id	sid	tid	token	lemma	pos
ejpam-4652	1	1	european	european	PROPN
ejpam-4652	1	2	journal	journal	PROPN
ejpam-4652	1	3	of	of	ADP
ejpam-4652	1	4	pure	pure	ADJ
ejpam-4652	1	5	and	and	CCONJ
ejpam-4652	1	6	applied	apply	VERB
ejpam-4652	1	7	mathematics	mathematic	NOUN
ejpam-4652	1	8	vol	vol	NOUN
ejpam-4652	1	9	.	.	PUNCT
ejpam-4652	2	1	16	16	NUM
ejpam-4652	2	2	,	,	PUNCT
ejpam-4652	2	3	no	no	INTJ
ejpam-4652	2	4	.	.	NOUN
ejpam-4652	2	5	1	1	NUM
ejpam-4652	2	6	,	,	PUNCT
ejpam-4652	2	7	2023	2023	NUM
ejpam-4652	2	8	,	,	PUNCT
ejpam-4652	2	9	363	363	NUM
ejpam-4652	2	10	-	-	SYM
ejpam-4652	2	11	372	372	NUM
ejpam-4652	2	12	issn	issn	PROPN
ejpam-4652	2	13	1307	1307	NUM
ejpam-4652	2	14	-	-	SYM
ejpam-4652	2	15	5543	5543	NUM
ejpam-4652	2	16	–	–	PUNCT
ejpam-4652	2	17	ejpam.com	ejpam.com	X
ejpam-4652	2	18	published	publish	VERB
ejpam-4652	2	19	by	by	ADP
ejpam-4652	2	20	new	new	PROPN
ejpam-4652	2	21	york	york	PROPN
ejpam-4652	2	22	business	business	PROPN
ejpam-4652	2	23	global	global	ADJ
ejpam-4652	2	24	strong	strong	ADJ
ejpam-4652	2	25	resolving	resolve	VERB
ejpam-4652	2	26	domination	domination	NOUN
ejpam-4652	2	27	in	in	ADP
ejpam-4652	2	28	the	the	DET
ejpam-4652	2	29	lexicographic	lexicographic	ADJ
ejpam-4652	2	30	product	product	NOUN
ejpam-4652	2	31	of	of	ADP
ejpam-4652	2	32	graphs	graphs	PROPN
ejpam-4652	2	33	gerald	gerald	PROPN
ejpam-4652	2	34	b.	b.	PROPN
ejpam-4652	2	35	monsanto1,∗	monsanto1,∗	PROPN
ejpam-4652	2	36	,	,	PUNCT
ejpam-4652	2	37	penelyn	penelyn	NOUN
ejpam-4652	2	38	l.	l.	PROPN
ejpam-4652	2	39	acal2	acal2	PROPN
ejpam-4652	2	40	,	,	PUNCT
ejpam-4652	3	1	helen	helen	PROPN
ejpam-4652	3	2	m.	m.	PROPN
ejpam-4652	3	3	rara3	rara3	PROPN
ejpam-4652	3	4	1	1	NUM
ejpam-4652	3	5	college	college	NOUN
ejpam-4652	3	6	of	of	ADP
ejpam-4652	3	7	teacher	teacher	NOUN
ejpam-4652	3	8	education	education	NOUN
ejpam-4652	3	9	,	,	PUNCT
ejpam-4652	3	10	arts	art	NOUN
ejpam-4652	3	11	and	and	CCONJ
ejpam-4652	3	12	sciences	science	NOUN
ejpam-4652	3	13	,	,	PUNCT
ejpam-4652	3	14	visayas	visayas	PROPN
ejpam-4652	3	15	state	state	PROPN
ejpam-4652	3	16	university	university	PROPN
ejpam-4652	3	17	villaba	villaba	NOUN
ejpam-4652	3	18	,	,	PUNCT
ejpam-4652	3	19	6537	6537	NUM
ejpam-4652	3	20	villaba	villaba	NOUN
ejpam-4652	3	21	,	,	PUNCT
ejpam-4652	3	22	leyte	leyte	PROPN
ejpam-4652	3	23	,	,	PUNCT
ejpam-4652	3	24	philippines	philippines	PROPN
ejpam-4652	3	25	2	2	NUM
ejpam-4652	3	26	department	department	NOUN
ejpam-4652	3	27	of	of	ADP
ejpam-4652	3	28	mathematical	mathematical	ADJ
ejpam-4652	3	29	sciences	sciences	PROPN
ejpam-4652	3	30	,	,	PUNCT
ejpam-4652	3	31	university	university	NOUN
ejpam-4652	3	32	of	of	ADP
ejpam-4652	3	33	science	science	NOUN
ejpam-4652	3	34	and	and	CCONJ
ejpam-4652	3	35	technology	technology	NOUN
ejpam-4652	3	36	of	of	ADP
ejpam-4652	3	37	southern	southern	ADJ
ejpam-4652	3	38	philippines	philippine	NOUN
ejpam-4652	3	39	,	,	PUNCT
ejpam-4652	3	40	9023	9023	NUM
ejpam-4652	3	41	,	,	PUNCT
ejpam-4652	3	42	cagayan	cagayan	PROPN
ejpam-4652	3	43	de	de	PROPN
ejpam-4652	3	44	oro	oro	PROPN
ejpam-4652	3	45	city	city	NOUN
ejpam-4652	3	46	,	,	PUNCT
ejpam-4652	3	47	philippines	philippines	PROPN
ejpam-4652	3	48	3	3	NUM
ejpam-4652	3	49	department	department	NOUN
ejpam-4652	3	50	of	of	ADP
ejpam-4652	3	51	mathematics	mathematic	NOUN
ejpam-4652	3	52	and	and	CCONJ
ejpam-4652	3	53	statistics	statistic	NOUN
ejpam-4652	3	54	,	,	PUNCT
ejpam-4652	3	55	college	college	NOUN
ejpam-4652	3	56	of	of	ADP
ejpam-4652	3	57	science	science	NOUN
ejpam-4652	3	58	and	and	CCONJ
ejpam-4652	3	59	mathematics	mathematic	NOUN
ejpam-4652	3	60	,	,	PUNCT
ejpam-4652	3	61	center	center	NOUN
ejpam-4652	3	62	of	of	ADP
ejpam-4652	3	63	graph	graph	NOUN
ejpam-4652	3	64	theory	theory	NOUN
ejpam-4652	3	65	,	,	PUNCT
ejpam-4652	3	66	algebra	algebra	NOUN
ejpam-4652	3	67	,	,	PUNCT
ejpam-4652	3	68	and	and	CCONJ
ejpam-4652	3	69	analysis	analysis	NOUN
ejpam-4652	3	70	-	-	PUNCT
ejpam-4652	3	71	premier	premier	NOUN
ejpam-4652	3	72	research	research	NOUN
ejpam-4652	3	73	institute	institute	PROPN
ejpam-4652	3	74	of	of	ADP
ejpam-4652	3	75	science	science	NOUN
ejpam-4652	3	76	and	and	CCONJ
ejpam-4652	3	77	mathematics	mathematic	NOUN
ejpam-4652	3	78	,	,	PUNCT
ejpam-4652	3	79	mindanao	mindanao	PROPN
ejpam-4652	3	80	state	state	PROPN
ejpam-4652	3	81	university	university	PROPN
ejpam-4652	3	82	-	-	PUNCT
ejpam-4652	3	83	iligan	iligan	PROPN
ejpam-4652	3	84	institute	institute	PROPN
ejpam-4652	3	85	of	of	ADP
ejpam-4652	3	86	technology	technology	PROPN
ejpam-4652	3	87	,	,	PUNCT
ejpam-4652	3	88	9200	9200	NUM
ejpam-4652	3	89	iligan	iligan	ADJ
ejpam-4652	3	90	city	city	NOUN
ejpam-4652	3	91	,	,	PUNCT
ejpam-4652	3	92	philippines	philippine	NOUN
ejpam-4652	3	93	abstract	abstract	ADJ
ejpam-4652	3	94	.	.	PUNCT
ejpam-4652	4	1	let	let	VERB
ejpam-4652	4	2	g	g	PRON
ejpam-4652	4	3	be	be	AUX
ejpam-4652	4	4	a	a	DET
ejpam-4652	4	5	connected	connected	ADJ
ejpam-4652	4	6	graph	graph	NOUN
ejpam-4652	4	7	.	.	PUNCT
ejpam-4652	5	1	a	a	DET
ejpam-4652	5	2	subset	subset	NOUN
ejpam-4652	5	3	s	s	VERB
ejpam-4652	5	4	⊆	⊆	NUM
ejpam-4652	5	5	v	v	NOUN
ejpam-4652	5	6	(	(	PUNCT
ejpam-4652	5	7	g	g	NOUN
ejpam-4652	5	8	)	)	PUNCT
ejpam-4652	5	9	is	be	AUX
ejpam-4652	5	10	a	a	DET
ejpam-4652	5	11	strong	strong	ADJ
ejpam-4652	5	12	resolving	resolving	NOUN
ejpam-4652	5	13	dominating	dominating	NOUN
ejpam-4652	5	14	set	set	NOUN
ejpam-4652	5	15	of	of	ADP
ejpam-4652	5	16	g	g	PROPN
ejpam-4652	5	17	if	if	SCONJ
ejpam-4652	5	18	s	s	VERB
ejpam-4652	5	19	is	be	AUX
ejpam-4652	5	20	a	a	DET
ejpam-4652	5	21	dominating	dominating	NOUN
ejpam-4652	5	22	set	set	NOUN
ejpam-4652	5	23	and	and	CCONJ
ejpam-4652	5	24	for	for	ADP
ejpam-4652	5	25	every	every	DET
ejpam-4652	5	26	pair	pair	NOUN
ejpam-4652	5	27	of	of	ADP
ejpam-4652	5	28	vertices	vertex	NOUN
ejpam-4652	5	29	u	u	NOUN
ejpam-4652	5	30	,	,	PUNCT
ejpam-4652	5	31	v	v	NOUN
ejpam-4652	5	32	∈	∈	PROPN
ejpam-4652	5	33	v	v	NOUN
ejpam-4652	5	34	(	(	PUNCT
ejpam-4652	5	35	g	g	NOUN
ejpam-4652	5	36	)	)	PUNCT
ejpam-4652	5	37	,	,	PUNCT
ejpam-4652	5	38	there	there	PRON
ejpam-4652	5	39	exists	exist	VERB
ejpam-4652	5	40	a	a	DET
ejpam-4652	5	41	vertex	vertex	NOUN
ejpam-4652	5	42	w	w	ADP
ejpam-4652	5	43	∈	∈	NOUN
ejpam-4652	5	44	s	s	VERB
ejpam-4652	5	45	such	such	ADJ
ejpam-4652	5	46	that	that	SCONJ
ejpam-4652	5	47	u	u	PROPN
ejpam-4652	5	48	∈	∈	PROPN
ejpam-4652	5	49	ig[v	ig[v	PROPN
ejpam-4652	5	50	,	,	PUNCT
ejpam-4652	5	51	w	w	PROPN
ejpam-4652	5	52	]	]	PUNCT
ejpam-4652	5	53	or	or	CCONJ
ejpam-4652	5	54	ig[u	ig[u	PROPN
ejpam-4652	5	55	,	,	PUNCT
ejpam-4652	5	56	w	w	NOUN
ejpam-4652	5	57	]	]	X
ejpam-4652	5	58	.	.	PUNCT
ejpam-4652	6	1	the	the	DET
ejpam-4652	6	2	smallest	small	ADJ
ejpam-4652	6	3	cardinality	cardinality	NOUN
ejpam-4652	6	4	of	of	ADP
ejpam-4652	6	5	a	a	DET
ejpam-4652	6	6	strong	strong	ADJ
ejpam-4652	6	7	resolving	resolving	NOUN
ejpam-4652	6	8	dominating	dominating	NOUN
ejpam-4652	6	9	set	set	NOUN
ejpam-4652	6	10	of	of	ADP
ejpam-4652	6	11	g	g	PROPN
ejpam-4652	6	12	is	be	AUX
ejpam-4652	6	13	called	call	VERB
ejpam-4652	6	14	the	the	DET
ejpam-4652	6	15	strong	strong	ADJ
ejpam-4652	6	16	resolving	resolving	NOUN
ejpam-4652	6	17	domination	domination	NOUN
ejpam-4652	6	18	number	number	NOUN
ejpam-4652	6	19	of	of	ADP
ejpam-4652	6	20	g.	g.	PROPN
ejpam-4652	6	21	in	in	ADP
ejpam-4652	6	22	this	this	DET
ejpam-4652	6	23	paper	paper	NOUN
ejpam-4652	6	24	,	,	PUNCT
ejpam-4652	6	25	we	we	PRON
ejpam-4652	6	26	characterize	characterize	VERB
ejpam-4652	6	27	the	the	DET
ejpam-4652	6	28	strong	strong	ADJ
ejpam-4652	6	29	resolving	resolve	VERB
ejpam-4652	6	30	dominating	dominating	NOUN
ejpam-4652	6	31	sets	set	NOUN
ejpam-4652	6	32	in	in	ADP
ejpam-4652	6	33	the	the	DET
ejpam-4652	6	34	lexicographic	lexicographic	ADJ
ejpam-4652	6	35	product	product	NOUN
ejpam-4652	6	36	of	of	ADP
ejpam-4652	6	37	graphs	graph	NOUN
ejpam-4652	6	38	and	and	CCONJ
ejpam-4652	6	39	determine	determine	VERB
ejpam-4652	6	40	the	the	DET
ejpam-4652	6	41	corresponding	correspond	VERB
ejpam-4652	6	42	strong	strong	ADJ
ejpam-4652	6	43	resolving	resolving	NOUN
ejpam-4652	6	44	domination	domination	NOUN
ejpam-4652	6	45	number	number	NOUN
ejpam-4652	6	46	.	.	PUNCT
ejpam-4652	7	1	2020	2020	NUM
ejpam-4652	7	2	mathematics	mathematic	NOUN
ejpam-4652	7	3	subject	subject	NOUN
ejpam-4652	7	4	classifications	classification	NOUN
ejpam-4652	7	5	:	:	PUNCT
ejpam-4652	7	6	05c69	05c69	X
ejpam-4652	7	7	key	key	ADJ
ejpam-4652	7	8	words	word	NOUN
ejpam-4652	7	9	and	and	CCONJ
ejpam-4652	7	10	phrases	phrase	NOUN
ejpam-4652	7	11	:	:	PUNCT
ejpam-4652	7	12	strong	strong	ADJ
ejpam-4652	7	13	resolving	resolve	VERB
ejpam-4652	7	14	dominating	dominating	NOUN
ejpam-4652	7	15	set	set	NOUN
ejpam-4652	7	16	,	,	PUNCT
ejpam-4652	7	17	strong	strong	ADJ
ejpam-4652	7	18	resolving	resolve	VERB
ejpam-4652	7	19	domination	domination	NOUN
ejpam-4652	7	20	number	number	NOUN
ejpam-4652	7	21	,	,	PUNCT
ejpam-4652	7	22	lexicographic	lexicographic	ADJ
ejpam-4652	7	23	product	product	NOUN
ejpam-4652	7	24	1	1	NUM
ejpam-4652	7	25	.	.	PUNCT
ejpam-4652	8	1	introduction	introduction	NOUN
ejpam-4652	8	2	all	all	DET
ejpam-4652	8	3	graphs	graph	NOUN
ejpam-4652	8	4	considered	consider	VERB
ejpam-4652	8	5	in	in	ADP
ejpam-4652	8	6	this	this	DET
ejpam-4652	8	7	study	study	NOUN
ejpam-4652	8	8	are	be	AUX
ejpam-4652	8	9	finite	finite	ADJ
ejpam-4652	8	10	,	,	PUNCT
ejpam-4652	8	11	simple	simple	ADJ
ejpam-4652	8	12	,	,	PUNCT
ejpam-4652	8	13	and	and	CCONJ
ejpam-4652	8	14	undirected	undirected	ADJ
ejpam-4652	8	15	connected	connected	ADJ
ejpam-4652	8	16	graphs	graph	NOUN
ejpam-4652	8	17	,	,	PUNCT
ejpam-4652	8	18	that	that	ADV
ejpam-4652	8	19	is	is	ADV
ejpam-4652	8	20	,	,	PUNCT
ejpam-4652	8	21	without	without	ADP
ejpam-4652	8	22	loops	loop	NOUN
ejpam-4652	8	23	and	and	CCONJ
ejpam-4652	8	24	multiple	multiple	ADJ
ejpam-4652	8	25	edges	edge	NOUN
ejpam-4652	8	26	.	.	PUNCT
ejpam-4652	9	1	for	for	ADP
ejpam-4652	9	2	some	some	DET
ejpam-4652	9	3	basic	basic	ADJ
ejpam-4652	9	4	concepts	concept	NOUN
ejpam-4652	9	5	in	in	ADP
ejpam-4652	9	6	graph	graph	NOUN
ejpam-4652	9	7	theory	theory	NOUN
ejpam-4652	9	8	,	,	PUNCT
ejpam-4652	9	9	we	we	PRON
ejpam-4652	9	10	refer	refer	VERB
ejpam-4652	9	11	readers	reader	NOUN
ejpam-4652	9	12	to	to	ADP
ejpam-4652	9	13	[	[	X
ejpam-4652	9	14	7	7	NUM
ejpam-4652	9	15	]	]	PUNCT
ejpam-4652	9	16	.	.	PUNCT
ejpam-4652	10	1	let	let	VERB
ejpam-4652	10	2	g	g	NOUN
ejpam-4652	10	3	=	=	PUNCT
ejpam-4652	10	4	(	(	PUNCT
ejpam-4652	10	5	v	v	NOUN
ejpam-4652	10	6	(	(	PUNCT
ejpam-4652	10	7	g	g	NOUN
ejpam-4652	10	8	)	)	PUNCT
ejpam-4652	10	9	,	,	PUNCT
ejpam-4652	10	10	e(g	e(g	PROPN
ejpam-4652	10	11	)	)	PUNCT
ejpam-4652	10	12	)	)	PUNCT
ejpam-4652	11	1	be	be	AUX
ejpam-4652	11	2	a	a	DET
ejpam-4652	11	3	connected	connected	ADJ
ejpam-4652	11	4	graph	graph	NOUN
ejpam-4652	11	5	.	.	PUNCT
ejpam-4652	12	1	the	the	DET
ejpam-4652	12	2	open	open	ADJ
ejpam-4652	12	3	neighborhood	neighborhood	NOUN
ejpam-4652	12	4	of	of	ADP
ejpam-4652	12	5	v	v	NUM
ejpam-4652	12	6	∈	∈	NOUN
ejpam-4652	12	7	v	v	NOUN
ejpam-4652	12	8	(	(	PUNCT
ejpam-4652	12	9	g	g	NOUN
ejpam-4652	12	10	)	)	PUNCT
ejpam-4652	12	11	is	be	AUX
ejpam-4652	12	12	ng(v	ng(v	PUNCT
ejpam-4652	12	13	)	)	PUNCT
ejpam-4652	12	14	=	=	PRON
ejpam-4652	13	1	{	{	PUNCT
ejpam-4652	13	2	u	u	NOUN
ejpam-4652	13	3	∈	∈	PROPN
ejpam-4652	13	4	v	v	NOUN
ejpam-4652	13	5	(	(	PUNCT
ejpam-4652	13	6	g	g	NOUN
ejpam-4652	13	7	)	)	PUNCT
ejpam-4652	13	8	:	:	PUNCT
ejpam-4652	13	9	uv	uv	PROPN
ejpam-4652	13	10	∈	∈	PROPN
ejpam-4652	13	11	e(g	e(g	PROPN
ejpam-4652	13	12	)	)	PUNCT
ejpam-4652	13	13	}	}	PUNCT
ejpam-4652	13	14	.	.	PUNCT
ejpam-4652	14	1	any	any	DET
ejpam-4652	14	2	element	element	NOUN
ejpam-4652	14	3	u	u	NOUN
ejpam-4652	14	4	of	of	ADP
ejpam-4652	14	5	ng(v	ng(v	PUNCT
ejpam-4652	14	6	)	)	PUNCT
ejpam-4652	14	7	is	be	AUX
ejpam-4652	14	8	called	call	VERB
ejpam-4652	14	9	a	a	DET
ejpam-4652	14	10	neighbor	neighbor	NOUN
ejpam-4652	14	11	of	of	ADP
ejpam-4652	14	12	v.	v.	ADP
ejpam-4652	14	13	the	the	DET
ejpam-4652	14	14	closed	closed	ADJ
ejpam-4652	14	15	neighborhood	neighborhood	NOUN
ejpam-4652	14	16	of	of	ADP
ejpam-4652	14	17	v	v	NUM
ejpam-4652	14	18	∈	∈	NOUN
ejpam-4652	14	19	v	v	NOUN
ejpam-4652	14	20	(	(	PUNCT
ejpam-4652	14	21	g	g	NOUN
ejpam-4652	14	22	)	)	PUNCT
ejpam-4652	14	23	is	be	AUX
ejpam-4652	14	24	ng[v	ng[v	NOUN
ejpam-4652	14	25	]	]	X
ejpam-4652	14	26	=	=	SYM
ejpam-4652	14	27	ng(v	ng(v	X
ejpam-4652	14	28	)	)	PUNCT
ejpam-4652	14	29	∪	∪	ADP
ejpam-4652	14	30	{	{	PUNCT
ejpam-4652	14	31	v	v	NOUN
ejpam-4652	14	32	}	}	PUNCT
ejpam-4652	14	33	.	.	PUNCT
ejpam-4652	15	1	thus	thus	ADV
ejpam-4652	15	2	,	,	PUNCT
ejpam-4652	15	3	the	the	DET
ejpam-4652	15	4	degree	degree	NOUN
ejpam-4652	15	5	of	of	ADP
ejpam-4652	15	6	v	v	NUM
ejpam-4652	15	7	∈	∈	NOUN
ejpam-4652	15	8	v	v	NOUN
ejpam-4652	15	9	(	(	PUNCT
ejpam-4652	15	10	g	g	NOUN
ejpam-4652	15	11	)	)	PUNCT
ejpam-4652	15	12	is	be	AUX
ejpam-4652	15	13	given	give	VERB
ejpam-4652	15	14	by	by	ADP
ejpam-4652	15	15	degg(v	degg(v	PROPN
ejpam-4652	15	16	)	)	PUNCT
ejpam-4652	15	17	=	=	SYM
ejpam-4652	15	18	|ng(v)|	|ng(v)|	NOUN
ejpam-4652	15	19	.	.	PUNCT
ejpam-4652	15	20	customary	customary	ADJ
ejpam-4652	15	21	,	,	PUNCT
ejpam-4652	15	22	for	for	ADP
ejpam-4652	15	23	s	s	PROPN
ejpam-4652	15	24	⊆	⊆	NUM
ejpam-4652	15	25	v	v	NOUN
ejpam-4652	15	26	(	(	PUNCT
ejpam-4652	15	27	g	g	NOUN
ejpam-4652	15	28	)	)	PUNCT
ejpam-4652	15	29	,	,	PUNCT
ejpam-4652	15	30	ng(s	ng(s	NUM
ejpam-4652	15	31	)	)	PUNCT
ejpam-4652	16	1	=	=	SYM
ejpam-4652	17	1	⋃	⋃	ADP
ejpam-4652	17	2	v∈s	v∈s	NOUN
ejpam-4652	17	3	ng(v	ng(v	NOUN
ejpam-4652	17	4	)	)	PUNCT
ejpam-4652	17	5	and	and	CCONJ
ejpam-4652	17	6	ng[s	ng[	NOUN
ejpam-4652	17	7	]	]	PUNCT
ejpam-4652	17	8	=	=	PUNCT
ejpam-4652	17	9	⋃	⋃	VERB
ejpam-4652	17	10	v∈s	v∈s	ADJ
ejpam-4652	17	11	ng[v	ng[v	NOUN
ejpam-4652	17	12	]	]	PUNCT
ejpam-4652	17	13	.	.	PUNCT
ejpam-4652	18	1	doi	doi	NOUN
ejpam-4652	18	2	:	:	PUNCT
ejpam-4652	18	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4652	https://doi.org/10.29020/nybg.ejpam.v16i1.4652	PROPN
ejpam-4652	18	4	email	email	NOUN
ejpam-4652	18	5	addresses	address	NOUN
ejpam-4652	18	6	:	:	PUNCT
ejpam-4652	18	7	gerald.monsanto@vsu.edu.ph	gerald.monsanto@vsu.edu.ph	PROPN
ejpam-4652	18	8	(	(	PUNCT
ejpam-4652	18	9	g.	g.	PROPN
ejpam-4652	18	10	monsanto	monsanto	PROPN
ejpam-4652	18	11	)	)	PUNCT
ejpam-4652	18	12	,	,	PUNCT
ejpam-4652	18	13	penelyn.acal@g.msuiit.edu.ph	penelyn.acal@g.msuiit.edu.ph	PROPN
ejpam-4652	18	14	(	(	PUNCT
ejpam-4652	18	15	p.	p.	NOUN
ejpam-4652	18	16	acal	acal	ADJ
ejpam-4652	18	17	)	)	PUNCT
ejpam-4652	18	18	,	,	PUNCT
ejpam-4652	18	19	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4652	18	20	(	(	PUNCT
ejpam-4652	18	21	h.	h.	PROPN
ejpam-4652	18	22	rara	rara	PROPN
ejpam-4652	18	23	)	)	PUNCT
ejpam-4652	18	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4652	19	1	363	363	NUM
ejpam-4652	19	2	©	©	PROPN
ejpam-4652	19	3	2023	2023	NUM
ejpam-4652	19	4	ejpam	ejpam	NOUN
ejpam-4652	19	5	all	all	DET
ejpam-4652	19	6	rights	right	NOUN
ejpam-4652	19	7	reserved	reserve	VERB
ejpam-4652	19	8	.	.	PUNCT
ejpam-4652	20	1	g.	g.	PROPN
ejpam-4652	20	2	monsanto	monsanto	PROPN
ejpam-4652	20	3	,	,	PUNCT
ejpam-4652	20	4	p.	p.	PROPN
ejpam-4652	20	5	acal	acal	PROPN
ejpam-4652	20	6	,	,	PUNCT
ejpam-4652	20	7	h.	h.	PROPN
ejpam-4652	20	8	rara	rara	PROPN
ejpam-4652	20	9	/	/	SYM
ejpam-4652	20	10	eur	eur	PROPN
ejpam-4652	20	11	.	.	PUNCT
ejpam-4652	21	1	j.	j.	PROPN
ejpam-4652	21	2	pure	pure	PROPN
ejpam-4652	21	3	appl	appl	PROPN
ejpam-4652	21	4	.	.	PROPN
ejpam-4652	21	5	math	math	PROPN
ejpam-4652	21	6	,	,	PUNCT
ejpam-4652	21	7	16	16	NUM
ejpam-4652	21	8	(	(	PUNCT
ejpam-4652	21	9	1	1	NUM
ejpam-4652	21	10	)	)	PUNCT
ejpam-4652	21	11	(	(	PUNCT
ejpam-4652	21	12	2023	2023	NUM
ejpam-4652	21	13	)	)	PUNCT
ejpam-4652	21	14	,	,	PUNCT
ejpam-4652	21	15	363	363	NUM
ejpam-4652	21	16	-	-	SYM
ejpam-4652	21	17	372	372	NUM
ejpam-4652	21	18	364	364	NUM
ejpam-4652	21	19	a	a	DET
ejpam-4652	21	20	nonempty	nonempty	ADJ
ejpam-4652	21	21	set	set	VERB
ejpam-4652	21	22	s	s	PROPN
ejpam-4652	21	23	⊆	⊆	NUM
ejpam-4652	21	24	v	v	NOUN
ejpam-4652	21	25	(	(	PUNCT
ejpam-4652	21	26	g	g	NOUN
ejpam-4652	21	27	)	)	PUNCT
ejpam-4652	21	28	is	be	AUX
ejpam-4652	21	29	a	a	DET
ejpam-4652	21	30	dominating	dominating	NOUN
ejpam-4652	21	31	set	set	VERB
ejpam-4652	21	32	in	in	ADP
ejpam-4652	21	33	graph	graph	NOUN
ejpam-4652	21	34	g	g	NOUN
ejpam-4652	21	35	if	if	SCONJ
ejpam-4652	21	36	ng[s	ng[	NOUN
ejpam-4652	21	37	]	]	PUNCT
ejpam-4652	21	38	=	=	SYM
ejpam-4652	21	39	v	v	NOUN
ejpam-4652	21	40	(	(	PUNCT
ejpam-4652	21	41	g	g	NOUN
ejpam-4652	21	42	)	)	PUNCT
ejpam-4652	21	43	.	.	PUNCT
ejpam-4652	22	1	otherwise	otherwise	ADV
ejpam-4652	22	2	,	,	PUNCT
ejpam-4652	22	3	we	we	PRON
ejpam-4652	22	4	say	say	VERB
ejpam-4652	22	5	s	s	PRON
ejpam-4652	22	6	is	be	AUX
ejpam-4652	22	7	a	a	DET
ejpam-4652	22	8	non	non	ADJ
ejpam-4652	22	9	-	-	ADJ
ejpam-4652	22	10	dominating	dominating	ADJ
ejpam-4652	22	11	set	set	NOUN
ejpam-4652	22	12	of	of	ADP
ejpam-4652	22	13	g.	g.	PROPN
ejpam-4652	22	14	the	the	DET
ejpam-4652	22	15	domination	domination	NOUN
ejpam-4652	22	16	number	number	NOUN
ejpam-4652	22	17	of	of	ADP
ejpam-4652	22	18	a	a	DET
ejpam-4652	22	19	graph	graph	NOUN
ejpam-4652	22	20	g	g	NOUN
ejpam-4652	22	21	,	,	PUNCT
ejpam-4652	22	22	denoted	denote	VERB
ejpam-4652	22	23	by	by	ADP
ejpam-4652	22	24	γ(g	γ(g	PROPN
ejpam-4652	22	25	)	)	PUNCT
ejpam-4652	22	26	,	,	PUNCT
ejpam-4652	22	27	is	be	AUX
ejpam-4652	22	28	given	give	VERB
ejpam-4652	22	29	by	by	ADP
ejpam-4652	22	30	γ(g	γ(g	PROPN
ejpam-4652	22	31	)	)	PUNCT
ejpam-4652	23	1	=	=	SYM
ejpam-4652	23	2	min|s|	min|s|	PROPN
ejpam-4652	23	3	:	:	PUNCT
ejpam-4652	23	4	s	s	VERB
ejpam-4652	23	5	is	be	AUX
ejpam-4652	23	6	a	a	DET
ejpam-4652	23	7	dominating	dominating	NOUN
ejpam-4652	23	8	set	set	NOUN
ejpam-4652	23	9	of	of	ADP
ejpam-4652	23	10	g.	g.	PROPN
ejpam-4652	23	11	if	if	SCONJ
ejpam-4652	23	12	s	s	X
ejpam-4652	23	13	is	be	AUX
ejpam-4652	23	14	a	a	DET
ejpam-4652	23	15	dominating	dominating	NOUN
ejpam-4652	23	16	set	set	NOUN
ejpam-4652	23	17	of	of	ADP
ejpam-4652	23	18	g	g	PROPN
ejpam-4652	23	19	and	and	CCONJ
ejpam-4652	23	20	if	if	SCONJ
ejpam-4652	23	21	|s|	|s|	PROPN
ejpam-4652	23	22	=	=	SYM
ejpam-4652	23	23	γ(g	γ(g	PROPN
ejpam-4652	23	24	)	)	PUNCT
ejpam-4652	23	25	,	,	PUNCT
ejpam-4652	23	26	then	then	ADV
ejpam-4652	23	27	s	s	VERB
ejpam-4652	23	28	is	be	AUX
ejpam-4652	23	29	called	call	VERB
ejpam-4652	23	30	a	a	DET
ejpam-4652	23	31	minimum	minimum	ADJ
ejpam-4652	23	32	dominating	dominating	NOUN
ejpam-4652	23	33	set	set	NOUN
ejpam-4652	23	34	or	or	CCONJ
ejpam-4652	23	35	a	a	DET
ejpam-4652	23	36	γ	γ	NOUN
ejpam-4652	23	37	-	-	PUNCT
ejpam-4652	23	38	set	set	NOUN
ejpam-4652	23	39	of	of	ADP
ejpam-4652	23	40	g.	g.	PROPN
ejpam-4652	23	41	a	a	DET
ejpam-4652	23	42	vertex	vertex	NOUN
ejpam-4652	23	43	w	w	ADP
ejpam-4652	23	44	∈	∈	NOUN
ejpam-4652	23	45	s	s	PART
ejpam-4652	23	46	strongly	strongly	ADV
ejpam-4652	23	47	resolves	resolve	VERB
ejpam-4652	23	48	two	two	NUM
ejpam-4652	23	49	different	different	ADJ
ejpam-4652	23	50	vertices	vertex	NOUN
ejpam-4652	23	51	u	u	NOUN
ejpam-4652	23	52	,	,	PUNCT
ejpam-4652	23	53	v	v	NOUN
ejpam-4652	23	54	∈	∈	PROPN
ejpam-4652	23	55	v	v	NOUN
ejpam-4652	23	56	(	(	PUNCT
ejpam-4652	23	57	g	g	NOUN
ejpam-4652	23	58	)	)	PUNCT
ejpam-4652	23	59	if	if	SCONJ
ejpam-4652	23	60	v	v	NUM
ejpam-4652	23	61	∈	∈	PROPN
ejpam-4652	23	62	ig[u	ig[u	PROPN
ejpam-4652	23	63	,	,	PUNCT
ejpam-4652	23	64	w	w	NOUN
ejpam-4652	23	65	]	]	PUNCT
ejpam-4652	23	66	or	or	CCONJ
ejpam-4652	23	67	u	u	PROPN
ejpam-4652	23	68	∈	∈	PROPN
ejpam-4652	23	69	ig[v	ig[v	PROPN
ejpam-4652	23	70	,	,	PUNCT
ejpam-4652	23	71	w	w	PROPN
ejpam-4652	23	72	]	]	X
ejpam-4652	23	73	.	.	PUNCT
ejpam-4652	24	1	a	a	DET
ejpam-4652	24	2	set	set	NOUN
ejpam-4652	24	3	w	w	NOUN
ejpam-4652	24	4	of	of	ADP
ejpam-4652	24	5	vertices	vertex	NOUN
ejpam-4652	24	6	in	in	ADP
ejpam-4652	24	7	g	g	PROPN
ejpam-4652	24	8	is	be	AUX
ejpam-4652	24	9	a	a	DET
ejpam-4652	24	10	strong	strong	ADJ
ejpam-4652	24	11	resolving	resolving	NOUN
ejpam-4652	24	12	set	set	NOUN
ejpam-4652	24	13	of	of	ADP
ejpam-4652	24	14	g	g	NOUN
ejpam-4652	24	15	if	if	SCONJ
ejpam-4652	24	16	every	every	DET
ejpam-4652	24	17	two	two	NUM
ejpam-4652	24	18	vertices	vertex	NOUN
ejpam-4652	24	19	of	of	ADP
ejpam-4652	24	20	g	g	NOUN
ejpam-4652	24	21	are	be	AUX
ejpam-4652	24	22	strongly	strongly	ADV
ejpam-4652	24	23	resolved	resolve	VERB
ejpam-4652	24	24	by	by	ADP
ejpam-4652	24	25	some	some	DET
ejpam-4652	24	26	vertices	vertex	NOUN
ejpam-4652	24	27	of	of	ADP
ejpam-4652	24	28	w	w	PROPN
ejpam-4652	24	29	.	.	PUNCT
ejpam-4652	25	1	the	the	DET
ejpam-4652	25	2	smallest	small	ADJ
ejpam-4652	25	3	cardinality	cardinality	NOUN
ejpam-4652	25	4	of	of	ADP
ejpam-4652	25	5	a	a	DET
ejpam-4652	25	6	strong	strong	ADJ
ejpam-4652	25	7	resolving	resolving	NOUN
ejpam-4652	25	8	set	set	NOUN
ejpam-4652	25	9	of	of	ADP
ejpam-4652	25	10	g	g	PROPN
ejpam-4652	25	11	is	be	AUX
ejpam-4652	25	12	called	call	VERB
ejpam-4652	25	13	the	the	DET
ejpam-4652	25	14	strong	strong	ADJ
ejpam-4652	25	15	metric	metric	ADJ
ejpam-4652	25	16	dimension	dimension	NOUN
ejpam-4652	25	17	of	of	ADP
ejpam-4652	25	18	g	g	NOUN
ejpam-4652	25	19	and	and	CCONJ
ejpam-4652	25	20	is	be	AUX
ejpam-4652	25	21	denoted	denote	VERB
ejpam-4652	25	22	by	by	ADP
ejpam-4652	25	23	sdim(g	sdim(g	PROPN
ejpam-4652	25	24	)	)	PUNCT
ejpam-4652	25	25	.	.	PUNCT
ejpam-4652	26	1	a	a	DET
ejpam-4652	26	2	subset	subset	NOUN
ejpam-4652	26	3	s	s	VERB
ejpam-4652	26	4	⊆	⊆	NUM
ejpam-4652	26	5	v	v	NOUN
ejpam-4652	26	6	(	(	PUNCT
ejpam-4652	26	7	g	g	NOUN
ejpam-4652	26	8	)	)	PUNCT
ejpam-4652	26	9	is	be	AUX
ejpam-4652	26	10	a	a	DET
ejpam-4652	26	11	strong	strong	ADJ
ejpam-4652	26	12	resolving	resolving	NOUN
ejpam-4652	26	13	dominating	dominating	NOUN
ejpam-4652	26	14	set	set	NOUN
ejpam-4652	26	15	of	of	ADP
ejpam-4652	26	16	g	g	PROPN
ejpam-4652	26	17	if	if	SCONJ
ejpam-4652	26	18	it	it	PRON
ejpam-4652	26	19	is	be	AUX
ejpam-4652	26	20	both	both	PRON
ejpam-4652	26	21	strong	strong	ADJ
ejpam-4652	26	22	resolving	resolving	NOUN
ejpam-4652	26	23	and	and	CCONJ
ejpam-4652	26	24	dominating	dominating	NOUN
ejpam-4652	26	25	.	.	PUNCT
ejpam-4652	27	1	the	the	DET
ejpam-4652	27	2	smallest	small	ADJ
ejpam-4652	27	3	cardinality	cardinality	NOUN
ejpam-4652	27	4	of	of	ADP
ejpam-4652	27	5	a	a	DET
ejpam-4652	27	6	strong	strong	ADJ
ejpam-4652	27	7	resolving	resolving	NOUN
ejpam-4652	27	8	dominating	dominating	NOUN
ejpam-4652	27	9	set	set	NOUN
ejpam-4652	27	10	of	of	ADP
ejpam-4652	27	11	g	g	PROPN
ejpam-4652	27	12	is	be	AUX
ejpam-4652	27	13	called	call	VERB
ejpam-4652	27	14	the	the	DET
ejpam-4652	27	15	strong	strong	ADJ
ejpam-4652	27	16	resolving	resolving	NOUN
ejpam-4652	27	17	domination	domination	NOUN
ejpam-4652	27	18	number	number	NOUN
ejpam-4652	27	19	of	of	ADP
ejpam-4652	27	20	g	g	NOUN
ejpam-4652	27	21	and	and	CCONJ
ejpam-4652	27	22	is	be	AUX
ejpam-4652	27	23	denoted	denote	VERB
ejpam-4652	27	24	by	by	ADP
ejpam-4652	27	25	γsr(g	γsr(g	PROPN
ejpam-4652	27	26	)	)	PUNCT
ejpam-4652	27	27	.	.	PUNCT
ejpam-4652	28	1	a	a	DET
ejpam-4652	28	2	strong	strong	ADJ
ejpam-4652	28	3	resolving	resolve	VERB
ejpam-4652	28	4	dominating	dominating	NOUN
ejpam-4652	28	5	set	set	NOUN
ejpam-4652	28	6	of	of	ADP
ejpam-4652	28	7	cardinality	cardinality	PROPN
ejpam-4652	28	8	γsr(g	γsr(g	NOUN
ejpam-4652	28	9	)	)	PUNCT
ejpam-4652	28	10	is	be	AUX
ejpam-4652	28	11	called	call	VERB
ejpam-4652	28	12	a	a	DET
ejpam-4652	28	13	γsr	γsr	PROPN
ejpam-4652	28	14	-	-	PUNCT
ejpam-4652	28	15	set	set	NOUN
ejpam-4652	28	16	of	of	ADP
ejpam-4652	28	17	g.	g.	PROPN
ejpam-4652	28	18	a	a	DET
ejpam-4652	28	19	clique	clique	NOUN
ejpam-4652	28	20	in	in	ADP
ejpam-4652	28	21	a	a	DET
ejpam-4652	28	22	graph	graph	NOUN
ejpam-4652	28	23	g	g	NOUN
ejpam-4652	28	24	is	be	AUX
ejpam-4652	28	25	a	a	DET
ejpam-4652	28	26	complete	complete	ADJ
ejpam-4652	28	27	induced	induce	VERB
ejpam-4652	28	28	subgraph	subgraph	NOUN
ejpam-4652	28	29	of	of	ADP
ejpam-4652	28	30	g.	g.	PROPN
ejpam-4652	28	31	a	a	DET
ejpam-4652	28	32	clique	clique	NOUN
ejpam-4652	28	33	c	c	PROPN
ejpam-4652	28	34	in	in	ADP
ejpam-4652	28	35	g	g	PROPN
ejpam-4652	28	36	is	be	AUX
ejpam-4652	28	37	called	call	VERB
ejpam-4652	28	38	a	a	DET
ejpam-4652	28	39	superclique	superclique	NOUN
ejpam-4652	28	40	if	if	SCONJ
ejpam-4652	28	41	for	for	ADP
ejpam-4652	28	42	every	every	DET
ejpam-4652	28	43	pair	pair	NOUN
ejpam-4652	28	44	of	of	ADP
ejpam-4652	28	45	distinct	distinct	ADJ
ejpam-4652	28	46	vertices	vertex	NOUN
ejpam-4652	28	47	u	u	NOUN
ejpam-4652	28	48	,	,	PUNCT
ejpam-4652	28	49	v	v	NOUN
ejpam-4652	28	50	∈	∈	ADJ
ejpam-4652	28	51	c	c	NOUN
ejpam-4652	28	52	,	,	PUNCT
ejpam-4652	28	53	there	there	PRON
ejpam-4652	28	54	exists	exist	VERB
ejpam-4652	28	55	w	w	PROPN
ejpam-4652	28	56	∈	∈	PROPN
ejpam-4652	28	57	v	v	ADP
ejpam-4652	28	58	(	(	PUNCT
ejpam-4652	28	59	g	g	NOUN
ejpam-4652	28	60	)	)	PUNCT
ejpam-4652	28	61	\	\	PUNCT
ejpam-4652	29	1	c	c	NOUN
ejpam-4652	29	2	such	such	ADJ
ejpam-4652	29	3	that	that	PRON
ejpam-4652	29	4	w	w	PROPN
ejpam-4652	29	5	∈	∈	PROPN
ejpam-4652	29	6	ng(u	ng(u	NOUN
ejpam-4652	29	7	)	)	PUNCT
ejpam-4652	29	8	\	\	NOUN
ejpam-4652	29	9	ng(v	ng(v	PUNCT
ejpam-4652	29	10	)	)	PUNCT
ejpam-4652	29	11	or	or	CCONJ
ejpam-4652	29	12	w	w	PROPN
ejpam-4652	29	13	∈	∈	PROPN
ejpam-4652	29	14	ng(v	ng(v	NOUN
ejpam-4652	29	15	)	)	PUNCT
ejpam-4652	29	16	\	\	NOUN
ejpam-4652	29	17	ng(u	ng(u	NOUN
ejpam-4652	29	18	)	)	PUNCT
ejpam-4652	29	19	.	.	PUNCT
ejpam-4652	30	1	a	a	DET
ejpam-4652	30	2	superclique	superclique	ADJ
ejpam-4652	30	3	c	c	NOUN
ejpam-4652	30	4	in	in	ADP
ejpam-4652	30	5	g	g	PROPN
ejpam-4652	30	6	is	be	AUX
ejpam-4652	30	7	called	call	VERB
ejpam-4652	30	8	a	a	DET
