id	sid	tid	token	lemma	pos
ejpam-4480	1	1	european	european	PROPN
ejpam-4480	1	2	journal	journal	PROPN
ejpam-4480	1	3	of	of	ADP
ejpam-4480	1	4	pure	pure	ADJ
ejpam-4480	1	5	and	and	CCONJ
ejpam-4480	1	6	applied	apply	VERB
ejpam-4480	1	7	mathematics	mathematic	NOUN
ejpam-4480	1	8	vol	vol	NOUN
ejpam-4480	1	9	.	.	PROPN
ejpam-4480	2	1	15	15	NUM
ejpam-4480	2	2	,	,	PUNCT
ejpam-4480	2	3	no	no	INTJ
ejpam-4480	2	4	.	.	NOUN
ejpam-4480	2	5	3	3	NUM
ejpam-4480	2	6	,	,	PUNCT
ejpam-4480	2	7	2022	2022	NUM
ejpam-4480	2	8	,	,	PUNCT
ejpam-4480	2	9	1217	1217	NUM
ejpam-4480	2	10	-	-	SYM
ejpam-4480	2	11	1228	1228	NUM
ejpam-4480	2	12	issn	issn	PROPN
ejpam-4480	2	13	1307	1307	NUM
ejpam-4480	2	14	-	-	SYM
ejpam-4480	2	15	5543	5543	NUM
ejpam-4480	2	16	–	–	PUNCT
ejpam-4480	2	17	ejpam.com	ejpam.com	X
ejpam-4480	2	18	published	publish	VERB
ejpam-4480	2	19	by	by	ADP
ejpam-4480	2	20	new	new	PROPN
ejpam-4480	2	21	york	york	PROPN
ejpam-4480	2	22	business	business	PROPN
ejpam-4480	2	23	global	global	ADJ
ejpam-4480	2	24	supercliques	superclique	NOUN
ejpam-4480	2	25	in	in	ADP
ejpam-4480	2	26	a	a	DET
ejpam-4480	2	27	graph	graph	NOUN
ejpam-4480	2	28	ramil	ramil	PROPN
ejpam-4480	2	29	h.	h.	PROPN
ejpam-4480	2	30	dela	dela	PROPN
ejpam-4480	2	31	cerna1,∗	cerna1,∗	PROPN
ejpam-4480	2	32	,	,	PUNCT
ejpam-4480	2	33	sergio	sergio	PROPN
ejpam-4480	2	34	r.	r.	PROPN
ejpam-4480	2	35	canoy	canoy	PROPN
ejpam-4480	2	36	,	,	PUNCT
ejpam-4480	2	37	jr.1	jr.1	PROPN
ejpam-4480	2	38	1	1	NUM
ejpam-4480	2	39	department	department	NOUN
ejpam-4480	2	40	of	of	ADP
ejpam-4480	2	41	mathematics	mathematic	NOUN
ejpam-4480	2	42	and	and	CCONJ
ejpam-4480	2	43	statistics	statistic	NOUN
ejpam-4480	2	44	,	,	PUNCT
ejpam-4480	2	45	college	college	NOUN
ejpam-4480	2	46	of	of	ADP
ejpam-4480	2	47	science	science	NOUN
ejpam-4480	2	48	and	and	CCONJ
ejpam-4480	2	49	mathematics	mathematic	NOUN
ejpam-4480	2	50	,	,	PUNCT
ejpam-4480	2	51	center	center	NOUN
ejpam-4480	2	52	for	for	ADP
ejpam-4480	2	53	graph	graph	NOUN
ejpam-4480	2	54	theory	theory	NOUN
ejpam-4480	2	55	,	,	PUNCT
ejpam-4480	2	56	algebra	algebra	NOUN
ejpam-4480	2	57	and	and	CCONJ
ejpam-4480	2	58	analysis	analysis	NOUN
ejpam-4480	2	59	-	-	PUNCT
ejpam-4480	2	60	prism	prism	NOUN
ejpam-4480	2	61	,	,	PUNCT
ejpam-4480	2	62	msu	msu	PROPN
ejpam-4480	2	63	-	-	PUNCT
ejpam-4480	2	64	iligan	iligan	PROPN
ejpam-4480	2	65	institute	institute	PROPN
ejpam-4480	2	66	of	of	ADP
ejpam-4480	2	67	technology	technology	PROPN
ejpam-4480	2	68	,	,	PUNCT
ejpam-4480	2	69	9200	9200	NUM
ejpam-4480	2	70	iligan	iligan	ADJ
ejpam-4480	2	71	city	city	NOUN
ejpam-4480	2	72	,	,	PUNCT
ejpam-4480	2	73	philippines	philippine	NOUN
ejpam-4480	2	74	abstract	abstract	ADJ
ejpam-4480	2	75	.	.	PUNCT
ejpam-4480	3	1	a	a	DET
ejpam-4480	3	2	set	set	NOUN
ejpam-4480	3	3	s	s	NOUN
ejpam-4480	3	4	⊆	⊆	NUM
ejpam-4480	3	5	v	v	NOUN
ejpam-4480	3	6	(	(	PUNCT
ejpam-4480	3	7	g	g	NOUN
ejpam-4480	3	8	)	)	PUNCT
ejpam-4480	3	9	of	of	ADP
ejpam-4480	3	10	a	a	DET
ejpam-4480	3	11	(	(	PUNCT
ejpam-4480	3	12	simple	simple	ADJ
ejpam-4480	3	13	)	)	PUNCT
ejpam-4480	3	14	undirected	undirected	ADJ
ejpam-4480	3	15	graph	graph	NOUN
ejpam-4480	3	16	g	g	PROPN
ejpam-4480	3	17	is	be	AUX
ejpam-4480	3	18	a	a	DET
ejpam-4480	3	19	superclique	superclique	NOUN
ejpam-4480	3	20	in	in	ADP
ejpam-4480	3	21	g	g	PROPN
ejpam-4480	3	22	if	if	SCONJ
ejpam-4480	3	23	it	it	PRON
ejpam-4480	3	24	is	be	AUX
ejpam-4480	3	25	a	a	DET
ejpam-4480	3	26	clique	clique	NOUN
ejpam-4480	3	27	and	and	CCONJ
ejpam-4480	3	28	for	for	ADP
ejpam-4480	3	29	every	every	DET
ejpam-4480	3	30	pair	pair	NOUN
ejpam-4480	3	31	of	of	ADP
ejpam-4480	3	32	distinct	distinct	ADJ
ejpam-4480	3	33	vertices	vertex	NOUN
ejpam-4480	3	34	v	v	ADP
ejpam-4480	3	35	,	,	PUNCT
ejpam-4480	3	36	w	w	PROPN
ejpam-4480	3	37	∈	∈	PROPN
ejpam-4480	3	38	s	s	NOUN
ejpam-4480	3	39	,	,	PUNCT
ejpam-4480	3	40	there	there	PRON
ejpam-4480	3	41	exists	exist	VERB
ejpam-4480	3	42	u	u	PROPN
ejpam-4480	3	43	∈	∈	PROPN
ejpam-4480	3	44	v	v	ADP
ejpam-4480	3	45	(	(	PUNCT
ejpam-4480	3	46	g	g	NOUN
ejpam-4480	3	47	)	)	PUNCT
ejpam-4480	3	48	\	\	PUNCT
ejpam-4480	4	1	s	s	VERB
ejpam-4480	4	2	such	such	ADJ
ejpam-4480	4	3	that	that	SCONJ
ejpam-4480	4	4	u	u	PROPN
ejpam-4480	4	5	∈	∈	PROPN
ejpam-4480	4	6	ng(v	ng(v	PUNCT
ejpam-4480	4	7	)	)	PUNCT
ejpam-4480	4	8	\	\	NOUN
ejpam-4480	4	9	ng(w	ng(w	NOUN
ejpam-4480	4	10	)	)	PUNCT
ejpam-4480	4	11	or	or	CCONJ
ejpam-4480	4	12	u	u	PROPN
ejpam-4480	4	13	∈	∈	PROPN
ejpam-4480	4	14	ng(w	ng(w	NOUN
ejpam-4480	4	15	)	)	PUNCT
ejpam-4480	4	16	\	\	NOUN
ejpam-4480	4	17	ng(v	ng(v	PUNCT
ejpam-4480	4	18	)	)	PUNCT
ejpam-4480	4	19	.	.	PUNCT
ejpam-4480	5	1	the	the	DET
ejpam-4480	5	2	maximum	maximum	PROPN
ejpam-4480	5	3	cardinality	cardinality	NOUN
ejpam-4480	5	4	among	among	ADP
ejpam-4480	5	5	the	the	DET
ejpam-4480	5	6	supercliques	superclique	NOUN
ejpam-4480	5	7	in	in	ADP
ejpam-4480	5	8	g	g	NOUN
ejpam-4480	5	9	,	,	PUNCT
ejpam-4480	5	10	denoted	denote	VERB
ejpam-4480	5	11	by	by	ADP
ejpam-4480	5	12	ωs(g	ωs(g	NOUN
ejpam-4480	5	13	)	)	PUNCT
ejpam-4480	5	14	,	,	PUNCT
ejpam-4480	5	15	is	be	AUX
ejpam-4480	5	16	called	call	VERB
ejpam-4480	5	17	the	the	DET
ejpam-4480	5	18	superclique	superclique	ADJ
ejpam-4480	5	19	number	number	NOUN
ejpam-4480	5	20	of	of	ADP
ejpam-4480	5	21	g.	g.	PROPN
ejpam-4480	5	22	in	in	ADP
ejpam-4480	5	23	this	this	DET
ejpam-4480	5	24	paper	paper	NOUN
ejpam-4480	5	25	,	,	PUNCT
ejpam-4480	5	26	we	we	PRON
ejpam-4480	5	27	determine	determine	VERB
ejpam-4480	5	28	the	the	DET
ejpam-4480	5	29	superclique	superclique	ADJ
ejpam-4480	5	30	numbers	number	NOUN
ejpam-4480	5	31	of	of	ADP
ejpam-4480	5	32	some	some	DET
ejpam-4480	5	33	graphs	graph	NOUN
ejpam-4480	5	34	including	include	VERB
ejpam-4480	5	35	those	those	PRON
ejpam-4480	5	36	resulting	result	VERB
ejpam-4480	5	37	from	from	ADP
ejpam-4480	5	38	some	some	DET
ejpam-4480	5	39	binary	binary	ADJ
ejpam-4480	5	40	operations	operation	NOUN
ejpam-4480	5	41	of	of	ADP
ejpam-4480	5	42	graphs	graph	NOUN
ejpam-4480	5	43	.	.	PUNCT
ejpam-4480	6	1	we	we	PRON
ejpam-4480	6	2	will	will	AUX
ejpam-4480	6	3	also	also	ADV
ejpam-4480	6	4	show	show	VERB
ejpam-4480	6	5	that	that	SCONJ
ejpam-4480	6	6	the	the	DET
ejpam-4480	6	7	difference	difference	NOUN
ejpam-4480	6	8	of	of	ADP
ejpam-4480	6	9	the	the	DET
ejpam-4480	6	10	clique	clique	NOUN
ejpam-4480	6	11	number	number	NOUN
ejpam-4480	6	12	and	and	CCONJ
ejpam-4480	6	13	the	the	DET
ejpam-4480	6	14	superclique	superclique	ADJ
ejpam-4480	6	15	number	number	NOUN
ejpam-4480	6	16	can	can	AUX
ejpam-4480	6	17	be	be	AUX
ejpam-4480	6	18	made	make	VERB
ejpam-4480	6	19	arbitrarily	arbitrarily	ADV
ejpam-4480	6	20	large	large	ADJ
ejpam-4480	6	21	.	.	PUNCT
ejpam-4480	7	1	2020	2020	NUM
ejpam-4480	7	2	mathematics	mathematic	NOUN
ejpam-4480	7	3	subject	subject	NOUN
ejpam-4480	7	4	classifications	classification	NOUN
ejpam-4480	7	5	:	:	PUNCT
ejpam-4480	7	6	05c69	05c69	X
ejpam-4480	7	7	key	key	ADJ
ejpam-4480	7	8	words	word	NOUN
ejpam-4480	7	9	and	and	CCONJ
ejpam-4480	7	10	phrases	phrase	NOUN
ejpam-4480	7	11	:	:	PUNCT
ejpam-4480	7	12	clique	clique	NOUN
ejpam-4480	7	13	,	,	PUNCT
ejpam-4480	7	14	clique	clique	ADJ
ejpam-4480	7	15	number	number	NOUN
ejpam-4480	7	16	,	,	PUNCT
ejpam-4480	7	17	superclique	superclique	ADJ
ejpam-4480	7	18	,	,	PUNCT
ejpam-4480	7	19	superclique	superclique	ADJ
ejpam-4480	7	20	number	number	NOUN
ejpam-4480	7	21	1	1	NUM
ejpam-4480	7	22	.	.	PUNCT
ejpam-4480	8	1	introduction	introduction	NOUN
ejpam-4480	8	2	clique	clique	NOUN
ejpam-4480	8	3	is	be	AUX
ejpam-4480	8	4	one	one	NUM
ejpam-4480	8	5	of	of	ADP
ejpam-4480	8	6	the	the	DET
ejpam-4480	8	7	basic	basic	ADJ
ejpam-4480	8	8	concepts	concept	NOUN
ejpam-4480	8	9	in	in	ADP
ejpam-4480	8	10	graph	graph	NOUN
ejpam-4480	8	11	theory	theory	NOUN
ejpam-4480	8	12	.	.	PUNCT
ejpam-4480	9	1	this	this	DET
ejpam-4480	9	2	concept	concept	NOUN
ejpam-4480	9	3	was	be	AUX
ejpam-4480	9	4	used	use	VERB
ejpam-4480	9	5	in	in	ADP
ejpam-4480	9	6	many	many	ADJ
ejpam-4480	9	7	mathematical	mathematical	ADJ
ejpam-4480	9	8	problems	problem	NOUN
ejpam-4480	9	9	and	and	CCONJ
ejpam-4480	9	10	constructions	construction	NOUN
ejpam-4480	9	11	on	on	ADP
ejpam-4480	9	12	graphs	graph	NOUN
ejpam-4480	9	13	.	.	PUNCT
ejpam-4480	10	1	the	the	DET
ejpam-4480	10	2	term	term	NOUN
ejpam-4480	10	3	clique	clique	NOUN
ejpam-4480	10	4	was	be	AUX
ejpam-4480	10	5	introduced	introduce	VERB
ejpam-4480	10	6	by	by	ADP
ejpam-4480	10	7	luce	luce	PROPN
ejpam-4480	10	8	and	and	CCONJ
ejpam-4480	10	9	perry	perry	NOUN
ejpam-4480	11	1	[	[	X
ejpam-4480	11	2	12	12	NUM
ejpam-4480	11	3	]	]	PUNCT
ejpam-4480	11	4	.	.	PUNCT
ejpam-4480	12	1	in	in	ADP
ejpam-4480	12	2	a	a	DET
ejpam-4480	12	3	study	study	NOUN
ejpam-4480	12	4	in	in	ADP
ejpam-4480	12	5	[	[	X
ejpam-4480	12	6	8	8	NUM
ejpam-4480	12	7	]	]	PUNCT
ejpam-4480	12	8	,	,	PUNCT
ejpam-4480	12	9	gaquing	gaquing	NOUN
ejpam-4480	12	10	and	and	CCONJ
ejpam-4480	12	11	canoy	canoy	NOUN
ejpam-4480	12	12	characterized	characterize	VERB
ejpam-4480	12	13	the	the	DET
ejpam-4480	12	14	cliques	clique	NOUN
ejpam-4480	12	15	in	in	ADP
ejpam-4480	12	16	the	the	DET
ejpam-4480	12	17	lexicographic	lexicographic	ADJ
ejpam-4480	12	18	and	and	CCONJ
ejpam-4480	12	19	cartesian	cartesian	ADJ
ejpam-4480	12	20	products	product	NOUN
ejpam-4480	12	21	of	of	ADP
ejpam-4480	12	22	graphs	graph	NOUN
ejpam-4480	12	23	.	.	PUNCT
ejpam-4480	13	1	from	from	ADP
ejpam-4480	13	2	the	the	DET
ejpam-4480	13	3	characterizations	characterization	NOUN
ejpam-4480	13	4	,	,	PUNCT
ejpam-4480	13	5	the	the	DET
ejpam-4480	13	6	corresponding	corresponding	ADJ
ejpam-4480	13	7	clique	clique	ADJ
ejpam-4480	13	8	numbers	number	NOUN
ejpam-4480	13	9	of	of	ADP
ejpam-4480	13	10	these	these	DET
ejpam-4480	13	11	graphs	graph	NOUN
ejpam-4480	13	12	have	have	AUX
ejpam-4480	13	13	been	be	AUX
ejpam-4480	13	14	subsequently	subsequently	ADV
ejpam-4480	13	15	determined	determine	VERB
ejpam-4480	13	16	.	.	PUNCT
ejpam-4480	14	1	some	some	DET
ejpam-4480	14	2	studies	study	NOUN
ejpam-4480	14	3	involving	involve	VERB
ejpam-4480	14	4	cliques	clique	NOUN
ejpam-4480	14	5	can	can	AUX
ejpam-4480	14	6	be	be	AUX
ejpam-4480	14	7	found	find	VERB
ejpam-4480	14	8	in	in	ADP
ejpam-4480	14	9	[	[	X
ejpam-4480	14	10	5	5	NUM
ejpam-4480	14	11	]	]	PUNCT
ejpam-4480	14	12	,	,	PUNCT
ejpam-4480	14	13	[	[	X
ejpam-4480	14	14	6	6	NUM
ejpam-4480	14	15	]	]	PUNCT
ejpam-4480	14	16	,	,	PUNCT
ejpam-4480	14	17	[	[	X
ejpam-4480	14	18	14	14	NUM
ejpam-4480	14	19	]	]	PUNCT
ejpam-4480	14	20	,	,	PUNCT
ejpam-4480	14	21	and	and	CCONJ
ejpam-4480	14	22	[	[	X
ejpam-4480	14	23	17	17	NUM
ejpam-4480	14	24	]	]	PUNCT
ejpam-4480	14	25	.	.	PUNCT
ejpam-4480	15	1	with	with	ADP
ejpam-4480	15	2	the	the	DET
ejpam-4480	15	3	objective	objective	NOUN
ejpam-4480	15	4	of	of	ADP
ejpam-4480	15	5	identifying	identify	VERB
ejpam-4480	15	6	the	the	DET
ejpam-4480	15	7	exact	exact	ADJ
ejpam-4480	15	8	location	location	NOUN
ejpam-4480	15	9	of	of	ADP
ejpam-4480	15	10	an	an	DET
ejpam-4480	15	11	intruder	intruder	NOUN
ejpam-4480	15	12	in	in	ADP
ejpam-4480	15	13	a	a	DET
ejpam-4480	15	14	network	network	NOUN
ejpam-4480	15	15	,	,	PUNCT
ejpam-4480	15	16	slater	slater	NOUN
ejpam-4480	15	17	[	[	X
ejpam-4480	15	18	19	19	NUM
ejpam-4480	15	19	]	]	PUNCT
ejpam-4480	15	20	introduced	introduce	VERB
ejpam-4480	15	21	the	the	DET
ejpam-4480	15	22	concepts	concept	NOUN
ejpam-4480	15	23	of	of	ADP
ejpam-4480	15	24	resolving	resolve	VERB
ejpam-4480	15	25	set	set	VERB
ejpam-4480	15	26	and	and	CCONJ
ejpam-4480	15	27	metric	metric	ADJ
ejpam-4480	15	28	dimension	dimension	NOUN
ejpam-4480	15	29	.	.	PUNCT
ejpam-4480	16	1	these	these	DET
ejpam-4480	16	2	concepts	concept	NOUN
ejpam-4480	16	3	were	be	AUX
ejpam-4480	16	4	independently	independently	ADV
ejpam-4480	16	5	considered	consider	VERB
ejpam-4480	16	6	by	by	ADP
ejpam-4480	16	7	harary	harary	NOUN
ejpam-4480	16	8	and	and	CCONJ
ejpam-4480	16	9	melter	melter	NOUN
ejpam-4480	16	10	in	in	ADP
ejpam-4480	16	11	[	[	X
ejpam-4480	16	12	10	10	NUM
ejpam-4480	16	13	]	]	PUNCT
ejpam-4480	16	14	.	.	PUNCT
ejpam-4480	17	1	later	later	ADV
ejpam-4480	17	2	,	,	PUNCT
ejpam-4480	17	3	chartrand	chartrand	PROPN
ejpam-4480	17	4	et	et	PROPN
ejpam-4480	17	5	al	al	PROPN
ejpam-4480	17	6	.	.	PUNCT
ejpam-4480	18	1	(	(	PUNCT
ejpam-4480	18	2	see	see	VERB
ejpam-4480	18	3	[	[	X
ejpam-4480	18	4	4	4	NUM
ejpam-4480	18	5	]	]	PUNCT
ejpam-4480	18	6	)	)	PUNCT
ejpam-4480	18	7	also	also	ADV
ejpam-4480	18	8	studied	study	VERB
ejpam-4480	18	9	resolving	resolve	VERB
ejpam-4480	18	10	set	set	VERB
ejpam-4480	18	11	and	and	CCONJ
ejpam-4480	18	12	metric	metric	ADJ
ejpam-4480	18	13	dimension	dimension	NOUN
ejpam-4480	18	14	of	of	ADP
ejpam-4480	18	15	a	a	DET
ejpam-4480	18	16	graph	graph	NOUN
ejpam-4480	18	17	.	.	PUNCT
ejpam-4480	18	18	oellermann	oellermann	NOUN
ejpam-4480	18	19	and	and	CCONJ
ejpam-4480	18	20	fransen	fransen	ADJ
ejpam-4480	19	1	[	[	X
ejpam-4480	19	2	15	15	NUM
ejpam-4480	19	3	]	]	PUNCT
ejpam-4480	19	4	considered	consider	VERB
ejpam-4480	19	5	the	the	DET
ejpam-4480	19	6	metric	metric	ADJ
ejpam-4480	19	7	dimension	dimension	NOUN
ejpam-4480	19	8	of	of	ADP
ejpam-4480	19	9	cartesian	cartesian	ADJ
ejpam-4480	19	10	products	product	NOUN
ejpam-4480	19	11	of	of	ADP
ejpam-4480	19	12	graphs	graph	NOUN
ejpam-4480	19	13	.	.	PUNCT
ejpam-4480	20	1	it	it	PRON
ejpam-4480	20	2	is	be	AUX
ejpam-4480	20	3	known	know	VERB
ejpam-4480	20	4	that	that	SCONJ
ejpam-4480	20	5	the	the	DET
ejpam-4480	20	6	problem	problem	NOUN
ejpam-4480	20	7	of	of	ADP
ejpam-4480	20	8	finding	find	VERB
ejpam-4480	20	9	the	the	DET
ejpam-4480	20	10	metric	metric	ADJ
ejpam-4480	20	11	dimension	dimension	NOUN
ejpam-4480	20	12	of	of	ADP
ejpam-4480	20	13	a	a	DET
ejpam-4480	20	14	graph	graph	NOUN
ejpam-4480	20	15	is	be	AUX
ejpam-4480	20	16	np	np	INTJ
ejpam-4480	20	17	-	-	ADJ
ejpam-4480	20	18	hard	hard	ADJ
ejpam-4480	20	19	(	(	PUNCT
ejpam-4480	20	20	see	see	VERB
ejpam-4480	20	21	[	[	X
ejpam-4480	20	22	9	9	NUM
ejpam-4480	20	23	]	]	NUM
ejpam-4480	20	24	)	)	PUNCT
ejpam-4480	20	25	.	.	PUNCT
ejpam-4480	21	1	in	in	ADP
ejpam-4480	21	2	2003	2003	NUM
ejpam-4480	21	3	,	,	PUNCT
ejpam-4480	21	4	brigham	brigham	PROPN
ejpam-4480	21	5	et	et	PROPN
ejpam-4480	21	6	al	al	PROPN
ejpam-4480	21	7	.	.	PUNCT
ejpam-4480	22	1	[	[	X
ejpam-4480	22	2	2	2	X
ejpam-4480	22	3	]	]	PUNCT
ejpam-4480	22	4	combined	combine	VERB
ejpam-4480	22	5	the	the	DET
ejpam-4480	22	6	concepts	concept	NOUN
ejpam-4480	22	7	of	of	ADP
ejpam-4480	22	8	resolving	resolving	NOUN
ejpam-4480	22	9	and	and	CCONJ
ejpam-4480	22	10	domination	domination	NOUN
ejpam-4480	22	11	.	.	PUNCT
ejpam-4480	23	1	in	in	ADP
ejpam-4480	23	2	their	their	PRON
ejpam-4480	23	3	article	article	NOUN
ejpam-4480	23	4	,	,	PUNCT
ejpam-4480	23	5	they	they	PRON
ejpam-4480	23	6	defined	define	VERB
ejpam-4480	23	7	∗corresponding	∗corresponde	VERB
ejpam-4480	23	8	author	author	NOUN
ejpam-4480	23	9	.	.	PUNCT
ejpam-4480	24	1	doi	doi	NOUN
ejpam-4480	24	2	:	:	PUNCT
ejpam-4480	24	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4480	https://doi.org/10.29020/nybg.ejpam.v15i3.4480	NOUN
ejpam-4480	24	4	email	email	NOUN
ejpam-4480	24	5	addresses	address	NOUN
ejpam-4480	24	6	:	:	PUNCT
ejpam-4480	24	7	ramil.delacerna@g.msuiit.edu.ph	ramil.delacerna@g.msuiit.edu.ph	PROPN
ejpam-4480	24	8	(	(	PUNCT
ejpam-4480	24	9	r.	r.	PROPN
ejpam-4480	24	10	dela	dela	PROPN
ejpam-4480	24	11	cerna	cerna	PROPN
ejpam-4480	24	12	)	)	PUNCT
ejpam-4480	24	13	,	,	PUNCT
ejpam-4480	24	14	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4480	24	15	(	(	PUNCT
ejpam-4480	24	16	s.	s.	PROPN
ejpam-4480	24	17	canoy	canoy	PROPN
ejpam-4480	24	18	,	,	PUNCT
ejpam-4480	24	19	jr	jr	PROPN
ejpam-4480	24	20	.	.	PUNCT
ejpam-4480	24	21	)	)	PUNCT
ejpam-4480	24	22	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4480	25	1	1217	1217	NUM
ejpam-4480	26	1	©	©	ADP
ejpam-4480	26	2	2022	2022	NUM
ejpam-4480	26	3	ejpam	ejpam	VERB
ejpam-4480	26	4	all	all	DET
ejpam-4480	26	5	rights	right	NOUN
ejpam-4480	26	6	reserved	reserve	VERB
ejpam-4480	26	7	.	.	PUNCT
ejpam-4480	27	1	r.	r.	PROPN
ejpam-4480	27	2	dela	dela	PROPN
ejpam-4480	27	3	cerna	cerna	PROPN
ejpam-4480	27	4	,	,	PUNCT
ejpam-4480	27	5	s.	s.	PROPN
ejpam-4480	27	6	canoy	canoy	PROPN
ejpam-4480	27	7	,	,	PUNCT
ejpam-4480	27	8	jr	jr	PROPN
ejpam-4480	27	9	.	.	PROPN
ejpam-4480	27	10	/	/	SYM
ejpam-4480	27	11	eur	eur	PROPN
ejpam-4480	27	12	.	.	PUNCT
ejpam-4480	28	1	j.	j.	PROPN
ejpam-4480	28	2	pure	pure	PROPN
ejpam-4480	28	3	appl	appl	PROPN
ejpam-4480	28	4	.	.	PROPN
ejpam-4480	28	5	math	math	PROPN
ejpam-4480	28	6	,	,	PUNCT
ejpam-4480	28	7	15	15	NUM
ejpam-4480	28	8	(	(	PUNCT
ejpam-4480	28	9	3	3	NUM
ejpam-4480	28	10	)	)	PUNCT
ejpam-4480	28	11	(	(	PUNCT
ejpam-4480	28	12	2022	2022	NUM
ejpam-4480	28	13	)	)	PUNCT
ejpam-4480	28	14	,	,	PUNCT
ejpam-4480	28	15	1217	1217	NUM
ejpam-4480	28	16	-	-	SYM
ejpam-4480	28	17	1228	1228	NUM
ejpam-4480	28	18	1218	1218	NUM
ejpam-4480	28	19	resolving	resolve	VERB
ejpam-4480	28	20	dominating	dominating	NOUN
ejpam-4480	28	21	set	set	VERB
ejpam-4480	28	22	as	as	ADP
ejpam-4480	28	23	a	a	DET
ejpam-4480	28	24	set	set	NOUN
ejpam-4480	28	25	that	that	PRON
ejpam-4480	28	26	is	be	AUX
ejpam-4480	28	27	both	both	PRON
ejpam-4480	28	28	resolving	resolve	VERB
ejpam-4480	28	29	and	and	CCONJ
ejpam-4480	28	30	dominating	dominating	NOUN
ejpam-4480	28	31	.	.	PUNCT
ejpam-4480	29	1	along	along	ADP
ejpam-4480	29	2	with	with	ADP
ejpam-4480	29	3	the	the	DET
ejpam-4480	29	4	concept	concept	NOUN
ejpam-4480	29	5	,	,	PUNCT
ejpam-4480	29	6	they	they	PRON
ejpam-4480	29	7	also	also	ADV
ejpam-4480	29	8	studied	study	VERB
ejpam-4480	29	9	the	the	DET
ejpam-4480	29	10	parameter	parameter	NOUN
ejpam-4480	29	11	called	call	VERB
ejpam-4480	29	12	resolving	resolve	VERB
ejpam-4480	29	13	domination	domination	NOUN
ejpam-4480	29	14	number	number	NOUN
ejpam-4480	29	15	of	of	ADP
ejpam-4480	29	16	a	a	DET
ejpam-4480	29	17	graph	graph	NOUN
ejpam-4480	29	18	.	.	PUNCT
ejpam-4480	30	1	a	a	DET
ejpam-4480	30	2	more	more	ADV
ejpam-4480	30	3	restrictive	restrictive	ADJ
ejpam-4480	30	4	concept	concept	NOUN
ejpam-4480	30	5	of	of	ADP
ejpam-4480	30	6	resolving	resolve	VERB
ejpam-4480	30	7	set	set	NOUN
ejpam-4480	30	8	,	,	PUNCT
ejpam-4480	30	9	called	call	VERB
ejpam-4480	30	10	strong	strong	ADJ
ejpam-4480	30	11	resolving	resolving	NOUN
ejpam-4480	30	12	set	set	NOUN
ejpam-4480	30	13	,	,	PUNCT
ejpam-4480	30	14	and	and	CCONJ
ejpam-4480	30	15	its	its	PRON
ejpam-4480	30	16	associated	associated	ADJ
ejpam-4480	30	17	invariant	invariant	NOUN
ejpam-4480	30	18	(	(	PUNCT
ejpam-4480	30	19	the	the	DET
ejpam-4480	30	20	strong	strong	ADJ
ejpam-4480	30	21	metric	metric	ADJ
ejpam-4480	30	22	dimension	dimension	NOUN
ejpam-4480	30	23	)	)	PUNCT
ejpam-4480	30	24	were	be	AUX
ejpam-4480	30	25	introduced	introduce	VERB
ejpam-4480	30	26	in	in	ADP
ejpam-4480	30	27	[	[	X
ejpam-4480	30	28	18	18	NUM
ejpam-4480	30	29	]	]	PUNCT
ejpam-4480	30	30	.	.	PUNCT
ejpam-4480	31	1	the	the	DET
ejpam-4480	31	2	invariant	invariant	PROPN
ejpam-4480	31	3	was	be	AUX
ejpam-4480	31	4	revisited	revisit	VERB
ejpam-4480	31	5	and	and	CCONJ
ejpam-4480	31	6	studied	study	VERB
ejpam-4480	31	7	by	by	ADP
ejpam-4480	31	8	oellermann	oellermann	NOUN
ejpam-4480	31	9	and	and	CCONJ
ejpam-4480	31	10	fransen	fransen	VERB
ejpam-4480	31	11	in	in	ADP
ejpam-4480	31	12	[	[	X
ejpam-4480	31	13	16	16	NUM
ejpam-4480	31	14	]	]	PUNCT
ejpam-4480	31	15	for	for	ADP
ejpam-4480	31	16	graphs	graph	NOUN
ejpam-4480	31	17	and	and	CCONJ
ejpam-4480	31	18	digraphs	digraph	NOUN
ejpam-4480	31	19	.	.	PUNCT
ejpam-4480	32	1	recently	recently	ADV
ejpam-4480	32	2	,	,	PUNCT
ejpam-4480	32	3	acal	acal	ADJ
ejpam-4480	32	4	,	,	PUNCT
ejpam-4480	32	5	sumaoy	sumaoy	NOUN
ejpam-4480	32	6	,	,	PUNCT
ejpam-4480	32	7	and	and	CCONJ
ejpam-4480	32	8	rara	rara	NOUN
ejpam-4480	32	9	in	in	ADP
ejpam-4480	32	10	[	[	X
ejpam-4480	32	11	1	1	NUM
ejpam-4480	32	12	]	]	PUNCT
ejpam-4480	32	13	,	,	PUNCT
ejpam-4480	32	14	[	[	X
ejpam-4480	32	15	13	13	NUM
ejpam-4480	32	16	]	]	PUNCT
ejpam-4480	32	17	,	,	PUNCT
ejpam-4480	32	18	and	and	CCONJ
ejpam-4480	32	19	[	[	X
ejpam-4480	32	20	20	20	NUM
ejpam-4480	32	21	]	]	PUNCT
ejpam-4480	32	22	investigated	investigate	VERB
ejpam-4480	32	23	the	the	DET
ejpam-4480	32	24	concepts	concept	NOUN
ejpam-4480	32	25	of	of	ADP
ejpam-4480	32	26	strong	strong	ADJ
ejpam-4480	32	27	connected	connected	ADJ
ejpam-4480	32	28	resolving	resolving	NOUN
ejpam-4480	32	29	domination	domination	NOUN
ejpam-4480	32	30	and	and	CCONJ
ejpam-4480	32	31	restrained	restrained	ADJ
ejpam-4480	32	32	resolving	resolve	VERB
ejpam-4480	32	33	domination	domination	NOUN
ejpam-4480	32	34	of	of	ADP
ejpam-4480	32	35	graphs	graph	NOUN
ejpam-4480	32	36	under	under	ADP
ejpam-4480	32	37	some	some	DET
ejpam-4480	32	38	binary	binary	ADJ
ejpam-4480	32	39	operations	operation	NOUN
ejpam-4480	32	40	.	.	PUNCT
ejpam-4480	33	1	in	in	ADP
ejpam-4480	33	2	these	these	DET
ejpam-4480	33	3	studies	study	NOUN
ejpam-4480	33	4	,	,	PUNCT
ejpam-4480	33	5	they	they	PRON
ejpam-4480	33	6	specifically	specifically	ADV
ejpam-4480	33	7	introduced	introduce	VERB
ejpam-4480	33	8	the	the	DET
ejpam-4480	33	9	concept	concept	NOUN
ejpam-4480	33	10	of	of	ADP
ejpam-4480	33	11	superclique	superclique	NOUN
ejpam-4480	33	12	and	and	CCONJ
ejpam-4480	33	13	determined	determine	VERB
ejpam-4480	33	14	the	the	DET
ejpam-4480	33	15	values	value	NOUN
ejpam-4480	33	16	of	of	ADP
ejpam-4480	33	17	the	the	DET
ejpam-4480	33	18	invariants	invariant	NOUN
ejpam-4480	33	19	for	for	ADP
ejpam-4480	33	20	the	the	DET
ejpam-4480	33	21	join	join	NOUN
ejpam-4480	33	22	and	and	CCONJ
ejpam-4480	33	23	corona	corona	PROPN
ejpam-4480	33	24	,	,	PUNCT
ejpam-4480	33	25	and	and	CCONJ
ejpam-4480	33	26	lexicographic	lexicographic	ADJ
ejpam-4480	33	27	product	product	NOUN
ejpam-4480	33	28	of	of	ADP
ejpam-4480	33	29	two	two	NUM
ejpam-4480	33	30	graphs	graph	NOUN
ejpam-4480	33	31	in	in	ADP
ejpam-4480	33	32	terms	term	NOUN
ejpam-4480	33	33	of	of	ADP
ejpam-4480	33	34	the	the	DET
ejpam-4480	33	35	superclique	superclique	ADJ
ejpam-4480	33	36	number	number	NOUN
ejpam-4480	33	37	of	of	ADP
ejpam-4480	33	38	a	a	DET
ejpam-4480	33	39	graph	graph	NOUN
ejpam-4480	33	40	.	.	PUNCT
ejpam-4480	34	1	this	this	DET
ejpam-4480	34	2	work	work	NOUN
ejpam-4480	34	3	is	be	AUX
ejpam-4480	34	4	therefore	therefore	ADV
ejpam-4480	34	5	motivated	motivate	VERB
ejpam-4480	34	6	by	by	ADP
ejpam-4480	34	7	the	the	DET
ejpam-4480	34	8	recent	recent	ADJ
ejpam-4480	34	9	studies	study	NOUN
ejpam-4480	34	10	on	on	ADP
ejpam-4480	34	11	these	these	DET
ejpam-4480	34	12	variations	variation	NOUN
ejpam-4480	34	13	of	of	ADP
ejpam-4480	34	14	strong	strong	ADJ
ejpam-4480	34	15	resolving	resolving	NOUN
ejpam-4480	34	16	set	set	VERB
ejpam-4480	34	17	and	and	CCONJ
ejpam-4480	34	18	strong	strong	ADJ
ejpam-4480	34	19	metric	metric	ADJ
ejpam-4480	34	20	dimension	dimension	NOUN
ejpam-4480	34	21	that	that	PRON
ejpam-4480	34	22	utilize	utilize	VERB
ejpam-4480	34	23	the	the	DET
ejpam-4480	34	24	concepts	concept	NOUN
ejpam-4480	34	25	of	of	ADP
ejpam-4480	34	26	superclique	superclique	ADJ
ejpam-4480	34	27	and	and	CCONJ
ejpam-4480	34	28	superclique	superclique	ADJ
ejpam-4480	34	29	number	number	NOUN
ejpam-4480	34	30	.	.	PUNCT
ejpam-4480	35	1	other	other	ADJ
ejpam-4480	35	2	works	work	NOUN
ejpam-4480	35	3	on	on	ADP
ejpam-4480	35	4	graph	graph	NOUN
ejpam-4480	35	5	-	-	PUNCT
ejpam-4480	35	6	theoretic	theoretic	ADJ
ejpam-4480	35	7	parameters	parameter	NOUN
ejpam-4480	35	8	that	that	PRON
ejpam-4480	35	9	involved	involve	VERB
ejpam-4480	35	10	some	some	DET
ejpam-4480	35	11	binary	binary	ADJ
ejpam-4480	35	12	operations	operation	NOUN
ejpam-4480	35	13	can	can	AUX
ejpam-4480	35	14	be	be	AUX
ejpam-4480	35	15	found	find	VERB
ejpam-4480	35	16	in	in	ADP
ejpam-4480	35	17	[	[	X
ejpam-4480	35	18	3	3	NUM
ejpam-4480	35	19	]	]	PUNCT
ejpam-4480	35	20	,	,	PUNCT
ejpam-4480	35	21	[	[	X
ejpam-4480	35	22	7	7	NUM
ejpam-4480	35	23	]	]	PUNCT
ejpam-4480	35	24	,	,	PUNCT
ejpam-4480	35	25	and	and	CCONJ
ejpam-4480	35	26	[	[	X
ejpam-4480	35	27	11	11	NUM
ejpam-4480	35	28	]	]	SYM
ejpam-4480	35	29	.	.	PUNCT
ejpam-4480	36	1	2	2	X
ejpam-4480	36	2	.	.	NOUN
ejpam-4480	36	3	terminologies	terminology	NOUN
ejpam-4480	36	4	and	and	CCONJ
ejpam-4480	36	5	notations	notation	NOUN
ejpam-4480	36	6	let	let	VERB
ejpam-4480	36	7	g	g	NOUN
ejpam-4480	36	8	=	=	SYM
ejpam-4480	36	9	(	(	PUNCT
ejpam-4480	36	10	v	v	NOUN
ejpam-4480	36	11	(	(	PUNCT
ejpam-4480	36	12	g	g	NOUN
ejpam-4480	36	13	)	)	PUNCT
ejpam-4480	36	14	,	,	PUNCT
ejpam-4480	36	15	e(g	e(g	PROPN
ejpam-4480	36	16	)	)	PUNCT
ejpam-4480	36	17	)	)	PUNCT
ejpam-4480	36	18	be	be	AUX
ejpam-4480	36	19	a	a	DET
ejpam-4480	36	20	simple	simple	ADJ
ejpam-4480	36	21	undirected	undirected	ADJ
ejpam-4480	36	22	graph	graph	NOUN
ejpam-4480	36	23	.	.	PUNCT
ejpam-4480	37	1	the	the	DET
ejpam-4480	37	2	distance	distance	NOUN
ejpam-4480	37	3	between	between	ADP
ejpam-4480	37	4	two	two	NUM
ejpam-4480	37	5	vertices	vertex	NOUN
ejpam-4480	37	6	u	u	NOUN
ejpam-4480	37	7	and	and	CCONJ
ejpam-4480	37	8	v	v	NOUN
ejpam-4480	37	9	of	of	ADP
ejpam-4480	37	10	g	g	NOUN
ejpam-4480	37	11	,	,	PUNCT
ejpam-4480	37	12	denoted	denote	VERB
ejpam-4480	37	13	by	by	ADP
ejpam-4480	37	14	dg(u	dg(u	NOUN
ejpam-4480	37	15	,	,	PUNCT
ejpam-4480	37	16	v	v	NOUN
ejpam-4480	37	17	)	)	PUNCT
ejpam-4480	37	18	,	,	PUNCT
ejpam-4480	37	19	is	be	AUX
ejpam-4480	37	20	equal	equal	ADJ
ejpam-4480	37	21	to	to	ADP
ejpam-4480	37	22	the	the	DET
ejpam-4480	37	23	length	length	NOUN
ejpam-4480	37	24	of	of	ADP
ejpam-4480	37	25	a	a	DET
ejpam-4480	37	26	shortest	short	ADJ
ejpam-4480	37	27	path	path	NOUN
ejpam-4480	37	28	connecting	connect	VERB
ejpam-4480	37	29	u	u	NOUN
ejpam-4480	37	30	and	and	CCONJ
ejpam-4480	37	31	v.	v.	ADP
ejpam-4480	37	32	any	any	DET
ejpam-4480	37	33	path	path	NOUN
ejpam-4480	37	34	connecting	connect	VERB
ejpam-4480	37	35	u	u	NOUN
ejpam-4480	37	36	and	and	CCONJ
ejpam-4480	37	37	v	v	NOUN
ejpam-4480	37	38	of	of	ADP
ejpam-4480	37	39	length	length	NOUN
ejpam-4480	37	40	dg(u	dg(u	ADJ
ejpam-4480	37	41	,	,	PUNCT
ejpam-4480	37	42	v	v	NOUN
ejpam-4480	37	43	)	)	PUNCT
ejpam-4480	37	44	is	be	AUX
ejpam-4480	37	45	called	call	VERB
ejpam-4480	37	46	a	a	DET
ejpam-4480	37	47	u	u	NOUN
ejpam-4480	37	48	-	-	NOUN
ejpam-4480	37	49	v	v	ADJ
ejpam-4480	37	50	geodesic	geodesic	NOUN
ejpam-4480	37	51	.	.	PUNCT
ejpam-4480	38	1	the	the	DET
ejpam-4480	38	2	open	open	ADJ
ejpam-4480	38	3	neighbourhood	neighbourhood	NOUN
ejpam-4480	38	4	of	of	ADP
ejpam-4480	38	5	a	a	DET
ejpam-4480	38	6	vertex	vertex	NOUN
ejpam-4480	38	7	v	v	NOUN
ejpam-4480	38	8	of	of	ADP
ejpam-4480	38	9	g	g	PROPN
ejpam-4480	38	10	is	be	AUX
ejpam-4480	38	11	the	the	DET
ejpam-4480	38	12	set	set	NOUN
ejpam-4480	38	13	ng(v	ng(v	PUNCT
ejpam-4480	38	14	)	)	PUNCT
ejpam-4480	38	15	=	=	SYM
ejpam-4480	39	1	{	{	PUNCT
ejpam-4480	39	2	u	u	NOUN
ejpam-4480	39	3	∈	∈	PROPN
ejpam-4480	39	4	v	v	NOUN
ejpam-4480	39	5	(	(	PUNCT
ejpam-4480	39	6	g	g	NOUN
ejpam-4480	39	7	)	)	PUNCT
ejpam-4480	39	8	:	:	PUNCT
ejpam-4480	39	9	uv	uv	PROPN
ejpam-4480	39	10	∈	∈	PROPN
ejpam-4480	39	11	e(g	e(g	PROPN
ejpam-4480	39	12	)	)	PUNCT
ejpam-4480	39	13	}	}	PUNCT
ejpam-4480	39	14	and	and	CCONJ
ejpam-4480	39	15	its	its	PRON
ejpam-4480	39	16	closed	closed	ADJ
ejpam-4480	39	17	neighbourhood	neighbourhood	NOUN
ejpam-4480	39	18	is	be	AUX
ejpam-4480	39	19	the	the	DET
ejpam-4480	39	20	set	set	NOUN
ejpam-4480	39	21	ng[v	ng[v	NOUN
ejpam-4480	39	22	]	]	X
ejpam-4480	39	23	=	=	SYM
ejpam-4480	39	24	ng(v	ng(v	X
ejpam-4480	39	25	)	)	PUNCT
ejpam-4480	39	26	∪	∪	ADP
ejpam-4480	39	27	{	{	PUNCT
ejpam-4480	39	28	v	v	NOUN
ejpam-4480	39	29	}	}	PUNCT
ejpam-4480	39	30	.	.	PUNCT
ejpam-4480	40	1	the	the	DET
ejpam-4480	40	2	open	open	ADJ
ejpam-4480	40	3	neighbourhood	neighbourhood	NOUN
ejpam-4480	40	4	of	of	ADP
ejpam-4480	40	5	a	a	DET
ejpam-4480	40	6	subset	subset	NOUN
ejpam-4480	40	7	s	s	NOUN
ejpam-4480	40	8	of	of	ADP
ejpam-4480	40	9	v	v	NOUN
ejpam-4480	40	10	(	(	PUNCT
ejpam-4480	40	11	g	g	NOUN
ejpam-4480	40	12	)	)	PUNCT
ejpam-4480	40	13	is	be	AUX
ejpam-4480	40	14	the	the	DET
ejpam-4480	40	15	set	set	NOUN
ejpam-4480	40	16	ng(s	ng(s	NOUN
ejpam-4480	40	17	)	)	PUNCT
ejpam-4480	40	18	=	=	SYM
ejpam-4480	40	19	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-4480	40	20	)	)	PUNCT
ejpam-4480	40	21	and	and	CCONJ
ejpam-4480	40	22	its	its	PRON
ejpam-4480	40	23	closed	closed	ADJ
ejpam-4480	40	24	neighbourhood	neighbourhood	NOUN
ejpam-4480	40	25	is	be	AUX
ejpam-4480	40	26	the	the	DET
ejpam-4480	40	27	set	set	VERB
ejpam-4480	40	28	ng[s	ng[	NOUN
ejpam-4480	40	29	]	]	PUNCT
ejpam-4480	40	30	=	=	SYM
ejpam-4480	40	31	ng(s	ng(s	X
ejpam-4480	40	32	)	)	PUNCT
ejpam-4480	40	33	∪	∪	ADP
ejpam-4480	40	34	s.	s.	PROPN
ejpam-4480	40	35	the	the	DET
ejpam-4480	40	36	degree	degree	NOUN
ejpam-4480	40	37	of	of	ADP
ejpam-4480	40	38	v	v	NOUN
ejpam-4480	40	39	,	,	PUNCT
ejpam-4480	40	40	denoted	denote	VERB
ejpam-4480	40	41	by	by	ADP
ejpam-4480	40	42	degg(v	degg(v	PROPN
ejpam-4480	40	43	)	)	PUNCT
ejpam-4480	40	44	,	,	PUNCT
ejpam-4480	40	45	is	be	AUX
ejpam-4480	40	46	equal	equal	ADJ
ejpam-4480	40	47	to	to	ADP
ejpam-4480	40	48	|ng(v)|	|ng(v)|	NOUN
ejpam-4480	40	49	.	.	PUNCT
ejpam-4480	41	1	a	a	DET
ejpam-4480	41	2	set	set	NOUN
ejpam-4480	41	3	s	s	NOUN
ejpam-4480	41	4	⊆	⊆	NUM
ejpam-4480	41	5	v	v	NOUN
ejpam-4480	41	6	(	(	PUNCT
ejpam-4480	41	7	g	g	NOUN
ejpam-4480	41	8	)	)	PUNCT
ejpam-4480	41	9	is	be	AUX
ejpam-4480	41	10	a	a	DET
ejpam-4480	41	11	dominating	dominating	NOUN
ejpam-4480	41	12	set	set	NOUN
ejpam-4480	41	13	of	of	ADP
ejpam-4480	41	14	g	g	PROPN
ejpam-4480	41	15	if	if	SCONJ
ejpam-4480	41	16	ng[s	ng[	NOUN
ejpam-4480	41	17	]	]	PUNCT
ejpam-4480	41	18	=	=	SYM
ejpam-4480	41	19	v	v	NOUN
ejpam-4480	41	20	(	(	PUNCT
ejpam-4480	41	21	g	g	NOUN
ejpam-4480	41	22	)	)	PUNCT
ejpam-4480	41	23	.	.	PUNCT
ejpam-4480	42	1	the	the	DET
ejpam-4480	42	2	smallest	small	ADJ
ejpam-4480	42	3	cardinality	cardinality	NOUN
ejpam-4480	42	4	of	of	ADP
ejpam-4480	42	5	a	a	DET
ejpam-4480	42	6	dominating	dominating	NOUN
ejpam-4480	42	7	set	set	NOUN
ejpam-4480	42	8	of	of	ADP
ejpam-4480	42	9	g	g	NOUN
ejpam-4480	42	10	,	,	PUNCT
ejpam-4480	42	11	denoted	denote	VERB
ejpam-4480	42	12	by	by	ADP
ejpam-4480	42	13	γ(g	γ(g	PROPN
ejpam-4480	42	14	)	)	PUNCT
ejpam-4480	42	15	,	,	PUNCT
ejpam-4480	42	16	is	be	AUX
ejpam-4480	42	17	called	call	VERB
ejpam-4480	42	18	the	the	DET
ejpam-4480	42	19	domination	domination	NOUN
ejpam-4480	42	20	number	number	NOUN
ejpam-4480	42	21	of	of	ADP
ejpam-4480	42	22	g.	g.	PROPN
ejpam-4480	42	23	a	a	DET
ejpam-4480	42	24	dominating	dominating	NOUN
ejpam-4480	42	25	set	set	NOUN
ejpam-4480	42	26	of	of	ADP
ejpam-4480	42	27	g	g	NOUN
ejpam-4480	42	28	with	with	ADP
ejpam-4480	42	29	with	with	ADP
ejpam-4480	42	30	cardinality	cardinality	PROPN
ejpam-4480	42	31	γ(g	γ(g	PROPN
ejpam-4480	42	32	)	)	PUNCT
ejpam-4480	42	33	is	be	AUX
ejpam-4480	42	34	called	call	VERB
ejpam-4480	42	35	a	a	DET
ejpam-4480	42	36	γ	γ	NOUN
ejpam-4480	42	37	-	-	PUNCT
ejpam-4480	42	38	set	set	NOUN
ejpam-4480	42	39	of	of	ADP
ejpam-4480	42	40	g.	g.	PROPN
ejpam-4480	42	41	a	a	DET
ejpam-4480	42	42	set	set	NOUN
ejpam-4480	42	43	s	s	PROPN
ejpam-4480	42	44	⊆	⊆	NUM
ejpam-4480	42	45	v	v	NOUN
ejpam-4480	42	46	(	(	PUNCT
ejpam-4480	42	47	g	g	NOUN
ejpam-4480	42	48	)	)	PUNCT
ejpam-4480	42	49	is	be	AUX
ejpam-4480	42	50	a	a	DET
ejpam-4480	42	51	clique	clique	NOUN
ejpam-4480	42	52	in	in	ADP
ejpam-4480	42	53	a	a	DET
ejpam-4480	42	54	graph	graph	NOUN
ejpam-4480	42	55	g	g	NOUN
ejpam-4480	42	56	if	if	SCONJ
ejpam-4480	42	57	the	the	DET
ejpam-4480	42	58	graph	graph	NOUN
ejpam-4480	42	59	g[s	g[	NOUN
ejpam-4480	42	60	]	]	PUNCT
ejpam-4480	42	61	induced	induce	VERB
ejpam-4480	42	62	by	by	ADP
ejpam-4480	42	63	s	s	PROPN
ejpam-4480	42	64	is	be	AUX
ejpam-4480	42	65	a	a	DET
ejpam-4480	42	66	complete	complete	ADJ
ejpam-4480	42	67	subgraph	subgraph	NOUN
ejpam-4480	42	68	of	of	ADP
ejpam-4480	42	69	g.	g.	PROPN
ejpam-4480	43	1	a	a	DET
ejpam-4480	43	2	clique	clique	NOUN
ejpam-4480	43	3	c	c	PROPN
ejpam-4480	43	4	in	in	ADP
ejpam-4480	43	5	g	g	PROPN
ejpam-4480	43	6	is	be	AUX
ejpam-4480	43	7	called	call	VERB
ejpam-4480	43	8	a	a	DET
ejpam-4480	43	9	superclique	superclique	NOUN
ejpam-4480	43	10	if	if	SCONJ
ejpam-4480	43	11	for	for	ADP
ejpam-4480	43	12	every	every	DET
ejpam-4480	43	13	pair	pair	NOUN
ejpam-4480	43	14	of	of	ADP
ejpam-4480	43	15	distinct	distinct	ADJ
ejpam-4480	43	16	vertices	vertex	NOUN
ejpam-4480	43	17	u	u	NOUN
ejpam-4480	43	18	,	,	PUNCT
ejpam-4480	43	19	v	v	NOUN
ejpam-4480	43	20	∈	∈	ADJ
ejpam-4480	43	21	c	c	NOUN
ejpam-4480	43	22	,	,	PUNCT
ejpam-4480	43	23	there	there	PRON
ejpam-4480	43	24	exists	exist	VERB
ejpam-4480	43	25	w	w	PROPN
ejpam-4480	43	26	∈	∈	PROPN
ejpam-4480	43	27	v	v	NOUN
ejpam-4480	43	28	(	(	PUNCT
ejpam-4480	43	29	g)\c	g)\c	VERB
ejpam-4480	43	30	such	such	DET
ejpam-4480	43	31	that	that	DET
ejpam-4480	43	32	w	w	PROPN
ejpam-4480	43	33	∈	∈	PROPN
ejpam-4480	43	34	ng(u)\ng(v	ng(u)\ng(v	NOUN
ejpam-4480	43	35	)	)	PUNCT
ejpam-4480	43	36	or	or	CCONJ
ejpam-4480	43	37	w	w	PROPN
ejpam-4480	43	38	∈	∈	PROPN
ejpam-4480	43	39	ng(v)\ng(u	ng(v)\ng(u	ADJ
ejpam-4480	43	40	)	)	PUNCT
ejpam-4480	43	41	.	.	PUNCT
ejpam-4480	44	1	a	a	DET
ejpam-4480	44	2	superclique	superclique	NOUN
ejpam-4480	44	3	c	c	PROPN
ejpam-4480	44	4	ing	ing	NOUN
ejpam-4480	44	5	is	be	AUX
ejpam-4480	44	6	called	call	VERB
ejpam-4480	44	7	a	a	DET
ejpam-4480	44	8	point	point	NOUN
ejpam-4480	44	9	-	-	PUNCT
ejpam-4480	44	10	wise	wise	ADJ
ejpam-4480	44	11	non	non	ADJ
ejpam-4480	44	12	-	-	ADJ
ejpam-4480	44	13	dominated	dominate	VERB
ejpam-4480	44	14	superclique	superclique	NOUN
ejpam-4480	44	15	if	if	SCONJ
ejpam-4480	44	16	for	for	ADP
ejpam-4480	44	17	every	every	DET
ejpam-4480	44	18	u	u	PROPN
ejpam-4480	44	19	∈	∈	PROPN
ejpam-4480	44	20	c	c	NOUN
ejpam-4480	44	21	,	,	PUNCT
ejpam-4480	44	22	there	there	PRON
ejpam-4480	44	23	exists	exist	VERB
ejpam-4480	44	24	v	v	ADP
ejpam-4480	44	25	∈	∈	PROPN
ejpam-4480	44	26	v	v	NOUN
ejpam-4480	44	27	(	(	PUNCT
