id	sid	tid	token	lemma	pos
ejpam-4651	1	1	european	european	PROPN
ejpam-4651	1	2	journal	journal	PROPN
ejpam-4651	1	3	of	of	ADP
ejpam-4651	1	4	pure	pure	ADJ
ejpam-4651	1	5	and	and	CCONJ
ejpam-4651	1	6	applied	apply	VERB
ejpam-4651	1	7	mathematics	mathematic	NOUN
ejpam-4651	1	8	vol	vol	NOUN
ejpam-4651	1	9	.	.	PUNCT
ejpam-4651	2	1	16	16	NUM
ejpam-4651	2	2	,	,	PUNCT
ejpam-4651	2	3	no	no	INTJ
ejpam-4651	2	4	.	.	NOUN
ejpam-4651	2	5	1	1	NUM
ejpam-4651	2	6	,	,	PUNCT
ejpam-4651	2	7	2023	2023	NUM
ejpam-4651	2	8	,	,	PUNCT
ejpam-4651	2	9	243	243	NUM
ejpam-4651	2	10	-	-	SYM
ejpam-4651	2	11	252	252	NUM
ejpam-4651	2	12	issn	issn	PROPN
ejpam-4651	2	13	1307	1307	NUM
ejpam-4651	2	14	-	-	SYM
ejpam-4651	2	15	5543	5543	NUM
ejpam-4651	2	16	–	–	PUNCT
ejpam-4651	2	17	ejpam.com	ejpam.com	X
ejpam-4651	2	18	published	publish	VERB
ejpam-4651	2	19	by	by	ADP
ejpam-4651	2	20	new	new	PROPN
ejpam-4651	2	21	york	york	PROPN
ejpam-4651	2	22	business	business	PROPN
ejpam-4651	2	23	global	global	ADJ
ejpam-4651	2	24	cliques	clique	NOUN
ejpam-4651	2	25	and	and	CCONJ
ejpam-4651	2	26	supercliques	superclique	NOUN
ejpam-4651	2	27	in	in	ADP
ejpam-4651	2	28	a	a	DET
ejpam-4651	2	29	graph	graph	NOUN
ejpam-4651	2	30	sergio	sergio	PROPN
ejpam-4651	2	31	r.	r.	PROPN
ejpam-4651	2	32	canoy	canoy	PROPN
ejpam-4651	2	33	,	,	PUNCT
ejpam-4651	2	34	jr.1,∗	jr.1,∗	PROPN
ejpam-4651	2	35	,	,	PUNCT
ejpam-4651	2	36	ramil	ramil	PROPN
ejpam-4651	2	37	h.	h.	PROPN
ejpam-4651	2	38	dela	dela	PROPN
ejpam-4651	2	39	cerna1	cerna1	PROPN
ejpam-4651	2	40	,	,	PUNCT
ejpam-4651	2	41	armalene	armalene	VERB
ejpam-4651	2	42	abragan1	abragan1	PROPN
ejpam-4651	2	43	1	1	NUM
ejpam-4651	2	44	department	department	NOUN
ejpam-4651	2	45	of	of	ADP
ejpam-4651	2	46	mathematics	mathematic	NOUN
ejpam-4651	2	47	and	and	CCONJ
ejpam-4651	2	48	statistics	statistic	NOUN
ejpam-4651	2	49	,	,	PUNCT
ejpam-4651	2	50	college	college	NOUN
ejpam-4651	2	51	of	of	ADP
ejpam-4651	2	52	science	science	NOUN
ejpam-4651	2	53	and	and	CCONJ
ejpam-4651	2	54	mathematics	mathematic	NOUN
ejpam-4651	2	55	,	,	PUNCT
ejpam-4651	2	56	center	center	NOUN
ejpam-4651	2	57	for	for	ADP
ejpam-4651	2	58	graph	graph	NOUN
ejpam-4651	2	59	theory	theory	NOUN
ejpam-4651	2	60	,	,	PUNCT
ejpam-4651	2	61	algebra	algebra	NOUN
ejpam-4651	2	62	and	and	CCONJ
ejpam-4651	2	63	analysis	analysis	NOUN
ejpam-4651	2	64	-	-	PUNCT
ejpam-4651	2	65	prism	prism	NOUN
ejpam-4651	2	66	,	,	PUNCT
ejpam-4651	2	67	msu	msu	PROPN
ejpam-4651	2	68	-	-	PUNCT
ejpam-4651	2	69	iligan	iligan	PROPN
ejpam-4651	2	70	institute	institute	PROPN
ejpam-4651	2	71	of	of	ADP
ejpam-4651	2	72	technology	technology	PROPN
ejpam-4651	2	73	,	,	PUNCT
ejpam-4651	2	74	9200	9200	NUM
ejpam-4651	2	75	iligan	iligan	ADJ
ejpam-4651	2	76	city	city	NOUN
ejpam-4651	2	77	,	,	PUNCT
ejpam-4651	2	78	philippines	philippine	NOUN
ejpam-4651	2	79	abstract	abstract	ADJ
ejpam-4651	2	80	.	.	PUNCT
ejpam-4651	3	1	a	a	DET
ejpam-4651	3	2	set	set	NOUN
ejpam-4651	3	3	s	s	NOUN
ejpam-4651	3	4	⊆	⊆	NUM
ejpam-4651	3	5	v	v	NOUN
ejpam-4651	3	6	(	(	PUNCT
ejpam-4651	3	7	g	g	NOUN
ejpam-4651	3	8	)	)	PUNCT
ejpam-4651	3	9	of	of	ADP
ejpam-4651	3	10	an	an	DET
ejpam-4651	3	11	undirected	undirected	ADJ
ejpam-4651	3	12	graph	graph	NOUN
ejpam-4651	3	13	g	g	PROPN
ejpam-4651	3	14	is	be	AUX
ejpam-4651	3	15	a	a	DET
ejpam-4651	3	16	clique	clique	NOUN
ejpam-4651	3	17	if	if	SCONJ
ejpam-4651	3	18	every	every	DET
ejpam-4651	3	19	two	two	NUM
ejpam-4651	3	20	distinct	distinct	ADJ
ejpam-4651	3	21	vertices	vertex	NOUN
ejpam-4651	3	22	in	in	ADP
ejpam-4651	3	23	s	s	NOUN
ejpam-4651	3	24	are	be	AUX
ejpam-4651	3	25	adjacent	adjacent	ADJ
ejpam-4651	3	26	.	.	PUNCT
ejpam-4651	4	1	a	a	DET
ejpam-4651	4	2	clique	clique	NOUN
ejpam-4651	4	3	is	be	AUX
ejpam-4651	4	4	a	a	DET
ejpam-4651	4	5	superclique	superclique	NOUN
ejpam-4651	4	6	if	if	SCONJ
ejpam-4651	4	7	for	for	ADP
ejpam-4651	4	8	every	every	DET
ejpam-4651	4	9	pair	pair	NOUN
ejpam-4651	4	10	of	of	ADP
ejpam-4651	4	11	distinct	distinct	ADJ
ejpam-4651	4	12	vertices	vertex	NOUN
ejpam-4651	4	13	v	v	ADP
ejpam-4651	4	14	,	,	PUNCT
ejpam-4651	4	15	w	w	PROPN
ejpam-4651	4	16	∈	∈	PROPN
ejpam-4651	4	17	s	s	NOUN
ejpam-4651	4	18	,	,	PUNCT
ejpam-4651	4	19	there	there	PRON
ejpam-4651	4	20	exists	exist	VERB
ejpam-4651	4	21	u	u	PROPN
ejpam-4651	4	22	∈	∈	PROPN
ejpam-4651	4	23	v	v	ADP
ejpam-4651	4	24	(	(	PUNCT
ejpam-4651	4	25	g	g	NOUN
ejpam-4651	4	26	)	)	PUNCT
ejpam-4651	4	27	\s	\	VERB
ejpam-4651	4	28	such	such	ADJ
ejpam-4651	4	29	that	that	SCONJ
ejpam-4651	4	30	u	u	PROPN
ejpam-4651	4	31	∈	∈	PROPN
ejpam-4651	4	32	ng(v	ng(v	PUNCT
ejpam-4651	4	33	)	)	PUNCT
ejpam-4651	4	34	\ng(w	\ng(w	NUM
ejpam-4651	4	35	)	)	PUNCT
ejpam-4651	4	36	or	or	CCONJ
ejpam-4651	4	37	u	u	PROPN
ejpam-4651	4	38	∈	∈	PROPN
ejpam-4651	4	39	ng(w	ng(w	NOUN
ejpam-4651	4	40	)	)	PUNCT
ejpam-4651	4	41	\ng(v	\ng(v	NOUN
ejpam-4651	4	42	)	)	PUNCT
ejpam-4651	4	43	.	.	PUNCT
ejpam-4651	5	1	the	the	DET
ejpam-4651	5	2	maximum	maximum	ADJ
ejpam-4651	5	3	cardinality	cardinality	NOUN
ejpam-4651	5	4	of	of	ADP
ejpam-4651	5	5	a	a	DET
ejpam-4651	5	6	clique	clique	NOUN
ejpam-4651	5	7	(	(	PUNCT
ejpam-4651	5	8	resp	resp	NOUN
ejpam-4651	5	9	.	.	PUNCT
ejpam-4651	6	1	superclique	superclique	NOUN
ejpam-4651	6	2	)	)	PUNCT
ejpam-4651	6	3	in	in	ADP
ejpam-4651	6	4	g	g	PROPN
ejpam-4651	6	5	is	be	AUX
ejpam-4651	6	6	called	call	VERB
ejpam-4651	6	7	the	the	DET
ejpam-4651	6	8	clique	clique	NOUN
ejpam-4651	6	9	(	(	PUNCT
ejpam-4651	6	10	resp	resp	NOUN
ejpam-4651	6	11	.	.	PUNCT
ejpam-4651	7	1	superclique	superclique	ADJ
ejpam-4651	7	2	)	)	PUNCT
ejpam-4651	7	3	number	number	NOUN
ejpam-4651	7	4	of	of	ADP
ejpam-4651	7	5	g.	g.	PROPN
ejpam-4651	7	6	in	in	ADP
ejpam-4651	7	7	this	this	DET
ejpam-4651	7	8	paper	paper	NOUN
ejpam-4651	7	9	,	,	PUNCT
ejpam-4651	7	10	we	we	PRON
ejpam-4651	7	11	determine	determine	VERB
ejpam-4651	7	12	the	the	DET
ejpam-4651	7	13	clique	clique	NOUN
ejpam-4651	7	14	and	and	CCONJ
ejpam-4651	7	15	superclique	superclique	ADJ
ejpam-4651	7	16	numbers	number	NOUN
ejpam-4651	7	17	of	of	ADP
ejpam-4651	7	18	some	some	DET
ejpam-4651	7	19	graphs	graph	NOUN
ejpam-4651	7	20	.	.	PUNCT
ejpam-4651	8	1	2020	2020	NUM
ejpam-4651	8	2	mathematics	mathematic	NOUN
ejpam-4651	8	3	subject	subject	NOUN
ejpam-4651	8	4	classifications	classification	NOUN
ejpam-4651	8	5	:	:	PUNCT
ejpam-4651	8	6	05c69	05c69	X
ejpam-4651	8	7	key	key	ADJ
ejpam-4651	8	8	words	word	NOUN
ejpam-4651	8	9	and	and	CCONJ
ejpam-4651	8	10	phrases	phrase	NOUN
ejpam-4651	8	11	:	:	PUNCT
ejpam-4651	8	12	clique	clique	NOUN
ejpam-4651	8	13	,	,	PUNCT
ejpam-4651	8	14	clique	clique	ADJ
ejpam-4651	8	15	number	number	NOUN
ejpam-4651	8	16	,	,	PUNCT
ejpam-4651	8	17	superclique	superclique	ADJ
ejpam-4651	8	18	,	,	PUNCT
ejpam-4651	8	19	superclique	superclique	ADJ
ejpam-4651	8	20	number	number	NOUN
ejpam-4651	8	21	1	1	NUM
ejpam-4651	8	22	.	.	PUNCT
ejpam-4651	9	1	introduction	introduction	NOUN
ejpam-4651	9	2	recently	recently	ADV
ejpam-4651	9	3	,	,	PUNCT
ejpam-4651	9	4	dela	dela	PROPN
ejpam-4651	9	5	cerna	cerna	NOUN
ejpam-4651	9	6	and	and	CCONJ
ejpam-4651	9	7	canoy	canoy	ADJ
ejpam-4651	9	8	(	(	PUNCT
ejpam-4651	9	9	see	see	VERB
ejpam-4651	9	10	[	[	X
ejpam-4651	9	11	3	3	NUM
ejpam-4651	9	12	]	]	PUNCT
ejpam-4651	9	13	)	)	PUNCT
ejpam-4651	9	14	initiated	initiate	VERB
ejpam-4651	9	15	the	the	DET
ejpam-4651	9	16	study	study	NOUN
ejpam-4651	9	17	of	of	ADP
ejpam-4651	9	18	the	the	DET
ejpam-4651	9	19	concept	concept	NOUN
ejpam-4651	9	20	of	of	ADP
ejpam-4651	9	21	superclique	superclique	NOUN
ejpam-4651	9	22	in	in	ADP
ejpam-4651	9	23	a	a	DET
ejpam-4651	9	24	graph	graph	NOUN
ejpam-4651	9	25	.	.	PUNCT
ejpam-4651	10	1	it	it	PRON
ejpam-4651	10	2	is	be	AUX
ejpam-4651	10	3	known	know	VERB
ejpam-4651	10	4	that	that	SCONJ
ejpam-4651	10	5	the	the	DET
ejpam-4651	10	6	superclique	superclique	ADJ
ejpam-4651	10	7	number	number	NOUN
ejpam-4651	10	8	of	of	ADP
ejpam-4651	10	9	a	a	DET
ejpam-4651	10	10	graph	graph	NOUN
ejpam-4651	10	11	is	be	AUX
ejpam-4651	10	12	at	at	ADP
ejpam-4651	10	13	most	most	ADV
ejpam-4651	10	14	equal	equal	ADJ
ejpam-4651	10	15	to	to	ADP
ejpam-4651	10	16	the	the	DET
ejpam-4651	10	17	clique	clique	ADJ
ejpam-4651	10	18	number	number	NOUN
ejpam-4651	10	19	of	of	ADP
ejpam-4651	10	20	the	the	DET
ejpam-4651	10	21	graph	graph	NOUN
ejpam-4651	10	22	.	.	PUNCT
ejpam-4651	11	1	moreover	moreover	ADV
ejpam-4651	11	2	,	,	PUNCT
ejpam-4651	11	3	it	it	PRON
ejpam-4651	11	4	was	be	AUX
ejpam-4651	11	5	shown	show	VERB
ejpam-4651	11	6	that	that	SCONJ
ejpam-4651	11	7	any	any	DET
ejpam-4651	11	8	two	two	NUM
ejpam-4651	11	9	positive	positive	ADJ
ejpam-4651	11	10	integers	integer	NOUN
ejpam-4651	11	11	a	a	PRON
ejpam-4651	11	12	and	and	CCONJ
ejpam-4651	11	13	b	b	NOUN
ejpam-4651	11	14	with	with	ADP
ejpam-4651	11	15	2	2	NUM
ejpam-4651	11	16	≤	≤	NOUN
ejpam-4651	11	17	a	a	DET
ejpam-4651	11	18	≤	≤	NUM
ejpam-4651	11	19	b	b	NOUN
ejpam-4651	11	20	are	be	AUX
ejpam-4651	11	21	,	,	PUNCT
ejpam-4651	11	22	respectively	respectively	ADV
ejpam-4651	11	23	,	,	PUNCT
ejpam-4651	11	24	realizable	realizable	ADJ
ejpam-4651	11	25	as	as	ADP
ejpam-4651	11	26	the	the	DET
ejpam-4651	11	27	superclique	superclique	ADJ
ejpam-4651	11	28	number	number	NOUN
ejpam-4651	11	29	and	and	CCONJ
ejpam-4651	11	30	clique	clique	ADJ
ejpam-4651	11	31	number	number	NOUN
ejpam-4651	11	32	of	of	ADP
ejpam-4651	11	33	a	a	DET
ejpam-4651	11	34	connected	connected	ADJ
ejpam-4651	11	35	graph	graph	NOUN
ejpam-4651	11	36	.	.	PUNCT
ejpam-4651	12	1	this	this	DET
ejpam-4651	12	2	result	result	NOUN
ejpam-4651	12	3	also	also	ADV
ejpam-4651	12	4	implies	imply	VERB
ejpam-4651	12	5	that	that	SCONJ
ejpam-4651	12	6	the	the	DET
ejpam-4651	12	7	difference	difference	NOUN
ejpam-4651	12	8	of	of	ADP
ejpam-4651	12	9	the	the	DET
ejpam-4651	12	10	clique	clique	NOUN
ejpam-4651	12	11	number	number	NOUN
ejpam-4651	12	12	and	and	CCONJ
ejpam-4651	12	13	the	the	DET
ejpam-4651	12	14	superclique	superclique	ADJ
ejpam-4651	12	15	number	number	NOUN
ejpam-4651	12	16	can	can	AUX
ejpam-4651	12	17	be	be	AUX
ejpam-4651	12	18	made	make	VERB
ejpam-4651	12	19	arbitrarily	arbitrarily	ADV
ejpam-4651	12	20	large	large	ADJ
ejpam-4651	12	21	.	.	PUNCT
ejpam-4651	13	1	as	as	SCONJ
ejpam-4651	13	2	pointed	point	VERB
ejpam-4651	13	3	out	out	ADP
ejpam-4651	13	4	in	in	ADP
ejpam-4651	13	5	an	an	DET
ejpam-4651	13	6	earlier	early	ADJ
ejpam-4651	13	7	study	study	NOUN
ejpam-4651	13	8	,	,	PUNCT
ejpam-4651	13	9	superclique	superclique	ADJ
ejpam-4651	13	10	and	and	CCONJ
ejpam-4651	13	11	superclique	superclique	ADJ
ejpam-4651	13	12	number	number	NOUN
ejpam-4651	13	13	were	be	AUX
ejpam-4651	13	14	introduced	introduce	VERB
ejpam-4651	13	15	and	and	CCONJ
ejpam-4651	13	16	first	first	ADV
ejpam-4651	13	17	used	use	VERB
ejpam-4651	13	18	in	in	ADP
ejpam-4651	13	19	the	the	DET
ejpam-4651	13	20	study	study	NOUN
ejpam-4651	13	21	of	of	ADP
ejpam-4651	13	22	acal	acal	ADJ
ejpam-4651	13	23	,	,	PUNCT
ejpam-4651	13	24	monsanto	monsanto	PROPN
ejpam-4651	13	25	,	,	PUNCT
ejpam-4651	13	26	sumaoy	sumaoy	NOUN
ejpam-4651	13	27	,	,	PUNCT
ejpam-4651	13	28	and	and	CCONJ
ejpam-4651	13	29	rara	rara	NOUN
ejpam-4651	13	30	in	in	ADP
ejpam-4651	13	31	[	[	X
ejpam-4651	13	32	1	1	NUM
ejpam-4651	13	33	]	]	PUNCT
ejpam-4651	13	34	,	,	PUNCT
ejpam-4651	13	35	[	[	X
ejpam-4651	13	36	14	14	NUM
ejpam-4651	13	37	]	]	PUNCT
ejpam-4651	13	38	,	,	PUNCT
ejpam-4651	13	39	and	and	CCONJ
ejpam-4651	13	40	[	[	X
ejpam-4651	13	41	21	21	NUM
ejpam-4651	13	42	]	]	PUNCT
ejpam-4651	13	43	when	when	SCONJ
ejpam-4651	13	44	they	they	PRON
ejpam-4651	13	45	investigated	investigate	VERB
ejpam-4651	13	46	some	some	DET
ejpam-4651	13	47	variations	variation	NOUN
ejpam-4651	13	48	of	of	ADP
ejpam-4651	13	49	resolving	resolve	VERB
ejpam-4651	13	50	domination	domination	NOUN
ejpam-4651	13	51	for	for	ADP
ejpam-4651	13	52	graphs	graph	NOUN
ejpam-4651	13	53	under	under	ADP
ejpam-4651	13	54	some	some	DET
ejpam-4651	13	55	binary	binary	ADJ
ejpam-4651	13	56	operations	operation	NOUN
ejpam-4651	13	57	.	.	PUNCT
ejpam-4651	14	1	their	their	PRON
ejpam-4651	14	2	study	study	NOUN
ejpam-4651	14	3	was	be	AUX
ejpam-4651	14	4	motivated	motivate	VERB
ejpam-4651	14	5	by	by	ADP
ejpam-4651	14	6	the	the	DET
ejpam-4651	14	7	concepts	concept	NOUN
ejpam-4651	14	8	of	of	ADP
ejpam-4651	14	9	strong	strong	ADJ
ejpam-4651	14	10	resolving	resolving	NOUN
ejpam-4651	14	11	set	set	NOUN
ejpam-4651	14	12	,	,	PUNCT
ejpam-4651	14	13	strong	strong	ADJ
ejpam-4651	14	14	metric	metric	ADJ
ejpam-4651	14	15	dimension	dimension	NOUN
ejpam-4651	14	16	,	,	PUNCT
ejpam-4651	14	17	and	and	CCONJ
ejpam-4651	14	18	resolving	resolve	VERB
ejpam-4651	14	19	domination	domination	NOUN
ejpam-4651	14	20	which	which	PRON
ejpam-4651	14	21	were	be	AUX
ejpam-4651	14	22	introduced	introduce	VERB
ejpam-4651	14	23	and	and	CCONJ
ejpam-4651	14	24	studied	study	VERB
ejpam-4651	14	25	in	in	ADP
ejpam-4651	14	26	[	[	X
ejpam-4651	14	27	2	2	NUM
ejpam-4651	14	28	]	]	PUNCT
ejpam-4651	14	29	,	,	PUNCT
ejpam-4651	14	30	[	[	X
ejpam-4651	14	31	16	16	NUM
ejpam-4651	14	32	]	]	PUNCT
ejpam-4651	14	33	,	,	PUNCT
ejpam-4651	14	34	and	and	CCONJ
ejpam-4651	14	35	[	[	X
ejpam-4651	14	36	19	19	NUM
ejpam-4651	14	37	]	]	PUNCT
ejpam-4651	14	38	.	.	PUNCT
ejpam-4651	15	1	these	these	DET
ejpam-4651	15	2	latter	latter	ADJ
ejpam-4651	15	3	studies	study	NOUN
ejpam-4651	15	4	,	,	PUNCT
ejpam-4651	15	5	in	in	ADP
ejpam-4651	15	6	turn	turn	NOUN
ejpam-4651	15	7	,	,	PUNCT
ejpam-4651	15	8	came	come	VERB
ejpam-4651	15	9	after	after	ADP
ejpam-4651	15	10	slater	slater	NOUN
ejpam-4651	15	11	in	in	ADP
ejpam-4651	15	12	[	[	X
ejpam-4651	15	13	20	20	NUM
ejpam-4651	15	14	]	]	PUNCT
ejpam-4651	15	15	introduced	introduce	VERB
ejpam-4651	15	16	the	the	DET
ejpam-4651	15	17	concepts	concept	NOUN
ejpam-4651	15	18	of	of	ADP
ejpam-4651	15	19	resolving	resolve	VERB
ejpam-4651	15	20	set	set	VERB
ejpam-4651	15	21	and	and	CCONJ
ejpam-4651	15	22	metric	metric	ADJ
ejpam-4651	15	23	dimension	dimension	NOUN
ejpam-4651	15	24	.	.	PUNCT
ejpam-4651	16	1	the	the	DET
ejpam-4651	16	2	same	same	ADJ
ejpam-4651	16	3	concepts	concept	NOUN
ejpam-4651	16	4	were	be	AUX
ejpam-4651	16	5	also	also	ADV
ejpam-4651	16	6	independently	independently	ADV
ejpam-4651	16	7	investigated	investigate	VERB
ejpam-4651	16	8	by	by	ADP
ejpam-4651	16	9	harary	harary	NOUN
ejpam-4651	16	10	and	and	CCONJ
ejpam-4651	16	11	melter	melter	NOUN
ejpam-4651	16	12	in	in	ADP
ejpam-4651	16	13	[	[	X
ejpam-4651	16	14	9	9	NUM
ejpam-4651	16	15	]	]	PUNCT
ejpam-4651	16	16	.	.	PUNCT
ejpam-4651	17	1	chartrand	chartrand	PROPN
ejpam-4651	17	2	et	et	PROPN
ejpam-4651	17	3	al	al	PROPN
ejpam-4651	17	4	.	.	PUNCT
ejpam-4651	18	1	(	(	PUNCT
ejpam-4651	18	2	see	see	VERB
ejpam-4651	18	3	[	[	X
ejpam-4651	18	4	4	4	NUM
ejpam-4651	18	5	]	]	PUNCT
ejpam-4651	18	6	)	)	PUNCT
ejpam-4651	18	7	also	also	ADV
ejpam-4651	18	8	studied	study	VERB
ejpam-4651	18	9	resolving	resolve	VERB
ejpam-4651	18	10	set	set	VERB
ejpam-4651	18	11	and	and	CCONJ
ejpam-4651	18	12	metric	metric	ADJ
ejpam-4651	18	13	dimension	dimension	NOUN
ejpam-4651	18	14	of	of	ADP
ejpam-4651	18	15	a	a	DET
ejpam-4651	18	16	graph	graph	NOUN
ejpam-4651	18	17	.	.	PUNCT
ejpam-4651	19	1	domination	domination	NOUN
ejpam-4651	19	2	and	and	CCONJ
ejpam-4651	19	3	some	some	DET
ejpam-4651	19	4	variations	variation	NOUN
ejpam-4651	19	5	of	of	ADP
ejpam-4651	19	6	domination	domination	NOUN
ejpam-4651	19	7	are	be	AUX
ejpam-4651	19	8	found	find	VERB
ejpam-4651	19	9	in	in	ADP
ejpam-4651	19	10	[	[	X
ejpam-4651	19	11	10	10	NUM
ejpam-4651	19	12	]	]	PUNCT
ejpam-4651	19	13	.	.	PUNCT
ejpam-4651	20	1	other	other	ADJ
ejpam-4651	20	2	studies	study	NOUN
ejpam-4651	20	3	on	on	ADP
ejpam-4651	20	4	domination	domination	NOUN
ejpam-4651	20	5	are	be	AUX
ejpam-4651	20	6	in	in	ADP
ejpam-4651	20	7	[	[	X
ejpam-4651	20	8	11	11	NUM
ejpam-4651	20	9	]	]	PUNCT
ejpam-4651	20	10	,	,	PUNCT
ejpam-4651	20	11	[	[	X
ejpam-4651	20	12	12	12	NUM
ejpam-4651	20	13	]	]	PUNCT
ejpam-4651	20	14	,	,	PUNCT
ejpam-4651	20	15	[	[	X
ejpam-4651	20	16	17	17	NUM
ejpam-4651	20	17	]	]	PUNCT
ejpam-4651	20	18	,	,	PUNCT
ejpam-4651	20	19	and	and	CCONJ
ejpam-4651	20	20	[	[	X
ejpam-4651	20	21	22	22	NUM
ejpam-4651	20	22	]	]	PUNCT
ejpam-4651	20	23	.	.	PUNCT
ejpam-4651	21	1	some	some	DET
ejpam-4651	21	2	studies	study	NOUN
ejpam-4651	21	3	involving	involve	VERB
ejpam-4651	21	4	cliques	clique	NOUN
ejpam-4651	21	5	can	can	AUX
ejpam-4651	21	6	be	be	AUX
ejpam-4651	21	7	found	find	VERB
ejpam-4651	21	8	in	in	ADP
ejpam-4651	21	9	[	[	X
ejpam-4651	21	10	5	5	NUM
ejpam-4651	21	11	]	]	PUNCT
ejpam-4651	21	12	,	,	PUNCT
ejpam-4651	21	13	[	[	X
ejpam-4651	21	14	6	6	NUM
ejpam-4651	21	15	]	]	PUNCT
ejpam-4651	21	16	,	,	PUNCT
ejpam-4651	21	17	[	[	X
ejpam-4651	21	18	7	7	NUM
ejpam-4651	21	19	]	]	PUNCT
ejpam-4651	21	20	,	,	PUNCT
ejpam-4651	21	21	[	[	X
ejpam-4651	21	22	8	8	NUM
ejpam-4651	21	23	]	]	PUNCT
ejpam-4651	21	24	,	,	PUNCT
ejpam-4651	21	25	[	[	X
ejpam-4651	21	26	13	13	NUM
ejpam-4651	21	27	]	]	PUNCT
ejpam-4651	21	28	,	,	PUNCT
ejpam-4651	21	29	[	[	X
ejpam-4651	21	30	15	15	NUM
ejpam-4651	21	31	]	]	PUNCT
ejpam-4651	21	32	,	,	PUNCT
ejpam-4651	21	33	[	[	X
ejpam-4651	21	34	18	18	NUM
ejpam-4651	21	35	]	]	PUNCT
ejpam-4651	21	36	,	,	PUNCT
ejpam-4651	21	37	and	and	CCONJ
ejpam-4651	21	38	[	[	X
ejpam-4651	21	39	23	23	NUM
ejpam-4651	21	40	]	]	PUNCT
ejpam-4651	21	41	.	.	PUNCT
ejpam-4651	22	1	∗corresponding	∗corresponde	VERB
ejpam-4651	22	2	author	author	NOUN
ejpam-4651	22	3	.	.	PUNCT
ejpam-4651	23	1	doi	doi	NOUN
ejpam-4651	23	2	:	:	PUNCT
ejpam-4651	23	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4651	https://doi.org/10.29020/nybg.ejpam.v16i1.4651	ADP
ejpam-4651	23	4	email	email	NOUN
ejpam-4651	23	5	addresses	address	VERB
ejpam-4651	23	6	:	:	PUNCT
ejpam-4651	23	7	,	,	PUNCT
ejpam-4651	23	8	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4651	23	9	(	(	PUNCT
ejpam-4651	23	10	s.	s.	PROPN
ejpam-4651	23	11	canoy	canoy	PROPN
ejpam-4651	23	12	,	,	PUNCT
ejpam-4651	23	13	jr	jr	PROPN
ejpam-4651	23	14	.	.	PROPN
ejpam-4651	23	15	)	)	PUNCT
ejpam-4651	23	16	,	,	PUNCT
ejpam-4651	23	17	ramil.delacerna@g.msuiit.edu.ph	ramil.delacerna@g.msuiit.edu.ph	PROPN
ejpam-4651	23	18	(	(	PUNCT
ejpam-4651	23	19	r.	r.	PROPN
ejpam-4651	23	20	dela	dela	PROPN
ejpam-4651	23	21	cerna	cerna	PROPN
ejpam-4651	23	22	)	)	PUNCT
ejpam-4651	23	23	,	,	PUNCT
ejpam-4651	23	24	armalene.abragan@g.msuiit.edu.ph	armalene.abragan@g.msuiit.edu.ph	PROPN
ejpam-4651	23	25	(	(	PUNCT
ejpam-4651	23	26	a.	a.	NOUN
ejpam-4651	23	27	abragan	abragan	PROPN
ejpam-4651	23	28	)	)	PUNCT
ejpam-4651	23	29	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4651	24	1	243	243	NUM
ejpam-4651	25	1	©	©	PROPN
ejpam-4651	25	2	2023	2023	NUM
ejpam-4651	25	3	ejpam	ejpam	NOUN
ejpam-4651	25	4	all	all	DET
ejpam-4651	25	5	rights	right	NOUN
ejpam-4651	25	6	reserved	reserve	VERB
ejpam-4651	25	7	.	.	PUNCT
ejpam-4651	26	1	s.	s.	PROPN
ejpam-4651	26	2	canoy	canoy	PROPN
ejpam-4651	26	3	,	,	PUNCT
ejpam-4651	26	4	jr	jr	PROPN
ejpam-4651	26	5	.	.	PROPN
ejpam-4651	26	6	,	,	PUNCT
ejpam-4651	26	7	r.	r.	PROPN
ejpam-4651	26	8	dela	dela	PROPN
ejpam-4651	26	9	cerna	cerna	PROPN
ejpam-4651	26	10	,	,	PUNCT
ejpam-4651	26	11	a.	a.	NOUN
ejpam-4651	26	12	abragan	abragan	PROPN
ejpam-4651	26	13	/	/	SYM
ejpam-4651	26	14	eur	eur	PROPN
ejpam-4651	26	15	.	.	PUNCT
ejpam-4651	27	1	j.	j.	PROPN
ejpam-4651	27	2	pure	pure	PROPN
ejpam-4651	27	3	appl	appl	PROPN
ejpam-4651	27	4	.	.	PROPN
ejpam-4651	27	5	math	math	PROPN
ejpam-4651	27	6	,	,	PUNCT
ejpam-4651	27	7	16	16	NUM
ejpam-4651	27	8	(	(	PUNCT
ejpam-4651	27	9	1	1	NUM
ejpam-4651	27	10	)	)	PUNCT
ejpam-4651	27	11	(	(	PUNCT
ejpam-4651	27	12	2023	2023	NUM
ejpam-4651	27	13	)	)	PUNCT
ejpam-4651	27	14	,	,	PUNCT
ejpam-4651	27	15	243	243	NUM
ejpam-4651	27	16	-	-	SYM
ejpam-4651	27	17	252	252	NUM
ejpam-4651	27	18	244	244	NUM
ejpam-4651	27	19	2	2	NUM
ejpam-4651	27	20	.	.	PUNCT
ejpam-4651	27	21	terminologies	terminology	NOUN
ejpam-4651	27	22	and	and	CCONJ
ejpam-4651	27	23	notations	notation	NOUN
ejpam-4651	27	24	let	let	VERB
ejpam-4651	27	25	g	g	NOUN
ejpam-4651	27	26	=	=	SYM
ejpam-4651	27	27	(	(	PUNCT
ejpam-4651	27	28	v	v	NOUN
ejpam-4651	27	29	(	(	PUNCT
ejpam-4651	27	30	g	g	NOUN
ejpam-4651	27	31	)	)	PUNCT
ejpam-4651	27	32	,	,	PUNCT
ejpam-4651	27	33	e(g	e(g	PROPN
ejpam-4651	27	34	)	)	PUNCT
ejpam-4651	27	35	)	)	PUNCT
ejpam-4651	27	36	be	be	AUX
ejpam-4651	27	37	a	a	DET
ejpam-4651	27	38	simple	simple	ADJ
ejpam-4651	27	39	undirected	undirected	ADJ
ejpam-4651	27	40	graph	graph	NOUN
ejpam-4651	27	41	.	.	PUNCT
ejpam-4651	28	1	the	the	DET
ejpam-4651	28	2	distance	distance	NOUN
ejpam-4651	28	3	between	between	ADP
ejpam-4651	28	4	two	two	NUM
ejpam-4651	28	5	vertices	vertex	NOUN
ejpam-4651	28	6	u	u	NOUN
ejpam-4651	28	7	and	and	CCONJ
ejpam-4651	28	8	v	v	NOUN
ejpam-4651	28	9	of	of	ADP
ejpam-4651	28	10	g	g	NOUN
ejpam-4651	28	11	,	,	PUNCT
ejpam-4651	28	12	denoted	denote	VERB
ejpam-4651	28	13	by	by	ADP
ejpam-4651	28	14	dg(u	dg(u	NOUN
ejpam-4651	28	15	,	,	PUNCT
ejpam-4651	28	16	v	v	NOUN
ejpam-4651	28	17	)	)	PUNCT
ejpam-4651	28	18	,	,	PUNCT
ejpam-4651	28	19	is	be	AUX
ejpam-4651	28	20	equal	equal	ADJ
ejpam-4651	28	21	to	to	ADP
ejpam-4651	28	22	the	the	DET
ejpam-4651	28	23	length	length	NOUN
ejpam-4651	28	24	of	of	ADP
ejpam-4651	28	25	a	a	DET
ejpam-4651	28	26	shortest	short	ADJ
ejpam-4651	28	27	path	path	NOUN
ejpam-4651	28	28	connecting	connect	VERB
ejpam-4651	28	29	u	u	NOUN
ejpam-4651	28	30	and	and	CCONJ
ejpam-4651	28	31	v.	v.	ADP
ejpam-4651	28	32	any	any	DET
ejpam-4651	28	33	path	path	NOUN
ejpam-4651	28	34	connecting	connect	VERB
ejpam-4651	28	35	u	u	NOUN
ejpam-4651	28	36	and	and	CCONJ
ejpam-4651	28	37	v	v	NOUN
ejpam-4651	28	38	of	of	ADP
ejpam-4651	28	39	length	length	NOUN
ejpam-4651	28	40	dg(u	dg(u	ADJ
ejpam-4651	28	41	,	,	PUNCT
ejpam-4651	28	42	v	v	NOUN
ejpam-4651	28	43	)	)	PUNCT
ejpam-4651	28	44	is	be	AUX
ejpam-4651	28	45	called	call	VERB
ejpam-4651	28	46	a	a	DET
ejpam-4651	28	47	u	u	NOUN
ejpam-4651	28	48	-	-	NOUN
ejpam-4651	28	49	v	v	ADJ
ejpam-4651	28	50	geodesic	geodesic	NOUN
ejpam-4651	28	51	.	.	PUNCT
ejpam-4651	29	1	the	the	DET
ejpam-4651	29	2	open	open	ADJ
ejpam-4651	29	3	neighbourhood	neighbourhood	NOUN
ejpam-4651	29	4	of	of	ADP
ejpam-4651	29	5	a	a	DET
ejpam-4651	29	6	vertex	vertex	NOUN
ejpam-4651	29	7	v	v	NOUN
ejpam-4651	29	8	of	of	ADP
ejpam-4651	29	9	g	g	PROPN
ejpam-4651	29	10	is	be	AUX
ejpam-4651	29	11	the	the	DET
ejpam-4651	29	12	set	set	NOUN
ejpam-4651	29	13	ng(v	ng(v	PUNCT
ejpam-4651	29	14	)	)	PUNCT
ejpam-4651	29	15	=	=	SYM
ejpam-4651	30	1	{	{	PUNCT
ejpam-4651	30	2	u	u	NOUN
ejpam-4651	30	3	∈	∈	PROPN
ejpam-4651	30	4	v	v	NOUN
ejpam-4651	30	5	(	(	PUNCT
ejpam-4651	30	6	g	g	NOUN
ejpam-4651	30	7	)	)	PUNCT
ejpam-4651	30	8	:	:	PUNCT
ejpam-4651	30	9	uv	uv	PROPN
ejpam-4651	30	10	∈	∈	PROPN
ejpam-4651	30	11	e(g	e(g	PROPN
ejpam-4651	30	12	)	)	PUNCT
ejpam-4651	30	13	}	}	PUNCT
ejpam-4651	30	14	and	and	CCONJ
ejpam-4651	30	15	its	its	PRON
ejpam-4651	30	16	closed	closed	ADJ
ejpam-4651	30	17	neighbourhood	neighbourhood	NOUN
ejpam-4651	30	18	is	be	AUX
ejpam-4651	30	19	the	the	DET
ejpam-4651	30	20	set	set	NOUN
ejpam-4651	30	21	ng[v	ng[v	NOUN
ejpam-4651	30	22	]	]	X
ejpam-4651	30	23	=	=	SYM
ejpam-4651	30	24	ng(v	ng(v	X
ejpam-4651	30	25	)	)	PUNCT
ejpam-4651	30	26	∪	∪	ADP
ejpam-4651	30	27	{	{	PUNCT
ejpam-4651	30	28	v	v	NOUN
ejpam-4651	30	29	}	}	PUNCT
ejpam-4651	30	30	.	.	PUNCT
ejpam-4651	31	1	the	the	DET
ejpam-4651	31	2	open	open	ADJ
ejpam-4651	31	3	neighbourhood	neighbourhood	NOUN
ejpam-4651	31	4	of	of	ADP
ejpam-4651	31	5	a	a	DET
ejpam-4651	31	6	subset	subset	NOUN
ejpam-4651	31	7	s	s	NOUN
ejpam-4651	31	8	of	of	ADP
ejpam-4651	31	9	v	v	NOUN
ejpam-4651	31	10	(	(	PUNCT
ejpam-4651	31	11	g	g	NOUN
ejpam-4651	31	12	)	)	PUNCT
ejpam-4651	31	13	is	be	AUX
ejpam-4651	31	14	the	the	DET
ejpam-4651	31	15	set	set	NOUN
ejpam-4651	31	16	ng(s	ng(s	NOUN
ejpam-4651	31	17	)	)	PUNCT
ejpam-4651	31	18	=	=	SYM
ejpam-4651	31	19	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-4651	31	20	)	)	PUNCT
ejpam-4651	31	21	and	and	CCONJ
ejpam-4651	31	22	its	its	PRON
ejpam-4651	31	23	closed	closed	ADJ
ejpam-4651	31	24	neighbourhood	neighbourhood	NOUN
ejpam-4651	31	25	is	be	AUX
ejpam-4651	31	26	the	the	DET
ejpam-4651	31	27	set	set	VERB
ejpam-4651	31	28	ng[s	ng[	NOUN
ejpam-4651	31	29	]	]	PUNCT
ejpam-4651	31	30	=	=	SYM
ejpam-4651	31	31	ng(s	ng(s	X
ejpam-4651	31	32	)	)	PUNCT
ejpam-4651	31	33	∪	∪	ADP
ejpam-4651	31	34	s.	s.	PROPN
ejpam-4651	31	35	the	the	DET
ejpam-4651	31	36	degree	degree	NOUN
ejpam-4651	31	37	of	of	ADP
ejpam-4651	31	38	v	v	NOUN
ejpam-4651	31	39	,	,	PUNCT
ejpam-4651	31	40	denoted	denote	VERB
ejpam-4651	31	41	by	by	ADP
ejpam-4651	31	42	degg(v	degg(v	PROPN
ejpam-4651	31	43	)	)	PUNCT
ejpam-4651	31	44	,	,	PUNCT
ejpam-4651	31	45	is	be	AUX
ejpam-4651	31	46	equal	equal	ADJ
ejpam-4651	31	47	to	to	ADP
ejpam-4651	31	48	|ng(v)|	|ng(v)|	NOUN
ejpam-4651	31	49	.	.	PUNCT
ejpam-4651	32	1	a	a	DET
ejpam-4651	32	2	set	set	NOUN
ejpam-4651	32	3	s	s	NOUN
ejpam-4651	32	4	⊆	⊆	NUM
ejpam-4651	32	5	v	v	NOUN
ejpam-4651	32	6	(	(	PUNCT
ejpam-4651	32	7	g	g	NOUN
ejpam-4651	32	8	)	)	PUNCT
ejpam-4651	32	9	is	be	AUX
ejpam-4651	32	10	a	a	DET
ejpam-4651	32	11	dominating	dominating	NOUN
ejpam-4651	32	12	set	set	NOUN
ejpam-4651	32	13	of	of	ADP
ejpam-4651	32	14	g	g	PROPN
ejpam-4651	32	15	if	if	SCONJ
ejpam-4651	32	16	ng[s	ng[	NOUN
ejpam-4651	32	17	]	]	PUNCT
ejpam-4651	32	18	=	=	SYM
ejpam-4651	32	19	v	v	NOUN
ejpam-4651	32	20	(	(	PUNCT
ejpam-4651	32	21	g	g	NOUN
ejpam-4651	32	22	)	)	PUNCT
ejpam-4651	32	23	.	.	PUNCT
ejpam-4651	33	1	the	the	DET
ejpam-4651	33	2	smallest	small	ADJ
ejpam-4651	33	3	cardinality	cardinality	NOUN
ejpam-4651	33	4	of	of	ADP
ejpam-4651	33	5	a	a	DET
ejpam-4651	33	6	dominating	dominating	NOUN
ejpam-4651	33	7	set	set	NOUN
ejpam-4651	33	8	of	of	ADP
ejpam-4651	33	9	g	g	NOUN
ejpam-4651	33	10	,	,	PUNCT
ejpam-4651	33	11	denoted	denote	VERB
ejpam-4651	33	12	by	by	ADP
ejpam-4651	33	13	γ(g	γ(g	PROPN
ejpam-4651	33	14	)	)	PUNCT
ejpam-4651	33	15	,	,	PUNCT
ejpam-4651	33	16	is	be	AUX
ejpam-4651	33	17	called	call	VERB
ejpam-4651	33	18	the	the	DET
ejpam-4651	33	19	domination	domination	NOUN
ejpam-4651	33	20	number	number	NOUN
ejpam-4651	33	21	of	of	ADP
ejpam-4651	33	22	g.	g.	PROPN
ejpam-4651	33	23	a	a	DET
ejpam-4651	33	24	dominating	dominating	NOUN
ejpam-4651	33	25	set	set	NOUN
ejpam-4651	33	26	of	of	ADP
ejpam-4651	33	27	g	g	NOUN
ejpam-4651	33	28	with	with	ADP
ejpam-4651	33	29	with	with	ADP
ejpam-4651	33	30	cardinality	cardinality	PROPN
ejpam-4651	33	31	γ(g	γ(g	PROPN
ejpam-4651	33	32	)	)	PUNCT
