id	sid	tid	token	lemma	pos
ejpam-3625	1	1	european	european	PROPN
ejpam-3625	1	2	journal	journal	PROPN
ejpam-3625	1	3	of	of	ADP
ejpam-3625	1	4	pure	pure	ADJ
ejpam-3625	1	5	and	and	CCONJ
ejpam-3625	1	6	applied	apply	VERB
ejpam-3625	1	7	mathematics	mathematic	NOUN
ejpam-3625	1	8	vol	vol	NOUN
ejpam-3625	1	9	.	.	PROPN
ejpam-3625	2	1	13	13	NUM
ejpam-3625	2	2	,	,	PUNCT
ejpam-3625	2	3	no	no	INTJ
ejpam-3625	2	4	.	.	NOUN
ejpam-3625	2	5	1	1	NUM
ejpam-3625	2	6	,	,	PUNCT
ejpam-3625	2	7	2020	2020	NUM
ejpam-3625	2	8	,	,	PUNCT
ejpam-3625	2	9	170	170	NUM
ejpam-3625	2	10	-	-	SYM
ejpam-3625	2	11	179	179	NUM
ejpam-3625	2	12	issn	issn	PROPN
ejpam-3625	2	13	1307	1307	NUM
ejpam-3625	2	14	-	-	SYM
ejpam-3625	2	15	5543	5543	NUM
ejpam-3625	2	16	–	–	PUNCT
ejpam-3625	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3625	2	18	published	publish	VERB
ejpam-3625	2	19	by	by	ADP
ejpam-3625	2	20	new	new	PROPN
ejpam-3625	2	21	york	york	PROPN
ejpam-3625	2	22	business	business	PROPN
ejpam-3625	2	23	global	global	ADJ
ejpam-3625	2	24	on	on	ADP
ejpam-3625	2	25	strong	strong	ADJ
ejpam-3625	2	26	resolving	resolving	NOUN
ejpam-3625	2	27	domination	domination	NOUN
ejpam-3625	2	28	in	in	ADP
ejpam-3625	2	29	the	the	DET
ejpam-3625	2	30	join	join	NOUN
ejpam-3625	2	31	and	and	CCONJ
ejpam-3625	2	32	corona	corona	NOUN
ejpam-3625	2	33	of	of	ADP
ejpam-3625	2	34	graphs	graphs	PROPN
ejpam-3625	2	35	gerald	gerald	PROPN
ejpam-3625	2	36	b.	b.	PROPN
ejpam-3625	2	37	monsanto1,∗	monsanto1,∗	PROPN
ejpam-3625	2	38	,	,	PUNCT
ejpam-3625	2	39	penelyn	penelyn	NOUN
ejpam-3625	2	40	l.	l.	PROPN
ejpam-3625	2	41	acal2	acal2	PROPN
ejpam-3625	2	42	,	,	PUNCT
ejpam-3625	2	43	helen	helen	PROPN
ejpam-3625	2	44	m.	m.	PROPN
ejpam-3625	2	45	rara3	rara3	PROPN
ejpam-3625	2	46	1	1	NUM
ejpam-3625	2	47	department	department	NOUN
ejpam-3625	2	48	of	of	ADP
ejpam-3625	2	49	teacher	teacher	NOUN
ejpam-3625	2	50	education	education	NOUN
ejpam-3625	2	51	,	,	PUNCT
ejpam-3625	2	52	visayas	visayas	PROPN
ejpam-3625	2	53	state	state	PROPN
ejpam-3625	2	54	university	university	PROPN
ejpam-3625	2	55	-	-	PUNCT
ejpam-3625	2	56	villaba	villaba	NOUN
ejpam-3625	2	57	,	,	PUNCT
ejpam-3625	2	58	6537	6537	NUM
ejpam-3625	2	59	villaba	villaba	NOUN
ejpam-3625	2	60	,	,	PUNCT
ejpam-3625	2	61	leyte	leyte	PROPN
ejpam-3625	2	62	,	,	PUNCT
ejpam-3625	2	63	philippines	philippines	PROPN
ejpam-3625	2	64	2	2	NUM
ejpam-3625	2	65	department	department	NOUN
ejpam-3625	2	66	of	of	ADP
ejpam-3625	2	67	mathematical	mathematical	ADJ
ejpam-3625	2	68	sciences	sciences	PROPN
ejpam-3625	2	69	,	,	PUNCT
ejpam-3625	2	70	university	university	NOUN
ejpam-3625	2	71	of	of	ADP
ejpam-3625	2	72	science	science	NOUN
ejpam-3625	2	73	and	and	CCONJ
ejpam-3625	2	74	technology	technology	NOUN
ejpam-3625	2	75	of	of	ADP
ejpam-3625	2	76	southern	southern	ADJ
ejpam-3625	2	77	philippines	philippine	NOUN
ejpam-3625	2	78	,	,	PUNCT
ejpam-3625	2	79	9023	9023	NUM
ejpam-3625	2	80	,	,	PUNCT
ejpam-3625	2	81	cagayan	cagayan	PROPN
ejpam-3625	2	82	de	de	PROPN
ejpam-3625	2	83	oro	oro	PROPN
ejpam-3625	2	84	city	city	NOUN
ejpam-3625	2	85	,	,	PUNCT
ejpam-3625	2	86	philippines	philippines	PROPN
ejpam-3625	2	87	3	3	NUM
ejpam-3625	2	88	department	department	NOUN
ejpam-3625	2	89	of	of	ADP
ejpam-3625	2	90	mathematics	mathematic	NOUN
ejpam-3625	2	91	and	and	CCONJ
ejpam-3625	2	92	statistics	statistic	NOUN
ejpam-3625	2	93	,	,	PUNCT
ejpam-3625	2	94	college	college	NOUN
ejpam-3625	2	95	of	of	ADP
ejpam-3625	2	96	science	science	NOUN
ejpam-3625	2	97	and	and	CCONJ
ejpam-3625	2	98	mathematics	mathematic	NOUN
ejpam-3625	2	99	,	,	PUNCT
ejpam-3625	2	100	center	center	NOUN
ejpam-3625	2	101	of	of	ADP
ejpam-3625	2	102	graph	graph	NOUN
ejpam-3625	2	103	theory	theory	NOUN
ejpam-3625	2	104	,	,	PUNCT
ejpam-3625	2	105	algebra	algebra	NOUN
ejpam-3625	2	106	,	,	PUNCT
ejpam-3625	2	107	and	and	CCONJ
ejpam-3625	2	108	analysis	analysis	NOUN
ejpam-3625	2	109	-	-	PUNCT
ejpam-3625	2	110	premier	premier	NOUN
ejpam-3625	2	111	research	research	NOUN
ejpam-3625	2	112	institute	institute	PROPN
ejpam-3625	2	113	of	of	ADP
ejpam-3625	2	114	science	science	NOUN
ejpam-3625	2	115	and	and	CCONJ
ejpam-3625	2	116	mathematics	mathematic	NOUN
ejpam-3625	2	117	,	,	PUNCT
ejpam-3625	2	118	mindanao	mindanao	PROPN
ejpam-3625	2	119	state	state	PROPN
ejpam-3625	2	120	university	university	PROPN
ejpam-3625	2	121	-	-	PUNCT
ejpam-3625	2	122	iligan	iligan	PROPN
ejpam-3625	2	123	institute	institute	PROPN
ejpam-3625	2	124	of	of	ADP
ejpam-3625	2	125	technology	technology	PROPN
ejpam-3625	2	126	,	,	PUNCT
ejpam-3625	2	127	9200	9200	NUM
ejpam-3625	2	128	iligan	iligan	ADJ
ejpam-3625	2	129	city	city	NOUN
ejpam-3625	2	130	,	,	PUNCT
ejpam-3625	2	131	philippines	philippine	NOUN
ejpam-3625	2	132	abstract	abstract	ADJ
ejpam-3625	2	133	.	.	PUNCT
ejpam-3625	3	1	let	let	VERB
ejpam-3625	3	2	g	g	PRON
ejpam-3625	3	3	be	be	AUX
ejpam-3625	3	4	a	a	DET
ejpam-3625	3	5	connected	connected	ADJ
ejpam-3625	3	6	graph	graph	NOUN
ejpam-3625	3	7	.	.	PUNCT
ejpam-3625	4	1	a	a	DET
ejpam-3625	4	2	subset	subset	NOUN
ejpam-3625	4	3	s	s	VERB
ejpam-3625	4	4	⊆	⊆	NUM
ejpam-3625	4	5	v	v	NOUN
ejpam-3625	4	6	(	(	PUNCT
ejpam-3625	4	7	g	g	NOUN
ejpam-3625	4	8	)	)	PUNCT
ejpam-3625	4	9	is	be	AUX
ejpam-3625	4	10	a	a	DET
ejpam-3625	4	11	strong	strong	ADJ
ejpam-3625	4	12	resolving	resolving	NOUN
ejpam-3625	4	13	dominating	dominating	NOUN
ejpam-3625	4	14	set	set	NOUN
ejpam-3625	4	15	of	of	ADP
ejpam-3625	4	16	g	g	PROPN
ejpam-3625	4	17	if	if	SCONJ
ejpam-3625	4	18	s	s	VERB
ejpam-3625	4	19	is	be	AUX
ejpam-3625	4	20	a	a	DET
ejpam-3625	4	21	dominating	dominating	NOUN
ejpam-3625	4	22	set	set	NOUN
ejpam-3625	4	23	and	and	CCONJ
ejpam-3625	4	24	for	for	ADP
ejpam-3625	4	25	every	every	DET
ejpam-3625	4	26	pair	pair	NOUN
ejpam-3625	4	27	of	of	ADP
ejpam-3625	4	28	vertices	vertex	NOUN
ejpam-3625	4	29	u	u	NOUN
ejpam-3625	4	30	,	,	PUNCT
ejpam-3625	4	31	v	v	NOUN
ejpam-3625	4	32	∈	∈	PROPN
ejpam-3625	4	33	v	v	NOUN
ejpam-3625	4	34	(	(	PUNCT
ejpam-3625	4	35	g	g	NOUN
ejpam-3625	4	36	)	)	PUNCT
ejpam-3625	4	37	,	,	PUNCT
ejpam-3625	4	38	there	there	PRON
ejpam-3625	4	39	exists	exist	VERB
ejpam-3625	4	40	a	a	DET
ejpam-3625	4	41	vertex	vertex	NOUN
ejpam-3625	4	42	w	w	ADP
ejpam-3625	4	43	∈	∈	NOUN
ejpam-3625	4	44	s	s	VERB
ejpam-3625	4	45	such	such	ADJ
ejpam-3625	4	46	that	that	SCONJ
ejpam-3625	4	47	u	u	PROPN
ejpam-3625	4	48	∈	∈	PROPN
ejpam-3625	4	49	ig[v	ig[v	PROPN
ejpam-3625	4	50	,	,	PUNCT
ejpam-3625	4	51	w	w	PROPN
ejpam-3625	4	52	]	]	PUNCT
ejpam-3625	4	53	or	or	CCONJ
ejpam-3625	4	54	v	v	ADP
ejpam-3625	4	55	∈	∈	PROPN
ejpam-3625	4	56	ig[u	ig[u	NOUN
ejpam-3625	4	57	,	,	PUNCT
ejpam-3625	4	58	w	w	NOUN
ejpam-3625	4	59	]	]	X
ejpam-3625	4	60	.	.	PUNCT
ejpam-3625	5	1	the	the	DET
ejpam-3625	5	2	smallest	small	ADJ
ejpam-3625	5	3	cardinality	cardinality	NOUN
ejpam-3625	5	4	of	of	ADP
ejpam-3625	5	5	a	a	DET
ejpam-3625	5	6	strong	strong	ADJ
ejpam-3625	5	7	resolving	resolving	NOUN
ejpam-3625	5	8	dominating	dominating	NOUN
ejpam-3625	5	9	set	set	NOUN
ejpam-3625	5	10	of	of	ADP
ejpam-3625	5	11	g	g	PROPN
ejpam-3625	5	12	is	be	AUX
ejpam-3625	5	13	called	call	VERB
ejpam-3625	5	14	the	the	DET
ejpam-3625	5	15	strong	strong	ADJ
ejpam-3625	5	16	resolving	resolving	NOUN
ejpam-3625	5	17	domination	domination	NOUN
ejpam-3625	5	18	number	number	NOUN
ejpam-3625	5	19	of	of	ADP
ejpam-3625	5	20	g.	g.	PROPN
ejpam-3625	5	21	in	in	ADP
ejpam-3625	5	22	this	this	DET
ejpam-3625	5	23	paper	paper	NOUN
ejpam-3625	5	24	,	,	PUNCT
ejpam-3625	5	25	we	we	PRON
ejpam-3625	5	26	characterize	characterize	VERB
ejpam-3625	5	27	the	the	DET
ejpam-3625	5	28	strong	strong	ADJ
ejpam-3625	5	29	resolving	resolve	VERB
ejpam-3625	5	30	dominating	dominating	NOUN
ejpam-3625	5	31	sets	set	NOUN
ejpam-3625	5	32	in	in	ADP
ejpam-3625	5	33	the	the	DET
ejpam-3625	5	34	join	join	NOUN
ejpam-3625	5	35	and	and	CCONJ
ejpam-3625	5	36	corona	corona	NOUN
ejpam-3625	5	37	of	of	ADP
ejpam-3625	5	38	graphs	graph	NOUN
ejpam-3625	5	39	and	and	CCONJ
ejpam-3625	5	40	determine	determine	VERB
ejpam-3625	5	41	the	the	DET
ejpam-3625	5	42	bounds	bound	NOUN
ejpam-3625	5	43	or	or	CCONJ
ejpam-3625	5	44	exact	exact	ADJ
ejpam-3625	5	45	values	value	NOUN
ejpam-3625	5	46	of	of	ADP
ejpam-3625	5	47	the	the	DET
ejpam-3625	5	48	strong	strong	ADJ
ejpam-3625	5	49	resolving	resolving	NOUN
ejpam-3625	5	50	domination	domination	NOUN
ejpam-3625	5	51	number	number	NOUN
ejpam-3625	5	52	of	of	ADP
ejpam-3625	5	53	these	these	DET
ejpam-3625	5	54	graphs	graph	NOUN
ejpam-3625	5	55	.	.	PUNCT
ejpam-3625	6	1	2020	2020	NUM
ejpam-3625	6	2	mathematics	mathematic	NOUN
ejpam-3625	6	3	subject	subject	NOUN
ejpam-3625	6	4	classifications	classification	NOUN
ejpam-3625	6	5	:	:	PUNCT
ejpam-3625	6	6	05c69	05c69	X
ejpam-3625	6	7	key	key	ADJ
ejpam-3625	6	8	words	word	NOUN
ejpam-3625	6	9	and	and	CCONJ
ejpam-3625	6	10	phrases	phrase	NOUN
ejpam-3625	6	11	:	:	PUNCT
ejpam-3625	6	12	strong	strong	ADJ
ejpam-3625	6	13	resolving	resolve	VERB
ejpam-3625	6	14	dominating	dominating	NOUN
ejpam-3625	6	15	set	set	NOUN
ejpam-3625	6	16	,	,	PUNCT
ejpam-3625	6	17	strong	strong	ADJ
ejpam-3625	6	18	resolving	resolve	VERB
ejpam-3625	6	19	domination	domination	NOUN
ejpam-3625	6	20	number	number	NOUN
ejpam-3625	6	21	,	,	PUNCT
ejpam-3625	6	22	join	join	NOUN
ejpam-3625	6	23	,	,	PUNCT
ejpam-3625	6	24	corona	corona	PROPN
ejpam-3625	6	25	1	1	NUM
ejpam-3625	6	26	.	.	PUNCT
ejpam-3625	7	1	introduction	introduction	NOUN
ejpam-3625	7	2	all	all	DET
ejpam-3625	7	3	graphs	graph	NOUN
ejpam-3625	7	4	considered	consider	VERB
ejpam-3625	7	5	in	in	ADP
ejpam-3625	7	6	this	this	DET
ejpam-3625	7	7	study	study	NOUN
ejpam-3625	7	8	are	be	AUX
ejpam-3625	7	9	finite	finite	ADJ
ejpam-3625	7	10	,	,	PUNCT
ejpam-3625	7	11	simple	simple	ADJ
ejpam-3625	7	12	,	,	PUNCT
ejpam-3625	7	13	and	and	CCONJ
ejpam-3625	7	14	undirected	undirected	ADJ
ejpam-3625	7	15	connected	connected	ADJ
ejpam-3625	7	16	graphs	graph	NOUN
ejpam-3625	7	17	,	,	PUNCT
ejpam-3625	7	18	that	that	ADV
ejpam-3625	7	19	is	is	ADV
ejpam-3625	7	20	,	,	PUNCT
ejpam-3625	7	21	without	without	ADP
ejpam-3625	7	22	loops	loop	NOUN
ejpam-3625	7	23	and	and	CCONJ
ejpam-3625	7	24	multiple	multiple	ADJ
ejpam-3625	7	25	edges	edge	NOUN
ejpam-3625	7	26	.	.	PUNCT
ejpam-3625	8	1	for	for	ADP
ejpam-3625	8	2	some	some	DET
ejpam-3625	8	3	basic	basic	ADJ
ejpam-3625	8	4	concepts	concept	NOUN
ejpam-3625	8	5	in	in	ADP
ejpam-3625	8	6	graph	graph	NOUN
ejpam-3625	8	7	theory	theory	NOUN
ejpam-3625	8	8	,	,	PUNCT
ejpam-3625	8	9	we	we	PRON
ejpam-3625	8	10	refer	refer	VERB
ejpam-3625	8	11	readers	reader	NOUN
ejpam-3625	8	12	to	to	ADP
ejpam-3625	8	13	[	[	X
ejpam-3625	8	14	4	4	NUM
ejpam-3625	8	15	]	]	PUNCT
ejpam-3625	8	16	.	.	PUNCT
ejpam-3625	9	1	let	let	VERB
ejpam-3625	9	2	g	g	NOUN
ejpam-3625	9	3	=	=	PUNCT
ejpam-3625	9	4	(	(	PUNCT
ejpam-3625	9	5	v	v	NOUN
ejpam-3625	9	6	(	(	PUNCT
ejpam-3625	9	7	g	g	NOUN
ejpam-3625	9	8	)	)	PUNCT
ejpam-3625	9	9	,	,	PUNCT
ejpam-3625	9	10	e(g	e(g	PROPN
ejpam-3625	9	11	)	)	PUNCT
ejpam-3625	9	12	)	)	PUNCT
ejpam-3625	10	1	be	be	AUX
ejpam-3625	10	2	a	a	DET
ejpam-3625	10	3	connected	connected	ADJ
ejpam-3625	10	4	graph	graph	NOUN
ejpam-3625	10	5	.	.	PUNCT
ejpam-3625	11	1	the	the	DET
ejpam-3625	11	2	open	open	ADJ
ejpam-3625	11	3	neighborhood	neighborhood	NOUN
ejpam-3625	11	4	ng(v	ng(v	PUNCT
ejpam-3625	11	5	)	)	PUNCT
ejpam-3625	11	6	=	=	PRON
ejpam-3625	11	7	{	{	PUNCT
ejpam-3625	11	8	u	u	NOUN
ejpam-3625	11	9	∈	∈	PROPN
ejpam-3625	11	10	v	v	NOUN
ejpam-3625	11	11	(	(	PUNCT
ejpam-3625	11	12	g	g	NOUN
ejpam-3625	11	13	)	)	PUNCT
ejpam-3625	11	14	:	:	PUNCT
ejpam-3625	11	15	uv	uv	PROPN
ejpam-3625	11	16	∈	∈	PROPN
ejpam-3625	11	17	e(g	e(g	PROPN
ejpam-3625	11	18	)	)	PUNCT
ejpam-3625	11	19	}	}	PUNCT
ejpam-3625	11	20	.	.	PUNCT
ejpam-3625	12	1	any	any	DET
ejpam-3625	12	2	element	element	NOUN
ejpam-3625	12	3	u	u	NOUN
ejpam-3625	12	4	of	of	ADP
ejpam-3625	12	5	ng(v	ng(v	PUNCT
ejpam-3625	12	6	)	)	PUNCT
ejpam-3625	12	7	is	be	AUX
ejpam-3625	12	8	called	call	VERB
ejpam-3625	12	9	a	a	DET
ejpam-3625	12	10	neighbor	neighbor	NOUN
ejpam-3625	12	11	of	of	ADP
ejpam-3625	12	12	v.	v.	ADP
ejpam-3625	12	13	the	the	DET
ejpam-3625	12	14	closed	closed	ADJ
ejpam-3625	12	15	neighborhood	neighborhood	NOUN
ejpam-3625	12	16	ng[v	ng[v	NOUN
ejpam-3625	12	17	]	]	X
ejpam-3625	12	18	=	=	SYM
ejpam-3625	12	19	ng(v	ng(v	X
ejpam-3625	12	20	)	)	PUNCT
ejpam-3625	12	21	∪	∪	ADP
ejpam-3625	12	22	{	{	PUNCT
ejpam-3625	12	23	v	v	NOUN
ejpam-3625	12	24	}	}	PUNCT
ejpam-3625	12	25	.	.	PUNCT
ejpam-3625	13	1	thus	thus	ADV
ejpam-3625	13	2	,	,	PUNCT
ejpam-3625	13	3	the	the	DET
ejpam-3625	13	4	degree	degree	NOUN
ejpam-3625	13	5	of	of	ADP
ejpam-3625	13	6	v	v	NOUN
ejpam-3625	13	7	is	be	AUX
ejpam-3625	13	8	given	give	VERB
ejpam-3625	13	9	by	by	ADP
ejpam-3625	13	10	degg(v	degg(v	PROPN
ejpam-3625	13	11	)	)	PUNCT
ejpam-3625	13	12	=	=	SYM
ejpam-3625	13	13	|ng(v)|	|ng(v)|	NOUN
ejpam-3625	13	14	.	.	PUNCT
ejpam-3625	14	1	customarily	customarily	ADV
ejpam-3625	14	2	,	,	PUNCT
ejpam-3625	14	3	for	for	ADP
ejpam-3625	14	4	s	s	PROPN
ejpam-3625	14	5	⊆	⊆	NUM
ejpam-3625	14	6	v	v	NOUN
ejpam-3625	14	7	(	(	PUNCT
ejpam-3625	14	8	g	g	NOUN
ejpam-3625	14	9	)	)	PUNCT
ejpam-3625	14	10	,	,	PUNCT
ejpam-3625	14	11	ng(s	ng(s	NUM
ejpam-3625	14	12	)	)	PUNCT
ejpam-3625	15	1	=	=	SYM
ejpam-3625	16	1	⋃	⋃	ADP
ejpam-3625	16	2	v∈s	v∈s	NOUN
ejpam-3625	16	3	ng(v	ng(v	NOUN
ejpam-3625	16	4	)	)	PUNCT
ejpam-3625	16	5	and	and	CCONJ
ejpam-3625	16	6	ng[s	ng[	NOUN
ejpam-3625	16	7	]	]	PUNCT
ejpam-3625	16	8	=	=	PUNCT
ejpam-3625	16	9	⋃	⋃	VERB
ejpam-3625	16	10	v∈s	v∈s	ADJ
ejpam-3625	16	11	ng[v	ng[v	NOUN
ejpam-3625	16	12	]	]	PUNCT
ejpam-3625	16	13	.	.	PUNCT
ejpam-3625	17	1	∗corresponding	∗corresponde	VERB
ejpam-3625	17	2	author	author	NOUN
ejpam-3625	17	3	.	.	PUNCT
ejpam-3625	18	1	doi	doi	NOUN
ejpam-3625	18	2	:	:	PUNCT
ejpam-3625	18	3	https://doi.org/10.29020/nybg.ejpam.v13i1.3625	https://doi.org/10.29020/nybg.ejpam.v13i1.3625	PRON
ejpam-3625	18	4	email	email	NOUN
ejpam-3625	18	5	addresses	address	NOUN
ejpam-3625	18	6	:	:	PUNCT
ejpam-3625	18	7	monger2006@yahoo.com	monger2006@yahoo.com	X
ejpam-3625	18	8	(	(	PUNCT
ejpam-3625	18	9	g.	g.	PROPN
ejpam-3625	18	10	monsanto	monsanto	PROPN
ejpam-3625	18	11	)	)	PUNCT
ejpam-3625	18	12	,	,	PUNCT
ejpam-3625	18	13	penelyn.acal@g.msuiit.edu.ph	penelyn.acal@g.msuiit.edu.ph	PROPN
ejpam-3625	18	14	(	(	PUNCT
ejpam-3625	18	15	p.	p.	NOUN
ejpam-3625	18	16	acal	acal	ADJ
ejpam-3625	18	17	)	)	PUNCT
ejpam-3625	18	18	,	,	PUNCT
ejpam-3625	18	19	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-3625	18	20	(	(	PUNCT
ejpam-3625	18	21	h.	h.	PROPN
ejpam-3625	18	22	rara	rara	PROPN
ejpam-3625	18	23	)	)	PUNCT
ejpam-3625	18	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3625	19	1	170	170	NUM
ejpam-3625	19	2	c	c	X
ejpam-3625	19	3	©	©	NOUN
ejpam-3625	19	4	2020	2020	NUM
ejpam-3625	19	5	ejpam	ejpam	VERB
ejpam-3625	19	6	all	all	DET
ejpam-3625	19	7	rights	right	NOUN
ejpam-3625	19	8	reserved	reserve	VERB
ejpam-3625	19	9	.	.	PUNCT
ejpam-3625	20	1	g.	g.	PROPN
ejpam-3625	20	2	monsanto	monsanto	PROPN
ejpam-3625	20	3	,	,	PUNCT
ejpam-3625	20	4	p.	p.	PROPN
ejpam-3625	20	5	acal	acal	PROPN
ejpam-3625	20	6	,	,	PUNCT
ejpam-3625	20	7	h.	h.	PROPN
ejpam-3625	20	8	rara	rara	PROPN
ejpam-3625	20	9	/	/	SYM
ejpam-3625	20	10	eur	eur	PROPN
ejpam-3625	20	11	.	.	PUNCT
ejpam-3625	21	1	j.	j.	PROPN
ejpam-3625	21	2	pure	pure	PROPN
ejpam-3625	21	3	appl	appl	PROPN
ejpam-3625	21	4	.	.	PROPN
ejpam-3625	21	5	math	math	PROPN
ejpam-3625	21	6	,	,	PUNCT
ejpam-3625	21	7	13	13	NUM
ejpam-3625	21	8	(	(	PUNCT
ejpam-3625	21	9	1	1	NUM
ejpam-3625	21	10	)	)	PUNCT
ejpam-3625	21	11	(	(	PUNCT
ejpam-3625	21	12	2020	2020	NUM
ejpam-3625	21	13	)	)	PUNCT
ejpam-3625	21	14	,	,	PUNCT
ejpam-3625	21	15	170	170	NUM
ejpam-3625	21	16	-	-	SYM
ejpam-3625	21	17	179	179	NUM
ejpam-3625	21	18	171	171	NUM
ejpam-3625	21	19	a	a	DET
ejpam-3625	21	20	nonempty	nonempty	ADJ
ejpam-3625	21	21	set	set	VERB
ejpam-3625	21	22	s	s	PROPN
ejpam-3625	21	23	⊆	⊆	NUM
ejpam-3625	21	24	v	v	NOUN
ejpam-3625	21	25	(	(	PUNCT
ejpam-3625	21	26	g	g	NOUN
ejpam-3625	21	27	)	)	PUNCT
ejpam-3625	21	28	is	be	AUX
ejpam-3625	21	29	a	a	DET
ejpam-3625	21	30	dominating	dominating	NOUN
ejpam-3625	21	31	set	set	VERB
ejpam-3625	21	32	in	in	ADP
ejpam-3625	21	33	graph	graph	NOUN
ejpam-3625	21	34	g	g	NOUN
ejpam-3625	21	35	if	if	SCONJ
ejpam-3625	21	36	ng[s	ng[	NOUN
ejpam-3625	21	37	]	]	PUNCT
ejpam-3625	21	38	=	=	SYM
ejpam-3625	21	39	v	v	NOUN
ejpam-3625	21	40	(	(	PUNCT
ejpam-3625	21	41	g	g	NOUN
ejpam-3625	21	42	)	)	PUNCT
ejpam-3625	21	43	.	.	PUNCT
ejpam-3625	22	1	otherwise	otherwise	ADV
ejpam-3625	22	2	,	,	PUNCT
ejpam-3625	22	3	we	we	PRON
ejpam-3625	22	4	say	say	VERB
ejpam-3625	22	5	s	s	PRON
ejpam-3625	22	6	is	be	AUX
ejpam-3625	22	7	a	a	DET
ejpam-3625	22	8	non	non	ADJ
ejpam-3625	22	9	-	-	ADJ
ejpam-3625	22	10	dominating	dominating	ADJ
ejpam-3625	22	11	set	set	NOUN
ejpam-3625	22	12	of	of	ADP
ejpam-3625	22	13	g.	g.	PROPN
ejpam-3625	22	14	the	the	DET
ejpam-3625	22	15	domination	domination	NOUN
ejpam-3625	22	16	number	number	NOUN
ejpam-3625	22	17	of	of	ADP
ejpam-3625	22	18	a	a	DET
ejpam-3625	22	19	graph	graph	NOUN
ejpam-3625	22	20	g	g	NOUN
ejpam-3625	22	21	,	,	PUNCT
ejpam-3625	22	22	denoted	denote	VERB
ejpam-3625	22	23	by	by	ADP
ejpam-3625	22	24	γ(g	γ(g	PROPN
ejpam-3625	22	25	)	)	PUNCT
ejpam-3625	22	26	,	,	PUNCT
ejpam-3625	22	27	is	be	AUX
ejpam-3625	22	28	given	give	VERB
ejpam-3625	22	29	by	by	ADP
ejpam-3625	22	30	γ(g	γ(g	PROPN
ejpam-3625	22	31	)	)	PUNCT
ejpam-3625	23	1	=	=	NOUN
ejpam-3625	23	2	min{|s|	min{|s|	NOUN
ejpam-3625	23	3	:	:	PUNCT
ejpam-3625	23	4	s	s	VERB
ejpam-3625	23	5	is	be	AUX
ejpam-3625	23	6	a	a	DET
ejpam-3625	23	7	dominating	dominating	NOUN
ejpam-3625	23	8	set	set	NOUN
ejpam-3625	23	9	of	of	ADP
ejpam-3625	23	10	g	g	NOUN
ejpam-3625	23	11	}	}	PUNCT
ejpam-3625	23	12	.	.	PUNCT
ejpam-3625	24	1	if	if	SCONJ
ejpam-3625	24	2	|s|	|s|	PROPN
ejpam-3625	24	3	=	=	SYM
ejpam-3625	24	4	γ(g	γ(g	PROPN
ejpam-3625	24	5	)	)	PUNCT
ejpam-3625	24	6	,	,	PUNCT
ejpam-3625	24	7	then	then	ADV
ejpam-3625	24	8	s	s	VERB
ejpam-3625	24	9	is	be	AUX
ejpam-3625	24	10	said	say	VERB
ejpam-3625	24	11	to	to	PART
ejpam-3625	24	12	be	be	AUX
ejpam-3625	24	13	a	a	DET
ejpam-3625	24	14	minimum	minimum	ADJ
ejpam-3625	24	15	dominating	dominating	NOUN
ejpam-3625	24	16	set	set	NOUN
ejpam-3625	24	17	or	or	CCONJ
ejpam-3625	24	18	γ	γ	NOUN
ejpam-3625	24	19	-	-	PUNCT
ejpam-3625	24	20	set	set	NOUN
ejpam-3625	24	21	of	of	ADP
ejpam-3625	24	22	g.	g.	PROPN
ejpam-3625	24	23	a	a	DET
ejpam-3625	24	24	vertex	vertex	NOUN
ejpam-3625	24	25	w	w	ADP
ejpam-3625	24	26	∈	∈	NOUN
ejpam-3625	24	27	s	s	PART
ejpam-3625	24	28	strongly	strongly	ADV
ejpam-3625	24	29	resolves	resolve	VERB
ejpam-3625	24	30	two	two	NUM
ejpam-3625	24	31	different	different	ADJ
ejpam-3625	24	32	vertices	vertex	NOUN
ejpam-3625	24	33	u	u	NOUN
ejpam-3625	24	34	,	,	PUNCT
ejpam-3625	24	35	v	v	NOUN
ejpam-3625	24	36	∈	∈	PROPN
ejpam-3625	24	37	v	v	NOUN
ejpam-3625	24	38	(	(	PUNCT
ejpam-3625	24	39	g	g	NOUN
ejpam-3625	24	40	)	)	PUNCT
ejpam-3625	24	41	if	if	SCONJ
ejpam-3625	24	42	v	v	NUM
ejpam-3625	24	43	∈	∈	PROPN
ejpam-3625	24	44	ig[u	ig[u	PROPN
ejpam-3625	24	45	,	,	PUNCT
ejpam-3625	24	46	w	w	NOUN
ejpam-3625	24	47	]	]	PUNCT
ejpam-3625	24	48	or	or	CCONJ
ejpam-3625	24	49	if	if	SCONJ
ejpam-3625	24	50	u	u	PROPN
ejpam-3625	24	51	∈	∈	PROPN
ejpam-3625	24	52	ig[v	ig[v	PROPN
ejpam-3625	24	53	,	,	PUNCT
ejpam-3625	24	54	w	w	PROPN
ejpam-3625	24	55	]	]	X
ejpam-3625	24	56	.	.	PUNCT
ejpam-3625	25	1	a	a	DET
ejpam-3625	25	2	set	set	NOUN
ejpam-3625	25	3	w	w	NOUN
ejpam-3625	25	4	of	of	ADP
ejpam-3625	25	5	vertices	vertex	NOUN
ejpam-3625	25	6	in	in	ADP
ejpam-3625	25	7	g	g	PROPN
ejpam-3625	25	8	is	be	AUX
ejpam-3625	25	9	a	a	DET
ejpam-3625	25	10	strong	strong	ADJ
ejpam-3625	25	11	resolving	resolving	NOUN
ejpam-3625	25	12	set	set	NOUN
ejpam-3625	25	13	of	of	ADP
ejpam-3625	25	14	g	g	NOUN
ejpam-3625	25	15	if	if	SCONJ
ejpam-3625	25	16	every	every	DET
ejpam-3625	25	17	two	two	NUM
ejpam-3625	25	18	vertices	vertex	NOUN
ejpam-3625	25	19	of	of	ADP
ejpam-3625	25	20	g	g	NOUN
ejpam-3625	25	21	are	be	AUX
ejpam-3625	25	22	strongly	strongly	ADV
ejpam-3625	25	23	resolved	resolve	VERB
ejpam-3625	25	24	by	by	ADP
ejpam-3625	25	25	some	some	DET
ejpam-3625	25	26	vertex	vertex	NOUN
ejpam-3625	25	27	of	of	ADP
ejpam-3625	25	28	w	w	PROPN
ejpam-3625	25	29	.	.	PUNCT
ejpam-3625	26	1	the	the	DET
ejpam-3625	26	2	smallest	small	ADJ
ejpam-3625	26	3	cardinality	cardinality	NOUN
ejpam-3625	26	4	of	of	ADP
ejpam-3625	26	5	a	a	DET
ejpam-3625	26	6	strong	strong	ADJ
ejpam-3625	26	7	resolving	resolving	NOUN
ejpam-3625	26	8	set	set	NOUN
ejpam-3625	26	9	of	of	ADP
ejpam-3625	26	10	g	g	PROPN
ejpam-3625	26	11	is	be	AUX
ejpam-3625	26	12	called	call	VERB
ejpam-3625	26	13	the	the	DET
ejpam-3625	26	14	strong	strong	ADJ
ejpam-3625	26	15	metric	metric	ADJ
ejpam-3625	26	16	dimension	dimension	NOUN
ejpam-3625	26	17	of	of	ADP
ejpam-3625	26	18	g	g	NOUN
ejpam-3625	26	19	and	and	CCONJ
ejpam-3625	26	20	is	be	AUX
ejpam-3625	26	21	denoted	denote	VERB
ejpam-3625	26	22	by	by	ADP
ejpam-3625	26	23	sdim(g	sdim(g	PROPN
ejpam-3625	26	24	)	)	PUNCT
ejpam-3625	26	25	.	.	PUNCT
ejpam-3625	27	1	a	a	DET
ejpam-3625	27	2	subset	subset	NOUN
ejpam-3625	27	3	s	s	VERB
ejpam-3625	27	4	⊆	⊆	NUM
ejpam-3625	27	5	v	v	NOUN
ejpam-3625	27	6	(	(	PUNCT
ejpam-3625	27	7	g	g	NOUN
ejpam-3625	27	8	)	)	PUNCT
ejpam-3625	27	9	is	be	AUX
ejpam-3625	27	10	a	a	DET
ejpam-3625	27	11	strong	strong	ADJ
ejpam-3625	27	12	resolving	resolving	NOUN
ejpam-3625	27	13	dominating	dominating	NOUN
ejpam-3625	27	14	set	set	NOUN
ejpam-3625	27	15	of	of	ADP
ejpam-3625	27	16	g	g	PROPN
ejpam-3625	27	17	if	if	SCONJ
ejpam-3625	27	18	it	it	PRON
ejpam-3625	27	19	is	be	AUX
ejpam-3625	27	20	both	both	PRON
ejpam-3625	27	21	strong	strong	ADJ
ejpam-3625	27	22	resolving	resolving	NOUN
ejpam-3625	27	23	and	and	CCONJ
ejpam-3625	27	24	dominating	dominating	NOUN
ejpam-3625	27	25	.	.	PUNCT
ejpam-3625	28	1	the	the	DET
ejpam-3625	28	2	smallest	small	ADJ
ejpam-3625	28	3	cardinality	cardinality	NOUN
ejpam-3625	28	4	of	of	ADP
ejpam-3625	28	5	a	a	DET
ejpam-3625	28	6	strong	strong	ADJ
ejpam-3625	28	7	resolving	resolving	NOUN
ejpam-3625	28	8	dominating	dominating	NOUN
ejpam-3625	28	9	set	set	NOUN
ejpam-3625	28	10	of	of	ADP
ejpam-3625	28	11	g	g	PROPN
ejpam-3625	28	12	is	be	AUX
ejpam-3625	28	13	called	call	VERB
ejpam-3625	28	14	the	the	DET
ejpam-3625	28	15	strong	strong	ADJ
ejpam-3625	28	16	resolving	resolving	NOUN
ejpam-3625	28	17	domination	domination	NOUN
ejpam-3625	28	18	number	number	NOUN
ejpam-3625	28	19	of	of	ADP
ejpam-3625	28	20	g	g	NOUN
ejpam-3625	28	21	and	and	CCONJ
ejpam-3625	28	22	is	be	AUX
ejpam-3625	28	23	denoted	denote	VERB
ejpam-3625	28	24	by	by	ADP
ejpam-3625	28	25	γsr(g	γsr(g	PROPN
ejpam-3625	28	26	)	)	PUNCT
ejpam-3625	28	27	.	.	PUNCT
ejpam-3625	29	1	a	a	DET
ejpam-3625	29	2	strong	strong	ADJ
ejpam-3625	29	3	resolving	resolve	VERB
ejpam-3625	29	4	dominating	dominating	NOUN
ejpam-3625	29	5	set	set	NOUN
ejpam-3625	29	6	of	of	ADP
ejpam-3625	29	7	cardinality	cardinality	PROPN
ejpam-3625	29	8	γsr(g	γsr(g	NOUN
ejpam-3625	29	9	)	)	PUNCT
ejpam-3625	29	10	is	be	AUX
ejpam-3625	29	11	called	call	VERB
ejpam-3625	29	12	a	a	DET
ejpam-3625	29	13	γsr	γsr	PROPN
ejpam-3625	29	14	-	-	PUNCT
ejpam-3625	29	15	set	set	NOUN
ejpam-3625	29	16	of	of	ADP
ejpam-3625	29	17	g.	g.	PROPN
ejpam-3625	29	18	a	a	DET
ejpam-3625	29	19	clique	clique	NOUN
ejpam-3625	29	20	in	in	ADP
ejpam-3625	29	21	a	a	DET
ejpam-3625	29	22	graph	graph	NOUN
ejpam-3625	29	23	g	g	NOUN
ejpam-3625	29	24	is	be	AUX
ejpam-3625	29	25	a	a	DET
ejpam-3625	29	26	complete	complete	ADJ
ejpam-3625	29	27	induced	induce	VERB
ejpam-3625	29	28	subgraph	subgraph	NOUN
ejpam-3625	29	29	of	of	ADP
ejpam-3625	29	30	g.	g.	PROPN
ejpam-3625	29	31	a	a	DET
ejpam-3625	29	32	clique	clique	NOUN
ejpam-3625	29	33	c	c	PROPN
ejpam-3625	29	34	in	in	ADP
ejpam-3625	29	35	g	g	PROPN
ejpam-3625	29	36	is	be	AUX
ejpam-3625	29	37	called	call	VERB
ejpam-3625	29	38	a	a	DET
ejpam-3625	29	39	superclique	superclique	NOUN
ejpam-3625	29	40	if	if	SCONJ
ejpam-3625	29	41	for	for	ADP
ejpam-3625	29	42	every	every	DET
ejpam-3625	29	43	pair	pair	NOUN
ejpam-3625	29	44	of	of	ADP
ejpam-3625	29	45	distinct	distinct	ADJ
ejpam-3625	29	46	vertices	vertex	NOUN
ejpam-3625	29	47	u	u	NOUN
ejpam-3625	29	48	,	,	PUNCT
ejpam-3625	29	49	v	v	NOUN
ejpam-3625	29	50	∈	∈	ADJ
ejpam-3625	29	51	c	c	NOUN
ejpam-3625	29	52	,	,	PUNCT
ejpam-3625	29	53	there	there	PRON
ejpam-3625	29	54	exists	exist	VERB
ejpam-3625	29	55	w	w	PROPN
ejpam-3625	29	56	∈	∈	PROPN
ejpam-3625	29	57	v	v	ADP
ejpam-3625	29	58	(	(	PUNCT
ejpam-3625	29	59	g	g	NOUN
ejpam-3625	29	60	)	)	PUNCT
ejpam-3625	29	61	\	\	PUNCT
ejpam-3625	30	1	c	c	NOUN
ejpam-3625	30	2	such	such	ADJ
ejpam-3625	30	3	that	that	PRON
ejpam-3625	30	4	w	w	PROPN
ejpam-3625	30	5	∈	∈	PROPN
ejpam-3625	30	6	ng(u	ng(u	NOUN
ejpam-3625	30	7	)	)	PUNCT
ejpam-3625	30	8	\	\	NOUN
ejpam-3625	30	9	ng(v	ng(v	PUNCT
ejpam-3625	30	10	)	)	PUNCT
ejpam-3625	30	11	or	or	CCONJ
ejpam-3625	30	12	w	w	PROPN
ejpam-3625	30	13	∈	∈	PROPN
ejpam-3625	30	14	ng(v	ng(v	NOUN
ejpam-3625	30	15	)	)	PUNCT
ejpam-3625	30	16	\	\	NOUN
ejpam-3625	30	17	ng(u	ng(u	NOUN
ejpam-3625	30	18	)	)	PUNCT
ejpam-3625	30	19	.	.	PUNCT
ejpam-3625	31	1	a	a	DET
ejpam-3625	31	2	superclique	superclique	ADJ
ejpam-3625	31	3	c	c	NOUN
ejpam-3625	31	4	in	in	ADP
ejpam-3625	31	5	g	g	PROPN
ejpam-3625	31	6	is	be	AUX
ejpam-3625	31	7	called	call	VERB
ejpam-3625	31	8	a	a	DET
ejpam-3625	31	9	dominated	dominate	VERB
ejpam-3625	31	10	superclique	superclique	NOUN
ejpam-3625	31	11	if	if	SCONJ
ejpam-3625	31	12	for	for	ADP
ejpam-3625	31	13	every	every	DET
ejpam-3625	31	14	u	u	PROPN
ejpam-3625	31	15	∈	∈	PROPN
ejpam-3625	31	16	c	c	NOUN
ejpam-3625	31	17	,	,	PUNCT
ejpam-3625	31	18	there	there	PRON
ejpam-3625	31	19	exists	exist	VERB
ejpam-3625	31	20	v	v	ADP
ejpam-3625	31	21	∈	∈	PROPN
ejpam-3625	31	22	v	v	NOUN
ejpam-3625	31	23	(	(	PUNCT
ejpam-3625	31	24	g	g	NOUN
ejpam-3625	31	25	)	)	PUNCT
ejpam-3625	31	26	\	\	PUNCT
ejpam-3625	32	1	c	c	NOUN
ejpam-3625	32	2	such	such	ADJ
ejpam-3625	32	3	that	that	DET
ejpam-3625	32	4	uv	uv	PROPN
ejpam-3625	32	5	∈	∈	PROPN
ejpam-3625	32	6	e(g	e(g	PROPN
ejpam-3625	32	7	)	)	PUNCT
ejpam-3625	33	1	[	[	X
ejpam-3625	33	2	3	3	NUM
ejpam-3625	33	3	]	]	PUNCT
ejpam-3625	33	4	.	.	PUNCT
ejpam-3625	34	1	a	a	DET
ejpam-3625	34	2	superclique	superclique	ADJ
ejpam-3625	34	3	(	(	PUNCT
ejpam-3625	34	4	resp	resp	NOUN
ejpam-3625	34	5	.	.	PUNCT
ejpam-3625	35	1	dominated	dominate	VERB
ejpam-3625	35	2	superclique	superclique	NOUN
ejpam-3625	35	3	)	)	PUNCT
ejpam-3625	35	4	c	c	NOUN
ejpam-3625	35	5	is	be	AUX
ejpam-3625	35	6	maximum	maximum	ADJ
ejpam-3625	35	7	in	in	ADP
ejpam-3625	35	8	g	g	PROPN
ejpam-3625	35	9	if	if	SCONJ
ejpam-3625	35	10	|c|	|c|	PROPN
ejpam-3625	35	11	≥	≥	NOUN
ejpam-3625	35	12	|c∗|	|c∗|	VERB
ejpam-3625	35	13	for	for	ADP
ejpam-3625	35	14	all	all	DET
ejpam-3625	35	15	supercliques	superclique	NOUN
ejpam-3625	35	16	(	(	PUNCT
ejpam-3625	35	17	resp	resp	NOUN
ejpam-3625	35	18	.	.	PUNCT
ejpam-3625	36	1	dominated	dominate	VERB
ejpam-3625	36	2	supercliques	superclique	NOUN
ejpam-3625	36	3	)	)	PUNCT
ejpam-3625	36	4	c∗	c∗	NOUN
ejpam-3625	36	5	in	in	ADP
ejpam-3625	36	6	g.	g.	PROPN
ejpam-3625	36	7	the	the	DET
ejpam-3625	36	8	superclique	superclique	NOUN
ejpam-3625	36	9	(	(	PUNCT
ejpam-3625	36	10	resp	resp	NOUN
ejpam-3625	36	11	.	.	PUNCT
ejpam-3625	37	1	dominated	dominate	VERB
ejpam-3625	37	2	superclique	superclique	NOUN
ejpam-3625	37	3	)	)	PUNCT
ejpam-3625	37	4	number	number	NOUN
ejpam-3625	37	5	,	,	PUNCT
ejpam-3625	37	6	ωs(g	ωs(g	NUM
ejpam-3625	37	7	)	)	PUNCT
ejpam-3625	37	8	(	(	PUNCT
ejpam-3625	37	9	resp	resp	NOUN
ejpam-3625	37	10	.	.	PUNCT
ejpam-3625	37	11	ωds(g	ωds(g	X
ejpam-3625	37	12	)	)	PUNCT
ejpam-3625	37	13	)	)	PUNCT
ejpam-3625	37	14	of	of	ADP
ejpam-3625	37	15	g	g	PROPN
ejpam-3625	37	16	is	be	AUX
ejpam-3625	37	17	the	the	DET
ejpam-3625	37	18	cardinality	cardinality	NOUN
ejpam-3625	37	19	of	of	ADP
ejpam-3625	37	20	a	a	DET
ejpam-3625	37	21	maximum	maximum	ADJ
ejpam-3625	37	22	superclique	superclique	NOUN