ejpam-4480	44	28	g	g	NOUN
ejpam-4480	44	29	)	)	PUNCT
ejpam-4480	44	30	\c	\c	ADP
ejpam-4480	45	1	such	such	ADJ
ejpam-4480	45	2	that	that	DET
ejpam-4480	45	3	uv	uv	NOUN
ejpam-4480	45	4	/∈	/∈	PUNCT
ejpam-4480	45	5	e(g	e(g	PROPN
ejpam-4480	45	6	)	)	PUNCT
ejpam-4480	45	7	.	.	PUNCT
ejpam-4480	46	1	a	a	DET
ejpam-4480	46	2	superclique	superclique	ADJ
ejpam-4480	46	3	(	(	PUNCT
ejpam-4480	46	4	resp	resp	NOUN
ejpam-4480	46	5	.	.	PUNCT
ejpam-4480	47	1	point	point	NOUN
ejpam-4480	47	2	-	-	PUNCT
ejpam-4480	47	3	wise	wise	ADJ
ejpam-4480	47	4	non	non	ADJ
ejpam-4480	47	5	-	-	ADJ
ejpam-4480	47	6	dominated	dominate	VERB
ejpam-4480	47	7	superclique	superclique	NOUN
ejpam-4480	47	8	)	)	PUNCT
ejpam-4480	48	1	c	c	NOUN
ejpam-4480	48	2	is	be	AUX
ejpam-4480	48	3	maximum	maximum	ADJ
ejpam-4480	48	4	in	in	ADP
ejpam-4480	48	5	g	g	PROPN
ejpam-4480	48	6	if	if	SCONJ
ejpam-4480	48	7	|c|	|c|	PROPN
ejpam-4480	48	8	≥	≥	PRON
ejpam-4480	48	9	|c	|c	VERB
ejpam-4480	48	10	′|	′|	NUM
ejpam-4480	48	11	for	for	ADP
ejpam-4480	48	12	all	all	DET
ejpam-4480	48	13	supercliques	superclique	NOUN
ejpam-4480	48	14	(	(	PUNCT
ejpam-4480	48	15	resp	resp	NOUN
ejpam-4480	48	16	.	.	PUNCT
ejpam-4480	49	1	pointwise	pointwise	PROPN
ejpam-4480	49	2	nondominated	nondominate	VERB
ejpam-4480	49	3	supercliques	superclique	NOUN
ejpam-4480	49	4	)	)	PUNCT
ejpam-4480	50	1	c	c	NOUN
ejpam-4480	50	2	′	′	NOUN
ejpam-4480	50	3	in	in	ADP
ejpam-4480	50	4	g.	g.	PROPN
ejpam-4480	51	1	the	the	DET
ejpam-4480	51	2	superclique	superclique	ADJ
ejpam-4480	51	3	number	number	NOUN
ejpam-4480	51	4	(	(	PUNCT
ejpam-4480	51	5	resp	resp	NOUN
ejpam-4480	51	6	.	.	PUNCT
ejpam-4480	52	1	pointwise	pointwise	VERB
ejpam-4480	52	2	non	non	ADJ
ejpam-4480	52	3	-	-	ADJ
ejpam-4480	52	4	dominated	dominate	VERB
ejpam-4480	52	5	superclique	superclique	ADJ
ejpam-4480	52	6	number	number	NOUN
ejpam-4480	52	7	)	)	PUNCT
ejpam-4480	52	8	,	,	PUNCT
ejpam-4480	52	9	denoted	denote	VERB
ejpam-4480	52	10	by	by	ADP
ejpam-4480	52	11	ωs(g	ωs(g	NOUN
ejpam-4480	52	12	)	)	PUNCT
ejpam-4480	52	13	(	(	PUNCT
ejpam-4480	52	14	resp	resp	NOUN
ejpam-4480	52	15	.	.	PUNCT
ejpam-4480	53	1	ωpnds(g	ωpnds(g	NUM
ejpam-4480	53	2	)	)	PUNCT
ejpam-4480	53	3	)	)	PUNCT
ejpam-4480	53	4	of	of	ADP
ejpam-4480	53	5	g	g	PROPN
ejpam-4480	53	6	is	be	AUX
ejpam-4480	53	7	the	the	DET
ejpam-4480	53	8	cardinality	cardinality	NOUN
ejpam-4480	53	9	of	of	ADP
ejpam-4480	53	10	a	a	DET
ejpam-4480	53	11	maximum	maximum	ADJ
ejpam-4480	53	12	superclique	superclique	NOUN
ejpam-4480	53	13	(	(	PUNCT
ejpam-4480	53	14	resp	resp	NOUN
ejpam-4480	53	15	.	.	PUNCT
ejpam-4480	54	1	maximum	maximum	PROPN
ejpam-4480	54	2	pointwise	pointwise	PROPN
ejpam-4480	54	3	non	non	ADJ
ejpam-4480	54	4	-	-	ADJ
ejpam-4480	54	5	dominated	dominate	VERB
ejpam-4480	54	6	superclique	superclique	NOUN
ejpam-4480	54	7	)	)	PUNCT
ejpam-4480	54	8	in	in	ADP
ejpam-4480	54	9	g.	g.	PROPN
ejpam-4480	54	10	the	the	DET
ejpam-4480	54	11	shadow	shadow	NOUN
ejpam-4480	54	12	graph	graph	NOUN
ejpam-4480	54	13	s(g	s(g	PROPN
ejpam-4480	54	14	)	)	PUNCT
ejpam-4480	54	15	of	of	ADP
ejpam-4480	54	16	a	a	DET
ejpam-4480	54	17	graph	graph	NOUN
ejpam-4480	54	18	g	g	NOUN
ejpam-4480	54	19	is	be	AUX
ejpam-4480	54	20	the	the	DET
ejpam-4480	54	21	graph	graph	NOUN
ejpam-4480	54	22	obtained	obtain	VERB
ejpam-4480	54	23	by	by	ADP
ejpam-4480	54	24	taking	take	VERB
ejpam-4480	54	25	two	two	NUM
ejpam-4480	54	26	copies	copy	NOUN
ejpam-4480	54	27	of	of	ADP
ejpam-4480	54	28	g	g	NOUN
ejpam-4480	54	29	,	,	PUNCT
ejpam-4480	54	30	say	say	VERB
ejpam-4480	54	31	g1	g1	PROPN
ejpam-4480	54	32	and	and	CCONJ
ejpam-4480	54	33	g2	g2	PROPN
ejpam-4480	54	34	,	,	PUNCT
ejpam-4480	54	35	and	and	CCONJ
ejpam-4480	54	36	joining	join	VERB
ejpam-4480	54	37	each	each	DET
ejpam-4480	54	38	vertex	vertex	NOUN
ejpam-4480	54	39	u	u	NOUN
ejpam-4480	54	40	∈	∈	PROPN
ejpam-4480	54	41	v	v	NOUN
ejpam-4480	54	42	(	(	PUNCT
ejpam-4480	54	43	g1	g1	PROPN
ejpam-4480	54	44	)	)	PUNCT
ejpam-4480	54	45	to	to	ADP
ejpam-4480	54	46	the	the	DET
ejpam-4480	54	47	neighbors	neighbor	NOUN
ejpam-4480	54	48	of	of	ADP
ejpam-4480	54	49	the	the	DET
ejpam-4480	54	50	corresponding	corresponding	ADJ
ejpam-4480	54	51	vertex	vertex	NOUN
ejpam-4480	54	52	u′	u′	PROPN
ejpam-4480	54	53	∈	∈	PROPN
ejpam-4480	54	54	v	v	NOUN
ejpam-4480	54	55	(	(	PUNCT
ejpam-4480	54	56	g2	g2	PROPN
ejpam-4480	54	57	)	)	PUNCT
ejpam-4480	54	58	.	.	PUNCT
ejpam-4480	55	1	for	for	ADP
ejpam-4480	55	2	a	a	DET
ejpam-4480	55	3	graph	graph	NOUN
ejpam-4480	55	4	g	g	NOUN
ejpam-4480	55	5	,	,	PUNCT
ejpam-4480	55	6	the	the	DET
ejpam-4480	55	7	complementary	complementary	ADJ
ejpam-4480	55	8	prism	prism	NOUN
ejpam-4480	55	9	,	,	PUNCT
ejpam-4480	55	10	denoted	denote	VERB
ejpam-4480	55	11	by	by	ADP
ejpam-4480	55	12	gg	gg	PROPN
ejpam-4480	55	13	,	,	PUNCT
ejpam-4480	55	14	is	be	AUX
ejpam-4480	55	15	formed	form	VERB
ejpam-4480	55	16	from	from	ADP
ejpam-4480	55	17	the	the	DET
ejpam-4480	55	18	disjoint	disjoint	PROPN
ejpam-4480	55	19	union	union	NOUN
ejpam-4480	55	20	of	of	ADP
ejpam-4480	55	21	g	g	PROPN
ejpam-4480	55	22	and	and	CCONJ
ejpam-4480	55	23	its	its	PRON
ejpam-4480	55	24	complement	complement	NOUN
ejpam-4480	55	25	g	g	NOUN
ejpam-4480	55	26	by	by	ADP
ejpam-4480	55	27	adding	add	VERB
ejpam-4480	55	28	a	a	DET
ejpam-4480	55	29	perfect	perfect	ADJ
ejpam-4480	55	30	matching	matching	NOUN
ejpam-4480	55	31	between	between	ADP
ejpam-4480	55	32	corresponding	corresponding	ADJ
ejpam-4480	55	33	vertices	vertex	NOUN
ejpam-4480	55	34	of	of	ADP
ejpam-4480	55	35	g	g	PROPN
ejpam-4480	55	36	and	and	CCONJ
ejpam-4480	55	37	g.	g.	NOUN
ejpam-4480	55	38	for	for	ADP
ejpam-4480	55	39	each	each	DET
ejpam-4480	55	40	v	v	NUM
ejpam-4480	55	41	∈	∈	PROPN
ejpam-4480	55	42	v	v	NOUN
ejpam-4480	55	43	(	(	PUNCT
ejpam-4480	55	44	g	g	NOUN
ejpam-4480	55	45	)	)	PUNCT
ejpam-4480	55	46	,	,	PUNCT
ejpam-4480	55	47	let	let	VERB
ejpam-4480	55	48	v	v	PART
ejpam-4480	55	49	denote	denote	VERB
ejpam-4480	55	50	the	the	DET
ejpam-4480	55	51	vertex	vertex	NOUN
ejpam-4480	55	52	corresponding	correspond	VERB
ejpam-4480	55	53	to	to	ADP
ejpam-4480	55	54	v	v	NOUN
ejpam-4480	55	55	in	in	ADP
ejpam-4480	55	56	g.	g.	PROPN
ejpam-4480	55	57	in	in	ADP
ejpam-4480	55	58	simple	simple	ADJ
ejpam-4480	55	59	terms	term	NOUN
ejpam-4480	55	60	,	,	PUNCT
ejpam-4480	55	61	the	the	DET
ejpam-4480	55	62	graph	graph	NOUN
ejpam-4480	55	63	gg	gg	NOUN
ejpam-4480	55	64	is	be	AUX
ejpam-4480	55	65	formed	form	VERB
ejpam-4480	55	66	from	from	ADP
ejpam-4480	55	67	g	g	PROPN
ejpam-4480	55	68	∪g	∪g	NUM
ejpam-4480	55	69	by	by	ADP
ejpam-4480	55	70	adding	add	VERB
ejpam-4480	55	71	the	the	DET
ejpam-4480	55	72	edge	edge	NOUN
ejpam-4480	55	73	vv	vv	NOUN
ejpam-4480	55	74	for	for	ADP
ejpam-4480	55	75	every	every	DET
ejpam-4480	55	76	vertex	vertex	NOUN
ejpam-4480	55	77	v	v	ADP
ejpam-4480	55	78	∈	∈	NOUN
ejpam-4480	55	79	v	v	NOUN
ejpam-4480	55	80	(	(	PUNCT
ejpam-4480	55	81	g	g	NOUN
ejpam-4480	55	82	)	)	PUNCT
ejpam-4480	55	83	.	.	PUNCT
ejpam-4480	56	1	r.	r.	PROPN
ejpam-4480	56	2	dela	dela	PROPN
ejpam-4480	56	3	cerna	cerna	PROPN
ejpam-4480	56	4	,	,	PUNCT
ejpam-4480	56	5	s.	s.	PROPN
ejpam-4480	56	6	canoy	canoy	PROPN
ejpam-4480	56	7	,	,	PUNCT
ejpam-4480	56	8	jr	jr	PROPN
ejpam-4480	56	9	.	.	PROPN
ejpam-4480	56	10	/	/	SYM
ejpam-4480	56	11	eur	eur	PROPN
ejpam-4480	56	12	.	.	PUNCT
ejpam-4480	57	1	j.	j.	PROPN
ejpam-4480	57	2	pure	pure	PROPN
ejpam-4480	57	3	appl	appl	PROPN
ejpam-4480	57	4	.	.	PROPN
ejpam-4480	57	5	math	math	PROPN
ejpam-4480	57	6	,	,	PUNCT
ejpam-4480	57	7	15	15	NUM
ejpam-4480	57	8	(	(	PUNCT
ejpam-4480	57	9	3	3	NUM
ejpam-4480	57	10	)	)	PUNCT
ejpam-4480	57	11	(	(	PUNCT
ejpam-4480	57	12	2022	2022	NUM
ejpam-4480	57	13	)	)	PUNCT
ejpam-4480	57	14	,	,	PUNCT
ejpam-4480	57	15	1217	1217	NUM
ejpam-4480	57	16	-	-	SYM
ejpam-4480	57	17	1228	1228	NUM
ejpam-4480	57	18	1219	1219	NUM
ejpam-4480	57	19	let	let	VERB
ejpam-4480	57	20	g	g	NOUN
ejpam-4480	57	21	and	and	CCONJ
ejpam-4480	57	22	h	h	PROPN
ejpam-4480	57	23	be	be	AUX
ejpam-4480	57	24	graphs	graph	NOUN
ejpam-4480	57	25	.	.	PUNCT
ejpam-4480	58	1	the	the	DET
ejpam-4480	58	2	join	join	NOUN
ejpam-4480	58	3	of	of	ADP
ejpam-4480	58	4	g	g	PROPN
ejpam-4480	58	5	and	and	CCONJ
ejpam-4480	58	6	h	h	NOUN
ejpam-4480	58	7	,	,	PUNCT
ejpam-4480	58	8	denoted	denote	VERB
ejpam-4480	58	9	by	by	ADP
ejpam-4480	58	10	g	g	PROPN
ejpam-4480	58	11	+	+	NOUN
ejpam-4480	58	12	h	h	NOUN
ejpam-4480	58	13	is	be	AUX
ejpam-4480	58	14	the	the	DET
ejpam-4480	58	15	graph	graph	NOUN
ejpam-4480	58	16	with	with	ADP
ejpam-4480	58	17	vertex	vertex	NOUN
ejpam-4480	58	18	set	set	VERB
ejpam-4480	58	19	v	v	NOUN
ejpam-4480	58	20	(	(	PUNCT
ejpam-4480	58	21	g+h	g+h	NOUN
ejpam-4480	58	22	)	)	PUNCT
ejpam-4480	58	23	=	=	SYM
ejpam-4480	58	24	v	v	NOUN
ejpam-4480	58	25	(	(	PUNCT
ejpam-4480	58	26	g)∪	g)∪	VERB
ejpam-4480	58	27	v	v	NUM
ejpam-4480	58	28	(	(	PUNCT
ejpam-4480	58	29	h	h	NOUN
ejpam-4480	58	30	)	)	PUNCT
ejpam-4480	58	31	and	and	CCONJ
ejpam-4480	58	32	edge	edge	NOUN
ejpam-4480	58	33	set	set	VERB
ejpam-4480	58	34	e(g+h	e(g+h	NUM
ejpam-4480	58	35	)	)	PUNCT
ejpam-4480	59	1	=	=	SYM
ejpam-4480	59	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-4480	59	3	{	{	PUNCT
ejpam-4480	59	4	uv	uv	NOUN
ejpam-4480	59	5	:	:	PUNCT
ejpam-4480	59	6	u	u	PROPN
ejpam-4480	59	7	∈	∈	PROPN
ejpam-4480	59	8	v	v	ADP
ejpam-4480	59	9	(	(	PUNCT
ejpam-4480	59	10	g	g	NOUN
ejpam-4480	59	11	)	)	PUNCT
ejpam-4480	59	12	,	,	PUNCT
ejpam-4480	59	13	v	v	X
ejpam-4480	59	14	∈	∈	PROPN
ejpam-4480	59	15	v	v	NOUN
ejpam-4480	59	16	(	(	PUNCT
ejpam-4480	59	17	h	h	NOUN
ejpam-4480	59	18	)	)	PUNCT
ejpam-4480	59	19	}	}	PUNCT
ejpam-4480	59	20	.	.	PUNCT
ejpam-4480	60	1	the	the	DET
ejpam-4480	60	2	corona	corona	NOUN
ejpam-4480	60	3	of	of	ADP
ejpam-4480	60	4	g	g	PROPN
ejpam-4480	60	5	andh	andh	NOUN
ejpam-4480	60	6	,	,	PUNCT
ejpam-4480	60	7	denoted	denote	VERB
ejpam-4480	60	8	by	by	ADP
ejpam-4480	60	9	g	g	PROPN
ejpam-4480	60	10	◦	◦	NOUN
ejpam-4480	60	11	h	h	NOUN
ejpam-4480	60	12	,	,	PUNCT
ejpam-4480	60	13	is	be	AUX
ejpam-4480	60	14	the	the	DET
ejpam-4480	60	15	graph	graph	NOUN
ejpam-4480	60	16	obtained	obtain	VERB
ejpam-4480	60	17	from	from	ADP
ejpam-4480	60	18	g	g	NOUN
ejpam-4480	60	19	by	by	ADP
ejpam-4480	60	20	taking	take	VERB
ejpam-4480	60	21	a	a	DET
ejpam-4480	60	22	copy	copy	NOUN
ejpam-4480	60	23	hv	hv	PROPN
ejpam-4480	60	24	of	of	ADP
ejpam-4480	60	25	h	h	PROPN
ejpam-4480	60	26	and	and	CCONJ
ejpam-4480	60	27	forming	form	VERB
ejpam-4480	60	28	the	the	DET
ejpam-4480	60	29	join	join	NOUN
ejpam-4480	60	30	⟨v⟩+hv	⟨v⟩+hv	PROPN
ejpam-4480	60	31	=	=	PROPN
ejpam-4480	60	32	v+hv	v+hv	PROPN
ejpam-4480	60	33	for	for	ADP
ejpam-4480	60	34	each	each	DET
ejpam-4480	60	35	v	v	NUM
ejpam-4480	60	36	∈	∈	PROPN
ejpam-4480	60	37	v	v	NOUN
ejpam-4480	60	38	(	(	PUNCT
ejpam-4480	60	39	g	g	NOUN
ejpam-4480	60	40	)	)	PUNCT
ejpam-4480	60	41	.	.	PUNCT
ejpam-4480	61	1	the	the	DET
ejpam-4480	61	2	lexicographic	lexicographic	ADJ
ejpam-4480	61	3	product	product	NOUN
ejpam-4480	61	4	of	of	ADP
ejpam-4480	61	5	graphs	graph	NOUN
ejpam-4480	61	6	g	g	PROPN
ejpam-4480	61	7	and	and	CCONJ
ejpam-4480	61	8	h	h	NOUN
ejpam-4480	61	9	,	,	PUNCT
ejpam-4480	61	10	denoted	denote	VERB
ejpam-4480	61	11	by	by	ADP
ejpam-4480	61	12	g[h	g[h	NOUN
ejpam-4480	61	13	]	]	PUNCT
ejpam-4480	61	14	,	,	PUNCT
ejpam-4480	61	15	is	be	AUX
ejpam-4480	61	16	the	the	DET
ejpam-4480	61	17	graph	graph	NOUN
ejpam-4480	61	18	with	with	ADP
ejpam-4480	61	19	vertex	vertex	NOUN
ejpam-4480	61	20	set	set	VERB
ejpam-4480	61	21	v	v	NOUN
ejpam-4480	61	22	(	(	PUNCT
ejpam-4480	61	23	g[h	g[h	PROPN
ejpam-4480	61	24	]	]	PUNCT
ejpam-4480	61	25	)	)	PUNCT
ejpam-4480	61	26	=	=	SYM
ejpam-4480	61	27	v	v	X
ejpam-4480	61	28	(	(	PUNCT
ejpam-4480	61	29	g)×v	g)×v	PROPN
ejpam-4480	61	30	(	(	PUNCT
ejpam-4480	61	31	h	h	NOUN
ejpam-4480	61	32	)	)	PUNCT
ejpam-4480	61	33	such	such	ADJ
ejpam-4480	61	34	that	that	SCONJ
ejpam-4480	61	35	(	(	PUNCT
ejpam-4480	61	36	v	v	NOUN
ejpam-4480	61	37	,	,	PUNCT
ejpam-4480	61	38	a)(u	a)(u	ADJ
ejpam-4480	61	39	,	,	PUNCT
ejpam-4480	61	40	b	b	X
ejpam-4480	61	41	)	)	PUNCT
ejpam-4480	61	42	∈	∈	NOUN
ejpam-4480	61	43	e(g[h	e(g[h	NOUN
ejpam-4480	61	44	]	]	PUNCT
ejpam-4480	61	45	)	)	PUNCT
ejpam-4480	62	1	if	if	SCONJ
ejpam-4480	62	2	and	and	CCONJ
ejpam-4480	62	3	only	only	ADV
ejpam-4480	62	4	if	if	SCONJ
ejpam-4480	62	5	either	either	DET
ejpam-4480	62	6	uv	uv	PROPN
ejpam-4480	62	7	∈	∈	PROPN
ejpam-4480	62	8	e(g	e(g	PROPN
ejpam-4480	62	9	)	)	PUNCT
ejpam-4480	62	10	or	or	CCONJ
ejpam-4480	62	11	u	u	X
ejpam-4480	62	12	=	=	PROPN
ejpam-4480	62	13	v	v	PROPN
ejpam-4480	62	14	and	and	CCONJ
ejpam-4480	62	15	ab	ab	PROPN
ejpam-4480	62	16	∈	∈	PROPN
ejpam-4480	62	17	e(h	e(h	PROPN
ejpam-4480	62	18	)	)	PUNCT
ejpam-4480	62	19	.	.	PUNCT
ejpam-4480	63	1	the	the	DET
ejpam-4480	63	2	cartesian	cartesian	ADJ
ejpam-4480	63	3	product	product	NOUN
ejpam-4480	63	4	of	of	ADP
ejpam-4480	63	5	g	g	PROPN
ejpam-4480	63	6	and	and	CCONJ
ejpam-4480	63	7	h	h	NOUN
ejpam-4480	63	8	,	,	PUNCT
ejpam-4480	63	9	denoted	denote	VERB
ejpam-4480	63	10	by	by	ADP
ejpam-4480	63	11	g	g	PROPN
ejpam-4480	63	12	□	□	PROPN
ejpam-4480	63	13	h	h	NOUN
ejpam-4480	63	14	,	,	PUNCT
ejpam-4480	63	15	is	be	AUX
ejpam-4480	63	16	the	the	DET
ejpam-4480	63	17	graph	graph	NOUN
ejpam-4480	63	18	with	with	ADP
ejpam-4480	63	19	vertex	vertex	NOUN
ejpam-4480	63	20	set	set	VERB
ejpam-4480	63	21	v	v	NOUN
ejpam-4480	63	22	(	(	PUNCT
ejpam-4480	63	23	g[h	g[h	PROPN
ejpam-4480	63	24	]	]	PUNCT
ejpam-4480	63	25	)	)	PUNCT
ejpam-4480	63	26	=	=	SYM
ejpam-4480	63	27	v	v	X
ejpam-4480	63	28	(	(	PUNCT
ejpam-4480	63	29	g	g	NOUN
ejpam-4480	63	30	)	)	PUNCT
ejpam-4480	63	31	×	×	NOUN
ejpam-4480	63	32	v	v	NOUN
ejpam-4480	63	33	(	(	PUNCT
ejpam-4480	63	34	h	h	NOUN
ejpam-4480	63	35	)	)	PUNCT
ejpam-4480	63	36	such	such	ADJ
ejpam-4480	63	37	that	that	SCONJ
ejpam-4480	63	38	(	(	PUNCT
ejpam-4480	63	39	v	v	NOUN
ejpam-4480	63	40	,	,	PUNCT
ejpam-4480	63	41	a)(u	a)(u	ADJ
ejpam-4480	63	42	,	,	PUNCT
ejpam-4480	63	43	b	b	X
ejpam-4480	63	44	)	)	PUNCT
ejpam-4480	63	45	∈	∈	NOUN
ejpam-4480	63	46	e(g[h	e(g[h	NOUN
ejpam-4480	63	47	]	]	PUNCT
ejpam-4480	63	48	)	)	PUNCT
ejpam-4480	63	49	if	if	SCONJ
ejpam-4480	63	50	and	and	CCONJ
ejpam-4480	63	51	only	only	ADV
ejpam-4480	63	52	if	if	SCONJ
ejpam-4480	63	53	either	either	DET
ejpam-4480	63	54	uv	uv	PROPN
ejpam-4480	63	55	∈	∈	PROPN
ejpam-4480	63	56	e(g	e(g	PROPN
ejpam-4480	63	57	)	)	PUNCT
ejpam-4480	63	58	and	and	CCONJ
ejpam-4480	63	59	a	a	DET
ejpam-4480	63	60	=	=	SYM
ejpam-4480	63	61	b	b	NOUN
ejpam-4480	63	62	or	or	CCONJ
ejpam-4480	63	63	u	u	PROPN
ejpam-4480	63	64	=	=	PROPN
ejpam-4480	63	65	v	v	PROPN
ejpam-4480	63	66	and	and	CCONJ
ejpam-4480	63	67	ab	ab	PROPN
ejpam-4480	63	68	∈	∈	PROPN
ejpam-4480	63	69	e(h	e(h	PROPN
ejpam-4480	63	70	)	)	PUNCT
ejpam-4480	63	71	.	.	PUNCT
ejpam-4480	64	1	we	we	PRON
ejpam-4480	64	2	note	note	VERB
ejpam-4480	64	3	that	that	SCONJ
ejpam-4480	64	4	every	every	DET
ejpam-4480	64	5	non	non	ADJ
ejpam-4480	64	6	-	-	ADJ
ejpam-4480	64	7	empty	empty	ADJ
ejpam-4480	64	8	subset	subset	NOUN
ejpam-4480	64	9	c	c	NOUN
ejpam-4480	64	10	of	of	ADP
ejpam-4480	64	11	v	v	PROPN
ejpam-4480	64	12	(	(	PUNCT
ejpam-4480	64	13	g	g	NOUN
ejpam-4480	64	14	)	)	PUNCT
ejpam-4480	64	15	×	×	NOUN
ejpam-4480	64	16	v	v	NOUN
ejpam-4480	64	17	(	(	PUNCT
ejpam-4480	64	18	h	h	NOUN
ejpam-4480	64	19	)	)	PUNCT
ejpam-4480	64	20	can	can	AUX
ejpam-4480	64	21	be	be	AUX
ejpam-4480	64	22	expressed	express	VERB
ejpam-4480	64	23	as	as	ADP
ejpam-4480	64	24	c	c	X
ejpam-4480	64	25	=	=	SYM
ejpam-4480	64	26	∪x∈s	∪x∈s	PROPN
ejpam-4480	65	1	[	[	X
ejpam-4480	65	2	{	{	PUNCT
ejpam-4480	65	3	x	x	NOUN
ejpam-4480	65	4	}	}	PUNCT
ejpam-4480	65	5	×	×	PROPN
ejpam-4480	65	6	tx	tx	PROPN
ejpam-4480	65	7	]	]	X
ejpam-4480	65	8	,	,	PUNCT
ejpam-4480	65	9	where	where	SCONJ
ejpam-4480	65	10	s	s	VERB
ejpam-4480	65	11	⊆	⊆	NUM
ejpam-4480	65	12	v	v	NOUN
ejpam-4480	65	13	(	(	PUNCT
ejpam-4480	65	14	g	g	NOUN
ejpam-4480	65	15	)	)	PUNCT
ejpam-4480	65	16	and	and	CCONJ
ejpam-4480	65	17	tx	tx	VERB
ejpam-4480	65	18	=	=	PUNCT
ejpam-4480	65	19	{	{	PUNCT
ejpam-4480	65	20	a	a	DET
ejpam-4480	65	21	∈	∈	PROPN
ejpam-4480	65	22	v	v	ADP
ejpam-4480	65	23	(	(	PUNCT
ejpam-4480	65	24	h	h	NOUN
ejpam-4480	65	25	)	)	PUNCT
ejpam-4480	65	26	:	:	PUNCT
ejpam-4480	65	27	(	(	PUNCT
ejpam-4480	65	28	x	x	X
ejpam-4480	65	29	,	,	PUNCT
ejpam-4480	65	30	a	a	PRON
ejpam-4480	65	31	)	)	PUNCT
ejpam-4480	65	32	∈	∈	PROPN
ejpam-4480	65	33	c	c	NOUN
ejpam-4480	65	34	}	}	PUNCT
ejpam-4480	65	35	for	for	ADP
ejpam-4480	65	36	each	each	DET
ejpam-4480	65	37	x	x	PROPN
ejpam-4480	65	38	∈	∈	PROPN
ejpam-4480	65	39	s.	s.	PROPN
ejpam-4480	65	40	3	3	NUM
ejpam-4480	65	41	.	.	PROPN
ejpam-4480	65	42	results	result	VERB
ejpam-4480	65	43	two	two	NUM
ejpam-4480	65	44	adjacent	adjacent	ADJ
ejpam-4480	65	45	vertices	vertex	NOUN
ejpam-4480	65	46	v	v	NOUN
ejpam-4480	65	47	and	and	CCONJ
ejpam-4480	65	48	w	w	NOUN
ejpam-4480	65	49	of	of	ADP
ejpam-4480	65	50	a	a	DET
ejpam-4480	65	51	graph	graph	NOUN
ejpam-4480	65	52	g	g	NOUN
ejpam-4480	65	53	are	be	AUX
ejpam-4480	65	54	true	true	ADJ
ejpam-4480	65	55	twins	twin	NOUN
ejpam-4480	65	56	if	if	SCONJ
ejpam-4480	65	57	ng[v	ng[v	NOUN
ejpam-4480	65	58	]	]	X
ejpam-4480	65	59	=	=	SYM
ejpam-4480	65	60	ng[w	ng[w	PROPN
ejpam-4480	65	61	]	]	PUNCT
ejpam-4480	65	62	.	.	PUNCT
ejpam-4480	66	1	theorem	theorem	NOUN
ejpam-4480	66	2	1	1	X
ejpam-4480	66	3	.	.	PUNCT
ejpam-4480	67	1	let	let	VERB
ejpam-4480	67	2	g	g	NOUN
ejpam-4480	67	3	be	be	AUX
ejpam-4480	67	4	any	any	DET
ejpam-4480	67	5	graph	graph	NOUN
ejpam-4480	67	6	.	.	PUNCT
ejpam-4480	68	1	then	then	ADV
ejpam-4480	68	2	each	each	PRON
ejpam-4480	68	3	of	of	ADP
ejpam-4480	68	4	the	the	DET
ejpam-4480	68	5	following	following	ADJ
ejpam-4480	68	6	statements	statement	NOUN
ejpam-4480	68	7	holds	hold	VERB
ejpam-4480	68	8	:	:	PUNCT
ejpam-4480	68	9	(	(	PUNCT
ejpam-4480	68	10	i	i	NOUN
ejpam-4480	68	11	)	)	PUNCT
ejpam-4480	68	12	g	g	PROPN
ejpam-4480	68	13	admits	admit	VERB
ejpam-4480	68	14	a	a	DET
ejpam-4480	68	15	superclique	superclique	NOUN
ejpam-4480	68	16	and	and	CCONJ
ejpam-4480	68	17	1	1	NUM
ejpam-4480	68	18	≤	≤	NOUN
ejpam-4480	68	19	ωs(g	ωs(g	NOUN
ejpam-4480	68	20	)	)	PUNCT
ejpam-4480	68	21	≤	≤	NUM
ejpam-4480	68	22	ω(g	ω(g	NOUN
ejpam-4480	68	23	)	)	PUNCT
ejpam-4480	68	24	.	.	PUNCT
ejpam-4480	69	1	(	(	PUNCT
ejpam-4480	69	2	ii	ii	NOUN
ejpam-4480	69	3	)	)	PUNCT
ejpam-4480	69	4	ωs(g	ωs(g	PUNCT
ejpam-4480	69	5	)	)	PUNCT
ejpam-4480	69	6	=	=	SYM
ejpam-4480	69	7	1	1	NUM
ejpam-4480	69	8	if	if	SCONJ
ejpam-4480	69	9	and	and	CCONJ
ejpam-4480	69	10	only	only	ADV
ejpam-4480	69	11	if	if	SCONJ
ejpam-4480	69	12	every	every	DET
ejpam-4480	69	13	component	component	NOUN
ejpam-4480	69	14	of	of	ADP
ejpam-4480	69	15	g	g	PROPN
ejpam-4480	69	16	is	be	AUX
ejpam-4480	69	17	complete	complete	ADJ
ejpam-4480	69	18	.	.	PUNCT
ejpam-4480	70	1	(	(	PUNCT
ejpam-4480	70	2	iii	iii	NOUN
ejpam-4480	70	3	)	)	PUNCT
ejpam-4480	70	4	ωs(g	ωs(g	PUNCT
ejpam-4480	70	5	)	)	PUNCT
ejpam-4480	70	6	=	=	SYM
ejpam-4480	70	7	ω(g	ω(g	NOUN
ejpam-4480	70	8	)	)	PUNCT
ejpam-4480	70	9	if	if	SCONJ
ejpam-4480	70	10	and	and	CCONJ
ejpam-4480	70	11	only	only	ADV
ejpam-4480	70	12	if	if	SCONJ
ejpam-4480	70	13	g	g	PROPN
ejpam-4480	70	14	has	have	VERB
ejpam-4480	70	15	a	a	DET
ejpam-4480	70	16	maximum	maximum	ADJ
ejpam-4480	70	17	clique	clique	NOUN
ejpam-4480	70	18	containing	contain	VERB
ejpam-4480	70	19	no	no	DET
ejpam-4480	70	20	true	true	ADJ
ejpam-4480	70	21	twin	twin	ADJ
ejpam-4480	70	22	vertices	vertex	NOUN
ejpam-4480	70	23	.	.	PUNCT
ejpam-4480	71	1	proof	proof	NOUN
ejpam-4480	71	2	.	.	PUNCT
ejpam-4480	72	1	g	g	PROPN
ejpam-4480	72	2	admits	admit	VERB
ejpam-4480	72	3	a	a	DET
ejpam-4480	72	4	superclique	superclique	NOUN
ejpam-4480	72	5	because	because	SCONJ
ejpam-4480	72	6	every	every	DET
ejpam-4480	72	7	singleton	singleton	NOUN
ejpam-4480	72	8	subset	subset	NOUN
ejpam-4480	72	9	of	of	ADP
ejpam-4480	72	10	v	v	PROPN
ejpam-4480	72	11	(	(	PUNCT
ejpam-4480	72	12	g	g	NOUN
ejpam-4480	72	13	)	)	PUNCT
ejpam-4480	72	14	is	be	AUX
ejpam-4480	72	15	a	a	DET
ejpam-4480	72	16	superclique	superclique	NOUN
ejpam-4480	72	17	in	in	ADP
ejpam-4480	72	18	g.	g.	PROPN
ejpam-4480	72	19	moreover	moreover	ADV
ejpam-4480	72	20	,	,	PUNCT
ejpam-4480	72	21	since	since	SCONJ
ejpam-4480	72	22	every	every	DET
ejpam-4480	72	23	superclique	superclique	NOUN
ejpam-4480	72	24	is	be	AUX
ejpam-4480	72	25	a	a	DET
ejpam-4480	72	26	clique	clique	NOUN
ejpam-4480	72	27	,	,	PUNCT
ejpam-4480	72	28	(	(	PUNCT
ejpam-4480	72	29	i	i	NOUN
ejpam-4480	72	30	)	)	PUNCT
ejpam-4480	72	31	holds	hold	VERB
ejpam-4480	72	32	.	.	PUNCT
ejpam-4480	73	1	suppose	suppose	VERB
ejpam-4480	73	2	that	that	SCONJ
ejpam-4480	73	3	ωs(g	ωs(g	NUM
ejpam-4480	73	4	)	)	PUNCT
ejpam-4480	73	5	=	=	SYM
ejpam-4480	73	6	1	1	X
ejpam-4480	73	7	.	.	PUNCT
ejpam-4480	73	8	suppose	suppose	VERB
ejpam-4480	73	9	further	far	ADV
ejpam-4480	73	10	that	that	SCONJ
ejpam-4480	73	11	g	g	PROPN
ejpam-4480	73	12	has	have	VERB
ejpam-4480	73	13	a	a	DET
ejpam-4480	73	14	component	component	NOUN
ejpam-4480	73	15	h	h	NOUN
ejpam-4480	73	16	which	which	PRON
ejpam-4480	73	17	is	be	AUX
ejpam-4480	73	18	not	not	PART
ejpam-4480	73	19	complete	complete	ADJ
ejpam-4480	73	20	.	.	PUNCT
ejpam-4480	74	1	then	then	ADV
ejpam-4480	74	2	there	there	PRON
ejpam-4480	74	3	exist	exist	VERB
ejpam-4480	74	4	vertices	vertex	NOUN
ejpam-4480	74	5	x	x	X
ejpam-4480	74	6	,	,	PUNCT
ejpam-4480	74	7	y	y	PROPN
ejpam-4480	74	8	∈	∈	PROPN
ejpam-4480	74	9	v	v	ADP
ejpam-4480	74	10	(	(	PUNCT
ejpam-4480	74	11	h	h	NOUN
ejpam-4480	74	12	)	)	PUNCT
ejpam-4480	74	13	such	such	ADJ
ejpam-4480	74	14	that	that	SCONJ
ejpam-4480	74	15	dh(x	dh(x	NOUN
ejpam-4480	74	16	,	,	PUNCT
ejpam-4480	74	17	y	y	NOUN
ejpam-4480	74	18	)	)	PUNCT
ejpam-4480	74	19	=	=	SYM
ejpam-4480	75	1	dg(x	dg(x	X
ejpam-4480	75	2	,	,	PUNCT
ejpam-4480	75	3	y	y	NOUN
ejpam-4480	75	4	)	)	PUNCT
ejpam-4480	75	5	=	=	SYM
ejpam-4480	76	1	2	2	X
ejpam-4480	76	2	.	.	X
ejpam-4480	76	3	let	let	VERB
ejpam-4480	76	4	z	z	NOUN
ejpam-4480	76	5	∈	∈	PROPN
ejpam-4480	76	6	ng(x	ng(x	NUM
ejpam-4480	76	7	)	)	PUNCT
ejpam-4480	76	8	∩	∩	NOUN
ejpam-4480	76	9	ng(y	ng(y	NOUN
ejpam-4480	76	10	)	)	PUNCT
ejpam-4480	76	11	.	.	PUNCT
ejpam-4480	77	1	then	then	ADV
ejpam-4480	77	2	s	s	VERB
ejpam-4480	77	3	=	=	SYM
ejpam-4480	77	4	{	{	PUNCT
ejpam-4480	77	5	x	x	NOUN
ejpam-4480	77	6	,	,	PUNCT
ejpam-4480	77	7	z	z	NOUN
ejpam-4480	77	8	}	}	PUNCT
ejpam-4480	77	9	is	be	AUX
ejpam-4480	77	10	a	a	DET
ejpam-4480	77	11	superclique	superclique	NOUN
ejpam-4480	77	12	in	in	ADP
ejpam-4480	77	13	g.	g.	PROPN
ejpam-4480	77	14	hence	hence	ADV
ejpam-4480	77	15	,	,	PUNCT
ejpam-4480	77	16	ωs(g	ωs(g	PUNCT
ejpam-4480	77	17	)	)	PUNCT
ejpam-4480	77	18	≥	≥	NOUN
ejpam-4480	77	19	|s|	|s|	NOUN
ejpam-4480	77	20	=	=	SYM
ejpam-4480	77	21	2	2	NUM
ejpam-4480	77	22	>	>	SYM
ejpam-4480	77	23	1	1	NUM
ejpam-4480	77	24	,	,	PUNCT
ejpam-4480	77	25	contrary	contrary	ADV
ejpam-4480	77	26	to	to	ADP
ejpam-4480	77	27	our	our	PRON
ejpam-4480	77	28	assumption	assumption	NOUN
ejpam-4480	77	29	that	that	SCONJ
ejpam-4480	77	30	ωs(g	ωs(g	PUNCT
ejpam-4480	77	31	)	)	PUNCT
ejpam-4480	77	32	=	=	SYM
ejpam-4480	77	33	1	1	X
ejpam-4480	77	34	.	.	PUNCT
ejpam-4480	77	35	thus	thus	ADV
ejpam-4480	77	36	,	,	PUNCT
ejpam-4480	77	37	every	every	DET
ejpam-4480	77	38	component	component	NOUN
ejpam-4480	77	39	of	of	ADP
ejpam-4480	77	40	g	g	PROPN
ejpam-4480	77	41	is	be	AUX
ejpam-4480	77	42	complete	complete	ADJ
ejpam-4480	77	43	.	.	PUNCT
ejpam-4480	78	1	the	the	DET
ejpam-4480	78	2	converse	converse	NOUN
ejpam-4480	78	3	is	be	AUX
ejpam-4480	78	4	easy	easy	ADJ
ejpam-4480	78	5	.	.	PUNCT
ejpam-4480	79	1	next	next	ADV
ejpam-4480	79	2	,	,	PUNCT
ejpam-4480	79	3	suppose	suppose	VERB
ejpam-4480	79	4	that	that	SCONJ
ejpam-4480	79	5	ωs(g	ωs(g	NUM
ejpam-4480	79	6	)	)	PUNCT
ejpam-4480	79	7	=	=	SYM
ejpam-4480	79	8	ω(g	ω(g	NOUN
ejpam-4480	79	9	)	)	PUNCT
ejpam-4480	79	10	.	.	PUNCT
ejpam-4480	80	1	let	let	VERB
ejpam-4480	80	2	s	s	PRON
ejpam-4480	80	3	be	be	AUX
ejpam-4480	80	4	a	a	DET
ejpam-4480	80	5	superclique	superclique	NOUN
ejpam-4480	80	6	in	in	ADP
ejpam-4480	80	7	g	g	PROPN
ejpam-4480	80	8	such	such	ADJ
ejpam-4480	80	9	that	that	DET
ejpam-4480	80	10	|s|	|s|	PROPN
ejpam-4480	80	11	=	=	NOUN
ejpam-4480	80	12	ωs(g	ωs(g	NUM
ejpam-4480	80	13	)	)	PUNCT
ejpam-4480	80	14	.	.	PUNCT
ejpam-4480	81	1	the	the	DET
ejpam-4480	81	2	assumption	assumption	NOUN
ejpam-4480	81	3	ωs(g	ωs(g	PUNCT
ejpam-4480	81	4	)	)	PUNCT
ejpam-4480	81	5	=	=	SYM
ejpam-4480	81	6	ω(g	ω(g	NOUN
ejpam-4480	81	7	)	)	PUNCT
ejpam-4480	81	8	would	would	AUX
ejpam-4480	81	9	imply	imply	VERB
ejpam-4480	81	10	that	that	DET
ejpam-4480	81	11	s	s	VERB
ejpam-4480	81	12	is	be	AUX
ejpam-4480	81	13	a	a	DET
ejpam-4480	81	14	maximum	maximum	ADJ
ejpam-4480	81	15	clique	clique	NOUN
ejpam-4480	81	16	of	of	ADP
ejpam-4480	81	17	g.	g.	PROPN
ejpam-4480	81	18	suppose	suppose	VERB
ejpam-4480	81	19	s	s	NOUN
ejpam-4480	81	20	contains	contain	VERB
ejpam-4480	81	21	true	true	ADJ
ejpam-4480	81	22	twin	twin	ADJ
ejpam-4480	81	23	vertices	vertex	NOUN
ejpam-4480	81	24	,	,	PUNCT
ejpam-4480	81	25	say	say	VERB
ejpam-4480	81	26	v	v	NOUN
ejpam-4480	81	27	and	and	CCONJ
ejpam-4480	81	28	w.	w.	NOUN
ejpam-4480	81	29	then	then	ADV
ejpam-4480	81	30	(	(	PUNCT
ejpam-4480	81	31	v	v	NOUN
ejpam-4480	81	32	(	(	PUNCT
ejpam-4480	81	33	g	g	NOUN
ejpam-4480	81	34	)	)	PUNCT
ejpam-4480	81	35	\	\	PROPN
ejpam-4480	82	1	s	s	X
ejpam-4480	82	2	)	)	PUNCT
ejpam-4480	82	3	∩	∩	NOUN
ejpam-4480	82	4	(	(	PUNCT
ejpam-4480	82	5	ng(v	ng(v	NOUN
ejpam-4480	82	6	)	)	PUNCT
ejpam-4480	82	7	\ng(w	\ng(w	NUM
ejpam-4480	82	8	)	)	PUNCT
ejpam-4480	82	9	)	)	PUNCT
ejpam-4480	83	1	=	=	SYM
ejpam-4480	83	2	(	(	PUNCT
ejpam-4480	83	3	v	v	NOUN
ejpam-4480	83	4	(	(	PUNCT
ejpam-4480	83	5	g	g	NOUN
ejpam-4480	83	6	)	)	PUNCT
ejpam-4480	83	7	\	\	PROPN
ejpam-4480	83	8	s	s	X
ejpam-4480	83	9	)	)	PUNCT
ejpam-4480	83	10	∩	∩	NOUN
ejpam-4480	83	11	(	(	PUNCT
ejpam-4480	83	12	ng(w	ng(w	NOUN
ejpam-4480	83	13	)	)	PUNCT
ejpam-4480	83	14	\ng(v	\ng(v	NOUN
ejpam-4480	83	15	)	)	PUNCT
ejpam-4480	83	16	)	)	PUNCT
ejpam-4480	84	1	=	=	NOUN
ejpam-4480	84	2	∅	∅	NOUN
ejpam-4480	84	3	,	,	PUNCT
ejpam-4480	84	4	contrary	contrary	ADJ
ejpam-4480	84	5	to	to	ADP
ejpam-4480	84	6	the	the	DET
ejpam-4480	84	7	assumption	assumption	NOUN
ejpam-4480	84	8	that	that	SCONJ
ejpam-4480	84	9	s	s	VERB
ejpam-4480	84	10	is	be	AUX
ejpam-4480	84	11	a	a	DET
ejpam-4480	84	12	superclique	superclique	NOUN
ejpam-4480	84	13	in	in	ADP
ejpam-4480	84	14	g.	g.	PROPN
ejpam-4480	84	15	thus	thus	ADV
ejpam-4480	84	16	,	,	PUNCT
ejpam-4480	84	17	s	s	VERB
ejpam-4480	84	18	does	do	AUX
ejpam-4480	84	19	not	not	PART
ejpam-4480	84	20	contain	contain	VERB
ejpam-4480	84	21	true	true	ADJ
ejpam-4480	84	22	twin	twin	ADJ
ejpam-4480	84	23	vertices	vertex	NOUN
ejpam-4480	84	24	.	.	PUNCT
ejpam-4480	85	1	conversely	conversely	ADV
ejpam-4480	85	2	,	,	PUNCT
ejpam-4480	85	3	suppose	suppose	VERB
ejpam-4480	85	4	that	that	SCONJ
ejpam-4480	85	5	g	g	PROPN
ejpam-4480	85	6	has	have	VERB
ejpam-4480	85	7	a	a	DET
ejpam-4480	85	8	maximum	maximum	ADJ
ejpam-4480	85	9	clique	clique	NOUN
ejpam-4480	85	10	s	s	AUX
ejpam-4480	85	11	containing	contain	VERB
ejpam-4480	85	12	no	no	DET
ejpam-4480	85	13	true	true	ADJ
ejpam-4480	85	14	twin	twin	ADJ
ejpam-4480	85	15	vertices	vertex	NOUN
ejpam-4480	85	16	.	.	PUNCT
ejpam-4480	86	1	then	then	ADV
ejpam-4480	86	2	clearly	clearly	ADV
ejpam-4480	86	3	,	,	PUNCT
ejpam-4480	86	4	s	s	VERB
ejpam-4480	86	5	is	be	AUX
ejpam-4480	86	6	a	a	DET
ejpam-4480	86	7	superclique	superclique	NOUN
ejpam-4480	86	8	in	in	ADP
ejpam-4480	86	9	g.	g.	PROPN
ejpam-4480	86	10	this	this	PRON
ejpam-4480	86	11	implies	imply	VERB
ejpam-4480	86	12	that	that	SCONJ
ejpam-4480	86	13	ωs(g	ωs(g	PUNCT
ejpam-4480	86	14	)	)	PUNCT
ejpam-4480	86	15	=	=	SYM
ejpam-4480	86	16	ω(g	ω(g	NOUN
ejpam-4480	86	17	)	)	PUNCT
ejpam-4480	86	18	.	.	PUNCT
ejpam-4480	87	1	remark	remark	PROPN
ejpam-4480	87	2	1	1	NUM
ejpam-4480	87	3	.	.	PUNCT
ejpam-4480	88	1	each	each	PRON
ejpam-4480	88	2	of	of	ADP
ejpam-4480	88	3	the	the	DET
ejpam-4480	88	4	following	following	ADJ
ejpam-4480	88	5	statements	statement	NOUN
ejpam-4480	88	6	holds	hold	VERB
ejpam-4480	88	7	:	:	PUNCT
ejpam-4480	88	8	(	(	PUNCT
ejpam-4480	88	9	i	i	NOUN
ejpam-4480	88	10	)	)	PUNCT
ejpam-4480	88	11	for	for	ADP
ejpam-4480	88	12	any	any	DET
ejpam-4480	88	13	positive	positive	ADJ
ejpam-4480	88	14	integer	integer	NOUN
ejpam-4480	88	15	n	n	CCONJ
ejpam-4480	88	16	,	,	PUNCT
ejpam-4480	88	17	ωs(kn	ωs(kn	PROPN
ejpam-4480	88	18	)	)	PUNCT
ejpam-4480	88	19	=	=	SYM
ejpam-4480	89	1	1	1	X
ejpam-4480	89	2	.	.	X
ejpam-4480	89	3	r.	r.	PROPN
ejpam-4480	89	4	dela	dela	PROPN
ejpam-4480	89	5	cerna	cerna	PROPN
ejpam-4480	89	6	,	,	PUNCT
ejpam-4480	89	7	s.	s.	PROPN
ejpam-4480	89	8	canoy	canoy	PROPN
ejpam-4480	89	9	,	,	PUNCT
ejpam-4480	89	10	jr	jr	PROPN
ejpam-4480	89	11	.	.	PROPN
ejpam-4480	89	12	/	/	SYM
ejpam-4480	89	13	eur	eur	PROPN
ejpam-4480	89	14	.	.	PUNCT
ejpam-4480	90	1	j.	j.	PROPN
ejpam-4480	90	2	pure	pure	PROPN
ejpam-4480	90	3	appl	appl	PROPN
ejpam-4480	90	4	.	.	PROPN
ejpam-4480	90	5	math	math	PROPN
ejpam-4480	90	6	,	,	PUNCT
ejpam-4480	90	7	15	15	NUM
ejpam-4480	90	8	(	(	PUNCT
ejpam-4480	90	9	3	3	NUM
ejpam-4480	90	10	)	)	PUNCT
ejpam-4480	90	11	(	(	PUNCT
ejpam-4480	90	12	2022	2022	NUM
ejpam-4480	90	13	)	)	PUNCT
ejpam-4480	90	14	,	,	PUNCT
ejpam-4480	90	15	1217	1217	NUM
ejpam-4480	90	16	-	-	SYM
ejpam-4480	90	17	1228	1228	NUM
ejpam-4480	90	18	1220	1220	NUM
ejpam-4480	90	19	(	(	PUNCT
ejpam-4480	90	20	ii	ii	NOUN
ejpam-4480	90	21	)	)	PUNCT
ejpam-4480	90	22	for	for	ADP
ejpam-4480	90	23	any	any	DET
ejpam-4480	90	24	positive	positive	ADJ
ejpam-4480	90	25	integer	integer	NOUN
ejpam-4480	90	26	n	n	PRON
ejpam-4480	90	27	≥	≥	NOUN
ejpam-4480	90	28	2	2	NUM
ejpam-4480	90	29	,	,	PUNCT
ejpam-4480	90	30	ωs(pn	ωs(pn	NOUN
ejpam-4480	90	31	)	)	PUNCT
ejpam-4480	90	32	=	=	PRON
ejpam-4480	90	33	{	{	PUNCT
ejpam-4480	90	34	1	1	NUM
ejpam-4480	90	35	if	if	SCONJ
ejpam-4480	90	36	n	n	NOUN
ejpam-4480	90	37	=	=	SYM
ejpam-4480	90	38	2	2	NUM
ejpam-4480	90	39	2	2	NUM
ejpam-4480	90	40	if	if	SCONJ
ejpam-4480	90	41	n	n	PRON
ejpam-4480	90	42	≥	≥	NOUN
ejpam-4480	90	43	3	3	NUM
ejpam-4480	90	44	.	.	PUNCT
ejpam-4480	90	45	(	(	PUNCT
ejpam-4480	90	46	iii	iii	NOUN
ejpam-4480	90	47	)	)	PUNCT
ejpam-4480	90	48	for	for	ADP
ejpam-4480	90	49	any	any	DET
ejpam-4480	90	50	positive	positive	ADJ
ejpam-4480	90	51	integer	integer	NOUN
ejpam-4480	90	52	n	n	PRON
ejpam-4480	90	53	≥	≥	NOUN
ejpam-4480	90	54	3	3	NUM
ejpam-4480	90	55	,	,	PUNCT
ejpam-4480	90	56	ωs(cn	ωs(cn	NOUN
ejpam-4480	90	57	)	)	PUNCT
ejpam-4480	90	58	=	=	PRON
ejpam-4480	90	59	{	{	PUNCT
ejpam-4480	90	60	1	1	NUM
ejpam-4480	90	61	if	if	SCONJ
ejpam-4480	90	62	n	n	ADJ
ejpam-4480	90	63	=	=	SYM
ejpam-4480	90	64	3	3	NUM
ejpam-4480	90	65	2	2	NUM
ejpam-4480	91	1	if	if	SCONJ
ejpam-4480	91	2	n	n	PRON
ejpam-4480	91	3	≥	≥	NOUN
ejpam-4480	91	4	4	4	NUM
ejpam-4480	91	5	.	.	PUNCT
ejpam-4480	91	6	theorem	theorem	NOUN
ejpam-4480	91	7	2	2	NUM
ejpam-4480	91	8	.	.	PUNCT
ejpam-4480	91	9	let	let	VERB
ejpam-4480	91	10	a	a	PRON
ejpam-4480	91	11	and	and	CCONJ
ejpam-4480	91	12	b	b	NOUN
ejpam-4480	91	13	be	be	AUX
ejpam-4480	91	14	positive	positive	ADJ
ejpam-4480	91	15	integers	integer	NOUN
ejpam-4480	91	16	such	such	ADJ
ejpam-4480	91	17	that	that	SCONJ
ejpam-4480	91	18	2	2	NUM
ejpam-4480	91	19	≤	≤	NUM
ejpam-4480	91	20	a	a	DET
ejpam-4480	91	21	≤	≤	PROPN
ejpam-4480	91	22	b.	b.	NOUN
ejpam-4480	92	1	then	then	ADV
ejpam-4480	92	2	there	there	PRON
ejpam-4480	92	3	exists	exist	VERB
ejpam-4480	92	4	a	a	DET
ejpam-4480	92	5	connected	connected	ADJ
ejpam-4480	92	6	graph	graph	NOUN
ejpam-4480	92	7	g	g	ADP
ejpam-4480	92	8	such	such	ADJ
ejpam-4480	92	9	that	that	SCONJ
ejpam-4480	92	10	ωs(g	ωs(g	PUNCT
ejpam-4480	92	11	)	)	PUNCT
ejpam-4480	92	12	=	=	SYM
ejpam-4480	92	13	a	a	PRON
ejpam-4480	92	14	and	and	CCONJ
ejpam-4480	92	15	ω(g	ω(g	NOUN
ejpam-4480	92	16	)	)	PUNCT
ejpam-4480	92	17	=	=	SYM
ejpam-4480	92	18	b.	b.	NOUN
ejpam-4480	92	19	proof	proof	NOUN
ejpam-4480	92	20	.	.	PUNCT
ejpam-4480	93	1	consider	consider	VERB
ejpam-4480	93	2	the	the	DET
ejpam-4480	93	3	following	follow	VERB
ejpam-4480	93	4	cases	case	NOUN
ejpam-4480	93	5	:	:	PUNCT
ejpam-4480	93	6	case	case	NOUN
ejpam-4480	93	7	1	1	NUM
ejpam-4480	93	8	.	.	PUNCT
ejpam-4480	94	1	a	a	PRON
ejpam-4480	94	2	=	=	X
ejpam-4480	94	3	b.	b.	PROPN
ejpam-4480	94	4	consider	consider	VERB
ejpam-4480	94	5	the	the	DET
ejpam-4480	94	6	graph	graph	NOUN
ejpam-4480	94	7	g	g	NOUN
ejpam-4480	94	8	in	in	ADP
ejpam-4480	94	9	figure	figure	NOUN
ejpam-4480	94	10	1	1	NUM
ejpam-4480	94	11	obtained	obtain	VERB
ejpam-4480	94	12	from	from	ADP
ejpam-4480	94	13	the	the	DET
ejpam-4480	94	14	complete	complete	ADJ
ejpam-4480	94	15	graph	graph	NOUN
ejpam-4480	94	16	ka	ka	X
ejpam-4480	94	17	by	by	ADP
ejpam-4480	94	18	adding	add	VERB
ejpam-4480	94	19	the	the	DET
ejpam-4480	94	20	a	a	DET
ejpam-4480	94	21	pendant	pendant	ADJ
ejpam-4480	94	22	vertices	vertex	NOUN
ejpam-4480	94	23	.	.	PUNCT
ejpam-4480	95	1	then	then	ADV
ejpam-4480	95	2	clearly	clearly	ADV
ejpam-4480	95	3	,	,	PUNCT
ejpam-4480	95	4	ωs(g	ωs(g	PUNCT
ejpam-4480	95	5	)	)	PUNCT
ejpam-4480	95	6	=	=	SYM
ejpam-4480	95	7	ω(g	ω(g	NOUN
ejpam-4480	95	8	)	)	PUNCT
ejpam-4480	95	9	=	=	SYM
ejpam-4480	95	10	a.	a.	NOUN
ejpam-4480	95	11	....................................	....................................	PUNCT
ejpam-4480	95	12	....................................	....................................	PUNCT
ejpam-4480	96	1	....................................	....................................	PUNCT
ejpam-4480	96	2	....................................	....................................	PUNCT
ejpam-4480	97	1	........................................................................	........................................................................	PUNCT
ejpam-4480	97	2	....................................	....................................	PUNCT
