id	sid	tid	token	lemma	pos
ejpam-4112	1	1	european	european	PROPN
ejpam-4112	1	2	journal	journal	PROPN
ejpam-4112	1	3	of	of	ADP
ejpam-4112	1	4	pure	pure	ADJ
ejpam-4112	1	5	and	and	CCONJ
ejpam-4112	1	6	applied	apply	VERB
ejpam-4112	1	7	mathematics	mathematic	NOUN
ejpam-4112	1	8	vol	vol	NOUN
ejpam-4112	1	9	.	.	PUNCT
ejpam-4112	2	1	14	14	NUM
ejpam-4112	2	2	,	,	PUNCT
ejpam-4112	2	3	no	no	INTJ
ejpam-4112	2	4	.	.	NOUN
ejpam-4112	2	5	4	4	NUM
ejpam-4112	2	6	,	,	PUNCT
ejpam-4112	2	7	2021	2021	NUM
ejpam-4112	2	8	,	,	PUNCT
ejpam-4112	2	9	1367	1367	NUM
ejpam-4112	2	10	-	-	SYM
ejpam-4112	2	11	1378	1378	NUM
ejpam-4112	2	12	issn	issn	PROPN
ejpam-4112	2	13	1307	1307	NUM
ejpam-4112	2	14	-	-	SYM
ejpam-4112	2	15	5543	5543	NUM
ejpam-4112	2	16	–	–	PUNCT
ejpam-4112	3	1	ejpam.com	ejpam.com	X
ejpam-4112	3	2	published	publish	VERB
ejpam-4112	3	3	by	by	ADP
ejpam-4112	3	4	new	new	PROPN
ejpam-4112	3	5	york	york	PROPN
ejpam-4112	3	6	business	business	PROPN
ejpam-4112	3	7	global	global	PROPN
ejpam-4112	3	8	on	on	ADP
ejpam-4112	3	9	restrained	restrained	ADJ
ejpam-4112	3	10	strong	strong	ADJ
ejpam-4112	3	11	resolving	resolving	NOUN
ejpam-4112	3	12	domination	domination	NOUN
ejpam-4112	3	13	in	in	ADP
ejpam-4112	3	14	graphs	graph	NOUN
ejpam-4112	3	15	helyn	helyn	NOUN
ejpam-4112	3	16	c.	c.	PROPN
ejpam-4112	3	17	sumaoy1	sumaoy1	PROPN
ejpam-4112	3	18	,	,	PUNCT
ejpam-4112	3	19	helen	helen	PROPN
ejpam-4112	3	20	m.	m.	PROPN
ejpam-4112	3	21	rara2,∗	rara2,∗	PROPN
ejpam-4112	3	22	1	1	NUM
ejpam-4112	3	23	department	department	NOUN
ejpam-4112	3	24	of	of	ADP
ejpam-4112	3	25	mathematics	mathematic	NOUN
ejpam-4112	3	26	and	and	CCONJ
ejpam-4112	3	27	statistics	statistic	NOUN
ejpam-4112	3	28	,	,	PUNCT
ejpam-4112	3	29	college	college	NOUN
ejpam-4112	3	30	of	of	ADP
ejpam-4112	3	31	science	science	NOUN
ejpam-4112	3	32	and	and	CCONJ
ejpam-4112	3	33	mathematics	mathematic	NOUN
ejpam-4112	3	34	,	,	PUNCT
ejpam-4112	3	35	center	center	NOUN
ejpam-4112	3	36	of	of	ADP
ejpam-4112	3	37	graph	graph	NOUN
ejpam-4112	3	38	theory	theory	NOUN
ejpam-4112	3	39	,	,	PUNCT
ejpam-4112	3	40	algebra	algebra	NOUN
ejpam-4112	3	41	,	,	PUNCT
ejpam-4112	3	42	mindanao	mindanao	PROPN
ejpam-4112	3	43	state	state	PROPN
ejpam-4112	3	44	university	university	PROPN
ejpam-4112	3	45	-	-	PUNCT
ejpam-4112	3	46	iligan	iligan	PROPN
ejpam-4112	3	47	institute	institute	PROPN
ejpam-4112	3	48	of	of	ADP
ejpam-4112	3	49	technology	technology	PROPN
ejpam-4112	3	50	,	,	PUNCT
ejpam-4112	3	51	9200	9200	NUM
ejpam-4112	3	52	iligan	iligan	ADJ
ejpam-4112	3	53	city	city	NOUN
ejpam-4112	3	54	,	,	PUNCT
ejpam-4112	3	55	philippines	philippine	VERB
ejpam-4112	3	56	2	2	NUM
ejpam-4112	3	57	analysis	analysis	NOUN
ejpam-4112	3	58	-	-	PUNCT
ejpam-4112	3	59	premier	premier	NOUN
ejpam-4112	3	60	research	research	NOUN
ejpam-4112	3	61	institute	institute	PROPN
ejpam-4112	3	62	of	of	ADP
ejpam-4112	3	63	science	science	NOUN
ejpam-4112	3	64	and	and	CCONJ
ejpam-4112	3	65	mathematics	mathematic	NOUN
ejpam-4112	3	66	,	,	PUNCT
ejpam-4112	3	67	mindanao	mindanao	PROPN
ejpam-4112	3	68	state	state	PROPN
ejpam-4112	3	69	universityiligan	universityiligan	PROPN
ejpam-4112	3	70	institute	institute	PROPN
ejpam-4112	3	71	of	of	ADP
ejpam-4112	3	72	technology	technology	PROPN
ejpam-4112	3	73	,	,	PUNCT
ejpam-4112	3	74	9200	9200	NUM
ejpam-4112	3	75	iligan	iligan	ADJ
ejpam-4112	3	76	city	city	NOUN
ejpam-4112	3	77	,	,	PUNCT
ejpam-4112	3	78	philippines	philippine	NOUN
ejpam-4112	3	79	abstract	abstract	ADJ
ejpam-4112	3	80	.	.	PUNCT
ejpam-4112	4	1	a	a	DET
ejpam-4112	4	2	set	set	NOUN
ejpam-4112	4	3	s	s	NOUN
ejpam-4112	4	4	⊆	⊆	NUM
ejpam-4112	4	5	v	v	NOUN
ejpam-4112	4	6	(	(	PUNCT
ejpam-4112	4	7	g	g	NOUN
ejpam-4112	4	8	)	)	PUNCT
ejpam-4112	4	9	is	be	AUX
ejpam-4112	4	10	a	a	DET
ejpam-4112	4	11	restrained	restrained	ADJ
ejpam-4112	4	12	strong	strong	ADJ
ejpam-4112	4	13	resolving	resolve	VERB
ejpam-4112	4	14	dominating	dominating	NOUN
ejpam-4112	4	15	set	set	VERB
ejpam-4112	4	16	in	in	ADP
ejpam-4112	4	17	g	g	PROPN
ejpam-4112	4	18	if	if	SCONJ
ejpam-4112	4	19	s	s	VERB
ejpam-4112	4	20	is	be	AUX
ejpam-4112	4	21	a	a	DET
ejpam-4112	4	22	strong	strong	ADJ
ejpam-4112	4	23	resolving	resolving	NOUN
ejpam-4112	4	24	dominating	dominating	NOUN
ejpam-4112	4	25	set	set	VERB
ejpam-4112	4	26	in	in	ADP
ejpam-4112	4	27	g	g	PROPN
ejpam-4112	4	28	and	and	CCONJ
ejpam-4112	4	29	s	s	PART
ejpam-4112	4	30	=	=	SYM
ejpam-4112	4	31	v	v	X
ejpam-4112	4	32	(	(	PUNCT
ejpam-4112	4	33	g	g	NOUN
ejpam-4112	4	34	)	)	PUNCT
ejpam-4112	4	35	or	or	CCONJ
ejpam-4112	4	36	⟨v	⟨v	NUM
ejpam-4112	4	37	(	(	PUNCT
ejpam-4112	4	38	g	g	NOUN
ejpam-4112	4	39	)	)	PUNCT
ejpam-4112	4	40	\	\	PROPN
ejpam-4112	4	41	s⟩	s⟩	NOUN
ejpam-4112	4	42	has	have	VERB
ejpam-4112	4	43	no	no	DET
ejpam-4112	4	44	isolated	isolated	ADJ
ejpam-4112	4	45	vertex	vertex	NOUN
ejpam-4112	4	46	.	.	PUNCT
ejpam-4112	5	1	the	the	DET
ejpam-4112	5	2	restrained	restrained	ADJ
ejpam-4112	5	3	strong	strong	ADJ
ejpam-4112	5	4	resolving	resolve	VERB
ejpam-4112	5	5	domination	domination	NOUN
ejpam-4112	5	6	number	number	NOUN
ejpam-4112	5	7	of	of	ADP
ejpam-4112	5	8	g	g	NOUN
ejpam-4112	5	9	,	,	PUNCT
ejpam-4112	5	10	denoted	denote	VERB
ejpam-4112	5	11	by	by	ADP
ejpam-4112	5	12	γrsr(g	γrsr(g	PROPN
ejpam-4112	5	13	)	)	PUNCT
ejpam-4112	5	14	,	,	PUNCT
ejpam-4112	5	15	is	be	AUX
ejpam-4112	5	16	the	the	DET
ejpam-4112	5	17	smallest	small	ADJ
ejpam-4112	5	18	cardinality	cardinality	NOUN
ejpam-4112	5	19	of	of	ADP
ejpam-4112	5	20	a	a	DET
ejpam-4112	5	21	restrained	restrain	VERB
ejpam-4112	5	22	strong	strong	ADJ
ejpam-4112	5	23	resolving	resolve	VERB
ejpam-4112	5	24	dominating	dominating	NOUN
ejpam-4112	5	25	set	set	VERB
ejpam-4112	5	26	in	in	ADP
ejpam-4112	5	27	g.	g.	PROPN
ejpam-4112	5	28	in	in	ADP
ejpam-4112	5	29	this	this	DET
ejpam-4112	5	30	paper	paper	NOUN
ejpam-4112	5	31	,	,	PUNCT
ejpam-4112	5	32	we	we	PRON
ejpam-4112	5	33	present	present	VERB
ejpam-4112	5	34	characterizations	characterization	NOUN
ejpam-4112	5	35	of	of	ADP
ejpam-4112	5	36	the	the	DET
ejpam-4112	5	37	restrained	restrained	ADJ
ejpam-4112	5	38	strong	strong	ADJ
ejpam-4112	5	39	resolving	resolve	VERB
ejpam-4112	5	40	dominating	dominating	NOUN
ejpam-4112	5	41	sets	set	NOUN
ejpam-4112	5	42	in	in	ADP
ejpam-4112	5	43	the	the	DET
ejpam-4112	5	44	join	join	NOUN
ejpam-4112	5	45	,	,	PUNCT
ejpam-4112	5	46	corona	corona	NOUN
ejpam-4112	5	47	and	and	CCONJ
ejpam-4112	5	48	lexicographic	lexicographic	ADJ
ejpam-4112	5	49	product	product	NOUN
ejpam-4112	5	50	of	of	ADP
ejpam-4112	5	51	two	two	NUM
ejpam-4112	5	52	graphs	graph	NOUN
ejpam-4112	5	53	and	and	CCONJ
ejpam-4112	5	54	determine	determine	VERB
ejpam-4112	5	55	the	the	DET
ejpam-4112	5	56	exact	exact	ADJ
ejpam-4112	5	57	value	value	NOUN
ejpam-4112	5	58	of	of	ADP
ejpam-4112	5	59	the	the	DET
ejpam-4112	5	60	restrained	restrain	VERB
ejpam-4112	5	61	strong	strong	ADJ
ejpam-4112	5	62	resolving	resolve	VERB
ejpam-4112	5	63	domination	domination	NOUN
ejpam-4112	5	64	number	number	NOUN
ejpam-4112	5	65	of	of	ADP
ejpam-4112	5	66	each	each	PRON
ejpam-4112	5	67	of	of	ADP
ejpam-4112	5	68	these	these	DET
ejpam-4112	5	69	graphs	graph	NOUN
ejpam-4112	5	70	.	.	PUNCT
ejpam-4112	6	1	2020	2020	NUM
ejpam-4112	6	2	mathematics	mathematic	NOUN
ejpam-4112	6	3	subject	subject	NOUN
ejpam-4112	6	4	classifications	classification	NOUN
ejpam-4112	6	5	:	:	PUNCT
ejpam-4112	6	6	05c69	05c69	X
ejpam-4112	6	7	key	key	ADJ
ejpam-4112	6	8	words	word	NOUN
ejpam-4112	6	9	and	and	CCONJ
ejpam-4112	6	10	phrases	phrase	NOUN
ejpam-4112	6	11	:	:	PUNCT
ejpam-4112	6	12	restrained	restrain	VERB
ejpam-4112	6	13	strong	strong	ADJ
ejpam-4112	6	14	resolving	resolve	VERB
ejpam-4112	6	15	dominating	dominating	NOUN
ejpam-4112	6	16	set	set	NOUN
ejpam-4112	6	17	,	,	PUNCT
ejpam-4112	6	18	restrained	restrain	VERB
ejpam-4112	6	19	strong	strong	ADJ
ejpam-4112	6	20	resolving	resolve	VERB
ejpam-4112	6	21	domination	domination	NOUN
ejpam-4112	6	22	number	number	NOUN
ejpam-4112	6	23	,	,	PUNCT
ejpam-4112	6	24	join	join	NOUN
ejpam-4112	6	25	,	,	PUNCT
ejpam-4112	6	26	corona	corona	PROPN
ejpam-4112	6	27	,	,	PUNCT
ejpam-4112	6	28	lexicographic	lexicographic	ADJ
ejpam-4112	6	29	product	product	NOUN
ejpam-4112	6	30	1	1	NUM
ejpam-4112	6	31	.	.	PUNCT
ejpam-4112	7	1	introduction	introduction	NOUN
ejpam-4112	7	2	domination	domination	NOUN
ejpam-4112	7	3	in	in	ADP
ejpam-4112	7	4	graphs	graph	NOUN
ejpam-4112	7	5	was	be	AUX
ejpam-4112	7	6	first	first	ADV
ejpam-4112	7	7	introduced	introduce	VERB
ejpam-4112	7	8	by	by	ADP
ejpam-4112	7	9	c.	c.	PROPN
ejpam-4112	7	10	berge	berge	PROPN
ejpam-4112	7	11	in	in	ADP
ejpam-4112	7	12	1958	1958	NUM
ejpam-4112	7	13	[	[	X
ejpam-4112	7	14	1	1	NUM
ejpam-4112	7	15	]	]	PUNCT
ejpam-4112	7	16	.	.	PUNCT
ejpam-4112	8	1	there	there	PRON
ejpam-4112	8	2	are	be	VERB
ejpam-4112	8	3	many	many	ADJ
ejpam-4112	8	4	studies	study	NOUN
ejpam-4112	8	5	involving	involve	VERB
ejpam-4112	8	6	domination	domination	NOUN
ejpam-4112	8	7	and	and	CCONJ
ejpam-4112	8	8	its	its	PRON
ejpam-4112	8	9	variations	variation	NOUN
ejpam-4112	8	10	.	.	PUNCT
ejpam-4112	9	1	slater	slater	NOUN
ejpam-4112	10	1	[	[	X
ejpam-4112	10	2	8	8	NUM
ejpam-4112	10	3	]	]	PUNCT
ejpam-4112	10	4	introduced	introduce	VERB
ejpam-4112	10	5	and	and	CCONJ
ejpam-4112	10	6	studied	study	VERB
ejpam-4112	10	7	the	the	DET
ejpam-4112	10	8	concept	concept	NOUN
ejpam-4112	10	9	of	of	ADP
ejpam-4112	10	10	resolving	resolve	VERB
ejpam-4112	10	11	set	set	NOUN
ejpam-4112	10	12	.	.	PUNCT
ejpam-4112	11	1	in	in	ADP
ejpam-4112	11	2	2003	2003	NUM
ejpam-4112	11	3	,	,	PUNCT
ejpam-4112	11	4	robert	robert	PROPN
ejpam-4112	11	5	brigham	brigham	PROPN
ejpam-4112	11	6	et	et	PROPN
ejpam-4112	11	7	al	al	PROPN
ejpam-4112	11	8	.	.	PUNCT
ejpam-4112	12	1	[	[	X
ejpam-4112	12	2	18	18	NUM
ejpam-4112	12	3	]	]	PUNCT
ejpam-4112	12	4	linked	link	VERB
ejpam-4112	12	5	the	the	DET
ejpam-4112	12	6	concepts	concept	NOUN
ejpam-4112	12	7	of	of	ADP
ejpam-4112	12	8	resolving	resolving	NOUN
ejpam-4112	12	9	and	and	CCONJ
ejpam-4112	12	10	domination	domination	NOUN
ejpam-4112	12	11	.	.	PUNCT
ejpam-4112	13	1	in	in	ADP
ejpam-4112	13	2	their	their	PRON
ejpam-4112	13	3	article	article	NOUN
ejpam-4112	13	4	,	,	PUNCT
ejpam-4112	13	5	they	they	PRON
ejpam-4112	13	6	defined	define	VERB
ejpam-4112	13	7	a	a	DET
ejpam-4112	13	8	resolving	resolve	VERB
ejpam-4112	13	9	dominating	dominating	NOUN
ejpam-4112	13	10	set	set	VERB
ejpam-4112	13	11	as	as	ADP
ejpam-4112	13	12	a	a	DET
ejpam-4112	13	13	set	set	NOUN
ejpam-4112	13	14	that	that	PRON
ejpam-4112	13	15	is	be	AUX
ejpam-4112	13	16	both	both	PRON
ejpam-4112	13	17	resolving	resolve	VERB
ejpam-4112	13	18	and	and	CCONJ
ejpam-4112	13	19	dominating	dominating	NOUN
ejpam-4112	13	20	.	.	PUNCT
ejpam-4112	14	1	resolving	resolve	VERB
ejpam-4112	14	2	sets	set	NOUN
ejpam-4112	14	3	and	and	CCONJ
ejpam-4112	14	4	resolving	resolve	VERB
ejpam-4112	14	5	dominating	dominating	NOUN
ejpam-4112	14	6	sets	set	NOUN
ejpam-4112	14	7	were	be	AUX
ejpam-4112	14	8	further	far	ADV
ejpam-4112	14	9	studied	study	VERB
ejpam-4112	14	10	in	in	ADP
ejpam-4112	14	11	[	[	X
ejpam-4112	14	12	2	2	NUM
ejpam-4112	14	13	,	,	PUNCT
ejpam-4112	14	14	3	3	NUM
ejpam-4112	14	15	]	]	PUNCT
ejpam-4112	14	16	.	.	PUNCT
ejpam-4112	15	1	oellermann	oellermann	PROPN
ejpam-4112	15	2	,	,	PUNCT
ejpam-4112	15	3	o.	o.	NOUN
ejpam-4112	15	4	r	r	NOUN
ejpam-4112	15	5	,	,	PUNCT
ejpam-4112	15	6	and	and	CCONJ
ejpam-4112	15	7	peters	peters	PROPN
ejpam-4112	15	8	-	-	PUNCT
ejpam-4112	15	9	fransen	fransen	PROPN
ejpam-4112	15	10	,	,	PUNCT
ejpam-4112	15	11	j.	j.	PROPN
ejpam-4112	16	1	[	[	X
ejpam-4112	16	2	6	6	NUM
ejpam-4112	16	3	]	]	PUNCT
ejpam-4112	16	4	introduced	introduce	VERB
ejpam-4112	16	5	and	and	CCONJ
ejpam-4112	16	6	studied	study	VERB
ejpam-4112	16	7	the	the	DET
ejpam-4112	16	8	concept	concept	NOUN
ejpam-4112	16	9	of	of	ADP
ejpam-4112	16	10	strong	strong	ADJ
ejpam-4112	16	11	resolving	resolving	NOUN
ejpam-4112	16	12	set	set	NOUN
ejpam-4112	16	13	.	.	PUNCT
ejpam-4112	17	1	domke	domke	PROPN
ejpam-4112	17	2	et	et	PROPN
ejpam-4112	17	3	.	.	PUNCT
ejpam-4112	18	1	al	al	PROPN
ejpam-4112	19	1	[	[	X
ejpam-4112	19	2	7	7	NUM
ejpam-4112	19	3	]	]	PUNCT
ejpam-4112	19	4	introduced	introduce	VERB
ejpam-4112	19	5	and	and	CCONJ
ejpam-4112	19	6	investigated	investigate	VERB
ejpam-4112	19	7	the	the	DET
ejpam-4112	19	8	concept	concept	NOUN
ejpam-4112	19	9	of	of	ADP
ejpam-4112	19	10	restrained	restrained	ADJ
ejpam-4112	19	11	domination	domination	NOUN
ejpam-4112	19	12	in	in	ADP
ejpam-4112	19	13	graphs	graph	NOUN
ejpam-4112	19	14	.	.	PUNCT
ejpam-4112	20	1	khuller	khuller	NOUN
ejpam-4112	20	2	,	,	PUNCT
ejpam-4112	20	3	et	et	NOUN
ejpam-4112	20	4	.	.	PUNCT
ejpam-4112	21	1	al	al	PROPN
ejpam-4112	21	2	.	.	PUNCT
ejpam-4112	22	1	[	[	X
ejpam-4112	22	2	11	11	NUM
ejpam-4112	22	3	]	]	PUNCT
ejpam-4112	22	4	introduced	introduce	VERB
ejpam-4112	22	5	the	the	DET
ejpam-4112	22	6	concept	concept	NOUN
ejpam-4112	22	7	of	of	ADP
ejpam-4112	22	8	metric	metric	ADJ
ejpam-4112	22	9	dimension	dimension	NOUN
ejpam-4112	22	10	and	and	CCONJ
ejpam-4112	22	11	this	this	PRON
ejpam-4112	22	12	has	have	AUX
ejpam-4112	22	13	grown	grow	VERB
ejpam-4112	22	14	to	to	PART
ejpam-4112	22	15	become	become	VERB
ejpam-4112	22	16	an	an	DET
ejpam-4112	22	17	interesting	interesting	ADJ
ejpam-4112	22	18	topic	topic	NOUN
ejpam-4112	22	19	in	in	ADP
ejpam-4112	22	20	graph	graph	NOUN
ejpam-4112	22	21	theory	theory	NOUN
ejpam-4112	22	22	.	.	PUNCT
ejpam-4112	23	1	in	in	ADP
ejpam-4112	23	2	line	line	NOUN
ejpam-4112	23	3	with	with	ADP
ejpam-4112	23	4	this	this	PRON
ejpam-4112	23	5	,	,	PUNCT
ejpam-4112	23	6	sebo	sebo	NOUN
ejpam-4112	23	7	and	and	CCONJ
ejpam-4112	23	8	tannier	tannier	NOUN
ejpam-4112	23	9	[	[	X
ejpam-4112	23	10	13	13	NUM
ejpam-4112	23	11	]	]	PUNCT
ejpam-4112	23	12	introduced	introduce	VERB
ejpam-4112	23	13	the	the	DET
ejpam-4112	23	14	concept	concept	NOUN
ejpam-4112	23	15	of	of	ADP
ejpam-4112	23	16	strong	strong	ADJ
ejpam-4112	23	17	metric	metric	ADJ
ejpam-4112	23	18	dimension	dimension	NOUN
ejpam-4112	23	19	,	,	PUNCT
ejpam-4112	23	20	a	a	DET
ejpam-4112	23	21	concept	concept	NOUN
ejpam-4112	23	22	which	which	PRON
ejpam-4112	23	23	is	be	AUX
ejpam-4112	23	24	more	more	ADV
ejpam-4112	23	25	restrictive	restrictive	ADJ
ejpam-4112	23	26	than	than	ADP
ejpam-4112	23	27	∗corresponding	∗corresponde	VERB
ejpam-4112	23	28	author	author	NOUN
ejpam-4112	23	29	.	.	PUNCT
ejpam-4112	24	1	doi	doi	NOUN
ejpam-4112	24	2	:	:	PUNCT
ejpam-4112	24	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4112	https://doi.org/10.29020/nybg.ejpam.v14i4.4112	ADJ
ejpam-4112	24	4	email	email	NOUN
ejpam-4112	24	5	addresses	address	NOUN
ejpam-4112	24	6	:	:	PUNCT
ejpam-4112	24	7	helyn.sumaoy@g.msuiit.edu.ph	helyn.sumaoy@g.msuiit.edu.ph	PROPN
ejpam-4112	24	8	(	(	PUNCT
ejpam-4112	24	9	h.	h.	NOUN
ejpam-4112	24	10	sumaoy	sumaoy	PROPN
ejpam-4112	24	11	)	)	PUNCT
ejpam-4112	24	12	,	,	PUNCT
ejpam-4112	24	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4112	24	14	,	,	PUNCT
ejpam-4112	24	15	helenrara@gmail.com	helenrara@gmail.com	PROPN
ejpam-4112	24	16	(	(	PUNCT
ejpam-4112	24	17	h.	h.	PROPN
ejpam-4112	24	18	rara	rara	PROPN
ejpam-4112	24	19	)	)	PUNCT
ejpam-4112	24	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4112	24	21	1367	1367	NUM
ejpam-4112	25	1	©	©	PROPN
ejpam-4112	25	2	2021	2021	NUM
ejpam-4112	25	3	ejpam	ejpam	VERB
ejpam-4112	25	4	all	all	DET
ejpam-4112	25	5	rights	right	NOUN
ejpam-4112	25	6	reserved	reserve	VERB
ejpam-4112	25	7	.	.	PUNCT
ejpam-4112	26	1	h.	h.	PROPN
ejpam-4112	26	2	sumaoy	sumaoy	PROPN
ejpam-4112	26	3	,	,	PUNCT
ejpam-4112	26	4	h.	h.	PROPN
ejpam-4112	26	5	rara	rara	PROPN
ejpam-4112	26	6	/	/	SYM
ejpam-4112	26	7	eur	eur	PROPN
ejpam-4112	26	8	.	.	PUNCT
ejpam-4112	27	1	j.	j.	PROPN
ejpam-4112	27	2	pure	pure	PROPN
ejpam-4112	27	3	appl	appl	PROPN
ejpam-4112	27	4	.	.	PROPN
ejpam-4112	27	5	math	math	PROPN
ejpam-4112	27	6	,	,	PUNCT
ejpam-4112	27	7	14	14	NUM
ejpam-4112	27	8	(	(	PUNCT
ejpam-4112	27	9	4	4	NUM
ejpam-4112	27	10	)	)	PUNCT
ejpam-4112	27	11	(	(	PUNCT
ejpam-4112	27	12	2021	2021	NUM
ejpam-4112	27	13	)	)	PUNCT
ejpam-4112	27	14	,	,	PUNCT
ejpam-4112	27	15	1367	1367	NUM
ejpam-4112	27	16	-	-	SYM
ejpam-4112	27	17	1378	1378	NUM
ejpam-4112	27	18	1368	1368	NUM
ejpam-4112	27	19	metric	metric	ADJ
ejpam-4112	27	20	dimension	dimension	NOUN
ejpam-4112	27	21	.	.	PUNCT
ejpam-4112	28	1	after	after	ADP
ejpam-4112	28	2	its	its	PRON
ejpam-4112	28	3	introduction	introduction	NOUN
ejpam-4112	28	4	,	,	PUNCT
ejpam-4112	28	5	slater	slater	NOUN
ejpam-4112	28	6	in	in	ADP
ejpam-4112	28	7	[	[	X
ejpam-4112	28	8	8	8	NUM
ejpam-4112	28	9	]	]	PUNCT
ejpam-4112	28	10	studied	study	VERB
ejpam-4112	28	11	it	it	PRON
ejpam-4112	28	12	and	and	CCONJ
ejpam-4112	28	13	discovered	discover	VERB
ejpam-4112	28	14	its	its	PRON
ejpam-4112	28	15	usefulness	usefulness	NOUN
ejpam-4112	28	16	when	when	SCONJ
ejpam-4112	28	17	working	work	VERB
ejpam-4112	28	18	with	with	ADP
ejpam-4112	28	19	the	the	DET
ejpam-4112	28	20	united	united	PROPN
ejpam-4112	28	21	states	states	PROPN
ejpam-4112	28	22	sonar	sonar	NOUN
ejpam-4112	28	23	and	and	CCONJ
ejpam-4112	28	24	coast	coast	NOUN
ejpam-4112	28	25	guard	guard	PROPN
ejpam-4112	28	26	loran	loran	NOUN
ejpam-4112	28	27	(	(	PUNCT
ejpam-4112	28	28	long	long	ADJ
ejpam-4112	28	29	range	range	NOUN
ejpam-4112	28	30	aids	aid	NOUN
ejpam-4112	28	31	to	to	ADP
ejpam-4112	28	32	navigation	navigation	NOUN
ejpam-4112	28	33	)	)	PUNCT
ejpam-4112	28	34	stations	station	NOUN
ejpam-4112	28	35	.	.	PUNCT
ejpam-4112	29	1	its	its	PRON
ejpam-4112	29	2	applications	application	NOUN
ejpam-4112	29	3	arise	arise	VERB
ejpam-4112	29	4	in	in	ADP
ejpam-4112	29	5	many	many	ADJ
ejpam-4112	29	6	diverse	diverse	ADJ
ejpam-4112	29	7	fields	field	NOUN
ejpam-4112	29	8	including	include	VERB
ejpam-4112	29	9	chemistry	chemistry	NOUN
ejpam-4112	29	10	,	,	PUNCT
ejpam-4112	29	11	for	for	ADP
ejpam-4112	29	12	representing	represent	VERB
ejpam-4112	29	13	chemical	chemical	NOUN
ejpam-4112	29	14	compounds	compound	NOUN
ejpam-4112	29	15	[	[	X
ejpam-4112	29	16	10	10	NUM
ejpam-4112	29	17	]	]	PUNCT
ejpam-4112	29	18	,	,	PUNCT
ejpam-4112	29	19	the	the	DET
ejpam-4112	29	20	robot	robot	NOUN
ejpam-4112	29	21	navigation	navigation	NOUN
ejpam-4112	30	1	[	[	X
ejpam-4112	30	2	11	11	NUM
ejpam-4112	30	3	]	]	PUNCT
ejpam-4112	30	4	and	and	CCONJ
ejpam-4112	30	5	geographical	geographical	ADJ
ejpam-4112	30	6	routing	routing	NOUN
ejpam-4112	30	7	protocols	protocol	NOUN
ejpam-4112	31	1	[	[	X
ejpam-4112	31	2	12	12	NUM
ejpam-4112	31	3	]	]	PUNCT
ejpam-4112	31	4	,	,	PUNCT
ejpam-4112	31	5	to	to	PART
ejpam-4112	31	6	name	name	VERB
ejpam-4112	31	7	a	a	DET
ejpam-4112	31	8	few	few	ADJ
ejpam-4112	31	9	.	.	PUNCT
ejpam-4112	32	1	in	in	ADP
ejpam-4112	32	2	[	[	X
ejpam-4112	32	3	13	13	NUM
ejpam-4112	32	4	]	]	PUNCT
ejpam-4112	32	5	,	,	PUNCT
ejpam-4112	32	6	an	an	DET
ejpam-4112	32	7	invariant	invariant	NOUN
ejpam-4112	32	8	called	call	VERB
ejpam-4112	32	9	the	the	DET
ejpam-4112	32	10	strong	strong	ADJ
ejpam-4112	32	11	metric	metric	ADJ
ejpam-4112	32	12	dimension	dimension	NOUN
ejpam-4112	32	13	,	,	PUNCT
ejpam-4112	32	14	was	be	AUX
ejpam-4112	32	15	presented	present	VERB
ejpam-4112	32	16	where	where	SCONJ
ejpam-4112	32	17	the	the	DET
ejpam-4112	32	18	authors	author	NOUN
ejpam-4112	32	19	illustrated	illustrate	VERB
ejpam-4112	32	20	its	its	PRON
ejpam-4112	32	21	application	application	NOUN
ejpam-4112	32	22	to	to	ADP
ejpam-4112	32	23	combinatorial	combinatorial	ADJ
ejpam-4112	32	24	search	search	NOUN
ejpam-4112	32	25	.	.	PUNCT
ejpam-4112	33	1	along	along	ADP
ejpam-4112	33	2	with	with	ADP
ejpam-4112	33	3	the	the	DET
ejpam-4112	33	4	increasing	increase	VERB
ejpam-4112	33	5	discovery	discovery	NOUN
ejpam-4112	33	6	of	of	ADP
ejpam-4112	33	7	its	its	PRON
ejpam-4112	33	8	applications	application	NOUN
ejpam-4112	33	9	,	,	PUNCT
ejpam-4112	33	10	theoretical	theoretical	ADJ
ejpam-4112	33	11	studies	study	NOUN
ejpam-4112	33	12	on	on	ADP
ejpam-4112	33	13	this	this	DET
ejpam-4112	33	14	invariant	invariant	NOUN
ejpam-4112	33	15	also	also	ADV
ejpam-4112	33	16	appear	appear	VERB
ejpam-4112	33	17	in	in	ADP
ejpam-4112	33	18	several	several	ADJ
ejpam-4112	33	19	number	number	NOUN
ejpam-4112	33	20	of	of	ADP
ejpam-4112	33	21	other	other	ADJ
ejpam-4112	33	22	papers	paper	NOUN
ejpam-4112	33	23	including	include	VERB
ejpam-4112	33	24	[	[	X
ejpam-4112	33	25	14	14	NUM
ejpam-4112	33	26	]	]	PUNCT
ejpam-4112	33	27	,	,	PUNCT
ejpam-4112	33	28	[	[	X
ejpam-4112	33	29	15	15	NUM
ejpam-4112	33	30	]	]	PUNCT
ejpam-4112	33	31	,	,	PUNCT
ejpam-4112	33	32	[	[	X
ejpam-4112	33	33	16	16	NUM
ejpam-4112	33	34	]	]	PUNCT
ejpam-4112	33	35	,	,	PUNCT
ejpam-4112	33	36	[	[	X
ejpam-4112	33	37	17	17	NUM
ejpam-4112	33	38	]	]	PUNCT
ejpam-4112	33	39	.	.	PUNCT
ejpam-4112	34	1	this	this	DET
ejpam-4112	34	2	paper	paper	NOUN
ejpam-4112	34	3	intends	intend	VERB
ejpam-4112	34	4	to	to	PART
ejpam-4112	34	5	generate	generate	VERB
ejpam-4112	34	6	additional	additional	ADJ
ejpam-4112	34	7	theoretical	theoretical	ADJ
ejpam-4112	34	8	results	result	NOUN
ejpam-4112	34	9	and	and	CCONJ
ejpam-4112	34	10	help	help	VERB
ejpam-4112	34	11	widen	widen	VERB
ejpam-4112	34	12	the	the	DET
ejpam-4112	34	13	pool	pool	NOUN
ejpam-4112	34	14	of	of	ADP
ejpam-4112	34	15	existing	exist	VERB
ejpam-4112	34	16	studies	study	NOUN
ejpam-4112	34	17	from	from	ADP
ejpam-4112	34	18	where	where	SCONJ
ejpam-4112	34	19	new	new	ADJ
ejpam-4112	34	20	researchers	researcher	NOUN
ejpam-4112	34	21	may	may	AUX
ejpam-4112	34	22	draw	draw	VERB
ejpam-4112	34	23	new	new	ADJ
ejpam-4112	34	24	insights	insight	NOUN
ejpam-4112	34	25	and	and	CCONJ
ejpam-4112	34	26	directions	direction	NOUN
ejpam-4112	34	27	for	for	ADP
ejpam-4112	34	28	further	further	ADJ
ejpam-4112	34	29	investigation	investigation	NOUN
ejpam-4112	34	30	.	.	PUNCT
ejpam-4112	35	1	in	in	ADP
ejpam-4112	35	2	this	this	DET
ejpam-4112	35	3	study	study	NOUN
ejpam-4112	35	4	,	,	PUNCT
ejpam-4112	35	5	we	we	PRON
ejpam-4112	35	6	investigate	investigate	VERB
ejpam-4112	35	7	the	the	DET
ejpam-4112	35	8	concept	concept	NOUN
ejpam-4112	35	9	of	of	ADP
ejpam-4112	35	10	restrained	restrained	ADJ
ejpam-4112	35	11	strong	strong	ADJ
ejpam-4112	35	12	resolving	resolving	NOUN
ejpam-4112	35	13	domination	domination	NOUN
ejpam-4112	35	14	in	in	ADP
ejpam-4112	35	15	the	the	DET
ejpam-4112	35	16	join	join	NOUN
ejpam-4112	35	17	,	,	PUNCT
ejpam-4112	35	18	corona	corona	PROPN
ejpam-4112	35	19	,	,	PUNCT
ejpam-4112	35	20	and	and	CCONJ
ejpam-4112	35	21	lexicographic	lexicographic	ADJ
ejpam-4112	35	22	product	product	NOUN
ejpam-4112	35	23	of	of	ADP
ejpam-4112	35	24	graphs	graph	NOUN
ejpam-4112	35	25	.	.	PUNCT
ejpam-4112	36	1	readers	reader	NOUN
ejpam-4112	36	2	are	be	AUX
ejpam-4112	36	3	referred	refer	VERB
ejpam-4112	36	4	to	to	ADP
ejpam-4112	36	5	[	[	X
ejpam-4112	36	6	9	9	NUM
ejpam-4112	36	7	]	]	PUNCT
ejpam-4112	36	8	for	for	ADP
ejpam-4112	36	9	elementary	elementary	ADJ
ejpam-4112	36	10	graph	graph	NOUN
ejpam-4112	36	11	theory	theory	NOUN
ejpam-4112	36	12	concepts	concept	NOUN
ejpam-4112	36	13	.	.	PUNCT
ejpam-4112	37	1	let	let	VERB
ejpam-4112	37	2	g	g	PROPN
ejpam-4112	37	3	=	=	PUNCT
ejpam-4112	37	4	(	(	PUNCT
ejpam-4112	37	5	v	v	NOUN
ejpam-4112	37	6	(	(	PUNCT
ejpam-4112	37	7	g	g	NOUN
ejpam-4112	37	8	)	)	PUNCT
ejpam-4112	37	9	,	,	PUNCT
ejpam-4112	37	10	e(g	e(g	PROPN
ejpam-4112	37	11	)	)	PUNCT
ejpam-4112	37	12	)	)	PUNCT
ejpam-4112	38	1	be	be	AUX
ejpam-4112	38	2	a	a	DET
ejpam-4112	38	3	graph	graph	NOUN
ejpam-4112	38	4	.	.	PUNCT
ejpam-4112	39	1	the	the	DET
ejpam-4112	39	2	open	open	ADJ
ejpam-4112	39	3	neighborhood	neighborhood	NOUN
ejpam-4112	39	4	of	of	ADP
ejpam-4112	39	5	v	v	NUM
ejpam-4112	39	6	∈	∈	NOUN
ejpam-4112	39	7	v	v	NOUN
ejpam-4112	39	8	(	(	PUNCT
ejpam-4112	39	9	g	g	NOUN
ejpam-4112	39	10	)	)	PUNCT
ejpam-4112	39	11	is	be	AUX
ejpam-4112	39	12	ng(v	ng(v	PUNCT
ejpam-4112	39	13	)	)	PUNCT
ejpam-4112	39	14	=	=	PRON
ejpam-4112	40	1	{	{	PUNCT
ejpam-4112	40	2	u	u	NOUN
ejpam-4112	40	3	∈	∈	PROPN
ejpam-4112	40	4	v	v	NOUN
ejpam-4112	40	5	(	(	PUNCT
ejpam-4112	40	6	g	g	NOUN
ejpam-4112	40	7	)	)	PUNCT
ejpam-4112	40	8	:	:	PUNCT
ejpam-4112	40	9	uv	uv	PROPN
ejpam-4112	40	10	∈	∈	PROPN
ejpam-4112	40	11	e(g	e(g	PROPN
ejpam-4112	40	12	)	)	PUNCT
ejpam-4112	40	13	}	}	PUNCT
ejpam-4112	40	14	.	.	PUNCT
ejpam-4112	41	1	an	an	DET
ejpam-4112	41	2	element	element	NOUN
ejpam-4112	41	3	u	u	NOUN
ejpam-4112	41	4	∈	∈	PROPN
ejpam-4112	41	5	ng(v	ng(v	PUNCT
ejpam-4112	41	6	)	)	PUNCT
ejpam-4112	41	7	is	be	AUX
ejpam-4112	41	8	called	call	VERB
ejpam-4112	41	9	a	a	DET
ejpam-4112	41	10	neighbor	neighbor	NOUN
ejpam-4112	41	11	of	of	ADP
ejpam-4112	41	12	v.	v.	ADP
ejpam-4112	41	13	the	the	DET
ejpam-4112	41	14	closed	closed	ADJ
ejpam-4112	41	15	neighborhood	neighborhood	NOUN
ejpam-4112	41	16	v	v	ADP
ejpam-4112	41	17	∈	∈	NOUN
ejpam-4112	41	18	v	v	NOUN
ejpam-4112	41	19	(	(	PUNCT
ejpam-4112	41	20	g	g	NOUN
ejpam-4112	41	21	)	)	PUNCT
ejpam-4112	41	22	is	be	AUX
ejpam-4112	41	23	ng[v	ng[v	NOUN
ejpam-4112	41	24	]	]	X
ejpam-4112	41	25	=	=	SYM
ejpam-4112	41	26	ng(v	ng(v	X
ejpam-4112	41	27	)	)	PUNCT
ejpam-4112	41	28	∪	∪	ADP
ejpam-4112	41	29	{	{	PUNCT
ejpam-4112	41	30	v	v	NOUN
ejpam-4112	41	31	}	}	PUNCT
ejpam-4112	41	32	.	.	PUNCT
ejpam-4112	42	1	thus	thus	ADV
ejpam-4112	42	2	,	,	PUNCT
ejpam-4112	42	3	the	the	DET
ejpam-4112	42	4	degree	degree	NOUN
ejpam-4112	42	5	of	of	ADP
ejpam-4112	42	6	v	v	NUM
ejpam-4112	42	7	∈	∈	NOUN
ejpam-4112	42	8	v	v	NOUN
ejpam-4112	42	9	(	(	PUNCT
ejpam-4112	42	10	g	g	NOUN
ejpam-4112	42	11	)	)	PUNCT
ejpam-4112	42	12	is	be	AUX
ejpam-4112	42	13	given	give	VERB
ejpam-4112	42	14	by	by	ADP
ejpam-4112	42	15	degg(v	degg(v	PROPN
ejpam-4112	42	16	)	)	PUNCT
ejpam-4112	42	17	=	=	SYM
ejpam-4112	42	18	|ng(v)|	|ng(v)|	NOUN
ejpam-4112	42	19	.	.	PUNCT
ejpam-4112	43	1	for	for	ADP
