14	s2	s2	VERB
ejpam-5713	220	15	=	=	SYM
ejpam-5713	220	16	{	{	PUNCT
ejpam-5713	220	17	v1	v1	PROPN
ejpam-5713	220	18	,	,	PUNCT
ejpam-5713	220	19	v2	v2	PROPN
ejpam-5713	220	20	,	,	PUNCT
ejpam-5713	220	21	·	·	PUNCT
ejpam-5713	220	22	·	·	PUNCT
ejpam-5713	220	23	·	·	PUNCT
ejpam-5713	220	24	,	,	PUNCT
ejpam-5713	220	25	va+1	va+1	X
ejpam-5713	220	26	}	}	PUNCT
ejpam-5713	220	27	is	be	AUX
ejpam-5713	220	28	a	a	DET
ejpam-5713	220	29	βs	βs	NOUN
ejpam-5713	220	30	-	-	PUNCT
ejpam-5713	220	31	set	set	NOUN
ejpam-5713	220	32	in	in	ADP
ejpam-5713	220	33	g.	g.	PROPN
ejpam-5713	220	34	thus	thus	ADV
ejpam-5713	220	35	,	,	PUNCT
ejpam-5713	220	36	βs(g	βs(g	PUNCT
ejpam-5713	220	37	)	)	PUNCT
ejpam-5713	220	38	=	=	SYM
ejpam-5713	221	1	a	a	DET
ejpam-5713	221	2	+	+	NUM
ejpam-5713	221	3	1	1	NUM
ejpam-5713	221	4	=	=	SYM
ejpam-5713	221	5	b.	b.	PROPN
ejpam-5713	221	6	suppose	suppose	VERB
ejpam-5713	221	7	m	m	VERB
ejpam-5713	221	8	≥	≥	PROPN
ejpam-5713	221	9	2	2	NUM
ejpam-5713	221	10	.	.	X
ejpam-5713	221	11	note	note	VERB
ejpam-5713	221	12	that	that	SCONJ
ejpam-5713	221	13	the	the	DET
ejpam-5713	221	14	set	set	NOUN
ejpam-5713	221	15	s3	s3	NOUN
ejpam-5713	221	16	=	=	SYM
ejpam-5713	221	17	{	{	PUNCT
ejpam-5713	221	18	v1	v1	PROPN
ejpam-5713	221	19	,	,	PUNCT
ejpam-5713	221	20	v2	v2	PROPN
ejpam-5713	221	21	,	,	PUNCT
ejpam-5713	221	22	·	·	PUNCT
ejpam-5713	221	23	·	·	PUNCT
ejpam-5713	221	24	·	·	PUNCT
ejpam-5713	221	25	,	,	PUNCT
ejpam-5713	221	26	va+1	va+1	PROPN
ejpam-5713	221	27	,	,	PUNCT
ejpam-5713	221	28	x2	x2	PROPN
ejpam-5713	221	29	,	,	PUNCT
ejpam-5713	221	30	·	·	PUNCT
ejpam-5713	221	31	·	·	PUNCT
ejpam-5713	221	32	·	·	PUNCT
ejpam-5713	221	33	,	,	PUNCT
ejpam-5713	221	34	xm	xm	PROPN
ejpam-5713	221	35	}	}	PUNCT
ejpam-5713	221	36	is	be	AUX
ejpam-5713	221	37	a	a	DET
ejpam-5713	221	38	super	super	ADJ
ejpam-5713	221	39	vertex	vertex	NOUN
ejpam-5713	221	40	cover	cover	NOUN
ejpam-5713	221	41	of	of	ADP
ejpam-5713	221	42	g.	g.	PROPN
ejpam-5713	221	43	it	it	PRON
ejpam-5713	221	44	follows	follow	VERB
ejpam-5713	221	45	that	that	SCONJ
ejpam-5713	221	46	β(g	β(g	PROPN
ejpam-5713	221	47	)	)	PUNCT
ejpam-5713	221	48	≤	≤	NUM
ejpam-5713	221	49	|s3|	|s3|	NOUN
ejpam-5713	221	50	=	=	PUNCT
ejpam-5713	221	51	a	a	DET
ejpam-5713	221	52	+	+	NUM
ejpam-5713	221	53	1	1	NUM
ejpam-5713	221	54	+	+	NUM
ejpam-5713	221	55	m	m	VERB
ejpam-5713	221	56	−	−	NUM
ejpam-5713	222	1	1	1	NUM
ejpam-5713	222	2	=	=	SYM
ejpam-5713	222	3	a	a	DET
ejpam-5713	222	4	+	+	NOUN
ejpam-5713	222	5	m	m	NOUN
ejpam-5713	222	6	=	=	ADJ
ejpam-5713	222	7	b.	b.	PROPN
ejpam-5713	222	8	let	let	VERB
ejpam-5713	222	9	s0	s0	PROPN
ejpam-5713	222	10	be	be	AUX
ejpam-5713	222	11	a	a	DET
ejpam-5713	222	12	βs	βs	NOUN
ejpam-5713	222	13	-	-	PUNCT
ejpam-5713	222	14	set	set	NOUN
ejpam-5713	222	15	in	in	ADP
ejpam-5713	222	16	g.	g.	PROPN
ejpam-5713	222	17	if	if	SCONJ
ejpam-5713	222	18	v1	v1	PROPN
ejpam-5713	222	19	/∈	/∈	PUNCT
ejpam-5713	223	1	s0	s0	PROPN
ejpam-5713	223	2	,	,	PUNCT
ejpam-5713	223	3	then	then	ADV
ejpam-5713	223	4	s0	s0	PROPN
ejpam-5713	223	5	=	=	PUNCT
ejpam-5713	223	6	{	{	PUNCT
ejpam-5713	223	7	v2	v2	PROPN
ejpam-5713	223	8	,	,	PUNCT
ejpam-5713	223	9	·	·	PUNCT
ejpam-5713	223	10	·	·	PUNCT
ejpam-5713	223	11	·	·	PUNCT
ejpam-5713	223	12	,	,	PUNCT
ejpam-5713	223	13	va+1	va+1	PROPN
ejpam-5713	223	14	,	,	PUNCT
ejpam-5713	223	15	x1	x1	PROPN
ejpam-5713	223	16	,	,	PUNCT
ejpam-5713	223	17	x2	x2	PROPN
ejpam-5713	223	18	,	,	PUNCT
ejpam-5713	223	19	·	·	PUNCT
ejpam-5713	223	20	·	·	PUNCT
ejpam-5713	223	21	·	·	PUNCT
ejpam-5713	223	22	,	,	PUNCT
ejpam-5713	223	23	xm	xm	PROPN
ejpam-5713	223	24	}	}	PUNCT
ejpam-5713	223	25	because	because	SCONJ
ejpam-5713	223	26	s0	s0	PROPN
ejpam-5713	223	27	is	be	AUX
ejpam-5713	223	28	a	a	DET
ejpam-5713	223	29	vertex	vertex	NOUN
ejpam-5713	223	30	cover	cover	NOUN
ejpam-5713	223	31	of	of	ADP
ejpam-5713	223	32	g.	g.	PROPN
ejpam-5713	223	33	thus	thus	ADV
ejpam-5713	223	34	,	,	PUNCT
ejpam-5713	223	35	β(g	β(g	PROPN
ejpam-5713	223	36	)	)	PUNCT
ejpam-5713	223	37	=	=	SYM
ejpam-5713	223	38	|s|	|s|	PROPN
ejpam-5713	223	39	=	=	SYM
ejpam-5713	223	40	m+	m+	NUM
ejpam-5713	223	41	a	a	DET
ejpam-5713	223	42	=	=	NOUN
ejpam-5713	223	43	b−	b−	PROPN
ejpam-5713	223	44	a+	a+	PUNCT
ejpam-5713	223	45	a	a	PRON
ejpam-5713	223	46	=	=	X
ejpam-5713	223	47	b.	b.	PROPN
ejpam-5713	223	48	suppose	suppose	VERB
ejpam-5713	223	49	v1	v1	PROPN
ejpam-5713	223	50	∈	∈	PROPN
ejpam-5713	223	51	s.	s.	PROPN
ejpam-5713	223	52	since	since	SCONJ
ejpam-5713	223	53	s	s	PROPN
ejpam-5713	223	54	is	be	AUX
ejpam-5713	223	55	a	a	DET
ejpam-5713	223	56	vertex	vertex	NOUN
ejpam-5713	223	57	cover	cover	NOUN
ejpam-5713	223	58	,	,	PUNCT
ejpam-5713	223	59	|v	|v	PROPN
ejpam-5713	223	60	(	(	PUNCT
ejpam-5713	223	61	ka+1	ka+1	PROPN
ejpam-5713	223	62	)	)	PUNCT
ejpam-5713	223	63	\	\	PROPN
ejpam-5713	224	1	s|	s|	VERB
ejpam-5713	224	2	≤	≤	NUM
ejpam-5713	224	3	1	1	NUM
ejpam-5713	224	4	.	.	PUNCT
ejpam-5713	225	1	if	if	SCONJ
ejpam-5713	225	2	|v	|v	PROPN
ejpam-5713	225	3	(	(	PUNCT
ejpam-5713	225	4	ka+1	ka+1	PROPN
ejpam-5713	225	5	)	)	PUNCT
ejpam-5713	225	6	\	\	NOUN
ejpam-5713	225	7	s|	s|	NOUN
ejpam-5713	225	8	=	=	SYM
ejpam-5713	225	9	0	0	NUM
ejpam-5713	225	10	,	,	PUNCT
ejpam-5713	225	11	then	then	ADV
ejpam-5713	225	12	|s	|s	PROPN
ejpam-5713	225	13	∩	∩	NOUN
ejpam-5713	225	14	{	{	PUNCT
ejpam-5713	225	15	x1	x1	PROPN
ejpam-5713	225	16	,	,	PUNCT
ejpam-5713	225	17	x2	x2	PROPN
ejpam-5713	225	18	,	,	PUNCT
ejpam-5713	225	19	·	·	PUNCT
ejpam-5713	225	20	·	·	PUNCT
ejpam-5713	225	21	·	·	PUNCT
ejpam-5713	225	22	,	,	PUNCT
ejpam-5713	225	23	xm}|	xm}|	NUM
ejpam-5713	226	1	=	=	SYM
ejpam-5713	226	2	m−	m−	PROPN
ejpam-5713	226	3	1	1	NUM
ejpam-5713	226	4	because	because	SCONJ
ejpam-5713	226	5	s	s	NOUN
ejpam-5713	226	6	is	be	AUX
ejpam-5713	226	7	a	a	DET
ejpam-5713	226	8	super	super	ADJ
ejpam-5713	226	9	dominating	dominating	NOUN
ejpam-5713	226	10	set	set	VERB
ejpam-5713	226	11	in	in	ADP
ejpam-5713	226	12	g.	g.	PROPN
ejpam-5713	226	13	again	again	ADV
ejpam-5713	226	14	,	,	PUNCT
ejpam-5713	226	15	since	since	SCONJ
ejpam-5713	226	16	s	s	NOUN
ejpam-5713	226	17	is	be	AUX
ejpam-5713	226	18	a	a	DET
ejpam-5713	226	19	super	super	ADJ
ejpam-5713	226	20	dominating	dominating	NOUN
ejpam-5713	226	21	set	set	NOUN
ejpam-5713	226	22	,	,	PUNCT
ejpam-5713	226	23	|s	|s	PROPN
ejpam-5713	226	24	∩	∩	NOUN
ejpam-5713	226	25	{	{	PUNCT
ejpam-5713	226	26	x1	x1	PROPN
ejpam-5713	226	27	,	,	PUNCT
ejpam-5713	226	28	x2	x2	PROPN
ejpam-5713	226	29	,	,	PUNCT
ejpam-5713	226	30	·	·	PUNCT
ejpam-5713	226	31	·	·	PUNCT
ejpam-5713	226	32	·	·	PUNCT
ejpam-5713	226	33	,	,	PUNCT
ejpam-5713	226	34	xm}|	xm}|	X
ejpam-5713	227	1	=	=	NOUN
ejpam-5713	227	2	m	m	VERB
ejpam-5713	227	3	whenever	whenever	SCONJ
ejpam-5713	227	4	|v	|v	PROPN
ejpam-5713	227	5	(	(	PUNCT
ejpam-5713	227	6	ka+1	ka+1	PROPN
ejpam-5713	227	7	)	)	PUNCT
ejpam-5713	227	8	\	\	NOUN
ejpam-5713	227	9	s|	s|	NOUN
ejpam-5713	227	10	=	=	SYM
ejpam-5713	227	11	1	1	X
ejpam-5713	227	12	.	.	PUNCT
ejpam-5713	227	13	in	in	ADP
ejpam-5713	227	14	both	both	DET
ejpam-5713	227	15	cases	case	NOUN
ejpam-5713	227	16	,	,	PUNCT
ejpam-5713	227	17	we	we	PRON
ejpam-5713	227	18	have	have	VERB
ejpam-5713	227	19	βs(g	βs(g	PUNCT
ejpam-5713	227	20	)	)	PUNCT
ejpam-5713	227	21	=	=	SYM
ejpam-5713	227	22	|s0|	|s0|	NOUN
ejpam-5713	227	23	=	=	PROPN
ejpam-5713	227	24	b.	b.	PROPN
ejpam-5713	227	25	............	............	PUNCT
ejpam-5713	227	26	...........	...........	PUNCT
ejpam-5713	227	27	...........	...........	PUNCT
ejpam-5713	227	28	...........	...........	PUNCT
ejpam-5713	227	29	...........	...........	PUNCT
ejpam-5713	227	30	...........	...........	PUNCT
ejpam-5713	227	31	...........	...........	PUNCT
ejpam-5713	227	32	...........	...........	PUNCT
ejpam-5713	227	33	...........	...........	PUNCT
ejpam-5713	227	34	...........	...........	PUNCT
ejpam-5713	227	35	....................................	....................................	PUNCT
ejpam-5713	227	36	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5713	227	37	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-5713	228	1	....................................	....................................	PUNCT
ejpam-5713	228	2	...................................................................................................................................................	...................................................................................................................................................	PUNCT
ejpam-5713	229	1	....................................	....................................	PUNCT
ejpam-5713	229	2	....................................	....................................	PUNCT
ejpam-5713	229	3	............	............	PUNCT
ejpam-5713	229	4	...........	...........	PUNCT
ejpam-5713	230	1	...........	...........	PUNCT
ejpam-5713	230	2	...........	...........	PUNCT
ejpam-5713	230	3	...........	...........	PUNCT
ejpam-5713	230	4	...........	...........	PUNCT
ejpam-5713	230	5	...........	...........	PUNCT
ejpam-5713	230	6	...........	...........	PUNCT
ejpam-5713	230	7	...........	...........	PUNCT
ejpam-5713	230	8	...........	...........	PUNCT
ejpam-5713	230	9	....................................	....................................	PUNCT
ejpam-5713	230	10	....................................	....................................	PUNCT
ejpam-5713	230	11	.....................	.....................	PUNCT
ejpam-5713	230	12	....................	....................	PUNCT
ejpam-5713	230	13	....................	....................	PUNCT
ejpam-5713	230	14	....................	....................	PUNCT
ejpam-5713	230	15	....................	....................	PUNCT
ejpam-5713	230	16	....................	....................	PUNCT
ejpam-5713	230	17	....................	....................	PUNCT
ejpam-5713	230	18	....................	....................	PUNCT
ejpam-5713	230	19	....................	....................	PUNCT
ejpam-5713	230	20	....................	....................	PUNCT
ejpam-5713	230	21	........	........	PUNCT
ejpam-5713	231	1	....................................	....................................	PUNCT
ejpam-5713	231	2	....................................	....................................	PUNCT
ejpam-5713	232	1	.........................................................................................................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-5713	232	2	.....................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................	PUNCT
ejpam-5713	232	3	....................................	....................................	PUNCT
ejpam-5713	232	4	....................................	....................................	PUNCT
ejpam-5713	233	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5713	233	2	.....................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................	PUNCT
ejpam-5713	234	1	....................................	....................................	PUNCT
ejpam-5713	234	2	....................................	....................................	PUNCT
ejpam-5713	235	1	.....................................................................................................................................................................................................	.....................................................................................................................................................................................................	PUNCT
ejpam-5713	235	2	....................................	....................................	PUNCT
ejpam-5713	235	3	................................................................................................................................................................................	................................................................................................................................................................................	PUNCT
ejpam-5713	235	4	....................................	....................................	PUNCT
ejpam-5713	236	1	.........	.........	PUNCT
ejpam-5713	236	2	........	........	PUNCT
ejpam-5713	236	3	........	........	PUNCT
ejpam-5713	236	4	........	........	PUNCT
ejpam-5713	236	5	........	........	PUNCT
ejpam-5713	236	6	........	........	PUNCT
ejpam-5713	236	7	........	........	PUNCT
ejpam-5713	236	8	........	........	PUNCT
ejpam-5713	236	9	........	........	PUNCT
ejpam-5713	236	10	........	........	PUNCT
ejpam-5713	236	11	........	........	PUNCT
ejpam-5713	236	12	........	........	PUNCT
ejpam-5713	236	13	........	........	PUNCT
ejpam-5713	236	14	........	........	PUNCT
ejpam-5713	236	15	........	........	PUNCT
ejpam-5713	236	16	........	........	PUNCT
ejpam-5713	236	17	........	........	PUNCT
ejpam-5713	236	18	........	........	PUNCT
ejpam-5713	236	19	........	........	PUNCT
ejpam-5713	236	20	........	........	PUNCT
ejpam-5713	236	21	.	.	PUNCT
ejpam-5713	237	1	....................................	....................................	PUNCT
ejpam-5713	237	2	....................................	....................................	PUNCT
ejpam-5713	238	1	...........	...........	PUNCT
ejpam-5713	238	2	..........	..........	PUNCT
ejpam-5713	239	1	..........	..........	PUNCT
ejpam-5713	239	2	..........	..........	PUNCT
ejpam-5713	240	1	..........	..........	PUNCT
ejpam-5713	240	2	..........	..........	PUNCT
ejpam-5713	241	1	..........	..........	PUNCT
ejpam-5713	241	2	..........	..........	PUNCT
ejpam-5713	242	1	..........	..........	PUNCT
ejpam-5713	242	2	..........	..........	PUNCT
ejpam-5713	243	1	..........	..........	PUNCT
ejpam-5713	243	2	..........	..........	PUNCT
ejpam-5713	244	1	..........	..........	PUNCT
ejpam-5713	244	2	..........	..........	PUNCT
ejpam-5713	245	1	..........	..........	PUNCT
ejpam-5713	245	2	..........	..........	PUNCT
ejpam-5713	246	1	..........	..........	PUNCT
ejpam-5713	246	2	..........	..........	PUNCT
ejpam-5713	247	1	..........	..........	PUNCT
ejpam-5713	247	2	......	......	PUNCT
ejpam-5713	248	1	....................................	....................................	PUNCT
ejpam-5713	248	2	....................................	....................................	PUNCT
ejpam-5713	249	1	.....................	.....................	PUNCT
ejpam-5713	249	2	....................	....................	PUNCT
ejpam-5713	249	3	....................	....................	PUNCT
ejpam-5713	249	4	....................	....................	PUNCT
ejpam-5713	249	5	....................	....................	PUNCT
ejpam-5713	249	6	....................	....................	PUNCT
ejpam-5713	249	7	....................	....................	PUNCT
ejpam-5713	249	8	....................	....................	PUNCT
ejpam-5713	249	9	....................	....................	PUNCT
ejpam-5713	249	10	....................	....................	PUNCT
ejpam-5713	249	11	........	........	PUNCT
ejpam-5713	250	1	....................................	....................................	PUNCT
ejpam-5713	250	2	....................................	....................................	PUNCT
ejpam-5713	250	3	.........	.........	PUNCT
ejpam-5713	250	4	........	........	PUNCT
ejpam-5713	250	5	........	........	PUNCT
ejpam-5713	250	6	........	........	PUNCT
ejpam-5713	250	7	........	........	PUNCT
ejpam-5713	250	8	........	........	PUNCT
ejpam-5713	250	9	........	........	PUNCT
ejpam-5713	250	10	........	........	PUNCT
ejpam-5713	250	11	........	........	PUNCT
ejpam-5713	250	12	........	........	PUNCT
ejpam-5713	250	13	........	........	PUNCT
ejpam-5713	250	14	........	........	PUNCT
ejpam-5713	250	15	........	........	PUNCT
ejpam-5713	250	16	........	........	PUNCT
ejpam-5713	250	17	........	........	PUNCT
ejpam-5713	250	18	........	........	PUNCT
ejpam-5713	250	19	........	........	PUNCT
ejpam-5713	250	20	........	........	PUNCT
ejpam-5713	250	21	........	........	PUNCT
ejpam-5713	250	22	........	........	PUNCT
ejpam-5713	250	23	.	.	PUNCT
ejpam-5713	251	1	....................................	....................................	PUNCT
ejpam-5713	251	2	....................................	....................................	PUNCT
ejpam-5713	252	1	..........	..........	PUNCT
ejpam-5713	252	2	.........	.........	PUNCT
ejpam-5713	253	1	.........	.........	PUNCT
ejpam-5713	253	2	.........	.........	PUNCT
ejpam-5713	254	1	.........	.........	PUNCT
ejpam-5713	254	2	.........	.........	PUNCT
ejpam-5713	255	1	.........	.........	PUNCT
ejpam-5713	255	2	.........	.........	PUNCT
ejpam-5713	256	1	.........	.........	PUNCT
ejpam-5713	256	2	.........	.........	PUNCT
ejpam-5713	257	1	.........	.........	PUNCT
ejpam-5713	257	2	.........	.........	PUNCT
ejpam-5713	258	1	.........	.........	PUNCT
ejpam-5713	258	2	....................................	....................................	PUNCT
ejpam-5713	259	1	....................................	....................................	PUNCT
ejpam-5713	259	2	..............	..............	PUNCT
ejpam-5713	259	3	.............	.............	PUNCT
ejpam-5713	259	4	.............	.............	PUNCT
ejpam-5713	259	5	.............	.............	PUNCT
ejpam-5713	260	1	.........	.........	PUNCT
ejpam-5713	260	2	....................................	....................................	PUNCT
ejpam-5713	261	1	....................................	....................................	PUNCT
ejpam-5713	261	2	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-5713	262	1	....................................	....................................	PUNCT
ejpam-5713	262	2	.....................................	.....................................	PUNCT
ejpam-5713	262	3	.	.	PUNCT
ejpam-5713	262	4	.	.	PUNCT
ejpam-5713	263	1	v1	v1	PROPN
ejpam-5713	263	2	v2v3	v2v3	NUM
ejpam-5713	263	3	v4	v4	PROPN
ejpam-5713	263	4	v5	v5	PROPN
ejpam-5713	263	5	va+1	va+1	PROPN
ejpam-5713	263	6	...	...	PUNCT
ejpam-5713	264	1	x1	x1	NUM
ejpam-5713	265	1	x2	x2	NOUN
ejpam-5713	265	2	xm	xm	PROPN
ejpam-5713	265	3	figure	figure	NOUN