ejpam-4651	33	33	is	be	AUX
ejpam-4651	33	34	called	call	VERB
ejpam-4651	33	35	a	a	DET
ejpam-4651	33	36	γ	γ	NOUN
ejpam-4651	33	37	-	-	PUNCT
ejpam-4651	33	38	set	set	NOUN
ejpam-4651	33	39	of	of	ADP
ejpam-4651	33	40	g.	g.	PROPN
ejpam-4651	33	41	a	a	DET
ejpam-4651	33	42	set	set	NOUN
ejpam-4651	33	43	s	s	PROPN
ejpam-4651	33	44	⊆	⊆	NUM
ejpam-4651	33	45	v	v	NOUN
ejpam-4651	33	46	(	(	PUNCT
ejpam-4651	33	47	g	g	NOUN
ejpam-4651	33	48	)	)	PUNCT
ejpam-4651	33	49	is	be	AUX
ejpam-4651	33	50	a	a	DET
ejpam-4651	33	51	clique	clique	NOUN
ejpam-4651	33	52	in	in	ADP
ejpam-4651	33	53	a	a	DET
ejpam-4651	33	54	graph	graph	NOUN
ejpam-4651	33	55	g	g	NOUN
ejpam-4651	33	56	if	if	SCONJ
ejpam-4651	33	57	the	the	DET
ejpam-4651	33	58	graph	graph	NOUN
ejpam-4651	33	59	g[s	g[	NOUN
ejpam-4651	33	60	]	]	PUNCT
ejpam-4651	33	61	=	=	SYM
ejpam-4651	33	62	⟨s⟩	⟨s⟩	PROPN
ejpam-4651	33	63	induced	induce	VERB
ejpam-4651	33	64	by	by	ADP
ejpam-4651	33	65	s	s	PROPN
ejpam-4651	33	66	is	be	AUX
ejpam-4651	33	67	a	a	DET
ejpam-4651	33	68	complete	complete	ADJ
ejpam-4651	33	69	subgraph	subgraph	NOUN
ejpam-4651	33	70	of	of	ADP
ejpam-4651	33	71	g.	g.	PROPN
ejpam-4651	33	72	a	a	DET
ejpam-4651	33	73	clique	clique	NOUN
ejpam-4651	33	74	c	c	PROPN
ejpam-4651	33	75	in	in	ADP
ejpam-4651	33	76	g	g	PROPN
ejpam-4651	33	77	is	be	AUX
ejpam-4651	33	78	called	call	VERB
ejpam-4651	33	79	a	a	DET
ejpam-4651	33	80	superclique	superclique	NOUN
ejpam-4651	33	81	if	if	SCONJ
ejpam-4651	33	82	for	for	ADP
ejpam-4651	33	83	every	every	DET
ejpam-4651	33	84	pair	pair	NOUN
ejpam-4651	33	85	of	of	ADP
ejpam-4651	33	86	distinct	distinct	ADJ
ejpam-4651	33	87	vertices	vertex	NOUN
ejpam-4651	33	88	u	u	NOUN
ejpam-4651	33	89	,	,	PUNCT
ejpam-4651	33	90	v	v	NOUN
ejpam-4651	33	91	∈	∈	ADJ
ejpam-4651	33	92	c	c	NOUN
ejpam-4651	33	93	,	,	PUNCT
ejpam-4651	33	94	there	there	PRON
ejpam-4651	33	95	exists	exist	VERB
ejpam-4651	33	96	w	w	PROPN
ejpam-4651	33	97	∈	∈	PROPN
ejpam-4651	33	98	v	v	ADP
ejpam-4651	33	99	(	(	PUNCT
ejpam-4651	33	100	g	g	NOUN
ejpam-4651	33	101	)	)	PUNCT
ejpam-4651	33	102	\	\	PUNCT
ejpam-4651	34	1	c	c	NOUN
ejpam-4651	34	2	such	such	ADJ
ejpam-4651	34	3	that	that	PRON
ejpam-4651	34	4	w	w	PROPN
ejpam-4651	34	5	∈	∈	PROPN
ejpam-4651	34	6	ng(u	ng(u	NOUN
ejpam-4651	34	7	)	)	PUNCT
ejpam-4651	34	8	\	\	NOUN
ejpam-4651	34	9	ng(v	ng(v	PUNCT
ejpam-4651	34	10	)	)	PUNCT
ejpam-4651	34	11	or	or	CCONJ
ejpam-4651	34	12	w	w	PROPN
ejpam-4651	34	13	∈	∈	PROPN
ejpam-4651	34	14	ng(v)\ng(u	ng(v)\ng(u	ADJ
ejpam-4651	34	15	)	)	PUNCT
ejpam-4651	34	16	.	.	PUNCT
ejpam-4651	35	1	the	the	DET
ejpam-4651	35	2	clique	clique	ADJ
ejpam-4651	35	3	number	number	NOUN
ejpam-4651	35	4	(	(	PUNCT
ejpam-4651	35	5	resp	resp	NOUN
ejpam-4651	35	6	.	.	PUNCT
ejpam-4651	36	1	superclique	superclique	ADJ
ejpam-4651	36	2	number	number	NOUN
ejpam-4651	36	3	)	)	PUNCT
ejpam-4651	36	4	of	of	ADP
ejpam-4651	36	5	g	g	NOUN
ejpam-4651	36	6	,	,	PUNCT
ejpam-4651	36	7	denoted	denote	VERB
ejpam-4651	36	8	by	by	ADP
ejpam-4651	36	9	ω(g	ω(g	NOUN
ejpam-4651	36	10	)	)	PUNCT
ejpam-4651	36	11	(	(	PUNCT
ejpam-4651	36	12	resp	resp	NOUN
ejpam-4651	36	13	.	.	PUNCT
ejpam-4651	36	14	ωs(g	ωs(g	PUNCT
ejpam-4651	36	15	)	)	PUNCT
ejpam-4651	36	16	)	)	PUNCT
ejpam-4651	37	1	,	,	PUNCT
ejpam-4651	37	2	is	be	AUX
ejpam-4651	37	3	the	the	DET
ejpam-4651	37	4	largest	large	ADJ
ejpam-4651	37	5	cardinality	cardinality	NOUN
ejpam-4651	37	6	of	of	ADP
ejpam-4651	37	7	a	a	DET
ejpam-4651	37	8	clique	clique	NOUN
ejpam-4651	37	9	(	(	PUNCT
ejpam-4651	37	10	resp	resp	NOUN
ejpam-4651	37	11	.	.	PUNCT
ejpam-4651	38	1	superclique	superclique	NOUN
ejpam-4651	38	2	)	)	PUNCT
ejpam-4651	38	3	in	in	ADP
ejpam-4651	38	4	g.	g.	PROPN
ejpam-4651	38	5	any	any	DET
ejpam-4651	38	6	clique	clique	NOUN
ejpam-4651	38	7	(	(	PUNCT
ejpam-4651	38	8	resp	resp	NOUN
ejpam-4651	38	9	.	.	PUNCT
ejpam-4651	39	1	superclique	superclique	NOUN
ejpam-4651	39	2	)	)	PUNCT
ejpam-4651	39	3	in	in	ADP
ejpam-4651	39	4	g	g	PROPN
ejpam-4651	39	5	with	with	ADP
ejpam-4651	39	6	cardinality	cardinality	NOUN
ejpam-4651	39	7	ω(g	ω(g	NOUN
ejpam-4651	39	8	)	)	PUNCT
ejpam-4651	39	9	(	(	PUNCT
ejpam-4651	39	10	resp	resp	NOUN
ejpam-4651	39	11	.	.	PUNCT
ejpam-4651	39	12	ωs(g	ωs(g	PUNCT
ejpam-4651	39	13	)	)	PUNCT
ejpam-4651	39	14	)	)	PUNCT
ejpam-4651	39	15	is	be	AUX
ejpam-4651	39	16	called	call	VERB
ejpam-4651	39	17	a	a	DET
ejpam-4651	39	18	maximum	maximum	ADJ
ejpam-4651	39	19	clique	clique	NOUN
ejpam-4651	39	20	or	or	CCONJ
ejpam-4651	39	21	ω	ω	VERB
ejpam-4651	39	22	-	-	PUNCT
ejpam-4651	39	23	set	set	VERB
ejpam-4651	39	24	(	(	PUNCT
ejpam-4651	39	25	resp	resp	NOUN
ejpam-4651	39	26	.	.	PUNCT
ejpam-4651	40	1	maximum	maximum	ADJ
ejpam-4651	40	2	superclique	superclique	NOUN
ejpam-4651	40	3	or	or	CCONJ
ejpam-4651	40	4	ωs	ω	NOUN
ejpam-4651	40	5	-	-	PUNCT
ejpam-4651	40	6	set	set	NOUN
ejpam-4651	40	7	)	)	PUNCT
ejpam-4651	40	8	.	.	PUNCT
ejpam-4651	41	1	letg	letg	PROPN
ejpam-4651	41	2	andh	andh	NOUN
ejpam-4651	41	3	be	be	VERB
ejpam-4651	41	4	graphs	graph	NOUN
ejpam-4651	41	5	.	.	PUNCT
ejpam-4651	42	1	the	the	DET
ejpam-4651	42	2	edge	edge	NOUN
ejpam-4651	42	3	corona	corona	NOUN
ejpam-4651	42	4	g⋄h	g⋄h	PROPN
ejpam-4651	42	5	of	of	ADP
ejpam-4651	42	6	graphsg	graphsg	NOUN
ejpam-4651	42	7	andh	andh	NOUN
ejpam-4651	42	8	is	be	AUX
ejpam-4651	42	9	the	the	DET
ejpam-4651	42	10	graph	graph	NOUN
ejpam-4651	42	11	obtained	obtain	VERB
ejpam-4651	42	12	by	by	ADP
ejpam-4651	42	13	taking	take	VERB
ejpam-4651	42	14	one	one	NUM
ejpam-4651	42	15	copy	copy	NOUN
ejpam-4651	42	16	of	of	ADP
ejpam-4651	42	17	g	g	PROPN
ejpam-4651	42	18	and	and	CCONJ
ejpam-4651	42	19	|e(g)|	|e(g)|	ADJ
ejpam-4651	42	20	copies	copy	NOUN
ejpam-4651	42	21	of	of	ADP
ejpam-4651	42	22	h	h	NOUN
ejpam-4651	42	23	and	and	CCONJ
ejpam-4651	42	24	joining	join	VERB
ejpam-4651	42	25	each	each	PRON
ejpam-4651	42	26	of	of	ADP
ejpam-4651	42	27	the	the	DET
ejpam-4651	42	28	end	end	NOUN
ejpam-4651	42	29	vertices	vertice	VERB
ejpam-4651	42	30	u	u	NOUN
ejpam-4651	42	31	and	and	CCONJ
ejpam-4651	42	32	v	v	NOUN
ejpam-4651	42	33	of	of	ADP
ejpam-4651	42	34	every	every	DET
ejpam-4651	42	35	edge	edge	NOUN
ejpam-4651	42	36	uv	uv	NOUN
ejpam-4651	42	37	in	in	ADP
ejpam-4651	42	38	g	g	NOUN
ejpam-4651	42	39	to	to	ADP
ejpam-4651	42	40	every	every	DET
ejpam-4651	42	41	vertex	vertex	NOUN
ejpam-4651	42	42	of	of	ADP
ejpam-4651	42	43	the	the	DET
ejpam-4651	42	44	copy	copy	NOUN
ejpam-4651	42	45	huv	huv	PROPN
ejpam-4651	42	46	of	of	ADP
ejpam-4651	42	47	h.	h.	PROPN
ejpam-4651	42	48	(	(	PUNCT
ejpam-4651	42	49	that	that	PRON
ejpam-4651	42	50	is	be	AUX
ejpam-4651	42	51	forming	form	VERB
ejpam-4651	42	52	the	the	DET
ejpam-4651	42	53	join	join	NOUN
ejpam-4651	42	54	⟨{u	⟨{u	PROPN
ejpam-4651	42	55	,	,	PUNCT
ejpam-4651	42	56	v}⟩+huv	v}⟩+huv	NOUN
ejpam-4651	42	57	for	for	ADP
ejpam-4651	42	58	each	each	DET
ejpam-4651	42	59	uv	uv	PROPN
ejpam-4651	42	60	∈	∈	PROPN
ejpam-4651	42	61	e(g	e(g	PROPN
ejpam-4651	42	62	)	)	PUNCT
ejpam-4651	42	63	)	)	PUNCT
ejpam-4651	42	64	.	.	PUNCT
ejpam-4651	43	1	the	the	DET
ejpam-4651	43	2	tensor	tensor	NOUN
ejpam-4651	43	3	product	product	NOUN
ejpam-4651	43	4	g⊠h	g⊠h	VERB
ejpam-4651	43	5	of	of	ADP
ejpam-4651	43	6	graphs	graph	NOUN
ejpam-4651	43	7	g	g	NOUN
ejpam-4651	44	1	and	and	CCONJ
ejpam-4651	44	2	h	h	NOUN
ejpam-4651	44	3	is	be	AUX
ejpam-4651	44	4	the	the	DET
ejpam-4651	44	5	graph	graph	NOUN
ejpam-4651	44	6	with	with	ADP
ejpam-4651	44	7	vertex	vertex	NOUN
ejpam-4651	44	8	set	set	VERB
ejpam-4651	44	9	v	v	NOUN
ejpam-4651	44	10	(	(	PUNCT
ejpam-4651	44	11	g)×v	g)×v	PROPN
ejpam-4651	44	12	(	(	PUNCT
ejpam-4651	44	13	h	h	NOUN
ejpam-4651	44	14	)	)	PUNCT
ejpam-4651	44	15	and	and	CCONJ
ejpam-4651	44	16	(	(	PUNCT
ejpam-4651	44	17	u	u	NOUN
ejpam-4651	44	18	,	,	PUNCT
ejpam-4651	44	19	v	v	NOUN
ejpam-4651	44	20	)	)	PUNCT
ejpam-4651	44	21	is	be	AUX
ejpam-4651	44	22	adjacent	adjacent	ADJ
ejpam-4651	44	23	with	with	ADP
ejpam-4651	44	24	(	(	PUNCT
ejpam-4651	44	25	u′	u′	PROPN
ejpam-4651	44	26	,	,	PUNCT
ejpam-4651	44	27	v′	v′	PROPN
ejpam-4651	44	28	)	)	PUNCT
ejpam-4651	45	1	whenever	whenever	SCONJ
ejpam-4651	45	2	uu′	uu′	PROPN
ejpam-4651	45	3	∈	∈	PROPN
ejpam-4651	45	4	e(g	e(g	PROPN
ejpam-4651	45	5	)	)	PUNCT
ejpam-4651	45	6	and	and	CCONJ
ejpam-4651	45	7	uv′	uv′	X
ejpam-4651	45	8	∈	∈	PROPN
ejpam-4651	45	9	e(h	e(h	PROPN
ejpam-4651	45	10	)	)	PUNCT
ejpam-4651	45	11	.	.	PUNCT
ejpam-4651	46	1	the	the	DET
ejpam-4651	46	2	strong	strong	ADJ
ejpam-4651	46	3	product	product	NOUN
ejpam-4651	46	4	g⊗h	g⊗h	NOUN
ejpam-4651	46	5	of	of	ADP
ejpam-4651	46	6	graphs	graph	NOUN
ejpam-4651	46	7	g	g	PROPN
ejpam-4651	46	8	and	and	CCONJ
ejpam-4651	46	9	h	h	NOUN
ejpam-4651	46	10	is	be	AUX
ejpam-4651	46	11	the	the	DET
ejpam-4651	46	12	graph	graph	NOUN
ejpam-4651	46	13	with	with	ADP
ejpam-4651	46	14	vertex	vertex	NOUN
ejpam-4651	46	15	set	set	VERB
ejpam-4651	46	16	v	v	NOUN
ejpam-4651	46	17	(	(	PUNCT
ejpam-4651	46	18	g)×	g)×	NOUN
ejpam-4651	46	19	v	v	NOUN
ejpam-4651	46	20	(	(	PUNCT
ejpam-4651	46	21	h	h	NOUN
ejpam-4651	46	22	)	)	PUNCT
ejpam-4651	46	23	and	and	CCONJ
ejpam-4651	46	24	(	(	PUNCT
ejpam-4651	46	25	u	u	NOUN
ejpam-4651	46	26	,	,	PUNCT
ejpam-4651	46	27	v	v	NOUN
ejpam-4651	46	28	)	)	PUNCT
ejpam-4651	46	29	is	be	AUX
ejpam-4651	46	30	adjacent	adjacent	ADJ
ejpam-4651	46	31	with	with	ADP
ejpam-4651	46	32	(	(	PUNCT
ejpam-4651	46	33	u′	u′	PROPN
ejpam-4651	46	34	,	,	PUNCT
ejpam-4651	46	35	v′	v′	PROPN
ejpam-4651	46	36	)	)	PUNCT
ejpam-4651	47	1	whenever	whenever	SCONJ
ejpam-4651	47	2	[	[	X
ejpam-4651	47	3	uu′	uu′	PROPN
ejpam-4651	47	4	∈	∈	PROPN
ejpam-4651	47	5	e(g	e(g	PROPN
ejpam-4651	47	6	)	)	PUNCT
ejpam-4651	47	7	and	and	CCONJ
ejpam-4651	47	8	v	v	NOUN
ejpam-4651	47	9	=	=	SYM
ejpam-4651	47	10	v′	v′	NOUN
ejpam-4651	47	11	]	]	PUNCT
ejpam-4651	47	12	or	or	CCONJ
ejpam-4651	47	13	[	[	X
ejpam-4651	47	14	vv′	vv′	NOUN
ejpam-4651	47	15	∈	∈	PROPN
ejpam-4651	47	16	e(h	e(h	PROPN
ejpam-4651	47	17	)	)	PUNCT
ejpam-4651	47	18	and	and	CCONJ
ejpam-4651	47	19	u	u	X
ejpam-4651	47	20	=	=	SYM
ejpam-4651	47	21	u′	u′	PROPN
ejpam-4651	47	22	]	]	PUNCT
ejpam-4651	47	23	or	or	CCONJ
ejpam-4651	47	24	[	[	X
ejpam-4651	47	25	uu′	uu′	PROPN
ejpam-4651	47	26	∈	∈	PROPN
ejpam-4651	47	27	e(g	e(g	PROPN
ejpam-4651	47	28	)	)	PUNCT
ejpam-4651	47	29	and	and	CCONJ
ejpam-4651	47	30	vv′	vv′	PROPN
ejpam-4651	47	31	∈	∈	PROPN
ejpam-4651	47	32	e(h	e(h	PROPN
ejpam-4651	47	33	)	)	PUNCT
ejpam-4651	47	34	]	]	PUNCT
ejpam-4651	47	35	.	.	PUNCT
ejpam-4651	48	1	we	we	PRON
ejpam-4651	48	2	note	note	VERB
ejpam-4651	48	3	that	that	SCONJ
ejpam-4651	48	4	every	every	DET
ejpam-4651	48	5	non	non	ADJ
ejpam-4651	48	6	-	-	ADJ
ejpam-4651	48	7	empty	empty	ADJ
ejpam-4651	48	8	subset	subset	NOUN
ejpam-4651	48	9	c	c	NOUN
ejpam-4651	48	10	of	of	ADP
ejpam-4651	48	11	v	v	PROPN
ejpam-4651	48	12	(	(	PUNCT
ejpam-4651	48	13	g)×	g)×	NOUN
ejpam-4651	48	14	v	v	NOUN
ejpam-4651	48	15	(	(	PUNCT
ejpam-4651	48	16	h	h	NOUN
ejpam-4651	48	17	)	)	PUNCT
ejpam-4651	48	18	can	can	AUX
ejpam-4651	48	19	be	be	AUX
ejpam-4651	48	20	expressed	express	VERB
ejpam-4651	48	21	as	as	ADP
ejpam-4651	48	22	c	c	X
ejpam-4651	48	23	=	=	SYM
ejpam-4651	48	24	∪x∈s	∪x∈s	PROPN
ejpam-4651	49	1	[	[	X
ejpam-4651	49	2	{	{	PUNCT
ejpam-4651	49	3	x	x	NOUN
ejpam-4651	49	4	}	}	PUNCT
ejpam-4651	49	5	×	×	PROPN
ejpam-4651	49	6	tx	tx	PROPN
ejpam-4651	49	7	]	]	X
ejpam-4651	49	8	,	,	PUNCT
ejpam-4651	49	9	where	where	SCONJ
ejpam-4651	49	10	s	s	VERB
ejpam-4651	49	11	⊆	⊆	NUM
ejpam-4651	49	12	v	v	NOUN
ejpam-4651	49	13	(	(	PUNCT
ejpam-4651	49	14	g	g	NOUN
ejpam-4651	49	15	)	)	PUNCT
ejpam-4651	49	16	and	and	CCONJ
ejpam-4651	49	17	tx	tx	VERB
ejpam-4651	49	18	=	=	PUNCT
ejpam-4651	49	19	{	{	PUNCT
ejpam-4651	49	20	a	a	DET
ejpam-4651	49	21	∈	∈	PROPN
ejpam-4651	49	22	v	v	ADP
ejpam-4651	49	23	(	(	PUNCT
ejpam-4651	49	24	h	h	NOUN
ejpam-4651	49	25	)	)	PUNCT
ejpam-4651	49	26	:	:	PUNCT
ejpam-4651	49	27	(	(	PUNCT
ejpam-4651	49	28	x	x	X
ejpam-4651	49	29	,	,	PUNCT
ejpam-4651	49	30	a	a	PRON
ejpam-4651	49	31	)	)	PUNCT
ejpam-4651	49	32	∈	∈	PROPN
ejpam-4651	49	33	c	c	NOUN
ejpam-4651	49	34	}	}	PUNCT
ejpam-4651	49	35	for	for	ADP
ejpam-4651	49	36	each	each	DET
ejpam-4651	49	37	x	x	PROPN
ejpam-4651	49	38	∈	∈	PROPN
ejpam-4651	49	39	s.	s.	PROPN
ejpam-4651	49	40	3	3	X
ejpam-4651	49	41	.	.	PROPN
ejpam-4651	49	42	results	result	VERB
ejpam-4651	49	43	the	the	DET
ejpam-4651	49	44	first	first	ADJ
ejpam-4651	49	45	result	result	NOUN
ejpam-4651	49	46	is	be	AUX
ejpam-4651	49	47	found	find	VERB
ejpam-4651	49	48	in	in	ADP
ejpam-4651	49	49	[	[	X
ejpam-4651	49	50	3	3	NUM
ejpam-4651	49	51	]	]	PUNCT
ejpam-4651	49	52	.	.	PUNCT
ejpam-4651	50	1	recall	recall	VERB
ejpam-4651	50	2	that	that	SCONJ
ejpam-4651	50	3	two	two	NUM
ejpam-4651	50	4	adjacent	adjacent	ADJ
ejpam-4651	50	5	vertices	vertex	NOUN
ejpam-4651	50	6	v	v	NOUN
ejpam-4651	50	7	and	and	CCONJ
ejpam-4651	50	8	w	w	NOUN
ejpam-4651	50	9	of	of	ADP
ejpam-4651	50	10	a	a	DET
ejpam-4651	50	11	graph	graph	NOUN
ejpam-4651	50	12	g	g	NOUN
ejpam-4651	50	13	are	be	AUX
ejpam-4651	50	14	true	true	ADJ
ejpam-4651	50	15	twins	twin	NOUN
ejpam-4651	50	16	if	if	SCONJ
ejpam-4651	50	17	ng[v	ng[v	NOUN
ejpam-4651	50	18	]	]	X
ejpam-4651	50	19	=	=	SYM
ejpam-4651	50	20	ng[w	ng[w	PROPN
ejpam-4651	50	21	]	]	PUNCT
ejpam-4651	50	22	.	.	PUNCT
ejpam-4651	51	1	theorem	theorem	NOUN
ejpam-4651	51	2	1	1	X
ejpam-4651	51	3	.	.	PUNCT
ejpam-4651	52	1	let	let	VERB
ejpam-4651	52	2	g	g	NOUN
ejpam-4651	52	3	be	be	AUX
ejpam-4651	52	4	any	any	DET
ejpam-4651	52	5	graph	graph	NOUN
ejpam-4651	52	6	.	.	PUNCT
ejpam-4651	53	1	then	then	ADV
ejpam-4651	53	2	each	each	PRON
ejpam-4651	53	3	of	of	ADP
ejpam-4651	53	4	the	the	DET
ejpam-4651	53	5	following	following	ADJ
ejpam-4651	53	6	statements	statement	NOUN
ejpam-4651	53	7	holds	hold	VERB
ejpam-4651	53	8	:	:	PUNCT
ejpam-4651	53	9	(	(	PUNCT
ejpam-4651	53	10	i	i	NOUN
ejpam-4651	53	11	)	)	PUNCT
ejpam-4651	53	12	g	g	PROPN
ejpam-4651	53	13	admits	admit	VERB
ejpam-4651	53	14	a	a	DET
ejpam-4651	53	15	superclique	superclique	NOUN
ejpam-4651	53	16	and	and	CCONJ
ejpam-4651	53	17	1	1	NUM
ejpam-4651	53	18	≤	≤	NOUN
ejpam-4651	53	19	ωs(g	ωs(g	NOUN
ejpam-4651	53	20	)	)	PUNCT
ejpam-4651	53	21	≤	≤	NUM
ejpam-4651	53	22	ω(g	ω(g	NOUN
ejpam-4651	53	23	)	)	PUNCT
ejpam-4651	53	24	.	.	PUNCT
ejpam-4651	54	1	(	(	PUNCT
ejpam-4651	54	2	ii	ii	NOUN
ejpam-4651	54	3	)	)	PUNCT
ejpam-4651	54	4	ωs(g	ωs(g	PUNCT
ejpam-4651	54	5	)	)	PUNCT
ejpam-4651	54	6	=	=	SYM
ejpam-4651	54	7	1	1	NUM
ejpam-4651	54	8	if	if	SCONJ
ejpam-4651	54	9	and	and	CCONJ
ejpam-4651	54	10	only	only	ADV
ejpam-4651	54	11	if	if	SCONJ
ejpam-4651	54	12	every	every	DET
ejpam-4651	54	13	component	component	NOUN
ejpam-4651	54	14	of	of	ADP
ejpam-4651	54	15	g	g	PROPN
ejpam-4651	54	16	is	be	AUX
ejpam-4651	54	17	complete	complete	ADJ
ejpam-4651	54	18	.	.	PUNCT
ejpam-4651	55	1	(	(	PUNCT
ejpam-4651	55	2	iii	iii	NOUN
ejpam-4651	55	3	)	)	PUNCT
ejpam-4651	55	4	ωs(g	ωs(g	PUNCT
ejpam-4651	55	5	)	)	PUNCT
ejpam-4651	55	6	=	=	SYM
ejpam-4651	55	7	ω(g	ω(g	NOUN
ejpam-4651	55	8	)	)	PUNCT
ejpam-4651	55	9	if	if	SCONJ
ejpam-4651	55	10	and	and	CCONJ
ejpam-4651	55	11	only	only	ADV
ejpam-4651	55	12	if	if	SCONJ
ejpam-4651	55	13	g	g	PROPN
ejpam-4651	55	14	has	have	VERB
ejpam-4651	55	15	a	a	DET
ejpam-4651	55	16	maximum	maximum	ADJ
ejpam-4651	55	17	clique	clique	NOUN
ejpam-4651	55	18	containing	contain	VERB
ejpam-4651	55	19	no	no	DET
ejpam-4651	55	20	true	true	ADJ
ejpam-4651	55	21	twin	twin	ADJ
ejpam-4651	55	22	vertices	vertex	NOUN
ejpam-4651	55	23	.	.	PUNCT
ejpam-4651	56	1	theorem	theorem	NOUN
ejpam-4651	56	2	2	2	NUM
ejpam-4651	56	3	.	.	PUNCT
ejpam-4651	57	1	let	let	VERB
ejpam-4651	57	2	g	g	PRON
ejpam-4651	57	3	be	be	AUX
ejpam-4651	57	4	a	a	DET
ejpam-4651	57	5	nontrivial	nontrivial	ADJ
ejpam-4651	57	6	connected	connect	VERB
ejpam-4651	57	7	graph	graph	NOUN
ejpam-4651	57	8	and	and	CCONJ
ejpam-4651	57	9	h	h	NOUN
ejpam-4651	57	10	be	be	AUX
ejpam-4651	57	11	any	any	DET
ejpam-4651	57	12	graph	graph	NOUN
ejpam-4651	57	13	.	.	PUNCT
ejpam-4651	58	1	then	then	ADV
ejpam-4651	58	2	s	s	VERB
ejpam-4651	58	3	is	be	AUX
ejpam-4651	58	4	clique	clique	NOUN
ejpam-4651	58	5	in	in	ADP
ejpam-4651	58	6	g	g	PROPN
ejpam-4651	58	7	⋄h	⋄h	NOUN
ejpam-4651	58	8	if	if	SCONJ
ejpam-4651	59	1	and	and	CCONJ
ejpam-4651	59	2	only	only	ADV
ejpam-4651	59	3	if	if	SCONJ
ejpam-4651	59	4	one	one	NUM
ejpam-4651	59	5	of	of	ADP
ejpam-4651	59	6	the	the	DET
ejpam-4651	59	7	following	follow	VERB
ejpam-4651	59	8	holds	hold	NOUN
ejpam-4651	59	9	:	:	PUNCT
ejpam-4651	59	10	s.	s.	PROPN
ejpam-4651	59	11	canoy	canoy	PROPN
ejpam-4651	59	12	,	,	PUNCT
ejpam-4651	59	13	jr	jr	PROPN
ejpam-4651	59	14	.	.	PROPN
ejpam-4651	59	15	,	,	PUNCT
ejpam-4651	59	16	r.	r.	PROPN
ejpam-4651	59	17	dela	dela	PROPN
ejpam-4651	59	18	cerna	cerna	PROPN
ejpam-4651	59	19	,	,	PUNCT
ejpam-4651	59	20	a.	a.	NOUN
ejpam-4651	59	21	abragan	abragan	PROPN
ejpam-4651	59	22	/	/	SYM
ejpam-4651	59	23	eur	eur	PROPN
ejpam-4651	59	24	.	.	PUNCT
ejpam-4651	60	1	j.	j.	PROPN
ejpam-4651	60	2	pure	pure	PROPN
ejpam-4651	60	3	appl	appl	PROPN
ejpam-4651	60	4	.	.	PROPN
ejpam-4651	60	5	math	math	PROPN
ejpam-4651	60	6	,	,	PUNCT
ejpam-4651	60	7	16	16	NUM
ejpam-4651	60	8	(	(	PUNCT
ejpam-4651	60	9	1	1	NUM
ejpam-4651	60	10	)	)	PUNCT
ejpam-4651	60	11	(	(	PUNCT
ejpam-4651	60	12	2023	2023	NUM
ejpam-4651	60	13	)	)	PUNCT
ejpam-4651	60	14	,	,	PUNCT
ejpam-4651	60	15	243	243	NUM
ejpam-4651	60	16	-	-	SYM
ejpam-4651	60	17	252	252	NUM
ejpam-4651	60	18	245	245	NUM
ejpam-4651	60	19	(	(	PUNCT
ejpam-4651	60	20	i	i	NOUN
ejpam-4651	60	21	)	)	PUNCT
ejpam-4651	60	22	s	s	AUX
ejpam-4651	60	23	is	be	AUX
ejpam-4651	60	24	a	a	DET
ejpam-4651	60	25	clique	clique	NOUN
ejpam-4651	60	26	in	in	ADP
ejpam-4651	60	27	g.	g.	PROPN
ejpam-4651	60	28	(	(	PUNCT
ejpam-4651	60	29	ii	ii	PROPN
ejpam-4651	60	30	)	)	PUNCT
ejpam-4651	60	31	s	s	VERB
ejpam-4651	60	32	is	be	AUX
ejpam-4651	60	33	clique	clique	ADJ
ejpam-4651	60	34	in	in	ADP
ejpam-4651	60	35	huv	huv	PROPN
ejpam-4651	60	36	for	for	ADP
ejpam-4651	60	37	some	some	DET
ejpam-4651	60	38	uv	uv	PROPN
ejpam-4651	60	39	∈	∈	PROPN
ejpam-4651	60	40	e(g	e(g	PROPN
ejpam-4651	60	41	)	)	PUNCT
ejpam-4651	60	42	.	.	PUNCT
ejpam-4651	61	1	(	(	PUNCT
ejpam-4651	61	2	iii	iii	X
ejpam-4651	61	3	)	)	PUNCT
ejpam-4651	61	4	s	s	PART
ejpam-4651	61	5	=	=	PROPN
ejpam-4651	61	6	suv∪d	suv∪d	PROPN
ejpam-4651	61	7	,	,	PUNCT
ejpam-4651	61	8	where	where	SCONJ
ejpam-4651	61	9	suv	suv	PROPN
ejpam-4651	61	10	is	be	AUX
ejpam-4651	61	11	a	a	DET
ejpam-4651	61	12	clique	clique	NOUN
ejpam-4651	61	13	in	in	ADP
ejpam-4651	61	14	huv	huv	PROPN
ejpam-4651	61	15	and	and	CCONJ
ejpam-4651	61	16	∅	∅	NOUN
ejpam-4651	61	17	̸=	̸=	PROPN
ejpam-4651	61	18	d	d	NOUN
ejpam-4651	61	19	⊆	⊆	NUM
ejpam-4651	61	20	{	{	PUNCT
ejpam-4651	61	21	u	u	NOUN
ejpam-4651	61	22	,	,	PUNCT
ejpam-4651	61	23	v	v	NOUN
ejpam-4651	61	24	}	}	PUNCT
ejpam-4651	61	25	for	for	ADP
ejpam-4651	61	26	some	some	DET
ejpam-4651	61	27	uv	uv	PROPN
ejpam-4651	61	28	∈	∈	PROPN
ejpam-4651	61	29	e(g	e(g	PROPN
ejpam-4651	61	30	)	)	PUNCT
ejpam-4651	61	31	.	.	PUNCT
ejpam-4651	62	1	proof	proof	NOUN
ejpam-4651	62	2	.	.	PUNCT
ejpam-4651	63	1	suppose	suppose	VERB
ejpam-4651	63	2	s	s	NOUN
ejpam-4651	63	3	is	be	AUX
ejpam-4651	63	4	a	a	DET
ejpam-4651	63	5	clique	clique	NOUN
ejpam-4651	63	6	in	in	ADP
ejpam-4651	63	7	g	g	PROPN
ejpam-4651	63	8	⋄	⋄	PROPN
ejpam-4651	63	9	h.	h.	NOUN
ejpam-4651	64	1	if	if	SCONJ
ejpam-4651	64	2	s	s	VERB
ejpam-4651	64	3	⊆	⊆	NUM
ejpam-4651	64	4	v	v	NOUN
ejpam-4651	64	5	(	(	PUNCT
ejpam-4651	64	6	g	g	NOUN
ejpam-4651	64	7	)	)	PUNCT
ejpam-4651	64	8	,	,	PUNCT
ejpam-4651	64	9	then	then	ADV
ejpam-4651	64	10	s	s	VERB
ejpam-4651	64	11	is	be	AUX
ejpam-4651	64	12	a	a	DET
ejpam-4651	64	13	clique	clique	NOUN
ejpam-4651	64	14	in	in	ADP
ejpam-4651	64	15	g	g	PROPN
ejpam-4651	64	16	and	and	CCONJ
ejpam-4651	64	17	(	(	PUNCT
ejpam-4651	64	18	i	i	NOUN
ejpam-4651	64	19	)	)	PUNCT
ejpam-4651	64	20	holds	hold	VERB
ejpam-4651	64	21	.	.	PUNCT
ejpam-4651	65	1	suppose	suppose	VERB
ejpam-4651	65	2	that	that	SCONJ
ejpam-4651	65	3	s	s	VERB
ejpam-4651	65	4	⊆	⊆	NUM
ejpam-4651	65	5	v	v	NOUN
ejpam-4651	65	6	(	(	PUNCT
ejpam-4651	65	7	huv	huv	PROPN
ejpam-4651	65	8	)	)	PUNCT
ejpam-4651	65	9	for	for	ADP
ejpam-4651	65	10	some	some	DET
ejpam-4651	65	11	uv	uv	PROPN
ejpam-4651	65	12	∈	∈	PROPN
ejpam-4651	65	13	e(g	e(g	PROPN
ejpam-4651	65	14	)	)	PUNCT
ejpam-4651	65	15	.	.	PUNCT
ejpam-4651	66	1	since	since	SCONJ
ejpam-4651	66	2	s	s	PROPN
ejpam-4651	66	3	is	be	AUX
ejpam-4651	66	4	a	a	DET
ejpam-4651	66	5	clique	clique	NOUN
ejpam-4651	66	6	in	in	ADP
ejpam-4651	66	7	g	g	PROPN
ejpam-4651	66	8	⋄h	⋄h	PROPN
ejpam-4651	66	9	,	,	PUNCT
ejpam-4651	66	10	suv	suv	PROPN
ejpam-4651	66	11	is	be	AUX
ejpam-4651	66	12	a	a	DET
ejpam-4651	66	13	clique	clique	NOUN
ejpam-4651	66	14	in	in	ADP
ejpam-4651	66	15	huv	huv	PROPN
ejpam-4651	66	16	.	.	PUNCT
ejpam-4651	67	1	hence	hence	ADV
ejpam-4651	67	2	,	,	PUNCT
ejpam-4651	67	3	(	(	PUNCT
ejpam-4651	67	4	ii	ii	NOUN
ejpam-4651	67	5	)	)	PUNCT
ejpam-4651	67	6	holds	hold	VERB
ejpam-4651	67	7	.	.	PUNCT
ejpam-4651	68	1	suppose	suppose	VERB
ejpam-4651	68	2	now	now	ADV
ejpam-4651	68	3	that	that	SCONJ
ejpam-4651	68	4	d	d	X
ejpam-4651	68	5	=	=	SYM
ejpam-4651	68	6	s	s	NOUN
ejpam-4651	68	7	∩	∩	NOUN
ejpam-4651	68	8	{	{	PUNCT
ejpam-4651	68	9	u	u	NOUN
ejpam-4651	68	10	,	,	PUNCT
ejpam-4651	68	11	v	v	NOUN
ejpam-4651	68	12	}	}	PUNCT
ejpam-4651	68	13	=	=	NOUN
ejpam-4651	68	14	̸	̸	ADJ
ejpam-4651	68	15	∅	∅	NOUN
ejpam-4651	68	16	and	and	CCONJ
ejpam-4651	68	17	suv	suv	PROPN
ejpam-4651	68	18	=	=	PROPN
ejpam-4651	68	19	s	s	PROPN
ejpam-4651	68	20	∩	∩	ADJ
ejpam-4651	68	21	v	v	X
ejpam-4651	68	22	(	(	PUNCT
ejpam-4651	68	23	huv	huv	PROPN
ejpam-4651	68	24	)	)	PUNCT
ejpam-4651	68	25	̸=	̸=	PROPN
ejpam-4651	68	26	∅	∅	NOUN
ejpam-4651	68	27	for	for	ADP
ejpam-4651	68	28	some	some	DET
ejpam-4651	68	29	uv	uv	PROPN
ejpam-4651	68	30	∈	∈	PROPN
ejpam-4651	68	31	e(g	e(g	PROPN
ejpam-4651	68	32	)	)	PUNCT
ejpam-4651	68	33	.	.	PUNCT
ejpam-4651	69	1	then	then	ADV
ejpam-4651	69	2	clearly	clearly	ADV
ejpam-4651	69	3	,	,	PUNCT
ejpam-4651	69	4	suv	suv	PROPN
ejpam-4651	69	5	is	be	AUX
ejpam-4651	69	6	a	a	DET
ejpam-4651	69	7	clique	clique	NOUN
ejpam-4651	69	8	in	in	ADP
ejpam-4651	69	9	huv	huv	PROPN
ejpam-4651	69	10	and	and	CCONJ
ejpam-4651	69	11	s	s	PROPN
ejpam-4651	69	12	=	=	PROPN
ejpam-4651	69	13	suv	suv	PROPN
ejpam-4651	69	14	∪d	∪d	NUM
ejpam-4651	69	15	.	.	PUNCT
ejpam-4651	70	1	thus	thus	ADV
ejpam-4651	70	2	,	,	PUNCT
ejpam-4651	70	3	(	(	PUNCT
ejpam-4651	70	4	iii	iii	NOUN
ejpam-4651	70	5	)	)	PUNCT
ejpam-4651	70	6	holds	hold	VERB
ejpam-4651	70	7	.	.	PUNCT
ejpam-4651	71	1	the	the	DET
ejpam-4651	71	2	converse	converse	NOUN
ejpam-4651	71	3	is	be	AUX
ejpam-4651	71	4	clear	clear	ADJ
ejpam-4651	71	5	.	.	PUNCT
ejpam-4651	72	1	the	the	DET
ejpam-4651	72	2	next	next	ADJ
ejpam-4651	72	3	result	result	NOUN
ejpam-4651	72	4	is	be	AUX
ejpam-4651	72	5	immediate	immediate	ADJ
ejpam-4651	72	6	from	from	ADP
ejpam-4651	72	7	theorem	theorem	ADJ
ejpam-4651	72	8	2	2	NUM
ejpam-4651	73	1	.	.	PUNCT
ejpam-4651	73	2	corollary	corollary	ADJ
ejpam-4651	73	3	1	1	NUM
ejpam-4651	73	4	.	.	PUNCT
ejpam-4651	74	1	let	let	VERB
ejpam-4651	74	2	g	g	PRON
ejpam-4651	74	3	be	be	AUX
ejpam-4651	74	4	a	a	DET
ejpam-4651	74	5	nontrivial	nontrivial	ADJ
ejpam-4651	74	6	connected	connect	VERB
ejpam-4651	74	7	graph	graph	NOUN
ejpam-4651	74	8	and	and	CCONJ
ejpam-4651	74	9	let	let	VERB
ejpam-4651	74	10	h	h	NOUN
ejpam-4651	74	11	be	be	AUX
ejpam-4651	74	12	any	any	DET
ejpam-4651	74	13	graph	graph	NOUN
ejpam-4651	74	14	.	.	PUNCT
ejpam-4651	75	1	then	then	ADV
ejpam-4651	75	2	ω(g	ω(g	PROPN
ejpam-4651	75	3	⋄h	⋄h	PROPN
ejpam-4651	75	4	)	)	PUNCT
ejpam-4651	75	5	=	=	SYM
ejpam-4651	75	6	max{ω(g	max{ω(g	PROPN
ejpam-4651	75	7	)	)	PUNCT
ejpam-4651	75	8	,	,	PUNCT
ejpam-4651	75	9	ω(h	ω(h	NUM
ejpam-4651	75	10	)	)	PUNCT
ejpam-4651	76	1	+	+	CCONJ
ejpam-4651	76	2	2	2	NUM
ejpam-4651	76	3	}	}	PUNCT
ejpam-4651	76	4	.	.	PUNCT
ejpam-4651	77	1	theorem	theorem	NOUN
ejpam-4651	77	2	3	3	X
ejpam-4651	77	3	.	.	PUNCT
ejpam-4651	78	1	let	let	VERB
ejpam-4651	78	2	g	g	PRON
ejpam-4651	78	3	be	be	AUX
ejpam-4651	78	4	a	a	DET
ejpam-4651	78	5	nontrivial	nontrivial	ADJ
ejpam-4651	78	6	connected	connect	VERB
ejpam-4651	78	7	graph	graph	NOUN
ejpam-4651	78	8	such	such	ADJ
ejpam-4651	78	9	that	that	SCONJ
ejpam-4651	78	10	g	g	PROPN
ejpam-4651	78	11	̸=	̸=	PROPN
ejpam-4651	78	12	k2	k2	NOUN
ejpam-4651	78	13	and	and	CCONJ
ejpam-4651	78	14	let	let	VERB
ejpam-4651	78	15	h	h	NOUN
ejpam-4651	78	16	be	be	AUX
ejpam-4651	78	17	any	any	DET
ejpam-4651	78	18	graph	graph	NOUN
ejpam-4651	78	19	.	.	PUNCT
ejpam-4651	79	1	then	then	ADV
ejpam-4651	79	2	s	s	VERB
ejpam-4651	79	3	is	be	AUX
ejpam-4651	79	4	superclique	superclique	ADJ
ejpam-4651	79	5	in	in	ADP
ejpam-4651	79	6	g	g	PROPN
ejpam-4651	79	7	⋄h	⋄h	NOUN
ejpam-4651	79	8	if	if	SCONJ
ejpam-4651	80	1	and	and	CCONJ
ejpam-4651	80	2	only	only	ADV
ejpam-4651	80	3	if	if	SCONJ
ejpam-4651	80	4	one	one	NUM
ejpam-4651	80	5	of	of	ADP
ejpam-4651	80	6	the	the	DET
ejpam-4651	80	7	following	follow	VERB
ejpam-4651	80	8	holds	hold	VERB
ejpam-4651	80	9	:	:	PUNCT
ejpam-4651	80	10	(	(	PUNCT
ejpam-4651	80	11	i	i	NOUN
ejpam-4651	80	12	)	)	PUNCT
ejpam-4651	80	13	s	s	VERB
ejpam-4651	80	14	is	be	AUX
ejpam-4651	80	15	a	a	DET
ejpam-4651	80	16	clique	clique	NOUN
ejpam-4651	80	17	in	in	ADP
ejpam-4651	80	18	g.	g.	PROPN
ejpam-4651	80	19	(	(	PUNCT
ejpam-4651	80	20	ii	ii	PROPN
ejpam-4651	80	21	)	)	PUNCT
ejpam-4651	80	22	s	s	VERB
ejpam-4651	80	23	is	be	AUX
ejpam-4651	80	24	superclique	superclique	ADJ
ejpam-4651	80	25	in	in	ADP
ejpam-4651	80	26	huv	huv	PROPN
ejpam-4651	80	27	for	for	ADP
ejpam-4651	80	28	some	some	DET
ejpam-4651	80	29	uv	uv	PROPN
ejpam-4651	80	30	∈	∈	PROPN
ejpam-4651	80	31	e(g	e(g	PROPN
ejpam-4651	80	32	)	)	PUNCT
ejpam-4651	80	33	.	.	PUNCT
ejpam-4651	81	1	(	(	PUNCT
ejpam-4651	81	2	iii	iii	X
ejpam-4651	81	3	)	)	PUNCT
ejpam-4651	81	4	s	s	PART
ejpam-4651	81	5	=	=	X
ejpam-4651	81	6	suv	suv	PROPN
ejpam-4651	81	7	∪	∪	ADP
ejpam-4651	81	8	d	d	PROPN
ejpam-4651	81	9	for	for	ADP
ejpam-4651	81	10	some	some	DET
ejpam-4651	81	11	uv	uv	PROPN
ejpam-4651	81	12	∈	∈	PROPN
ejpam-4651	81	13	e(g	e(g	PROPN
ejpam-4651	81	14	)	)	PUNCT
ejpam-4651	81	15	,	,	PUNCT
ejpam-4651	81	16	where	where	SCONJ
ejpam-4651	81	17	suv	suv	PROPN
ejpam-4651	81	18	is	be	AUX
ejpam-4651	81	19	a	a	DET
ejpam-4651	81	20	superclique	superclique	NOUN
ejpam-4651	81	21	in	in	ADP
ejpam-4651	81	22	huv	huv	PROPN
ejpam-4651	81	23	and	and	CCONJ
ejpam-4651	81	24	d	d	PROPN
ejpam-4651	81	25	is	be	AUX
ejpam-4651	81	26	a	a	DET