ejpam-4112	43	2	s	s	PROPN
ejpam-4112	43	3	⊆	⊆	NUM
ejpam-4112	43	4	v	v	NOUN
ejpam-4112	43	5	(	(	PUNCT
ejpam-4112	43	6	g	g	NOUN
ejpam-4112	43	7	)	)	PUNCT
ejpam-4112	43	8	,	,	PUNCT
ejpam-4112	43	9	ng(s	ng(s	NUM
ejpam-4112	43	10	)	)	PUNCT
ejpam-4112	43	11	=	=	SYM
ejpam-4112	43	12	⋃	⋃	ADP
ejpam-4112	43	13	v∈s	v∈s	NOUN
ejpam-4112	43	14	ng(v	ng(v	NOUN
ejpam-4112	43	15	)	)	PUNCT
ejpam-4112	43	16	and	and	CCONJ
ejpam-4112	43	17	ng[s	ng[	NOUN
ejpam-4112	43	18	]	]	PUNCT
ejpam-4112	43	19	=	=	PUNCT
ejpam-4112	43	20	⋃	⋃	VERB
ejpam-4112	43	21	v∈s	v∈s	ADJ
ejpam-4112	43	22	ng[v	ng[v	NOUN
ejpam-4112	43	23	]	]	PUNCT
ejpam-4112	43	24	.	.	PUNCT
ejpam-4112	44	1	a	a	DET
ejpam-4112	44	2	clique	clique	NOUN
ejpam-4112	44	3	in	in	ADP
ejpam-4112	44	4	a	a	DET
ejpam-4112	44	5	graph	graph	NOUN
ejpam-4112	44	6	g	g	NOUN
ejpam-4112	44	7	is	be	AUX
ejpam-4112	44	8	a	a	DET
ejpam-4112	44	9	complete	complete	ADJ
ejpam-4112	44	10	induced	induced	ADJ
ejpam-4112	44	11	subgraph	subgraph	NOUN
ejpam-4112	44	12	.	.	PUNCT
ejpam-4112	45	1	a	a	DET
ejpam-4112	45	2	set	set	NOUN
ejpam-4112	45	3	c	c	NOUN
ejpam-4112	45	4	⊆	⊆	NUM
ejpam-4112	45	5	v	v	NOUN
ejpam-4112	45	6	(	(	PUNCT
ejpam-4112	45	7	g	g	NOUN
ejpam-4112	45	8	)	)	PUNCT
ejpam-4112	45	9	is	be	AUX
ejpam-4112	45	10	called	call	VERB
ejpam-4112	45	11	a	a	DET
ejpam-4112	45	12	superclique	superclique	NOUN
ejpam-4112	45	13	in	in	ADP
ejpam-4112	45	14	g	g	PROPN
ejpam-4112	45	15	if	if	SCONJ
ejpam-4112	45	16	⟨c⟩	⟨c⟩	PROPN
ejpam-4112	45	17	is	be	AUX
ejpam-4112	45	18	a	a	DET
ejpam-4112	45	19	clique	clique	NOUN
ejpam-4112	45	20	and	and	CCONJ
ejpam-4112	45	21	for	for	ADP
ejpam-4112	45	22	every	every	DET
ejpam-4112	45	23	pair	pair	NOUN
ejpam-4112	45	24	of	of	ADP
ejpam-4112	45	25	distinct	distinct	ADJ
ejpam-4112	45	26	vertices	vertex	NOUN
ejpam-4112	45	27	u	u	NOUN
ejpam-4112	45	28	,	,	PUNCT
ejpam-4112	45	29	v	v	NOUN
ejpam-4112	45	30	∈	∈	ADJ
ejpam-4112	45	31	c	c	NOUN
ejpam-4112	45	32	,	,	PUNCT
ejpam-4112	45	33	there	there	PRON
ejpam-4112	45	34	exists	exist	VERB
ejpam-4112	45	35	w	w	PROPN
ejpam-4112	45	36	∈	∈	PROPN
ejpam-4112	45	37	v	v	ADP
ejpam-4112	45	38	(	(	PUNCT
ejpam-4112	45	39	g	g	NOUN
ejpam-4112	45	40	)	)	PUNCT
ejpam-4112	45	41	\	\	PUNCT
ejpam-4112	46	1	c	c	NOUN
ejpam-4112	46	2	such	such	ADJ
ejpam-4112	46	3	that	that	PRON
ejpam-4112	46	4	w	w	PROPN
ejpam-4112	46	5	∈	∈	PROPN
ejpam-4112	46	6	ng(u	ng(u	NOUN
ejpam-4112	46	7	)	)	PUNCT
ejpam-4112	46	8	\	\	NOUN
ejpam-4112	46	9	ng(v	ng(v	PUNCT
ejpam-4112	46	10	)	)	PUNCT
ejpam-4112	46	11	or	or	CCONJ
ejpam-4112	46	12	w	w	PROPN
ejpam-4112	46	13	∈	∈	PROPN
ejpam-4112	46	14	ng(v	ng(v	NOUN
ejpam-4112	46	15	)	)	PUNCT
ejpam-4112	46	16	\	\	NOUN
ejpam-4112	46	17	ng(u	ng(u	NOUN
ejpam-4112	46	18	)	)	PUNCT
ejpam-4112	46	19	.	.	PUNCT
ejpam-4112	47	1	a	a	DET
ejpam-4112	47	2	superclique	superclique	NOUN
ejpam-4112	47	3	c	c	NOUN
ejpam-4112	47	4	is	be	AUX
ejpam-4112	47	5	maximum	maximum	ADJ
ejpam-4112	47	6	in	in	ADP
ejpam-4112	47	7	g	g	PROPN
ejpam-4112	47	8	if	if	SCONJ
ejpam-4112	47	9	|c|	|c|	PROPN
ejpam-4112	47	10	≥	≥	NOUN
ejpam-4112	47	11	|c∗|	|c∗|	VERB
ejpam-4112	47	12	for	for	SCONJ
ejpam-4112	47	13	all	all	DET
ejpam-4112	47	14	supercliques	superclique	NOUN
ejpam-4112	47	15	c∗	c∗	PROPN
ejpam-4112	47	16	in	in	ADP
ejpam-4112	47	17	g.	g.	PROPN
ejpam-4112	47	18	the	the	DET
ejpam-4112	47	19	superclique	superclique	ADJ
ejpam-4112	47	20	number	number	NOUN
ejpam-4112	47	21	ωs(g	ωs(g	NUM
ejpam-4112	47	22	)	)	PUNCT
ejpam-4112	47	23	of	of	ADP
ejpam-4112	47	24	g	g	PROPN
ejpam-4112	47	25	is	be	AUX
ejpam-4112	47	26	the	the	DET
ejpam-4112	47	27	cardinality	cardinality	NOUN
ejpam-4112	47	28	of	of	ADP
ejpam-4112	47	29	a	a	DET
ejpam-4112	47	30	maximum	maximum	ADJ
ejpam-4112	47	31	superclique	superclique	NOUN
ejpam-4112	47	32	in	in	ADP
ejpam-4112	47	33	g.	g.	PROPN
ejpam-4112	47	34	a	a	DET
ejpam-4112	47	35	superclique	superclique	NOUN
ejpam-4112	47	36	c	c	NOUN
ejpam-4112	47	37	is	be	AUX
ejpam-4112	47	38	called	call	VERB
ejpam-4112	47	39	a	a	DET
ejpam-4112	47	40	dominated	dominate	VERB
ejpam-4112	47	41	superclique	superclique	NOUN
ejpam-4112	47	42	if	if	SCONJ
ejpam-4112	47	43	for	for	ADP
ejpam-4112	47	44	every	every	DET
ejpam-4112	47	45	u	u	NOUN
ejpam-4112	47	46	∈	∈	PROPN
ejpam-4112	47	47	c	c	NOUN
ejpam-4112	47	48	there	there	PRON
ejpam-4112	47	49	exists	exist	VERB
ejpam-4112	47	50	v	v	ADP
ejpam-4112	47	51	∈	∈	PROPN
ejpam-4112	47	52	v	v	NOUN
ejpam-4112	47	53	(	(	PUNCT
ejpam-4112	47	54	g	g	NOUN
ejpam-4112	47	55	)	)	PUNCT
ejpam-4112	47	56	\	\	PUNCT
ejpam-4112	48	1	c	c	NOUN
ejpam-4112	48	2	such	such	ADJ
ejpam-4112	48	3	that	that	DET
ejpam-4112	48	4	uv	uv	PROPN
ejpam-4112	48	5	∈	∈	PROPN
ejpam-4112	48	6	e(g	e(g	PROPN
ejpam-4112	48	7	)	)	PUNCT
ejpam-4112	48	8	.	.	PUNCT
ejpam-4112	49	1	the	the	DET
ejpam-4112	49	2	dominated	dominate	VERB
ejpam-4112	49	3	superclique	superclique	NOUN
ejpam-4112	49	4	number	number	NOUN
ejpam-4112	49	5	ωds(g	ωds(g	PROPN
ejpam-4112	49	6	)	)	PUNCT
ejpam-4112	49	7	,	,	PUNCT
ejpam-4112	49	8	of	of	ADP
ejpam-4112	49	9	g	g	PROPN
ejpam-4112	49	10	is	be	AUX
ejpam-4112	49	11	the	the	DET
ejpam-4112	49	12	cardinality	cardinality	NOUN
ejpam-4112	49	13	of	of	ADP
ejpam-4112	49	14	a	a	DET
ejpam-4112	49	15	maximum	maximum	ADV
ejpam-4112	49	16	dominated	dominate	VERB
ejpam-4112	49	17	superclique	superclique	NOUN
ejpam-4112	49	18	in	in	ADP
ejpam-4112	49	19	g.	g.	PROPN
ejpam-4112	49	20	a	a	DET
ejpam-4112	49	21	vertex	vertex	NOUN
ejpam-4112	49	22	x	x	X
ejpam-4112	49	23	of	of	ADP
ejpam-4112	49	24	a	a	DET
ejpam-4112	49	25	graph	graph	NOUN
ejpam-4112	49	26	g	g	NOUN
ejpam-4112	49	27	is	be	AUX
ejpam-4112	49	28	said	say	VERB
ejpam-4112	49	29	to	to	PART
ejpam-4112	49	30	resolve	resolve	VERB
ejpam-4112	49	31	two	two	NUM
ejpam-4112	49	32	vertices	vertex	NOUN
ejpam-4112	49	33	u	u	NOUN
ejpam-4112	49	34	and	and	CCONJ
ejpam-4112	49	35	v	v	NOUN
ejpam-4112	49	36	of	of	ADP
ejpam-4112	49	37	g	g	PROPN
ejpam-4112	49	38	if	if	SCONJ
ejpam-4112	49	39	dg(x	dg(x	NUM
ejpam-4112	49	40	,	,	PUNCT
ejpam-4112	49	41	u	u	NOUN
ejpam-4112	49	42	)	)	PUNCT
ejpam-4112	49	43	̸=	̸=	PROPN
ejpam-4112	49	44	dg(x	dg(x	NUM
ejpam-4112	49	45	,	,	PUNCT
ejpam-4112	49	46	v	v	NOUN
ejpam-4112	49	47	)	)	PUNCT
ejpam-4112	49	48	.	.	PUNCT
ejpam-4112	50	1	for	for	ADP
ejpam-4112	50	2	an	an	DET
ejpam-4112	50	3	ordered	order	VERB
ejpam-4112	50	4	set	set	NOUN
ejpam-4112	50	5	w	w	NOUN
ejpam-4112	50	6	=	=	PUNCT
ejpam-4112	50	7	{	{	PUNCT
ejpam-4112	50	8	x1	x1	PROPN
ejpam-4112	50	9	,	,	PUNCT
ejpam-4112	50	10	...	...	PUNCT
ejpam-4112	50	11	,	,	PUNCT
ejpam-4112	50	12	xk	xk	ADJ
ejpam-4112	50	13	}	}	PUNCT
ejpam-4112	50	14	⊆	⊆	NUM
ejpam-4112	50	15	v	v	NOUN
ejpam-4112	50	16	(	(	PUNCT
ejpam-4112	50	17	g	g	NOUN
ejpam-4112	50	18	)	)	PUNCT
ejpam-4112	50	19	and	and	CCONJ
ejpam-4112	50	20	a	a	DET
ejpam-4112	50	21	vertex	vertex	NOUN
ejpam-4112	50	22	v	v	NOUN
ejpam-4112	50	23	in	in	ADP
ejpam-4112	50	24	g	g	PROPN
ejpam-4112	50	25	,	,	PUNCT
ejpam-4112	50	26	the	the	DET
ejpam-4112	50	27	k	k	NOUN
ejpam-4112	50	28	-	-	NOUN
ejpam-4112	50	29	vector	vector	NOUN
ejpam-4112	50	30	rg(v	rg(v	NOUN
ejpam-4112	50	31	/	/	SYM
ejpam-4112	50	32	w	w	NOUN
ejpam-4112	50	33	)	)	PUNCT
ejpam-4112	50	34	=	=	SYM
ejpam-4112	50	35	(	(	PUNCT
ejpam-4112	50	36	dg(v	dg(v	X
ejpam-4112	50	37	,	,	PUNCT
ejpam-4112	50	38	x1	x1	PROPN
ejpam-4112	50	39	)	)	PUNCT
ejpam-4112	50	40	,	,	PUNCT
ejpam-4112	50	41	dg(v	dg(v	X
ejpam-4112	50	42	,	,	PUNCT
ejpam-4112	50	43	x2	x2	PROPN
ejpam-4112	50	44	)	)	PUNCT
ejpam-4112	50	45	,	,	PUNCT
ejpam-4112	50	46	...	...	PUNCT
ejpam-4112	50	47	,	,	PUNCT
ejpam-4112	50	48	dg(v	dg(v	X
ejpam-4112	50	49	,	,	PUNCT
ejpam-4112	50	50	xk	xk	NOUN
ejpam-4112	50	51	)	)	PUNCT
ejpam-4112	50	52	)	)	PUNCT
ejpam-4112	50	53	is	be	AUX
ejpam-4112	50	54	called	call	VERB
ejpam-4112	50	55	the	the	DET
ejpam-4112	50	56	representation	representation	NOUN
ejpam-4112	50	57	of	of	ADP
ejpam-4112	50	58	v	v	NOUN
ejpam-4112	50	59	with	with	ADP
ejpam-4112	50	60	respect	respect	NOUN
ejpam-4112	50	61	to	to	ADP
ejpam-4112	50	62	w	w	PROPN
ejpam-4112	50	63	.	.	PUNCT
ejpam-4112	51	1	the	the	DET
ejpam-4112	51	2	set	set	NOUN
ejpam-4112	51	3	w	w	NOUN
ejpam-4112	51	4	is	be	AUX
ejpam-4112	51	5	a	a	DET
ejpam-4112	51	6	resolving	resolving	NOUN
ejpam-4112	51	7	set	set	VERB
ejpam-4112	51	8	for	for	ADP
ejpam-4112	51	9	g	g	PROPN
ejpam-4112	51	10	if	if	SCONJ
ejpam-4112	52	1	and	and	CCONJ
ejpam-4112	52	2	only	only	ADV
ejpam-4112	52	3	if	if	SCONJ
ejpam-4112	52	4	no	no	DET
ejpam-4112	52	5	two	two	NUM
ejpam-4112	52	6	vertices	vertex	NOUN
ejpam-4112	52	7	of	of	ADP
ejpam-4112	52	8	g	g	NOUN
ejpam-4112	52	9	have	have	VERB
ejpam-4112	52	10	the	the	DET
ejpam-4112	52	11	same	same	ADJ
ejpam-4112	52	12	representation	representation	NOUN
ejpam-4112	52	13	with	with	ADP
ejpam-4112	52	14	respect	respect	NOUN
ejpam-4112	52	15	to	to	ADP
ejpam-4112	52	16	w	w	PROPN
ejpam-4112	52	17	.	.	PUNCT
ejpam-4112	53	1	the	the	DET
ejpam-4112	53	2	metric	metric	ADJ
ejpam-4112	53	3	dimension	dimension	NOUN
ejpam-4112	53	4	of	of	ADP
ejpam-4112	53	5	g	g	NOUN
ejpam-4112	53	6	,	,	PUNCT
ejpam-4112	53	7	denoted	denote	VERB
ejpam-4112	53	8	by	by	ADP
ejpam-4112	53	9	dim(g	dim(g	PROPN
ejpam-4112	53	10	)	)	PUNCT
ejpam-4112	53	11	,	,	PUNCT
ejpam-4112	53	12	is	be	AUX
ejpam-4112	53	13	the	the	DET
ejpam-4112	53	14	minimum	minimum	ADJ
ejpam-4112	53	15	cardinality	cardinality	NOUN
ejpam-4112	53	16	over	over	ADP
ejpam-4112	53	17	all	all	DET
ejpam-4112	53	18	resolving	resolve	VERB
ejpam-4112	53	19	sets	set	NOUN
ejpam-4112	53	20	of	of	ADP
ejpam-4112	53	21	g.	g.	PROPN
ejpam-4112	53	22	a	a	DET
ejpam-4112	53	23	resolving	resolve	VERB
ejpam-4112	53	24	set	set	NOUN
ejpam-4112	53	25	of	of	ADP
ejpam-4112	53	26	cardinality	cardinality	PROPN
ejpam-4112	53	27	dim(g	dim(g	PROPN
ejpam-4112	53	28	)	)	PUNCT
ejpam-4112	53	29	is	be	AUX
ejpam-4112	53	30	called	call	VERB
ejpam-4112	53	31	a	a	DET
ejpam-4112	53	32	basis	basis	NOUN
ejpam-4112	53	33	.	.	PUNCT
ejpam-4112	54	1	a	a	DET
ejpam-4112	54	2	set	set	NOUN
ejpam-4112	54	3	s	s	NOUN
ejpam-4112	54	4	⊆	⊆	NUM
ejpam-4112	54	5	v	v	NOUN
ejpam-4112	54	6	(	(	PUNCT
ejpam-4112	54	7	g	g	NOUN
ejpam-4112	54	8	)	)	PUNCT
ejpam-4112	54	9	of	of	ADP
ejpam-4112	54	10	vertices	vertex	NOUN
ejpam-4112	54	11	of	of	ADP
ejpam-4112	54	12	g	g	PROPN
ejpam-4112	54	13	is	be	AUX
ejpam-4112	54	14	a	a	DET
ejpam-4112	54	15	dominating	dominating	NOUN
ejpam-4112	54	16	set	set	NOUN
ejpam-4112	54	17	if	if	SCONJ
ejpam-4112	54	18	every	every	DET
ejpam-4112	54	19	u	u	PROPN
ejpam-4112	54	20	∈	∈	PROPN
ejpam-4112	54	21	v	v	NOUN
ejpam-4112	54	22	(	(	PUNCT
ejpam-4112	54	23	g	g	NOUN
ejpam-4112	54	24	)	)	PUNCT
ejpam-4112	54	25	\	\	PROPN
ejpam-4112	55	1	s	s	PART
ejpam-4112	55	2	is	be	AUX
ejpam-4112	55	3	adjacent	adjacent	ADJ
ejpam-4112	55	4	to	to	ADP
ejpam-4112	55	5	at	at	ADV
ejpam-4112	55	6	least	least	ADV
ejpam-4112	55	7	one	one	NUM
ejpam-4112	55	8	vertex	vertex	NOUN
ejpam-4112	55	9	v	v	ADP
ejpam-4112	55	10	∈	∈	NOUN
ejpam-4112	55	11	s.	s.	PROPN
ejpam-4112	56	1	the	the	DET
ejpam-4112	56	2	domination	domination	NOUN
ejpam-4112	56	3	number	number	NOUN
ejpam-4112	56	4	of	of	ADP
ejpam-4112	56	5	a	a	DET
ejpam-4112	56	6	graph	graph	NOUN
ejpam-4112	56	7	g	g	NOUN
ejpam-4112	56	8	,	,	PUNCT
ejpam-4112	56	9	denoted	denote	VERB
ejpam-4112	56	10	by	by	ADP
ejpam-4112	56	11	γ(g	γ(g	PROPN
ejpam-4112	56	12	)	)	PUNCT
ejpam-4112	56	13	,	,	PUNCT
ejpam-4112	56	14	is	be	AUX
ejpam-4112	56	15	given	give	VERB
ejpam-4112	56	16	by	by	ADP
ejpam-4112	56	17	γ(g	γ(g	PROPN
ejpam-4112	56	18	)	)	PUNCT
ejpam-4112	57	1	=	=	NOUN
ejpam-4112	57	2	min{|s|	min{|s|	NOUN
ejpam-4112	57	3	:	:	PUNCT
ejpam-4112	57	4	s	s	VERB
ejpam-4112	57	5	is	be	AUX
ejpam-4112	57	6	a	a	DET
ejpam-4112	57	7	dominating	dominating	NOUN
ejpam-4112	57	8	set	set	NOUN
ejpam-4112	57	9	of	of	ADP
ejpam-4112	57	10	g	g	NOUN
ejpam-4112	57	11	}	}	PUNCT
ejpam-4112	57	12	.	.	PUNCT
ejpam-4112	58	1	a	a	DET
ejpam-4112	58	2	subset	subset	NOUN
ejpam-4112	58	3	s	s	VERB
ejpam-4112	58	4	⊆	⊆	NUM
ejpam-4112	58	5	v	v	NOUN
ejpam-4112	58	6	(	(	PUNCT
ejpam-4112	58	7	g	g	NOUN
ejpam-4112	58	8	)	)	PUNCT
ejpam-4112	58	9	is	be	AUX
ejpam-4112	58	10	a	a	DET
ejpam-4112	58	11	strong	strong	ADJ
ejpam-4112	58	12	resolving	resolving	NOUN
ejpam-4112	58	13	dominating	dominating	NOUN
ejpam-4112	58	14	set	set	NOUN
ejpam-4112	58	15	of	of	ADP
ejpam-4112	58	16	g	g	PROPN
ejpam-4112	58	17	if	if	SCONJ
ejpam-4112	58	18	s	s	VERB
ejpam-4112	58	19	is	be	AUX
ejpam-4112	58	20	a	a	DET
ejpam-4112	58	21	dominating	dominating	NOUN
ejpam-4112	58	22	set	set	NOUN
ejpam-4112	58	23	and	and	CCONJ
ejpam-4112	58	24	for	for	ADP
ejpam-4112	58	25	every	every	DET
ejpam-4112	58	26	pair	pair	NOUN
ejpam-4112	58	27	of	of	ADP
ejpam-4112	58	28	vertices	vertex	NOUN
ejpam-4112	58	29	u	u	NOUN
ejpam-4112	58	30	,	,	PUNCT
ejpam-4112	58	31	v	v	NOUN
ejpam-4112	58	32	∈	∈	PROPN
ejpam-4112	58	33	v	v	NOUN
ejpam-4112	58	34	(	(	PUNCT
ejpam-4112	58	35	g	g	NOUN
ejpam-4112	58	36	)	)	PUNCT
ejpam-4112	58	37	,	,	PUNCT
ejpam-4112	58	38	there	there	PRON
ejpam-4112	58	39	exists	exist	VERB
ejpam-4112	58	40	a	a	DET
ejpam-4112	58	41	vertex	vertex	NOUN
ejpam-4112	58	42	w	w	ADP
ejpam-4112	58	43	∈	∈	NOUN
ejpam-4112	58	44	s	s	VERB
ejpam-4112	58	45	such	such	ADJ
ejpam-4112	58	46	that	that	SCONJ
ejpam-4112	58	47	u	u	PROPN
ejpam-4112	58	48	∈	∈	PROPN
ejpam-4112	58	49	ig[v	ig[v	PROPN
ejpam-4112	58	50	,	,	PUNCT
ejpam-4112	58	51	w	w	PROPN
ejpam-4112	58	52	]	]	PUNCT
ejpam-4112	58	53	or	or	CCONJ
ejpam-4112	58	54	v	v	ADP
ejpam-4112	58	55	∈	∈	PROPN
ejpam-4112	58	56	ig[u	ig[u	NOUN
ejpam-4112	58	57	,	,	PUNCT
ejpam-4112	58	58	w	w	NOUN
ejpam-4112	58	59	]	]	X
ejpam-4112	58	60	.	.	PUNCT
ejpam-4112	59	1	the	the	DET
ejpam-4112	59	2	smallest	small	ADJ
ejpam-4112	59	3	cardinality	cardinality	NOUN
ejpam-4112	59	4	of	of	ADP
ejpam-4112	59	5	a	a	DET
ejpam-4112	59	6	strong	strong	ADJ
ejpam-4112	59	7	resolving	resolving	NOUN
ejpam-4112	59	8	dominating	dominating	NOUN
ejpam-4112	59	9	set	set	NOUN
ejpam-4112	59	10	of	of	ADP
ejpam-4112	59	11	g	g	PROPN
ejpam-4112	59	12	is	be	AUX
ejpam-4112	59	13	called	call	VERB
ejpam-4112	59	14	the	the	DET
ejpam-4112	59	15	strong	strong	ADJ
ejpam-4112	59	16	resolving	resolving	NOUN
ejpam-4112	59	17	domination	domination	NOUN
ejpam-4112	59	18	number	number	NOUN
ejpam-4112	59	19	of	of	ADP
ejpam-4112	59	20	g	g	NOUN
ejpam-4112	59	21	and	and	CCONJ
ejpam-4112	59	22	is	be	AUX
ejpam-4112	59	23	denoted	denote	VERB
ejpam-4112	59	24	by	by	ADP
ejpam-4112	59	25	γsr(g	γsr(g	PROPN
ejpam-4112	59	26	)	)	PUNCT
ejpam-4112	59	27	.	.	PUNCT
ejpam-4112	60	1	a	a	DET
ejpam-4112	60	2	strong	strong	ADJ
ejpam-4112	60	3	resolving	resolve	VERB
ejpam-4112	60	4	dominating	dominating	NOUN
ejpam-4112	60	5	set	set	NOUN
ejpam-4112	60	6	of	of	ADP
ejpam-4112	60	7	cardinality	cardinality	PROPN
ejpam-4112	60	8	γsr(g	γsr(g	NOUN
ejpam-4112	60	9	)	)	PUNCT
ejpam-4112	60	10	is	be	AUX
ejpam-4112	60	11	called	call	VERB
ejpam-4112	60	12	a	a	DET
ejpam-4112	60	13	γsr	γsr	PROPN
ejpam-4112	60	14	-	-	PUNCT
ejpam-4112	60	15	set	set	NOUN
ejpam-4112	60	16	of	of	ADP
ejpam-4112	60	17	g.	g.	PROPN
ejpam-4112	60	18	h.	h.	PROPN
ejpam-4112	60	19	sumaoy	sumaoy	PROPN
ejpam-4112	60	20	,	,	PUNCT
ejpam-4112	60	21	h.	h.	PROPN
ejpam-4112	60	22	rara	rara	PROPN
ejpam-4112	60	23	/	/	SYM
ejpam-4112	60	24	eur	eur	PROPN
ejpam-4112	60	25	.	.	PUNCT
ejpam-4112	61	1	j.	j.	PROPN
ejpam-4112	61	2	pure	pure	PROPN
ejpam-4112	61	3	appl	appl	PROPN
ejpam-4112	61	4	.	.	PROPN
ejpam-4112	61	5	math	math	PROPN
ejpam-4112	61	6	,	,	PUNCT
ejpam-4112	61	7	14	14	NUM
ejpam-4112	61	8	(	(	PUNCT
ejpam-4112	61	9	4	4	NUM
ejpam-4112	61	10	)	)	PUNCT
ejpam-4112	61	11	(	(	PUNCT
ejpam-4112	61	12	2021	2021	NUM
ejpam-4112	61	13	)	)	PUNCT
ejpam-4112	61	14	,	,	PUNCT
ejpam-4112	61	15	1367	1367	NUM
ejpam-4112	61	16	-	-	SYM
ejpam-4112	61	17	1378	1378	NUM
ejpam-4112	61	18	1369	1369	NUM
ejpam-4112	61	19	a	a	DET
ejpam-4112	61	20	set	set	NOUN
ejpam-4112	61	21	s	s	NOUN
ejpam-4112	61	22	⊆	⊆	NUM
ejpam-4112	61	23	v	v	NOUN
ejpam-4112	61	24	(	(	PUNCT
ejpam-4112	61	25	g	g	NOUN
ejpam-4112	61	26	)	)	PUNCT
ejpam-4112	61	27	is	be	AUX
ejpam-4112	61	28	a	a	DET
ejpam-4112	61	29	restrained	restrained	ADJ
ejpam-4112	61	30	dominating	dominating	NOUN
ejpam-4112	61	31	set	set	NOUN
ejpam-4112	61	32	of	of	ADP
ejpam-4112	61	33	g	g	PROPN
ejpam-4112	61	34	if	if	SCONJ
ejpam-4112	61	35	s	s	VERB
ejpam-4112	61	36	is	be	AUX
ejpam-4112	61	37	a	a	DET
ejpam-4112	61	38	dominating	dominating	NOUN
ejpam-4112	61	39	set	set	NOUN
ejpam-4112	61	40	of	of	ADP
ejpam-4112	61	41	g	g	PROPN
ejpam-4112	61	42	and	and	CCONJ
ejpam-4112	61	43	for	for	ADP
ejpam-4112	61	44	every	every	PRON
ejpam-4112	61	45	v	v	NUM
ejpam-4112	61	46	∈	∈	PROPN
ejpam-4112	61	47	v	v	NOUN
ejpam-4112	61	48	(	(	PUNCT
ejpam-4112	61	49	g	g	NOUN
ejpam-4112	61	50	)	)	PUNCT
ejpam-4112	61	51	\	\	PROPN
ejpam-4112	62	1	s	s	VERB
ejpam-4112	62	2	there	there	PRON
ejpam-4112	62	3	exists	exist	VERB
ejpam-4112	62	4	u	u	PROPN
ejpam-4112	62	5	∈	∈	PROPN
ejpam-4112	62	6	(	(	PUNCT
ejpam-4112	62	7	v	v	NOUN
ejpam-4112	62	8	(	(	PUNCT
ejpam-4112	62	9	g	g	NOUN
ejpam-4112	62	10	)	)	PUNCT
ejpam-4112	62	11	\	\	PROPN
ejpam-4112	62	12	s	s	X
ejpam-4112	62	13	)	)	PUNCT
ejpam-4112	62	14	∩ng(v	∩ng(v	PROPN
ejpam-4112	62	15	)	)	PUNCT
ejpam-4112	62	16	.	.	PUNCT
ejpam-4112	63	1	equivalently	equivalently	ADV
ejpam-4112	63	2	,	,	PUNCT
ejpam-4112	63	3	a	a	DET
ejpam-4112	63	4	dominating	dominating	NOUN
ejpam-4112	63	5	subset	subset	NOUN
ejpam-4112	63	6	s	s	PROPN
ejpam-4112	63	7	of	of	ADP
ejpam-4112	63	8	v	v	NOUN
ejpam-4112	63	9	(	(	PUNCT
ejpam-4112	63	10	g	g	NOUN
ejpam-4112	63	11	)	)	PUNCT
ejpam-4112	63	12	is	be	AUX
ejpam-4112	63	13	a	a	DET
ejpam-4112	63	14	restrained	restrained	ADJ
ejpam-4112	63	15	dominating	dominating	NOUN
ejpam-4112	63	16	set	set	NOUN
ejpam-4112	63	17	of	of	ADP
ejpam-4112	63	18	graph	graph	NOUN
ejpam-4112	63	19	g	g	NOUN
ejpam-4112	63	20	if	if	SCONJ
ejpam-4112	63	21	s	s	VERB
ejpam-4112	63	22	=	=	SYM
ejpam-4112	63	23	v	v	X
ejpam-4112	63	24	(	(	PUNCT
ejpam-4112	63	25	g	g	NOUN
ejpam-4112	63	26	)	)	PUNCT
ejpam-4112	63	27	or	or	CCONJ
ejpam-4112	63	28	⟨v	⟨v	NUM
ejpam-4112	63	29	(	(	PUNCT
ejpam-4112	63	30	g	g	NOUN
ejpam-4112	63	31	)	)	PUNCT
ejpam-4112	63	32	\	\	PROPN
ejpam-4112	63	33	s⟩	s⟩	NOUN
ejpam-4112	63	34	has	have	VERB
ejpam-4112	63	35	no	no	DET
ejpam-4112	63	36	isolated	isolated	ADJ
ejpam-4112	63	37	vertex	vertex	NOUN
ejpam-4112	63	38	.	.	PUNCT
ejpam-4112	64	1	the	the	DET
ejpam-4112	64	2	restrained	restrained	ADJ
ejpam-4112	64	3	domination	domination	NOUN
ejpam-4112	64	4	number	number	NOUN
ejpam-4112	64	5	of	of	ADP
ejpam-4112	64	6	g	g	NOUN
ejpam-4112	64	7	,	,	PUNCT
ejpam-4112	64	8	denoted	denote	VERB
ejpam-4112	64	9	by	by	ADP
ejpam-4112	64	10	γr(g	γr(g	PROPN
ejpam-4112	64	11	)	)	PUNCT
ejpam-4112	64	12	is	be	AUX
ejpam-4112	64	13	the	the	DET
ejpam-4112	64	14	minimum	minimum	ADJ
ejpam-4112	64	15	cardinality	cardinality	NOUN
ejpam-4112	64	16	of	of	ADP
ejpam-4112	64	17	a	a	DET
ejpam-4112	64	18	restrained	restrained	ADJ
ejpam-4112	64	19	dominating	dominating	NOUN
ejpam-4112	64	20	set	set	NOUN
ejpam-4112	64	21	of	of	ADP
ejpam-4112	64	22	g.	g.	PROPN
ejpam-4112	64	23	any	any	DET
ejpam-4112	64	24	restrained	restrain	VERB
ejpam-4112	64	25	dominating	dominating	NOUN
ejpam-4112	64	26	set	set	NOUN
ejpam-4112	64	27	of	of	ADP
ejpam-4112	64	28	g	g	PROPN
ejpam-4112	64	29	of	of	ADP
ejpam-4112	64	30	cardinality	cardinality	PROPN
ejpam-4112	64	31	γr(g	γr(g	PROPN
ejpam-4112	64	32	)	)	PUNCT
ejpam-4112	64	33	is	be	AUX
ejpam-4112	64	34	referred	refer	VERB
ejpam-4112	64	35	to	to	ADP
ejpam-4112	64	36	as	as	ADP
ejpam-4112	64	37	a	a	DET
ejpam-4112	64	38	γr	γr	PROPN
ejpam-4112	64	39	-	-	PUNCT
ejpam-4112	64	40	set	set	NOUN
ejpam-4112	64	41	of	of	ADP
ejpam-4112	64	42	g.	g.	PROPN
ejpam-4112	64	43	the	the	DET
ejpam-4112	64	44	join	join	NOUN
ejpam-4112	64	45	of	of	ADP
ejpam-4112	64	46	two	two	NUM
ejpam-4112	64	47	graphs	graph	NOUN
ejpam-4112	64	48	g	g	NOUN
ejpam-4112	64	49	and	and	CCONJ
ejpam-4112	64	50	h	h	NOUN
ejpam-4112	64	51	is	be	AUX
ejpam-4112	64	52	the	the	DET
ejpam-4112	64	53	graph	graph	NOUN
ejpam-4112	64	54	g	g	NOUN
ejpam-4112	64	55	+	+	CCONJ
ejpam-4112	64	56	h	h	NOUN
ejpam-4112	64	57	with	with	ADP
ejpam-4112	64	58	vertex	vertex	NOUN
ejpam-4112	64	59	set	set	VERB
ejpam-4112	64	60	v	v	NOUN
ejpam-4112	64	61	(	(	PUNCT
ejpam-4112	64	62	g	g	PROPN
ejpam-4112	64	63	+	+	NOUN
ejpam-4112	64	64	h	h	NOUN
ejpam-4112	64	65	)	)	PUNCT
ejpam-4112	65	1	=	=	NOUN
ejpam-4112	65	2	v	v	X
ejpam-4112	65	3	(	(	PUNCT
ejpam-4112	65	4	g	g	NOUN
ejpam-4112	65	5	)	)	PUNCT
ejpam-4112	65	6	•	•	ADP
ejpam-4112	65	7	∪	∪	X
ejpam-4112	65	8	v	v	NOUN
ejpam-4112	65	9	(	(	PUNCT
ejpam-4112	65	10	h	h	NOUN
ejpam-4112	65	11	)	)	PUNCT
ejpam-4112	65	12	and	and	CCONJ
ejpam-4112	65	13	edge	edge	NOUN
ejpam-4112	65	14	set	set	VERB
ejpam-4112	65	15	e(g	e(g	PROPN
ejpam-4112	66	1	+	+	CCONJ
ejpam-4112	66	2	h	h	NOUN
ejpam-4112	66	3	)	)	PUNCT
ejpam-4112	66	4	=	=	SYM
ejpam-4112	66	5	e(g	e(g	PROPN
ejpam-4112	66	6	)	)	PUNCT
ejpam-4112	67	1	•	•	ADP
ejpam-4112	67	2	∪	∪	ADP
ejpam-4112	67	3	e(h	e(h	PROPN
ejpam-4112	67	4	)	)	PUNCT
ejpam-4112	67	5	∪	∪	NOUN
ejpam-4112	67	6	{	{	PUNCT
ejpam-4112	67	7	uv	uv	NOUN
ejpam-4112	67	8	:	:	PUNCT
ejpam-4112	67	9	u	u	PROPN
ejpam-4112	67	10	∈	∈	PROPN
ejpam-4112	67	11	v	v	ADP
ejpam-4112	67	12	(	(	PUNCT
ejpam-4112	67	13	g	g	NOUN
ejpam-4112	67	14	)	)	PUNCT
ejpam-4112	67	15	,	,	PUNCT
ejpam-4112	67	16	v	v	X
ejpam-4112	67	17	∈	∈	PROPN
ejpam-4112	67	18	v	v	NOUN
ejpam-4112	67	19	(	(	PUNCT
ejpam-4112	67	20	h	h	NOUN
ejpam-4112	67	21	)	)	PUNCT
ejpam-4112	67	22	}	}	PUNCT
ejpam-4112	67	23	.	.	PUNCT
ejpam-4112	68	1	the	the	DET
ejpam-4112	68	2	corona	corona	NOUN
ejpam-4112	68	3	of	of	ADP
ejpam-4112	68	4	two	two	NUM
ejpam-4112	68	5	graphs	graph	NOUN
ejpam-4112	68	6	g	g	NOUN
ejpam-4112	68	7	and	and	CCONJ
ejpam-4112	68	8	h	h	NOUN
ejpam-4112	68	9	,	,	PUNCT
ejpam-4112	68	10	denoted	denote	VERB
ejpam-4112	68	11	by	by	ADP
ejpam-4112	68	12	g	g	PROPN
ejpam-4112	68	13	◦	◦	NOUN
ejpam-4112	68	14	h	h	NOUN
ejpam-4112	68	15	,	,	PUNCT
ejpam-4112	68	16	is	be	AUX
ejpam-4112	68	17	the	the	DET
ejpam-4112	68	18	graph	graph	NOUN
ejpam-4112	68	19	obtained	obtain	VERB
ejpam-4112	68	20	by	by	ADP
ejpam-4112	68	21	taking	take	VERB
ejpam-4112	68	22	one	one	NUM
ejpam-4112	68	23	copy	copy	NOUN
ejpam-4112	68	24	of	of	ADP
ejpam-4112	68	25	g	g	NOUN
ejpam-4112	68	26	of	of	ADP
ejpam-4112	68	27	order	order	NOUN
ejpam-4112	68	28	n	n	NOUN
ejpam-4112	68	29	and	and	CCONJ
ejpam-4112	68	30	n	n	PRON
ejpam-4112	68	31	copies	copy	NOUN
ejpam-4112	68	32	of	of	ADP
ejpam-4112	68	33	h	h	NOUN
ejpam-4112	68	34	,	,	PUNCT
ejpam-4112	68	35	and	and	CCONJ
ejpam-4112	68	36	then	then	ADV
ejpam-4112	68	37	joining	join	VERB
ejpam-4112	68	38	every	every	DET
ejpam-4112	68	39	vertex	vertex	NOUN
ejpam-4112	68	40	of	of	ADP
ejpam-4112	68	41	the	the	DET
ejpam-4112	68	42	ith	ith	PROPN
ejpam-4112	68	43	copy	copy	NOUN
ejpam-4112	68	44	of	of	ADP
ejpam-4112	68	45	h	h	NOUN
ejpam-4112	68	46	to	to	ADP
ejpam-4112	68	47	the	the	DET
ejpam-4112	68	48	ith	ith	PROPN
ejpam-4112	68	49	vertex	vertex	NOUN
ejpam-4112	68	50	of	of	ADP
ejpam-4112	68	51	g.	g.	PROPN
ejpam-4112	68	52	for	for	ADP
ejpam-4112	68	53	v	v	NOUN
ejpam-4112	68	54	∈	∈	PROPN
ejpam-4112	68	55	v	v	NOUN
ejpam-4112	68	56	(	(	PUNCT
ejpam-4112	68	57	g	g	NOUN
ejpam-4112	68	58	)	)	PUNCT
ejpam-4112	68	59	,	,	PUNCT
ejpam-4112	68	60	denote	denote	VERB
ejpam-4112	68	61	by	by	ADP
ejpam-4112	68	62	hv	hv	PROPN
ejpam-4112	68	63	the	the	DET
ejpam-4112	68	64	copy	copy	NOUN
ejpam-4112	68	65	of	of	ADP
ejpam-4112	68	66	h	h	NOUN
ejpam-4112	68	67	whose	whose	DET
ejpam-4112	68	68	vertices	vertex	NOUN
ejpam-4112	68	69	are	be	AUX
ejpam-4112	68	70	attached	attach	VERB
ejpam-4112	68	71	one	one	NUM
ejpam-4112	68	72	by	by	ADP
ejpam-4112	68	73	one	one	NUM
ejpam-4112	68	74	to	to	ADP
ejpam-4112	68	75	the	the	DET
ejpam-4112	68	76	vertex	vertex	NOUN
ejpam-4112	68	77	v.	v.	ADP
ejpam-4112	68	78	subsequently	subsequently	ADV
ejpam-4112	68	79	,	,	PUNCT
ejpam-4112	68	80	denote	denote	VERB
ejpam-4112	68	81	by	by	ADP
ejpam-4112	68	82	v+hv	v+hv	NOUN
ejpam-4112	68	83	the	the	DET
ejpam-4112	68	84	subgraph	subgraph	NOUN
ejpam-4112	68	85	of	of	ADP
ejpam-4112	68	86	the	the	DET
ejpam-4112	68	87	corona	corona	NOUN
ejpam-4112	68	88	g	g	PROPN
ejpam-4112	68	89	◦	◦	NOUN
ejpam-4112	68	90	h	h	NOUN
ejpam-4112	68	91	corresponding	correspond	VERB
ejpam-4112	68	92	to	to	ADP
ejpam-4112	68	93	the	the	DET
ejpam-4112	68	94	join	join	NOUN
ejpam-4112	68	95	⟨{v}⟩	⟨{v}⟩	AUX
ejpam-4112	68	96	+	+	CCONJ
ejpam-4112	68	97	hv	hv	PROPN
ejpam-4112	68	98	,	,	PUNCT
ejpam-4112	68	99	v	v	NOUN
ejpam-4112	68	100	∈	∈	PROPN
ejpam-4112	68	101	v	v	NOUN
ejpam-4112	68	102	(	(	PUNCT
ejpam-4112	68	103	g	g	NOUN
ejpam-4112	68	104	)	)	PUNCT
ejpam-4112	68	105	.	.	PUNCT
ejpam-4112	69	1	the	the	DET
ejpam-4112	69	2	lexicographic	lexicographic	ADJ
ejpam-4112	69	3	product	product	NOUN
ejpam-4112	69	4	of	of	ADP
ejpam-4112	69	5	two	two	NUM
ejpam-4112	69	6	graphs	graph	NOUN
ejpam-4112	69	7	g	g	NOUN
ejpam-4112	69	8	and	and	CCONJ
ejpam-4112	69	9	h	h	NOUN
ejpam-4112	69	10	,	,	PUNCT
ejpam-4112	69	11	denoted	denote	VERB
ejpam-4112	69	12	by	by	ADP
ejpam-4112	69	13	g[h	g[h	NOUN
ejpam-4112	69	14	]	]	PUNCT
ejpam-4112	69	15	,	,	PUNCT
ejpam-4112	69	16	is	be	AUX
ejpam-4112	69	17	the	the	DET
ejpam-4112	69	18	graph	graph	NOUN
ejpam-4112	69	19	with	with	ADP
ejpam-4112	69	20	vertexset	vertexset	ADJ
ejpam-4112	69	21	v	v	NOUN
ejpam-4112	69	22	(	(	PUNCT
ejpam-4112	69	23	g[h	g[h	PROPN
ejpam-4112	69	24	]	]	PUNCT
ejpam-4112	69	25	)	)	PUNCT
ejpam-4112	69	26	=	=	SYM
ejpam-4112	69	27	v	v	X
ejpam-4112	69	28	(	(	PUNCT
ejpam-4112	69	29	g	g	NOUN
ejpam-4112	69	30	)	)	PUNCT
ejpam-4112	69	31	×	×	NOUN
ejpam-4112	69	32	v	v	NOUN
ejpam-4112	69	33	(	(	PUNCT
ejpam-4112	69	34	h	h	NOUN
ejpam-4112	69	35	)	)	PUNCT