ejpam-5713	265	4	2	2	NUM
ejpam-5713	265	5	therefore	therefore	ADV
ejpam-5713	265	6	,	,	PUNCT
ejpam-5713	265	7	the	the	DET
ejpam-5713	265	8	assertion	assertion	NOUN
ejpam-5713	265	9	holds	hold	VERB
ejpam-5713	265	10	.	.	PUNCT
ejpam-5713	266	1	the	the	DET
ejpam-5713	266	2	next	next	ADJ
ejpam-5713	266	3	result	result	NOUN
ejpam-5713	266	4	is	be	AUX
ejpam-5713	266	5	a	a	DET
ejpam-5713	266	6	consequence	consequence	NOUN
ejpam-5713	266	7	of	of	ADP
ejpam-5713	266	8	theorem	theorem	ADJ
ejpam-5713	266	9	3	3	NUM
ejpam-5713	266	10	.	.	PUNCT
ejpam-5713	266	11	corollary	corollary	ADJ
ejpam-5713	266	12	2	2	NUM
ejpam-5713	266	13	.	.	PUNCT
ejpam-5713	267	1	let	let	VERB
ejpam-5713	267	2	n	n	PRON
ejpam-5713	267	3	be	be	AUX
ejpam-5713	267	4	a	a	DET
ejpam-5713	267	5	positive	positive	ADJ
ejpam-5713	267	6	integer	integer	NOUN
ejpam-5713	267	7	.	.	PUNCT
ejpam-5713	268	1	then	then	ADV
ejpam-5713	268	2	there	there	PRON
ejpam-5713	268	3	exists	exist	VERB
ejpam-5713	268	4	a	a	DET
ejpam-5713	268	5	connected	connected	ADJ
ejpam-5713	268	6	graph	graph	NOUN
ejpam-5713	268	7	g	g	ADP
ejpam-5713	268	8	such	such	ADJ
ejpam-5713	268	9	that	that	PRON
ejpam-5713	268	10	βs(g	βs(g	PUNCT
ejpam-5713	268	11	)	)	PUNCT
ejpam-5713	268	12	−	−	ADP
ejpam-5713	269	1	β(g	β(g	PROPN
ejpam-5713	269	2	)	)	PUNCT
ejpam-5713	269	3	=	=	VERB
ejpam-5713	270	1	n.	n.	NOUN
ejpam-5713	270	2	in	in	ADP
ejpam-5713	270	3	other	other	ADJ
ejpam-5713	270	4	words	word	NOUN
ejpam-5713	270	5	,	,	PUNCT
ejpam-5713	270	6	the	the	DET
ejpam-5713	270	7	difference	difference	NOUN
ejpam-5713	270	8	βs(g	βs(g	PUNCT
ejpam-5713	270	9	)	)	PUNCT
ejpam-5713	270	10	−	−	ADP
ejpam-5713	271	1	β(g	β(g	PROPN
ejpam-5713	271	2	)	)	PUNCT
ejpam-5713	271	3	can	can	AUX
ejpam-5713	271	4	be	be	AUX
ejpam-5713	271	5	made	make	VERB
ejpam-5713	271	6	arbitrarily	arbitrarily	ADV
ejpam-5713	271	7	large	large	ADJ
ejpam-5713	271	8	.	.	PUNCT
ejpam-5713	272	1	theorem	theorem	ADJ
ejpam-5713	272	2	4	4	NUM
ejpam-5713	272	3	.	.	PUNCT
ejpam-5713	273	1	let	let	VERB
ejpam-5713	273	2	g	g	NOUN
ejpam-5713	274	1	and	and	CCONJ
ejpam-5713	274	2	h	h	NOUN
ejpam-5713	274	3	be	be	VERB
ejpam-5713	274	4	any	any	DET
ejpam-5713	274	5	graphs	graph	NOUN
ejpam-5713	274	6	.	.	PUNCT
ejpam-5713	275	1	a	a	DET
ejpam-5713	275	2	set	set	NOUN
ejpam-5713	275	3	c	c	NOUN
ejpam-5713	275	4	⊆	⊆	NUM
ejpam-5713	275	5	v	v	NOUN
ejpam-5713	275	6	(	(	PUNCT
ejpam-5713	275	7	g	g	PROPN
ejpam-5713	275	8	+	+	NOUN
ejpam-5713	275	9	h	h	NOUN
ejpam-5713	275	10	)	)	PUNCT
ejpam-5713	275	11	is	be	AUX
ejpam-5713	275	12	a	a	DET
ejpam-5713	275	13	super	super	ADJ
ejpam-5713	275	14	vertex	vertex	NOUN
ejpam-5713	275	15	cover	cover	NOUN
ejpam-5713	275	16	of	of	ADP
ejpam-5713	275	17	g+h	g+h	PROPN
ejpam-5713	276	1	if	if	SCONJ
ejpam-5713	276	2	and	and	CCONJ
ejpam-5713	276	3	only	only	ADV
ejpam-5713	276	4	if	if	SCONJ
ejpam-5713	276	5	c	c	NOUN
ejpam-5713	276	6	=	=	NOUN
ejpam-5713	276	7	cg	cg	NOUN
ejpam-5713	276	8	∪	∪	NOUN
ejpam-5713	276	9	ch	ch	NOUN
ejpam-5713	276	10	and	and	CCONJ
ejpam-5713	276	11	satisfies	satisfy	VERB
ejpam-5713	276	12	one	one	NUM
ejpam-5713	276	13	of	of	ADP
ejpam-5713	276	14	the	the	DET
ejpam-5713	276	15	following	following	ADJ
ejpam-5713	276	16	conditions	condition	NOUN
ejpam-5713	276	17	:	:	PUNCT
ejpam-5713	276	18	(	(	PUNCT
ejpam-5713	276	19	i	i	NOUN
ejpam-5713	276	20	)	)	PUNCT
ejpam-5713	276	21	cg	cg	NOUN
ejpam-5713	276	22	=	=	SYM
ejpam-5713	276	23	v	v	PROPN
ejpam-5713	276	24	(	(	PUNCT
ejpam-5713	276	25	g	g	NOUN
ejpam-5713	276	26	)	)	PUNCT
ejpam-5713	276	27	and	and	CCONJ
ejpam-5713	276	28	ch	ch	NOUN
ejpam-5713	276	29	is	be	AUX
ejpam-5713	276	30	a	a	DET
ejpam-5713	276	31	super	super	ADJ
ejpam-5713	276	32	vertex	vertex	NOUN
ejpam-5713	276	33	cover	cover	NOUN
ejpam-5713	276	34	of	of	ADP
ejpam-5713	276	35	h.	h.	PROPN
ejpam-5713	276	36	(	(	PUNCT
ejpam-5713	276	37	ii	ii	PROPN
ejpam-5713	276	38	)	)	PUNCT
ejpam-5713	276	39	cg	cg	NOUN
ejpam-5713	276	40	=	=	SYM
ejpam-5713	276	41	v	v	PROPN
ejpam-5713	276	42	(	(	PUNCT
ejpam-5713	276	43	g	g	NOUN
ejpam-5713	276	44	)	)	PUNCT
ejpam-5713	276	45	and	and	CCONJ
ejpam-5713	276	46	ch	ch	NOUN
ejpam-5713	276	47	=	=	SYM
ejpam-5713	276	48	v	v	PROPN
ejpam-5713	276	49	(	(	PUNCT
ejpam-5713	276	50	h	h	NOUN
ejpam-5713	276	51	)	)	PUNCT
ejpam-5713	276	52	\	\	NOUN
ejpam-5713	276	53	{	{	PUNCT
ejpam-5713	276	54	q	q	NOUN
ejpam-5713	276	55	}	}	PUNCT
ejpam-5713	276	56	where	where	SCONJ
ejpam-5713	276	57	q	q	NOUN
ejpam-5713	276	58	is	be	AUX
ejpam-5713	276	59	an	an	DET
ejpam-5713	276	60	isolated	isolated	ADJ
ejpam-5713	276	61	vertex	vertex	NOUN
ejpam-5713	276	62	in	in	ADP
ejpam-5713	276	63	h.	h.	PROPN
ejpam-5713	276	64	(	(	PUNCT
ejpam-5713	276	65	iii	iii	NOUN
ejpam-5713	276	66	)	)	PUNCT
ejpam-5713	276	67	ch	ch	NOUN
ejpam-5713	276	68	=	=	SYM
ejpam-5713	276	69	v	v	PROPN
ejpam-5713	276	70	(	(	PUNCT
ejpam-5713	276	71	h	h	NOUN
ejpam-5713	276	72	)	)	PUNCT
ejpam-5713	276	73	and	and	CCONJ
ejpam-5713	276	74	cg	cg	NOUN
ejpam-5713	276	75	is	be	AUX
ejpam-5713	276	76	a	a	DET
ejpam-5713	276	77	super	super	ADJ
ejpam-5713	276	78	vertex	vertex	NOUN
ejpam-5713	276	79	cover	cover	NOUN
ejpam-5713	276	80	of	of	ADP
ejpam-5713	276	81	g.	g.	PROPN
ejpam-5713	276	82	s.	s.	PROPN
ejpam-5713	276	83	r.	r.	PROPN
ejpam-5713	276	84	canoy	canoy	PROPN
ejpam-5713	276	85	et	et	PROPN
ejpam-5713	276	86	al	al	PROPN
ejpam-5713	276	87	.	.	PUNCT
ejpam-5713	276	88	/	/	SYM
ejpam-5713	276	89	eur	eur	PROPN
ejpam-5713	276	90	.	.	PUNCT
ejpam-5713	277	1	j.	j.	PROPN
ejpam-5713	277	2	pure	pure	PROPN
ejpam-5713	277	3	appl	appl	PROPN
ejpam-5713	277	4	.	.	PROPN
ejpam-5713	277	5	math	math	PROPN
ejpam-5713	277	6	,	,	PUNCT
ejpam-5713	277	7	18	18	NUM
ejpam-5713	277	8	(	(	PUNCT
ejpam-5713	277	9	1	1	NUM
ejpam-5713	277	10	)	)	PUNCT
ejpam-5713	277	11	(	(	PUNCT
ejpam-5713	277	12	2025	2025	NUM
ejpam-5713	277	13	)	)	PUNCT
ejpam-5713	277	14	,	,	PUNCT
ejpam-5713	277	15	5713	5713	NUM
ejpam-5713	277	16	8	8	NUM
ejpam-5713	277	17	of	of	ADP
ejpam-5713	277	18	13	13	NUM
ejpam-5713	277	19	(	(	PUNCT
ejpam-5713	277	20	iv	iv	NOUN
ejpam-5713	277	21	)	)	PUNCT
ejpam-5713	277	22	ch	ch	NOUN
ejpam-5713	277	23	=	=	SYM
ejpam-5713	277	24	v	v	PROPN
ejpam-5713	277	25	(	(	PUNCT
ejpam-5713	277	26	h	h	NOUN
ejpam-5713	277	27	)	)	PUNCT
ejpam-5713	277	28	and	and	CCONJ
ejpam-5713	277	29	cg	cg	NOUN
ejpam-5713	277	30	=	=	NOUN
ejpam-5713	277	31	v	v	PROPN
ejpam-5713	277	32	(	(	PUNCT
ejpam-5713	277	33	g	g	NOUN
ejpam-5713	277	34	)	)	PUNCT
ejpam-5713	277	35	\	\	NOUN
ejpam-5713	277	36	{	{	PUNCT
ejpam-5713	277	37	x	x	X
ejpam-5713	277	38	}	}	PUNCT
ejpam-5713	277	39	where	where	SCONJ
ejpam-5713	277	40	x	x	PRON
ejpam-5713	277	41	is	be	AUX
ejpam-5713	277	42	an	an	DET
ejpam-5713	277	43	isolated	isolated	ADJ
ejpam-5713	277	44	vertex	vertex	NOUN
ejpam-5713	277	45	in	in	ADP
ejpam-5713	277	46	g.	g.	PROPN
ejpam-5713	277	47	proof	proof	PROPN
ejpam-5713	277	48	.	.	PUNCT
ejpam-5713	278	1	suppose	suppose	VERB
ejpam-5713	278	2	c	c	NOUN
ejpam-5713	278	3	is	be	AUX
ejpam-5713	278	4	super	super	ADJ
ejpam-5713	278	5	vertex	vertex	NOUN
ejpam-5713	278	6	cover	cover	NOUN
ejpam-5713	278	7	of	of	ADP
ejpam-5713	278	8	g	g	PROPN
ejpam-5713	278	9	+	+	CCONJ
ejpam-5713	278	10	h.	h.	PROPN
ejpam-5713	278	11	let	let	VERB
ejpam-5713	278	12	cg	cg	NOUN
ejpam-5713	278	13	=	=	PUNCT
ejpam-5713	278	14	c	c	PROPN
ejpam-5713	278	15	∩	∩	X
ejpam-5713	278	16	v	v	X
ejpam-5713	278	17	(	(	PUNCT
ejpam-5713	278	18	g	g	NOUN
ejpam-5713	278	19	)	)	PUNCT
ejpam-5713	278	20	and	and	CCONJ
ejpam-5713	278	21	ch	ch	NOUN
ejpam-5713	278	22	=	=	SYM
ejpam-5713	278	23	c	c	PROPN
ejpam-5713	278	24	∩	∩	X
ejpam-5713	278	25	v	v	X
ejpam-5713	278	26	(	(	PUNCT
ejpam-5713	278	27	h	h	NOUN
ejpam-5713	278	28	)	)	PUNCT
ejpam-5713	278	29	.	.	PUNCT
ejpam-5713	279	1	suppose	suppose	VERB
ejpam-5713	279	2	cg	cg	PRON
ejpam-5713	279	3	̸=	̸=	PROPN
ejpam-5713	279	4	v	v	NOUN
ejpam-5713	279	5	(	(	PUNCT
ejpam-5713	279	6	g	g	NOUN
ejpam-5713	279	7	)	)	PUNCT
ejpam-5713	279	8	and	and	CCONJ
ejpam-5713	279	9	ch	ch	PROPN
ejpam-5713	279	10	̸=	̸=	PROPN
ejpam-5713	279	11	v	v	NOUN
ejpam-5713	279	12	(	(	PUNCT
ejpam-5713	279	13	h	h	NOUN
ejpam-5713	279	14	)	)	PUNCT
ejpam-5713	279	15	.	.	PUNCT
ejpam-5713	280	1	pick	pick	VERB
ejpam-5713	280	2	any	any	DET
ejpam-5713	280	3	v	v	NOUN
ejpam-5713	280	4	∈	∈	PROPN
ejpam-5713	280	5	v	v	NOUN
ejpam-5713	280	6	(	(	PUNCT
ejpam-5713	280	7	g	g	NOUN
ejpam-5713	280	8	)	)	PUNCT
ejpam-5713	280	9	\	\	PROPN
ejpam-5713	280	10	cg	cg	NOUN
ejpam-5713	280	11	and	and	CCONJ
ejpam-5713	280	12	p	p	NOUN
ejpam-5713	280	13	∈	∈	PROPN
ejpam-5713	280	14	v	v	ADP
ejpam-5713	280	15	(	(	PUNCT
ejpam-5713	280	16	h	h	NOUN
ejpam-5713	280	17	)	)	PUNCT
ejpam-5713	280	18	\	\	PROPN
ejpam-5713	280	19	ch	ch	NOUN
ejpam-5713	280	20	.	.	PUNCT
ejpam-5713	281	1	then	then	ADV
ejpam-5713	281	2	e	e	X
ejpam-5713	281	3	=	=	SYM
ejpam-5713	281	4	vp	vp	PROPN
ejpam-5713	281	5	∈	∈	PROPN
ejpam-5713	281	6	e(g	e(g	PROPN
ejpam-5713	281	7	)	)	PUNCT
ejpam-5713	281	8	and	and	CCONJ
ejpam-5713	281	9	none	none	NOUN
ejpam-5713	281	10	of	of	ADP
ejpam-5713	281	11	v	v	NOUN
ejpam-5713	281	12	and	and	CCONJ
ejpam-5713	281	13	p	p	NOUN
ejpam-5713	281	14	is	be	AUX
ejpam-5713	281	15	in	in	ADP
ejpam-5713	281	16	c.	c.	PROPN
ejpam-5713	281	17	this	this	PRON
ejpam-5713	281	18	implies	imply	VERB
ejpam-5713	281	19	that	that	SCONJ
ejpam-5713	281	20	c	c	PROPN
ejpam-5713	281	21	is	be	AUX
ejpam-5713	281	22	not	not	PART
ejpam-5713	281	23	a	a	DET
ejpam-5713	281	24	vertex	vertex	NOUN
ejpam-5713	281	25	cover	cover	NOUN
ejpam-5713	281	26	in	in	ADP
ejpam-5713	281	27	g	g	PROPN
ejpam-5713	282	1	+	+	CCONJ
ejpam-5713	282	2	h	h	NOUN
ejpam-5713	282	3	,	,	PUNCT
ejpam-5713	282	4	a	a	DET
ejpam-5713	282	5	contradiction	contradiction	NOUN
ejpam-5713	282	6	.	.	PUNCT
ejpam-5713	283	1	thus	thus	ADV
ejpam-5713	283	2	,	,	PUNCT
ejpam-5713	283	3	cg	cg	NOUN
ejpam-5713	283	4	=	=	SYM
ejpam-5713	283	5	v	v	NOUN
ejpam-5713	283	6	(	(	PUNCT
ejpam-5713	283	7	g	g	NOUN
ejpam-5713	283	8	)	)	PUNCT
ejpam-5713	283	9	or	or	CCONJ
ejpam-5713	283	10	ch	ch	NOUN
ejpam-5713	283	11	=	=	SYM
ejpam-5713	283	12	v	v	PROPN
ejpam-5713	283	13	(	(	PUNCT
ejpam-5713	283	14	h	h	NOUN
ejpam-5713	283	15	)	)	PUNCT
ejpam-5713	283	16	.	.	PUNCT
ejpam-5713	284	1	suppose	suppose	VERB
ejpam-5713	284	2	cg	cg	NOUN
ejpam-5713	284	3	=	=	SYM
ejpam-5713	284	4	v	v	PROPN
ejpam-5713	284	5	(	(	PUNCT
ejpam-5713	284	6	g	g	NOUN
ejpam-5713	284	7	)	)	PUNCT
ejpam-5713	284	8	and	and	CCONJ
ejpam-5713	284	9	let	let	VERB
ejpam-5713	284	10	ab	ab	PROPN
ejpam-5713	284	11	∈	∈	PROPN
ejpam-5713	284	12	e(h	e(h	PROPN
ejpam-5713	284	13	)	)	PUNCT
ejpam-5713	284	14	.	.	PUNCT
ejpam-5713	285	1	since	since	SCONJ
ejpam-5713	285	2	c	c	PROPN
ejpam-5713	285	3	is	be	AUX
ejpam-5713	285	4	a	a	DET
ejpam-5713	285	5	vertex	vertex	NOUN
ejpam-5713	285	6	cover	cover	NOUN
ejpam-5713	285	7	of	of	ADP
ejpam-5713	285	8	g	g	PROPN
ejpam-5713	285	9	+	+	CCONJ
ejpam-5713	285	10	h	h	NOUN
ejpam-5713	285	11	,	,	PUNCT
ejpam-5713	285	12	it	it	PRON
ejpam-5713	285	13	follows	follow	VERB
ejpam-5713	285	14	that	that	SCONJ
ejpam-5713	285	15	a	a	DET
ejpam-5713	285	16	∈	∈	PROPN
ejpam-5713	285	17	ch	ch	NOUN
ejpam-5713	285	18	or	or	CCONJ
ejpam-5713	285	19	b	b	NOUN
ejpam-5713	285	20	∈	∈	PROPN
ejpam-5713	285	21	ch	ch	NOUN
ejpam-5713	285	22	.	.	PUNCT
ejpam-5713	286	1	this	this	PRON
ejpam-5713	286	2	implies	imply	VERB
ejpam-5713	286	3	that	that	SCONJ
ejpam-5713	286	4	ch	ch	NOUN
ejpam-5713	286	5	is	be	AUX
ejpam-5713	286	6	a	a	DET
ejpam-5713	286	7	vertex	vertex	NOUN
ejpam-5713	286	8	cover	cover	NOUN
ejpam-5713	286	9	of	of	ADP
ejpam-5713	286	10	h.	h.	NOUN
ejpam-5713	286	11	if	if	SCONJ
ejpam-5713	286	12	ch	ch	NOUN
ejpam-5713	286	13	is	be	AUX
ejpam-5713	286	14	a	a	DET
ejpam-5713	286	15	super	super	ADJ
ejpam-5713	286	16	dominating	dominating	NOUN
ejpam-5713	286	17	set	set	NOUN
ejpam-5713	286	18	in	in	ADP
ejpam-5713	286	19	h	h	NOUN
ejpam-5713	286	20	,	,	PUNCT
ejpam-5713	286	21	then	then	ADV
ejpam-5713	286	22	(	(	PUNCT
ejpam-5713	286	23	i	i	NOUN
ejpam-5713	286	24	)	)	PUNCT
ejpam-5713	286	25	holds	hold	VERB
ejpam-5713	286	26	.	.	PUNCT
ejpam-5713	287	1	so	so	ADV
ejpam-5713	287	2	suppose	suppose	VERB
ejpam-5713	287	3	that	that	SCONJ
ejpam-5713	287	4	ch	ch	NOUN
ejpam-5713	287	5	is	be	AUX
ejpam-5713	287	6	not	not	PART
ejpam-5713	287	7	a	a	DET
ejpam-5713	287	8	super	super	ADJ
ejpam-5713	287	9	dominating	dominating	NOUN
ejpam-5713	287	10	set	set	NOUN
ejpam-5713	287	11	in	in	ADP
ejpam-5713	287	12	h.	h.	PROPN
ejpam-5713	287	13	then	then	ADV
ejpam-5713	287	14	there	there	PRON
ejpam-5713	287	15	exists	exist	VERB
ejpam-5713	287	16	a	a	DET
ejpam-5713	287	17	vertex	vertex	NOUN
ejpam-5713	287	18	q	q	X
ejpam-5713	287	19	∈	∈	PROPN
ejpam-5713	287	20	v	v	ADP
ejpam-5713	287	21	(	(	PUNCT
ejpam-5713	287	22	h	h	NOUN
ejpam-5713	287	23	)	)	PUNCT
ejpam-5713	287	24	\	\	PROPN
ejpam-5713	287	25	ch	ch	NOUN
ejpam-5713	287	26	such	such	ADJ
ejpam-5713	287	27	that	that	PRON
ejpam-5713	287	28	for	for	ADP
ejpam-5713	287	29	all	all	DET
ejpam-5713	287	30	z	z	NOUN
ejpam-5713	287	31	∈	∈	PROPN
ejpam-5713	287	32	ch	ch	NOUN
ejpam-5713	287	33	,	,	PUNCT
ejpam-5713	287	34	we	we	PRON
ejpam-5713	287	35	have	have	VERB
ejpam-5713	287	36	nh(z)∩[v	nh(z)∩[v	NOUN
ejpam-5713	287	37	(	(	PUNCT
ejpam-5713	287	38	h)\ch	h)\ch	PROPN
ejpam-5713	287	39	]	]	X
ejpam-5713	287	40	̸=	̸=	PROPN
ejpam-5713	287	41	{	{	PUNCT
ejpam-5713	287	42	q	q	NOUN
ejpam-5713	287	43	}	}	PUNCT
ejpam-5713	287	44	.	.	PUNCT
ejpam-5713	288	1	suppose	suppose	VERB
ejpam-5713	288	2	q	q	NOUN
ejpam-5713	288	3	is	be	AUX
ejpam-5713	288	4	not	not	PART
ejpam-5713	288	5	an	an	DET
ejpam-5713	288	6	isolated	isolated	ADJ
ejpam-5713	288	7	vertex	vertex	NOUN
ejpam-5713	288	8	in	in	ADP
ejpam-5713	288	9	h.	h.	PROPN
ejpam-5713	288	10	let	let	VERB
ejpam-5713	288	11	z0	z0	PROPN
ejpam-5713	288	12	∈	∈	PROPN
ejpam-5713	288	13	ch∩nh(q	ch∩nh(q	PROPN
ejpam-5713	288	14	)	)	PUNCT
ejpam-5713	288	15	(	(	PUNCT
ejpam-5713	288	16	z0	z0	PROPN
ejpam-5713	288	17	exists	exist	VERB
ejpam-5713	288	18	because	because	SCONJ
ejpam-5713	288	19	ch	ch	NOUN
ejpam-5713	288	20	is	be	AUX
ejpam-5713	288	21	a	a	DET
ejpam-5713	288	22	vertex	vertex	NOUN
ejpam-5713	288	23	cover	cover	NOUN
ejpam-5713	288	24	of	of	ADP
ejpam-5713	288	25	h	h	NOUN
ejpam-5713	288	26	)	)	PUNCT
ejpam-5713	288	27	.	.	PUNCT
ejpam-5713	289	1	then	then	ADV
ejpam-5713	289	2	nh(z0	nh(z0	NOUN
ejpam-5713	289	3	)	)	PUNCT
ejpam-5713	289	4	∩	∩	NOUN
ejpam-5713	289	5	[	[	X
ejpam-5713	289	6	v	v	X
ejpam-5713	289	7	(	(	PUNCT
ejpam-5713	289	8	h	h	NOUN
ejpam-5713	289	9	)	)	PUNCT
ejpam-5713	289	10	\	\	PROPN
ejpam-5713	289	11	ch	ch	NOUN
ejpam-5713	289	12	]	]	PUNCT
ejpam-5713	289	13	̸=	̸=	PROPN
ejpam-5713	289	14	{	{	PUNCT
ejpam-5713	289	15	q	q	NOUN
ejpam-5713	289	16	}	}	PUNCT
ejpam-5713	289	17	.	.	PUNCT
ejpam-5713	290	1	it	it	PRON
ejpam-5713	290	2	follows	follow	VERB
ejpam-5713	290	3	that	that	SCONJ
ejpam-5713	290	4	there	there	PRON
ejpam-5713	290	5	exists	exist	VERB
ejpam-5713	290	6	t	t	PROPN
ejpam-5713	290	7	∈	∈	PROPN
ejpam-5713	290	8	nh(z0	nh(z0	PRON
ejpam-5713	290	9	)	)	PUNCT
ejpam-5713	290	10	∩	∩	NOUN
ejpam-5713	291	1	[	[	X
ejpam-5713	291	2	v	v	X
ejpam-5713	291	3	(	(	PUNCT
ejpam-5713	291	4	h	h	NOUN
ejpam-5713	291	5	)	)	PUNCT
ejpam-5713	291	6	\	\	PROPN
ejpam-5713	291	7	ch	ch	NOUN
ejpam-5713	291	8	]	]	PUNCT
ejpam-5713	291	9	such	such	ADJ
ejpam-5713	291	10	that	that	SCONJ
ejpam-5713	291	11	q	q	PROPN
ejpam-5713	291	12	̸=	̸=	PROPN
ejpam-5713	291	13	t.	t.	NOUN
ejpam-5713	291	14	this	this	PRON
ejpam-5713	291	15	implies	imply	VERB
ejpam-5713	291	16	that	that	SCONJ
ejpam-5713	291	17	ng+h(w	ng+h(w	NOUN
ejpam-5713	291	18	)	)	PUNCT
ejpam-5713	291	19	∩	∩	NOUN
ejpam-5713	292	1	[	[	X
ejpam-5713	292	2	v	v	X
ejpam-5713	292	3	(	(	PUNCT
ejpam-5713	292	4	g+h	g+h	NOUN
ejpam-5713	292	5	)	)	PUNCT
ejpam-5713	292	6	\	\	PUNCT
ejpam-5713	293	1	c	c	X
ejpam-5713	293	2	]	]	X
ejpam-5713	293	3	̸=	̸=	PROPN
ejpam-5713	293	4	{	{	PUNCT
ejpam-5713	293	5	q	q	X
ejpam-5713	293	6	}	}	PUNCT
ejpam-5713	293	7	for	for	ADP
ejpam-5713	293	8	all	all	DET
ejpam-5713	293	9	w	w	PROPN
ejpam-5713	293	10	∈	∈	PROPN
ejpam-5713	293	11	c	c	NOUN
ejpam-5713	293	12	,	,	PUNCT
ejpam-5713	293	13	contrary	contrary	ADV
ejpam-5713	293	14	to	to	ADP
ejpam-5713	293	15	the	the	DET
ejpam-5713	293	16	assumption	assumption	NOUN
ejpam-5713	293	17	that	that	SCONJ
ejpam-5713	293	18	c	c	PROPN
ejpam-5713	293	19	is	be	AUX
ejpam-5713	293	20	a	a	DET
ejpam-5713	293	21	super	super	ADJ
ejpam-5713	293	22	dominating	dominating	NOUN
ejpam-5713	293	23	set	set	NOUN
ejpam-5713	293	24	in	in	ADP
ejpam-5713	293	25	g	g	PROPN
ejpam-5713	293	26	+	+	PROPN
ejpam-5713	293	27	h.	h.	PROPN
ejpam-5713	293	28	thus	thus	ADV
ejpam-5713	293	29	,	,	PUNCT
ejpam-5713	293	30	q	q	X
ejpam-5713	293	31	is	be	AUX
ejpam-5713	293	32	an	an	DET
ejpam-5713	293	33	isolated	isolated	ADJ
ejpam-5713	293	34	vertex	vertex	NOUN
ejpam-5713	293	35	in	in	ADP
ejpam-5713	293	36	h.	h.	PROPN
ejpam-5713	293	37	since	since	SCONJ
ejpam-5713	293	38	c	c	PROPN
ejpam-5713	293	39	is	be	AUX
ejpam-5713	293	40	a	a	DET
ejpam-5713	293	41	super	super	ADJ
ejpam-5713	293	42	dominating	dominating	NOUN
ejpam-5713	293	43	set	set	NOUN
ejpam-5713	293	44	in	in	ADP
ejpam-5713	293	45	g+h	g+h	PROPN
ejpam-5713	293	46	,	,	PUNCT
ejpam-5713	293	47	and	and	CCONJ
ejpam-5713	293	48	q	q	PROPN
ejpam-5713	293	49	/∈	/∈	PUNCT
ejpam-5713	293	50	nh	nh	PROPN
ejpam-5713	294	1	[	[	X
ejpam-5713	294	2	ch	ch	X
ejpam-5713	294	3	]	]	X
ejpam-5713	294	4	,	,	PUNCT
ejpam-5713	294	5	it	it	PRON
ejpam-5713	294	6	follows	follow	VERB
ejpam-5713	294	7	that	that	DET
ejpam-5713	294	8	ch	ch	NOUN
ejpam-5713	294	9	=	=	SYM
ejpam-5713	294	10	v	v	PROPN
ejpam-5713	294	11	(	(	PUNCT
ejpam-5713	294	12	h	h	NOUN
ejpam-5713	294	13	)	)	PUNCT
ejpam-5713	294	14	\	\	NOUN
ejpam-5713	294	15	{	{	PUNCT
ejpam-5713	294	16	q	q	NOUN
ejpam-5713	294	17	}	}	PUNCT
ejpam-5713	294	18	.	.	PUNCT
ejpam-5713	295	1	this	this	PRON
ejpam-5713	295	2	shows	show	VERB
ejpam-5713	295	3	that	that	SCONJ
ejpam-5713	295	4	(	(	PUNCT
ejpam-5713	295	5	ii	ii	NOUN
ejpam-5713	295	6	)	)	PUNCT
ejpam-5713	295	7	holds	hold	VERB
ejpam-5713	295	8	.	.	PUNCT
ejpam-5713	296	1	similarly	similarly	ADV
ejpam-5713	296	2	,	,	PUNCT
ejpam-5713	296	3	(	(	PUNCT
