id	sid	tid	token	lemma	pos
ejpam-5658	1	1	european	european	PROPN
ejpam-5658	1	2	journal	journal	PROPN
ejpam-5658	1	3	of	of	ADP
ejpam-5658	1	4	pure	pure	ADJ
ejpam-5658	1	5	and	and	CCONJ
ejpam-5658	1	6	applied	applied	ADJ
ejpam-5658	1	7	mathematics	mathematic	NOUN
ejpam-5658	1	8	2025	2025	NUM
ejpam-5658	1	9	,	,	PUNCT
ejpam-5658	1	10	vol	vol	NOUN
ejpam-5658	1	11	.	.	PROPN
ejpam-5658	1	12	18	18	NUM
ejpam-5658	1	13	,	,	PUNCT
ejpam-5658	1	14	issue	issue	NOUN
ejpam-5658	1	15	1	1	NUM
ejpam-5658	1	16	,	,	PUNCT
ejpam-5658	1	17	article	article	NOUN
ejpam-5658	1	18	number	number	NOUN
ejpam-5658	1	19	5658	5658	NUM
ejpam-5658	1	20	issn	issn	PROPN
ejpam-5658	1	21	1307	1307	NUM
ejpam-5658	1	22	-	-	SYM
ejpam-5658	1	23	5543	5543	NUM
ejpam-5658	1	24	–	–	PUNCT
ejpam-5658	1	25	ejpam.com	ejpam.com	X
ejpam-5658	1	26	published	publish	VERB
ejpam-5658	1	27	by	by	ADP
ejpam-5658	1	28	new	new	PROPN
ejpam-5658	1	29	york	york	PROPN
ejpam-5658	1	30	business	business	PROPN
ejpam-5658	1	31	global	global	PROPN
ejpam-5658	1	32	another	another	DET
ejpam-5658	1	33	look	look	NOUN
ejpam-5658	1	34	at	at	ADP
ejpam-5658	1	35	hop	hop	ADJ
ejpam-5658	1	36	independence	independence	NOUN
ejpam-5658	1	37	in	in	ADP
ejpam-5658	1	38	graphs	graph	NOUN
ejpam-5658	1	39	jesica	jesica	PROPN
ejpam-5658	1	40	m.	m.	PROPN
ejpam-5658	1	41	anoche	anoche	PROPN
ejpam-5658	1	42	1	1	NUM
ejpam-5658	1	43	,	,	PUNCT
ejpam-5658	1	44	sergio	sergio	PROPN
ejpam-5658	1	45	r.	r.	PROPN
ejpam-5658	1	46	canoy	canoy	PROPN
ejpam-5658	1	47	,	,	PUNCT
ejpam-5658	1	48	jr.1,2	jr.1,2	ADJ
ejpam-5658	1	49	1	1	NUM
ejpam-5658	1	50	department	department	NOUN
ejpam-5658	1	51	of	of	ADP
ejpam-5658	1	52	mathematics	mathematic	NOUN
ejpam-5658	1	53	and	and	CCONJ
ejpam-5658	1	54	statistics	statistic	NOUN
ejpam-5658	1	55	,	,	PUNCT
ejpam-5658	1	56	college	college	NOUN
ejpam-5658	1	57	of	of	ADP
ejpam-5658	1	58	science	science	NOUN
ejpam-5658	1	59	and	and	CCONJ
ejpam-5658	1	60	mathematics	mathematic	NOUN
ejpam-5658	1	61	,	,	PUNCT
ejpam-5658	1	62	msu	msu	PROPN
ejpam-5658	1	63	-	-	PUNCT
ejpam-5658	1	64	iligan	iligan	PROPN
ejpam-5658	1	65	institute	institute	PROPN
ejpam-5658	1	66	of	of	ADP
ejpam-5658	1	67	technology	technology	PROPN
ejpam-5658	1	68	,	,	PUNCT
ejpam-5658	1	69	9200	9200	NUM
ejpam-5658	1	70	iligan	iligan	ADJ
ejpam-5658	1	71	city	city	NOUN
ejpam-5658	1	72	,	,	PUNCT
ejpam-5658	1	73	philippines	philippine	NOUN
ejpam-5658	1	74	2	2	NUM
ejpam-5658	1	75	center	center	NOUN
ejpam-5658	1	76	of	of	ADP
ejpam-5658	1	77	mathematical	mathematical	ADJ
ejpam-5658	1	78	and	and	CCONJ
ejpam-5658	1	79	theoretical	theoretical	ADJ
ejpam-5658	1	80	physical	physical	ADJ
ejpam-5658	1	81	sciences	science	NOUN
ejpam-5658	1	82	-	-	PUNCT
ejpam-5658	1	83	prism	prism	NOUN
ejpam-5658	1	84	,	,	PUNCT
ejpam-5658	1	85	msu	msu	PROPN
ejpam-5658	1	86	-	-	PUNCT
ejpam-5658	1	87	iligan	iligan	PROPN
ejpam-5658	1	88	institute	institute	PROPN
ejpam-5658	1	89	of	of	ADP
ejpam-5658	1	90	technology	technology	PROPN
ejpam-5658	1	91	,	,	PUNCT
ejpam-5658	1	92	9200	9200	NUM
ejpam-5658	1	93	iligan	iligan	ADJ
ejpam-5658	1	94	city	city	NOUN
ejpam-5658	1	95	,	,	PUNCT
ejpam-5658	1	96	philippines	philippine	NOUN
ejpam-5658	1	97	abstract	abstract	ADJ
ejpam-5658	1	98	.	.	PUNCT
ejpam-5658	2	1	a	a	DET
ejpam-5658	2	2	set	set	NOUN
ejpam-5658	2	3	s	s	NOUN
ejpam-5658	2	4	⊆	⊆	NUM
ejpam-5658	2	5	v	v	NOUN
ejpam-5658	2	6	(	(	PUNCT
ejpam-5658	2	7	g	g	NOUN
ejpam-5658	2	8	)	)	PUNCT
ejpam-5658	2	9	is	be	AUX
ejpam-5658	2	10	a	a	DET
ejpam-5658	2	11	hop	hop	NOUN
ejpam-5658	2	12	independent	independent	ADJ
ejpam-5658	2	13	set	set	NOUN
ejpam-5658	2	14	in	in	ADP
ejpam-5658	2	15	an	an	DET
ejpam-5658	2	16	undirected	undirected	ADJ
ejpam-5658	2	17	graph	graph	NOUN
ejpam-5658	2	18	g	g	NOUN
ejpam-5658	2	19	if	if	SCONJ
ejpam-5658	2	20	dg(v	dg(v	NOUN
ejpam-5658	2	21	,	,	PUNCT
ejpam-5658	2	22	w	w	NOUN
ejpam-5658	2	23	)	)	PUNCT
ejpam-5658	2	24	̸=	̸=	PROPN
ejpam-5658	2	25	2	2	NUM
ejpam-5658	2	26	for	for	ADP
ejpam-5658	2	27	any	any	DET
ejpam-5658	2	28	two	two	NUM
ejpam-5658	2	29	distinct	distinct	ADJ
ejpam-5658	2	30	vertices	vertex	NOUN
ejpam-5658	2	31	v	v	ADP
ejpam-5658	2	32	,	,	PUNCT
ejpam-5658	2	33	w	w	PROPN
ejpam-5658	2	34	∈	∈	PROPN
ejpam-5658	2	35	s.	s.	PROPN
ejpam-5658	2	36	the	the	DET
ejpam-5658	2	37	maximum	maximum	PROPN
ejpam-5658	2	38	cardinality	cardinality	NOUN
ejpam-5658	2	39	among	among	ADP
ejpam-5658	2	40	the	the	DET
ejpam-5658	2	41	hop	hop	NOUN
ejpam-5658	2	42	independent	independent	ADJ
ejpam-5658	2	43	sets	set	NOUN
ejpam-5658	2	44	in	in	ADP
ejpam-5658	2	45	g	g	NOUN
ejpam-5658	2	46	,	,	PUNCT
ejpam-5658	2	47	denoted	denote	VERB
ejpam-5658	2	48	by	by	ADP
ejpam-5658	2	49	αh(g	αh(g	NOUN
ejpam-5658	2	50	)	)	PUNCT
ejpam-5658	2	51	,	,	PUNCT
ejpam-5658	2	52	is	be	AUX
ejpam-5658	2	53	called	call	VERB
ejpam-5658	2	54	the	the	DET
ejpam-5658	2	55	hop	hop	NOUN
ejpam-5658	2	56	independence	independence	NOUN
ejpam-5658	2	57	number	number	NOUN
ejpam-5658	2	58	of	of	ADP
ejpam-5658	2	59	g.	g.	PROPN
ejpam-5658	2	60	the	the	DET
ejpam-5658	2	61	hop	hop	NOUN
ejpam-5658	2	62	independent	independent	ADJ
ejpam-5658	2	63	sets	set	NOUN
ejpam-5658	2	64	in	in	ADP
ejpam-5658	2	65	the	the	DET
ejpam-5658	2	66	shadow	shadow	NOUN
ejpam-5658	2	67	graph	graph	NOUN
ejpam-5658	2	68	,	,	PUNCT
ejpam-5658	2	69	complementary	complementary	ADJ
ejpam-5658	2	70	prism	prism	NOUN
ejpam-5658	2	71	,	,	PUNCT
ejpam-5658	2	72	edge	edge	NOUN
ejpam-5658	2	73	corona	corona	NOUN
ejpam-5658	2	74	and	and	CCONJ
ejpam-5658	2	75	disjunctive	disjunctive	ADJ
ejpam-5658	2	76	products	product	NOUN
ejpam-5658	2	77	of	of	ADP
ejpam-5658	2	78	two	two	NUM
ejpam-5658	2	79	graphs	graph	NOUN
ejpam-5658	2	80	are	be	AUX
ejpam-5658	2	81	characterized	characterize	VERB
ejpam-5658	2	82	.	.	PUNCT
ejpam-5658	3	1	these	these	DET
ejpam-5658	3	2	characterizations	characterization	NOUN
ejpam-5658	3	3	are	be	AUX
ejpam-5658	3	4	used	use	VERB
ejpam-5658	3	5	to	to	PART
ejpam-5658	3	6	determine	determine	VERB
ejpam-5658	3	7	the	the	DET
ejpam-5658	3	8	exact	exact	ADJ
ejpam-5658	3	9	or	or	CCONJ
ejpam-5658	3	10	sharp	sharp	ADJ
ejpam-5658	3	11	bounds	bound	NOUN
ejpam-5658	3	12	of	of	ADP
ejpam-5658	3	13	the	the	DET
ejpam-5658	3	14	hop	hop	NOUN
ejpam-5658	3	15	independence	independence	NOUN
ejpam-5658	3	16	numbers	number	NOUN
ejpam-5658	3	17	of	of	ADP
ejpam-5658	3	18	these	these	DET
ejpam-5658	3	19	graphs	graph	NOUN
ejpam-5658	3	20	.	.	PUNCT
ejpam-5658	4	1	furthermore	furthermore	ADV
ejpam-5658	4	2	,	,	PUNCT
ejpam-5658	4	3	we	we	PRON
ejpam-5658	4	4	show	show	VERB
ejpam-5658	4	5	that	that	SCONJ
ejpam-5658	4	6	the	the	DET
ejpam-5658	4	7	hop	hop	NOUN
ejpam-5658	4	8	independent	independent	ADJ
ejpam-5658	4	9	set	set	VERB
ejpam-5658	4	10	decision	decision	NOUN
ejpam-5658	4	11	problem	problem	NOUN
ejpam-5658	4	12	(	(	PUNCT
ejpam-5658	4	13	hisp	hisp	NOUN
ejpam-5658	4	14	)	)	PUNCT
ejpam-5658	4	15	is	be	AUX
ejpam-5658	4	16	np	np	ADV
ejpam-5658	4	17	-complete	-complete	ADJ
ejpam-5658	4	18	.	.	PUNCT
ejpam-5658	5	1	2020	2020	NUM
ejpam-5658	5	2	mathematics	mathematic	NOUN
ejpam-5658	5	3	subject	subject	NOUN
ejpam-5658	5	4	classifications	classification	NOUN
ejpam-5658	5	5	:	:	PUNCT
ejpam-5658	5	6	05c69	05c69	X
ejpam-5658	5	7	key	key	ADJ
ejpam-5658	5	8	words	word	NOUN
ejpam-5658	5	9	and	and	CCONJ
ejpam-5658	5	10	phrases	phrase	NOUN
ejpam-5658	5	11	:	:	PUNCT
ejpam-5658	5	12	hop	hop	NOUN
ejpam-5658	5	13	independence	independence	NOUN
ejpam-5658	5	14	number	number	NOUN
ejpam-5658	5	15	,	,	PUNCT
ejpam-5658	5	16	shadow	shadow	NOUN
ejpam-5658	5	17	graph	graph	NOUN
ejpam-5658	5	18	,	,	PUNCT
ejpam-5658	5	19	complementary	complementary	ADJ
ejpam-5658	5	20	prism	prism	NOUN
ejpam-5658	5	21	,	,	PUNCT
ejpam-5658	5	22	edge	edge	NOUN
ejpam-5658	5	23	corona	corona	NOUN
ejpam-5658	5	24	,	,	PUNCT
ejpam-5658	5	25	disjunction	disjunction	NOUN
ejpam-5658	5	26	,	,	PUNCT
ejpam-5658	5	27	strong	strong	ADJ
ejpam-5658	5	28	product	product	NOUN
ejpam-5658	5	29	1	1	NUM
ejpam-5658	5	30	.	.	PUNCT
ejpam-5658	6	1	introduction	introduction	NOUN
ejpam-5658	6	2	hop	hop	PROPN
ejpam-5658	6	3	domination	domination	NOUN
ejpam-5658	6	4	is	be	AUX
ejpam-5658	6	5	a	a	DET
ejpam-5658	6	6	domination	domination	NOUN
ejpam-5658	6	7	-	-	PUNCT
ejpam-5658	6	8	related	relate	VERB
ejpam-5658	6	9	concept	concept	NOUN
ejpam-5658	6	10	introduced	introduce	VERB
ejpam-5658	6	11	and	and	CCONJ
ejpam-5658	6	12	studied	study	VERB
ejpam-5658	6	13	by	by	ADP
ejpam-5658	6	14	natarajan	natarajan	PROPN
ejpam-5658	6	15	and	and	CCONJ
ejpam-5658	6	16	ayyaswamy	ayyaswamy	ADV
ejpam-5658	6	17	in	in	ADP
ejpam-5658	6	18	[	[	X
ejpam-5658	6	19	7	7	NUM
ejpam-5658	6	20	]	]	PUNCT
ejpam-5658	6	21	.	.	PUNCT
ejpam-5658	7	1	this	this	DET
ejpam-5658	7	2	parameter	parameter	NOUN
ejpam-5658	7	3	has	have	AUX
ejpam-5658	7	4	been	be	AUX
ejpam-5658	7	5	widely	widely	ADV
ejpam-5658	7	6	studied	study	VERB
ejpam-5658	7	7	since	since	SCONJ
ejpam-5658	7	8	its	its	PRON
ejpam-5658	7	9	introduction	introduction	NOUN
ejpam-5658	7	10	and	and	CCONJ
ejpam-5658	7	11	some	some	DET
ejpam-5658	7	12	variations	variation	NOUN
ejpam-5658	7	13	of	of	ADP
ejpam-5658	7	14	the	the	DET
ejpam-5658	7	15	concept	concept	NOUN
ejpam-5658	7	16	have	have	AUX
ejpam-5658	7	17	been	be	AUX
ejpam-5658	7	18	defined	define	VERB
ejpam-5658	7	19	and	and	CCONJ
ejpam-5658	7	20	investigated	investigate	VERB
ejpam-5658	7	21	(	(	PUNCT
ejpam-5658	7	22	see	see	VERB
ejpam-5658	7	23	for	for	ADP
ejpam-5658	7	24	example	example	NOUN
ejpam-5658	8	1	[	[	X
ejpam-5658	8	2	1	1	NUM
ejpam-5658	8	3	]	]	PUNCT
ejpam-5658	8	4	,	,	PUNCT
ejpam-5658	8	5	[	[	X
ejpam-5658	8	6	2	2	NUM
ejpam-5658	8	7	]	]	PUNCT
ejpam-5658	8	8	,	,	PUNCT
ejpam-5658	8	9	[	[	X
ejpam-5658	8	10	5	5	NUM
ejpam-5658	8	11	]	]	PUNCT
ejpam-5658	8	12	,	,	PUNCT
ejpam-5658	8	13	[	[	X
ejpam-5658	8	14	8	8	NUM
ejpam-5658	8	15	]	]	PUNCT
ejpam-5658	8	16	,	,	PUNCT
ejpam-5658	8	17	[	[	X
ejpam-5658	8	18	9	9	NUM
ejpam-5658	8	19	]	]	PUNCT
ejpam-5658	8	20	,	,	PUNCT
ejpam-5658	8	21	and	and	CCONJ
ejpam-5658	8	22	[	[	X
ejpam-5658	8	23	10	10	NUM
ejpam-5658	8	24	]	]	NUM
ejpam-5658	8	25	)	)	PUNCT
ejpam-5658	8	26	.	.	PUNCT
ejpam-5658	9	1	recently	recently	ADV
ejpam-5658	9	2	,	,	PUNCT
ejpam-5658	9	3	hassan	hassan	PROPN
ejpam-5658	9	4	et	et	PROPN
ejpam-5658	9	5	al	al	PROPN
ejpam-5658	9	6	.	.	PUNCT
ejpam-5658	10	1	[	[	X
ejpam-5658	10	2	4	4	X
ejpam-5658	10	3	]	]	PUNCT
ejpam-5658	10	4	introduced	introduce	VERB
ejpam-5658	10	5	an	an	DET
ejpam-5658	10	6	independent	independent	ADJ
ejpam-5658	10	7	-	-	PUNCT
ejpam-5658	10	8	type	type	NOUN
ejpam-5658	10	9	parameter	parameter	NOUN
ejpam-5658	10	10	called	call	VERB
ejpam-5658	10	11	hop	hop	NOUN
ejpam-5658	10	12	independence	independence	NOUN
ejpam-5658	10	13	.	.	PUNCT
ejpam-5658	11	1	as	as	SCONJ
ejpam-5658	11	2	mentioned	mention	VERB
ejpam-5658	11	3	in	in	ADP
ejpam-5658	11	4	the	the	DET
ejpam-5658	11	5	paper	paper	NOUN
ejpam-5658	11	6	,	,	PUNCT
ejpam-5658	11	7	the	the	DET
ejpam-5658	11	8	motivation	motivation	NOUN
ejpam-5658	11	9	of	of	ADP
ejpam-5658	11	10	such	such	ADJ
ejpam-5658	11	11	study	study	NOUN
ejpam-5658	11	12	is	be	AUX
ejpam-5658	11	13	the	the	DET
ejpam-5658	11	14	ever	ever	ADV
ejpam-5658	11	15	increasing	increase	VERB
ejpam-5658	11	16	figure	figure	NOUN
ejpam-5658	11	17	of	of	ADP
ejpam-5658	11	18	research	research	NOUN
ejpam-5658	11	19	on	on	ADP
ejpam-5658	11	20	hop	hop	NOUN
ejpam-5658	11	21	-	-	PUNCT
ejpam-5658	11	22	domination	domination	NOUN
ejpam-5658	11	23	related	relate	VERB
ejpam-5658	11	24	topics	topic	NOUN
ejpam-5658	11	25	.	.	PUNCT
ejpam-5658	12	1	it	it	PRON
ejpam-5658	12	2	’s	’	VERB
ejpam-5658	12	3	worth	worth	ADJ
ejpam-5658	12	4	noting	note	VERB
ejpam-5658	12	5	that	that	SCONJ
ejpam-5658	12	6	the	the	DET
ejpam-5658	12	7	hop	hop	NOUN
ejpam-5658	12	8	independence	independence	NOUN
ejpam-5658	12	9	number	number	NOUN
ejpam-5658	12	10	provides	provide	VERB
ejpam-5658	12	11	a	a	DET
ejpam-5658	12	12	sharp	sharp	ADJ
ejpam-5658	12	13	upper	upper	ADJ
ejpam-5658	12	14	bound	bind	VERB
ejpam-5658	12	15	for	for	ADP
ejpam-5658	12	16	the	the	DET
ejpam-5658	12	17	hop	hop	NOUN
ejpam-5658	12	18	domination	domination	NOUN
ejpam-5658	12	19	number	number	NOUN
ejpam-5658	12	20	of	of	ADP
ejpam-5658	12	21	a	a	DET
ejpam-5658	12	22	graph	graph	NOUN
ejpam-5658	12	23	.	.	PUNCT
ejpam-5658	13	1	the	the	DET
ejpam-5658	13	2	authors	author	NOUN
ejpam-5658	13	3	also	also	ADV
ejpam-5658	13	4	showed	show	VERB
ejpam-5658	13	5	that	that	SCONJ
ejpam-5658	13	6	the	the	DET
ejpam-5658	13	7	absolute	absolute	ADJ
ejpam-5658	13	8	difference	difference	NOUN
ejpam-5658	13	9	of	of	ADP
ejpam-5658	13	10	the	the	DET
ejpam-5658	13	11	(	(	PUNCT
ejpam-5658	13	12	ordinary	ordinary	ADJ
ejpam-5658	13	13	)	)	PUNCT
ejpam-5658	13	14	independence	independence	NOUN
ejpam-5658	13	15	number	number	NOUN
ejpam-5658	13	16	and	and	CCONJ
ejpam-5658	13	17	the	the	DET
ejpam-5658	13	18	hop	hop	NOUN
ejpam-5658	13	19	independence	independence	NOUN
ejpam-5658	13	20	number	number	NOUN
ejpam-5658	13	21	can	can	AUX
ejpam-5658	13	22	be	be	AUX
ejpam-5658	13	23	made	make	VERB
ejpam-5658	13	24	arbitrarily	arbitrarily	ADV
ejpam-5658	13	25	large	large	ADJ
ejpam-5658	13	26	.	.	PUNCT
ejpam-5658	14	1	moreover	moreover	ADV
ejpam-5658	14	2	,	,	PUNCT
ejpam-5658	14	3	hop	hop	NOUN
ejpam-5658	14	4	independent	independent	ADJ
ejpam-5658	14	5	sets	set	NOUN
ejpam-5658	14	6	in	in	ADP
ejpam-5658	14	7	the	the	DET
ejpam-5658	14	8	join	join	NOUN
ejpam-5658	14	9	,	,	PUNCT
ejpam-5658	14	10	corona	corona	PROPN
ejpam-5658	14	11	,	,	PUNCT
ejpam-5658	14	12	lexicographic	lexicographic	ADJ
ejpam-5658	14	13	product	product	NOUN
ejpam-5658	14	14	,	,	PUNCT
ejpam-5658	14	15	and	and	CCONJ
ejpam-5658	14	16	cartesian	cartesian	ADJ
ejpam-5658	14	17	product	product	NOUN
ejpam-5658	14	18	of	of	ADP
ejpam-5658	14	19	two	two	NUM
ejpam-5658	14	20	graphs	graph	NOUN
ejpam-5658	14	21	have	have	AUX
ejpam-5658	14	22	been	be	AUX
ejpam-5658	14	23	characterized	characterize	VERB
ejpam-5658	14	24	.	.	PUNCT
ejpam-5658	15	1	subsequently	subsequently	ADV
ejpam-5658	15	2	,	,	PUNCT
ejpam-5658	15	3	sharp	sharp	ADJ
ejpam-5658	15	4	bounds	bound	NOUN
ejpam-5658	15	5	(	(	PUNCT
ejpam-5658	15	6	exact	exact	ADJ
ejpam-5658	15	7	values	value	NOUN
ejpam-5658	15	8	for	for	ADP
ejpam-5658	15	9	others	other	NOUN
ejpam-5658	15	10	)	)	PUNCT
ejpam-5658	15	11	doi	doi	NOUN
ejpam-5658	15	12	:	:	PUNCT
ejpam-5658	15	13	https://doi.org/10.29020/nybg.ejpam.v18i1.5658	https://doi.org/10.29020/nybg.ejpam.v18i1.5658	PRON
ejpam-5658	15	14	email	email	NOUN
ejpam-5658	15	15	addresses	address	NOUN
ejpam-5658	15	16	:	:	PUNCT
ejpam-5658	15	17	jesica.anoche@g.msuiit.edu.ph	jesica.anoche@g.msuiit.edu.ph	PROPN
ejpam-5658	15	18	(	(	PUNCT
ejpam-5658	15	19	j.	j.	PROPN
ejpam-5658	15	20	anoche	anoche	PROPN
ejpam-5658	15	21	)	)	PUNCT
ejpam-5658	15	22	,	,	PUNCT
ejpam-5658	15	23	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-5658	15	24	(	(	PUNCT
ejpam-5658	15	25	s.	s.	PROPN
ejpam-5658	15	26	canoy	canoy	PROPN
ejpam-5658	15	27	,	,	PUNCT
ejpam-5658	15	28	jr	jr	PROPN
ejpam-5658	15	29	.	.	PUNCT
ejpam-5658	15	30	)	)	PUNCT
ejpam-5658	15	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5658	16	1	1	1	NUM
ejpam-5658	16	2	copyright	copyright	NOUN
ejpam-5658	16	3	:	:	PUNCT
ejpam-5658	16	4	©	©	PROPN
ejpam-5658	16	5	2025	2025	NUM
ejpam-5658	16	6	the	the	DET
ejpam-5658	16	7	author(s	author(s	NOUN
ejpam-5658	16	8	)	)	PUNCT
ejpam-5658	16	9	.	.	PUNCT
ejpam-5658	17	1	(	(	PUNCT
ejpam-5658	17	2	cc	cc	NOUN
ejpam-5658	17	3	by	by	ADP
ejpam-5658	17	4	-	-	PUNCT
ejpam-5658	17	5	nc	nc	PROPN
ejpam-5658	17	6	4.0	4.0	NUM
ejpam-5658	17	7	)	)	PUNCT
ejpam-5658	17	8	j.	j.	PROPN
ejpam-5658	17	9	anoche	anoche	PROPN
ejpam-5658	17	10	,	,	PUNCT
ejpam-5658	17	11	s.	s.	PROPN
ejpam-5658	17	12	canoy	canoy	PROPN
ejpam-5658	17	13	,	,	PUNCT
ejpam-5658	17	14	jr	jr	PROPN
ejpam-5658	17	15	.	.	PROPN
ejpam-5658	17	16	/	/	SYM
ejpam-5658	17	17	eur	eur	PROPN
ejpam-5658	17	18	.	.	PUNCT
ejpam-5658	18	1	j.	j.	PROPN
ejpam-5658	18	2	pure	pure	PROPN
ejpam-5658	18	3	appl	appl	PROPN
ejpam-5658	18	4	.	.	PROPN
ejpam-5658	18	5	math	math	PROPN
ejpam-5658	18	6	,	,	PUNCT
ejpam-5658	18	7	18	18	NUM
ejpam-5658	18	8	(	(	PUNCT
ejpam-5658	18	9	1	1	NUM
ejpam-5658	18	10	)	)	PUNCT
ejpam-5658	18	11	(	(	PUNCT
ejpam-5658	18	12	2025	2025	NUM
ejpam-5658	18	13	)	)	PUNCT
ejpam-5658	18	14	,	,	PUNCT
ejpam-5658	18	15	5658	5658	NUM
ejpam-5658	18	16	2	2	NUM
ejpam-5658	18	17	of	of	ADP
ejpam-5658	18	18	15	15	NUM
ejpam-5658	18	19	of	of	ADP
ejpam-5658	18	20	the	the	DET
ejpam-5658	18	21	hop	hop	NOUN
ejpam-5658	18	22	independence	independence	NOUN
ejpam-5658	18	23	numbers	number	NOUN
ejpam-5658	18	24	of	of	ADP
ejpam-5658	18	25	these	these	DET
ejpam-5658	18	26	graphs	graph	NOUN
ejpam-5658	18	27	have	have	AUX
ejpam-5658	18	28	been	be	AUX
ejpam-5658	18	29	obtained	obtain	VERB
ejpam-5658	18	30	.	.	PUNCT
ejpam-5658	19	1	in	in	ADP
ejpam-5658	19	2	[	[	X
ejpam-5658	19	3	3	3	NUM
ejpam-5658	19	4	]	]	PUNCT
ejpam-5658	19	5	,	,	PUNCT
ejpam-5658	19	6	the	the	DET
ejpam-5658	19	7	authors	author	NOUN
ejpam-5658	19	8	used	use	VERB
ejpam-5658	19	9	the	the	DET
ejpam-5658	19	10	concept	concept	NOUN
ejpam-5658	19	11	of	of	ADP
ejpam-5658	19	12	hop	hop	NOUN
ejpam-5658	19	13	independence	independence	NOUN
ejpam-5658	19	14	to	to	PART
ejpam-5658	19	15	define	define	VERB
ejpam-5658	19	16	a	a	DET
ejpam-5658	19	17	variation	variation	NOUN
ejpam-5658	19	18	of	of	ADP
ejpam-5658	19	19	hop	hop	NOUN
ejpam-5658	19	20	domination	domination	NOUN
ejpam-5658	19	21	.	.	PUNCT
ejpam-5658	20	1	karp	karp	PROPN
ejpam-5658	20	2	in	in	ADP
ejpam-5658	20	3	[	[	X
ejpam-5658	20	4	6	6	NUM
ejpam-5658	20	5	]	]	PUNCT
ejpam-5658	20	6	,	,	PUNCT
ejpam-5658	20	7	as	as	ADP
ejpam-5658	20	8	one	one	NUM
ejpam-5658	20	9	of	of	ADP
ejpam-5658	20	10	his	his	PRON
ejpam-5658	20	11	many	many	ADJ
ejpam-5658	20	12	original	original	ADJ
ejpam-5658	20	13	problems	problem	NOUN
ejpam-5658	20	14	,	,	PUNCT
ejpam-5658	20	15	showed	show	VERB
ejpam-5658	20	16	that	that	SCONJ
ejpam-5658	20	17	the	the	DET
ejpam-5658	20	18	clique	clique	ADJ
ejpam-5658	20	19	decision	decision	NOUN
ejpam-5658	20	20	problem	problem	NOUN
ejpam-5658	20	21	is	be	AUX
ejpam-5658	20	22	np	np	ADP
ejpam-5658	20	23	-complete	-complete	ADJ
ejpam-5658	20	24	.	.	PUNCT
ejpam-5658	21	1	we	we	PRON
ejpam-5658	21	2	shall	shall	AUX
ejpam-5658	21	3	use	use	VERB
ejpam-5658	21	4	this	this	DET
ejpam-5658	21	5	result	result	NOUN
ejpam-5658	21	6	to	to	PART
ejpam-5658	21	7	show	show	VERB
ejpam-5658	21	8	that	that	SCONJ
ejpam-5658	21	9	the	the	DET
ejpam-5658	21	10	hop	hop	PROPN
ejpam-5658	21	11	independence	independence	NOUN
ejpam-5658	21	12	decision	decision	NOUN
ejpam-5658	21	13	problem	problem	NOUN
ejpam-5658	21	14	is	be	AUX
ejpam-5658	21	15	also	also	ADV
ejpam-5658	21	16	np	np	ADP
ejpam-5658	21	17	-complete	-complete	ADJ
ejpam-5658	21	18	.	.	PUNCT
ejpam-5658	22	1	2	2	X
ejpam-5658	22	2	.	.	X
ejpam-5658	22	3	terminology	terminology	NOUN
ejpam-5658	22	4	and	and	CCONJ
ejpam-5658	22	5	notation	notation	NOUN
ejpam-5658	22	6	for	for	ADP
ejpam-5658	22	7	any	any	DET
ejpam-5658	22	8	two	two	NUM
ejpam-5658	22	9	vertices	vertex	NOUN
ejpam-5658	22	10	u	u	NOUN
ejpam-5658	22	11	and	and	CCONJ
ejpam-5658	22	12	v	v	NOUN
ejpam-5658	22	13	in	in	ADP
ejpam-5658	22	14	an	an	DET
ejpam-5658	22	15	undirected	undirected	ADJ
ejpam-5658	22	16	connected	connected	ADJ
ejpam-5658	22	17	graph	graph	NOUN
ejpam-5658	22	18	g	g	PROPN
ejpam-5658	22	19	,	,	PUNCT
ejpam-5658	22	20	the	the	DET
ejpam-5658	22	21	distance	distance	NOUN
ejpam-5658	22	22	dg(u	dg(u	X
ejpam-5658	22	23	,	,	PUNCT
ejpam-5658	22	24	v	v	NOUN
ejpam-5658	22	25	)	)	PUNCT
ejpam-5658	22	26	is	be	AUX
ejpam-5658	22	27	the	the	DET
ejpam-5658	22	28	length	length	NOUN
ejpam-5658	22	29	of	of	ADP
ejpam-5658	22	30	a	a	DET
ejpam-5658	22	31	shortest	short	ADJ
ejpam-5658	22	32	path	path	NOUN
ejpam-5658	22	33	joining	join	VERB
ejpam-5658	22	34	u	u	NOUN
ejpam-5658	22	35	and	and	CCONJ
ejpam-5658	22	36	v.	v.	ADP
ejpam-5658	22	37	any	any	DET
ejpam-5658	22	38	u	u	NOUN
ejpam-5658	22	39	-	-	NOUN
ejpam-5658	22	40	v	v	ADJ
ejpam-5658	22	41	path	path	NOUN
ejpam-5658	22	42	of	of	ADP
ejpam-5658	22	43	length	length	NOUN
ejpam-5658	22	44	dg(u	dg(u	PROPN
ejpam-5658	22	45	,	,	PUNCT
ejpam-5658	22	46	v	v	NOUN
ejpam-5658	22	47	)	)	PUNCT
ejpam-5658	22	48	is	be	AUX
ejpam-5658	22	49	called	call	VERB
ejpam-5658	22	50	a	a	DET
ejpam-5658	22	51	u	u	NOUN
ejpam-5658	22	52	-	-	NOUN
ejpam-5658	22	53	v	v	ADJ
ejpam-5658	22	54	geodesic	geodesic	NOUN
ejpam-5658	22	55	.	.	PUNCT
ejpam-5658	23	1	the	the	DET
ejpam-5658	23	2	distance	distance	NOUN
ejpam-5658	23	3	between	between	ADP
ejpam-5658	23	4	two	two	NUM
ejpam-5658	23	5	subsets	subset	NOUN
ejpam-5658	23	6	a	a	PRON
ejpam-5658	23	7	and	and	CCONJ
ejpam-5658	23	8	b	b	NOUN
ejpam-5658	23	9	of	of	ADP
ejpam-5658	23	10	v	v	NOUN
ejpam-5658	23	11	(	(	PUNCT
ejpam-5658	23	12	g	g	NOUN
ejpam-5658	23	13	)	)	PUNCT
ejpam-5658	23	14	is	be	AUX
ejpam-5658	23	15	given	give	VERB
ejpam-5658	23	16	by	by	ADP
ejpam-5658	23	17	dg(a	dg(a	PROPN
ejpam-5658	23	18	,	,	PUNCT
ejpam-5658	23	19	b	b	NOUN
ejpam-5658	23	20	)	)	PUNCT
ejpam-5658	23	21	=	=	SYM
ejpam-5658	23	22	min{dg(a	min{dg(a	PROPN
ejpam-5658	23	23	,	,	PUNCT
ejpam-5658	23	24	b	b	NOUN
ejpam-5658	23	25	)	)	PUNCT
ejpam-5658	23	26	:	:	PUNCT
ejpam-5658	23	27	a	a	DET
ejpam-5658	23	28	∈	∈	PROPN
ejpam-5658	23	29	a	a	PRON
ejpam-5658	23	30	and	and	CCONJ
ejpam-5658	23	31	b	b	NOUN
ejpam-5658	23	32	∈	∈	PROPN
ejpam-5658	23	33	b	b	NOUN
ejpam-5658	23	34	}	}	PUNCT
ejpam-5658	23	35	.	.	PUNCT
ejpam-5658	24	1	the	the	DET
ejpam-5658	24	2	open	open	ADJ
ejpam-5658	24	3	neighborhood	neighborhood	NOUN
ejpam-5658	24	4	of	of	ADP
ejpam-5658	24	5	a	a	DET
ejpam-5658	24	6	point	point	NOUN
ejpam-5658	24	7	u	u	NOUN
ejpam-5658	24	8	is	be	AUX
ejpam-5658	24	9	the	the	DET
ejpam-5658	24	10	set	set	NOUN
ejpam-5658	24	11	ng(u	ng(u	NOUN
ejpam-5658	24	12	)	)	PUNCT
ejpam-5658	24	13	consisting	consist	VERB
ejpam-5658	24	14	of	of	ADP
ejpam-5658	24	15	all	all	DET
ejpam-5658	24	16	points	point	NOUN
ejpam-5658	24	17	v	v	NUM
ejpam-5658	24	18	which	which	PRON
ejpam-5658	24	19	are	be	AUX
ejpam-5658	24	20	adjacent	adjacent	ADJ
ejpam-5658	24	21	to	to	PART
ejpam-5658	24	22	u.	u.	VERB
ejpam-5658	24	23	the	the	DET
ejpam-5658	24	24	closed	closed	ADJ
ejpam-5658	24	25	neighborhood	neighborhood	NOUN
ejpam-5658	24	26	of	of	ADP
ejpam-5658	24	27	u	u	NOUN
ejpam-5658	24	28	is	be	AUX
ejpam-5658	24	29	ng[u	ng[u	PROPN
ejpam-5658	24	30	]	]	X
ejpam-5658	24	31	=	=	SYM
ejpam-5658	24	32	ng(u	ng(u	PROPN
ejpam-5658	24	33	)	)	PUNCT
ejpam-5658	24	34	∪	∪	NOUN
ejpam-5658	24	35	{	{	PUNCT
ejpam-5658	24	36	u	u	NOUN
ejpam-5658	24	37	}	}	PUNCT
ejpam-5658	24	38	.	.	PUNCT
ejpam-5658	25	1	for	for	ADP
ejpam-5658	25	2	any	any	DET
ejpam-5658	25	3	a	a	DET
ejpam-5658	25	4	⊆	⊆	NUM
ejpam-5658	25	5	v	v	NOUN
ejpam-5658	25	6	(	(	PUNCT
ejpam-5658	25	7	g	g	NOUN
ejpam-5658	25	8	)	)	PUNCT
ejpam-5658	25	9	,	,	PUNCT
ejpam-5658	25	10	ng(a	ng(a	X
ejpam-5658	25	11	)	)	PUNCT
ejpam-5658	25	12	=	=	PUNCT
ejpam-5658	25	13	⋃	⋃	NOUN
ejpam-5658	25	14	v∈a	v∈a	NOUN
ejpam-5658	25	15	ng(v	ng(v	PUNCT
ejpam-5658	25	16	)	)	PUNCT
ejpam-5658	25	17	is	be	AUX
ejpam-5658	25	18	called	call	VERB
ejpam-5658	25	19	the	the	DET
ejpam-5658	25	20	open	open	ADJ
ejpam-5658	25	21	neighborhood	neighborhood	NOUN
ejpam-5658	25	22	of	of	ADP
ejpam-5658	25	23	a	a	PRON
ejpam-5658	25	24	and	and	CCONJ
ejpam-5658	25	25	ng[a	ng[a	NOUN
ejpam-5658	25	26	]	]	X
ejpam-5658	25	27	=	=	PUNCT
ejpam-5658	25	28	ng(a	ng(a	X
ejpam-5658	25	29	)	)	PUNCT
ejpam-5658	25	30	∪	∪	ADP
ejpam-5658	25	31	a	a	PRON
ejpam-5658	25	32	is	be	AUX
ejpam-5658	25	33	called	call	VERB
ejpam-5658	25	34	the	the	DET
ejpam-5658	25	35	closed	closed	ADJ
ejpam-5658	25	36	neighborhood	neighborhood	NOUN
ejpam-5658	25	37	of	of	ADP
ejpam-5658	25	38	a.	a.	NOUN
ejpam-5658	25	39	a	a	DET
ejpam-5658	25	40	vertex	vertex	NOUN
ejpam-5658	25	41	v	v	NOUN
ejpam-5658	25	42	of	of	ADP
ejpam-5658	25	43	g	g	PROPN
ejpam-5658	25	44	is	be	AUX
ejpam-5658	25	45	isolated	isolate	VERB
ejpam-5658	25	46	if	if	SCONJ
ejpam-5658	25	47	|ng(v)|	|ng(v)|	NOUN
ejpam-5658	25	48	=	=	SYM
ejpam-5658	25	49	0	0	NUM
ejpam-5658	25	50	.	.	PUNCT
ejpam-5658	26	1	the	the	DET
ejpam-5658	26	2	open	open	ADJ
ejpam-5658	26	3	hop	hop	NOUN
ejpam-5658	26	4	neighborhood	neighborhood	NOUN
ejpam-5658	26	5	of	of	ADP
ejpam-5658	26	6	a	a	DET
ejpam-5658	26	7	point	point	NOUN
ejpam-5658	26	8	u	u	NOUN
ejpam-5658	26	9	is	be	AUX
ejpam-5658	26	10	the	the	DET
ejpam-5658	26	11	set	set	ADJ
ejpam-5658	26	12	n2	n2	ADJ
ejpam-5658	26	13	g(u	g(u	PROPN
ejpam-5658	26	14	)	)	PUNCT
ejpam-5658	26	15	=	=	PRON
ejpam-5658	26	16	{	{	PUNCT
ejpam-5658	26	17	v	v	NUM
ejpam-5658	26	18	∈	∈	NOUN
ejpam-5658	26	19	v	v	NOUN
ejpam-5658	26	20	(	(	PUNCT
ejpam-5658	26	21	g	g	NOUN
ejpam-5658	26	22	)	)	PUNCT
ejpam-5658	26	23	:	:	PUNCT
ejpam-5658	26	24	dg(v	dg(v	X
ejpam-5658	26	25	,	,	PUNCT
ejpam-5658	26	26	u	u	NOUN
ejpam-5658	26	27	)	)	PUNCT
ejpam-5658	26	28	=	=	SYM
ejpam-5658	26	29	2	2	NUM
ejpam-5658	26	30	}	}	PUNCT
ejpam-5658	26	31	.	.	PUNCT
ejpam-5658	27	1	the	the	DET
ejpam-5658	27	2	closed	closed	ADJ
ejpam-5658	27	3	hop	hop	NOUN
ejpam-5658	27	4	neighborhood	neighborhood	NOUN
ejpam-5658	27	5	of	of	ADP
ejpam-5658	27	6	u	u	NOUN
ejpam-5658	27	7	is	be	AUX
ejpam-5658	27	8	n2	n2	ADJ
ejpam-5658	27	9	g[u	g[u	X
ejpam-5658	27	10	]	]	X
ejpam-5658	27	11	=	=	SYM
ejpam-5658	27	12	n2	n2	ADJ
ejpam-5658	27	13	g(u	g(u	PROPN
ejpam-5658	27	14	)	)	PUNCT
ejpam-5658	27	15	∪	∪	NOUN
ejpam-5658	27	16	{	{	PUNCT
ejpam-5658	27	17	u	u	NOUN
ejpam-5658	27	18	}	}	PUNCT
ejpam-5658	27	19	.	.	PUNCT
ejpam-5658	28	1	for	for	ADP
ejpam-5658	28	2	any	any	DET
ejpam-5658	28	3	a	a	DET
ejpam-5658	28	4	⊆	⊆	NUM
ejpam-5658	28	5	v	v	NOUN
ejpam-5658	28	6	(	(	PUNCT
ejpam-5658	28	7	g	g	NOUN
ejpam-5658	28	8	)	)	PUNCT
ejpam-5658	28	9	,	,	PUNCT
ejpam-5658	28	10	n2	n2	PROPN
ejpam-5658	28	11	g(a	g(a	PROPN
ejpam-5658	28	12	)	)	PUNCT
ejpam-5658	28	13	=	=	NOUN
ejpam-5658	28	14	⋃	⋃	PROPN
ejpam-5658	28	15	v∈a	v∈a	NOUN
ejpam-5658	28	16	n2	n2	ADJ
ejpam-5658	28	17	g(v	g(v	PROPN
ejpam-5658	28	18	)	)	PUNCT
ejpam-5658	28	19	is	be	AUX
ejpam-5658	28	20	called	call	VERB
ejpam-5658	28	21	the	the	DET
ejpam-5658	28	22	open	open	ADJ
ejpam-5658	28	23	hop	hop	NOUN
ejpam-5658	28	24	neighborhood	neighborhood	NOUN
ejpam-5658	28	25	of	of	ADP
ejpam-5658	28	26	a	a	DET
ejpam-5658	28	27	and	and	CCONJ
ejpam-5658	28	28	n2	n2	ADJ
ejpam-5658	28	29	g[a	g[a	NOUN
ejpam-5658	28	30	]	]	X
ejpam-5658	28	31	=	=	SYM
ejpam-5658	28	32	n2	n2	PROPN
ejpam-5658	28	33	g(a)∪a	g(a)∪a	PROPN
ejpam-5658	28	34	is	be	AUX
ejpam-5658	28	35	called	call	VERB
ejpam-5658	28	36	the	the	DET
ejpam-5658	28	37	closed	closed	ADJ
ejpam-5658	28	38	hop	hop	NOUN
ejpam-5658	28	39	neighborhood	neighborhood	NOUN
ejpam-5658	28	40	of	of	ADP
ejpam-5658	28	41	a.	a.	NOUN
ejpam-5658	28	42	a	a	DET
ejpam-5658	28	43	set	set	NOUN
ejpam-5658	28	44	s	s	NOUN
ejpam-5658	28	45	⊆	⊆	NUM
ejpam-5658	28	46	v	v	NOUN
ejpam-5658	28	47	(	(	PUNCT
ejpam-5658	28	48	g	g	NOUN
ejpam-5658	28	49	)	)	PUNCT
ejpam-5658	28	50	is	be	AUX
ejpam-5658	28	51	a	a	DET
ejpam-5658	28	52	hop	hop	NOUN
ejpam-5658	28	53	dominating	dominating	NOUN
ejpam-5658	28	54	set	set	NOUN
ejpam-5658	28	55	if	if	SCONJ
ejpam-5658	28	56	n2	n2	ADJ
ejpam-5658	28	57	g[s	g[s	PROPN
ejpam-5658	28	58	]	]	X
ejpam-5658	28	59	=	=	SYM
ejpam-5658	28	60	v	v	NOUN
ejpam-5658	28	61	(	(	PUNCT
ejpam-5658	28	62	g	g	NOUN
ejpam-5658	28	63	)	)	PUNCT
ejpam-5658	28	64	.	.	PUNCT
ejpam-5658	29	1	the	the	DET
ejpam-5658	29	2	minimum	minimum	ADJ
ejpam-5658	29	3	cardinality	cardinality	NOUN
ejpam-5658	29	4	of	of	ADP
ejpam-5658	29	5	a	a	DET
ejpam-5658	29	6	hop	hop	NOUN
ejpam-5658	29	7	dominating	dominating	NOUN
ejpam-5658	29	8	set	set	NOUN
ejpam-5658	29	9	of	of	ADP
ejpam-5658	29	10	a	a	DET
ejpam-5658	29	11	graph	graph	NOUN
ejpam-5658	29	12	g	g	NOUN
ejpam-5658	29	13	,	,	PUNCT
ejpam-5658	29	14	denoted	denote	VERB
ejpam-5658	29	15	by	by	ADP
ejpam-5658	29	16	γh(g	γh(g	NOUN
ejpam-5658	29	17	)	)	PUNCT
ejpam-5658	29	18	,	,	PUNCT
ejpam-5658	29	19	is	be	AUX
ejpam-5658	29	20	called	call	VERB
ejpam-5658	29	21	the	the	DET
ejpam-5658	29	22	hop	hop	NOUN
ejpam-5658	29	23	domination	domination	NOUN
ejpam-5658	29	24	number	number	NOUN
ejpam-5658	29	25	of	of	ADP
ejpam-5658	29	26	g.	g.	PROPN
ejpam-5658	29	27	a	a	DET
ejpam-5658	29	28	set	set	NOUN
ejpam-5658	29	29	s	s	PROPN
ejpam-5658	29	30	⊆	⊆	NUM
ejpam-5658	29	31	v	v	NOUN
ejpam-5658	29	32	(	(	PUNCT
ejpam-5658	29	33	g	g	NOUN
ejpam-5658	29	34	)	)	PUNCT
ejpam-5658	29	35	is	be	AUX
ejpam-5658	29	36	an	an	DET
ejpam-5658	29	37	independent	independent	ADJ
ejpam-5658	29	38	set	set	NOUN
ejpam-5658	29	39	of	of	ADP
ejpam-5658	29	40	g	g	PROPN
ejpam-5658	29	41	if	if	SCONJ
ejpam-5658	29	42	no	no	DET
ejpam-5658	29	43	two	two	NUM
ejpam-5658	29	44	pair	pair	NOUN
ejpam-5658	29	45	of	of	ADP
ejpam-5658	29	46	distinct	distinct	ADJ
ejpam-5658	29	47	vertices	vertex	NOUN
ejpam-5658	29	48	of	of	ADP
ejpam-5658	29	49	s	s	NOUN
ejpam-5658	29	50	are	be	AUX
ejpam-5658	29	51	adjacent	adjacent	ADJ
ejpam-5658	29	52	.	.	PUNCT
ejpam-5658	30	1	the	the	DET
ejpam-5658	30	2	maximum	maximum	ADJ
ejpam-5658	30	3	cardinality	cardinality	NOUN
ejpam-5658	30	4	of	of	ADP
ejpam-5658	30	5	an	an	DET
ejpam-5658	30	6	independent	independent	ADJ
ejpam-5658	30	7	set	set	NOUN
ejpam-5658	30	8	of	of	ADP
ejpam-5658	30	9	g	g	NOUN
ejpam-5658	30	10	,	,	PUNCT
ejpam-5658	30	11	denoted	denote	VERB
ejpam-5658	30	12	by	by	ADP
ejpam-5658	30	13	α(g	α(g	NOUN
ejpam-5658	30	14	)	)	PUNCT
ejpam-5658	30	15	,	,	PUNCT
ejpam-5658	30	16	is	be	AUX
ejpam-5658	30	17	called	call	VERB
ejpam-5658	30	18	the	the	DET
ejpam-5658	30	19	independence	independence	NOUN
ejpam-5658	30	20	number	number	NOUN
ejpam-5658	30	21	of	of	ADP
ejpam-5658	30	22	g.	g.	PROPN
ejpam-5658	30	23	set	set	PROPN
ejpam-5658	30	24	s	s	VERB
ejpam-5658	30	25	is	be	AUX
ejpam-5658	30	26	a	a	DET
ejpam-5658	30	27	hop	hop	NOUN
ejpam-5658	30	28	independent	independent	ADJ
ejpam-5658	30	29	set	set	NOUN
ejpam-5658	30	30	of	of	ADP
ejpam-5658	30	31	g	g	PROPN
ejpam-5658	30	32	if	if	SCONJ
ejpam-5658	30	33	dg(v	dg(v	NOUN
ejpam-5658	30	34	,	,	PUNCT
ejpam-5658	30	35	w	w	NOUN
ejpam-5658	30	36	)	)	PUNCT
ejpam-5658	30	37	̸=	̸=	PROPN
ejpam-5658	30	38	2	2	NUM
ejpam-5658	30	39	for	for	ADP
ejpam-5658	30	40	any	any	DET
ejpam-5658	30	41	two	two	NUM
ejpam-5658	30	42	distinct	distinct	ADJ
ejpam-5658	30	43	vertices	vertex	NOUN
ejpam-5658	30	44	v	v	NOUN
ejpam-5658	30	45	and	and	CCONJ
ejpam-5658	30	46	w	w	PROPN
ejpam-5658	30	47	of	of	ADP
ejpam-5658	30	48	s.	s.	PROPN
ejpam-5658	30	49	the	the	DET
ejpam-5658	30	50	maximum	maximum	PROPN
ejpam-5658	30	51	cardinality	cardinality	NOUN
ejpam-5658	30	52	of	of	ADP
ejpam-5658	30	53	a	a	DET
ejpam-5658	30	54	hop	hop	NOUN
ejpam-5658	30	55	independent	independent	ADJ
ejpam-5658	30	56	set	set	NOUN
ejpam-5658	30	57	of	of	ADP
ejpam-5658	30	58	g	g	NOUN
ejpam-5658	30	59	,	,	PUNCT
ejpam-5658	30	60	denoted	denote	VERB
ejpam-5658	30	61	by	by	ADP
ejpam-5658	30	62	αh(g	αh(g	NOUN
ejpam-5658	30	63	)	)	PUNCT
ejpam-5658	30	64	,	,	PUNCT
ejpam-5658	30	65	is	be	AUX
ejpam-5658	30	66	called	call	VERB
ejpam-5658	30	67	the	the	DET
ejpam-5658	30	68	hop	hop	NOUN
ejpam-5658	30	69	independence	independence	NOUN
ejpam-5658	30	70	number	number	NOUN
ejpam-5658	30	71	of	of	ADP
ejpam-5658	30	72	g.	g.	PROPN
ejpam-5658	30	73	any	any	DET
ejpam-5658	30	74	independent	independent	ADJ
ejpam-5658	30	75	(	(	PUNCT
ejpam-5658	30	76	hop	hop	NOUN
ejpam-5658	30	77	independent	independent	ADJ
ejpam-5658	30	78	)	)	PUNCT
ejpam-5658	30	79	set	set	VERB
ejpam-5658	30	80	with	with	ADP
ejpam-5658	30	81	cardinality	cardinality	NOUN
ejpam-5658	30	82	α(g	α(g	NUM
ejpam-5658	30	83	)	)	PUNCT
ejpam-5658	30	84	(	(	PUNCT
ejpam-5658	30	85	resp	resp	NOUN
ejpam-5658	30	86	.	.	PUNCT
ejpam-5658	30	87	αh(g	αh(g	NOUN
ejpam-5658	30	88	)	)	PUNCT
ejpam-5658	30	89	)	)	PUNCT
ejpam-5658	30	90	is	be	AUX
ejpam-5658	30	91	referred	refer	VERB
ejpam-5658	30	92	to	to	ADP
ejpam-5658	30	93	as	as	ADP
ejpam-5658	30	94	a	a	DET
ejpam-5658	30	95	maximum	maximum	ADJ
ejpam-5658	30	96	independent	independent	ADJ
ejpam-5658	30	97	set	set	NOUN
ejpam-5658	30	98	or	or	CCONJ
ejpam-5658	30	99	α	α	NOUN
ejpam-5658	30	100	-	-	PUNCT
ejpam-5658	30	101	set	set	VERB
ejpam-5658	30	102	(	(	PUNCT
ejpam-5658	30	103	resp	resp	NOUN
ejpam-5658	30	104	.	.	PUNCT
ejpam-5658	31	1	maximum	maximum	ADJ
ejpam-5658	31	2	hop	hop	PROPN
ejpam-5658	31	3	independent	independent	ADJ
ejpam-5658	31	4	set	set	NOUN
ejpam-5658	31	5	or	or	CCONJ
ejpam-5658	31	6	αh	αh	NOUN
ejpam-5658	31	7	-	-	PUNCT
ejpam-5658	31	8	set	set	NOUN
ejpam-5658	31	9	)	)	PUNCT
ejpam-5658	31	10	of	of	ADP
ejpam-5658	31	11	g.	g.	PROPN
ejpam-5658	31	12	a	a	DET
ejpam-5658	31	13	set	set	NOUN
ejpam-5658	31	14	s	s	PART
ejpam-5658	31	15	is	be	AUX
ejpam-5658	31	16	clique	clique	NOUN
ejpam-5658	31	17	of	of	ADP
ejpam-5658	31	18	a	a	DET
ejpam-5658	31	19	graph	graph	NOUN
ejpam-5658	31	20	g	g	NOUN
ejpam-5658	31	21	if	if	SCONJ
ejpam-5658	31	22	the	the	DET
ejpam-5658	31	23	graph	graph	NOUN
ejpam-5658	31	24	⟨s⟩	⟨s⟩	VERB
ejpam-5658	31	25	induced	induce	VERB
ejpam-5658	31	26	by	by	ADP
ejpam-5658	31	27	s	s	PROPN
ejpam-5658	31	28	is	be	AUX
ejpam-5658	31	29	a	a	DET
ejpam-5658	31	30	complete	complete	ADJ
ejpam-5658	31	31	graph	graph	NOUN
ejpam-5658	31	32	.	.	PUNCT
ejpam-5658	32	1	the	the	DET
ejpam-5658	32	2	maximum	maximum	ADJ
ejpam-5658	32	3	size	size	NOUN
ejpam-5658	32	4	or	or	CCONJ
ejpam-5658	32	5	cardinality	cardinality	NOUN
ejpam-5658	32	6	of	of	ADP
ejpam-5658	32	7	a	a	DET
ejpam-5658	32	8	clique	clique	NOUN
ejpam-5658	32	9	of	of	ADP
ejpam-5658	32	10	g	g	NOUN
ejpam-5658	32	11	,	,	PUNCT
ejpam-5658	32	12	denoted	denote	VERB
ejpam-5658	32	13	by	by	ADP
ejpam-5658	32	14	ω(g	ω(g	NOUN
ejpam-5658	32	15	)	)	PUNCT
ejpam-5658	32	16	,	,	PUNCT
ejpam-5658	32	17	is	be	AUX
ejpam-5658	32	18	called	call	VERB
ejpam-5658	32	19	the	the	DET
ejpam-5658	32	20	clique	clique	ADJ
ejpam-5658	32	21	number	number	NOUN
ejpam-5658	32	22	of	of	ADP
ejpam-5658	32	23	g.	g.	PROPN
ejpam-5658	32	24	any	any	DET
ejpam-5658	32	25	clique	clique	NOUN
ejpam-5658	32	26	in	in	ADP
ejpam-5658	32	27	g	g	PROPN
ejpam-5658	32	28	with	with	ADP
ejpam-5658	32	29	cardinality	cardinality	NOUN
ejpam-5658	32	30	ω(g	ω(g	NOUN
ejpam-5658	32	31	)	)	PUNCT
ejpam-5658	32	32	is	be	AUX
ejpam-5658	32	33	called	call	VERB
ejpam-5658	32	34	an	an	DET
ejpam-5658	32	35	ω	ω	NOUN
ejpam-5658	32	36	-	-	PUNCT
ejpam-5658	32	37	set	set	NOUN
ejpam-5658	32	38	in	in	ADP
ejpam-5658	32	39	g.	g.	PROPN
ejpam-5658	32	40	a	a	DET
ejpam-5658	32	41	matching	matching	NOUN
ejpam-5658	32	42	of	of	ADP
ejpam-5658	32	43	a	a	DET
ejpam-5658	32	44	graph	graph	NOUN
ejpam-5658	32	45	g	g	NOUN
ejpam-5658	32	46	is	be	AUX
ejpam-5658	32	47	a	a	DET
ejpam-5658	32	48	set	set	NOUN
ejpam-5658	32	49	m	m	NOUN
ejpam-5658	32	50	=	=	SYM
ejpam-5658	32	51	{	{	PUNCT
ejpam-5658	32	52	e1	e1	PROPN
ejpam-5658	32	53	,	,	PUNCT
ejpam-5658	32	54	e2	e2	PROPN
ejpam-5658	32	55	,	,	PUNCT
ejpam-5658	32	56	·	·	PUNCT
ejpam-5658	32	57	·	·	PUNCT
ejpam-5658	32	58	·	·	PUNCT
ejpam-5658	32	59	,	,	PUNCT
ejpam-5658	32	60	en	en	ADP
ejpam-5658	32	61	}	}	PUNCT
ejpam-5658	32	62	⊆	⊆	NUM
ejpam-5658	32	63	e(g	e(g	NOUN
ejpam-5658	32	64	)	)	PUNCT
ejpam-5658	32	65	such	such	ADJ
ejpam-5658	32	66	that	that	SCONJ
ejpam-5658	32	67	each	each	DET
ejpam-5658	32	68	vertex	vertex	NOUN
ejpam-5658	32	69	v	v	ADP
ejpam-5658	32	70	∈	∈	PROPN
ejpam-5658	32	71	v	v	NOUN
ejpam-5658	32	72	(	(	PUNCT
ejpam-5658	32	73	g	g	NOUN
ejpam-5658	32	74	)	)	PUNCT
ejpam-5658	32	75	appears	appear	VERB
ejpam-5658	32	76	in	in	ADP
ejpam-5658	32	77	at	at	ADP
ejpam-5658	32	78	most	most	ADV
ejpam-5658	32	79	one	one	NUM
ejpam-5658	32	80	edge	edge	NOUN
ejpam-5658	32	81	in	in	ADP
ejpam-5658	32	82	m	m	PROPN
ejpam-5658	32	83	(	(	PUNCT
ejpam-5658	32	84	i.e.	i.e.	X
ejpam-5658	32	85	,	,	PUNCT
ejpam-5658	32	86	the	the	DET
ejpam-5658	32	87	edges	edge	NOUN
ejpam-5658	32	88	in	in	ADP
ejpam-5658	32	89	m	m	PROPN
ejpam-5658	32	90	do	do	AUX
ejpam-5658	32	91	not	not	PART
ejpam-5658	32	92	have	have	VERB
ejpam-5658	32	93	a	a	DET
ejpam-5658	32	94	common	common	ADJ
ejpam-5658	32	95	vertex	vertex	NOUN
ejpam-5658	32	96	)	)	PUNCT
ejpam-5658	32	97	.	.	PUNCT
ejpam-5658	33	1	a	a	DET
ejpam-5658	33	2	matching	matching	NOUN
ejpam-5658	33	3	m	m	NOUN
ejpam-5658	33	4	is	be	AUX
ejpam-5658	33	5	maximum	maximum	ADJ
ejpam-5658	33	6	if	if	SCONJ
ejpam-5658	33	7	m	m	NOUN
ejpam-5658	33	8	∪{e	∪{e	PROPN
ejpam-5658	33	9	}	}	PUNCT
ejpam-5658	33	10	is	be	AUX
ejpam-5658	33	11	not	not	PART
ejpam-5658	33	12	a	a	DET
ejpam-5658	33	13	matching	matching	NOUN
ejpam-5658	33	14	for	for	ADP
ejpam-5658	33	15	any	any	DET
ejpam-5658	33	16	e	e	NOUN
ejpam-5658	33	17	∈	∈	PROPN
ejpam-5658	33	18	e(g)\m	e(g)\m	NOUN
ejpam-5658	33	19	.	.	PUNCT
ejpam-5658	34	1	the	the	DET
ejpam-5658	34	2	matching	match	VERB
ejpam-5658	34	3	number	number	NOUN
ejpam-5658	34	4	of	of	ADP
ejpam-5658	34	5	a	a	DET
ejpam-5658	34	6	graph	graph	NOUN
ejpam-5658	34	7	g	g	NOUN
ejpam-5658	34	8	,	,	PUNCT
ejpam-5658	34	9	denoted	denote	VERB
ejpam-5658	34	10	by	by	ADP
ejpam-5658	34	11	ν(g	ν(g	NOUN
ejpam-5658	34	12	)	)	PUNCT
ejpam-5658	34	13	is	be	AUX
ejpam-5658	34	14	the	the	DET
ejpam-5658	34	15	size	size	NOUN
ejpam-5658	34	16	of	of	ADP
ejpam-5658	34	17	a	a	DET
ejpam-5658	34	18	maximum	maximum	ADJ
ejpam-5658	34	19	matching	matching	NOUN
ejpam-5658	34	20	in	in	ADP
ejpam-5658	34	21	g.	g.	PROPN
ejpam-5658	34	22	letg	letg	PROPN
ejpam-5658	34	23	andh	andh	NOUN
ejpam-5658	34	24	be	be	VERB
ejpam-5658	34	25	undirected	undirected	ADJ
ejpam-5658	34	26	graphs	graph	NOUN
ejpam-5658	34	27	.	.	PUNCT
ejpam-5658	35	1	the	the	DET
ejpam-5658	35	2	shadow	shadow	NOUN
ejpam-5658	35	3	graph	graph	VERB
ejpam-5658	35	4	d2(g	d2(g	PROPN
ejpam-5658	35	5	)	)	PUNCT
ejpam-5658	35	6	ofg	ofg	PROPN
ejpam-5658	35	7	is	be	AUX
ejpam-5658	35	8	the	the	DET
ejpam-5658	35	9	graph	graph	NOUN
ejpam-5658	35	10	obtained	obtain	VERB
ejpam-5658	35	11	by	by	ADP
ejpam-5658	35	12	taking	take	VERB
ejpam-5658	35	13	two	two	NUM
ejpam-5658	35	14	copies	copy	NOUN
ejpam-5658	35	15	of	of	ADP
ejpam-5658	35	16	g	g	NOUN
ejpam-5658	35	17	,	,	PUNCT
ejpam-5658	35	18	say	say	VERB
ejpam-5658	35	19	g1	g1	PROPN
ejpam-5658	35	20	and	and	CCONJ
ejpam-5658	35	21	g2	g2	PROPN
ejpam-5658	35	22	,	,	PUNCT
ejpam-5658	35	23	and	and	CCONJ
ejpam-5658	35	24	then	then	ADV
ejpam-5658	35	25	joining	join	VERB
ejpam-5658	35	26	each	each	DET
ejpam-5658	35	27	vertex	vertex	NOUN
ejpam-5658	35	28	v	v	ADP
ejpam-5658	35	29	∈	∈	PROPN
ejpam-5658	35	30	v	v	NOUN
ejpam-5658	35	31	(	(	PUNCT
ejpam-5658	35	32	g1	g1	PROPN
ejpam-5658	35	33	)	)	PUNCT
ejpam-5658	35	34	to	to	ADP
ejpam-5658	35	35	the	the	DET
ejpam-5658	35	36	neighbors	neighbor	NOUN
ejpam-5658	35	37	of	of	ADP
ejpam-5658	35	38	v′	v′	PROPN
ejpam-5658	35	39	∈	∈	PROPN
ejpam-5658	35	40	v	v	PROPN
ejpam-5658	35	41	(	(	PUNCT
ejpam-5658	35	42	g2	g2	PROPN
ejpam-5658	35	43	)	)	PUNCT
ejpam-5658	35	44	,	,	PUNCT
ejpam-5658	35	45	where	where	SCONJ
ejpam-5658	35	46	v′	v′	NOUN
ejpam-5658	35	47	is	be	AUX
ejpam-5658	35	48	the	the	DET
ejpam-5658	35	49	vertex	vertex	NOUN
ejpam-5658	35	50	in	in	ADP
ejpam-5658	35	51	v	v	PROPN
ejpam-5658	35	52	(	(	PUNCT
ejpam-5658	35	53	g2	g2	PROPN
ejpam-5658	35	54	)	)	PUNCT
ejpam-5658	35	55	corresponding	correspond	VERB
ejpam-5658	35	56	to	to	ADP
ejpam-5658	35	57	v	v	NUM
ejpam-5658	35	58	,	,	PUNCT
ejpam-5658	35	59	i.e.	i.e.	X
ejpam-5658	35	60	,	,	PUNCT
ejpam-5658	35	61	v	v	NOUN
ejpam-5658	35	62	and	and	CCONJ
ejpam-5658	35	63	v′	v′	PROPN
ejpam-5658	35	64	represent	represent	VERB
ejpam-5658	35	65	the	the	DET
ejpam-5658	35	66	same	same	ADJ
ejpam-5658	35	67	vertex	vertex	NOUN
ejpam-5658	35	68	in	in	ADP
ejpam-5658	35	69	g.	g.	PROPN
ejpam-5658	35	70	the	the	DET
ejpam-5658	35	71	complementary	complementary	ADJ
ejpam-5658	35	72	prism	prism	NOUN
ejpam-5658	35	73	of	of	ADP
ejpam-5658	35	74	graph	graph	NOUN
ejpam-5658	35	75	g	g	NOUN
ejpam-5658	35	76	,	,	PUNCT
ejpam-5658	35	77	denoted	denote	VERB
ejpam-5658	35	78	j.	j.	PROPN
ejpam-5658	35	79	anoche	anoche	PROPN
ejpam-5658	35	80	,	,	PUNCT
ejpam-5658	35	81	s.	s.	PROPN
ejpam-5658	35	82	canoy	canoy	PROPN
ejpam-5658	35	83	,	,	PUNCT
ejpam-5658	35	84	jr	jr	PROPN
ejpam-5658	35	85	.	.	PROPN
ejpam-5658	35	86	/	/	SYM
ejpam-5658	35	87	eur	eur	PROPN
ejpam-5658	35	88	.	.	PUNCT
ejpam-5658	36	1	j.	j.	PROPN
ejpam-5658	36	2	pure	pure	PROPN
ejpam-5658	36	3	appl	appl	PROPN
ejpam-5658	36	4	.	.	PROPN
ejpam-5658	36	5	math	math	PROPN
ejpam-5658	36	6	,	,	PUNCT
ejpam-5658	36	7	18	18	NUM
ejpam-5658	36	8	(	(	PUNCT
ejpam-5658	36	9	1	1	NUM
ejpam-5658	36	10	)	)	PUNCT
ejpam-5658	36	11	(	(	PUNCT
ejpam-5658	36	12	2025	2025	NUM
ejpam-5658	36	13	)	)	PUNCT
ejpam-5658	36	14	,	,	PUNCT
ejpam-5658	36	15	5658	5658	NUM
ejpam-5658	36	16	3	3	NUM
ejpam-5658	36	17	of	of	ADP
ejpam-5658	36	18	15	15	NUM
ejpam-5658	36	19	by	by	ADP
ejpam-5658	36	20	gg	gg	PROPN
ejpam-5658	36	21	,	,	PUNCT
ejpam-5658	36	22	is	be	AUX
ejpam-5658	36	23	the	the	DET
ejpam-5658	36	24	graph	graph	NOUN
ejpam-5658	36	25	obtained	obtain	VERB
ejpam-5658	36	26	from	from	ADP
ejpam-5658	36	27	the	the	DET
ejpam-5658	36	28	disjoint	disjoint	PROPN
ejpam-5658	36	29	union	union	NOUN
ejpam-5658	36	30	of	of	ADP
ejpam-5658	36	31	g	g	PROPN
ejpam-5658	36	32	and	and	CCONJ
ejpam-5658	36	33	g	g	NOUN
ejpam-5658	36	34	by	by	ADP
ejpam-5658	36	35	adding	add	VERB
ejpam-5658	36	36	the	the	DET
ejpam-5658	36	37	edges	edge	NOUN
ejpam-5658	36	38	vv	vv	ADP
ejpam-5658	36	39	,	,	PUNCT
ejpam-5658	36	40	where	where	SCONJ
ejpam-5658	36	41	v	v	X
ejpam-5658	36	42	∈	∈	PROPN
ejpam-5658	36	43	v	v	NOUN
ejpam-5658	36	44	(	(	PUNCT
ejpam-5658	36	45	g	g	NOUN
ejpam-5658	36	46	)	)	PUNCT
ejpam-5658	36	47	and	and	CCONJ
ejpam-5658	36	48	v	v	NOUN
ejpam-5658	36	49	is	be	AUX
ejpam-5658	36	50	the	the	DET
ejpam-5658	36	51	vertex	vertex	NOUN
ejpam-5658	36	52	of	of	ADP
ejpam-5658	36	53	g	g	PROPN
ejpam-5658	36	54	corresponding	correspond	VERB
ejpam-5658	36	55	to	to	ADP
ejpam-5658	36	56	vertex	vertex	NOUN
ejpam-5658	36	57	v.	v.	ADP
ejpam-5658	36	58	the	the	DET
ejpam-5658	36	59	disjunction	disjunction	NOUN
ejpam-5658	36	60	of	of	ADP
ejpam-5658	36	61	graphs	graph	NOUN