ejpam-4112	69	36	such	such	ADJ
ejpam-4112	69	37	that	that	SCONJ
ejpam-4112	69	38	(	(	PUNCT
ejpam-4112	69	39	u1	u1	NOUN
ejpam-4112	69	40	,	,	PUNCT
ejpam-4112	69	41	u2)(v1	u2)(v1	NOUN
ejpam-4112	69	42	,	,	PUNCT
ejpam-4112	69	43	v2	v2	NOUN
ejpam-4112	69	44	)	)	PUNCT
ejpam-4112	69	45	∈	∈	NOUN
ejpam-4112	69	46	e(g[h	e(g[h	NOUN
ejpam-4112	69	47	]	]	PUNCT
ejpam-4112	69	48	)	)	PUNCT
ejpam-4112	69	49	if	if	SCONJ
ejpam-4112	69	50	either	either	CCONJ
ejpam-4112	69	51	u1v1	u1v1	PROPN
ejpam-4112	69	52	∈	∈	PROPN
ejpam-4112	69	53	e(g	e(g	PROPN
ejpam-4112	69	54	)	)	PUNCT
ejpam-4112	69	55	or	or	CCONJ
ejpam-4112	69	56	u1	u1	NOUN
ejpam-4112	69	57	=	=	SYM
ejpam-4112	69	58	v1	v1	NOUN
ejpam-4112	69	59	and	and	CCONJ
ejpam-4112	69	60	u2v2	u2v2	ADJ
ejpam-4112	69	61	∈	∈	PROPN
ejpam-4112	69	62	e(h	e(h	PROPN
ejpam-4112	69	63	)	)	PUNCT
ejpam-4112	69	64	.	.	PUNCT
ejpam-4112	70	1	2	2	X
ejpam-4112	70	2	.	.	X
ejpam-4112	70	3	preliminary	preliminary	ADJ
ejpam-4112	70	4	results	result	NOUN
ejpam-4112	70	5	this	this	DET
ejpam-4112	70	6	section	section	NOUN
ejpam-4112	70	7	presents	present	VERB
ejpam-4112	70	8	some	some	PRON
ejpam-4112	70	9	of	of	ADP
ejpam-4112	70	10	the	the	DET
ejpam-4112	70	11	important	important	ADJ
ejpam-4112	70	12	known	know	VERB
ejpam-4112	70	13	results	result	NOUN
ejpam-4112	70	14	in	in	ADP
ejpam-4112	70	15	strong	strong	ADJ
ejpam-4112	70	16	resolving	resolving	NOUN
ejpam-4112	70	17	domination	domination	NOUN
ejpam-4112	70	18	of	of	ADP
ejpam-4112	70	19	graphs	graph	NOUN
ejpam-4112	70	20	and	and	CCONJ
ejpam-4112	70	21	some	some	DET
ejpam-4112	70	22	properties	property	NOUN
ejpam-4112	70	23	of	of	ADP
ejpam-4112	70	24	restrained	restrained	ADJ
ejpam-4112	70	25	strong	strong	ADJ
ejpam-4112	70	26	resolving	resolve	VERB
ejpam-4112	70	27	dominating	dominating	NOUN
ejpam-4112	70	28	set	set	VERB
ejpam-4112	70	29	in	in	ADP
ejpam-4112	70	30	a	a	DET
ejpam-4112	70	31	graph	graph	NOUN
ejpam-4112	70	32	.	.	PUNCT
ejpam-4112	71	1	theorem	theorem	NOUN
ejpam-4112	71	2	1	1	NUM
ejpam-4112	71	3	.	.	PUNCT
ejpam-4112	72	1	[	[	X
ejpam-4112	72	2	3	3	X
ejpam-4112	72	3	]	]	PUNCT
ejpam-4112	72	4	let	let	VERB
ejpam-4112	72	5	g	g	PRON
ejpam-4112	72	6	be	be	AUX
ejpam-4112	72	7	a	a	DET
ejpam-4112	72	8	nontrivial	nontrivial	ADJ
ejpam-4112	72	9	connected	connect	VERB
ejpam-4112	72	10	graph	graph	NOUN
ejpam-4112	72	11	of	of	ADP
ejpam-4112	72	12	order	order	NOUN
ejpam-4112	72	13	n	n	PRON
ejpam-4112	72	14	with	with	ADP
ejpam-4112	72	15	γ(g	γ(g	PROPN
ejpam-4112	72	16	)	)	PUNCT
ejpam-4112	73	1	̸=	̸=	PROPN
ejpam-4112	73	2	1	1	NUM
ejpam-4112	73	3	and	and	CCONJ
ejpam-4112	73	4	k1	k1	NOUN
ejpam-4112	73	5	=	=	SYM
ejpam-4112	73	6	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4112	73	7	then	then	ADV
ejpam-4112	73	8	s	s	VERB
ejpam-4112	73	9	⊆	⊆	NUM
ejpam-4112	73	10	v	v	NOUN
ejpam-4112	73	11	(	(	PUNCT
ejpam-4112	73	12	k1	k1	NOUN
ejpam-4112	73	13	+	+	CCONJ
ejpam-4112	73	14	g	g	NOUN
ejpam-4112	73	15	)	)	PUNCT
ejpam-4112	73	16	is	be	AUX
ejpam-4112	73	17	a	a	DET
ejpam-4112	73	18	strong	strong	ADJ
ejpam-4112	73	19	resolving	resolving	NOUN
ejpam-4112	73	20	dominating	dominating	NOUN
ejpam-4112	73	21	set	set	NOUN
ejpam-4112	73	22	of	of	ADP
ejpam-4112	73	23	k1	k1	NOUN
ejpam-4112	73	24	+	+	CCONJ
ejpam-4112	73	25	g	g	NOUN
ejpam-4112	73	26	if	if	SCONJ
ejpam-4112	74	1	and	and	CCONJ
ejpam-4112	74	2	only	only	ADV
ejpam-4112	74	3	if	if	SCONJ
ejpam-4112	74	4	s	s	VERB
ejpam-4112	74	5	=	=	SYM
ejpam-4112	74	6	v	v	X
ejpam-4112	74	7	(	(	PUNCT
ejpam-4112	74	8	g	g	NOUN
ejpam-4112	74	9	)	)	PUNCT
ejpam-4112	74	10	;	;	PUNCT
ejpam-4112	74	11	or	or	CCONJ
ejpam-4112	74	12	s	s	X
ejpam-4112	74	13	=	=	SYM
ejpam-4112	74	14	v	v	PROPN
ejpam-4112	74	15	(	(	PUNCT
ejpam-4112	74	16	k1	k1	NOUN
ejpam-4112	74	17	+	+	PROPN
ejpam-4112	74	18	g	g	NOUN
ejpam-4112	74	19	)	)	PUNCT
ejpam-4112	74	20	\	\	NOUN
ejpam-4112	75	1	c	c	NOUN
ejpam-4112	75	2	or	or	CCONJ
ejpam-4112	75	3	s	s	NOUN
ejpam-4112	75	4	=	=	SYM
ejpam-4112	75	5	v	v	PROPN
ejpam-4112	75	6	(	(	PUNCT
ejpam-4112	75	7	g	g	NOUN
ejpam-4112	75	8	)	)	PUNCT
ejpam-4112	75	9	\	\	PROPN
ejpam-4112	75	10	c∗	c∗	NOUN
ejpam-4112	75	11	where	where	SCONJ
ejpam-4112	75	12	c	c	PROPN
ejpam-4112	75	13	is	be	AUX
ejpam-4112	75	14	a	a	DET
ejpam-4112	75	15	superclique	superclique	ADJ
ejpam-4112	75	16	and	and	CCONJ
ejpam-4112	75	17	c∗	c∗	NOUN
ejpam-4112	75	18	is	be	AUX
ejpam-4112	75	19	dominated	dominate	VERB
ejpam-4112	75	20	superclique	superclique	NOUN
ejpam-4112	75	21	in	in	ADP
ejpam-4112	75	22	g.	g.	PROPN
ejpam-4112	75	23	theorem	theorem	PROPN
ejpam-4112	75	24	2	2	NUM
ejpam-4112	75	25	.	.	PUNCT
ejpam-4112	76	1	[	[	X
ejpam-4112	76	2	3	3	X
ejpam-4112	76	3	]	]	PUNCT
ejpam-4112	76	4	let	let	VERB
ejpam-4112	76	5	g	g	PRON
ejpam-4112	76	6	be	be	AUX
ejpam-4112	76	7	a	a	DET
ejpam-4112	76	8	nontrivial	nontrivial	ADJ
ejpam-4112	76	9	connected	connect	VERB
ejpam-4112	76	10	graph	graph	NOUN
ejpam-4112	76	11	of	of	ADP
ejpam-4112	76	12	order	order	NOUN
ejpam-4112	76	13	n	n	PRON
ejpam-4112	76	14	with	with	ADP
ejpam-4112	76	15	γ(g	γ(g	PROPN
ejpam-4112	76	16	)	)	PUNCT
ejpam-4112	76	17	=	=	SYM
ejpam-4112	76	18	1	1	NUM
ejpam-4112	76	19	and	and	CCONJ
ejpam-4112	76	20	k1	k1	NOUN
ejpam-4112	77	1	=	=	SYM
ejpam-4112	77	2	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4112	77	3	then	then	ADV
ejpam-4112	77	4	s	s	VERB
ejpam-4112	77	5	⊆	⊆	NUM
ejpam-4112	77	6	v	v	NOUN
ejpam-4112	77	7	(	(	PUNCT
ejpam-4112	77	8	k1	k1	NOUN
ejpam-4112	77	9	+	+	CCONJ
ejpam-4112	77	10	g	g	NOUN
ejpam-4112	77	11	)	)	PUNCT
ejpam-4112	77	12	is	be	AUX
ejpam-4112	77	13	a	a	DET
ejpam-4112	77	14	strong	strong	ADJ
ejpam-4112	77	15	connected	connected	ADJ
ejpam-4112	77	16	resolving	resolve	VERB
ejpam-4112	77	17	dominating	dominating	NOUN
ejpam-4112	77	18	set	set	NOUN
ejpam-4112	77	19	of	of	ADP
ejpam-4112	77	20	k1	k1	NOUN
ejpam-4112	78	1	+	+	ADP
ejpam-4112	78	2	g	g	PROPN
ejpam-4112	78	3	if	if	SCONJ
ejpam-4112	78	4	and	and	CCONJ
ejpam-4112	78	5	only	only	ADV
ejpam-4112	78	6	if	if	SCONJ
ejpam-4112	78	7	s	s	VERB
ejpam-4112	78	8	=	=	SYM
ejpam-4112	78	9	v	v	X
ejpam-4112	78	10	(	(	PUNCT
ejpam-4112	78	11	g	g	NOUN
ejpam-4112	78	12	)	)	PUNCT
ejpam-4112	78	13	or	or	CCONJ
ejpam-4112	78	14	s	s	X
ejpam-4112	78	15	=	=	SYM
ejpam-4112	78	16	v	v	PROPN
ejpam-4112	78	17	(	(	PUNCT
ejpam-4112	78	18	k1	k1	NOUN
ejpam-4112	78	19	+	+	PROPN
ejpam-4112	78	20	g	g	NOUN
ejpam-4112	78	21	)	)	PUNCT
ejpam-4112	78	22	\c	\c	NOUN
ejpam-4112	78	23	or	or	CCONJ
ejpam-4112	78	24	s	s	NOUN
ejpam-4112	78	25	=	=	PUNCT
ejpam-4112	78	26	(	(	PUNCT
ejpam-4112	78	27	v	v	NOUN
ejpam-4112	78	28	(	(	PUNCT
ejpam-4112	78	29	g	g	NOUN
ejpam-4112	78	30	)	)	PUNCT
ejpam-4112	78	31	\	\	PROPN
ejpam-4112	78	32	c∗	c∗	PROPN
ejpam-4112	78	33	)	)	PUNCT
ejpam-4112	78	34	∪	∪	NOUN
ejpam-4112	78	35	{	{	PUNCT
ejpam-4112	78	36	x	x	SYM
ejpam-4112	78	37	∈	∈	PROPN
ejpam-4112	78	38	c∗	c∗	NOUN
ejpam-4112	78	39	:	:	PUNCT
ejpam-4112	78	40	deg(x	deg(x	X
ejpam-4112	78	41	)	)	PUNCT
ejpam-4112	79	1	=	=	PUNCT
ejpam-4112	79	2	n−	n−	NOUN
ejpam-4112	79	3	1	1	NUM
ejpam-4112	79	4	}	}	PUNCT
ejpam-4112	79	5	where	where	SCONJ
ejpam-4112	79	6	c	c	NOUN
ejpam-4112	79	7	and	and	CCONJ
ejpam-4112	79	8	c∗	c∗	PROPN
ejpam-4112	79	9	are	be	AUX
ejpam-4112	79	10	superclique	superclique	ADJ
ejpam-4112	79	11	and	and	CCONJ
ejpam-4112	79	12	dominated	dominate	VERB
ejpam-4112	79	13	superclique	superclique	NOUN
ejpam-4112	79	14	,	,	PUNCT
ejpam-4112	79	15	respectively	respectively	ADV
ejpam-4112	79	16	in	in	ADP
ejpam-4112	79	17	g.	g.	PROPN
ejpam-4112	79	18	theorem	theorem	VERB
ejpam-4112	79	19	3	3	NUM
ejpam-4112	79	20	.	.	PUNCT
ejpam-4112	80	1	[	[	X
ejpam-4112	80	2	3	3	X
ejpam-4112	80	3	]	]	PUNCT
ejpam-4112	80	4	let	let	VERB
ejpam-4112	80	5	k1	k1	NOUN
ejpam-4112	80	6	=	=	SYM
ejpam-4112	80	7	⟨v⟩	⟨v⟩	PROPN
ejpam-4112	80	8	and	and	CCONJ
ejpam-4112	80	9	g	g	PROPN
ejpam-4112	80	10	be	be	AUX
ejpam-4112	80	11	a	a	DET
ejpam-4112	80	12	disconnected	disconnected	ADJ
ejpam-4112	80	13	graph	graph	NOUN
ejpam-4112	80	14	whose	whose	DET
ejpam-4112	80	15	components	component	NOUN
ejpam-4112	80	16	are	be	AUX
ejpam-4112	80	17	gi	gi	ADJ
ejpam-4112	80	18	for	for	ADP
ejpam-4112	80	19	i	i	PROPN
ejpam-4112	80	20	=	=	NOUN
ejpam-4112	80	21	1	1	NUM
ejpam-4112	80	22	,	,	PUNCT
ejpam-4112	80	23	2	2	NUM
ejpam-4112	80	24	,	,	PUNCT
ejpam-4112	80	25	.	.	PUNCT
ejpam-4112	80	26	.	.	PUNCT
ejpam-4112	80	27	.	.	PUNCT
ejpam-4112	81	1	,	,	PUNCT
ejpam-4112	81	2	m.	m.	NOUN
ejpam-4112	81	3	a	a	DET
ejpam-4112	81	4	proper	proper	ADJ
ejpam-4112	81	5	subset	subset	NOUN
ejpam-4112	81	6	s	s	NOUN
ejpam-4112	81	7	of	of	ADP
ejpam-4112	81	8	v	v	NOUN
ejpam-4112	81	9	(	(	PUNCT
ejpam-4112	81	10	k1	k1	NOUN
ejpam-4112	81	11	+	+	NOUN
ejpam-4112	81	12	g	g	NOUN
ejpam-4112	81	13	)	)	PUNCT
ejpam-4112	81	14	is	be	AUX
ejpam-4112	81	15	a	a	DET
ejpam-4112	81	16	strong	strong	ADJ
ejpam-4112	81	17	resolving	resolving	NOUN
ejpam-4112	81	18	dominating	dominating	NOUN
ejpam-4112	81	19	set	set	NOUN
ejpam-4112	81	20	of	of	ADP
ejpam-4112	81	21	k1	k1	NOUN
ejpam-4112	82	1	+	+	ADP
ejpam-4112	82	2	g	g	PROPN
ejpam-4112	82	3	if	if	SCONJ
ejpam-4112	82	4	and	and	CCONJ
ejpam-4112	82	5	only	only	ADV
ejpam-4112	82	6	if	if	SCONJ
ejpam-4112	82	7	s	s	VERB
ejpam-4112	82	8	=	=	SYM
ejpam-4112	82	9	v	v	X
ejpam-4112	82	10	(	(	PUNCT
ejpam-4112	82	11	g	g	NOUN
ejpam-4112	82	12	)	)	PUNCT
ejpam-4112	82	13	or	or	CCONJ
ejpam-4112	82	14	s	s	X
ejpam-4112	82	15	=	=	SYM
ejpam-4112	82	16	v	v	PROPN
ejpam-4112	82	17	(	(	PUNCT
ejpam-4112	82	18	g	g	NOUN
ejpam-4112	82	19	)	)	PUNCT
ejpam-4112	82	20	\	\	PROPN
ejpam-4112	82	21	c∗	c∗	PROPN
ejpam-4112	82	22	i	i	PROPN
ejpam-4112	82	23	or	or	CCONJ
ejpam-4112	82	24	s	s	NOUN
ejpam-4112	82	25	=	=	SYM
ejpam-4112	82	26	v	v	PROPN
ejpam-4112	82	27	(	(	PUNCT
ejpam-4112	82	28	k1	k1	NOUN
ejpam-4112	82	29	+	+	PROPN
ejpam-4112	82	30	g	g	NOUN
ejpam-4112	82	31	)	)	PUNCT
ejpam-4112	82	32	\	\	PROPN
ejpam-4112	82	33	ci	ci	PROPN
ejpam-4112	82	34	where	where	SCONJ
ejpam-4112	82	35	ci	ci	PROPN
ejpam-4112	82	36	is	be	AUX
ejpam-4112	82	37	a	a	DET
ejpam-4112	82	38	superclique	superclique	NOUN
ejpam-4112	82	39	in	in	ADP
ejpam-4112	82	40	gi	gi	NOUN
ejpam-4112	82	41	,	,	PUNCT
ejpam-4112	82	42	for	for	ADP
ejpam-4112	82	43	i	i	PROPN
ejpam-4112	82	44	=	=	SYM
ejpam-4112	82	45	1	1	NUM
ejpam-4112	82	46	,	,	PUNCT
ejpam-4112	82	47	2	2	NUM
ejpam-4112	82	48	,	,	PUNCT
ejpam-4112	82	49	.	.	PUNCT
ejpam-4112	82	50	.	.	PUNCT
ejpam-4112	83	1	.	.	PUNCT
ejpam-4112	84	1	,	,	PUNCT
ejpam-4112	84	2	m	m	NOUN
ejpam-4112	84	3	and	and	CCONJ
ejpam-4112	84	4	c∗	c∗	PROPN
ejpam-4112	84	5	i	i	PRON
ejpam-4112	84	6	is	be	AUX
ejpam-4112	84	7	a	a	DET
ejpam-4112	84	8	dominated	dominate	VERB
ejpam-4112	84	9	superclique	superclique	NOUN
ejpam-4112	84	10	of	of	ADP
ejpam-4112	84	11	gi	gi	NOUN
ejpam-4112	84	12	.	.	PUNCT
ejpam-4112	85	1	theorem	theorem	ADJ
ejpam-4112	85	2	4	4	NUM
ejpam-4112	85	3	.	.	PUNCT
ejpam-4112	86	1	[	[	X
ejpam-4112	86	2	3	3	X
ejpam-4112	86	3	]	]	PUNCT
ejpam-4112	86	4	let	let	VERB
ejpam-4112	86	5	g	g	PRON
ejpam-4112	86	6	be	be	AUX
ejpam-4112	86	7	a	a	DET
ejpam-4112	86	8	nontrivial	nontrivial	ADJ
ejpam-4112	86	9	connected	connect	VERB
ejpam-4112	86	10	graph	graph	NOUN
ejpam-4112	86	11	and	and	CCONJ
ejpam-4112	86	12	h	h	NOUN
ejpam-4112	86	13	a	a	DET
ejpam-4112	86	14	connected	connected	ADJ
ejpam-4112	86	15	graph	graph	NOUN
ejpam-4112	86	16	.	.	PUNCT
ejpam-4112	87	1	a	a	DET
ejpam-4112	87	2	proper	proper	ADJ
ejpam-4112	87	3	subset	subset	NOUN
ejpam-4112	87	4	s	s	NOUN
ejpam-4112	87	5	of	of	ADP
ejpam-4112	87	6	v	v	NOUN
ejpam-4112	87	7	(	(	PUNCT
ejpam-4112	87	8	g	g	PROPN
ejpam-4112	87	9	◦	◦	NOUN
ejpam-4112	87	10	h	h	NOUN
ejpam-4112	87	11	)	)	PUNCT
ejpam-4112	87	12	is	be	AUX
ejpam-4112	87	13	a	a	DET
ejpam-4112	87	14	strong	strong	ADJ
ejpam-4112	87	15	resolving	resolving	NOUN
ejpam-4112	87	16	dominating	dominating	NOUN
ejpam-4112	87	17	set	set	NOUN
ejpam-4112	87	18	of	of	ADP
ejpam-4112	87	19	g	g	PROPN
ejpam-4112	87	20	◦	◦	NOUN
ejpam-4112	87	21	h	h	NOUN
ejpam-4112	87	22	if	if	SCONJ
ejpam-4112	88	1	and	and	CCONJ
ejpam-4112	88	2	only	only	ADV
ejpam-4112	88	3	if	if	SCONJ
ejpam-4112	88	4	one	one	NUM
ejpam-4112	88	5	of	of	ADP
ejpam-4112	88	6	the	the	DET
ejpam-4112	88	7	following	follow	VERB
ejpam-4112	88	8	holds	hold	NOUN
ejpam-4112	88	9	:	:	PUNCT
ejpam-4112	88	10	h.	h.	NOUN
ejpam-4112	88	11	sumaoy	sumaoy	NOUN
ejpam-4112	88	12	,	,	PUNCT
ejpam-4112	88	13	h.	h.	PROPN
ejpam-4112	88	14	rara	rara	PROPN
ejpam-4112	88	15	/	/	SYM
ejpam-4112	88	16	eur	eur	PROPN
ejpam-4112	88	17	.	.	PUNCT
ejpam-4112	89	1	j.	j.	PROPN
ejpam-4112	89	2	pure	pure	PROPN
ejpam-4112	89	3	appl	appl	PROPN
ejpam-4112	89	4	.	.	PROPN
ejpam-4112	89	5	math	math	PROPN
ejpam-4112	89	6	,	,	PUNCT
ejpam-4112	89	7	14	14	NUM
ejpam-4112	89	8	(	(	PUNCT
ejpam-4112	89	9	4	4	NUM
ejpam-4112	89	10	)	)	PUNCT
ejpam-4112	89	11	(	(	PUNCT
ejpam-4112	89	12	2021	2021	NUM
ejpam-4112	89	13	)	)	PUNCT
ejpam-4112	89	14	,	,	PUNCT
ejpam-4112	89	15	1367	1367	NUM
ejpam-4112	89	16	-	-	SYM
ejpam-4112	89	17	1378	1378	NUM
ejpam-4112	89	18	1370	1370	NUM
ejpam-4112	89	19	(	(	PUNCT
ejpam-4112	89	20	i	i	NOUN
ejpam-4112	89	21	)	)	PUNCT
ejpam-4112	89	22	s	s	PART
ejpam-4112	89	23	=	=	PUNCT
ejpam-4112	89	24	a	a	DET
ejpam-4112	89	25	∪	∪	X
ejpam-4112	89	26	(	(	PUNCT
ejpam-4112	89	27	⋃	⋃	NOUN
ejpam-4112	89	28	u∈v	u∈v	NOUN
ejpam-4112	89	29	(	(	PUNCT
ejpam-4112	89	30	g	g	NOUN
ejpam-4112	89	31	)	)	PUNCT
ejpam-4112	89	32	v	v	NOUN
ejpam-4112	89	33	(	(	PUNCT
ejpam-4112	89	34	hu	hu	PROPN
ejpam-4112	89	35	)	)	PUNCT
ejpam-4112	89	36	)	)	PUNCT
ejpam-4112	89	37	where	where	SCONJ
ejpam-4112	89	38	a	a	DET
ejpam-4112	89	39	⊆	⊆	NUM
ejpam-4112	89	40	v	v	NOUN
ejpam-4112	89	41	(	(	PUNCT
ejpam-4112	89	42	g	g	NOUN
ejpam-4112	89	43	)	)	PUNCT
ejpam-4112	89	44	;	;	PUNCT
ejpam-4112	89	45	(	(	PUNCT
ejpam-4112	89	46	ii	ii	NOUN
ejpam-4112	89	47	)	)	PUNCT
ejpam-4112	89	48	s	s	PART
ejpam-4112	89	49	=	=	PUNCT
ejpam-4112	89	50	a	a	DET
ejpam-4112	89	51	∪	∪	X
ejpam-4112	89	52	(	(	PUNCT
ejpam-4112	89	53	⋃	⋃	NOUN
ejpam-4112	89	54	u∈v	u∈v	NOUN
ejpam-4112	89	55	(	(	PUNCT
ejpam-4112	89	56	g)\{v	g)\{v	PROPN
ejpam-4112	89	57	}	}	PUNCT
ejpam-4112	89	58	v	v	PROPN
ejpam-4112	89	59	(	(	PUNCT
ejpam-4112	89	60	hu	hu	PROPN
ejpam-4112	89	61	)	)	PUNCT
ejpam-4112	89	62	)	)	PUNCT
ejpam-4112	90	1	∪bv	∪bv	NOUN
ejpam-4112	90	2	for	for	ADP
ejpam-4112	90	3	a	a	DET
ejpam-4112	90	4	unique	unique	ADJ
ejpam-4112	90	5	vertex	vertex	NOUN
ejpam-4112	90	6	v	v	NOUN
ejpam-4112	90	7	in	in	ADP
ejpam-4112	90	8	g	g	PROPN
ejpam-4112	90	9	,	,	PUNCT
ejpam-4112	90	10	where	where	SCONJ
ejpam-4112	90	11	a	a	DET
ejpam-4112	90	12	⊆	⊆	NUM
ejpam-4112	90	13	v	v	NOUN
ejpam-4112	90	14	(	(	PUNCT
ejpam-4112	90	15	g	g	NOUN
ejpam-4112	90	16	)	)	PUNCT
ejpam-4112	90	17	\	\	NOUN
ejpam-4112	90	18	{	{	PUNCT
ejpam-4112	90	19	v	v	NOUN
ejpam-4112	90	20	}	}	PUNCT
ejpam-4112	90	21	and	and	CCONJ
ejpam-4112	90	22	bv	bv	PROPN
ejpam-4112	90	23	is	be	AUX
ejpam-4112	90	24	a	a	DET
ejpam-4112	90	25	strong	strong	ADJ
ejpam-4112	90	26	resolving	resolving	NOUN
ejpam-4112	90	27	dominating	dominating	NOUN
ejpam-4112	90	28	set	set	NOUN
ejpam-4112	90	29	of	of	ADP
ejpam-4112	90	30	hv	hv	PROPN
ejpam-4112	90	31	if	if	SCONJ
ejpam-4112	90	32	γ(h	γ(h	NOUN
ejpam-4112	90	33	)	)	PUNCT
ejpam-4112	90	34	=	=	SYM
ejpam-4112	90	35	1	1	NUM
ejpam-4112	90	36	or	or	CCONJ
ejpam-4112	90	37	bv	bv	PROPN
ejpam-4112	90	38	is	be	AUX
ejpam-4112	90	39	a	a	DET
ejpam-4112	90	40	strong	strong	ADJ
ejpam-4112	90	41	resolving	resolving	NOUN
ejpam-4112	90	42	dominating	dominating	NOUN
ejpam-4112	90	43	set	set	NOUN
ejpam-4112	90	44	of	of	ADP
ejpam-4112	90	45	⟨v⟩+hv	⟨v⟩+hv	PROPN
ejpam-4112	90	46	if	if	SCONJ
ejpam-4112	90	47	γ(h	γ(h	NOUN
ejpam-4112	90	48	)	)	PUNCT
ejpam-4112	90	49	̸=	̸=	PROPN
ejpam-4112	90	50	1	1	NUM
ejpam-4112	90	51	.	.	PUNCT
ejpam-4112	91	1	theorem	theorem	VERB
ejpam-4112	91	2	5	5	NUM
ejpam-4112	91	3	.	.	PUNCT
ejpam-4112	92	1	[	[	X
ejpam-4112	92	2	3	3	X
ejpam-4112	92	3	]	]	PUNCT
ejpam-4112	92	4	let	let	VERB
ejpam-4112	92	5	g	g	NOUN
ejpam-4112	92	6	and	and	CCONJ
ejpam-4112	92	7	h	h	PROPN
ejpam-4112	92	8	be	be	VERB
ejpam-4112	92	9	non	non	ADJ
ejpam-4112	92	10	-	-	ADJ
ejpam-4112	92	11	trivial	trivial	ADJ
ejpam-4112	92	12	connected	connected	ADJ
ejpam-4112	92	13	graphs	graph	NOUN
ejpam-4112	92	14	of	of	ADP
ejpam-4112	92	15	orders	order	NOUN
ejpam-4112	92	16	m	m	VERB
ejpam-4112	92	17	and	and	CCONJ
ejpam-4112	92	18	n	n	CCONJ
ejpam-4112	92	19	,	,	PUNCT
ejpam-4112	92	20	respectively	respectively	ADV
ejpam-4112	92	21	.	.	PUNCT
ejpam-4112	93	1	a	a	DET
ejpam-4112	93	2	proper	proper	ADJ
ejpam-4112	93	3	subset	subset	NOUN
ejpam-4112	93	4	s	s	NOUN
ejpam-4112	93	5	of	of	ADP
ejpam-4112	93	6	v	v	NOUN
ejpam-4112	93	7	(	(	PUNCT
ejpam-4112	93	8	g+h	g+h	PROPN
ejpam-4112	93	9	)	)	PUNCT
ejpam-4112	93	10	is	be	AUX
ejpam-4112	93	11	a	a	DET
ejpam-4112	93	12	strong	strong	ADJ
ejpam-4112	93	13	resolving	resolving	NOUN
ejpam-4112	93	14	dominating	dominating	NOUN
ejpam-4112	93	15	set	set	NOUN
ejpam-4112	93	16	of	of	ADP
ejpam-4112	93	17	g+h	g+h	PROPN
ejpam-4112	93	18	if	if	SCONJ
ejpam-4112	93	19	and	and	CCONJ
ejpam-4112	93	20	only	only	ADV
ejpam-4112	93	21	if	if	SCONJ
ejpam-4112	93	22	at	at	ADV
ejpam-4112	93	23	least	least	ADJ
ejpam-4112	93	24	one	one	NUM
ejpam-4112	93	25	of	of	ADP
ejpam-4112	93	26	the	the	DET
ejpam-4112	93	27	following	follow	VERB
ejpam-4112	93	28	is	be	AUX
ejpam-4112	93	29	satisfied	satisfied	ADJ
ejpam-4112	93	30	:	:	PUNCT
ejpam-4112	93	31	(	(	PUNCT
ejpam-4112	93	32	i	i	NOUN
ejpam-4112	93	33	)	)	PUNCT
ejpam-4112	93	34	s	s	PART
ejpam-4112	93	35	=	=	SYM
ejpam-4112	93	36	v	v	PROPN
ejpam-4112	93	37	(	(	PUNCT
ejpam-4112	93	38	g+h	g+h	NOUN
ejpam-4112	93	39	)	)	PUNCT
ejpam-4112	93	40	\	\	PROPN
ejpam-4112	94	1	cg	cg	NOUN
ejpam-4112	94	2	where	where	SCONJ
ejpam-4112	94	3	cg	cg	NOUN
ejpam-4112	94	4	is	be	AUX
ejpam-4112	94	5	a	a	DET
ejpam-4112	94	6	superclique	superclique	NOUN
ejpam-4112	94	7	of	of	ADP
ejpam-4112	94	8	g.	g.	PROPN
ejpam-4112	94	9	(	(	PUNCT
ejpam-4112	94	10	ii	ii	PROPN
ejpam-4112	94	11	)	)	PUNCT
ejpam-4112	94	12	s	s	PART
ejpam-4112	94	13	=	=	SYM
ejpam-4112	94	14	v	v	PROPN
ejpam-4112	94	15	(	(	PUNCT
ejpam-4112	94	16	g+h	g+h	NOUN
ejpam-4112	94	17	)	)	PUNCT
ejpam-4112	94	18	\	\	PROPN
ejpam-4112	95	1	ch	ch	NOUN
ejpam-4112	95	2	where	where	SCONJ
ejpam-4112	95	3	ch	ch	NOUN
ejpam-4112	95	4	is	be	AUX
ejpam-4112	95	5	a	a	DET
ejpam-4112	95	6	superclique	superclique	NOUN
ejpam-4112	95	7	of	of	ADP
ejpam-4112	95	8	g.	g.	PROPN
ejpam-4112	95	9	(	(	PUNCT
ejpam-4112	95	10	iii	iii	PROPN
ejpam-4112	95	11	)	)	PUNCT
ejpam-4112	95	12	if	if	SCONJ
ejpam-4112	95	13	γ(g	γ(g	PROPN
ejpam-4112	95	14	)	)	PUNCT
ejpam-4112	95	15	=	=	SYM
ejpam-4112	95	16	1	1	NUM
ejpam-4112	95	17	and	and	CCONJ
ejpam-4112	95	18	γ(h	γ(h	NOUN
ejpam-4112	95	19	)	)	PUNCT
ejpam-4112	95	20	=	=	SYM
ejpam-4112	95	21	1	1	NUM
ejpam-4112	95	22	,	,	PUNCT
ejpam-4112	95	23	s	s	PART
ejpam-4112	95	24	=	=	PUNCT
ejpam-4112	96	1	[	[	X
ejpam-4112	96	2	v	v	X
ejpam-4112	96	3	(	(	PUNCT
ejpam-4112	96	4	g+h	g+h	NOUN
ejpam-4112	96	5	)	)	PUNCT
ejpam-4112	96	6	\	\	PUNCT
ejpam-4112	97	1	(	(	PUNCT
ejpam-4112	97	2	cg	cg	NOUN
ejpam-4112	97	3	∪	∪	PROPN
ejpam-4112	97	4	ch	ch	NOUN
ejpam-4112	97	5	)	)	PUNCT
ejpam-4112	97	6	]	]	PUNCT
ejpam-4112	97	7	∪	∪	X
ejpam-4112	97	8	{	{	PUNCT
ejpam-4112	97	9	z	z	PROPN
ejpam-4112	97	10	∈	∈	PROPN
ejpam-4112	97	11	cg	cg	NOUN
ejpam-4112	97	12	:	:	PUNCT
ejpam-4112	97	13	degg(z	degg(z	NOUN
ejpam-4112	97	14	)	)	PUNCT
ejpam-4112	98	1	=	=	SYM
ejpam-4112	98	2	m−	m−	PROPN
ejpam-4112	98	3	1	1	NUM
ejpam-4112	98	4	}	}	PUNCT
ejpam-4112	98	5	or	or	CCONJ
ejpam-4112	98	6	s	s	NOUN
ejpam-4112	98	7	=	=	PUNCT
ejpam-4112	99	1	[	[	X
ejpam-4112	99	2	v	v	X
ejpam-4112	99	3	(	(	PUNCT
ejpam-4112	99	4	g+h	g+h	NOUN
ejpam-4112	99	5	)	)	PUNCT
ejpam-4112	99	6	\	\	PUNCT
ejpam-4112	100	1	(	(	PUNCT
ejpam-4112	100	2	cg	cg	NOUN
ejpam-4112	100	3	∪	∪	PROPN
ejpam-4112	100	4	ch	ch	NOUN
ejpam-4112	100	5	)	)	PUNCT
ejpam-4112	100	6	]	]	PUNCT
ejpam-4112	101	1	∪	∪	X
ejpam-4112	101	2	{	{	PUNCT
ejpam-4112	101	3	w	w	PROPN
ejpam-4112	101	4	∈	∈	PROPN
ejpam-4112	101	5	ch	ch	NOUN
ejpam-4112	101	6	:	:	PUNCT
ejpam-4112	101	7	degh(w	degh(w	PROPN
ejpam-4112	101	8	)	)	PUNCT
ejpam-4112	101	9	=	=	PUNCT
ejpam-4112	101	10	n−	n−	NOUN
ejpam-4112	101	11	1	1	NUM
ejpam-4112	101	12	}	}	PUNCT
ejpam-4112	101	13	where	where	SCONJ
ejpam-4112	101	14	cg	cg	NOUN
ejpam-4112	101	15	and	and	CCONJ
ejpam-4112	101	16	ch	ch	NOUN
ejpam-4112	101	17	are	be	AUX
ejpam-4112	101	18	supercliques	superclique	NOUN
ejpam-4112	101	19	in	in	ADP
ejpam-4112	101	20	g	g	PROPN
ejpam-4112	101	21	and	and	CCONJ
ejpam-4112	101	22	h	h	NOUN
ejpam-4112	101	23	,	,	PUNCT
ejpam-4112	101	24	respectively	respectively	ADV
ejpam-4112	101	25	.	.	PUNCT
ejpam-4112	102	1	(	(	PUNCT
ejpam-4112	102	2	iv	iv	X
ejpam-4112	102	3	)	)	PUNCT
ejpam-4112	102	4	if	if	SCONJ
ejpam-4112	102	5	γ(g	γ(g	PROPN
ejpam-4112	102	6	)	)	PUNCT
ejpam-4112	102	7	̸=	̸=	PROPN
ejpam-4112	102	8	1	1	NUM
ejpam-4112	102	9	and	and	CCONJ
ejpam-4112	102	10	γ(h	γ(h	NOUN
ejpam-4112	102	11	)	)	PUNCT
ejpam-4112	102	12	̸=	̸=	PROPN
ejpam-4112	102	13	1	1	NUM
ejpam-4112	102	14	,	,	PUNCT
ejpam-4112	102	15	s	s	VERB
ejpam-4112	102	16	=	=	PUNCT
ejpam-4112	103	1	[	[	X
ejpam-4112	103	2	v	v	X
ejpam-4112	103	3	(	(	PUNCT
ejpam-4112	103	4	g+h	g+h	NOUN
ejpam-4112	103	5	)	)	PUNCT
ejpam-4112	103	6	\	\	PUNCT
ejpam-4112	104	1	(	(	PUNCT
ejpam-4112	104	2	cg	cg	NOUN
ejpam-4112	104	3	∪	∪	PROPN
ejpam-4112	104	4	ch	ch	NOUN
ejpam-4112	104	5	)	)	PUNCT
ejpam-4112	104	6	]	]	PUNCT
ejpam-4112	105	1	=	=	PUNCT
ejpam-4112	105	2	(	(	PUNCT
ejpam-4112	105	3	v	v	NOUN
ejpam-4112	105	4	(	(	PUNCT
ejpam-4112	105	5	g	g	NOUN
ejpam-4112	105	6	)	)	PUNCT
ejpam-4112	105	7	\	\	PROPN
ejpam-4112	105	8	cg	cg	NOUN
ejpam-4112	105	9	)	)	PUNCT
ejpam-4112	105	10	∪	∪	NOUN
ejpam-4112	105	11	(	(	PUNCT
ejpam-4112	105	12	v	v	NOUN
ejpam-4112	105	13	(	(	PUNCT
ejpam-4112	105	14	h	h	NOUN
ejpam-4112	105	15	)	)	PUNCT
ejpam-4112	105	16	\	\	PROPN
ejpam-4112	105	17	ch	ch	NOUN
ejpam-4112	105	18	)	)	PUNCT
ejpam-4112	105	19	where	where	SCONJ
ejpam-4112	105	20	cg	cg	NOUN
ejpam-4112	105	21	and	and	CCONJ
ejpam-4112	105	22	ch	ch	NOUN
ejpam-4112	105	23	are	be	AUX
ejpam-4112	105	24	supercliques	superclique	NOUN
ejpam-4112	105	25	in	in	ADP
ejpam-4112	105	26	g	g	PROPN
ejpam-4112	105	27	and	and	CCONJ
ejpam-4112	105	28	h	h	NOUN
ejpam-4112	105	29	,	,	PUNCT
ejpam-4112	105	30	respectively	respectively	ADV
ejpam-4112	105	31	.	.	PUNCT
ejpam-4112	106	1	lemma	lemma	PROPN
ejpam-4112	106	2	1	1	NUM
ejpam-4112	106	3	.	.	PUNCT
ejpam-4112	107	1	[	[	X
ejpam-4112	107	2	2	2	X
ejpam-4112	107	3	]	]	PUNCT
ejpam-4112	107	4	let	let	VERB
ejpam-4112	107	5	g	g	PRON
ejpam-4112	107	6	be	be	AUX
ejpam-4112	107	7	a	a	DET
ejpam-4112	107	8	nontrivial	nontrivial	ADJ
ejpam-4112	107	9	connected	connect	VERB
ejpam-4112	107	10	graph	graph	NOUN
ejpam-4112	107	11	with	with	ADP
ejpam-4112	107	12	diam(g	diam(g	NOUN
ejpam-4112	107	13	)	)	PUNCT
ejpam-4112	107	14	≤	≤	NOUN
ejpam-4112	107	15	2	2	NUM
ejpam-4112	107	16	.	.	PUNCT
ejpam-4112	108	1	then	then	ADV
ejpam-4112	108	2	s	s	VERB
ejpam-4112	108	3	=	=	SYM
ejpam-4112	108	4	v	v	PROPN
ejpam-4112	108	5	(	(	PUNCT
ejpam-4112	108	6	g	g	NOUN
ejpam-4112	108	7	)	)	PUNCT
ejpam-4112	108	8	\	\	PUNCT
ejpam-4112	109	1	c	c	NOUN
ejpam-4112	109	2	is	be	AUX
ejpam-4112	109	3	a	a	DET
ejpam-4112	109	4	strong	strong	ADJ
ejpam-4112	109	5	resolving	resolving	NOUN
ejpam-4112	109	6	set	set	NOUN
ejpam-4112	109	7	of	of	ADP
ejpam-4112	109	8	g	g	PROPN
ejpam-4112	109	9	if	if	SCONJ
ejpam-4112	110	1	and	and	CCONJ
ejpam-4112	110	2	only	only	ADV
ejpam-4112	110	3	if	if	SCONJ
ejpam-4112	110	4	c	c	NOUN
ejpam-4112	110	5	=	=	SYM
ejpam-4112	110	6	∅	∅	NOUN
ejpam-4112	110	7	or	or	CCONJ
ejpam-4112	110	8	c	c	NOUN
ejpam-4112	110	9	is	be	AUX
ejpam-4112	110	10	a	a	DET
ejpam-4112	110	11	superclique	superclique	NOUN
ejpam-4112	110	12	in	in	ADP
ejpam-4112	110	13	g.	g.	PROPN
ejpam-4112	110	14	in	in	ADP
ejpam-4112	110	15	particular	particular	ADJ
ejpam-4112	110	16	,	,	PUNCT
ejpam-4112	110	17	sdim(g	sdim(g	PROPN
ejpam-4112	110	18	)	)	PUNCT
ejpam-4112	110	19	=	=	SYM
ejpam-4112	110	20	|v	|v	PROPN
ejpam-4112	110	21	(	(	PUNCT
ejpam-4112	110	22	g)|	g)|	NOUN
ejpam-4112	110	23	−	−	NOUN
ejpam-4112	110	24	ωs(g	ωs(g	NUM
ejpam-4112	110	25	)	)	PUNCT
ejpam-4112	110	26	.	.	PUNCT
ejpam-4112	111	1	theorem	theorem	VERB
ejpam-4112	111	2	6	6	NUM
ejpam-4112	111	3	.	.	PUNCT
ejpam-4112	112	1	[	[	X
ejpam-4112	112	2	2	2	X
ejpam-4112	112	3	]	]	PUNCT
ejpam-4112	112	4	let	let	VERB
ejpam-4112	112	5	g	g	PROPN
ejpam-4112	112	6	=	=	PROPN
ejpam-4112	112	7	kn	kn	PROPN
ejpam-4112	112	8	for	for	ADP
ejpam-4112	112	9	n	n	PROPN
ejpam-4112	112	10	>	>	SYM
ejpam-4112	112	11	1	1	NUM
ejpam-4112	112	12	and	and	CCONJ
ejpam-4112	112	13	h	h	DET
ejpam-4112	112	14	a	a	DET
ejpam-4112	112	15	nontrivial	nontrivial	ADJ
ejpam-4112	112	16	connected	connect	VERB
ejpam-4112	112	17	graph	graph	NOUN
ejpam-4112	112	18	with	with	ADP
ejpam-4112	112	19	γ(h	γ(h	NOUN
ejpam-4112	112	20	)	)	PUNCT
ejpam-4112	112	21	̸=	̸=	PROPN
ejpam-4112	112	22	1	1	NUM
ejpam-4112	112	23	.	.	PUNCT
ejpam-4112	113	1	a	a	DET
ejpam-4112	113	2	subset	subset	NOUN
ejpam-4112	113	3	s	s	X
ejpam-4112	113	4	of	of	ADP
ejpam-4112	113	5	v	v	NOUN
ejpam-4112	113	6	(	(	PUNCT
ejpam-4112	113	7	g[h	g[h	PROPN
ejpam-4112	113	8	]	]	PUNCT
ejpam-4112	113	9	)	)	PUNCT
ejpam-4112	113	10	is	be	AUX
ejpam-4112	113	11	a	a	DET
ejpam-4112	113	12	strong	strong	ADJ
ejpam-4112	113	13	resolving	resolving	NOUN
ejpam-4112	113	14	set	set	NOUN
ejpam-4112	113	15	of	of	ADP
ejpam-4112	113	16	g[h	g[h	NOUN
ejpam-4112	113	17	]	]	PUNCT
ejpam-4112	113	18	if	if	SCONJ
ejpam-4112	113	19	and	and	CCONJ
ejpam-4112	113	20	only	only	ADV
ejpam-4112	113	21	s	s	VERB
ejpam-4112	113	22	=	=	SYM
ejpam-4112	113	23	v	v	NOUN
ejpam-4112	113	24	(	(	PUNCT