ejpam-4652	30	9	dominated	dominate	VERB
ejpam-4652	30	10	superclique	superclique	NOUN
ejpam-4652	30	11	if	if	SCONJ
ejpam-4652	30	12	for	for	ADP
ejpam-4652	30	13	every	every	DET
ejpam-4652	30	14	u	u	PROPN
ejpam-4652	30	15	∈	∈	PROPN
ejpam-4652	30	16	c	c	NOUN
ejpam-4652	30	17	,	,	PUNCT
ejpam-4652	30	18	there	there	PRON
ejpam-4652	30	19	exists	exist	VERB
ejpam-4652	30	20	v	v	ADP
ejpam-4652	30	21	∈	∈	PROPN
ejpam-4652	30	22	v	v	NOUN
ejpam-4652	30	23	(	(	PUNCT
ejpam-4652	30	24	g)\c	g)\c	VERB
ejpam-4652	30	25	such	such	DET
ejpam-4652	30	26	that	that	PRON
ejpam-4652	30	27	uv	uv	PROPN
ejpam-4652	30	28	∈	∈	PROPN
ejpam-4652	30	29	e(g).[5	e(g).[5	NOUN
ejpam-4652	30	30	]	]	PUNCT
ejpam-4652	30	31	a	a	DET
ejpam-4652	30	32	superclique	superclique	NOUN
ejpam-4652	30	33	(	(	PUNCT
ejpam-4652	30	34	resp	resp	NOUN
ejpam-4652	30	35	.	.	PUNCT
ejpam-4652	31	1	dominated	dominate	VERB
ejpam-4652	31	2	superclique	superclique	NOUN
ejpam-4652	31	3	)	)	PUNCT
ejpam-4652	31	4	c	c	NOUN
ejpam-4652	31	5	is	be	AUX
ejpam-4652	31	6	maximum	maximum	ADJ
ejpam-4652	31	7	in	in	ADP
ejpam-4652	31	8	g	g	PROPN
ejpam-4652	31	9	if	if	SCONJ
ejpam-4652	31	10	|c|	|c|	PROPN
ejpam-4652	31	11	≥	≥	NOUN
ejpam-4652	31	12	|c∗|	|c∗|	VERB
ejpam-4652	31	13	for	for	ADP
ejpam-4652	31	14	all	all	DET
ejpam-4652	31	15	supercliques	superclique	NOUN
ejpam-4652	31	16	(	(	PUNCT
ejpam-4652	31	17	resp	resp	NOUN
ejpam-4652	31	18	.	.	PUNCT
ejpam-4652	32	1	dominated	dominate	VERB
ejpam-4652	32	2	supercliques	superclique	NOUN
ejpam-4652	32	3	)	)	PUNCT
ejpam-4652	32	4	c∗	c∗	NOUN
ejpam-4652	32	5	in	in	ADP
ejpam-4652	32	6	g.	g.	PROPN
ejpam-4652	32	7	the	the	DET
ejpam-4652	32	8	superclique	superclique	NOUN
ejpam-4652	32	9	(	(	PUNCT
ejpam-4652	32	10	resp	resp	NOUN
ejpam-4652	32	11	.	.	PUNCT
ejpam-4652	33	1	dominated	dominate	VERB
ejpam-4652	33	2	superclique	superclique	NOUN
ejpam-4652	33	3	)	)	PUNCT
ejpam-4652	33	4	number	number	NOUN
ejpam-4652	33	5	,	,	PUNCT
ejpam-4652	33	6	ωs(g	ωs(g	NUM
ejpam-4652	33	7	)	)	PUNCT
ejpam-4652	33	8	(	(	PUNCT
ejpam-4652	33	9	resp	resp	NOUN
ejpam-4652	33	10	.	.	PUNCT
ejpam-4652	34	1	ωds	ωds	NOUN
ejpam-4652	34	2	)	)	PUNCT
ejpam-4652	34	3	of	of	ADP
ejpam-4652	34	4	g	g	PROPN
ejpam-4652	34	5	is	be	AUX
ejpam-4652	34	6	the	the	DET
ejpam-4652	34	7	cardinality	cardinality	NOUN
ejpam-4652	34	8	of	of	ADP
ejpam-4652	34	9	a	a	DET
ejpam-4652	34	10	maximum	maximum	ADJ
ejpam-4652	34	11	superclique	superclique	NOUN
ejpam-4652	34	12	(	(	PUNCT
ejpam-4652	34	13	resp	resp	NOUN
ejpam-4652	34	14	.	.	PUNCT
ejpam-4652	35	1	maximum	maximum	ADJ
ejpam-4652	35	2	dominated	dominate	VERB
ejpam-4652	35	3	superclique	superclique	NOUN
ejpam-4652	35	4	)	)	PUNCT
ejpam-4652	35	5	in	in	ADP
ejpam-4652	35	6	g.	g.	PROPN
ejpam-4652	35	7	a	a	DET
ejpam-4652	35	8	vertex	vertex	NOUN
ejpam-4652	35	9	u	u	NOUN
ejpam-4652	35	10	of	of	ADP
ejpam-4652	35	11	g	g	PROPN
ejpam-4652	35	12	is	be	AUX
ejpam-4652	35	13	maximally	maximally	ADV
ejpam-4652	35	14	distant	distant	ADJ
ejpam-4652	35	15	from	from	ADP
ejpam-4652	35	16	vertex	vertex	NOUN
ejpam-4652	35	17	v	v	NOUN
ejpam-4652	35	18	of	of	ADP
ejpam-4652	35	19	g	g	NOUN
ejpam-4652	35	20	,	,	PUNCT
ejpam-4652	35	21	u	u	PROPN
ejpam-4652	35	22	̸=	̸=	PROPN
ejpam-4652	35	23	v	v	NOUN
ejpam-4652	35	24	,	,	PUNCT
ejpam-4652	35	25	if	if	SCONJ
ejpam-4652	35	26	for	for	ADP
ejpam-4652	35	27	every	every	DET
ejpam-4652	35	28	vertex	vertex	NOUN
ejpam-4652	35	29	w	w	PROPN
ejpam-4652	35	30	∈	∈	PROPN
ejpam-4652	35	31	ng(u	ng(u	NOUN
ejpam-4652	35	32	)	)	PUNCT
ejpam-4652	35	33	,	,	PUNCT
ejpam-4652	35	34	dg(v	dg(v	X
ejpam-4652	35	35	,	,	PUNCT
ejpam-4652	35	36	w	w	NOUN
ejpam-4652	35	37	)	)	PUNCT
ejpam-4652	35	38	≤	≤	NOUN
ejpam-4652	35	39	dg(u	dg(u	ADJ
ejpam-4652	35	40	,	,	PUNCT
ejpam-4652	35	41	v	v	NOUN
ejpam-4652	35	42	)	)	PUNCT
ejpam-4652	35	43	.	.	PUNCT
ejpam-4652	36	1	if	if	SCONJ
ejpam-4652	36	2	u	u	NOUN
ejpam-4652	36	3	is	be	AUX
ejpam-4652	36	4	maximally	maximally	ADV
ejpam-4652	36	5	distant	distant	ADJ
ejpam-4652	36	6	from	from	ADP
ejpam-4652	36	7	v	v	NOUN
ejpam-4652	36	8	and	and	CCONJ
ejpam-4652	36	9	v	v	NOUN
ejpam-4652	36	10	is	be	AUX
ejpam-4652	36	11	maximally	maximally	ADV
ejpam-4652	36	12	distant	distant	ADJ
ejpam-4652	36	13	from	from	ADP
ejpam-4652	36	14	u	u	NOUN
ejpam-4652	36	15	,	,	PUNCT
ejpam-4652	36	16	then	then	ADV
ejpam-4652	36	17	we	we	PRON
ejpam-4652	36	18	say	say	VERB
ejpam-4652	36	19	that	that	SCONJ
ejpam-4652	36	20	u	u	PROPN
ejpam-4652	36	21	and	and	CCONJ
ejpam-4652	36	22	v	v	NOUN
ejpam-4652	36	23	are	be	AUX
ejpam-4652	36	24	mutually	mutually	ADV
ejpam-4652	36	25	maximally	maximally	ADV
ejpam-4652	36	26	distant	distant	ADJ
ejpam-4652	36	27	,	,	PUNCT
ejpam-4652	36	28	denoted	denote	VERB
ejpam-4652	36	29	by	by	ADP
ejpam-4652	36	30	ummdv	ummdv	NOUN
ejpam-4652	36	31	.	.	PUNCT
ejpam-4652	37	1	in	in	ADP
ejpam-4652	37	2	recent	recent	ADJ
ejpam-4652	37	3	years	year	NOUN
ejpam-4652	37	4	,	,	PUNCT
ejpam-4652	37	5	the	the	DET
ejpam-4652	37	6	concept	concept	NOUN
ejpam-4652	37	7	of	of	ADP
ejpam-4652	37	8	domination	domination	NOUN
ejpam-4652	37	9	in	in	ADP
ejpam-4652	37	10	graphs	graph	NOUN
ejpam-4652	37	11	has	have	AUX
ejpam-4652	37	12	been	be	AUX
ejpam-4652	37	13	studied	study	VERB
ejpam-4652	37	14	extensively	extensively	ADV
ejpam-4652	37	15	and	and	CCONJ
ejpam-4652	37	16	several	several	ADJ
ejpam-4652	37	17	research	research	NOUN
ejpam-4652	37	18	papers	paper	NOUN
ejpam-4652	37	19	have	have	AUX
ejpam-4652	37	20	been	be	AUX
ejpam-4652	37	21	published	publish	VERB
ejpam-4652	37	22	on	on	ADP
ejpam-4652	37	23	this	this	DET
ejpam-4652	37	24	topic	topic	NOUN
ejpam-4652	37	25	.	.	PUNCT
ejpam-4652	38	1	the	the	DET
ejpam-4652	38	2	said	say	VERB
ejpam-4652	38	3	concept	concept	NOUN
ejpam-4652	38	4	was	be	AUX
ejpam-4652	38	5	not	not	PART
ejpam-4652	38	6	formally	formally	ADV
ejpam-4652	38	7	defined	define	VERB
ejpam-4652	38	8	mathematically	mathematically	ADV
ejpam-4652	38	9	until	until	ADP
ejpam-4652	38	10	the	the	DET
ejpam-4652	38	11	publications	publication	NOUN
ejpam-4652	38	12	of	of	ADP
ejpam-4652	38	13	the	the	DET
ejpam-4652	38	14	books	book	NOUN
ejpam-4652	38	15	by	by	ADP
ejpam-4652	38	16	claude	claude	PROPN
ejpam-4652	38	17	berge	berge	NOUN
ejpam-4652	39	1	[	[	X
ejpam-4652	39	2	3	3	X
ejpam-4652	39	3	]	]	PUNCT
ejpam-4652	39	4	in	in	ADP
ejpam-4652	39	5	1958	1958	NUM
ejpam-4652	39	6	and	and	CCONJ
ejpam-4652	39	7	oystein	oystein	ADJ
ejpam-4652	39	8	ore	ore	NOUN
ejpam-4652	39	9	in	in	ADP
ejpam-4652	39	10	1962	1962	NUM
ejpam-4652	39	11	.	.	PUNCT
ejpam-4652	40	1	in	in	ADP
ejpam-4652	40	2	1977	1977	NUM
ejpam-4652	40	3	,	,	PUNCT
ejpam-4652	40	4	a	a	DET
ejpam-4652	40	5	survey	survey	NOUN
ejpam-4652	40	6	paper	paper	NOUN
ejpam-4652	40	7	by	by	ADP
ejpam-4652	40	8	cockayne	cockayne	NOUN
ejpam-4652	40	9	and	and	CCONJ
ejpam-4652	40	10	hedetniemi	hedetniemi	X
ejpam-4652	40	11	[	[	X
ejpam-4652	40	12	4	4	NUM
ejpam-4652	40	13	]	]	PUNCT
ejpam-4652	40	14	began	begin	VERB
ejpam-4652	40	15	to	to	PART
ejpam-4652	40	16	study	study	VERB
ejpam-4652	40	17	the	the	DET
ejpam-4652	40	18	concept	concept	NOUN
ejpam-4652	40	19	of	of	ADP
ejpam-4652	40	20	domination	domination	NOUN
ejpam-4652	40	21	.	.	PUNCT
ejpam-4652	41	1	on	on	ADP
ejpam-4652	41	2	the	the	DET
ejpam-4652	41	3	other	other	ADJ
ejpam-4652	41	4	hand	hand	NOUN
ejpam-4652	41	5	,	,	PUNCT
ejpam-4652	41	6	the	the	DET
ejpam-4652	41	7	problem	problem	NOUN
ejpam-4652	41	8	of	of	ADP
ejpam-4652	41	9	uniquely	uniquely	ADV
ejpam-4652	41	10	recognizing	recognize	VERB
ejpam-4652	41	11	the	the	DET
ejpam-4652	41	12	possible	possible	ADJ
ejpam-4652	41	13	position	position	NOUN
ejpam-4652	41	14	of	of	ADP
ejpam-4652	41	15	an	an	DET
ejpam-4652	41	16	intruder	intruder	NOUN
ejpam-4652	41	17	such	such	ADJ
ejpam-4652	41	18	as	as	ADP
ejpam-4652	41	19	fault	fault	NOUN
ejpam-4652	41	20	in	in	ADP
ejpam-4652	41	21	a	a	DET
ejpam-4652	41	22	computer	computer	NOUN
ejpam-4652	41	23	network	network	NOUN
ejpam-4652	41	24	and	and	CCONJ
ejpam-4652	41	25	spoiled	spoiled	ADJ
ejpam-4652	41	26	device	device	NOUN
ejpam-4652	41	27	was	be	AUX
ejpam-4652	41	28	the	the	DET
ejpam-4652	41	29	principal	principal	ADJ
ejpam-4652	41	30	motivation	motivation	NOUN
ejpam-4652	41	31	in	in	ADP
ejpam-4652	41	32	introducing	introduce	VERB
ejpam-4652	41	33	the	the	DET
ejpam-4652	41	34	concept	concept	NOUN
ejpam-4652	41	35	of	of	ADP
ejpam-4652	41	36	metric	metric	ADJ
ejpam-4652	41	37	dimension	dimension	NOUN
ejpam-4652	41	38	in	in	ADP
ejpam-4652	41	39	graphs	graph	NOUN
ejpam-4652	41	40	.	.	PUNCT
ejpam-4652	42	1	slater	slater	NOUN
ejpam-4652	43	1	[	[	X
ejpam-4652	43	2	10	10	NUM
ejpam-4652	43	3	]	]	PUNCT
ejpam-4652	43	4	brought	bring	VERB
ejpam-4652	43	5	in	in	ADP
ejpam-4652	43	6	the	the	DET
ejpam-4652	43	7	notion	notion	NOUN
ejpam-4652	43	8	of	of	ADP
ejpam-4652	43	9	locating	locate	VERB
ejpam-4652	43	10	sets	set	NOUN
ejpam-4652	43	11	and	and	CCONJ
ejpam-4652	43	12	its	its	PRON
ejpam-4652	43	13	minimum	minimum	ADJ
ejpam-4652	43	14	cardinality	cardinality	NOUN
ejpam-4652	43	15	as	as	ADP
ejpam-4652	43	16	locating	locate	VERB
ejpam-4652	43	17	number	number	NOUN
ejpam-4652	43	18	.	.	PUNCT
ejpam-4652	44	1	the	the	DET
ejpam-4652	44	2	same	same	ADJ
ejpam-4652	44	3	concept	concept	NOUN
ejpam-4652	44	4	was	be	AUX
ejpam-4652	44	5	also	also	ADV
ejpam-4652	44	6	introduced	introduce	VERB
ejpam-4652	44	7	by	by	ADP
ejpam-4652	44	8	harary	harary	NOUN
ejpam-4652	44	9	and	and	CCONJ
ejpam-4652	44	10	melter	melter	NOUN
ejpam-4652	45	1	[	[	X
ejpam-4652	45	2	7	7	NUM
ejpam-4652	45	3	]	]	PUNCT
ejpam-4652	45	4	but	but	CCONJ
ejpam-4652	45	5	using	use	VERB
ejpam-4652	45	6	the	the	DET
ejpam-4652	45	7	terms	term	NOUN
ejpam-4652	45	8	resolving	resolve	VERB
ejpam-4652	45	9	sets	set	NOUN
ejpam-4652	45	10	and	and	CCONJ
ejpam-4652	45	11	metric	metric	ADJ
ejpam-4652	45	12	dimension	dimension	NOUN
ejpam-4652	45	13	to	to	PART
ejpam-4652	45	14	refer	refer	VERB
ejpam-4652	45	15	to	to	ADP
ejpam-4652	45	16	locating	locate	VERB
ejpam-4652	45	17	sets	set	NOUN
ejpam-4652	45	18	and	and	CCONJ
ejpam-4652	45	19	locating	locate	VERB
ejpam-4652	45	20	number	number	NOUN
ejpam-4652	45	21	,	,	PUNCT
ejpam-4652	45	22	respectively	respectively	ADV
ejpam-4652	45	23	.	.	PUNCT
ejpam-4652	46	1	however	however	ADV
ejpam-4652	46	2	,	,	PUNCT
ejpam-4652	46	3	in	in	ADP
ejpam-4652	46	4	recent	recent	ADJ
ejpam-4652	46	5	studies	study	NOUN
ejpam-4652	46	6	,	,	PUNCT
ejpam-4652	46	7	locating	locate	VERB
ejpam-4652	46	8	sets	set	NOUN
ejpam-4652	46	9	and	and	CCONJ
ejpam-4652	46	10	resolving	resolve	VERB
ejpam-4652	46	11	sets	set	NOUN
ejpam-4652	46	12	are	be	AUX
ejpam-4652	46	13	defined	define	VERB
ejpam-4652	46	14	differently	differently	ADV
ejpam-4652	46	15	.	.	PUNCT
ejpam-4652	47	1	in	in	ADP
ejpam-4652	47	2	2013	2013	NUM
ejpam-4652	47	3	,	,	PUNCT
ejpam-4652	47	4	canoy	canoy	NOUN
ejpam-4652	47	5	and	and	CCONJ
ejpam-4652	47	6	omega	omega	NOUN
ejpam-4652	47	7	[	[	X
ejpam-4652	47	8	8	8	NUM
ejpam-4652	47	9	]	]	PUNCT
ejpam-4652	47	10	,	,	PUNCT
ejpam-4652	47	11	defined	define	VERB
ejpam-4652	47	12	a	a	DET
ejpam-4652	47	13	locating	locating	NOUN
ejpam-4652	47	14	set	set	VERB
ejpam-4652	47	15	as	as	ADP
ejpam-4652	47	16	a	a	DET
ejpam-4652	47	17	subset	subset	NOUN
ejpam-4652	47	18	s	s	NOUN
ejpam-4652	47	19	of	of	ADP
ejpam-4652	47	20	v	v	NOUN
ejpam-4652	47	21	(	(	PUNCT
ejpam-4652	47	22	g	g	NOUN
ejpam-4652	47	23	)	)	PUNCT
ejpam-4652	47	24	in	in	ADP
ejpam-4652	47	25	a	a	DET
ejpam-4652	47	26	connected	connected	ADJ
ejpam-4652	47	27	graph	graph	NOUN
ejpam-4652	47	28	g	g	NOUN
ejpam-4652	47	29	satisfying	satisfy	VERB
ejpam-4652	47	30	that	that	SCONJ
ejpam-4652	47	31	ng(u	ng(u	NOUN
ejpam-4652	47	32	)	)	PUNCT
ejpam-4652	47	33	∩	∩	NOUN
ejpam-4652	47	34	s	s	PART
ejpam-4652	47	35	̸=	̸=	PROPN
ejpam-4652	47	36	ng(v	ng(v	NUM
ejpam-4652	47	37	)	)	PUNCT
ejpam-4652	47	38	∩	∩	NOUN
ejpam-4652	47	39	s	s	PART
ejpam-4652	47	40	for	for	ADP
ejpam-4652	47	41	all	all	DET
ejpam-4652	47	42	u	u	NOUN
ejpam-4652	47	43	,	,	PUNCT
ejpam-4652	47	44	v	v	NOUN
ejpam-4652	47	45	∈	∈	PROPN
ejpam-4652	47	46	v	v	NOUN
ejpam-4652	47	47	(	(	PUNCT
ejpam-4652	47	48	g	g	NOUN
ejpam-4652	47	49	)	)	PUNCT
ejpam-4652	47	50	\	\	PUNCT
ejpam-4652	48	1	s.	s.	PROPN
ejpam-4652	48	2	meanwhile	meanwhile	ADV
ejpam-4652	48	3	,	,	PUNCT
ejpam-4652	48	4	bailey	bailey	PROPN
ejpam-4652	48	5	et	et	PROPN
ejpam-4652	48	6	al	al	PROPN
ejpam-4652	48	7	.	.	PUNCT
ejpam-4652	49	1	[	[	X
ejpam-4652	49	2	2	2	X
ejpam-4652	49	3	]	]	PUNCT
ejpam-4652	49	4	defined	define	VERB
ejpam-4652	49	5	a	a	DET
ejpam-4652	49	6	resolving	resolving	NOUN
ejpam-4652	49	7	set	set	VERB
ejpam-4652	49	8	as	as	ADP
ejpam-4652	49	9	a	a	DET
ejpam-4652	49	10	set	set	NOUN
ejpam-4652	49	11	of	of	ADP
ejpam-4652	49	12	vertices	vertex	NOUN
ejpam-4652	49	13	s	s	PART
ejpam-4652	49	14	in	in	ADP
ejpam-4652	49	15	a	a	DET
ejpam-4652	49	16	graph	graph	NOUN
ejpam-4652	49	17	g	g	ADP
ejpam-4652	49	18	such	such	ADJ
ejpam-4652	49	19	that	that	PRON
ejpam-4652	49	20	for	for	ADP
ejpam-4652	49	21	any	any	DET
ejpam-4652	49	22	two	two	NUM
ejpam-4652	49	23	vertices	vertex	NOUN
ejpam-4652	49	24	u	u	NOUN
ejpam-4652	49	25	,	,	PUNCT
ejpam-4652	49	26	v	v	NOUN
ejpam-4652	49	27	,	,	PUNCT
ejpam-4652	49	28	there	there	PRON
ejpam-4652	49	29	exists	exist	VERB
ejpam-4652	49	30	x	x	X
ejpam-4652	49	31	∈	∈	PROPN
ejpam-4652	49	32	s	s	VERB
ejpam-4652	49	33	such	such	ADJ
ejpam-4652	49	34	that	that	SCONJ
ejpam-4652	49	35	the	the	DET
ejpam-4652	49	36	distances	distance	NOUN
ejpam-4652	49	37	d(u	d(u	PROPN
ejpam-4652	49	38	,	,	PUNCT
ejpam-4652	49	39	x	x	NOUN
ejpam-4652	49	40	)	)	PUNCT
ejpam-4652	49	41	̸=	̸=	PROPN
ejpam-4652	49	42	d(v	d(v	PROPN
ejpam-4652	49	43	,	,	PUNCT
ejpam-4652	49	44	x	x	NOUN
ejpam-4652	49	45	)	)	PUNCT
ejpam-4652	49	46	.	.	PUNCT
ejpam-4652	50	1	in	in	ADP
ejpam-4652	50	2	2007	2007	NUM
ejpam-4652	50	3	,	,	PUNCT
ejpam-4652	50	4	oellerman	oellerman	NOUN
ejpam-4652	50	5	and	and	CCONJ
ejpam-4652	50	6	peter	peter	PROPN
ejpam-4652	50	7	-	-	PUNCT
ejpam-4652	50	8	fransen	fransen	PROPN
ejpam-4652	50	9	[	[	X
ejpam-4652	50	10	9	9	NUM
ejpam-4652	50	11	]	]	PUNCT
ejpam-4652	50	12	introduced	introduce	VERB
ejpam-4652	50	13	the	the	DET
ejpam-4652	50	14	strong	strong	ADJ
ejpam-4652	50	15	resolving	resolving	NOUN
ejpam-4652	50	16	graph	graph	NOUN
ejpam-4652	50	17	gsr	gsr	NOUN
ejpam-4652	50	18	of	of	ADP
ejpam-4652	50	19	a	a	DET
ejpam-4652	50	20	connected	connected	ADJ
ejpam-4652	50	21	graph	graph	NOUN
ejpam-4652	50	22	g	g	NOUN
ejpam-4652	50	23	as	as	ADP
ejpam-4652	50	24	a	a	DET
ejpam-4652	50	25	tool	tool	NOUN
ejpam-4652	50	26	to	to	PART
ejpam-4652	50	27	study	study	VERB
ejpam-4652	50	28	the	the	DET
ejpam-4652	50	29	strong	strong	ADJ
ejpam-4652	50	30	metric	metric	ADJ
ejpam-4652	50	31	dimension	dimension	NOUN
ejpam-4652	50	32	of	of	ADP
ejpam-4652	50	33	g.	g.	PROPN
ejpam-4652	50	34	this	this	DET
ejpam-4652	50	35	study	study	NOUN
ejpam-4652	50	36	aims	aim	VERB
ejpam-4652	50	37	to	to	PART
ejpam-4652	50	38	define	define	VERB
ejpam-4652	50	39	and	and	CCONJ
ejpam-4652	50	40	characterize	characterize	VERB
ejpam-4652	50	41	the	the	DET
ejpam-4652	50	42	strong	strong	ADJ
ejpam-4652	50	43	resolving	resolve	VERB
ejpam-4652	50	44	dominating	dominating	NOUN
ejpam-4652	50	45	sets	set	NOUN
ejpam-4652	50	46	in	in	ADP
ejpam-4652	50	47	g.	g.	PROPN
ejpam-4652	50	48	monsanto	monsanto	PROPN
ejpam-4652	50	49	,	,	PUNCT
ejpam-4652	50	50	p.	p.	PROPN
ejpam-4652	50	51	acal	acal	PROPN
ejpam-4652	50	52	,	,	PUNCT
ejpam-4652	50	53	h.	h.	PROPN
ejpam-4652	50	54	rara	rara	PROPN
ejpam-4652	50	55	/	/	SYM
ejpam-4652	50	56	eur	eur	PROPN
ejpam-4652	50	57	.	.	PUNCT
ejpam-4652	51	1	j.	j.	PROPN
ejpam-4652	51	2	pure	pure	PROPN
ejpam-4652	51	3	appl	appl	PROPN
ejpam-4652	51	4	.	.	PROPN
ejpam-4652	51	5	math	math	PROPN
ejpam-4652	51	6	,	,	PUNCT
ejpam-4652	51	7	16	16	NUM
ejpam-4652	51	8	(	(	PUNCT
ejpam-4652	51	9	1	1	NUM
ejpam-4652	51	10	)	)	PUNCT
ejpam-4652	51	11	(	(	PUNCT
ejpam-4652	51	12	2023	2023	NUM
ejpam-4652	51	13	)	)	PUNCT
ejpam-4652	51	14	,	,	PUNCT
ejpam-4652	51	15	363	363	NUM
ejpam-4652	51	16	-	-	SYM
ejpam-4652	51	17	372	372	NUM
ejpam-4652	51	18	365	365	NUM
ejpam-4652	51	19	the	the	DET
ejpam-4652	51	20	lexicographic	lexicographic	ADJ
ejpam-4652	51	21	product	product	NOUN
ejpam-4652	51	22	of	of	ADP
ejpam-4652	51	23	graphs	graph	NOUN
ejpam-4652	51	24	and	and	CCONJ
ejpam-4652	51	25	determine	determine	VERB
ejpam-4652	51	26	their	their	PRON
ejpam-4652	51	27	corresponding	correspond	VERB
ejpam-4652	51	28	strong	strong	ADJ
ejpam-4652	51	29	resolving	resolving	NOUN
ejpam-4652	51	30	domination	domination	NOUN
ejpam-4652	51	31	number	number	NOUN
ejpam-4652	51	32	.	.	PUNCT
ejpam-4652	52	1	2	2	X
ejpam-4652	52	2	.	.	X
ejpam-4652	52	3	preliminary	preliminary	ADJ
ejpam-4652	52	4	results	result	NOUN
ejpam-4652	52	5	remark	remark	VERB
ejpam-4652	52	6	1	1	NUM
ejpam-4652	52	7	.	.	PUNCT
ejpam-4652	53	1	[	[	X
ejpam-4652	53	2	1	1	X
ejpam-4652	53	3	]	]	PUNCT
ejpam-4652	53	4	every	every	DET
ejpam-4652	53	5	strong	strong	ADJ
ejpam-4652	53	6	resolving	resolve	VERB
ejpam-4652	53	7	dominating	dominating	NOUN
ejpam-4652	53	8	set	set	NOUN
ejpam-4652	53	9	of	of	ADP
ejpam-4652	53	10	a	a	DET
ejpam-4652	53	11	connected	connected	ADJ
ejpam-4652	53	12	graph	graph	NOUN
ejpam-4652	53	13	g	g	PROPN
ejpam-4652	53	14	is	be	AUX
ejpam-4652	53	15	a	a	DET
ejpam-4652	53	16	dominating	dominating	NOUN
ejpam-4652	53	17	set	set	NOUN
ejpam-4652	53	18	of	of	ADP
ejpam-4652	53	19	g.	g.	PROPN
ejpam-4652	53	20	hence	hence	ADV
ejpam-4652	53	21	,	,	PUNCT
ejpam-4652	53	22	γ(g	γ(g	PROPN
ejpam-4652	53	23	)	)	PUNCT
ejpam-4652	53	24	≤	≤	NOUN
ejpam-4652	53	25	γsr(g	γsr(g	NOUN
ejpam-4652	53	26	)	)	PUNCT
ejpam-4652	53	27	.	.	PUNCT
ejpam-4652	54	1	remark	remark	NOUN
ejpam-4652	54	2	2	2	NUM
ejpam-4652	54	3	.	.	PUNCT
ejpam-4652	55	1	[	[	X
ejpam-4652	55	2	1	1	X
ejpam-4652	55	3	]	]	PUNCT
ejpam-4652	55	4	every	every	DET
ejpam-4652	55	5	strong	strong	ADJ
ejpam-4652	55	6	resolving	resolve	VERB
ejpam-4652	55	7	dominating	dominating	NOUN
ejpam-4652	55	8	set	set	NOUN
ejpam-4652	55	9	of	of	ADP
ejpam-4652	55	10	a	a	DET
ejpam-4652	55	11	connected	connected	ADJ
ejpam-4652	55	12	graph	graph	NOUN
ejpam-4652	55	13	g	g	PROPN
ejpam-4652	55	14	is	be	AUX
ejpam-4652	55	15	a	a	DET
ejpam-4652	55	16	strong	strong	ADJ
ejpam-4652	55	17	resolving	resolving	NOUN
ejpam-4652	55	18	set	set	NOUN
ejpam-4652	55	19	of	of	ADP
ejpam-4652	55	20	g.	g.	PROPN
ejpam-4652	55	21	hence	hence	ADV
ejpam-4652	55	22	,	,	PUNCT
ejpam-4652	55	23	sdim(g	sdim(g	PROPN
ejpam-4652	55	24	)	)	PUNCT
ejpam-4652	55	25	≤	≤	NOUN
ejpam-4652	55	26	γsr(g	γsr(g	NOUN
ejpam-4652	55	27	)	)	PUNCT
ejpam-4652	55	28	.	.	PUNCT
ejpam-4652	56	1	remark	remark	PROPN
ejpam-4652	56	2	3	3	NUM
ejpam-4652	56	3	.	.	PUNCT
ejpam-4652	57	1	for	for	ADP
ejpam-4652	57	2	any	any	DET
ejpam-4652	57	3	connected	connected	ADJ
ejpam-4652	57	4	graph	graph	NOUN
ejpam-4652	57	5	g	g	NOUN
ejpam-4652	57	6	of	of	ADP
ejpam-4652	57	7	order	order	NOUN
ejpam-4652	57	8	n	n	PRON
ejpam-4652	57	9	≥	≥	NOUN
ejpam-4652	57	10	2	2	NUM
ejpam-4652	57	11	,	,	PUNCT
ejpam-4652	57	12	1	1	NUM
ejpam-4652	57	13	≤	≤	NUM
ejpam-4652	57	14	γsr(g	γsr(g	NOUN
ejpam-4652	57	15	)	)	PUNCT
ejpam-4652	57	16	≤	≤	NUM
ejpam-4652	57	17	n−	n−	NOUN
ejpam-4652	57	18	1	1	NUM
ejpam-4652	57	19	.	.	PUNCT
ejpam-4652	57	20	example	example	NOUN
ejpam-4652	58	1	1	1	NUM
ejpam-4652	58	2	.	.	PUNCT
ejpam-4652	58	3	γsr(p2	γsr(p2	NUM
ejpam-4652	58	4	)	)	PUNCT
ejpam-4652	58	5	=	=	SYM
ejpam-4652	58	6	1	1	NUM
ejpam-4652	58	7	and	and	CCONJ
ejpam-4652	58	8	γsr(kn	γsr(kn	NOUN
ejpam-4652	58	9	)	)	PUNCT
ejpam-4652	58	10	=	=	PUNCT
ejpam-4652	59	1	n−	n−	NOUN
ejpam-4652	59	2	1	1	NUM
ejpam-4652	59	3	for	for	ADP
ejpam-4652	59	4	n	n	PRON
ejpam-4652	59	5	≥	≥	NUM
ejpam-4652	59	6	2	2	NUM
ejpam-4652	59	7	.	.	PUNCT
ejpam-4652	59	8	remark	remark	NOUN
ejpam-4652	59	9	4	4	NUM
ejpam-4652	59	10	.	.	PUNCT
ejpam-4652	60	1	[	[	X
ejpam-4652	60	2	1	1	X
ejpam-4652	60	3	]	]	PUNCT
ejpam-4652	60	4	any	any	DET
ejpam-4652	60	5	superset	superset	NOUN
ejpam-4652	60	6	of	of	ADP
ejpam-4652	60	7	a	a	DET
ejpam-4652	60	8	strong	strong	ADJ
ejpam-4652	60	9	resolving	resolving	NOUN
ejpam-4652	60	10	dominating	dominating	NOUN
ejpam-4652	60	11	set	set	NOUN
ejpam-4652	60	12	is	be	AUX
ejpam-4652	60	13	a	a	DET
ejpam-4652	60	14	strong	strong	ADJ
ejpam-4652	60	15	resolving	resolve	VERB
ejpam-4652	60	16	dominating	dominating	NOUN
ejpam-4652	60	17	set	set	NOUN
ejpam-4652	60	18	.	.	PUNCT
ejpam-4652	61	1	proposition	proposition	NOUN
ejpam-4652	61	2	1	1	NUM
ejpam-4652	61	3	.	.	PUNCT
ejpam-4652	62	1	every	every	DET
ejpam-4652	62	2	strong	strong	ADJ
ejpam-4652	62	3	resolving	resolving	NOUN
ejpam-4652	62	4	set	set	NOUN
ejpam-4652	62	5	of	of	ADP
ejpam-4652	62	6	a	a	DET
ejpam-4652	62	7	connected	connected	ADJ
ejpam-4652	62	8	graph	graph	NOUN
ejpam-4652	62	9	g	g	PROPN
ejpam-4652	62	10	is	be	AUX
ejpam-4652	62	11	a	a	DET
ejpam-4652	62	12	resolving	resolving	NOUN
ejpam-4652	62	13	set	set	NOUN
ejpam-4652	62	14	.	.	PUNCT
ejpam-4652	63	1	proof	proof	NOUN
ejpam-4652	63	2	:	:	PUNCT
ejpam-4652	63	3	let	let	VERB
ejpam-4652	63	4	s	s	PRON
ejpam-4652	63	5	⊆	⊆	NUM
ejpam-4652	63	6	v	v	NOUN
ejpam-4652	63	7	(	(	PUNCT
ejpam-4652	63	8	g	g	NOUN
ejpam-4652	63	9	)	)	PUNCT
ejpam-4652	63	10	is	be	AUX
ejpam-4652	63	11	a	a	DET
ejpam-4652	63	12	strong	strong	ADJ
ejpam-4652	63	13	resolving	resolving	NOUN
ejpam-4652	63	14	set	set	NOUN
ejpam-4652	63	15	of	of	ADP
ejpam-4652	63	16	g.	g.	PROPN
ejpam-4652	63	17	then	then	ADV
ejpam-4652	63	18	for	for	ADP
ejpam-4652	63	19	any	any	DET
ejpam-4652	63	20	pair	pair	NOUN
ejpam-4652	63	21	of	of	ADP
ejpam-4652	63	22	distinct	distinct	ADJ
ejpam-4652	63	23	vertices	vertex	NOUN
ejpam-4652	63	24	u	u	NOUN
ejpam-4652	63	25	,	,	PUNCT
ejpam-4652	63	26	v	v	NOUN
ejpam-4652	63	27	∈	∈	PROPN
ejpam-4652	63	28	v	v	NOUN
ejpam-4652	63	29	(	(	PUNCT
ejpam-4652	63	30	g	g	NOUN
ejpam-4652	63	31	)	)	PUNCT
ejpam-4652	63	32	,	,	PUNCT
ejpam-4652	63	33	there	there	PRON
ejpam-4652	63	34	exists	exist	VERB
ejpam-4652	63	35	w	w	PROPN
ejpam-4652	63	36	∈	∈	PROPN
ejpam-4652	63	37	s	s	VERB
ejpam-4652	63	38	such	such	ADJ
ejpam-4652	63	39	that	that	SCONJ
ejpam-4652	63	40	u	u	PROPN
ejpam-4652	63	41	∈	∈	PROPN
ejpam-4652	63	42	ig[v	ig[v	PROPN
ejpam-4652	63	43	,	,	PUNCT
ejpam-4652	63	44	w	w	PROPN
ejpam-4652	63	45	]	]	PUNCT
ejpam-4652	63	46	or	or	CCONJ
ejpam-4652	63	47	v	v	ADP
ejpam-4652	63	48	∈	∈	PROPN
ejpam-4652	63	49	ig[u	ig[u	NOUN
ejpam-4652	63	50	,	,	PUNCT
ejpam-4652	63	51	w	w	NOUN
ejpam-4652	63	52	]	]	X
ejpam-4652	63	53	.	.	PUNCT
ejpam-4652	64	1	if	if	SCONJ
ejpam-4652	64	2	u	u	PROPN
ejpam-4652	64	3	∈	∈	PROPN
ejpam-4652	64	4	ig[v	ig[v	PROPN
ejpam-4652	64	5	,	,	PUNCT
ejpam-4652	64	6	w	w	PROPN
ejpam-4652	64	7	]	]	X
ejpam-4652	64	8	,	,	PUNCT
ejpam-4652	64	9	then	then	ADV
ejpam-4652	64	10	dg(u	dg(u	X
ejpam-4652	64	11	,	,	PUNCT
ejpam-4652	64	12	w	w	NOUN
ejpam-4652	64	13	)	)	PUNCT
ejpam-4652	64	14	<	<	X
ejpam-4652	64	15	dg(v	dg(v	X
ejpam-4652	64	16	,	,	PUNCT
ejpam-4652	64	17	w	w	NOUN
ejpam-4652	64	18	)	)	PUNCT
ejpam-4652	64	19	.	.	PUNCT
ejpam-4652	65	1	thus	thus	ADV
ejpam-4652	65	2	,	,	PUNCT
ejpam-4652	65	3	rg(u	rg(u	X
ejpam-4652	65	4	/	/	SYM
ejpam-4652	65	5	s	s	X
ejpam-4652	65	6	)	)	PUNCT
ejpam-4652	65	7	̸=	̸=	PROPN
ejpam-4652	65	8	rg(v	rg(v	NOUN
ejpam-4652	65	9	/	/	SYM
ejpam-4652	65	10	s	s	NOUN
ejpam-4652	65	11	)	)	PUNCT
ejpam-4652	65	12	,	,	PUNCT
ejpam-4652	65	13	showing	show	VERB
ejpam-4652	65	14	that	that	SCONJ
ejpam-4652	65	15	w	w	NOUN
ejpam-4652	65	16	resolves	resolve	NOUN
ejpam-4652	65	17	u	u	NOUN
ejpam-4652	65	18	and	and	CCONJ
ejpam-4652	65	19	v.	v.	ADP
ejpam-4652	65	20	hence	hence	ADV
ejpam-4652	65	21	,	,	PUNCT
ejpam-4652	65	22	s	s	VERB
ejpam-4652	65	23	is	be	AUX
ejpam-4652	65	24	a	a	DET
ejpam-4652	65	25	resolving	resolving	NOUN
ejpam-4652	65	26	set	set	NOUN
ejpam-4652	65	27	of	of	ADP
ejpam-4652	65	28	g.	g.	PROPN
ejpam-4652	65	29	proposition	proposition	PROPN
ejpam-4652	65	30	2	2	NUM
ejpam-4652	65	31	.	.	PUNCT
ejpam-4652	66	1	every	every	DET
ejpam-4652	66	2	strong	strong	ADJ
ejpam-4652	66	3	resolving	resolve	VERB
ejpam-4652	66	4	dominating	dominating	NOUN
ejpam-4652	66	5	set	set	NOUN
ejpam-4652	66	6	of	of	ADP
ejpam-4652	66	7	a	a	DET
ejpam-4652	66	8	connected	connected	ADJ
ejpam-4652	66	9	graph	graph	NOUN
ejpam-4652	66	10	g	g	PROPN
ejpam-4652	66	11	is	be	AUX
ejpam-4652	66	12	a	a	DET
ejpam-4652	66	13	resolving	resolve	VERB
ejpam-4652	66	14	dominating	dominating	NOUN
ejpam-4652	66	15	set	set	NOUN
ejpam-4652	66	16	.	.	PUNCT
ejpam-4652	67	1	hence	hence	ADV
ejpam-4652	67	2	,	,	PUNCT
ejpam-4652	67	3	γr(g	γr(g	PROPN
ejpam-4652	67	4	)	)	PUNCT
ejpam-4652	67	5	≤	≤	NUM
ejpam-4652	67	6	γsr(g	γsr(g	NOUN
ejpam-4652	67	7	)	)	PUNCT
ejpam-4652	67	8	.	.	PUNCT
ejpam-4652	68	1	proof	proof	NOUN
ejpam-4652	68	2	:	:	PUNCT
ejpam-4652	68	3	follows	follow	VERB
ejpam-4652	68	4	from	from	ADP
ejpam-4652	68	5	proposition	proposition	NOUN
ejpam-4652	68	6	1	1	NUM
ejpam-4652	68	7	.	.	PUNCT
ejpam-4652	68	8	remark	remark	NOUN
ejpam-4652	68	9	5	5	NUM
ejpam-4652	68	10	.	.	PUNCT
ejpam-4652	69	1	the	the	DET
ejpam-4652	69	2	converse	converse	NOUN
ejpam-4652	69	3	of	of	ADP
ejpam-4652	69	4	proposition	proposition	NOUN
ejpam-4652	69	5	2	2	NUM
ejpam-4652	69	6	is	be	AUX
ejpam-4652	69	7	not	not	PART
ejpam-4652	69	8	true	true	ADJ
ejpam-4652	69	9	.	.	PUNCT
ejpam-4652	70	1	to	to	PART
ejpam-4652	70	2	see	see	VERB
ejpam-4652	70	3	this	this	PRON
ejpam-4652	70	4	,	,	PUNCT
ejpam-4652	70	5	consider	consider	VERB
ejpam-4652	70	6	the	the	DET
ejpam-4652	70	7	graph	graph	NOUN
ejpam-4652	70	8	in	in	ADP
ejpam-4652	70	9	figure	figure	NOUN
ejpam-4652	70	10	1	1	NUM
ejpam-4652	70	11	,	,	PUNCT
ejpam-4652	70	12	the	the	DET
ejpam-4652	70	13	set	set	NOUN
ejpam-4652	70	14	w	w	NOUN
ejpam-4652	70	15	=	=	PUNCT
ejpam-4652	70	16	{	{	PUNCT
ejpam-4652	70	17	v2	v2	PROPN