ejpam-5713	296	4	iii	iii	NOUN
ejpam-5713	296	5	)	)	PUNCT
ejpam-5713	296	6	or	or	CCONJ
ejpam-5713	296	7	(	(	PUNCT
ejpam-5713	296	8	iv	iv	X
ejpam-5713	296	9	)	)	PUNCT
ejpam-5713	296	10	holds	hold	NOUN
ejpam-5713	296	11	.	.	PUNCT
ejpam-5713	297	1	conversely	conversely	ADV
ejpam-5713	297	2	,	,	PUNCT
ejpam-5713	297	3	suppose	suppose	VERB
ejpam-5713	297	4	that	that	SCONJ
ejpam-5713	297	5	c	c	AUX
ejpam-5713	297	6	=	=	PUNCT
ejpam-5713	297	7	cg	cg	NOUN
ejpam-5713	297	8	∪	∪	PROPN
ejpam-5713	297	9	ch	ch	PROPN
ejpam-5713	297	10	.	.	PUNCT
ejpam-5713	297	11	suppose	suppose	VERB
ejpam-5713	297	12	that	that	SCONJ
ejpam-5713	297	13	(	(	PUNCT
ejpam-5713	297	14	i	i	NOUN
ejpam-5713	297	15	)	)	PUNCT
ejpam-5713	297	16	holds	hold	VERB
ejpam-5713	297	17	.	.	PUNCT
ejpam-5713	298	1	then	then	ADV
ejpam-5713	298	2	clearly	clearly	ADV
ejpam-5713	298	3	,	,	PUNCT
ejpam-5713	298	4	c	c	PROPN
ejpam-5713	298	5	is	be	AUX
ejpam-5713	298	6	a	a	DET
ejpam-5713	298	7	super	super	ADJ
ejpam-5713	298	8	vertex	vertex	NOUN
ejpam-5713	298	9	cover	cover	NOUN
ejpam-5713	298	10	of	of	ADP
ejpam-5713	298	11	g+h	g+h	PROPN
ejpam-5713	298	12	.	.	PUNCT
ejpam-5713	299	1	suppose	suppose	VERB
ejpam-5713	299	2	(	(	PUNCT
ejpam-5713	299	3	ii	ii	NOUN
ejpam-5713	299	4	)	)	PUNCT
ejpam-5713	299	5	holds	hold	VERB
ejpam-5713	299	6	.	.	PUNCT
ejpam-5713	300	1	since	since	SCONJ
ejpam-5713	300	2	v	v	NOUN
ejpam-5713	300	3	(	(	PUNCT
ejpam-5713	300	4	g	g	NOUN
ejpam-5713	300	5	)	)	PUNCT
ejpam-5713	300	6	⊂	⊂	PROPN
ejpam-5713	301	1	c	c	X
ejpam-5713	301	2	,	,	PUNCT
ejpam-5713	301	3	every	every	DET
ejpam-5713	301	4	edge	edge	NOUN
ejpam-5713	301	5	of	of	ADP
ejpam-5713	301	6	the	the	DET
ejpam-5713	301	7	form	form	NOUN
ejpam-5713	301	8	vw	vw	PROPN
ejpam-5713	301	9	or	or	CCONJ
ejpam-5713	301	10	vq	vq	NOUN
ejpam-5713	301	11	,	,	PUNCT
ejpam-5713	301	12	where	where	SCONJ
ejpam-5713	301	13	v	v	NOUN
ejpam-5713	301	14	,	,	PUNCT
ejpam-5713	301	15	w	w	PROPN
ejpam-5713	301	16	∈	∈	PROPN
ejpam-5713	301	17	v	v	ADP
ejpam-5713	301	18	(	(	PUNCT
ejpam-5713	301	19	g	g	NOUN
ejpam-5713	301	20	)	)	PUNCT
ejpam-5713	301	21	,	,	PUNCT
ejpam-5713	301	22	is	be	AUX
ejpam-5713	301	23	incident	incident	NOUN
ejpam-5713	301	24	to	to	ADP
ejpam-5713	301	25	a	a	DET
ejpam-5713	301	26	vertex	vertex	NOUN
ejpam-5713	301	27	in	in	ADP
ejpam-5713	301	28	c.	c.	PROPN
ejpam-5713	301	29	now	now	ADV
ejpam-5713	301	30	let	let	VERB
ejpam-5713	301	31	ab	ab	PROPN
ejpam-5713	301	32	∈	∈	PROPN
ejpam-5713	301	33	e(h	e(h	PROPN
ejpam-5713	301	34	)	)	PUNCT
ejpam-5713	301	35	.	.	PUNCT
ejpam-5713	302	1	since	since	SCONJ
ejpam-5713	302	2	ch	ch	NOUN
ejpam-5713	302	3	=	=	SYM
ejpam-5713	302	4	v	v	PROPN
ejpam-5713	302	5	(	(	PUNCT
ejpam-5713	302	6	h)\{q	h)\{q	PROPN
ejpam-5713	302	7	}	}	PUNCT
ejpam-5713	302	8	,	,	PUNCT
ejpam-5713	302	9	a	a	DET
ejpam-5713	302	10	,	,	PUNCT
ejpam-5713	302	11	b	b	PROPN
ejpam-5713	302	12	∈	∈	PROPN
ejpam-5713	302	13	ch	ch	NOUN
ejpam-5713	302	14	⊂	⊂	PROPN
ejpam-5713	302	15	c.	c.	PROPN
ejpam-5713	302	16	hence	hence	ADV
ejpam-5713	302	17	,	,	PUNCT
ejpam-5713	302	18	c	c	PROPN
ejpam-5713	302	19	is	be	AUX
ejpam-5713	302	20	a	a	DET
ejpam-5713	302	21	vertex	vertex	NOUN
ejpam-5713	302	22	cover	cover	NOUN
ejpam-5713	302	23	of	of	ADP
ejpam-5713	302	24	g+h	g+h	PROPN
ejpam-5713	302	25	.	.	PUNCT
ejpam-5713	303	1	since	since	SCONJ
ejpam-5713	303	2	v	v	NOUN
ejpam-5713	303	3	(	(	PUNCT
ejpam-5713	303	4	g+h)\c	g+h)\c	X
ejpam-5713	303	5	=	=	PUNCT
ejpam-5713	303	6	{	{	PUNCT
ejpam-5713	303	7	q	q	X
ejpam-5713	303	8	}	}	PUNCT
ejpam-5713	303	9	,	,	PUNCT
ejpam-5713	303	10	pick	pick	VERB
ejpam-5713	303	11	any	any	DET
ejpam-5713	303	12	y	y	PROPN
ejpam-5713	303	13	∈	∈	PROPN
ejpam-5713	303	14	cg	cg	NOUN
ejpam-5713	303	15	=	=	SYM
ejpam-5713	303	16	v	v	NOUN
ejpam-5713	303	17	(	(	PUNCT
ejpam-5713	303	18	g	g	NOUN
ejpam-5713	303	19	)	)	PUNCT
ejpam-5713	303	20	.	.	PUNCT
ejpam-5713	304	1	then	then	ADV
ejpam-5713	304	2	yq	yq	PROPN
ejpam-5713	304	3	∈	∈	PROPN
ejpam-5713	304	4	e(g	e(g	PROPN
ejpam-5713	305	1	+	+	NOUN
ejpam-5713	305	2	h	h	NOUN
ejpam-5713	305	3	)	)	PUNCT
ejpam-5713	305	4	and	and	CCONJ
ejpam-5713	305	5	ng+h(y	ng+h(y	NUM
ejpam-5713	305	6	)	)	PUNCT
ejpam-5713	305	7	∩	∩	NOUN
ejpam-5713	306	1	[	[	X
ejpam-5713	306	2	v	v	X
ejpam-5713	306	3	(	(	PUNCT
ejpam-5713	306	4	g	g	PROPN
ejpam-5713	306	5	+	+	NOUN
ejpam-5713	306	6	h	h	NOUN
ejpam-5713	306	7	)	)	PUNCT
ejpam-5713	306	8	\	\	PUNCT
ejpam-5713	307	1	c	c	X
ejpam-5713	307	2	]	]	X
ejpam-5713	307	3	=	=	X
ejpam-5713	307	4	{	{	PUNCT
ejpam-5713	307	5	q	q	X
ejpam-5713	307	6	}	}	PUNCT
ejpam-5713	307	7	.	.	PUNCT
ejpam-5713	308	1	thus	thus	ADV
ejpam-5713	308	2	,	,	PUNCT
ejpam-5713	308	3	c	c	PROPN
ejpam-5713	308	4	is	be	AUX
ejpam-5713	308	5	a	a	DET
ejpam-5713	308	6	super	super	ADJ
ejpam-5713	308	7	dominating	dominating	NOUN
ejpam-5713	308	8	set	set	NOUN
ejpam-5713	308	9	in	in	ADP
ejpam-5713	308	10	g	g	PROPN
ejpam-5713	308	11	+	+	CCONJ
ejpam-5713	308	12	h.	h.	PROPN
ejpam-5713	308	13	therefore	therefore	ADV
ejpam-5713	308	14	,	,	PUNCT
ejpam-5713	308	15	c	c	PROPN
ejpam-5713	308	16	is	be	AUX
ejpam-5713	308	17	a	a	DET
ejpam-5713	308	18	super	super	ADJ
ejpam-5713	308	19	vertex	vertex	NOUN
ejpam-5713	308	20	cover	cover	NOUN
ejpam-5713	308	21	in	in	ADP
ejpam-5713	308	22	g+h	g+h	PROPN
ejpam-5713	308	23	.	.	PUNCT
ejpam-5713	309	1	the	the	DET
ejpam-5713	309	2	same	same	ADJ
ejpam-5713	309	3	conclusion	conclusion	NOUN
ejpam-5713	309	4	holds	hold	VERB
ejpam-5713	309	5	for	for	ADP
ejpam-5713	309	6	c	c	PROPN
ejpam-5713	309	7	if	if	SCONJ
ejpam-5713	309	8	(	(	PUNCT
ejpam-5713	309	9	iii	iii	NOUN
ejpam-5713	309	10	)	)	PUNCT
ejpam-5713	309	11	or	or	CCONJ
ejpam-5713	309	12	(	(	PUNCT
ejpam-5713	309	13	iv	iv	X
ejpam-5713	309	14	)	)	PUNCT
ejpam-5713	309	15	holds	hold	NOUN
ejpam-5713	309	16	.	.	PUNCT
ejpam-5713	310	1	corollary	corollary	ADJ
ejpam-5713	310	2	3	3	X
ejpam-5713	310	3	.	.	PUNCT
ejpam-5713	311	1	let	let	VERB
ejpam-5713	311	2	g	g	NOUN
ejpam-5713	312	1	and	and	CCONJ
ejpam-5713	312	2	h	h	NOUN
ejpam-5713	312	3	be	be	VERB
ejpam-5713	312	4	any	any	DET
ejpam-5713	312	5	two	two	NUM
ejpam-5713	312	6	graphs	graph	NOUN
ejpam-5713	312	7	of	of	ADP
ejpam-5713	312	8	orders	order	NOUN
ejpam-5713	312	9	m	m	VERB
ejpam-5713	312	10	and	and	CCONJ
ejpam-5713	312	11	n	n	CCONJ
ejpam-5713	312	12	,	,	PUNCT
ejpam-5713	312	13	respectively	respectively	ADV
ejpam-5713	312	14	.	.	PUNCT
ejpam-5713	313	1	then	then	ADV
ejpam-5713	313	2	βs(g+h	βs(g+h	X
ejpam-5713	313	3	)	)	PUNCT
ejpam-5713	314	1	=	=	SYM
ejpam-5713	315	1	m+	m+	NUM
ejpam-5713	315	2	n−	n−	NOUN
ejpam-5713	315	3	1	1	NUM
ejpam-5713	315	4	if	if	SCONJ
ejpam-5713	315	5	and	and	CCONJ
ejpam-5713	315	6	only	only	ADV
ejpam-5713	315	7	if	if	SCONJ
ejpam-5713	315	8	one	one	NUM
ejpam-5713	315	9	of	of	ADP
ejpam-5713	315	10	the	the	DET
ejpam-5713	315	11	following	follow	VERB
ejpam-5713	315	12	holds	hold	VERB
ejpam-5713	315	13	:	:	PUNCT
ejpam-5713	315	14	(	(	PUNCT
ejpam-5713	315	15	i	i	NOUN
ejpam-5713	315	16	)	)	PUNCT
ejpam-5713	315	17	βs(g	βs(g	PUNCT
ejpam-5713	315	18	)	)	PUNCT
ejpam-5713	316	1	=	=	SYM
ejpam-5713	316	2	m−	m−	PROPN
ejpam-5713	316	3	1	1	NUM
ejpam-5713	316	4	and	and	CCONJ
ejpam-5713	316	5	βs(h	βs(h	PRON
ejpam-5713	316	6	)	)	PUNCT
ejpam-5713	317	1	=	=	PUNCT
ejpam-5713	317	2	n−	n−	NOUN
ejpam-5713	317	3	1	1	NUM
ejpam-5713	317	4	.	.	PUNCT
ejpam-5713	317	5	(	(	PUNCT
ejpam-5713	317	6	ii	ii	NOUN
ejpam-5713	317	7	)	)	PUNCT
ejpam-5713	317	8	βs(g	βs(g	PUNCT
ejpam-5713	317	9	)	)	PUNCT
ejpam-5713	318	1	=	=	SYM
ejpam-5713	318	2	m−	m−	PROPN
ejpam-5713	318	3	1	1	NUM
ejpam-5713	318	4	and	and	CCONJ
ejpam-5713	318	5	h	h	NOUN
ejpam-5713	318	6	=	=	SYM
ejpam-5713	318	7	kn	kn	PROPN
ejpam-5713	318	8	(	(	PUNCT
ejpam-5713	318	9	or	or	CCONJ
ejpam-5713	318	10	βs(h	βs(h	PUNCT
ejpam-5713	318	11	)	)	PUNCT
ejpam-5713	318	12	=	=	PUNCT
ejpam-5713	318	13	n−	n−	NOUN
ejpam-5713	318	14	1	1	NUM
ejpam-5713	318	15	and	and	CCONJ
ejpam-5713	318	16	g	g	NOUN
ejpam-5713	318	17	=	=	SYM
ejpam-5713	318	18	km	km	PROPN
ejpam-5713	318	19	)	)	PUNCT
ejpam-5713	318	20	.	.	PUNCT
ejpam-5713	319	1	(	(	PUNCT
ejpam-5713	319	2	iii	iii	X
ejpam-5713	319	3	)	)	PUNCT
ejpam-5713	319	4	g	g	NOUN
ejpam-5713	319	5	=	=	SYM
ejpam-5713	319	6	km	km	PROPN
ejpam-5713	319	7	and	and	CCONJ
ejpam-5713	319	8	h	h	NOUN
ejpam-5713	320	1	=	=	SYM
ejpam-5713	320	2	kn	kn	PROPN
ejpam-5713	320	3	.	.	PUNCT
ejpam-5713	321	1	in	in	ADP
ejpam-5713	321	2	particular	particular	ADJ
ejpam-5713	321	3	,	,	PUNCT
ejpam-5713	321	4	βs(km	βs(km	PROPN
ejpam-5713	321	5	,	,	PUNCT
ejpam-5713	321	6	n	n	CCONJ
ejpam-5713	321	7	)	)	PUNCT
ejpam-5713	321	8	=	=	SYM
ejpam-5713	322	1	m+	m+	NUM
ejpam-5713	322	2	n−	n−	NOUN
ejpam-5713	322	3	1	1	NUM
ejpam-5713	322	4	for	for	ADP
ejpam-5713	322	5	m	m	PROPN
ejpam-5713	322	6	,	,	PUNCT
ejpam-5713	322	7	n	n	PRON
ejpam-5713	322	8	≥	≥	NOUN
ejpam-5713	322	9	1	1	NUM
ejpam-5713	322	10	.	.	PUNCT
ejpam-5713	323	1	proof	proof	NOUN
ejpam-5713	323	2	.	.	PUNCT
ejpam-5713	324	1	suppose	suppose	VERB
ejpam-5713	324	2	βs(g	βs(g	PUNCT
ejpam-5713	324	3	+	+	NUM
ejpam-5713	324	4	h	h	X
ejpam-5713	324	5	)	)	PUNCT
ejpam-5713	324	6	=	=	NOUN
ejpam-5713	325	1	m	m	VERB
ejpam-5713	325	2	+	+	NOUN
ejpam-5713	325	3	n	n	CCONJ
ejpam-5713	325	4	−	−	NUM
ejpam-5713	325	5	1	1	NUM
ejpam-5713	326	1	and	and	CCONJ
ejpam-5713	326	2	let	let	VERB
ejpam-5713	326	3	c	c	PRON
ejpam-5713	326	4	be	be	AUX
ejpam-5713	326	5	a	a	DET
ejpam-5713	326	6	βs	βs	NOUN
ejpam-5713	326	7	-	-	PUNCT
ejpam-5713	326	8	set	set	NOUN
ejpam-5713	326	9	in	in	ADP
ejpam-5713	326	10	g	g	PROPN
ejpam-5713	326	11	+	+	CCONJ
ejpam-5713	326	12	h.	h.	PROPN
ejpam-5713	326	13	suppose	suppose	VERB
ejpam-5713	326	14	βs(g	βs(g	PUNCT
ejpam-5713	326	15	)	)	PUNCT
ejpam-5713	327	1	<	<	X
ejpam-5713	327	2	m−1	m−1	PROPN
ejpam-5713	327	3	or	or	CCONJ
ejpam-5713	327	4	βs(h	βs(h	NUM
ejpam-5713	327	5	)	)	PUNCT
ejpam-5713	327	6	<	<	X
ejpam-5713	327	7	n−1	n−1	PROPN
ejpam-5713	327	8	,	,	PUNCT
ejpam-5713	327	9	say	say	VERB
ejpam-5713	327	10	βs(g	βs(g	PUNCT
ejpam-5713	327	11	)	)	PUNCT
ejpam-5713	327	12	<	<	X
ejpam-5713	328	1	m−1	m−1	PROPN
ejpam-5713	328	2	.	.	PUNCT
ejpam-5713	329	1	let	let	VERB
ejpam-5713	329	2	sg	sg	PART
ejpam-5713	329	3	be	be	AUX
ejpam-5713	329	4	a	a	DET
ejpam-5713	329	5	βs	βs	ADV
ejpam-5713	329	6	-	-	PUNCT
ejpam-5713	329	7	set	set	VERB
ejpam-5713	329	8	ing	ing	NOUN
ejpam-5713	329	9	.	.	PUNCT
ejpam-5713	330	1	by	by	ADP
ejpam-5713	330	2	theorem	theorem	NOUN
ejpam-5713	330	3	4	4	NUM
ejpam-5713	330	4	,	,	PUNCT
ejpam-5713	330	5	c	c	X
ejpam-5713	330	6	=	=	SYM
ejpam-5713	330	7	sg∪v	sg∪v	PROPN
ejpam-5713	330	8	(	(	PUNCT
ejpam-5713	330	9	h	h	NOUN
ejpam-5713	330	10	)	)	PUNCT
ejpam-5713	330	11	is	be	AUX
ejpam-5713	330	12	a	a	DET
ejpam-5713	330	13	super	super	ADJ
ejpam-5713	330	14	vertex	vertex	NOUN
ejpam-5713	330	15	cover	cover	NOUN
ejpam-5713	330	16	ofg+h	ofg+h	PROPN
ejpam-5713	330	17	.	.	PUNCT
ejpam-5713	331	1	hence	hence	ADV
ejpam-5713	331	2	,	,	PUNCT
ejpam-5713	331	3	βs(g+h	βs(g+h	SYM
ejpam-5713	331	4	)	)	PUNCT
ejpam-5713	331	5	≤	≤	NOUN
ejpam-5713	331	6	|c|	|c|	PROPN
ejpam-5713	331	7	=	=	SYM
ejpam-5713	331	8	n+βs(g	n+βs(g	X
ejpam-5713	331	9	)	)	PUNCT
ejpam-5713	331	10	<	<	X
ejpam-5713	331	11	|c|	|c|	PROPN
ejpam-5713	331	12	,	,	PUNCT
ejpam-5713	331	13	a	a	DET
ejpam-5713	331	14	contradiction	contradiction	NOUN
ejpam-5713	331	15	.	.	PUNCT
ejpam-5713	332	1	it	it	PRON
ejpam-5713	332	2	follows	follow	VERB
ejpam-5713	332	3	that	that	SCONJ
ejpam-5713	332	4	βs(g	βs(g	PUNCT
ejpam-5713	332	5	)	)	PUNCT
ejpam-5713	332	6	≥	≥	NOUN
ejpam-5713	332	7	m−1	m−1	PROPN
ejpam-5713	332	8	and	and	CCONJ
ejpam-5713	332	9	βs(h	βs(h	NUM
ejpam-5713	332	10	)	)	PUNCT
ejpam-5713	332	11	≥	≥	NOUN
ejpam-5713	333	1	n−1	n−1	PROPN
ejpam-5713	333	2	.	.	PROPN
ejpam-5713	333	3	suppose	suppose	VERB
ejpam-5713	333	4	βs(g	βs(g	PUNCT
ejpam-5713	333	5	)	)	PUNCT
ejpam-5713	334	1	=	=	SYM
ejpam-5713	334	2	m−1	m−1	PROPN
ejpam-5713	334	3	.	.	PUNCT
ejpam-5713	335	1	if	if	SCONJ
ejpam-5713	335	2	βs(h	βs(h	PRON
ejpam-5713	335	3	)	)	PUNCT
ejpam-5713	335	4	=	=	PUNCT
ejpam-5713	335	5	n−	n−	NOUN
ejpam-5713	335	6	1	1	NUM
ejpam-5713	335	7	,	,	PUNCT
ejpam-5713	335	8	then	then	ADV
ejpam-5713	335	9	(	(	PUNCT
ejpam-5713	335	10	i	i	NOUN
ejpam-5713	335	11	)	)	PUNCT
ejpam-5713	335	12	holds	hold	VERB
ejpam-5713	335	13	.	.	PUNCT
ejpam-5713	336	1	suppose	suppose	VERB
ejpam-5713	336	2	βs(h	βs(h	PUNCT
ejpam-5713	336	3	)	)	PUNCT
ejpam-5713	336	4	=	=	VERB
ejpam-5713	337	1	n.	n.	NOUN
ejpam-5713	337	2	then	then	ADV
ejpam-5713	337	3	h	h	NOUN
ejpam-5713	338	1	=	=	SYM
ejpam-5713	338	2	kn	kn	PROPN
ejpam-5713	338	3	by	by	ADP
ejpam-5713	338	4	theorem	theorem	ADJ
ejpam-5713	338	5	2(iii	2(iii	NUM
ejpam-5713	338	6	)	)	PUNCT
ejpam-5713	338	7	.	.	PUNCT
ejpam-5713	339	1	hence	hence	ADV
ejpam-5713	339	2	,	,	PUNCT
ejpam-5713	339	3	(	(	PUNCT
ejpam-5713	339	4	ii	ii	NOUN
ejpam-5713	339	5	)	)	PUNCT
ejpam-5713	339	6	holds	hold	VERB
ejpam-5713	339	7	.	.	PUNCT
ejpam-5713	340	1	if	if	SCONJ
ejpam-5713	340	2	βs(g	βs(g	PUNCT
ejpam-5713	340	3	)	)	PUNCT
ejpam-5713	340	4	=	=	SYM
ejpam-5713	340	5	m	m	PROPN
ejpam-5713	340	6	,	,	PUNCT
ejpam-5713	340	7	then	then	ADV
ejpam-5713	340	8	(	(	PUNCT
ejpam-5713	340	9	ii	ii	NOUN
ejpam-5713	340	10	)	)	PUNCT
ejpam-5713	340	11	or	or	CCONJ
ejpam-5713	340	12	(	(	PUNCT
ejpam-5713	340	13	iii	iii	NOUN
ejpam-5713	340	14	)	)	PUNCT
ejpam-5713	340	15	holds	hold	VERB
ejpam-5713	340	16	.	.	PUNCT
ejpam-5713	341	1	for	for	ADP
ejpam-5713	341	2	the	the	DET
ejpam-5713	341	3	converse	converse	NOUN
ejpam-5713	341	4	,	,	PUNCT
ejpam-5713	341	5	suppose	suppose	VERB
ejpam-5713	341	6	(	(	PUNCT
ejpam-5713	341	7	i	i	NOUN
ejpam-5713	341	8	)	)	PUNCT
ejpam-5713	341	9	holds	hold	VERB
ejpam-5713	341	10	.	.	PUNCT
ejpam-5713	342	1	by	by	ADP
ejpam-5713	342	2	theorem	theorem	NOUN
ejpam-5713	342	3	4	4	NUM
ejpam-5713	342	4	,	,	PUNCT
ejpam-5713	342	5	it	it	PRON
ejpam-5713	342	6	follows	follow	VERB
ejpam-5713	342	7	that	that	SCONJ
ejpam-5713	342	8	βs(g	βs(g	PUNCT
ejpam-5713	342	9	+	+	NUM
ejpam-5713	342	10	h	h	X
ejpam-5713	342	11	)	)	PUNCT
ejpam-5713	342	12	=	=	SYM
ejpam-5713	343	1	m+	m+	NUM
ejpam-5713	343	2	n−	n−	NOUN
ejpam-5713	343	3	1	1	NUM
ejpam-5713	343	4	.	.	PUNCT
ejpam-5713	344	1	next	next	ADV
ejpam-5713	344	2	,	,	PUNCT
ejpam-5713	344	3	suppose	suppose	VERB
ejpam-5713	344	4	(	(	PUNCT
ejpam-5713	344	5	ii	ii	NOUN
ejpam-5713	344	6	)	)	PUNCT
ejpam-5713	344	7	holds	hold	NOUN
ejpam-5713	344	8	,	,	PUNCT
ejpam-5713	344	9	i.e.	i.e.	X
ejpam-5713	344	10	,	,	PUNCT
ejpam-5713	344	11	βs(g	βs(g	PUNCT
ejpam-5713	344	12	)	)	PUNCT
ejpam-5713	344	13	=	=	SYM
ejpam-5713	345	1	m−	m−	PROPN
ejpam-5713	345	2	1	1	NUM
ejpam-5713	345	3	and	and	CCONJ
ejpam-5713	345	4	h	h	NOUN
ejpam-5713	346	1	=	=	SYM
ejpam-5713	346	2	kn	kn	PROPN
ejpam-5713	346	3	.	.	PUNCT
ejpam-5713	347	1	if	if	SCONJ
ejpam-5713	347	2	c	c	PROPN
ejpam-5713	347	3	is	be	AUX
ejpam-5713	347	4	a	a	DET
ejpam-5713	347	5	βs	βs	NOUN
ejpam-5713	347	6	-	-	PUNCT
ejpam-5713	347	7	set	set	NOUN
ejpam-5713	347	8	in	in	ADP
ejpam-5713	347	9	g+h	g+h	PROPN
ejpam-5713	347	10	,	,	PUNCT
ejpam-5713	347	11	then	then	ADV
ejpam-5713	347	12	c	c	PROPN
ejpam-5713	347	13	satisfies	satisfie	NOUN
ejpam-5713	347	14	(	(	PUNCT
ejpam-5713	347	15	ii	ii	NOUN
ejpam-5713	347	16	)	)	PUNCT
ejpam-5713	347	17	or	or	CCONJ
ejpam-5713	347	18	(	(	PUNCT
ejpam-5713	347	19	iii	iii	NOUN
ejpam-5713	347	20	)	)	PUNCT
ejpam-5713	347	21	or	or	CCONJ
ejpam-5713	347	22	(	(	PUNCT
ejpam-5713	347	23	iv	iv	X
ejpam-5713	347	24	)	)	PUNCT
ejpam-5713	347	25	(	(	PUNCT
ejpam-5713	347	26	in	in	ADP
ejpam-5713	347	27	case	case	NOUN
ejpam-5713	347	28	g	g	NOUN
ejpam-5713	347	29	has	have	VERB
ejpam-5713	347	30	an	an	DET
ejpam-5713	347	31	isolated	isolated	ADJ
ejpam-5713	347	32	vertex	vertex	NOUN
ejpam-5713	347	33	)	)	PUNCT
ejpam-5713	347	34	of	of	ADP
ejpam-5713	347	35	theorem	theorem	PROPN
ejpam-5713	347	36	s.	s.	PROPN
ejpam-5713	347	37	r.	r.	PROPN
ejpam-5713	347	38	canoy	canoy	PROPN
ejpam-5713	347	39	et	et	PROPN
ejpam-5713	347	40	al	al	PROPN
ejpam-5713	347	41	.	.	PUNCT
ejpam-5713	347	42	/	/	SYM
ejpam-5713	347	43	eur	eur	PROPN
ejpam-5713	347	44	.	.	PUNCT
ejpam-5713	348	1	j.	j.	PROPN
ejpam-5713	348	2	pure	pure	PROPN
ejpam-5713	348	3	appl	appl	PROPN
ejpam-5713	348	4	.	.	PROPN
ejpam-5713	348	5	math	math	PROPN
ejpam-5713	348	6	,	,	PUNCT
ejpam-5713	348	7	18	18	NUM
ejpam-5713	348	8	(	(	PUNCT
ejpam-5713	348	9	1	1	NUM
ejpam-5713	348	10	)	)	PUNCT
ejpam-5713	348	11	(	(	PUNCT
ejpam-5713	348	12	2025	2025	NUM
ejpam-5713	348	13	)	)	PUNCT
ejpam-5713	348	14	,	,	PUNCT
ejpam-5713	348	15	5713	5713	NUM
ejpam-5713	348	16	9	9	NUM
ejpam-5713	348	17	of	of	ADP
ejpam-5713	348	18	13	13	NUM
ejpam-5713	348	19	4	4	NUM
ejpam-5713	348	20	.	.	PUNCT
ejpam-5713	349	1	that	that	PRON
ejpam-5713	349	2	is	be	AUX
ejpam-5713	349	3	,	,	PUNCT
ejpam-5713	349	4	c	c	PROPN
ejpam-5713	349	5	=	=	SYM
ejpam-5713	349	6	v	v	PROPN
ejpam-5713	349	7	(	(	PUNCT
ejpam-5713	349	8	h	h	NOUN
ejpam-5713	349	9	)	)	PUNCT
ejpam-5713	349	10	∪	∪	PROPN
ejpam-5713	349	11	cg	cg	NOUN
ejpam-5713	349	12	,	,	PUNCT
ejpam-5713	349	13	where	where	SCONJ
ejpam-5713	349	14	cg	cg	NOUN
ejpam-5713	349	15	is	be	AUX
ejpam-5713	349	16	βs	βs	ADV
ejpam-5713	349	17	-	-	PUNCT
ejpam-5713	349	18	set	set	VERB
ejpam-5713	349	19	in	in	ADP
ejpam-5713	349	20	g	g	NOUN
ejpam-5713	349	21	,	,	PUNCT
ejpam-5713	349	22	or	or	CCONJ
ejpam-5713	349	23	c	c	NOUN
ejpam-5713	349	24	=	=	SYM
ejpam-5713	349	25	v	v	PROPN
ejpam-5713	349	26	(	(	PUNCT
ejpam-5713	349	27	g	g	NOUN
ejpam-5713	349	28	)	)	PUNCT
ejpam-5713	349	29	∪	∪	ADP
ejpam-5713	349	30	[	[	X
ejpam-5713	349	31	v	v	X
ejpam-5713	349	32	(	(	PUNCT
ejpam-5713	349	33	kn	kn	PROPN
ejpam-5713	349	34	)	)	PUNCT
ejpam-5713	349	35	\	\	PROPN
ejpam-5713	349	36	{	{	PUNCT
ejpam-5713	349	37	q	q	NOUN
ejpam-5713	349	38	}	}	PUNCT
ejpam-5713	349	39	for	for	ADP
ejpam-5713	349	40	a	a	DET
ejpam-5713	349	41	q	q	X
ejpam-5713	349	42	∈	∈	PROPN
ejpam-5713	349	43	v	v	NOUN
ejpam-5713	349	44	(	(	PUNCT
ejpam-5713	349	45	kn	kn	PROPN
ejpam-5713	349	46	)	)	PUNCT
ejpam-5713	349	47	or	or	CCONJ
ejpam-5713	349	48	c	c	NOUN
ejpam-5713	349	49	=	=	SYM
ejpam-5713	349	50	v	v	PROPN
ejpam-5713	349	51	(	(	PUNCT
ejpam-5713	349	52	h	h	NOUN
ejpam-5713	349	53	)	)	PUNCT