ejpam-4112	113	25	g[h	g[h	PROPN
ejpam-4112	113	26	]	]	PUNCT
ejpam-4112	113	27	)	)	PUNCT
ejpam-4112	113	28	\	\	PUNCT
ejpam-4112	113	29	(	(	PUNCT
ejpam-4112	113	30	a×c	a×c	PROPN
ejpam-4112	113	31	)	)	PUNCT
ejpam-4112	113	32	,	,	PUNCT
ejpam-4112	113	33	where	where	SCONJ
ejpam-4112	113	34	a	a	PRON
ejpam-4112	113	35	is	be	AUX
ejpam-4112	113	36	a	a	DET
ejpam-4112	113	37	subset	subset	NOUN
ejpam-4112	113	38	of	of	ADP
ejpam-4112	113	39	v	v	NOUN
ejpam-4112	113	40	(	(	PUNCT
ejpam-4112	113	41	g	g	NOUN
ejpam-4112	113	42	)	)	PUNCT
ejpam-4112	113	43	and	and	CCONJ
ejpam-4112	113	44	c	c	NOUN
ejpam-4112	113	45	=	=	SYM
ejpam-4112	113	46	∅	∅	NOUN
ejpam-4112	113	47	or	or	CCONJ
ejpam-4112	113	48	c	c	NOUN
ejpam-4112	113	49	is	be	AUX
ejpam-4112	113	50	a	a	DET
ejpam-4112	113	51	superclique	superclique	NOUN
ejpam-4112	113	52	in	in	ADP
ejpam-4112	113	53	h.	h.	PROPN
ejpam-4112	113	54	remark	remark	PROPN
ejpam-4112	113	55	1	1	NUM
ejpam-4112	113	56	.	.	PUNCT
ejpam-4112	114	1	every	every	DET
ejpam-4112	114	2	restrained	restrain	VERB
ejpam-4112	114	3	strong	strong	ADJ
ejpam-4112	114	4	resolving	resolve	VERB
ejpam-4112	114	5	dominating	dominating	NOUN
ejpam-4112	114	6	set	set	NOUN
ejpam-4112	114	7	of	of	ADP
ejpam-4112	114	8	a	a	DET
ejpam-4112	114	9	connected	connected	ADJ
ejpam-4112	114	10	graph	graph	NOUN
ejpam-4112	114	11	g	g	PROPN
ejpam-4112	114	12	is	be	AUX
ejpam-4112	114	13	a	a	DET
ejpam-4112	114	14	strong	strong	ADJ
ejpam-4112	114	15	resolving	resolve	VERB
ejpam-4112	114	16	dominating	dominating	NOUN
ejpam-4112	114	17	set	set	NOUN
ejpam-4112	114	18	.	.	PUNCT
ejpam-4112	115	1	hence	hence	ADV
ejpam-4112	115	2	,	,	PUNCT
ejpam-4112	115	3	γsr(g	γsr(g	NOUN
ejpam-4112	115	4	)	)	PUNCT
ejpam-4112	115	5	≤	≤	NOUN
ejpam-4112	115	6	γrsr(g	γrsr(g	PROPN
ejpam-4112	115	7	)	)	PUNCT
ejpam-4112	115	8	.	.	PUNCT
ejpam-4112	116	1	also	also	ADV
ejpam-4112	116	2	,	,	PUNCT
ejpam-4112	116	3	every	every	DET
ejpam-4112	116	4	restrained	restrain	VERB
ejpam-4112	116	5	strong	strong	ADJ
ejpam-4112	116	6	resolving	resolve	VERB
ejpam-4112	116	7	dominating	dominating	NOUN
ejpam-4112	116	8	set	set	NOUN
ejpam-4112	116	9	of	of	ADP
ejpam-4112	116	10	g	g	PROPN
ejpam-4112	116	11	is	be	AUX
ejpam-4112	116	12	a	a	DET
ejpam-4112	116	13	restrained	restrained	ADJ
ejpam-4112	116	14	dominating	dominating	NOUN
ejpam-4112	116	15	set	set	NOUN
ejpam-4112	116	16	.	.	PUNCT
ejpam-4112	117	1	thus	thus	ADV
ejpam-4112	117	2	,	,	PUNCT
ejpam-4112	117	3	γr(g	γr(g	NUM
ejpam-4112	117	4	)	)	PUNCT
ejpam-4112	117	5	≤	≤	NUM
ejpam-4112	117	6	γrsr(g	γrsr(g	PROPN
ejpam-4112	117	7	)	)	PUNCT
ejpam-4112	117	8	.	.	PUNCT
ejpam-4112	118	1	remark	remark	PROPN
ejpam-4112	118	2	2	2	NUM
ejpam-4112	118	3	.	.	PUNCT
ejpam-4112	119	1	for	for	ADP
ejpam-4112	119	2	any	any	DET
ejpam-4112	119	3	connected	connected	ADJ
ejpam-4112	119	4	graph	graph	NOUN
ejpam-4112	119	5	g	g	NOUN
ejpam-4112	119	6	of	of	ADP
ejpam-4112	119	7	order	order	NOUN
ejpam-4112	119	8	n	n	CCONJ
ejpam-4112	119	9	,	,	PUNCT
ejpam-4112	119	10	1	1	NUM
ejpam-4112	119	11	≤	≤	NUM
ejpam-4112	119	12	γrsr(g	γrsr(g	PROPN
ejpam-4112	119	13	)	)	PUNCT
ejpam-4112	119	14	≤	≤	PROPN
ejpam-4112	119	15	n.	n.	NOUN
ejpam-4112	119	16	moreover	moreover	ADV
ejpam-4112	119	17	,	,	PUNCT
ejpam-4112	119	18	γ(g	γ(g	PROPN
ejpam-4112	119	19	)	)	PUNCT
ejpam-4112	120	1	=	=	PUNCT
ejpam-4112	120	2	1	1	NUM
ejpam-4112	120	3	if	if	SCONJ
ejpam-4112	120	4	and	and	CCONJ
ejpam-4112	120	5	only	only	ADV
ejpam-4112	120	6	if	if	SCONJ
ejpam-4112	120	7	g	g	PROPN
ejpam-4112	120	8	is	be	AUX
ejpam-4112	120	9	a	a	DET
ejpam-4112	120	10	non	non	ADJ
ejpam-4112	120	11	-	-	ADJ
ejpam-4112	120	12	trivial	trivial	ADJ
ejpam-4112	120	13	graph	graph	NOUN
ejpam-4112	120	14	and	and	CCONJ
ejpam-4112	120	15	γrsr(kn	γrsr(kn	NOUN
ejpam-4112	120	16	)	)	PUNCT
ejpam-4112	120	17	=	=	SYM
ejpam-4112	120	18	n	n	PROPN
ejpam-4112	120	19	for	for	ADP
ejpam-4112	120	20	n	n	PRON
ejpam-4112	120	21	≥	≥	NUM
ejpam-4112	120	22	1	1	NUM
ejpam-4112	120	23	.	.	PUNCT
ejpam-4112	121	1	proposition	proposition	NOUN
ejpam-4112	121	2	1	1	NUM
ejpam-4112	121	3	.	.	PUNCT
ejpam-4112	122	1	let	let	VERB
ejpam-4112	122	2	g	g	PRON
ejpam-4112	122	3	be	be	AUX
ejpam-4112	122	4	a	a	DET
ejpam-4112	122	5	nontrivial	nontrivial	ADJ
ejpam-4112	122	6	connected	connect	VERB
ejpam-4112	122	7	graph	graph	NOUN
ejpam-4112	122	8	with	with	ADP
ejpam-4112	122	9	diam(g	diam(g	NOUN
ejpam-4112	122	10	)	)	PUNCT
ejpam-4112	122	11	≤	≤	NOUN
ejpam-4112	122	12	2	2	NUM
ejpam-4112	122	13	.	.	PUNCT
ejpam-4112	123	1	then	then	ADV
ejpam-4112	123	2	s	s	VERB
ejpam-4112	123	3	⊆	⊆	NUM
ejpam-4112	123	4	v	v	NOUN
ejpam-4112	123	5	(	(	PUNCT
ejpam-4112	123	6	g	g	NOUN
ejpam-4112	123	7	)	)	PUNCT
ejpam-4112	123	8	is	be	AUX
ejpam-4112	123	9	a	a	DET
ejpam-4112	123	10	restrained	restrained	ADJ
ejpam-4112	123	11	strong	strong	ADJ
ejpam-4112	123	12	resolving	resolve	VERB
ejpam-4112	123	13	dominating	dominating	NOUN
ejpam-4112	123	14	set	set	NOUN
ejpam-4112	123	15	of	of	ADP
ejpam-4112	123	16	g	g	PROPN
ejpam-4112	123	17	if	if	SCONJ
ejpam-4112	124	1	and	and	CCONJ
ejpam-4112	124	2	only	only	ADV
ejpam-4112	124	3	if	if	SCONJ
ejpam-4112	124	4	s	s	VERB
ejpam-4112	124	5	=	=	SYM
ejpam-4112	124	6	v	v	NOUN
ejpam-4112	124	7	(	(	PUNCT
ejpam-4112	124	8	g)\c	g)\c	VERB
ejpam-4112	124	9	where	where	SCONJ
ejpam-4112	124	10	c	c	NOUN
ejpam-4112	124	11	=	=	SYM
ejpam-4112	124	12	∅	∅	NOUN
ejpam-4112	124	13	or	or	CCONJ
ejpam-4112	124	14	c	c	NOUN
ejpam-4112	124	15	is	be	AUX
ejpam-4112	124	16	a	a	DET
ejpam-4112	124	17	nonsingleton	nonsingleton	NOUN
ejpam-4112	124	18	dominated	dominate	VERB
ejpam-4112	124	19	superclique	superclique	NOUN
ejpam-4112	124	20	in	in	ADP
ejpam-4112	124	21	g.	g.	PROPN
ejpam-4112	124	22	in	in	ADP
ejpam-4112	124	23	particular	particular	ADJ
ejpam-4112	124	24	,	,	PUNCT
ejpam-4112	124	25	γrsr(g	γrsr(g	PROPN
ejpam-4112	124	26	)	)	PUNCT
ejpam-4112	124	27	=	=	SYM
ejpam-4112	125	1	|v	|v	PROPN
ejpam-4112	125	2	(	(	PUNCT
ejpam-4112	125	3	g)|	g)|	PROPN
ejpam-4112	125	4	−	−	PROPN
ejpam-4112	125	5	ωds(g	ωds(g	PROPN
ejpam-4112	125	6	)	)	PUNCT
ejpam-4112	125	7	.	.	PUNCT
ejpam-4112	126	1	h.	h.	PROPN
ejpam-4112	126	2	sumaoy	sumaoy	PROPN
ejpam-4112	126	3	,	,	PUNCT
ejpam-4112	126	4	h.	h.	PROPN
ejpam-4112	126	5	rara	rara	PROPN
ejpam-4112	126	6	/	/	SYM
ejpam-4112	126	7	eur	eur	PROPN
ejpam-4112	126	8	.	.	PUNCT
ejpam-4112	127	1	j.	j.	PROPN
ejpam-4112	127	2	pure	pure	PROPN
ejpam-4112	127	3	appl	appl	PROPN
ejpam-4112	127	4	.	.	PROPN
ejpam-4112	127	5	math	math	PROPN
ejpam-4112	127	6	,	,	PUNCT
ejpam-4112	127	7	14	14	NUM
ejpam-4112	127	8	(	(	PUNCT
ejpam-4112	127	9	4	4	NUM
ejpam-4112	127	10	)	)	PUNCT
ejpam-4112	127	11	(	(	PUNCT
ejpam-4112	127	12	2021	2021	NUM
ejpam-4112	127	13	)	)	PUNCT
ejpam-4112	127	14	,	,	PUNCT
ejpam-4112	127	15	1367	1367	NUM
ejpam-4112	127	16	-	-	SYM
ejpam-4112	127	17	1378	1378	NUM
ejpam-4112	127	18	1371	1371	NUM
ejpam-4112	127	19	proof	proof	NOUN
ejpam-4112	127	20	:	:	PUNCT
ejpam-4112	127	21	let	let	VERB
ejpam-4112	127	22	s	s	PRON
ejpam-4112	127	23	be	be	AUX
ejpam-4112	127	24	a	a	DET
ejpam-4112	127	25	restrained	restrained	ADJ
ejpam-4112	127	26	strong	strong	ADJ
ejpam-4112	127	27	resolving	resolve	VERB
ejpam-4112	127	28	dominating	dominating	NOUN
ejpam-4112	127	29	set	set	NOUN
ejpam-4112	127	30	of	of	ADP
ejpam-4112	127	31	g.	g.	PROPN
ejpam-4112	127	32	let	let	VERB
ejpam-4112	127	33	c	c	NOUN
ejpam-4112	127	34	=	=	SYM
ejpam-4112	127	35	v	v	PROPN
ejpam-4112	127	36	(	(	PUNCT
ejpam-4112	127	37	g	g	NOUN
ejpam-4112	127	38	)	)	PUNCT
ejpam-4112	127	39	\	\	PUNCT
ejpam-4112	128	1	s.	s.	PROPN
ejpam-4112	128	2	then	then	ADV
ejpam-4112	128	3	,	,	PUNCT
ejpam-4112	128	4	s	s	NOUN
ejpam-4112	128	5	=	=	SYM
ejpam-4112	128	6	v	v	X
ejpam-4112	128	7	(	(	PUNCT
ejpam-4112	128	8	g	g	NOUN
ejpam-4112	128	9	)	)	PUNCT
ejpam-4112	128	10	\	\	PROPN
ejpam-4112	128	11	c.	c.	NOUN
ejpam-4112	128	12	since	since	SCONJ
ejpam-4112	128	13	s	s	PROPN
ejpam-4112	128	14	is	be	AUX
ejpam-4112	128	15	a	a	DET
ejpam-4112	128	16	strong	strong	ADJ
ejpam-4112	128	17	resolving	resolving	NOUN
ejpam-4112	128	18	,	,	PUNCT
ejpam-4112	128	19	by	by	ADP
ejpam-4112	128	20	lemma	lemma	PROPN
ejpam-4112	128	21	1	1	NUM
ejpam-4112	128	22	,	,	PUNCT
ejpam-4112	128	23	c	c	NOUN
ejpam-4112	128	24	=	=	SYM
ejpam-4112	128	25	∅	∅	NOUN
ejpam-4112	128	26	or	or	CCONJ
ejpam-4112	128	27	c	c	NOUN
ejpam-4112	128	28	is	be	AUX
ejpam-4112	128	29	a	a	DET
ejpam-4112	128	30	superclique	superclique	NOUN
ejpam-4112	128	31	in	in	ADP
ejpam-4112	128	32	g.	g.	PROPN
ejpam-4112	128	33	since	since	SCONJ
ejpam-4112	128	34	s	s	PROPN
ejpam-4112	128	35	is	be	AUX
ejpam-4112	128	36	restrained	restrain	VERB
ejpam-4112	128	37	dominating	dominating	NOUN
ejpam-4112	128	38	,	,	PUNCT
ejpam-4112	128	39	s	s	PART
ejpam-4112	128	40	=	=	SYM
ejpam-4112	128	41	v	v	X
ejpam-4112	128	42	(	(	PUNCT
ejpam-4112	128	43	g	g	NOUN
ejpam-4112	128	44	)	)	PUNCT
ejpam-4112	128	45	or	or	CCONJ
ejpam-4112	128	46	v	v	NOUN
ejpam-4112	128	47	(	(	PUNCT
ejpam-4112	128	48	g	g	NOUN
ejpam-4112	128	49	)	)	PUNCT
ejpam-4112	128	50	\s	\s	NOUN
ejpam-4112	128	51	has	have	AUX
ejpam-4112	128	52	no	no	DET
ejpam-4112	128	53	isolated	isolated	ADJ
ejpam-4112	128	54	vertex	vertex	NOUN
ejpam-4112	128	55	.	.	PUNCT
ejpam-4112	129	1	thus	thus	ADV
ejpam-4112	129	2	,	,	PUNCT
ejpam-4112	129	3	c	c	NOUN
ejpam-4112	129	4	=	=	SYM
ejpam-4112	129	5	∅	∅	NOUN
ejpam-4112	129	6	or	or	CCONJ
ejpam-4112	129	7	c	c	NOUN
ejpam-4112	129	8	is	be	AUX
ejpam-4112	129	9	a	a	DET
ejpam-4112	129	10	singleton	singleton	NOUN
ejpam-4112	129	11	dominated	dominate	VERB
ejpam-4112	129	12	superclique	superclique	NOUN
ejpam-4112	129	13	in	in	ADP
ejpam-4112	129	14	g.	g.	PROPN
ejpam-4112	129	15	the	the	DET
ejpam-4112	129	16	converse	converse	NOUN
ejpam-4112	129	17	follows	follow	VERB
ejpam-4112	129	18	immediately	immediately	ADV
ejpam-4112	129	19	from	from	ADP
ejpam-4112	129	20	lemma	lemma	PROPN
ejpam-4112	129	21	1	1	NUM
ejpam-4112	129	22	,	,	PUNCT
ejpam-4112	129	23	definition	definition	NOUN
ejpam-4112	129	24	of	of	ADP
ejpam-4112	129	25	dominated	dominate	VERB
ejpam-4112	129	26	superclique	superclique	NOUN
ejpam-4112	129	27	and	and	CCONJ
ejpam-4112	129	28	definition	definition	NOUN
ejpam-4112	129	29	of	of	ADP
ejpam-4112	129	30	restrained	restrained	ADJ
ejpam-4112	129	31	dominating	dominating	NOUN
ejpam-4112	129	32	set	set	NOUN
ejpam-4112	129	33	.	.	PUNCT
ejpam-4112	130	1	suppose	suppose	VERB
ejpam-4112	130	2	s	s	PRON
ejpam-4112	130	3	is	be	AUX
ejpam-4112	130	4	a	a	DET
ejpam-4112	130	5	γrsr	γrsr	NOUN
ejpam-4112	130	6	-	-	PUNCT
ejpam-4112	130	7	set	set	NOUN
ejpam-4112	130	8	of	of	ADP
ejpam-4112	130	9	g.	g.	PROPN
ejpam-4112	130	10	then	then	ADV
ejpam-4112	130	11	,	,	PUNCT
ejpam-4112	130	12	s	s	NOUN
ejpam-4112	130	13	=	=	SYM
ejpam-4112	130	14	v	v	NOUN
ejpam-4112	130	15	(	(	PUNCT
ejpam-4112	130	16	g)\c	g)\c	NOUN
ejpam-4112	130	17	where	where	SCONJ
ejpam-4112	130	18	c	c	PROPN
ejpam-4112	130	19	is	be	AUX
ejpam-4112	130	20	a	a	DET
ejpam-4112	130	21	nonsingleton	nonsingleton	NOUN
ejpam-4112	130	22	dominated	dominate	VERB
ejpam-4112	130	23	superclique	superclique	NOUN
ejpam-4112	130	24	in	in	ADP
ejpam-4112	130	25	g	g	PROPN
ejpam-4112	130	26	and	and	CCONJ
ejpam-4112	130	27	|c|	|c|	PROPN
ejpam-4112	130	28	=	=	SYM
ejpam-4112	130	29	ωds(g	ωds(g	PROPN
ejpam-4112	130	30	)	)	PUNCT
ejpam-4112	130	31	.	.	PUNCT
ejpam-4112	131	1	thus	thus	ADV
ejpam-4112	131	2	,	,	PUNCT
ejpam-4112	131	3	γrsr(g	γrsr(g	PROPN
ejpam-4112	131	4	)	)	PUNCT
ejpam-4112	131	5	=	=	SYM
ejpam-4112	131	6	|s|	|s|	PROPN
ejpam-4112	131	7	=	=	PUNCT
ejpam-4112	131	8	|v	|v	PROPN
ejpam-4112	131	9	(	(	PUNCT
ejpam-4112	131	10	g)|	g)|	PROPN
ejpam-4112	131	11	−	−	PROPN
ejpam-4112	131	12	|c|	|c|	PROPN
ejpam-4112	131	13	=	=	SYM
ejpam-4112	131	14	|v	|v	PROPN
ejpam-4112	131	15	(	(	PUNCT
ejpam-4112	131	16	g)|	g)|	PROPN
ejpam-4112	131	17	−	−	PROPN
ejpam-4112	131	18	ωds(g	ωds(g	PROPN
ejpam-4112	131	19	)	)	PUNCT
ejpam-4112	131	20	.	.	PUNCT
ejpam-4112	132	1	3	3	X
ejpam-4112	132	2	.	.	X
ejpam-4112	132	3	restrained	restrain	VERB
ejpam-4112	132	4	strong	strong	ADJ
ejpam-4112	132	5	resolving	resolving	NOUN
ejpam-4112	132	6	domination	domination	NOUN
ejpam-4112	132	7	in	in	ADP
ejpam-4112	132	8	the	the	DET
ejpam-4112	132	9	join	join	NOUN
ejpam-4112	132	10	of	of	ADP
ejpam-4112	132	11	graphs	graph	NOUN
ejpam-4112	132	12	theorem	theorem	VERB
ejpam-4112	132	13	7	7	NUM
ejpam-4112	132	14	.	.	PUNCT
ejpam-4112	133	1	let	let	VERB
ejpam-4112	133	2	g	g	PRON
ejpam-4112	133	3	be	be	AUX
ejpam-4112	133	4	a	a	DET
ejpam-4112	133	5	nontrivial	nontrivial	ADJ
ejpam-4112	133	6	connected	connect	VERB
ejpam-4112	133	7	graph	graph	NOUN
ejpam-4112	133	8	of	of	ADP
ejpam-4112	133	9	order	order	NOUN
ejpam-4112	133	10	n	n	PRON
ejpam-4112	133	11	with	with	ADP
ejpam-4112	133	12	γ(g	γ(g	PROPN
ejpam-4112	133	13	)	)	PUNCT
ejpam-4112	133	14	̸=	̸=	PROPN
ejpam-4112	133	15	1	1	NUM
ejpam-4112	133	16	.	.	PUNCT
ejpam-4112	134	1	then	then	ADV
ejpam-4112	134	2	s	s	VERB
ejpam-4112	134	3	⊆	⊆	NUM
ejpam-4112	134	4	v	v	NOUN
ejpam-4112	134	5	(	(	PUNCT
ejpam-4112	134	6	k1	k1	NOUN
ejpam-4112	134	7	+	+	CCONJ
ejpam-4112	134	8	g	g	NOUN
ejpam-4112	134	9	)	)	PUNCT
ejpam-4112	134	10	is	be	AUX
ejpam-4112	134	11	a	a	DET
ejpam-4112	134	12	restrained	restrained	ADJ
ejpam-4112	134	13	strong	strong	ADJ
ejpam-4112	134	14	resolving	resolve	VERB
ejpam-4112	134	15	dominating	dominating	NOUN
ejpam-4112	134	16	set	set	NOUN
ejpam-4112	134	17	of	of	ADP
ejpam-4112	134	18	k1	k1	NOUN
ejpam-4112	134	19	+	+	CCONJ
ejpam-4112	134	20	g	g	NOUN
ejpam-4112	134	21	if	if	SCONJ
ejpam-4112	134	22	and	and	CCONJ
ejpam-4112	134	23	only	only	ADV
ejpam-4112	134	24	if	if	SCONJ
ejpam-4112	134	25	s	s	VERB
ejpam-4112	134	26	=	=	SYM
ejpam-4112	134	27	v	v	X
ejpam-4112	134	28	(	(	PUNCT
ejpam-4112	134	29	g	g	NOUN
ejpam-4112	134	30	)	)	PUNCT
ejpam-4112	134	31	\	\	NOUN
ejpam-4112	135	1	c	c	PROPN
ejpam-4112	135	2	or	or	CCONJ
ejpam-4112	135	3	s	s	NOUN
ejpam-4112	135	4	=	=	SYM
ejpam-4112	135	5	v	v	PROPN
ejpam-4112	135	6	(	(	PUNCT
ejpam-4112	135	7	k1	k1	NOUN
ejpam-4112	135	8	+	+	PROPN
ejpam-4112	135	9	g	g	NOUN
ejpam-4112	135	10	)	)	PUNCT
ejpam-4112	135	11	\	\	PROPN
ejpam-4112	135	12	c∗	c∗	NOUN
ejpam-4112	135	13	where	where	SCONJ
ejpam-4112	135	14	c	c	PROPN
ejpam-4112	135	15	is	be	AUX
ejpam-4112	135	16	a	a	DET
ejpam-4112	135	17	non	non	ADJ
ejpam-4112	135	18	-	-	ADJ
ejpam-4112	135	19	singleton	singleton	ADJ
ejpam-4112	135	20	dominated	dominate	VERB
ejpam-4112	135	21	superclique	superclique	NOUN
ejpam-4112	135	22	and	and	CCONJ
ejpam-4112	135	23	c∗	c∗	NOUN
ejpam-4112	135	24	=	=	SYM
ejpam-4112	135	25	∅	∅	NOUN
ejpam-4112	135	26	or	or	CCONJ
ejpam-4112	135	27	c∗	c∗	NOUN
ejpam-4112	135	28	is	be	AUX
ejpam-4112	135	29	non	non	ADJ
ejpam-4112	135	30	-	-	ADJ
ejpam-4112	135	31	singleton	singleton	ADJ
ejpam-4112	135	32	dominated	dominate	VERB
ejpam-4112	135	33	superclique	superclique	NOUN
ejpam-4112	135	34	of	of	ADP
ejpam-4112	135	35	g.	g.	PROPN
ejpam-4112	135	36	proof	proof	NOUN
ejpam-4112	135	37	:	:	PUNCT
ejpam-4112	135	38	let	let	VERB
ejpam-4112	135	39	s	s	PRON
ejpam-4112	135	40	be	be	AUX
ejpam-4112	135	41	a	a	DET
ejpam-4112	135	42	restrained	restrain	VERB
ejpam-4112	135	43	strong	strong	ADJ
ejpam-4112	135	44	resolving	resolving	NOUN
ejpam-4112	135	45	set	set	NOUN
ejpam-4112	135	46	of	of	ADP
ejpam-4112	135	47	k1	k1	PROPN
ejpam-4112	135	48	+	+	CCONJ
ejpam-4112	135	49	g.	g.	NOUN
ejpam-4112	135	50	since	since	SCONJ
ejpam-4112	135	51	s	s	PROPN
ejpam-4112	135	52	is	be	AUX
ejpam-4112	135	53	strong	strong	ADJ
ejpam-4112	135	54	resolving	resolve	VERB
ejpam-4112	135	55	dominating	dominating	NOUN
ejpam-4112	135	56	set	set	VERB
ejpam-4112	135	57	by	by	ADP
ejpam-4112	135	58	theorem	theorem	NOUN
ejpam-4112	135	59	1	1	NUM
ejpam-4112	135	60	,	,	PUNCT
ejpam-4112	135	61	s	s	PART
ejpam-4112	135	62	=	=	SYM
ejpam-4112	135	63	v	v	X
ejpam-4112	135	64	(	(	PUNCT
ejpam-4112	135	65	g	g	NOUN
ejpam-4112	135	66	)	)	PUNCT
ejpam-4112	135	67	or	or	CCONJ
ejpam-4112	135	68	s	s	X
ejpam-4112	135	69	=	=	SYM
ejpam-4112	135	70	v	v	PROPN
ejpam-4112	135	71	(	(	PUNCT
ejpam-4112	135	72	g	g	NOUN
ejpam-4112	135	73	)	)	PUNCT
ejpam-4112	135	74	\	\	NOUN
ejpam-4112	136	1	c	c	PROPN
ejpam-4112	136	2	or	or	CCONJ
ejpam-4112	136	3	s	s	NOUN
ejpam-4112	136	4	=	=	SYM
ejpam-4112	136	5	v	v	PROPN
ejpam-4112	136	6	(	(	PUNCT
ejpam-4112	136	7	k1	k1	NOUN
ejpam-4112	136	8	+	+	CCONJ
ejpam-4112	136	9	g	g	NOUN
ejpam-4112	136	10	)	)	PUNCT
ejpam-4112	136	11	\	\	PROPN
ejpam-4112	136	12	c∗	c∗	NOUN
ejpam-4112	136	13	where	where	SCONJ
ejpam-4112	136	14	c	c	PROPN
ejpam-4112	136	15	is	be	AUX
ejpam-4112	136	16	a	a	DET
ejpam-4112	136	17	dominated	dominate	VERB
ejpam-4112	136	18	superclique	superclique	NOUN
ejpam-4112	136	19	and	and	CCONJ
ejpam-4112	136	20	c∗	c∗	NOUN
ejpam-4112	136	21	is	be	AUX
ejpam-4112	136	22	a	a	DET
ejpam-4112	136	23	superclique	superclique	NOUN
ejpam-4112	136	24	in	in	ADP
ejpam-4112	136	25	g.	g.	PROPN
ejpam-4112	136	26	since	since	SCONJ
ejpam-4112	136	27	s	s	PROPN
ejpam-4112	136	28	is	be	AUX
ejpam-4112	136	29	restrained	restrain	VERB
ejpam-4112	136	30	dominating	dominating	NOUN
ejpam-4112	136	31	,	,	PUNCT
ejpam-4112	136	32	s	s	PART
ejpam-4112	136	33	=	=	SYM
ejpam-4112	136	34	v	v	PROPN
ejpam-4112	136	35	(	(	PUNCT
ejpam-4112	136	36	g+k1	g+k1	NOUN
ejpam-4112	136	37	)	)	PUNCT
ejpam-4112	136	38	or	or	CCONJ
ejpam-4112	136	39	v	v	NOUN
ejpam-4112	136	40	(	(	PUNCT
ejpam-4112	136	41	g+k1	g+k1	NOUN
ejpam-4112	136	42	)	)	PUNCT
ejpam-4112	136	43	\	\	PROPN
ejpam-4112	137	1	s	s	PART
ejpam-4112	137	2	has	have	VERB
ejpam-4112	137	3	no	no	DET
ejpam-4112	137	4	isolated	isolated	ADJ
ejpam-4112	137	5	vertex	vertex	NOUN
ejpam-4112	137	6	.	.	PUNCT
ejpam-4112	138	1	hence	hence	ADV
ejpam-4112	138	2	,	,	PUNCT
ejpam-4112	138	3	s	s	VERB
ejpam-4112	138	4	̸=	̸=	PROPN
ejpam-4112	138	5	v	v	NOUN
ejpam-4112	138	6	(	(	PUNCT
ejpam-4112	138	7	g	g	NOUN
ejpam-4112	138	8	)	)	PUNCT
ejpam-4112	138	9	and	and	CCONJ
ejpam-4112	138	10	s	s	VERB
ejpam-4112	138	11	=	=	SYM
ejpam-4112	138	12	v	v	X
ejpam-4112	138	13	(	(	PUNCT
ejpam-4112	138	14	g	g	NOUN
ejpam-4112	138	15	)	)	PUNCT
ejpam-4112	138	16	\	\	NOUN
ejpam-4112	139	1	c	c	PROPN
ejpam-4112	139	2	or	or	CCONJ
ejpam-4112	139	3	s	s	NOUN
ejpam-4112	139	4	=	=	SYM
ejpam-4112	139	5	v	v	PROPN
ejpam-4112	139	6	(	(	PUNCT
ejpam-4112	139	7	k1	k1	NOUN
ejpam-4112	139	8	+	+	PROPN
ejpam-4112	139	9	g	g	NOUN
ejpam-4112	139	10	)	)	PUNCT
ejpam-4112	139	11	\	\	PROPN
ejpam-4112	139	12	c∗	c∗	NOUN
ejpam-4112	139	13	where	where	SCONJ
ejpam-4112	139	14	c	c	PROPN
ejpam-4112	139	15	is	be	AUX
ejpam-4112	139	16	dominated	dominate	VERB
ejpam-4112	139	17	supeclique	supeclique	NOUN
ejpam-4112	139	18	and	and	CCONJ
ejpam-4112	139	19	c∗	c∗	NOUN
ejpam-4112	139	20	=	=	SYM
ejpam-4112	139	21	∅	∅	NOUN
ejpam-4112	139	22	or	or	CCONJ
ejpam-4112	139	23	c∗	c∗	NOUN
ejpam-4112	139	24	is	be	AUX
ejpam-4112	139	25	a	a	DET
ejpam-4112	139	26	nonsingleton	nonsingleton	NOUN
ejpam-4112	139	27	superclique	superclique	NOUN
ejpam-4112	139	28	of	of	ADP
ejpam-4112	139	29	g.	g.	PROPN
ejpam-4112	139	30	the	the	DET
ejpam-4112	139	31	converse	converse	NOUN
ejpam-4112	139	32	follows	follow	VERB
ejpam-4112	139	33	immediately	immediately	ADV
ejpam-4112	139	34	from	from	ADP
ejpam-4112	139	35	theorem	theorem	ADJ
ejpam-4112	139	36	1	1	NUM
ejpam-4112	139	37	,	,	PUNCT
ejpam-4112	139	38	definitions	definition	NOUN
ejpam-4112	139	39	of	of	ADP
ejpam-4112	139	40	dominated	dominate	VERB
ejpam-4112	139	41	superclique	superclique	NOUN
ejpam-4112	139	42	and	and	CCONJ
ejpam-4112	139	43	restrained	restrained	ADJ
ejpam-4112	139	44	dominating	dominating	NOUN
ejpam-4112	139	45	set	set	NOUN
ejpam-4112	139	46	of	of	ADP
ejpam-4112	139	47	a	a	DET
ejpam-4112	139	48	graph	graph	NOUN
ejpam-4112	139	49	.	.	PUNCT
ejpam-4112	140	1	theorem	theorem	NOUN
ejpam-4112	140	2	8	8	NUM
ejpam-4112	140	3	.	.	PUNCT
ejpam-4112	141	1	let	let	VERB
ejpam-4112	141	2	g	g	PRON
ejpam-4112	141	3	be	be	AUX
ejpam-4112	141	4	a	a	DET
ejpam-4112	141	5	nontrivial	nontrivial	ADJ
ejpam-4112	141	6	connected	connect	VERB
ejpam-4112	141	7	graph	graph	NOUN
ejpam-4112	141	8	of	of	ADP
ejpam-4112	141	9	order	order	NOUN
ejpam-4112	141	10	n	n	PRON
ejpam-4112	141	11	with	with	ADP
ejpam-4112	141	12	γ(g	γ(g	PROPN
ejpam-4112	141	13	)	)	PUNCT
ejpam-4112	141	14	=	=	SYM
ejpam-4112	141	15	1	1	NUM
ejpam-4112	141	16	and	and	CCONJ
ejpam-4112	141	17	k1	k1	NOUN
ejpam-4112	142	1	=	=	SYM
ejpam-4112	142	2	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4112	142	3	then	then	ADV
ejpam-4112	142	4	s	s	VERB
ejpam-4112	142	5	⊆	⊆	NUM
ejpam-4112	142	6	v	v	NOUN
ejpam-4112	142	7	(	(	PUNCT
ejpam-4112	142	8	k1+g	k1+g	NOUN
ejpam-4112	142	9	)	)	PUNCT
ejpam-4112	142	10	is	be	AUX
ejpam-4112	142	11	a	a	DET
ejpam-4112	142	12	restrained	restrained	ADJ
ejpam-4112	142	13	strong	strong	ADJ
ejpam-4112	142	14	resolving	resolve	VERB
ejpam-4112	142	15	dominating	dominating	NOUN
ejpam-4112	142	16	set	set	NOUN
ejpam-4112	142	17	of	of	ADP
ejpam-4112	142	18	k1+g	k1+g	NOUN
ejpam-4112	142	19	if	if	SCONJ
ejpam-4112	142	20	and	and	CCONJ
ejpam-4112	142	21	only	only	ADV
ejpam-4112	142	22	if	if	SCONJ
ejpam-4112	142	23	s	s	VERB
ejpam-4112	142	24	=	=	SYM
ejpam-4112	142	25	v	v	PROPN
ejpam-4112	142	26	(	(	PUNCT
ejpam-4112	142	27	k1	k1	NOUN
ejpam-4112	142	28	+	+	PROPN
ejpam-4112	142	29	g	g	NOUN
ejpam-4112	142	30	)	)	PUNCT
ejpam-4112	142	31	\c	\c	NOUN
ejpam-4112	142	32	or	or	CCONJ
ejpam-4112	142	33	s	s	NOUN
ejpam-4112	142	34	=	=	PUNCT
ejpam-4112	142	35	(	(	PUNCT
ejpam-4112	142	36	v	v	NOUN
ejpam-4112	142	37	(	(	PUNCT
ejpam-4112	142	38	g	g	NOUN
ejpam-4112	142	39	)	)	PUNCT
ejpam-4112	142	40	\c∗)∪	\c∗)∪	NOUN
ejpam-4112	142	41	{	{	PUNCT
ejpam-4112	142	42	x	x	PROPN
ejpam-4112	142	43	∈	∈	PROPN
ejpam-4112	142	44	c∗	c∗	NOUN
ejpam-4112	142	45	:	:	PUNCT
ejpam-4112	142	46	degg(x	degg(x	X
ejpam-4112	142	47	)	)	PUNCT
ejpam-4112	142	48	=	=	PUNCT
ejpam-4112	142	49	n−	n−	NOUN
ejpam-4112	142	50	1	1	NUM
ejpam-4112	142	51	}	}	PUNCT
ejpam-4112	142	52	where	where	SCONJ
ejpam-4112	142	53	c	c	NOUN
ejpam-4112	142	54	=	=	SYM
ejpam-4112	142	55	∅	∅	NOUN
ejpam-4112	142	56	or	or	CCONJ
ejpam-4112	142	57	c	c	NOUN
ejpam-4112	142	58	is	be	AUX
ejpam-4112	142	59	nonsingleton	nonsingleton	NOUN
ejpam-4112	142	60	superclique	superclique	NOUN
ejpam-4112	142	61	of	of	ADP
ejpam-4112	142	62	g	g	NOUN
ejpam-4112	142	63	and	and	CCONJ
ejpam-4112	142	64	c∗	c∗	PROPN
ejpam-4112	142	65	is	be	AUX
ejpam-4112	142	66	a	a	DET
ejpam-4112	142	67	superclique	superclique	NOUN
ejpam-4112	142	68	of	of	ADP
ejpam-4112	142	69	g.	g.	NOUN
ejpam-4112	142	70	proof	proof	NOUN
ejpam-4112	142	71	:	:	PUNCT
ejpam-4112	142	72	let	let	VERB
ejpam-4112	142	73	s	s	PRON
ejpam-4112	142	74	be	be	AUX
ejpam-4112	142	75	a	a	DET
ejpam-4112	142	76	restrained	restrained	ADJ
ejpam-4112	142	77	strong	strong	ADJ
ejpam-4112	142	78	resolving	resolve	VERB
ejpam-4112	142	79	dominating	dominating	NOUN
ejpam-4112	142	80	set	set	NOUN
ejpam-4112	142	81	of	of	ADP
ejpam-4112	142	82	k1	k1	PROPN
ejpam-4112	143	1	+	+	PROPN
ejpam-4112	143	2	g.	g.	PROPN
ejpam-4112	143	3	then	then	ADV
ejpam-4112	143	4	by	by	ADP
ejpam-4112	143	5	theorem	theorem	NOUN
ejpam-4112	143	6	2	2	NUM
ejpam-4112	143	7	,	,	PUNCT
ejpam-4112	143	8	s	s	PART
ejpam-4112	143	9	=	=	SYM
ejpam-4112	143	10	v	v	X
ejpam-4112	143	11	(	(	PUNCT
ejpam-4112	143	12	g	g	NOUN
ejpam-4112	143	13	)	)	PUNCT
ejpam-4112	143	14	or	or	CCONJ
ejpam-4112	143	15	s	s	X
ejpam-4112	143	16	=	=	SYM
ejpam-4112	143	17	v	v	PROPN
ejpam-4112	143	18	(	(	PUNCT
ejpam-4112	143	19	k1	k1	NOUN
ejpam-4112	143	20	+	+	PROPN
ejpam-4112	143	21	g	g	NOUN
ejpam-4112	143	22	)	)	PUNCT
ejpam-4112	143	23	\c	\c	NOUN
ejpam-4112	143	24	or	or	CCONJ
ejpam-4112	143	25	s	s	NOUN
ejpam-4112	143	26	=	=	PUNCT
ejpam-4112	143	27	(	(	PUNCT
ejpam-4112	143	28	v	v	NOUN
ejpam-4112	143	29	(	(	PUNCT
ejpam-4112	143	30	g	g	NOUN
ejpam-4112	143	31	)	)	PUNCT
ejpam-4112	143	32	\c∗)∪	\c∗)∪	NOUN
ejpam-4112	143	33	{	{	PUNCT
ejpam-4112	143	34	x	x	PROPN
ejpam-4112	143	35	∈	∈	PROPN
ejpam-4112	143	36	c∗	c∗	NOUN
ejpam-4112	143	37	:	:	PUNCT
ejpam-4112	143	38	degg(x	degg(x	X
ejpam-4112	143	39	)	)	PUNCT
ejpam-4112	143	40	=	=	SYM
ejpam-4112	144	1	n	n	CCONJ
ejpam-4112	144	2	−	−	NOUN
ejpam-4112	144	3	1	1	NUM
ejpam-4112	144	4	}	}	PUNCT
ejpam-4112	144	5	where	where	SCONJ
ejpam-4112	144	6	c	c	NOUN
ejpam-4112	144	7	and	and	CCONJ
ejpam-4112	144	8	c∗	c∗	PROPN
ejpam-4112	144	9	are	be	AUX
ejpam-4112	144	10	superclique	superclique	ADJ
ejpam-4112	144	11	and	and	CCONJ
ejpam-4112	144	12	dominated	dominate	VERB
ejpam-4112	144	13	superclique	superclique	NOUN
ejpam-4112	144	14	of	of	ADP
ejpam-4112	144	15	g	g	NOUN
ejpam-4112	144	16	,	,	PUNCT
ejpam-4112	144	17	respectively	respectively	ADV
ejpam-4112	144	18	.	.	PUNCT
ejpam-4112	145	1	since	since	SCONJ
ejpam-4112	145	2	s	s	NOUN
ejpam-4112	145	3	is	be	AUX
ejpam-4112	145	4	restrained	restrain	VERB
ejpam-4112	145	5	dominating	dominating	NOUN
ejpam-4112	145	6	,	,	PUNCT
ejpam-4112	145	7	s	s	PART
ejpam-4112	145	8	=	=	SYM
ejpam-4112	145	9	v	v	PROPN
ejpam-4112	145	10	(	(	PUNCT
ejpam-4112	145	11	k1+g	k1+g	NOUN
ejpam-4112	145	12	)	)	PUNCT
ejpam-4112	145	13	or	or	CCONJ
ejpam-4112	145	14	v	v	NOUN
ejpam-4112	145	15	(	(	PUNCT
ejpam-4112	145	16	k1+g)\s	k1+g)\s	NOUN
ejpam-4112	145	17	has	have	VERB
ejpam-4112	145	18	no	no	DET
ejpam-4112	145	19	isolated	isolated	ADJ
ejpam-4112	145	20	vertex	vertex	NOUN
ejpam-4112	145	21	.	.	PUNCT
ejpam-4112	146	1	thus	thus	ADV
ejpam-4112	146	2	,	,	PUNCT
ejpam-4112	146	3	s	s	VERB
ejpam-4112	146	4	̸=	̸=	PROPN
ejpam-4112	146	5	v	v	NOUN
ejpam-4112	146	6	(	(	PUNCT
ejpam-4112	146	7	g	g	NOUN
ejpam-4112	146	8	)	)	PUNCT
ejpam-4112	146	9	,	,	PUNCT
ejpam-4112	146	10	c	c	NOUN
ejpam-4112	146	11	=	=	SYM
ejpam-4112	146	12	∅	∅	NOUN
ejpam-4112	146	13	or	or	CCONJ
ejpam-4112	146	14	c	c	NOUN
ejpam-4112	146	15	is	be	AUX
ejpam-4112	146	16	non	non	ADJ