ejpam-5658	36	62	g	g	PROPN
ejpam-5658	36	63	and	and	CCONJ
ejpam-5658	36	64	h	h	NOUN
ejpam-5658	36	65	,	,	PUNCT
ejpam-5658	36	66	denoted	denote	VERB
ejpam-5658	36	67	by	by	ADP
ejpam-5658	36	68	g	g	PROPN
ejpam-5658	36	69	∨	∨	NUM
ejpam-5658	36	70	h	h	NOUN
ejpam-5658	36	71	,	,	PUNCT
ejpam-5658	36	72	is	be	AUX
ejpam-5658	36	73	the	the	DET
ejpam-5658	36	74	graph	graph	NOUN
ejpam-5658	36	75	with	with	ADP
ejpam-5658	36	76	v	v	NOUN
ejpam-5658	36	77	(	(	PUNCT
ejpam-5658	36	78	g	g	PROPN
ejpam-5658	36	79	∨	∨	NUM
ejpam-5658	36	80	h	h	NOUN
ejpam-5658	36	81	)	)	PUNCT
ejpam-5658	37	1	=	=	NOUN
ejpam-5658	37	2	v	v	X
ejpam-5658	37	3	(	(	PUNCT
ejpam-5658	37	4	g	g	NOUN
ejpam-5658	37	5	)	)	PUNCT
ejpam-5658	37	6	×	×	NOUN
ejpam-5658	37	7	v	v	NOUN
ejpam-5658	37	8	(	(	PUNCT
ejpam-5658	37	9	h	h	NOUN
ejpam-5658	37	10	)	)	PUNCT
ejpam-5658	37	11	and	and	CCONJ
ejpam-5658	37	12	(	(	PUNCT
ejpam-5658	37	13	x	x	X
ejpam-5658	37	14	,	,	PUNCT
ejpam-5658	37	15	p)(y	p)(y	PROPN
ejpam-5658	37	16	,	,	PUNCT
ejpam-5658	37	17	q	q	X
ejpam-5658	37	18	)	)	PUNCT
ejpam-5658	37	19	∈	∈	PROPN
ejpam-5658	37	20	e(g	e(g	PROPN
ejpam-5658	37	21	∨	∨	NUM
ejpam-5658	37	22	h	h	NOUN
ejpam-5658	37	23	)	)	PUNCT
ejpam-5658	37	24	if	if	SCONJ
ejpam-5658	37	25	and	and	CCONJ
ejpam-5658	37	26	only	only	ADV
ejpam-5658	37	27	if	if	SCONJ
ejpam-5658	37	28	xy	xy	PROPN
ejpam-5658	37	29	∈	∈	PROPN
ejpam-5658	37	30	e(g	e(g	PROPN
ejpam-5658	37	31	)	)	PUNCT
ejpam-5658	37	32	or	or	CCONJ
ejpam-5658	37	33	pq	pq	NOUN
ejpam-5658	37	34	∈	∈	PROPN
ejpam-5658	37	35	e(h	e(h	PROPN
ejpam-5658	37	36	)	)	PUNCT
ejpam-5658	37	37	.	.	PUNCT
ejpam-5658	38	1	the	the	DET
ejpam-5658	38	2	edge	edge	NOUN
ejpam-5658	38	3	corona	corona	PROPN
ejpam-5658	38	4	g	g	PROPN
ejpam-5658	38	5	⋄	⋄	PROPN
ejpam-5658	38	6	h	h	NOUN
ejpam-5658	38	7	of	of	ADP
ejpam-5658	38	8	g	g	PROPN
ejpam-5658	38	9	and	and	CCONJ
ejpam-5658	38	10	h	h	NOUN
ejpam-5658	38	11	is	be	AUX
ejpam-5658	38	12	the	the	DET
ejpam-5658	38	13	graph	graph	NOUN
ejpam-5658	38	14	obtained	obtain	VERB
ejpam-5658	38	15	by	by	ADP
ejpam-5658	38	16	taking	take	VERB
ejpam-5658	38	17	one	one	NUM
ejpam-5658	38	18	copy	copy	NOUN
ejpam-5658	38	19	of	of	ADP
ejpam-5658	38	20	g	g	PROPN
ejpam-5658	38	21	and	and	CCONJ
ejpam-5658	38	22	|e(g)|	|e(g)|	ADJ
ejpam-5658	38	23	copies	copy	NOUN
ejpam-5658	38	24	of	of	ADP
ejpam-5658	38	25	h	h	NOUN
ejpam-5658	38	26	,	,	PUNCT
ejpam-5658	38	27	and	and	CCONJ
ejpam-5658	38	28	then	then	ADV
ejpam-5658	38	29	joining	join	VERB
ejpam-5658	38	30	two	two	NUM
ejpam-5658	38	31	end	end	NOUN
ejpam-5658	38	32	-	-	PUNCT
ejpam-5658	38	33	vertices	vertex	NOUN
ejpam-5658	38	34	of	of	ADP
ejpam-5658	38	35	the	the	DET
ejpam-5658	38	36	i	i	PROPN
ejpam-5658	38	37	-	-	PUNCT
ejpam-5658	38	38	th	th	X
ejpam-5658	38	39	edge	edge	NOUN
ejpam-5658	38	40	of	of	ADP
ejpam-5658	38	41	g	g	NOUN
ejpam-5658	38	42	to	to	ADP
ejpam-5658	38	43	every	every	DET
ejpam-5658	38	44	vertex	vertex	NOUN
ejpam-5658	38	45	in	in	ADP
ejpam-5658	38	46	the	the	DET
ejpam-5658	38	47	i	i	PROPN
ejpam-5658	38	48	-	-	PUNCT
ejpam-5658	38	49	th	th	PROPN
ejpam-5658	38	50	copy	copy	NOUN
ejpam-5658	38	51	of	of	ADP
ejpam-5658	38	52	h.	h.	PROPN
ejpam-5658	38	53	the	the	DET
ejpam-5658	38	54	strong	strong	ADJ
ejpam-5658	38	55	product	product	NOUN
ejpam-5658	38	56	g	g	PROPN
ejpam-5658	38	57	⊠	⊠	PROPN
ejpam-5658	38	58	h	h	NOUN
ejpam-5658	38	59	of	of	ADP
ejpam-5658	38	60	graphs	graph	NOUN
ejpam-5658	38	61	g	g	NOUN
ejpam-5658	38	62	and	and	CCONJ
ejpam-5658	38	63	h	h	NOUN
ejpam-5658	38	64	is	be	AUX
ejpam-5658	38	65	the	the	DET
ejpam-5658	38	66	graph	graph	NOUN
ejpam-5658	38	67	with	with	ADP
ejpam-5658	38	68	vertex	vertex	NOUN
ejpam-5658	38	69	set	set	VERB
ejpam-5658	38	70	v	v	NOUN
ejpam-5658	38	71	(	(	PUNCT
ejpam-5658	38	72	g	g	NOUN
ejpam-5658	38	73	)	)	PUNCT
ejpam-5658	38	74	×	×	NOUN
ejpam-5658	38	75	v	v	NOUN
ejpam-5658	38	76	(	(	PUNCT
ejpam-5658	38	77	h	h	NOUN
ejpam-5658	38	78	)	)	PUNCT
ejpam-5658	38	79	and	and	CCONJ
ejpam-5658	38	80	(	(	PUNCT
ejpam-5658	38	81	u	u	NOUN
ejpam-5658	38	82	,	,	PUNCT
ejpam-5658	38	83	v	v	NOUN
ejpam-5658	38	84	)	)	PUNCT
ejpam-5658	38	85	is	be	AUX
ejpam-5658	38	86	adjacent	adjacent	ADJ
ejpam-5658	38	87	with	with	ADP
ejpam-5658	38	88	(	(	PUNCT
ejpam-5658	38	89	u′	u′	PROPN
ejpam-5658	38	90	,	,	PUNCT
ejpam-5658	38	91	v′	v′	PROPN
ejpam-5658	38	92	)	)	PUNCT
ejpam-5658	39	1	whenever	whenever	SCONJ
ejpam-5658	39	2	[	[	X
ejpam-5658	39	3	uu′	uu′	PROPN
ejpam-5658	39	4	∈	∈	PROPN
ejpam-5658	39	5	e(g	e(g	PROPN
ejpam-5658	39	6	)	)	PUNCT
ejpam-5658	39	7	and	and	CCONJ
ejpam-5658	39	8	v	v	NOUN
ejpam-5658	39	9	=	=	SYM
ejpam-5658	39	10	v′	v′	NOUN
ejpam-5658	39	11	]	]	PUNCT
ejpam-5658	39	12	or	or	CCONJ
ejpam-5658	39	13	[	[	X
ejpam-5658	39	14	vv′	vv′	NOUN
ejpam-5658	39	15	∈	∈	PROPN
ejpam-5658	39	16	e(h	e(h	PROPN
ejpam-5658	39	17	)	)	PUNCT
ejpam-5658	39	18	and	and	CCONJ
ejpam-5658	39	19	u	u	X
ejpam-5658	39	20	=	=	SYM
ejpam-5658	39	21	u′	u′	PROPN
ejpam-5658	39	22	]	]	PUNCT
ejpam-5658	39	23	or	or	CCONJ
ejpam-5658	39	24	[	[	X
ejpam-5658	39	25	uu′	uu′	PROPN
ejpam-5658	39	26	∈	∈	PROPN
ejpam-5658	39	27	e(g	e(g	PROPN
ejpam-5658	39	28	)	)	PUNCT
ejpam-5658	39	29	and	and	CCONJ
ejpam-5658	39	30	vv′	vv′	PROPN
ejpam-5658	39	31	∈	∈	PROPN
ejpam-5658	39	32	e(h	e(h	PROPN
ejpam-5658	39	33	)	)	PUNCT
ejpam-5658	39	34	]	]	PUNCT
ejpam-5658	39	35	.	.	PUNCT
ejpam-5658	40	1	3	3	X
ejpam-5658	40	2	.	.	NOUN
ejpam-5658	40	3	results	result	NOUN
ejpam-5658	40	4	proposition	proposition	NOUN
ejpam-5658	40	5	1	1	NUM
ejpam-5658	40	6	(	(	PUNCT
ejpam-5658	40	7	[	[	X
ejpam-5658	40	8	4	4	NUM
ejpam-5658	40	9	]	]	NUM
ejpam-5658	40	10	)	)	PUNCT
ejpam-5658	40	11	.	.	PUNCT
ejpam-5658	41	1	let	let	VERB
ejpam-5658	41	2	g	g	PRON
ejpam-5658	41	3	be	be	AUX
ejpam-5658	41	4	any	any	DET
ejpam-5658	41	5	graph	graph	NOUN
ejpam-5658	41	6	on	on	ADP
ejpam-5658	41	7	n	n	DET
ejpam-5658	41	8	vertices	vertex	NOUN
ejpam-5658	41	9	.	.	PUNCT
ejpam-5658	42	1	if	if	SCONJ
ejpam-5658	42	2	s	s	NOUN
ejpam-5658	42	3	is	be	AUX
ejpam-5658	42	4	a	a	DET
ejpam-5658	42	5	maximun	maximun	PROPN
ejpam-5658	42	6	hop	hop	PROPN
ejpam-5658	42	7	independent	independent	ADJ
ejpam-5658	42	8	set	set	NOUN
ejpam-5658	42	9	of	of	ADP
ejpam-5658	42	10	g	g	NOUN
ejpam-5658	42	11	,	,	PUNCT
ejpam-5658	42	12	then	then	ADV
ejpam-5658	42	13	s	s	VERB
ejpam-5658	42	14	is	be	AUX
ejpam-5658	42	15	a	a	DET
ejpam-5658	42	16	hop	hop	NOUN
ejpam-5658	42	17	dominating	dominating	NOUN
ejpam-5658	42	18	set	set	NOUN
ejpam-5658	42	19	.	.	PUNCT
ejpam-5658	43	1	in	in	ADP
ejpam-5658	43	2	particular	particular	ADJ
ejpam-5658	43	3	,	,	PUNCT
ejpam-5658	43	4	γh(g	γh(g	NOUN
ejpam-5658	43	5	)	)	PUNCT
ejpam-5658	43	6	≤	≤	NOUN
ejpam-5658	43	7	αh(g	αh(g	NOUN
ejpam-5658	43	8	)	)	PUNCT
ejpam-5658	43	9	.	.	PUNCT
ejpam-5658	44	1	theorem	theorem	ADJ
ejpam-5658	44	2	1	1	NUM
ejpam-5658	44	3	(	(	PUNCT
ejpam-5658	44	4	[	[	X
ejpam-5658	44	5	4	4	NUM
ejpam-5658	44	6	]	]	NUM
ejpam-5658	44	7	)	)	PUNCT
ejpam-5658	44	8	.	.	PUNCT
ejpam-5658	45	1	let	let	VERB
ejpam-5658	45	2	g	g	PRON
ejpam-5658	45	3	be	be	AUX
ejpam-5658	45	4	any	any	DET
ejpam-5658	45	5	graph	graph	NOUN
ejpam-5658	45	6	on	on	ADP
ejpam-5658	45	7	n	n	DET
ejpam-5658	45	8	vertices	vertex	NOUN
ejpam-5658	45	9	.	.	PUNCT
ejpam-5658	46	1	if	if	SCONJ
ejpam-5658	46	2	s	s	PROPN
ejpam-5658	46	3	is	be	AUX
ejpam-5658	46	4	a	a	DET
ejpam-5658	46	5	hop	hop	NOUN
ejpam-5658	46	6	independent	independent	ADJ
ejpam-5658	46	7	set	set	NOUN
ejpam-5658	46	8	of	of	ADP
ejpam-5658	46	9	g	g	NOUN
ejpam-5658	46	10	,	,	PUNCT
ejpam-5658	46	11	then	then	ADV
ejpam-5658	46	12	every	every	DET
ejpam-5658	46	13	component	component	NOUN
ejpam-5658	46	14	of	of	ADP
ejpam-5658	46	15	⟨s⟩	⟨s⟩	PROPN
ejpam-5658	46	16	is	be	AUX
ejpam-5658	46	17	complete	complete	ADJ
ejpam-5658	46	18	.	.	PUNCT
ejpam-5658	47	1	moreover	moreover	ADV
ejpam-5658	47	2	,	,	PUNCT
ejpam-5658	47	3	(	(	PUNCT
ejpam-5658	47	4	i	i	NOUN
ejpam-5658	47	5	)	)	PUNCT
ejpam-5658	47	6	αh(g	αh(g	NOUN
ejpam-5658	47	7	)	)	PUNCT
ejpam-5658	48	1	=	=	SYM
ejpam-5658	48	2	n	n	NOUN
ejpam-5658	48	3	if	if	SCONJ
ejpam-5658	48	4	and	and	CCONJ
ejpam-5658	48	5	only	only	ADV
ejpam-5658	48	6	if	if	SCONJ
ejpam-5658	48	7	every	every	DET
ejpam-5658	48	8	component	component	NOUN
ejpam-5658	48	9	of	of	ADP
ejpam-5658	48	10	g	g	PROPN
ejpam-5658	48	11	is	be	AUX
ejpam-5658	48	12	complete	complete	ADJ
ejpam-5658	48	13	;	;	PUNCT
ejpam-5658	48	14	and	and	CCONJ
ejpam-5658	48	15	(	(	PUNCT
ejpam-5658	48	16	ii	ii	NOUN
ejpam-5658	48	17	)	)	PUNCT
ejpam-5658	48	18	for	for	ADP
ejpam-5658	48	19	n	n	X
ejpam-5658	48	20	≥	≥	NUM
ejpam-5658	48	21	3	3	NUM
ejpam-5658	48	22	,	,	PUNCT
ejpam-5658	48	23	αh(g	αh(g	NOUN
ejpam-5658	48	24	)	)	PUNCT
ejpam-5658	48	25	=	=	SYM
ejpam-5658	48	26	n	n	CCONJ
ejpam-5658	48	27	−	−	PROPN
ejpam-5658	48	28	1	1	NUM
ejpam-5658	48	29	if	if	SCONJ
ejpam-5658	48	30	and	and	CCONJ
ejpam-5658	48	31	only	only	ADV
ejpam-5658	48	32	if	if	SCONJ
ejpam-5658	48	33	all	all	PRON
ejpam-5658	48	34	but	but	SCONJ
ejpam-5658	48	35	a	a	DET
ejpam-5658	48	36	single	single	ADJ
ejpam-5658	48	37	component	component	NOUN
ejpam-5658	48	38	c	c	PROPN
ejpam-5658	48	39	of	of	ADP
ejpam-5658	48	40	g	g	PROPN
ejpam-5658	48	41	are	be	AUX
ejpam-5658	48	42	complete	complete	ADJ
ejpam-5658	48	43	and	and	CCONJ
ejpam-5658	48	44	c	c	NOUN
ejpam-5658	48	45	\	\	PROPN
ejpam-5658	48	46	v	v	NOUN
ejpam-5658	48	47	is	be	AUX
ejpam-5658	48	48	a	a	DET
ejpam-5658	48	49	complete	complete	ADJ
ejpam-5658	48	50	graph	graph	NOUN
ejpam-5658	48	51	for	for	ADP
ejpam-5658	48	52	some	some	DET
ejpam-5658	48	53	vertex	vertex	NOUN
ejpam-5658	48	54	v	v	ADP
ejpam-5658	48	55	∈	∈	NOUN
ejpam-5658	48	56	v	v	NOUN
ejpam-5658	48	57	(	(	PUNCT
ejpam-5658	48	58	c	c	NOUN
ejpam-5658	48	59	)	)	PUNCT
ejpam-5658	48	60	.	.	PUNCT
ejpam-5658	49	1	corollary	corollary	ADJ
ejpam-5658	49	2	1	1	NUM
ejpam-5658	49	3	(	(	PUNCT
ejpam-5658	49	4	[	[	X
ejpam-5658	49	5	4	4	NUM
ejpam-5658	49	6	]	]	NUM
ejpam-5658	49	7	)	)	PUNCT
ejpam-5658	49	8	.	.	PUNCT
ejpam-5658	50	1	let	let	VERB
ejpam-5658	50	2	g	g	PRON
ejpam-5658	50	3	be	be	AUX
ejpam-5658	50	4	a	a	DET
ejpam-5658	50	5	connected	connected	ADJ
ejpam-5658	50	6	graph	graph	NOUN
ejpam-5658	50	7	on	on	ADP
ejpam-5658	50	8	n	n	DET
ejpam-5658	50	9	vertices	vertex	NOUN
ejpam-5658	50	10	.	.	PUNCT
ejpam-5658	51	1	then	then	ADV
ejpam-5658	51	2	(	(	PUNCT
ejpam-5658	51	3	i	i	NOUN
ejpam-5658	51	4	)	)	PUNCT
ejpam-5658	51	5	αh(g	αh(g	NOUN
ejpam-5658	51	6	)	)	PUNCT
ejpam-5658	51	7	=	=	SYM
ejpam-5658	52	1	n	n	NOUN
ejpam-5658	52	2	if	if	SCONJ
ejpam-5658	52	3	and	and	CCONJ
ejpam-5658	52	4	only	only	ADV
ejpam-5658	52	5	if	if	SCONJ
ejpam-5658	52	6	g	g	PROPN
ejpam-5658	52	7	=	=	SYM
ejpam-5658	52	8	kn	kn	PROPN
ejpam-5658	52	9	;	;	PUNCT
ejpam-5658	52	10	and	and	CCONJ
ejpam-5658	52	11	(	(	PUNCT
ejpam-5658	52	12	ii	ii	NOUN
ejpam-5658	52	13	)	)	PUNCT
ejpam-5658	52	14	for	for	ADP
ejpam-5658	52	15	n	n	X
ejpam-5658	52	16	≥	≥	NUM
ejpam-5658	52	17	3	3	NUM
ejpam-5658	52	18	,	,	PUNCT
ejpam-5658	52	19	αh(g	αh(g	NOUN
ejpam-5658	52	20	)	)	PUNCT
ejpam-5658	52	21	=	=	SYM
ejpam-5658	52	22	n−	n−	NOUN
ejpam-5658	52	23	1	1	NUM
ejpam-5658	52	24	if	if	SCONJ
ejpam-5658	52	25	and	and	CCONJ
ejpam-5658	52	26	only	only	ADV
ejpam-5658	52	27	if	if	SCONJ
ejpam-5658	52	28	g	g	PROPN
ejpam-5658	52	29	̸=	̸=	PROPN
ejpam-5658	52	30	kn	kn	PROPN
ejpam-5658	52	31	and	and	CCONJ
ejpam-5658	52	32	there	there	PRON
ejpam-5658	52	33	exists	exist	VERB
ejpam-5658	52	34	v	v	ADP
ejpam-5658	52	35	∈	∈	PROPN
ejpam-5658	52	36	v	v	NOUN
ejpam-5658	52	37	(	(	PUNCT
ejpam-5658	52	38	g	g	NOUN
ejpam-5658	52	39	)	)	PUNCT
ejpam-5658	52	40	such	such	ADJ
ejpam-5658	52	41	that	that	SCONJ
ejpam-5658	52	42	g	g	PROPN
ejpam-5658	52	43	\	\	PROPN
ejpam-5658	52	44	v	v	PROPN
ejpam-5658	52	45	=	=	SYM
ejpam-5658	52	46	kn−1	kn−1	PROPN
ejpam-5658	52	47	.	.	PROPN
ejpam-5658	52	48	observation	observation	NOUN
ejpam-5658	52	49	1	1	NUM
ejpam-5658	52	50	:	:	PUNCT
ejpam-5658	52	51	let	let	VERB
ejpam-5658	52	52	g	g	PRON
ejpam-5658	52	53	be	be	AUX
ejpam-5658	52	54	a	a	DET
ejpam-5658	52	55	graph	graph	NOUN
ejpam-5658	52	56	of	of	ADP
ejpam-5658	52	57	order	order	NOUN
ejpam-5658	52	58	n.	n.	NOUN
ejpam-5658	52	59	(	(	PUNCT
ejpam-5658	52	60	i	i	NOUN
ejpam-5658	52	61	)	)	PUNCT
ejpam-5658	52	62	∅	∅	NOUN
ejpam-5658	52	63	and	and	CCONJ
ejpam-5658	52	64	cliques	clique	NOUN
ejpam-5658	52	65	in	in	ADP
ejpam-5658	52	66	g	g	PROPN
ejpam-5658	52	67	are	be	AUX
ejpam-5658	52	68	hop	hop	ADV
ejpam-5658	52	69	independent	independent	ADJ
ejpam-5658	52	70	sets	set	NOUN
ejpam-5658	52	71	.	.	PUNCT
ejpam-5658	53	1	(	(	PUNCT
ejpam-5658	53	2	ii	ii	NOUN
ejpam-5658	53	3	)	)	PUNCT
ejpam-5658	53	4	if	if	SCONJ
ejpam-5658	53	5	s	s	VERB
ejpam-5658	53	6	is	be	AUX
ejpam-5658	53	7	a	a	DET
ejpam-5658	53	8	hop	hop	NOUN
ejpam-5658	53	9	independent	independent	ADJ
ejpam-5658	53	10	set	set	NOUN
ejpam-5658	53	11	in	in	ADP
ejpam-5658	53	12	g	g	PROPN
ejpam-5658	53	13	and	and	CCONJ
ejpam-5658	53	14	i	i	PRON
ejpam-5658	53	15	⊆	⊆	NUM
ejpam-5658	53	16	i(g	i(g	NOUN
ejpam-5658	53	17	)	)	PUNCT
ejpam-5658	53	18	,	,	PUNCT
ejpam-5658	53	19	where	where	SCONJ
ejpam-5658	53	20	i(g	i(g	NOUN
ejpam-5658	53	21	)	)	PUNCT
ejpam-5658	53	22	denotes	denote	VERB
ejpam-5658	53	23	the	the	DET
ejpam-5658	53	24	set	set	NOUN
ejpam-5658	53	25	consisting	consisting	NOUN
ejpam-5658	53	26	of	of	ADP
ejpam-5658	53	27	the	the	DET
ejpam-5658	53	28	isolated	isolate	VERB
ejpam-5658	53	29	vertices	vertex	NOUN
ejpam-5658	53	30	of	of	ADP
ejpam-5658	53	31	g	g	NOUN
ejpam-5658	53	32	,	,	PUNCT
ejpam-5658	53	33	then	then	ADV
ejpam-5658	53	34	s	s	VERB
ejpam-5658	53	35	∪	∪	ADP
ejpam-5658	54	1	i	i	PRON
ejpam-5658	54	2	is	be	AUX
ejpam-5658	54	3	also	also	ADV
ejpam-5658	54	4	hop	hop	ADV
ejpam-5658	54	5	independent	independent	ADJ
ejpam-5658	54	6	in	in	ADP
ejpam-5658	54	7	g.	g.	PROPN
ejpam-5658	54	8	moreover	moreover	ADV
ejpam-5658	54	9	,	,	PUNCT
ejpam-5658	54	10	if	if	SCONJ
ejpam-5658	54	11	s	s	VERB
ejpam-5658	54	12	is	be	AUX
ejpam-5658	54	13	an	an	DET
ejpam-5658	54	14	αh	αh	NOUN
ejpam-5658	54	15	-	-	PUNCT
ejpam-5658	54	16	set	set	NOUN
ejpam-5658	54	17	in	in	ADP
ejpam-5658	54	18	g	g	NOUN
ejpam-5658	54	19	,	,	PUNCT
ejpam-5658	54	20	then	then	ADV
ejpam-5658	54	21	i(g	i(g	ADV
ejpam-5658	54	22	)	)	PUNCT
ejpam-5658	55	1	⊆	⊆	NUM
ejpam-5658	55	2	s.	s.	PROPN
ejpam-5658	55	3	observation	observation	NOUN
ejpam-5658	55	4	2	2	NUM
ejpam-5658	55	5	:	:	PUNCT
ejpam-5658	55	6	let	let	VERB
ejpam-5658	55	7	g1	g1	PROPN
ejpam-5658	55	8	,	,	PUNCT
ejpam-5658	55	9	g2	g2	PROPN
ejpam-5658	55	10	,	,	PUNCT
ejpam-5658	55	11	·	·	PUNCT
ejpam-5658	55	12	·	·	PUNCT
ejpam-5658	55	13	·	·	PUNCT
ejpam-5658	55	14	,	,	PUNCT
ejpam-5658	55	15	gk	gk	PROPN
ejpam-5658	55	16	be	be	AUX
ejpam-5658	55	17	the	the	DET
ejpam-5658	55	18	components	component	NOUN
ejpam-5658	55	19	of	of	ADP
ejpam-5658	55	20	graph	graph	NOUN
ejpam-5658	55	21	g	g	PROPN
ejpam-5658	55	22	,	,	PUNCT
ejpam-5658	55	23	where	where	SCONJ
ejpam-5658	55	24	k	k	PROPN
ejpam-5658	55	25	≥	≥	NUM
ejpam-5658	55	26	1	1	NUM
ejpam-5658	55	27	.	.	PUNCT
ejpam-5658	56	1	then	then	ADV
ejpam-5658	56	2	s	s	VERB
ejpam-5658	56	3	is	be	AUX
ejpam-5658	56	4	hop	hop	NOUN
ejpam-5658	56	5	independent	independent	ADJ
ejpam-5658	56	6	in	in	ADP
ejpam-5658	56	7	g	g	PROPN
ejpam-5658	56	8	if	if	SCONJ
ejpam-5658	57	1	and	and	CCONJ
ejpam-5658	57	2	only	only	ADV
ejpam-5658	57	3	if	if	SCONJ
ejpam-5658	57	4	sj	sj	ADP
ejpam-5658	57	5	=	=	SYM
ejpam-5658	57	6	s∩v	s∩v	PROPN
ejpam-5658	57	7	(	(	PUNCT
ejpam-5658	57	8	gj	gj	NOUN
ejpam-5658	57	9	)	)	PUNCT
ejpam-5658	57	10	is	be	AUX
ejpam-5658	57	11	hop	hop	ADV
ejpam-5658	57	12	independent	independent	ADJ
ejpam-5658	57	13	in	in	ADP
ejpam-5658	57	14	gj	gj	NOUN
ejpam-5658	57	15	for	for	ADP
ejpam-5658	57	16	each	each	DET
ejpam-5658	57	17	j	j	PROPN
ejpam-5658	57	18	∈	∈	PROPN
ejpam-5658	57	19	{	{	PUNCT
ejpam-5658	57	20	1	1	NUM
ejpam-5658	57	21	,	,	PUNCT
ejpam-5658	57	22	2	2	NUM
ejpam-5658	57	23	,	,	PUNCT
ejpam-5658	57	24	·	·	PUNCT
ejpam-5658	57	25	·	·	PUNCT
ejpam-5658	57	26	·	·	PUNCT
ejpam-5658	57	27	,	,	PUNCT
ejpam-5658	57	28	k	k	NOUN
ejpam-5658	57	29	}	}	PUNCT
ejpam-5658	57	30	.	.	PUNCT
ejpam-5658	58	1	moreover	moreover	ADV
ejpam-5658	58	2	,	,	PUNCT
ejpam-5658	58	3	αh(g	αh(g	NOUN
ejpam-5658	58	4	)	)	PUNCT
ejpam-5658	59	1	=	=	SYM
ejpam-5658	60	1	∑k	∑k	PROPN
ejpam-5658	60	2	i=1	i=1	PROPN
ejpam-5658	60	3	αh(gj	αh(gj	PROPN
ejpam-5658	60	4	)	)	PUNCT
ejpam-5658	60	5	.	.	PUNCT
ejpam-5658	61	1	j.	j.	PROPN
ejpam-5658	61	2	anoche	anoche	PROPN
ejpam-5658	61	3	,	,	PUNCT
ejpam-5658	61	4	s.	s.	PROPN
ejpam-5658	61	5	canoy	canoy	PROPN
ejpam-5658	61	6	,	,	PUNCT
ejpam-5658	61	7	jr	jr	PROPN
ejpam-5658	61	8	.	.	PROPN
ejpam-5658	61	9	/	/	SYM
ejpam-5658	61	10	eur	eur	PROPN
ejpam-5658	61	11	.	.	PUNCT
ejpam-5658	62	1	j.	j.	PROPN
ejpam-5658	62	2	pure	pure	PROPN
ejpam-5658	62	3	appl	appl	PROPN
ejpam-5658	62	4	.	.	PROPN
ejpam-5658	62	5	math	math	PROPN
ejpam-5658	62	6	,	,	PUNCT
ejpam-5658	62	7	18	18	NUM
ejpam-5658	62	8	(	(	PUNCT
ejpam-5658	62	9	1	1	NUM
ejpam-5658	62	10	)	)	PUNCT
ejpam-5658	62	11	(	(	PUNCT
ejpam-5658	62	12	2025	2025	NUM
ejpam-5658	62	13	)	)	PUNCT
ejpam-5658	62	14	,	,	PUNCT
ejpam-5658	62	15	5658	5658	NUM
ejpam-5658	62	16	4	4	NUM
ejpam-5658	62	17	of	of	ADP
ejpam-5658	62	18	15	15	NUM
ejpam-5658	62	19	4	4	NUM
ejpam-5658	62	20	.	.	PUNCT
ejpam-5658	63	1	shadow	shadow	NOUN
ejpam-5658	63	2	graph	graph	VERB
ejpam-5658	63	3	if	if	SCONJ
ejpam-5658	63	4	g1	g1	PROPN
ejpam-5658	63	5	and	and	CCONJ
ejpam-5658	63	6	g2	g2	PROPN
ejpam-5658	63	7	are	be	AUX
ejpam-5658	63	8	the	the	DET
ejpam-5658	63	9	copies	copy	NOUN
ejpam-5658	63	10	of	of	ADP
ejpam-5658	63	11	graph	graph	NOUN
ejpam-5658	63	12	g	g	PROPN
ejpam-5658	63	13	in	in	ADP
ejpam-5658	63	14	the	the	DET
ejpam-5658	63	15	definition	definition	NOUN
ejpam-5658	63	16	of	of	ADP
ejpam-5658	63	17	the	the	DET
ejpam-5658	63	18	shadow	shadow	NOUN
ejpam-5658	63	19	graph	graph	VERB
ejpam-5658	63	20	d2(g	d2(g	PROPN
ejpam-5658	63	21	)	)	PUNCT
ejpam-5658	63	22	and	and	CCONJ
ejpam-5658	63	23	if	if	SCONJ
ejpam-5658	63	24	sg1	sg1	PROPN
ejpam-5658	63	25	⊆	⊆	PROPN
ejpam-5658	63	26	v	v	NOUN
ejpam-5658	63	27	(	(	PUNCT
ejpam-5658	63	28	g1	g1	PROPN
ejpam-5658	63	29	)	)	PUNCT
ejpam-5658	63	30	and	and	CCONJ
ejpam-5658	63	31	sg2	sg2	PROPN
ejpam-5658	63	32	⊆	⊆	NUM
ejpam-5658	63	33	v	v	PROPN
ejpam-5658	63	34	(	(	PUNCT
ejpam-5658	63	35	g2	g2	PROPN
ejpam-5658	63	36	)	)	PUNCT
ejpam-5658	63	37	,	,	PUNCT
ejpam-5658	63	38	then	then	ADV
ejpam-5658	63	39	the	the	DET
ejpam-5658	63	40	sets	set	NOUN
ejpam-5658	63	41	s′	s′	VERB
ejpam-5658	63	42	g1	g1	NOUN
ejpam-5658	63	43	and	and	CCONJ
ejpam-5658	63	44	s′	s′	ADJ
ejpam-5658	63	45	g2	g2	PROPN
ejpam-5658	63	46	are	be	AUX
ejpam-5658	63	47	the	the	DET
ejpam-5658	63	48	sets	set	NOUN
ejpam-5658	63	49	given	give	VERB
ejpam-5658	63	50	by	by	ADP
ejpam-5658	63	51	s′	s′	ADJ
ejpam-5658	63	52	g1	g1	NOUN
ejpam-5658	63	53	=	=	PUNCT
ejpam-5658	63	54	{	{	PUNCT
ejpam-5658	63	55	a′	a′	PROPN
ejpam-5658	63	56	∈	∈	PROPN
ejpam-5658	63	57	v	v	ADP
ejpam-5658	63	58	(	(	PUNCT
ejpam-5658	63	59	g2	g2	PROPN
ejpam-5658	63	60	)	)	PUNCT
ejpam-5658	63	61	:	:	PUNCT
ejpam-5658	63	62	a	a	DET
ejpam-5658	63	63	∈	∈	NOUN
ejpam-5658	63	64	sg1	sg1	NOUN
ejpam-5658	63	65	}	}	PUNCT
ejpam-5658	63	66	and	and	CCONJ
ejpam-5658	63	67	s′	s′	ADJ
ejpam-5658	63	68	g2	g2	PROPN
ejpam-5658	63	69	=	=	PRON
ejpam-5658	63	70	{	{	PUNCT
ejpam-5658	63	71	a	a	DET
ejpam-5658	63	72	∈	∈	PROPN
ejpam-5658	63	73	v	v	NOUN
ejpam-5658	63	74	(	(	PUNCT
ejpam-5658	63	75	g1	g1	PROPN
ejpam-5658	63	76	)	)	PUNCT
ejpam-5658	63	77	:	:	PUNCT
ejpam-5658	63	78	a	a	DET
ejpam-5658	63	79	′	′	NUM
ejpam-5658	63	80	∈	∈	PROPN
ejpam-5658	63	81	sg2	sg2	PROPN
ejpam-5658	63	82	}	}	PUNCT
ejpam-5658	63	83	.	.	PUNCT
ejpam-5658	64	1	we	we	PRON
ejpam-5658	64	2	denote	denote	VERB
ejpam-5658	64	3	by	by	ADP
ejpam-5658	64	4	i(g	i(g	NOUN
ejpam-5658	64	5	)	)	PUNCT
ejpam-5658	64	6	the	the	DET
ejpam-5658	64	7	set	set	NOUN
ejpam-5658	64	8	containing	contain	VERB
ejpam-5658	64	9	all	all	DET
ejpam-5658	64	10	the	the	DET
ejpam-5658	64	11	isolated	isolated	ADJ
ejpam-5658	64	12	vertices	vertex	NOUN
ejpam-5658	64	13	of	of	ADP
ejpam-5658	64	14	g.	g.	PROPN
ejpam-5658	64	15	theorem	theorem	NOUN
ejpam-5658	64	16	2	2	X
ejpam-5658	64	17	.	.	PUNCT
ejpam-5658	65	1	let	let	VERB
ejpam-5658	65	2	g	g	PRON
ejpam-5658	65	3	be	be	AUX
ejpam-5658	65	4	a	a	DET
ejpam-5658	65	5	graph	graph	NOUN
ejpam-5658	65	6	.	.	PUNCT
ejpam-5658	66	1	then	then	ADV
ejpam-5658	66	2	a	a	DET
ejpam-5658	66	3	subset	subset	NOUN
ejpam-5658	66	4	s	s	X
ejpam-5658	66	5	of	of	ADP
ejpam-5658	66	6	v	v	NOUN
ejpam-5658	66	7	(	(	PUNCT
ejpam-5658	66	8	d2(g	d2(g	PROPN
ejpam-5658	66	9	)	)	PUNCT
ejpam-5658	66	10	)	)	PUNCT
ejpam-5658	66	11	is	be	AUX
ejpam-5658	66	12	hop	hop	ADV
ejpam-5658	66	13	independent	independent	ADJ
ejpam-5658	66	14	in	in	ADP
ejpam-5658	66	15	d2(g	d2(g	PROPN
ejpam-5658	66	16	)	)	PUNCT
ejpam-5658	66	17	if	if	SCONJ
ejpam-5658	67	1	and	and	CCONJ
ejpam-5658	67	2	only	only	ADV
ejpam-5658	67	3	if	if	SCONJ
ejpam-5658	67	4	one	one	NUM
ejpam-5658	67	5	of	of	ADP
ejpam-5658	67	6	the	the	DET
ejpam-5658	67	7	following	follow	VERB
ejpam-5658	67	8	conditions	condition	NOUN
ejpam-5658	67	9	holds	hold	VERB
ejpam-5658	67	10	:	:	PUNCT
ejpam-5658	67	11	(	(	PUNCT
ejpam-5658	67	12	i	i	NOUN
ejpam-5658	67	13	)	)	PUNCT
ejpam-5658	67	14	s	s	VERB
ejpam-5658	67	15	is	be	AUX
ejpam-5658	67	16	a	a	DET
ejpam-5658	67	17	hop	hop	NOUN
ejpam-5658	67	18	independent	independent	ADJ
ejpam-5658	67	19	set	set	NOUN
ejpam-5658	67	20	in	in	ADP
ejpam-5658	67	21	g1	g1	PROPN
ejpam-5658	67	22	.	.	PUNCT
ejpam-5658	68	1	(	(	PUNCT
ejpam-5658	68	2	ii	ii	X
ejpam-5658	68	3	)	)	PUNCT
ejpam-5658	68	4	s	s	VERB
ejpam-5658	68	5	is	be	AUX
ejpam-5658	68	6	a	a	DET
ejpam-5658	68	7	hop	hop	NOUN
ejpam-5658	68	8	independent	independent	ADJ
ejpam-5658	68	9	set	set	NOUN
ejpam-5658	68	10	in	in	ADP
ejpam-5658	68	11	g2	g2	PROPN
ejpam-5658	68	12	.	.	PUNCT
ejpam-5658	69	1	(	(	PUNCT
ejpam-5658	69	2	iii	iii	X
ejpam-5658	69	3	)	)	PUNCT
ejpam-5658	69	4	s	s	PART
ejpam-5658	69	5	=	=	NOUN
ejpam-5658	69	6	sg1	sg1	NOUN
ejpam-5658	69	7	∪	∪	ADP
ejpam-5658	69	8	sg2	sg2	PROPN
ejpam-5658	69	9	∪	∪	PROPN
ejpam-5658	69	10	i1	i1	PROPN
ejpam-5658	69	11	∪	∪	PROPN
ejpam-5658	69	12	i2	i2	PROPN
ejpam-5658	69	13	and	and	CCONJ
ejpam-5658	69	14	satisfies	satisfy	VERB
ejpam-5658	69	15	the	the	DET
ejpam-5658	69	16	following	follow	VERB
ejpam-5658	69	17	conditions	condition	NOUN
ejpam-5658	69	18	:	:	PUNCT
ejpam-5658	69	19	(	(	PUNCT
ejpam-5658	69	20	a	a	X
ejpam-5658	69	21	)	)	PUNCT
ejpam-5658	69	22	i1	i1	PROPN
ejpam-5658	69	23	⊆	⊆	NUM
ejpam-5658	69	24	i(g1	i(g1	PROPN
ejpam-5658	69	25	)	)	PUNCT
ejpam-5658	69	26	and	and	CCONJ
ejpam-5658	69	27	i2	i2	PROPN
ejpam-5658	69	28	⊆	⊆	NUM
ejpam-5658	69	29	i(g2	i(g2	NOUN
ejpam-5658	69	30	)	)	PUNCT
ejpam-5658	69	31	.	.	PUNCT
ejpam-5658	70	1	(	(	PUNCT
ejpam-5658	70	2	b	b	X
ejpam-5658	70	3	)	)	PUNCT
ejpam-5658	70	4	sg1	sg1	NOUN
ejpam-5658	70	5	and	and	CCONJ
ejpam-5658	70	6	sg2	sg2	PROPN
ejpam-5658	70	7	are	be	AUX
ejpam-5658	70	8	hop	hop	ADV
ejpam-5658	70	9	independent	independent	ADJ
ejpam-5658	70	10	sets	set	NOUN
ejpam-5658	70	11	in	in	ADP
ejpam-5658	70	12	g1	g1	PROPN
ejpam-5658	70	13	and	and	CCONJ
ejpam-5658	70	14	g2	g2	PROPN
ejpam-5658	70	15	,	,	PUNCT
ejpam-5658	70	16	respectively	respectively	ADV
ejpam-5658	70	17	,	,	PUNCT
ejpam-5658	70	18	not	not	PART
ejpam-5658	70	19	containing	contain	VERB
ejpam-5658	70	20	isolated	isolated	ADJ
ejpam-5658	70	21	vertices	vertex	NOUN
ejpam-5658	70	22	.	.	PUNCT
ejpam-5658	71	1	(	(	PUNCT
ejpam-5658	71	2	c	c	X
ejpam-5658	71	3	)	)	PUNCT
ejpam-5658	71	4	sg1	sg1	NOUN
ejpam-5658	71	5	∩	∩	NOUN
ejpam-5658	71	6	s′	s′	VERB
ejpam-5658	71	7	g2	g2	PROPN
ejpam-5658	71	8	=	=	PUNCT
ejpam-5658	71	9	∅	∅	NOUN
ejpam-5658	71	10	and	and	CCONJ
ejpam-5658	71	11	s′	s′	ADJ
ejpam-5658	71	12	g1	g1	PROPN
ejpam-5658	71	13	∩	∩	PROPN
ejpam-5658	71	14	sg2	sg2	PROPN
ejpam-5658	71	15	=	=	PROPN
ejpam-5658	71	16	∅.	∅.	PROPN
ejpam-5658	71	17	(	(	PUNCT
ejpam-5658	71	18	d	d	NOUN
ejpam-5658	71	19	)	)	PUNCT
ejpam-5658	71	20	sg1	sg1	NOUN
ejpam-5658	71	21	∪	∪	ADP
ejpam-5658	71	22	s′	s′	ADJ
ejpam-5658	71	23	g2	g2	PROPN
ejpam-5658	71	24	and	and	CCONJ
ejpam-5658	71	25	s′	s′	ADJ
ejpam-5658	71	26	g1	g1	PROPN
ejpam-5658	71	27	∪	∪	ADP
ejpam-5658	71	28	sg2	sg2	PROPN
ejpam-5658	71	29	are	be	AUX
ejpam-5658	71	30	hop	hop	ADV
ejpam-5658	71	31	independent	independent	ADJ
ejpam-5658	71	32	sets	set	NOUN
ejpam-5658	71	33	in	in	ADP
ejpam-5658	71	34	g1	g1	PROPN
ejpam-5658	71	35	and	and	CCONJ
ejpam-5658	71	36	g2	g2	PROPN
ejpam-5658	71	37	,	,	PUNCT
ejpam-5658	71	38	respectively	respectively	ADV
ejpam-5658	71	39	.	.	PUNCT
ejpam-5658	72	1	proof	proof	NOUN
ejpam-5658	72	2	.	.	PUNCT
ejpam-5658	73	1	suppose	suppose	VERB
ejpam-5658	73	2	s	s	PRON
ejpam-5658	73	3	is	be	AUX
ejpam-5658	73	4	a	a	DET
ejpam-5658	73	5	hop	hop	NOUN
ejpam-5658	73	6	independent	independent	ADJ
ejpam-5658	73	7	set	set	NOUN
ejpam-5658	73	8	in	in	ADP
ejpam-5658	73	9	d2(g	d2(g	NOUN
ejpam-5658	73	10	)	)	PUNCT
ejpam-5658	73	11	.	.	PUNCT
ejpam-5658	74	1	if	if	SCONJ
ejpam-5658	74	2	s	s	ADP
ejpam-5658	74	3	∩	∩	ADJ
ejpam-5658	74	4	v	v	X
ejpam-5658	74	5	(	(	PUNCT
ejpam-5658	74	6	g2	g2	PROPN
ejpam-5658	74	7	)	)	PUNCT
ejpam-5658	74	8	=	=	NOUN
ejpam-5658	75	1	∅	∅	NOUN
ejpam-5658	75	2	,	,	PUNCT
ejpam-5658	75	3	then	then	ADV
ejpam-5658	75	4	s	s	VERB
ejpam-5658	75	5	⊆	⊆	NUM
ejpam-5658	75	6	v	v	NOUN
ejpam-5658	75	7	(	(	PUNCT
ejpam-5658	75	8	g1	g1	PROPN
ejpam-5658	75	9	)	)	PUNCT
ejpam-5658	75	10	.	.	PUNCT
ejpam-5658	76	1	since	since	SCONJ
ejpam-5658	76	2	s	s	PROPN
ejpam-5658	76	3	is	be	AUX
ejpam-5658	76	4	hop	hop	NOUN
ejpam-5658	76	5	independent	independent	ADJ
ejpam-5658	76	6	in	in	ADP
ejpam-5658	76	7	d2(g	d2(g	PROPN
ejpam-5658	76	8	)	)	PUNCT
ejpam-5658	76	9	,	,	PUNCT
ejpam-5658	76	10	it	it	PRON
ejpam-5658	76	11	follows	follow	VERB
ejpam-5658	76	12	that	that	SCONJ
ejpam-5658	76	13	s	s	VERB
ejpam-5658	76	14	is	be	AUX
ejpam-5658	76	15	hop	hop	ADV
ejpam-5658	76	16	independent	independent	ADJ
ejpam-5658	76	17	in	in	ADP
ejpam-5658	76	18	g1	g1	PROPN
ejpam-5658	76	19	.	.	PUNCT
ejpam-5658	77	1	this	this	PRON
ejpam-5658	77	2	shows	show	VERB
ejpam-5658	77	3	that	that	SCONJ
ejpam-5658	77	4	(	(	PUNCT
ejpam-5658	77	5	i	i	NOUN
ejpam-5658	77	6	)	)	PUNCT
ejpam-5658	77	7	holds	hold	VERB
ejpam-5658	77	8	.	.	PUNCT
ejpam-5658	78	1	similarly	similarly	ADV
ejpam-5658	78	2	,	,	PUNCT
ejpam-5658	78	3	(	(	PUNCT
ejpam-5658	78	4	ii	ii	NOUN
ejpam-5658	78	5	)	)	PUNCT
ejpam-5658	78	6	holds	hold	VERB
ejpam-5658	78	7	if	if	SCONJ
ejpam-5658	78	8	s	s	ADP
ejpam-5658	78	9	∩	∩	ADJ
ejpam-5658	78	10	v	v	X
ejpam-5658	78	11	(	(	PUNCT
ejpam-5658	78	12	g1	g1	PROPN
ejpam-5658	78	13	)	)	PUNCT
ejpam-5658	78	14	=	=	PUNCT
ejpam-5658	78	15	∅.	∅.	ADP
ejpam-5658	78	16	next	next	ADV
ejpam-5658	78	17	,	,	PUNCT
ejpam-5658	78	18	suppose	suppose	VERB
ejpam-5658	78	19	that	that	SCONJ
ejpam-5658	78	20	s	s	VERB
ejpam-5658	78	21	∩	∩	ADJ
ejpam-5658	78	22	v	v	NOUN
ejpam-5658	78	23	(	(	PUNCT
ejpam-5658	78	24	g1	g1	PROPN
ejpam-5658	78	25	)	)	PUNCT
ejpam-5658	78	26	̸=	̸=	PROPN
ejpam-5658	78	27	∅	∅	NOUN
ejpam-5658	78	28	and	and	CCONJ
ejpam-5658	78	29	s	s	VERB
ejpam-5658	78	30	∩	∩	ADJ
ejpam-5658	78	31	v	v	X
ejpam-5658	78	32	(	(	PUNCT
ejpam-5658	78	33	g2	g2	PROPN
ejpam-5658	78	34	)	)	PUNCT
ejpam-5658	78	35	̸=	̸=	PROPN
ejpam-5658	78	36	∅.	∅.	ADV
ejpam-5658	78	37	let	let	VERB
ejpam-5658	78	38	i1	i1	PROPN
ejpam-5658	78	39	=	=	PROPN
ejpam-5658	78	40	i(g1	i(g1	PROPN
ejpam-5658	78	41	)	)	PUNCT
ejpam-5658	78	42	∩	∩	PROPN
ejpam-5658	78	43	s	s	SYM
ejpam-5658	78	44	,	,	PUNCT
ejpam-5658	78	45	i2	i2	NOUN
ejpam-5658	78	46	=	=	PUNCT
ejpam-5658	78	47	i(g2	i(g2	NOUN
ejpam-5658	78	48	)	)	PUNCT
ejpam-5658	78	49	∩	∩	NOUN
ejpam-5658	78	50	s	s	NOUN
ejpam-5658	78	51	,	,	PUNCT
ejpam-5658	78	52	sg1	sg1	NOUN
ejpam-5658	78	53	=	=	SYM
ejpam-5658	78	54	s	s	NOUN
ejpam-5658	78	55	∩	∩	X
ejpam-5658	78	56	(	(	PUNCT
ejpam-5658	78	57	v	v	NOUN
ejpam-5658	78	58	(	(	PUNCT
ejpam-5658	78	59	g1	g1	PROPN
ejpam-5658	78	60	)	)	PUNCT
ejpam-5658	78	61	\	\	PROPN
ejpam-5658	78	62	i1	i1	PROPN
ejpam-5658	78	63	)	)	PUNCT
ejpam-5658	78	64	,	,	PUNCT
ejpam-5658	78	65	and	and	CCONJ
ejpam-5658	78	66	sg2	sg2	PROPN
ejpam-5658	78	67	=	=	PROPN
ejpam-5658	78	68	s	s	PROPN
ejpam-5658	78	69	∩	∩	NOUN
ejpam-5658	78	70	(	(	PUNCT
ejpam-5658	78	71	v	v	X
ejpam-5658	78	72	(	(	PUNCT
ejpam-5658	78	73	g2	g2	PROPN
ejpam-5658	78	74	)	)	PUNCT
ejpam-5658	78	75	\	\	PROPN
ejpam-5658	78	76	i2	i2	PROPN
ejpam-5658	78	77	)	)	PUNCT
ejpam-5658	78	78	.	.	PUNCT
ejpam-5658	79	1	then	then	ADV
ejpam-5658	79	2	s	s	VERB
ejpam-5658	79	3	=	=	PUNCT
ejpam-5658	79	4	sg1	sg1	PROPN
ejpam-5658	79	5	∪	∪	ADP
ejpam-5658	79	6	sg2	sg2	PROPN
ejpam-5658	79	7	∪	∪	PROPN
ejpam-5658	79	8	i1	i1	PROPN
ejpam-5658	79	9	∪	∪	PROPN
ejpam-5658	79	10	i2	i2	PROPN
ejpam-5658	79	11	.	.	PUNCT
ejpam-5658	80	1	clearly	clearly	ADV
ejpam-5658	80	2	,	,	PUNCT
ejpam-5658	80	3	(	(	PUNCT
ejpam-5658	80	4	a	a	PRON
ejpam-5658	80	5	)	)	PUNCT
ejpam-5658	80	6	holds	hold	NOUN
ejpam-5658	80	7	.	.	PUNCT
ejpam-5658	81	1	since	since	SCONJ
ejpam-5658	81	2	s	s	PROPN
ejpam-5658	81	3	is	be	AUX
ejpam-5658	81	4	a	a	DET
ejpam-5658	81	5	hop	hop	NOUN
ejpam-5658	81	6	independent	independent	ADJ
ejpam-5658	81	7	set	set	NOUN
ejpam-5658	81	8	in	in	ADP
ejpam-5658	81	9	d2(g	d2(g	PROPN
ejpam-5658	81	10	)	)	PUNCT
ejpam-5658	81	11	,	,	PUNCT
ejpam-5658	81	12	property	property	NOUN
ejpam-5658	81	13	(	(	PUNCT
ejpam-5658	81	14	b	b	NOUN
ejpam-5658	81	15	)	)	PUNCT
ejpam-5658	81	16	also	also	ADV
ejpam-5658	81	17	holds	hold	VERB
ejpam-5658	81	18	.	.	PUNCT
ejpam-5658	82	1	now	now	ADV
ejpam-5658	82	2	,	,	PUNCT
ejpam-5658	82	3	if	if	SCONJ
ejpam-5658	82	4	sg1	sg1	NOUN
ejpam-5658	82	5	=	=	SYM
ejpam-5658	82	6	∅	∅	NOUN
ejpam-5658	82	7	or	or	CCONJ
ejpam-5658	82	8	sg2	sg2	PROPN
ejpam-5658	82	9	=	=	PUNCT
ejpam-5658	82	10	∅	∅	NOUN
ejpam-5658	82	11	,	,	PUNCT
ejpam-5658	82	12	then	then	ADV
ejpam-5658	82	13	(	(	PUNCT
ejpam-5658	82	14	c	c	NOUN
ejpam-5658	82	15	)	)	PUNCT
ejpam-5658	82	16	and	and	CCONJ
ejpam-5658	82	17	(	(	PUNCT
ejpam-5658	82	18	d	d	X
ejpam-5658	82	19	)	)	PUNCT
ejpam-5658	82	20	hold	hold	NOUN
ejpam-5658	82	21	.	.	PUNCT
ejpam-5658	83	1	so	so	ADV
ejpam-5658	83	2	suppose	suppose	VERB
ejpam-5658	83	3	sg1	sg1	NOUN
ejpam-5658	83	4	̸=	̸=	PROPN
ejpam-5658	83	5	∅	∅	NOUN
ejpam-5658	83	6	and	and	CCONJ
ejpam-5658	83	7	sg2	sg2	PROPN
ejpam-5658	83	8	̸=	̸=	PROPN
ejpam-5658	83	9	∅.	∅.	ADV
ejpam-5658	83	10	suppose	suppose	VERB
ejpam-5658	83	11	further	far	ADV
ejpam-5658	83	12	that	that	SCONJ
ejpam-5658	83	13	sg1	sg1	NOUN
ejpam-5658	83	14	∩	∩	NOUN
ejpam-5658	83	15	s′	s′	VERB
ejpam-5658	83	16	g2	g2	PROPN
ejpam-5658	83	17	̸=	̸=	PROPN
ejpam-5658	83	18	∅	∅	NOUN
ejpam-5658	83	19	,	,	PUNCT
ejpam-5658	83	20	say	say	VERB
ejpam-5658	83	21	v	v	NUM
ejpam-5658	83	22	∈	∈	PROPN
ejpam-5658	83	23	sg1	sg1	NOUN
ejpam-5658	83	24	∩	∩	NOUN
ejpam-5658	83	25	s′	s′	ADJ
ejpam-5658	83	26	g2	g2	PROPN
ejpam-5658	83	27	.	.	PUNCT
ejpam-5658	84	1	then	then	ADV
ejpam-5658	84	2	v	v	X
ejpam-5658	84	3	,	,	PUNCT
ejpam-5658	84	4	v′	v′	PROPN
ejpam-5658	84	5	∈	∈	PROPN
ejpam-5658	84	6	s.	s.	PROPN
ejpam-5658	84	7	since	since	SCONJ
ejpam-5658	84	8	v	v	PROPN
ejpam-5658	84	9	/∈	/∈	PUNCT
ejpam-5658	84	10	i(g1	i(g1	PROPN
ejpam-5658	84	11	)	)	PUNCT
ejpam-5658	84	12	,	,	PUNCT
ejpam-5658	84	13	there	there	PRON
ejpam-5658	84	14	exists	exist	VERB
ejpam-5658	84	15	w	w	PROPN
ejpam-5658	84	16	∈	∈	PROPN
ejpam-5658	84	17	ng1(v	ng1(v	PRON
ejpam-5658	84	18	)	)	PUNCT
ejpam-5658	84	19	.	.	PUNCT
ejpam-5658	85	1	it	it	PRON
ejpam-5658	85	2	follows	follow	VERB
ejpam-5658	85	3	that	that	SCONJ
ejpam-5658	85	4	dd2(g)(w	dd2(g)(w	NOUN
ejpam-5658	85	5	,	,	PUNCT
ejpam-5658	85	6	v	v	NOUN
ejpam-5658	85	7	′	′	NOUN
ejpam-5658	85	8	)	)	PUNCT
ejpam-5658	85	9	=	=	SYM
ejpam-5658	86	1	1	1	X
ejpam-5658	86	2	.	.	PUNCT
ejpam-5658	86	3	thus	thus	ADV
ejpam-5658	86	4	,	,	PUNCT
ejpam-5658	86	5	dd2(g)(v	dd2(g)(v	PROPN
ejpam-5658	86	6	,	,	PUNCT
ejpam-5658	86	7	v	v	NOUN
ejpam-5658	86	8	′	′	NOUN
ejpam-5658	86	9	)	)	PUNCT
ejpam-5658	86	10	=	=	SYM
ejpam-5658	86	11	2	2	NUM
ejpam-5658	86	12	,	,	PUNCT
ejpam-5658	86	13	contradicting	contradict	VERB
ejpam-5658	86	14	the	the	DET
ejpam-5658	86	15	assumption	assumption	NOUN
ejpam-5658	86	16	that	that	SCONJ
ejpam-5658	86	17	s	s	VERB
ejpam-5658	86	18	is	be	AUX
ejpam-5658	86	19	hop	hop	NOUN
ejpam-5658	86	20	independent	independent	ADJ
ejpam-5658	86	21	in	in	ADP
ejpam-5658	86	22	d2(g	d2(g	PROPN
ejpam-5658	86	23	)	)	PUNCT
ejpam-5658	86	24	.	.	PUNCT
ejpam-5658	87	1	therefore	therefore	ADV
ejpam-5658	87	2	,	,	PUNCT
ejpam-5658	87	3	sg1	sg1	PROPN
ejpam-5658	87	4	∩	∩	NOUN
ejpam-5658	87	5	s′	s′	VERB
ejpam-5658	87	6	g2	g2	PROPN
ejpam-5658	87	7	=	=	PUNCT
ejpam-5658	87	8	∅.	∅.	PRON
ejpam-5658	87	9	similarly	similarly	ADV
ejpam-5658	87	10	,	,	PUNCT
ejpam-5658	87	11	s′	s′	ADJ
ejpam-5658	87	12	g1	g1	PROPN
ejpam-5658	87	13	∩	∩	PROPN
ejpam-5658	87	14	sg2	sg2	PROPN
ejpam-5658	87	15	=	=	SYM
ejpam-5658	87	16	∅	∅	NOUN
ejpam-5658	87	17	,	,	PUNCT
ejpam-5658	87	18	showing	show	VERB
ejpam-5658	87	19	that	that	SCONJ
ejpam-5658	87	20	(	(	PUNCT
ejpam-5658	87	21	c	c	X
ejpam-5658	87	22	)	)	PUNCT
ejpam-5658	87	23	holds	hold	NOUN
ejpam-5658	87	24	.	.	PUNCT
ejpam-5658	88	1	finally	finally	ADV
ejpam-5658	88	2	,	,	PUNCT
ejpam-5658	88	3	suppose	suppose	VERB
ejpam-5658	88	4	that	that	SCONJ
ejpam-5658	88	5	sg1	sg1	PROPN
ejpam-5658	88	6	∪	∪	ADP
ejpam-5658	88	7	s′	s′	ADJ
ejpam-5658	88	8	g2	g2	PROPN
ejpam-5658	88	9	is	be	AUX
ejpam-5658	88	10	not	not	PART
ejpam-5658	88	11	hop	hop	ADV
ejpam-5658	88	12	independent	independent	ADJ
ejpam-5658	88	13	in	in	ADP
ejpam-5658	88	14	g1	g1	PROPN
ejpam-5658	88	15	.	.	PUNCT
ejpam-5658	89	1	since	since	SCONJ
ejpam-5658	89	2	sg1	sg1	PROPN
ejpam-5658	89	3	and	and	CCONJ
ejpam-5658	89	4	sg2	sg2	PROPN
ejpam-5658	89	5	are	be	AUX
ejpam-5658	89	6	hop	hop	ADV
ejpam-5658	89	7	independent	independent	ADJ
ejpam-5658	89	8	in	in	ADP
ejpam-5658	89	9	g1	g1	PROPN
ejpam-5658	89	10	and	and	CCONJ
ejpam-5658	89	11	g2	g2	PROPN
ejpam-5658	89	12	,	,	PUNCT
ejpam-5658	89	13	respectively	respectively	ADV
ejpam-5658	89	14	,	,	PUNCT
ejpam-5658	89	15	according	accord	VERB
ejpam-5658	89	16	to	to	ADP
ejpam-5658	89	17	(	(	PUNCT
ejpam-5658	89	18	b	b	NOUN
ejpam-5658	89	19	)	)	PUNCT
ejpam-5658	89	20	,	,	PUNCT
ejpam-5658	89	21	there	there	PRON
ejpam-5658	89	22	exist	exist	VERB
ejpam-5658	89	23	x	x	SYM
ejpam-5658	89	24	∈	∈	NOUN
ejpam-5658	89	25	sg1	sg1	NOUN
ejpam-5658	89	26	and	and	CCONJ
ejpam-5658	89	27	y	y	PROPN
ejpam-5658	89	28	∈	∈	PROPN
ejpam-5658	89	29	s′	s′	PUNCT
ejpam-5658	89	30	g2	g2	PROPN
ejpam-5658	89	31	such	such	ADJ
ejpam-5658	89	32	that	that	DET
ejpam-5658	89	33	dd2(g)(x	dd2(g)(x	NOUN
ejpam-5658	89	34	,	,	PUNCT
ejpam-5658	89	35	y	y	NOUN
ejpam-5658	89	36	)	)	PUNCT
ejpam-5658	89	37	=	=	SYM
ejpam-5658	90	1	2	2	X
ejpam-5658	90	2	.	.	X
ejpam-5658	91	1	this	this	PRON
ejpam-5658	91	2	,	,	PUNCT
ejpam-5658	91	3	however	however	ADV
ejpam-5658	91	4	,	,	PUNCT
ejpam-5658	91	5	would	would	AUX
ejpam-5658	91	6	imply	imply	VERB
ejpam-5658	91	7	that	that	DET
ejpam-5658	91	8	dd2(g)(x	dd2(g)(x	NOUN
ejpam-5658	91	9	,	,	PUNCT
ejpam-5658	91	10	y	y	PROPN
ejpam-5658	91	11	′	′	NOUN
ejpam-5658	91	12	)	)	PUNCT
ejpam-5658	92	1	=	=	SYM
ejpam-5658	92	2	2	2	NUM
ejpam-5658	92	3	,	,	PUNCT
ejpam-5658	92	4	contradicting	contradict	VERB
ejpam-5658	92	5	the	the	DET
ejpam-5658	92	6	fact	fact	NOUN
ejpam-5658	92	7	that	that	SCONJ
ejpam-5658	92	8	y′	y′	NOUN
ejpam-5658	92	9	∈	∈	PROPN
ejpam-5658	92	10	sg2	sg2	PROPN
ejpam-5658	92	11	and	and	CCONJ
ejpam-5658	92	12	s	s	PROPN
ejpam-5658	92	13	is	be	AUX
ejpam-5658	92	14	a	a	DET
ejpam-5658	92	15	hop	hop	NOUN
ejpam-5658	92	16	independent	independent	ADJ
ejpam-5658	92	17	set	set	NOUN
ejpam-5658	92	18	in	in	ADP
ejpam-5658	92	19	d2(g	d2(g	PROPN
ejpam-5658	92	20	)	)	PUNCT
ejpam-5658	92	21	.	.	PUNCT
ejpam-5658	93	1	hence	hence	ADV
ejpam-5658	93	2	,	,	PUNCT
ejpam-5658	93	3	sg1	sg1	PROPN
ejpam-5658	93	4	∪	∪	ADP
ejpam-5658	93	5	s′	s′	ADJ
ejpam-5658	93	6	g2	g2	PROPN
ejpam-5658	93	7	is	be	AUX
ejpam-5658	93	8	hop	hop	ADV
ejpam-5658	93	9	independent	independent	ADJ
ejpam-5658	93	10	in	in	ADP
ejpam-5658	93	11	g1	g1	PROPN
ejpam-5658	93	12	.	.	PUNCT
ejpam-5658	94	1	similarly	similarly	ADV
ejpam-5658	94	2	,	,	PUNCT
ejpam-5658	94	3	s′	s′	ADJ
ejpam-5658	94	4	g1	g1	PROPN
ejpam-5658	94	5	∪	∪	ADP
ejpam-5658	94	6	sg2	sg2	PROPN
ejpam-5658	94	7	is	be	AUX
ejpam-5658	94	8	hop	hop	ADV
ejpam-5658	94	9	independent	independent	ADJ
ejpam-5658	94	10	in	in	ADP
ejpam-5658	94	11	g2	g2	PROPN
ejpam-5658	94	12	.	.	PUNCT
ejpam-5658	95	1	this	this	PRON
ejpam-5658	95	2	shows	show	VERB
ejpam-5658	95	3	that	that	SCONJ
ejpam-5658	95	4	(	(	PUNCT
ejpam-5658	95	5	d	d	X
ejpam-5658	95	6	)	)	PUNCT
ejpam-5658	95	7	holds	hold	VERB
ejpam-5658	95	8	.	.	PUNCT
ejpam-5658	96	1	conversely	conversely	ADV
ejpam-5658	96	2	,	,	PUNCT
ejpam-5658	96	3	if	if	SCONJ
ejpam-5658	96	4	(	(	PUNCT
ejpam-5658	96	5	i	i	NOUN
ejpam-5658	96	6	)	)	PUNCT
ejpam-5658	96	7	or	or	CCONJ
ejpam-5658	96	8	(	(	PUNCT
ejpam-5658	96	9	ii	ii	NOUN
ejpam-5658	96	10	)	)	PUNCT
ejpam-5658	96	11	holds	hold	VERB
ejpam-5658	96	12	,	,	PUNCT
ejpam-5658	96	13	then	then	ADV
ejpam-5658	96	14	s	s	VERB
ejpam-5658	96	15	is	be	AUX
ejpam-5658	96	16	a	a	DET
ejpam-5658	96	17	hop	hop	NOUN
ejpam-5658	96	18	independent	independent	ADJ
ejpam-5658	96	19	set	set	NOUN
ejpam-5658	96	20	in	in	ADP
ejpam-5658	96	21	d2(g	d2(g	PROPN
ejpam-5658	96	22	)	)	PUNCT
ejpam-5658	96	23	.	.	PUNCT
ejpam-5658	97	1	suppose	suppose	VERB
ejpam-5658	97	2	now	now	ADV
ejpam-5658	97	3	that	that	SCONJ
ejpam-5658	97	4	(	(	PUNCT
ejpam-5658	97	5	iii	iii	NOUN
ejpam-5658	97	6	)	)	PUNCT
ejpam-5658	97	7	holds	hold	VERB
ejpam-5658	97	8	.	.	PUNCT
ejpam-5658	98	1	since	since	SCONJ
ejpam-5658	98	2	(	(	PUNCT
ejpam-5658	98	3	b	b	NOUN
ejpam-5658	98	4	)	)	PUNCT
ejpam-5658	98	5	holds	hold	NOUN
ejpam-5658	98	6	,	,	PUNCT
ejpam-5658	98	7	sg1	sg1	NOUN
ejpam-5658	98	8	∪	∪	PROPN
ejpam-5658	98	9	i1	i1	PROPN
ejpam-5658	98	10	and	and	CCONJ
ejpam-5658	98	11	sg2	sg2	PROPN
ejpam-5658	98	12	∪	∪	PROPN
ejpam-5658	98	13	i2	i2	PROPN
ejpam-5658	98	14	are	be	AUX
ejpam-5658	98	15	hop	hop	ADV
ejpam-5658	98	16	independent	independent	ADJ
ejpam-5658	98	17	sets	set	NOUN
ejpam-5658	98	18	in	in	ADP
ejpam-5658	98	19	g1	g1	PROPN
ejpam-5658	98	20	and	and	CCONJ
ejpam-5658	98	21	g2	g2	PROPN
ejpam-5658	98	22	,	,	PUNCT
ejpam-5658	98	23	respectively	respectively	ADV
ejpam-5658	98	24	(	(	PUNCT
ejpam-5658	98	25	and	and	CCONJ
ejpam-5658	98	26	hence	hence	ADV
ejpam-5658	98	27	,	,	PUNCT
ejpam-5658	98	28	in	in	ADP
ejpam-5658	98	29	d2(g	d2(g	PROPN
ejpam-5658	98	30	)	)	PUNCT
ejpam-5658	98	31	)	)	PUNCT
ejpam-5658	98	32	.	.	PUNCT
ejpam-5658	99	1	let	let	VERB
ejpam-5658	99	2	x	x	PUNCT
ejpam-5658	99	3	∈	∈	NOUN
ejpam-5658	99	4	sg1	sg1	NOUN
ejpam-5658	99	5	and	and	CCONJ
ejpam-5658	99	6	y′	y′	NOUN
ejpam-5658	99	7	∈	∈	PROPN
ejpam-5658	99	8	sg2	sg2	PROPN
ejpam-5658	99	9	.	.	PUNCT
ejpam-5658	100	1	then	then	ADV
ejpam-5658	100	2	y	y	PROPN
ejpam-5658	100	3	∈	∈	PROPN
ejpam-5658	100	4	s′	s′	VERB
ejpam-5658	100	5	g2	g2	PROPN
ejpam-5658	100	6	and	and	CCONJ
ejpam-5658	100	7	by	by	ADP
ejpam-5658	100	8	(	(	PUNCT
ejpam-5658	100	9	c	c	NOUN
ejpam-5658	100	10	)	)	PUNCT
ejpam-5658	100	11	,	,	PUNCT
ejpam-5658	100	12	x	x	X
ejpam-5658	100	13	̸=	̸=	PROPN
ejpam-5658	100	14	y.	y.	NOUN
ejpam-5658	100	15	by	by	ADP
ejpam-5658	100	16	property	property	NOUN
ejpam-5658	100	17	(	(	PUNCT
ejpam-5658	100	18	d	d	NOUN
ejpam-5658	100	19	)	)	PUNCT
ejpam-5658	100	20	,	,	PUNCT
ejpam-5658	100	21	dd2(g)(x	dd2(g)(x	PROPN
ejpam-5658	100	22	,	,	PUNCT
ejpam-5658	100	23	y	y	PROPN
ejpam-5658	100	24	′	′	NUM
ejpam-5658	100	25	)	)	PUNCT
ejpam-5658	101	1	=	=	SYM
ejpam-5658	101	2	dd2(g)(x	dd2(g)(x	PROPN
ejpam-5658	101	3	,	,	PUNCT
ejpam-5658	101	4	y	y	NOUN
ejpam-5658	101	5	)	)	PUNCT
ejpam-5658	101	6	̸=	̸=	PROPN
ejpam-5658	101	7	2	2	NUM
ejpam-5658	101	8	.	.	PUNCT
ejpam-5658	102	1	therefore	therefore	ADV
ejpam-5658	102	2	,	,	PUNCT
ejpam-5658	102	3	s	s	VERB
ejpam-5658	102	4	is	be	AUX
ejpam-5658	102	5	a	a	DET
ejpam-5658	102	6	hop	hop	NOUN
ejpam-5658	102	7	independent	independent	ADJ
ejpam-5658	102	8	set	set	NOUN
ejpam-5658	102	9	in	in	ADP
ejpam-5658	102	10	d2(g	d2(g	PROPN
ejpam-5658	102	11	)	)	PUNCT
ejpam-5658	102	12	.	.	PUNCT
ejpam-5658	103	1	j.	j.	PROPN
ejpam-5658	103	2	anoche	anoche	PROPN
ejpam-5658	103	3	,	,	PUNCT
ejpam-5658	103	4	s.	s.	PROPN
ejpam-5658	103	5	canoy	canoy	PROPN
ejpam-5658	103	6	,	,	PUNCT
ejpam-5658	103	7	jr	jr	PROPN
ejpam-5658	103	8	.	.	PROPN
ejpam-5658	103	9	/	/	SYM
ejpam-5658	103	10	eur	eur	PROPN
ejpam-5658	103	11	.	.	PUNCT
ejpam-5658	104	1	j.	j.	PROPN
ejpam-5658	104	2	pure	pure	PROPN
ejpam-5658	104	3	appl	appl	PROPN
ejpam-5658	104	4	.	.	PROPN
ejpam-5658	104	5	math	math	PROPN
ejpam-5658	104	6	,	,	PUNCT
ejpam-5658	104	7	18	18	NUM
ejpam-5658	104	8	(	(	PUNCT
ejpam-5658	104	9	1	1	NUM
ejpam-5658	104	10	)	)	PUNCT
ejpam-5658	104	11	(	(	PUNCT
ejpam-5658	104	12	2025	2025	NUM
ejpam-5658	104	13	)	)	PUNCT
ejpam-5658	104	14	,	,	PUNCT
ejpam-5658	104	15	5658	5658	NUM
ejpam-5658	104	16	5	5	NUM
ejpam-5658	104	17	of	of	ADP
ejpam-5658	104	18	15	15	NUM
ejpam-5658	104	19	corollary	corollary	ADJ
ejpam-5658	104	20	2	2	NUM
ejpam-5658	104	21	.	.	PUNCT
ejpam-5658	105	1	let	let	VERB
ejpam-5658	105	2	g	g	PRON
ejpam-5658	105	3	be	be	AUX
ejpam-5658	105	4	a	a	DET
ejpam-5658	105	5	graph	graph	NOUN
ejpam-5658	105	6	.	.	PUNCT
ejpam-5658	106	1	then	then	ADV
ejpam-5658	106	2	αh(d2(g	αh(d2(g	NOUN
ejpam-5658	106	3	)	)	PUNCT
ejpam-5658	106	4	)	)	PUNCT
ejpam-5658	107	1	=	=	NOUN
ejpam-5658	107	2	αh(g	αh(g	NOUN
ejpam-5658	107	3	)	)	PUNCT
ejpam-5658	107	4	+	+	CCONJ
ejpam-5658	108	1	|i(g)|	|i(g)|	NOUN
ejpam-5658	108	2	.	.	PUNCT
ejpam-5658	108	3	proof	proof	NOUN
ejpam-5658	108	4	.	.	PUNCT
ejpam-5658	109	1	if	if	SCONJ
ejpam-5658	109	2	g	g	PROPN
ejpam-5658	109	3	is	be	AUX
ejpam-5658	109	4	an	an	DET
ejpam-5658	109	5	empty	empty	ADJ
ejpam-5658	109	6	graph	graph	NOUN
ejpam-5658	109	7	,	,	PUNCT
ejpam-5658	109	8	then	then	ADV
ejpam-5658	109	9	d2(g	d2(g	NUM
ejpam-5658	109	10	)	)	PUNCT
ejpam-5658	109	11	is	be	AUX
ejpam-5658	109	12	an	an	DET