ejpam-4480	98	1	........................................................................	........................................................................	PUNCT
ejpam-4480	98	2	....................................	....................................	PUNCT
ejpam-4480	99	1	........................................................................	........................................................................	PUNCT
ejpam-4480	99	2	....................................	....................................	PUNCT
ejpam-4480	100	1	....................................	....................................	PUNCT
ejpam-4480	100	2	....................................	....................................	PUNCT
ejpam-4480	101	1	...........	...........	PUNCT
ejpam-4480	101	2	..........	..........	PUNCT
ejpam-4480	102	1	..........	..........	PUNCT
ejpam-4480	102	2	..........	..........	PUNCT
ejpam-4480	103	1	..........	..........	PUNCT
ejpam-4480	103	2	..........	..........	PUNCT
ejpam-4480	104	1	..........	..........	PUNCT
ejpam-4480	104	2	..........	..........	PUNCT
ejpam-4480	105	1	..........	..........	PUNCT
ejpam-4480	105	2	..........	..........	PUNCT
ejpam-4480	106	1	..........	..........	PUNCT
ejpam-4480	106	2	..........	..........	PUNCT
ejpam-4480	107	1	..........	..........	PUNCT
ejpam-4480	107	2	..	..	PUNCT
ejpam-4480	108	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4480	108	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4480	109	1	...........	...........	PUNCT
ejpam-4480	109	2	..........	..........	PUNCT
ejpam-4480	110	1	..........	..........	PUNCT
ejpam-4480	110	2	..........	..........	PUNCT
ejpam-4480	111	1	..........	..........	PUNCT
ejpam-4480	111	2	..........	..........	PUNCT
ejpam-4480	112	1	..........	..........	PUNCT
ejpam-4480	112	2	..........	..........	PUNCT
ejpam-4480	113	1	..........	..........	PUNCT
ejpam-4480	113	2	..........	..........	PUNCT
ejpam-4480	114	1	..........	..........	PUNCT
ejpam-4480	114	2	..........	..........	PUNCT
ejpam-4480	115	1	..........	..........	PUNCT
ejpam-4480	115	2	..	..	PUNCT
ejpam-4480	115	3	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4480	115	4	...........	...........	PUNCT
ejpam-4480	116	1	..........	..........	PUNCT
ejpam-4480	116	2	..........	..........	PUNCT
ejpam-4480	117	1	..........	..........	PUNCT
ejpam-4480	117	2	..........	..........	PUNCT
ejpam-4480	118	1	..........	..........	PUNCT
ejpam-4480	118	2	..........	..........	PUNCT
ejpam-4480	119	1	..........	..........	PUNCT
ejpam-4480	119	2	..........	..........	PUNCT
ejpam-4480	120	1	..........	..........	PUNCT
ejpam-4480	120	2	..........	..........	PUNCT
ejpam-4480	121	1	..........	..........	PUNCT
ejpam-4480	121	2	..........	..........	PUNCT
ejpam-4480	122	1	..	..	PUNCT
ejpam-4480	122	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4480	123	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4480	123	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4480	123	3	................................................................................................................................................	................................................................................................................................................	PUNCT
ejpam-4480	124	1	..........	..........	PUNCT
ejpam-4480	124	2	..........	..........	PUNCT
ejpam-4480	125	1	..........	..........	PUNCT
ejpam-4480	125	2	..........	..........	PUNCT
ejpam-4480	126	1	..........	..........	PUNCT
ejpam-4480	126	2	..........	..........	PUNCT
ejpam-4480	127	1	..........	..........	PUNCT
ejpam-4480	127	2	..........	..........	PUNCT
ejpam-4480	128	1	..........	..........	PUNCT
ejpam-4480	128	2	..........	..........	PUNCT
ejpam-4480	129	1	..........	..........	PUNCT
ejpam-4480	130	1	..........	..........	PUNCT
ejpam-4480	131	1	..	..	PUNCT
ejpam-4480	132	1	•	•	NUM
ejpam-4480	132	2	•	•	NOUN
ejpam-4480	132	3	•	•	NOUN
ejpam-4480	132	4	.....................	.....................	PUNCT
ejpam-4480	132	5	....................	....................	PUNCT
ejpam-4480	132	6	....................	....................	PUNCT
ejpam-4480	132	7	....................	....................	PUNCT
ejpam-4480	132	8	....................	....................	PUNCT
ejpam-4480	132	9	....................	....................	PUNCT
ejpam-4480	132	10	....................	....................	PUNCT
ejpam-4480	132	11	....................	....................	PUNCT
ejpam-4480	132	12	....................	....................	PUNCT
ejpam-4480	132	13	....................	....................	PUNCT
ejpam-4480	132	14	....................	....................	PUNCT
ejpam-4480	132	15	....................	....................	PUNCT
ejpam-4480	132	16	....................	....................	PUNCT
ejpam-4480	132	17	...........	...........	PUNCT
ejpam-4480	132	18	...........	...........	PUNCT
ejpam-4480	132	19	..........	..........	PUNCT
ejpam-4480	132	20	..........	..........	PUNCT
ejpam-4480	133	1	..........	..........	PUNCT
ejpam-4480	133	2	..........	..........	PUNCT
ejpam-4480	134	1	..........	..........	PUNCT
ejpam-4480	134	2	..........	..........	PUNCT
ejpam-4480	135	1	..........	..........	PUNCT
ejpam-4480	135	2	..........	..........	PUNCT
ejpam-4480	136	1	..........	..........	PUNCT
ejpam-4480	136	2	..........	..........	PUNCT
ejpam-4480	137	1	..........	..........	PUNCT
ejpam-4480	137	2	..........	..........	PUNCT
ejpam-4480	138	1	..........	..........	PUNCT
ejpam-4480	138	2	..........	..........	PUNCT
ejpam-4480	139	1	..........	..........	PUNCT
ejpam-4480	139	2	..........	..........	PUNCT
ejpam-4480	140	1	..........	..........	PUNCT
ejpam-4480	140	2	..........	..........	PUNCT
ejpam-4480	141	1	..........	..........	PUNCT
ejpam-4480	141	2	..........	..........	PUNCT
ejpam-4480	142	1	..........	..........	PUNCT
ejpam-4480	142	2	..........	..........	PUNCT
ejpam-4480	143	1	..........	..........	PUNCT
ejpam-4480	143	2	..........	..........	PUNCT
ejpam-4480	144	1	..........	..........	PUNCT
ejpam-4480	144	2	..........	..........	PUNCT
ejpam-4480	145	1	......	......	PUNCT
ejpam-4480	145	2	.........	.........	PUNCT
ejpam-4480	145	3	........	........	PUNCT
ejpam-4480	145	4	........	........	PUNCT
ejpam-4480	145	5	........	........	PUNCT
ejpam-4480	145	6	........	........	PUNCT
ejpam-4480	145	7	........	........	PUNCT
ejpam-4480	145	8	........	........	PUNCT
ejpam-4480	145	9	........	........	PUNCT
ejpam-4480	145	10	........	........	PUNCT
ejpam-4480	145	11	........	........	PUNCT
ejpam-4480	145	12	........	........	PUNCT
ejpam-4480	145	13	........	........	PUNCT
ejpam-4480	145	14	........	........	PUNCT
ejpam-4480	145	15	........	........	PUNCT
ejpam-4480	145	16	........	........	PUNCT
ejpam-4480	145	17	........	........	PUNCT
ejpam-4480	145	18	........	........	PUNCT
ejpam-4480	145	19	........	........	PUNCT
ejpam-4480	145	20	........	........	PUNCT
ejpam-4480	145	21	........	........	PUNCT
ejpam-4480	145	22	........	........	PUNCT
ejpam-4480	145	23	........	........	PUNCT
ejpam-4480	145	24	........	........	PUNCT
ejpam-4480	145	25	........	........	PUNCT
ejpam-4480	145	26	........	........	PUNCT
ejpam-4480	145	27	........	........	PUNCT
ejpam-4480	145	28	........	........	PUNCT
ejpam-4480	145	29	...	...	PUNCT
ejpam-4480	145	30	.........	.........	PUNCT
ejpam-4480	145	31	........	........	PUNCT
ejpam-4480	145	32	........	........	PUNCT
ejpam-4480	145	33	........	........	PUNCT
ejpam-4480	145	34	........	........	PUNCT
ejpam-4480	145	35	........	........	PUNCT
ejpam-4480	145	36	........	........	PUNCT
ejpam-4480	145	37	........	........	PUNCT
ejpam-4480	145	38	........	........	PUNCT
ejpam-4480	145	39	........	........	PUNCT
ejpam-4480	145	40	........	........	PUNCT
ejpam-4480	145	41	........	........	PUNCT
ejpam-4480	145	42	........	........	PUNCT
ejpam-4480	145	43	........	........	PUNCT
ejpam-4480	145	44	........	........	PUNCT
ejpam-4480	145	45	........	........	PUNCT
ejpam-4480	145	46	........	........	PUNCT
ejpam-4480	145	47	........	........	PUNCT
ejpam-4480	145	48	........	........	PUNCT
ejpam-4480	145	49	........	........	PUNCT
ejpam-4480	145	50	........	........	PUNCT
ejpam-4480	145	51	........	........	PUNCT
ejpam-4480	145	52	........	........	PUNCT
ejpam-4480	145	53	........	........	PUNCT
ejpam-4480	145	54	........	........	PUNCT
ejpam-4480	145	55	........	........	PUNCT
ejpam-4480	145	56	........	........	PUNCT
ejpam-4480	146	1	........................................................................................................................................................................................................................................................................................	........................................................................................................................................................................................................................................................................................	PROPN
ejpam-4480	146	2	................................................................................................................................................................................................................................................................................	................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4480	147	1	.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4480	147	2	....................	....................	PUNCT
ejpam-4480	147	3	....................	....................	PUNCT
ejpam-4480	147	4	....................	....................	PUNCT
ejpam-4480	147	5	....................	....................	PUNCT
ejpam-4480	147	6	....................	....................	PUNCT
ejpam-4480	147	7	....................	....................	PUNCT
ejpam-4480	147	8	....................	....................	PUNCT
ejpam-4480	147	9	....................	....................	PUNCT
ejpam-4480	147	10	....................	....................	PUNCT
ejpam-4480	147	11	....................	....................	PUNCT
ejpam-4480	147	12	....................	....................	PUNCT
ejpam-4480	147	13	....................	....................	PUNCT
ejpam-4480	148	1	...........	...........	PUNCT
ejpam-4480	149	1	xa	xa	PROPN
ejpam-4480	150	1	x2	x2	PROPN
ejpam-4480	150	2	x3	x3	PROPN
ejpam-4480	150	3	x4	x4	PROPN
ejpam-4480	150	4	x5	x5	PROPN
ejpam-4480	150	5	x1	x1	PROPN
ejpam-4480	150	6	g	g	NOUN
ejpam-4480	150	7	:	:	PUNCT
ejpam-4480	150	8	figure	figure	NOUN
ejpam-4480	150	9	1	1	NUM
ejpam-4480	150	10	:	:	PUNCT
ejpam-4480	150	11	a	a	DET
ejpam-4480	150	12	graph	graph	NOUN
ejpam-4480	150	13	g	g	NOUN
ejpam-4480	150	14	with	with	ADP
ejpam-4480	150	15	ωs(g	ωs(g	NOUN
ejpam-4480	150	16	)	)	PUNCT
ejpam-4480	150	17	=	=	SYM
ejpam-4480	150	18	ω(g	ω(g	NOUN
ejpam-4480	150	19	)	)	PUNCT
ejpam-4480	150	20	case	case	NOUN
ejpam-4480	150	21	2	2	NUM
ejpam-4480	150	22	.	.	PUNCT
ejpam-4480	151	1	a	a	DET
ejpam-4480	151	2	<	<	X
ejpam-4480	151	3	b.	b.	NOUN
ejpam-4480	151	4	consider	consider	VERB
ejpam-4480	151	5	the	the	DET
ejpam-4480	151	6	graph	graph	NOUN
ejpam-4480	151	7	g	g	NOUN
ejpam-4480	151	8	in	in	ADP
ejpam-4480	151	9	figure	figure	NOUN
ejpam-4480	151	10	2	2	NUM
ejpam-4480	151	11	where	where	SCONJ
ejpam-4480	151	12	g[{x1	g[{x1	PROPN
ejpam-4480	151	13	,	,	PUNCT
ejpam-4480	151	14	x2	x2	PROPN
ejpam-4480	151	15	,	,	PUNCT
ejpam-4480	151	16	.	.	PUNCT
ejpam-4480	151	17	.	.	PUNCT
ejpam-4480	152	1	.	.	PUNCT
ejpam-4480	153	1	,	,	PUNCT
ejpam-4480	153	2	xa	xa	PROPN
ejpam-4480	153	3	}	}	PUNCT
ejpam-4480	153	4	]	]	PUNCT
ejpam-4480	154	1	=	=	PUNCT
ejpam-4480	154	2	ka	ka	PROPN
ejpam-4480	154	3	and	and	CCONJ
ejpam-4480	154	4	g[{y1	g[{y1	PROPN
ejpam-4480	154	5	,	,	PUNCT
ejpam-4480	154	6	y2	y2	PROPN
ejpam-4480	154	7	,	,	PUNCT
ejpam-4480	154	8	.	.	PUNCT
ejpam-4480	154	9	.	.	PUNCT
ejpam-4480	155	1	.	.	PUNCT
ejpam-4480	156	1	,	,	PUNCT
ejpam-4480	156	2	yb	yb	PROPN
ejpam-4480	156	3	}	}	PUNCT
ejpam-4480	156	4	]	]	PUNCT
ejpam-4480	157	1	=	=	SYM
ejpam-4480	157	2	kb	kb	PROPN
ejpam-4480	157	3	.	.	PUNCT
ejpam-4480	158	1	let	let	VERB
ejpam-4480	158	2	s1	s1	PROPN
ejpam-4480	158	3	=	=	PUNCT
ejpam-4480	158	4	{	{	PUNCT
ejpam-4480	158	5	x1	x1	PROPN
ejpam-4480	158	6	,	,	PUNCT
ejpam-4480	158	7	x2	x2	PROPN
ejpam-4480	158	8	,	,	PUNCT
ejpam-4480	158	9	.	.	PUNCT
ejpam-4480	158	10	.	.	PUNCT
ejpam-4480	159	1	.	.	PUNCT
ejpam-4480	160	1	,	,	PUNCT
ejpam-4480	160	2	xa	xa	PROPN
ejpam-4480	160	3	}	}	PUNCT
ejpam-4480	160	4	and	and	CCONJ
ejpam-4480	160	5	s2	s2	VERB
ejpam-4480	160	6	=	=	SYM
ejpam-4480	160	7	{	{	PUNCT
ejpam-4480	160	8	y1	y1	PROPN
ejpam-4480	160	9	,	,	PUNCT
ejpam-4480	160	10	y2	y2	PROPN
ejpam-4480	160	11	,	,	PUNCT
ejpam-4480	160	12	.	.	PUNCT
ejpam-4480	160	13	.	.	PUNCT
ejpam-4480	161	1	.	.	PUNCT
ejpam-4480	162	1	,	,	PUNCT
ejpam-4480	162	2	yb	yb	PROPN
ejpam-4480	162	3	}	}	PUNCT
ejpam-4480	162	4	.	.	PUNCT
ejpam-4480	163	1	clearly	clearly	ADV
ejpam-4480	163	2	,	,	PUNCT
ejpam-4480	163	3	s2	s2	PROPN
ejpam-4480	163	4	is	be	AUX
ejpam-4480	163	5	the	the	DET
ejpam-4480	163	6	(	(	PUNCT
ejpam-4480	163	7	only	only	ADJ
ejpam-4480	163	8	)	)	PUNCT
ejpam-4480	163	9	maximum	maximum	ADJ
ejpam-4480	163	10	clique	clique	NOUN
ejpam-4480	163	11	in	in	ADP
ejpam-4480	163	12	g	g	PROPN
ejpam-4480	163	13	and	and	CCONJ
ejpam-4480	163	14	so	so	ADV
ejpam-4480	163	15	ω(g	ω(g	NOUN
ejpam-4480	163	16	)	)	PUNCT
ejpam-4480	163	17	=	=	SYM
ejpam-4480	163	18	b.	b.	PROPN
ejpam-4480	163	19	since	since	SCONJ
ejpam-4480	163	20	s2	s2	PROPN
ejpam-4480	163	21	has	have	VERB
ejpam-4480	163	22	true	true	ADJ
ejpam-4480	163	23	twin	twin	ADJ
ejpam-4480	163	24	vertices	vertex	NOUN
ejpam-4480	163	25	,	,	PUNCT
ejpam-4480	163	26	it	it	PRON
ejpam-4480	163	27	is	be	AUX
ejpam-4480	163	28	not	not	PART
ejpam-4480	163	29	a	a	DET
ejpam-4480	163	30	superclique	superclique	NOUN
ejpam-4480	163	31	in	in	ADP
ejpam-4480	163	32	g	g	PROPN
ejpam-4480	163	33	(	(	PUNCT
ejpam-4480	163	34	hence	hence	ADV
ejpam-4480	163	35	,	,	PUNCT
ejpam-4480	163	36	ωs(g	ωs(g	PUNCT
ejpam-4480	163	37	)	)	PUNCT
ejpam-4480	163	38	̸=	̸=	PROPN
ejpam-4480	163	39	ω(g	ω(g	NOUN
ejpam-4480	163	40	)	)	PUNCT
ejpam-4480	163	41	)	)	PUNCT
ejpam-4480	163	42	by	by	ADP
ejpam-4480	163	43	theorem	theorem	NOUN
ejpam-4480	163	44	1(iii	1(iii	NUM
ejpam-4480	163	45	)	)	PUNCT
ejpam-4480	163	46	.	.	PUNCT
ejpam-4480	164	1	also	also	ADV
ejpam-4480	164	2	,	,	PUNCT
ejpam-4480	164	3	the	the	DET
ejpam-4480	164	4	only	only	ADJ
ejpam-4480	164	5	subsets	subset	NOUN
ejpam-4480	164	6	of	of	ADP
ejpam-4480	164	7	s2	s2	PROPN
ejpam-4480	164	8	that	that	PRON
ejpam-4480	164	9	are	be	AUX
ejpam-4480	164	10	supercliques	superclique	NOUN
ejpam-4480	164	11	in	in	ADP
ejpam-4480	164	12	g	g	PROPN
ejpam-4480	164	13	are	be	AUX
ejpam-4480	164	14	the	the	DET
ejpam-4480	164	15	singletons	singleton	NOUN
ejpam-4480	164	16	and	and	CCONJ
ejpam-4480	164	17	the	the	DET
ejpam-4480	164	18	sets	set	NOUN
ejpam-4480	164	19	{	{	PUNCT
ejpam-4480	164	20	y1	y1	NOUN
ejpam-4480	164	21	,	,	PUNCT
ejpam-4480	164	22	yi	yi	NOUN
ejpam-4480	164	23	}	}	PUNCT
ejpam-4480	164	24	where	where	SCONJ
ejpam-4480	164	25	i	i	PRON
ejpam-4480	164	26	∈	∈	PROPN
ejpam-4480	164	27	{	{	PUNCT
ejpam-4480	164	28	2	2	NUM
ejpam-4480	164	29	,	,	PUNCT
ejpam-4480	164	30	3	3	NUM
ejpam-4480	164	31	,	,	PUNCT
ejpam-4480	164	32	.	.	PUNCT
ejpam-4480	164	33	.	.	PUNCT
ejpam-4480	165	1	.	.	PUNCT
ejpam-4480	166	1	,	,	PUNCT
ejpam-4480	166	2	b	b	X
ejpam-4480	166	3	}	}	PUNCT
ejpam-4480	166	4	.	.	PUNCT
ejpam-4480	167	1	it	it	PRON
ejpam-4480	167	2	can	can	AUX
ejpam-4480	167	3	easily	easily	ADV
ejpam-4480	167	4	be	be	AUX
ejpam-4480	167	5	verified	verify	VERB
ejpam-4480	167	6	that	that	SCONJ
ejpam-4480	167	7	s1	s1	NOUN
ejpam-4480	167	8	is	be	AUX
ejpam-4480	167	9	a	a	DET
ejpam-4480	167	10	maximum	maximum	ADJ
ejpam-4480	167	11	superclique	superclique	NOUN
ejpam-4480	167	12	in	in	ADP
ejpam-4480	167	13	g.	g.	PROPN
ejpam-4480	167	14	consequently	consequently	ADV
ejpam-4480	167	15	,	,	PUNCT
ejpam-4480	167	16	ωs(g	ωs(g	PUNCT
ejpam-4480	167	17	)	)	PUNCT
ejpam-4480	167	18	=	=	SYM
ejpam-4480	167	19	a.	a.	PROPN
ejpam-4480	167	20	r.	r.	PROPN
ejpam-4480	167	21	dela	dela	PROPN
ejpam-4480	167	22	cerna	cerna	PROPN
ejpam-4480	167	23	,	,	PUNCT
ejpam-4480	167	24	s.	s.	PROPN
ejpam-4480	167	25	canoy	canoy	PROPN
ejpam-4480	167	26	,	,	PUNCT
ejpam-4480	167	27	jr	jr	PROPN
ejpam-4480	167	28	.	.	PROPN
ejpam-4480	167	29	/	/	SYM
ejpam-4480	167	30	eur	eur	PROPN
ejpam-4480	167	31	.	.	PUNCT
ejpam-4480	168	1	j.	j.	PROPN
ejpam-4480	168	2	pure	pure	PROPN
ejpam-4480	168	3	appl	appl	PROPN
ejpam-4480	168	4	.	.	PROPN
ejpam-4480	168	5	math	math	PROPN
ejpam-4480	168	6	,	,	PUNCT
ejpam-4480	168	7	15	15	NUM
ejpam-4480	168	8	(	(	PUNCT
ejpam-4480	168	9	3	3	NUM
ejpam-4480	168	10	)	)	PUNCT
ejpam-4480	168	11	(	(	PUNCT
ejpam-4480	168	12	2022	2022	NUM
ejpam-4480	168	13	)	)	PUNCT
ejpam-4480	168	14	,	,	PUNCT
ejpam-4480	168	15	1217	1217	NUM
ejpam-4480	168	16	-	-	SYM
ejpam-4480	168	17	1228	1228	NUM
ejpam-4480	168	18	1221	1221	NUM
ejpam-4480	168	19	....................................	....................................	PUNCT
ejpam-4480	168	20	....................................	....................................	PUNCT
ejpam-4480	169	1	....................................	....................................	PUNCT
ejpam-4480	169	2	....................................	....................................	PUNCT
ejpam-4480	170	1	........................................................................	........................................................................	PUNCT
ejpam-4480	170	2	....................................	....................................	PUNCT
ejpam-4480	171	1	........................................................................	........................................................................	PUNCT
ejpam-4480	171	2	....................................	....................................	PUNCT
ejpam-4480	172	1	....................................	....................................	PUNCT
ejpam-4480	172	2	....................................	....................................	PUNCT
ejpam-4480	173	1	....................................	....................................	PUNCT
ejpam-4480	173	2	....................................	....................................	PUNCT
ejpam-4480	174	1	....................................	....................................	PUNCT
ejpam-4480	174	2	........................................................................	........................................................................	PUNCT
ejpam-4480	175	1	....................................	....................................	PUNCT
ejpam-4480	175	2	........................................................................	........................................................................	PUNCT
ejpam-4480	176	1	....................................	....................................	PUNCT
ejpam-4480	176	2	....................................	....................................	PUNCT
ejpam-4480	177	1	....................................	....................................	PUNCT
ejpam-4480	177	2	....................................	....................................	PUNCT
ejpam-4480	178	1	...........	...........	PUNCT
ejpam-4480	178	2	..........	..........	PUNCT
ejpam-4480	179	1	..........	..........	PUNCT
ejpam-4480	179	2	..........	..........	PUNCT
ejpam-4480	180	1	..........	..........	PUNCT
ejpam-4480	180	2	..........	..........	PUNCT
ejpam-4480	181	1	..........	..........	PUNCT
ejpam-4480	181	2	..........	..........	PUNCT
ejpam-4480	182	1	..........	..........	PUNCT
ejpam-4480	182	2	..........	..........	PUNCT
ejpam-4480	183	1	..........	..........	PUNCT
ejpam-4480	183	2	..........	..........	PUNCT
ejpam-4480	184	1	..........	..........	PUNCT
ejpam-4480	184	2	..	..	PUNCT
ejpam-4480	185	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4480	185	2	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4480	186	1	...........	...........	PUNCT
ejpam-4480	186	2	..........	..........	PUNCT
ejpam-4480	187	1	..........	..........	PUNCT
ejpam-4480	187	2	..........	..........	PUNCT
ejpam-4480	188	1	..........	..........	PUNCT
ejpam-4480	188	2	..........	..........	PUNCT
ejpam-4480	189	1	..........	..........	PUNCT
ejpam-4480	189	2	..........	..........	PUNCT
ejpam-4480	190	1	..........	..........	PUNCT
ejpam-4480	190	2	..........	..........	PUNCT
ejpam-4480	191	1	..........	..........	PUNCT
ejpam-4480	191	2	..........	..........	PUNCT
ejpam-4480	192	1	..........	..........	PUNCT
ejpam-4480	192	2	..	..	PUNCT
ejpam-4480	192	3	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4480	192	4	...........	...........	PUNCT
ejpam-4480	193	1	..........	..........	PUNCT
ejpam-4480	193	2	..........	..........	PUNCT
ejpam-4480	194	1	..........	..........	PUNCT
ejpam-4480	194	2	..........	..........	PUNCT
ejpam-4480	195	1	..........	..........	PUNCT
ejpam-4480	195	2	..........	..........	PUNCT
ejpam-4480	196	1	..........	..........	PUNCT
ejpam-4480	196	2	..........	..........	PUNCT
ejpam-4480	197	1	..........	..........	PUNCT
ejpam-4480	197	2	..........	..........	PUNCT
ejpam-4480	198	1	..........	..........	PUNCT
ejpam-4480	198	2	..........	..........	PUNCT
ejpam-4480	199	1	..	..	PUNCT
ejpam-4480	199	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4480	200	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4480	200	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4480	201	1	...........	...........	PUNCT
ejpam-4480	201	2	..........	..........	PUNCT
ejpam-4480	202	1	..........	..........	PUNCT
ejpam-4480	202	2	..........	..........	PUNCT
ejpam-4480	203	1	..........	..........	PUNCT
ejpam-4480	203	2	..........	..........	PUNCT
ejpam-4480	204	1	..........	..........	PUNCT
ejpam-4480	204	2	..........	..........	PUNCT
ejpam-4480	205	1	..........	..........	PUNCT
ejpam-4480	205	2	..........	..........	PUNCT
ejpam-4480	206	1	..........	..........	PUNCT
ejpam-4480	206	2	..........	..........	PUNCT
ejpam-4480	207	1	..........	..........	PUNCT
ejpam-4480	208	1	..	..	PUNCT
ejpam-4480	209	1	•	•	NUM
ejpam-4480	209	2	•	•	NUM
ejpam-4480	209	3	•	•	NUM
ejpam-4480	209	4	•	•	NUM
ejpam-4480	209	5	•	•	NOUN
ejpam-4480	209	6	•	•	NOUN
ejpam-4480	209	7	.....................	.....................	PUNCT
ejpam-4480	209	8	....................	....................	PUNCT
ejpam-4480	209	9	....................	....................	PUNCT
ejpam-4480	209	10	....................	....................	PUNCT
ejpam-4480	209	11	....................	....................	PUNCT
ejpam-4480	209	12	....................	....................	PUNCT
ejpam-4480	209	13	....................	....................	PUNCT
ejpam-4480	209	14	....................	....................	PUNCT
ejpam-4480	209	15	....................	....................	PUNCT
ejpam-4480	209	16	....................	....................	PUNCT
ejpam-4480	209	17	....................	....................	PUNCT
ejpam-4480	209	18	....................	....................	PUNCT
ejpam-4480	209	19	....................	....................	PUNCT
ejpam-4480	209	20	...........	...........	PUNCT
ejpam-4480	209	21	...........	...........	PUNCT
ejpam-4480	209	22	..........	..........	PUNCT
ejpam-4480	209	23	..........	..........	PUNCT
ejpam-4480	210	1	..........	..........	PUNCT
ejpam-4480	210	2	..........	..........	PUNCT
ejpam-4480	211	1	..........	..........	PUNCT
ejpam-4480	211	2	..........	..........	PUNCT
ejpam-4480	212	1	..........	..........	PUNCT
ejpam-4480	212	2	..........	..........	PUNCT
ejpam-4480	213	1	..........	..........	PUNCT
ejpam-4480	213	2	..........	..........	PUNCT
ejpam-4480	214	1	..........	..........	PUNCT
ejpam-4480	214	2	..........	..........	PUNCT
ejpam-4480	215	1	..........	..........	PUNCT
ejpam-4480	215	2	..........	..........	PUNCT
ejpam-4480	216	1	..........	..........	PUNCT
ejpam-4480	216	2	..........	..........	PUNCT
ejpam-4480	217	1	..........	..........	PUNCT
ejpam-4480	217	2	..........	..........	PUNCT
ejpam-4480	218	1	..........	..........	PUNCT
ejpam-4480	218	2	..........	..........	PUNCT
ejpam-4480	219	1	..........	..........	PUNCT
ejpam-4480	219	2	..........	..........	PUNCT
ejpam-4480	220	1	..........	..........	PUNCT
ejpam-4480	220	2	..........	..........	PUNCT
ejpam-4480	221	1	..........	..........	PUNCT
ejpam-4480	221	2	..........	..........	PUNCT
ejpam-4480	222	1	......	......	PUNCT
ejpam-4480	222	2	.........	.........	PUNCT
ejpam-4480	222	3	........	........	PUNCT
ejpam-4480	222	4	........	........	PUNCT
ejpam-4480	222	5	........	........	PUNCT
ejpam-4480	222	6	........	........	PUNCT
ejpam-4480	222	7	........	........	PUNCT
ejpam-4480	222	8	........	........	PUNCT
ejpam-4480	222	9	........	........	PUNCT
ejpam-4480	222	10	........	........	PUNCT
ejpam-4480	222	11	........	........	PUNCT
ejpam-4480	222	12	........	........	PUNCT
ejpam-4480	222	13	........	........	PUNCT
ejpam-4480	222	14	........	........	PUNCT
ejpam-4480	222	15	........	........	PUNCT
ejpam-4480	222	16	........	........	PUNCT
ejpam-4480	222	17	........	........	PUNCT
ejpam-4480	222	18	........	........	PUNCT
ejpam-4480	222	19	........	........	PUNCT
ejpam-4480	222	20	........	........	PUNCT
ejpam-4480	222	21	........	........	PUNCT
ejpam-4480	222	22	........	........	PUNCT
ejpam-4480	222	23	........	........	PUNCT
ejpam-4480	222	24	........	........	PUNCT
ejpam-4480	222	25	........	........	PUNCT
ejpam-4480	222	26	........	........	PUNCT
ejpam-4480	222	27	........	........	PUNCT
ejpam-4480	222	28	........	........	PUNCT
ejpam-4480	222	29	...	...	PUNCT
ejpam-4480	222	30	.........	.........	PUNCT
ejpam-4480	222	31	........	........	PUNCT
ejpam-4480	222	32	........	........	PUNCT
ejpam-4480	222	33	........	........	PUNCT
ejpam-4480	222	34	........	........	PUNCT
ejpam-4480	222	35	........	........	PUNCT
ejpam-4480	222	36	........	........	PUNCT
ejpam-4480	222	37	........	........	PUNCT
ejpam-4480	222	38	........	........	PUNCT
ejpam-4480	222	39	........	........	PUNCT
ejpam-4480	222	40	........	........	PUNCT
ejpam-4480	222	41	........	........	PUNCT
ejpam-4480	222	42	........	........	PUNCT
ejpam-4480	222	43	........	........	PUNCT
ejpam-4480	222	44	........	........	PUNCT
ejpam-4480	222	45	........	........	PUNCT
ejpam-4480	222	46	........	........	PUNCT
ejpam-4480	222	47	........	........	PUNCT
ejpam-4480	222	48	........	........	PUNCT
ejpam-4480	222	49	........	........	PUNCT
ejpam-4480	222	50	........	........	PUNCT
ejpam-4480	222	51	........	........	PUNCT
ejpam-4480	222	52	........	........	PUNCT
ejpam-4480	222	53	........	........	PUNCT
ejpam-4480	222	54	........	........	PUNCT
ejpam-4480	222	55	........	........	PUNCT
ejpam-4480	222	56	........	........	PUNCT
ejpam-4480	223	1	........................................................................................................................................................................................................................................................................................	........................................................................................................................................................................................................................................................................................	PROPN
ejpam-4480	223	2	................................................................................................................................................................................................................................................................................	................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4480	224	1	.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4480	224	2	....................	....................	PUNCT
ejpam-4480	224	3	....................	....................	PUNCT
ejpam-4480	224	4	....................	....................	PUNCT
ejpam-4480	224	5	....................	....................	PUNCT
ejpam-4480	224	6	....................	....................	PUNCT
ejpam-4480	224	7	....................	....................	PUNCT
ejpam-4480	224	8	....................	....................	PUNCT
ejpam-4480	224	9	....................	....................	PUNCT
ejpam-4480	224	10	....................	....................	PUNCT
ejpam-4480	224	11	....................	....................	PUNCT
ejpam-4480	224	12	....................	....................	PUNCT
ejpam-4480	224	13	....................	....................	PUNCT
ejpam-4480	225	1	...........	...........	PUNCT
ejpam-4480	225	2	...............................................................................................................................................................................................	...............................................................................................................................................................................................	PUNCT
ejpam-4480	225	3	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4480	225	4	.........	.........	PUNCT
ejpam-4480	226	1	........	........	PUNCT
ejpam-4480	226	2	........	........	PUNCT
ejpam-4480	226	3	........	........	PUNCT
ejpam-4480	226	4	........	........	PUNCT
ejpam-4480	226	5	........	........	PUNCT
ejpam-4480	226	6	........	........	PUNCT
ejpam-4480	226	7	........	........	PUNCT
ejpam-4480	226	8	........	........	PUNCT
ejpam-4480	226	9	........	........	PUNCT
ejpam-4480	226	10	........	........	PUNCT
ejpam-4480	226	11	........	........	PUNCT
ejpam-4480	226	12	.......	.......	PUNCT
ejpam-4480	226	13	...........	...........	PUNCT
ejpam-4480	227	1	..........	..........	PUNCT
ejpam-4480	227	2	..........	..........	PUNCT
ejpam-4480	228	1	..........	..........	PUNCT
ejpam-4480	228	2	..........	..........	PUNCT
ejpam-4480	229	1	..........	..........	PUNCT
ejpam-4480	229	2	..........	..........	PUNCT
ejpam-4480	230	1	..........	..........	PUNCT
ejpam-4480	230	2	..........	..........	PUNCT
ejpam-4480	231	1	..........	..........	PUNCT
ejpam-4480	231	2	..........	..........	PUNCT
ejpam-4480	232	1	..........	..........	PUNCT
ejpam-4480	232	2	..........	..........	PUNCT
ejpam-4480	233	1	..	..	PUNCT
ejpam-4480	233	2	...............................................................................................................................................................................................	...............................................................................................................................................................................................	PUNCT
ejpam-4480	234	1	.............................................................................................................................	.............................................................................................................................	PUNCT
ejpam-4480	234	2	...........	...........	PUNCT
ejpam-4480	234	3	..........	..........	PUNCT
ejpam-4480	235	1	..........	..........	PUNCT
ejpam-4480	235	2	..........	..........	PUNCT
ejpam-4480	236	1	..........	..........	PUNCT
ejpam-4480	236	2	..........	..........	PUNCT
ejpam-4480	237	1	..........	..........	PUNCT
ejpam-4480	237	2	..........	..........	PUNCT
ejpam-4480	238	1	..........	..........	PUNCT
ejpam-4480	238	2	..........	..........	PUNCT
ejpam-4480	239	1	..........	..........	PUNCT
ejpam-4480	239	2	..........	..........	PUNCT
ejpam-4480	240	1	....	....	PUNCT
ejpam-4480	240	2	...........................................................................................................................................................................................................................................................................................................	...........................................................................................................................................................................................................................................................................................................	X
ejpam-4480	240	3	......................................................................................................................................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4480	240	4	............................................................................................................................................................................................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4480	240	5	........	........	PUNCT
ejpam-4480	240	6	........	........	PUNCT
ejpam-4480	240	7	........	........	PUNCT
ejpam-4480	240	8	........	........	PUNCT
ejpam-4480	240	9	........	........	PUNCT
ejpam-4480	240	10	........	........	PUNCT
ejpam-4480	240	11	........	........	PUNCT
ejpam-4480	240	12	........	........	PUNCT
ejpam-4480	240	13	........	........	PUNCT
ejpam-4480	240	14	........	........	PUNCT
ejpam-4480	240	15	........	........	PUNCT
ejpam-4480	240	16	........	........	PUNCT
ejpam-4480	240	17	........	........	PUNCT
ejpam-4480	240	18	........	........	PUNCT
ejpam-4480	240	19	........	........	PUNCT
ejpam-4480	240	20	........	........	PUNCT
ejpam-4480	240	21	........	........	PUNCT
ejpam-4480	240	22	........	........	PUNCT
ejpam-4480	240	23	........	........	PUNCT
ejpam-4480	240	24	........	........	PUNCT
ejpam-4480	240	25	........	........	PUNCT
ejpam-4480	240	26	........	........	PUNCT
ejpam-4480	240	27	........	........	PUNCT