ejpam-4112	146	17	-	-	ADJ
ejpam-4112	146	18	singleton	singleton	ADJ
ejpam-4112	146	19	dominated	dominate	VERB
ejpam-4112	146	20	superclique	superclique	NOUN
ejpam-4112	146	21	of	of	ADP
ejpam-4112	146	22	g	g	PROPN
ejpam-4112	146	23	and	and	CCONJ
ejpam-4112	146	24	c∗	c∗	PROPN
ejpam-4112	146	25	is	be	AUX
ejpam-4112	146	26	a	a	DET
ejpam-4112	146	27	superclique	superclique	NOUN
ejpam-4112	146	28	of	of	ADP
ejpam-4112	146	29	g.	g.	PROPN
ejpam-4112	146	30	the	the	DET
ejpam-4112	146	31	converse	converse	NOUN
ejpam-4112	146	32	follows	follow	VERB
ejpam-4112	146	33	immediately	immediately	ADV
ejpam-4112	146	34	from	from	ADP
ejpam-4112	146	35	theorem	theorem	ADJ
ejpam-4112	146	36	2	2	NUM
ejpam-4112	146	37	,	,	PUNCT
ejpam-4112	146	38	definitions	definition	NOUN
ejpam-4112	146	39	of	of	ADP
ejpam-4112	146	40	superclique	superclique	ADJ
ejpam-4112	146	41	and	and	CCONJ
ejpam-4112	146	42	restrained	restrained	ADJ
ejpam-4112	146	43	dominating	dominating	NOUN
ejpam-4112	146	44	set	set	NOUN
ejpam-4112	146	45	of	of	ADP
ejpam-4112	146	46	a	a	DET
ejpam-4112	146	47	graph	graph	NOUN
ejpam-4112	146	48	.	.	PUNCT
ejpam-4112	147	1	the	the	DET
ejpam-4112	147	2	next	next	ADJ
ejpam-4112	147	3	results	result	NOUN
ejpam-4112	147	4	follow	follow	VERB
ejpam-4112	147	5	immediately	immediately	ADV
ejpam-4112	147	6	from	from	ADP
ejpam-4112	147	7	theorem	theorem	ADJ
ejpam-4112	147	8	7	7	NUM
ejpam-4112	147	9	.	.	PUNCT
ejpam-4112	147	10	corollary	corollary	ADJ
ejpam-4112	147	11	1	1	NUM
ejpam-4112	147	12	.	.	PUNCT
ejpam-4112	148	1	let	let	VERB
ejpam-4112	148	2	g	g	PRON
ejpam-4112	148	3	be	be	AUX
ejpam-4112	148	4	a	a	DET
ejpam-4112	148	5	nontrivial	nontrivial	ADJ
ejpam-4112	148	6	connected	connect	VERB
ejpam-4112	148	7	graph	graph	NOUN
ejpam-4112	148	8	of	of	ADP
ejpam-4112	148	9	order	order	NOUN
ejpam-4112	148	10	n.	n.	NOUN
ejpam-4112	148	11	then	then	ADV
ejpam-4112	148	12	γrsr(k1	γrsr(k1	ADP
ejpam-4112	148	13	+	+	NOUN
ejpam-4112	148	14	g	g	NOUN
ejpam-4112	148	15	)	)	PUNCT
ejpam-4112	148	16	=	=	PRON
ejpam-4112	148	17	{	{	PUNCT
ejpam-4112	148	18	n−	n−	NOUN
ejpam-4112	148	19	ωs(g	ωs(g	PUNCT
ejpam-4112	148	20	)	)	PUNCT
ejpam-4112	149	1	+	+	CCONJ
ejpam-4112	149	2	1	1	NUM
ejpam-4112	149	3	,	,	PUNCT
ejpam-4112	149	4	if	if	SCONJ
ejpam-4112	149	5	γ(g	γ(g	PROPN
ejpam-4112	149	6	)	)	PUNCT
ejpam-4112	149	7	=	=	SYM
ejpam-4112	149	8	1	1	NUM
ejpam-4112	149	9	n−	n−	NOUN
ejpam-4112	149	10	ωds(g	ωds(g	PROPN
ejpam-4112	149	11	)	)	PUNCT
ejpam-4112	149	12	,	,	PUNCT
ejpam-4112	149	13	if	if	SCONJ
ejpam-4112	149	14	γ(g	γ(g	NOUN
ejpam-4112	149	15	)	)	PUNCT
ejpam-4112	149	16	̸=	̸=	PROPN
ejpam-4112	149	17	1	1	NUM
ejpam-4112	149	18	.	.	PUNCT
ejpam-4112	149	19	h.	h.	NOUN
ejpam-4112	149	20	sumaoy	sumaoy	PROPN
ejpam-4112	149	21	,	,	PUNCT
ejpam-4112	149	22	h.	h.	PROPN
ejpam-4112	149	23	rara	rara	PROPN
ejpam-4112	149	24	/	/	SYM
ejpam-4112	149	25	eur	eur	PROPN
ejpam-4112	149	26	.	.	PUNCT
ejpam-4112	150	1	j.	j.	PROPN
ejpam-4112	150	2	pure	pure	PROPN
ejpam-4112	150	3	appl	appl	PROPN
ejpam-4112	150	4	.	.	PROPN
ejpam-4112	150	5	math	math	PROPN
ejpam-4112	150	6	,	,	PUNCT
ejpam-4112	150	7	14	14	NUM
ejpam-4112	150	8	(	(	PUNCT
ejpam-4112	150	9	4	4	NUM
ejpam-4112	150	10	)	)	PUNCT
ejpam-4112	150	11	(	(	PUNCT
ejpam-4112	150	12	2021	2021	NUM
ejpam-4112	150	13	)	)	PUNCT
ejpam-4112	150	14	,	,	PUNCT
ejpam-4112	150	15	1367	1367	NUM
ejpam-4112	150	16	-	-	SYM
ejpam-4112	150	17	1378	1378	NUM
ejpam-4112	150	18	1372	1372	NUM
ejpam-4112	150	19	corollary	corollary	NOUN
ejpam-4112	150	20	2	2	NUM
ejpam-4112	150	21	.	.	PUNCT
ejpam-4112	151	1	let	let	VERB
ejpam-4112	151	2	g	g	PRON
ejpam-4112	151	3	be	be	AUX
ejpam-4112	151	4	a	a	DET
ejpam-4112	151	5	connected	connected	ADJ
ejpam-4112	151	6	graph	graph	NOUN
ejpam-4112	151	7	with	with	ADP
ejpam-4112	151	8	diam(g	diam(g	NOUN
ejpam-4112	151	9	)	)	PUNCT
ejpam-4112	151	10	≤	≤	NOUN
ejpam-4112	151	11	2	2	NUM
ejpam-4112	151	12	.	.	PUNCT
ejpam-4112	152	1	then	then	ADV
ejpam-4112	152	2	γrsr(k1	γrsr(k1	ADP
ejpam-4112	153	1	+	+	NOUN
ejpam-4112	153	2	g	g	NOUN
ejpam-4112	153	3	)	)	PUNCT
ejpam-4112	153	4	=	=	NOUN
ejpam-4112	153	5	{	{	PUNCT
ejpam-4112	153	6	sdim(g	sdim(g	PROPN
ejpam-4112	153	7	)	)	PUNCT
ejpam-4112	154	1	+	+	CCONJ
ejpam-4112	154	2	1	1	NUM
ejpam-4112	154	3	,	,	PUNCT
ejpam-4112	154	4	if	if	SCONJ
ejpam-4112	154	5	γ(g	γ(g	PROPN
ejpam-4112	154	6	)	)	PUNCT
ejpam-4112	154	7	=	=	SYM
ejpam-4112	154	8	1	1	NUM
ejpam-4112	154	9	γsr(g	γsr(g	NOUN
ejpam-4112	154	10	)	)	PUNCT
ejpam-4112	154	11	,	,	PUNCT
ejpam-4112	154	12	if	if	SCONJ
ejpam-4112	154	13	γ(g	γ(g	NOUN
ejpam-4112	154	14	)	)	PUNCT
ejpam-4112	154	15	̸=	̸=	PROPN
ejpam-4112	154	16	1	1	NUM
ejpam-4112	154	17	.	.	PUNCT
ejpam-4112	154	18	corollary	corollary	ADJ
ejpam-4112	154	19	3	3	X
ejpam-4112	154	20	.	.	PUNCT
ejpam-4112	155	1	let	let	VERB
ejpam-4112	155	2	pn	pn	VERB
ejpam-4112	155	3	=	=	PUNCT
ejpam-4112	156	1	[	[	X
ejpam-4112	156	2	v1	v1	NOUN
ejpam-4112	156	3	,	,	PUNCT
ejpam-4112	156	4	v2	v2	NOUN
ejpam-4112	156	5	,	,	PUNCT
ejpam-4112	156	6	.	.	PUNCT
ejpam-4112	156	7	.	.	PUNCT
ejpam-4112	156	8	.	.	PUNCT
ejpam-4112	157	1	,	,	PUNCT
ejpam-4112	157	2	vn	vn	X
ejpam-4112	157	3	]	]	PUNCT
ejpam-4112	157	4	and	and	CCONJ
ejpam-4112	157	5	cm	cm	NOUN
ejpam-4112	157	6	=	=	PUNCT
ejpam-4112	158	1	[	[	X
ejpam-4112	158	2	c1	c1	PROPN
ejpam-4112	158	3	,	,	PUNCT
ejpam-4112	158	4	c2	c2	PROPN
ejpam-4112	158	5	,	,	PUNCT
ejpam-4112	158	6	.	.	PUNCT
ejpam-4112	158	7	.	.	PUNCT
ejpam-4112	158	8	.	.	PUNCT
ejpam-4112	159	1	cm	cm	NOUN
ejpam-4112	159	2	,	,	PUNCT
ejpam-4112	159	3	c1	c1	NOUN
ejpam-4112	159	4	]	]	PUNCT
ejpam-4112	159	5	where	where	SCONJ
ejpam-4112	159	6	n	n	X
ejpam-4112	159	7	,	,	PUNCT
ejpam-4112	159	8	m	m	VERB
ejpam-4112	159	9	≥	≥	NOUN
ejpam-4112	159	10	3	3	NUM
ejpam-4112	159	11	.	.	PUNCT
ejpam-4112	160	1	(	(	PUNCT
ejpam-4112	160	2	i	i	NOUN
ejpam-4112	160	3	)	)	PUNCT
ejpam-4112	160	4	the	the	DET
ejpam-4112	160	5	sets	set	NOUN
ejpam-4112	160	6	v	v	X
ejpam-4112	160	7	(	(	PUNCT
ejpam-4112	160	8	pn	pn	NOUN
ejpam-4112	160	9	)	)	PUNCT
ejpam-4112	160	10	\	\	PROPN
ejpam-4112	160	11	{	{	PUNCT
ejpam-4112	160	12	vi	vi	PROPN
ejpam-4112	160	13	,	,	PUNCT
ejpam-4112	160	14	vi+1	vi+1	PRON
ejpam-4112	160	15	}	}	PUNCT
ejpam-4112	160	16	for	for	ADP
ejpam-4112	160	17	i	i	PROPN
ejpam-4112	160	18	=	=	SYM
ejpam-4112	160	19	2	2	NUM
ejpam-4112	160	20	,	,	PUNCT
ejpam-4112	160	21	3	3	NUM
ejpam-4112	160	22	,	,	PUNCT
ejpam-4112	160	23	.	.	PUNCT
ejpam-4112	160	24	.	.	PUNCT
ejpam-4112	160	25	.	.	PUNCT
ejpam-4112	161	1	,	,	PUNCT
ejpam-4112	161	2	n−	n−	NOUN
ejpam-4112	161	3	2	2	NUM
ejpam-4112	161	4	,	,	PUNCT
ejpam-4112	161	5	v	v	PROPN
ejpam-4112	161	6	(	(	PUNCT
ejpam-4112	161	7	pn	pn	NOUN
ejpam-4112	161	8	)	)	PUNCT
ejpam-4112	161	9	\	\	PROPN
ejpam-4112	161	10	{	{	PUNCT
ejpam-4112	161	11	vj	vj	PROPN
ejpam-4112	161	12	}	}	PUNCT
ejpam-4112	161	13	for	for	ADP
ejpam-4112	161	14	j	j	PROPN
ejpam-4112	161	15	=	=	SYM
ejpam-4112	161	16	1	1	NUM
ejpam-4112	161	17	,	,	PUNCT
ejpam-4112	161	18	2	2	NUM
ejpam-4112	161	19	,	,	PUNCT
ejpam-4112	161	20	.	.	PUNCT
ejpam-4112	161	21	.	.	PUNCT
ejpam-4112	162	1	.	.	PUNCT
ejpam-4112	163	1	,	,	PUNCT
ejpam-4112	163	2	n	n	PROPN
ejpam-4112	163	3	and	and	CCONJ
ejpam-4112	163	4	v	v	ADP
ejpam-4112	163	5	(	(	PUNCT
ejpam-4112	163	6	pn)∪{v	pn)∪{v	PROPN
ejpam-4112	163	7	}	}	PUNCT
ejpam-4112	163	8	\	\	NOUN
ejpam-4112	163	9	{	{	PUNCT
ejpam-4112	163	10	vk	vk	PROPN
ejpam-4112	163	11	,	,	PUNCT
ejpam-4112	163	12	vk+1	vk+1	VERB
ejpam-4112	163	13	}	}	PUNCT
ejpam-4112	163	14	for	for	ADP
ejpam-4112	163	15	k	k	PROPN
ejpam-4112	163	16	=	=	SYM
ejpam-4112	163	17	1	1	NUM
ejpam-4112	163	18	,	,	PUNCT
ejpam-4112	163	19	2	2	NUM
ejpam-4112	163	20	,	,	PUNCT
ejpam-4112	163	21	.	.	PUNCT
ejpam-4112	163	22	.	.	PUNCT
ejpam-4112	164	1	.	.	PUNCT
ejpam-4112	165	1	,	,	PUNCT
ejpam-4112	165	2	n−	n−	NOUN
ejpam-4112	165	3	1	1	NUM
ejpam-4112	165	4	are	be	AUX
ejpam-4112	165	5	the	the	DET
ejpam-4112	165	6	restrained	restrain	VERB
ejpam-4112	165	7	strong	strong	ADJ
ejpam-4112	165	8	resolving	resolve	VERB
ejpam-4112	165	9	dominating	dominating	NOUN
ejpam-4112	165	10	sets	set	NOUN
ejpam-4112	165	11	of	of	ADP
ejpam-4112	165	12	⟨v⟩+	⟨v⟩+	INTJ
ejpam-4112	165	13	pn	pn	PROPN
ejpam-4112	165	14	.	.	PROPN
ejpam-4112	165	15	(	(	PUNCT
ejpam-4112	165	16	ii	ii	NOUN
ejpam-4112	165	17	)	)	PUNCT
ejpam-4112	165	18	the	the	DET
ejpam-4112	165	19	sets	set	NOUN
ejpam-4112	165	20	v	v	ADP
ejpam-4112	165	21	(	(	PUNCT
ejpam-4112	165	22	cm	cm	NOUN
ejpam-4112	165	23	)	)	PUNCT
ejpam-4112	165	24	\	\	NOUN
ejpam-4112	165	25	{	{	PUNCT
ejpam-4112	165	26	ci	ci	PROPN
ejpam-4112	165	27	,	,	PUNCT
ejpam-4112	165	28	ci+1	ci+1	ADJ
ejpam-4112	165	29	}	}	PUNCT
ejpam-4112	165	30	,	,	PUNCT
ejpam-4112	165	31	(	(	PUNCT
ejpam-4112	165	32	v	v	NOUN
ejpam-4112	165	33	(	(	PUNCT
ejpam-4112	165	34	cm)∪	cm)∪	VERB
ejpam-4112	165	35	{	{	PUNCT
ejpam-4112	165	36	v	v	NOUN
ejpam-4112	165	37	}	}	PUNCT
ejpam-4112	165	38	)	)	PUNCT
ejpam-4112	165	39	\	\	PROPN
ejpam-4112	165	40	{	{	PUNCT
ejpam-4112	165	41	ci	ci	PROPN
ejpam-4112	165	42	,	,	PUNCT
ejpam-4112	165	43	ci+1	ci+1	ADJ
ejpam-4112	165	44	}	}	PUNCT
ejpam-4112	165	45	,	,	PUNCT
ejpam-4112	165	46	v	v	INTJ
ejpam-4112	165	47	(	(	PUNCT
ejpam-4112	165	48	cm	cm	NOUN
ejpam-4112	165	49	)	)	PUNCT
ejpam-4112	165	50	\	\	NOUN
ejpam-4112	165	51	{	{	PUNCT
ejpam-4112	165	52	vi	vi	NOUN
ejpam-4112	165	53	}	}	PUNCT
ejpam-4112	165	54	,	,	PUNCT
ejpam-4112	165	55	v	v	INTJ
ejpam-4112	165	56	(	(	PUNCT
ejpam-4112	165	57	cm	cm	NOUN
ejpam-4112	165	58	)	)	PUNCT
ejpam-4112	165	59	\	\	NOUN
ejpam-4112	165	60	{	{	PUNCT
ejpam-4112	165	61	vm	vm	NOUN
ejpam-4112	165	62	}	}	PUNCT
ejpam-4112	165	63	,	,	PUNCT
ejpam-4112	165	64	v	v	INTJ
ejpam-4112	165	65	(	(	PUNCT
ejpam-4112	165	66	cm	cm	NOUN
ejpam-4112	165	67	)	)	PUNCT
ejpam-4112	165	68	\	\	NOUN
ejpam-4112	165	69	{	{	PUNCT
ejpam-4112	165	70	ci	ci	PROPN
ejpam-4112	165	71	,	,	PUNCT
ejpam-4112	165	72	cm	cm	NOUN
ejpam-4112	165	73	}	}	PUNCT
ejpam-4112	165	74	and	and	CCONJ
ejpam-4112	165	75	(	(	PUNCT
ejpam-4112	165	76	v	v	NOUN
ejpam-4112	165	77	(	(	PUNCT
ejpam-4112	165	78	cm)∪	cm)∪	VERB
ejpam-4112	165	79	{	{	PUNCT
ejpam-4112	165	80	v	v	NOUN
ejpam-4112	165	81	}	}	PUNCT
ejpam-4112	165	82	\	\	NOUN
ejpam-4112	165	83	{	{	PUNCT
ejpam-4112	165	84	c1	c1	NOUN
ejpam-4112	165	85	,	,	PUNCT
ejpam-4112	165	86	cm	cm	NOUN
ejpam-4112	165	87	}	}	PUNCT
ejpam-4112	165	88	)	)	PUNCT
ejpam-4112	165	89	for	for	ADP
ejpam-4112	165	90	i	i	PROPN
ejpam-4112	165	91	=	=	SYM
ejpam-4112	165	92	1	1	NUM
ejpam-4112	165	93	,	,	PUNCT
ejpam-4112	165	94	2	2	NUM
ejpam-4112	165	95	,	,	PUNCT
ejpam-4112	165	96	.	.	PUNCT
ejpam-4112	165	97	.	.	PUNCT
ejpam-4112	165	98	.	.	PUNCT
ejpam-4112	166	1	,	,	PUNCT
ejpam-4112	166	2	m−	m−	PROPN
ejpam-4112	166	3	1	1	NUM
ejpam-4112	166	4	,	,	PUNCT
ejpam-4112	166	5	are	be	AUX
ejpam-4112	166	6	the	the	DET
ejpam-4112	166	7	restrained	restrain	VERB
ejpam-4112	166	8	strong	strong	ADJ
ejpam-4112	166	9	resolving	resolve	VERB
ejpam-4112	166	10	dominating	dominating	NOUN
ejpam-4112	166	11	sets	set	NOUN
ejpam-4112	166	12	of	of	ADP
ejpam-4112	166	13	⟨v⟩+	⟨v⟩+	INTJ
ejpam-4112	166	14	cn	cn	PROPN
ejpam-4112	166	15	.	.	PUNCT
ejpam-4112	166	16	theorem	theorem	NOUN
ejpam-4112	166	17	9	9	NUM
ejpam-4112	166	18	.	.	PUNCT
ejpam-4112	167	1	let	let	VERB
ejpam-4112	167	2	g	g	PRON
ejpam-4112	167	3	be	be	AUX
ejpam-4112	167	4	a	a	DET
ejpam-4112	167	5	disconnected	disconnected	ADJ
ejpam-4112	167	6	graph	graph	NOUN
ejpam-4112	167	7	whose	whose	DET
ejpam-4112	167	8	components	component	NOUN
ejpam-4112	167	9	are	be	AUX
ejpam-4112	167	10	gi	gi	ADJ
ejpam-4112	167	11	for	for	ADP
ejpam-4112	167	12	i	i	PROPN
ejpam-4112	167	13	=	=	NOUN
ejpam-4112	167	14	1	1	NUM
ejpam-4112	167	15	,	,	PUNCT
ejpam-4112	167	16	2	2	NUM
ejpam-4112	167	17	,	,	PUNCT
ejpam-4112	167	18	.	.	PUNCT
ejpam-4112	167	19	.	.	PUNCT
ejpam-4112	168	1	.	.	PUNCT
ejpam-4112	169	1	,	,	PUNCT
ejpam-4112	169	2	n.	n.	PROPN
ejpam-4112	169	3	a	a	DET
ejpam-4112	169	4	subset	subset	NOUN
ejpam-4112	169	5	s	s	NOUN
ejpam-4112	169	6	of	of	ADP
ejpam-4112	169	7	v	v	NOUN
ejpam-4112	169	8	(	(	PUNCT
ejpam-4112	169	9	k1	k1	NOUN
ejpam-4112	170	1	+	+	NOUN
ejpam-4112	170	2	g	g	NOUN
ejpam-4112	170	3	)	)	PUNCT
ejpam-4112	170	4	is	be	AUX
ejpam-4112	170	5	a	a	DET
ejpam-4112	170	6	restrained	restrained	ADJ
ejpam-4112	170	7	strong	strong	ADJ
ejpam-4112	170	8	resolving	resolve	VERB
ejpam-4112	170	9	dominating	dominating	NOUN
ejpam-4112	170	10	set	set	NOUN
ejpam-4112	170	11	of	of	ADP
ejpam-4112	170	12	k1	k1	NOUN
ejpam-4112	171	1	+	+	ADP
ejpam-4112	171	2	g	g	PROPN
ejpam-4112	171	3	if	if	SCONJ
ejpam-4112	171	4	and	and	CCONJ
ejpam-4112	171	5	only	only	ADV
ejpam-4112	171	6	if	if	SCONJ
ejpam-4112	171	7	s	s	VERB
ejpam-4112	171	8	=	=	SYM
ejpam-4112	171	9	v	v	X
ejpam-4112	171	10	(	(	PUNCT
ejpam-4112	171	11	g	g	NOUN
ejpam-4112	171	12	)	)	PUNCT
ejpam-4112	171	13	\	\	PROPN
ejpam-4112	171	14	ci	ci	NOUN
ejpam-4112	171	15	or	or	CCONJ
ejpam-4112	171	16	s	s	NOUN
ejpam-4112	171	17	=	=	X
ejpam-4112	171	18	v	v	PROPN
ejpam-4112	171	19	(	(	PUNCT
ejpam-4112	171	20	k1	k1	NOUN
ejpam-4112	171	21	+	+	CCONJ
ejpam-4112	171	22	g	g	NOUN
ejpam-4112	171	23	)	)	PUNCT
ejpam-4112	172	1	\	\	PROPN
ejpam-4112	172	2	c∗	c∗	PROPN
ejpam-4112	172	3	i	i	PRON
ejpam-4112	172	4	where	where	SCONJ
ejpam-4112	172	5	ci	ci	PROPN
ejpam-4112	172	6	is	be	AUX
ejpam-4112	172	7	a	a	DET
ejpam-4112	172	8	dominated	dominate	VERB
ejpam-4112	172	9	superclique	superclique	NOUN
ejpam-4112	172	10	of	of	ADP
ejpam-4112	172	11	gi	gi	NOUN
ejpam-4112	172	12	and	and	CCONJ
ejpam-4112	172	13	c∗	c∗	PROPN
ejpam-4112	173	1	i	i	NOUN
ejpam-4112	173	2	=	=	NOUN
ejpam-4112	173	3	∅	∅	NOUN
ejpam-4112	173	4	or	or	CCONJ
ejpam-4112	173	5	c∗	c∗	NOUN
ejpam-4112	173	6	i	i	PRON
ejpam-4112	173	7	is	be	AUX
ejpam-4112	173	8	a	a	DET
ejpam-4112	173	9	nonsingleton	nonsingleton	NOUN
ejpam-4112	173	10	superclique	superclique	NOUN
ejpam-4112	173	11	of	of	ADP
ejpam-4112	173	12	g.	g.	PROPN
ejpam-4112	173	13	proof	proof	NOUN
ejpam-4112	173	14	:	:	PUNCT
ejpam-4112	173	15	let	let	VERB
ejpam-4112	173	16	s	s	PRON
ejpam-4112	173	17	be	be	AUX
ejpam-4112	173	18	a	a	DET
ejpam-4112	173	19	restrained	restrained	ADJ
ejpam-4112	173	20	strong	strong	ADJ
ejpam-4112	173	21	resolving	resolve	VERB
ejpam-4112	173	22	dominating	dominating	NOUN
ejpam-4112	173	23	set	set	NOUN
ejpam-4112	173	24	of	of	ADP
ejpam-4112	173	25	k1	k1	PROPN
ejpam-4112	173	26	+	+	PROPN
ejpam-4112	173	27	g.	g.	PROPN
ejpam-4112	173	28	then	then	ADV
ejpam-4112	173	29	by	by	ADP
ejpam-4112	173	30	theorem	theorem	NOUN
ejpam-4112	173	31	3	3	NUM
ejpam-4112	173	32	s	s	NOUN
ejpam-4112	173	33	=	=	X
ejpam-4112	173	34	v	v	X
ejpam-4112	173	35	(	(	PUNCT
ejpam-4112	173	36	g	g	NOUN
ejpam-4112	173	37	)	)	PUNCT
ejpam-4112	173	38	or	or	CCONJ
ejpam-4112	173	39	s	s	X
ejpam-4112	173	40	=	=	SYM
ejpam-4112	173	41	v	v	PROPN
ejpam-4112	173	42	(	(	PUNCT
ejpam-4112	173	43	g	g	NOUN
ejpam-4112	173	44	)	)	PUNCT
ejpam-4112	173	45	\	\	PROPN
ejpam-4112	173	46	ci	ci	NOUN
ejpam-4112	173	47	or	or	CCONJ
ejpam-4112	173	48	s	s	NOUN
ejpam-4112	173	49	=	=	X
ejpam-4112	173	50	v	v	PROPN
ejpam-4112	173	51	(	(	PUNCT
ejpam-4112	173	52	k1	k1	NOUN
ejpam-4112	173	53	+	+	CCONJ
ejpam-4112	173	54	g	g	NOUN
ejpam-4112	173	55	)	)	PUNCT
ejpam-4112	173	56	\	\	PROPN
ejpam-4112	173	57	c∗	c∗	PROPN
ejpam-4112	173	58	i	i	PRON
ejpam-4112	173	59	where	where	SCONJ
ejpam-4112	173	60	ci	ci	PROPN
ejpam-4112	173	61	is	be	AUX
ejpam-4112	173	62	a	a	DET
ejpam-4112	173	63	dominated	dominate	VERB
ejpam-4112	173	64	superclique	superclique	NOUN
ejpam-4112	173	65	of	of	ADP
ejpam-4112	173	66	gi	gi	NOUN
ejpam-4112	173	67	and	and	CCONJ
ejpam-4112	173	68	c∗	c∗	PROPN
ejpam-4112	174	1	i	i	NOUN
ejpam-4112	174	2	=	=	NOUN
ejpam-4112	174	3	∅	∅	NOUN
ejpam-4112	174	4	or	or	CCONJ
ejpam-4112	174	5	c∗	c∗	NOUN
ejpam-4112	174	6	i	i	PRON
ejpam-4112	174	7	is	be	AUX
ejpam-4112	174	8	a	a	DET
ejpam-4112	174	9	nonsingleton	nonsingleton	NOUN
ejpam-4112	174	10	superclique	superclique	NOUN
ejpam-4112	174	11	in	in	ADP
ejpam-4112	174	12	gi	gi	NOUN
ejpam-4112	174	13	.	.	PUNCT
ejpam-4112	175	1	since	since	SCONJ
ejpam-4112	175	2	s	s	NOUN
ejpam-4112	175	3	is	be	AUX
ejpam-4112	175	4	restrained	restrain	VERB
ejpam-4112	175	5	dominating	dominating	NOUN
ejpam-4112	175	6	,	,	PUNCT
ejpam-4112	175	7	s	s	PART
ejpam-4112	175	8	=	=	SYM
ejpam-4112	175	9	v	v	PROPN
ejpam-4112	175	10	(	(	PUNCT
ejpam-4112	175	11	k1	k1	NOUN
ejpam-4112	175	12	+	+	CCONJ
ejpam-4112	175	13	g	g	NOUN
ejpam-4112	175	14	)	)	PUNCT
ejpam-4112	175	15	or	or	CCONJ
ejpam-4112	175	16	v	v	NOUN
ejpam-4112	175	17	(	(	PUNCT
ejpam-4112	175	18	k1	k1	NOUN
ejpam-4112	175	19	+	+	CCONJ
ejpam-4112	175	20	g	g	NOUN
ejpam-4112	175	21	)	)	PUNCT
ejpam-4112	175	22	\	\	PUNCT
ejpam-4112	176	1	s	s	PART
ejpam-4112	176	2	has	have	VERB
ejpam-4112	176	3	no	no	DET
ejpam-4112	176	4	isolated	isolated	ADJ
ejpam-4112	176	5	vertex	vertex	NOUN
ejpam-4112	176	6	.	.	PUNCT
ejpam-4112	177	1	hence	hence	ADV
ejpam-4112	177	2	,	,	PUNCT
ejpam-4112	177	3	s	s	VERB
ejpam-4112	177	4	̸=	̸=	PROPN
ejpam-4112	177	5	v	v	NOUN
ejpam-4112	177	6	(	(	PUNCT
ejpam-4112	177	7	g	g	NOUN
ejpam-4112	177	8	)	)	PUNCT
ejpam-4112	177	9	and	and	CCONJ
ejpam-4112	177	10	c∗	c∗	PROPN
ejpam-4112	177	11	i	i	NOUN
ejpam-4112	177	12	=	=	NOUN
ejpam-4112	177	13	∅	∅	NOUN
ejpam-4112	177	14	or	or	CCONJ
ejpam-4112	177	15	c∗	c∗	NOUN
ejpam-4112	177	16	i	i	PRON
ejpam-4112	177	17	is	be	AUX
ejpam-4112	177	18	nonsingleton	nonsingleton	ADJ
ejpam-4112	177	19	.	.	PUNCT
ejpam-4112	178	1	therefore	therefore	ADV
ejpam-4112	178	2	,	,	PUNCT
ejpam-4112	178	3	s	s	VERB
ejpam-4112	178	4	=	=	SYM
ejpam-4112	178	5	v	v	NOUN
ejpam-4112	178	6	(	(	PUNCT
ejpam-4112	178	7	g)\c1	g)\c1	NOUN
ejpam-4112	178	8	or	or	CCONJ
ejpam-4112	178	9	s	s	NOUN
ejpam-4112	178	10	=	=	SYM
ejpam-4112	178	11	v	v	PROPN
ejpam-4112	178	12	(	(	PUNCT
ejpam-4112	178	13	k1	k1	NOUN
ejpam-4112	178	14	+	+	PROPN
ejpam-4112	178	15	g	g	NOUN
ejpam-4112	178	16	)	)	PUNCT
ejpam-4112	178	17	\c∗	\c∗	PROPN
ejpam-4112	179	1	i	i	PRON
ejpam-4112	179	2	where	where	SCONJ
ejpam-4112	179	3	ci	ci	PROPN
ejpam-4112	179	4	is	be	AUX
ejpam-4112	179	5	a	a	DET
ejpam-4112	179	6	dominated	dominate	VERB
ejpam-4112	179	7	superclique	superclique	NOUN
ejpam-4112	179	8	in	in	ADP
ejpam-4112	179	9	gi	gi	NOUN
ejpam-4112	179	10	and	and	CCONJ
ejpam-4112	179	11	c∗	c∗	PROPN
ejpam-4112	179	12	i	i	PRON
ejpam-4112	179	13	is	be	AUX
ejpam-4112	179	14	a	a	DET
ejpam-4112	179	15	nonsingleton	nonsingleton	NOUN
ejpam-4112	179	16	superclique	superclique	NOUN
ejpam-4112	179	17	in	in	ADP
ejpam-4112	179	18	gi	gi	NOUN
ejpam-4112	179	19	.	.	PUNCT
ejpam-4112	180	1	the	the	DET
ejpam-4112	180	2	converse	converse	NOUN
ejpam-4112	180	3	follows	follow	VERB
ejpam-4112	180	4	immediately	immediately	ADV
ejpam-4112	180	5	from	from	ADP
ejpam-4112	180	6	theorem	theorem	ADJ
ejpam-4112	180	7	3	3	NUM
ejpam-4112	180	8	,	,	PUNCT
ejpam-4112	180	9	definitions	definition	NOUN
ejpam-4112	180	10	of	of	ADP
ejpam-4112	180	11	dominated	dominate	VERB
ejpam-4112	180	12	superclique	superclique	NOUN
ejpam-4112	180	13	and	and	CCONJ
ejpam-4112	180	14	restrained	restrained	ADJ
ejpam-4112	180	15	dominating	dominating	NOUN
ejpam-4112	180	16	set	set	NOUN
ejpam-4112	180	17	of	of	ADP
ejpam-4112	180	18	a	a	DET
ejpam-4112	180	19	graph	graph	NOUN
ejpam-4112	180	20	.	.	PUNCT
ejpam-4112	181	1	corollary	corollary	ADJ
ejpam-4112	181	2	4	4	NUM
ejpam-4112	181	3	.	.	PUNCT
ejpam-4112	182	1	let	let	VERB
ejpam-4112	182	2	gi	gi	PART
ejpam-4112	182	3	be	be	AUX
ejpam-4112	182	4	connected	connect	VERB
ejpam-4112	182	5	graphs	graph	NOUN
ejpam-4112	182	6	of	of	ADP
ejpam-4112	182	7	order	order	NOUN
ejpam-4112	182	8	ni	ni	PROPN
ejpam-4112	182	9	and	and	CCONJ
ejpam-4112	182	10	g	g	PROPN
ejpam-4112	182	11	be	be	VERB
ejpam-4112	182	12	a	a	DET
ejpam-4112	182	13	disconnected	disconnected	ADJ
ejpam-4112	182	14	graph	graph	NOUN
ejpam-4112	182	15	whose	whose	DET
ejpam-4112	182	16	components	component	NOUN
ejpam-4112	182	17	are	be	AUX
ejpam-4112	182	18	gi	gi	ADJ
ejpam-4112	182	19	for	for	ADP
ejpam-4112	182	20	i	i	PROPN
ejpam-4112	182	21	=	=	NOUN
ejpam-4112	182	22	1	1	NUM
ejpam-4112	182	23	,	,	PUNCT
ejpam-4112	182	24	2	2	NUM
ejpam-4112	182	25	,	,	PUNCT
ejpam-4112	182	26	.	.	PUNCT
ejpam-4112	182	27	.	.	PUNCT
ejpam-4112	183	1	.	.	PUNCT
ejpam-4112	184	1	,	,	PUNCT
ejpam-4112	184	2	m.	m.	NOUN
ejpam-4112	184	3	then	then	ADV
ejpam-4112	184	4	,	,	PUNCT
ejpam-4112	184	5	γrsr(k1	γrsr(k1	ADP
ejpam-4112	184	6	+	+	CCONJ
ejpam-4112	184	7	g	g	NOUN
ejpam-4112	184	8	)	)	PUNCT
ejpam-4112	185	1	=	=	PUNCT
ejpam-4112	185	2	∑m	∑m	PROPN
ejpam-4112	185	3	i=1	i=1	PROPN
ejpam-4112	185	4	ni	ni	PROPN
ejpam-4112	186	1	−	−	PROPN
ejpam-4112	186	2	rg	rg	INTJ
ejpam-4112	186	3	where	where	SCONJ
ejpam-4112	186	4	rg	rg	PROPN
ejpam-4112	186	5	=	=	PUNCT
ejpam-4112	186	6	max	max	PROPN
ejpam-4112	186	7	{	{	PUNCT
ejpam-4112	186	8	max{ωds(gi)},max{ωs(gi	max{ωds(gi)},max{ωs(gi	PROPN
ejpam-4112	186	9	)	)	PUNCT
ejpam-4112	187	1	+	+	CCONJ
ejpam-4112	187	2	1	1	NUM
ejpam-4112	187	3	}	}	PUNCT
ejpam-4112	187	4	:	:	PUNCT
ejpam-4112	187	5	i	i	PRON
ejpam-4112	187	6	=	=	NOUN
ejpam-4112	187	7	1	1	NUM
ejpam-4112	187	8	,	,	PUNCT
ejpam-4112	187	9	2	2	NUM
ejpam-4112	187	10	,	,	PUNCT
ejpam-4112	187	11	.	.	PUNCT
ejpam-4112	187	12	.	.	PUNCT
ejpam-4112	187	13	.	.	PUNCT
ejpam-4112	188	1	,	,	PUNCT
ejpam-4112	188	2	m	m	VERB
ejpam-4112	188	3	}	}	PUNCT
ejpam-4112	188	4	.	.	PUNCT
ejpam-4112	189	1	in	in	ADP
ejpam-4112	189	2	the	the	DET
ejpam-4112	189	3	join	join	NOUN
ejpam-4112	189	4	of	of	ADP
ejpam-4112	189	5	two	two	NUM
ejpam-4112	189	6	graphs	graph	NOUN
ejpam-4112	189	7	g	g	NOUN
ejpam-4112	189	8	and	and	CCONJ
ejpam-4112	189	9	h	h	NOUN
ejpam-4112	189	10	,	,	PUNCT
ejpam-4112	189	11	the	the	DET
ejpam-4112	189	12	results	result	NOUN
ejpam-4112	189	13	theorem	theorem	VERB
ejpam-4112	189	14	7	7	NUM
ejpam-4112	189	15	and	and	CCONJ
ejpam-4112	189	16	theorem	theorem	VERB
ejpam-4112	189	17	8	8	NUM
ejpam-4112	189	18	have	have	AUX
ejpam-4112	189	19	already	already	ADV
ejpam-4112	189	20	considered	consider	VERB
ejpam-4112	189	21	the	the	DET
ejpam-4112	189	22	case	case	NOUN
ejpam-4112	189	23	when	when	SCONJ
ejpam-4112	189	24	g	g	PROPN
ejpam-4112	189	25	or	or	CCONJ
ejpam-4112	189	26	h	h	NOUN
ejpam-4112	189	27	is	be	AUX
ejpam-4112	189	28	trivial	trivial	ADJ
ejpam-4112	189	29	.	.	PUNCT
ejpam-4112	190	1	hence	hence	ADV
ejpam-4112	190	2	,	,	PUNCT
ejpam-4112	190	3	the	the	DET
ejpam-4112	190	4	next	next	ADJ
ejpam-4112	190	5	results	result	NOUN
ejpam-4112	190	6	,	,	PUNCT
ejpam-4112	190	7	considered	consider	VERB
ejpam-4112	190	8	the	the	DET
ejpam-4112	190	9	characterizations	characterization	NOUN
ejpam-4112	190	10	of	of	ADP
ejpam-4112	190	11	the	the	DET
ejpam-4112	190	12	restrained	restrained	ADJ
ejpam-4112	190	13	strong	strong	ADJ
ejpam-4112	190	14	resolving	resolve	VERB
ejpam-4112	190	15	dominating	dominating	NOUN
ejpam-4112	190	16	sets	set	NOUN
ejpam-4112	190	17	of	of	ADP
ejpam-4112	190	18	nontrivial	nontrivial	ADJ
ejpam-4112	190	19	connected	connect	VERB
ejpam-4112	190	20	graphs	graph	NOUN
ejpam-4112	190	21	g	g	PROPN
ejpam-4112	190	22	and	and	CCONJ
ejpam-4112	190	23	h.	h.	PROPN
ejpam-4112	190	24	theorem	theorem	VERB
ejpam-4112	190	25	10	10	NUM
ejpam-4112	190	26	.	.	PUNCT
ejpam-4112	191	1	letg	letg	NOUN
ejpam-4112	191	2	andh	andh	NOUN
ejpam-4112	191	3	be	be	VERB
ejpam-4112	191	4	nontrivial	nontrivial	ADJ
ejpam-4112	191	5	connected	connect	VERB
ejpam-4112	191	6	graphs	graph	NOUN
ejpam-4112	191	7	of	of	ADP
ejpam-4112	191	8	ordersm	ordersm	NOUN
ejpam-4112	191	9	and	and	CCONJ
ejpam-4112	191	10	n	n	CCONJ
ejpam-4112	191	11	,	,	PUNCT
ejpam-4112	191	12	respectively	respectively	ADV
ejpam-4112	191	13	.	.	PUNCT
ejpam-4112	192	1	a	a	DET
ejpam-4112	192	2	subset	subset	NOUN
ejpam-4112	192	3	s	s	X
ejpam-4112	192	4	of	of	ADP
ejpam-4112	192	5	v	v	NOUN
ejpam-4112	192	6	(	(	PUNCT
ejpam-4112	192	7	g	g	PROPN
ejpam-4112	192	8	+	+	NOUN
ejpam-4112	192	9	h	h	NOUN
ejpam-4112	192	10	)	)	PUNCT
ejpam-4112	192	11	is	be	AUX
ejpam-4112	192	12	a	a	DET
ejpam-4112	192	13	restrained	restrained	ADJ
ejpam-4112	192	14	strong	strong	ADJ
ejpam-4112	192	15	resolving	resolve	VERB
ejpam-4112	192	16	dominating	dominating	NOUN
ejpam-4112	192	17	set	set	NOUN
ejpam-4112	192	18	of	of	ADP
ejpam-4112	192	19	g	g	PROPN
ejpam-4112	192	20	+	+	PROPN
ejpam-4112	192	21	h	h	NOUN
ejpam-4112	192	22	if	if	SCONJ
ejpam-4112	193	1	and	and	CCONJ
ejpam-4112	193	2	only	only	ADV
ejpam-4112	193	3	if	if	SCONJ
ejpam-4112	193	4	at	at	ADV
ejpam-4112	193	5	least	least	ADJ
ejpam-4112	193	6	one	one	NUM
ejpam-4112	193	7	of	of	ADP
ejpam-4112	193	8	the	the	DET
ejpam-4112	193	9	following	follow	VERB
ejpam-4112	193	10	is	be	AUX
ejpam-4112	193	11	satisfied	satisfied	ADJ
ejpam-4112	193	12	:	:	PUNCT
ejpam-4112	193	13	(	(	PUNCT
ejpam-4112	193	14	i	i	NOUN
ejpam-4112	193	15	)	)	PUNCT
ejpam-4112	193	16	s	s	PART
ejpam-4112	193	17	=	=	SYM
ejpam-4112	193	18	v	v	PROPN
ejpam-4112	193	19	(	(	PUNCT
ejpam-4112	193	20	g+h	g+h	NOUN
ejpam-4112	193	21	)	)	PUNCT
ejpam-4112	193	22	\	\	PROPN
ejpam-4112	194	1	cg	cg	NOUN
ejpam-4112	194	2	where	where	SCONJ
ejpam-4112	194	3	cg	cg	NOUN
ejpam-4112	194	4	is	be	AUX
ejpam-4112	194	5	a	a	DET
ejpam-4112	194	6	nonsingleton	nonsingleton	NOUN
ejpam-4112	194	7	superclique	superclique	NOUN
ejpam-4112	194	8	of	of	ADP
ejpam-4112	194	9	g.	g.	PROPN
ejpam-4112	194	10	(	(	PUNCT
ejpam-4112	194	11	ii	ii	PROPN
ejpam-4112	194	12	)	)	PUNCT
ejpam-4112	194	13	s	s	PART
ejpam-4112	194	14	=	=	SYM
ejpam-4112	194	15	v	v	PROPN
ejpam-4112	194	16	(	(	PUNCT
ejpam-4112	194	17	g+h	g+h	NOUN
ejpam-4112	194	18	)	)	PUNCT
ejpam-4112	194	19	\	\	PROPN
ejpam-4112	195	1	ch	ch	NOUN
ejpam-4112	195	2	where	where	SCONJ
ejpam-4112	195	3	ch	ch	NOUN
ejpam-4112	195	4	is	be	AUX
ejpam-4112	195	5	a	a	DET
ejpam-4112	195	6	nonsingleton	nonsingleton	NOUN