ejpam-5658	109	13	empty	empty	ADJ
ejpam-5658	109	14	graph	graph	NOUN
ejpam-5658	109	15	.	.	PUNCT
ejpam-5658	110	1	hence	hence	ADV
ejpam-5658	110	2	,	,	PUNCT
ejpam-5658	110	3	αh(g	αh(g	NOUN
ejpam-5658	110	4	)	)	PUNCT
ejpam-5658	110	5	=	=	SYM
ejpam-5658	110	6	|i(d2(g))|	|i(d2(g))|	X
ejpam-5658	110	7	=	=	SYM
ejpam-5658	110	8	|i(g1)|+	|i(g1)|+	NOUN
ejpam-5658	110	9	|i(g2)|	|i(g2)|	PROPN
ejpam-5658	110	10	=	=	PRON
ejpam-5658	110	11	αh(g	αh(g	NOUN
ejpam-5658	110	12	)	)	PUNCT
ejpam-5658	110	13	+	+	CCONJ
ejpam-5658	111	1	|i(g)|	|i(g)|	NOUN
ejpam-5658	111	2	.	.	PUNCT
ejpam-5658	111	3	suppose	suppose	VERB
ejpam-5658	111	4	that	that	SCONJ
ejpam-5658	111	5	g	g	PROPN
ejpam-5658	111	6	has	have	VERB
ejpam-5658	111	7	an	an	DET
ejpam-5658	111	8	edge	edge	NOUN
ejpam-5658	111	9	.	.	PUNCT
ejpam-5658	112	1	let	let	VERB
ejpam-5658	112	2	s	s	PRON
ejpam-5658	112	3	be	be	AUX
ejpam-5658	112	4	an	an	DET
ejpam-5658	112	5	αh	αh	NOUN
ejpam-5658	112	6	-	-	PUNCT
ejpam-5658	112	7	set	set	VERB
ejpam-5658	112	8	in	in	ADP
ejpam-5658	112	9	g1	g1	PROPN
ejpam-5658	112	10	.	.	PUNCT
ejpam-5658	113	1	then	then	ADV
ejpam-5658	113	2	s∗	s∗	PROPN
ejpam-5658	113	3	=	=	SYM
ejpam-5658	113	4	s	s	PART
ejpam-5658	113	5	∪	∪	X
ejpam-5658	113	6	i(g2	i(g2	NOUN
ejpam-5658	113	7	)	)	PUNCT
ejpam-5658	113	8	is	be	AUX
ejpam-5658	113	9	a	a	DET
ejpam-5658	113	10	hop	hop	NOUN
ejpam-5658	113	11	independent	independent	ADJ
ejpam-5658	113	12	set	set	NOUN
ejpam-5658	113	13	in	in	ADP
ejpam-5658	113	14	d2(g	d2(g	PROPN
ejpam-5658	113	15	)	)	PUNCT
ejpam-5658	113	16	.	.	PUNCT
ejpam-5658	114	1	this	this	PRON
ejpam-5658	114	2	implies	imply	VERB
ejpam-5658	114	3	that	that	SCONJ
ejpam-5658	114	4	αh(g	αh(g	NOUN
ejpam-5658	114	5	)	)	PUNCT
ejpam-5658	114	6	≥	≥	NOUN
ejpam-5658	114	7	|s∗|	|s∗|	NUM
ejpam-5658	114	8	=	=	NOUN
ejpam-5658	114	9	αh(g	αh(g	NOUN
ejpam-5658	114	10	)	)	PUNCT
ejpam-5658	115	1	+	+	CCONJ
ejpam-5658	116	1	|i(g)|	|i(g)|	NOUN
ejpam-5658	116	2	.	.	PUNCT
ejpam-5658	117	1	next	next	ADV
ejpam-5658	117	2	,	,	PUNCT
ejpam-5658	117	3	suppose	suppose	VERB
ejpam-5658	117	4	that	that	SCONJ
ejpam-5658	117	5	q	q	NOUN
ejpam-5658	117	6	is	be	AUX
ejpam-5658	117	7	αh	αh	ADV
ejpam-5658	117	8	-	-	PUNCT
ejpam-5658	117	9	set	set	VERB
ejpam-5658	117	10	in	in	ADP
ejpam-5658	117	11	d2(g	d2(g	PROPN
ejpam-5658	117	12	)	)	PUNCT
ejpam-5658	117	13	.	.	PUNCT
ejpam-5658	118	1	then	then	ADV
ejpam-5658	118	2	i(d2(g	i(d2(g	NOUN
ejpam-5658	118	3	)	)	PUNCT
ejpam-5658	118	4	)	)	PUNCT
ejpam-5658	119	1	=	=	SYM
ejpam-5658	119	2	i(g1)∪i(g2	i(g1)∪i(g2	PROPN
ejpam-5658	119	3	)	)	PUNCT
ejpam-5658	119	4	⊂	⊂	PROPN
ejpam-5658	119	5	q.	q.	PROPN
ejpam-5658	119	6	let	let	VERB
ejpam-5658	119	7	qg1	qg1	ADV
ejpam-5658	119	8	=	=	PUNCT
ejpam-5658	119	9	(	(	PUNCT
ejpam-5658	119	10	q∩	q∩	NOUN
ejpam-5658	119	11	v	v	NOUN
ejpam-5658	119	12	(	(	PUNCT
ejpam-5658	119	13	g1))\i(g1	g1))\i(g1	PROPN
ejpam-5658	119	14	)	)	PUNCT
ejpam-5658	119	15	and	and	CCONJ
ejpam-5658	119	16	qg2	qg2	NOUN
ejpam-5658	120	1	=	=	SYM
ejpam-5658	120	2	(	(	PUNCT
ejpam-5658	120	3	q∩v	q∩v	X
ejpam-5658	120	4	(	(	PUNCT
ejpam-5658	120	5	g2))\i(g2	g2))\i(g2	PROPN
ejpam-5658	120	6	)	)	PUNCT
ejpam-5658	120	7	.	.	PUNCT
ejpam-5658	121	1	then	then	ADV
ejpam-5658	121	2	q	q	X
ejpam-5658	121	3	=	=	SYM
ejpam-5658	121	4	qg1∪qg2∪i(g1)∪i(g2	qg1∪qg2∪i(g1)∪i(g2	PROPN
ejpam-5658	121	5	)	)	PUNCT
ejpam-5658	121	6	.	.	PUNCT
ejpam-5658	122	1	from	from	ADP
ejpam-5658	122	2	property	property	NOUN
ejpam-5658	122	3	(	(	PUNCT
ejpam-5658	122	4	d	d	NOUN
ejpam-5658	122	5	)	)	PUNCT
ejpam-5658	122	6	,	,	PUNCT
ejpam-5658	122	7	qg1	qg1	ADV
ejpam-5658	122	8	∪q′	∪q′	PRON
ejpam-5658	122	9	g2	g2	PROPN
ejpam-5658	122	10	is	be	AUX
ejpam-5658	122	11	a	a	DET
ejpam-5658	122	12	hop	hop	NOUN
ejpam-5658	122	13	independent	independent	ADJ
ejpam-5658	122	14	set	set	NOUN
ejpam-5658	122	15	in	in	ADP
ejpam-5658	122	16	g1	g1	PROPN
ejpam-5658	122	17	.	.	PUNCT
ejpam-5658	123	1	it	it	PRON
ejpam-5658	123	2	follows	follow	VERB
ejpam-5658	123	3	that	that	SCONJ
ejpam-5658	123	4	qg1	qg1	ADV
ejpam-5658	123	5	∪q′	∪q′	NUM
ejpam-5658	123	6	g2	g2	PROPN
ejpam-5658	123	7	∪i(g1	∪i(g1	PROPN
ejpam-5658	123	8	)	)	PUNCT
ejpam-5658	123	9	is	be	AUX
ejpam-5658	123	10	a	a	DET
ejpam-5658	123	11	hop	hop	NOUN
ejpam-5658	123	12	independent	independent	ADJ
ejpam-5658	123	13	set	set	NOUN
ejpam-5658	123	14	in	in	ADP
ejpam-5658	123	15	g1	g1	PROPN
ejpam-5658	123	16	.	.	PUNCT
ejpam-5658	124	1	thus	thus	ADV
ejpam-5658	124	2	,	,	PUNCT
ejpam-5658	124	3	αh(d2(g	αh(d2(g	NOUN
ejpam-5658	124	4	)	)	PUNCT
ejpam-5658	124	5	)	)	PUNCT
ejpam-5658	125	1	=	=	SYM
ejpam-5658	125	2	|q|	|q|	VERB
ejpam-5658	125	3	=	=	SYM
ejpam-5658	125	4	|qg1	|qg1	ADP
ejpam-5658	125	5	∪qg2	∪qg2	PROPN
ejpam-5658	125	6	∪	∪	PROPN
ejpam-5658	125	7	i(g1	i(g1	NOUN
ejpam-5658	125	8	)	)	PUNCT
ejpam-5658	125	9	∪	∪	X
ejpam-5658	126	1	i(g2)|	i(g2)|	PROPN
ejpam-5658	126	2	=	=	SYM
ejpam-5658	126	3	|qg1	|qg1	ADP
ejpam-5658	126	4	∪qg2	∪qg2	PROPN
ejpam-5658	126	5	∪	∪	PROPN
ejpam-5658	126	6	i(g1)|+	i(g1)|+	NOUN
ejpam-5658	126	7	|i(g2)|	|i(g2)|	PROPN
ejpam-5658	126	8	=	=	SYM
ejpam-5658	126	9	|qg1	|qg1	ADP
ejpam-5658	126	10	∪q′	∪q′	VERB
ejpam-5658	126	11	g2	g2	PROPN
ejpam-5658	126	12	∪	∪	PROPN
ejpam-5658	126	13	i(g1)|+	i(g1)|+	PROPN
ejpam-5658	126	14	|i(g2)|	|i(g2)|	PROPN
ejpam-5658	126	15	≤	≤	NOUN
ejpam-5658	126	16	αh(g	αh(g	NOUN
ejpam-5658	126	17	)	)	PUNCT
ejpam-5658	126	18	+	+	CCONJ
ejpam-5658	127	1	|i(g)|	|i(g)|	NOUN
ejpam-5658	127	2	.	.	PUNCT
ejpam-5658	128	1	this	this	PRON
ejpam-5658	128	2	establishes	establish	VERB
ejpam-5658	128	3	the	the	DET
ejpam-5658	128	4	desired	desire	VERB
ejpam-5658	128	5	equality	equality	NOUN
ejpam-5658	128	6	.	.	PUNCT
ejpam-5658	129	1	5	5	X
ejpam-5658	129	2	.	.	X
ejpam-5658	129	3	edge	edge	NOUN
ejpam-5658	129	4	corona	corona	NOUN
ejpam-5658	129	5	of	of	ADP
ejpam-5658	129	6	two	two	NUM
ejpam-5658	129	7	graphs	graph	NOUN
ejpam-5658	129	8	for	for	ADP
ejpam-5658	129	9	every	every	DET
ejpam-5658	129	10	edge	edge	NOUN
ejpam-5658	129	11	e	e	NOUN
ejpam-5658	129	12	=	=	NOUN
ejpam-5658	129	13	uv	uv	NOUN
ejpam-5658	129	14	of	of	ADP
ejpam-5658	129	15	g	g	NOUN
ejpam-5658	129	16	,	,	PUNCT
ejpam-5658	129	17	denote	denote	VERB
ejpam-5658	129	18	by	by	ADP
ejpam-5658	129	19	he	he	PRON
ejpam-5658	129	20	=	=	PUNCT
ejpam-5658	129	21	huv	huv	PROPN
ejpam-5658	130	1	the	the	DET
ejpam-5658	130	2	copy	copy	NOUN
ejpam-5658	130	3	of	of	ADP
ejpam-5658	130	4	h	h	NOUN
ejpam-5658	130	5	where	where	SCONJ
ejpam-5658	130	6	the	the	DET
ejpam-5658	130	7	vertices	vertex	NOUN
ejpam-5658	130	8	are	be	AUX
ejpam-5658	130	9	joined	join	VERB
ejpam-5658	130	10	to	to	PART
ejpam-5658	130	11	vertices	vertice	VERB
ejpam-5658	130	12	u	u	PRON
ejpam-5658	130	13	and	and	CCONJ
ejpam-5658	130	14	v.	v.	ADP
ejpam-5658	130	15	theorem	theorem	ADJ
ejpam-5658	130	16	3	3	X
ejpam-5658	130	17	.	.	PUNCT
ejpam-5658	131	1	let	let	VERB
ejpam-5658	131	2	g	g	PRON
ejpam-5658	131	3	be	be	AUX
ejpam-5658	131	4	a	a	DET
ejpam-5658	131	5	non	non	ADJ
ejpam-5658	131	6	-	-	ADJ
ejpam-5658	131	7	trivial	trivial	ADJ
ejpam-5658	131	8	connected	connected	ADJ
ejpam-5658	131	9	graph	graph	NOUN
ejpam-5658	131	10	and	and	CCONJ
ejpam-5658	131	11	let	let	VERB
ejpam-5658	131	12	h	h	NOUN
ejpam-5658	131	13	be	be	AUX
ejpam-5658	131	14	any	any	DET
ejpam-5658	131	15	graph	graph	NOUN
ejpam-5658	131	16	.	.	PUNCT
ejpam-5658	132	1	then	then	ADV
ejpam-5658	132	2	s	s	VERB
ejpam-5658	132	3	is	be	AUX
ejpam-5658	132	4	a	a	DET
ejpam-5658	132	5	hop	hop	NOUN
ejpam-5658	132	6	independent	independent	ADJ
ejpam-5658	132	7	set	set	NOUN
ejpam-5658	132	8	in	in	ADP
ejpam-5658	132	9	g	g	PROPN
ejpam-5658	132	10	⋄	⋄	PROPN
ejpam-5658	132	11	h	h	NOUN
ejpam-5658	133	1	if	if	SCONJ
ejpam-5658	133	2	and	and	CCONJ
ejpam-5658	133	3	only	only	ADV
ejpam-5658	133	4	if	if	SCONJ
ejpam-5658	133	5	s	s	VERB
ejpam-5658	133	6	=	=	NOUN
ejpam-5658	133	7	a	a	DET
ejpam-5658	133	8	∪	∪	X
ejpam-5658	133	9	(	(	PUNCT
ejpam-5658	133	10	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-5658	133	11	)	)	PUNCT
ejpam-5658	133	12	and	and	CCONJ
ejpam-5658	133	13	satisfies	satisfy	VERB
ejpam-5658	133	14	the	the	DET
ejpam-5658	133	15	following	follow	VERB
ejpam-5658	133	16	conditions	condition	NOUN
ejpam-5658	133	17	:	:	PUNCT
ejpam-5658	133	18	(	(	PUNCT
ejpam-5658	133	19	i	i	NOUN
ejpam-5658	133	20	)	)	PUNCT
ejpam-5658	133	21	a	a	PRON
ejpam-5658	133	22	is	be	AUX
ejpam-5658	133	23	a	a	DET
ejpam-5658	133	24	hop	hop	NOUN
ejpam-5658	133	25	independent	independent	ADJ
ejpam-5658	133	26	set	set	NOUN
ejpam-5658	133	27	in	in	ADP
ejpam-5658	133	28	g.	g.	PROPN
ejpam-5658	133	29	(	(	PUNCT
ejpam-5658	133	30	ii	ii	PROPN
ejpam-5658	133	31	)	)	PUNCT
ejpam-5658	133	32	if	if	SCONJ
ejpam-5658	133	33	suv	suv	PROPN
ejpam-5658	133	34	̸=	̸=	PROPN
ejpam-5658	133	35	∅	∅	NOUN
ejpam-5658	133	36	,	,	PUNCT
ejpam-5658	133	37	then	then	ADV
ejpam-5658	133	38	suv	suv	PROPN
ejpam-5658	133	39	is	be	AUX
ejpam-5658	133	40	a	a	DET
ejpam-5658	133	41	clique	clique	NOUN
ejpam-5658	133	42	in	in	ADP
ejpam-5658	133	43	huv	huv	PROPN
ejpam-5658	133	44	.	.	PUNCT
ejpam-5658	134	1	(	(	PUNCT
ejpam-5658	134	2	iii	iii	X
ejpam-5658	134	3	)	)	PUNCT
ejpam-5658	134	4	suv	suv	NOUN
ejpam-5658	134	5	=	=	PUNCT
ejpam-5658	134	6	∅	∅	NOUN
ejpam-5658	134	7	whenever	whenever	SCONJ
ejpam-5658	134	8	any	any	PRON
ejpam-5658	134	9	of	of	ADP
ejpam-5658	134	10	the	the	DET
ejpam-5658	134	11	following	following	NOUN
ejpam-5658	134	12	holds	hold	VERB
ejpam-5658	134	13	:	:	PUNCT
ejpam-5658	134	14	(	(	PUNCT
ejpam-5658	134	15	a	a	X
ejpam-5658	134	16	)	)	PUNCT
ejpam-5658	134	17	{	{	PUNCT
ejpam-5658	134	18	u	u	NOUN
ejpam-5658	134	19	,	,	PUNCT
ejpam-5658	134	20	v	v	NOUN
ejpam-5658	134	21	}	}	PUNCT
ejpam-5658	134	22	∩ng(a	∩ng(a	NOUN
ejpam-5658	134	23	)	)	PUNCT
ejpam-5658	134	24	)	)	PUNCT
ejpam-5658	135	1	̸=	̸=	PROPN
ejpam-5658	135	2	∅	∅	NOUN
ejpam-5658	135	3	(	(	PUNCT
ejpam-5658	135	4	b	b	NOUN
ejpam-5658	135	5	)	)	PUNCT
ejpam-5658	135	6	suw	suw	NOUN
ejpam-5658	135	7	̸=	̸=	PROPN
ejpam-5658	135	8	∅	∅	NOUN
ejpam-5658	135	9	for	for	ADP
ejpam-5658	135	10	some	some	DET
ejpam-5658	135	11	w	w	PROPN
ejpam-5658	135	12	∈	∈	PROPN
ejpam-5658	135	13	ng(u	ng(u	NOUN
ejpam-5658	135	14	)	)	PUNCT
ejpam-5658	135	15	(	(	PUNCT
ejpam-5658	135	16	c	c	X
ejpam-5658	135	17	)	)	PUNCT
ejpam-5658	135	18	svz	svz	NOUN
ejpam-5658	135	19	̸=	̸=	PROPN
ejpam-5658	135	20	∅	∅	NOUN
ejpam-5658	135	21	for	for	ADP
ejpam-5658	135	22	some	some	DET
ejpam-5658	135	23	z	z	NOUN
ejpam-5658	135	24	∈	∈	PROPN
ejpam-5658	135	25	ng(v	ng(v	PUNCT
ejpam-5658	135	26	)	)	PUNCT
ejpam-5658	135	27	proof	proof	NOUN
ejpam-5658	135	28	.	.	PUNCT
ejpam-5658	136	1	suppose	suppose	VERB
ejpam-5658	136	2	s	s	PRON
ejpam-5658	136	3	is	be	AUX
ejpam-5658	136	4	a	a	DET
ejpam-5658	136	5	hop	hop	NOUN
ejpam-5658	136	6	independent	independent	ADJ
ejpam-5658	136	7	set	set	NOUN
ejpam-5658	136	8	in	in	ADP
ejpam-5658	136	9	g	g	PROPN
ejpam-5658	136	10	⋄	⋄	PROPN
ejpam-5658	136	11	h	h	NOUN
ejpam-5658	136	12	and	and	CCONJ
ejpam-5658	136	13	let	let	VERB
ejpam-5658	136	14	a	a	DET
ejpam-5658	136	15	=	=	X
ejpam-5658	136	16	s	s	NOUN
ejpam-5658	136	17	∩	∩	ADJ
ejpam-5658	136	18	v	v	X
ejpam-5658	136	19	(	(	PUNCT
ejpam-5658	136	20	g	g	NOUN
ejpam-5658	136	21	)	)	PUNCT
ejpam-5658	136	22	and	and	CCONJ
ejpam-5658	136	23	suv	suv	PROPN
ejpam-5658	136	24	=	=	PROPN
ejpam-5658	136	25	s	s	PROPN
ejpam-5658	136	26	∩	∩	ADJ
ejpam-5658	136	27	v	v	X
ejpam-5658	136	28	(	(	PUNCT
ejpam-5658	136	29	huv	huv	PROPN
ejpam-5658	136	30	)	)	PUNCT
ejpam-5658	136	31	for	for	ADP
ejpam-5658	136	32	each	each	DET
ejpam-5658	136	33	uv	uv	PROPN
ejpam-5658	136	34	∈	∈	PROPN
ejpam-5658	136	35	e(g	e(g	PROPN
ejpam-5658	136	36	)	)	PUNCT
ejpam-5658	136	37	.	.	PUNCT
ejpam-5658	137	1	then	then	ADV
ejpam-5658	137	2	s	s	VERB
ejpam-5658	137	3	=	=	PUNCT
ejpam-5658	137	4	a	a	DET
ejpam-5658	137	5	∪	∪	X
ejpam-5658	137	6	(	(	PUNCT
ejpam-5658	137	7	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-5658	137	8	)	)	PUNCT
ejpam-5658	137	9	.	.	PUNCT
ejpam-5658	138	1	since	since	SCONJ
ejpam-5658	138	2	s	s	PROPN
ejpam-5658	138	3	is	be	AUX
ejpam-5658	138	4	a	a	DET
ejpam-5658	138	5	hop	hop	NOUN
ejpam-5658	138	6	independent	independent	ADJ
ejpam-5658	138	7	set	set	NOUN
ejpam-5658	138	8	in	in	ADP
ejpam-5658	138	9	g	g	PROPN
ejpam-5658	138	10	⋄	⋄	PROPN
ejpam-5658	138	11	h	h	NOUN
ejpam-5658	138	12	,	,	PUNCT
ejpam-5658	138	13	a	a	PRON
ejpam-5658	138	14	is	be	AUX
ejpam-5658	138	15	a	a	DET
ejpam-5658	138	16	hop	hop	NOUN
ejpam-5658	138	17	independent	independent	ADJ
ejpam-5658	138	18	set	set	NOUN
ejpam-5658	138	19	in	in	ADP
ejpam-5658	138	20	g.	g.	PROPN
ejpam-5658	138	21	this	this	PRON
ejpam-5658	138	22	shows	show	VERB
ejpam-5658	138	23	that	that	SCONJ
ejpam-5658	138	24	(	(	PUNCT
ejpam-5658	138	25	i	i	NOUN
ejpam-5658	138	26	)	)	PUNCT
ejpam-5658	138	27	holds	hold	VERB
ejpam-5658	138	28	.	.	PUNCT
ejpam-5658	139	1	j.	j.	PROPN
ejpam-5658	139	2	anoche	anoche	PROPN
ejpam-5658	139	3	,	,	PUNCT
ejpam-5658	139	4	s.	s.	PROPN
ejpam-5658	139	5	canoy	canoy	PROPN
ejpam-5658	139	6	,	,	PUNCT
ejpam-5658	139	7	jr	jr	PROPN
ejpam-5658	139	8	.	.	PROPN
ejpam-5658	139	9	/	/	SYM
ejpam-5658	139	10	eur	eur	PROPN
ejpam-5658	139	11	.	.	PUNCT
ejpam-5658	140	1	j.	j.	PROPN
ejpam-5658	140	2	pure	pure	PROPN
ejpam-5658	140	3	appl	appl	PROPN
ejpam-5658	140	4	.	.	PROPN
ejpam-5658	140	5	math	math	PROPN
ejpam-5658	140	6	,	,	PUNCT
ejpam-5658	140	7	18	18	NUM
ejpam-5658	140	8	(	(	PUNCT
ejpam-5658	140	9	1	1	NUM
ejpam-5658	140	10	)	)	PUNCT
ejpam-5658	140	11	(	(	PUNCT
ejpam-5658	140	12	2025	2025	NUM
ejpam-5658	140	13	)	)	PUNCT
ejpam-5658	140	14	,	,	PUNCT
ejpam-5658	140	15	5658	5658	NUM
ejpam-5658	140	16	6	6	NUM
ejpam-5658	140	17	of	of	ADP
ejpam-5658	140	18	15	15	NUM
ejpam-5658	140	19	next	next	ADV
ejpam-5658	140	20	,	,	PUNCT
ejpam-5658	140	21	let	let	VERB
ejpam-5658	140	22	uv	uv	PRON
ejpam-5658	140	23	∈	∈	PROPN
ejpam-5658	140	24	e(g	e(g	PROPN
ejpam-5658	140	25	)	)	PUNCT
ejpam-5658	140	26	and	and	CCONJ
ejpam-5658	140	27	suv	suv	PROPN
ejpam-5658	140	28	̸=	̸=	PROPN
ejpam-5658	140	29	∅.	∅.	ADV
ejpam-5658	140	30	if	if	SCONJ
ejpam-5658	140	31	suv	suv	PROPN
ejpam-5658	140	32	is	be	AUX
ejpam-5658	140	33	not	not	PART
ejpam-5658	140	34	a	a	DET
ejpam-5658	140	35	clique	clique	NOUN
ejpam-5658	140	36	in	in	ADP
ejpam-5658	140	37	huv	huv	PROPN
ejpam-5658	140	38	,	,	PUNCT
ejpam-5658	140	39	then	then	ADV
ejpam-5658	140	40	there	there	PRON
ejpam-5658	140	41	exist	exist	VERB
ejpam-5658	140	42	p	p	PRON
ejpam-5658	140	43	,	,	PUNCT
ejpam-5658	140	44	q	q	PROPN
ejpam-5658	140	45	∈	∈	PROPN
ejpam-5658	140	46	suv	suv	NOUN
ejpam-5658	140	47	such	such	ADJ
ejpam-5658	140	48	that	that	PRON
ejpam-5658	140	49	dhuv(p	dhuv(p	PROPN
ejpam-5658	140	50	,	,	PUNCT
ejpam-5658	140	51	q	q	X
ejpam-5658	140	52	)	)	PUNCT
ejpam-5658	140	53	̸=	̸=	NOUN
ejpam-5658	140	54	1	1	NUM
ejpam-5658	140	55	.	.	PUNCT
ejpam-5658	141	1	it	it	PRON
ejpam-5658	141	2	follows	follow	VERB
ejpam-5658	141	3	that	that	SCONJ
ejpam-5658	141	4	dg⋄h(p	dg⋄h(p	NOUN
ejpam-5658	141	5	,	,	PUNCT
ejpam-5658	141	6	q	q	NOUN
ejpam-5658	141	7	)	)	PUNCT
ejpam-5658	141	8	=	=	SYM
ejpam-5658	141	9	2	2	NUM
ejpam-5658	141	10	,	,	PUNCT
ejpam-5658	141	11	contrary	contrary	ADV
ejpam-5658	141	12	to	to	ADP
ejpam-5658	141	13	the	the	DET
ejpam-5658	141	14	assumption	assumption	NOUN
ejpam-5658	141	15	that	that	SCONJ
ejpam-5658	141	16	s	s	VERB
ejpam-5658	141	17	is	be	AUX
ejpam-5658	141	18	hop	hop	NOUN
ejpam-5658	141	19	independent	independent	ADJ
ejpam-5658	141	20	in	in	ADP
ejpam-5658	141	21	g	g	PROPN
ejpam-5658	141	22	⋄	⋄	PROPN
ejpam-5658	141	23	h.	h.	PROPN
ejpam-5658	141	24	thus	thus	ADV
ejpam-5658	141	25	,	,	PUNCT
ejpam-5658	141	26	suv	suv	PROPN
ejpam-5658	141	27	is	be	AUX
ejpam-5658	141	28	a	a	DET
ejpam-5658	141	29	clique	clique	NOUN
ejpam-5658	141	30	in	in	ADP
ejpam-5658	141	31	huv	huv	PROPN
ejpam-5658	141	32	,	,	PUNCT
ejpam-5658	141	33	showing	show	VERB
ejpam-5658	141	34	that	that	SCONJ
ejpam-5658	141	35	(	(	PUNCT
ejpam-5658	141	36	ii	ii	NOUN
ejpam-5658	141	37	)	)	PUNCT
ejpam-5658	141	38	holds	hold	VERB
ejpam-5658	141	39	.	.	PUNCT
ejpam-5658	142	1	finally	finally	ADV
ejpam-5658	142	2	,	,	PUNCT
ejpam-5658	142	3	suppose	suppose	VERB
ejpam-5658	142	4	that	that	SCONJ
ejpam-5658	142	5	uv	uv	PROPN
ejpam-5658	142	6	∈	∈	PROPN
ejpam-5658	142	7	v	v	ADP
ejpam-5658	142	8	(	(	PUNCT
ejpam-5658	142	9	g	g	NOUN
ejpam-5658	142	10	)	)	PUNCT
ejpam-5658	142	11	.	.	PUNCT
ejpam-5658	143	1	since	since	SCONJ
ejpam-5658	143	2	s	s	PROPN
ejpam-5658	143	3	is	be	AUX
ejpam-5658	143	4	hop	hop	NOUN
ejpam-5658	143	5	independent	independent	ADJ
ejpam-5658	143	6	in	in	ADP
ejpam-5658	143	7	g⋄h	g⋄h	PROPN
ejpam-5658	143	8	,	,	PUNCT
ejpam-5658	143	9	suv	suv	NOUN
ejpam-5658	143	10	=	=	PUNCT
ejpam-5658	143	11	∅	∅	NOUN
ejpam-5658	143	12	whenever	whenever	SCONJ
ejpam-5658	143	13	(	(	PUNCT
ejpam-5658	143	14	a	a	X
ejpam-5658	143	15	)	)	PUNCT
ejpam-5658	143	16	or	or	CCONJ
ejpam-5658	143	17	(	(	PUNCT
ejpam-5658	143	18	b	b	NOUN
ejpam-5658	143	19	)	)	PUNCT
ejpam-5658	143	20	or	or	CCONJ
ejpam-5658	143	21	(	(	PUNCT
ejpam-5658	143	22	c	c	NOUN
ejpam-5658	143	23	)	)	PUNCT
ejpam-5658	143	24	holds	hold	NOUN
ejpam-5658	143	25	.	.	PUNCT
ejpam-5658	144	1	this	this	PRON
ejpam-5658	144	2	shows	show	VERB
ejpam-5658	144	3	that	that	SCONJ
ejpam-5658	144	4	(	(	PUNCT
ejpam-5658	144	5	iii	iii	NOUN
ejpam-5658	144	6	)	)	PUNCT
ejpam-5658	144	7	holds	hold	VERB
ejpam-5658	144	8	.	.	PUNCT
ejpam-5658	145	1	for	for	ADP
ejpam-5658	145	2	the	the	DET
ejpam-5658	145	3	converse	converse	NOUN
ejpam-5658	145	4	,	,	PUNCT
ejpam-5658	145	5	suppose	suppose	VERB
ejpam-5658	145	6	that	that	SCONJ
ejpam-5658	145	7	s	s	VERB
ejpam-5658	145	8	has	have	VERB
ejpam-5658	145	9	the	the	DET
ejpam-5658	145	10	given	give	VERB
ejpam-5658	145	11	form	form	NOUN
ejpam-5658	145	12	and	and	CCONJ
ejpam-5658	145	13	satisfies	satisfie	NOUN
ejpam-5658	145	14	(	(	PUNCT
ejpam-5658	145	15	i	i	NOUN
ejpam-5658	145	16	)	)	PUNCT
ejpam-5658	145	17	,	,	PUNCT
ejpam-5658	145	18	(	(	PUNCT
ejpam-5658	145	19	ii	ii	NOUN
ejpam-5658	145	20	)	)	PUNCT
ejpam-5658	145	21	,	,	PUNCT
ejpam-5658	145	22	and	and	CCONJ
ejpam-5658	145	23	(	(	PUNCT
ejpam-5658	145	24	iii	iii	NOUN
ejpam-5658	145	25	)	)	PUNCT
ejpam-5658	145	26	.	.	PUNCT
ejpam-5658	146	1	let	let	VERB
ejpam-5658	146	2	a	a	DET
ejpam-5658	146	3	,	,	PUNCT
ejpam-5658	146	4	b	b	PROPN
ejpam-5658	146	5	∈	∈	PROPN
ejpam-5658	146	6	s	s	NOUN
ejpam-5658	146	7	,	,	PUNCT
ejpam-5658	146	8	where	where	SCONJ
ejpam-5658	146	9	a	a	DET
ejpam-5658	146	10	̸=	̸=	PROPN
ejpam-5658	146	11	b	b	NUM
ejpam-5658	146	12	,	,	PUNCT
ejpam-5658	146	13	and	and	CCONJ
ejpam-5658	146	14	let	let	VERB
ejpam-5658	146	15	uv	uv	INTJ
ejpam-5658	146	16	,	,	PUNCT
ejpam-5658	146	17	xy	xy	PROPN
ejpam-5658	146	18	∈	∈	PROPN
ejpam-5658	146	19	e(g	e(g	PROPN
ejpam-5658	146	20	)	)	PUNCT
ejpam-5658	146	21	such	such	ADJ
ejpam-5658	146	22	that	that	SCONJ
ejpam-5658	146	23	a	a	DET
ejpam-5658	146	24	∈	∈	PROPN
ejpam-5658	146	25	v	v	NOUN
ejpam-5658	146	26	(	(	PUNCT
ejpam-5658	146	27	⟨{u	⟨{u	PROPN
ejpam-5658	146	28	,	,	PUNCT
ejpam-5658	146	29	v}⟩	v}⟩	PROPN
ejpam-5658	146	30	+	+	CCONJ
ejpam-5658	146	31	huv	huv	PROPN
ejpam-5658	146	32	)	)	PUNCT
ejpam-5658	146	33	and	and	CCONJ
ejpam-5658	146	34	b	b	X
ejpam-5658	146	35	∈	∈	PROPN
ejpam-5658	146	36	v	v	NOUN
ejpam-5658	146	37	(	(	PUNCT
ejpam-5658	146	38	⟨{x	⟨{x	PROPN
ejpam-5658	146	39	,	,	PUNCT
ejpam-5658	146	40	y}⟩+hxy	y}⟩+hxy	NOUN
ejpam-5658	146	41	)	)	PUNCT
ejpam-5658	146	42	.	.	PUNCT
ejpam-5658	147	1	if	if	SCONJ
ejpam-5658	147	2	a	a	PRON
ejpam-5658	147	3	,	,	PUNCT
ejpam-5658	147	4	b	b	PROPN
ejpam-5658	147	5	∈	∈	PROPN
ejpam-5658	147	6	a	a	DET
ejpam-5658	147	7	,	,	PUNCT
ejpam-5658	147	8	then	then	ADV
ejpam-5658	147	9	dg⋄h(a	dg⋄h(a	PROPN
ejpam-5658	147	10	,	,	PUNCT
ejpam-5658	147	11	b	b	NOUN
ejpam-5658	147	12	)	)	PUNCT
ejpam-5658	147	13	̸=	̸=	PROPN
ejpam-5658	147	14	2	2	NUM
ejpam-5658	147	15	because	because	SCONJ
ejpam-5658	147	16	of	of	ADP
ejpam-5658	147	17	(	(	PUNCT
ejpam-5658	147	18	i	i	NOUN
ejpam-5658	147	19	)	)	PUNCT
ejpam-5658	147	20	.	.	PUNCT
ejpam-5658	147	21	suppose	suppose	VERB
ejpam-5658	147	22	that	that	SCONJ
ejpam-5658	147	23	a	a	PRON
ejpam-5658	147	24	or	or	CCONJ
ejpam-5658	147	25	b	b	NOUN
ejpam-5658	147	26	is	be	AUX
ejpam-5658	147	27	not	not	PART
ejpam-5658	147	28	in	in	ADP
ejpam-5658	147	29	a.	a.	NOUN
ejpam-5658	147	30	consider	consider	VERB
ejpam-5658	147	31	the	the	DET
ejpam-5658	147	32	following	follow	VERB
ejpam-5658	147	33	cases	case	NOUN
ejpam-5658	147	34	:	:	PUNCT
ejpam-5658	147	35	case	case	NOUN
ejpam-5658	147	36	1	1	NUM
ejpam-5658	147	37	.	.	PUNCT
ejpam-5658	148	1	uv	uv	NOUN
ejpam-5658	148	2	̸=	̸=	PROPN
ejpam-5658	148	3	xy	xy	PROPN
ejpam-5658	148	4	.	.	PUNCT
ejpam-5658	149	1	suppose	suppose	VERB
ejpam-5658	149	2	first	first	ADV
ejpam-5658	149	3	that	that	SCONJ
ejpam-5658	149	4	uv	uv	NOUN
ejpam-5658	149	5	and	and	CCONJ
ejpam-5658	149	6	xy	xy	PROPN
ejpam-5658	149	7	have	have	VERB
ejpam-5658	149	8	a	a	DET
ejpam-5658	149	9	common	common	ADJ
ejpam-5658	149	10	vertex	vertex	NOUN
ejpam-5658	149	11	,	,	PUNCT
ejpam-5658	149	12	say	say	VERB
ejpam-5658	149	13	x	x	PUNCT
ejpam-5658	149	14	=	=	PUNCT
ejpam-5658	149	15	v.	v.	ADP
ejpam-5658	149	16	by	by	ADP
ejpam-5658	149	17	(	(	PUNCT
ejpam-5658	149	18	iii	iii	NOUN
ejpam-5658	149	19	)	)	PUNCT
ejpam-5658	149	20	,	,	PUNCT
ejpam-5658	149	21	suv	suv	PROPN
ejpam-5658	149	22	and	and	CCONJ
ejpam-5658	149	23	sxy	sxy	PROPN
ejpam-5658	149	24	can	can	AUX
ejpam-5658	149	25	not	not	PART
ejpam-5658	149	26	be	be	AUX
ejpam-5658	149	27	both	both	PRON
ejpam-5658	149	28	nonempty	nonempty	ADJ
ejpam-5658	149	29	.	.	PUNCT
ejpam-5658	150	1	assume	assume	VERB
ejpam-5658	150	2	that	that	SCONJ
ejpam-5658	150	3	sxy	sxy	PROPN
ejpam-5658	150	4	=	=	PUNCT
ejpam-5658	150	5	∅.	∅.	AUX
ejpam-5658	150	6	suppose	suppose	VERB
ejpam-5658	150	7	b	b	PROPN
ejpam-5658	150	8	=	=	SYM
ejpam-5658	150	9	y.	y.	PROPN
ejpam-5658	150	10	then	then	ADV
ejpam-5658	150	11	suv	suv	PROPN
ejpam-5658	150	12	=	=	NOUN
ejpam-5658	150	13	∅	∅	NOUN
ejpam-5658	150	14	by	by	ADP
ejpam-5658	150	15	(	(	PUNCT
ejpam-5658	150	16	iii	iii	NOUN
ejpam-5658	150	17	)	)	PUNCT
ejpam-5658	150	18	.	.	PUNCT
ejpam-5658	151	1	it	it	PRON
ejpam-5658	151	2	follows	follow	VERB
ejpam-5658	151	3	that	that	SCONJ
ejpam-5658	151	4	a	a	DET
ejpam-5658	151	5	∈	∈	PROPN
ejpam-5658	151	6	{	{	PUNCT
ejpam-5658	151	7	u	u	NOUN
ejpam-5658	151	8	,	,	PUNCT
ejpam-5658	151	9	v	v	NOUN
ejpam-5658	151	10	}	}	PUNCT
ejpam-5658	151	11	,	,	PUNCT
ejpam-5658	151	12	contrary	contrary	ADV
ejpam-5658	151	13	to	to	ADP
ejpam-5658	151	14	our	our	PRON
ejpam-5658	151	15	assumption	assumption	NOUN
ejpam-5658	151	16	that	that	SCONJ
ejpam-5658	151	17	a	a	PRON
ejpam-5658	151	18	or	or	CCONJ
ejpam-5658	151	19	b	b	NOUN
ejpam-5658	151	20	is	be	AUX
ejpam-5658	151	21	not	not	PART
ejpam-5658	151	22	in	in	ADP
ejpam-5658	151	23	a.	a.	NOUN
ejpam-5658	151	24	hence	hence	ADV
ejpam-5658	151	25	,	,	PUNCT
ejpam-5658	151	26	b	b	X
ejpam-5658	151	27	=	=	SYM
ejpam-5658	151	28	x	x	PROPN
ejpam-5658	151	29	,	,	PUNCT
ejpam-5658	151	30	a	a	DET
ejpam-5658	151	31	∈	∈	PROPN
ejpam-5658	151	32	suv	suv	NOUN
ejpam-5658	151	33	,	,	PUNCT
ejpam-5658	151	34	and	and	CCONJ
ejpam-5658	151	35	ab	ab	PROPN
ejpam-5658	151	36	∈	∈	PROPN
ejpam-5658	151	37	e(g	e(g	PROPN
ejpam-5658	151	38	⋄h	⋄h	PROPN
ejpam-5658	151	39	)	)	PUNCT
ejpam-5658	151	40	.	.	PUNCT
ejpam-5658	152	1	so	so	ADV
ejpam-5658	152	2	suppose	suppose	VERB
ejpam-5658	152	3	uv	uv	NOUN
ejpam-5658	152	4	and	and	CCONJ
ejpam-5658	152	5	xy	xy	PROPN
ejpam-5658	152	6	do	do	AUX
ejpam-5658	152	7	not	not	PART
ejpam-5658	152	8	have	have	VERB
ejpam-5658	152	9	a	a	DET
ejpam-5658	152	10	common	common	ADJ
ejpam-5658	152	11	vertex	vertex	NOUN
ejpam-5658	152	12	.	.	PUNCT
ejpam-5658	153	1	assume	assume	VERB
ejpam-5658	153	2	first	first	ADV
ejpam-5658	153	3	that	that	SCONJ
ejpam-5658	153	4	one	one	NUM
ejpam-5658	153	5	of	of	ADP
ejpam-5658	153	6	a	a	PRON
ejpam-5658	153	7	and	and	CCONJ
ejpam-5658	153	8	b	b	NOUN
ejpam-5658	153	9	is	be	AUX
ejpam-5658	153	10	in	in	ADP
ejpam-5658	153	11	a	a	PRON
ejpam-5658	153	12	,	,	PUNCT
ejpam-5658	153	13	say	say	VERB
ejpam-5658	153	14	a	a	DET
ejpam-5658	153	15	=	=	X
ejpam-5658	153	16	u	u	NOUN
ejpam-5658	153	17	∈	∈	PROPN
ejpam-5658	153	18	a.	a.	NOUN
ejpam-5658	153	19	then	then	ADV
ejpam-5658	153	20	b	b	PROPN
ejpam-5658	153	21	∈	∈	PROPN
ejpam-5658	153	22	sxy	sxy	PROPN
ejpam-5658	153	23	.	.	PUNCT
ejpam-5658	154	1	by	by	ADP
ejpam-5658	154	2	(	(	PUNCT
ejpam-5658	154	3	iii	iii	NOUN
ejpam-5658	154	4	)	)	PUNCT
ejpam-5658	154	5	,	,	PUNCT
ejpam-5658	154	6	x	x	X
ejpam-5658	154	7	,	,	PUNCT
ejpam-5658	154	8	y	y	PROPN
ejpam-5658	154	9	/∈	/∈	PUNCT
ejpam-5658	154	10	ng(a	ng(a	NUM
ejpam-5658	154	11	)	)	PUNCT
ejpam-5658	154	12	.	.	PUNCT
ejpam-5658	155	1	this	this	PRON
ejpam-5658	155	2	implies	imply	VERB
ejpam-5658	155	3	that	that	SCONJ
ejpam-5658	155	4	dg⋄h(a	dg⋄h(a	NOUN
ejpam-5658	155	5	,	,	PUNCT
ejpam-5658	155	6	b	b	NOUN
ejpam-5658	155	7	)	)	PUNCT
ejpam-5658	155	8	̸=	̸=	PROPN
ejpam-5658	155	9	2	2	NUM
ejpam-5658	155	10	.	.	PUNCT
ejpam-5658	156	1	next	next	ADV
ejpam-5658	156	2	,	,	PUNCT
ejpam-5658	156	3	suppose	suppose	VERB
ejpam-5658	156	4	that	that	SCONJ
ejpam-5658	156	5	a	a	DET
ejpam-5658	156	6	∈	∈	PROPN
ejpam-5658	156	7	suv	suv	NOUN
ejpam-5658	156	8	and	and	CCONJ
ejpam-5658	156	9	b	b	PROPN
ejpam-5658	156	10	∈	∈	PROPN
ejpam-5658	156	11	sxy	sxy	PROPN
ejpam-5658	156	12	.	.	PUNCT
ejpam-5658	157	1	since	since	SCONJ
ejpam-5658	157	2	uv	uv	NOUN
ejpam-5658	157	3	and	and	CCONJ
ejpam-5658	157	4	xy	xy	PROPN
ejpam-5658	157	5	do	do	AUX
ejpam-5658	157	6	not	not	PART
ejpam-5658	157	7	have	have	VERB
ejpam-5658	157	8	a	a	DET
ejpam-5658	157	9	common	common	ADJ
ejpam-5658	157	10	vertex	vertex	NOUN
ejpam-5658	157	11	,	,	PUNCT
ejpam-5658	157	12	dg⋄h(a	dg⋄h(a	NOUN
ejpam-5658	157	13	,	,	PUNCT
ejpam-5658	157	14	b	b	NOUN
ejpam-5658	157	15	)	)	PUNCT
ejpam-5658	157	16	̸=	̸=	PROPN
ejpam-5658	157	17	2	2	NUM
ejpam-5658	157	18	.	.	PUNCT
ejpam-5658	157	19	case	case	NOUN
ejpam-5658	157	20	2	2	NUM
ejpam-5658	157	21	.	.	PUNCT
ejpam-5658	158	1	uv	uv	NOUN
ejpam-5658	158	2	=	=	NOUN
ejpam-5658	159	1	xy	xy	PROPN
ejpam-5658	159	2	.	.	PUNCT
ejpam-5658	160	1	if	if	SCONJ
ejpam-5658	160	2	a	a	DET
ejpam-5658	160	3	∈	∈	PROPN
ejpam-5658	160	4	{	{	PUNCT
ejpam-5658	160	5	u	u	NOUN
ejpam-5658	160	6	,	,	PUNCT
ejpam-5658	160	7	v	v	NOUN
ejpam-5658	160	8	}	}	PUNCT
ejpam-5658	160	9	,	,	PUNCT
ejpam-5658	160	10	then	then	ADV
ejpam-5658	160	11	b	b	PROPN
ejpam-5658	160	12	∈	∈	PROPN
ejpam-5658	160	13	suv	suv	PROPN
ejpam-5658	160	14	and	and	CCONJ
ejpam-5658	160	15	dg⋄h(a	dg⋄h(a	PROPN
ejpam-5658	160	16	,	,	PUNCT
ejpam-5658	160	17	b	b	NOUN
ejpam-5658	160	18	)	)	PUNCT
ejpam-5658	160	19	=	=	SYM
ejpam-5658	160	20	1	1	X
ejpam-5658	160	21	.	.	X
ejpam-5658	160	22	if	if	SCONJ
ejpam-5658	160	23	a	a	PRON
ejpam-5658	160	24	,	,	PUNCT
ejpam-5658	160	25	b	b	PROPN
ejpam-5658	160	26	∈	∈	PROPN
ejpam-5658	160	27	suv	suv	PROPN
ejpam-5658	160	28	,	,	PUNCT
ejpam-5658	160	29	then	then	ADV
ejpam-5658	160	30	dg⋄h(a	dg⋄h(a	PROPN
ejpam-5658	160	31	,	,	PUNCT
ejpam-5658	160	32	b	b	NOUN
ejpam-5658	160	33	)	)	PUNCT
ejpam-5658	160	34	=	=	SYM
ejpam-5658	160	35	1	1	NUM
ejpam-5658	160	36	by	by	ADP
ejpam-5658	160	37	(	(	PUNCT
ejpam-5658	160	38	ii	ii	NOUN
ejpam-5658	160	39	)	)	PUNCT
ejpam-5658	160	40	.	.	PUNCT
ejpam-5658	161	1	therefore	therefore	ADV
ejpam-5658	161	2	,	,	PUNCT
ejpam-5658	161	3	s	s	VERB
ejpam-5658	161	4	is	be	AUX
ejpam-5658	161	5	a	a	DET
ejpam-5658	161	6	hop	hop	NOUN
ejpam-5658	161	7	independent	independent	ADJ
ejpam-5658	161	8	set	set	NOUN
ejpam-5658	161	9	in	in	ADP
ejpam-5658	161	10	g	g	PROPN
ejpam-5658	161	11	⋄h	⋄h	PROPN
ejpam-5658	161	12	.	.	PUNCT
ejpam-5658	162	1	lemma	lemma	PROPN
ejpam-5658	162	2	1	1	X
ejpam-5658	162	3	.	.	PUNCT
ejpam-5658	163	1	let	let	VERB
ejpam-5658	163	2	g	g	PRON
ejpam-5658	163	3	be	be	AUX
ejpam-5658	163	4	a	a	DET
ejpam-5658	163	5	connected	connected	ADJ
ejpam-5658	163	6	graph	graph	NOUN
ejpam-5658	163	7	of	of	ADP
ejpam-5658	163	8	order	order	NOUN
ejpam-5658	163	9	n	n	PRON
ejpam-5658	163	10	≥	≥	NOUN
ejpam-5658	163	11	3	3	NUM
ejpam-5658	163	12	.	.	PUNCT
ejpam-5658	163	13	then	then	ADV
ejpam-5658	163	14	ν(g	ν(g	NOUN
ejpam-5658	163	15	)	)	PUNCT
ejpam-5658	163	16	=	=	PUNCT
ejpam-5658	163	17	1	1	NUM
ejpam-5658	163	18	if	if	SCONJ
ejpam-5658	163	19	and	and	CCONJ
ejpam-5658	163	20	only	only	ADV
ejpam-5658	163	21	if	if	SCONJ
ejpam-5658	163	22	g	g	NOUN
ejpam-5658	163	23	=	=	PUNCT
ejpam-5658	163	24	k3	k3	X
ejpam-5658	163	25	or	or	CCONJ
ejpam-5658	163	26	g	g	NOUN
ejpam-5658	163	27	=	=	PUNCT
ejpam-5658	163	28	k1,n−1	k1,n−1	PROPN
ejpam-5658	163	29	.	.	PUNCT
ejpam-5658	164	1	furthermore	furthermore	ADV
ejpam-5658	164	2	,	,	PUNCT
ejpam-5658	164	3	if	if	SCONJ
ejpam-5658	164	4	ν(g	ν(g	NOUN
ejpam-5658	164	5	)	)	PUNCT
ejpam-5658	164	6	=	=	SYM
ejpam-5658	164	7	1	1	NUM
ejpam-5658	164	8	and	and	CCONJ
ejpam-5658	164	9	αh(g	αh(g	NOUN
ejpam-5658	164	10	)	)	PUNCT
ejpam-5658	164	11	>	>	X
ejpam-5658	165	1	2	2	NUM
ejpam-5658	165	2	,	,	PUNCT
ejpam-5658	165	3	then	then	ADV
ejpam-5658	165	4	g	g	PROPN
ejpam-5658	165	5	=	=	SYM
ejpam-5658	165	6	k3	k3	PROPN
ejpam-5658	165	7	.	.	PUNCT
ejpam-5658	166	1	proof	proof	NOUN
ejpam-5658	166	2	.	.	PUNCT
ejpam-5658	167	1	suppose	suppose	VERB
ejpam-5658	167	2	that	that	SCONJ
ejpam-5658	167	3	ν(g	ν(g	PROPN
ejpam-5658	167	4	)	)	PUNCT
ejpam-5658	167	5	=	=	PUNCT
ejpam-5658	168	1	1	1	X
ejpam-5658	168	2	.	.	PUNCT
ejpam-5658	169	1	if	if	SCONJ
ejpam-5658	169	2	n	n	NOUN
ejpam-5658	169	3	=	=	SYM
ejpam-5658	169	4	3	3	NUM
ejpam-5658	169	5	,	,	PUNCT
ejpam-5658	169	6	then	then	ADV
ejpam-5658	169	7	g	g	PROPN
ejpam-5658	169	8	∈	∈	PROPN
ejpam-5658	169	9	{	{	PUNCT
ejpam-5658	169	10	k3	k3	PROPN
ejpam-5658	169	11	,	,	PUNCT
ejpam-5658	169	12	p3	p3	PROPN
ejpam-5658	169	13	}	}	PUNCT
ejpam-5658	169	14	.	.	PUNCT
ejpam-5658	170	1	suppose	suppose	VERB
ejpam-5658	170	2	n	n	PRON
ejpam-5658	170	3	≥	≥	X
ejpam-5658	170	4	4	4	NUM
ejpam-5658	170	5	and	and	CCONJ
ejpam-5658	170	6	let	let	VERB
ejpam-5658	170	7	m	m	VERB
ejpam-5658	170	8	=	=	PRON
ejpam-5658	170	9	{	{	PUNCT
ejpam-5658	170	10	uv	uv	NOUN
ejpam-5658	170	11	}	}	PUNCT
ejpam-5658	170	12	be	be	AUX
ejpam-5658	170	13	a	a	DET
ejpam-5658	170	14	maximum	maximum	ADJ
ejpam-5658	170	15	matching	matching	NOUN
ejpam-5658	170	16	in	in	ADP
ejpam-5658	170	17	g.	g.	PROPN
ejpam-5658	170	18	let	let	VERB
ejpam-5658	170	19	x	x	SYM
ejpam-5658	170	20	∈	∈	PROPN
ejpam-5658	170	21	v	v	X
ejpam-5658	170	22	(	(	PUNCT
ejpam-5658	170	23	g	g	NOUN
ejpam-5658	170	24	)	)	PUNCT
ejpam-5658	170	25	\	\	NOUN
ejpam-5658	170	26	{	{	PUNCT
ejpam-5658	170	27	u	u	NOUN
ejpam-5658	170	28	,	,	PUNCT
ejpam-5658	170	29	v	v	NOUN
ejpam-5658	170	30	}	}	PUNCT
ejpam-5658	170	31	.	.	PUNCT
ejpam-5658	171	1	since	since	SCONJ
ejpam-5658	171	2	ν(g	ν(g	NOUN
ejpam-5658	171	3	)	)	PUNCT
ejpam-5658	171	4	=	=	SYM
ejpam-5658	171	5	1	1	NUM
ejpam-5658	171	6	,	,	PUNCT
ejpam-5658	171	7	xu	xu	PROPN
ejpam-5658	171	8	∈	∈	PROPN
ejpam-5658	171	9	e(g	e(g	PROPN
ejpam-5658	171	10	)	)	PUNCT
ejpam-5658	171	11	or	or	CCONJ
ejpam-5658	171	12	xv	xv	PROPN
ejpam-5658	171	13	∈	∈	PROPN
ejpam-5658	171	14	e(g	e(g	PROPN
ejpam-5658	171	15	)	)	PUNCT
ejpam-5658	171	16	.	.	PUNCT
ejpam-5658	172	1	assume	assume	VERB
ejpam-5658	172	2	that	that	SCONJ
ejpam-5658	172	3	xu	xu	PROPN
ejpam-5658	172	4	∈	∈	PROPN
ejpam-5658	172	5	e(g	e(g	PROPN
ejpam-5658	172	6	)	)	PUNCT
ejpam-5658	172	7	.	.	PUNCT
ejpam-5658	173	1	suppose	suppose	VERB
ejpam-5658	173	2	further	far	ADV
ejpam-5658	173	3	that	that	SCONJ
ejpam-5658	173	4	xv	xv	PROPN
ejpam-5658	173	5	∈	∈	PROPN
ejpam-5658	173	6	e(g	e(g	PROPN
ejpam-5658	173	7	)	)	PUNCT
ejpam-5658	173	8	.	.	PUNCT
ejpam-5658	174	1	then	then	ADV
ejpam-5658	174	2	⟨{x	⟨{x	PROPN
ejpam-5658	174	3	,	,	PUNCT
ejpam-5658	174	4	u	u	NOUN
ejpam-5658	174	5	,	,	PUNCT
ejpam-5658	174	6	v}⟩	v}⟩	PROPN
ejpam-5658	174	7	is	be	AUX
ejpam-5658	174	8	(	(	PUNCT
ejpam-5658	174	9	isomorphic	isomorphic	ADJ
ejpam-5658	174	10	to	to	PART
ejpam-5658	174	11	)	)	PUNCT
ejpam-5658	174	12	k3	k3	PROPN
ejpam-5658	174	13	.	.	PUNCT
ejpam-5658	175	1	next	next	ADV
ejpam-5658	175	2	,	,	PUNCT
ejpam-5658	175	3	let	let	VERB
ejpam-5658	175	4	y	y	PROPN
ejpam-5658	175	5	∈	∈	PROPN
ejpam-5658	175	6	v	v	PROPN
ejpam-5658	175	7	(	(	PUNCT
ejpam-5658	175	8	g)\{x	g)\{x	PROPN
ejpam-5658	175	9	,	,	PUNCT
ejpam-5658	175	10	u	u	NOUN
ejpam-5658	175	11	,	,	PUNCT
ejpam-5658	175	12	v	v	NOUN
ejpam-5658	175	13	}	}	PUNCT
ejpam-5658	175	14	.	.	PUNCT
ejpam-5658	176	1	since	since	SCONJ
ejpam-5658	176	2	g	g	PROPN
ejpam-5658	176	3	is	be	AUX
ejpam-5658	176	4	connected	connect	VERB
ejpam-5658	176	5	and	and	CCONJ
ejpam-5658	176	6	n	n	PRON
ejpam-5658	176	7	≥	≥	NOUN
ejpam-5658	176	8	4	4	NUM
ejpam-5658	176	9	,	,	PUNCT
ejpam-5658	176	10	pick	pick	VERB
ejpam-5658	176	11	any	any	DET
ejpam-5658	176	12	y	y	PROPN
ejpam-5658	176	13	∈	∈	PROPN
ejpam-5658	176	14	ng({x	ng({x	PROPN
ejpam-5658	176	15	,	,	PUNCT
ejpam-5658	176	16	u	u	NOUN
ejpam-5658	176	17	,	,	PUNCT
ejpam-5658	176	18	v	v	NOUN
ejpam-5658	176	19	}	}	PUNCT
ejpam-5658	176	20	)	)	PUNCT
ejpam-5658	176	21	.	.	PUNCT
ejpam-5658	177	1	we	we	PRON
ejpam-5658	177	2	may	may	AUX
ejpam-5658	177	3	assume	assume	VERB
ejpam-5658	177	4	that	that	SCONJ
ejpam-5658	177	5	xy	xy	PROPN
ejpam-5658	177	6	∈	∈	PROPN
ejpam-5658	177	7	e(g	e(g	PROPN
ejpam-5658	177	8	)	)	PUNCT
ejpam-5658	177	9	.	.	PUNCT
ejpam-5658	178	1	then	then	ADV
ejpam-5658	178	2	xy	xy	PROPN
ejpam-5658	179	1	and	and	CCONJ
ejpam-5658	179	2	uv	uv	PROPN
ejpam-5658	179	3	do	do	AUX
ejpam-5658	179	4	not	not	PART
ejpam-5658	179	5	have	have	VERB
ejpam-5658	179	6	a	a	DET
ejpam-5658	179	7	common	common	ADJ
ejpam-5658	179	8	vertex	vertex	NOUN
ejpam-5658	179	9	.	.	PUNCT
ejpam-5658	180	1	this	this	PRON
ejpam-5658	180	2	implies	imply	VERB
ejpam-5658	180	3	thatm∪{xy	thatm∪{xy	NOUN
ejpam-5658	180	4	}	}	PUNCT
ejpam-5658	180	5	is	be	AUX
ejpam-5658	180	6	a	a	DET
ejpam-5658	180	7	matching	matching	NOUN
ejpam-5658	180	8	in	in	ADP
ejpam-5658	180	9	g	g	NOUN
ejpam-5658	180	10	,	,	PUNCT
ejpam-5658	180	11	contradicting	contradict	VERB
ejpam-5658	180	12	the	the	DET
ejpam-5658	180	13	maximality	maximality	NOUN
ejpam-5658	180	14	of	of	ADP
ejpam-5658	180	15	m	m	PROPN
ejpam-5658	180	16	.	.	PUNCT
ejpam-5658	181	1	thus	thus	ADV
ejpam-5658	181	2	,	,	PUNCT
ejpam-5658	181	3	xv	xv	PROPN
ejpam-5658	181	4	/∈	/∈	PUNCT
ejpam-5658	181	5	e(g	e(g	PROPN
ejpam-5658	181	6	)	)	PUNCT
ejpam-5658	181	7	.	.	PUNCT
ejpam-5658	182	1	now	now	ADV
ejpam-5658	182	2	let	let	VERB
ejpam-5658	182	3	z	z	NOUN
ejpam-5658	182	4	∈	∈	PROPN
ejpam-5658	182	5	v	v	ADP
ejpam-5658	182	6	(	(	PUNCT
ejpam-5658	182	7	g	g	NOUN
ejpam-5658	182	8	)	)	PUNCT
ejpam-5658	182	9	\	\	NOUN
ejpam-5658	183	1	{	{	PUNCT
ejpam-5658	183	2	u	u	NOUN
ejpam-5658	183	3	,	,	PUNCT
ejpam-5658	183	4	x	x	NOUN
ejpam-5658	183	5	}	}	PUNCT
ejpam-5658	183	6	.	.	PUNCT
ejpam-5658	184	1	since	since	SCONJ
ejpam-5658	184	2	m	m	PROPN
ejpam-5658	184	3	=	=	SYM
ejpam-5658	184	4	{	{	PUNCT
ejpam-5658	184	5	uv	uv	NOUN
ejpam-5658	184	6	}	}	PUNCT
ejpam-5658	184	7	is	be	AUX
ejpam-5658	184	8	a	a	DET
ejpam-5658	184	9	maximum	maximum	ADJ
ejpam-5658	184	10	matching	matching	NOUN
ejpam-5658	184	11	in	in	ADP
ejpam-5658	184	12	g	g	NOUN
ejpam-5658	184	13	,	,	PUNCT
ejpam-5658	184	14	zu	zu	PROPN
ejpam-5658	184	15	∈	∈	PROPN
ejpam-5658	184	16	e(g	e(g	PROPN
ejpam-5658	184	17	)	)	PUNCT
ejpam-5658	184	18	and	and	CCONJ
ejpam-5658	184	19	xz	xz	PROPN
ejpam-5658	184	20	/∈	/∈	PUNCT
ejpam-5658	185	1	e(g	e(g	PROPN
ejpam-5658	185	2	)	)	PUNCT
ejpam-5658	185	3	.	.	PUNCT
ejpam-5658	186	1	therefore	therefore	ADV
ejpam-5658	186	2	,	,	PUNCT
ejpam-5658	186	3	g	g	PROPN
ejpam-5658	186	4	=	=	PUNCT
ejpam-5658	186	5	k1,n−1	k1,n−1	PROPN
ejpam-5658	186	6	.	.	PUNCT
ejpam-5658	187	1	the	the	DET
ejpam-5658	187	2	converse	converse	NOUN
ejpam-5658	187	3	is	be	AUX
ejpam-5658	187	4	clear	clear	ADJ
ejpam-5658	187	5	.	.	PUNCT
ejpam-5658	188	1	for	for	ADP
ejpam-5658	188	2	the	the	DET
ejpam-5658	188	3	second	second	ADJ
ejpam-5658	188	4	part	part	NOUN
ejpam-5658	188	5	,	,	PUNCT
ejpam-5658	188	6	suppose	suppose	VERB
ejpam-5658	188	7	that	that	SCONJ
ejpam-5658	188	8	ν(g	ν(g	PROPN
ejpam-5658	188	9	)	)	PUNCT
ejpam-5658	188	10	=	=	SYM
ejpam-5658	188	11	1	1	NUM
ejpam-5658	188	12	and	and	CCONJ
ejpam-5658	188	13	αh(g	αh(g	NOUN
ejpam-5658	188	14	)	)	PUNCT
ejpam-5658	188	15	>	>	X
ejpam-5658	189	1	2	2	X
ejpam-5658	189	2	.	.	PUNCT
ejpam-5658	189	3	since	since	SCONJ
ejpam-5658	189	4	αh(k1,n−1	αh(k1,n−1	PROPN
ejpam-5658	189	5	)	)	PUNCT
ejpam-5658	189	6	=	=	SYM
ejpam-5658	189	7	2	2	NUM
ejpam-5658	189	8	for	for	ADP
ejpam-5658	189	9	all	all	DET
ejpam-5658	189	10	n	n	PRON
ejpam-5658	189	11	≥	≥	NOUN
ejpam-5658	189	12	3	3	NUM
ejpam-5658	189	13	,	,	PUNCT
ejpam-5658	189	14	it	it	PRON
ejpam-5658	189	15	follows	follow	VERB
ejpam-5658	189	16	from	from	ADP
ejpam-5658	189	17	the	the	DET
ejpam-5658	189	18	first	first	ADJ
ejpam-5658	189	19	part	part	NOUN
ejpam-5658	189	20	that	that	PRON
ejpam-5658	189	21	g	g	NOUN
ejpam-5658	189	22	=	=	SYM
ejpam-5658	189	23	k3	k3	PROPN
ejpam-5658	189	24	.	.	PUNCT
ejpam-5658	190	1	corollary	corollary	ADJ
ejpam-5658	190	2	3	3	X
ejpam-5658	190	3	.	.	PUNCT
ejpam-5658	191	1	let	let	VERB
ejpam-5658	191	2	g	g	PRON
ejpam-5658	191	3	be	be	AUX
ejpam-5658	191	4	a	a	DET
ejpam-5658	191	5	non	non	ADJ
ejpam-5658	191	6	-	-	ADJ
ejpam-5658	191	7	trivial	trivial	ADJ
ejpam-5658	191	8	connected	connected	ADJ
ejpam-5658	191	9	graph	graph	NOUN
ejpam-5658	191	10	and	and	CCONJ
ejpam-5658	191	11	let	let	VERB
ejpam-5658	191	12	h	h	NOUN
ejpam-5658	191	13	be	be	AUX
ejpam-5658	191	14	any	any	DET
ejpam-5658	191	15	graph	graph	NOUN
ejpam-5658	191	16	.	.	PUNCT
ejpam-5658	192	1	(	(	PUNCT
ejpam-5658	192	2	i	i	NOUN
ejpam-5658	192	3	)	)	PUNCT
ejpam-5658	192	4	if	if	SCONJ
ejpam-5658	192	5	ν(g	ν(g	NOUN
ejpam-5658	192	6	)	)	PUNCT
ejpam-5658	192	7	=	=	SYM
ejpam-5658	193	1	1	1	NUM
ejpam-5658	193	2	,	,	PUNCT
ejpam-5658	193	3	then	then	ADV
ejpam-5658	193	4	αh(g	αh(g	ADP
ejpam-5658	193	5	⋄h	⋄h	X
ejpam-5658	193	6	)	)	PUNCT
ejpam-5658	193	7	=	=	SYM
ejpam-5658	193	8	2	2	NUM
ejpam-5658	193	9	+	+	NUM
ejpam-5658	193	10	ω(h	ω(h	NUM
ejpam-5658	193	11	)	)	PUNCT
ejpam-5658	193	12	.	.	PUNCT
ejpam-5658	194	1	(	(	PUNCT
ejpam-5658	194	2	ii	ii	NOUN
ejpam-5658	194	3	)	)	PUNCT
ejpam-5658	194	4	if	if	SCONJ
ejpam-5658	194	5	ν(g	ν(g	PROPN
ejpam-5658	194	6	)	)	PUNCT
ejpam-5658	194	7	≥	≥	NOUN
ejpam-5658	194	8	2	2	NUM
ejpam-5658	194	9	,	,	PUNCT
ejpam-5658	194	10	then	then	ADV
ejpam-5658	194	11	αh(g	αh(g	ADP
ejpam-5658	194	12	⋄h	⋄h	PROPN
ejpam-5658	194	13	)	)	PUNCT
ejpam-5658	194	14	≥	≥	PROPN
ejpam-5658	194	15	max{αh(g	max{αh(g	NOUN
ejpam-5658	194	16	)	)	PUNCT
ejpam-5658	194	17	,	,	PUNCT
ejpam-5658	194	18	ν(g)ω(h	ν(g)ω(h	PROPN
ejpam-5658	194	19	)	)	PUNCT
ejpam-5658	194	20	}	}	PUNCT
ejpam-5658	194	21	.	.	PUNCT
ejpam-5658	195	1	j.	j.	PROPN
ejpam-5658	195	2	anoche	anoche	PROPN
ejpam-5658	195	3	,	,	PUNCT
ejpam-5658	195	4	s.	s.	PROPN
ejpam-5658	195	5	canoy	canoy	PROPN
ejpam-5658	195	6	,	,	PUNCT
ejpam-5658	195	7	jr	jr	PROPN
ejpam-5658	195	8	.	.	PROPN
ejpam-5658	195	9	/	/	SYM
ejpam-5658	195	10	eur	eur	PROPN
ejpam-5658	195	11	.	.	PUNCT
ejpam-5658	196	1	j.	j.	PROPN
ejpam-5658	196	2	pure	pure	PROPN
ejpam-5658	196	3	appl	appl	PROPN
ejpam-5658	196	4	.	.	PROPN
ejpam-5658	196	5	math	math	PROPN
ejpam-5658	196	6	,	,	PUNCT
ejpam-5658	196	7	18	18	NUM
ejpam-5658	196	8	(	(	PUNCT
ejpam-5658	196	9	1	1	NUM
ejpam-5658	196	10	)	)	PUNCT
ejpam-5658	196	11	(	(	PUNCT
ejpam-5658	196	12	2025	2025	NUM
ejpam-5658	196	13	)	)	PUNCT
ejpam-5658	196	14	,	,	PUNCT
ejpam-5658	196	15	5658	5658	NUM
ejpam-5658	196	16	7	7	NUM
ejpam-5658	196	17	of	of	ADP
ejpam-5658	196	18	15	15	NUM
ejpam-5658	196	19	proof	proof	NOUN
ejpam-5658	196	20	.	.	PUNCT
ejpam-5658	197	1	(	(	PUNCT
ejpam-5658	197	2	i	i	NOUN
ejpam-5658	197	3	)	)	PUNCT
ejpam-5658	197	4	assume	assume	VERB
ejpam-5658	197	5	that	that	SCONJ
ejpam-5658	197	6	ν(g	ν(g	PRON
ejpam-5658	197	7	)	)	PUNCT
ejpam-5658	197	8	=	=	SYM
ejpam-5658	198	1	1	1	NUM
ejpam-5658	198	2	,	,	PUNCT
ejpam-5658	198	3	saym	saym	X
ejpam-5658	198	4	′	′	VERB
ejpam-5658	199	1	=	=	SYM
ejpam-5658	199	2	{	{	PUNCT
ejpam-5658	199	3	pq	pq	INTJ
ejpam-5658	199	4	}	}	PUNCT
ejpam-5658	199	5	is	be	AUX
ejpam-5658	199	6	a	a	DET
ejpam-5658	199	7	maximum	maximum	ADJ
ejpam-5658	199	8	matching	match	VERB
ejpam-5658	199	9	ing	ing	NOUN
ejpam-5658	199	10	.	.	PUNCT
ejpam-5658	200	1	clearly	clearly	ADV
ejpam-5658	200	2	,	,	PUNCT
ejpam-5658	200	3	αh(g	αh(g	ADP
ejpam-5658	200	4	⋄	⋄	PROPN
ejpam-5658	200	5	h	h	NOUN
ejpam-5658	200	6	)	)	PUNCT
ejpam-5658	200	7	=	=	SYM
ejpam-5658	200	8	2	2	NUM
ejpam-5658	200	9	+	+	NUM
ejpam-5658	200	10	ω(h	ω(h	NUM
ejpam-5658	200	11	)	)	PUNCT
ejpam-5658	200	12	if	if	SCONJ
ejpam-5658	200	13	g	g	PROPN
ejpam-5658	200	14	=	=	SYM
ejpam-5658	200	15	⟨{p	⟨{p	PROPN
ejpam-5658	200	16	,	,	PUNCT
ejpam-5658	200	17	q}⟩	q}⟩	PROPN
ejpam-5658	200	18	=	=	SYM
ejpam-5658	200	19	k2	k2	PROPN
ejpam-5658	200	20	.	.	PUNCT
ejpam-5658	200	21	suppose	suppose	VERB
ejpam-5658	200	22	g	g	PROPN
ejpam-5658	200	23	̸=	̸=	PROPN
ejpam-5658	200	24	k2	k2	PROPN
ejpam-5658	200	25	.	.	PUNCT
ejpam-5658	201	1	let	let	VERB
ejpam-5658	201	2	s0	s0	PROPN
ejpam-5658	201	3	=	=	PUNCT
ejpam-5658	201	4	{	{	PUNCT
ejpam-5658	201	5	p	p	X
ejpam-5658	201	6	,	,	PUNCT
ejpam-5658	201	7	q	q	ADJ
ejpam-5658	201	8	}	}	PUNCT
ejpam-5658	201	9	∪	∪	ADJ
ejpam-5658	201	10	spq	spq	NOUN
ejpam-5658	201	11	,	,	PUNCT
ejpam-5658	201	12	where	where	SCONJ
ejpam-5658	201	13	spq	spq	NOUN
ejpam-5658	201	14	is	be	AUX
ejpam-5658	201	15	a	a	DET
ejpam-5658	201	16	maximum	maximum	ADJ
ejpam-5658	201	17	clique	clique	NOUN
ejpam-5658	201	18	in	in	ADP
ejpam-5658	201	19	h.	h.	PROPN
ejpam-5658	201	20	then	then	ADV
ejpam-5658	201	21	,	,	PUNCT
ejpam-5658	201	22	by	by	ADP
ejpam-5658	201	23	theorem	theorem	NOUN
ejpam-5658	201	24	3	3	NUM
ejpam-5658	201	25	,	,	PUNCT
ejpam-5658	201	26	s0	s0	PROPN
ejpam-5658	201	27	is	be	AUX
ejpam-5658	201	28	a	a	DET
ejpam-5658	201	29	hop	hop	NOUN
ejpam-5658	201	30	independent	independent	ADJ
ejpam-5658	201	31	set	set	NOUN
ejpam-5658	201	32	in	in	ADP
ejpam-5658	201	33	g	g	PROPN