ejpam-4651	81	27	nonempty	nonempty	ADJ
ejpam-4651	81	28	subset	subset	NOUN
ejpam-4651	81	29	of	of	ADP
ejpam-4651	81	30	{	{	PUNCT
ejpam-4651	81	31	u	u	NOUN
ejpam-4651	81	32	,	,	PUNCT
ejpam-4651	81	33	v	v	NOUN
ejpam-4651	81	34	}	}	PUNCT
ejpam-4651	81	35	such	such	ADJ
ejpam-4651	81	36	that	that	SCONJ
ejpam-4651	81	37	d	d	NOUN
ejpam-4651	81	38	=	=	SYM
ejpam-4651	81	39	{	{	PUNCT
ejpam-4651	81	40	u	u	NOUN
ejpam-4651	81	41	}	}	PUNCT
ejpam-4651	81	42	if	if	SCONJ
ejpam-4651	81	43	degg(v	degg(v	VERB
ejpam-4651	81	44	)	)	PUNCT
ejpam-4651	81	45	=	=	SYM
ejpam-4651	81	46	1	1	NUM
ejpam-4651	81	47	and	and	CCONJ
ejpam-4651	81	48	d	d	NOUN
ejpam-4651	81	49	=	=	SYM
ejpam-4651	81	50	{	{	PUNCT
ejpam-4651	81	51	v	v	NOUN
ejpam-4651	81	52	}	}	PUNCT
ejpam-4651	81	53	if	if	SCONJ
ejpam-4651	81	54	degg(u	degg(u	NUM
ejpam-4651	81	55	)	)	PUNCT
ejpam-4651	82	1	=	=	SYM
ejpam-4651	82	2	1	1	X
ejpam-4651	82	3	.	.	PUNCT
ejpam-4651	82	4	proof	proof	NOUN
ejpam-4651	82	5	.	.	PUNCT
ejpam-4651	83	1	suppose	suppose	VERB
ejpam-4651	83	2	s	s	PRON
ejpam-4651	83	3	is	be	AUX
ejpam-4651	83	4	a	a	DET
ejpam-4651	83	5	superclique	superclique	NOUN
ejpam-4651	83	6	in	in	ADP
ejpam-4651	83	7	g	g	PROPN
ejpam-4651	83	8	⋄h	⋄h	PROPN
ejpam-4651	83	9	.	.	PUNCT
ejpam-4651	84	1	then	then	ADV
ejpam-4651	84	2	s	s	VERB
ejpam-4651	84	3	is	be	AUX
ejpam-4651	84	4	a	a	DET
ejpam-4651	84	5	clique	clique	NOUN
ejpam-4651	84	6	in	in	ADP
ejpam-4651	84	7	g	g	PROPN
ejpam-4651	84	8	⋄h	⋄h	PROPN
ejpam-4651	84	9	.	.	PUNCT
ejpam-4651	85	1	if	if	SCONJ
ejpam-4651	85	2	s	s	VERB
ejpam-4651	85	3	⊆	⊆	NUM
ejpam-4651	85	4	v	v	NOUN
ejpam-4651	85	5	(	(	PUNCT
ejpam-4651	85	6	g	g	NOUN
ejpam-4651	85	7	)	)	PUNCT
ejpam-4651	85	8	or	or	CCONJ
ejpam-4651	85	9	s	s	PRON
ejpam-4651	85	10	⊆	⊆	NUM
ejpam-4651	85	11	v	v	NOUN
ejpam-4651	85	12	(	(	PUNCT
ejpam-4651	85	13	huv	huv	PROPN
ejpam-4651	85	14	)	)	PUNCT
ejpam-4651	85	15	for	for	ADP
ejpam-4651	85	16	some	some	DET
ejpam-4651	85	17	uv	uv	PROPN
ejpam-4651	85	18	∈	∈	PROPN
ejpam-4651	85	19	e(g	e(g	PROPN
ejpam-4651	85	20	)	)	PUNCT
ejpam-4651	85	21	,	,	PUNCT
ejpam-4651	85	22	then	then	ADV
ejpam-4651	85	23	s	s	VERB
ejpam-4651	85	24	is	be	AUX
ejpam-4651	85	25	a	a	DET
ejpam-4651	85	26	clique	clique	NOUN
ejpam-4651	85	27	in	in	ADP
ejpam-4651	85	28	g	g	PROPN
ejpam-4651	85	29	or	or	CCONJ
ejpam-4651	85	30	huv	huv	PROPN
ejpam-4651	85	31	,	,	PUNCT
ejpam-4651	85	32	respectively	respectively	ADV
ejpam-4651	85	33	,	,	PUNCT
ejpam-4651	85	34	by	by	ADP
ejpam-4651	85	35	(	(	PUNCT
ejpam-4651	85	36	i	i	NOUN
ejpam-4651	85	37	)	)	PUNCT
ejpam-4651	85	38	and	and	CCONJ
ejpam-4651	85	39	(	(	PUNCT
ejpam-4651	85	40	ii	ii	NOUN
ejpam-4651	85	41	)	)	PUNCT
ejpam-4651	85	42	of	of	ADP
ejpam-4651	85	43	theorem	theorem	NOUN
ejpam-4651	85	44	2	2	X
ejpam-4651	85	45	.	.	PUNCT
ejpam-4651	85	46	suppose	suppose	VERB
ejpam-4651	85	47	s	s	X
ejpam-4651	85	48	=	=	PUNCT
ejpam-4651	85	49	suv	suv	PROPN
ejpam-4651	85	50	for	for	ADP
ejpam-4651	85	51	some	some	DET
ejpam-4651	85	52	uv	uv	PROPN
ejpam-4651	85	53	∈	∈	PROPN
ejpam-4651	85	54	e(g	e(g	PROPN
ejpam-4651	85	55	)	)	PUNCT
ejpam-4651	85	56	and	and	CCONJ
ejpam-4651	85	57	let	let	VERB
ejpam-4651	85	58	a	a	DET
ejpam-4651	85	59	,	,	PUNCT
ejpam-4651	85	60	b	b	PROPN
ejpam-4651	85	61	∈	∈	PROPN
ejpam-4651	85	62	suv	suv	PROPN
ejpam-4651	85	63	.	.	PUNCT
ejpam-4651	86	1	since	since	SCONJ
ejpam-4651	86	2	s	s	PROPN
ejpam-4651	86	3	is	be	AUX
ejpam-4651	86	4	a	a	DET
ejpam-4651	86	5	superclique	superclique	NOUN
ejpam-4651	86	6	in	in	ADP
ejpam-4651	86	7	g	g	PROPN
ejpam-4651	86	8	⋄h	⋄h	PROPN
ejpam-4651	86	9	,	,	PUNCT
ejpam-4651	86	10	there	there	PRON
ejpam-4651	86	11	exists	exist	VERB
ejpam-4651	86	12	c	c	PROPN
ejpam-4651	86	13	∈	∈	PROPN
ejpam-4651	86	14	v	v	NOUN
ejpam-4651	86	15	(	(	PUNCT
ejpam-4651	86	16	g	g	PROPN
ejpam-4651	86	17	⋄h	⋄h	PROPN
ejpam-4651	86	18	)	)	PUNCT
ejpam-4651	86	19	\	\	PROPN
ejpam-4651	87	1	s	s	VERB
ejpam-4651	87	2	such	such	ADJ
ejpam-4651	87	3	that	that	SCONJ
ejpam-4651	87	4	c	c	PROPN
ejpam-4651	87	5	∈	∈	PROPN
ejpam-4651	87	6	ng⋄h(a	ng⋄h(a	NOUN
ejpam-4651	87	7	)	)	PUNCT
ejpam-4651	87	8	\ng⋄h(b	\ng⋄h(b	NOUN
ejpam-4651	87	9	)	)	PUNCT
ejpam-4651	87	10	or	or	CCONJ
ejpam-4651	87	11	c	c	PROPN
ejpam-4651	87	12	∈	∈	PROPN
ejpam-4651	87	13	ng⋄h(b	ng⋄h(b	PROPN
ejpam-4651	87	14	)	)	PUNCT
ejpam-4651	87	15	\ng⋄h(a	\ng⋄h(a	NOUN
ejpam-4651	87	16	)	)	PUNCT
ejpam-4651	87	17	.	.	PUNCT
ejpam-4651	88	1	this	this	PRON
ejpam-4651	88	2	implies	imply	VERB
ejpam-4651	88	3	that	that	SCONJ
ejpam-4651	88	4	c	c	PROPN
ejpam-4651	88	5	∈	∈	PROPN
ejpam-4651	88	6	v	v	PROPN
ejpam-4651	88	7	(	(	PUNCT
ejpam-4651	88	8	huv	huv	PROPN
ejpam-4651	88	9	)	)	PUNCT
ejpam-4651	88	10	\suv	\suv	NOUN
ejpam-4651	88	11	and	and	CCONJ
ejpam-4651	88	12	c	c	NOUN
ejpam-4651	88	13	∈	∈	PROPN
ejpam-4651	88	14	nhuv(a	nhuv(a	PROPN
ejpam-4651	88	15	)	)	PUNCT
ejpam-4651	88	16	\nhuv(b	\nhuv(b	X
ejpam-4651	88	17	)	)	PUNCT
ejpam-4651	88	18	or	or	CCONJ
ejpam-4651	88	19	c	c	NOUN
ejpam-4651	88	20	∈	∈	PROPN
ejpam-4651	88	21	nhuv(b	nhuv(b	PROPN
ejpam-4651	88	22	)	)	PUNCT
ejpam-4651	88	23	\	\	PROPN
ejpam-4651	89	1	nhuv(a	nhuv(a	NOUN
ejpam-4651	89	2	)	)	PUNCT
ejpam-4651	89	3	.	.	PUNCT
ejpam-4651	90	1	hence	hence	ADV
ejpam-4651	90	2	,	,	PUNCT
ejpam-4651	90	3	suv	suv	PROPN
ejpam-4651	90	4	is	be	AUX
ejpam-4651	90	5	a	a	DET
ejpam-4651	90	6	superclique	superclique	NOUN
ejpam-4651	90	7	in	in	ADP
ejpam-4651	90	8	huv	huv	PROPN
ejpam-4651	90	9	,	,	PUNCT
ejpam-4651	90	10	showing	show	VERB
ejpam-4651	90	11	that	that	SCONJ
ejpam-4651	90	12	(	(	PUNCT
ejpam-4651	90	13	i	i	NOUN
ejpam-4651	90	14	)	)	PUNCT
ejpam-4651	90	15	or	or	CCONJ
ejpam-4651	90	16	(	(	PUNCT
ejpam-4651	90	17	ii	ii	NOUN
ejpam-4651	90	18	)	)	PUNCT
ejpam-4651	90	19	holds	hold	VERB
ejpam-4651	90	20	.	.	PUNCT
ejpam-4651	91	1	next	next	ADV
ejpam-4651	91	2	,	,	PUNCT
ejpam-4651	91	3	suppose	suppose	VERB
ejpam-4651	91	4	that	that	SCONJ
ejpam-4651	91	5	s	s	VERB
ejpam-4651	91	6	∩	∩	NOUN
ejpam-4651	91	7	{	{	PUNCT
ejpam-4651	91	8	u	u	NOUN
ejpam-4651	91	9	,	,	PUNCT
ejpam-4651	91	10	v	v	NOUN
ejpam-4651	91	11	}	}	PUNCT
ejpam-4651	91	12	̸=	̸=	PROPN
ejpam-4651	91	13	∅	∅	NOUN
ejpam-4651	91	14	and	and	CCONJ
ejpam-4651	91	15	s	s	VERB
ejpam-4651	91	16	∩	∩	ADJ
ejpam-4651	91	17	v	v	X
ejpam-4651	91	18	(	(	PUNCT
ejpam-4651	91	19	huv	huv	PROPN
ejpam-4651	91	20	)	)	PUNCT
ejpam-4651	91	21	̸=	̸=	PROPN
ejpam-4651	91	22	∅	∅	NOUN
ejpam-4651	91	23	for	for	ADP
ejpam-4651	91	24	some	some	DET
ejpam-4651	91	25	uv	uv	NOUN
ejpam-4651	91	26	∈	∈	PROPN
ejpam-4651	91	27	v	v	NOUN
ejpam-4651	91	28	(	(	PUNCT
ejpam-4651	91	29	g	g	NOUN
ejpam-4651	91	30	)	)	PUNCT
ejpam-4651	91	31	.	.	PUNCT
ejpam-4651	92	1	then	then	ADV
ejpam-4651	92	2	s	s	VERB
ejpam-4651	92	3	=	=	PROPN
ejpam-4651	92	4	suv	suv	PROPN
ejpam-4651	92	5	∪d	∪d	NUM
ejpam-4651	92	6	,	,	PUNCT
ejpam-4651	92	7	where	where	SCONJ
ejpam-4651	92	8	suv	suv	PROPN
ejpam-4651	92	9	is	be	AUX
ejpam-4651	92	10	a	a	DET
ejpam-4651	92	11	clique	clique	NOUN
ejpam-4651	92	12	in	in	ADP
ejpam-4651	92	13	huv	huv	PROPN
ejpam-4651	92	14	and	and	CCONJ
ejpam-4651	92	15	∅	∅	NOUN
ejpam-4651	92	16	̸=	̸=	PROPN
ejpam-4651	92	17	d	d	NOUN
ejpam-4651	92	18	⊆	⊆	NUM
ejpam-4651	92	19	{	{	PUNCT
ejpam-4651	92	20	u	u	NOUN
ejpam-4651	92	21	,	,	PUNCT
ejpam-4651	92	22	v	v	NOUN
ejpam-4651	92	23	}	}	PUNCT
ejpam-4651	92	24	for	for	ADP
ejpam-4651	92	25	some	some	DET
ejpam-4651	92	26	uv	uv	PROPN
ejpam-4651	92	27	∈	∈	PROPN
ejpam-4651	92	28	e(g	e(g	PROPN
ejpam-4651	92	29	)	)	PUNCT
ejpam-4651	92	30	,	,	PUNCT
ejpam-4651	92	31	by	by	ADP
ejpam-4651	92	32	theorem	theorem	NOUN
ejpam-4651	92	33	2(iii	2(iii	NUM
ejpam-4651	92	34	)	)	PUNCT
ejpam-4651	92	35	.	.	PUNCT
ejpam-4651	93	1	again	again	ADV
ejpam-4651	93	2	,	,	PUNCT
ejpam-4651	93	3	since	since	SCONJ
ejpam-4651	93	4	s	s	NOUN
ejpam-4651	93	5	is	be	AUX
ejpam-4651	93	6	a	a	DET
ejpam-4651	93	7	superclique	superclique	NOUN
ejpam-4651	93	8	in	in	ADP
ejpam-4651	93	9	g	g	PROPN
ejpam-4651	93	10	⋄	⋄	PROPN
ejpam-4651	93	11	h	h	NOUN
ejpam-4651	93	12	,	,	PUNCT
ejpam-4651	93	13	suv	suv	PROPN
ejpam-4651	93	14	is	be	AUX
ejpam-4651	93	15	a	a	DET
ejpam-4651	93	16	superclique	superclique	NOUN
ejpam-4651	93	17	in	in	ADP
ejpam-4651	93	18	huv	huv	PROPN
ejpam-4651	93	19	.	.	PUNCT
ejpam-4651	94	1	suppose	suppose	VERB
ejpam-4651	94	2	now	now	ADV
ejpam-4651	94	3	that	that	SCONJ
ejpam-4651	94	4	degg(u	degg(u	VERB
ejpam-4651	94	5	)	)	PUNCT
ejpam-4651	94	6	=	=	SYM
ejpam-4651	94	7	1	1	NUM
ejpam-4651	94	8	or	or	CCONJ
ejpam-4651	94	9	degg(v	degg(v	PROPN
ejpam-4651	94	10	)	)	PUNCT
ejpam-4651	94	11	=	=	SYM
ejpam-4651	94	12	1	1	NUM
ejpam-4651	94	13	,	,	PUNCT
ejpam-4651	94	14	say	say	VERB
ejpam-4651	94	15	degg(v	degg(v	VERB
ejpam-4651	94	16	)	)	PUNCT
ejpam-4651	94	17	=	=	SYM
ejpam-4651	94	18	1	1	X
ejpam-4651	94	19	.	.	X
ejpam-4651	94	20	pick	pick	VERB
ejpam-4651	94	21	any	any	DET
ejpam-4651	94	22	x	x	SYM
ejpam-4651	94	23	∈	∈	PROPN
ejpam-4651	94	24	suv	suv	PROPN
ejpam-4651	94	25	.	.	PUNCT
ejpam-4651	95	1	then	then	ADV
ejpam-4651	95	2	ng⋄h(x)∩	ng⋄h(x)∩	X
ejpam-4651	96	1	[	[	X
ejpam-4651	96	2	v	v	X
ejpam-4651	96	3	(	(	PUNCT
ejpam-4651	96	4	g	g	PROPN
ejpam-4651	96	5	⋄h	⋄h	PROPN
ejpam-4651	96	6	)	)	PUNCT
ejpam-4651	96	7	\	\	PUNCT
ejpam-4651	97	1	s	s	X
ejpam-4651	97	2	]	]	X
ejpam-4651	97	3	=	=	PUNCT
ejpam-4651	97	4	ng⋄h(u)∩	ng⋄h(u)∩	PROPN
ejpam-4651	98	1	[	[	X
ejpam-4651	98	2	v	v	X
ejpam-4651	98	3	(	(	PUNCT
ejpam-4651	98	4	g	g	PROPN
ejpam-4651	98	5	⋄h	⋄h	PROPN
ejpam-4651	98	6	)	)	PUNCT
ejpam-4651	98	7	\	\	PROPN
ejpam-4651	99	1	s	s	PART
ejpam-4651	99	2	]	]	X
ejpam-4651	99	3	.	.	PUNCT
ejpam-4651	100	1	thus	thus	ADV
ejpam-4651	100	2	,	,	PUNCT
ejpam-4651	100	3	u	u	PROPN
ejpam-4651	100	4	/∈	/∈	PROPN
ejpam-4651	100	5	d.	d.	PROPN
ejpam-4651	100	6	therefore	therefore	ADV
ejpam-4651	100	7	,	,	PUNCT
ejpam-4651	100	8	|d|	|d|	PROPN
ejpam-4651	100	9	=	=	SYM
ejpam-4651	100	10	1	1	X
ejpam-4651	100	11	.	.	PUNCT
ejpam-4651	101	1	in	in	ADP
ejpam-4651	101	2	particular	particular	ADJ
ejpam-4651	101	3	,	,	PUNCT
ejpam-4651	101	4	d	d	AUX
ejpam-4651	101	5	=	=	PRON
ejpam-4651	101	6	{	{	PUNCT
ejpam-4651	101	7	u	u	NOUN
ejpam-4651	101	8	}	}	PUNCT
ejpam-4651	101	9	showing	show	VERB
ejpam-4651	101	10	that	that	SCONJ
ejpam-4651	101	11	(	(	PUNCT
ejpam-4651	101	12	iii	iii	NOUN
ejpam-4651	101	13	)	)	PUNCT
ejpam-4651	101	14	holds	hold	VERB
ejpam-4651	101	15	.	.	PUNCT
ejpam-4651	102	1	for	for	ADP
ejpam-4651	102	2	the	the	DET
ejpam-4651	102	3	converse	converse	NOUN
ejpam-4651	102	4	,	,	PUNCT
ejpam-4651	102	5	suppose	suppose	VERB
ejpam-4651	102	6	first	first	ADV
ejpam-4651	102	7	that	that	SCONJ
ejpam-4651	102	8	(	(	PUNCT
ejpam-4651	102	9	i	i	NOUN
ejpam-4651	102	10	)	)	PUNCT
ejpam-4651	102	11	holds	hold	VERB
ejpam-4651	102	12	.	.	PUNCT
ejpam-4651	103	1	let	let	VERB
ejpam-4651	103	2	u	u	NOUN
ejpam-4651	103	3	,	,	PUNCT
ejpam-4651	103	4	v	v	PROPN
ejpam-4651	103	5	∈	∈	NOUN
ejpam-4651	103	6	s	s	VERB
ejpam-4651	103	7	with	with	ADP
ejpam-4651	103	8	u	u	NOUN
ejpam-4651	103	9	̸=	̸=	PROPN
ejpam-4651	103	10	v.	v.	ADV
ejpam-4651	103	11	since	since	SCONJ
ejpam-4651	103	12	g	g	PROPN
ejpam-4651	103	13	is	be	AUX
ejpam-4651	103	14	connected	connect	VERB
ejpam-4651	103	15	and	and	CCONJ
ejpam-4651	103	16	g	g	PROPN
ejpam-4651	103	17	̸=	̸=	PROPN
ejpam-4651	103	18	k2	k2	PROPN
ejpam-4651	103	19	,	,	PUNCT
ejpam-4651	103	20	degg(u	degg(u	PROPN
ejpam-4651	103	21	)	)	PUNCT
ejpam-4651	103	22	≥	≥	NOUN
ejpam-4651	103	23	2	2	NUM
ejpam-4651	103	24	or	or	CCONJ
ejpam-4651	103	25	degg(v	degg(v	PROPN
ejpam-4651	103	26	)	)	PUNCT
ejpam-4651	103	27	≥	≥	NOUN
ejpam-4651	104	1	2	2	NUM
ejpam-4651	104	2	.	.	X
ejpam-4651	104	3	assume	assume	VERB
ejpam-4651	104	4	that	that	SCONJ
ejpam-4651	104	5	degg(u	degg(u	PROPN
ejpam-4651	104	6	)	)	PUNCT
ejpam-4651	104	7	≥	≥	NOUN
ejpam-4651	104	8	2	2	NUM
ejpam-4651	104	9	.	.	PUNCT
ejpam-4651	105	1	let	let	VERB
ejpam-4651	105	2	w	w	PROPN
ejpam-4651	105	3	∈	∈	PROPN
ejpam-4651	105	4	ng(u	ng(u	NOUN
ejpam-4651	105	5	)	)	PUNCT
ejpam-4651	105	6	\	\	NOUN
ejpam-4651	105	7	{	{	PUNCT
ejpam-4651	105	8	v	v	NOUN
ejpam-4651	105	9	}	}	PUNCT
ejpam-4651	105	10	and	and	CCONJ
ejpam-4651	105	11	pick	pick	VERB
ejpam-4651	105	12	any	any	DET
ejpam-4651	105	13	q	q	PROPN
ejpam-4651	105	14	∈	∈	PROPN
ejpam-4651	105	15	v	v	NOUN
ejpam-4651	105	16	(	(	PUNCT
ejpam-4651	105	17	huw	huw	PROPN
ejpam-4651	105	18	)	)	PUNCT
ejpam-4651	105	19	.	.	PUNCT
ejpam-4651	106	1	then	then	ADV
ejpam-4651	106	2	q	q	PROPN
ejpam-4651	106	3	∈	∈	PROPN
ejpam-4651	106	4	v	v	NOUN
ejpam-4651	106	5	(	(	PUNCT
ejpam-4651	106	6	g	g	PROPN
ejpam-4651	106	7	⋄	⋄	PROPN
ejpam-4651	106	8	h	h	PROPN
ejpam-4651	106	9	)	)	PUNCT
ejpam-4651	106	10	\	\	PROPN
ejpam-4651	106	11	s	s	PROPN
ejpam-4651	106	12	and	and	CCONJ
ejpam-4651	106	13	q	q	PROPN
ejpam-4651	106	14	∈	∈	PROPN
ejpam-4651	106	15	ng⋄h(u)\ng⋄h(v	ng⋄h(u)\ng⋄h(v	NOUN
ejpam-4651	106	16	)	)	PUNCT
ejpam-4651	106	17	.	.	PUNCT
ejpam-4651	107	1	therefore	therefore	ADV
ejpam-4651	107	2	,	,	PUNCT
ejpam-4651	107	3	s	s	VERB
ejpam-4651	107	4	is	be	AUX
ejpam-4651	107	5	a	a	DET
ejpam-4651	107	6	superclique	superclique	NOUN
ejpam-4651	107	7	in	in	ADP
ejpam-4651	107	8	g⋄h	g⋄h	PROPN
ejpam-4651	107	9	.	.	PUNCT
ejpam-4651	108	1	next	next	ADV
ejpam-4651	108	2	,	,	PUNCT
ejpam-4651	108	3	suppose	suppose	VERB
ejpam-4651	108	4	that	that	SCONJ
ejpam-4651	108	5	(	(	PUNCT
ejpam-4651	108	6	ii	ii	NOUN
ejpam-4651	108	7	)	)	PUNCT
ejpam-4651	108	8	holds	hold	VERB
ejpam-4651	108	9	.	.	PUNCT
ejpam-4651	109	1	s.	s.	PROPN
ejpam-4651	109	2	canoy	canoy	PROPN
ejpam-4651	109	3	,	,	PUNCT
ejpam-4651	109	4	jr	jr	PROPN
ejpam-4651	109	5	.	.	PROPN
ejpam-4651	109	6	,	,	PUNCT
ejpam-4651	109	7	r.	r.	PROPN
ejpam-4651	109	8	dela	dela	PROPN
ejpam-4651	109	9	cerna	cerna	PROPN
ejpam-4651	109	10	,	,	PUNCT
ejpam-4651	109	11	a.	a.	NOUN
ejpam-4651	109	12	abragan	abragan	PROPN
ejpam-4651	109	13	/	/	SYM
ejpam-4651	109	14	eur	eur	PROPN
ejpam-4651	109	15	.	.	PUNCT
ejpam-4651	110	1	j.	j.	PROPN
ejpam-4651	110	2	pure	pure	PROPN
ejpam-4651	110	3	appl	appl	PROPN
ejpam-4651	110	4	.	.	PROPN
ejpam-4651	110	5	math	math	PROPN
ejpam-4651	110	6	,	,	PUNCT
ejpam-4651	110	7	16	16	NUM
ejpam-4651	110	8	(	(	PUNCT
ejpam-4651	110	9	1	1	NUM
ejpam-4651	110	10	)	)	PUNCT
ejpam-4651	110	11	(	(	PUNCT
ejpam-4651	110	12	2023	2023	NUM
ejpam-4651	110	13	)	)	PUNCT
ejpam-4651	110	14	,	,	PUNCT
ejpam-4651	110	15	243	243	NUM
ejpam-4651	110	16	-	-	SYM
ejpam-4651	110	17	252	252	NUM
ejpam-4651	110	18	246	246	NUM
ejpam-4651	110	19	since	since	SCONJ
ejpam-4651	110	20	s	s	PROPN
ejpam-4651	110	21	is	be	AUX
ejpam-4651	110	22	a	a	DET
ejpam-4651	110	23	superclique	superclique	NOUN
ejpam-4651	110	24	in	in	ADP
ejpam-4651	110	25	huv	huv	PROPN
ejpam-4651	110	26	,	,	PUNCT
ejpam-4651	110	27	it	it	PRON
ejpam-4651	110	28	is	be	AUX
ejpam-4651	110	29	a	a	DET
ejpam-4651	110	30	superclique	superclique	NOUN
ejpam-4651	110	31	in	in	ADP
ejpam-4651	110	32	g	g	PROPN
ejpam-4651	110	33	⋄h	⋄h	PROPN
ejpam-4651	110	34	.	.	PUNCT
ejpam-4651	111	1	finally	finally	ADV
ejpam-4651	111	2	,	,	PUNCT
ejpam-4651	111	3	suppose	suppose	VERB
ejpam-4651	111	4	that	that	SCONJ
ejpam-4651	111	5	(	(	PUNCT
ejpam-4651	111	6	iii	iii	NOUN
ejpam-4651	111	7	)	)	PUNCT
ejpam-4651	111	8	holds	hold	VERB
ejpam-4651	111	9	.	.	PUNCT
ejpam-4651	112	1	by	by	ADP
ejpam-4651	112	2	theorem	theorem	ADJ
ejpam-4651	112	3	2(iii	2(iii	NUM
ejpam-4651	112	4	)	)	PUNCT
ejpam-4651	112	5	,	,	PUNCT
ejpam-4651	112	6	s	s	VERB
ejpam-4651	112	7	is	be	AUX
ejpam-4651	112	8	a	a	DET
ejpam-4651	112	9	clique	clique	NOUN
ejpam-4651	112	10	in	in	ADP
ejpam-4651	112	11	g	g	PROPN
ejpam-4651	112	12	⋄h	⋄h	PROPN
ejpam-4651	112	13	.	.	PUNCT
ejpam-4651	113	1	let	let	VERB
ejpam-4651	113	2	x	x	PRON
ejpam-4651	113	3	,	,	PUNCT
ejpam-4651	113	4	y	y	PROPN
ejpam-4651	113	5	∈	∈	PROPN
ejpam-4651	113	6	s	s	PART
ejpam-4651	113	7	with	with	ADP
ejpam-4651	113	8	x	x	PART
ejpam-4651	113	9	̸=	̸=	PROPN
ejpam-4651	113	10	y.	y.	NOUN
ejpam-4651	113	11	if	if	SCONJ
ejpam-4651	113	12	x	x	PRON
ejpam-4651	113	13	,	,	PUNCT
ejpam-4651	113	14	y	y	PROPN
ejpam-4651	113	15	∈	∈	PROPN
ejpam-4651	113	16	suv	suv	PROPN
ejpam-4651	113	17	,	,	PUNCT
ejpam-4651	113	18	then	then	ADV
ejpam-4651	113	19	there	there	PRON
ejpam-4651	113	20	exists	exist	VERB
ejpam-4651	113	21	z	z	PROPN
ejpam-4651	113	22	∈	∈	PROPN
ejpam-4651	113	23	v	v	PROPN
ejpam-4651	113	24	(	(	PUNCT
ejpam-4651	113	25	huv	huv	PROPN
ejpam-4651	113	26	\	\	PROPN
ejpam-4651	113	27	suv	suv	PROPN
ejpam-4651	113	28	)	)	PUNCT
ejpam-4651	113	29	⊆	⊆	NUM
ejpam-4651	113	30	v	v	NOUN
ejpam-4651	113	31	(	(	PUNCT
ejpam-4651	113	32	g	g	PROPN
ejpam-4651	113	33	⋄h	⋄h	PROPN
ejpam-4651	113	34	)	)	PUNCT
ejpam-4651	113	35	\	\	PROPN
ejpam-4651	114	1	s	s	VERB
ejpam-4651	115	1	such	such	ADJ
ejpam-4651	115	2	that	that	SCONJ
ejpam-4651	115	3	z	z	PROPN
ejpam-4651	115	4	∈	∈	PROPN
ejpam-4651	115	5	nhuv(x	nhuv(x	NOUN
ejpam-4651	115	6	)	)	PUNCT
ejpam-4651	115	7	\nhuv(y	\nhuv(y	PROPN
ejpam-4651	115	8	)	)	PUNCT
ejpam-4651	116	1	or	or	CCONJ
ejpam-4651	116	2	z	z	NOUN
ejpam-4651	116	3	∈	∈	PROPN
ejpam-4651	116	4	nhuv(y	nhuv(y	NOUN
ejpam-4651	116	5	)	)	PUNCT
ejpam-4651	116	6	\nhuv(x	\nhuv(x	PUNCT
ejpam-4651	116	7	)	)	PUNCT
ejpam-4651	116	8	because	because	SCONJ
ejpam-4651	116	9	suv	suv	PROPN
ejpam-4651	116	10	is	be	AUX
ejpam-4651	116	11	a	a	DET
ejpam-4651	116	12	superclique	superclique	NOUN
ejpam-4651	116	13	in	in	ADP
ejpam-4651	116	14	huv	huv	PROPN
ejpam-4651	116	15	.	.	PUNCT
ejpam-4651	117	1	therefore	therefore	ADV
ejpam-4651	117	2	,	,	PUNCT
ejpam-4651	117	3	z	z	PROPN
ejpam-4651	117	4	∈	∈	PROPN
ejpam-4651	117	5	v	v	NOUN
ejpam-4651	117	6	(	(	PUNCT
ejpam-4651	117	7	g	g	PROPN
ejpam-4651	117	8	⋄h	⋄h	PROPN
ejpam-4651	117	9	)	)	PUNCT
ejpam-4651	117	10	\	\	PROPN
ejpam-4651	118	1	s	s	PROPN
ejpam-4651	118	2	and	and	CCONJ
ejpam-4651	118	3	z	z	PROPN
ejpam-4651	118	4	∈	∈	PROPN
ejpam-4651	118	5	ng⋄h(x	ng⋄h(x	PROPN
ejpam-4651	118	6	)	)	PUNCT
ejpam-4651	118	7	\	\	PROPN
ejpam-4651	119	1	ng⋄h(y	ng⋄h(y	PROPN
ejpam-4651	119	2	)	)	PUNCT
ejpam-4651	119	3	or	or	CCONJ
ejpam-4651	119	4	z	z	NOUN
ejpam-4651	119	5	∈	∈	PROPN
ejpam-4651	119	6	ng⋄h(y	ng⋄h(y	PROPN
ejpam-4651	119	7	)	)	PUNCT
ejpam-4651	119	8	\	\	PROPN
ejpam-4651	119	9	ng⋄h(x	ng⋄h(x	PROPN
ejpam-4651	119	10	)	)	PUNCT
ejpam-4651	119	11	.	.	PUNCT
ejpam-4651	120	1	suppose	suppose	VERB
ejpam-4651	120	2	x	x	SYM
ejpam-4651	120	3	∈	∈	PROPN
ejpam-4651	120	4	d	d	NOUN
ejpam-4651	120	5	and	and	CCONJ
ejpam-4651	120	6	y	y	PROPN
ejpam-4651	120	7	∈	∈	PROPN
ejpam-4651	120	8	suv	suv	PROPN
ejpam-4651	120	9	.	.	PROPN
ejpam-4651	121	1	assume	assume	VERB
ejpam-4651	121	2	,	,	PUNCT
ejpam-4651	121	3	without	without	ADP
ejpam-4651	121	4	lost	lose	VERB
ejpam-4651	121	5	of	of	ADP
ejpam-4651	121	6	generality	generality	NOUN
ejpam-4651	121	7	,	,	PUNCT
ejpam-4651	121	8	that	that	SCONJ
ejpam-4651	121	9	x	x	X
ejpam-4651	121	10	=	=	PUNCT
ejpam-4651	121	11	u.	u.	PROPN
ejpam-4651	121	12	then	then	ADV
ejpam-4651	121	13	degg(u	degg(u	PROPN
ejpam-4651	121	14	)	)	PUNCT
ejpam-4651	121	15	≥	≥	NOUN
ejpam-4651	121	16	2	2	NUM
ejpam-4651	121	17	.	.	PUNCT
ejpam-4651	122	1	let	let	VERB
ejpam-4651	122	2	w	w	PROPN
ejpam-4651	122	3	∈	∈	PROPN
ejpam-4651	122	4	ng(u	ng(u	NOUN
ejpam-4651	122	5	)	)	PUNCT
ejpam-4651	122	6	\	\	NOUN
ejpam-4651	122	7	{	{	PUNCT
ejpam-4651	122	8	v	v	NOUN
ejpam-4651	122	9	}	}	PUNCT
ejpam-4651	122	10	.	.	PUNCT
ejpam-4651	123	1	then	then	ADV
ejpam-4651	123	2	w	w	PROPN
ejpam-4651	123	3	∈	∈	PROPN
ejpam-4651	123	4	v	v	ADP
ejpam-4651	123	5	(	(	PUNCT
ejpam-4651	123	6	g	g	PROPN
ejpam-4651	123	7	⋄h	⋄h	PROPN
ejpam-4651	123	8	)	)	PUNCT
ejpam-4651	123	9	\	\	PROPN
ejpam-4651	123	10	s	s	PROPN
ejpam-4651	123	11	and	and	CCONJ
ejpam-4651	123	12	w	w	PROPN
ejpam-4651	123	13	∈	∈	PROPN
ejpam-4651	123	14	ng⋄h(x	ng⋄h(x	PROPN
ejpam-4651	123	15	)	)	PUNCT
ejpam-4651	123	16	\ng⋄h(y	\ng⋄h(y	NOUN
ejpam-4651	123	17	)	)	PUNCT
ejpam-4651	123	18	.	.	PUNCT
ejpam-4651	124	1	lastly	lastly	ADV
ejpam-4651	124	2	,	,	PUNCT
ejpam-4651	124	3	suppose	suppose	VERB
ejpam-4651	124	4	that	that	SCONJ
ejpam-4651	124	5	x	x	NOUN
ejpam-4651	124	6	,	,	PUNCT
ejpam-4651	124	7	y	y	PROPN
ejpam-4651	124	8	∈	∈	PROPN
ejpam-4651	124	9	d	d	X
ejpam-4651	124	10	.	.	PUNCT
ejpam-4651	125	1	in	in	ADP
ejpam-4651	125	2	particular	particular	ADJ
ejpam-4651	125	3	,	,	PUNCT
ejpam-4651	125	4	let	let	VERB
ejpam-4651	125	5	x	x	SYM
ejpam-4651	125	6	=	=	PUNCT
ejpam-4651	125	7	u	u	NOUN
ejpam-4651	125	8	and	and	CCONJ
ejpam-4651	125	9	y	y	PROPN
ejpam-4651	125	10	=	=	PROPN
ejpam-4651	126	1	v.	v.	CCONJ
ejpam-4651	126	2	then	then	ADV
ejpam-4651	126	3	,	,	PUNCT
ejpam-4651	126	4	by	by	ADP
ejpam-4651	126	5	assumption	assumption	NOUN
ejpam-4651	126	6	,	,	PUNCT
ejpam-4651	126	7	degg(u	degg(u	PROPN
ejpam-4651	126	8	)	)	PUNCT
ejpam-4651	126	9	≥	≥	NOUN
ejpam-4651	126	10	2	2	NUM
ejpam-4651	126	11	and	and	CCONJ
ejpam-4651	126	12	degg(v	degg(v	PROPN
ejpam-4651	126	13	)	)	PUNCT
ejpam-4651	126	14	≥	≥	NOUN
ejpam-4651	126	15	2	2	NUM
ejpam-4651	126	16	.	.	PUNCT
ejpam-4651	127	1	let	let	VERB
ejpam-4651	127	2	z	z	PROPN
ejpam-4651	127	3	∈	∈	PROPN
ejpam-4651	127	4	ng(u	ng(u	NOUN
ejpam-4651	127	5	)	)	PUNCT
ejpam-4651	127	6	\	\	NOUN
ejpam-4651	127	7	{	{	PUNCT
ejpam-4651	127	8	v	v	NOUN
ejpam-4651	127	9	}	}	PUNCT
ejpam-4651	127	10	and	and	CCONJ
ejpam-4651	127	11	choose	choose	VERB
ejpam-4651	127	12	any	any	DET
ejpam-4651	127	13	p	p	PROPN
ejpam-4651	127	14	∈	∈	PROPN
ejpam-4651	127	15	v	v	ADP
ejpam-4651	127	16	(	(	PUNCT
ejpam-4651	127	17	huz	huz	NOUN
ejpam-4651	127	18	)	)	PUNCT
ejpam-4651	127	19	.	.	PUNCT
ejpam-4651	128	1	then	then	ADV
ejpam-4651	128	2	p	p	PROPN
ejpam-4651	128	3	∈	∈	PROPN
ejpam-4651	128	4	v	v	NOUN
ejpam-4651	128	5	(	(	PUNCT
ejpam-4651	128	6	g	g	PROPN
ejpam-4651	128	7	⋄	⋄	PROPN
ejpam-4651	128	8	h	h	PROPN
ejpam-4651	128	9	)	)	PUNCT
ejpam-4651	128	10	\	\	PROPN
ejpam-4651	129	1	s	s	PART
ejpam-4651	129	2	and	and	CCONJ
ejpam-4651	129	3	p	p	PROPN
ejpam-4651	129	4	∈	∈	PROPN
ejpam-4651	129	5	ng⋄h(x	ng⋄h(x	PROPN
ejpam-4651	129	6	)	)	PUNCT
ejpam-4651	129	7	\ng⋄h(y	\ng⋄h(y	NOUN
ejpam-4651	129	8	)	)	PUNCT
ejpam-4651	129	9	.	.	PUNCT
ejpam-4651	130	1	therefore	therefore	ADV
ejpam-4651	130	2	,	,	PUNCT
ejpam-4651	130	3	in	in	ADP
ejpam-4651	130	4	either	either	DET
ejpam-4651	130	5	case	case	NOUN
ejpam-4651	130	6	,	,	PUNCT
ejpam-4651	130	7	s	s	VERB
ejpam-4651	130	8	is	be	AUX
ejpam-4651	130	9	a	a	DET
ejpam-4651	130	10	superclique	superclique	NOUN
ejpam-4651	130	11	in	in	ADP
ejpam-4651	130	12	g	g	PROPN
ejpam-4651	130	13	⋄h	⋄h	PROPN
ejpam-4651	130	14	.	.	PUNCT
ejpam-4651	131	1	corollary	corollary	ADJ
ejpam-4651	131	2	2	2	NUM
ejpam-4651	131	3	.	.	PUNCT
ejpam-4651	132	1	let	let	VERB
ejpam-4651	132	2	g	g	PRON
ejpam-4651	132	3	be	be	AUX
ejpam-4651	132	4	a	a	DET
ejpam-4651	132	5	nontrivial	nontrivial	ADJ
ejpam-4651	132	6	connected	connect	VERB
ejpam-4651	132	7	graph	graph	NOUN
ejpam-4651	132	8	such	such	ADJ
ejpam-4651	132	9	that	that	SCONJ
ejpam-4651	132	10	g	g	PROPN
ejpam-4651	132	11	is	be	AUX
ejpam-4651	132	12	not	not	PART
ejpam-4651	132	13	a	a	DET
ejpam-4651	132	14	star	star	NOUN
ejpam-4651	132	15	and	and	CCONJ
ejpam-4651	132	16	let	let	VERB
ejpam-4651	132	17	h	h	NOUN
ejpam-4651	132	18	be	be	AUX
ejpam-4651	132	19	any	any	DET
ejpam-4651	132	20	graph	graph	NOUN
ejpam-4651	132	21	.	.	PUNCT
ejpam-4651	133	1	then	then	ADV
ejpam-4651	133	2	ωs(g	ωs(g	PUNCT
ejpam-4651	133	3	⋄h	⋄h	X
ejpam-4651	133	4	)	)	PUNCT
ejpam-4651	133	5	=	=	SYM
ejpam-4651	133	6	max{ω(g	max{ω(g	PROPN
ejpam-4651	133	7	)	)	PUNCT
ejpam-4651	133	8	,	,	PUNCT
ejpam-4651	133	9	ωs(h	ωs(h	NUM
ejpam-4651	133	10	)	)	PUNCT
ejpam-4651	133	11	+	+	CCONJ
ejpam-4651	133	12	2	2	NUM
ejpam-4651	133	13	}	}	PUNCT
ejpam-4651	133	14	.	.	PUNCT
ejpam-4651	134	1	proof	proof	NOUN
ejpam-4651	134	2	.	.	PUNCT
ejpam-4651	135	1	let	let	VERB
ejpam-4651	135	2	s	s	PRON
ejpam-4651	135	3	be	be	AUX
ejpam-4651	135	4	a	a	DET
ejpam-4651	135	5	maximum	maximum	ADJ
ejpam-4651	135	6	clique	clique	NOUN
ejpam-4651	135	7	in	in	ADP
ejpam-4651	135	8	g	g	PROPN
ejpam-4651	135	9	and	and	CCONJ
ejpam-4651	135	10	let	let	VERB
ejpam-4651	135	11	u	u	NOUN
ejpam-4651	135	12	,	,	PUNCT
ejpam-4651	135	13	v	v	PROPN
ejpam-4651	135	14	∈	∈	PROPN
ejpam-4651	135	15	v	v	NOUN
ejpam-4651	135	16	(	(	PUNCT
ejpam-4651	135	17	g	g	NOUN
ejpam-4651	135	18	)	)	PUNCT
ejpam-4651	135	19	with	with	ADP
ejpam-4651	135	20	degg(u	degg(u	PROPN
ejpam-4651	135	21	)	)	PUNCT
ejpam-4651	135	22	≥	≥	NOUN
ejpam-4651	135	23	2	2	NUM
ejpam-4651	135	24	and	and	CCONJ
ejpam-4651	135	25	degg(v	degg(v	PROPN
ejpam-4651	135	26	)	)	PUNCT
ejpam-4651	135	27	≥	≥	NUM
ejpam-4651	135	28	2	2	NUM
ejpam-4651	135	29	(	(	PUNCT
ejpam-4651	135	30	these	these	DET
ejpam-4651	135	31	vertices	vertex	NOUN
ejpam-4651	135	32	exist	exist	VERB
ejpam-4651	135	33	because	because	SCONJ
ejpam-4651	135	34	g	g	PROPN
ejpam-4651	135	35	is	be	AUX
ejpam-4651	135	36	not	not	PART
ejpam-4651	135	37	a	a	DET
ejpam-4651	135	38	star	star	NOUN
ejpam-4651	135	39	)	)	PUNCT
ejpam-4651	135	40	.	.	PUNCT
ejpam-4651	136	1	let	let	VERB
ejpam-4651	136	2	suv	suv	PROPN
ejpam-4651	136	3	be	be	AUX
ejpam-4651	136	4	a	a	DET
ejpam-4651	136	5	maximum	maximum	ADJ
ejpam-4651	136	6	superclique	superclique	NOUN
ejpam-4651	136	7	in	in	ADP
ejpam-4651	136	8	huv	huv	PROPN
ejpam-4651	136	9	.	.	PUNCT
ejpam-4651	137	1	then	then	ADV
ejpam-4651	137	2	s	s	VERB
ejpam-4651	137	3	and	and	CCONJ
ejpam-4651	137	4	s∗	s∗	PROPN
ejpam-4651	137	5	=	=	SYM
ejpam-4651	137	6	suv	suv	PROPN
ejpam-4651	137	7	∪	∪	X
ejpam-4651	137	8	{	{	PUNCT
ejpam-4651	137	9	u	u	NOUN
ejpam-4651	137	10	,	,	PUNCT
ejpam-4651	137	11	v	v	NOUN
ejpam-4651	137	12	}	}	PUNCT
ejpam-4651	137	13	are	be	AUX
ejpam-4651	137	14	supercliques	superclique	NOUN
ejpam-4651	137	15	in	in	ADP
ejpam-4651	137	16	g	g	PROPN
ejpam-4651	137	17	⋄h	⋄h	NOUN
ejpam-4651	137	18	by	by	ADP
ejpam-4651	137	19	theorem	theorem	NOUN
ejpam-4651	137	20	3	3	NUM
ejpam-4651	137	21	.	.	PUNCT
ejpam-4651	138	1	this	this	PRON
ejpam-4651	138	2	implies	imply	VERB
ejpam-4651	138	3	that	that	SCONJ
ejpam-4651	138	4	ωs(g	ωs(g	PUNCT
ejpam-4651	138	5	⋄h	⋄h	PROPN
ejpam-4651	138	6	)	)	PUNCT
ejpam-4651	138	7	≥	≥	NOUN
ejpam-4651	138	8	max{|s|	max{|s|	NOUN
ejpam-4651	138	9	,	,	PUNCT
ejpam-4651	138	10	|s∗|	|s∗|	NUM
ejpam-4651	138	11	}	}	PUNCT
ejpam-4651	138	12	=	=	SYM
ejpam-4651	138	13	max{ω(g	max{ω(g	PROPN
ejpam-4651	138	14	)	)	PUNCT
ejpam-4651	138	15	,	,	PUNCT
ejpam-4651	138	16	ωs(h	ωs(h	NUM
ejpam-4651	138	17	)	)	PUNCT
ejpam-4651	138	18	+	+	CCONJ
ejpam-4651	138	19	2	2	NUM
ejpam-4651	138	20	}	}	PUNCT
ejpam-4651	138	21	.	.	PUNCT
ejpam-4651	139	1	on	on	ADP
ejpam-4651	139	2	the	the	DET
ejpam-4651	139	3	other	other	ADJ