ejpam-4112	195	7	superclique	superclique	NOUN
ejpam-4112	195	8	of	of	ADP
ejpam-4112	195	9	g.	g.	PROPN
ejpam-4112	195	10	h.	h.	PROPN
ejpam-4112	195	11	sumaoy	sumaoy	PROPN
ejpam-4112	195	12	,	,	PUNCT
ejpam-4112	195	13	h.	h.	PROPN
ejpam-4112	195	14	rara	rara	PROPN
ejpam-4112	195	15	/	/	SYM
ejpam-4112	195	16	eur	eur	PROPN
ejpam-4112	195	17	.	.	PUNCT
ejpam-4112	196	1	j.	j.	PROPN
ejpam-4112	196	2	pure	pure	PROPN
ejpam-4112	196	3	appl	appl	PROPN
ejpam-4112	196	4	.	.	PROPN
ejpam-4112	196	5	math	math	PROPN
ejpam-4112	196	6	,	,	PUNCT
ejpam-4112	196	7	14	14	NUM
ejpam-4112	196	8	(	(	PUNCT
ejpam-4112	196	9	4	4	NUM
ejpam-4112	196	10	)	)	PUNCT
ejpam-4112	196	11	(	(	PUNCT
ejpam-4112	196	12	2021	2021	NUM
ejpam-4112	196	13	)	)	PUNCT
ejpam-4112	196	14	,	,	PUNCT
ejpam-4112	196	15	1367	1367	NUM
ejpam-4112	196	16	-	-	SYM
ejpam-4112	196	17	1378	1378	NUM
ejpam-4112	196	18	1373	1373	NUM
ejpam-4112	196	19	(	(	PUNCT
ejpam-4112	196	20	iii	iii	NOUN
ejpam-4112	196	21	)	)	PUNCT
ejpam-4112	196	22	if	if	SCONJ
ejpam-4112	196	23	γ(g	γ(g	PROPN
ejpam-4112	196	24	)	)	PUNCT
ejpam-4112	196	25	=	=	SYM
ejpam-4112	196	26	1	1	NUM
ejpam-4112	196	27	and	and	CCONJ
ejpam-4112	196	28	γ(h	γ(h	NOUN
ejpam-4112	196	29	)	)	PUNCT
ejpam-4112	196	30	=	=	SYM
ejpam-4112	197	1	1	1	NUM
ejpam-4112	197	2	,	,	PUNCT
ejpam-4112	197	3	s	s	PART
ejpam-4112	197	4	=	=	PUNCT
ejpam-4112	198	1	[	[	X
ejpam-4112	198	2	v	v	X
ejpam-4112	198	3	(	(	PUNCT
ejpam-4112	198	4	g+h	g+h	NOUN
ejpam-4112	198	5	)	)	PUNCT
ejpam-4112	198	6	\	\	PUNCT
ejpam-4112	199	1	(	(	PUNCT
ejpam-4112	199	2	cg	cg	NOUN
ejpam-4112	199	3	∪	∪	PROPN
ejpam-4112	199	4	ch	ch	NOUN
ejpam-4112	199	5	)	)	PUNCT
ejpam-4112	199	6	]	]	PUNCT
ejpam-4112	199	7	∪	∪	X
ejpam-4112	199	8	{	{	PUNCT
ejpam-4112	199	9	z	z	PROPN
ejpam-4112	199	10	∈	∈	PROPN
ejpam-4112	199	11	cg	cg	NOUN
ejpam-4112	199	12	:	:	PUNCT
ejpam-4112	199	13	degg(z	degg(z	NOUN
ejpam-4112	199	14	)	)	PUNCT
ejpam-4112	200	1	=	=	SYM
ejpam-4112	200	2	m−	m−	PROPN
ejpam-4112	200	3	1	1	NUM
ejpam-4112	200	4	}	}	PUNCT
ejpam-4112	200	5	or	or	CCONJ
ejpam-4112	200	6	s	s	NOUN
ejpam-4112	200	7	=	=	PUNCT
ejpam-4112	201	1	[	[	X
ejpam-4112	201	2	v	v	X
ejpam-4112	201	3	(	(	PUNCT
ejpam-4112	201	4	g+h	g+h	NOUN
ejpam-4112	201	5	)	)	PUNCT
ejpam-4112	201	6	\	\	PUNCT
ejpam-4112	202	1	(	(	PUNCT
ejpam-4112	202	2	cg	cg	NOUN
ejpam-4112	202	3	∪	∪	PROPN
ejpam-4112	202	4	ch	ch	NOUN
ejpam-4112	202	5	)	)	PUNCT
ejpam-4112	202	6	]	]	PUNCT
ejpam-4112	203	1	∪	∪	X
ejpam-4112	203	2	{	{	PUNCT
ejpam-4112	203	3	w	w	PROPN
ejpam-4112	203	4	∈	∈	PROPN
ejpam-4112	203	5	ch	ch	NOUN
ejpam-4112	203	6	:	:	PUNCT
ejpam-4112	203	7	degh(w	degh(w	PROPN
ejpam-4112	203	8	)	)	PUNCT
ejpam-4112	203	9	=	=	PUNCT
ejpam-4112	203	10	n−	n−	NOUN
ejpam-4112	203	11	1	1	NUM
ejpam-4112	203	12	}	}	PUNCT
ejpam-4112	203	13	where	where	SCONJ
ejpam-4112	203	14	cg	cg	NOUN
ejpam-4112	203	15	and	and	CCONJ
ejpam-4112	203	16	ch	ch	NOUN
ejpam-4112	203	17	are	be	AUX
ejpam-4112	203	18	supercliques	superclique	NOUN
ejpam-4112	203	19	in	in	ADP
ejpam-4112	203	20	g	g	PROPN
ejpam-4112	203	21	and	and	CCONJ
ejpam-4112	203	22	h	h	NOUN
ejpam-4112	203	23	,	,	PUNCT
ejpam-4112	203	24	respectively	respectively	ADV
ejpam-4112	203	25	.	.	PUNCT
ejpam-4112	204	1	(	(	PUNCT
ejpam-4112	204	2	iv	iv	X
ejpam-4112	204	3	)	)	PUNCT
ejpam-4112	204	4	if	if	SCONJ
ejpam-4112	204	5	γ(g	γ(g	PROPN
ejpam-4112	204	6	)	)	PUNCT
ejpam-4112	204	7	̸=	̸=	PROPN
ejpam-4112	204	8	1	1	NUM
ejpam-4112	204	9	and	and	CCONJ
ejpam-4112	204	10	γ(h	γ(h	NOUN
ejpam-4112	204	11	)	)	PUNCT
ejpam-4112	204	12	̸=	̸=	PROPN
ejpam-4112	204	13	1	1	NUM
ejpam-4112	204	14	,	,	PUNCT
ejpam-4112	204	15	s	s	VERB
ejpam-4112	204	16	=	=	PUNCT
ejpam-4112	205	1	[	[	X
ejpam-4112	205	2	v	v	X
ejpam-4112	205	3	(	(	PUNCT
ejpam-4112	205	4	g+h	g+h	NOUN
ejpam-4112	205	5	)	)	PUNCT
ejpam-4112	205	6	\	\	PUNCT
ejpam-4112	206	1	(	(	PUNCT
ejpam-4112	206	2	cg	cg	NOUN
ejpam-4112	206	3	∪	∪	PROPN
ejpam-4112	206	4	ch	ch	NOUN
ejpam-4112	206	5	)	)	PUNCT
ejpam-4112	206	6	]	]	PUNCT
ejpam-4112	207	1	=	=	PUNCT
ejpam-4112	207	2	(	(	PUNCT
ejpam-4112	207	3	v	v	NOUN
ejpam-4112	207	4	(	(	PUNCT
ejpam-4112	207	5	g	g	NOUN
ejpam-4112	207	6	)	)	PUNCT
ejpam-4112	207	7	\	\	PROPN
ejpam-4112	207	8	cg	cg	NOUN
ejpam-4112	207	9	)	)	PUNCT
ejpam-4112	207	10	∪	∪	NOUN
ejpam-4112	207	11	(	(	PUNCT
ejpam-4112	207	12	v	v	NOUN
ejpam-4112	207	13	(	(	PUNCT
ejpam-4112	207	14	h	h	NOUN
ejpam-4112	207	15	)	)	PUNCT
ejpam-4112	207	16	\	\	PROPN
ejpam-4112	207	17	ch	ch	NOUN
ejpam-4112	207	18	)	)	PUNCT
ejpam-4112	207	19	where	where	SCONJ
ejpam-4112	207	20	cg	cg	NOUN
ejpam-4112	207	21	and	and	CCONJ
ejpam-4112	207	22	ch	ch	NOUN
ejpam-4112	207	23	are	be	AUX
ejpam-4112	207	24	supercliques	superclique	NOUN
ejpam-4112	207	25	in	in	ADP
ejpam-4112	207	26	g	g	PROPN
ejpam-4112	207	27	and	and	CCONJ
ejpam-4112	207	28	h	h	NOUN
ejpam-4112	207	29	,	,	PUNCT
ejpam-4112	207	30	respectively	respectively	ADV
ejpam-4112	207	31	.	.	PUNCT
ejpam-4112	208	1	proof	proof	NOUN
ejpam-4112	208	2	:	:	PUNCT
ejpam-4112	208	3	let	let	VERB
ejpam-4112	208	4	s	s	PRON
ejpam-4112	208	5	be	be	AUX
ejpam-4112	208	6	a	a	DET
ejpam-4112	208	7	restrained	restrained	ADJ
ejpam-4112	208	8	strong	strong	ADJ
ejpam-4112	208	9	resolving	resolve	VERB
ejpam-4112	208	10	dominating	dominating	NOUN
ejpam-4112	208	11	set	set	NOUN
ejpam-4112	208	12	of	of	ADP
ejpam-4112	208	13	g+h	g+h	PROPN
ejpam-4112	208	14	.	.	PUNCT
ejpam-4112	209	1	by	by	ADP
ejpam-4112	209	2	theorem	theorem	NOUN
ejpam-4112	209	3	5	5	NUM
ejpam-4112	209	4	(	(	PUNCT
ejpam-4112	209	5	a	a	NOUN
ejpam-4112	209	6	)	)	PUNCT
ejpam-4112	209	7	s	s	PART
ejpam-4112	209	8	=	=	SYM
ejpam-4112	209	9	v	v	PROPN
ejpam-4112	209	10	(	(	PUNCT
ejpam-4112	209	11	g+h	g+h	NOUN
ejpam-4112	209	12	)	)	PUNCT
ejpam-4112	209	13	\	\	PROPN
ejpam-4112	210	1	cg	cg	NOUN
ejpam-4112	210	2	where	where	SCONJ
ejpam-4112	210	3	cg	cg	NOUN
ejpam-4112	210	4	is	be	AUX
ejpam-4112	210	5	a	a	DET
ejpam-4112	210	6	superclique	superclique	NOUN
ejpam-4112	210	7	of	of	ADP
ejpam-4112	210	8	g.	g.	PROPN
ejpam-4112	210	9	(	(	PUNCT
ejpam-4112	210	10	b	b	X
ejpam-4112	210	11	)	)	PUNCT
ejpam-4112	210	12	s	s	PART
ejpam-4112	210	13	=	=	SYM
ejpam-4112	210	14	v	v	PROPN
ejpam-4112	210	15	(	(	PUNCT
ejpam-4112	210	16	g+h	g+h	NOUN
ejpam-4112	210	17	)	)	PUNCT
ejpam-4112	210	18	\	\	PROPN
ejpam-4112	211	1	ch	ch	NOUN
ejpam-4112	211	2	where	where	SCONJ
ejpam-4112	211	3	ch	ch	NOUN
ejpam-4112	211	4	is	be	AUX
ejpam-4112	211	5	a	a	DET
ejpam-4112	211	6	superclique	superclique	NOUN
ejpam-4112	211	7	of	of	ADP
ejpam-4112	211	8	g.	g.	PROPN
ejpam-4112	211	9	(	(	PUNCT
ejpam-4112	211	10	c	c	X
ejpam-4112	211	11	)	)	PUNCT
ejpam-4112	211	12	if	if	SCONJ
ejpam-4112	211	13	γ(g	γ(g	PROPN
ejpam-4112	211	14	)	)	PUNCT
ejpam-4112	211	15	=	=	SYM
ejpam-4112	211	16	1	1	NUM
ejpam-4112	211	17	and	and	CCONJ
ejpam-4112	211	18	γ(h	γ(h	NOUN
ejpam-4112	211	19	)	)	PUNCT
ejpam-4112	211	20	=	=	SYM
ejpam-4112	211	21	1	1	NUM
ejpam-4112	211	22	,	,	PUNCT
ejpam-4112	211	23	s	s	PART
ejpam-4112	211	24	=	=	PUNCT
ejpam-4112	212	1	[	[	X
ejpam-4112	212	2	v	v	X
ejpam-4112	212	3	(	(	PUNCT
ejpam-4112	212	4	g+h	g+h	NOUN
ejpam-4112	212	5	)	)	PUNCT
ejpam-4112	212	6	\	\	PUNCT
ejpam-4112	213	1	(	(	PUNCT
ejpam-4112	213	2	cg	cg	NOUN
ejpam-4112	213	3	∪	∪	PROPN
ejpam-4112	213	4	ch	ch	NOUN
ejpam-4112	213	5	)	)	PUNCT
ejpam-4112	213	6	]	]	PUNCT
ejpam-4112	213	7	∪	∪	X
ejpam-4112	213	8	{	{	PUNCT
ejpam-4112	213	9	z	z	PROPN
ejpam-4112	213	10	∈	∈	PROPN
ejpam-4112	213	11	cg	cg	NOUN
ejpam-4112	213	12	:	:	PUNCT
ejpam-4112	213	13	degg(z	degg(z	NOUN
ejpam-4112	213	14	)	)	PUNCT
ejpam-4112	214	1	=	=	SYM
ejpam-4112	214	2	m−	m−	PROPN
ejpam-4112	214	3	1	1	NUM
ejpam-4112	214	4	}	}	PUNCT
ejpam-4112	214	5	or	or	CCONJ
ejpam-4112	214	6	s	s	NOUN
ejpam-4112	214	7	=	=	PUNCT
ejpam-4112	215	1	[	[	X
ejpam-4112	215	2	v	v	X
ejpam-4112	215	3	(	(	PUNCT
ejpam-4112	215	4	g+h	g+h	NOUN
ejpam-4112	215	5	)	)	PUNCT
ejpam-4112	215	6	\	\	PUNCT
ejpam-4112	216	1	(	(	PUNCT
ejpam-4112	216	2	cg	cg	NOUN
ejpam-4112	216	3	∪	∪	PROPN
ejpam-4112	216	4	ch	ch	NOUN
ejpam-4112	216	5	)	)	PUNCT
ejpam-4112	216	6	]	]	PUNCT
ejpam-4112	217	1	∪	∪	X
ejpam-4112	217	2	{	{	PUNCT
ejpam-4112	217	3	w	w	PROPN
ejpam-4112	217	4	∈	∈	PROPN
ejpam-4112	217	5	ch	ch	NOUN
ejpam-4112	217	6	:	:	PUNCT
ejpam-4112	217	7	degh(w	degh(w	PROPN
ejpam-4112	217	8	)	)	PUNCT
ejpam-4112	217	9	=	=	PUNCT
ejpam-4112	217	10	n−	n−	NOUN
ejpam-4112	217	11	1	1	NUM
ejpam-4112	217	12	}	}	PUNCT
ejpam-4112	217	13	where	where	SCONJ
ejpam-4112	217	14	⟨cg⟩	⟨cg⟩	NUM
ejpam-4112	217	15	and	and	CCONJ
ejpam-4112	217	16	ch	ch	NOUN
ejpam-4112	217	17	are	be	AUX
ejpam-4112	217	18	supercliques	superclique	NOUN
ejpam-4112	217	19	in	in	ADP
ejpam-4112	217	20	g	g	PROPN
ejpam-4112	217	21	and	and	CCONJ
ejpam-4112	217	22	h	h	NOUN
ejpam-4112	217	23	,	,	PUNCT
ejpam-4112	217	24	respectively	respectively	ADV
ejpam-4112	217	25	.	.	PUNCT
ejpam-4112	218	1	(	(	PUNCT
ejpam-4112	218	2	d	d	X
ejpam-4112	218	3	)	)	PUNCT
ejpam-4112	218	4	if	if	SCONJ
ejpam-4112	218	5	γ(g	γ(g	NOUN
ejpam-4112	218	6	)	)	PUNCT
ejpam-4112	218	7	̸=	̸=	PROPN
ejpam-4112	218	8	1	1	NUM
ejpam-4112	218	9	and	and	CCONJ
ejpam-4112	218	10	γ(h	γ(h	NOUN
ejpam-4112	218	11	)	)	PUNCT
ejpam-4112	218	12	̸=	̸=	PROPN
ejpam-4112	218	13	1	1	NUM
ejpam-4112	218	14	,	,	PUNCT
ejpam-4112	218	15	s	s	VERB
ejpam-4112	218	16	=	=	PUNCT
ejpam-4112	219	1	[	[	X
ejpam-4112	219	2	v	v	X
ejpam-4112	219	3	(	(	PUNCT
ejpam-4112	219	4	g+h	g+h	NOUN
ejpam-4112	219	5	)	)	PUNCT
ejpam-4112	219	6	\	\	PUNCT
ejpam-4112	220	1	(	(	PUNCT
ejpam-4112	220	2	cg	cg	NOUN
ejpam-4112	220	3	∪	∪	PROPN
ejpam-4112	220	4	ch	ch	NOUN
ejpam-4112	220	5	)	)	PUNCT
ejpam-4112	220	6	]	]	PUNCT
ejpam-4112	221	1	=	=	PUNCT
ejpam-4112	221	2	(	(	PUNCT
ejpam-4112	221	3	v	v	NOUN
ejpam-4112	221	4	(	(	PUNCT
ejpam-4112	221	5	g	g	NOUN
ejpam-4112	221	6	)	)	PUNCT
ejpam-4112	221	7	\	\	PROPN
ejpam-4112	221	8	cg	cg	NOUN
ejpam-4112	221	9	)	)	PUNCT
ejpam-4112	221	10	∪	∪	NOUN
ejpam-4112	221	11	(	(	PUNCT
ejpam-4112	221	12	v	v	NOUN
ejpam-4112	221	13	(	(	PUNCT
ejpam-4112	221	14	h	h	NOUN
ejpam-4112	221	15	)	)	PUNCT
ejpam-4112	221	16	\	\	PROPN
ejpam-4112	221	17	ch	ch	NOUN
ejpam-4112	221	18	)	)	PUNCT
ejpam-4112	221	19	where	where	SCONJ
ejpam-4112	221	20	cg	cg	NOUN
ejpam-4112	221	21	and	and	CCONJ
ejpam-4112	221	22	ch	ch	NOUN
ejpam-4112	221	23	are	be	AUX
ejpam-4112	221	24	supercliques	superclique	NOUN
ejpam-4112	221	25	in	in	ADP
ejpam-4112	221	26	g	g	PROPN
ejpam-4112	221	27	and	and	CCONJ
ejpam-4112	221	28	h	h	NOUN
ejpam-4112	221	29	,	,	PUNCT
ejpam-4112	221	30	respectively	respectively	ADV
ejpam-4112	221	31	.	.	PUNCT
ejpam-4112	222	1	since	since	SCONJ
ejpam-4112	222	2	s	s	NOUN
ejpam-4112	222	3	is	be	AUX
ejpam-4112	222	4	a	a	DET
ejpam-4112	222	5	restrained	restrain	VERB
ejpam-4112	222	6	dominating	dominating	NOUN
ejpam-4112	222	7	set	set	NOUN
ejpam-4112	222	8	of	of	ADP
ejpam-4112	222	9	g+h	g+h	PROPN
ejpam-4112	222	10	,	,	PUNCT
ejpam-4112	222	11	(	(	PUNCT
ejpam-4112	222	12	i	i	NOUN
ejpam-4112	222	13	)	)	PUNCT
ejpam-4112	222	14	,	,	PUNCT
ejpam-4112	222	15	(	(	PUNCT
ejpam-4112	222	16	ii	ii	NOUN
ejpam-4112	222	17	)	)	PUNCT
ejpam-4112	222	18	,	,	PUNCT
ejpam-4112	222	19	(	(	PUNCT
ejpam-4112	222	20	iii	iii	NOUN
ejpam-4112	222	21	)	)	PUNCT
ejpam-4112	222	22	,	,	PUNCT
ejpam-4112	222	23	(	(	PUNCT
ejpam-4112	222	24	iv	iv	X
ejpam-4112	222	25	)	)	PUNCT
ejpam-4112	222	26	hold	hold	NOUN
ejpam-4112	222	27	.	.	PUNCT
ejpam-4112	223	1	the	the	DET
ejpam-4112	223	2	converse	converse	NOUN
ejpam-4112	223	3	immediately	immediately	ADV
ejpam-4112	223	4	follows	follow	VERB
ejpam-4112	223	5	from	from	ADP
ejpam-4112	223	6	theorem	theorem	ADJ
ejpam-4112	223	7	5	5	NUM
ejpam-4112	223	8	and	and	CCONJ
ejpam-4112	223	9	from	from	ADP
ejpam-4112	223	10	definition	definition	NOUN
ejpam-4112	223	11	of	of	ADP
ejpam-4112	223	12	restrained	restrained	ADJ
ejpam-4112	223	13	dominating	dominating	NOUN
ejpam-4112	223	14	set	set	NOUN
ejpam-4112	223	15	of	of	ADP
ejpam-4112	223	16	a	a	DET
ejpam-4112	223	17	graph	graph	NOUN
ejpam-4112	223	18	.	.	PUNCT
ejpam-4112	224	1	corollary	corollary	ADJ
ejpam-4112	224	2	5	5	NUM
ejpam-4112	224	3	.	.	PUNCT
ejpam-4112	225	1	let	let	VERB
ejpam-4112	225	2	g	g	NOUN
ejpam-4112	225	3	andh	andh	NOUN
ejpam-4112	225	4	be	be	AUX
ejpam-4112	225	5	nontrivial	nontrivial	ADJ
ejpam-4112	225	6	connected	connect	VERB
ejpam-4112	225	7	graphs	graph	NOUN
ejpam-4112	225	8	of	of	ADP
ejpam-4112	225	9	ordersm	ordersm	NOUN
ejpam-4112	225	10	and	and	CCONJ
ejpam-4112	225	11	n	n	CCONJ
ejpam-4112	225	12	,	,	PUNCT
ejpam-4112	225	13	respectively	respectively	ADV
ejpam-4112	225	14	.	.	PUNCT
ejpam-4112	226	1	then	then	ADV
ejpam-4112	226	2	sdim(g+h	sdim(g+h	NOUN
ejpam-4112	226	3	)	)	PUNCT
ejpam-4112	226	4	=	=	PUNCT
ejpam-4112	227	1			PROPN
ejpam-4112	227	2	(	(	PUNCT
ejpam-4112	227	3	m−	m−	PROPN
ejpam-4112	227	4	ωs(g	ωs(g	PUNCT
ejpam-4112	227	5	)	)	PUNCT
ejpam-4112	227	6	)	)	PUNCT
ejpam-4112	228	1	+	+	CCONJ
ejpam-4112	228	2	(	(	PUNCT
ejpam-4112	228	3	n−	n−	NOUN
ejpam-4112	228	4	ωs(h	ωs(h	NUM
ejpam-4112	228	5	)	)	PUNCT
ejpam-4112	228	6	)	)	PUNCT
ejpam-4112	229	1	+	+	CCONJ
ejpam-4112	229	2	1	1	NUM
ejpam-4112	229	3	,	,	PUNCT
ejpam-4112	229	4	if	if	SCONJ
ejpam-4112	229	5	γ(g	γ(g	PROPN
ejpam-4112	229	6	)	)	PUNCT
ejpam-4112	229	7	=	=	SYM
ejpam-4112	229	8	1	1	NUM
ejpam-4112	229	9	or	or	CCONJ
ejpam-4112	229	10	γ(h	γ(h	NOUN
ejpam-4112	229	11	)	)	PUNCT
ejpam-4112	229	12	=	=	SYM
ejpam-4112	229	13	1	1	X
ejpam-4112	229	14	(	(	PUNCT
ejpam-4112	229	15	m−	m−	PROPN
ejpam-4112	229	16	ωs(g	ωs(g	NUM
ejpam-4112	229	17	)	)	PUNCT
ejpam-4112	229	18	)	)	PUNCT
ejpam-4112	230	1	+	+	CCONJ
ejpam-4112	230	2	(	(	PUNCT
ejpam-4112	230	3	n−	n−	NOUN
ejpam-4112	230	4	ωs(h	ωs(h	NUM
ejpam-4112	230	5	)	)	PUNCT
ejpam-4112	230	6	)	)	PUNCT
ejpam-4112	230	7	,	,	PUNCT
ejpam-4112	230	8	if	if	SCONJ
ejpam-4112	230	9	γ(g	γ(g	NOUN
ejpam-4112	230	10	)	)	PUNCT
ejpam-4112	230	11	̸=	̸=	PROPN
ejpam-4112	230	12	1	1	NUM
ejpam-4112	230	13	and	and	CCONJ
ejpam-4112	230	14	γ(h	γ(h	NOUN
ejpam-4112	230	15	)	)	PUNCT
ejpam-4112	230	16	̸=	̸=	PROPN
ejpam-4112	230	17	1	1	NUM
ejpam-4112	230	18	.	.	NOUN
ejpam-4112	230	19	4	4	NUM
ejpam-4112	230	20	.	.	X
ejpam-4112	230	21	restrained	restrain	VERB
ejpam-4112	230	22	strong	strong	ADJ
ejpam-4112	230	23	resolving	resolving	NOUN
ejpam-4112	230	24	domination	domination	NOUN
ejpam-4112	230	25	in	in	ADP
ejpam-4112	230	26	the	the	DET
ejpam-4112	230	27	corona	corona	NOUN
ejpam-4112	230	28	of	of	ADP
ejpam-4112	230	29	graphs	graph	NOUN
ejpam-4112	230	30	this	this	DET
ejpam-4112	230	31	section	section	NOUN
ejpam-4112	230	32	gives	give	VERB
ejpam-4112	230	33	characterization	characterization	NOUN
ejpam-4112	230	34	of	of	ADP
ejpam-4112	230	35	the	the	DET
ejpam-4112	230	36	restrained	restrained	ADJ
ejpam-4112	230	37	strong	strong	ADJ
ejpam-4112	230	38	resolving	resolve	VERB
ejpam-4112	230	39	dominating	dominating	NOUN
ejpam-4112	230	40	sets	set	NOUN
ejpam-4112	230	41	in	in	ADP
ejpam-4112	230	42	the	the	DET
ejpam-4112	230	43	corona	corona	NOUN
ejpam-4112	230	44	of	of	ADP
ejpam-4112	230	45	graphs	graph	NOUN
ejpam-4112	230	46	as	as	ADV
ejpam-4112	230	47	well	well	ADV
ejpam-4112	230	48	as	as	ADP
ejpam-4112	230	49	its	its	PRON
ejpam-4112	230	50	restrained	restrained	ADJ
ejpam-4112	230	51	strong	strong	ADJ
ejpam-4112	230	52	resolving	resolve	VERB
ejpam-4112	230	53	domination	domination	NOUN
ejpam-4112	230	54	number	number	NOUN
ejpam-4112	230	55	.	.	PUNCT
ejpam-4112	231	1	theorem	theorem	NOUN
ejpam-4112	231	2	11	11	NUM
ejpam-4112	231	3	.	.	PUNCT
ejpam-4112	232	1	let	let	VERB
ejpam-4112	232	2	g	g	PRON
ejpam-4112	232	3	be	be	AUX
ejpam-4112	232	4	a	a	DET
ejpam-4112	232	5	nontrivial	nontrivial	ADJ
ejpam-4112	232	6	connected	connect	VERB
ejpam-4112	232	7	graph	graph	NOUN
ejpam-4112	232	8	and	and	CCONJ
ejpam-4112	232	9	h	h	NOUN
ejpam-4112	232	10	a	a	DET
ejpam-4112	232	11	connected	connected	ADJ
ejpam-4112	232	12	graph	graph	NOUN
ejpam-4112	232	13	.	.	PUNCT
ejpam-4112	233	1	a	a	DET
ejpam-4112	233	2	proper	proper	ADJ
ejpam-4112	233	3	subset	subset	NOUN
ejpam-4112	233	4	s	s	VERB
ejpam-4112	233	5	⊆	⊆	NUM
ejpam-4112	233	6	v	v	NOUN
ejpam-4112	233	7	(	(	PUNCT
ejpam-4112	233	8	g	g	PROPN
ejpam-4112	233	9	◦	◦	NOUN
ejpam-4112	233	10	h	h	NOUN
ejpam-4112	233	11	)	)	PUNCT
ejpam-4112	233	12	of	of	ADP
ejpam-4112	233	13	a	a	DET
ejpam-4112	233	14	restrained	restrained	ADJ
ejpam-4112	233	15	strong	strong	ADJ
ejpam-4112	233	16	resolving	resolve	VERB
ejpam-4112	233	17	dominating	dominating	NOUN
ejpam-4112	233	18	set	set	NOUN
ejpam-4112	233	19	of	of	ADP
ejpam-4112	233	20	g	g	PROPN
ejpam-4112	233	21	◦	◦	NOUN
ejpam-4112	233	22	h	h	NOUN
ejpam-4112	233	23	if	if	SCONJ
ejpam-4112	233	24	and	and	CCONJ
ejpam-4112	233	25	only	only	ADV
ejpam-4112	233	26	if	if	SCONJ
ejpam-4112	233	27	one	one	NUM
ejpam-4112	233	28	of	of	ADP
ejpam-4112	233	29	the	the	DET
ejpam-4112	233	30	following	follow	VERB
ejpam-4112	233	31	holds	hold	VERB
ejpam-4112	233	32	:	:	PUNCT
ejpam-4112	233	33	(	(	PUNCT
ejpam-4112	233	34	i	i	NOUN
ejpam-4112	233	35	)	)	PUNCT
ejpam-4112	233	36	s	s	PART
ejpam-4112	233	37	=	=	PUNCT
ejpam-4112	233	38	a	a	DET
ejpam-4112	233	39	∪	∪	X
ejpam-4112	233	40	(	(	PUNCT
ejpam-4112	233	41	⋃	⋃	NOUN
ejpam-4112	233	42	u∈v	u∈v	NOUN
ejpam-4112	233	43	(	(	PUNCT
ejpam-4112	233	44	g	g	NOUN
ejpam-4112	233	45	)	)	PUNCT
ejpam-4112	233	46	v	v	NOUN
ejpam-4112	233	47	(	(	PUNCT
ejpam-4112	233	48	hu	hu	PROPN
ejpam-4112	233	49	)	)	PUNCT
ejpam-4112	233	50	)	)	PUNCT
ejpam-4112	233	51	where	where	SCONJ
ejpam-4112	233	52	a	a	DET
ejpam-4112	233	53	⊆	⊆	NUM
ejpam-4112	233	54	v	v	NOUN
ejpam-4112	233	55	(	(	PUNCT
ejpam-4112	233	56	g	g	NOUN
ejpam-4112	233	57	)	)	PUNCT
ejpam-4112	233	58	and	and	CCONJ
ejpam-4112	233	59	v	v	X
ejpam-4112	233	60	(	(	PUNCT
ejpam-4112	233	61	g	g	NOUN
ejpam-4112	233	62	)	)	PUNCT
ejpam-4112	233	63	\a	\a	VERB
ejpam-4112	233	64	has	have	VERB
ejpam-4112	233	65	no	no	DET
ejpam-4112	233	66	isolated	isolated	ADJ
ejpam-4112	233	67	vertex	vertex	NOUN
ejpam-4112	233	68	.	.	PUNCT
ejpam-4112	234	1	h.	h.	PROPN
ejpam-4112	234	2	sumaoy	sumaoy	PROPN
ejpam-4112	234	3	,	,	PUNCT
ejpam-4112	234	4	h.	h.	PROPN
ejpam-4112	234	5	rara	rara	PROPN
ejpam-4112	234	6	/	/	SYM
ejpam-4112	234	7	eur	eur	PROPN
ejpam-4112	234	8	.	.	PUNCT
ejpam-4112	235	1	j.	j.	PROPN
ejpam-4112	235	2	pure	pure	PROPN
ejpam-4112	235	3	appl	appl	PROPN
ejpam-4112	235	4	.	.	PROPN
ejpam-4112	235	5	math	math	PROPN
ejpam-4112	235	6	,	,	PUNCT
ejpam-4112	235	7	14	14	NUM
ejpam-4112	235	8	(	(	PUNCT
ejpam-4112	235	9	4	4	NUM
ejpam-4112	235	10	)	)	PUNCT
ejpam-4112	235	11	(	(	PUNCT
ejpam-4112	235	12	2021	2021	NUM
ejpam-4112	235	13	)	)	PUNCT
ejpam-4112	235	14	,	,	PUNCT
ejpam-4112	235	15	1367	1367	NUM
ejpam-4112	235	16	-	-	SYM
ejpam-4112	235	17	1378	1378	NUM
ejpam-4112	235	18	1374	1374	NUM
ejpam-4112	235	19	(	(	PUNCT
ejpam-4112	235	20	ii	ii	NOUN
ejpam-4112	235	21	)	)	PUNCT
ejpam-4112	235	22	s	s	PART
ejpam-4112	235	23	=	=	PUNCT
ejpam-4112	235	24	a∪	a∪	PROPN
ejpam-4112	235	25	(	(	PUNCT
ejpam-4112	235	26	⋃	⋃	NOUN
ejpam-4112	235	27	u∈v	u∈v	NOUN
ejpam-4112	235	28	(	(	PUNCT
ejpam-4112	235	29	g)\{v	g)\{v	PROPN
ejpam-4112	235	30	}	}	PUNCT
ejpam-4112	235	31	v	v	PROPN
ejpam-4112	235	32	(	(	PUNCT
ejpam-4112	235	33	hu	hu	PROPN
ejpam-4112	235	34	)	)	PUNCT
ejpam-4112	235	35	)	)	PUNCT
ejpam-4112	236	1	∪bv	∪bv	NOUN
ejpam-4112	236	2	for	for	ADP
ejpam-4112	236	3	a	a	DET
ejpam-4112	236	4	unique	unique	ADJ
ejpam-4112	236	5	vertex	vertex	NOUN
ejpam-4112	236	6	v	v	NOUN
ejpam-4112	236	7	in	in	ADP
ejpam-4112	236	8	g	g	PROPN
ejpam-4112	236	9	,	,	PUNCT
ejpam-4112	236	10	where	where	SCONJ
ejpam-4112	236	11	a	a	DET
ejpam-4112	236	12	=	=	SYM
ejpam-4112	236	13	v	v	X
ejpam-4112	236	14	(	(	PUNCT
ejpam-4112	236	15	g	g	NOUN
ejpam-4112	236	16	)	)	PUNCT
ejpam-4112	236	17	\	\	NOUN
ejpam-4112	236	18	{	{	PUNCT
ejpam-4112	236	19	v	v	NOUN
ejpam-4112	236	20	}	}	PUNCT
ejpam-4112	236	21	or	or	CCONJ
ejpam-4112	236	22	v	v	NOUN
ejpam-4112	236	23	(	(	PUNCT
ejpam-4112	236	24	g	g	NOUN
ejpam-4112	236	25	)	)	PUNCT
ejpam-4112	236	26	\	\	PUNCT
ejpam-4112	237	1	(	(	PUNCT
ejpam-4112	237	2	a	a	DET
ejpam-4112	237	3	∪	∪	ADJ
ejpam-4112	237	4	{	{	PUNCT
ejpam-4112	237	5	v	v	NOUN
ejpam-4112	237	6	}	}	PUNCT
ejpam-4112	237	7	)	)	PUNCT
ejpam-4112	237	8	has	have	VERB
ejpam-4112	237	9	no	no	DET
ejpam-4112	237	10	isolated	isolated	ADJ
ejpam-4112	237	11	vertex	vertex	NOUN
ejpam-4112	237	12	and	and	CCONJ
ejpam-4112	237	13	bv	bv	PROPN
ejpam-4112	237	14	is	be	AUX
ejpam-4112	237	15	a	a	DET
ejpam-4112	237	16	strong	strong	ADJ
ejpam-4112	237	17	resolving	resolving	NOUN
ejpam-4112	237	18	dominating	dominating	NOUN
ejpam-4112	237	19	set	set	NOUN
ejpam-4112	237	20	of	of	ADP
ejpam-4112	237	21	hv	hv	PROPN
ejpam-4112	237	22	+	+	X
ejpam-4112	237	23	⟨v⟩	⟨v⟩	PROPN
ejpam-4112	238	1	if	if	SCONJ
ejpam-4112	238	2	v	v	NUM
ejpam-4112	238	3	∈	∈	PROPN
ejpam-4112	238	4	s	s	NOUN
ejpam-4112	238	5	and	and	CCONJ
ejpam-4112	238	6	bv	bv	PROPN
ejpam-4112	238	7	is	be	AUX
ejpam-4112	238	8	a	a	DET
ejpam-4112	238	9	strong	strong	ADJ
ejpam-4112	238	10	resolving	resolving	NOUN
ejpam-4112	238	11	set	set	VERB
ejpam-4112	238	12	where	where	SCONJ
ejpam-4112	238	13	v	v	NOUN
ejpam-4112	238	14	(	(	PUNCT
ejpam-4112	238	15	hv	hv	PROPN
ejpam-4112	238	16	)	)	PUNCT
ejpam-4112	238	17	\	\	PROPN
ejpam-4112	238	18	bv	bv	PROPN
ejpam-4112	238	19	has	have	VERB
ejpam-4112	238	20	no	no	DET
ejpam-4112	238	21	isolated	isolated	ADJ
ejpam-4112	238	22	vertex	vertex	NOUN
ejpam-4112	238	23	if	if	SCONJ
ejpam-4112	238	24	v	v	NOUN
ejpam-4112	238	25	∈	∈	PROPN
ejpam-4112	238	26	s.	s.	PROPN
ejpam-4112	238	27	proof	proof	NOUN
ejpam-4112	238	28	:	:	PUNCT
ejpam-4112	238	29	suppose	suppose	VERB
ejpam-4112	238	30	s	s	NOUN
ejpam-4112	238	31	is	be	AUX
ejpam-4112	238	32	a	a	DET
ejpam-4112	238	33	restrained	restrained	ADJ
ejpam-4112	238	34	resolving	resolving	NOUN
ejpam-4112	238	35	dominating	dominating	NOUN
ejpam-4112	238	36	set	set	NOUN
ejpam-4112	238	37	of	of	ADP
ejpam-4112	238	38	g	g	PROPN
ejpam-4112	238	39	◦	◦	NOUN
ejpam-4112	238	40	h.	h.	NOUN
ejpam-4112	239	1	then	then	ADV
ejpam-4112	239	2	s	s	VERB
ejpam-4112	239	3	is	be	AUX
ejpam-4112	239	4	a	a	DET
ejpam-4112	239	5	strong	strong	ADJ
ejpam-4112	239	6	resolving	resolving	NOUN
ejpam-4112	239	7	dominating	dominating	NOUN
ejpam-4112	239	8	and	and	CCONJ
ejpam-4112	239	9	by	by	ADP
ejpam-4112	239	10	theorem	theorem	VERB
ejpam-4112	239	11	4	4	NUM
ejpam-4112	239	12	one	one	NUM
ejpam-4112	239	13	of	of	ADP
ejpam-4112	239	14	the	the	DET
ejpam-4112	239	15	following	following	NOUN
ejpam-4112	239	16	holds	hold	VERB
ejpam-4112	239	17	:	:	PUNCT
ejpam-4112	239	18	(	(	PUNCT
ejpam-4112	239	19	a	a	X
ejpam-4112	239	20	)	)	PUNCT
ejpam-4112	239	21	s	s	NOUN
ejpam-4112	239	22	=	=	PUNCT
ejpam-4112	239	23	a	a	DET
ejpam-4112	239	24	∪	∪	X
ejpam-4112	239	25	(	(	PUNCT
ejpam-4112	239	26	⋃	⋃	NOUN
ejpam-4112	239	27	u∈v	u∈v	NOUN
ejpam-4112	239	28	(	(	PUNCT
ejpam-4112	239	29	g	g	NOUN
ejpam-4112	239	30	)	)	PUNCT
ejpam-4112	239	31	v	v	NOUN
ejpam-4112	239	32	(	(	PUNCT
ejpam-4112	239	33	hu	hu	PROPN
ejpam-4112	239	34	)	)	PUNCT
ejpam-4112	239	35	)	)	PUNCT
ejpam-4112	239	36	where	where	SCONJ
ejpam-4112	239	37	a	a	DET
ejpam-4112	239	38	⊆	⊆	NUM
ejpam-4112	239	39	v	v	NOUN
ejpam-4112	239	40	(	(	PUNCT
ejpam-4112	239	41	g	g	NOUN
ejpam-4112	239	42	)	)	PUNCT
ejpam-4112	239	43	;	;	PUNCT
ejpam-4112	239	44	(	(	PUNCT
ejpam-4112	239	45	b	b	X
ejpam-4112	239	46	)	)	PUNCT
ejpam-4112	239	47	s	s	PART
ejpam-4112	239	48	=	=	PUNCT
ejpam-4112	239	49	a∪	a∪	PROPN
ejpam-4112	239	50	(	(	PUNCT
ejpam-4112	239	51	⋃	⋃	NOUN
ejpam-4112	239	52	u∈v	u∈v	NOUN
ejpam-4112	239	53	(	(	PUNCT
ejpam-4112	239	54	g)\{v	g)\{v	PROPN
ejpam-4112	239	55	}	}	PUNCT
ejpam-4112	239	56	v	v	PROPN
ejpam-4112	239	57	(	(	PUNCT
ejpam-4112	239	58	hu	hu	PROPN
ejpam-4112	239	59	)	)	PUNCT
ejpam-4112	239	60	)	)	PUNCT
ejpam-4112	239	61	∪bv	∪bv	NOUN
ejpam-4112	239	62	for	for	ADP
ejpam-4112	239	63	a	a	DET
ejpam-4112	239	64	unique	unique	ADJ
ejpam-4112	239	65	vertex	vertex	NOUN
ejpam-4112	239	66	v	v	NOUN
ejpam-4112	239	67	in	in	ADP
ejpam-4112	239	68	g	g	PROPN
ejpam-4112	239	69	,	,	PUNCT
ejpam-4112	239	70	where	where	SCONJ
ejpam-4112	239	71	a	a	DET
ejpam-4112	239	72	⊆	⊆	NUM
ejpam-4112	239	73	v	v	NOUN
ejpam-4112	239	74	(	(	PUNCT
ejpam-4112	239	75	g)\{v	g)\{v	PROPN
ejpam-4112	239	76	}	}	PUNCT
ejpam-4112	239	77	and	and	CCONJ
ejpam-4112	239	78	bv	bv	PROPN
ejpam-4112	239	79	is	be	AUX
ejpam-4112	239	80	a	a	DET
ejpam-4112	239	81	strong	strong	ADJ
ejpam-4112	239	82	resolving	resolving	NOUN
ejpam-4112	239	83	dominating	dominating	NOUN
ejpam-4112	239	84	set	set	NOUN
ejpam-4112	239	85	of	of	ADP
ejpam-4112	239	86	hv	hv	PROPN
ejpam-4112	239	87	if	if	SCONJ
ejpam-4112	239	88	γ(h	γ(h	NOUN
ejpam-4112	239	89	)	)	PUNCT
ejpam-4112	239	90	=	=	SYM
ejpam-4112	239	91	1	1	NUM
ejpam-4112	239	92	or	or	CCONJ
ejpam-4112	239	93	bv	bv	PROPN
ejpam-4112	239	94	is	be	AUX
ejpam-4112	239	95	a	a	DET
ejpam-4112	239	96	strong	strong	ADJ
ejpam-4112	239	97	resolving	resolving	NOUN
ejpam-4112	239	98	dominating	dominating	NOUN
ejpam-4112	239	99	set	set	NOUN
ejpam-4112	239	100	of	of	ADP
ejpam-4112	239	101	⟨v⟩+hv	⟨v⟩+hv	PROPN
ejpam-4112	239	102	if	if	SCONJ
ejpam-4112	239	103	γ(h	γ(h	NOUN
ejpam-4112	239	104	)	)	PUNCT
ejpam-4112	239	105	̸=	̸=	PROPN
ejpam-4112	239	106	1	1	NUM
ejpam-4112	239	107	.	.	PUNCT
ejpam-4112	240	1	suppose	suppose	VERB
ejpam-4112	240	2	(	(	PUNCT
ejpam-4112	240	3	a	a	PRON
ejpam-4112	240	4	)	)	PUNCT
ejpam-4112	240	5	holds	hold	NOUN
ejpam-4112	240	6	.	.	PUNCT
ejpam-4112	241	1	since	since	SCONJ
ejpam-4112	241	2	s	s	PROPN
ejpam-4112	241	3	is	be	AUX
ejpam-4112	241	4	a	a	DET
ejpam-4112	241	5	proper	proper	ADJ
ejpam-4112	241	6	restrained	restrained	ADJ
ejpam-4112	241	7	dominating	dominating	NOUN
ejpam-4112	241	8	subset	subset	NOUN
ejpam-4112	241	9	of	of	ADP
ejpam-4112	241	10	g	g	PROPN
ejpam-4112	241	11	◦	◦	NOUN