ejpam-5713	349	54	∪	∪	ADP
ejpam-5713	349	55	[	[	X
ejpam-5713	349	56	v	v	X
ejpam-5713	349	57	(	(	PUNCT
ejpam-5713	349	58	g	g	NOUN
ejpam-5713	349	59	)	)	PUNCT
ejpam-5713	349	60	\	\	NOUN
ejpam-5713	349	61	{	{	PUNCT
ejpam-5713	349	62	x	x	X
ejpam-5713	349	63	}	}	PUNCT
ejpam-5713	349	64	if	if	SCONJ
ejpam-5713	349	65	x	x	PRON
ejpam-5713	349	66	is	be	AUX
ejpam-5713	349	67	an	an	DET
ejpam-5713	349	68	isolated	isolated	ADJ
ejpam-5713	349	69	vertex	vertex	NOUN
ejpam-5713	349	70	in	in	ADP
ejpam-5713	349	71	g.	g.	PROPN
ejpam-5713	349	72	this	this	PRON
ejpam-5713	349	73	implies	imply	VERB
ejpam-5713	349	74	that	that	SCONJ
ejpam-5713	349	75	βs(g	βs(g	PUNCT
ejpam-5713	349	76	+	+	NOUN
ejpam-5713	349	77	h	h	NOUN
ejpam-5713	349	78	)	)	PUNCT
ejpam-5713	349	79	=	=	NOUN
ejpam-5713	349	80	m	m	VERB
ejpam-5713	349	81	+	+	NOUN
ejpam-5713	349	82	n	n	CCONJ
ejpam-5713	349	83	−	−	PROPN
ejpam-5713	349	84	1	1	NUM
ejpam-5713	349	85	.	.	PUNCT
ejpam-5713	350	1	lastly	lastly	ADV
ejpam-5713	350	2	,	,	PUNCT
ejpam-5713	350	3	suppose	suppose	VERB
ejpam-5713	350	4	(	(	PUNCT
ejpam-5713	350	5	iii	iii	NOUN
ejpam-5713	350	6	)	)	PUNCT
ejpam-5713	350	7	holds	hold	VERB
ejpam-5713	350	8	.	.	PUNCT
ejpam-5713	351	1	since	since	SCONJ
ejpam-5713	351	2	βs(g	βs(g	PUNCT
ejpam-5713	351	3	)	)	PUNCT
ejpam-5713	351	4	=	=	SYM
ejpam-5713	351	5	m	m	NOUN
ejpam-5713	351	6	and	and	CCONJ
ejpam-5713	351	7	βs(h	βs(h	PRON
ejpam-5713	351	8	)	)	PUNCT
ejpam-5713	351	9	=	=	SYM
ejpam-5713	351	10	n	n	PROPN
ejpam-5713	351	11	and	and	CCONJ
ejpam-5713	351	12	c	c	PROPN
ejpam-5713	351	13	is	be	AUX
ejpam-5713	351	14	a	a	DET
ejpam-5713	351	15	βs	βs	NOUN
ejpam-5713	351	16	-	-	PUNCT
ejpam-5713	351	17	set	set	NOUN
ejpam-5713	351	18	in	in	ADP
ejpam-5713	351	19	g	g	PROPN
ejpam-5713	351	20	+	+	PROPN
ejpam-5713	351	21	h	h	NOUN
ejpam-5713	351	22	,	,	PUNCT
ejpam-5713	351	23	c	c	NOUN
ejpam-5713	351	24	satisfies	satisfie	NOUN
ejpam-5713	351	25	(	(	PUNCT
ejpam-5713	351	26	ii	ii	NOUN
ejpam-5713	351	27	)	)	PUNCT
ejpam-5713	351	28	or	or	CCONJ
ejpam-5713	351	29	(	(	PUNCT
ejpam-5713	351	30	iv	iv	X
ejpam-5713	351	31	)	)	PUNCT
ejpam-5713	351	32	of	of	ADP
ejpam-5713	351	33	theorem	theorem	ADJ
ejpam-5713	351	34	4	4	NUM
ejpam-5713	351	35	.	.	PUNCT
ejpam-5713	351	36	therefore	therefore	ADV
ejpam-5713	351	37	,	,	PUNCT
ejpam-5713	351	38	βs(g+h	βs(g+h	SYM
ejpam-5713	351	39	)	)	PUNCT
ejpam-5713	352	1	=	=	SYM
ejpam-5713	353	1	m+	m+	NUM
ejpam-5713	353	2	n−	n−	NOUN
ejpam-5713	353	3	1	1	NUM
ejpam-5713	353	4	.	.	PUNCT
ejpam-5713	353	5	corollary	corollary	ADJ
ejpam-5713	353	6	4	4	NUM
ejpam-5713	353	7	.	.	PUNCT
ejpam-5713	354	1	let	let	VERB
ejpam-5713	354	2	g	g	NOUN
ejpam-5713	354	3	and	and	CCONJ
ejpam-5713	354	4	h	h	NOUN
ejpam-5713	354	5	be	be	VERB
ejpam-5713	354	6	any	any	DET
ejpam-5713	354	7	two	two	NUM
ejpam-5713	354	8	graphs	graph	NOUN
ejpam-5713	354	9	of	of	ADP
ejpam-5713	354	10	orders	order	NOUN
ejpam-5713	354	11	m	m	VERB
ejpam-5713	354	12	and	and	CCONJ
ejpam-5713	354	13	n	n	CCONJ
ejpam-5713	354	14	,	,	PUNCT
ejpam-5713	354	15	respectively	respectively	ADV
ejpam-5713	354	16	,	,	PUNCT
ejpam-5713	354	17	such	such	ADJ
ejpam-5713	354	18	that	that	PRON
ejpam-5713	354	19	βs(g+h	βs(g+h	NOUN
ejpam-5713	354	20	)	)	PUNCT
ejpam-5713	354	21	̸=	̸=	PROPN
ejpam-5713	354	22	m+	m+	NUM
ejpam-5713	354	23	n−	n−	NOUN
ejpam-5713	354	24	1	1	NUM
ejpam-5713	354	25	.	.	PUNCT
ejpam-5713	355	1	then	then	ADV
ejpam-5713	355	2	βs(g+h	βs(g+h	PRON
ejpam-5713	355	3	)	)	PUNCT
ejpam-5713	355	4	=	=	NOUN
ejpam-5713	355	5	min{m+	min{m+	PROPN
ejpam-5713	355	6	βs(h	βs(h	PUNCT
ejpam-5713	355	7	)	)	PUNCT
ejpam-5713	355	8	,	,	PUNCT
ejpam-5713	355	9	n+	n+	NUM
ejpam-5713	355	10	βs(g	βs(g	PUNCT
ejpam-5713	355	11	)	)	PUNCT
ejpam-5713	355	12	}	}	PUNCT
ejpam-5713	355	13	.	.	PUNCT
ejpam-5713	356	1	proof	proof	NOUN
ejpam-5713	356	2	.	.	PUNCT
ejpam-5713	357	1	let	let	VERB
ejpam-5713	357	2	d1	d1	PROPN
ejpam-5713	357	3	and	and	CCONJ
ejpam-5713	357	4	d2	d2	PROPN
ejpam-5713	357	5	be	be	AUX
ejpam-5713	357	6	βs	β	NOUN
ejpam-5713	357	7	-	-	PUNCT
ejpam-5713	357	8	sets	set	NOUN
ejpam-5713	357	9	in	in	ADP
ejpam-5713	357	10	g	g	PROPN
ejpam-5713	357	11	and	and	CCONJ
ejpam-5713	357	12	h	h	NOUN
ejpam-5713	357	13	,	,	PUNCT
ejpam-5713	357	14	respectively	respectively	ADV
ejpam-5713	357	15	.	.	PUNCT
ejpam-5713	358	1	then	then	ADV
ejpam-5713	358	2	c1	c1	PROPN
ejpam-5713	358	3	=	=	PROPN
ejpam-5713	358	4	d2	d2	PROPN
ejpam-5713	358	5	∪v	∪v	PUNCT
ejpam-5713	358	6	(	(	PUNCT
ejpam-5713	358	7	g	g	NOUN
ejpam-5713	358	8	)	)	PUNCT
ejpam-5713	358	9	and	and	CCONJ
ejpam-5713	358	10	c2	c2	PROPN
ejpam-5713	358	11	=	=	PUNCT
ejpam-5713	358	12	d1	d1	PROPN
ejpam-5713	358	13	∪	∪	ADP
ejpam-5713	358	14	v	v	NOUN
ejpam-5713	358	15	(	(	PUNCT
ejpam-5713	358	16	h	h	NOUN
ejpam-5713	358	17	)	)	PUNCT
ejpam-5713	358	18	are	be	AUX
ejpam-5713	358	19	super	super	ADJ
ejpam-5713	358	20	vertex	vertex	NOUN
ejpam-5713	358	21	covers	cover	NOUN
ejpam-5713	358	22	of	of	ADP
ejpam-5713	358	23	g+h	g+h	PROPN
ejpam-5713	358	24	by	by	ADP
ejpam-5713	358	25	theorem	theorem	NOUN
ejpam-5713	358	26	4	4	NUM
ejpam-5713	358	27	.	.	PUNCT
ejpam-5713	359	1	therefore	therefore	ADV
ejpam-5713	359	2	,	,	PUNCT
ejpam-5713	359	3	βs(g+h	βs(g+h	SYM
ejpam-5713	359	4	)	)	PUNCT
ejpam-5713	359	5	≤	≤	NOUN
ejpam-5713	359	6	min{|c1|	min{|c1|	PROPN
ejpam-5713	359	7	,	,	PUNCT
ejpam-5713	359	8	|c2|	|c2|	NOUN
ejpam-5713	359	9	}	}	PUNCT
ejpam-5713	359	10	=	=	SYM
ejpam-5713	359	11	min{m+	min{m+	PROPN
ejpam-5713	359	12	βs(h	βs(h	NUM
ejpam-5713	359	13	)	)	PUNCT
ejpam-5713	359	14	,	,	PUNCT
ejpam-5713	359	15	n+	n+	NUM
ejpam-5713	359	16	βs(g	βs(g	PUNCT
ejpam-5713	359	17	)	)	PUNCT
ejpam-5713	359	18	}	}	PUNCT
ejpam-5713	359	19	.	.	PUNCT
ejpam-5713	360	1	next	next	ADV
ejpam-5713	360	2	,	,	PUNCT
ejpam-5713	360	3	let	let	VERB
ejpam-5713	360	4	c	c	PRON
ejpam-5713	360	5	be	be	AUX
ejpam-5713	360	6	a	a	DET
ejpam-5713	360	7	βs	βs	NOUN
ejpam-5713	360	8	-	-	PUNCT
ejpam-5713	360	9	set	set	NOUN
ejpam-5713	360	10	in	in	ADP
ejpam-5713	360	11	g	g	PROPN
ejpam-5713	360	12	+	+	CCONJ
ejpam-5713	360	13	h.	h.	PROPN
ejpam-5713	360	14	since	since	SCONJ
ejpam-5713	360	15	βs(g	βs(g	PUNCT
ejpam-5713	360	16	+	+	NUM
ejpam-5713	360	17	h	h	X
ejpam-5713	360	18	)	)	PUNCT
ejpam-5713	360	19	̸=	̸=	PROPN
ejpam-5713	360	20	m	m	PROPN
ejpam-5713	360	21	+	+	NOUN
ejpam-5713	360	22	n	n	CCONJ
ejpam-5713	360	23	−	−	PROPN
ejpam-5713	360	24	1	1	NUM
ejpam-5713	360	25	,	,	PUNCT
ejpam-5713	360	26	βs(g	βs(g	PUNCT
ejpam-5713	360	27	)	)	PUNCT
ejpam-5713	360	28	<	<	X
ejpam-5713	360	29	m	m	VERB
ejpam-5713	360	30	−	−	NUM
ejpam-5713	360	31	1	1	NUM
ejpam-5713	360	32	or	or	CCONJ
ejpam-5713	360	33	βs(h	βs(h	NUM
ejpam-5713	360	34	)	)	PUNCT
ejpam-5713	360	35	<	<	X
ejpam-5713	360	36	n−	n−	NOUN
ejpam-5713	360	37	1	1	NUM
ejpam-5713	360	38	by	by	ADP
ejpam-5713	360	39	corollary	corollary	ADJ
ejpam-5713	360	40	3	3	NUM
ejpam-5713	360	41	.	.	PUNCT
ejpam-5713	361	1	this	this	PRON
ejpam-5713	361	2	implies	imply	VERB
ejpam-5713	361	3	that	that	SCONJ
ejpam-5713	361	4	c	c	PROPN
ejpam-5713	361	5	satisfies	satisfie	NOUN
ejpam-5713	361	6	(	(	PUNCT
ejpam-5713	361	7	i	i	NOUN
ejpam-5713	361	8	)	)	PUNCT
ejpam-5713	361	9	or	or	CCONJ
ejpam-5713	361	10	(	(	PUNCT
ejpam-5713	361	11	iii	iii	NOUN
ejpam-5713	361	12	)	)	PUNCT
ejpam-5713	361	13	of	of	ADP
ejpam-5713	361	14	theorem	theorem	ADJ
ejpam-5713	361	15	4	4	NUM
ejpam-5713	361	16	,	,	PUNCT
ejpam-5713	361	17	i.e.	i.e.	X
ejpam-5713	361	18	,	,	PUNCT
ejpam-5713	361	19	c	c	NOUN
ejpam-5713	361	20	=	=	SYM
ejpam-5713	361	21	v	v	PROPN
ejpam-5713	361	22	(	(	PUNCT
ejpam-5713	361	23	g	g	NOUN
ejpam-5713	361	24	)	)	PUNCT
ejpam-5713	361	25	∪	∪	NOUN
ejpam-5713	361	26	ch	ch	NOUN
ejpam-5713	361	27	or	or	CCONJ
ejpam-5713	361	28	c	c	NOUN
ejpam-5713	361	29	=	=	SYM
ejpam-5713	361	30	v	v	PROPN
ejpam-5713	361	31	(	(	PUNCT
ejpam-5713	361	32	h	h	NOUN
ejpam-5713	361	33	)	)	PUNCT
ejpam-5713	361	34	∪	∪	PROPN
ejpam-5713	361	35	cg	cg	NOUN
ejpam-5713	361	36	,	,	PUNCT
ejpam-5713	361	37	where	where	SCONJ
ejpam-5713	361	38	cg	cg	NOUN
ejpam-5713	361	39	and	and	CCONJ
ejpam-5713	361	40	ch	ch	NOUN
ejpam-5713	361	41	are	be	AUX
ejpam-5713	361	42	super	super	ADJ
ejpam-5713	361	43	vertex	vertex	NOUN
ejpam-5713	361	44	covers	cover	NOUN
ejpam-5713	361	45	of	of	ADP
ejpam-5713	361	46	g	g	PROPN
ejpam-5713	361	47	and	and	CCONJ
ejpam-5713	361	48	h	h	NOUN
ejpam-5713	361	49	,	,	PUNCT
ejpam-5713	361	50	respectively	respectively	ADV
ejpam-5713	361	51	.	.	PUNCT
ejpam-5713	362	1	it	it	PRON
ejpam-5713	362	2	follows	follow	VERB
ejpam-5713	362	3	that	that	SCONJ
ejpam-5713	362	4	βs(g	βs(g	PUNCT
ejpam-5713	362	5	+	+	NUM
ejpam-5713	362	6	h	h	X
ejpam-5713	362	7	)	)	PUNCT
ejpam-5713	362	8	=	=	SYM
ejpam-5713	362	9	|c|	|c|	PROPN
ejpam-5713	362	10	≥	≥	NOUN
ejpam-5713	362	11	min{m	min{m	NOUN
ejpam-5713	362	12	+	+	CCONJ
ejpam-5713	362	13	βs(h	βs(h	NUM
ejpam-5713	362	14	)	)	PUNCT
ejpam-5713	362	15	,	,	PUNCT
ejpam-5713	362	16	n	n	PROPN
ejpam-5713	362	17	+	+	X
ejpam-5713	362	18	βs(g	βs(g	PUNCT
ejpam-5713	362	19	)	)	PUNCT
ejpam-5713	362	20	}	}	PUNCT
ejpam-5713	362	21	.	.	PUNCT
ejpam-5713	363	1	this	this	PRON
ejpam-5713	363	2	establishes	establish	VERB
ejpam-5713	363	3	the	the	DET
ejpam-5713	363	4	desired	desire	VERB
ejpam-5713	363	5	equality	equality	NOUN
ejpam-5713	363	6	.	.	PUNCT
ejpam-5713	364	1	the	the	DET
ejpam-5713	364	2	next	next	ADJ
ejpam-5713	364	3	result	result	NOUN
ejpam-5713	364	4	is	be	AUX
ejpam-5713	364	5	immediate	immediate	ADJ
ejpam-5713	364	6	from	from	ADP
ejpam-5713	364	7	theorem	theorem	ADJ
ejpam-5713	364	8	4	4	NUM
ejpam-5713	364	9	and	and	CCONJ
ejpam-5713	364	10	corollary	corollary	ADJ
ejpam-5713	364	11	1(i	1(i	NUM
ejpam-5713	364	12	)	)	PUNCT
ejpam-5713	364	13	.	.	PUNCT
ejpam-5713	365	1	corollary	corollary	ADJ
ejpam-5713	365	2	5	5	NUM
ejpam-5713	365	3	.	.	PUNCT
ejpam-5713	366	1	let	let	VERB
ejpam-5713	366	2	g	g	PRON
ejpam-5713	366	3	be	be	AUX
ejpam-5713	366	4	a	a	DET
ejpam-5713	366	5	graph	graph	NOUN
ejpam-5713	366	6	of	of	ADP
ejpam-5713	366	7	order	order	NOUN
ejpam-5713	366	8	m	m	VERB
ejpam-5713	366	9	and	and	CCONJ
ejpam-5713	366	10	let	let	VERB
ejpam-5713	366	11	n	n	PRON
ejpam-5713	366	12	be	be	AUX
ejpam-5713	366	13	any	any	DET
ejpam-5713	366	14	positive	positive	ADJ
ejpam-5713	366	15	integer	integer	NOUN
ejpam-5713	366	16	.	.	PUNCT
ejpam-5713	367	1	then	then	ADV
ejpam-5713	367	2	βs(kn+g	βs(kn+g	NOUN
ejpam-5713	367	3	)	)	PUNCT
ejpam-5713	367	4	=	=	PUNCT
ejpam-5713	367	5	min{n+βs(g),m+n−1	min{n+βs(g),m+n−1	PROPN
ejpam-5713	367	6	}	}	PUNCT
ejpam-5713	367	7	.	.	PUNCT
ejpam-5713	368	1	in	in	ADP
ejpam-5713	368	2	particular	particular	ADJ
ejpam-5713	368	3	,	,	PUNCT
ejpam-5713	368	4	βs(k1+g	βs(k1+g	NOUN
ejpam-5713	368	5	)	)	PUNCT
ejpam-5713	368	6	=	=	SYM
ejpam-5713	368	7	min{1+βs(g),m	min{1+βs(g),m	ADJ
ejpam-5713	368	8	}	}	PUNCT
ejpam-5713	368	9	.	.	PUNCT
ejpam-5713	369	1	moreover	moreover	ADV
ejpam-5713	369	2	,	,	PUNCT
ejpam-5713	369	3	each	each	PRON
ejpam-5713	369	4	of	of	ADP
ejpam-5713	369	5	the	the	DET
ejpam-5713	369	6	following	follow	VERB
ejpam-5713	369	7	holds	hold	VERB
ejpam-5713	369	8	:	:	PUNCT
ejpam-5713	369	9	(	(	PUNCT
ejpam-5713	369	10	i	i	NOUN
ejpam-5713	369	11	)	)	PUNCT
ejpam-5713	369	12	βs(fn	βs(fn	PROPN
ejpam-5713	369	13	)	)	PUNCT
ejpam-5713	369	14	=	=	PUNCT
ejpam-5713	369	15	βs(k1	βs(k1	PROPN
ejpam-5713	370	1	+	+	CCONJ
ejpam-5713	370	2	pn	pn	NOUN
ejpam-5713	370	3	)	)	PUNCT
ejpam-5713	370	4	=	=	SYM
ejpam-5713	370	5	1	1	NUM
ejpam-5713	370	6	+	+	NUM
ejpam-5713	370	7	βs(pn	βs(pn	NUM
ejpam-5713	370	8	)	)	PUNCT
ejpam-5713	370	9	for	for	ADP
ejpam-5713	370	10	n	n	X
ejpam-5713	370	11	≥	≥	NUM
ejpam-5713	370	12	2	2	NUM
ejpam-5713	370	13	.	.	PUNCT
ejpam-5713	370	14	(	(	PUNCT
ejpam-5713	370	15	ii	ii	NOUN
ejpam-5713	370	16	)	)	PUNCT
ejpam-5713	370	17	βs(wn	βs(wn	PROPN
ejpam-5713	370	18	)	)	PUNCT
ejpam-5713	370	19	=	=	SYM
ejpam-5713	370	20	βs(k1	βs(k1	PROPN
ejpam-5713	371	1	+	+	CCONJ
ejpam-5713	371	2	cn	cn	ADJ
ejpam-5713	371	3	)	)	PUNCT
ejpam-5713	371	4	=	=	SYM
ejpam-5713	371	5	1	1	NUM
ejpam-5713	371	6	+	+	NUM
ejpam-5713	371	7	βs(cn	βs(cn	NOUN
ejpam-5713	371	8	)	)	PUNCT
ejpam-5713	371	9	for	for	ADP
ejpam-5713	371	10	n	n	X
ejpam-5713	371	11	≥	≥	NUM
ejpam-5713	371	12	3	3	NUM
ejpam-5713	371	13	.	.	PUNCT
ejpam-5713	371	14	theorem	theorem	NOUN
ejpam-5713	371	15	5	5	NUM
ejpam-5713	371	16	.	.	PUNCT
ejpam-5713	372	1	let	let	VERB
ejpam-5713	372	2	g	g	PRON
ejpam-5713	372	3	be	be	AUX
ejpam-5713	372	4	a	a	DET
ejpam-5713	372	5	non	non	ADJ
ejpam-5713	372	6	-	-	ADJ
ejpam-5713	372	7	trivial	trivial	ADJ
ejpam-5713	372	8	connected	connected	ADJ
ejpam-5713	372	9	graph	graph	NOUN
ejpam-5713	372	10	and	and	CCONJ
ejpam-5713	372	11	let	let	VERB
ejpam-5713	372	12	h	h	NOUN
ejpam-5713	372	13	be	be	AUX
ejpam-5713	372	14	any	any	DET
ejpam-5713	372	15	graph	graph	NOUN
ejpam-5713	372	16	.	.	PUNCT
ejpam-5713	373	1	then	then	ADV
ejpam-5713	373	2	s	s	VERB
ejpam-5713	373	3	⊆	⊆	NUM
ejpam-5713	373	4	v	v	NOUN
ejpam-5713	373	5	(	(	PUNCT
ejpam-5713	373	6	g	g	PROPN
ejpam-5713	373	7	◦	◦	NOUN
ejpam-5713	373	8	h	h	NOUN
ejpam-5713	373	9	)	)	PUNCT
ejpam-5713	373	10	is	be	AUX
ejpam-5713	373	11	a	a	DET
ejpam-5713	373	12	super	super	ADJ
ejpam-5713	373	13	vertex	vertex	NOUN
ejpam-5713	373	14	cover	cover	NOUN
ejpam-5713	373	15	in	in	ADP
ejpam-5713	373	16	g	g	PROPN
ejpam-5713	373	17	◦	◦	NOUN
ejpam-5713	373	18	h	h	NOUN
ejpam-5713	373	19	if	if	SCONJ
ejpam-5713	374	1	and	and	CCONJ
ejpam-5713	374	2	only	only	ADV
ejpam-5713	374	3	if	if	SCONJ
ejpam-5713	374	4	s	s	VERB
ejpam-5713	374	5	=	=	NOUN
ejpam-5713	374	6	a	a	DET
ejpam-5713	374	7	∪	∪	X
ejpam-5713	374	8	(	(	PUNCT
ejpam-5713	374	9	∪v∈v	∪v∈v	X
ejpam-5713	374	10	(	(	PUNCT
ejpam-5713	374	11	g)sv	g)sv	PROPN
ejpam-5713	374	12	)	)	PUNCT
ejpam-5713	374	13	and	and	CCONJ
ejpam-5713	374	14	satisfies	satisfy	VERB
ejpam-5713	374	15	the	the	DET
ejpam-5713	374	16	following	follow	VERB
ejpam-5713	374	17	conditions	condition	NOUN
ejpam-5713	374	18	:	:	PUNCT
ejpam-5713	374	19	(	(	PUNCT
ejpam-5713	374	20	i	i	NOUN
ejpam-5713	374	21	)	)	PUNCT
ejpam-5713	374	22	a	a	PRON
ejpam-5713	374	23	is	be	AUX
ejpam-5713	374	24	a	a	DET
ejpam-5713	374	25	vertex	vertex	NOUN
ejpam-5713	374	26	cover	cover	NOUN
ejpam-5713	374	27	in	in	ADP
ejpam-5713	374	28	g.	g.	PROPN
ejpam-5713	374	29	(	(	PUNCT
ejpam-5713	374	30	ii	ii	PROPN
ejpam-5713	374	31	)	)	PUNCT
ejpam-5713	374	32	for	for	ADP
ejpam-5713	374	33	each	each	DET
ejpam-5713	374	34	v	v	ADP
ejpam-5713	374	35	∈	∈	PROPN
ejpam-5713	375	1	a	a	DET
ejpam-5713	375	2	∩ng(v	∩ng(v	PROPN
ejpam-5713	375	3	(	(	PUNCT
ejpam-5713	375	4	g	g	NOUN
ejpam-5713	375	5	)	)	PUNCT
ejpam-5713	375	6	\a	\a	NUM
ejpam-5713	375	7	)	)	PUNCT
ejpam-5713	376	1	,	,	PUNCT
ejpam-5713	376	2	it	it	PRON
ejpam-5713	376	3	holds	hold	VERB
ejpam-5713	376	4	that	that	SCONJ
ejpam-5713	376	5	sv	sv	PROPN
ejpam-5713	376	6	is	be	AUX
ejpam-5713	376	7	a	a	DET
ejpam-5713	376	8	super	super	ADJ
ejpam-5713	376	9	vertex	vertex	NOUN
ejpam-5713	376	10	cover	cover	NOUN
ejpam-5713	376	11	in	in	ADP
ejpam-5713	376	12	hv	hv	PROPN
ejpam-5713	376	13	.	.	PUNCT
ejpam-5713	377	1	(	(	PUNCT
ejpam-5713	377	2	iii	iii	NOUN
ejpam-5713	377	3	)	)	PUNCT
ejpam-5713	377	4	for	for	ADP
ejpam-5713	377	5	each	each	PRON
ejpam-5713	377	6	v	v	ADP
ejpam-5713	377	7	∈	∈	PRON
ejpam-5713	377	8	a	a	DET
ejpam-5713	377	9	\	\	NOUN
ejpam-5713	377	10	ng(v	ng(v	PUNCT
ejpam-5713	377	11	(	(	PUNCT
ejpam-5713	377	12	g	g	NOUN
ejpam-5713	377	13	)	)	PUNCT
ejpam-5713	377	14	\	\	PROPN
ejpam-5713	378	1	a	a	X
ejpam-5713	378	2	)	)	PUNCT
ejpam-5713	378	3	,	,	PUNCT
ejpam-5713	378	4	it	it	PRON
ejpam-5713	378	5	holds	hold	VERB
ejpam-5713	378	6	that	that	SCONJ
ejpam-5713	378	7	sv	sv	PROPN
ejpam-5713	378	8	is	be	AUX
ejpam-5713	378	9	a	a	DET
ejpam-5713	378	10	super	super	ADJ
ejpam-5713	378	11	vertex	vertex	NOUN
ejpam-5713	378	12	cover	cover	NOUN
ejpam-5713	378	13	in	in	ADP
ejpam-5713	378	14	hv	hv	PROPN
ejpam-5713	378	15	or	or	CCONJ
ejpam-5713	378	16	sv	sv	PROPN
ejpam-5713	378	17	=	=	SYM
ejpam-5713	378	18	v	v	PROPN
ejpam-5713	378	19	(	(	PUNCT
ejpam-5713	378	20	hv	hv	PROPN
ejpam-5713	378	21	)	)	PUNCT
ejpam-5713	378	22	\	\	NOUN
ejpam-5713	378	23	{	{	PUNCT
ejpam-5713	378	24	qv	qv	INTJ
ejpam-5713	378	25	}	}	PUNCT
ejpam-5713	378	26	for	for	ADP
ejpam-5713	378	27	some	some	DET
ejpam-5713	378	28	isolated	isolate	VERB
ejpam-5713	378	29	vertex	vertex	NOUN
ejpam-5713	378	30	qv	qv	X
ejpam-5713	378	31	in	in	ADP
ejpam-5713	378	32	hv	hv	PROPN
ejpam-5713	378	33	.	.	PUNCT
ejpam-5713	379	1	(	(	PUNCT
ejpam-5713	379	2	iv	iv	X
ejpam-5713	379	3	)	)	PUNCT
ejpam-5713	379	4	for	for	ADP
ejpam-5713	379	5	each	each	DET
ejpam-5713	379	6	v	v	NOUN
ejpam-5713	379	7	/∈	/∈	PUNCT
ejpam-5713	380	1	a	a	X
ejpam-5713	380	2	,	,	PUNCT
ejpam-5713	380	3	it	it	PRON
ejpam-5713	380	4	holds	hold	VERB
ejpam-5713	380	5	that	that	PRON
ejpam-5713	380	6	sv	sv	PROPN
ejpam-5713	380	7	=	=	SYM
ejpam-5713	380	8	v	v	PROPN
ejpam-5713	380	9	(	(	PUNCT
ejpam-5713	380	10	hv	hv	PROPN
ejpam-5713	380	11	)	)	PUNCT
ejpam-5713	380	12	.	.	PUNCT
ejpam-5713	381	1	proof	proof	NOUN
ejpam-5713	381	2	.	.	PUNCT
ejpam-5713	382	1	suppose	suppose	VERB
ejpam-5713	382	2	s	s	PRON
ejpam-5713	382	3	is	be	AUX
ejpam-5713	382	4	a	a	DET
ejpam-5713	382	5	super	super	ADJ
ejpam-5713	382	6	vertex	vertex	NOUN
ejpam-5713	382	7	cover	cover	NOUN
ejpam-5713	382	8	in	in	ADP
ejpam-5713	382	9	g	g	PROPN
ejpam-5713	382	10	◦	◦	PROPN
ejpam-5713	382	11	h.	h.	PROPN
ejpam-5713	382	12	let	let	VERB
ejpam-5713	382	13	a	a	DET
ejpam-5713	382	14	=	=	SYM
ejpam-5713	382	15	c	c	NOUN
ejpam-5713	382	16	∩	∩	X
ejpam-5713	382	17	v	v	X
ejpam-5713	382	18	(	(	PUNCT
ejpam-5713	382	19	g	g	NOUN
ejpam-5713	382	20	)	)	PUNCT
ejpam-5713	382	21	and	and	CCONJ
ejpam-5713	382	22	let	let	VERB
ejpam-5713	382	23	sv	sv	INTJ
ejpam-5713	382	24	=	=	VERB
ejpam-5713	382	25	c∩v	c∩v	NOUN
ejpam-5713	382	26	(	(	PUNCT
ejpam-5713	382	27	hv	hv	PROPN
ejpam-5713	382	28	)	)	PUNCT
ejpam-5713	382	29	for	for	ADP
ejpam-5713	382	30	each	each	DET
ejpam-5713	382	31	v	v	NUM
ejpam-5713	382	32	∈	∈	PROPN
ejpam-5713	382	33	v	v	NOUN
ejpam-5713	382	34	(	(	PUNCT
ejpam-5713	382	35	g	g	NOUN
ejpam-5713	382	36	)	)	PUNCT
ejpam-5713	382	37	.	.	PUNCT
ejpam-5713	383	1	then	then	ADV
ejpam-5713	383	2	s	s	VERB