ejpam-5658	201	34	⋄h	⋄h	PROPN
ejpam-5658	201	35	.	.	PUNCT
ejpam-5658	202	1	this	this	PRON
ejpam-5658	202	2	implies	imply	VERB
ejpam-5658	202	3	that	that	SCONJ
ejpam-5658	202	4	αh(g	αh(g	DET
ejpam-5658	202	5	⋄h	⋄h	NOUN
ejpam-5658	202	6	)	)	PUNCT
ejpam-5658	202	7	≥	≥	NOUN
ejpam-5658	202	8	|s0|	|s0|	NOUN
ejpam-5658	202	9	=	=	SYM
ejpam-5658	202	10	2	2	NUM
ejpam-5658	202	11	+	+	NUM
ejpam-5658	202	12	ω(h	ω(h	NUM
ejpam-5658	202	13	)	)	PUNCT
ejpam-5658	202	14	.	.	PUNCT
ejpam-5658	203	1	on	on	ADP
ejpam-5658	203	2	the	the	DET
ejpam-5658	203	3	other	other	ADJ
ejpam-5658	203	4	hand	hand	NOUN
ejpam-5658	203	5	,	,	PUNCT
ejpam-5658	203	6	if	if	SCONJ
ejpam-5658	203	7	s∗	s∗	PROPN
ejpam-5658	203	8	is	be	AUX
ejpam-5658	203	9	an	an	DET
ejpam-5658	203	10	αh	αh	NOUN
ejpam-5658	203	11	-	-	PUNCT
ejpam-5658	203	12	set	set	NOUN
ejpam-5658	203	13	in	in	ADP
ejpam-5658	203	14	g⋄h	g⋄h	PROPN
ejpam-5658	203	15	,	,	PUNCT
ejpam-5658	203	16	then	then	ADV
ejpam-5658	203	17	s∗	s∗	PROPN
ejpam-5658	203	18	=	=	SYM
ejpam-5658	203	19	a∪(∪uv∈e(g)suv	a∪(∪uv∈e(g)suv	PROPN
ejpam-5658	203	20	)	)	PUNCT
ejpam-5658	203	21	and	and	CCONJ
ejpam-5658	203	22	satisifes	satisife	VERB
ejpam-5658	203	23	conditions	condition	NOUN
ejpam-5658	203	24	(	(	PUNCT
ejpam-5658	203	25	i	i	NOUN
ejpam-5658	203	26	)	)	PUNCT
ejpam-5658	203	27	,	,	PUNCT
ejpam-5658	203	28	(	(	PUNCT
ejpam-5658	203	29	ii	ii	NOUN
ejpam-5658	203	30	)	)	PUNCT
ejpam-5658	203	31	,	,	PUNCT
ejpam-5658	203	32	and	and	CCONJ
ejpam-5658	203	33	(	(	PUNCT
ejpam-5658	203	34	iii	iii	NOUN
ejpam-5658	203	35	)	)	PUNCT
ejpam-5658	203	36	of	of	ADP
ejpam-5658	203	37	theorem	theorem	NOUN
ejpam-5658	203	38	3	3	X
ejpam-5658	203	39	.	.	PUNCT
ejpam-5658	203	40	suppose	suppose	VERB
ejpam-5658	203	41	there	there	PRON
ejpam-5658	203	42	exists	exist	VERB
ejpam-5658	203	43	an	an	DET
ejpam-5658	203	44	st	st	PROPN
ejpam-5658	203	45	∈	∈	PROPN
ejpam-5658	203	46	e(g	e(g	PROPN
ejpam-5658	203	47	)	)	PUNCT
ejpam-5658	203	48	such	such	ADJ
ejpam-5658	203	49	that	that	SCONJ
ejpam-5658	203	50	sst	sst	PROPN
ejpam-5658	203	51	̸=	̸=	PROPN
ejpam-5658	203	52	∅.	∅.	NOUN
ejpam-5658	203	53	without	without	ADP
ejpam-5658	203	54	loss	loss	NOUN
ejpam-5658	203	55	of	of	ADP
ejpam-5658	203	56	generality	generality	NOUN
ejpam-5658	203	57	,	,	PUNCT
ejpam-5658	203	58	we	we	PRON
ejpam-5658	203	59	may	may	AUX
ejpam-5658	203	60	assume	assume	VERB
ejpam-5658	203	61	that	that	SCONJ
ejpam-5658	203	62	st	st	PROPN
ejpam-5658	203	63	=	=	SYM
ejpam-5658	203	64	pq	pq	PROPN
ejpam-5658	203	65	,	,	PUNCT
ejpam-5658	203	66	i.e.	i.e.	X
ejpam-5658	203	67	,	,	PUNCT
ejpam-5658	203	68	sst	sst	NOUN
ejpam-5658	203	69	=	=	PUNCT
ejpam-5658	203	70	spq	spq	NOUN
ejpam-5658	203	71	̸=	̸=	PROPN
ejpam-5658	203	72	∅.	∅.	NOUN
ejpam-5658	203	73	then	then	ADV
ejpam-5658	203	74	spq	spq	NOUN
ejpam-5658	203	75	is	be	AUX
ejpam-5658	203	76	a	a	DET
ejpam-5658	203	77	clique	clique	NOUN
ejpam-5658	203	78	in	in	ADP
ejpam-5658	203	79	hpq	hpq	PROPN
ejpam-5658	203	80	by	by	ADP
ejpam-5658	203	81	(	(	PUNCT
ejpam-5658	203	82	ii	ii	NOUN
ejpam-5658	203	83	)	)	PUNCT
ejpam-5658	203	84	.	.	PUNCT
ejpam-5658	204	1	let	let	VERB
ejpam-5658	204	2	kl	kl	PROPN
ejpam-5658	204	3	∈	∈	PROPN
ejpam-5658	204	4	e(g)\m	e(g)\m	VERB
ejpam-5658	204	5	′.	′.	NOUN
ejpam-5658	204	6	since	since	SCONJ
ejpam-5658	204	7	m	m	PROPN
ejpam-5658	204	8	′	′	NUM
ejpam-5658	204	9	is	be	AUX
ejpam-5658	204	10	a	a	DET
ejpam-5658	204	11	maximum	maximum	ADJ
ejpam-5658	204	12	matching	matching	NOUN
ejpam-5658	204	13	in	in	ADP
ejpam-5658	204	14	g	g	PROPN
ejpam-5658	204	15	(	(	PUNCT
ejpam-5658	204	16	or	or	CCONJ
ejpam-5658	204	17	since	since	SCONJ
ejpam-5658	204	18	ν(g	ν(g	NOUN
ejpam-5658	204	19	)	)	PUNCT
ejpam-5658	204	20	=	=	SYM
ejpam-5658	205	1	1	1	NUM
ejpam-5658	205	2	)	)	PUNCT
ejpam-5658	205	3	,	,	PUNCT
ejpam-5658	205	4	pq	pq	PROPN
ejpam-5658	205	5	and	and	CCONJ
ejpam-5658	205	6	kl	kl	PROPN
ejpam-5658	205	7	must	must	AUX
ejpam-5658	205	8	have	have	VERB
ejpam-5658	205	9	a	a	DET
ejpam-5658	205	10	common	common	ADJ
ejpam-5658	205	11	vertex	vertex	NOUN
ejpam-5658	205	12	.	.	PUNCT
ejpam-5658	206	1	we	we	PRON
ejpam-5658	206	2	may	may	AUX
ejpam-5658	206	3	assume	assume	VERB
ejpam-5658	206	4	that	that	SCONJ
ejpam-5658	206	5	k	k	PROPN
ejpam-5658	207	1	=	=	PUNCT
ejpam-5658	207	2	p.	p.	NOUN
ejpam-5658	207	3	then	then	ADV
ejpam-5658	207	4	skl	skl	NOUN
ejpam-5658	207	5	=	=	SYM
ejpam-5658	207	6	∅	∅	NOUN
ejpam-5658	207	7	by	by	ADP
ejpam-5658	207	8	(	(	PUNCT
ejpam-5658	207	9	iii	iii	NOUN
ejpam-5658	207	10	)	)	PUNCT
ejpam-5658	207	11	.	.	PUNCT
ejpam-5658	208	1	also	also	ADV
ejpam-5658	208	2	,	,	PUNCT
ejpam-5658	208	3	since	since	SCONJ
ejpam-5658	208	4	w	w	PROPN
ejpam-5658	208	5	∈	∈	PROPN
ejpam-5658	208	6	ng({p	ng({p	NOUN
ejpam-5658	208	7	,	,	PUNCT
ejpam-5658	208	8	q	q	NOUN
ejpam-5658	208	9	}	}	PUNCT
ejpam-5658	208	10	)	)	PUNCT
ejpam-5658	208	11	for	for	ADP
ejpam-5658	208	12	all	all	PRON
ejpam-5658	208	13	w	w	PROPN
ejpam-5658	208	14	∈	∈	PROPN
ejpam-5658	208	15	v	v	ADP
ejpam-5658	208	16	(	(	PUNCT
ejpam-5658	208	17	g	g	NOUN
ejpam-5658	208	18	)	)	PUNCT
ejpam-5658	208	19	\	\	NOUN
ejpam-5658	208	20	{	{	PUNCT
ejpam-5658	208	21	p	p	X
ejpam-5658	208	22	,	,	PUNCT
ejpam-5658	208	23	q	q	ADJ
ejpam-5658	208	24	}	}	PUNCT
ejpam-5658	208	25	and	and	CCONJ
ejpam-5658	208	26	spq	spq	NOUN
ejpam-5658	208	27	̸=	̸=	PROPN
ejpam-5658	208	28	∅	∅	NOUN
ejpam-5658	208	29	,	,	PUNCT
ejpam-5658	208	30	it	it	PRON
ejpam-5658	208	31	follows	follow	VERB
ejpam-5658	208	32	from	from	ADP
ejpam-5658	208	33	(	(	PUNCT
ejpam-5658	208	34	iii	iii	NOUN
ejpam-5658	208	35	)	)	PUNCT
ejpam-5658	208	36	that	that	PRON
ejpam-5658	209	1	w	w	PROPN
ejpam-5658	209	2	/∈	/∈	PUNCT
ejpam-5658	209	3	a	a	PRON
ejpam-5658	209	4	for	for	ADP
ejpam-5658	209	5	all	all	DET
ejpam-5658	209	6	w	w	PROPN
ejpam-5658	209	7	∈	∈	PROPN
ejpam-5658	209	8	v	v	ADP
ejpam-5658	209	9	(	(	PUNCT
ejpam-5658	209	10	g	g	NOUN
ejpam-5658	209	11	)	)	PUNCT
ejpam-5658	209	12	\	\	NOUN
ejpam-5658	209	13	{	{	PUNCT
ejpam-5658	209	14	p	p	X
ejpam-5658	209	15	,	,	PUNCT
ejpam-5658	209	16	q	q	NOUN
ejpam-5658	209	17	}	}	PUNCT
ejpam-5658	209	18	.	.	PUNCT
ejpam-5658	210	1	this	this	PRON
ejpam-5658	210	2	implies	imply	VERB
ejpam-5658	210	3	that	that	SCONJ
ejpam-5658	210	4	a	a	DET
ejpam-5658	210	5	⊆	⊆	NUM
ejpam-5658	210	6	{	{	PUNCT
ejpam-5658	210	7	p	p	X
ejpam-5658	210	8	,	,	PUNCT
ejpam-5658	210	9	q	q	NOUN
ejpam-5658	210	10	}	}	PUNCT
ejpam-5658	210	11	.	.	PUNCT
ejpam-5658	211	1	hence	hence	ADV
ejpam-5658	211	2	,	,	PUNCT
ejpam-5658	211	3	αh(g	αh(g	PRON
ejpam-5658	211	4	⋄h	⋄h	NOUN
ejpam-5658	211	5	)	)	PUNCT
ejpam-5658	211	6	=	=	PUNCT
ejpam-5658	212	1	|a|+	|a|+	VERB
ejpam-5658	212	2	|spq|	|spq|	NOUN
ejpam-5658	212	3	≤	≤	ADV
ejpam-5658	212	4	2	2	NUM
ejpam-5658	212	5	+	+	NOUN
ejpam-5658	212	6	ω(h	ω(h	NUM
ejpam-5658	212	7	)	)	PUNCT
ejpam-5658	212	8	.	.	PUNCT
ejpam-5658	213	1	next	next	ADV
ejpam-5658	213	2	,	,	PUNCT
ejpam-5658	213	3	suppose	suppose	VERB
ejpam-5658	213	4	that	that	SCONJ
ejpam-5658	213	5	suv	suv	PROPN
ejpam-5658	213	6	=	=	NOUN
ejpam-5658	213	7	∅	∅	NOUN
ejpam-5658	213	8	for	for	ADP
ejpam-5658	213	9	all	all	DET
ejpam-5658	213	10	uv	uv	PROPN
ejpam-5658	213	11	∈	∈	PROPN
ejpam-5658	213	12	e(g	e(g	PROPN
ejpam-5658	213	13	)	)	PUNCT
ejpam-5658	213	14	.	.	PUNCT
ejpam-5658	214	1	then	then	ADV
ejpam-5658	214	2	s∗	s∗	PROPN
ejpam-5658	214	3	=	=	PUNCT
ejpam-5658	214	4	a.	a.	NOUN
ejpam-5658	214	5	since	since	SCONJ
ejpam-5658	214	6	g	g	PROPN
ejpam-5658	214	7	is	be	AUX
ejpam-5658	214	8	a	a	DET
ejpam-5658	214	9	non	non	ADJ
ejpam-5658	214	10	-	-	ADJ
ejpam-5658	214	11	trivial	trivial	ADJ
ejpam-5658	214	12	connected	connected	ADJ
ejpam-5658	214	13	graph	graph	NOUN
ejpam-5658	214	14	,	,	PUNCT
ejpam-5658	214	15	|a|	|a|	PROPN
ejpam-5658	214	16	≥	≥	NOUN
ejpam-5658	214	17	2	2	NUM
ejpam-5658	214	18	.	.	PUNCT
ejpam-5658	214	19	clearly	clearly	ADV
ejpam-5658	214	20	,	,	PUNCT
ejpam-5658	214	21	αh(g	αh(g	PRON
ejpam-5658	214	22	⋄h	⋄h	NOUN
ejpam-5658	214	23	)	)	PUNCT
ejpam-5658	215	1	=	=	SYM
ejpam-5658	215	2	|a|	|a|	NOUN
ejpam-5658	215	3	≤	≤	ADV
ejpam-5658	215	4	2	2	NUM
ejpam-5658	215	5	+	+	NOUN
ejpam-5658	215	6	ω(h	ω(h	NUM
ejpam-5658	215	7	)	)	PUNCT
ejpam-5658	215	8	if	if	SCONJ
ejpam-5658	215	9	|a|	|a|	PROPN
ejpam-5658	215	10	=	=	SYM
ejpam-5658	215	11	2	2	X
ejpam-5658	215	12	.	.	PUNCT
ejpam-5658	216	1	so	so	ADV
ejpam-5658	216	2	suppose	suppose	VERB
ejpam-5658	216	3	|a|	|a|	PROPN
ejpam-5658	216	4	>	>	X
ejpam-5658	216	5	2	2	NUM
ejpam-5658	216	6	.	.	PUNCT
ejpam-5658	216	7	since	since	SCONJ
ejpam-5658	216	8	a	a	PRON
ejpam-5658	216	9	is	be	AUX
ejpam-5658	216	10	a	a	DET
ejpam-5658	216	11	hop	hop	NOUN
ejpam-5658	216	12	independent	independent	ADJ
ejpam-5658	216	13	set	set	NOUN
ejpam-5658	216	14	in	in	ADP
ejpam-5658	216	15	g	g	PROPN
ejpam-5658	216	16	and	and	CCONJ
ejpam-5658	216	17	|a|	|a|	PROPN
ejpam-5658	216	18	>	>	X
ejpam-5658	216	19	2	2	NUM
ejpam-5658	216	20	,	,	PUNCT
ejpam-5658	216	21	it	it	PRON
ejpam-5658	216	22	follows	follow	VERB
ejpam-5658	216	23	from	from	ADP
ejpam-5658	216	24	lemma	lemma	PROPN
ejpam-5658	216	25	1	1	NUM
ejpam-5658	216	26	that	that	PRON
ejpam-5658	216	27	g	g	NOUN
ejpam-5658	216	28	=	=	SYM
ejpam-5658	216	29	k3	k3	PROPN
ejpam-5658	216	30	.	.	PUNCT
ejpam-5658	217	1	hence	hence	ADV
ejpam-5658	217	2	,	,	PUNCT
ejpam-5658	217	3	αh(g	αh(g	PRON
ejpam-5658	217	4	⋄h	⋄h	X
ejpam-5658	217	5	)	)	PUNCT
ejpam-5658	218	1	=	=	SYM
ejpam-5658	218	2	|a|	|a|	PROPN
ejpam-5658	218	3	=	=	SYM
ejpam-5658	218	4	3	3	NUM
ejpam-5658	218	5	≤	≤	NUM
ejpam-5658	218	6	2	2	NUM
ejpam-5658	218	7	+	+	NOUN
ejpam-5658	218	8	ω(h	ω(h	NUM
ejpam-5658	218	9	)	)	PUNCT
ejpam-5658	218	10	.	.	PUNCT
ejpam-5658	219	1	accordingly	accordingly	ADV
ejpam-5658	219	2	,	,	PUNCT
ejpam-5658	219	3	αh(g	αh(g	PRON
ejpam-5658	219	4	⋄h	⋄h	NOUN
ejpam-5658	219	5	)	)	PUNCT
ejpam-5658	219	6	=	=	SYM
ejpam-5658	219	7	2	2	NUM
ejpam-5658	219	8	+	+	NUM
ejpam-5658	219	9	ω(h	ω(h	NUM
ejpam-5658	219	10	)	)	PUNCT
ejpam-5658	219	11	.	.	PUNCT
ejpam-5658	220	1	(	(	PUNCT
ejpam-5658	220	2	ii	ii	NOUN
ejpam-5658	220	3	)	)	PUNCT
ejpam-5658	220	4	suppose	suppose	VERB
ejpam-5658	220	5	now	now	ADV
ejpam-5658	220	6	that	that	SCONJ
ejpam-5658	220	7	ν(g	ν(g	PROPN
ejpam-5658	220	8	)	)	PUNCT
ejpam-5658	220	9	≥	≥	NOUN
ejpam-5658	220	10	2	2	X
ejpam-5658	220	11	.	.	PUNCT
ejpam-5658	221	1	let	let	VERB
ejpam-5658	221	2	s	s	PRON
ejpam-5658	221	3	be	be	AUX
ejpam-5658	221	4	an	an	DET
ejpam-5658	221	5	αh	αh	NOUN
ejpam-5658	221	6	-	-	PUNCT
ejpam-5658	221	7	set	set	NOUN
ejpam-5658	221	8	in	in	ADP
ejpam-5658	221	9	g.	g.	PROPN
ejpam-5658	221	10	then	then	ADV
ejpam-5658	221	11	s	s	VERB
ejpam-5658	221	12	is	be	AUX
ejpam-5658	221	13	a	a	DET
ejpam-5658	221	14	hop	hop	NOUN
ejpam-5658	221	15	independent	independent	ADJ
ejpam-5658	221	16	set	set	NOUN
ejpam-5658	221	17	in	in	ADP
ejpam-5658	221	18	g	g	PROPN
ejpam-5658	221	19	⋄	⋄	PROPN
ejpam-5658	221	20	h	h	NOUN
ejpam-5658	221	21	by	by	ADP
ejpam-5658	221	22	theorem	theorem	NOUN
ejpam-5658	221	23	3	3	X
ejpam-5658	221	24	.	.	PUNCT
ejpam-5658	222	1	it	it	PRON
ejpam-5658	222	2	follows	follow	VERB
ejpam-5658	222	3	that	that	SCONJ
ejpam-5658	222	4	αh(g	αh(g	NUM
ejpam-5658	222	5	⋄	⋄	PROPN
ejpam-5658	222	6	h	h	PROPN
ejpam-5658	222	7	)	)	PUNCT
ejpam-5658	222	8	≥	≥	NOUN
ejpam-5658	222	9	|s|	|s|	NOUN
ejpam-5658	222	10	=	=	NOUN
ejpam-5658	222	11	αh(g	αh(g	NOUN
ejpam-5658	222	12	)	)	PUNCT
ejpam-5658	222	13	.	.	PUNCT
ejpam-5658	223	1	next	next	ADV
ejpam-5658	223	2	,	,	PUNCT
ejpam-5658	223	3	let	let	VERB
ejpam-5658	223	4	m	m	PRON
ejpam-5658	223	5	be	be	AUX
ejpam-5658	223	6	a	a	DET
ejpam-5658	223	7	maximum	maximum	ADJ
ejpam-5658	223	8	matching	matching	NOUN
ejpam-5658	223	9	in	in	ADP
ejpam-5658	223	10	g.	g.	PROPN
ejpam-5658	223	11	let	let	VERB
ejpam-5658	223	12	suv	suv	PROPN
ejpam-5658	223	13	be	be	AUX
ejpam-5658	223	14	a	a	DET
ejpam-5658	223	15	maximum	maximum	ADJ
ejpam-5658	223	16	clique	clique	NOUN
ejpam-5658	223	17	in	in	ADP
ejpam-5658	223	18	huv	huv	PROPN
ejpam-5658	223	19	for	for	ADP
ejpam-5658	223	20	each	each	DET
ejpam-5658	223	21	uv	uv	NOUN
ejpam-5658	223	22	∈	∈	PROPN
ejpam-5658	223	23	m	m	VERB
ejpam-5658	223	24	and	and	CCONJ
ejpam-5658	223	25	set	set	VERB
ejpam-5658	223	26	sxy	sxy	NOUN
ejpam-5658	223	27	=	=	NOUN
ejpam-5658	223	28	∅	∅	NOUN
ejpam-5658	223	29	for	for	ADP
ejpam-5658	223	30	each	each	DET
ejpam-5658	223	31	xy	xy	PROPN
ejpam-5658	223	32	∈	∈	PROPN
ejpam-5658	223	33	e(g	e(g	PROPN
ejpam-5658	223	34	)	)	PUNCT
ejpam-5658	223	35	\	\	PROPN
ejpam-5658	224	1	m	m	VERB
ejpam-5658	224	2	.	.	PUNCT
ejpam-5658	225	1	then	then	ADV
ejpam-5658	225	2	s	s	VERB
ejpam-5658	225	3	=	=	SYM
ejpam-5658	225	4	∪uv∈e(g)suv	∪uv∈e(g)suv	PROPN
ejpam-5658	225	5	=	=	SYM
ejpam-5658	225	6	∪uv∈msuv	∪uv∈msuv	PROPN
ejpam-5658	225	7	is	be	AUX
ejpam-5658	225	8	a	a	DET
ejpam-5658	225	9	hop	hop	NOUN
ejpam-5658	225	10	independent	independent	ADJ
ejpam-5658	225	11	set	set	NOUN
ejpam-5658	225	12	in	in	ADP
ejpam-5658	225	13	g	g	NOUN
ejpam-5658	225	14	⋄h	⋄h	NOUN
ejpam-5658	225	15	by	by	ADP
ejpam-5658	225	16	theorem	theorem	NOUN
ejpam-5658	225	17	3	3	NUM
ejpam-5658	225	18	.	.	PUNCT
ejpam-5658	225	19	thus	thus	ADV
ejpam-5658	225	20	,	,	PUNCT
ejpam-5658	225	21	αh(g	αh(g	PRON
ejpam-5658	225	22	⋄h	⋄h	PROPN
ejpam-5658	225	23	)	)	PUNCT
ejpam-5658	225	24	≥	≥	NOUN
ejpam-5658	225	25	|s|	|s|	NOUN
ejpam-5658	225	26	=	=	PUNCT
ejpam-5658	225	27	ν(g)ω(h	ν(g)ω(h	PROPN
ejpam-5658	225	28	)	)	PUNCT
ejpam-5658	225	29	.	.	PUNCT
ejpam-5658	226	1	therefore	therefore	ADV
ejpam-5658	226	2	,	,	PUNCT
ejpam-5658	226	3	αh(g	αh(g	PRON
ejpam-5658	226	4	⋄h	⋄h	PROPN
ejpam-5658	226	5	)	)	PUNCT
ejpam-5658	226	6	≥	≥	PROPN
ejpam-5658	226	7	max{αh(g	max{αh(g	NOUN
ejpam-5658	226	8	)	)	PUNCT
ejpam-5658	226	9	,	,	PUNCT
ejpam-5658	226	10	ν(g)ω(h	ν(g)ω(h	PROPN
ejpam-5658	226	11	)	)	PUNCT
ejpam-5658	226	12	}	}	PUNCT
ejpam-5658	226	13	.	.	PUNCT
ejpam-5658	227	1	remark	remark	NOUN
ejpam-5658	227	2	1	1	NUM
ejpam-5658	227	3	.	.	PUNCT
ejpam-5658	228	1	the	the	DET
ejpam-5658	228	2	lower	lower	ADV
ejpam-5658	228	3	bound	bind	VERB
ejpam-5658	228	4	given	give	VERB
ejpam-5658	228	5	in	in	ADP
ejpam-5658	228	6	corollary	corollary	ADJ
ejpam-5658	228	7	3	3	NUM
ejpam-5658	228	8	is	be	AUX
ejpam-5658	228	9	tight	tight	ADJ
ejpam-5658	228	10	.	.	PUNCT
ejpam-5658	229	1	however	however	ADV
ejpam-5658	229	2	,	,	PUNCT
ejpam-5658	229	3	strict	strict	ADJ
ejpam-5658	229	4	inequality	inequality	NOUN
ejpam-5658	229	5	is	be	AUX
ejpam-5658	229	6	also	also	ADV
ejpam-5658	229	7	attainable	attainable	ADJ
ejpam-5658	229	8	.	.	PUNCT
ejpam-5658	230	1	to	to	PART
ejpam-5658	230	2	see	see	VERB
ejpam-5658	230	3	this	this	PRON
ejpam-5658	230	4	,	,	PUNCT
ejpam-5658	230	5	consider	consider	VERB
ejpam-5658	230	6	k5	k5	PROPN
ejpam-5658	230	7	⋄	⋄	PROPN
ejpam-5658	230	8	p3	p3	PROPN
ejpam-5658	230	9	,	,	PUNCT
ejpam-5658	230	10	c4	c4	NOUN
ejpam-5658	230	11	⋄	⋄	PROPN
ejpam-5658	230	12	p3	p3	PROPN
ejpam-5658	230	13	,	,	PUNCT
ejpam-5658	230	14	and	and	CCONJ
ejpam-5658	230	15	g	g	PROPN
ejpam-5658	230	16	⋄	⋄	PROPN
ejpam-5658	230	17	p3	p3	PROPN
ejpam-5658	230	18	,	,	PUNCT
ejpam-5658	230	19	where	where	SCONJ
ejpam-5658	230	20	g	g	PROPN
ejpam-5658	230	21	is	be	AUX
ejpam-5658	230	22	the	the	DET
ejpam-5658	230	23	graph	graph	NOUN
ejpam-5658	230	24	in	in	ADP
ejpam-5658	230	25	figure	figure	NOUN
ejpam-5658	230	26	3	3	NUM
ejpam-5658	230	27	.	.	PUNCT
ejpam-5658	230	28	.........	.........	PUNCT
ejpam-5658	230	29	........	........	PUNCT
ejpam-5658	230	30	........	........	PUNCT
ejpam-5658	230	31	........	........	PUNCT
ejpam-5658	230	32	........	........	PUNCT
ejpam-5658	230	33	........	........	PUNCT
ejpam-5658	230	34	........	........	PUNCT
ejpam-5658	230	35	........	........	PUNCT
ejpam-5658	230	36	........	........	PUNCT
ejpam-5658	230	37	........	........	PUNCT
ejpam-5658	230	38	........	........	PUNCT
ejpam-5658	230	39	........	........	PUNCT
ejpam-5658	230	40	.......	.......	PUNCT
ejpam-5658	231	1	....................................	....................................	PUNCT
ejpam-5658	231	2	..........................................................................................................................................................	..........................................................................................................................................................	PUNCT
ejpam-5658	231	3	....................................	....................................	PUNCT
ejpam-5658	232	1	....................................	....................................	PUNCT
ejpam-5658	232	2	...................	...................	PUNCT
ejpam-5658	233	1	..................	..................	PUNCT
ejpam-5658	233	2	..................	..................	PUNCT
ejpam-5658	234	1	..................	..................	PUNCT
ejpam-5658	234	2	..................	..................	PUNCT
ejpam-5658	235	1	..................	..................	PUNCT
ejpam-5658	235	2	.........	.........	PUNCT
ejpam-5658	236	1	....................................	....................................	PUNCT
ejpam-5658	236	2	....................................	....................................	PUNCT
ejpam-5658	237	1	...................	...................	PUNCT
ejpam-5658	237	2	..................	..................	PUNCT
ejpam-5658	238	1	..................	..................	PUNCT
ejpam-5658	238	2	..................	..................	PUNCT
ejpam-5658	239	1	..................	..................	PUNCT
ejpam-5658	239	2	..................	..................	PUNCT
ejpam-5658	240	1	.........	.........	PUNCT
ejpam-5658	240	2	....................................	....................................	PUNCT
ejpam-5658	241	1	....................................	....................................	PUNCT
ejpam-5658	241	2	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-5658	242	1	....................................	....................................	PUNCT
ejpam-5658	242	2	....................................	....................................	PUNCT
ejpam-5658	242	3	.........	.........	PUNCT
ejpam-5658	242	4	........	........	PUNCT
ejpam-5658	242	5	........	........	PUNCT
ejpam-5658	242	6	........	........	PUNCT
ejpam-5658	242	7	........	........	PUNCT
ejpam-5658	242	8	........	........	PUNCT
ejpam-5658	242	9	........	........	PUNCT
ejpam-5658	242	10	........	........	PUNCT
ejpam-5658	242	11	........	........	PUNCT
ejpam-5658	242	12	........	........	PUNCT
ejpam-5658	242	13	........	........	PUNCT
ejpam-5658	242	14	........	........	PUNCT
ejpam-5658	242	15	.......	.......	PUNCT
ejpam-5658	242	16	....................................	....................................	PUNCT
ejpam-5658	243	1	....................................	....................................	PUNCT
ejpam-5658	243	2	figure	figure	NOUN
ejpam-5658	243	3	3	3	NUM
ejpam-5658	243	4	clearly	clearly	ADV
ejpam-5658	243	5	,	,	PUNCT
ejpam-5658	243	6	αh(k5	αh(k5	PROPN
ejpam-5658	243	7	)	)	PUNCT
ejpam-5658	243	8	=	=	SYM
ejpam-5658	243	9	5	5	NUM
ejpam-5658	243	10	,	,	PUNCT
ejpam-5658	243	11	αh(c4	αh(c4	NOUN
ejpam-5658	243	12	)	)	PUNCT
ejpam-5658	243	13	=	=	SYM
ejpam-5658	243	14	2	2	NUM
ejpam-5658	243	15	,	,	PUNCT
ejpam-5658	243	16	αh(g	αh(g	NOUN
ejpam-5658	243	17	)	)	PUNCT
ejpam-5658	243	18	=	=	SYM
ejpam-5658	243	19	3	3	NUM
ejpam-5658	243	20	,	,	PUNCT
ejpam-5658	243	21	ν(k5	ν(k5	PROPN
ejpam-5658	243	22	)	)	PUNCT
ejpam-5658	243	23	=	=	SYM
ejpam-5658	243	24	ν(c4	ν(c4	NOUN
ejpam-5658	243	25	)	)	PUNCT
ejpam-5658	243	26	=	=	SYM
ejpam-5658	244	1	ν(g	ν(g	PROPN
ejpam-5658	244	2	)	)	PUNCT
ejpam-5658	244	3	=	=	SYM
ejpam-5658	244	4	2	2	NUM
ejpam-5658	244	5	,	,	PUNCT
ejpam-5658	244	6	and	and	CCONJ
ejpam-5658	244	7	ω(p3	ω(p3	NOUN
ejpam-5658	244	8	)	)	PUNCT
ejpam-5658	244	9	=	=	SYM
ejpam-5658	245	1	2	2	X
ejpam-5658	245	2	.	.	X
ejpam-5658	245	3	it	it	PRON
ejpam-5658	245	4	can	can	AUX
ejpam-5658	245	5	be	be	AUX
ejpam-5658	245	6	verified	verify	VERB
ejpam-5658	245	7	easily	easily	ADV
ejpam-5658	245	8	that	that	SCONJ
ejpam-5658	245	9	αh(k5	αh(k5	DET
ejpam-5658	245	10	⋄p3	⋄p3	NOUN
ejpam-5658	245	11	)	)	PUNCT
ejpam-5658	245	12	=	=	SYM
ejpam-5658	245	13	αh(k5	αh(k5	PROPN
ejpam-5658	245	14	)	)	PUNCT
ejpam-5658	245	15	=	=	SYM
ejpam-5658	245	16	5	5	NUM
ejpam-5658	245	17	>	>	SYM
ejpam-5658	245	18	4	4	NUM
ejpam-5658	245	19	=	=	SYM
ejpam-5658	245	20	ν(k5)ω(p3	ν(k5)ω(p3	PROPN
ejpam-5658	245	21	)	)	PUNCT
ejpam-5658	245	22	,	,	PUNCT
ejpam-5658	245	23	αh(c4	αh(c4	ADP
ejpam-5658	245	24	⋄p3	⋄p3	ADJ
ejpam-5658	245	25	)	)	PUNCT
ejpam-5658	245	26	=	=	SYM
ejpam-5658	245	27	ν(c4)ω(p3	ν(c4)ω(p3	PROPN
ejpam-5658	245	28	)	)	PUNCT
ejpam-5658	245	29	=	=	PUNCT
ejpam-5658	245	30	4	4	NUM
ejpam-5658	245	31	>	>	SYM
ejpam-5658	245	32	2	2	NUM
ejpam-5658	245	33	=	=	SYM
ejpam-5658	245	34	αh(c4	αh(c4	NOUN
ejpam-5658	245	35	)	)	PUNCT
ejpam-5658	245	36	,	,	PUNCT
ejpam-5658	245	37	and	and	CCONJ
ejpam-5658	245	38	αh(g	αh(g	ADP
ejpam-5658	245	39	⋄	⋄	PROPN
ejpam-5658	245	40	p3	p3	PROPN
ejpam-5658	245	41	)	)	PUNCT
ejpam-5658	245	42	=	=	PUNCT
ejpam-5658	245	43	6	6	NUM
ejpam-5658	245	44	>	>	SYM
ejpam-5658	245	45	4	4	NUM
ejpam-5658	245	46	=	=	SYM
ejpam-5658	245	47	max{αh(g	max{αh(g	NOUN
ejpam-5658	245	48	)	)	PUNCT
ejpam-5658	245	49	,	,	PUNCT
ejpam-5658	245	50	ν(g)ω(p3	ν(g)ω(p3	NOUN
ejpam-5658	245	51	)	)	PUNCT
ejpam-5658	245	52	}	}	PUNCT
ejpam-5658	245	53	.	.	PUNCT
ejpam-5658	246	1	j.	j.	PROPN
ejpam-5658	246	2	anoche	anoche	PROPN
ejpam-5658	246	3	,	,	PUNCT
ejpam-5658	246	4	s.	s.	PROPN
ejpam-5658	246	5	canoy	canoy	PROPN
ejpam-5658	246	6	,	,	PUNCT
ejpam-5658	246	7	jr	jr	PROPN
ejpam-5658	246	8	.	.	PROPN
ejpam-5658	246	9	/	/	SYM
ejpam-5658	246	10	eur	eur	PROPN
ejpam-5658	246	11	.	.	PUNCT
ejpam-5658	247	1	j.	j.	PROPN
ejpam-5658	247	2	pure	pure	PROPN
ejpam-5658	247	3	appl	appl	PROPN
ejpam-5658	247	4	.	.	PROPN
ejpam-5658	247	5	math	math	PROPN
ejpam-5658	247	6	,	,	PUNCT
ejpam-5658	247	7	18	18	NUM
ejpam-5658	247	8	(	(	PUNCT
ejpam-5658	247	9	1	1	NUM
ejpam-5658	247	10	)	)	PUNCT
ejpam-5658	247	11	(	(	PUNCT
ejpam-5658	247	12	2025	2025	NUM
ejpam-5658	247	13	)	)	PUNCT
ejpam-5658	247	14	,	,	PUNCT
ejpam-5658	247	15	5658	5658	NUM
ejpam-5658	247	16	8	8	NUM
ejpam-5658	247	17	of	of	ADP
ejpam-5658	247	18	15	15	NUM
ejpam-5658	247	19	6	6	NUM
ejpam-5658	247	20	.	.	PUNCT
ejpam-5658	247	21	complementary	complementary	ADJ
ejpam-5658	247	22	prism	prism	NOUN
ejpam-5658	247	23	theorem	theorem	VERB
ejpam-5658	247	24	4	4	NUM
ejpam-5658	247	25	.	.	PUNCT
ejpam-5658	248	1	let	let	VERB
ejpam-5658	248	2	g	g	PRON
ejpam-5658	248	3	be	be	AUX
ejpam-5658	248	4	a	a	DET
ejpam-5658	248	5	graph	graph	NOUN
ejpam-5658	248	6	.	.	PUNCT
ejpam-5658	249	1	then	then	ADV
ejpam-5658	249	2	s	s	VERB
ejpam-5658	249	3	is	be	AUX
ejpam-5658	249	4	a	a	DET
ejpam-5658	249	5	hop	hop	NOUN
ejpam-5658	249	6	independent	independent	ADJ
ejpam-5658	249	7	set	set	NOUN
ejpam-5658	249	8	in	in	ADP
ejpam-5658	249	9	gg	gg	PROPN
ejpam-5658	249	10	if	if	SCONJ
ejpam-5658	249	11	and	and	CCONJ
ejpam-5658	249	12	only	only	ADV
ejpam-5658	249	13	if	if	SCONJ
ejpam-5658	249	14	one	one	NUM
ejpam-5658	249	15	of	of	ADP
ejpam-5658	249	16	the	the	DET
ejpam-5658	249	17	following	follow	VERB
ejpam-5658	249	18	holds	hold	NOUN
ejpam-5658	249	19	.	.	PUNCT
ejpam-5658	250	1	(	(	PUNCT
ejpam-5658	250	2	i	i	NOUN
ejpam-5658	250	3	)	)	PUNCT
ejpam-5658	250	4	s	s	AUX
ejpam-5658	250	5	is	be	AUX
ejpam-5658	250	6	a	a	DET
ejpam-5658	250	7	hop	hop	NOUN
ejpam-5658	250	8	independent	independent	ADJ
ejpam-5658	250	9	set	set	NOUN
ejpam-5658	250	10	in	in	ADP
ejpam-5658	250	11	g.	g.	PROPN
ejpam-5658	250	12	(	(	PUNCT
ejpam-5658	250	13	ii	ii	PROPN
ejpam-5658	250	14	)	)	PUNCT
ejpam-5658	250	15	s	s	VERB
ejpam-5658	250	16	is	be	AUX
ejpam-5658	250	17	a	a	DET
ejpam-5658	250	18	hop	hop	NOUN
ejpam-5658	250	19	independent	independent	ADJ
ejpam-5658	250	20	set	set	NOUN
ejpam-5658	250	21	in	in	ADP
ejpam-5658	250	22	g.	g.	PROPN
ejpam-5658	250	23	(	(	PUNCT
ejpam-5658	250	24	iii	iii	X
ejpam-5658	250	25	)	)	PUNCT
ejpam-5658	250	26	s	s	PART
ejpam-5658	250	27	=	=	PUNCT
ejpam-5658	250	28	{	{	PUNCT
ejpam-5658	250	29	v	v	NOUN
ejpam-5658	250	30	,	,	PUNCT
ejpam-5658	250	31	v	v	NOUN
ejpam-5658	250	32	}	}	PUNCT
ejpam-5658	250	33	for	for	ADP
ejpam-5658	250	34	some	some	DET
ejpam-5658	250	35	v	v	ADP
ejpam-5658	250	36	∈	∈	NOUN
ejpam-5658	250	37	v	v	NOUN
ejpam-5658	250	38	(	(	PUNCT
ejpam-5658	250	39	g	g	NOUN
ejpam-5658	250	40	)	)	PUNCT
ejpam-5658	250	41	.	.	PUNCT
ejpam-5658	251	1	proof	proof	NOUN
ejpam-5658	251	2	.	.	PUNCT
ejpam-5658	252	1	suppose	suppose	VERB
ejpam-5658	252	2	s	s	PRON
ejpam-5658	252	3	is	be	AUX
ejpam-5658	252	4	a	a	DET
ejpam-5658	252	5	hop	hop	NOUN
ejpam-5658	252	6	independent	independent	ADJ
ejpam-5658	252	7	set	set	NOUN
ejpam-5658	252	8	in	in	ADP
ejpam-5658	252	9	gg	gg	PROPN
ejpam-5658	252	10	.	.	PUNCT
ejpam-5658	253	1	if	if	SCONJ
ejpam-5658	253	2	s	s	VERB
ejpam-5658	253	3	⊆	⊆	NUM
ejpam-5658	253	4	v	v	NOUN
ejpam-5658	253	5	(	(	PUNCT
ejpam-5658	253	6	g	g	NOUN
ejpam-5658	253	7	)	)	PUNCT
ejpam-5658	253	8	,	,	PUNCT
ejpam-5658	253	9	then	then	ADV
ejpam-5658	253	10	s	s	VERB
ejpam-5658	253	11	is	be	AUX
ejpam-5658	253	12	a	a	DET
ejpam-5658	253	13	hop	hop	NOUN
ejpam-5658	253	14	independent	independent	ADJ
ejpam-5658	253	15	set	set	NOUN
ejpam-5658	253	16	in	in	ADP
ejpam-5658	253	17	g.	g.	PROPN
ejpam-5658	253	18	if	if	SCONJ
ejpam-5658	253	19	s	s	VERB
ejpam-5658	253	20	⊆	⊆	NUM
ejpam-5658	253	21	v	v	NOUN
ejpam-5658	253	22	(	(	PUNCT
ejpam-5658	253	23	g	g	NOUN
ejpam-5658	253	24	)	)	PUNCT
ejpam-5658	253	25	,	,	PUNCT
ejpam-5658	253	26	then	then	ADV
ejpam-5658	253	27	s	s	VERB
ejpam-5658	253	28	is	be	AUX
ejpam-5658	253	29	a	a	DET
ejpam-5658	253	30	hop	hop	NOUN
ejpam-5658	253	31	independent	independent	ADJ
ejpam-5658	253	32	set	set	NOUN
ejpam-5658	253	33	in	in	ADP
ejpam-5658	253	34	g.	g.	PROPN
ejpam-5658	253	35	hence	hence	ADV
ejpam-5658	253	36	,	,	PUNCT
ejpam-5658	253	37	(	(	PUNCT
ejpam-5658	253	38	i	i	NOUN
ejpam-5658	253	39	)	)	PUNCT
ejpam-5658	253	40	or	or	CCONJ
ejpam-5658	253	41	(	(	PUNCT
ejpam-5658	253	42	ii	ii	NOUN
ejpam-5658	253	43	)	)	PUNCT
ejpam-5658	253	44	holds	hold	VERB
ejpam-5658	253	45	.	.	PUNCT
ejpam-5658	254	1	suppose	suppose	VERB
ejpam-5658	254	2	s	s	VERB
ejpam-5658	254	3	∩	∩	ADJ
ejpam-5658	254	4	v	v	X
ejpam-5658	254	5	(	(	PUNCT
ejpam-5658	254	6	g	g	NOUN
ejpam-5658	254	7	)	)	PUNCT
ejpam-5658	254	8	̸=	̸=	PROPN
ejpam-5658	254	9	∅	∅	NOUN
ejpam-5658	254	10	and	and	CCONJ
ejpam-5658	254	11	s	s	VERB
ejpam-5658	254	12	∩	∩	ADJ
ejpam-5658	254	13	v	v	ADJ
ejpam-5658	254	14	(	(	PUNCT
ejpam-5658	254	15	g	g	NOUN
ejpam-5658	254	16	)	)	PUNCT
ejpam-5658	254	17	̸=	̸=	PROPN
ejpam-5658	254	18	∅.	∅.	ADV
ejpam-5658	254	19	let	let	VERB
ejpam-5658	254	20	v	v	NUM
ejpam-5658	254	21	∈	∈	NOUN
ejpam-5658	254	22	s	s	PART
ejpam-5658	254	23	∩	∩	ADJ
ejpam-5658	254	24	v	v	X
ejpam-5658	254	25	(	(	PUNCT
ejpam-5658	254	26	g	g	NOUN
ejpam-5658	254	27	)	)	PUNCT
ejpam-5658	254	28	and	and	CCONJ
ejpam-5658	254	29	let	let	VERB
ejpam-5658	254	30	w	w	PROPN
ejpam-5658	254	31	∈	∈	PROPN
ejpam-5658	254	32	s	s	PART
ejpam-5658	254	33	∩	∩	ADJ
ejpam-5658	254	34	v	v	X
ejpam-5658	254	35	(	(	PUNCT
ejpam-5658	254	36	g	g	NOUN
ejpam-5658	254	37	)	)	PUNCT
ejpam-5658	254	38	.	.	PUNCT
ejpam-5658	255	1	suppose	suppose	VERB
ejpam-5658	255	2	w	w	ADP
ejpam-5658	255	3	̸=	̸=	PROPN
ejpam-5658	255	4	v.	v.	CCONJ
ejpam-5658	255	5	then	then	ADV
ejpam-5658	255	6	v	v	ADP
ejpam-5658	255	7	̸=	̸=	PROPN
ejpam-5658	255	8	w.	w.	NOUN
ejpam-5658	255	9	since	since	SCONJ
ejpam-5658	255	10	vw	vw	PROPN
ejpam-5658	255	11	∈	∈	PROPN
ejpam-5658	255	12	e(g	e(g	PROPN
ejpam-5658	255	13	)	)	PUNCT
ejpam-5658	256	1	if	if	SCONJ
ejpam-5658	256	2	and	and	CCONJ
ejpam-5658	256	3	only	only	ADV
ejpam-5658	256	4	if	if	SCONJ
ejpam-5658	256	5	v	v	PROPN
ejpam-5658	256	6	w	w	PROPN
ejpam-5658	256	7	/∈	/∈	PUNCT
ejpam-5658	256	8	e(g	e(g	PROPN
ejpam-5658	256	9	)	)	PUNCT
ejpam-5658	256	10	,	,	PUNCT
ejpam-5658	256	11	it	it	PRON
ejpam-5658	256	12	follows	follow	VERB
ejpam-5658	256	13	that	that	SCONJ
ejpam-5658	256	14	dgg(v	dgg(v	PROPN
ejpam-5658	256	15	,	,	PUNCT
ejpam-5658	256	16	w	w	NOUN
ejpam-5658	256	17	)	)	PUNCT
ejpam-5658	256	18	=	=	SYM
ejpam-5658	256	19	2	2	NUM
ejpam-5658	256	20	,	,	PUNCT
ejpam-5658	256	21	contrary	contrary	ADV
ejpam-5658	256	22	to	to	ADP
ejpam-5658	256	23	the	the	DET
ejpam-5658	256	24	assumption	assumption	NOUN
ejpam-5658	256	25	that	that	SCONJ
ejpam-5658	256	26	s	s	VERB
ejpam-5658	256	27	is	be	AUX
ejpam-5658	256	28	a	a	DET
ejpam-5658	256	29	hop	hop	NOUN
ejpam-5658	256	30	independent	independent	ADJ
ejpam-5658	256	31	set	set	NOUN
ejpam-5658	256	32	in	in	ADP
ejpam-5658	256	33	gg	gg	PROPN
ejpam-5658	256	34	.	.	PUNCT
ejpam-5658	257	1	thus	thus	ADV
ejpam-5658	257	2	,	,	PUNCT
ejpam-5658	257	3	w	w	PROPN
ejpam-5658	257	4	=	=	PUNCT
ejpam-5658	257	5	v.	v.	CCONJ
ejpam-5658	257	6	suppose	suppose	VERB
ejpam-5658	257	7	there	there	PRON
ejpam-5658	257	8	exists	exist	VERB
ejpam-5658	257	9	x	x	X
ejpam-5658	257	10	∈	∈	PROPN
ejpam-5658	257	11	(	(	PUNCT
ejpam-5658	257	12	s	s	X
ejpam-5658	257	13	∩	∩	ADJ
ejpam-5658	257	14	v	v	ADJ
ejpam-5658	257	15	(	(	PUNCT
ejpam-5658	257	16	g	g	NOUN
ejpam-5658	257	17	)	)	PUNCT
ejpam-5658	257	18	)	)	PUNCT
ejpam-5658	257	19	\	\	PROPN
ejpam-5658	258	1	{	{	PUNCT
ejpam-5658	258	2	v	v	NOUN
ejpam-5658	258	3	}	}	PUNCT
ejpam-5658	258	4	.	.	PUNCT
ejpam-5658	259	1	then	then	ADV
ejpam-5658	259	2	dgg(x	dgg(x	PRON
ejpam-5658	259	3	,	,	PUNCT
ejpam-5658	259	4	v	v	NOUN
ejpam-5658	259	5	)	)	PUNCT
ejpam-5658	259	6	=	=	SYM
ejpam-5658	259	7	2	2	NUM
ejpam-5658	259	8	which	which	PRON
ejpam-5658	259	9	is	be	AUX
ejpam-5658	259	10	not	not	PART
ejpam-5658	259	11	possible	possible	ADJ
ejpam-5658	259	12	.	.	PUNCT
ejpam-5658	260	1	thus	thus	ADV
ejpam-5658	260	2	,	,	PUNCT
ejpam-5658	260	3	s	s	VERB
ejpam-5658	260	4	∩v	∩v	NOUN
ejpam-5658	260	5	(	(	PUNCT
ejpam-5658	260	6	g	g	NOUN
ejpam-5658	260	7	)	)	PUNCT
ejpam-5658	260	8	=	=	PRON
ejpam-5658	260	9	{	{	PUNCT
ejpam-5658	260	10	v	v	NOUN
ejpam-5658	260	11	}	}	PUNCT
ejpam-5658	260	12	.	.	PUNCT
ejpam-5658	261	1	similarly	similarly	ADV
ejpam-5658	261	2	,	,	PUNCT
ejpam-5658	261	3	s	s	AUX
ejpam-5658	261	4	∩v	∩v	NOUN
ejpam-5658	261	5	(	(	PUNCT
ejpam-5658	261	6	g	g	NOUN
ejpam-5658	261	7	)	)	PUNCT
ejpam-5658	261	8	=	=	PRON
ejpam-5658	261	9	{	{	PUNCT
ejpam-5658	261	10	v	v	NOUN
ejpam-5658	261	11	}	}	PUNCT
ejpam-5658	261	12	.	.	PUNCT
ejpam-5658	262	1	this	this	PRON
ejpam-5658	262	2	shows	show	VERB
ejpam-5658	262	3	that	that	SCONJ
ejpam-5658	262	4	(	(	PUNCT
ejpam-5658	262	5	iii	iii	NOUN
ejpam-5658	262	6	)	)	PUNCT
ejpam-5658	262	7	holds	hold	VERB
ejpam-5658	262	8	.	.	PUNCT
ejpam-5658	263	1	the	the	DET
ejpam-5658	263	2	converse	converse	NOUN
ejpam-5658	263	3	is	be	AUX
ejpam-5658	263	4	clear	clear	ADJ
ejpam-5658	263	5	.	.	PUNCT
ejpam-5658	264	1	the	the	DET
ejpam-5658	264	2	next	next	ADJ
ejpam-5658	264	3	result	result	NOUN
ejpam-5658	264	4	is	be	AUX
ejpam-5658	264	5	immediate	immediate	ADJ
ejpam-5658	264	6	from	from	ADP
ejpam-5658	264	7	theorem	theorem	ADJ
ejpam-5658	264	8	4	4	NUM
ejpam-5658	264	9	.	.	PUNCT
ejpam-5658	264	10	corollary	corollary	ADJ
ejpam-5658	264	11	4	4	NUM
ejpam-5658	264	12	.	.	PUNCT
ejpam-5658	265	1	let	let	VERB
ejpam-5658	265	2	g	g	PRON
ejpam-5658	265	3	be	be	AUX
ejpam-5658	265	4	a	a	DET
ejpam-5658	265	5	graph	graph	NOUN
ejpam-5658	265	6	.	.	PUNCT
ejpam-5658	266	1	then	then	ADV
ejpam-5658	266	2	αh(gg	αh(gg	PROPN
ejpam-5658	266	3	)	)	PUNCT
ejpam-5658	267	1	=	=	SYM
ejpam-5658	267	2	max{2	max{2	PROPN
ejpam-5658	267	3	,	,	PUNCT
ejpam-5658	267	4	αh(g	αh(g	NOUN
ejpam-5658	267	5	)	)	PUNCT
ejpam-5658	267	6	,	,	PUNCT
ejpam-5658	267	7	αh(g	αh(g	NOUN
ejpam-5658	267	8	}	}	PUNCT
ejpam-5658	267	9	.	.	PUNCT
ejpam-5658	268	1	7	7	X
ejpam-5658	268	2	.	.	X
ejpam-5658	268	3	disjunction	disjunction	NOUN
ejpam-5658	268	4	of	of	ADP
ejpam-5658	268	5	two	two	NUM
ejpam-5658	268	6	graphs	graph	NOUN
ejpam-5658	268	7	theorem	theorem	VERB
ejpam-5658	268	8	5	5	NUM
ejpam-5658	268	9	.	.	PUNCT
ejpam-5658	269	1	let	let	VERB
ejpam-5658	269	2	g	g	NOUN
ejpam-5658	269	3	and	and	CCONJ
ejpam-5658	269	4	h	h	PROPN
ejpam-5658	269	5	be	be	VERB
ejpam-5658	269	6	non	non	ADJ
ejpam-5658	269	7	-	-	ADJ
ejpam-5658	269	8	trivial	trivial	ADJ
ejpam-5658	269	9	connected	connected	ADJ
ejpam-5658	269	10	graphs	graph	NOUN
ejpam-5658	269	11	.	.	PUNCT
ejpam-5658	270	1	then	then	ADV
ejpam-5658	270	2	c	c	X
ejpam-5658	270	3	=	=	SYM
ejpam-5658	270	4	∪x∈s({x	∪x∈s({x	ADJ
ejpam-5658	270	5	}	}	PUNCT
ejpam-5658	270	6	×	×	NOUN
ejpam-5658	270	7	tx	tx	PROPN
ejpam-5658	270	8	)	)	PUNCT
ejpam-5658	270	9	is	be	AUX
ejpam-5658	270	10	a	a	DET
ejpam-5658	270	11	hop	hop	NOUN
ejpam-5658	270	12	independent	independent	ADJ
ejpam-5658	270	13	set	set	NOUN
ejpam-5658	270	14	in	in	ADP
ejpam-5658	270	15	g	g	PROPN
ejpam-5658	270	16	∨h	∨h	NOUN
ejpam-5658	270	17	if	if	SCONJ
ejpam-5658	270	18	and	and	CCONJ
ejpam-5658	270	19	only	only	ADV
ejpam-5658	270	20	if	if	SCONJ
ejpam-5658	270	21	following	follow	VERB
ejpam-5658	270	22	conditions	condition	NOUN
ejpam-5658	270	23	hold	hold	VERB
ejpam-5658	270	24	.	.	PUNCT
ejpam-5658	271	1	(	(	PUNCT
ejpam-5658	271	2	i	i	NOUN
ejpam-5658	271	3	)	)	PUNCT
ejpam-5658	271	4	s	s	VERB
ejpam-5658	271	5	is	be	AUX
ejpam-5658	271	6	a	a	DET
ejpam-5658	271	7	hop	hop	NOUN
ejpam-5658	271	8	independent	independent	ADJ
ejpam-5658	271	9	set	set	NOUN
ejpam-5658	271	10	in	in	ADP
ejpam-5658	271	11	g.	g.	PROPN
ejpam-5658	271	12	(	(	PUNCT
ejpam-5658	271	13	ii	ii	PROPN
ejpam-5658	271	14	)	)	PUNCT
ejpam-5658	271	15	tx	tx	PROPN
ejpam-5658	271	16	is	be	AUX
ejpam-5658	271	17	a	a	DET
ejpam-5658	271	18	clique	clique	NOUN
ejpam-5658	271	19	in	in	ADP
ejpam-5658	271	20	h	h	NOUN
ejpam-5658	271	21	for	for	ADP
ejpam-5658	271	22	every	every	DET
ejpam-5658	271	23	x	x	PROPN
ejpam-5658	271	24	∈	∈	PROPN
ejpam-5658	271	25	s.	s.	PROPN
ejpam-5658	271	26	(	(	PUNCT
ejpam-5658	271	27	iii	iii	PROPN
ejpam-5658	271	28	)	)	PUNCT
ejpam-5658	271	29	if	if	SCONJ
ejpam-5658	271	30	x	x	X
ejpam-5658	271	31	,	,	PUNCT
ejpam-5658	271	32	y	y	PROPN
ejpam-5658	271	33	∈	∈	PROPN
ejpam-5658	271	34	s	s	X
ejpam-5658	271	35	and	and	CCONJ
ejpam-5658	271	36	dg(x	dg(x	NUM
ejpam-5658	271	37	,	,	PUNCT
ejpam-5658	271	38	y	y	PROPN
ejpam-5658	271	39	)	)	PUNCT
ejpam-5658	271	40	≥	≥	NOUN
ejpam-5658	271	41	3	3	NUM
ejpam-5658	271	42	,	,	PUNCT
ejpam-5658	271	43	then	then	ADV
ejpam-5658	271	44	tx	tx	PROPN
ejpam-5658	271	45	∩	∩	ADJ
ejpam-5658	271	46	ty	ty	ADJ
ejpam-5658	271	47	=	=	NOUN
ejpam-5658	271	48	∅	∅	NOUN
ejpam-5658	271	49	and	and	CCONJ
ejpam-5658	271	50	dh(tx	dh(tx	PROPN
ejpam-5658	271	51	,	,	PUNCT
ejpam-5658	271	52	ty	ty	NOUN
ejpam-5658	271	53	)	)	PUNCT
ejpam-5658	271	54	≥	≥	NOUN
ejpam-5658	271	55	3	3	NUM
ejpam-5658	271	56	.	.	PUNCT
ejpam-5658	271	57	(	(	PUNCT
ejpam-5658	271	58	iv	iv	X
ejpam-5658	271	59	)	)	PUNCT
ejpam-5658	271	60	∪x∈s0tx	∪x∈s0tx	PROPN
ejpam-5658	271	61	is	be	AUX
ejpam-5658	271	62	a	a	DET
ejpam-5658	271	63	hop	hop	NOUN
ejpam-5658	271	64	independent	independent	ADJ
ejpam-5658	271	65	set	set	NOUN
ejpam-5658	271	66	in	in	ADP
ejpam-5658	271	67	h	h	NOUN
ejpam-5658	271	68	for	for	ADP
ejpam-5658	271	69	every	every	DET
ejpam-5658	271	70	independet	independet	NOUN
ejpam-5658	271	71	set	set	VERB
ejpam-5658	271	72	s0	s0	PROPN
ejpam-5658	271	73	⊆	⊆	NUM
ejpam-5658	271	74	s.	s.	PROPN
ejpam-5658	271	75	proof	proof	PROPN
ejpam-5658	271	76	.	.	PUNCT
ejpam-5658	272	1	suppose	suppose	VERB
ejpam-5658	272	2	c	c	NOUN
ejpam-5658	272	3	is	be	AUX
ejpam-5658	272	4	a	a	DET
ejpam-5658	272	5	hop	hop	NOUN
ejpam-5658	272	6	independent	independent	ADJ
ejpam-5658	272	7	set	set	NOUN
ejpam-5658	272	8	in	in	ADP
ejpam-5658	272	9	g∨h	g∨h	PROPN
ejpam-5658	272	10	.	.	PUNCT
ejpam-5658	273	1	suppose	suppose	VERB
ejpam-5658	273	2	s	s	NOUN
ejpam-5658	273	3	is	be	AUX
ejpam-5658	273	4	not	not	PART
ejpam-5658	273	5	hop	hop	ADV
ejpam-5658	273	6	independent	independent	ADJ
ejpam-5658	273	7	in	in	ADP
ejpam-5658	273	8	g.	g.	PROPN
ejpam-5658	273	9	then	then	ADV
ejpam-5658	273	10	there	there	PRON
ejpam-5658	273	11	exist	exist	VERB
ejpam-5658	273	12	u	u	NOUN
ejpam-5658	273	13	,	,	PUNCT
ejpam-5658	273	14	v	v	PROPN
ejpam-5658	273	15	∈	∈	NOUN
ejpam-5658	273	16	s	s	VERB
ejpam-5658	273	17	such	such	ADJ
ejpam-5658	273	18	that	that	DET
ejpam-5658	273	19	dg(u	dg(u	ADJ
ejpam-5658	273	20	,	,	PUNCT
ejpam-5658	273	21	v	v	NOUN
ejpam-5658	273	22	)	)	PUNCT
ejpam-5658	274	1	=	=	SYM
ejpam-5658	274	2	2	2	X
ejpam-5658	274	3	.	.	X
ejpam-5658	274	4	let	let	VERB
ejpam-5658	274	5	w	w	PROPN
ejpam-5658	274	6	∈	∈	PROPN
ejpam-5658	274	7	ng(u	ng(u	NOUN
ejpam-5658	274	8	)	)	PUNCT
ejpam-5658	274	9	∩ng(v	∩ng(v	PROPN
ejpam-5658	274	10	)	)	PUNCT
ejpam-5658	274	11	,	,	PUNCT
ejpam-5658	274	12	a	a	DET
ejpam-5658	274	13	∈	∈	PROPN
ejpam-5658	274	14	tu	tu	X
ejpam-5658	274	15	and	and	CCONJ
ejpam-5658	274	16	b	b	PROPN
ejpam-5658	274	17	∈	∈	PROPN
ejpam-5658	274	18	tv	tv	NOUN
ejpam-5658	274	19	.	.	PUNCT
ejpam-5658	275	1	if	if	SCONJ
ejpam-5658	275	2	a	a	DET
ejpam-5658	275	3	=	=	SYM
ejpam-5658	275	4	b	b	NOUN
ejpam-5658	275	5	,	,	PUNCT
ejpam-5658	275	6	then	then	ADV
ejpam-5658	275	7	[	[	X
ejpam-5658	275	8	(	(	PUNCT
ejpam-5658	275	9	u	u	NOUN
ejpam-5658	275	10	,	,	PUNCT
ejpam-5658	275	11	a	a	PRON
ejpam-5658	275	12	)	)	PUNCT
ejpam-5658	275	13	,	,	PUNCT
ejpam-5658	275	14	(	(	PUNCT
ejpam-5658	275	15	w	w	NOUN
ejpam-5658	275	16	,	,	PUNCT
ejpam-5658	275	17	a	a	NOUN
ejpam-5658	275	18	)	)	PUNCT
ejpam-5658	275	19	,	,	PUNCT
ejpam-5658	275	20	(	(	PUNCT
ejpam-5658	275	21	v	v	NOUN
ejpam-5658	275	22	,	,	PUNCT
ejpam-5658	275	23	a	a	PRON
ejpam-5658	275	24	)	)	PUNCT
ejpam-5658	275	25	]	]	PUNCT
ejpam-5658	275	26	is	be	AUX
ejpam-5658	275	27	a	a	DET
ejpam-5658	275	28	(	(	PUNCT
ejpam-5658	275	29	u	u	NOUN
ejpam-5658	275	30	,	,	PUNCT
ejpam-5658	275	31	a)-(v	a)-(v	PROPN
ejpam-5658	275	32	,	,	PUNCT
ejpam-5658	275	33	b	b	NOUN
ejpam-5658	275	34	)	)	PUNCT
ejpam-5658	275	35	geodesic	geodesic	NOUN
ejpam-5658	275	36	in	in	ADP
ejpam-5658	275	37	g∨h	g∨h	PROPN
ejpam-5658	275	38	.	.	PUNCT
ejpam-5658	276	1	if	if	SCONJ
ejpam-5658	276	2	a	a	DET
ejpam-5658	276	3	̸=	̸=	PROPN
ejpam-5658	276	4	b	b	PROPN
ejpam-5658	276	5	,	,	PUNCT
ejpam-5658	276	6	then	then	ADV
ejpam-5658	276	7	[	[	X
ejpam-5658	276	8	(	(	PUNCT
ejpam-5658	276	9	u	u	NOUN
ejpam-5658	276	10	,	,	PUNCT
ejpam-5658	276	11	a	a	PRON
ejpam-5658	276	12	)	)	PUNCT
ejpam-5658	276	13	,	,	PUNCT
ejpam-5658	276	14	(	(	PUNCT
ejpam-5658	276	15	w	w	PROPN
ejpam-5658	276	16	,	,	PUNCT
ejpam-5658	276	17	b	b	NOUN
ejpam-5658	276	18	)	)	PUNCT
ejpam-5658	276	19	,	,	PUNCT
ejpam-5658	276	20	(	(	PUNCT
ejpam-5658	276	21	v	v	NOUN
ejpam-5658	276	22	,	,	PUNCT
ejpam-5658	276	23	b	b	NOUN
ejpam-5658	276	24	)	)	PUNCT
ejpam-5658	276	25	]	]	PUNCT
ejpam-5658	276	26	is	be	AUX
ejpam-5658	276	27	a	a	DET
ejpam-5658	276	28	(	(	PUNCT
ejpam-5658	276	29	u	u	NOUN
ejpam-5658	276	30	,	,	PUNCT
ejpam-5658	276	31	a)-(v	a)-(v	PROPN
ejpam-5658	276	32	,	,	PUNCT
ejpam-5658	276	33	b	b	NOUN
ejpam-5658	276	34	)	)	PUNCT
ejpam-5658	276	35	geodesic	geodesic	NOUN
ejpam-5658	276	36	in	in	ADP
ejpam-5658	276	37	g	g	PROPN
ejpam-5658	276	38	∨	∨	PROPN
ejpam-5658	276	39	h.	h.	PROPN
ejpam-5658	276	40	both	both	DET
ejpam-5658	276	41	cases	case	NOUN
ejpam-5658	276	42	are	be	AUX
ejpam-5658	276	43	contrary	contrary	ADJ
ejpam-5658	276	44	to	to	ADP
ejpam-5658	276	45	the	the	DET
ejpam-5658	276	46	assumption	assumption	NOUN
ejpam-5658	276	47	that	that	SCONJ
ejpam-5658	276	48	c	c	PROPN
ejpam-5658	276	49	is	be	AUX
ejpam-5658	276	50	a	a	DET
ejpam-5658	276	51	hop	hop	NOUN
ejpam-5658	276	52	independent	independent	ADJ
ejpam-5658	276	53	set	set	NOUN
ejpam-5658	276	54	in	in	ADP
ejpam-5658	276	55	g	g	PROPN
ejpam-5658	276	56	∨h	∨h	NOUN
ejpam-5658	276	57	.	.	PUNCT
ejpam-5658	277	1	hence	hence	ADV
ejpam-5658	277	2	,	,	PUNCT
ejpam-5658	277	3	s	s	VERB
ejpam-5658	277	4	is	be	AUX
ejpam-5658	277	5	hop	hop	NOUN
ejpam-5658	277	6	independent	independent	ADJ
ejpam-5658	277	7	in	in	ADP
ejpam-5658	277	8	g	g	PROPN
ejpam-5658	277	9	,	,	PUNCT
ejpam-5658	277	10	showing	show	VERB
ejpam-5658	277	11	that	that	SCONJ
ejpam-5658	277	12	(	(	PUNCT
ejpam-5658	277	13	i	i	NOUN
ejpam-5658	277	14	)	)	PUNCT
ejpam-5658	277	15	holds	hold	VERB
ejpam-5658	277	16	.	.	PUNCT
ejpam-5658	278	1	now	now	ADV
ejpam-5658	278	2	,	,	PUNCT
ejpam-5658	278	3	let	let	VERB
ejpam-5658	278	4	x	x	PUNCT
ejpam-5658	278	5	∈	∈	NOUN
ejpam-5658	278	6	s	s	PART
ejpam-5658	278	7	and	and	CCONJ
ejpam-5658	278	8	let	let	VERB
ejpam-5658	278	9	p	p	PRON
ejpam-5658	278	10	,	,	PUNCT
ejpam-5658	278	11	q	q	PROPN
ejpam-5658	278	12	∈	∈	PROPN
ejpam-5658	278	13	tx	tx	NOUN
ejpam-5658	278	14	where	where	SCONJ
ejpam-5658	278	15	p	p	PROPN
ejpam-5658	278	16	̸=	̸=	PROPN
ejpam-5658	278	17	q.	q.	NOUN
ejpam-5658	278	18	since	since	SCONJ
ejpam-5658	278	19	c	c	PROPN
ejpam-5658	278	20	is	be	AUX
ejpam-5658	278	21	a	a	DET
ejpam-5658	278	22	hop	hop	NOUN
ejpam-5658	278	23	independent	independent	ADJ
ejpam-5658	278	24	set	set	NOUN
ejpam-5658	278	25	in	in	ADP
ejpam-5658	278	26	g	g	PROPN
ejpam-5658	278	27	∨	∨	NUM
ejpam-5658	278	28	h	h	NOUN
ejpam-5658	278	29	,	,	PUNCT
ejpam-5658	278	30	dg∨h((x	dg∨h((x	NOUN
ejpam-5658	278	31	,	,	PUNCT
ejpam-5658	278	32	p	p	NOUN
ejpam-5658	278	33	)	)	PUNCT
ejpam-5658	278	34	,	,	PUNCT
ejpam-5658	278	35	(	(	PUNCT
ejpam-5658	278	36	x	x	X
ejpam-5658	278	37	,	,	PUNCT
ejpam-5658	278	38	q	q	NOUN
ejpam-5658	278	39	)	)	PUNCT
ejpam-5658	278	40	)	)	PUNCT
ejpam-5658	279	1	̸=	̸=	PROPN
ejpam-5658	279	2	2	2	NUM
ejpam-5658	279	3	.	.	PUNCT
ejpam-5658	279	4	from	from	ADP
ejpam-5658	279	5	the	the	DET
ejpam-5658	279	6	fact	fact	NOUN
ejpam-5658	279	7	that	that	SCONJ
ejpam-5658	279	8	1	1	NUM
ejpam-5658	279	9	≤	≤	NOUN
ejpam-5658	279	10	dg∨h((x	dg∨h((x	NOUN
ejpam-5658	279	11	,	,	PUNCT
ejpam-5658	279	12	p	p	NOUN
ejpam-5658	279	13	)	)	PUNCT
ejpam-5658	279	14	,	,	PUNCT
ejpam-5658	279	15	(	(	PUNCT
ejpam-5658	279	16	x	x	X
ejpam-5658	279	17	,	,	PUNCT
ejpam-5658	279	18	q	q	NOUN
ejpam-5658	279	19	)	)	PUNCT
ejpam-5658	279	20	)	)	PUNCT
ejpam-5658	279	21	≤	≤	NUM
ejpam-5658	279	22	2	2	NUM
ejpam-5658	279	23	and	and	CCONJ
ejpam-5658	279	24	because	because	SCONJ
ejpam-5658	279	25	(	(	PUNCT
ejpam-5658	279	26	x	x	X
ejpam-5658	279	27	,	,	PUNCT