ejpam-4112	241	12	h	h	NOUN
ejpam-4112	241	13	,	,	PUNCT
ejpam-4112	241	14	v	v	NOUN
ejpam-4112	241	15	(	(	PUNCT
ejpam-4112	241	16	g	g	PROPN
ejpam-4112	241	17	◦	◦	NOUN
ejpam-4112	241	18	h	h	NOUN
ejpam-4112	241	19	)	)	PUNCT
ejpam-4112	241	20	\	\	PROPN
ejpam-4112	241	21	s	s	PART
ejpam-4112	241	22	=	=	SYM
ejpam-4112	241	23	v	v	X
ejpam-4112	241	24	(	(	PUNCT
ejpam-4112	241	25	g	g	NOUN
ejpam-4112	241	26	)	)	PUNCT
ejpam-4112	241	27	\a	\a	VERB
ejpam-4112	241	28	has	have	VERB
ejpam-4112	241	29	no	no	DET
ejpam-4112	241	30	isolated	isolated	ADJ
ejpam-4112	241	31	vertex	vertex	NOUN
ejpam-4112	241	32	.	.	PUNCT
ejpam-4112	242	1	thus	thus	ADV
ejpam-4112	242	2	,	,	PUNCT
ejpam-4112	242	3	(	(	PUNCT
ejpam-4112	242	4	i	i	NOUN
ejpam-4112	242	5	)	)	PUNCT
ejpam-4112	242	6	holds	hold	VERB
ejpam-4112	242	7	.	.	PUNCT
ejpam-4112	243	1	on	on	ADP
ejpam-4112	243	2	the	the	DET
ejpam-4112	243	3	other	other	ADJ
ejpam-4112	243	4	hand	hand	NOUN
ejpam-4112	243	5	if	if	SCONJ
ejpam-4112	243	6	(	(	PUNCT
ejpam-4112	243	7	b	b	NOUN
ejpam-4112	243	8	)	)	PUNCT
ejpam-4112	243	9	holds	hold	VERB
ejpam-4112	243	10	,	,	PUNCT
ejpam-4112	243	11	then	then	ADV
ejpam-4112	243	12	since	since	SCONJ
ejpam-4112	243	13	s	s	NOUN
ejpam-4112	243	14	is	be	AUX
ejpam-4112	243	15	a	a	DET
ejpam-4112	243	16	restrained	restrain	VERB
ejpam-4112	243	17	dominating	dominating	NOUN
ejpam-4112	243	18	set	set	NOUN
ejpam-4112	243	19	and	and	CCONJ
ejpam-4112	243	20	v	v	NOUN
ejpam-4112	243	21	(	(	PUNCT
ejpam-4112	243	22	g	g	PROPN
ejpam-4112	243	23	◦	◦	NOUN
ejpam-4112	243	24	h	h	NOUN
ejpam-4112	243	25	)	)	PUNCT
ejpam-4112	243	26	\	\	PROPN
ejpam-4112	244	1	s	s	PART
ejpam-4112	244	2	=	=	SYM
ejpam-4112	244	3	(	(	PUNCT
ejpam-4112	244	4	v	v	NOUN
ejpam-4112	244	5	(	(	PUNCT
ejpam-4112	244	6	g)\a)∪	g)\a)∪	PROPN
ejpam-4112	244	7	(	(	PUNCT
ejpam-4112	244	8	v	v	NOUN
ejpam-4112	244	9	(	(	PUNCT
ejpam-4112	244	10	hv+	hv+	NOUN
ejpam-4112	244	11	⟨v⟩)\bv	⟨v⟩)\bv	NOUN
ejpam-4112	244	12	)	)	PUNCT
ejpam-4112	244	13	,	,	PUNCT
ejpam-4112	244	14	a	a	DET
ejpam-4112	244	15	=	=	SYM
ejpam-4112	244	16	v	v	NOUN
ejpam-4112	244	17	(	(	PUNCT
ejpam-4112	244	18	g)\{v	g)\{v	PROPN
ejpam-4112	244	19	}	}	PUNCT
ejpam-4112	244	20	or	or	CCONJ
ejpam-4112	244	21	v	v	NOUN
ejpam-4112	244	22	(	(	PUNCT
ejpam-4112	244	23	g)\	g)\	PROPN
ejpam-4112	244	24	(	(	PUNCT
ejpam-4112	244	25	a∪{v	a∪{v	NOUN
ejpam-4112	244	26	}	}	PUNCT
ejpam-4112	244	27	)	)	PUNCT
ejpam-4112	244	28	has	have	VERB
ejpam-4112	244	29	no	no	DET
ejpam-4112	244	30	isolated	isolated	ADJ
ejpam-4112	244	31	vertex	vertex	NOUN
ejpam-4112	244	32	and	and	CCONJ
ejpam-4112	244	33	bv	bv	PROPN
ejpam-4112	244	34	is	be	AUX
ejpam-4112	244	35	a	a	DET
ejpam-4112	244	36	strong	strong	ADJ
ejpam-4112	244	37	resolving	resolving	NOUN
ejpam-4112	244	38	dominating	dominating	NOUN
ejpam-4112	244	39	set	set	NOUN
ejpam-4112	244	40	of	of	ADP
ejpam-4112	244	41	hv	hv	PROPN
ejpam-4112	244	42	+	+	PROPN
ejpam-4112	244	43	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4112	244	44	since	since	SCONJ
ejpam-4112	244	45	v	v	NUM
ejpam-4112	244	46	∈	∈	PROPN
ejpam-4112	244	47	s	s	NOUN
ejpam-4112	244	48	,	,	PUNCT
ejpam-4112	244	49	v	v	PROPN
ejpam-4112	244	50	(	(	PUNCT
ejpam-4112	244	51	hv	hv	NOUN
ejpam-4112	244	52	)	)	PUNCT
ejpam-4112	244	53	\bv	\bv	NOUN
ejpam-4112	244	54	has	have	VERB
ejpam-4112	244	55	no	no	DET
ejpam-4112	244	56	isolated	isolated	ADJ
ejpam-4112	244	57	vertex	vertex	NOUN
ejpam-4112	244	58	and	and	CCONJ
ejpam-4112	244	59	bv	bv	PROPN
ejpam-4112	244	60	is	be	AUX
ejpam-4112	244	61	a	a	DET
ejpam-4112	244	62	strong	strong	ADJ
ejpam-4112	244	63	resolving	resolving	NOUN
ejpam-4112	244	64	dominating	dominating	NOUN
ejpam-4112	244	65	set	set	NOUN
ejpam-4112	244	66	of	of	ADP
ejpam-4112	244	67	hv	hv	PROPN
ejpam-4112	244	68	+	+	X
ejpam-4112	244	69	⟨v⟩	⟨v⟩	PROPN
ejpam-4112	245	1	if	if	SCONJ
ejpam-4112	245	2	v	v	NUM
ejpam-4112	245	3	∈	∈	PROPN
ejpam-4112	245	4	s	s	NOUN
ejpam-4112	245	5	and	and	CCONJ
ejpam-4112	245	6	bv	bv	PROPN
ejpam-4112	245	7	is	be	AUX
ejpam-4112	245	8	strong	strong	ADJ
ejpam-4112	245	9	resolving	resolve	VERB
ejpam-4112	245	10	set	set	NOUN
ejpam-4112	245	11	of	of	ADP
ejpam-4112	245	12	hv	hv	PROPN
ejpam-4112	245	13	and	and	CCONJ
ejpam-4112	246	1	v	v	PROPN
ejpam-4112	246	2	(	(	PUNCT
ejpam-4112	246	3	hv	hv	PROPN
ejpam-4112	246	4	)	)	PUNCT
ejpam-4112	246	5	\	\	PROPN
ejpam-4112	246	6	bv	bv	PROPN
ejpam-4112	246	7	has	have	VERB
ejpam-4112	246	8	no	no	DET
ejpam-4112	246	9	isolated	isolated	ADJ
ejpam-4112	246	10	vertex	vertex	NOUN
ejpam-4112	246	11	if	if	SCONJ
ejpam-4112	246	12	v	v	NOUN
ejpam-4112	246	13	∈	∈	PROPN
ejpam-4112	246	14	s.	s.	PROPN
ejpam-4112	246	15	hence	hence	ADV
ejpam-4112	246	16	,	,	PUNCT
ejpam-4112	246	17	(	(	PUNCT
ejpam-4112	246	18	ii	ii	NOUN
ejpam-4112	246	19	)	)	PUNCT
ejpam-4112	246	20	holds	hold	VERB
ejpam-4112	246	21	.	.	PUNCT
ejpam-4112	247	1	conversely	conversely	ADV
ejpam-4112	247	2	,	,	PUNCT
ejpam-4112	247	3	suppose	suppose	VERB
ejpam-4112	247	4	(	(	PUNCT
ejpam-4112	247	5	i	i	NOUN
ejpam-4112	247	6	)	)	PUNCT
ejpam-4112	247	7	and	and	CCONJ
ejpam-4112	247	8	(	(	PUNCT
ejpam-4112	247	9	ii	ii	NOUN
ejpam-4112	247	10	)	)	PUNCT
ejpam-4112	247	11	hold	hold	NOUN
ejpam-4112	247	12	.	.	PUNCT
ejpam-4112	248	1	by	by	ADP
ejpam-4112	248	2	theorem	theorem	NOUN
ejpam-4112	248	3	4	4	NUM
ejpam-4112	248	4	,	,	PUNCT
ejpam-4112	248	5	s	s	VERB
ejpam-4112	248	6	is	be	AUX
ejpam-4112	248	7	a	a	DET
ejpam-4112	248	8	strong	strong	ADJ
ejpam-4112	248	9	resolving	resolving	NOUN
ejpam-4112	248	10	dominating	dominating	NOUN
ejpam-4112	248	11	set	set	NOUN
ejpam-4112	248	12	of	of	ADP
ejpam-4112	248	13	g	g	PROPN
ejpam-4112	248	14	◦	◦	NOUN
ejpam-4112	248	15	h.	h.	NOUN
ejpam-4112	248	16	if	if	SCONJ
ejpam-4112	248	17	(	(	PUNCT
ejpam-4112	248	18	i	i	NOUN
ejpam-4112	248	19	)	)	PUNCT
ejpam-4112	248	20	holds	hold	VERB
ejpam-4112	248	21	,	,	PUNCT
ejpam-4112	248	22	then	then	ADV
ejpam-4112	248	23	v	v	INTJ
ejpam-4112	248	24	(	(	PUNCT
ejpam-4112	248	25	g	g	PROPN
ejpam-4112	248	26	◦	◦	NOUN
ejpam-4112	248	27	h	h	NOUN
ejpam-4112	248	28	)	)	PUNCT
ejpam-4112	248	29	\	\	PROPN
ejpam-4112	249	1	s	s	PART
ejpam-4112	249	2	=	=	SYM
ejpam-4112	249	3	v	v	NOUN
ejpam-4112	249	4	(	(	PUNCT
ejpam-4112	249	5	g	g	NOUN
ejpam-4112	249	6	)	)	PUNCT
ejpam-4112	249	7	\	\	NOUN
ejpam-4112	250	1	a	a	PRON
ejpam-4112	250	2	has	have	VERB
ejpam-4112	250	3	no	no	DET
ejpam-4112	250	4	isolated	isolated	ADJ
ejpam-4112	250	5	vertex	vertex	NOUN
ejpam-4112	250	6	.	.	PUNCT
ejpam-4112	251	1	if	if	SCONJ
ejpam-4112	251	2	(	(	PUNCT
ejpam-4112	251	3	ii	ii	NOUN
ejpam-4112	251	4	)	)	PUNCT
ejpam-4112	251	5	holds	hold	VERB
ejpam-4112	251	6	then	then	ADV
ejpam-4112	251	7	v	v	X
ejpam-4112	251	8	(	(	PUNCT
ejpam-4112	251	9	g	g	PROPN
ejpam-4112	251	10	◦	◦	NOUN
ejpam-4112	251	11	h	h	NOUN
ejpam-4112	251	12	)	)	PUNCT
ejpam-4112	251	13	\s	\s	NOUN
ejpam-4112	251	14	=	=	PUNCT
ejpam-4112	251	15	(	(	PUNCT
ejpam-4112	251	16	v	v	NOUN
ejpam-4112	251	17	(	(	PUNCT
ejpam-4112	251	18	g	g	NOUN
ejpam-4112	251	19	)	)	PUNCT
ejpam-4112	251	20	\a)∪	\a)∪	PROPN
ejpam-4112	251	21	(	(	PUNCT
ejpam-4112	251	22	v	v	NOUN
ejpam-4112	251	23	(	(	PUNCT
ejpam-4112	251	24	hv	hv	PROPN
ejpam-4112	251	25	+	+	PROPN
ejpam-4112	251	26	⟨v⟩	⟨v⟩	PROPN
ejpam-4112	251	27	)	)	PUNCT
ejpam-4112	251	28	\bv	\bv	NOUN
ejpam-4112	251	29	)	)	PUNCT
ejpam-4112	251	30	.	.	PUNCT
ejpam-4112	252	1	since	since	SCONJ
ejpam-4112	252	2	a	a	DET
ejpam-4112	252	3	=	=	SYM
ejpam-4112	252	4	v	v	NOUN
ejpam-4112	252	5	(	(	PUNCT
ejpam-4112	252	6	g	g	NOUN
ejpam-4112	252	7	)	)	PUNCT
ejpam-4112	252	8	\	\	NOUN
ejpam-4112	252	9	{	{	PUNCT
ejpam-4112	252	10	v	v	NOUN
ejpam-4112	252	11	}	}	PUNCT
ejpam-4112	252	12	or	or	CCONJ
ejpam-4112	252	13	v	v	NOUN
ejpam-4112	252	14	(	(	PUNCT
ejpam-4112	252	15	g	g	NOUN
ejpam-4112	252	16	)	)	PUNCT
ejpam-4112	252	17	\	\	PUNCT
ejpam-4112	252	18	(	(	PUNCT
ejpam-4112	252	19	a∪	a∪	X
ejpam-4112	252	20	{	{	PUNCT
ejpam-4112	252	21	v	v	NOUN
ejpam-4112	252	22	}	}	PUNCT
ejpam-4112	252	23	)	)	PUNCT
ejpam-4112	252	24	has	have	VERB
ejpam-4112	252	25	no	no	DET
ejpam-4112	252	26	isolated	isolated	ADJ
ejpam-4112	252	27	vertex	vertex	NOUN
ejpam-4112	252	28	,	,	PUNCT
ejpam-4112	252	29	v	v	NOUN
ejpam-4112	252	30	(	(	PUNCT
ejpam-4112	252	31	g+h	g+h	NOUN
ejpam-4112	252	32	)	)	PUNCT
ejpam-4112	252	33	\	\	PUNCT
ejpam-4112	253	1	s	s	PART
ejpam-4112	253	2	has	have	VERB
ejpam-4112	253	3	no	no	DET
ejpam-4112	253	4	isolated	isolated	ADJ
ejpam-4112	253	5	vertex	vertex	NOUN
ejpam-4112	253	6	.	.	PUNCT
ejpam-4112	254	1	in	in	ADP
ejpam-4112	254	2	either	either	DET
ejpam-4112	254	3	case	case	NOUN
ejpam-4112	254	4	,	,	PUNCT
ejpam-4112	254	5	v	v	NOUN
ejpam-4112	254	6	(	(	PUNCT
ejpam-4112	254	7	g	g	PROPN
ejpam-4112	254	8	◦	◦	NOUN
ejpam-4112	254	9	h	h	NOUN
ejpam-4112	254	10	)	)	PUNCT
ejpam-4112	254	11	\	\	PROPN
ejpam-4112	255	1	s	s	PART
ejpam-4112	255	2	has	have	VERB
ejpam-4112	255	3	no	no	DET
ejpam-4112	255	4	isolated	isolated	ADJ
ejpam-4112	255	5	vertex	vertex	NOUN
ejpam-4112	255	6	.	.	PUNCT
ejpam-4112	256	1	therefore	therefore	ADV
ejpam-4112	256	2	s	s	VERB
ejpam-4112	256	3	is	be	AUX
ejpam-4112	256	4	a	a	DET
ejpam-4112	256	5	restrained	restrain	VERB
ejpam-4112	256	6	strong	strong	ADJ
ejpam-4112	256	7	resolving	resolve	VERB
ejpam-4112	256	8	dominating	dominating	NOUN
ejpam-4112	256	9	set	set	NOUN
ejpam-4112	256	10	of	of	ADP
ejpam-4112	256	11	g	g	PROPN
ejpam-4112	256	12	◦	◦	NOUN
ejpam-4112	256	13	h.	h.	PROPN
ejpam-4112	256	14	corollary	corollary	ADJ
ejpam-4112	256	15	6	6	NUM
ejpam-4112	256	16	.	.	PUNCT
ejpam-4112	257	1	let	let	VERB
ejpam-4112	257	2	g	g	NOUN
ejpam-4112	257	3	andh	andh	NOUN
ejpam-4112	257	4	be	be	AUX
ejpam-4112	257	5	nontrivial	nontrivial	ADJ
ejpam-4112	257	6	connected	connect	VERB
ejpam-4112	257	7	graphs	graph	NOUN
ejpam-4112	257	8	of	of	ADP
ejpam-4112	257	9	ordersm	ordersm	NOUN
ejpam-4112	257	10	and	and	CCONJ
ejpam-4112	257	11	n	n	CCONJ
ejpam-4112	257	12	,	,	PUNCT
ejpam-4112	257	13	respectively	respectively	ADV
ejpam-4112	257	14	.	.	PUNCT
ejpam-4112	258	1	then	then	ADV
ejpam-4112	258	2	,	,	PUNCT
ejpam-4112	258	3	γrsr(g	γrsr(g	PROPN
ejpam-4112	258	4	◦	◦	NOUN
ejpam-4112	258	5	h	h	NOUN
ejpam-4112	258	6	)	)	PUNCT
ejpam-4112	258	7	=	=	PUNCT
ejpam-4112	259	1	(	(	PUNCT
ejpam-4112	259	2	m−	m−	PROPN
ejpam-4112	259	3	1)n+	1)n+	NUM
ejpam-4112	259	4	γsr(h	γsr(h	PROPN
ejpam-4112	259	5	+	+	NOUN
ejpam-4112	259	6	k1	k1	NOUN
ejpam-4112	259	7	)	)	PUNCT
ejpam-4112	259	8	.	.	PUNCT
ejpam-4112	260	1	proof	proof	NOUN
ejpam-4112	260	2	:	:	PUNCT
ejpam-4112	260	3	let	let	VERB
ejpam-4112	260	4	s	s	PRON
ejpam-4112	260	5	be	be	AUX
ejpam-4112	260	6	a	a	DET
ejpam-4112	260	7	γrsr	γrsr	NOUN
ejpam-4112	260	8	-	-	PUNCT
ejpam-4112	260	9	set	set	NOUN
ejpam-4112	260	10	of	of	ADP
ejpam-4112	260	11	g	g	PROPN
ejpam-4112	260	12	◦	◦	NOUN
ejpam-4112	260	13	h.	h.	NOUN
ejpam-4112	260	14	then	then	ADV
ejpam-4112	260	15	by	by	ADP
ejpam-4112	260	16	theorem	theorem	ADJ
ejpam-4112	260	17	11	11	NUM
ejpam-4112	260	18	(	(	PUNCT
ejpam-4112	260	19	ii	ii	NOUN
ejpam-4112	260	20	)	)	PUNCT
ejpam-4112	260	21	,	,	PUNCT
ejpam-4112	260	22	s	s	PART
ejpam-4112	260	23	=	=	PUNCT
ejpam-4112	260	24	⋃	⋃	NOUN
ejpam-4112	260	25	u∈v	u∈v	NOUN
ejpam-4112	260	26	(	(	PUNCT
ejpam-4112	260	27	g)\{v	g)\{v	PROPN
ejpam-4112	260	28	}	}	PUNCT
ejpam-4112	260	29	v	v	PROPN
ejpam-4112	260	30	(	(	PUNCT
ejpam-4112	260	31	hu	hu	PROPN
ejpam-4112	260	32	)	)	PUNCT
ejpam-4112	261	1	⋃	⋃	PUNCT
ejpam-4112	261	2	bv	bv	PROPN
ejpam-4112	261	3	for	for	ADP
ejpam-4112	261	4	a	a	DET
ejpam-4112	261	5	unique	unique	ADJ
ejpam-4112	261	6	vertex	vertex	NOUN
ejpam-4112	261	7	v	v	NOUN
ejpam-4112	261	8	in	in	ADP
ejpam-4112	261	9	g	g	PROPN
ejpam-4112	261	10	and	and	CCONJ
ejpam-4112	261	11	bv	bv	PROPN
ejpam-4112	261	12	is	be	AUX
ejpam-4112	261	13	a	a	DET
ejpam-4112	261	14	strong	strong	ADJ
ejpam-4112	261	15	resolving	resolving	NOUN
ejpam-4112	261	16	dominating	dominating	NOUN
ejpam-4112	261	17	set	set	NOUN
ejpam-4112	261	18	of	of	ADP
ejpam-4112	261	19	hv	hv	PROPN
ejpam-4112	261	20	.	.	PUNCT
ejpam-4112	262	1	hence	hence	ADV
ejpam-4112	262	2	,	,	PUNCT
ejpam-4112	262	3	γrsr(g	γrsr(g	PROPN
ejpam-4112	262	4	◦	◦	NOUN
ejpam-4112	262	5	h	h	NOUN
ejpam-4112	262	6	)	)	PUNCT
ejpam-4112	262	7	=	=	SYM
ejpam-4112	262	8	|s|	|s|	PROPN
ejpam-4112	262	9	=	=	PUNCT
ejpam-4112	262	10	|v	|v	X
ejpam-4112	262	11	(	(	PUNCT
ejpam-4112	262	12	h)||v	h)||v	PROPN
ejpam-4112	262	13	(	(	PUNCT
ejpam-4112	262	14	g	g	NOUN
ejpam-4112	262	15	)	)	PUNCT
ejpam-4112	262	16	\	\	NOUN
ejpam-4112	262	17	{	{	PUNCT
ejpam-4112	262	18	v}|+	v}|+	PROPN
ejpam-4112	262	19	|bv|	|bv|	PROPN
ejpam-4112	262	20	≥	≥	NUM
ejpam-4112	262	21	(	(	PUNCT
ejpam-4112	262	22	m−	m−	PROPN
ejpam-4112	262	23	1)n+	1)n+	NUM
ejpam-4112	262	24	γsr(h	γsr(h	PROPN
ejpam-4112	262	25	)	)	PUNCT
ejpam-4112	262	26	h.	h.	PROPN
ejpam-4112	262	27	sumaoy	sumaoy	NOUN
ejpam-4112	262	28	,	,	PUNCT
ejpam-4112	262	29	h.	h.	PROPN
ejpam-4112	262	30	rara	rara	PROPN
ejpam-4112	262	31	/	/	SYM
ejpam-4112	262	32	eur	eur	PROPN
ejpam-4112	262	33	.	.	PUNCT
ejpam-4112	263	1	j.	j.	PROPN
ejpam-4112	263	2	pure	pure	PROPN
ejpam-4112	263	3	appl	appl	PROPN
ejpam-4112	263	4	.	.	PROPN
ejpam-4112	263	5	math	math	PROPN
ejpam-4112	263	6	,	,	PUNCT
ejpam-4112	263	7	14	14	NUM
ejpam-4112	263	8	(	(	PUNCT
ejpam-4112	263	9	4	4	NUM
ejpam-4112	263	10	)	)	PUNCT
ejpam-4112	263	11	(	(	PUNCT
ejpam-4112	263	12	2021	2021	NUM
ejpam-4112	263	13	)	)	PUNCT
ejpam-4112	263	14	,	,	PUNCT
ejpam-4112	263	15	1367	1367	NUM
ejpam-4112	263	16	-	-	SYM
ejpam-4112	263	17	1378	1378	NUM
ejpam-4112	263	18	1375	1375	NUM
ejpam-4112	263	19	let	let	VERB
ejpam-4112	263	20	cv	cv	PROPN
ejpam-4112	263	21	be	be	AUX
ejpam-4112	263	22	a	a	DET
ejpam-4112	263	23	minimum	minimum	ADJ
ejpam-4112	263	24	strong	strong	ADJ
ejpam-4112	263	25	resolving	resolving	NOUN
ejpam-4112	263	26	dominating	dominating	NOUN
ejpam-4112	263	27	set	set	NOUN
ejpam-4112	263	28	of	of	ADP
ejpam-4112	263	29	hv	hv	PROPN
ejpam-4112	263	30	.	.	PROPN
ejpam-4112	264	1	for	for	ADP
ejpam-4112	264	2	a	a	DET
ejpam-4112	264	3	unique	unique	ADJ
ejpam-4112	264	4	vertex	vertex	NOUN
ejpam-4112	264	5	v	v	ADP
ejpam-4112	264	6	∈	∈	NOUN
ejpam-4112	264	7	v	v	NOUN
ejpam-4112	264	8	(	(	PUNCT
ejpam-4112	264	9	g	g	NOUN
ejpam-4112	264	10	)	)	PUNCT
ejpam-4112	264	11	,	,	PUNCT
ejpam-4112	264	12	let	let	VERB
ejpam-4112	264	13	⟨bv⟩	⟨bv⟩	VERB
ejpam-4112	264	14	∼=	∼=	PROPN
ejpam-4112	264	15	⟨cv⟩.	⟨cv⟩.	PUNCT
ejpam-4112	264	16	then	then	ADV
ejpam-4112	264	17	by	by	ADP
ejpam-4112	264	18	theorem	theorem	VERB
ejpam-4112	264	19	11	11	NUM
ejpam-4112	264	20	s	s	NOUN
ejpam-4112	264	21	=	=	PUNCT
ejpam-4112	264	22	(	(	PUNCT
ejpam-4112	264	23	⋃	⋃	NOUN
ejpam-4112	264	24	u∈v	u∈v	NOUN
ejpam-4112	264	25	(	(	PUNCT
ejpam-4112	264	26	g)\{v	g)\{v	PROPN
ejpam-4112	264	27	}	}	PUNCT
ejpam-4112	264	28	v	v	PROPN
ejpam-4112	264	29	(	(	PUNCT
ejpam-4112	264	30	hu	hu	PROPN
ejpam-4112	264	31	)	)	PUNCT
ejpam-4112	264	32	)	)	PUNCT
ejpam-4112	265	1	⋃	⋃	ADP
ejpam-4112	265	2	bv	bv	PROPN
ejpam-4112	265	3	is	be	AUX
ejpam-4112	265	4	a	a	DET
ejpam-4112	265	5	restrained	restrained	ADJ
ejpam-4112	265	6	strong	strong	ADJ
ejpam-4112	265	7	resolving	resolve	VERB
ejpam-4112	265	8	dominating	dominating	NOUN
ejpam-4112	265	9	set	set	NOUN
ejpam-4112	265	10	of	of	ADP
ejpam-4112	265	11	g	g	PROPN
ejpam-4112	265	12	◦	◦	NOUN
ejpam-4112	265	13	h.	h.	PROPN
ejpam-4112	265	14	thus	thus	ADV
ejpam-4112	265	15	,	,	PUNCT
ejpam-4112	265	16	γrsr(g	γrsr(g	PROPN
ejpam-4112	265	17	◦	◦	NOUN
ejpam-4112	265	18	h	h	NOUN
ejpam-4112	265	19	)	)	PUNCT
ejpam-4112	265	20	≤	≤	NUM
ejpam-4112	265	21	|s|	|s|	PROPN
ejpam-4112	265	22	=	=	PUNCT
ejpam-4112	265	23	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4112	265	24	⋃	⋃	NOUN
ejpam-4112	265	25	u∈v	u∈v	NOUN
ejpam-4112	265	26	(	(	PUNCT
ejpam-4112	265	27	g)\{v	g)\{v	PROPN
ejpam-4112	265	28	}	}	PUNCT
ejpam-4112	265	29	v	v	PROPN
ejpam-4112	265	30	(	(	PUNCT
ejpam-4112	265	31	hu	hu	PROPN
ejpam-4112	265	32	)	)	PUNCT
ejpam-4112	265	33	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-4112	265	34	|bv|	|bv|	PROPN
ejpam-4112	265	35	=	=	PUNCT
ejpam-4112	265	36	(	(	PUNCT
ejpam-4112	265	37	m−	m−	PROPN
ejpam-4112	265	38	1)(n	1)(n	NUM
ejpam-4112	265	39	)	)	PUNCT
ejpam-4112	265	40	+	+	NUM
ejpam-4112	265	41	|cv|	|cv|	NOUN
ejpam-4112	265	42	=	=	SYM
ejpam-4112	265	43	(	(	PUNCT
ejpam-4112	265	44	m−	m−	PROPN
ejpam-4112	265	45	1)(n	1)(n	NUM
ejpam-4112	265	46	)	)	PUNCT
ejpam-4112	265	47	+	+	CCONJ
ejpam-4112	265	48	γsr(h	γsr(h	PROPN
ejpam-4112	265	49	)	)	PUNCT
ejpam-4112	265	50	therefore	therefore	ADV
ejpam-4112	265	51	,	,	PUNCT
ejpam-4112	265	52	γrsr(g	γrsr(g	PROPN
ejpam-4112	265	53	◦	◦	NOUN
ejpam-4112	265	54	h	h	NOUN
ejpam-4112	265	55	)	)	PUNCT
ejpam-4112	265	56	=	=	PUNCT
ejpam-4112	266	1	(	(	PUNCT
ejpam-4112	266	2	m−	m−	PROPN
ejpam-4112	266	3	1)n+	1)n+	NUM
ejpam-4112	266	4	γsr(h	γsr(h	PROPN
ejpam-4112	266	5	)	)	PUNCT
ejpam-4112	266	6	.	.	PUNCT
ejpam-4112	267	1	5	5	X
ejpam-4112	267	2	.	.	X
ejpam-4112	267	3	restrained	restrain	VERB
ejpam-4112	267	4	strong	strong	ADJ
ejpam-4112	267	5	resolving	resolving	NOUN
ejpam-4112	267	6	domination	domination	NOUN
ejpam-4112	267	7	in	in	ADP
ejpam-4112	267	8	the	the	DET
ejpam-4112	267	9	lexicographic	lexicographic	ADJ
ejpam-4112	267	10	product	product	NOUN
ejpam-4112	267	11	of	of	ADP
ejpam-4112	267	12	graphs	graph	NOUN
ejpam-4112	267	13	lemma	lemma	PROPN
ejpam-4112	267	14	2	2	X
ejpam-4112	267	15	.	.	PUNCT
ejpam-4112	268	1	let	let	VERB
ejpam-4112	268	2	g	g	PROPN
ejpam-4112	268	3	=	=	PROPN
ejpam-4112	268	4	kn	kn	PROPN
ejpam-4112	268	5	for	for	ADP
ejpam-4112	268	6	n	n	PROPN
ejpam-4112	268	7	>	>	SYM
ejpam-4112	268	8	1	1	NUM
ejpam-4112	268	9	and	and	CCONJ
ejpam-4112	268	10	h	h	DET
ejpam-4112	268	11	a	a	DET
ejpam-4112	268	12	nontrivial	nontrivial	ADJ
ejpam-4112	268	13	connected	connect	VERB
ejpam-4112	268	14	graph	graph	NOUN
ejpam-4112	268	15	with	with	ADP
ejpam-4112	268	16	γ(h	γ(h	NOUN
ejpam-4112	268	17	)	)	PUNCT
ejpam-4112	268	18	̸=	̸=	PROPN
ejpam-4112	268	19	1	1	NUM
ejpam-4112	268	20	.	.	PUNCT
ejpam-4112	269	1	then	then	ADV
ejpam-4112	269	2	a×c	a×c	PROPN
ejpam-4112	269	3	⊆	⊆	NUM
ejpam-4112	269	4	v	v	NOUN
ejpam-4112	269	5	(	(	PUNCT
ejpam-4112	269	6	g[h	g[h	PROPN
ejpam-4112	269	7	]	]	PUNCT
ejpam-4112	269	8	)	)	PUNCT
ejpam-4112	269	9	is	be	AUX
ejpam-4112	269	10	a	a	DET
ejpam-4112	269	11	dominated	dominate	VERB
ejpam-4112	269	12	superclique	superclique	NOUN
ejpam-4112	269	13	in	in	ADP
ejpam-4112	269	14	g[h	g[h	NOUN
ejpam-4112	269	15	]	]	PUNCT
ejpam-4112	269	16	if	if	SCONJ
ejpam-4112	270	1	and	and	CCONJ
ejpam-4112	270	2	only	only	ADV
ejpam-4112	270	3	if	if	SCONJ
ejpam-4112	270	4	a	a	PRON
ejpam-4112	270	5	is	be	AUX
ejpam-4112	270	6	a	a	DET
ejpam-4112	270	7	nonempty	nonempty	ADJ
ejpam-4112	270	8	subset	subset	NOUN
ejpam-4112	270	9	of	of	ADP
ejpam-4112	270	10	v	v	NOUN
ejpam-4112	270	11	(	(	PUNCT
ejpam-4112	270	12	g	g	NOUN
ejpam-4112	270	13	)	)	PUNCT
ejpam-4112	270	14	and	and	CCONJ
ejpam-4112	270	15	c	c	PROPN
ejpam-4112	270	16	is	be	AUX
ejpam-4112	270	17	a	a	DET
ejpam-4112	270	18	superclique	superclique	NOUN
ejpam-4112	270	19	in	in	ADP
ejpam-4112	270	20	h.	h.	NOUN
ejpam-4112	270	21	proof	proof	NOUN
ejpam-4112	270	22	:	:	PUNCT
ejpam-4112	270	23	let	let	VERB
ejpam-4112	270	24	g	g	PROPN
ejpam-4112	270	25	=	=	PROPN
ejpam-4112	270	26	kn	kn	PROPN
ejpam-4112	270	27	for	for	ADP
ejpam-4112	270	28	n	n	PROPN
ejpam-4112	270	29	>	>	SYM
ejpam-4112	270	30	1	1	NUM
ejpam-4112	270	31	and	and	CCONJ
ejpam-4112	270	32	h	h	DET
ejpam-4112	270	33	a	a	DET
ejpam-4112	270	34	nontrivial	nontrivial	ADJ
ejpam-4112	270	35	connected	connect	VERB
ejpam-4112	270	36	graph	graph	NOUN
ejpam-4112	270	37	with	with	ADP
ejpam-4112	270	38	γ(h	γ(h	NOUN
ejpam-4112	270	39	)	)	PUNCT
ejpam-4112	270	40	̸=	̸=	PROPN
ejpam-4112	270	41	1	1	NUM
ejpam-4112	270	42	.	.	PUNCT
ejpam-4112	271	1	suppose	suppose	VERB
ejpam-4112	271	2	a×	a×	PUNCT
ejpam-4112	271	3	c	c	NOUN
ejpam-4112	271	4	⊆	⊆	NUM
ejpam-4112	271	5	v	v	NOUN
ejpam-4112	271	6	(	(	PUNCT
ejpam-4112	271	7	g[h	g[h	PROPN
ejpam-4112	271	8	]	]	PUNCT
ejpam-4112	271	9	)	)	PUNCT
ejpam-4112	271	10	is	be	AUX
ejpam-4112	271	11	a	a	DET
ejpam-4112	271	12	dominated	dominate	VERB
ejpam-4112	271	13	superclique	superclique	NOUN
ejpam-4112	271	14	in	in	ADP
ejpam-4112	271	15	g[h	g[h	NOUN
ejpam-4112	271	16	]	]	PUNCT
ejpam-4112	271	17	.	.	PUNCT
ejpam-4112	272	1	by	by	ADP
ejpam-4112	272	2	a	a	DET
ejpam-4112	272	3	lemma	lemma	PROPN
ejpam-4112	272	4	in	in	ADP
ejpam-4112	272	5	[	[	PUNCT
ejpam-4112	272	6	3	3	NUM
ejpam-4112	272	7	]	]	PUNCT
ejpam-4112	272	8	,	,	PUNCT
ejpam-4112	272	9	a	a	PRON
ejpam-4112	272	10	is	be	AUX
ejpam-4112	272	11	a	a	DET
ejpam-4112	272	12	nonempty	nonempty	ADJ
ejpam-4112	272	13	subset	subset	NOUN
ejpam-4112	272	14	of	of	ADP
ejpam-4112	272	15	v	v	NOUN
ejpam-4112	272	16	(	(	PUNCT
ejpam-4112	272	17	g	g	NOUN
ejpam-4112	272	18	)	)	PUNCT
ejpam-4112	272	19	and	and	CCONJ
ejpam-4112	272	20	c	c	PROPN
ejpam-4112	272	21	is	be	AUX
ejpam-4112	272	22	a	a	DET
ejpam-4112	272	23	superclique	superclique	NOUN
ejpam-4112	272	24	in	in	ADP
ejpam-4112	272	25	h.	h.	NOUN
ejpam-4112	272	26	conversely	conversely	ADV
ejpam-4112	272	27	,	,	PUNCT
ejpam-4112	272	28	suppose	suppose	VERB
ejpam-4112	272	29	a	a	DET
ejpam-4112	272	30	⊆	⊆	NUM
ejpam-4112	272	31	v	v	NOUN
ejpam-4112	272	32	(	(	PUNCT
ejpam-4112	272	33	g	g	NOUN
ejpam-4112	272	34	)	)	PUNCT
ejpam-4112	272	35	,	,	PUNCT
ejpam-4112	272	36	a	a	DET
ejpam-4112	272	37	̸=	̸=	PROPN
ejpam-4112	272	38	∅	∅	NOUN
ejpam-4112	272	39	and	and	CCONJ
ejpam-4112	272	40	c	c	NOUN
ejpam-4112	272	41	is	be	AUX
ejpam-4112	272	42	a	a	DET
ejpam-4112	272	43	superclique	superclique	NOUN
ejpam-4112	272	44	in	in	ADP
ejpam-4112	272	45	h.	h.	PROPN
ejpam-4112	273	1	then	then	ADV
ejpam-4112	273	2	a×	a×	VERB
ejpam-4112	273	3	c	c	NOUN
ejpam-4112	273	4	⊆	⊆	NUM
ejpam-4112	273	5	v	v	NOUN
ejpam-4112	273	6	(	(	PUNCT
ejpam-4112	273	7	g[h	g[h	PROPN
ejpam-4112	273	8	]	]	PUNCT
ejpam-4112	273	9	)	)	PUNCT
ejpam-4112	273	10	is	be	AUX
ejpam-4112	273	11	a	a	DET
ejpam-4112	273	12	superclique	superclique	NOUN
ejpam-4112	273	13	in	in	ADP
ejpam-4112	273	14	g[h	g[h	NOUN
ejpam-4112	273	15	]	]	PUNCT
ejpam-4112	273	16	by	by	ADP
ejpam-4112	273	17	a	a	DET
ejpam-4112	273	18	lemma	lemma	PROPN
ejpam-4112	273	19	in	in	ADP
ejpam-4112	273	20	[	[	X
ejpam-4112	273	21	3	3	NUM
ejpam-4112	273	22	]	]	PUNCT
ejpam-4112	273	23	.	.	PUNCT
ejpam-4112	274	1	we	we	PRON
ejpam-4112	274	2	show	show	VERB
ejpam-4112	274	3	that	that	SCONJ
ejpam-4112	274	4	a×	a×	PROPN
ejpam-4112	274	5	c	c	PROPN
ejpam-4112	274	6	is	be	AUX
ejpam-4112	274	7	a	a	DET
ejpam-4112	274	8	dominated	dominate	VERB
ejpam-4112	274	9	superclique	superclique	NOUN
ejpam-4112	274	10	.	.	PUNCT
ejpam-4112	275	1	let	let	VERB
ejpam-4112	275	2	(	(	PUNCT
ejpam-4112	275	3	a	a	PRON
ejpam-4112	275	4	,	,	PUNCT
ejpam-4112	275	5	b	b	NOUN
ejpam-4112	275	6	)	)	PUNCT
ejpam-4112	275	7	∈	∈	PROPN
ejpam-4112	275	8	a×c	a×c	PROPN
ejpam-4112	275	9	.	.	PUNCT
ejpam-4112	276	1	then	then	ADV
ejpam-4112	276	2	a	a	DET
ejpam-4112	276	3	∈	∈	PROPN
ejpam-4112	276	4	a	a	PRON
ejpam-4112	276	5	and	and	CCONJ
ejpam-4112	276	6	b	b	PROPN
ejpam-4112	276	7	∈	∈	PROPN
ejpam-4112	276	8	c.	c.	NOUN
ejpam-4112	276	9	since	since	SCONJ
ejpam-4112	276	10	γ(h	γ(h	NOUN
ejpam-4112	276	11	)	)	PUNCT
ejpam-4112	276	12	̸=	̸=	PROPN
ejpam-4112	276	13	1	1	NUM
ejpam-4112	276	14	,	,	PUNCT
ejpam-4112	276	15	there	there	PRON
ejpam-4112	276	16	exists	exist	VERB
ejpam-4112	276	17	d	d	X
ejpam-4112	276	18	∈	∈	PROPN
ejpam-4112	276	19	v	v	PROPN
ejpam-4112	276	20	(	(	PUNCT
ejpam-4112	276	21	h)\nh(b	h)\nh(b	PROPN
ejpam-4112	276	22	)	)	PUNCT
ejpam-4112	276	23	.	.	PUNCT
ejpam-4112	277	1	hence	hence	ADV
ejpam-4112	277	2	,	,	PUNCT
ejpam-4112	277	3	d	d	PROPN
ejpam-4112	277	4	/∈	/∈	PROPN
ejpam-4112	277	5	c.	c.	NOUN
ejpam-4112	277	6	since	since	SCONJ
ejpam-4112	277	7	g	g	PROPN
ejpam-4112	277	8	=	=	PROPN
ejpam-4112	277	9	kn	kn	PROPN
ejpam-4112	277	10	for	for	ADP
ejpam-4112	277	11	n	n	PROPN
ejpam-4112	277	12	>	>	X
ejpam-4112	277	13	1	1	NUM
ejpam-4112	277	14	,	,	PUNCT
ejpam-4112	277	15	a	a	DET
ejpam-4112	277	16	vertex	vertex	NOUN
ejpam-4112	277	17	v	v	ADP
ejpam-4112	277	18	∈	∈	NOUN
ejpam-4112	277	19	v	v	NOUN
ejpam-4112	277	20	(	(	PUNCT
ejpam-4112	277	21	kn)\{a	kn)\{a	PROPN
ejpam-4112	277	22	}	}	PUNCT
ejpam-4112	277	23	exists	exist	VERB
ejpam-4112	277	24	where	where	SCONJ
ejpam-4112	277	25	av	av	PROPN
ejpam-4112	277	26	∈	∈	PROPN
ejpam-4112	277	27	e(kn	e(kn	NUM
ejpam-4112	277	28	)	)	PUNCT
ejpam-4112	277	29	.	.	PUNCT
ejpam-4112	278	1	thus	thus	ADV
ejpam-4112	278	2	,	,	PUNCT
ejpam-4112	278	3	(	(	PUNCT
ejpam-4112	278	4	v	v	NOUN
ejpam-4112	278	5	,	,	PUNCT
ejpam-4112	278	6	d	d	NOUN
ejpam-4112	278	7	)	)	PUNCT
ejpam-4112	278	8	/∈	/∈	PUNCT
ejpam-4112	279	1	a	a	DET
ejpam-4112	279	2	×	×	NOUN
ejpam-4112	279	3	c	c	NOUN
ejpam-4112	279	4	and	and	CCONJ
ejpam-4112	279	5	(	(	PUNCT
ejpam-4112	279	6	a	a	PRON
ejpam-4112	279	7	,	,	PUNCT
ejpam-4112	279	8	b)(v	b)(v	PROPN
ejpam-4112	279	9	,	,	PUNCT
ejpam-4112	279	10	d	d	X
ejpam-4112	279	11	)	)	PUNCT
ejpam-4112	279	12	∈	∈	NOUN
ejpam-4112	279	13	e(g[h	e(g[h	NOUN
ejpam-4112	279	14	]	]	PUNCT
ejpam-4112	279	15	)	)	PUNCT
ejpam-4112	279	16	.	.	PUNCT
ejpam-4112	280	1	therefore	therefore	ADV
ejpam-4112	280	2	,	,	PUNCT
ejpam-4112	280	3	a×	a×	PROPN
ejpam-4112	280	4	c	c	PROPN
ejpam-4112	280	5	is	be	AUX
ejpam-4112	280	6	a	a	DET
ejpam-4112	280	7	dominated	dominate	VERB
ejpam-4112	280	8	superclique	superclique	NOUN
ejpam-4112	280	9	in	in	ADP
ejpam-4112	280	10	g[h	g[h	NOUN
ejpam-4112	280	11	]	]	PUNCT
ejpam-4112	280	12	.	.	PUNCT
ejpam-4112	281	1	theorem	theorem	NOUN
ejpam-4112	281	2	12	12	NUM
ejpam-4112	281	3	.	.	PUNCT
ejpam-4112	282	1	let	let	VERB
ejpam-4112	282	2	g	g	PROPN
ejpam-4112	282	3	=	=	PROPN
ejpam-4112	282	4	kn	kn	PROPN
ejpam-4112	282	5	for	for	ADP