ejpam-4651	139	4	hand	hand	NOUN
ejpam-4651	139	5	,	,	PUNCT
ejpam-4651	139	6	if	if	SCONJ
ejpam-4651	139	7	s0	s0	PROPN
ejpam-4651	139	8	is	be	AUX
ejpam-4651	139	9	a	a	DET
ejpam-4651	139	10	maximum	maximum	ADJ
ejpam-4651	139	11	superclique	superclique	NOUN
ejpam-4651	139	12	in	in	ADP
ejpam-4651	139	13	g	g	PROPN
ejpam-4651	139	14	⋄h	⋄h	PROPN
ejpam-4651	139	15	,	,	PUNCT
ejpam-4651	139	16	then	then	ADV
ejpam-4651	139	17	s0	s0	PROPN
ejpam-4651	139	18	is	be	AUX
ejpam-4651	139	19	a	a	DET
ejpam-4651	139	20	clique	clique	NOUN
ejpam-4651	139	21	in	in	ADP
ejpam-4651	139	22	g	g	PROPN
ejpam-4651	139	23	or	or	CCONJ
ejpam-4651	139	24	s0	s0	PROPN
ejpam-4651	139	25	=	=	PUNCT
ejpam-4651	139	26	suv	suv	PROPN
ejpam-4651	139	27	∪d	∪d	PUNCT
ejpam-4651	139	28	for	for	ADP
ejpam-4651	139	29	some	some	DET
ejpam-4651	139	30	uv	uv	PROPN
ejpam-4651	139	31	∈	∈	PROPN
ejpam-4651	139	32	e(g	e(g	NOUN
ejpam-4651	139	33	)	)	PUNCT
ejpam-4651	139	34	satisfying	satisfy	VERB
ejpam-4651	139	35	the	the	DET
ejpam-4651	139	36	conditions	condition	NOUN
ejpam-4651	139	37	in	in	ADP
ejpam-4651	139	38	theorem	theorem	NOUN
ejpam-4651	139	39	3(iii	3(iii	NUM
ejpam-4651	139	40	)	)	PUNCT
ejpam-4651	139	41	.	.	PUNCT
ejpam-4651	140	1	hence	hence	ADV
ejpam-4651	140	2	,	,	PUNCT
ejpam-4651	140	3	ωs(g	ωs(g	PUNCT
ejpam-4651	140	4	⋄h	⋄h	NUM
ejpam-4651	140	5	)	)	PUNCT
ejpam-4651	140	6	=	=	PRON
ejpam-4651	140	7	|s0|	|s0|	VERB
ejpam-4651	140	8	≤	≤	ADJ
ejpam-4651	140	9	max{ω(g	max{ω(g	PROPN
ejpam-4651	140	10	)	)	PUNCT
ejpam-4651	140	11	,	,	PUNCT
ejpam-4651	140	12	ωs(h	ωs(h	NUM
ejpam-4651	140	13	)	)	PUNCT
ejpam-4651	140	14	+	+	CCONJ
ejpam-4651	140	15	2	2	NUM
ejpam-4651	140	16	}	}	PUNCT
ejpam-4651	140	17	,	,	PUNCT
ejpam-4651	140	18	establishing	establish	VERB
ejpam-4651	140	19	the	the	DET
ejpam-4651	140	20	desired	desire	VERB
ejpam-4651	140	21	equality	equality	NOUN
ejpam-4651	140	22	.	.	PUNCT
ejpam-4651	141	1	theorem	theorem	ADJ
ejpam-4651	141	2	4	4	NUM
ejpam-4651	141	3	.	.	PUNCT
ejpam-4651	142	1	let	let	VERB
ejpam-4651	142	2	g	g	NOUN
ejpam-4651	142	3	=	=	PROPN
ejpam-4651	142	4	k1,m	k1,m	PROPN
ejpam-4651	142	5	=	=	PUNCT
ejpam-4651	142	6	⟨v0⟩+km	⟨v0⟩+km	PROPN
ejpam-4651	142	7	,	,	PUNCT
ejpam-4651	142	8	where	where	SCONJ
ejpam-4651	142	9	m	m	PROPN
ejpam-4651	142	10	≥	≥	NOUN
ejpam-4651	142	11	2	2	NUM
ejpam-4651	142	12	,	,	PUNCT
ejpam-4651	142	13	and	and	CCONJ
ejpam-4651	142	14	let	let	VERB
ejpam-4651	142	15	h	h	NOUN
ejpam-4651	142	16	be	be	AUX
ejpam-4651	142	17	any	any	DET
ejpam-4651	142	18	graph	graph	NOUN
ejpam-4651	142	19	.	.	PUNCT
ejpam-4651	143	1	then	then	ADV
ejpam-4651	143	2	s	s	VERB
ejpam-4651	143	3	is	be	AUX
ejpam-4651	143	4	a	a	DET
ejpam-4651	143	5	superclique	superclique	NOUN
ejpam-4651	143	6	in	in	ADP
ejpam-4651	143	7	g	g	NOUN
ejpam-4651	143	8	⋄h	⋄h	NOUN
ejpam-4651	143	9	if	if	SCONJ
ejpam-4651	144	1	and	and	CCONJ
ejpam-4651	144	2	only	only	ADV
ejpam-4651	144	3	if	if	SCONJ
ejpam-4651	144	4	one	one	NUM
ejpam-4651	144	5	of	of	ADP
ejpam-4651	144	6	the	the	DET
ejpam-4651	144	7	following	follow	VERB
ejpam-4651	144	8	holds	hold	VERB
ejpam-4651	144	9	:	:	PUNCT
ejpam-4651	144	10	(	(	PUNCT
ejpam-4651	144	11	i	i	NOUN
ejpam-4651	144	12	)	)	PUNCT
ejpam-4651	144	13	s	s	VERB
ejpam-4651	144	14	is	be	AUX
ejpam-4651	144	15	a	a	DET
ejpam-4651	144	16	clique	clique	NOUN
ejpam-4651	144	17	in	in	ADP
ejpam-4651	144	18	g.	g.	PROPN
ejpam-4651	144	19	(	(	PUNCT
ejpam-4651	144	20	ii	ii	PROPN
ejpam-4651	144	21	)	)	PUNCT
ejpam-4651	144	22	s	s	VERB
ejpam-4651	144	23	is	be	AUX
ejpam-4651	144	24	a	a	DET
ejpam-4651	144	25	superclique	superclique	NOUN
ejpam-4651	144	26	in	in	ADP
ejpam-4651	144	27	huv0	huv0	ADV
ejpam-4651	144	28	for	for	ADP
ejpam-4651	144	29	some	some	DET
ejpam-4651	144	30	u	u	NOUN
ejpam-4651	144	31	∈	∈	PROPN
ejpam-4651	144	32	v	v	ADP
ejpam-4651	144	33	(	(	PUNCT
ejpam-4651	144	34	g	g	NOUN
ejpam-4651	144	35	)	)	PUNCT
ejpam-4651	144	36	\	\	NOUN
ejpam-4651	144	37	{	{	PUNCT
ejpam-4651	144	38	v0	v0	NOUN
ejpam-4651	144	39	}	}	PUNCT
ejpam-4651	144	40	.	.	PUNCT
ejpam-4651	145	1	(	(	PUNCT
ejpam-4651	145	2	iii	iii	X
ejpam-4651	145	3	)	)	PUNCT
ejpam-4651	145	4	s	s	PART
ejpam-4651	145	5	=	=	NOUN
ejpam-4651	145	6	suv0	suv0	PROPN
ejpam-4651	145	7	∪	∪	X
ejpam-4651	145	8	{	{	PUNCT
ejpam-4651	145	9	v0	v0	NOUN
ejpam-4651	145	10	}	}	PUNCT
ejpam-4651	145	11	for	for	ADP
ejpam-4651	145	12	some	some	DET
ejpam-4651	145	13	u	u	PROPN
ejpam-4651	145	14	∈	∈	PROPN
ejpam-4651	145	15	v	v	ADP
ejpam-4651	145	16	(	(	PUNCT
ejpam-4651	145	17	g	g	NOUN
ejpam-4651	145	18	)	)	PUNCT
ejpam-4651	145	19	\	\	NOUN
ejpam-4651	145	20	{	{	PUNCT
ejpam-4651	145	21	v0	v0	NOUN
ejpam-4651	145	22	}	}	PUNCT
ejpam-4651	145	23	,	,	PUNCT
ejpam-4651	145	24	where	where	SCONJ
ejpam-4651	145	25	suv0	suv0	PROPN
ejpam-4651	145	26	is	be	AUX
ejpam-4651	145	27	a	a	DET
ejpam-4651	145	28	superclique	superclique	NOUN
ejpam-4651	145	29	in	in	ADP
ejpam-4651	145	30	huv0	huv0	ADV
ejpam-4651	145	31	.	.	PUNCT
ejpam-4651	146	1	proof	proof	NOUN
ejpam-4651	146	2	.	.	PUNCT
ejpam-4651	147	1	suppose	suppose	VERB
ejpam-4651	147	2	s	s	PRON
ejpam-4651	147	3	is	be	AUX
ejpam-4651	147	4	a	a	DET
ejpam-4651	147	5	superclique	superclique	NOUN
ejpam-4651	147	6	in	in	ADP
ejpam-4651	147	7	g	g	PROPN
ejpam-4651	147	8	⋄h	⋄h	PROPN
ejpam-4651	147	9	.	.	PUNCT
ejpam-4651	148	1	then	then	ADV
ejpam-4651	148	2	(	(	PUNCT
ejpam-4651	148	3	i	i	NOUN
ejpam-4651	148	4	)	)	PUNCT
ejpam-4651	148	5	,	,	PUNCT
ejpam-4651	148	6	(	(	PUNCT
ejpam-4651	148	7	ii	ii	NOUN
ejpam-4651	148	8	)	)	PUNCT
ejpam-4651	148	9	,	,	PUNCT
ejpam-4651	148	10	or	or	CCONJ
ejpam-4651	148	11	(	(	PUNCT
ejpam-4651	148	12	iii	iii	X
ejpam-4651	148	13	)	)	PUNCT
ejpam-4651	148	14	holds	hold	VERB
ejpam-4651	148	15	by	by	ADP
ejpam-4651	148	16	theorem	theorem	NOUN
ejpam-4651	148	17	3	3	NUM
ejpam-4651	148	18	.	.	PUNCT
ejpam-4651	149	1	the	the	DET
ejpam-4651	149	2	converse	converse	NOUN
ejpam-4651	149	3	also	also	ADV
ejpam-4651	149	4	follows	follow	VERB
ejpam-4651	149	5	from	from	ADP
ejpam-4651	149	6	theorem	theorem	ADJ
ejpam-4651	149	7	3	3	NUM
ejpam-4651	149	8	.	.	PUNCT
ejpam-4651	149	9	corollary	corollary	ADJ
ejpam-4651	149	10	3	3	X
ejpam-4651	149	11	.	.	PUNCT
ejpam-4651	150	1	let	let	VERB
ejpam-4651	150	2	g	g	NOUN
ejpam-4651	150	3	=	=	PROPN
ejpam-4651	150	4	k1,m	k1,m	PROPN
ejpam-4651	150	5	,	,	PUNCT
ejpam-4651	150	6	where	where	SCONJ
ejpam-4651	150	7	m	m	PROPN
ejpam-4651	150	8	≥	≥	NOUN
ejpam-4651	150	9	2	2	NUM
ejpam-4651	150	10	,	,	PUNCT
ejpam-4651	150	11	and	and	CCONJ
ejpam-4651	150	12	let	let	VERB
ejpam-4651	150	13	h	h	NOUN
ejpam-4651	150	14	be	be	AUX
ejpam-4651	150	15	any	any	DET
ejpam-4651	150	16	graph	graph	NOUN
ejpam-4651	150	17	.	.	PUNCT
ejpam-4651	151	1	then	then	ADV
ejpam-4651	151	2	ωs(g	ωs(g	PUNCT
ejpam-4651	151	3	⋄h	⋄h	X
ejpam-4651	151	4	)	)	PUNCT
ejpam-4651	151	5	=	=	SYM
ejpam-4651	151	6	ωs(h	ωs(h	X
ejpam-4651	151	7	)	)	PUNCT
ejpam-4651	151	8	+	+	NUM
ejpam-4651	151	9	1	1	X
ejpam-4651	151	10	.	.	X
ejpam-4651	151	11	s.	s.	PROPN
ejpam-4651	151	12	canoy	canoy	PROPN
ejpam-4651	151	13	,	,	PUNCT
ejpam-4651	151	14	jr	jr	PROPN
ejpam-4651	151	15	.	.	PROPN
ejpam-4651	151	16	,	,	PUNCT
ejpam-4651	151	17	r.	r.	PROPN
ejpam-4651	151	18	dela	dela	PROPN
ejpam-4651	151	19	cerna	cerna	PROPN
ejpam-4651	151	20	,	,	PUNCT
ejpam-4651	151	21	a.	a.	NOUN
ejpam-4651	151	22	abragan	abragan	PROPN
ejpam-4651	151	23	/	/	SYM
ejpam-4651	151	24	eur	eur	PROPN
ejpam-4651	151	25	.	.	PUNCT
ejpam-4651	152	1	j.	j.	PROPN
ejpam-4651	152	2	pure	pure	PROPN
ejpam-4651	152	3	appl	appl	PROPN
ejpam-4651	152	4	.	.	PROPN
ejpam-4651	152	5	math	math	PROPN
ejpam-4651	152	6	,	,	PUNCT
ejpam-4651	152	7	16	16	NUM
ejpam-4651	152	8	(	(	PUNCT
ejpam-4651	152	9	1	1	NUM
ejpam-4651	152	10	)	)	PUNCT
ejpam-4651	152	11	(	(	PUNCT
ejpam-4651	152	12	2023	2023	NUM
ejpam-4651	152	13	)	)	PUNCT
ejpam-4651	152	14	,	,	PUNCT
ejpam-4651	152	15	243	243	NUM
ejpam-4651	152	16	-	-	SYM
ejpam-4651	152	17	252	252	NUM
ejpam-4651	152	18	247	247	NUM
ejpam-4651	152	19	proof	proof	NOUN
ejpam-4651	152	20	.	.	PUNCT
ejpam-4651	153	1	clearly	clearly	ADV
ejpam-4651	153	2	,	,	PUNCT
ejpam-4651	153	3	ω(g	ω(g	NOUN
ejpam-4651	153	4	)	)	PUNCT
ejpam-4651	153	5	=	=	SYM
ejpam-4651	154	1	2	2	X
ejpam-4651	154	2	.	.	PUNCT
ejpam-4651	154	3	since	since	SCONJ
ejpam-4651	154	4	ωs(h	ωs(h	NUM
ejpam-4651	154	5	)	)	PUNCT
ejpam-4651	154	6	≥	≥	NOUN
ejpam-4651	154	7	1	1	NUM
ejpam-4651	154	8	,	,	PUNCT
ejpam-4651	154	9	it	it	PRON
ejpam-4651	154	10	follows	follow	VERB
ejpam-4651	154	11	that	that	SCONJ
ejpam-4651	154	12	ω(g	ω(g	NOUN
ejpam-4651	154	13	)	)	PUNCT
ejpam-4651	154	14	≤	≤	NOUN
ejpam-4651	154	15	ωs(h	ωs(h	PUNCT
ejpam-4651	154	16	)	)	PUNCT
ejpam-4651	154	17	+	+	NUM
ejpam-4651	155	1	1	1	X
ejpam-4651	155	2	.	.	X
ejpam-4651	155	3	the	the	DET
ejpam-4651	155	4	desired	desire	VERB
ejpam-4651	155	5	equality	equality	NOUN
ejpam-4651	155	6	now	now	ADV
ejpam-4651	155	7	follows	follow	VERB
ejpam-4651	155	8	from	from	ADP
ejpam-4651	155	9	theorem	theorem	ADJ
ejpam-4651	155	10	4	4	NUM
ejpam-4651	155	11	.	.	PUNCT
ejpam-4651	155	12	theorem	theorem	NOUN
ejpam-4651	155	13	5	5	NUM
ejpam-4651	155	14	.	.	PUNCT
ejpam-4651	156	1	let	let	VERB
ejpam-4651	156	2	g	g	NOUN
ejpam-4651	156	3	and	and	CCONJ
ejpam-4651	156	4	h	h	NOUN
ejpam-4651	156	5	be	be	AUX
ejpam-4651	156	6	nontrivial	nontrivial	ADJ
ejpam-4651	156	7	connected	connected	ADJ
ejpam-4651	156	8	graphs	graph	NOUN
ejpam-4651	156	9	.	.	PUNCT
ejpam-4651	157	1	then	then	ADV
ejpam-4651	157	2	c	c	X
ejpam-4651	157	3	=	=	SYM
ejpam-4651	157	4	∪x∈s({x	∪x∈s({x	ADJ
ejpam-4651	157	5	}	}	PUNCT
ejpam-4651	157	6	×	×	PROPN
ejpam-4651	157	7	tx	tx	PROPN
ejpam-4651	157	8	)	)	PUNCT
ejpam-4651	157	9	,	,	PUNCT
ejpam-4651	157	10	where	where	SCONJ
ejpam-4651	157	11	s	s	VERB
ejpam-4651	157	12	⊆	⊆	NUM
ejpam-4651	157	13	v	v	NOUN
ejpam-4651	157	14	(	(	PUNCT
ejpam-4651	157	15	g	g	NOUN
ejpam-4651	157	16	)	)	PUNCT
ejpam-4651	157	17	and	and	CCONJ
ejpam-4651	157	18	tx	tx	VERB
ejpam-4651	157	19	⊆	⊆	NUM
ejpam-4651	157	20	v	v	NOUN
ejpam-4651	157	21	(	(	PUNCT
ejpam-4651	157	22	h	h	NOUN
ejpam-4651	157	23	)	)	PUNCT
ejpam-4651	157	24	for	for	ADP
ejpam-4651	157	25	each	each	DET
ejpam-4651	157	26	x	x	SYM
ejpam-4651	157	27	∈	∈	PROPN
ejpam-4651	157	28	s	s	NOUN
ejpam-4651	157	29	,	,	PUNCT
ejpam-4651	157	30	is	be	AUX
ejpam-4651	157	31	a	a	DET
ejpam-4651	157	32	clique	clique	NOUN
ejpam-4651	157	33	in	in	ADP
ejpam-4651	157	34	g	g	PROPN
ejpam-4651	157	35	⊠h	⊠h	PROPN
ejpam-4651	157	36	if	if	SCONJ
ejpam-4651	157	37	and	and	CCONJ
ejpam-4651	157	38	only	only	ADV
ejpam-4651	157	39	if	if	SCONJ
ejpam-4651	157	40	the	the	DET
ejpam-4651	157	41	following	follow	VERB
ejpam-4651	157	42	statements	statement	NOUN
ejpam-4651	157	43	hold	hold	VERB
ejpam-4651	157	44	:	:	PUNCT
ejpam-4651	157	45	(	(	PUNCT
ejpam-4651	157	46	i	i	NOUN
ejpam-4651	157	47	)	)	PUNCT
ejpam-4651	157	48	s	s	AUX
ejpam-4651	157	49	is	be	AUX
ejpam-4651	157	50	a	a	DET
ejpam-4651	157	51	clique	clique	NOUN
ejpam-4651	157	52	in	in	ADP
ejpam-4651	157	53	g.	g.	PROPN
ejpam-4651	157	54	(	(	PUNCT
ejpam-4651	157	55	ii	ii	PROPN
ejpam-4651	157	56	)	)	PUNCT
ejpam-4651	157	57	|tx|	|tx|	NOUN
ejpam-4651	157	58	=	=	SYM
ejpam-4651	157	59	1	1	NUM
ejpam-4651	157	60	for	for	ADP
ejpam-4651	157	61	each	each	DET
ejpam-4651	157	62	x	x	SYM
ejpam-4651	157	63	∈	∈	PROPN
ejpam-4651	157	64	s	s	PART
ejpam-4651	157	65	,	,	PUNCT
ejpam-4651	157	66	tx	tx	ADP
ejpam-4651	157	67	̸=	̸=	PROPN
ejpam-4651	157	68	ty	ty	INTJ
ejpam-4651	157	69	if	if	SCONJ
ejpam-4651	157	70	x	x	PROPN
ejpam-4651	157	71	̸=	̸=	PROPN
ejpam-4651	157	72	y	y	PROPN
ejpam-4651	157	73	,	,	PUNCT
ejpam-4651	157	74	and	and	CCONJ
ejpam-4651	157	75	∪x∈stx	∪x∈stx	NOUN
ejpam-4651	157	76	is	be	AUX
ejpam-4651	157	77	a	a	DET
ejpam-4651	157	78	clique	clique	NOUN
ejpam-4651	157	79	in	in	ADP
ejpam-4651	157	80	h.	h.	PROPN
ejpam-4651	157	81	proof	proof	PROPN
ejpam-4651	157	82	.	.	PUNCT
ejpam-4651	158	1	suppose	suppose	VERB
ejpam-4651	158	2	c	c	NOUN
ejpam-4651	158	3	is	be	AUX
ejpam-4651	158	4	a	a	DET
ejpam-4651	158	5	clique	clique	NOUN
ejpam-4651	158	6	in	in	ADP
ejpam-4651	158	7	g⊠h	g⊠h	NOUN
ejpam-4651	158	8	.	.	PUNCT
ejpam-4651	159	1	let	let	VERB
ejpam-4651	159	2	x	x	PRON
ejpam-4651	159	3	,	,	PUNCT
ejpam-4651	159	4	y	y	PROPN
ejpam-4651	159	5	∈	∈	PROPN
ejpam-4651	159	6	s	s	VERB
ejpam-4651	159	7	such	such	ADJ
ejpam-4651	159	8	that	that	SCONJ
ejpam-4651	159	9	x	x	SYM
ejpam-4651	159	10	̸=	̸=	PROPN
ejpam-4651	159	11	y	y	PROPN
ejpam-4651	159	12	and	and	CCONJ
ejpam-4651	159	13	let	let	VERB
ejpam-4651	159	14	a	a	DET
ejpam-4651	159	15	∈	∈	PROPN
ejpam-4651	159	16	tx	tx	NOUN
ejpam-4651	159	17	and	and	CCONJ
ejpam-4651	159	18	b	b	X
ejpam-4651	159	19	∈	∈	PROPN
ejpam-4651	160	1	ty	ty	INTJ
ejpam-4651	160	2	.	.	PUNCT
ejpam-4651	161	1	then	then	ADV
ejpam-4651	161	2	(	(	PUNCT
ejpam-4651	161	3	x	x	X
ejpam-4651	161	4	,	,	PUNCT
ejpam-4651	161	5	a)(y	a)(y	PROPN
ejpam-4651	161	6	,	,	PUNCT
ejpam-4651	161	7	b	b	X
ejpam-4651	161	8	)	)	PUNCT
ejpam-4651	161	9	∈	∈	PROPN
ejpam-4651	161	10	c	c	NOUN
ejpam-4651	161	11	and	and	CCONJ
ejpam-4651	161	12	(	(	PUNCT
ejpam-4651	161	13	x	x	NOUN
ejpam-4651	161	14	,	,	PUNCT
ejpam-4651	161	15	a	a	PRON
ejpam-4651	161	16	)	)	PUNCT
ejpam-4651	161	17	̸=	̸=	PROPN
ejpam-4651	161	18	(	(	PUNCT
ejpam-4651	161	19	y	y	PROPN
ejpam-4651	161	20	,	,	PUNCT
ejpam-4651	161	21	b	b	NOUN
ejpam-4651	161	22	)	)	PUNCT
ejpam-4651	161	23	.	.	PUNCT
ejpam-4651	162	1	it	it	PRON
ejpam-4651	162	2	follows	follow	VERB
ejpam-4651	162	3	that	that	SCONJ
ejpam-4651	162	4	(	(	PUNCT
ejpam-4651	162	5	x	x	X
ejpam-4651	162	6	,	,	PUNCT
ejpam-4651	162	7	a)(y	a)(y	PROPN
ejpam-4651	162	8	,	,	PUNCT
ejpam-4651	162	9	b	b	X
ejpam-4651	162	10	)	)	PUNCT
ejpam-4651	162	11	∈	∈	PROPN
ejpam-4651	162	12	e(g	e(g	PROPN
ejpam-4651	162	13	⊠h	⊠h	PROPN
ejpam-4651	162	14	)	)	PUNCT
ejpam-4651	162	15	.	.	PUNCT
ejpam-4651	163	1	hence	hence	ADV
ejpam-4651	163	2	,	,	PUNCT
ejpam-4651	163	3	xy	xy	PROPN
ejpam-4651	163	4	∈	∈	PROPN
ejpam-4651	163	5	e(g	e(g	PROPN
ejpam-4651	163	6	)	)	PUNCT
ejpam-4651	163	7	,	,	PUNCT
ejpam-4651	163	8	showing	show	VERB
ejpam-4651	163	9	that	that	SCONJ
ejpam-4651	163	10	s	s	VERB
ejpam-4651	163	11	is	be	AUX
ejpam-4651	163	12	a	a	DET
ejpam-4651	163	13	clique	clique	NOUN
ejpam-4651	163	14	in	in	ADP
ejpam-4651	163	15	g.	g.	PROPN
ejpam-4651	163	16	thus	thus	ADV
ejpam-4651	163	17	,	,	PUNCT
ejpam-4651	163	18	(	(	PUNCT
ejpam-4651	163	19	i	i	NOUN
ejpam-4651	163	20	)	)	PUNCT
ejpam-4651	163	21	holds	hold	VERB
ejpam-4651	163	22	.	.	PUNCT
ejpam-4651	164	1	next	next	ADV
ejpam-4651	164	2	,	,	PUNCT
ejpam-4651	164	3	let	let	VERB
ejpam-4651	164	4	x	x	PUNCT
ejpam-4651	164	5	∈	∈	NOUN
ejpam-4651	164	6	s	s	PART
ejpam-4651	164	7	and	and	CCONJ
ejpam-4651	164	8	suppose	suppose	VERB
ejpam-4651	164	9	that	that	SCONJ
ejpam-4651	164	10	|tx|	|tx|	PROPN
ejpam-4651	164	11	≥	≥	NUM
ejpam-4651	164	12	2	2	NUM
ejpam-4651	164	13	.	.	PUNCT
ejpam-4651	165	1	let	let	VERB
ejpam-4651	165	2	p	p	PRON
ejpam-4651	165	3	,	,	PUNCT
ejpam-4651	165	4	q	q	PROPN
ejpam-4651	165	5	∈	∈	PROPN
ejpam-4651	165	6	tx	tx	VERB
ejpam-4651	165	7	such	such	ADJ
ejpam-4651	165	8	that	that	SCONJ
ejpam-4651	165	9	p	p	PROPN
ejpam-4651	165	10	̸=	̸=	PROPN
ejpam-4651	165	11	q.	q.	NOUN
ejpam-4651	165	12	then	then	ADV
ejpam-4651	165	13	(	(	PUNCT
ejpam-4651	165	14	x	x	X
ejpam-4651	165	15	,	,	PUNCT
ejpam-4651	165	16	p)(x	p)(x	NOUN
ejpam-4651	165	17	,	,	PUNCT
ejpam-4651	165	18	q	q	X
ejpam-4651	165	19	)	)	PUNCT
ejpam-4651	165	20	∈	∈	PROPN
ejpam-4651	165	21	c	c	NOUN
ejpam-4651	165	22	and	and	CCONJ
ejpam-4651	165	23	(	(	PUNCT
ejpam-4651	165	24	x	x	NOUN
ejpam-4651	165	25	,	,	PUNCT
ejpam-4651	165	26	p	p	NOUN
ejpam-4651	165	27	)	)	PUNCT
ejpam-4651	165	28	̸=	̸=	PROPN
ejpam-4651	165	29	(	(	PUNCT
ejpam-4651	165	30	x	x	X
ejpam-4651	165	31	,	,	PUNCT
ejpam-4651	165	32	q	q	NOUN
ejpam-4651	165	33	)	)	PUNCT
ejpam-4651	165	34	.	.	PUNCT
ejpam-4651	166	1	since	since	SCONJ
ejpam-4651	166	2	c	c	PROPN
ejpam-4651	166	3	is	be	AUX
ejpam-4651	166	4	a	a	DET
ejpam-4651	166	5	clique	clique	NOUN
ejpam-4651	166	6	in	in	ADP
ejpam-4651	166	7	g⊠h	g⊠h	NOUN
ejpam-4651	166	8	,	,	PUNCT
ejpam-4651	166	9	(	(	PUNCT
ejpam-4651	166	10	x	x	X
ejpam-4651	166	11	,	,	PUNCT
ejpam-4651	166	12	p)(x	p)(x	NOUN
ejpam-4651	166	13	,	,	PUNCT
ejpam-4651	166	14	q	q	X
ejpam-4651	166	15	)	)	PUNCT
ejpam-4651	166	16	∈	∈	NOUN
ejpam-4651	166	17	e(g⊠h	e(g⊠h	NOUN
ejpam-4651	166	18	)	)	PUNCT
ejpam-4651	166	19	which	which	PRON
ejpam-4651	166	20	is	be	AUX
ejpam-4651	166	21	not	not	PART
ejpam-4651	166	22	possible	possible	ADJ
ejpam-4651	166	23	.	.	PUNCT
ejpam-4651	167	1	it	it	PRON
ejpam-4651	167	2	follows	follow	VERB
ejpam-4651	167	3	that	that	SCONJ
ejpam-4651	167	4	|tx|	|tx|	NOUN
ejpam-4651	167	5	=	=	SYM
ejpam-4651	167	6	1	1	NUM
ejpam-4651	167	7	for	for	ADP
ejpam-4651	167	8	each	each	DET
ejpam-4651	167	9	x	x	PROPN
ejpam-4651	167	10	∈	∈	PROPN
ejpam-4651	167	11	s.	s.	PROPN
ejpam-4651	167	12	now	now	ADV
ejpam-4651	167	13	,	,	PUNCT
ejpam-4651	167	14	let	let	VERB
ejpam-4651	167	15	s	s	NOUN
ejpam-4651	167	16	,	,	PUNCT
ejpam-4651	167	17	t	t	PROPN
ejpam-4651	167	18	∈	∈	PROPN
ejpam-4651	167	19	∪x∈stx	∪x∈stx	NOUN
ejpam-4651	167	20	such	such	ADJ
ejpam-4651	167	21	that	that	PRON
ejpam-4651	167	22	s	s	VERB
ejpam-4651	167	23	̸=	̸=	PROPN
ejpam-4651	167	24	t.	t.	NOUN
ejpam-4651	167	25	then	then	ADV
ejpam-4651	167	26	s	s	VERB
ejpam-4651	167	27	∈	∈	PROPN
ejpam-4651	167	28	tv	tv	NOUN
ejpam-4651	167	29	and	and	CCONJ
ejpam-4651	167	30	t	t	NOUN
ejpam-4651	167	31	∈	∈	PROPN
ejpam-4651	167	32	tw	tw	NOUN
ejpam-4651	167	33	for	for	ADP
ejpam-4651	167	34	some	some	DET
ejpam-4651	167	35	v	v	NOUN
ejpam-4651	167	36	,	,	PUNCT
ejpam-4651	167	37	w	w	PROPN
ejpam-4651	167	38	∈	∈	PROPN
ejpam-4651	167	39	s	s	VERB
ejpam-4651	167	40	with	with	ADP
ejpam-4651	167	41	v	v	NOUN
ejpam-4651	167	42	̸=	̸=	PROPN
ejpam-4651	167	43	w.	w.	NOUN
ejpam-4651	167	44	since	since	SCONJ
ejpam-4651	167	45	(	(	PUNCT
ejpam-4651	167	46	v	v	NOUN
ejpam-4651	167	47	,	,	PUNCT
ejpam-4651	167	48	s	s	PART
ejpam-4651	167	49	)	)	PUNCT
ejpam-4651	167	50	,	,	PUNCT
ejpam-4651	167	51	(	(	PUNCT
ejpam-4651	167	52	w	w	PROPN
ejpam-4651	167	53	,	,	PUNCT
ejpam-4651	167	54	t	t	PROPN
ejpam-4651	167	55	)	)	PUNCT
ejpam-4651	167	56	∈	∈	PROPN
ejpam-4651	167	57	c	c	PROPN
ejpam-4651	167	58	and	and	CCONJ
ejpam-4651	167	59	c	c	PROPN
ejpam-4651	167	60	is	be	AUX
ejpam-4651	167	61	a	a	DET
ejpam-4651	167	62	clique	clique	NOUN
ejpam-4651	167	63	in	in	ADP
ejpam-4651	167	64	g	g	PROPN
ejpam-4651	167	65	⊠	⊠	PROPN
ejpam-4651	167	66	h	h	NOUN
ejpam-4651	167	67	,	,	PUNCT
ejpam-4651	167	68	(	(	PUNCT
ejpam-4651	167	69	v	v	NOUN
ejpam-4651	167	70	,	,	PUNCT
ejpam-4651	167	71	s)(w	s)(w	PROPN
ejpam-4651	167	72	,	,	PUNCT
ejpam-4651	167	73	t	t	PROPN
ejpam-4651	167	74	)	)	PUNCT
ejpam-4651	167	75	∈	∈	PROPN
ejpam-4651	167	76	e(g	e(g	PROPN
ejpam-4651	167	77	⊠	⊠	PROPN
ejpam-4651	167	78	h	h	PROPN
ejpam-4651	167	79	)	)	PUNCT
ejpam-4651	167	80	.	.	PUNCT
ejpam-4651	168	1	this	this	PRON
ejpam-4651	168	2	implies	imply	VERB
ejpam-4651	168	3	that	that	SCONJ
ejpam-4651	168	4	st	st	PROPN
ejpam-4651	168	5	∈	∈	PROPN
ejpam-4651	168	6	e(h	e(h	PROPN
ejpam-4651	168	7	)	)	PUNCT
ejpam-4651	168	8	.	.	PUNCT
ejpam-4651	169	1	therefore	therefore	ADV
ejpam-4651	169	2	,	,	PUNCT
ejpam-4651	169	3	∪x∈stx	∪x∈stx	NOUN
ejpam-4651	169	4	is	be	AUX
ejpam-4651	169	5	a	a	DET
ejpam-4651	169	6	clique	clique	NOUN
ejpam-4651	169	7	in	in	ADP
ejpam-4651	169	8	h	h	NOUN
ejpam-4651	169	9	,	,	PUNCT
ejpam-4651	169	10	showing	show	VERB
ejpam-4651	169	11	that	that	SCONJ
ejpam-4651	169	12	(	(	PUNCT
ejpam-4651	169	13	ii	ii	NOUN
ejpam-4651	169	14	)	)	PUNCT
ejpam-4651	169	15	holds	hold	VERB
ejpam-4651	169	16	.	.	PUNCT
ejpam-4651	170	1	conversely	conversely	ADV
ejpam-4651	170	2	,	,	PUNCT
ejpam-4651	170	3	suppose	suppose	VERB
ejpam-4651	170	4	that	that	SCONJ
ejpam-4651	170	5	c	c	PROPN
ejpam-4651	170	6	satisfies	satisfy	VERB
ejpam-4651	170	7	(	(	PUNCT
ejpam-4651	170	8	i	i	NOUN
ejpam-4651	170	9	)	)	PUNCT
ejpam-4651	170	10	and	and	CCONJ
ejpam-4651	170	11	(	(	PUNCT
ejpam-4651	170	12	ii	ii	NOUN
ejpam-4651	170	13	)	)	PUNCT
ejpam-4651	170	14	.	.	PUNCT
ejpam-4651	171	1	let	let	VERB
ejpam-4651	171	2	(	(	PUNCT
ejpam-4651	171	3	v	v	NOUN
ejpam-4651	171	4	,	,	PUNCT
ejpam-4651	171	5	p	p	NOUN
ejpam-4651	171	6	)	)	PUNCT
ejpam-4651	171	7	,	,	PUNCT
ejpam-4651	171	8	(	(	PUNCT
ejpam-4651	171	9	w	w	NOUN
ejpam-4651	171	10	,	,	PUNCT
ejpam-4651	171	11	q	q	NOUN
ejpam-4651	171	12	)	)	PUNCT
ejpam-4651	171	13	∈	∈	PROPN
ejpam-4651	171	14	c	c	NOUN
ejpam-4651	171	15	such	such	ADJ
ejpam-4651	171	16	that	that	PRON
ejpam-4651	171	17	(	(	PUNCT
ejpam-4651	171	18	v	v	NOUN
ejpam-4651	171	19	,	,	PUNCT
ejpam-4651	171	20	p	p	NOUN
ejpam-4651	171	21	)	)	PUNCT
ejpam-4651	171	22	̸=	̸=	PROPN
ejpam-4651	171	23	(	(	PUNCT
ejpam-4651	171	24	w	w	PROPN
ejpam-4651	171	25	,	,	PUNCT
ejpam-4651	171	26	q	q	NOUN
ejpam-4651	171	27	)	)	PUNCT
ejpam-4651	171	28	.	.	PUNCT
ejpam-4651	172	1	if	if	SCONJ
ejpam-4651	172	2	v	v	NUM
ejpam-4651	172	3	=	=	SYM
ejpam-4651	172	4	w	w	NOUN
ejpam-4651	172	5	,	,	PUNCT
ejpam-4651	172	6	then	then	ADV
ejpam-4651	172	7	p	p	PROPN
ejpam-4651	172	8	̸=	̸=	PROPN
ejpam-4651	172	9	q	q	PROPN
ejpam-4651	172	10	and	and	CCONJ
ejpam-4651	172	11	p	p	X
ejpam-4651	172	12	,	,	PUNCT
ejpam-4651	172	13	q	q	PROPN
ejpam-4651	172	14	∈	∈	PROPN
ejpam-4651	172	15	tv	tv	NOUN
ejpam-4651	172	16	contrary	contrary	ADV
ejpam-4651	172	17	to	to	ADP
ejpam-4651	172	18	the	the	DET
ejpam-4651	172	19	assumption	assumption	NOUN
ejpam-4651	172	20	that	that	SCONJ
ejpam-4651	172	21	|tx|	|tx|	NOUN
ejpam-4651	172	22	=	=	SYM
ejpam-4651	172	23	1	1	NUM
ejpam-4651	172	24	for	for	ADP
ejpam-4651	172	25	all	all	DET
ejpam-4651	172	26	x	x	PROPN
ejpam-4651	172	27	∈	∈	PROPN
ejpam-4651	172	28	s.	s.	PROPN
ejpam-4651	172	29	thus	thus	ADV
ejpam-4651	172	30	,	,	PUNCT
ejpam-4651	172	31	v	v	ADP
ejpam-4651	172	32	̸=	̸=	PROPN
ejpam-4651	172	33	w	w	PROPN
ejpam-4651	172	34	and	and	CCONJ
ejpam-4651	172	35	p	p	PROPN
ejpam-4651	172	36	̸=	̸=	PROPN
ejpam-4651	172	37	q.	q.	NOUN
ejpam-4651	172	38	since	since	SCONJ
ejpam-4651	172	39	s	s	PROPN
ejpam-4651	172	40	and	and	CCONJ
ejpam-4651	172	41	∪x∈stx	∪x∈stx	NOUN
ejpam-4651	172	42	are	be	AUX
ejpam-4651	172	43	cliques	clique	NOUN
ejpam-4651	172	44	in	in	ADP
ejpam-4651	172	45	g	g	PROPN
ejpam-4651	172	46	and	and	CCONJ
ejpam-4651	172	47	h	h	NOUN
ejpam-4651	172	48	,	,	PUNCT
ejpam-4651	172	49	respectively	respectively	ADV
ejpam-4651	172	50	,	,	PUNCT
ejpam-4651	172	51	vw	vw	PROPN
ejpam-4651	172	52	∈	∈	PROPN
ejpam-4651	172	53	e(g	e(g	PROPN
ejpam-4651	172	54	)	)	PUNCT
ejpam-4651	172	55	and	and	CCONJ
ejpam-4651	172	56	pq	pq	NOUN
ejpam-4651	172	57	∈	∈	PROPN
ejpam-4651	172	58	e(h	e(h	PROPN
ejpam-4651	172	59	)	)	PUNCT
ejpam-4651	172	60	.	.	PUNCT
ejpam-4651	173	1	thus	thus	ADV
ejpam-4651	173	2	,	,	PUNCT
ejpam-4651	173	3	(	(	PUNCT
ejpam-4651	173	4	v	v	NOUN
ejpam-4651	173	5	,	,	PUNCT
ejpam-4651	173	6	p	p	NOUN
ejpam-4651	173	7	)	)	PUNCT
ejpam-4651	173	8	,	,	PUNCT
ejpam-4651	173	9	(	(	PUNCT
ejpam-4651	173	10	w	w	NOUN
ejpam-4651	173	11	,	,	PUNCT
ejpam-4651	173	12	q	q	NOUN
ejpam-4651	173	13	)	)	PUNCT
ejpam-4651	173	14	∈	∈	PROPN
ejpam-4651	173	15	e(g	e(g	PROPN
ejpam-4651	173	16	⊠h	⊠h	PROPN
ejpam-4651	173	17	)	)	PUNCT
ejpam-4651	173	18	.	.	PUNCT
ejpam-4651	174	1	therefore	therefore	ADV
ejpam-4651	174	2	,	,	PUNCT
ejpam-4651	174	3	c	c	PROPN
ejpam-4651	174	4	is	be	AUX
ejpam-4651	174	5	a	a	DET
ejpam-4651	174	6	clique	clique	NOUN
ejpam-4651	174	7	in	in	ADP
ejpam-4651	174	8	(	(	PUNCT
ejpam-4651	174	9	g⊠h	g⊠h	NOUN
ejpam-4651	174	10	)	)	PUNCT
ejpam-4651	174	11	.	.	PUNCT
ejpam-4651	175	1	corollary	corollary	ADJ
ejpam-4651	175	2	4	4	NUM
ejpam-4651	175	3	.	.	PUNCT
ejpam-4651	176	1	let	let	VERB
ejpam-4651	176	2	g	g	NOUN
ejpam-4651	176	3	and	and	CCONJ
ejpam-4651	176	4	h	h	NOUN
ejpam-4651	176	5	be	be	AUX
ejpam-4651	176	6	nontrivial	nontrivial	ADJ
ejpam-4651	176	7	connected	connected	ADJ
ejpam-4651	176	8	graphs	graph	NOUN
ejpam-4651	176	9	.	.	PUNCT
ejpam-4651	177	1	then	then	ADV
ejpam-4651	177	2	ω(g⊠h	ω(g⊠h	NUM
ejpam-4651	177	3	)	)	PUNCT
ejpam-4651	177	4	=	=	SYM
ejpam-4651	177	5	min{ω(g	min{ω(g	PROPN
ejpam-4651	177	6	)	)	PUNCT
ejpam-4651	177	7	,	,	PUNCT
ejpam-4651	177	8	ω(h	ω(h	NUM
ejpam-4651	177	9	)	)	PUNCT
ejpam-4651	177	10	}	}	PUNCT
ejpam-4651	177	11	.	.	PUNCT
ejpam-4651	178	1	proof	proof	NOUN
ejpam-4651	178	2	.	.	PUNCT
ejpam-4651	179	1	let	let	VERB
ejpam-4651	179	2	s	s	PRON
ejpam-4651	179	3	and	and	CCONJ
ejpam-4651	179	4	d	d	AUX
ejpam-4651	179	5	be	be	AUX
ejpam-4651	179	6	maximum	maximum	ADJ
ejpam-4651	179	7	cliques	clique	NOUN
ejpam-4651	179	8	in	in	ADP
ejpam-4651	179	9	g	g	PROPN
ejpam-4651	179	10	and	and	CCONJ
ejpam-4651	179	11	h.	h.	PROPN
ejpam-4651	179	12	suppose	suppose	VERB
ejpam-4651	179	13	first	first	ADV
ejpam-4651	179	14	that	that	SCONJ
ejpam-4651	179	15	ω(g	ω(g	NOUN
ejpam-4651	179	16	)	)	PUNCT
ejpam-4651	179	17	=	=	SYM
ejpam-4651	179	18	|s|	|s|	PROPN
ejpam-4651	179	19	≤	≤	NUM
ejpam-4651	179	20	|d|	|d|	PROPN
ejpam-4651	179	21	=	=	SYM
ejpam-4651	179	22	ω(h	ω(h	NUM
ejpam-4651	179	23	)	)	PUNCT
ejpam-4651	179	24	.	.	PUNCT
ejpam-4651	180	1	let	let	VERB
ejpam-4651	180	2	d′	d′	PRON
ejpam-4651	180	3	⊆	⊆	NUM
ejpam-4651	180	4	d	d	ADP
ejpam-4651	180	5	such	such	ADJ
ejpam-4651	180	6	that	that	DET
ejpam-4651	180	7	|s|	|s|	PROPN
ejpam-4651	180	8	=	=	PROPN
ejpam-4651	180	9	|d′|	|d′|	PROPN
ejpam-4651	180	10	.	.	PUNCT
ejpam-4651	181	1	let	let	VERB
ejpam-4651	181	2	s	s	PRON
ejpam-4651	181	3	=	=	NOUN
ejpam-4651	181	4	{	{	PUNCT
ejpam-4651	181	5	v1	v1	PROPN
ejpam-4651	181	6	,	,	PUNCT
ejpam-4651	181	7	v2	v2	PROPN
ejpam-4651	181	8	,	,	PUNCT
ejpam-4651	181	9	.	.	PUNCT
ejpam-4651	181	10	.	.	PUNCT
ejpam-4651	182	1	.	.	PUNCT
ejpam-4651	183	1	,	,	PUNCT
ejpam-4651	183	2	vk	vk	VERB
ejpam-4651	183	3	}	}	PUNCT
ejpam-4651	183	4	and	and	CCONJ
ejpam-4651	183	5	d′	d′	NUM
ejpam-4651	183	6	=	=	SYM
ejpam-4651	183	7	{	{	PUNCT
ejpam-4651	183	8	a1	a1	PROPN
ejpam-4651	183	9	,	,	PUNCT
ejpam-4651	183	10	a2	a2	PROPN
ejpam-4651	183	11	,	,	PUNCT
ejpam-4651	183	12	.	.	PUNCT
ejpam-4651	183	13	.	.	PUNCT
ejpam-4651	184	1	.	.	PUNCT
ejpam-4651	185	1	,	,	PUNCT
ejpam-4651	185	2	ak	ak	PROPN
ejpam-4651	185	3	}	}	PUNCT
ejpam-4651	185	4	.	.	PUNCT
ejpam-4651	186	1	set	set	VERB
ejpam-4651	186	2	tvj	tvj	NOUN
ejpam-4651	186	3	=	=	SYM
ejpam-4651	186	4	{	{	PUNCT
ejpam-4651	186	5	aj	aj	PROPN
ejpam-4651	186	6	}	}	PUNCT
ejpam-4651	186	7	for	for	ADP
ejpam-4651	186	8	each	each	DET
ejpam-4651	186	9	j	j	PROPN
ejpam-4651	186	10	∈	∈	PROPN
ejpam-4651	187	1	[	[	X
ejpam-4651	187	2	k	k	X