ejpam-4652	70	18	,	,	PUNCT
ejpam-4652	70	19	v5	v5	PROPN
ejpam-4652	70	20	}	}	PUNCT
ejpam-4652	70	21	is	be	AUX
ejpam-4652	70	22	a	a	DET
ejpam-4652	70	23	resolving	resolving	NOUN
ejpam-4652	70	24	set	set	VERB
ejpam-4652	70	25	since	since	SCONJ
ejpam-4652	70	26	the	the	DET
ejpam-4652	70	27	representation	representation	NOUN
ejpam-4652	70	28	of	of	ADP
ejpam-4652	70	29	each	each	DET
ejpam-4652	70	30	vertex	vertex	NOUN
ejpam-4652	70	31	in	in	ADP
ejpam-4652	70	32	g	g	NOUN
ejpam-4652	70	33	,	,	PUNCT
ejpam-4652	70	34	with	with	SCONJ
ejpam-4652	70	35	respect	respect	NOUN
ejpam-4652	70	36	to	to	ADP
ejpam-4652	70	37	w	w	NOUN
ejpam-4652	70	38	is	be	AUX
ejpam-4652	70	39	unique	unique	ADJ
ejpam-4652	70	40	.	.	PUNCT
ejpam-4652	71	1	these	these	DET
ejpam-4652	71	2	representations	representation	NOUN
ejpam-4652	71	3	are	be	AUX
ejpam-4652	71	4	as	as	SCONJ
ejpam-4652	71	5	follows	follow	VERB
ejpam-4652	71	6	:	:	PUNCT
ejpam-4652	71	7	rg(v1	rg(v1	VERB
ejpam-4652	71	8	/	/	SYM
ejpam-4652	71	9	w	w	NOUN
ejpam-4652	71	10	)	)	PUNCT
ejpam-4652	72	1	=	=	SYM
ejpam-4652	72	2	(	(	PUNCT
ejpam-4652	72	3	1	1	NUM
ejpam-4652	72	4	,	,	PUNCT
ejpam-4652	72	5	2	2	NUM
ejpam-4652	72	6	)	)	PUNCT
ejpam-4652	72	7	,	,	PUNCT
ejpam-4652	72	8	rg(v2	rg(v2	NOUN
ejpam-4652	72	9	/	/	SYM
ejpam-4652	72	10	w	w	NOUN
ejpam-4652	72	11	)	)	PUNCT
ejpam-4652	73	1	=	=	SYM
ejpam-4652	73	2	(	(	PUNCT
ejpam-4652	73	3	0	0	NUM
ejpam-4652	73	4	,	,	PUNCT
ejpam-4652	73	5	1	1	NUM
ejpam-4652	73	6	)	)	PUNCT
ejpam-4652	73	7	,	,	PUNCT
ejpam-4652	73	8	rg(v3	rg(v3	NOUN
ejpam-4652	73	9	/	/	SYM
ejpam-4652	73	10	w	w	PROPN
ejpam-4652	73	11	)	)	PUNCT
ejpam-4652	73	12	,	,	PUNCT
ejpam-4652	73	13	rg(v4	rg(v4	PROPN
ejpam-4652	73	14	/	/	SYM
ejpam-4652	73	15	w	w	NOUN
ejpam-4652	73	16	)	)	PUNCT
ejpam-4652	74	1	=	=	SYM
ejpam-4652	74	2	(	(	PUNCT
ejpam-4652	74	3	2	2	NUM
ejpam-4652	74	4	,	,	PUNCT
ejpam-4652	74	5	1	1	NUM
ejpam-4652	74	6	)	)	PUNCT
ejpam-4652	74	7	and	and	CCONJ
ejpam-4652	74	8	rg(v5	rg(v5	PROPN
ejpam-4652	74	9	/	/	SYM
ejpam-4652	74	10	w	w	NOUN
ejpam-4652	74	11	)	)	PUNCT
ejpam-4652	74	12	=	=	SYM
ejpam-4652	74	13	(	(	PUNCT
ejpam-4652	74	14	1	1	NUM
ejpam-4652	74	15	,	,	PUNCT
ejpam-4652	74	16	0	0	NUM
ejpam-4652	74	17	)	)	PUNCT
ejpam-4652	74	18	.	.	PUNCT
ejpam-4652	75	1	however	however	ADV
ejpam-4652	75	2	,	,	PUNCT
ejpam-4652	75	3	none	none	NOUN
ejpam-4652	75	4	among	among	ADP
ejpam-4652	75	5	the	the	DET
ejpam-4652	75	6	vertices	vertex	NOUN
ejpam-4652	75	7	in	in	ADP
ejpam-4652	75	8	w	w	NOUN
ejpam-4652	75	9	strongly	strongly	ADV
ejpam-4652	75	10	resolves	resolve	VERB
ejpam-4652	75	11	the	the	DET
ejpam-4652	75	12	vertices	vertex	NOUN
ejpam-4652	75	13	v1	v1	NOUN
ejpam-4652	75	14	and	and	CCONJ
ejpam-4652	75	15	v3	v3	PROPN
ejpam-4652	75	16	.	.	PUNCT
ejpam-4652	76	1	thus	thus	ADV
ejpam-4652	76	2	,	,	PUNCT
ejpam-4652	76	3	w	w	PROPN
ejpam-4652	76	4	is	be	AUX
ejpam-4652	76	5	a	a	DET
ejpam-4652	76	6	resolving	resolving	NOUN
ejpam-4652	76	7	set	set	NOUN
ejpam-4652	76	8	but	but	CCONJ
ejpam-4652	76	9	it	it	PRON
ejpam-4652	76	10	is	be	AUX
ejpam-4652	76	11	not	not	PART
ejpam-4652	76	12	a	a	DET
ejpam-4652	76	13	strong	strong	ADJ
ejpam-4652	76	14	resolving	resolving	NOUN
ejpam-4652	76	15	set	set	NOUN
ejpam-4652	76	16	of	of	ADP
ejpam-4652	76	17	g.	g.	PROPN
ejpam-4652	76	18	in	in	ADP
ejpam-4652	76	19	the	the	DET
ejpam-4652	76	20	same	same	ADJ
ejpam-4652	76	21	graph	graph	NOUN
ejpam-4652	76	22	,	,	PUNCT
ejpam-4652	76	23	it	it	PRON
ejpam-4652	76	24	is	be	AUX
ejpam-4652	76	25	easy	easy	ADJ
ejpam-4652	76	26	to	to	PART
ejpam-4652	76	27	verify	verify	VERB
ejpam-4652	76	28	that	that	SCONJ
ejpam-4652	76	29	the	the	DET
ejpam-4652	76	30	set	set	NOUN
ejpam-4652	76	31	{	{	PUNCT
ejpam-4652	76	32	v1	v1	NOUN
ejpam-4652	76	33	,	,	PUNCT
ejpam-4652	76	34	v3	v3	PROPN
ejpam-4652	76	35	}	}	PUNCT
ejpam-4652	76	36	is	be	AUX
ejpam-4652	76	37	a	a	DET
ejpam-4652	76	38	strong	strong	ADJ
ejpam-4652	76	39	resolving	resolving	NOUN
ejpam-4652	76	40	set	set	NOUN
ejpam-4652	76	41	of	of	ADP
ejpam-4652	76	42	g	g	NOUN
ejpam-4652	76	43	,	,	PUNCT
ejpam-4652	76	44	hence	hence	ADV
ejpam-4652	76	45	a	a	DET
ejpam-4652	76	46	resolving	resolving	NOUN
ejpam-4652	76	47	set	set	VERB
ejpam-4652	76	48	as	as	ADV
ejpam-4652	76	49	well	well	ADV
ejpam-4652	76	50	.	.	PUNCT
ejpam-4652	77	1	figure	figure	NOUN
ejpam-4652	77	2	1	1	NUM
ejpam-4652	77	3	.	.	PUNCT
ejpam-4652	78	1	a	a	DET
ejpam-4652	78	2	strong	strong	ADJ
ejpam-4652	78	3	resolving	resolving	NOUN
ejpam-4652	78	4	set	set	VERB
ejpam-4652	78	5	{	{	PUNCT
ejpam-4652	78	6	v1	v1	NOUN
ejpam-4652	78	7	,	,	PUNCT
ejpam-4652	78	8	v3	v3	PROPN
ejpam-4652	78	9	}	}	PUNCT
ejpam-4652	78	10	of	of	ADP
ejpam-4652	78	11	g	g	PROPN
ejpam-4652	78	12	g.	g.	PROPN
ejpam-4652	78	13	monsanto	monsanto	PROPN
ejpam-4652	78	14	,	,	PUNCT
ejpam-4652	78	15	p.	p.	PROPN
ejpam-4652	78	16	acal	acal	PROPN
ejpam-4652	78	17	,	,	PUNCT
ejpam-4652	78	18	h.	h.	PROPN
ejpam-4652	78	19	rara	rara	PROPN
ejpam-4652	78	20	/	/	SYM
ejpam-4652	78	21	eur	eur	PROPN
ejpam-4652	78	22	.	.	PUNCT
ejpam-4652	79	1	j.	j.	PROPN
ejpam-4652	79	2	pure	pure	PROPN
ejpam-4652	79	3	appl	appl	PROPN
ejpam-4652	79	4	.	.	PROPN
ejpam-4652	79	5	math	math	PROPN
ejpam-4652	79	6	,	,	PUNCT
ejpam-4652	79	7	16	16	NUM
ejpam-4652	79	8	(	(	PUNCT
ejpam-4652	79	9	1	1	NUM
ejpam-4652	79	10	)	)	PUNCT
ejpam-4652	79	11	(	(	PUNCT
ejpam-4652	79	12	2023	2023	NUM
ejpam-4652	79	13	)	)	PUNCT
ejpam-4652	79	14	,	,	PUNCT
ejpam-4652	79	15	363	363	NUM
ejpam-4652	79	16	-	-	SYM
ejpam-4652	79	17	372	372	NUM
ejpam-4652	79	18	366	366	NUM
ejpam-4652	79	19	proposition	proposition	NOUN
ejpam-4652	79	20	3	3	NUM
ejpam-4652	79	21	.	.	PUNCT
ejpam-4652	80	1	[	[	X
ejpam-4652	80	2	1	1	X
ejpam-4652	80	3	]	]	PUNCT
ejpam-4652	80	4	let	let	VERB
ejpam-4652	80	5	g	g	PRON
ejpam-4652	80	6	be	be	AUX
ejpam-4652	80	7	a	a	DET
ejpam-4652	80	8	connected	connected	ADJ
ejpam-4652	80	9	graph	graph	NOUN
ejpam-4652	80	10	of	of	ADP
ejpam-4652	80	11	order	order	NOUN
ejpam-4652	80	12	n	n	PRON
ejpam-4652	80	13	≥	≥	NOUN
ejpam-4652	80	14	2	2	NUM
ejpam-4652	80	15	.	.	PUNCT
ejpam-4652	81	1	then	then	ADV
ejpam-4652	81	2	,	,	PUNCT
ejpam-4652	81	3	(	(	PUNCT
ejpam-4652	81	4	i	i	NOUN
ejpam-4652	81	5	)	)	PUNCT
ejpam-4652	81	6	γsr(pn	γsr(pn	PROPN
ejpam-4652	81	7	)	)	PUNCT
ejpam-4652	81	8	=	=	PUNCT
ejpam-4652	82	1	⌈	⌈	SYM
ejpam-4652	82	2	n+1	n+1	PROPN
ejpam-4652	82	3	3	3	NUM
ejpam-4652	82	4	⌉	⌉	X
ejpam-4652	82	5	(	(	PUNCT
ejpam-4652	82	6	ii	ii	NOUN
ejpam-4652	82	7	)	)	PUNCT
ejpam-4652	82	8	γsr(kn	γsr(kn	NOUN
ejpam-4652	82	9	)	)	PUNCT
ejpam-4652	83	1	=	=	PUNCT
ejpam-4652	83	2	n−	n−	NOUN
ejpam-4652	83	3	1	1	NUM
ejpam-4652	83	4	(	(	PUNCT
ejpam-4652	83	5	iii	iii	NOUN
ejpam-4652	83	6	)	)	PUNCT
ejpam-4652	83	7	γsr(cn	γsr(cn	NOUN
ejpam-4652	83	8	)	)	PUNCT
ejpam-4652	83	9	=	=	PUNCT
ejpam-4652	83	10			NUM
ejpam-4652	83	11	2	2	NUM
ejpam-4652	83	12	,	,	PUNCT
ejpam-4652	83	13	if	if	SCONJ
ejpam-4652	83	14	n	n	NOUN
ejpam-4652	83	15	=	=	SYM
ejpam-4652	83	16	3	3	NUM
ejpam-4652	83	17	n−	n−	NOUN
ejpam-4652	83	18	2	2	NUM
ejpam-4652	83	19	,	,	PUNCT
ejpam-4652	83	20	if	if	SCONJ
ejpam-4652	83	21	n	n	PROPN
ejpam-4652	83	22	>	>	X
ejpam-4652	83	23	3	3	NUM
ejpam-4652	83	24	and	and	CCONJ
ejpam-4652	83	25	n	n	PRON
ejpam-4652	83	26	is	be	AUX
ejpam-4652	83	27	odd	odd	ADJ
ejpam-4652	83	28	n	n	PRON
ejpam-4652	83	29	2	2	NUM
ejpam-4652	83	30	,	,	PUNCT
ejpam-4652	83	31	if	if	SCONJ
ejpam-4652	83	32	n	n	PROPN
ejpam-4652	83	33	>	>	X
ejpam-4652	83	34	3	3	NUM
ejpam-4652	83	35	and	and	CCONJ
ejpam-4652	83	36	n	n	PRON
ejpam-4652	83	37	is	be	AUX
ejpam-4652	83	38	even	even	ADV
ejpam-4652	83	39	.	.	PUNCT
ejpam-4652	84	1	remark	remark	PROPN
ejpam-4652	84	2	6	6	NUM
ejpam-4652	84	3	.	.	PUNCT
ejpam-4652	85	1	let	let	VERB
ejpam-4652	85	2	g	g	PRON
ejpam-4652	85	3	be	be	AUX
ejpam-4652	85	4	a	a	DET
ejpam-4652	85	5	connected	connected	ADJ
ejpam-4652	85	6	graph	graph	NOUN
ejpam-4652	85	7	(	(	PUNCT
ejpam-4652	85	8	i	i	NOUN
ejpam-4652	85	9	)	)	PUNCT
ejpam-4652	85	10	a	a	DET
ejpam-4652	85	11	set	set	NOUN
ejpam-4652	85	12	{	{	PUNCT
ejpam-4652	85	13	u	u	NOUN
ejpam-4652	85	14	}	}	PUNCT
ejpam-4652	85	15	⊂	⊂	PROPN
ejpam-4652	85	16	v	v	X
ejpam-4652	85	17	(	(	PUNCT
ejpam-4652	85	18	g	g	NOUN
ejpam-4652	85	19	)	)	PUNCT
ejpam-4652	85	20	induces	induce	VERB
ejpam-4652	85	21	a	a	DET
ejpam-4652	85	22	dominated	dominate	VERB
ejpam-4652	85	23	superclique	superclique	NOUN
ejpam-4652	85	24	of	of	ADP
ejpam-4652	85	25	g.	g.	PROPN
ejpam-4652	85	26	(	(	PUNCT
ejpam-4652	85	27	ii	ii	PROPN
ejpam-4652	85	28	)	)	PUNCT
ejpam-4652	85	29	a	a	DET
ejpam-4652	85	30	clique	clique	NOUN
ejpam-4652	85	31	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	85	32	of	of	ADP
ejpam-4652	85	33	g	g	PROPN
ejpam-4652	85	34	is	be	AUX
ejpam-4652	85	35	a	a	DET
ejpam-4652	85	36	dominated	dominate	VERB
ejpam-4652	85	37	superclique	superclique	NOUN
ejpam-4652	85	38	of	of	ADP
ejpam-4652	85	39	g	g	PROPN
ejpam-4652	85	40	if	if	SCONJ
ejpam-4652	85	41	ng[u	ng[u	PROPN
ejpam-4652	85	42	]	]	PUNCT
ejpam-4652	85	43	̸=	̸=	PROPN
ejpam-4652	85	44	ng[v	ng[v	X
ejpam-4652	85	45	]	]	PUNCT
ejpam-4652	85	46	for	for	ADP
ejpam-4652	85	47	every	every	DET
ejpam-4652	85	48	pair	pair	NOUN
ejpam-4652	85	49	of	of	ADP
ejpam-4652	85	50	distinct	distinct	ADJ
ejpam-4652	85	51	vertices	vertex	NOUN
ejpam-4652	85	52	u	u	NOUN
ejpam-4652	85	53	,	,	PUNCT
ejpam-4652	85	54	v	v	NOUN
ejpam-4652	85	55	∈	∈	NOUN
ejpam-4652	85	56	c	c	NOUN
ejpam-4652	85	57	and	and	CCONJ
ejpam-4652	85	58	v	v	NOUN
ejpam-4652	85	59	(	(	PUNCT
ejpam-4652	85	60	g	g	NOUN
ejpam-4652	85	61	)	)	PUNCT
ejpam-4652	85	62	\	\	PUNCT
ejpam-4652	86	1	c	c	NOUN
ejpam-4652	86	2	is	be	AUX
ejpam-4652	86	3	a	a	DET
ejpam-4652	86	4	dominating	dominating	NOUN
ejpam-4652	86	5	set	set	NOUN
ejpam-4652	86	6	of	of	ADP
ejpam-4652	86	7	g.	g.	PROPN
ejpam-4652	86	8	(	(	PUNCT
ejpam-4652	86	9	iii	iii	NOUN
ejpam-4652	86	10	)	)	PUNCT
ejpam-4652	86	11	every	every	DET
ejpam-4652	86	12	dominated	dominate	VERB
ejpam-4652	86	13	superclique	superclique	NOUN
ejpam-4652	86	14	of	of	ADP
ejpam-4652	86	15	g	g	PROPN
ejpam-4652	86	16	is	be	AUX
ejpam-4652	86	17	a	a	DET
ejpam-4652	86	18	superclique	superclique	NOUN
ejpam-4652	86	19	of	of	ADP
ejpam-4652	86	20	g.	g.	PROPN
ejpam-4652	86	21	example	example	NOUN
ejpam-4652	87	1	2	2	X
ejpam-4652	87	2	.	.	PUNCT
ejpam-4652	88	1	let	let	VERB
ejpam-4652	88	2	n	n	PRON
ejpam-4652	88	3	be	be	AUX
ejpam-4652	88	4	a	a	DET
ejpam-4652	88	5	positive	positive	ADJ
ejpam-4652	88	6	integer	integer	NOUN
ejpam-4652	88	7	.	.	PUNCT
ejpam-4652	89	1	(	(	PUNCT
ejpam-4652	89	2	i	i	NOUN
ejpam-4652	89	3	)	)	PUNCT
ejpam-4652	89	4	ωds(kn	ωds(kn	NUM
ejpam-4652	89	5	)	)	PUNCT
ejpam-4652	89	6	=	=	SYM
ejpam-4652	89	7	ωs(kn	ωs(kn	NOUN
ejpam-4652	89	8	)	)	PUNCT
ejpam-4652	89	9	=	=	SYM
ejpam-4652	90	1	1	1	X
ejpam-4652	90	2	.	.	PUNCT
ejpam-4652	90	3	(	(	PUNCT
ejpam-4652	90	4	ii	ii	NOUN
ejpam-4652	90	5	)	)	PUNCT
ejpam-4652	90	6	if	if	SCONJ
ejpam-4652	90	7	pn	pn	PROPN
ejpam-4652	90	8	=	=	PUNCT
ejpam-4652	90	9	[	[	X
ejpam-4652	90	10	v1	v1	NOUN
ejpam-4652	90	11	,	,	PUNCT
ejpam-4652	90	12	v2	v2	NOUN
ejpam-4652	90	13	,	,	PUNCT
ejpam-4652	90	14	.	.	PUNCT
ejpam-4652	90	15	.	.	PUNCT
ejpam-4652	90	16	.	.	PUNCT
ejpam-4652	91	1	,	,	PUNCT
ejpam-4652	91	2	vn	vn	X
ejpam-4652	91	3	]	]	PUNCT
ejpam-4652	91	4	for	for	ADP
ejpam-4652	91	5	n	n	X
ejpam-4652	91	6	≥	≥	NOUN
ejpam-4652	91	7	4	4	NUM
ejpam-4652	91	8	,	,	PUNCT
ejpam-4652	91	9	then	then	ADV
ejpam-4652	91	10	the	the	DET
ejpam-4652	91	11	dominated	dominate	VERB
ejpam-4652	91	12	supercliques	superclique	NOUN
ejpam-4652	91	13	of	of	ADP
ejpam-4652	91	14	pn	pn	PROPN
ejpam-4652	91	15	are	be	AUX
ejpam-4652	91	16	induced	induce	VERB
ejpam-4652	91	17	from	from	ADP
ejpam-4652	91	18	the	the	DET
ejpam-4652	91	19	singletons	singleton	NOUN
ejpam-4652	91	20	{	{	PUNCT
ejpam-4652	91	21	vj	vj	INTJ
ejpam-4652	91	22	}	}	PUNCT
ejpam-4652	91	23	for	for	ADP
ejpam-4652	91	24	all	all	DET
ejpam-4652	91	25	j	j	NOUN
ejpam-4652	91	26	=	=	SYM
ejpam-4652	91	27	1	1	NUM
ejpam-4652	91	28	,	,	PUNCT
ejpam-4652	91	29	2	2	NUM
ejpam-4652	91	30	,	,	PUNCT
ejpam-4652	91	31	.	.	PUNCT
ejpam-4652	91	32	.	.	PUNCT
ejpam-4652	92	1	.	.	PUNCT
ejpam-4652	93	1	,	,	PUNCT
ejpam-4652	93	2	n	n	PROPN
ejpam-4652	93	3	and	and	CCONJ
ejpam-4652	93	4	{	{	PUNCT
ejpam-4652	93	5	vi	vi	PROPN
ejpam-4652	93	6	,	,	PUNCT
ejpam-4652	93	7	vi+1	vi+1	PRON
ejpam-4652	93	8	}	}	PUNCT
ejpam-4652	93	9	for	for	ADP
ejpam-4652	93	10	i	i	PROPN
ejpam-4652	93	11	=	=	SYM
ejpam-4652	93	12	2	2	NUM
ejpam-4652	93	13	,	,	PUNCT
ejpam-4652	93	14	3	3	NUM
ejpam-4652	93	15	,	,	PUNCT
ejpam-4652	93	16	.	.	PUNCT
ejpam-4652	93	17	.	.	PUNCT
ejpam-4652	94	1	.	.	PUNCT
ejpam-4652	95	1	,	,	PUNCT
ejpam-4652	95	2	n−	n−	NOUN
ejpam-4652	95	3	2	2	NUM
ejpam-4652	95	4	.	.	PUNCT
ejpam-4652	95	5	(	(	PUNCT
ejpam-4652	95	6	iii	iii	X
ejpam-4652	95	7	)	)	PUNCT
ejpam-4652	95	8	the	the	DET
ejpam-4652	95	9	dominated	dominate	VERB
ejpam-4652	95	10	supercliques	superclique	NOUN
ejpam-4652	95	11	of	of	ADP
ejpam-4652	95	12	a	a	DET
ejpam-4652	95	13	cycle	cycle	NOUN
ejpam-4652	95	14	cn	cn	NOUN
ejpam-4652	95	15	for	for	ADP
ejpam-4652	95	16	n	n	X
ejpam-4652	95	17	≥	≥	NUM
ejpam-4652	95	18	4	4	NUM
ejpam-4652	95	19	,	,	PUNCT
ejpam-4652	95	20	are	be	AUX
ejpam-4652	95	21	⟨{uj}⟩	⟨{uj}⟩	PROPN
ejpam-4652	95	22	and	and	CCONJ
ejpam-4652	95	23	induced	induce	VERB
ejpam-4652	95	24	from	from	ADP
ejpam-4652	95	25	{	{	PUNCT
ejpam-4652	95	26	ui	ui	PROPN
ejpam-4652	95	27	,	,	PUNCT
ejpam-4652	95	28	uj	uj	PROPN
ejpam-4652	95	29	}	}	PUNCT
ejpam-4652	95	30	⊆	⊆	NUM
ejpam-4652	95	31	v	v	NOUN
ejpam-4652	95	32	(	(	PUNCT
ejpam-4652	95	33	cn	cn	PROPN
ejpam-4652	95	34	)	)	PUNCT
ejpam-4652	95	35	where	where	SCONJ
ejpam-4652	95	36	uiuj	uiuj	ADJ
ejpam-4652	95	37	∈	∈	PROPN
ejpam-4652	95	38	e(cn	e(cn	NOUN
ejpam-4652	95	39	)	)	PUNCT
ejpam-4652	95	40	.	.	PUNCT
ejpam-4652	96	1	(	(	PUNCT
ejpam-4652	96	2	iv	iv	X
ejpam-4652	96	3	)	)	PUNCT
ejpam-4652	96	4	the	the	DET
ejpam-4652	96	5	dominated	dominate	VERB
ejpam-4652	96	6	supercliques	superclique	NOUN
ejpam-4652	96	7	of	of	ADP
ejpam-4652	96	8	a	a	DET
ejpam-4652	96	9	complete	complete	ADJ
ejpam-4652	96	10	bipartite	bipartite	NOUN
ejpam-4652	96	11	graph	graph	NOUN
ejpam-4652	96	12	km	km	PROPN
ejpam-4652	96	13	,	,	PUNCT
ejpam-4652	96	14	n	n	PRON
ejpam-4652	96	15	are	be	AUX
ejpam-4652	96	16	the	the	DET
ejpam-4652	96	17	singleton	singleton	PROPN
ejpam-4652	96	18	sets	set	NOUN
ejpam-4652	96	19	{	{	PUNCT
ejpam-4652	96	20	v	v	NOUN
ejpam-4652	96	21	}	}	PUNCT
ejpam-4652	96	22	⊂	⊂	PROPN
ejpam-4652	96	23	v	v	X
ejpam-4652	96	24	(	(	PUNCT
ejpam-4652	96	25	km	km	PROPN
ejpam-4652	96	26	,	,	PUNCT
ejpam-4652	96	27	n	n	CCONJ
ejpam-4652	96	28	)	)	PUNCT
ejpam-4652	96	29	and	and	CCONJ
ejpam-4652	96	30	n	n	CCONJ
ejpam-4652	96	31	̸=	̸=	PROPN
ejpam-4652	96	32	1	1	NUM
ejpam-4652	96	33	,	,	PUNCT
ejpam-4652	96	34	m	m	VERB
ejpam-4652	96	35	̸=	̸=	PROPN
ejpam-4652	96	36	1	1	NUM
ejpam-4652	96	37	.	.	PUNCT
ejpam-4652	97	1	(	(	PUNCT
ejpam-4652	97	2	v	v	NOUN
ejpam-4652	97	3	)	)	PUNCT
ejpam-4652	97	4	the	the	DET
ejpam-4652	97	5	maximum	maximum	ADJ
ejpam-4652	97	6	dominated	dominate	VERB
ejpam-4652	97	7	supercliques	superclique	NOUN
ejpam-4652	97	8	of	of	ADP
ejpam-4652	97	9	a	a	DET
ejpam-4652	97	10	complete	complete	ADJ
ejpam-4652	97	11	bipartite	bipartite	NOUN
ejpam-4652	97	12	graph	graph	NOUN
ejpam-4652	97	13	km	km	PROPN
ejpam-4652	97	14	,	,	PUNCT
ejpam-4652	97	15	n	n	PRON
ejpam-4652	97	16	are	be	AUX
ejpam-4652	97	17	induced	induce	VERB
ejpam-4652	97	18	from	from	ADP
ejpam-4652	97	19	the	the	DET
ejpam-4652	97	20	sets	set	NOUN
ejpam-4652	97	21	{	{	PUNCT
ejpam-4652	97	22	xi	xi	PROPN
ejpam-4652	97	23	,	,	PUNCT
ejpam-4652	97	24	xj	xj	ADJ
ejpam-4652	97	25	}	}	PUNCT
ejpam-4652	97	26	⊆	⊆	NUM
ejpam-4652	97	27	v	v	NOUN
ejpam-4652	97	28	(	(	PUNCT
ejpam-4652	97	29	km	km	PROPN
ejpam-4652	97	30	,	,	PUNCT
ejpam-4652	97	31	n	n	CCONJ
ejpam-4652	97	32	)	)	PUNCT
ejpam-4652	97	33	where	where	SCONJ
ejpam-4652	97	34	xixj	xixj	PROPN
ejpam-4652	97	35	∈	∈	PROPN
ejpam-4652	97	36	e(km	e(km	PROPN
ejpam-4652	97	37	,	,	PUNCT
ejpam-4652	97	38	n	n	CCONJ
ejpam-4652	97	39	)	)	PUNCT
ejpam-4652	97	40	and	and	CCONJ
ejpam-4652	97	41	n	n	CCONJ
ejpam-4652	97	42	̸=	̸=	PROPN
ejpam-4652	97	43	1	1	NUM
ejpam-4652	97	44	,	,	PUNCT
ejpam-4652	97	45	m	m	VERB
ejpam-4652	97	46	̸=	̸=	PROPN
ejpam-4652	97	47	1	1	NUM
ejpam-4652	97	48	.	.	PUNCT
ejpam-4652	98	1	theorem	theorem	NOUN
ejpam-4652	98	2	1	1	NUM
ejpam-4652	98	3	.	.	PUNCT
ejpam-4652	99	1	let	let	VERB
ejpam-4652	99	2	g	g	PRON
ejpam-4652	99	3	be	be	AUX
ejpam-4652	99	4	a	a	DET
ejpam-4652	99	5	connected	connected	ADJ
ejpam-4652	99	6	graph	graph	NOUN
ejpam-4652	99	7	of	of	ADP
ejpam-4652	99	8	order	order	NOUN
ejpam-4652	99	9	n.	n.	NOUN
ejpam-4652	99	10	then	then	ADV
ejpam-4652	99	11	ωds(g	ωds(g	PROPN
ejpam-4652	99	12	)	)	PUNCT
ejpam-4652	99	13	=	=	SYM
ejpam-4652	99	14	1	1	NUM
ejpam-4652	99	15	if	if	SCONJ
ejpam-4652	99	16	and	and	CCONJ
ejpam-4652	99	17	only	only	ADV
ejpam-4652	99	18	if	if	SCONJ
ejpam-4652	99	19	γ(g	γ(g	PROPN
ejpam-4652	99	20	)	)	PUNCT
ejpam-4652	100	1	=	=	SYM
ejpam-4652	100	2	kn	kn	NOUN
ejpam-4652	100	3	or	or	CCONJ
ejpam-4652	100	4	g	g	PROPN
ejpam-4652	100	5	=	=	PUNCT
ejpam-4652	100	6	k1,n−1	k1,n−1	ADJ
ejpam-4652	100	7	.	.	PUNCT
ejpam-4652	101	1	proof	proof	NOUN
ejpam-4652	101	2	:	:	PUNCT
ejpam-4652	101	3	suppose	suppose	VERB
ejpam-4652	101	4	ωds(g	ωds(g	X
ejpam-4652	101	5	)	)	PUNCT
ejpam-4652	101	6	=	=	SYM
ejpam-4652	102	1	1	1	X
ejpam-4652	102	2	.	.	PUNCT
ejpam-4652	103	1	if	if	SCONJ
ejpam-4652	103	2	n	n	NOUN
ejpam-4652	103	3	=	=	SYM
ejpam-4652	103	4	1	1	NUM
ejpam-4652	103	5	or	or	CCONJ
ejpam-4652	103	6	n	n	NOUN
ejpam-4652	103	7	=	=	SYM
ejpam-4652	103	8	2	2	NUM
ejpam-4652	103	9	,	,	PUNCT
ejpam-4652	103	10	then	then	ADV
ejpam-4652	103	11	g	g	PROPN
ejpam-4652	103	12	=	=	PROPN
ejpam-4652	103	13	kn	kn	PROPN
ejpam-4652	103	14	.	.	PUNCT
ejpam-4652	104	1	if	if	SCONJ
ejpam-4652	104	2	n	n	NUM
ejpam-4652	104	3	=	=	SYM
ejpam-4652	104	4	3	3	NUM
ejpam-4652	104	5	,	,	PUNCT
ejpam-4652	104	6	then	then	ADV
ejpam-4652	104	7	g	g	NOUN
ejpam-4652	104	8	=	=	PUNCT
ejpam-4652	104	9	k3	k3	X
ejpam-4652	104	10	or	or	CCONJ
ejpam-4652	104	11	g	g	PROPN
ejpam-4652	104	12	=	=	SYM
ejpam-4652	104	13	k1,2	k1,2	PROPN
ejpam-4652	104	14	.	.	PUNCT
ejpam-4652	104	15	suppose	suppose	VERB
ejpam-4652	104	16	n	n	PRON
ejpam-4652	104	17	≥	≥	X
ejpam-4652	104	18	4	4	NUM
ejpam-4652	104	19	and	and	CCONJ
ejpam-4652	104	20	g	g	PROPN
ejpam-4652	104	21	̸=	̸=	PROPN
ejpam-4652	104	22	kn	kn	PROPN
ejpam-4652	104	23	.	.	PUNCT
ejpam-4652	105	1	then	then	ADV
ejpam-4652	105	2	there	there	PRON
ejpam-4652	105	3	exist	exist	VERB
ejpam-4652	105	4	distinct	distinct	ADJ
ejpam-4652	105	5	vertices	vertex	NOUN
ejpam-4652	105	6	a	a	PRON
ejpam-4652	105	7	and	and	CCONJ
ejpam-4652	105	8	b	b	NOUN
ejpam-4652	105	9	of	of	ADP
ejpam-4652	105	10	g	g	NOUN
ejpam-4652	105	11	such	such	ADJ
ejpam-4652	105	12	that	that	PRON
ejpam-4652	105	13	dg(a	dg(a	PROPN
ejpam-4652	105	14	,	,	PUNCT
ejpam-4652	105	15	b	b	X
ejpam-4652	105	16	)	)	PUNCT
ejpam-4652	105	17	=	=	SYM
ejpam-4652	105	18	2	2	X
ejpam-4652	105	19	.	.	X
ejpam-4652	105	20	let	let	VERB
ejpam-4652	105	21	v	v	NUM
ejpam-4652	105	22	∈	∈	PROPN
ejpam-4652	105	23	ng(a	ng(a	NOUN
ejpam-4652	105	24	)	)	PUNCT
ejpam-4652	105	25	∩	∩	NOUN
ejpam-4652	105	26	ng(b	ng(b	NOUN
ejpam-4652	105	27	)	)	PUNCT
ejpam-4652	105	28	.	.	PUNCT
ejpam-4652	106	1	since	since	SCONJ
ejpam-4652	106	2	{	{	PUNCT
ejpam-4652	106	3	a	a	DET
ejpam-4652	106	4	,	,	PUNCT
ejpam-4652	106	5	v	v	NOUN
ejpam-4652	106	6	}	}	PUNCT
ejpam-4652	106	7	is	be	AUX
ejpam-4652	106	8	a	a	DET
ejpam-4652	106	9	superclique	superclique	ADJ
ejpam-4652	106	10	and	and	CCONJ
ejpam-4652	106	11	ωds(g	ωds(g	NUM
ejpam-4652	106	12	)	)	PUNCT
ejpam-4652	106	13	=	=	SYM
ejpam-4652	106	14	1	1	NUM
ejpam-4652	106	15	,	,	PUNCT
ejpam-4652	106	16	|ng(a)|	|ng(a)|	PROPN
ejpam-4652	106	17	=	=	SYM
ejpam-4652	106	18	1	1	X
ejpam-4652	106	19	.	.	PUNCT
ejpam-4652	106	20	similarly	similarly	ADV
ejpam-4652	106	21	,	,	PUNCT
ejpam-4652	106	22	|ng(b)|	|ng(b)|	NOUN
ejpam-4652	106	23	=	=	SYM
ejpam-4652	106	24	1	1	X
ejpam-4652	106	25	.	.	PUNCT
ejpam-4652	106	26	suppose	suppose	VERB
ejpam-4652	106	27	there	there	PRON
ejpam-4652	106	28	exists	exist	VERB
ejpam-4652	106	29	y	y	PROPN
ejpam-4652	106	30	∈	∈	PROPN
ejpam-4652	106	31	v	v	PROPN
ejpam-4652	106	32	(	(	PUNCT
ejpam-4652	106	33	g)\ng(v	g)\ng(v	PROPN
ejpam-4652	106	34	)	)	PUNCT
ejpam-4652	106	35	.	.	PUNCT
ejpam-4652	107	1	we	we	PRON
ejpam-4652	107	2	may	may	AUX
ejpam-4652	107	3	assume	assume	VERB
ejpam-4652	107	4	that	that	SCONJ
ejpam-4652	107	5	dg(y	dg(y	ADJ
ejpam-4652	107	6	,	,	PUNCT
ejpam-4652	107	7	v	v	NOUN
ejpam-4652	107	8	)	)	PUNCT
ejpam-4652	107	9	=	=	SYM
ejpam-4652	107	10	2	2	X
ejpam-4652	107	11	.	.	X
ejpam-4652	107	12	let	let	VERB
ejpam-4652	107	13	z	z	NOUN
ejpam-4652	107	14	∈	∈	PROPN
ejpam-4652	107	15	ng(y	ng(y	NOUN
ejpam-4652	107	16	)	)	PUNCT
ejpam-4652	107	17	∩	∩	NOUN
ejpam-4652	107	18	ng(v	ng(v	NUM
ejpam-4652	107	19	)	)	PUNCT
ejpam-4652	107	20	.	.	PUNCT
ejpam-4652	108	1	then	then	ADV
ejpam-4652	108	2	{	{	PUNCT
ejpam-4652	108	3	z	z	NOUN
ejpam-4652	108	4	,	,	PUNCT
ejpam-4652	108	5	v	v	NOUN
ejpam-4652	108	6	}	}	PUNCT
ejpam-4652	108	7	is	be	AUX
ejpam-4652	108	8	a	a	DET
ejpam-4652	108	9	dominated	dominate	VERB
ejpam-4652	108	10	superclique	superclique	NOUN
ejpam-4652	108	11	of	of	ADP
ejpam-4652	108	12	g	g	NOUN
ejpam-4652	108	13	,	,	PUNCT
ejpam-4652	108	14	contrary	contrary	ADV
ejpam-4652	108	15	to	to	ADP
ejpam-4652	108	16	the	the	DET
ejpam-4652	108	17	assumption	assumption	NOUN
ejpam-4652	108	18	that	that	SCONJ
ejpam-4652	108	19	ωds(g	ωds(g	X
ejpam-4652	108	20	)	)	PUNCT
ejpam-4652	108	21	=	=	SYM
ejpam-4652	109	1	1	1	X
ejpam-4652	109	2	.	.	PUNCT
ejpam-4652	110	1	hence	hence	ADV
ejpam-4652	110	2	,	,	PUNCT
ejpam-4652	110	3	x	x	SYM
ejpam-4652	110	4	∈	∈	NOUN
ejpam-4652	110	5	ng(v	ng(v	PUNCT
ejpam-4652	110	6	)	)	PUNCT
ejpam-4652	110	7	for	for	ADP
ejpam-4652	110	8	all	all	PRON
ejpam-4652	110	9	x	x	SYM
ejpam-4652	110	10	∈	∈	PROPN
ejpam-4652	110	11	v	v	NOUN
ejpam-4652	110	12	(	(	PUNCT
ejpam-4652	110	13	g	g	NOUN
ejpam-4652	110	14	)	)	PUNCT
ejpam-4652	110	15	\	\	NOUN
ejpam-4652	110	16	{	{	PUNCT
ejpam-4652	110	17	v	v	NOUN
ejpam-4652	110	18	}	}	PUNCT
ejpam-4652	110	19	.	.	PUNCT
ejpam-4652	111	1	also	also	ADV
ejpam-4652	111	2	,	,	PUNCT
ejpam-4652	111	3	for	for	ADP
ejpam-4652	111	4	any	any	DET
ejpam-4652	111	5	distinct	distinct	ADJ
ejpam-4652	111	6	vertices	vertex	NOUN
ejpam-4652	111	7	x	x	X
ejpam-4652	111	8	,	,	PUNCT
ejpam-4652	111	9	y	y	PROPN
ejpam-4652	111	10	∈	∈	PROPN
ejpam-4652	111	11	v	v	ADP
ejpam-4652	111	12	(	(	PUNCT
ejpam-4652	111	13	g	g	NOUN
ejpam-4652	111	14	)	)	PUNCT
ejpam-4652	111	15	\	\	NOUN
ejpam-4652	111	16	{	{	PUNCT
ejpam-4652	111	17	v	v	NOUN
ejpam-4652	111	18	}	}	PUNCT
ejpam-4652	111	19	,	,	PUNCT
ejpam-4652	111	20	xy	xy	PROPN
ejpam-4652	111	21	/∈	/∈	PUNCT
ejpam-4652	111	22	e(g	e(g	PROPN
ejpam-4652	111	23	)	)	PUNCT
ejpam-4652	111	24	.	.	PUNCT
ejpam-4652	112	1	therefore	therefore	ADV
ejpam-4652	112	2	,	,	PUNCT
ejpam-4652	112	3	g	g	PROPN
ejpam-4652	112	4	=	=	PROPN
ejpam-4652	112	5	⟨v⟩+	⟨v⟩+	PROPN
ejpam-4652	112	6	⋃	⋃	NOUN
ejpam-4652	112	7	x∈v	x∈v	PROPN
ejpam-4652	112	8	(	(	PUNCT
ejpam-4652	112	9	g)\{v	g)\{v	PROPN
ejpam-4652	112	10	}	}	PUNCT
ejpam-4652	112	11	⟨x⟩	⟨x⟩	X
ejpam-4652	112	12	=	=	PUNCT
ejpam-4652	112	13	k1,n−1	k1,n−1	PROPN
ejpam-4652	112	14	.	.	PUNCT
ejpam-4652	113	1	for	for	ADP
ejpam-4652	113	2	the	the	DET
ejpam-4652	113	3	converse	converse	NOUN
ejpam-4652	113	4	,	,	PUNCT
ejpam-4652	113	5	suppose	suppose	VERB
ejpam-4652	113	6	g	g	PROPN
ejpam-4652	113	7	=	=	PROPN
ejpam-4652	113	8	kn	kn	PROPN
ejpam-4652	113	9	or	or	CCONJ
ejpam-4652	113	10	g	g	PROPN
ejpam-4652	113	11	=	=	PUNCT
ejpam-4652	113	12	k1,n−1	k1,n−1	PROPN
ejpam-4652	113	13	.	.	PUNCT
ejpam-4652	114	1	then	then	ADV
ejpam-4652	114	2	,	,	PUNCT
ejpam-4652	114	3	clearly	clearly	ADV
ejpam-4652	114	4	,	,	PUNCT
ejpam-4652	114	5	ωds(g	ωds(g	PROPN
ejpam-4652	114	6	)	)	PUNCT
ejpam-4652	114	7	=	=	SYM
ejpam-4652	114	8	1	1	X
ejpam-4652	114	9	.	.	PUNCT
ejpam-4652	114	10	g.	g.	PROPN
ejpam-4652	114	11	monsanto	monsanto	PROPN
ejpam-4652	114	12	,	,	PUNCT
ejpam-4652	114	13	p.	p.	PROPN
ejpam-4652	114	14	acal	acal	PROPN
ejpam-4652	114	15	,	,	PUNCT
ejpam-4652	114	16	h.	h.	PROPN
ejpam-4652	114	17	rara	rara	PROPN
ejpam-4652	114	18	/	/	SYM
ejpam-4652	114	19	eur	eur	PROPN
ejpam-4652	114	20	.	.	PUNCT
ejpam-4652	115	1	j.	j.	PROPN
ejpam-4652	115	2	pure	pure	PROPN
ejpam-4652	115	3	appl	appl	PROPN
ejpam-4652	115	4	.	.	PROPN
ejpam-4652	115	5	math	math	PROPN
ejpam-4652	115	6	,	,	PUNCT
ejpam-4652	115	7	16	16	NUM
ejpam-4652	115	8	(	(	PUNCT
ejpam-4652	115	9	1	1	NUM
ejpam-4652	115	10	)	)	PUNCT
ejpam-4652	115	11	(	(	PUNCT
ejpam-4652	115	12	2023	2023	NUM
ejpam-4652	115	13	)	)	PUNCT
ejpam-4652	115	14	,	,	PUNCT
ejpam-4652	115	15	363	363	NUM
ejpam-4652	115	16	-	-	SYM
ejpam-4652	115	17	372	372	NUM
ejpam-4652	115	18	367	367	NUM
ejpam-4652	115	19	3	3	NUM
ejpam-4652	115	20	.	.	PUNCT
ejpam-4652	116	1	strong	strong	ADJ
ejpam-4652	116	2	resolving	resolving	NOUN
ejpam-4652	116	3	domination	domination	NOUN
ejpam-4652	116	4	in	in	ADP
ejpam-4652	116	5	the	the	DET
ejpam-4652	116	6	lexicographic	lexicographic	ADJ
ejpam-4652	116	7	product	product	NOUN
ejpam-4652	116	8	of	of	ADP
ejpam-4652	116	9	graphs	graph	NOUN
ejpam-4652	116	10	lemma	lemma	PROPN
ejpam-4652	116	11	1	1	X
ejpam-4652	116	12	.	.	PUNCT
ejpam-4652	117	1	let	let	VERB
ejpam-4652	117	2	g	g	PROPN
ejpam-4652	117	3	=	=	PROPN
ejpam-4652	117	4	kn	kn	PROPN
ejpam-4652	117	5	for	for	ADP
ejpam-4652	117	6	n	n	PROPN
ejpam-4652	117	7	>	>	SYM
ejpam-4652	117	8	1	1	NUM
ejpam-4652	117	9	and	and	CCONJ
ejpam-4652	117	10	h	h	DET
ejpam-4652	117	11	a	a	DET
ejpam-4652	117	12	non	non	ADJ