ejpam-3625	37	23	(	(	PUNCT
ejpam-3625	37	24	resp	resp	NOUN
ejpam-3625	37	25	.	.	PUNCT
ejpam-3625	38	1	maximum	maximum	ADJ
ejpam-3625	38	2	dominated	dominate	VERB
ejpam-3625	38	3	superclique	superclique	NOUN
ejpam-3625	38	4	)	)	PUNCT
ejpam-3625	38	5	in	in	ADP
ejpam-3625	38	6	g.	g.	PROPN
ejpam-3625	38	7	in	in	ADP
ejpam-3625	38	8	recent	recent	ADJ
ejpam-3625	38	9	years	year	NOUN
ejpam-3625	38	10	,	,	PUNCT
ejpam-3625	38	11	the	the	DET
ejpam-3625	38	12	concept	concept	NOUN
ejpam-3625	38	13	of	of	ADP
ejpam-3625	38	14	domination	domination	NOUN
ejpam-3625	38	15	in	in	ADP
ejpam-3625	38	16	graphs	graph	NOUN
ejpam-3625	38	17	has	have	AUX
ejpam-3625	38	18	been	be	AUX
ejpam-3625	38	19	studied	study	VERB
ejpam-3625	38	20	extensively	extensively	ADV
ejpam-3625	38	21	and	and	CCONJ
ejpam-3625	38	22	several	several	ADJ
ejpam-3625	38	23	research	research	NOUN
ejpam-3625	38	24	papers	paper	NOUN
ejpam-3625	38	25	have	have	AUX
ejpam-3625	38	26	been	be	AUX
ejpam-3625	38	27	published	publish	VERB
ejpam-3625	38	28	on	on	ADP
ejpam-3625	38	29	this	this	DET
ejpam-3625	38	30	topic	topic	NOUN
ejpam-3625	38	31	.	.	PUNCT
ejpam-3625	39	1	the	the	DET
ejpam-3625	39	2	said	say	VERB
ejpam-3625	39	3	concept	concept	NOUN
ejpam-3625	39	4	was	be	AUX
ejpam-3625	39	5	not	not	PART
ejpam-3625	39	6	formally	formally	ADV
ejpam-3625	39	7	defined	define	VERB
ejpam-3625	39	8	mathematically	mathematically	ADV
ejpam-3625	39	9	until	until	ADP
ejpam-3625	39	10	the	the	DET
ejpam-3625	39	11	publications	publication	NOUN
ejpam-3625	39	12	of	of	ADP
ejpam-3625	39	13	the	the	DET
ejpam-3625	39	14	books	book	NOUN
ejpam-3625	39	15	by	by	ADP
ejpam-3625	39	16	claude	claude	PROPN
ejpam-3625	39	17	berge	berge	NOUN
ejpam-3625	40	1	[	[	X
ejpam-3625	40	2	1	1	X
ejpam-3625	40	3	]	]	PUNCT
ejpam-3625	40	4	in	in	ADP
ejpam-3625	40	5	1958	1958	NUM
ejpam-3625	40	6	and	and	CCONJ
ejpam-3625	40	7	oystein	oystein	ADJ
ejpam-3625	40	8	ore	ore	NOUN
ejpam-3625	40	9	in	in	ADP
ejpam-3625	40	10	1962	1962	NUM
ejpam-3625	40	11	.	.	PUNCT
ejpam-3625	41	1	in	in	ADP
ejpam-3625	41	2	1977	1977	NUM
ejpam-3625	41	3	,	,	PUNCT
ejpam-3625	41	4	a	a	DET
ejpam-3625	41	5	survey	survey	NOUN
ejpam-3625	41	6	paper	paper	NOUN
ejpam-3625	41	7	by	by	ADP
ejpam-3625	41	8	cockayne	cockayne	NOUN
ejpam-3625	41	9	and	and	CCONJ
ejpam-3625	41	10	hedetniemi	hedetniemi	NOUN
ejpam-3625	41	11	[	[	X
ejpam-3625	41	12	2	2	NUM
ejpam-3625	41	13	]	]	PUNCT
ejpam-3625	41	14	began	begin	VERB
ejpam-3625	41	15	to	to	PART
ejpam-3625	41	16	study	study	VERB
ejpam-3625	41	17	the	the	DET
ejpam-3625	41	18	concept	concept	NOUN
ejpam-3625	41	19	of	of	ADP
ejpam-3625	41	20	domination	domination	NOUN
ejpam-3625	41	21	.	.	PUNCT
ejpam-3625	42	1	on	on	ADP
ejpam-3625	42	2	the	the	DET
ejpam-3625	42	3	other	other	ADJ
ejpam-3625	42	4	hand	hand	NOUN
ejpam-3625	42	5	,	,	PUNCT
ejpam-3625	42	6	the	the	DET
ejpam-3625	42	7	problem	problem	NOUN
ejpam-3625	42	8	of	of	ADP
ejpam-3625	42	9	uniquely	uniquely	ADV
ejpam-3625	42	10	recognizing	recognize	VERB
ejpam-3625	42	11	the	the	DET
ejpam-3625	42	12	possible	possible	ADJ
ejpam-3625	42	13	position	position	NOUN
ejpam-3625	42	14	of	of	ADP
ejpam-3625	42	15	an	an	DET
ejpam-3625	42	16	intruder	intruder	NOUN
ejpam-3625	42	17	such	such	ADJ
ejpam-3625	42	18	as	as	ADP
ejpam-3625	42	19	fault	fault	NOUN
ejpam-3625	42	20	in	in	ADP
ejpam-3625	42	21	a	a	DET
ejpam-3625	42	22	computer	computer	NOUN
ejpam-3625	42	23	network	network	NOUN
ejpam-3625	42	24	and	and	CCONJ
ejpam-3625	42	25	spoiled	spoiled	ADJ
ejpam-3625	42	26	device	device	NOUN
ejpam-3625	42	27	was	be	AUX
ejpam-3625	42	28	the	the	DET
ejpam-3625	42	29	principal	principal	ADJ
ejpam-3625	42	30	motivation	motivation	NOUN
ejpam-3625	42	31	in	in	ADP
ejpam-3625	42	32	introducing	introduce	VERB
ejpam-3625	42	33	the	the	DET
ejpam-3625	42	34	concept	concept	NOUN
ejpam-3625	42	35	of	of	ADP
ejpam-3625	42	36	metric	metric	ADJ
ejpam-3625	42	37	dimension	dimension	NOUN
ejpam-3625	42	38	in	in	ADP
ejpam-3625	42	39	graphs	graph	NOUN
ejpam-3625	42	40	.	.	PUNCT
ejpam-3625	43	1	slater	slater	NOUN
ejpam-3625	44	1	[	[	X
ejpam-3625	44	2	6	6	NUM
ejpam-3625	44	3	]	]	PUNCT
ejpam-3625	44	4	brought	bring	VERB
ejpam-3625	44	5	in	in	ADP
ejpam-3625	44	6	the	the	DET
ejpam-3625	44	7	notion	notion	NOUN
ejpam-3625	44	8	of	of	ADP
ejpam-3625	44	9	locating	locate	VERB
ejpam-3625	44	10	sets	set	NOUN
ejpam-3625	44	11	and	and	CCONJ
ejpam-3625	44	12	its	its	PRON
ejpam-3625	44	13	minimal	minimal	ADJ
ejpam-3625	44	14	cardinality	cardinality	NOUN
ejpam-3625	44	15	as	as	ADP
ejpam-3625	44	16	locating	locate	VERB
ejpam-3625	44	17	number	number	NOUN
ejpam-3625	44	18	.	.	PUNCT
ejpam-3625	45	1	the	the	DET
ejpam-3625	45	2	same	same	ADJ
ejpam-3625	45	3	concept	concept	NOUN
ejpam-3625	45	4	was	be	AUX
ejpam-3625	45	5	also	also	ADV
ejpam-3625	45	6	introduced	introduce	VERB
ejpam-3625	45	7	by	by	ADP
ejpam-3625	45	8	harary	harary	NOUN
ejpam-3625	45	9	and	and	CCONJ
ejpam-3625	45	10	melter	melter	NOUN
ejpam-3625	45	11	[	[	X
ejpam-3625	45	12	4	4	NUM
ejpam-3625	45	13	]	]	PUNCT
ejpam-3625	45	14	but	but	CCONJ
ejpam-3625	45	15	using	use	VERB
ejpam-3625	45	16	the	the	DET
ejpam-3625	45	17	terms	term	NOUN
ejpam-3625	45	18	resolving	resolve	VERB
ejpam-3625	45	19	sets	set	NOUN
ejpam-3625	45	20	and	and	CCONJ
ejpam-3625	45	21	metric	metric	ADJ
ejpam-3625	45	22	dimension	dimension	NOUN
ejpam-3625	45	23	to	to	PART
ejpam-3625	45	24	refer	refer	VERB
ejpam-3625	45	25	to	to	ADP
ejpam-3625	45	26	locating	locate	VERB
ejpam-3625	45	27	sets	set	NOUN
ejpam-3625	45	28	and	and	CCONJ
ejpam-3625	45	29	locating	locate	VERB
ejpam-3625	45	30	number	number	NOUN
ejpam-3625	45	31	,	,	PUNCT
ejpam-3625	45	32	respectively	respectively	ADV
ejpam-3625	45	33	.	.	PUNCT
ejpam-3625	46	1	in	in	ADP
ejpam-3625	46	2	2007	2007	NUM
ejpam-3625	46	3	,	,	PUNCT
ejpam-3625	46	4	oellerman	oellerman	NOUN
ejpam-3625	46	5	and	and	CCONJ
ejpam-3625	46	6	peter	peter	PROPN
ejpam-3625	46	7	-	-	PUNCT
ejpam-3625	46	8	fransen	fransen	PROPN
ejpam-3625	46	9	[	[	X
ejpam-3625	46	10	5	5	NUM
ejpam-3625	46	11	]	]	PUNCT
ejpam-3625	46	12	introduced	introduce	VERB
ejpam-3625	46	13	the	the	DET
ejpam-3625	46	14	strong	strong	ADJ
ejpam-3625	46	15	resolving	resolving	NOUN
ejpam-3625	46	16	graph	graph	NOUN
ejpam-3625	46	17	gsr	gsr	NOUN
ejpam-3625	46	18	of	of	ADP
ejpam-3625	46	19	a	a	DET
ejpam-3625	46	20	connected	connected	ADJ
ejpam-3625	46	21	graph	graph	NOUN
ejpam-3625	46	22	g	g	NOUN
ejpam-3625	46	23	as	as	ADP
ejpam-3625	46	24	a	a	DET
ejpam-3625	46	25	tool	tool	NOUN
ejpam-3625	46	26	to	to	PART
ejpam-3625	46	27	study	study	VERB
ejpam-3625	46	28	the	the	DET
ejpam-3625	46	29	strong	strong	ADJ
ejpam-3625	46	30	metric	metric	ADJ
ejpam-3625	46	31	dimension	dimension	NOUN
ejpam-3625	46	32	of	of	ADP
ejpam-3625	46	33	g.	g.	PROPN
ejpam-3625	46	34	this	this	DET
ejpam-3625	46	35	study	study	NOUN
ejpam-3625	46	36	aims	aim	VERB
ejpam-3625	46	37	to	to	PART
ejpam-3625	46	38	define	define	VERB
ejpam-3625	46	39	and	and	CCONJ
ejpam-3625	46	40	characterize	characterize	VERB
ejpam-3625	46	41	the	the	DET
ejpam-3625	46	42	strong	strong	ADJ
ejpam-3625	46	43	resolving	resolve	VERB
ejpam-3625	46	44	dominating	dominating	NOUN
ejpam-3625	46	45	sets	set	NOUN
ejpam-3625	46	46	and	and	CCONJ
ejpam-3625	46	47	determine	determine	VERB
ejpam-3625	46	48	the	the	DET
ejpam-3625	46	49	exact	exact	ADJ
ejpam-3625	46	50	values	value	NOUN
ejpam-3625	46	51	or	or	CCONJ
ejpam-3625	46	52	bounds	bound	NOUN
ejpam-3625	46	53	in	in	ADP
ejpam-3625	46	54	the	the	DET
ejpam-3625	46	55	join	join	NOUN
ejpam-3625	46	56	and	and	CCONJ
ejpam-3625	46	57	corona	corona	NOUN
ejpam-3625	46	58	of	of	ADP
ejpam-3625	46	59	two	two	NUM
ejpam-3625	46	60	graphs	graph	NOUN
ejpam-3625	46	61	.	.	PUNCT
ejpam-3625	47	1	2	2	X
ejpam-3625	47	2	.	.	X
ejpam-3625	47	3	preliminary	preliminary	ADJ
ejpam-3625	47	4	results	result	NOUN
ejpam-3625	47	5	remark	remark	VERB
ejpam-3625	47	6	1	1	NUM
ejpam-3625	47	7	.	.	PUNCT
ejpam-3625	48	1	every	every	DET
ejpam-3625	48	2	strong	strong	ADJ
ejpam-3625	48	3	resolving	resolve	VERB
ejpam-3625	48	4	dominating	dominating	NOUN
ejpam-3625	48	5	set	set	NOUN
ejpam-3625	48	6	of	of	ADP
ejpam-3625	48	7	a	a	DET
ejpam-3625	48	8	connected	connected	ADJ
ejpam-3625	48	9	graph	graph	NOUN
ejpam-3625	48	10	g	g	PROPN
ejpam-3625	48	11	is	be	AUX
ejpam-3625	48	12	a	a	DET
ejpam-3625	48	13	dominating	dominating	NOUN
ejpam-3625	48	14	set	set	NOUN
ejpam-3625	48	15	.	.	PUNCT
ejpam-3625	49	1	hence	hence	ADV
ejpam-3625	49	2	,	,	PUNCT
ejpam-3625	49	3	γ(g	γ(g	PROPN
ejpam-3625	49	4	)	)	PUNCT
ejpam-3625	49	5	≤	≤	NOUN
ejpam-3625	49	6	γsr(g	γsr(g	NOUN
ejpam-3625	49	7	)	)	PUNCT
ejpam-3625	49	8	.	.	PUNCT
ejpam-3625	50	1	remark	remark	NOUN
ejpam-3625	50	2	2	2	NUM
ejpam-3625	50	3	.	.	PUNCT
ejpam-3625	51	1	every	every	DET
ejpam-3625	51	2	strong	strong	ADJ
ejpam-3625	51	3	resolving	resolve	VERB
ejpam-3625	51	4	dominating	dominating	NOUN
ejpam-3625	51	5	set	set	NOUN
ejpam-3625	51	6	of	of	ADP
ejpam-3625	51	7	a	a	DET
ejpam-3625	51	8	connected	connected	ADJ
ejpam-3625	51	9	graph	graph	NOUN
ejpam-3625	51	10	g	g	PROPN
ejpam-3625	51	11	is	be	AUX
ejpam-3625	51	12	a	a	DET
ejpam-3625	51	13	strong	strong	ADJ
ejpam-3625	51	14	resolving	resolving	NOUN
ejpam-3625	51	15	set	set	NOUN
ejpam-3625	51	16	.	.	PUNCT
ejpam-3625	52	1	thus	thus	ADV
ejpam-3625	52	2	,	,	PUNCT
ejpam-3625	52	3	sdim(g	sdim(g	PROPN
ejpam-3625	52	4	)	)	PUNCT
ejpam-3625	52	5	≤	≤	NOUN
ejpam-3625	52	6	γsr(g	γsr(g	NOUN
ejpam-3625	52	7	)	)	PUNCT
ejpam-3625	52	8	.	.	PUNCT
ejpam-3625	53	1	g.	g.	PROPN
ejpam-3625	53	2	monsanto	monsanto	PROPN
ejpam-3625	53	3	,	,	PUNCT
ejpam-3625	53	4	p.	p.	PROPN
ejpam-3625	53	5	acal	acal	PROPN
ejpam-3625	53	6	,	,	PUNCT
ejpam-3625	53	7	h.	h.	PROPN
ejpam-3625	53	8	rara	rara	PROPN
ejpam-3625	53	9	/	/	SYM
ejpam-3625	53	10	eur	eur	PROPN
ejpam-3625	53	11	.	.	PUNCT
ejpam-3625	54	1	j.	j.	PROPN
ejpam-3625	54	2	pure	pure	PROPN
ejpam-3625	54	3	appl	appl	PROPN
ejpam-3625	54	4	.	.	PROPN
ejpam-3625	54	5	math	math	PROPN
ejpam-3625	54	6	,	,	PUNCT
ejpam-3625	54	7	13	13	NUM
ejpam-3625	54	8	(	(	PUNCT
ejpam-3625	54	9	1	1	NUM
ejpam-3625	54	10	)	)	PUNCT
ejpam-3625	54	11	(	(	PUNCT
ejpam-3625	54	12	2020	2020	NUM
ejpam-3625	54	13	)	)	PUNCT
ejpam-3625	54	14	,	,	PUNCT
ejpam-3625	54	15	170	170	NUM
ejpam-3625	54	16	-	-	SYM
ejpam-3625	54	17	179	179	NUM
ejpam-3625	54	18	172	172	NUM
ejpam-3625	54	19	remark	remark	NOUN
ejpam-3625	54	20	3	3	NUM
ejpam-3625	54	21	.	.	PUNCT
ejpam-3625	55	1	for	for	ADP
ejpam-3625	55	2	any	any	DET
ejpam-3625	55	3	connected	connected	ADJ
ejpam-3625	55	4	graph	graph	NOUN
ejpam-3625	55	5	g	g	NOUN
ejpam-3625	55	6	of	of	ADP
ejpam-3625	55	7	order	order	NOUN
ejpam-3625	55	8	n	n	CCONJ
ejpam-3625	55	9	,	,	PUNCT
ejpam-3625	55	10	1	1	NUM
ejpam-3625	55	11	≤	≤	NUM
ejpam-3625	55	12	γsr(g	γsr(g	NOUN
ejpam-3625	55	13	)	)	PUNCT
ejpam-3625	55	14	≤	≤	NUM
ejpam-3625	55	15	n−	n−	NOUN
ejpam-3625	55	16	1	1	NUM
ejpam-3625	55	17	.	.	PUNCT
ejpam-3625	55	18	remark	remark	NOUN
ejpam-3625	55	19	4	4	NUM
ejpam-3625	55	20	.	.	PUNCT
ejpam-3625	56	1	any	any	DET
ejpam-3625	56	2	superset	superset	NOUN
ejpam-3625	56	3	of	of	ADP
ejpam-3625	56	4	a	a	DET
ejpam-3625	56	5	strong	strong	ADJ
ejpam-3625	56	6	resolving	resolving	NOUN
ejpam-3625	56	7	dominating	dominating	NOUN
ejpam-3625	56	8	set	set	NOUN
ejpam-3625	56	9	is	be	AUX
ejpam-3625	56	10	a	a	DET
ejpam-3625	56	11	strong	strong	ADJ
ejpam-3625	56	12	resolving	resolve	VERB
ejpam-3625	56	13	dominating	dominating	NOUN
ejpam-3625	56	14	set	set	NOUN
ejpam-3625	56	15	.	.	PUNCT
ejpam-3625	57	1	proposition	proposition	NOUN
ejpam-3625	57	2	1	1	NUM
ejpam-3625	57	3	.	.	PUNCT
ejpam-3625	58	1	let	let	VERB
ejpam-3625	58	2	g	g	PRON
ejpam-3625	58	3	be	be	AUX
ejpam-3625	58	4	a	a	DET
ejpam-3625	58	5	connected	connected	ADJ
ejpam-3625	58	6	graph	graph	NOUN
ejpam-3625	58	7	of	of	ADP
ejpam-3625	58	8	order	order	NOUN
ejpam-3625	58	9	n	n	PRON
ejpam-3625	58	10	≥	≥	NOUN
ejpam-3625	58	11	2	2	NUM
ejpam-3625	58	12	.	.	PUNCT
ejpam-3625	59	1	then	then	ADV
ejpam-3625	59	2	,	,	PUNCT
ejpam-3625	59	3	(	(	PUNCT
ejpam-3625	59	4	i	i	NOUN
ejpam-3625	59	5	)	)	PUNCT
ejpam-3625	59	6	γsr(pn	γsr(pn	PROPN
ejpam-3625	59	7	)	)	PUNCT
ejpam-3625	59	8	=	=	PUNCT
ejpam-3625	60	1	⌈	⌈	SYM
ejpam-3625	60	2	n+1	n+1	PROPN
ejpam-3625	60	3	3	3	NUM
ejpam-3625	60	4	⌉	⌉	X
ejpam-3625	60	5	(	(	PUNCT
ejpam-3625	60	6	ii	ii	NOUN
ejpam-3625	60	7	)	)	PUNCT
ejpam-3625	60	8	γsr(kn	γsr(kn	NOUN
ejpam-3625	60	9	)	)	PUNCT
ejpam-3625	61	1	=	=	PUNCT
ejpam-3625	61	2	n−	n−	NOUN
ejpam-3625	61	3	1	1	NUM
ejpam-3625	61	4	(	(	PUNCT
ejpam-3625	61	5	iii	iii	NOUN
ejpam-3625	61	6	)	)	PUNCT
ejpam-3625	61	7	γsr(cn	γsr(cn	NOUN
ejpam-3625	61	8	)	)	PUNCT
ejpam-3625	62	1	=	=	PUNCT
ejpam-3625	63	1			NOUN
ejpam-3625	63	2	2	2	NUM
ejpam-3625	63	3	,	,	PUNCT
ejpam-3625	63	4	if	if	SCONJ
ejpam-3625	63	5	n	n	NOUN
ejpam-3625	63	6	=	=	SYM
ejpam-3625	63	7	3	3	NUM
ejpam-3625	63	8	n−	n−	NOUN
ejpam-3625	63	9	2	2	NUM
ejpam-3625	63	10	,	,	PUNCT
ejpam-3625	63	11	if	if	SCONJ
ejpam-3625	63	12	n	n	PROPN
ejpam-3625	63	13	>	>	X
ejpam-3625	63	14	3	3	NUM
ejpam-3625	63	15	and	and	CCONJ
ejpam-3625	63	16	n	n	PRON
ejpam-3625	63	17	is	be	AUX
ejpam-3625	63	18	odd⌈	odd⌈	NUM
ejpam-3625	63	19	n	n	DET
ejpam-3625	63	20	2	2	NUM
ejpam-3625	63	21	⌉	⌉	NOUN
ejpam-3625	63	22	,	,	PUNCT
ejpam-3625	63	23	if	if	SCONJ
ejpam-3625	63	24	n	n	PROPN
ejpam-3625	63	25	>	>	X
ejpam-3625	63	26	3	3	NUM
ejpam-3625	63	27	and	and	CCONJ
ejpam-3625	63	28	n	n	PRON
ejpam-3625	63	29	is	be	AUX
ejpam-3625	63	30	even	even	ADV
ejpam-3625	63	31	proposition	proposition	NOUN
ejpam-3625	63	32	2	2	NUM
ejpam-3625	63	33	.	.	PUNCT
ejpam-3625	64	1	let	let	VERB
ejpam-3625	64	2	g	g	PRON
ejpam-3625	64	3	be	be	AUX
ejpam-3625	64	4	a	a	DET
ejpam-3625	64	5	connected	connected	ADJ
ejpam-3625	64	6	graph	graph	NOUN
ejpam-3625	64	7	of	of	ADP
ejpam-3625	64	8	order	order	NOUN
ejpam-3625	64	9	n	n	NOUN
ejpam-3625	64	10	and	and	CCONJ
ejpam-3625	64	11	let	let	VERB
ejpam-3625	64	12	a	a	DET
ejpam-3625	64	13	=	=	SYM
ejpam-3625	64	14	{	{	PUNCT
ejpam-3625	64	15	x	x	PROPN
ejpam-3625	64	16	∈	∈	PROPN
ejpam-3625	64	17	v	v	NOUN
ejpam-3625	64	18	(	(	PUNCT
ejpam-3625	64	19	g	g	NOUN
ejpam-3625	64	20	)	)	PUNCT
ejpam-3625	64	21	:	:	PUNCT
ejpam-3625	65	1	degg(x	degg(x	X
ejpam-3625	65	2	)	)	PUNCT
ejpam-3625	65	3	=	=	PUNCT
ejpam-3625	65	4	n−	n−	NOUN
ejpam-3625	65	5	1	1	NUM
ejpam-3625	65	6	}	}	PUNCT
ejpam-3625	65	7	.	.	PUNCT
ejpam-3625	66	1	if	if	SCONJ
ejpam-3625	66	2	a	a	DET
ejpam-3625	66	3	6=	6=	NOUN
ejpam-3625	66	4	∅	∅	NOUN
ejpam-3625	66	5	and	and	CCONJ
ejpam-3625	66	6	c	c	NOUN
ejpam-3625	66	7	is	be	AUX
ejpam-3625	66	8	a	a	DET
ejpam-3625	66	9	superclique	superclique	NOUN
ejpam-3625	66	10	in	in	ADP
ejpam-3625	66	11	g	g	NOUN
ejpam-3625	66	12	,	,	PUNCT
ejpam-3625	66	13	then	then	ADV
ejpam-3625	66	14	|c	|c	VERB
ejpam-3625	66	15	∩	∩	NOUN
ejpam-3625	66	16	a|	a|	PROPN
ejpam-3625	66	17	≤	≤	NOUN
ejpam-3625	66	18	1	1	NUM
ejpam-3625	66	19	.	.	PUNCT
ejpam-3625	67	1	moreover	moreover	ADV
ejpam-3625	67	2	,	,	PUNCT
ejpam-3625	67	3	if	if	SCONJ
ejpam-3625	67	4	c	c	PROPN
ejpam-3625	67	5	is	be	AUX
ejpam-3625	67	6	a	a	DET
ejpam-3625	67	7	maximum	maximum	ADJ
ejpam-3625	67	8	superclique	superclique	NOUN
ejpam-3625	67	9	of	of	ADP
ejpam-3625	67	10	g	g	NOUN
ejpam-3625	67	11	,	,	PUNCT
ejpam-3625	67	12	then	then	ADV
ejpam-3625	67	13	|c	|c	VERB
ejpam-3625	67	14	∩a|	∩a|	PUNCT
ejpam-3625	67	15	=	=	SYM
ejpam-3625	67	16	1	1	X
ejpam-3625	67	17	.	.	NOUN
ejpam-3625	67	18	remark	remark	NOUN
ejpam-3625	67	19	5	5	NUM
ejpam-3625	67	20	.	.	PUNCT
ejpam-3625	68	1	let	let	VERB
ejpam-3625	68	2	g	g	PRON
ejpam-3625	68	3	be	be	AUX
ejpam-3625	68	4	a	a	DET
ejpam-3625	68	5	nontrivial	nontrivial	ADJ
ejpam-3625	68	6	connected	connect	VERB
ejpam-3625	68	7	graph	graph	NOUN
ejpam-3625	68	8	with	with	ADP
ejpam-3625	68	9	diam(g	diam(g	NOUN
ejpam-3625	68	10	)	)	PUNCT
ejpam-3625	68	11	≤	≤	NOUN
ejpam-3625	68	12	2	2	NUM
ejpam-3625	68	13	.	.	X
ejpam-3625	69	1	for	for	ADP
ejpam-3625	69	2	distinct	distinct	ADJ
ejpam-3625	69	3	vertices	vertex	NOUN
ejpam-3625	69	4	u	u	NOUN
ejpam-3625	69	5	,	,	PUNCT
ejpam-3625	69	6	v	v	NOUN
ejpam-3625	69	7	,	,	PUNCT
ejpam-3625	69	8	w	w	PROPN
ejpam-3625	69	9	∈	∈	PROPN
ejpam-3625	69	10	g	g	PROPN
ejpam-3625	69	11	,	,	PUNCT
ejpam-3625	69	12	u	u	PROPN
ejpam-3625	69	13	∈	∈	PROPN
ejpam-3625	69	14	ig[v	ig[v	PROPN
ejpam-3625	69	15	,	,	PUNCT
ejpam-3625	69	16	w	w	PROPN
ejpam-3625	69	17	]	]	X
ejpam-3625	69	18	if	if	SCONJ
ejpam-3625	69	19	and	and	CCONJ
ejpam-3625	69	20	only	only	ADV
ejpam-3625	69	21	if	if	SCONJ
ejpam-3625	69	22	dg(v	dg(v	NOUN
ejpam-3625	69	23	,	,	PUNCT
ejpam-3625	69	24	w	w	NOUN
ejpam-3625	69	25	)	)	PUNCT
ejpam-3625	69	26	=	=	SYM
ejpam-3625	69	27	2	2	NUM
ejpam-3625	69	28	and	and	CCONJ
ejpam-3625	69	29	u	u	PROPN
ejpam-3625	69	30	∈	∈	PROPN
ejpam-3625	69	31	ng(v	ng(v	NOUN
ejpam-3625	69	32	)	)	PUNCT
ejpam-3625	69	33	∩ng(w	∩ng(w	PROPN
ejpam-3625	69	34	)	)	PUNCT
ejpam-3625	69	35	.	.	PUNCT
ejpam-3625	70	1	proposition	proposition	NOUN
ejpam-3625	70	2	3	3	X
ejpam-3625	70	3	.	.	PUNCT
ejpam-3625	71	1	let	let	VERB
ejpam-3625	71	2	g	g	PRON
ejpam-3625	71	3	be	be	AUX
ejpam-3625	71	4	a	a	DET
ejpam-3625	71	5	nontrivial	nontrivial	ADJ
ejpam-3625	71	6	connected	connect	VERB
ejpam-3625	71	7	graph	graph	NOUN
ejpam-3625	71	8	with	with	ADP
ejpam-3625	71	9	diam(g	diam(g	NOUN
ejpam-3625	71	10	)	)	PUNCT
ejpam-3625	71	11	≤	≤	NOUN
ejpam-3625	71	12	2	2	NUM
ejpam-3625	71	13	.	.	PUNCT
ejpam-3625	72	1	then	then	ADV
ejpam-3625	72	2	s	s	VERB
ejpam-3625	72	3	=	=	SYM
ejpam-3625	72	4	v	v	PROPN
ejpam-3625	72	5	(	(	PUNCT
ejpam-3625	72	6	g	g	NOUN
ejpam-3625	72	7	)	)	PUNCT
ejpam-3625	72	8	\c	\c	NOUN
ejpam-3625	72	9	is	be	AUX
ejpam-3625	72	10	a	a	DET
ejpam-3625	72	11	strong	strong	ADJ
ejpam-3625	72	12	resolving	resolving	NOUN
ejpam-3625	72	13	set	set	NOUN
ejpam-3625	72	14	of	of	ADP
ejpam-3625	72	15	g	g	PROPN
ejpam-3625	72	16	if	if	SCONJ
ejpam-3625	72	17	and	and	CCONJ
ejpam-3625	72	18	only	only	ADV
ejpam-3625	72	19	if	if	SCONJ
ejpam-3625	72	20	c	c	NOUN
ejpam-3625	72	21	=	=	SYM
ejpam-3625	72	22	∅	∅	NOUN
ejpam-3625	72	23	or	or	CCONJ
ejpam-3625	72	24	c	c	NOUN
ejpam-3625	72	25	is	be	AUX
ejpam-3625	72	26	a	a	DET
ejpam-3625	72	27	superclique	superclique	NOUN
ejpam-3625	72	28	in	in	ADP
ejpam-3625	72	29	g.	g.	PROPN
ejpam-3625	72	30	in	in	ADP
ejpam-3625	72	31	particular	particular	ADJ
ejpam-3625	72	32	,	,	PUNCT
ejpam-3625	72	33	sdim(g	sdim(g	PROPN
ejpam-3625	72	34	)	)	PUNCT
ejpam-3625	72	35	=	=	SYM
ejpam-3625	72	36	|v	|v	PROPN
ejpam-3625	72	37	(	(	PUNCT
ejpam-3625	72	38	g)|	g)|	NOUN
ejpam-3625	72	39	−	−	NOUN
ejpam-3625	72	40	ωs(g	ωs(g	PUNCT
ejpam-3625	72	41	)	)	PUNCT
ejpam-3625	72	42	.	.	PUNCT
ejpam-3625	73	1	proof	proof	NOUN
ejpam-3625	73	2	:	:	PUNCT
ejpam-3625	73	3	assume	assume	VERB
ejpam-3625	73	4	that	that	SCONJ
ejpam-3625	73	5	s	s	VERB
ejpam-3625	73	6	is	be	AUX
ejpam-3625	73	7	a	a	DET
ejpam-3625	73	8	strong	strong	ADJ
ejpam-3625	73	9	resolving	resolving	NOUN
ejpam-3625	73	10	set	set	NOUN
ejpam-3625	73	11	of	of	ADP
ejpam-3625	73	12	g.	g.	PROPN
ejpam-3625	73	13	if	if	SCONJ
ejpam-3625	73	14	s∩v	s∩v	PROPN
ejpam-3625	73	15	(	(	PUNCT
ejpam-3625	73	16	g	g	NOUN
ejpam-3625	73	17	)	)	PUNCT
ejpam-3625	73	18	=	=	NOUN
ejpam-3625	73	19	v	v	X
ejpam-3625	73	20	(	(	PUNCT
ejpam-3625	73	21	g	g	NOUN
ejpam-3625	73	22	)	)	PUNCT
ejpam-3625	73	23	,	,	PUNCT
ejpam-3625	73	24	then	then	ADV
ejpam-3625	73	25	c	c	X
ejpam-3625	73	26	=	=	PUNCT
ejpam-3625	73	27	∅.	∅.	ADV
ejpam-3625	73	28	suppose	suppose	VERB
ejpam-3625	73	29	s	s	X
ejpam-3625	73	30	(	(	PUNCT
ejpam-3625	73	31	v	v	NOUN
ejpam-3625	73	32	(	(	PUNCT
ejpam-3625	73	33	g	g	NOUN
ejpam-3625	73	34	)	)	PUNCT
ejpam-3625	73	35	.	.	PUNCT
ejpam-3625	74	1	let	let	VERB
ejpam-3625	74	2	c	c	NOUN
ejpam-3625	74	3	=	=	SYM
ejpam-3625	74	4	v	v	PROPN
ejpam-3625	74	5	(	(	PUNCT
ejpam-3625	74	6	g	g	NOUN
ejpam-3625	74	7	)	)	PUNCT
ejpam-3625	74	8	\	\	PUNCT
ejpam-3625	75	1	s.	s.	PROPN
ejpam-3625	75	2	then	then	ADV
ejpam-3625	75	3	s	s	VERB
ejpam-3625	75	4	=	=	SYM
ejpam-3625	75	5	v	v	PROPN
ejpam-3625	75	6	(	(	PUNCT
ejpam-3625	75	7	g	g	NOUN
ejpam-3625	75	8	)	)	PUNCT
ejpam-3625	75	9	\	\	PROPN
ejpam-3625	75	10	c.	c.	PROPN
ejpam-3625	75	11	let	let	VERB
ejpam-3625	75	12	x	x	PRON
ejpam-3625	75	13	,	,	PUNCT
ejpam-3625	75	14	y	y	PROPN
ejpam-3625	75	15	∈	∈	PROPN
ejpam-3625	75	16	c	c	PROPN
ejpam-3625	75	17	,	,	PUNCT
ejpam-3625	75	18	where	where	SCONJ
ejpam-3625	75	19	x	x	PUNCT
ejpam-3625	75	20	6=	6=	ADP
ejpam-3625	75	21	y.	y.	NOUN
ejpam-3625	75	22	since	since	SCONJ
ejpam-3625	75	23	s	s	PROPN
ejpam-3625	75	24	is	be	AUX
ejpam-3625	75	25	a	a	DET
ejpam-3625	75	26	strong	strong	ADJ
ejpam-3625	75	27	resolving	resolving	NOUN
ejpam-3625	75	28	set	set	NOUN
ejpam-3625	75	29	of	of	ADP
ejpam-3625	75	30	g	g	NOUN
ejpam-3625	75	31	,	,	PUNCT
ejpam-3625	75	32	x	x	PROPN
ejpam-3625	75	33	and	and	CCONJ
ejpam-3625	75	34	y	y	PROPN
ejpam-3625	75	35	are	be	AUX
ejpam-3625	75	36	strongly	strongly	ADV
ejpam-3625	75	37	resolved	resolve	VERB
ejpam-3625	75	38	by	by	ADP
ejpam-3625	75	39	some	some	DET
ejpam-3625	75	40	z	z	PROPN
ejpam-3625	75	41	∈	∈	PROPN
ejpam-3625	75	42	s.	s.	PROPN
ejpam-3625	75	43	we	we	PRON
ejpam-3625	75	44	may	may	AUX
ejpam-3625	75	45	assume	assume	VERB
ejpam-3625	75	46	that	that	SCONJ
ejpam-3625	75	47	x	x	PROPN
ejpam-3625	75	48	∈	∈	PROPN
ejpam-3625	75	49	ig[y	ig[y	PROPN
ejpam-3625	75	50	,	,	PUNCT
ejpam-3625	75	51	z	z	NOUN
ejpam-3625	75	52	]	]	X
ejpam-3625	75	53	.	.	PUNCT
ejpam-3625	76	1	then	then	ADV
ejpam-3625	76	2	dg(y	dg(y	ADJ
ejpam-3625	76	3	,	,	PUNCT
ejpam-3625	76	4	z	z	NOUN
ejpam-3625	76	5	)	)	PUNCT
ejpam-3625	76	6	=	=	SYM
ejpam-3625	76	7	2	2	NUM
ejpam-3625	76	8	and	and	CCONJ
ejpam-3625	76	9	x	x	NOUN
ejpam-3625	76	10	∈	∈	PROPN
ejpam-3625	76	11	ng(y	ng(y	NOUN
ejpam-3625	76	12	)	)	PUNCT
ejpam-3625	76	13	∩	∩	NOUN
ejpam-3625	76	14	ng(z	ng(z	NUM
ejpam-3625	76	15	)	)	PUNCT
ejpam-3625	76	16	by	by	ADP
ejpam-3625	76	17	remark	remark	NOUN
ejpam-3625	76	18	5	5	NUM
ejpam-3625	76	19	.	.	PUNCT
ejpam-3625	77	1	thus	thus	ADV
ejpam-3625	77	2	,	,	PUNCT
ejpam-3625	77	3	z	z	PROPN
ejpam-3625	77	4	∈	∈	PROPN
ejpam-3625	77	5	ng(x	ng(x	NUM
ejpam-3625	77	6	)	)	PUNCT
ejpam-3625	77	7	\ng(y	\ng(y	NOUN
ejpam-3625	77	8	)	)	PUNCT
ejpam-3625	77	9	,	,	PUNCT
ejpam-3625	77	10	showing	show	VERB
ejpam-3625	77	11	that	that	SCONJ
ejpam-3625	77	12	c	c	PROPN
ejpam-3625	77	13	is	be	AUX
ejpam-3625	77	14	a	a	DET
ejpam-3625	77	15	superclique	superclique	NOUN
ejpam-3625	77	16	in	in	ADP
ejpam-3625	77	17	g.	g.	NOUN
ejpam-3625	77	18	conversely	conversely	ADV
ejpam-3625	77	19	,	,	PUNCT
ejpam-3625	77	20	assume	assume	VERB
ejpam-3625	77	21	that	that	SCONJ
ejpam-3625	77	22	s	s	VERB
ejpam-3625	77	23	=	=	SYM
ejpam-3625	77	24	v	v	X
ejpam-3625	77	25	(	(	PUNCT
ejpam-3625	77	26	g	g	NOUN
ejpam-3625	77	27	)	)	PUNCT
ejpam-3625	77	28	\	\	PUNCT
ejpam-3625	78	1	c	c	X
ejpam-3625	78	2	,	,	PUNCT
ejpam-3625	78	3	where	where	SCONJ
ejpam-3625	78	4	c	c	PROPN
ejpam-3625	78	5	is	be	AUX
ejpam-3625	78	6	a	a	DET
ejpam-3625	78	7	superclique	superclique	NOUN
ejpam-3625	78	8	in	in	ADP
ejpam-3625	78	9	g.	g.	PROPN
ejpam-3625	78	10	let	let	VERB
ejpam-3625	78	11	x	x	PRON
ejpam-3625	78	12	,	,	PUNCT
ejpam-3625	78	13	y	y	PROPN
ejpam-3625	78	14	/∈	/∈	PUNCT
ejpam-3625	79	1	s	s	X
ejpam-3625	79	2	,	,	PUNCT
ejpam-3625	79	3	where	where	SCONJ
ejpam-3625	79	4	x	x	PUNCT
ejpam-3625	79	5	6=	6=	ADP
ejpam-3625	79	6	y.	y.	PROPN
ejpam-3625	79	7	then	then	ADV
ejpam-3625	79	8	x	x	PRON
ejpam-3625	79	9	,	,	PUNCT
ejpam-3625	79	10	y	y	PROPN
ejpam-3625	79	11	∈	∈	PROPN
ejpam-3625	79	12	c.	c.	NOUN
ejpam-3625	79	13	since	since	SCONJ
ejpam-3625	79	14	c	c	PROPN
ejpam-3625	79	15	is	be	AUX
ejpam-3625	79	16	a	a	DET
ejpam-3625	79	17	superclique	superclique	NOUN
ejpam-3625	79	18	in	in	ADP
ejpam-3625	79	19	g	g	NOUN
ejpam-3625	79	20	,	,	PUNCT
ejpam-3625	79	21	there	there	PRON
ejpam-3625	79	22	exists	exist	VERB
ejpam-3625	79	23	z	z	PROPN
ejpam-3625	79	24	∈	∈	PROPN
ejpam-3625	79	25	s	s	VERB
ejpam-3625	79	26	such	such	ADJ
ejpam-3625	79	27	that	that	SCONJ
ejpam-3625	79	28	z	z	PROPN
ejpam-3625	79	29	∈	∈	PROPN
ejpam-3625	79	30	ng(x)\ng(y	ng(x)\ng(y	NOUN
ejpam-3625	79	31	)	)	PUNCT
ejpam-3625	79	32	or	or	CCONJ
ejpam-3625	79	33	z	z	NOUN
ejpam-3625	79	34	∈	∈	PROPN
ejpam-3625	79	35	ng(y)\ng(x	ng(y)\ng(x	NOUN
ejpam-3625	79	36	)	)	PUNCT
ejpam-3625	79	37	.	.	PUNCT
ejpam-3625	80	1	since	since	SCONJ
ejpam-3625	80	2	diam(g	diam(g	NOUN
ejpam-3625	80	3	)	)	PUNCT
ejpam-3625	80	4	=	=	SYM
ejpam-3625	80	5	2	2	NUM
ejpam-3625	80	6	,	,	PUNCT
ejpam-3625	80	7	dg(y	dg(y	ADJ
ejpam-3625	80	8	,	,	PUNCT
ejpam-3625	80	9	z	z	NOUN
ejpam-3625	80	10	)	)	PUNCT
ejpam-3625	80	11	=	=	SYM
ejpam-3625	80	12	2	2	NUM
ejpam-3625	80	13	or	or	CCONJ
ejpam-3625	80	14	dg(x	dg(x	NUM
ejpam-3625	80	15	,	,	PUNCT
ejpam-3625	80	16	z	z	NOUN
ejpam-3625	80	17	)	)	PUNCT
ejpam-3625	80	18	=	=	SYM
ejpam-3625	80	19	2	2	X
ejpam-3625	80	20	.	.	PUNCT
ejpam-3625	80	21	by	by	ADP
ejpam-3625	80	22	remark	remark	NOUN
ejpam-3625	80	23	5	5	NUM
ejpam-3625	80	24	,	,	PUNCT
ejpam-3625	80	25	x	x	SYM
ejpam-3625	80	26	∈	∈	PROPN
ejpam-3625	80	27	ig[y	ig[y	PROPN
ejpam-3625	80	28	,	,	PUNCT
ejpam-3625	80	29	z	z	NOUN
ejpam-3625	80	30	]	]	X
ejpam-3625	80	31	or	or	CCONJ
ejpam-3625	80	32	y	y	PROPN
ejpam-3625	80	33	∈	∈	PROPN
ejpam-3625	80	34	ig[x	ig[x	PROPN
ejpam-3625	80	35	,	,	PUNCT
ejpam-3625	80	36	z	z	NOUN
ejpam-3625	80	37	]	]	X
ejpam-3625	80	38	.	.	PUNCT
ejpam-3625	81	1	hence	hence	ADV
ejpam-3625	81	2	,	,	PUNCT
ejpam-3625	81	3	s	s	VERB
ejpam-3625	81	4	is	be	AUX
ejpam-3625	81	5	a	a	DET
ejpam-3625	81	6	strong	strong	ADJ
ejpam-3625	81	7	resolving	resolving	NOUN
ejpam-3625	81	8	set	set	NOUN
ejpam-3625	81	9	of	of	ADP
ejpam-3625	81	10	g.	g.	PROPN
ejpam-3625	81	11	suppose	suppose	VERB
ejpam-3625	81	12	s	s	VERB
ejpam-3625	81	13	is	be	AUX
ejpam-3625	81	14	a	a	DET
ejpam-3625	81	15	strong	strong	ADJ
ejpam-3625	81	16	resolving	resolving	NOUN
ejpam-3625	81	17	set	set	NOUN
ejpam-3625	81	18	of	of	ADP
ejpam-3625	81	19	g.	g.	PROPN
ejpam-3625	81	20	then	then	ADV
ejpam-3625	81	21	s	s	VERB
ejpam-3625	81	22	=	=	SYM
ejpam-3625	81	23	v	v	PROPN
ejpam-3625	81	24	(	(	PUNCT
ejpam-3625	81	25	g)\c	g)\c	PROPN
ejpam-3625	81	26	,	,	PUNCT
ejpam-3625	81	27	where	where	SCONJ
ejpam-3625	81	28	c	c	PROPN
ejpam-3625	81	29	is	be	AUX
ejpam-3625	81	30	a	a	DET
ejpam-3625	81	31	superclique	superclique	NOUN
ejpam-3625	81	32	in	in	ADP
ejpam-3625	81	33	g	g	PROPN
ejpam-3625	81	34	and	and	CCONJ
ejpam-3625	81	35	|c|	|c|	PROPN
ejpam-3625	81	36	=	=	PUNCT
ejpam-3625	81	37	ωs(g	ωs(g	NUM
ejpam-3625	81	38	)	)	PUNCT
ejpam-3625	81	39	.	.	PUNCT
ejpam-3625	82	1	thus	thus	ADV
ejpam-3625	82	2	,	,	PUNCT
ejpam-3625	82	3	sdim(g	sdim(g	PROPN
ejpam-3625	82	4	)	)	PUNCT
ejpam-3625	82	5	=	=	SYM
ejpam-3625	82	6	|s|	|s|	PROPN
ejpam-3625	82	7	=	=	PUNCT
ejpam-3625	82	8	|v	|v	PROPN
ejpam-3625	82	9	(	(	PUNCT
ejpam-3625	82	10	g)|	g)|	PROPN
ejpam-3625	82	11	−	−	PROPN
ejpam-3625	82	12	|c|	|c|	PROPN
ejpam-3625	82	13	=	=	SYM
ejpam-3625	82	14	|v	|v	PROPN
ejpam-3625	82	15	(	(	PUNCT
ejpam-3625	82	16	g)|	g)|	NOUN
ejpam-3625	82	17	−	−	NOUN
ejpam-3625	82	18	ωs(g	ωs(g	NUM
ejpam-3625	82	19	)	)	PUNCT
ejpam-3625	82	20	.	.	PUNCT
ejpam-3625	83	1	3	3	X
ejpam-3625	83	2	.	.	X
ejpam-3625	83	3	on	on	ADP
ejpam-3625	83	4	strong	strong	ADJ
ejpam-3625	83	5	resolving	resolving	NOUN
ejpam-3625	83	6	domination	domination	NOUN
ejpam-3625	83	7	in	in	ADP
ejpam-3625	83	8	the	the	DET
ejpam-3625	83	9	join	join	NOUN
ejpam-3625	83	10	of	of	ADP
ejpam-3625	83	11	graphs	graph	NOUN
ejpam-3625	83	12	the	the	DET
ejpam-3625	83	13	join	join	NOUN
ejpam-3625	83	14	of	of	ADP
ejpam-3625	83	15	two	two	NUM
ejpam-3625	83	16	graphs	graph	NOUN
ejpam-3625	83	17	g	g	NOUN
ejpam-3625	83	18	and	and	CCONJ
ejpam-3625	83	19	h	h	NOUN
ejpam-3625	83	20	is	be	AUX
ejpam-3625	83	21	the	the	DET
ejpam-3625	83	22	graph	graph	NOUN
ejpam-3625	83	23	g	g	NOUN
ejpam-3625	83	24	+	+	CCONJ
ejpam-3625	83	25	h	h	NOUN
ejpam-3625	83	26	with	with	ADP
ejpam-3625	83	27	vertex	vertex	NOUN
ejpam-3625	83	28	set	set	VERB
ejpam-3625	83	29	v	v	NOUN
ejpam-3625	83	30	(	(	PUNCT
ejpam-3625	83	31	g	g	PROPN
ejpam-3625	83	32	+	+	NOUN