ejpam-4651	187	3	]	]	X
ejpam-4651	187	4	.	.	PUNCT
ejpam-4651	188	1	then	then	ADV
ejpam-4651	188	2	c	c	X
ejpam-4651	188	3	=	=	SYM
ejpam-4651	188	4	∪k	∪k	NUM
ejpam-4651	188	5	j=1({vj	j=1({vj	PROPN
ejpam-4651	188	6	}	}	PUNCT
ejpam-4651	188	7	×	×	PROPN
ejpam-4651	188	8	tvj	tvj	NOUN
ejpam-4651	188	9	)	)	PUNCT
ejpam-4651	188	10	is	be	AUX
ejpam-4651	188	11	a	a	DET
ejpam-4651	188	12	clique	clique	NOUN
ejpam-4651	188	13	in	in	ADP
ejpam-4651	188	14	g	g	PROPN
ejpam-4651	188	15	⊠h	⊠h	PROPN
ejpam-4651	188	16	by	by	ADP
ejpam-4651	188	17	theorem	theorem	NOUN
ejpam-4651	188	18	5	5	NUM
ejpam-4651	188	19	.	.	PUNCT
ejpam-4651	188	20	consequently	consequently	ADV
ejpam-4651	188	21	,	,	PUNCT
ejpam-4651	188	22	ω(g	ω(g	PROPN
ejpam-4651	188	23	⊠h	⊠h	NUM
ejpam-4651	188	24	)	)	PUNCT
ejpam-4651	188	25	≥	≥	NOUN
ejpam-4651	188	26	|c|	|c|	PROPN
ejpam-4651	188	27	=	=	SYM
ejpam-4651	188	28	|s|	|s|	PROPN
ejpam-4651	188	29	=	=	PUNCT
ejpam-4651	188	30	ω(g	ω(g	NOUN
ejpam-4651	188	31	)	)	PUNCT
ejpam-4651	188	32	.	.	PUNCT
ejpam-4651	189	1	a	a	DET
ejpam-4651	189	2	similar	similar	ADJ
ejpam-4651	189	3	argument	argument	NOUN
ejpam-4651	189	4	can	can	AUX
ejpam-4651	189	5	be	be	AUX
ejpam-4651	189	6	used	use	VERB
ejpam-4651	189	7	to	to	PART
ejpam-4651	189	8	show	show	VERB
ejpam-4651	189	9	that	that	SCONJ
ejpam-4651	189	10	ω(g⊠h	ω(g⊠h	NUM
ejpam-4651	189	11	)	)	PUNCT
ejpam-4651	189	12	≥	≥	NOUN
ejpam-4651	189	13	|d|	|d|	NOUN
ejpam-4651	189	14	=	=	SYM
ejpam-4651	189	15	ω(g	ω(g	PROPN
ejpam-4651	189	16	)	)	PUNCT
ejpam-4651	189	17	if	if	SCONJ
ejpam-4651	189	18	|d|	|d|	PROPN
ejpam-4651	189	19	≤	≤	PROPN
ejpam-4651	189	20	|s|	|s|	PROPN
ejpam-4651	189	21	.	.	PUNCT
ejpam-4651	189	22	suppose	suppose	VERB
ejpam-4651	189	23	now	now	ADV
ejpam-4651	189	24	that	that	SCONJ
ejpam-4651	189	25	c0	c0	PROPN
ejpam-4651	189	26	=	=	SYM
ejpam-4651	189	27	∪x∈s0({x	∪x∈s0({x	PROPN
ejpam-4651	189	28	}	}	PUNCT
ejpam-4651	189	29	×rx	×rx	PROPN
ejpam-4651	189	30	)	)	PUNCT
ejpam-4651	189	31	is	be	AUX
ejpam-4651	189	32	a	a	DET
ejpam-4651	189	33	maximum	maximum	ADJ
ejpam-4651	189	34	clique	clique	NOUN
ejpam-4651	189	35	in	in	ADP
ejpam-4651	189	36	g⊠h	g⊠h	NOUN
ejpam-4651	189	37	.	.	PUNCT
ejpam-4651	190	1	then	then	ADV
ejpam-4651	190	2	s	s	VERB
ejpam-4651	190	3	is	be	AUX
ejpam-4651	190	4	a	a	DET
ejpam-4651	190	5	clique	clique	NOUN
ejpam-4651	190	6	in	in	ADP
ejpam-4651	190	7	g	g	PROPN
ejpam-4651	190	8	,	,	PUNCT
ejpam-4651	190	9	|rx|	|rx|	NOUN
ejpam-4651	190	10	=	=	NOUN
ejpam-4651	190	11	1	1	NUM
ejpam-4651	190	12	for	for	ADP
ejpam-4651	190	13	each	each	DET
ejpam-4651	190	14	x	x	SYM
ejpam-4651	190	15	∈	∈	PROPN
ejpam-4651	190	16	s	s	NOUN
ejpam-4651	190	17	,	,	PUNCT
ejpam-4651	190	18	rx	rx	ADP
ejpam-4651	190	19	̸=	̸=	PROPN
ejpam-4651	190	20	ry	ry	VERB
ejpam-4651	190	21	if	if	SCONJ
ejpam-4651	190	22	x	x	PROPN
ejpam-4651	190	23	̸=	̸=	PROPN
ejpam-4651	190	24	y	y	PROPN
ejpam-4651	190	25	,	,	PUNCT
ejpam-4651	190	26	and	and	CCONJ
ejpam-4651	190	27	∪x∈srx	∪x∈srx	NOUN
ejpam-4651	190	28	is	be	AUX
ejpam-4651	190	29	a	a	DET
ejpam-4651	190	30	clique	clique	NOUN
ejpam-4651	190	31	in	in	ADP
ejpam-4651	190	32	h	h	NOUN
ejpam-4651	190	33	by	by	ADP
ejpam-4651	190	34	theorem	theorem	NOUN
ejpam-4651	190	35	5	5	NUM
ejpam-4651	190	36	.	.	PUNCT
ejpam-4651	191	1	it	it	PRON
ejpam-4651	191	2	follows	follow	VERB
ejpam-4651	191	3	that	that	SCONJ
ejpam-4651	191	4	ω(g⊠h	ω(g⊠h	NUM
ejpam-4651	191	5	)	)	PUNCT
ejpam-4651	191	6	=	=	SYM
ejpam-4651	191	7	|c0|	|c0|	NOUN
ejpam-4651	191	8	=	=	PUNCT
ejpam-4651	191	9	∑	∑	PROPN
ejpam-4651	191	10	x∈s	x∈s	PROPN
ejpam-4651	191	11	|rx|	|rx|	PROPN
ejpam-4651	191	12	=	=	SYM
ejpam-4651	191	13	|s|	|s|	PROPN
ejpam-4651	191	14	=	=	SYM
ejpam-4651	191	15	|	|	ADV
ejpam-4651	191	16	∪x∈s	∪x∈s	ADJ
ejpam-4651	191	17	rx|	rx|	NOUN
ejpam-4651	191	18	≤	≤	NUM
ejpam-4651	191	19	min{ω(g	min{ω(g	NUM
ejpam-4651	191	20	)	)	PUNCT
ejpam-4651	191	21	,	,	PUNCT
ejpam-4651	191	22	ω(h	ω(h	NUM
ejpam-4651	191	23	)	)	PUNCT
ejpam-4651	191	24	}	}	PUNCT
ejpam-4651	191	25	.	.	PUNCT
ejpam-4651	192	1	this	this	PRON
ejpam-4651	192	2	establishes	establish	VERB
ejpam-4651	192	3	the	the	DET
ejpam-4651	192	4	desired	desire	VERB
ejpam-4651	192	5	equality	equality	NOUN
ejpam-4651	192	6	.	.	PUNCT
ejpam-4651	193	1	s.	s.	PROPN
ejpam-4651	193	2	canoy	canoy	PROPN
ejpam-4651	193	3	,	,	PUNCT
ejpam-4651	193	4	jr	jr	PROPN
ejpam-4651	193	5	.	.	PROPN
ejpam-4651	193	6	,	,	PUNCT
ejpam-4651	193	7	r.	r.	PROPN
ejpam-4651	193	8	dela	dela	PROPN
ejpam-4651	193	9	cerna	cerna	PROPN
ejpam-4651	193	10	,	,	PUNCT
ejpam-4651	193	11	a.	a.	NOUN
ejpam-4651	193	12	abragan	abragan	PROPN
ejpam-4651	193	13	/	/	SYM
ejpam-4651	193	14	eur	eur	PROPN
ejpam-4651	193	15	.	.	PUNCT
ejpam-4651	194	1	j.	j.	PROPN
ejpam-4651	194	2	pure	pure	PROPN
ejpam-4651	194	3	appl	appl	PROPN
ejpam-4651	194	4	.	.	PROPN
ejpam-4651	194	5	math	math	PROPN
ejpam-4651	194	6	,	,	PUNCT
ejpam-4651	194	7	16	16	NUM
ejpam-4651	194	8	(	(	PUNCT
ejpam-4651	194	9	1	1	NUM
ejpam-4651	194	10	)	)	PUNCT
ejpam-4651	194	11	(	(	PUNCT
ejpam-4651	194	12	2023	2023	NUM
ejpam-4651	194	13	)	)	PUNCT
ejpam-4651	194	14	,	,	PUNCT
ejpam-4651	194	15	243	243	NUM
ejpam-4651	194	16	-	-	SYM
ejpam-4651	194	17	252	252	NUM
ejpam-4651	194	18	248	248	NUM
ejpam-4651	194	19	theorem	theorem	NOUN
ejpam-4651	194	20	6	6	NUM
ejpam-4651	194	21	.	.	PUNCT
ejpam-4651	195	1	let	let	VERB
ejpam-4651	195	2	g	g	NOUN
ejpam-4651	195	3	and	and	CCONJ
ejpam-4651	195	4	h	h	NOUN
ejpam-4651	195	5	be	be	AUX
ejpam-4651	195	6	nontrivial	nontrivial	ADJ
ejpam-4651	195	7	connected	connect	VERB
ejpam-4651	195	8	graphs	graph	NOUN
ejpam-4651	195	9	such	such	ADJ
ejpam-4651	195	10	that	that	SCONJ
ejpam-4651	195	11	g	g	PROPN
ejpam-4651	195	12	̸=	̸=	PROPN
ejpam-4651	195	13	k2	k2	NOUN
ejpam-4651	195	14	or	or	CCONJ
ejpam-4651	195	15	h	h	NOUN
ejpam-4651	195	16	̸=	̸=	PROPN
ejpam-4651	195	17	k2	k2	NOUN
ejpam-4651	195	18	.	.	PUNCT
ejpam-4651	196	1	then	then	ADV
ejpam-4651	196	2	c	c	X
ejpam-4651	196	3	=	=	SYM
ejpam-4651	196	4	∪x∈s({x	∪x∈s({x	ADJ
ejpam-4651	196	5	}	}	PUNCT
ejpam-4651	196	6	×	×	PROPN
ejpam-4651	196	7	tx	tx	PROPN
ejpam-4651	196	8	)	)	PUNCT
ejpam-4651	196	9	,	,	PUNCT
ejpam-4651	196	10	where	where	SCONJ
ejpam-4651	196	11	s	s	VERB
ejpam-4651	196	12	⊆	⊆	NUM
ejpam-4651	196	13	v	v	NOUN
ejpam-4651	196	14	(	(	PUNCT
ejpam-4651	196	15	g	g	NOUN
ejpam-4651	196	16	)	)	PUNCT
ejpam-4651	196	17	and	and	CCONJ
ejpam-4651	196	18	tx	tx	VERB
ejpam-4651	196	19	⊆	⊆	NUM
ejpam-4651	196	20	v	v	NOUN
ejpam-4651	196	21	(	(	PUNCT
ejpam-4651	196	22	h	h	NOUN
ejpam-4651	196	23	)	)	PUNCT
ejpam-4651	196	24	for	for	ADP
ejpam-4651	196	25	each	each	DET
ejpam-4651	196	26	x	x	SYM
ejpam-4651	196	27	∈	∈	PROPN
ejpam-4651	196	28	s	s	NOUN
ejpam-4651	196	29	,	,	PUNCT
ejpam-4651	196	30	is	be	AUX
ejpam-4651	196	31	a	a	DET
ejpam-4651	196	32	superclique	superclique	NOUN
ejpam-4651	196	33	in	in	ADP
ejpam-4651	196	34	g⊠h	g⊠h	NOUN
ejpam-4651	196	35	if	if	SCONJ
ejpam-4651	196	36	and	and	CCONJ
ejpam-4651	196	37	only	only	ADV
ejpam-4651	196	38	if	if	SCONJ
ejpam-4651	196	39	it	it	PRON
ejpam-4651	196	40	is	be	AUX
ejpam-4651	196	41	a	a	DET
ejpam-4651	196	42	clique	clique	NOUN
ejpam-4651	196	43	.	.	PUNCT
ejpam-4651	197	1	proof	proof	NOUN
ejpam-4651	197	2	.	.	PUNCT
ejpam-4651	198	1	since	since	SCONJ
ejpam-4651	198	2	every	every	DET
ejpam-4651	198	3	superclique	superclique	NOUN
ejpam-4651	198	4	is	be	AUX
ejpam-4651	198	5	a	a	DET
ejpam-4651	198	6	clique	clique	NOUN
ejpam-4651	198	7	,	,	PUNCT
ejpam-4651	198	8	it	it	PRON
ejpam-4651	198	9	remains	remain	VERB
ejpam-4651	198	10	to	to	PART
ejpam-4651	198	11	show	show	VERB
ejpam-4651	198	12	that	that	SCONJ
ejpam-4651	198	13	the	the	DET
ejpam-4651	198	14	converse	converse	NOUN
ejpam-4651	198	15	is	be	AUX
ejpam-4651	198	16	true	true	ADJ
ejpam-4651	198	17	.	.	PUNCT
ejpam-4651	199	1	to	to	ADP
ejpam-4651	199	2	this	this	DET
ejpam-4651	199	3	end	end	NOUN
ejpam-4651	199	4	,	,	PUNCT
ejpam-4651	199	5	suppose	suppose	VERB
ejpam-4651	199	6	that	that	SCONJ
ejpam-4651	199	7	c	c	PROPN
ejpam-4651	199	8	is	be	AUX
ejpam-4651	199	9	a	a	DET
ejpam-4651	199	10	clique	clique	NOUN
ejpam-4651	199	11	in	in	ADP
ejpam-4651	199	12	g⊠h	g⊠h	NOUN
ejpam-4651	199	13	.	.	PUNCT
ejpam-4651	200	1	then	then	ADV
ejpam-4651	200	2	c	c	X
ejpam-4651	200	3	satisfies	satisfie	NOUN
ejpam-4651	200	4	(	(	PUNCT
ejpam-4651	200	5	i	i	NOUN
ejpam-4651	200	6	)	)	PUNCT
ejpam-4651	200	7	and	and	CCONJ
ejpam-4651	200	8	(	(	PUNCT
ejpam-4651	200	9	ii	ii	NOUN
ejpam-4651	200	10	)	)	PUNCT
ejpam-4651	200	11	of	of	ADP
ejpam-4651	200	12	theorem	theorem	NOUN
ejpam-4651	200	13	5	5	NUM
ejpam-4651	200	14	.	.	PUNCT
ejpam-4651	201	1	let	let	VERB
ejpam-4651	201	2	(	(	PUNCT
ejpam-4651	201	3	v	v	NOUN
ejpam-4651	201	4	,	,	PUNCT
ejpam-4651	201	5	p	p	NOUN
ejpam-4651	201	6	)	)	PUNCT
ejpam-4651	201	7	,	,	PUNCT
ejpam-4651	201	8	(	(	PUNCT
ejpam-4651	201	9	w	w	NOUN
ejpam-4651	201	10	,	,	PUNCT
ejpam-4651	201	11	q	q	NOUN
ejpam-4651	201	12	)	)	PUNCT
ejpam-4651	201	13	∈	∈	PROPN
ejpam-4651	201	14	c	c	NOUN
ejpam-4651	201	15	such	such	ADJ
ejpam-4651	201	16	that	that	PRON
ejpam-4651	201	17	(	(	PUNCT
ejpam-4651	201	18	v	v	NOUN
ejpam-4651	201	19	,	,	PUNCT
ejpam-4651	201	20	p	p	NOUN
ejpam-4651	201	21	)	)	PUNCT
ejpam-4651	201	22	̸=	̸=	PROPN
ejpam-4651	201	23	(	(	PUNCT
ejpam-4651	201	24	w	w	PROPN
ejpam-4651	201	25	,	,	PUNCT
ejpam-4651	201	26	q	q	NOUN
ejpam-4651	201	27	)	)	PUNCT
ejpam-4651	201	28	.	.	PUNCT
ejpam-4651	202	1	then	then	ADV
ejpam-4651	202	2	(	(	PUNCT
ejpam-4651	202	3	v	v	NOUN
ejpam-4651	202	4	,	,	PUNCT
ejpam-4651	202	5	p	p	NOUN
ejpam-4651	202	6	)	)	PUNCT
ejpam-4651	202	7	,	,	PUNCT
ejpam-4651	202	8	(	(	PUNCT
ejpam-4651	202	9	w	w	NOUN
ejpam-4651	202	10	,	,	PUNCT
ejpam-4651	202	11	q	q	NOUN
ejpam-4651	202	12	)	)	PUNCT
ejpam-4651	202	13	∈	∈	PROPN
ejpam-4651	202	14	c.	c.	NOUN
ejpam-4651	202	15	hence	hence	ADV
ejpam-4651	202	16	,	,	PUNCT
ejpam-4651	202	17	vw	vw	PROPN
ejpam-4651	202	18	∈	∈	PROPN
ejpam-4651	202	19	e(g	e(g	PROPN
ejpam-4651	202	20	)	)	PUNCT
ejpam-4651	202	21	and	and	CCONJ
ejpam-4651	202	22	pq	pq	NOUN
ejpam-4651	202	23	∈	∈	PROPN
ejpam-4651	202	24	e(h	e(h	PROPN
ejpam-4651	202	25	)	)	PUNCT
ejpam-4651	202	26	.	.	PUNCT
ejpam-4651	203	1	suppose	suppose	VERB
ejpam-4651	203	2	g	g	PROPN
ejpam-4651	203	3	̸=	̸=	PROPN
ejpam-4651	203	4	k2	k2	NOUN
ejpam-4651	203	5	.	.	PUNCT
ejpam-4651	204	1	since	since	SCONJ
ejpam-4651	204	2	g	g	PROPN
ejpam-4651	204	3	is	be	AUX
ejpam-4651	204	4	connected	connect	VERB
ejpam-4651	204	5	,	,	PUNCT
ejpam-4651	204	6	degg(v	degg(v	PROPN
ejpam-4651	204	7	)	)	PUNCT
ejpam-4651	204	8	≥	≥	NOUN
ejpam-4651	204	9	2	2	NUM
ejpam-4651	204	10	or	or	CCONJ
ejpam-4651	204	11	degg(w	degg(w	PROPN
ejpam-4651	204	12	)	)	PUNCT
ejpam-4651	204	13	≥	≥	NOUN
ejpam-4651	205	1	2	2	NUM
ejpam-4651	205	2	.	.	X
ejpam-4651	205	3	assume	assume	VERB
ejpam-4651	205	4	that	that	SCONJ
ejpam-4651	205	5	degg(v	degg(v	PROPN
ejpam-4651	205	6	)	)	PUNCT
ejpam-4651	205	7	≥	≥	NOUN
ejpam-4651	205	8	2	2	NUM
ejpam-4651	205	9	and	and	CCONJ
ejpam-4651	205	10	let	let	VERB
ejpam-4651	205	11	z	z	PROPN
ejpam-4651	205	12	∈	∈	PROPN
ejpam-4651	205	13	ng(v	ng(v	PUNCT
ejpam-4651	205	14	)	)	PUNCT
ejpam-4651	205	15	\	\	NOUN
ejpam-4651	205	16	{	{	PUNCT
ejpam-4651	205	17	w	w	NOUN
ejpam-4651	205	18	}	}	PUNCT
ejpam-4651	205	19	.	.	PUNCT
ejpam-4651	206	1	since	since	SCONJ
ejpam-4651	206	2	c	c	PROPN
ejpam-4651	206	3	is	be	AUX
ejpam-4651	206	4	a	a	DET
ejpam-4651	206	5	clique	clique	NOUN
ejpam-4651	206	6	and	and	CCONJ
ejpam-4651	206	7	(	(	PUNCT
ejpam-4651	206	8	z	z	NOUN
ejpam-4651	206	9	,	,	PUNCT
ejpam-4651	206	10	q)(w	q)(w	NOUN
ejpam-4651	206	11	,	,	PUNCT
ejpam-4651	206	12	q	q	NOUN
ejpam-4651	206	13	)	)	PUNCT
ejpam-4651	206	14	/∈	/∈	PUNCT
ejpam-4651	207	1	e(g⊠h	e(g⊠h	X
ejpam-4651	207	2	)	)	PUNCT
ejpam-4651	208	1	,	,	PUNCT
ejpam-4651	208	2	it	it	PRON
ejpam-4651	208	3	follows	follow	VERB
ejpam-4651	208	4	that	that	SCONJ
ejpam-4651	208	5	(	(	PUNCT
ejpam-4651	208	6	z	z	NOUN
ejpam-4651	208	7	,	,	PUNCT
ejpam-4651	208	8	q	q	NOUN
ejpam-4651	208	9	)	)	PUNCT
ejpam-4651	208	10	/∈	/∈	PUNCT
ejpam-4651	209	1	c.	c.	PROPN
ejpam-4651	209	2	hence	hence	ADV
ejpam-4651	209	3	,	,	PUNCT
ejpam-4651	209	4	(	(	PUNCT
ejpam-4651	209	5	z	z	NOUN
ejpam-4651	209	6	,	,	PUNCT
ejpam-4651	209	7	q	q	X
ejpam-4651	209	8	)	)	PUNCT
ejpam-4651	209	9	∈	∈	PROPN
ejpam-4651	209	10	ng⊠h((v	ng⊠h((v	PROPN
ejpam-4651	209	11	,	,	PUNCT
ejpam-4651	209	12	p	p	NOUN
ejpam-4651	209	13	)	)	PUNCT
ejpam-4651	209	14	)	)	PUNCT
ejpam-4651	209	15	\ng⊠h((w	\ng⊠h((w	PROPN
ejpam-4651	209	16	,	,	PUNCT
ejpam-4651	209	17	q	q	NOUN
ejpam-4651	209	18	)	)	PUNCT
ejpam-4651	209	19	)	)	PUNCT
ejpam-4651	209	20	.	.	PUNCT
ejpam-4651	210	1	next	next	ADV
ejpam-4651	210	2	,	,	PUNCT
ejpam-4651	210	3	suppose	suppose	VERB
ejpam-4651	210	4	that	that	SCONJ
ejpam-4651	210	5	h	h	PROPN
ejpam-4651	210	6	̸=	̸=	PROPN
ejpam-4651	210	7	k2	k2	NOUN
ejpam-4651	210	8	.	.	PUNCT
ejpam-4651	211	1	then	then	ADV
ejpam-4651	211	2	degh(p	degh(p	PROPN
ejpam-4651	211	3	)	)	PUNCT
ejpam-4651	211	4	≥	≥	NOUN
ejpam-4651	211	5	2	2	NUM
ejpam-4651	211	6	or	or	CCONJ
ejpam-4651	211	7	degh(q	degh(q	NOUN
ejpam-4651	211	8	)	)	PUNCT
ejpam-4651	211	9	≥	≥	NOUN
ejpam-4651	212	1	2	2	NUM
ejpam-4651	212	2	.	.	X
ejpam-4651	212	3	assume	assume	VERB
ejpam-4651	212	4	that	that	SCONJ
ejpam-4651	212	5	degh(p	degh(p	NOUN
ejpam-4651	212	6	)	)	PUNCT
ejpam-4651	212	7	≥	≥	NOUN
ejpam-4651	212	8	2	2	NUM
ejpam-4651	212	9	and	and	CCONJ
ejpam-4651	212	10	let	let	VERB
ejpam-4651	212	11	t	t	PROPN
ejpam-4651	212	12	∈	∈	PROPN
ejpam-4651	212	13	nh(p	nh(p	PROPN
ejpam-4651	212	14	)	)	PUNCT
ejpam-4651	212	15	\	\	NOUN
ejpam-4651	212	16	{	{	PUNCT
ejpam-4651	212	17	q	q	NOUN
ejpam-4651	212	18	}	}	PUNCT
ejpam-4651	212	19	.	.	PUNCT
ejpam-4651	213	1	since	since	SCONJ
ejpam-4651	213	2	c	c	PROPN
ejpam-4651	213	3	is	be	AUX
ejpam-4651	213	4	a	a	DET
ejpam-4651	213	5	clique	clique	NOUN
ejpam-4651	213	6	and	and	CCONJ
ejpam-4651	213	7	(	(	PUNCT
ejpam-4651	213	8	w	w	NOUN
ejpam-4651	213	9	,	,	PUNCT
ejpam-4651	213	10	t)(w	t)(w	NOUN
ejpam-4651	213	11	,	,	PUNCT
ejpam-4651	213	12	q	q	NOUN
ejpam-4651	213	13	)	)	PUNCT
ejpam-4651	213	14	/∈	/∈	PUNCT
ejpam-4651	214	1	e(g	e(g	PROPN
ejpam-4651	214	2	⊠h	⊠h	PROPN
ejpam-4651	214	3	)	)	PUNCT
ejpam-4651	214	4	,	,	PUNCT
ejpam-4651	214	5	it	it	PRON
ejpam-4651	214	6	follows	follow	VERB
ejpam-4651	214	7	that	that	SCONJ
ejpam-4651	214	8	(	(	PUNCT
ejpam-4651	214	9	w	w	PROPN
ejpam-4651	214	10	,	,	PUNCT
ejpam-4651	214	11	t	t	PROPN
ejpam-4651	214	12	)	)	PUNCT
ejpam-4651	214	13	/∈	/∈	PUNCT
ejpam-4651	215	1	c.	c.	PROPN
ejpam-4651	215	2	hence	hence	ADV
ejpam-4651	215	3	,	,	PUNCT
ejpam-4651	215	4	(	(	PUNCT
ejpam-4651	215	5	w	w	PROPN
ejpam-4651	215	6	,	,	PUNCT
ejpam-4651	215	7	t	t	PROPN
ejpam-4651	215	8	)	)	PUNCT
ejpam-4651	215	9	∈	∈	PROPN
ejpam-4651	215	10	ng⊠h((v	ng⊠h((v	PROPN
ejpam-4651	215	11	,	,	PUNCT
ejpam-4651	215	12	p))\ng⊠h((w	p))\ng⊠h((w	NOUN
ejpam-4651	215	13	,	,	PUNCT
ejpam-4651	215	14	q	q	NOUN
ejpam-4651	215	15	)	)	PUNCT
ejpam-4651	215	16	)	)	PUNCT
ejpam-4651	215	17	.	.	PUNCT
ejpam-4651	216	1	in	in	ADP
ejpam-4651	216	2	either	either	DET
ejpam-4651	216	3	case	case	NOUN
ejpam-4651	216	4	,	,	PUNCT
ejpam-4651	216	5	c	c	PROPN
ejpam-4651	216	6	is	be	AUX
ejpam-4651	216	7	a	a	DET
ejpam-4651	216	8	superclique	superclique	NOUN
ejpam-4651	216	9	in	in	ADP
ejpam-4651	216	10	g⊠h	g⊠h	NOUN
ejpam-4651	216	11	.	.	PUNCT
ejpam-4651	217	1	it	it	PRON
ejpam-4651	217	2	is	be	AUX
ejpam-4651	217	3	clear	clear	ADJ
ejpam-4651	217	4	that	that	SCONJ
ejpam-4651	217	5	ωs(k2	ωs(k2	NUM
ejpam-4651	217	6	⊠k2	⊠k2	NOUN
ejpam-4651	217	7	)	)	PUNCT
ejpam-4651	217	8	=	=	PUNCT
ejpam-4651	217	9	ωs(k2	ωs(k2	NOUN
ejpam-4651	217	10	∪k2	∪k2	X
ejpam-4651	217	11	)	)	PUNCT
ejpam-4651	218	1	=	=	SYM
ejpam-4651	218	2	1	1	X
ejpam-4651	218	3	.	.	X
ejpam-4651	218	4	corollary	corollary	ADJ
ejpam-4651	218	5	5	5	NUM
ejpam-4651	218	6	.	.	PUNCT
ejpam-4651	219	1	let	let	VERB
ejpam-4651	219	2	g	g	NOUN
ejpam-4651	219	3	and	and	CCONJ
ejpam-4651	219	4	h	h	NOUN
ejpam-4651	219	5	be	be	AUX
ejpam-4651	219	6	nontrivial	nontrivial	ADJ
ejpam-4651	219	7	connected	connect	VERB
ejpam-4651	219	8	graphs	graph	NOUN
ejpam-4651	219	9	such	such	ADJ
ejpam-4651	219	10	that	that	SCONJ
ejpam-4651	219	11	g	g	PROPN
ejpam-4651	219	12	̸=	̸=	PROPN
ejpam-4651	219	13	k2	k2	NOUN
ejpam-4651	219	14	or	or	CCONJ
ejpam-4651	219	15	h	h	NOUN
ejpam-4651	219	16	̸=	̸=	PROPN
ejpam-4651	219	17	k2	k2	NOUN
ejpam-4651	219	18	.	.	PUNCT
ejpam-4651	220	1	then	then	ADV
ejpam-4651	220	2	ωs(g⊠h	ωs(g⊠h	NOUN
ejpam-4651	220	3	)	)	PUNCT
ejpam-4651	220	4	=	=	SYM
ejpam-4651	220	5	ω(g⊠h	ω(g⊠h	NUM
ejpam-4651	220	6	)	)	PUNCT
ejpam-4651	220	7	=	=	SYM
ejpam-4651	220	8	min{ω(g	min{ω(g	PROPN
ejpam-4651	220	9	)	)	PUNCT
ejpam-4651	220	10	,	,	PUNCT
ejpam-4651	220	11	ω(h	ω(h	NUM
ejpam-4651	220	12	)	)	PUNCT
ejpam-4651	220	13	}	}	PUNCT
ejpam-4651	220	14	.	.	PUNCT
ejpam-4651	221	1	theorem	theorem	VERB
ejpam-4651	221	2	7	7	NUM
ejpam-4651	221	3	.	.	PUNCT
ejpam-4651	222	1	let	let	VERB
ejpam-4651	222	2	g	g	NOUN
ejpam-4651	222	3	and	and	CCONJ
ejpam-4651	222	4	h	h	NOUN
ejpam-4651	222	5	be	be	AUX
ejpam-4651	222	6	nontrivial	nontrivial	ADJ
ejpam-4651	222	7	connected	connected	ADJ
ejpam-4651	222	8	graphs	graph	NOUN
ejpam-4651	222	9	.	.	PUNCT
ejpam-4651	223	1	then	then	ADV
ejpam-4651	223	2	c	c	X
ejpam-4651	223	3	=	=	SYM
ejpam-4651	223	4	∪x∈s({x	∪x∈s({x	ADJ
ejpam-4651	223	5	}	}	PUNCT
ejpam-4651	223	6	×	×	PROPN
ejpam-4651	223	7	tx	tx	PROPN
ejpam-4651	223	8	)	)	PUNCT
ejpam-4651	223	9	,	,	PUNCT
ejpam-4651	223	10	where	where	SCONJ
ejpam-4651	223	11	s	s	VERB
ejpam-4651	223	12	⊆	⊆	NUM
ejpam-4651	223	13	v	v	NOUN
ejpam-4651	223	14	(	(	PUNCT
ejpam-4651	223	15	g	g	NOUN
ejpam-4651	223	16	)	)	PUNCT
ejpam-4651	223	17	and	and	CCONJ
ejpam-4651	223	18	tx	tx	VERB
ejpam-4651	223	19	⊆	⊆	NUM
ejpam-4651	223	20	v	v	NOUN
ejpam-4651	223	21	(	(	PUNCT
ejpam-4651	223	22	h	h	NOUN
ejpam-4651	223	23	)	)	PUNCT
ejpam-4651	223	24	for	for	ADP
ejpam-4651	223	25	each	each	DET
ejpam-4651	223	26	x	x	SYM
ejpam-4651	223	27	∈	∈	PROPN
ejpam-4651	223	28	s	s	NOUN
ejpam-4651	223	29	,	,	PUNCT
ejpam-4651	223	30	is	be	AUX
ejpam-4651	223	31	a	a	DET
ejpam-4651	223	32	clique	clique	NOUN
ejpam-4651	223	33	in	in	ADP
ejpam-4651	223	34	g	g	PROPN
ejpam-4651	223	35	⊗h	⊗h	NOUN
ejpam-4651	223	36	if	if	SCONJ
ejpam-4651	223	37	and	and	CCONJ
ejpam-4651	223	38	only	only	ADV
ejpam-4651	223	39	if	if	SCONJ
ejpam-4651	223	40	the	the	DET
ejpam-4651	223	41	following	follow	VERB
ejpam-4651	223	42	statements	statement	NOUN
ejpam-4651	223	43	hold	hold	VERB
ejpam-4651	223	44	:	:	PUNCT
ejpam-4651	223	45	(	(	PUNCT
ejpam-4651	223	46	i	i	NOUN
ejpam-4651	223	47	)	)	PUNCT
ejpam-4651	223	48	s	s	AUX
ejpam-4651	223	49	is	be	AUX
ejpam-4651	223	50	a	a	DET
ejpam-4651	223	51	clique	clique	NOUN
ejpam-4651	223	52	in	in	ADP
ejpam-4651	223	53	g.	g.	PROPN
ejpam-4651	223	54	(	(	PUNCT
ejpam-4651	223	55	ii	ii	PROPN
ejpam-4651	223	56	)	)	PUNCT
ejpam-4651	223	57	tx	tx	PROPN
ejpam-4651	223	58	is	be	AUX
ejpam-4651	223	59	a	a	DET
ejpam-4651	223	60	clique	clique	NOUN
ejpam-4651	223	61	in	in	ADP
ejpam-4651	223	62	h	h	NOUN
ejpam-4651	223	63	for	for	ADP
ejpam-4651	223	64	each	each	DET
ejpam-4651	223	65	x	x	PROPN
ejpam-4651	223	66	∈	∈	PROPN
ejpam-4651	223	67	s.	s.	PROPN
ejpam-4651	223	68	(	(	PUNCT
ejpam-4651	223	69	iii	iii	NOUN
ejpam-4651	223	70	)	)	PUNCT
ejpam-4651	223	71	∪x∈stx	∪x∈stx	NOUN
ejpam-4651	223	72	is	be	AUX
ejpam-4651	223	73	a	a	DET
ejpam-4651	223	74	clique	clique	NOUN
ejpam-4651	223	75	in	in	ADP
ejpam-4651	223	76	h.	h.	PROPN
ejpam-4651	223	77	proof	proof	PROPN
ejpam-4651	223	78	.	.	PUNCT
ejpam-4651	224	1	suppose	suppose	VERB
ejpam-4651	224	2	c	c	NOUN
ejpam-4651	224	3	is	be	AUX
ejpam-4651	224	4	a	a	DET
ejpam-4651	224	5	clique	clique	NOUN
ejpam-4651	224	6	in	in	ADP
ejpam-4651	224	7	g⊗h	g⊗h	PROPN
ejpam-4651	224	8	.	.	PUNCT
ejpam-4651	225	1	let	let	VERB
ejpam-4651	225	2	x	x	PRON
ejpam-4651	225	3	,	,	PUNCT
ejpam-4651	225	4	y	y	PROPN
ejpam-4651	225	5	∈	∈	PROPN
ejpam-4651	225	6	s	s	VERB
ejpam-4651	225	7	such	such	ADJ
ejpam-4651	225	8	that	that	SCONJ
ejpam-4651	225	9	x	x	SYM
ejpam-4651	225	10	̸=	̸=	PROPN
ejpam-4651	225	11	y	y	PROPN
ejpam-4651	225	12	and	and	CCONJ
ejpam-4651	225	13	let	let	VERB
ejpam-4651	225	14	a	a	DET
ejpam-4651	225	15	∈	∈	PROPN
ejpam-4651	225	16	tx	tx	NOUN
ejpam-4651	225	17	and	and	CCONJ
ejpam-4651	225	18	b	b	X
ejpam-4651	225	19	∈	∈	PROPN
ejpam-4651	226	1	ty	ty	INTJ
ejpam-4651	226	2	.	.	PUNCT
ejpam-4651	227	1	then	then	ADV
ejpam-4651	227	2	(	(	PUNCT
ejpam-4651	227	3	x	x	X
ejpam-4651	227	4	,	,	PUNCT
ejpam-4651	227	5	a)(y	a)(y	PROPN
ejpam-4651	227	6	,	,	PUNCT
ejpam-4651	227	7	b	b	X
ejpam-4651	227	8	)	)	PUNCT
ejpam-4651	227	9	∈	∈	PROPN
ejpam-4651	227	10	c	c	NOUN
ejpam-4651	227	11	and	and	CCONJ
ejpam-4651	227	12	(	(	PUNCT
ejpam-4651	227	13	x	x	NOUN
ejpam-4651	227	14	,	,	PUNCT
ejpam-4651	227	15	a	a	PRON
ejpam-4651	227	16	)	)	PUNCT
ejpam-4651	227	17	̸=	̸=	PROPN
ejpam-4651	227	18	(	(	PUNCT
ejpam-4651	227	19	y	y	PROPN
ejpam-4651	227	20	,	,	PUNCT
ejpam-4651	227	21	b	b	NOUN
ejpam-4651	227	22	)	)	PUNCT
ejpam-4651	227	23	.	.	PUNCT
ejpam-4651	228	1	by	by	ADP
ejpam-4651	228	2	assumption	assumption	NOUN
ejpam-4651	228	3	,	,	PUNCT
ejpam-4651	228	4	(	(	PUNCT
ejpam-4651	228	5	x	x	X
ejpam-4651	228	6	,	,	PUNCT
ejpam-4651	228	7	a)(y	a)(y	PROPN
ejpam-4651	228	8	,	,	PUNCT
ejpam-4651	228	9	b	b	X
ejpam-4651	228	10	)	)	PUNCT
ejpam-4651	228	11	∈	∈	NOUN
ejpam-4651	228	12	e(g⊗h	e(g⊗h	NOUN
ejpam-4651	228	13	)	)	PUNCT
ejpam-4651	228	14	.	.	PUNCT
ejpam-4651	229	1	this	this	PRON
ejpam-4651	229	2	implies	imply	VERB
ejpam-4651	229	3	that	that	SCONJ
ejpam-4651	229	4	xy	xy	PROPN
ejpam-4651	229	5	∈	∈	PROPN
ejpam-4651	229	6	e(g	e(g	PROPN
ejpam-4651	229	7	)	)	PUNCT
ejpam-4651	229	8	,	,	PUNCT
ejpam-4651	229	9	showing	show	VERB
ejpam-4651	229	10	that	that	SCONJ
ejpam-4651	229	11	(	(	PUNCT
ejpam-4651	229	12	i	i	NOUN
ejpam-4651	229	13	)	)	PUNCT
ejpam-4651	229	14	is	be	AUX
ejpam-4651	229	15	true	true	ADJ
ejpam-4651	229	16	.	.	PUNCT
ejpam-4651	230	1	let	let	VERB
ejpam-4651	230	2	x	x	PUNCT
ejpam-4651	230	3	∈	∈	NOUN
ejpam-4651	230	4	s	s	PART
ejpam-4651	230	5	and	and	CCONJ
ejpam-4651	230	6	let	let	VERB
ejpam-4651	230	7	p	p	PRON
ejpam-4651	230	8	,	,	PUNCT
ejpam-4651	230	9	q	q	PROPN
ejpam-4651	230	10	∈	∈	PROPN
ejpam-4651	230	11	tx	tx	VERB
ejpam-4651	230	12	such	such	ADJ
ejpam-4651	230	13	that	that	SCONJ
ejpam-4651	230	14	p	p	PROPN
ejpam-4651	230	15	̸=	̸=	PROPN
ejpam-4651	230	16	q.	q.	NOUN
ejpam-4651	230	17	then	then	ADV
ejpam-4651	230	18	(	(	PUNCT
ejpam-4651	230	19	x	x	X
ejpam-4651	230	20	,	,	PUNCT
ejpam-4651	230	21	p)(x	p)(x	NOUN
ejpam-4651	230	22	,	,	PUNCT
ejpam-4651	230	23	q	q	X
ejpam-4651	230	24	)	)	PUNCT
ejpam-4651	230	25	∈	∈	PROPN
ejpam-4651	230	26	c	c	NOUN
ejpam-4651	230	27	and	and	CCONJ
ejpam-4651	230	28	(	(	PUNCT
ejpam-4651	230	29	x	x	NOUN
ejpam-4651	230	30	,	,	PUNCT
ejpam-4651	230	31	p	p	NOUN
ejpam-4651	230	32	)	)	PUNCT
ejpam-4651	230	33	̸=	̸=	PROPN
ejpam-4651	230	34	(	(	PUNCT
ejpam-4651	230	35	x	x	X
ejpam-4651	230	36	,	,	PUNCT
ejpam-4651	230	37	q	q	NOUN
ejpam-4651	230	38	)	)	PUNCT
ejpam-4651	230	39	.	.	PUNCT
ejpam-4651	231	1	since	since	SCONJ
ejpam-4651	231	2	c	c	PROPN
ejpam-4651	231	3	is	be	AUX
ejpam-4651	231	4	a	a	DET
ejpam-4651	231	5	clique	clique	NOUN
ejpam-4651	231	6	in	in	ADP
ejpam-4651	231	7	g⊗h	g⊗h	PROPN
ejpam-4651	231	8	,	,	PUNCT
ejpam-4651	231	9	(	(	PUNCT
ejpam-4651	231	10	x	x	X
ejpam-4651	231	11	,	,	PUNCT
ejpam-4651	231	12	p)(x	p)(x	NOUN
ejpam-4651	231	13	,	,	PUNCT
ejpam-4651	231	14	q	q	X
ejpam-4651	231	15	)	)	PUNCT
ejpam-4651	231	16	∈	∈	NOUN
ejpam-4651	231	17	e(g⊗h	e(g⊗h	NOUN
ejpam-4651	231	18	)	)	PUNCT
ejpam-4651	231	19	.	.	PUNCT
ejpam-4651	232	1	adjacency	adjacency	PROPN
ejpam-4651	232	2	in	in	ADP
ejpam-4651	232	3	g⊗h	g⊗h	PROPN
ejpam-4651	232	4	would	would	AUX
ejpam-4651	232	5	imply	imply	VERB
ejpam-4651	232	6	that	that	SCONJ
ejpam-4651	232	7	pq	pq	PROPN
ejpam-4651	232	8	∈	∈	PROPN
ejpam-4651	232	9	e(h	e(h	PROPN
ejpam-4651	232	10	)	)	PUNCT
ejpam-4651	232	11	.	.	PUNCT
ejpam-4651	233	1	this	this	PRON
ejpam-4651	233	2	shows	show	VERB
ejpam-4651	233	3	that	that	SCONJ
ejpam-4651	233	4	tx	tx	PROPN
ejpam-4651	233	5	is	be	AUX
ejpam-4651	233	6	a	a	DET
ejpam-4651	233	7	clique	clique	NOUN
ejpam-4651	233	8	in	in	ADP
ejpam-4651	233	9	h	h	NOUN
ejpam-4651	233	10	as	as	ADP
ejpam-4651	233	11	asserted	assert	VERB
ejpam-4651	233	12	in	in	ADP
ejpam-4651	233	13	(	(	PUNCT
ejpam-4651	233	14	ii	ii	NOUN
ejpam-4651	233	15	)	)	PUNCT
ejpam-4651	233	16	.	.	PUNCT
ejpam-4651	234	1	next	next	ADV
ejpam-4651	234	2	,	,	PUNCT
ejpam-4651	234	3	let	let	VERB
ejpam-4651	234	4	s	s	NOUN
ejpam-4651	234	5	,	,	PUNCT
ejpam-4651	234	6	t	t	PROPN
ejpam-4651	234	7	∈	∈	PROPN
ejpam-4651	234	8	∪x∈stx	∪x∈stx	NOUN
ejpam-4651	234	9	such	such	ADJ
ejpam-4651	234	10	that	that	PRON
ejpam-4651	234	11	s	s	VERB
ejpam-4651	234	12	̸=	̸=	PROPN
ejpam-4651	234	13	t.	t.	NOUN
ejpam-4651	234	14	if	if	SCONJ
ejpam-4651	234	15	s	s	PROPN
ejpam-4651	234	16	,	,	PUNCT
ejpam-4651	234	17	t	t	PROPN
ejpam-4651	234	18	∈	∈	PROPN
ejpam-4651	234	19	tx	tx	PROPN
ejpam-4651	234	20	for	for	ADP
ejpam-4651	234	21	x	x	PROPN
ejpam-4651	234	22	∈	∈	PROPN
ejpam-4651	234	23	s	s	NOUN
ejpam-4651	234	24	,	,	PUNCT
ejpam-4651	234	25	then	then	ADV
ejpam-4651	234	26	st	st	PROPN
ejpam-4651	234	27	∈	∈	PROPN
ejpam-4651	234	28	e(h	e(h	PROPN
ejpam-4651	234	29	)	)	PUNCT
ejpam-4651	234	30	because	because	SCONJ
ejpam-4651	234	31	tx	tx	PROPN
ejpam-4651	234	32	is	be	AUX
ejpam-4651	234	33	a	a	DET
ejpam-4651	234	34	clique	clique	NOUN
ejpam-4651	234	35	.	.	PUNCT
ejpam-4651	235	1	suppose	suppose	VERB
ejpam-4651	235	2	s	s	X
ejpam-4651	235	3	∈	∈	PROPN
ejpam-4651	235	4	tv	tv	NOUN
ejpam-4651	235	5	and	and	CCONJ
ejpam-4651	235	6	t	t	NOUN
ejpam-4651	235	7	∈	∈	PROPN
ejpam-4651	235	8	tw	tw	NOUN
ejpam-4651	235	9	for	for	ADP
ejpam-4651	235	10	some	some	DET
ejpam-4651	235	11	v	v	NOUN
ejpam-4651	235	12	,	,	PUNCT
ejpam-4651	235	13	w	w	PROPN
ejpam-4651	235	14	∈	∈	PROPN
ejpam-4651	235	15	s	s	VERB
ejpam-4651	235	16	with	with	ADP
ejpam-4651	235	17	v	v	NOUN
ejpam-4651	235	18	̸=	̸=	PROPN
ejpam-4651	235	19	w.	w.	NOUN
ejpam-4651	235	20	since	since	SCONJ
ejpam-4651	235	21	s	s	PROPN
ejpam-4651	235	22	is	be	AUX
ejpam-4651	235	23	a	a	DET
ejpam-4651	235	24	clique	clique	NOUN
ejpam-4651	235	25	in	in	ADP
ejpam-4651	235	26	g	g	PROPN
ejpam-4651	235	27	,	,	PUNCT
ejpam-4651	235	28	vw	vw	PROPN
ejpam-4651	235	29	∈	∈	PROPN
ejpam-4651	235	30	e(g	e(g	PROPN
ejpam-4651	235	31	)	)	PUNCT
ejpam-4651	235	32	.	.	PUNCT
ejpam-4651	236	1	also	also	ADV