ejpam-4652	117	13	-	-	ADJ
ejpam-4652	117	14	trivial	trivial	ADJ
ejpam-4652	117	15	connected	connected	ADJ
ejpam-4652	117	16	graph	graph	NOUN
ejpam-4652	117	17	with	with	ADP
ejpam-4652	117	18	γ(h	γ(h	NOUN
ejpam-4652	117	19	)	)	PUNCT
ejpam-4652	117	20	̸=	̸=	PROPN
ejpam-4652	117	21	1	1	NUM
ejpam-4652	117	22	.	.	PUNCT
ejpam-4652	118	1	then	then	ADV
ejpam-4652	118	2	a×c	a×c	PROPN
ejpam-4652	118	3	⊆	⊆	NUM
ejpam-4652	118	4	v	v	NOUN
ejpam-4652	118	5	(	(	PUNCT
ejpam-4652	118	6	g[h	g[h	PROPN
ejpam-4652	118	7	]	]	PUNCT
ejpam-4652	118	8	)	)	PUNCT
ejpam-4652	118	9	is	be	AUX
ejpam-4652	118	10	a	a	DET
ejpam-4652	118	11	superclique	superclique	NOUN
ejpam-4652	118	12	in	in	ADP
ejpam-4652	118	13	g[h	g[h	NOUN
ejpam-4652	118	14	]	]	PUNCT
ejpam-4652	118	15	if	if	SCONJ
ejpam-4652	119	1	and	and	CCONJ
ejpam-4652	119	2	only	only	ADV
ejpam-4652	119	3	if	if	SCONJ
ejpam-4652	119	4	a	a	PRON
ejpam-4652	119	5	is	be	AUX
ejpam-4652	119	6	a	a	DET
ejpam-4652	119	7	nonempty	nonempty	ADJ
ejpam-4652	119	8	subset	subset	NOUN
ejpam-4652	119	9	of	of	ADP
ejpam-4652	119	10	v	v	NOUN
ejpam-4652	119	11	(	(	PUNCT
ejpam-4652	119	12	g	g	NOUN
ejpam-4652	119	13	)	)	PUNCT
ejpam-4652	119	14	and	and	CCONJ
ejpam-4652	119	15	c	c	PROPN
ejpam-4652	119	16	is	be	AUX
ejpam-4652	119	17	a	a	DET
ejpam-4652	119	18	superclique	superclique	NOUN
ejpam-4652	119	19	in	in	ADP
ejpam-4652	119	20	h.	h.	NOUN
ejpam-4652	119	21	proof	proof	NOUN
ejpam-4652	119	22	:	:	PUNCT
ejpam-4652	119	23	let	let	VERB
ejpam-4652	119	24	g	g	PROPN
ejpam-4652	119	25	=	=	PROPN
ejpam-4652	119	26	kn	kn	PROPN
ejpam-4652	119	27	for	for	ADP
ejpam-4652	119	28	n	n	PROPN
ejpam-4652	119	29	>	>	SYM
ejpam-4652	119	30	1	1	NUM
ejpam-4652	119	31	and	and	CCONJ
ejpam-4652	119	32	h	h	DET
ejpam-4652	119	33	a	a	DET
ejpam-4652	119	34	non	non	ADJ
ejpam-4652	119	35	-	-	ADJ
ejpam-4652	119	36	trivial	trivial	ADJ
ejpam-4652	119	37	connected	connected	ADJ
ejpam-4652	119	38	graph	graph	NOUN
ejpam-4652	119	39	.	.	PUNCT
ejpam-4652	120	1	suppose	suppose	VERB
ejpam-4652	120	2	a	a	DET
ejpam-4652	120	3	×	×	NOUN
ejpam-4652	120	4	c	c	NOUN
ejpam-4652	120	5	⊆	⊆	NUM
ejpam-4652	120	6	v	v	NOUN
ejpam-4652	120	7	(	(	PUNCT
ejpam-4652	120	8	g[h	g[h	PROPN
ejpam-4652	120	9	]	]	PUNCT
ejpam-4652	120	10	)	)	PUNCT
ejpam-4652	120	11	is	be	AUX
ejpam-4652	120	12	a	a	DET
ejpam-4652	120	13	superclique	superclique	NOUN
ejpam-4652	120	14	in	in	ADP
ejpam-4652	120	15	g[h	g[h	NOUN
ejpam-4652	120	16	]	]	PUNCT
ejpam-4652	120	17	.	.	PUNCT
ejpam-4652	121	1	then	then	ADV
ejpam-4652	121	2	a	a	DET
ejpam-4652	121	3	⊆	⊆	NUM
ejpam-4652	121	4	v	v	NOUN
ejpam-4652	121	5	(	(	PUNCT
ejpam-4652	121	6	g	g	NOUN
ejpam-4652	121	7	)	)	PUNCT
ejpam-4652	121	8	,	,	PUNCT
ejpam-4652	121	9	c	c	PROPN
ejpam-4652	121	10	⊆	⊆	NUM
ejpam-4652	121	11	v	v	X
ejpam-4652	121	12	(	(	PUNCT
ejpam-4652	121	13	h	h	NOUN
ejpam-4652	121	14	)	)	PUNCT
ejpam-4652	121	15	,	,	PUNCT
ejpam-4652	121	16	a	a	DET
ejpam-4652	121	17	̸=	̸=	PROPN
ejpam-4652	121	18	∅	∅	NOUN
ejpam-4652	121	19	and	and	CCONJ
ejpam-4652	121	20	c	c	ADP
ejpam-4652	121	21	̸=	̸=	PROPN
ejpam-4652	121	22	∅.	∅.	ADV
ejpam-4652	121	23	if	if	SCONJ
ejpam-4652	121	24	|c|	|c|	PROPN
ejpam-4652	121	25	=	=	SYM
ejpam-4652	121	26	1	1	NUM
ejpam-4652	121	27	,	,	PUNCT
ejpam-4652	121	28	then	then	ADV
ejpam-4652	121	29	we	we	PRON
ejpam-4652	121	30	are	be	AUX
ejpam-4652	121	31	done	do	VERB
ejpam-4652	121	32	.	.	PUNCT
ejpam-4652	122	1	suppose	suppose	VERB
ejpam-4652	122	2	|c|	|c|	PROPN
ejpam-4652	122	3	≥	≥	NUM
ejpam-4652	122	4	2	2	X
ejpam-4652	122	5	.	.	PUNCT
ejpam-4652	123	1	let	let	VERB
ejpam-4652	123	2	x	x	PRON
ejpam-4652	123	3	,	,	PUNCT
ejpam-4652	123	4	y	y	PROPN
ejpam-4652	123	5	∈	∈	PROPN
ejpam-4652	123	6	c	c	AUX
ejpam-4652	123	7	,	,	PUNCT
ejpam-4652	123	8	x	x	PROPN
ejpam-4652	123	9	̸=	̸=	PROPN
ejpam-4652	123	10	y.	y.	NOUN
ejpam-4652	123	11	since	since	SCONJ
ejpam-4652	123	12	a	a	DET
ejpam-4652	123	13	×	×	NOUN
ejpam-4652	123	14	c	c	NOUN
ejpam-4652	123	15	is	be	AUX
ejpam-4652	123	16	a	a	DET
ejpam-4652	123	17	superclique	superclique	NOUN
ejpam-4652	123	18	in	in	ADP
ejpam-4652	123	19	g[h	g[h	NOUN
ejpam-4652	123	20	]	]	PUNCT
ejpam-4652	123	21	,	,	PUNCT
ejpam-4652	123	22	(	(	PUNCT
ejpam-4652	123	23	v	v	NOUN
ejpam-4652	123	24	,	,	PUNCT
ejpam-4652	123	25	x)(v	x)(v	PROPN
ejpam-4652	123	26	,	,	PUNCT
ejpam-4652	123	27	y	y	NOUN
ejpam-4652	123	28	)	)	PUNCT
ejpam-4652	123	29	∈	∈	NOUN
ejpam-4652	123	30	e(g[h	e(g[h	NOUN
ejpam-4652	123	31	]	]	PUNCT
ejpam-4652	123	32	)	)	PUNCT
ejpam-4652	123	33	for	for	ADP
ejpam-4652	123	34	all	all	PRON
ejpam-4652	123	35	v	v	ADP
ejpam-4652	123	36	∈	∈	PRON
ejpam-4652	123	37	a	a	PRON
ejpam-4652	123	38	and	and	CCONJ
ejpam-4652	123	39	there	there	PRON
ejpam-4652	123	40	exists	exist	VERB
ejpam-4652	123	41	(	(	PUNCT
ejpam-4652	123	42	w	w	PROPN
ejpam-4652	123	43	,	,	PUNCT
ejpam-4652	123	44	z	z	NOUN
ejpam-4652	123	45	)	)	PUNCT
ejpam-4652	123	46	∈	∈	NOUN
ejpam-4652	123	47	v	v	NOUN
ejpam-4652	123	48	(	(	PUNCT
ejpam-4652	123	49	g[h	g[h	PROPN
ejpam-4652	123	50	]	]	PUNCT
ejpam-4652	123	51	)	)	PUNCT
ejpam-4652	123	52	\	\	PUNCT
ejpam-4652	124	1	(	(	PUNCT
ejpam-4652	124	2	a	a	DET
ejpam-4652	124	3	×	×	NOUN
ejpam-4652	124	4	c	c	NOUN
ejpam-4652	124	5	)	)	PUNCT
ejpam-4652	124	6	such	such	ADJ
ejpam-4652	124	7	that	that	SCONJ
ejpam-4652	124	8	(	(	PUNCT
ejpam-4652	124	9	w	w	PROPN
ejpam-4652	124	10	,	,	PUNCT
ejpam-4652	124	11	z	z	NOUN
ejpam-4652	124	12	)	)	PUNCT
ejpam-4652	124	13	∈	∈	PROPN
ejpam-4652	124	14	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	124	15	,	,	PUNCT
ejpam-4652	124	16	x	x	NOUN
ejpam-4652	124	17	)	)	PUNCT
ejpam-4652	124	18	)	)	PUNCT
ejpam-4652	124	19	\	\	PROPN
ejpam-4652	124	20	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	124	21	,	,	PUNCT
ejpam-4652	124	22	y	y	NOUN
ejpam-4652	124	23	)	)	PUNCT
ejpam-4652	124	24	)	)	PUNCT
ejpam-4652	124	25	or	or	CCONJ
ejpam-4652	124	26	(	(	PUNCT
ejpam-4652	124	27	w	w	PROPN
ejpam-4652	124	28	,	,	PUNCT
ejpam-4652	124	29	z	z	NOUN
ejpam-4652	124	30	)	)	PUNCT
ejpam-4652	124	31	∈	∈	PROPN
ejpam-4652	124	32	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	124	33	,	,	PUNCT
ejpam-4652	124	34	y	y	NOUN
ejpam-4652	124	35	)	)	PUNCT
ejpam-4652	124	36	)	)	PUNCT
ejpam-4652	124	37	\	\	PROPN
ejpam-4652	124	38	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	124	39	,	,	PUNCT
ejpam-4652	124	40	x	x	NOUN
ejpam-4652	124	41	)	)	PUNCT
ejpam-4652	124	42	)	)	PUNCT
ejpam-4652	124	43	.	.	PUNCT
ejpam-4652	125	1	hence	hence	ADV
ejpam-4652	125	2	,	,	PUNCT
ejpam-4652	125	3	xy	xy	PROPN
ejpam-4652	125	4	∈	∈	PROPN
ejpam-4652	125	5	e(h	e(h	PROPN
ejpam-4652	125	6	)	)	PUNCT
ejpam-4652	125	7	.	.	PUNCT
ejpam-4652	126	1	since	since	SCONJ
ejpam-4652	126	2	g	g	PROPN
ejpam-4652	126	3	is	be	AUX
ejpam-4652	126	4	complete	complete	ADJ
ejpam-4652	126	5	,	,	PUNCT
ejpam-4652	126	6	v	v	NOUN
ejpam-4652	126	7	=	=	SYM
ejpam-4652	126	8	w	w	PROPN
ejpam-4652	126	9	and	and	CCONJ
ejpam-4652	126	10	z	z	NOUN
ejpam-4652	126	11	∈	∈	PROPN
ejpam-4652	126	12	nh(x	nh(x	NUM
ejpam-4652	126	13	)	)	PUNCT
ejpam-4652	126	14	\	\	NOUN
ejpam-4652	126	15	nh(y	nh(y	PUNCT
ejpam-4652	126	16	)	)	PUNCT
ejpam-4652	126	17	or	or	CCONJ
ejpam-4652	126	18	z	z	NOUN
ejpam-4652	126	19	∈	∈	PROPN
ejpam-4652	126	20	nh(y	nh(y	NOUN
ejpam-4652	126	21	)	)	PUNCT
ejpam-4652	126	22	\	\	NOUN
ejpam-4652	127	1	nh(x	nh(x	NUM
ejpam-4652	127	2	)	)	PUNCT
ejpam-4652	127	3	,	,	PUNCT
ejpam-4652	127	4	where	where	SCONJ
ejpam-4652	127	5	z	z	PROPN
ejpam-4652	127	6	∈	∈	PROPN
ejpam-4652	127	7	v	v	ADP
ejpam-4652	127	8	(	(	PUNCT
ejpam-4652	127	9	h	h	NOUN
ejpam-4652	127	10	)	)	PUNCT
ejpam-4652	127	11	\	\	PROPN
ejpam-4652	127	12	c.	c.	PROPN
ejpam-4652	127	13	thus	thus	ADV
ejpam-4652	127	14	,	,	PUNCT
ejpam-4652	127	15	c	c	PROPN
ejpam-4652	127	16	is	be	AUX
ejpam-4652	127	17	a	a	DET
ejpam-4652	127	18	superclique	superclique	NOUN
ejpam-4652	127	19	in	in	ADP
ejpam-4652	127	20	h.	h.	NOUN
ejpam-4652	127	21	conversely	conversely	ADV
ejpam-4652	127	22	,	,	PUNCT
ejpam-4652	127	23	suppose	suppose	VERB
ejpam-4652	127	24	a	a	DET
ejpam-4652	127	25	⊆	⊆	NUM
ejpam-4652	127	26	v	v	NOUN
ejpam-4652	127	27	(	(	PUNCT
ejpam-4652	127	28	g	g	NOUN
ejpam-4652	127	29	)	)	PUNCT
ejpam-4652	127	30	,	,	PUNCT
ejpam-4652	127	31	a	a	DET
ejpam-4652	127	32	̸=	̸=	PROPN
ejpam-4652	127	33	∅	∅	NOUN
ejpam-4652	127	34	and	and	CCONJ
ejpam-4652	127	35	c	c	NOUN
ejpam-4652	127	36	is	be	AUX
ejpam-4652	127	37	a	a	DET
ejpam-4652	127	38	superclique	superclique	NOUN
ejpam-4652	127	39	in	in	ADP
ejpam-4652	127	40	h.	h.	PROPN
ejpam-4652	128	1	then	then	ADV
ejpam-4652	128	2	a×c	a×c	PROPN
ejpam-4652	128	3	⊆	⊆	NUM
ejpam-4652	128	4	v	v	NOUN
ejpam-4652	128	5	(	(	PUNCT
ejpam-4652	128	6	g[h	g[h	PROPN
ejpam-4652	128	7	]	]	PUNCT
ejpam-4652	128	8	)	)	PUNCT
ejpam-4652	128	9	and	and	CCONJ
ejpam-4652	128	10	a×c	a×c	PROPN
ejpam-4652	128	11	̸=	̸=	PROPN
ejpam-4652	128	12	∅.	∅.	VERB
ejpam-4652	128	13	if	if	SCONJ
ejpam-4652	128	14	|a×c|	|a×c|	NUM
ejpam-4652	128	15	=	=	SYM
ejpam-4652	128	16	1	1	NUM
ejpam-4652	128	17	,	,	PUNCT
ejpam-4652	128	18	then	then	ADV
ejpam-4652	128	19	we	we	PRON
ejpam-4652	128	20	are	be	AUX
ejpam-4652	128	21	done	do	VERB
ejpam-4652	128	22	.	.	PUNCT
ejpam-4652	129	1	suppose	suppose	VERB
ejpam-4652	129	2	|a×c|	|a×c|	NUM
ejpam-4652	129	3	≥	≥	NOUN
ejpam-4652	129	4	2	2	NUM
ejpam-4652	129	5	.	.	PUNCT
ejpam-4652	130	1	let	let	VERB
ejpam-4652	130	2	(	(	PUNCT
ejpam-4652	130	3	u	u	NOUN
ejpam-4652	130	4	,	,	PUNCT
ejpam-4652	130	5	x	x	NOUN
ejpam-4652	130	6	)	)	PUNCT
ejpam-4652	130	7	,	,	PUNCT
ejpam-4652	130	8	(	(	PUNCT
ejpam-4652	130	9	v	v	NOUN
ejpam-4652	130	10	,	,	PUNCT
ejpam-4652	130	11	y	y	NOUN
ejpam-4652	130	12	)	)	PUNCT
ejpam-4652	130	13	∈	∈	NOUN
ejpam-4652	131	1	a×	a×	PUNCT
ejpam-4652	131	2	c	c	X
ejpam-4652	131	3	,	,	PUNCT
ejpam-4652	131	4	(	(	PUNCT
ejpam-4652	131	5	u	u	NOUN
ejpam-4652	131	6	,	,	PUNCT
ejpam-4652	131	7	x	x	NOUN
ejpam-4652	131	8	)	)	PUNCT
ejpam-4652	131	9	̸=	̸=	PROPN
ejpam-4652	131	10	(	(	PUNCT
ejpam-4652	131	11	v	v	NOUN
ejpam-4652	131	12	,	,	PUNCT
ejpam-4652	131	13	y	y	PROPN
ejpam-4652	131	14	)	)	PUNCT
ejpam-4652	131	15	.	.	PUNCT
ejpam-4652	132	1	consider	consider	VERB
ejpam-4652	132	2	the	the	DET
ejpam-4652	132	3	following	follow	VERB
ejpam-4652	132	4	cases	case	NOUN
ejpam-4652	132	5	:	:	PUNCT
ejpam-4652	132	6	case	case	NOUN
ejpam-4652	132	7	1	1	NUM
ejpam-4652	132	8	.	.	X
ejpam-4652	133	1	u	u	NOUN
ejpam-4652	134	1	=	=	NOUN
ejpam-4652	135	1	v	v	X
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ejpam-4652	135	4	̸=	̸=	PROPN
ejpam-4652	135	5	y.	y.	NOUN
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ejpam-4652	135	7	x	x	X
ejpam-4652	135	8	,	,	PUNCT
ejpam-4652	135	9	y	y	PROPN
ejpam-4652	135	10	∈	∈	PROPN
ejpam-4652	135	11	c	c	PROPN
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ejpam-4652	135	13	c	c	PROPN
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ejpam-4652	135	15	a	a	DET
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ejpam-4652	135	17	in	in	ADP
ejpam-4652	135	18	h	h	NOUN
ejpam-4652	135	19	,	,	PUNCT
ejpam-4652	135	20	xy	xy	PROPN
ejpam-4652	135	21	∈	∈	PROPN
ejpam-4652	135	22	e(h	e(h	PROPN
ejpam-4652	135	23	)	)	PUNCT
ejpam-4652	135	24	and	and	CCONJ
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ejpam-4652	135	27	z	z	PROPN
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ejpam-4652	135	29	v	v	ADP
ejpam-4652	135	30	(	(	PUNCT
ejpam-4652	135	31	h	h	NOUN
ejpam-4652	135	32	)	)	PUNCT
ejpam-4652	135	33	\	\	PUNCT
ejpam-4652	136	1	c	c	NOUN
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ejpam-4652	136	3	that	that	SCONJ
ejpam-4652	136	4	z	z	PROPN
ejpam-4652	136	5	∈	∈	PROPN
ejpam-4652	136	6	nh(x	nh(x	PUNCT
ejpam-4652	136	7	)	)	PUNCT
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ejpam-4652	136	9	nh(y	nh(y	PUNCT
ejpam-4652	136	10	)	)	PUNCT
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ejpam-4652	136	12	z	z	NOUN
ejpam-4652	136	13	∈	∈	PROPN
ejpam-4652	136	14	nh(y	nh(y	NOUN
ejpam-4652	136	15	)	)	PUNCT
ejpam-4652	136	16	\	\	NOUN
ejpam-4652	136	17	nh(x	nh(x	NUM
ejpam-4652	136	18	)	)	PUNCT
ejpam-4652	136	19	.	.	PUNCT
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ejpam-4652	137	6	x)(v	x)(v	PROPN
ejpam-4652	137	7	,	,	PUNCT
ejpam-4652	137	8	y	y	NOUN
ejpam-4652	137	9	)	)	PUNCT
ejpam-4652	137	10	∈	∈	NOUN
ejpam-4652	137	11	e(g[h	e(g[h	NOUN
ejpam-4652	137	12	]	]	PUNCT
ejpam-4652	137	13	)	)	PUNCT
ejpam-4652	137	14	,	,	PUNCT
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ejpam-4652	137	16	u	u	NOUN
ejpam-4652	137	17	,	,	PUNCT
ejpam-4652	137	18	z	z	NOUN
ejpam-4652	137	19	)	)	PUNCT
ejpam-4652	137	20	/∈	/∈	PUNCT
ejpam-4652	138	1	a×c	a×c	PROPN
ejpam-4652	138	2	and	and	CCONJ
ejpam-4652	138	3	(	(	PUNCT
ejpam-4652	138	4	u	u	NOUN
ejpam-4652	138	5	,	,	PUNCT
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ejpam-4652	138	9	ng[h]((u	ng[h]((u	NOUN
ejpam-4652	138	10	,	,	PUNCT
ejpam-4652	138	11	x))\ng[h]((v	x))\ng[h]((v	PROPN
ejpam-4652	138	12	,	,	PUNCT
ejpam-4652	138	13	y	y	NOUN
ejpam-4652	138	14	)	)	PUNCT
ejpam-4652	138	15	)	)	PUNCT
ejpam-4652	138	16	or	or	CCONJ
ejpam-4652	138	17	(	(	PUNCT
ejpam-4652	138	18	u	u	NOUN
ejpam-4652	138	19	,	,	PUNCT
ejpam-4652	138	20	z	z	NOUN
ejpam-4652	138	21	)	)	PUNCT
ejpam-4652	138	22	∈	∈	PROPN
ejpam-4652	138	23	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	138	24	,	,	PUNCT
ejpam-4652	138	25	y))\	y))\	PROPN
ejpam-4652	138	26	ng[h]((u	ng[h]((u	NOUN
ejpam-4652	138	27	,	,	PUNCT
ejpam-4652	138	28	x	x	NOUN
ejpam-4652	138	29	)	)	PUNCT
ejpam-4652	138	30	)	)	PUNCT
ejpam-4652	138	31	.	.	PUNCT
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ejpam-4652	139	2	2	2	NUM
ejpam-4652	139	3	.	.	X
ejpam-4652	140	1	u	u	NOUN
ejpam-4652	140	2	̸=	̸=	PROPN
ejpam-4652	140	3	v	v	NUM
ejpam-4652	140	4	subcase	subcase	NOUN
ejpam-4652	140	5	2.1	2.1	NUM
ejpam-4652	140	6	x	x	X
ejpam-4652	140	7	=	=	SYM
ejpam-4652	140	8	y	y	PROPN
ejpam-4652	140	9	since	since	SCONJ
ejpam-4652	140	10	γ(h	γ(h	NOUN
ejpam-4652	140	11	)	)	PUNCT
ejpam-4652	140	12	̸=	̸=	PROPN
ejpam-4652	140	13	1	1	NUM
ejpam-4652	140	14	,	,	PUNCT
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ejpam-4652	140	17	z	z	PROPN
ejpam-4652	140	18	∈	∈	PROPN
ejpam-4652	140	19	v	v	ADP
ejpam-4652	140	20	(	(	PUNCT
ejpam-4652	140	21	h	h	NOUN
ejpam-4652	140	22	)	)	PUNCT
ejpam-4652	140	23	such	such	ADJ
ejpam-4652	140	24	that	that	SCONJ
ejpam-4652	140	25	z	z	NOUN
ejpam-4652	140	26	/∈	/∈	PUNCT
ejpam-4652	140	27	nh(x	nh(x	NUM
ejpam-4652	140	28	)	)	PUNCT
ejpam-4652	140	29	.	.	PUNCT
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ejpam-4652	141	4	x	x	PROPN
ejpam-4652	141	5	∈	∈	PROPN
ejpam-4652	141	6	c	c	PROPN
ejpam-4652	141	7	and	and	CCONJ
ejpam-4652	141	8	z	z	NOUN
ejpam-4652	141	9	/∈	/∈	PUNCT
ejpam-4652	142	1	c	c	X
ejpam-4652	142	2	,	,	PUNCT
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ejpam-4652	142	5	(	(	PUNCT
ejpam-4652	142	6	u	u	NOUN
ejpam-4652	142	7	,	,	PUNCT
ejpam-4652	142	8	z	z	NOUN
ejpam-4652	142	9	)	)	PUNCT
ejpam-4652	142	10	/∈	/∈	PUNCT
ejpam-4652	143	1	a	a	DET
ejpam-4652	143	2	×	×	NOUN
ejpam-4652	143	3	c	c	NOUN
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ejpam-4652	143	5	(	(	PUNCT
ejpam-4652	143	6	u	u	NOUN
ejpam-4652	143	7	,	,	PUNCT
ejpam-4652	143	8	z	z	NOUN
ejpam-4652	143	9	)	)	PUNCT
ejpam-4652	143	10	∈	∈	PROPN
ejpam-4652	143	11	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	143	12	,	,	PUNCT
ejpam-4652	143	13	x	x	NOUN
ejpam-4652	143	14	)	)	PUNCT
ejpam-4652	143	15	)	)	PUNCT
ejpam-4652	143	16	\	\	NOUN
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ejpam-4652	143	18	,	,	PUNCT
ejpam-4652	143	19	x	x	NOUN
ejpam-4652	143	20	)	)	PUNCT
ejpam-4652	143	21	)	)	PUNCT
ejpam-4652	143	22	.	.	PUNCT
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ejpam-4652	144	2	g	g	PROPN
ejpam-4652	144	3	is	be	AUX
ejpam-4652	144	4	complete	complete	ADJ
ejpam-4652	144	5	and	and	CCONJ
ejpam-4652	144	6	u	u	NOUN
ejpam-4652	144	7	̸=	̸=	PROPN
ejpam-4652	144	8	v	v	NOUN
ejpam-4652	144	9	,	,	PUNCT
ejpam-4652	144	10	(	(	PUNCT
ejpam-4652	144	11	u	u	NOUN
ejpam-4652	144	12	,	,	PUNCT
ejpam-4652	144	13	x)(v	x)(v	PROPN
ejpam-4652	144	14	,	,	PUNCT
ejpam-4652	144	15	x	x	X
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ejpam-4652	144	18	e(g[h	e(g[h	NOUN
ejpam-4652	144	19	]	]	PUNCT
ejpam-4652	144	20	)	)	PUNCT
ejpam-4652	144	21	.	.	PUNCT
ejpam-4652	145	1	subcase	subcase	PROPN
ejpam-4652	145	2	2.2	2.2	NUM
ejpam-4652	145	3	x	x	SYM
ejpam-4652	145	4	̸=	̸=	PROPN
ejpam-4652	145	5	y	y	PROPN
ejpam-4652	145	6	since	since	SCONJ
ejpam-4652	145	7	x	x	X
ejpam-4652	145	8	,	,	PUNCT
ejpam-4652	145	9	y	y	PROPN
ejpam-4652	145	10	∈	∈	PROPN
ejpam-4652	145	11	c	c	PROPN
ejpam-4652	145	12	and	and	CCONJ
ejpam-4652	145	13	c	c	PROPN
ejpam-4652	145	14	is	be	AUX
ejpam-4652	145	15	a	a	DET
ejpam-4652	145	16	superclique	superclique	NOUN
ejpam-4652	145	17	in	in	ADP
ejpam-4652	145	18	h	h	NOUN
ejpam-4652	145	19	,	,	PUNCT
ejpam-4652	145	20	xy	xy	PROPN
ejpam-4652	145	21	∈	∈	PROPN
ejpam-4652	145	22	e(h	e(h	PROPN
ejpam-4652	145	23	)	)	PUNCT
ejpam-4652	145	24	and	and	CCONJ
ejpam-4652	145	25	there	there	PRON
ejpam-4652	145	26	exists	exist	VERB
ejpam-4652	145	27	z	z	NOUN
ejpam-4652	145	28	/∈	/∈	PUNCT
ejpam-4652	146	1	c	c	NOUN
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ejpam-4652	146	3	that	that	SCONJ
ejpam-4652	146	4	z	z	PROPN
ejpam-4652	146	5	∈	∈	PROPN
ejpam-4652	146	6	nh(x)\nh(y	nh(x)\nh(y	NOUN
ejpam-4652	146	7	)	)	PUNCT
ejpam-4652	146	8	or	or	CCONJ
ejpam-4652	146	9	z	z	NOUN
ejpam-4652	146	10	∈	∈	PROPN
ejpam-4652	146	11	nh(y)\nh(x	nh(y)\nh(x	NOUN
ejpam-4652	146	12	)	)	PUNCT
ejpam-4652	146	13	.	.	PUNCT
ejpam-4652	147	1	hence	hence	ADV
ejpam-4652	147	2	,	,	PUNCT
ejpam-4652	147	3	(	(	PUNCT
ejpam-4652	147	4	v	v	NOUN
ejpam-4652	147	5	,	,	PUNCT
ejpam-4652	147	6	z	z	NOUN
ejpam-4652	147	7	)	)	PUNCT
ejpam-4652	147	8	∈	∈	PROPN
ejpam-4652	147	9	ng[h]((u	ng[h]((u	NOUN
ejpam-4652	147	10	,	,	PUNCT
ejpam-4652	147	11	x))\ng[h]((v	x))\ng[h]((v	PROPN
ejpam-4652	147	12	,	,	PUNCT
ejpam-4652	147	13	y	y	NOUN
ejpam-4652	147	14	)	)	PUNCT
ejpam-4652	147	15	)	)	PUNCT
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ejpam-4652	147	17	(	(	PUNCT
ejpam-4652	147	18	v	v	NOUN
ejpam-4652	147	19	,	,	PUNCT
ejpam-4652	147	20	z	z	NOUN
ejpam-4652	147	21	)	)	PUNCT
ejpam-4652	147	22	∈	∈	PROPN
ejpam-4652	147	23	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	147	24	,	,	PUNCT
ejpam-4652	147	25	y	y	NOUN
ejpam-4652	147	26	)	)	PUNCT
ejpam-4652	147	27	)	)	PUNCT
ejpam-4652	148	1	\ng[h]((u	\ng[h]((u	PROPN
ejpam-4652	148	2	,	,	PUNCT
ejpam-4652	148	3	x	x	NOUN
ejpam-4652	148	4	)	)	PUNCT
ejpam-4652	148	5	)	)	PUNCT
ejpam-4652	148	6	for	for	ADP
ejpam-4652	148	7	some	some	PRON
ejpam-4652	148	8	(	(	PUNCT
ejpam-4652	148	9	v	v	NOUN
ejpam-4652	148	10	,	,	PUNCT
ejpam-4652	148	11	z	z	NOUN
ejpam-4652	148	12	)	)	PUNCT
ejpam-4652	148	13	/∈	/∈	PUNCT
ejpam-4652	149	1	a×	a×	PROPN
ejpam-4652	149	2	c.	c.	NOUN
ejpam-4652	149	3	in	in	ADP
ejpam-4652	149	4	any	any	DET
ejpam-4652	149	5	case	case	NOUN
ejpam-4652	149	6	,	,	PUNCT
ejpam-4652	149	7	a×	a×	PROPN
ejpam-4652	149	8	c	c	PROPN
ejpam-4652	149	9	is	be	AUX
ejpam-4652	149	10	a	a	DET
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ejpam-4652	149	12	in	in	ADP
ejpam-4652	149	13	g[h	g[h	NOUN
ejpam-4652	149	14	]	]	PUNCT
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ejpam-4652	151	1	[	[	X
ejpam-4652	151	2	6	6	NUM
ejpam-4652	151	3	]	]	PUNCT
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ejpam-4652	151	5	g	g	PROPN
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ejpam-4652	151	11	.	.	PUNCT
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ejpam-4652	152	2	c	c	PROPN
ejpam-4652	152	3	⊆	⊆	NUM
ejpam-4652	152	4	v	v	NOUN
ejpam-4652	152	5	(	(	PUNCT
ejpam-4652	152	6	g+h	g+h	PROPN
ejpam-4652	152	7	)	)	PUNCT
ejpam-4652	152	8	is	be	AUX
ejpam-4652	152	9	a	a	DET
ejpam-4652	152	10	dominating	dominating	NOUN
ejpam-4652	152	11	set	set	VERB
ejpam-4652	152	12	in	in	ADP
ejpam-4652	152	13	g+h	g+h	PROPN
ejpam-4652	152	14	if	if	SCONJ
ejpam-4652	152	15	and	and	CCONJ
ejpam-4652	152	16	only	only	ADV
ejpam-4652	152	17	if	if	SCONJ
ejpam-4652	152	18	at	at	ADV
ejpam-4652	152	19	least	least	ADJ
ejpam-4652	152	20	one	one	NUM
ejpam-4652	152	21	of	of	ADP
ejpam-4652	152	22	the	the	DET
ejpam-4652	152	23	following	follow	VERB
ejpam-4652	152	24	is	be	AUX
ejpam-4652	152	25	true	true	ADJ
ejpam-4652	152	26	:	:	PUNCT
ejpam-4652	152	27	(	(	PUNCT
ejpam-4652	152	28	i	i	NOUN
ejpam-4652	152	29	)	)	PUNCT
ejpam-4652	152	30	c	c	PROPN
ejpam-4652	152	31	∩	∩	PROPN
ejpam-4652	152	32	v	v	X
ejpam-4652	152	33	(	(	PUNCT
ejpam-4652	152	34	g	g	NOUN
ejpam-4652	152	35	)	)	PUNCT
ejpam-4652	152	36	is	be	AUX
ejpam-4652	152	37	a	a	DET
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ejpam-4652	152	39	set	set	VERB
ejpam-4652	152	40	in	in	ADP
ejpam-4652	152	41	g.	g.	PROPN
ejpam-4652	152	42	(	(	PUNCT
ejpam-4652	152	43	ii	ii	PROPN
ejpam-4652	152	44	)	)	PUNCT
ejpam-4652	152	45	c	c	NOUN
ejpam-4652	152	46	∩	∩	PROPN
ejpam-4652	152	47	v	v	X
ejpam-4652	152	48	(	(	PUNCT
ejpam-4652	152	49	h	h	NOUN
ejpam-4652	152	50	)	)	PUNCT
ejpam-4652	152	51	is	be	AUX
ejpam-4652	152	52	a	a	DET
ejpam-4652	152	53	dominating	dominating	NOUN
ejpam-4652	152	54	set	set	NOUN
ejpam-4652	152	55	in	in	ADP
ejpam-4652	152	56	h.	h.	PROPN
ejpam-4652	152	57	(	(	PUNCT
ejpam-4652	152	58	iii	iii	NOUN
ejpam-4652	152	59	)	)	PUNCT
ejpam-4652	152	60	c	c	NOUN
ejpam-4652	152	61	∩	∩	X
ejpam-4652	152	62	v	v	X
ejpam-4652	152	63	(	(	PUNCT
ejpam-4652	152	64	g	g	NOUN
ejpam-4652	152	65	)	)	PUNCT
ejpam-4652	152	66	̸=	̸=	PROPN
ejpam-4652	152	67	∅	∅	NOUN
ejpam-4652	152	68	and	and	CCONJ
ejpam-4652	152	69	c	c	NOUN
ejpam-4652	152	70	∩	∩	ADJ
ejpam-4652	152	71	v	v	X
ejpam-4652	152	72	(	(	PUNCT
ejpam-4652	152	73	h	h	NOUN
ejpam-4652	152	74	)	)	PUNCT
ejpam-4652	152	75	̸=	̸=	PROPN
ejpam-4652	152	76	∅.	∅.	ADV
ejpam-4652	152	77	theorem	theorem	ADJ
ejpam-4652	152	78	3	3	NUM
ejpam-4652	152	79	.	.	PUNCT
ejpam-4652	153	1	[	[	X
ejpam-4652	153	2	6	6	NUM
ejpam-4652	153	3	]	]	PUNCT
ejpam-4652	153	4	let	let	VERB
ejpam-4652	153	5	g	g	PROPN
ejpam-4652	153	6	and	and	CCONJ
ejpam-4652	153	7	h	h	NOUN
ejpam-4652	153	8	be	be	AUX
ejpam-4652	153	9	connected	connect	VERB
ejpam-4652	153	10	graphs	graph	NOUN
ejpam-4652	153	11	.	.	PUNCT
ejpam-4652	154	1	then	then	ADV
ejpam-4652	154	2	c	c	PROPN
ejpam-4652	154	3	⊆	⊆	NUM
ejpam-4652	154	4	v	v	NOUN
ejpam-4652	154	5	(	(	PUNCT
ejpam-4652	154	6	g+h	g+h	PROPN
ejpam-4652	154	7	)	)	PUNCT
ejpam-4652	154	8	is	be	AUX
ejpam-4652	154	9	a	a	DET
ejpam-4652	154	10	dominating	dominating	NOUN
ejpam-4652	154	11	set	set	VERB
ejpam-4652	154	12	in	in	ADP
ejpam-4652	154	13	g[h	g[h	PROPN
ejpam-4652	154	14	]	]	PUNCT
ejpam-4652	154	15	if	if	SCONJ
ejpam-4652	155	1	and	and	CCONJ
ejpam-4652	155	2	only	only	ADV
ejpam-4652	155	3	if	if	SCONJ
ejpam-4652	155	4	c	c	NOUN
ejpam-4652	155	5	=	=	SYM
ejpam-4652	155	6	⋃	⋃	PROPN
ejpam-4652	155	7	x∈s	x∈s	NOUN
ejpam-4652	155	8	(	(	PUNCT
ejpam-4652	155	9	{	{	PUNCT
ejpam-4652	155	10	x	x	NOUN
ejpam-4652	155	11	}	}	PUNCT
ejpam-4652	155	12	×	×	PROPN
ejpam-4652	155	13	tx	tx	PROPN
ejpam-4652	155	14	)	)	PUNCT
ejpam-4652	155	15	and	and	CCONJ
ejpam-4652	155	16	either	either	CCONJ
ejpam-4652	155	17	(	(	PUNCT
ejpam-4652	155	18	i	i	NOUN
ejpam-4652	155	19	)	)	PUNCT
ejpam-4652	155	20	s	s	VERB
ejpam-4652	155	21	is	be	AUX
ejpam-4652	155	22	a	a	DET
ejpam-4652	155	23	total	total	ADJ
ejpam-4652	155	24	dominating	dominating	NOUN
ejpam-4652	155	25	set	set	NOUN
ejpam-4652	155	26	in	in	ADP
ejpam-4652	155	27	g	g	PROPN
ejpam-4652	155	28	or	or	CCONJ
ejpam-4652	155	29	g.	g.	PROPN
ejpam-4652	155	30	monsanto	monsanto	PROPN
ejpam-4652	155	31	,	,	PUNCT
ejpam-4652	155	32	p.	p.	PROPN
ejpam-4652	155	33	acal	acal	PROPN
ejpam-4652	155	34	,	,	PUNCT
ejpam-4652	155	35	h.	h.	PROPN
ejpam-4652	155	36	rara	rara	PROPN
ejpam-4652	155	37	/	/	SYM
ejpam-4652	155	38	eur	eur	PROPN
ejpam-4652	155	39	.	.	PUNCT
ejpam-4652	156	1	j.	j.	PROPN
ejpam-4652	156	2	pure	pure	PROPN
ejpam-4652	156	3	appl	appl	PROPN
ejpam-4652	156	4	.	.	PROPN
ejpam-4652	156	5	math	math	PROPN
ejpam-4652	156	6	,	,	PUNCT
ejpam-4652	156	7	16	16	NUM
ejpam-4652	156	8	(	(	PUNCT
ejpam-4652	156	9	1	1	NUM
ejpam-4652	156	10	)	)	PUNCT
ejpam-4652	156	11	(	(	PUNCT
ejpam-4652	156	12	2023	2023	NUM
ejpam-4652	156	13	)	)	PUNCT
ejpam-4652	156	14	,	,	PUNCT
ejpam-4652	156	15	363	363	NUM
ejpam-4652	156	16	-	-	SYM
ejpam-4652	156	17	372	372	NUM
ejpam-4652	156	18	368	368	NUM
ejpam-4652	156	19	(	(	PUNCT
ejpam-4652	156	20	ii	ii	NOUN
ejpam-4652	156	21	)	)	PUNCT
ejpam-4652	156	22	s	s	VERB
ejpam-4652	156	23	is	be	AUX
ejpam-4652	156	24	a	a	DET
ejpam-4652	156	25	dominating	dominating	NOUN
ejpam-4652	156	26	set	set	NOUN
ejpam-4652	156	27	in	in	ADP
ejpam-4652	156	28	g	g	PROPN
ejpam-4652	156	29	and	and	CCONJ
ejpam-4652	156	30	tx	tx	PROPN
ejpam-4652	156	31	is	be	AUX
ejpam-4652	156	32	a	a	DET
ejpam-4652	156	33	dominating	dominating	NOUN
ejpam-4652	156	34	set	set	VERB
ejpam-4652	156	35	in	in	ADP
ejpam-4652	156	36	h	h	NOUN
ejpam-4652	156	37	for	for	ADP
ejpam-4652	156	38	every	every	DET
ejpam-4652	156	39	x	x	SYM
ejpam-4652	156	40	∈	∈	PROPN
ejpam-4652	156	41	s	s	PART
ejpam-4652	156	42	\ng(s	\ng(s	NOUN
ejpam-4652	156	43	)	)	PUNCT
ejpam-4652	156	44	.	.	PUNCT
ejpam-4652	157	1	lemma	lemma	PROPN
ejpam-4652	157	2	2	2	X
ejpam-4652	157	3	.	.	PUNCT
ejpam-4652	157	4	let	let	VERB
ejpam-4652	157	5	g	g	PROPN
ejpam-4652	157	6	=	=	PROPN
ejpam-4652	157	7	kn	kn	PROPN
ejpam-4652	157	8	for	for	ADP
ejpam-4652	157	9	n	n	PROPN
ejpam-4652	157	10	>	>	SYM
ejpam-4652	157	11	1	1	NUM
ejpam-4652	157	12	and	and	CCONJ
ejpam-4652	157	13	h	h	DET
ejpam-4652	157	14	a	a	DET
ejpam-4652	157	15	non	non	ADJ
ejpam-4652	157	16	-	-	ADJ
ejpam-4652	157	17	trivial	trivial	ADJ
ejpam-4652	157	18	connected	connected	ADJ
ejpam-4652	157	19	graph	graph	NOUN