ejpam-4480	240	28	........	........	PUNCT
ejpam-4480	240	29	........	........	PUNCT
ejpam-4480	240	30	........	........	PUNCT
ejpam-4480	240	31	........	........	PUNCT
ejpam-4480	240	32	........	........	PUNCT
ejpam-4480	240	33	........	........	PUNCT
ejpam-4480	240	34	........	........	PUNCT
ejpam-4480	240	35	........	........	PUNCT
ejpam-4480	240	36	........	........	PUNCT
ejpam-4480	240	37	........	........	PUNCT
ejpam-4480	240	38	........	........	PUNCT
ejpam-4480	240	39	........	........	PUNCT
ejpam-4480	240	40	........	........	PUNCT
ejpam-4480	240	41	........	........	PUNCT
ejpam-4480	240	42	........	........	PUNCT
ejpam-4480	240	43	........	........	PUNCT
ejpam-4480	240	44	........	........	PUNCT
ejpam-4480	240	45	.......	.......	PUNCT
ejpam-4480	241	1	..........	..........	PUNCT
ejpam-4480	241	2	.........	.........	PUNCT
ejpam-4480	242	1	.........	.........	PUNCT
ejpam-4480	242	2	.........	.........	PUNCT
ejpam-4480	243	1	.........	.........	PUNCT
ejpam-4480	243	2	.........	.........	PUNCT
ejpam-4480	244	1	.........	.........	PUNCT
ejpam-4480	244	2	.........	.........	PUNCT
ejpam-4480	245	1	.........	.........	PUNCT
ejpam-4480	245	2	.........	.........	PUNCT
ejpam-4480	246	1	.........	.........	PUNCT
ejpam-4480	246	2	.........	.........	PUNCT
ejpam-4480	247	1	.........	.........	PUNCT
ejpam-4480	247	2	.........	.........	PUNCT
ejpam-4480	248	1	.........	.........	PUNCT
ejpam-4480	248	2	.........	.........	PUNCT
ejpam-4480	249	1	.........	.........	PUNCT
ejpam-4480	249	2	.........	.........	PUNCT
ejpam-4480	250	1	.........	.........	PUNCT
ejpam-4480	250	2	.........	.........	PUNCT
ejpam-4480	251	1	.........	.........	PUNCT
ejpam-4480	251	2	.........	.........	PUNCT
ejpam-4480	252	1	.........	.........	PUNCT
ejpam-4480	252	2	.........	.........	PUNCT
ejpam-4480	253	1	.........	.........	PUNCT
ejpam-4480	253	2	.....	.....	PUNCT
ejpam-4480	253	3	............................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................	PUNCT
ejpam-4480	253	4	.........	.........	PUNCT
ejpam-4480	253	5	........	........	PUNCT
ejpam-4480	253	6	........	........	PUNCT
ejpam-4480	253	7	........	........	PUNCT
ejpam-4480	253	8	........	........	PUNCT
ejpam-4480	253	9	........	........	PUNCT
ejpam-4480	253	10	........	........	PUNCT
ejpam-4480	253	11	........	........	PUNCT
ejpam-4480	253	12	........	........	PUNCT
ejpam-4480	253	13	........	........	PUNCT
ejpam-4480	253	14	........	........	PUNCT
ejpam-4480	253	15	........	........	PUNCT
ejpam-4480	253	16	........	........	PUNCT
ejpam-4480	253	17	........	........	PUNCT
ejpam-4480	253	18	........	........	PUNCT
ejpam-4480	253	19	........	........	PUNCT
ejpam-4480	253	20	........	........	PUNCT
ejpam-4480	253	21	........	........	PUNCT
ejpam-4480	253	22	........	........	PUNCT
ejpam-4480	253	23	........	........	PUNCT
ejpam-4480	253	24	........	........	PUNCT
ejpam-4480	253	25	........	........	PUNCT
ejpam-4480	253	26	........	........	PUNCT
ejpam-4480	253	27	........	........	PUNCT
ejpam-4480	253	28	........	........	PUNCT
ejpam-4480	253	29	........	........	PUNCT
ejpam-4480	253	30	........	........	PUNCT
ejpam-4480	253	31	........	........	PUNCT
ejpam-4480	253	32	........	........	PUNCT
ejpam-4480	253	33	........	........	PUNCT
ejpam-4480	253	34	........	........	PUNCT
ejpam-4480	253	35	........	........	PUNCT
ejpam-4480	253	36	........	........	PUNCT
ejpam-4480	253	37	........	........	PUNCT
ejpam-4480	253	38	........	........	PUNCT
ejpam-4480	253	39	........	........	PUNCT
ejpam-4480	253	40	........	........	PUNCT
ejpam-4480	253	41	........	........	PUNCT
ejpam-4480	253	42	........	........	PUNCT
ejpam-4480	253	43	........	........	PUNCT
ejpam-4480	253	44	........	........	PUNCT
ejpam-4480	253	45	.......	.......	PUNCT
ejpam-4480	254	1	..........	..........	PUNCT
ejpam-4480	254	2	.........	.........	PUNCT
ejpam-4480	255	1	.........	.........	PUNCT
ejpam-4480	255	2	.........	.........	PUNCT
ejpam-4480	256	1	.........	.........	PUNCT
ejpam-4480	256	2	.........	.........	PUNCT
ejpam-4480	257	1	.........	.........	PUNCT
ejpam-4480	257	2	.........	.........	PUNCT
ejpam-4480	258	1	.........	.........	PUNCT
ejpam-4480	258	2	.........	.........	PUNCT
ejpam-4480	259	1	.........	.........	PUNCT
ejpam-4480	259	2	.........	.........	PUNCT
ejpam-4480	260	1	.........	.........	PUNCT
ejpam-4480	260	2	.........	.........	PUNCT
ejpam-4480	261	1	.........	.........	PUNCT
ejpam-4480	261	2	.........	.........	PUNCT
ejpam-4480	262	1	.........	.........	PUNCT
ejpam-4480	262	2	.........	.........	PUNCT
ejpam-4480	263	1	.........	.........	PUNCT
ejpam-4480	263	2	.........	.........	PUNCT
ejpam-4480	264	1	.........	.........	PUNCT
ejpam-4480	264	2	.........	.........	PUNCT
ejpam-4480	265	1	.........	.........	PUNCT
ejpam-4480	265	2	.........	.........	PUNCT
ejpam-4480	266	1	.........	.........	PUNCT
ejpam-4480	266	2	.........	.........	PUNCT
ejpam-4480	267	1	.........	.........	PUNCT
ejpam-4480	267	2	.........	.........	PUNCT
ejpam-4480	268	1	.........	.........	PUNCT
ejpam-4480	268	2	.........	.........	PUNCT
ejpam-4480	269	1	.........	.........	PUNCT
ejpam-4480	269	2	.........	.........	PUNCT
ejpam-4480	270	1	.........	.........	PUNCT
ejpam-4480	270	2	.........	.........	PUNCT
ejpam-4480	271	1	.........	.........	PUNCT
ejpam-4480	271	2	.........	.........	PUNCT
ejpam-4480	272	1	.........	.........	PUNCT
ejpam-4480	272	2	.........	.........	PUNCT
ejpam-4480	273	1	.........	.........	PUNCT
ejpam-4480	273	2	.........	.........	PUNCT
ejpam-4480	274	1	.........	.........	PUNCT
ejpam-4480	274	2	.........	.........	PUNCT
ejpam-4480	274	3	........	........	PUNCT
ejpam-4480	275	1	..............	..............	PUNCT
ejpam-4480	275	2	.............	.............	PUNCT
ejpam-4480	275	3	.............	.............	PUNCT
ejpam-4480	275	4	.............	.............	PUNCT
ejpam-4480	275	5	.............	.............	PUNCT
ejpam-4480	275	6	.............	.............	PUNCT
ejpam-4480	275	7	.............	.............	PUNCT
ejpam-4480	275	8	.............	.............	PUNCT
ejpam-4480	275	9	.............	.............	PUNCT
ejpam-4480	275	10	.............	.............	PUNCT
ejpam-4480	275	11	.............	.............	PUNCT
ejpam-4480	275	12	.............	.............	PUNCT
ejpam-4480	275	13	.............	.............	PUNCT
ejpam-4480	275	14	.............	.............	PUNCT
ejpam-4480	275	15	.............	.............	PUNCT
ejpam-4480	275	16	.............	.............	PUNCT
ejpam-4480	275	17	.............	.............	PUNCT
ejpam-4480	275	18	.............	.............	PUNCT
ejpam-4480	275	19	.............	.............	PUNCT
ejpam-4480	275	20	.............	.............	PUNCT
ejpam-4480	275	21	.............	.............	PUNCT
ejpam-4480	275	22	.............	.............	PUNCT
ejpam-4480	275	23	.............	.............	PUNCT
ejpam-4480	275	24	.............	.............	PUNCT
ejpam-4480	275	25	.............	.............	PUNCT
ejpam-4480	275	26	.............	.............	PUNCT
ejpam-4480	275	27	.......	.......	PUNCT
ejpam-4480	275	28	......................	......................	PUNCT
ejpam-4480	276	1	.....................	.....................	PUNCT
ejpam-4480	276	2	.....................	.....................	PUNCT
ejpam-4480	277	1	.....................	.....................	PUNCT
ejpam-4480	277	2	.....................	.....................	PUNCT
ejpam-4480	277	3	.....................	.....................	PUNCT
ejpam-4480	277	4	.....................	.....................	PUNCT
ejpam-4480	277	5	.....................	.....................	PUNCT
ejpam-4480	277	6	.....................	.....................	PUNCT
ejpam-4480	277	7	.....................	.....................	PUNCT
ejpam-4480	277	8	.....................	.....................	PUNCT
ejpam-4480	277	9	.....................	.....................	PUNCT
ejpam-4480	277	10	.....................	.....................	PUNCT
ejpam-4480	277	11	............	............	PUNCT
ejpam-4480	278	1	..........	..........	PUNCT
ejpam-4480	278	2	.........	.........	PUNCT
ejpam-4480	279	1	.........	.........	PUNCT
ejpam-4480	279	2	.........	.........	PUNCT
ejpam-4480	280	1	.........	.........	PUNCT
ejpam-4480	280	2	.........	.........	PUNCT
ejpam-4480	281	1	.........	.........	PUNCT
ejpam-4480	281	2	.........	.........	PUNCT
ejpam-4480	282	1	.........	.........	PUNCT
ejpam-4480	282	2	.........	.........	PUNCT
ejpam-4480	283	1	.........	.........	PUNCT
ejpam-4480	283	2	.........	.........	PUNCT
ejpam-4480	284	1	.........	.........	PUNCT
ejpam-4480	284	2	.........	.........	PUNCT
ejpam-4480	285	1	.........	.........	PUNCT
ejpam-4480	285	2	.........	.........	PUNCT
ejpam-4480	286	1	.........	.........	PUNCT
ejpam-4480	286	2	.........	.........	PUNCT
ejpam-4480	287	1	.........	.........	PUNCT
ejpam-4480	287	2	.........	.........	PUNCT
ejpam-4480	288	1	.........	.........	PUNCT
ejpam-4480	288	2	.........	.........	PUNCT
ejpam-4480	289	1	.........	.........	PUNCT
ejpam-4480	289	2	.........	.........	PUNCT
ejpam-4480	290	1	.........	.........	PUNCT
ejpam-4480	290	2	.........	.........	PUNCT
ejpam-4480	290	3	.	.	PUNCT
ejpam-4480	291	1	..............	..............	PUNCT
ejpam-4480	291	2	.............	.............	PUNCT
ejpam-4480	291	3	.............	.............	PUNCT
ejpam-4480	291	4	.............	.............	PUNCT
ejpam-4480	291	5	.............	.............	PUNCT
ejpam-4480	291	6	.............	.............	PUNCT
ejpam-4480	291	7	.............	.............	PUNCT
ejpam-4480	291	8	.............	.............	PUNCT
ejpam-4480	291	9	.............	.............	PUNCT
ejpam-4480	291	10	.............	.............	PUNCT
ejpam-4480	291	11	.............	.............	PUNCT
ejpam-4480	291	12	.............	.............	PUNCT
ejpam-4480	291	13	.............	.............	PUNCT
ejpam-4480	291	14	.............	.............	PUNCT
ejpam-4480	291	15	.............	.............	PUNCT
ejpam-4480	291	16	.............	.............	PUNCT
ejpam-4480	291	17	.............	.............	PUNCT
ejpam-4480	291	18	.............	.............	PUNCT
ejpam-4480	291	19	.............	.............	PUNCT
ejpam-4480	291	20	.............	.............	PUNCT
ejpam-4480	291	21	.............	.............	PUNCT
ejpam-4480	291	22	.............	.............	PUNCT
ejpam-4480	291	23	.............	.............	PUNCT
ejpam-4480	291	24	.............	.............	PUNCT
ejpam-4480	291	25	.............	.............	PUNCT
ejpam-4480	291	26	.............	.............	PUNCT
ejpam-4480	291	27	.............	.............	PUNCT
ejpam-4480	292	1	......	......	PUNCT
ejpam-4480	292	2	...........................	...........................	PUNCT
ejpam-4480	293	1	..........................	..........................	PUNCT
ejpam-4480	293	2	..........................	..........................	PUNCT
ejpam-4480	294	1	..........................	..........................	PUNCT
ejpam-4480	294	2	..........................	..........................	PUNCT
ejpam-4480	295	1	..........................	..........................	PUNCT
ejpam-4480	295	2	..........................	..........................	PUNCT
ejpam-4480	296	1	..........................	..........................	PUNCT
ejpam-4480	296	2	..........................	..........................	PUNCT
ejpam-4480	297	1	..........................	..........................	PUNCT
ejpam-4480	297	2	..........................	..........................	PUNCT
ejpam-4480	298	1	..........................	..........................	PUNCT
ejpam-4480	298	2	..........................	..........................	PUNCT
ejpam-4480	299	1	..........................	..........................	PUNCT
ejpam-4480	299	2	...............................................................................................................................................................................................................................................................................................................................................................	...............................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4480	299	3	......................	......................	PUNCT
ejpam-4480	300	1	.....................	.....................	PUNCT
ejpam-4480	300	2	.....................	.....................	PUNCT
ejpam-4480	300	3	.....................	.....................	PUNCT
ejpam-4480	300	4	.....................	.....................	PUNCT
ejpam-4480	300	5	.....................	.....................	PUNCT
ejpam-4480	300	6	.....................	.....................	PUNCT
ejpam-4480	300	7	.....................	.....................	PUNCT
ejpam-4480	300	8	.....................	.....................	PUNCT
ejpam-4480	300	9	.....................	.....................	PUNCT
ejpam-4480	300	10	.....................	.....................	PUNCT
ejpam-4480	300	11	.....................	.....................	PUNCT
ejpam-4480	300	12	.....................	.....................	PUNCT
ejpam-4480	301	1	.....................	.....................	PUNCT
ejpam-4480	301	2	..................................................................................................................................................................................................................................................................................................................................................................	..................................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4480	302	1	............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................	PROPN
ejpam-4480	302	2	..........................................................................................................................................................................................................................................................................................................................................................	..........................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4480	302	3	.......................................................................................................................................................................................................................................	.......................................................................................................................................................................................................................................	PUNCT
ejpam-4480	303	1	xa	xa	PROPN
ejpam-4480	304	1	x2	x2	PROPN
ejpam-4480	304	2	x3	x3	PROPN
ejpam-4480	304	3	x4	x4	PROPN
ejpam-4480	305	1	x5	x5	PROPN
ejpam-4480	305	2	x1	x1	PROPN
ejpam-4480	305	3	=	=	SYM
ejpam-4480	305	4	y1	y1	ADJ
ejpam-4480	305	5	y2	y2	NOUN
ejpam-4480	305	6	y3	y3	NOUN
ejpam-4480	305	7	y4	y4	PROPN
ejpam-4480	305	8	y5y6	y5y6	ADP
ejpam-4480	305	9	y7	y7	PROPN
ejpam-4480	305	10	yb	yb	PROPN
ejpam-4480	305	11	g∗	g∗	PROPN
ejpam-4480	305	12	:	:	PUNCT
ejpam-4480	305	13	figure	figure	NOUN
ejpam-4480	305	14	2	2	NUM
ejpam-4480	305	15	:	:	PUNCT
ejpam-4480	305	16	a	a	DET
ejpam-4480	305	17	graph	graph	NOUN
ejpam-4480	305	18	g	g	NOUN
ejpam-4480	305	19	with	with	ADP
ejpam-4480	305	20	ωs(g	ωs(g	NOUN
ejpam-4480	305	21	)	)	PUNCT
ejpam-4480	305	22	<	<	X
ejpam-4480	305	23	ω(g	ω(g	NOUN
ejpam-4480	305	24	)	)	PUNCT
ejpam-4480	305	25	therefore	therefore	ADV
ejpam-4480	305	26	,	,	PUNCT
ejpam-4480	305	27	the	the	DET
ejpam-4480	305	28	assertion	assertion	NOUN
ejpam-4480	305	29	holds	hold	VERB
ejpam-4480	305	30	.	.	PUNCT
ejpam-4480	306	1	corollary	corollary	ADJ
ejpam-4480	306	2	1	1	NUM
ejpam-4480	306	3	.	.	PUNCT
ejpam-4480	307	1	let	let	VERB
ejpam-4480	307	2	n	n	PRON
ejpam-4480	307	3	be	be	AUX
ejpam-4480	307	4	a	a	DET
ejpam-4480	307	5	positive	positive	ADJ
ejpam-4480	307	6	integer	integer	NOUN
ejpam-4480	307	7	.	.	PUNCT
ejpam-4480	308	1	then	then	ADV
ejpam-4480	308	2	there	there	PRON
ejpam-4480	308	3	exists	exist	VERB
ejpam-4480	308	4	a	a	DET
ejpam-4480	308	5	connected	connected	ADJ
ejpam-4480	308	6	graph	graph	NOUN
ejpam-4480	308	7	g	g	ADP
ejpam-4480	308	8	such	such	ADJ
ejpam-4480	308	9	that	that	SCONJ
ejpam-4480	308	10	ω(g)−	ω(g)−	NOUN
ejpam-4480	308	11	ωs(g	ωs(g	PUNCT
ejpam-4480	308	12	)	)	PUNCT
ejpam-4480	308	13	=	=	VERB
ejpam-4480	308	14	n.	n.	NOUN
ejpam-4480	308	15	in	in	ADP
ejpam-4480	308	16	other	other	ADJ
ejpam-4480	308	17	words	word	NOUN
ejpam-4480	308	18	,	,	PUNCT
ejpam-4480	308	19	the	the	DET
ejpam-4480	308	20	difference	difference	NOUN
ejpam-4480	308	21	ω	ω	NOUN
ejpam-4480	308	22	−	−	NOUN
ejpam-4480	308	23	ωs	ωs	PROPN
ejpam-4480	308	24	can	can	AUX
ejpam-4480	308	25	be	be	AUX
ejpam-4480	308	26	made	make	VERB
ejpam-4480	308	27	arbitrarily	arbitrarily	ADV
ejpam-4480	308	28	large	large	ADJ
ejpam-4480	308	29	.	.	PUNCT
ejpam-4480	309	1	proof	proof	NOUN
ejpam-4480	309	2	.	.	PUNCT
ejpam-4480	310	1	let	let	VERB
ejpam-4480	310	2	n	n	PRON
ejpam-4480	310	3	be	be	AUX
ejpam-4480	310	4	a	a	DET
ejpam-4480	310	5	positive	positive	ADJ
ejpam-4480	310	6	integer	integer	NOUN
ejpam-4480	310	7	.	.	PUNCT
ejpam-4480	311	1	by	by	ADP
ejpam-4480	311	2	theorem	theorem	NOUN
ejpam-4480	311	3	2	2	NUM
ejpam-4480	311	4	,	,	PUNCT
ejpam-4480	311	5	there	there	PRON
ejpam-4480	311	6	exists	exist	VERB
ejpam-4480	311	7	a	a	DET
ejpam-4480	311	8	connected	connected	ADJ
ejpam-4480	311	9	graph	graph	NOUN
ejpam-4480	311	10	g	g	NOUN
ejpam-4480	311	11	with	with	ADP
ejpam-4480	311	12	ωs(g	ωs(g	PUNCT
ejpam-4480	311	13	)	)	PUNCT
ejpam-4480	311	14	=	=	SYM
ejpam-4480	311	15	n+	n+	ADP
ejpam-4480	311	16	1	1	NUM
ejpam-4480	311	17	and	and	CCONJ
ejpam-4480	311	18	ω(g	ω(g	NOUN
ejpam-4480	311	19	)	)	PUNCT
ejpam-4480	311	20	=	=	SYM
ejpam-4480	311	21	2n+	2n+	NUM
ejpam-4480	311	22	1	1	NUM
ejpam-4480	311	23	.	.	PUNCT
ejpam-4480	312	1	thus	thus	ADV
ejpam-4480	312	2	,	,	PUNCT
ejpam-4480	312	3	ω(g)−	ω(g)−	NOUN
ejpam-4480	312	4	ωs(g	ωs(g	NUM
ejpam-4480	312	5	)	)	PUNCT
ejpam-4480	312	6	=	=	SYM
ejpam-4480	312	7	n.	n.	NOUN
ejpam-4480	312	8	theorem	theorem	NOUN
ejpam-4480	312	9	3	3	X
ejpam-4480	312	10	.	.	PUNCT
ejpam-4480	313	1	let	let	VERB
ejpam-4480	313	2	g	g	PRON
ejpam-4480	313	3	be	be	AUX
ejpam-4480	313	4	a	a	DET
ejpam-4480	313	5	non	non	ADJ
ejpam-4480	313	6	-	-	ADJ
ejpam-4480	313	7	trivial	trivial	ADJ
ejpam-4480	313	8	connected	connected	ADJ
ejpam-4480	313	9	graph	graph	NOUN
ejpam-4480	313	10	and	and	CCONJ
ejpam-4480	313	11	let	let	VERB
ejpam-4480	313	12	g1	g1	PROPN
ejpam-4480	313	13	and	and	CCONJ
ejpam-4480	313	14	g2	g2	PROPN
ejpam-4480	313	15	be	be	VERB
ejpam-4480	313	16	two	two	NUM
ejpam-4480	313	17	copies	copy	NOUN
ejpam-4480	313	18	of	of	ADP
ejpam-4480	313	19	g	g	NOUN
ejpam-4480	313	20	in	in	ADP
ejpam-4480	313	21	the	the	DET
ejpam-4480	313	22	definition	definition	NOUN
ejpam-4480	313	23	of	of	ADP
ejpam-4480	313	24	s(g	s(g	PROPN
ejpam-4480	313	25	)	)	PUNCT
ejpam-4480	313	26	.	.	PUNCT
ejpam-4480	314	1	then	then	ADV
ejpam-4480	314	2	c	c	PROPN
ejpam-4480	314	3	is	be	AUX
ejpam-4480	314	4	a	a	DET
ejpam-4480	314	5	superclique	superclique	NOUN
ejpam-4480	314	6	in	in	ADP
ejpam-4480	314	7	s(g	s(g	PROPN
ejpam-4480	314	8	)	)	PUNCT
ejpam-4480	314	9	if	if	SCONJ
ejpam-4480	314	10	and	and	CCONJ
ejpam-4480	314	11	only	only	ADV
ejpam-4480	314	12	if	if	SCONJ
ejpam-4480	314	13	one	one	NUM
ejpam-4480	314	14	of	of	ADP
ejpam-4480	314	15	the	the	DET
ejpam-4480	314	16	following	follow	VERB
ejpam-4480	314	17	holds	hold	VERB
ejpam-4480	314	18	:	:	PUNCT
ejpam-4480	314	19	(	(	PUNCT
ejpam-4480	314	20	i	i	NOUN
ejpam-4480	314	21	)	)	PUNCT
ejpam-4480	314	22	c	c	PROPN
ejpam-4480	314	23	is	be	AUX
ejpam-4480	314	24	a	a	DET
ejpam-4480	314	25	clique	clique	NOUN
ejpam-4480	314	26	in	in	ADP
ejpam-4480	314	27	g1	g1	PROPN
ejpam-4480	314	28	.	.	PUNCT
ejpam-4480	315	1	(	(	PUNCT
ejpam-4480	315	2	ii	ii	NOUN
ejpam-4480	315	3	)	)	PUNCT
ejpam-4480	315	4	c	c	PROPN
ejpam-4480	315	5	is	be	AUX
ejpam-4480	315	6	a	a	DET
ejpam-4480	315	7	clique	clique	NOUN
ejpam-4480	315	8	in	in	ADP
ejpam-4480	315	9	g2	g2	PROPN
ejpam-4480	315	10	.	.	PUNCT
ejpam-4480	316	1	(	(	PUNCT
ejpam-4480	316	2	iii	iii	X
ejpam-4480	316	3	)	)	PUNCT
ejpam-4480	316	4	c	c	NOUN
ejpam-4480	316	5	=	=	SYM
ejpam-4480	316	6	cg1	cg1	NOUN
ejpam-4480	316	7	∪	∪	ADJ
ejpam-4480	316	8	cg2	cg2	NOUN
ejpam-4480	316	9	,	,	PUNCT
ejpam-4480	316	10	where	where	SCONJ
ejpam-4480	316	11	cg1	cg1	NOUN
ejpam-4480	316	12	and	and	CCONJ
ejpam-4480	316	13	cg2	cg2	PROPN
ejpam-4480	316	14	are	be	AUX
ejpam-4480	316	15	cliques	clique	NOUN
ejpam-4480	316	16	in	in	ADP
ejpam-4480	316	17	g1	g1	PROPN
ejpam-4480	316	18	and	and	CCONJ
ejpam-4480	316	19	g2	g2	PROPN
ejpam-4480	316	20	,	,	PUNCT
ejpam-4480	316	21	respectively	respectively	ADV
ejpam-4480	316	22	,	,	PUNCT
ejpam-4480	316	23	and	and	CCONJ
ejpam-4480	316	24	satisfy	satisfy	VERB
ejpam-4480	316	25	the	the	DET
ejpam-4480	316	26	following	follow	VERB
ejpam-4480	316	27	conditions	condition	NOUN
ejpam-4480	316	28	:	:	PUNCT
ejpam-4480	316	29	(	(	PUNCT
ejpam-4480	316	30	a	a	X
ejpam-4480	316	31	)	)	PUNCT
ejpam-4480	316	32	v′	v′	NOUN
ejpam-4480	316	33	/∈	/∈	PUNCT
ejpam-4480	317	1	cg2	cg2	PROPN
ejpam-4480	317	2	whenever	whenever	SCONJ
ejpam-4480	317	3	v	v	X
ejpam-4480	317	4	∈	∈	NOUN
ejpam-4480	317	5	cg1	cg1	NOUN
ejpam-4480	317	6	,	,	PUNCT
ejpam-4480	317	7	and	and	CCONJ
ejpam-4480	317	8	(	(	PUNCT
ejpam-4480	317	9	b	b	NOUN
ejpam-4480	317	10	)	)	PUNCT
ejpam-4480	317	11	vw	vw	PROPN
ejpam-4480	317	12	∈	∈	PROPN
ejpam-4480	317	13	e(g1	e(g1	ADJ
ejpam-4480	317	14	)	)	PUNCT
ejpam-4480	317	15	for	for	ADP
ejpam-4480	317	16	each	each	DET
ejpam-4480	317	17	v	v	ADP
ejpam-4480	317	18	∈	∈	NOUN
ejpam-4480	317	19	cg1	cg1	NOUN
ejpam-4480	317	20	and	and	CCONJ
ejpam-4480	317	21	w′	w′	PROPN
ejpam-4480	317	22	∈	∈	PROPN
ejpam-4480	317	23	cg2	cg2	PROPN
ejpam-4480	317	24	.	.	PUNCT
ejpam-4480	318	1	r.	r.	PROPN
ejpam-4480	318	2	dela	dela	PROPN
ejpam-4480	318	3	cerna	cerna	PROPN
ejpam-4480	318	4	,	,	PUNCT
ejpam-4480	318	5	s.	s.	PROPN
ejpam-4480	318	6	canoy	canoy	PROPN
ejpam-4480	318	7	,	,	PUNCT
ejpam-4480	318	8	jr	jr	PROPN
ejpam-4480	318	9	.	.	PROPN
ejpam-4480	318	10	/	/	SYM
ejpam-4480	318	11	eur	eur	PROPN
ejpam-4480	318	12	.	.	PUNCT
ejpam-4480	319	1	j.	j.	PROPN
ejpam-4480	319	2	pure	pure	PROPN
ejpam-4480	319	3	appl	appl	PROPN
ejpam-4480	319	4	.	.	PROPN
ejpam-4480	319	5	math	math	PROPN
ejpam-4480	319	6	,	,	PUNCT
ejpam-4480	319	7	15	15	NUM
ejpam-4480	319	8	(	(	PUNCT
ejpam-4480	319	9	3	3	NUM
ejpam-4480	319	10	)	)	PUNCT
ejpam-4480	319	11	(	(	PUNCT
ejpam-4480	319	12	2022	2022	NUM
ejpam-4480	319	13	)	)	PUNCT
ejpam-4480	319	14	,	,	PUNCT
ejpam-4480	319	15	1217	1217	NUM
ejpam-4480	319	16	-	-	SYM
ejpam-4480	319	17	1228	1228	NUM
ejpam-4480	319	18	1222	1222	NUM
ejpam-4480	319	19	proof	proof	NOUN
ejpam-4480	319	20	.	.	PUNCT
ejpam-4480	320	1	let	let	VERB
ejpam-4480	320	2	c	c	PRON
ejpam-4480	320	3	be	be	AUX
ejpam-4480	320	4	a	a	DET
ejpam-4480	320	5	superclique	superclique	NOUN
ejpam-4480	320	6	in	in	ADP
ejpam-4480	320	7	s(g	s(g	PROPN
ejpam-4480	320	8	)	)	PUNCT
ejpam-4480	320	9	and	and	CCONJ
ejpam-4480	320	10	set	set	VERB
ejpam-4480	320	11	cg1	cg1	NOUN
ejpam-4480	320	12	=	=	SYM
ejpam-4480	320	13	c∩v	c∩v	NOUN
ejpam-4480	320	14	(	(	PUNCT
ejpam-4480	320	15	g1	g1	PROPN
ejpam-4480	320	16	)	)	PUNCT
ejpam-4480	320	17	and	and	CCONJ
ejpam-4480	320	18	cg2	cg2	NOUN
ejpam-4480	320	19	=	=	SYM
ejpam-4480	320	20	c∩v	c∩v	NOUN
ejpam-4480	320	21	(	(	PUNCT
ejpam-4480	320	22	g2	g2	PROPN
ejpam-4480	320	23	)	)	PUNCT
ejpam-4480	320	24	.	.	PUNCT
ejpam-4480	321	1	if	if	SCONJ
ejpam-4480	321	2	cg2	cg2	NOUN
ejpam-4480	321	3	=	=	SYM
ejpam-4480	321	4	∅	∅	NOUN
ejpam-4480	321	5	or	or	CCONJ
ejpam-4480	321	6	cg1	cg1	NOUN
ejpam-4480	321	7	=	=	NOUN
ejpam-4480	321	8	∅	∅	NOUN
ejpam-4480	321	9	,	,	PUNCT
ejpam-4480	321	10	then	then	ADV
ejpam-4480	321	11	(	(	PUNCT
ejpam-4480	321	12	i	i	NOUN
ejpam-4480	321	13	)	)	PUNCT
ejpam-4480	321	14	or	or	CCONJ
ejpam-4480	321	15	(	(	PUNCT
ejpam-4480	321	16	ii	ii	NOUN
ejpam-4480	321	17	)	)	PUNCT
ejpam-4480	321	18	holds	hold	VERB
ejpam-4480	321	19	.	.	PUNCT
ejpam-4480	322	1	so	so	ADV
ejpam-4480	322	2	suppose	suppose	VERB
ejpam-4480	322	3	that	that	SCONJ
ejpam-4480	322	4	cg1	cg1	NOUN
ejpam-4480	322	5	̸=	̸=	PROPN
ejpam-4480	322	6	∅	∅	NOUN
ejpam-4480	322	7	and	and	CCONJ
ejpam-4480	322	8	cg2	cg2	PROPN
ejpam-4480	322	9	̸=	̸=	PROPN
ejpam-4480	322	10	∅.	∅.	VERB
ejpam-4480	322	11	then	then	ADV
ejpam-4480	322	12	cg1	cg1	INTJ
ejpam-4480	323	1	and	and	CCONJ
ejpam-4480	323	2	cg2	cg2	PROPN
ejpam-4480	323	3	are	be	AUX
ejpam-4480	323	4	cliques	clique	NOUN
ejpam-4480	323	5	in	in	ADP
ejpam-4480	323	6	g1	g1	PROPN
ejpam-4480	323	7	and	and	CCONJ
ejpam-4480	323	8	g2	g2	PROPN
ejpam-4480	323	9	,	,	PUNCT
ejpam-4480	323	10	respectively	respectively	ADV
ejpam-4480	323	11	.	.	PUNCT
ejpam-4480	324	1	let	let	VERB
ejpam-4480	324	2	v	v	NUM
ejpam-4480	324	3	∈	∈	NOUN
ejpam-4480	324	4	cg1	cg1	NOUN
ejpam-4480	324	5	.	.	PUNCT
ejpam-4480	325	1	then	then	ADV
ejpam-4480	325	2	vv′	vv′	PROPN
ejpam-4480	325	3	/∈	/∈	PUNCT
ejpam-4480	326	1	v	v	X
ejpam-4480	326	2	(	(	PUNCT
ejpam-4480	326	3	s(g	s(g	PROPN
ejpam-4480	326	4	)	)	PUNCT
ejpam-4480	326	5	)	)	PUNCT
ejpam-4480	326	6	by	by	ADP
ejpam-4480	326	7	definition	definition	NOUN
ejpam-4480	326	8	of	of	ADP
ejpam-4480	326	9	s(g	s(g	PROPN
ejpam-4480	326	10	)	)	PUNCT
ejpam-4480	326	11	.	.	PUNCT
ejpam-4480	327	1	hence	hence	ADV
ejpam-4480	327	2	,	,	PUNCT
ejpam-4480	327	3	v′	v′	PROPN
ejpam-4480	327	4	/∈	/∈	PUNCT
ejpam-4480	327	5	cg2	cg2	NOUN
ejpam-4480	327	6	,	,	PUNCT
ejpam-4480	327	7	showing	show	VERB
ejpam-4480	327	8	that	that	SCONJ
ejpam-4480	327	9	(	(	PUNCT
ejpam-4480	327	10	a	a	X
ejpam-4480	327	11	)	)	PUNCT
ejpam-4480	327	12	holds	hold	NOUN
ejpam-4480	327	13	.	.	PUNCT
ejpam-4480	328	1	next	next	ADV
ejpam-4480	328	2	,	,	PUNCT
ejpam-4480	328	3	let	let	VERB
ejpam-4480	328	4	v	v	NUM
ejpam-4480	328	5	∈	∈	NOUN
ejpam-4480	328	6	cg1	cg1	NOUN
ejpam-4480	328	7	and	and	CCONJ
ejpam-4480	328	8	w′	w′	NOUN
ejpam-4480	328	9	∈	∈	PROPN
ejpam-4480	328	10	cg2	cg2	NOUN
ejpam-4480	328	11	.	.	PUNCT
ejpam-4480	329	1	since	since	SCONJ
ejpam-4480	329	2	c	c	PROPN
ejpam-4480	329	3	is	be	AUX
ejpam-4480	329	4	a	a	DET
ejpam-4480	329	5	clique	clique	NOUN
ejpam-4480	329	6	in	in	ADP
ejpam-4480	329	7	s(g	s(g	PROPN
ejpam-4480	329	8	)	)	PUNCT
ejpam-4480	329	9	,	,	PUNCT
ejpam-4480	329	10	vw′	vw′	PROPN
ejpam-4480	329	11	∈	∈	PROPN
ejpam-4480	329	12	e(s(g	e(s(g	PROPN
ejpam-4480	329	13	)	)	PUNCT
ejpam-4480	329	14	)	)	PUNCT
ejpam-4480	329	15	.	.	PUNCT
ejpam-4480	330	1	the	the	DET
ejpam-4480	330	2	definition	definition	NOUN
ejpam-4480	330	3	of	of	ADP
ejpam-4480	330	4	s(g	s(g	PROPN
ejpam-4480	330	5	)	)	PUNCT
ejpam-4480	330	6	will	will	AUX
ejpam-4480	330	7	now	now	ADV
ejpam-4480	330	8	imply	imply	VERB
ejpam-4480	330	9	that	that	SCONJ
ejpam-4480	330	10	vw	vw	PROPN
ejpam-4480	330	11	∈	∈	PROPN
ejpam-4480	330	12	e(g1	e(g1	ADV
ejpam-4480	330	13	)	)	PUNCT
ejpam-4480	330	14	showing	show	VERB
ejpam-4480	330	15	that	that	SCONJ
ejpam-4480	330	16	(	(	PUNCT
ejpam-4480	330	17	b	b	X
ejpam-4480	330	18	)	)	PUNCT
ejpam-4480	330	19	holds	hold	VERB
ejpam-4480	330	20	.	.	PUNCT
ejpam-4480	331	1	therefore	therefore	ADV
ejpam-4480	331	2	,	,	PUNCT
ejpam-4480	331	3	(	(	PUNCT
ejpam-4480	331	4	iii	iii	X
ejpam-4480	331	5	)	)	PUNCT
ejpam-4480	331	6	holds	hold	VERB
ejpam-4480	331	7	.	.	PUNCT
ejpam-4480	332	1	for	for	ADP
ejpam-4480	332	2	the	the	DET
ejpam-4480	332	3	converse	converse	NOUN
ejpam-4480	332	4	,	,	PUNCT
ejpam-4480	332	5	suppose	suppose	VERB
ejpam-4480	332	6	that	that	SCONJ
ejpam-4480	332	7	(	(	PUNCT
ejpam-4480	332	8	i	i	NOUN
ejpam-4480	332	9	)	)	PUNCT
ejpam-4480	332	10	holds	hold	VERB
ejpam-4480	332	11	.	.	PUNCT
ejpam-4480	333	1	let	let	VERB
ejpam-4480	333	2	v	v	NOUN
ejpam-4480	333	3	,	,	PUNCT
ejpam-4480	333	4	w	w	PROPN
ejpam-4480	333	5	∈	∈	PROPN
ejpam-4480	333	6	c	c	NOUN
ejpam-4480	333	7	with	with	ADP
ejpam-4480	333	8	v	v	NOUN
ejpam-4480	333	9	̸=	̸=	PROPN
ejpam-4480	333	10	w.	w.	NOUN
ejpam-4480	333	11	then	then	ADV
ejpam-4480	333	12	v′	v′	VERB
ejpam-4480	333	13	∈	∈	PROPN
ejpam-4480	333	14	v	v	NOUN
ejpam-4480	333	15	(	(	PUNCT
ejpam-4480	333	16	s(g	s(g	PROPN
ejpam-4480	333	17	)	)	PUNCT
ejpam-4480	333	18	)	)	PUNCT
ejpam-4480	333	19	\	\	PROPN
ejpam-4480	334	1	c	c	PROPN
ejpam-4480	334	2	and	and	CCONJ
ejpam-4480	334	3	v′	v′	PROPN
ejpam-4480	334	4	∈	∈	PROPN
ejpam-4480	334	5	ns(g)(w	ns(g)(w	NOUN
ejpam-4480	334	6	)	)	PUNCT
ejpam-4480	334	7	\	\	PROPN
ejpam-4480	334	8	ns(g)(v	ns(g)(v	PROPN
ejpam-4480	334	9	)	)	PUNCT
ejpam-4480	334	10	by	by	ADP
ejpam-4480	334	11	the	the	DET
ejpam-4480	334	12	adjacency	adjacency	NOUN
ejpam-4480	334	13	in	in	ADP
ejpam-4480	334	14	s(g	s(g	PROPN
ejpam-4480	334	15	)	)	PUNCT
ejpam-4480	334	16	.	.	PUNCT
ejpam-4480	335	1	hence	hence	ADV
ejpam-4480	335	2	,	,	PUNCT
ejpam-4480	335	3	c	c	PROPN
ejpam-4480	335	4	is	be	AUX
ejpam-4480	335	5	a	a	DET
ejpam-4480	335	6	superclique	superclique	NOUN
ejpam-4480	335	7	in	in	ADP
ejpam-4480	335	8	s(g	s(g	PROPN
ejpam-4480	335	9	)	)	PUNCT
ejpam-4480	335	10	.	.	PUNCT
ejpam-4480	336	1	the	the	DET
ejpam-4480	336	2	same	same	ADJ
ejpam-4480	336	3	conclusion	conclusion	NOUN
ejpam-4480	336	4	can	can	AUX
ejpam-4480	336	5	be	be	AUX
ejpam-4480	336	6	made	make	VERB
ejpam-4480	336	7	if	if	SCONJ
ejpam-4480	336	8	(	(	PUNCT
ejpam-4480	336	9	ii	ii	NOUN
ejpam-4480	336	10	)	)	PUNCT
ejpam-4480	336	11	holds	hold	VERB
ejpam-4480	336	12	.	.	PUNCT
ejpam-4480	337	1	next	next	ADV
ejpam-4480	337	2	,	,	PUNCT
ejpam-4480	337	3	suppose	suppose	VERB
ejpam-4480	337	4	that	that	SCONJ
ejpam-4480	337	5	(	(	PUNCT
ejpam-4480	337	6	iii	iii	NOUN
ejpam-4480	337	7	)	)	PUNCT
ejpam-4480	337	8	holds	hold	VERB
ejpam-4480	337	9	.	.	PUNCT
ejpam-4480	338	1	then	then	ADV
ejpam-4480	338	2	,	,	PUNCT
ejpam-4480	338	3	by	by	ADP
ejpam-4480	338	4	(	(	PUNCT
ejpam-4480	338	5	a	a	X
ejpam-4480	338	6	)	)	PUNCT
ejpam-4480	338	7	and	and	CCONJ
ejpam-4480	338	8	(	(	PUNCT
ejpam-4480	338	9	b	b	NOUN
ejpam-4480	338	10	)	)	PUNCT
ejpam-4480	338	11	,	,	PUNCT
ejpam-4480	338	12	c	c	PROPN
ejpam-4480	338	13	is	be	AUX
ejpam-4480	338	14	a	a	DET
ejpam-4480	338	15	clique	clique	NOUN
ejpam-4480	338	16	of	of	ADP
ejpam-4480	338	17	s(g	s(g	PROPN
ejpam-4480	338	18	)	)	PUNCT
ejpam-4480	338	19	.	.	PUNCT
ejpam-4480	339	1	let	let	VERB
ejpam-4480	339	2	x	x	PRON
ejpam-4480	339	3	,	,	PUNCT
ejpam-4480	339	4	y	y	PROPN
ejpam-4480	339	5	∈	∈	PROPN
ejpam-4480	339	6	c	c	NOUN
ejpam-4480	339	7	with	with	ADP
ejpam-4480	339	8	x	x	PUNCT
ejpam-4480	339	9	̸=	̸=	PROPN
ejpam-4480	339	10	y.	y.	NOUN
ejpam-4480	339	11	if	if	SCONJ
ejpam-4480	339	12	x	x	PRON
ejpam-4480	339	13	,	,	PUNCT
ejpam-4480	339	14	y	y	PROPN
ejpam-4480	339	15	∈	∈	PROPN
ejpam-4480	339	16	cg1	cg1	NOUN
ejpam-4480	339	17	,	,	PUNCT
ejpam-4480	340	1	then	then	ADV
ejpam-4480	340	2	x′	x′	PROPN
ejpam-4480	340	3	∈	∈	PROPN
ejpam-4480	340	4	v	v	NOUN
ejpam-4480	340	5	(	(	PUNCT
ejpam-4480	340	6	s(g	s(g	PROPN
ejpam-4480	340	7	)	)	PUNCT
ejpam-4480	340	8	)	)	PUNCT
ejpam-4480	340	9	\	\	PROPN
ejpam-4480	341	1	c	c	X
ejpam-4480	341	2	by	by	ADP
ejpam-4480	341	3	(	(	PUNCT
ejpam-4480	341	4	a	a	NOUN
ejpam-4480	341	5	)	)	PUNCT
ejpam-4480	341	6	and	and	CCONJ
ejpam-4480	341	7	x′	x′	PROPN
ejpam-4480	341	8	∈	∈	PROPN
ejpam-4480	341	9	ns(g)(y	ns(g)(y	PROPN
ejpam-4480	341	10	)	)	PUNCT
ejpam-4480	341	11	because	because	SCONJ
ejpam-4480	341	12	xy	xy	PROPN
ejpam-4480	341	13	∈	∈	PROPN
ejpam-4480	341	14	e(g1	e(g1	ADJ
ejpam-4480	341	15	)	)	PUNCT
ejpam-4480	341	16	.	.	PUNCT
ejpam-4480	342	1	it	it	PRON
ejpam-4480	342	2	follows	follow	VERB
ejpam-4480	342	3	that	that	SCONJ
ejpam-4480	342	4	x	x	X
ejpam-4480	342	5	′	′	NUM
ejpam-4480	342	6	∈	∈	PROPN
ejpam-4480	342	7	ns(g)(y	ns(g)(y	PROPN
ejpam-4480	342	8	)	)	PUNCT
ejpam-4480	342	9	\ns(g)(x	\ns(g)(x	PROPN
ejpam-4480	342	10	)	)	PUNCT
ejpam-4480	342	11	.	.	PUNCT
ejpam-4480	343	1	suppose	suppose	VERB
ejpam-4480	343	2	x	x	PRON
ejpam-4480	343	3	,	,	PUNCT
ejpam-4480	343	4	y	y	PROPN
ejpam-4480	343	5	∈	∈	PROPN
ejpam-4480	343	6	cg2	cg2	NOUN
ejpam-4480	343	7	,	,	PUNCT
ejpam-4480	343	8	say	say	VERB
ejpam-4480	343	9	x	x	X
ejpam-4480	343	10	=	=	SYM
ejpam-4480	343	11	v′	v′	PROPN
ejpam-4480	343	12	and	and	CCONJ
ejpam-4480	343	13	y	y	NOUN
ejpam-4480	343	14	=	=	PUNCT
ejpam-4480	343	15	w′	w′	PROPN
ejpam-4480	343	16	where	where	SCONJ
ejpam-4480	343	17	v	v	NOUN
ejpam-4480	343	18	,	,	PUNCT
ejpam-4480	343	19	w	w	PROPN
ejpam-4480	343	20	∈	∈	PROPN
ejpam-4480	343	21	v	v	X
ejpam-4480	343	22	(	(	PUNCT
ejpam-4480	343	23	g1	g1	PROPN
ejpam-4480	343	24	)	)	PUNCT
ejpam-4480	343	25	.	.	PUNCT
ejpam-4480	344	1	then	then	ADV
ejpam-4480	344	2	v	v	X
ejpam-4480	344	3	∈	∈	PROPN
ejpam-4480	344	4	v	v	NOUN
ejpam-4480	344	5	(	(	PUNCT
ejpam-4480	344	6	s(g	s(g	PROPN
ejpam-4480	344	7	)	)	PUNCT
ejpam-4480	344	8	)	)	PUNCT
ejpam-4480	344	9	\	\	PROPN
ejpam-4480	345	1	c	c	X
ejpam-4480	345	2	by	by	ADP
ejpam-4480	345	3	(	(	PUNCT
ejpam-4480	345	4	a	a	NOUN
ejpam-4480	345	5	)	)	PUNCT
ejpam-4480	345	6	and	and	CCONJ
ejpam-4480	345	7	v	v	ADP
ejpam-4480	345	8	∈	∈	PROPN
ejpam-4480	345	9	ns(g)(w	ns(g)(w	ADJ
ejpam-4480	345	10	′	′	NOUN
ejpam-4480	345	11	)	)	PUNCT
ejpam-4480	345	12	because	because	SCONJ
ejpam-4480	345	13	v′w′	v′w′	NOUN
ejpam-4480	345	14	∈	∈	PROPN
ejpam-4480	345	15	e(g2	e(g2	X
ejpam-4480	345	16	)	)	PUNCT
ejpam-4480	345	17	.	.	PUNCT
ejpam-4480	346	1	hence	hence	ADV
ejpam-4480	346	2	,	,	PUNCT
ejpam-4480	346	3	v	v	PROPN
ejpam-4480	346	4	∈	∈	PROPN
ejpam-4480	346	5	ns(g)(w	ns(g)(w	ADJ
ejpam-4480	346	6	′	′	NOUN
ejpam-4480	346	7	)	)	PUNCT
ejpam-4480	346	8	\	\	PROPN
ejpam-4480	346	9	ns(g)(v	ns(g)(v	X
ejpam-4480	346	10	′	′	NUM
ejpam-4480	346	11	)	)	PUNCT
ejpam-4480	346	12	.	.	PUNCT
ejpam-4480	347	1	suppose	suppose	VERB
ejpam-4480	347	2	x	x	SYM
ejpam-4480	347	3	∈	∈	NOUN
ejpam-4480	347	4	cg1	cg1	NOUN