ejpam-3625	83	33	h	h	NOUN
ejpam-3625	83	34	)	)	PUNCT
ejpam-3625	84	1	=	=	NOUN
ejpam-3625	84	2	v	v	X
ejpam-3625	84	3	(	(	PUNCT
ejpam-3625	84	4	g	g	NOUN
ejpam-3625	84	5	)	)	PUNCT
ejpam-3625	84	6	•	•	ADP
ejpam-3625	84	7	∪	∪	X
ejpam-3625	84	8	v	v	NOUN
ejpam-3625	84	9	(	(	PUNCT
ejpam-3625	84	10	h	h	NOUN
ejpam-3625	84	11	)	)	PUNCT
ejpam-3625	84	12	and	and	CCONJ
ejpam-3625	84	13	edge	edge	NOUN
ejpam-3625	84	14	set	set	VERB
ejpam-3625	84	15	e(g+h	e(g+h	NUM
ejpam-3625	84	16	)	)	PUNCT
ejpam-3625	84	17	=	=	SYM
ejpam-3625	84	18	e(g	e(g	PROPN
ejpam-3625	84	19	)	)	PUNCT
ejpam-3625	85	1	•	•	ADP
ejpam-3625	85	2	∪	∪	ADP
ejpam-3625	85	3	e(h	e(h	PROPN
ejpam-3625	85	4	)	)	PUNCT
ejpam-3625	85	5	∪	∪	NOUN
ejpam-3625	85	6	{	{	PUNCT
ejpam-3625	85	7	uv	uv	NOUN
ejpam-3625	85	8	:	:	PUNCT
ejpam-3625	85	9	u	u	PROPN
ejpam-3625	85	10	∈	∈	PROPN
ejpam-3625	85	11	v	v	ADP
ejpam-3625	85	12	(	(	PUNCT
ejpam-3625	85	13	g	g	NOUN
ejpam-3625	85	14	)	)	PUNCT
ejpam-3625	85	15	,	,	PUNCT
ejpam-3625	85	16	v	v	X
ejpam-3625	85	17	∈	∈	PROPN
ejpam-3625	85	18	v	v	NOUN
ejpam-3625	85	19	(	(	PUNCT
ejpam-3625	85	20	h	h	NOUN
ejpam-3625	85	21	)	)	PUNCT
ejpam-3625	85	22	}	}	PUNCT
ejpam-3625	85	23	.	.	PUNCT
ejpam-3625	86	1	g.	g.	PROPN
ejpam-3625	86	2	monsanto	monsanto	PROPN
ejpam-3625	86	3	,	,	PUNCT
ejpam-3625	86	4	p.	p.	PROPN
ejpam-3625	86	5	acal	acal	PROPN
ejpam-3625	86	6	,	,	PUNCT
ejpam-3625	86	7	h.	h.	PROPN
ejpam-3625	86	8	rara	rara	PROPN
ejpam-3625	86	9	/	/	SYM
ejpam-3625	86	10	eur	eur	PROPN
ejpam-3625	86	11	.	.	PUNCT
ejpam-3625	87	1	j.	j.	PROPN
ejpam-3625	87	2	pure	pure	PROPN
ejpam-3625	87	3	appl	appl	PROPN
ejpam-3625	87	4	.	.	PROPN
ejpam-3625	87	5	math	math	PROPN
ejpam-3625	87	6	,	,	PUNCT
ejpam-3625	87	7	13	13	NUM
ejpam-3625	87	8	(	(	PUNCT
ejpam-3625	87	9	1	1	NUM
ejpam-3625	87	10	)	)	PUNCT
ejpam-3625	87	11	(	(	PUNCT
ejpam-3625	87	12	2020	2020	NUM
ejpam-3625	87	13	)	)	PUNCT
ejpam-3625	87	14	,	,	PUNCT
ejpam-3625	87	15	170	170	NUM
ejpam-3625	87	16	-	-	SYM
ejpam-3625	87	17	179	179	NUM
ejpam-3625	87	18	173	173	NUM
ejpam-3625	87	19	remark	remark	NOUN
ejpam-3625	87	20	6	6	NUM
ejpam-3625	87	21	.	.	PUNCT
ejpam-3625	88	1	for	for	ADP
ejpam-3625	88	2	the	the	DET
ejpam-3625	88	3	joins	join	NOUN
ejpam-3625	88	4	〈	〈	PROPN
ejpam-3625	88	5	v〉+pn	v〉+pn	NOUN
ejpam-3625	88	6	and	and	CCONJ
ejpam-3625	88	7	〈	〈	PROPN
ejpam-3625	88	8	w〉+cn	w〉+cn	NOUN
ejpam-3625	88	9	,	,	PUNCT
ejpam-3625	88	10	it	it	PRON
ejpam-3625	88	11	can	can	AUX
ejpam-3625	88	12	be	be	AUX
ejpam-3625	88	13	verified	verify	VERB
ejpam-3625	88	14	that	that	SCONJ
ejpam-3625	88	15	γsr	γsr	PROPN
ejpam-3625	88	16	(	(	PUNCT
ejpam-3625	88	17	〈	〈	PROPN
ejpam-3625	88	18	v〉+pn	v〉+pn	X
ejpam-3625	88	19	)	)	PUNCT
ejpam-3625	88	20	=	=	SYM
ejpam-3625	88	21	n−1	n−1	PROPN
ejpam-3625	88	22	for	for	ADP
ejpam-3625	88	23	n	n	X
ejpam-3625	88	24	≥	≥	NOUN
ejpam-3625	88	25	3	3	NUM
ejpam-3625	88	26	and	and	CCONJ
ejpam-3625	88	27	γsr	γsr	PROPN
ejpam-3625	88	28	(	(	PUNCT
ejpam-3625	88	29	〈	〈	PROPN
ejpam-3625	88	30	w〉+	w〉+	PROPN
ejpam-3625	88	31	cn	cn	PROPN
ejpam-3625	88	32	)	)	PUNCT
ejpam-3625	89	1	=	=	PUNCT
ejpam-3625	89	2	n−	n−	NOUN
ejpam-3625	89	3	2	2	NUM
ejpam-3625	89	4	for	for	ADP
ejpam-3625	89	5	n	n	X
ejpam-3625	89	6	≥	≥	NUM
ejpam-3625	89	7	4	4	NUM
ejpam-3625	89	8	.	.	PUNCT
ejpam-3625	89	9	proposition	proposition	NOUN
ejpam-3625	89	10	4	4	NUM
ejpam-3625	89	11	.	.	PUNCT
ejpam-3625	90	1	let	let	VERB
ejpam-3625	90	2	g	g	PRON
ejpam-3625	90	3	be	be	AUX
ejpam-3625	90	4	a	a	DET
ejpam-3625	90	5	connected	connected	ADJ
ejpam-3625	90	6	graph	graph	NOUN
ejpam-3625	90	7	with	with	ADP
ejpam-3625	90	8	γ(g	γ(g	PROPN
ejpam-3625	90	9	)	)	PUNCT
ejpam-3625	90	10	6=	6=	ADP
ejpam-3625	90	11	1	1	NUM
ejpam-3625	90	12	and	and	CCONJ
ejpam-3625	90	13	let	let	VERB
ejpam-3625	90	14	k1	k1	NOUN
ejpam-3625	90	15	=	=	PUNCT
ejpam-3625	90	16	〈	〈	PROPN
ejpam-3625	90	17	v	v	NOUN
ejpam-3625	90	18	〉	〉	PROPN
ejpam-3625	90	19	.	.	PUNCT
ejpam-3625	91	1	then	then	ADV
ejpam-3625	91	2	c	c	PROPN
ejpam-3625	91	3	⊆	⊆	NUM
ejpam-3625	91	4	v	v	NOUN
ejpam-3625	91	5	(	(	PUNCT
ejpam-3625	91	6	k1	k1	NOUN
ejpam-3625	91	7	+	+	NOUN
ejpam-3625	91	8	g	g	NOUN
ejpam-3625	91	9	)	)	PUNCT
ejpam-3625	91	10	is	be	AUX
ejpam-3625	91	11	a	a	DET
ejpam-3625	91	12	superclique	superclique	NOUN
ejpam-3625	91	13	of	of	ADP
ejpam-3625	91	14	k1	k1	NOUN
ejpam-3625	92	1	+	+	ADP
ejpam-3625	92	2	g	g	PROPN
ejpam-3625	92	3	if	if	SCONJ
ejpam-3625	92	4	and	and	CCONJ
ejpam-3625	92	5	only	only	ADV
ejpam-3625	92	6	if	if	SCONJ
ejpam-3625	92	7	|c|	|c|	PROPN
ejpam-3625	92	8	=	=	SYM
ejpam-3625	92	9	1	1	NUM
ejpam-3625	92	10	or	or	CCONJ
ejpam-3625	92	11	|c|	|c|	PROPN
ejpam-3625	92	12	≥	≥	NUM
ejpam-3625	92	13	2	2	NUM
ejpam-3625	92	14	and	and	CCONJ
ejpam-3625	92	15	c	c	NOUN
ejpam-3625	92	16	\	\	X
ejpam-3625	92	17	{	{	PUNCT
ejpam-3625	92	18	v	v	NOUN
ejpam-3625	92	19	}	}	PUNCT
ejpam-3625	92	20	is	be	AUX
ejpam-3625	92	21	a	a	DET
ejpam-3625	92	22	superclique	superclique	NOUN
ejpam-3625	92	23	of	of	ADP
ejpam-3625	92	24	g.	g.	PROPN
ejpam-3625	92	25	proof	proof	NOUN
ejpam-3625	92	26	:	:	PUNCT
ejpam-3625	92	27	the	the	DET
ejpam-3625	92	28	conditions	condition	NOUN
ejpam-3625	92	29	follow	follow	VERB
ejpam-3625	92	30	immediately	immediately	ADV
ejpam-3625	92	31	if	if	SCONJ
ejpam-3625	92	32	c	c	PROPN
ejpam-3625	92	33	⊆	⊆	NUM
ejpam-3625	92	34	v	v	X
ejpam-3625	92	35	(	(	PUNCT
ejpam-3625	92	36	k1+g	k1+g	NOUN
ejpam-3625	92	37	)	)	PUNCT
ejpam-3625	92	38	is	be	AUX
ejpam-3625	92	39	a	a	DET
ejpam-3625	92	40	superclique	superclique	NOUN
ejpam-3625	92	41	of	of	ADP
ejpam-3625	92	42	k1+g	k1+g	NOUN
ejpam-3625	92	43	.	.	PUNCT
ejpam-3625	93	1	for	for	ADP
ejpam-3625	93	2	the	the	DET
ejpam-3625	93	3	converse	converse	NOUN
ejpam-3625	93	4	,	,	PUNCT
ejpam-3625	93	5	the	the	DET
ejpam-3625	93	6	case	case	NOUN
ejpam-3625	93	7	when	when	SCONJ
ejpam-3625	93	8	|c|	|c|	PROPN
ejpam-3625	93	9	=	=	SYM
ejpam-3625	93	10	1	1	NUM
ejpam-3625	93	11	is	be	AUX
ejpam-3625	93	12	obvious	obvious	ADJ
ejpam-3625	93	13	.	.	PUNCT
ejpam-3625	94	1	suppose	suppose	VERB
ejpam-3625	94	2	|c|	|c|	PROPN
ejpam-3625	94	3	≥	≥	NUM
ejpam-3625	94	4	2	2	NUM
ejpam-3625	94	5	.	.	PUNCT
ejpam-3625	95	1	since	since	SCONJ
ejpam-3625	95	2	c	c	PROPN
ejpam-3625	95	3	\	\	PROPN
ejpam-3625	95	4	{	{	PUNCT
ejpam-3625	95	5	v	v	NOUN
ejpam-3625	95	6	}	}	PUNCT
ejpam-3625	95	7	is	be	AUX
ejpam-3625	95	8	a	a	DET
ejpam-3625	95	9	superclique	superclique	NOUN
ejpam-3625	95	10	of	of	ADP
ejpam-3625	95	11	g	g	NOUN
ejpam-3625	95	12	,	,	PUNCT
ejpam-3625	95	13	we	we	PRON
ejpam-3625	95	14	only	only	ADV
ejpam-3625	95	15	need	need	VERB
ejpam-3625	95	16	to	to	PART
ejpam-3625	95	17	consider	consider	VERB
ejpam-3625	95	18	the	the	DET
ejpam-3625	95	19	pair	pair	NOUN
ejpam-3625	95	20	of	of	ADP
ejpam-3625	95	21	distinct	distinct	ADJ
ejpam-3625	95	22	vertices	vertex	NOUN
ejpam-3625	95	23	z	z	NOUN
ejpam-3625	95	24	,	,	PUNCT
ejpam-3625	95	25	v	v	PROPN
ejpam-3625	95	26	∈	∈	PROPN
ejpam-3625	95	27	c.	c.	NOUN
ejpam-3625	95	28	since	since	SCONJ
ejpam-3625	95	29	γ(g	γ(g	PROPN
ejpam-3625	95	30	)	)	PUNCT
ejpam-3625	95	31	6=	6=	ADP
ejpam-3625	96	1	1	1	NUM
ejpam-3625	96	2	,	,	PUNCT
ejpam-3625	96	3	there	there	PRON
ejpam-3625	96	4	exists	exist	VERB
ejpam-3625	96	5	w	w	PROPN
ejpam-3625	96	6	∈	∈	PROPN
ejpam-3625	96	7	v	v	ADP
ejpam-3625	96	8	(	(	PUNCT
ejpam-3625	96	9	g	g	NOUN
ejpam-3625	96	10	)	)	PUNCT
ejpam-3625	96	11	such	such	ADJ
ejpam-3625	96	12	that	that	SCONJ
ejpam-3625	96	13	zw	zw	PROPN
ejpam-3625	96	14	/∈	/∈	PUNCT
ejpam-3625	96	15	e(g	e(g	PROPN
ejpam-3625	96	16	)	)	PUNCT
ejpam-3625	96	17	.	.	PUNCT
ejpam-3625	97	1	since	since	SCONJ
ejpam-3625	97	2	diam(k1	diam(k1	PROPN
ejpam-3625	97	3	+	+	CCONJ
ejpam-3625	97	4	g	g	NOUN
ejpam-3625	97	5	)	)	PUNCT
ejpam-3625	97	6	=	=	SYM
ejpam-3625	97	7	2	2	NUM
ejpam-3625	97	8	,	,	PUNCT
ejpam-3625	97	9	dg(z	dg(z	NUM
ejpam-3625	97	10	,	,	PUNCT
ejpam-3625	97	11	w	w	NOUN
ejpam-3625	97	12	)	)	PUNCT
ejpam-3625	97	13	=	=	SYM
ejpam-3625	97	14	2	2	X
ejpam-3625	97	15	.	.	X
ejpam-3625	97	16	hence	hence	ADV
ejpam-3625	97	17	,	,	PUNCT
ejpam-3625	97	18	z	z	PROPN
ejpam-3625	97	19	∈	∈	PROPN
ejpam-3625	97	20	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-3625	97	21	)	)	PUNCT
ejpam-3625	97	22	,	,	PUNCT
ejpam-3625	97	23	showing	show	VERB
ejpam-3625	97	24	that	that	SCONJ
ejpam-3625	97	25	c	c	PROPN
ejpam-3625	97	26	is	be	AUX
ejpam-3625	97	27	a	a	DET
ejpam-3625	97	28	superclique	superclique	NOUN
ejpam-3625	97	29	of	of	ADP
ejpam-3625	97	30	k1+g	k1+g	NOUN
ejpam-3625	97	31	.	.	PUNCT
ejpam-3625	98	1	theorem	theorem	NOUN
ejpam-3625	98	2	1	1	NUM
ejpam-3625	98	3	.	.	PUNCT
ejpam-3625	99	1	let	let	VERB
ejpam-3625	99	2	g	g	PRON
ejpam-3625	99	3	be	be	AUX
ejpam-3625	99	4	a	a	DET
ejpam-3625	99	5	nontrivial	nontrivial	ADJ
ejpam-3625	99	6	connected	connect	VERB
ejpam-3625	99	7	graph	graph	NOUN
ejpam-3625	99	8	of	of	ADP
ejpam-3625	99	9	order	order	NOUN
ejpam-3625	99	10	n	n	PRON
ejpam-3625	99	11	with	with	ADP
ejpam-3625	99	12	γ(g	γ(g	PROPN
ejpam-3625	99	13	)	)	PUNCT
ejpam-3625	99	14	6=	6=	ADP
ejpam-3625	99	15	1	1	NUM
ejpam-3625	99	16	and	and	CCONJ
ejpam-3625	99	17	k1	k1	NOUN
ejpam-3625	99	18	=	=	SYM
ejpam-3625	99	19	〈	〈	PROPN
ejpam-3625	99	20	v	v	NOUN
ejpam-3625	99	21	〉	〉	PROPN
ejpam-3625	99	22	.	.	PUNCT
ejpam-3625	100	1	then	then	ADV
ejpam-3625	100	2	s	s	VERB
ejpam-3625	100	3	⊆	⊆	NUM
ejpam-3625	100	4	v	v	NOUN
ejpam-3625	100	5	(	(	PUNCT
ejpam-3625	100	6	k1	k1	NOUN
ejpam-3625	100	7	+	+	NOUN
ejpam-3625	100	8	g	g	NOUN
ejpam-3625	100	9	)	)	PUNCT
ejpam-3625	100	10	is	be	AUX
ejpam-3625	100	11	a	a	DET
ejpam-3625	100	12	strong	strong	ADJ
ejpam-3625	100	13	resolving	resolving	NOUN
ejpam-3625	100	14	dominating	dominating	NOUN
ejpam-3625	100	15	set	set	NOUN
ejpam-3625	100	16	of	of	ADP
ejpam-3625	100	17	k1	k1	NOUN
ejpam-3625	101	1	+	+	ADP
ejpam-3625	101	2	g	g	PROPN
ejpam-3625	101	3	if	if	SCONJ
ejpam-3625	101	4	and	and	CCONJ
ejpam-3625	101	5	only	only	ADV
ejpam-3625	101	6	if	if	SCONJ
ejpam-3625	101	7	s	s	VERB
ejpam-3625	101	8	=	=	SYM
ejpam-3625	101	9	v	v	X
ejpam-3625	101	10	(	(	PUNCT
ejpam-3625	101	11	g	g	NOUN
ejpam-3625	101	12	)	)	PUNCT
ejpam-3625	101	13	,	,	PUNCT
ejpam-3625	101	14	or	or	CCONJ
ejpam-3625	101	15	s	s	VERB
ejpam-3625	101	16	=	=	SYM
ejpam-3625	101	17	v	v	PROPN
ejpam-3625	101	18	(	(	PUNCT
ejpam-3625	101	19	k1	k1	NOUN
ejpam-3625	101	20	+	+	CCONJ
ejpam-3625	101	21	g	g	NOUN
ejpam-3625	101	22	)	)	PUNCT
ejpam-3625	101	23	\	\	NOUN
ejpam-3625	102	1	c	c	NOUN
ejpam-3625	102	2	or	or	CCONJ
ejpam-3625	102	3	s	s	NOUN
ejpam-3625	102	4	=	=	SYM
ejpam-3625	102	5	v	v	PROPN
ejpam-3625	102	6	(	(	PUNCT
ejpam-3625	102	7	g	g	NOUN
ejpam-3625	102	8	)	)	PUNCT
ejpam-3625	102	9	\	\	PROPN
ejpam-3625	102	10	c∗	c∗	NOUN
ejpam-3625	102	11	where	where	SCONJ
ejpam-3625	102	12	c	c	NOUN
ejpam-3625	102	13	and	and	CCONJ
ejpam-3625	102	14	c∗	c∗	PROPN
ejpam-3625	102	15	are	be	AUX
ejpam-3625	102	16	superclique	superclique	ADJ
ejpam-3625	102	17	and	and	CCONJ
ejpam-3625	102	18	dominated	dominate	VERB
ejpam-3625	102	19	superclique	superclique	NOUN
ejpam-3625	102	20	,	,	PUNCT
ejpam-3625	102	21	respectively	respectively	ADV
ejpam-3625	102	22	,	,	PUNCT
ejpam-3625	102	23	in	in	ADP
ejpam-3625	102	24	g.	g.	PROPN
ejpam-3625	102	25	proof	proof	NOUN
ejpam-3625	102	26	:	:	PUNCT
ejpam-3625	102	27	let	let	VERB
ejpam-3625	102	28	s	s	PRON
ejpam-3625	102	29	be	be	AUX
ejpam-3625	102	30	a	a	DET
ejpam-3625	102	31	strong	strong	ADJ
ejpam-3625	102	32	resolving	resolving	NOUN
ejpam-3625	102	33	dominating	dominating	NOUN
ejpam-3625	102	34	set	set	NOUN
ejpam-3625	102	35	of	of	ADP
ejpam-3625	102	36	k1	k1	PROPN
ejpam-3625	102	37	+	+	CCONJ
ejpam-3625	102	38	g.	g.	PROPN
ejpam-3625	102	39	suppose	suppose	VERB
ejpam-3625	102	40	γ(g	γ(g	NOUN
ejpam-3625	102	41	)	)	PUNCT
ejpam-3625	102	42	6=	6=	ADP
ejpam-3625	103	1	1	1	X
ejpam-3625	103	2	.	.	PUNCT
ejpam-3625	104	1	if	if	SCONJ
ejpam-3625	104	2	v	v	NUM
ejpam-3625	104	3	/∈	/∈	SYM
ejpam-3625	104	4	s	s	X
ejpam-3625	104	5	,	,	PUNCT
ejpam-3625	104	6	then	then	ADV
ejpam-3625	104	7	s	s	X
ejpam-3625	104	8	(	(	PUNCT
ejpam-3625	104	9	v	v	NOUN
ejpam-3625	104	10	(	(	PUNCT
ejpam-3625	104	11	g	g	NOUN
ejpam-3625	104	12	)	)	PUNCT
ejpam-3625	104	13	.	.	PUNCT
ejpam-3625	105	1	by	by	ADP
ejpam-3625	105	2	proposition	proposition	NOUN
ejpam-3625	105	3	3	3	NUM
ejpam-3625	105	4	,	,	PUNCT
ejpam-3625	105	5	s	s	PART
ejpam-3625	105	6	=	=	SYM
ejpam-3625	105	7	v	v	PROPN
ejpam-3625	105	8	(	(	PUNCT
ejpam-3625	105	9	k1	k1	NOUN
ejpam-3625	105	10	+	+	PROPN
ejpam-3625	105	11	g)\	g)\	PROPN
ejpam-3625	105	12	(	(	PUNCT
ejpam-3625	105	13	c	c	NOUN
ejpam-3625	105	14	∪{v	∪{v	NOUN
ejpam-3625	105	15	}	}	PUNCT
ejpam-3625	105	16	)	)	PUNCT
ejpam-3625	106	1	=	=	SYM
ejpam-3625	106	2	v	v	X
ejpam-3625	106	3	(	(	PUNCT
ejpam-3625	106	4	g)\c	g)\c	PROPN
ejpam-3625	106	5	,	,	PUNCT
ejpam-3625	106	6	where	where	SCONJ
ejpam-3625	106	7	s	s	NOUN
ejpam-3625	106	8	is	be	AUX
ejpam-3625	106	9	a	a	DET
ejpam-3625	106	10	dominating	dominating	NOUN
ejpam-3625	106	11	set	set	VERB
ejpam-3625	106	12	in	in	ADP
ejpam-3625	106	13	k1	k1	NOUN
ejpam-3625	106	14	+	+	PROPN
ejpam-3625	106	15	g	g	PROPN
ejpam-3625	106	16	and	and	CCONJ
ejpam-3625	106	17	c∪{v	c∪{v	NOUN
ejpam-3625	106	18	}	}	PUNCT
ejpam-3625	106	19	is	be	AUX
ejpam-3625	106	20	a	a	DET
ejpam-3625	106	21	superclique	superclique	NOUN
ejpam-3625	106	22	in	in	ADP
ejpam-3625	106	23	k1	k1	PROPN
ejpam-3625	106	24	+	+	PROPN
ejpam-3625	106	25	g.	g.	NOUN
ejpam-3625	106	26	by	by	ADP
ejpam-3625	106	27	proposition	proposition	NOUN
ejpam-3625	106	28	4	4	NUM
ejpam-3625	106	29	,	,	PUNCT
ejpam-3625	106	30	c	c	PROPN
ejpam-3625	106	31	is	be	AUX
ejpam-3625	106	32	a	a	DET
ejpam-3625	106	33	superclique	superclique	NOUN
ejpam-3625	106	34	in	in	ADP
ejpam-3625	106	35	g.	g.	PROPN
ejpam-3625	106	36	since	since	SCONJ
ejpam-3625	106	37	{	{	PUNCT
ejpam-3625	106	38	v	v	NOUN
ejpam-3625	106	39	}	}	PUNCT
ejpam-3625	106	40	is	be	AUX
ejpam-3625	106	41	a	a	DET
ejpam-3625	106	42	superclique	superclique	NOUN
ejpam-3625	106	43	in	in	ADP
ejpam-3625	106	44	k1	k1	NOUN
ejpam-3625	107	1	+	+	PROPN
ejpam-3625	107	2	g	g	NOUN
ejpam-3625	107	3	,	,	PUNCT
ejpam-3625	107	4	s	s	PART
ejpam-3625	107	5	=	=	SYM
ejpam-3625	107	6	v	v	PROPN
ejpam-3625	107	7	(	(	PUNCT
ejpam-3625	107	8	k1	k1	NOUN
ejpam-3625	107	9	+	+	PROPN
ejpam-3625	107	10	g	g	NOUN
ejpam-3625	107	11	)	)	PUNCT
ejpam-3625	107	12	\	\	NOUN
ejpam-3625	108	1	{	{	PUNCT
ejpam-3625	108	2	v	v	NOUN
ejpam-3625	108	3	}	}	PUNCT
ejpam-3625	108	4	=	=	SYM
ejpam-3625	108	5	v	v	NOUN
ejpam-3625	108	6	(	(	PUNCT
ejpam-3625	108	7	g	g	NOUN
ejpam-3625	108	8	)	)	PUNCT
ejpam-3625	108	9	.	.	PUNCT
ejpam-3625	109	1	on	on	ADP
ejpam-3625	109	2	the	the	DET
ejpam-3625	109	3	other	other	ADJ
ejpam-3625	109	4	hand	hand	NOUN
ejpam-3625	109	5	,	,	PUNCT
ejpam-3625	109	6	if	if	SCONJ
ejpam-3625	109	7	v	v	NUM
ejpam-3625	109	8	∈	∈	NOUN
ejpam-3625	109	9	s	s	NOUN
ejpam-3625	109	10	and	and	CCONJ
ejpam-3625	109	11	c	c	NOUN
ejpam-3625	109	12	=	=	SYM
ejpam-3625	109	13	v	v	PROPN
ejpam-3625	109	14	(	(	PUNCT
ejpam-3625	109	15	k1	k1	NOUN
ejpam-3625	109	16	+	+	PROPN
ejpam-3625	109	17	g	g	NOUN
ejpam-3625	109	18	)	)	PUNCT
ejpam-3625	109	19	\s	\s	NOUN
ejpam-3625	109	20	,	,	PUNCT
ejpam-3625	109	21	then	then	ADV
ejpam-3625	109	22	s	s	VERB
ejpam-3625	109	23	=	=	SYM
ejpam-3625	109	24	v	v	PROPN
ejpam-3625	109	25	(	(	PUNCT
ejpam-3625	109	26	k1	k1	NOUN
ejpam-3625	109	27	+	+	PROPN
ejpam-3625	109	28	g	g	NOUN
ejpam-3625	109	29	)	)	PUNCT
ejpam-3625	109	30	\c	\c	NOUN
ejpam-3625	109	31	where	where	SCONJ
ejpam-3625	109	32	c	c	NOUN
ejpam-3625	109	33	is	be	AUX
ejpam-3625	109	34	a	a	DET
ejpam-3625	109	35	superclique	superclique	NOUN
ejpam-3625	109	36	in	in	ADP
ejpam-3625	109	37	k1	k1	NOUN
ejpam-3625	110	1	+	+	PROPN
ejpam-3625	110	2	g	g	NOUN
ejpam-3625	110	3	by	by	ADP
ejpam-3625	110	4	proposition	proposition	NOUN
ejpam-3625	110	5	3	3	NUM
ejpam-3625	110	6	.	.	PUNCT
ejpam-3625	111	1	by	by	ADP
ejpam-3625	111	2	proposition	proposition	NOUN
ejpam-3625	111	3	4	4	NUM
ejpam-3625	111	4	,	,	PUNCT
ejpam-3625	111	5	c	c	NOUN
ejpam-3625	111	6	\	\	PROPN
ejpam-3625	111	7	{	{	PUNCT
ejpam-3625	111	8	v	v	NOUN
ejpam-3625	111	9	}	}	PUNCT
ejpam-3625	111	10	=	=	PUNCT
ejpam-3625	111	11	c	c	NOUN
ejpam-3625	111	12	is	be	AUX
ejpam-3625	111	13	a	a	DET
ejpam-3625	111	14	superclique	superclique	NOUN
ejpam-3625	111	15	in	in	ADP
ejpam-3625	111	16	g.	g.	NOUN
ejpam-3625	111	17	conversely	conversely	ADV
ejpam-3625	111	18	,	,	PUNCT
ejpam-3625	111	19	the	the	DET
ejpam-3625	111	20	case	case	NOUN
ejpam-3625	111	21	when	when	SCONJ
ejpam-3625	111	22	s	s	VERB
ejpam-3625	111	23	=	=	SYM
ejpam-3625	111	24	v	v	X
ejpam-3625	111	25	(	(	PUNCT
ejpam-3625	111	26	g	g	NOUN
ejpam-3625	111	27	)	)	PUNCT
ejpam-3625	111	28	and	and	CCONJ
ejpam-3625	111	29	s	s	X
ejpam-3625	111	30	=	=	SYM
ejpam-3625	111	31	v	v	PROPN
ejpam-3625	111	32	(	(	PUNCT
ejpam-3625	111	33	k1	k1	NOUN
ejpam-3625	111	34	+	+	CCONJ
ejpam-3625	111	35	g	g	NOUN
ejpam-3625	111	36	)	)	PUNCT
ejpam-3625	111	37	\	\	PUNCT
ejpam-3625	112	1	c	c	NOUN
ejpam-3625	112	2	follows	follow	VERB
ejpam-3625	112	3	immediately	immediately	ADV
ejpam-3625	112	4	from	from	ADP
ejpam-3625	112	5	proposition	proposition	NOUN
ejpam-3625	112	6	3	3	NUM
ejpam-3625	112	7	.	.	PUNCT
ejpam-3625	113	1	suppose	suppose	VERB
ejpam-3625	113	2	s	s	VERB
ejpam-3625	113	3	=	=	SYM
ejpam-3625	113	4	v	v	PROPN
ejpam-3625	113	5	(	(	PUNCT
ejpam-3625	113	6	g	g	NOUN
ejpam-3625	113	7	)	)	PUNCT
ejpam-3625	113	8	\	\	PROPN
ejpam-3625	113	9	c∗	c∗	PROPN
ejpam-3625	113	10	,	,	PUNCT
ejpam-3625	113	11	where	where	SCONJ
ejpam-3625	113	12	c∗	c∗	PROPN
ejpam-3625	113	13	is	be	AUX
ejpam-3625	113	14	a	a	DET
ejpam-3625	113	15	dominated	dominate	VERB
ejpam-3625	113	16	superclique	superclique	NOUN
ejpam-3625	113	17	in	in	ADP
ejpam-3625	113	18	g.	g.	NOUN
ejpam-3625	113	19	by	by	ADP
ejpam-3625	113	20	proposition	proposition	NOUN
ejpam-3625	113	21	4	4	NUM
ejpam-3625	113	22	,	,	PUNCT
ejpam-3625	113	23	c	c	NOUN
ejpam-3625	113	24	∪	∪	X
ejpam-3625	113	25	{	{	PUNCT
ejpam-3625	113	26	v	v	NOUN
ejpam-3625	113	27	}	}	PUNCT
ejpam-3625	113	28	is	be	AUX
ejpam-3625	113	29	a	a	DET
ejpam-3625	113	30	superclique	superclique	NOUN
ejpam-3625	113	31	of	of	ADP
ejpam-3625	113	32	k1	k1	NOUN
ejpam-3625	113	33	+	+	CCONJ
ejpam-3625	113	34	g.	g.	NOUN
ejpam-3625	113	35	since	since	SCONJ
ejpam-3625	113	36	v	v	NUM
ejpam-3625	113	37	/∈	/∈	SYM
ejpam-3625	113	38	s	s	X
ejpam-3625	113	39	,	,	PUNCT
ejpam-3625	113	40	s	s	PART
ejpam-3625	113	41	=	=	SYM
ejpam-3625	113	42	v	v	X
ejpam-3625	113	43	(	(	PUNCT
ejpam-3625	113	44	g	g	NOUN
ejpam-3625	113	45	)	)	PUNCT
ejpam-3625	113	46	\	\	PROPN
ejpam-3625	113	47	c∗	c∗	PROPN
ejpam-3625	113	48	=	=	SYM
ejpam-3625	113	49	v	v	PROPN
ejpam-3625	113	50	(	(	PUNCT
ejpam-3625	113	51	k1	k1	NOUN
ejpam-3625	113	52	+	+	CCONJ
ejpam-3625	113	53	g	g	NOUN
ejpam-3625	113	54	)	)	PUNCT
ejpam-3625	113	55	\	\	PUNCT
ejpam-3625	114	1	(	(	PUNCT
ejpam-3625	114	2	c	c	NOUN
ejpam-3625	114	3	∪	∪	X
ejpam-3625	114	4	{	{	PUNCT
ejpam-3625	114	5	v	v	NOUN
ejpam-3625	114	6	}	}	PUNCT
ejpam-3625	114	7	)	)	PUNCT
ejpam-3625	114	8	.	.	PUNCT
ejpam-3625	115	1	by	by	ADP
ejpam-3625	115	2	proposition	proposition	NOUN
ejpam-3625	115	3	3	3	NUM
ejpam-3625	115	4	,	,	PUNCT
ejpam-3625	115	5	s	s	VERB
ejpam-3625	115	6	is	be	AUX
ejpam-3625	115	7	a	a	DET
ejpam-3625	115	8	strong	strong	ADJ
ejpam-3625	115	9	resolving	resolving	NOUN
ejpam-3625	115	10	dominating	dominating	NOUN
ejpam-3625	115	11	set	set	NOUN
ejpam-3625	115	12	of	of	ADP
ejpam-3625	115	13	k1	k1	PROPN
ejpam-3625	115	14	+	+	PROPN
ejpam-3625	115	15	g.	g.	PROPN
ejpam-3625	115	16	theorem	theorem	NOUN
ejpam-3625	115	17	2	2	X
ejpam-3625	115	18	.	.	PUNCT
ejpam-3625	116	1	let	let	VERB
ejpam-3625	116	2	g	g	PRON
ejpam-3625	116	3	be	be	AUX
ejpam-3625	116	4	a	a	DET
ejpam-3625	116	5	nontrivial	nontrivial	ADJ
ejpam-3625	116	6	connected	connect	VERB
ejpam-3625	116	7	graph	graph	NOUN
ejpam-3625	116	8	of	of	ADP
ejpam-3625	116	9	order	order	NOUN
ejpam-3625	116	10	n	n	PRON
ejpam-3625	116	11	with	with	ADP
ejpam-3625	116	12	γ(g	γ(g	PROPN
ejpam-3625	116	13	)	)	PUNCT
ejpam-3625	116	14	=	=	SYM
ejpam-3625	116	15	1	1	NUM
ejpam-3625	116	16	and	and	CCONJ
ejpam-3625	116	17	k1	k1	NOUN
ejpam-3625	116	18	=	=	SYM
ejpam-3625	116	19	〈	〈	PROPN
ejpam-3625	116	20	v	v	NOUN
ejpam-3625	116	21	〉	〉	PROPN
ejpam-3625	116	22	.	.	PUNCT
ejpam-3625	117	1	then	then	ADV
ejpam-3625	117	2	s	s	VERB
ejpam-3625	117	3	⊆	⊆	NUM
ejpam-3625	117	4	v	v	NOUN
ejpam-3625	117	5	(	(	PUNCT
ejpam-3625	117	6	k1	k1	NOUN
ejpam-3625	117	7	+	+	CCONJ
ejpam-3625	117	8	g	g	NOUN
ejpam-3625	117	9	)	)	PUNCT
ejpam-3625	117	10	is	be	AUX
ejpam-3625	117	11	a	a	DET
ejpam-3625	117	12	strong	strong	ADJ
ejpam-3625	117	13	resolving	resolving	NOUN
ejpam-3625	117	14	dominating	dominating	NOUN
ejpam-3625	117	15	set	set	NOUN
ejpam-3625	117	16	of	of	ADP
ejpam-3625	117	17	k1	k1	NOUN
ejpam-3625	117	18	+	+	CCONJ
ejpam-3625	117	19	g	g	NOUN
ejpam-3625	117	20	if	if	SCONJ
ejpam-3625	117	21	and	and	CCONJ
ejpam-3625	117	22	only	only	ADV
ejpam-3625	117	23	if	if	SCONJ
ejpam-3625	117	24	s	s	VERB
ejpam-3625	117	25	=	=	SYM
ejpam-3625	117	26	v	v	X
ejpam-3625	117	27	(	(	PUNCT
ejpam-3625	117	28	g	g	NOUN
ejpam-3625	117	29	)	)	PUNCT
ejpam-3625	117	30	or	or	CCONJ
ejpam-3625	117	31	s	s	X
ejpam-3625	117	32	=	=	SYM
ejpam-3625	117	33	v	v	PROPN
ejpam-3625	117	34	(	(	PUNCT
ejpam-3625	117	35	k1	k1	NOUN
ejpam-3625	117	36	+	+	PROPN
ejpam-3625	117	37	g	g	NOUN
ejpam-3625	117	38	)	)	PUNCT
ejpam-3625	117	39	\	\	NOUN
ejpam-3625	118	1	c	c	PROPN
ejpam-3625	118	2	or	or	CCONJ
ejpam-3625	118	3	s	s	NOUN
ejpam-3625	118	4	=	=	PUNCT
ejpam-3625	118	5	(	(	PUNCT
ejpam-3625	118	6	v	v	NOUN
ejpam-3625	118	7	(	(	PUNCT
ejpam-3625	118	8	g	g	NOUN
ejpam-3625	118	9	)	)	PUNCT
ejpam-3625	118	10	\	\	PROPN
ejpam-3625	118	11	c∗	c∗	PROPN
ejpam-3625	118	12	)	)	PUNCT
ejpam-3625	118	13	∪	∪	NOUN
ejpam-3625	118	14	{	{	PUNCT
ejpam-3625	118	15	x	x	SYM
ejpam-3625	118	16	∈	∈	PROPN
ejpam-3625	118	17	c∗	c∗	NOUN
ejpam-3625	118	18	:	:	PUNCT
ejpam-3625	118	19	deg(x	deg(x	X
ejpam-3625	118	20	)	)	PUNCT
ejpam-3625	119	1	=	=	PUNCT
ejpam-3625	119	2	n−	n−	NOUN
ejpam-3625	119	3	1	1	NUM
ejpam-3625	119	4	}	}	PUNCT
ejpam-3625	119	5	where	where	SCONJ
ejpam-3625	119	6	c	c	NOUN
ejpam-3625	119	7	and	and	CCONJ
ejpam-3625	119	8	c∗	c∗	PROPN
ejpam-3625	119	9	are	be	AUX
ejpam-3625	119	10	superclique	superclique	ADJ
ejpam-3625	119	11	and	and	CCONJ
ejpam-3625	119	12	dominated	dominate	VERB
ejpam-3625	119	13	superclique	superclique	NOUN
ejpam-3625	119	14	,	,	PUNCT
ejpam-3625	119	15	respectively	respectively	ADV
ejpam-3625	119	16	,	,	PUNCT
ejpam-3625	119	17	in	in	ADP
ejpam-3625	119	18	g.	g.	PROPN
ejpam-3625	119	19	proof	proof	NOUN
ejpam-3625	119	20	:	:	PUNCT
ejpam-3625	119	21	let	let	VERB
ejpam-3625	119	22	s	s	PRON
ejpam-3625	119	23	be	be	AUX
ejpam-3625	119	24	a	a	DET
ejpam-3625	119	25	strong	strong	ADJ
ejpam-3625	119	26	resolving	resolving	NOUN
ejpam-3625	119	27	dominating	dominating	NOUN
ejpam-3625	119	28	set	set	NOUN
ejpam-3625	119	29	of	of	ADP
ejpam-3625	119	30	k1	k1	PROPN
ejpam-3625	119	31	+	+	CCONJ
ejpam-3625	119	32	g.	g.	PROPN
ejpam-3625	119	33	suppose	suppose	VERB
ejpam-3625	119	34	γ(g	γ(g	NOUN
ejpam-3625	119	35	)	)	PUNCT
ejpam-3625	119	36	=	=	PUNCT
ejpam-3625	120	1	1	1	X
ejpam-3625	120	2	.	.	X
ejpam-3625	121	1	if	if	SCONJ
ejpam-3625	121	2	v	v	NUM
ejpam-3625	121	3	∈	∈	PROPN
ejpam-3625	121	4	s	s	NOUN
ejpam-3625	121	5	and	and	CCONJ
ejpam-3625	121	6	c	c	NOUN
ejpam-3625	121	7	=	=	SYM
ejpam-3625	121	8	v	v	PROPN
ejpam-3625	121	9	(	(	PUNCT
ejpam-3625	121	10	k1+g)\s	k1+g)\s	PROPN
ejpam-3625	121	11	,	,	PUNCT
ejpam-3625	121	12	then	then	ADV
ejpam-3625	121	13	s	s	VERB
ejpam-3625	121	14	=	=	SYM
ejpam-3625	121	15	v	v	PROPN
ejpam-3625	121	16	(	(	PUNCT
ejpam-3625	121	17	k1+g)\c	k1+g)\c	NOUN
ejpam-3625	121	18	=	=	X
ejpam-3625	121	19	{	{	PUNCT
ejpam-3625	121	20	v}∪(v	v}∪(v	X
ejpam-3625	121	21	(	(	PUNCT
ejpam-3625	121	22	g)\c	g)\c	NOUN
ejpam-3625	121	23	)	)	PUNCT
ejpam-3625	121	24	.	.	PUNCT
ejpam-3625	122	1	by	by	ADP
ejpam-3625	122	2	proposition	proposition	NOUN
ejpam-3625	122	3	3	3	NUM
ejpam-3625	122	4	,	,	PUNCT
ejpam-3625	122	5	c	c	PROPN
ejpam-3625	122	6	is	be	AUX
ejpam-3625	122	7	a	a	DET
ejpam-3625	122	8	superclique	superclique	NOUN
ejpam-3625	122	9	in	in	ADP
ejpam-3625	122	10	k1	k1	PROPN
ejpam-3625	122	11	+	+	CCONJ
ejpam-3625	122	12	g.	g.	NOUN
ejpam-3625	122	13	hence	hence	ADV
ejpam-3625	122	14	for	for	ADP
ejpam-3625	122	15	x	x	X
ejpam-3625	122	16	,	,	PUNCT
ejpam-3625	122	17	y	y	PROPN
ejpam-3625	122	18	∈	∈	PROPN
ejpam-3625	122	19	c	c	AUX
ejpam-3625	122	20	,	,	PUNCT
ejpam-3625	122	21	x	x	SYM
ejpam-3625	122	22	6=	6=	NUM
ejpam-3625	122	23	y	y	PROPN
ejpam-3625	122	24	,	,	PUNCT
ejpam-3625	122	25	there	there	PRON
ejpam-3625	122	26	exists	exist	VERB
ejpam-3625	122	27	w	w	PROPN
ejpam-3625	122	28	∈	∈	PROPN
ejpam-3625	122	29	v	v	ADP
ejpam-3625	122	30	(	(	PUNCT
ejpam-3625	122	31	g	g	NOUN
ejpam-3625	122	32	)	)	PUNCT
ejpam-3625	122	33	\	\	PUNCT
ejpam-3625	123	1	c	c	NOUN
ejpam-3625	123	2	such	such	ADJ
ejpam-3625	123	3	that	that	PRON
ejpam-3625	123	4	w	w	PROPN
ejpam-3625	123	5	∈	∈	PROPN
ejpam-3625	123	6	ng(x	ng(x	NUM
ejpam-3625	123	7	)	)	PUNCT
ejpam-3625	123	8	\	\	NOUN
ejpam-3625	123	9	ng(y	ng(y	NOUN
ejpam-3625	123	10	)	)	PUNCT
ejpam-3625	123	11	or	or	CCONJ
ejpam-3625	123	12	w	w	PROPN
ejpam-3625	123	13	∈	∈	PROPN
ejpam-3625	123	14	ng(y	ng(y	NOUN
ejpam-3625	123	15	)	)	PUNCT
ejpam-3625	123	16	\	\	NOUN
ejpam-3625	123	17	ng(x	ng(x	NUM
ejpam-3625	123	18	)	)	PUNCT
ejpam-3625	123	19	,	,	PUNCT
ejpam-3625	123	20	showing	show	VERB
ejpam-3625	123	21	that	that	SCONJ
ejpam-3625	123	22	c	c	PROPN
ejpam-3625	123	23	is	be	AUX
ejpam-3625	123	24	a	a	DET
ejpam-3625	123	25	superclique	superclique	NOUN
ejpam-3625	123	26	in	in	ADP
ejpam-3625	123	27	g.	g.	PROPN
ejpam-3625	123	28	on	on	ADP
ejpam-3625	123	29	the	the	DET
ejpam-3625	123	30	other	other	ADJ
ejpam-3625	123	31	hand	hand	NOUN
ejpam-3625	123	32	,	,	PUNCT
ejpam-3625	123	33	if	if	SCONJ
ejpam-3625	123	34	v	v	NUM
ejpam-3625	123	35	/∈	/∈	PUNCT
ejpam-3625	123	36	s	s	X
ejpam-3625	123	37	,	,	PUNCT
ejpam-3625	123	38	then	then	ADV
ejpam-3625	123	39	s	s	X
ejpam-3625	123	40	(	(	PUNCT
ejpam-3625	123	41	v	v	NOUN
ejpam-3625	123	42	(	(	PUNCT
ejpam-3625	123	43	g	g	NOUN
ejpam-3625	123	44	)	)	PUNCT
ejpam-3625	123	45	.	.	PUNCT
ejpam-3625	124	1	let	let	VERB
ejpam-3625	124	2	c	c	NOUN
ejpam-3625	124	3	=	=	SYM
ejpam-3625	124	4	v	v	PROPN
ejpam-3625	124	5	(	(	PUNCT
ejpam-3625	124	6	k1	k1	NOUN
ejpam-3625	124	7	+	+	CCONJ
ejpam-3625	124	8	g	g	NOUN
ejpam-3625	124	9	)	)	PUNCT
ejpam-3625	124	10	\	\	NOUN
ejpam-3625	125	1	s.	s.	PROPN
ejpam-3625	125	2	hence	hence	ADV
ejpam-3625	125	3	,	,	PUNCT
ejpam-3625	125	4	s	s	NOUN
ejpam-3625	125	5	=	=	SYM
ejpam-3625	125	6	v	v	PROPN
ejpam-3625	125	7	(	(	PUNCT
ejpam-3625	125	8	k1	k1	NOUN
ejpam-3625	125	9	+	+	NOUN
ejpam-3625	125	10	g)\c	g)\c	NOUN
ejpam-3625	125	11	=	=	SYM
ejpam-3625	125	12	v	v	NOUN
ejpam-3625	125	13	(	(	PUNCT
ejpam-3625	125	14	g)\c	g)\c	NOUN
ejpam-3625	125	15	.	.	PUNCT
ejpam-3625	126	1	by	by	ADP
ejpam-3625	126	2	proposition	proposition	NOUN
ejpam-3625	126	3	3	3	NUM
ejpam-3625	126	4	,	,	PUNCT
ejpam-3625	126	5	c	c	PROPN
ejpam-3625	126	6	is	be	AUX
ejpam-3625	126	7	a	a	DET
ejpam-3625	126	8	superclique	superclique	NOUN
ejpam-3625	126	9	in	in	ADP
ejpam-3625	126	10	k1	k1	PROPN
ejpam-3625	126	11	+	+	PROPN
ejpam-3625	126	12	g.	g.	PROPN
ejpam-3625	126	13	hence	hence	ADV
ejpam-3625	126	14	,	,	PUNCT
ejpam-3625	126	15	c	c	PROPN
ejpam-3625	126	16	is	be	AUX
ejpam-3625	126	17	also	also	ADV
ejpam-3625	126	18	a	a	DET
ejpam-3625	126	19	superclique	superclique	NOUN
ejpam-3625	126	20	in	in	ADP
ejpam-3625	126	21	g.	g.	PROPN
ejpam-3625	126	22	since	since	SCONJ
ejpam-3625	126	23	γ(g	γ(g	PROPN
ejpam-3625	126	24	)	)	PUNCT
ejpam-3625	127	1	=	=	SYM
ejpam-3625	127	2	1	1	NUM
ejpam-3625	127	3	,	,	PUNCT
ejpam-3625	127	4	ag	ag	PROPN
ejpam-3625	127	5	=	=	SYM
ejpam-3625	127	6	{	{	PUNCT
ejpam-3625	127	7	z	z	PROPN
ejpam-3625	127	8	∈	∈	PROPN
ejpam-3625	127	9	v	v	NOUN
ejpam-3625	127	10	(	(	PUNCT
ejpam-3625	127	11	g	g	NOUN
ejpam-3625	127	12	)	)	PUNCT
ejpam-3625	127	13	;	;	PUNCT
ejpam-3625	127	14	degg(z	degg(z	X