ejpam-5658	279	28	p	p	NOUN
ejpam-5658	279	29	)	)	PUNCT
ejpam-5658	279	30	̸=	̸=	PROPN
ejpam-5658	279	31	(	(	PUNCT
ejpam-5658	279	32	x	x	X
ejpam-5658	279	33	,	,	PUNCT
ejpam-5658	279	34	q	q	NOUN
ejpam-5658	279	35	)	)	PUNCT
ejpam-5658	279	36	,	,	PUNCT
ejpam-5658	279	37	we	we	PRON
ejpam-5658	279	38	must	must	AUX
ejpam-5658	279	39	have	have	AUX
ejpam-5658	279	40	dg∨h((x	dg∨h((x	VERB
ejpam-5658	279	41	,	,	PUNCT
ejpam-5658	279	42	p	p	NOUN
ejpam-5658	279	43	)	)	PUNCT
ejpam-5658	279	44	,	,	PUNCT
ejpam-5658	279	45	(	(	PUNCT
ejpam-5658	279	46	x	x	X
ejpam-5658	279	47	,	,	PUNCT
ejpam-5658	279	48	q	q	NOUN
ejpam-5658	279	49	)	)	PUNCT
ejpam-5658	279	50	)	)	PUNCT
ejpam-5658	280	1	=	=	PUNCT
ejpam-5658	280	2	1	1	X
ejpam-5658	280	3	.	.	PUNCT
ejpam-5658	281	1	this	this	PRON
ejpam-5658	281	2	implies	imply	VERB
ejpam-5658	281	3	that	that	SCONJ
ejpam-5658	281	4	pq	pq	PROPN
ejpam-5658	281	5	∈	∈	PROPN
ejpam-5658	281	6	e(g	e(g	PROPN
ejpam-5658	281	7	)	)	PUNCT
ejpam-5658	281	8	.	.	PUNCT
ejpam-5658	282	1	therefore	therefore	ADV
ejpam-5658	282	2	,	,	PUNCT
ejpam-5658	282	3	tx	tx	PROPN
ejpam-5658	282	4	is	be	AUX
ejpam-5658	282	5	a	a	DET
ejpam-5658	282	6	clique	clique	NOUN
ejpam-5658	282	7	in	in	ADP
ejpam-5658	282	8	h	h	NOUN
ejpam-5658	282	9	,	,	PUNCT
ejpam-5658	282	10	showing	show	VERB
ejpam-5658	282	11	that	that	SCONJ
ejpam-5658	282	12	(	(	PUNCT
ejpam-5658	282	13	ii	ii	NOUN
ejpam-5658	282	14	)	)	PUNCT
ejpam-5658	282	15	holds	hold	VERB
ejpam-5658	282	16	.	.	PUNCT
ejpam-5658	283	1	j.	j.	PROPN
ejpam-5658	283	2	anoche	anoche	PROPN
ejpam-5658	283	3	,	,	PUNCT
ejpam-5658	283	4	s.	s.	PROPN
ejpam-5658	283	5	canoy	canoy	PROPN
ejpam-5658	283	6	,	,	PUNCT
ejpam-5658	283	7	jr	jr	PROPN
ejpam-5658	283	8	.	.	PROPN
ejpam-5658	283	9	/	/	SYM
ejpam-5658	283	10	eur	eur	PROPN
ejpam-5658	283	11	.	.	PUNCT
ejpam-5658	284	1	j.	j.	PROPN
ejpam-5658	284	2	pure	pure	PROPN
ejpam-5658	284	3	appl	appl	PROPN
ejpam-5658	284	4	.	.	PROPN
ejpam-5658	284	5	math	math	PROPN
ejpam-5658	284	6	,	,	PUNCT
ejpam-5658	284	7	18	18	NUM
ejpam-5658	284	8	(	(	PUNCT
ejpam-5658	284	9	1	1	NUM
ejpam-5658	284	10	)	)	PUNCT
ejpam-5658	284	11	(	(	PUNCT
ejpam-5658	284	12	2025	2025	NUM
ejpam-5658	284	13	)	)	PUNCT
ejpam-5658	284	14	,	,	PUNCT
ejpam-5658	284	15	5658	5658	NUM
ejpam-5658	284	16	9	9	NUM
ejpam-5658	284	17	of	of	ADP
ejpam-5658	284	18	15	15	NUM
ejpam-5658	284	19	next	next	ADJ
ejpam-5658	284	20	,	,	PUNCT
ejpam-5658	284	21	let	let	VERB
ejpam-5658	284	22	x	x	PRON
ejpam-5658	284	23	,	,	PUNCT
ejpam-5658	284	24	y	y	PROPN
ejpam-5658	284	25	∈	∈	PROPN
ejpam-5658	284	26	s	s	VERB
ejpam-5658	284	27	with	with	ADP
ejpam-5658	284	28	dg(x	dg(x	PROPN
ejpam-5658	284	29	,	,	PUNCT
ejpam-5658	284	30	y	y	PROPN
ejpam-5658	284	31	)	)	PUNCT
ejpam-5658	284	32	≥	≥	NOUN
ejpam-5658	284	33	3	3	NUM
ejpam-5658	284	34	.	.	PUNCT
ejpam-5658	284	35	suppose	suppose	VERB
ejpam-5658	284	36	tx	tx	PROPN
ejpam-5658	284	37	∩	∩	PROPN
ejpam-5658	284	38	ty	ty	NUM
ejpam-5658	284	39	̸=	̸=	PROPN
ejpam-5658	284	40	∅	∅	NOUN
ejpam-5658	284	41	,	,	PUNCT
ejpam-5658	284	42	say	say	VERB
ejpam-5658	284	43	t	t	PROPN
ejpam-5658	284	44	∈	∈	PROPN
ejpam-5658	284	45	tx	tx	PROPN
ejpam-5658	284	46	∩	∩	PROPN
ejpam-5658	285	1	ty	ty	X
ejpam-5658	285	2	.	.	PUNCT
ejpam-5658	286	1	let	let	VERB
ejpam-5658	286	2	s	s	PRON
ejpam-5658	286	3	∈	∈	PROPN
ejpam-5658	286	4	nh(t	nh(t	NUM
ejpam-5658	286	5	)	)	PUNCT
ejpam-5658	286	6	.	.	PUNCT
ejpam-5658	287	1	then	then	ADV
ejpam-5658	287	2	[	[	X
ejpam-5658	287	3	(	(	PUNCT
ejpam-5658	287	4	x	x	NOUN
ejpam-5658	287	5	,	,	PUNCT
ejpam-5658	287	6	t	t	PROPN
ejpam-5658	287	7	)	)	PUNCT
ejpam-5658	287	8	,	,	PUNCT
ejpam-5658	287	9	(	(	PUNCT
ejpam-5658	287	10	y	y	PROPN
ejpam-5658	287	11	,	,	PUNCT
ejpam-5658	287	12	s	s	PART
ejpam-5658	287	13	)	)	PUNCT
ejpam-5658	287	14	,	,	PUNCT
ejpam-5658	287	15	(	(	PUNCT
ejpam-5658	287	16	y	y	PROPN
ejpam-5658	287	17	,	,	PUNCT
ejpam-5658	287	18	t	t	PROPN
ejpam-5658	287	19	)	)	PUNCT
ejpam-5658	287	20	]	]	PUNCT
ejpam-5658	287	21	is	be	AUX
ejpam-5658	287	22	an	an	DET
ejpam-5658	287	23	(	(	PUNCT
ejpam-5658	287	24	x	x	NOUN
ejpam-5658	287	25	,	,	PUNCT
ejpam-5658	287	26	t)-(y	t)-(y	PROPN
ejpam-5658	287	27	,	,	PUNCT
ejpam-5658	287	28	t	t	PROPN
ejpam-5658	287	29	)	)	PUNCT
ejpam-5658	287	30	geodesic	geodesic	NOUN
ejpam-5658	287	31	in	in	ADP
ejpam-5658	287	32	g	g	PROPN
ejpam-5658	287	33	∨h	∨h	NOUN
ejpam-5658	287	34	,	,	PUNCT
ejpam-5658	287	35	contrary	contrary	ADV
ejpam-5658	287	36	to	to	ADP
ejpam-5658	287	37	the	the	DET
ejpam-5658	287	38	assumption	assumption	NOUN
ejpam-5658	287	39	that	that	SCONJ
ejpam-5658	287	40	c	c	PROPN
ejpam-5658	287	41	is	be	AUX
ejpam-5658	287	42	hop	hop	ADV
ejpam-5658	287	43	independent	independent	ADJ
ejpam-5658	287	44	in	in	ADP
ejpam-5658	287	45	g	g	PROPN
ejpam-5658	287	46	∨	∨	PROPN
ejpam-5658	287	47	h.	h.	PROPN
ejpam-5658	287	48	thus	thus	ADV
ejpam-5658	287	49	,	,	PUNCT
ejpam-5658	287	50	tx	tx	PROPN
ejpam-5658	287	51	∩	∩	ADJ
ejpam-5658	287	52	ty	ty	ADJ
ejpam-5658	287	53	=	=	PUNCT
ejpam-5658	287	54	∅.	∅.	AUX
ejpam-5658	287	55	let	let	VERB
ejpam-5658	287	56	a1	a1	PROPN
ejpam-5658	287	57	∈	∈	PROPN
ejpam-5658	287	58	tx	tx	PROPN
ejpam-5658	287	59	and	and	CCONJ
ejpam-5658	287	60	a2	a2	PROPN
ejpam-5658	287	61	∈	∈	PROPN
ejpam-5658	288	1	ty	ty	PRON
ejpam-5658	288	2	.	.	PUNCT
ejpam-5658	288	3	suppose	suppose	VERB
ejpam-5658	288	4	dh(a1	dh(a1	PROPN
ejpam-5658	288	5	,	,	PUNCT
ejpam-5658	288	6	a2	a2	PROPN
ejpam-5658	288	7	)	)	PUNCT
ejpam-5658	288	8	=	=	SYM
ejpam-5658	288	9	2	2	NUM
ejpam-5658	288	10	and	and	CCONJ
ejpam-5658	288	11	let	let	VERB
ejpam-5658	288	12	q	q	PROPN
ejpam-5658	288	13	∈	∈	PROPN
ejpam-5658	288	14	nh(a1	nh(a1	NOUN
ejpam-5658	288	15	,	,	PUNCT
ejpam-5658	288	16	a2	a2	PROPN
ejpam-5658	288	17	)	)	PUNCT
ejpam-5658	288	18	.	.	PUNCT
ejpam-5658	289	1	then	then	ADV
ejpam-5658	289	2	[	[	X
ejpam-5658	289	3	(	(	PUNCT
ejpam-5658	289	4	x	x	NOUN
ejpam-5658	289	5	,	,	PUNCT
ejpam-5658	289	6	a1	a1	NOUN
ejpam-5658	289	7	)	)	PUNCT
ejpam-5658	289	8	,	,	PUNCT
ejpam-5658	289	9	(	(	PUNCT
ejpam-5658	289	10	y	y	NOUN
ejpam-5658	289	11	,	,	PUNCT
ejpam-5658	289	12	q	q	NOUN
ejpam-5658	289	13	)	)	PUNCT
ejpam-5658	289	14	,	,	PUNCT
ejpam-5658	289	15	(	(	PUNCT
ejpam-5658	289	16	y	y	PROPN
ejpam-5658	289	17	,	,	PUNCT
ejpam-5658	289	18	a2	a2	PROPN
ejpam-5658	289	19	)	)	PUNCT
ejpam-5658	289	20	]	]	PUNCT
ejpam-5658	289	21	is	be	AUX
ejpam-5658	289	22	an	an	DET
ejpam-5658	289	23	(	(	PUNCT
ejpam-5658	289	24	x	x	NOUN
ejpam-5658	289	25	,	,	PUNCT
ejpam-5658	289	26	a1)-(y	a1)-(y	PROPN
ejpam-5658	289	27	,	,	PUNCT
ejpam-5658	289	28	a2	a2	PROPN
ejpam-5658	289	29	)	)	PUNCT
ejpam-5658	289	30	geodesic	geodesic	NOUN
ejpam-5658	289	31	in	in	ADP
ejpam-5658	289	32	g	g	PROPN
ejpam-5658	289	33	∨	∨	NUM
ejpam-5658	289	34	h	h	NOUN
ejpam-5658	289	35	,	,	PUNCT
ejpam-5658	289	36	a	a	DET
ejpam-5658	289	37	contradiction	contradiction	NOUN
ejpam-5658	289	38	.	.	PUNCT
ejpam-5658	290	1	this	this	PRON
ejpam-5658	290	2	implies	imply	VERB
ejpam-5658	290	3	that	that	SCONJ
ejpam-5658	290	4	dh(a1	dh(a1	PROPN
ejpam-5658	290	5	,	,	PUNCT
ejpam-5658	290	6	a2	a2	PROPN
ejpam-5658	290	7	)	)	PUNCT
ejpam-5658	290	8	̸=	̸=	PROPN
ejpam-5658	290	9	2	2	NUM
ejpam-5658	290	10	.	.	PUNCT
ejpam-5658	291	1	since	since	SCONJ
ejpam-5658	291	2	a1	a1	NOUN
ejpam-5658	291	3	and	and	CCONJ
ejpam-5658	291	4	a2	a2	PROPN
ejpam-5658	291	5	were	be	AUX
ejpam-5658	291	6	arbitrarily	arbitrarily	ADV
ejpam-5658	291	7	chosen	choose	VERB
ejpam-5658	291	8	,	,	PUNCT
ejpam-5658	291	9	it	it	PRON
ejpam-5658	291	10	follows	follow	VERB
ejpam-5658	291	11	that	that	SCONJ
ejpam-5658	291	12	dh(tx	dh(tx	PROPN
ejpam-5658	291	13	,	,	PUNCT
ejpam-5658	291	14	ty	ty	NOUN
ejpam-5658	291	15	)	)	PUNCT
ejpam-5658	291	16	≥	≥	NOUN
ejpam-5658	291	17	3	3	NUM
ejpam-5658	291	18	,	,	PUNCT
ejpam-5658	291	19	showing	show	VERB
ejpam-5658	291	20	that	that	SCONJ
ejpam-5658	291	21	(	(	PUNCT
ejpam-5658	291	22	iii	iii	NOUN
ejpam-5658	291	23	)	)	PUNCT
ejpam-5658	291	24	holds	hold	VERB
ejpam-5658	291	25	.	.	PUNCT
ejpam-5658	292	1	finally	finally	ADV
ejpam-5658	292	2	,	,	PUNCT
ejpam-5658	292	3	suppose	suppose	VERB
ejpam-5658	292	4	that	that	SCONJ
ejpam-5658	292	5	s0	s0	PROPN
ejpam-5658	292	6	is	be	AUX
ejpam-5658	292	7	an	an	DET
ejpam-5658	292	8	independent	independent	ADJ
ejpam-5658	292	9	subset	subset	NOUN
ejpam-5658	292	10	of	of	ADP
ejpam-5658	292	11	s.	s.	PROPN
ejpam-5658	292	12	suppose	suppose	VERB
ejpam-5658	292	13	∪x∈s0tx	∪x∈s0tx	NUM
ejpam-5658	292	14	is	be	AUX
ejpam-5658	292	15	not	not	PART
ejpam-5658	292	16	hop	hop	ADV
ejpam-5658	292	17	independent	independent	ADJ
ejpam-5658	292	18	in	in	ADP
ejpam-5658	292	19	h.	h.	PROPN
ejpam-5658	292	20	then	then	ADV
ejpam-5658	292	21	there	there	PRON
ejpam-5658	292	22	exist	exist	VERB
ejpam-5658	292	23	c	c	NOUN
ejpam-5658	292	24	,	,	PUNCT
ejpam-5658	292	25	d	d	PROPN
ejpam-5658	292	26	∈	∈	PROPN
ejpam-5658	292	27	∪x∈s0tx	∪x∈s0tx	PROPN
ejpam-5658	292	28	with	with	ADP
ejpam-5658	292	29	dh(c	dh(c	PROPN
ejpam-5658	292	30	,	,	PUNCT
ejpam-5658	292	31	d	d	NOUN
ejpam-5658	292	32	)	)	PUNCT
ejpam-5658	293	1	=	=	SYM
ejpam-5658	293	2	2	2	X
ejpam-5658	293	3	.	.	PUNCT
ejpam-5658	293	4	by	by	ADP
ejpam-5658	293	5	(	(	PUNCT
ejpam-5658	293	6	ii	ii	NOUN
ejpam-5658	293	7	)	)	PUNCT
ejpam-5658	293	8	,	,	PUNCT
ejpam-5658	293	9	it	it	PRON
ejpam-5658	293	10	follows	follow	VERB
ejpam-5658	293	11	that	that	SCONJ
ejpam-5658	293	12	c	c	PROPN
ejpam-5658	293	13	∈	∈	PROPN
ejpam-5658	293	14	tz	tz	PROPN
ejpam-5658	293	15	and	and	CCONJ
ejpam-5658	293	16	d	d	PROPN
ejpam-5658	293	17	∈	∈	PROPN
ejpam-5658	293	18	tw	tw	NOUN
ejpam-5658	293	19	,	,	PUNCT
ejpam-5658	293	20	where	where	SCONJ
ejpam-5658	293	21	z	z	NOUN
ejpam-5658	293	22	̸=	̸=	PROPN
ejpam-5658	293	23	w	w	PROPN
ejpam-5658	293	24	and	and	CCONJ
ejpam-5658	293	25	z	z	PROPN
ejpam-5658	293	26	,	,	PUNCT
ejpam-5658	293	27	w	w	PROPN
ejpam-5658	293	28	∈	∈	PROPN
ejpam-5658	293	29	s0	s0	PROPN
ejpam-5658	293	30	.	.	PUNCT
ejpam-5658	294	1	let	let	VERB
ejpam-5658	294	2	r	r	NOUN
ejpam-5658	294	3	∈	∈	PROPN
ejpam-5658	294	4	nh(c)∩nh(d	nh(c)∩nh(d	PROPN
ejpam-5658	294	5	)	)	PUNCT
ejpam-5658	294	6	.	.	PUNCT
ejpam-5658	295	1	then	then	ADV
ejpam-5658	295	2	[	[	X
ejpam-5658	295	3	(	(	PUNCT
ejpam-5658	295	4	z	z	NOUN
ejpam-5658	295	5	,	,	PUNCT
ejpam-5658	295	6	c	c	NOUN
ejpam-5658	295	7	)	)	PUNCT
ejpam-5658	295	8	,	,	PUNCT
ejpam-5658	295	9	(	(	PUNCT
ejpam-5658	295	10	w	w	NOUN
ejpam-5658	295	11	,	,	PUNCT
ejpam-5658	295	12	r	r	NOUN
ejpam-5658	295	13	)	)	PUNCT
ejpam-5658	295	14	,	,	PUNCT
ejpam-5658	295	15	(	(	PUNCT
ejpam-5658	295	16	w	w	NOUN
ejpam-5658	295	17	,	,	PUNCT
ejpam-5658	295	18	d	d	NOUN
ejpam-5658	295	19	)	)	PUNCT
ejpam-5658	295	20	]	]	PUNCT
ejpam-5658	295	21	is	be	AUX
ejpam-5658	295	22	a	a	DET
ejpam-5658	295	23	(	(	PUNCT
ejpam-5658	295	24	z	z	NOUN
ejpam-5658	295	25	,	,	PUNCT
ejpam-5658	295	26	c)-(w	c)-(w	PROPN
ejpam-5658	295	27	,	,	PUNCT
ejpam-5658	295	28	d	d	X
ejpam-5658	295	29	)	)	PUNCT
ejpam-5658	295	30	geodesic	geodesic	NOUN
ejpam-5658	295	31	in	in	ADP
ejpam-5658	295	32	g	g	PROPN
ejpam-5658	295	33	∨h	∨h	NOUN
ejpam-5658	295	34	which	which	PRON
ejpam-5658	295	35	is	be	AUX
ejpam-5658	295	36	not	not	PART
ejpam-5658	295	37	possible	possible	ADJ
ejpam-5658	295	38	.	.	PUNCT
ejpam-5658	296	1	therefore	therefore	ADV
ejpam-5658	296	2	,	,	PUNCT
ejpam-5658	296	3	∪x∈s0tx	∪x∈s0tx	PROPN
ejpam-5658	296	4	is	be	AUX
ejpam-5658	296	5	hop	hop	ADV
ejpam-5658	296	6	independent	independent	ADJ
ejpam-5658	296	7	in	in	ADP
ejpam-5658	296	8	h	h	NOUN
ejpam-5658	296	9	,	,	PUNCT
ejpam-5658	296	10	showing	show	VERB
ejpam-5658	296	11	that	that	SCONJ
ejpam-5658	296	12	(	(	PUNCT
ejpam-5658	296	13	iv	iv	X
ejpam-5658	296	14	)	)	PUNCT
ejpam-5658	296	15	holds	hold	NOUN
ejpam-5658	296	16	.	.	PUNCT
ejpam-5658	297	1	for	for	ADP
ejpam-5658	297	2	the	the	DET
ejpam-5658	297	3	converse	converse	NOUN
ejpam-5658	297	4	,	,	PUNCT
ejpam-5658	297	5	suppose	suppose	VERB
ejpam-5658	297	6	that	that	SCONJ
ejpam-5658	297	7	c	c	PROPN
ejpam-5658	297	8	satisfies	satisfy	VERB
ejpam-5658	297	9	properties	property	NOUN
ejpam-5658	297	10	(	(	PUNCT
ejpam-5658	297	11	i	i	NOUN
ejpam-5658	297	12	)	)	PUNCT
ejpam-5658	297	13	,	,	PUNCT
ejpam-5658	297	14	(	(	PUNCT
ejpam-5658	297	15	ii	ii	NOUN
ejpam-5658	297	16	)	)	PUNCT
ejpam-5658	297	17	,	,	PUNCT
ejpam-5658	297	18	(	(	PUNCT
ejpam-5658	297	19	iii	iii	NOUN
ejpam-5658	297	20	)	)	PUNCT
ejpam-5658	297	21	,	,	PUNCT
ejpam-5658	297	22	and	and	CCONJ
ejpam-5658	297	23	(	(	PUNCT
ejpam-5658	297	24	iv	iv	X
ejpam-5658	297	25	)	)	PUNCT
ejpam-5658	297	26	.	.	PUNCT
ejpam-5658	298	1	let	let	VERB
ejpam-5658	298	2	(	(	PUNCT
ejpam-5658	298	3	v	v	NOUN
ejpam-5658	298	4	,	,	PUNCT
ejpam-5658	298	5	p	p	NOUN
ejpam-5658	298	6	)	)	PUNCT
ejpam-5658	298	7	,	,	PUNCT
ejpam-5658	298	8	(	(	PUNCT
ejpam-5658	298	9	w	w	NOUN
ejpam-5658	298	10	,	,	PUNCT
ejpam-5658	298	11	q	q	NOUN
ejpam-5658	298	12	)	)	PUNCT
ejpam-5658	298	13	∈	∈	PROPN
ejpam-5658	298	14	c	c	NOUN
ejpam-5658	298	15	such	such	ADJ
ejpam-5658	298	16	that	that	PRON
ejpam-5658	298	17	(	(	PUNCT
ejpam-5658	298	18	v	v	NOUN
ejpam-5658	298	19	,	,	PUNCT
ejpam-5658	298	20	p	p	NOUN
ejpam-5658	298	21	)	)	PUNCT
ejpam-5658	298	22	̸=	̸=	PROPN
ejpam-5658	298	23	(	(	PUNCT
ejpam-5658	298	24	w	w	PROPN
ejpam-5658	298	25	,	,	PUNCT
ejpam-5658	298	26	q	q	NOUN
ejpam-5658	298	27	)	)	PUNCT
ejpam-5658	298	28	.	.	PUNCT
ejpam-5658	299	1	consider	consider	VERB
ejpam-5658	299	2	the	the	DET
ejpam-5658	299	3	following	follow	VERB
ejpam-5658	299	4	cases	case	NOUN
ejpam-5658	299	5	:	:	PUNCT
ejpam-5658	299	6	case	case	NOUN
ejpam-5658	299	7	1	1	NUM
ejpam-5658	299	8	.	.	PUNCT
ejpam-5658	299	9	v	v	NOUN
ejpam-5658	299	10	=	=	PUNCT
ejpam-5658	299	11	w.	w.	PROPN
ejpam-5658	299	12	then	then	ADV
ejpam-5658	299	13	p	p	X
ejpam-5658	299	14	,	,	PUNCT
ejpam-5658	299	15	q	q	PROPN
ejpam-5658	299	16	∈	∈	PROPN
ejpam-5658	299	17	tv	tv	NOUN
ejpam-5658	299	18	and	and	CCONJ
ejpam-5658	299	19	p	p	PROPN
ejpam-5658	299	20	̸=	̸=	PROPN
ejpam-5658	299	21	q.	q.	NOUN
ejpam-5658	299	22	by	by	ADP
ejpam-5658	299	23	property	property	NOUN
ejpam-5658	299	24	(	(	PUNCT
ejpam-5658	299	25	ii	ii	NOUN
ejpam-5658	299	26	)	)	PUNCT
ejpam-5658	299	27	,	,	PUNCT
ejpam-5658	299	28	dh(p	dh(p	PROPN
ejpam-5658	299	29	,	,	PUNCT
ejpam-5658	299	30	q	q	X
ejpam-5658	299	31	)	)	PUNCT
ejpam-5658	299	32	=	=	SYM
ejpam-5658	299	33	1	1	X
ejpam-5658	299	34	.	.	X
ejpam-5658	300	1	hence	hence	ADV
ejpam-5658	300	2	,	,	PUNCT
ejpam-5658	300	3	dg∨h((v	dg∨h((v	PROPN
ejpam-5658	300	4	,	,	PUNCT
ejpam-5658	300	5	p	p	NOUN
ejpam-5658	300	6	)	)	PUNCT
ejpam-5658	300	7	,	,	PUNCT
ejpam-5658	300	8	(	(	PUNCT
ejpam-5658	300	9	w	w	NOUN
ejpam-5658	300	10	,	,	PUNCT
ejpam-5658	300	11	q	q	NOUN
ejpam-5658	300	12	)	)	PUNCT
ejpam-5658	300	13	)	)	PUNCT
ejpam-5658	301	1	=	=	SYM
ejpam-5658	301	2	1	1	X
ejpam-5658	301	3	.	.	X
ejpam-5658	301	4	case	case	NOUN
ejpam-5658	301	5	2	2	NUM
ejpam-5658	301	6	.	.	X
ejpam-5658	301	7	v	v	ADP
ejpam-5658	301	8	̸=	̸=	PROPN
ejpam-5658	301	9	w.	w.	PROPN
ejpam-5658	301	10	suppose	suppose	VERB
ejpam-5658	301	11	first	first	ADV
ejpam-5658	301	12	that	that	PRON
ejpam-5658	301	13	dg(v	dg(v	NOUN
ejpam-5658	301	14	,	,	PUNCT
ejpam-5658	301	15	w	w	NOUN
ejpam-5658	301	16	)	)	PUNCT
ejpam-5658	301	17	=	=	SYM
ejpam-5658	302	1	1	1	X
ejpam-5658	302	2	.	.	PUNCT
ejpam-5658	302	3	then	then	ADV
ejpam-5658	302	4	dg∨h((v	dg∨h((v	PROPN
ejpam-5658	302	5	,	,	PUNCT
ejpam-5658	302	6	p	p	NOUN
ejpam-5658	302	7	)	)	PUNCT
ejpam-5658	302	8	,	,	PUNCT
ejpam-5658	302	9	(	(	PUNCT
ejpam-5658	302	10	w	w	NOUN
ejpam-5658	302	11	,	,	PUNCT
ejpam-5658	302	12	q	q	NOUN
ejpam-5658	302	13	)	)	PUNCT
ejpam-5658	302	14	)	)	PUNCT
ejpam-5658	302	15	=	=	PUNCT
ejpam-5658	303	1	1	1	X
ejpam-5658	303	2	.	.	PUNCT
ejpam-5658	304	1	next	next	ADV
ejpam-5658	304	2	,	,	PUNCT
ejpam-5658	304	3	suppose	suppose	VERB
ejpam-5658	304	4	that	that	SCONJ
ejpam-5658	304	5	dg(v	dg(v	NOUN
ejpam-5658	304	6	,	,	PUNCT
ejpam-5658	304	7	w	w	NOUN
ejpam-5658	304	8	)	)	PUNCT
ejpam-5658	304	9	>	>	X
ejpam-5658	304	10	1	1	X
ejpam-5658	304	11	.	.	PUNCT
ejpam-5658	305	1	by	by	ADP
ejpam-5658	305	2	property	property	NOUN
ejpam-5658	305	3	(	(	PUNCT
ejpam-5658	305	4	i	i	NOUN
ejpam-5658	305	5	)	)	PUNCT
ejpam-5658	305	6	,	,	PUNCT
ejpam-5658	305	7	we	we	PRON
ejpam-5658	305	8	must	must	AUX
ejpam-5658	305	9	have	have	VERB
ejpam-5658	305	10	dg(v	dg(v	NOUN
ejpam-5658	305	11	,	,	PUNCT
ejpam-5658	305	12	w	w	NOUN
ejpam-5658	305	13	)	)	PUNCT
ejpam-5658	305	14	≥	≥	NOUN
ejpam-5658	305	15	3	3	NUM
ejpam-5658	305	16	.	.	PUNCT
ejpam-5658	306	1	now	now	ADV
ejpam-5658	306	2	,	,	PUNCT
ejpam-5658	306	3	by	by	ADP
ejpam-5658	306	4	property	property	NOUN
ejpam-5658	306	5	(	(	PUNCT
ejpam-5658	306	6	iii	iii	NOUN
ejpam-5658	306	7	)	)	PUNCT
ejpam-5658	306	8	,	,	PUNCT
ejpam-5658	306	9	p	p	PROPN
ejpam-5658	306	10	̸=	̸=	PROPN
ejpam-5658	306	11	q.	q.	NOUN
ejpam-5658	306	12	if	if	SCONJ
ejpam-5658	306	13	dh(p	dh(p	NOUN
ejpam-5658	306	14	,	,	PUNCT
ejpam-5658	306	15	q	q	X
ejpam-5658	306	16	)	)	PUNCT
ejpam-5658	306	17	=	=	SYM
ejpam-5658	306	18	1	1	NUM
ejpam-5658	306	19	,	,	PUNCT
ejpam-5658	306	20	then	then	ADV
ejpam-5658	306	21	dg∨h((v	dg∨h((v	PROPN
ejpam-5658	306	22	,	,	PUNCT
ejpam-5658	306	23	p	p	NOUN
ejpam-5658	306	24	)	)	PUNCT
ejpam-5658	306	25	,	,	PUNCT
ejpam-5658	306	26	(	(	PUNCT
ejpam-5658	306	27	w	w	NOUN
ejpam-5658	306	28	,	,	PUNCT
ejpam-5658	306	29	q	q	NOUN
ejpam-5658	306	30	)	)	PUNCT
ejpam-5658	306	31	)	)	PUNCT
ejpam-5658	307	1	=	=	SYM
ejpam-5658	307	2	1	1	X
ejpam-5658	307	3	.	.	PUNCT
ejpam-5658	307	4	suppose	suppose	VERB
ejpam-5658	307	5	dh(p	dh(p	NOUN
ejpam-5658	307	6	,	,	PUNCT
ejpam-5658	307	7	q	q	X
ejpam-5658	307	8	)	)	PUNCT
ejpam-5658	307	9	̸=	̸=	PROPN
ejpam-5658	307	10	1	1	NUM
ejpam-5658	307	11	.	.	PUNCT
ejpam-5658	308	1	then	then	ADV
ejpam-5658	308	2	,	,	PUNCT
ejpam-5658	308	3	by	by	ADP
ejpam-5658	308	4	property	property	NOUN
ejpam-5658	308	5	(	(	PUNCT
ejpam-5658	308	6	iv	iv	X
ejpam-5658	308	7	)	)	PUNCT
ejpam-5658	308	8	(	(	PUNCT
ejpam-5658	308	9	using	use	VERB
ejpam-5658	308	10	the	the	DET
ejpam-5658	308	11	fact	fact	NOUN
ejpam-5658	308	12	that	that	SCONJ
ejpam-5658	308	13	s0	s0	NOUN
ejpam-5658	308	14	=	=	PUNCT
ejpam-5658	308	15	{	{	PUNCT
ejpam-5658	308	16	v	v	NOUN
ejpam-5658	308	17	,	,	PUNCT
ejpam-5658	308	18	w	w	NOUN
ejpam-5658	308	19	}	}	PUNCT
ejpam-5658	308	20	is	be	AUX
ejpam-5658	308	21	an	an	DET
ejpam-5658	308	22	independent	independent	ADJ
ejpam-5658	308	23	set	set	NOUN
ejpam-5658	308	24	)	)	PUNCT
ejpam-5658	308	25	,	,	PUNCT
ejpam-5658	308	26	dh(p	dh(p	PROPN
ejpam-5658	308	27	,	,	PUNCT
ejpam-5658	308	28	q	q	X
ejpam-5658	308	29	)	)	PUNCT
ejpam-5658	308	30	≥	≥	NOUN
ejpam-5658	308	31	3	3	NUM
ejpam-5658	308	32	.	.	PUNCT
ejpam-5658	309	1	therefore	therefore	ADV
ejpam-5658	309	2	,	,	PUNCT
ejpam-5658	309	3	dg∨h((v	dg∨h((v	PROPN
ejpam-5658	309	4	,	,	PUNCT
ejpam-5658	309	5	p	p	NOUN
ejpam-5658	309	6	)	)	PUNCT
ejpam-5658	309	7	,	,	PUNCT
ejpam-5658	309	8	(	(	PUNCT
ejpam-5658	309	9	w	w	NOUN
ejpam-5658	309	10	,	,	PUNCT
ejpam-5658	309	11	q	q	NOUN
ejpam-5658	309	12	)	)	PUNCT
ejpam-5658	309	13	)	)	PUNCT
ejpam-5658	309	14	≥	≥	NOUN
ejpam-5658	310	1	3	3	X
ejpam-5658	310	2	.	.	PUNCT
ejpam-5658	310	3	accordingly	accordingly	ADV
ejpam-5658	310	4	,	,	PUNCT
ejpam-5658	310	5	c	c	PROPN
ejpam-5658	310	6	is	be	AUX
ejpam-5658	310	7	a	a	DET
ejpam-5658	310	8	hop	hop	NOUN
ejpam-5658	310	9	independent	independent	ADJ
ejpam-5658	310	10	set	set	NOUN
ejpam-5658	310	11	in	in	ADP
ejpam-5658	310	12	g	g	PROPN
ejpam-5658	310	13	∨h	∨h	NOUN
ejpam-5658	310	14	.	.	PUNCT
ejpam-5658	311	1	a	a	DET
ejpam-5658	311	2	sequence	sequence	NOUN
ejpam-5658	311	3	of	of	ADP
ejpam-5658	311	4	cliques	clique	NOUN
ejpam-5658	311	5	⟨sq1	⟨sq1	NOUN
ejpam-5658	311	6	,	,	PUNCT
ejpam-5658	311	7	sq2	sq2	PROPN
ejpam-5658	311	8	,	,	PUNCT
ejpam-5658	311	9	·	·	PUNCT
ejpam-5658	311	10	·	·	PUNCT
ejpam-5658	311	11	·	·	PUNCT
ejpam-5658	311	12	,	,	PUNCT
ejpam-5658	311	13	sqm⟩	sqm⟩	NOUN
ejpam-5658	311	14	in	in	ADP
ejpam-5658	311	15	an	an	DET
ejpam-5658	311	16	undirected	undirected	ADJ
ejpam-5658	311	17	graph	graph	NOUN
ejpam-5658	311	18	g	g	NOUN
ejpam-5658	311	19	,	,	PUNCT
ejpam-5658	311	20	where	where	SCONJ
ejpam-5658	311	21	each	each	DET
ejpam-5658	311	22	qj	qj	PROPN
ejpam-5658	311	23	=	=	PUNCT
ejpam-5658	311	24	|sqj	|sqj	PROPN
ejpam-5658	311	25	|	|	ADV
ejpam-5658	311	26	,	,	PUNCT
ejpam-5658	311	27	is	be	AUX
ejpam-5658	311	28	a	a	DET
ejpam-5658	311	29	decreasing	decrease	VERB
ejpam-5658	311	30	d3	d3	NOUN
ejpam-5658	311	31	-	-	PUNCT
ejpam-5658	311	32	sequence	sequence	NOUN
ejpam-5658	311	33	if	if	SCONJ
ejpam-5658	311	34	dg(sqi	dg(sqi	PROPN
ejpam-5658	311	35	,	,	PUNCT
ejpam-5658	311	36	sqj	sqj	PROPN
ejpam-5658	311	37	)	)	PUNCT
ejpam-5658	311	38	≥	≥	NOUN
ejpam-5658	311	39	3	3	NUM
ejpam-5658	311	40	for	for	ADP
ejpam-5658	311	41	every	every	DET
ejpam-5658	311	42	pair	pair	NOUN
ejpam-5658	311	43	of	of	ADP
ejpam-5658	311	44	distinct	distinct	ADJ
ejpam-5658	311	45	indices	index	NOUN
ejpam-5658	312	1	i	i	PRON
ejpam-5658	312	2	,	,	PUNCT
ejpam-5658	312	3	j	j	PROPN
ejpam-5658	312	4	∈	∈	PROPN
ejpam-5658	312	5	{	{	PUNCT
ejpam-5658	312	6	1	1	NUM
ejpam-5658	312	7	,	,	PUNCT
ejpam-5658	312	8	2	2	NUM
ejpam-5658	312	9	,	,	PUNCT
ejpam-5658	312	10	·	·	PUNCT
ejpam-5658	312	11	·	·	PUNCT
ejpam-5658	312	12	·	·	PUNCT
ejpam-5658	312	13	,	,	PUNCT
ejpam-5658	312	14	m	m	VERB
ejpam-5658	312	15	}	}	PUNCT
ejpam-5658	312	16	and	and	CCONJ
ejpam-5658	312	17	q1	q1	PROPN
ejpam-5658	312	18	≥	≥	PROPN
ejpam-5658	312	19	q2	q2	PROPN
ejpam-5658	312	20	≥	≥	NUM
ejpam-5658	312	21	.	.	PUNCT
ejpam-5658	312	22	.	.	PUNCT
ejpam-5658	312	23	.	.	PUNCT
ejpam-5658	313	1	≥	≥	PROPN
ejpam-5658	314	1	qm	qm	PROPN
ejpam-5658	314	2	.	.	PUNCT
ejpam-5658	315	1	it	it	PRON
ejpam-5658	315	2	is	be	AUX
ejpam-5658	315	3	a	a	DET
ejpam-5658	315	4	maximum	maximum	ADJ
ejpam-5658	315	5	decreasing	decrease	VERB
ejpam-5658	315	6	d3	d3	NOUN
ejpam-5658	315	7	-	-	PUNCT
ejpam-5658	315	8	sequence	sequence	NOUN
ejpam-5658	315	9	if	if	SCONJ
ejpam-5658	315	10	for	for	ADP
ejpam-5658	315	11	every	every	DET
ejpam-5658	315	12	decreasing	decrease	VERB
ejpam-5658	315	13	d3	d3	NOUN
ejpam-5658	315	14	-	-	PUNCT
ejpam-5658	315	15	sequence	sequence	NOUN
ejpam-5658	315	16	of	of	ADP
ejpam-5658	315	17	cliques	clique	NOUN
ejpam-5658	315	18	⟨st1	⟨st1	NOUN
ejpam-5658	315	19	,	,	PUNCT
ejpam-5658	315	20	st2	st2	NOUN
ejpam-5658	315	21	,	,	PUNCT
ejpam-5658	315	22	·	·	PUNCT
ejpam-5658	315	23	·	·	PUNCT
ejpam-5658	315	24	·	·	PUNCT
ejpam-5658	315	25	,	,	PUNCT
ejpam-5658	315	26	sts⟩	sts⟩	NOUN
ejpam-5658	315	27	in	in	ADP
ejpam-5658	315	28	g	g	PROPN
ejpam-5658	315	29	,	,	PUNCT
ejpam-5658	315	30	it	it	PRON
ejpam-5658	315	31	holds	hold	VERB
ejpam-5658	315	32	that	that	PRON
ejpam-5658	315	33	s	s	VERB
ejpam-5658	315	34	≤	≤	NOUN
ejpam-5658	315	35	m	m	PROPN
ejpam-5658	315	36	and	and	CCONJ
ejpam-5658	315	37	tj	tj	PROPN
ejpam-5658	315	38	≤	≤	PROPN
ejpam-5658	315	39	qj	qj	PROPN
ejpam-5658	315	40	for	for	ADP
ejpam-5658	315	41	each	each	DET
ejpam-5658	315	42	j	j	PROPN
ejpam-5658	315	43	∈	∈	PROPN
ejpam-5658	315	44	{	{	PUNCT
ejpam-5658	315	45	1	1	NUM
ejpam-5658	315	46	,	,	PUNCT
ejpam-5658	315	47	2	2	NUM
ejpam-5658	315	48	,	,	PUNCT
ejpam-5658	315	49	.	.	PUNCT
ejpam-5658	315	50	.	.	PUNCT
ejpam-5658	316	1	.	.	PUNCT
ejpam-5658	317	1	,	,	PUNCT
ejpam-5658	317	2	s	s	X
ejpam-5658	317	3	}	}	PUNCT
ejpam-5658	317	4	.	.	PUNCT
ejpam-5658	318	1	corollary	corollary	ADJ
ejpam-5658	318	2	5	5	NUM
ejpam-5658	318	3	.	.	PUNCT
ejpam-5658	319	1	let	let	VERB
ejpam-5658	319	2	g	g	NOUN
ejpam-5658	319	3	and	and	CCONJ
ejpam-5658	319	4	h	h	PROPN
ejpam-5658	319	5	be	be	VERB
ejpam-5658	319	6	non	non	ADJ
ejpam-5658	319	7	-	-	ADJ
ejpam-5658	319	8	trivial	trivial	ADJ
ejpam-5658	319	9	connected	connected	ADJ
ejpam-5658	319	10	graphs	graph	NOUN
ejpam-5658	319	11	and	and	CCONJ
ejpam-5658	319	12	let	let	VERB
ejpam-5658	319	13	⟨sq1	⟨sq1	VERB
ejpam-5658	319	14	,	,	PUNCT
ejpam-5658	319	15	sq2	sq2	PROPN
ejpam-5658	319	16	,	,	PUNCT
ejpam-5658	319	17	·	·	PUNCT
ejpam-5658	319	18	·	·	PUNCT
ejpam-5658	319	19	·	·	PUNCT
ejpam-5658	319	20	,	,	PUNCT
ejpam-5658	319	21	sqm⟩	sqm⟩	NOUN
ejpam-5658	319	22	and	and	CCONJ
ejpam-5658	319	23	⟨dp1	⟨dp1	PROPN
ejpam-5658	319	24	,	,	PUNCT
ejpam-5658	319	25	dp2	dp2	PROPN
ejpam-5658	319	26	,	,	PUNCT
ejpam-5658	319	27	·	·	PUNCT
ejpam-5658	319	28	·	·	PUNCT
ejpam-5658	319	29	·	·	PUNCT
ejpam-5658	319	30	,	,	PUNCT
ejpam-5658	319	31	dpr⟩	dpr⟩	NOUN
ejpam-5658	319	32	be	be	AUX
ejpam-5658	319	33	maximum	maximum	ADV
ejpam-5658	319	34	decreasing	decrease	VERB
ejpam-5658	319	35	d3	d3	NOUN
ejpam-5658	319	36	-	-	PUNCT
ejpam-5658	319	37	sequences	sequence	NOUN
ejpam-5658	319	38	of	of	ADP
ejpam-5658	319	39	cliques	clique	NOUN
ejpam-5658	319	40	in	in	ADP
ejpam-5658	319	41	g	g	PROPN
ejpam-5658	319	42	and	and	CCONJ
ejpam-5658	319	43	h	h	NOUN
ejpam-5658	319	44	,	,	PUNCT
ejpam-5658	319	45	respectively	respectively	ADV
ejpam-5658	319	46	.	.	PUNCT
ejpam-5658	320	1	then	then	ADV
ejpam-5658	320	2	αh(g	αh(g	ADP
ejpam-5658	320	3	∨h	∨h	NOUN
ejpam-5658	320	4	)	)	PUNCT
ejpam-5658	321	1	=	=	SYM
ejpam-5658	322	1	ρhg∑	ρhg∑	PROPN
ejpam-5658	322	2	k=1	k=1	PROPN
ejpam-5658	322	3	qkpk	qkpk	PROPN
ejpam-5658	322	4	,	,	PUNCT
ejpam-5658	322	5	where	where	SCONJ
ejpam-5658	322	6	ρhg	ρhg	NOUN
ejpam-5658	322	7	=	=	SYM
ejpam-5658	322	8	min{m	min{m	PROPN
ejpam-5658	322	9	,	,	PUNCT
ejpam-5658	322	10	r	r	NOUN
ejpam-5658	322	11	}	}	PUNCT
ejpam-5658	322	12	.	.	PUNCT
ejpam-5658	323	1	proof	proof	NOUN
ejpam-5658	323	2	.	.	PUNCT
ejpam-5658	324	1	let	let	VERB
ejpam-5658	324	2	⟨sq1	⟨sq1	VERB
ejpam-5658	324	3	,	,	PUNCT
ejpam-5658	324	4	sq2	sq2	PROPN
ejpam-5658	324	5	,	,	PUNCT
ejpam-5658	324	6	·	·	PUNCT
ejpam-5658	324	7	·	·	PUNCT
ejpam-5658	324	8	·	·	PUNCT
ejpam-5658	324	9	,	,	PUNCT
ejpam-5658	324	10	sqm⟩	sqm⟩	NOUN
ejpam-5658	324	11	and	and	CCONJ
ejpam-5658	324	12	⟨dp1	⟨dp1	PROPN
ejpam-5658	324	13	,	,	PUNCT
ejpam-5658	324	14	dp2	dp2	PROPN
ejpam-5658	324	15	,	,	PUNCT
ejpam-5658	324	16	·	·	PUNCT
ejpam-5658	324	17	·	·	PUNCT
ejpam-5658	324	18	·	·	PUNCT
ejpam-5658	324	19	,	,	PUNCT
ejpam-5658	324	20	dpr⟩	dpr⟩	NOUN
ejpam-5658	324	21	be	be	AUX
ejpam-5658	324	22	maximum	maximum	ADV
ejpam-5658	324	23	decreasing	decrease	VERB
ejpam-5658	324	24	d3sequences	d3sequence	NOUN
ejpam-5658	324	25	of	of	ADP
ejpam-5658	324	26	cliques	clique	NOUN
ejpam-5658	324	27	in	in	ADP
ejpam-5658	324	28	g	g	PROPN
ejpam-5658	324	29	and	and	CCONJ
ejpam-5658	324	30	h	h	NOUN
ejpam-5658	324	31	,	,	PUNCT
ejpam-5658	324	32	respectively	respectively	ADV
ejpam-5658	324	33	.	.	PUNCT
ejpam-5658	325	1	then	then	ADV
ejpam-5658	325	2	s	s	PART
ejpam-5658	325	3	=	=	NOUN
ejpam-5658	325	4	∪ρhg	∪ρhg	NOUN
ejpam-5658	325	5	k=1sqk	k=1sqk	NOUN
ejpam-5658	325	6	is	be	AUX
ejpam-5658	325	7	a	a	DET
ejpam-5658	325	8	hop	hop	NOUN
ejpam-5658	325	9	dominating	dominating	NOUN
ejpam-5658	325	10	set	set	VERB
ejpam-5658	325	11	ing	ing	NOUN
ejpam-5658	325	12	.	.	PUNCT
ejpam-5658	326	1	for	for	ADP
ejpam-5658	326	2	each	each	DET
ejpam-5658	326	3	x	x	SYM
ejpam-5658	326	4	∈	∈	PROPN
ejpam-5658	326	5	s	s	NOUN
ejpam-5658	326	6	,	,	PUNCT
ejpam-5658	326	7	set	set	VERB
ejpam-5658	326	8	tx	tx	PROPN
ejpam-5658	326	9	=	=	SYM
ejpam-5658	326	10	dpj	dpj	NOUN
ejpam-5658	326	11	if	if	SCONJ
ejpam-5658	326	12	x	x	PROPN
ejpam-5658	326	13	∈	∈	PROPN
ejpam-5658	326	14	sqj	sqj	NOUN
ejpam-5658	326	15	,	,	PUNCT
ejpam-5658	326	16	where	where	SCONJ
ejpam-5658	326	17	1	1	NUM
ejpam-5658	326	18	≤	≤	NUM
ejpam-5658	326	19	j	j	PROPN
ejpam-5658	326	20	≤	≤	NOUN
ejpam-5658	326	21	ρhg	ρhg	NOUN
ejpam-5658	326	22	.	.	PUNCT
ejpam-5658	327	1	then	then	ADV
ejpam-5658	327	2	c	c	X
ejpam-5658	327	3	=	=	SYM
ejpam-5658	327	4	∪x∈s({x}×tx	∪x∈s({x}×tx	PROPN
ejpam-5658	327	5	)	)	PUNCT
ejpam-5658	327	6	j.	j.	PROPN
ejpam-5658	327	7	anoche	anoche	PROPN
ejpam-5658	327	8	,	,	PUNCT
ejpam-5658	327	9	s.	s.	PROPN
ejpam-5658	327	10	canoy	canoy	PROPN
ejpam-5658	327	11	,	,	PUNCT
ejpam-5658	327	12	jr	jr	PROPN
ejpam-5658	327	13	.	.	PROPN
ejpam-5658	327	14	/	/	SYM
ejpam-5658	327	15	eur	eur	PROPN
ejpam-5658	327	16	.	.	PUNCT
ejpam-5658	328	1	j.	j.	PROPN
ejpam-5658	328	2	pure	pure	PROPN
ejpam-5658	328	3	appl	appl	PROPN
ejpam-5658	328	4	.	.	PROPN
ejpam-5658	328	5	math	math	PROPN
ejpam-5658	328	6	,	,	PUNCT
ejpam-5658	328	7	18	18	NUM
ejpam-5658	328	8	(	(	PUNCT
ejpam-5658	328	9	1	1	NUM
ejpam-5658	328	10	)	)	PUNCT
ejpam-5658	328	11	(	(	PUNCT
ejpam-5658	328	12	2025	2025	NUM
ejpam-5658	328	13	)	)	PUNCT
ejpam-5658	328	14	,	,	PUNCT
ejpam-5658	328	15	5658	5658	NUM
ejpam-5658	328	16	10	10	NUM
ejpam-5658	328	17	of	of	ADP
ejpam-5658	328	18	15	15	NUM
ejpam-5658	328	19	is	be	AUX
ejpam-5658	328	20	a	a	DET
ejpam-5658	328	21	hop	hop	NOUN
ejpam-5658	328	22	independent	independent	ADJ
ejpam-5658	328	23	set	set	NOUN
ejpam-5658	328	24	in	in	ADP
ejpam-5658	328	25	g	g	PROPN
ejpam-5658	328	26	∨h	∨h	NOUN
ejpam-5658	328	27	by	by	ADP
ejpam-5658	328	28	theorem	theorem	NOUN
ejpam-5658	328	29	5	5	NUM
ejpam-5658	328	30	.	.	PUNCT
ejpam-5658	329	1	this	this	PRON
ejpam-5658	329	2	implies	imply	VERB
ejpam-5658	329	3	that	that	SCONJ
ejpam-5658	329	4	αh(g	αh(g	NOUN
ejpam-5658	329	5	∨h	∨h	NOUN
ejpam-5658	329	6	)	)	PUNCT
ejpam-5658	329	7	≥	≥	NOUN
ejpam-5658	329	8	|c|	|c|	PROPN
ejpam-5658	329	9	=	=	PUNCT
ejpam-5658	329	10	∑	∑	PROPN
ejpam-5658	329	11	x∈s	x∈s	PROPN
ejpam-5658	329	12	|tx|	|tx|	PROPN
ejpam-5658	329	13	=	=	PUNCT
ejpam-5658	329	14	ρhg∑	ρhg∑	PUNCT
ejpam-5658	329	15	k=1	k=1	PUNCT
ejpam-5658	329	16	∑	∑	PUNCT
ejpam-5658	329	17	x∈sqk	x∈sqk	NOUN
ejpam-5658	329	18	|tx|	|tx|	NOUN
ejpam-5658	329	19	=	=	SYM
ejpam-5658	329	20	ρhg∑	ρhg∑	PUNCT
ejpam-5658	330	1	k=1	k=1	PUNCT
ejpam-5658	330	2	∑	∑	PUNCT
ejpam-5658	330	3	x∈sqk	x∈sqk	PROPN
ejpam-5658	330	4	|dpk	|dpk	NOUN
ejpam-5658	330	5	|	|	NOUN
ejpam-5658	330	6	=	=	SYM
ejpam-5658	330	7	ρhg∑	ρhg∑	PROPN
ejpam-5658	330	8	k=1	k=1	PROPN
ejpam-5658	330	9	qkpk	qkpk	VERB
ejpam-5658	330	10	.	.	PUNCT
ejpam-5658	331	1	on	on	ADP
ejpam-5658	331	2	the	the	DET
ejpam-5658	331	3	other	other	ADJ
ejpam-5658	331	4	hand	hand	NOUN
ejpam-5658	331	5	,	,	PUNCT
ejpam-5658	331	6	suppose	suppose	VERB
ejpam-5658	331	7	c0	c0	PROPN
ejpam-5658	331	8	=	=	SYM
ejpam-5658	331	9	∪x∈s0({x}×rx	∪x∈s0({x}×rx	PROPN
ejpam-5658	331	10	)	)	PUNCT
ejpam-5658	331	11	is	be	AUX
ejpam-5658	331	12	an	an	DET
ejpam-5658	331	13	αh	αh	NOUN
ejpam-5658	331	14	-	-	PUNCT
ejpam-5658	331	15	set	set	VERB
ejpam-5658	331	16	in	in	ADP
ejpam-5658	331	17	g∨h	g∨h	PROPN
ejpam-5658	331	18	.	.	PUNCT
ejpam-5658	332	1	then	then	ADV
ejpam-5658	332	2	,	,	PUNCT
ejpam-5658	332	3	by	by	ADP
ejpam-5658	332	4	(	(	PUNCT
ejpam-5658	332	5	i	i	NOUN
ejpam-5658	332	6	)	)	PUNCT
ejpam-5658	332	7	and	and	CCONJ
ejpam-5658	332	8	(	(	PUNCT
ejpam-5658	332	9	ii	ii	NOUN
ejpam-5658	332	10	)	)	PUNCT
ejpam-5658	332	11	of	of	ADP
ejpam-5658	332	12	theorem	theorem	ADJ
ejpam-5658	332	13	5	5	NUM
ejpam-5658	332	14	,	,	PUNCT
ejpam-5658	332	15	s0	s0	PROPN
ejpam-5658	332	16	is	be	AUX
ejpam-5658	332	17	a	a	DET
ejpam-5658	332	18	hop	hop	NOUN
ejpam-5658	332	19	independent	independent	ADJ
ejpam-5658	332	20	set	set	NOUN
ejpam-5658	332	21	in	in	ADP
ejpam-5658	332	22	g	g	NOUN
ejpam-5658	332	23	and	and	CCONJ
ejpam-5658	332	24	rx	rx	VERB
ejpam-5658	332	25	is	be	AUX
ejpam-5658	332	26	a	a	DET
ejpam-5658	332	27	clique	clique	NOUN
ejpam-5658	332	28	in	in	ADP
ejpam-5658	332	29	h	h	NOUN
ejpam-5658	332	30	for	for	ADP
ejpam-5658	332	31	each	each	DET
ejpam-5658	332	32	x	x	SYM
ejpam-5658	332	33	∈	∈	PROPN
ejpam-5658	332	34	s0	s0	PROPN
ejpam-5658	332	35	.	.	PUNCT
ejpam-5658	333	1	by	by	ADP
ejpam-5658	333	2	theorem	theorem	NOUN
ejpam-5658	333	3	1	1	NUM
ejpam-5658	333	4	,	,	PUNCT
ejpam-5658	333	5	the	the	DET
ejpam-5658	333	6	components	component	NOUN
ejpam-5658	333	7	of	of	ADP
ejpam-5658	333	8	s0	s0	PROPN
ejpam-5658	333	9	are	be	AUX
ejpam-5658	333	10	cliques	clique	NOUN
ejpam-5658	333	11	in	in	ADP
ejpam-5658	333	12	g.	g.	PROPN
ejpam-5658	333	13	let	let	VERB
ejpam-5658	333	14	gr1	gr1	PROPN
ejpam-5658	333	15	,	,	PUNCT
ejpam-5658	333	16	gr2	gr2	PROPN
ejpam-5658	333	17	,	,	PUNCT
ejpam-5658	333	18	·	·	PUNCT
ejpam-5658	333	19	·	·	PUNCT
ejpam-5658	333	20	·	·	PUNCT
ejpam-5658	333	21	,	,	PUNCT
ejpam-5658	333	22	and	and	CCONJ
ejpam-5658	333	23	grn	grn	PROPN
ejpam-5658	333	24	be	be	VERB
ejpam-5658	333	25	the	the	DET
ejpam-5658	333	26	components	component	NOUN
ejpam-5658	333	27	of	of	ADP
ejpam-5658	333	28	g	g	NOUN
ejpam-5658	333	29	,	,	PUNCT
ejpam-5658	333	30	where	where	SCONJ
ejpam-5658	333	31	r1	r1	PROPN
ejpam-5658	333	32	≥	≥	NUM
ejpam-5658	333	33	r2	r2	PROPN
ejpam-5658	333	34	·	·	PUNCT
ejpam-5658	333	35	·	·	PUNCT
ejpam-5658	333	36	·	·	PUNCT
ejpam-5658	333	37	≥	≥	NUM
ejpam-5658	333	38	rn	rn	PROPN
ejpam-5658	333	39	,	,	PUNCT
ejpam-5658	333	40	where	where	SCONJ
ejpam-5658	333	41	rj	rj	PROPN
ejpam-5658	333	42	=	=	PROPN
ejpam-5658	333	43	|v	|v	PROPN
ejpam-5658	333	44	(	(	PUNCT
ejpam-5658	333	45	grj	grj	NOUN
ejpam-5658	333	46	)	)	PUNCT
ejpam-5658	333	47	|	|	ADV
ejpam-5658	333	48	for	for	ADP
ejpam-5658	333	49	each	each	DET
ejpam-5658	333	50	j	j	PROPN
ejpam-5658	333	51	∈	∈	PROPN
ejpam-5658	333	52	{	{	PUNCT
ejpam-5658	333	53	1	1	NUM
ejpam-5658	333	54	,	,	PUNCT
ejpam-5658	333	55	2	2	NUM
ejpam-5658	333	56	,	,	PUNCT
ejpam-5658	333	57	·	·	PUNCT
ejpam-5658	333	58	·	·	PUNCT
ejpam-5658	333	59	·	·	PUNCT
ejpam-5658	333	60	,	,	PUNCT
ejpam-5658	333	61	n	n	CCONJ
ejpam-5658	333	62	}	}	PUNCT
ejpam-5658	333	63	.	.	PUNCT
ejpam-5658	334	1	by	by	ADP
ejpam-5658	334	2	(	(	PUNCT
ejpam-5658	334	3	iii	iii	NOUN
ejpam-5658	334	4	)	)	PUNCT
ejpam-5658	334	5	of	of	ADP
ejpam-5658	334	6	theorem	theorem	NOUN
ejpam-5658	334	7	5	5	NUM
ejpam-5658	334	8	,	,	PUNCT
ejpam-5658	334	9	⟨v	⟨v	NUM
ejpam-5658	334	10	(	(	PUNCT
ejpam-5658	334	11	gr1	gr1	PROPN
ejpam-5658	334	12	)	)	PUNCT
ejpam-5658	334	13	,	,	PUNCT
ejpam-5658	334	14	v	v	X
ejpam-5658	334	15	(	(	PUNCT
ejpam-5658	334	16	gr2	gr2	PROPN
ejpam-5658	334	17	)	)	PUNCT
ejpam-5658	334	18	,	,	PUNCT
ejpam-5658	334	19	·	·	PUNCT
ejpam-5658	334	20	·	·	PUNCT
ejpam-5658	334	21	·	·	PUNCT
ejpam-5658	334	22	,	,	PUNCT
ejpam-5658	334	23	v	v	X
ejpam-5658	334	24	(	(	PUNCT
ejpam-5658	334	25	grn)⟩	grn)⟩	PROPN
ejpam-5658	334	26	is	be	AUX
ejpam-5658	334	27	a	a	DET
ejpam-5658	334	28	decreasing	decrease	VERB
ejpam-5658	334	29	d3	d3	NOUN
ejpam-5658	334	30	-	-	PUNCT
ejpam-5658	334	31	sequence	sequence	NOUN
ejpam-5658	334	32	of	of	ADP
ejpam-5658	334	33	cliques	clique	NOUN
ejpam-5658	334	34	in	in	ADP
ejpam-5658	334	35	g.	g.	PROPN
ejpam-5658	334	36	hence	hence	ADV
ejpam-5658	334	37	,	,	PUNCT
ejpam-5658	334	38	n	n	PRON
ejpam-5658	334	39	≤	≤	NOUN
ejpam-5658	334	40	m	m	PROPN
ejpam-5658	334	41	and	and	CCONJ
ejpam-5658	334	42	v	v	X
ejpam-5658	334	43	(	(	PUNCT
ejpam-5658	334	44	grj	grj	NOUN
ejpam-5658	334	45	)	)	PUNCT
ejpam-5658	334	46	⊆	⊆	NUM
ejpam-5658	334	47	sqj	sqj	NOUN
ejpam-5658	334	48	for	for	ADP
ejpam-5658	334	49	each	each	DET
ejpam-5658	334	50	j	j	PROPN
ejpam-5658	334	51	∈	∈	PROPN
ejpam-5658	334	52	{	{	PUNCT
ejpam-5658	334	53	1	1	NUM
ejpam-5658	334	54	,	,	PUNCT
ejpam-5658	334	55	2	2	NUM
ejpam-5658	334	56	,	,	PUNCT
ejpam-5658	334	57	·	·	PUNCT
ejpam-5658	334	58	·	·	PUNCT
ejpam-5658	334	59	·	·	PUNCT
ejpam-5658	334	60	,	,	PUNCT
ejpam-5658	334	61	n	n	CCONJ
ejpam-5658	334	62	}	}	PUNCT
ejpam-5658	334	63	.	.	PUNCT
ejpam-5658	335	1	since	since	SCONJ
ejpam-5658	335	2	c0	c0	PROPN
ejpam-5658	335	3	is	be	AUX
ejpam-5658	335	4	an	an	DET
ejpam-5658	335	5	αh	αh	NOUN
ejpam-5658	335	6	-	-	PUNCT
ejpam-5658	335	7	set	set	NOUN
ejpam-5658	335	8	in	in	ADP
ejpam-5658	335	9	g	g	PROPN
ejpam-5658	335	10	∨h	∨h	NOUN
ejpam-5658	335	11	,	,	PUNCT
ejpam-5658	335	12	it	it	PRON
ejpam-5658	335	13	follows	follow	VERB
ejpam-5658	335	14	that	that	SCONJ
ejpam-5658	335	15	for	for	ADP
ejpam-5658	335	16	each	each	DET
ejpam-5658	335	17	j	j	NOUN
ejpam-5658	335	18	with	with	ADP
ejpam-5658	335	19	1	1	NUM
ejpam-5658	335	20	≤	≤	NUM
ejpam-5658	335	21	j	j	PROPN
ejpam-5658	335	22	≤	≤	PROPN
ejpam-5658	335	23	n	n	CCONJ
ejpam-5658	335	24	and	and	CCONJ
ejpam-5658	335	25	for	for	ADP
ejpam-5658	335	26	each	each	DET
ejpam-5658	335	27	x	x	SYM
ejpam-5658	335	28	∈	∈	PROPN
ejpam-5658	335	29	v	v	NOUN
ejpam-5658	335	30	(	(	PUNCT
ejpam-5658	335	31	grj	grj	NOUN
ejpam-5658	335	32	)	)	PUNCT
ejpam-5658	335	33	,	,	PUNCT
ejpam-5658	335	34	rx	rx	VERB
ejpam-5658	335	35	=	=	PUNCT
ejpam-5658	335	36	qtj	qtj	PROPN
ejpam-5658	335	37	and	and	CCONJ
ejpam-5658	335	38	tj	tj	NOUN
ejpam-5658	335	39	≥	≥	NOUN
ejpam-5658	335	40	tj+1	tj+1	ADJ
ejpam-5658	335	41	for	for	ADP
ejpam-5658	335	42	j	j	PROPN
ejpam-5658	335	43	∈	∈	PROPN
ejpam-5658	335	44	{	{	PUNCT
ejpam-5658	335	45	1	1	NUM
ejpam-5658	335	46	,	,	PUNCT
ejpam-5658	335	47	2	2	NUM
ejpam-5658	335	48	,	,	PUNCT
ejpam-5658	335	49	·	·	PUNCT
ejpam-5658	335	50	·	·	PUNCT
ejpam-5658	335	51	·	·	PUNCT
ejpam-5658	335	52	,	,	PUNCT
ejpam-5658	336	1	n	n	CCONJ
ejpam-5658	336	2	−	−	PROPN
ejpam-5658	336	3	1	1	NUM
ejpam-5658	336	4	}	}	PUNCT
ejpam-5658	336	5	.	.	PUNCT
ejpam-5658	337	1	thus	thus	ADV
ejpam-5658	337	2	,	,	PUNCT
ejpam-5658	337	3	⟨qt1	⟨qt1	NOUN
ejpam-5658	337	4	,	,	PUNCT
ejpam-5658	337	5	qt2	qt2	PROPN
ejpam-5658	337	6	,	,	PUNCT
ejpam-5658	337	7	·	·	PUNCT
ejpam-5658	337	8	·	·	PUNCT
ejpam-5658	337	9	·	·	PUNCT
ejpam-5658	337	10	,	,	PUNCT
ejpam-5658	337	11	qtn⟩	qtn⟩	NOUN
ejpam-5658	337	12	is	be	AUX
ejpam-5658	337	13	a	a	DET
ejpam-5658	337	14	decreasing	decrease	VERB
ejpam-5658	337	15	d3	d3	NOUN
ejpam-5658	337	16	-	-	PUNCT
ejpam-5658	337	17	sequence	sequence	NOUN
ejpam-5658	337	18	of	of	ADP
ejpam-5658	337	19	cliques	clique	NOUN
ejpam-5658	337	20	in	in	ADP
ejpam-5658	337	21	h.	h.	PROPN
ejpam-5658	337	22	hence	hence	ADV
ejpam-5658	337	23	,	,	PUNCT
ejpam-5658	337	24	n	n	CCONJ
ejpam-5658	337	25	≤	≤	NOUN
ejpam-5658	337	26	r	r	NOUN
ejpam-5658	337	27	and	and	CCONJ
ejpam-5658	337	28	qtj	qtj	PROPN
ejpam-5658	337	29	⊆	⊆	NUM
ejpam-5658	337	30	dpj	dpj	NOUN
ejpam-5658	337	31	for	for	ADP
ejpam-5658	337	32	each	each	DET
ejpam-5658	337	33	j	j	PROPN
ejpam-5658	337	34	∈	∈	PROPN
ejpam-5658	337	35	{	{	PUNCT
ejpam-5658	337	36	1	1	NUM
ejpam-5658	337	37	,	,	PUNCT
ejpam-5658	337	38	2	2	NUM
ejpam-5658	337	39	,	,	PUNCT
ejpam-5658	337	40	·	·	PUNCT
ejpam-5658	337	41	·	·	PUNCT
ejpam-5658	337	42	·	·	PUNCT
ejpam-5658	337	43	,	,	PUNCT
ejpam-5658	337	44	n	n	CCONJ
ejpam-5658	337	45	}	}	PUNCT
ejpam-5658	337	46	.	.	PUNCT
ejpam-5658	338	1	it	it	PRON
ejpam-5658	338	2	follows	follow	VERB
ejpam-5658	338	3	that	that	SCONJ
ejpam-5658	338	4	n	n	CCONJ
ejpam-5658	338	5	≤	≤	NOUN
ejpam-5658	338	6	ρhg	ρhg	NOUN
ejpam-5658	338	7	.	.	PUNCT
ejpam-5658	339	1	therefore	therefore	ADV
ejpam-5658	339	2	,	,	PUNCT
ejpam-5658	339	3	αh(g	αh(g	ADP
ejpam-5658	339	4	∨h	∨h	NOUN
ejpam-5658	339	5	)	)	PUNCT
ejpam-5658	339	6	=	=	SYM
ejpam-5658	339	7	|c0|	|c0|	NOUN
ejpam-5658	339	8	=	=	SYM
ejpam-5658	339	9	∑	∑	PUNCT
ejpam-5658	339	10	x∈s0	x∈s0	PROPN
ejpam-5658	339	11	|rx|	|rx|	PROPN
ejpam-5658	339	12	=	=	PUNCT
ejpam-5658	339	13	n∑	n∑	NOUN
ejpam-5658	340	1	k=1	k=1	PROPN
ejpam-5658	340	2	rktk	rktk	VERB
ejpam-5658	340	3	≤	≤	NOUN
ejpam-5658	340	4	ρhg∑	ρhg∑	X
ejpam-5658	340	5	k=1	k=1	PROPN
ejpam-5658	340	6	qkpk	qkpk	PROPN
ejpam-5658	340	7	.	.	PUNCT
ejpam-5658	341	1	this	this	PRON
ejpam-5658	341	2	proves	prove	VERB
ejpam-5658	341	3	the	the	DET
ejpam-5658	341	4	desired	desire	VERB
ejpam-5658	341	5	equality	equality	NOUN
ejpam-5658	341	6	.	.	PUNCT
ejpam-5658	342	1	corollary	corollary	ADJ
ejpam-5658	342	2	6	6	NUM
ejpam-5658	342	3	.	.	PUNCT
ejpam-5658	343	1	let	let	VERB
ejpam-5658	343	2	g	g	NOUN
ejpam-5658	343	3	and	and	CCONJ
ejpam-5658	343	4	h	h	PROPN
ejpam-5658	343	5	be	be	VERB
ejpam-5658	343	6	non	non	ADJ
ejpam-5658	343	7	-	-	ADJ
ejpam-5658	343	8	trivial	trivial	ADJ
ejpam-5658	343	9	connected	connected	ADJ
ejpam-5658	343	10	graphs	graph	NOUN
ejpam-5658	343	11	.	.	PUNCT
ejpam-5658	344	1	if	if	SCONJ
ejpam-5658	344	2	g	g	PROPN
ejpam-5658	344	3	or	or	CCONJ
ejpam-5658	344	4	in	in	ADP
ejpam-5658	344	5	h	h	NOUN
ejpam-5658	344	6	has	have	VERB
ejpam-5658	344	7	a	a	DET
ejpam-5658	344	8	maximum	maximum	ADJ
ejpam-5658	344	9	decreasing	decrease	VERB
ejpam-5658	344	10	d3	d3	NOUN
ejpam-5658	344	11	-	-	PUNCT
ejpam-5658	344	12	sequence	sequence	NOUN
ejpam-5658	344	13	consisting	consist	VERB
ejpam-5658	344	14	of	of	ADP
ejpam-5658	344	15	a	a	DET
ejpam-5658	344	16	single	single	ADJ
ejpam-5658	344	17	clique	clique	NOUN
ejpam-5658	344	18	as	as	ADP
ejpam-5658	344	19	a	a	DET
ejpam-5658	344	20	term	term	NOUN
ejpam-5658	344	21	,	,	PUNCT
ejpam-5658	344	22	then	then	ADV
ejpam-5658	344	23	αh(g∨h	αh(g∨h	PROPN
ejpam-5658	344	24	)	)	PUNCT
ejpam-5658	344	25	=	=	SYM
ejpam-5658	344	26	ω(g)ω(h	ω(g)ω(h	PROPN
ejpam-5658	344	27	)	)	PUNCT
ejpam-5658	344	28	.	.	PUNCT
ejpam-5658	345	1	proof	proof	NOUN
ejpam-5658	345	2	.	.	PUNCT
ejpam-5658	346	1	suppose	suppose	VERB
ejpam-5658	346	2	,	,	PUNCT
ejpam-5658	346	3	without	without	ADP
ejpam-5658	346	4	loss	loss	NOUN
ejpam-5658	346	5	of	of	ADP
ejpam-5658	346	6	generality	generality	NOUN
ejpam-5658	346	7	,	,	PUNCT
ejpam-5658	346	8	that	that	SCONJ
ejpam-5658	346	9	⟨sq⟩	⟨sq⟩	NOUN
ejpam-5658	346	10	is	be	AUX
ejpam-5658	346	11	a	a	DET
ejpam-5658	346	12	maximum	maximum	ADJ
ejpam-5658	346	13	d3	d3	NOUN
ejpam-5658	346	14	-	-	PUNCT
ejpam-5658	346	15	sequence	sequence	NOUN
ejpam-5658	346	16	of	of	ADP
ejpam-5658	346	17	a	a	DET
ejpam-5658	346	18	single	single	ADJ
ejpam-5658	346	19	clique	clique	NOUN
ejpam-5658	346	20	in	in	ADP
ejpam-5658	346	21	g.	g.	PROPN
ejpam-5658	346	22	then	then	ADV
ejpam-5658	346	23	ρhg	ρhg	VERB
ejpam-5658	346	24	=	=	SYM
ejpam-5658	346	25	1	1	NUM
ejpam-5658	346	26	and	and	CCONJ
ejpam-5658	346	27	sq	sq	PROPN
ejpam-5658	346	28	is	be	AUX
ejpam-5658	346	29	a	a	DET
ejpam-5658	346	30	maximum	maximum	ADJ
ejpam-5658	346	31	clique	clique	NOUN
ejpam-5658	346	32	in	in	ADP
ejpam-5658	346	33	g.	g.	PROPN
ejpam-5658	346	34	let	let	VERB
ejpam-5658	346	35	d	d	PRON
ejpam-5658	346	36	be	be	AUX
ejpam-5658	346	37	a	a	DET
ejpam-5658	346	38	maximum	maximum	ADJ
ejpam-5658	346	39	clique	clique	NOUN
ejpam-5658	346	40	in	in	ADP
ejpam-5658	346	41	h.	h.	PROPN
ejpam-5658	346	42	then	then	ADV
ejpam-5658	346	43	αh(g	αh(g	ADP
ejpam-5658	346	44	∨h	∨h	NOUN
ejpam-5658	346	45	)	)	PUNCT
ejpam-5658	347	1	=	=	SYM