ejpam-4651	236	2	,	,	PUNCT
ejpam-4651	236	3	since	since	SCONJ
ejpam-4651	236	4	c	c	PROPN
ejpam-4651	236	5	is	be	AUX
ejpam-4651	236	6	a	a	DET
ejpam-4651	236	7	clique	clique	NOUN
ejpam-4651	236	8	in	in	ADP
ejpam-4651	236	9	g⊗h	g⊗h	PROPN
ejpam-4651	236	10	,	,	PUNCT
ejpam-4651	236	11	(	(	PUNCT
ejpam-4651	236	12	v	v	NOUN
ejpam-4651	236	13	,	,	PUNCT
ejpam-4651	236	14	s)(w	s)(w	PROPN
ejpam-4651	236	15	,	,	PUNCT
ejpam-4651	236	16	t	t	PROPN
ejpam-4651	236	17	)	)	PUNCT
ejpam-4651	236	18	∈	∈	PROPN
ejpam-4651	236	19	e(g⊗h	e(g⊗h	NOUN
ejpam-4651	236	20	)	)	PUNCT
ejpam-4651	236	21	.	.	PUNCT
ejpam-4651	237	1	consequently	consequently	ADV
ejpam-4651	237	2	,	,	PUNCT
ejpam-4651	237	3	st	st	PROPN
ejpam-4651	237	4	∈	∈	PROPN
ejpam-4651	237	5	e(h	e(h	PROPN
ejpam-4651	237	6	)	)	PUNCT
ejpam-4651	237	7	by	by	ADP
ejpam-4651	237	8	the	the	DET
ejpam-4651	237	9	definition	definition	NOUN
ejpam-4651	237	10	of	of	ADP
ejpam-4651	237	11	the	the	DET
ejpam-4651	237	12	adjacency	adjacency	NOUN
ejpam-4651	237	13	in	in	ADP
ejpam-4651	237	14	g⊗h	g⊗h	PROPN
ejpam-4651	237	15	.	.	PUNCT
ejpam-4651	238	1	this	this	PRON
ejpam-4651	238	2	proves	prove	VERB
ejpam-4651	238	3	(	(	PUNCT
ejpam-4651	238	4	iii	iii	NOUN
ejpam-4651	238	5	)	)	PUNCT
ejpam-4651	238	6	.	.	PUNCT
ejpam-4651	239	1	for	for	ADP
ejpam-4651	239	2	the	the	DET
ejpam-4651	239	3	converse	converse	NOUN
ejpam-4651	239	4	,	,	PUNCT
ejpam-4651	239	5	suppose	suppose	VERB
ejpam-4651	239	6	that	that	SCONJ
ejpam-4651	239	7	c	c	PROPN
ejpam-4651	239	8	satisfies	satisfy	VERB
ejpam-4651	239	9	(	(	PUNCT
ejpam-4651	239	10	i	i	NOUN
ejpam-4651	239	11	)	)	PUNCT
ejpam-4651	239	12	,	,	PUNCT
ejpam-4651	239	13	(	(	PUNCT
ejpam-4651	239	14	ii	ii	NOUN
ejpam-4651	239	15	)	)	PUNCT
ejpam-4651	239	16	,	,	PUNCT
ejpam-4651	239	17	and	and	CCONJ
ejpam-4651	239	18	(	(	PUNCT
ejpam-4651	239	19	iii	iii	NOUN
ejpam-4651	239	20	)	)	PUNCT
ejpam-4651	239	21	.	.	PUNCT
ejpam-4651	240	1	let	let	VERB
ejpam-4651	240	2	(	(	PUNCT
ejpam-4651	240	3	x	x	X
ejpam-4651	240	4	,	,	PUNCT
ejpam-4651	240	5	p	p	NOUN
ejpam-4651	240	6	)	)	PUNCT
ejpam-4651	240	7	,	,	PUNCT
ejpam-4651	240	8	(	(	PUNCT
ejpam-4651	240	9	y	y	NOUN
ejpam-4651	240	10	,	,	PUNCT
ejpam-4651	240	11	q	q	X
ejpam-4651	240	12	)	)	PUNCT
ejpam-4651	240	13	∈	∈	PROPN
ejpam-4651	240	14	c	c	NOUN
ejpam-4651	240	15	such	such	ADJ
ejpam-4651	240	16	that	that	PRON
ejpam-4651	240	17	(	(	PUNCT
ejpam-4651	240	18	x	x	X
ejpam-4651	240	19	,	,	PUNCT
ejpam-4651	240	20	p	p	NOUN
ejpam-4651	240	21	)	)	PUNCT
ejpam-4651	240	22	̸=	̸=	PROPN
ejpam-4651	240	23	(	(	PUNCT
ejpam-4651	240	24	y	y	PROPN
ejpam-4651	240	25	,	,	PUNCT
ejpam-4651	240	26	q	q	NOUN
ejpam-4651	240	27	)	)	PUNCT
ejpam-4651	240	28	.	.	PUNCT
ejpam-4651	241	1	if	if	SCONJ
ejpam-4651	241	2	x	x	X
ejpam-4651	241	3	=	=	SYM
ejpam-4651	241	4	y	y	PROPN
ejpam-4651	241	5	,	,	PUNCT
ejpam-4651	241	6	then	then	ADV
ejpam-4651	241	7	p	p	PROPN
ejpam-4651	241	8	̸=	̸=	PROPN
ejpam-4651	241	9	q	q	PROPN
ejpam-4651	241	10	and	and	CCONJ
ejpam-4651	241	11	p	p	X
ejpam-4651	241	12	,	,	PUNCT
ejpam-4651	241	13	q	q	PROPN
ejpam-4651	241	14	∈	∈	PROPN
ejpam-4651	241	15	tx	tx	PROPN
ejpam-4651	241	16	.	.	PUNCT
ejpam-4651	242	1	it	it	PRON
ejpam-4651	242	2	follows	follow	VERB
ejpam-4651	242	3	from	from	ADP
ejpam-4651	242	4	(	(	PUNCT
ejpam-4651	242	5	ii	ii	NOUN
ejpam-4651	242	6	)	)	PUNCT
ejpam-4651	242	7	that	that	PRON
ejpam-4651	242	8	pq	pq	PROPN
ejpam-4651	242	9	∈	∈	PROPN
ejpam-4651	242	10	e(h	e(h	PROPN
ejpam-4651	242	11	)	)	PUNCT
ejpam-4651	242	12	.	.	PUNCT
ejpam-4651	243	1	hence	hence	ADV
ejpam-4651	243	2	,	,	PUNCT
ejpam-4651	243	3	(	(	PUNCT
ejpam-4651	243	4	x	x	X
ejpam-4651	243	5	,	,	PUNCT
ejpam-4651	243	6	p)(y	p)(y	PROPN
ejpam-4651	243	7	,	,	PUNCT
ejpam-4651	243	8	q	q	X
ejpam-4651	243	9	)	)	PUNCT
ejpam-4651	243	10	∈	∈	PROPN
ejpam-4651	243	11	e(g	e(g	PROPN
ejpam-4651	243	12	⊗	⊗	PROPN
ejpam-4651	243	13	h	h	PROPN
ejpam-4651	243	14	)	)	PUNCT
ejpam-4651	243	15	.	.	PUNCT
ejpam-4651	243	16	suppose	suppose	VERB
ejpam-4651	243	17	now	now	ADV
ejpam-4651	243	18	that	that	SCONJ
ejpam-4651	243	19	x	x	X
ejpam-4651	243	20	̸=	̸=	PROPN
ejpam-4651	243	21	y.	y.	NOUN
ejpam-4651	243	22	then	then	ADV
ejpam-4651	243	23	xy	xy	PROPN
ejpam-4651	243	24	∈	∈	PROPN
ejpam-4651	243	25	e(g	e(g	PROPN
ejpam-4651	243	26	)	)	PUNCT
ejpam-4651	243	27	by	by	ADP
ejpam-4651	243	28	(	(	PUNCT
ejpam-4651	243	29	i	i	NOUN
ejpam-4651	243	30	)	)	PUNCT
ejpam-4651	243	31	.	.	PUNCT
ejpam-4651	244	1	if	if	SCONJ
ejpam-4651	244	2	p	p	NOUN
ejpam-4651	244	3	=	=	NOUN
ejpam-4651	244	4	q	q	ADJ
ejpam-4651	244	5	,	,	PUNCT
ejpam-4651	244	6	then	then	ADV
ejpam-4651	244	7	(	(	PUNCT
ejpam-4651	244	8	x	x	X
ejpam-4651	244	9	,	,	PUNCT
ejpam-4651	244	10	p)(y	p)(y	PROPN
ejpam-4651	244	11	,	,	PUNCT
ejpam-4651	244	12	q	q	X
ejpam-4651	244	13	)	)	PUNCT
ejpam-4651	244	14	∈	∈	PROPN
ejpam-4651	244	15	e(g	e(g	PROPN
ejpam-4651	244	16	⊗	⊗	PROPN
ejpam-4651	244	17	h	h	PROPN
ejpam-4651	244	18	)	)	PUNCT
ejpam-4651	244	19	by	by	ADP
ejpam-4651	244	20	the	the	DET
ejpam-4651	244	21	definition	definition	NOUN
ejpam-4651	244	22	of	of	ADP
ejpam-4651	244	23	g	g	PROPN
ejpam-4651	244	24	⊗	⊗	PROPN
ejpam-4651	244	25	h.	h.	PROPN
ejpam-4651	244	26	suppose	suppose	VERB
ejpam-4651	244	27	p	p	X
ejpam-4651	244	28	̸=	̸=	PROPN
ejpam-4651	244	29	q.	q.	VERB
ejpam-4651	244	30	the	the	DET
ejpam-4651	244	31	assumption	assumption	NOUN
ejpam-4651	244	32	that	that	SCONJ
ejpam-4651	244	33	(	(	PUNCT
ejpam-4651	244	34	iii	iii	NOUN
ejpam-4651	244	35	)	)	PUNCT
ejpam-4651	244	36	holds	hold	NOUN
ejpam-4651	244	37	would	would	AUX
ejpam-4651	244	38	imply	imply	VERB
ejpam-4651	244	39	that	that	SCONJ
ejpam-4651	244	40	tx	tx	PROPN
ejpam-4651	244	41	∪	∪	NOUN
ejpam-4651	245	1	ty	ty	PROPN
ejpam-4651	245	2	is	be	AUX
ejpam-4651	245	3	a	a	DET
ejpam-4651	245	4	clique	clique	NOUN
ejpam-4651	245	5	in	in	ADP
ejpam-4651	245	6	h.	h.	PROPN
ejpam-4651	245	7	thus	thus	ADV
ejpam-4651	245	8	,	,	PUNCT
ejpam-4651	245	9	pq	pq	PROPN
ejpam-4651	245	10	∈	∈	PROPN
ejpam-4651	245	11	e(g	e(g	PROPN
ejpam-4651	245	12	)	)	PUNCT
ejpam-4651	245	13	and	and	CCONJ
ejpam-4651	245	14	(	(	PUNCT
ejpam-4651	245	15	x	x	X
ejpam-4651	245	16	,	,	PUNCT
ejpam-4651	245	17	p)(y	p)(y	PROPN
ejpam-4651	245	18	,	,	PUNCT
ejpam-4651	245	19	q	q	X
ejpam-4651	245	20	)	)	PUNCT
ejpam-4651	245	21	∈	∈	NOUN
ejpam-4651	245	22	e(g⊗h	e(g⊗h	NOUN
ejpam-4651	245	23	)	)	PUNCT
ejpam-4651	245	24	.	.	PUNCT
ejpam-4651	246	1	this	this	PRON
ejpam-4651	246	2	proves	prove	VERB
ejpam-4651	246	3	that	that	SCONJ
ejpam-4651	246	4	c	c	PROPN
ejpam-4651	246	5	is	be	AUX
ejpam-4651	246	6	a	a	DET
ejpam-4651	246	7	clique	clique	NOUN
ejpam-4651	246	8	in	in	ADP
ejpam-4651	246	9	g⊗h	g⊗h	PROPN
ejpam-4651	246	10	.	.	PUNCT
ejpam-4651	247	1	s.	s.	PROPN
ejpam-4651	247	2	canoy	canoy	PROPN
ejpam-4651	247	3	,	,	PUNCT
ejpam-4651	247	4	jr	jr	PROPN
ejpam-4651	247	5	.	.	PROPN
ejpam-4651	247	6	,	,	PUNCT
ejpam-4651	247	7	r.	r.	PROPN
ejpam-4651	247	8	dela	dela	PROPN
ejpam-4651	247	9	cerna	cerna	PROPN
ejpam-4651	247	10	,	,	PUNCT
ejpam-4651	247	11	a.	a.	NOUN
ejpam-4651	247	12	abragan	abragan	PROPN
ejpam-4651	247	13	/	/	SYM
ejpam-4651	247	14	eur	eur	PROPN
ejpam-4651	247	15	.	.	PUNCT
ejpam-4651	248	1	j.	j.	PROPN
ejpam-4651	248	2	pure	pure	PROPN
ejpam-4651	248	3	appl	appl	PROPN
ejpam-4651	248	4	.	.	PROPN
ejpam-4651	248	5	math	math	PROPN
ejpam-4651	248	6	,	,	PUNCT
ejpam-4651	248	7	16	16	NUM
ejpam-4651	248	8	(	(	PUNCT
ejpam-4651	248	9	1	1	NUM
ejpam-4651	248	10	)	)	PUNCT
ejpam-4651	248	11	(	(	PUNCT
ejpam-4651	248	12	2023	2023	NUM
ejpam-4651	248	13	)	)	PUNCT
ejpam-4651	248	14	,	,	PUNCT
ejpam-4651	248	15	243	243	NUM
ejpam-4651	248	16	-	-	SYM
ejpam-4651	248	17	252	252	NUM
ejpam-4651	248	18	249	249	NUM
ejpam-4651	248	19	corollary	corollary	ADJ
ejpam-4651	248	20	6	6	NUM
ejpam-4651	248	21	.	.	PUNCT
ejpam-4651	249	1	let	let	VERB
ejpam-4651	249	2	g	g	NOUN
ejpam-4651	249	3	and	and	CCONJ
ejpam-4651	249	4	h	h	NOUN
ejpam-4651	249	5	be	be	AUX
ejpam-4651	249	6	nontrivial	nontrivial	ADJ
ejpam-4651	249	7	connected	connected	ADJ
ejpam-4651	249	8	graphs	graph	NOUN
ejpam-4651	249	9	.	.	PUNCT
ejpam-4651	250	1	then	then	ADV
ejpam-4651	250	2	ω(g⊗h	ω(g⊗h	NOUN
ejpam-4651	250	3	)	)	PUNCT
ejpam-4651	250	4	=	=	SYM
ejpam-4651	250	5	ω(g)ω(h	ω(g)ω(h	PROPN
ejpam-4651	250	6	)	)	PUNCT
ejpam-4651	250	7	.	.	PUNCT
ejpam-4651	251	1	proof	proof	NOUN
ejpam-4651	251	2	.	.	PUNCT
ejpam-4651	252	1	let	let	VERB
ejpam-4651	252	2	s	s	PRON
ejpam-4651	252	3	and	and	CCONJ
ejpam-4651	252	4	d	d	AUX
ejpam-4651	252	5	be	be	AUX
ejpam-4651	252	6	maximum	maximum	ADJ
ejpam-4651	252	7	cliques	clique	NOUN
ejpam-4651	252	8	in	in	ADP
ejpam-4651	252	9	g	g	PROPN
ejpam-4651	252	10	and	and	CCONJ
ejpam-4651	252	11	h	h	NOUN
ejpam-4651	252	12	,	,	PUNCT
ejpam-4651	252	13	respectively	respectively	ADV
ejpam-4651	252	14	.	.	PUNCT
ejpam-4651	253	1	set	set	VERB
ejpam-4651	253	2	tx	tx	PROPN
ejpam-4651	254	1	=	=	SYM
ejpam-4651	255	1	d	d	PROPN
ejpam-4651	255	2	for	for	ADP
ejpam-4651	255	3	each	each	DET
ejpam-4651	255	4	x	x	SYM
ejpam-4651	255	5	∈	∈	PROPN
ejpam-4651	255	6	s.	s.	PROPN
ejpam-4651	255	7	then	then	ADV
ejpam-4651	255	8	c	c	X
ejpam-4651	255	9	=	=	SYM
ejpam-4651	255	10	∪x∈s({x	∪x∈s({x	ADJ
ejpam-4651	255	11	}	}	PUNCT
ejpam-4651	255	12	×	×	NOUN
ejpam-4651	255	13	tx	tx	PROPN
ejpam-4651	255	14	)	)	PUNCT
ejpam-4651	256	1	=	=	SYM
ejpam-4651	256	2	s	s	PART
ejpam-4651	256	3	×	×	NOUN
ejpam-4651	256	4	d	d	NOUN
ejpam-4651	256	5	is	be	AUX
ejpam-4651	256	6	a	a	DET
ejpam-4651	256	7	clique	clique	NOUN
ejpam-4651	256	8	in	in	ADP
ejpam-4651	256	9	g	g	PROPN
ejpam-4651	256	10	⊗	⊗	PROPN
ejpam-4651	256	11	h	h	NOUN
ejpam-4651	256	12	by	by	ADP
ejpam-4651	256	13	theorem	theorem	NOUN
ejpam-4651	256	14	7	7	NUM
ejpam-4651	256	15	.	.	PUNCT
ejpam-4651	256	16	therefore	therefore	ADV
ejpam-4651	256	17	,	,	PUNCT
ejpam-4651	256	18	ω(g⊗h	ω(g⊗h	NOUN
ejpam-4651	256	19	)	)	PUNCT
ejpam-4651	256	20	≥	≥	NOUN
ejpam-4651	256	21	|c|	|c|	PROPN
ejpam-4651	256	22	=	=	SYM
ejpam-4651	256	23	|s||d|	|s||d|	PROPN
ejpam-4651	256	24	=	=	SYM
ejpam-4651	256	25	ω(g)ω(h	ω(g)ω(h	PROPN
ejpam-4651	256	26	)	)	PUNCT
ejpam-4651	256	27	.	.	PUNCT
ejpam-4651	257	1	next	next	ADV
ejpam-4651	257	2	,	,	PUNCT
ejpam-4651	257	3	suppose	suppose	VERB
ejpam-4651	257	4	that	that	SCONJ
ejpam-4651	257	5	c0	c0	PROPN
ejpam-4651	257	6	=	=	SYM
ejpam-4651	257	7	∪x∈s0({x	∪x∈s0({x	PROPN
ejpam-4651	257	8	}	}	PUNCT
ejpam-4651	257	9	×	×	NOUN
ejpam-4651	257	10	rx	rx	NOUN
ejpam-4651	257	11	)	)	PUNCT
ejpam-4651	257	12	is	be	AUX
ejpam-4651	257	13	a	a	DET
ejpam-4651	257	14	maximum	maximum	ADJ
ejpam-4651	257	15	clique	clique	NOUN
ejpam-4651	257	16	in	in	ADP
ejpam-4651	257	17	g	g	PROPN
ejpam-4651	257	18	⊗h	⊗h	NOUN
ejpam-4651	257	19	.	.	PUNCT
ejpam-4651	258	1	then	then	ADV
ejpam-4651	258	2	c0	c0	PROPN
ejpam-4651	258	3	satisfies	satisfy	VERB
ejpam-4651	258	4	properties	property	NOUN
ejpam-4651	258	5	(	(	PUNCT
ejpam-4651	258	6	i	i	NOUN
ejpam-4651	258	7	)	)	PUNCT
ejpam-4651	258	8	,	,	PUNCT
ejpam-4651	258	9	(	(	PUNCT
ejpam-4651	258	10	ii	ii	NOUN
ejpam-4651	258	11	)	)	PUNCT
ejpam-4651	258	12	,	,	PUNCT
ejpam-4651	258	13	and	and	CCONJ
ejpam-4651	258	14	(	(	PUNCT
ejpam-4651	258	15	iii	iii	NOUN
ejpam-4651	258	16	)	)	PUNCT
ejpam-4651	258	17	of	of	ADP
ejpam-4651	258	18	theorem	theorem	NOUN
ejpam-4651	258	19	7	7	NUM
ejpam-4651	258	20	.	.	PUNCT
ejpam-4651	259	1	it	it	PRON
ejpam-4651	259	2	follows	follow	VERB
ejpam-4651	259	3	that	that	SCONJ
ejpam-4651	259	4	ω(g⊗h	ω(g⊗h	NOUN
ejpam-4651	259	5	)	)	PUNCT
ejpam-4651	259	6	=	=	SYM
ejpam-4651	259	7	|c0|	|c0|	NOUN
ejpam-4651	259	8	=	=	SYM
ejpam-4651	259	9	∑	∑	PUNCT
ejpam-4651	259	10	x∈s0	x∈s0	PROPN
ejpam-4651	259	11	|rx|	|rx|	PROPN
ejpam-4651	259	12	≤	≤	ADJ
ejpam-4651	259	13	|s0|ω(h	|s0|ω(h	PROPN
ejpam-4651	259	14	)	)	PUNCT
ejpam-4651	259	15	≤	≤	NUM
ejpam-4651	259	16	ω(g)ω(h	ω(g)ω(h	NOUN
ejpam-4651	259	17	)	)	PUNCT
ejpam-4651	259	18	.	.	PUNCT
ejpam-4651	260	1	this	this	PRON
ejpam-4651	260	2	establishes	establish	VERB
ejpam-4651	260	3	the	the	DET
ejpam-4651	260	4	desired	desire	VERB
ejpam-4651	260	5	equality	equality	NOUN
ejpam-4651	260	6	.	.	PUNCT
ejpam-4651	261	1	theorem	theorem	VERB
ejpam-4651	261	2	8	8	NUM
ejpam-4651	261	3	.	.	PUNCT
ejpam-4651	262	1	let	let	VERB
ejpam-4651	262	2	g	g	NOUN
ejpam-4651	262	3	and	and	CCONJ
ejpam-4651	262	4	h	h	PROPN
ejpam-4651	262	5	be	be	VERB
ejpam-4651	262	6	non	non	ADJ
ejpam-4651	262	7	-	-	ADJ
ejpam-4651	262	8	trivial	trivial	ADJ
ejpam-4651	262	9	connected	connected	ADJ
ejpam-4651	262	10	graphs	graph	NOUN
ejpam-4651	262	11	.	.	PUNCT
ejpam-4651	263	1	then	then	ADV
ejpam-4651	263	2	c	c	X
ejpam-4651	263	3	=	=	SYM
ejpam-4651	263	4	∪x∈s({x	∪x∈s({x	ADJ
ejpam-4651	263	5	}	}	PUNCT
ejpam-4651	263	6	×	×	PROPN
ejpam-4651	263	7	tx	tx	PROPN
ejpam-4651	263	8	)	)	PUNCT
ejpam-4651	263	9	,	,	PUNCT
ejpam-4651	263	10	where	where	SCONJ
ejpam-4651	263	11	s	s	VERB
ejpam-4651	263	12	⊆	⊆	NUM
ejpam-4651	263	13	v	v	NOUN
ejpam-4651	263	14	(	(	PUNCT
ejpam-4651	263	15	g	g	NOUN
ejpam-4651	263	16	)	)	PUNCT
ejpam-4651	263	17	and	and	CCONJ
ejpam-4651	263	18	tx	tx	VERB
ejpam-4651	263	19	⊆	⊆	NUM
ejpam-4651	263	20	v	v	NOUN
ejpam-4651	263	21	(	(	PUNCT
ejpam-4651	263	22	h	h	NOUN
ejpam-4651	263	23	)	)	PUNCT
ejpam-4651	263	24	for	for	ADP
ejpam-4651	263	25	each	each	DET
ejpam-4651	263	26	x	x	SYM
ejpam-4651	263	27	∈	∈	PROPN
ejpam-4651	263	28	s	s	NOUN
ejpam-4651	263	29	,	,	PUNCT
ejpam-4651	263	30	is	be	AUX
ejpam-4651	263	31	a	a	DET
ejpam-4651	263	32	superclique	superclique	NOUN
ejpam-4651	263	33	in	in	ADP
ejpam-4651	263	34	g⊗h	g⊗h	NOUN
ejpam-4651	263	35	if	if	SCONJ
ejpam-4651	264	1	and	and	CCONJ
ejpam-4651	264	2	only	only	ADV
ejpam-4651	264	3	if	if	SCONJ
ejpam-4651	264	4	it	it	PRON
ejpam-4651	264	5	satisfies	satisfy	VERB
ejpam-4651	264	6	the	the	DET
ejpam-4651	264	7	following	follow	VERB
ejpam-4651	264	8	conditions	condition	NOUN
ejpam-4651	264	9	:	:	PUNCT
ejpam-4651	264	10	(	(	PUNCT
ejpam-4651	264	11	i	i	NOUN
ejpam-4651	264	12	)	)	PUNCT
ejpam-4651	264	13	s	s	AUX
ejpam-4651	264	14	is	be	AUX
ejpam-4651	264	15	a	a	DET
ejpam-4651	264	16	clique	clique	NOUN
ejpam-4651	264	17	in	in	ADP
ejpam-4651	264	18	g.	g.	PROPN
ejpam-4651	264	19	(	(	PUNCT
ejpam-4651	264	20	ii	ii	PROPN
ejpam-4651	264	21	)	)	PUNCT
ejpam-4651	264	22	tx	tx	PROPN
ejpam-4651	264	23	is	be	AUX
ejpam-4651	264	24	a	a	DET
ejpam-4651	264	25	superclique	superclique	NOUN
ejpam-4651	264	26	in	in	ADP
ejpam-4651	264	27	h	h	NOUN
ejpam-4651	264	28	for	for	ADP
ejpam-4651	264	29	each	each	DET
ejpam-4651	264	30	x	x	PROPN
ejpam-4651	264	31	∈	∈	PROPN
ejpam-4651	264	32	s.	s.	PROPN
ejpam-4651	264	33	(	(	PUNCT
ejpam-4651	264	34	iii	iii	NOUN
ejpam-4651	264	35	)	)	PUNCT
ejpam-4651	264	36	∪x∈stx	∪x∈stx	NOUN
ejpam-4651	264	37	is	be	AUX
ejpam-4651	264	38	a	a	DET
ejpam-4651	264	39	clique	clique	NOUN
ejpam-4651	264	40	in	in	ADP
ejpam-4651	264	41	h.	h.	PROPN
ejpam-4651	264	42	(	(	PUNCT
ejpam-4651	264	43	iv	iv	X
ejpam-4651	264	44	)	)	PUNCT
ejpam-4651	264	45	for	for	ADP
ejpam-4651	264	46	each	each	DET
ejpam-4651	264	47	distinct	distinct	ADJ
ejpam-4651	264	48	pairs	pair	NOUN
ejpam-4651	264	49	of	of	ADP
ejpam-4651	264	50	vertices	vertex	NOUN
ejpam-4651	264	51	v	v	ADP
ejpam-4651	264	52	,	,	PUNCT
ejpam-4651	264	53	w	w	PROPN
ejpam-4651	264	54	∈	∈	PROPN
ejpam-4651	264	55	s	s	VERB
ejpam-4651	264	56	such	such	ADJ
ejpam-4651	264	57	that	that	SCONJ
ejpam-4651	264	58	tw	tw	NOUN
ejpam-4651	264	59	∩	∩	ADJ
ejpam-4651	264	60	tv	tv	NOUN
ejpam-4651	264	61	̸=	̸=	PROPN
ejpam-4651	264	62	∅	∅	NOUN
ejpam-4651	264	63	,	,	PUNCT
ejpam-4651	264	64	there	there	PRON
ejpam-4651	264	65	exists	exist	VERB
ejpam-4651	264	66	u	u	PROPN
ejpam-4651	264	67	∈	∈	PROPN
ejpam-4651	264	68	v	v	ADP
ejpam-4651	264	69	(	(	PUNCT
ejpam-4651	264	70	g	g	NOUN
ejpam-4651	264	71	)	)	PUNCT
ejpam-4651	264	72	\	\	PUNCT
ejpam-4651	265	1	s	s	VERB
ejpam-4651	265	2	such	such	ADJ
ejpam-4651	265	3	that	that	SCONJ
ejpam-4651	265	4	u	u	PROPN
ejpam-4651	265	5	∈	∈	PROPN
ejpam-4651	265	6	ng(v	ng(v	PUNCT
ejpam-4651	265	7	)	)	PUNCT
ejpam-4651	265	8	\ng(w	\ng(w	NUM
ejpam-4651	265	9	)	)	PUNCT
ejpam-4651	265	10	or	or	CCONJ
ejpam-4651	265	11	u	u	PROPN
ejpam-4651	265	12	∈	∈	PROPN
ejpam-4651	265	13	ng(w	ng(w	NOUN
ejpam-4651	265	14	)	)	PUNCT
ejpam-4651	265	15	\ng(v	\ng(v	NOUN
ejpam-4651	265	16	)	)	PUNCT
ejpam-4651	265	17	.	.	PUNCT
ejpam-4651	266	1	(	(	PUNCT
ejpam-4651	266	2	v	v	NOUN
ejpam-4651	266	3	)	)	PUNCT
ejpam-4651	266	4	for	for	ADP
ejpam-4651	266	5	each	each	DET
ejpam-4651	266	6	pair	pair	NOUN
ejpam-4651	266	7	of	of	ADP
ejpam-4651	266	8	distinct	distinct	ADJ
ejpam-4651	266	9	vertices	vertex	NOUN
ejpam-4651	266	10	v	v	ADP
ejpam-4651	266	11	,	,	PUNCT
ejpam-4651	266	12	w	w	PROPN
ejpam-4651	266	13	∈	∈	PROPN
ejpam-4651	266	14	s	s	VERB
ejpam-4651	266	15	such	such	ADJ
ejpam-4651	266	16	that	that	SCONJ
ejpam-4651	266	17	ng[v	ng[v	PROPN
ejpam-4651	266	18	]	]	X
ejpam-4651	267	1	=	=	SYM
ejpam-4651	267	2	ng[w	ng[w	PROPN
ejpam-4651	267	3	]	]	PUNCT
ejpam-4651	267	4	,	,	PUNCT
ejpam-4651	267	5	and	and	CCONJ
ejpam-4651	267	6	for	for	ADP
ejpam-4651	267	7	each	each	DET
ejpam-4651	267	8	distinct	distinct	ADJ
ejpam-4651	267	9	vertices	vertex	NOUN
ejpam-4651	267	10	a	a	PRON
ejpam-4651	267	11	and	and	CCONJ
ejpam-4651	267	12	b	b	NOUN
ejpam-4651	267	13	such	such	ADJ
ejpam-4651	267	14	that	that	SCONJ
ejpam-4651	267	15	a	a	DET
ejpam-4651	267	16	∈	∈	PROPN
ejpam-4651	267	17	tv	tv	NOUN
ejpam-4651	267	18	and	and	CCONJ
ejpam-4651	267	19	b	b	PROPN
ejpam-4651	267	20	∈	∈	PROPN
ejpam-4651	267	21	tw	tw	NOUN
ejpam-4651	267	22	,	,	PUNCT
ejpam-4651	267	23	there	there	PRON
ejpam-4651	267	24	exists	exist	VERB
ejpam-4651	267	25	c	c	PROPN
ejpam-4651	267	26	∈	∈	PROPN
ejpam-4651	267	27	v	v	PROPN
ejpam-4651	267	28	(	(	PUNCT
ejpam-4651	267	29	h	h	NOUN
ejpam-4651	267	30	)	)	PUNCT
ejpam-4651	267	31	such	such	ADJ
ejpam-4651	267	32	that	that	SCONJ
ejpam-4651	268	1	[	[	X
ejpam-4651	268	2	c	c	NOUN
ejpam-4651	268	3	/∈	/∈	PUNCT
ejpam-4651	268	4	tv	tv	NOUN
ejpam-4651	268	5	and	and	CCONJ
ejpam-4651	268	6	c	c	NOUN
ejpam-4651	268	7	∈	∈	PROPN
ejpam-4651	268	8	nh(a	nh(a	PROPN
ejpam-4651	268	9	)	)	PUNCT
ejpam-4651	268	10	\nh(b	\nh(b	NUM
ejpam-4651	268	11	)	)	PUNCT
ejpam-4651	268	12	]	]	PUNCT
ejpam-4651	268	13	or	or	CCONJ
ejpam-4651	268	14	[	[	X
ejpam-4651	268	15	c	c	X
ejpam-4651	268	16	/∈	/∈	PUNCT
ejpam-4651	268	17	tw	tw	NOUN
ejpam-4651	268	18	and	and	CCONJ
ejpam-4651	268	19	c	c	NOUN
ejpam-4651	268	20	∈	∈	PROPN
ejpam-4651	268	21	nh(b	nh(b	NOUN
ejpam-4651	268	22	)	)	PUNCT
ejpam-4651	268	23	\nh(a	\nh(a	NOUN
ejpam-4651	268	24	)	)	PUNCT
ejpam-4651	268	25	]	]	PUNCT
ejpam-4651	268	26	.	.	PUNCT
ejpam-4651	269	1	proof	proof	NOUN
ejpam-4651	269	2	.	.	PUNCT
ejpam-4651	270	1	suppose	suppose	VERB
ejpam-4651	270	2	c	c	NOUN
ejpam-4651	270	3	is	be	AUX
ejpam-4651	270	4	superclique	superclique	ADJ
ejpam-4651	270	5	in	in	ADP
ejpam-4651	270	6	g⊗h	g⊗h	PROPN
ejpam-4651	270	7	.	.	PUNCT
ejpam-4651	271	1	since	since	SCONJ
ejpam-4651	271	2	c	c	PROPN
ejpam-4651	271	3	is	be	AUX
ejpam-4651	271	4	a	a	DET
ejpam-4651	271	5	clique	clique	NOUN
ejpam-4651	271	6	,	,	PUNCT
ejpam-4651	271	7	each	each	DET
ejpam-4651	271	8	tx	tx	PROPN
ejpam-4651	271	9	is	be	AUX
ejpam-4651	271	10	clique	clique	ADJ
ejpam-4651	271	11	in	in	ADP
ejpam-4651	271	12	h	h	NOUN
ejpam-4651	271	13	,	,	PUNCT
ejpam-4651	271	14	and	and	CCONJ
ejpam-4651	271	15	(	(	PUNCT
ejpam-4651	271	16	i	i	NOUN
ejpam-4651	271	17	)	)	PUNCT
ejpam-4651	271	18	and	and	CCONJ
ejpam-4651	271	19	(	(	PUNCT
ejpam-4651	271	20	iii	iii	X
ejpam-4651	271	21	)	)	PUNCT
ejpam-4651	271	22	hold	hold	NOUN
ejpam-4651	271	23	by	by	ADP
ejpam-4651	271	24	theorem	theorem	NOUN
ejpam-4651	271	25	7	7	NUM
ejpam-4651	271	26	.	.	PUNCT
ejpam-4651	272	1	let	let	VERB
ejpam-4651	272	2	x	x	PUNCT
ejpam-4651	272	3	∈	∈	PROPN
ejpam-4651	272	4	s	s	X
ejpam-4651	272	5	and	and	CCONJ
ejpam-4651	272	6	p	p	X
ejpam-4651	272	7	,	,	PUNCT
ejpam-4651	272	8	q	q	PROPN
ejpam-4651	272	9	∈	∈	PROPN
ejpam-4651	272	10	tx	tx	VERB
ejpam-4651	272	11	such	such	ADJ
ejpam-4651	272	12	that	that	SCONJ
ejpam-4651	272	13	p	p	PROPN
ejpam-4651	272	14	̸=	̸=	PROPN
ejpam-4651	272	15	q.	q.	NOUN
ejpam-4651	272	16	since	since	SCONJ
ejpam-4651	272	17	tx	tx	PROPN
ejpam-4651	272	18	is	be	AUX
ejpam-4651	272	19	a	a	DET
ejpam-4651	272	20	clique	clique	NOUN
ejpam-4651	272	21	,	,	PUNCT
ejpam-4651	272	22	pq	pq	NOUN
ejpam-4651	272	23	∈	∈	PROPN
ejpam-4651	272	24	e(h	e(h	PROPN
ejpam-4651	272	25	)	)	PUNCT
ejpam-4651	272	26	.	.	PUNCT
ejpam-4651	273	1	also	also	ADV
ejpam-4651	273	2	,	,	PUNCT
ejpam-4651	273	3	since	since	SCONJ
ejpam-4651	273	4	c	c	PROPN
ejpam-4651	273	5	is	be	AUX
ejpam-4651	273	6	a	a	DET
ejpam-4651	273	7	superclique	superclique	NOUN
ejpam-4651	273	8	in	in	ADP
ejpam-4651	273	9	⊗h	⊗h	NOUN
ejpam-4651	273	10	,	,	PUNCT
ejpam-4651	273	11	we	we	PRON
ejpam-4651	273	12	may	may	AUX
ejpam-4651	273	13	assume	assume	VERB
ejpam-4651	273	14	that	that	SCONJ
ejpam-4651	273	15	there	there	PRON
ejpam-4651	273	16	exists	exist	VERB
ejpam-4651	273	17	(	(	PUNCT
ejpam-4651	273	18	u	u	NOUN
ejpam-4651	273	19	,	,	PUNCT
ejpam-4651	273	20	t	t	PROPN
ejpam-4651	273	21	)	)	PUNCT
ejpam-4651	273	22	∈	∈	PROPN
ejpam-4651	273	23	v	v	ADP
ejpam-4651	273	24	(	(	PUNCT
ejpam-4651	273	25	g⊗h	g⊗h	NOUN
ejpam-4651	273	26	)	)	PUNCT
ejpam-4651	273	27	\c	\c	ADP
ejpam-4651	273	28	such	such	ADJ
ejpam-4651	273	29	that	that	PRON
ejpam-4651	273	30	(	(	PUNCT
ejpam-4651	273	31	u	u	NOUN
ejpam-4651	273	32	,	,	PUNCT
ejpam-4651	273	33	t	t	PROPN
ejpam-4651	273	34	)	)	PUNCT
ejpam-4651	273	35	∈	∈	PROPN
ejpam-4651	273	36	ng⊗h((x	ng⊗h((x	PROPN
ejpam-4651	273	37	,	,	PUNCT
ejpam-4651	273	38	p	p	NOUN
ejpam-4651	273	39	)	)	PUNCT
ejpam-4651	273	40	)	)	PUNCT
ejpam-4651	273	41	\ng⊗h((x	\ng⊗h((x	NOUN
ejpam-4651	273	42	,	,	PUNCT
ejpam-4651	273	43	q	q	NOUN
ejpam-4651	273	44	)	)	PUNCT
ejpam-4651	273	45	)	)	PUNCT
ejpam-4651	273	46	.	.	PUNCT
ejpam-4651	274	1	suppose	suppose	VERB
ejpam-4651	274	2	first	first	ADV
ejpam-4651	274	3	that	that	SCONJ
ejpam-4651	274	4	u	u	PRON
ejpam-4651	274	5	̸=	̸=	PROPN
ejpam-4651	274	6	x.	x.	NOUN
ejpam-4651	274	7	then	then	ADV
ejpam-4651	274	8	ux	ux	PROPN
ejpam-4651	274	9	∈	∈	PROPN
ejpam-4651	274	10	e(g	e(g	PROPN
ejpam-4651	274	11	)	)	PUNCT
ejpam-4651	274	12	.	.	PUNCT
ejpam-4651	275	1	if	if	SCONJ
ejpam-4651	275	2	p	p	PROPN
ejpam-4651	275	3	=	=	PROPN
ejpam-4651	275	4	t	t	PROPN
ejpam-4651	275	5	,	,	PUNCT
ejpam-4651	275	6	then	then	ADV
ejpam-4651	275	7	(	(	PUNCT
ejpam-4651	275	8	u	u	NOUN
ejpam-4651	275	9	,	,	PUNCT
ejpam-4651	275	10	t)(x	t)(x	PROPN
ejpam-4651	275	11	,	,	PUNCT
ejpam-4651	275	12	q	q	X
ejpam-4651	275	13	)	)	PUNCT
ejpam-4651	275	14	∈	∈	PROPN
ejpam-4651	275	15	e(g	e(g	PROPN
ejpam-4651	275	16	⊗	⊗	PROPN
ejpam-4651	275	17	h	h	PROPN
ejpam-4651	275	18	)	)	PUNCT
ejpam-4651	275	19	,	,	PUNCT
ejpam-4651	275	20	a	a	DET
ejpam-4651	275	21	contradiction	contradiction	NOUN
ejpam-4651	275	22	.	.	PUNCT
ejpam-4651	276	1	thus	thus	ADV
ejpam-4651	276	2	,	,	PUNCT
ejpam-4651	276	3	pt	pt	PROPN
ejpam-4651	276	4	∈	∈	PROPN
ejpam-4651	276	5	e(h	e(h	PROPN
ejpam-4651	276	6	)	)	PUNCT
ejpam-4651	276	7	because	because	SCONJ
ejpam-4651	276	8	(	(	PUNCT
ejpam-4651	276	9	u	u	NOUN
ejpam-4651	276	10	,	,	PUNCT
ejpam-4651	276	11	t	t	PROPN
ejpam-4651	276	12	)	)	PUNCT
ejpam-4651	276	13	∈	∈	PROPN
ejpam-4651	276	14	ng⊗h((x	ng⊗h((x	PROPN
ejpam-4651	276	15	,	,	PUNCT
ejpam-4651	276	16	p	p	NOUN
ejpam-4651	276	17	)	)	PUNCT
ejpam-4651	276	18	)	)	PUNCT
ejpam-4651	276	19	.	.	PUNCT
ejpam-4651	277	1	since	since	SCONJ
ejpam-4651	277	2	(	(	PUNCT
ejpam-4651	277	3	u	u	NOUN
ejpam-4651	277	4	,	,	PUNCT
ejpam-4651	277	5	t	t	PROPN
ejpam-4651	277	6	)	)	PUNCT
ejpam-4651	277	7	/∈	/∈	PUNCT
ejpam-4651	278	1	ng⊗h((x	ng⊗h((x	NOUN
ejpam-4651	278	2	,	,	PUNCT
ejpam-4651	278	3	q	q	NOUN
ejpam-4651	278	4	)	)	PUNCT
ejpam-4651	278	5	)	)	PUNCT
ejpam-4651	278	6	,	,	PUNCT
ejpam-4651	278	7	t	t	PROPN
ejpam-4651	278	8	̸=	̸=	PROPN
ejpam-4651	278	9	q	q	PROPN
ejpam-4651	278	10	and	and	CCONJ
ejpam-4651	278	11	tq	tq	ADV
ejpam-4651	278	12	/∈	/∈	PUNCT
ejpam-4651	278	13	e(h	e(h	PROPN
ejpam-4651	278	14	)	)	PUNCT
ejpam-4651	278	15	.	.	PUNCT
ejpam-4651	279	1	this	this	PRON
ejpam-4651	279	2	implies	imply	VERB
ejpam-4651	279	3	that	that	SCONJ
ejpam-4651	279	4	t	t	PROPN
ejpam-4651	279	5	∈	∈	PROPN
ejpam-4651	279	6	v	v	ADP
ejpam-4651	279	7	(	(	PUNCT
ejpam-4651	279	8	h	h	NOUN
ejpam-4651	279	9	)	)	PUNCT
ejpam-4651	279	10	\	\	PROPN
ejpam-4651	279	11	tx	tx	PROPN
ejpam-4651	279	12	and	and	CCONJ
ejpam-4651	279	13	t	t	PROPN
ejpam-4651	279	14	∈	∈	PROPN
ejpam-4651	279	15	nh(p	nh(p	PROPN
ejpam-4651	279	16	)	)	PUNCT
ejpam-4651	279	17	\	\	NOUN
ejpam-4651	279	18	nh(q	nh(q	NUM
ejpam-4651	279	19	)	)	PUNCT
ejpam-4651	279	20	.	.	PUNCT
ejpam-4651	280	1	next	next	ADV
ejpam-4651	280	2	,	,	PUNCT
ejpam-4651	280	3	suppose	suppose	VERB
ejpam-4651	280	4	that	that	SCONJ
ejpam-4651	280	5	u	u	PRON
ejpam-4651	280	6	=	=	NOUN
ejpam-4651	280	7	x.	x.	NOUN
ejpam-4651	280	8	then	then	ADV
ejpam-4651	280	9	pt	pt	PROPN
ejpam-4651	280	10	∈	∈	PROPN
ejpam-4651	280	11	e(h	e(h	PROPN
ejpam-4651	280	12	)	)	PUNCT
ejpam-4651	280	13	and	and	CCONJ
ejpam-4651	280	14	qt	qt	NOUN
ejpam-4651	280	15	/∈	/∈	PUNCT
ejpam-4651	281	1	e(h	e(h	PROPN
ejpam-4651	281	2	)	)	PUNCT
ejpam-4651	281	3	.	.	PUNCT
ejpam-4651	282	1	it	it	PRON
ejpam-4651	282	2	follows	follow	VERB
ejpam-4651	282	3	that	that	SCONJ
ejpam-4651	282	4	t	t	PROPN
ejpam-4651	282	5	∈	∈	PROPN
ejpam-4651	282	6	v	v	ADP
ejpam-4651	282	7	(	(	PUNCT
ejpam-4651	282	8	h	h	NOUN
ejpam-4651	282	9	)	)	PUNCT
ejpam-4651	282	10	\	\	PROPN
ejpam-4651	282	11	tx	tx	PROPN
ejpam-4651	282	12	and	and	CCONJ
ejpam-4651	282	13	t	t	PROPN
ejpam-4651	282	14	∈	∈	PROPN
ejpam-4651	282	15	nh(p)\nh(q	nh(p)\nh(q	NOUN
ejpam-4651	282	16	)	)	PUNCT
ejpam-4651	282	17	.	.	PUNCT
ejpam-4651	283	1	in	in	ADP
ejpam-4651	283	2	either	either	DET
ejpam-4651	283	3	case	case	NOUN
ejpam-4651	283	4	,	,	PUNCT
ejpam-4651	283	5	tx	tx	PROPN
ejpam-4651	283	6	is	be	AUX
ejpam-4651	283	7	a	a	DET
ejpam-4651	283	8	superclique	superclique	NOUN
ejpam-4651	283	9	in	in	ADP
ejpam-4651	283	10	h	h	NOUN
ejpam-4651	283	11	,	,	PUNCT
ejpam-4651	283	12	showing	show	VERB
ejpam-4651	283	13	that	that	SCONJ
ejpam-4651	283	14	(	(	PUNCT
ejpam-4651	283	15	ii	ii	NOUN
ejpam-4651	283	16	)	)	PUNCT
ejpam-4651	283	17	holds	hold	VERB
ejpam-4651	283	18	.	.	PUNCT
ejpam-4651	284	1	next	next	ADV
ejpam-4651	284	2	,	,	PUNCT
ejpam-4651	284	3	suppose	suppose	VERB
ejpam-4651	284	4	that	that	SCONJ
ejpam-4651	284	5	v	v	NOUN
ejpam-4651	284	6	,	,	PUNCT
ejpam-4651	284	7	w	w	PROPN
ejpam-4651	284	8	∈	∈	PROPN
ejpam-4651	284	9	s	s	VERB
ejpam-4651	284	10	such	such	ADJ