ejpam-4652	157	20	with	with	ADP
ejpam-4652	157	21	γ(h	γ(h	NOUN
ejpam-4652	157	22	)	)	PUNCT
ejpam-4652	157	23	̸=	̸=	PROPN
ejpam-4652	157	24	1	1	NUM
ejpam-4652	157	25	.	.	PUNCT
ejpam-4652	158	1	then	then	ADV
ejpam-4652	158	2	a×c	a×c	PROPN
ejpam-4652	158	3	⊆	⊆	NUM
ejpam-4652	158	4	v	v	NOUN
ejpam-4652	158	5	(	(	PUNCT
ejpam-4652	158	6	g[h	g[h	PROPN
ejpam-4652	158	7	]	]	PUNCT
ejpam-4652	158	8	)	)	PUNCT
ejpam-4652	158	9	induces	induce	VERB
ejpam-4652	158	10	a	a	DET
ejpam-4652	158	11	dominated	dominate	VERB
ejpam-4652	158	12	superclique	superclique	NOUN
ejpam-4652	158	13	in	in	ADP
ejpam-4652	158	14	g[h	g[h	NOUN
ejpam-4652	158	15	]	]	PUNCT
ejpam-4652	158	16	if	if	SCONJ
ejpam-4652	158	17	and	and	CCONJ
ejpam-4652	158	18	only	only	ADV
ejpam-4652	158	19	if	if	SCONJ
ejpam-4652	158	20	one	one	NUM
ejpam-4652	158	21	of	of	ADP
ejpam-4652	158	22	the	the	DET
ejpam-4652	158	23	following	follow	VERB
ejpam-4652	158	24	hold	hold	NOUN
ejpam-4652	158	25	:	:	PUNCT
ejpam-4652	158	26	(	(	PUNCT
ejpam-4652	158	27	i	i	NOUN
ejpam-4652	158	28	)	)	PUNCT
ejpam-4652	158	29	a	a	DET
ejpam-4652	158	30	⊆	⊆	NUM
ejpam-4652	158	31	v	v	NOUN
ejpam-4652	158	32	(	(	PUNCT
ejpam-4652	158	33	g	g	NOUN
ejpam-4652	158	34	)	)	PUNCT
ejpam-4652	158	35	with	with	ADP
ejpam-4652	158	36	1	1	NUM
ejpam-4652	158	37	≤	≤	NUM
ejpam-4652	158	38	|a|	|a|	NOUN
ejpam-4652	158	39	≤	≤	NUM
ejpam-4652	158	40	n−	n−	NOUN
ejpam-4652	158	41	2	2	NUM
ejpam-4652	158	42	and	and	CCONJ
ejpam-4652	158	43	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	158	44	is	be	AUX
ejpam-4652	158	45	a	a	DET
ejpam-4652	158	46	superclique	superclique	NOUN
ejpam-4652	158	47	of	of	ADP
ejpam-4652	158	48	h.	h.	PROPN
ejpam-4652	158	49	(	(	PUNCT
ejpam-4652	158	50	ii	ii	PROPN
ejpam-4652	158	51	)	)	PUNCT
ejpam-4652	158	52	a	a	DET
ejpam-4652	158	53	⊆	⊆	NUM
ejpam-4652	158	54	v	v	NOUN
ejpam-4652	158	55	(	(	PUNCT
ejpam-4652	158	56	g	g	NOUN
ejpam-4652	158	57	)	)	PUNCT
ejpam-4652	158	58	with	with	ADP
ejpam-4652	158	59	|a|	|a|	NOUN
ejpam-4652	158	60	=	=	SYM
ejpam-4652	158	61	n−	n−	PROPN
ejpam-4652	158	62	1	1	NUM
ejpam-4652	158	63	and	and	CCONJ
ejpam-4652	158	64	⟨v	⟨v	NUM
ejpam-4652	158	65	(	(	PUNCT
ejpam-4652	158	66	h	h	NOUN
ejpam-4652	158	67	)	)	PUNCT
ejpam-4652	158	68	\	\	NOUN
ejpam-4652	158	69	c⟩	c⟩	PRON
ejpam-4652	158	70	is	be	AUX
ejpam-4652	158	71	a	a	DET
ejpam-4652	158	72	dominated	dominate	VERB
ejpam-4652	158	73	superclique	superclique	NOUN
ejpam-4652	158	74	of	of	ADP
ejpam-4652	158	75	h.	h.	NOUN
ejpam-4652	158	76	proof	proof	NOUN
ejpam-4652	158	77	:	:	PUNCT
ejpam-4652	158	78	let	let	VERB
ejpam-4652	158	79	g	g	PROPN
ejpam-4652	158	80	=	=	PROPN
ejpam-4652	158	81	kn	kn	PROPN
ejpam-4652	158	82	for	for	ADP
ejpam-4652	158	83	n	n	PROPN
ejpam-4652	158	84	>	>	SYM
ejpam-4652	158	85	1	1	NUM
ejpam-4652	158	86	and	and	CCONJ
ejpam-4652	158	87	h	h	DET
ejpam-4652	158	88	a	a	DET
ejpam-4652	158	89	nontrivial	nontrivial	ADJ
ejpam-4652	158	90	connected	connect	VERB
ejpam-4652	158	91	graph	graph	NOUN
ejpam-4652	158	92	with	with	ADP
ejpam-4652	158	93	γ(h	γ(h	NOUN
ejpam-4652	158	94	)	)	PUNCT
ejpam-4652	158	95	̸=	̸=	PROPN
ejpam-4652	158	96	1	1	NUM
ejpam-4652	158	97	.	.	PUNCT
ejpam-4652	158	98	suppose	suppose	VERB
ejpam-4652	158	99	a	a	DET
ejpam-4652	158	100	×	×	NOUN
ejpam-4652	158	101	c	c	NOUN
ejpam-4652	158	102	⊆	⊆	NUM
ejpam-4652	158	103	v	v	NOUN
ejpam-4652	158	104	(	(	PUNCT
ejpam-4652	158	105	g[h	g[h	PROPN
ejpam-4652	158	106	]	]	PUNCT
ejpam-4652	158	107	)	)	PUNCT
ejpam-4652	158	108	induces	induce	VERB
ejpam-4652	158	109	a	a	DET
ejpam-4652	158	110	dominated	dominate	VERB
ejpam-4652	158	111	superclique	superclique	NOUN
ejpam-4652	158	112	of	of	ADP
ejpam-4652	158	113	g[h	g[h	NOUN
ejpam-4652	158	114	]	]	PUNCT
ejpam-4652	158	115	.	.	PUNCT
ejpam-4652	159	1	by	by	ADP
ejpam-4652	159	2	remark	remark	PROPN
ejpam-4652	159	3	6(ii	6(ii	PROPN
ejpam-4652	159	4	)	)	PUNCT
ejpam-4652	159	5	,	,	PUNCT
ejpam-4652	159	6	v	v	X
ejpam-4652	159	7	(	(	PUNCT
ejpam-4652	159	8	g[h	g[h	PROPN
ejpam-4652	159	9	]	]	PUNCT
ejpam-4652	159	10	)	)	PUNCT
ejpam-4652	159	11	\	\	PUNCT
ejpam-4652	160	1	(	(	PUNCT
ejpam-4652	160	2	a	a	DET
ejpam-4652	160	3	×	×	NOUN
ejpam-4652	160	4	c	c	NOUN
ejpam-4652	160	5	)	)	PUNCT
ejpam-4652	160	6	=	=	SYM
ejpam-4652	161	1	(	(	PUNCT
ejpam-4652	161	2	v	v	NOUN
ejpam-4652	161	3	(	(	PUNCT
ejpam-4652	161	4	g	g	NOUN
ejpam-4652	161	5	)	)	PUNCT
ejpam-4652	161	6	\	\	PROPN
ejpam-4652	162	1	a	a	DET
ejpam-4652	162	2	)	)	PUNCT
ejpam-4652	162	3	×	×	NOUN
ejpam-4652	162	4	(	(	PUNCT
ejpam-4652	162	5	v	v	NOUN
ejpam-4652	162	6	(	(	PUNCT
ejpam-4652	162	7	h	h	NOUN
ejpam-4652	162	8	)	)	PUNCT
ejpam-4652	162	9	\	\	PROPN
ejpam-4652	162	10	c	c	X
ejpam-4652	162	11	)	)	PUNCT
ejpam-4652	162	12	is	be	AUX
ejpam-4652	162	13	a	a	DET
ejpam-4652	162	14	dominating	dominating	NOUN
ejpam-4652	162	15	set	set	NOUN
ejpam-4652	162	16	of	of	ADP
ejpam-4652	162	17	g[h	g[h	NOUN
ejpam-4652	162	18	]	]	PUNCT
ejpam-4652	162	19	.	.	PUNCT
ejpam-4652	163	1	thus	thus	ADV
ejpam-4652	163	2	,	,	PUNCT
ejpam-4652	163	3	by	by	ADP
ejpam-4652	163	4	theorem	theorem	NOUN
ejpam-4652	163	5	2	2	NUM
ejpam-4652	163	6	,	,	PUNCT
ejpam-4652	163	7	v	v	NOUN
ejpam-4652	163	8	(	(	PUNCT
ejpam-4652	163	9	g	g	NOUN
ejpam-4652	163	10	)	)	PUNCT
ejpam-4652	163	11	\a	\a	VERB
ejpam-4652	163	12	is	be	AUX
ejpam-4652	163	13	a	a	DET
ejpam-4652	163	14	total	total	ADJ
ejpam-4652	163	15	dominating	dominating	NOUN
ejpam-4652	163	16	set	set	NOUN
ejpam-4652	163	17	of	of	ADP
ejpam-4652	163	18	g	g	PROPN
ejpam-4652	163	19	or	or	CCONJ
ejpam-4652	163	20	v	v	NOUN
ejpam-4652	163	21	(	(	PUNCT
ejpam-4652	163	22	g	g	NOUN
ejpam-4652	163	23	)	)	PUNCT
ejpam-4652	163	24	\a	\a	VERB
ejpam-4652	163	25	is	be	AUX
ejpam-4652	163	26	a	a	DET
ejpam-4652	163	27	dominating	dominating	NOUN
ejpam-4652	163	28	set	set	NOUN
ejpam-4652	163	29	of	of	ADP
ejpam-4652	163	30	g	g	PROPN
ejpam-4652	163	31	and	and	CCONJ
ejpam-4652	163	32	v	v	PROPN
ejpam-4652	163	33	(	(	PUNCT
ejpam-4652	163	34	h	h	NOUN
ejpam-4652	163	35	)	)	PUNCT
ejpam-4652	163	36	\	\	PUNCT
ejpam-4652	164	1	c	c	NOUN
ejpam-4652	164	2	is	be	AUX
ejpam-4652	164	3	a	a	DET
ejpam-4652	164	4	dominating	dominating	NOUN
ejpam-4652	164	5	set	set	NOUN
ejpam-4652	164	6	of	of	ADP
ejpam-4652	164	7	h.	h.	PROPN
ejpam-4652	164	8	since	since	SCONJ
ejpam-4652	164	9	g	g	PROPN
ejpam-4652	164	10	=	=	PROPN
ejpam-4652	164	11	kn	kn	PROPN
ejpam-4652	164	12	,	,	PUNCT
ejpam-4652	164	13	1	1	NUM
ejpam-4652	164	14	≤	≤	NUM
ejpam-4652	164	15	|a|	|a|	NOUN
ejpam-4652	164	16	≤	≤	NOUN
ejpam-4652	164	17	n	n	CCONJ
ejpam-4652	164	18	−	−	PROPN
ejpam-4652	164	19	2	2	NUM
ejpam-4652	164	20	or	or	CCONJ
ejpam-4652	164	21	|a|	|a|	NOUN
ejpam-4652	164	22	=	=	PROPN
ejpam-4652	164	23	n	n	CCONJ
ejpam-4652	164	24	−	−	PROPN
ejpam-4652	164	25	1	1	NUM
ejpam-4652	164	26	and	and	CCONJ
ejpam-4652	164	27	v	v	NOUN
ejpam-4652	164	28	(	(	PUNCT
ejpam-4652	164	29	h	h	NOUN
ejpam-4652	164	30	)	)	PUNCT
ejpam-4652	164	31	\	\	PUNCT
ejpam-4652	165	1	c	c	NOUN
ejpam-4652	165	2	is	be	AUX
ejpam-4652	165	3	a	a	DET
ejpam-4652	165	4	dominating	dominating	NOUN
ejpam-4652	165	5	set	set	NOUN
ejpam-4652	165	6	of	of	ADP
ejpam-4652	165	7	h.	h.	PROPN
ejpam-4652	165	8	by	by	ADP
ejpam-4652	165	9	lemma	lemma	PROPN
ejpam-4652	165	10	1	1	NUM
ejpam-4652	165	11	,	,	PUNCT
ejpam-4652	165	12	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	165	13	is	be	AUX
ejpam-4652	165	14	a	a	DET
ejpam-4652	165	15	superclique	superclique	NOUN
ejpam-4652	165	16	of	of	ADP
ejpam-4652	165	17	h.	h.	NOUN
ejpam-4652	165	18	thus	thus	ADV
ejpam-4652	165	19	,	,	PUNCT
ejpam-4652	165	20	(	(	PUNCT
ejpam-4652	165	21	i	i	NOUN
ejpam-4652	165	22	)	)	PUNCT
ejpam-4652	165	23	and	and	CCONJ
ejpam-4652	165	24	(	(	PUNCT
ejpam-4652	165	25	ii	ii	NOUN
ejpam-4652	165	26	)	)	PUNCT
ejpam-4652	165	27	hold	hold	VERB
ejpam-4652	165	28	.	.	PUNCT
ejpam-4652	166	1	the	the	DET
ejpam-4652	166	2	converse	converse	NOUN
ejpam-4652	166	3	follows	follow	VERB
ejpam-4652	166	4	immediately	immediately	ADV
ejpam-4652	166	5	from	from	ADP
ejpam-4652	166	6	theorem	theorem	ADJ
ejpam-4652	166	7	3	3	NUM
ejpam-4652	166	8	and	and	CCONJ
ejpam-4652	166	9	lemma	lemma	PROPN
ejpam-4652	166	10	1	1	NUM
ejpam-4652	166	11	.	.	PUNCT
ejpam-4652	166	12	proposition	proposition	NOUN
ejpam-4652	166	13	4	4	NUM
ejpam-4652	166	14	.	.	PUNCT
ejpam-4652	167	1	[	[	X
ejpam-4652	167	2	1	1	X
ejpam-4652	167	3	]	]	PUNCT
ejpam-4652	167	4	let	let	VERB
ejpam-4652	167	5	g	g	PRON
ejpam-4652	167	6	be	be	AUX
ejpam-4652	167	7	a	a	DET
ejpam-4652	167	8	non	non	ADJ
ejpam-4652	167	9	-	-	ADJ
ejpam-4652	167	10	trivial	trivial	ADJ
ejpam-4652	167	11	connected	connected	ADJ
ejpam-4652	167	12	graph	graph	NOUN
ejpam-4652	167	13	with	with	ADP
ejpam-4652	167	14	diam(g	diam(g	NOUN
ejpam-4652	167	15	)	)	PUNCT
ejpam-4652	167	16	≤	≤	NOUN
ejpam-4652	167	17	2	2	NUM
ejpam-4652	167	18	.	.	PUNCT
ejpam-4652	168	1	then	then	ADV
ejpam-4652	168	2	w	w	PROPN
ejpam-4652	168	3	⊆	⊆	NUM
ejpam-4652	168	4	v	v	ADP
ejpam-4652	168	5	(	(	PUNCT
ejpam-4652	168	6	g	g	NOUN
ejpam-4652	168	7	)	)	PUNCT
ejpam-4652	168	8	\c	\c	NOUN
ejpam-4652	168	9	is	be	AUX
ejpam-4652	168	10	a	a	DET
ejpam-4652	168	11	strong	strong	ADJ
ejpam-4652	168	12	resolving	resolving	NOUN
ejpam-4652	168	13	set	set	NOUN
ejpam-4652	168	14	of	of	ADP
ejpam-4652	168	15	g	g	PROPN
ejpam-4652	168	16	if	if	SCONJ
ejpam-4652	169	1	and	and	CCONJ
ejpam-4652	169	2	only	only	ADV
ejpam-4652	169	3	if	if	SCONJ
ejpam-4652	169	4	c	c	NOUN
ejpam-4652	169	5	=	=	SYM
ejpam-4652	169	6	∅	∅	NOUN
ejpam-4652	169	7	or	or	CCONJ
ejpam-4652	169	8	c	c	NOUN
ejpam-4652	169	9	is	be	AUX
ejpam-4652	169	10	a	a	DET
ejpam-4652	169	11	superclique	superclique	NOUN
ejpam-4652	169	12	in	in	ADP
ejpam-4652	169	13	g.	g.	PROPN
ejpam-4652	169	14	in	in	ADP
ejpam-4652	169	15	particular	particular	ADJ
ejpam-4652	169	16	,	,	PUNCT
ejpam-4652	169	17	sdim(g	sdim(g	PROPN
ejpam-4652	169	18	)	)	PUNCT
ejpam-4652	169	19	=	=	SYM
ejpam-4652	169	20	|v	|v	PROPN
ejpam-4652	169	21	(	(	PUNCT
ejpam-4652	169	22	g)|	g)|	NOUN
ejpam-4652	169	23	−	−	NOUN
ejpam-4652	169	24	ωs(g	ωs(g	NUM
ejpam-4652	169	25	)	)	PUNCT
ejpam-4652	169	26	.	.	PUNCT
ejpam-4652	170	1	theorem	theorem	ADJ
ejpam-4652	170	2	4	4	NUM
ejpam-4652	170	3	.	.	PUNCT
ejpam-4652	171	1	let	let	VERB
ejpam-4652	171	2	g	g	PROPN
ejpam-4652	171	3	=	=	PROPN
ejpam-4652	171	4	kn	kn	PROPN
ejpam-4652	171	5	for	for	ADP
ejpam-4652	171	6	n	n	PROPN
ejpam-4652	171	7	>	>	SYM
ejpam-4652	171	8	1	1	NUM
ejpam-4652	171	9	and	and	CCONJ
ejpam-4652	171	10	h	h	DET
ejpam-4652	171	11	a	a	DET
ejpam-4652	171	12	non	non	ADJ
ejpam-4652	171	13	-	-	ADJ
ejpam-4652	171	14	trivial	trivial	ADJ
ejpam-4652	171	15	connected	connected	ADJ
ejpam-4652	171	16	graph	graph	NOUN
ejpam-4652	171	17	with	with	ADP
ejpam-4652	171	18	γ(h	γ(h	NOUN
ejpam-4652	171	19	)	)	PUNCT
ejpam-4652	171	20	̸=	̸=	PROPN
ejpam-4652	171	21	1	1	NUM
ejpam-4652	171	22	.	.	PUNCT
ejpam-4652	172	1	a	a	DET
ejpam-4652	172	2	subset	subset	NOUN
ejpam-4652	172	3	s	s	X
ejpam-4652	172	4	of	of	ADP
ejpam-4652	172	5	v	v	NOUN
ejpam-4652	172	6	(	(	PUNCT
ejpam-4652	172	7	g[h	g[h	PROPN
ejpam-4652	172	8	]	]	PUNCT
ejpam-4652	172	9	)	)	PUNCT
ejpam-4652	172	10	is	be	AUX
ejpam-4652	172	11	a	a	DET
ejpam-4652	172	12	strong	strong	ADJ
ejpam-4652	172	13	resolving	resolving	NOUN
ejpam-4652	172	14	dominating	dominating	NOUN
ejpam-4652	172	15	set	set	NOUN
ejpam-4652	172	16	of	of	ADP
ejpam-4652	172	17	g[h	g[h	PROPN
ejpam-4652	172	18	]	]	PUNCT
ejpam-4652	172	19	if	if	SCONJ
ejpam-4652	172	20	and	and	CCONJ
ejpam-4652	172	21	only	only	ADV
ejpam-4652	172	22	if	if	SCONJ
ejpam-4652	172	23	s	s	VERB
ejpam-4652	172	24	=	=	SYM
ejpam-4652	172	25	v	v	NOUN
ejpam-4652	172	26	(	(	PUNCT
ejpam-4652	172	27	g[h	g[h	PROPN
ejpam-4652	172	28	]	]	PUNCT
ejpam-4652	172	29	)	)	PUNCT
ejpam-4652	172	30	\	\	PUNCT
ejpam-4652	173	1	(	(	PUNCT
ejpam-4652	173	2	a×	a×	NOUN
ejpam-4652	173	3	c	c	NOUN
ejpam-4652	173	4	)	)	PUNCT
ejpam-4652	173	5	satisying	satisye	VERB
ejpam-4652	173	6	either	either	PRON
ejpam-4652	173	7	of	of	ADP
ejpam-4652	173	8	the	the	DET
ejpam-4652	173	9	following	following	NOUN
ejpam-4652	173	10	:	:	PUNCT
ejpam-4652	173	11	(	(	PUNCT
ejpam-4652	173	12	i	i	NOUN
ejpam-4652	173	13	)	)	PUNCT
ejpam-4652	173	14	a	a	DET
ejpam-4652	173	15	⊆	⊆	NUM
ejpam-4652	173	16	v	v	NOUN
ejpam-4652	173	17	(	(	PUNCT
ejpam-4652	173	18	g	g	NOUN
ejpam-4652	173	19	)	)	PUNCT
ejpam-4652	173	20	with	with	ADP
ejpam-4652	173	21	1	1	NUM
ejpam-4652	173	22	≤	≤	NUM
ejpam-4652	173	23	|a|	|a|	NOUN
ejpam-4652	173	24	≤	≤	NUM
ejpam-4652	173	25	n−	n−	NOUN
ejpam-4652	173	26	2	2	NUM
ejpam-4652	173	27	and	and	CCONJ
ejpam-4652	173	28	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	173	29	is	be	AUX
ejpam-4652	173	30	a	a	DET
ejpam-4652	173	31	superclique	superclique	NOUN
ejpam-4652	173	32	of	of	ADP
ejpam-4652	173	33	h.	h.	PROPN
ejpam-4652	173	34	(	(	PUNCT
ejpam-4652	173	35	ii	ii	PROPN
ejpam-4652	173	36	)	)	PUNCT
ejpam-4652	173	37	a	a	DET
ejpam-4652	173	38	⊆	⊆	NUM
ejpam-4652	173	39	v	v	NOUN
ejpam-4652	173	40	(	(	PUNCT
ejpam-4652	173	41	g	g	NOUN
ejpam-4652	173	42	)	)	PUNCT
ejpam-4652	173	43	with	with	ADP
ejpam-4652	173	44	|a|	|a|	NOUN
ejpam-4652	173	45	=	=	SYM
ejpam-4652	173	46	n−	n−	PROPN
ejpam-4652	173	47	1	1	NUM
ejpam-4652	173	48	and	and	CCONJ
ejpam-4652	173	49	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	173	50	is	be	AUX
ejpam-4652	173	51	a	a	DET
ejpam-4652	173	52	dominated	dominate	VERB
ejpam-4652	173	53	superclique	superclique	NOUN
ejpam-4652	173	54	of	of	ADP
ejpam-4652	173	55	g[h	g[h	NOUN
ejpam-4652	173	56	]	]	PUNCT
ejpam-4652	173	57	.	.	PUNCT
ejpam-4652	174	1	proof	proof	NOUN
ejpam-4652	174	2	:	:	PUNCT
ejpam-4652	174	3	let	let	VERB
ejpam-4652	174	4	s	s	PRON
ejpam-4652	174	5	be	be	AUX
ejpam-4652	174	6	a	a	DET
ejpam-4652	174	7	strong	strong	ADJ
ejpam-4652	174	8	resolving	resolving	NOUN
ejpam-4652	174	9	dominating	dominating	NOUN
ejpam-4652	174	10	set	set	NOUN
ejpam-4652	174	11	of	of	ADP
ejpam-4652	174	12	g[h	g[h	NOUN
ejpam-4652	174	13	]	]	PUNCT
ejpam-4652	174	14	.	.	PUNCT
ejpam-4652	175	1	since	since	SCONJ
ejpam-4652	175	2	diam(g[h	diam(g[h	PROPN
ejpam-4652	175	3	]	]	PUNCT
ejpam-4652	175	4	)	)	PUNCT
ejpam-4652	175	5	=	=	SYM
ejpam-4652	175	6	2	2	X
ejpam-4652	175	7	,	,	PUNCT
ejpam-4652	175	8	by	by	ADP
ejpam-4652	175	9	proposition	proposition	NOUN
ejpam-4652	175	10	4	4	NUM
ejpam-4652	175	11	,	,	PUNCT
ejpam-4652	175	12	s	s	PART
ejpam-4652	175	13	=	=	SYM
ejpam-4652	175	14	v	v	NOUN
ejpam-4652	175	15	(	(	PUNCT
ejpam-4652	175	16	g[h	g[h	PROPN
ejpam-4652	175	17	]	]	PUNCT
ejpam-4652	175	18	)	)	PUNCT
ejpam-4652	175	19	\	\	PROPN
ejpam-4652	175	20	c0	c0	NOUN
ejpam-4652	175	21	,	,	PUNCT
ejpam-4652	175	22	where	where	SCONJ
ejpam-4652	175	23	c0	c0	PROPN
ejpam-4652	175	24	=	=	SYM
ejpam-4652	175	25	∅	∅	NOUN
ejpam-4652	175	26	or	or	CCONJ
ejpam-4652	175	27	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	175	28	is	be	AUX
ejpam-4652	175	29	a	a	DET
ejpam-4652	175	30	superclique	superclique	NOUN
ejpam-4652	175	31	of	of	ADP
ejpam-4652	175	32	g[h	g[h	NOUN
ejpam-4652	175	33	]	]	PUNCT
ejpam-4652	175	34	.	.	PUNCT
ejpam-4652	176	1	by	by	ADP
ejpam-4652	176	2	lemma	lemma	PROPN
ejpam-4652	176	3	2	2	NUM
ejpam-4652	176	4	,	,	PUNCT
ejpam-4652	176	5	(	(	PUNCT
ejpam-4652	176	6	i	i	NOUN
ejpam-4652	176	7	)	)	PUNCT
ejpam-4652	176	8	and	and	CCONJ
ejpam-4652	176	9	(	(	PUNCT
ejpam-4652	176	10	ii	ii	NOUN
ejpam-4652	176	11	)	)	PUNCT
ejpam-4652	176	12	follow	follow	VERB
ejpam-4652	176	13	.	.	PUNCT
ejpam-4652	177	1	for	for	ADP
ejpam-4652	177	2	the	the	DET
ejpam-4652	177	3	converse	converse	NOUN
ejpam-4652	177	4	,	,	PUNCT
ejpam-4652	177	5	suppose	suppose	VERB
ejpam-4652	177	6	s	s	VERB
ejpam-4652	177	7	=	=	SYM
ejpam-4652	177	8	v	v	PROPN
ejpam-4652	177	9	(	(	PUNCT
ejpam-4652	177	10	g[h	g[h	PROPN
ejpam-4652	177	11	]	]	PUNCT
ejpam-4652	177	12	)	)	PUNCT
ejpam-4652	177	13	\	\	PUNCT
ejpam-4652	178	1	(	(	PUNCT
ejpam-4652	178	2	a×	a×	NOUN
ejpam-4652	178	3	c	c	X
ejpam-4652	178	4	)	)	PUNCT
ejpam-4652	178	5	satisfying	satisfy	VERB
ejpam-4652	178	6	condition	condition	NOUN
ejpam-4652	178	7	(	(	PUNCT
ejpam-4652	178	8	i	i	NOUN
ejpam-4652	178	9	)	)	PUNCT
ejpam-4652	178	10	or	or	CCONJ
ejpam-4652	178	11	(	(	PUNCT
ejpam-4652	178	12	ii	ii	NOUN
ejpam-4652	178	13	)	)	PUNCT
ejpam-4652	178	14	.	.	PUNCT
ejpam-4652	179	1	by	by	ADP
ejpam-4652	179	2	lemma	lemma	PROPN
ejpam-4652	179	3	2	2	NUM
ejpam-4652	179	4	,	,	PUNCT
ejpam-4652	179	5	⟨a×	⟨a×	NOUN
ejpam-4652	179	6	c⟩	c⟩	ADV
ejpam-4652	179	7	is	be	AUX
ejpam-4652	179	8	a	a	DET
ejpam-4652	179	9	dominated	dominate	VERB
ejpam-4652	179	10	superclique	superclique	NOUN
ejpam-4652	179	11	of	of	ADP
ejpam-4652	179	12	g[h	g[h	NOUN
ejpam-4652	179	13	]	]	PUNCT
ejpam-4652	179	14	.	.	PUNCT
ejpam-4652	180	1	since	since	SCONJ
ejpam-4652	180	2	diam(g[h	diam(g[h	PROPN
ejpam-4652	180	3	]	]	PUNCT
ejpam-4652	180	4	)	)	PUNCT
ejpam-4652	180	5	=	=	SYM
ejpam-4652	180	6	2	2	NUM
ejpam-4652	180	7	,	,	PUNCT
ejpam-4652	180	8	s	s	VERB
ejpam-4652	180	9	is	be	AUX
ejpam-4652	180	10	a	a	DET
ejpam-4652	180	11	strong	strong	ADJ
ejpam-4652	180	12	resolving	resolving	NOUN
ejpam-4652	180	13	dominating	dominating	NOUN
ejpam-4652	180	14	set	set	NOUN
ejpam-4652	180	15	of	of	ADP
ejpam-4652	180	16	g[h	g[h	PROPN
ejpam-4652	180	17	]	]	PUNCT
ejpam-4652	180	18	by	by	ADP
ejpam-4652	180	19	proposition	proposition	NOUN
ejpam-4652	180	20	4	4	NUM
ejpam-4652	180	21	.	.	PUNCT
ejpam-4652	181	1	lemma	lemma	PROPN
ejpam-4652	181	2	3	3	X
ejpam-4652	181	3	.	.	PUNCT
ejpam-4652	182	1	let	let	VERB
ejpam-4652	182	2	g	g	PROPN
ejpam-4652	182	3	=	=	PROPN
ejpam-4652	182	4	kn	kn	PROPN
ejpam-4652	182	5	for	for	ADP
ejpam-4652	182	6	n	n	PROPN
ejpam-4652	182	7	>	>	SYM
ejpam-4652	182	8	1	1	NUM
ejpam-4652	182	9	and	and	CCONJ
ejpam-4652	182	10	h	h	DET
ejpam-4652	182	11	a	a	DET
ejpam-4652	182	12	non	non	ADJ
ejpam-4652	182	13	-	-	ADJ
ejpam-4652	182	14	trivial	trivial	ADJ
ejpam-4652	182	15	connected	connected	ADJ
ejpam-4652	182	16	graph	graph	NOUN
ejpam-4652	182	17	with	with	ADP
ejpam-4652	182	18	γ(h	γ(h	NOUN
ejpam-4652	182	19	)	)	PUNCT
ejpam-4652	182	20	=	=	SYM
ejpam-4652	183	1	1	1	X
ejpam-4652	183	2	.	.	PUNCT
ejpam-4652	184	1	then	then	ADV
ejpam-4652	184	2	a×c	a×c	PROPN
ejpam-4652	184	3	⊆	⊆	NUM
ejpam-4652	184	4	v	v	NOUN
ejpam-4652	184	5	(	(	PUNCT
ejpam-4652	184	6	g[h	g[h	PROPN
ejpam-4652	184	7	]	]	PUNCT
ejpam-4652	184	8	)	)	PUNCT
ejpam-4652	184	9	is	be	AUX
ejpam-4652	184	10	a	a	DET
ejpam-4652	184	11	superclique	superclique	NOUN
ejpam-4652	184	12	in	in	ADP
ejpam-4652	184	13	g[h	g[h	NOUN
ejpam-4652	184	14	]	]	PUNCT
ejpam-4652	184	15	if	if	SCONJ
ejpam-4652	185	1	and	and	CCONJ
ejpam-4652	185	2	only	only	ADV
ejpam-4652	185	3	if	if	SCONJ
ejpam-4652	185	4	a	a	PRON
ejpam-4652	185	5	is	be	AUX
ejpam-4652	185	6	a	a	DET
ejpam-4652	185	7	nonempty	nonempty	ADJ
ejpam-4652	185	8	subset	subset	NOUN
ejpam-4652	185	9	of	of	ADP
ejpam-4652	185	10	v	v	NOUN
ejpam-4652	185	11	(	(	PUNCT
ejpam-4652	185	12	g	g	NOUN
ejpam-4652	185	13	)	)	PUNCT
ejpam-4652	185	14	and	and	CCONJ
ejpam-4652	185	15	c	c	PROPN
ejpam-4652	185	16	is	be	AUX
ejpam-4652	185	17	a	a	DET
ejpam-4652	185	18	superclique	superclique	NOUN
ejpam-4652	185	19	in	in	ADP
ejpam-4652	185	20	h	h	NOUN
ejpam-4652	185	21	such	such	ADJ
ejpam-4652	185	22	that	that	PRON
ejpam-4652	185	23	|a|	|a|	PROPN
ejpam-4652	185	24	=	=	SYM
ejpam-4652	185	25	1	1	NUM
ejpam-4652	185	26	whenever	whenever	SCONJ
ejpam-4652	185	27	c	c	NOUN
ejpam-4652	185	28	∩c∗	∩c∗	SYM
ejpam-4652	185	29	̸=	̸=	PROPN
ejpam-4652	185	30	∅	∅	NOUN
ejpam-4652	185	31	for	for	ADP
ejpam-4652	185	32	some	some	DET
ejpam-4652	185	33	γ	γ	NOUN
ejpam-4652	185	34	-	-	PUNCT
ejpam-4652	185	35	set	set	ADJ
ejpam-4652	185	36	c∗	c∗	NOUN
ejpam-4652	185	37	of	of	ADP
ejpam-4652	185	38	h.	h.	PROPN
ejpam-4652	185	39	proof	proof	PROPN
ejpam-4652	185	40	:	:	PUNCT
ejpam-4652	185	41	suppose	suppose	VERB
ejpam-4652	185	42	a	a	DET
ejpam-4652	185	43	×	×	NOUN
ejpam-4652	185	44	c	c	NOUN
ejpam-4652	185	45	⊆	⊆	NUM
ejpam-4652	185	46	v	v	NOUN
ejpam-4652	185	47	(	(	PUNCT
ejpam-4652	185	48	g[h	g[h	PROPN
ejpam-4652	185	49	]	]	PUNCT
ejpam-4652	185	50	)	)	PUNCT
ejpam-4652	185	51	is	be	AUX
ejpam-4652	185	52	a	a	DET
ejpam-4652	185	53	superclique	superclique	NOUN
ejpam-4652	185	54	in	in	ADP
ejpam-4652	185	55	g[h	g[h	NOUN
ejpam-4652	185	56	]	]	PUNCT
ejpam-4652	185	57	.	.	PUNCT
ejpam-4652	186	1	then	then	ADV
ejpam-4652	186	2	a	a	DET
ejpam-4652	186	3	⊆	⊆	NUM
ejpam-4652	186	4	v	v	NOUN
ejpam-4652	186	5	(	(	PUNCT
ejpam-4652	186	6	g	g	NOUN
ejpam-4652	186	7	)	)	PUNCT
ejpam-4652	186	8	,	,	PUNCT
ejpam-4652	186	9	c	c	PROPN
ejpam-4652	186	10	⊆	⊆	NUM
ejpam-4652	186	11	v	v	X
ejpam-4652	186	12	(	(	PUNCT
ejpam-4652	186	13	h	h	NOUN
ejpam-4652	186	14	)	)	PUNCT
ejpam-4652	186	15	,	,	PUNCT
ejpam-4652	186	16	a	a	DET
ejpam-4652	186	17	̸=	̸=	PROPN
ejpam-4652	186	18	∅	∅	NOUN
ejpam-4652	186	19	and	and	CCONJ
ejpam-4652	186	20	c	c	ADP
ejpam-4652	186	21	̸=	̸=	PROPN
ejpam-4652	186	22	∅.	∅.	ADV
ejpam-4652	186	23	if	if	SCONJ
ejpam-4652	186	24	|c|	|c|	PROPN
ejpam-4652	186	25	=	=	SYM
ejpam-4652	186	26	1	1	NUM
ejpam-4652	186	27	,	,	PUNCT
ejpam-4652	186	28	then	then	ADV
ejpam-4652	186	29	c	c	PROPN
ejpam-4652	186	30	is	be	AUX
ejpam-4652	186	31	a	a	DET
ejpam-4652	186	32	superclique	superclique	NOUN
ejpam-4652	186	33	in	in	ADP
ejpam-4652	186	34	h.	h.	PROPN
ejpam-4652	186	35	suppose	suppose	VERB
ejpam-4652	186	36	|c|	|c|	PROPN
ejpam-4652	186	37	≥	≥	NUM
ejpam-4652	186	38	2	2	NUM
ejpam-4652	186	39	and	and	CCONJ
ejpam-4652	186	40	x	x	NOUN
ejpam-4652	186	41	,	,	PUNCT
ejpam-4652	186	42	y	y	PROPN
ejpam-4652	186	43	∈	∈	PROPN
ejpam-4652	186	44	c	c	X
ejpam-4652	186	45	where	where	SCONJ
ejpam-4652	186	46	x	x	X
ejpam-4652	186	47	̸=	̸=	PROPN
ejpam-4652	186	48	y.	y.	PROPN
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ejpam-4652	186	50	(	(	PUNCT
ejpam-4652	186	51	u	u	NOUN
ejpam-4652	186	52	,	,	PUNCT
ejpam-4652	186	53	x)(u	x)(u	PROPN
ejpam-4652	186	54	,	,	PUNCT
ejpam-4652	186	55	y	y	NOUN
ejpam-4652	186	56	)	)	PUNCT
ejpam-4652	186	57	∈	∈	PROPN
ejpam-4652	187	1	a×c	a×c	PROPN
ejpam-4652	187	2	for	for	ADP
ejpam-4652	187	3	all	all	DET
ejpam-4652	187	4	u	u	PROPN
ejpam-4652	187	5	∈	∈	PROPN
ejpam-4652	187	6	a.	a.	NOUN
ejpam-4652	187	7	since	since	SCONJ
ejpam-4652	187	8	(	(	PUNCT
ejpam-4652	187	9	u	u	NOUN
ejpam-4652	187	10	,	,	PUNCT
ejpam-4652	187	11	x	x	NOUN
ejpam-4652	187	12	)	)	PUNCT
ejpam-4652	187	13	̸=	̸=	PROPN
ejpam-4652	187	14	(	(	PUNCT
ejpam-4652	187	15	u	u	NOUN
ejpam-4652	187	16	,	,	PUNCT
ejpam-4652	187	17	y	y	PROPN
ejpam-4652	187	18	)	)	PUNCT
ejpam-4652	187	19	and	and	CCONJ
ejpam-4652	187	20	a×	a×	PROPN
ejpam-4652	187	21	c	c	PROPN
ejpam-4652	187	22	is	be	AUX
ejpam-4652	187	23	a	a	DET
ejpam-4652	187	24	superclique	superclique	ADJ
ejpam-4652	187	25	ing[h	ing[h	NOUN
ejpam-4652	187	26	]	]	X
ejpam-4652	187	27	,	,	PUNCT
ejpam-4652	187	28	(	(	PUNCT
ejpam-4652	187	29	u	u	NOUN
ejpam-4652	187	30	,	,	PUNCT
ejpam-4652	187	31	x)(u	x)(u	PROPN
ejpam-4652	187	32	,	,	PUNCT
ejpam-4652	187	33	y	y	NOUN
ejpam-4652	187	34	)	)	PUNCT
ejpam-4652	187	35	∈	∈	NOUN
ejpam-4652	187	36	e(g[h	e(g[h	NOUN
ejpam-4652	187	37	]	]	PUNCT
ejpam-4652	187	38	)	)	PUNCT
ejpam-4652	187	39	and	and	CCONJ
ejpam-4652	187	40	(	(	PUNCT
ejpam-4652	187	41	w	w	PROPN
ejpam-4652	187	42	,	,	PUNCT
ejpam-4652	187	43	z	z	NOUN
ejpam-4652	187	44	)	)	PUNCT
ejpam-4652	187	45	∈	∈	PROPN
ejpam-4652	187	46	ng[h]((u	ng[h]((u	NOUN
ejpam-4652	187	47	,	,	PUNCT
ejpam-4652	187	48	x))\ng[h]((u	x))\ng[h]((u	PROPN
ejpam-4652	187	49	,	,	PUNCT
ejpam-4652	187	50	y	y	NOUN
ejpam-4652	187	51	)	)	PUNCT
ejpam-4652	187	52	)	)	PUNCT
ejpam-4652	188	1	g.	g.	PROPN
ejpam-4652	188	2	monsanto	monsanto	PROPN
ejpam-4652	188	3	,	,	PUNCT
ejpam-4652	188	4	p.	p.	PROPN
ejpam-4652	188	5	acal	acal	PROPN
ejpam-4652	188	6	,	,	PUNCT
ejpam-4652	188	7	h.	h.	PROPN
ejpam-4652	188	8	rara	rara	PROPN
ejpam-4652	188	9	/	/	SYM
ejpam-4652	188	10	eur	eur	PROPN
ejpam-4652	188	11	.	.	PUNCT
ejpam-4652	189	1	j.	j.	PROPN
ejpam-4652	189	2	pure	pure	PROPN
ejpam-4652	189	3	appl	appl	PROPN
ejpam-4652	189	4	.	.	PROPN
ejpam-4652	189	5	math	math	PROPN
ejpam-4652	189	6	,	,	PUNCT
ejpam-4652	189	7	16	16	NUM
ejpam-4652	189	8	(	(	PUNCT
ejpam-4652	189	9	1	1	NUM
ejpam-4652	189	10	)	)	PUNCT
ejpam-4652	189	11	(	(	PUNCT
ejpam-4652	189	12	2023	2023	NUM
ejpam-4652	189	13	)	)	PUNCT
ejpam-4652	189	14	,	,	PUNCT
ejpam-4652	189	15	363	363	NUM
ejpam-4652	189	16	-	-	SYM
ejpam-4652	189	17	372	372	NUM
ejpam-4652	189	18	369	369	NUM
ejpam-4652	189	19	or	or	CCONJ
ejpam-4652	189	20	(	(	PUNCT
ejpam-4652	189	21	w	w	PROPN
ejpam-4652	189	22	,	,	PUNCT
ejpam-4652	189	23	z	z	NOUN
ejpam-4652	189	24	)	)	PUNCT
ejpam-4652	189	25	∈	∈	PROPN
ejpam-4652	189	26	ng[h]((u	ng[h]((u	NOUN
ejpam-4652	189	27	,	,	PUNCT
ejpam-4652	189	28	y	y	NOUN
ejpam-4652	189	29	)	)	PUNCT
ejpam-4652	189	30	)	)	PUNCT
ejpam-4652	189	31	\	\	NOUN
ejpam-4652	189	32	ng[h]((u	ng[h]((u	NOUN
ejpam-4652	189	33	,	,	PUNCT
ejpam-4652	189	34	x	x	NOUN
ejpam-4652	189	35	)	)	PUNCT
ejpam-4652	189	36	)	)	PUNCT
ejpam-4652	189	37	for	for	ADP
ejpam-4652	189	38	some	some	PRON
ejpam-4652	189	39	(	(	PUNCT
ejpam-4652	189	40	w	w	PROPN
ejpam-4652	189	41	,	,	PUNCT
ejpam-4652	189	42	z	z	NOUN
ejpam-4652	189	43	)	)	PUNCT
ejpam-4652	189	44	∈	∈	NOUN
ejpam-4652	189	45	v	v	NOUN
ejpam-4652	189	46	(	(	PUNCT
ejpam-4652	189	47	g[h	g[h	PROPN
ejpam-4652	189	48	]	]	PUNCT
ejpam-4652	189	49	)	)	PUNCT
ejpam-4652	189	50	\	\	PUNCT
ejpam-4652	190	1	(	(	PUNCT
ejpam-4652	190	2	a	a	DET
ejpam-4652	190	3	×	×	NOUN
ejpam-4652	190	4	c	c	NOUN
ejpam-4652	190	5	)	)	PUNCT
ejpam-4652	190	6	.	.	PUNCT
ejpam-4652	191	1	thus	thus	ADV
ejpam-4652	191	2	,	,	PUNCT
ejpam-4652	191	3	xy	xy	PROPN
ejpam-4652	191	4	∈	∈	PROPN
ejpam-4652	191	5	e(h	e(h	PROPN
ejpam-4652	191	6	)	)	PUNCT
ejpam-4652	191	7	,	,	PUNCT
ejpam-4652	191	8	w	w	NOUN
ejpam-4652	191	9	=	=	SYM
ejpam-4652	191	10	u	u	PROPN