ejpam-5658	347	2	|sq||d|	|sq||d|	PROPN
ejpam-5658	347	3	=	=	SYM
ejpam-5658	347	4	ω(g)ω(h	ω(g)ω(h	PROPN
ejpam-5658	347	5	)	)	PUNCT
ejpam-5658	347	6	by	by	ADP
ejpam-5658	347	7	corollary	corollary	ADJ
ejpam-5658	347	8	5	5	NUM
ejpam-5658	347	9	.	.	PUNCT
ejpam-5658	347	10	example	example	NOUN
ejpam-5658	348	1	1	1	NUM
ejpam-5658	348	2	.	.	X
ejpam-5658	348	3	for	for	ADP
ejpam-5658	348	4	any	any	DET
ejpam-5658	348	5	non	non	ADJ
ejpam-5658	348	6	-	-	ADJ
ejpam-5658	348	7	trivial	trivial	ADJ
ejpam-5658	348	8	connected	connected	ADJ
ejpam-5658	348	9	graph	graph	NOUN
ejpam-5658	348	10	h	h	NOUN
ejpam-5658	348	11	,	,	PUNCT
ejpam-5658	348	12	αh(kn	αh(kn	PROPN
ejpam-5658	348	13	∨h	∨h	ADJ
ejpam-5658	348	14	)	)	PUNCT
ejpam-5658	349	1	=	=	SYM
ejpam-5658	349	2	nω(h	nω(h	X
ejpam-5658	349	3	)	)	PUNCT
ejpam-5658	349	4	and	and	CCONJ
ejpam-5658	349	5	αh(p3	αh(p3	X
ejpam-5658	349	6	∨	∨	NUM
ejpam-5658	349	7	h	h	NOUN
ejpam-5658	349	8	)	)	PUNCT
ejpam-5658	350	1	=	=	SYM
ejpam-5658	350	2	2ω(h	2ω(h	PROPN
ejpam-5658	350	3	)	)	PUNCT
ejpam-5658	350	4	.	.	PUNCT
ejpam-5658	351	1	8	8	X
ejpam-5658	351	2	.	.	X
ejpam-5658	351	3	strong	strong	ADJ
ejpam-5658	351	4	product	product	NOUN
ejpam-5658	351	5	of	of	ADP
ejpam-5658	351	6	two	two	NUM
ejpam-5658	351	7	graphs	graph	NOUN
ejpam-5658	351	8	theorem	theorem	VERB
ejpam-5658	351	9	6	6	NUM
ejpam-5658	351	10	.	.	PUNCT
ejpam-5658	352	1	let	let	VERB
ejpam-5658	352	2	g	g	NOUN
ejpam-5658	352	3	and	and	CCONJ
ejpam-5658	352	4	h	h	PROPN
ejpam-5658	352	5	be	be	VERB
ejpam-5658	352	6	non	non	ADJ
ejpam-5658	352	7	-	-	ADJ
ejpam-5658	352	8	trivial	trivial	ADJ
ejpam-5658	352	9	connected	connected	ADJ
ejpam-5658	352	10	graphs	graph	NOUN
ejpam-5658	352	11	.	.	PUNCT
ejpam-5658	353	1	then	then	ADV
ejpam-5658	353	2	c	c	X
ejpam-5658	353	3	=	=	SYM
ejpam-5658	353	4	∪x∈s({x	∪x∈s({x	ADJ
ejpam-5658	353	5	}	}	PUNCT
ejpam-5658	353	6	×	×	NOUN
ejpam-5658	353	7	tx	tx	PROPN
ejpam-5658	353	8	)	)	PUNCT
ejpam-5658	353	9	where	where	SCONJ
ejpam-5658	353	10	s	s	VERB
ejpam-5658	353	11	⊆	⊆	NUM
ejpam-5658	353	12	v	v	NOUN
ejpam-5658	353	13	(	(	PUNCT
ejpam-5658	353	14	g	g	NOUN
ejpam-5658	353	15	)	)	PUNCT
ejpam-5658	353	16	and	and	CCONJ
ejpam-5658	353	17	tx	tx	VERB
ejpam-5658	353	18	⊆	⊆	NUM
ejpam-5658	353	19	v	v	NOUN
ejpam-5658	353	20	(	(	PUNCT
ejpam-5658	353	21	h	h	NOUN
ejpam-5658	353	22	)	)	PUNCT
ejpam-5658	353	23	for	for	ADP
ejpam-5658	353	24	every	every	DET
ejpam-5658	353	25	x	x	SYM
ejpam-5658	353	26	∈	∈	PROPN
ejpam-5658	353	27	s	s	NOUN
ejpam-5658	353	28	,	,	PUNCT
ejpam-5658	353	29	is	be	AUX
ejpam-5658	353	30	a	a	DET
ejpam-5658	353	31	hop	hop	NOUN
ejpam-5658	353	32	independent	independent	ADJ
ejpam-5658	353	33	set	set	NOUN
ejpam-5658	353	34	in	in	ADP
ejpam-5658	353	35	g	g	PROPN
ejpam-5658	353	36	⊠h	⊠h	PROPN
ejpam-5658	353	37	if	if	SCONJ
ejpam-5658	353	38	and	and	CCONJ
ejpam-5658	353	39	only	only	ADV
ejpam-5658	353	40	if	if	SCONJ
ejpam-5658	353	41	following	follow	VERB
ejpam-5658	353	42	conditions	condition	NOUN
ejpam-5658	353	43	hold	hold	VERB
ejpam-5658	353	44	.	.	PUNCT
ejpam-5658	354	1	(	(	PUNCT
ejpam-5658	354	2	i	i	NOUN
ejpam-5658	354	3	)	)	PUNCT
ejpam-5658	354	4	tx	tx	PROPN
ejpam-5658	354	5	is	be	AUX
ejpam-5658	354	6	a	a	DET
ejpam-5658	354	7	hop	hop	NOUN
ejpam-5658	354	8	independent	independent	ADJ
ejpam-5658	354	9	set	set	NOUN
ejpam-5658	354	10	in	in	ADP
ejpam-5658	354	11	h	h	NOUN
ejpam-5658	354	12	for	for	ADP
ejpam-5658	354	13	every	every	DET
ejpam-5658	354	14	x	x	PROPN
ejpam-5658	354	15	∈	∈	PROPN
ejpam-5658	354	16	s.	s.	PROPN
ejpam-5658	354	17	(	(	PUNCT
ejpam-5658	354	18	ii	ii	PROPN
ejpam-5658	354	19	)	)	PUNCT
ejpam-5658	354	20	tx∪ty	tx∪ty	PROPN
ejpam-5658	354	21	is	be	AUX
ejpam-5658	354	22	hop	hop	ADV
ejpam-5658	354	23	independent	independent	ADJ
ejpam-5658	354	24	in	in	ADP
ejpam-5658	354	25	h	h	NOUN
ejpam-5658	354	26	for	for	ADP
ejpam-5658	354	27	every	every	DET
ejpam-5658	354	28	pair	pair	NOUN
ejpam-5658	354	29	of	of	ADP
ejpam-5658	354	30	vertices	vertex	NOUN
ejpam-5658	354	31	x	x	X
ejpam-5658	354	32	,	,	PUNCT
ejpam-5658	354	33	y	y	PROPN
ejpam-5658	354	34	∈	∈	PROPN
ejpam-5658	354	35	s	s	VERB
ejpam-5658	354	36	with	with	ADP
ejpam-5658	354	37	dg(x	dg(x	PROPN
ejpam-5658	354	38	,	,	PUNCT
ejpam-5658	354	39	y	y	NOUN
ejpam-5658	354	40	)	)	PUNCT
ejpam-5658	354	41	≤	≤	NOUN
ejpam-5658	354	42	2	2	NUM
ejpam-5658	354	43	.	.	PUNCT
ejpam-5658	355	1	(	(	PUNCT
ejpam-5658	355	2	iii	iii	X
ejpam-5658	355	3	)	)	PUNCT
ejpam-5658	355	4	tx∩ty	tx∩ty	PROPN
ejpam-5658	355	5	=	=	X
ejpam-5658	355	6	∅	∅	NOUN
ejpam-5658	355	7	and	and	CCONJ
ejpam-5658	355	8	dh(tx	dh(tx	PROPN
ejpam-5658	355	9	,	,	PUNCT
ejpam-5658	355	10	ty	ty	NOUN
ejpam-5658	355	11	)	)	PUNCT
ejpam-5658	355	12	≥	≥	NOUN
ejpam-5658	355	13	3	3	NUM
ejpam-5658	355	14	for	for	ADP
ejpam-5658	355	15	every	every	DET
ejpam-5658	355	16	pair	pair	NOUN
ejpam-5658	355	17	of	of	ADP
ejpam-5658	355	18	vertices	vertex	NOUN
ejpam-5658	355	19	x	x	X
ejpam-5658	355	20	,	,	PUNCT
ejpam-5658	355	21	y	y	PROPN
ejpam-5658	355	22	∈	∈	PROPN
ejpam-5658	355	23	s	s	VERB
ejpam-5658	355	24	with	with	ADP
ejpam-5658	355	25	dg(x	dg(x	PROPN
ejpam-5658	355	26	,	,	PUNCT
ejpam-5658	355	27	y	y	NOUN
ejpam-5658	355	28	)	)	PUNCT
ejpam-5658	355	29	=	=	SYM
ejpam-5658	355	30	2	2	X
ejpam-5658	355	31	.	.	PUNCT
ejpam-5658	355	32	j.	j.	PROPN
ejpam-5658	355	33	anoche	anoche	PROPN
ejpam-5658	355	34	,	,	PUNCT
ejpam-5658	355	35	s.	s.	PROPN
ejpam-5658	355	36	canoy	canoy	PROPN
ejpam-5658	355	37	,	,	PUNCT
ejpam-5658	355	38	jr	jr	PROPN
ejpam-5658	355	39	.	.	PROPN
ejpam-5658	355	40	/	/	SYM
ejpam-5658	355	41	eur	eur	PROPN
ejpam-5658	355	42	.	.	PUNCT
ejpam-5658	356	1	j.	j.	PROPN
ejpam-5658	356	2	pure	pure	PROPN
ejpam-5658	356	3	appl	appl	PROPN
ejpam-5658	356	4	.	.	PROPN
ejpam-5658	356	5	math	math	PROPN
ejpam-5658	356	6	,	,	PUNCT
ejpam-5658	356	7	18	18	NUM
ejpam-5658	356	8	(	(	PUNCT
ejpam-5658	356	9	1	1	NUM
ejpam-5658	356	10	)	)	PUNCT
ejpam-5658	356	11	(	(	PUNCT
ejpam-5658	356	12	2025	2025	NUM
ejpam-5658	356	13	)	)	PUNCT
ejpam-5658	356	14	,	,	PUNCT
ejpam-5658	356	15	5658	5658	NUM
ejpam-5658	356	16	11	11	NUM
ejpam-5658	356	17	of	of	ADP
ejpam-5658	356	18	15	15	NUM
ejpam-5658	356	19	proof	proof	NOUN
ejpam-5658	356	20	.	.	PUNCT
ejpam-5658	357	1	suppose	suppose	VERB
ejpam-5658	357	2	c	c	NOUN
ejpam-5658	357	3	is	be	AUX
ejpam-5658	357	4	a	a	DET
ejpam-5658	357	5	hop	hop	NOUN
ejpam-5658	357	6	independent	independent	ADJ
ejpam-5658	357	7	set	set	NOUN
ejpam-5658	357	8	in	in	ADP
ejpam-5658	357	9	g⊠h	g⊠h	NOUN
ejpam-5658	357	10	.	.	PUNCT
ejpam-5658	358	1	let	let	VERB
ejpam-5658	358	2	x	x	PUNCT
ejpam-5658	358	3	∈	∈	PROPN
ejpam-5658	358	4	s	s	X
ejpam-5658	358	5	and	and	CCONJ
ejpam-5658	358	6	a	a	DET
ejpam-5658	358	7	,	,	PUNCT
ejpam-5658	358	8	b	b	X
ejpam-5658	358	9	∈	∈	PROPN
ejpam-5658	358	10	tx	tx	VERB
ejpam-5658	358	11	such	such	ADJ
ejpam-5658	358	12	that	that	SCONJ
ejpam-5658	358	13	a	a	DET
ejpam-5658	358	14	̸=	̸=	PROPN
ejpam-5658	358	15	b.	b.	NOUN
ejpam-5658	358	16	if	if	SCONJ
ejpam-5658	358	17	ab	ab	PROPN
ejpam-5658	358	18	∈	∈	PROPN
ejpam-5658	358	19	e(g	e(g	PROPN
ejpam-5658	358	20	)	)	PUNCT
ejpam-5658	358	21	,	,	PUNCT
ejpam-5658	358	22	then	then	ADV
ejpam-5658	358	23	(	(	PUNCT
ejpam-5658	358	24	x	x	NOUN
ejpam-5658	358	25	,	,	PUNCT
ejpam-5658	358	26	a)(x	a)(x	PROPN
ejpam-5658	358	27	,	,	PUNCT
ejpam-5658	358	28	b	b	X
ejpam-5658	358	29	)	)	PUNCT
ejpam-5658	358	30	∈	∈	NOUN
ejpam-5658	358	31	e(g⊠h	e(g⊠h	NUM
ejpam-5658	358	32	)	)	PUNCT
ejpam-5658	358	33	.	.	PUNCT
ejpam-5658	359	1	suppose	suppose	VERB
ejpam-5658	359	2	ab	ab	PROPN
ejpam-5658	359	3	/∈	/∈	PUNCT
ejpam-5658	359	4	e(g	e(g	PROPN
ejpam-5658	359	5	)	)	PUNCT
ejpam-5658	359	6	.	.	PUNCT
ejpam-5658	360	1	then	then	ADV
ejpam-5658	360	2	(	(	PUNCT
ejpam-5658	360	3	x	x	NOUN
ejpam-5658	360	4	,	,	PUNCT
ejpam-5658	360	5	a)(x	a)(x	PROPN
ejpam-5658	360	6	,	,	PUNCT
ejpam-5658	360	7	b	b	NOUN
ejpam-5658	360	8	)	)	PUNCT
ejpam-5658	360	9	/∈	/∈	PUNCT
ejpam-5658	360	10	e(g	e(g	PROPN
ejpam-5658	360	11	⊠h	⊠h	PROPN
ejpam-5658	360	12	)	)	PUNCT
ejpam-5658	360	13	.	.	PUNCT
ejpam-5658	361	1	since	since	SCONJ
ejpam-5658	361	2	c	c	PROPN
ejpam-5658	361	3	is	be	AUX
ejpam-5658	361	4	hop	hop	ADV
ejpam-5658	361	5	independent	independent	ADJ
ejpam-5658	361	6	in	in	ADP
ejpam-5658	361	7	g	g	PROPN
ejpam-5658	361	8	⊠h	⊠h	PROPN
ejpam-5658	361	9	,	,	PUNCT
ejpam-5658	361	10	dg⊠h((x	dg⊠h((x	PROPN
ejpam-5658	361	11	,	,	PUNCT
ejpam-5658	361	12	a	a	PRON
ejpam-5658	361	13	)	)	PUNCT
ejpam-5658	361	14	,	,	PUNCT
ejpam-5658	361	15	(	(	PUNCT
ejpam-5658	361	16	x	x	NOUN
ejpam-5658	361	17	,	,	PUNCT
ejpam-5658	361	18	b	b	NOUN
ejpam-5658	361	19	)	)	PUNCT
ejpam-5658	361	20	)	)	PUNCT
ejpam-5658	361	21	≥	≥	NOUN
ejpam-5658	362	1	3	3	X
ejpam-5658	362	2	.	.	PUNCT
ejpam-5658	363	1	this	this	PRON
ejpam-5658	363	2	implies	imply	VERB
ejpam-5658	363	3	that	that	SCONJ
ejpam-5658	363	4	dh(a	dh(a	ADJ
ejpam-5658	363	5	,	,	PUNCT
ejpam-5658	363	6	b	b	NOUN
ejpam-5658	363	7	)	)	PUNCT
ejpam-5658	363	8	≥	≥	NOUN
ejpam-5658	363	9	3	3	NUM
ejpam-5658	363	10	,	,	PUNCT
ejpam-5658	363	11	showing	show	VERB
ejpam-5658	363	12	that	that	SCONJ
ejpam-5658	363	13	tx	tx	PROPN
ejpam-5658	363	14	is	be	AUX
ejpam-5658	363	15	hop	hop	ADV
ejpam-5658	363	16	independent	independent	ADJ
ejpam-5658	363	17	in	in	ADP
ejpam-5658	363	18	h.	h.	PROPN
ejpam-5658	363	19	this	this	PRON
ejpam-5658	363	20	shows	show	VERB
ejpam-5658	363	21	that	that	SCONJ
ejpam-5658	363	22	(	(	PUNCT
ejpam-5658	363	23	i	i	NOUN
ejpam-5658	363	24	)	)	PUNCT
ejpam-5658	363	25	holds	hold	VERB
ejpam-5658	363	26	.	.	PUNCT
ejpam-5658	364	1	next	next	ADV
ejpam-5658	364	2	,	,	PUNCT
ejpam-5658	364	3	let	let	VERB
ejpam-5658	364	4	x	x	PRON
ejpam-5658	364	5	,	,	PUNCT
ejpam-5658	364	6	y	y	PROPN
ejpam-5658	364	7	∈	∈	PROPN
ejpam-5658	364	8	s	s	VERB
ejpam-5658	364	9	with	with	ADP
ejpam-5658	364	10	dg(x	dg(x	PROPN
ejpam-5658	364	11	,	,	PUNCT
ejpam-5658	364	12	y	y	NOUN
ejpam-5658	364	13	)	)	PUNCT
ejpam-5658	364	14	≤	≤	NOUN
ejpam-5658	364	15	2	2	NUM
ejpam-5658	364	16	and	and	CCONJ
ejpam-5658	364	17	suppose	suppose	VERB
ejpam-5658	364	18	that	that	SCONJ
ejpam-5658	364	19	tx	tx	PROPN
ejpam-5658	364	20	∪	∪	NOUN
ejpam-5658	364	21	ty	ty	PRON
ejpam-5658	364	22	is	be	AUX
ejpam-5658	364	23	not	not	PART
ejpam-5658	364	24	hop	hop	ADV
ejpam-5658	364	25	independent	independent	ADJ
ejpam-5658	364	26	in	in	ADP
ejpam-5658	364	27	h.	h.	PROPN
ejpam-5658	364	28	by	by	ADP
ejpam-5658	364	29	(	(	PUNCT
ejpam-5658	364	30	i	i	NOUN
ejpam-5658	364	31	)	)	PUNCT
ejpam-5658	364	32	,	,	PUNCT
ejpam-5658	364	33	it	it	PRON
ejpam-5658	364	34	follows	follow	VERB
ejpam-5658	364	35	that	that	SCONJ
ejpam-5658	364	36	there	there	PRON
ejpam-5658	364	37	exist	exist	VERB
ejpam-5658	364	38	p	p	PROPN
ejpam-5658	364	39	∈	∈	PROPN
ejpam-5658	364	40	tx	tx	NOUN
ejpam-5658	364	41	and	and	CCONJ
ejpam-5658	364	42	q	q	ADJ
ejpam-5658	364	43	∈	∈	NOUN
ejpam-5658	365	1	ty	ty	INTJ
ejpam-5658	365	2	such	such	ADJ
ejpam-5658	365	3	that	that	SCONJ
ejpam-5658	365	4	dh(p	dh(p	NOUN
ejpam-5658	365	5	,	,	PUNCT
ejpam-5658	365	6	q	q	X
ejpam-5658	365	7	)	)	PUNCT
ejpam-5658	365	8	=	=	SYM
ejpam-5658	365	9	2	2	X
ejpam-5658	365	10	.	.	PUNCT
ejpam-5658	365	11	let	let	VERB
ejpam-5658	365	12	t	t	PROPN
ejpam-5658	365	13	∈	∈	PROPN
ejpam-5658	365	14	nh(p	nh(p	PROPN
ejpam-5658	365	15	)	)	PUNCT
ejpam-5658	365	16	∩nh(q	∩nh(q	NOUN
ejpam-5658	365	17	)	)	PUNCT
ejpam-5658	365	18	.	.	PUNCT
ejpam-5658	366	1	suppose	suppose	VERB
ejpam-5658	366	2	first	first	ADV
ejpam-5658	366	3	that	that	SCONJ
ejpam-5658	366	4	dg(x	dg(x	PROPN
ejpam-5658	366	5	,	,	PUNCT
ejpam-5658	366	6	y	y	NOUN
ejpam-5658	366	7	)	)	PUNCT
ejpam-5658	366	8	=	=	SYM
ejpam-5658	367	1	1	1	X
ejpam-5658	367	2	.	.	PUNCT
ejpam-5658	368	1	then	then	ADV
ejpam-5658	368	2	[	[	X
ejpam-5658	368	3	(	(	PUNCT
ejpam-5658	368	4	x	x	INTJ
ejpam-5658	368	5	,	,	PUNCT
ejpam-5658	368	6	p)(y	p)(y	PROPN
ejpam-5658	368	7	,	,	PUNCT
ejpam-5658	368	8	t	t	PROPN
ejpam-5658	368	9	)	)	PUNCT
ejpam-5658	368	10	,	,	PUNCT
ejpam-5658	368	11	(	(	PUNCT
ejpam-5658	368	12	y	y	NOUN
ejpam-5658	368	13	,	,	PUNCT
ejpam-5658	368	14	q	q	NOUN
ejpam-5658	368	15	)	)	PUNCT
ejpam-5658	368	16	]	]	PUNCT
ejpam-5658	368	17	is	be	AUX
ejpam-5658	368	18	an	an	DET
ejpam-5658	368	19	(	(	PUNCT
ejpam-5658	368	20	x	x	NOUN
ejpam-5658	368	21	,	,	PUNCT
ejpam-5658	368	22	p)(y	p)(y	PROPN
ejpam-5658	368	23	,	,	PUNCT
ejpam-5658	368	24	q	q	ADJ
ejpam-5658	368	25	)	)	PUNCT
ejpam-5658	368	26	geodesic	geodesic	NOUN
ejpam-5658	368	27	.	.	PUNCT
ejpam-5658	369	1	suppose	suppose	VERB
ejpam-5658	369	2	dg(x	dg(x	PROPN
ejpam-5658	369	3	,	,	PUNCT
ejpam-5658	369	4	y	y	NOUN
ejpam-5658	369	5	)	)	PUNCT
ejpam-5658	369	6	=	=	SYM
ejpam-5658	369	7	2	2	NUM
ejpam-5658	369	8	and	and	CCONJ
ejpam-5658	369	9	let	let	VERB
ejpam-5658	369	10	z	z	NOUN
ejpam-5658	369	11	∈	∈	PROPN
ejpam-5658	369	12	ng(x)∩ng(y	ng(x)∩ng(y	PROPN
ejpam-5658	369	13	)	)	PUNCT
ejpam-5658	369	14	.	.	PUNCT
ejpam-5658	370	1	then	then	ADV
ejpam-5658	370	2	[	[	X
ejpam-5658	370	3	(	(	PUNCT
ejpam-5658	370	4	x	x	X
ejpam-5658	370	5	,	,	PUNCT
ejpam-5658	370	6	p)(z	p)(z	PROPN
ejpam-5658	370	7	,	,	PUNCT
ejpam-5658	370	8	t	t	PROPN
ejpam-5658	370	9	)	)	PUNCT
ejpam-5658	370	10	,	,	PUNCT
ejpam-5658	370	11	(	(	PUNCT
ejpam-5658	370	12	y	y	NOUN
ejpam-5658	370	13	,	,	PUNCT
ejpam-5658	370	14	q	q	NOUN
ejpam-5658	370	15	)	)	PUNCT
ejpam-5658	370	16	]	]	PUNCT
ejpam-5658	370	17	is	be	AUX
ejpam-5658	370	18	an	an	DET
ejpam-5658	370	19	(	(	PUNCT
ejpam-5658	370	20	x	x	NOUN
ejpam-5658	370	21	,	,	PUNCT
ejpam-5658	370	22	p)-(y	p)-(y	ADJ
ejpam-5658	370	23	,	,	PUNCT
ejpam-5658	370	24	q	q	ADJ
ejpam-5658	370	25	)	)	PUNCT
ejpam-5658	370	26	geodesic	geodesic	NOUN
ejpam-5658	370	27	.	.	PUNCT
ejpam-5658	371	1	in	in	ADP
ejpam-5658	371	2	both	both	DET
ejpam-5658	371	3	cases	case	NOUN
ejpam-5658	371	4	,	,	PUNCT
ejpam-5658	371	5	we	we	PRON
ejpam-5658	371	6	have	have	VERB
ejpam-5658	371	7	dg⊠h((x	dg⊠h((x	NOUN
ejpam-5658	371	8	,	,	PUNCT
ejpam-5658	371	9	p	p	NOUN
ejpam-5658	371	10	)	)	PUNCT
ejpam-5658	371	11	,	,	PUNCT
ejpam-5658	371	12	(	(	PUNCT
ejpam-5658	371	13	y	y	NOUN
ejpam-5658	371	14	,	,	PUNCT
ejpam-5658	371	15	q	q	NOUN
ejpam-5658	371	16	)	)	PUNCT
ejpam-5658	371	17	)	)	PUNCT
ejpam-5658	372	1	=	=	SYM
ejpam-5658	372	2	2	2	NUM
ejpam-5658	372	3	,	,	PUNCT
ejpam-5658	372	4	contrary	contrary	ADJ
ejpam-5658	372	5	to	to	ADP
ejpam-5658	372	6	our	our	PRON
ejpam-5658	372	7	assumption	assumption	NOUN
ejpam-5658	372	8	that	that	SCONJ
ejpam-5658	372	9	c	c	PROPN
ejpam-5658	372	10	is	be	AUX
ejpam-5658	372	11	hop	hop	ADV
ejpam-5658	372	12	independent	independent	ADJ
ejpam-5658	372	13	.	.	PUNCT
ejpam-5658	373	1	thus	thus	ADV
ejpam-5658	373	2	,	,	PUNCT
ejpam-5658	373	3	tx	tx	PROPN
ejpam-5658	373	4	∪	∪	X
ejpam-5658	373	5	ty	ty	PROPN
ejpam-5658	373	6	is	be	AUX
ejpam-5658	373	7	hop	hop	ADV
ejpam-5658	373	8	independent	independent	ADJ
ejpam-5658	373	9	in	in	ADP
ejpam-5658	373	10	h	h	NOUN
ejpam-5658	373	11	,	,	PUNCT
ejpam-5658	373	12	showing	show	VERB
ejpam-5658	373	13	that	that	SCONJ
ejpam-5658	373	14	(	(	PUNCT
ejpam-5658	373	15	ii	ii	NOUN
ejpam-5658	373	16	)	)	PUNCT
ejpam-5658	373	17	holds	hold	VERB
ejpam-5658	373	18	.	.	PUNCT
ejpam-5658	374	1	finally	finally	ADV
ejpam-5658	374	2	,	,	PUNCT
ejpam-5658	374	3	let	let	VERB
ejpam-5658	374	4	x	x	PRON
ejpam-5658	374	5	,	,	PUNCT
ejpam-5658	374	6	y	y	PROPN
ejpam-5658	374	7	∈	∈	PROPN
ejpam-5658	374	8	s	s	VERB
ejpam-5658	374	9	such	such	ADJ
ejpam-5658	374	10	that	that	DET
ejpam-5658	374	11	dg(x	dg(x	NOUN
ejpam-5658	374	12	,	,	PUNCT
ejpam-5658	374	13	y	y	NOUN
ejpam-5658	374	14	)	)	PUNCT
ejpam-5658	374	15	=	=	SYM
ejpam-5658	375	1	2	2	X
ejpam-5658	375	2	.	.	X
ejpam-5658	375	3	let	let	VERB
ejpam-5658	375	4	z	z	NOUN
ejpam-5658	375	5	∈	∈	PROPN
ejpam-5658	375	6	ng(x	ng(x	NUM
ejpam-5658	375	7	)	)	PUNCT
ejpam-5658	375	8	∩	∩	NOUN
ejpam-5658	375	9	ng(y	ng(y	NOUN
ejpam-5658	375	10	)	)	PUNCT
ejpam-5658	375	11	.	.	PUNCT
ejpam-5658	376	1	suppose	suppose	VERB
ejpam-5658	376	2	there	there	PRON
ejpam-5658	376	3	exists	exist	VERB
ejpam-5658	376	4	t	t	PROPN
ejpam-5658	376	5	∈	∈	PROPN
ejpam-5658	376	6	tx	tx	PROPN
ejpam-5658	376	7	∩	∩	PROPN
ejpam-5658	376	8	ty	ty	X
ejpam-5658	376	9	.	.	PUNCT
ejpam-5658	376	10	then	then	ADV
ejpam-5658	376	11	dg⊠h((x	dg⊠h((x	PROPN
ejpam-5658	376	12	,	,	PUNCT
ejpam-5658	376	13	t	t	PROPN
ejpam-5658	376	14	)	)	PUNCT
ejpam-5658	376	15	,	,	PUNCT
ejpam-5658	376	16	(	(	PUNCT
ejpam-5658	376	17	y	y	PROPN
ejpam-5658	376	18	,	,	PUNCT
ejpam-5658	376	19	t	t	PROPN
ejpam-5658	376	20	)	)	PUNCT
ejpam-5658	376	21	)	)	PUNCT
ejpam-5658	377	1	=	=	SYM
ejpam-5658	377	2	2	2	NUM
ejpam-5658	377	3	which	which	PRON
ejpam-5658	377	4	is	be	AUX
ejpam-5658	377	5	not	not	PART
ejpam-5658	377	6	possible	possible	ADJ
ejpam-5658	377	7	.	.	PUNCT
ejpam-5658	378	1	hence	hence	ADV
ejpam-5658	378	2	,	,	PUNCT
ejpam-5658	378	3	tx	tx	PROPN
ejpam-5658	378	4	∩	∩	ADJ
ejpam-5658	378	5	ty	ty	AUX
ejpam-5658	378	6	=	=	PUNCT
ejpam-5658	378	7	∅.	∅.	AUX
ejpam-5658	378	8	suppose	suppose	VERB
ejpam-5658	378	9	dh(tx	dh(tx	PROPN
ejpam-5658	378	10	,	,	PUNCT
ejpam-5658	378	11	ty	ty	INTJ
ejpam-5658	378	12	)	)	PUNCT
ejpam-5658	378	13	=	=	SYM
ejpam-5658	379	1	1	1	X
ejpam-5658	379	2	.	.	PUNCT
ejpam-5658	380	1	then	then	ADV
ejpam-5658	380	2	this	this	PRON
ejpam-5658	380	3	would	would	AUX
ejpam-5658	380	4	imply	imply	VERB
ejpam-5658	380	5	that	that	SCONJ
ejpam-5658	380	6	there	there	PRON
ejpam-5658	380	7	exist	exist	VERB
ejpam-5658	380	8	c	c	PROPN
ejpam-5658	380	9	∈	∈	PROPN
ejpam-5658	380	10	tx	tx	PROPN
ejpam-5658	380	11	and	and	CCONJ
ejpam-5658	380	12	d	d	PROPN
ejpam-5658	380	13	∈	∈	PROPN
ejpam-5658	380	14	ty	ty	INTJ
ejpam-5658	380	15	with	with	ADP
ejpam-5658	380	16	dh(c	dh(c	PROPN
ejpam-5658	380	17	,	,	PUNCT
ejpam-5658	380	18	d	d	NOUN
ejpam-5658	380	19	)	)	PUNCT
ejpam-5658	380	20	=	=	SYM
ejpam-5658	380	21	1	1	X
ejpam-5658	380	22	.	.	PUNCT
ejpam-5658	380	23	consequently	consequently	ADV
ejpam-5658	380	24	,	,	PUNCT
ejpam-5658	380	25	[	[	X
ejpam-5658	380	26	(	(	PUNCT
ejpam-5658	380	27	x	x	NOUN
ejpam-5658	380	28	,	,	PUNCT
ejpam-5658	380	29	c	c	NOUN
ejpam-5658	380	30	)	)	PUNCT
ejpam-5658	380	31	,	,	PUNCT
ejpam-5658	380	32	(	(	PUNCT
ejpam-5658	380	33	z	z	X
ejpam-5658	380	34	,	,	PUNCT
ejpam-5658	380	35	d	d	NOUN
ejpam-5658	380	36	)	)	PUNCT
ejpam-5658	380	37	,	,	PUNCT
ejpam-5658	380	38	(	(	PUNCT
ejpam-5658	380	39	y	y	NOUN
ejpam-5658	380	40	,	,	PUNCT
ejpam-5658	380	41	d	d	NOUN
ejpam-5658	380	42	)	)	PUNCT
ejpam-5658	380	43	]	]	PUNCT
ejpam-5658	380	44	is	be	AUX
ejpam-5658	380	45	an	an	DET
ejpam-5658	380	46	(	(	PUNCT
ejpam-5658	380	47	x	x	NOUN
ejpam-5658	380	48	,	,	PUNCT
ejpam-5658	380	49	c)-(y	c)-(y	PROPN
ejpam-5658	380	50	,	,	PUNCT
ejpam-5658	380	51	d	d	NOUN
ejpam-5658	380	52	)	)	PUNCT
ejpam-5658	380	53	geodesic	geodesic	NOUN
ejpam-5658	380	54	in	in	ADP
ejpam-5658	380	55	g⊠h	g⊠h	NOUN
ejpam-5658	380	56	.	.	PUNCT
ejpam-5658	381	1	if	if	SCONJ
ejpam-5658	381	2	dh(tx	dh(tx	PROPN
ejpam-5658	381	3	,	,	PUNCT
ejpam-5658	381	4	ty	ty	INTJ
ejpam-5658	381	5	)	)	PUNCT
ejpam-5658	381	6	=	=	SYM
ejpam-5658	381	7	2	2	NUM
ejpam-5658	381	8	,	,	PUNCT
ejpam-5658	381	9	then	then	ADV
ejpam-5658	381	10	there	there	PRON
ejpam-5658	381	11	exist	exist	VERB
ejpam-5658	381	12	g	g	PROPN
ejpam-5658	381	13	∈	∈	PROPN
ejpam-5658	381	14	tx	tx	PROPN
ejpam-5658	381	15	and	and	CCONJ
ejpam-5658	381	16	h	h	NOUN
ejpam-5658	381	17	∈	∈	PROPN
ejpam-5658	381	18	ty	ty	INTJ
ejpam-5658	381	19	with	with	ADP
ejpam-5658	381	20	dh(g	dh(g	NOUN
ejpam-5658	381	21	,	,	PUNCT
ejpam-5658	381	22	h	h	NOUN
ejpam-5658	381	23	)	)	PUNCT
ejpam-5658	382	1	=	=	SYM
ejpam-5658	382	2	2	2	X
ejpam-5658	382	3	.	.	X
ejpam-5658	382	4	let	let	VERB
ejpam-5658	382	5	l	l	NOUN
ejpam-5658	382	6	∈	∈	PROPN
ejpam-5658	382	7	nh(g)∩nh(h	nh(g)∩nh(h	NOUN
ejpam-5658	382	8	)	)	PUNCT
ejpam-5658	382	9	.	.	PUNCT
ejpam-5658	383	1	then	then	ADV
ejpam-5658	383	2	[	[	X
ejpam-5658	383	3	(	(	PUNCT
ejpam-5658	383	4	x	x	NOUN
ejpam-5658	383	5	,	,	PUNCT
ejpam-5658	383	6	g	g	NOUN
ejpam-5658	383	7	)	)	PUNCT
ejpam-5658	383	8	,	,	PUNCT
ejpam-5658	383	9	(	(	PUNCT
ejpam-5658	383	10	z	z	X
ejpam-5658	383	11	,	,	PUNCT
ejpam-5658	383	12	l	l	NOUN
ejpam-5658	383	13	)	)	PUNCT
ejpam-5658	383	14	,	,	PUNCT
ejpam-5658	383	15	(	(	PUNCT
ejpam-5658	383	16	y	y	NOUN
ejpam-5658	383	17	,	,	PUNCT
ejpam-5658	383	18	h	h	NOUN
ejpam-5658	383	19	)	)	PUNCT
ejpam-5658	383	20	]	]	PUNCT
ejpam-5658	383	21	is	be	AUX
ejpam-5658	383	22	an	an	DET
ejpam-5658	383	23	(	(	PUNCT
ejpam-5658	383	24	x	x	NOUN
ejpam-5658	383	25	,	,	PUNCT
ejpam-5658	383	26	c)-(y	c)-(y	PROPN
ejpam-5658	383	27	,	,	PUNCT
ejpam-5658	383	28	d	d	NOUN
ejpam-5658	383	29	)	)	PUNCT
ejpam-5658	383	30	geodesic	geodesic	NOUN
ejpam-5658	383	31	in	in	ADP
ejpam-5658	383	32	g⊠h	g⊠h	NOUN
ejpam-5658	383	33	.	.	PUNCT
ejpam-5658	384	1	in	in	ADP
ejpam-5658	384	2	any	any	DET
ejpam-5658	384	3	case	case	NOUN
ejpam-5658	384	4	,	,	PUNCT
ejpam-5658	384	5	we	we	PRON
ejpam-5658	384	6	get	get	VERB
ejpam-5658	384	7	a	a	DET
ejpam-5658	384	8	contradiction	contradiction	NOUN
ejpam-5658	384	9	.	.	PUNCT
ejpam-5658	385	1	therefore	therefore	ADV
ejpam-5658	385	2	,	,	PUNCT
ejpam-5658	385	3	(	(	PUNCT
ejpam-5658	385	4	iii	iii	X
ejpam-5658	385	5	)	)	PUNCT
ejpam-5658	385	6	holds	hold	VERB
ejpam-5658	385	7	.	.	PUNCT
ejpam-5658	386	1	for	for	ADP
ejpam-5658	386	2	the	the	DET
ejpam-5658	386	3	converse	converse	NOUN
ejpam-5658	386	4	,	,	PUNCT
ejpam-5658	386	5	suppose	suppose	VERB
ejpam-5658	386	6	that	that	SCONJ
ejpam-5658	386	7	c	c	PROPN
ejpam-5658	386	8	satisfies	satisfy	VERB
ejpam-5658	386	9	properties	property	NOUN
ejpam-5658	386	10	(	(	PUNCT
ejpam-5658	386	11	i	i	NOUN
ejpam-5658	386	12	)	)	PUNCT
ejpam-5658	386	13	,	,	PUNCT
ejpam-5658	386	14	(	(	PUNCT
ejpam-5658	386	15	ii	ii	NOUN
ejpam-5658	386	16	)	)	PUNCT
ejpam-5658	386	17	,	,	PUNCT
ejpam-5658	386	18	(	(	PUNCT
ejpam-5658	386	19	iii	iii	NOUN
ejpam-5658	386	20	)	)	PUNCT
ejpam-5658	386	21	,	,	PUNCT
ejpam-5658	386	22	and	and	CCONJ
ejpam-5658	386	23	(	(	PUNCT
ejpam-5658	386	24	iv	iv	X
ejpam-5658	386	25	)	)	PUNCT
ejpam-5658	386	26	.	.	PUNCT
ejpam-5658	387	1	let	let	VERB
ejpam-5658	387	2	(	(	PUNCT
ejpam-5658	387	3	v	v	NOUN
ejpam-5658	387	4	,	,	PUNCT
ejpam-5658	387	5	p	p	NOUN
ejpam-5658	387	6	)	)	PUNCT
ejpam-5658	387	7	,	,	PUNCT
ejpam-5658	387	8	(	(	PUNCT
ejpam-5658	387	9	w	w	NOUN
ejpam-5658	387	10	,	,	PUNCT
ejpam-5658	387	11	q	q	NOUN
ejpam-5658	387	12	)	)	PUNCT
ejpam-5658	387	13	∈	∈	PROPN
ejpam-5658	387	14	c	c	NOUN
ejpam-5658	387	15	such	such	ADJ
ejpam-5658	387	16	that	that	PRON
ejpam-5658	387	17	(	(	PUNCT
ejpam-5658	387	18	v	v	NOUN
ejpam-5658	387	19	,	,	PUNCT
ejpam-5658	387	20	p	p	NOUN
ejpam-5658	387	21	)	)	PUNCT
ejpam-5658	387	22	̸=	̸=	PROPN
ejpam-5658	387	23	(	(	PUNCT
ejpam-5658	387	24	w	w	PROPN
ejpam-5658	387	25	,	,	PUNCT
ejpam-5658	387	26	q	q	NOUN
ejpam-5658	387	27	)	)	PUNCT
ejpam-5658	387	28	.	.	PUNCT
ejpam-5658	388	1	consider	consider	VERB
ejpam-5658	388	2	the	the	DET
ejpam-5658	388	3	following	follow	VERB
ejpam-5658	388	4	cases	case	NOUN
ejpam-5658	388	5	:	:	PUNCT
ejpam-5658	388	6	case	case	NOUN
ejpam-5658	388	7	1	1	NUM
ejpam-5658	388	8	.	.	PUNCT
ejpam-5658	388	9	v	v	NOUN
ejpam-5658	388	10	=	=	PUNCT
ejpam-5658	388	11	w.	w.	PROPN
ejpam-5658	388	12	then	then	ADV
ejpam-5658	388	13	p	p	X
ejpam-5658	388	14	,	,	PUNCT
ejpam-5658	388	15	q	q	PROPN
ejpam-5658	388	16	∈	∈	PROPN
ejpam-5658	388	17	tv	tv	NOUN
ejpam-5658	388	18	and	and	CCONJ
ejpam-5658	388	19	p	p	PROPN
ejpam-5658	388	20	̸=	̸=	PROPN
ejpam-5658	388	21	q.	q.	NOUN
ejpam-5658	388	22	by	by	ADP
ejpam-5658	388	23	condition	condition	NOUN
ejpam-5658	388	24	(	(	PUNCT
ejpam-5658	388	25	i	i	NOUN
ejpam-5658	388	26	)	)	PUNCT
ejpam-5658	388	27	,	,	PUNCT
ejpam-5658	388	28	dh(p	dh(p	PROPN
ejpam-5658	388	29	,	,	PUNCT
ejpam-5658	388	30	q	q	X
ejpam-5658	388	31	)	)	PUNCT
ejpam-5658	388	32	̸=	̸=	PROPN
ejpam-5658	388	33	2	2	NUM
ejpam-5658	388	34	.	.	PUNCT
ejpam-5658	389	1	hence	hence	ADV
ejpam-5658	389	2	,	,	PUNCT
ejpam-5658	389	3	dg⊠h((v	dg⊠h((v	NOUN
ejpam-5658	389	4	,	,	PUNCT
ejpam-5658	389	5	p	p	NOUN
ejpam-5658	389	6	)	)	PUNCT
ejpam-5658	389	7	,	,	PUNCT
ejpam-5658	389	8	(	(	PUNCT
ejpam-5658	389	9	w	w	NOUN
ejpam-5658	389	10	,	,	PUNCT
ejpam-5658	389	11	q	q	NOUN
ejpam-5658	389	12	)	)	PUNCT
ejpam-5658	389	13	)	)	PUNCT
ejpam-5658	390	1	̸=	̸=	PROPN
ejpam-5658	390	2	2	2	NUM
ejpam-5658	390	3	.	.	PUNCT
ejpam-5658	390	4	case	case	NOUN
ejpam-5658	390	5	2	2	NUM
ejpam-5658	390	6	.	.	NOUN
ejpam-5658	390	7	v	v	ADP
ejpam-5658	390	8	̸=	̸=	PROPN
ejpam-5658	390	9	w.	w.	PROPN
ejpam-5658	390	10	suppose	suppose	VERB
ejpam-5658	390	11	first	first	ADV
ejpam-5658	390	12	that	that	SCONJ
ejpam-5658	390	13	vw	vw	PROPN
ejpam-5658	390	14	∈	∈	PROPN
ejpam-5658	390	15	e(g	e(g	PROPN
ejpam-5658	390	16	)	)	PUNCT
ejpam-5658	390	17	.	.	PUNCT
ejpam-5658	391	1	if	if	SCONJ
ejpam-5658	391	2	p	p	NOUN
ejpam-5658	391	3	=	=	NOUN
ejpam-5658	391	4	q	q	ADJ
ejpam-5658	391	5	,	,	PUNCT
ejpam-5658	391	6	then	then	ADV
ejpam-5658	391	7	dg⊠h((v	dg⊠h((v	VERB
ejpam-5658	391	8	,	,	PUNCT
ejpam-5658	391	9	p	p	NOUN
ejpam-5658	391	10	)	)	PUNCT
ejpam-5658	391	11	,	,	PUNCT
ejpam-5658	391	12	(	(	PUNCT
ejpam-5658	391	13	w	w	NOUN
ejpam-5658	391	14	,	,	PUNCT
ejpam-5658	391	15	q	q	NOUN
ejpam-5658	391	16	)	)	PUNCT
ejpam-5658	391	17	)	)	PUNCT
ejpam-5658	392	1	=	=	SYM
ejpam-5658	392	2	1	1	X
ejpam-5658	392	3	.	.	PUNCT
ejpam-5658	392	4	suppose	suppose	VERB
ejpam-5658	392	5	p	p	X
ejpam-5658	392	6	̸=	̸=	PROPN
ejpam-5658	392	7	q.	q.	NOUN
ejpam-5658	392	8	if	if	SCONJ
ejpam-5658	392	9	pq	pq	PROPN
ejpam-5658	392	10	∈	∈	PROPN
ejpam-5658	392	11	e(h	e(h	PROPN
ejpam-5658	392	12	)	)	PUNCT
ejpam-5658	392	13	,	,	PUNCT
ejpam-5658	392	14	then	then	ADV
ejpam-5658	392	15	dg⊠h((v	dg⊠h((v	VERB
ejpam-5658	392	16	,	,	PUNCT
ejpam-5658	392	17	p	p	NOUN
ejpam-5658	392	18	)	)	PUNCT
ejpam-5658	392	19	,	,	PUNCT
ejpam-5658	392	20	(	(	PUNCT
ejpam-5658	392	21	w	w	NOUN
ejpam-5658	392	22	,	,	PUNCT
ejpam-5658	392	23	q	q	NOUN
ejpam-5658	392	24	)	)	PUNCT
ejpam-5658	392	25	)	)	PUNCT
ejpam-5658	393	1	=	=	SYM
ejpam-5658	393	2	1	1	X
ejpam-5658	393	3	.	.	PUNCT
ejpam-5658	393	4	suppose	suppose	VERB
ejpam-5658	393	5	pq	pq	INTJ
ejpam-5658	393	6	/∈	/∈	PUNCT
ejpam-5658	393	7	e(h	e(h	PROPN
ejpam-5658	393	8	)	)	PUNCT
ejpam-5658	393	9	.	.	PUNCT
ejpam-5658	394	1	by	by	ADP
ejpam-5658	394	2	(	(	PUNCT
ejpam-5658	394	3	ii	ii	NOUN
ejpam-5658	394	4	)	)	PUNCT
ejpam-5658	394	5	,	,	PUNCT
ejpam-5658	394	6	tv	tv	NOUN
ejpam-5658	394	7	∪	∪	NOUN
ejpam-5658	394	8	tw	tw	PROPN
ejpam-5658	394	9	is	be	AUX
ejpam-5658	394	10	a	a	DET
ejpam-5658	394	11	hop	hop	NOUN
ejpam-5658	394	12	independent	independent	ADJ
ejpam-5658	394	13	set	set	NOUN
ejpam-5658	394	14	.	.	PUNCT
ejpam-5658	395	1	it	it	PRON
ejpam-5658	395	2	follows	follow	VERB
ejpam-5658	395	3	that	that	SCONJ
ejpam-5658	395	4	dh(p	dh(p	NOUN
ejpam-5658	395	5	,	,	PUNCT
ejpam-5658	395	6	q	q	X
ejpam-5658	395	7	)	)	PUNCT
ejpam-5658	395	8	≥	≥	NOUN
ejpam-5658	395	9	3	3	NUM
ejpam-5658	395	10	.	.	PUNCT
ejpam-5658	395	11	thus	thus	ADV
ejpam-5658	395	12	,	,	PUNCT
ejpam-5658	395	13	dg⊠h((v	dg⊠h((v	NOUN
ejpam-5658	395	14	,	,	PUNCT
ejpam-5658	395	15	p	p	NOUN
ejpam-5658	395	16	)	)	PUNCT
ejpam-5658	395	17	,	,	PUNCT
ejpam-5658	395	18	(	(	PUNCT
ejpam-5658	395	19	w	w	NOUN
ejpam-5658	395	20	,	,	PUNCT
ejpam-5658	395	21	q	q	NOUN
ejpam-5658	395	22	)	)	PUNCT
ejpam-5658	395	23	)	)	PUNCT
ejpam-5658	395	24	≥	≥	NOUN
ejpam-5658	396	1	3	3	NUM
ejpam-5658	396	2	.	.	PUNCT
ejpam-5658	397	1	next	next	ADV
ejpam-5658	397	2	,	,	PUNCT
ejpam-5658	397	3	suppose	suppose	VERB
ejpam-5658	397	4	that	that	SCONJ
ejpam-5658	397	5	vw	vw	PROPN
ejpam-5658	397	6	/∈	/∈	PUNCT
ejpam-5658	397	7	e(g	e(g	PROPN
ejpam-5658	397	8	)	)	PUNCT
ejpam-5658	397	9	.	.	PUNCT
ejpam-5658	398	1	if	if	SCONJ
ejpam-5658	398	2	dg(v	dg(v	NOUN
ejpam-5658	398	3	,	,	PUNCT
ejpam-5658	398	4	w	w	NOUN
ejpam-5658	398	5	)	)	PUNCT
ejpam-5658	398	6	≥	≥	NOUN
ejpam-5658	398	7	3	3	NUM
ejpam-5658	398	8	,	,	PUNCT
ejpam-5658	398	9	then	then	ADV
ejpam-5658	398	10	dg⊠h((v	dg⊠h((v	VERB
ejpam-5658	398	11	,	,	PUNCT
ejpam-5658	398	12	p	p	NOUN
ejpam-5658	398	13	)	)	PUNCT
ejpam-5658	398	14	,	,	PUNCT
ejpam-5658	398	15	(	(	PUNCT
ejpam-5658	398	16	w	w	NOUN
ejpam-5658	398	17	,	,	PUNCT
ejpam-5658	398	18	q	q	NOUN
ejpam-5658	398	19	)	)	PUNCT
ejpam-5658	398	20	)	)	PUNCT
ejpam-5658	398	21	≥	≥	NOUN
ejpam-5658	399	1	3	3	X
ejpam-5658	399	2	.	.	PUNCT
ejpam-5658	400	1	if	if	SCONJ
ejpam-5658	400	2	dg(v	dg(v	NOUN
ejpam-5658	400	3	,	,	PUNCT
ejpam-5658	400	4	w	w	NOUN
ejpam-5658	400	5	)	)	PUNCT
ejpam-5658	400	6	=	=	SYM
ejpam-5658	400	7	2	2	NUM
ejpam-5658	400	8	,	,	PUNCT
ejpam-5658	400	9	then	then	ADV
ejpam-5658	400	10	tv	tv	NOUN
ejpam-5658	400	11	∩	∩	ADJ
ejpam-5658	400	12	tw	tw	NOUN
ejpam-5658	400	13	=	=	SYM
ejpam-5658	400	14	∅	∅	NOUN
ejpam-5658	400	15	by	by	ADP
ejpam-5658	400	16	(	(	PUNCT
ejpam-5658	400	17	iii	iii	NOUN
ejpam-5658	400	18	)	)	PUNCT
ejpam-5658	400	19	.	.	PUNCT
ejpam-5658	401	1	hence	hence	ADV
ejpam-5658	401	2	,	,	PUNCT
ejpam-5658	401	3	p	p	PROPN
ejpam-5658	401	4	̸=	̸=	PROPN
ejpam-5658	401	5	q	q	PROPN
ejpam-5658	401	6	and	and	CCONJ
ejpam-5658	401	7	dh(p	dh(p	PROPN
ejpam-5658	401	8	,	,	PUNCT
ejpam-5658	401	9	q	q	X
ejpam-5658	401	10	)	)	PUNCT
ejpam-5658	401	11	≥	≥	NOUN
ejpam-5658	401	12	3	3	NUM
ejpam-5658	401	13	by	by	ADP
ejpam-5658	401	14	(	(	PUNCT
ejpam-5658	401	15	ii	ii	NOUN
ejpam-5658	401	16	)	)	PUNCT
ejpam-5658	401	17	.	.	PUNCT
ejpam-5658	402	1	therefore	therefore	ADV
ejpam-5658	402	2	,	,	PUNCT
ejpam-5658	402	3	dg⊠h((v	dg⊠h((v	NOUN
ejpam-5658	402	4	,	,	PUNCT
ejpam-5658	402	5	p	p	NOUN
ejpam-5658	402	6	)	)	PUNCT
ejpam-5658	402	7	,	,	PUNCT
ejpam-5658	402	8	(	(	PUNCT
ejpam-5658	402	9	w	w	NOUN
ejpam-5658	402	10	,	,	PUNCT
ejpam-5658	402	11	q	q	NOUN
ejpam-5658	402	12	)	)	PUNCT
ejpam-5658	402	13	)	)	PUNCT
ejpam-5658	402	14	≥	≥	NOUN
ejpam-5658	402	15	3	3	X
ejpam-5658	402	16	.	.	PUNCT
ejpam-5658	402	17	accordingly	accordingly	ADV
ejpam-5658	402	18	,	,	PUNCT
ejpam-5658	402	19	c	c	PROPN
ejpam-5658	402	20	is	be	AUX
ejpam-5658	402	21	a	a	DET
ejpam-5658	402	22	hop	hop	NOUN
ejpam-5658	402	23	independent	independent	ADJ
ejpam-5658	402	24	set	set	NOUN
ejpam-5658	402	25	in	in	ADP
ejpam-5658	402	26	g⊠h	g⊠h	NOUN
ejpam-5658	402	27	.	.	PUNCT
ejpam-5658	403	1	corollary	corollary	ADJ
ejpam-5658	403	2	7	7	NUM
ejpam-5658	403	3	.	.	PUNCT
ejpam-5658	404	1	let	let	VERB
ejpam-5658	404	2	g	g	NOUN
ejpam-5658	404	3	and	and	CCONJ
ejpam-5658	404	4	h	h	PROPN
ejpam-5658	404	5	be	be	VERB
ejpam-5658	404	6	non	non	ADJ
ejpam-5658	404	7	-	-	ADJ
ejpam-5658	404	8	trivial	trivial	ADJ
ejpam-5658	404	9	connected	connected	ADJ
ejpam-5658	404	10	graphs	graph	NOUN
ejpam-5658	404	11	and	and	CCONJ
ejpam-5658	404	12	let	let	VERB
ejpam-5658	404	13	⟨sq1	⟨sq1	VERB
ejpam-5658	404	14	,	,	PUNCT
ejpam-5658	404	15	sq2	sq2	PROPN
ejpam-5658	404	16	,	,	PUNCT
ejpam-5658	404	17	·	·	PUNCT
ejpam-5658	404	18	·	·	PUNCT
ejpam-5658	404	19	·	·	PUNCT
ejpam-5658	404	20	,	,	PUNCT
ejpam-5658	404	21	sqm⟩	sqm⟩	NOUN
ejpam-5658	404	22	and	and	CCONJ
ejpam-5658	404	23	⟨dp1	⟨dp1	PROPN
ejpam-5658	404	24	,	,	PUNCT
ejpam-5658	404	25	dp2	dp2	PROPN
ejpam-5658	404	26	,	,	PUNCT
ejpam-5658	404	27	·	·	PUNCT
ejpam-5658	404	28	·	·	PUNCT
ejpam-5658	404	29	·	·	PUNCT
ejpam-5658	404	30	,	,	PUNCT
ejpam-5658	404	31	dpr⟩	dpr⟩	NOUN
ejpam-5658	404	32	be	be	AUX
ejpam-5658	404	33	maximum	maximum	ADV
ejpam-5658	404	34	decreasing	decrease	VERB
ejpam-5658	404	35	d3	d3	NOUN
ejpam-5658	404	36	-	-	PUNCT
ejpam-5658	404	37	sequences	sequence	NOUN
ejpam-5658	404	38	of	of	ADP
ejpam-5658	404	39	cliques	clique	NOUN
ejpam-5658	404	40	in	in	ADP
ejpam-5658	404	41	g	g	PROPN
ejpam-5658	404	42	and	and	CCONJ
ejpam-5658	404	43	h	h	NOUN
ejpam-5658	404	44	,	,	PUNCT
ejpam-5658	404	45	respectively	respectively	ADV
ejpam-5658	404	46	.	.	PUNCT
ejpam-5658	405	1	then	then	ADV
ejpam-5658	405	2	αh(g⊠h	αh(g⊠h	NOUN
ejpam-5658	405	3	)	)	PUNCT
ejpam-5658	405	4	≥	≥	NOUN
ejpam-5658	405	5	m∑	m∑	X
ejpam-5658	405	6	i=1	i=1	PRON
ejpam-5658	405	7	r∑	r∑	NOUN
ejpam-5658	405	8	j=1	j=1	PROPN
ejpam-5658	405	9	qipj	qipj	NOUN
ejpam-5658	405	10	.	.	PUNCT
ejpam-5658	406	1	proof	proof	NOUN
ejpam-5658	406	2	.	.	PUNCT
ejpam-5658	407	1	let	let	VERB
ejpam-5658	407	2	⟨sq1	⟨sq1	VERB
ejpam-5658	407	3	,	,	PUNCT
ejpam-5658	407	4	sq2	sq2	PROPN
ejpam-5658	407	5	,	,	PUNCT
ejpam-5658	407	6	·	·	PUNCT
ejpam-5658	407	7	·	·	PUNCT
ejpam-5658	407	8	·	·	PUNCT
ejpam-5658	407	9	,	,	PUNCT
ejpam-5658	407	10	sqm⟩	sqm⟩	NOUN
ejpam-5658	407	11	and	and	CCONJ
ejpam-5658	407	12	⟨dp1	⟨dp1	PROPN
ejpam-5658	407	13	,	,	PUNCT
ejpam-5658	407	14	dp2	dp2	PROPN
ejpam-5658	407	15	,	,	PUNCT
ejpam-5658	407	16	·	·	PUNCT
ejpam-5658	407	17	·	·	PUNCT
ejpam-5658	407	18	·	·	PUNCT
ejpam-5658	407	19	,	,	PUNCT
ejpam-5658	407	20	dpr⟩	dpr⟩	NOUN
ejpam-5658	407	21	be	be	AUX
ejpam-5658	407	22	maximum	maximum	ADV
ejpam-5658	407	23	decreasing	decrease	VERB
ejpam-5658	407	24	d3sequences	d3sequence	NOUN
ejpam-5658	407	25	of	of	ADP
ejpam-5658	407	26	cliques	clique	NOUN
ejpam-5658	407	27	in	in	ADP
ejpam-5658	407	28	g	g	PROPN
ejpam-5658	407	29	and	and	CCONJ
ejpam-5658	407	30	h	h	NOUN
ejpam-5658	407	31	,	,	PUNCT
ejpam-5658	407	32	respectively	respectively	ADV
ejpam-5658	407	33	.	.	PUNCT
ejpam-5658	408	1	let	let	VERB
ejpam-5658	408	2	s	s	PRON
ejpam-5658	408	3	=	=	PUNCT
ejpam-5658	408	4	∪m	∪m	PUNCT
ejpam-5658	408	5	i=1sqi	i=1sqi	PROPN
ejpam-5658	408	6	and	and	CCONJ
ejpam-5658	408	7	for	for	ADP
ejpam-5658	408	8	each	each	DET
ejpam-5658	408	9	x	x	SYM
ejpam-5658	408	10	∈	∈	PROPN
ejpam-5658	408	11	s	s	NOUN
ejpam-5658	408	12	,	,	PUNCT
ejpam-5658	408	13	set	set	VERB
ejpam-5658	408	14	rx	rx	ADJ
ejpam-5658	408	15	=	=	PUNCT
ejpam-5658	408	16	∪r	∪r	PROPN
ejpam-5658	408	17	j=1dpj	j=1dpj	PROPN
ejpam-5658	408	18	.	.	PUNCT
ejpam-5658	409	1	then	then	ADV
ejpam-5658	409	2	each	each	PRON
ejpam-5658	409	3	rx	rx	VERB
ejpam-5658	409	4	is	be	AUX
ejpam-5658	409	5	a	a	DET
ejpam-5658	409	6	hop	hop	NOUN
ejpam-5658	409	7	independent	independent	ADJ
ejpam-5658	409	8	set	set	NOUN
ejpam-5658	409	9	in	in	ADP
ejpam-5658	409	10	h.	h.	PROPN
ejpam-5658	409	11	clearly	clearly	ADV
ejpam-5658	409	12	,	,	PUNCT
ejpam-5658	409	13	condition	condition	NOUN
ejpam-5658	409	14	(	(	PUNCT
ejpam-5658	409	15	ii	ii	NOUN
ejpam-5658	409	16	)	)	PUNCT
ejpam-5658	409	17	of	of	ADP
ejpam-5658	409	18	theorem	theorem	NOUN
ejpam-5658	409	19	6	6	NUM
ejpam-5658	409	20	is	be	AUX
ejpam-5658	409	21	satisfied	satisfied	ADJ
ejpam-5658	409	22	.	.	PUNCT
ejpam-5658	410	1	moreover	moreover	ADV
ejpam-5658	410	2	,	,	PUNCT
ejpam-5658	410	3	because	because	SCONJ
ejpam-5658	410	4	s	s	NOUN
ejpam-5658	410	5	is	be	AUX
ejpam-5658	410	6	a	a	DET
ejpam-5658	410	7	hop	hop	NOUN
ejpam-5658	410	8	independent	independent	ADJ
ejpam-5658	410	9	set	set	NOUN
ejpam-5658	410	10	,	,	PUNCT
ejpam-5658	410	11	condition	condition	NOUN
ejpam-5658	410	12	(	(	PUNCT
ejpam-5658	410	13	iii	iii	NOUN
ejpam-5658	410	14	)	)	PUNCT
ejpam-5658	410	15	of	of	ADP
ejpam-5658	410	16	j.	j.	PROPN
ejpam-5658	410	17	anoche	anoche	PROPN
ejpam-5658	410	18	,	,	PUNCT
ejpam-5658	410	19	s.	s.	PROPN
ejpam-5658	410	20	canoy	canoy	PROPN
ejpam-5658	410	21	,	,	PUNCT
ejpam-5658	410	22	jr	jr	PROPN
ejpam-5658	410	23	.	.	PROPN
ejpam-5658	410	24	/	/	SYM
ejpam-5658	410	25	eur	eur	PROPN
ejpam-5658	410	26	.	.	PUNCT
ejpam-5658	411	1	j.	j.	PROPN
ejpam-5658	411	2	pure	pure	PROPN
ejpam-5658	411	3	appl	appl	PROPN
ejpam-5658	411	4	.	.	PROPN
ejpam-5658	411	5	math	math	PROPN
ejpam-5658	411	6	,	,	PUNCT
ejpam-5658	411	7	18	18	NUM
ejpam-5658	411	8	(	(	PUNCT
ejpam-5658	411	9	1	1	NUM
ejpam-5658	411	10	)	)	PUNCT
ejpam-5658	411	11	(	(	PUNCT
ejpam-5658	411	12	2025	2025	NUM
ejpam-5658	411	13	)	)	PUNCT
ejpam-5658	411	14	,	,	PUNCT
ejpam-5658	411	15	5658	5658	NUM
ejpam-5658	411	16	12	12	NUM
ejpam-5658	411	17	of	of	ADP
ejpam-5658	411	18	15	15	NUM
ejpam-5658	411	19	theorem	theorem	NOUN
ejpam-5658	411	20	6	6	NUM
ejpam-5658	411	21	also	also	ADV
ejpam-5658	411	22	holds	hold	VERB
ejpam-5658	411	23	.	.	PUNCT
ejpam-5658	412	1	thus	thus	ADV
ejpam-5658	412	2	,	,	PUNCT
ejpam-5658	412	3	c	c	NOUN
ejpam-5658	412	4	=	=	SYM
ejpam-5658	412	5	∪x∈s({x	∪x∈s({x	ADJ
ejpam-5658	412	6	}	}	PUNCT
ejpam-5658	412	7	×	×	NOUN
ejpam-5658	412	8	tx	tx	PROPN
ejpam-5658	412	9	)	)	PUNCT
ejpam-5658	412	10	is	be	AUX
ejpam-5658	412	11	a	a	DET
ejpam-5658	412	12	hop	hop	NOUN
ejpam-5658	412	13	independent	independent	ADJ
ejpam-5658	412	14	set	set	NOUN
ejpam-5658	412	15	in	in	ADP
ejpam-5658	412	16	g⊠h	g⊠h	NOUN
ejpam-5658	412	17	and	and	CCONJ
ejpam-5658	412	18	αh(g⊠h	αh(g⊠h	NOUN
ejpam-5658	412	19	)	)	PUNCT
ejpam-5658	412	20	≥	≥	NOUN
ejpam-5658	412	21	|c|	|c|	PROPN
ejpam-5658	412	22	=	=	PUNCT
ejpam-5658	412	23	∑	∑	PROPN
ejpam-5658	412	24	x∈s	x∈s	PROPN
ejpam-5658	412	25	|rx|	|rx|	PROPN
ejpam-5658	412	26	=	=	PUNCT
ejpam-5658	412	27	m∑	m∑	INTJ
ejpam-5658	412	28	i=1	i=1	PROPN
ejpam-5658	412	29	∑	∑	PROPN
ejpam-5658	412	30	x∈sqi	x∈sqi	PROPN
ejpam-5658	412	31	|	|	ADV
ejpam-5658	412	32	∪r	∪r	PROPN
ejpam-5658	412	33	j=1	j=1	PROPN
ejpam-5658	412	34	dpj	dpj	NOUN
ejpam-5658	412	35	|	|	ADV
ejpam-5658	412	36	=	=	PUNCT
ejpam-5658	412	37	m∑	m∑	CCONJ
ejpam-5658	413	1	i=1	i=1	PROPN
ejpam-5658	413	2	qi	qi	NOUN
ejpam-5658	413	3	r∑	r∑	NOUN
ejpam-5658	413	4	j=1	j=1	PROPN
ejpam-5658	413	5	pj	pj	PROPN
ejpam-5658	414	1	=	=	PUNCT
ejpam-5658	414	2	m∑	m∑	INTJ
ejpam-5658	414	3	i=1	i=1	NOUN
ejpam-5658	414	4	r∑	r∑	NOUN
ejpam-5658	414	5	j=1	j=1	ADJ
ejpam-5658	414	6	qipj	qipj	NOUN
ejpam-5658	414	7	.	.	PUNCT
ejpam-5658	415	1	this	this	PRON
ejpam-5658	415	2	proves	prove	VERB
ejpam-5658	415	3	the	the	DET
ejpam-5658	415	4	assertion	assertion	NOUN
ejpam-5658	415	5	.	.	PUNCT
ejpam-5658	416	1	remark	remark	NOUN
ejpam-5658	416	2	2	2	NUM
ejpam-5658	416	3	.	.	PUNCT
ejpam-5658	417	1	the	the	DET
ejpam-5658	417	2	bound	bind	VERB
ejpam-5658	417	3	given	give	VERB
ejpam-5658	417	4	in	in	ADP
ejpam-5658	417	5	corollary	corollary	ADJ
ejpam-5658	417	6	7	7	NUM
ejpam-5658	417	7	is	be	AUX
ejpam-5658	417	8	tight	tight	ADJ
ejpam-5658	417	9	.	.	PUNCT
ejpam-5658	418	1	consider	consider	VERB
ejpam-5658	418	2	graphs	graph	NOUN
ejpam-5658	418	3	g	g	NOUN
ejpam-5658	418	4	=	=	PUNCT
ejpam-5658	418	5	p6	p6	NOUN
ejpam-5658	418	6	=	=	PUNCT
ejpam-5658	419	1	[	[	X
ejpam-5658	419	2	v1	v1	NOUN
ejpam-5658	419	3	,	,	PUNCT
ejpam-5658	419	4	v2	v2	PROPN
ejpam-5658	419	5	,	,	PUNCT
ejpam-5658	419	6	v3	v3	PROPN
ejpam-5658	419	7	,	,	PUNCT
ejpam-5658	419	8	v4	v4	PROPN
ejpam-5658	419	9	,	,	PUNCT
ejpam-5658	419	10	v5	v5	PROPN
ejpam-5658	419	11	,	,	PUNCT
ejpam-5658	419	12	v6	v6	NOUN
ejpam-5658	419	13	]	]	PUNCT
ejpam-5658	419	14	,	,	PUNCT
ejpam-5658	419	15	h	h	NOUN
ejpam-5658	419	16	=	=	PUNCT
ejpam-5658	419	17	p6	p6	VERB
ejpam-5658	419	18	=	=	PUNCT
ejpam-5658	420	1	[	[	X
ejpam-5658	420	2	p1	p1	NOUN
ejpam-5658	420	3	,	,	PUNCT
ejpam-5658	420	4	p2	p2	NOUN
ejpam-5658	420	5	,	,	PUNCT
ejpam-5658	420	6	p3	p3	NOUN
ejpam-5658	420	7	,	,	PUNCT
ejpam-5658	420	8	p4	p4	ADJ
ejpam-5658	420	9	,	,	PUNCT
ejpam-5658	420	10	p5	p5	ADJ
ejpam-5658	420	11	,	,	PUNCT
ejpam-5658	420	12	p6	p6	PROPN
ejpam-5658	420	13	]	]	PUNCT
ejpam-5658	420	14	,	,	PUNCT
ejpam-5658	420	15	and	and	CCONJ
ejpam-5658	420	16	the	the	DET
ejpam-5658	420	17	strong	strong	ADJ
ejpam-5658	420	18	product	product	NOUN
ejpam-5658	420	19	p6	p6	VERB
ejpam-5658	420	20	⊠	⊠	PROPN
ejpam-5658	420	21	p6	p6	NOUN
ejpam-5658	420	22	in	in	ADP
ejpam-5658	420	23	figure	figure	NOUN
ejpam-5658	420	24	4	4	NUM
ejpam-5658	420	25	.	.	PUNCT
ejpam-5658	421	1	the	the	DET
ejpam-5658	421	2	sequences	sequence	NOUN
ejpam-5658	421	3	⟨{v1	⟨{v1	NOUN
ejpam-5658	421	4	,	,	PUNCT
ejpam-5658	421	5	v2	v2	PROPN
ejpam-5658	421	6	}	}	PUNCT
ejpam-5658	421	7	,	,	PUNCT
ejpam-5658	421	8	{	{	PUNCT
ejpam-5658	421	9	v5	v5	NOUN
ejpam-5658	421	10	,	,	PUNCT
ejpam-5658	421	11	v6}⟩	v6}⟩	NOUN
ejpam-5658	421	12	and	and	CCONJ
ejpam-5658	421	13	⟨{p1	⟨{p1	NOUN
ejpam-5658	421	14	,	,	PUNCT
ejpam-5658	421	15	p2	p2	PROPN
ejpam-5658	421	16	}	}	PUNCT
ejpam-5658	421	17	,	,	PUNCT
ejpam-5658	421	18	{	{	PUNCT
ejpam-5658	421	19	p5	p5	ADJ
ejpam-5658	421	20	,	,	PUNCT
ejpam-5658	421	21	p6}⟩	p6}⟩	NOUN
ejpam-5658	421	22	are	be	AUX
ejpam-5658	421	23	maximum	maximum	ADJ
ejpam-5658	421	24	(	(	PUNCT
ejpam-5658	421	25	decreasing	decrease	VERB
ejpam-5658	421	26	)	)	PUNCT
ejpam-5658	421	27	d3	d3	PROPN
ejpam-5658	421	28	-	-	PUNCT
ejpam-5658	421	29	sequences	sequence	NOUN
ejpam-5658	421	30	of	of	ADP
ejpam-5658	421	31	cliques	clique	NOUN
ejpam-5658	421	32	in	in	ADP
ejpam-5658	421	33	g	g	PROPN
ejpam-5658	421	34	and	and	CCONJ
ejpam-5658	421	35	h	h	NOUN
ejpam-5658	421	36	,	,	PUNCT
ejpam-5658	421	37	respectively	respectively	ADV
ejpam-5658	421	38	.	.	PUNCT
ejpam-5658	422	1	clearly	clearly	ADV
ejpam-5658	422	2	,	,	PUNCT
ejpam-5658	422	3	αh(g⊠h	αh(g⊠h	NOUN
ejpam-5658	422	4	)	)	PUNCT
ejpam-5658	422	5	=	=	NOUN
ejpam-5658	422	6	|{v1	|{v1	NOUN
ejpam-5658	422	7	,	,	PUNCT
ejpam-5658	422	8	v2}||{p1	v2}||{p1	NOUN
ejpam-5658	422	9	,	,	PUNCT
ejpam-5658	422	10	p2}|+	p2}|+	NOUN
ejpam-5658	422	11	|{v1	|{v1	NOUN
ejpam-5658	422	12	,	,	PUNCT
ejpam-5658	422	13	v2}||{p5	v2}||{p5	PROPN
ejpam-5658	422	14	,	,	PUNCT
ejpam-5658	422	15	p6}|+	p6}|+	NOUN
ejpam-5658	422	16	|{v5	|{v5	PROPN
ejpam-5658	422	17	,	,	PUNCT
ejpam-5658	422	18	v6}||{p1	v6}||{p1	PROPN
ejpam-5658	422	19	,	,	PUNCT
ejpam-5658	422	20	p2}|+	p2}|+	NOUN
ejpam-5658	422	21	|{v5	|{v5	NOUN
ejpam-5658	422	22	,	,	PUNCT
ejpam-5658	422	23	v6}||{p5	v6}||{p5	PROPN
ejpam-5658	422	24	,	,	PUNCT
ejpam-5658	422	25	p6}|	p6}|	PROPN
ejpam-5658	422	26	=	=	SYM
ejpam-5658	422	27	16	16	NUM
ejpam-5658	422	28	.	.	PUNCT
ejpam-5658	423	1	j.	j.	PROPN
ejpam-5658	423	2	anoche	anoche	PROPN
ejpam-5658	423	3	,	,	PUNCT
ejpam-5658	423	4	s.	s.	PROPN
ejpam-5658	423	5	canoy	canoy	PROPN
ejpam-5658	423	6	,	,	PUNCT
ejpam-5658	423	7	jr	jr	PROPN
ejpam-5658	423	8	.	.	PROPN
ejpam-5658	423	9	/	/	SYM
ejpam-5658	423	10	eur	eur	PROPN
ejpam-5658	423	11	.	.	PUNCT
ejpam-5658	424	1	j.	j.	PROPN
ejpam-5658	424	2	pure	pure	PROPN
ejpam-5658	424	3	appl	appl	PROPN
ejpam-5658	424	4	.	.	PROPN
ejpam-5658	424	5	math	math	PROPN
ejpam-5658	424	6	,	,	PUNCT
ejpam-5658	424	7	18	18	NUM
ejpam-5658	424	8	(	(	PUNCT
ejpam-5658	424	9	1	1	NUM
ejpam-5658	424	10	)	)	PUNCT
ejpam-5658	424	11	(	(	PUNCT
ejpam-5658	424	12	2025	2025	NUM
ejpam-5658	424	13	)	)	PUNCT