ejpam-3625	127	15	)	)	PUNCT
ejpam-3625	127	16	=	=	PUNCT
ejpam-3625	127	17	n−	n−	NOUN
ejpam-3625	127	18	1	1	NUM
ejpam-3625	127	19	}	}	PUNCT
ejpam-3625	127	20	6=	6=	ADP
ejpam-3625	127	21	∅.	∅.	ADP
ejpam-3625	127	22	by	by	ADP
ejpam-3625	127	23	proposition	proposition	NOUN
ejpam-3625	127	24	2	2	NUM
ejpam-3625	127	25	,	,	PUNCT
ejpam-3625	127	26	|c	|c	ADJ
ejpam-3625	127	27	∩	∩	NOUN
ejpam-3625	127	28	ag|	ag|	NOUN
ejpam-3625	127	29	=	=	SYM
ejpam-3625	127	30	1	1	X
ejpam-3625	127	31	.	.	PUNCT
ejpam-3625	128	1	let	let	VERB
ejpam-3625	128	2	z	z	NOUN
ejpam-3625	128	3	∈	∈	PROPN
ejpam-3625	128	4	c	c	PROPN
ejpam-3625	128	5	∩	∩	PROPN
ejpam-3625	128	6	ag	ag	PROPN
ejpam-3625	128	7	.	.	PROPN
ejpam-3625	129	1	since	since	SCONJ
ejpam-3625	129	2	dk1+g(z	dk1+g(z	NOUN
ejpam-3625	129	3	,	,	PUNCT
ejpam-3625	129	4	v	v	NOUN
ejpam-3625	129	5	)	)	PUNCT
ejpam-3625	129	6	=	=	SYM
ejpam-3625	129	7	1	1	NUM
ejpam-3625	129	8	and	and	CCONJ
ejpam-3625	129	9	dk1+g(v	dk1+g(v	ADJ
ejpam-3625	129	10	)	)	PUNCT
ejpam-3625	129	11	=	=	SYM
ejpam-3625	129	12	n	n	CCONJ
ejpam-3625	129	13	,	,	PUNCT
ejpam-3625	129	14	none	none	NOUN
ejpam-3625	129	15	of	of	ADP
ejpam-3625	129	16	the	the	DET
ejpam-3625	129	17	elements	element	NOUN
ejpam-3625	129	18	in	in	ADP
ejpam-3625	129	19	s	s	PRON
ejpam-3625	129	20	strongly	strongly	ADV
ejpam-3625	129	21	resolves	resolve	NOUN
ejpam-3625	129	22	z	z	NOUN
ejpam-3625	129	23	and	and	CCONJ
ejpam-3625	129	24	v	v	NOUN
ejpam-3625	129	25	,	,	PUNCT
ejpam-3625	129	26	a	a	DET
ejpam-3625	129	27	contradiction	contradiction	NOUN
ejpam-3625	129	28	.	.	PUNCT
ejpam-3625	130	1	hence	hence	ADV
ejpam-3625	130	2	,	,	PUNCT
ejpam-3625	130	3	z	z	PROPN
ejpam-3625	130	4	∈	∈	PROPN
ejpam-3625	130	5	s.	s.	PROPN
ejpam-3625	130	6	thus	thus	ADV
ejpam-3625	130	7	,	,	PUNCT
ejpam-3625	130	8	s	s	VERB
ejpam-3625	130	9	=	=	PUNCT
ejpam-3625	130	10	(	(	PUNCT
ejpam-3625	130	11	v	v	NOUN
ejpam-3625	130	12	(	(	PUNCT
ejpam-3625	130	13	g	g	NOUN
ejpam-3625	130	14	)	)	PUNCT
ejpam-3625	130	15	\	\	PUNCT
ejpam-3625	131	1	c	c	X
ejpam-3625	131	2	)	)	PUNCT
ejpam-3625	131	3	∪	∪	NOUN
ejpam-3625	131	4	{	{	PUNCT
ejpam-3625	131	5	z	z	NOUN
ejpam-3625	131	6	}	}	PUNCT
ejpam-3625	131	7	.	.	PUNCT
ejpam-3625	132	1	in	in	ADP
ejpam-3625	132	2	addition	addition	NOUN
ejpam-3625	132	3	,	,	PUNCT
ejpam-3625	132	4	since	since	SCONJ
ejpam-3625	132	5	{	{	PUNCT
ejpam-3625	132	6	v	v	NOUN
ejpam-3625	132	7	}	}	PUNCT
ejpam-3625	132	8	is	be	AUX
ejpam-3625	132	9	a	a	DET
ejpam-3625	132	10	superclique	superclique	NOUN
ejpam-3625	132	11	in	in	ADP
ejpam-3625	132	12	k1	k1	NOUN
ejpam-3625	132	13	+	+	CCONJ
ejpam-3625	132	14	g	g	NOUN
ejpam-3625	132	15	,	,	PUNCT
ejpam-3625	132	16	s	s	PART
ejpam-3625	132	17	=	=	PROPN
ejpam-3625	132	18	g.	g.	PROPN
ejpam-3625	132	19	monsanto	monsanto	PROPN
ejpam-3625	132	20	,	,	PUNCT
ejpam-3625	132	21	p.	p.	PROPN
ejpam-3625	132	22	acal	acal	PROPN
ejpam-3625	132	23	,	,	PUNCT
ejpam-3625	132	24	h.	h.	PROPN
ejpam-3625	132	25	rara	rara	PROPN
ejpam-3625	132	26	/	/	SYM
ejpam-3625	132	27	eur	eur	PROPN
ejpam-3625	132	28	.	.	PUNCT
ejpam-3625	133	1	j.	j.	PROPN
ejpam-3625	133	2	pure	pure	PROPN
ejpam-3625	133	3	appl	appl	PROPN
ejpam-3625	133	4	.	.	PROPN
ejpam-3625	133	5	math	math	PROPN
ejpam-3625	133	6	,	,	PUNCT
ejpam-3625	133	7	13	13	NUM
ejpam-3625	133	8	(	(	PUNCT
ejpam-3625	133	9	1	1	NUM
ejpam-3625	133	10	)	)	PUNCT
ejpam-3625	133	11	(	(	PUNCT
ejpam-3625	133	12	2020	2020	NUM
ejpam-3625	133	13	)	)	PUNCT
ejpam-3625	133	14	,	,	PUNCT
ejpam-3625	133	15	170	170	NUM
ejpam-3625	133	16	-	-	SYM
ejpam-3625	133	17	179	179	NUM
ejpam-3625	133	18	174	174	NUM
ejpam-3625	133	19	v	v	NOUN
ejpam-3625	133	20	(	(	PUNCT
ejpam-3625	133	21	k1	k1	NOUN
ejpam-3625	133	22	+	+	PROPN
ejpam-3625	133	23	g	g	NOUN
ejpam-3625	133	24	)	)	PUNCT
ejpam-3625	133	25	\	\	NOUN
ejpam-3625	133	26	{	{	PUNCT
ejpam-3625	133	27	v	v	NOUN
ejpam-3625	133	28	}	}	PUNCT
ejpam-3625	133	29	=	=	SYM
ejpam-3625	133	30	v	v	NOUN
ejpam-3625	133	31	(	(	PUNCT
ejpam-3625	133	32	g	g	NOUN
ejpam-3625	133	33	)	)	PUNCT
ejpam-3625	133	34	.	.	PUNCT
ejpam-3625	134	1	similarly	similarly	ADV
ejpam-3625	134	2	,	,	PUNCT
ejpam-3625	134	3	if	if	SCONJ
ejpam-3625	134	4	c∗	c∗	PROPN
ejpam-3625	134	5	=	=	SYM
ejpam-3625	134	6	v	v	PROPN
ejpam-3625	134	7	(	(	PUNCT
ejpam-3625	134	8	g	g	NOUN
ejpam-3625	134	9	)	)	PUNCT
ejpam-3625	134	10	\s	\s	NOUN
ejpam-3625	134	11	,	,	PUNCT
ejpam-3625	134	12	then	then	ADV
ejpam-3625	134	13	c∗	c∗	PROPN
ejpam-3625	134	14	is	be	AUX
ejpam-3625	134	15	a	a	DET
ejpam-3625	134	16	dominated	dominate	VERB
ejpam-3625	134	17	superclique	superclique	NOUN
ejpam-3625	134	18	in	in	ADP
ejpam-3625	134	19	g.	g.	PROPN
ejpam-3625	134	20	for	for	ADP
ejpam-3625	134	21	the	the	DET
ejpam-3625	134	22	converse	converse	NOUN
ejpam-3625	134	23	,	,	PUNCT
ejpam-3625	134	24	the	the	DET
ejpam-3625	134	25	case	case	NOUN
ejpam-3625	134	26	when	when	SCONJ
ejpam-3625	134	27	s	s	VERB
ejpam-3625	134	28	=	=	SYM
ejpam-3625	134	29	v	v	X
ejpam-3625	134	30	(	(	PUNCT
ejpam-3625	134	31	g	g	NOUN
ejpam-3625	134	32	)	)	PUNCT
ejpam-3625	134	33	is	be	AUX
ejpam-3625	134	34	trivial	trivial	ADJ
ejpam-3625	134	35	.	.	PUNCT
ejpam-3625	135	1	suppose	suppose	VERB
ejpam-3625	135	2	s	s	VERB
ejpam-3625	135	3	=	=	SYM
ejpam-3625	135	4	v	v	PROPN
ejpam-3625	135	5	(	(	PUNCT
ejpam-3625	135	6	k1	k1	NOUN
ejpam-3625	135	7	+	+	CCONJ
ejpam-3625	135	8	g	g	NOUN
ejpam-3625	135	9	)	)	PUNCT
ejpam-3625	135	10	\	\	PUNCT
ejpam-3625	136	1	c	c	X
ejpam-3625	136	2	,	,	PUNCT
ejpam-3625	136	3	where	where	SCONJ
ejpam-3625	136	4	c	c	PROPN
ejpam-3625	136	5	is	be	AUX
ejpam-3625	136	6	a	a	DET
ejpam-3625	136	7	superclique	superclique	NOUN
ejpam-3625	136	8	in	in	ADP
ejpam-3625	136	9	g.	g.	PROPN
ejpam-3625	136	10	let	let	VERB
ejpam-3625	136	11	x	x	PRON
ejpam-3625	136	12	,	,	PUNCT
ejpam-3625	136	13	y	y	PROPN
ejpam-3625	136	14	/∈	/∈	PUNCT
ejpam-3625	137	1	s	s	X
ejpam-3625	137	2	,	,	PUNCT
ejpam-3625	137	3	x	x	SYM
ejpam-3625	137	4	6=	6=	ADP
ejpam-3625	137	5	y.	y.	NOUN
ejpam-3625	137	6	then	then	ADV
ejpam-3625	137	7	x	x	PRON
ejpam-3625	137	8	,	,	PUNCT
ejpam-3625	137	9	y	y	PROPN
ejpam-3625	137	10	∈	∈	PROPN
ejpam-3625	137	11	c	c	NOUN
ejpam-3625	138	1	and	and	CCONJ
ejpam-3625	138	2	there	there	PRON
ejpam-3625	138	3	exists	exist	VERB
ejpam-3625	138	4	w	w	PROPN
ejpam-3625	138	5	∈	∈	PROPN
ejpam-3625	138	6	v	v	ADP
ejpam-3625	138	7	(	(	PUNCT
ejpam-3625	138	8	g	g	NOUN
ejpam-3625	138	9	)	)	PUNCT
ejpam-3625	138	10	\	\	PUNCT
ejpam-3625	139	1	c	c	NOUN
ejpam-3625	139	2	such	such	ADJ
ejpam-3625	139	3	that	that	SCONJ
ejpam-3625	139	4	xy	xy	PROPN
ejpam-3625	139	5	∈	∈	PROPN
ejpam-3625	139	6	e(g	e(g	PROPN
ejpam-3625	139	7	)	)	PUNCT
ejpam-3625	139	8	and	and	CCONJ
ejpam-3625	139	9	w	w	PROPN
ejpam-3625	139	10	∈	∈	PROPN
ejpam-3625	139	11	ng(x	ng(x	NUM
ejpam-3625	139	12	)	)	PUNCT
ejpam-3625	139	13	\	\	NOUN
ejpam-3625	139	14	ng(y	ng(y	NOUN
ejpam-3625	139	15	)	)	PUNCT
ejpam-3625	139	16	or	or	CCONJ
ejpam-3625	139	17	w	w	PROPN
ejpam-3625	139	18	∈	∈	PROPN
ejpam-3625	139	19	ng(y	ng(y	NOUN
ejpam-3625	139	20	)	)	PUNCT
ejpam-3625	139	21	\	\	NOUN
ejpam-3625	139	22	ng(x	ng(x	NUM
ejpam-3625	139	23	)	)	PUNCT
ejpam-3625	139	24	.	.	PUNCT
ejpam-3625	140	1	by	by	ADP
ejpam-3625	140	2	remark	remark	NOUN
ejpam-3625	140	3	5	5	NUM
ejpam-3625	140	4	,	,	PUNCT
ejpam-3625	140	5	x	x	SYM
ejpam-3625	140	6	∈	∈	NOUN
ejpam-3625	140	7	ik1+g[y	ik1+g[y	NOUN
ejpam-3625	140	8	,	,	PUNCT
ejpam-3625	140	9	w	w	NOUN
ejpam-3625	140	10	]	]	PUNCT
ejpam-3625	140	11	or	or	CCONJ
ejpam-3625	140	12	y	y	PROPN
ejpam-3625	140	13	∈	∈	PROPN
ejpam-3625	140	14	ik1+g[x	ik1+g[x	PROPN
ejpam-3625	140	15	,	,	PUNCT
ejpam-3625	140	16	w	w	PROPN
ejpam-3625	140	17	]	]	X
ejpam-3625	140	18	,	,	PUNCT
ejpam-3625	140	19	showing	show	VERB
ejpam-3625	140	20	that	that	SCONJ
ejpam-3625	140	21	s	s	VERB
ejpam-3625	140	22	is	be	AUX
ejpam-3625	140	23	a	a	DET
ejpam-3625	140	24	strong	strong	ADJ
ejpam-3625	140	25	resolving	resolving	NOUN
ejpam-3625	140	26	dominating	dominating	NOUN
ejpam-3625	140	27	set	set	NOUN
ejpam-3625	140	28	of	of	ADP
ejpam-3625	140	29	k1	k1	PROPN
ejpam-3625	141	1	+	+	PROPN
ejpam-3625	141	2	g.	g.	PROPN
ejpam-3625	141	3	suppose	suppose	VERB
ejpam-3625	141	4	s	s	VERB
ejpam-3625	141	5	=	=	SYM
ejpam-3625	141	6	(	(	PUNCT
ejpam-3625	141	7	v	v	NOUN
ejpam-3625	141	8	(	(	PUNCT
ejpam-3625	141	9	g	g	NOUN
ejpam-3625	141	10	)	)	PUNCT
ejpam-3625	141	11	\	\	PROPN
ejpam-3625	141	12	c∗	c∗	PROPN
ejpam-3625	141	13	)	)	PUNCT
ejpam-3625	141	14	∪	∪	NOUN
ejpam-3625	141	15	{	{	PUNCT
ejpam-3625	141	16	z	z	PROPN
ejpam-3625	141	17	∈	∈	PROPN
ejpam-3625	141	18	c∗	c∗	NOUN
ejpam-3625	141	19	;	;	PUNCT
ejpam-3625	141	20	degg(z	degg(z	PROPN
ejpam-3625	141	21	)	)	PUNCT
ejpam-3625	141	22	=	=	PUNCT
ejpam-3625	141	23	n−	n−	NOUN
ejpam-3625	141	24	1	1	NUM
ejpam-3625	141	25	}	}	PUNCT
ejpam-3625	141	26	,	,	PUNCT
ejpam-3625	141	27	where	where	SCONJ
ejpam-3625	141	28	c∗	c∗	PROPN
ejpam-3625	141	29	is	be	AUX
ejpam-3625	141	30	a	a	DET
ejpam-3625	141	31	dominated	dominate	VERB
ejpam-3625	141	32	superclique	superclique	NOUN
ejpam-3625	141	33	in	in	ADP
ejpam-3625	141	34	g.	g.	PROPN
ejpam-3625	141	35	let	let	VERB
ejpam-3625	141	36	x	x	PRON
ejpam-3625	141	37	,	,	PUNCT
ejpam-3625	141	38	y	y	PROPN
ejpam-3625	141	39	/∈	/∈	PUNCT
ejpam-3625	142	1	s	s	X
ejpam-3625	142	2	,	,	PUNCT
ejpam-3625	142	3	x	x	SYM
ejpam-3625	142	4	6=	6=	ADP
ejpam-3625	142	5	y.	y.	NOUN
ejpam-3625	142	6	then	then	ADV
ejpam-3625	142	7	x	x	PRON
ejpam-3625	142	8	,	,	PUNCT
ejpam-3625	142	9	y	y	PROPN
ejpam-3625	142	10	∈	∈	PROPN
ejpam-3625	142	11	c∗.	c∗.	NOUN
ejpam-3625	142	12	by	by	ADP
ejpam-3625	142	13	the	the	DET
ejpam-3625	142	14	same	same	ADJ
ejpam-3625	142	15	argument	argument	NOUN
ejpam-3625	142	16	above	above	ADV
ejpam-3625	142	17	,	,	PUNCT
ejpam-3625	142	18	there	there	PRON
ejpam-3625	142	19	exists	exist	VERB
ejpam-3625	142	20	w	w	PROPN
ejpam-3625	142	21	∈	∈	PROPN
ejpam-3625	142	22	s	s	VERB
ejpam-3625	142	23	that	that	SCONJ
ejpam-3625	142	24	strongly	strongly	ADV
ejpam-3625	142	25	resolves	resolve	VERB
ejpam-3625	142	26	x	x	PUNCT
ejpam-3625	142	27	and	and	CCONJ
ejpam-3625	142	28	y.	y.	PROPN
ejpam-3625	142	29	now	now	ADV
ejpam-3625	142	30	,	,	PUNCT
ejpam-3625	142	31	consider	consider	VERB
ejpam-3625	142	32	the	the	DET
ejpam-3625	142	33	vertices	vertex	NOUN
ejpam-3625	142	34	x	x	PUNCT
ejpam-3625	142	35	and	and	CCONJ
ejpam-3625	143	1	v.	v.	ADV
ejpam-3625	143	2	since	since	SCONJ
ejpam-3625	143	3	x	x	PROPN
ejpam-3625	143	4	/∈	/∈	PROPN
ejpam-3625	143	5	s	s	NOUN
ejpam-3625	143	6	,	,	PUNCT
ejpam-3625	143	7	then	then	ADV
ejpam-3625	143	8	degg(x	degg(x	NOUN
ejpam-3625	143	9	)	)	PUNCT
ejpam-3625	143	10	<	<	X
ejpam-3625	143	11	n	n	CCONJ
ejpam-3625	143	12	−	−	PROPN
ejpam-3625	143	13	1	1	NUM
ejpam-3625	143	14	.	.	PUNCT
ejpam-3625	144	1	hence	hence	ADV
ejpam-3625	144	2	,	,	PUNCT
ejpam-3625	144	3	there	there	PRON
ejpam-3625	144	4	exists	exist	VERB
ejpam-3625	144	5	z	z	PROPN
ejpam-3625	144	6	∈	∈	PROPN
ejpam-3625	144	7	v	v	ADP
ejpam-3625	144	8	(	(	PUNCT
ejpam-3625	144	9	g	g	NOUN
ejpam-3625	144	10	)	)	PUNCT
ejpam-3625	144	11	such	such	ADJ
ejpam-3625	144	12	that	that	SCONJ
ejpam-3625	144	13	xz	xz	PROPN
ejpam-3625	144	14	/∈	/∈	PUNCT
ejpam-3625	144	15	e(g	e(g	PROPN
ejpam-3625	144	16	)	)	PUNCT
ejpam-3625	144	17	.	.	PUNCT
ejpam-3625	145	1	it	it	PRON
ejpam-3625	145	2	follows	follow	VERB
ejpam-3625	145	3	that	that	SCONJ
ejpam-3625	145	4	v	v	X
ejpam-3625	145	5	∈	∈	PROPN
ejpam-3625	145	6	ik1+g[x	ik1+g[x	NOUN
ejpam-3625	145	7	,	,	PUNCT
ejpam-3625	145	8	z	z	NOUN
ejpam-3625	145	9	]	]	X
ejpam-3625	145	10	.	.	PUNCT
ejpam-3625	146	1	thus	thus	ADV
ejpam-3625	146	2	,	,	PUNCT
ejpam-3625	146	3	s	s	VERB
ejpam-3625	146	4	is	be	AUX
ejpam-3625	146	5	a	a	DET
ejpam-3625	146	6	strong	strong	ADJ
ejpam-3625	146	7	resolving	resolving	NOUN
ejpam-3625	146	8	dominating	dominating	NOUN
ejpam-3625	146	9	set	set	NOUN
ejpam-3625	146	10	of	of	ADP
ejpam-3625	146	11	k1+g	k1+g	PROPN
ejpam-3625	146	12	.	.	PUNCT
ejpam-3625	146	13	corollary	corollary	ADJ
ejpam-3625	147	1	1	1	NUM
ejpam-3625	147	2	.	.	PUNCT
ejpam-3625	148	1	let	let	VERB
ejpam-3625	148	2	pn	pn	VERB
ejpam-3625	148	3	=	=	PUNCT
ejpam-3625	149	1	[	[	X
ejpam-3625	149	2	v1	v1	NOUN
ejpam-3625	149	3	,	,	PUNCT
ejpam-3625	149	4	v2	v2	NOUN
ejpam-3625	149	5	,	,	PUNCT
ejpam-3625	149	6	.	.	PUNCT
ejpam-3625	149	7	.	.	PUNCT
ejpam-3625	149	8	.	.	PUNCT
ejpam-3625	150	1	,	,	PUNCT
ejpam-3625	150	2	vn	vn	X
ejpam-3625	150	3	]	]	PUNCT
ejpam-3625	150	4	and	and	CCONJ
ejpam-3625	150	5	cm	cm	NOUN
ejpam-3625	150	6	=	=	PUNCT
ejpam-3625	151	1	[	[	X
ejpam-3625	151	2	c1	c1	PROPN
ejpam-3625	151	3	,	,	PUNCT
ejpam-3625	151	4	c2	c2	PROPN
ejpam-3625	151	5	,	,	PUNCT
ejpam-3625	151	6	.	.	PUNCT
ejpam-3625	151	7	.	.	PUNCT
ejpam-3625	151	8	.	.	PUNCT
ejpam-3625	152	1	,	,	PUNCT
ejpam-3625	152	2	cm	cm	NOUN
ejpam-3625	152	3	,	,	PUNCT
ejpam-3625	152	4	c1	c1	NOUN
ejpam-3625	152	5	]	]	PUNCT
ejpam-3625	152	6	where	where	SCONJ
ejpam-3625	152	7	n	n	X
ejpam-3625	152	8	,	,	PUNCT
ejpam-3625	152	9	m	m	VERB
ejpam-3625	152	10	≥	≥	NOUN
ejpam-3625	152	11	3	3	NUM
ejpam-3625	152	12	.	.	PUNCT
ejpam-3625	153	1	(	(	PUNCT
ejpam-3625	153	2	i	i	NOUN
ejpam-3625	153	3	)	)	PUNCT
ejpam-3625	153	4	the	the	DET
ejpam-3625	153	5	sets	set	NOUN
ejpam-3625	153	6	v	v	X
ejpam-3625	153	7	(	(	PUNCT
ejpam-3625	153	8	pn	pn	NOUN
ejpam-3625	153	9	)	)	PUNCT
ejpam-3625	153	10	\	\	PROPN
ejpam-3625	153	11	{	{	PUNCT
ejpam-3625	153	12	vi	vi	PROPN
ejpam-3625	153	13	,	,	PUNCT
ejpam-3625	153	14	vi+1	vi+1	PRON
ejpam-3625	153	15	}	}	PUNCT
ejpam-3625	153	16	,	,	PUNCT
ejpam-3625	153	17	for	for	ADP
ejpam-3625	153	18	i	i	PROPN
ejpam-3625	153	19	=	=	NOUN
ejpam-3625	153	20	2	2	NUM
ejpam-3625	153	21	.	.	PUNCT
ejpam-3625	153	22	.	.	PUNCT
ejpam-3625	153	23	.	.	PUNCT
ejpam-3625	154	1	,	,	PUNCT
ejpam-3625	154	2	n−	n−	NOUN
ejpam-3625	154	3	2	2	NUM
ejpam-3625	154	4	are	be	AUX
ejpam-3625	154	5	the	the	DET
ejpam-3625	154	6	strong	strong	ADJ
ejpam-3625	154	7	resolving	resolve	VERB
ejpam-3625	154	8	dominating	dominating	NOUN
ejpam-3625	154	9	sets	set	NOUN
ejpam-3625	154	10	of	of	ADP
ejpam-3625	154	11	〈	〈	PROPN
ejpam-3625	154	12	v〉+	v〉+	PROPN
ejpam-3625	154	13	pn	pn	PROPN
ejpam-3625	154	14	.	.	PUNCT
ejpam-3625	155	1	(	(	PUNCT
ejpam-3625	155	2	ii	ii	X
ejpam-3625	155	3	)	)	PUNCT
ejpam-3625	155	4	the	the	DET
ejpam-3625	155	5	sets	set	NOUN
ejpam-3625	155	6	v	v	X
ejpam-3625	155	7	(	(	PUNCT
ejpam-3625	155	8	cm)\{ci	cm)\{ci	NOUN
ejpam-3625	155	9	,	,	PUNCT
ejpam-3625	155	10	ci+1	ci+1	ADJ
ejpam-3625	155	11	}	}	PUNCT
ejpam-3625	155	12	and	and	CCONJ
ejpam-3625	155	13	v	v	X
ejpam-3625	155	14	(	(	PUNCT
ejpam-3625	155	15	cm)\{c1	cm)\{c1	NOUN
ejpam-3625	155	16	,	,	PUNCT
ejpam-3625	155	17	cm	cm	NOUN
ejpam-3625	155	18	}	}	PUNCT
ejpam-3625	155	19	,	,	PUNCT
ejpam-3625	155	20	for	for	ADP
ejpam-3625	155	21	i	i	PROPN
ejpam-3625	155	22	=	=	SYM
ejpam-3625	155	23	1	1	NUM
ejpam-3625	155	24	,	,	PUNCT
ejpam-3625	155	25	2	2	NUM
ejpam-3625	155	26	.	.	PUNCT
ejpam-3625	155	27	.	.	PUNCT
ejpam-3625	155	28	.	.	PUNCT
ejpam-3625	156	1	,	,	PUNCT
ejpam-3625	156	2	m−1	m−1	PROPN
ejpam-3625	156	3	are	be	AUX
ejpam-3625	156	4	the	the	DET
ejpam-3625	156	5	strong	strong	ADJ
ejpam-3625	156	6	resolving	resolve	VERB
ejpam-3625	156	7	dominating	dominating	NOUN
ejpam-3625	156	8	sets	set	NOUN
ejpam-3625	156	9	of	of	ADP
ejpam-3625	156	10	〈	〈	PROPN
ejpam-3625	156	11	v〉+	v〉+	PROPN
ejpam-3625	156	12	cm	cm	NOUN
ejpam-3625	156	13	.	.	PUNCT
ejpam-3625	157	1	corollary	corollary	ADJ
ejpam-3625	157	2	2	2	NUM
ejpam-3625	157	3	.	.	PUNCT
ejpam-3625	158	1	let	let	VERB
ejpam-3625	158	2	g	g	PRON
ejpam-3625	158	3	be	be	AUX
ejpam-3625	158	4	a	a	DET
ejpam-3625	158	5	nontrivial	nontrivial	ADJ
ejpam-3625	158	6	connected	connect	VERB
ejpam-3625	158	7	graph	graph	NOUN
ejpam-3625	158	8	of	of	ADP
ejpam-3625	158	9	order	order	NOUN
ejpam-3625	158	10	n.	n.	NOUN
ejpam-3625	158	11	then	then	ADV
ejpam-3625	158	12	(	(	PUNCT
ejpam-3625	158	13	i	i	NOUN
ejpam-3625	158	14	)	)	PUNCT
ejpam-3625	158	15	for	for	ADP
ejpam-3625	158	16	γ(g	γ(g	PROPN
ejpam-3625	158	17	)	)	PUNCT
ejpam-3625	159	1	=	=	SYM
ejpam-3625	159	2	1	1	NUM
ejpam-3625	159	3	,	,	PUNCT
ejpam-3625	159	4	we	we	PRON
ejpam-3625	159	5	have	have	VERB
ejpam-3625	159	6	γsr(k1	γsr(k1	PUNCT
ejpam-3625	160	1	+	+	NOUN
ejpam-3625	160	2	g	g	NOUN
ejpam-3625	160	3	)	)	PUNCT
ejpam-3625	160	4	=	=	VERB
ejpam-3625	160	5	n−	n−	NOUN
ejpam-3625	160	6	ωs(g	ωs(g	PUNCT
ejpam-3625	160	7	)	)	PUNCT
ejpam-3625	161	1	+	+	CCONJ
ejpam-3625	161	2	1	1	NUM
ejpam-3625	161	3	;	;	PUNCT
ejpam-3625	161	4	(	(	PUNCT
ejpam-3625	161	5	ii	ii	NOUN
ejpam-3625	161	6	)	)	PUNCT
ejpam-3625	161	7	for	for	ADP
ejpam-3625	161	8	γ(g	γ(g	PROPN
ejpam-3625	161	9	)	)	PUNCT
ejpam-3625	161	10	6=	6=	ADP
ejpam-3625	161	11	1	1	NUM
ejpam-3625	161	12	,	,	PUNCT
ejpam-3625	161	13	we	we	PRON
ejpam-3625	161	14	have	have	VERB
ejpam-3625	161	15	γsr(k1	γsr(k1	PUNCT
ejpam-3625	162	1	+	+	NOUN
ejpam-3625	162	2	g	g	NOUN
ejpam-3625	162	3	)	)	PUNCT
ejpam-3625	163	1	=	=	SYM
ejpam-3625	163	2	min	min	NOUN
ejpam-3625	163	3	{	{	PUNCT
ejpam-3625	163	4	γsr(g	γsr(g	NOUN
ejpam-3625	163	5	)	)	PUNCT
ejpam-3625	163	6	,	,	PUNCT
ejpam-3625	163	7	n−	n−	NOUN
ejpam-3625	163	8	ωs(g	ωs(g	PUNCT
ejpam-3625	163	9	)	)	PUNCT
ejpam-3625	163	10	}	}	PUNCT
ejpam-3625	163	11	.	.	PUNCT
ejpam-3625	164	1	the	the	DET
ejpam-3625	164	2	next	next	ADJ
ejpam-3625	164	3	result	result	NOUN
ejpam-3625	164	4	follows	follow	VERB
ejpam-3625	164	5	from	from	ADP
ejpam-3625	164	6	proposition	proposition	NOUN
ejpam-3625	164	7	3	3	NUM
ejpam-3625	164	8	,	,	PUNCT
ejpam-3625	164	9	theorem	theorem	VERB
ejpam-3625	164	10	1	1	NUM
ejpam-3625	164	11	and	and	CCONJ
ejpam-3625	164	12	theorem	theorem	VERB
ejpam-3625	164	13	2	2	NUM
ejpam-3625	164	14	.	.	PUNCT
ejpam-3625	164	15	corollary	corollary	ADJ
ejpam-3625	164	16	3	3	X
ejpam-3625	164	17	.	.	PUNCT
ejpam-3625	165	1	let	let	VERB
ejpam-3625	165	2	g	g	PRON
ejpam-3625	165	3	be	be	AUX
ejpam-3625	165	4	nontrivial	nontrivial	ADJ
ejpam-3625	165	5	connected	connected	ADJ
ejpam-3625	165	6	graph	graph	NOUN
ejpam-3625	165	7	with	with	ADP
ejpam-3625	165	8	diam(g	diam(g	NOUN
ejpam-3625	165	9	)	)	PUNCT
ejpam-3625	165	10	≤	≤	NOUN
ejpam-3625	165	11	2	2	NUM
ejpam-3625	165	12	.	.	PUNCT
ejpam-3625	166	1	then	then	ADV
ejpam-3625	166	2	(	(	PUNCT
ejpam-3625	166	3	i	i	NOUN
ejpam-3625	166	4	)	)	PUNCT
ejpam-3625	166	5	for	for	ADP
ejpam-3625	166	6	γ(g	γ(g	PROPN
ejpam-3625	166	7	)	)	PUNCT
ejpam-3625	166	8	=	=	SYM
ejpam-3625	166	9	1	1	NUM
ejpam-3625	166	10	,	,	PUNCT
ejpam-3625	166	11	we	we	PRON
ejpam-3625	166	12	have	have	VERB
ejpam-3625	166	13	γsr(k1	γsr(k1	PUNCT
ejpam-3625	167	1	+	+	NOUN
ejpam-3625	167	2	g	g	NOUN
ejpam-3625	167	3	)	)	PUNCT
ejpam-3625	167	4	=	=	SYM
ejpam-3625	167	5	sdim(g	sdim(g	PROPN
ejpam-3625	167	6	)	)	PUNCT
ejpam-3625	167	7	+	+	CCONJ
ejpam-3625	167	8	1	1	NUM
ejpam-3625	167	9	;	;	PUNCT
ejpam-3625	167	10	(	(	PUNCT
ejpam-3625	167	11	ii	ii	NOUN
ejpam-3625	167	12	)	)	PUNCT
ejpam-3625	167	13	for	for	ADP
ejpam-3625	167	14	γ(g	γ(g	PROPN
ejpam-3625	167	15	)	)	PUNCT
ejpam-3625	167	16	6=	6=	ADP
ejpam-3625	167	17	1	1	NUM
ejpam-3625	167	18	,	,	PUNCT
ejpam-3625	167	19	we	we	PRON
ejpam-3625	167	20	have	have	VERB
ejpam-3625	167	21	γsr(k1	γsr(k1	PUNCT
ejpam-3625	168	1	+	+	NOUN
ejpam-3625	168	2	g	g	NOUN
ejpam-3625	168	3	)	)	PUNCT
ejpam-3625	169	1	=	=	SYM
ejpam-3625	169	2	min	min	NOUN
ejpam-3625	169	3	{	{	PUNCT
ejpam-3625	169	4	γsr(g	γsr(g	NOUN
ejpam-3625	169	5	)	)	PUNCT
ejpam-3625	169	6	,	,	PUNCT
ejpam-3625	169	7	sdim(g	sdim(g	PROPN
ejpam-3625	169	8	)	)	PUNCT
ejpam-3625	170	1	+	+	CCONJ
ejpam-3625	170	2	1	1	NUM
ejpam-3625	170	3	}	}	PUNCT
ejpam-3625	170	4	.	.	PUNCT
ejpam-3625	171	1	the	the	DET
ejpam-3625	171	2	following	follow	VERB
ejpam-3625	171	3	theorem	theorem	NOUN
ejpam-3625	171	4	gives	give	VERB
ejpam-3625	171	5	a	a	DET
ejpam-3625	171	6	characterization	characterization	NOUN
ejpam-3625	171	7	of	of	ADP
ejpam-3625	171	8	the	the	DET
ejpam-3625	171	9	strong	strong	ADJ
ejpam-3625	171	10	resolving	resolve	VERB
ejpam-3625	171	11	dominating	dominating	NOUN
ejpam-3625	171	12	sets	set	NOUN
ejpam-3625	171	13	in	in	ADP
ejpam-3625	171	14	the	the	DET
ejpam-3625	171	15	join	join	NOUN
ejpam-3625	171	16	of	of	ADP
ejpam-3625	171	17	k1	k1	PROPN
ejpam-3625	171	18	and	and	CCONJ
ejpam-3625	171	19	a	a	DET
ejpam-3625	171	20	disconnected	disconnected	ADJ
ejpam-3625	171	21	graph	graph	NOUN
ejpam-3625	171	22	g.	g.	NOUN
ejpam-3625	171	23	theorem	theorem	NOUN
ejpam-3625	171	24	3	3	X
ejpam-3625	171	25	.	.	PUNCT
ejpam-3625	172	1	let	let	VERB
ejpam-3625	172	2	k1	k1	NOUN
ejpam-3625	172	3	=	=	PUNCT
ejpam-3625	172	4	〈	〈	PROPN
ejpam-3625	172	5	v	v	NOUN
ejpam-3625	172	6	〉	〉	NOUN
ejpam-3625	172	7	and	and	CCONJ
ejpam-3625	172	8	g	g	PROPN
ejpam-3625	172	9	be	be	AUX
ejpam-3625	172	10	a	a	DET
ejpam-3625	172	11	disconnected	disconnected	ADJ
ejpam-3625	172	12	graph	graph	NOUN
ejpam-3625	172	13	whose	whose	DET
ejpam-3625	172	14	components	component	NOUN
ejpam-3625	172	15	are	be	AUX
ejpam-3625	172	16	gi	gi	ADJ
ejpam-3625	172	17	for	for	ADP
ejpam-3625	172	18	i	i	PROPN
ejpam-3625	172	19	=	=	NOUN
ejpam-3625	172	20	1	1	NUM
ejpam-3625	172	21	,	,	PUNCT
ejpam-3625	172	22	2	2	NUM
ejpam-3625	172	23	,	,	PUNCT
ejpam-3625	172	24	.	.	PUNCT
ejpam-3625	172	25	.	.	PUNCT
ejpam-3625	172	26	.	.	PUNCT
ejpam-3625	173	1	,	,	PUNCT
ejpam-3625	173	2	m.	m.	NOUN
ejpam-3625	173	3	a	a	DET
ejpam-3625	173	4	proper	proper	ADJ
ejpam-3625	173	5	subset	subset	NOUN
ejpam-3625	173	6	s	s	NOUN
ejpam-3625	173	7	of	of	ADP
ejpam-3625	173	8	v	v	NOUN
ejpam-3625	173	9	(	(	PUNCT
ejpam-3625	173	10	k1	k1	NOUN
ejpam-3625	173	11	+	+	CCONJ
ejpam-3625	173	12	g	g	NOUN
ejpam-3625	173	13	)	)	PUNCT
ejpam-3625	173	14	is	be	AUX
ejpam-3625	173	15	a	a	DET
ejpam-3625	173	16	strong	strong	ADJ
ejpam-3625	173	17	resolving	resolving	NOUN
ejpam-3625	173	18	dominating	dominating	NOUN
ejpam-3625	173	19	set	set	NOUN
ejpam-3625	173	20	of	of	ADP
ejpam-3625	173	21	k1	k1	NOUN
ejpam-3625	173	22	+	+	CCONJ
ejpam-3625	173	23	g	g	NOUN
ejpam-3625	173	24	if	if	SCONJ
ejpam-3625	174	1	and	and	CCONJ
ejpam-3625	174	2	only	only	ADV
ejpam-3625	174	3	if	if	SCONJ
ejpam-3625	174	4	s	s	VERB
ejpam-3625	174	5	=	=	SYM
ejpam-3625	174	6	v	v	X
ejpam-3625	174	7	(	(	PUNCT
ejpam-3625	174	8	g	g	NOUN
ejpam-3625	174	9	)	)	PUNCT
ejpam-3625	174	10	or	or	CCONJ
ejpam-3625	174	11	s	s	X
ejpam-3625	174	12	=	=	SYM
ejpam-3625	174	13	v	v	PROPN
ejpam-3625	174	14	(	(	PUNCT
ejpam-3625	174	15	g	g	NOUN
ejpam-3625	174	16	)	)	PUNCT
ejpam-3625	174	17	\	\	NOUN
ejpam-3625	174	18	c∗i	c∗i	PUNCT
ejpam-3625	174	19	or	or	CCONJ
ejpam-3625	174	20	s	s	X
ejpam-3625	174	21	=	=	SYM
ejpam-3625	174	22	v	v	PROPN
ejpam-3625	174	23	(	(	PUNCT
ejpam-3625	174	24	k1	k1	NOUN
ejpam-3625	174	25	+	+	CCONJ
ejpam-3625	174	26	g	g	NOUN
ejpam-3625	174	27	)	)	PUNCT
ejpam-3625	174	28	\	\	PROPN
ejpam-3625	175	1	ci	ci	PROPN
ejpam-3625	175	2	where	where	SCONJ
ejpam-3625	175	3	ci	ci	PROPN
ejpam-3625	175	4	is	be	AUX
ejpam-3625	175	5	a	a	DET
ejpam-3625	175	6	superclique	superclique	NOUN
ejpam-3625	175	7	in	in	ADP
ejpam-3625	175	8	gi	gi	NOUN
ejpam-3625	175	9	,	,	PUNCT
ejpam-3625	175	10	for	for	ADP
ejpam-3625	175	11	i	i	PROPN
ejpam-3625	175	12	=	=	SYM
ejpam-3625	175	13	1	1	NUM
ejpam-3625	175	14	,	,	PUNCT
ejpam-3625	175	15	2	2	NUM
ejpam-3625	175	16	,	,	PUNCT
ejpam-3625	175	17	.	.	PUNCT
ejpam-3625	175	18	.	.	PUNCT
ejpam-3625	176	1	.	.	PUNCT
ejpam-3625	177	1	,	,	PUNCT
ejpam-3625	177	2	m	m	VERB
ejpam-3625	177	3	and	and	CCONJ
ejpam-3625	177	4	c∗i	c∗i	NUM
ejpam-3625	177	5	is	be	AUX
ejpam-3625	177	6	a	a	DET
ejpam-3625	177	7	dominated	dominate	VERB
ejpam-3625	177	8	superclique	superclique	NOUN
ejpam-3625	177	9	of	of	ADP
ejpam-3625	177	10	gi	gi	NOUN
ejpam-3625	177	11	.	.	PUNCT
ejpam-3625	178	1	proof	proof	NOUN
ejpam-3625	178	2	:	:	PUNCT
ejpam-3625	178	3	let	let	VERB
ejpam-3625	178	4	s	s	PRON
ejpam-3625	178	5	be	be	AUX
ejpam-3625	178	6	a	a	DET
ejpam-3625	178	7	strong	strong	ADJ
ejpam-3625	178	8	resolving	resolving	NOUN
ejpam-3625	178	9	dominating	dominating	NOUN
ejpam-3625	178	10	set	set	NOUN
ejpam-3625	178	11	of	of	ADP
ejpam-3625	178	12	k1+g	k1+g	PROPN
ejpam-3625	178	13	.	.	PUNCT
ejpam-3625	178	14	suppose	suppose	VERB
ejpam-3625	178	15	v	v	X
ejpam-3625	178	16	/∈	/∈	PUNCT
ejpam-3625	179	1	s.	s.	PROPN
ejpam-3625	179	2	then	then	ADV
ejpam-3625	179	3	s	s	PROPN
ejpam-3625	179	4	(	(	PUNCT
ejpam-3625	179	5	v	v	NOUN
ejpam-3625	179	6	(	(	PUNCT
ejpam-3625	179	7	g	g	NOUN
ejpam-3625	179	8	)	)	PUNCT
ejpam-3625	179	9	.	.	PUNCT
ejpam-3625	180	1	let	let	VERB
ejpam-3625	180	2	ci	ci	NOUN
ejpam-3625	180	3	=	=	VERB
ejpam-3625	180	4	v	v	PROPN
ejpam-3625	180	5	(	(	PUNCT
ejpam-3625	180	6	k1	k1	NOUN
ejpam-3625	180	7	+	+	NOUN
ejpam-3625	180	8	g)\s	g)\s	NOUN
ejpam-3625	180	9	,	,	PUNCT
ejpam-3625	180	10	for	for	ADP
ejpam-3625	180	11	i	i	PROPN
ejpam-3625	180	12	=	=	SYM
ejpam-3625	180	13	1	1	NUM
ejpam-3625	180	14	,	,	PUNCT
ejpam-3625	180	15	2	2	NUM
ejpam-3625	180	16	,	,	PUNCT
ejpam-3625	180	17	.	.	PUNCT
ejpam-3625	180	18	.	.	PUNCT
ejpam-3625	181	1	.	.	PUNCT
ejpam-3625	182	1	,	,	PUNCT
ejpam-3625	182	2	m.	m.	NOUN
ejpam-3625	182	3	then	then	ADV
ejpam-3625	182	4	s	s	VERB
ejpam-3625	182	5	=	=	SYM
ejpam-3625	182	6	v	v	PROPN
ejpam-3625	182	7	(	(	PUNCT
ejpam-3625	182	8	k1	k1	NOUN
ejpam-3625	182	9	+	+	PROPN
ejpam-3625	182	10	g)\ci	g)\ci	PROPN
ejpam-3625	182	11	=	=	SYM
ejpam-3625	182	12	v	v	PROPN
ejpam-3625	182	13	(	(	PUNCT
ejpam-3625	182	14	g)\ci	g)\ci	PROPN
ejpam-3625	182	15	.	.	PUNCT
ejpam-3625	183	1	let	let	VERB
ejpam-3625	183	2	x	x	PRON
ejpam-3625	183	3	,	,	PUNCT
ejpam-3625	183	4	y	y	PROPN
ejpam-3625	183	5	∈	∈	PROPN
ejpam-3625	183	6	ci	ci	PROPN
ejpam-3625	183	7	,	,	PUNCT
ejpam-3625	183	8	x	x	PROPN
ejpam-3625	183	9	6=	6=	ADP
ejpam-3625	183	10	y.	y.	NOUN
ejpam-3625	183	11	since	since	SCONJ
ejpam-3625	183	12	dk1+g(w	dk1+g(w	PROPN
ejpam-3625	183	13	,	,	PUNCT
ejpam-3625	183	14	x	x	NOUN
ejpam-3625	183	15	)	)	PUNCT
ejpam-3625	183	16	=	=	SYM
ejpam-3625	183	17	dk1+g(w	dk1+g(w	PROPN
ejpam-3625	183	18	,	,	PUNCT
ejpam-3625	183	19	y	y	PROPN
ejpam-3625	183	20	)	)	PUNCT
ejpam-3625	183	21	,	,	PUNCT
ejpam-3625	183	22	for	for	ADP
ejpam-3625	183	23	all	all	DET
ejpam-3625	183	24	w	w	PROPN
ejpam-3625	183	25	∈	∈	PROPN
ejpam-3625	183	26	v	v	ADP
ejpam-3625	183	27	(	(	PUNCT
ejpam-3625	183	28	g	g	NOUN
ejpam-3625	183	29	)	)	PUNCT
ejpam-3625	183	30	\	\	PROPN
ejpam-3625	183	31	v	v	X
ejpam-3625	183	32	(	(	PUNCT
ejpam-3625	183	33	gi	gi	INTJ
ejpam-3625	183	34	)	)	PUNCT
ejpam-3625	183	35	,	,	PUNCT
ejpam-3625	183	36	there	there	PRON
ejpam-3625	183	37	exists	exist	VERB
ejpam-3625	183	38	z	z	PROPN
ejpam-3625	183	39	∈	∈	PROPN
ejpam-3625	183	40	v	v	ADP
ejpam-3625	183	41	(	(	PUNCT
ejpam-3625	183	42	gi	gi	INTJ
ejpam-3625	183	43	)	)	PUNCT
ejpam-3625	183	44	\	\	PROPN
ejpam-3625	183	45	ci	ci	NOUN
ejpam-3625	183	46	such	such	ADJ
ejpam-3625	183	47	that	that	SCONJ
ejpam-3625	183	48	x	x	SYM
ejpam-3625	183	49	∈	∈	PRON
ejpam-3625	183	50	igi	igi	NOUN
ejpam-3625	184	1	[	[	X
ejpam-3625	184	2	y	y	PROPN
ejpam-3625	184	3	,	,	PUNCT
ejpam-3625	184	4	z	z	NOUN
ejpam-3625	184	5	]	]	X
ejpam-3625	184	6	or	or	CCONJ
ejpam-3625	184	7	y	y	PROPN
ejpam-3625	184	8	∈	∈	PROPN
ejpam-3625	184	9	igi	igi	NOUN
ejpam-3625	185	1	[	[	X
ejpam-3625	185	2	x	x	X
ejpam-3625	185	3	,	,	PUNCT
ejpam-3625	185	4	z	z	NOUN
ejpam-3625	185	5	]	]	X
ejpam-3625	185	6	.	.	PUNCT
ejpam-3625	186	1	by	by	ADP
ejpam-3625	186	2	remark	remark	NOUN
ejpam-3625	186	3	5	5	NUM
ejpam-3625	186	4	,	,	PUNCT
ejpam-3625	186	5	g.	g.	PROPN
ejpam-3625	186	6	monsanto	monsanto	PROPN
ejpam-3625	186	7	,	,	PUNCT
ejpam-3625	186	8	p.	p.	PROPN
ejpam-3625	186	9	acal	acal	PROPN
ejpam-3625	186	10	,	,	PUNCT
ejpam-3625	186	11	h.	h.	PROPN
ejpam-3625	186	12	rara	rara	PROPN
ejpam-3625	186	13	/	/	SYM
ejpam-3625	186	14	eur	eur	PROPN
ejpam-3625	186	15	.	.	PUNCT
ejpam-3625	187	1	j.	j.	PROPN
ejpam-3625	187	2	pure	pure	PROPN
ejpam-3625	187	3	appl	appl	PROPN
ejpam-3625	187	4	.	.	PROPN
ejpam-3625	187	5	math	math	PROPN
ejpam-3625	187	6	,	,	PUNCT
ejpam-3625	187	7	13	13	NUM
ejpam-3625	187	8	(	(	PUNCT
ejpam-3625	187	9	1	1	NUM
ejpam-3625	187	10	)	)	PUNCT
ejpam-3625	187	11	(	(	PUNCT
ejpam-3625	187	12	2020	2020	NUM