ejpam-4480	347	5	and	and	CCONJ
ejpam-4480	347	6	y	y	PROPN
ejpam-4480	347	7	∈	∈	PROPN
ejpam-4480	347	8	cg2	cg2	NOUN
ejpam-4480	347	9	,	,	PUNCT
ejpam-4480	347	10	say	say	VERB
ejpam-4480	347	11	y	y	PROPN
ejpam-4480	347	12	=	=	SYM
ejpam-4480	347	13	z′	z′	PROPN
ejpam-4480	347	14	,	,	PUNCT
ejpam-4480	347	15	where	where	SCONJ
ejpam-4480	347	16	z	z	PROPN
ejpam-4480	347	17	∈	∈	PROPN
ejpam-4480	347	18	v	v	NOUN
ejpam-4480	347	19	(	(	PUNCT
ejpam-4480	347	20	g1	g1	PROPN
ejpam-4480	347	21	)	)	PUNCT
ejpam-4480	347	22	.	.	PUNCT
ejpam-4480	348	1	by	by	ADP
ejpam-4480	348	2	(	(	PUNCT
ejpam-4480	348	3	b	b	NOUN
ejpam-4480	348	4	)	)	PUNCT
ejpam-4480	348	5	,	,	PUNCT
ejpam-4480	348	6	z	z	NOUN
ejpam-4480	348	7	∈	∈	PROPN
ejpam-4480	349	1	[	[	X
ejpam-4480	349	2	v	v	X
ejpam-4480	349	3	(	(	PUNCT
ejpam-4480	349	4	s(g))\c]∩ng(x	s(g))\c]∩ng(x	PUNCT
ejpam-4480	349	5	)	)	PUNCT
ejpam-4480	349	6	.	.	PUNCT
ejpam-4480	350	1	thus	thus	ADV
ejpam-4480	350	2	,	,	PUNCT
ejpam-4480	350	3	z	z	PROPN
ejpam-4480	350	4	∈	∈	PROPN
ejpam-4480	350	5	ns(g)(x)\ns(g)(y	ns(g)(x)\ns(g)(y	PROPN
ejpam-4480	350	6	)	)	PUNCT
ejpam-4480	350	7	.	.	PUNCT
ejpam-4480	351	1	this	this	PRON
ejpam-4480	351	2	shows	show	VERB
ejpam-4480	351	3	that	that	SCONJ
ejpam-4480	351	4	c	c	PROPN
ejpam-4480	351	5	is	be	AUX
ejpam-4480	351	6	a	a	DET
ejpam-4480	351	7	superclique	superclique	NOUN
ejpam-4480	351	8	in	in	ADP
ejpam-4480	351	9	s(g	s(g	PROPN
ejpam-4480	351	10	)	)	PUNCT
ejpam-4480	351	11	.	.	PUNCT
ejpam-4480	352	1	corollary	corollary	ADJ
ejpam-4480	352	2	2	2	NUM
ejpam-4480	352	3	.	.	PUNCT
ejpam-4480	353	1	let	let	VERB
ejpam-4480	353	2	g	g	PRON
ejpam-4480	353	3	be	be	AUX
ejpam-4480	353	4	a	a	DET
ejpam-4480	353	5	connected	connected	ADJ
ejpam-4480	353	6	graph	graph	NOUN
ejpam-4480	353	7	.	.	PUNCT
ejpam-4480	354	1	then	then	ADV
ejpam-4480	354	2	ωs(s(g	ωs(s(g	NUM
ejpam-4480	354	3	)	)	PUNCT
ejpam-4480	354	4	)	)	PUNCT
ejpam-4480	354	5	=	=	SYM
ejpam-4480	354	6	ω(g	ω(g	NOUN
ejpam-4480	354	7	)	)	PUNCT
ejpam-4480	354	8	.	.	PUNCT
ejpam-4480	355	1	proof	proof	NOUN
ejpam-4480	355	2	.	.	PUNCT
ejpam-4480	356	1	if	if	SCONJ
ejpam-4480	356	2	g	g	PROPN
ejpam-4480	356	3	=	=	SYM
ejpam-4480	356	4	k1	k1	PROPN
ejpam-4480	356	5	,	,	PUNCT
ejpam-4480	356	6	then	then	ADV
ejpam-4480	356	7	s(g	s(g	PROPN
ejpam-4480	356	8	)	)	PUNCT
ejpam-4480	356	9	=	=	SYM
ejpam-4480	356	10	k2	k2	X
ejpam-4480	356	11	(	(	PUNCT
ejpam-4480	356	12	empty	empty	ADJ
ejpam-4480	356	13	graph	graph	NOUN
ejpam-4480	356	14	)	)	PUNCT
ejpam-4480	356	15	.	.	PUNCT
ejpam-4480	357	1	it	it	PRON
ejpam-4480	357	2	follows	follow	VERB
ejpam-4480	357	3	that	that	PRON
ejpam-4480	357	4	ωs(s(g	ωs(s(g	VERB
ejpam-4480	357	5	)	)	PUNCT
ejpam-4480	357	6	)	)	PUNCT
ejpam-4480	358	1	=	=	SYM
ejpam-4480	358	2	ω(g	ω(g	NOUN
ejpam-4480	358	3	)	)	PUNCT
ejpam-4480	358	4	=	=	SYM
ejpam-4480	359	1	1	1	X
ejpam-4480	359	2	.	.	PUNCT
ejpam-4480	360	1	next	next	ADV
ejpam-4480	360	2	,	,	PUNCT
ejpam-4480	360	3	suppose	suppose	VERB
ejpam-4480	360	4	that	that	SCONJ
ejpam-4480	360	5	g	g	PROPN
ejpam-4480	360	6	is	be	AUX
ejpam-4480	360	7	non	non	ADJ
ejpam-4480	360	8	-	-	ADJ
ejpam-4480	360	9	trivial	trivial	ADJ
ejpam-4480	360	10	.	.	PUNCT
ejpam-4480	361	1	let	let	VERB
ejpam-4480	361	2	c	c	PRON
ejpam-4480	361	3	be	be	AUX
ejpam-4480	361	4	a	a	DET
ejpam-4480	361	5	superclique	superclique	NOUN
ejpam-4480	361	6	in	in	ADP
ejpam-4480	361	7	s(g	s(g	PROPN
ejpam-4480	361	8	)	)	PUNCT
ejpam-4480	361	9	of	of	ADP
ejpam-4480	361	10	the	the	DET
ejpam-4480	361	11	form	form	NOUN
ejpam-4480	361	12	given	give	VERB
ejpam-4480	361	13	in	in	ADP
ejpam-4480	361	14	theorem	theorem	ADJ
ejpam-4480	361	15	3(iii	3(iii	NUM
ejpam-4480	361	16	)	)	PUNCT
ejpam-4480	361	17	.	.	PUNCT
ejpam-4480	362	1	then	then	ADV
ejpam-4480	362	2	c	c	X
ejpam-4480	362	3	=	=	PUNCT
ejpam-4480	362	4	cg1	cg1	NOUN
ejpam-4480	362	5	∪	∪	NOUN
ejpam-4480	362	6	cg2	cg2	NOUN
ejpam-4480	362	7	,	,	PUNCT
ejpam-4480	362	8	where	where	SCONJ
ejpam-4480	362	9	cg1	cg1	NOUN
ejpam-4480	362	10	and	and	CCONJ
ejpam-4480	362	11	cg2	cg2	PROPN
ejpam-4480	362	12	are	be	AUX
ejpam-4480	362	13	cliques	clique	NOUN
ejpam-4480	362	14	in	in	ADP
ejpam-4480	362	15	g1	g1	PROPN
ejpam-4480	362	16	and	and	CCONJ
ejpam-4480	362	17	g2	g2	PROPN
ejpam-4480	362	18	,	,	PUNCT
ejpam-4480	362	19	respectively	respectively	ADV
ejpam-4480	362	20	,	,	PUNCT
ejpam-4480	362	21	and	and	CCONJ
ejpam-4480	362	22	satisfy	satisfy	VERB
ejpam-4480	362	23	conditions	condition	NOUN
ejpam-4480	362	24	(	(	PUNCT
ejpam-4480	362	25	a	a	X
ejpam-4480	362	26	)	)	PUNCT
ejpam-4480	362	27	and	and	CCONJ
ejpam-4480	362	28	(	(	PUNCT
ejpam-4480	362	29	b	b	NOUN
ejpam-4480	362	30	)	)	PUNCT
ejpam-4480	362	31	.	.	PUNCT
ejpam-4480	363	1	set	set	VERB
ejpam-4480	363	2	c∗	c∗	PROPN
ejpam-4480	363	3	g1	g1	PROPN
ejpam-4480	363	4	=	=	SYM
ejpam-4480	363	5	{	{	PUNCT
ejpam-4480	363	6	v	v	NUM
ejpam-4480	363	7	∈	∈	NOUN
ejpam-4480	363	8	v	v	NOUN
ejpam-4480	363	9	(	(	PUNCT
ejpam-4480	363	10	g1	g1	PROPN
ejpam-4480	363	11	)	)	PUNCT
ejpam-4480	363	12	:	:	PUNCT
ejpam-4480	364	1	v	v	X
ejpam-4480	364	2	′	′	NUM
ejpam-4480	364	3	∈	∈	PROPN
ejpam-4480	364	4	cg2	cg2	PROPN
ejpam-4480	364	5	}	}	PUNCT
ejpam-4480	364	6	.	.	PUNCT
ejpam-4480	365	1	then	then	ADV
ejpam-4480	365	2	|c∗	|c∗	PROPN
ejpam-4480	365	3	g1	g1	PROPN
ejpam-4480	365	4	|	|	ADV
ejpam-4480	365	5	=	=	PUNCT
ejpam-4480	365	6	|cg2	|cg2	CCONJ
ejpam-4480	365	7	|	|	NOUN
ejpam-4480	365	8	.	.	PUNCT
ejpam-4480	366	1	by	by	ADP
ejpam-4480	366	2	condition	condition	NOUN
ejpam-4480	366	3	(	(	PUNCT
ejpam-4480	366	4	a	a	X
ejpam-4480	366	5	)	)	PUNCT
ejpam-4480	366	6	,	,	PUNCT
ejpam-4480	366	7	cg1	cg1	X
ejpam-4480	366	8	∩	∩	ADJ
ejpam-4480	366	9	c∗	c∗	PROPN
ejpam-4480	366	10	g1	g1	PROPN
ejpam-4480	366	11	=	=	PUNCT
ejpam-4480	366	12	∅.	∅.	AUX
ejpam-4480	366	13	let	let	VERB
ejpam-4480	366	14	c∗	c∗	NOUN
ejpam-4480	366	15	=	=	PUNCT
ejpam-4480	366	16	cg1	cg1	NOUN
ejpam-4480	366	17	∪	∪	NOUN
ejpam-4480	366	18	c∗	c∗	ADJ
ejpam-4480	366	19	g1	g1	NOUN
ejpam-4480	366	20	and	and	CCONJ
ejpam-4480	366	21	let	let	VERB
ejpam-4480	366	22	x	x	PRON
ejpam-4480	366	23	,	,	PUNCT
ejpam-4480	366	24	y	y	PROPN
ejpam-4480	366	25	∈	∈	PROPN
ejpam-4480	366	26	c∗	c∗	NOUN
ejpam-4480	366	27	with	with	ADP
ejpam-4480	366	28	x	x	PROPN
ejpam-4480	366	29	̸=	̸=	PROPN
ejpam-4480	366	30	y.	y.	NOUN
ejpam-4480	366	31	if	if	SCONJ
ejpam-4480	366	32	x	x	PRON
ejpam-4480	366	33	,	,	PUNCT
ejpam-4480	366	34	y	y	PROPN
ejpam-4480	366	35	∈	∈	PROPN
ejpam-4480	366	36	cg1	cg1	NOUN
ejpam-4480	366	37	,	,	PUNCT
ejpam-4480	366	38	then	then	ADV
ejpam-4480	366	39	xy	xy	PROPN
ejpam-4480	366	40	∈	∈	PROPN
ejpam-4480	366	41	e(g1	e(g1	ADJ
ejpam-4480	366	42	)	)	PUNCT
ejpam-4480	366	43	.	.	PUNCT
ejpam-4480	367	1	suppose	suppose	VERB
ejpam-4480	367	2	x	x	PRON
ejpam-4480	367	3	,	,	PUNCT
ejpam-4480	367	4	y	y	PROPN
ejpam-4480	367	5	∈	∈	PROPN
ejpam-4480	367	6	c∗	c∗	PROPN
ejpam-4480	367	7	g1	g1	PROPN
ejpam-4480	367	8	.	.	PUNCT
ejpam-4480	368	1	then	then	ADV
ejpam-4480	368	2	x′	x′	NUM
ejpam-4480	368	3	,	,	PUNCT
ejpam-4480	368	4	y′	y′	NOUN
ejpam-4480	368	5	∈	∈	PROPN
ejpam-4480	368	6	cg2	cg2	NOUN
ejpam-4480	368	7	.	.	PUNCT
ejpam-4480	369	1	since	since	SCONJ
ejpam-4480	369	2	cg2	cg2	PROPN
ejpam-4480	369	3	is	be	AUX
ejpam-4480	369	4	a	a	DET
ejpam-4480	369	5	clique	clique	NOUN
ejpam-4480	369	6	in	in	ADP
ejpam-4480	369	7	g2	g2	PROPN
ejpam-4480	369	8	,	,	PUNCT
ejpam-4480	369	9	x	x	SYM
ejpam-4480	369	10	′y′	′y′	PROPN
ejpam-4480	369	11	∈	∈	PROPN
ejpam-4480	369	12	e(g2	e(g2	X
ejpam-4480	369	13	)	)	PUNCT
ejpam-4480	369	14	.	.	PUNCT
ejpam-4480	370	1	this	this	PRON
ejpam-4480	370	2	implies	imply	VERB
ejpam-4480	370	3	that	that	SCONJ
ejpam-4480	370	4	xy	xy	PROPN
ejpam-4480	370	5	∈	∈	PROPN
ejpam-4480	370	6	e(g1	e(g1	ADJ
ejpam-4480	370	7	)	)	PUNCT
ejpam-4480	370	8	.	.	PUNCT
ejpam-4480	371	1	finally	finally	ADV
ejpam-4480	371	2	,	,	PUNCT
ejpam-4480	371	3	suppose	suppose	VERB
ejpam-4480	371	4	that	that	SCONJ
ejpam-4480	371	5	x	x	PUNCT
ejpam-4480	371	6	∈	∈	NOUN
ejpam-4480	371	7	cg1	cg1	NOUN
ejpam-4480	371	8	and	and	CCONJ
ejpam-4480	371	9	y	y	PROPN
ejpam-4480	371	10	∈	∈	PROPN
ejpam-4480	371	11	c∗	c∗	PROPN
ejpam-4480	371	12	g1	g1	PROPN
ejpam-4480	371	13	.	.	PUNCT
ejpam-4480	372	1	then	then	ADV
ejpam-4480	372	2	y′	y′	NOUN
ejpam-4480	372	3	∈	∈	PROPN
ejpam-4480	372	4	cg2	cg2	NOUN
ejpam-4480	372	5	.	.	PUNCT
ejpam-4480	373	1	by	by	ADP
ejpam-4480	373	2	condition	condition	NOUN
ejpam-4480	373	3	(	(	PUNCT
ejpam-4480	373	4	b	b	NOUN
ejpam-4480	373	5	)	)	PUNCT
ejpam-4480	373	6	,	,	PUNCT
ejpam-4480	373	7	it	it	PRON
ejpam-4480	373	8	follows	follow	VERB
ejpam-4480	373	9	that	that	SCONJ
ejpam-4480	373	10	xy	xy	PROPN
ejpam-4480	373	11	∈	∈	PROPN
ejpam-4480	373	12	e(g1	e(g1	ADJ
ejpam-4480	373	13	)	)	PUNCT
ejpam-4480	373	14	.	.	PUNCT
ejpam-4480	374	1	therefore	therefore	ADV
ejpam-4480	374	2	,	,	PUNCT
ejpam-4480	374	3	c∗	c∗	PROPN
ejpam-4480	374	4	is	be	AUX
ejpam-4480	374	5	a	a	DET
ejpam-4480	374	6	clique	clique	NOUN
ejpam-4480	374	7	in	in	ADP
ejpam-4480	374	8	g1	g1	PROPN
ejpam-4480	374	9	and	and	CCONJ
ejpam-4480	374	10	|c|	|c|	PROPN
ejpam-4480	374	11	=	=	SYM
ejpam-4480	374	12	|c∗|	|c∗|	VERB
ejpam-4480	374	13	≤	≤	NOUN
ejpam-4480	374	14	ω(g1	ω(g1	NOUN
ejpam-4480	374	15	)	)	PUNCT
ejpam-4480	374	16	=	=	SYM
ejpam-4480	374	17	ω(g	ω(g	NOUN
ejpam-4480	374	18	)	)	PUNCT
ejpam-4480	374	19	.	.	PUNCT
ejpam-4480	375	1	the	the	DET
ejpam-4480	375	2	desired	desire	VERB
ejpam-4480	375	3	result	result	NOUN
ejpam-4480	375	4	now	now	ADV
ejpam-4480	375	5	follows	follow	VERB
ejpam-4480	375	6	from	from	ADP
ejpam-4480	375	7	theorem	theorem	ADJ
ejpam-4480	375	8	3	3	NUM
ejpam-4480	375	9	.	.	PUNCT
ejpam-4480	375	10	theorem	theorem	NOUN
ejpam-4480	375	11	4	4	NUM
ejpam-4480	375	12	.	.	PUNCT
ejpam-4480	376	1	let	let	VERB
ejpam-4480	376	2	g	g	PRON
ejpam-4480	376	3	be	be	AUX
ejpam-4480	376	4	a	a	DET
ejpam-4480	376	5	non	non	ADJ
ejpam-4480	376	6	-	-	ADJ
ejpam-4480	376	7	trivial	trivial	ADJ
ejpam-4480	376	8	graph	graph	NOUN
ejpam-4480	376	9	.	.	PUNCT
ejpam-4480	377	1	then	then	ADV
ejpam-4480	377	2	c	c	PROPN
ejpam-4480	377	3	is	be	AUX
ejpam-4480	377	4	a	a	DET
ejpam-4480	377	5	superclique	superclique	NOUN
ejpam-4480	377	6	in	in	ADP
ejpam-4480	377	7	gg	gg	PROPN
ejpam-4480	377	8	if	if	SCONJ
ejpam-4480	378	1	and	and	CCONJ
ejpam-4480	378	2	only	only	ADV
ejpam-4480	378	3	if	if	SCONJ
ejpam-4480	378	4	one	one	NUM
ejpam-4480	378	5	of	of	ADP
ejpam-4480	378	6	the	the	DET
ejpam-4480	378	7	following	follow	VERB
ejpam-4480	378	8	holds	hold	VERB
ejpam-4480	378	9	:	:	PUNCT
ejpam-4480	378	10	(	(	PUNCT
ejpam-4480	378	11	i	i	NOUN
ejpam-4480	378	12	)	)	PUNCT
ejpam-4480	378	13	c	c	PROPN
ejpam-4480	378	14	is	be	AUX
ejpam-4480	378	15	a	a	DET
ejpam-4480	378	16	clique	clique	NOUN
ejpam-4480	378	17	in	in	ADP
ejpam-4480	378	18	g.	g.	PROPN
ejpam-4480	378	19	(	(	PUNCT
ejpam-4480	378	20	ii	ii	PROPN
ejpam-4480	378	21	)	)	PUNCT
ejpam-4480	378	22	c	c	PROPN
ejpam-4480	378	23	is	be	AUX
ejpam-4480	378	24	a	a	DET
ejpam-4480	378	25	clique	clique	NOUN
ejpam-4480	378	26	in	in	ADP
ejpam-4480	378	27	g.	g.	PROPN
ejpam-4480	378	28	(	(	PUNCT
ejpam-4480	378	29	iii	iii	X
ejpam-4480	378	30	)	)	PUNCT
ejpam-4480	378	31	c	c	NOUN
ejpam-4480	378	32	=	=	SYM
ejpam-4480	378	33	{	{	PUNCT
ejpam-4480	378	34	v	v	NOUN
ejpam-4480	378	35	,	,	PUNCT
ejpam-4480	378	36	v	v	NOUN
ejpam-4480	378	37	}	}	PUNCT
ejpam-4480	378	38	for	for	ADP
ejpam-4480	378	39	some	some	DET
ejpam-4480	378	40	v	v	ADP
ejpam-4480	378	41	∈	∈	NOUN
ejpam-4480	378	42	v	v	NOUN
ejpam-4480	378	43	(	(	PUNCT
ejpam-4480	378	44	g	g	NOUN
ejpam-4480	378	45	)	)	PUNCT
ejpam-4480	378	46	.	.	PUNCT
ejpam-4480	379	1	proof	proof	NOUN
ejpam-4480	379	2	.	.	PUNCT
ejpam-4480	380	1	let	let	VERB
ejpam-4480	380	2	c	c	PRON
ejpam-4480	380	3	be	be	AUX
ejpam-4480	380	4	a	a	DET
ejpam-4480	380	5	superclique	superclique	NOUN
ejpam-4480	380	6	in	in	ADP
ejpam-4480	380	7	gg	gg	NOUN
ejpam-4480	380	8	and	and	CCONJ
ejpam-4480	380	9	set	set	VERB
ejpam-4480	380	10	cg	cg	NOUN
ejpam-4480	380	11	=	=	PUNCT
ejpam-4480	380	12	c	c	PROPN
ejpam-4480	380	13	∩	∩	X
ejpam-4480	380	14	v	v	X
ejpam-4480	380	15	(	(	PUNCT
ejpam-4480	380	16	g	g	NOUN
ejpam-4480	380	17	)	)	PUNCT
ejpam-4480	380	18	and	and	CCONJ
ejpam-4480	380	19	cg	cg	X
ejpam-4480	380	20	=	=	SYM
ejpam-4480	380	21	c	c	PROPN
ejpam-4480	380	22	∩	∩	X
ejpam-4480	380	23	v	v	X
ejpam-4480	380	24	(	(	PUNCT
ejpam-4480	380	25	g	g	NOUN
ejpam-4480	380	26	)	)	PUNCT
ejpam-4480	380	27	.	.	PUNCT
ejpam-4480	381	1	if	if	SCONJ
ejpam-4480	381	2	cg	cg	NOUN
ejpam-4480	381	3	=	=	NOUN
ejpam-4480	381	4	∅	∅	NOUN
ejpam-4480	381	5	or	or	CCONJ
ejpam-4480	381	6	cg	cg	NOUN
ejpam-4480	381	7	=	=	NOUN
ejpam-4480	381	8	∅	∅	NOUN
ejpam-4480	381	9	,	,	PUNCT
ejpam-4480	381	10	then	then	ADV
ejpam-4480	381	11	c	c	PROPN
ejpam-4480	381	12	is	be	AUX
ejpam-4480	381	13	a	a	DET
ejpam-4480	381	14	clique	clique	NOUN
ejpam-4480	381	15	in	in	ADP
ejpam-4480	381	16	g	g	PROPN
ejpam-4480	381	17	or	or	CCONJ
ejpam-4480	381	18	g	g	NOUN
ejpam-4480	381	19	,	,	PUNCT
ejpam-4480	381	20	showing	show	VERB
ejpam-4480	381	21	that	that	SCONJ
ejpam-4480	381	22	(	(	PUNCT
ejpam-4480	381	23	i	i	NOUN
ejpam-4480	381	24	)	)	PUNCT
ejpam-4480	381	25	or	or	CCONJ
ejpam-4480	381	26	(	(	PUNCT
ejpam-4480	381	27	ii	ii	NOUN
ejpam-4480	381	28	)	)	PUNCT
ejpam-4480	381	29	holds	hold	VERB
ejpam-4480	381	30	.	.	PUNCT
ejpam-4480	382	1	suppose	suppose	VERB
ejpam-4480	382	2	that	that	SCONJ
ejpam-4480	382	3	cg	cg	NOUN
ejpam-4480	382	4	̸=	̸=	PROPN
ejpam-4480	382	5	∅	∅	NOUN
ejpam-4480	382	6	and	and	CCONJ
ejpam-4480	382	7	cg	cg	NOUN
ejpam-4480	382	8	̸=	̸=	PROPN
ejpam-4480	382	9	∅.	∅.	ADV
ejpam-4480	382	10	let	let	VERB
ejpam-4480	382	11	v	v	ADP
ejpam-4480	382	12	∈	∈	PROPN
ejpam-4480	382	13	cg	cg	NOUN
ejpam-4480	382	14	and	and	CCONJ
ejpam-4480	382	15	w	w	PROPN
ejpam-4480	382	16	∈	∈	PROPN
ejpam-4480	382	17	cg	cg	NOUN
ejpam-4480	382	18	.	.	PUNCT
ejpam-4480	383	1	since	since	SCONJ
ejpam-4480	383	2	c	c	PROPN
ejpam-4480	383	3	is	be	AUX
ejpam-4480	383	4	a	a	DET
ejpam-4480	383	5	clique	clique	NOUN
ejpam-4480	383	6	,	,	PUNCT
ejpam-4480	383	7	vw	vw	PROPN
ejpam-4480	383	8	∈	∈	PROPN
ejpam-4480	383	9	e(gg	e(gg	PROPN
ejpam-4480	383	10	)	)	PUNCT
ejpam-4480	383	11	.	.	PUNCT
ejpam-4480	384	1	r.	r.	PROPN
ejpam-4480	384	2	dela	dela	PROPN
ejpam-4480	384	3	cerna	cerna	PROPN
ejpam-4480	384	4	,	,	PUNCT
ejpam-4480	384	5	s.	s.	PROPN
ejpam-4480	384	6	canoy	canoy	PROPN
ejpam-4480	384	7	,	,	PUNCT
ejpam-4480	384	8	jr	jr	PROPN
ejpam-4480	384	9	.	.	PROPN
ejpam-4480	384	10	/	/	SYM
ejpam-4480	384	11	eur	eur	PROPN
ejpam-4480	384	12	.	.	PUNCT
ejpam-4480	385	1	j.	j.	PROPN
ejpam-4480	385	2	pure	pure	PROPN
ejpam-4480	385	3	appl	appl	PROPN
ejpam-4480	385	4	.	.	PROPN
ejpam-4480	385	5	math	math	PROPN
ejpam-4480	385	6	,	,	PUNCT
ejpam-4480	385	7	15	15	NUM
ejpam-4480	385	8	(	(	PUNCT
ejpam-4480	385	9	3	3	NUM
ejpam-4480	385	10	)	)	PUNCT
ejpam-4480	385	11	(	(	PUNCT
ejpam-4480	385	12	2022	2022	NUM
ejpam-4480	385	13	)	)	PUNCT
ejpam-4480	385	14	,	,	PUNCT
ejpam-4480	385	15	1217	1217	NUM
ejpam-4480	385	16	-	-	SYM
ejpam-4480	385	17	1228	1228	NUM
ejpam-4480	385	18	1223	1223	NUM
ejpam-4480	385	19	hence	hence	ADV
ejpam-4480	385	20	,	,	PUNCT
ejpam-4480	385	21	by	by	ADP
ejpam-4480	385	22	definition	definition	NOUN
ejpam-4480	385	23	of	of	ADP
ejpam-4480	385	24	gg	gg	PROPN
ejpam-4480	385	25	,	,	PUNCT
ejpam-4480	385	26	w	w	PROPN
ejpam-4480	385	27	=	=	PUNCT
ejpam-4480	386	1	v.	v.	CCONJ
ejpam-4480	386	2	now	now	ADV
ejpam-4480	386	3	,	,	PUNCT
ejpam-4480	386	4	because	because	SCONJ
ejpam-4480	386	5	v	v	NUM
ejpam-4480	386	6	/∈	/∈	PUNCT
ejpam-4480	386	7	ngg(u	ngg(u	PROPN
ejpam-4480	386	8	)	)	PUNCT
ejpam-4480	386	9	for	for	ADP
ejpam-4480	386	10	all	all	DET
ejpam-4480	386	11	u	u	PROPN
ejpam-4480	386	12	∈	∈	PROPN
ejpam-4480	386	13	ng(v	ng(v	NOUN
ejpam-4480	386	14	)	)	PUNCT
ejpam-4480	386	15	,	,	PUNCT
ejpam-4480	386	16	it	it	PRON
ejpam-4480	386	17	follows	follow	VERB
ejpam-4480	386	18	that	that	DET
ejpam-4480	386	19	cg	cg	NOUN
ejpam-4480	386	20	=	=	INTJ
ejpam-4480	386	21	{	{	PUNCT
ejpam-4480	386	22	v	v	NOUN
ejpam-4480	386	23	}	}	PUNCT
ejpam-4480	386	24	.	.	PUNCT
ejpam-4480	387	1	similarly	similarly	ADV
ejpam-4480	387	2	,	,	PUNCT
ejpam-4480	387	3	cg	cg	NOUN
ejpam-4480	387	4	=	=	SYM
ejpam-4480	387	5	{	{	PUNCT
ejpam-4480	387	6	v	v	NOUN
ejpam-4480	387	7	}	}	PUNCT
ejpam-4480	387	8	.	.	PUNCT
ejpam-4480	388	1	thus	thus	ADV
ejpam-4480	388	2	,	,	PUNCT
ejpam-4480	388	3	c	c	X
ejpam-4480	388	4	=	=	PRON
ejpam-4480	388	5	{	{	PUNCT
ejpam-4480	388	6	v	v	NOUN
ejpam-4480	388	7	,	,	PUNCT
ejpam-4480	388	8	v	v	NOUN
ejpam-4480	388	9	}	}	PUNCT
ejpam-4480	388	10	,	,	PUNCT
ejpam-4480	388	11	showing	show	VERB
ejpam-4480	388	12	that	that	SCONJ
ejpam-4480	388	13	(	(	PUNCT
ejpam-4480	388	14	iii	iii	NOUN
ejpam-4480	388	15	)	)	PUNCT
ejpam-4480	388	16	holds	hold	VERB
ejpam-4480	388	17	.	.	PUNCT
ejpam-4480	389	1	for	for	ADP
ejpam-4480	389	2	the	the	DET
ejpam-4480	389	3	converse	converse	NOUN
ejpam-4480	389	4	,	,	PUNCT
ejpam-4480	389	5	suppose	suppose	VERB
ejpam-4480	389	6	first	first	ADV
ejpam-4480	389	7	that	that	SCONJ
ejpam-4480	389	8	(	(	PUNCT
ejpam-4480	389	9	i	i	NOUN
ejpam-4480	389	10	)	)	PUNCT
ejpam-4480	389	11	holds	hold	VERB
ejpam-4480	389	12	.	.	PUNCT
ejpam-4480	390	1	then	then	ADV
ejpam-4480	390	2	c	c	PROPN
ejpam-4480	390	3	is	be	AUX
ejpam-4480	390	4	a	a	DET
ejpam-4480	390	5	clique	clique	NOUN
ejpam-4480	390	6	in	in	ADP
ejpam-4480	390	7	gg	gg	PROPN
ejpam-4480	390	8	.	.	PUNCT
ejpam-4480	391	1	let	let	VERB
ejpam-4480	391	2	p	p	PRON
ejpam-4480	391	3	,	,	PUNCT
ejpam-4480	391	4	q	q	PROPN
ejpam-4480	391	5	∈	∈	PROPN
ejpam-4480	391	6	c	c	NOUN
ejpam-4480	391	7	with	with	ADP
ejpam-4480	391	8	p	p	PROPN
ejpam-4480	391	9	̸=	̸=	PROPN
ejpam-4480	391	10	q.	q.	NOUN
ejpam-4480	391	11	then	then	ADV
ejpam-4480	391	12	p	p	PROPN
ejpam-4480	391	13	∈	∈	PROPN
ejpam-4480	391	14	ngg(p	ngg(p	PROPN
ejpam-4480	391	15	)	)	PUNCT
ejpam-4480	391	16	\ngg(q	\ngg(q	NOUN
ejpam-4480	391	17	)	)	PUNCT
ejpam-4480	391	18	.	.	PUNCT
ejpam-4480	392	1	this	this	PRON
ejpam-4480	392	2	implies	imply	VERB
ejpam-4480	392	3	that	that	SCONJ
ejpam-4480	392	4	c	c	PROPN
ejpam-4480	392	5	is	be	AUX
ejpam-4480	392	6	a	a	DET
ejpam-4480	392	7	superclique	superclique	NOUN
ejpam-4480	392	8	in	in	ADP
ejpam-4480	392	9	gg	gg	NOUN
ejpam-4480	392	10	.	.	PUNCT
ejpam-4480	393	1	the	the	DET
ejpam-4480	393	2	same	same	ADJ
ejpam-4480	393	3	conclusion	conclusion	NOUN
ejpam-4480	393	4	holds	hold	VERB
ejpam-4480	393	5	if	if	SCONJ
ejpam-4480	393	6	(	(	PUNCT
ejpam-4480	393	7	ii	ii	NOUN
ejpam-4480	393	8	)	)	PUNCT
ejpam-4480	393	9	is	be	AUX
ejpam-4480	393	10	assumed	assume	VERB
ejpam-4480	393	11	.	.	PUNCT
ejpam-4480	394	1	suppose	suppose	VERB
ejpam-4480	394	2	now	now	ADV
ejpam-4480	394	3	that	that	SCONJ
ejpam-4480	394	4	(	(	PUNCT
ejpam-4480	394	5	iii	iii	NOUN
ejpam-4480	394	6	)	)	PUNCT
ejpam-4480	394	7	holds	hold	NOUN
ejpam-4480	394	8	,	,	PUNCT
ejpam-4480	394	9	i.e.	i.e.	X
ejpam-4480	394	10	,	,	PUNCT
ejpam-4480	394	11	c	c	X
ejpam-4480	394	12	=	=	SYM
ejpam-4480	394	13	{	{	PUNCT
ejpam-4480	394	14	v	v	NOUN
ejpam-4480	394	15	,	,	PUNCT
ejpam-4480	394	16	v	v	NOUN
ejpam-4480	394	17	}	}	PUNCT
ejpam-4480	394	18	for	for	ADP
ejpam-4480	394	19	some	some	DET
ejpam-4480	394	20	v	v	ADP
ejpam-4480	394	21	∈	∈	NOUN
ejpam-4480	394	22	v	v	NOUN
ejpam-4480	394	23	(	(	PUNCT
ejpam-4480	394	24	g	g	NOUN
ejpam-4480	394	25	)	)	PUNCT
ejpam-4480	394	26	.	.	PUNCT
ejpam-4480	395	1	pick	pick	VERB
ejpam-4480	395	2	any	any	DET
ejpam-4480	395	3	w	w	PROPN
ejpam-4480	395	4	∈	∈	PROPN
ejpam-4480	395	5	v	v	ADP
ejpam-4480	395	6	(	(	PUNCT
ejpam-4480	395	7	g	g	NOUN
ejpam-4480	395	8	)	)	PUNCT
ejpam-4480	395	9	\	\	NOUN
ejpam-4480	395	10	{	{	PUNCT
ejpam-4480	395	11	v	v	NOUN
ejpam-4480	395	12	}	}	PUNCT
ejpam-4480	395	13	.	.	PUNCT
ejpam-4480	396	1	if	if	SCONJ
ejpam-4480	396	2	w	w	PROPN
ejpam-4480	396	3	∈	∈	PROPN
ejpam-4480	396	4	ng(v	ng(v	NOUN
ejpam-4480	396	5	)	)	PUNCT
ejpam-4480	396	6	,	,	PUNCT
ejpam-4480	396	7	then	then	ADV
ejpam-4480	396	8	w	w	PROPN
ejpam-4480	396	9	∈	∈	PROPN
ejpam-4480	396	10	ngg(v	ngg(v	PROPN
ejpam-4480	396	11	)	)	PUNCT
ejpam-4480	396	12	\ngg(v	\ngg(v	PROPN
ejpam-4480	396	13	)	)	PUNCT
ejpam-4480	396	14	.	.	PUNCT
ejpam-4480	397	1	if	if	SCONJ
ejpam-4480	397	2	w	w	PROPN
ejpam-4480	397	3	/∈	/∈	PUNCT
ejpam-4480	397	4	ng(v	ng(v	NUM
ejpam-4480	397	5	)	)	PUNCT
ejpam-4480	397	6	,	,	PUNCT
ejpam-4480	397	7	then	then	ADV
ejpam-4480	397	8	w	w	PROPN
ejpam-4480	397	9	∈	∈	PROPN
ejpam-4480	397	10	ngg(v	ngg(v	PROPN
ejpam-4480	397	11	)	)	PUNCT
ejpam-4480	397	12	\ngg(v	\ngg(v	PROPN
ejpam-4480	397	13	)	)	PUNCT
ejpam-4480	397	14	.	.	PUNCT
ejpam-4480	398	1	thus	thus	ADV
ejpam-4480	398	2	,	,	PUNCT
ejpam-4480	398	3	c	c	PROPN
ejpam-4480	398	4	is	be	AUX
ejpam-4480	398	5	a	a	DET
ejpam-4480	398	6	superclique	superclique	NOUN
ejpam-4480	398	7	in	in	ADP
ejpam-4480	398	8	gg	gg	NOUN
ejpam-4480	398	9	.	.	PUNCT
ejpam-4480	399	1	the	the	DET
ejpam-4480	399	2	next	next	ADJ
ejpam-4480	399	3	results	result	NOUN
ejpam-4480	399	4	are	be	AUX
ejpam-4480	399	5	immediate	immediate	ADJ
ejpam-4480	399	6	from	from	ADP
ejpam-4480	399	7	theorem	theorem	ADJ
ejpam-4480	399	8	4	4	NUM
ejpam-4480	399	9	.	.	PUNCT
ejpam-4480	399	10	corollary	corollary	ADJ
ejpam-4480	399	11	3	3	X
ejpam-4480	399	12	.	.	PUNCT
ejpam-4480	400	1	let	let	VERB
ejpam-4480	400	2	g	g	PRON
ejpam-4480	400	3	be	be	AUX
ejpam-4480	400	4	a	a	DET
ejpam-4480	400	5	non	non	ADJ
ejpam-4480	400	6	-	-	ADJ
ejpam-4480	400	7	trivial	trivial	ADJ
ejpam-4480	400	8	graph	graph	NOUN
ejpam-4480	400	9	.	.	PUNCT
ejpam-4480	401	1	then	then	ADV
ejpam-4480	401	2	ωs(gg	ωs(gg	PROPN
ejpam-4480	401	3	)	)	PUNCT
ejpam-4480	402	1	=	=	SYM
ejpam-4480	402	2	max{2	max{2	PROPN
ejpam-4480	402	3	,	,	PUNCT
ejpam-4480	402	4	ω(g	ω(g	NOUN
ejpam-4480	402	5	)	)	PUNCT
ejpam-4480	402	6	,	,	PUNCT
ejpam-4480	402	7	ω(g	ω(g	NOUN
ejpam-4480	402	8	)	)	PUNCT
ejpam-4480	402	9	}	}	PUNCT
ejpam-4480	402	10	.	.	PUNCT
ejpam-4480	403	1	corollary	corollary	ADJ
ejpam-4480	403	2	4	4	NUM
ejpam-4480	403	3	.	.	PUNCT
ejpam-4480	404	1	let	let	VERB
ejpam-4480	404	2	g	g	NOUN
ejpam-4480	404	3	be	be	AUX
ejpam-4480	404	4	any	any	DET
ejpam-4480	404	5	graph	graph	NOUN
ejpam-4480	404	6	.	.	PUNCT
ejpam-4480	405	1	then	then	ADV
ejpam-4480	405	2	c	c	PROPN
ejpam-4480	405	3	is	be	AUX
ejpam-4480	405	4	a	a	DET
ejpam-4480	405	5	superclique	superclique	NOUN
ejpam-4480	405	6	in	in	ADP
ejpam-4480	405	7	gg	gg	PROPN
ejpam-4480	405	8	if	if	SCONJ
ejpam-4480	406	1	and	and	CCONJ
ejpam-4480	406	2	only	only	ADV
ejpam-4480	406	3	if	if	SCONJ
ejpam-4480	406	4	it	it	PRON
ejpam-4480	406	5	is	be	AUX
ejpam-4480	406	6	a	a	DET
ejpam-4480	406	7	clique	clique	NOUN
ejpam-4480	406	8	in	in	ADP
ejpam-4480	406	9	gg	gg	PROPN
ejpam-4480	406	10	.	.	PUNCT
ejpam-4480	407	1	in	in	ADP
ejpam-4480	407	2	particular	particular	ADJ
ejpam-4480	407	3	,	,	PUNCT
ejpam-4480	407	4	ωs(gg	ωs(gg	ADJ
ejpam-4480	407	5	)	)	PUNCT
ejpam-4480	407	6	=	=	SYM
ejpam-4480	408	1	ω(gg	ω(gg	PROPN
ejpam-4480	408	2	)	)	PUNCT
ejpam-4480	408	3	.	.	PUNCT
ejpam-4480	409	1	theorem	theorem	NOUN
ejpam-4480	409	2	5	5	NUM
ejpam-4480	409	3	.	.	PUNCT
ejpam-4480	410	1	let	let	VERB
ejpam-4480	410	2	g	g	NOUN
ejpam-4480	410	3	and	and	CCONJ
ejpam-4480	410	4	h	h	NOUN
ejpam-4480	410	5	be	be	VERB
ejpam-4480	410	6	any	any	DET
ejpam-4480	410	7	two	two	NUM
ejpam-4480	410	8	graphs	graph	NOUN
ejpam-4480	410	9	.	.	PUNCT
ejpam-4480	411	1	then	then	ADV
ejpam-4480	411	2	c	c	PROPN
ejpam-4480	411	3	⊆	⊆	NUM
ejpam-4480	411	4	v	v	NOUN
ejpam-4480	411	5	(	(	PUNCT
ejpam-4480	411	6	g	g	PROPN
ejpam-4480	411	7	+	+	NOUN
ejpam-4480	411	8	h	h	NOUN
ejpam-4480	411	9	)	)	PUNCT
ejpam-4480	411	10	is	be	AUX
ejpam-4480	411	11	a	a	DET
ejpam-4480	411	12	superclique	superclique	NOUN
ejpam-4480	411	13	in	in	ADP
ejpam-4480	411	14	g+h	g+h	PROPN
ejpam-4480	411	15	if	if	SCONJ
ejpam-4480	411	16	and	and	CCONJ
ejpam-4480	411	17	only	only	ADV
ejpam-4480	411	18	if	if	SCONJ
ejpam-4480	411	19	one	one	NUM
ejpam-4480	411	20	of	of	ADP
ejpam-4480	411	21	the	the	DET
ejpam-4480	411	22	following	following	ADJ
ejpam-4480	411	23	statements	statement	NOUN
ejpam-4480	411	24	holds	hold	VERB
ejpam-4480	411	25	:	:	PUNCT
ejpam-4480	411	26	(	(	PUNCT
ejpam-4480	411	27	i	i	NOUN
ejpam-4480	411	28	)	)	PUNCT
ejpam-4480	411	29	c	c	PROPN
ejpam-4480	411	30	is	be	AUX
ejpam-4480	411	31	a	a	DET
ejpam-4480	411	32	superclique	superclique	NOUN
ejpam-4480	411	33	in	in	ADP
ejpam-4480	411	34	g.	g.	PROPN
ejpam-4480	411	35	(	(	PUNCT
ejpam-4480	411	36	ii	ii	PROPN
ejpam-4480	411	37	)	)	PUNCT
ejpam-4480	411	38	c	c	PROPN
ejpam-4480	411	39	is	be	AUX
ejpam-4480	411	40	a	a	DET
ejpam-4480	411	41	superclique	superclique	NOUN
ejpam-4480	411	42	in	in	ADP
ejpam-4480	411	43	h.	h.	PROPN
ejpam-4480	411	44	(	(	PUNCT
ejpam-4480	411	45	iii	iii	NOUN
ejpam-4480	411	46	)	)	PUNCT
ejpam-4480	411	47	c	c	NOUN
ejpam-4480	412	1	=	=	PUNCT
ejpam-4480	412	2	cg	cg	NOUN
ejpam-4480	412	3	∪	∪	NOUN
ejpam-4480	412	4	ch	ch	NOUN
ejpam-4480	412	5	,	,	PUNCT
ejpam-4480	412	6	where	where	SCONJ
ejpam-4480	412	7	cg	cg	NOUN
ejpam-4480	412	8	and	and	CCONJ
ejpam-4480	412	9	ch	ch	NOUN
ejpam-4480	412	10	are	be	AUX
ejpam-4480	412	11	supercliques	superclique	NOUN
ejpam-4480	412	12	in	in	ADP
ejpam-4480	412	13	g	g	PROPN
ejpam-4480	412	14	and	and	CCONJ
ejpam-4480	412	15	h	h	NOUN
ejpam-4480	412	16	,	,	PUNCT
ejpam-4480	412	17	respectively	respectively	ADV
ejpam-4480	412	18	,	,	PUNCT
ejpam-4480	412	19	and	and	CCONJ
ejpam-4480	412	20	at	at	ADV
ejpam-4480	412	21	least	least	ADJ
ejpam-4480	412	22	one	one	NUM
ejpam-4480	412	23	of	of	ADP
ejpam-4480	412	24	them	they	PRON
ejpam-4480	412	25	is	be	AUX
ejpam-4480	412	26	pointwise	pointwise	ADJ
ejpam-4480	412	27	non	non	ADJ
ejpam-4480	412	28	-	-	ADJ
ejpam-4480	412	29	dominated	dominated	ADJ
ejpam-4480	412	30	.	.	PUNCT
ejpam-4480	413	1	proof	proof	NOUN
ejpam-4480	413	2	.	.	PUNCT
ejpam-4480	414	1	suppose	suppose	VERB
ejpam-4480	414	2	c	c	NOUN
ejpam-4480	414	3	is	be	AUX
ejpam-4480	414	4	a	a	DET
ejpam-4480	414	5	superclique	superclique	NOUN
ejpam-4480	414	6	in	in	ADP
ejpam-4480	414	7	g+h	g+h	PROPN
ejpam-4480	414	8	.	.	PUNCT
ejpam-4480	415	1	set	set	VERB
ejpam-4480	415	2	cg	cg	NOUN
ejpam-4480	415	3	=	=	PUNCT
ejpam-4480	415	4	c	c	NOUN
ejpam-4480	415	5	∩v	∩v	NOUN
ejpam-4480	415	6	(	(	PUNCT
ejpam-4480	415	7	g	g	NOUN
ejpam-4480	415	8	)	)	PUNCT
ejpam-4480	415	9	and	and	CCONJ
ejpam-4480	416	1	ch	ch	NOUN
ejpam-4480	416	2	=	=	PUNCT
ejpam-4480	416	3	c	c	PROPN
ejpam-4480	416	4	∩v	∩v	NOUN
ejpam-4480	416	5	(	(	PUNCT
ejpam-4480	416	6	h	h	NOUN
ejpam-4480	416	7	)	)	PUNCT
ejpam-4480	416	8	.	.	PUNCT
ejpam-4480	417	1	if	if	SCONJ
ejpam-4480	417	2	one	one	NUM
ejpam-4480	417	3	of	of	ADP
ejpam-4480	417	4	cg	cg	NOUN
ejpam-4480	417	5	and	and	CCONJ
ejpam-4480	417	6	ch	ch	NOUN
ejpam-4480	417	7	is	be	AUX
ejpam-4480	417	8	empty	empty	ADJ
ejpam-4480	417	9	,	,	PUNCT
ejpam-4480	417	10	say	say	VERB
ejpam-4480	417	11	ch	ch	NOUN
ejpam-4480	417	12	=	=	NOUN
ejpam-4480	417	13	∅	∅	NOUN
ejpam-4480	417	14	,	,	PUNCT
ejpam-4480	417	15	then	then	ADV
ejpam-4480	417	16	clearly	clearly	ADV
ejpam-4480	417	17	,	,	PUNCT
ejpam-4480	417	18	cg	cg	NOUN
ejpam-4480	417	19	is	be	AUX
ejpam-4480	417	20	a	a	DET
ejpam-4480	417	21	superclique	superclique	NOUN
ejpam-4480	417	22	in	in	ADP
ejpam-4480	417	23	g.	g.	PROPN
ejpam-4480	417	24	thus	thus	ADV
ejpam-4480	417	25	,	,	PUNCT
ejpam-4480	417	26	(	(	PUNCT
ejpam-4480	417	27	i	i	NOUN
ejpam-4480	417	28	)	)	PUNCT
ejpam-4480	417	29	or	or	CCONJ
ejpam-4480	417	30	(	(	PUNCT
ejpam-4480	417	31	ii	ii	NOUN
ejpam-4480	417	32	)	)	PUNCT
ejpam-4480	417	33	holds	hold	VERB
ejpam-4480	417	34	.	.	PUNCT
ejpam-4480	418	1	suppose	suppose	VERB
ejpam-4480	418	2	that	that	SCONJ
ejpam-4480	418	3	cg	cg	NOUN
ejpam-4480	418	4	̸=	̸=	PROPN
ejpam-4480	418	5	∅	∅	NOUN
ejpam-4480	418	6	and	and	CCONJ
ejpam-4480	418	7	ch	ch	NOUN
ejpam-4480	418	8	̸=	̸=	PROPN
ejpam-4480	418	9	∅.	∅.	ADV
ejpam-4480	418	10	since	since	SCONJ
ejpam-4480	418	11	c	c	PROPN
ejpam-4480	418	12	is	be	AUX
ejpam-4480	418	13	a	a	DET
ejpam-4480	418	14	clique	clique	NOUN
ejpam-4480	418	15	,	,	PUNCT
ejpam-4480	418	16	cg	cg	NOUN
ejpam-4480	418	17	and	and	CCONJ
ejpam-4480	418	18	ch	ch	NOUN
ejpam-4480	418	19	are	be	AUX
ejpam-4480	418	20	cliques	clique	NOUN
ejpam-4480	418	21	in	in	ADP
ejpam-4480	418	22	g	g	PROPN
ejpam-4480	418	23	and	and	CCONJ
ejpam-4480	418	24	h	h	NOUN
ejpam-4480	418	25	,	,	PUNCT
ejpam-4480	418	26	respectively	respectively	ADV
ejpam-4480	418	27	.	.	PUNCT
ejpam-4480	419	1	let	let	VERB
ejpam-4480	419	2	v	v	NOUN
ejpam-4480	419	3	,	,	PUNCT
ejpam-4480	419	4	w	w	PROPN
ejpam-4480	419	5	∈	∈	PROPN
ejpam-4480	419	6	cg	cg	NOUN
ejpam-4480	419	7	such	such	ADJ
ejpam-4480	419	8	that	that	PRON
ejpam-4480	419	9	v	v	ADP
ejpam-4480	419	10	̸=	̸=	PROPN
ejpam-4480	419	11	w.	w.	NOUN
ejpam-4480	419	12	since	since	SCONJ
ejpam-4480	419	13	c	c	PROPN
ejpam-4480	419	14	is	be	AUX
ejpam-4480	419	15	a	a	DET
ejpam-4480	419	16	superclique	superclique	NOUN
ejpam-4480	419	17	in	in	ADP
ejpam-4480	419	18	g+h	g+h	PROPN
ejpam-4480	419	19	,	,	PUNCT
ejpam-4480	419	20	there	there	PRON
ejpam-4480	419	21	exists	exist	VERB
ejpam-4480	419	22	z	z	PROPN
ejpam-4480	419	23	∈	∈	PROPN
ejpam-4480	419	24	v	v	PROPN
ejpam-4480	419	25	(	(	PUNCT
ejpam-4480	419	26	g+h	g+h	NOUN
ejpam-4480	419	27	)	)	PUNCT
ejpam-4480	419	28	\	\	PUNCT
ejpam-4480	420	1	c	c	NOUN
ejpam-4480	420	2	such	such	ADJ
ejpam-4480	420	3	that	that	SCONJ
ejpam-4480	420	4	z	z	PROPN
ejpam-4480	420	5	∈	∈	PROPN
ejpam-4480	420	6	ng+h(v	ng+h(v	NOUN
ejpam-4480	420	7	)	)	PUNCT
ejpam-4480	420	8	\ng+h(w	\ng+h(w	NUM
ejpam-4480	420	9	)	)	PUNCT
ejpam-4480	420	10	or	or	CCONJ
ejpam-4480	420	11	z	z	NOUN
ejpam-4480	420	12	∈	∈	PROPN
ejpam-4480	420	13	ng+h(w	ng+h(w	PROPN
ejpam-4480	420	14	)	)	PUNCT
ejpam-4480	420	15	\	\	PUNCT
ejpam-4480	420	16	ng+h(v	ng+h(v	PROPN
ejpam-4480	420	17	)	)	PUNCT
ejpam-4480	420	18	.	.	PUNCT
ejpam-4480	421	1	since	since	SCONJ
ejpam-4480	421	2	v	v	NOUN
ejpam-4480	421	3	(	(	PUNCT
ejpam-4480	421	4	h	h	NOUN
ejpam-4480	421	5	)	)	PUNCT
ejpam-4480	421	6	\	\	PROPN
ejpam-4480	421	7	ch	ch	NOUN
ejpam-4480	421	8	⊆	⊆	NUM
ejpam-4480	421	9	ng+h(v	ng+h(v	NOUN
ejpam-4480	421	10	)	)	PUNCT
ejpam-4480	421	11	∩	∩	NOUN
ejpam-4480	421	12	ng+h(w	ng+h(w	NUM
ejpam-4480	421	13	)	)	PUNCT
ejpam-4480	421	14	,	,	PUNCT
ejpam-4480	421	15	it	it	PRON
ejpam-4480	421	16	follows	follow	VERB
ejpam-4480	421	17	that	that	SCONJ
ejpam-4480	421	18	z	z	PROPN
ejpam-4480	421	19	∈	∈	PROPN
ejpam-4480	421	20	v	v	ADP
ejpam-4480	421	21	(	(	PUNCT
ejpam-4480	421	22	g	g	NOUN
ejpam-4480	421	23	)	)	PUNCT
ejpam-4480	421	24	\	\	PROPN
ejpam-4480	422	1	cg	cg	NOUN
ejpam-4480	422	2	.	.	PUNCT
ejpam-4480	423	1	hence	hence	ADV
ejpam-4480	423	2	,	,	PUNCT
ejpam-4480	423	3	z	z	PROPN
ejpam-4480	423	4	∈	∈	PROPN
ejpam-4480	423	5	ng(v	ng(v	PUNCT
ejpam-4480	423	6	)	)	PUNCT
ejpam-4480	423	7	\ng(w	\ng(w	NUM
ejpam-4480	423	8	)	)	PUNCT
ejpam-4480	423	9	or	or	CCONJ
ejpam-4480	423	10	z	z	NOUN
ejpam-4480	423	11	∈	∈	PROPN
ejpam-4480	423	12	ng(w	ng(w	NOUN
ejpam-4480	423	13	)	)	PUNCT
ejpam-4480	423	14	\ng(v	\ng(v	NOUN
ejpam-4480	423	15	)	)	PUNCT
ejpam-4480	423	16	,	,	PUNCT
ejpam-4480	423	17	showing	show	VERB
ejpam-4480	423	18	that	that	DET
ejpam-4480	423	19	cg	cg	NOUN
ejpam-4480	423	20	is	be	AUX
ejpam-4480	423	21	a	a	DET
ejpam-4480	423	22	superclique	superclique	NOUN
ejpam-4480	423	23	in	in	ADP
ejpam-4480	423	24	g.	g.	NOUN
ejpam-4480	423	25	similarly	similarly	ADV
ejpam-4480	423	26	,	,	PUNCT
ejpam-4480	423	27	ch	ch	NOUN
ejpam-4480	423	28	is	be	AUX
ejpam-4480	423	29	a	a	DET
ejpam-4480	423	30	superclique	superclique	NOUN
ejpam-4480	423	31	in	in	ADP
ejpam-4480	423	32	h.	h.	PROPN
ejpam-4480	423	33	suppose	suppose	VERB
ejpam-4480	423	34	now	now	ADV
ejpam-4480	423	35	that	that	SCONJ
ejpam-4480	423	36	both	both	CCONJ
ejpam-4480	423	37	cg	cg	NOUN
ejpam-4480	423	38	and	and	CCONJ
ejpam-4480	423	39	ch	ch	NOUN
ejpam-4480	423	40	are	be	AUX
ejpam-4480	423	41	not	not	PART
ejpam-4480	423	42	pointwise	pointwise	ADJ
ejpam-4480	423	43	non	non	ADJ
ejpam-4480	423	44	-	-	ADJ
ejpam-4480	423	45	dominated	dominated	ADJ
ejpam-4480	423	46	supercliques	superclique	NOUN
ejpam-4480	423	47	in	in	ADP
ejpam-4480	423	48	g	g	PROPN
ejpam-4480	423	49	and	and	CCONJ
ejpam-4480	423	50	h	h	NOUN
ejpam-4480	423	51	,	,	PUNCT
ejpam-4480	423	52	respectively	respectively	ADV
ejpam-4480	423	53	.	.	PUNCT
ejpam-4480	424	1	then	then	ADV
ejpam-4480	424	2	there	there	PRON
ejpam-4480	424	3	exist	exist	VERB
ejpam-4480	424	4	a	a	DET
ejpam-4480	424	5	∈	∈	PROPN
ejpam-4480	424	6	cg	cg	NOUN
ejpam-4480	424	7	and	and	CCONJ
ejpam-4480	424	8	b	b	PROPN
ejpam-4480	424	9	∈	∈	PROPN
ejpam-4480	424	10	ch	ch	NOUN
ejpam-4480	424	11	such	such	ADJ
ejpam-4480	424	12	that	that	DET
ejpam-4480	424	13	v	v	NOUN
ejpam-4480	424	14	(	(	PUNCT
ejpam-4480	424	15	g	g	NOUN
ejpam-4480	424	16	)	)	PUNCT
ejpam-4480	424	17	\	\	PROPN
ejpam-4480	424	18	cg	cg	NOUN
ejpam-4480	424	19	⊆	⊆	NUM
ejpam-4480	424	20	ng(a	ng(a	NOUN
ejpam-4480	424	21	)	)	PUNCT
ejpam-4480	424	22	and	and	CCONJ
ejpam-4480	424	23	v	v	NOUN
ejpam-4480	424	24	(	(	PUNCT
ejpam-4480	424	25	h	h	NOUN
ejpam-4480	424	26	)	)	PUNCT
ejpam-4480	424	27	\	\	PROPN
ejpam-4480	424	28	ch	ch	NOUN
ejpam-4480	424	29	⊆	⊆	NUM
ejpam-4480	424	30	ng(b	ng(b	NOUN
ejpam-4480	424	31	)	)	PUNCT
ejpam-4480	424	32	.	.	PUNCT
ejpam-4480	425	1	this	this	PRON
ejpam-4480	425	2	would	would	AUX
ejpam-4480	425	3	imply	imply	VERB
ejpam-4480	425	4	that	that	PRON
ejpam-4480	425	5	v	v	NOUN
ejpam-4480	425	6	(	(	PUNCT
ejpam-4480	425	7	g+h	g+h	NOUN
ejpam-4480	425	8	)	)	PUNCT
ejpam-4480	425	9	\c	\c	NOUN
ejpam-4480	425	10	⊆	⊆	NUM
ejpam-4480	425	11	ng+h(a)∩ng+h(b	ng+h(a)∩ng+h(b	ADJ
ejpam-4480	425	12	)	)	PUNCT
ejpam-4480	425	13	,	,	PUNCT
ejpam-4480	425	14	contradicting	contradict	VERB
ejpam-4480	425	15	the	the	DET
ejpam-4480	425	16	assumption	assumption	NOUN
ejpam-4480	425	17	that	that	SCONJ
ejpam-4480	425	18	c	c	PROPN
ejpam-4480	425	19	is	be	AUX
ejpam-4480	425	20	a	a	DET
ejpam-4480	425	21	superclique	superclique	NOUN
ejpam-4480	425	22	in	in	ADP