ejpam-4652	191	11	and	and	CCONJ
ejpam-4652	191	12	z	z	NOUN
ejpam-4652	191	13	∈	∈	PROPN
ejpam-4652	191	14	nh(x)\nh(y	nh(x)\nh(y	NOUN
ejpam-4652	191	15	)	)	PUNCT
ejpam-4652	191	16	or	or	CCONJ
ejpam-4652	191	17	z	z	NOUN
ejpam-4652	191	18	∈	∈	PROPN
ejpam-4652	191	19	nh(y)\nh(x	nh(y)\nh(x	PROPN
ejpam-4652	191	20	)	)	PUNCT
ejpam-4652	191	21	,	,	PUNCT
ejpam-4652	191	22	where	where	SCONJ
ejpam-4652	191	23	z	z	NOUN
ejpam-4652	191	24	/∈	/∈	PUNCT
ejpam-4652	191	25	c.	c.	PROPN
ejpam-4652	191	26	hence	hence	ADV
ejpam-4652	191	27	,	,	PUNCT
ejpam-4652	191	28	c	c	PROPN
ejpam-4652	191	29	is	be	AUX
ejpam-4652	191	30	a	a	DET
ejpam-4652	191	31	superclique	superclique	NOUN
ejpam-4652	191	32	in	in	ADP
ejpam-4652	191	33	h.	h.	NOUN
ejpam-4652	191	34	let	let	VERB
ejpam-4652	191	35	a	a	DET
ejpam-4652	191	36	∈	∈	NOUN
ejpam-4652	191	37	c	c	NOUN
ejpam-4652	191	38	where	where	SCONJ
ejpam-4652	191	39	{	{	PUNCT
ejpam-4652	191	40	a	a	PRON
ejpam-4652	191	41	}	}	PUNCT
ejpam-4652	191	42	is	be	AUX
ejpam-4652	191	43	a	a	DET
ejpam-4652	191	44	γ	γ	NOUN
ejpam-4652	191	45	-	-	PUNCT
ejpam-4652	191	46	set	set	NOUN
ejpam-4652	191	47	of	of	ADP
ejpam-4652	191	48	h.	h.	PROPN
ejpam-4652	191	49	suppose	suppose	VERB
ejpam-4652	191	50	|a|	|a|	PROPN
ejpam-4652	191	51	≥	≥	NOUN
ejpam-4652	191	52	2	2	NUM
ejpam-4652	191	53	and	and	CCONJ
ejpam-4652	191	54	let	let	VERB
ejpam-4652	191	55	u	u	NOUN
ejpam-4652	191	56	,	,	PUNCT
ejpam-4652	191	57	v	v	ADP
ejpam-4652	191	58	∈	∈	PROPN
ejpam-4652	191	59	a	a	PRON
ejpam-4652	191	60	,	,	PUNCT
ejpam-4652	191	61	where	where	SCONJ
ejpam-4652	191	62	u	u	NOUN
ejpam-4652	191	63	̸=	̸=	PROPN
ejpam-4652	191	64	v.	v.	CCONJ
ejpam-4652	191	65	then	then	ADV
ejpam-4652	191	66	(	(	PUNCT
ejpam-4652	191	67	u	u	NOUN
ejpam-4652	191	68	,	,	PUNCT
ejpam-4652	191	69	a	a	PRON
ejpam-4652	191	70	)	)	PUNCT
ejpam-4652	191	71	,	,	PUNCT
ejpam-4652	191	72	(	(	PUNCT
ejpam-4652	191	73	v	v	NOUN
ejpam-4652	191	74	,	,	PUNCT
ejpam-4652	191	75	a	a	PRON
ejpam-4652	191	76	)	)	PUNCT
ejpam-4652	191	77	∈	∈	PROPN
ejpam-4652	191	78	a	a	DET
ejpam-4652	191	79	×	×	NOUN
ejpam-4652	191	80	c	c	NOUN
ejpam-4652	191	81	,	,	PUNCT
ejpam-4652	191	82	(	(	PUNCT
ejpam-4652	191	83	u	u	NOUN
ejpam-4652	191	84	,	,	PUNCT
ejpam-4652	191	85	a	a	PRON
ejpam-4652	191	86	)	)	PUNCT
ejpam-4652	191	87	̸=	̸=	PROPN
ejpam-4652	191	88	(	(	PUNCT
ejpam-4652	191	89	v	v	NOUN
ejpam-4652	191	90	,	,	PUNCT
ejpam-4652	191	91	a	a	PRON
ejpam-4652	191	92	)	)	PUNCT
ejpam-4652	191	93	.	.	PUNCT
ejpam-4652	192	1	since	since	SCONJ
ejpam-4652	192	2	a	a	DET
ejpam-4652	192	3	×	×	NOUN
ejpam-4652	192	4	c	c	NOUN
ejpam-4652	192	5	is	be	AUX
ejpam-4652	192	6	a	a	DET
ejpam-4652	192	7	superclique	superclique	NOUN
ejpam-4652	192	8	,	,	PUNCT
ejpam-4652	192	9	there	there	PRON
ejpam-4652	192	10	exists	exist	VERB
ejpam-4652	192	11	(	(	PUNCT
ejpam-4652	192	12	w	w	PROPN
ejpam-4652	192	13	,	,	PUNCT
ejpam-4652	192	14	b	b	NOUN
ejpam-4652	192	15	)	)	PUNCT
ejpam-4652	192	16	∈	∈	NOUN
ejpam-4652	192	17	v	v	NOUN
ejpam-4652	192	18	(	(	PUNCT
ejpam-4652	192	19	g[h	g[h	PROPN
ejpam-4652	192	20	]	]	PUNCT
ejpam-4652	192	21	)	)	PUNCT
ejpam-4652	192	22	\	\	PUNCT
ejpam-4652	193	1	(	(	PUNCT
ejpam-4652	193	2	a×c	a×c	PROPN
ejpam-4652	193	3	)	)	PUNCT
ejpam-4652	194	1	such	such	ADJ
ejpam-4652	194	2	that	that	SCONJ
ejpam-4652	194	3	(	(	PUNCT
ejpam-4652	194	4	w	w	PROPN
ejpam-4652	194	5	,	,	PUNCT
ejpam-4652	194	6	b	b	NOUN
ejpam-4652	194	7	)	)	PUNCT
ejpam-4652	194	8	∈	∈	PROPN
ejpam-4652	194	9	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	194	10	,	,	PUNCT
ejpam-4652	194	11	a	a	PRON
ejpam-4652	194	12	)	)	PUNCT
ejpam-4652	194	13	)	)	PUNCT
ejpam-4652	194	14	\ng[h]((u	\ng[h]((u	PROPN
ejpam-4652	194	15	,	,	PUNCT
ejpam-4652	194	16	a	a	NOUN
ejpam-4652	194	17	)	)	PUNCT
ejpam-4652	194	18	)	)	PUNCT
ejpam-4652	194	19	or	or	CCONJ
ejpam-4652	194	20	(	(	PUNCT
ejpam-4652	194	21	w	w	PROPN
ejpam-4652	194	22	,	,	PUNCT
ejpam-4652	194	23	b	b	NOUN
ejpam-4652	194	24	)	)	PUNCT
ejpam-4652	194	25	∈	∈	PROPN
ejpam-4652	194	26	ng[h]((u	ng[h]((u	NOUN
ejpam-4652	194	27	,	,	PUNCT
ejpam-4652	194	28	a	a	PRON
ejpam-4652	194	29	)	)	PUNCT
ejpam-4652	194	30	)	)	PUNCT
ejpam-4652	194	31	\ng[h]((v	\ng[h]((v	NOUN
ejpam-4652	194	32	,	,	PUNCT
ejpam-4652	194	33	a	a	PRON
ejpam-4652	194	34	)	)	PUNCT
ejpam-4652	194	35	)	)	PUNCT
ejpam-4652	194	36	.	.	PUNCT
ejpam-4652	195	1	since	since	SCONJ
ejpam-4652	195	2	g	g	PROPN
ejpam-4652	195	3	is	be	AUX
ejpam-4652	195	4	complete	complete	ADJ
ejpam-4652	195	5	,	,	PUNCT
ejpam-4652	195	6	w	w	PROPN
ejpam-4652	195	7	=	=	PUNCT
ejpam-4652	195	8	u	u	NOUN
ejpam-4652	195	9	w	w	NOUN
ejpam-4652	195	10	=	=	SYM
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ejpam-4652	195	13	b	b	PROPN
ejpam-4652	195	14	/∈	/∈	PUNCT
ejpam-4652	195	15	nh(a	nh(a	NUM
ejpam-4652	195	16	)	)	PUNCT
ejpam-4652	195	17	.	.	PUNCT
ejpam-4652	196	1	this	this	PRON
ejpam-4652	196	2	is	be	AUX
ejpam-4652	196	3	a	a	DET
ejpam-4652	196	4	contrdiction	contrdiction	NOUN
ejpam-4652	196	5	since	since	SCONJ
ejpam-4652	196	6	{	{	PUNCT
ejpam-4652	196	7	a	a	PRON
ejpam-4652	196	8	}	}	PUNCT
ejpam-4652	196	9	is	be	AUX
ejpam-4652	196	10	a	a	DET
ejpam-4652	196	11	γ	γ	NOUN
ejpam-4652	196	12	-	-	PUNCT
ejpam-4652	196	13	set	set	NOUN
ejpam-4652	196	14	of	of	ADP
ejpam-4652	196	15	h.	h.	PROPN
ejpam-4652	196	16	thus	thus	ADV
ejpam-4652	196	17	,	,	PUNCT
ejpam-4652	196	18	|a|	|a|	PROPN
ejpam-4652	196	19	≤	≤	NOUN
ejpam-4652	196	20	1	1	NUM
ejpam-4652	196	21	.	.	PUNCT
ejpam-4652	197	1	since	since	SCONJ
ejpam-4652	197	2	a	a	DET
ejpam-4652	197	3	̸=	̸=	PROPN
ejpam-4652	197	4	∅	∅	NOUN
ejpam-4652	197	5	,	,	PUNCT
ejpam-4652	197	6	|a|	|a|	PROPN
ejpam-4652	197	7	=	=	SYM
ejpam-4652	197	8	1	1	NUM
ejpam-4652	197	9	.	.	PUNCT
ejpam-4652	197	10	coversely	coversely	ADV
ejpam-4652	197	11	,	,	PUNCT
ejpam-4652	197	12	suppose	suppose	VERB
ejpam-4652	197	13	a	a	DET
ejpam-4652	197	14	⊆	⊆	NUM
ejpam-4652	197	15	v	v	NOUN
ejpam-4652	197	16	(	(	PUNCT
ejpam-4652	197	17	g	g	NOUN
ejpam-4652	197	18	)	)	PUNCT
ejpam-4652	197	19	,	,	PUNCT
ejpam-4652	197	20	a	a	DET
ejpam-4652	197	21	̸=	̸=	PROPN
ejpam-4652	197	22	∅	∅	NOUN
ejpam-4652	197	23	and	and	CCONJ
ejpam-4652	197	24	c	c	NOUN
ejpam-4652	197	25	is	be	AUX
ejpam-4652	197	26	a	a	DET
ejpam-4652	197	27	superclique	superclique	NOUN
ejpam-4652	197	28	in	in	ADP
ejpam-4652	197	29	h	h	NOUN
ejpam-4652	197	30	such	such	ADJ
ejpam-4652	197	31	that	that	DET
ejpam-4652	197	32	|a|	|a|	PROPN
ejpam-4652	197	33	=	=	SYM
ejpam-4652	197	34	1	1	NUM
ejpam-4652	197	35	whenever	whenever	SCONJ
ejpam-4652	197	36	c	c	X
ejpam-4652	197	37	∩	∩	ADJ
ejpam-4652	197	38	c∗	c∗	PROPN
ejpam-4652	197	39	̸=	̸=	PROPN
ejpam-4652	197	40	∅	∅	NOUN
ejpam-4652	197	41	for	for	ADP
ejpam-4652	197	42	some	some	DET
ejpam-4652	197	43	γ	γ	NOUN
ejpam-4652	197	44	-	-	PUNCT
ejpam-4652	197	45	set	set	ADJ
ejpam-4652	197	46	c∗	c∗	NOUN
ejpam-4652	197	47	of	of	ADP
ejpam-4652	197	48	h.	h.	PROPN
ejpam-4652	197	49	then	then	ADV
ejpam-4652	197	50	a×	a×	VERB
ejpam-4652	197	51	c	c	NOUN
ejpam-4652	197	52	⊆	⊆	NUM
ejpam-4652	197	53	v	v	NOUN
ejpam-4652	197	54	(	(	PUNCT
ejpam-4652	197	55	g[h	g[h	PROPN
ejpam-4652	197	56	]	]	PUNCT
ejpam-4652	197	57	)	)	PUNCT
ejpam-4652	197	58	and	and	CCONJ
ejpam-4652	198	1	a×	a×	PROPN
ejpam-4652	198	2	c	c	VERB
ejpam-4652	198	3	̸=	̸=	PROPN
ejpam-4652	198	4	∅.	∅.	ADV
ejpam-4652	198	5	if	if	SCONJ
ejpam-4652	198	6	|a	|a	VERB
ejpam-4652	198	7	×	×	PROPN
ejpam-4652	198	8	c|	c|	PROPN
ejpam-4652	198	9	=	=	SYM
ejpam-4652	198	10	1	1	NUM
ejpam-4652	198	11	,	,	PUNCT
ejpam-4652	198	12	then	then	ADV
ejpam-4652	198	13	we	we	PRON
ejpam-4652	198	14	are	be	AUX
ejpam-4652	198	15	done	do	VERB
ejpam-4652	198	16	.	.	PUNCT
ejpam-4652	199	1	suppose	suppose	VERB
ejpam-4652	199	2	|a	|a	PROPN
ejpam-4652	199	3	×	×	PROPN
ejpam-4652	199	4	c|	c|	PROPN
ejpam-4652	199	5	≥	≥	NOUN
ejpam-4652	199	6	2	2	X
ejpam-4652	199	7	.	.	PUNCT
ejpam-4652	200	1	let	let	VERB
ejpam-4652	200	2	(	(	PUNCT
ejpam-4652	200	3	u	u	NOUN
ejpam-4652	200	4	,	,	PUNCT
ejpam-4652	200	5	x	x	NOUN
ejpam-4652	200	6	)	)	PUNCT
ejpam-4652	200	7	,	,	PUNCT
ejpam-4652	200	8	(	(	PUNCT
ejpam-4652	200	9	v	v	NOUN
ejpam-4652	200	10	,	,	PUNCT
ejpam-4652	200	11	y	y	NOUN
ejpam-4652	200	12	)	)	PUNCT
ejpam-4652	200	13	∈	∈	PROPN
ejpam-4652	200	14	a	a	DET
ejpam-4652	200	15	×	×	NOUN
ejpam-4652	200	16	c	c	NOUN
ejpam-4652	200	17	,	,	PUNCT
ejpam-4652	200	18	(	(	PUNCT
ejpam-4652	200	19	u	u	NOUN
ejpam-4652	200	20	,	,	PUNCT
ejpam-4652	200	21	x	x	NOUN
ejpam-4652	200	22	)	)	PUNCT
ejpam-4652	200	23	̸=	̸=	PROPN
ejpam-4652	200	24	(	(	PUNCT
ejpam-4652	200	25	v	v	NOUN
ejpam-4652	200	26	,	,	PUNCT
ejpam-4652	200	27	y	y	PROPN
ejpam-4652	200	28	)	)	PUNCT
ejpam-4652	200	29	.	.	PUNCT
ejpam-4652	201	1	consider	consider	VERB
ejpam-4652	201	2	the	the	DET
ejpam-4652	201	3	following	follow	VERB
ejpam-4652	201	4	cases	case	NOUN
ejpam-4652	201	5	:	:	PUNCT
ejpam-4652	201	6	case	case	NOUN
ejpam-4652	201	7	1	1	NUM
ejpam-4652	201	8	.	.	X
ejpam-4652	202	1	u	u	NOUN
ejpam-4652	203	1	=	=	NOUN
ejpam-4652	204	1	v	v	X
ejpam-4652	204	2	then	then	ADV
ejpam-4652	204	3	x	x	PART
ejpam-4652	204	4	̸=	̸=	PROPN
ejpam-4652	204	5	y.	y.	NOUN
ejpam-4652	204	6	since	since	SCONJ
ejpam-4652	204	7	x	x	X
ejpam-4652	204	8	,	,	PUNCT
ejpam-4652	204	9	y	y	PROPN
ejpam-4652	204	10	∈	∈	PROPN
ejpam-4652	204	11	c	c	PROPN
ejpam-4652	204	12	and	and	CCONJ
ejpam-4652	204	13	c	c	PROPN
ejpam-4652	204	14	is	be	AUX
ejpam-4652	204	15	a	a	DET
ejpam-4652	204	16	superclique	superclique	NOUN
ejpam-4652	204	17	in	in	ADP
ejpam-4652	204	18	h	h	NOUN
ejpam-4652	204	19	,	,	PUNCT
ejpam-4652	204	20	xy	xy	PROPN
ejpam-4652	204	21	∈	∈	PROPN
ejpam-4652	204	22	e(h	e(h	PROPN
ejpam-4652	204	23	)	)	PUNCT
ejpam-4652	204	24	and	and	CCONJ
ejpam-4652	204	25	there	there	PRON
ejpam-4652	204	26	exists	exist	VERB
ejpam-4652	204	27	z	z	PROPN
ejpam-4652	204	28	∈	∈	PROPN
ejpam-4652	204	29	nh(x	nh(x	NUM
ejpam-4652	204	30	)	)	PUNCT
ejpam-4652	204	31	\	\	NOUN
ejpam-4652	204	32	nh(y	nh(y	PUNCT
ejpam-4652	204	33	)	)	PUNCT
ejpam-4652	204	34	or	or	CCONJ
ejpam-4652	204	35	z	z	NOUN
ejpam-4652	204	36	∈	∈	PROPN
ejpam-4652	204	37	nh(y	nh(y	NOUN
ejpam-4652	204	38	)	)	PUNCT
ejpam-4652	204	39	\	\	NOUN
ejpam-4652	204	40	nh(x	nh(x	PUNCT
ejpam-4652	204	41	)	)	PUNCT
ejpam-4652	204	42	for	for	ADP
ejpam-4652	204	43	some	some	PRON
ejpam-4652	204	44	z	z	NOUN
ejpam-4652	204	45	∈	∈	PROPN
ejpam-4652	204	46	v	v	ADP
ejpam-4652	204	47	(	(	PUNCT
ejpam-4652	204	48	h	h	NOUN
ejpam-4652	204	49	)	)	PUNCT
ejpam-4652	204	50	\	\	PROPN
ejpam-4652	204	51	c.	c.	PROPN
ejpam-4652	204	52	hence	hence	ADV
ejpam-4652	204	53	,	,	PUNCT
ejpam-4652	204	54	(	(	PUNCT
ejpam-4652	204	55	u	u	NOUN
ejpam-4652	204	56	,	,	PUNCT
ejpam-4652	204	57	x)(v	x)(v	PROPN
ejpam-4652	204	58	,	,	PUNCT
ejpam-4652	204	59	y	y	NOUN
ejpam-4652	204	60	)	)	PUNCT
ejpam-4652	204	61	∈	∈	NOUN
ejpam-4652	204	62	e(g[h	e(g[h	NOUN
ejpam-4652	204	63	]	]	PUNCT
ejpam-4652	204	64	)	)	PUNCT
ejpam-4652	204	65	and	and	CCONJ
ejpam-4652	204	66	(	(	PUNCT
ejpam-4652	204	67	u	u	NOUN
ejpam-4652	204	68	,	,	PUNCT
ejpam-4652	204	69	z	z	NOUN
ejpam-4652	204	70	)	)	PUNCT
ejpam-4652	204	71	∈	∈	PROPN
ejpam-4652	204	72	ng[h]((u	ng[h]((u	NOUN
ejpam-4652	204	73	,	,	PUNCT
ejpam-4652	204	74	x))\ng[h]((v	x))\ng[h]((v	PROPN
ejpam-4652	204	75	,	,	PUNCT
ejpam-4652	204	76	y	y	NOUN
ejpam-4652	204	77	)	)	PUNCT
ejpam-4652	204	78	)	)	PUNCT
ejpam-4652	204	79	or	or	CCONJ
ejpam-4652	204	80	(	(	PUNCT
ejpam-4652	204	81	u	u	NOUN
ejpam-4652	204	82	,	,	PUNCT
ejpam-4652	204	83	z	z	NOUN
ejpam-4652	204	84	)	)	PUNCT
ejpam-4652	204	85	∈	∈	PROPN
ejpam-4652	204	86	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	204	87	,	,	PUNCT
ejpam-4652	204	88	y))\ng[h]((u	y))\ng[h]((u	PROPN
ejpam-4652	204	89	,	,	PUNCT
ejpam-4652	204	90	x	x	NOUN
ejpam-4652	204	91	)	)	PUNCT
ejpam-4652	204	92	)	)	PUNCT
ejpam-4652	204	93	,	,	PUNCT
ejpam-4652	204	94	where	where	SCONJ
ejpam-4652	204	95	(	(	PUNCT
ejpam-4652	204	96	u	u	NOUN
ejpam-4652	204	97	,	,	PUNCT
ejpam-4652	204	98	z	z	NOUN
ejpam-4652	204	99	)	)	PUNCT
ejpam-4652	204	100	∈	∈	NOUN
ejpam-4652	204	101	v	v	NOUN
ejpam-4652	204	102	(	(	PUNCT
ejpam-4652	204	103	g[h	g[h	PROPN
ejpam-4652	204	104	]	]	PUNCT
ejpam-4652	204	105	)	)	PUNCT
ejpam-4652	204	106	\	\	PROPN
ejpam-4652	204	107	c.	c.	NOUN
ejpam-4652	204	108	case	case	NOUN
ejpam-4652	204	109	2	2	NUM
ejpam-4652	204	110	.	.	X
ejpam-4652	204	111	u	u	NOUN
ejpam-4652	204	112	̸=	̸=	PROPN
ejpam-4652	204	113	v	v	NUM
ejpam-4652	204	114	subcase	subcase	NOUN
ejpam-4652	204	115	2.1	2.1	NUM
ejpam-4652	204	116	.	.	PUNCT
ejpam-4652	205	1	x	x	X
ejpam-4652	205	2	=	=	PUNCT
ejpam-4652	205	3	y	y	PROPN
ejpam-4652	205	4	since	since	SCONJ
ejpam-4652	205	5	u	u	PROPN
ejpam-4652	205	6	,	,	PUNCT
ejpam-4652	205	7	v	v	ADP
ejpam-4652	205	8	∈	∈	PROPN
ejpam-4652	205	9	a	a	PRON
ejpam-4652	205	10	,	,	PUNCT
ejpam-4652	205	11	u	u	PROPN
ejpam-4652	205	12	̸=	̸=	PROPN
ejpam-4652	205	13	v	v	NOUN
ejpam-4652	205	14	,	,	PUNCT
ejpam-4652	205	15	|a|	|a|	PROPN
ejpam-4652	205	16	≥	≥	NOUN
ejpam-4652	205	17	2	2	NUM
ejpam-4652	205	18	.	.	PUNCT
ejpam-4652	205	19	by	by	ADP
ejpam-4652	205	20	assumption	assumption	NOUN
ejpam-4652	205	21	,	,	PUNCT
ejpam-4652	206	1	if	if	SCONJ
ejpam-4652	206	2	x	x	SYM
ejpam-4652	206	3	∈	∈	PROPN
ejpam-4652	206	4	c	c	NOUN
ejpam-4652	206	5	,	,	PUNCT
ejpam-4652	206	6	then	then	ADV
ejpam-4652	206	7	{	{	PUNCT
ejpam-4652	206	8	x	x	X
ejpam-4652	206	9	}	}	PUNCT
ejpam-4652	206	10	is	be	AUX
ejpam-4652	206	11	not	not	PART
ejpam-4652	206	12	a	a	DET
ejpam-4652	206	13	γ	γ	NOUN
ejpam-4652	206	14	-	-	PUNCT
ejpam-4652	206	15	set	set	NOUN
ejpam-4652	206	16	of	of	ADP
ejpam-4652	206	17	h.	h.	PROPN
ejpam-4652	206	18	thus	thus	ADV
ejpam-4652	206	19	,	,	PUNCT
ejpam-4652	206	20	there	there	PRON
ejpam-4652	206	21	exists	exist	VERB
ejpam-4652	206	22	z	z	PROPN
ejpam-4652	206	23	∈	∈	PROPN
ejpam-4652	206	24	v	v	ADP
ejpam-4652	206	25	(	(	PUNCT
ejpam-4652	206	26	h	h	NOUN
ejpam-4652	206	27	)	)	PUNCT
ejpam-4652	206	28	\	\	NOUN
ejpam-4652	206	29	nh(x	nh(x	NUM
ejpam-4652	206	30	)	)	PUNCT
ejpam-4652	206	31	.	.	PUNCT
ejpam-4652	207	1	hence	hence	ADV
ejpam-4652	207	2	,	,	PUNCT
ejpam-4652	207	3	(	(	PUNCT
ejpam-4652	207	4	u	u	NOUN
ejpam-4652	207	5	,	,	PUNCT
ejpam-4652	207	6	z	z	NOUN
ejpam-4652	207	7	)	)	PUNCT
ejpam-4652	207	8	∈	∈	NOUN
ejpam-4652	207	9	v	v	NOUN
ejpam-4652	207	10	(	(	PUNCT
ejpam-4652	207	11	g[h	g[h	PROPN
ejpam-4652	207	12	]	]	PUNCT
ejpam-4652	207	13	)	)	PUNCT
ejpam-4652	207	14	\	\	PUNCT
ejpam-4652	208	1	(	(	PUNCT
ejpam-4652	208	2	a	a	DET
ejpam-4652	208	3	×	×	NOUN
ejpam-4652	208	4	c	c	NOUN
ejpam-4652	208	5	)	)	PUNCT
ejpam-4652	208	6	and	and	CCONJ
ejpam-4652	208	7	(	(	PUNCT
ejpam-4652	208	8	u	u	NOUN
ejpam-4652	208	9	,	,	PUNCT
ejpam-4652	208	10	z	z	NOUN
ejpam-4652	208	11	)	)	PUNCT
ejpam-4652	208	12	∈	∈	PROPN
ejpam-4652	208	13	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	208	14	,	,	PUNCT
ejpam-4652	208	15	y	y	NOUN
ejpam-4652	208	16	)	)	PUNCT
ejpam-4652	208	17	)	)	PUNCT
ejpam-4652	209	1	\ng[h]((u	\ng[h]((u	PROPN
ejpam-4652	209	2	,	,	PUNCT
ejpam-4652	209	3	x	x	NOUN
ejpam-4652	209	4	)	)	PUNCT
ejpam-4652	209	5	)	)	PUNCT
ejpam-4652	209	6	.	.	PUNCT
ejpam-4652	210	1	since	since	SCONJ
ejpam-4652	210	2	g	g	PROPN
ejpam-4652	210	3	is	be	AUX
ejpam-4652	210	4	complete	complete	ADJ
ejpam-4652	210	5	,	,	PUNCT
ejpam-4652	210	6	(	(	PUNCT
ejpam-4652	210	7	u	u	NOUN
ejpam-4652	210	8	,	,	PUNCT
ejpam-4652	210	9	x)(v	x)(v	PROPN
ejpam-4652	210	10	,	,	PUNCT
ejpam-4652	210	11	y	y	NOUN
ejpam-4652	210	12	)	)	PUNCT
ejpam-4652	210	13	∈	∈	NOUN
ejpam-4652	210	14	e(g[h	e(g[h	NOUN
ejpam-4652	210	15	]	]	PUNCT
ejpam-4652	210	16	)	)	PUNCT
ejpam-4652	210	17	.	.	PUNCT
ejpam-4652	211	1	subcase	subcase	PROPN
ejpam-4652	211	2	2.2	2.2	NUM
ejpam-4652	211	3	.	.	PUNCT
ejpam-4652	212	1	x	x	X
ejpam-4652	212	2	̸=	̸=	PROPN
ejpam-4652	212	3	y	y	PROPN
ejpam-4652	212	4	since	since	SCONJ
ejpam-4652	212	5	x	x	X
ejpam-4652	212	6	,	,	PUNCT
ejpam-4652	212	7	y	y	PROPN
ejpam-4652	212	8	∈	∈	PROPN
ejpam-4652	212	9	c	c	PROPN
ejpam-4652	212	10	and	and	CCONJ
ejpam-4652	212	11	c	c	PROPN
ejpam-4652	212	12	is	be	AUX
ejpam-4652	212	13	a	a	DET
ejpam-4652	212	14	superclique	superclique	NOUN
ejpam-4652	212	15	in	in	ADP
ejpam-4652	212	16	h	h	NOUN
ejpam-4652	212	17	,	,	PUNCT
ejpam-4652	212	18	xy	xy	PROPN
ejpam-4652	212	19	∈	∈	PROPN
ejpam-4652	212	20	e(h	e(h	PROPN
ejpam-4652	212	21	)	)	PUNCT
ejpam-4652	212	22	and	and	CCONJ
ejpam-4652	212	23	z	z	NOUN
ejpam-4652	212	24	∈	∈	PROPN
ejpam-4652	212	25	nh(x	nh(x	NUM
ejpam-4652	212	26	)	)	PUNCT
ejpam-4652	212	27	\	\	NOUN
ejpam-4652	212	28	nh(y	nh(y	PUNCT
ejpam-4652	212	29	)	)	PUNCT
ejpam-4652	212	30	or	or	CCONJ
ejpam-4652	212	31	z	z	NOUN
ejpam-4652	212	32	∈	∈	PROPN
ejpam-4652	212	33	nh(y	nh(y	NOUN
ejpam-4652	212	34	)	)	PUNCT
ejpam-4652	212	35	\	\	NOUN
ejpam-4652	212	36	nh(x	nh(x	PUNCT
ejpam-4652	212	37	)	)	PUNCT
ejpam-4652	212	38	for	for	ADP
ejpam-4652	212	39	some	some	PRON
ejpam-4652	212	40	z	z	NOUN
ejpam-4652	212	41	∈	∈	PROPN
ejpam-4652	212	42	v	v	ADP
ejpam-4652	212	43	(	(	PUNCT
ejpam-4652	212	44	h	h	NOUN
ejpam-4652	212	45	)	)	PUNCT
ejpam-4652	212	46	\	\	PROPN
ejpam-4652	212	47	c.	c.	PROPN
ejpam-4652	212	48	thus	thus	ADV
ejpam-4652	212	49	,	,	PUNCT
ejpam-4652	212	50	(	(	PUNCT
ejpam-4652	212	51	u	u	NOUN
ejpam-4652	212	52	,	,	PUNCT
ejpam-4652	212	53	z	z	NOUN
ejpam-4652	212	54	)	)	PUNCT
ejpam-4652	212	55	∈	∈	PROPN
ejpam-4652	212	56	ng[h]((v	ng[h]((v	NOUN
ejpam-4652	212	57	,	,	PUNCT
ejpam-4652	212	58	y	y	NOUN
ejpam-4652	212	59	)	)	PUNCT
ejpam-4652	212	60	)	)	PUNCT
ejpam-4652	212	61	\	\	NOUN
ejpam-4652	212	62	ng[h]((u	ng[h]((u	NOUN
ejpam-4652	212	63	,	,	PUNCT
ejpam-4652	212	64	x	x	NOUN
ejpam-4652	212	65	)	)	PUNCT
ejpam-4652	212	66	)	)	PUNCT
ejpam-4652	212	67	where	where	SCONJ
ejpam-4652	212	68	(	(	PUNCT
ejpam-4652	212	69	u	u	NOUN
ejpam-4652	212	70	,	,	PUNCT
ejpam-4652	212	71	z	z	NOUN
ejpam-4652	212	72	)	)	PUNCT
ejpam-4652	212	73	∈	∈	NOUN
ejpam-4652	212	74	v	v	NOUN
ejpam-4652	212	75	(	(	PUNCT
ejpam-4652	212	76	g[h	g[h	PROPN
ejpam-4652	212	77	]	]	PUNCT
ejpam-4652	212	78	)	)	PUNCT
ejpam-4652	212	79	\	\	PUNCT
ejpam-4652	213	1	(	(	PUNCT
ejpam-4652	213	2	a×c	a×c	PROPN
ejpam-4652	213	3	)	)	PUNCT
ejpam-4652	213	4	.	.	PUNCT
ejpam-4652	214	1	since	since	SCONJ
ejpam-4652	214	2	g	g	PROPN
ejpam-4652	214	3	is	be	AUX
ejpam-4652	214	4	complete	complete	ADJ
ejpam-4652	214	5	and	and	CCONJ
ejpam-4652	214	6	u	u	NOUN
ejpam-4652	214	7	̸=	̸=	PROPN
ejpam-4652	214	8	v	v	NOUN
ejpam-4652	214	9	,	,	PUNCT
ejpam-4652	214	10	(	(	PUNCT
ejpam-4652	214	11	u	u	NOUN
ejpam-4652	214	12	,	,	PUNCT
ejpam-4652	214	13	x)(v	x)(v	PROPN
ejpam-4652	214	14	,	,	PUNCT
ejpam-4652	214	15	y	y	NOUN
ejpam-4652	214	16	)	)	PUNCT
ejpam-4652	214	17	∈	∈	NOUN
ejpam-4652	214	18	e(g[h	e(g[h	NOUN
ejpam-4652	214	19	]	]	PUNCT
ejpam-4652	214	20	)	)	PUNCT
ejpam-4652	214	21	.	.	PUNCT
ejpam-4652	215	1	in	in	ADP
ejpam-4652	215	2	any	any	DET
ejpam-4652	215	3	case	case	NOUN
ejpam-4652	215	4	,	,	PUNCT
ejpam-4652	215	5	a×	a×	PROPN
ejpam-4652	215	6	c	c	PROPN
ejpam-4652	215	7	is	be	AUX
ejpam-4652	215	8	a	a	DET
ejpam-4652	215	9	superclique	superclique	NOUN
ejpam-4652	215	10	in	in	ADP
ejpam-4652	215	11	g[h	g[h	NOUN
ejpam-4652	215	12	]	]	PUNCT
ejpam-4652	215	13	.	.	PUNCT
ejpam-4652	216	1	the	the	DET
ejpam-4652	216	2	next	next	ADJ
ejpam-4652	216	3	result	result	NOUN
ejpam-4652	216	4	follows	follow	VERB
ejpam-4652	216	5	immediately	immediately	ADV
ejpam-4652	216	6	from	from	ADP
ejpam-4652	216	7	lemma	lemma	PROPN
ejpam-4652	216	8	3	3	NUM
ejpam-4652	216	9	and	and	CCONJ
ejpam-4652	216	10	theorem	theorem	VERB
ejpam-4652	216	11	2	2	NUM
ejpam-4652	216	12	.	.	PUNCT
ejpam-4652	217	1	lemma	lemma	PROPN
ejpam-4652	217	2	4	4	X
ejpam-4652	217	3	.	.	PUNCT
ejpam-4652	218	1	let	let	VERB
ejpam-4652	218	2	g	g	PROPN
ejpam-4652	218	3	=	=	PROPN
ejpam-4652	218	4	kn	kn	PROPN
ejpam-4652	218	5	for	for	ADP
ejpam-4652	218	6	n	n	PROPN
ejpam-4652	218	7	>	>	SYM
ejpam-4652	218	8	1	1	NUM
ejpam-4652	218	9	and	and	CCONJ
ejpam-4652	218	10	h	h	DET
ejpam-4652	218	11	a	a	DET
ejpam-4652	218	12	non	non	ADJ
ejpam-4652	218	13	-	-	ADJ
ejpam-4652	218	14	trivial	trivial	ADJ
ejpam-4652	218	15	connected	connected	ADJ
ejpam-4652	218	16	graph	graph	NOUN
ejpam-4652	218	17	with	with	ADP
ejpam-4652	218	18	γ(h	γ(h	NOUN
ejpam-4652	218	19	)	)	PUNCT
ejpam-4652	218	20	=	=	SYM
ejpam-4652	219	1	1	1	X
ejpam-4652	219	2	.	.	PUNCT
ejpam-4652	220	1	then	then	ADV
ejpam-4652	220	2	a×c	a×c	PROPN
ejpam-4652	220	3	⊆	⊆	NUM
ejpam-4652	220	4	v	v	NOUN
ejpam-4652	220	5	(	(	PUNCT
ejpam-4652	220	6	g[h	g[h	PROPN
ejpam-4652	220	7	]	]	PUNCT
ejpam-4652	220	8	)	)	PUNCT
ejpam-4652	220	9	induces	induce	VERB
ejpam-4652	220	10	a	a	DET
ejpam-4652	220	11	dominated	dominate	VERB
ejpam-4652	220	12	superclique	superclique	NOUN
ejpam-4652	220	13	of	of	ADP
ejpam-4652	220	14	g[h	g[h	NOUN
ejpam-4652	220	15	]	]	PUNCT
ejpam-4652	220	16	if	if	SCONJ
ejpam-4652	220	17	and	and	CCONJ
ejpam-4652	220	18	only	only	ADV
ejpam-4652	220	19	if	if	SCONJ
ejpam-4652	220	20	the	the	DET
ejpam-4652	220	21	following	follow	VERB
ejpam-4652	220	22	hold	hold	NOUN
ejpam-4652	220	23	:	:	PUNCT
ejpam-4652	220	24	(	(	PUNCT
ejpam-4652	220	25	i	i	NOUN
ejpam-4652	220	26	)	)	PUNCT
ejpam-4652	220	27	a	a	DET
ejpam-4652	220	28	⊆	⊆	NUM
ejpam-4652	220	29	v	v	NOUN
ejpam-4652	220	30	(	(	PUNCT
ejpam-4652	220	31	g	g	NOUN
ejpam-4652	220	32	)	)	PUNCT
ejpam-4652	220	33	with	with	ADP
ejpam-4652	220	34	1	1	NUM
ejpam-4652	220	35	≤	≤	NUM
ejpam-4652	220	36	|a|	|a|	NOUN
ejpam-4652	220	37	≤	≤	NOUN
ejpam-4652	220	38	n	n	CCONJ
ejpam-4652	220	39	−	−	PROPN
ejpam-4652	220	40	2	2	NUM
ejpam-4652	220	41	and	and	CCONJ
ejpam-4652	220	42	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	220	43	is	be	AUX
ejpam-4652	220	44	a	a	DET
ejpam-4652	220	45	superclique	superclique	NOUN
ejpam-4652	220	46	of	of	ADP
ejpam-4652	220	47	h	h	NOUN
ejpam-4652	220	48	such	such	ADJ
ejpam-4652	220	49	that	that	PRON
ejpam-4652	220	50	|a|	|a|	PROPN
ejpam-4652	220	51	=	=	SYM
ejpam-4652	220	52	1	1	NUM
ejpam-4652	220	53	whenever	whenever	SCONJ
ejpam-4652	220	54	c	c	X
ejpam-4652	220	55	∩	∩	ADJ
ejpam-4652	220	56	c∗	c∗	PROPN
ejpam-4652	220	57	̸=	̸=	PROPN
ejpam-4652	220	58	∅	∅	NOUN
ejpam-4652	220	59	for	for	ADP
ejpam-4652	220	60	some	some	DET
ejpam-4652	220	61	γ	γ	NOUN
ejpam-4652	220	62	-	-	PUNCT
ejpam-4652	220	63	set	set	ADJ
ejpam-4652	220	64	c∗	c∗	NOUN
ejpam-4652	220	65	of	of	ADP
ejpam-4652	220	66	h.	h.	PROPN
ejpam-4652	220	67	(	(	PUNCT
ejpam-4652	220	68	ii	ii	PROPN
ejpam-4652	220	69	)	)	PUNCT
ejpam-4652	220	70	a	a	DET
ejpam-4652	220	71	⊆	⊆	NUM
ejpam-4652	220	72	v	v	NOUN
ejpam-4652	220	73	(	(	PUNCT
ejpam-4652	220	74	g	g	NOUN
ejpam-4652	220	75	)	)	PUNCT
ejpam-4652	220	76	with	with	ADP
ejpam-4652	220	77	|a|	|a|	NOUN
ejpam-4652	220	78	=	=	SYM
ejpam-4652	220	79	n−	n−	PROPN
ejpam-4652	220	80	1	1	NUM
ejpam-4652	220	81	and	and	CCONJ
ejpam-4652	220	82	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	220	83	is	be	AUX
ejpam-4652	220	84	a	a	DET
ejpam-4652	220	85	dominated	dominate	VERB
ejpam-4652	220	86	superclique	superclique	NOUN
ejpam-4652	220	87	of	of	ADP
ejpam-4652	220	88	g[h	g[h	NOUN
ejpam-4652	220	89	]	]	PUNCT
ejpam-4652	220	90	.	.	PUNCT
ejpam-4652	221	1	theorem	theorem	NOUN
ejpam-4652	221	2	5	5	NUM
ejpam-4652	221	3	.	.	PUNCT
ejpam-4652	222	1	let	let	VERB
ejpam-4652	222	2	g	g	PROPN
ejpam-4652	222	3	=	=	PROPN
ejpam-4652	222	4	kn	kn	PROPN
ejpam-4652	222	5	for	for	ADP
ejpam-4652	222	6	n	n	PROPN
ejpam-4652	222	7	>	>	SYM
ejpam-4652	222	8	1	1	NUM
ejpam-4652	222	9	and	and	CCONJ
ejpam-4652	222	10	h	h	DET
ejpam-4652	222	11	a	a	DET
ejpam-4652	222	12	non	non	ADJ
ejpam-4652	222	13	-	-	ADJ
ejpam-4652	222	14	trivial	trivial	ADJ
ejpam-4652	222	15	connected	connected	ADJ
ejpam-4652	222	16	graph	graph	NOUN
ejpam-4652	222	17	with	with	ADP
ejpam-4652	222	18	γ(h	γ(h	NOUN
ejpam-4652	222	19	)	)	PUNCT
ejpam-4652	222	20	=	=	SYM
ejpam-4652	223	1	1	1	X
ejpam-4652	223	2	.	.	PUNCT
ejpam-4652	223	3	a	a	DET
ejpam-4652	223	4	subset	subset	NOUN
ejpam-4652	223	5	s	s	X
ejpam-4652	223	6	of	of	ADP
ejpam-4652	223	7	v	v	NOUN
ejpam-4652	223	8	(	(	PUNCT
ejpam-4652	223	9	g[h	g[h	PROPN
ejpam-4652	223	10	]	]	PUNCT
ejpam-4652	223	11	)	)	PUNCT
ejpam-4652	223	12	is	be	AUX
ejpam-4652	223	13	a	a	DET
ejpam-4652	223	14	strong	strong	ADJ
ejpam-4652	223	15	resolving	resolving	NOUN
ejpam-4652	223	16	dominating	dominating	NOUN
ejpam-4652	223	17	set	set	NOUN
ejpam-4652	223	18	of	of	ADP
ejpam-4652	223	19	g[h	g[h	PROPN
ejpam-4652	223	20	]	]	PUNCT
ejpam-4652	223	21	if	if	SCONJ
ejpam-4652	223	22	and	and	CCONJ
ejpam-4652	223	23	only	only	ADV
ejpam-4652	223	24	if	if	SCONJ
ejpam-4652	223	25	the	the	DET
ejpam-4652	223	26	following	follow	VERB
ejpam-4652	223	27	hold	hold	NOUN
ejpam-4652	223	28	:	:	PUNCT
ejpam-4652	223	29	(	(	PUNCT
ejpam-4652	223	30	i	i	NOUN
ejpam-4652	223	31	)	)	PUNCT
ejpam-4652	223	32	a	a	DET
ejpam-4652	223	33	⊆	⊆	NUM
ejpam-4652	223	34	v	v	NOUN
ejpam-4652	223	35	(	(	PUNCT
ejpam-4652	223	36	g	g	NOUN
ejpam-4652	223	37	)	)	PUNCT
ejpam-4652	223	38	with	with	ADP
ejpam-4652	223	39	1	1	NUM
ejpam-4652	223	40	≤	≤	NUM
ejpam-4652	223	41	|a|	|a|	NOUN
ejpam-4652	223	42	≤	≤	NOUN
ejpam-4652	223	43	n	n	CCONJ
ejpam-4652	223	44	−	−	PROPN
ejpam-4652	223	45	2	2	NUM
ejpam-4652	223	46	and	and	CCONJ
ejpam-4652	223	47	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	223	48	is	be	AUX
ejpam-4652	223	49	a	a	DET
ejpam-4652	223	50	superclique	superclique	NOUN
ejpam-4652	223	51	of	of	ADP
ejpam-4652	223	52	h	h	NOUN
ejpam-4652	223	53	such	such	ADJ
ejpam-4652	223	54	that	that	PRON
ejpam-4652	223	55	|a|	|a|	PROPN
ejpam-4652	223	56	=	=	SYM
ejpam-4652	223	57	1	1	NUM
ejpam-4652	223	58	whenever	whenever	SCONJ
ejpam-4652	223	59	c	c	X
ejpam-4652	223	60	∩	∩	ADJ
ejpam-4652	223	61	c∗	c∗	PROPN
ejpam-4652	223	62	̸=	̸=	PROPN
ejpam-4652	223	63	∅	∅	NOUN
ejpam-4652	223	64	for	for	ADP
ejpam-4652	223	65	some	some	DET