ejpam-5713	383	3	=	=	SYM
ejpam-5713	383	4	a∪(∪v∈v	a∪(∪v∈v	PROPN
ejpam-5713	383	5	(	(	PUNCT
ejpam-5713	383	6	g)sv	g)sv	PROPN
ejpam-5713	383	7	)	)	PUNCT
ejpam-5713	383	8	.	.	PUNCT
ejpam-5713	384	1	let	let	VERB
ejpam-5713	384	2	ab	ab	PROPN
ejpam-5713	384	3	∈	∈	PROPN
ejpam-5713	384	4	e(g	e(g	PROPN
ejpam-5713	384	5	)	)	PUNCT
ejpam-5713	385	1	⊂	⊂	PROPN
ejpam-5713	385	2	e(g	e(g	PROPN
ejpam-5713	385	3	◦	◦	NOUN
ejpam-5713	385	4	h	h	NOUN
ejpam-5713	385	5	)	)	PUNCT
ejpam-5713	385	6	.	.	PUNCT
ejpam-5713	386	1	s.	s.	PROPN
ejpam-5713	386	2	r.	r.	PROPN
ejpam-5713	386	3	canoy	canoy	PROPN
ejpam-5713	386	4	et	et	PROPN
ejpam-5713	386	5	al	al	PROPN
ejpam-5713	386	6	.	.	PUNCT
ejpam-5713	386	7	/	/	SYM
ejpam-5713	386	8	eur	eur	PROPN
ejpam-5713	386	9	.	.	PUNCT
ejpam-5713	387	1	j.	j.	PROPN
ejpam-5713	387	2	pure	pure	PROPN
ejpam-5713	387	3	appl	appl	PROPN
ejpam-5713	387	4	.	.	PROPN
ejpam-5713	387	5	math	math	PROPN
ejpam-5713	387	6	,	,	PUNCT
ejpam-5713	387	7	18	18	NUM
ejpam-5713	387	8	(	(	PUNCT
ejpam-5713	387	9	1	1	NUM
ejpam-5713	387	10	)	)	PUNCT
ejpam-5713	387	11	(	(	PUNCT
ejpam-5713	387	12	2025	2025	NUM
ejpam-5713	387	13	)	)	PUNCT
ejpam-5713	387	14	,	,	PUNCT
ejpam-5713	387	15	5713	5713	NUM
ejpam-5713	387	16	10	10	NUM
ejpam-5713	387	17	of	of	ADP
ejpam-5713	387	18	13	13	NUM
ejpam-5713	387	19	since	since	SCONJ
ejpam-5713	387	20	s	s	NOUN
ejpam-5713	387	21	is	be	AUX
ejpam-5713	387	22	a	a	DET
ejpam-5713	387	23	vertex	vertex	NOUN
ejpam-5713	387	24	cover	cover	NOUN
ejpam-5713	387	25	in	in	ADP
ejpam-5713	387	26	g	g	NOUN
ejpam-5713	387	27	◦	◦	NOUN
ejpam-5713	387	28	h	h	NOUN
ejpam-5713	387	29	,	,	PUNCT
ejpam-5713	387	30	it	it	PRON
ejpam-5713	387	31	follows	follow	VERB
ejpam-5713	387	32	that	that	SCONJ
ejpam-5713	387	33	a	a	DET
ejpam-5713	387	34	∈	∈	PROPN
ejpam-5713	387	35	a	a	DET
ejpam-5713	387	36	or	or	CCONJ
ejpam-5713	387	37	b	b	NOUN
ejpam-5713	387	38	∈	∈	NOUN
ejpam-5713	387	39	a.	a.	NOUN
ejpam-5713	387	40	hence	hence	ADV
ejpam-5713	387	41	,	,	PUNCT
ejpam-5713	387	42	a	a	PRON
ejpam-5713	387	43	is	be	AUX
ejpam-5713	387	44	a	a	DET
ejpam-5713	387	45	vertex	vertex	NOUN
ejpam-5713	387	46	cover	cover	NOUN
ejpam-5713	387	47	in	in	ADP
ejpam-5713	387	48	g	g	NOUN
ejpam-5713	387	49	,	,	PUNCT
ejpam-5713	387	50	showing	show	VERB
ejpam-5713	387	51	that	that	SCONJ
ejpam-5713	387	52	(	(	PUNCT
ejpam-5713	387	53	i	i	NOUN
ejpam-5713	387	54	)	)	PUNCT
ejpam-5713	387	55	holds	hold	VERB
ejpam-5713	387	56	.	.	PUNCT
ejpam-5713	388	1	let	let	VERB
ejpam-5713	388	2	v	v	NUM
ejpam-5713	388	3	∈	∈	PROPN
ejpam-5713	388	4	a∩ng(v	a∩ng(v	X
ejpam-5713	388	5	(	(	PUNCT
ejpam-5713	388	6	g	g	NOUN
ejpam-5713	388	7	)	)	PUNCT
ejpam-5713	388	8	\a	\a	NUM
ejpam-5713	388	9	)	)	PUNCT
ejpam-5713	388	10	and	and	CCONJ
ejpam-5713	388	11	let	let	VERB
ejpam-5713	388	12	pq	pq	INTJ
ejpam-5713	388	13	∈	∈	PROPN
ejpam-5713	388	14	e(hv	e(hv	PROPN
ejpam-5713	388	15	)	)	PUNCT
ejpam-5713	389	1	⊂	⊂	PROPN
ejpam-5713	389	2	e(g	e(g	PROPN
ejpam-5713	389	3	◦	◦	NOUN
ejpam-5713	389	4	h	h	NOUN
ejpam-5713	389	5	)	)	PUNCT
ejpam-5713	389	6	.	.	PUNCT
ejpam-5713	390	1	again	again	ADV
ejpam-5713	390	2	,	,	PUNCT
ejpam-5713	390	3	because	because	SCONJ
ejpam-5713	390	4	s	s	NOUN
ejpam-5713	390	5	is	be	AUX
ejpam-5713	390	6	a	a	DET
ejpam-5713	390	7	vertex	vertex	NOUN
ejpam-5713	390	8	cover	cover	NOUN
ejpam-5713	390	9	in	in	ADP
ejpam-5713	390	10	g	g	PROPN
ejpam-5713	390	11	◦	◦	NOUN
ejpam-5713	390	12	h	h	NOUN
ejpam-5713	390	13	,	,	PUNCT
ejpam-5713	390	14	p	p	PROPN
ejpam-5713	390	15	∈	∈	PROPN
ejpam-5713	390	16	sv	sv	NOUN
ejpam-5713	390	17	or	or	CCONJ
ejpam-5713	390	18	q	q	PROPN
ejpam-5713	390	19	∈	∈	PROPN
ejpam-5713	390	20	sv	sv	PROPN
ejpam-5713	390	21	.	.	PUNCT
ejpam-5713	391	1	this	this	PRON
ejpam-5713	391	2	implies	imply	VERB
ejpam-5713	391	3	that	that	SCONJ
ejpam-5713	391	4	sv	sv	PROPN
ejpam-5713	391	5	is	be	AUX
ejpam-5713	391	6	a	a	DET
ejpam-5713	391	7	vertex	vertex	NOUN
ejpam-5713	391	8	cover	cover	NOUN
ejpam-5713	391	9	in	in	ADP
ejpam-5713	391	10	hv	hv	PROPN
ejpam-5713	391	11	.	.	PUNCT
ejpam-5713	392	1	now	now	ADV
ejpam-5713	392	2	,	,	PUNCT
ejpam-5713	392	3	let	let	VERB
ejpam-5713	392	4	t	t	PROPN
ejpam-5713	392	5	∈	∈	PROPN
ejpam-5713	392	6	v	v	X
ejpam-5713	392	7	(	(	PUNCT
ejpam-5713	392	8	hv	hv	PROPN
ejpam-5713	392	9	)	)	PUNCT
ejpam-5713	392	10	\	\	PROPN
ejpam-5713	393	1	sv	sv	PROPN
ejpam-5713	393	2	.	.	PUNCT
ejpam-5713	394	1	since	since	SCONJ
ejpam-5713	394	2	s	s	PROPN
ejpam-5713	394	3	is	be	AUX
ejpam-5713	394	4	a	a	DET
ejpam-5713	394	5	super	super	ADJ
ejpam-5713	394	6	dominating	dominating	NOUN
ejpam-5713	394	7	set	set	NOUN
ejpam-5713	394	8	in	in	ADP
ejpam-5713	394	9	g	g	PROPN
ejpam-5713	394	10	◦	◦	NOUN
ejpam-5713	394	11	h	h	NOUN
ejpam-5713	394	12	,	,	PUNCT
ejpam-5713	394	13	there	there	PRON
ejpam-5713	394	14	exists	exist	VERB
ejpam-5713	394	15	x	x	X
ejpam-5713	394	16	∈	∈	PROPN
ejpam-5713	394	17	c	c	NOUN
ejpam-5713	394	18	such	such	ADJ
ejpam-5713	394	19	that	that	PRON
ejpam-5713	394	20	ng	ng	PROPN
ejpam-5713	394	21	◦	◦	PROPN
ejpam-5713	394	22	h(x	h(x	PROPN
ejpam-5713	394	23	)	)	PUNCT
ejpam-5713	394	24	∩	∩	NOUN
ejpam-5713	395	1	[	[	X
ejpam-5713	395	2	v	v	X
ejpam-5713	395	3	(	(	PUNCT
ejpam-5713	395	4	g	g	PROPN
ejpam-5713	395	5	◦	◦	NOUN
ejpam-5713	395	6	h	h	NOUN
ejpam-5713	395	7	)	)	PUNCT
ejpam-5713	395	8	\	\	PUNCT
ejpam-5713	395	9	c	c	X
ejpam-5713	395	10	]	]	X
ejpam-5713	395	11	=	=	SYM
ejpam-5713	395	12	{	{	PUNCT
ejpam-5713	395	13	t	t	NOUN
ejpam-5713	395	14	}	}	PUNCT
ejpam-5713	395	15	.	.	PUNCT
ejpam-5713	396	1	since	since	SCONJ
ejpam-5713	396	2	v	v	NUM
ejpam-5713	396	3	∈	∈	NOUN
ejpam-5713	396	4	ng(v	ng(v	PUNCT
ejpam-5713	396	5	(	(	PUNCT
ejpam-5713	396	6	g	g	NOUN
ejpam-5713	396	7	)	)	PUNCT
ejpam-5713	396	8	\	\	PROPN
ejpam-5713	397	1	a	a	PRON
ejpam-5713	397	2	,	,	PUNCT
ejpam-5713	397	3	x	x	PROPN
ejpam-5713	397	4	̸=	̸=	PROPN
ejpam-5713	397	5	v.	v.	ADP
ejpam-5713	397	6	this	this	PRON
ejpam-5713	397	7	implies	imply	VERB
ejpam-5713	397	8	that	that	SCONJ
ejpam-5713	397	9	x	x	SYM
ejpam-5713	397	10	∈	∈	PROPN
ejpam-5713	397	11	sv	sv	NOUN
ejpam-5713	397	12	and	and	CCONJ
ejpam-5713	397	13	nhv(x	nhv(x	PROPN
ejpam-5713	397	14	)	)	PUNCT
ejpam-5713	397	15	∩	∩	NOUN
ejpam-5713	397	16	[	[	X
ejpam-5713	397	17	v	v	X
ejpam-5713	397	18	(	(	PUNCT
ejpam-5713	397	19	hv	hv	NOUN
ejpam-5713	397	20	)	)	PUNCT
ejpam-5713	397	21	\	\	PUNCT
ejpam-5713	398	1	sv	sv	ADP
ejpam-5713	398	2	]	]	X
ejpam-5713	398	3	=	=	X
ejpam-5713	398	4	{	{	PUNCT
ejpam-5713	398	5	t	t	NOUN
ejpam-5713	398	6	}	}	PUNCT
ejpam-5713	398	7	.	.	PUNCT
ejpam-5713	399	1	thus	thus	ADV
ejpam-5713	399	2	,	,	PUNCT
ejpam-5713	399	3	sv	sv	PROPN
ejpam-5713	399	4	is	be	AUX
ejpam-5713	399	5	a	a	DET
ejpam-5713	399	6	super	super	ADJ
ejpam-5713	399	7	dominating	dominating	NOUN
ejpam-5713	399	8	set	set	NOUN
ejpam-5713	399	9	in	in	ADP
ejpam-5713	399	10	hv	hv	PROPN
ejpam-5713	399	11	.	.	PUNCT
ejpam-5713	400	1	this	this	PRON
ejpam-5713	400	2	shows	show	VERB
ejpam-5713	400	3	that	that	SCONJ
ejpam-5713	400	4	(	(	PUNCT
ejpam-5713	400	5	ii	ii	NOUN
ejpam-5713	400	6	)	)	PUNCT
ejpam-5713	400	7	holds	hold	VERB
ejpam-5713	400	8	.	.	PUNCT
ejpam-5713	401	1	suppose	suppose	VERB
ejpam-5713	401	2	now	now	ADV
ejpam-5713	401	3	that	that	SCONJ
ejpam-5713	401	4	v	v	NUM
ejpam-5713	401	5	∈	∈	PROPN
ejpam-5713	401	6	a\ng(v	a\ng(v	NOUN
ejpam-5713	401	7	(	(	PUNCT
ejpam-5713	401	8	g)\a	g)\a	NOUN
ejpam-5713	401	9	)	)	PUNCT
ejpam-5713	401	10	.	.	PUNCT
ejpam-5713	402	1	clearly	clearly	ADV
ejpam-5713	402	2	,	,	PUNCT
ejpam-5713	402	3	sv	sv	PROPN
ejpam-5713	402	4	is	be	AUX
ejpam-5713	402	5	a	a	DET
ejpam-5713	402	6	vertex	vertex	NOUN
ejpam-5713	402	7	cover	cover	NOUN
ejpam-5713	402	8	in	in	ADP
ejpam-5713	402	9	hv	hv	PROPN
ejpam-5713	402	10	.	.	PUNCT
ejpam-5713	403	1	if	if	SCONJ
ejpam-5713	403	2	sv	sv	PROPN
ejpam-5713	403	3	is	be	AUX
ejpam-5713	403	4	a	a	DET
ejpam-5713	403	5	super	super	ADJ
ejpam-5713	403	6	dominating	dominating	NOUN
ejpam-5713	403	7	set	set	NOUN
ejpam-5713	403	8	in	in	ADP
ejpam-5713	403	9	hv	hv	PROPN
ejpam-5713	403	10	,	,	PUNCT
ejpam-5713	403	11	then	then	ADV
ejpam-5713	403	12	(	(	PUNCT
ejpam-5713	403	13	iii	iii	NOUN
ejpam-5713	403	14	)	)	PUNCT
ejpam-5713	403	15	holds	hold	VERB
ejpam-5713	403	16	.	.	PUNCT
ejpam-5713	404	1	so	so	ADV
ejpam-5713	404	2	suppose	suppose	VERB
ejpam-5713	404	3	sv	sv	PROPN
ejpam-5713	404	4	is	be	AUX
ejpam-5713	404	5	not	not	PART
ejpam-5713	404	6	a	a	DET
ejpam-5713	404	7	super	super	ADJ
ejpam-5713	404	8	dominating	dominating	NOUN
ejpam-5713	404	9	set	set	NOUN
ejpam-5713	404	10	in	in	ADP
ejpam-5713	404	11	hv	hv	PROPN
ejpam-5713	404	12	.	.	PUNCT
ejpam-5713	405	1	then	then	ADV
ejpam-5713	405	2	there	there	PRON
ejpam-5713	405	3	exists	exist	VERB
ejpam-5713	405	4	qv	qv	INTJ
ejpam-5713	405	5	∈	∈	PROPN
ejpam-5713	405	6	v	v	PROPN
ejpam-5713	405	7	(	(	PUNCT
ejpam-5713	405	8	hv	hv	PROPN
ejpam-5713	405	9	)	)	PUNCT
ejpam-5713	405	10	\	\	PROPN
ejpam-5713	406	1	sv	sv	ADP
ejpam-5713	406	2	such	such	ADJ
ejpam-5713	406	3	that	that	PRON
ejpam-5713	406	4	for	for	ADP
ejpam-5713	406	5	all	all	DET
ejpam-5713	406	6	z	z	NOUN
ejpam-5713	406	7	∈	∈	PROPN
ejpam-5713	406	8	sv	sv	NOUN
ejpam-5713	406	9	,	,	PUNCT
ejpam-5713	406	10	we	we	PRON
ejpam-5713	406	11	have	have	VERB
ejpam-5713	406	12	nh(z	nh(z	NOUN
ejpam-5713	406	13	)	)	PUNCT
ejpam-5713	406	14	∩	∩	NOUN
ejpam-5713	407	1	[	[	X
ejpam-5713	407	2	v	v	X
ejpam-5713	407	3	(	(	PUNCT
ejpam-5713	407	4	hv	hv	NOUN
ejpam-5713	407	5	)	)	PUNCT
ejpam-5713	407	6	\	\	PUNCT
ejpam-5713	408	1	sv	sv	ADP
ejpam-5713	408	2	]	]	X
ejpam-5713	408	3	̸=	̸=	PROPN
ejpam-5713	408	4	{	{	PUNCT
ejpam-5713	408	5	qv	qv	PROPN
ejpam-5713	408	6	}	}	PUNCT
ejpam-5713	408	7	.	.	PUNCT
ejpam-5713	409	1	following	follow	VERB
ejpam-5713	409	2	a	a	DET
ejpam-5713	409	3	previous	previous	ADJ
ejpam-5713	409	4	argument	argument	NOUN
ejpam-5713	409	5	(	(	PUNCT
ejpam-5713	409	6	see	see	VERB
ejpam-5713	409	7	proof	proof	NOUN
ejpam-5713	409	8	of	of	ADP
ejpam-5713	409	9	theorem	theorem	NOUN
ejpam-5713	409	10	4	4	NUM
ejpam-5713	409	11	)	)	PUNCT
ejpam-5713	409	12	,	,	PUNCT
ejpam-5713	409	13	it	it	PRON
ejpam-5713	409	14	can	can	AUX
ejpam-5713	409	15	be	be	AUX
ejpam-5713	409	16	shown	show	VERB
ejpam-5713	409	17	that	that	SCONJ
ejpam-5713	409	18	qv	qv	PROPN
ejpam-5713	409	19	is	be	AUX
ejpam-5713	409	20	an	an	DET
ejpam-5713	409	21	isolated	isolated	ADJ
ejpam-5713	409	22	vertex	vertex	NOUN
ejpam-5713	409	23	in	in	ADP
ejpam-5713	409	24	hv	hv	PROPN
ejpam-5713	409	25	and	and	CCONJ
ejpam-5713	409	26	sv	sv	PROPN
ejpam-5713	409	27	=	=	SYM
ejpam-5713	409	28	v	v	PROPN
ejpam-5713	409	29	(	(	PUNCT
ejpam-5713	409	30	h	h	NOUN
ejpam-5713	409	31	)	)	PUNCT
ejpam-5713	409	32	\	\	NOUN
ejpam-5713	409	33	{	{	PUNCT
ejpam-5713	409	34	qv	qv	INTJ
ejpam-5713	409	35	}	}	PUNCT
ejpam-5713	409	36	.	.	PUNCT
ejpam-5713	410	1	this	this	PRON
ejpam-5713	410	2	shows	show	VERB
ejpam-5713	410	3	that	that	SCONJ
ejpam-5713	410	4	(	(	PUNCT
ejpam-5713	410	5	iii	iii	NOUN
ejpam-5713	410	6	)	)	PUNCT
ejpam-5713	410	7	holds	hold	VERB
ejpam-5713	410	8	.	.	PUNCT
ejpam-5713	411	1	finally	finally	ADV
ejpam-5713	411	2	,	,	PUNCT
ejpam-5713	411	3	let	let	VERB
ejpam-5713	411	4	v	v	NOUN
ejpam-5713	411	5	/∈	/∈	VERB
ejpam-5713	411	6	a	a	PRON
ejpam-5713	411	7	and	and	CCONJ
ejpam-5713	411	8	let	let	VERB
ejpam-5713	411	9	s	s	PRON
ejpam-5713	411	10	∈	∈	NOUN
ejpam-5713	411	11	v	v	X
ejpam-5713	411	12	(	(	PUNCT
ejpam-5713	411	13	hv	hv	PROPN
ejpam-5713	411	14	)	)	PUNCT
ejpam-5713	411	15	.	.	PUNCT
ejpam-5713	412	1	since	since	SCONJ
ejpam-5713	412	2	c	c	PROPN
ejpam-5713	412	3	is	be	AUX
ejpam-5713	412	4	a	a	DET
ejpam-5713	412	5	vertex	vertex	NOUN
ejpam-5713	412	6	cover	cover	NOUN
ejpam-5713	412	7	in	in	ADP
ejpam-5713	412	8	g	g	PROPN
ejpam-5713	412	9	◦	◦	NOUN
ejpam-5713	412	10	h	h	NOUN
ejpam-5713	412	11	,	,	PUNCT
ejpam-5713	412	12	v	v	NOUN
ejpam-5713	412	13	/∈	/∈	PROPN
ejpam-5713	412	14	a	a	NOUN
ejpam-5713	412	15	,	,	PUNCT
ejpam-5713	412	16	and	and	CCONJ
ejpam-5713	412	17	vs	vs	ADP
ejpam-5713	412	18	∈	∈	PROPN
ejpam-5713	412	19	e(g	e(g	PROPN
ejpam-5713	412	20	◦	◦	PROPN
ejpam-5713	412	21	h	h	NOUN
ejpam-5713	412	22	)	)	PUNCT
ejpam-5713	412	23	,	,	PUNCT
ejpam-5713	412	24	we	we	PRON
ejpam-5713	412	25	must	must	AUX
ejpam-5713	412	26	have	have	VERB
ejpam-5713	412	27	s	s	X
ejpam-5713	412	28	∈	∈	PROPN
ejpam-5713	412	29	sv	sv	PROPN
ejpam-5713	412	30	.	.	PUNCT
ejpam-5713	413	1	as	as	SCONJ
ejpam-5713	413	2	v	v	NOUN
ejpam-5713	413	3	was	be	AUX
ejpam-5713	413	4	arbitrarily	arbitrarily	ADV
ejpam-5713	413	5	chosen	choose	VERB
ejpam-5713	413	6	,	,	PUNCT
ejpam-5713	413	7	we	we	PRON
ejpam-5713	413	8	have	have	VERB
ejpam-5713	413	9	sv	sv	NOUN
ejpam-5713	413	10	=	=	SYM
ejpam-5713	413	11	v	v	PROPN
ejpam-5713	413	12	(	(	PUNCT
ejpam-5713	413	13	hv	hv	PROPN
ejpam-5713	413	14	)	)	PUNCT
ejpam-5713	413	15	,	,	PUNCT
ejpam-5713	413	16	showing	show	VERB
ejpam-5713	413	17	that	that	SCONJ
ejpam-5713	413	18	(	(	PUNCT
ejpam-5713	413	19	iv	iv	X
ejpam-5713	413	20	)	)	PUNCT
ejpam-5713	413	21	holds	hold	NOUN
ejpam-5713	413	22	.	.	PUNCT
ejpam-5713	414	1	for	for	ADP
ejpam-5713	414	2	the	the	DET
ejpam-5713	414	3	converse	converse	NOUN
ejpam-5713	414	4	,	,	PUNCT
ejpam-5713	414	5	suppose	suppose	VERB
ejpam-5713	414	6	that	that	SCONJ
ejpam-5713	414	7	s	s	VERB
ejpam-5713	414	8	has	have	VERB
ejpam-5713	414	9	the	the	DET
ejpam-5713	414	10	given	give	VERB
ejpam-5713	414	11	form	form	NOUN
ejpam-5713	414	12	and	and	CCONJ
ejpam-5713	414	13	satisties	satistie	NOUN
ejpam-5713	414	14	conditions	condition	NOUN
ejpam-5713	414	15	(	(	PUNCT
ejpam-5713	414	16	i	i	NOUN
ejpam-5713	414	17	)	)	PUNCT
ejpam-5713	414	18	,	,	PUNCT
ejpam-5713	414	19	(	(	PUNCT
ejpam-5713	414	20	ii	ii	NOUN
ejpam-5713	414	21	)	)	PUNCT
ejpam-5713	414	22	,	,	PUNCT
ejpam-5713	414	23	(	(	PUNCT
ejpam-5713	414	24	iii	iii	NOUN
ejpam-5713	414	25	)	)	PUNCT
ejpam-5713	414	26	,	,	PUNCT
ejpam-5713	414	27	and	and	CCONJ
ejpam-5713	414	28	(	(	PUNCT
ejpam-5713	414	29	iv	iv	X
ejpam-5713	414	30	)	)	PUNCT
ejpam-5713	414	31	.	.	PUNCT
ejpam-5713	415	1	let	let	VERB
ejpam-5713	415	2	xy	xy	PROPN
ejpam-5713	415	3	∈	∈	PROPN
ejpam-5713	415	4	e(g	e(g	PROPN
ejpam-5713	415	5	◦	◦	PROPN
ejpam-5713	415	6	h	h	NOUN
ejpam-5713	415	7	)	)	PUNCT
ejpam-5713	415	8	.	.	PUNCT
ejpam-5713	416	1	if	if	SCONJ
ejpam-5713	416	2	x	x	X
ejpam-5713	416	3	,	,	PUNCT
ejpam-5713	416	4	y	y	PROPN
ejpam-5713	416	5	∈	∈	PROPN
ejpam-5713	416	6	v	v	NOUN
ejpam-5713	416	7	(	(	PUNCT
ejpam-5713	416	8	g	g	NOUN
ejpam-5713	416	9	)	)	PUNCT
ejpam-5713	416	10	,	,	PUNCT
ejpam-5713	416	11	then	then	ADV
ejpam-5713	416	12	x	x	SYM
ejpam-5713	416	13	∈	∈	PROPN
ejpam-5713	416	14	a	a	PRON
ejpam-5713	416	15	or	or	CCONJ
ejpam-5713	416	16	y	y	PROPN
ejpam-5713	416	17	∈	∈	PROPN
ejpam-5713	416	18	a	a	DET
ejpam-5713	416	19	because	because	SCONJ
ejpam-5713	416	20	of	of	ADP
ejpam-5713	416	21	(	(	PUNCT
ejpam-5713	416	22	i	i	NOUN
ejpam-5713	416	23	)	)	PUNCT
ejpam-5713	416	24	.	.	PUNCT
ejpam-5713	417	1	suppose	suppose	VERB
ejpam-5713	417	2	at	at	ADP
ejpam-5713	417	3	most	most	ADJ
ejpam-5713	417	4	one	one	NUM
ejpam-5713	417	5	of	of	ADP
ejpam-5713	417	6	x	x	PUNCT
ejpam-5713	417	7	and	and	CCONJ
ejpam-5713	417	8	y	y	PROPN
ejpam-5713	417	9	is	be	AUX
ejpam-5713	417	10	in	in	ADP
ejpam-5713	417	11	v	v	NOUN
ejpam-5713	417	12	(	(	PUNCT
ejpam-5713	417	13	g	g	NOUN
ejpam-5713	417	14	)	)	PUNCT
ejpam-5713	417	15	.	.	PUNCT
ejpam-5713	418	1	we	we	PRON
ejpam-5713	418	2	may	may	AUX
ejpam-5713	418	3	assume	assume	VERB
ejpam-5713	418	4	that	that	SCONJ
ejpam-5713	418	5	x	x	PUNCT
ejpam-5713	418	6	∈	∈	NOUN
ejpam-5713	418	7	v	v	X
ejpam-5713	418	8	(	(	PUNCT
ejpam-5713	418	9	g	g	NOUN
ejpam-5713	418	10	)	)	PUNCT
ejpam-5713	418	11	.	.	PUNCT
ejpam-5713	419	1	then	then	ADV
ejpam-5713	419	2	y	y	PROPN
ejpam-5713	419	3	∈	∈	PROPN
ejpam-5713	419	4	v	v	PROPN
ejpam-5713	419	5	(	(	PUNCT
ejpam-5713	419	6	hx	hx	PROPN
ejpam-5713	419	7	)	)	PUNCT
ejpam-5713	419	8	.	.	PUNCT
ejpam-5713	420	1	if	if	SCONJ
ejpam-5713	420	2	x	x	SYM
ejpam-5713	420	3	∈	∈	PROPN
ejpam-5713	420	4	a	a	PRON
ejpam-5713	420	5	,	,	PUNCT
ejpam-5713	420	6	then	then	ADV
ejpam-5713	420	7	xy	xy	PROPN
ejpam-5713	420	8	is	be	AUX
ejpam-5713	420	9	incident	incident	NOUN
ejpam-5713	420	10	to	to	ADP
ejpam-5713	420	11	x	x	SYM
ejpam-5713	420	12	∈	∈	PROPN
ejpam-5713	420	13	c.	c.	NOUN
ejpam-5713	420	14	if	if	SCONJ
ejpam-5713	420	15	x	x	X
ejpam-5713	420	16	/∈	/∈	NOUN
ejpam-5713	421	1	a	a	PRON
ejpam-5713	421	2	,	,	PUNCT
ejpam-5713	421	3	then	then	ADV
ejpam-5713	421	4	sx	sx	PROPN
ejpam-5713	421	5	=	=	PUNCT
ejpam-5713	421	6	v	v	PROPN
ejpam-5713	421	7	(	(	PUNCT
ejpam-5713	421	8	hx	hx	PROPN
ejpam-5713	421	9	)	)	PUNCT
ejpam-5713	421	10	by	by	ADP
ejpam-5713	421	11	(	(	PUNCT
ejpam-5713	421	12	iv	iv	X
ejpam-5713	421	13	)	)	PUNCT
ejpam-5713	421	14	.	.	PUNCT
ejpam-5713	422	1	it	it	PRON
ejpam-5713	422	2	follows	follow	VERB
ejpam-5713	422	3	that	that	SCONJ
ejpam-5713	422	4	y	y	PROPN
ejpam-5713	422	5	∈	∈	PROPN
ejpam-5713	422	6	sv	sv	PROPN
ejpam-5713	422	7	.	.	PUNCT
ejpam-5713	423	1	hence	hence	ADV
ejpam-5713	423	2	,	,	PUNCT
ejpam-5713	423	3	xy	xy	PROPN
ejpam-5713	423	4	is	be	AUX
ejpam-5713	423	5	incident	incident	NOUN
ejpam-5713	423	6	to	to	ADP
ejpam-5713	423	7	y	y	PROPN
ejpam-5713	423	8	∈	∈	PROPN
ejpam-5713	423	9	c.	c.	PROPN
ejpam-5713	423	10	suppose	suppose	VERB
ejpam-5713	423	11	now	now	ADV
ejpam-5713	423	12	that	that	SCONJ
ejpam-5713	423	13	x	x	X
ejpam-5713	423	14	,	,	PUNCT
ejpam-5713	423	15	y	y	PROPN
ejpam-5713	423	16	∈	∈	PROPN
ejpam-5713	423	17	v	v	PROPN
ejpam-5713	423	18	(	(	PUNCT
ejpam-5713	423	19	hv	hv	PROPN
ejpam-5713	423	20	)	)	PUNCT
ejpam-5713	423	21	for	for	ADP
ejpam-5713	423	22	some	some	DET
ejpam-5713	423	23	v	v	ADP
ejpam-5713	423	24	∈	∈	PROPN
ejpam-5713	423	25	v	v	NOUN
ejpam-5713	423	26	(	(	PUNCT
ejpam-5713	423	27	g	g	NOUN
ejpam-5713	423	28	)	)	PUNCT
ejpam-5713	423	29	.	.	PUNCT
ejpam-5713	424	1	if	if	SCONJ
ejpam-5713	424	2	v	v	NUM
ejpam-5713	424	3	/∈	/∈	NOUN
ejpam-5713	425	1	a	a	PRON
ejpam-5713	425	2	,	,	PUNCT
ejpam-5713	425	3	then	then	ADV
ejpam-5713	425	4	sv	sv	PROPN
ejpam-5713	425	5	=	=	SYM
ejpam-5713	425	6	v	v	PROPN
ejpam-5713	425	7	(	(	PUNCT
ejpam-5713	425	8	hv	hv	PROPN
ejpam-5713	425	9	)	)	PUNCT
ejpam-5713	425	10	.	.	PUNCT