ejpam-4480	425	23	g+h	g+h	PROPN
ejpam-4480	425	24	.	.	PUNCT
ejpam-4480	426	1	therefore	therefore	ADV
ejpam-4480	426	2	,	,	PUNCT
ejpam-4480	426	3	cg	cg	NOUN
ejpam-4480	426	4	or	or	CCONJ
ejpam-4480	426	5	ch	ch	NOUN
ejpam-4480	426	6	is	be	AUX
ejpam-4480	426	7	a	a	DET
ejpam-4480	426	8	pointwise	pointwise	ADJ
ejpam-4480	426	9	non	non	ADJ
ejpam-4480	426	10	-	-	ADJ
ejpam-4480	426	11	dominated	dominate	VERB
ejpam-4480	426	12	superclique	superclique	NOUN
ejpam-4480	426	13	,	,	PUNCT
ejpam-4480	426	14	showing	show	VERB
ejpam-4480	426	15	that	that	SCONJ
ejpam-4480	426	16	(	(	PUNCT
ejpam-4480	426	17	iii	iii	NOUN
ejpam-4480	426	18	)	)	PUNCT
ejpam-4480	426	19	holds	hold	VERB
ejpam-4480	426	20	.	.	PUNCT
ejpam-4480	427	1	for	for	ADP
ejpam-4480	427	2	the	the	DET
ejpam-4480	427	3	converse	converse	NOUN
ejpam-4480	427	4	,	,	PUNCT
ejpam-4480	427	5	suppose	suppose	VERB
ejpam-4480	427	6	that	that	SCONJ
ejpam-4480	427	7	(	(	PUNCT
ejpam-4480	427	8	i	i	NOUN
ejpam-4480	427	9	)	)	PUNCT
ejpam-4480	427	10	or	or	CCONJ
ejpam-4480	427	11	(	(	PUNCT
ejpam-4480	427	12	ii	ii	NOUN
ejpam-4480	427	13	)	)	PUNCT
ejpam-4480	427	14	holds	hold	VERB
ejpam-4480	427	15	.	.	PUNCT
ejpam-4480	428	1	then	then	ADV
ejpam-4480	428	2	clearly	clearly	ADV
ejpam-4480	428	3	,	,	PUNCT
ejpam-4480	428	4	c	c	PROPN
ejpam-4480	428	5	is	be	AUX
ejpam-4480	428	6	a	a	DET
ejpam-4480	428	7	superclique	superclique	NOUN
ejpam-4480	428	8	in	in	ADP
ejpam-4480	428	9	g+h	g+h	PROPN
ejpam-4480	428	10	.	.	PUNCT
ejpam-4480	429	1	next	next	ADV
ejpam-4480	429	2	,	,	PUNCT
ejpam-4480	429	3	suppose	suppose	VERB
ejpam-4480	429	4	that	that	SCONJ
ejpam-4480	429	5	(	(	PUNCT
ejpam-4480	429	6	iii	iii	NOUN
ejpam-4480	429	7	)	)	PUNCT
ejpam-4480	429	8	holds	hold	NOUN
ejpam-4480	429	9	,	,	PUNCT
ejpam-4480	429	10	i.e.	i.e.	X
ejpam-4480	429	11	,	,	PUNCT
ejpam-4480	429	12	c	c	X
ejpam-4480	429	13	=	=	SYM
ejpam-4480	429	14	cg	cg	NOUN
ejpam-4480	429	15	∪ch	∪ch	NOUN
ejpam-4480	429	16	and	and	CCONJ
ejpam-4480	429	17	satisfies	satisfy	VERB
ejpam-4480	429	18	the	the	DET
ejpam-4480	429	19	given	give	VERB
ejpam-4480	429	20	property	property	NOUN
ejpam-4480	429	21	.	.	PUNCT
ejpam-4480	430	1	assume	assume	VERB
ejpam-4480	430	2	that	that	SCONJ
ejpam-4480	430	3	ch	ch	NOUN
ejpam-4480	430	4	is	be	AUX
ejpam-4480	430	5	a	a	DET
ejpam-4480	430	6	pointwise	pointwise	ADJ
ejpam-4480	430	7	non	non	ADJ
ejpam-4480	430	8	-	-	ADJ
ejpam-4480	430	9	dominated	dominated	ADJ
ejpam-4480	430	10	superclique	superclique	NOUN
ejpam-4480	430	11	in	in	ADP
ejpam-4480	430	12	h.	h.	PROPN
ejpam-4480	430	13	let	let	VERB
ejpam-4480	430	14	v	v	NOUN
ejpam-4480	430	15	,	,	PUNCT
ejpam-4480	430	16	w	w	PROPN
ejpam-4480	430	17	∈	∈	PROPN
ejpam-4480	430	18	v	v	NOUN
ejpam-4480	430	19	(	(	PUNCT
ejpam-4480	430	20	g+h)\c	g+h)\c	VERB
ejpam-4480	430	21	such	such	ADJ
ejpam-4480	430	22	that	that	PRON
ejpam-4480	430	23	v	v	ADP
ejpam-4480	430	24	̸=	̸=	PROPN
ejpam-4480	430	25	v.	v.	ADP
ejpam-4480	430	26	suppose	suppose	VERB
ejpam-4480	430	27	first	first	ADV
ejpam-4480	430	28	that	that	PRON
ejpam-4480	430	29	v	v	NOUN
ejpam-4480	430	30	,	,	PUNCT
ejpam-4480	430	31	w	w	PROPN
ejpam-4480	430	32	∈	∈	PROPN
ejpam-4480	430	33	cg	cg	NOUN
ejpam-4480	430	34	.	.	PUNCT
ejpam-4480	431	1	since	since	SCONJ
ejpam-4480	431	2	cg	cg	NOUN
ejpam-4480	431	3	is	be	AUX
ejpam-4480	431	4	a	a	DET
ejpam-4480	431	5	superclique	superclique	NOUN
ejpam-4480	431	6	in	in	ADP
ejpam-4480	431	7	g	g	NOUN
ejpam-4480	431	8	,	,	PUNCT
ejpam-4480	431	9	there	there	PRON
ejpam-4480	431	10	exists	exist	VERB
ejpam-4480	431	11	y	y	PROPN
ejpam-4480	431	12	∈	∈	PROPN
ejpam-4480	431	13	v	v	ADP
ejpam-4480	431	14	(	(	PUNCT
ejpam-4480	431	15	g	g	NOUN
ejpam-4480	431	16	)	)	PUNCT
ejpam-4480	431	17	\	\	PROPN
ejpam-4480	431	18	cg	cg	NOUN
ejpam-4480	431	19	such	such	ADJ
ejpam-4480	431	20	that	that	SCONJ
ejpam-4480	431	21	y	y	PROPN
ejpam-4480	431	22	∈	∈	PROPN
ejpam-4480	431	23	ng(v	ng(v	PUNCT
ejpam-4480	431	24	)	)	PUNCT
ejpam-4480	431	25	\	\	NOUN
ejpam-4480	431	26	ng(w	ng(w	NOUN
ejpam-4480	431	27	)	)	PUNCT
ejpam-4480	431	28	or	or	CCONJ
ejpam-4480	431	29	y	y	PROPN
ejpam-4480	431	30	∈	∈	PROPN
ejpam-4480	431	31	ng(w	ng(w	NOUN
ejpam-4480	431	32	)	)	PUNCT
ejpam-4480	431	33	\	\	NOUN
ejpam-4480	431	34	ng(v	ng(v	PUNCT
ejpam-4480	431	35	)	)	PUNCT
ejpam-4480	431	36	.	.	PUNCT
ejpam-4480	432	1	hence	hence	ADV
ejpam-4480	432	2	,	,	PUNCT
ejpam-4480	432	3	r.	r.	PROPN
ejpam-4480	432	4	dela	dela	PROPN
ejpam-4480	432	5	cerna	cerna	PROPN
ejpam-4480	432	6	,	,	PUNCT
ejpam-4480	432	7	s.	s.	PROPN
ejpam-4480	432	8	canoy	canoy	PROPN
ejpam-4480	432	9	,	,	PUNCT
ejpam-4480	432	10	jr	jr	PROPN
ejpam-4480	432	11	.	.	PROPN
ejpam-4480	432	12	/	/	SYM
ejpam-4480	432	13	eur	eur	PROPN
ejpam-4480	432	14	.	.	PUNCT
ejpam-4480	433	1	j.	j.	PROPN
ejpam-4480	433	2	pure	pure	PROPN
ejpam-4480	433	3	appl	appl	PROPN
ejpam-4480	433	4	.	.	PROPN
ejpam-4480	433	5	math	math	PROPN
ejpam-4480	433	6	,	,	PUNCT
ejpam-4480	433	7	15	15	NUM
ejpam-4480	433	8	(	(	PUNCT
ejpam-4480	433	9	3	3	NUM
ejpam-4480	433	10	)	)	PUNCT
ejpam-4480	433	11	(	(	PUNCT
ejpam-4480	433	12	2022	2022	NUM
ejpam-4480	433	13	)	)	PUNCT
ejpam-4480	433	14	,	,	PUNCT
ejpam-4480	433	15	1217	1217	NUM
ejpam-4480	433	16	-	-	SYM
ejpam-4480	433	17	1228	1228	NUM
ejpam-4480	433	18	1224	1224	NUM
ejpam-4480	433	19	y	y	PROPN
ejpam-4480	433	20	∈	∈	PROPN
ejpam-4480	433	21	v	v	PROPN
ejpam-4480	433	22	(	(	PUNCT
ejpam-4480	433	23	g+h	g+h	NOUN
ejpam-4480	433	24	)	)	PUNCT
ejpam-4480	433	25	\	\	PROPN
ejpam-4480	434	1	c	c	PROPN
ejpam-4480	434	2	and	and	CCONJ
ejpam-4480	434	3	y	y	PROPN
ejpam-4480	434	4	∈	∈	PROPN
ejpam-4480	434	5	ng+h(v	ng+h(v	ADV
ejpam-4480	434	6	)	)	PUNCT
ejpam-4480	434	7	\ng+h(w	\ng+h(w	NUM
ejpam-4480	434	8	)	)	PUNCT
ejpam-4480	434	9	or	or	CCONJ
ejpam-4480	434	10	y	y	PROPN
ejpam-4480	434	11	∈	∈	PROPN
ejpam-4480	434	12	ng+h(w	ng+h(w	PROPN
ejpam-4480	434	13	)	)	PUNCT
ejpam-4480	434	14	\ng+h(v	\ng+h(v	NOUN
ejpam-4480	434	15	)	)	PUNCT
ejpam-4480	434	16	.	.	PUNCT
ejpam-4480	435	1	similarly	similarly	ADV
ejpam-4480	435	2	,	,	PUNCT
ejpam-4480	435	3	if	if	SCONJ
ejpam-4480	435	4	v	v	ADP
ejpam-4480	435	5	,	,	PUNCT
ejpam-4480	435	6	w	w	PROPN
ejpam-4480	435	7	∈	∈	PROPN
ejpam-4480	435	8	v	v	ADP
ejpam-4480	435	9	(	(	PUNCT
ejpam-4480	435	10	h	h	NOUN
ejpam-4480	435	11	)	)	PUNCT
ejpam-4480	435	12	\	\	PROPN
ejpam-4480	435	13	ch	ch	NOUN
ejpam-4480	435	14	,	,	PUNCT
ejpam-4480	435	15	then	then	ADV
ejpam-4480	435	16	there	there	PRON
ejpam-4480	435	17	exists	exist	VERB
ejpam-4480	435	18	p	p	PROPN
ejpam-4480	435	19	∈	∈	PROPN
ejpam-4480	435	20	v	v	NOUN
ejpam-4480	435	21	(	(	PUNCT
ejpam-4480	435	22	g	g	PROPN
ejpam-4480	435	23	+	+	NOUN
ejpam-4480	435	24	h	h	NOUN
ejpam-4480	435	25	)	)	PUNCT
ejpam-4480	435	26	\	\	PROPN
ejpam-4480	435	27	c	c	NOUN
ejpam-4480	435	28	and	and	CCONJ
ejpam-4480	435	29	p	p	NOUN
ejpam-4480	435	30	∈	∈	PROPN
ejpam-4480	435	31	ng+h(v	ng+h(v	ADV
ejpam-4480	435	32	)	)	PUNCT
ejpam-4480	435	33	\	\	PROPN
ejpam-4480	435	34	ng+h(w	ng+h(w	PROPN
ejpam-4480	435	35	)	)	PUNCT
ejpam-4480	435	36	or	or	CCONJ
ejpam-4480	435	37	p	p	PRON
ejpam-4480	435	38	∈	∈	PROPN
ejpam-4480	435	39	ng+h(w	ng+h(w	NUM
ejpam-4480	435	40	)	)	PUNCT
ejpam-4480	435	41	\	\	PUNCT
ejpam-4480	436	1	ng+h(v	ng+h(v	PROPN
ejpam-4480	436	2	)	)	PUNCT
ejpam-4480	436	3	.	.	PUNCT
ejpam-4480	437	1	suppose	suppose	VERB
ejpam-4480	437	2	now	now	ADV
ejpam-4480	437	3	that	that	SCONJ
ejpam-4480	437	4	v	v	ADP
ejpam-4480	437	5	∈	∈	PROPN
ejpam-4480	437	6	cg	cg	NOUN
ejpam-4480	437	7	and	and	CCONJ
ejpam-4480	437	8	w	w	PROPN
ejpam-4480	437	9	∈	∈	PROPN
ejpam-4480	437	10	ch	ch	NOUN
ejpam-4480	437	11	.	.	PUNCT
ejpam-4480	438	1	since	since	SCONJ
ejpam-4480	438	2	ch	ch	PROPN
ejpam-4480	438	3	is	be	AUX
ejpam-4480	438	4	pointwise	pointwise	ADJ
ejpam-4480	438	5	non	non	ADJ
ejpam-4480	438	6	-	-	ADJ
ejpam-4480	438	7	dominated	dominated	ADJ
ejpam-4480	438	8	,	,	PUNCT
ejpam-4480	438	9	there	there	PRON
ejpam-4480	438	10	exists	exist	VERB
ejpam-4480	438	11	q	q	PROPN
ejpam-4480	438	12	∈	∈	PROPN
ejpam-4480	438	13	v	v	ADP
ejpam-4480	438	14	(	(	PUNCT
ejpam-4480	438	15	h	h	NOUN
ejpam-4480	438	16	)	)	PUNCT
ejpam-4480	438	17	\	\	PROPN
ejpam-4480	438	18	ch	ch	NOUN
ejpam-4480	438	19	such	such	ADJ
ejpam-4480	438	20	that	that	DET
ejpam-4480	438	21	q	q	NOUN
ejpam-4480	438	22	/∈	/∈	PUNCT
ejpam-4480	438	23	nh(v	nh(v	NOUN
ejpam-4480	438	24	)	)	PUNCT
ejpam-4480	438	25	.	.	PUNCT
ejpam-4480	439	1	it	it	PRON
ejpam-4480	439	2	follows	follow	VERB
ejpam-4480	439	3	that	that	SCONJ
ejpam-4480	439	4	q	q	PROPN
ejpam-4480	439	5	∈	∈	PROPN
ejpam-4480	439	6	ng+h(v	ng+h(v	NOUN
ejpam-4480	439	7	)	)	PUNCT
ejpam-4480	439	8	\ng+h(w	\ng+h(w	NUM
ejpam-4480	439	9	)	)	PUNCT
ejpam-4480	439	10	.	.	PUNCT
ejpam-4480	440	1	accordingly	accordingly	ADV
ejpam-4480	440	2	,	,	PUNCT
ejpam-4480	440	3	c	c	PROPN
ejpam-4480	440	4	is	be	AUX
ejpam-4480	440	5	a	a	DET
ejpam-4480	440	6	superclique	superclique	NOUN
ejpam-4480	440	7	in	in	ADP
ejpam-4480	440	8	g+h	g+h	PROPN
ejpam-4480	440	9	.	.	PUNCT
ejpam-4480	441	1	corollary	corollary	ADJ
ejpam-4480	441	2	5	5	NUM
ejpam-4480	441	3	.	.	PUNCT
ejpam-4480	442	1	let	let	VERB
ejpam-4480	442	2	g	g	PRON
ejpam-4480	442	3	be	be	AUX
ejpam-4480	442	4	a	a	DET
ejpam-4480	442	5	non	non	ADJ
ejpam-4480	442	6	-	-	ADJ
ejpam-4480	442	7	complete	complete	ADJ
ejpam-4480	442	8	graph	graph	NOUN
ejpam-4480	442	9	and	and	CCONJ
ejpam-4480	442	10	let	let	VERB
ejpam-4480	442	11	n	n	PRON
ejpam-4480	442	12	be	be	AUX
ejpam-4480	442	13	a	a	DET
ejpam-4480	442	14	positive	positive	ADJ
ejpam-4480	442	15	integer	integer	NOUN
ejpam-4480	442	16	.	.	PUNCT
ejpam-4480	443	1	then	then	ADV
ejpam-4480	443	2	c	c	PROPN
ejpam-4480	443	3	⊆	⊆	NUM
ejpam-4480	443	4	v	v	PROPN
ejpam-4480	443	5	(	(	PUNCT
ejpam-4480	443	6	kn+g	kn+g	NOUN
ejpam-4480	443	7	)	)	PUNCT
ejpam-4480	443	8	is	be	AUX
ejpam-4480	443	9	a	a	DET
ejpam-4480	443	10	superclique	superclique	NOUN
ejpam-4480	443	11	in	in	ADP
ejpam-4480	443	12	kn+g	kn+g	PROPN
ejpam-4480	444	1	if	if	SCONJ
ejpam-4480	444	2	and	and	CCONJ
ejpam-4480	444	3	only	only	ADV
ejpam-4480	444	4	if	if	SCONJ
ejpam-4480	444	5	one	one	NUM
ejpam-4480	444	6	of	of	ADP
ejpam-4480	444	7	the	the	DET
ejpam-4480	444	8	following	following	ADJ
ejpam-4480	444	9	statements	statement	NOUN
ejpam-4480	444	10	holds	hold	VERB
ejpam-4480	444	11	:	:	PUNCT
ejpam-4480	444	12	(	(	PUNCT
ejpam-4480	444	13	i	i	NOUN
ejpam-4480	444	14	)	)	PUNCT
ejpam-4480	444	15	c	c	PROPN
ejpam-4480	444	16	is	be	AUX
ejpam-4480	444	17	a	a	DET
ejpam-4480	444	18	superclique	superclique	NOUN
ejpam-4480	444	19	in	in	ADP
ejpam-4480	444	20	g.	g.	PROPN
ejpam-4480	444	21	(	(	PUNCT
ejpam-4480	444	22	ii	ii	PROPN
ejpam-4480	444	23	)	)	PUNCT
ejpam-4480	444	24	c	c	NOUN
ejpam-4480	445	1	=	=	PRON
ejpam-4480	445	2	{	{	PUNCT
ejpam-4480	445	3	p	p	X
ejpam-4480	445	4	}	}	PUNCT
ejpam-4480	445	5	for	for	ADP
ejpam-4480	445	6	some	some	DET
ejpam-4480	445	7	p	p	NOUN
ejpam-4480	445	8	∈	∈	PROPN
ejpam-4480	445	9	v	v	NOUN
ejpam-4480	445	10	(	(	PUNCT
ejpam-4480	445	11	kn	kn	PROPN
ejpam-4480	445	12	)	)	PUNCT
ejpam-4480	445	13	.	.	PUNCT
ejpam-4480	446	1	(	(	PUNCT
ejpam-4480	446	2	iii	iii	X
ejpam-4480	446	3	)	)	PUNCT
ejpam-4480	446	4	c	c	NOUN
ejpam-4480	446	5	=	=	SYM
ejpam-4480	446	6	cg∪{p	cg∪{p	NOUN
ejpam-4480	446	7	}	}	PUNCT
ejpam-4480	446	8	for	for	ADP
ejpam-4480	446	9	some	some	DET
ejpam-4480	446	10	pointwise	pointwise	ADJ
ejpam-4480	446	11	non	non	ADJ
ejpam-4480	446	12	-	-	ADJ
ejpam-4480	446	13	dominated	dominate	VERB
ejpam-4480	446	14	superclique	superclique	ADJ
ejpam-4480	446	15	cg	cg	NOUN
ejpam-4480	446	16	in	in	ADP
ejpam-4480	446	17	g	g	PROPN
ejpam-4480	446	18	and	and	CCONJ
ejpam-4480	446	19	p	p	NOUN
ejpam-4480	446	20	∈	∈	PROPN
ejpam-4480	446	21	v	v	ADP
ejpam-4480	446	22	(	(	PUNCT
ejpam-4480	446	23	kn	kn	PROPN
ejpam-4480	446	24	)	)	PUNCT
ejpam-4480	446	25	.	.	PUNCT
ejpam-4480	447	1	proof	proof	NOUN
ejpam-4480	447	2	.	.	PUNCT
ejpam-4480	448	1	since	since	SCONJ
ejpam-4480	448	2	the	the	DET
ejpam-4480	448	3	only	only	ADJ
ejpam-4480	448	4	supercliques	superclique	NOUN
ejpam-4480	448	5	in	in	ADP
ejpam-4480	448	6	kn	kn	PROPN
ejpam-4480	448	7	are	be	AUX
ejpam-4480	448	8	the	the	DET
ejpam-4480	448	9	singleton	singleton	PROPN
ejpam-4480	448	10	subsets	subset	NOUN
ejpam-4480	448	11	of	of	ADP
ejpam-4480	448	12	v	v	PROPN
ejpam-4480	448	13	(	(	PUNCT
ejpam-4480	448	14	kn	kn	PROPN
ejpam-4480	448	15	)	)	PUNCT
ejpam-4480	448	16	and	and	CCONJ
ejpam-4480	448	17	none	none	NOUN
ejpam-4480	448	18	of	of	ADP
ejpam-4480	448	19	these	these	DET
ejpam-4480	448	20	sets	set	NOUN
ejpam-4480	448	21	is	be	AUX
ejpam-4480	448	22	pointwise	pointwise	ADJ
ejpam-4480	448	23	non	non	ADJ
ejpam-4480	448	24	-	-	ADJ
ejpam-4480	448	25	dominated	dominated	ADJ
ejpam-4480	448	26	,	,	PUNCT
ejpam-4480	448	27	c	c	PROPN
ejpam-4480	448	28	⊆	⊆	NUM
ejpam-4480	448	29	v	v	X
ejpam-4480	448	30	(	(	PUNCT
ejpam-4480	448	31	kn	kn	NOUN
ejpam-4480	448	32	+	+	CCONJ
ejpam-4480	448	33	g	g	NOUN
ejpam-4480	448	34	)	)	PUNCT
ejpam-4480	448	35	is	be	AUX
ejpam-4480	448	36	a	a	DET
ejpam-4480	448	37	superclique	superclique	NOUN
ejpam-4480	448	38	in	in	ADP
ejpam-4480	448	39	kn	kn	PROPN
ejpam-4480	448	40	+	+	CCONJ
ejpam-4480	448	41	g	g	PROPN
ejpam-4480	448	42	if	if	SCONJ
ejpam-4480	448	43	and	and	CCONJ
ejpam-4480	448	44	only	only	ADV
ejpam-4480	448	45	if	if	SCONJ
ejpam-4480	448	46	(	(	PUNCT
ejpam-4480	448	47	i	i	NOUN
ejpam-4480	448	48	)	)	PUNCT
ejpam-4480	448	49	,	,	PUNCT
ejpam-4480	448	50	(	(	PUNCT
ejpam-4480	448	51	ii	ii	NOUN
ejpam-4480	448	52	)	)	PUNCT
ejpam-4480	448	53	,	,	PUNCT
ejpam-4480	448	54	or	or	CCONJ
ejpam-4480	448	55	(	(	PUNCT
ejpam-4480	448	56	iii	iii	X
ejpam-4480	448	57	)	)	PUNCT
ejpam-4480	448	58	holds	hold	VERB
ejpam-4480	448	59	by	by	ADP
ejpam-4480	448	60	theorem	theorem	NOUN
ejpam-4480	448	61	5	5	NUM
ejpam-4480	448	62	.	.	PUNCT
ejpam-4480	449	1	the	the	DET
ejpam-4480	449	2	next	next	ADJ
ejpam-4480	449	3	result	result	NOUN
ejpam-4480	449	4	is	be	AUX
ejpam-4480	449	5	a	a	DET
ejpam-4480	449	6	consequence	consequence	NOUN
ejpam-4480	449	7	of	of	ADP
ejpam-4480	449	8	theorem	theorem	ADJ
ejpam-4480	449	9	5	5	NUM
ejpam-4480	449	10	and	and	CCONJ
ejpam-4480	449	11	corollary	corollary	ADJ
ejpam-4480	449	12	5	5	NUM
ejpam-4480	449	13	.	.	PUNCT
ejpam-4480	449	14	corollary	corollary	ADJ
ejpam-4480	449	15	6	6	NUM
ejpam-4480	449	16	.	.	PUNCT
ejpam-4480	450	1	let	let	VERB
ejpam-4480	450	2	g	g	NOUN
ejpam-4480	450	3	and	and	CCONJ
ejpam-4480	450	4	h	h	NOUN
ejpam-4480	450	5	be	be	VERB
ejpam-4480	450	6	any	any	DET
ejpam-4480	450	7	two	two	NUM
ejpam-4480	450	8	graphs	graph	NOUN
ejpam-4480	450	9	and	and	CCONJ
ejpam-4480	450	10	let	let	VERB
ejpam-4480	450	11	n	n	PRON
ejpam-4480	450	12	be	be	AUX
ejpam-4480	450	13	a	a	DET
ejpam-4480	450	14	positive	positive	ADJ
ejpam-4480	450	15	integer	integer	NOUN
ejpam-4480	450	16	.	.	PUNCT
ejpam-4480	451	1	then	then	ADV
ejpam-4480	451	2	ωs(g+h	ωs(g+h	NUM
ejpam-4480	451	3	)	)	PUNCT
ejpam-4480	451	4	=	=	NUM
ejpam-4480	451	5			NOUN
ejpam-4480	451	6	max{ωs(g	max{ωs(g	PROPN
ejpam-4480	451	7	)	)	PUNCT
ejpam-4480	452	1	+	+	CCONJ
ejpam-4480	452	2	ωpnds(h	ωpnds(h	NOUN
ejpam-4480	452	3	)	)	PUNCT
ejpam-4480	452	4	,	,	PUNCT
ejpam-4480	452	5	ωs(h	ωs(h	NUM
ejpam-4480	452	6	)	)	PUNCT
ejpam-4480	453	1	+	+	CCONJ
ejpam-4480	453	2	ωpnds(g	ωpnds(g	NUM
ejpam-4480	453	3	)	)	PUNCT
ejpam-4480	453	4	}	}	PUNCT
ejpam-4480	453	5	if	if	SCONJ
ejpam-4480	453	6	g	g	PROPN
ejpam-4480	453	7	and	and	CCONJ
ejpam-4480	453	8	h	h	NOUN
ejpam-4480	453	9	are	be	AUX
ejpam-4480	453	10	non	non	ADJ
ejpam-4480	453	11	-	-	ADJ
ejpam-4480	453	12	complete	complete	ADJ
ejpam-4480	453	13	max{ωs(g	max{ωs(g	PROPN
ejpam-4480	453	14	)	)	PUNCT
ejpam-4480	453	15	,	,	PUNCT
ejpam-4480	453	16	ωpnds(g	ωpnds(g	ADP
ejpam-4480	453	17	)	)	PUNCT
ejpam-4480	453	18	+	+	NOUN
ejpam-4480	453	19	1	1	X
ejpam-4480	453	20	}	}	PUNCT
ejpam-4480	453	21	if	if	SCONJ
ejpam-4480	453	22	g	g	PROPN
ejpam-4480	453	23	is	be	AUX
ejpam-4480	453	24	non	non	ADJ
ejpam-4480	453	25	-	-	ADJ
ejpam-4480	453	26	complete	complete	ADJ
ejpam-4480	453	27	and	and	CCONJ
ejpam-4480	453	28	h	h	NOUN
ejpam-4480	453	29	=	=	SYM
ejpam-4480	453	30	kn	kn	PROPN
ejpam-4480	453	31	.	.	PUNCT
ejpam-4480	453	32	theorem	theorem	VERB
ejpam-4480	453	33	6	6	NUM
ejpam-4480	453	34	.	.	PUNCT
ejpam-4480	454	1	let	let	VERB
ejpam-4480	454	2	g	g	PRON
ejpam-4480	454	3	be	be	AUX
ejpam-4480	454	4	a	a	DET
ejpam-4480	454	5	non	non	ADJ
ejpam-4480	454	6	-	-	ADJ
ejpam-4480	454	7	trivial	trivial	ADJ
ejpam-4480	454	8	connected	connected	ADJ
ejpam-4480	454	9	graph	graph	NOUN
ejpam-4480	454	10	and	and	CCONJ
ejpam-4480	454	11	let	let	VERB
ejpam-4480	454	12	h	h	NOUN
ejpam-4480	454	13	be	be	AUX
ejpam-4480	454	14	any	any	DET
ejpam-4480	454	15	graph	graph	NOUN
ejpam-4480	454	16	.	.	PUNCT
ejpam-4480	455	1	then	then	ADV
ejpam-4480	455	2	c	c	PROPN
ejpam-4480	455	3	⊆	⊆	NUM
ejpam-4480	455	4	v	v	NOUN
ejpam-4480	455	5	(	(	PUNCT
ejpam-4480	455	6	g	g	PROPN
ejpam-4480	455	7	◦	◦	NOUN
ejpam-4480	455	8	h	h	NOUN
ejpam-4480	455	9	)	)	PUNCT
ejpam-4480	455	10	is	be	AUX
ejpam-4480	455	11	a	a	DET
ejpam-4480	455	12	superclique	superclique	NOUN
ejpam-4480	455	13	in	in	ADP
ejpam-4480	455	14	g	g	PROPN
ejpam-4480	455	15	◦	◦	NOUN
ejpam-4480	455	16	h	h	NOUN
ejpam-4480	455	17	if	if	SCONJ
ejpam-4480	456	1	and	and	CCONJ
ejpam-4480	456	2	only	only	ADV
ejpam-4480	456	3	if	if	SCONJ
ejpam-4480	456	4	one	one	NUM
ejpam-4480	456	5	of	of	ADP
ejpam-4480	456	6	the	the	DET
ejpam-4480	456	7	following	following	ADJ
ejpam-4480	456	8	statements	statement	NOUN
ejpam-4480	456	9	holds	hold	VERB
ejpam-4480	456	10	:	:	PUNCT
ejpam-4480	456	11	(	(	PUNCT
ejpam-4480	456	12	i	i	NOUN
ejpam-4480	456	13	)	)	PUNCT
ejpam-4480	456	14	c	c	PROPN
ejpam-4480	456	15	is	be	AUX
ejpam-4480	456	16	a	a	DET
ejpam-4480	456	17	clique	clique	NOUN
ejpam-4480	456	18	in	in	ADP
ejpam-4480	456	19	g.	g.	PROPN
ejpam-4480	456	20	(	(	PUNCT
ejpam-4480	456	21	ii	ii	PROPN
ejpam-4480	456	22	)	)	PUNCT
ejpam-4480	456	23	c	c	PROPN
ejpam-4480	456	24	is	be	AUX
ejpam-4480	456	25	a	a	DET
ejpam-4480	456	26	superclique	superclique	NOUN
ejpam-4480	456	27	in	in	ADP
ejpam-4480	456	28	hv	hv	NOUN
ejpam-4480	456	29	for	for	ADP
ejpam-4480	456	30	some	some	DET
ejpam-4480	456	31	v	v	NUM
ejpam-4480	456	32	∈	∈	PROPN
ejpam-4480	456	33	v	v	NOUN
ejpam-4480	456	34	(	(	PUNCT
ejpam-4480	456	35	g	g	NOUN
ejpam-4480	456	36	)	)	PUNCT
ejpam-4480	456	37	.	.	PUNCT
ejpam-4480	457	1	(	(	PUNCT
ejpam-4480	457	2	iii	iii	X
ejpam-4480	457	3	)	)	PUNCT
ejpam-4480	457	4	c	c	NOUN
ejpam-4480	457	5	=	=	SYM
ejpam-4480	457	6	cv	cv	PROPN
ejpam-4480	457	7	∪	∪	X
ejpam-4480	457	8	{	{	PUNCT
ejpam-4480	457	9	v	v	NOUN
ejpam-4480	457	10	}	}	PUNCT
ejpam-4480	457	11	for	for	ADP
ejpam-4480	457	12	some	some	DET
ejpam-4480	457	13	v	v	ADP
ejpam-4480	457	14	∈	∈	PROPN
ejpam-4480	457	15	v	v	NOUN
ejpam-4480	457	16	(	(	PUNCT
ejpam-4480	457	17	g	g	NOUN
ejpam-4480	457	18	)	)	PUNCT
ejpam-4480	457	19	and	and	CCONJ
ejpam-4480	457	20	superclique	superclique	ADJ
ejpam-4480	457	21	cv	cv	PROPN
ejpam-4480	457	22	in	in	ADP
ejpam-4480	457	23	hv	hv	PROPN
ejpam-4480	457	24	.	.	PUNCT
ejpam-4480	458	1	proof	proof	NOUN
ejpam-4480	458	2	.	.	PUNCT
ejpam-4480	459	1	suppose	suppose	VERB
ejpam-4480	459	2	c	c	NOUN
ejpam-4480	459	3	is	be	AUX
ejpam-4480	459	4	a	a	DET
ejpam-4480	459	5	superclique	superclique	NOUN
ejpam-4480	459	6	in	in	ADP
ejpam-4480	459	7	g	g	PROPN
ejpam-4480	459	8	◦	◦	NOUN
ejpam-4480	459	9	h.	h.	NOUN
ejpam-4480	459	10	if	if	SCONJ
ejpam-4480	459	11	c	c	PROPN
ejpam-4480	459	12	⊆	⊆	NUM
ejpam-4480	459	13	v	v	X
ejpam-4480	459	14	(	(	PUNCT
ejpam-4480	459	15	g	g	NOUN
ejpam-4480	459	16	)	)	PUNCT
ejpam-4480	459	17	,	,	PUNCT
ejpam-4480	459	18	then	then	ADV
ejpam-4480	459	19	c	c	PROPN
ejpam-4480	459	20	is	be	AUX
ejpam-4480	459	21	a	a	DET
ejpam-4480	459	22	clique	clique	NOUN
ejpam-4480	459	23	in	in	ADP
ejpam-4480	459	24	g.	g.	PROPN
ejpam-4480	459	25	so	so	ADV
ejpam-4480	459	26	suppose	suppose	VERB
ejpam-4480	459	27	that	that	SCONJ
ejpam-4480	459	28	c	c	PROPN
ejpam-4480	459	29	∩	∩	PROPN
ejpam-4480	459	30	v	v	PROPN
ejpam-4480	459	31	(	(	PUNCT
ejpam-4480	459	32	hv	hv	NOUN
ejpam-4480	459	33	)	)	PUNCT
ejpam-4480	459	34	̸=	̸=	PROPN
ejpam-4480	459	35	∅	∅	NOUN
ejpam-4480	459	36	for	for	ADP
ejpam-4480	459	37	some	some	PRON
ejpam-4480	459	38	v	v	ADP
ejpam-4480	459	39	∈	∈	NOUN
ejpam-4480	459	40	v	v	NOUN
ejpam-4480	459	41	(	(	PUNCT
ejpam-4480	459	42	g	g	NOUN
ejpam-4480	459	43	)	)	PUNCT
ejpam-4480	459	44	.	.	PUNCT
ejpam-4480	460	1	then	then	ADV
ejpam-4480	460	2	c	c	PROPN
ejpam-4480	460	3	is	be	AUX
ejpam-4480	460	4	a	a	DET
ejpam-4480	460	5	clique	clique	NOUN
ejpam-4480	460	6	in	in	ADP
ejpam-4480	460	7	v	v	PROPN
ejpam-4480	460	8	+	+	PROPN
ejpam-4480	460	9	hv	hv	PROPN
ejpam-4480	460	10	.	.	PUNCT
ejpam-4480	460	11	suppose	suppose	VERB
ejpam-4480	460	12	first	first	ADV
ejpam-4480	460	13	that	that	SCONJ
ejpam-4480	460	14	c	c	PROPN
ejpam-4480	460	15	⊆	⊆	NUM
ejpam-4480	460	16	v	v	X
ejpam-4480	460	17	(	(	PUNCT
ejpam-4480	460	18	hv	hv	PROPN
ejpam-4480	460	19	)	)	PUNCT
ejpam-4480	460	20	and	and	CCONJ
ejpam-4480	460	21	let	let	VERB
ejpam-4480	460	22	x	x	PRON
ejpam-4480	460	23	,	,	PUNCT
ejpam-4480	460	24	y	y	PROPN
ejpam-4480	460	25	∈	∈	PROPN
ejpam-4480	460	26	c	c	X
ejpam-4480	460	27	where	where	SCONJ
ejpam-4480	460	28	x	x	X
ejpam-4480	460	29	̸=	̸=	PROPN
ejpam-4480	460	30	y.	y.	NOUN
ejpam-4480	460	31	since	since	SCONJ
ejpam-4480	460	32	c	c	PROPN
ejpam-4480	460	33	is	be	AUX
ejpam-4480	460	34	a	a	DET
ejpam-4480	460	35	superclique	superclique	NOUN
ejpam-4480	460	36	in	in	ADP
ejpam-4480	460	37	g	g	PROPN
ejpam-4480	460	38	◦	◦	NOUN
ejpam-4480	460	39	h	h	NOUN
ejpam-4480	460	40	,	,	PUNCT
ejpam-4480	460	41	there	there	PRON
ejpam-4480	460	42	exists	exist	VERB
ejpam-4480	460	43	z	z	PROPN
ejpam-4480	460	44	∈	∈	PROPN
ejpam-4480	460	45	v	v	NOUN
ejpam-4480	460	46	(	(	PUNCT
ejpam-4480	460	47	g	g	NOUN
ejpam-4480	460	48	◦	◦	NOUN
ejpam-4480	460	49	h)\c	h)\c	NOUN
ejpam-4480	460	50	such	such	DET
ejpam-4480	460	51	that	that	SCONJ
ejpam-4480	460	52	z	z	PROPN
ejpam-4480	460	53	∈	∈	PROPN
ejpam-4480	460	54	ng	ng	PROPN
ejpam-4480	460	55	◦	◦	NOUN
ejpam-4480	460	56	h(x)\ng	h(x)\ng	NOUN
ejpam-4480	460	57	◦	◦	NOUN
ejpam-4480	460	58	h(y	h(y	NUM
ejpam-4480	460	59	)	)	PUNCT
ejpam-4480	460	60	or	or	CCONJ
ejpam-4480	460	61	z	z	PROPN
ejpam-4480	460	62	∈	∈	PROPN
ejpam-4480	460	63	ng	ng	PROPN
ejpam-4480	460	64	◦	◦	NOUN
ejpam-4480	460	65	h(y)\ng	h(y)\ng	NOUN
ejpam-4480	460	66	◦	◦	NOUN
ejpam-4480	460	67	h(x	h(x	PROPN
ejpam-4480	460	68	)	)	PUNCT
ejpam-4480	460	69	.	.	PUNCT
ejpam-4480	461	1	since	since	SCONJ
ejpam-4480	461	2	v	v	NUM
ejpam-4480	461	3	∈	∈	PROPN
ejpam-4480	461	4	ng	ng	PROPN
ejpam-4480	461	5	◦	◦	NOUN
ejpam-4480	461	6	h(x	h(x	PROPN
ejpam-4480	461	7	)	)	PUNCT
ejpam-4480	461	8	∩	∩	PROPN
ejpam-4480	461	9	ng	ng	PROPN
ejpam-4480	461	10	◦	◦	NOUN
ejpam-4480	461	11	h(y	h(y	ADV
ejpam-4480	461	12	)	)	PUNCT
ejpam-4480	461	13	,	,	PUNCT
ejpam-4480	461	14	z	z	PROPN
ejpam-4480	461	15	̸=	̸=	PROPN
ejpam-4480	461	16	v.	v.	ADP
ejpam-4480	461	17	hence	hence	ADV
ejpam-4480	461	18	,	,	PUNCT
ejpam-4480	461	19	z	z	PROPN
ejpam-4480	461	20	∈	∈	PROPN
ejpam-4480	461	21	v	v	ADP
ejpam-4480	461	22	(	(	PUNCT
ejpam-4480	461	23	hv	hv	PROPN
ejpam-4480	461	24	)	)	PUNCT
ejpam-4480	461	25	\	\	PROPN
ejpam-4480	461	26	c	c	PROPN
ejpam-4480	461	27	and	and	CCONJ
ejpam-4480	461	28	z	z	PROPN
ejpam-4480	461	29	∈	∈	PROPN
ejpam-4480	461	30	nhv(x	nhv(x	PROPN
ejpam-4480	461	31	)	)	PUNCT
ejpam-4480	461	32	\	\	PROPN
ejpam-4480	461	33	nhv(y	nhv(y	PROPN
ejpam-4480	461	34	)	)	PUNCT
ejpam-4480	461	35	r.	r.	PROPN
ejpam-4480	461	36	dela	dela	PROPN
ejpam-4480	461	37	cerna	cerna	PROPN
ejpam-4480	461	38	,	,	PUNCT
ejpam-4480	461	39	s.	s.	PROPN
ejpam-4480	461	40	canoy	canoy	PROPN
ejpam-4480	461	41	,	,	PUNCT
ejpam-4480	461	42	jr	jr	PROPN
ejpam-4480	461	43	.	.	PROPN
ejpam-4480	461	44	/	/	SYM
ejpam-4480	461	45	eur	eur	PROPN
ejpam-4480	461	46	.	.	PUNCT
ejpam-4480	462	1	j.	j.	PROPN
ejpam-4480	462	2	pure	pure	PROPN
ejpam-4480	462	3	appl	appl	PROPN
ejpam-4480	462	4	.	.	PROPN
ejpam-4480	462	5	math	math	PROPN
ejpam-4480	462	6	,	,	PUNCT
ejpam-4480	462	7	15	15	NUM
ejpam-4480	462	8	(	(	PUNCT
ejpam-4480	462	9	3	3	NUM
ejpam-4480	462	10	)	)	PUNCT
ejpam-4480	462	11	(	(	PUNCT
ejpam-4480	462	12	2022	2022	NUM
ejpam-4480	462	13	)	)	PUNCT
ejpam-4480	462	14	,	,	PUNCT
ejpam-4480	462	15	1217	1217	NUM
ejpam-4480	462	16	-	-	SYM
ejpam-4480	462	17	1228	1228	NUM
ejpam-4480	462	18	1225	1225	NUM
ejpam-4480	462	19	or	or	CCONJ
ejpam-4480	462	20	z	z	NOUN
ejpam-4480	462	21	∈	∈	PROPN
ejpam-4480	462	22	nhv(y	nhv(y	PROPN
ejpam-4480	462	23	)	)	PUNCT
ejpam-4480	462	24	\	\	NOUN
ejpam-4480	462	25	nhv(x	nhv(x	PROPN
ejpam-4480	462	26	)	)	PUNCT
ejpam-4480	462	27	.	.	PUNCT
ejpam-4480	463	1	this	this	PRON
ejpam-4480	463	2	shows	show	VERB
ejpam-4480	463	3	that	that	SCONJ
ejpam-4480	463	4	c	c	PROPN
ejpam-4480	463	5	is	be	AUX
ejpam-4480	463	6	a	a	DET
ejpam-4480	463	7	superclique	superclique	NOUN
ejpam-4480	463	8	in	in	ADP
ejpam-4480	463	9	hv	hv	PROPN
ejpam-4480	463	10	.	.	PUNCT
ejpam-4480	464	1	next	next	ADV
ejpam-4480	464	2	,	,	PUNCT
ejpam-4480	464	3	suppose	suppose	VERB
ejpam-4480	464	4	that	that	SCONJ
ejpam-4480	464	5	v	v	PROPN
ejpam-4480	464	6	∈	∈	PROPN
ejpam-4480	464	7	c.	c.	NOUN
ejpam-4480	464	8	then	then	ADV
ejpam-4480	464	9	c	c	X
ejpam-4480	464	10	=	=	SYM
ejpam-4480	464	11	{	{	PUNCT
ejpam-4480	464	12	v	v	NOUN
ejpam-4480	464	13	}	}	PUNCT
ejpam-4480	464	14	∪	∪	NOUN
ejpam-4480	464	15	cv	cv	PROPN
ejpam-4480	464	16	where	where	SCONJ
ejpam-4480	464	17	cv	cv	PROPN
ejpam-4480	464	18	=	=	SYM
ejpam-4480	464	19	c	c	PROPN
ejpam-4480	464	20	∩	∩	X
ejpam-4480	464	21	v	v	X
ejpam-4480	464	22	(	(	PUNCT
ejpam-4480	464	23	hv	hv	PROPN
ejpam-4480	464	24	)	)	PUNCT
ejpam-4480	464	25	.	.	PUNCT
ejpam-4480	465	1	it	it	PRON
ejpam-4480	465	2	is	be	AUX
ejpam-4480	465	3	routine	routine	ADJ
ejpam-4480	465	4	to	to	PART
ejpam-4480	465	5	show	show	VERB
ejpam-4480	465	6	that	that	SCONJ
ejpam-4480	465	7	cv	cv	PROPN
ejpam-4480	465	8	is	be	AUX
ejpam-4480	465	9	a	a	DET
ejpam-4480	465	10	superclique	superclique	NOUN
ejpam-4480	465	11	in	in	ADP
ejpam-4480	465	12	hv	hv	PROPN
ejpam-4480	465	13	.	.	PUNCT
ejpam-4480	466	1	for	for	ADP
ejpam-4480	466	2	the	the	DET
ejpam-4480	466	3	converse	converse	NOUN
ejpam-4480	466	4	,	,	PUNCT
ejpam-4480	466	5	suppose	suppose	VERB
ejpam-4480	466	6	first	first	ADV
ejpam-4480	466	7	that	that	SCONJ
ejpam-4480	466	8	c	c	PROPN
ejpam-4480	466	9	is	be	AUX
ejpam-4480	466	10	a	a	DET
ejpam-4480	466	11	clique	clique	NOUN
ejpam-4480	466	12	in	in	ADP
ejpam-4480	466	13	g.	g.	PROPN
ejpam-4480	466	14	let	let	VERB
ejpam-4480	466	15	a	a	DET
ejpam-4480	466	16	,	,	PUNCT
ejpam-4480	466	17	b	b	X
ejpam-4480	466	18	∈	∈	PROPN
ejpam-4480	466	19	c	c	NOUN
ejpam-4480	466	20	where	where	SCONJ
ejpam-4480	466	21	a	a	DET
ejpam-4480	466	22	̸=	̸=	PROPN
ejpam-4480	466	23	b.	b.	NOUN
ejpam-4480	466	24	pick	pick	VERB
ejpam-4480	466	25	any	any	DET
ejpam-4480	466	26	c	c	PROPN
ejpam-4480	466	27	∈	∈	PROPN
ejpam-4480	466	28	v	v	PROPN
ejpam-4480	466	29	(	(	PUNCT
ejpam-4480	466	30	ha	ha	INTJ
ejpam-4480	466	31	)	)	PUNCT
ejpam-4480	466	32	.	.	PUNCT
ejpam-4480	467	1	then	then	ADV
ejpam-4480	467	2	c	c	PROPN
ejpam-4480	467	3	∈	∈	PROPN
ejpam-4480	467	4	v	v	NOUN
ejpam-4480	467	5	(	(	PUNCT
ejpam-4480	467	6	g	g	PROPN
ejpam-4480	467	7	◦	◦	NOUN
ejpam-4480	467	8	h	h	NOUN
ejpam-4480	467	9	)	)	PUNCT
ejpam-4480	467	10	\	\	PROPN
ejpam-4480	467	11	c	c	PROPN
ejpam-4480	467	12	and	and	CCONJ
ejpam-4480	467	13	c	c	PROPN
ejpam-4480	467	14	∈∈	∈∈	NOUN
ejpam-4480	467	15	ng	ng	PROPN
ejpam-4480	467	16	◦	◦	PROPN
ejpam-4480	467	17	h(a	h(a	PROPN
ejpam-4480	467	18	)	)	PUNCT
ejpam-4480	467	19	\	\	PROPN
ejpam-4480	468	1	ng	ng	PROPN
ejpam-4480	468	2	◦	◦	PROPN
ejpam-4480	468	3	h(b	h(b	PROPN
ejpam-4480	468	4	)	)	PUNCT
ejpam-4480	468	5	.	.	PUNCT
ejpam-4480	469	1	thus	thus	ADV
ejpam-4480	469	2	,	,	PUNCT
ejpam-4480	469	3	c	c	PROPN
ejpam-4480	469	4	is	be	AUX
ejpam-4480	469	5	a	a	DET
ejpam-4480	469	6	superclique	superclique	NOUN
ejpam-4480	469	7	in	in	ADP
ejpam-4480	469	8	g	g	PROPN
ejpam-4480	469	9	◦	◦	NOUN
ejpam-4480	469	10	h.	h.	PROPN
ejpam-4480	469	11	next	next	ADV
ejpam-4480	469	12	,	,	PUNCT
ejpam-4480	469	13	suppose	suppose	VERB
ejpam-4480	469	14	that	that	SCONJ
ejpam-4480	469	15	c	c	PROPN
ejpam-4480	469	16	is	be	AUX
ejpam-4480	469	17	a	a	DET
ejpam-4480	469	18	superclique	superclique	NOUN
ejpam-4480	469	19	in	in	ADP
ejpam-4480	469	20	hv	hv	NOUN
ejpam-4480	469	21	for	for	ADP
ejpam-4480	469	22	some	some	DET
ejpam-4480	469	23	v	v	NUM
ejpam-4480	469	24	∈	∈	PROPN
ejpam-4480	469	25	v	v	NOUN
ejpam-4480	469	26	(	(	PUNCT
ejpam-4480	469	27	g	g	NOUN
ejpam-4480	469	28	)	)	PUNCT
ejpam-4480	469	29	.	.	PUNCT
ejpam-4480	470	1	then	then	ADV
ejpam-4480	470	2	clearly	clearly	ADV
ejpam-4480	470	3	,	,	PUNCT
ejpam-4480	470	4	c	c	PROPN
ejpam-4480	470	5	is	be	AUX
ejpam-4480	470	6	a	a	DET
ejpam-4480	470	7	superclique	superclique	NOUN
ejpam-4480	470	8	in	in	ADP
ejpam-4480	470	9	g	g	PROPN
ejpam-4480	470	10	◦	◦	NOUN
ejpam-4480	470	11	h.	h.	PROPN
ejpam-4480	470	12	finally	finally	ADV
ejpam-4480	470	13	,	,	PUNCT
ejpam-4480	470	14	suppose	suppose	VERB
ejpam-4480	470	15	that	that	SCONJ
ejpam-4480	470	16	c	c	PROPN
ejpam-4480	470	17	=	=	SYM
ejpam-4480	470	18	cv	cv	PROPN
ejpam-4480	470	19	∪	∪	X
ejpam-4480	470	20	{	{	PUNCT
ejpam-4480	470	21	v	v	NOUN
ejpam-4480	470	22	}	}	PUNCT
ejpam-4480	470	23	for	for	ADP
ejpam-4480	470	24	some	some	DET
ejpam-4480	470	25	v	v	ADP
ejpam-4480	470	26	∈	∈	PROPN
ejpam-4480	470	27	v	v	NOUN
ejpam-4480	470	28	(	(	PUNCT
ejpam-4480	470	29	g	g	NOUN
ejpam-4480	470	30	)	)	PUNCT
ejpam-4480	470	31	and	and	CCONJ
ejpam-4480	470	32	superclique	superclique	ADJ
ejpam-4480	470	33	cv	cv	PROPN
ejpam-4480	470	34	in	in	ADP
ejpam-4480	470	35	hv	hv	PROPN
ejpam-4480	470	36	.	.	PUNCT
ejpam-4480	471	1	let	let	VERB
ejpam-4480	471	2	p	p	PRON
ejpam-4480	471	3	,	,	PUNCT
ejpam-4480	471	4	q	q	PROPN
ejpam-4480	471	5	∈	∈	PROPN
ejpam-4480	471	6	c	c	NOUN
ejpam-4480	471	7	where	where	SCONJ
ejpam-4480	471	8	p	p	NOUN
ejpam-4480	471	9	̸=	̸=	PROPN
ejpam-4480	471	10	q.	q.	VERB
ejpam-4480	471	11	if	if	SCONJ
ejpam-4480	471	12	p	p	X
ejpam-4480	471	13	,	,	PUNCT
ejpam-4480	471	14	q	q	PROPN
ejpam-4480	471	15	∈	∈	PROPN
ejpam-4480	471	16	cv	cv	PROPN
ejpam-4480	471	17	,	,	PUNCT
ejpam-4480	471	18	then	then	ADV
ejpam-4480	471	19	there	there	PRON
ejpam-4480	471	20	exists	exist	VERB
ejpam-4480	472	1	t	t	PROPN
ejpam-4480	472	2	∈	∈	PROPN
ejpam-4480	472	3	v	v	PROPN
ejpam-4480	472	4	(	(	PUNCT
ejpam-4480	472	5	hv	hv	PROPN
ejpam-4480	472	6	)	)	PUNCT
ejpam-4480	472	7	\	\	PROPN
ejpam-4480	472	8	cv	cv	PROPN
ejpam-4480	472	9	such	such	ADJ
ejpam-4480	472	10	that	that	SCONJ
ejpam-4480	472	11	t	t	PROPN
ejpam-4480	472	12	∈	∈	PROPN
ejpam-4480	472	13	nhv(p	nhv(p	PROPN
ejpam-4480	472	14	)	)	PUNCT
ejpam-4480	472	15	\nhv(q	\nhv(q	NOUN
ejpam-4480	472	16	)	)	PUNCT
ejpam-4480	472	17	or	or	CCONJ
ejpam-4480	472	18	t	t	NOUN
ejpam-4480	472	19	∈	∈	PROPN
ejpam-4480	472	20	nhv(q	nhv(q	PROPN
ejpam-4480	472	21	)	)	PUNCT
ejpam-4480	472	22	\nhv(p	\nhv(p	NOUN
ejpam-4480	472	23	)	)	PUNCT
ejpam-4480	472	24	because	because	SCONJ
ejpam-4480	472	25	cv	cv	PROPN
ejpam-4480	472	26	is	be	AUX
ejpam-4480	472	27	a	a	DET
ejpam-4480	472	28	superclique	superclique	NOUN
ejpam-4480	472	29	in	in	ADP
ejpam-4480	472	30	hv	hv	PROPN
ejpam-4480	472	31	.	.	PUNCT
ejpam-4480	473	1	it	it	PRON
ejpam-4480	473	2	follows	follow	VERB
ejpam-4480	473	3	that	that	SCONJ
ejpam-4480	473	4	t	t	PROPN
ejpam-4480	473	5	∈	∈	PROPN
ejpam-4480	473	6	v	v	ADP
ejpam-4480	473	7	(	(	PUNCT
ejpam-4480	473	8	g	g	PROPN
ejpam-4480	473	9	◦	◦	NOUN
ejpam-4480	473	10	h	h	NOUN
ejpam-4480	473	11	)	)	PUNCT
ejpam-4480	473	12	\	\	PROPN
ejpam-4480	473	13	c	c	PROPN
ejpam-4480	473	14	and	and	CCONJ
ejpam-4480	473	15	t	t	PROPN
ejpam-4480	473	16	∈	∈	PROPN
ejpam-4480	473	17	ng	ng	PROPN
ejpam-4480	473	18	◦	◦	NOUN
ejpam-4480	473	19	h(p	h(p	NOUN
ejpam-4480	473	20	)	)	PUNCT
ejpam-4480	473	21	\	\	PROPN
ejpam-4480	474	1	ng	ng	PROPN
ejpam-4480	474	2	◦	◦	NOUN
ejpam-4480	474	3	h(q	h(q	ADV
ejpam-4480	474	4	)	)	PUNCT
ejpam-4480	474	5	or	or	CCONJ
ejpam-4480	474	6	t	t	PROPN
ejpam-4480	474	7	∈	∈	PROPN
ejpam-4480	474	8	ng	ng	PROPN
ejpam-4480	474	9	◦	◦	NOUN
ejpam-4480	474	10	h(q	h(q	ADV
ejpam-4480	474	11	)	)	PUNCT
ejpam-4480	474	12	\	\	PROPN
ejpam-4480	475	1	ng	ng	PROPN
ejpam-4480	475	2	◦	◦	NOUN
ejpam-4480	475	3	h(p	h(p	NOUN
ejpam-4480	475	4	)	)	PUNCT
ejpam-4480	475	5	.	.	PUNCT
ejpam-4480	476	1	suppose	suppose	VERB
ejpam-4480	476	2	p	p	X
ejpam-4480	476	3	=	=	PUNCT
ejpam-4480	476	4	v.	v.	CCONJ
ejpam-4480	476	5	choose	choose	VERB
ejpam-4480	476	6	any	any	DET
ejpam-4480	476	7	w	w	NOUN
ejpam-4480	476	8	∈	∈	PROPN
ejpam-4480	476	9	ng(v	ng(v	NOUN
ejpam-4480	476	10	)	)	PUNCT
ejpam-4480	476	11	.	.	PUNCT
ejpam-4480	477	1	then	then	ADV
ejpam-4480	477	2	w	w	PROPN
ejpam-4480	477	3	∈	∈	PROPN
ejpam-4480	477	4	ng	ng	PROPN
ejpam-4480	477	5	◦	◦	NOUN
ejpam-4480	477	6	h(p	h(p	NOUN
ejpam-4480	477	7	)	)	PUNCT
ejpam-4480	477	8	\	\	PROPN
ejpam-4480	477	9	ng	ng	PROPN
ejpam-4480	477	10	◦	◦	NOUN
ejpam-4480	477	11	h(q	h(q	ADV
ejpam-4480	477	12	)	)	PUNCT
ejpam-4480	477	13	.	.	PUNCT
ejpam-4480	478	1	this	this	PRON
ejpam-4480	478	2	proves	prove	VERB
ejpam-4480	478	3	that	that	SCONJ
ejpam-4480	478	4	c	c	PROPN
ejpam-4480	478	5	is	be	AUX
ejpam-4480	478	6	a	a	DET
ejpam-4480	478	7	superclique	superclique	NOUN
ejpam-4480	478	8	in	in	ADP
ejpam-4480	478	9	g	g	PROPN
ejpam-4480	478	10	◦	◦	NOUN
ejpam-4480	478	11	h.	h.	NOUN
ejpam-4480	478	12	the	the	DET
ejpam-4480	478	13	next	next	ADJ
ejpam-4480	478	14	result	result	NOUN
ejpam-4480	478	15	is	be	AUX
ejpam-4480	478	16	a	a	DET
ejpam-4480	478	17	consequence	consequence	NOUN
ejpam-4480	478	18	of	of	ADP
ejpam-4480	478	19	theorem	theorem	ADJ
ejpam-4480	478	20	6	6	NUM
ejpam-4480	478	21	.	.	PUNCT
ejpam-4480	478	22	corollary	corollary	ADJ
ejpam-4480	478	23	7	7	NUM
ejpam-4480	478	24	.	.	PUNCT
ejpam-4480	479	1	let	let	VERB
ejpam-4480	479	2	g	g	PRON