ejpam-5658	424	14	,	,	PUNCT
ejpam-5658	424	15	5658	5658	NUM
ejpam-5658	424	16	13	13	NUM
ejpam-5658	424	17	of	of	ADP
ejpam-5658	424	18	15	15	NUM
ejpam-5658	424	19	.........	.........	PUNCT
ejpam-5658	424	20	........	........	PUNCT
ejpam-5658	424	21	........	........	PUNCT
ejpam-5658	424	22	........	........	PUNCT
ejpam-5658	424	23	........	........	PUNCT
ejpam-5658	424	24	........	........	PUNCT
ejpam-5658	424	25	........	........	PUNCT
ejpam-5658	424	26	........	........	PUNCT
ejpam-5658	424	27	........	........	PUNCT
ejpam-5658	424	28	........	........	PUNCT
ejpam-5658	424	29	........	........	PUNCT
ejpam-5658	424	30	........	........	PUNCT
ejpam-5658	424	31	.......	.......	PUNCT
ejpam-5658	424	32	....................................	....................................	PUNCT
ejpam-5658	424	33	.........	.........	PUNCT
ejpam-5658	424	34	........	........	PUNCT
ejpam-5658	424	35	........	........	PUNCT
ejpam-5658	424	36	........	........	PUNCT
ejpam-5658	424	37	........	........	PUNCT
ejpam-5658	424	38	........	........	PUNCT
ejpam-5658	424	39	........	........	PUNCT
ejpam-5658	424	40	........	........	PUNCT
ejpam-5658	424	41	........	........	PUNCT
ejpam-5658	424	42	........	........	PUNCT
ejpam-5658	424	43	........	........	PUNCT
ejpam-5658	424	44	........	........	PUNCT
ejpam-5658	424	45	.......	.......	PUNCT
ejpam-5658	424	46	....................................	....................................	PUNCT
ejpam-5658	424	47	.........	.........	PUNCT
ejpam-5658	424	48	........	........	PUNCT
ejpam-5658	424	49	........	........	PUNCT
ejpam-5658	424	50	........	........	PUNCT
ejpam-5658	424	51	........	........	PUNCT
ejpam-5658	424	52	........	........	PUNCT
ejpam-5658	424	53	........	........	PUNCT
ejpam-5658	424	54	........	........	PUNCT
ejpam-5658	424	55	........	........	PUNCT
ejpam-5658	424	56	........	........	PUNCT
ejpam-5658	424	57	........	........	PUNCT
ejpam-5658	424	58	........	........	PUNCT
ejpam-5658	424	59	.......	.......	PUNCT
ejpam-5658	424	60	....................................	....................................	PUNCT
ejpam-5658	424	61	.........	.........	PUNCT
ejpam-5658	424	62	........	........	PUNCT
ejpam-5658	424	63	........	........	PUNCT
ejpam-5658	424	64	........	........	PUNCT
ejpam-5658	424	65	........	........	PUNCT
ejpam-5658	424	66	........	........	PUNCT
ejpam-5658	424	67	........	........	PUNCT
ejpam-5658	424	68	........	........	PUNCT
ejpam-5658	424	69	........	........	PUNCT
ejpam-5658	424	70	........	........	PUNCT
ejpam-5658	424	71	........	........	PUNCT
ejpam-5658	424	72	........	........	PUNCT
ejpam-5658	424	73	.......	.......	PUNCT
ejpam-5658	424	74	....................................	....................................	PUNCT
ejpam-5658	424	75	.........	.........	PUNCT
ejpam-5658	424	76	........	........	PUNCT
ejpam-5658	424	77	........	........	PUNCT
ejpam-5658	424	78	........	........	PUNCT
ejpam-5658	424	79	........	........	PUNCT
ejpam-5658	424	80	........	........	PUNCT
ejpam-5658	424	81	........	........	PUNCT
ejpam-5658	424	82	........	........	PUNCT
ejpam-5658	424	83	........	........	PUNCT
ejpam-5658	424	84	........	........	PUNCT
ejpam-5658	424	85	........	........	PUNCT
ejpam-5658	424	86	........	........	PUNCT
ejpam-5658	424	87	.......	.......	PUNCT
ejpam-5658	424	88	....................................	....................................	PUNCT
ejpam-5658	425	1	....................................	....................................	PUNCT
ejpam-5658	425	2	.........	.........	PUNCT
ejpam-5658	425	3	........	........	PUNCT
ejpam-5658	425	4	........	........	PUNCT
ejpam-5658	425	5	........	........	PUNCT
ejpam-5658	425	6	........	........	PUNCT
ejpam-5658	425	7	........	........	PUNCT
ejpam-5658	425	8	........	........	PUNCT
ejpam-5658	425	9	........	........	PUNCT
ejpam-5658	425	10	........	........	PUNCT
ejpam-5658	425	11	........	........	PUNCT
ejpam-5658	425	12	........	........	PUNCT
ejpam-5658	425	13	........	........	PUNCT
ejpam-5658	425	14	.......	.......	PUNCT
ejpam-5658	426	1	....................................	....................................	PUNCT
ejpam-5658	426	2	.........	.........	PUNCT
ejpam-5658	427	1	........	........	PUNCT
ejpam-5658	427	2	........	........	PUNCT
ejpam-5658	427	3	........	........	PUNCT
ejpam-5658	427	4	........	........	PUNCT
ejpam-5658	427	5	........	........	PUNCT
ejpam-5658	427	6	........	........	PUNCT
ejpam-5658	427	7	........	........	PUNCT
ejpam-5658	427	8	........	........	PUNCT
ejpam-5658	427	9	........	........	PUNCT
ejpam-5658	427	10	........	........	PUNCT
ejpam-5658	427	11	........	........	PUNCT
ejpam-5658	427	12	.......	.......	PUNCT
ejpam-5658	427	13	....................................	....................................	PUNCT
ejpam-5658	427	14	.........	.........	PUNCT
ejpam-5658	427	15	........	........	PUNCT
ejpam-5658	427	16	........	........	PUNCT
ejpam-5658	427	17	........	........	PUNCT
ejpam-5658	427	18	........	........	PUNCT
ejpam-5658	427	19	........	........	PUNCT
ejpam-5658	427	20	........	........	PUNCT
ejpam-5658	427	21	........	........	PUNCT
ejpam-5658	427	22	........	........	PUNCT
ejpam-5658	427	23	........	........	PUNCT
ejpam-5658	427	24	........	........	PUNCT
ejpam-5658	427	25	........	........	PUNCT
ejpam-5658	427	26	.......	.......	PUNCT
ejpam-5658	427	27	....................................	....................................	PUNCT
ejpam-5658	427	28	.........	.........	PUNCT
ejpam-5658	427	29	........	........	PUNCT
ejpam-5658	427	30	........	........	PUNCT
ejpam-5658	427	31	........	........	PUNCT
ejpam-5658	427	32	........	........	PUNCT
ejpam-5658	427	33	........	........	PUNCT
ejpam-5658	427	34	........	........	PUNCT
ejpam-5658	427	35	........	........	PUNCT
ejpam-5658	427	36	........	........	PUNCT
ejpam-5658	427	37	........	........	PUNCT
ejpam-5658	427	38	........	........	PUNCT
ejpam-5658	427	39	........	........	PUNCT
ejpam-5658	427	40	.......	.......	PUNCT
ejpam-5658	427	41	....................................	....................................	PUNCT
ejpam-5658	427	42	.........	.........	PUNCT
ejpam-5658	427	43	........	........	PUNCT
ejpam-5658	427	44	........	........	PUNCT
ejpam-5658	427	45	........	........	PUNCT
ejpam-5658	427	46	........	........	PUNCT
ejpam-5658	427	47	........	........	PUNCT
ejpam-5658	427	48	........	........	PUNCT
ejpam-5658	427	49	........	........	PUNCT
ejpam-5658	427	50	........	........	PUNCT
ejpam-5658	427	51	........	........	PUNCT
ejpam-5658	427	52	........	........	PUNCT
ejpam-5658	427	53	........	........	PUNCT
ejpam-5658	427	54	.......	.......	PUNCT
ejpam-5658	427	55	....................................	....................................	PUNCT
ejpam-5658	428	1	....................................	....................................	PUNCT
ejpam-5658	428	2	.........	.........	PUNCT
ejpam-5658	428	3	........	........	PUNCT
ejpam-5658	428	4	........	........	PUNCT
ejpam-5658	428	5	........	........	PUNCT
ejpam-5658	428	6	........	........	PUNCT
ejpam-5658	428	7	........	........	PUNCT
ejpam-5658	428	8	........	........	PUNCT
ejpam-5658	428	9	........	........	PUNCT
ejpam-5658	428	10	........	........	PUNCT
ejpam-5658	428	11	........	........	PUNCT
ejpam-5658	428	12	........	........	PUNCT
ejpam-5658	428	13	........	........	PUNCT
ejpam-5658	428	14	.......	.......	PUNCT
ejpam-5658	429	1	....................................	....................................	PUNCT
ejpam-5658	429	2	.........	.........	PUNCT
ejpam-5658	430	1	........	........	PUNCT
ejpam-5658	430	2	........	........	PUNCT
ejpam-5658	430	3	........	........	PUNCT
ejpam-5658	430	4	........	........	PUNCT
ejpam-5658	430	5	........	........	PUNCT
ejpam-5658	430	6	........	........	PUNCT
ejpam-5658	430	7	........	........	PUNCT
ejpam-5658	430	8	........	........	PUNCT
ejpam-5658	430	9	........	........	PUNCT
ejpam-5658	430	10	........	........	PUNCT
ejpam-5658	430	11	........	........	PUNCT
ejpam-5658	430	12	.......	.......	PUNCT
ejpam-5658	430	13	....................................	....................................	PUNCT
ejpam-5658	430	14	.........	.........	PUNCT
ejpam-5658	430	15	........	........	PUNCT
ejpam-5658	430	16	........	........	PUNCT
ejpam-5658	430	17	........	........	PUNCT
ejpam-5658	430	18	........	........	PUNCT
ejpam-5658	430	19	........	........	PUNCT
ejpam-5658	430	20	........	........	PUNCT
ejpam-5658	430	21	........	........	PUNCT
ejpam-5658	430	22	........	........	PUNCT
ejpam-5658	430	23	........	........	PUNCT
ejpam-5658	430	24	........	........	PUNCT
ejpam-5658	430	25	........	........	PUNCT
ejpam-5658	430	26	.......	.......	PUNCT
ejpam-5658	430	27	....................................	....................................	PUNCT
ejpam-5658	430	28	.........	.........	PUNCT
ejpam-5658	430	29	........	........	PUNCT
ejpam-5658	430	30	........	........	PUNCT
ejpam-5658	430	31	........	........	PUNCT
ejpam-5658	430	32	........	........	PUNCT
ejpam-5658	430	33	........	........	PUNCT
ejpam-5658	430	34	........	........	PUNCT
ejpam-5658	430	35	........	........	PUNCT
ejpam-5658	430	36	........	........	PUNCT
ejpam-5658	430	37	........	........	PUNCT
ejpam-5658	430	38	........	........	PUNCT
ejpam-5658	430	39	........	........	PUNCT
ejpam-5658	430	40	.......	.......	PUNCT
ejpam-5658	430	41	....................................	....................................	PUNCT
ejpam-5658	430	42	.........	.........	PUNCT
ejpam-5658	430	43	........	........	PUNCT
ejpam-5658	430	44	........	........	PUNCT
ejpam-5658	430	45	........	........	PUNCT
ejpam-5658	430	46	........	........	PUNCT
ejpam-5658	430	47	........	........	PUNCT
ejpam-5658	430	48	........	........	PUNCT
ejpam-5658	430	49	........	........	PUNCT
ejpam-5658	430	50	........	........	PUNCT
ejpam-5658	430	51	........	........	PUNCT
ejpam-5658	430	52	........	........	PUNCT
ejpam-5658	430	53	........	........	PUNCT
ejpam-5658	430	54	.......	.......	PUNCT
ejpam-5658	430	55	....................................	....................................	PUNCT
ejpam-5658	431	1	....................................	....................................	PUNCT
ejpam-5658	431	2	.........	.........	PUNCT
ejpam-5658	431	3	........	........	PUNCT
ejpam-5658	431	4	........	........	PUNCT
ejpam-5658	431	5	........	........	PUNCT
ejpam-5658	431	6	........	........	PUNCT
ejpam-5658	431	7	........	........	PUNCT
ejpam-5658	431	8	........	........	PUNCT
ejpam-5658	431	9	........	........	PUNCT
ejpam-5658	431	10	........	........	PUNCT
ejpam-5658	431	11	........	........	PUNCT
ejpam-5658	431	12	........	........	PUNCT
ejpam-5658	431	13	........	........	PUNCT
ejpam-5658	431	14	.......	.......	PUNCT
ejpam-5658	432	1	....................................	....................................	PUNCT
ejpam-5658	432	2	.........	.........	PUNCT
ejpam-5658	433	1	........	........	PUNCT
ejpam-5658	433	2	........	........	PUNCT
ejpam-5658	433	3	........	........	PUNCT
ejpam-5658	433	4	........	........	PUNCT
ejpam-5658	433	5	........	........	PUNCT
ejpam-5658	433	6	........	........	PUNCT
ejpam-5658	433	7	........	........	PUNCT
ejpam-5658	433	8	........	........	PUNCT
ejpam-5658	433	9	........	........	PUNCT
ejpam-5658	433	10	........	........	PUNCT
ejpam-5658	433	11	........	........	PUNCT
ejpam-5658	433	12	.......	.......	PUNCT
ejpam-5658	433	13	....................................	....................................	PUNCT
ejpam-5658	433	14	.........	.........	PUNCT
ejpam-5658	433	15	........	........	PUNCT
ejpam-5658	433	16	........	........	PUNCT
ejpam-5658	433	17	........	........	PUNCT
ejpam-5658	433	18	........	........	PUNCT
ejpam-5658	433	19	........	........	PUNCT
ejpam-5658	433	20	........	........	PUNCT
ejpam-5658	433	21	........	........	PUNCT
ejpam-5658	433	22	........	........	PUNCT
ejpam-5658	433	23	........	........	PUNCT
ejpam-5658	433	24	........	........	PUNCT
ejpam-5658	433	25	........	........	PUNCT
ejpam-5658	433	26	.......	.......	PUNCT
ejpam-5658	433	27	....................................	....................................	PUNCT
ejpam-5658	433	28	.........	.........	PUNCT
ejpam-5658	433	29	........	........	PUNCT
ejpam-5658	433	30	........	........	PUNCT
ejpam-5658	433	31	........	........	PUNCT
ejpam-5658	433	32	........	........	PUNCT
ejpam-5658	433	33	........	........	PUNCT
ejpam-5658	433	34	........	........	PUNCT
ejpam-5658	433	35	........	........	PUNCT
ejpam-5658	433	36	........	........	PUNCT
ejpam-5658	433	37	........	........	PUNCT
ejpam-5658	433	38	........	........	PUNCT
ejpam-5658	433	39	........	........	PUNCT
ejpam-5658	433	40	.......	.......	PUNCT
ejpam-5658	433	41	....................................	....................................	PUNCT
ejpam-5658	433	42	.........	.........	PUNCT
ejpam-5658	433	43	........	........	PUNCT
ejpam-5658	433	44	........	........	PUNCT
ejpam-5658	433	45	........	........	PUNCT
ejpam-5658	433	46	........	........	PUNCT
ejpam-5658	433	47	........	........	PUNCT
ejpam-5658	433	48	........	........	PUNCT
ejpam-5658	433	49	........	........	PUNCT
ejpam-5658	433	50	........	........	PUNCT
ejpam-5658	433	51	........	........	PUNCT
ejpam-5658	433	52	........	........	PUNCT
ejpam-5658	433	53	........	........	PUNCT
ejpam-5658	433	54	.......	.......	PUNCT
ejpam-5658	434	1	....................................	....................................	PUNCT
ejpam-5658	434	2	....................................	....................................	PUNCT
ejpam-5658	435	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	435	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	435	3	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	436	1	....................................	....................................	PUNCT
ejpam-5658	436	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	436	3	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	436	4	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	437	1	....................................	....................................	PUNCT
ejpam-5658	437	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	437	3	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	437	4	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	438	1	....................................	....................................	PUNCT
ejpam-5658	438	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	438	3	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	438	4	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	439	1	....................................	....................................	PUNCT
ejpam-5658	439	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	439	3	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	439	4	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	440	1	....................................	....................................	PUNCT
ejpam-5658	440	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	440	3	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	440	4	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	441	1	....................................	....................................	PUNCT
ejpam-5658	441	2	............	............	PUNCT
ejpam-5658	441	3	...........	...........	PUNCT
ejpam-5658	441	4	...........	...........	PUNCT
ejpam-5658	441	5	...........	...........	PUNCT
ejpam-5658	441	6	...........	...........	PUNCT
ejpam-5658	441	7	...........	...........	PUNCT
ejpam-5658	441	8	...........	...........	PUNCT
ejpam-5658	441	9	...........	...........	PUNCT
ejpam-5658	441	10	...........	...........	PUNCT
ejpam-5658	441	11	...........	...........	PUNCT
ejpam-5658	441	12	...........	...........	PUNCT
ejpam-5658	441	13	...........	...........	PUNCT
ejpam-5658	441	14	...........	...........	PUNCT
ejpam-5658	441	15	........	........	PUNCT
ejpam-5658	441	16	....................................	....................................	PUNCT
ejpam-5658	441	17	............	............	PUNCT
ejpam-5658	441	18	...........	...........	PUNCT
ejpam-5658	441	19	...........	...........	PUNCT
ejpam-5658	441	20	...........	...........	PUNCT
ejpam-5658	441	21	...........	...........	PUNCT
ejpam-5658	441	22	...........	...........	PUNCT
ejpam-5658	441	23	...........	...........	PUNCT
ejpam-5658	441	24	...........	...........	PUNCT
ejpam-5658	441	25	...........	...........	PUNCT
ejpam-5658	441	26	...........	...........	PUNCT
ejpam-5658	441	27	...........	...........	PUNCT
ejpam-5658	441	28	...........	...........	PUNCT
ejpam-5658	441	29	...........	...........	PUNCT
ejpam-5658	441	30	........	........	PUNCT
ejpam-5658	441	31	....................................	....................................	PUNCT
ejpam-5658	441	32	............	............	PUNCT
ejpam-5658	441	33	...........	...........	PUNCT
ejpam-5658	441	34	...........	...........	PUNCT
ejpam-5658	441	35	...........	...........	PUNCT
ejpam-5658	441	36	...........	...........	PUNCT
ejpam-5658	441	37	...........	...........	PUNCT
ejpam-5658	441	38	...........	...........	PUNCT
ejpam-5658	441	39	...........	...........	PUNCT
ejpam-5658	441	40	...........	...........	PUNCT
ejpam-5658	441	41	...........	...........	PUNCT
ejpam-5658	441	42	...........	...........	PUNCT
ejpam-5658	441	43	...........	...........	PUNCT
ejpam-5658	441	44	...........	...........	PUNCT
ejpam-5658	441	45	........	........	PUNCT
ejpam-5658	441	46	....................................	....................................	PUNCT
ejpam-5658	442	1	....................................	....................................	PUNCT
ejpam-5658	442	2	............	............	PUNCT
ejpam-5658	442	3	...........	...........	PUNCT
ejpam-5658	442	4	...........	...........	PUNCT
ejpam-5658	442	5	...........	...........	PUNCT
ejpam-5658	442	6	...........	...........	PUNCT
ejpam-5658	442	7	...........	...........	PUNCT
ejpam-5658	442	8	...........	...........	PUNCT
ejpam-5658	442	9	...........	...........	PUNCT
ejpam-5658	442	10	...........	...........	PUNCT
ejpam-5658	442	11	...........	...........	PUNCT
ejpam-5658	442	12	...........	...........	PUNCT
ejpam-5658	442	13	...........	...........	PUNCT
ejpam-5658	442	14	...........	...........	PUNCT
ejpam-5658	442	15	........	........	PUNCT
ejpam-5658	442	16	....................................	....................................	PUNCT
ejpam-5658	442	17	............	............	PUNCT
ejpam-5658	442	18	...........	...........	PUNCT
ejpam-5658	442	19	...........	...........	PUNCT
ejpam-5658	442	20	...........	...........	PUNCT
ejpam-5658	442	21	...........	...........	PUNCT
ejpam-5658	442	22	...........	...........	PUNCT
ejpam-5658	442	23	...........	...........	PUNCT
ejpam-5658	442	24	...........	...........	PUNCT
ejpam-5658	442	25	...........	...........	PUNCT
ejpam-5658	442	26	...........	...........	PUNCT
ejpam-5658	442	27	...........	...........	PUNCT
ejpam-5658	442	28	...........	...........	PUNCT
ejpam-5658	442	29	...........	...........	PUNCT
ejpam-5658	442	30	........	........	PUNCT
ejpam-5658	442	31	....................................	....................................	PUNCT
ejpam-5658	442	32	............	............	PUNCT
ejpam-5658	442	33	...........	...........	PUNCT
ejpam-5658	442	34	...........	...........	PUNCT
ejpam-5658	442	35	...........	...........	PUNCT
ejpam-5658	442	36	...........	...........	PUNCT
ejpam-5658	442	37	...........	...........	PUNCT
ejpam-5658	442	38	...........	...........	PUNCT
ejpam-5658	442	39	...........	...........	PUNCT
ejpam-5658	442	40	...........	...........	PUNCT
ejpam-5658	442	41	...........	...........	PUNCT
ejpam-5658	442	42	...........	...........	PUNCT
ejpam-5658	442	43	...........	...........	PUNCT
ejpam-5658	442	44	...........	...........	PUNCT
ejpam-5658	442	45	........	........	PUNCT
ejpam-5658	442	46	....................................	....................................	PUNCT
ejpam-5658	443	1	....................................	....................................	PUNCT
ejpam-5658	443	2	............	............	PUNCT
ejpam-5658	443	3	...........	...........	PUNCT
ejpam-5658	443	4	...........	...........	PUNCT
ejpam-5658	443	5	...........	...........	PUNCT
ejpam-5658	443	6	...........	...........	PUNCT
ejpam-5658	443	7	...........	...........	PUNCT
ejpam-5658	443	8	...........	...........	PUNCT
ejpam-5658	443	9	...........	...........	PUNCT
ejpam-5658	443	10	...........	...........	PUNCT
ejpam-5658	443	11	...........	...........	PUNCT
ejpam-5658	443	12	...........	...........	PUNCT
ejpam-5658	443	13	...........	...........	PUNCT
ejpam-5658	443	14	...........	...........	PUNCT
ejpam-5658	443	15	........	........	PUNCT
ejpam-5658	443	16	....................................	....................................	PUNCT
ejpam-5658	443	17	............	............	PUNCT
ejpam-5658	443	18	...........	...........	PUNCT
ejpam-5658	443	19	...........	...........	PUNCT
ejpam-5658	443	20	...........	...........	PUNCT
ejpam-5658	443	21	...........	...........	PUNCT
ejpam-5658	443	22	...........	...........	PUNCT
ejpam-5658	443	23	...........	...........	PUNCT
ejpam-5658	443	24	...........	...........	PUNCT
ejpam-5658	443	25	...........	...........	PUNCT
ejpam-5658	443	26	...........	...........	PUNCT
ejpam-5658	443	27	...........	...........	PUNCT
ejpam-5658	443	28	...........	...........	PUNCT
ejpam-5658	443	29	...........	...........	PUNCT
ejpam-5658	443	30	........	........	PUNCT
ejpam-5658	443	31	....................................	....................................	PUNCT
ejpam-5658	443	32	............	............	PUNCT
ejpam-5658	443	33	...........	...........	PUNCT
ejpam-5658	443	34	...........	...........	PUNCT
ejpam-5658	443	35	...........	...........	PUNCT
ejpam-5658	443	36	...........	...........	PUNCT
ejpam-5658	443	37	...........	...........	PUNCT
ejpam-5658	443	38	...........	...........	PUNCT
ejpam-5658	443	39	...........	...........	PUNCT
ejpam-5658	443	40	...........	...........	PUNCT
ejpam-5658	443	41	...........	...........	PUNCT
ejpam-5658	443	42	...........	...........	PUNCT
ejpam-5658	443	43	...........	...........	PUNCT
ejpam-5658	443	44	...........	...........	PUNCT
ejpam-5658	443	45	........	........	PUNCT
ejpam-5658	443	46	....................................	....................................	PUNCT
ejpam-5658	444	1	....................................	....................................	PUNCT
ejpam-5658	444	2	............	............	PUNCT
ejpam-5658	444	3	...........	...........	PUNCT
ejpam-5658	444	4	...........	...........	PUNCT
ejpam-5658	444	5	...........	...........	PUNCT
ejpam-5658	444	6	...........	...........	PUNCT
ejpam-5658	444	7	...........	...........	PUNCT
ejpam-5658	444	8	...........	...........	PUNCT
ejpam-5658	444	9	...........	...........	PUNCT
ejpam-5658	444	10	...........	...........	PUNCT
ejpam-5658	444	11	...........	...........	PUNCT
ejpam-5658	444	12	...........	...........	PUNCT
ejpam-5658	444	13	...........	...........	PUNCT
ejpam-5658	444	14	...........	...........	PUNCT
ejpam-5658	444	15	........	........	PUNCT
ejpam-5658	444	16	....................................	....................................	PUNCT
ejpam-5658	444	17	............	............	PUNCT
ejpam-5658	444	18	...........	...........	PUNCT
ejpam-5658	444	19	...........	...........	PUNCT
ejpam-5658	444	20	...........	...........	PUNCT
ejpam-5658	444	21	...........	...........	PUNCT
ejpam-5658	444	22	...........	...........	PUNCT
ejpam-5658	444	23	...........	...........	PUNCT
ejpam-5658	444	24	...........	...........	PUNCT
ejpam-5658	444	25	...........	...........	PUNCT
ejpam-5658	444	26	...........	...........	PUNCT
ejpam-5658	444	27	...........	...........	PUNCT
ejpam-5658	444	28	...........	...........	PUNCT
ejpam-5658	444	29	...........	...........	PUNCT
ejpam-5658	444	30	........	........	PUNCT
ejpam-5658	444	31	....................................	....................................	PUNCT
ejpam-5658	444	32	....................................	....................................	PUNCT
ejpam-5658	444	33	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	445	1	....................................	....................................	PUNCT
ejpam-5658	445	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	445	3	....................................	....................................	PUNCT
ejpam-5658	445	4	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	445	5	....................................	....................................	PUNCT
ejpam-5658	446	1	....................................	....................................	PUNCT
ejpam-5658	446	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	447	1	....................................	....................................	PUNCT
ejpam-5658	447	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	447	3	....................................	....................................	PUNCT
ejpam-5658	447	4	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	447	5	....................................	....................................	PUNCT
ejpam-5658	448	1	....................................	....................................	PUNCT
ejpam-5658	448	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	449	1	....................................	....................................	PUNCT
ejpam-5658	449	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	449	3	....................................	....................................	PUNCT
ejpam-5658	449	4	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	449	5	....................................	....................................	PUNCT
ejpam-5658	450	1	....................................	....................................	PUNCT
ejpam-5658	450	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	451	1	....................................	....................................	PUNCT
ejpam-5658	451	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	451	3	....................................	....................................	PUNCT
ejpam-5658	452	1	....................................	....................................	PUNCT
ejpam-5658	452	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	452	3	....................................	....................................	PUNCT
ejpam-5658	453	1	....................................	....................................	PUNCT
ejpam-5658	453	2	............	............	PUNCT
ejpam-5658	453	3	...........	...........	PUNCT
ejpam-5658	453	4	...........	...........	PUNCT
ejpam-5658	453	5	...........	...........	PUNCT
ejpam-5658	453	6	...........	...........	PUNCT
ejpam-5658	453	7	...........	...........	PUNCT
ejpam-5658	453	8	...........	...........	PUNCT
ejpam-5658	453	9	...........	...........	PUNCT
ejpam-5658	453	10	...........	...........	PUNCT
ejpam-5658	453	11	...........	...........	PUNCT
ejpam-5658	453	12	...........	...........	PUNCT
ejpam-5658	453	13	...........	...........	PUNCT
ejpam-5658	453	14	...........	...........	PUNCT
ejpam-5658	453	15	........	........	PUNCT
ejpam-5658	453	16	....................................	....................................	PUNCT
ejpam-5658	454	1	....................................	....................................	PUNCT
ejpam-5658	454	2	............	............	PUNCT
ejpam-5658	454	3	...........	...........	PUNCT
ejpam-5658	454	4	...........	...........	PUNCT
ejpam-5658	454	5	...........	...........	PUNCT
ejpam-5658	454	6	...........	...........	PUNCT
ejpam-5658	454	7	...........	...........	PUNCT
ejpam-5658	454	8	...........	...........	PUNCT
ejpam-5658	454	9	...........	...........	PUNCT
ejpam-5658	454	10	...........	...........	PUNCT
ejpam-5658	454	11	...........	...........	PUNCT
ejpam-5658	454	12	...........	...........	PUNCT
ejpam-5658	454	13	...........	...........	PUNCT
ejpam-5658	454	14	...........	...........	PUNCT
ejpam-5658	454	15	........	........	PUNCT
ejpam-5658	454	16	....................................	....................................	PUNCT
ejpam-5658	454	17	............	............	PUNCT
ejpam-5658	454	18	...........	...........	PUNCT
ejpam-5658	454	19	...........	...........	PUNCT
ejpam-5658	454	20	...........	...........	PUNCT
ejpam-5658	454	21	...........	...........	PUNCT
ejpam-5658	454	22	...........	...........	PUNCT
ejpam-5658	454	23	...........	...........	PUNCT
ejpam-5658	454	24	...........	...........	PUNCT
ejpam-5658	454	25	...........	...........	PUNCT
ejpam-5658	454	26	...........	...........	PUNCT
ejpam-5658	454	27	...........	...........	PUNCT
ejpam-5658	454	28	...........	...........	PUNCT
ejpam-5658	454	29	...........	...........	PUNCT
ejpam-5658	454	30	........	........	PUNCT
ejpam-5658	454	31	....................................	....................................	PUNCT
ejpam-5658	454	32	....................................	....................................	PUNCT
ejpam-5658	454	33	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	454	34	....................................	....................................	PUNCT
ejpam-5658	455	1	....................................	....................................	PUNCT
ejpam-5658	455	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	456	1	....................................	....................................	PUNCT
ejpam-5658	456	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	456	3	....................................	....................................	PUNCT
ejpam-5658	457	1	....................................	....................................	PUNCT
ejpam-5658	457	2	............	............	PUNCT
ejpam-5658	457	3	...........	...........	PUNCT
ejpam-5658	457	4	...........	...........	PUNCT
ejpam-5658	457	5	...........	...........	PUNCT
ejpam-5658	457	6	...........	...........	PUNCT
ejpam-5658	457	7	...........	...........	PUNCT
ejpam-5658	457	8	...........	...........	PUNCT
ejpam-5658	457	9	...........	...........	PUNCT
ejpam-5658	457	10	...........	...........	PUNCT
ejpam-5658	457	11	...........	...........	PUNCT
ejpam-5658	457	12	...........	...........	PUNCT
ejpam-5658	457	13	...........	...........	PUNCT
ejpam-5658	457	14	...........	...........	PUNCT
ejpam-5658	457	15	........	........	PUNCT
ejpam-5658	457	16	....................................	....................................	PUNCT
ejpam-5658	457	17	....................................	....................................	PUNCT
ejpam-5658	457	18	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	458	1	....................................	....................................	PUNCT
ejpam-5658	458	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	459	1	....................................	....................................	PUNCT
ejpam-5658	459	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	460	1	....................................	....................................	PUNCT
ejpam-5658	460	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	461	1	....................................	....................................	PUNCT
ejpam-5658	461	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	462	1	....................................	....................................	PUNCT
ejpam-5658	462	2	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	463	1	....................................	....................................	PUNCT
ejpam-5658	463	2	.........	.........	PUNCT
ejpam-5658	464	1	........	........	PUNCT
ejpam-5658	464	2	........	........	PUNCT
ejpam-5658	464	3	........	........	PUNCT
ejpam-5658	464	4	........	........	PUNCT
ejpam-5658	464	5	........	........	PUNCT
ejpam-5658	464	6	........	........	PUNCT
ejpam-5658	464	7	........	........	PUNCT
ejpam-5658	464	8	........	........	PUNCT
ejpam-5658	464	9	........	........	PUNCT
ejpam-5658	464	10	........	........	PUNCT
ejpam-5658	464	11	........	........	PUNCT
ejpam-5658	464	12	.......	.......	PUNCT
ejpam-5658	464	13	....................................	....................................	PUNCT
ejpam-5658	464	14	.........	.........	PUNCT
ejpam-5658	464	15	........	........	PUNCT
ejpam-5658	464	16	........	........	PUNCT
ejpam-5658	464	17	........	........	PUNCT
ejpam-5658	464	18	........	........	PUNCT
ejpam-5658	464	19	........	........	PUNCT
ejpam-5658	464	20	........	........	PUNCT
ejpam-5658	464	21	........	........	PUNCT
ejpam-5658	464	22	........	........	PUNCT
ejpam-5658	464	23	........	........	PUNCT
ejpam-5658	464	24	........	........	PUNCT
ejpam-5658	464	25	........	........	PUNCT
ejpam-5658	464	26	.......	.......	PUNCT
ejpam-5658	464	27	....................................	....................................	PUNCT
ejpam-5658	464	28	.........	.........	PUNCT
ejpam-5658	464	29	........	........	PUNCT
ejpam-5658	464	30	........	........	PUNCT
ejpam-5658	464	31	........	........	PUNCT
ejpam-5658	464	32	........	........	PUNCT
ejpam-5658	464	33	........	........	PUNCT
ejpam-5658	464	34	........	........	PUNCT
ejpam-5658	464	35	........	........	PUNCT
ejpam-5658	464	36	........	........	PUNCT
ejpam-5658	464	37	........	........	PUNCT
ejpam-5658	464	38	........	........	PUNCT
ejpam-5658	464	39	........	........	PUNCT
ejpam-5658	464	40	.......	.......	PUNCT
ejpam-5658	464	41	....................................	....................................	PUNCT
ejpam-5658	464	42	.........	.........	PUNCT
ejpam-5658	464	43	........	........	PUNCT
ejpam-5658	464	44	........	........	PUNCT
ejpam-5658	464	45	........	........	PUNCT
ejpam-5658	464	46	........	........	PUNCT
ejpam-5658	464	47	........	........	PUNCT
ejpam-5658	464	48	........	........	PUNCT
ejpam-5658	464	49	........	........	PUNCT
ejpam-5658	464	50	........	........	PUNCT
ejpam-5658	464	51	........	........	PUNCT
ejpam-5658	464	52	........	........	PUNCT
ejpam-5658	464	53	........	........	PUNCT
ejpam-5658	464	54	.......	.......	PUNCT
ejpam-5658	464	55	....................................	....................................	PUNCT
ejpam-5658	464	56	.........	.........	PUNCT
ejpam-5658	464	57	........	........	PUNCT
ejpam-5658	464	58	........	........	PUNCT
ejpam-5658	464	59	........	........	PUNCT
ejpam-5658	464	60	........	........	PUNCT
ejpam-5658	464	61	........	........	PUNCT
ejpam-5658	464	62	........	........	PUNCT
ejpam-5658	464	63	........	........	PUNCT
ejpam-5658	464	64	........	........	PUNCT
ejpam-5658	464	65	........	........	PUNCT
ejpam-5658	464	66	........	........	PUNCT
ejpam-5658	464	67	........	........	PUNCT
ejpam-5658	464	68	.......	.......	PUNCT
ejpam-5658	465	1	....................................	....................................	PUNCT
ejpam-5658	465	2	....................................	....................................	PUNCT
ejpam-5658	466	1	.........	.........	PUNCT
ejpam-5658	466	2	........	........	PUNCT
ejpam-5658	466	3	........	........	PUNCT
ejpam-5658	466	4	........	........	PUNCT
ejpam-5658	466	5	........	........	PUNCT
ejpam-5658	466	6	........	........	PUNCT
ejpam-5658	466	7	........	........	PUNCT
ejpam-5658	466	8	........	........	PUNCT
ejpam-5658	466	9	........	........	PUNCT
ejpam-5658	466	10	........	........	PUNCT
ejpam-5658	466	11	........	........	PUNCT
ejpam-5658	466	12	........	........	PUNCT
ejpam-5658	466	13	.......	.......	PUNCT
ejpam-5658	467	1	....................................	....................................	PUNCT
ejpam-5658	467	2	.........	.........	PUNCT
ejpam-5658	468	1	........	........	PUNCT
ejpam-5658	468	2	........	........	PUNCT
ejpam-5658	468	3	........	........	PUNCT
ejpam-5658	468	4	........	........	PUNCT
ejpam-5658	468	5	........	........	PUNCT
ejpam-5658	468	6	........	........	PUNCT
ejpam-5658	468	7	........	........	PUNCT
ejpam-5658	468	8	........	........	PUNCT
ejpam-5658	468	9	........	........	PUNCT
ejpam-5658	468	10	........	........	PUNCT
ejpam-5658	468	11	........	........	PUNCT
ejpam-5658	468	12	.......	.......	PUNCT
ejpam-5658	468	13	....................................	....................................	PUNCT
ejpam-5658	468	14	.........	.........	PUNCT
ejpam-5658	468	15	........	........	PUNCT
ejpam-5658	468	16	........	........	PUNCT
ejpam-5658	468	17	........	........	PUNCT
ejpam-5658	468	18	........	........	PUNCT
ejpam-5658	468	19	........	........	PUNCT
ejpam-5658	468	20	........	........	PUNCT
ejpam-5658	468	21	........	........	PUNCT
ejpam-5658	468	22	........	........	PUNCT
ejpam-5658	468	23	........	........	PUNCT
ejpam-5658	468	24	........	........	PUNCT
ejpam-5658	468	25	........	........	PUNCT
ejpam-5658	468	26	.......	.......	PUNCT
ejpam-5658	468	27	....................................	....................................	PUNCT
ejpam-5658	468	28	.........	.........	PUNCT
ejpam-5658	468	29	........	........	PUNCT
ejpam-5658	468	30	........	........	PUNCT
ejpam-5658	468	31	........	........	PUNCT
ejpam-5658	468	32	........	........	PUNCT
ejpam-5658	468	33	........	........	PUNCT
ejpam-5658	468	34	........	........	PUNCT
ejpam-5658	468	35	........	........	PUNCT
ejpam-5658	468	36	........	........	PUNCT
ejpam-5658	468	37	........	........	PUNCT
ejpam-5658	468	38	........	........	PUNCT
ejpam-5658	468	39	........	........	PUNCT
ejpam-5658	468	40	.......	.......	PUNCT
ejpam-5658	468	41	....................................	....................................	PUNCT
ejpam-5658	468	42	.........	.........	PUNCT
ejpam-5658	468	43	........	........	PUNCT
ejpam-5658	468	44	........	........	PUNCT
ejpam-5658	468	45	........	........	PUNCT
ejpam-5658	468	46	........	........	PUNCT
ejpam-5658	468	47	........	........	PUNCT
ejpam-5658	468	48	........	........	PUNCT
ejpam-5658	468	49	........	........	PUNCT
ejpam-5658	468	50	........	........	PUNCT
ejpam-5658	468	51	........	........	PUNCT
ejpam-5658	468	52	........	........	PUNCT
ejpam-5658	468	53	........	........	PUNCT
ejpam-5658	468	54	.......	.......	PUNCT
ejpam-5658	469	1	....................................	....................................	PUNCT
ejpam-5658	469	2	....................................	....................................	PUNCT
ejpam-5658	470	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	470	2	....................................	....................................	PUNCT
ejpam-5658	471	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	471	2	....................................	....................................	PUNCT
ejpam-5658	472	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	472	2	....................................	....................................	PUNCT
ejpam-5658	473	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	473	2	....................................	....................................	PUNCT
ejpam-5658	474	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	474	2	....................................	....................................	PUNCT
ejpam-5658	475	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-5658	475	2	....................................	....................................	PUNCT
ejpam-5658	475	3	............	............	PUNCT
ejpam-5658	475	4	...........	...........	PUNCT
ejpam-5658	475	5	...........	...........	PUNCT
ejpam-5658	475	6	...........	...........	PUNCT
ejpam-5658	475	7	...........	...........	PUNCT
ejpam-5658	475	8	...........	...........	PUNCT
ejpam-5658	475	9	...........	...........	PUNCT
ejpam-5658	475	10	...........	...........	PUNCT
ejpam-5658	475	11	...........	...........	PUNCT
ejpam-5658	475	12	...........	...........	PUNCT
ejpam-5658	475	13	...........	...........	PUNCT
ejpam-5658	475	14	...........	...........	PUNCT
ejpam-5658	475	15	...........	...........	PUNCT
ejpam-5658	475	16	........	........	PUNCT
ejpam-5658	475	17	....................................	....................................	PUNCT
ejpam-5658	476	1	....................................	....................................	PUNCT
ejpam-5658	476	2	............	............	PUNCT
ejpam-5658	476	3	...........	...........	PUNCT
ejpam-5658	476	4	...........	...........	PUNCT
ejpam-5658	476	5	...........	...........	PUNCT
ejpam-5658	476	6	...........	...........	PUNCT
ejpam-5658	476	7	...........	...........	PUNCT
ejpam-5658	476	8	...........	...........	PUNCT
ejpam-5658	476	9	...........	...........	PUNCT
ejpam-5658	476	10	...........	...........	PUNCT
ejpam-5658	476	11	...........	...........	PUNCT
ejpam-5658	476	12	...........	...........	PUNCT
ejpam-5658	476	13	...........	...........	PUNCT
ejpam-5658	476	14	...........	...........	PUNCT
ejpam-5658	476	15	........	........	PUNCT
ejpam-5658	476	16	....................................	....................................	PUNCT
ejpam-5658	477	1	....................................	....................................	PUNCT
ejpam-5658	477	2	............	............	PUNCT
ejpam-5658	477	3	...........	...........	PUNCT
ejpam-5658	477	4	...........	...........	PUNCT
ejpam-5658	477	5	...........	...........	PUNCT
ejpam-5658	477	6	...........	...........	PUNCT
ejpam-5658	477	7	...........	...........	PUNCT
ejpam-5658	477	8	...........	...........	PUNCT
ejpam-5658	477	9	...........	...........	PUNCT
ejpam-5658	477	10	...........	...........	PUNCT
ejpam-5658	477	11	...........	...........	PUNCT
ejpam-5658	477	12	...........	...........	PUNCT
ejpam-5658	477	13	...........	...........	PUNCT
ejpam-5658	477	14	...........	...........	PUNCT
ejpam-5658	477	15	........	........	PUNCT
ejpam-5658	477	16	....................................	....................................	PUNCT
ejpam-5658	478	1	....................................	....................................	PUNCT
ejpam-5658	478	2	............	............	PUNCT
ejpam-5658	478	3	...........	...........	PUNCT
ejpam-5658	478	4	...........	...........	PUNCT