ejpam-5713	426	1	hence	hence	ADV
ejpam-5713	426	2	,	,	PUNCT
ejpam-5713	426	3	x	x	PRON
ejpam-5713	426	4	,	,	PUNCT
ejpam-5713	426	5	y	y	PROPN
ejpam-5713	426	6	∈	∈	PROPN
ejpam-5713	426	7	sv	sv	PROPN
ejpam-5713	426	8	⊂	⊂	PROPN
ejpam-5713	426	9	c.	c.	PROPN
ejpam-5713	426	10	suppose	suppose	VERB
ejpam-5713	426	11	that	that	SCONJ
ejpam-5713	426	12	v	v	X
ejpam-5713	426	13	∈	∈	PROPN
ejpam-5713	426	14	a∩ng(v	a∩ng(v	PRON
ejpam-5713	426	15	(	(	PUNCT
ejpam-5713	426	16	g)\a	g)\a	NOUN
ejpam-5713	426	17	)	)	PUNCT
ejpam-5713	426	18	.	.	PUNCT
ejpam-5713	427	1	by	by	ADP
ejpam-5713	427	2	(	(	PUNCT
ejpam-5713	427	3	ii	ii	NOUN
ejpam-5713	427	4	)	)	PUNCT
ejpam-5713	427	5	,	,	PUNCT
ejpam-5713	427	6	sv	sv	PROPN
ejpam-5713	427	7	is	be	AUX
ejpam-5713	427	8	a	a	DET
ejpam-5713	427	9	super	super	ADJ
ejpam-5713	427	10	vertex	vertex	NOUN
ejpam-5713	427	11	cover	cover	NOUN
ejpam-5713	427	12	in	in	ADP
ejpam-5713	427	13	hv	hv	PROPN
ejpam-5713	427	14	.	.	PUNCT
ejpam-5713	428	1	this	this	PRON
ejpam-5713	428	2	implies	imply	VERB
ejpam-5713	428	3	that	that	SCONJ
ejpam-5713	428	4	x	x	PUNCT
ejpam-5713	428	5	∈	∈	NOUN
ejpam-5713	428	6	sv	sv	NOUN
ejpam-5713	428	7	or	or	CCONJ
ejpam-5713	428	8	y	y	PROPN
ejpam-5713	428	9	∈	∈	PROPN
ejpam-5713	428	10	sv	sv	INTJ
ejpam-5713	428	11	.	.	PUNCT
ejpam-5713	429	1	if	if	SCONJ
ejpam-5713	429	2	v	v	NUM
ejpam-5713	429	3	∈	∈	PRON
ejpam-5713	429	4	a	a	DET
ejpam-5713	429	5	\	\	NOUN
ejpam-5713	429	6	ng(v	ng(v	PUNCT
ejpam-5713	429	7	(	(	PUNCT
ejpam-5713	429	8	g	g	NOUN
ejpam-5713	429	9	)	)	PUNCT
ejpam-5713	429	10	\	\	PROPN
ejpam-5713	430	1	a	a	PRON
ejpam-5713	430	2	)	)	PUNCT
ejpam-5713	430	3	,	,	PUNCT
ejpam-5713	430	4	then	then	ADV
ejpam-5713	430	5	sv	sv	INTJ
ejpam-5713	430	6	=	=	SYM
ejpam-5713	430	7	v	v	PROPN
ejpam-5713	430	8	(	(	PUNCT
ejpam-5713	430	9	hv	hv	PROPN
ejpam-5713	430	10	)	)	PUNCT
ejpam-5713	430	11	\	\	NOUN
ejpam-5713	430	12	{	{	PUNCT
ejpam-5713	430	13	qv	qv	INTJ
ejpam-5713	430	14	}	}	PUNCT
ejpam-5713	430	15	for	for	ADP
ejpam-5713	430	16	some	some	DET
ejpam-5713	430	17	isolated	isolate	VERB
ejpam-5713	430	18	vertex	vertex	NOUN
ejpam-5713	430	19	qv	qv	X
ejpam-5713	430	20	in	in	ADP
ejpam-5713	430	21	hv	hv	PROPN
ejpam-5713	430	22	.	.	PUNCT
ejpam-5713	431	1	since	since	SCONJ
ejpam-5713	431	2	xy	xy	PROPN
ejpam-5713	431	3	∈	∈	PROPN
ejpam-5713	431	4	e(g	e(g	PROPN
ejpam-5713	431	5	◦	◦	PROPN
ejpam-5713	431	6	h	h	NOUN
ejpam-5713	431	7	)	)	PUNCT
ejpam-5713	431	8	,	,	PUNCT
ejpam-5713	431	9	x	x	X
ejpam-5713	431	10	̸=	̸=	PROPN
ejpam-5713	431	11	qv	qv	X
ejpam-5713	431	12	and	and	CCONJ
ejpam-5713	431	13	y	y	PROPN
ejpam-5713	431	14	̸=	̸=	PROPN
ejpam-5713	431	15	qv	qv	VERB
ejpam-5713	431	16	.	.	PUNCT
ejpam-5713	432	1	hence	hence	ADV
ejpam-5713	432	2	,	,	PUNCT
ejpam-5713	432	3	x	x	PRON
ejpam-5713	432	4	,	,	PUNCT
ejpam-5713	432	5	y	y	PROPN
ejpam-5713	432	6	∈	∈	PROPN
ejpam-5713	432	7	sv	sv	PROPN
ejpam-5713	432	8	⊂	⊂	PROPN
ejpam-5713	432	9	c.	c.	PROPN
ejpam-5713	432	10	therefore	therefore	ADV
ejpam-5713	432	11	,	,	PUNCT
ejpam-5713	432	12	c	c	PROPN
ejpam-5713	432	13	is	be	AUX
ejpam-5713	432	14	a	a	DET
ejpam-5713	432	15	vertex	vertex	NOUN
ejpam-5713	432	16	cover	cover	NOUN
ejpam-5713	432	17	in	in	ADP
ejpam-5713	432	18	g	g	PROPN
ejpam-5713	432	19	◦	◦	NOUN
ejpam-5713	432	20	h.	h.	PROPN
ejpam-5713	432	21	next	next	ADV
ejpam-5713	432	22	,	,	PUNCT
ejpam-5713	432	23	let	let	VERB
ejpam-5713	432	24	p	p	PRON
ejpam-5713	432	25	∈	∈	PROPN
ejpam-5713	432	26	v	v	NOUN
ejpam-5713	432	27	(	(	PUNCT
ejpam-5713	432	28	g	g	PROPN
ejpam-5713	432	29	◦	◦	NOUN
ejpam-5713	432	30	h	h	NOUN
ejpam-5713	432	31	)	)	PUNCT
ejpam-5713	432	32	\	\	NOUN
ejpam-5713	432	33	c	c	NOUN
ejpam-5713	432	34	and	and	CCONJ
ejpam-5713	432	35	let	let	VERB
ejpam-5713	432	36	v	v	NUM
ejpam-5713	432	37	∈	∈	PROPN
ejpam-5713	432	38	v	v	NOUN
ejpam-5713	432	39	(	(	PUNCT
ejpam-5713	432	40	g	g	NOUN
ejpam-5713	432	41	)	)	PUNCT
ejpam-5713	432	42	such	such	ADJ
ejpam-5713	432	43	that	that	SCONJ
ejpam-5713	432	44	p	p	PROPN
ejpam-5713	432	45	∈	∈	PROPN
ejpam-5713	432	46	v	v	ADP
ejpam-5713	432	47	(	(	PUNCT
ejpam-5713	432	48	v	v	NOUN
ejpam-5713	432	49	+	+	CCONJ
ejpam-5713	432	50	hv	hv	NOUN
ejpam-5713	432	51	)	)	PUNCT
ejpam-5713	432	52	.	.	PUNCT
ejpam-5713	433	1	if	if	SCONJ
ejpam-5713	433	2	p	p	PROPN
ejpam-5713	433	3	=	=	SYM
ejpam-5713	433	4	v	v	NOUN
ejpam-5713	433	5	,	,	PUNCT
ejpam-5713	433	6	then	then	ADV
ejpam-5713	433	7	p	p	X
ejpam-5713	433	8	/∈	/∈	NOUN
ejpam-5713	433	9	a.	a.	NOUN
ejpam-5713	433	10	by	by	ADP
ejpam-5713	433	11	(	(	PUNCT
ejpam-5713	433	12	iv	iv	X
ejpam-5713	433	13	)	)	PUNCT
ejpam-5713	433	14	,	,	PUNCT
ejpam-5713	433	15	sv	sv	PROPN
ejpam-5713	433	16	=	=	SYM
ejpam-5713	433	17	v	v	PROPN
ejpam-5713	433	18	(	(	PUNCT
ejpam-5713	433	19	hv	hv	PROPN
ejpam-5713	433	20	)	)	PUNCT
ejpam-5713	433	21	.	.	PUNCT
ejpam-5713	434	1	pick	pick	VERB
ejpam-5713	434	2	any	any	DET
ejpam-5713	434	3	q	q	PROPN
ejpam-5713	434	4	∈	∈	PROPN
ejpam-5713	434	5	sv	sv	PROPN
ejpam-5713	434	6	.	.	PUNCT
ejpam-5713	435	1	then	then	ADV
ejpam-5713	435	2	ng	ng	PROPN
ejpam-5713	435	3	◦	◦	PROPN
ejpam-5713	435	4	h(q)∩	h(q)∩	NOUN
ejpam-5713	435	5	[	[	X
ejpam-5713	435	6	v	v	X
ejpam-5713	435	7	(	(	PUNCT
ejpam-5713	435	8	g	g	PROPN
ejpam-5713	435	9	◦	◦	NOUN
ejpam-5713	435	10	h	h	NOUN
ejpam-5713	435	11	)	)	PUNCT
ejpam-5713	435	12	\c	\c	NOUN
ejpam-5713	435	13	]	]	PUNCT
ejpam-5713	436	1	=	=	PUNCT
ejpam-5713	436	2	{	{	PUNCT
ejpam-5713	436	3	p	p	X
ejpam-5713	436	4	}	}	PUNCT
ejpam-5713	436	5	.	.	PUNCT
ejpam-5713	437	1	suppose	suppose	VERB
ejpam-5713	437	2	p	p	X
ejpam-5713	437	3	∈	∈	PROPN
ejpam-5713	437	4	v	v	ADP
ejpam-5713	437	5	(	(	PUNCT
ejpam-5713	437	6	hv	hv	PROPN
ejpam-5713	437	7	)	)	PUNCT
ejpam-5713	437	8	.	.	PUNCT
ejpam-5713	438	1	then	then	ADV
ejpam-5713	438	2	p	p	PROPN
ejpam-5713	438	3	∈	∈	PROPN
ejpam-5713	438	4	v	v	ADP
ejpam-5713	438	5	(	(	PUNCT
ejpam-5713	438	6	hv	hv	NOUN
ejpam-5713	438	7	)	)	PUNCT
ejpam-5713	438	8	\sv	\sv	PROPN
ejpam-5713	438	9	.	.	PUNCT
ejpam-5713	439	1	this	this	PRON
ejpam-5713	439	2	implies	imply	VERB
ejpam-5713	439	3	that	that	SCONJ
ejpam-5713	439	4	v	v	NUM
ejpam-5713	439	5	∈	∈	PRON
ejpam-5713	439	6	a	a	PRON
ejpam-5713	439	7	(	(	PUNCT
ejpam-5713	439	8	otherwise	otherwise	ADV
ejpam-5713	439	9	sv	sv	PROPN
ejpam-5713	439	10	=	=	SYM
ejpam-5713	439	11	v	v	PROPN
ejpam-5713	439	12	(	(	PUNCT
ejpam-5713	439	13	hv	hv	NOUN
ejpam-5713	439	14	)	)	PUNCT
ejpam-5713	439	15	by	by	ADP
ejpam-5713	439	16	(	(	PUNCT
ejpam-5713	439	17	iv	iv	X
ejpam-5713	439	18	)	)	PUNCT
ejpam-5713	439	19	,	,	PUNCT
ejpam-5713	439	20	a	a	DET
ejpam-5713	439	21	contradiction	contradiction	NOUN
ejpam-5713	439	22	)	)	PUNCT
ejpam-5713	439	23	.	.	PUNCT
ejpam-5713	440	1	if	if	SCONJ
ejpam-5713	440	2	v	v	NUM
ejpam-5713	440	3	∈	∈	PROPN
ejpam-5713	440	4	a	a	DET
ejpam-5713	440	5	∩	∩	NOUN
ejpam-5713	440	6	ng(v	ng(v	PRON
ejpam-5713	440	7	(	(	PUNCT
ejpam-5713	440	8	g	g	NOUN
ejpam-5713	440	9	)	)	PUNCT
ejpam-5713	440	10	\	\	PROPN
ejpam-5713	441	1	a	a	PRON
ejpam-5713	441	2	)	)	PUNCT
ejpam-5713	441	3	,	,	PUNCT
ejpam-5713	441	4	then	then	ADV
ejpam-5713	441	5	sv	sv	PROPN
ejpam-5713	441	6	is	be	AUX
ejpam-5713	441	7	a	a	DET
ejpam-5713	441	8	super	super	ADJ
ejpam-5713	441	9	dominating	dominating	NOUN
ejpam-5713	441	10	set	set	NOUN
ejpam-5713	441	11	in	in	ADP
ejpam-5713	441	12	hv	hv	PROPN
ejpam-5713	441	13	by	by	ADP
ejpam-5713	441	14	(	(	PUNCT
ejpam-5713	441	15	ii	ii	NOUN
ejpam-5713	441	16	)	)	PUNCT
ejpam-5713	441	17	.	.	PUNCT
ejpam-5713	442	1	hence	hence	ADV
ejpam-5713	442	2	,	,	PUNCT
ejpam-5713	442	3	there	there	PRON
ejpam-5713	442	4	exists	exist	VERB
ejpam-5713	442	5	d	d	X
ejpam-5713	442	6	∈	∈	PROPN
ejpam-5713	442	7	sv	sv	PROPN
ejpam-5713	443	1	⊂	⊂	PROPN
ejpam-5713	443	2	c	c	PROPN
ejpam-5713	444	1	such	such	ADJ
ejpam-5713	444	2	that	that	SCONJ
ejpam-5713	444	3	ng	ng	PROPN
ejpam-5713	444	4	◦	◦	PROPN
ejpam-5713	444	5	h(d)∩	h(d)∩	PROPN
ejpam-5713	444	6	[	[	X
ejpam-5713	444	7	v	v	X
ejpam-5713	444	8	(	(	PUNCT
ejpam-5713	444	9	g	g	PROPN
ejpam-5713	444	10	◦	◦	NOUN
ejpam-5713	444	11	h	h	NOUN
ejpam-5713	444	12	)	)	PUNCT
ejpam-5713	444	13	\c	\c	NOUN
ejpam-5713	444	14	]	]	PUNCT
ejpam-5713	445	1	=	=	SYM
ejpam-5713	445	2	nhv(d)∩	nhv(d)∩	X
ejpam-5713	445	3	[	[	X
ejpam-5713	445	4	v	v	X
ejpam-5713	445	5	(	(	PUNCT
ejpam-5713	445	6	hv	hv	NOUN
ejpam-5713	445	7	)	)	PUNCT
ejpam-5713	445	8	\	\	PUNCT
ejpam-5713	446	1	sv	sv	ADP
ejpam-5713	446	2	]	]	X
ejpam-5713	446	3	=	=	X
ejpam-5713	446	4	{	{	PUNCT
ejpam-5713	446	5	p	p	X
ejpam-5713	446	6	}	}	PUNCT
ejpam-5713	446	7	.	.	PUNCT
ejpam-5713	447	1	if	if	SCONJ
ejpam-5713	447	2	v	v	NUM
ejpam-5713	447	3	∈	∈	PRON
ejpam-5713	447	4	a	a	DET
ejpam-5713	447	5	\ng(v	\ng(v	NOUN
ejpam-5713	447	6	(	(	PUNCT
ejpam-5713	447	7	g	g	NOUN
ejpam-5713	447	8	)	)	PUNCT
ejpam-5713	447	9	\a	\a	NUM
ejpam-5713	447	10	)	)	PUNCT
ejpam-5713	447	11	,	,	PUNCT
ejpam-5713	447	12	then	then	ADV
ejpam-5713	447	13	sv	sv	INTJ
ejpam-5713	447	14	=	=	SYM
ejpam-5713	447	15	v	v	PROPN
ejpam-5713	447	16	(	(	PUNCT
ejpam-5713	447	17	hv	hv	PROPN
ejpam-5713	447	18	)	)	PUNCT
ejpam-5713	447	19	\	\	NOUN
ejpam-5713	447	20	{	{	PUNCT
ejpam-5713	447	21	qv	qv	INTJ
ejpam-5713	447	22	}	}	PUNCT
ejpam-5713	447	23	for	for	ADP
ejpam-5713	447	24	some	some	DET
ejpam-5713	447	25	isolated	isolate	VERB
ejpam-5713	447	26	vertex	vertex	NOUN
ejpam-5713	447	27	qv	qv	X
ejpam-5713	447	28	in	in	ADP
ejpam-5713	447	29	hv	hv	PROPN
ejpam-5713	447	30	.	.	PUNCT
ejpam-5713	448	1	it	it	PRON
ejpam-5713	448	2	follows	follow	VERB
ejpam-5713	448	3	that	that	SCONJ
ejpam-5713	448	4	p	p	PROPN
ejpam-5713	448	5	=	=	X
ejpam-5713	448	6	qv	qv	PROPN
ejpam-5713	448	7	.	.	PUNCT
ejpam-5713	449	1	clearly	clearly	ADV
ejpam-5713	449	2	,	,	PUNCT
ejpam-5713	449	3	ng	ng	PROPN
ejpam-5713	449	4	◦	◦	PROPN
ejpam-5713	449	5	h(v	h(v	NOUN
ejpam-5713	449	6	)	)	PUNCT
ejpam-5713	449	7	∩	∩	NOUN
ejpam-5713	450	1	[	[	X
ejpam-5713	450	2	v	v	X
ejpam-5713	450	3	(	(	PUNCT
ejpam-5713	450	4	g	g	PROPN
ejpam-5713	450	5	◦	◦	NOUN
ejpam-5713	450	6	h	h	NOUN
ejpam-5713	450	7	)	)	PUNCT
ejpam-5713	450	8	\	\	PUNCT
ejpam-5713	450	9	c	c	X
ejpam-5713	450	10	]	]	X
ejpam-5713	450	11	=	=	X
ejpam-5713	450	12	{	{	PUNCT
ejpam-5713	450	13	p	p	X
ejpam-5713	450	14	}	}	PUNCT
ejpam-5713	450	15	.	.	PUNCT
ejpam-5713	451	1	therefore	therefore	ADV
ejpam-5713	451	2	,	,	PUNCT
ejpam-5713	451	3	c	c	PROPN
ejpam-5713	451	4	is	be	AUX
ejpam-5713	451	5	a	a	DET
ejpam-5713	451	6	super	super	ADJ
ejpam-5713	451	7	dominating	dominating	NOUN
ejpam-5713	451	8	set	set	NOUN
ejpam-5713	451	9	in	in	ADP
ejpam-5713	451	10	g	g	PROPN
ejpam-5713	451	11	◦	◦	PROPN
ejpam-5713	451	12	h.	h.	NOUN
ejpam-5713	451	13	accordingly	accordingly	ADV
ejpam-5713	451	14	,	,	PUNCT
ejpam-5713	451	15	c	c	PROPN
ejpam-5713	451	16	is	be	AUX
ejpam-5713	451	17	a	a	DET
ejpam-5713	451	18	super	super	ADJ
ejpam-5713	451	19	vertex	vertex	NOUN
ejpam-5713	451	20	cover	cover	NOUN
ejpam-5713	451	21	in	in	ADP
ejpam-5713	451	22	g	g	PROPN
ejpam-5713	451	23	◦	◦	NOUN
ejpam-5713	451	24	h.	h.	NOUN
ejpam-5713	451	25	corollary	corollary	ADJ
ejpam-5713	451	26	6	6	NUM
ejpam-5713	451	27	.	.	PUNCT
ejpam-5713	452	1	let	let	VERB
ejpam-5713	452	2	g	g	NOUN
ejpam-5713	452	3	and	and	CCONJ
ejpam-5713	452	4	h	h	PROPN
ejpam-5713	452	5	be	be	VERB
ejpam-5713	452	6	non	non	ADJ
ejpam-5713	452	7	-	-	ADJ
ejpam-5713	452	8	trivial	trivial	ADJ
ejpam-5713	452	9	connected	connected	ADJ
ejpam-5713	452	10	graphs	graph	NOUN
ejpam-5713	452	11	of	of	ADP
ejpam-5713	452	12	orders	order	NOUN
ejpam-5713	452	13	m	m	VERB
ejpam-5713	452	14	and	and	CCONJ
ejpam-5713	452	15	n	n	CCONJ
ejpam-5713	452	16	,	,	PUNCT
ejpam-5713	452	17	respectively	respectively	ADV
ejpam-5713	452	18	.	.	PUNCT
ejpam-5713	453	1	then	then	ADV
ejpam-5713	453	2	βs(g	βs(g	PUNCT
ejpam-5713	453	3	◦	◦	NOUN
ejpam-5713	453	4	h	h	NOUN
ejpam-5713	453	5	)	)	PUNCT
ejpam-5713	453	6	=	=	SYM
ejpam-5713	453	7	(	(	PUNCT
ejpam-5713	454	1	βs(h)−	βs(h)−	PROPN
ejpam-5713	454	2	n+	n+	NUM
ejpam-5713	454	3	1)β(g	1)β(g	NUM
ejpam-5713	454	4	)	)	PUNCT
ejpam-5713	455	1	+	+	PROPN
ejpam-5713	455	2	mn	mn	PROPN
ejpam-5713	455	3	.	.	PUNCT
ejpam-5713	455	4	proof	proof	NOUN
ejpam-5713	455	5	.	.	PUNCT
ejpam-5713	456	1	let	let	VERB
ejpam-5713	456	2	a	a	DET
ejpam-5713	456	3	be	be	AUX
ejpam-5713	456	4	a	a	DET
ejpam-5713	456	5	β	β	NOUN
ejpam-5713	456	6	-	-	VERB
ejpam-5713	456	7	set	set	VERB
ejpam-5713	456	8	in	in	ADP
ejpam-5713	456	9	g	g	PROPN
ejpam-5713	456	10	,	,	PUNCT
ejpam-5713	456	11	sv	sv	PROPN
ejpam-5713	456	12	a	a	DET
ejpam-5713	456	13	βs	βs	NOUN
ejpam-5713	456	14	-	-	PUNCT
ejpam-5713	456	15	set	set	NOUN
ejpam-5713	456	16	in	in	ADP
ejpam-5713	456	17	hv	hv	PROPN
ejpam-5713	456	18	for	for	ADP
ejpam-5713	456	19	each	each	DET
ejpam-5713	456	20	v	v	ADP
ejpam-5713	456	21	∈	∈	PROPN
ejpam-5713	456	22	a	a	PRON
ejpam-5713	456	23	,	,	PUNCT
ejpam-5713	456	24	and	and	CCONJ
ejpam-5713	456	25	sw	sw	PROPN
ejpam-5713	456	26	=	=	SYM
ejpam-5713	456	27	v	v	PROPN
ejpam-5713	456	28	(	(	PUNCT
ejpam-5713	456	29	hv	hv	PROPN
ejpam-5713	456	30	)	)	PUNCT
ejpam-5713	456	31	for	for	ADP
ejpam-5713	456	32	each	each	PRON
ejpam-5713	456	33	v	v	NUM
ejpam-5713	456	34	∈	∈	PROPN
ejpam-5713	456	35	v	v	NOUN
ejpam-5713	456	36	(	(	PUNCT
ejpam-5713	456	37	g	g	NOUN
ejpam-5713	456	38	)	)	PUNCT
ejpam-5713	456	39	\	\	NOUN
ejpam-5713	456	40	a.	a.	NOUN
ejpam-5713	456	41	then	then	ADV
ejpam-5713	456	42	s	s	VERB
ejpam-5713	456	43	=	=	PUNCT
ejpam-5713	456	44	a	a	DET
ejpam-5713	456	45	∪	∪	X
ejpam-5713	456	46	(	(	PUNCT
ejpam-5713	456	47	∪v∈v	∪v∈v	X
ejpam-5713	456	48	(	(	PUNCT
ejpam-5713	456	49	g)sv	g)sv	PROPN
ejpam-5713	456	50	)	)	PUNCT
ejpam-5713	456	51	is	be	AUX
ejpam-5713	456	52	a	a	DET
ejpam-5713	456	53	super	super	ADJ
ejpam-5713	456	54	vertex	vertex	NOUN
ejpam-5713	456	55	cover	cover	NOUN
ejpam-5713	456	56	of	of	ADP
ejpam-5713	456	57	g	g	PROPN
ejpam-5713	456	58	◦	◦	NOUN
ejpam-5713	456	59	h	h	NOUN
ejpam-5713	456	60	by	by	ADP
ejpam-5713	456	61	theorem	theorem	NOUN
ejpam-5713	456	62	5	5	NUM
ejpam-5713	456	63	.	.	PUNCT
ejpam-5713	457	1	it	it	PRON
ejpam-5713	457	2	follows	follow	VERB
ejpam-5713	457	3	that	that	SCONJ
ejpam-5713	457	4	βs(g	βs(g	PUNCT
ejpam-5713	457	5	◦	◦	NOUN
ejpam-5713	457	6	h	h	NOUN
ejpam-5713	457	7	)	)	PUNCT
ejpam-5713	457	8	≤	≤	NUM
ejpam-5713	457	9	|s|	|s|	NOUN
ejpam-5713	457	10	=	=	SYM
ejpam-5713	457	11	|a|+	|a|+	NOUN
ejpam-5713	457	12	∑	∑	PUNCT
ejpam-5713	457	13	v∈a	v∈a	NOUN
ejpam-5713	457	14	|sv|+	|sv|+	SYM
ejpam-5713	457	15	∑	∑	PROPN
ejpam-5713	457	16	v∈v	v∈v	NOUN
ejpam-5713	457	17	(	(	PUNCT
ejpam-5713	457	18	g)\a	g)\a	NOUN
ejpam-5713	457	19	|sv|	|sv|	PROPN
ejpam-5713	457	20	s.	s.	PROPN
ejpam-5713	457	21	r.	r.	PROPN
ejpam-5713	457	22	canoy	canoy	PROPN
ejpam-5713	457	23	et	et	PROPN
ejpam-5713	457	24	al	al	PROPN
ejpam-5713	457	25	.	.	PUNCT
ejpam-5713	457	26	/	/	SYM
ejpam-5713	457	27	eur	eur	PROPN
ejpam-5713	457	28	.	.	PUNCT
ejpam-5713	458	1	j.	j.	PROPN
ejpam-5713	458	2	pure	pure	PROPN
ejpam-5713	458	3	appl	appl	PROPN
ejpam-5713	458	4	.	.	PROPN
ejpam-5713	458	5	math	math	PROPN
ejpam-5713	458	6	,	,	PUNCT
ejpam-5713	458	7	18	18	NUM
ejpam-5713	458	8	(	(	PUNCT
ejpam-5713	458	9	1	1	NUM
ejpam-5713	458	10	)	)	PUNCT
ejpam-5713	458	11	(	(	PUNCT
ejpam-5713	458	12	2025	2025	NUM
ejpam-5713	458	13	)	)	PUNCT
ejpam-5713	458	14	,	,	PUNCT
ejpam-5713	458	15	5713	5713	NUM
ejpam-5713	458	16	11	11	NUM
ejpam-5713	458	17	of	of	ADP
ejpam-5713	458	18	13	13	NUM
ejpam-5713	458	19	=	=	SYM
ejpam-5713	458	20	β(g	β(g	PROPN
ejpam-5713	458	21	)	)	PUNCT
ejpam-5713	459	1	+	+	CCONJ
ejpam-5713	459	2	β(g)βs(h	β(g)βs(h	NOUN
ejpam-5713	459	3	)	)	PUNCT
ejpam-5713	459	4	+	+	CCONJ
ejpam-5713	459	5	n(m−	n(m−	PROPN
ejpam-5713	459	6	β(g	β(g	PROPN
ejpam-5713	459	7	)	)	PUNCT
ejpam-5713	459	8	)	)	PUNCT
ejpam-5713	460	1	=	=	PRON
ejpam-5713	460	2	(	(	PUNCT
ejpam-5713	460	3	βs(h)−	βs(h)−	PROPN
ejpam-5713	460	4	n+	n+	NUM
ejpam-5713	460	5	1)β(g	1)β(g	NUM
ejpam-5713	460	6	)	)	PUNCT
ejpam-5713	461	1	+	+	PROPN
ejpam-5713	461	2	mn	mn	PROPN
ejpam-5713	461	3	.	.	PROPN
ejpam-5713	462	1	on	on	ADP
ejpam-5713	462	2	the	the	DET
ejpam-5713	462	3	other	other	ADJ
ejpam-5713	462	4	hand	hand	NOUN
ejpam-5713	462	5	,	,	PUNCT
ejpam-5713	462	6	let	let	VERB
ejpam-5713	462	7	c0	c0	NOUN
ejpam-5713	462	8	be	be	AUX
ejpam-5713	462	9	a	a	DET
ejpam-5713	462	10	βs	βs	NOUN
ejpam-5713	462	11	-	-	PUNCT
ejpam-5713	462	12	set	set	NOUN
ejpam-5713	462	13	in	in	ADP
ejpam-5713	462	14	g	g	PROPN
ejpam-5713	462	15	◦	◦	PROPN
ejpam-5713	462	16	h.	h.	PROPN
ejpam-5713	462	17	then	then	ADV
ejpam-5713	462	18	c0	c0	PROPN
ejpam-5713	462	19	=	=	SYM
ejpam-5713	462	20	a0	a0	PROPN
ejpam-5713	462	21	∪	∪	ADV
ejpam-5713	462	22	(	(	PUNCT
ejpam-5713	462	23	∪v∈v	∪v∈v	X
ejpam-5713	462	24	(	(	PUNCT
ejpam-5713	462	25	g)s	g)s	NOUN
ejpam-5713	462	26	′	′	NUM
ejpam-5713	462	27	v	v	NOUN
ejpam-5713	462	28	)	)	PUNCT
ejpam-5713	462	29	and	and	CCONJ
ejpam-5713	462	30	satisfies	satisfy	VERB
ejpam-5713	462	31	properties	property	NOUN
ejpam-5713	462	32	(	(	PUNCT
ejpam-5713	462	33	i	i	NOUN
ejpam-5713	462	34	)	)	PUNCT
ejpam-5713	462	35	,	,	PUNCT
ejpam-5713	462	36	(	(	PUNCT
ejpam-5713	462	37	ii	ii	NOUN
ejpam-5713	462	38	)	)	PUNCT
ejpam-5713	462	39	,	,	PUNCT
ejpam-5713	462	40	(	(	PUNCT
ejpam-5713	462	41	iii	iii	NOUN
ejpam-5713	462	42	)	)	PUNCT
ejpam-5713	462	43	,	,	PUNCT
ejpam-5713	462	44	and	and	CCONJ
ejpam-5713	462	45	(	(	PUNCT
ejpam-5713	462	46	iv	iv	X
ejpam-5713	462	47	)	)	PUNCT
ejpam-5713	462	48	of	of	ADP
ejpam-5713	462	49	theorem	theorem	NOUN
ejpam-5713	462	50	5	5	NUM
ejpam-5713	462	51	.	.	PUNCT
ejpam-5713	462	52	hence	hence	ADV
ejpam-5713	462	53	,	,	PUNCT
ejpam-5713	462	54	a0	a0	PROPN
ejpam-5713	462	55	is	be	AUX
ejpam-5713	462	56	a	a	DET
ejpam-5713	462	57	vertex	vertex	NOUN
ejpam-5713	462	58	cover	cover	NOUN
ejpam-5713	462	59	of	of	ADP
ejpam-5713	462	60	g	g	NOUN
ejpam-5713	462	61	by	by	ADP
ejpam-5713	462	62	(	(	PUNCT
ejpam-5713	462	63	i	i	NOUN
ejpam-5713	462	64	)	)	PUNCT
ejpam-5713	462	65	and	and	CCONJ
ejpam-5713	462	66	s′	s′	PROPN
ejpam-5713	462	67	v	v	PROPN
ejpam-5713	462	68	=	=	SYM
ejpam-5713	462	69	v	v	PROPN
ejpam-5713	462	70	(	(	PUNCT
ejpam-5713	462	71	hv	hv	PROPN
ejpam-5713	462	72	)	)	PUNCT
ejpam-5713	462	73	for	for	ADP
ejpam-5713	462	74	each	each	PRON
ejpam-5713	462	75	v	v	NUM
ejpam-5713	462	76	∈	∈	PROPN