ejpam-4652	223	66	γ	γ	NOUN
ejpam-4652	223	67	-	-	PUNCT
ejpam-4652	223	68	set	set	ADJ
ejpam-4652	223	69	c∗	c∗	NOUN
ejpam-4652	223	70	of	of	ADP
ejpam-4652	223	71	h.	h.	PROPN
ejpam-4652	223	72	(	(	PUNCT
ejpam-4652	223	73	ii	ii	PROPN
ejpam-4652	223	74	)	)	PUNCT
ejpam-4652	223	75	a	a	DET
ejpam-4652	223	76	⊆	⊆	NUM
ejpam-4652	223	77	v	v	NOUN
ejpam-4652	223	78	(	(	PUNCT
ejpam-4652	223	79	g	g	NOUN
ejpam-4652	223	80	)	)	PUNCT
ejpam-4652	223	81	with	with	ADP
ejpam-4652	223	82	|a|	|a|	NOUN
ejpam-4652	223	83	=	=	SYM
ejpam-4652	223	84	n−	n−	PROPN
ejpam-4652	223	85	1	1	NUM
ejpam-4652	223	86	and	and	CCONJ
ejpam-4652	223	87	⟨c⟩	⟨c⟩	PROPN
ejpam-4652	223	88	is	be	AUX
ejpam-4652	223	89	a	a	DET
ejpam-4652	223	90	dominated	dominate	VERB
ejpam-4652	223	91	superclique	superclique	NOUN
ejpam-4652	223	92	of	of	ADP
ejpam-4652	223	93	g[h	g[h	NOUN
ejpam-4652	223	94	]	]	PUNCT
ejpam-4652	223	95	.	.	PUNCT
ejpam-4652	224	1	g.	g.	PROPN
ejpam-4652	224	2	monsanto	monsanto	PROPN
ejpam-4652	224	3	,	,	PUNCT
ejpam-4652	224	4	p.	p.	PROPN
ejpam-4652	224	5	acal	acal	PROPN
ejpam-4652	224	6	,	,	PUNCT
ejpam-4652	224	7	h.	h.	PROPN
ejpam-4652	224	8	rara	rara	PROPN
ejpam-4652	224	9	/	/	SYM
ejpam-4652	224	10	eur	eur	PROPN
ejpam-4652	224	11	.	.	PUNCT
ejpam-4652	225	1	j.	j.	PROPN
ejpam-4652	225	2	pure	pure	PROPN
ejpam-4652	225	3	appl	appl	PROPN
ejpam-4652	225	4	.	.	PROPN
ejpam-4652	225	5	math	math	PROPN
ejpam-4652	225	6	,	,	PUNCT
ejpam-4652	225	7	16	16	NUM
ejpam-4652	225	8	(	(	PUNCT
ejpam-4652	225	9	1	1	NUM
ejpam-4652	225	10	)	)	PUNCT
ejpam-4652	225	11	(	(	PUNCT
ejpam-4652	225	12	2023	2023	NUM
ejpam-4652	225	13	)	)	PUNCT
ejpam-4652	225	14	,	,	PUNCT
ejpam-4652	225	15	363	363	NUM
ejpam-4652	225	16	-	-	SYM
ejpam-4652	225	17	372	372	NUM
ejpam-4652	225	18	370	370	NUM
ejpam-4652	225	19	proof	proof	NOUN
ejpam-4652	225	20	:	:	PUNCT
ejpam-4652	225	21	the	the	DET
ejpam-4652	225	22	proof	proof	NOUN
ejpam-4652	225	23	is	be	AUX
ejpam-4652	225	24	similar	similar	ADJ
ejpam-4652	225	25	to	to	ADP
ejpam-4652	225	26	the	the	DET
ejpam-4652	225	27	proof	proof	NOUN
ejpam-4652	225	28	of	of	ADP
ejpam-4652	225	29	theorem	theorem	NOUN
ejpam-4652	225	30	4	4	NUM
ejpam-4652	225	31	and	and	CCONJ
ejpam-4652	225	32	by	by	ADP
ejpam-4652	225	33	using	use	VERB
ejpam-4652	225	34	lemma	lemma	PROPN
ejpam-4652	225	35	4	4	NUM
ejpam-4652	225	36	corollary	corollary	NOUN
ejpam-4652	225	37	1	1	NUM
ejpam-4652	225	38	.	.	PUNCT
ejpam-4652	226	1	let	let	VERB
ejpam-4652	226	2	g	g	PROPN
ejpam-4652	226	3	=	=	PROPN
ejpam-4652	226	4	kn	kn	PROPN
ejpam-4652	226	5	for	for	ADP
ejpam-4652	226	6	n	n	PROPN
ejpam-4652	226	7	>	>	SYM
ejpam-4652	226	8	1	1	NUM
ejpam-4652	226	9	and	and	CCONJ
ejpam-4652	226	10	h	h	DET
ejpam-4652	226	11	a	a	DET
ejpam-4652	226	12	non	non	ADJ
ejpam-4652	226	13	-	-	ADJ
ejpam-4652	226	14	trivial	trivial	ADJ
ejpam-4652	226	15	connected	connected	ADJ
ejpam-4652	226	16	graph	graph	NOUN
ejpam-4652	226	17	of	of	ADP
ejpam-4652	226	18	order	order	NOUN
ejpam-4652	226	19	m.	m.	NOUN
ejpam-4652	226	20	then	then	ADV
ejpam-4652	226	21	γsr	γsr	PROPN
ejpam-4652	226	22	(	(	PUNCT
ejpam-4652	226	23	g[h	g[h	PROPN
ejpam-4652	226	24	]	]	PUNCT
ejpam-4652	226	25	)	)	PUNCT
ejpam-4652	227	1	=	=	SYM
ejpam-4652	227	2	nm−	nm−	PROPN
ejpam-4652	227	3	ωs	ωs	PROPN
ejpam-4652	227	4	(	(	PUNCT
ejpam-4652	227	5	g[h	g[h	PROPN
ejpam-4652	227	6	]	]	PUNCT
ejpam-4652	227	7	)	)	PUNCT
ejpam-4652	227	8	.	.	PUNCT
ejpam-4652	228	1	proof	proof	NOUN
ejpam-4652	228	2	:	:	PUNCT
ejpam-4652	228	3	let	let	VERB
ejpam-4652	228	4	s	s	PRON
ejpam-4652	228	5	be	be	AUX
ejpam-4652	228	6	a	a	DET
ejpam-4652	228	7	strong	strong	ADJ
ejpam-4652	228	8	metric	metric	ADJ
ejpam-4652	228	9	basis	basis	NOUN
ejpam-4652	228	10	of	of	ADP
ejpam-4652	228	11	g[h	g[h	NOUN
ejpam-4652	228	12	]	]	PUNCT
ejpam-4652	228	13	.	.	PUNCT
ejpam-4652	229	1	then	then	ADV
ejpam-4652	229	2	s	s	VERB
ejpam-4652	229	3	is	be	AUX
ejpam-4652	229	4	a	a	DET
ejpam-4652	229	5	strong	strong	ADJ
ejpam-4652	229	6	resolving	resolving	NOUN
ejpam-4652	229	7	set	set	NOUN
ejpam-4652	229	8	of	of	ADP
ejpam-4652	229	9	g[h	g[h	NOUN
ejpam-4652	229	10	]	]	PUNCT
ejpam-4652	229	11	.	.	PUNCT
ejpam-4652	230	1	by	by	ADP
ejpam-4652	230	2	lemma	lemma	PROPN
ejpam-4652	230	3	1	1	NUM
ejpam-4652	230	4	,	,	PUNCT
ejpam-4652	230	5	s	s	PART
ejpam-4652	230	6	=	=	SYM
ejpam-4652	230	7	v	v	NOUN
ejpam-4652	230	8	(	(	PUNCT
ejpam-4652	230	9	g[h	g[h	PROPN
ejpam-4652	230	10	]	]	PUNCT
ejpam-4652	230	11	)	)	PUNCT
ejpam-4652	230	12	\	\	PUNCT
ejpam-4652	231	1	(	(	PUNCT
ejpam-4652	231	2	a	a	DET
ejpam-4652	231	3	×	×	NOUN
ejpam-4652	231	4	c	c	NOUN
ejpam-4652	231	5	)	)	PUNCT
ejpam-4652	231	6	,	,	PUNCT
ejpam-4652	231	7	where	where	SCONJ
ejpam-4652	231	8	a	a	DET
ejpam-4652	231	9	×	×	NOUN
ejpam-4652	231	10	c	c	NOUN
ejpam-4652	231	11	is	be	AUX
ejpam-4652	231	12	a	a	DET
ejpam-4652	231	13	superclique	superclique	NOUN
ejpam-4652	231	14	of	of	ADP
ejpam-4652	231	15	g[h	g[h	NOUN
ejpam-4652	231	16	]	]	PUNCT
ejpam-4652	231	17	.	.	PUNCT
ejpam-4652	232	1	since	since	SCONJ
ejpam-4652	232	2	s	s	PROPN
ejpam-4652	232	3	is	be	AUX
ejpam-4652	232	4	a	a	DET
ejpam-4652	232	5	strong	strong	ADJ
ejpam-4652	232	6	resolving	resolve	VERB
ejpam-4652	232	7	dominating	dominating	NOUN
ejpam-4652	232	8	set	set	NOUN
ejpam-4652	232	9	,	,	PUNCT
ejpam-4652	232	10	a×c	a×c	PROPN
ejpam-4652	232	11	is	be	AUX
ejpam-4652	232	12	a	a	DET
ejpam-4652	232	13	maximum	maximum	ADJ
ejpam-4652	232	14	dominated	dominate	VERB
ejpam-4652	232	15	superclique	superclique	NOUN
ejpam-4652	232	16	.	.	PUNCT
ejpam-4652	233	1	hence	hence	ADV
ejpam-4652	233	2	,	,	PUNCT
ejpam-4652	233	3	γsr(g[h	γsr(g[h	NOUN
ejpam-4652	233	4	]	]	PUNCT
ejpam-4652	233	5	)	)	PUNCT
ejpam-4652	233	6	=	=	SYM
ejpam-4652	233	7	|s|	|s|	PROPN
ejpam-4652	233	8	=	=	SYM
ejpam-4652	233	9	|v	|v	PROPN
ejpam-4652	233	10	(	(	PUNCT
ejpam-4652	233	11	g[h])|	g[h])|	PROPN
ejpam-4652	233	12	−	−	PROPN
ejpam-4652	233	13	|a×	|a×	ADJ
ejpam-4652	233	14	c|	c|	PROPN
ejpam-4652	233	15	=	=	SYM
ejpam-4652	233	16	nm−	nm−	PROPN
ejpam-4652	233	17	ωds(g[h	ωds(g[h	NUM
ejpam-4652	233	18	]	]	NUM
ejpam-4652	233	19	)	)	PUNCT
ejpam-4652	233	20	.	.	PUNCT
ejpam-4652	234	1	the	the	DET
ejpam-4652	234	2	next	next	ADJ
ejpam-4652	234	3	result	result	NOUN
ejpam-4652	234	4	follows	follow	VERB
ejpam-4652	234	5	immediately	immediately	ADV
ejpam-4652	234	6	from	from	ADP
ejpam-4652	234	7	lemma	lemma	PROPN
ejpam-4652	234	8	1	1	NUM
ejpam-4652	234	9	and	and	CCONJ
ejpam-4652	234	10	corollary	corollary	ADJ
ejpam-4652	234	11	1	1	NUM
ejpam-4652	234	12	.	.	PUNCT
ejpam-4652	234	13	corollary	corollary	ADJ
ejpam-4652	234	14	2	2	NUM
ejpam-4652	234	15	.	.	PUNCT
ejpam-4652	235	1	let	let	VERB
ejpam-4652	235	2	g	g	PROPN
ejpam-4652	235	3	=	=	PROPN
ejpam-4652	235	4	kn	kn	PROPN
ejpam-4652	235	5	for	for	ADP
ejpam-4652	235	6	n	n	PROPN
ejpam-4652	235	7	>	>	SYM
ejpam-4652	235	8	1	1	NUM
ejpam-4652	235	9	and	and	CCONJ
ejpam-4652	235	10	h	h	DET
ejpam-4652	235	11	a	a	DET
ejpam-4652	235	12	non	non	ADJ
ejpam-4652	235	13	-	-	ADJ
ejpam-4652	235	14	trivial	trivial	ADJ
ejpam-4652	235	15	connected	connected	ADJ
ejpam-4652	235	16	graph	graph	NOUN
ejpam-4652	235	17	of	of	ADP
ejpam-4652	235	18	order	order	NOUN
ejpam-4652	235	19	m.	m.	NOUN
ejpam-4652	235	20	then	then	ADV
ejpam-4652	235	21	γsr	γsr	PROPN
ejpam-4652	235	22	(	(	PUNCT
ejpam-4652	235	23	g[h	g[h	PROPN
ejpam-4652	235	24	]	]	PUNCT
ejpam-4652	235	25	)	)	PUNCT
ejpam-4652	236	1	=	=	PUNCT
ejpam-4652	236	2	nm−	nm−	PROPN
ejpam-4652	236	3	ωds	ωds	NOUN
ejpam-4652	236	4	(	(	PUNCT
ejpam-4652	236	5	g[h	g[h	PROPN
ejpam-4652	236	6	]	]	PUNCT
ejpam-4652	236	7	)	)	PUNCT
ejpam-4652	236	8	.	.	PUNCT
ejpam-4652	237	1	theorem	theorem	ADJ
ejpam-4652	237	2	6	6	NUM
ejpam-4652	237	3	.	.	PUNCT
ejpam-4652	238	1	let	let	VERB
ejpam-4652	238	2	g	g	PRON
ejpam-4652	238	3	be	be	AUX
ejpam-4652	238	4	a	a	DET
ejpam-4652	238	5	non	non	ADJ
ejpam-4652	238	6	-	-	ADJ
ejpam-4652	238	7	trivial	trivial	ADJ
ejpam-4652	238	8	connected	connected	ADJ
ejpam-4652	238	9	graph	graph	NOUN
ejpam-4652	238	10	andh	andh	NOUN
ejpam-4652	238	11	be	be	AUX
ejpam-4652	238	12	non	non	ADJ
ejpam-4652	238	13	-	-	ADJ
ejpam-4652	238	14	trivial	trivial	ADJ
ejpam-4652	238	15	complete	complete	ADJ
ejpam-4652	238	16	graph	graph	NOUN
ejpam-4652	238	17	.	.	PUNCT
ejpam-4652	239	1	a	a	DET
ejpam-4652	239	2	subset	subset	NOUN
ejpam-4652	239	3	c	c	NOUN
ejpam-4652	239	4	=	=	SYM
ejpam-4652	239	5	(	(	PUNCT
ejpam-4652	239	6	⋃	⋃	PROPN
ejpam-4652	239	7	x∈s	x∈s	X
ejpam-4652	239	8	{	{	PUNCT
ejpam-4652	239	9	{	{	PUNCT
ejpam-4652	239	10	x	x	NOUN
ejpam-4652	239	11	}	}	PUNCT
ejpam-4652	239	12	×	×	NOUN
ejpam-4652	239	13	tx	tx	PROPN
ejpam-4652	239	14	}	}	PUNCT
ejpam-4652	239	15	)	)	PUNCT
ejpam-4652	239	16	⋃	⋃	NOUN
ejpam-4652	239	17	⋃	⋃	PROPN
ejpam-4652	239	18	x∈wg	x∈wg	NOUN
ejpam-4652	239	19	{	{	PUNCT
ejpam-4652	239	20	{	{	PUNCT
ejpam-4652	239	21	x	x	NOUN
ejpam-4652	239	22	}	}	PUNCT
ejpam-4652	239	23	×	×	NOUN
ejpam-4652	239	24	(	(	PUNCT
ejpam-4652	239	25	v	v	NOUN
ejpam-4652	239	26	(	(	PUNCT
ejpam-4652	239	27	h	h	NOUN
ejpam-4652	239	28	)	)	PUNCT
ejpam-4652	239	29	\	\	PUNCT
ejpam-4652	239	30	tx	tx	PROPN
ejpam-4652	239	31	)	)	PUNCT
ejpam-4652	239	32	}	}	PUNCT
ejpam-4652	239	33			PROPN
ejpam-4652	239	34	of	of	ADP
ejpam-4652	239	35	v	v	NOUN
ejpam-4652	239	36	(	(	PUNCT
ejpam-4652	239	37	g[h	g[h	PROPN
ejpam-4652	239	38	]	]	PUNCT
ejpam-4652	239	39	)	)	PUNCT
ejpam-4652	239	40	where	where	SCONJ
ejpam-4652	239	41	wg	wg	VERB
ejpam-4652	239	42	⊆	⊆	NUM
ejpam-4652	239	43	s	s	NOUN
ejpam-4652	239	44	and	and	CCONJ
ejpam-4652	239	45	tx	tx	VERB
ejpam-4652	239	46	⊆	⊆	NUM
ejpam-4652	239	47	v	v	NOUN
ejpam-4652	239	48	(	(	PUNCT
ejpam-4652	239	49	h	h	NOUN
ejpam-4652	239	50	)	)	PUNCT
ejpam-4652	239	51	,	,	PUNCT
ejpam-4652	239	52	∀x	∀x	VERB
ejpam-4652	239	53	∈	∈	PROPN
ejpam-4652	239	54	s	s	NOUN
ejpam-4652	239	55	,	,	PUNCT
ejpam-4652	239	56	is	be	AUX
ejpam-4652	239	57	a	a	DET
ejpam-4652	239	58	strong	strong	ADJ
ejpam-4652	239	59	resolving	resolving	NOUN
ejpam-4652	239	60	dominating	dominating	NOUN
ejpam-4652	239	61	set	set	NOUN
ejpam-4652	239	62	of	of	ADP
ejpam-4652	239	63	g[h	g[h	PROPN
ejpam-4652	239	64	]	]	PUNCT
ejpam-4652	239	65	if	if	SCONJ
ejpam-4652	239	66	and	and	CCONJ
ejpam-4652	239	67	only	only	ADV
ejpam-4652	239	68	if	if	SCONJ
ejpam-4652	239	69	(	(	PUNCT
ejpam-4652	239	70	i	i	NOUN
ejpam-4652	239	71	)	)	PUNCT
ejpam-4652	239	72	s	s	PART
ejpam-4652	239	73	=	=	SYM
ejpam-4652	239	74	v	v	NOUN
ejpam-4652	239	75	(	(	PUNCT
ejpam-4652	239	76	g	g	NOUN
ejpam-4652	239	77	)	)	PUNCT
ejpam-4652	239	78	.	.	PUNCT
ejpam-4652	240	1	(	(	PUNCT
ejpam-4652	240	2	ii	ii	NOUN
ejpam-4652	240	3	)	)	PUNCT
ejpam-4652	240	4	v	v	NOUN
ejpam-4652	240	5	(	(	PUNCT
ejpam-4652	240	6	h	h	NOUN
ejpam-4652	240	7	)	)	PUNCT
ejpam-4652	240	8	\	\	PROPN
ejpam-4652	241	1	tx	tx	PROPN
ejpam-4652	241	2	is	be	AUX
ejpam-4652	241	3	a	a	DET
ejpam-4652	241	4	superclique	superclique	NOUN
ejpam-4652	241	5	of	of	ADP
ejpam-4652	241	6	h.	h.	PROPN
ejpam-4652	241	7	(	(	PUNCT
ejpam-4652	241	8	iii	iii	X
ejpam-4652	241	9	)	)	PUNCT
ejpam-4652	241	10	wg	wg	PROPN
ejpam-4652	241	11	is	be	AUX
ejpam-4652	241	12	a	a	DET
ejpam-4652	241	13	strong	strong	ADJ
ejpam-4652	241	14	resolving	resolving	NOUN
ejpam-4652	241	15	set	set	NOUN
ejpam-4652	241	16	of	of	ADP
ejpam-4652	241	17	g.	g.	PROPN
ejpam-4652	241	18	proof	proof	PROPN
ejpam-4652	241	19	:	:	PUNCT
ejpam-4652	241	20	let	let	VERB
ejpam-4652	241	21	c	c	PART
ejpam-4652	241	22	be	be	AUX
ejpam-4652	241	23	a	a	DET
ejpam-4652	241	24	strong	strong	ADJ
ejpam-4652	241	25	resolving	resolving	NOUN
ejpam-4652	241	26	dominating	dominating	NOUN
ejpam-4652	241	27	set	set	NOUN
ejpam-4652	241	28	of	of	ADP
ejpam-4652	241	29	g[h	g[h	PROPN
ejpam-4652	241	30	]	]	PUNCT
ejpam-4652	241	31	.	.	PUNCT
ejpam-4652	242	1	suppose	suppose	VERB
ejpam-4652	242	2	there	there	PRON
ejpam-4652	242	3	exists	exist	VERB
ejpam-4652	242	4	x	x	X
ejpam-4652	242	5	∈	∈	PROPN
ejpam-4652	242	6	v	v	X
ejpam-4652	242	7	(	(	PUNCT
ejpam-4652	242	8	g	g	NOUN
ejpam-4652	242	9	)	)	PUNCT
ejpam-4652	242	10	\	\	PUNCT
ejpam-4652	243	1	s.	s.	PROPN
ejpam-4652	243	2	let	let	VERB
ejpam-4652	243	3	p	p	PRON
ejpam-4652	243	4	,	,	PUNCT
ejpam-4652	243	5	q	q	PROPN
ejpam-4652	243	6	∈	∈	PROPN
ejpam-4652	243	7	v	v	ADP
ejpam-4652	243	8	(	(	PUNCT
ejpam-4652	243	9	h	h	NOUN
ejpam-4652	243	10	)	)	PUNCT
ejpam-4652	243	11	with	with	ADP
ejpam-4652	243	12	dh(p	dh(p	NOUN
ejpam-4652	243	13	,	,	PUNCT
ejpam-4652	243	14	q	q	NOUN
ejpam-4652	243	15	)	)	PUNCT
ejpam-4652	243	16	=	=	SYM
ejpam-4652	243	17	diam(h	diam(h	NOUN
ejpam-4652	243	18	)	)	PUNCT
ejpam-4652	243	19	.	.	PUNCT
ejpam-4652	244	1	then	then	ADV
ejpam-4652	244	2	(	(	PUNCT
ejpam-4652	244	3	x	x	X
ejpam-4652	244	4	,	,	PUNCT
ejpam-4652	244	5	p	p	X
ejpam-4652	244	6	)	)	PUNCT
ejpam-4652	244	7	mmd	mmd	NOUN
ejpam-4652	244	8	(	(	PUNCT
ejpam-4652	244	9	x	x	X
ejpam-4652	244	10	,	,	PUNCT
ejpam-4652	244	11	p	p	NOUN
ejpam-4652	244	12	)	)	PUNCT
ejpam-4652	244	13	implying	imply	VERB
ejpam-4652	244	14	that	that	SCONJ
ejpam-4652	244	15	(	(	PUNCT
ejpam-4652	244	16	x	x	X
ejpam-4652	244	17	,	,	PUNCT
ejpam-4652	244	18	p	p	NOUN
ejpam-4652	244	19	)	)	PUNCT
ejpam-4652	244	20	and	and	CCONJ
ejpam-4652	244	21	(	(	PUNCT
ejpam-4652	244	22	x	x	X
ejpam-4652	244	23	,	,	PUNCT
ejpam-4652	244	24	q	q	X
ejpam-4652	244	25	)	)	PUNCT
ejpam-4652	244	26	can	can	AUX
ejpam-4652	244	27	not	not	PART
ejpam-4652	244	28	be	be	AUX
ejpam-4652	244	29	resolved	resolve	VERB
ejpam-4652	244	30	by	by	ADP
ejpam-4652	244	31	c	c	PROPN
ejpam-4652	244	32	since	since	SCONJ
ejpam-4652	244	33	(	(	PUNCT
ejpam-4652	244	34	x	x	X
ejpam-4652	244	35	,	,	PUNCT
ejpam-4652	244	36	p)(x	p)(x	NOUN
ejpam-4652	244	37	,	,	PUNCT
ejpam-4652	244	38	q	q	NOUN
ejpam-4652	244	39	)	)	PUNCT
ejpam-4652	244	40	/∈	/∈	PUNCT
ejpam-4652	245	1	c.	c.	PROPN
ejpam-4652	245	2	hence	hence	ADV
ejpam-4652	245	3	,	,	PUNCT
ejpam-4652	245	4	s	s	NOUN
ejpam-4652	245	5	=	=	SYM
ejpam-4652	245	6	v	v	X
ejpam-4652	245	7	(	(	PUNCT
ejpam-4652	245	8	g	g	NOUN
ejpam-4652	245	9	)	)	PUNCT
ejpam-4652	245	10	and	and	CCONJ
ejpam-4652	245	11	(	(	PUNCT
ejpam-4652	245	12	i	i	NOUN
ejpam-4652	245	13	)	)	PUNCT
ejpam-4652	245	14	holds	hold	VERB
ejpam-4652	245	15	.	.	PUNCT
ejpam-4652	246	1	let	let	VERB
ejpam-4652	246	2	u	u	NOUN
ejpam-4652	246	3	,	,	PUNCT
ejpam-4652	246	4	v	v	PROPN
ejpam-4652	246	5	∈	∈	PROPN
ejpam-4652	246	6	v	v	NOUN
ejpam-4652	246	7	(	(	PUNCT
ejpam-4652	246	8	h	h	NOUN
ejpam-4652	246	9	)	)	PUNCT
ejpam-4652	246	10	\	\	PUNCT
ejpam-4652	247	1	tx	tx	PROPN
ejpam-4652	247	2	,	,	PUNCT
ejpam-4652	247	3	u	u	PROPN
ejpam-4652	247	4	̸=	̸=	PROPN
ejpam-4652	247	5	v.	v.	CCONJ
ejpam-4652	247	6	then	then	ADV
ejpam-4652	247	7	(	(	PUNCT
ejpam-4652	247	8	x	x	X
ejpam-4652	247	9	,	,	PUNCT
ejpam-4652	247	10	u	u	NOUN
ejpam-4652	247	11	)	)	PUNCT
ejpam-4652	247	12	,	,	PUNCT
ejpam-4652	247	13	(	(	PUNCT
ejpam-4652	247	14	x	x	NOUN
ejpam-4652	247	15	,	,	PUNCT
ejpam-4652	247	16	v	v	NOUN
ejpam-4652	247	17	)	)	PUNCT
ejpam-4652	247	18	/∈	/∈	PUNCT
ejpam-4652	248	1	c.	c.	NOUN
ejpam-4652	248	2	since	since	SCONJ
ejpam-4652	248	3	c	c	PROPN
ejpam-4652	248	4	is	be	AUX
ejpam-4652	248	5	a	a	DET
ejpam-4652	248	6	strong	strong	ADJ
ejpam-4652	248	7	resolving	resolving	NOUN
ejpam-4652	248	8	dominating	dominating	NOUN
ejpam-4652	248	9	set	set	NOUN
ejpam-4652	248	10	of	of	ADP
ejpam-4652	248	11	g[h	g[h	PROPN
ejpam-4652	248	12	]	]	PUNCT
ejpam-4652	248	13	,	,	PUNCT
ejpam-4652	248	14	(	(	PUNCT
ejpam-4652	248	15	x	x	NOUN
ejpam-4652	248	16	,	,	PUNCT
ejpam-4652	248	17	u	u	NOUN
ejpam-4652	248	18	)	)	PUNCT
ejpam-4652	248	19	and	and	CCONJ
ejpam-4652	248	20	(	(	PUNCT
ejpam-4652	248	21	x	x	NOUN
ejpam-4652	248	22	,	,	PUNCT
ejpam-4652	248	23	v	v	NOUN
ejpam-4652	248	24	)	)	PUNCT
ejpam-4652	248	25	can	can	AUX
ejpam-4652	248	26	be	be	AUX
ejpam-4652	248	27	strongly	strongly	ADV
ejpam-4652	248	28	resolved	resolve	VERB
ejpam-4652	248	29	by	by	ADP
ejpam-4652	248	30	(	(	PUNCT
ejpam-4652	248	31	y	y	PROPN
ejpam-4652	248	32	,	,	PUNCT
ejpam-4652	248	33	w	w	NOUN
ejpam-4652	248	34	)	)	PUNCT
ejpam-4652	248	35	∈	∈	PROPN
ejpam-4652	248	36	c.	c.	NOUN
ejpam-4652	249	1	if	if	SCONJ
ejpam-4652	249	2	(	(	PUNCT
ejpam-4652	249	3	x	x	NOUN
ejpam-4652	249	4	,	,	PUNCT
ejpam-4652	249	5	u	u	NOUN
ejpam-4652	249	6	)	)	PUNCT
ejpam-4652	249	7	∈	∈	PROPN
ejpam-4652	249	8	ig[h][(x	ig[h][(x	PROPN
ejpam-4652	249	9	,	,	PUNCT
ejpam-4652	249	10	v	v	NOUN
ejpam-4652	249	11	)	)	PUNCT
ejpam-4652	249	12	,	,	PUNCT
ejpam-4652	249	13	(	(	PUNCT
ejpam-4652	249	14	y	y	NOUN
ejpam-4652	249	15	,	,	PUNCT
ejpam-4652	249	16	w	w	PROPN
ejpam-4652	249	17	)	)	PUNCT
ejpam-4652	249	18	]	]	PUNCT
ejpam-4652	249	19	,	,	PUNCT
ejpam-4652	249	20	then	then	ADV
ejpam-4652	249	21	dg[h]((x	dg[h]((x	NOUN
ejpam-4652	249	22	,	,	PUNCT
ejpam-4652	249	23	v	v	NOUN
ejpam-4652	249	24	)	)	PUNCT
ejpam-4652	249	25	,	,	PUNCT
ejpam-4652	249	26	(	(	PUNCT
ejpam-4652	249	27	x	x	NOUN
ejpam-4652	249	28	,	,	PUNCT
ejpam-4652	249	29	u	u	NOUN
ejpam-4652	249	30	)	)	PUNCT
ejpam-4652	249	31	)	)	PUNCT
ejpam-4652	250	1	+	+	CCONJ
ejpam-4652	250	2	dg[h]((x	dg[h]((x	X
ejpam-4652	250	3	,	,	PUNCT
ejpam-4652	250	4	u	u	NOUN
ejpam-4652	250	5	)	)	PUNCT
ejpam-4652	250	6	,	,	PUNCT
ejpam-4652	250	7	(	(	PUNCT
ejpam-4652	250	8	y	y	NOUN
ejpam-4652	250	9	,	,	PUNCT
ejpam-4652	250	10	w	w	NOUN
ejpam-4652	250	11	)	)	PUNCT
ejpam-4652	250	12	)	)	PUNCT
ejpam-4652	251	1	=	=	PUNCT
ejpam-4652	251	2	dg[h]((x	dg[h]((x	X
ejpam-4652	251	3	,	,	PUNCT
ejpam-4652	251	4	v	v	NOUN
ejpam-4652	251	5	)	)	PUNCT
ejpam-4652	251	6	,	,	PUNCT
ejpam-4652	251	7	(	(	PUNCT
ejpam-4652	251	8	y	y	NOUN
ejpam-4652	251	9	,	,	PUNCT
ejpam-4652	251	10	w	w	NOUN
ejpam-4652	251	11	)	)	PUNCT
ejpam-4652	251	12	)	)	PUNCT
ejpam-4652	251	13	implying	imply	VERB
ejpam-4652	251	14	that	that	SCONJ
ejpam-4652	251	15	x	x	NOUN
ejpam-4652	251	16	=	=	SYM
ejpam-4652	251	17	y	y	PROPN
ejpam-4652	251	18	and	and	CCONJ
ejpam-4652	251	19	w	w	PROPN
ejpam-4652	251	20	∈	∈	PROPN
ejpam-4652	251	21	nh(u	nh(u	X
ejpam-4652	251	22	)	)	PUNCT
ejpam-4652	251	23	\	\	NOUN
ejpam-4652	251	24	nh(v	nh(v	NOUN
ejpam-4652	251	25	)	)	PUNCT
ejpam-4652	251	26	.	.	PUNCT
ejpam-4652	252	1	similarly	similarly	ADV
ejpam-4652	252	2	,	,	PUNCT
ejpam-4652	252	3	if	if	SCONJ
ejpam-4652	252	4	(	(	PUNCT
ejpam-4652	252	5	x	x	NOUN
ejpam-4652	252	6	,	,	PUNCT
ejpam-4652	252	7	v	v	NOUN
ejpam-4652	252	8	)	)	PUNCT
ejpam-4652	252	9	∈	∈	PROPN
ejpam-4652	252	10	ig[h][(x	ig[h][(x	PROPN
ejpam-4652	252	11	,	,	PUNCT
ejpam-4652	252	12	u	u	NOUN
ejpam-4652	252	13	)	)	PUNCT
ejpam-4652	252	14	,	,	PUNCT
ejpam-4652	252	15	(	(	PUNCT
ejpam-4652	252	16	y	y	NOUN
ejpam-4652	252	17	,	,	PUNCT
ejpam-4652	252	18	v	v	NOUN
ejpam-4652	252	19	)	)	PUNCT
ejpam-4652	252	20	]	]	PUNCT
ejpam-4652	252	21	,	,	PUNCT
ejpam-4652	252	22	then	then	ADV
ejpam-4652	252	23	x	x	X
ejpam-4652	252	24	=	=	SYM
ejpam-4652	252	25	y	y	PROPN
ejpam-4652	252	26	and	and	CCONJ
ejpam-4652	252	27	w	w	PROPN
ejpam-4652	252	28	∈	∈	PROPN
ejpam-4652	252	29	nh(v	nh(v	NOUN
ejpam-4652	252	30	)	)	PUNCT
ejpam-4652	252	31	\nh(u	\nh(u	NUM
ejpam-4652	252	32	)	)	PUNCT
ejpam-4652	252	33	.	.	PUNCT
ejpam-4652	253	1	hence	hence	ADV
ejpam-4652	253	2	,	,	PUNCT
ejpam-4652	253	3	v	v	INTJ
ejpam-4652	253	4	(	(	PUNCT
ejpam-4652	253	5	h	h	NOUN
ejpam-4652	253	6	)	)	PUNCT
ejpam-4652	253	7	\	\	PROPN
ejpam-4652	253	8	tx	tx	PROPN
ejpam-4652	253	9	is	be	AUX
ejpam-4652	253	10	a	a	DET
ejpam-4652	253	11	superclique	superclique	NOUN
ejpam-4652	253	12	of	of	ADP
ejpam-4652	253	13	h.	h.	NOUN
ejpam-4652	253	14	thus	thus	ADV
ejpam-4652	253	15	,	,	PUNCT
ejpam-4652	253	16	(	(	PUNCT
ejpam-4652	253	17	ii	ii	NOUN
ejpam-4652	253	18	)	)	PUNCT
ejpam-4652	253	19	holds	hold	VERB
ejpam-4652	253	20	.	.	PUNCT
ejpam-4652	254	1	g.	g.	PROPN
ejpam-4652	254	2	monsanto	monsanto	PROPN
ejpam-4652	254	3	,	,	PUNCT
ejpam-4652	254	4	p.	p.	PROPN
ejpam-4652	254	5	acal	acal	PROPN
ejpam-4652	254	6	,	,	PUNCT
ejpam-4652	254	7	h.	h.	PROPN
ejpam-4652	254	8	rara	rara	PROPN
ejpam-4652	254	9	/	/	SYM
ejpam-4652	254	10	eur	eur	PROPN
ejpam-4652	254	11	.	.	PUNCT
ejpam-4652	255	1	j.	j.	PROPN
ejpam-4652	255	2	pure	pure	PROPN
ejpam-4652	255	3	appl	appl	PROPN
ejpam-4652	255	4	.	.	PROPN
ejpam-4652	255	5	math	math	PROPN
ejpam-4652	255	6	,	,	PUNCT
ejpam-4652	255	7	16	16	NUM
ejpam-4652	255	8	(	(	PUNCT
ejpam-4652	255	9	1	1	NUM
ejpam-4652	255	10	)	)	PUNCT
ejpam-4652	255	11	(	(	PUNCT
ejpam-4652	255	12	2023	2023	NUM
ejpam-4652	255	13	)	)	PUNCT
ejpam-4652	255	14	,	,	PUNCT
ejpam-4652	255	15	363	363	NUM
ejpam-4652	255	16	-	-	SYM
ejpam-4652	255	17	372	372	NUM
ejpam-4652	255	18	371	371	NUM
ejpam-4652	255	19	let	let	VERB
ejpam-4652	255	20	p	p	PRON
ejpam-4652	255	21	,	,	PUNCT
ejpam-4652	255	22	q	q	PROPN
ejpam-4652	255	23	∈	∈	PROPN
ejpam-4652	255	24	v	v	ADP
ejpam-4652	255	25	(	(	PUNCT
ejpam-4652	255	26	g	g	NOUN
ejpam-4652	255	27	)	)	PUNCT
ejpam-4652	255	28	\	\	PROPN
ejpam-4652	256	1	wg	wg	PROPN
ejpam-4652	256	2	.	.	PUNCT
ejpam-4652	257	1	then	then	ADV
ejpam-4652	257	2	(	(	PUNCT
ejpam-4652	257	3	p	p	X
ejpam-4652	257	4	,	,	PUNCT
ejpam-4652	257	5	r	r	NOUN
ejpam-4652	257	6	)	)	PUNCT
ejpam-4652	257	7	,	,	PUNCT
ejpam-4652	257	8	(	(	PUNCT
ejpam-4652	257	9	q	q	X
ejpam-4652	257	10	,	,	PUNCT
ejpam-4652	257	11	r	r	NOUN
ejpam-4652	257	12	)	)	PUNCT
ejpam-4652	257	13	/∈	/∈	PUNCT
ejpam-4652	258	1	c	c	X
ejpam-4652	258	2	,	,	PUNCT
ejpam-4652	258	3	where	where	SCONJ
ejpam-4652	258	4	r	r	NOUN
ejpam-4652	258	5	/∈	/∈	PUNCT
ejpam-4652	258	6	tp	tp	NOUN
ejpam-4652	258	7	,	,	PUNCT
ejpam-4652	258	8	tq	tq	INTJ
ejpam-4652	258	9	.	.	PUNCT
ejpam-4652	259	1	hence	hence	ADV
ejpam-4652	259	2	,	,	PUNCT
ejpam-4652	259	3	there	there	PRON
ejpam-4652	259	4	exists	exist	VERB
ejpam-4652	259	5	(	(	PUNCT
ejpam-4652	259	6	s	s	X
ejpam-4652	259	7	,	,	PUNCT
ejpam-4652	259	8	t	t	PROPN
ejpam-4652	259	9	)	)	PUNCT
ejpam-4652	259	10	∈	∈	PROPN
ejpam-4652	259	11	c	c	NOUN
ejpam-4652	259	12	that	that	PRON
ejpam-4652	259	13	resolves	resolve	VERB
ejpam-4652	259	14	(	(	PUNCT
ejpam-4652	259	15	p	p	X
ejpam-4652	259	16	,	,	PUNCT
ejpam-4652	259	17	r	r	NOUN
ejpam-4652	259	18	)	)	PUNCT
ejpam-4652	259	19	and	and	CCONJ
ejpam-4652	259	20	(	(	PUNCT
ejpam-4652	259	21	q	q	X
ejpam-4652	259	22	,	,	PUNCT
ejpam-4652	259	23	r	r	NOUN
ejpam-4652	259	24	)	)	PUNCT
ejpam-4652	259	25	.	.	PUNCT
ejpam-4652	260	1	if	if	SCONJ
ejpam-4652	260	2	(	(	PUNCT
ejpam-4652	260	3	p	p	X
ejpam-4652	260	4	,	,	PUNCT
ejpam-4652	260	5	r	r	NOUN
ejpam-4652	260	6	)	)	PUNCT
ejpam-4652	260	7	∈	∈	NOUN
ejpam-4652	260	8	ig[h][(q	ig[h][(q	PROPN
ejpam-4652	260	9	,	,	PUNCT
ejpam-4652	260	10	r	r	NOUN
ejpam-4652	260	11	)	)	PUNCT
ejpam-4652	260	12	,	,	PUNCT
ejpam-4652	260	13	(	(	PUNCT
ejpam-4652	260	14	s	s	X
ejpam-4652	260	15	,	,	PUNCT
ejpam-4652	260	16	t	t	PROPN
ejpam-4652	260	17	)	)	PUNCT
ejpam-4652	260	18	]	]	PUNCT
ejpam-4652	260	19	,	,	PUNCT
ejpam-4652	260	20	then	then	ADV
ejpam-4652	260	21	dg[h]((q	dg[h]((q	NOUN
ejpam-4652	260	22	,	,	PUNCT
ejpam-4652	260	23	r	r	NOUN
ejpam-4652	260	24	)	)	PUNCT
ejpam-4652	260	25	,	,	PUNCT
ejpam-4652	260	26	(	(	PUNCT
ejpam-4652	260	27	p	p	X
ejpam-4652	260	28	,	,	PUNCT
ejpam-4652	260	29	r	r	NOUN
ejpam-4652	260	30	)	)	PUNCT
ejpam-4652	260	31	)	)	PUNCT
ejpam-4652	261	1	+	+	CCONJ
ejpam-4652	261	2	dg[h]((p	dg[h]((p	NOUN
ejpam-4652	261	3	,	,	PUNCT
ejpam-4652	261	4	r	r	NOUN
ejpam-4652	261	5	)	)	PUNCT
ejpam-4652	261	6	,	,	PUNCT
ejpam-4652	261	7	(	(	PUNCT
ejpam-4652	261	8	s	s	X
ejpam-4652	261	9	,	,	PUNCT
ejpam-4652	261	10	t	t	PROPN
ejpam-4652	261	11	)	)	PUNCT
ejpam-4652	261	12	)	)	PUNCT
ejpam-4652	262	1	=	=	PUNCT
ejpam-4652	262	2	dg[h]((q	dg[h]((q	NOUN
ejpam-4652	262	3	,	,	PUNCT
ejpam-4652	262	4	r	r	NOUN
ejpam-4652	262	5	)	)	PUNCT
ejpam-4652	262	6	,	,	PUNCT
ejpam-4652	262	7	(	(	PUNCT
ejpam-4652	262	8	s	s	X
ejpam-4652	262	9	,	,	PUNCT
ejpam-4652	262	10	t	t	PROPN
ejpam-4652	262	11	)	)	PUNCT
ejpam-4652	262	12	)	)	PUNCT
ejpam-4652	263	1	implying	imply	VERB
ejpam-4652	263	2	that	that	SCONJ
ejpam-4652	263	3	r	r	NOUN
ejpam-4652	263	4	=	=	SYM
ejpam-4652	263	5	t	t	PROPN
ejpam-4652	263	6	and	and	CCONJ
ejpam-4652	263	7	p	p	NOUN
ejpam-4652	263	8	∈	∈	PROPN
ejpam-4652	263	9	ig[q	ig[q	PROPN
ejpam-4652	263	10	,	,	PUNCT
ejpam-4652	263	11	s	s	PART
ejpam-4652	263	12	]	]	PUNCT
ejpam-4652	263	13	.	.	PUNCT
ejpam-4652	264	1	similarly	similarly	ADV
ejpam-4652	264	2	,	,	PUNCT
ejpam-4652	264	3	if	if	SCONJ
ejpam-4652	264	4	(	(	PUNCT
ejpam-4652	264	5	q	q	ADJ
ejpam-4652	264	6	,	,	PUNCT
ejpam-4652	264	7	r	r	NOUN
ejpam-4652	264	8	)	)	PUNCT
ejpam-4652	264	9	∈	∈	NOUN
ejpam-4652	264	10	ig[h][(p	ig[h][(p	PROPN
ejpam-4652	264	11	,	,	PUNCT
ejpam-4652	264	12	r	r	NOUN
ejpam-4652	264	13	)	)	PUNCT
ejpam-4652	264	14	,	,	PUNCT
ejpam-4652	264	15	(	(	PUNCT
ejpam-4652	264	16	s	s	X
ejpam-4652	264	17	,	,	PUNCT
ejpam-4652	264	18	t	t	PROPN
ejpam-4652	264	19	)	)	PUNCT
ejpam-4652	264	20	]	]	PUNCT
ejpam-4652	264	21	,	,	PUNCT
ejpam-4652	264	22	then	then	ADV
ejpam-4652	264	23	r	r	NOUN
ejpam-4652	264	24	=	=	SYM
ejpam-4652	264	25	t	t	PROPN
ejpam-4652	264	26	and	and	CCONJ
ejpam-4652	264	27	q	q	PROPN
ejpam-4652	264	28	∈	∈	PROPN
ejpam-4652	264	29	ig[p	ig[p	PROPN
ejpam-4652	264	30	,	,	PUNCT
ejpam-4652	264	31	s	s	PART
ejpam-4652	264	32	]	]	X
ejpam-4652	264	33	.	.	PUNCT
ejpam-4652	265	1	hence	hence	ADV
ejpam-4652	265	2	,	,	PUNCT
ejpam-4652	265	3	s	s	VERB
ejpam-4652	265	4	strongly	strongly	ADV
ejpam-4652	265	5	resolves	resolve	VERB
ejpam-4652	265	6	p	p	NOUN
ejpam-4652	265	7	and	and	CCONJ
ejpam-4652	265	8	q.	q.	PROPN
ejpam-4652	265	9	therefore	therefore	ADV
ejpam-4652	265	10	,	,	PUNCT
ejpam-4652	265	11	wg	wg	PROPN
ejpam-4652	265	12	is	be	AUX
ejpam-4652	265	13	a	a	DET
ejpam-4652	265	14	strongly	strongly	ADV
ejpam-4652	265	15	resolving	resolve	VERB
ejpam-4652	265	16	dominating	dominating	NOUN
ejpam-4652	265	17	set	set	NOUN
ejpam-4652	265	18	of	of	ADP
ejpam-4652	265	19	g	g	PROPN
ejpam-4652	265	20	and	and	CCONJ
ejpam-4652	265	21	(	(	PUNCT