ejpam-4480	479	3	be	be	AUX
ejpam-4480	479	4	a	a	DET
ejpam-4480	479	5	non	non	ADJ
ejpam-4480	479	6	-	-	ADJ
ejpam-4480	479	7	trivial	trivial	ADJ
ejpam-4480	479	8	connected	connected	ADJ
ejpam-4480	479	9	graph	graph	NOUN
ejpam-4480	479	10	and	and	CCONJ
ejpam-4480	479	11	let	let	VERB
ejpam-4480	479	12	h	h	NOUN
ejpam-4480	479	13	be	be	AUX
ejpam-4480	479	14	any	any	DET
ejpam-4480	479	15	graph	graph	NOUN
ejpam-4480	479	16	.	.	PUNCT
ejpam-4480	480	1	then	then	ADV
ejpam-4480	480	2	ωs(g	ωs(g	PUNCT
ejpam-4480	480	3	◦	◦	NOUN
ejpam-4480	480	4	h	h	NOUN
ejpam-4480	480	5	)	)	PUNCT
ejpam-4480	480	6	=	=	SYM
ejpam-4480	480	7	max{ω(g	max{ω(g	PROPN
ejpam-4480	480	8	)	)	PUNCT
ejpam-4480	480	9	,	,	PUNCT
ejpam-4480	480	10	ωs(h	ωs(h	NUM
ejpam-4480	480	11	)	)	PUNCT
ejpam-4480	480	12	+	+	CCONJ
ejpam-4480	480	13	1	1	NUM
ejpam-4480	480	14	}	}	PUNCT
ejpam-4480	480	15	.	.	PUNCT
ejpam-4480	481	1	gaquing	gaque	VERB
ejpam-4480	481	2	and	and	CCONJ
ejpam-4480	481	3	canoy	canoy	ADJ
ejpam-4480	481	4	in	in	ADP
ejpam-4480	481	5	[	[	X
ejpam-4480	481	6	8	8	NUM
ejpam-4480	481	7	]	]	PUNCT
ejpam-4480	481	8	obtained	obtain	VERB
ejpam-4480	481	9	the	the	DET
ejpam-4480	481	10	next	next	ADJ
ejpam-4480	481	11	result	result	NOUN
ejpam-4480	481	12	.	.	PUNCT
ejpam-4480	482	1	theorem	theorem	VERB
ejpam-4480	482	2	7	7	NUM
ejpam-4480	482	3	.	.	PUNCT
ejpam-4480	483	1	let	let	VERB
ejpam-4480	483	2	g	g	NOUN
ejpam-4480	484	1	and	and	CCONJ
ejpam-4480	484	2	h	h	NOUN
ejpam-4480	484	3	be	be	VERB
ejpam-4480	484	4	any	any	DET
ejpam-4480	484	5	connected	connected	ADJ
ejpam-4480	484	6	non	non	ADJ
ejpam-4480	484	7	-	-	ADJ
ejpam-4480	484	8	trivial	trivial	ADJ
ejpam-4480	484	9	graphs	graph	NOUN
ejpam-4480	484	10	.	.	PUNCT
ejpam-4480	485	1	then	then	ADV
ejpam-4480	485	2	c	c	NOUN
ejpam-4480	485	3	=	=	PUNCT
ejpam-4480	485	4	⋃	⋃	PROPN
ejpam-4480	485	5	x∈s	x∈s	NOUN
ejpam-4480	486	1	[	[	X
ejpam-4480	486	2	{	{	PUNCT
ejpam-4480	486	3	x}×tx	x}×tx	X
ejpam-4480	486	4	]	]	X
ejpam-4480	486	5	,	,	PUNCT
ejpam-4480	486	6	where	where	SCONJ
ejpam-4480	486	7	s	s	VERB
ejpam-4480	486	8	⊆	⊆	NUM
ejpam-4480	486	9	v	v	NOUN
ejpam-4480	486	10	(	(	PUNCT
ejpam-4480	486	11	g	g	NOUN
ejpam-4480	486	12	)	)	PUNCT
ejpam-4480	486	13	and	and	CCONJ
ejpam-4480	486	14	tx	tx	VERB
ejpam-4480	486	15	⊆	⊆	NUM
ejpam-4480	486	16	v	v	NOUN
ejpam-4480	486	17	(	(	PUNCT
ejpam-4480	486	18	h	h	NOUN
ejpam-4480	486	19	)	)	PUNCT
ejpam-4480	486	20	for	for	ADP
ejpam-4480	486	21	each	each	DET
ejpam-4480	486	22	x	x	SYM
ejpam-4480	486	23	∈	∈	PROPN
ejpam-4480	486	24	s	s	NOUN
ejpam-4480	486	25	,	,	PUNCT
ejpam-4480	486	26	is	be	AUX
ejpam-4480	486	27	a	a	DET
ejpam-4480	486	28	clique	clique	NOUN
ejpam-4480	486	29	in	in	ADP
ejpam-4480	486	30	g[h	g[h	PROPN
ejpam-4480	486	31	]	]	PUNCT
ejpam-4480	486	32	if	if	SCONJ
ejpam-4480	486	33	and	and	CCONJ
ejpam-4480	486	34	only	only	ADV
ejpam-4480	486	35	if	if	SCONJ
ejpam-4480	486	36	s	s	VERB
ejpam-4480	486	37	a	a	DET
ejpam-4480	486	38	clique	clique	NOUN
ejpam-4480	486	39	in	in	ADP
ejpam-4480	486	40	g	g	PROPN
ejpam-4480	486	41	and	and	CCONJ
ejpam-4480	486	42	tx	tx	PROPN
ejpam-4480	486	43	is	be	AUX
ejpam-4480	486	44	a	a	DET
ejpam-4480	486	45	clique	clique	NOUN
ejpam-4480	486	46	in	in	ADP
ejpam-4480	486	47	h	h	NOUN
ejpam-4480	486	48	for	for	ADP
ejpam-4480	486	49	each	each	DET
ejpam-4480	486	50	x	x	PROPN
ejpam-4480	486	51	∈	∈	PROPN
ejpam-4480	486	52	s.	s.	PROPN
ejpam-4480	486	53	in	in	ADP
ejpam-4480	486	54	particular	particular	ADJ
ejpam-4480	486	55	,	,	PUNCT
ejpam-4480	486	56	ω(g[h	ω(g[h	X
ejpam-4480	486	57	]	]	PUNCT
ejpam-4480	486	58	)	)	PUNCT
ejpam-4480	486	59	=	=	SYM
ejpam-4480	486	60	ω(g)ω(h	ω(g)ω(h	PROPN
ejpam-4480	486	61	)	)	PUNCT
ejpam-4480	486	62	.	.	PUNCT
ejpam-4480	487	1	theorem	theorem	VERB
ejpam-4480	487	2	8	8	NUM
ejpam-4480	487	3	.	.	PUNCT
ejpam-4480	488	1	let	let	VERB
ejpam-4480	488	2	g	g	NOUN
ejpam-4480	489	1	and	and	CCONJ
ejpam-4480	489	2	h	h	NOUN
ejpam-4480	489	3	be	be	VERB
ejpam-4480	489	4	any	any	DET
ejpam-4480	489	5	connected	connected	ADJ
ejpam-4480	489	6	non	non	ADJ
ejpam-4480	489	7	-	-	ADJ
ejpam-4480	489	8	trivial	trivial	ADJ
ejpam-4480	489	9	graphs	graph	NOUN
ejpam-4480	489	10	.	.	PUNCT
ejpam-4480	490	1	then	then	ADV
ejpam-4480	490	2	c	c	NOUN
ejpam-4480	490	3	=	=	PUNCT
ejpam-4480	490	4	⋃	⋃	PROPN
ejpam-4480	490	5	x∈s	x∈s	NOUN
ejpam-4480	491	1	[	[	X
ejpam-4480	491	2	{	{	PUNCT
ejpam-4480	491	3	x}×tx	x}×tx	X
ejpam-4480	491	4	]	]	X
ejpam-4480	491	5	,	,	PUNCT
ejpam-4480	491	6	where	where	SCONJ
ejpam-4480	491	7	s	s	VERB
ejpam-4480	491	8	⊆	⊆	NUM
ejpam-4480	491	9	v	v	NOUN
ejpam-4480	491	10	(	(	PUNCT
ejpam-4480	491	11	g	g	NOUN
ejpam-4480	491	12	)	)	PUNCT
ejpam-4480	491	13	and	and	CCONJ
ejpam-4480	491	14	tx	tx	VERB
ejpam-4480	491	15	⊆	⊆	NUM
ejpam-4480	491	16	v	v	NOUN
ejpam-4480	491	17	(	(	PUNCT
ejpam-4480	491	18	h	h	NOUN
ejpam-4480	491	19	)	)	PUNCT
ejpam-4480	491	20	for	for	ADP
ejpam-4480	491	21	each	each	DET
ejpam-4480	491	22	x	x	SYM
ejpam-4480	491	23	∈	∈	PROPN
ejpam-4480	491	24	s	s	NOUN
ejpam-4480	491	25	,	,	PUNCT
ejpam-4480	491	26	is	be	AUX
ejpam-4480	491	27	a	a	DET
ejpam-4480	491	28	superclique	superclique	NOUN
ejpam-4480	491	29	in	in	ADP
ejpam-4480	491	30	g[h	g[h	NOUN
ejpam-4480	491	31	]	]	PUNCT
ejpam-4480	491	32	if	if	SCONJ
ejpam-4480	491	33	and	and	CCONJ
ejpam-4480	491	34	only	only	ADV
ejpam-4480	491	35	if	if	SCONJ
ejpam-4480	491	36	s	s	VERB
ejpam-4480	491	37	a	a	DET
ejpam-4480	491	38	superclique	superclique	NOUN
ejpam-4480	491	39	in	in	ADP
ejpam-4480	491	40	g	g	PROPN
ejpam-4480	491	41	and	and	CCONJ
ejpam-4480	491	42	tx	tx	PROPN
ejpam-4480	491	43	is	be	AUX
ejpam-4480	491	44	a	a	DET
ejpam-4480	491	45	superclique	superclique	NOUN
ejpam-4480	491	46	in	in	ADP
ejpam-4480	491	47	h	h	NOUN
ejpam-4480	491	48	for	for	ADP
ejpam-4480	491	49	each	each	DET
ejpam-4480	491	50	x	x	SYM
ejpam-4480	491	51	∈	∈	PROPN
ejpam-4480	491	52	s.	s.	PROPN
ejpam-4480	491	53	proof	proof	PROPN
ejpam-4480	491	54	.	.	PUNCT
ejpam-4480	492	1	suppose	suppose	VERB
ejpam-4480	492	2	c	c	NOUN
ejpam-4480	492	3	is	be	AUX
ejpam-4480	492	4	a	a	DET
ejpam-4480	492	5	superclique	superclique	NOUN
ejpam-4480	492	6	in	in	ADP
ejpam-4480	492	7	g[h	g[h	NOUN
ejpam-4480	492	8	]	]	PUNCT
ejpam-4480	492	9	.	.	PUNCT
ejpam-4480	493	1	then	then	ADV
ejpam-4480	493	2	s	s	VERB
ejpam-4480	493	3	and	and	CCONJ
ejpam-4480	493	4	each	each	DET
ejpam-4480	493	5	tx	tx	PROPN
ejpam-4480	493	6	are	be	AUX
ejpam-4480	493	7	cliques	clique	NOUN
ejpam-4480	493	8	in	in	ADP
ejpam-4480	493	9	g	g	PROPN
ejpam-4480	493	10	and	and	CCONJ
ejpam-4480	493	11	h	h	NOUN
ejpam-4480	493	12	,	,	PUNCT
ejpam-4480	493	13	respectively	respectively	ADV
ejpam-4480	493	14	,	,	PUNCT
ejpam-4480	493	15	by	by	ADP
ejpam-4480	493	16	theorem	theorem	NOUN
ejpam-4480	493	17	7	7	NUM
ejpam-4480	493	18	.	.	PUNCT
ejpam-4480	494	1	let	let	VERB
ejpam-4480	494	2	x	x	PRON
ejpam-4480	494	3	,	,	PUNCT
ejpam-4480	494	4	y	y	PROPN
ejpam-4480	494	5	∈	∈	PROPN
ejpam-4480	494	6	s	s	PART
ejpam-4480	494	7	with	with	ADP
ejpam-4480	494	8	x	x	PART
ejpam-4480	494	9	̸=	̸=	PROPN
ejpam-4480	494	10	y.	y.	NOUN
ejpam-4480	494	11	choose	choose	VERB
ejpam-4480	494	12	any	any	DET
ejpam-4480	494	13	a	a	DET
ejpam-4480	494	14	∈	∈	PROPN
ejpam-4480	494	15	tx	tx	NOUN
ejpam-4480	494	16	and	and	CCONJ
ejpam-4480	494	17	b	b	X
ejpam-4480	494	18	∈	∈	PROPN
ejpam-4480	495	1	ty	ty	INTJ
ejpam-4480	495	2	.	.	PUNCT
ejpam-4480	496	1	then	then	ADV
ejpam-4480	496	2	(	(	PUNCT
ejpam-4480	496	3	x	x	X
ejpam-4480	496	4	,	,	PUNCT
ejpam-4480	496	5	a	a	PRON
ejpam-4480	496	6	)	)	PUNCT
ejpam-4480	496	7	,	,	PUNCT
ejpam-4480	496	8	(	(	PUNCT
ejpam-4480	496	9	y	y	PROPN
ejpam-4480	496	10	,	,	PUNCT
ejpam-4480	496	11	b	b	NOUN
ejpam-4480	496	12	)	)	PUNCT
ejpam-4480	496	13	∈	∈	PROPN
ejpam-4480	496	14	c.	c.	NOUN
ejpam-4480	496	15	since	since	SCONJ
ejpam-4480	496	16	c	c	PROPN
ejpam-4480	496	17	is	be	AUX
ejpam-4480	496	18	a	a	DET
ejpam-4480	496	19	superclique	superclique	NOUN
ejpam-4480	496	20	in	in	ADP
ejpam-4480	496	21	g[h	g[h	PROPN
ejpam-4480	496	22	]	]	PUNCT
ejpam-4480	496	23	,	,	PUNCT
ejpam-4480	496	24	there	there	PRON
ejpam-4480	496	25	exists	exist	VERB
ejpam-4480	496	26	(	(	PUNCT
ejpam-4480	496	27	z	z	NOUN
ejpam-4480	496	28	,	,	PUNCT
ejpam-4480	496	29	c	c	NOUN
ejpam-4480	496	30	)	)	PUNCT
ejpam-4480	496	31	∈	∈	NOUN
ejpam-4480	496	32	v	v	NOUN
ejpam-4480	496	33	(	(	PUNCT
ejpam-4480	496	34	g[h	g[h	PROPN
ejpam-4480	496	35	]	]	PUNCT
ejpam-4480	496	36	)	)	PUNCT
ejpam-4480	497	1	\c	\c	ADP
ejpam-4480	497	2	such	such	ADJ
ejpam-4480	497	3	that	that	PRON
ejpam-4480	497	4	(	(	PUNCT
ejpam-4480	497	5	z	z	NOUN
ejpam-4480	497	6	,	,	PUNCT
ejpam-4480	497	7	c	c	NOUN
ejpam-4480	497	8	)	)	PUNCT
ejpam-4480	497	9	∈	∈	PROPN
ejpam-4480	497	10	ng[h]((x	ng[h]((x	NOUN
ejpam-4480	497	11	,	,	PUNCT
ejpam-4480	497	12	a	a	PRON
ejpam-4480	497	13	)	)	PUNCT
ejpam-4480	497	14	)	)	PUNCT
ejpam-4480	497	15	\	\	PROPN
ejpam-4480	497	16	ng[h]((y	ng[h]((y	PROPN
ejpam-4480	497	17	,	,	PUNCT
ejpam-4480	497	18	b	b	NOUN
ejpam-4480	497	19	)	)	PUNCT
ejpam-4480	497	20	)	)	PUNCT
ejpam-4480	497	21	or	or	CCONJ
ejpam-4480	497	22	(	(	PUNCT
ejpam-4480	497	23	z	z	NOUN
ejpam-4480	497	24	,	,	PUNCT
ejpam-4480	497	25	c	c	NOUN
ejpam-4480	497	26	)	)	PUNCT
ejpam-4480	497	27	∈	∈	PROPN
ejpam-4480	497	28	ng[h]((y	ng[h]((y	NOUN
ejpam-4480	497	29	,	,	PUNCT
ejpam-4480	497	30	b	b	NOUN
ejpam-4480	497	31	)	)	PUNCT
ejpam-4480	497	32	)	)	PUNCT
ejpam-4480	497	33	\	\	PROPN
ejpam-4480	498	1	ng[h]((x	ng[h]((x	NOUN
ejpam-4480	498	2	,	,	PUNCT
ejpam-4480	498	3	a	a	PRON
ejpam-4480	498	4	)	)	PUNCT
ejpam-4480	498	5	)	)	PUNCT
ejpam-4480	498	6	.	.	PUNCT
ejpam-4480	499	1	since	since	SCONJ
ejpam-4480	499	2	{	{	PUNCT
ejpam-4480	499	3	x}×	x}×	PROPN
ejpam-4480	499	4	(	(	PUNCT
ejpam-4480	499	5	v	v	NOUN
ejpam-4480	499	6	(	(	PUNCT
ejpam-4480	499	7	h	h	NOUN
ejpam-4480	499	8	)	)	PUNCT
ejpam-4480	499	9	\	\	PUNCT
ejpam-4480	499	10	tx	tx	PROPN
ejpam-4480	499	11	)	)	PUNCT
ejpam-4480	499	12	⊆	⊆	NUM
ejpam-4480	499	13	ng[h]((y	ng[h]((y	NOUN
ejpam-4480	499	14	,	,	PUNCT
ejpam-4480	499	15	b	b	NOUN
ejpam-4480	499	16	)	)	PUNCT
ejpam-4480	499	17	)	)	PUNCT
ejpam-4480	499	18	and	and	CCONJ
ejpam-4480	499	19	{	{	PUNCT
ejpam-4480	499	20	y}×	y}×	PROPN
ejpam-4480	499	21	(	(	PUNCT
ejpam-4480	499	22	v	v	PROPN
ejpam-4480	499	23	(	(	PUNCT
ejpam-4480	499	24	h	h	NOUN
ejpam-4480	499	25	)	)	PUNCT
ejpam-4480	499	26	\	\	NOUN
ejpam-4480	500	1	ty	ty	NUM
ejpam-4480	500	2	)	)	PUNCT
ejpam-4480	500	3	⊆	⊆	NUM
ejpam-4480	500	4	ng[h]((x	ng[h]((x	NOUN
ejpam-4480	500	5	,	,	PUNCT
ejpam-4480	500	6	b	b	NOUN
ejpam-4480	500	7	)	)	PUNCT
ejpam-4480	500	8	)	)	PUNCT
ejpam-4480	500	9	,	,	PUNCT
ejpam-4480	500	10	it	it	PRON
ejpam-4480	500	11	follows	follow	VERB
ejpam-4480	500	12	that	that	PRON
ejpam-4480	500	13	z	z	NOUN
ejpam-4480	500	14	/∈	/∈	PUNCT
ejpam-4480	501	1	{	{	PUNCT
ejpam-4480	501	2	x	x	NOUN
ejpam-4480	501	3	,	,	PUNCT
ejpam-4480	501	4	y	y	NOUN
ejpam-4480	501	5	}	}	PUNCT
ejpam-4480	501	6	and	and	CCONJ
ejpam-4480	501	7	z	z	NOUN
ejpam-4480	501	8	∈	∈	PROPN
ejpam-4480	501	9	v	v	ADP
ejpam-4480	501	10	(	(	PUNCT
ejpam-4480	501	11	g	g	NOUN
ejpam-4480	501	12	)	)	PUNCT
ejpam-4480	501	13	\	\	NOUN
ejpam-4480	502	1	s.	s.	PROPN
ejpam-4480	502	2	hence	hence	ADV
ejpam-4480	502	3	,	,	PUNCT
ejpam-4480	502	4	z	z	PROPN
ejpam-4480	502	5	∈	∈	PROPN
ejpam-4480	502	6	ng(x	ng(x	NUM
ejpam-4480	502	7	)	)	PUNCT
ejpam-4480	502	8	\	\	NOUN
ejpam-4480	502	9	ng(y	ng(y	NOUN
ejpam-4480	502	10	)	)	PUNCT
ejpam-4480	502	11	or	or	CCONJ
ejpam-4480	502	12	z	z	NOUN
ejpam-4480	502	13	∈	∈	PROPN
ejpam-4480	502	14	ng(y	ng(y	NOUN
ejpam-4480	502	15	)	)	PUNCT
ejpam-4480	502	16	\	\	NOUN
ejpam-4480	502	17	ng(x	ng(x	NUM
ejpam-4480	502	18	)	)	PUNCT
ejpam-4480	502	19	,	,	PUNCT
ejpam-4480	502	20	showing	show	VERB
ejpam-4480	502	21	that	that	SCONJ
ejpam-4480	502	22	s	s	VERB
ejpam-4480	502	23	is	be	AUX
ejpam-4480	502	24	a	a	DET
ejpam-4480	502	25	superclique	superclique	NOUN
ejpam-4480	502	26	in	in	ADP
ejpam-4480	502	27	g.	g.	PROPN
ejpam-4480	502	28	next	next	ADV
ejpam-4480	502	29	,	,	PUNCT
ejpam-4480	502	30	let	let	VERB
ejpam-4480	502	31	x	x	PUNCT
ejpam-4480	502	32	∈	∈	NOUN
ejpam-4480	502	33	s	s	PART
ejpam-4480	502	34	and	and	CCONJ
ejpam-4480	502	35	let	let	VERB
ejpam-4480	502	36	p	p	PRON
ejpam-4480	502	37	,	,	PUNCT
ejpam-4480	502	38	q	q	PROPN
ejpam-4480	502	39	∈	∈	PROPN
ejpam-4480	502	40	tx	tx	NOUN
ejpam-4480	502	41	with	with	ADP
ejpam-4480	502	42	p	p	PROPN
ejpam-4480	502	43	̸=	̸=	PROPN
ejpam-4480	502	44	q.	q.	NOUN
ejpam-4480	502	45	then	then	ADV
ejpam-4480	502	46	(	(	PUNCT
ejpam-4480	502	47	x	x	X
ejpam-4480	502	48	,	,	PUNCT
ejpam-4480	502	49	p	p	NOUN
ejpam-4480	502	50	)	)	PUNCT
ejpam-4480	502	51	,	,	PUNCT
ejpam-4480	502	52	(	(	PUNCT
ejpam-4480	502	53	x	x	X
ejpam-4480	502	54	,	,	PUNCT
ejpam-4480	502	55	q	q	ADJ
ejpam-4480	502	56	)	)	PUNCT
ejpam-4480	502	57	∈	∈	PROPN
ejpam-4480	502	58	c.	c.	NOUN
ejpam-4480	502	59	since	since	SCONJ
ejpam-4480	502	60	c	c	PROPN
ejpam-4480	502	61	is	be	AUX
ejpam-4480	502	62	a	a	DET
ejpam-4480	502	63	superclique	superclique	NOUN
ejpam-4480	502	64	in	in	ADP
ejpam-4480	502	65	g[h	g[h	PROPN
ejpam-4480	502	66	]	]	PUNCT
ejpam-4480	502	67	,	,	PUNCT
ejpam-4480	502	68	there	there	PRON
ejpam-4480	502	69	exists	exist	VERB
ejpam-4480	502	70	(	(	PUNCT
ejpam-4480	502	71	w	w	PROPN
ejpam-4480	502	72	,	,	PUNCT
ejpam-4480	502	73	t	t	PROPN
ejpam-4480	502	74	)	)	PUNCT
ejpam-4480	502	75	∈	∈	PROPN
ejpam-4480	502	76	v	v	NOUN
ejpam-4480	502	77	(	(	PUNCT
ejpam-4480	502	78	g[h	g[h	PROPN
ejpam-4480	502	79	]	]	PUNCT
ejpam-4480	502	80	)	)	PUNCT
ejpam-4480	502	81	\	\	PUNCT
ejpam-4480	503	1	c	c	NOUN
ejpam-4480	503	2	such	such	ADJ
ejpam-4480	503	3	that	that	DET
ejpam-4480	503	4	(	(	PUNCT
ejpam-4480	503	5	w	w	PROPN
ejpam-4480	503	6	,	,	PUNCT
ejpam-4480	503	7	t	t	PROPN
ejpam-4480	503	8	)	)	PUNCT
ejpam-4480	503	9	∈	∈	PROPN
ejpam-4480	503	10	ng[h]((x	ng[h]((x	NOUN
ejpam-4480	503	11	,	,	PUNCT
ejpam-4480	503	12	p	p	NOUN
ejpam-4480	503	13	)	)	PUNCT
ejpam-4480	503	14	)	)	PUNCT
ejpam-4480	503	15	\	\	PROPN
ejpam-4480	504	1	ng[h]((x	ng[h]((x	NOUN
ejpam-4480	504	2	,	,	PUNCT
ejpam-4480	504	3	q	q	NOUN
ejpam-4480	504	4	)	)	PUNCT
ejpam-4480	504	5	)	)	PUNCT
ejpam-4480	504	6	or	or	CCONJ
ejpam-4480	504	7	(	(	PUNCT
ejpam-4480	504	8	w	w	PROPN
ejpam-4480	504	9	,	,	PUNCT
ejpam-4480	504	10	t	t	PROPN
ejpam-4480	504	11	)	)	PUNCT
ejpam-4480	504	12	∈	∈	PROPN
ejpam-4480	504	13	ng[h]((x	ng[h]((x	NOUN
ejpam-4480	504	14	,	,	PUNCT
ejpam-4480	504	15	q	q	NOUN
ejpam-4480	504	16	)	)	PUNCT
ejpam-4480	504	17	)	)	PUNCT
ejpam-4480	504	18	\	\	PROPN
ejpam-4480	504	19	ng[h]((x	ng[h]((x	NOUN
ejpam-4480	504	20	,	,	PUNCT
ejpam-4480	504	21	p	p	NOUN
ejpam-4480	504	22	)	)	PUNCT
ejpam-4480	504	23	)	)	PUNCT
ejpam-4480	504	24	.	.	PUNCT
ejpam-4480	505	1	this	this	PRON
ejpam-4480	505	2	would	would	AUX
ejpam-4480	505	3	imply	imply	VERB
ejpam-4480	505	4	that	that	PRON
ejpam-4480	505	5	w	w	PROPN
ejpam-4480	505	6	=	=	SYM
ejpam-4480	505	7	x	x	PROPN
ejpam-4480	505	8	,	,	PUNCT
ejpam-4480	505	9	t	t	PROPN
ejpam-4480	505	10	∈	∈	PROPN
ejpam-4480	505	11	v	v	PROPN
ejpam-4480	505	12	(	(	PUNCT
ejpam-4480	505	13	h)\tx	h)\tx	PROPN
ejpam-4480	505	14	,	,	PUNCT
ejpam-4480	505	15	and	and	CCONJ
ejpam-4480	505	16	t	t	PROPN
ejpam-4480	505	17	∈	∈	PROPN
ejpam-4480	505	18	nh(p)\nh(q	nh(p)\nh(q	NOUN
ejpam-4480	505	19	)	)	PUNCT
ejpam-4480	505	20	or	or	CCONJ
ejpam-4480	505	21	t	t	PROPN
ejpam-4480	505	22	∈	∈	PROPN
ejpam-4480	505	23	nh(q)\nh(p	nh(q)\nh(p	NOUN
ejpam-4480	505	24	)	)	PUNCT
ejpam-4480	505	25	.	.	PUNCT
ejpam-4480	506	1	therefore	therefore	ADV
ejpam-4480	506	2	,	,	PUNCT
ejpam-4480	506	3	tx	tx	PROPN
ejpam-4480	506	4	is	be	AUX
ejpam-4480	506	5	a	a	DET
ejpam-4480	506	6	superclique	superclique	NOUN
ejpam-4480	506	7	in	in	ADP
ejpam-4480	506	8	h.	h.	NOUN
ejpam-4480	506	9	for	for	ADP
ejpam-4480	506	10	the	the	DET
ejpam-4480	506	11	converse	converse	NOUN
ejpam-4480	506	12	,	,	PUNCT
ejpam-4480	506	13	suppose	suppose	VERB
ejpam-4480	506	14	that	that	SCONJ
ejpam-4480	506	15	s	s	VERB
ejpam-4480	506	16	a	a	DET
ejpam-4480	506	17	superclique	superclique	NOUN
ejpam-4480	506	18	in	in	ADP
ejpam-4480	506	19	g	g	PROPN
ejpam-4480	506	20	and	and	CCONJ
ejpam-4480	506	21	tx	tx	PROPN
ejpam-4480	506	22	is	be	AUX
ejpam-4480	506	23	a	a	DET
ejpam-4480	506	24	superclique	superclique	NOUN
ejpam-4480	506	25	in	in	ADP
ejpam-4480	506	26	h	h	NOUN
ejpam-4480	506	27	for	for	ADP
ejpam-4480	506	28	each	each	DET
ejpam-4480	506	29	x	x	SYM
ejpam-4480	506	30	∈	∈	PROPN
ejpam-4480	506	31	s.	s.	PROPN
ejpam-4480	506	32	by	by	ADP
ejpam-4480	506	33	theorem	theorem	NOUN
ejpam-4480	506	34	7	7	NUM
ejpam-4480	506	35	,	,	PUNCT
ejpam-4480	506	36	c	c	PROPN
ejpam-4480	506	37	is	be	AUX
ejpam-4480	506	38	a	a	DET
ejpam-4480	506	39	clique	clique	NOUN
ejpam-4480	506	40	in	in	ADP
ejpam-4480	506	41	g[h	g[h	PROPN
ejpam-4480	506	42	]	]	PUNCT
ejpam-4480	506	43	.	.	PUNCT
ejpam-4480	507	1	let	let	VERB
ejpam-4480	507	2	(	(	PUNCT
ejpam-4480	507	3	v	v	NOUN
ejpam-4480	507	4	,	,	PUNCT
ejpam-4480	507	5	a	a	PRON
ejpam-4480	507	6	)	)	PUNCT
ejpam-4480	507	7	,	,	PUNCT
ejpam-4480	507	8	(	(	PUNCT
ejpam-4480	507	9	w	w	PROPN
ejpam-4480	507	10	,	,	PUNCT
ejpam-4480	507	11	b	b	NOUN
ejpam-4480	507	12	)	)	PUNCT
ejpam-4480	507	13	∈	∈	PROPN
ejpam-4480	507	14	c	c	NOUN
ejpam-4480	507	15	with	with	ADP
ejpam-4480	507	16	(	(	PUNCT
ejpam-4480	507	17	v	v	NOUN
ejpam-4480	507	18	,	,	PUNCT
ejpam-4480	507	19	a	a	PRON
ejpam-4480	507	20	)	)	PUNCT
ejpam-4480	507	21	̸=	̸=	PROPN
ejpam-4480	507	22	(	(	PUNCT
ejpam-4480	507	23	w	w	PROPN
ejpam-4480	507	24	,	,	PUNCT
ejpam-4480	507	25	b	b	NOUN
ejpam-4480	507	26	)	)	PUNCT
ejpam-4480	507	27	and	and	CCONJ
ejpam-4480	507	28	consider	consider	VERB
ejpam-4480	507	29	the	the	DET
ejpam-4480	507	30	following	follow	VERB
ejpam-4480	507	31	cases	case	NOUN
ejpam-4480	507	32	:	:	PUNCT
ejpam-4480	507	33	r.	r.	PROPN
ejpam-4480	507	34	dela	dela	PROPN
ejpam-4480	507	35	cerna	cerna	PROPN
ejpam-4480	507	36	,	,	PUNCT
ejpam-4480	507	37	s.	s.	PROPN
ejpam-4480	507	38	canoy	canoy	PROPN
ejpam-4480	507	39	,	,	PUNCT
ejpam-4480	507	40	jr	jr	PROPN
ejpam-4480	507	41	.	.	PROPN
ejpam-4480	507	42	/	/	SYM
ejpam-4480	507	43	eur	eur	PROPN
ejpam-4480	507	44	.	.	PUNCT
ejpam-4480	508	1	j.	j.	PROPN
ejpam-4480	508	2	pure	pure	PROPN
ejpam-4480	508	3	appl	appl	PROPN
ejpam-4480	508	4	.	.	PROPN
ejpam-4480	508	5	math	math	PROPN
ejpam-4480	508	6	,	,	PUNCT
ejpam-4480	508	7	15	15	NUM
ejpam-4480	508	8	(	(	PUNCT
ejpam-4480	508	9	3	3	NUM
ejpam-4480	508	10	)	)	PUNCT
ejpam-4480	508	11	(	(	PUNCT
ejpam-4480	508	12	2022	2022	NUM
ejpam-4480	508	13	)	)	PUNCT
ejpam-4480	508	14	,	,	PUNCT
ejpam-4480	508	15	1217	1217	NUM
ejpam-4480	508	16	-	-	SYM
ejpam-4480	508	17	1228	1228	NUM
ejpam-4480	508	18	1226	1226	NUM
ejpam-4480	508	19	case	case	NOUN
ejpam-4480	508	20	1	1	NUM
ejpam-4480	508	21	.	.	PUNCT
ejpam-4480	509	1	v	v	NOUN
ejpam-4480	509	2	=	=	PUNCT
ejpam-4480	509	3	w.	w.	PROPN
ejpam-4480	509	4	then	then	ADV
ejpam-4480	509	5	a	a	DET
ejpam-4480	509	6	,	,	PUNCT
ejpam-4480	509	7	b	b	PROPN
ejpam-4480	509	8	∈	∈	PROPN
ejpam-4480	509	9	tv	tv	NOUN
ejpam-4480	509	10	and	and	CCONJ
ejpam-4480	509	11	a	a	DET
ejpam-4480	509	12	̸=	̸=	PROPN
ejpam-4480	509	13	b.	b.	NOUN
ejpam-4480	509	14	since	since	SCONJ
ejpam-4480	509	15	tv	tv	NOUN
ejpam-4480	509	16	is	be	AUX
ejpam-4480	509	17	a	a	DET
ejpam-4480	509	18	superclique	superclique	NOUN
ejpam-4480	509	19	in	in	ADP
ejpam-4480	509	20	h	h	NOUN
ejpam-4480	509	21	,	,	PUNCT
ejpam-4480	509	22	there	there	PRON
ejpam-4480	509	23	exists	exist	VERB
ejpam-4480	509	24	d	d	X
ejpam-4480	509	25	∈	∈	PROPN
ejpam-4480	509	26	v	v	ADP
ejpam-4480	509	27	(	(	PUNCT
ejpam-4480	509	28	h	h	NOUN
ejpam-4480	509	29	)	)	PUNCT
ejpam-4480	509	30	\	\	NOUN
ejpam-4480	509	31	tv	tv	NOUN
ejpam-4480	509	32	such	such	ADJ
ejpam-4480	509	33	that	that	SCONJ
ejpam-4480	509	34	d	d	PROPN
ejpam-4480	509	35	∈	∈	PROPN
ejpam-4480	509	36	nh(a	nh(a	NUM
ejpam-4480	509	37	)	)	PUNCT
ejpam-4480	509	38	\nh(b	\nh(b	NUM
ejpam-4480	509	39	)	)	PUNCT
ejpam-4480	509	40	or	or	CCONJ
ejpam-4480	509	41	d	d	PROPN
ejpam-4480	509	42	∈	∈	PROPN
ejpam-4480	509	43	nh(b	nh(b	NOUN
ejpam-4480	509	44	)	)	PUNCT
ejpam-4480	509	45	\nh(a	\nh(a	NUM
ejpam-4480	509	46	)	)	PUNCT
ejpam-4480	509	47	.	.	PUNCT
ejpam-4480	510	1	it	it	PRON
ejpam-4480	510	2	follows	follow	VERB
ejpam-4480	510	3	that	that	SCONJ
ejpam-4480	510	4	(	(	PUNCT
ejpam-4480	510	5	v	v	NOUN
ejpam-4480	510	6	,	,	PUNCT
ejpam-4480	510	7	d	d	NOUN
ejpam-4480	510	8	)	)	PUNCT
ejpam-4480	510	9	∈	∈	NOUN
ejpam-4480	510	10	v	v	NOUN
ejpam-4480	510	11	(	(	PUNCT
ejpam-4480	510	12	g[h	g[h	PROPN
ejpam-4480	510	13	]	]	PUNCT
ejpam-4480	510	14	)	)	PUNCT
ejpam-4480	510	15	\	\	PROPN
ejpam-4480	511	1	c	c	PROPN
ejpam-4480	511	2	and	and	CCONJ
ejpam-4480	511	3	(	(	PUNCT
ejpam-4480	511	4	v	v	NOUN
ejpam-4480	511	5	,	,	PUNCT
ejpam-4480	511	6	d	d	NOUN
ejpam-4480	511	7	)	)	PUNCT
ejpam-4480	511	8	∈	∈	PROPN
ejpam-4480	511	9	ng[h]((v	ng[h]((v	NOUN
ejpam-4480	511	10	,	,	PUNCT
ejpam-4480	511	11	a	a	PRON
ejpam-4480	511	12	)	)	PUNCT
ejpam-4480	511	13	)	)	PUNCT
ejpam-4480	511	14	\ng[h]((v	\ng[h]((v	PROPN
ejpam-4480	511	15	,	,	PUNCT
ejpam-4480	511	16	b	b	NOUN
ejpam-4480	511	17	)	)	PUNCT
ejpam-4480	511	18	)	)	PUNCT
ejpam-4480	511	19	or	or	CCONJ
ejpam-4480	511	20	(	(	PUNCT
ejpam-4480	511	21	v	v	NOUN
ejpam-4480	511	22	,	,	PUNCT
ejpam-4480	511	23	d	d	NOUN
ejpam-4480	511	24	)	)	PUNCT
ejpam-4480	511	25	∈	∈	PROPN
ejpam-4480	511	26	ng[h]((v	ng[h]((v	NOUN
ejpam-4480	511	27	,	,	PUNCT
ejpam-4480	511	28	b	b	NOUN
ejpam-4480	511	29	)	)	PUNCT
ejpam-4480	511	30	)	)	PUNCT
ejpam-4480	511	31	\ng[h]((v	\ng[h]((v	NOUN
ejpam-4480	511	32	,	,	PUNCT
ejpam-4480	511	33	a	a	PRON
ejpam-4480	511	34	)	)	PUNCT
ejpam-4480	511	35	)	)	PUNCT
ejpam-4480	511	36	.	.	PUNCT
ejpam-4480	512	1	case	case	NOUN
ejpam-4480	512	2	2	2	NUM
ejpam-4480	512	3	.	.	NOUN
ejpam-4480	512	4	v	v	ADP
ejpam-4480	512	5	̸=	̸=	PROPN
ejpam-4480	512	6	w.	w.	NOUN
ejpam-4480	512	7	since	since	SCONJ
ejpam-4480	512	8	v	v	NOUN
ejpam-4480	512	9	,	,	PUNCT
ejpam-4480	512	10	w	w	PROPN
ejpam-4480	512	11	∈	∈	PROPN
ejpam-4480	512	12	s	s	PART
ejpam-4480	512	13	and	and	CCONJ
ejpam-4480	512	14	s	s	VERB
ejpam-4480	512	15	is	be	AUX
ejpam-4480	512	16	a	a	DET
ejpam-4480	512	17	superclique	superclique	NOUN
ejpam-4480	512	18	in	in	ADP
ejpam-4480	512	19	g	g	NOUN
ejpam-4480	512	20	,	,	PUNCT
ejpam-4480	512	21	there	there	PRON
ejpam-4480	512	22	exists	exist	VERB
ejpam-4480	512	23	u	u	PROPN
ejpam-4480	512	24	∈	∈	PROPN
ejpam-4480	512	25	v	v	NOUN
ejpam-4480	512	26	(	(	PUNCT
ejpam-4480	512	27	g)\s	g)\s	VERB
ejpam-4480	512	28	such	such	ADJ
ejpam-4480	512	29	that	that	SCONJ
ejpam-4480	512	30	u	u	PROPN
ejpam-4480	512	31	∈	∈	PROPN
ejpam-4480	512	32	ng(v)\	ng(v)\	NOUN
ejpam-4480	512	33	ng(w	ng(w	NOUN
ejpam-4480	512	34	)	)	PUNCT
ejpam-4480	512	35	or	or	CCONJ
ejpam-4480	512	36	u	u	PROPN
ejpam-4480	512	37	∈	∈	PROPN
ejpam-4480	512	38	ng(w	ng(w	NOUN
ejpam-4480	512	39	)	)	PUNCT
ejpam-4480	512	40	\	\	NOUN
ejpam-4480	512	41	ng(v	ng(v	PUNCT
ejpam-4480	512	42	)	)	PUNCT
ejpam-4480	512	43	.	.	PUNCT
ejpam-4480	513	1	then	then	ADV
ejpam-4480	513	2	(	(	PUNCT
ejpam-4480	513	3	u	u	NOUN
ejpam-4480	513	4	,	,	PUNCT
ejpam-4480	513	5	a	a	PRON
ejpam-4480	513	6	)	)	PUNCT
ejpam-4480	513	7	∈	∈	NOUN
ejpam-4480	513	8	v	v	NOUN
ejpam-4480	513	9	(	(	PUNCT
ejpam-4480	513	10	g[h	g[h	PROPN
ejpam-4480	513	11	]	]	PUNCT
ejpam-4480	513	12	)	)	PUNCT
ejpam-4480	513	13	\	\	PROPN
ejpam-4480	514	1	c	c	PROPN
ejpam-4480	514	2	and	and	CCONJ
ejpam-4480	514	3	(	(	PUNCT
ejpam-4480	514	4	u	u	NOUN
ejpam-4480	514	5	,	,	PUNCT
ejpam-4480	514	6	a	a	PRON
ejpam-4480	514	7	)	)	PUNCT
ejpam-4480	514	8	∈	∈	PROPN
ejpam-4480	514	9	ng[h]((v	ng[h]((v	NOUN
ejpam-4480	514	10	,	,	PUNCT
ejpam-4480	514	11	a	a	PRON
ejpam-4480	514	12	)	)	PUNCT
ejpam-4480	514	13	)	)	PUNCT
ejpam-4480	514	14	\	\	PROPN
ejpam-4480	514	15	ng[h]((v	ng[h]((v	NOUN
ejpam-4480	514	16	,	,	PUNCT
ejpam-4480	514	17	b	b	NOUN
ejpam-4480	514	18	)	)	PUNCT
ejpam-4480	514	19	)	)	PUNCT
ejpam-4480	514	20	or	or	CCONJ
ejpam-4480	514	21	(	(	PUNCT
ejpam-4480	514	22	u	u	NOUN
ejpam-4480	514	23	,	,	PUNCT
ejpam-4480	514	24	a	a	PRON
ejpam-4480	514	25	)	)	PUNCT
ejpam-4480	514	26	∈	∈	PROPN
ejpam-4480	514	27	ng[h]((v	ng[h]((v	NOUN
ejpam-4480	514	28	,	,	PUNCT
ejpam-4480	514	29	b	b	NOUN
ejpam-4480	514	30	)	)	PUNCT
ejpam-4480	514	31	)	)	PUNCT
ejpam-4480	514	32	\ng[h]((v	\ng[h]((v	NOUN
ejpam-4480	514	33	,	,	PUNCT
ejpam-4480	514	34	a	a	PRON
ejpam-4480	514	35	)	)	PUNCT
ejpam-4480	514	36	)	)	PUNCT
ejpam-4480	514	37	.	.	PUNCT
ejpam-4480	515	1	accordingly	accordingly	ADV
ejpam-4480	515	2	,	,	PUNCT
ejpam-4480	515	3	c	c	PROPN
ejpam-4480	515	4	is	be	AUX
ejpam-4480	515	5	a	a	DET
ejpam-4480	515	6	superclique	superclique	NOUN
ejpam-4480	515	7	in	in	ADP
ejpam-4480	515	8	g[h	g[h	NOUN
ejpam-4480	515	9	]	]	PUNCT
ejpam-4480	515	10	.	.	PUNCT
ejpam-4480	516	1	corollary	corollary	ADJ
ejpam-4480	516	2	8	8	NUM
ejpam-4480	516	3	.	.	PUNCT
ejpam-4480	517	1	let	let	VERB
ejpam-4480	517	2	g	g	NOUN
ejpam-4480	517	3	and	and	CCONJ
ejpam-4480	517	4	h	h	NOUN
ejpam-4480	517	5	be	be	VERB
ejpam-4480	517	6	any	any	DET
ejpam-4480	517	7	connected	connected	ADJ
ejpam-4480	517	8	non	non	ADJ
ejpam-4480	517	9	-	-	ADJ
ejpam-4480	517	10	trivial	trivial	ADJ
ejpam-4480	517	11	graphs	graph	NOUN
ejpam-4480	517	12	.	.	PUNCT
ejpam-4480	518	1	then	then	ADV
ejpam-4480	518	2	ωs(g[h	ωs(g[h	VERB
ejpam-4480	518	3	]	]	PUNCT
ejpam-4480	518	4	)	)	PUNCT
ejpam-4480	518	5	=	=	SYM
ejpam-4480	518	6	ωs(g)ωs(h	ωs(g)ωs(h	PROPN
ejpam-4480	518	7	)	)	PUNCT
ejpam-4480	518	8	.	.	PUNCT
ejpam-4480	519	1	proof	proof	NOUN
ejpam-4480	519	2	.	.	PUNCT
ejpam-4480	520	1	let	let	VERB
ejpam-4480	520	2	s	s	PRON
ejpam-4480	520	3	and	and	CCONJ
ejpam-4480	520	4	d	d	AUX
ejpam-4480	520	5	be	be	AUX
ejpam-4480	520	6	ωs	ω	NOUN
ejpam-4480	520	7	-	-	NOUN
ejpam-4480	520	8	sets	set	NOUN
ejpam-4480	520	9	in	in	ADP
ejpam-4480	520	10	g	g	PROPN
ejpam-4480	520	11	and	and	CCONJ
ejpam-4480	520	12	h	h	NOUN
ejpam-4480	520	13	,	,	PUNCT
ejpam-4480	520	14	respectively	respectively	ADV
ejpam-4480	520	15	.	.	PUNCT
ejpam-4480	521	1	then	then	ADV
ejpam-4480	521	2	c0	c0	PROPN
ejpam-4480	521	3	=	=	PROPN
ejpam-4480	521	4	s	s	PART
ejpam-4480	521	5	×	×	PROPN
ejpam-4480	521	6	d	d	NOUN
ejpam-4480	521	7	is	be	AUX
ejpam-4480	521	8	a	a	DET
ejpam-4480	521	9	superclique	superclique	NOUN
ejpam-4480	521	10	in	in	ADP
ejpam-4480	521	11	g[h	g[h	NOUN
ejpam-4480	521	12	]	]	PUNCT
ejpam-4480	521	13	by	by	ADP
ejpam-4480	521	14	theorem	theorem	NOUN
ejpam-4480	521	15	8	8	NUM
ejpam-4480	521	16	.	.	PUNCT
ejpam-4480	522	1	it	it	PRON
ejpam-4480	522	2	follows	follow	VERB
ejpam-4480	522	3	that	that	SCONJ
ejpam-4480	522	4	ωs(g[h	ωs(g[h	NOUN
ejpam-4480	522	5	]	]	PUNCT
ejpam-4480	522	6	)	)	PUNCT
ejpam-4480	522	7	≥	≥	NOUN
ejpam-4480	522	8	|c0|	|c0|	NOUN
ejpam-4480	522	9	=	=	SYM
ejpam-4480	522	10	|s||d|	|s||d|	PROPN
ejpam-4480	522	11	=	=	SYM
ejpam-4480	522	12	ωs(g)ωs(h	ωs(g)ωs(h	PROPN
ejpam-4480	522	13	)	)	PUNCT
ejpam-4480	522	14	.	.	PUNCT
ejpam-4480	523	1	now	now	ADV
ejpam-4480	523	2	,	,	PUNCT
ejpam-4480	523	3	let	let	VERB
ejpam-4480	523	4	c	c	PRON
ejpam-4480	523	5	be	be	AUX
ejpam-4480	523	6	an	an	DET
ejpam-4480	523	7	ωs	ωs	ADV
ejpam-4480	523	8	-	-	PUNCT
ejpam-4480	523	9	set	set	NOUN
ejpam-4480	523	10	in	in	ADP
ejpam-4480	523	11	g[h	g[h	NOUN
ejpam-4480	523	12	]	]	PUNCT
ejpam-4480	523	13	.	.	PUNCT
ejpam-4480	524	1	then	then	ADV
ejpam-4480	524	2	c	c	NOUN
ejpam-4480	524	3	=	=	PUNCT
ejpam-4480	524	4	⋃	⋃	PROPN
ejpam-4480	524	5	x∈s	x∈s	NOUN
ejpam-4480	525	1	[	[	X
ejpam-4480	525	2	{	{	PUNCT
ejpam-4480	525	3	x	x	NOUN
ejpam-4480	525	4	}	}	PUNCT
ejpam-4480	525	5	×	×	PROPN
ejpam-4480	525	6	tx	tx	PROPN
ejpam-4480	525	7	]	]	PUNCT
ejpam-4480	525	8	and	and	CCONJ
ejpam-4480	525	9	s	s	X
ejpam-4480	525	10	and	and	CCONJ
ejpam-4480	525	11	each	each	DET
ejpam-4480	525	12	tx	tx	PROPN
ejpam-4480	525	13	are	be	AUX
ejpam-4480	525	14	supercliques	superclique	NOUN
ejpam-4480	525	15	in	in	ADP
ejpam-4480	525	16	g	g	PROPN
ejpam-4480	525	17	and	and	CCONJ
ejpam-4480	525	18	h	h	NOUN
ejpam-4480	525	19	,	,	PUNCT
ejpam-4480	525	20	respectively	respectively	ADV
ejpam-4480	525	21	,	,	PUNCT
ejpam-4480	525	22	by	by	ADP
ejpam-4480	525	23	theorem	theorem	NOUN
ejpam-4480	525	24	8	8	NUM
ejpam-4480	525	25	.	.	PUNCT
ejpam-4480	526	1	hence	hence	ADV
ejpam-4480	526	2	,	,	PUNCT
ejpam-4480	526	3	ωs(g[h	ωs(g[h	NOUN
ejpam-4480	526	4	]	]	NOUN
ejpam-4480	526	5	)	)	PUNCT
ejpam-4480	526	6	=	=	SYM
ejpam-4480	526	7	|c|	|c|	PROPN
ejpam-4480	526	8	=	=	PUNCT
ejpam-4480	526	9	∑	∑	PROPN
ejpam-4480	526	10	x∈s	x∈s	PROPN
ejpam-4480	526	11	|tx|	|tx|	NOUN
ejpam-4480	526	12	≤	≤	NUM
ejpam-4480	526	13	ωs(g)ωs(h	ωs(g)ωs(h	NUM
ejpam-4480	526	14	)	)	PUNCT
ejpam-4480	526	15	.	.	PUNCT
ejpam-4480	527	1	this	this	PRON
ejpam-4480	527	2	establishes	establish	VERB
ejpam-4480	527	3	the	the	DET
ejpam-4480	527	4	desired	desire	VERB
ejpam-4480	527	5	equality	equality	NOUN
ejpam-4480	527	6	.	.	PUNCT
ejpam-4480	528	1	the	the	DET
ejpam-4480	528	2	next	next	ADJ
ejpam-4480	528	3	result	result	NOUN
ejpam-4480	528	4	is	be	AUX
ejpam-4480	528	5	also	also	ADV
ejpam-4480	528	6	obtained	obtain	VERB
ejpam-4480	528	7	from	from	ADP
ejpam-4480	528	8	[	[	X
ejpam-4480	528	9	8	8	NUM
ejpam-4480	528	10	]	]	PUNCT
ejpam-4480	528	11	.	.	PUNCT
ejpam-4480	529	1	theorem	theorem	NOUN
ejpam-4480	529	2	9	9	NUM
ejpam-4480	529	3	.	.	PUNCT
ejpam-4480	530	1	let	let	VERB
ejpam-4480	530	2	g	g	NOUN
ejpam-4480	531	1	and	and	CCONJ
ejpam-4480	531	2	h	h	NOUN
ejpam-4480	531	3	be	be	VERB
ejpam-4480	531	4	any	any	DET
ejpam-4480	531	5	connected	connected	ADJ
ejpam-4480	531	6	graphs	graph	NOUN
ejpam-4480	531	7	.	.	PUNCT
ejpam-4480	532	1	then	then	ADV
ejpam-4480	532	2	c	c	PROPN
ejpam-4480	532	3	is	be	AUX
ejpam-4480	532	4	a	a	DET
ejpam-4480	532	5	clique	clique	NOUN
ejpam-4480	532	6	in	in	ADP
ejpam-4480	532	7	g	g	NOUN
ejpam-4480	532	8	□	□	PROPN
ejpam-4480	532	9	h	h	NOUN
ejpam-4480	532	10	if	if	SCONJ
ejpam-4480	533	1	and	and	CCONJ
ejpam-4480	533	2	only	only	ADV
ejpam-4480	533	3	if	if	SCONJ
ejpam-4480	533	4	c	c	NOUN
ejpam-4480	533	5	=	=	SYM
ejpam-4480	533	6	s	s	PROPN
ejpam-4480	533	7	×	×	NOUN
ejpam-4480	533	8	{	{	PUNCT
ejpam-4480	533	9	a	a	NOUN
ejpam-4480	533	10	}	}	PUNCT
ejpam-4480	533	11	for	for	ADP
ejpam-4480	533	12	some	some	DET
ejpam-4480	533	13	a	a	DET
ejpam-4480	533	14	∈	∈	PROPN
ejpam-4480	533	15	v	v	ADP
ejpam-4480	533	16	(	(	PUNCT
ejpam-4480	533	17	h	h	NOUN
ejpam-4480	533	18	)	)	PUNCT
ejpam-4480	533	19	and	and	CCONJ
ejpam-4480	533	20	clique	clique	NOUN
ejpam-4480	533	21	s	s	X
ejpam-4480	533	22	in	in	ADP
ejpam-4480	533	23	g	g	PROPN
ejpam-4480	533	24	or	or	CCONJ
ejpam-4480	533	25	c	c	NOUN
ejpam-4480	533	26	=	=	SYM
ejpam-4480	533	27	{	{	PUNCT
ejpam-4480	533	28	x	x	NOUN
ejpam-4480	533	29	}	}	PUNCT
ejpam-4480	533	30	×	×	NOUN
ejpam-4480	533	31	r	r	NOUN
ejpam-4480	533	32	for	for	ADP
ejpam-4480	533	33	some	some	DET
ejpam-4480	533	34	x	x	SYM
ejpam-4480	533	35	∈	∈	PROPN
ejpam-4480	533	36	v	v	ADP
ejpam-4480	533	37	(	(	PUNCT
ejpam-4480	533	38	g	g	NOUN
ejpam-4480	533	39	)	)	PUNCT
ejpam-4480	533	40	and	and	CCONJ
ejpam-4480	533	41	clique	clique	NOUN
ejpam-4480	533	42	r	r	NOUN
ejpam-4480	533	43	in	in	ADP
ejpam-4480	533	44	h.	h.	PROPN
ejpam-4480	533	45	in	in	ADP
ejpam-4480	533	46	particular	particular	ADJ
ejpam-4480	533	47	,	,	PUNCT
ejpam-4480	533	48	ω(g	ω(g	NOUN
ejpam-4480	533	49	□	□	SYM
ejpam-4480	533	50	h	h	NOUN
ejpam-4480	533	51	)	)	PUNCT
ejpam-4480	533	52	=	=	SYM
ejpam-4480	533	53	max{ω(g	max{ω(g	PROPN
ejpam-4480	533	54	)	)	PUNCT
ejpam-4480	533	55	,	,	PUNCT
ejpam-4480	533	56	ω(h	ω(h	NUM
ejpam-4480	533	57	)	)	PUNCT
ejpam-4480	533	58	}	}	PUNCT
ejpam-4480	533	59	.	.	PUNCT
ejpam-4480	534	1	theorem	theorem	ADJ
ejpam-4480	534	2	10	10	NUM
ejpam-4480	534	3	.	.	PUNCT
ejpam-4480	535	1	let	let	VERB
ejpam-4480	535	2	g	g	NOUN
ejpam-4480	536	1	and	and	CCONJ
ejpam-4480	536	2	h	h	NOUN
ejpam-4480	536	3	be	be	VERB
ejpam-4480	536	4	any	any	DET
ejpam-4480	536	5	connected	connected	ADJ
ejpam-4480	536	6	non	non	ADJ
ejpam-4480	536	7	-	-	ADJ
ejpam-4480	536	8	trivial	trivial	ADJ
ejpam-4480	536	9	graphs	graph	NOUN
ejpam-4480	536	10	.	.	PUNCT
ejpam-4480	537	1	then	then	ADV
ejpam-4480	537	2	c	c	PROPN
ejpam-4480	537	3	is	be	AUX
ejpam-4480	537	4	a	a	DET
ejpam-4480	537	5	superclique	superclique	NOUN
ejpam-4480	537	6	in	in	ADP
ejpam-4480	537	7	g	g	NOUN
ejpam-4480	537	8	□	□	PROPN
ejpam-4480	537	9	h	h	NOUN
ejpam-4480	537	10	if	if	SCONJ
ejpam-4480	538	1	and	and	CCONJ
ejpam-4480	538	2	only	only	ADV
ejpam-4480	538	3	if	if	SCONJ
ejpam-4480	538	4	c	c	NOUN
ejpam-4480	538	5	=	=	SYM
ejpam-4480	538	6	s×{a	s×{a	ADV
ejpam-4480	538	7	}	}	PUNCT
ejpam-4480	538	8	for	for	ADP
ejpam-4480	538	9	some	some	DET
ejpam-4480	538	10	a	a	DET
ejpam-4480	538	11	∈	∈	PROPN
ejpam-4480	538	12	v	v	ADP
ejpam-4480	538	13	(	(	PUNCT
ejpam-4480	538	14	h	h	NOUN
ejpam-4480	538	15	)	)	PUNCT
ejpam-4480	538	16	and	and	CCONJ
ejpam-4480	538	17	clique	clique	NOUN
ejpam-4480	538	18	s	s	X
ejpam-4480	538	19	in	in	ADP
ejpam-4480	538	20	g	g	PROPN
ejpam-4480	538	21	or	or	CCONJ
ejpam-4480	538	22	c	c	NOUN
ejpam-4480	538	23	=	=	SYM
ejpam-4480	538	24	{	{	PUNCT
ejpam-4480	538	25	x}×r	x}×r	PROPN
ejpam-4480	538	26	for	for	ADP
ejpam-4480	538	27	some	some	DET
ejpam-4480	538	28	x	x	SYM
ejpam-4480	538	29	∈	∈	PROPN
ejpam-4480	538	30	v	v	ADP
ejpam-4480	538	31	(	(	PUNCT
ejpam-4480	538	32	g	g	NOUN
ejpam-4480	538	33	)	)	PUNCT
ejpam-4480	538	34	and	and	CCONJ
ejpam-4480	538	35	clique	clique	NOUN
ejpam-4480	538	36	r	r	NOUN
ejpam-4480	538	37	in	in	ADP
ejpam-4480	538	38	h.	h.	PROPN
ejpam-4480	538	39	proof	proof	NOUN
ejpam-4480	538	40	.	.	PUNCT
ejpam-4480	539	1	suppose	suppose	VERB
ejpam-4480	539	2	c	c	NOUN
ejpam-4480	539	3	is	be	AUX
ejpam-4480	539	4	a	a	DET
ejpam-4480	539	5	superclique	superclique	NOUN
ejpam-4480	539	6	in	in	ADP
ejpam-4480	539	7	g[h	g[h	NOUN
ejpam-4480	539	8	]	]	PUNCT
ejpam-4480	539	9	.	.	PUNCT
ejpam-4480	540	1	since	since	SCONJ
ejpam-4480	540	2	c	c	PROPN
ejpam-4480	540	3	is	be	AUX
ejpam-4480	540	4	a	a	DET