ejpam-5713	462	77	v	v	NOUN
ejpam-5713	462	78	(	(	PUNCT
ejpam-5713	462	79	g	g	NOUN
ejpam-5713	462	80	)	)	PUNCT
ejpam-5713	462	81	\a	\a	VERB
ejpam-5713	462	82	by	by	ADP
ejpam-5713	462	83	(	(	PUNCT
ejpam-5713	462	84	iv	iv	X
ejpam-5713	462	85	)	)	PUNCT
ejpam-5713	462	86	.	.	PUNCT
ejpam-5713	463	1	note	note	VERB
ejpam-5713	463	2	that	that	SCONJ
ejpam-5713	463	3	since	since	SCONJ
ejpam-5713	463	4	h	h	NOUN
ejpam-5713	463	5	is	be	AUX
ejpam-5713	463	6	a	a	DET
ejpam-5713	463	7	(	(	PUNCT
ejpam-5713	463	8	non	non	ADJ
ejpam-5713	463	9	-	-	ADJ
ejpam-5713	463	10	trivial	trivial	ADJ
ejpam-5713	463	11	)	)	PUNCT
ejpam-5713	463	12	connected	connected	ADJ
ejpam-5713	463	13	graph	graph	NOUN
ejpam-5713	463	14	,	,	PUNCT
ejpam-5713	463	15	s′	s′	X
ejpam-5713	463	16	v	v	NOUN
ejpam-5713	463	17	is	be	AUX
ejpam-5713	463	18	a	a	DET
ejpam-5713	463	19	super	super	ADJ
ejpam-5713	463	20	vertex	vertex	NOUN
ejpam-5713	463	21	cover	cover	NOUN
ejpam-5713	463	22	in	in	ADP
ejpam-5713	463	23	hv	hv	PROPN
ejpam-5713	463	24	for	for	ADP
ejpam-5713	463	25	each	each	DET
ejpam-5713	463	26	v	v	NUM
ejpam-5713	463	27	∈	∈	PROPN
ejpam-5713	463	28	v	v	NOUN
ejpam-5713	463	29	(	(	PUNCT
ejpam-5713	463	30	g	g	NOUN
ejpam-5713	463	31	)	)	PUNCT
ejpam-5713	463	32	by	by	ADP
ejpam-5713	463	33	(	(	PUNCT
ejpam-5713	463	34	ii	ii	NOUN
ejpam-5713	463	35	)	)	PUNCT
ejpam-5713	463	36	and	and	CCONJ
ejpam-5713	463	37	(	(	PUNCT
ejpam-5713	463	38	iii	iii	NOUN
ejpam-5713	463	39	)	)	PUNCT
ejpam-5713	463	40	.	.	PUNCT
ejpam-5713	464	1	hence	hence	ADV
ejpam-5713	464	2	,	,	PUNCT
ejpam-5713	464	3	βs(g	βs(g	PUNCT
ejpam-5713	464	4	◦	◦	NOUN
ejpam-5713	464	5	h	h	NOUN
ejpam-5713	464	6	)	)	PUNCT
ejpam-5713	464	7	=	=	SYM
ejpam-5713	464	8	|s0|	|s0|	NOUN
ejpam-5713	464	9	=	=	SYM
ejpam-5713	464	10	|a0|+	|a0|+	ADP
ejpam-5713	464	11	∑	∑	PUNCT
ejpam-5713	464	12	v∈a0	v∈a0	NOUN
ejpam-5713	464	13	|s′	|s′	NOUN
ejpam-5713	464	14	v|+	v|+	PROPN
ejpam-5713	464	15	∑	∑	PUNCT
ejpam-5713	464	16	v∈v	v∈v	PROPN
ejpam-5713	464	17	(	(	PUNCT
ejpam-5713	464	18	g)\a0	g)\a0	PROPN
ejpam-5713	464	19	|s′	|s′	PROPN
ejpam-5713	464	20	v|	v|	ADV
ejpam-5713	464	21	≥	≥	X
ejpam-5713	464	22	|a0|+	|a0|+	SYM
ejpam-5713	464	23	∑	∑	NOUN
ejpam-5713	464	24	v∈a0	v∈a0	NOUN
ejpam-5713	464	25	βs(h	βs(h	PUNCT
ejpam-5713	464	26	)	)	PUNCT
ejpam-5713	465	1	+	+	CCONJ
ejpam-5713	465	2	∑	∑	PUNCT
ejpam-5713	465	3	v∈v	v∈v	PROPN
ejpam-5713	465	4	(	(	PUNCT
ejpam-5713	465	5	g)\a0	g)\a0	NOUN
ejpam-5713	465	6	n	n	NOUN
ejpam-5713	465	7	=	=	SYM
ejpam-5713	465	8	|a0|+	|a0|+	X
ejpam-5713	465	9	|a0|βs(h	|a0|βs(h	PROPN
ejpam-5713	465	10	)	)	PUNCT
ejpam-5713	465	11	+	+	CCONJ
ejpam-5713	465	12	(	(	PUNCT
ejpam-5713	465	13	m−	m−	PROPN
ejpam-5713	465	14	|a0|)n	|a0|)n	PROPN
ejpam-5713	465	15	=	=	SYM
ejpam-5713	465	16	(	(	PUNCT
ejpam-5713	465	17	βs(h)−	βs(h)−	PROPN
ejpam-5713	465	18	n+	n+	NUM
ejpam-5713	465	19	1)|a0|+mn	1)|a0|+mn	NUM
ejpam-5713	465	20	≥	≥	NOUN
ejpam-5713	465	21	(	(	PUNCT
ejpam-5713	465	22	βs(h)−	βs(h)−	PROPN
ejpam-5713	465	23	n+	n+	NUM
ejpam-5713	465	24	1)β(g	1)β(g	NUM
ejpam-5713	465	25	)	)	PUNCT
ejpam-5713	465	26	+	+	PROPN
ejpam-5713	465	27	mn	mn	PROPN
ejpam-5713	465	28	.	.	PUNCT
ejpam-5713	466	1	this	this	PRON
ejpam-5713	466	2	establishes	establish	VERB
ejpam-5713	466	3	the	the	DET
ejpam-5713	466	4	desired	desire	VERB
ejpam-5713	466	5	equality	equality	NOUN
ejpam-5713	466	6	.	.	PUNCT
ejpam-5713	467	1	4	4	X
ejpam-5713	467	2	.	.	X
ejpam-5713	467	3	conclusion	conclusion	VERB
ejpam-5713	467	4	the	the	DET
ejpam-5713	467	5	variant	variant	ADJ
ejpam-5713	467	6	super	super	ADJ
ejpam-5713	467	7	vertex	vertex	NOUN
ejpam-5713	467	8	cover	cover	NOUN
ejpam-5713	467	9	of	of	ADP
ejpam-5713	467	10	the	the	DET
ejpam-5713	467	11	standard	standard	ADJ
ejpam-5713	467	12	vertex	vertex	NOUN
ejpam-5713	467	13	cover	cover	NOUN
ejpam-5713	467	14	had	have	AUX
ejpam-5713	467	15	been	be	AUX
ejpam-5713	467	16	introduced	introduce	VERB
ejpam-5713	467	17	and	and	CCONJ
ejpam-5713	467	18	initially	initially	ADV
ejpam-5713	467	19	investigated	investigate	VERB
ejpam-5713	467	20	in	in	ADP
ejpam-5713	467	21	this	this	DET
ejpam-5713	467	22	study	study	NOUN
ejpam-5713	467	23	.	.	PUNCT
ejpam-5713	468	1	for	for	ADP
ejpam-5713	468	2	a	a	DET
ejpam-5713	468	3	non	non	ADJ
ejpam-5713	468	4	-	-	ADJ
ejpam-5713	468	5	empty	empty	ADJ
ejpam-5713	468	6	graphg	graphg	NOUN
ejpam-5713	468	7	,	,	PUNCT
ejpam-5713	468	8	its	its	PRON
ejpam-5713	468	9	super	super	ADJ
ejpam-5713	468	10	vertex	vertex	NOUN
ejpam-5713	468	11	cover	cover	NOUN
ejpam-5713	468	12	number	number	NOUN
ejpam-5713	468	13	is	be	AUX
ejpam-5713	468	14	at	at	ADP
ejpam-5713	468	15	least	least	ADJ
ejpam-5713	468	16	equal	equal	ADJ
ejpam-5713	468	17	to	to	ADP
ejpam-5713	468	18	the	the	DET
ejpam-5713	468	19	maximum	maximum	NOUN
ejpam-5713	468	20	of	of	ADP
ejpam-5713	468	21	the	the	DET
ejpam-5713	468	22	super	super	ADJ
ejpam-5713	468	23	domination	domination	NOUN
ejpam-5713	468	24	number	number	NOUN
ejpam-5713	468	25	and	and	CCONJ
ejpam-5713	468	26	the	the	DET
ejpam-5713	468	27	vertex	vertex	NOUN
ejpam-5713	468	28	cover	cover	NOUN
ejpam-5713	468	29	number	number	NOUN
ejpam-5713	468	30	of	of	ADP
ejpam-5713	468	31	the	the	DET
ejpam-5713	468	32	graph	graph	NOUN
ejpam-5713	468	33	and	and	CCONJ
ejpam-5713	468	34	at	at	ADP
ejpam-5713	468	35	most	most	ADV
ejpam-5713	468	36	equal	equal	ADJ
ejpam-5713	468	37	to	to	ADP
ejpam-5713	468	38	|v	|v	PROPN
ejpam-5713	468	39	(	(	PUNCT
ejpam-5713	468	40	g)|	g)|	INTJ
ejpam-5713	468	41	−	−	NOUN
ejpam-5713	468	42	1	1	NUM
ejpam-5713	468	43	.	.	PUNCT
ejpam-5713	469	1	it	it	PRON
ejpam-5713	469	2	was	be	AUX
ejpam-5713	469	3	shown	show	VERB
ejpam-5713	469	4	that	that	SCONJ
ejpam-5713	469	5	the	the	DET
ejpam-5713	469	6	difference	difference	NOUN
ejpam-5713	469	7	of	of	ADP
ejpam-5713	469	8	the	the	DET
ejpam-5713	469	9	super	super	ADJ
ejpam-5713	469	10	vertex	vertex	NOUN
ejpam-5713	469	11	cover	cover	NOUN
ejpam-5713	469	12	number	number	NOUN
ejpam-5713	469	13	and	and	CCONJ
ejpam-5713	469	14	the	the	DET
ejpam-5713	469	15	vertex	vertex	NOUN
ejpam-5713	469	16	cover	cover	NOUN
ejpam-5713	469	17	number	number	NOUN
ejpam-5713	469	18	can	can	AUX
ejpam-5713	469	19	be	be	AUX
ejpam-5713	469	20	made	make	VERB
ejpam-5713	469	21	arbitrarily	arbitrarily	ADV
ejpam-5713	469	22	large	large	ADJ
ejpam-5713	469	23	.	.	PUNCT
ejpam-5713	470	1	in	in	ADP
ejpam-5713	470	2	this	this	DET
ejpam-5713	470	3	study	study	NOUN
ejpam-5713	470	4	,	,	PUNCT
ejpam-5713	470	5	the	the	DET
ejpam-5713	470	6	super	super	ADJ
ejpam-5713	470	7	vertex	vertex	NOUN
ejpam-5713	470	8	cover	cover	NOUN
ejpam-5713	470	9	numbers	number	NOUN
ejpam-5713	470	10	of	of	ADP
ejpam-5713	470	11	some	some	DET
ejpam-5713	470	12	graphs	graph	NOUN
ejpam-5713	470	13	,	,	PUNCT
ejpam-5713	470	14	including	include	VERB
ejpam-5713	470	15	the	the	DET
ejpam-5713	470	16	join	join	NOUN
ejpam-5713	470	17	and	and	CCONJ
ejpam-5713	470	18	the	the	DET
ejpam-5713	470	19	corona	corona	NOUN
ejpam-5713	470	20	of	of	ADP
ejpam-5713	470	21	two	two	NUM
ejpam-5713	470	22	graphs	graph	NOUN
ejpam-5713	470	23	,	,	PUNCT
ejpam-5713	470	24	had	have	AUX
ejpam-5713	470	25	been	be	AUX
ejpam-5713	470	26	obtained	obtain	VERB
ejpam-5713	470	27	.	.	PUNCT
ejpam-5713	471	1	further	further	ADJ
ejpam-5713	471	2	study	study	NOUN
ejpam-5713	471	3	or	or	CCONJ
ejpam-5713	471	4	investigation	investigation	NOUN
ejpam-5713	471	5	of	of	ADP
ejpam-5713	471	6	the	the	DET
ejpam-5713	471	7	newly	newly	ADV
ejpam-5713	471	8	defined	define	VERB
ejpam-5713	471	9	parameter	parameter	NOUN
ejpam-5713	471	10	is	be	AUX
ejpam-5713	471	11	recommended	recommend	VERB
ejpam-5713	471	12	.	.	PUNCT
ejpam-5713	472	1	in	in	ADP
ejpam-5713	472	2	particular	particular	ADJ
ejpam-5713	472	3	,	,	PUNCT
ejpam-5713	472	4	it	it	PRON
ejpam-5713	472	5	may	may	AUX
ejpam-5713	472	6	be	be	AUX
ejpam-5713	472	7	interesting	interesting	ADJ
ejpam-5713	472	8	to	to	PART
ejpam-5713	472	9	determine	determine	VERB
ejpam-5713	472	10	the	the	DET
ejpam-5713	472	11	value	value	NOUN
ejpam-5713	472	12	of	of	ADP
ejpam-5713	472	13	the	the	DET
ejpam-5713	472	14	parameter	parameter	NOUN
ejpam-5713	472	15	for	for	ADP
ejpam-5713	472	16	graphs	graph	NOUN
ejpam-5713	472	17	resulting	result	VERB
ejpam-5713	472	18	from	from	ADP
ejpam-5713	472	19	other	other	ADJ
ejpam-5713	472	20	binary	binary	ADJ
ejpam-5713	472	21	operations	operation	NOUN
ejpam-5713	472	22	.	.	PUNCT
ejpam-5713	473	1	moreover	moreover	ADV
ejpam-5713	473	2	,	,	PUNCT
ejpam-5713	473	3	while	while	SCONJ
ejpam-5713	473	4	the	the	DET
ejpam-5713	473	5	vertex	vertex	NOUN
ejpam-5713	473	6	cover	cover	NOUN
ejpam-5713	473	7	problem	problem	NOUN
ejpam-5713	473	8	is	be	AUX
ejpam-5713	473	9	np	np	ADP
ejpam-5713	473	10	-complete	-complete	ADJ
ejpam-5713	473	11	,	,	PUNCT
ejpam-5713	473	12	it	it	PRON
ejpam-5713	473	13	remains	remain	VERB
ejpam-5713	473	14	open	open	ADJ
ejpam-5713	473	15	to	to	PART
ejpam-5713	473	16	show	show	VERB
ejpam-5713	473	17	whether	whether	SCONJ
ejpam-5713	473	18	or	or	CCONJ
ejpam-5713	473	19	not	not	PART
ejpam-5713	473	20	the	the	DET
ejpam-5713	473	21	super	super	ADJ
ejpam-5713	473	22	vertex	vertex	NOUN
ejpam-5713	473	23	cover	cover	NOUN
ejpam-5713	473	24	problem	problem	NOUN
ejpam-5713	473	25	is	be	AUX
ejpam-5713	473	26	np	np	ADP
ejpam-5713	473	27	-complete	-complete	ADJ
ejpam-5713	473	28	.	.	PUNCT
ejpam-5713	474	1	acknowledgements	acknowledgement	NOUN
ejpam-5713	474	2	the	the	DET
ejpam-5713	474	3	authors	author	NOUN
ejpam-5713	474	4	would	would	AUX
ejpam-5713	474	5	like	like	VERB
ejpam-5713	474	6	to	to	PART
ejpam-5713	474	7	thank	thank	VERB
ejpam-5713	474	8	the	the	DET
ejpam-5713	474	9	referees	referee	NOUN
ejpam-5713	474	10	for	for	ADP
ejpam-5713	474	11	reading	read	VERB
ejpam-5713	474	12	the	the	DET
ejpam-5713	474	13	paper	paper	NOUN
ejpam-5713	474	14	and	and	CCONJ
ejpam-5713	474	15	giving	give	VERB
ejpam-5713	474	16	their	their	PRON
ejpam-5713	474	17	respective	respective	ADJ
ejpam-5713	474	18	comments	comment	NOUN
ejpam-5713	474	19	and	and	CCONJ
ejpam-5713	474	20	suggestions	suggestion	NOUN
ejpam-5713	474	21	.	.	PUNCT
ejpam-5713	475	1	the	the	DET
ejpam-5713	475	2	authors	author	NOUN
ejpam-5713	475	3	are	be	AUX
ejpam-5713	475	4	grateful	grateful	ADJ
ejpam-5713	475	5	to	to	ADP
ejpam-5713	475	6	msu	msu	PROPN
ejpam-5713	475	7	-	-	PUNCT
ejpam-5713	475	8	iligan	iligan	PROPN
ejpam-5713	475	9	institute	institute	PROPN
ejpam-5713	475	10	of	of	ADP
ejpam-5713	475	11	technology	technology	PROPN
ejpam-5713	475	12	,	,	PUNCT
ejpam-5713	475	13	iligan	iligan	PROPN
ejpam-5713	475	14	city	city	PROPN
ejpam-5713	475	15	,	,	PUNCT
ejpam-5713	475	16	ateneo	ateneo	PROPN
ejpam-5713	475	17	de	de	PROPN
ejpam-5713	475	18	davao	davao	PROPN
ejpam-5713	475	19	university	university	PROPN
ejpam-5713	475	20	,	,	PUNCT
ejpam-5713	475	21	msu	msu	PROPN
ejpam-5713	475	22	tawi	tawi	PROPN
ejpam-5713	475	23	-	-	PUNCT
ejpam-5713	475	24	tawi	tawi	PROPN
ejpam-5713	475	25	college	college	PROPN
ejpam-5713	475	26	of	of	ADP
ejpam-5713	475	27	technology	technology	NOUN
ejpam-5713	475	28	and	and	CCONJ
ejpam-5713	475	29	oceanography	oceanography	NOUN
ejpam-5713	475	30	,	,	PUNCT
ejpam-5713	475	31	and	and	CCONJ
ejpam-5713	475	32	korea	korea	PROPN
ejpam-5713	475	33	university	university	PROPN
ejpam-5713	475	34	for	for	ADP
ejpam-5713	475	35	the	the	DET
ejpam-5713	475	36	financial	financial	ADJ
ejpam-5713	475	37	support	support	NOUN
ejpam-5713	475	38	they	they	PRON
ejpam-5713	475	39	have	have	AUX
ejpam-5713	475	40	extended	extend	VERB
ejpam-5713	475	41	for	for	ADP
ejpam-5713	475	42	the	the	DET
ejpam-5713	475	43	conduct	conduct	NOUN
ejpam-5713	475	44	of	of	ADP
ejpam-5713	475	45	this	this	DET
ejpam-5713	475	46	research	research	NOUN
ejpam-5713	475	47	.	.	PUNCT
ejpam-5713	476	1	s.	s.	PROPN
ejpam-5713	476	2	r.	r.	PROPN
ejpam-5713	476	3	canoy	canoy	PROPN
ejpam-5713	476	4	et	et	PROPN
ejpam-5713	476	5	al	al	PROPN
ejpam-5713	476	6	.	.	PUNCT
ejpam-5713	476	7	/	/	SYM
ejpam-5713	476	8	eur	eur	PROPN
ejpam-5713	476	9	.	.	PUNCT
ejpam-5713	477	1	j.	j.	PROPN
ejpam-5713	477	2	pure	pure	PROPN
ejpam-5713	477	3	appl	appl	PROPN
ejpam-5713	477	4	.	.	PROPN
ejpam-5713	477	5	math	math	PROPN
ejpam-5713	477	6	,	,	PUNCT
ejpam-5713	477	7	18	18	NUM
ejpam-5713	477	8	(	(	PUNCT
ejpam-5713	477	9	1	1	NUM
ejpam-5713	477	10	)	)	PUNCT
ejpam-5713	477	11	(	(	PUNCT
ejpam-5713	477	12	2025	2025	NUM
ejpam-5713	477	13	)	)	PUNCT
ejpam-5713	477	14	,	,	PUNCT
ejpam-5713	477	15	5713	5713	NUM
ejpam-5713	477	16	12	12	NUM
ejpam-5713	477	17	of	of	ADP
ejpam-5713	477	18	13	13	NUM
ejpam-5713	477	19	references	reference	NOUN
ejpam-5713	477	20	[	[	X
ejpam-5713	477	21	1	1	NUM
ejpam-5713	477	22	]	]	PUNCT
ejpam-5713	477	23	d.	d.	PROPN
ejpam-5713	477	24	angel	angel	NOUN
ejpam-5713	477	25	and	and	CCONJ
ejpam-5713	477	26	a.	a.	NOUN
ejpam-5713	477	27	amutha	amutha	PROPN
ejpam-5713	477	28	.	.	PUNCT
ejpam-5713	478	1	vertex	vertex	NOUN
ejpam-5713	478	2	covering	covering	NOUN
ejpam-5713	478	3	and	and	CCONJ
ejpam-5713	478	4	strong	strong	ADJ
ejpam-5713	478	5	covering	covering	NOUN
ejpam-5713	478	6	of	of	ADP
ejpam-5713	478	7	flower	flower	NOUN
ejpam-5713	478	8	like	like	ADP
ejpam-5713	478	9	network	network	NOUN
ejpam-5713	478	10	structures	structure	NOUN
ejpam-5713	478	11	.	.	PUNCT
ejpam-5713	479	1	procedia	procedia	NOUN
ejpam-5713	479	2	computer	computer	NOUN
ejpam-5713	479	3	science	science	NOUN
ejpam-5713	479	4	,	,	PUNCT
ejpam-5713	479	5	87:164–171	87:164–171	PROPN
ejpam-5713	479	6	,	,	PUNCT
ejpam-5713	479	7	2016	2016	NUM
ejpam-5713	479	8	.	.	PUNCT
ejpam-5713	480	1	[	[	X
ejpam-5713	480	2	2	2	NUM
ejpam-5713	480	3	]	]	X
ejpam-5713	480	4	b.	b.	PROPN
ejpam-5713	480	5	behsaz	behsaz	PROPN
ejpam-5713	480	6	,	,	PUNCT
ejpam-5713	480	7	p.	p.	PROPN
ejpam-5713	480	8	hatami	hatami	PROPN
ejpam-5713	480	9	,	,	PUNCT
ejpam-5713	480	10	and	and	CCONJ
ejpam-5713	480	11	e.s	e.s	PROPN
ejpam-5713	480	12	.	.	PROPN
ejpam-5713	480	13	mahmoodian	mahmoodian	PROPN
ejpam-5713	480	14	.	.	PUNCT
ejpam-5713	481	1	on	on	ADP
ejpam-5713	481	2	minimum	minimum	ADJ
ejpam-5713	481	3	vertex	vertex	NOUN
ejpam-5713	481	4	cover	cover	NOUN
ejpam-5713	481	5	of	of	ADP
ejpam-5713	481	6	generalized	generalized	ADJ
ejpam-5713	481	7	petersen	petersen	NOUN
ejpam-5713	481	8	graphs	graph	NOUN
ejpam-5713	481	9	.	.	PUNCT
ejpam-5713	482	1	australian	australian	ADJ
ejpam-5713	482	2	journal	journal	NOUN
ejpam-5713	482	3	of	of	ADP
ejpam-5713	482	4	combinatorics	combinatoric	NOUN
ejpam-5713	482	5	,	,	PUNCT
ejpam-5713	482	6	40:253–264	40:253–264	NUM
ejpam-5713	482	7	,	,	PUNCT
ejpam-5713	482	8	2008	2008	NUM
ejpam-5713	482	9	.	.	PUNCT
ejpam-5713	483	1	[	[	X
ejpam-5713	483	2	3	3	X
ejpam-5713	483	3	]	]	X
ejpam-5713	483	4	v.	v.	X
ejpam-5713	483	5	bilar	bilar	PROPN
ejpam-5713	483	6	,	,	PUNCT
ejpam-5713	483	7	m.a	m.a	PROPN
ejpam-5713	483	8	.	.	PROPN
ejpam-5713	483	9	bonsocan	bonsocan	PROPN
ejpam-5713	483	10	,	,	PUNCT
ejpam-5713	483	11	j.	j.	PROPN
ejpam-5713	483	12	hassan	hassan	PROPN
ejpam-5713	483	13	,	,	PUNCT
ejpam-5713	483	14	and	and	CCONJ
ejpam-5713	483	15	s.	s.	PROPN
ejpam-5713	483	16	dagondon	dagondon	PROPN
ejpam-5713	483	17	.	.	PUNCT
ejpam-5713	484	1	vertex	vertex	NOUN
ejpam-5713	484	2	cover	cover	VERB
ejpam-5713	484	3	hop	hop	NOUN
ejpam-5713	484	4	dominating	dominating	NOUN
ejpam-5713	484	5	sets	set	NOUN
ejpam-5713	484	6	in	in	ADP
ejpam-5713	484	7	graphs	graph	NOUN
ejpam-5713	484	8	.	.	PUNCT
ejpam-5713	485	1	eur	eur	PROPN
ejpam-5713	485	2	.	.	PUNCT
ejpam-5713	486	1	j.	j.	PROPN
ejpam-5713	486	2	pure	pure	PROPN
ejpam-5713	486	3	appl	appl	PROPN
ejpam-5713	486	4	.	.	PUNCT
ejpam-5713	486	5	math	math	PROPN
ejpam-5713	486	6	.	.	PUNCT
ejpam-5713	486	7	,	,	PUNCT
ejpam-5713	486	8	17(1):93–104	17(1):93–104	NUM
ejpam-5713	486	9	,	,	PUNCT
ejpam-5713	486	10	2024	2024	NUM
ejpam-5713	486	11	.	.	PUNCT
ejpam-5713	487	1	[	[	X
ejpam-5713	487	2	4	4	NUM
ejpam-5713	487	3	]	]	X
ejpam-5713	487	4	f.	f.	PROPN
ejpam-5713	487	5	buckley	buckley	PROPN
ejpam-5713	487	6	and	and	CCONJ
ejpam-5713	487	7	f.	f.	PROPN
ejpam-5713	487	8	harary	harary	PROPN
ejpam-5713	487	9	.	.	PUNCT
ejpam-5713	488	1	distance	distance	NOUN
ejpam-5713	488	2	in	in	ADP
ejpam-5713	488	3	graphs	graph	NOUN
ejpam-5713	488	4	.	.	PUNCT
ejpam-5713	489	1	addison	addison	PROPN
ejpam-5713	489	2	-	-	PUNCT
ejpam-5713	489	3	wesley	wesley	PROPN
ejpam-5713	489	4	,	,	PUNCT
ejpam-5713	489	5	redwood	redwood	NOUN
ejpam-5713	489	6	city	city	NOUN
ejpam-5713	489	7	,	,	PUNCT
ejpam-5713	489	8	1990	1990	NUM
ejpam-5713	489	9	.	.	PUNCT
ejpam-5713	490	1	[	[	X
ejpam-5713	490	2	5	5	NUM
ejpam-5713	490	3	]	]	X
ejpam-5713	490	4	c.	c.	NOUN
ejpam-5713	490	5	bujtas	bujtas	PROPN
ejpam-5713	490	6	,	,	PUNCT
ejpam-5713	490	7	n.	n.	NOUN
ejpam-5713	490	8	ghanbari	ghanbari	NOUN
ejpam-5713	490	9	,	,	PUNCT
ejpam-5713	490	10	and	and	CCONJ
ejpam-5713	490	11	s.	s.	PROPN
ejpam-5713	490	12	klavzar	klavzar	PROPN
ejpam-5713	490	13	.	.	PUNCT
ejpam-5713	491	1	computational	computational	ADJ
ejpam-5713	491	2	complexity	complexity	NOUN
ejpam-5713	491	3	aspects	aspect	NOUN
ejpam-5713	491	4	of	of	ADP
ejpam-5713	491	5	super	super	ADJ
ejpam-5713	491	6	domination	domination	NOUN
ejpam-5713	491	7	.	.	PUNCT
ejpam-5713	492	1	theoretical	theoretical	ADJ
ejpam-5713	492	2	computer	computer	NOUN
ejpam-5713	492	3	science	science	NOUN
ejpam-5713	492	4	,	,	PUNCT
ejpam-5713	492	5	975:1–13	975:1–13	NUM
ejpam-5713	492	6	,	,	PUNCT
ejpam-5713	492	7	2023	2023	NUM
ejpam-5713	492	8	.	.	PUNCT
ejpam-5713	493	1	[	[	X
ejpam-5713	493	2	6	6	NUM
ejpam-5713	493	3	]	]	X
ejpam-5713	493	4	m.r	m.r	PROPN
ejpam-5713	493	5	.	.	PROPN
ejpam-5713	493	6	garey	garey	PROPN
ejpam-5713	493	7	and	and	CCONJ
ejpam-5713	493	8	d.s	d.s	PROPN
ejpam-5713	493	9	.	.	PROPN
ejpam-5713	493	10	johnson	johnson	PROPN
ejpam-5713	493	11	.	.	PUNCT
ejpam-5713	494	1	the	the	DET
ejpam-5713	494	2	rectilinear	rectilinear	PROPN
ejpam-5713	494	3	steiner	steiner	PROPN
ejpam-5713	494	4	tree	tree	NOUN
ejpam-5713	494	5	problem	problem	NOUN
ejpam-5713	494	6	is	be	AUX
ejpam-5713	494	7	np	np	NOUN
ejpam-5713	494	8	-	-	PUNCT
ejpam-5713	494	9	complete	complete	ADJ
ejpam-5713	494	10	.	.	PUNCT
ejpam-5713	495	1	siam	siam	PROPN
ejpam-5713	495	2	journal	journal	PROPN