ejpam-4651	284	11	that	that	PRON
ejpam-4651	284	12	v	v	ADP
ejpam-4651	284	13	̸=	̸=	PROPN
ejpam-4651	284	14	w	w	NOUN
ejpam-4651	284	15	and	and	CCONJ
ejpam-4651	284	16	tv∩tw	tv∩tw	NOUN
ejpam-4651	284	17	̸=	̸=	PROPN
ejpam-4651	284	18	∅	∅	NOUN
ejpam-4651	284	19	,	,	PUNCT
ejpam-4651	284	20	say	say	VERB
ejpam-4651	284	21	p	p	PROPN
ejpam-4651	284	22	∈	∈	PROPN
ejpam-4651	284	23	tv∩tw	tv∩tw	NOUN
ejpam-4651	284	24	.	.	PUNCT
ejpam-4651	285	1	again	again	ADV
ejpam-4651	285	2	,	,	PUNCT
ejpam-4651	285	3	since	since	SCONJ
ejpam-4651	285	4	c	c	NOUN
ejpam-4651	285	5	is	be	AUX
ejpam-4651	285	6	a	a	DET
ejpam-4651	285	7	superclique	superclique	ADJ
ejpam-4651	285	8	and	and	CCONJ
ejpam-4651	285	9	(	(	PUNCT
ejpam-4651	285	10	v	v	NOUN
ejpam-4651	285	11	,	,	PUNCT
ejpam-4651	285	12	p	p	NOUN
ejpam-4651	285	13	)	)	PUNCT
ejpam-4651	285	14	,	,	PUNCT
ejpam-4651	285	15	(	(	PUNCT
ejpam-4651	285	16	w	w	X
ejpam-4651	285	17	,	,	PUNCT
ejpam-4651	285	18	p	p	NOUN
ejpam-4651	285	19	)	)	PUNCT
ejpam-4651	285	20	∈	∈	PROPN
ejpam-4651	285	21	c	c	NOUN
ejpam-4651	285	22	,	,	PUNCT
ejpam-4651	285	23	we	we	PRON
ejpam-4651	285	24	may	may	AUX
ejpam-4651	285	25	assume	assume	VERB
ejpam-4651	285	26	that	that	SCONJ
ejpam-4651	285	27	there	there	PRON
ejpam-4651	285	28	exists	exist	VERB
ejpam-4651	285	29	(	(	PUNCT
ejpam-4651	285	30	z	z	NOUN
ejpam-4651	285	31	,	,	PUNCT
ejpam-4651	285	32	s	s	X
ejpam-4651	285	33	)	)	PUNCT
ejpam-4651	285	34	∈	∈	NOUN
ejpam-4651	285	35	v	v	NOUN
ejpam-4651	285	36	(	(	PUNCT
ejpam-4651	285	37	g⊗h)\c	g⊗h)\c	NOUN
ejpam-4651	285	38	such	such	ADJ
ejpam-4651	285	39	that	that	SCONJ
ejpam-4651	285	40	(	(	PUNCT
ejpam-4651	285	41	z	z	NOUN
ejpam-4651	285	42	,	,	PUNCT
ejpam-4651	285	43	s	s	NOUN
ejpam-4651	285	44	)	)	PUNCT
ejpam-4651	285	45	∈	∈	PROPN
ejpam-4651	285	46	ng⊗h((v	ng⊗h((v	NOUN
ejpam-4651	285	47	,	,	PUNCT
ejpam-4651	285	48	p	p	NOUN
ejpam-4651	285	49	)	)	PUNCT
ejpam-4651	285	50	)	)	PUNCT
ejpam-4651	285	51	\ng⊗h((w	\ng⊗h((w	NOUN
ejpam-4651	285	52	,	,	PUNCT
ejpam-4651	285	53	p	p	NOUN
ejpam-4651	285	54	)	)	PUNCT
ejpam-4651	285	55	)	)	PUNCT
ejpam-4651	285	56	.	.	PUNCT
ejpam-4651	286	1	suppose	suppose	VERB
ejpam-4651	287	1	z	z	NOUN
ejpam-4651	287	2	=	=	PUNCT
ejpam-4651	288	1	v.	v.	CCONJ
ejpam-4651	288	2	then	then	ADV
ejpam-4651	288	3	ps	ps	PROPN
ejpam-4651	288	4	∈	∈	PROPN
ejpam-4651	288	5	e(h	e(h	PROPN
ejpam-4651	288	6	)	)	PUNCT
ejpam-4651	288	7	because	because	SCONJ
ejpam-4651	288	8	(	(	PUNCT
ejpam-4651	288	9	z	z	X
ejpam-4651	288	10	,	,	PUNCT
ejpam-4651	288	11	s	s	NOUN
ejpam-4651	288	12	)	)	PUNCT
ejpam-4651	288	13	∈	∈	PROPN
ejpam-4651	288	14	ng⊗h((v	ng⊗h((v	NOUN
ejpam-4651	288	15	,	,	PUNCT
ejpam-4651	288	16	p	p	NOUN
ejpam-4651	288	17	)	)	PUNCT
ejpam-4651	288	18	)	)	PUNCT
ejpam-4651	288	19	.	.	PUNCT
ejpam-4651	289	1	further	far	ADV
ejpam-4651	289	2	,	,	PUNCT
ejpam-4651	289	3	since	since	SCONJ
ejpam-4651	289	4	vw	vw	PROPN
ejpam-4651	289	5	∈	∈	PROPN
ejpam-4651	289	6	e(g	e(g	PROPN
ejpam-4651	289	7	)	)	PUNCT
ejpam-4651	289	8	,	,	PUNCT
ejpam-4651	289	9	(	(	PUNCT
ejpam-4651	289	10	z	z	X
ejpam-4651	289	11	,	,	PUNCT
ejpam-4651	289	12	s	s	X
ejpam-4651	289	13	)	)	PUNCT
ejpam-4651	289	14	∈	∈	PROPN
ejpam-4651	289	15	ng⊗h((w	ng⊗h((w	PROPN
ejpam-4651	289	16	,	,	PUNCT
ejpam-4651	289	17	p	p	NOUN
ejpam-4651	289	18	)	)	PUNCT
ejpam-4651	289	19	)	)	PUNCT
ejpam-4651	289	20	,	,	PUNCT
ejpam-4651	289	21	a	a	DET
ejpam-4651	289	22	contradiction	contradiction	NOUN
ejpam-4651	289	23	.	.	PUNCT
ejpam-4651	290	1	thus	thus	ADV
ejpam-4651	290	2	,	,	PUNCT
ejpam-4651	290	3	z	z	PROPN
ejpam-4651	290	4	̸=	̸=	PROPN
ejpam-4651	290	5	v.	v.	ADP
ejpam-4651	290	6	this	this	PRON
ejpam-4651	290	7	implies	imply	VERB
ejpam-4651	290	8	that	that	SCONJ
ejpam-4651	290	9	zv	zv	PROPN
ejpam-4651	290	10	∈	∈	PROPN
ejpam-4651	290	11	e(g	e(g	PROPN
ejpam-4651	290	12	)	)	PUNCT
ejpam-4651	290	13	.	.	PUNCT
ejpam-4651	291	1	suppose	suppose	VERB
ejpam-4651	291	2	zw	zw	PROPN
ejpam-4651	291	3	∈	∈	PROPN
ejpam-4651	291	4	e(g	e(g	PROPN
ejpam-4651	291	5	)	)	PUNCT
ejpam-4651	291	6	.	.	PUNCT
ejpam-4651	292	1	if	if	SCONJ
ejpam-4651	292	2	p	p	PROPN
ejpam-4651	292	3	=	=	SYM
ejpam-4651	292	4	s	s	PROPN
ejpam-4651	292	5	,	,	PUNCT
ejpam-4651	292	6	then	then	ADV
ejpam-4651	292	7	s.	s.	PROPN
ejpam-4651	292	8	canoy	canoy	PROPN
ejpam-4651	292	9	,	,	PUNCT
ejpam-4651	292	10	jr	jr	PROPN
ejpam-4651	292	11	.	.	PROPN
ejpam-4651	292	12	,	,	PUNCT
ejpam-4651	293	1	r.	r.	PROPN
ejpam-4651	293	2	dela	dela	PROPN
ejpam-4651	293	3	cerna	cerna	PROPN
ejpam-4651	293	4	,	,	PUNCT
ejpam-4651	293	5	a.	a.	NOUN
ejpam-4651	293	6	abragan	abragan	PROPN
ejpam-4651	293	7	/	/	SYM
ejpam-4651	293	8	eur	eur	PROPN
ejpam-4651	293	9	.	.	PUNCT
ejpam-4651	294	1	j.	j.	PROPN
ejpam-4651	294	2	pure	pure	PROPN
ejpam-4651	294	3	appl	appl	PROPN
ejpam-4651	294	4	.	.	PROPN
ejpam-4651	294	5	math	math	PROPN
ejpam-4651	294	6	,	,	PUNCT
ejpam-4651	294	7	16	16	NUM
ejpam-4651	294	8	(	(	PUNCT
ejpam-4651	294	9	1	1	NUM
ejpam-4651	294	10	)	)	PUNCT
ejpam-4651	294	11	(	(	PUNCT
ejpam-4651	294	12	2023	2023	NUM
ejpam-4651	294	13	)	)	PUNCT
ejpam-4651	294	14	,	,	PUNCT
ejpam-4651	294	15	243	243	NUM
ejpam-4651	294	16	-	-	SYM
ejpam-4651	294	17	252	252	NUM
ejpam-4651	294	18	250	250	NUM
ejpam-4651	294	19	(	(	PUNCT
ejpam-4651	294	20	z	z	NOUN
ejpam-4651	294	21	,	,	PUNCT
ejpam-4651	294	22	s	s	NOUN
ejpam-4651	294	23	)	)	PUNCT
ejpam-4651	294	24	∈	∈	PROPN
ejpam-4651	294	25	ng⊗h((w	ng⊗h((w	PROPN
ejpam-4651	294	26	,	,	PUNCT
ejpam-4651	294	27	p	p	NOUN
ejpam-4651	294	28	)	)	PUNCT
ejpam-4651	294	29	)	)	PUNCT
ejpam-4651	294	30	.	.	PUNCT
ejpam-4651	295	1	if	if	SCONJ
ejpam-4651	295	2	p	p	PRON
ejpam-4651	295	3	̸=	̸=	PROPN
ejpam-4651	295	4	s	s	PART
ejpam-4651	295	5	,	,	PUNCT
ejpam-4651	295	6	then	then	ADV
ejpam-4651	295	7	ps	ps	PROPN
ejpam-4651	295	8	∈	∈	PROPN
ejpam-4651	295	9	e(h	e(h	PROPN
ejpam-4651	295	10	)	)	PUNCT
ejpam-4651	295	11	since	since	SCONJ
ejpam-4651	295	12	(	(	PUNCT
ejpam-4651	295	13	z	z	NOUN
ejpam-4651	295	14	,	,	PUNCT
ejpam-4651	295	15	s	s	NOUN
ejpam-4651	295	16	)	)	PUNCT
ejpam-4651	295	17	∈	∈	PROPN
ejpam-4651	295	18	ng⊗h((v	ng⊗h((v	NOUN
ejpam-4651	295	19	,	,	PUNCT
ejpam-4651	295	20	p	p	NOUN
ejpam-4651	295	21	)	)	PUNCT
ejpam-4651	295	22	)	)	PUNCT
ejpam-4651	295	23	.	.	PUNCT
ejpam-4651	296	1	hence	hence	ADV
ejpam-4651	296	2	,	,	PUNCT
ejpam-4651	296	3	(	(	PUNCT
ejpam-4651	296	4	z	z	X
ejpam-4651	296	5	,	,	PUNCT
ejpam-4651	296	6	s	s	X
ejpam-4651	296	7	)	)	PUNCT
ejpam-4651	296	8	∈	∈	PROPN
ejpam-4651	296	9	ng⊗h((w	ng⊗h((w	PROPN
ejpam-4651	296	10	,	,	PUNCT
ejpam-4651	296	11	p	p	NOUN
ejpam-4651	296	12	)	)	PUNCT
ejpam-4651	296	13	)	)	PUNCT
ejpam-4651	296	14	.	.	PUNCT
ejpam-4651	297	1	in	in	ADP
ejpam-4651	297	2	either	either	DET
ejpam-4651	297	3	case	case	NOUN
ejpam-4651	297	4	,	,	PUNCT
ejpam-4651	297	5	we	we	PRON
ejpam-4651	297	6	get	get	VERB
ejpam-4651	297	7	a	a	DET
ejpam-4651	297	8	contradiction	contradiction	NOUN
ejpam-4651	297	9	.	.	PUNCT
ejpam-4651	298	1	therefore	therefore	ADV
ejpam-4651	298	2	,	,	PUNCT
ejpam-4651	298	3	zw	zw	PROPN
ejpam-4651	298	4	/∈	/∈	PUNCT
ejpam-4651	298	5	e(g	e(g	PROPN
ejpam-4651	298	6	)	)	PUNCT
ejpam-4651	298	7	,	,	PUNCT
ejpam-4651	298	8	that	that	ADV
ejpam-4651	298	9	is	be	AUX
ejpam-4651	298	10	,	,	PUNCT
ejpam-4651	298	11	z	z	PROPN
ejpam-4651	298	12	∈	∈	PROPN
ejpam-4651	298	13	v	v	ADP
ejpam-4651	298	14	(	(	PUNCT
ejpam-4651	298	15	g	g	NOUN
ejpam-4651	298	16	)	)	PUNCT
ejpam-4651	298	17	\	\	PROPN
ejpam-4651	299	1	s	s	PROPN
ejpam-4651	299	2	and	and	CCONJ
ejpam-4651	299	3	z	z	NOUN
ejpam-4651	299	4	∈	∈	PROPN
ejpam-4651	299	5	ng(v	ng(v	PUNCT
ejpam-4651	299	6	)	)	PUNCT
ejpam-4651	299	7	\ng(w	\ng(w	PUNCT
ejpam-4651	299	8	)	)	PUNCT
ejpam-4651	299	9	,	,	PUNCT
ejpam-4651	299	10	showing	show	VERB
ejpam-4651	299	11	that	that	SCONJ
ejpam-4651	299	12	(	(	PUNCT
ejpam-4651	299	13	iv	iv	X
ejpam-4651	299	14	)	)	PUNCT
ejpam-4651	299	15	holds	hold	NOUN
ejpam-4651	299	16	.	.	PUNCT
ejpam-4651	300	1	for	for	ADP
ejpam-4651	300	2	the	the	DET
ejpam-4651	300	3	converse	converse	NOUN
ejpam-4651	300	4	,	,	PUNCT
ejpam-4651	300	5	suppose	suppose	VERB
ejpam-4651	300	6	that	that	SCONJ
ejpam-4651	300	7	c	c	PROPN
ejpam-4651	300	8	satisfies	satisfy	VERB
ejpam-4651	300	9	(	(	PUNCT
ejpam-4651	300	10	i	i	NOUN
ejpam-4651	300	11	)	)	PUNCT
ejpam-4651	300	12	,	,	PUNCT
ejpam-4651	300	13	(	(	PUNCT
ejpam-4651	300	14	ii	ii	NOUN
ejpam-4651	300	15	)	)	PUNCT
ejpam-4651	300	16	,	,	PUNCT
ejpam-4651	300	17	(	(	PUNCT
ejpam-4651	300	18	iii	iii	NOUN
ejpam-4651	300	19	)	)	PUNCT
ejpam-4651	300	20	,	,	PUNCT
ejpam-4651	300	21	and	and	CCONJ
ejpam-4651	300	22	(	(	PUNCT
ejpam-4651	300	23	iv	iv	X
ejpam-4651	300	24	)	)	PUNCT
ejpam-4651	300	25	.	.	PUNCT
ejpam-4651	301	1	then	then	ADV
ejpam-4651	301	2	c	c	PROPN
ejpam-4651	301	3	is	be	AUX
ejpam-4651	301	4	a	a	DET
ejpam-4651	301	5	clique	clique	NOUN
ejpam-4651	301	6	by	by	ADP
ejpam-4651	301	7	theorem	theorem	NOUN
ejpam-4651	301	8	7	7	NUM
ejpam-4651	301	9	.	.	PUNCT
ejpam-4651	302	1	let	let	VERB
ejpam-4651	302	2	(	(	PUNCT
ejpam-4651	302	3	x	x	X
ejpam-4651	302	4	,	,	PUNCT
ejpam-4651	302	5	a	a	PRON
ejpam-4651	302	6	)	)	PUNCT
ejpam-4651	302	7	,	,	PUNCT
ejpam-4651	302	8	(	(	PUNCT
ejpam-4651	302	9	z	z	X
ejpam-4651	302	10	,	,	PUNCT
ejpam-4651	302	11	b	b	NOUN
ejpam-4651	302	12	)	)	PUNCT
ejpam-4651	302	13	∈	∈	PROPN
ejpam-4651	302	14	c	c	NOUN
ejpam-4651	302	15	such	such	ADJ
ejpam-4651	302	16	that	that	PRON
ejpam-4651	302	17	(	(	PUNCT
ejpam-4651	302	18	x	x	NOUN
ejpam-4651	302	19	,	,	PUNCT
ejpam-4651	302	20	a	a	PRON
ejpam-4651	302	21	)	)	PUNCT
ejpam-4651	302	22	̸=	̸=	PROPN
ejpam-4651	302	23	(	(	PUNCT
ejpam-4651	302	24	z	z	PROPN
ejpam-4651	302	25	,	,	PUNCT
ejpam-4651	302	26	b	b	NOUN
ejpam-4651	302	27	)	)	PUNCT
ejpam-4651	302	28	.	.	PUNCT
ejpam-4651	303	1	consider	consider	VERB
ejpam-4651	303	2	the	the	DET
ejpam-4651	303	3	following	follow	VERB
ejpam-4651	303	4	cases	case	NOUN
ejpam-4651	303	5	:	:	PUNCT
ejpam-4651	303	6	case	case	NOUN
ejpam-4651	303	7	1	1	NUM
ejpam-4651	303	8	.	.	PUNCT
ejpam-4651	303	9	x	x	X
ejpam-4651	304	1	=	=	PUNCT
ejpam-4651	304	2	z.	z.	PROPN
ejpam-4651	304	3	then	then	ADV
ejpam-4651	304	4	a	a	DET
ejpam-4651	304	5	,	,	PUNCT
ejpam-4651	304	6	b	b	PROPN
ejpam-4651	304	7	∈	∈	PROPN
ejpam-4651	304	8	tx	tx	PROPN
ejpam-4651	304	9	and	and	CCONJ
ejpam-4651	304	10	a	a	DET
ejpam-4651	304	11	̸=	̸=	PROPN
ejpam-4651	304	12	b	b	PROPN
ejpam-4651	304	13	since	since	SCONJ
ejpam-4651	304	14	tx	tx	PROPN
ejpam-4651	304	15	is	be	AUX
ejpam-4651	304	16	a	a	DET
ejpam-4651	304	17	clique	clique	NOUN
ejpam-4651	304	18	,	,	PUNCT
ejpam-4651	304	19	ab	ab	PROPN
ejpam-4651	304	20	∈	∈	PROPN
ejpam-4651	304	21	e(h	e(h	PROPN
ejpam-4651	304	22	)	)	PUNCT
ejpam-4651	304	23	.	.	PUNCT
ejpam-4651	305	1	moreover	moreover	ADV
ejpam-4651	305	2	,	,	PUNCT
ejpam-4651	305	3	since	since	SCONJ
ejpam-4651	305	4	tx	tx	PROPN
ejpam-4651	305	5	is	be	AUX
ejpam-4651	305	6	a	a	DET
ejpam-4651	305	7	superclique	superclique	NOUN
ejpam-4651	305	8	,	,	PUNCT
ejpam-4651	305	9	we	we	PRON
ejpam-4651	305	10	may	may	AUX
ejpam-4651	305	11	assume	assume	VERB
ejpam-4651	305	12	that	that	SCONJ
ejpam-4651	305	13	there	there	PRON
ejpam-4651	305	14	exists	exist	VERB
ejpam-4651	305	15	p	p	PROPN
ejpam-4651	305	16	∈	∈	PROPN
ejpam-4651	305	17	v	v	ADP
ejpam-4651	305	18	(	(	PUNCT
ejpam-4651	305	19	h	h	NOUN
ejpam-4651	305	20	)	)	PUNCT
ejpam-4651	305	21	\	\	PUNCT
ejpam-4651	306	1	tx	tx	ADP
ejpam-4651	306	2	such	such	ADJ
ejpam-4651	306	3	that	that	SCONJ
ejpam-4651	306	4	p	p	PROPN
ejpam-4651	306	5	∈	∈	PROPN
ejpam-4651	306	6	nh(a	nh(a	NUM
ejpam-4651	306	7	)	)	PUNCT
ejpam-4651	306	8	\nh(b	\nh(b	NUM
ejpam-4651	306	9	)	)	PUNCT
ejpam-4651	306	10	.	.	PUNCT
ejpam-4651	307	1	hence	hence	ADV
ejpam-4651	307	2	,	,	PUNCT
ejpam-4651	307	3	(	(	PUNCT
ejpam-4651	307	4	x	x	X
ejpam-4651	307	5	,	,	PUNCT
ejpam-4651	307	6	p	p	NOUN
ejpam-4651	307	7	)	)	PUNCT
ejpam-4651	307	8	∈	∈	PROPN
ejpam-4651	307	9	v	v	NOUN
ejpam-4651	307	10	(	(	PUNCT
ejpam-4651	307	11	g⊗h	g⊗h	NOUN
ejpam-4651	307	12	)	)	PUNCT
ejpam-4651	307	13	\	\	PROPN
ejpam-4651	307	14	c	c	PROPN
ejpam-4651	307	15	and	and	CCONJ
ejpam-4651	307	16	(	(	PUNCT
ejpam-4651	307	17	x	x	NOUN
ejpam-4651	307	18	,	,	PUNCT
ejpam-4651	307	19	p	p	NOUN
ejpam-4651	307	20	)	)	PUNCT
ejpam-4651	307	21	∈	∈	PROPN
ejpam-4651	307	22	ng⊗h((x	ng⊗h((x	PROPN
ejpam-4651	307	23	,	,	PUNCT
ejpam-4651	307	24	a	a	PRON
ejpam-4651	307	25	)	)	PUNCT
ejpam-4651	307	26	)	)	PUNCT
ejpam-4651	307	27	\ng⊗h((x	\ng⊗h((x	NOUN
ejpam-4651	307	28	,	,	PUNCT
ejpam-4651	307	29	b	b	NOUN
ejpam-4651	307	30	)	)	PUNCT
ejpam-4651	307	31	)	)	PUNCT
ejpam-4651	307	32	.	.	PUNCT
ejpam-4651	308	1	case	case	NOUN
ejpam-4651	308	2	2	2	NUM
ejpam-4651	308	3	.	.	PUNCT
ejpam-4651	308	4	x	x	X
ejpam-4651	309	1	̸=	̸=	PROPN
ejpam-4651	309	2	z.	z.	PROPN
ejpam-4651	309	3	then	then	ADV
ejpam-4651	309	4	xz	xz	PROPN
ejpam-4651	309	5	∈	∈	PROPN
ejpam-4651	309	6	e(g	e(g	PROPN
ejpam-4651	309	7	)	)	PUNCT
ejpam-4651	309	8	because	because	SCONJ
ejpam-4651	309	9	s	s	VERB
ejpam-4651	309	10	is	be	AUX
ejpam-4651	309	11	a	a	DET
ejpam-4651	309	12	clique	clique	NOUN
ejpam-4651	309	13	in	in	ADP
ejpam-4651	309	14	g.	g.	PROPN
ejpam-4651	309	15	suppose	suppose	VERB
ejpam-4651	309	16	a	a	DET
ejpam-4651	309	17	=	=	PROPN
ejpam-4651	309	18	b.	b.	PROPN
ejpam-4651	309	19	then	then	ADV
ejpam-4651	309	20	a	a	DET
ejpam-4651	309	21	∈	∈	PROPN
ejpam-4651	309	22	tx	tx	PROPN
ejpam-4651	309	23	∩	∩	PROPN
ejpam-4651	309	24	tz	tz	PROPN
ejpam-4651	309	25	.	.	PUNCT
ejpam-4651	309	26	by	by	ADP
ejpam-4651	309	27	(	(	PUNCT
ejpam-4651	309	28	iv	iv	X
ejpam-4651	309	29	)	)	PUNCT
ejpam-4651	309	30	,	,	PUNCT
ejpam-4651	309	31	we	we	PRON
ejpam-4651	309	32	may	may	AUX
ejpam-4651	309	33	assume	assume	VERB
ejpam-4651	309	34	that	that	SCONJ
ejpam-4651	309	35	there	there	PRON
ejpam-4651	309	36	exists	exist	VERB
ejpam-4651	309	37	y	y	PROPN
ejpam-4651	309	38	∈	∈	PROPN
ejpam-4651	309	39	v	v	ADP
ejpam-4651	309	40	(	(	PUNCT
ejpam-4651	309	41	g	g	NOUN
ejpam-4651	309	42	)	)	PUNCT
ejpam-4651	309	43	\	\	PUNCT
ejpam-4651	310	1	s	s	VERB
ejpam-4651	310	2	such	such	ADJ
ejpam-4651	310	3	that	that	SCONJ
ejpam-4651	310	4	y	y	PROPN
ejpam-4651	310	5	∈	∈	PROPN
ejpam-4651	310	6	ng(x	ng(x	NUM
ejpam-4651	310	7	)	)	PUNCT
ejpam-4651	310	8	\	\	NOUN
ejpam-4651	310	9	ng(z	ng(z	PROPN
ejpam-4651	310	10	)	)	PUNCT
ejpam-4651	310	11	.	.	PUNCT
ejpam-4651	311	1	it	it	PRON
ejpam-4651	311	2	follows	follow	VERB
ejpam-4651	311	3	that	that	SCONJ
ejpam-4651	311	4	(	(	PUNCT
ejpam-4651	311	5	y	y	NOUN
ejpam-4651	311	6	,	,	PUNCT
ejpam-4651	311	7	a	a	PRON
ejpam-4651	311	8	)	)	PUNCT
ejpam-4651	311	9	∈	∈	NOUN
ejpam-4651	311	10	v	v	NOUN
ejpam-4651	311	11	(	(	PUNCT
ejpam-4651	311	12	g	g	PROPN
ejpam-4651	311	13	⊗h	⊗h	PROPN
ejpam-4651	311	14	)	)	PUNCT
ejpam-4651	311	15	\	\	PROPN
ejpam-4651	312	1	c	c	PROPN
ejpam-4651	312	2	and	and	CCONJ
ejpam-4651	312	3	(	(	PUNCT
ejpam-4651	312	4	y	y	PROPN
ejpam-4651	312	5	,	,	PUNCT
ejpam-4651	312	6	a	a	PRON
ejpam-4651	312	7	)	)	PUNCT
ejpam-4651	312	8	∈	∈	PROPN
ejpam-4651	312	9	ng⊗h(x	ng⊗h(x	PROPN
ejpam-4651	312	10	,	,	PUNCT
ejpam-4651	312	11	a	a	PRON
ejpam-4651	312	12	)	)	PUNCT
ejpam-4651	312	13	\ng⊗h(z	\ng⊗h(z	PROPN
ejpam-4651	312	14	,	,	PUNCT
ejpam-4651	312	15	b	b	NOUN
ejpam-4651	312	16	)	)	PUNCT
ejpam-4651	312	17	.	.	PUNCT
ejpam-4651	313	1	finally	finally	ADV
ejpam-4651	313	2	,	,	PUNCT
ejpam-4651	313	3	suppose	suppose	VERB
ejpam-4651	313	4	that	that	SCONJ
ejpam-4651	313	5	a	a	DET
ejpam-4651	313	6	̸=	̸=	PROPN
ejpam-4651	313	7	b.	b.	NOUN
ejpam-4651	313	8	then	then	ADV
ejpam-4651	313	9	ab	ab	PROPN
ejpam-4651	313	10	∈	∈	PROPN
ejpam-4651	313	11	e(g	e(g	PROPN
ejpam-4651	313	12	)	)	PUNCT
ejpam-4651	313	13	by	by	ADP
ejpam-4651	313	14	(	(	PUNCT
ejpam-4651	313	15	iii	iii	NOUN
ejpam-4651	313	16	)	)	PUNCT
ejpam-4651	313	17	.	.	PUNCT
ejpam-4651	313	18	suppose	suppose	VERB
ejpam-4651	314	1	ng[x	ng[x	PROPN
ejpam-4651	314	2	]	]	PUNCT
ejpam-4651	314	3	̸=	̸=	PROPN
ejpam-4651	314	4	ng[z	ng[z	PROPN
ejpam-4651	314	5	]	]	PUNCT
ejpam-4651	314	6	.	.	PUNCT
ejpam-4651	315	1	we	we	PRON
ejpam-4651	315	2	may	may	AUX
ejpam-4651	315	3	assume	assume	VERB
ejpam-4651	315	4	that	that	SCONJ
ejpam-4651	315	5	there	there	PRON
ejpam-4651	315	6	exists	exist	VERB
ejpam-4651	315	7	v	v	ADP
ejpam-4651	315	8	∈	∈	PROPN
ejpam-4651	315	9	ng(x	ng(x	NUM
ejpam-4651	315	10	)	)	PUNCT
ejpam-4651	315	11	\	\	NOUN
ejpam-4651	315	12	ng(z	ng(z	PROPN
ejpam-4651	315	13	)	)	PUNCT
ejpam-4651	315	14	.	.	PUNCT
ejpam-4651	316	1	clearly	clearly	ADV
ejpam-4651	316	2	,	,	PUNCT
ejpam-4651	316	3	v	v	PROPN
ejpam-4651	316	4	∈	∈	PROPN
ejpam-4651	316	5	v	v	NOUN
ejpam-4651	316	6	(	(	PUNCT
ejpam-4651	316	7	g	g	NOUN
ejpam-4651	316	8	)	)	PUNCT
ejpam-4651	316	9	\	\	NOUN
ejpam-4651	317	1	s.	s.	PROPN
ejpam-4651	317	2	hence	hence	ADV
ejpam-4651	317	3	,	,	PUNCT
ejpam-4651	317	4	(	(	PUNCT
ejpam-4651	317	5	v	v	NOUN
ejpam-4651	317	6	,	,	PUNCT
ejpam-4651	317	7	a	a	PRON
ejpam-4651	317	8	)	)	PUNCT
ejpam-4651	317	9	∈	∈	NOUN
ejpam-4651	317	10	v	v	NOUN
ejpam-4651	317	11	(	(	PUNCT
ejpam-4651	317	12	g	g	PROPN
ejpam-4651	317	13	⊗	⊗	PROPN
ejpam-4651	317	14	h	h	NOUN
ejpam-4651	317	15	)	)	PUNCT
ejpam-4651	317	16	\	\	PROPN
ejpam-4651	318	1	c	c	PROPN
ejpam-4651	318	2	and	and	CCONJ
ejpam-4651	318	3	(	(	PUNCT
ejpam-4651	318	4	v	v	NOUN
ejpam-4651	318	5	,	,	PUNCT
ejpam-4651	318	6	a	a	PRON
ejpam-4651	318	7	)	)	PUNCT
ejpam-4651	318	8	∈	∈	PROPN
ejpam-4651	318	9	ng⊗h(x	ng⊗h(x	PROPN
ejpam-4651	318	10	,	,	PUNCT
ejpam-4651	318	11	a	a	PRON
ejpam-4651	318	12	)	)	PUNCT
ejpam-4651	318	13	\ng⊗h(z	\ng⊗h(z	PROPN
ejpam-4651	318	14	,	,	PUNCT
ejpam-4651	318	15	b	b	NOUN
ejpam-4651	318	16	)	)	PUNCT
ejpam-4651	318	17	.	.	PUNCT
ejpam-4651	319	1	if	if	SCONJ
ejpam-4651	319	2	ng[x	ng[x	PROPN
ejpam-4651	319	3	]	]	X
ejpam-4651	319	4	=	=	PUNCT
ejpam-4651	319	5	ng[z	ng[z	PROPN
ejpam-4651	319	6	]	]	PUNCT
ejpam-4651	319	7	,	,	PUNCT
ejpam-4651	319	8	then	then	ADV
ejpam-4651	319	9	there	there	PRON
ejpam-4651	319	10	exists	exist	VERB
ejpam-4651	319	11	c	c	PROPN
ejpam-4651	319	12	∈	∈	PROPN
ejpam-4651	319	13	v	v	PROPN
ejpam-4651	319	14	(	(	PUNCT
ejpam-4651	319	15	h	h	NOUN
ejpam-4651	319	16	)	)	PUNCT
ejpam-4651	319	17	such	such	ADJ
ejpam-4651	319	18	that	that	SCONJ
ejpam-4651	320	1	[	[	X
ejpam-4651	320	2	c	c	X
ejpam-4651	320	3	∈	∈	PROPN
ejpam-4651	320	4	v	v	NOUN
ejpam-4651	320	5	(	(	PUNCT
ejpam-4651	320	6	h)\tx	h)\tx	NOUN
ejpam-4651	320	7	and	and	CCONJ
ejpam-4651	320	8	c	c	NOUN
ejpam-4651	320	9	∈	∈	PROPN
ejpam-4651	320	10	nh(a)\nh(b	nh(a)\nh(b	NOUN
ejpam-4651	320	11	)	)	PUNCT
ejpam-4651	320	12	]	]	PUNCT
ejpam-4651	320	13	or	or	CCONJ
ejpam-4651	320	14	[	[	X
ejpam-4651	320	15	c	c	X
ejpam-4651	320	16	∈	∈	PROPN
ejpam-4651	320	17	v	v	NOUN
ejpam-4651	320	18	(	(	PUNCT
ejpam-4651	320	19	h)\tz	h)\tz	PROPN
ejpam-4651	320	20	and	and	CCONJ
ejpam-4651	320	21	c	c	PROPN
ejpam-4651	320	22	∈	∈	PROPN
ejpam-4651	320	23	nh(b)\nh(a	nh(b)\nh(a	NOUN
ejpam-4651	320	24	)	)	PUNCT
ejpam-4651	320	25	]	]	PUNCT
ejpam-4651	320	26	by	by	ADP
ejpam-4651	320	27	property	property	NOUN
ejpam-4651	320	28	(	(	PUNCT
ejpam-4651	320	29	v	v	NOUN
ejpam-4651	320	30	)	)	PUNCT
ejpam-4651	320	31	.	.	PUNCT
ejpam-4651	321	1	assume	assume	VERB
ejpam-4651	321	2	that	that	SCONJ
ejpam-4651	321	3	c	c	PROPN
ejpam-4651	321	4	∈	∈	PROPN
ejpam-4651	321	5	v	v	PROPN
ejpam-4651	321	6	(	(	PUNCT
ejpam-4651	321	7	h	h	NOUN
ejpam-4651	321	8	)	)	PUNCT
ejpam-4651	321	9	\	\	NOUN
ejpam-4651	321	10	tx	tx	PROPN
ejpam-4651	321	11	and	and	CCONJ
ejpam-4651	321	12	c	c	NOUN
ejpam-4651	321	13	∈	∈	PROPN
ejpam-4651	321	14	nh(a	nh(a	PROPN
ejpam-4651	321	15	)	)	PUNCT
ejpam-4651	321	16	\nh(b	\nh(b	NUM
ejpam-4651	321	17	)	)	PUNCT
ejpam-4651	321	18	.	.	PUNCT
ejpam-4651	322	1	then	then	ADV
ejpam-4651	322	2	(	(	PUNCT
ejpam-4651	322	3	x	x	X
ejpam-4651	322	4	,	,	PUNCT
ejpam-4651	322	5	c	c	NOUN
ejpam-4651	322	6	)	)	PUNCT
ejpam-4651	322	7	∈	∈	NOUN
ejpam-4651	322	8	v	v	NOUN
ejpam-4651	322	9	(	(	PUNCT
ejpam-4651	322	10	g⊗h	g⊗h	NOUN
ejpam-4651	322	11	)	)	PUNCT
ejpam-4651	322	12	\c	\c	NOUN
ejpam-4651	322	13	and	and	CCONJ
ejpam-4651	322	14	(	(	PUNCT
ejpam-4651	322	15	x	x	NOUN
ejpam-4651	322	16	,	,	PUNCT
ejpam-4651	322	17	c	c	NOUN
ejpam-4651	322	18	)	)	PUNCT
ejpam-4651	322	19	∈	∈	PROPN
ejpam-4651	322	20	ng⊗h(x	ng⊗h(x	PROPN
ejpam-4651	322	21	,	,	PUNCT
ejpam-4651	322	22	a	a	PRON
ejpam-4651	322	23	)	)	PUNCT
ejpam-4651	322	24	\ng⊗h(z	\ng⊗h(z	PROPN
ejpam-4651	322	25	,	,	PUNCT
ejpam-4651	322	26	b	b	NOUN
ejpam-4651	322	27	)	)	PUNCT
ejpam-4651	322	28	.	.	PUNCT
ejpam-4651	323	1	accordingly	accordingly	ADV
ejpam-4651	323	2	,	,	PUNCT
ejpam-4651	323	3	c	c	PROPN
ejpam-4651	323	4	is	be	AUX
ejpam-4651	323	5	a	a	DET
ejpam-4651	323	6	superclique	superclique	NOUN
ejpam-4651	323	7	in	in	ADP
ejpam-4651	323	8	g⊗h	g⊗h	PROPN
ejpam-4651	323	9	.	.	PUNCT
ejpam-4651	324	1	corollary	corollary	ADJ
ejpam-4651	324	2	7	7	PROPN
ejpam-4651	324	3	.	.	PUNCT
ejpam-4651	325	1	let	let	VERB
ejpam-4651	325	2	g	g	NOUN
ejpam-4651	325	3	and	and	CCONJ
ejpam-4651	325	4	h	h	PROPN
ejpam-4651	325	5	be	be	VERB
ejpam-4651	325	6	non	non	ADJ
ejpam-4651	325	7	-	-	ADJ
ejpam-4651	325	8	trivial	trivial	ADJ
ejpam-4651	325	9	connected	connected	ADJ
ejpam-4651	325	10	graphs	graph	NOUN
ejpam-4651	325	11	.	.	PUNCT
ejpam-4651	326	1	then	then	ADV
ejpam-4651	326	2	ωs(g)ωs(h	ωs(g)ωs(h	PROPN
ejpam-4651	326	3	)	)	PUNCT
ejpam-4651	326	4	≤	≤	NOUN
ejpam-4651	326	5	ωs(g⊗h	ωs(g⊗h	ADJ
ejpam-4651	326	6	)	)	PUNCT
ejpam-4651	326	7	≤	≤	NUM
ejpam-4651	326	8	ω(g)ωs(h	ω(g)ωs(h	NOUN
ejpam-4651	326	9	)	)	PUNCT
ejpam-4651	326	10	.	.	PUNCT
ejpam-4651	327	1	moreover	moreover	ADV
ejpam-4651	327	2	,	,	PUNCT
ejpam-4651	327	3	if	if	SCONJ
ejpam-4651	327	4	ωs(g	ωs(g	NUM
ejpam-4651	327	5	)	)	PUNCT
ejpam-4651	327	6	=	=	SYM
ejpam-4651	327	7	ω(g	ω(g	NOUN
ejpam-4651	327	8	)	)	PUNCT
ejpam-4651	327	9	,	,	PUNCT
ejpam-4651	327	10	then	then	ADV
ejpam-4651	327	11	ωs(g⊗h	ωs(g⊗h	ADJ
ejpam-4651	327	12	)	)	PUNCT
ejpam-4651	327	13	=	=	SYM
ejpam-4651	327	14	ωs(g)ωs(h	ωs(g)ωs(h	PROPN
ejpam-4651	327	15	)	)	PUNCT
ejpam-4651	327	16	.	.	PUNCT
ejpam-4651	328	1	proof	proof	NOUN
ejpam-4651	328	2	.	.	PUNCT
ejpam-4651	329	1	let	let	VERB
ejpam-4651	329	2	s	s	PRON
ejpam-4651	329	3	and	and	CCONJ
ejpam-4651	329	4	d	d	AUX
ejpam-4651	329	5	be	be	AUX
ejpam-4651	329	6	ωs	ω	NOUN
ejpam-4651	329	7	-	-	NOUN
ejpam-4651	329	8	sets	set	NOUN
ejpam-4651	329	9	in	in	ADP
ejpam-4651	329	10	g	g	PROPN
ejpam-4651	329	11	and	and	CCONJ
ejpam-4651	329	12	h	h	NOUN
ejpam-4651	329	13	,	,	PUNCT
ejpam-4651	329	14	repectively	repectively	ADV
ejpam-4651	329	15	.	.	PUNCT
ejpam-4651	330	1	set	set	VERB
ejpam-4651	330	2	tx	tx	PROPN
ejpam-4651	331	1	=	=	SYM
ejpam-4651	332	1	d	d	PROPN
ejpam-4651	332	2	for	for	ADP
ejpam-4651	332	3	each	each	DET
ejpam-4651	332	4	x	x	SYM
ejpam-4651	332	5	∈	∈	PROPN
ejpam-4651	332	6	s.	s.	PROPN
ejpam-4651	332	7	then	then	ADV
ejpam-4651	332	8	c	c	X
ejpam-4651	332	9	=	=	SYM
ejpam-4651	332	10	∪x∈s({x	∪x∈s({x	ADJ
ejpam-4651	332	11	}	}	PUNCT
ejpam-4651	332	12	×	×	NOUN
ejpam-4651	332	13	tx	tx	PROPN
ejpam-4651	332	14	)	)	PUNCT
ejpam-4651	333	1	=	=	SYM
ejpam-4651	333	2	s	s	PART
ejpam-4651	333	3	×d	×d	NOUN
ejpam-4651	333	4	is	be	AUX
ejpam-4651	333	5	a	a	DET
ejpam-4651	333	6	superclique	superclique	NOUN
ejpam-4651	333	7	in	in	ADP
ejpam-4651	333	8	g⊗h	g⊗h	NOUN
ejpam-4651	333	9	by	by	ADP
ejpam-4651	333	10	theorem	theorem	NOUN
ejpam-4651	333	11	8	8	NUM
ejpam-4651	333	12	.	.	PUNCT
ejpam-4651	334	1	therefore	therefore	ADV
ejpam-4651	334	2	,	,	PUNCT
ejpam-4651	334	3	ωs(g⊗h	ωs(g⊗h	ADJ
ejpam-4651	334	4	)	)	PUNCT
ejpam-4651	334	5	≥	≥	PROPN
ejpam-4651	334	6	|c|	|c|	PROPN
ejpam-4651	334	7	=	=	SYM
ejpam-4651	334	8	|s||d|	|s||d|	PROPN
ejpam-4651	334	9	=	=	SYM
ejpam-4651	334	10	ωs(g)ωs(h	ωs(g)ωs(h	PROPN
ejpam-4651	334	11	)	)	PUNCT
ejpam-4651	334	12	.	.	PUNCT
ejpam-4651	335	1	on	on	ADP
ejpam-4651	335	2	the	the	DET
ejpam-4651	335	3	other	other	ADJ
ejpam-4651	335	4	hand	hand	NOUN
ejpam-4651	335	5	,	,	PUNCT
ejpam-4651	335	6	suppose	suppose	VERB
ejpam-4651	335	7	that	that	SCONJ
ejpam-4651	335	8	c	c	NOUN
ejpam-4651	335	9	′	′	NUM
ejpam-4651	335	10	=	=	SYM
ejpam-4651	335	11	∪x∈s′({x	∪x∈s′({x	NUM
ejpam-4651	335	12	}	}	PUNCT
ejpam-4651	335	13	×dx	×dx	PROPN
ejpam-4651	335	14	)	)	PUNCT
ejpam-4651	335	15	is	be	AUX
ejpam-4651	335	16	an	an	DET
ejpam-4651	335	17	ωs	ωs	ADV
ejpam-4651	335	18	-	-	PUNCT
ejpam-4651	335	19	set	set	VERB
ejpam-4651	335	20	in	in	ADP
ejpam-4651	335	21	g⊗h	g⊗h	PROPN
ejpam-4651	335	22	.	.	PUNCT
ejpam-4651	336	1	then	then	ADV
ejpam-4651	336	2	s′	s′	PROPN
ejpam-4651	336	3	is	be	AUX
ejpam-4651	336	4	a	a	DET
ejpam-4651	336	5	clique	clique	NOUN
ejpam-4651	336	6	in	in	ADP
ejpam-4651	336	7	g	g	PROPN
ejpam-4651	336	8	and	and	CCONJ
ejpam-4651	336	9	each	each	DET
ejpam-4651	336	10	dx	dx	PROPN
ejpam-4651	336	11	is	be	AUX
ejpam-4651	336	12	a	a	DET
ejpam-4651	336	13	superclique	superclique	NOUN
ejpam-4651	336	14	in	in	ADP
ejpam-4651	336	15	h	h	NOUN
ejpam-4651	336	16	by	by	ADP
ejpam-4651	336	17	theorem	theorem	NOUN
ejpam-4651	336	18	8	8	NUM
ejpam-4651	336	19	.	.	PUNCT
ejpam-4651	337	1	it	it	PRON
ejpam-4651	337	2	follows	follow	VERB
ejpam-4651	337	3	that	that	SCONJ
ejpam-4651	337	4	ωs(g⊗h	ωs(g⊗h	ADJ
ejpam-4651	337	5	)	)	PUNCT
ejpam-4651	338	1	=	=	NOUN
ejpam-4651	338	2	|c	|c	VERB
ejpam-4651	338	3	′|	′|	NUM
ejpam-4651	338	4	≤	≤	NUM
ejpam-4651	338	5	ω(g)ωs(h	ω(g)ωs(h	NOUN
ejpam-4651	338	6	)	)	PUNCT
ejpam-4651	338	7	.	.	PUNCT
ejpam-4651	339	1	this	this	PRON
ejpam-4651	339	2	proves	prove	VERB
ejpam-4651	339	3	the	the	DET
ejpam-4651	339	4	assertion	assertion	NOUN
ejpam-4651	339	5	.	.	PUNCT
ejpam-4651	340	1	example	example	NOUN
ejpam-4651	341	1	1	1	NUM
ejpam-4651	341	2	.	.	X
ejpam-4651	342	1	for	for	ADP
ejpam-4651	342	2	any	any	DET
ejpam-4651	342	3	two	two	NUM
ejpam-4651	342	4	positive	positive	ADJ
ejpam-4651	342	5	integers	integer	NOUN
ejpam-4651	342	6	m	m	VERB
ejpam-4651	342	7	≥	≥	NOUN
ejpam-4651	342	8	3	3	NUM
ejpam-4651	342	9	and	and	CCONJ
ejpam-4651	342	10	n	n	PRON
ejpam-4651	342	11	≥	≥	NOUN
ejpam-4651	342	12	3	3	NUM
ejpam-4651	342	13	,	,	PUNCT
ejpam-4651	342	14	ωs(pm	ωs(pm	ADJ
ejpam-4651	342	15	⊗	⊗	PROPN
ejpam-4651	342	16	pn	pn	NOUN
ejpam-4651	342	17	)	)	PUNCT
ejpam-4651	342	18	=	=	SYM
ejpam-4651	342	19	4	4	NUM
ejpam-4651	342	20	=	=	SYM
ejpam-4651	342	21	ωs(pm)ωs(pn	ωs(pm)ωs(pn	NUM
ejpam-4651	342	22	)	)	PUNCT
ejpam-4651	342	23	=	=	SYM
ejpam-4651	342	24	ω(pm)ωs(pn	ω(pm)ωs(pn	NUM
ejpam-4651	342	25	)	)	PUNCT
ejpam-4651	342	26	.	.	PUNCT
ejpam-4651	342	27	note	note	VERB
ejpam-4651	342	28	that	that	SCONJ
ejpam-4651	342	29	ωs(p2	ωs(p2	ADP
ejpam-4651	342	30	⊗	⊗	PROPN