ejpam-3625	187	13	)	)	PUNCT
ejpam-3625	187	14	,	,	PUNCT
ejpam-3625	187	15	170	170	NUM
ejpam-3625	187	16	-	-	SYM
ejpam-3625	187	17	179	179	NUM
ejpam-3625	187	18	175	175	NUM
ejpam-3625	187	19	x	x	SYM
ejpam-3625	187	20	∈	∈	PROPN
ejpam-3625	187	21	ngi(y	ngi(y	PROPN
ejpam-3625	187	22	)	)	PUNCT
ejpam-3625	187	23	\ngi(z	\ngi(z	NOUN
ejpam-3625	187	24	)	)	PUNCT
ejpam-3625	187	25	or	or	CCONJ
ejpam-3625	187	26	y	y	PROPN
ejpam-3625	187	27	∈	∈	PROPN
ejpam-3625	187	28	ngi(x	ngi(x	PROPN
ejpam-3625	187	29	)	)	PUNCT
ejpam-3625	187	30	\ngi(z	\ngi(z	NOUN
ejpam-3625	187	31	)	)	PUNCT
ejpam-3625	187	32	.	.	PUNCT
ejpam-3625	188	1	thus	thus	ADV
ejpam-3625	188	2	,	,	PUNCT
ejpam-3625	188	3	ci	ci	PROPN
ejpam-3625	188	4	is	be	AUX
ejpam-3625	188	5	a	a	DET
ejpam-3625	188	6	superclique	superclique	NOUN
ejpam-3625	188	7	in	in	ADP
ejpam-3625	188	8	gi	gi	NOUN
ejpam-3625	188	9	.	.	PUNCT
ejpam-3625	189	1	since	since	SCONJ
ejpam-3625	189	2	{	{	PUNCT
ejpam-3625	189	3	v	v	NOUN
ejpam-3625	189	4	}	}	PUNCT
ejpam-3625	189	5	is	be	AUX
ejpam-3625	189	6	a	a	DET
ejpam-3625	189	7	superclique	superclique	NOUN
ejpam-3625	189	8	in	in	ADP
ejpam-3625	189	9	k1	k1	NOUN
ejpam-3625	189	10	+	+	PROPN
ejpam-3625	189	11	g	g	NOUN
ejpam-3625	189	12	,	,	PUNCT
ejpam-3625	189	13	by	by	ADP
ejpam-3625	189	14	proposition	proposition	NOUN
ejpam-3625	189	15	3	3	NUM
ejpam-3625	189	16	,	,	PUNCT
ejpam-3625	189	17	s	s	PART
ejpam-3625	189	18	=	=	PUNCT
ejpam-3625	189	19	(	(	PUNCT
ejpam-3625	189	20	v	v	NOUN
ejpam-3625	189	21	(	(	PUNCT
ejpam-3625	189	22	k1	k1	NOUN
ejpam-3625	189	23	+	+	NOUN
ejpam-3625	189	24	g	g	NOUN
ejpam-3625	189	25	)	)	PUNCT
ejpam-3625	189	26	\	\	NOUN
ejpam-3625	189	27	{	{	PUNCT
ejpam-3625	189	28	v	v	NOUN
ejpam-3625	189	29	}	}	PUNCT
ejpam-3625	189	30	)	)	PUNCT
ejpam-3625	190	1	=	=	SYM
ejpam-3625	190	2	v	v	X
ejpam-3625	190	3	(	(	PUNCT
ejpam-3625	190	4	g	g	NOUN
ejpam-3625	190	5	)	)	PUNCT
ejpam-3625	190	6	.	.	PUNCT
ejpam-3625	191	1	on	on	ADP
ejpam-3625	191	2	the	the	DET
ejpam-3625	191	3	other	other	ADJ
ejpam-3625	191	4	hand	hand	NOUN
ejpam-3625	191	5	,	,	PUNCT
ejpam-3625	191	6	if	if	SCONJ
ejpam-3625	191	7	v	v	NUM
ejpam-3625	191	8	∈	∈	PROPN
ejpam-3625	191	9	s	s	X
ejpam-3625	191	10	and	and	CCONJ
ejpam-3625	191	11	ci	ci	NOUN
ejpam-3625	191	12	=	=	SYM
ejpam-3625	191	13	v	v	PROPN
ejpam-3625	191	14	(	(	PUNCT
ejpam-3625	191	15	k1	k1	NOUN
ejpam-3625	191	16	+	+	CCONJ
ejpam-3625	191	17	g	g	NOUN
ejpam-3625	191	18	)	)	PUNCT
ejpam-3625	191	19	\	\	PROPN
ejpam-3625	192	1	s	s	X
ejpam-3625	192	2	,	,	PUNCT
ejpam-3625	192	3	for	for	ADP
ejpam-3625	192	4	i	i	PROPN
ejpam-3625	192	5	=	=	SYM
ejpam-3625	192	6	1	1	NUM
ejpam-3625	192	7	,	,	PUNCT
ejpam-3625	192	8	2	2	NUM
ejpam-3625	192	9	,	,	PUNCT
ejpam-3625	192	10	.	.	PUNCT
ejpam-3625	192	11	.	.	PUNCT
ejpam-3625	192	12	.	.	PUNCT
ejpam-3625	193	1	,	,	PUNCT
ejpam-3625	193	2	m	m	PROPN
ejpam-3625	193	3	,	,	PUNCT
ejpam-3625	193	4	then	then	ADV
ejpam-3625	193	5	s	s	VERB
ejpam-3625	193	6	=	=	SYM
ejpam-3625	193	7	v	v	PROPN
ejpam-3625	193	8	(	(	PUNCT
ejpam-3625	193	9	k1	k1	NOUN
ejpam-3625	193	10	+	+	CCONJ
ejpam-3625	193	11	g	g	NOUN
ejpam-3625	193	12	)	)	PUNCT
ejpam-3625	193	13	\	\	PROPN
ejpam-3625	193	14	ci	ci	PROPN
ejpam-3625	193	15	,	,	PUNCT
ejpam-3625	193	16	where	where	SCONJ
ejpam-3625	193	17	ci	ci	PROPN
ejpam-3625	193	18	is	be	AUX
ejpam-3625	193	19	a	a	DET
ejpam-3625	193	20	superclique	superclique	NOUN
ejpam-3625	193	21	in	in	ADP
ejpam-3625	193	22	k1	k1	NOUN
ejpam-3625	193	23	+	+	CCONJ
ejpam-3625	193	24	g	g	NOUN
ejpam-3625	193	25	,	,	PUNCT
ejpam-3625	193	26	by	by	ADP
ejpam-3625	193	27	proposition	proposition	NOUN
ejpam-3625	193	28	3	3	NUM
ejpam-3625	193	29	.	.	PUNCT
ejpam-3625	194	1	hence	hence	ADV
ejpam-3625	194	2	,	,	PUNCT
ejpam-3625	194	3	ci	ci	PROPN
ejpam-3625	194	4	is	be	AUX
ejpam-3625	194	5	a	a	DET
ejpam-3625	194	6	superclique	superclique	NOUN
ejpam-3625	194	7	in	in	ADP
ejpam-3625	194	8	gi	gi	NOUN
ejpam-3625	194	9	.	.	PUNCT
ejpam-3625	195	1	similarly	similarly	ADV
ejpam-3625	195	2	,	,	PUNCT
ejpam-3625	195	3	if	if	SCONJ
ejpam-3625	195	4	c∗i	c∗i	NUM
ejpam-3625	195	5	=	=	SYM
ejpam-3625	195	6	v	v	X
ejpam-3625	195	7	(	(	PUNCT
ejpam-3625	195	8	g	g	NOUN
ejpam-3625	195	9	)	)	PUNCT
ejpam-3625	195	10	\	\	PROPN
ejpam-3625	195	11	s	s	PART
ejpam-3625	195	12	for	for	ADP
ejpam-3625	195	13	i	i	PROPN
ejpam-3625	195	14	=	=	SYM
ejpam-3625	195	15	1	1	NUM
ejpam-3625	195	16	,	,	PUNCT
ejpam-3625	195	17	2	2	NUM
ejpam-3625	195	18	,	,	PUNCT
ejpam-3625	195	19	.	.	PUNCT
ejpam-3625	195	20	.	.	PUNCT
ejpam-3625	195	21	.	.	PUNCT
ejpam-3625	196	1	,	,	PUNCT
ejpam-3625	196	2	m	m	VERB
ejpam-3625	196	3	where	where	SCONJ
ejpam-3625	196	4	c∗i	c∗i	VERB
ejpam-3625	196	5	is	be	AUX
ejpam-3625	196	6	a	a	DET
ejpam-3625	196	7	dominated	dominate	VERB
ejpam-3625	196	8	superclique	superclique	NOUN
ejpam-3625	196	9	of	of	ADP
ejpam-3625	196	10	gi	gi	NOUN
ejpam-3625	196	11	and	and	CCONJ
ejpam-3625	196	12	since	since	SCONJ
ejpam-3625	196	13	s	s	NOUN
ejpam-3625	196	14	is	be	AUX
ejpam-3625	196	15	dominating	dominate	VERB
ejpam-3625	196	16	,	,	PUNCT
ejpam-3625	196	17	then	then	ADV
ejpam-3625	196	18	v	v	X
ejpam-3625	196	19	(	(	PUNCT
ejpam-3625	196	20	gi	gi	INTJ
ejpam-3625	196	21	)	)	PUNCT
ejpam-3625	196	22	\	\	NOUN
ejpam-3625	196	23	c∗i	c∗i	NUM
ejpam-3625	196	24	is	be	AUX
ejpam-3625	196	25	a	a	DET
ejpam-3625	196	26	dominating	dominating	NOUN
ejpam-3625	196	27	set	set	NOUN
ejpam-3625	196	28	of	of	ADP
ejpam-3625	196	29	gi	gi	PROPN
ejpam-3625	196	30	.	.	PUNCT
ejpam-3625	197	1	for	for	ADP
ejpam-3625	197	2	the	the	DET
ejpam-3625	197	3	converse	converse	NOUN
ejpam-3625	197	4	,	,	PUNCT
ejpam-3625	197	5	if	if	SCONJ
ejpam-3625	197	6	s	s	VERB
ejpam-3625	197	7	=	=	SYM
ejpam-3625	197	8	v	v	X
ejpam-3625	197	9	(	(	PUNCT
ejpam-3625	197	10	g	g	NOUN
ejpam-3625	197	11	)	)	PUNCT
ejpam-3625	197	12	,	,	PUNCT
ejpam-3625	197	13	then	then	ADV
ejpam-3625	197	14	we	we	PRON
ejpam-3625	197	15	are	be	AUX
ejpam-3625	197	16	done	do	VERB
ejpam-3625	197	17	.	.	PUNCT
ejpam-3625	198	1	suppose	suppose	VERB
ejpam-3625	198	2	s	s	VERB
ejpam-3625	198	3	=	=	SYM
ejpam-3625	198	4	v	v	PROPN
ejpam-3625	198	5	(	(	PUNCT
ejpam-3625	198	6	g	g	NOUN
ejpam-3625	198	7	)	)	PUNCT
ejpam-3625	198	8	\	\	NOUN
ejpam-3625	198	9	c∗i	c∗i	PUNCT
ejpam-3625	198	10	,	,	PUNCT
ejpam-3625	198	11	or	or	CCONJ
ejpam-3625	198	12	s	s	NOUN
ejpam-3625	198	13	=	=	SYM
ejpam-3625	198	14	v	v	PROPN
ejpam-3625	198	15	(	(	PUNCT
ejpam-3625	198	16	k1	k1	NOUN
ejpam-3625	198	17	+	+	PROPN
ejpam-3625	198	18	g)\ci	g)\ci	PROPN
ejpam-3625	198	19	,	,	PUNCT
ejpam-3625	198	20	where	where	SCONJ
ejpam-3625	198	21	ci	ci	PROPN
ejpam-3625	198	22	and	and	CCONJ
ejpam-3625	198	23	c∗i	c∗i	NUM
ejpam-3625	198	24	are	be	AUX
ejpam-3625	198	25	superclique	superclique	ADJ
ejpam-3625	198	26	and	and	CCONJ
ejpam-3625	198	27	dominated	dominate	VERB
ejpam-3625	198	28	superclique	superclique	NOUN
ejpam-3625	198	29	,	,	PUNCT
ejpam-3625	198	30	respectively	respectively	ADV
ejpam-3625	198	31	,	,	PUNCT
ejpam-3625	198	32	in	in	ADP
ejpam-3625	198	33	gi	gi	NOUN
ejpam-3625	198	34	for	for	ADP
ejpam-3625	198	35	i	i	PRON
ejpam-3625	198	36	=	=	NOUN
ejpam-3625	198	37	1	1	NUM
ejpam-3625	198	38	,	,	PUNCT
ejpam-3625	198	39	2	2	NUM
ejpam-3625	198	40	,	,	PUNCT
ejpam-3625	198	41	.	.	PUNCT
ejpam-3625	198	42	.	.	PUNCT
ejpam-3625	199	1	.	.	PUNCT
ejpam-3625	200	1	,	,	PUNCT
ejpam-3625	200	2	m.	m.	NOUN
ejpam-3625	200	3	then	then	ADV
ejpam-3625	200	4	by	by	ADP
ejpam-3625	200	5	theorem	theorem	NOUN
ejpam-3625	200	6	1	1	NUM
ejpam-3625	200	7	and	and	CCONJ
ejpam-3625	200	8	theorem	theorem	VERB
ejpam-3625	200	9	2	2	NUM
ejpam-3625	200	10	,	,	PUNCT
ejpam-3625	200	11	v	v	PROPN
ejpam-3625	200	12	(	(	PUNCT
ejpam-3625	200	13	gi	gi	NOUN
ejpam-3625	200	14	)	)	PUNCT
ejpam-3625	200	15	\	\	NOUN
ejpam-3625	201	1	c∗i	c∗i	NUM
ejpam-3625	201	2	is	be	AUX
ejpam-3625	201	3	a	a	DET
ejpam-3625	201	4	strong	strong	ADJ
ejpam-3625	201	5	resolving	resolving	NOUN
ejpam-3625	201	6	dominating	dominating	NOUN
ejpam-3625	201	7	set	set	NOUN
ejpam-3625	201	8	of	of	ADP
ejpam-3625	201	9	k1	k1	PROPN
ejpam-3625	201	10	+	+	CCONJ
ejpam-3625	201	11	gi	gi	NOUN
ejpam-3625	201	12	.	.	PUNCT
ejpam-3625	202	1	by	by	ADP
ejpam-3625	202	2	remark	remark	NOUN
ejpam-3625	202	3	4	4	NUM
ejpam-3625	202	4	,	,	PUNCT
ejpam-3625	202	5	s	s	PART
ejpam-3625	202	6	=	=	SYM
ejpam-3625	202	7	v	v	PROPN
ejpam-3625	202	8	(	(	PUNCT
ejpam-3625	202	9	k1	k1	NOUN
ejpam-3625	202	10	+	+	CCONJ
ejpam-3625	202	11	g	g	NOUN
ejpam-3625	202	12	)	)	PUNCT
ejpam-3625	202	13	\	\	PROPN
ejpam-3625	202	14	ci	ci	PROPN
ejpam-3625	202	15	is	be	AUX
ejpam-3625	202	16	a	a	DET
ejpam-3625	202	17	strong	strong	ADJ
ejpam-3625	202	18	resolving	resolving	NOUN
ejpam-3625	202	19	dominating	dominating	NOUN
ejpam-3625	202	20	set	set	NOUN
ejpam-3625	202	21	of	of	ADP
ejpam-3625	202	22	k1	k1	PROPN
ejpam-3625	203	1	+	+	PROPN
ejpam-3625	203	2	g.	g.	PROPN
ejpam-3625	203	3	corollary	corollary	NOUN
ejpam-3625	203	4	4	4	NUM
ejpam-3625	203	5	.	.	PUNCT
ejpam-3625	204	1	let	let	VERB
ejpam-3625	204	2	gi	gi	PART
ejpam-3625	204	3	be	be	AUX
ejpam-3625	204	4	connected	connect	VERB
ejpam-3625	204	5	graphs	graph	NOUN
ejpam-3625	204	6	of	of	ADP
ejpam-3625	204	7	orders	order	NOUN
ejpam-3625	204	8	ni	ni	PROPN
ejpam-3625	204	9	and	and	CCONJ
ejpam-3625	204	10	g	g	PROPN
ejpam-3625	204	11	be	be	VERB
ejpam-3625	204	12	a	a	DET
ejpam-3625	204	13	disconnected	disconnected	ADJ
ejpam-3625	204	14	graph	graph	NOUN
ejpam-3625	204	15	whose	whose	DET
ejpam-3625	204	16	components	component	NOUN
ejpam-3625	204	17	are	be	AUX
ejpam-3625	204	18	gi	gi	ADJ
ejpam-3625	204	19	for	for	ADP
ejpam-3625	204	20	i	i	PROPN
ejpam-3625	204	21	=	=	NOUN
ejpam-3625	204	22	1	1	NUM
ejpam-3625	204	23	,	,	PUNCT
ejpam-3625	204	24	2	2	NUM
ejpam-3625	204	25	,	,	PUNCT
ejpam-3625	204	26	.	.	PUNCT
ejpam-3625	204	27	.	.	PUNCT
ejpam-3625	205	1	.	.	PUNCT
ejpam-3625	206	1	,	,	PUNCT
ejpam-3625	206	2	m	m	VERB
ejpam-3625	206	3	and	and	CCONJ
ejpam-3625	206	4	si	si	PROPN
ejpam-3625	206	5	=	=	ADJ
ejpam-3625	206	6	v	v	PROPN
ejpam-3625	206	7	(	(	PUNCT
ejpam-3625	206	8	gi	gi	INTJ
ejpam-3625	206	9	)	)	PUNCT
ejpam-3625	206	10	\ci	\ci	PROPN
ejpam-3625	206	11	where	where	SCONJ
ejpam-3625	206	12	ci	ci	PROPN
ejpam-3625	206	13	is	be	AUX
ejpam-3625	206	14	a	a	DET
ejpam-3625	206	15	maximum	maximum	ADV
ejpam-3625	206	16	dominated	dominate	VERB
ejpam-3625	206	17	superclique	superclique	NOUN
ejpam-3625	206	18	of	of	ADP
ejpam-3625	206	19	gi	gi	NOUN
ejpam-3625	206	20	.	.	PUNCT
ejpam-3625	207	1	then	then	ADV
ejpam-3625	207	2	γsr(k1	γsr(k1	PUNCT
ejpam-3625	208	1	+	+	NOUN
ejpam-3625	208	2	g	g	NOUN
ejpam-3625	208	3	)	)	PUNCT
ejpam-3625	208	4	=	=	PUNCT
ejpam-3625	208	5	m∑	m∑	CCONJ
ejpam-3625	208	6	i=1	i=1	PROPN
ejpam-3625	208	7	ni	ni	PROPN
ejpam-3625	208	8	−max	−max	PRON
ejpam-3625	208	9	{	{	PUNCT
ejpam-3625	208	10	γsr(gi	γsr(gi	NOUN
ejpam-3625	208	11	)	)	PUNCT
ejpam-3625	208	12	,	,	PUNCT
ejpam-3625	208	13	ωds(gi	ωds(gi	NOUN
ejpam-3625	208	14	)	)	PUNCT
ejpam-3625	209	1	+	+	CCONJ
ejpam-3625	209	2	1	1	NUM
ejpam-3625	209	3	∣∣i	∣∣i	ADJ
ejpam-3625	209	4	=	=	SYM
ejpam-3625	209	5	1	1	NUM
ejpam-3625	209	6	,	,	PUNCT
ejpam-3625	209	7	2	2	NUM
ejpam-3625	209	8	,	,	PUNCT
ejpam-3625	209	9	.	.	PUNCT
ejpam-3625	209	10	.	.	PUNCT
ejpam-3625	209	11	.	.	PUNCT
ejpam-3625	210	1	,	,	PUNCT
ejpam-3625	210	2	m	m	VERB
ejpam-3625	210	3	}	}	PUNCT
ejpam-3625	210	4	.	.	PUNCT
ejpam-3625	211	1	in	in	ADP
ejpam-3625	211	2	the	the	DET
ejpam-3625	211	3	join	join	NOUN
ejpam-3625	211	4	of	of	ADP
ejpam-3625	211	5	two	two	NUM
ejpam-3625	211	6	graphs	graph	NOUN
ejpam-3625	211	7	g	g	NOUN
ejpam-3625	211	8	and	and	CCONJ
ejpam-3625	211	9	h	h	NOUN
ejpam-3625	211	10	,	,	PUNCT
ejpam-3625	211	11	the	the	DET
ejpam-3625	211	12	previous	previous	ADJ
ejpam-3625	211	13	results	result	NOUN
ejpam-3625	211	14	have	have	AUX
ejpam-3625	211	15	already	already	ADV
ejpam-3625	211	16	considered	consider	VERB
ejpam-3625	211	17	the	the	DET
ejpam-3625	211	18	case	case	NOUN
ejpam-3625	211	19	when	when	SCONJ
ejpam-3625	211	20	g	g	PROPN
ejpam-3625	211	21	or	or	CCONJ
ejpam-3625	211	22	h	h	NOUN
ejpam-3625	211	23	is	be	AUX
ejpam-3625	211	24	trivial	trivial	ADJ
ejpam-3625	211	25	.	.	PUNCT
ejpam-3625	212	1	hence	hence	ADV
ejpam-3625	212	2	,	,	PUNCT
ejpam-3625	212	3	in	in	ADP
ejpam-3625	212	4	the	the	DET
ejpam-3625	212	5	following	following	NOUN
ejpam-3625	212	6	theorem	theorem	NOUN
ejpam-3625	212	7	,	,	PUNCT
ejpam-3625	212	8	a	a	DET
ejpam-3625	212	9	characterization	characterization	NOUN
ejpam-3625	212	10	of	of	ADP
ejpam-3625	212	11	the	the	DET
ejpam-3625	212	12	strong	strong	ADJ
ejpam-3625	212	13	resolving	resolve	VERB
ejpam-3625	212	14	dominating	dominating	NOUN
ejpam-3625	212	15	sets	set	NOUN
ejpam-3625	212	16	in	in	ADP
ejpam-3625	212	17	the	the	DET
ejpam-3625	212	18	join	join	NOUN
ejpam-3625	212	19	of	of	ADP
ejpam-3625	212	20	nontrivial	nontrivial	ADJ
ejpam-3625	212	21	connected	connect	VERB
ejpam-3625	212	22	graphs	graph	NOUN
ejpam-3625	212	23	g	g	NOUN
ejpam-3625	212	24	and	and	CCONJ
ejpam-3625	212	25	h	h	NOUN
ejpam-3625	212	26	is	be	AUX
ejpam-3625	212	27	considered	consider	VERB
ejpam-3625	212	28	.	.	PUNCT
ejpam-3625	213	1	theorem	theorem	ADJ
ejpam-3625	213	2	4	4	NUM
ejpam-3625	213	3	.	.	PUNCT
ejpam-3625	214	1	let	let	VERB
ejpam-3625	214	2	g	g	NOUN
ejpam-3625	214	3	and	and	CCONJ
ejpam-3625	214	4	h	h	NOUN
ejpam-3625	214	5	be	be	AUX
ejpam-3625	214	6	nontrivial	nontrivial	ADJ
ejpam-3625	214	7	connected	connect	VERB
ejpam-3625	214	8	graphs	graph	NOUN
ejpam-3625	214	9	of	of	ADP
ejpam-3625	214	10	orders	order	NOUN
ejpam-3625	214	11	m	m	VERB
ejpam-3625	214	12	and	and	CCONJ
ejpam-3625	214	13	n	n	CCONJ
ejpam-3625	214	14	,	,	PUNCT
ejpam-3625	214	15	respectively	respectively	ADV
ejpam-3625	214	16	.	.	PUNCT
ejpam-3625	215	1	a	a	DET
ejpam-3625	215	2	proper	proper	ADJ
ejpam-3625	215	3	subset	subset	NOUN
ejpam-3625	215	4	s	s	NOUN
ejpam-3625	215	5	of	of	ADP
ejpam-3625	215	6	v	v	NOUN
ejpam-3625	215	7	(	(	PUNCT
ejpam-3625	215	8	g+h	g+h	PROPN
ejpam-3625	215	9	)	)	PUNCT
ejpam-3625	215	10	is	be	AUX
ejpam-3625	215	11	a	a	DET
ejpam-3625	215	12	strong	strong	ADJ
ejpam-3625	215	13	resolving	resolving	NOUN
ejpam-3625	215	14	dominating	dominating	NOUN
ejpam-3625	215	15	set	set	NOUN
ejpam-3625	215	16	of	of	ADP
ejpam-3625	215	17	g+h	g+h	PROPN
ejpam-3625	215	18	if	if	SCONJ
ejpam-3625	215	19	and	and	CCONJ
ejpam-3625	215	20	only	only	ADV
ejpam-3625	215	21	if	if	SCONJ
ejpam-3625	215	22	at	at	ADV
ejpam-3625	215	23	least	least	ADJ
ejpam-3625	215	24	one	one	NUM
ejpam-3625	215	25	of	of	ADP
ejpam-3625	215	26	the	the	DET
ejpam-3625	215	27	following	follow	VERB
ejpam-3625	215	28	is	be	AUX
ejpam-3625	215	29	satisfied	satisfied	ADJ
ejpam-3625	215	30	:	:	PUNCT
ejpam-3625	215	31	(	(	PUNCT
ejpam-3625	215	32	i	i	NOUN
ejpam-3625	215	33	)	)	PUNCT
ejpam-3625	215	34	s	s	PART
ejpam-3625	215	35	=	=	SYM
ejpam-3625	215	36	v	v	PROPN
ejpam-3625	215	37	(	(	PUNCT
ejpam-3625	215	38	g+h	g+h	NOUN
ejpam-3625	215	39	)	)	PUNCT
ejpam-3625	215	40	\	\	PROPN
ejpam-3625	216	1	cg	cg	NOUN
ejpam-3625	216	2	where	where	SCONJ
ejpam-3625	216	3	cg	cg	NOUN
ejpam-3625	216	4	is	be	AUX
ejpam-3625	216	5	a	a	DET
ejpam-3625	216	6	superclique	superclique	NOUN
ejpam-3625	216	7	in	in	ADP
ejpam-3625	216	8	g.	g.	PROPN
ejpam-3625	216	9	(	(	PUNCT
ejpam-3625	216	10	ii	ii	PROPN
ejpam-3625	216	11	)	)	PUNCT
ejpam-3625	216	12	s	s	PART
ejpam-3625	216	13	=	=	SYM
ejpam-3625	216	14	v	v	PROPN
ejpam-3625	216	15	(	(	PUNCT
ejpam-3625	216	16	g+h	g+h	NOUN
ejpam-3625	216	17	)	)	PUNCT
ejpam-3625	216	18	\	\	PROPN
ejpam-3625	217	1	ch	ch	NOUN
ejpam-3625	217	2	where	where	SCONJ
ejpam-3625	217	3	ch	ch	NOUN
ejpam-3625	217	4	is	be	AUX
ejpam-3625	217	5	a	a	DET
ejpam-3625	217	6	superclique	superclique	NOUN
ejpam-3625	217	7	in	in	ADP
ejpam-3625	217	8	h.	h.	PROPN
ejpam-3625	217	9	(	(	PUNCT
ejpam-3625	217	10	iii	iii	X
ejpam-3625	217	11	)	)	PUNCT
ejpam-3625	217	12	if	if	SCONJ
ejpam-3625	217	13	γ(g	γ(g	PROPN
ejpam-3625	217	14	)	)	PUNCT
ejpam-3625	217	15	=	=	SYM
ejpam-3625	217	16	1	1	NUM
ejpam-3625	217	17	and	and	CCONJ
ejpam-3625	217	18	γ(h	γ(h	NOUN
ejpam-3625	217	19	)	)	PUNCT
ejpam-3625	217	20	=	=	SYM
ejpam-3625	217	21	1	1	NUM
ejpam-3625	217	22	,	,	PUNCT
ejpam-3625	217	23	s	s	PART
ejpam-3625	217	24	=	=	PUNCT
ejpam-3625	218	1	[	[	X
ejpam-3625	218	2	v	v	X
ejpam-3625	218	3	(	(	PUNCT
ejpam-3625	218	4	g+h	g+h	NOUN
ejpam-3625	218	5	)	)	PUNCT
ejpam-3625	218	6	\	\	PUNCT
ejpam-3625	219	1	(	(	PUNCT
ejpam-3625	219	2	cg	cg	NOUN
ejpam-3625	219	3	∪	∪	PROPN
ejpam-3625	219	4	ch	ch	NOUN
ejpam-3625	219	5	)	)	PUNCT
ejpam-3625	219	6	]	]	PUNCT
ejpam-3625	219	7	∪	∪	X
ejpam-3625	219	8	{	{	PUNCT
ejpam-3625	219	9	z	z	PROPN
ejpam-3625	219	10	∈	∈	PROPN
ejpam-3625	219	11	cg	cg	NOUN
ejpam-3625	219	12	:	:	PUNCT
ejpam-3625	219	13	degg(z	degg(z	NOUN
ejpam-3625	219	14	)	)	PUNCT
ejpam-3625	220	1	=	=	SYM
ejpam-3625	220	2	m−	m−	PROPN
ejpam-3625	220	3	1	1	NUM
ejpam-3625	220	4	}	}	PUNCT
ejpam-3625	220	5	,	,	PUNCT
ejpam-3625	220	6	or	or	CCONJ
ejpam-3625	220	7	s	s	VERB
ejpam-3625	220	8	=	=	PUNCT
ejpam-3625	221	1	[	[	X
ejpam-3625	221	2	v	v	X
ejpam-3625	221	3	(	(	PUNCT
ejpam-3625	221	4	g+h	g+h	NOUN
ejpam-3625	221	5	)	)	PUNCT
ejpam-3625	221	6	\	\	PUNCT
ejpam-3625	222	1	(	(	PUNCT
ejpam-3625	222	2	cg	cg	NOUN
ejpam-3625	222	3	∪	∪	PROPN
ejpam-3625	222	4	ch	ch	NOUN
ejpam-3625	222	5	)	)	PUNCT
ejpam-3625	222	6	]	]	PUNCT
ejpam-3625	223	1	∪	∪	X
ejpam-3625	223	2	{	{	PUNCT
ejpam-3625	223	3	w	w	PROPN
ejpam-3625	223	4	∈	∈	PROPN
ejpam-3625	223	5	ch	ch	NOUN
ejpam-3625	223	6	:	:	PUNCT
ejpam-3625	223	7	degh(w	degh(w	PROPN
ejpam-3625	223	8	)	)	PUNCT
ejpam-3625	223	9	=	=	PUNCT
ejpam-3625	223	10	n−	n−	NOUN
ejpam-3625	223	11	1	1	NUM
ejpam-3625	223	12	}	}	PUNCT
ejpam-3625	223	13	where	where	SCONJ
ejpam-3625	223	14	cg	cg	NOUN
ejpam-3625	223	15	and	and	CCONJ
ejpam-3625	223	16	ch	ch	NOUN
ejpam-3625	223	17	are	be	AUX
ejpam-3625	223	18	supercliques	superclique	NOUN
ejpam-3625	223	19	in	in	ADP
ejpam-3625	223	20	g	g	PROPN
ejpam-3625	223	21	and	and	CCONJ
ejpam-3625	223	22	h	h	NOUN
ejpam-3625	223	23	,	,	PUNCT
ejpam-3625	223	24	respectively	respectively	ADV
ejpam-3625	223	25	.	.	PUNCT
ejpam-3625	224	1	(	(	PUNCT
ejpam-3625	224	2	iv	iv	X
ejpam-3625	224	3	)	)	PUNCT
ejpam-3625	224	4	if	if	SCONJ
ejpam-3625	224	5	γ(g	γ(g	PROPN
ejpam-3625	224	6	)	)	PUNCT
ejpam-3625	224	7	6=	6=	ADP
ejpam-3625	224	8	1	1	NUM
ejpam-3625	224	9	and	and	CCONJ
ejpam-3625	224	10	γ(h	γ(h	NOUN
ejpam-3625	224	11	)	)	PUNCT
ejpam-3625	224	12	6=	6=	ADP
ejpam-3625	224	13	1	1	NUM
ejpam-3625	224	14	,	,	PUNCT
ejpam-3625	224	15	s	s	VERB
ejpam-3625	224	16	=	=	PUNCT
ejpam-3625	225	1	[	[	X
ejpam-3625	225	2	v	v	X
ejpam-3625	225	3	(	(	PUNCT
ejpam-3625	225	4	g+h	g+h	NOUN
ejpam-3625	225	5	)	)	PUNCT
ejpam-3625	225	6	\	\	PUNCT
ejpam-3625	226	1	(	(	PUNCT
ejpam-3625	226	2	cg	cg	NOUN
ejpam-3625	226	3	∪	∪	PROPN
ejpam-3625	226	4	ch	ch	NOUN
ejpam-3625	226	5	)	)	PUNCT
ejpam-3625	226	6	]	]	PUNCT
ejpam-3625	227	1	=	=	PUNCT
ejpam-3625	227	2	(	(	PUNCT
ejpam-3625	227	3	v	v	NOUN
ejpam-3625	227	4	(	(	PUNCT
ejpam-3625	227	5	g	g	NOUN
ejpam-3625	227	6	)	)	PUNCT
ejpam-3625	227	7	\	\	PROPN
ejpam-3625	227	8	cg	cg	NOUN
ejpam-3625	227	9	)	)	PUNCT
ejpam-3625	227	10	∪	∪	NOUN
ejpam-3625	227	11	(	(	PUNCT
ejpam-3625	227	12	v	v	NOUN
ejpam-3625	227	13	(	(	PUNCT
ejpam-3625	227	14	h	h	NOUN
ejpam-3625	227	15	)	)	PUNCT
ejpam-3625	227	16	\	\	PROPN
ejpam-3625	227	17	ch	ch	NOUN
ejpam-3625	227	18	)	)	PUNCT
ejpam-3625	227	19	,	,	PUNCT
ejpam-3625	227	20	where	where	SCONJ
ejpam-3625	227	21	cg	cg	NOUN
ejpam-3625	227	22	and	and	CCONJ
ejpam-3625	227	23	ch	ch	NOUN
ejpam-3625	227	24	are	be	AUX
ejpam-3625	227	25	supercliques	superclique	NOUN
ejpam-3625	227	26	in	in	ADP
ejpam-3625	227	27	g	g	PROPN
ejpam-3625	227	28	and	and	CCONJ
ejpam-3625	227	29	h	h	NOUN
ejpam-3625	227	30	,	,	PUNCT
ejpam-3625	227	31	respectively	respectively	ADV
ejpam-3625	227	32	.	.	PUNCT
ejpam-3625	228	1	g.	g.	PROPN
ejpam-3625	228	2	monsanto	monsanto	PROPN
ejpam-3625	228	3	,	,	PUNCT
ejpam-3625	228	4	p.	p.	PROPN
ejpam-3625	228	5	acal	acal	PROPN
ejpam-3625	228	6	,	,	PUNCT
ejpam-3625	228	7	h.	h.	PROPN
ejpam-3625	228	8	rara	rara	PROPN
ejpam-3625	228	9	/	/	SYM
ejpam-3625	228	10	eur	eur	PROPN
ejpam-3625	228	11	.	.	PUNCT
ejpam-3625	229	1	j.	j.	PROPN
ejpam-3625	229	2	pure	pure	PROPN
ejpam-3625	229	3	appl	appl	PROPN
ejpam-3625	229	4	.	.	PROPN
ejpam-3625	229	5	math	math	PROPN
ejpam-3625	229	6	,	,	PUNCT
ejpam-3625	229	7	13	13	NUM
ejpam-3625	229	8	(	(	PUNCT
ejpam-3625	229	9	1	1	NUM
ejpam-3625	229	10	)	)	PUNCT
ejpam-3625	229	11	(	(	PUNCT
ejpam-3625	229	12	2020	2020	NUM
ejpam-3625	229	13	)	)	PUNCT
ejpam-3625	229	14	,	,	PUNCT
ejpam-3625	229	15	170	170	NUM
ejpam-3625	229	16	-	-	SYM
ejpam-3625	229	17	179	179	NUM
ejpam-3625	229	18	176	176	NUM
ejpam-3625	229	19	proof	proof	NOUN
ejpam-3625	229	20	:	:	PUNCT
ejpam-3625	229	21	let	let	VERB
ejpam-3625	229	22	s	s	PRON
ejpam-3625	229	23	be	be	AUX
ejpam-3625	229	24	a	a	DET
ejpam-3625	229	25	strong	strong	ADJ
ejpam-3625	229	26	resolving	resolving	NOUN
ejpam-3625	229	27	dominating	dominating	NOUN
ejpam-3625	229	28	set	set	NOUN
ejpam-3625	229	29	of	of	ADP
ejpam-3625	229	30	g+h	g+h	PROPN
ejpam-3625	229	31	.	.	PUNCT
ejpam-3625	230	1	since	since	SCONJ
ejpam-3625	230	2	dg+h(x	dg+h(x	PROPN
ejpam-3625	230	3	,	,	PUNCT
ejpam-3625	230	4	y	y	NOUN
ejpam-3625	230	5	)	)	PUNCT
ejpam-3625	230	6	=	=	SYM
ejpam-3625	230	7	1	1	NUM
ejpam-3625	230	8	,	,	PUNCT
ejpam-3625	230	9	for	for	ADP
ejpam-3625	230	10	each	each	DET
ejpam-3625	230	11	x	x	SYM
ejpam-3625	230	12	∈	∈	PROPN
ejpam-3625	230	13	v	v	ADP
ejpam-3625	230	14	(	(	PUNCT
ejpam-3625	230	15	g	g	NOUN
ejpam-3625	230	16	)	)	PUNCT
ejpam-3625	230	17	and	and	CCONJ
ejpam-3625	230	18	y	y	PROPN
ejpam-3625	230	19	∈	∈	PROPN
ejpam-3625	230	20	v	v	ADP
ejpam-3625	230	21	(	(	PUNCT
ejpam-3625	230	22	h	h	NOUN
ejpam-3625	230	23	)	)	PUNCT
ejpam-3625	230	24	,	,	PUNCT
ejpam-3625	230	25	none	none	NOUN
ejpam-3625	230	26	of	of	ADP
ejpam-3625	230	27	the	the	DET
ejpam-3625	230	28	vertices	vertex	NOUN
ejpam-3625	230	29	in	in	ADP
ejpam-3625	230	30	v	v	ADP
ejpam-3625	230	31	(	(	PUNCT
ejpam-3625	230	32	g	g	NOUN
ejpam-3625	230	33	)	)	PUNCT
ejpam-3625	230	34	and	and	CCONJ
ejpam-3625	230	35	v	v	NOUN
ejpam-3625	230	36	(	(	PUNCT
ejpam-3625	230	37	h	h	NOUN
ejpam-3625	230	38	)	)	PUNCT
ejpam-3625	230	39	strongly	strongly	ADV
ejpam-3625	230	40	resolves	resolve	VERB
ejpam-3625	230	41	any	any	DET
ejpam-3625	230	42	pair	pair	NOUN
ejpam-3625	230	43	of	of	ADP
ejpam-3625	230	44	distinct	distinct	ADJ
ejpam-3625	230	45	vertices	vertex	NOUN
ejpam-3625	230	46	in	in	ADP
ejpam-3625	230	47	v	v	ADP
ejpam-3625	230	48	(	(	PUNCT
ejpam-3625	230	49	h	h	NOUN
ejpam-3625	230	50	)	)	PUNCT
ejpam-3625	230	51	and	and	CCONJ
ejpam-3625	230	52	v	v	X
ejpam-3625	230	53	(	(	PUNCT
ejpam-3625	230	54	g	g	NOUN
ejpam-3625	230	55	)	)	PUNCT
ejpam-3625	230	56	,	,	PUNCT
ejpam-3625	230	57	respectively	respectively	ADV
ejpam-3625	230	58	.	.	PUNCT
ejpam-3625	231	1	thus	thus	ADV
ejpam-3625	231	2	,	,	PUNCT
ejpam-3625	231	3	s	s	AUX
ejpam-3625	231	4	∩	∩	ADJ
ejpam-3625	231	5	v	v	ADJ
ejpam-3625	231	6	(	(	PUNCT
ejpam-3625	231	7	g	g	NOUN
ejpam-3625	231	8	)	)	PUNCT
ejpam-3625	231	9	6=	6=	ADP
ejpam-3625	231	10	∅	∅	NOUN
ejpam-3625	231	11	and	and	CCONJ
ejpam-3625	231	12	s	s	X
ejpam-3625	231	13	∩	∩	ADJ
ejpam-3625	231	14	v	v	ADJ
ejpam-3625	231	15	(	(	PUNCT
ejpam-3625	231	16	h	h	NOUN
ejpam-3625	231	17	)	)	PUNCT
ejpam-3625	231	18	6=	6=	ADP
ejpam-3625	231	19	∅.	∅.	ADP
ejpam-3625	231	20	if	if	SCONJ
ejpam-3625	231	21	s	s	ADP
ejpam-3625	231	22	∩	∩	ADJ
ejpam-3625	231	23	v	v	ADJ
ejpam-3625	231	24	(	(	PUNCT
ejpam-3625	231	25	h	h	NOUN
ejpam-3625	231	26	)	)	PUNCT
ejpam-3625	231	27	=	=	NOUN
ejpam-3625	231	28	v	v	X
ejpam-3625	231	29	(	(	PUNCT
ejpam-3625	231	30	h	h	NOUN
ejpam-3625	231	31	)	)	PUNCT
ejpam-3625	231	32	,	,	PUNCT
ejpam-3625	231	33	then	then	ADV
ejpam-3625	231	34	s	s	PROPN
ejpam-3625	231	35	6=	6=	PROPN
ejpam-3625	231	36	v	v	ADP
ejpam-3625	231	37	(	(	PUNCT
ejpam-3625	231	38	g	g	NOUN
ejpam-3625	231	39	)	)	PUNCT
ejpam-3625	231	40	.	.	PUNCT
ejpam-3625	232	1	let	let	VERB
ejpam-3625	232	2	cg	cg	NOUN
ejpam-3625	232	3	=	=	NOUN
ejpam-3625	232	4	v	v	X
ejpam-3625	232	5	(	(	PUNCT
ejpam-3625	232	6	g	g	NOUN
ejpam-3625	232	7	)	)	PUNCT
ejpam-3625	232	8	\	\	NOUN
ejpam-3625	233	1	s.	s.	PROPN
ejpam-3625	233	2	hence	hence	ADV
ejpam-3625	233	3	,	,	PUNCT
ejpam-3625	233	4	s	s	NOUN
ejpam-3625	233	5	=	=	SYM
ejpam-3625	233	6	v	v	NOUN
ejpam-3625	233	7	(	(	PUNCT
ejpam-3625	233	8	g	g	PROPN
ejpam-3625	233	9	+	+	NOUN
ejpam-3625	233	10	h	h	NOUN
ejpam-3625	233	11	)	)	PUNCT
ejpam-3625	233	12	\	\	PROPN
ejpam-3625	233	13	cg	cg	NOUN
ejpam-3625	233	14	.	.	PUNCT
ejpam-3625	234	1	let	let	VERB
ejpam-3625	234	2	u	u	NOUN
ejpam-3625	234	3	,	,	PUNCT
ejpam-3625	234	4	v	v	PROPN
ejpam-3625	234	5	∈	∈	PROPN
ejpam-3625	234	6	cg	cg	NOUN
ejpam-3625	234	7	,	,	PUNCT
ejpam-3625	234	8	u	u	PROPN
ejpam-3625	234	9	6=	6=	PROPN
ejpam-3625	234	10	v.	v.	CCONJ
ejpam-3625	234	11	then	then	ADV
ejpam-3625	234	12	there	there	PRON
ejpam-3625	234	13	exists	exist	VERB
ejpam-3625	234	14	w	w	PROPN
ejpam-3625	234	15	∈	∈	PROPN
ejpam-3625	234	16	s	s	PART
ejpam-3625	234	17	∩	∩	ADJ
ejpam-3625	234	18	v	v	X
ejpam-3625	234	19	(	(	PUNCT
ejpam-3625	234	20	g	g	NOUN
ejpam-3625	234	21	)	)	PUNCT
ejpam-3625	234	22	such	such	ADJ
ejpam-3625	234	23	that	that	SCONJ
ejpam-3625	234	24	u	u	PROPN
ejpam-3625	234	25	∈	∈	NOUN
ejpam-3625	234	26	ig+h	ig+h	PROPN
ejpam-3625	235	1	[	[	X
ejpam-3625	235	2	v	v	NOUN
ejpam-3625	235	3	,	,	PUNCT
ejpam-3625	235	4	w	w	NOUN
ejpam-3625	235	5	]	]	PUNCT
ejpam-3625	235	6	or	or	CCONJ
ejpam-3625	235	7	v	v	ADP
ejpam-3625	235	8	∈	∈	NOUN
ejpam-3625	235	9	ig+h	ig+h	PROPN
ejpam-3625	235	10	[	[	NOUN
ejpam-3625	235	11	u	u	NOUN
ejpam-3625	235	12	,	,	PUNCT
ejpam-3625	235	13	w	w	NOUN
ejpam-3625	235	14	]	]	PUNCT
ejpam-3625	235	15	.	.	PUNCT
ejpam-3625	236	1	by	by	ADP
ejpam-3625	236	2	remark	remark	NOUN
ejpam-3625	236	3	5	5	NUM
ejpam-3625	236	4	,	,	PUNCT
ejpam-3625	236	5	w	w	PROPN
ejpam-3625	236	6	∈	∈	PROPN
ejpam-3625	236	7	ng(u)\ng(v	ng(u)\ng(v	NOUN
ejpam-3625	236	8	)	)	PUNCT
ejpam-3625	236	9	or	or	CCONJ
ejpam-3625	236	10	w	w	PROPN
ejpam-3625	236	11	∈	∈	PROPN
ejpam-3625	236	12	ng(v)\ng(u	ng(v)\ng(u	ADJ
ejpam-3625	236	13	)	)	PUNCT
ejpam-3625	236	14	.	.	PUNCT
ejpam-3625	237	1	thus	thus	ADV
ejpam-3625	237	2	,	,	PUNCT
ejpam-3625	237	3	cg	cg	NOUN
ejpam-3625	237	4	is	be	AUX
ejpam-3625	237	5	a	a	DET
ejpam-3625	237	6	superclique	superclique	NOUN
ejpam-3625	237	7	in	in	ADP
ejpam-3625	237	8	g.	g.	NOUN
ejpam-3625	237	9	similarly	similarly	ADV
ejpam-3625	237	10	,	,	PUNCT
ejpam-3625	237	11	s	s	VERB
ejpam-3625	237	12	∩	∩	ADJ
ejpam-3625	237	13	v	v	ADJ
ejpam-3625	237	14	(	(	PUNCT
ejpam-3625	237	15	g	g	NOUN
ejpam-3625	237	16	)	)	PUNCT
ejpam-3625	237	17	=	=	NOUN
ejpam-3625	237	18	v	v	X
ejpam-3625	237	19	(	(	PUNCT
ejpam-3625	237	20	g	g	NOUN
ejpam-3625	237	21	)	)	PUNCT
ejpam-3625	237	22	.	.	PUNCT
ejpam-3625	238	1	on	on	ADP
ejpam-3625	238	2	the	the	DET
ejpam-3625	238	3	other	other	ADJ
ejpam-3625	238	4	hand	hand	NOUN
ejpam-3625	238	5	,	,	PUNCT
ejpam-3625	238	6	if	if	SCONJ
ejpam-3625	238	7	s	s	ADP
ejpam-3625	238	8	∩	∩	ADJ
ejpam-3625	238	9	v	v	X
ejpam-3625	238	10	(	(	PUNCT
ejpam-3625	238	11	g	g	NOUN
ejpam-3625	238	12	)	)	PUNCT
ejpam-3625	238	13	6=	6=	ADP
ejpam-3625	238	14	v	v	ADP
ejpam-3625	238	15	(	(	PUNCT
ejpam-3625	238	16	g	g	NOUN
ejpam-3625	238	17	)	)	PUNCT
ejpam-3625	238	18	,	,	PUNCT
ejpam-3625	238	19	s	s	VERB
ejpam-3625	238	20	∩	∩	ADJ
ejpam-3625	238	21	v	v	ADJ
ejpam-3625	238	22	(	(	PUNCT
ejpam-3625	238	23	h	h	NOUN
ejpam-3625	238	24	)	)	PUNCT
ejpam-3625	238	25	6=	6=	ADP
ejpam-3625	238	26	v	v	ADP
ejpam-3625	238	27	(	(	PUNCT
ejpam-3625	238	28	h	h	NOUN
ejpam-3625	238	29	)	)	PUNCT
ejpam-3625	238	30	,	,	PUNCT
ejpam-3625	238	31	cg	cg	NOUN
ejpam-3625	238	32	=	=	SYM
ejpam-3625	238	33	v	v	NOUN
ejpam-3625	238	34	(	(	PUNCT
ejpam-3625	238	35	g	g	NOUN
ejpam-3625	238	36	)	)	PUNCT
ejpam-3625	238	37	\	\	PROPN
ejpam-3625	238	38	s	s	PART
ejpam-3625	238	39	and	and	CCONJ
ejpam-3625	238	40	ch	ch	NOUN
ejpam-3625	238	41	=	=	SYM
ejpam-3625	238	42	v	v	PROPN
ejpam-3625	238	43	(	(	PUNCT