ejpam-5713	495	3	on	on	ADP
ejpam-5713	495	4	applied	apply	VERB
ejpam-5713	495	5	mathematics	mathematic	NOUN
ejpam-5713	495	6	,	,	PUNCT
ejpam-5713	495	7	32:826–834	32:826–834	NUM
ejpam-5713	495	8	,	,	PUNCT
ejpam-5713	495	9	1977	1977	NUM
ejpam-5713	495	10	.	.	PUNCT
ejpam-5713	496	1	[	[	X
ejpam-5713	496	2	7	7	X
ejpam-5713	496	3	]	]	X
ejpam-5713	496	4	m.r	m.r	PROPN
ejpam-5713	496	5	.	.	PROPN
ejpam-5713	496	6	garey	garey	PROPN
ejpam-5713	496	7	,	,	PUNCT
ejpam-5713	496	8	d.s	d.s	PROPN
ejpam-5713	496	9	.	.	PROPN
ejpam-5713	496	10	johnson	johnson	PROPN
ejpam-5713	496	11	,	,	PUNCT
ejpam-5713	496	12	and	and	CCONJ
ejpam-5713	496	13	l.	l.	PROPN
ejpam-5713	496	14	stockmeyer	stockmeyer	PROPN
ejpam-5713	496	15	.	.	PUNCT
ejpam-5713	497	1	some	some	PRON
ejpam-5713	497	2	simplified	simplified	ADJ
ejpam-5713	497	3	npcomplete	npcomplete	ADJ
ejpam-5713	497	4	problems	problem	NOUN
ejpam-5713	497	5	.	.	PUNCT
ejpam-5713	498	1	proceedings	proceeding	NOUN
ejpam-5713	498	2	of	of	ADP
ejpam-5713	498	3	the	the	DET
ejpam-5713	498	4	sixth	sixth	ADJ
ejpam-5713	498	5	annual	annual	ADJ
ejpam-5713	498	6	acm	acm	NOUN
ejpam-5713	498	7	symposium	symposium	NOUN
ejpam-5713	498	8	on	on	ADP
ejpam-5713	498	9	theory	theory	NOUN
ejpam-5713	498	10	of	of	ADP
ejpam-5713	498	11	computing	computing	NOUN
ejpam-5713	498	12	,	,	PUNCT
ejpam-5713	498	13	pages	page	NOUN
ejpam-5713	498	14	47	47	NUM
ejpam-5713	498	15	–	–	PUNCT
ejpam-5713	498	16	63	63	NUM
ejpam-5713	498	17	,	,	PUNCT
ejpam-5713	498	18	1974	1974	NUM
ejpam-5713	498	19	.	.	PUNCT
ejpam-5713	499	1	[	[	X
ejpam-5713	499	2	8	8	X
ejpam-5713	499	3	]	]	X
ejpam-5713	499	4	j.	j.	PROPN
ejpam-5713	499	5	hassan	hassan	PROPN
ejpam-5713	499	6	,	,	PUNCT
ejpam-5713	499	7	m.	m.	NOUN
ejpam-5713	499	8	a.	a.	PROPN
ejpam-5713	499	9	bonsocan	bonsocan	PROPN
ejpam-5713	499	10	,	,	PUNCT
ejpam-5713	499	11	r.	r.	PROPN
ejpam-5713	499	12	rasid	rasid	PROPN
ejpam-5713	499	13	,	,	PUNCT
ejpam-5713	499	14	and	and	CCONJ
ejpam-5713	499	15	a.	a.	NOUN
ejpam-5713	499	16	sappari	sappari	PROPN
ejpam-5713	499	17	.	.	PUNCT
ejpam-5713	500	1	certified	certify	VERB
ejpam-5713	500	2	vertex	vertex	NOUN
ejpam-5713	500	3	cover	cover	NOUN
ejpam-5713	500	4	of	of	ADP
ejpam-5713	500	5	a	a	DET
ejpam-5713	500	6	graph	graph	NOUN
ejpam-5713	500	7	.	.	PUNCT
ejpam-5713	501	1	ur	ur	INTJ
ejpam-5713	501	2	.	.	PUNCT
ejpam-5713	502	1	j.	j.	PROPN
ejpam-5713	502	2	pure	pure	PROPN
ejpam-5713	502	3	appl	appl	PROPN
ejpam-5713	502	4	.	.	PUNCT
ejpam-5713	502	5	math	math	PROPN
ejpam-5713	502	6	.	.	PUNCT
ejpam-5713	502	7	,	,	PUNCT
ejpam-5713	502	8	17(2):1038–1045	17(2):1038–1045	NUM
ejpam-5713	502	9	,	,	PUNCT
ejpam-5713	502	10	2024	2024	NUM
ejpam-5713	502	11	.	.	PUNCT
ejpam-5713	503	1	[	[	X
ejpam-5713	503	2	9	9	NUM
ejpam-5713	503	3	]	]	X
ejpam-5713	503	4	m.	m.	NOUN
ejpam-5713	503	5	henning	henning	PROPN
ejpam-5713	503	6	and	and	CCONJ
ejpam-5713	503	7	a.	a.	PROPN
ejpam-5713	503	8	yeo	yeo	PROPN
ejpam-5713	503	9	.	.	PROPN
ejpam-5713	504	1	identifying	identify	VERB
ejpam-5713	504	2	vertex	vertex	NOUN
ejpam-5713	504	3	covers	cover	VERB
ejpam-5713	504	4	in	in	ADP
ejpam-5713	504	5	graphs	graph	NOUN
ejpam-5713	504	6	.	.	PUNCT
ejpam-5713	505	1	the	the	DET
ejpam-5713	505	2	electric	electric	ADJ
ejpam-5713	505	3	journal	journal	PROPN
ejpam-5713	505	4	in	in	ADP
ejpam-5713	505	5	mathematics	mathematic	NOUN
ejpam-5713	505	6	,	,	PUNCT
ejpam-5713	505	7	,	,	PUNCT
ejpam-5713	505	8	19(4):1038–1045	19(4):1038–1045	NUM
ejpam-5713	505	9	.	.	NOUN
ejpam-5713	505	10	,	,	PUNCT
ejpam-5713	505	11	2012	2012	NUM
ejpam-5713	505	12	.	.	PUNCT
ejpam-5713	506	1	[	[	X
ejpam-5713	506	2	10	10	NUM
ejpam-5713	506	3	]	]	X
ejpam-5713	506	4	s.	s.	PROPN
ejpam-5713	506	5	canoy	canoy	PROPN
ejpam-5713	506	6	jr	jr	PROPN
ejpam-5713	506	7	and	and	CCONJ
ejpam-5713	506	8	r.	r.	PROPN
ejpam-5713	506	9	artes	artes	PROPN
ejpam-5713	506	10	jr	jr	PROPN
ejpam-5713	506	11	.	.	PROPN
ejpam-5713	506	12	vertex	vertex	NOUN
ejpam-5713	506	13	and	and	CCONJ
ejpam-5713	506	14	edge	edge	NOUN
ejpam-5713	506	15	covering	cover	VERB
ejpam-5713	506	16	numbers	number	NOUN
ejpam-5713	506	17	of	of	ADP
ejpam-5713	506	18	a	a	DET
ejpam-5713	506	19	graph	graph	NOUN
ejpam-5713	506	20	:	:	PUNCT
ejpam-5713	506	21	revisited	revisit	VERB
ejpam-5713	506	22	.	.	PUNCT
ejpam-5713	507	1	congressus	congressus	PROPN
ejpam-5713	507	2	numerantium	numerantium	PROPN
ejpam-5713	507	3	,	,	PUNCT
ejpam-5713	507	4	167:65	167:65	NUM
ejpam-5713	507	5	,	,	PUNCT
ejpam-5713	507	6	2004	2004	NUM
ejpam-5713	507	7	.	.	PUNCT
ejpam-5713	508	1	[	[	X
ejpam-5713	508	2	11	11	NUM
ejpam-5713	508	3	]	]	X
ejpam-5713	508	4	r.m	r.m	PROPN
ejpam-5713	508	5	.	.	PROPN
ejpam-5713	508	6	karp	karp	PROPN
ejpam-5713	508	7	.	.	PUNCT
ejpam-5713	509	1	reducibility	reducibility	PROPN
ejpam-5713	509	2	among	among	ADP
ejpam-5713	509	3	combinatorial	combinatorial	ADJ
ejpam-5713	509	4	problems	problem	NOUN
ejpam-5713	509	5	,	,	PUNCT
ejpam-5713	509	6	complexity	complexity	NOUN
ejpam-5713	509	7	of	of	ADP
ejpam-5713	509	8	computer	computer	NOUN
ejpam-5713	509	9	computations	computation	NOUN
ejpam-5713	509	10	.	.	PUNCT
ejpam-5713	510	1	plenum	plenum	PROPN
ejpam-5713	510	2	press	press	PROPN
ejpam-5713	510	3	,	,	PUNCT
ejpam-5713	510	4	new	new	PROPN
ejpam-5713	510	5	york	york	PROPN
ejpam-5713	510	6	,	,	PUNCT
ejpam-5713	510	7	pages	page	NOUN
ejpam-5713	510	8	85–103	85–103	NUM
ejpam-5713	510	9	,	,	PUNCT
ejpam-5713	510	10	1972	1972	NUM
ejpam-5713	510	11	.	.	PUNCT
ejpam-5713	511	1	[	[	X
ejpam-5713	511	2	12	12	NUM
ejpam-5713	511	3	]	]	X
ejpam-5713	511	4	d.	d.	PROPN
ejpam-5713	511	5	klein	klein	PROPN
ejpam-5713	511	6	,	,	PUNCT
ejpam-5713	511	7	j.	j.	PROPN
ejpam-5713	511	8	velazquez	velazquez	PROPN
ejpam-5713	511	9	,	,	PUNCT
ejpam-5713	511	10	and	and	CCONJ
ejpam-5713	511	11	e.	e.	PROPN
ejpam-5713	511	12	yi	yi	PROPN
ejpam-5713	511	13	.	.	PUNCT
ejpam-5713	512	1	on	on	ADP
ejpam-5713	512	2	the	the	DET
ejpam-5713	512	3	super	super	ADJ
ejpam-5713	512	4	domination	domination	NOUN
ejpam-5713	512	5	number	number	NOUN
ejpam-5713	512	6	of	of	ADP
ejpam-5713	512	7	graphs	graph	NOUN
ejpam-5713	512	8	.	.	PUNCT
ejpam-5713	513	1	communications	communication	NOUN
ejpam-5713	513	2	in	in	ADP
ejpam-5713	513	3	combinatorics	combinatoric	NOUN
ejpam-5713	513	4	and	and	CCONJ
ejpam-5713	513	5	optimization	optimization	NOUN
ejpam-5713	513	6	,	,	PUNCT
ejpam-5713	513	7	5(2):83–96	5(2):83–96	NUM
ejpam-5713	513	8	,	,	PUNCT
ejpam-5713	513	9	2020	2020	NUM
ejpam-5713	513	10	.	.	PUNCT
ejpam-5713	514	1	[	[	X
ejpam-5713	514	2	13	13	NUM
ejpam-5713	514	3	]	]	PUNCT
ejpam-5713	514	4	m.	m.	NOUN
ejpam-5713	514	5	lemanska	lemanska	PROPN
ejpam-5713	514	6	,	,	PUNCT
ejpam-5713	514	7	v.	v.	ADP
ejpam-5713	514	8	swaminathan	swaminathan	ADV
ejpam-5713	514	9	,	,	PUNCT
ejpam-5713	514	10	and	and	CCONJ
ejpam-5713	514	11	y.	y.	PROPN
ejpam-5713	514	12	b.	b.	PROPN
ejpam-5713	514	13	venkatakrishnan	venkatakrishnan	PROPN
ejpam-5713	514	14	.	.	PUNCT
ejpam-5713	515	1	computational	computational	ADJ
ejpam-5713	515	2	complexity	complexity	NOUN
ejpam-5713	515	3	aspects	aspect	NOUN
ejpam-5713	515	4	of	of	ADP
ejpam-5713	515	5	super	super	ADJ
ejpam-5713	515	6	domination	domination	NOUN
ejpam-5713	515	7	.	.	PUNCT
ejpam-5713	516	1	proceedings	proceeding	NOUN
ejpam-5713	516	2	of	of	ADP
ejpam-5713	516	3	the	the	DET
ejpam-5713	516	4	national	national	PROPN
ejpam-5713	516	5	academy	academy	PROPN
ejpam-5713	516	6	of	of	ADP
ejpam-5713	516	7	sciences	sciences	PROPN
ejpam-5713	516	8	,	,	PUNCT
ejpam-5713	516	9	india	india	PROPN
ejpam-5713	516	10	section	section	PROPN
ejpam-5713	516	11	a	a	PRON
ejpam-5713	516	12	:	:	PUNCT
ejpam-5713	516	13	physical	physical	ADJ
ejpam-5713	516	14	sciences	science	NOUN
ejpam-5713	516	15	,	,	PUNCT
ejpam-5713	516	16	85:353–357	85:353–357	NUM
ejpam-5713	516	17	,	,	PUNCT
ejpam-5713	516	18	2015	2015	NUM
ejpam-5713	516	19	.	.	PUNCT
ejpam-5713	517	1	[	[	X
ejpam-5713	517	2	14	14	NUM
ejpam-5713	517	3	]	]	X
ejpam-5713	517	4	r.	r.	PROPN
ejpam-5713	517	5	liguarda	liguarda	PROPN
ejpam-5713	517	6	and	and	CCONJ
ejpam-5713	517	7	s.	s.	PROPN
ejpam-5713	517	8	canoy	canoy	PROPN
ejpam-5713	517	9	jr	jr	PROPN
ejpam-5713	517	10	.	.	PROPN
ejpam-5713	517	11	connected	connect	VERB
ejpam-5713	517	12	super	super	ADJ
ejpam-5713	517	13	domination	domination	NOUN
ejpam-5713	517	14	in	in	ADP
ejpam-5713	517	15	graphs	graph	NOUN
ejpam-5713	517	16	.	.	PUNCT
ejpam-5713	518	1	advances	advance	NOUN
ejpam-5713	518	2	and	and	CCONJ
ejpam-5713	518	3	applications	application	NOUN
ejpam-5713	518	4	in	in	ADP
ejpam-5713	518	5	discrete	discrete	ADJ
ejpam-5713	518	6	mathematics	mathematic	NOUN
ejpam-5713	518	7	,	,	PUNCT
ejpam-5713	518	8	19(3):273–288	19(3):273–288	NUM
ejpam-5713	518	9	,	,	PUNCT
ejpam-5713	518	10	2018	2018	NUM
ejpam-5713	518	11	.	.	PUNCT
ejpam-5713	519	1	[	[	X
ejpam-5713	519	2	15	15	NUM
ejpam-5713	519	3	]	]	X
ejpam-5713	519	4	m.	m.	NOUN
ejpam-5713	519	5	marathe	marathe	PROPN
ejpam-5713	519	6	,	,	PUNCT
ejpam-5713	519	7	r.	r.	PROPN
ejpam-5713	519	8	ravi	ravi	PROPN
ejpam-5713	519	9	,	,	PUNCT
ejpam-5713	519	10	and	and	CCONJ
ejpam-5713	519	11	c.	c.	PROPN
ejpam-5713	519	12	p.	p.	PROPN
ejpam-5713	519	13	rangan	rangan	PROPN
ejpam-5713	519	14	.	.	PUNCT
ejpam-5713	520	1	generalized	generalize	VERB
ejpam-5713	520	2	vertex	vertex	NOUN
ejpam-5713	520	3	covering	cover	VERB
ejpam-5713	520	4	in	in	ADP
ejpam-5713	520	5	interval	interval	NOUN
ejpam-5713	520	6	graphs	graph	NOUN
ejpam-5713	520	7	.	.	PUNCT
ejpam-5713	521	1	discrete	discrete	ADJ
ejpam-5713	521	2	applied	applied	ADJ
ejpam-5713	521	3	mathematics	mathematic	NOUN
ejpam-5713	521	4	,	,	PUNCT
ejpam-5713	521	5	39:87–93	39:87–93	PROPN
ejpam-5713	521	6	,	,	PUNCT
ejpam-5713	521	7	1992	1992	NUM
ejpam-5713	521	8	.	.	PUNCT
ejpam-5713	522	1	[	[	X
ejpam-5713	522	2	16	16	NUM
ejpam-5713	522	3	]	]	X
ejpam-5713	522	4	s.	s.	PROPN
ejpam-5713	522	5	paraico	paraico	PROPN
ejpam-5713	522	6	and	and	CCONJ
ejpam-5713	522	7	s.	s.	PROPN
ejpam-5713	522	8	canoy	canoy	PROPN
ejpam-5713	522	9	jr	jr	PROPN
ejpam-5713	522	10	.	.	PUNCT
ejpam-5713	522	11	super	super	ADJ
ejpam-5713	522	12	dominating	dominating	NOUN
ejpam-5713	522	13	sets	set	NOUN
ejpam-5713	522	14	in	in	ADP
ejpam-5713	522	15	some	some	DET
ejpam-5713	522	16	products	product	NOUN
ejpam-5713	522	17	of	of	ADP
ejpam-5713	522	18	graphs	graph	NOUN
ejpam-5713	522	19	.	.	PUNCT
ejpam-5713	523	1	far	far	PROPN
ejpam-5713	523	2	east	east	PROPN
ejpam-5713	523	3	journal	journal	PROPN
ejpam-5713	523	4	of	of	ADP
ejpam-5713	523	5	mathematical	mathematical	ADJ
ejpam-5713	523	6	sciences	sciences	PROPN
ejpam-5713	523	7	,	,	PUNCT
ejpam-5713	523	8	23(2):187–199	23(2):187–199	NUM
ejpam-5713	523	9	,	,	PUNCT
ejpam-5713	523	10	2015	2015	NUM
ejpam-5713	523	11	.	.	PUNCT
ejpam-5713	524	1	[	[	X
ejpam-5713	524	2	17	17	NUM
ejpam-5713	524	3	]	]	X
ejpam-5713	524	4	s.	s.	PROPN
ejpam-5713	524	5	paraico	paraico	PROPN
ejpam-5713	524	6	and	and	CCONJ
ejpam-5713	524	7	s.	s.	PROPN
ejpam-5713	524	8	canoy	canoy	PROPN
ejpam-5713	524	9	jr	jr	PROPN
ejpam-5713	524	10	.	.	PUNCT
ejpam-5713	524	11	super	super	PROPN
ejpam-5713	524	12	domination	domination	NOUN
ejpam-5713	524	13	in	in	ADP
ejpam-5713	524	14	graphs	graph	NOUN
ejpam-5713	524	15	.	.	PUNCT
ejpam-5713	525	1	journal	journal	NOUN
ejpam-5713	525	2	of	of	ADP
ejpam-5713	525	3	analysis	analysis	NOUN
ejpam-5713	525	4	&	&	CCONJ
ejpam-5713	525	5	applications	application	NOUN
ejpam-5713	525	6	,	,	PUNCT
ejpam-5713	525	7	15(2):149	15(2):149	NOUN
ejpam-5713	525	8	,	,	PUNCT
ejpam-5713	525	9	2017	2017	NUM
ejpam-5713	525	10	.	.	PUNCT
ejpam-5713	526	1	[	[	X
ejpam-5713	526	2	18	18	NUM
ejpam-5713	526	3	]	]	PUNCT
ejpam-5713	526	4	p.	p.	NOUN
ejpam-5713	526	5	pushpam	pushpam	NOUN
ejpam-5713	526	6	and	and	CCONJ
ejpam-5713	526	7	c.	c.	PROPN
ejpam-5713	526	8	suseendran	suseendran	PROPN
ejpam-5713	526	9	.	.	PUNCT
ejpam-5713	527	1	secure	secure	ADJ
ejpam-5713	527	2	vertex	vertex	NOUN
ejpam-5713	527	3	cover	cover	NOUN
ejpam-5713	527	4	of	of	ADP
ejpam-5713	527	5	a	a	DET
ejpam-5713	527	6	graph	graph	NOUN
ejpam-5713	527	7	.	.	PUNCT
ejpam-5713	528	1	discrete	discrete	ADJ
ejpam-5713	528	2	mathematics	mathematic	NOUN
ejpam-5713	528	3	,	,	PUNCT
ejpam-5713	528	4	algorithms	algorithm	NOUN
ejpam-5713	528	5	and	and	CCONJ
ejpam-5713	528	6	applications	application	NOUN
ejpam-5713	528	7	,	,	PUNCT
ejpam-5713	528	8	9(2	9(2	NUM
ejpam-5713	528	9	)	)	PUNCT
ejpam-5713	528	10	,	,	PUNCT
ejpam-5713	528	11	2017	2017	NUM
ejpam-5713	528	12	.	.	PUNCT
ejpam-5713	529	1	[	[	X
ejpam-5713	529	2	19	19	NUM
ejpam-5713	529	3	]	]	X
ejpam-5713	529	4	l.	l.	PROPN
ejpam-5713	529	5	sathikala	sathikala	PROPN
ejpam-5713	529	6	,	,	PUNCT
ejpam-5713	529	7	k.	k.	PROPN
ejpam-5713	529	8	k.	k.	PROPN
ejpam-5713	529	9	basari	basari	PROPN
ejpam-5713	529	10	,	,	PUNCT
ejpam-5713	529	11	and	and	CCONJ
ejpam-5713	529	12	k.	k.	PROPN
ejpam-5713	529	13	subramanian	subramanian	PROPN
ejpam-5713	529	14	.	.	PROPN
ejpam-5713	530	1	connected	connect	VERB
ejpam-5713	530	2	and	and	CCONJ
ejpam-5713	530	3	total	total	ADJ
ejpam-5713	530	4	vertex	vertex	NOUN
ejpam-5713	530	5	covering	cover	VERB
ejpam-5713	530	6	in	in	ADP
ejpam-5713	530	7	graphs	graph	NOUN
ejpam-5713	530	8	.	.	PUNCT
ejpam-5713	531	1	turkish	turkish	ADJ
ejpam-5713	531	2	journal	journal	NOUN
ejpam-5713	531	3	of	of	ADP
ejpam-5713	531	4	computer	computer	NOUN
ejpam-5713	531	5	and	and	CCONJ
ejpam-5713	531	6	mathematics	mathematic	NOUN
ejpam-5713	531	7	education	education	NOUN
ejpam-5713	531	8	,	,	PUNCT
ejpam-5713	531	9	12(2):2180–2185	12(2):2180–2185	NUM
ejpam-5713	531	10	,	,	PUNCT
ejpam-5713	531	11	2021	2021	NUM
ejpam-5713	531	12	.	.	PUNCT
ejpam-5713	532	1	[	[	X
ejpam-5713	532	2	20	20	NUM
ejpam-5713	532	3	]	]	PUNCT
ejpam-5713	532	4	s.	s.	PROPN
ejpam-5713	532	5	sitthiwirattham	sitthiwirattham	PROPN
ejpam-5713	532	6	.	.	PUNCT
ejpam-5713	533	1	vertex	vertex	NOUN
ejpam-5713	533	2	covering	covering	NOUN
ejpam-5713	533	3	and	and	CCONJ
ejpam-5713	533	4	independent	independent	ADJ
ejpam-5713	533	5	number	number	NOUN
ejpam-5713	533	6	on	on	ADP
ejpam-5713	533	7	difference	difference	NOUN
ejpam-5713	533	8	graphs	graph	NOUN
ejpam-5713	533	9	.	.	PUNCT
ejpam-5713	534	1	s.	s.	PROPN
ejpam-5713	534	2	r.	r.	PROPN
ejpam-5713	534	3	canoy	canoy	PROPN
ejpam-5713	534	4	et	et	PROPN
ejpam-5713	534	5	al	al	PROPN
ejpam-5713	534	6	.	.	PUNCT
ejpam-5713	534	7	/	/	SYM
ejpam-5713	534	8	eur	eur	PROPN
ejpam-5713	534	9	.	.	PUNCT
ejpam-5713	535	1	j.	j.	PROPN
ejpam-5713	535	2	pure	pure	PROPN
ejpam-5713	535	3	appl	appl	PROPN
ejpam-5713	535	4	.	.	PROPN
ejpam-5713	535	5	math	math	PROPN
ejpam-5713	535	6	,	,	PUNCT
ejpam-5713	535	7	18	18	NUM
ejpam-5713	535	8	(	(	PUNCT
ejpam-5713	535	9	1	1	NUM
ejpam-5713	535	10	)	)	PUNCT
ejpam-5713	535	11	(	(	PUNCT
ejpam-5713	535	12	2025	2025	NUM
ejpam-5713	535	13	)	)	PUNCT
ejpam-5713	535	14	,	,	PUNCT
ejpam-5713	535	15	5713	5713	NUM
ejpam-5713	535	16	13	13	NUM
ejpam-5713	535	17	of	of	ADP
ejpam-5713	535	18	13	13	NUM
ejpam-5713	535	19	international	international	ADJ
ejpam-5713	535	20	journal	journal	NOUN
ejpam-5713	535	21	of	of	ADP
ejpam-5713	535	22	pure	pure	ADJ
ejpam-5713	535	23	and	and	CCONJ
ejpam-5713	535	24	applied	applied	ADJ
ejpam-5713	535	25	mathematics	mathematic	NOUN
ejpam-5713	535	26	,	,	PUNCT
ejpam-5713	535	27	77(4):543–547	77(4):543–547	NOUN
ejpam-5713	535	28	,	,	PUNCT
ejpam-5713	535	29	2012	2012	NUM
ejpam-5713	535	30	.	.	PUNCT
ejpam-5713	536	1	[	[	X
ejpam-5713	536	2	21	21	NUM
ejpam-5713	536	3	]	]	X
ejpam-5713	536	4	c.	c.	PROPN
ejpam-5713	536	5	toregas	toregas	PROPN
ejpam-5713	536	6	,	,	PUNCT
ejpam-5713	536	7	,	,	PUNCT
ejpam-5713	536	8	r.	r.	PROPN
ejpam-5713	536	9	swain	swain	PROPN
ejpam-5713	536	10	,	,	PUNCT
ejpam-5713	536	11	c.	c.	PROPN
ejpam-5713	536	12	revelle	revelle	PROPN
ejpam-5713	536	13	,	,	PUNCT
ejpam-5713	536	14	and	and	CCONJ
ejpam-5713	536	15	l.	l.	PROPN
ejpam-5713	536	16	bercman	bercman	PROPN
ejpam-5713	536	17	.	.	PUNCT
ejpam-5713	537	1	the	the	DET
ejpam-5713	537	2	location	location	NOUN
ejpam-5713	537	3	of	of	ADP
ejpam-5713	537	4	emergency	emergency	NOUN
ejpam-5713	537	5	service	service	NOUN
ejpam-5713	537	6	facilities	facility	NOUN
ejpam-5713	537	7	.	.	PUNCT
ejpam-5713	538	1	journal	journal	NOUN
ejpam-5713	538	2	of	of	ADP
ejpam-5713	538	3	the	the	DET
ejpam-5713	538	4	operations	operation	NOUN
ejpam-5713	538	5	research	research	NOUN
ejpam-5713	538	6	society	society	NOUN
ejpam-5713	538	7	of	of	ADP
ejpam-5713	538	8	america	america	PROPN
ejpam-5713	538	9	,	,	PUNCT
ejpam-5713	538	10	19(6	19(6	NUM
ejpam-5713	538	11	)	)	PUNCT
ejpam-5713	538	12	,	,	PUNCT
ejpam-5713	538	13	1971	1971	NUM
ejpam-5713	538	14	.	.	PUNCT
ejpam-5713	539	1	[	[	X
ejpam-5713	539	2	22	22	NUM
ejpam-5713	539	3	]	]	X
ejpam-5713	540	1	j.	j.	PROPN
ejpam-5713	540	2	uy	uy	PROPN
ejpam-5713	540	3	.	.	PUNCT
ejpam-5713	541	1	vertex	vertex	PROPN
ejpam-5713	541	2	cover	cover	NOUN
ejpam-5713	541	3	of	of	ADP
ejpam-5713	541	4	graphs	graph	NOUN
ejpam-5713	541	5	.	.	PUNCT
ejpam-5713	542	1	journal	journal	NOUN
ejpam-5713	542	2	of	of	ADP
ejpam-5713	542	3	research	research	NOUN
ejpam-5713	542	4	in	in	ADP
ejpam-5713	542	5	science	science	NOUN
ejpam-5713	542	6	and	and	CCONJ
ejpam-5713	542	7	engineering	engineering	NOUN
ejpam-5713	542	8	,	,	PUNCT
ejpam-5713	542	9	1:49–53	1:49–53	NUM
ejpam-5713	542	10	,	,	PUNCT
ejpam-5713	542	11	2003	2003	NUM
ejpam-5713	542	12	.	.	PUNCT
ejpam-5713	543	1	[	[	X
ejpam-5713	543	2	23	23	NUM
ejpam-5713	543	3	]	]	PUNCT
ejpam-5713	543	4	j.	j.	PROPN
ejpam-5713	543	5	uy	uy	PROPN
ejpam-5713	543	6	and	and	CCONJ
ejpam-5713	543	7	v.	v.	ADP
ejpam-5713	543	8	abregana	abregana	PROPN
ejpam-5713	543	9	.	.	PUNCT
ejpam-5713	544	1	revisiting	revisit	VERB
ejpam-5713	544	2	the	the	DET
ejpam-5713	544	3	vertex	vertex	NOUN
ejpam-5713	544	4	cover	cover	NOUN
ejpam-5713	544	5	of	of	ADP
ejpam-5713	544	6	graphs	graph	NOUN
ejpam-5713	544	7	.	.	PUNCT
ejpam-5713	545	1	applied	apply	VERB
ejpam-5713	545	2	mathematical	mathematical	ADJ
ejpam-5713	545	3	sciences	science	NOUN
ejpam-5713	545	4	,	,	PUNCT
ejpam-5713	545	5	9:5707	9:5707	NUM
ejpam-5713	545	6	–	–	PUNCT
ejpam-5713	545	7	5714	5714	NUM
ejpam-5713	545	8	,	,	PUNCT
ejpam-5713	545	9	2015	2015	NUM
ejpam-5713	545	10	.	.	PUNCT