ejpam-4480	540	5	clique	clique	NOUN
ejpam-4480	540	6	,	,	PUNCT
ejpam-4480	540	7	c	c	X
ejpam-4480	540	8	=	=	SYM
ejpam-4480	540	9	s	s	PROPN
ejpam-4480	540	10	×	×	NOUN
ejpam-4480	540	11	{	{	PUNCT
ejpam-4480	540	12	a	a	NOUN
ejpam-4480	540	13	}	}	PUNCT
ejpam-4480	540	14	for	for	ADP
ejpam-4480	540	15	some	some	DET
ejpam-4480	540	16	a	a	DET
ejpam-4480	540	17	∈	∈	PROPN
ejpam-4480	540	18	v	v	ADP
ejpam-4480	540	19	(	(	PUNCT
ejpam-4480	540	20	h	h	NOUN
ejpam-4480	540	21	)	)	PUNCT
ejpam-4480	540	22	and	and	CCONJ
ejpam-4480	540	23	clique	clique	NOUN
ejpam-4480	540	24	s	s	X
ejpam-4480	540	25	in	in	ADP
ejpam-4480	540	26	g	g	PROPN
ejpam-4480	540	27	or	or	CCONJ
ejpam-4480	540	28	c	c	NOUN
ejpam-4480	540	29	=	=	SYM
ejpam-4480	540	30	{	{	PUNCT
ejpam-4480	540	31	x	x	NOUN
ejpam-4480	540	32	}	}	PUNCT
ejpam-4480	540	33	×	×	NOUN
ejpam-4480	540	34	r	r	NOUN
ejpam-4480	540	35	for	for	ADP
ejpam-4480	540	36	some	some	DET
ejpam-4480	540	37	x	x	SYM
ejpam-4480	540	38	∈	∈	PROPN
ejpam-4480	540	39	v	v	ADP
ejpam-4480	540	40	(	(	PUNCT
ejpam-4480	540	41	g	g	NOUN
ejpam-4480	540	42	)	)	PUNCT
ejpam-4480	540	43	and	and	CCONJ
ejpam-4480	540	44	clique	clique	NOUN
ejpam-4480	540	45	r	r	NOUN
ejpam-4480	540	46	in	in	ADP
ejpam-4480	540	47	h	h	NOUN
ejpam-4480	540	48	by	by	ADP
ejpam-4480	540	49	theorem	theorem	NOUN
ejpam-4480	540	50	9	9	NUM
ejpam-4480	540	51	.	.	PUNCT
ejpam-4480	541	1	for	for	ADP
ejpam-4480	541	2	the	the	DET
ejpam-4480	541	3	converse	converse	NOUN
ejpam-4480	541	4	,	,	PUNCT
ejpam-4480	541	5	suppose	suppose	VERB
ejpam-4480	541	6	that	that	SCONJ
ejpam-4480	541	7	c	c	AUX
ejpam-4480	541	8	=	=	SYM
ejpam-4480	541	9	s	s	PROPN
ejpam-4480	541	10	×	×	NOUN
ejpam-4480	541	11	{	{	PUNCT
ejpam-4480	541	12	a	a	NOUN
ejpam-4480	541	13	}	}	PUNCT
ejpam-4480	541	14	for	for	ADP
ejpam-4480	541	15	some	some	DET
ejpam-4480	541	16	a	a	DET
ejpam-4480	541	17	∈	∈	PROPN
ejpam-4480	541	18	v	v	ADP
ejpam-4480	541	19	(	(	PUNCT
ejpam-4480	541	20	h	h	NOUN
ejpam-4480	541	21	)	)	PUNCT
ejpam-4480	541	22	and	and	CCONJ
ejpam-4480	541	23	clique	clique	NOUN
ejpam-4480	541	24	s	s	PROPN
ejpam-4480	541	25	in	in	ADP
ejpam-4480	541	26	g.	g.	PROPN
ejpam-4480	541	27	then	then	ADV
ejpam-4480	541	28	c	c	PROPN
ejpam-4480	541	29	is	be	AUX
ejpam-4480	541	30	a	a	DET
ejpam-4480	541	31	clique	clique	NOUN
ejpam-4480	541	32	in	in	ADP
ejpam-4480	541	33	g	g	PROPN
ejpam-4480	541	34	□	□	PROPN
ejpam-4480	541	35	h	h	NOUN
ejpam-4480	541	36	by	by	ADP
ejpam-4480	541	37	theorem	theorem	NOUN
ejpam-4480	541	38	9	9	NUM
ejpam-4480	541	39	.	.	PUNCT
ejpam-4480	542	1	let	let	VERB
ejpam-4480	542	2	(	(	PUNCT
ejpam-4480	542	3	v	v	NOUN
ejpam-4480	542	4	,	,	PUNCT
ejpam-4480	542	5	a	a	PRON
ejpam-4480	542	6	)	)	PUNCT
ejpam-4480	542	7	,	,	PUNCT
ejpam-4480	542	8	(	(	PUNCT
ejpam-4480	542	9	w	w	NOUN
ejpam-4480	542	10	,	,	PUNCT
ejpam-4480	542	11	a	a	PRON
ejpam-4480	542	12	)	)	PUNCT
ejpam-4480	542	13	∈	∈	PROPN
ejpam-4480	542	14	c	c	NOUN
ejpam-4480	543	1	such	such	ADJ
ejpam-4480	543	2	that	that	PRON
ejpam-4480	543	3	v	v	AUX
ejpam-4480	543	4	̸=	̸=	PROPN
ejpam-4480	543	5	w.	w.	NOUN
ejpam-4480	543	6	choose	choose	VERB
ejpam-4480	543	7	references	reference	NOUN
ejpam-4480	543	8	1227	1227	NUM
ejpam-4480	543	9	any	any	DET
ejpam-4480	543	10	b	b	PROPN
ejpam-4480	543	11	∈	∈	PROPN
ejpam-4480	543	12	nh(a	nh(a	NUM
ejpam-4480	543	13	)	)	PUNCT
ejpam-4480	543	14	.	.	PUNCT
ejpam-4480	544	1	then	then	ADV
ejpam-4480	544	2	(	(	PUNCT
ejpam-4480	544	3	v	v	NOUN
ejpam-4480	544	4	,	,	PUNCT
ejpam-4480	544	5	b	b	NOUN
ejpam-4480	544	6	)	)	PUNCT
ejpam-4480	544	7	∈	∈	NOUN
ejpam-4480	544	8	v	v	NOUN
ejpam-4480	544	9	(	(	PUNCT
ejpam-4480	544	10	g	g	NOUN
ejpam-4480	544	11	□	□	NOUN
ejpam-4480	544	12	h	h	NOUN
ejpam-4480	544	13	)	)	PUNCT
ejpam-4480	544	14	\	\	PROPN
ejpam-4480	544	15	c	c	PROPN
ejpam-4480	544	16	and	and	CCONJ
ejpam-4480	544	17	(	(	PUNCT
ejpam-4480	544	18	v	v	NOUN
ejpam-4480	544	19	,	,	PUNCT
ejpam-4480	544	20	b	b	NOUN
ejpam-4480	544	21	)	)	PUNCT
ejpam-4480	544	22	∈	∈	PROPN
ejpam-4480	544	23	ng	ng	PROPN
ejpam-4480	544	24	□	□	PROPN
ejpam-4480	544	25	h((v	h((v	NOUN
ejpam-4480	544	26	,	,	PUNCT
ejpam-4480	544	27	a	a	PRON
ejpam-4480	544	28	)	)	PUNCT
ejpam-4480	544	29	)	)	PUNCT
ejpam-4480	544	30	\	\	PROPN
ejpam-4480	545	1	ng	ng	PROPN
ejpam-4480	545	2	□	□	PROPN
ejpam-4480	545	3	h((w	h((w	PROPN
ejpam-4480	545	4	,	,	PUNCT
ejpam-4480	545	5	a	a	PRON
ejpam-4480	545	6	)	)	PUNCT
ejpam-4480	545	7	)	)	PUNCT
ejpam-4480	545	8	.	.	PUNCT
ejpam-4480	546	1	next	next	ADV
ejpam-4480	546	2	,	,	PUNCT
ejpam-4480	546	3	suppose	suppose	VERB
ejpam-4480	546	4	that	that	SCONJ
ejpam-4480	546	5	c	c	AUX
ejpam-4480	546	6	=	=	PRON
ejpam-4480	546	7	{	{	PUNCT
ejpam-4480	546	8	x	x	NOUN
ejpam-4480	546	9	}	}	PUNCT
ejpam-4480	546	10	×	×	NOUN
ejpam-4480	546	11	r	r	NOUN
ejpam-4480	546	12	for	for	ADP
ejpam-4480	546	13	some	some	DET
ejpam-4480	546	14	x	x	SYM
ejpam-4480	546	15	∈	∈	PROPN
ejpam-4480	546	16	v	v	ADP
ejpam-4480	546	17	(	(	PUNCT
ejpam-4480	546	18	g	g	NOUN
ejpam-4480	546	19	)	)	PUNCT
ejpam-4480	546	20	and	and	CCONJ
ejpam-4480	546	21	clique	clique	NOUN
ejpam-4480	546	22	r	r	NOUN
ejpam-4480	546	23	in	in	ADP
ejpam-4480	546	24	h.	h.	PROPN
ejpam-4480	546	25	again	again	ADV
ejpam-4480	546	26	,	,	PUNCT
ejpam-4480	546	27	c	c	PROPN
ejpam-4480	546	28	is	be	AUX
ejpam-4480	546	29	a	a	DET
ejpam-4480	546	30	clique	clique	NOUN
ejpam-4480	546	31	in	in	ADP
ejpam-4480	546	32	g	g	PROPN
ejpam-4480	546	33	□	□	PROPN
ejpam-4480	546	34	h	h	NOUN
ejpam-4480	546	35	by	by	ADP
ejpam-4480	546	36	theorem	theorem	NOUN
ejpam-4480	546	37	9	9	NUM
ejpam-4480	546	38	.	.	PUNCT
ejpam-4480	547	1	let	let	VERB
ejpam-4480	547	2	(	(	PUNCT
ejpam-4480	547	3	x	x	X
ejpam-4480	547	4	,	,	PUNCT
ejpam-4480	547	5	p	p	NOUN
ejpam-4480	547	6	)	)	PUNCT
ejpam-4480	547	7	,	,	PUNCT
ejpam-4480	547	8	(	(	PUNCT
ejpam-4480	547	9	x	x	X
ejpam-4480	547	10	,	,	PUNCT
ejpam-4480	547	11	q	q	NOUN
ejpam-4480	547	12	)	)	PUNCT
ejpam-4480	547	13	∈	∈	PROPN
ejpam-4480	547	14	c	c	NOUN
ejpam-4480	547	15	with	with	ADP
ejpam-4480	547	16	p	p	NOUN
ejpam-4480	547	17	̸=	̸=	PROPN
ejpam-4480	547	18	q.	q.	NOUN
ejpam-4480	547	19	choose	choose	VERB
ejpam-4480	547	20	any	any	DET
ejpam-4480	547	21	y	y	PROPN
ejpam-4480	547	22	∈	∈	PROPN
ejpam-4480	547	23	ng(x	ng(x	NUM
ejpam-4480	547	24	)	)	PUNCT
ejpam-4480	547	25	.	.	PUNCT
ejpam-4480	548	1	then	then	ADV
ejpam-4480	548	2	(	(	PUNCT
ejpam-4480	548	3	y	y	PROPN
ejpam-4480	548	4	,	,	PUNCT
ejpam-4480	548	5	p	p	NOUN
ejpam-4480	548	6	)	)	PUNCT
ejpam-4480	548	7	∈	∈	PROPN
ejpam-4480	548	8	v	v	NOUN
ejpam-4480	548	9	(	(	PUNCT
ejpam-4480	548	10	g	g	NOUN
ejpam-4480	548	11	□	□	NOUN
ejpam-4480	548	12	h	h	NOUN
ejpam-4480	548	13	)	)	PUNCT
ejpam-4480	548	14	\	\	PROPN
ejpam-4480	548	15	c	c	PROPN
ejpam-4480	548	16	and	and	CCONJ
ejpam-4480	548	17	(	(	PUNCT
ejpam-4480	548	18	y	y	PROPN
ejpam-4480	548	19	,	,	PUNCT
ejpam-4480	548	20	p	p	NOUN
ejpam-4480	548	21	)	)	PUNCT
ejpam-4480	548	22	∈	∈	PROPN
ejpam-4480	548	23	ng	ng	PROPN
ejpam-4480	548	24	□	□	PROPN
ejpam-4480	548	25	h((x	h((x	NOUN
ejpam-4480	548	26	,	,	PUNCT
ejpam-4480	548	27	p	p	NOUN
ejpam-4480	548	28	)	)	PUNCT
ejpam-4480	548	29	)	)	PUNCT
ejpam-4480	549	1	\ng	\ng	PROPN
ejpam-4480	549	2	□	□	NOUN
ejpam-4480	549	3	h((x	h((x	NOUN
ejpam-4480	549	4	,	,	PUNCT
ejpam-4480	549	5	q	q	NOUN
ejpam-4480	549	6	)	)	PUNCT
ejpam-4480	549	7	)	)	PUNCT
ejpam-4480	549	8	.	.	PUNCT
ejpam-4480	550	1	in	in	ADP
ejpam-4480	550	2	either	either	DET
ejpam-4480	550	3	case	case	NOUN
ejpam-4480	550	4	,	,	PUNCT
ejpam-4480	550	5	we	we	PRON
ejpam-4480	550	6	find	find	VERB
ejpam-4480	550	7	that	that	SCONJ
ejpam-4480	550	8	c	c	PROPN
ejpam-4480	550	9	is	be	AUX
ejpam-4480	550	10	a	a	DET
ejpam-4480	550	11	superclique	superclique	NOUN
ejpam-4480	550	12	in	in	ADP
ejpam-4480	550	13	g	g	PROPN
ejpam-4480	550	14	□	□	PROPN
ejpam-4480	550	15	h.	h.	NOUN
ejpam-4480	550	16	the	the	DET
ejpam-4480	550	17	next	next	ADJ
ejpam-4480	550	18	result	result	NOUN
ejpam-4480	550	19	follows	follow	VERB
ejpam-4480	550	20	from	from	ADP
ejpam-4480	550	21	theorem	theorem	ADJ
ejpam-4480	550	22	9	9	NUM
ejpam-4480	550	23	and	and	CCONJ
ejpam-4480	550	24	theorem	theorem	VERB
ejpam-4480	550	25	10	10	NUM
ejpam-4480	550	26	.	.	PUNCT
ejpam-4480	551	1	corollary	corollary	ADJ
ejpam-4480	551	2	9	9	NUM
ejpam-4480	551	3	.	.	PUNCT
ejpam-4480	552	1	let	let	VERB
ejpam-4480	552	2	g	g	NOUN
ejpam-4480	552	3	and	and	CCONJ
ejpam-4480	552	4	h	h	PROPN
ejpam-4480	552	5	be	be	VERB
ejpam-4480	552	6	non	non	ADJ
ejpam-4480	552	7	-	-	ADJ
ejpam-4480	552	8	trivial	trivial	ADJ
ejpam-4480	552	9	connected	connected	ADJ
ejpam-4480	552	10	graphs	graph	NOUN
ejpam-4480	552	11	.	.	PUNCT
ejpam-4480	553	1	then	then	ADV
ejpam-4480	553	2	ωs(g	ωs(g	NOUN
ejpam-4480	553	3	□	□	SYM
ejpam-4480	553	4	h	h	NOUN
ejpam-4480	553	5	)	)	PUNCT
ejpam-4480	553	6	=	=	SYM
ejpam-4480	553	7	ω(g	ω(g	NOUN
ejpam-4480	553	8	□	□	PUNCT
ejpam-4480	553	9	h	h	NOUN
ejpam-4480	553	10	)	)	PUNCT
ejpam-4480	553	11	=	=	SYM
ejpam-4480	553	12	max{ω(g	max{ω(g	PROPN
ejpam-4480	553	13	)	)	PUNCT
ejpam-4480	553	14	,	,	PUNCT
ejpam-4480	553	15	ω(h	ω(h	NUM
ejpam-4480	553	16	)	)	PUNCT
ejpam-4480	553	17	}	}	PUNCT
ejpam-4480	553	18	.	.	PUNCT
ejpam-4480	554	1	4	4	X
ejpam-4480	554	2	.	.	X
ejpam-4480	554	3	conclusion	conclusion	NOUN
ejpam-4480	554	4	any	any	DET
ejpam-4480	554	5	graph	graph	NOUN
ejpam-4480	554	6	admits	admit	VERB
ejpam-4480	554	7	a	a	DET
ejpam-4480	554	8	superclique	superclique	NOUN
ejpam-4480	554	9	and	and	CCONJ
ejpam-4480	554	10	the	the	DET
ejpam-4480	554	11	superclique	superclique	ADJ
ejpam-4480	554	12	number	number	NOUN
ejpam-4480	554	13	of	of	ADP
ejpam-4480	554	14	a	a	DET
ejpam-4480	554	15	graph	graph	NOUN
ejpam-4480	554	16	does	do	AUX
ejpam-4480	554	17	not	not	PART
ejpam-4480	554	18	exceed	exceed	VERB
ejpam-4480	554	19	the	the	DET
ejpam-4480	554	20	clique	clique	ADJ
ejpam-4480	554	21	number	number	NOUN
ejpam-4480	554	22	of	of	ADP
ejpam-4480	554	23	the	the	DET
ejpam-4480	554	24	graph	graph	NOUN
ejpam-4480	554	25	.	.	PUNCT
ejpam-4480	555	1	it	it	PRON
ejpam-4480	555	2	is	be	AUX
ejpam-4480	555	3	shown	show	VERB
ejpam-4480	555	4	that	that	SCONJ
ejpam-4480	555	5	the	the	DET
ejpam-4480	555	6	difference	difference	NOUN
ejpam-4480	555	7	of	of	ADP
ejpam-4480	555	8	the	the	DET
ejpam-4480	555	9	clique	clique	ADJ
ejpam-4480	555	10	number	number	NOUN
ejpam-4480	555	11	and	and	CCONJ
ejpam-4480	555	12	superclique	superclique	ADJ
ejpam-4480	555	13	number	number	NOUN
ejpam-4480	555	14	can	can	AUX
ejpam-4480	555	15	be	be	AUX
ejpam-4480	555	16	made	make	VERB
ejpam-4480	555	17	arbitrarily	arbitrarily	ADV
ejpam-4480	555	18	large	large	ADJ
ejpam-4480	555	19	.	.	PUNCT
ejpam-4480	556	1	supercliques	superclique	NOUN
ejpam-4480	556	2	in	in	ADP
ejpam-4480	556	3	the	the	DET
ejpam-4480	556	4	join	join	NOUN
ejpam-4480	556	5	,	,	PUNCT
ejpam-4480	556	6	corona	corona	PROPN
ejpam-4480	556	7	,	,	PUNCT
ejpam-4480	556	8	lexicographic	lexicographic	ADJ
ejpam-4480	556	9	product	product	NOUN
ejpam-4480	556	10	,	,	PUNCT
ejpam-4480	556	11	and	and	CCONJ
ejpam-4480	556	12	cartesian	cartesian	ADJ
ejpam-4480	556	13	product	product	NOUN
ejpam-4480	556	14	of	of	ADP
ejpam-4480	556	15	two	two	NUM
ejpam-4480	556	16	graphs	graph	NOUN
ejpam-4480	556	17	have	have	AUX
ejpam-4480	556	18	been	be	AUX
ejpam-4480	556	19	characterized	characterize	VERB
ejpam-4480	556	20	.	.	PUNCT
ejpam-4480	557	1	from	from	ADP
ejpam-4480	557	2	these	these	DET
ejpam-4480	557	3	characterizations	characterization	NOUN
ejpam-4480	557	4	,	,	PUNCT
ejpam-4480	557	5	respective	respective	ADJ
ejpam-4480	557	6	superclique	superclique	ADJ
ejpam-4480	557	7	numbers	number	NOUN
ejpam-4480	557	8	have	have	AUX
ejpam-4480	557	9	been	be	AUX
ejpam-4480	557	10	determined	determine	VERB
ejpam-4480	557	11	.	.	PUNCT
ejpam-4480	558	1	this	this	DET
ejpam-4480	558	2	new	new	ADJ
ejpam-4480	558	3	invariant	invariant	NOUN
ejpam-4480	558	4	can	can	AUX
ejpam-4480	558	5	also	also	ADV
ejpam-4480	558	6	be	be	AUX
ejpam-4480	558	7	studied	study	VERB
ejpam-4480	558	8	for	for	ADP
ejpam-4480	558	9	graphs	graph	NOUN
ejpam-4480	558	10	under	under	ADP
ejpam-4480	558	11	other	other	ADJ
ejpam-4480	558	12	binary	binary	ADJ
ejpam-4480	558	13	operations	operation	NOUN
ejpam-4480	558	14	.	.	PUNCT
ejpam-4480	559	1	moreover	moreover	ADV
ejpam-4480	559	2	,	,	PUNCT
ejpam-4480	559	3	it	it	PRON
ejpam-4480	559	4	may	may	AUX
ejpam-4480	559	5	be	be	AUX
ejpam-4480	559	6	possible	possible	ADJ
ejpam-4480	559	7	that	that	SCONJ
ejpam-4480	559	8	the	the	DET
ejpam-4480	559	9	invariant	invariant	NOUN
ejpam-4480	559	10	has	have	VERB
ejpam-4480	559	11	relationship	relationship	NOUN
ejpam-4480	559	12	with	with	ADP
ejpam-4480	559	13	other	other	ADJ
ejpam-4480	559	14	graph	graph	NOUN
ejpam-4480	559	15	-	-	PUNCT
ejpam-4480	559	16	theoretic	theoretic	NOUN
ejpam-4480	559	17	parameters	parameter	NOUN
ejpam-4480	559	18	apart	apart	ADV
ejpam-4480	559	19	from	from	ADP
ejpam-4480	559	20	the	the	DET
ejpam-4480	559	21	ones	one	NOUN
ejpam-4480	559	22	involving	involve	VERB
ejpam-4480	559	23	the	the	DET
ejpam-4480	559	24	strong	strong	ADJ
ejpam-4480	559	25	metric	metric	ADJ
ejpam-4480	559	26	dimension	dimension	NOUN
ejpam-4480	559	27	.	.	PUNCT
ejpam-4480	560	1	acknowledgements	acknowledgement	NOUN
ejpam-4480	560	2	the	the	DET
ejpam-4480	560	3	authors	author	NOUN
ejpam-4480	560	4	would	would	AUX
ejpam-4480	560	5	like	like	VERB
ejpam-4480	560	6	to	to	PART
ejpam-4480	560	7	thank	thank	VERB
ejpam-4480	560	8	the	the	DET
ejpam-4480	560	9	referees	referee	NOUN
ejpam-4480	560	10	for	for	ADP
ejpam-4480	560	11	the	the	DET
ejpam-4480	560	12	suggestions	suggestion	NOUN
ejpam-4480	560	13	and	and	CCONJ
ejpam-4480	560	14	comments	comment	NOUN
ejpam-4480	560	15	that	that	PRON
ejpam-4480	560	16	helped	helped	AUX
ejpam-4480	560	17	improve	improve	VERB
ejpam-4480	560	18	the	the	DET
ejpam-4480	560	19	paper	paper	NOUN
ejpam-4480	560	20	.	.	PUNCT
ejpam-4480	561	1	also	also	ADV
ejpam-4480	561	2	,	,	PUNCT
ejpam-4480	561	3	the	the	DET
ejpam-4480	561	4	authors	author	NOUN
ejpam-4480	561	5	would	would	AUX
ejpam-4480	561	6	like	like	VERB
ejpam-4480	561	7	to	to	PART
ejpam-4480	561	8	extend	extend	VERB
ejpam-4480	561	9	their	their	PRON
ejpam-4480	561	10	thankfulness	thankfulness	NOUN
ejpam-4480	561	11	to	to	ADP
ejpam-4480	561	12	the	the	DET
ejpam-4480	561	13	department	department	PROPN
ejpam-4480	561	14	of	of	ADP
ejpam-4480	561	15	science	science	NOUN
ejpam-4480	561	16	and	and	CCONJ
ejpam-4480	561	17	technology	technology	NOUN
ejpam-4480	561	18	accelerated	accelerate	VERB
ejpam-4480	561	19	science	science	NOUN
ejpam-4480	561	20	and	and	CCONJ
ejpam-4480	561	21	technology	technology	NOUN
ejpam-4480	561	22	human	human	ADJ
ejpam-4480	561	23	resource	resource	NOUN
ejpam-4480	561	24	development	development	NOUN
ejpam-4480	561	25	program	program	NOUN
ejpam-4480	561	26	(	(	PUNCT
ejpam-4480	561	27	dost	dost	NOUN
ejpam-4480	561	28	-	-	PUNCT
ejpam-4480	561	29	asthrdp)-philippines	asthrdp)-philippine	NOUN
ejpam-4480	561	30	,	,	PUNCT
ejpam-4480	561	31	and	and	CCONJ
ejpam-4480	561	32	msu	msu	PROPN
ejpam-4480	561	33	-	-	PUNCT
ejpam-4480	561	34	iligan	iligan	PROPN
ejpam-4480	561	35	institute	institute	PROPN
ejpam-4480	561	36	of	of	ADP
ejpam-4480	561	37	technology	technology	NOUN
ejpam-4480	561	38	for	for	ADP
ejpam-4480	561	39	funding	fund	VERB
ejpam-4480	561	40	this	this	DET
ejpam-4480	561	41	research	research	NOUN
ejpam-4480	561	42	.	.	PUNCT
ejpam-4480	562	1	references	reference	NOUN
ejpam-4480	562	2	[	[	X
ejpam-4480	562	3	1	1	NUM
ejpam-4480	562	4	]	]	PUNCT
ejpam-4480	562	5	p.	p.	NOUN
ejpam-4480	562	6	acal	acal	ADJ
ejpam-4480	562	7	and	and	CCONJ
ejpam-4480	562	8	h.	h.	PROPN
ejpam-4480	562	9	rara	rara	PROPN
ejpam-4480	562	10	.	.	PUNCT
ejpam-4480	563	1	the	the	DET
ejpam-4480	563	2	strong	strong	ADJ
ejpam-4480	563	3	connected	connected	ADJ
ejpam-4480	563	4	metric	metric	ADJ
ejpam-4480	563	5	dimension	dimension	NOUN
ejpam-4480	563	6	in	in	ADP
ejpam-4480	563	7	the	the	DET
ejpam-4480	563	8	join	join	NOUN
ejpam-4480	563	9	and	and	CCONJ
ejpam-4480	563	10	corona	corona	NOUN
ejpam-4480	563	11	of	of	ADP
ejpam-4480	563	12	graphs	graph	NOUN
ejpam-4480	563	13	.	.	PUNCT
ejpam-4480	564	1	advances	advance	NOUN
ejpam-4480	564	2	and	and	CCONJ
ejpam-4480	564	3	applications	application	NOUN
ejpam-4480	564	4	in	in	ADP
ejpam-4480	564	5	discrete	discrete	ADJ
ejpam-4480	564	6	mathematics	mathematic	NOUN
ejpam-4480	564	7	,	,	PUNCT
ejpam-4480	564	8	21(1):91–101	21(1):91–101	NUM
ejpam-4480	564	9	,	,	PUNCT
ejpam-4480	564	10	2019	2019	NUM
ejpam-4480	564	11	.	.	PUNCT
ejpam-4480	565	1	[	[	X
ejpam-4480	565	2	2	2	NUM
ejpam-4480	565	3	]	]	X
ejpam-4480	565	4	r.	r.	PROPN
ejpam-4480	565	5	brigham	brigham	PROPN
ejpam-4480	565	6	,	,	PUNCT
ejpam-4480	565	7	g.	g.	PROPN
ejpam-4480	565	8	chartrand	chartrand	PROPN
ejpam-4480	565	9	,	,	PUNCT
ejpam-4480	565	10	r.	r.	PROPN
ejpam-4480	565	11	dutton	dutton	PROPN
ejpam-4480	565	12	,	,	PUNCT
ejpam-4480	565	13	and	and	CCONJ
ejpam-4480	565	14	p.	p.	PROPN
ejpam-4480	565	15	zhang	zhang	PROPN
ejpam-4480	565	16	.	.	PUNCT
ejpam-4480	566	1	resolving	resolve	VERB
ejpam-4480	566	2	domination	domination	NOUN
ejpam-4480	566	3	in	in	ADP
ejpam-4480	566	4	graphs	graph	NOUN
ejpam-4480	566	5	.	.	PUNCT
ejpam-4480	567	1	mathematica	mathematica	PROPN
ejpam-4480	567	2	bohemica	bohemica	PROPN
ejpam-4480	567	3	,	,	PUNCT
ejpam-4480	567	4	128(1):25–36	128(1):25–36	NUM
ejpam-4480	567	5	,	,	PUNCT
ejpam-4480	567	6	2003	2003	NUM
ejpam-4480	567	7	.	.	PUNCT
ejpam-4480	568	1	[	[	X
ejpam-4480	568	2	3	3	X
ejpam-4480	568	3	]	]	X
ejpam-4480	568	4	g.	g.	NOUN
ejpam-4480	568	5	cagaanan	cagaanan	PROPN
ejpam-4480	568	6	and	and	CCONJ
ejpam-4480	568	7	s.	s.	PROPN
ejpam-4480	568	8	canoy	canoy	PROPN
ejpam-4480	568	9	jr	jr	PROPN
ejpam-4480	568	10	.	.	PROPN
ejpam-4480	568	11	on	on	ADP
ejpam-4480	568	12	the	the	DET
ejpam-4480	568	13	geodetic	geodetic	ADJ
ejpam-4480	568	14	covers	cover	NOUN
ejpam-4480	568	15	and	and	CCONJ
ejpam-4480	568	16	geodetic	geodetic	ADJ
ejpam-4480	568	17	bases	basis	NOUN
ejpam-4480	568	18	of	of	ADP
ejpam-4480	568	19	the	the	DET
ejpam-4480	568	20	composition	composition	NOUN
ejpam-4480	568	21	g[km	g[km	PROPN
ejpam-4480	568	22	]	]	PUNCT
ejpam-4480	568	23	.	.	PUNCT
ejpam-4480	568	24	ars	ars	PROPN
ejpam-4480	568	25	combinatoria	combinatoria	PROPN
ejpam-4480	568	26	,	,	PUNCT
ejpam-4480	568	27	79:33–45	79:33–45	NUM
ejpam-4480	568	28	,	,	PUNCT
ejpam-4480	568	29	2006	2006	NUM
ejpam-4480	568	30	.	.	PUNCT
ejpam-4480	569	1	[	[	X
ejpam-4480	569	2	4	4	X
ejpam-4480	569	3	]	]	X
ejpam-4480	569	4	g.	g.	PROPN
ejpam-4480	569	5	chartrand	chartrand	PROPN
ejpam-4480	569	6	,	,	PUNCT
ejpam-4480	569	7	l.	l.	PROPN
ejpam-4480	569	8	eroh	eroh	PROPN
ejpam-4480	569	9	,	,	PUNCT
ejpam-4480	569	10	m.	m.	NOUN
ejpam-4480	569	11	johnson	johnson	PROPN
ejpam-4480	569	12	,	,	PUNCT
ejpam-4480	569	13	and	and	CCONJ
ejpam-4480	569	14	o.r	o.r	PROPN
ejpam-4480	569	15	.	.	PROPN
ejpam-4480	569	16	oellermann	oellermann	PROPN
ejpam-4480	569	17	.	.	PUNCT
ejpam-4480	570	1	resolvability	resolvability	NOUN
ejpam-4480	570	2	in	in	ADP
ejpam-4480	570	3	graphs	graph	NOUN
ejpam-4480	570	4	and	and	CCONJ
ejpam-4480	570	5	the	the	DET
ejpam-4480	570	6	metric	metric	ADJ
ejpam-4480	570	7	dimension	dimension	NOUN
ejpam-4480	570	8	of	of	ADP
ejpam-4480	570	9	a	a	DET
ejpam-4480	570	10	graph	graph	NOUN
ejpam-4480	570	11	the	the	DET
ejpam-4480	570	12	metric	metric	ADJ
ejpam-4480	570	13	dimension	dimension	NOUN
ejpam-4480	570	14	of	of	ADP
ejpam-4480	570	15	a	a	DET
ejpam-4480	570	16	graph	graph	NOUN
ejpam-4480	570	17	.	.	PUNCT
ejpam-4480	571	1	discrete	discrete	ADJ
ejpam-4480	571	2	applied	apply	VERB
ejpam-4480	571	3	mathematics	mathematic	NOUN
ejpam-4480	571	4	,	,	PUNCT
ejpam-4480	571	5	105:99–113	105:99–113	NUM
ejpam-4480	571	6	,	,	PUNCT
ejpam-4480	571	7	2000	2000	NUM
ejpam-4480	571	8	.	.	PUNCT
ejpam-4480	572	1	references	reference	NOUN
ejpam-4480	572	2	1228	1228	NUM
ejpam-4480	572	3	[	[	X
ejpam-4480	572	4	5	5	NUM
ejpam-4480	572	5	]	]	X
ejpam-4480	572	6	m.b	m.b	PROPN
ejpam-4480	572	7	.	.	PROPN
ejpam-4480	572	8	cozzens	cozzen	NOUN
ejpam-4480	572	9	and	and	CCONJ
ejpam-4480	572	10	l.l	l.l	PROPN
ejpam-4480	572	11	.	.	PROPN
ejpam-4480	572	12	kelleher	kelleher	PROPN
ejpam-4480	572	13	.	.	PUNCT
ejpam-4480	573	1	dominating	dominate	VERB
ejpam-4480	573	2	cliques	clique	NOUN
ejpam-4480	573	3	in	in	ADP
ejpam-4480	573	4	graphs	graph	NOUN
ejpam-4480	573	5	.	.	PUNCT
ejpam-4480	574	1	discrete	discrete	ADJ
ejpam-4480	574	2	mathematics	mathematic	NOUN
ejpam-4480	574	3	,	,	PUNCT
ejpam-4480	574	4	86:101–116	86:101–116	PROPN
ejpam-4480	574	5	,	,	PUNCT
ejpam-4480	574	6	1990	1990	NUM
ejpam-4480	574	7	.	.	PUNCT
ejpam-4480	575	1	[	[	X
ejpam-4480	575	2	6	6	NUM
ejpam-4480	575	3	]	]	X
ejpam-4480	575	4	t.v	t.v	PROPN
ejpam-4480	575	5	.	.	PROPN
ejpam-4480	575	6	daniel	daniel	PROPN
ejpam-4480	575	7	and	and	CCONJ
ejpam-4480	575	8	s.	s.	PROPN
ejpam-4480	575	9	canoy	canoy	PROPN
ejpam-4480	575	10	jr	jr	PROPN
ejpam-4480	575	11	.	.	PROPN
ejpam-4480	575	12	clique	clique	PROPN
ejpam-4480	575	13	domination	domination	NOUN
ejpam-4480	575	14	in	in	ADP
ejpam-4480	575	15	a	a	DET
ejpam-4480	575	16	graph	graph	NOUN
ejpam-4480	575	17	.	.	PUNCT
ejpam-4480	576	1	applied	apply	VERB
ejpam-4480	576	2	mathematical	mathematical	ADJ
ejpam-4480	576	3	sciences	science	NOUN
ejpam-4480	576	4	,	,	PUNCT
ejpam-4480	576	5	9(116):5749–5755	9(116):5749–5755	NUM
ejpam-4480	576	6	,	,	PUNCT
ejpam-4480	576	7	2015	2015	NUM
ejpam-4480	576	8	.	.	PUNCT
ejpam-4480	577	1	[	[	X
ejpam-4480	577	2	7	7	X
ejpam-4480	577	3	]	]	X
ejpam-4480	577	4	r.	r.	NOUN
ejpam-4480	577	5	eballe	eballe	PROPN
ejpam-4480	577	6	and	and	CCONJ
ejpam-4480	577	7	s.	s.	PROPN
ejpam-4480	577	8	canoy	canoy	PROPN
ejpam-4480	577	9	jr	jr	PROPN
ejpam-4480	577	10	.	.	PROPN
ejpam-4480	577	11	steiner	steiner	PROPN
ejpam-4480	577	12	sets	set	NOUN
ejpam-4480	577	13	in	in	ADP
ejpam-4480	577	14	the	the	DET
ejpam-4480	577	15	join	join	NOUN
ejpam-4480	577	16	and	and	CCONJ
ejpam-4480	577	17	composition	composition	NOUN
ejpam-4480	577	18	of	of	ADP
ejpam-4480	577	19	graphs	graph	NOUN
ejpam-4480	577	20	.	.	PUNCT
ejpam-4480	578	1	congresus	congresus	PROPN
ejpam-4480	578	2	numerantium	numerantium	PROPN
ejpam-4480	578	3	,	,	PUNCT
ejpam-4480	578	4	170:65–73	170:65–73	NUM
ejpam-4480	578	5	,	,	PUNCT
ejpam-4480	578	6	2004	2004	NUM
ejpam-4480	578	7	.	.	PUNCT
ejpam-4480	579	1	[	[	X
ejpam-4480	579	2	8	8	NUM
ejpam-4480	579	3	]	]	X
ejpam-4480	579	4	n.	n.	NOUN
ejpam-4480	579	5	gaquing	gaquing	NOUN
ejpam-4480	579	6	and	and	CCONJ
ejpam-4480	579	7	s.	s.	PROPN
ejpam-4480	579	8	canoy	canoy	PROPN
ejpam-4480	579	9	jr	jr	PROPN
ejpam-4480	579	10	.	.	PROPN
ejpam-4480	580	1	on	on	ADP
ejpam-4480	580	2	cliques	clique	NOUN
ejpam-4480	580	3	and	and	CCONJ
ejpam-4480	580	4	forcing	force	VERB
ejpam-4480	580	5	m	m	NOUN
ejpam-4480	580	6	-	-	PUNCT
ejpam-4480	580	7	convexity	convexity	NOUN
ejpam-4480	580	8	numbers	number	NOUN
ejpam-4480	580	9	of	of	ADP
ejpam-4480	580	10	graphs	graph	NOUN
ejpam-4480	580	11	.	.	PUNCT
ejpam-4480	581	1	ars	ars	PROPN
ejpam-4480	581	2	combinatoria	combinatoria	PROPN
ejpam-4480	581	3	,	,	PUNCT
ejpam-4480	581	4	103:321–331	103:321–331	NUM
ejpam-4480	581	5	,	,	PUNCT
ejpam-4480	581	6	2012	2012	NUM
ejpam-4480	581	7	.	.	PUNCT
ejpam-4480	582	1	[	[	X
ejpam-4480	582	2	9	9	NUM
ejpam-4480	582	3	]	]	X
ejpam-4480	582	4	m.r	m.r	PROPN
ejpam-4480	582	5	.	.	PROPN
ejpam-4480	582	6	garey	garey	PROPN
ejpam-4480	582	7	and	and	CCONJ
ejpam-4480	582	8	d.s	d.s	PROPN
ejpam-4480	582	9	.	.	PROPN
ejpam-4480	582	10	johnson	johnson	PROPN
ejpam-4480	582	11	.	.	PUNCT
ejpam-4480	583	1	computers	computer	NOUN
ejpam-4480	583	2	and	and	CCONJ
ejpam-4480	583	3	intractability	intractability	NOUN
ejpam-4480	583	4	:	:	PUNCT
ejpam-4480	583	5	a	a	DET
ejpam-4480	583	6	guide	guide	NOUN
ejpam-4480	583	7	to	to	ADP
ejpam-4480	583	8	the	the	DET
ejpam-4480	583	9	theory	theory	NOUN
ejpam-4480	583	10	of	of	ADP
ejpam-4480	583	11	np	np	DET
ejpam-4480	583	12	completeness	completeness	NOUN
ejpam-4480	583	13	.	.	PUNCT
ejpam-4480	584	1	freeman	freeman	PROPN
ejpam-4480	584	2	,	,	PUNCT
ejpam-4480	584	3	new	new	PROPN
ejpam-4480	584	4	york	york	PROPN
ejpam-4480	584	5	,	,	PUNCT
ejpam-4480	584	6	1979	1979	NUM
ejpam-4480	584	7	.	.	PUNCT
ejpam-4480	585	1	[	[	X
ejpam-4480	585	2	10	10	NUM
ejpam-4480	585	3	]	]	X
ejpam-4480	585	4	f.	f.	PROPN
ejpam-4480	585	5	harary	harary	PROPN
ejpam-4480	585	6	and	and	CCONJ
ejpam-4480	585	7	r.a	r.a	PROPN
ejpam-4480	585	8	.	.	PROPN
ejpam-4480	585	9	melter	melter	NOUN
ejpam-4480	585	10	.	.	PUNCT
ejpam-4480	586	1	on	on	ADP
ejpam-4480	586	2	the	the	DET
ejpam-4480	586	3	metric	metric	ADJ
ejpam-4480	586	4	dimension	dimension	NOUN
ejpam-4480	586	5	of	of	ADP
ejpam-4480	586	6	a	a	DET
ejpam-4480	586	7	graph	graph	NOUN
ejpam-4480	586	8	.	.	PUNCT
ejpam-4480	586	9	ars	ars	PROPN
ejpam-4480	586	10	combinatoria	combinatoria	NOUN
ejpam-4480	586	11	,	,	PUNCT
ejpam-4480	586	12	2:191–195	2:191–195	NUM
ejpam-4480	586	13	,	,	PUNCT
ejpam-4480	586	14	1976	1976	NUM
ejpam-4480	586	15	.	.	PUNCT
ejpam-4480	587	1	[	[	X
ejpam-4480	587	2	11	11	NUM
ejpam-4480	587	3	]	]	X
ejpam-4480	587	4	r.	r.	PROPN
ejpam-4480	587	5	hinampas	hinampas	PROPN
ejpam-4480	587	6	and	and	CCONJ
ejpam-4480	587	7	s.	s.	PROPN
ejpam-4480	587	8	canoy	canoy	PROPN
ejpam-4480	587	9	jr	jr	PROPN
ejpam-4480	587	10	.	.	PROPN
ejpam-4480	587	11	1	1	NUM
ejpam-4480	587	12	-	-	PUNCT
ejpam-4480	587	13	movable	movable	ADJ
ejpam-4480	587	14	domination	domination	NOUN
ejpam-4480	587	15	in	in	ADP
ejpam-4480	587	16	graphs	graph	NOUN
ejpam-4480	587	17	.	.	PUNCT
ejpam-4480	588	1	applied	apply	VERB
ejpam-4480	588	2	mathematical	mathematical	ADJ
ejpam-4480	588	3	sciences	sciences	PROPN
ejpam-4480	588	4	,	,	PUNCT
ejpam-4480	588	5	8(172):8565–8571	8(172):8565–8571	NUM
ejpam-4480	588	6	,	,	PUNCT
ejpam-4480	588	7	2014	2014	NUM
ejpam-4480	588	8	.	.	PUNCT
ejpam-4480	589	1	[	[	X
ejpam-4480	589	2	12	12	NUM
ejpam-4480	589	3	]	]	X
ejpam-4480	589	4	r.	r.	PROPN
ejpam-4480	589	5	luce	luce	PROPN
ejpam-4480	589	6	and	and	CCONJ
ejpam-4480	589	7	a.	a.	PROPN
ejpam-4480	589	8	perry	perry	PROPN
ejpam-4480	589	9	.	.	PUNCT
ejpam-4480	590	1	a	a	DET
ejpam-4480	590	2	method	method	NOUN
ejpam-4480	590	3	of	of	ADP
ejpam-4480	590	4	matrix	matrix	NOUN
ejpam-4480	590	5	analysis	analysis	NOUN
ejpam-4480	590	6	of	of	ADP
ejpam-4480	590	7	group	group	NOUN
ejpam-4480	590	8	structure	structure	NOUN
ejpam-4480	590	9	.	.	PUNCT
ejpam-4480	591	1	psychometrika	psychometrika	NOUN
ejpam-4480	591	2	,	,	PUNCT
ejpam-4480	591	3	14:95–116	14:95–116	NUM
ejpam-4480	591	4	,	,	PUNCT
ejpam-4480	591	5	1949	1949	NUM
ejpam-4480	591	6	.	.	PUNCT
ejpam-4480	592	1	[	[	X
ejpam-4480	592	2	13	13	NUM
ejpam-4480	592	3	]	]	X
ejpam-4480	592	4	g.	g.	PROPN
ejpam-4480	592	5	monsanto	monsanto	PROPN
ejpam-4480	592	6	,	,	PUNCT
ejpam-4480	592	7	p.	p.	NOUN
ejpam-4480	592	8	acal	acal	ADJ
ejpam-4480	592	9	,	,	PUNCT
ejpam-4480	592	10	and	and	CCONJ
ejpam-4480	592	11	h.	h.	PROPN
ejpam-4480	592	12	rara	rara	PROPN
ejpam-4480	592	13	.	.	PUNCT
ejpam-4480	593	1	on	on	ADP
ejpam-4480	593	2	strong	strong	ADJ
ejpam-4480	593	3	resolving	resolving	NOUN
ejpam-4480	593	4	domination	domination	NOUN
ejpam-4480	593	5	in	in	ADP
ejpam-4480	593	6	the	the	DET
ejpam-4480	593	7	join	join	NOUN
ejpam-4480	593	8	and	and	CCONJ
ejpam-4480	593	9	corona	corona	NOUN
ejpam-4480	593	10	of	of	ADP
ejpam-4480	593	11	graphs	graph	NOUN
ejpam-4480	593	12	.	.	PUNCT
ejpam-4480	594	1	european	european	ADJ
ejpam-4480	594	2	journal	journal	PROPN
ejpam-4480	594	3	of	of	ADP
ejpam-4480	594	4	pure	pure	ADJ
ejpam-4480	594	5	and	and	CCONJ
ejpam-4480	594	6	applied	applied	ADJ
ejpam-4480	594	7	mathematics	mathematic	NOUN
ejpam-4480	594	8	,	,	PUNCT
ejpam-4480	594	9	13(1):170–179	13(1):170–179	NUM
ejpam-4480	594	10	,	,	PUNCT
ejpam-4480	594	11	2020	2020	NUM
ejpam-4480	594	12	.	.	PUNCT
ejpam-4480	595	1	[	[	X
ejpam-4480	595	2	14	14	NUM
ejpam-4480	595	3	]	]	X
ejpam-4480	595	4	j.w	j.w	PROPN
ejpam-4480	595	5	.	.	PROPN
ejpam-4480	595	6	moon	moon	PROPN
ejpam-4480	595	7	and	and	CCONJ
ejpam-4480	595	8	l.	l.	PROPN
ejpam-4480	595	9	moser	moser	PROPN
ejpam-4480	595	10	.	.	PUNCT
ejpam-4480	596	1	on	on	ADP
ejpam-4480	596	2	clique	clique	NOUN
ejpam-4480	596	3	in	in	ADP
ejpam-4480	596	4	graphs	graph	NOUN
ejpam-4480	596	5	.	.	PUNCT
ejpam-4480	597	1	israel	israel	PROPN
ejpam-4480	597	2	j.	j.	PROPN
ejpam-4480	597	3	math	math	PROPN
ejpam-4480	597	4	.	.	PROPN
ejpam-4480	597	5	,	,	PUNCT
ejpam-4480	597	6	9:23–28	9:23–28	NUM
ejpam-4480	597	7	,	,	PUNCT
ejpam-4480	597	8	1965	1965	NUM
ejpam-4480	597	9	.	.	PUNCT
ejpam-4480	598	1	[	[	X
ejpam-4480	598	2	15	15	NUM
ejpam-4480	598	3	]	]	X
ejpam-4480	598	4	o.r	o.r	PROPN
ejpam-4480	598	5	.	.	PROPN
ejpam-4480	598	6	oellermann	oellermann	PROPN
ejpam-4480	598	7	and	and	CCONJ
ejpam-4480	598	8	j.	j.	PROPN
ejpam-4480	598	9	peters	peters	PROPN
ejpam-4480	598	10	-	-	PUNCT
ejpam-4480	598	11	fransen	fransen	PROPN
ejpam-4480	598	12	.	.	PUNCT
ejpam-4480	599	1	metric	metric	ADJ
ejpam-4480	599	2	dimension	dimension	NOUN
ejpam-4480	599	3	of	of	ADP
ejpam-4480	599	4	cartesian	cartesian	ADJ
ejpam-4480	599	5	products	product	NOUN
ejpam-4480	599	6	of	of	ADP
ejpam-4480	599	7	graphs	graph	NOUN
ejpam-4480	599	8	.	.	PUNCT
ejpam-4480	600	1	utilitas	utilitas	ADJ
ejpam-4480	600	2	math	math	NOUN
ejpam-4480	600	3	.	.	PUNCT
ejpam-4480	600	4	,	,	PUNCT
ejpam-4480	600	5	69:33–41	69:33–41	NUM
ejpam-4480	600	6	,	,	PUNCT
ejpam-4480	600	7	2006	2006	NUM
ejpam-4480	600	8	.	.	PUNCT
ejpam-4480	601	1	[	[	X
ejpam-4480	601	2	16	16	NUM
ejpam-4480	601	3	]	]	X
ejpam-4480	601	4	o.r	o.r	PROPN
ejpam-4480	601	5	.	.	PROPN
ejpam-4480	601	6	oellermann	oellermann	PROPN
ejpam-4480	601	7	and	and	CCONJ
ejpam-4480	601	8	j.	j.	PROPN
ejpam-4480	601	9	peters	peters	PROPN
ejpam-4480	601	10	-	-	PUNCT
ejpam-4480	601	11	fransen	fransen	PROPN
ejpam-4480	601	12	.	.	PUNCT
ejpam-4480	602	1	the	the	DET
ejpam-4480	602	2	strong	strong	ADJ
ejpam-4480	602	3	metric	metric	ADJ
ejpam-4480	602	4	dimension	dimension	NOUN
ejpam-4480	602	5	of	of	ADP
ejpam-4480	602	6	graphs	graph	NOUN
ejpam-4480	602	7	and	and	CCONJ
ejpam-4480	602	8	digraphs	digraph	NOUN
ejpam-4480	602	9	.	.	PUNCT
ejpam-4480	603	1	discrete	discrete	ADJ
ejpam-4480	603	2	applied	apply	VERB
ejpam-4480	603	3	mathematics	mathematic	NOUN
ejpam-4480	603	4	,	,	PUNCT
ejpam-4480	603	5	155:356–364	155:356–364	NUM
ejpam-4480	603	6	,	,	PUNCT
ejpam-4480	603	7	2007	2007	NUM
ejpam-4480	603	8	.	.	PUNCT
ejpam-4480	604	1	[	[	X
ejpam-4480	604	2	17	17	NUM
ejpam-4480	604	3	]	]	X
ejpam-4480	604	4	f.	f.	PROPN
ejpam-4480	604	5	roberts	roberts	PROPN
ejpam-4480	604	6	and	and	CCONJ
ejpam-4480	604	7	j.	j.	PROPN
ejpam-4480	604	8	spencer	spencer	PROPN
ejpam-4480	604	9	.	.	PUNCT
ejpam-4480	605	1	a	a	DET
ejpam-4480	605	2	characterization	characterization	NOUN
ejpam-4480	605	3	of	of	ADP
ejpam-4480	605	4	clique	clique	NOUN
ejpam-4480	605	5	graphs	graph	NOUN
ejpam-4480	605	6	.	.	PUNCT
ejpam-4480	606	1	journal	journal	NOUN
ejpam-4480	606	2	of	of	ADP
ejpam-4480	606	3	combinatorial	combinatorial	ADJ
ejpam-4480	606	4	theory	theory	NOUN
ejpam-4480	606	5	,	,	PUNCT
ejpam-4480	606	6	10:102–108	10:102–108	NUM
ejpam-4480	606	7	,	,	PUNCT
ejpam-4480	606	8	1971	1971	NUM
ejpam-4480	606	9	.	.	PUNCT
ejpam-4480	607	1	[	[	X
ejpam-4480	607	2	18	18	NUM
ejpam-4480	607	3	]	]	PUNCT
ejpam-4480	607	4	a.	a.	NOUN
ejpam-4480	607	5	sebo	sebo	NOUN
ejpam-4480	607	6	and	and	CCONJ
ejpam-4480	607	7	e.	e.	PROPN
ejpam-4480	607	8	tannier	tannier	PROPN
ejpam-4480	607	9	.	.	PUNCT
ejpam-4480	608	1	on	on	ADP
ejpam-4480	608	2	metric	metric	ADJ
ejpam-4480	608	3	generators	generator	NOUN
ejpam-4480	608	4	of	of	ADP
ejpam-4480	608	5	graphs	graph	NOUN
ejpam-4480	608	6	.	.	PUNCT
ejpam-4480	609	1	math	math	NOUN
ejpam-4480	609	2	.	.	PUNCT
ejpam-4480	610	1	oper	oper	PROPN
ejpam-4480	610	2	.	.	PUNCT
ejpam-4480	611	1	res	res	PROPN
ejpam-4480	611	2	.	.	PROPN
ejpam-4480	611	3	,	,	PUNCT
ejpam-4480	611	4	29:383	29:383	NUM
ejpam-4480	611	5	–	–	PUNCT
ejpam-4480	611	6	393	393	NUM
ejpam-4480	611	7	,	,	PUNCT
ejpam-4480	611	8	2004	2004	NUM
ejpam-4480	611	9	.	.	PUNCT
ejpam-4480	612	1	[	[	X
ejpam-4480	612	2	19	19	NUM
ejpam-4480	612	3	]	]	X
ejpam-4480	612	4	p.j	p.j	PROPN
ejpam-4480	612	5	.	.	PROPN
ejpam-4480	612	6	slater	slater	PROPN
ejpam-4480	612	7	.	.	PUNCT
ejpam-4480	613	1	dominating	dominating	NOUN
ejpam-4480	613	2	and	and	CCONJ
ejpam-4480	613	3	reference	reference	NOUN
ejpam-4480	613	4	sets	set	NOUN
ejpam-4480	613	5	in	in	ADP
ejpam-4480	613	6	graphs	graph	NOUN
ejpam-4480	613	7	.	.	PUNCT
ejpam-4480	614	1	j.	j.	PROPN
ejpam-4480	614	2	math	math	PROPN
ejpam-4480	614	3	.	.	PUNCT
ejpam-4480	615	1	phys	phy	NOUN
ejpam-4480	615	2	.	.	PUNCT
ejpam-4480	616	1	sci	sci	PROPN
ejpam-4480	616	2	.	.	PROPN
ejpam-4480	616	3	,	,	PUNCT
ejpam-4480	616	4	22:445–455	22:445–455	PROPN
ejpam-4480	616	5	,	,	PUNCT
ejpam-4480	616	6	1988	1988	NUM
ejpam-4480	616	7	.	.	PUNCT
ejpam-4480	617	1	[	[	X
ejpam-4480	617	2	20	20	NUM
ejpam-4480	617	3	]	]	X
ejpam-4480	617	4	h.	h.	NOUN
ejpam-4480	617	5	sumaoy	sumaoy	NOUN
ejpam-4480	617	6	and	and	CCONJ
ejpam-4480	617	7	h.	h.	PROPN
ejpam-4480	617	8	rara	rara	PROPN
ejpam-4480	617	9	.	.	PUNCT
ejpam-4480	618	1	on	on	ADP
ejpam-4480	618	2	restrained	restrained	ADJ
ejpam-4480	618	3	and	and	CCONJ
ejpam-4480	618	4	movable	movable	ADJ
ejpam-4480	618	5	strong	strong	ADJ
ejpam-4480	618	6	resolving	resolving	NOUN
ejpam-4480	618	7	domination	domination	NOUN
ejpam-4480	618	8	in	in	ADP
ejpam-4480	618	9	graphs	graph	NOUN
ejpam-4480	618	10	.	.	PUNCT
ejpam-4480	619	1	european	european	ADJ
ejpam-4480	619	2	journal	journal	PROPN
ejpam-4480	619	3	of	of	ADP
ejpam-4480	619	4	pure	pure	ADJ
ejpam-4480	619	5	and	and	CCONJ
ejpam-4480	619	6	applied	applied	ADJ
ejpam-4480	619	7	mathematics	mathematic	NOUN
ejpam-4480	619	8	,	,	PUNCT
ejpam-4480	619	9	14(4):1367–1378	14(4):1367–1378	NUM
ejpam-4480	619	10	,	,	PUNCT
ejpam-4480	619	11	2021	2021	NUM
ejpam-4480	619	12	.	.	PUNCT