ejpam-3625	238	44	h	h	NOUN
ejpam-3625	238	45	)	)	PUNCT
ejpam-3625	238	46	\	\	PROPN
ejpam-3625	239	1	s	s	X
ejpam-3625	239	2	,	,	PUNCT
ejpam-3625	239	3	then	then	ADV
ejpam-3625	239	4	s	s	VERB
ejpam-3625	239	5	=	=	SYM
ejpam-3625	239	6	v	v	PROPN
ejpam-3625	239	7	(	(	PUNCT
ejpam-3625	239	8	g+h)\	g+h)\	PROPN
ejpam-3625	239	9	(	(	PUNCT
ejpam-3625	239	10	cg∪ch	cg∪ch	PROPN
ejpam-3625	239	11	)	)	PUNCT
ejpam-3625	239	12	.	.	PUNCT
ejpam-3625	240	1	hence	hence	ADV
ejpam-3625	240	2	,	,	PUNCT
ejpam-3625	240	3	cg	cg	NOUN
ejpam-3625	240	4	and	and	CCONJ
ejpam-3625	240	5	ch	ch	NOUN
ejpam-3625	240	6	are	be	AUX
ejpam-3625	240	7	supercliques	superclique	NOUN
ejpam-3625	240	8	in	in	ADP
ejpam-3625	240	9	g	g	PROPN
ejpam-3625	240	10	and	and	CCONJ
ejpam-3625	240	11	h	h	NOUN
ejpam-3625	240	12	,	,	PUNCT
ejpam-3625	240	13	respectively	respectively	ADV
ejpam-3625	240	14	.	.	PUNCT
ejpam-3625	241	1	suppose	suppose	VERB
ejpam-3625	242	1	γ(g	γ(g	NOUN
ejpam-3625	242	2	)	)	PUNCT
ejpam-3625	243	1	=	=	SYM
ejpam-3625	243	2	1	1	NUM
ejpam-3625	243	3	and	and	CCONJ
ejpam-3625	243	4	γ(h	γ(h	NOUN
ejpam-3625	243	5	)	)	PUNCT
ejpam-3625	243	6	=	=	SYM
ejpam-3625	244	1	1	1	X
ejpam-3625	244	2	.	.	X
ejpam-3625	244	3	then	then	ADV
ejpam-3625	244	4	ag	ag	PROPN
ejpam-3625	244	5	=	=	PUNCT
ejpam-3625	244	6	{	{	PUNCT
ejpam-3625	244	7	zg	zg	PROPN
ejpam-3625	244	8	∈	∈	PROPN
ejpam-3625	244	9	v	v	NOUN
ejpam-3625	244	10	(	(	PUNCT
ejpam-3625	244	11	g	g	NOUN
ejpam-3625	244	12	)	)	PUNCT
ejpam-3625	244	13	;	;	PUNCT
ejpam-3625	244	14	degg(z	degg(z	X
ejpam-3625	244	15	)	)	PUNCT
ejpam-3625	244	16	=	=	SYM
ejpam-3625	244	17	m−	m−	PROPN
ejpam-3625	244	18	1	1	NUM
ejpam-3625	244	19	}	}	PUNCT
ejpam-3625	244	20	6=	6=	NUM
ejpam-3625	244	21	∅	∅	NOUN
ejpam-3625	244	22	and	and	CCONJ
ejpam-3625	244	23	ah	ah	INTJ
ejpam-3625	244	24	=	=	X
ejpam-3625	244	25	{	{	PUNCT
ejpam-3625	244	26	zh	zh	X
ejpam-3625	244	27	∈	∈	PROPN
ejpam-3625	244	28	v	v	NOUN
ejpam-3625	244	29	(	(	PUNCT
ejpam-3625	244	30	h	h	NOUN
ejpam-3625	244	31	)	)	PUNCT
ejpam-3625	244	32	;	;	PUNCT
ejpam-3625	244	33	degh(z	degh(z	X
ejpam-3625	244	34	)	)	PUNCT
ejpam-3625	244	35	=	=	SYM
ejpam-3625	244	36	m−	m−	PROPN
ejpam-3625	244	37	1	1	NUM
ejpam-3625	244	38	}	}	PUNCT
ejpam-3625	244	39	6=	6=	ADP
ejpam-3625	244	40	∅.	∅.	ADP
ejpam-3625	244	41	by	by	ADP
ejpam-3625	244	42	proposition	proposition	NOUN
ejpam-3625	244	43	2	2	NUM
ejpam-3625	244	44	,	,	PUNCT
ejpam-3625	244	45	|cg	|cg	NUM
ejpam-3625	244	46	∩	∩	NOUN
ejpam-3625	244	47	ag|	ag|	VERB
ejpam-3625	244	48	≤	≤	NOUN
ejpam-3625	244	49	1	1	NUM
ejpam-3625	244	50	and	and	CCONJ
ejpam-3625	244	51	|ch	|ch	NOUN
ejpam-3625	244	52	∩	∩	NOUN
ejpam-3625	244	53	ah	ah	INTJ
ejpam-3625	244	54	|	|	ADV
ejpam-3625	244	55	≤	≤	ADJ
ejpam-3625	244	56	1	1	NUM
ejpam-3625	244	57	.	.	PUNCT
ejpam-3625	245	1	hence	hence	ADV
ejpam-3625	245	2	,	,	PUNCT
ejpam-3625	245	3	we	we	PRON
ejpam-3625	245	4	may	may	AUX
ejpam-3625	245	5	assume	assume	VERB
ejpam-3625	245	6	that	that	SCONJ
ejpam-3625	245	7	there	there	PRON
ejpam-3625	245	8	exists	exist	VERB
ejpam-3625	245	9	zg	zg	PROPN
ejpam-3625	245	10	∈	∈	PROPN
ejpam-3625	245	11	cg	cg	NOUN
ejpam-3625	245	12	∩	∩	NOUN
ejpam-3625	245	13	ag	ag	PROPN
ejpam-3625	245	14	and	and	CCONJ
ejpam-3625	245	15	zh	zh	PROPN
ejpam-3625	245	16	∈	∈	PROPN
ejpam-3625	245	17	ch	ch	NOUN
ejpam-3625	245	18	∩	∩	PROPN
ejpam-3625	245	19	ah	ah	INTJ
ejpam-3625	245	20	.	.	PUNCT
ejpam-3625	246	1	then	then	ADV
ejpam-3625	246	2	none	none	NOUN
ejpam-3625	246	3	of	of	ADP
ejpam-3625	246	4	the	the	DET
ejpam-3625	246	5	vertices	vertex	NOUN
ejpam-3625	246	6	in	in	ADP
ejpam-3625	246	7	s	s	PART
ejpam-3625	246	8	∩	∩	ADJ
ejpam-3625	246	9	v	v	ADJ
ejpam-3625	246	10	(	(	PUNCT
ejpam-3625	246	11	g	g	NOUN
ejpam-3625	246	12	)	)	PUNCT
ejpam-3625	246	13	and	and	CCONJ
ejpam-3625	246	14	s	s	VERB
ejpam-3625	246	15	∩	∩	ADJ
ejpam-3625	246	16	v	v	ADJ
ejpam-3625	246	17	(	(	PUNCT
ejpam-3625	246	18	h	h	NOUN
ejpam-3625	246	19	)	)	PUNCT
ejpam-3625	246	20	strongly	strongly	ADV
ejpam-3625	246	21	resolves	resolve	VERB
ejpam-3625	246	22	zg	zg	PROPN
ejpam-3625	246	23	and	and	CCONJ
ejpam-3625	246	24	zh	zh	PROPN
ejpam-3625	246	25	,	,	PUNCT
ejpam-3625	246	26	a	a	DET
ejpam-3625	246	27	contradiction	contradiction	NOUN
ejpam-3625	246	28	.	.	PUNCT
ejpam-3625	247	1	thus	thus	ADV
ejpam-3625	247	2	zg	zg	PROPN
ejpam-3625	247	3	∈	∈	PROPN
ejpam-3625	247	4	s	s	PART
ejpam-3625	247	5	or	or	CCONJ
ejpam-3625	247	6	zh	zh	ADP
ejpam-3625	247	7	∈	∈	NOUN
ejpam-3625	247	8	s	s	PART
ejpam-3625	247	9	so	so	ADV
ejpam-3625	247	10	that	that	PRON
ejpam-3625	247	11	s	s	VERB
ejpam-3625	248	1	=	=	PUNCT
ejpam-3625	249	1	[	[	X
ejpam-3625	249	2	v	v	X
ejpam-3625	249	3	(	(	PUNCT
ejpam-3625	249	4	g	g	NOUN
ejpam-3625	249	5	+	+	NOUN
ejpam-3625	249	6	h	h	NOUN
ejpam-3625	249	7	)	)	PUNCT
ejpam-3625	249	8	\	\	PUNCT
ejpam-3625	249	9	(	(	PUNCT
ejpam-3625	249	10	cg	cg	NOUN
ejpam-3625	249	11	∪	∪	PROPN
ejpam-3625	249	12	ch	ch	NOUN
ejpam-3625	249	13	)	)	PUNCT
ejpam-3625	249	14	]	]	PUNCT
ejpam-3625	249	15	∪	∪	X
ejpam-3625	249	16	{	{	PUNCT
ejpam-3625	249	17	z	z	PROPN
ejpam-3625	249	18	∈	∈	PROPN
ejpam-3625	249	19	cg	cg	NOUN
ejpam-3625	249	20	:	:	PUNCT
ejpam-3625	249	21	degg(z	degg(z	NOUN
ejpam-3625	249	22	)	)	PUNCT
ejpam-3625	250	1	=	=	SYM
ejpam-3625	250	2	m−	m−	PROPN
ejpam-3625	250	3	1	1	NUM
ejpam-3625	250	4	}	}	PUNCT
ejpam-3625	250	5	,	,	PUNCT
ejpam-3625	250	6	or	or	CCONJ
ejpam-3625	250	7	s	s	VERB
ejpam-3625	250	8	=	=	PUNCT
ejpam-3625	251	1	[	[	X
ejpam-3625	251	2	v	v	X
ejpam-3625	251	3	(	(	PUNCT
ejpam-3625	251	4	g	g	NOUN
ejpam-3625	251	5	+	+	NOUN
ejpam-3625	251	6	h	h	NOUN
ejpam-3625	251	7	)	)	PUNCT
ejpam-3625	251	8	\	\	PUNCT
ejpam-3625	251	9	(	(	PUNCT
ejpam-3625	251	10	cg	cg	NOUN
ejpam-3625	251	11	∪	∪	PROPN
ejpam-3625	251	12	ch	ch	NOUN
ejpam-3625	251	13	)	)	PUNCT
ejpam-3625	251	14	]	]	PUNCT
ejpam-3625	251	15	∪	∪	X
ejpam-3625	251	16	{	{	PUNCT
ejpam-3625	251	17	w	w	PROPN
ejpam-3625	251	18	∈	∈	PROPN
ejpam-3625	251	19	ch	ch	NOUN
ejpam-3625	251	20	:	:	PUNCT
ejpam-3625	251	21	degh(w	degh(w	PROPN
ejpam-3625	251	22	)	)	PUNCT
ejpam-3625	251	23	=	=	PUNCT
ejpam-3625	251	24	n−	n−	NOUN
ejpam-3625	251	25	1	1	NUM
ejpam-3625	251	26	}	}	PUNCT
ejpam-3625	251	27	.	.	PUNCT
ejpam-3625	252	1	suppose	suppose	VERB
ejpam-3625	252	2	γ(g	γ(g	NOUN
ejpam-3625	252	3	)	)	PUNCT
ejpam-3625	252	4	6=	6=	ADP
ejpam-3625	252	5	1	1	NUM
ejpam-3625	252	6	or	or	CCONJ
ejpam-3625	252	7	γ(h	γ(h	NOUN
ejpam-3625	252	8	)	)	PUNCT
ejpam-3625	252	9	=	=	SYM
ejpam-3625	253	1	1	1	X
ejpam-3625	253	2	.	.	X
ejpam-3625	253	3	then	then	ADV
ejpam-3625	253	4	ag	ag	PROPN
ejpam-3625	253	5	=	=	PROPN
ejpam-3625	253	6	∅	∅	NOUN
ejpam-3625	253	7	or	or	CCONJ
ejpam-3625	253	8	ah	ah	INTJ
ejpam-3625	253	9	=	=	PUNCT
ejpam-3625	253	10	∅.	∅.	VERB
ejpam-3625	253	11	hence	hence	ADV
ejpam-3625	253	12	,	,	PUNCT
ejpam-3625	253	13	s	s	NOUN
ejpam-3625	253	14	=	=	SYM
ejpam-3625	253	15	v	v	PROPN
ejpam-3625	253	16	(	(	PUNCT
ejpam-3625	253	17	g+h	g+h	NOUN
ejpam-3625	253	18	)	)	PUNCT
ejpam-3625	253	19	\	\	PUNCT
ejpam-3625	254	1	(	(	PUNCT
ejpam-3625	254	2	cg	cg	NOUN
ejpam-3625	254	3	∪	∪	PROPN
ejpam-3625	254	4	ch	ch	NOUN
ejpam-3625	254	5	)	)	PUNCT
ejpam-3625	254	6	=	=	PUNCT
ejpam-3625	254	7	(	(	PUNCT
ejpam-3625	254	8	v	v	NOUN
ejpam-3625	254	9	(	(	PUNCT
ejpam-3625	254	10	g	g	NOUN
ejpam-3625	254	11	)	)	PUNCT
ejpam-3625	254	12	\	\	PROPN
ejpam-3625	254	13	cg	cg	NOUN
ejpam-3625	254	14	)	)	PUNCT
ejpam-3625	254	15	∪	∪	NOUN
ejpam-3625	254	16	(	(	PUNCT
ejpam-3625	254	17	v	v	NOUN
ejpam-3625	254	18	(	(	PUNCT
ejpam-3625	254	19	g	g	NOUN
ejpam-3625	254	20	)	)	PUNCT
ejpam-3625	254	21	\	\	PROPN
ejpam-3625	254	22	cg	cg	NOUN
ejpam-3625	254	23	)	)	PUNCT
ejpam-3625	254	24	.	.	PUNCT
ejpam-3625	255	1	conversely	conversely	ADV
ejpam-3625	255	2	,	,	PUNCT
ejpam-3625	255	3	suppose	suppose	VERB
ejpam-3625	255	4	s	s	PRON
ejpam-3625	255	5	satisfies	satisfie	NOUN
ejpam-3625	255	6	condition	condition	NOUN
ejpam-3625	255	7	(	(	PUNCT
ejpam-3625	255	8	i	i	NOUN
ejpam-3625	255	9	)	)	PUNCT
ejpam-3625	255	10	.	.	PUNCT
ejpam-3625	256	1	since	since	SCONJ
ejpam-3625	256	2	cg	cg	NOUN
ejpam-3625	256	3	is	be	AUX
ejpam-3625	256	4	a	a	DET
ejpam-3625	256	5	superclique	superclique	NOUN
ejpam-3625	256	6	in	in	ADP
ejpam-3625	256	7	g	g	NOUN
ejpam-3625	256	8	,	,	PUNCT
ejpam-3625	256	9	there	there	PRON
ejpam-3625	256	10	exists	exist	VERB
ejpam-3625	256	11	w	w	PROPN
ejpam-3625	256	12	∈	∈	PROPN
ejpam-3625	256	13	(	(	PUNCT
ejpam-3625	256	14	v	v	NOUN
ejpam-3625	256	15	(	(	PUNCT
ejpam-3625	256	16	g	g	NOUN
ejpam-3625	256	17	)	)	PUNCT
ejpam-3625	256	18	\cg	\cg	NUM
ejpam-3625	256	19	)	)	PUNCT
ejpam-3625	257	1	⊆	⊆	NUM
ejpam-3625	257	2	s	s	VERB
ejpam-3625	257	3	such	such	ADJ
ejpam-3625	257	4	that	that	SCONJ
ejpam-3625	257	5	u	u	PROPN
ejpam-3625	257	6	∈	∈	PROPN
ejpam-3625	257	7	ig[v	ig[v	PROPN
ejpam-3625	257	8	,	,	PUNCT
ejpam-3625	257	9	w	w	PROPN
ejpam-3625	257	10	]	]	PUNCT
ejpam-3625	257	11	or	or	CCONJ
ejpam-3625	257	12	v	v	ADP
ejpam-3625	257	13	∈	∈	PROPN
ejpam-3625	257	14	ig[u	ig[u	NOUN
ejpam-3625	257	15	,	,	PUNCT
ejpam-3625	257	16	w	w	NOUN
ejpam-3625	257	17	]	]	X
ejpam-3625	257	18	,	,	PUNCT
ejpam-3625	257	19	for	for	ADP
ejpam-3625	257	20	any	any	DET
ejpam-3625	257	21	u	u	NOUN
ejpam-3625	257	22	,	,	PUNCT
ejpam-3625	257	23	v	v	NOUN
ejpam-3625	257	24	/∈	/∈	SYM
ejpam-3625	257	25	s	s	X
ejpam-3625	257	26	,	,	PUNCT
ejpam-3625	257	27	u	u	PROPN
ejpam-3625	257	28	6=	6=	PROPN
ejpam-3625	257	29	v	v	NOUN
ejpam-3625	257	30	,	,	PUNCT
ejpam-3625	257	31	showing	show	VERB
ejpam-3625	257	32	that	that	SCONJ
ejpam-3625	257	33	w	w	NOUN
ejpam-3625	257	34	strongly	strongly	ADV
ejpam-3625	257	35	resolves	resolve	VERB
ejpam-3625	257	36	u	u	NOUN
ejpam-3625	257	37	,	,	PUNCT
ejpam-3625	257	38	v.	v.	ADP
ejpam-3625	257	39	a	a	DET
ejpam-3625	257	40	similar	similar	ADJ
ejpam-3625	257	41	argument	argument	NOUN
ejpam-3625	257	42	applies	apply	VERB
ejpam-3625	257	43	if	if	SCONJ
ejpam-3625	257	44	s	s	PROPN
ejpam-3625	257	45	satisfies	satisfie	NOUN
ejpam-3625	257	46	condition	condition	NOUN
ejpam-3625	257	47	(	(	PUNCT
ejpam-3625	257	48	ii	ii	NOUN
ejpam-3625	257	49	)	)	PUNCT
ejpam-3625	257	50	.	.	PUNCT
ejpam-3625	258	1	suppose	suppose	VERB
ejpam-3625	258	2	s	s	PRON
ejpam-3625	258	3	satisfies	satisfie	NOUN
ejpam-3625	258	4	condition	condition	NOUN
ejpam-3625	258	5	(	(	PUNCT
ejpam-3625	258	6	iii	iii	NOUN
ejpam-3625	258	7	)	)	PUNCT
ejpam-3625	258	8	or	or	CCONJ
ejpam-3625	258	9	(	(	PUNCT
ejpam-3625	258	10	iv	iv	X
ejpam-3625	258	11	)	)	PUNCT
ejpam-3625	258	12	.	.	PUNCT
ejpam-3625	259	1	let	let	VERB
ejpam-3625	259	2	u	u	NOUN
ejpam-3625	259	3	,	,	PUNCT
ejpam-3625	259	4	v	v	NOUN
ejpam-3625	259	5	/∈	/∈	SYM
ejpam-3625	259	6	s	s	X
ejpam-3625	259	7	,	,	PUNCT
ejpam-3625	259	8	u	u	PROPN
ejpam-3625	259	9	6=	6=	PROPN
ejpam-3625	259	10	v.	v.	ADP
ejpam-3625	259	11	if	if	SCONJ
ejpam-3625	259	12	u	u	PROPN
ejpam-3625	259	13	,	,	PUNCT
ejpam-3625	259	14	v	v	PROPN
ejpam-3625	259	15	∈	∈	PROPN
ejpam-3625	259	16	cg	cg	NOUN
ejpam-3625	259	17	or	or	CCONJ
ejpam-3625	259	18	u	u	NOUN
ejpam-3625	259	19	,	,	PUNCT
ejpam-3625	259	20	v	v	PROPN
ejpam-3625	259	21	∈	∈	PROPN
ejpam-3625	259	22	ch	ch	NOUN
ejpam-3625	259	23	,	,	PUNCT
ejpam-3625	259	24	then	then	ADV
ejpam-3625	259	25	we	we	PRON
ejpam-3625	259	26	are	be	AUX
ejpam-3625	259	27	done	do	VERB
ejpam-3625	259	28	.	.	PUNCT
ejpam-3625	260	1	consider	consider	VERB
ejpam-3625	260	2	the	the	DET
ejpam-3625	260	3	pair	pair	NOUN
ejpam-3625	260	4	u	u	NOUN
ejpam-3625	260	5	∈	∈	PROPN
ejpam-3625	260	6	v	v	ADP
ejpam-3625	260	7	(	(	PUNCT
ejpam-3625	260	8	g	g	NOUN
ejpam-3625	260	9	)	)	PUNCT
ejpam-3625	260	10	\	\	PROPN
ejpam-3625	261	1	s	s	PART
ejpam-3625	261	2	and	and	CCONJ
ejpam-3625	261	3	v	v	ADP
ejpam-3625	261	4	∈	∈	PROPN
ejpam-3625	261	5	v	v	NOUN
ejpam-3625	261	6	(	(	PUNCT
ejpam-3625	261	7	h	h	NOUN
ejpam-3625	261	8	)	)	PUNCT
ejpam-3625	261	9	\	\	NOUN
ejpam-3625	261	10	s.	s.	PROPN
ejpam-3625	261	11	since	since	SCONJ
ejpam-3625	261	12	cg	cg	PROPN
ejpam-3625	261	13	is	be	AUX
ejpam-3625	261	14	a	a	DET
ejpam-3625	261	15	superclique	superclique	NOUN
ejpam-3625	261	16	in	in	ADP
ejpam-3625	261	17	g	g	NOUN
ejpam-3625	261	18	,	,	PUNCT
ejpam-3625	261	19	there	there	PRON
ejpam-3625	261	20	exists	exist	VERB
ejpam-3625	261	21	z	z	PROPN
ejpam-3625	261	22	∈	∈	PROPN
ejpam-3625	261	23	(	(	PUNCT
ejpam-3625	261	24	v	v	NOUN
ejpam-3625	261	25	(	(	PUNCT
ejpam-3625	261	26	g	g	NOUN
ejpam-3625	261	27	)	)	PUNCT
ejpam-3625	261	28	\	\	PROPN
ejpam-3625	261	29	cg	cg	NOUN
ejpam-3625	261	30	)	)	PUNCT
ejpam-3625	261	31	⊆	⊆	NUM
ejpam-3625	261	32	s	s	VERB
ejpam-3625	261	33	such	such	ADJ
ejpam-3625	261	34	that	that	SCONJ
ejpam-3625	261	35	z	z	PROPN
ejpam-3625	261	36	∈	∈	PROPN
ejpam-3625	261	37	ng(u	ng(u	NOUN
ejpam-3625	261	38	)	)	PUNCT
ejpam-3625	261	39	\ng(v	\ng(v	NOUN
ejpam-3625	261	40	)	)	PUNCT
ejpam-3625	261	41	or	or	CCONJ
ejpam-3625	261	42	z	z	NOUN
ejpam-3625	261	43	∈	∈	PROPN
ejpam-3625	261	44	ng(v	ng(v	NOUN
ejpam-3625	261	45	)	)	PUNCT
ejpam-3625	261	46	\	\	NOUN
ejpam-3625	261	47	ng(u	ng(u	NOUN
ejpam-3625	261	48	)	)	PUNCT
ejpam-3625	261	49	.	.	PUNCT
ejpam-3625	262	1	hence	hence	ADV
ejpam-3625	262	2	,	,	PUNCT
ejpam-3625	262	3	u	u	PROPN
ejpam-3625	262	4	∈	∈	PROPN
ejpam-3625	262	5	ig[v	ig[v	PROPN
ejpam-3625	262	6	,	,	PUNCT
ejpam-3625	262	7	z	z	X
ejpam-3625	262	8	]	]	X
ejpam-3625	262	9	or	or	CCONJ
ejpam-3625	262	10	v	v	ADP
ejpam-3625	262	11	∈	∈	PROPN
ejpam-3625	262	12	ig[u	ig[u	NOUN
ejpam-3625	262	13	,	,	PUNCT
ejpam-3625	262	14	z	z	NOUN
ejpam-3625	262	15	]	]	X
ejpam-3625	262	16	.	.	PUNCT
ejpam-3625	263	1	thus	thus	ADV
ejpam-3625	263	2	,	,	PUNCT
ejpam-3625	263	3	s	s	VERB
ejpam-3625	263	4	is	be	AUX
ejpam-3625	263	5	a	a	DET
ejpam-3625	263	6	strong	strong	ADJ
ejpam-3625	263	7	resolving	resolving	NOUN
ejpam-3625	263	8	dominating	dominating	NOUN
ejpam-3625	263	9	set	set	NOUN
ejpam-3625	263	10	of	of	ADP
ejpam-3625	263	11	g+h	g+h	PROPN
ejpam-3625	263	12	.	.	PUNCT
ejpam-3625	264	1	corollary	corollary	ADJ
ejpam-3625	264	2	5	5	NUM
ejpam-3625	264	3	.	.	PUNCT
ejpam-3625	265	1	let	let	VERB
ejpam-3625	265	2	g	g	NOUN
ejpam-3625	265	3	and	and	CCONJ
ejpam-3625	265	4	h	h	NOUN
ejpam-3625	265	5	be	be	AUX
ejpam-3625	265	6	nontrivial	nontrivial	ADJ
ejpam-3625	265	7	connected	connect	VERB
ejpam-3625	265	8	graphs	graph	NOUN
ejpam-3625	265	9	of	of	ADP
ejpam-3625	265	10	orders	order	NOUN
ejpam-3625	265	11	m	m	VERB
ejpam-3625	265	12	and	and	CCONJ
ejpam-3625	265	13	n	n	CCONJ
ejpam-3625	265	14	,	,	PUNCT
ejpam-3625	265	15	respectively	respectively	ADV
ejpam-3625	265	16	.	.	PUNCT
ejpam-3625	266	1	then	then	ADV
ejpam-3625	266	2	γsr(g+h	γsr(g+h	VERB
ejpam-3625	266	3	)	)	PUNCT
ejpam-3625	267	1	=	=	PRON
ejpam-3625	267	2	{	{	PUNCT
ejpam-3625	267	3	(	(	PUNCT
ejpam-3625	267	4	m−	m−	PROPN
ejpam-3625	267	5	ωs(g	ωs(g	NUM
ejpam-3625	267	6	)	)	PUNCT
ejpam-3625	267	7	)	)	PUNCT
ejpam-3625	268	1	+	+	CCONJ
ejpam-3625	268	2	(	(	PUNCT
ejpam-3625	268	3	n−	n−	NOUN
ejpam-3625	268	4	ωs(h	ωs(h	NUM
ejpam-3625	268	5	)	)	PUNCT
ejpam-3625	268	6	)	)	PUNCT
ejpam-3625	269	1	+	+	CCONJ
ejpam-3625	269	2	1	1	NUM
ejpam-3625	269	3	,	,	PUNCT
ejpam-3625	269	4	if	if	SCONJ
ejpam-3625	269	5	γ(g	γ(g	PROPN
ejpam-3625	269	6	)	)	PUNCT
ejpam-3625	269	7	=	=	SYM
ejpam-3625	269	8	1	1	NUM
ejpam-3625	269	9	and	and	CCONJ
ejpam-3625	269	10	γ(h	γ(h	NOUN
ejpam-3625	269	11	)	)	PUNCT
ejpam-3625	269	12	=	=	SYM
ejpam-3625	269	13	1	1	X
ejpam-3625	269	14	(	(	PUNCT
ejpam-3625	269	15	m−	m−	PROPN
ejpam-3625	269	16	ωs(g	ωs(g	NUM
ejpam-3625	269	17	)	)	PUNCT
ejpam-3625	269	18	)	)	PUNCT
ejpam-3625	270	1	+	+	CCONJ
ejpam-3625	270	2	(	(	PUNCT
ejpam-3625	270	3	n−	n−	NOUN
ejpam-3625	270	4	ωs(h	ωs(h	NUM
ejpam-3625	270	5	)	)	PUNCT
ejpam-3625	270	6	)	)	PUNCT
ejpam-3625	270	7	,	,	PUNCT
ejpam-3625	270	8	if	if	SCONJ
ejpam-3625	270	9	γ(g	γ(g	PROPN
ejpam-3625	270	10	)	)	PUNCT
ejpam-3625	270	11	6=	6=	ADP
ejpam-3625	270	12	1	1	NUM
ejpam-3625	270	13	or	or	CCONJ
ejpam-3625	270	14	γ(h	γ(h	NOUN
ejpam-3625	270	15	)	)	PUNCT
ejpam-3625	270	16	6=	6=	ADP
ejpam-3625	270	17	1	1	X
ejpam-3625	270	18	.	.	X
ejpam-3625	270	19	remark	remark	NOUN
ejpam-3625	270	20	7	7	NUM
ejpam-3625	270	21	.	.	PUNCT
ejpam-3625	271	1	if	if	SCONJ
ejpam-3625	271	2	g	g	PROPN
ejpam-3625	271	3	is	be	AUX
ejpam-3625	271	4	a	a	DET
ejpam-3625	271	5	nontrivial	nontrivial	ADJ
ejpam-3625	271	6	connected	connect	VERB
ejpam-3625	271	7	graph	graph	NOUN
ejpam-3625	271	8	with	with	ADP
ejpam-3625	271	9	γ(g	γ(g	PROPN
ejpam-3625	271	10	)	)	PUNCT
ejpam-3625	271	11	=	=	SYM
ejpam-3625	271	12	1	1	NUM
ejpam-3625	271	13	,	,	PUNCT
ejpam-3625	271	14	then	then	ADV
ejpam-3625	271	15	diam(g	diam(g	NOUN
ejpam-3625	271	16	)	)	PUNCT
ejpam-3625	271	17	≤	≤	NOUN
ejpam-3625	271	18	2	2	NUM
ejpam-3625	271	19	.	.	PUNCT
ejpam-3625	271	20	corollary	corollary	ADJ
ejpam-3625	271	21	6	6	NUM
ejpam-3625	271	22	.	.	PUNCT
ejpam-3625	272	1	let	let	VERB
ejpam-3625	272	2	g	g	NOUN
ejpam-3625	272	3	and	and	CCONJ
ejpam-3625	272	4	h	h	NOUN
ejpam-3625	272	5	be	be	AUX
ejpam-3625	272	6	nontrivial	nontrivial	ADJ
ejpam-3625	272	7	connected	connect	VERB
ejpam-3625	272	8	graphs	graph	NOUN
ejpam-3625	272	9	with	with	ADP
ejpam-3625	272	10	γ(g	γ(g	PROPN
ejpam-3625	272	11	)	)	PUNCT
ejpam-3625	272	12	=	=	SYM
ejpam-3625	272	13	1	1	NUM
ejpam-3625	272	14	and	and	CCONJ
ejpam-3625	272	15	γ(h	γ(h	NOUN
ejpam-3625	272	16	)	)	PUNCT
ejpam-3625	272	17	=	=	SYM
ejpam-3625	273	1	1	1	X
ejpam-3625	273	2	.	.	PUNCT
ejpam-3625	273	3	then	then	ADV
ejpam-3625	273	4	γsr(g+h	γsr(g+h	VERB
ejpam-3625	273	5	)	)	PUNCT
ejpam-3625	273	6	=	=	SYM
ejpam-3625	273	7	sdim(g	sdim(g	PROPN
ejpam-3625	273	8	)	)	PUNCT
ejpam-3625	273	9	+	+	NUM
ejpam-3625	273	10	sdim(h	sdim(h	NOUN
ejpam-3625	273	11	)	)	PUNCT
ejpam-3625	273	12	+	+	NOUN
ejpam-3625	274	1	1	1	X
ejpam-3625	274	2	.	.	X
ejpam-3625	274	3	in	in	ADP
ejpam-3625	274	4	particular	particular	ADJ
ejpam-3625	274	5	,	,	PUNCT
ejpam-3625	274	6	g.	g.	PROPN
ejpam-3625	274	7	monsanto	monsanto	PROPN
ejpam-3625	274	8	,	,	PUNCT
ejpam-3625	274	9	p.	p.	PROPN
ejpam-3625	274	10	acal	acal	PROPN
ejpam-3625	274	11	,	,	PUNCT
ejpam-3625	274	12	h.	h.	PROPN
ejpam-3625	274	13	rara	rara	PROPN
ejpam-3625	274	14	/	/	SYM
ejpam-3625	274	15	eur	eur	PROPN
ejpam-3625	274	16	.	.	PUNCT
ejpam-3625	275	1	j.	j.	PROPN
ejpam-3625	275	2	pure	pure	PROPN
ejpam-3625	275	3	appl	appl	PROPN
ejpam-3625	275	4	.	.	PROPN
ejpam-3625	275	5	math	math	PROPN
ejpam-3625	275	6	,	,	PUNCT
ejpam-3625	275	7	13	13	NUM
ejpam-3625	275	8	(	(	PUNCT
ejpam-3625	275	9	1	1	NUM
ejpam-3625	275	10	)	)	PUNCT
ejpam-3625	275	11	(	(	PUNCT
ejpam-3625	275	12	2020	2020	NUM
ejpam-3625	275	13	)	)	PUNCT
ejpam-3625	275	14	,	,	PUNCT
ejpam-3625	275	15	170	170	NUM
ejpam-3625	275	16	-	-	SYM
ejpam-3625	275	17	179	179	NUM
ejpam-3625	275	18	177	177	NUM
ejpam-3625	275	19	(	(	PUNCT
ejpam-3625	275	20	i	i	NOUN
ejpam-3625	275	21	)	)	PUNCT
ejpam-3625	275	22	γsr(g+h	γsr(g+h	PROPN
ejpam-3625	275	23	)	)	PUNCT
ejpam-3625	276	1	=	=	SYM
ejpam-3625	276	2	3	3	NUM
ejpam-3625	276	3	for	for	ADP
ejpam-3625	276	4	g	g	NOUN
ejpam-3625	276	5	=	=	SYM
ejpam-3625	276	6	pm	pm	NOUN
ejpam-3625	276	7	and	and	CCONJ
ejpam-3625	276	8	h	h	NOUN
ejpam-3625	276	9	=	=	NOUN
ejpam-3625	276	10	pn	pn	PROPN
ejpam-3625	276	11	(	(	PUNCT
ejpam-3625	276	12	m	m	PROPN
ejpam-3625	276	13	≥	≥	NOUN
ejpam-3625	276	14	2	2	NUM
ejpam-3625	276	15	,	,	PUNCT
ejpam-3625	276	16	n	n	PRON
ejpam-3625	276	17	≥	≥	NOUN
ejpam-3625	276	18	2	2	NUM
ejpam-3625	276	19	)	)	PUNCT
ejpam-3625	276	20	;	;	PUNCT
ejpam-3625	276	21	(	(	PUNCT
ejpam-3625	276	22	ii	ii	NOUN
ejpam-3625	276	23	)	)	PUNCT
ejpam-3625	276	24	γsr(g+h	γsr(g+h	PROPN
ejpam-3625	276	25	)	)	PUNCT
ejpam-3625	277	1	=	=	PUNCT
ejpam-3625	277	2	⌈	⌈	NOUN
ejpam-3625	277	3	n	n	CCONJ
ejpam-3625	277	4	2	2	NUM
ejpam-3625	277	5	⌉	⌉	NOUN
ejpam-3625	277	6	+	+	CCONJ
ejpam-3625	277	7	2	2	NUM
ejpam-3625	277	8	for	for	ADP
ejpam-3625	277	9	g	g	NOUN
ejpam-3625	277	10	=	=	SYM
ejpam-3625	277	11	pm	pm	NOUN
ejpam-3625	277	12	and	and	CCONJ
ejpam-3625	277	13	h	h	NOUN
ejpam-3625	277	14	=	=	SYM
ejpam-3625	277	15	cn	cn	PROPN
ejpam-3625	277	16	(	(	PUNCT
ejpam-3625	277	17	m	m	PROPN
ejpam-3625	277	18	≥	≥	NOUN
ejpam-3625	277	19	2	2	NUM
ejpam-3625	277	20	,	,	PUNCT
ejpam-3625	277	21	n	n	PRON
ejpam-3625	277	22	≥	≥	NOUN
ejpam-3625	277	23	3	3	NUM
ejpam-3625	277	24	)	)	PUNCT
ejpam-3625	277	25	;	;	PUNCT
ejpam-3625	277	26	(	(	PUNCT
ejpam-3625	277	27	iii	iii	X
ejpam-3625	277	28	)	)	PUNCT
ejpam-3625	277	29	γsr(g+h	γsr(g+h	NOUN
ejpam-3625	277	30	)	)	PUNCT
ejpam-3625	278	1	=	=	SYM
ejpam-3625	278	2	4	4	NUM
ejpam-3625	278	3	for	for	ADP
ejpam-3625	278	4	g	g	NOUN
ejpam-3625	278	5	=	=	SYM
ejpam-3625	278	6	cm	cm	NOUN
ejpam-3625	278	7	and	and	CCONJ
ejpam-3625	278	8	h	h	NOUN
ejpam-3625	278	9	=	=	SYM
ejpam-3625	278	10	cn	cn	PROPN
ejpam-3625	278	11	(	(	PUNCT
ejpam-3625	278	12	m	m	PROPN
ejpam-3625	278	13	=	=	SYM
ejpam-3625	278	14	n	n	PROPN
ejpam-3625	278	15	=	=	SYM
ejpam-3625	278	16	3	3	NUM
ejpam-3625	278	17	)	)	PUNCT
ejpam-3625	278	18	(	(	PUNCT
ejpam-3625	278	19	iv	iv	X
ejpam-3625	278	20	)	)	PUNCT
ejpam-3625	278	21	γsr(g+h	γsr(g+h	PROPN
ejpam-3625	278	22	)	)	PUNCT
ejpam-3625	279	1	=	=	PUNCT
ejpam-3625	279	2	⌈	⌈	SYM
ejpam-3625	279	3	m	m	VERB
ejpam-3625	279	4	2	2	NUM
ejpam-3625	279	5	⌉	⌉	NOUN
ejpam-3625	279	6	+	+	CCONJ
ejpam-3625	279	7	⌈	⌈	SYM
ejpam-3625	279	8	n	n	PRON
ejpam-3625	279	9	2	2	NUM
ejpam-3625	279	10	⌉	⌉	NOUN
ejpam-3625	279	11	+	+	CCONJ
ejpam-3625	279	12	1	1	NUM
ejpam-3625	279	13	for	for	ADP
ejpam-3625	279	14	g	g	NOUN
ejpam-3625	279	15	=	=	SYM
ejpam-3625	279	16	cm	cm	NOUN
ejpam-3625	279	17	and	and	CCONJ
ejpam-3625	279	18	h	h	NOUN
ejpam-3625	279	19	=	=	SYM
ejpam-3625	279	20	cn	cn	PROPN
ejpam-3625	279	21	(	(	PUNCT
ejpam-3625	279	22	m	m	PROPN
ejpam-3625	279	23	,	,	PUNCT
ejpam-3625	279	24	n	n	PRON
ejpam-3625	279	25	≥	≥	NOUN
ejpam-3625	279	26	4	4	NUM
ejpam-3625	279	27	)	)	PUNCT
ejpam-3625	279	28	theorem	theorem	NOUN
ejpam-3625	279	29	5	5	NUM
ejpam-3625	279	30	.	.	PUNCT
ejpam-3625	280	1	let	let	VERB
ejpam-3625	280	2	g	g	PRON
ejpam-3625	280	3	be	be	AUX
ejpam-3625	280	4	a	a	DET
ejpam-3625	280	5	disconnected	disconnected	ADJ
ejpam-3625	280	6	graph	graph	NOUN
ejpam-3625	280	7	with	with	ADP
ejpam-3625	280	8	components	component	NOUN
ejpam-3625	280	9	g1	g1	PROPN
ejpam-3625	280	10	,	,	PUNCT
ejpam-3625	280	11	.	.	PUNCT
ejpam-3625	280	12	.	.	PUNCT
ejpam-3625	281	1	.	.	PUNCT
ejpam-3625	282	1	,	,	PUNCT
ejpam-3625	282	2	gn	gn	PROPN
ejpam-3625	282	3	and	and	CCONJ
ejpam-3625	282	4	h	h	DET
ejpam-3625	282	5	a	a	DET
ejpam-3625	282	6	disconnected	disconnected	ADJ
ejpam-3625	282	7	graph	graph	NOUN
ejpam-3625	282	8	with	with	ADP
ejpam-3625	282	9	components	component	NOUN
ejpam-3625	282	10	h1	h1	PROPN
ejpam-3625	282	11	,	,	PUNCT
ejpam-3625	282	12	.	.	PUNCT
ejpam-3625	282	13	.	.	PUNCT
ejpam-3625	283	1	.	.	PUNCT
ejpam-3625	284	1	,	,	PUNCT
ejpam-3625	284	2	hm	hm	INTJ
ejpam-3625	284	3	.	.	PUNCT
ejpam-3625	285	1	a	a	DET
ejpam-3625	285	2	proper	proper	ADJ
ejpam-3625	285	3	subset	subset	NOUN
ejpam-3625	285	4	s	s	NOUN
ejpam-3625	285	5	of	of	ADP
ejpam-3625	285	6	v	v	NOUN
ejpam-3625	285	7	(	(	PUNCT
ejpam-3625	285	8	g+h	g+h	PROPN
ejpam-3625	285	9	)	)	PUNCT
ejpam-3625	285	10	is	be	AUX
ejpam-3625	285	11	a	a	DET
ejpam-3625	285	12	strong	strong	ADJ
ejpam-3625	285	13	resolving	resolving	NOUN
ejpam-3625	285	14	dominating	dominating	NOUN
ejpam-3625	285	15	set	set	NOUN
ejpam-3625	285	16	of	of	ADP
ejpam-3625	285	17	g+h	g+h	PROPN
ejpam-3625	285	18	if	if	SCONJ
ejpam-3625	285	19	and	and	CCONJ
ejpam-3625	285	20	only	only	ADV
ejpam-3625	285	21	if	if	SCONJ
ejpam-3625	285	22	s	s	X
ejpam-3625	285	23	satisfies	satisfy	VERB
ejpam-3625	285	24	any	any	PRON
ejpam-3625	285	25	of	of	ADP
ejpam-3625	285	26	the	the	DET
ejpam-3625	285	27	following	following	NOUN
ejpam-3625	285	28	:	:	PUNCT
ejpam-3625	285	29	(	(	PUNCT
ejpam-3625	285	30	i	i	NOUN
ejpam-3625	285	31	)	)	PUNCT
ejpam-3625	285	32	s	s	PART
ejpam-3625	285	33	=	=	PUNCT
ejpam-3625	285	34	sg	sg	X
ejpam-3625	285	35	∪	∪	ADJ
ejpam-3625	285	36	v	v	PROPN
ejpam-3625	285	37	(	(	PUNCT
ejpam-3625	285	38	h	h	NOUN
ejpam-3625	285	39	)	)	PUNCT
ejpam-3625	285	40	where	where	SCONJ
ejpam-3625	285	41	v	v	X
ejpam-3625	285	42	(	(	PUNCT
ejpam-3625	285	43	g	g	NOUN
ejpam-3625	285	44	)	)	PUNCT
ejpam-3625	286	1	\	\	PROPN
ejpam-3625	287	1	sg	sg	PROPN
ejpam-3625	287	2	is	be	AUX
ejpam-3625	287	3	a	a	DET
ejpam-3625	287	4	superclique	superclique	NOUN
ejpam-3625	287	5	of	of	ADP
ejpam-3625	287	6	gi	gi	NOUN
ejpam-3625	287	7	for	for	ADP
ejpam-3625	287	8	some	some	DET
ejpam-3625	287	9	i	i	PRON
ejpam-3625	287	10	∈	∈	PROPN
ejpam-3625	287	11	{	{	PUNCT
ejpam-3625	287	12	1	1	NUM
ejpam-3625	287	13	,	,	PUNCT
ejpam-3625	287	14	2	2	NUM
ejpam-3625	287	15	,	,	PUNCT
ejpam-3625	287	16	.	.	PUNCT
ejpam-3625	287	17	.	.	PUNCT
ejpam-3625	288	1	.	.	PUNCT
ejpam-3625	289	1	,	,	PUNCT
ejpam-3625	289	2	n	n	CCONJ
ejpam-3625	289	3	}	}	PUNCT
ejpam-3625	289	4	;	;	PUNCT
ejpam-3625	289	5	(	(	PUNCT
ejpam-3625	289	6	ii	ii	NOUN
ejpam-3625	289	7	)	)	PUNCT
ejpam-3625	289	8	s	s	PART
ejpam-3625	290	1	=	=	PUNCT
ejpam-3625	290	2	sh	sh	PROPN
ejpam-3625	290	3	∪	∪	ADP
ejpam-3625	290	4	v	v	NOUN
ejpam-3625	290	5	(	(	PUNCT
ejpam-3625	290	6	g	g	NOUN
ejpam-3625	290	7	)	)	PUNCT
ejpam-3625	290	8	where	where	SCONJ
ejpam-3625	290	9	v	v	X
ejpam-3625	290	10	(	(	PUNCT
ejpam-3625	290	11	h	h	NOUN
ejpam-3625	290	12	)	)	PUNCT
ejpam-3625	290	13	\	\	PUNCT
ejpam-3625	291	1	sh	sh	PROPN
ejpam-3625	291	2	is	be	AUX
ejpam-3625	291	3	a	a	DET
ejpam-3625	291	4	superclique	superclique	NOUN
ejpam-3625	291	5	of	of	ADP
ejpam-3625	291	6	hj	hj	PROPN
ejpam-3625	291	7	for	for	ADP
ejpam-3625	291	8	some	some	DET
ejpam-3625	291	9	j	j	PROPN
ejpam-3625	291	10	∈	∈	PROPN
ejpam-3625	291	11	{	{	PUNCT
ejpam-3625	291	12	1	1	NUM
ejpam-3625	291	13	,	,	PUNCT
ejpam-3625	291	14	2	2	NUM
ejpam-3625	291	15	,	,	PUNCT
ejpam-3625	291	16	.	.	PUNCT
ejpam-3625	291	17	.	.	PUNCT
ejpam-3625	291	18	.	.	PUNCT
ejpam-3625	292	1	,	,	PUNCT
ejpam-3625	292	2	m	m	VERB
ejpam-3625	292	3	}	}	PUNCT
ejpam-3625	292	4	;	;	PUNCT
ejpam-3625	292	5	(	(	PUNCT
ejpam-3625	292	6	iii	iii	X
ejpam-3625	292	7	)	)	PUNCT
ejpam-3625	292	8	s	s	PART
ejpam-3625	292	9	=	=	PUNCT
ejpam-3625	292	10	sg	sg	X
ejpam-3625	292	11	∪	∪	ADJ
ejpam-3625	293	1	sh	sh	PROPN
ejpam-3625	293	2	,	,	PUNCT
ejpam-3625	293	3	where	where	SCONJ
ejpam-3625	293	4	v	v	X
ejpam-3625	293	5	(	(	PUNCT
ejpam-3625	293	6	g	g	NOUN
ejpam-3625	293	7	)	)	PUNCT
ejpam-3625	293	8	\	\	PROPN
ejpam-3625	293	9	sg	sg	NOUN
ejpam-3625	293	10	and	and	CCONJ
ejpam-3625	293	11	v	v	NOUN
ejpam-3625	293	12	(	(	PUNCT
ejpam-3625	293	13	h	h	NOUN
ejpam-3625	293	14	)	)	PUNCT
ejpam-3625	293	15	\	\	PUNCT
ejpam-3625	294	1	sh	sh	PROPN
ejpam-3625	294	2	are	be	AUX
ejpam-3625	294	3	supercliques	superclique	NOUN
ejpam-3625	294	4	of	of	ADP
ejpam-3625	294	5	gi	gi	PROPN
ejpam-3625	294	6	and	and	CCONJ
ejpam-3625	294	7	hj	hj	X
ejpam-3625	294	8	,	,	PUNCT
ejpam-3625	294	9	for	for	ADP
ejpam-3625	294	10	some	some	DET
ejpam-3625	294	11	i	i	PRON
ejpam-3625	294	12	∈	∈	PROPN
ejpam-3625	294	13	{	{	PUNCT
ejpam-3625	294	14	1	1	NUM
ejpam-3625	294	15	,	,	PUNCT
ejpam-3625	294	16	2	2	NUM
ejpam-3625	294	17	,	,	PUNCT
ejpam-3625	294	18	.	.	PUNCT
ejpam-3625	294	19	.	.	PUNCT
ejpam-3625	295	1	.	.	PUNCT
ejpam-3625	296	1	,	,	PUNCT
ejpam-3625	296	2	n	n	CCONJ
ejpam-3625	296	3	}	}	PUNCT
ejpam-3625	296	4	and	and	CCONJ
ejpam-3625	296	5	some	some	DET
ejpam-3625	296	6	j	j	PROPN
ejpam-3625	296	7	∈	∈	PROPN
ejpam-3625	296	8	{	{	PUNCT
ejpam-3625	296	9	1	1	NUM
ejpam-3625	296	10	,	,	PUNCT
ejpam-3625	296	11	2	2	NUM
ejpam-3625	296	12	,	,	PUNCT
ejpam-3625	296	13	.	.	PUNCT
ejpam-3625	296	14	.	.	PUNCT
ejpam-3625	297	1	.	.	PUNCT
ejpam-3625	298	1	,	,	PUNCT
ejpam-3625	298	2	m	m	VERB
ejpam-3625	298	3	}	}	PUNCT
ejpam-3625	298	4	.	.	PUNCT
ejpam-3625	299	1	proof	proof	NOUN
ejpam-3625	299	2	:	:	PUNCT
ejpam-3625	299	3	let	let	VERB
ejpam-3625	299	4	s	s	PRON
ejpam-3625	299	5	be	be	AUX
ejpam-3625	299	6	a	a	DET
ejpam-3625	299	7	strong	strong	ADJ
ejpam-3625	299	8	resolving	resolving	NOUN
ejpam-3625	299	9	dominating	dominating	NOUN
ejpam-3625	299	10	set	set	NOUN
ejpam-3625	299	11	of	of	ADP
ejpam-3625	299	12	g+h	g+h	PROPN
ejpam-3625	299	13	and	and	CCONJ