ejpam-4652	265	22	iii	iii	NOUN
ejpam-4652	265	23	)	)	PUNCT
ejpam-4652	265	24	holds	hold	VERB
ejpam-4652	265	25	.	.	PUNCT
ejpam-4652	266	1	for	for	ADP
ejpam-4652	266	2	the	the	DET
ejpam-4652	266	3	converse	converse	NOUN
ejpam-4652	266	4	,	,	PUNCT
ejpam-4652	266	5	suppose	suppose	VERB
ejpam-4652	266	6	c	c	NOUN
ejpam-4652	266	7	satisfies	satisfy	VERB
ejpam-4652	266	8	the	the	DET
ejpam-4652	266	9	given	give	VERB
ejpam-4652	266	10	property	property	NOUN
ejpam-4652	266	11	.	.	PUNCT
ejpam-4652	267	1	let	let	VERB
ejpam-4652	267	2	x	x	PUNCT
ejpam-4652	267	3	=	=	SYM
ejpam-4652	267	4	(	(	PUNCT
ejpam-4652	267	5	x1	x1	PROPN
ejpam-4652	267	6	,	,	PUNCT
ejpam-4652	267	7	x2	x2	PROPN
ejpam-4652	267	8	)	)	PUNCT
ejpam-4652	267	9	,	,	PUNCT
ejpam-4652	267	10	y	y	PROPN
ejpam-4652	267	11	=	=	SYM
ejpam-4652	267	12	(	(	PUNCT
ejpam-4652	267	13	y1	y1	INTJ
ejpam-4652	267	14	,	,	PUNCT
ejpam-4652	267	15	y2	y2	PROPN
ejpam-4652	267	16	)	)	PUNCT
ejpam-4652	267	17	/∈	/∈	PUNCT
ejpam-4652	268	1	c	c	X
ejpam-4652	268	2	,	,	PUNCT
ejpam-4652	268	3	x	x	PROPN
ejpam-4652	268	4	̸=	̸=	PROPN
ejpam-4652	268	5	y.	y.	NOUN
ejpam-4652	268	6	then	then	ADV
ejpam-4652	268	7	consider	consider	VERB
ejpam-4652	268	8	the	the	DET
ejpam-4652	268	9	following	follow	VERB
ejpam-4652	268	10	cases	case	NOUN
ejpam-4652	268	11	:	:	PUNCT
ejpam-4652	268	12	case	case	NOUN
ejpam-4652	268	13	1	1	NUM
ejpam-4652	268	14	.	.	PUNCT
ejpam-4652	269	1	x1	x1	PROPN
ejpam-4652	269	2	∈	∈	PROPN
ejpam-4652	269	3	v	v	ADP
ejpam-4652	269	4	(	(	PUNCT
ejpam-4652	269	5	g	g	NOUN
ejpam-4652	269	6	)	)	PUNCT
ejpam-4652	269	7	\wg	\wg	PROPN
ejpam-4652	269	8	and	and	CCONJ
ejpam-4652	269	9	y1	y1	NOUN
ejpam-4652	269	10	∈	∈	PROPN
ejpam-4652	269	11	v	v	ADP
ejpam-4652	269	12	(	(	PUNCT
ejpam-4652	269	13	g	g	NOUN
ejpam-4652	269	14	)	)	PUNCT
ejpam-4652	269	15	\wg	\wg	PROPN
ejpam-4652	269	16	,	,	PUNCT
ejpam-4652	269	17	x1	x1	PROPN
ejpam-4652	269	18	̸=	̸=	PROPN
ejpam-4652	269	19	y1	y1	PROPN
ejpam-4652	269	20	.	.	PUNCT
ejpam-4652	270	1	by	by	ADP
ejpam-4652	270	2	(	(	PUNCT
ejpam-4652	270	3	iii	iii	NOUN
ejpam-4652	270	4	)	)	PUNCT
ejpam-4652	270	5	,	,	PUNCT
ejpam-4652	270	6	there	there	PRON
ejpam-4652	270	7	exists	exist	VERB
ejpam-4652	270	8	z1	z1	PROPN
ejpam-4652	270	9	∈	∈	PROPN
ejpam-4652	270	10	v	v	ADP
ejpam-4652	270	11	(	(	PUNCT
ejpam-4652	270	12	g	g	NOUN
ejpam-4652	270	13	)	)	PUNCT
ejpam-4652	270	14	∩wg	∩wg	NOUN
ejpam-4652	270	15	that	that	PRON
ejpam-4652	270	16	resolves	resolve	VERB
ejpam-4652	270	17	x1	x1	PROPN
ejpam-4652	270	18	and	and	CCONJ
ejpam-4652	270	19	y1	y1	NOUN
ejpam-4652	270	20	.	.	PUNCT
ejpam-4652	271	1	if	if	SCONJ
ejpam-4652	271	2	x1	x1	PROPN
ejpam-4652	271	3	∈	∈	PROPN
ejpam-4652	271	4	ig[y1	ig[y1	PROPN
ejpam-4652	271	5	,	,	PUNCT
ejpam-4652	271	6	z1	z1	NOUN
ejpam-4652	271	7	]	]	PUNCT
ejpam-4652	271	8	,	,	PUNCT
ejpam-4652	271	9	then	then	ADV
ejpam-4652	271	10	dg(y1	dg(y1	PROPN
ejpam-4652	271	11	,	,	PUNCT
ejpam-4652	271	12	x1	x1	PROPN
ejpam-4652	271	13	)	)	PUNCT
ejpam-4652	271	14	+	+	NUM
ejpam-4652	271	15	dg(x1	dg(x1	NOUN
ejpam-4652	271	16	,	,	PUNCT
ejpam-4652	271	17	z1	z1	NOUN
ejpam-4652	271	18	)	)	PUNCT
ejpam-4652	271	19	=	=	SYM
ejpam-4652	271	20	dg(y1	dg(y1	PROPN
ejpam-4652	271	21	,	,	PUNCT
ejpam-4652	271	22	z1).(1	z1).(1	NOUN
ejpam-4652	271	23	)	)	PUNCT
ejpam-4652	271	24	choose	choose	VERB
ejpam-4652	271	25	z2	z2	PROPN
ejpam-4652	271	26	∈	∈	PROPN
ejpam-4652	271	27	v	v	ADP
ejpam-4652	271	28	(	(	PUNCT
ejpam-4652	271	29	h	h	NOUN
ejpam-4652	271	30	)	)	PUNCT
ejpam-4652	271	31	\	\	PROPN
ejpam-4652	271	32	tz1	tz1	PROPN
ejpam-4652	271	33	.	.	PUNCT
ejpam-4652	272	1	clearly	clearly	ADV
ejpam-4652	272	2	,	,	PUNCT
ejpam-4652	272	3	(	(	PUNCT
ejpam-4652	272	4	z1	z1	PROPN
ejpam-4652	272	5	,	,	PUNCT
ejpam-4652	272	6	z2	z2	PROPN
ejpam-4652	272	7	)	)	PUNCT
ejpam-4652	272	8	∈	∈	PROPN
ejpam-4652	272	9	c.	c.	NOUN
ejpam-4652	272	10	we	we	PRON
ejpam-4652	272	11	claim	claim	VERB
ejpam-4652	272	12	that	that	SCONJ
ejpam-4652	272	13	(	(	PUNCT
ejpam-4652	272	14	z1	z1	PROPN
ejpam-4652	272	15	,	,	PUNCT
ejpam-4652	272	16	z2	z2	NOUN
ejpam-4652	272	17	)	)	PUNCT
ejpam-4652	272	18	strongly	strongly	ADV
ejpam-4652	272	19	resolves	resolve	VERB
ejpam-4652	272	20	x	x	PUNCT
ejpam-4652	272	21	=	=	SYM
ejpam-4652	272	22	(	(	PUNCT
ejpam-4652	272	23	x1	x1	PROPN
ejpam-4652	272	24	,	,	PUNCT
ejpam-4652	272	25	x2	x2	PROPN
ejpam-4652	272	26	)	)	PUNCT
ejpam-4652	272	27	and	and	CCONJ
ejpam-4652	272	28	y	y	PROPN
ejpam-4652	272	29	=	=	SYM
ejpam-4652	272	30	(	(	PUNCT
ejpam-4652	272	31	y1	y1	INTJ
ejpam-4652	272	32	,	,	PUNCT
ejpam-4652	272	33	y2	y2	PROPN
ejpam-4652	272	34	)	)	PUNCT
ejpam-4652	272	35	in	in	ADP
ejpam-4652	272	36	g[h	g[h	NOUN
ejpam-4652	272	37	]	]	PUNCT
ejpam-4652	272	38	.	.	PUNCT
ejpam-4652	273	1	using	use	VERB
ejpam-4652	273	2	equation	equation	NOUN
ejpam-4652	273	3	1	1	NUM
ejpam-4652	273	4	,	,	PUNCT
ejpam-4652	273	5	we	we	PRON
ejpam-4652	273	6	have	have	VERB
ejpam-4652	273	7	dg[h]((y1	dg[h]((y1	NOUN
ejpam-4652	273	8	,	,	PUNCT
ejpam-4652	273	9	y2	y2	PROPN
ejpam-4652	273	10	)	)	PUNCT
ejpam-4652	273	11	,	,	PUNCT
ejpam-4652	273	12	(	(	PUNCT
ejpam-4652	273	13	x1	x1	X
ejpam-4652	273	14	,	,	PUNCT
ejpam-4652	273	15	x2	x2	PROPN
ejpam-4652	273	16	)	)	PUNCT
ejpam-4652	273	17	)	)	PUNCT
ejpam-4652	274	1	+	+	CCONJ
ejpam-4652	274	2	dg[h]((x1	dg[h]((x1	NOUN
ejpam-4652	274	3	,	,	PUNCT
ejpam-4652	274	4	x2	x2	PROPN
ejpam-4652	274	5	)	)	PUNCT
ejpam-4652	274	6	,	,	PUNCT
ejpam-4652	274	7	(	(	PUNCT
ejpam-4652	274	8	z1	z1	PROPN
ejpam-4652	274	9	,	,	PUNCT
ejpam-4652	274	10	z2	z2	NOUN
ejpam-4652	274	11	)	)	PUNCT
ejpam-4652	274	12	)	)	PUNCT
ejpam-4652	275	1	=	=	SYM
ejpam-4652	275	2	dg[h]((y1	dg[h]((y1	X
ejpam-4652	275	3	,	,	PUNCT
ejpam-4652	275	4	y2	y2	PROPN
ejpam-4652	275	5	)	)	PUNCT
ejpam-4652	275	6	,	,	PUNCT
ejpam-4652	275	7	(	(	PUNCT
ejpam-4652	275	8	z1	z1	PROPN
ejpam-4652	275	9	,	,	PUNCT
ejpam-4652	275	10	z2	z2	NOUN
ejpam-4652	275	11	)	)	PUNCT
ejpam-4652	275	12	)	)	PUNCT
ejpam-4652	276	1	implying	imply	VERB
ejpam-4652	276	2	that	that	SCONJ
ejpam-4652	276	3	(	(	PUNCT
ejpam-4652	276	4	x1	x1	ADJ
ejpam-4652	276	5	,	,	PUNCT
ejpam-4652	276	6	x2	x2	PROPN
ejpam-4652	276	7	)	)	PUNCT
ejpam-4652	276	8	∈	∈	PROPN
ejpam-4652	276	9	ig[h][(y1	ig[h][(y1	NOUN
ejpam-4652	276	10	,	,	PUNCT
ejpam-4652	276	11	y2	y2	PROPN
ejpam-4652	276	12	)	)	PUNCT
ejpam-4652	276	13	,	,	PUNCT
ejpam-4652	276	14	(	(	PUNCT
ejpam-4652	276	15	z1	z1	PROPN
ejpam-4652	276	16	,	,	PUNCT
ejpam-4652	276	17	z2	z2	PROPN
ejpam-4652	276	18	)	)	PUNCT
ejpam-4652	276	19	]	]	PUNCT
ejpam-4652	276	20	.	.	PUNCT
ejpam-4652	277	1	similarly	similarly	ADV
ejpam-4652	277	2	,	,	PUNCT
ejpam-4652	277	3	if	if	SCONJ
ejpam-4652	277	4	y1	y1	NOUN
ejpam-4652	277	5	∈	∈	PROPN
ejpam-4652	277	6	ig[x1	ig[x1	PROPN
ejpam-4652	277	7	,	,	PUNCT
ejpam-4652	277	8	z1	z1	NOUN
ejpam-4652	277	9	]	]	PUNCT
ejpam-4652	277	10	,	,	PUNCT
ejpam-4652	277	11	then	then	ADV
ejpam-4652	277	12	(	(	PUNCT
ejpam-4652	277	13	z1	z1	PROPN
ejpam-4652	277	14	,	,	PUNCT
ejpam-4652	277	15	z2	z2	NOUN
ejpam-4652	277	16	)	)	PUNCT
ejpam-4652	277	17	strongly	strongly	ADV
ejpam-4652	277	18	resolves	resolve	VERB
ejpam-4652	277	19	x	x	PUNCT
ejpam-4652	277	20	=	=	SYM
ejpam-4652	277	21	(	(	PUNCT
ejpam-4652	277	22	x1	x1	PROPN
ejpam-4652	277	23	,	,	PUNCT
ejpam-4652	277	24	x2	x2	PROPN
ejpam-4652	277	25	)	)	PUNCT
ejpam-4652	277	26	and	and	CCONJ
ejpam-4652	277	27	y	y	PROPN
ejpam-4652	277	28	=	=	SYM
ejpam-4652	277	29	(	(	PUNCT
ejpam-4652	277	30	y1	y1	INTJ
ejpam-4652	277	31	,	,	PUNCT
ejpam-4652	277	32	y2	y2	PROPN
ejpam-4652	277	33	)	)	PUNCT
ejpam-4652	277	34	.	.	PUNCT
ejpam-4652	278	1	case	case	NOUN
ejpam-4652	278	2	2	2	NUM
ejpam-4652	278	3	.	.	X
ejpam-4652	279	1	x1	x1	PROPN
ejpam-4652	279	2	=	=	PUNCT
ejpam-4652	280	1	y1	y1	INTJ
ejpam-4652	280	2	then	then	ADV
ejpam-4652	280	3	x2	x2	PROPN
ejpam-4652	280	4	̸=	̸=	PROPN
ejpam-4652	280	5	y2	y2	PROPN
ejpam-4652	280	6	since	since	SCONJ
ejpam-4652	280	7	x	x	PROPN
ejpam-4652	280	8	̸=	̸=	PROPN
ejpam-4652	280	9	y.	y.	NOUN
ejpam-4652	280	10	it	it	PRON
ejpam-4652	280	11	follows	follow	VERB
ejpam-4652	280	12	that	that	DET
ejpam-4652	280	13	tx1	tx1	NOUN
ejpam-4652	280	14	=	=	PUNCT
ejpam-4652	280	15	ty1	ty1	NOUN
ejpam-4652	280	16	.	.	PUNCT
ejpam-4652	280	17	note	note	VERB
ejpam-4652	280	18	that	that	SCONJ
ejpam-4652	280	19	x	x	X
ejpam-4652	280	20	=	=	SYM
ejpam-4652	280	21	(	(	PUNCT
ejpam-4652	280	22	x1	x1	PROPN
ejpam-4652	280	23	,	,	PUNCT
ejpam-4652	280	24	x2	x2	PROPN
ejpam-4652	280	25	)	)	PUNCT
ejpam-4652	280	26	and	and	CCONJ
ejpam-4652	280	27	y	y	PROPN
ejpam-4652	280	28	=	=	SYM
ejpam-4652	280	29	(	(	PUNCT
ejpam-4652	280	30	y1	y1	INTJ
ejpam-4652	280	31	,	,	PUNCT
ejpam-4652	280	32	y2	y2	PROPN
ejpam-4652	280	33	)	)	PUNCT
ejpam-4652	280	34	/∈	/∈	PUNCT
ejpam-4652	281	1	c	c	X
ejpam-4652	281	2	,	,	PUNCT
ejpam-4652	281	3	then	then	ADV
ejpam-4652	281	4	x2	x2	PROPN
ejpam-4652	281	5	/∈	/∈	PUNCT
ejpam-4652	281	6	tx1	tx1	NOUN
ejpam-4652	281	7	and	and	CCONJ
ejpam-4652	281	8	y2	y2	NOUN
ejpam-4652	281	9	/∈	/∈	PUNCT
ejpam-4652	282	1	ty1	ty1	INTJ
ejpam-4652	282	2	.	.	PUNCT
ejpam-4652	283	1	by	by	ADP
ejpam-4652	283	2	(	(	PUNCT
ejpam-4652	283	3	ii	ii	NOUN
ejpam-4652	283	4	)	)	PUNCT
ejpam-4652	283	5	,	,	PUNCT
ejpam-4652	283	6	there	there	PRON
ejpam-4652	283	7	exists	exist	VERB
ejpam-4652	283	8	z	z	PROPN
ejpam-4652	283	9	∈	∈	PROPN
ejpam-4652	283	10	tx1	tx1	NOUN
ejpam-4652	283	11	such	such	ADJ
ejpam-4652	283	12	that	that	SCONJ
ejpam-4652	283	13	z	z	PROPN
ejpam-4652	283	14	∈	∈	PROPN
ejpam-4652	283	15	ng(y2	ng(y2	PROPN
ejpam-4652	283	16	)	)	PUNCT
ejpam-4652	283	17	\	\	PROPN
ejpam-4652	283	18	ng(x2	ng(x2	NOUN
ejpam-4652	283	19	)	)	PUNCT
ejpam-4652	283	20	or	or	CCONJ
ejpam-4652	283	21	z	z	NOUN
ejpam-4652	283	22	∈	∈	PROPN
ejpam-4652	283	23	ng(x2	ng(x2	NOUN
ejpam-4652	283	24	)	)	PUNCT
ejpam-4652	283	25	\	\	NOUN
ejpam-4652	283	26	ng(y2	ng(y2	PROPN
ejpam-4652	283	27	)	)	PUNCT
ejpam-4652	283	28	.	.	PUNCT
ejpam-4652	284	1	clearly	clearly	ADV
ejpam-4652	284	2	,	,	PUNCT
ejpam-4652	284	3	(	(	PUNCT
ejpam-4652	284	4	x1	x1	PROPN
ejpam-4652	284	5	,	,	PUNCT
ejpam-4652	284	6	z	z	NOUN
ejpam-4652	284	7	)	)	PUNCT
ejpam-4652	284	8	∈	∈	PROPN
ejpam-4652	284	9	c	c	NOUN
ejpam-4652	284	10	and	and	CCONJ
ejpam-4652	284	11	either	either	CCONJ
ejpam-4652	284	12	(	(	PUNCT
ejpam-4652	284	13	y1	y1	INTJ
ejpam-4652	284	14	,	,	PUNCT
ejpam-4652	284	15	y2	y2	PROPN
ejpam-4652	284	16	)	)	PUNCT
ejpam-4652	284	17	∈	∈	PROPN
ejpam-4652	284	18	ig[h][(x1	ig[h][(x1	PROPN
ejpam-4652	284	19	,	,	PUNCT
ejpam-4652	284	20	x2	x2	PROPN
ejpam-4652	284	21	)	)	PUNCT
ejpam-4652	284	22	,	,	PUNCT
ejpam-4652	284	23	(	(	PUNCT
ejpam-4652	284	24	x1	x1	PROPN
ejpam-4652	284	25	,	,	PUNCT
ejpam-4652	284	26	z	z	NOUN
ejpam-4652	284	27	)	)	PUNCT
ejpam-4652	284	28	]	]	PUNCT
ejpam-4652	284	29	.	.	PUNCT
ejpam-4652	285	1	thus	thus	ADV
ejpam-4652	285	2	,	,	PUNCT
ejpam-4652	285	3	(	(	PUNCT
ejpam-4652	285	4	x1	x1	PROPN
ejpam-4652	285	5	,	,	PUNCT
ejpam-4652	285	6	z	z	NOUN
ejpam-4652	285	7	)	)	PUNCT
ejpam-4652	285	8	strongly	strongly	ADV
ejpam-4652	285	9	resolves	resolve	NOUN
ejpam-4652	285	10	(	(	PUNCT
ejpam-4652	285	11	x1	x1	PROPN
ejpam-4652	285	12	,	,	PUNCT
ejpam-4652	285	13	x2	x2	PROPN
ejpam-4652	285	14	)	)	PUNCT
ejpam-4652	285	15	and	and	CCONJ
ejpam-4652	285	16	(	(	PUNCT
ejpam-4652	285	17	y1	y1	INTJ
ejpam-4652	285	18	,	,	PUNCT
ejpam-4652	285	19	y2	y2	PROPN
ejpam-4652	285	20	)	)	PUNCT
ejpam-4652	285	21	.	.	PUNCT
ejpam-4652	286	1	the	the	DET
ejpam-4652	286	2	next	next	ADJ
ejpam-4652	286	3	result	result	NOUN
ejpam-4652	286	4	follows	follow	VERB
ejpam-4652	286	5	immediately	immediately	ADV
ejpam-4652	286	6	from	from	ADP
ejpam-4652	286	7	theorem	theorem	ADJ
ejpam-4652	286	8	6	6	NUM
ejpam-4652	286	9	.	.	PUNCT
ejpam-4652	286	10	theorem	theorem	VERB
ejpam-4652	286	11	7	7	NUM
ejpam-4652	286	12	.	.	PUNCT
ejpam-4652	287	1	let	let	VERB
ejpam-4652	287	2	g	g	PRON
ejpam-4652	287	3	be	be	AUX
ejpam-4652	287	4	a	a	DET
ejpam-4652	287	5	non	non	ADJ
ejpam-4652	287	6	-	-	ADJ
ejpam-4652	287	7	trivial	trivial	ADJ
ejpam-4652	287	8	connected	connected	ADJ
ejpam-4652	287	9	graph	graph	NOUN
ejpam-4652	287	10	andh	andh	NOUN
ejpam-4652	287	11	be	be	AUX
ejpam-4652	287	12	non	non	ADJ
ejpam-4652	287	13	-	-	ADJ
ejpam-4652	287	14	trivial	trivial	ADJ
ejpam-4652	287	15	complete	complete	ADJ
ejpam-4652	287	16	graph	graph	NOUN
ejpam-4652	287	17	.	.	PUNCT
ejpam-4652	288	1	a	a	DET
ejpam-4652	288	2	subset	subset	NOUN
ejpam-4652	288	3	c	c	NOUN
ejpam-4652	288	4	=	=	SYM
ejpam-4652	288	5	(	(	PUNCT
ejpam-4652	288	6	⋃	⋃	PROPN
ejpam-4652	288	7	x∈s	x∈s	X
ejpam-4652	288	8	{	{	PUNCT
ejpam-4652	288	9	{	{	PUNCT
ejpam-4652	288	10	x	x	NOUN
ejpam-4652	288	11	}	}	PUNCT
ejpam-4652	288	12	×	×	NOUN
ejpam-4652	288	13	tx	tx	PROPN
ejpam-4652	288	14	}	}	PUNCT
ejpam-4652	288	15	)	)	PUNCT
ejpam-4652	288	16	⋃	⋃	NOUN
ejpam-4652	288	17	⋃	⋃	PROPN
ejpam-4652	288	18	x∈wg	x∈wg	NOUN
ejpam-4652	288	19	{	{	PUNCT
ejpam-4652	288	20	{	{	PUNCT
ejpam-4652	288	21	x	x	NOUN
ejpam-4652	288	22	}	}	PUNCT
ejpam-4652	288	23	×	×	NOUN
ejpam-4652	288	24	(	(	PUNCT
ejpam-4652	288	25	v	v	NOUN
ejpam-4652	288	26	(	(	PUNCT
ejpam-4652	288	27	h	h	NOUN
ejpam-4652	288	28	)	)	PUNCT
ejpam-4652	288	29	\	\	PUNCT
ejpam-4652	288	30	tx	tx	PROPN
ejpam-4652	288	31	)	)	PUNCT
ejpam-4652	288	32	}	}	PUNCT
ejpam-4652	288	33			PROPN
ejpam-4652	288	34	of	of	ADP
ejpam-4652	288	35	v	v	NOUN
ejpam-4652	288	36	(	(	PUNCT
ejpam-4652	288	37	g[h	g[h	PROPN
ejpam-4652	288	38	]	]	PUNCT
ejpam-4652	288	39	)	)	PUNCT
ejpam-4652	288	40	where	where	SCONJ
ejpam-4652	288	41	wg	wg	VERB
ejpam-4652	288	42	⊆	⊆	NUM
ejpam-4652	288	43	s	s	NOUN
ejpam-4652	288	44	and	and	CCONJ
ejpam-4652	288	45	tx	tx	VERB
ejpam-4652	288	46	⊆	⊆	NUM
ejpam-4652	288	47	v	v	NOUN
ejpam-4652	288	48	(	(	PUNCT
ejpam-4652	288	49	h	h	NOUN
ejpam-4652	288	50	)	)	PUNCT
ejpam-4652	288	51	,	,	PUNCT
ejpam-4652	288	52	∀x	∀x	VERB
ejpam-4652	288	53	∈	∈	PROPN
ejpam-4652	288	54	s	s	NOUN
ejpam-4652	288	55	,	,	PUNCT
ejpam-4652	288	56	is	be	AUX
ejpam-4652	288	57	a	a	DET
ejpam-4652	288	58	strong	strong	ADJ
ejpam-4652	288	59	resolving	resolving	NOUN
ejpam-4652	288	60	dominating	dominating	NOUN
ejpam-4652	288	61	set	set	NOUN
ejpam-4652	288	62	of	of	ADP
ejpam-4652	288	63	g[h	g[h	PROPN
ejpam-4652	288	64	]	]	PUNCT
ejpam-4652	288	65	if	if	SCONJ
ejpam-4652	288	66	and	and	CCONJ
ejpam-4652	288	67	only	only	ADV
ejpam-4652	288	68	if	if	SCONJ
ejpam-4652	288	69	(	(	PUNCT
ejpam-4652	288	70	i	i	NOUN
ejpam-4652	288	71	)	)	PUNCT
ejpam-4652	288	72	s	s	PART
ejpam-4652	288	73	=	=	SYM
ejpam-4652	288	74	v	v	NOUN
ejpam-4652	288	75	(	(	PUNCT
ejpam-4652	288	76	g	g	NOUN
ejpam-4652	288	77	)	)	PUNCT
ejpam-4652	288	78	.	.	PUNCT
ejpam-4652	289	1	(	(	PUNCT
ejpam-4652	289	2	ii	ii	NOUN
ejpam-4652	289	3	)	)	PUNCT
ejpam-4652	289	4	v	v	NOUN
ejpam-4652	289	5	(	(	PUNCT
ejpam-4652	289	6	h	h	NOUN
ejpam-4652	289	7	)	)	PUNCT
ejpam-4652	289	8	\	\	PROPN
ejpam-4652	290	1	tx	tx	PROPN
ejpam-4652	290	2	is	be	AUX
ejpam-4652	290	3	a	a	DET
ejpam-4652	290	4	dominated	dominate	VERB
ejpam-4652	290	5	superclique	superclique	NOUN
ejpam-4652	290	6	of	of	ADP
ejpam-4652	290	7	h.	h.	PROPN
ejpam-4652	290	8	(	(	PUNCT
ejpam-4652	290	9	iii	iii	X
ejpam-4652	290	10	)	)	PUNCT
ejpam-4652	290	11	wg	wg	PROPN
ejpam-4652	290	12	is	be	AUX
ejpam-4652	290	13	a	a	DET
ejpam-4652	290	14	strong	strong	ADJ
ejpam-4652	290	15	resolving	resolving	NOUN
ejpam-4652	290	16	dominating	dominating	NOUN
ejpam-4652	290	17	set	set	NOUN
ejpam-4652	290	18	of	of	ADP
ejpam-4652	290	19	g.	g.	PROPN
ejpam-4652	290	20	acknowledgements	acknowledgement	NOUN
ejpam-4652	290	21	this	this	DET
ejpam-4652	290	22	research	research	NOUN
ejpam-4652	290	23	is	be	AUX
ejpam-4652	290	24	funded	fund	VERB
ejpam-4652	290	25	by	by	ADP
ejpam-4652	290	26	the	the	DET
ejpam-4652	290	27	commission	commission	NOUN
ejpam-4652	290	28	on	on	ADP
ejpam-4652	290	29	higher	high	ADJ
ejpam-4652	290	30	education	education	NOUN
ejpam-4652	290	31	(	(	PUNCT
ejpam-4652	290	32	ched	che	VERB
ejpam-4652	290	33	)	)	PUNCT
ejpam-4652	290	34	and	and	CCONJ
ejpam-4652	290	35	mindanao	mindanao	PROPN
ejpam-4652	290	36	state	state	PROPN
ejpam-4652	290	37	university	university	PROPN
ejpam-4652	290	38	-	-	PUNCT
ejpam-4652	290	39	iligan	iligan	PROPN
ejpam-4652	290	40	institute	institute	PROPN
ejpam-4652	290	41	of	of	ADP
ejpam-4652	290	42	technology	technology	PROPN
ejpam-4652	290	43	,	,	PUNCT
ejpam-4652	290	44	philippines	philippine	NOUN
ejpam-4652	290	45	.	.	PUNCT
ejpam-4652	291	1	references	reference	NOUN
ejpam-4652	291	2	372	372	NUM
ejpam-4652	291	3	references	reference	NOUN
ejpam-4652	291	4	[	[	X
ejpam-4652	291	5	1	1	NUM
ejpam-4652	291	6	]	]	X
ejpam-4652	291	7	p.l	p.l	PROPN
ejpam-4652	291	8	.	.	PROPN
ejpam-4652	291	9	acal	acal	PROPN
ejpam-4652	291	10	,	,	PUNCT
ejpam-4652	291	11	g.b	g.b	PROPN
ejpam-4652	291	12	.	.	PUNCT
ejpam-4652	291	13	monsanto	monsanto	PROPN
ejpam-4652	291	14	,	,	PUNCT
ejpam-4652	291	15	and	and	CCONJ
ejpam-4652	291	16	h.m	h.m	PROPN
ejpam-4652	291	17	.	.	PROPN
ejpam-4652	291	18	rara	rara	PROPN
ejpam-4652	291	19	.	.	PUNCT
ejpam-4652	292	1	on	on	ADP
ejpam-4652	292	2	strong	strong	ADJ
ejpam-4652	292	3	resolving	resolving	NOUN
ejpam-4652	292	4	domination	domination	NOUN
ejpam-4652	292	5	in	in	ADP
ejpam-4652	292	6	the	the	DET
ejpam-4652	292	7	join	join	NOUN
ejpam-4652	292	8	and	and	CCONJ
ejpam-4652	292	9	corona	corona	NOUN
ejpam-4652	292	10	of	of	ADP
ejpam-4652	292	11	graphs	graph	NOUN
ejpam-4652	292	12	.	.	PUNCT
ejpam-4652	293	1	european	european	ADJ
ejpam-4652	293	2	journal	journal	PROPN
ejpam-4652	293	3	of	of	ADP
ejpam-4652	293	4	pure	pure	ADJ
ejpam-4652	293	5	and	and	CCONJ
ejpam-4652	293	6	applied	applied	ADJ
ejpam-4652	293	7	mathematics	mathematic	NOUN
ejpam-4652	293	8	,	,	PUNCT
ejpam-4652	293	9	29:383–393	29:383–393	NUM
ejpam-4652	293	10	,	,	PUNCT
ejpam-4652	293	11	2020	2020	NUM
ejpam-4652	293	12	.	.	PUNCT
ejpam-4652	294	1	[	[	X
ejpam-4652	294	2	2	2	NUM
ejpam-4652	294	3	]	]	X
ejpam-4652	294	4	r.f	r.f	PROPN
ejpam-4652	294	5	.	.	PROPN
ejpam-4652	294	6	bailey	bailey	PROPN
ejpam-4652	294	7	,	,	PUNCT
ejpam-4652	294	8	j.cáceres	j.cáceres	PROPN
ejpam-4652	294	9	,	,	PUNCT
ejpam-4652	294	10	d.	d.	PROPN
ejpam-4652	294	11	garijo	garijo	PROPN
ejpam-4652	294	12	,	,	PUNCT
ejpam-4652	294	13	a.	a.	PROPN
ejpam-4652	294	14	gonzález	gonzález	PROPN
ejpam-4652	294	15	,	,	PUNCT
ejpam-4652	294	16	a.	a.	NOUN
ejpam-4652	294	17	márquez	márquez	PROPN
ejpam-4652	294	18	.	.	PROPN
ejpam-4652	294	19	k.	k.	PROPN
ejpam-4652	294	20	meagher	meagher	PROPN
ejpam-4652	294	21	,	,	PUNCT
ejpam-4652	294	22	and	and	CCONJ
ejpam-4652	294	23	m.l	m.l	PROPN
ejpam-4652	294	24	.	.	PROPN
ejpam-4652	294	25	puertas	puertas	PROPN
ejpam-4652	294	26	.	.	PUNCT
ejpam-4652	295	1	resolving	resolve	VERB
ejpam-4652	295	2	sets	set	NOUN
ejpam-4652	295	3	for	for	ADP
ejpam-4652	295	4	johnson	johnson	PROPN
ejpam-4652	295	5	and	and	CCONJ
ejpam-4652	295	6	kneser	kneser	NOUN
ejpam-4652	295	7	graphs	graph	NOUN
ejpam-4652	295	8	.	.	PUNCT
ejpam-4652	296	1	european	european	ADJ
ejpam-4652	296	2	journal	journal	PROPN
ejpam-4652	296	3	of	of	ADP
ejpam-4652	296	4	combinatorics	combinatoric	NOUN
ejpam-4652	296	5	,	,	PUNCT
ejpam-4652	296	6	34:736–751	34:736–751	NUM
ejpam-4652	296	7	,	,	PUNCT
ejpam-4652	296	8	2013	2013	NUM
ejpam-4652	296	9	.	.	PUNCT
ejpam-4652	297	1	[	[	X
ejpam-4652	297	2	3	3	X
ejpam-4652	297	3	]	]	X
ejpam-4652	297	4	c.	c.	PROPN
ejpam-4652	297	5	berge	berge	PROPN
ejpam-4652	297	6	.	.	PUNCT
ejpam-4652	298	1	theorie	theorie	PROPN
ejpam-4652	298	2	des	des	PROPN
ejpam-4652	298	3	graphes	graphes	PROPN
ejpam-4652	298	4	et	et	PROPN
ejpam-4652	298	5	ses	ses	PROPN
ejpam-4652	298	6	applications	application	NOUN
ejpam-4652	298	7	.	.	PUNCT
ejpam-4652	299	1	metheum	metheum	NOUN
ejpam-4652	299	2	and	and	CCONJ
ejpam-4652	299	3	wiley	wiley	PROPN
ejpam-4652	299	4	,	,	PUNCT
ejpam-4652	299	5	london	london	PROPN
ejpam-4652	299	6	and	and	CCONJ
ejpam-4652	299	7	new	new	PROPN
ejpam-4652	299	8	york	york	PROPN
ejpam-4652	299	9	,	,	PUNCT
ejpam-4652	299	10	1962	1962	NUM
ejpam-4652	299	11	.	.	PUNCT
ejpam-4652	300	1	[	[	X
ejpam-4652	300	2	4	4	X
ejpam-4652	300	3	]	]	X
ejpam-4652	300	4	e.	e.	PROPN
ejpam-4652	300	5	cockayne	cockayne	PROPN
ejpam-4652	300	6	and	and	CCONJ
ejpam-4652	300	7	s.	s.	PROPN
ejpam-4652	300	8	hedetniemi	hedetniemi	PROPN
ejpam-4652	300	9	.	.	PUNCT
ejpam-4652	301	1	towards	towards	ADP
ejpam-4652	301	2	a	a	DET
ejpam-4652	301	3	theory	theory	NOUN
ejpam-4652	301	4	of	of	ADP
ejpam-4652	301	5	domination	domination	NOUN
ejpam-4652	301	6	in	in	ADP
ejpam-4652	301	7	graphs	graph	NOUN
ejpam-4652	301	8	.	.	PUNCT
ejpam-4652	302	1	networks	network	NOUN
ejpam-4652	302	2	,	,	PUNCT
ejpam-4652	302	3	7(3):247–261	7(3):247–261	NUM
ejpam-4652	302	4	,	,	PUNCT
ejpam-4652	302	5	1977	1977	NUM
ejpam-4652	302	6	.	.	PUNCT
ejpam-4652	303	1	[	[	X
ejpam-4652	303	2	5	5	NUM
ejpam-4652	303	3	]	]	PUNCT
ejpam-4652	303	4	a.	a.	NOUN
ejpam-4652	303	5	cuivillas	cuivilla	NOUN
ejpam-4652	303	6	and	and	CCONJ
ejpam-4652	303	7	s.r	s.r	PROPN
ejpam-4652	303	8	.	.	PROPN
ejpam-4652	303	9	canoy	canoy	PROPN
ejpam-4652	303	10	jr	jr	PROPN
ejpam-4652	303	11	.	.	PROPN
ejpam-4652	303	12	restrained	restrain	VERB
ejpam-4652	303	13	double	double	ADJ
ejpam-4652	303	14	domination	domination	NOUN
ejpam-4652	303	15	in	in	ADP
ejpam-4652	303	16	the	the	DET
ejpam-4652	303	17	join	join	NOUN
ejpam-4652	303	18	and	and	CCONJ
ejpam-4652	303	19	corona	corona	NOUN
ejpam-4652	303	20	of	of	ADP
ejpam-4652	303	21	graphs	graph	NOUN
ejpam-4652	303	22	.	.	PUNCT
ejpam-4652	304	1	international	international	ADJ
ejpam-4652	304	2	journal	journal	PROPN
ejpam-4652	304	3	of	of	ADP
ejpam-4652	304	4	math	math	NOUN
ejpam-4652	304	5	.	.	PUNCT
ejpam-4652	305	1	analysis	analysis	NOUN
ejpam-4652	305	2	,	,	PUNCT
ejpam-4652	305	3	8(27):1339–1347	8(27):1339–1347	NUM
ejpam-4652	305	4	,	,	PUNCT
ejpam-4652	305	5	2014	2014	NUM
ejpam-4652	305	6	.	.	PUNCT
ejpam-4652	306	1	[	[	X
ejpam-4652	306	2	6	6	NUM
ejpam-4652	306	3	]	]	X
ejpam-4652	306	4	c.	c.	NOUN
ejpam-4652	306	5	go	go	NOUN
ejpam-4652	306	6	and	and	CCONJ
ejpam-4652	306	7	s.r	s.r	PROPN
ejpam-4652	306	8	.	.	PROPN
ejpam-4652	306	9	canoy	canoy	PROPN
ejpam-4652	306	10	jr	jr	PROPN
ejpam-4652	306	11	.	.	PUNCT
ejpam-4652	307	1	some	some	DET
ejpam-4652	307	2	types	type	NOUN
ejpam-4652	307	3	of	of	ADP
ejpam-4652	307	4	dominating	dominating	NOUN
ejpam-4652	307	5	sets	set	NOUN
ejpam-4652	307	6	and	and	CCONJ
ejpam-4652	307	7	domination	domination	NOUN
ejpam-4652	307	8	numbers	number	NOUN
ejpam-4652	307	9	in	in	ADP
ejpam-4652	307	10	graphs	graph	NOUN
ejpam-4652	307	11	.	.	PUNCT
ejpam-4652	308	1	[	[	X
ejpam-4652	308	2	7	7	X
ejpam-4652	308	3	]	]	X
ejpam-4652	308	4	f.	f.	PROPN
ejpam-4652	308	5	harary	harary	PROPN
ejpam-4652	308	6	.	.	PUNCT
ejpam-4652	309	1	graph	graph	NOUN
ejpam-4652	309	2	theory	theory	NOUN
ejpam-4652	309	3	.	.	PUNCT
ejpam-4652	310	1	addison	addison	PROPN
ejpam-4652	310	2	-	-	PUNCT
ejpam-4652	310	3	wesley	wesley	PROPN
ejpam-4652	310	4	publishing	publishing	PROPN
ejpam-4652	310	5	company	company	NOUN
ejpam-4652	310	6	,	,	PUNCT
ejpam-4652	310	7	usa	usa	PROPN
ejpam-4652	310	8	,	,	PUNCT
ejpam-4652	310	9	1969	1969	NUM
ejpam-4652	310	10	.	.	PUNCT
ejpam-4652	311	1	[	[	X
ejpam-4652	311	2	8	8	NUM
ejpam-4652	311	3	]	]	X
ejpam-4652	311	4	s.r	s.r	PROPN
ejpam-4652	311	5	.	.	PROPN
ejpam-4652	311	6	canoy	canoy	PROPN
ejpam-4652	311	7	jr	jr	PROPN
ejpam-4652	311	8	.	.	PROPN
ejpam-4652	311	9	and	and	CCONJ
ejpam-4652	311	10	s.a	s.a	PROPN
ejpam-4652	311	11	.	.	PROPN
ejpam-4652	311	12	omega	omega	NOUN
ejpam-4652	311	13	.	.	PUNCT
ejpam-4652	312	1	locating	locate	VERB
ejpam-4652	312	2	sets	set	NOUN
ejpam-4652	312	3	in	in	ADP
ejpam-4652	312	4	a	a	DET
ejpam-4652	312	5	graph	graph	NOUN
ejpam-4652	312	6	.	.	PUNCT
ejpam-4652	313	1	applied	apply	VERB
ejpam-4652	313	2	mathematical	mathematical	ADJ
ejpam-4652	313	3	sciences	science	NOUN
ejpam-4652	313	4	,	,	PUNCT
ejpam-4652	313	5	9(60):2957–2964	9(60):2957–2964	NUM
ejpam-4652	313	6	,	,	PUNCT
ejpam-4652	313	7	2015	2015	NUM
ejpam-4652	313	8	.	.	PUNCT
ejpam-4652	314	1	[	[	X
ejpam-4652	314	2	9	9	NUM
ejpam-4652	314	3	]	]	X
ejpam-4652	314	4	o.	o.	NOUN
ejpam-4652	314	5	oellerman	oellerman	PROPN
ejpam-4652	314	6	and	and	CCONJ
ejpam-4652	314	7	j.	j.	PROPN
ejpam-4652	314	8	peter	peter	PROPN
ejpam-4652	314	9	-	-	PUNCT
ejpam-4652	314	10	fransen	fransen	PROPN
ejpam-4652	314	11	.	.	PUNCT
ejpam-4652	315	1	the	the	DET
ejpam-4652	315	2	strong	strong	ADJ
ejpam-4652	315	3	metric	metric	ADJ
ejpam-4652	315	4	dimension	dimension	NOUN
ejpam-4652	315	5	of	of	ADP
ejpam-4652	315	6	graphs	graph	NOUN
ejpam-4652	315	7	and	and	CCONJ
ejpam-4652	315	8	digraphs	digraph	NOUN
ejpam-4652	315	9	.	.	PUNCT
ejpam-4652	316	1	discrete	discrete	ADJ
ejpam-4652	316	2	applied	apply	VERB
ejpam-4652	316	3	mathematics	mathematic	NOUN
ejpam-4652	316	4	,	,	PUNCT
ejpam-4652	316	5	155(3):356–364	155(3):356–364	NUM
ejpam-4652	316	6	,	,	PUNCT
ejpam-4652	316	7	2007	2007	NUM
ejpam-4652	316	8	.	.	PUNCT
ejpam-4652	317	1	[	[	X
ejpam-4652	317	2	10	10	NUM
ejpam-4652	317	3	]	]	X
ejpam-4652	317	4	p.	p.	NOUN
ejpam-4652	317	5	slater	slater	PROPN
ejpam-4652	317	6	.	.	PUNCT
ejpam-4652	318	1	dominating	dominating	NOUN
ejpam-4652	318	2	and	and	CCONJ
ejpam-4652	318	3	reference	reference	NOUN
ejpam-4652	318	4	sets	set	NOUN
ejpam-4652	318	5	in	in	ADP
ejpam-4652	318	6	a	a	DET
ejpam-4652	318	7	graph	graph	NOUN
ejpam-4652	318	8	.	.	PUNCT
ejpam-4652	319	1	journal	journal	NOUN
ejpam-4652	319	2	of	of	ADP
ejpam-4652	319	3	mathematics	mathematic	NOUN
ejpam-4652	319	4	and	and	CCONJ
ejpam-4652	319	5	physical	physical	ADJ
ejpam-4652	319	6	science	science	NOUN
ejpam-4652	319	7	,	,	PUNCT
ejpam-4652	319	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4652	319	9	,	,	PUNCT
ejpam-4652	319	10	1988	1988	NUM
ejpam-4652	319	11	.	.	PUNCT