ejpam-5658	478	5	...........	...........	PUNCT
ejpam-5658	478	6	...........	...........	PUNCT
ejpam-5658	478	7	...........	...........	PUNCT
ejpam-5658	478	8	...........	...........	PUNCT
ejpam-5658	478	9	...........	...........	PUNCT
ejpam-5658	478	10	...........	...........	PUNCT
ejpam-5658	478	11	...........	...........	PUNCT
ejpam-5658	478	12	...........	...........	PUNCT
ejpam-5658	478	13	...........	...........	PUNCT
ejpam-5658	478	14	...........	...........	PUNCT
ejpam-5658	478	15	........	........	PUNCT
ejpam-5658	478	16	....................................	....................................	PUNCT
ejpam-5658	479	1	....................................	....................................	PUNCT
ejpam-5658	479	2	............	............	PUNCT
ejpam-5658	479	3	...........	...........	PUNCT
ejpam-5658	479	4	...........	...........	PUNCT
ejpam-5658	479	5	...........	...........	PUNCT
ejpam-5658	479	6	...........	...........	PUNCT
ejpam-5658	479	7	...........	...........	PUNCT
ejpam-5658	479	8	...........	...........	PUNCT
ejpam-5658	479	9	...........	...........	PUNCT
ejpam-5658	479	10	...........	...........	PUNCT
ejpam-5658	479	11	...........	...........	PUNCT
ejpam-5658	479	12	...........	...........	PUNCT
ejpam-5658	479	13	...........	...........	PUNCT
ejpam-5658	479	14	...........	...........	PUNCT
ejpam-5658	479	15	........	........	PUNCT
ejpam-5658	479	16	....................................	....................................	PUNCT
ejpam-5658	479	17	................................................................................................................................................................................	................................................................................................................................................................................	PUNCT
ejpam-5658	479	18	....................................	....................................	PUNCT
ejpam-5658	479	19	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	479	20	....................................	....................................	PUNCT
ejpam-5658	480	1	....................................	....................................	PUNCT
ejpam-5658	480	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	480	3	....................................	....................................	PUNCT
ejpam-5658	481	1	....................................	....................................	PUNCT
ejpam-5658	481	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	481	3	....................................	....................................	PUNCT
ejpam-5658	482	1	....................................	....................................	PUNCT
ejpam-5658	482	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	482	3	....................................	....................................	PUNCT
ejpam-5658	483	1	....................................	....................................	PUNCT
ejpam-5658	483	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	483	3	....................................	....................................	PUNCT
ejpam-5658	484	1	....................................	....................................	PUNCT
ejpam-5658	484	2	............	............	PUNCT
ejpam-5658	484	3	...........	...........	PUNCT
ejpam-5658	484	4	...........	...........	PUNCT
ejpam-5658	484	5	...........	...........	PUNCT
ejpam-5658	484	6	...........	...........	PUNCT
ejpam-5658	484	7	...........	...........	PUNCT
ejpam-5658	484	8	...........	...........	PUNCT
ejpam-5658	484	9	...........	...........	PUNCT
ejpam-5658	484	10	...........	...........	PUNCT
ejpam-5658	484	11	...........	...........	PUNCT
ejpam-5658	484	12	...........	...........	PUNCT
ejpam-5658	484	13	...........	...........	PUNCT
ejpam-5658	484	14	...........	...........	PUNCT
ejpam-5658	484	15	........	........	PUNCT
ejpam-5658	484	16	....................................	....................................	PUNCT
ejpam-5658	485	1	....................................	....................................	PUNCT
ejpam-5658	485	2	............	............	PUNCT
ejpam-5658	485	3	...........	...........	PUNCT
ejpam-5658	485	4	...........	...........	PUNCT
ejpam-5658	485	5	...........	...........	PUNCT
ejpam-5658	485	6	...........	...........	PUNCT
ejpam-5658	485	7	...........	...........	PUNCT
ejpam-5658	485	8	...........	...........	PUNCT
ejpam-5658	485	9	...........	...........	PUNCT
ejpam-5658	485	10	...........	...........	PUNCT
ejpam-5658	485	11	...........	...........	PUNCT
ejpam-5658	485	12	...........	...........	PUNCT
ejpam-5658	485	13	...........	...........	PUNCT
ejpam-5658	485	14	...........	...........	PUNCT
ejpam-5658	485	15	........	........	PUNCT
ejpam-5658	485	16	....................................	....................................	PUNCT
ejpam-5658	486	1	....................................	....................................	PUNCT
ejpam-5658	486	2	............	............	PUNCT
ejpam-5658	486	3	...........	...........	PUNCT
ejpam-5658	486	4	...........	...........	PUNCT
ejpam-5658	486	5	...........	...........	PUNCT
ejpam-5658	486	6	...........	...........	PUNCT
ejpam-5658	486	7	...........	...........	PUNCT
ejpam-5658	486	8	...........	...........	PUNCT
ejpam-5658	486	9	...........	...........	PUNCT
ejpam-5658	486	10	...........	...........	PUNCT
ejpam-5658	486	11	...........	...........	PUNCT
ejpam-5658	486	12	...........	...........	PUNCT
ejpam-5658	486	13	...........	...........	PUNCT
ejpam-5658	486	14	...........	...........	PUNCT
ejpam-5658	486	15	........	........	PUNCT
ejpam-5658	486	16	....................................	....................................	PUNCT
ejpam-5658	487	1	....................................	....................................	PUNCT
ejpam-5658	487	2	............	............	PUNCT
ejpam-5658	487	3	...........	...........	PUNCT
ejpam-5658	487	4	...........	...........	PUNCT
ejpam-5658	487	5	...........	...........	PUNCT
ejpam-5658	487	6	...........	...........	PUNCT
ejpam-5658	487	7	...........	...........	PUNCT
ejpam-5658	487	8	...........	...........	PUNCT
ejpam-5658	487	9	...........	...........	PUNCT
ejpam-5658	487	10	...........	...........	PUNCT
ejpam-5658	487	11	...........	...........	PUNCT
ejpam-5658	487	12	...........	...........	PUNCT
ejpam-5658	487	13	...........	...........	PUNCT
ejpam-5658	487	14	...........	...........	PUNCT
ejpam-5658	487	15	........	........	PUNCT
ejpam-5658	487	16	....................................	....................................	PUNCT
ejpam-5658	488	1	....................................	....................................	PUNCT
ejpam-5658	488	2	............	............	PUNCT
ejpam-5658	488	3	...........	...........	PUNCT
ejpam-5658	488	4	...........	...........	PUNCT
ejpam-5658	488	5	...........	...........	PUNCT
ejpam-5658	488	6	...........	...........	PUNCT
ejpam-5658	488	7	...........	...........	PUNCT
ejpam-5658	488	8	...........	...........	PUNCT
ejpam-5658	488	9	...........	...........	PUNCT
ejpam-5658	488	10	...........	...........	PUNCT
ejpam-5658	488	11	...........	...........	PUNCT
ejpam-5658	488	12	...........	...........	PUNCT
ejpam-5658	488	13	...........	...........	PUNCT
ejpam-5658	488	14	...........	...........	PUNCT
ejpam-5658	488	15	........	........	PUNCT
ejpam-5658	488	16	....................................	....................................	PUNCT
ejpam-5658	488	17	................................................................................................................................................................................	................................................................................................................................................................................	PUNCT
ejpam-5658	488	18	....................................	....................................	PUNCT
ejpam-5658	488	19	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	488	20	....................................	....................................	PUNCT
ejpam-5658	489	1	....................................	....................................	PUNCT
ejpam-5658	489	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	489	3	....................................	....................................	PUNCT
ejpam-5658	490	1	....................................	....................................	PUNCT
ejpam-5658	490	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	490	3	....................................	....................................	PUNCT
ejpam-5658	491	1	....................................	....................................	PUNCT
ejpam-5658	491	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	491	3	....................................	....................................	PUNCT
ejpam-5658	492	1	....................................	....................................	PUNCT
ejpam-5658	492	2	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-5658	493	1	....................................	....................................	PUNCT
ejpam-5658	494	1	....................................	....................................	PUNCT
ejpam-5658	495	1	•	•	NUM
ejpam-5658	496	1	•	•	NUM
ejpam-5658	496	2	•	•	NUM
ejpam-5658	496	3	•	•	NUM
ejpam-5658	496	4	•	•	NUM
ejpam-5658	496	5	•	•	NUM
ejpam-5658	496	6	•	•	NUM
ejpam-5658	496	7	•	•	NUM
ejpam-5658	496	8	•	•	NUM
ejpam-5658	496	9	•	•	NUM
ejpam-5658	496	10	•	•	NUM
ejpam-5658	496	11	•	•	NUM
ejpam-5658	496	12	•	•	NUM
ejpam-5658	496	13	•	•	NUM
ejpam-5658	496	14	•	•	NOUN
ejpam-5658	496	15	•	•	NUM
ejpam-5658	496	16	figure	figure	NOUN
ejpam-5658	496	17	4	4	NUM
ejpam-5658	496	18	:	:	PUNCT
ejpam-5658	496	19	p6	p6	PROPN
ejpam-5658	496	20	⊠	⊠	PROPN
ejpam-5658	496	21	p6	p6	NOUN
ejpam-5658	496	22	v1	v1	PROPN
ejpam-5658	496	23	v2	v2	PROPN
ejpam-5658	496	24	v3	v3	PROPN
ejpam-5658	496	25	v4	v4	PROPN
ejpam-5658	496	26	v5	v5	PROPN
ejpam-5658	496	27	v6	v6	NOUN
ejpam-5658	496	28	p5	p5	ADJ
ejpam-5658	496	29	p6p4p3p2p1	p6p4p3p2p1	NOUN
ejpam-5658	496	30	we	we	PRON
ejpam-5658	496	31	now	now	ADV
ejpam-5658	496	32	show	show	VERB
ejpam-5658	496	33	that	that	SCONJ
ejpam-5658	496	34	the	the	DET
ejpam-5658	496	35	hop	hop	NOUN
ejpam-5658	496	36	independent	independent	ADJ
ejpam-5658	496	37	set	set	VERB
ejpam-5658	496	38	decision	decision	NOUN
ejpam-5658	496	39	problem	problem	NOUN
ejpam-5658	496	40	(	(	PUNCT
ejpam-5658	496	41	hisp	hisp	NOUN
ejpam-5658	496	42	)	)	PUNCT
ejpam-5658	496	43	is	be	AUX
ejpam-5658	496	44	np	np	ADP
ejpam-5658	496	45	-complete	-complete	ADJ
ejpam-5658	496	46	.	.	PUNCT
ejpam-5658	497	1	to	to	ADP
ejpam-5658	497	2	this	this	DET
ejpam-5658	497	3	end	end	NOUN
ejpam-5658	497	4	,	,	PUNCT
ejpam-5658	497	5	consider	consider	VERB
ejpam-5658	497	6	the	the	DET
ejpam-5658	497	7	following	follow	VERB
ejpam-5658	497	8	hop	hop	NOUN
ejpam-5658	497	9	independent	independent	ADJ
ejpam-5658	497	10	set	set	VERB
ejpam-5658	497	11	decision	decision	NOUN
ejpam-5658	497	12	problem	problem	NOUN
ejpam-5658	497	13	(	(	PUNCT
ejpam-5658	497	14	hisp	hisp	INTJ
ejpam-5658	497	15	):	):	PUNCT
ejpam-5658	497	16	instance	instance	NOUN
ejpam-5658	497	17	:	:	PUNCT
ejpam-5658	497	18	given	give	VERB
ejpam-5658	497	19	a	a	DET
ejpam-5658	497	20	graph	graph	NOUN
ejpam-5658	497	21	g	g	NOUN
ejpam-5658	497	22	=	=	PUNCT
ejpam-5658	497	23	(	(	PUNCT
ejpam-5658	497	24	v	v	NOUN
ejpam-5658	497	25	(	(	PUNCT
ejpam-5658	497	26	g	g	NOUN
ejpam-5658	497	27	)	)	PUNCT
ejpam-5658	497	28	,	,	PUNCT
ejpam-5658	497	29	e(g	e(g	PROPN
ejpam-5658	497	30	)	)	PUNCT
ejpam-5658	497	31	)	)	PUNCT
ejpam-5658	497	32	and	and	CCONJ
ejpam-5658	497	33	a	a	DET
ejpam-5658	497	34	positive	positive	ADJ
ejpam-5658	497	35	integer	integer	NOUN
ejpam-5658	497	36	k	k	PROPN
ejpam-5658	497	37	≤	≤	PROPN
ejpam-5658	497	38	|v	|v	X
ejpam-5658	497	39	(	(	PUNCT
ejpam-5658	497	40	g)|	g)|	NOUN
ejpam-5658	497	41	question	question	NOUN
ejpam-5658	497	42	:	:	PUNCT
ejpam-5658	497	43	does	do	AUX
ejpam-5658	497	44	g	g	PROPN
ejpam-5658	497	45	contain	contain	VERB
ejpam-5658	497	46	a	a	DET
ejpam-5658	497	47	hop	hop	NOUN
ejpam-5658	497	48	independent	independent	ADJ
ejpam-5658	497	49	set	set	NOUN
ejpam-5658	497	50	of	of	ADP
ejpam-5658	497	51	size	size	NOUN
ejpam-5658	497	52	k	k	X
ejpam-5658	497	53	?	?	PUNCT
ejpam-5658	498	1	on	on	ADP
ejpam-5658	498	2	the	the	DET
ejpam-5658	498	3	other	other	ADJ
ejpam-5658	498	4	hand	hand	NOUN
ejpam-5658	498	5	,	,	PUNCT
ejpam-5658	498	6	the	the	DET
ejpam-5658	498	7	clique	clique	ADJ
ejpam-5658	498	8	decision	decision	NOUN
ejpam-5658	498	9	problem	problem	NOUN
ejpam-5658	498	10	(	(	PUNCT
ejpam-5658	498	11	cp	cp	NOUN
ejpam-5658	498	12	)	)	PUNCT
ejpam-5658	498	13	is	be	AUX
ejpam-5658	498	14	stated	state	VERB
ejpam-5658	498	15	as	as	SCONJ
ejpam-5658	498	16	follows	follow	VERB
ejpam-5658	498	17	:	:	PUNCT
ejpam-5658	498	18	instance	instance	NOUN
ejpam-5658	498	19	:	:	PUNCT
ejpam-5658	498	20	given	give	VERB
ejpam-5658	498	21	a	a	DET
ejpam-5658	498	22	graph	graph	NOUN
ejpam-5658	498	23	g	g	NOUN
ejpam-5658	498	24	=	=	PUNCT
ejpam-5658	498	25	(	(	PUNCT
ejpam-5658	498	26	v	v	NOUN
ejpam-5658	498	27	(	(	PUNCT
ejpam-5658	498	28	g	g	NOUN
ejpam-5658	498	29	)	)	PUNCT
ejpam-5658	498	30	,	,	PUNCT
ejpam-5658	498	31	e(g	e(g	PROPN
ejpam-5658	498	32	)	)	PUNCT
ejpam-5658	498	33	)	)	PUNCT
ejpam-5658	498	34	and	and	CCONJ
ejpam-5658	498	35	a	a	DET
ejpam-5658	498	36	positive	positive	ADJ
ejpam-5658	498	37	integer	integer	NOUN
ejpam-5658	498	38	k	k	PROPN
ejpam-5658	498	39	≤	≤	PROPN
ejpam-5658	498	40	|v	|v	X
ejpam-5658	498	41	(	(	PUNCT
ejpam-5658	498	42	g)|	g)|	NOUN
ejpam-5658	498	43	question	question	NOUN
ejpam-5658	498	44	:	:	PUNCT
ejpam-5658	498	45	does	do	AUX
ejpam-5658	498	46	g	g	PROPN
ejpam-5658	498	47	contain	contain	VERB
ejpam-5658	498	48	a	a	DET
ejpam-5658	498	49	clique	clique	NOUN
ejpam-5658	498	50	of	of	ADP
ejpam-5658	498	51	size	size	NOUN
ejpam-5658	498	52	k	k	PROPN
ejpam-5658	498	53	?	?	PUNCT
ejpam-5658	498	54	theorem	theorem	VERB
ejpam-5658	498	55	7	7	NUM
ejpam-5658	498	56	(	(	PUNCT
ejpam-5658	498	57	[	[	X
ejpam-5658	498	58	6	6	NUM
ejpam-5658	498	59	]	]	NUM
ejpam-5658	498	60	)	)	PUNCT
ejpam-5658	498	61	.	.	PUNCT
ejpam-5658	499	1	the	the	DET
ejpam-5658	499	2	clique	clique	ADJ
ejpam-5658	499	3	problem	problem	NOUN
ejpam-5658	499	4	is	be	AUX
ejpam-5658	499	5	np	np	ADP
ejpam-5658	499	6	-complete	-complete	ADJ
ejpam-5658	499	7	.	.	PUNCT
ejpam-5658	500	1	theorem	theorem	ADJ
ejpam-5658	500	2	8	8	NUM
ejpam-5658	500	3	.	.	PUNCT
ejpam-5658	501	1	the	the	DET
ejpam-5658	501	2	hop	hop	PROPN
ejpam-5658	501	3	independent	independent	ADJ
ejpam-5658	501	4	set	set	NOUN
ejpam-5658	501	5	problem	problem	NOUN
ejpam-5658	501	6	is	be	AUX
ejpam-5658	501	7	np	np	ADP
ejpam-5658	501	8	-complete	-complete	ADJ
ejpam-5658	501	9	.	.	PUNCT
ejpam-5658	502	1	proof	proof	NOUN
ejpam-5658	502	2	.	.	PUNCT
ejpam-5658	503	1	given	give	VERB
ejpam-5658	503	2	a	a	DET
ejpam-5658	503	3	subset	subset	NOUN
ejpam-5658	503	4	s	s	NOUN
ejpam-5658	503	5	of	of	ADP
ejpam-5658	503	6	vertices	vertex	NOUN
ejpam-5658	503	7	of	of	ADP
ejpam-5658	503	8	g	g	NOUN
ejpam-5658	503	9	,	,	PUNCT
ejpam-5658	503	10	one	one	PRON
ejpam-5658	503	11	can	can	AUX
ejpam-5658	503	12	check	check	VERB
ejpam-5658	503	13	in	in	ADP
ejpam-5658	503	14	polynomial	polynomial	ADJ
ejpam-5658	503	15	time	time	NOUN
ejpam-5658	503	16	if	if	SCONJ
ejpam-5658	503	17	s	s	VERB
ejpam-5658	503	18	is	be	AUX
ejpam-5658	503	19	a	a	DET
ejpam-5658	503	20	hop	hop	NOUN
ejpam-5658	503	21	independent	independent	ADJ
ejpam-5658	503	22	set	set	NOUN
ejpam-5658	503	23	.	.	PUNCT
ejpam-5658	504	1	hence	hence	ADV
ejpam-5658	504	2	,	,	PUNCT
ejpam-5658	504	3	the	the	DET
ejpam-5658	504	4	hop	hop	NOUN
ejpam-5658	504	5	independent	independent	ADJ
ejpam-5658	504	6	set	set	NOUN
ejpam-5658	504	7	problem	problem	NOUN
ejpam-5658	504	8	is	be	AUX
ejpam-5658	504	9	np	np	INTJ
ejpam-5658	504	10	.	.	PUNCT
ejpam-5658	505	1	we	we	PRON
ejpam-5658	505	2	now	now	ADV
ejpam-5658	505	3	use	use	VERB
ejpam-5658	505	4	the	the	DET
ejpam-5658	505	5	clique	clique	ADJ
ejpam-5658	505	6	problem	problem	NOUN
ejpam-5658	505	7	(	(	PUNCT
ejpam-5658	505	8	cp	cp	NOUN
ejpam-5658	505	9	)	)	PUNCT
ejpam-5658	505	10	to	to	PART
ejpam-5658	505	11	show	show	VERB
ejpam-5658	505	12	that	that	PRON
ejpam-5658	505	13	hisp	hisp	NOUN
ejpam-5658	505	14	is	be	AUX
ejpam-5658	505	15	np	np	ADP
ejpam-5658	505	16	-hard	-hard	NOUN
ejpam-5658	505	17	.	.	PUNCT
ejpam-5658	506	1	to	to	ADP
ejpam-5658	506	2	this	this	DET
ejpam-5658	506	3	end	end	NOUN
ejpam-5658	506	4	,	,	PUNCT
ejpam-5658	506	5	let	let	VERB
ejpam-5658	506	6	g	g	NOUN
ejpam-5658	506	7	=	=	SYM
ejpam-5658	506	8	(	(	PUNCT
ejpam-5658	506	9	v	v	NOUN
ejpam-5658	506	10	(	(	PUNCT
ejpam-5658	506	11	g	g	NOUN
ejpam-5658	506	12	)	)	PUNCT
ejpam-5658	506	13	,	,	PUNCT
ejpam-5658	506	14	e(g	e(g	PROPN
ejpam-5658	506	15	)	)	PUNCT
ejpam-5658	506	16	be	be	AUX
ejpam-5658	506	17	a	a	DET
ejpam-5658	506	18	graph	graph	NOUN
ejpam-5658	506	19	with	with	ADP
ejpam-5658	506	20	v	v	NOUN
ejpam-5658	506	21	(	(	PUNCT
ejpam-5658	506	22	g	g	NOUN
ejpam-5658	506	23	)	)	PUNCT
ejpam-5658	506	24	=	=	SYM
ejpam-5658	506	25	{	{	PUNCT
ejpam-5658	506	26	v1	v1	PROPN
ejpam-5658	506	27	,	,	PUNCT
ejpam-5658	506	28	v2	v2	PROPN
ejpam-5658	506	29	,	,	PUNCT
ejpam-5658	506	30	...	...	PUNCT
ejpam-5658	506	31	,	,	PUNCT
ejpam-5658	506	32	vn	vn	INTJ
ejpam-5658	506	33	}	}	PUNCT
ejpam-5658	506	34	and	and	CCONJ
ejpam-5658	506	35	let	let	VERB
ejpam-5658	506	36	k	k	PRON
ejpam-5658	506	37	be	be	AUX
ejpam-5658	506	38	a	a	DET
ejpam-5658	506	39	positive	positive	ADJ
ejpam-5658	506	40	integer	integer	NOUN
ejpam-5658	506	41	with	with	ADP
ejpam-5658	506	42	k	k	PROPN
ejpam-5658	506	43	≤	≤	PROPN
ejpam-5658	506	44	|v	|v	X
ejpam-5658	506	45	(	(	PUNCT
ejpam-5658	506	46	g)|	g)|	NOUN
ejpam-5658	506	47	.	.	PUNCT
ejpam-5658	507	1	let	let	VERB
ejpam-5658	507	2	h	h	NOUN
ejpam-5658	507	3	=	=	PROPN
ejpam-5658	507	4	g+k1	g+k1	PROPN
ejpam-5658	507	5	,	,	PUNCT
ejpam-5658	507	6	where	where	SCONJ
ejpam-5658	507	7	v	v	NOUN
ejpam-5658	507	8	(	(	PUNCT
ejpam-5658	507	9	k1	k1	NOUN
ejpam-5658	507	10	)	)	PUNCT
ejpam-5658	507	11	=	=	SYM
ejpam-5658	507	12	{	{	PUNCT
ejpam-5658	507	13	v	v	NOUN
ejpam-5658	507	14	}	}	PUNCT
ejpam-5658	507	15	.	.	PUNCT
ejpam-5658	508	1	if	if	SCONJ
ejpam-5658	508	2	s	s	PROPN
ejpam-5658	508	3	is	be	AUX
ejpam-5658	508	4	a	a	DET
ejpam-5658	508	5	clique	clique	NOUN
ejpam-5658	508	6	in	in	ADP
ejpam-5658	508	7	g	g	PROPN
ejpam-5658	508	8	and	and	CCONJ
ejpam-5658	508	9	|s|	|s|	PROPN
ejpam-5658	508	10	=	=	SYM
ejpam-5658	508	11	k	k	PROPN
ejpam-5658	508	12	,	,	PUNCT
ejpam-5658	508	13	then	then	ADV
ejpam-5658	508	14	s′	s′	ADJ
ejpam-5658	508	15	=	=	SYM
ejpam-5658	508	16	s	s	PART
ejpam-5658	508	17	∪{v	∪{v	NOUN
ejpam-5658	508	18	}	}	PUNCT
ejpam-5658	508	19	is	be	AUX
ejpam-5658	508	20	a	a	DET
ejpam-5658	508	21	hop	hop	NOUN
ejpam-5658	508	22	independent	independent	ADJ
ejpam-5658	508	23	set	set	NOUN
ejpam-5658	508	24	in	in	ADP
ejpam-5658	508	25	h	h	NOUN
ejpam-5658	508	26	and	and	CCONJ
ejpam-5658	508	27	|s′|	|s′|	NOUN
ejpam-5658	508	28	=	=	PUNCT
ejpam-5658	509	1	k	k	PROPN
ejpam-5658	510	1	+	+	NOUN
ejpam-5658	510	2	1	1	X
ejpam-5658	510	3	.	.	PUNCT
ejpam-5658	510	4	conversely	conversely	ADV
ejpam-5658	510	5	,	,	PUNCT
ejpam-5658	510	6	suppose	suppose	VERB
ejpam-5658	510	7	s∗	s∗	PROPN
ejpam-5658	510	8	is	be	AUX
ejpam-5658	510	9	a	a	DET
ejpam-5658	510	10	hop	hop	NOUN
ejpam-5658	510	11	independent	independent	ADJ
ejpam-5658	510	12	set	set	NOUN
ejpam-5658	510	13	in	in	ADP
ejpam-5658	510	14	h	h	NOUN
ejpam-5658	510	15	with	with	ADP
ejpam-5658	510	16	|s∗|	|s∗|	NOUN
ejpam-5658	510	17	=	=	SYM
ejpam-5658	510	18	k+1	k+1	AUX
ejpam-5658	510	19	.	.	X
ejpam-5658	510	20	suppose	suppose	VERB
ejpam-5658	510	21	s∗	s∗	PROPN
ejpam-5658	510	22	is	be	AUX
ejpam-5658	510	23	not	not	PART
ejpam-5658	510	24	a	a	DET
ejpam-5658	510	25	clique	clique	NOUN
ejpam-5658	510	26	in	in	ADP
ejpam-5658	510	27	h.	h.	PROPN
ejpam-5658	510	28	then	then	ADV
ejpam-5658	510	29	,	,	PUNCT
ejpam-5658	510	30	by	by	ADP
ejpam-5658	510	31	theorem	theorem	NOUN
ejpam-5658	510	32	1	1	NUM
ejpam-5658	510	33	,	,	PUNCT
ejpam-5658	510	34	⟨s∗⟩	⟨s∗⟩	NOUN
ejpam-5658	510	35	has	have	VERB
ejpam-5658	510	36	at	at	ADV
ejpam-5658	510	37	least	least	ADV
ejpam-5658	510	38	two	two	NUM
ejpam-5658	510	39	complete	complete	ADJ
ejpam-5658	510	40	components	component	NOUN
ejpam-5658	510	41	,	,	PUNCT
ejpam-5658	510	42	say	say	VERB
ejpam-5658	510	43	h1	h1	NOUN
ejpam-5658	510	44	and	and	CCONJ
ejpam-5658	510	45	h2	h2	PROPN
ejpam-5658	510	46	.	.	PUNCT
ejpam-5658	511	1	pick	pick	VERB
ejpam-5658	511	2	x	x	SYM
ejpam-5658	511	3	∈	∈	PROPN
ejpam-5658	511	4	v	v	ADP
ejpam-5658	511	5	(	(	PUNCT
ejpam-5658	511	6	h1	h1	PROPN
ejpam-5658	511	7	)	)	PUNCT
ejpam-5658	511	8	and	and	CCONJ
ejpam-5658	511	9	y	y	PROPN
ejpam-5658	511	10	∈	∈	PROPN
ejpam-5658	511	11	v	v	PROPN
ejpam-5658	511	12	(	(	PUNCT
ejpam-5658	511	13	h2	h2	NOUN
ejpam-5658	511	14	)	)	PUNCT
ejpam-5658	511	15	.	.	PUNCT
ejpam-5658	512	1	then	then	ADV
ejpam-5658	512	2	j.	j.	PROPN
ejpam-5658	512	3	anoche	anoche	PROPN
ejpam-5658	512	4	,	,	PUNCT
ejpam-5658	512	5	s.	s.	PROPN
ejpam-5658	512	6	canoy	canoy	PROPN
ejpam-5658	512	7	,	,	PUNCT
ejpam-5658	512	8	jr	jr	PROPN
ejpam-5658	512	9	.	.	PROPN
ejpam-5658	512	10	/	/	SYM
ejpam-5658	512	11	eur	eur	PROPN
ejpam-5658	512	12	.	.	PUNCT
ejpam-5658	513	1	j.	j.	PROPN
ejpam-5658	513	2	pure	pure	PROPN
ejpam-5658	513	3	appl	appl	PROPN
ejpam-5658	513	4	.	.	PROPN
ejpam-5658	513	5	math	math	PROPN
ejpam-5658	513	6	,	,	PUNCT
ejpam-5658	513	7	18	18	NUM
ejpam-5658	513	8	(	(	PUNCT
ejpam-5658	513	9	1	1	NUM
ejpam-5658	513	10	)	)	PUNCT
ejpam-5658	513	11	(	(	PUNCT
ejpam-5658	513	12	2025	2025	NUM
ejpam-5658	513	13	)	)	PUNCT
ejpam-5658	513	14	,	,	PUNCT
ejpam-5658	513	15	5658	5658	NUM
ejpam-5658	513	16	14	14	NUM
ejpam-5658	513	17	of	of	ADP
ejpam-5658	513	18	15	15	NUM
ejpam-5658	513	19	dh(x	dh(x	NUM
ejpam-5658	513	20	,	,	PUNCT
ejpam-5658	513	21	y	y	NOUN
ejpam-5658	513	22	)	)	PUNCT
ejpam-5658	513	23	=	=	SYM
ejpam-5658	513	24	2	2	NUM
ejpam-5658	513	25	,	,	PUNCT
ejpam-5658	513	26	a	a	DET
ejpam-5658	513	27	contradiction	contradiction	NOUN
ejpam-5658	513	28	.	.	PUNCT
ejpam-5658	514	1	thus	thus	ADV
ejpam-5658	514	2	,	,	PUNCT
ejpam-5658	514	3	s∗	s∗	PROPN
ejpam-5658	514	4	is	be	AUX
ejpam-5658	514	5	a	a	DET
ejpam-5658	514	6	clique	clique	NOUN
ejpam-5658	514	7	in	in	ADP
ejpam-5658	514	8	h.	h.	PROPN
ejpam-5658	514	9	if	if	SCONJ
ejpam-5658	514	10	s∗	s∗	PROPN
ejpam-5658	514	11	⊆	⊆	NUM
ejpam-5658	514	12	v	v	NOUN
ejpam-5658	514	13	(	(	PUNCT
ejpam-5658	514	14	g	g	NOUN
ejpam-5658	514	15	)	)	PUNCT
ejpam-5658	514	16	,	,	PUNCT
ejpam-5658	514	17	then	then	ADV
ejpam-5658	514	18	s∗	s∗	VERB
ejpam-5658	514	19	\	\	PROPN
ejpam-5658	514	20	{	{	PUNCT
ejpam-5658	514	21	x	x	X
ejpam-5658	514	22	}	}	PUNCT
ejpam-5658	514	23	,	,	PUNCT
ejpam-5658	514	24	where	where	SCONJ
ejpam-5658	514	25	x	x	PUNCT
ejpam-5658	514	26	∈	∈	PROPN
ejpam-5658	514	27	s∗	s∗	PROPN
ejpam-5658	514	28	,	,	PUNCT
ejpam-5658	514	29	is	be	AUX
ejpam-5658	514	30	a	a	DET
ejpam-5658	514	31	clique	clique	NOUN
ejpam-5658	514	32	in	in	ADP
ejpam-5658	514	33	g	g	NOUN
ejpam-5658	514	34	with	with	ADP
ejpam-5658	514	35	size	size	NOUN
ejpam-5658	514	36	k.	k.	PROPN
ejpam-5658	514	37	suppose	suppose	VERB
ejpam-5658	515	1	v	v	ADP
ejpam-5658	515	2	∈	∈	PROPN
ejpam-5658	515	3	s∗.	s∗.	INTJ
ejpam-5658	515	4	then	then	ADV
ejpam-5658	515	5	s∗	s∗	PROPN
ejpam-5658	515	6	\	\	PROPN
ejpam-5658	515	7	{	{	PUNCT
ejpam-5658	515	8	v	v	NOUN
ejpam-5658	515	9	}	}	PUNCT
ejpam-5658	515	10	is	be	AUX
ejpam-5658	515	11	a	a	DET
ejpam-5658	515	12	clique	clique	NOUN
ejpam-5658	515	13	in	in	ADP
ejpam-5658	515	14	g	g	NOUN
ejpam-5658	515	15	with	with	ADP
ejpam-5658	515	16	size	size	NOUN
ejpam-5658	516	1	k.	k.	PROPN
ejpam-5658	517	1	therefore	therefore	ADV
ejpam-5658	517	2	,	,	PUNCT
ejpam-5658	517	3	g	g	PROPN
ejpam-5658	517	4	has	have	VERB
ejpam-5658	517	5	a	a	DET
ejpam-5658	517	6	clique	clique	NOUN
ejpam-5658	517	7	of	of	ADP
ejpam-5658	517	8	size	size	NOUN
ejpam-5658	517	9	k	k	PROPN
ejpam-5658	518	1	if	if	SCONJ
ejpam-5658	519	1	and	and	CCONJ
ejpam-5658	519	2	only	only	ADV
ejpam-5658	519	3	if	if	SCONJ
ejpam-5658	519	4	h	h	NOUN
ejpam-5658	519	5	has	have	VERB
ejpam-5658	519	6	a	a	DET
ejpam-5658	519	7	hop	hop	NOUN
ejpam-5658	519	8	independent	independent	ADJ
ejpam-5658	519	9	set	set	NOUN
ejpam-5658	519	10	of	of	ADP
ejpam-5658	519	11	size	size	NOUN
ejpam-5658	519	12	k	k	PROPN
ejpam-5658	520	1	+	+	PROPN
ejpam-5658	520	2	1	1	X
ejpam-5658	520	3	.	.	PUNCT
ejpam-5658	520	4	accordingly	accordingly	ADV
ejpam-5658	520	5	,	,	PUNCT
ejpam-5658	520	6	the	the	DET
ejpam-5658	520	7	hop	hop	NOUN
ejpam-5658	520	8	independent	independent	ADJ
ejpam-5658	520	9	set	set	NOUN
ejpam-5658	520	10	problem	problem	NOUN
ejpam-5658	520	11	is	be	AUX
ejpam-5658	520	12	np	np	ADP
ejpam-5658	520	13	-complete	-complete	ADJ
ejpam-5658	520	14	.	.	PUNCT
ejpam-5658	521	1	9	9	X
ejpam-5658	521	2	.	.	X
ejpam-5658	521	3	conclusion	conclusion	NOUN
ejpam-5658	521	4	the	the	DET
ejpam-5658	521	5	hop	hop	PROPN
ejpam-5658	521	6	independence	independence	NOUN
ejpam-5658	521	7	parameter	parameter	NOUN
ejpam-5658	521	8	has	have	AUX
ejpam-5658	521	9	been	be	AUX
ejpam-5658	521	10	explored	explore	VERB
ejpam-5658	521	11	for	for	ADP
ejpam-5658	521	12	the	the	DET
ejpam-5658	521	13	shadow	shadow	NOUN
ejpam-5658	521	14	graph	graph	NOUN
ejpam-5658	521	15	,	,	PUNCT
ejpam-5658	521	16	complementary	complementary	ADJ
ejpam-5658	521	17	prism	prism	NOUN
ejpam-5658	521	18	,	,	PUNCT
ejpam-5658	521	19	edge	edge	NOUN
ejpam-5658	521	20	corona	corona	NOUN
ejpam-5658	521	21	,	,	PUNCT
ejpam-5658	521	22	disjunction	disjunction	NOUN
ejpam-5658	521	23	,	,	PUNCT
ejpam-5658	521	24	and	and	CCONJ
ejpam-5658	521	25	strong	strong	ADJ
ejpam-5658	521	26	product	product	NOUN
ejpam-5658	521	27	of	of	ADP
ejpam-5658	521	28	two	two	NUM
ejpam-5658	521	29	graphs	graph	NOUN
ejpam-5658	521	30	.	.	PUNCT
ejpam-5658	522	1	it	it	PRON
ejpam-5658	522	2	is	be	AUX
ejpam-5658	522	3	conjectured	conjecture	VERB
ejpam-5658	522	4	that	that	SCONJ
ejpam-5658	522	5	the	the	DET
ejpam-5658	522	6	hop	hop	NOUN
ejpam-5658	522	7	independence	independence	NOUN
ejpam-5658	522	8	number	number	NOUN
ejpam-5658	522	9	of	of	ADP
ejpam-5658	522	10	the	the	DET
ejpam-5658	522	11	edge	edge	NOUN
ejpam-5658	522	12	corona	corona	NOUN
ejpam-5658	522	13	of	of	ADP
ejpam-5658	522	14	two	two	NUM
ejpam-5658	522	15	graphs	graph	NOUN
ejpam-5658	522	16	may	may	AUX
ejpam-5658	522	17	take	take	VERB
ejpam-5658	522	18	only	only	ADV
ejpam-5658	522	19	three	three	NUM
ejpam-5658	522	20	possible	possible	ADJ
ejpam-5658	522	21	values	value	NOUN
ejpam-5658	522	22	,	,	PUNCT
ejpam-5658	522	23	namely	namely	ADV
ejpam-5658	522	24	;	;	PUNCT
ejpam-5658	522	25	αh(g	αh(g	NOUN
ejpam-5658	522	26	)	)	PUNCT
ejpam-5658	522	27	,	,	PUNCT
ejpam-5658	522	28	ν(g)ω(g	ν(g)ω(g	NOUN
ejpam-5658	522	29	)	)	PUNCT
ejpam-5658	522	30	,	,	PUNCT
ejpam-5658	522	31	and	and	CCONJ
ejpam-5658	522	32	ν(g)ω(g	ν(g)ω(g	NOUN
ejpam-5658	522	33	)	)	PUNCT
ejpam-5658	523	1	+	+	CCONJ
ejpam-5658	523	2	2	2	X
ejpam-5658	523	3	.	.	X
ejpam-5658	523	4	it	it	PRON
ejpam-5658	523	5	is	be	AUX
ejpam-5658	523	6	also	also	ADV
ejpam-5658	523	7	conjectured	conjecture	VERB
ejpam-5658	523	8	that	that	SCONJ
ejpam-5658	523	9	the	the	DET
ejpam-5658	523	10	lower	lower	ADV
ejpam-5658	523	11	bound	bind	VERB
ejpam-5658	523	12	in	in	ADP
ejpam-5658	523	13	corollary	corollary	ADJ
ejpam-5658	523	14	7	7	NUM
ejpam-5658	523	15	is	be	AUX
ejpam-5658	523	16	the	the	DET
ejpam-5658	523	17	exact	exact	ADJ
ejpam-5658	523	18	value	value	NOUN
ejpam-5658	523	19	of	of	ADP
ejpam-5658	523	20	the	the	DET
ejpam-5658	523	21	parameter	parameter	NOUN
ejpam-5658	523	22	.	.	PUNCT
ejpam-5658	524	1	using	use	VERB
ejpam-5658	524	2	the	the	DET
ejpam-5658	524	3	fact	fact	NOUN
ejpam-5658	524	4	that	that	SCONJ
ejpam-5658	524	5	the	the	DET
ejpam-5658	524	6	clique	clique	ADJ
ejpam-5658	524	7	decision	decision	NOUN
ejpam-5658	524	8	problem	problem	NOUN
ejpam-5658	524	9	(	(	PUNCT
ejpam-5658	524	10	cp	cp	X
ejpam-5658	524	11	)	)	PUNCT
ejpam-5658	524	12	is	be	AUX
ejpam-5658	524	13	np	np	ADP
ejpam-5658	524	14	-complete	-complete	ADJ
ejpam-5658	524	15	,	,	PUNCT
ejpam-5658	524	16	it	it	PRON
ejpam-5658	524	17	was	be	AUX
ejpam-5658	524	18	shown	show	VERB
ejpam-5658	524	19	that	that	SCONJ
ejpam-5658	524	20	the	the	DET
ejpam-5658	524	21	hop	hop	NOUN
ejpam-5658	524	22	independent	independent	ADJ
ejpam-5658	524	23	set	set	NOUN
ejpam-5658	524	24	problem	problem	NOUN
ejpam-5658	524	25	(	(	PUNCT
ejpam-5658	524	26	hisp	hisp	NOUN
ejpam-5658	524	27	)	)	PUNCT
ejpam-5658	524	28	is	be	AUX
ejpam-5658	524	29	also	also	ADV
ejpam-5658	524	30	np	np	ADP
ejpam-5658	524	31	-complete	-complete	ADJ
ejpam-5658	524	32	.	.	PUNCT
ejpam-5658	525	1	acknowledgements	acknowledgement	NOUN
ejpam-5658	525	2	the	the	DET
ejpam-5658	525	3	authors	author	NOUN
ejpam-5658	525	4	would	would	AUX
ejpam-5658	525	5	like	like	VERB
ejpam-5658	525	6	to	to	PART
ejpam-5658	525	7	thank	thank	VERB
ejpam-5658	525	8	the	the	DET
ejpam-5658	525	9	referees	referee	NOUN
ejpam-5658	525	10	for	for	ADP
ejpam-5658	525	11	the	the	DET
ejpam-5658	525	12	comments	comment	NOUN
ejpam-5658	525	13	and	and	CCONJ
ejpam-5658	525	14	suggestions	suggestion	NOUN
ejpam-5658	525	15	they	they	PRON
ejpam-5658	525	16	offered	offer	VERB
ejpam-5658	525	17	us	we	PRON
ejpam-5658	525	18	which	which	PRON
ejpam-5658	525	19	led	lead	VERB
ejpam-5658	525	20	to	to	ADP
ejpam-5658	525	21	the	the	DET
ejpam-5658	525	22	improvement	improvement	NOUN
ejpam-5658	525	23	of	of	ADP
ejpam-5658	525	24	the	the	DET
ejpam-5658	525	25	paper	paper	NOUN
ejpam-5658	525	26	.	.	PUNCT
ejpam-5658	526	1	also	also	ADV
ejpam-5658	526	2	,	,	PUNCT
ejpam-5658	526	3	the	the	DET
ejpam-5658	526	4	authors	author	NOUN
ejpam-5658	526	5	would	would	AUX
ejpam-5658	526	6	like	like	VERB
ejpam-5658	526	7	to	to	PART
ejpam-5658	526	8	thank	thank	VERB
ejpam-5658	526	9	the	the	DET
ejpam-5658	526	10	department	department	NOUN
ejpam-5658	526	11	of	of	ADP
ejpam-5658	526	12	science	science	NOUN
ejpam-5658	526	13	and	and	CCONJ
ejpam-5658	526	14	technology	technology	NOUN
ejpam-5658	526	15	accelerated	accelerate	VERB
ejpam-5658	526	16	science	science	NOUN
ejpam-5658	526	17	and	and	CCONJ
ejpam-5658	526	18	technology	technology	NOUN
ejpam-5658	526	19	human	human	ADJ
ejpam-5658	526	20	resource	resource	NOUN
ejpam-5658	526	21	development	development	NOUN
ejpam-5658	526	22	program	program	NOUN
ejpam-5658	526	23	(	(	PUNCT
ejpam-5658	526	24	dost	dost	NOUN
ejpam-5658	526	25	-	-	PUNCT
ejpam-5658	526	26	asthrdp)-philippines	asthrdp)-philippine	NOUN
ejpam-5658	526	27	,	,	PUNCT
ejpam-5658	526	28	and	and	CCONJ
ejpam-5658	526	29	msu	msu	PROPN
ejpam-5658	526	30	-	-	PUNCT
ejpam-5658	526	31	iligan	iligan	PROPN
ejpam-5658	526	32	institute	institute	PROPN
ejpam-5658	526	33	of	of	ADP
ejpam-5658	526	34	technology	technology	NOUN
ejpam-5658	526	35	for	for	ADP
ejpam-5658	526	36	funding	fund	VERB
ejpam-5658	526	37	this	this	DET
ejpam-5658	526	38	research	research	NOUN
ejpam-5658	526	39	.	.	PUNCT
ejpam-5658	527	1	references	reference	NOUN
ejpam-5658	527	2	[	[	X
ejpam-5658	527	3	1	1	X
ejpam-5658	527	4	]	]	PUNCT
ejpam-5658	527	5	s.	s.	PROPN
ejpam-5658	527	6	arriola	arriola	PROPN
ejpam-5658	527	7	and	and	CCONJ
ejpam-5658	527	8	jr	jr	PROPN
ejpam-5658	527	9	.	.	PROPN
ejpam-5658	527	10	s.	s.	PROPN
ejpam-5658	527	11	canoy	canoy	PROPN
ejpam-5658	527	12	.	.	PUNCT
ejpam-5658	528	1	(	(	PUNCT
ejpam-5658	528	2	1	1	NUM
ejpam-5658	528	3	,	,	PUNCT
ejpam-5658	528	4	2)∗-domination	2)∗-domination	NOUN
ejpam-5658	528	5	in	in	ADP
ejpam-5658	528	6	graphs	graph	NOUN
ejpam-5658	528	7	.	.	PUNCT
ejpam-5658	529	1	advances	advance	NOUN
ejpam-5658	529	2	and	and	CCONJ
ejpam-5658	529	3	applications	application	NOUN
ejpam-5658	529	4	in	in	ADP
ejpam-5658	529	5	discrete	discrete	ADJ
ejpam-5658	529	6	mathematics	mathematic	NOUN
ejpam-5658	529	7	.	.	PUNCT
ejpam-5658	529	8	,	,	PUNCT
ejpam-5658	529	9	18(2):179–190	18(2):179–190	NUM
ejpam-5658	529	10	,	,	PUNCT
ejpam-5658	529	11	2017	2017	NUM
ejpam-5658	529	12	.	.	PUNCT
ejpam-5658	530	1	[	[	X
ejpam-5658	530	2	2	2	NUM
ejpam-5658	530	3	]	]	PUNCT
ejpam-5658	530	4	s.	s.	PROPN
ejpam-5658	530	5	ayyaswamy	ayyaswamy	PROPN
ejpam-5658	530	6	,	,	PUNCT
ejpam-5658	530	7	b.	b.	PROPN
ejpam-5658	530	8	krishnakumari	krishnakumari	PROPN
ejpam-5658	530	9	,	,	PUNCT
ejpam-5658	530	10	b.	b.	PROPN
ejpam-5658	530	11	natarjan	natarjan	PROPN
ejpam-5658	530	12	,	,	PUNCT
ejpam-5658	530	13	and	and	CCONJ
ejpam-5658	530	14	y.	y.	PROPN
ejpam-5658	530	15	venkatakrishnan	venkatakrishnan	PROPN
ejpam-5658	530	16	.	.	PUNCT
ejpam-5658	531	1	bounds	bound	NOUN
ejpam-5658	531	2	on	on	ADP
ejpam-5658	531	3	the	the	DET
ejpam-5658	531	4	hop	hop	NOUN
ejpam-5658	531	5	domination	domination	NOUN
ejpam-5658	531	6	number	number	NOUN
ejpam-5658	531	7	of	of	ADP
ejpam-5658	531	8	a	a	DET
ejpam-5658	531	9	tree	tree	NOUN
ejpam-5658	531	10	.	.	PUNCT
ejpam-5658	532	1	proceedings	proceeding	NOUN
ejpam-5658	532	2	-	-	PUNCT
ejpam-5658	532	3	mathematical	mathematical	ADJ
ejpam-5658	532	4	sciences	science	NOUN
ejpam-5658	532	5	,	,	PUNCT
ejpam-5658	532	6	125(4):449	125(4):449	NUM
ejpam-5658	532	7	–	–	PUNCT
ejpam-5658	532	8	455	455	NUM
ejpam-5658	532	9	,	,	PUNCT
ejpam-5658	532	10	2015	2015	NUM
ejpam-5658	532	11	.	.	PUNCT
ejpam-5658	533	1	[	[	X
ejpam-5658	533	2	3	3	X
ejpam-5658	533	3	]	]	X
ejpam-5658	533	4	j.	j.	PROPN
ejpam-5658	533	5	hassan1	hassan1	PROPN
ejpam-5658	533	6	and	and	CCONJ
ejpam-5658	533	7	jr	jr	PROPN
ejpam-5658	533	8	.	.	PROPN
ejpam-5658	533	9	s.	s.	PROPN
ejpam-5658	533	10	canoy	canoy	PROPN
ejpam-5658	533	11	.	.	PUNCT
ejpam-5658	534	1	hop	hop	PROPN
ejpam-5658	534	2	independent	independent	ADJ
ejpam-5658	534	3	hop	hop	NOUN
ejpam-5658	534	4	domination	domination	NOUN
ejpam-5658	534	5	in	in	ADP
ejpam-5658	534	6	graphs	graph	NOUN
ejpam-5658	534	7	.	.	PUNCT
ejpam-5658	535	1	eur	eur	PROPN
ejpam-5658	535	2	.	.	PUNCT
ejpam-5658	536	1	j.	j.	PROPN
ejpam-5658	536	2	pure	pure	PROPN
ejpam-5658	536	3	appl	appl	PROPN
ejpam-5658	536	4	.	.	PUNCT
ejpam-5658	536	5	math	math	PROPN
ejpam-5658	536	6	.	.	PUNCT
ejpam-5658	536	7	,	,	PUNCT
ejpam-5658	536	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-5658	536	9	,	,	PUNCT
ejpam-5658	536	10	2022	2022	NUM
ejpam-5658	536	11	.	.	PUNCT
ejpam-5658	537	1	[	[	X
ejpam-5658	537	2	4	4	X
ejpam-5658	537	3	]	]	PUNCT
ejpam-5658	537	4	j.	j.	PROPN
ejpam-5658	537	5	hassan1	hassan1	PROPN
ejpam-5658	537	6	,	,	PUNCT
ejpam-5658	537	7	jr	jr	PROPN
ejpam-5658	537	8	.	.	PROPN
ejpam-5658	537	9	s.	s.	PROPN
ejpam-5658	537	10	canoy	canoy	PROPN
ejpam-5658	537	11	,	,	PUNCT
ejpam-5658	537	12	and	and	CCONJ
ejpam-5658	537	13	a.	a.	PROPN
ejpam-5658	537	14	aradais	aradais	PROPN
ejpam-5658	537	15	.	.	PUNCT
ejpam-5658	538	1	hop	hop	PROPN
ejpam-5658	538	2	independent	independent	ADJ
ejpam-5658	538	3	sets	set	NOUN
ejpam-5658	538	4	in	in	ADP
ejpam-5658	538	5	graphs	graph	NOUN
ejpam-5658	538	6	.	.	PUNCT
ejpam-5658	539	1	eur	eur	PROPN
ejpam-5658	539	2	.	.	PUNCT
ejpam-5658	540	1	j.	j.	PROPN
ejpam-5658	540	2	pure	pure	PROPN
ejpam-5658	540	3	appl	appl	PROPN
ejpam-5658	540	4	.	.	PUNCT
ejpam-5658	540	5	math	math	PROPN
ejpam-5658	540	6	.	.	PUNCT
ejpam-5658	540	7	,	,	PUNCT
ejpam-5658	540	8	15(2):467–477	15(2):467–477	PROPN
ejpam-5658	540	9	,	,	PUNCT
ejpam-5658	540	10	2022	2022	NUM
ejpam-5658	540	11	.	.	PUNCT
ejpam-5658	541	1	[	[	X
ejpam-5658	541	2	5	5	NUM
ejpam-5658	541	3	]	]	PUNCT
ejpam-5658	541	4	m.	m.	NOUN
ejpam-5658	541	5	henning	henning	PROPN
ejpam-5658	541	6	and	and	CCONJ
ejpam-5658	541	7	n.	n.	PROPN
ejpam-5658	541	8	rad	rad	PROPN
ejpam-5658	541	9	.	.	PROPN
ejpam-5658	542	1	on	on	ADP
ejpam-5658	542	2	2	2	NUM
ejpam-5658	542	3	-	-	PUNCT
ejpam-5658	542	4	step	step	NOUN
ejpam-5658	542	5	and	and	CCONJ
ejpam-5658	542	6	hop	hop	NOUN
ejpam-5658	542	7	dominating	dominating	NOUN
ejpam-5658	542	8	sets	set	NOUN
ejpam-5658	542	9	in	in	ADP
ejpam-5658	542	10	graphs	graph	NOUN
ejpam-5658	542	11	.	.	PUNCT
ejpam-5658	543	1	graphs	graph	NOUN
ejpam-5658	543	2	and	and	CCONJ
ejpam-5658	543	3	combinatorics	combinatoric	NOUN
ejpam-5658	543	4	.	.	PUNCT
ejpam-5658	543	5	,	,	PUNCT
ejpam-5658	543	6	33(4):913–927	33(4):913–927	PROPN
ejpam-5658	543	7	,	,	PUNCT
ejpam-5658	543	8	2017	2017	NUM
ejpam-5658	543	9	.	.	PUNCT
ejpam-5658	544	1	[	[	X
ejpam-5658	544	2	6	6	NUM
ejpam-5658	544	3	]	]	PUNCT
ejpam-5658	544	4	r.	r.	PROPN
ejpam-5658	544	5	karp	karp	PROPN
ejpam-5658	544	6	.	.	PUNCT
ejpam-5658	545	1	reducibility	reducibility	PROPN
ejpam-5658	545	2	among	among	ADP
ejpam-5658	545	3	combinatorial	combinatorial	ADJ
ejpam-5658	545	4	problems	problem	NOUN
ejpam-5658	545	5	.	.	PUNCT
ejpam-5658	546	1	complexity	complexity	NOUN
ejpam-5658	546	2	of	of	ADP
ejpam-5658	546	3	computer	computer	NOUN
ejpam-5658	546	4	computations	computation	NOUN
ejpam-5658	546	5	(	(	PUNCT
ejpam-5658	546	6	pdf	pdf	NOUN
ejpam-5658	546	7	)	)	PUNCT
ejpam-5658	546	8	,	,	PUNCT
ejpam-5658	546	9	new	new	PROPN
ejpam-5658	546	10	york	york	PROPN
ejpam-5658	546	11	:	:	PUNCT
ejpam-5658	546	12	plenum	plenum	PROPN
ejpam-5658	546	13	,	,	PUNCT
ejpam-5658	546	14	pages	page	NOUN
ejpam-5658	546	15	85–103	85–103	NUM
ejpam-5658	546	16	,	,	PUNCT
ejpam-5658	546	17	1972	1972	NUM
ejpam-5658	546	18	.	.	PUNCT
ejpam-5658	547	1	[	[	X
ejpam-5658	547	2	7	7	X
ejpam-5658	547	3	]	]	X
ejpam-5658	547	4	c.	c.	PROPN
ejpam-5658	547	5	natarajan	natarajan	PROPN
ejpam-5658	547	6	and	and	CCONJ
ejpam-5658	547	7	s.	s.	PROPN
ejpam-5658	547	8	ayyaswamy	ayyaswamy	PROPN
ejpam-5658	547	9	.	.	PUNCT
ejpam-5658	548	1	hop	hop	PROPN
ejpam-5658	548	2	domination	domination	NOUN
ejpam-5658	548	3	in	in	ADP
ejpam-5658	548	4	graphs	graphs	PROPN
ejpam-5658	548	5	ii	ii	PROPN
ejpam-5658	548	6	.	.	PUNCT
ejpam-5658	548	7	versita	versita	PROPN
ejpam-5658	548	8	,	,	PUNCT
ejpam-5658	548	9	23(2):187	23(2):187	NUM
ejpam-5658	548	10	–	–	PUNCT
ejpam-5658	548	11	199	199	NUM
ejpam-5658	548	12	,	,	PUNCT
ejpam-5658	548	13	2015	2015	NUM
ejpam-5658	548	14	.	.	PUNCT
ejpam-5658	549	1	[	[	X
ejpam-5658	549	2	8	8	NUM
ejpam-5658	549	3	]	]	X
ejpam-5658	549	4	jr	jr	PROPN
ejpam-5658	549	5	.	.	PROPN
ejpam-5658	549	6	s.	s.	PROPN
ejpam-5658	549	7	canoy	canoy	PROPN
ejpam-5658	549	8	,	,	PUNCT
ejpam-5658	549	9	r.	r.	NOUN
ejpam-5658	549	10	mollejon	mollejon	NOUN
ejpam-5658	549	11	,	,	PUNCT
ejpam-5658	549	12	and	and	CCONJ
ejpam-5658	549	13	j.	j.	PROPN
ejpam-5658	549	14	g.	g.	PROPN
ejpam-5658	549	15	canoy	canoy	PROPN
ejpam-5658	549	16	.	.	PUNCT
ejpam-5658	550	1	hop	hop	PROPN
ejpam-5658	550	2	dominating	dominating	NOUN
ejpam-5658	550	3	sets	set	NOUN
ejpam-5658	550	4	in	in	ADP
ejpam-5658	550	5	graphs	graph	NOUN
ejpam-5658	550	6	under	under	ADP
ejpam-5658	550	7	binary	binary	ADJ
ejpam-5658	550	8	operations	operation	NOUN
ejpam-5658	550	9	.	.	PUNCT
ejpam-5658	551	1	eur	eur	PROPN
ejpam-5658	551	2	.	.	PUNCT
ejpam-5658	552	1	j.	j.	PROPN
ejpam-5658	552	2	pure	pure	PROPN
ejpam-5658	552	3	appl	appl	PROPN
ejpam-5658	552	4	.	.	PUNCT
ejpam-5658	552	5	math	math	PROPN
ejpam-5658	552	6	.	.	PUNCT
ejpam-5658	552	7	,	,	PUNCT
ejpam-5658	553	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-5658	553	2	,	,	PUNCT
ejpam-5658	553	3	2019	2019	NUM
ejpam-5658	553	4	.	.	PUNCT
ejpam-5658	554	1	j.	j.	PROPN
ejpam-5658	554	2	anoche	anoche	PROPN
ejpam-5658	554	3	,	,	PUNCT
ejpam-5658	554	4	s.	s.	PROPN
ejpam-5658	554	5	canoy	canoy	PROPN
ejpam-5658	554	6	,	,	PUNCT
ejpam-5658	554	7	jr	jr	PROPN
ejpam-5658	554	8	.	.	PROPN
ejpam-5658	554	9	/	/	SYM
ejpam-5658	554	10	eur	eur	PROPN
ejpam-5658	554	11	.	.	PUNCT
ejpam-5658	555	1	j.	j.	PROPN
ejpam-5658	555	2	pure	pure	PROPN
ejpam-5658	555	3	appl	appl	PROPN
ejpam-5658	555	4	.	.	PROPN
ejpam-5658	555	5	math	math	PROPN
ejpam-5658	555	6	,	,	PUNCT
ejpam-5658	555	7	18	18	NUM
ejpam-5658	555	8	(	(	PUNCT
ejpam-5658	555	9	1	1	NUM
ejpam-5658	555	10	)	)	PUNCT
ejpam-5658	555	11	(	(	PUNCT
ejpam-5658	555	12	2025	2025	NUM
ejpam-5658	555	13	)	)	PUNCT
ejpam-5658	555	14	,	,	PUNCT
ejpam-5658	555	15	5658	5658	NUM
ejpam-5658	555	16	15	15	NUM
ejpam-5658	555	17	of	of	ADP
ejpam-5658	555	18	15	15	NUM
ejpam-5658	555	19	[	[	SYM
ejpam-5658	555	20	9	9	NUM
ejpam-5658	555	21	]	]	SYM
ejpam-5658	555	22	jr	jr	PROPN
ejpam-5658	555	23	.	.	PROPN
ejpam-5658	555	24	s.	s.	PROPN
ejpam-5658	555	25	canoy	canoy	PROPN
ejpam-5658	555	26	and	and	CCONJ
ejpam-5658	555	27	g.	g.	PROPN
ejpam-5658	555	28	salasalan	salasalan	NOUN
ejpam-5658	555	29	.	.	PUNCT
ejpam-5658	556	1	locating	locate	VERB
ejpam-5658	556	2	-	-	PUNCT
ejpam-5658	556	3	hop	hop	NOUN
ejpam-5658	556	4	domination	domination	NOUN
ejpam-5658	556	5	in	in	ADP
ejpam-5658	556	6	graphs	graph	NOUN
ejpam-5658	556	7	.	.	PUNCT
ejpam-5658	557	1	kyungpook	kyungpook	PROPN
ejpam-5658	557	2	mathematical	mathematical	PROPN
ejpam-5658	557	3	journal	journal	PROPN
ejpam-5658	557	4	,	,	PUNCT
ejpam-5658	557	5	62:193–204	62:193–204	PROPN
ejpam-5658	557	6	,	,	PUNCT
ejpam-5658	557	7	2022	2022	NUM
ejpam-5658	557	8	.	.	PUNCT
ejpam-5658	558	1	[	[	X
ejpam-5658	558	2	10	10	NUM
ejpam-5658	558	3	]	]	X
ejpam-5658	558	4	g.	g.	NOUN
ejpam-5658	558	5	salasalan	salasalan	NOUN
ejpam-5658	558	6	and	and	CCONJ
ejpam-5658	558	7	jr	jr	PROPN
ejpam-5658	558	8	.	.	PROPN
ejpam-5658	558	9	s.	s.	PROPN
ejpam-5658	558	10	canoy	canoy	PROPN
ejpam-5658	558	11	.	.	PUNCT
ejpam-5658	559	1	global	global	ADJ
ejpam-5658	559	2	hop	hop	PROPN
ejpam-5658	559	3	domination	domination	PROPN
ejpam-5658	559	4	numbers	number	NOUN
ejpam-5658	559	5	of	of	ADP
ejpam-5658	559	6	graphs	graph	NOUN
ejpam-5658	559	7	.	.	PUNCT
ejpam-5658	560	1	eur	eur	PROPN
ejpam-5658	560	2	.	.	PUNCT
ejpam-5658	561	1	j.	j.	PROPN
ejpam-5658	561	2	pure	pure	PROPN
ejpam-5658	561	3	appl	appl	PROPN
ejpam-5658	561	4	.	.	PUNCT
ejpam-5658	561	5	math	math	PROPN
ejpam-5658	561	6	.	.	PUNCT
ejpam-5658	561	7	,	,	PUNCT
ejpam-5658	561	8	14(1):112–125	14(1):112–125	NUM
ejpam-5658	561	9	,	,	PUNCT
ejpam-5658	561	10	2021	2021	NUM
ejpam-5658	561	11	.	.	PUNCT