ejpam-4651	342	31	p3	p3	PROPN
ejpam-4651	342	32	)	)	PUNCT
ejpam-4651	342	33	=	=	SYM
ejpam-4651	342	34	ωs(p2)ωs(p3	ωs(p2)ωs(p3	NOUN
ejpam-4651	342	35	)	)	PUNCT
ejpam-4651	342	36	=	=	SYM
ejpam-4651	342	37	2	2	NUM
ejpam-4651	342	38	̸=	̸=	PROPN
ejpam-4651	342	39	4	4	NUM
ejpam-4651	342	40	=	=	SYM
ejpam-4651	342	41	ω(p2)ωs(p3	ω(p2)ωs(p3	NOUN
ejpam-4651	342	42	)	)	PUNCT
ejpam-4651	342	43	.	.	PUNCT
ejpam-4651	343	1	references	reference	NOUN
ejpam-4651	343	2	251	251	NUM
ejpam-4651	343	3	4	4	NUM
ejpam-4651	343	4	.	.	PUNCT
ejpam-4651	343	5	conclusion	conclusion	NOUN
ejpam-4651	343	6	cliques	clique	NOUN
ejpam-4651	343	7	and	and	CCONJ
ejpam-4651	343	8	supercliques	superclique	NOUN
ejpam-4651	343	9	in	in	ADP
ejpam-4651	343	10	the	the	DET
ejpam-4651	343	11	edge	edge	NOUN
ejpam-4651	343	12	corona	corona	NOUN
ejpam-4651	343	13	,	,	PUNCT
ejpam-4651	343	14	tensor	tensor	NOUN
ejpam-4651	343	15	product	product	NOUN
ejpam-4651	343	16	,	,	PUNCT
ejpam-4651	343	17	and	and	CCONJ
ejpam-4651	343	18	strong	strong	ADJ
ejpam-4651	343	19	product	product	NOUN
ejpam-4651	343	20	of	of	ADP
ejpam-4651	343	21	two	two	NUM
ejpam-4651	343	22	graphs	graph	NOUN
ejpam-4651	343	23	have	have	AUX
ejpam-4651	343	24	been	be	AUX
ejpam-4651	343	25	characterized	characterize	VERB
ejpam-4651	343	26	and	and	CCONJ
ejpam-4651	343	27	the	the	DET
ejpam-4651	343	28	corresponding	corresponding	ADJ
ejpam-4651	343	29	clique	clique	NOUN
ejpam-4651	343	30	and	and	CCONJ
ejpam-4651	343	31	supercliques	superclique	NOUN
ejpam-4651	343	32	numbers	number	NOUN
ejpam-4651	343	33	have	have	AUX
ejpam-4651	343	34	been	be	AUX
ejpam-4651	343	35	described	describe	VERB
ejpam-4651	343	36	.	.	PUNCT
ejpam-4651	344	1	these	these	DET
ejpam-4651	344	2	concepts	concept	NOUN
ejpam-4651	344	3	can	can	AUX
ejpam-4651	344	4	be	be	AUX
ejpam-4651	344	5	studied	study	VERB
ejpam-4651	344	6	further	far	ADV
ejpam-4651	344	7	for	for	ADP
ejpam-4651	344	8	other	other	ADJ
ejpam-4651	344	9	graphs	graph	NOUN
ejpam-4651	344	10	.	.	PUNCT
ejpam-4651	345	1	moreover	moreover	ADV
ejpam-4651	345	2	,	,	PUNCT
ejpam-4651	345	3	it	it	PRON
ejpam-4651	345	4	may	may	AUX
ejpam-4651	345	5	be	be	AUX
ejpam-4651	345	6	interesting	interesting	ADJ
ejpam-4651	345	7	to	to	PART
ejpam-4651	345	8	investigate	investigate	VERB
ejpam-4651	345	9	the	the	DET
ejpam-4651	345	10	complexity	complexity	NOUN
ejpam-4651	345	11	of	of	ADP
ejpam-4651	345	12	the	the	DET
ejpam-4651	345	13	superclique	superclique	ADJ
ejpam-4651	345	14	problem	problem	NOUN
ejpam-4651	345	15	.	.	PUNCT
ejpam-4651	346	1	acknowledgment	acknowledgment	NOUN
ejpam-4651	346	2	:	:	PUNCT
ejpam-4651	346	3	the	the	DET
ejpam-4651	346	4	authors	author	NOUN
ejpam-4651	346	5	would	would	AUX
ejpam-4651	346	6	like	like	VERB
ejpam-4651	346	7	to	to	PART
ejpam-4651	346	8	thank	thank	VERB
ejpam-4651	346	9	the	the	DET
ejpam-4651	346	10	referees	referee	NOUN
ejpam-4651	346	11	for	for	ADP
ejpam-4651	346	12	the	the	DET
ejpam-4651	346	13	suggestions	suggestion	NOUN
ejpam-4651	346	14	and	and	CCONJ
ejpam-4651	346	15	comments	comment	NOUN
ejpam-4651	346	16	that	that	PRON
ejpam-4651	346	17	helped	helped	AUX
ejpam-4651	346	18	improve	improve	VERB
ejpam-4651	346	19	the	the	DET
ejpam-4651	346	20	paper	paper	NOUN
ejpam-4651	346	21	.	.	PUNCT
ejpam-4651	347	1	the	the	DET
ejpam-4651	347	2	authors	author	NOUN
ejpam-4651	347	3	also	also	ADV
ejpam-4651	347	4	extend	extend	VERB
ejpam-4651	347	5	their	their	PRON
ejpam-4651	347	6	thankfulness	thankfulness	NOUN
ejpam-4651	347	7	to	to	ADP
ejpam-4651	347	8	the	the	DET
ejpam-4651	347	9	department	department	PROPN
ejpam-4651	347	10	of	of	ADP
ejpam-4651	347	11	science	science	NOUN
ejpam-4651	347	12	and	and	CCONJ
ejpam-4651	347	13	technology	technology	NOUN
ejpam-4651	347	14	accelerated	accelerate	VERB
ejpam-4651	347	15	science	science	NOUN
ejpam-4651	347	16	and	and	CCONJ
ejpam-4651	347	17	technology	technology	NOUN
ejpam-4651	347	18	human	human	ADJ
ejpam-4651	347	19	resource	resource	NOUN
ejpam-4651	347	20	development	development	NOUN
ejpam-4651	347	21	program	program	NOUN
ejpam-4651	347	22	(	(	PUNCT
ejpam-4651	347	23	dost	dost	NOUN
ejpam-4651	347	24	-	-	PUNCT
ejpam-4651	347	25	asthrdp)-philippines	asthrdp)-philippine	NOUN
ejpam-4651	347	26	,	,	PUNCT
ejpam-4651	347	27	and	and	CCONJ
ejpam-4651	347	28	msu	msu	PROPN
ejpam-4651	347	29	-	-	PUNCT
ejpam-4651	347	30	iligan	iligan	PROPN
ejpam-4651	347	31	institute	institute	PROPN
ejpam-4651	347	32	of	of	ADP
ejpam-4651	347	33	technology	technology	NOUN
ejpam-4651	347	34	for	for	ADP
ejpam-4651	347	35	funding	fund	VERB
ejpam-4651	347	36	this	this	DET
ejpam-4651	347	37	research	research	NOUN
ejpam-4651	347	38	.	.	PUNCT
ejpam-4651	348	1	references	reference	NOUN
ejpam-4651	348	2	[	[	X
ejpam-4651	348	3	1	1	NUM
ejpam-4651	348	4	]	]	PUNCT
ejpam-4651	348	5	p.	p.	NOUN
ejpam-4651	348	6	acal	acal	ADJ
ejpam-4651	348	7	and	and	CCONJ
ejpam-4651	348	8	h.	h.	PROPN
ejpam-4651	348	9	rara	rara	PROPN
ejpam-4651	348	10	.	.	PUNCT
ejpam-4651	349	1	the	the	DET
ejpam-4651	349	2	strong	strong	ADJ
ejpam-4651	349	3	connected	connected	ADJ
ejpam-4651	349	4	metric	metric	ADJ
ejpam-4651	349	5	dimension	dimension	NOUN
ejpam-4651	349	6	in	in	ADP
ejpam-4651	349	7	the	the	DET
ejpam-4651	349	8	join	join	NOUN
ejpam-4651	349	9	and	and	CCONJ
ejpam-4651	349	10	corona	corona	NOUN
ejpam-4651	349	11	of	of	ADP
ejpam-4651	349	12	graphs	graph	NOUN
ejpam-4651	349	13	.	.	PUNCT
ejpam-4651	350	1	advances	advance	NOUN
ejpam-4651	350	2	and	and	CCONJ
ejpam-4651	350	3	applications	application	NOUN
ejpam-4651	350	4	in	in	ADP
ejpam-4651	350	5	discrete	discrete	ADJ
ejpam-4651	350	6	mathematics	mathematic	NOUN
ejpam-4651	350	7	,	,	PUNCT
ejpam-4651	350	8	21(1):91–101	21(1):91–101	NUM
ejpam-4651	350	9	,	,	PUNCT
ejpam-4651	350	10	2019	2019	NUM
ejpam-4651	350	11	.	.	PUNCT
ejpam-4651	351	1	[	[	X
ejpam-4651	351	2	2	2	NUM
ejpam-4651	351	3	]	]	X
ejpam-4651	351	4	r.	r.	PROPN
ejpam-4651	351	5	brigham	brigham	PROPN
ejpam-4651	351	6	,	,	PUNCT
ejpam-4651	351	7	g.	g.	PROPN
ejpam-4651	351	8	chartrand	chartrand	PROPN
ejpam-4651	351	9	,	,	PUNCT
ejpam-4651	351	10	r.	r.	PROPN
ejpam-4651	351	11	dutton	dutton	PROPN
ejpam-4651	351	12	,	,	PUNCT
ejpam-4651	351	13	and	and	CCONJ
ejpam-4651	351	14	p.	p.	PROPN
ejpam-4651	351	15	zhang	zhang	PROPN
ejpam-4651	351	16	.	.	PUNCT
ejpam-4651	352	1	resolving	resolve	VERB
ejpam-4651	352	2	domination	domination	NOUN
ejpam-4651	352	3	in	in	ADP
ejpam-4651	352	4	graphs	graph	NOUN
ejpam-4651	352	5	.	.	PUNCT
ejpam-4651	353	1	mathematica	mathematica	PROPN
ejpam-4651	353	2	bohemica	bohemica	PROPN
ejpam-4651	353	3	,	,	PUNCT
ejpam-4651	353	4	128(1):25–36	128(1):25–36	NUM
ejpam-4651	353	5	,	,	PUNCT
ejpam-4651	353	6	2003	2003	NUM
ejpam-4651	353	7	.	.	PUNCT
ejpam-4651	354	1	[	[	X
ejpam-4651	354	2	3	3	X
ejpam-4651	354	3	]	]	X
ejpam-4651	354	4	r.	r.	PROPN
ejpam-4651	354	5	dela	dela	PROPN
ejpam-4651	354	6	cerna	cerna	PROPN
ejpam-4651	354	7	and	and	CCONJ
ejpam-4651	354	8	s.	s.	PROPN
ejpam-4651	354	9	canoy	canoy	PROPN
ejpam-4651	354	10	jr	jr	PROPN
ejpam-4651	354	11	.	.	PROPN
ejpam-4651	354	12	supercliques	superclique	NOUN
ejpam-4651	354	13	in	in	ADP
ejpam-4651	354	14	a	a	DET
ejpam-4651	354	15	graph	graph	NOUN
ejpam-4651	354	16	.	.	PUNCT
ejpam-4651	355	1	european	european	ADJ
ejpam-4651	355	2	journal	journal	PROPN
ejpam-4651	355	3	of	of	ADP
ejpam-4651	355	4	pure	pure	ADJ
ejpam-4651	355	5	and	and	CCONJ
ejpam-4651	355	6	applied	applied	ADJ
ejpam-4651	355	7	mathematics	mathematic	NOUN
ejpam-4651	355	8	,	,	PUNCT
ejpam-4651	355	9	15(3):1217–1228	15(3):1217–1228	NUM
ejpam-4651	355	10	,	,	PUNCT
ejpam-4651	355	11	2022	2022	NUM
ejpam-4651	355	12	.	.	PUNCT
ejpam-4651	356	1	[	[	X
ejpam-4651	356	2	4	4	X
ejpam-4651	356	3	]	]	X
ejpam-4651	356	4	g.	g.	PROPN
ejpam-4651	356	5	chartrand	chartrand	PROPN
ejpam-4651	356	6	,	,	PUNCT
ejpam-4651	356	7	l.	l.	PROPN
ejpam-4651	356	8	eroh	eroh	PROPN
ejpam-4651	356	9	,	,	PUNCT
ejpam-4651	356	10	m.	m.	NOUN
ejpam-4651	356	11	johnson	johnson	PROPN
ejpam-4651	356	12	,	,	PUNCT
ejpam-4651	356	13	and	and	CCONJ
ejpam-4651	356	14	o.r	o.r	PROPN
ejpam-4651	356	15	.	.	PROPN
ejpam-4651	356	16	oellermann	oellermann	PROPN
ejpam-4651	356	17	.	.	PUNCT
ejpam-4651	357	1	resolvability	resolvability	NOUN
ejpam-4651	357	2	in	in	ADP
ejpam-4651	357	3	graphs	graph	NOUN
ejpam-4651	357	4	and	and	CCONJ
ejpam-4651	357	5	the	the	DET
ejpam-4651	357	6	metric	metric	ADJ
ejpam-4651	357	7	dimension	dimension	NOUN
ejpam-4651	357	8	of	of	ADP
ejpam-4651	357	9	a	a	DET
ejpam-4651	357	10	graph	graph	NOUN
ejpam-4651	357	11	the	the	DET
ejpam-4651	357	12	metric	metric	ADJ
ejpam-4651	357	13	dimension	dimension	NOUN
ejpam-4651	357	14	of	of	ADP
ejpam-4651	357	15	a	a	DET
ejpam-4651	357	16	graph	graph	NOUN
ejpam-4651	357	17	.	.	PUNCT
ejpam-4651	358	1	discrete	discrete	ADJ
ejpam-4651	358	2	applied	apply	VERB
ejpam-4651	358	3	mathematics	mathematic	NOUN
ejpam-4651	358	4	,	,	PUNCT
ejpam-4651	358	5	105:99–113	105:99–113	NUM
ejpam-4651	358	6	,	,	PUNCT
ejpam-4651	358	7	2000	2000	NUM
ejpam-4651	358	8	.	.	PUNCT
ejpam-4651	359	1	[	[	X
ejpam-4651	359	2	5	5	NUM
ejpam-4651	359	3	]	]	X
ejpam-4651	359	4	m.b	m.b	PROPN
ejpam-4651	359	5	.	.	PROPN
ejpam-4651	359	6	cozzens	cozzen	NOUN
ejpam-4651	359	7	and	and	CCONJ
ejpam-4651	359	8	l.l	l.l	PROPN
ejpam-4651	359	9	.	.	PROPN
ejpam-4651	359	10	kelleher	kelleher	PROPN
ejpam-4651	359	11	.	.	PUNCT
ejpam-4651	360	1	dominating	dominate	VERB
ejpam-4651	360	2	cliques	clique	NOUN
ejpam-4651	360	3	in	in	ADP
ejpam-4651	360	4	graphs	graph	NOUN
ejpam-4651	360	5	.	.	PUNCT
ejpam-4651	361	1	discrete	discrete	ADJ
ejpam-4651	361	2	mathematics	mathematic	NOUN
ejpam-4651	361	3	,	,	PUNCT
ejpam-4651	361	4	86:101–116	86:101–116	PROPN
ejpam-4651	361	5	,	,	PUNCT
ejpam-4651	361	6	1990	1990	NUM
ejpam-4651	361	7	.	.	PUNCT
ejpam-4651	362	1	[	[	X
ejpam-4651	362	2	6	6	NUM
ejpam-4651	362	3	]	]	X
ejpam-4651	362	4	t.v	t.v	PROPN
ejpam-4651	362	5	.	.	PROPN
ejpam-4651	362	6	daniel	daniel	PROPN
ejpam-4651	362	7	and	and	CCONJ
ejpam-4651	362	8	s.	s.	PROPN
ejpam-4651	362	9	canoy	canoy	PROPN
ejpam-4651	362	10	jr	jr	PROPN
ejpam-4651	362	11	.	.	PROPN
ejpam-4651	362	12	clique	clique	PROPN
ejpam-4651	362	13	domination	domination	NOUN
ejpam-4651	362	14	in	in	ADP
ejpam-4651	362	15	a	a	DET
ejpam-4651	362	16	graph	graph	NOUN
ejpam-4651	362	17	.	.	PUNCT
ejpam-4651	363	1	applied	apply	VERB
ejpam-4651	363	2	mathematical	mathematical	ADJ
ejpam-4651	363	3	sciences	science	NOUN
ejpam-4651	363	4	,	,	PUNCT
ejpam-4651	363	5	9(116):5749–5755	9(116):5749–5755	NUM
ejpam-4651	363	6	,	,	PUNCT
ejpam-4651	363	7	2015	2015	NUM
ejpam-4651	363	8	.	.	PUNCT
ejpam-4651	364	1	[	[	X
ejpam-4651	364	2	7	7	X
ejpam-4651	364	3	]	]	X
ejpam-4651	364	4	t.v	t.v	PROPN
ejpam-4651	364	5	.	.	PROPN
ejpam-4651	364	6	daniel	daniel	PROPN
ejpam-4651	364	7	and	and	CCONJ
ejpam-4651	364	8	s.	s.	PROPN
ejpam-4651	364	9	canoy	canoy	PROPN
ejpam-4651	364	10	jr	jr	PROPN
ejpam-4651	364	11	.	.	PROPN
ejpam-4651	364	12	1	1	NUM
ejpam-4651	364	13	-	-	PUNCT
ejpam-4651	364	14	movable	movable	ADJ
ejpam-4651	364	15	clique	clique	NOUN
ejpam-4651	364	16	dominating	dominating	NOUN
ejpam-4651	364	17	sets	set	NOUN
ejpam-4651	364	18	of	of	ADP
ejpam-4651	364	19	a	a	DET
ejpam-4651	364	20	graph	graph	NOUN
ejpam-4651	364	21	.	.	PUNCT
ejpam-4651	365	1	applied	apply	VERB
ejpam-4651	365	2	mathematical	mathematical	ADJ
ejpam-4651	365	3	sciences	science	NOUN
ejpam-4651	365	4	,	,	PUNCT
ejpam-4651	365	5	106(2):463–471	106(2):463–471	NUM
ejpam-4651	365	6	,	,	PUNCT
ejpam-4651	365	7	2016	2016	NUM
ejpam-4651	365	8	.	.	PUNCT
ejpam-4651	366	1	[	[	X
ejpam-4651	366	2	8	8	NUM
ejpam-4651	366	3	]	]	X
ejpam-4651	366	4	n.	n.	NOUN
ejpam-4651	366	5	gaquing	gaquing	NOUN
ejpam-4651	366	6	and	and	CCONJ
ejpam-4651	366	7	s.	s.	PROPN
ejpam-4651	366	8	canoy	canoy	PROPN
ejpam-4651	366	9	jr	jr	PROPN
ejpam-4651	366	10	.	.	PROPN
ejpam-4651	367	1	on	on	ADP
ejpam-4651	367	2	cliques	clique	NOUN
ejpam-4651	367	3	and	and	CCONJ
ejpam-4651	367	4	forcing	force	VERB
ejpam-4651	367	5	m	m	NOUN
ejpam-4651	367	6	-	-	PUNCT
ejpam-4651	367	7	convexity	convexity	NOUN
ejpam-4651	367	8	numbers	number	NOUN
ejpam-4651	367	9	of	of	ADP
ejpam-4651	367	10	graphs	graph	NOUN
ejpam-4651	367	11	.	.	PUNCT
ejpam-4651	368	1	ars	ars	PROPN
ejpam-4651	368	2	combinatoria	combinatoria	PROPN
ejpam-4651	368	3	,	,	PUNCT
ejpam-4651	368	4	103:321–331	103:321–331	NUM
ejpam-4651	368	5	,	,	PUNCT
ejpam-4651	368	6	2012	2012	NUM
ejpam-4651	368	7	.	.	PUNCT
ejpam-4651	369	1	[	[	X
ejpam-4651	369	2	9	9	NUM
ejpam-4651	369	3	]	]	X
ejpam-4651	369	4	f.	f.	PROPN
ejpam-4651	369	5	harary	harary	PROPN
ejpam-4651	369	6	and	and	CCONJ
ejpam-4651	369	7	r.a	r.a	PROPN
ejpam-4651	369	8	.	.	PROPN
ejpam-4651	369	9	melter	melter	NOUN
ejpam-4651	369	10	.	.	PUNCT
ejpam-4651	370	1	on	on	ADP
ejpam-4651	370	2	the	the	DET
ejpam-4651	370	3	metric	metric	ADJ
ejpam-4651	370	4	dimension	dimension	NOUN
ejpam-4651	370	5	of	of	ADP
ejpam-4651	370	6	a	a	DET
ejpam-4651	370	7	graph	graph	NOUN
ejpam-4651	370	8	.	.	PUNCT
ejpam-4651	370	9	ars	ars	PROPN
ejpam-4651	370	10	combinatoria	combinatoria	NOUN
ejpam-4651	370	11	,	,	PUNCT
ejpam-4651	370	12	2:191–195	2:191–195	NUM
ejpam-4651	370	13	,	,	PUNCT
ejpam-4651	370	14	1976	1976	NUM
ejpam-4651	370	15	.	.	PUNCT
ejpam-4651	371	1	[	[	X
ejpam-4651	371	2	10	10	NUM
ejpam-4651	371	3	]	]	PUNCT
ejpam-4651	371	4	t.	t.	PROPN
ejpam-4651	371	5	w.	w.	PROPN
ejpam-4651	371	6	haynes	haynes	PROPN
ejpam-4651	371	7	,	,	PUNCT
ejpam-4651	371	8	s.t	s.t	PROPN
ejpam-4651	371	9	.	.	PROPN
ejpam-4651	371	10	hedetnieme	hedetnieme	PROPN
ejpam-4651	371	11	,	,	PUNCT
ejpam-4651	371	12	and	and	CCONJ
ejpam-4651	371	13	p.j	p.j	PROPN
ejpam-4651	371	14	.	.	PROPN
ejpam-4651	371	15	slater	slater	PROPN
ejpam-4651	371	16	.	.	PUNCT
ejpam-4651	372	1	fundamentals	fundamental	NOUN
ejpam-4651	372	2	of	of	ADP
ejpam-4651	372	3	domination	domination	NOUN
ejpam-4651	372	4	in	in	ADP
ejpam-4651	372	5	graphs	graph	NOUN
ejpam-4651	372	6	.	.	PUNCT
ejpam-4651	373	1	monographs	monograph	NOUN
ejpam-4651	373	2	and	and	CCONJ
ejpam-4651	373	3	textbooks	textbook	NOUN
ejpam-4651	373	4	in	in	ADP
ejpam-4651	373	5	pure	pure	ADJ
ejpam-4651	373	6	and	and	CCONJ
ejpam-4651	373	7	applied	applied	ADJ
ejpam-4651	373	8	mathematics	mathematic	NOUN
ejpam-4651	373	9	,	,	PUNCT
ejpam-4651	373	10	28	28	NUM
ejpam-4651	373	11	,	,	PUNCT
ejpam-4651	373	12	1998	1998	NUM
ejpam-4651	373	13	.	.	PUNCT
ejpam-4651	374	1	references	reference	NOUN
ejpam-4651	374	2	252	252	NUM
ejpam-4651	374	3	[	[	NOUN
ejpam-4651	374	4	11	11	NUM
ejpam-4651	374	5	]	]	X
ejpam-4651	374	6	r.	r.	PROPN
ejpam-4651	374	7	hinampas	hinampas	PROPN
ejpam-4651	374	8	and	and	CCONJ
ejpam-4651	374	9	s.	s.	PROPN
ejpam-4651	374	10	canoy	canoy	PROPN
ejpam-4651	374	11	jr	jr	PROPN
ejpam-4651	374	12	.	.	PROPN
ejpam-4651	374	13	1	1	NUM
ejpam-4651	374	14	-	-	PUNCT
ejpam-4651	374	15	movable	movable	ADJ
ejpam-4651	374	16	domination	domination	NOUN
ejpam-4651	374	17	in	in	ADP
ejpam-4651	374	18	graph	graph	NOUN
ejpam-4651	374	19	.	.	PUNCT
ejpam-4651	375	1	applied	apply	VERB
ejpam-4651	375	2	mathematical	mathematical	ADJ
ejpam-4651	375	3	sciences	sciences	PROPN
ejpam-4651	375	4	,	,	PUNCT
ejpam-4651	375	5	8(172):8565–8571	8(172):8565–8571	NUM
ejpam-4651	375	6	,	,	PUNCT
ejpam-4651	375	7	2014	2014	NUM
ejpam-4651	375	8	.	.	PUNCT
ejpam-4651	376	1	[	[	X
ejpam-4651	376	2	12	12	NUM
ejpam-4651	376	3	]	]	X
ejpam-4651	376	4	j.	j.	PROPN
ejpam-4651	376	5	lomarda	lomarda	PROPN
ejpam-4651	376	6	and	and	CCONJ
ejpam-4651	376	7	s.	s.	PROPN
ejpam-4651	376	8	canoy	canoy	PROPN
ejpam-4651	376	9	jr	jr	PROPN
ejpam-4651	376	10	.	.	PROPN
ejpam-4651	376	11	1	1	NUM
ejpam-4651	376	12	-	-	PUNCT
ejpam-4651	376	13	movable	movable	ADJ
ejpam-4651	376	14	total	total	ADJ
ejpam-4651	376	15	dominating	dominating	NOUN
ejpam-4651	376	16	sets	set	NOUN
ejpam-4651	376	17	in	in	ADP
ejpam-4651	376	18	graphs	graph	NOUN
ejpam-4651	376	19	.	.	PUNCT
ejpam-4651	377	1	international	international	ADJ
ejpam-4651	377	2	journal	journal	PROPN
ejpam-4651	377	3	of	of	ADP
ejpam-4651	377	4	mathematical	mathematical	ADJ
ejpam-4651	377	5	analysis	analysis	NOUN
ejpam-4651	377	6	,	,	PUNCT
ejpam-4651	377	7	8(55):2703–2709	8(55):2703–2709	NUM
ejpam-4651	377	8	,	,	PUNCT
ejpam-4651	377	9	2014	2014	NUM
ejpam-4651	377	10	.	.	PUNCT
ejpam-4651	378	1	[	[	X
ejpam-4651	378	2	13	13	NUM
ejpam-4651	378	3	]	]	X
ejpam-4651	378	4	c.	c.	PROPN
ejpam-4651	378	5	lu	lu	PROPN
ejpam-4651	378	6	,	,	PUNCT
ejpam-4651	378	7	j.	j.	PROPN
ejpam-4651	378	8	yu	yu	PROPN
ejpam-4651	378	9	,	,	PUNCT
ejpam-4651	378	10	h.	h.	PROPN
ejpam-4651	378	11	wei	wei	PROPN
ejpam-4651	378	12	,	,	PUNCT
ejpam-4651	378	13	and	and	CCONJ
ejpam-4651	378	14	y.	y.	PROPN
ejpam-4651	378	15	zhang	zhang	PROPN
ejpam-4651	378	16	.	.	PUNCT
ejpam-4651	379	1	on	on	ADP
ejpam-4651	379	2	cliques	clique	NOUN
ejpam-4651	379	3	in	in	ADP
ejpam-4651	379	4	graphs	graph	NOUN
ejpam-4651	379	5	.	.	PUNCT
ejpam-4651	380	1	ieee	ieee	NOUN
ejpam-4651	380	2	transactions	transaction	NOUN
ejpam-4651	380	3	on	on	ADP
ejpam-4651	380	4	knowledge	knowledge	NOUN
ejpam-4651	380	5	and	and	CCONJ
ejpam-4651	380	6	data	datum	NOUN
ejpam-4651	380	7	engineering	engineering	NOUN
ejpam-4651	380	8	,	,	PUNCT
ejpam-4651	380	9	34(9):4215–4230	34(9):4215–4230	NUM
ejpam-4651	380	10	,	,	PUNCT
ejpam-4651	380	11	2022	2022	NUM
ejpam-4651	380	12	.	.	PUNCT
ejpam-4651	381	1	[	[	X
ejpam-4651	381	2	14	14	NUM
ejpam-4651	381	3	]	]	X
ejpam-4651	381	4	g.	g.	PROPN
ejpam-4651	381	5	monsanto	monsanto	PROPN
ejpam-4651	381	6	,	,	PUNCT
ejpam-4651	381	7	p.	p.	NOUN
ejpam-4651	381	8	acal	acal	ADJ
ejpam-4651	381	9	,	,	PUNCT
ejpam-4651	381	10	and	and	CCONJ
ejpam-4651	381	11	h.	h.	PROPN
ejpam-4651	381	12	rara	rara	PROPN
ejpam-4651	381	13	.	.	PUNCT
ejpam-4651	382	1	on	on	ADP
ejpam-4651	382	2	strong	strong	ADJ
ejpam-4651	382	3	resolving	resolving	NOUN
ejpam-4651	382	4	domination	domination	NOUN
ejpam-4651	382	5	in	in	ADP
ejpam-4651	382	6	the	the	DET
ejpam-4651	382	7	join	join	NOUN
ejpam-4651	382	8	and	and	CCONJ
ejpam-4651	382	9	corona	corona	NOUN
ejpam-4651	382	10	of	of	ADP
ejpam-4651	382	11	graphs	graph	NOUN
ejpam-4651	382	12	.	.	PUNCT
ejpam-4651	383	1	european	european	ADJ
ejpam-4651	383	2	journal	journal	PROPN
ejpam-4651	383	3	of	of	ADP
ejpam-4651	383	4	pure	pure	ADJ
ejpam-4651	383	5	and	and	CCONJ
ejpam-4651	383	6	applied	applied	ADJ
ejpam-4651	383	7	mathematics	mathematic	NOUN
ejpam-4651	383	8	,	,	PUNCT
ejpam-4651	383	9	13(1):170–179	13(1):170–179	NUM
ejpam-4651	383	10	,	,	PUNCT
ejpam-4651	383	11	2020	2020	NUM
ejpam-4651	383	12	.	.	PUNCT
ejpam-4651	384	1	[	[	X
ejpam-4651	384	2	15	15	NUM
ejpam-4651	384	3	]	]	X
ejpam-4651	384	4	j.	j.	PROPN
ejpam-4651	384	5	moon	moon	PROPN
ejpam-4651	384	6	and	and	CCONJ
ejpam-4651	384	7	l.	l.	PROPN
ejpam-4651	384	8	moser	moser	PROPN
ejpam-4651	384	9	.	.	PUNCT
ejpam-4651	385	1	on	on	ADP
ejpam-4651	385	2	cliques	clique	NOUN
ejpam-4651	385	3	in	in	ADP
ejpam-4651	385	4	graphs	graph	NOUN
ejpam-4651	385	5	.	.	PUNCT
ejpam-4651	386	1	israel	israel	PROPN
ejpam-4651	386	2	journal	journal	PROPN
ejpam-4651	386	3	of	of	ADP
ejpam-4651	386	4	mathematics	mathematics	PROPN
ejpam-4651	386	5	,	,	PUNCT
ejpam-4651	386	6	3:23–28	3:23–28	NOUN
ejpam-4651	386	7	,	,	PUNCT
ejpam-4651	386	8	1965	1965	NUM
ejpam-4651	386	9	.	.	PUNCT
ejpam-4651	387	1	[	[	X
ejpam-4651	387	2	16	16	NUM
ejpam-4651	387	3	]	]	X
ejpam-4651	387	4	o.r	o.r	PROPN
ejpam-4651	387	5	.	.	PROPN
ejpam-4651	387	6	oellermann	oellermann	PROPN
ejpam-4651	387	7	and	and	CCONJ
ejpam-4651	387	8	j.	j.	PROPN
ejpam-4651	387	9	peters	peters	PROPN
ejpam-4651	387	10	-	-	PUNCT
ejpam-4651	387	11	fransen	fransen	PROPN
ejpam-4651	387	12	.	.	PUNCT
ejpam-4651	388	1	the	the	DET
ejpam-4651	388	2	strong	strong	ADJ
ejpam-4651	388	3	metric	metric	ADJ
ejpam-4651	388	4	dimension	dimension	NOUN
ejpam-4651	388	5	of	of	ADP
ejpam-4651	388	6	graphs	graph	NOUN
ejpam-4651	388	7	and	and	CCONJ
ejpam-4651	388	8	digraphs	digraph	NOUN
ejpam-4651	388	9	.	.	PUNCT
ejpam-4651	389	1	discrete	discrete	ADJ
ejpam-4651	389	2	applied	apply	VERB
ejpam-4651	389	3	mathematics	mathematic	NOUN
ejpam-4651	389	4	,	,	PUNCT
ejpam-4651	389	5	155:356–364	155:356–364	NUM
ejpam-4651	389	6	,	,	PUNCT
ejpam-4651	389	7	2007	2007	NUM
ejpam-4651	389	8	.	.	PUNCT
ejpam-4651	390	1	[	[	X
ejpam-4651	390	2	17	17	NUM
ejpam-4651	390	3	]	]	PUNCT
ejpam-4651	390	4	b.	b.	PROPN
ejpam-4651	390	5	omamalin	omamalin	PROPN
ejpam-4651	390	6	,	,	PUNCT
ejpam-4651	390	7	s.	s.	PROPN
ejpam-4651	390	8	canoy	canoy	PROPN
ejpam-4651	390	9	jr	jr	PROPN
ejpam-4651	390	10	.	.	PROPN
ejpam-4651	390	11	,	,	PUNCT
ejpam-4651	390	12	and	and	CCONJ
ejpam-4651	390	13	h.	h.	PROPN
ejpam-4651	390	14	rara	rara	PROPN
ejpam-4651	390	15	.	.	PUNCT
ejpam-4651	391	1	locating	locate	VERB
ejpam-4651	391	2	total	total	ADJ
ejpam-4651	391	3	dominating	dominating	NOUN
ejpam-4651	391	4	sets	set	NOUN
ejpam-4651	391	5	in	in	ADP
ejpam-4651	391	6	the	the	DET
ejpam-4651	391	7	join	join	NOUN
ejpam-4651	391	8	,	,	PUNCT
ejpam-4651	391	9	corona	corona	NOUN
ejpam-4651	391	10	and	and	CCONJ
ejpam-4651	391	11	composition	composition	NOUN
ejpam-4651	391	12	of	of	ADP
ejpam-4651	391	13	graphs	graph	NOUN
ejpam-4651	391	14	.	.	PUNCT
ejpam-4651	392	1	applied	apply	VERB
ejpam-4651	392	2	mathematical	mathematical	ADJ
ejpam-4651	392	3	sciences	science	NOUN
ejpam-4651	392	4	,	,	PUNCT
ejpam-4651	392	5	8(48):2363–2374	8(48):2363–2374	NUM
ejpam-4651	392	6	,	,	PUNCT
ejpam-4651	392	7	2014	2014	NUM
ejpam-4651	392	8	.	.	PUNCT
ejpam-4651	393	1	[	[	X
ejpam-4651	393	2	18	18	NUM
ejpam-4651	393	3	]	]	X
ejpam-4651	393	4	f.	f.	PROPN
ejpam-4651	393	5	roberts	roberts	PROPN
ejpam-4651	393	6	and	and	CCONJ
ejpam-4651	393	7	j.	j.	PROPN
ejpam-4651	393	8	spencer	spencer	PROPN
ejpam-4651	393	9	.	.	PUNCT
ejpam-4651	394	1	a	a	DET
ejpam-4651	394	2	characterization	characterization	NOUN
ejpam-4651	394	3	of	of	ADP
ejpam-4651	394	4	clique	clique	NOUN
ejpam-4651	394	5	graphs	graph	NOUN
ejpam-4651	394	6	.	.	PUNCT
ejpam-4651	395	1	journal	journal	NOUN
ejpam-4651	395	2	of	of	ADP
ejpam-4651	395	3	combinatorial	combinatorial	ADJ
ejpam-4651	395	4	theory	theory	NOUN
ejpam-4651	395	5	,	,	PUNCT
ejpam-4651	395	6	10:102–108	10:102–108	NUM
ejpam-4651	395	7	,	,	PUNCT
ejpam-4651	395	8	1971	1971	NUM
ejpam-4651	395	9	.	.	PUNCT
ejpam-4651	396	1	[	[	X
ejpam-4651	396	2	19	19	NUM
ejpam-4651	396	3	]	]	PUNCT
ejpam-4651	396	4	a.	a.	NOUN
ejpam-4651	396	5	sebo	sebo	NOUN
ejpam-4651	396	6	and	and	CCONJ
ejpam-4651	396	7	e.	e.	PROPN
ejpam-4651	396	8	tannier	tannier	PROPN
ejpam-4651	396	9	.	.	PUNCT
ejpam-4651	397	1	on	on	ADP
ejpam-4651	397	2	metric	metric	ADJ
ejpam-4651	397	3	generators	generator	NOUN
ejpam-4651	397	4	of	of	ADP
ejpam-4651	397	5	graphs	graph	NOUN
ejpam-4651	397	6	.	.	PUNCT
ejpam-4651	398	1	math	math	NOUN
ejpam-4651	398	2	.	.	PUNCT
ejpam-4651	399	1	oper	oper	PROPN
ejpam-4651	399	2	.	.	PUNCT
ejpam-4651	400	1	res	res	PROPN
ejpam-4651	400	2	.	.	PROPN
ejpam-4651	400	3	,	,	PUNCT
ejpam-4651	400	4	29:383	29:383	NUM
ejpam-4651	400	5	–	–	PUNCT
ejpam-4651	400	6	393	393	NUM
ejpam-4651	400	7	,	,	PUNCT
ejpam-4651	400	8	2004	2004	NUM
ejpam-4651	400	9	.	.	PUNCT
ejpam-4651	401	1	[	[	X
ejpam-4651	401	2	20	20	NUM
ejpam-4651	401	3	]	]	X
ejpam-4651	401	4	p.j	p.j	PROPN
ejpam-4651	401	5	.	.	PROPN
ejpam-4651	401	6	slater	slater	PROPN
ejpam-4651	401	7	.	.	PUNCT
ejpam-4651	402	1	dominating	dominating	NOUN
ejpam-4651	402	2	and	and	CCONJ
ejpam-4651	402	3	reference	reference	NOUN
ejpam-4651	402	4	sets	set	NOUN
ejpam-4651	402	5	in	in	ADP
ejpam-4651	402	6	graphs	graph	NOUN
ejpam-4651	402	7	.	.	PUNCT
ejpam-4651	403	1	j.	j.	PROPN
ejpam-4651	403	2	math	math	PROPN
ejpam-4651	403	3	.	.	PUNCT
ejpam-4651	404	1	phys	phy	NOUN
ejpam-4651	404	2	.	.	PUNCT
ejpam-4651	405	1	sci	sci	PROPN
ejpam-4651	405	2	.	.	PROPN
ejpam-4651	405	3	,	,	PUNCT
ejpam-4651	405	4	22:445–455	22:445–455	PROPN
ejpam-4651	405	5	,	,	PUNCT
ejpam-4651	405	6	1988	1988	NUM
ejpam-4651	405	7	.	.	PUNCT
ejpam-4651	406	1	[	[	X
ejpam-4651	406	2	21	21	NUM
ejpam-4651	406	3	]	]	X
ejpam-4651	406	4	h.	h.	NOUN
ejpam-4651	406	5	sumaoy	sumaoy	NOUN
ejpam-4651	406	6	and	and	CCONJ
ejpam-4651	406	7	h.	h.	PROPN
ejpam-4651	406	8	rara	rara	PROPN
ejpam-4651	406	9	.	.	PUNCT
ejpam-4651	407	1	on	on	ADP
ejpam-4651	407	2	restrained	restrained	ADJ
ejpam-4651	407	3	and	and	CCONJ
ejpam-4651	407	4	movable	movable	ADJ
ejpam-4651	407	5	strong	strong	ADJ
ejpam-4651	407	6	resolving	resolving	NOUN
ejpam-4651	407	7	domination	domination	NOUN
ejpam-4651	407	8	in	in	ADP
ejpam-4651	407	9	graphs	graph	NOUN
ejpam-4651	407	10	.	.	PUNCT
ejpam-4651	408	1	european	european	ADJ
ejpam-4651	408	2	journal	journal	PROPN
ejpam-4651	408	3	of	of	ADP
ejpam-4651	408	4	pure	pure	ADJ
ejpam-4651	408	5	and	and	CCONJ
ejpam-4651	408	6	applied	applied	ADJ
ejpam-4651	408	7	mathematics	mathematic	NOUN
ejpam-4651	408	8	,	,	PUNCT
ejpam-4651	408	9	14(4):1367–1378	14(4):1367–1378	NUM
ejpam-4651	408	10	,	,	PUNCT
ejpam-4651	408	11	2021	2021	NUM
ejpam-4651	408	12	.	.	PUNCT
ejpam-4651	409	1	[	[	X
ejpam-4651	409	2	22	22	NUM
ejpam-4651	409	3	]	]	X
ejpam-4651	409	4	b.	b.	PROPN
ejpam-4651	409	5	tubo	tubo	PROPN
ejpam-4651	409	6	and	and	CCONJ
ejpam-4651	409	7	s.	s.	PROPN
ejpam-4651	409	8	canoy	canoy	PROPN
ejpam-4651	409	9	jr	jr	PROPN
ejpam-4651	409	10	.	.	PROPN
ejpam-4651	409	11	restrained	restrain	VERB
ejpam-4651	409	12	perfect	perfect	ADJ
ejpam-4651	409	13	domination	domination	NOUN
ejpam-4651	409	14	in	in	ADP
ejpam-4651	409	15	graphs	graph	NOUN
ejpam-4651	409	16	.	.	PUNCT
ejpam-4651	410	1	applied	apply	VERB
ejpam-4651	410	2	mathematical	mathematical	ADJ
ejpam-4651	410	3	sciences	science	NOUN
ejpam-4651	410	4	,	,	PUNCT
ejpam-4651	410	5	9(25):1231–1240	9(25):1231–1240	NOUN
ejpam-4651	410	6	,	,	PUNCT
ejpam-4651	410	7	2015	2015	NUM
ejpam-4651	410	8	.	.	PUNCT
ejpam-4651	411	1	[	[	X
ejpam-4651	411	2	23	23	NUM
ejpam-4651	411	3	]	]	X
ejpam-4651	411	4	d.	d.	PROPN
ejpam-4651	411	5	wood	wood	PROPN
ejpam-4651	411	6	.	.	PUNCT
ejpam-4651	412	1	on	on	ADP
ejpam-4651	412	2	the	the	DET
ejpam-4651	412	3	maximum	maximum	ADJ
ejpam-4651	412	4	number	number	NOUN
ejpam-4651	412	5	of	of	ADP
ejpam-4651	412	6	cliques	clique	NOUN
ejpam-4651	412	7	in	in	ADP
ejpam-4651	412	8	a	a	DET
ejpam-4651	412	9	graph	graph	NOUN
ejpam-4651	412	10	.	.	PUNCT
ejpam-4651	412	11	graph	graph	NOUN
ejpam-4651	412	12	and	and	CCONJ
ejpam-4651	412	13	combinatorics	combinatoric	NOUN
ejpam-4651	412	14	,	,	PUNCT
ejpam-4651	412	15	23:337–352	23:337–352	PROPN
ejpam-4651	412	16	,	,	PUNCT
ejpam-4651	412	17	2007	2007	NUM
ejpam-4651	412	18	.	.	PUNCT