ejpam-3625	299	14	x	x	PUNCT
ejpam-3625	299	15	∈	∈	NOUN
ejpam-3625	299	16	gi	gi	NOUN
ejpam-3625	299	17	and	and	CCONJ
ejpam-3625	299	18	y	y	PROPN
ejpam-3625	299	19	∈	∈	PROPN
ejpam-3625	299	20	gk	gk	PROPN
ejpam-3625	299	21	,	,	PUNCT
ejpam-3625	299	22	i	i	PROPN
ejpam-3625	299	23	6=	6=	PROPN
ejpam-3625	299	24	k.	k.	PROPN
ejpam-3625	299	25	since	since	SCONJ
ejpam-3625	299	26	dg+h(x	dg+h(x	PROPN
ejpam-3625	299	27	,	,	PUNCT
ejpam-3625	299	28	y	y	NOUN
ejpam-3625	299	29	)	)	PUNCT
ejpam-3625	299	30	=	=	SYM
ejpam-3625	299	31	2	2	NUM
ejpam-3625	299	32	and	and	CCONJ
ejpam-3625	299	33	dg+h(x	dg+h(x	PROPN
ejpam-3625	299	34	,	,	PUNCT
ejpam-3625	299	35	h	h	NOUN
ejpam-3625	299	36	)	)	PUNCT
ejpam-3625	299	37	=	=	PUNCT
ejpam-3625	300	1	dg+h(y	dg+h(y	ADJ
ejpam-3625	300	2	,	,	PUNCT
ejpam-3625	300	3	h	h	NOUN
ejpam-3625	300	4	)	)	PUNCT
ejpam-3625	300	5	=	=	SYM
ejpam-3625	300	6	1	1	NUM
ejpam-3625	300	7	,	,	PUNCT
ejpam-3625	300	8	for	for	ADP
ejpam-3625	300	9	all	all	DET
ejpam-3625	300	10	h	h	NOUN
ejpam-3625	300	11	∈	∈	PROPN
ejpam-3625	300	12	v	v	ADP
ejpam-3625	300	13	(	(	PUNCT
ejpam-3625	300	14	h	h	NOUN
ejpam-3625	300	15	)	)	PUNCT
ejpam-3625	300	16	,	,	PUNCT
ejpam-3625	300	17	then	then	ADV
ejpam-3625	300	18	x	x	X
ejpam-3625	300	19	∈	∈	PROPN
ejpam-3625	300	20	s	s	PART
ejpam-3625	300	21	or	or	CCONJ
ejpam-3625	300	22	y	y	PROPN
ejpam-3625	300	23	∈	∈	PROPN
ejpam-3625	300	24	s.	s.	PROPN
ejpam-3625	300	25	hence	hence	ADV
ejpam-3625	300	26	,	,	PUNCT
ejpam-3625	300	27	s	s	VERB
ejpam-3625	300	28	∩	∩	ADJ
ejpam-3625	300	29	v	v	ADJ
ejpam-3625	300	30	(	(	PUNCT
ejpam-3625	300	31	g	g	NOUN
ejpam-3625	300	32	)	)	PUNCT
ejpam-3625	300	33	=	=	NOUN
ejpam-3625	300	34	∅.	∅.	ADP
ejpam-3625	300	35	similarly	similarly	ADV
ejpam-3625	300	36	,	,	PUNCT
ejpam-3625	300	37	s	s	VERB
ejpam-3625	300	38	∩	∩	ADJ
ejpam-3625	300	39	v	v	ADJ
ejpam-3625	300	40	(	(	PUNCT
ejpam-3625	300	41	h	h	NOUN
ejpam-3625	300	42	)	)	PUNCT
ejpam-3625	300	43	6=	6=	ADP
ejpam-3625	300	44	∅.	∅.	ADV
ejpam-3625	300	45	let	let	VERB
ejpam-3625	300	46	sg	sg	ADV
ejpam-3625	300	47	=	=	SYM
ejpam-3625	300	48	s	s	PART
ejpam-3625	300	49	∩	∩	ADJ
ejpam-3625	300	50	v	v	X
ejpam-3625	300	51	(	(	PUNCT
ejpam-3625	300	52	g	g	NOUN
ejpam-3625	300	53	)	)	PUNCT
ejpam-3625	300	54	and	and	CCONJ
ejpam-3625	300	55	sh	sh	INTJ
ejpam-3625	300	56	=	=	SYM
ejpam-3625	300	57	s	s	PROPN
ejpam-3625	300	58	∩	∩	ADJ
ejpam-3625	300	59	v	v	ADJ
ejpam-3625	300	60	(	(	PUNCT
ejpam-3625	300	61	h	h	NOUN
ejpam-3625	300	62	)	)	PUNCT
ejpam-3625	300	63	.	.	PUNCT
ejpam-3625	301	1	suppose	suppose	VERB
ejpam-3625	301	2	s	s	VERB
ejpam-3625	301	3	∩	∩	ADJ
ejpam-3625	301	4	v	v	X
ejpam-3625	301	5	(	(	PUNCT
ejpam-3625	301	6	h	h	NOUN
ejpam-3625	301	7	)	)	PUNCT
ejpam-3625	301	8	=	=	NOUN
ejpam-3625	301	9	v	v	X
ejpam-3625	301	10	(	(	PUNCT
ejpam-3625	301	11	h	h	NOUN
ejpam-3625	301	12	)	)	PUNCT
ejpam-3625	301	13	.	.	PUNCT
ejpam-3625	302	1	then	then	ADV
ejpam-3625	302	2	sg	sg	VERB
ejpam-3625	302	3	⊆	⊆	NUM
ejpam-3625	302	4	v	v	NOUN
ejpam-3625	302	5	(	(	PUNCT
ejpam-3625	302	6	g	g	NOUN
ejpam-3625	302	7	)	)	PUNCT
ejpam-3625	302	8	.	.	PUNCT
ejpam-3625	303	1	let	let	VERB
ejpam-3625	303	2	cg	cg	NOUN
ejpam-3625	303	3	=	=	NOUN
ejpam-3625	303	4	v	v	X
ejpam-3625	303	5	(	(	PUNCT
ejpam-3625	303	6	g	g	NOUN
ejpam-3625	303	7	)	)	PUNCT
ejpam-3625	303	8	\	\	PROPN
ejpam-3625	303	9	sg	sg	PROPN
ejpam-3625	303	10	.	.	PUNCT
ejpam-3625	304	1	then	then	ADV
ejpam-3625	304	2	s	s	VERB
ejpam-3625	304	3	=	=	PUNCT
ejpam-3625	304	4	sg	sg	X
ejpam-3625	304	5	∪	∪	ADJ
ejpam-3625	304	6	v	v	PROPN
ejpam-3625	304	7	(	(	PUNCT
ejpam-3625	304	8	h	h	NOUN
ejpam-3625	304	9	)	)	PUNCT
ejpam-3625	304	10	.	.	PUNCT
ejpam-3625	305	1	let	let	VERB
ejpam-3625	305	2	u	u	NOUN
ejpam-3625	305	3	,	,	PUNCT
ejpam-3625	305	4	v	v	NUM
ejpam-3625	305	5	/∈	/∈	INTJ
ejpam-3625	305	6	sg	sg	PROPN
ejpam-3625	305	7	,	,	PUNCT
ejpam-3625	305	8	u	u	PROPN
ejpam-3625	305	9	6=	6=	PROPN
ejpam-3625	305	10	v.	v.	ADP
ejpam-3625	305	11	hence	hence	ADV
ejpam-3625	305	12	,	,	PUNCT
ejpam-3625	305	13	u	u	NOUN
ejpam-3625	305	14	,	,	PUNCT
ejpam-3625	305	15	v	v	PROPN
ejpam-3625	305	16	∈	∈	PROPN
ejpam-3625	305	17	cg	cg	NOUN
ejpam-3625	305	18	.	.	PUNCT
ejpam-3625	306	1	since	since	SCONJ
ejpam-3625	306	2	s	s	PROPN
ejpam-3625	306	3	is	be	AUX
ejpam-3625	306	4	a	a	DET
ejpam-3625	306	5	strong	strong	ADJ
ejpam-3625	306	6	resolving	resolving	NOUN
ejpam-3625	306	7	dominating	dominating	NOUN
ejpam-3625	306	8	set	set	NOUN
ejpam-3625	306	9	of	of	ADP
ejpam-3625	306	10	g	g	PROPN
ejpam-3625	306	11	+	+	CCONJ
ejpam-3625	306	12	h	h	NOUN
ejpam-3625	306	13	,	,	PUNCT
ejpam-3625	306	14	cg	cg	NOUN
ejpam-3625	306	15	⊆	⊆	NUM
ejpam-3625	306	16	v	v	NOUN
ejpam-3625	306	17	(	(	PUNCT
ejpam-3625	306	18	gi	gi	INTJ
ejpam-3625	306	19	)	)	PUNCT
ejpam-3625	306	20	for	for	ADP
ejpam-3625	306	21	some	some	DET
ejpam-3625	306	22	i	i	PRON
ejpam-3625	306	23	∈	∈	PROPN
ejpam-3625	306	24	{	{	PUNCT
ejpam-3625	306	25	1	1	NUM
ejpam-3625	306	26	,	,	PUNCT
ejpam-3625	306	27	2	2	NUM
ejpam-3625	306	28	,	,	PUNCT
ejpam-3625	306	29	.	.	PUNCT
ejpam-3625	306	30	.	.	PUNCT
ejpam-3625	307	1	.	.	PUNCT
ejpam-3625	308	1	,	,	PUNCT
ejpam-3625	309	1	n	n	CCONJ
ejpam-3625	309	2	}	}	PUNCT
ejpam-3625	309	3	.	.	PUNCT
ejpam-3625	310	1	then	then	ADV
ejpam-3625	310	2	there	there	PRON
ejpam-3625	310	3	exists	exist	VERB
ejpam-3625	310	4	z	z	PROPN
ejpam-3625	310	5	∈	∈	PROPN
ejpam-3625	310	6	s	s	PART
ejpam-3625	310	7	∩	∩	ADJ
ejpam-3625	310	8	v	v	X
ejpam-3625	310	9	(	(	PUNCT
ejpam-3625	310	10	gi	gi	INTJ
ejpam-3625	310	11	)	)	PUNCT
ejpam-3625	310	12	such	such	ADJ
ejpam-3625	310	13	that	that	SCONJ
ejpam-3625	310	14	u	u	PROPN
ejpam-3625	310	15	∈	∈	NOUN
ejpam-3625	310	16	ig+h	ig+h	PROPN
ejpam-3625	311	1	[	[	X
ejpam-3625	311	2	v	v	NOUN
ejpam-3625	311	3	,	,	PUNCT
ejpam-3625	311	4	z	z	NOUN
ejpam-3625	311	5	]	]	X
ejpam-3625	311	6	or	or	CCONJ
ejpam-3625	311	7	v	v	ADP
ejpam-3625	311	8	∈	∈	NOUN
ejpam-3625	311	9	ig+h	ig+h	CCONJ
ejpam-3625	312	1	[	[	NOUN
ejpam-3625	312	2	u	u	NOUN
ejpam-3625	312	3	,	,	PUNCT
ejpam-3625	312	4	z	z	NOUN
ejpam-3625	312	5	]	]	PUNCT
ejpam-3625	312	6	.	.	PUNCT
ejpam-3625	313	1	it	it	PRON
ejpam-3625	313	2	follows	follow	VERB
ejpam-3625	313	3	from	from	ADP
ejpam-3625	313	4	remark	remark	NOUN
ejpam-3625	313	5	5	5	NUM
ejpam-3625	313	6	that	that	PRON
ejpam-3625	313	7	cg	cg	NOUN
ejpam-3625	313	8	is	be	AUX
ejpam-3625	313	9	a	a	DET
ejpam-3625	313	10	superclique	superclique	NOUN
ejpam-3625	313	11	of	of	ADP
ejpam-3625	313	12	gi	gi	NOUN
ejpam-3625	313	13	.	.	PUNCT
ejpam-3625	314	1	similarly	similarly	ADV
ejpam-3625	314	2	,	,	PUNCT
ejpam-3625	314	3	s	s	VERB
ejpam-3625	314	4	∩	∩	ADJ
ejpam-3625	314	5	v	v	ADJ
ejpam-3625	314	6	(	(	PUNCT
ejpam-3625	314	7	g	g	NOUN
ejpam-3625	314	8	)	)	PUNCT
ejpam-3625	314	9	=	=	NOUN
ejpam-3625	314	10	v	v	X
ejpam-3625	314	11	(	(	PUNCT
ejpam-3625	314	12	g	g	NOUN
ejpam-3625	314	13	)	)	PUNCT
ejpam-3625	314	14	.	.	PUNCT
ejpam-3625	315	1	on	on	ADP
ejpam-3625	315	2	the	the	DET
ejpam-3625	315	3	other	other	ADJ
ejpam-3625	315	4	hand	hand	NOUN
ejpam-3625	315	5	,	,	PUNCT
ejpam-3625	315	6	if	if	SCONJ
ejpam-3625	315	7	s	s	ADP
ejpam-3625	315	8	∩	∩	ADJ
ejpam-3625	315	9	v	v	X
ejpam-3625	315	10	(	(	PUNCT
ejpam-3625	315	11	g	g	NOUN
ejpam-3625	315	12	)	)	PUNCT
ejpam-3625	315	13	6=	6=	ADP
ejpam-3625	315	14	v	v	ADP
ejpam-3625	315	15	(	(	PUNCT
ejpam-3625	315	16	g	g	NOUN
ejpam-3625	315	17	)	)	PUNCT
ejpam-3625	315	18	,	,	PUNCT
ejpam-3625	315	19	s	s	VERB
ejpam-3625	315	20	∩	∩	ADJ
ejpam-3625	315	21	v	v	ADJ
ejpam-3625	315	22	(	(	PUNCT
ejpam-3625	315	23	h	h	NOUN
ejpam-3625	315	24	)	)	PUNCT
ejpam-3625	315	25	6=	6=	ADP
ejpam-3625	315	26	v	v	ADP
ejpam-3625	315	27	(	(	PUNCT
ejpam-3625	315	28	h	h	NOUN
ejpam-3625	315	29	)	)	PUNCT
ejpam-3625	315	30	,	,	PUNCT
ejpam-3625	315	31	cg	cg	NOUN
ejpam-3625	315	32	=	=	SYM
ejpam-3625	315	33	v	v	NOUN
ejpam-3625	315	34	(	(	PUNCT
ejpam-3625	315	35	g	g	NOUN
ejpam-3625	315	36	)	)	PUNCT
ejpam-3625	315	37	\	\	PROPN
ejpam-3625	315	38	sg	sg	NOUN
ejpam-3625	315	39	and	and	CCONJ
ejpam-3625	315	40	ch	ch	NOUN
ejpam-3625	315	41	=	=	SYM
ejpam-3625	315	42	v	v	PROPN
ejpam-3625	315	43	(	(	PUNCT
ejpam-3625	315	44	h	h	NOUN
ejpam-3625	315	45	)	)	PUNCT
ejpam-3625	315	46	\	\	PUNCT
ejpam-3625	316	1	sh	sh	INTJ
ejpam-3625	316	2	,	,	PUNCT
ejpam-3625	316	3	then	then	ADV
ejpam-3625	316	4	s	s	VERB
ejpam-3625	316	5	=	=	PUNCT
ejpam-3625	316	6	sg	sg	PROPN
ejpam-3625	316	7	∪sh	∪sh	NOUN
ejpam-3625	316	8	.	.	PUNCT
ejpam-3625	317	1	hence	hence	ADV
ejpam-3625	317	2	,	,	PUNCT
ejpam-3625	317	3	cg	cg	NOUN
ejpam-3625	317	4	and	and	CCONJ
ejpam-3625	317	5	ch	ch	NOUN
ejpam-3625	317	6	are	be	AUX
ejpam-3625	317	7	supercliques	superclique	NOUN
ejpam-3625	317	8	of	of	ADP
ejpam-3625	317	9	gi	gi	PROPN
ejpam-3625	317	10	and	and	CCONJ
ejpam-3625	317	11	hj	hj	VERB
ejpam-3625	317	12	for	for	ADP
ejpam-3625	317	13	some	some	DET
ejpam-3625	317	14	i	i	PRON
ejpam-3625	317	15	∈	∈	PROPN
ejpam-3625	317	16	{	{	PUNCT
ejpam-3625	317	17	1	1	NUM
ejpam-3625	317	18	,	,	PUNCT
ejpam-3625	317	19	2	2	NUM
ejpam-3625	317	20	,	,	PUNCT
ejpam-3625	317	21	.	.	PUNCT
ejpam-3625	317	22	.	.	PUNCT
ejpam-3625	318	1	.	.	PUNCT
ejpam-3625	319	1	,	,	PUNCT
ejpam-3625	319	2	n	n	CCONJ
ejpam-3625	319	3	}	}	PUNCT
ejpam-3625	319	4	and	and	CCONJ
ejpam-3625	319	5	j	j	PROPN
ejpam-3625	319	6	∈	∈	PROPN
ejpam-3625	319	7	{	{	PUNCT
ejpam-3625	319	8	1	1	NUM
ejpam-3625	319	9	,	,	PUNCT
ejpam-3625	319	10	2	2	NUM
ejpam-3625	319	11	,	,	PUNCT
ejpam-3625	319	12	.	.	PUNCT
ejpam-3625	319	13	.	.	PUNCT
ejpam-3625	320	1	.	.	PUNCT
ejpam-3625	321	1	,	,	PUNCT
ejpam-3625	321	2	m	m	VERB
ejpam-3625	321	3	}	}	PUNCT
ejpam-3625	321	4	.	.	PUNCT
ejpam-3625	322	1	conversely	conversely	ADV
ejpam-3625	322	2	,	,	PUNCT
ejpam-3625	322	3	suppose	suppose	VERB
ejpam-3625	322	4	s	s	PRON
ejpam-3625	322	5	satisfies	satisfie	NOUN
ejpam-3625	322	6	condition	condition	NOUN
ejpam-3625	322	7	(	(	PUNCT
ejpam-3625	322	8	i	i	NOUN
ejpam-3625	322	9	)	)	PUNCT
ejpam-3625	322	10	.	.	PUNCT
ejpam-3625	323	1	let	let	VERB
ejpam-3625	323	2	u	u	NOUN
ejpam-3625	323	3	,	,	PUNCT
ejpam-3625	323	4	v	v	NOUN
ejpam-3625	323	5	/∈	/∈	SYM
ejpam-3625	323	6	s	s	X
ejpam-3625	323	7	,	,	PUNCT
ejpam-3625	323	8	u	u	PROPN
ejpam-3625	323	9	6=	6=	PROPN
ejpam-3625	323	10	v.	v.	ADP
ejpam-3625	323	11	then	then	ADV
ejpam-3625	323	12	u	u	PROPN
ejpam-3625	323	13	,	,	PUNCT
ejpam-3625	323	14	v	v	PROPN
ejpam-3625	324	1	∈	∈	PROPN
ejpam-3625	324	2	cg	cg	NOUN
ejpam-3625	324	3	=	=	SYM
ejpam-3625	324	4	v	v	PROPN
ejpam-3625	324	5	(	(	PUNCT
ejpam-3625	324	6	g	g	NOUN
ejpam-3625	324	7	)	)	PUNCT
ejpam-3625	324	8	\	\	PROPN
ejpam-3625	324	9	sg	sg	PROPN
ejpam-3625	324	10	.	.	PUNCT
ejpam-3625	325	1	hence	hence	ADV
ejpam-3625	325	2	,	,	PUNCT
ejpam-3625	325	3	there	there	PRON
ejpam-3625	325	4	exists	exist	VERB
ejpam-3625	325	5	w	w	PROPN
ejpam-3625	325	6	∈	∈	PROPN
ejpam-3625	325	7	v	v	ADP
ejpam-3625	325	8	(	(	PUNCT
ejpam-3625	325	9	gi	gi	NOUN
ejpam-3625	325	10	)	)	PUNCT
ejpam-3625	325	11	\	\	PROPN
ejpam-3625	325	12	cg	cg	NOUN
ejpam-3625	325	13	such	such	ADJ
ejpam-3625	325	14	that	that	SCONJ
ejpam-3625	325	15	w	w	PROPN
ejpam-3625	325	16	∈	∈	PROPN
ejpam-3625	325	17	ng+h(u	ng+h(u	PROPN
ejpam-3625	325	18	)	)	PUNCT
ejpam-3625	325	19	\	\	PUNCT
ejpam-3625	326	1	ng+h(v	ng+h(v	PROPN
ejpam-3625	326	2	)	)	PUNCT
ejpam-3625	326	3	or	or	CCONJ
ejpam-3625	326	4	w	w	PROPN
ejpam-3625	326	5	∈	∈	PROPN
ejpam-3625	326	6	ng+h(v	ng+h(v	NOUN
ejpam-3625	326	7	)	)	PUNCT
ejpam-3625	326	8	\	\	PROPN
ejpam-3625	327	1	ng+h(u	ng+h(u	PROPN
ejpam-3625	327	2	)	)	PUNCT
ejpam-3625	327	3	.	.	PUNCT
ejpam-3625	328	1	by	by	ADP
ejpam-3625	328	2	remark	remark	NOUN
ejpam-3625	328	3	5	5	NUM
ejpam-3625	328	4	,	,	PUNCT
ejpam-3625	328	5	u	u	NOUN
ejpam-3625	328	6	∈	∈	NOUN
ejpam-3625	328	7	ig+h	ig+h	PROPN
ejpam-3625	329	1	[	[	X
ejpam-3625	329	2	v	v	NOUN
ejpam-3625	329	3	,	,	PUNCT
ejpam-3625	329	4	w	w	NOUN
ejpam-3625	329	5	]	]	PUNCT
ejpam-3625	329	6	or	or	CCONJ
ejpam-3625	329	7	v	v	ADP
ejpam-3625	329	8	∈	∈	NOUN
ejpam-3625	329	9	ig+h	ig+h	PROPN
ejpam-3625	329	10	[	[	NOUN
ejpam-3625	329	11	u	u	NOUN
ejpam-3625	329	12	,	,	PUNCT
ejpam-3625	329	13	w	w	NOUN
ejpam-3625	329	14	]	]	PUNCT
ejpam-3625	329	15	.	.	PUNCT
ejpam-3625	330	1	thus	thus	ADV
ejpam-3625	330	2	,	,	PUNCT
ejpam-3625	330	3	s	s	VERB
ejpam-3625	330	4	is	be	AUX
ejpam-3625	330	5	a	a	DET
ejpam-3625	330	6	strong	strong	ADJ
ejpam-3625	330	7	resolving	resolving	NOUN
ejpam-3625	330	8	dominating	dominating	NOUN
ejpam-3625	330	9	set	set	NOUN
ejpam-3625	330	10	of	of	ADP
ejpam-3625	330	11	g	g	PROPN
ejpam-3625	330	12	+	+	CCONJ
ejpam-3625	330	13	h.	h.	PROPN
ejpam-3625	330	14	similarly	similarly	ADV
ejpam-3625	330	15	,	,	PUNCT
ejpam-3625	330	16	the	the	DET
ejpam-3625	330	17	same	same	ADJ
ejpam-3625	330	18	conclusion	conclusion	NOUN
ejpam-3625	330	19	holds	hold	VERB
ejpam-3625	330	20	if	if	SCONJ
ejpam-3625	330	21	s	s	PROPN
ejpam-3625	330	22	satisfies	satisfie	NOUN
ejpam-3625	330	23	condition	condition	NOUN
ejpam-3625	330	24	(	(	PUNCT
ejpam-3625	330	25	ii	ii	NOUN
ejpam-3625	330	26	)	)	PUNCT
ejpam-3625	330	27	.	.	PUNCT
ejpam-3625	331	1	suppose	suppose	VERB
ejpam-3625	331	2	s	s	PRON
ejpam-3625	331	3	satisfies	satisfie	NOUN
ejpam-3625	331	4	condition	condition	NOUN
ejpam-3625	331	5	(	(	PUNCT
ejpam-3625	331	6	iii	iii	NOUN
ejpam-3625	331	7	)	)	PUNCT
ejpam-3625	331	8	.	.	PUNCT
ejpam-3625	332	1	let	let	VERB
ejpam-3625	332	2	u	u	NOUN
ejpam-3625	332	3	,	,	PUNCT
ejpam-3625	332	4	v	v	NOUN
ejpam-3625	332	5	/∈	/∈	SYM
ejpam-3625	332	6	s	s	X
ejpam-3625	332	7	,	,	PUNCT
ejpam-3625	332	8	u	u	PROPN
ejpam-3625	332	9	6=	6=	PROPN
ejpam-3625	332	10	v.	v.	ADP
ejpam-3625	332	11	if	if	SCONJ
ejpam-3625	332	12	u	u	PROPN
ejpam-3625	332	13	,	,	PUNCT
ejpam-3625	332	14	v	v	PROPN
ejpam-3625	332	15	∈	∈	PROPN
ejpam-3625	332	16	cg	cg	NOUN
ejpam-3625	332	17	or	or	CCONJ
ejpam-3625	332	18	u	u	NOUN
ejpam-3625	332	19	,	,	PUNCT
ejpam-3625	332	20	v	v	PROPN
ejpam-3625	332	21	∈	∈	PROPN
ejpam-3625	332	22	ch	ch	NOUN
ejpam-3625	332	23	,	,	PUNCT
ejpam-3625	332	24	then	then	ADV
ejpam-3625	332	25	we	we	PRON
ejpam-3625	332	26	are	be	AUX
ejpam-3625	332	27	done	do	VERB
ejpam-3625	332	28	.	.	PUNCT
ejpam-3625	333	1	assume	assume	VERB
ejpam-3625	333	2	u	u	PROPN
ejpam-3625	333	3	∈	∈	PROPN
ejpam-3625	333	4	cg	cg	NOUN
ejpam-3625	333	5	and	and	CCONJ
ejpam-3625	333	6	v	v	ADP
ejpam-3625	333	7	∈	∈	PROPN
ejpam-3625	333	8	ch	ch	NOUN
ejpam-3625	333	9	.	.	PUNCT
ejpam-3625	334	1	since	since	SCONJ
ejpam-3625	334	2	dg+h(u	dg+h(u	PROPN
ejpam-3625	334	3	,	,	PUNCT
ejpam-3625	334	4	u′	u′	PRON
ejpam-3625	334	5	)	)	PUNCT
ejpam-3625	334	6	=	=	SYM
ejpam-3625	334	7	2	2	NUM
ejpam-3625	334	8	for	for	ADP
ejpam-3625	334	9	u′	u′	PROPN
ejpam-3625	334	10	∈	∈	PROPN
ejpam-3625	334	11	gk	gk	PROPN
ejpam-3625	334	12	,	,	PUNCT
ejpam-3625	334	13	k	k	PROPN
ejpam-3625	334	14	6=	6=	PROPN
ejpam-3625	334	15	i	i	PROPN
ejpam-3625	334	16	and	and	CCONJ
ejpam-3625	334	17	dg+h(v	dg+h(v	PROPN
ejpam-3625	334	18	,	,	PUNCT
ejpam-3625	334	19	v′	v′	NUM
ejpam-3625	334	20	)	)	PUNCT
ejpam-3625	335	1	=	=	SYM
ejpam-3625	335	2	2	2	NUM
ejpam-3625	335	3	for	for	ADP
ejpam-3625	335	4	v′	v′	NOUN
ejpam-3625	335	5	∈	∈	PROPN
ejpam-3625	335	6	hp	hp	PROPN
ejpam-3625	335	7	,	,	PUNCT
ejpam-3625	335	8	p	p	PROPN
ejpam-3625	335	9	6=	6=	PROPN
ejpam-3625	335	10	j	j	PROPN
ejpam-3625	335	11	,	,	PUNCT
ejpam-3625	335	12	v	v	X
ejpam-3625	335	13	∈	∈	NOUN
ejpam-3625	335	14	ig+h	ig+h	NOUN
ejpam-3625	336	1	[	[	NOUN
ejpam-3625	336	2	u	u	NOUN
ejpam-3625	336	3	,	,	PUNCT
ejpam-3625	336	4	u′	u′	PRON
ejpam-3625	336	5	]	]	PUNCT
ejpam-3625	336	6	or	or	CCONJ
ejpam-3625	336	7	u	u	NOUN
ejpam-3625	336	8	∈	∈	NOUN
ejpam-3625	336	9	ig+h	ig+h	PROPN
ejpam-3625	336	10	[	[	X
ejpam-3625	336	11	v	v	NOUN
ejpam-3625	336	12	,	,	PUNCT
ejpam-3625	336	13	v′	v′	NOUN
ejpam-3625	336	14	]	]	PUNCT
ejpam-3625	336	15	.	.	PUNCT
ejpam-3625	337	1	thus	thus	ADV
ejpam-3625	337	2	,	,	PUNCT
ejpam-3625	337	3	s	s	VERB
ejpam-3625	337	4	is	be	AUX
ejpam-3625	337	5	a	a	DET
ejpam-3625	337	6	strong	strong	ADJ
ejpam-3625	337	7	resolving	resolving	NOUN
ejpam-3625	337	8	dominating	dominating	NOUN
ejpam-3625	337	9	set	set	NOUN
ejpam-3625	337	10	of	of	ADP
ejpam-3625	337	11	g+h	g+h	PROPN
ejpam-3625	337	12	.	.	PUNCT
ejpam-3625	338	1	4	4	X
ejpam-3625	338	2	.	.	X
ejpam-3625	338	3	on	on	ADP
ejpam-3625	338	4	strong	strong	ADJ
ejpam-3625	338	5	resolving	resolving	NOUN
ejpam-3625	338	6	domination	domination	NOUN
ejpam-3625	338	7	in	in	ADP
ejpam-3625	338	8	the	the	DET
ejpam-3625	338	9	corona	corona	NOUN
ejpam-3625	338	10	of	of	ADP
ejpam-3625	338	11	graphs	graph	NOUN
ejpam-3625	338	12	the	the	DET
ejpam-3625	338	13	corona	corona	NOUN
ejpam-3625	338	14	of	of	ADP
ejpam-3625	338	15	two	two	NUM
ejpam-3625	338	16	graphs	graph	NOUN
ejpam-3625	338	17	g	g	NOUN
ejpam-3625	338	18	and	and	CCONJ
ejpam-3625	338	19	h	h	NOUN
ejpam-3625	338	20	,	,	PUNCT
ejpam-3625	338	21	denoted	denote	VERB
ejpam-3625	338	22	by	by	ADP
ejpam-3625	338	23	g	g	PROPN
ejpam-3625	338	24	◦	◦	NOUN
ejpam-3625	338	25	h	h	NOUN
ejpam-3625	338	26	,	,	PUNCT
ejpam-3625	338	27	is	be	AUX
ejpam-3625	338	28	the	the	DET
ejpam-3625	338	29	graph	graph	NOUN
ejpam-3625	338	30	obtained	obtain	VERB
ejpam-3625	338	31	by	by	ADP
ejpam-3625	338	32	taking	take	VERB
ejpam-3625	338	33	one	one	NUM
ejpam-3625	338	34	copy	copy	NOUN
ejpam-3625	338	35	of	of	ADP
ejpam-3625	338	36	g	g	NOUN
ejpam-3625	338	37	of	of	ADP
ejpam-3625	338	38	order	order	NOUN
ejpam-3625	338	39	n	n	NOUN
ejpam-3625	338	40	and	and	CCONJ
ejpam-3625	338	41	n	n	PRON
ejpam-3625	338	42	copies	copy	NOUN
ejpam-3625	338	43	of	of	ADP
ejpam-3625	338	44	h	h	NOUN
ejpam-3625	338	45	,	,	PUNCT
ejpam-3625	338	46	and	and	CCONJ
ejpam-3625	338	47	then	then	ADV
ejpam-3625	338	48	joining	join	VERB
ejpam-3625	338	49	every	every	DET
ejpam-3625	338	50	vertex	vertex	NOUN
ejpam-3625	338	51	of	of	ADP
ejpam-3625	338	52	the	the	DET
ejpam-3625	338	53	ith	ith	PROPN
ejpam-3625	338	54	copy	copy	NOUN
ejpam-3625	338	55	of	of	ADP
ejpam-3625	338	56	h	h	NOUN
ejpam-3625	338	57	to	to	ADP
ejpam-3625	338	58	the	the	DET
ejpam-3625	338	59	ith	ith	PROPN
ejpam-3625	338	60	vertex	vertex	NOUN
ejpam-3625	338	61	of	of	ADP
ejpam-3625	338	62	g.	g.	PROPN
ejpam-3625	338	63	for	for	ADP
ejpam-3625	338	64	v	v	NOUN
ejpam-3625	338	65	∈	∈	PROPN
ejpam-3625	338	66	v	v	NOUN
ejpam-3625	338	67	(	(	PUNCT
ejpam-3625	338	68	g	g	NOUN
ejpam-3625	338	69	)	)	PUNCT
ejpam-3625	338	70	,	,	PUNCT
ejpam-3625	338	71	denote	denote	VERB
ejpam-3625	338	72	by	by	ADP
ejpam-3625	338	73	hv	hv	PROPN
ejpam-3625	338	74	the	the	DET
ejpam-3625	338	75	copy	copy	NOUN
ejpam-3625	338	76	of	of	ADP
ejpam-3625	338	77	h	h	NOUN
ejpam-3625	338	78	whose	whose	DET
ejpam-3625	338	79	vertices	vertex	NOUN
ejpam-3625	338	80	are	be	AUX
ejpam-3625	338	81	attached	attach	VERB
ejpam-3625	338	82	one	one	NUM
ejpam-3625	338	83	by	by	ADP
ejpam-3625	338	84	one	one	NUM
ejpam-3625	338	85	to	to	ADP
ejpam-3625	338	86	the	the	DET
ejpam-3625	338	87	vertex	vertex	NOUN
ejpam-3625	338	88	v.	v.	ADP
ejpam-3625	338	89	subsequently	subsequently	ADV
ejpam-3625	338	90	,	,	PUNCT
ejpam-3625	338	91	denote	denote	VERB
ejpam-3625	338	92	by	by	ADP
ejpam-3625	338	93	v+hv	v+hv	NOUN
ejpam-3625	338	94	the	the	DET
ejpam-3625	338	95	subgraph	subgraph	NOUN
ejpam-3625	338	96	of	of	ADP
ejpam-3625	338	97	the	the	DET
ejpam-3625	338	98	corona	corona	NOUN
ejpam-3625	338	99	g	g	PROPN
ejpam-3625	338	100	◦	◦	NOUN
ejpam-3625	338	101	h	h	NOUN
ejpam-3625	338	102	corresponding	correspond	VERB
ejpam-3625	338	103	to	to	ADP
ejpam-3625	338	104	the	the	DET
ejpam-3625	338	105	join	join	NOUN
ejpam-3625	338	106	〈	〈	PROPN
ejpam-3625	338	107	{	{	PUNCT
ejpam-3625	338	108	v}〉+hv	v}〉+hv	PROPN
ejpam-3625	338	109	,	,	PUNCT
ejpam-3625	338	110	v	v	NOUN
ejpam-3625	338	111	∈	∈	PROPN
ejpam-3625	338	112	v	v	NOUN
ejpam-3625	338	113	(	(	PUNCT
ejpam-3625	338	114	g	g	NOUN
ejpam-3625	338	115	)	)	PUNCT
ejpam-3625	338	116	.	.	PUNCT
ejpam-3625	339	1	g.	g.	PROPN
ejpam-3625	339	2	monsanto	monsanto	PROPN
ejpam-3625	339	3	,	,	PUNCT
ejpam-3625	339	4	p.	p.	PROPN
ejpam-3625	339	5	acal	acal	PROPN
ejpam-3625	339	6	,	,	PUNCT
ejpam-3625	339	7	h.	h.	PROPN
ejpam-3625	339	8	rara	rara	PROPN
ejpam-3625	339	9	/	/	SYM
ejpam-3625	339	10	eur	eur	PROPN
ejpam-3625	339	11	.	.	PUNCT
ejpam-3625	340	1	j.	j.	PROPN
ejpam-3625	340	2	pure	pure	PROPN
ejpam-3625	340	3	appl	appl	PROPN
ejpam-3625	340	4	.	.	PROPN
ejpam-3625	340	5	math	math	PROPN
ejpam-3625	340	6	,	,	PUNCT
ejpam-3625	340	7	13	13	NUM
ejpam-3625	340	8	(	(	PUNCT
ejpam-3625	340	9	1	1	NUM
ejpam-3625	340	10	)	)	PUNCT
ejpam-3625	340	11	(	(	PUNCT
ejpam-3625	340	12	2020	2020	NUM
ejpam-3625	340	13	)	)	PUNCT
ejpam-3625	340	14	,	,	PUNCT
ejpam-3625	340	15	170	170	NUM
ejpam-3625	340	16	-	-	SYM
ejpam-3625	340	17	179	179	NUM
ejpam-3625	340	18	178	178	NUM
ejpam-3625	340	19	remark	remark	NOUN
ejpam-3625	340	20	8	8	NUM
ejpam-3625	340	21	.	.	PUNCT
ejpam-3625	341	1	for	for	ADP
ejpam-3625	341	2	the	the	DET
ejpam-3625	341	3	coronas	coronas	PROPN
ejpam-3625	341	4	pn	pn	PROPN
ejpam-3625	341	5	◦	◦	PROPN
ejpam-3625	341	6	k1	k1	PROPN
ejpam-3625	341	7	and	and	CCONJ
ejpam-3625	341	8	cn	cn	PROPN
ejpam-3625	341	9	◦	◦	NOUN
ejpam-3625	341	10	k1	k1	PROPN
ejpam-3625	341	11	,	,	PUNCT
ejpam-3625	341	12	it	it	PRON
ejpam-3625	341	13	can	can	AUX
ejpam-3625	341	14	be	be	AUX
ejpam-3625	341	15	verified	verify	VERB
ejpam-3625	341	16	easily	easily	ADV
ejpam-3625	341	17	that	that	SCONJ
ejpam-3625	341	18	γsr(pn	γsr(pn	PROPN
ejpam-3625	341	19	◦	◦	NOUN
ejpam-3625	341	20	k1	k1	NOUN
ejpam-3625	341	21	)	)	PUNCT
ejpam-3625	341	22	=	=	SYM
ejpam-3625	341	23	γsr(cn	γsr(cn	NUM
ejpam-3625	341	24	◦	◦	NOUN
ejpam-3625	341	25	k1	k1	NOUN
ejpam-3625	341	26	)	)	PUNCT
ejpam-3625	341	27	=	=	SYM
ejpam-3625	341	28	n	n	CCONJ
ejpam-3625	341	29	,	,	PUNCT
ejpam-3625	341	30	∀n	∀n	NUM
ejpam-3625	341	31	≥	≥	NOUN
ejpam-3625	341	32	3	3	NUM
ejpam-3625	341	33	.	.	PUNCT
ejpam-3625	342	1	theorem	theorem	NOUN
ejpam-3625	342	2	6	6	NUM
ejpam-3625	342	3	.	.	PUNCT
ejpam-3625	343	1	let	let	VERB
ejpam-3625	343	2	g	g	PRON
ejpam-3625	343	3	be	be	AUX
ejpam-3625	343	4	a	a	DET
ejpam-3625	343	5	nontrivial	nontrivial	ADJ
ejpam-3625	343	6	connected	connect	VERB
ejpam-3625	343	7	graph	graph	NOUN
ejpam-3625	343	8	and	and	CCONJ
ejpam-3625	343	9	h	h	NOUN
ejpam-3625	343	10	a	a	DET
ejpam-3625	343	11	connected	connected	ADJ
ejpam-3625	343	12	graph	graph	NOUN
ejpam-3625	343	13	.	.	PUNCT
ejpam-3625	344	1	a	a	DET
ejpam-3625	344	2	proper	proper	ADJ
ejpam-3625	344	3	subset	subset	NOUN
ejpam-3625	344	4	s	s	NOUN
ejpam-3625	344	5	of	of	ADP
ejpam-3625	344	6	v	v	NOUN
ejpam-3625	344	7	(	(	PUNCT
ejpam-3625	344	8	g	g	PROPN
ejpam-3625	344	9	◦	◦	NOUN
ejpam-3625	344	10	h	h	NOUN
ejpam-3625	344	11	)	)	PUNCT
ejpam-3625	344	12	is	be	AUX
ejpam-3625	344	13	a	a	DET
ejpam-3625	344	14	strong	strong	ADJ
ejpam-3625	344	15	resolving	resolving	NOUN
ejpam-3625	344	16	dominating	dominating	NOUN
ejpam-3625	344	17	set	set	NOUN
ejpam-3625	344	18	of	of	ADP
ejpam-3625	344	19	g	g	PROPN
ejpam-3625	344	20	◦	◦	NOUN
ejpam-3625	344	21	h	h	NOUN
ejpam-3625	344	22	if	if	SCONJ
ejpam-3625	345	1	and	and	CCONJ
ejpam-3625	345	2	only	only	ADV
ejpam-3625	345	3	if	if	SCONJ
ejpam-3625	345	4	one	one	NUM
ejpam-3625	345	5	of	of	ADP
ejpam-3625	345	6	the	the	DET
ejpam-3625	345	7	following	follow	VERB
ejpam-3625	345	8	holds	hold	VERB
ejpam-3625	345	9	:	:	PUNCT
ejpam-3625	345	10	(	(	PUNCT
ejpam-3625	345	11	i	i	NOUN
ejpam-3625	345	12	)	)	PUNCT
ejpam-3625	345	13	s	s	PART
ejpam-3625	345	14	=	=	PUNCT
ejpam-3625	345	15	a	a	DET
ejpam-3625	345	16	∪	∪	X
ejpam-3625	345	17	(	(	PUNCT
ejpam-3625	345	18	∪u∈v	∪u∈v	PROPN
ejpam-3625	345	19	(	(	PUNCT
ejpam-3625	345	20	g	g	NOUN
ejpam-3625	345	21	)	)	PUNCT
ejpam-3625	345	22	v	v	NOUN
ejpam-3625	345	23	(	(	PUNCT
ejpam-3625	345	24	hu	hu	PROPN
ejpam-3625	345	25	)	)	PUNCT
ejpam-3625	345	26	)	)	PUNCT
ejpam-3625	345	27	where	where	SCONJ
ejpam-3625	345	28	a	a	DET
ejpam-3625	345	29	⊆	⊆	NUM
ejpam-3625	345	30	v	v	NOUN
ejpam-3625	345	31	(	(	PUNCT
ejpam-3625	345	32	g	g	NOUN
ejpam-3625	345	33	)	)	PUNCT
ejpam-3625	345	34	;	;	PUNCT
ejpam-3625	345	35	(	(	PUNCT
ejpam-3625	345	36	ii	ii	NOUN
ejpam-3625	345	37	)	)	PUNCT
ejpam-3625	345	38	s	s	PART
ejpam-3625	345	39	=	=	PUNCT
ejpam-3625	345	40	a	a	DET
ejpam-3625	345	41	∪	∪	X
ejpam-3625	345	42	(	(	PUNCT
ejpam-3625	345	43	∪u∈v	∪u∈v	PROPN
ejpam-3625	345	44	(	(	PUNCT
ejpam-3625	345	45	g)\{v}v	g)\{v}v	PROPN
ejpam-3625	345	46	(	(	PUNCT
ejpam-3625	345	47	hu	hu	PROPN
ejpam-3625	345	48	)	)	PUNCT
ejpam-3625	345	49	)	)	PUNCT
ejpam-3625	345	50	∪	∪	ADP
ejpam-3625	345	51	bv	bv	PROPN
ejpam-3625	345	52	for	for	ADP
ejpam-3625	345	53	a	a	DET
ejpam-3625	345	54	unique	unique	ADJ
ejpam-3625	345	55	v	v	ADP
ejpam-3625	345	56	∈	∈	NOUN
ejpam-3625	345	57	v	v	NOUN
ejpam-3625	345	58	(	(	PUNCT
ejpam-3625	345	59	g	g	NOUN
ejpam-3625	345	60	)	)	PUNCT
ejpam-3625	345	61	,	,	PUNCT
ejpam-3625	345	62	where	where	SCONJ
ejpam-3625	345	63	a	a	DET
ejpam-3625	345	64	⊆	⊆	NUM
ejpam-3625	345	65	v	v	NOUN
ejpam-3625	345	66	(	(	PUNCT
ejpam-3625	345	67	g	g	NOUN
ejpam-3625	345	68	)	)	PUNCT
ejpam-3625	345	69	\	\	NOUN
ejpam-3625	345	70	{	{	PUNCT
ejpam-3625	345	71	v	v	NOUN
ejpam-3625	345	72	}	}	PUNCT
ejpam-3625	345	73	and	and	CCONJ
ejpam-3625	345	74	bv	bv	PROPN
ejpam-3625	345	75	is	be	AUX
ejpam-3625	345	76	a	a	DET
ejpam-3625	345	77	strong	strong	ADJ
ejpam-3625	345	78	resolving	resolving	NOUN
ejpam-3625	345	79	dominating	dominating	NOUN
ejpam-3625	345	80	set	set	NOUN
ejpam-3625	345	81	of	of	ADP
ejpam-3625	345	82	hv	hv	PROPN
ejpam-3625	345	83	if	if	SCONJ
ejpam-3625	345	84	γ(h	γ(h	NOUN
ejpam-3625	345	85	)	)	PUNCT
ejpam-3625	345	86	=	=	SYM
ejpam-3625	345	87	1	1	NUM
ejpam-3625	345	88	or	or	CCONJ
ejpam-3625	345	89	bv	bv	PROPN
ejpam-3625	345	90	is	be	AUX
ejpam-3625	345	91	a	a	DET
ejpam-3625	345	92	strong	strong	ADJ
ejpam-3625	345	93	resolving	resolving	NOUN
ejpam-3625	345	94	dominating	dominating	NOUN
ejpam-3625	345	95	set	set	NOUN
ejpam-3625	345	96	of	of	ADP
ejpam-3625	345	97	〈	〈	PROPN
ejpam-3625	345	98	v〉+hv	v〉+hv	VERB
ejpam-3625	345	99	if	if	SCONJ
ejpam-3625	345	100	γ(h	γ(h	NOUN
ejpam-3625	345	101	)	)	PUNCT
ejpam-3625	345	102	6=	6=	ADP
ejpam-3625	345	103	1	1	NUM
ejpam-3625	345	104	;	;	PUNCT
ejpam-3625	345	105	(	(	PUNCT
ejpam-3625	345	106	iii	iii	X
ejpam-3625	345	107	)	)	PUNCT
ejpam-3625	345	108	s	s	PART
ejpam-3625	345	109	=	=	PUNCT
ejpam-3625	345	110	a	a	DET
ejpam-3625	345	111	∪	∪	X
ejpam-3625	345	112	(	(	PUNCT
ejpam-3625	345	113	∪u∈v	∪u∈v	PROPN
ejpam-3625	345	114	(	(	PUNCT
ejpam-3625	345	115	g)\{v}v	g)\{v}v	PROPN
ejpam-3625	345	116	(	(	PUNCT
ejpam-3625	345	117	hu	hu	PROPN
ejpam-3625	345	118	)	)	PUNCT
ejpam-3625	345	119	)	)	PUNCT
ejpam-3625	345	120	∪bv	∪bv	NOUN
ejpam-3625	345	121	for	for	ADP
ejpam-3625	345	122	a	a	DET
ejpam-3625	345	123	unique	unique	ADJ
ejpam-3625	345	124	v	v	ADP
ejpam-3625	345	125	∈	∈	NOUN
ejpam-3625	345	126	v	v	NOUN
ejpam-3625	345	127	(	(	PUNCT
ejpam-3625	345	128	g	g	NOUN
ejpam-3625	345	129	)	)	PUNCT
ejpam-3625	345	130	where	where	SCONJ
ejpam-3625	345	131	v	v	X
ejpam-3625	345	132	∈	∈	PRON
ejpam-3625	345	133	a	a	DET
ejpam-3625	345	134	⊆	⊆	NUM
ejpam-3625	345	135	v	v	NOUN
ejpam-3625	345	136	(	(	PUNCT
ejpam-3625	345	137	g	g	NOUN
ejpam-3625	345	138	)	)	PUNCT
ejpam-3625	345	139	and	and	CCONJ
ejpam-3625	345	140	bv	bv	PROPN
ejpam-3625	345	141	is	be	AUX
ejpam-3625	345	142	a	a	DET
ejpam-3625	345	143	strong	strong	ADJ
ejpam-3625	345	144	resolving	resolving	NOUN
ejpam-3625	345	145	set	set	NOUN
ejpam-3625	345	146	of	of	ADP
ejpam-3625	345	147	hv	hv	PROPN
ejpam-3625	345	148	if	if	SCONJ
ejpam-3625	345	149	γ(h	γ(h	NOUN
ejpam-3625	345	150	)	)	PUNCT
ejpam-3625	345	151	=	=	SYM
ejpam-3625	345	152	1	1	NUM
ejpam-3625	345	153	and	and	CCONJ
ejpam-3625	345	154	bv	bv	PROPN
ejpam-3625	345	155	is	be	AUX
ejpam-3625	345	156	a	a	DET
ejpam-3625	345	157	strong	strong	ADJ
ejpam-3625	345	158	resolving	resolving	NOUN
ejpam-3625	345	159	set	set	NOUN
ejpam-3625	345	160	of	of	ADP
ejpam-3625	345	161	〈	〈	PROPN
ejpam-3625	345	162	v〉+hv	v〉+hv	VERB
ejpam-3625	345	163	if	if	SCONJ
ejpam-3625	345	164	γ(h	γ(h	NOUN
ejpam-3625	345	165	)	)	PUNCT
ejpam-3625	345	166	6=	6=	ADP
ejpam-3625	345	167	1	1	X
ejpam-3625	345	168	.	.	X
ejpam-3625	346	1	proof	proof	NOUN
ejpam-3625	346	2	:	:	PUNCT
ejpam-3625	346	3	suppose	suppose	VERB
ejpam-3625	346	4	s	s	NOUN
ejpam-3625	346	5	is	be	AUX
ejpam-3625	346	6	a	a	DET
ejpam-3625	346	7	strong	strong	ADJ
ejpam-3625	346	8	resolving	resolving	NOUN
ejpam-3625	346	9	dominating	dominating	NOUN
ejpam-3625	346	10	set	set	NOUN
ejpam-3625	346	11	of	of	ADP
ejpam-3625	346	12	g	g	PROPN
ejpam-3625	346	13	◦	◦	PROPN
ejpam-3625	346	14	h.	h.	PROPN
ejpam-3625	346	15	let	let	VERB
ejpam-3625	346	16	a	a	DET
ejpam-3625	346	17	=	=	X
ejpam-3625	346	18	s	s	NOUN
ejpam-3625	346	19	∩	∩	ADJ
ejpam-3625	346	20	v	v	X
ejpam-3625	346	21	(	(	PUNCT
ejpam-3625	346	22	g	g	NOUN
ejpam-3625	346	23	)	)	PUNCT
ejpam-3625	346	24	and	and	CCONJ
ejpam-3625	346	25	bv	bv	PROPN
ejpam-3625	346	26	=	=	PROPN
ejpam-3625	346	27	s	s	PROPN
ejpam-3625	346	28	∩	∩	ADJ
ejpam-3625	346	29	v	v	X
ejpam-3625	346	30	(	(	PUNCT
ejpam-3625	346	31	hv	hv	PROPN
ejpam-3625	346	32	)	)	PUNCT
ejpam-3625	346	33	,	,	PUNCT
ejpam-3625	346	34	where	where	SCONJ
ejpam-3625	346	35	v	v	X
ejpam-3625	346	36	∈	∈	PROPN
ejpam-3625	346	37	v	v	NOUN
ejpam-3625	346	38	(	(	PUNCT
ejpam-3625	346	39	g	g	NOUN
ejpam-3625	346	40	)	)	PUNCT
ejpam-3625	346	41	.	.	PUNCT
ejpam-3625	347	1	consider	consider	VERB
ejpam-3625	347	2	the	the	DET
ejpam-3625	347	3	following	follow	VERB
ejpam-3625	347	4	cases	case	NOUN
ejpam-3625	347	5	:	:	PUNCT
ejpam-3625	347	6	case	case	NOUN
ejpam-3625	347	7	1	1	NUM
ejpam-3625	347	8	.	.	X
ejpam-3625	347	9	s	s	PART
ejpam-3625	347	10	∩	∩	ADJ
ejpam-3625	347	11	v	v	X
ejpam-3625	347	12	(	(	PUNCT
ejpam-3625	347	13	hv	hv	NOUN
ejpam-3625	347	14	)	)	PUNCT
ejpam-3625	347	15	=	=	NOUN
ejpam-3625	347	16	v	v	X
ejpam-3625	347	17	(	(	PUNCT
ejpam-3625	347	18	hv	hv	PROPN
ejpam-3625	347	19	)	)	PUNCT
ejpam-3625	347	20	then	then	ADV
ejpam-3625	347	21	bv	bv	PROPN
ejpam-3625	347	22	=	=	PROPN
ejpam-3625	347	23	hv	hv	PROPN
ejpam-3625	347	24	.	.	PUNCT
ejpam-3625	348	1	thus	thus	ADV
ejpam-3625	348	2	,	,	PUNCT
ejpam-3625	348	3	s	s	VERB
ejpam-3625	348	4	=	=	PUNCT
ejpam-3625	348	5	a	a	DET
ejpam-3625	348	6	∪	∪	X
ejpam-3625	348	7	(	(	PUNCT
ejpam-3625	348	8	∪u∈v	∪u∈v	PROPN
ejpam-3625	348	9	(	(	PUNCT
ejpam-3625	348	10	g	g	NOUN
ejpam-3625	348	11	)	)	PUNCT
ejpam-3625	348	12	v	v	NOUN
ejpam-3625	348	13	(	(	PUNCT
ejpam-3625	348	14	hu	hu	PROPN
ejpam-3625	348	15	)	)	PUNCT
ejpam-3625	348	16	)	)	PUNCT
ejpam-3625	348	17	.	.	PUNCT
ejpam-3625	349	1	case	case	NOUN
ejpam-3625	349	2	2	2	NUM
ejpam-3625	349	3	.	.	X
ejpam-3625	349	4	s	s	PART
ejpam-3625	349	5	∩	∩	ADJ
ejpam-3625	349	6	v	v	X
ejpam-3625	349	7	(	(	PUNCT
ejpam-3625	349	8	hv	hv	PROPN
ejpam-3625	349	9	)	)	PUNCT
ejpam-3625	349	10	6=	6=	ADP
ejpam-3625	349	11	v	v	PROPN
ejpam-3625	349	12	(	(	PUNCT
ejpam-3625	349	13	hv	hv	X
ejpam-3625	349	14	)	)	PUNCT
ejpam-3625	349	15	let	let	VERB
ejpam-3625	349	16	u	u	NOUN
ejpam-3625	349	17	,	,	PUNCT
ejpam-3625	349	18	v	v	PROPN
ejpam-3625	349	19	∈	∈	PROPN
ejpam-3625	349	20	v	v	NOUN
ejpam-3625	349	21	(	(	PUNCT
ejpam-3625	349	22	g	g	NOUN
ejpam-3625	349	23	)	)	PUNCT
ejpam-3625	349	24	,	,	PUNCT
ejpam-3625	349	25	u	u	PROPN
ejpam-3625	349	26	6=	6=	PROPN
ejpam-3625	349	27	v	v	ADP
ejpam-3625	349	28	such	such	ADJ
ejpam-3625	349	29	that	that	DET
ejpam-3625	349	30	s	s	NOUN
ejpam-3625	349	31	∩	∩	ADJ
ejpam-3625	349	32	v	v	X
ejpam-3625	349	33	(	(	PUNCT
ejpam-3625	349	34	hu	hu	PROPN
ejpam-3625	349	35	)	)	PUNCT
ejpam-3625	349	36	6=	6=	ADP
ejpam-3625	349	37	v	v	X
ejpam-3625	349	38	(	(	PUNCT
ejpam-3625	349	39	hu	hu	PROPN
ejpam-3625	349	40	)	)	PUNCT
ejpam-3625	349	41	and	and	CCONJ
ejpam-3625	349	42	s	s	X
ejpam-3625	349	43	∩	∩	ADJ
ejpam-3625	349	44	v	v	X
ejpam-3625	349	45	(	(	PUNCT
ejpam-3625	349	46	hv	hv	PROPN
ejpam-3625	349	47	)	)	PUNCT
ejpam-3625	349	48	6=	6=	ADP
ejpam-3625	349	49	v	v	PROPN
ejpam-3625	349	50	(	(	PUNCT
ejpam-3625	349	51	hv	hv	PROPN
ejpam-3625	349	52	)	)	PUNCT
ejpam-3625	349	53	.	.	PUNCT
ejpam-3625	350	1	pick	pick	VERB
ejpam-3625	350	2	pu	pu	PROPN
ejpam-3625	350	3	∈	∈	PROPN
ejpam-3625	350	4	v	v	PROPN
ejpam-3625	350	5	(	(	PUNCT
ejpam-3625	350	6	hu	hu	PROPN
ejpam-3625	350	7	)	)	PUNCT
ejpam-3625	350	8	\	\	PROPN
ejpam-3625	350	9	s	s	PART
ejpam-3625	350	10	and	and	CCONJ
ejpam-3625	350	11	pv	pv	NOUN
ejpam-3625	350	12	∈	∈	PROPN
ejpam-3625	350	13	v	v	ADP
ejpam-3625	350	14	(	(	PUNCT
ejpam-3625	350	15	hv	hv	PROPN
ejpam-3625	350	16	)	)	PUNCT
ejpam-3625	350	17	\	\	PUNCT
ejpam-3625	351	1	s.	s.	PROPN
ejpam-3625	351	2	then	then	ADV
ejpam-3625	351	3	,	,	PUNCT
ejpam-3625	351	4	none	none	NOUN
ejpam-3625	351	5	of	of	ADP
ejpam-3625	351	6	the	the	DET
ejpam-3625	351	7	vertices	vertex	NOUN
ejpam-3625	351	8	in	in	ADP
ejpam-3625	351	9	s	s	PRON
ejpam-3625	351	10	strongly	strongly	ADV
ejpam-3625	351	11	resolves	resolve	VERB
ejpam-3625	351	12	pu	pu	PROPN
ejpam-3625	351	13	and	and	CCONJ
ejpam-3625	351	14	pv	pv	INTJ
ejpam-3625	351	15	,	,	PUNCT
ejpam-3625	351	16	a	a	DET
ejpam-3625	351	17	contradiction	contradiction	NOUN
ejpam-3625	351	18	.	.	PUNCT
ejpam-3625	352	1	thus	thus	ADV
ejpam-3625	352	2	,	,	PUNCT
ejpam-3625	352	3	the	the	DET
ejpam-3625	352	4	vertex	vertex	NOUN
ejpam-3625	352	5	v	v	ADP
ejpam-3625	352	6	∈	∈	PROPN
ejpam-3625	352	7	v	v	NOUN
ejpam-3625	352	8	(	(	PUNCT
ejpam-3625	352	9	g	g	NOUN
ejpam-3625	352	10	)	)	PUNCT
ejpam-3625	352	11	such	such	ADJ
ejpam-3625	352	12	that	that	SCONJ
ejpam-3625	352	13	s	s	ADP
ejpam-3625	352	14	∩	∩	ADJ
ejpam-3625	352	15	v	v	X
ejpam-3625	352	16	(	(	PUNCT
ejpam-3625	352	17	hv	hv	PROPN
ejpam-3625	352	18	)	)	PUNCT
ejpam-3625	352	19	6=	6=	ADP
ejpam-3625	352	20	v	v	ADP
ejpam-3625	352	21	(	(	PUNCT
ejpam-3625	352	22	hv	hv	X
ejpam-3625	352	23	)	)	PUNCT
ejpam-3625	352	24	must	must	AUX
ejpam-3625	352	25	be	be	AUX
ejpam-3625	352	26	unique	unique	ADJ
ejpam-3625	352	27	.	.	PUNCT
ejpam-3625	353	1	hence	hence	ADV
ejpam-3625	353	2	,	,	PUNCT
ejpam-3625	353	3	s	s	VERB
ejpam-3625	353	4	=	=	PUNCT
ejpam-3625	353	5	a	a	DET
ejpam-3625	353	6	∪	∪	X
ejpam-3625	353	7	(	(	PUNCT
ejpam-3625	353	8	∪u∈v	∪u∈v	PROPN
ejpam-3625	353	9	(	(	PUNCT
ejpam-3625	353	10	g)\{v}v	g)\{v}v	PROPN
ejpam-3625	353	11	(	(	PUNCT
ejpam-3625	353	12	hu	hu	PROPN
ejpam-3625	353	13	)	)	PUNCT
ejpam-3625	353	14	)	)	PUNCT
ejpam-3625	354	1	∪bv	∪bv	PROPN
ejpam-3625	354	2	.	.	PROPN
ejpam-3625	355	1	subcase	subcase	PROPN
ejpam-3625	355	2	2.1	2.1	NUM
ejpam-3625	355	3	v	v	NOUN
ejpam-3625	355	4	∈	∈	NOUN
ejpam-3625	355	5	s	s	AUX
ejpam-3625	355	6	let	let	VERB
ejpam-3625	355	7	cv	cv	PROPN
ejpam-3625	355	8	=	=	SYM
ejpam-3625	355	9	v	v	PROPN
ejpam-3625	355	10	(	(	PUNCT
ejpam-3625	355	11	hv	hv	PROPN
ejpam-3625	355	12	)	)	PUNCT
ejpam-3625	355	13	\	\	PROPN
ejpam-3625	355	14	bv	bv	PROPN
ejpam-3625	355	15	.	.	PROPN
ejpam-3625	355	16	hence	hence	PROPN
ejpam-3625	355	17	,	,	PUNCT
ejpam-3625	356	1	bv	bv	PROPN
ejpam-3625	356	2	=	=	PROPN
ejpam-3625	356	3	v	v	PROPN
ejpam-3625	356	4	(	(	PUNCT
ejpam-3625	356	5	hv	hv	PROPN
ejpam-3625	356	6	)	)	PUNCT
ejpam-3625	356	7	\	\	PROPN
ejpam-3625	356	8	cv	cv	PROPN
ejpam-3625	356	9	.	.	PROPN
ejpam-3625	357	1	then	then	ADV
ejpam-3625	357	2	it	it	PRON
ejpam-3625	357	3	can	can	AUX
ejpam-3625	357	4	be	be	AUX
ejpam-3625	357	5	verified	verify	VERB
ejpam-3625	357	6	that	that	SCONJ
ejpam-3625	357	7	cv	cv	PROPN
ejpam-3625	357	8	is	be	AUX
ejpam-3625	357	9	a	a	DET
ejpam-3625	357	10	superclique	superclique	NOUN
ejpam-3625	357	11	in	in	ADP
ejpam-3625	357	12	hv	hv	PROPN
ejpam-3625	357	13	.	.	PUNCT
ejpam-3625	358	1	if	if	SCONJ
ejpam-3625	358	2	γ(h	γ(h	PROPN
ejpam-3625	358	3	)	)	PUNCT
ejpam-3625	359	1	6=	6=	ADP
ejpam-3625	359	2	1	1	NUM
ejpam-3625	359	3	,	,	PUNCT
ejpam-3625	359	4	by	by	ADP
ejpam-3625	359	5	theorem	theorem	NOUN
ejpam-3625	359	6	1	1	NUM
ejpam-3625	359	7	,	,	PUNCT
ejpam-3625	359	8	bv	bv	PROPN
ejpam-3625	359	9	is	be	AUX
ejpam-3625	359	10	a	a	DET
ejpam-3625	359	11	strong	strong	ADJ
ejpam-3625	359	12	resolving	resolving	NOUN
ejpam-3625	359	13	set	set	NOUN
ejpam-3625	359	14	of	of	ADP
ejpam-3625	359	15	{	{	PUNCT
ejpam-3625	359	16	v}+hv	v}+hv	NOUN
ejpam-3625	359	17	.	.	PUNCT
ejpam-3625	360	1	if	if	SCONJ
ejpam-3625	360	2	γ(h	γ(h	NOUN
ejpam-3625	360	3	)	)	PUNCT
ejpam-3625	360	4	=	=	SYM
ejpam-3625	360	5	1	1	NUM
ejpam-3625	360	6	,	,	PUNCT
ejpam-3625	360	7	then	then	ADV
ejpam-3625	360	8	by	by	ADP
ejpam-3625	360	9	remark	remark	NOUN
ejpam-3625	360	10	7	7	NUM
ejpam-3625	360	11	and	and	CCONJ
ejpam-3625	360	12	theorem	theorem	VERB
ejpam-3625	360	13	2	2	NUM
ejpam-3625	360	14	,	,	PUNCT
ejpam-3625	360	15	bv	bv	PROPN
ejpam-3625	360	16	is	be	AUX
ejpam-3625	360	17	a	a	DET
ejpam-3625	360	18	strong	strong	ADJ
ejpam-3625	360	19	resolving	resolving	NOUN
ejpam-3625	360	20	set	set	NOUN
ejpam-3625	360	21	of	of	ADP
ejpam-3625	360	22	hv	hv	PROPN
ejpam-3625	360	23	.	.	PROPN
ejpam-3625	360	24	subcase	subcase	PROPN
ejpam-3625	360	25	2.2	2.2	NUM
ejpam-3625	360	26	v	v	NOUN
ejpam-3625	360	27	/∈	/∈	PUNCT
ejpam-3625	360	28	s	s	PART
ejpam-3625	360	29	since	since	SCONJ
ejpam-3625	360	30	s	s	NOUN
ejpam-3625	360	31	is	be	AUX
ejpam-3625	360	32	a	a	DET
ejpam-3625	360	33	dominating	dominating	NOUN
ejpam-3625	360	34	set	set	NOUN
ejpam-3625	360	35	of	of	ADP
ejpam-3625	360	36	g	g	PROPN
ejpam-3625	360	37	◦	◦	NOUN
ejpam-3625	360	38	h	h	NOUN
ejpam-3625	360	39	,	,	PUNCT
ejpam-3625	360	40	bv	bv	PROPN
ejpam-3625	360	41	is	be	AUX
ejpam-3625	360	42	a	a	DET
ejpam-3625	360	43	dominating	dominating	NOUN
ejpam-3625	360	44	set	set	NOUN
ejpam-3625	360	45	of	of	ADP
ejpam-3625	360	46	hv	hv	PROPN
ejpam-3625	360	47	.	.	PUNCT
ejpam-3625	361	1	by	by	ADP
ejpam-3625	361	2	similar	similar	ADJ
ejpam-3625	361	3	argument	argument	NOUN
ejpam-3625	361	4	in	in	ADP
ejpam-3625	361	5	the	the	DET
ejpam-3625	361	6	proof	proof	NOUN
ejpam-3625	361	7	of	of	ADP
ejpam-3625	361	8	subcase	subcase	NOUN
ejpam-3625	361	9	2.1	2.1	NUM
ejpam-3625	361	10	,	,	PUNCT
ejpam-3625	361	11	bv	bv	PROPN
ejpam-3625	361	12	is	be	AUX
ejpam-3625	361	13	a	a	DET
ejpam-3625	361	14	strong	strong	ADJ
ejpam-3625	361	15	resolving	resolving	NOUN
ejpam-3625	361	16	dominating	dominating	NOUN
ejpam-3625	361	17	set	set	NOUN
ejpam-3625	361	18	of	of	ADP
ejpam-3625	361	19	hv	hv	PROPN
ejpam-3625	361	20	if	if	SCONJ
ejpam-3625	361	21	γ(h	γ(h	NOUN
ejpam-3625	361	22	)	)	PUNCT
ejpam-3625	361	23	=	=	SYM
ejpam-3625	361	24	1	1	NUM
ejpam-3625	361	25	or	or	CCONJ
ejpam-3625	361	26	bv	bv	PROPN
ejpam-3625	361	27	is	be	AUX
ejpam-3625	361	28	a	a	DET
ejpam-3625	361	29	strong	strong	ADJ
ejpam-3625	361	30	resolving	resolving	NOUN
ejpam-3625	361	31	dominating	dominating	NOUN
ejpam-3625	361	32	set	set	NOUN
ejpam-3625	361	33	of	of	ADP
ejpam-3625	361	34	〈	〈	PROPN
ejpam-3625	361	35	v〉+hv	v〉+hv	VERB
ejpam-3625	361	36	if	if	SCONJ
ejpam-3625	361	37	γ(h	γ(h	NOUN
ejpam-3625	361	38	)	)	PUNCT
ejpam-3625	361	39	6=	6=	ADP
ejpam-3625	361	40	1	1	X
ejpam-3625	361	41	.	.	PUNCT
ejpam-3625	361	42	conversely	conversely	ADV
ejpam-3625	361	43	,	,	PUNCT
ejpam-3625	361	44	suppose	suppose	VERB
ejpam-3625	361	45	(	(	PUNCT
ejpam-3625	361	46	i	i	NOUN
ejpam-3625	361	47	)	)	PUNCT
ejpam-3625	361	48	,	,	PUNCT
ejpam-3625	361	49	(	(	PUNCT
ejpam-3625	361	50	ii	ii	NOUN
ejpam-3625	361	51	)	)	PUNCT
ejpam-3625	361	52	and	and	CCONJ
ejpam-3625	361	53	(	(	PUNCT
ejpam-3625	361	54	iii	iii	NOUN
ejpam-3625	361	55	)	)	PUNCT
ejpam-3625	361	56	hold	hold	NOUN
ejpam-3625	361	57	.	.	PUNCT
ejpam-3625	362	1	consider	consider	VERB
ejpam-3625	362	2	the	the	DET
ejpam-3625	362	3	following	follow	VERB
ejpam-3625	362	4	cases	case	NOUN
ejpam-3625	362	5	:	:	PUNCT
ejpam-3625	362	6	case	case	NOUN
ejpam-3625	362	7	1	1	NUM
ejpam-3625	362	8	.	.	X
ejpam-3625	363	1	p	p	X
ejpam-3625	363	2	,	,	PUNCT
ejpam-3625	363	3	q	q	PROPN
ejpam-3625	363	4	∈	∈	PROPN
ejpam-3625	363	5	v	v	ADP
ejpam-3625	363	6	(	(	PUNCT
ejpam-3625	363	7	g	g	NOUN
ejpam-3625	363	8	)	)	PUNCT
ejpam-3625	363	9	\a	\a	VERB
ejpam-3625	363	10	let	let	VERB
ejpam-3625	363	11	p	p	PRON
ejpam-3625	363	12	,	,	PUNCT
ejpam-3625	363	13	q	q	PROPN
ejpam-3625	363	14	∈	∈	PROPN
ejpam-3625	363	15	v	v	NOUN
ejpam-3625	363	16	(	(	PUNCT
ejpam-3625	363	17	g	g	PROPN
ejpam-3625	363	18	◦	◦	NOUN
ejpam-3625	363	19	h	h	NOUN
ejpam-3625	363	20	)	)	PUNCT
ejpam-3625	363	21	\	\	PROPN
ejpam-3625	364	1	s	s	VERB
ejpam-3625	364	2	where	where	SCONJ
ejpam-3625	364	3	p	p	PROPN
ejpam-3625	364	4	6=	6=	PROPN
ejpam-3625	364	5	q	q	PROPN
ejpam-3625	364	6	and	and	CCONJ
ejpam-3625	364	7	p	p	NOUN
ejpam-3625	364	8	=	=	PROPN
ejpam-3625	364	9	v	v	NOUN
ejpam-3625	364	10	or	or	CCONJ
ejpam-3625	364	11	q	q	NOUN
ejpam-3625	364	12	=	=	ADJ
ejpam-3625	364	13	v	v	NOUN
ejpam-3625	364	14	,	,	PUNCT
ejpam-3625	364	15	but	but	CCONJ
ejpam-3625	364	16	not	not	PART
ejpam-3625	364	17	both	both	PRON
ejpam-3625	364	18	,	,	PUNCT
ejpam-3625	364	19	then	then	ADV
ejpam-3625	364	20	p	p	PROPN
ejpam-3625	364	21	∈	∈	PROPN
ejpam-3625	365	1	ig	ig	PROPN
ejpam-3625	365	2	◦	◦	NOUN
ejpam-3625	365	3	h	h	NOUN
ejpam-3625	366	1	[	[	X
ejpam-3625	366	2	q	q	X
ejpam-3625	366	3	,	,	PUNCT
ejpam-3625	366	4	z	z	X
ejpam-3625	366	5	]	]	X
ejpam-3625	366	6	or	or	CCONJ
ejpam-3625	366	7	q	q	PROPN
ejpam-3625	366	8	∈	∈	PROPN
ejpam-3625	366	9	ig	ig	PROPN
ejpam-3625	366	10	◦	◦	NOUN
ejpam-3625	366	11	h	h	NOUN
ejpam-3625	367	1	[	[	X
ejpam-3625	367	2	p	p	X
ejpam-3625	367	3	,	,	PUNCT
ejpam-3625	367	4	z	z	X
ejpam-3625	367	5	]	]	X
ejpam-3625	367	6	for	for	ADP
ejpam-3625	367	7	some	some	DET
ejpam-3625	367	8	z	z	PROPN
ejpam-3625	367	9	∈	∈	PROPN
ejpam-3625	367	10	bv	bv	PROPN
ejpam-3625	367	11	.	.	PROPN
ejpam-3625	367	12	on	on	ADP
ejpam-3625	367	13	the	the	DET
ejpam-3625	367	14	other	other	ADJ
ejpam-3625	367	15	hand	hand	NOUN
ejpam-3625	367	16	,	,	PUNCT
ejpam-3625	367	17	if	if	SCONJ
ejpam-3625	367	18	p	p	PROPN
ejpam-3625	367	19	6=	6=	NUM
ejpam-3625	367	20	v	v	NOUN
ejpam-3625	367	21	and	and	CCONJ
ejpam-3625	367	22	q	q	NOUN
ejpam-3625	367	23	6=	6=	PROPN
ejpam-3625	367	24	v	v	NOUN
ejpam-3625	367	25	,	,	PUNCT
ejpam-3625	367	26	then	then	ADV
ejpam-3625	367	27	q	q	PROPN
ejpam-3625	367	28	∈	∈	PROPN
ejpam-3625	367	29	ig	ig	PROPN
ejpam-3625	367	30	◦	◦	NOUN
ejpam-3625	367	31	h	h	NOUN
ejpam-3625	368	1	[	[	X
ejpam-3625	368	2	p	p	X
ejpam-3625	368	3	,	,	PUNCT
ejpam-3625	368	4	w	w	NOUN
ejpam-3625	368	5	]	]	X
ejpam-3625	368	6	for	for	ADP
ejpam-3625	368	7	some	some	PRON
ejpam-3625	368	8	w	w	PROPN
ejpam-3625	368	9	∈	∈	PROPN
ejpam-3625	368	10	v	v	NOUN
ejpam-3625	368	11	(	(	PUNCT
ejpam-3625	368	12	hq	hq	NOUN
ejpam-3625	368	13	)	)	PUNCT
ejpam-3625	369	1	⊂	⊂	PROPN
ejpam-3625	369	2	s	s	VERB
ejpam-3625	369	3	or	or	CCONJ
ejpam-3625	369	4	p	p	NOUN
ejpam-3625	369	5	∈	∈	PROPN
ejpam-3625	369	6	ig	ig	PROPN
ejpam-3625	369	7	◦	◦	NOUN
ejpam-3625	369	8	h	h	NOUN
ejpam-3625	370	1	[	[	X
ejpam-3625	370	2	q	q	X
ejpam-3625	370	3	,	,	PUNCT
ejpam-3625	370	4	r	r	NOUN
ejpam-3625	370	5	]	]	X
ejpam-3625	370	6	for	for	ADP
ejpam-3625	370	7	some	some	DET
ejpam-3625	370	8	r	r	NOUN
ejpam-3625	370	9	∈	∈	NOUN
ejpam-3625	370	10	v	v	NOUN
ejpam-3625	370	11	(	(	PUNCT
ejpam-3625	370	12	hp	hp	NOUN
ejpam-3625	370	13	)	)	PUNCT
ejpam-3625	370	14	\bv	\bv	NOUN
ejpam-3625	370	15	.	.	PUNCT
ejpam-3625	370	16	case	case	NOUN
ejpam-3625	370	17	2	2	NUM
ejpam-3625	370	18	.	.	X
ejpam-3625	371	1	p	p	X
ejpam-3625	371	2	,	,	PUNCT
ejpam-3625	371	3	q	q	PROPN
ejpam-3625	371	4	∈	∈	PROPN
ejpam-3625	371	5	v	v	ADP
ejpam-3625	371	6	(	(	PUNCT
ejpam-3625	371	7	hv	hv	NOUN
ejpam-3625	371	8	)	)	PUNCT
ejpam-3625	371	9	\bv	\bv	NOUN
ejpam-3625	371	10	since	since	SCONJ
ejpam-3625	371	11	bv	bv	PROPN
ejpam-3625	371	12	is	be	AUX
ejpam-3625	371	13	a	a	DET
ejpam-3625	371	14	strong	strong	ADJ
ejpam-3625	371	15	resolving	resolving	NOUN
ejpam-3625	371	16	set	set	NOUN
ejpam-3625	371	17	of	of	ADP
ejpam-3625	371	18	hv	hv	PROPN
ejpam-3625	371	19	,	,	PUNCT
ejpam-3625	371	20	there	there	PRON
ejpam-3625	371	21	exists	exist	VERB
ejpam-3625	371	22	t	t	PROPN
ejpam-3625	371	23	∈	∈	PROPN
ejpam-3625	371	24	bv	bv	PROPN
ejpam-3625	372	1	⊂	⊂	PROPN
ejpam-3625	372	2	s	s	VERB
ejpam-3625	372	3	that	that	SCONJ
ejpam-3625	372	4	strongly	strongly	ADV
ejpam-3625	372	5	resolves	resolve	VERB
ejpam-3625	372	6	p	p	NOUN
ejpam-3625	372	7	and	and	CCONJ
ejpam-3625	372	8	q.	q.	PROPN
ejpam-3625	372	9	case	case	NOUN
ejpam-3625	372	10	3	3	X
ejpam-3625	372	11	.	.	PUNCT
ejpam-3625	373	1	p	p	PROPN
ejpam-3625	373	2	∈	∈	PROPN
ejpam-3625	373	3	v	v	ADP
ejpam-3625	373	4	(	(	PUNCT
ejpam-3625	373	5	g	g	NOUN
ejpam-3625	373	6	)	)	PUNCT
ejpam-3625	373	7	\	\	PUNCT
ejpam-3625	374	1	(	(	PUNCT
ejpam-3625	374	2	a	a	DET
ejpam-3625	374	3	∪	∪	ADJ
ejpam-3625	374	4	{	{	PUNCT
ejpam-3625	374	5	v	v	NOUN
ejpam-3625	374	6	}	}	PUNCT
ejpam-3625	374	7	)	)	PUNCT
ejpam-3625	375	1	and	and	CCONJ
ejpam-3625	375	2	q	q	PROPN
ejpam-3625	375	3	∈	∈	PROPN
ejpam-3625	375	4	v	v	ADP
ejpam-3625	375	5	(	(	PUNCT
ejpam-3625	375	6	hv	hv	NOUN
ejpam-3625	375	7	)	)	PUNCT
ejpam-3625	375	8	\bv	\bv	NOUN
ejpam-3625	375	9	since	since	SCONJ
ejpam-3625	375	10	p	p	PROPN
ejpam-3625	375	11	6=	6=	PROPN
ejpam-3625	375	12	v	v	NOUN
ejpam-3625	375	13	,	,	PUNCT
ejpam-3625	375	14	then	then	ADV
ejpam-3625	375	15	v	v	X
ejpam-3625	375	16	(	(	PUNCT
ejpam-3625	375	17	hp	hp	PROPN
ejpam-3625	375	18	)	)	PUNCT
ejpam-3625	375	19	⊂	⊂	PROPN
ejpam-3625	375	20	s	s	PART
ejpam-3625	375	21	and	and	CCONJ
ejpam-3625	375	22	p	p	PROPN
ejpam-3625	375	23	∈	∈	PROPN
ejpam-3625	376	1	ig	ig	PROPN
ejpam-3625	376	2	◦	◦	NOUN
ejpam-3625	376	3	h	h	NOUN
ejpam-3625	377	1	[	[	X
ejpam-3625	377	2	q	q	X
ejpam-3625	377	3	,	,	PUNCT
ejpam-3625	377	4	z	z	X
ejpam-3625	377	5	]	]	X
ejpam-3625	377	6	for	for	ADP
ejpam-3625	377	7	all	all	DET
ejpam-3625	377	8	z	z	NOUN
ejpam-3625	377	9	∈	∈	PROPN
ejpam-3625	377	10	v	v	X
ejpam-3625	377	11	(	(	PUNCT
ejpam-3625	377	12	hp	hp	PROPN
ejpam-3625	377	13	)	)	PUNCT
ejpam-3625	377	14	.	.	PUNCT
ejpam-3625	378	1	references	reference	NOUN
ejpam-3625	378	2	179	179	NUM
ejpam-3625	378	3	case	case	NOUN
ejpam-3625	378	4	4	4	NUM
ejpam-3625	378	5	.	.	PUNCT
ejpam-3625	379	1	p	p	X
ejpam-3625	379	2	=	=	PUNCT
ejpam-3625	379	3	v	v	PROPN
ejpam-3625	379	4	,	,	PUNCT
ejpam-3625	379	5	q	q	PROPN
ejpam-3625	379	6	∈	∈	PROPN
ejpam-3625	379	7	v	v	ADP
ejpam-3625	379	8	(	(	PUNCT
ejpam-3625	379	9	hv	hv	NOUN
ejpam-3625	379	10	)	)	PUNCT
ejpam-3625	379	11	\bv	\bv	NOUN
ejpam-3625	379	12	let	let	VERB
ejpam-3625	379	13	t	t	PROPN
ejpam-3625	379	14	∈	∈	PROPN
ejpam-3625	379	15	ng(v	ng(v	PUNCT
ejpam-3625	379	16	)	)	PUNCT
ejpam-3625	379	17	.	.	PUNCT
ejpam-3625	380	1	then	then	ADV
ejpam-3625	380	2	v	v	INTJ
ejpam-3625	380	3	(	(	PUNCT
ejpam-3625	380	4	ht	ht	PROPN
ejpam-3625	380	5	)	)	PUNCT
ejpam-3625	380	6	⊂	⊂	PROPN
ejpam-3625	380	7	s	s	PART
ejpam-3625	380	8	and	and	CCONJ
ejpam-3625	380	9	p	p	PROPN
ejpam-3625	380	10	∈	∈	PROPN
ejpam-3625	381	1	ig	ig	PROPN
ejpam-3625	381	2	◦	◦	NOUN
ejpam-3625	381	3	h	h	NOUN
ejpam-3625	382	1	[	[	X
ejpam-3625	382	2	q	q	X
ejpam-3625	382	3	,	,	PUNCT
ejpam-3625	382	4	u	u	NOUN
ejpam-3625	382	5	]	]	X
ejpam-3625	382	6	,	,	PUNCT
ejpam-3625	382	7	for	for	ADP
ejpam-3625	382	8	some	some	DET
ejpam-3625	382	9	u	u	NOUN
ejpam-3625	382	10	∈	∈	PROPN
ejpam-3625	382	11	v	v	NOUN
ejpam-3625	382	12	(	(	PUNCT
ejpam-3625	382	13	ht	ht	PROPN
ejpam-3625	382	14	)	)	PUNCT
ejpam-3625	382	15	.	.	PUNCT
ejpam-3625	383	1	cases	case	NOUN
ejpam-3625	383	2	1	1	NUM
ejpam-3625	383	3	to	to	PART
ejpam-3625	383	4	4	4	NUM
ejpam-3625	383	5	imply	imply	VERB
ejpam-3625	383	6	that	that	SCONJ
ejpam-3625	383	7	s	s	VERB
ejpam-3625	383	8	is	be	AUX
ejpam-3625	383	9	a	a	DET
ejpam-3625	383	10	strong	strong	ADJ
ejpam-3625	383	11	resolving	resolving	NOUN
ejpam-3625	383	12	dominating	dominating	NOUN
ejpam-3625	383	13	set	set	NOUN
ejpam-3625	383	14	of	of	ADP
ejpam-3625	383	15	g	g	NOUN
ejpam-3625	383	16	◦	◦	NOUN
ejpam-3625	383	17	h	h	NOUN
ejpam-3625	383	18	and	and	CCONJ
ejpam-3625	383	19	(	(	PUNCT
ejpam-3625	383	20	i	i	NOUN
ejpam-3625	383	21	)	)	PUNCT
ejpam-3625	383	22	,	,	PUNCT
ejpam-3625	383	23	(	(	PUNCT
ejpam-3625	383	24	ii	ii	NOUN
ejpam-3625	383	25	)	)	PUNCT
ejpam-3625	383	26	,	,	PUNCT
ejpam-3625	383	27	(	(	PUNCT
ejpam-3625	383	28	iii	iii	X
ejpam-3625	383	29	)	)	PUNCT
ejpam-3625	383	30	imply	imply	VERB
ejpam-3625	383	31	that	that	SCONJ
ejpam-3625	383	32	s	s	VERB
ejpam-3625	383	33	is	be	AUX
ejpam-3625	383	34	a	a	DET
ejpam-3625	383	35	dominating	dominating	NOUN
ejpam-3625	383	36	set	set	NOUN
ejpam-3625	383	37	of	of	ADP
ejpam-3625	383	38	g	g	PROPN
ejpam-3625	383	39	◦	◦	NOUN
ejpam-3625	383	40	h.	h.	NOUN
ejpam-3625	383	41	accordingly	accordingly	ADV
ejpam-3625	383	42	,	,	PUNCT
ejpam-3625	383	43	s	s	VERB
ejpam-3625	383	44	is	be	AUX
ejpam-3625	383	45	a	a	DET
ejpam-3625	383	46	strong	strong	ADJ
ejpam-3625	383	47	resolving	resolving	NOUN
ejpam-3625	383	48	dominating	dominating	NOUN
ejpam-3625	383	49	set	set	NOUN
ejpam-3625	383	50	of	of	ADP
ejpam-3625	383	51	g	g	PROPN
ejpam-3625	383	52	◦	◦	NOUN
ejpam-3625	383	53	h.	h.	NOUN
ejpam-3625	383	54	corollary	corollary	ADJ
ejpam-3625	383	55	7	7	PROPN
ejpam-3625	383	56	.	.	PUNCT
ejpam-3625	384	1	let	let	VERB
ejpam-3625	384	2	g	g	NOUN
ejpam-3625	384	3	and	and	CCONJ
ejpam-3625	384	4	h	h	NOUN
ejpam-3625	384	5	be	be	AUX
ejpam-3625	384	6	connected	connect	VERB
ejpam-3625	384	7	graphs	graph	NOUN
ejpam-3625	384	8	of	of	ADP
ejpam-3625	384	9	orders	order	NOUN
ejpam-3625	384	10	m	m	VERB
ejpam-3625	384	11	and	and	CCONJ
ejpam-3625	384	12	n	n	CCONJ
ejpam-3625	384	13	,	,	PUNCT
ejpam-3625	384	14	respectively	respectively	ADV
ejpam-3625	384	15	γsr(g	γsr(g	ADP
ejpam-3625	384	16	◦	◦	NOUN
ejpam-3625	384	17	h	h	NOUN
ejpam-3625	384	18	)	)	PUNCT
ejpam-3625	385	1	=	=	PRON
ejpam-3625	385	2	{	{	PUNCT
ejpam-3625	385	3	(	(	PUNCT
ejpam-3625	385	4	m−	m−	PROPN
ejpam-3625	385	5	1)n+	1)n+	NUM
ejpam-3625	385	6	γsr(h	γsr(h	PROPN
ejpam-3625	385	7	)	)	PUNCT
ejpam-3625	385	8	,	,	PUNCT
ejpam-3625	385	9	if	if	SCONJ
ejpam-3625	385	10	γ(h	γ(h	NOUN
ejpam-3625	385	11	)	)	PUNCT
ejpam-3625	385	12	=	=	SYM
ejpam-3625	385	13	1	1	NUM
ejpam-3625	385	14	(	(	PUNCT
ejpam-3625	385	15	m−	m−	PROPN
ejpam-3625	385	16	1)n+	1)n+	NUM
ejpam-3625	385	17	γsr(k1	γsr(k1	PUNCT
ejpam-3625	386	1	+	+	NOUN
ejpam-3625	386	2	h	h	NOUN
ejpam-3625	386	3	)	)	PUNCT
ejpam-3625	386	4	,	,	PUNCT
ejpam-3625	386	5	if	if	SCONJ
ejpam-3625	386	6	γ(h	γ(h	NOUN
ejpam-3625	386	7	)	)	PUNCT
ejpam-3625	386	8	6=	6=	ADP
ejpam-3625	386	9	1	1	NUM
ejpam-3625	386	10	acknowledgements	acknowledgement	NOUN
ejpam-3625	386	11	this	this	DET
ejpam-3625	386	12	research	research	NOUN
ejpam-3625	386	13	is	be	AUX
ejpam-3625	386	14	funded	fund	VERB
ejpam-3625	386	15	by	by	ADP
ejpam-3625	386	16	the	the	DET
ejpam-3625	386	17	commission	commission	NOUN
ejpam-3625	386	18	on	on	ADP
ejpam-3625	386	19	higher	high	ADJ
ejpam-3625	386	20	education	education	NOUN
ejpam-3625	386	21	(	(	PUNCT
ejpam-3625	386	22	ched	che	VERB
ejpam-3625	386	23	)	)	PUNCT
ejpam-3625	386	24	and	and	CCONJ
ejpam-3625	386	25	mindanao	mindanao	PROPN
ejpam-3625	386	26	state	state	PROPN
ejpam-3625	386	27	university	university	PROPN
ejpam-3625	386	28	-	-	PUNCT
ejpam-3625	386	29	iligan	iligan	PROPN
ejpam-3625	386	30	institute	institute	PROPN
ejpam-3625	386	31	of	of	ADP
ejpam-3625	386	32	technology	technology	PROPN
ejpam-3625	386	33	,	,	PUNCT
ejpam-3625	386	34	philippines	philippine	NOUN
ejpam-3625	386	35	.	.	PUNCT
ejpam-3625	387	1	references	reference	NOUN
ejpam-3625	387	2	[	[	X
ejpam-3625	387	3	1	1	NUM
ejpam-3625	387	4	]	]	PUNCT
ejpam-3625	387	5	c.	c.	PROPN
ejpam-3625	387	6	berge	berge	PROPN
ejpam-3625	387	7	.	.	PUNCT
ejpam-3625	388	1	theorie	theorie	PROPN
ejpam-3625	388	2	des	des	PROPN
ejpam-3625	388	3	graphes	graphes	PROPN
ejpam-3625	388	4	et	et	PROPN
ejpam-3625	388	5	ses	ses	PROPN
ejpam-3625	388	6	applications	application	NOUN
ejpam-3625	388	7	.	.	PUNCT
ejpam-3625	389	1	metheun	metheun	NOUN
ejpam-3625	389	2	and	and	CCONJ
ejpam-3625	389	3	wiley	wiley	PROPN
ejpam-3625	389	4	,	,	PUNCT
ejpam-3625	389	5	london	london	PROPN
ejpam-3625	389	6	and	and	CCONJ
ejpam-3625	389	7	new	new	PROPN
ejpam-3625	389	8	york	york	PROPN
ejpam-3625	389	9	,	,	PUNCT
ejpam-3625	389	10	1962	1962	NUM
ejpam-3625	389	11	.	.	PUNCT
ejpam-3625	390	1	[	[	X
ejpam-3625	390	2	2	2	X
ejpam-3625	390	3	]	]	PUNCT
ejpam-3625	390	4	e.	e.	PROPN
ejpam-3625	390	5	cockayne	cockayne	PROPN
ejpam-3625	390	6	and	and	CCONJ
ejpam-3625	390	7	s.	s.	PROPN
ejpam-3625	390	8	hedetniemi	hedetniemi	PROPN
ejpam-3625	390	9	.	.	PUNCT
ejpam-3625	391	1	towards	towards	ADP
ejpam-3625	391	2	a	a	DET
ejpam-3625	391	3	theory	theory	NOUN
ejpam-3625	391	4	of	of	ADP
ejpam-3625	391	5	domination	domination	NOUN
ejpam-3625	391	6	in	in	ADP
ejpam-3625	391	7	graphs	graph	NOUN
ejpam-3625	391	8	.	.	PUNCT
ejpam-3625	392	1	networks	network	NOUN
ejpam-3625	392	2	,	,	PUNCT
ejpam-3625	392	3	7(3):247–261	7(3):247–261	NUM
ejpam-3625	392	4	,	,	PUNCT
ejpam-3625	392	5	1977	1977	NUM
ejpam-3625	392	6	.	.	PUNCT
ejpam-3625	393	1	[	[	X
ejpam-3625	393	2	3	3	NUM
ejpam-3625	393	3	]	]	PUNCT
ejpam-3625	393	4	a.	a.	NOUN
ejpam-3625	393	5	cuivillas	cuivilla	NOUN
ejpam-3625	393	6	and	and	CCONJ
ejpam-3625	393	7	jr	jr	PROPN
ejpam-3625	393	8	.	.	PROPN
ejpam-3625	393	9	s.	s.	PROPN
ejpam-3625	393	10	canoy	canoy	PROPN
ejpam-3625	393	11	.	.	PUNCT
ejpam-3625	394	1	restrained	restrained	ADJ
ejpam-3625	394	2	double	double	ADJ
ejpam-3625	394	3	domination	domination	NOUN
ejpam-3625	394	4	in	in	ADP
ejpam-3625	394	5	the	the	DET
ejpam-3625	394	6	join	join	NOUN
ejpam-3625	394	7	and	and	CCONJ
ejpam-3625	394	8	corona	corona	NOUN
ejpam-3625	394	9	of	of	ADP
ejpam-3625	394	10	graphs	graph	NOUN
ejpam-3625	394	11	.	.	PUNCT
ejpam-3625	395	1	international	international	ADJ
ejpam-3625	395	2	journal	journal	PROPN
ejpam-3625	395	3	of	of	ADP
ejpam-3625	395	4	math	math	NOUN
ejpam-3625	395	5	.	.	PUNCT
ejpam-3625	396	1	analysis	analysis	NOUN
ejpam-3625	396	2	,	,	PUNCT
ejpam-3625	396	3	8(27):1339–1347	8(27):1339–1347	NUM
ejpam-3625	396	4	,	,	PUNCT
ejpam-3625	396	5	2014	2014	NUM
ejpam-3625	396	6	.	.	PUNCT
ejpam-3625	397	1	[	[	X
ejpam-3625	397	2	4	4	NUM
ejpam-3625	397	3	]	]	PUNCT
ejpam-3625	397	4	f.	f.	PROPN
ejpam-3625	397	5	harary	harary	PROPN
ejpam-3625	397	6	.	.	PUNCT
ejpam-3625	398	1	graph	graph	NOUN
ejpam-3625	398	2	theory	theory	NOUN
ejpam-3625	398	3	.	.	PUNCT
ejpam-3625	399	1	addison	addison	PROPN
ejpam-3625	399	2	-	-	PUNCT
ejpam-3625	399	3	wesley	wesley	PROPN
ejpam-3625	399	4	publishing	publishing	PROPN
ejpam-3625	399	5	company	company	NOUN
ejpam-3625	399	6	,	,	PUNCT
ejpam-3625	399	7	usa	usa	PROPN
ejpam-3625	399	8	,	,	PUNCT
ejpam-3625	399	9	1969	1969	NUM
ejpam-3625	399	10	.	.	PUNCT
ejpam-3625	400	1	[	[	X
ejpam-3625	400	2	5	5	NUM
ejpam-3625	400	3	]	]	X
ejpam-3625	400	4	o.	o.	NOUN
ejpam-3625	400	5	oellermann	oellermann	PROPN
ejpam-3625	400	6	and	and	CCONJ
ejpam-3625	400	7	j.	j.	PROPN
ejpam-3625	400	8	peter	peter	PROPN
ejpam-3625	400	9	-	-	PUNCT
ejpam-3625	400	10	fransen	fransen	PROPN
ejpam-3625	400	11	.	.	PUNCT
ejpam-3625	401	1	the	the	DET
ejpam-3625	401	2	strong	strong	ADJ
ejpam-3625	401	3	metric	metric	ADJ
ejpam-3625	401	4	dimension	dimension	NOUN
ejpam-3625	401	5	of	of	ADP
ejpam-3625	401	6	graphs	graph	NOUN
ejpam-3625	401	7	and	and	CCONJ
ejpam-3625	401	8	digraphs	digraph	NOUN
ejpam-3625	401	9	.	.	PUNCT
ejpam-3625	402	1	discrete	discrete	ADJ
ejpam-3625	402	2	applied	apply	VERB
ejpam-3625	402	3	mathematics	mathematic	NOUN
ejpam-3625	402	4	,	,	PUNCT
ejpam-3625	402	5	155(3):356–364	155(3):356–364	NUM
ejpam-3625	402	6	,	,	PUNCT
ejpam-3625	402	7	2007	2007	NUM
ejpam-3625	402	8	.	.	PUNCT
ejpam-3625	403	1	[	[	X
ejpam-3625	403	2	6	6	NUM
ejpam-3625	403	3	]	]	PUNCT
ejpam-3625	403	4	p.	p.	NOUN
ejpam-3625	403	5	slater	slater	PROPN
ejpam-3625	403	6	.	.	PUNCT
ejpam-3625	404	1	dominating	dominating	NOUN
ejpam-3625	404	2	and	and	CCONJ
ejpam-3625	404	3	reference	reference	NOUN
ejpam-3625	404	4	sets	set	NOUN
ejpam-3625	404	5	in	in	ADP
ejpam-3625	404	6	a	a	DET
ejpam-3625	404	7	graph	graph	NOUN
ejpam-3625	404	8	.	.	PUNCT
ejpam-3625	405	1	journal	journal	NOUN
ejpam-3625	405	2	of	of	ADP
ejpam-3625	405	3	mathematics	mathematic	NOUN
ejpam-3625	405	4	and	and	CCONJ
ejpam-3625	405	5	physical	physical	ADJ
ejpam-3625	405	6	science	science	NOUN
ejpam-3625	405	7	,	,	PUNCT
ejpam-3625	405	8	22(4):445–455	22(4):445–455	PROPN
ejpam-3625	405	9	,	,	PUNCT
ejpam-3625	405	10	1988	1988	NUM
ejpam-3625	405	11	.	.	PUNCT