ejpam-4112	282	6	n	n	PROPN
ejpam-4112	282	7	>	>	SYM
ejpam-4112	282	8	1	1	NUM
ejpam-4112	282	9	and	and	CCONJ
ejpam-4112	282	10	h	h	DET
ejpam-4112	282	11	a	a	DET
ejpam-4112	282	12	nontrivial	nontrivial	ADJ
ejpam-4112	282	13	connected	connect	VERB
ejpam-4112	282	14	graph	graph	NOUN
ejpam-4112	282	15	with	with	ADP
ejpam-4112	282	16	γ(h	γ(h	NOUN
ejpam-4112	282	17	)	)	PUNCT
ejpam-4112	282	18	̸=	̸=	PROPN
ejpam-4112	282	19	1	1	NUM
ejpam-4112	282	20	.	.	PUNCT
ejpam-4112	283	1	a	a	DET
ejpam-4112	283	2	subset	subset	NOUN
ejpam-4112	283	3	s	s	X
ejpam-4112	283	4	of	of	ADP
ejpam-4112	283	5	v	v	NOUN
ejpam-4112	283	6	(	(	PUNCT
ejpam-4112	283	7	g[h	g[h	PROPN
ejpam-4112	283	8	]	]	PUNCT
ejpam-4112	283	9	)	)	PUNCT
ejpam-4112	283	10	is	be	AUX
ejpam-4112	283	11	a	a	DET
ejpam-4112	283	12	restrained	restrained	ADJ
ejpam-4112	283	13	strong	strong	ADJ
ejpam-4112	283	14	resolving	resolve	VERB
ejpam-4112	283	15	dominating	dominating	NOUN
ejpam-4112	283	16	set	set	NOUN
ejpam-4112	283	17	of	of	ADP
ejpam-4112	283	18	g[h	g[h	PROPN
ejpam-4112	283	19	]	]	PUNCT
ejpam-4112	283	20	if	if	SCONJ
ejpam-4112	283	21	and	and	CCONJ
ejpam-4112	283	22	only	only	ADV
ejpam-4112	283	23	if	if	SCONJ
ejpam-4112	283	24	s	s	VERB
ejpam-4112	283	25	=	=	SYM
ejpam-4112	283	26	v	v	NOUN
ejpam-4112	283	27	(	(	PUNCT
ejpam-4112	283	28	g[h	g[h	PROPN
ejpam-4112	283	29	]	]	PUNCT
ejpam-4112	283	30	)	)	PUNCT
ejpam-4112	283	31	\	\	PUNCT
ejpam-4112	284	1	(	(	PUNCT
ejpam-4112	284	2	a×	a×	NOUN
ejpam-4112	284	3	c	c	X
ejpam-4112	284	4	)	)	PUNCT
ejpam-4112	284	5	and	and	CCONJ
ejpam-4112	284	6	one	one	NUM
ejpam-4112	284	7	of	of	ADP
ejpam-4112	284	8	the	the	DET
ejpam-4112	284	9	following	follow	VERB
ejpam-4112	284	10	is	be	AUX
ejpam-4112	284	11	satisfied	satisfied	ADJ
ejpam-4112	284	12	:	:	PUNCT
ejpam-4112	284	13	(	(	PUNCT
ejpam-4112	284	14	i	i	NOUN
ejpam-4112	284	15	)	)	PUNCT
ejpam-4112	284	16	a	a	DET
ejpam-4112	284	17	⊆	⊆	NUM
ejpam-4112	284	18	v	v	NOUN
ejpam-4112	284	19	(	(	PUNCT
ejpam-4112	284	20	g	g	NOUN
ejpam-4112	284	21	)	)	PUNCT
ejpam-4112	284	22	and	and	CCONJ
ejpam-4112	284	23	c	c	NOUN
ejpam-4112	284	24	=	=	SYM
ejpam-4112	284	25	∅	∅	NOUN
ejpam-4112	284	26	(	(	PUNCT
ejpam-4112	284	27	ii	ii	NOUN
ejpam-4112	284	28	)	)	PUNCT
ejpam-4112	284	29	a	a	PRON
ejpam-4112	284	30	is	be	AUX
ejpam-4112	284	31	singleton	singleton	NOUN
ejpam-4112	284	32	subset	subset	NOUN
ejpam-4112	284	33	of	of	ADP
ejpam-4112	284	34	v	v	PROPN
ejpam-4112	284	35	(	(	PUNCT
ejpam-4112	284	36	g	g	NOUN
ejpam-4112	284	37	)	)	PUNCT
ejpam-4112	284	38	and	and	CCONJ
ejpam-4112	284	39	c	c	PROPN
ejpam-4112	284	40	is	be	AUX
ejpam-4112	284	41	a	a	DET
ejpam-4112	284	42	nonsingleton	nonsingleton	NOUN
ejpam-4112	284	43	suerclique	suerclique	NOUN
ejpam-4112	284	44	in	in	ADP
ejpam-4112	284	45	h.	h.	PROPN
ejpam-4112	284	46	(	(	PUNCT
ejpam-4112	284	47	iii	iii	X
ejpam-4112	284	48	)	)	PUNCT
ejpam-4112	284	49	a	a	PRON
ejpam-4112	284	50	is	be	AUX
ejpam-4112	284	51	nonempty	nonempty	ADJ
ejpam-4112	284	52	nonsingleton	nonsingleton	NOUN
ejpam-4112	284	53	subset	subset	NOUN
ejpam-4112	284	54	of	of	ADP
ejpam-4112	284	55	v	v	NOUN
ejpam-4112	284	56	(	(	PUNCT
ejpam-4112	284	57	g	g	NOUN
ejpam-4112	284	58	)	)	PUNCT
ejpam-4112	284	59	and	and	CCONJ
ejpam-4112	284	60	c	c	PROPN
ejpam-4112	284	61	is	be	AUX
ejpam-4112	284	62	a	a	DET
ejpam-4112	284	63	superclique	superclique	NOUN
ejpam-4112	284	64	in	in	ADP
ejpam-4112	284	65	h.	h.	NOUN
ejpam-4112	284	66	proof	proof	NOUN
ejpam-4112	284	67	:	:	PUNCT
ejpam-4112	284	68	let	let	VERB
ejpam-4112	284	69	s	s	PRON
ejpam-4112	284	70	be	be	AUX
ejpam-4112	284	71	a	a	DET
ejpam-4112	284	72	restrained	restrained	ADJ
ejpam-4112	284	73	strong	strong	ADJ
ejpam-4112	284	74	resolving	resolve	VERB
ejpam-4112	284	75	dominating	dominating	NOUN
ejpam-4112	284	76	set	set	NOUN
ejpam-4112	284	77	of	of	ADP
ejpam-4112	284	78	g[h	g[h	NOUN
ejpam-4112	284	79	]	]	PUNCT
ejpam-4112	284	80	.	.	PUNCT
ejpam-4112	285	1	by	by	ADP
ejpam-4112	285	2	theorem	theorem	NOUN
ejpam-4112	285	3	6	6	NUM
ejpam-4112	285	4	,	,	PUNCT
ejpam-4112	285	5	s	s	PART
ejpam-4112	285	6	=	=	SYM
ejpam-4112	285	7	v	v	NOUN
ejpam-4112	285	8	(	(	PUNCT
ejpam-4112	285	9	g[h	g[h	PROPN
ejpam-4112	285	10	]	]	PUNCT
ejpam-4112	285	11	)	)	PUNCT
ejpam-4112	285	12	\	\	PUNCT
ejpam-4112	286	1	(	(	PUNCT
ejpam-4112	286	2	a×	a×	NOUN
ejpam-4112	286	3	c	c	X
ejpam-4112	286	4	)	)	PUNCT
ejpam-4112	286	5	where	where	SCONJ
ejpam-4112	286	6	a	a	PRON
ejpam-4112	286	7	is	be	AUX
ejpam-4112	286	8	a	a	DET
ejpam-4112	286	9	subset	subset	NOUN
ejpam-4112	286	10	of	of	ADP
ejpam-4112	286	11	v	v	NOUN
ejpam-4112	286	12	(	(	PUNCT
ejpam-4112	286	13	g	g	NOUN
ejpam-4112	286	14	)	)	PUNCT
ejpam-4112	286	15	and	and	CCONJ
ejpam-4112	286	16	c	c	NOUN
ejpam-4112	286	17	=	=	SYM
ejpam-4112	286	18	∅	∅	NOUN
ejpam-4112	286	19	or	or	CCONJ
ejpam-4112	286	20	c	c	NOUN
ejpam-4112	286	21	is	be	AUX
ejpam-4112	286	22	a	a	DET
ejpam-4112	286	23	superclique	superclique	NOUN
ejpam-4112	286	24	in	in	ADP
ejpam-4112	286	25	h.	h.	NOUN
ejpam-4112	286	26	since	since	SCONJ
ejpam-4112	286	27	s	s	PROPN
ejpam-4112	286	28	is	be	AUX
ejpam-4112	286	29	restrained	restrain	VERB
ejpam-4112	286	30	strong	strong	ADJ
ejpam-4112	286	31	resolving	resolve	VERB
ejpam-4112	286	32	dominating	dominating	NOUN
ejpam-4112	286	33	,	,	PUNCT
ejpam-4112	286	34	s	s	PART
ejpam-4112	286	35	=	=	SYM
ejpam-4112	286	36	v	v	NOUN
ejpam-4112	286	37	(	(	PUNCT
ejpam-4112	286	38	g[h	g[h	PROPN
ejpam-4112	286	39	]	]	PUNCT
ejpam-4112	286	40	)	)	PUNCT
ejpam-4112	286	41	or	or	CCONJ
ejpam-4112	286	42	v	v	NOUN
ejpam-4112	286	43	(	(	PUNCT
ejpam-4112	286	44	g[h	g[h	PROPN
ejpam-4112	286	45	]	]	PUNCT
ejpam-4112	286	46	)	)	PUNCT
ejpam-4112	286	47	\	\	PROPN
ejpam-4112	287	1	s	s	PART
ejpam-4112	287	2	has	have	VERB
ejpam-4112	287	3	h.	h.	NOUN
ejpam-4112	287	4	sumaoy	sumaoy	NOUN
ejpam-4112	287	5	,	,	PUNCT
ejpam-4112	287	6	h.	h.	PROPN
ejpam-4112	287	7	rara	rara	PROPN
ejpam-4112	287	8	/	/	SYM
ejpam-4112	287	9	eur	eur	PROPN
ejpam-4112	287	10	.	.	PUNCT
ejpam-4112	288	1	j.	j.	PROPN
ejpam-4112	288	2	pure	pure	PROPN
ejpam-4112	288	3	appl	appl	PROPN
ejpam-4112	288	4	.	.	PROPN
ejpam-4112	288	5	math	math	PROPN
ejpam-4112	288	6	,	,	PUNCT
ejpam-4112	288	7	14	14	NUM
ejpam-4112	288	8	(	(	PUNCT
ejpam-4112	288	9	4	4	NUM
ejpam-4112	288	10	)	)	PUNCT
ejpam-4112	288	11	(	(	PUNCT
ejpam-4112	288	12	2021	2021	NUM
ejpam-4112	288	13	)	)	PUNCT
ejpam-4112	288	14	,	,	PUNCT
ejpam-4112	288	15	1367	1367	NUM
ejpam-4112	288	16	-	-	SYM
ejpam-4112	288	17	1378	1378	NUM
ejpam-4112	288	18	1376	1376	NUM
ejpam-4112	288	19	no	no	DET
ejpam-4112	288	20	isolated	isolated	ADJ
ejpam-4112	288	21	vertex	vertex	NOUN
ejpam-4112	288	22	.	.	PUNCT
ejpam-4112	289	1	if	if	SCONJ
ejpam-4112	289	2	s	s	VERB
ejpam-4112	289	3	=	=	SYM
ejpam-4112	289	4	v	v	NOUN
ejpam-4112	289	5	(	(	PUNCT
ejpam-4112	289	6	g[h	g[h	PROPN
ejpam-4112	289	7	]	]	PUNCT
ejpam-4112	289	8	)	)	PUNCT
ejpam-4112	289	9	then	then	ADV
ejpam-4112	289	10	a×c	a×c	ADP
ejpam-4112	289	11	=	=	PUNCT
ejpam-4112	289	12	∅	∅	NOUN
ejpam-4112	289	13	,	,	PUNCT
ejpam-4112	289	14	showing	show	VERB
ejpam-4112	289	15	that	that	SCONJ
ejpam-4112	289	16	a	a	DET
ejpam-4112	289	17	⊆	⊆	NUM
ejpam-4112	289	18	v	v	NOUN
ejpam-4112	289	19	(	(	PUNCT
ejpam-4112	289	20	g	g	NOUN
ejpam-4112	289	21	)	)	PUNCT
ejpam-4112	289	22	and	and	CCONJ
ejpam-4112	289	23	c	c	NOUN
ejpam-4112	289	24	=	=	PUNCT
ejpam-4112	289	25	∅.	∅.	VERB
ejpam-4112	289	26	thus	thus	ADV
ejpam-4112	289	27	,	,	PUNCT
ejpam-4112	289	28	(	(	PUNCT
ejpam-4112	289	29	i	i	NOUN
ejpam-4112	289	30	)	)	PUNCT
ejpam-4112	289	31	holds	hold	VERB
ejpam-4112	289	32	.	.	PUNCT
ejpam-4112	290	1	if	if	SCONJ
ejpam-4112	290	2	v	v	X
ejpam-4112	290	3	(	(	PUNCT
ejpam-4112	290	4	g[h	g[h	PROPN
ejpam-4112	290	5	]	]	PUNCT
ejpam-4112	290	6	)	)	PUNCT
ejpam-4112	290	7	\	\	PROPN
ejpam-4112	291	1	s	s	PART
ejpam-4112	291	2	has	have	VERB
ejpam-4112	291	3	no	no	DET
ejpam-4112	291	4	isolated	isolated	ADJ
ejpam-4112	291	5	vertex	vertex	NOUN
ejpam-4112	291	6	,	,	PUNCT
ejpam-4112	291	7	then	then	ADV
ejpam-4112	291	8	a	a	DET
ejpam-4112	291	9	×	×	NOUN
ejpam-4112	291	10	c	c	NOUN
ejpam-4112	291	11	is	be	AUX
ejpam-4112	291	12	a	a	DET
ejpam-4112	291	13	nonsingleton	nonsingleton	NOUN
ejpam-4112	291	14	dominated	dominate	VERB
ejpam-4112	291	15	superclique	superclique	NOUN
ejpam-4112	291	16	in	in	ADP
ejpam-4112	291	17	g[h	g[h	NOUN
ejpam-4112	291	18	]	]	PUNCT
ejpam-4112	291	19	.	.	PUNCT
ejpam-4112	292	1	this	this	PRON
ejpam-4112	292	2	implies	imply	VERB
ejpam-4112	292	3	that	that	SCONJ
ejpam-4112	292	4	a	a	PRON
ejpam-4112	292	5	is	be	AUX
ejpam-4112	292	6	a	a	DET
ejpam-4112	292	7	singleton	singleton	NOUN
ejpam-4112	292	8	subset	subset	NOUN
ejpam-4112	292	9	of	of	ADP
ejpam-4112	292	10	v	v	PROPN
ejpam-4112	292	11	(	(	PUNCT
ejpam-4112	292	12	g	g	NOUN
ejpam-4112	292	13	)	)	PUNCT
ejpam-4112	292	14	and	and	CCONJ
ejpam-4112	292	15	c	c	PROPN
ejpam-4112	292	16	is	be	AUX
ejpam-4112	292	17	a	a	DET
ejpam-4112	292	18	nonsingleton	nonsingleton	NOUN
ejpam-4112	292	19	superclique	superclique	NOUN
ejpam-4112	292	20	in	in	ADP
ejpam-4112	292	21	h	h	NOUN
ejpam-4112	292	22	or	or	CCONJ
ejpam-4112	292	23	a	a	PRON
ejpam-4112	292	24	is	be	AUX
ejpam-4112	292	25	nonempty	nonempty	ADJ
ejpam-4112	292	26	nonsingleton	nonsingleton	NOUN
ejpam-4112	292	27	subset	subset	NOUN
ejpam-4112	292	28	of	of	ADP
ejpam-4112	292	29	v	v	NOUN
ejpam-4112	292	30	(	(	PUNCT
ejpam-4112	292	31	g	g	NOUN
ejpam-4112	292	32	)	)	PUNCT
ejpam-4112	292	33	and	and	CCONJ
ejpam-4112	292	34	c	c	PROPN
ejpam-4112	292	35	is	be	AUX
ejpam-4112	292	36	a	a	DET
ejpam-4112	292	37	superclique	superclique	NOUN
ejpam-4112	292	38	in	in	ADP
ejpam-4112	292	39	h.	h.	PROPN
ejpam-4112	292	40	hence	hence	ADV
ejpam-4112	292	41	(	(	PUNCT
ejpam-4112	292	42	ii	ii	NOUN
ejpam-4112	292	43	)	)	PUNCT
ejpam-4112	292	44	or	or	CCONJ
ejpam-4112	292	45	(	(	PUNCT
ejpam-4112	292	46	iii	iii	NOUN
ejpam-4112	292	47	)	)	PUNCT
ejpam-4112	292	48	holds	hold	VERB
ejpam-4112	292	49	.	.	PUNCT
ejpam-4112	293	1	for	for	ADP
ejpam-4112	293	2	the	the	DET
ejpam-4112	293	3	converse	converse	NOUN
ejpam-4112	293	4	,	,	PUNCT
ejpam-4112	293	5	suppose	suppose	VERB
ejpam-4112	293	6	s	s	VERB
ejpam-4112	293	7	=	=	SYM
ejpam-4112	293	8	v	v	PROPN
ejpam-4112	293	9	(	(	PUNCT
ejpam-4112	293	10	g[h	g[h	PROPN
ejpam-4112	293	11	]	]	PUNCT
ejpam-4112	293	12	)	)	PUNCT
ejpam-4112	293	13	\	\	PUNCT
ejpam-4112	294	1	(	(	PUNCT
ejpam-4112	294	2	a	a	DET
ejpam-4112	294	3	×	×	NOUN
ejpam-4112	294	4	c	c	NOUN
ejpam-4112	294	5	)	)	PUNCT
ejpam-4112	294	6	,	,	PUNCT
ejpam-4112	294	7	where	where	SCONJ
ejpam-4112	294	8	a	a	PRON
ejpam-4112	294	9	and	and	CCONJ
ejpam-4112	294	10	c	c	NOUN
ejpam-4112	294	11	satisfy	satisfy	NOUN
ejpam-4112	294	12	(	(	PUNCT
ejpam-4112	294	13	i),(ii	i),(ii	PROPN
ejpam-4112	294	14	)	)	PUNCT
ejpam-4112	294	15	or	or	CCONJ
ejpam-4112	294	16	(	(	PUNCT
ejpam-4112	294	17	iii	iii	NOUN
ejpam-4112	294	18	)	)	PUNCT
ejpam-4112	294	19	.	.	PUNCT
ejpam-4112	295	1	then	then	ADV
ejpam-4112	295	2	,	,	PUNCT
ejpam-4112	295	3	either	either	CCONJ
ejpam-4112	295	4	a	a	DET
ejpam-4112	295	5	×	×	NOUN
ejpam-4112	295	6	c	c	NOUN
ejpam-4112	295	7	=	=	NOUN
ejpam-4112	295	8	∅	∅	NOUN
ejpam-4112	295	9	or	or	CCONJ
ejpam-4112	295	10	by	by	ADP
ejpam-4112	295	11	lemma	lemma	PROPN
ejpam-4112	295	12	2	2	NUM
ejpam-4112	295	13	,	,	PUNCT
ejpam-4112	295	14	a	a	DET
ejpam-4112	295	15	×	×	NOUN
ejpam-4112	295	16	c	c	NOUN
ejpam-4112	295	17	is	be	AUX
ejpam-4112	295	18	a	a	DET
ejpam-4112	295	19	nonsingleton	nonsingleton	NOUN
ejpam-4112	295	20	dominated	dominate	VERB
ejpam-4112	295	21	superclique	superclique	NOUN
ejpam-4112	295	22	in	in	ADP
ejpam-4112	295	23	g[h	g[h	NOUN
ejpam-4112	295	24	]	]	PUNCT
ejpam-4112	295	25	.	.	PUNCT
ejpam-4112	296	1	by	by	ADP
ejpam-4112	296	2	theorem	theorem	NOUN
ejpam-4112	296	3	6	6	NUM
ejpam-4112	296	4	,	,	PUNCT
ejpam-4112	296	5	s	s	VERB
ejpam-4112	296	6	is	be	AUX
ejpam-4112	296	7	a	a	DET
ejpam-4112	296	8	strong	strong	ADJ
ejpam-4112	296	9	resolving	resolving	NOUN
ejpam-4112	296	10	set	set	VERB
ejpam-4112	296	11	in	in	ADP
ejpam-4112	296	12	g[h	g[h	NOUN
ejpam-4112	296	13	]	]	PUNCT
ejpam-4112	296	14	.	.	PUNCT
ejpam-4112	297	1	since	since	SCONJ
ejpam-4112	297	2	a×c	a×c	PROPN
ejpam-4112	297	3	is	be	AUX
ejpam-4112	297	4	a	a	DET
ejpam-4112	297	5	dominated	dominate	VERB
ejpam-4112	297	6	superclique	superclique	NOUN
ejpam-4112	297	7	,	,	PUNCT
ejpam-4112	297	8	s	s	PART
ejpam-4112	297	9	is	be	AUX
ejpam-4112	297	10	a	a	DET
ejpam-4112	297	11	strong	strong	ADJ
ejpam-4112	297	12	resolving	resolving	NOUN
ejpam-4112	297	13	dominating	dominating	NOUN
ejpam-4112	297	14	set	set	NOUN
ejpam-4112	297	15	of	of	ADP
ejpam-4112	297	16	g[h	g[h	NOUN
ejpam-4112	297	17	]	]	PUNCT
ejpam-4112	297	18	.	.	PUNCT
ejpam-4112	298	1	if	if	SCONJ
ejpam-4112	298	2	(	(	PUNCT
ejpam-4112	298	3	i	i	NOUN
ejpam-4112	298	4	)	)	PUNCT
ejpam-4112	298	5	is	be	AUX
ejpam-4112	298	6	true	true	ADJ
ejpam-4112	298	7	,	,	PUNCT
ejpam-4112	298	8	then	then	ADV
ejpam-4112	298	9	a	a	DET
ejpam-4112	298	10	⊆	⊆	NUM
ejpam-4112	298	11	v	v	NOUN
ejpam-4112	298	12	(	(	PUNCT
ejpam-4112	298	13	g	g	NOUN
ejpam-4112	298	14	)	)	PUNCT
ejpam-4112	298	15	and	and	CCONJ
ejpam-4112	298	16	c	c	NOUN
ejpam-4112	298	17	=	=	SYM
ejpam-4112	298	18	∅	∅	NOUN
ejpam-4112	298	19	,	,	PUNCT
ejpam-4112	298	20	that	that	ADV
ejpam-4112	298	21	is	is	ADV
ejpam-4112	298	22	,	,	PUNCT
ejpam-4112	298	23	a	a	DET
ejpam-4112	298	24	×	×	NOUN
ejpam-4112	298	25	c	c	NOUN
ejpam-4112	298	26	=	=	NOUN
ejpam-4112	298	27	∅	∅	NOUN
ejpam-4112	298	28	and	and	CCONJ
ejpam-4112	298	29	s	s	NOUN
ejpam-4112	298	30	=	=	SYM
ejpam-4112	298	31	v	v	PROPN
ejpam-4112	298	32	(	(	PUNCT
ejpam-4112	298	33	g[h	g[h	PROPN
ejpam-4112	298	34	]	]	PUNCT
ejpam-4112	298	35	)	)	PUNCT
ejpam-4112	298	36	.	.	PUNCT
ejpam-4112	299	1	if	if	SCONJ
ejpam-4112	299	2	(	(	PUNCT
ejpam-4112	299	3	ii	ii	NOUN
ejpam-4112	299	4	)	)	PUNCT
ejpam-4112	299	5	or	or	CCONJ
ejpam-4112	299	6	(	(	PUNCT
ejpam-4112	299	7	iii	iii	X
ejpam-4112	299	8	)	)	PUNCT
ejpam-4112	299	9	is	be	AUX
ejpam-4112	299	10	satisfied	satisfied	ADJ
ejpam-4112	299	11	,	,	PUNCT
ejpam-4112	299	12	then	then	ADV
ejpam-4112	299	13	v	v	X
ejpam-4112	299	14	(	(	PUNCT
ejpam-4112	299	15	g[h	g[h	PROPN
ejpam-4112	299	16	]	]	PUNCT
ejpam-4112	299	17	)	)	PUNCT
ejpam-4112	299	18	\	\	PROPN
ejpam-4112	300	1	s	s	PART
ejpam-4112	300	2	has	have	VERB
ejpam-4112	300	3	no	no	DET
ejpam-4112	300	4	isolated	isolated	ADJ
ejpam-4112	300	5	vertex	vertex	NOUN
ejpam-4112	300	6	.	.	PUNCT
ejpam-4112	301	1	therefore	therefore	ADV
ejpam-4112	301	2	,	,	PUNCT
ejpam-4112	301	3	s	s	VERB
ejpam-4112	301	4	is	be	AUX
ejpam-4112	301	5	a	a	DET
ejpam-4112	301	6	restrained	restrained	ADJ
ejpam-4112	301	7	strong	strong	ADJ
ejpam-4112	301	8	resolving	resolve	VERB
ejpam-4112	301	9	dominating	dominate	VERB
ejpam-4112	301	10	set	set	VERB
ejpam-4112	301	11	g[h	g[h	PROPN
ejpam-4112	301	12	]	]	PUNCT
ejpam-4112	301	13	.	.	PUNCT
ejpam-4112	302	1	lemma	lemma	PROPN
ejpam-4112	302	2	3	3	X
ejpam-4112	302	3	.	.	PUNCT
ejpam-4112	303	1	let	let	VERB
ejpam-4112	303	2	g	g	PROPN
ejpam-4112	303	3	=	=	PROPN
ejpam-4112	303	4	kn	kn	PROPN
ejpam-4112	303	5	for	for	ADP
ejpam-4112	303	6	n	n	PROPN
ejpam-4112	303	7	>	>	SYM
ejpam-4112	303	8	1	1	NUM
ejpam-4112	303	9	and	and	CCONJ
ejpam-4112	303	10	h	h	DET
ejpam-4112	303	11	a	a	DET
ejpam-4112	303	12	nontrivial	nontrivial	ADJ
ejpam-4112	303	13	connected	connect	VERB
ejpam-4112	303	14	graph	graph	NOUN
ejpam-4112	303	15	with	with	ADP
ejpam-4112	303	16	γ(h	γ(h	NOUN
ejpam-4112	303	17	)	)	PUNCT
ejpam-4112	303	18	=	=	SYM
ejpam-4112	304	1	1	1	X
ejpam-4112	304	2	.	.	PUNCT
ejpam-4112	305	1	then	then	ADV
ejpam-4112	305	2	a×c	a×c	PROPN
ejpam-4112	305	3	⊆	⊆	NUM
ejpam-4112	305	4	v	v	NOUN
ejpam-4112	305	5	(	(	PUNCT
ejpam-4112	305	6	g[h	g[h	PROPN
ejpam-4112	305	7	]	]	PUNCT
ejpam-4112	305	8	)	)	PUNCT
ejpam-4112	305	9	is	be	AUX
ejpam-4112	305	10	a	a	DET
ejpam-4112	305	11	dominated	dominate	VERB
ejpam-4112	305	12	superclique	superclique	NOUN
ejpam-4112	305	13	of	of	ADP
ejpam-4112	305	14	g[h	g[h	NOUN
ejpam-4112	305	15	]	]	PUNCT
ejpam-4112	306	1	if	if	SCONJ
ejpam-4112	307	1	and	and	CCONJ
ejpam-4112	307	2	only	only	ADV
ejpam-4112	307	3	if	if	SCONJ
ejpam-4112	307	4	a	a	PRON
ejpam-4112	307	5	is	be	AUX
ejpam-4112	307	6	a	a	DET
ejpam-4112	307	7	nonempty	nonempty	ADJ
ejpam-4112	307	8	subset	subset	NOUN
ejpam-4112	307	9	of	of	ADP
ejpam-4112	307	10	v	v	NOUN
ejpam-4112	307	11	(	(	PUNCT
ejpam-4112	307	12	g	g	NOUN
ejpam-4112	307	13	)	)	PUNCT
ejpam-4112	307	14	and	and	CCONJ
ejpam-4112	307	15	c	c	PROPN
ejpam-4112	307	16	is	be	AUX
ejpam-4112	307	17	a	a	DET
ejpam-4112	307	18	superclique	superclique	NOUN
ejpam-4112	307	19	in	in	ADP
ejpam-4112	307	20	h	h	NOUN
ejpam-4112	307	21	such	such	ADJ
ejpam-4112	307	22	that	that	DET
ejpam-4112	307	23	|a|	|a|	PROPN
ejpam-4112	307	24	=	=	SYM
ejpam-4112	307	25	1	1	NUM
ejpam-4112	307	26	whenever	whenever	SCONJ
ejpam-4112	307	27	c	c	X
ejpam-4112	307	28	∩	∩	ADJ
ejpam-4112	307	29	c∗	c∗	PROPN
ejpam-4112	307	30	̸=	̸=	PROPN
ejpam-4112	307	31	∅	∅	NOUN
ejpam-4112	307	32	for	for	ADP
ejpam-4112	307	33	some	some	DET
ejpam-4112	307	34	γ	γ	NOUN
ejpam-4112	307	35	-	-	PUNCT
ejpam-4112	307	36	set	set	ADJ
ejpam-4112	307	37	c∗	c∗	NOUN
ejpam-4112	307	38	of	of	ADP
ejpam-4112	307	39	h.	h.	PROPN
ejpam-4112	307	40	proof	proof	NOUN
ejpam-4112	307	41	:	:	PUNCT
ejpam-4112	307	42	suppose	suppose	VERB
ejpam-4112	307	43	a×c	a×c	PROPN
ejpam-4112	307	44	⊆	⊆	NUM
ejpam-4112	307	45	v	v	NOUN
ejpam-4112	307	46	(	(	PUNCT
ejpam-4112	307	47	g[h	g[h	PROPN
ejpam-4112	307	48	]	]	PUNCT
ejpam-4112	307	49	)	)	PUNCT
ejpam-4112	307	50	is	be	AUX
ejpam-4112	307	51	a	a	DET
ejpam-4112	307	52	dominated	dominate	VERB
ejpam-4112	307	53	superclique	superclique	NOUN
ejpam-4112	307	54	in	in	ADP
ejpam-4112	307	55	g[h	g[h	NOUN
ejpam-4112	307	56	]	]	PUNCT
ejpam-4112	307	57	.	.	PUNCT
ejpam-4112	308	1	then	then	ADV
ejpam-4112	308	2	a×c	a×c	PROPN
ejpam-4112	308	3	̸=	̸=	PROPN
ejpam-4112	308	4	∅.	∅.	ADV
ejpam-4112	308	5	by	by	ADP
ejpam-4112	308	6	a	a	DET
ejpam-4112	308	7	lemma	lemma	PROPN
ejpam-4112	308	8	in	in	ADP
ejpam-4112	308	9	[	[	PUNCT
ejpam-4112	308	10	3	3	NUM
ejpam-4112	308	11	]	]	PUNCT
ejpam-4112	308	12	,	,	PUNCT
ejpam-4112	308	13	a	a	PRON
ejpam-4112	308	14	is	be	AUX
ejpam-4112	308	15	a	a	DET
ejpam-4112	308	16	nonempty	nonempty	ADJ
ejpam-4112	308	17	subset	subset	NOUN
ejpam-4112	308	18	of	of	ADP
ejpam-4112	308	19	v	v	NOUN
ejpam-4112	308	20	(	(	PUNCT
ejpam-4112	308	21	g	g	NOUN
ejpam-4112	308	22	)	)	PUNCT
ejpam-4112	308	23	and	and	CCONJ
ejpam-4112	308	24	c	c	PROPN
ejpam-4112	308	25	is	be	AUX
ejpam-4112	308	26	a	a	DET
ejpam-4112	308	27	superclique	superclique	NOUN
ejpam-4112	308	28	in	in	ADP
ejpam-4112	308	29	h	h	NOUN
ejpam-4112	308	30	such	such	ADJ
ejpam-4112	308	31	that	that	DET
ejpam-4112	308	32	|a|	|a|	PROPN
ejpam-4112	308	33	=	=	SYM
ejpam-4112	308	34	1	1	NUM
ejpam-4112	308	35	whenever	whenever	SCONJ
ejpam-4112	308	36	c	c	X
ejpam-4112	308	37	∩	∩	ADJ
ejpam-4112	308	38	c∗	c∗	PROPN
ejpam-4112	308	39	̸=	̸=	PROPN
ejpam-4112	308	40	∅	∅	NOUN
ejpam-4112	308	41	for	for	ADP
ejpam-4112	308	42	some	some	DET
ejpam-4112	308	43	γ	γ	NOUN
ejpam-4112	308	44	-	-	PUNCT
ejpam-4112	308	45	set	set	ADJ
ejpam-4112	308	46	c∗	c∗	NOUN
ejpam-4112	308	47	of	of	ADP
ejpam-4112	308	48	h.	h.	NOUN
ejpam-4112	308	49	conversely	conversely	ADV
ejpam-4112	308	50	,	,	PUNCT
ejpam-4112	308	51	suppose	suppose	VERB
ejpam-4112	308	52	a	a	DET
ejpam-4112	308	53	⊆	⊆	NUM
ejpam-4112	308	54	v	v	NOUN
ejpam-4112	308	55	(	(	PUNCT
ejpam-4112	308	56	g	g	NOUN
ejpam-4112	308	57	)	)	PUNCT
ejpam-4112	308	58	and	and	CCONJ
ejpam-4112	308	59	a	a	DET
ejpam-4112	308	60	̸=	̸=	PROPN
ejpam-4112	308	61	∅	∅	NOUN
ejpam-4112	308	62	and	and	CCONJ
ejpam-4112	308	63	c	c	NOUN
ejpam-4112	308	64	is	be	AUX
ejpam-4112	308	65	a	a	DET
ejpam-4112	308	66	superclique	superclique	NOUN
ejpam-4112	308	67	in	in	ADP
ejpam-4112	308	68	h	h	NOUN
ejpam-4112	308	69	such	such	ADJ
ejpam-4112	308	70	that	that	DET
ejpam-4112	308	71	|a|	|a|	PROPN
ejpam-4112	308	72	=	=	SYM
ejpam-4112	308	73	1	1	NUM
ejpam-4112	308	74	whenever	whenever	SCONJ
ejpam-4112	308	75	c	c	X
ejpam-4112	308	76	∩	∩	ADJ
ejpam-4112	308	77	c∗	c∗	PROPN
ejpam-4112	308	78	̸=	̸=	PROPN
ejpam-4112	308	79	∅	∅	NOUN
ejpam-4112	308	80	for	for	ADP
ejpam-4112	308	81	some	some	DET
ejpam-4112	308	82	γ	γ	NOUN
ejpam-4112	308	83	-	-	PUNCT
ejpam-4112	308	84	set	set	ADJ
ejpam-4112	308	85	c∗	c∗	NOUN
ejpam-4112	308	86	of	of	ADP
ejpam-4112	308	87	h.	h.	PROPN
ejpam-4112	308	88	then	then	ADV
ejpam-4112	308	89	by	by	ADP
ejpam-4112	308	90	a	a	DET
ejpam-4112	308	91	lemma	lemma	PROPN
ejpam-4112	308	92	in	in	ADP
ejpam-4112	308	93	[	[	PUNCT
ejpam-4112	308	94	3	3	NUM
ejpam-4112	308	95	]	]	PUNCT
ejpam-4112	308	96	,	,	PUNCT
ejpam-4112	308	97	a	a	DET
ejpam-4112	308	98	×	×	NOUN
ejpam-4112	308	99	c	c	NOUN
ejpam-4112	308	100	is	be	AUX
ejpam-4112	308	101	a	a	DET
ejpam-4112	308	102	superclique	superclique	NOUN
ejpam-4112	308	103	in	in	ADP
ejpam-4112	308	104	g[h	g[h	NOUN
ejpam-4112	308	105	]	]	PUNCT
ejpam-4112	308	106	.	.	PUNCT
ejpam-4112	309	1	we	we	PRON
ejpam-4112	309	2	show	show	VERB
ejpam-4112	309	3	that	that	SCONJ
ejpam-4112	309	4	a	a	DET
ejpam-4112	309	5	×	×	NOUN
ejpam-4112	309	6	c	c	NOUN
ejpam-4112	309	7	is	be	AUX
ejpam-4112	309	8	a	a	DET
ejpam-4112	309	9	dominated	dominate	VERB
ejpam-4112	309	10	superclique	superclique	NOUN
ejpam-4112	309	11	in	in	ADP
ejpam-4112	309	12	g[h	g[h	NOUN
ejpam-4112	309	13	]	]	PUNCT
ejpam-4112	309	14	.	.	PUNCT
ejpam-4112	310	1	let	let	VERB
ejpam-4112	310	2	(	(	PUNCT
ejpam-4112	310	3	a	a	PRON
ejpam-4112	310	4	,	,	PUNCT
ejpam-4112	310	5	b	b	NOUN
ejpam-4112	310	6	)	)	PUNCT
ejpam-4112	310	7	∈	∈	PROPN
ejpam-4112	310	8	a	a	DET
ejpam-4112	310	9	×	×	NOUN
ejpam-4112	310	10	c.	c.	NOUN
ejpam-4112	310	11	then	then	ADV
ejpam-4112	310	12	a	a	DET
ejpam-4112	310	13	∈	∈	PROPN
ejpam-4112	310	14	a	a	DET
ejpam-4112	310	15	and	and	CCONJ
ejpam-4112	310	16	b	b	PROPN
ejpam-4112	310	17	∈	∈	PROPN
ejpam-4112	310	18	c.	c.	NOUN
ejpam-4112	310	19	if	if	SCONJ
ejpam-4112	310	20	c	c	PROPN
ejpam-4112	310	21	∩	∩	ADJ
ejpam-4112	310	22	c∗	c∗	NOUN
ejpam-4112	310	23	=	=	NOUN
ejpam-4112	310	24	∅	∅	NOUN
ejpam-4112	310	25	for	for	ADP
ejpam-4112	310	26	all	all	DET
ejpam-4112	310	27	γ	γ	PROPN
ejpam-4112	310	28	-	-	PUNCT
ejpam-4112	310	29	set	set	ADJ
ejpam-4112	310	30	c∗	c∗	NOUN
ejpam-4112	310	31	of	of	ADP
ejpam-4112	310	32	h	h	NOUN
ejpam-4112	310	33	,	,	PUNCT
ejpam-4112	310	34	then	then	ADV
ejpam-4112	310	35	there	there	PRON
ejpam-4112	310	36	exists	exist	VERB
ejpam-4112	310	37	d	d	X
ejpam-4112	310	38	∈	∈	PROPN
ejpam-4112	310	39	v	v	ADP
ejpam-4112	310	40	(	(	PUNCT
ejpam-4112	310	41	h	h	NOUN
ejpam-4112	310	42	)	)	PUNCT
ejpam-4112	310	43	\nh(b	\nh(b	NUM
ejpam-4112	310	44	)	)	PUNCT
ejpam-4112	310	45	.	.	PUNCT
ejpam-4112	311	1	thus	thus	ADV
ejpam-4112	311	2	,	,	PUNCT
ejpam-4112	311	3	d	d	PROPN
ejpam-4112	311	4	/∈	/∈	PROPN
ejpam-4112	311	5	c.	c.	NOUN
ejpam-4112	311	6	since	since	SCONJ
ejpam-4112	311	7	g	g	PROPN
ejpam-4112	311	8	=	=	PROPN
ejpam-4112	311	9	kn	kn	PROPN
ejpam-4112	311	10	for	for	ADP
ejpam-4112	311	11	n	n	PROPN
ejpam-4112	311	12	>	>	X
ejpam-4112	311	13	1	1	NUM
ejpam-4112	311	14	,	,	PUNCT
ejpam-4112	311	15	a	a	DET
ejpam-4112	311	16	vertex	vertex	NOUN
ejpam-4112	311	17	y	y	PROPN
ejpam-4112	311	18	∈	∈	PROPN
ejpam-4112	311	19	(	(	PUNCT
ejpam-4112	311	20	v	v	NOUN
ejpam-4112	311	21	(	(	PUNCT
ejpam-4112	311	22	kn	kn	PROPN
ejpam-4112	311	23	)	)	PUNCT
ejpam-4112	311	24	\	\	PROPN
ejpam-4112	311	25	{	{	PUNCT
ejpam-4112	311	26	a	a	NOUN
ejpam-4112	311	27	}	}	PUNCT
ejpam-4112	311	28	)	)	PUNCT
ejpam-4112	311	29	∪ng(a	∪ng(a	PROPN
ejpam-4112	311	30	)	)	PUNCT
ejpam-4112	311	31	exists	exist	VERB
ejpam-4112	311	32	.	.	PUNCT
ejpam-4112	312	1	this	this	PRON
ejpam-4112	312	2	implies	imply	VERB
ejpam-4112	312	3	that	that	SCONJ
ejpam-4112	312	4	(	(	PUNCT
ejpam-4112	312	5	y	y	NOUN
ejpam-4112	312	6	,	,	PUNCT
ejpam-4112	312	7	d	d	NOUN
ejpam-4112	312	8	)	)	PUNCT
ejpam-4112	312	9	∈	∈	PROPN
ejpam-4112	313	1	[	[	X
ejpam-4112	313	2	v	v	X
ejpam-4112	313	3	(	(	PUNCT
ejpam-4112	313	4	g[h	g[h	PROPN
ejpam-4112	313	5	]	]	PUNCT
ejpam-4112	313	6	)	)	PUNCT
ejpam-4112	313	7	\	\	PUNCT
ejpam-4112	314	1	(	(	PUNCT
ejpam-4112	314	2	a×	a×	NOUN
ejpam-4112	314	3	c	c	NOUN
ejpam-4112	314	4	)	)	PUNCT
ejpam-4112	314	5	]	]	PUNCT
ejpam-4112	315	1	∩ng[h]((a	∩ng[h]((a	PROPN
ejpam-4112	315	2	,	,	PUNCT
ejpam-4112	315	3	b	b	NOUN
ejpam-4112	315	4	)	)	PUNCT
ejpam-4112	315	5	)	)	PUNCT
ejpam-4112	315	6	.	.	PUNCT
ejpam-4112	316	1	suppose	suppose	VERB
ejpam-4112	316	2	,	,	PUNCT
ejpam-4112	316	3	that	that	SCONJ
ejpam-4112	316	4	c	c	PROPN
ejpam-4112	316	5	∩	∩	ADJ
ejpam-4112	316	6	c∗	c∗	PROPN
ejpam-4112	316	7	̸=	̸=	PROPN
ejpam-4112	316	8	∅	∅	NOUN
ejpam-4112	316	9	for	for	ADP
ejpam-4112	316	10	some	some	DET
ejpam-4112	316	11	γ	γ	NOUN
ejpam-4112	316	12	-	-	PUNCT
ejpam-4112	316	13	set	set	ADJ
ejpam-4112	316	14	c∗	c∗	NOUN
ejpam-4112	316	15	of	of	ADP
ejpam-4112	316	16	h.	h.	PROPN
ejpam-4112	316	17	then	then	ADV
ejpam-4112	316	18	|a|	|a|	PROPN
ejpam-4112	316	19	=	=	SYM
ejpam-4112	316	20	1	1	X
ejpam-4112	316	21	.	.	PUNCT
ejpam-4112	317	1	let	let	VERB
ejpam-4112	317	2	w	w	PROPN
ejpam-4112	317	3	∈	∈	PROPN
ejpam-4112	317	4	a	a	PRON
ejpam-4112	317	5	and	and	CCONJ
ejpam-4112	317	6	p	p	NOUN
ejpam-4112	317	7	∈	∈	PROPN
ejpam-4112	317	8	c	c	NOUN
ejpam-4112	317	9	∩	∩	X
ejpam-4112	317	10	c∗.	c∗.	NOUN
ejpam-4112	317	11	since	since	SCONJ
ejpam-4112	317	12	g	g	PROPN
ejpam-4112	317	13	=	=	PROPN
ejpam-4112	317	14	kn	kn	PROPN
ejpam-4112	317	15	for	for	ADP
ejpam-4112	317	16	n	n	PROPN
ejpam-4112	317	17	>	>	X
ejpam-4112	317	18	1	1	NUM
ejpam-4112	317	19	,	,	PUNCT
ejpam-4112	317	20	there	there	PRON
ejpam-4112	317	21	exists	exist	VERB
ejpam-4112	317	22	u	u	PROPN
ejpam-4112	317	23	∈	∈	PROPN
ejpam-4112	317	24	(	(	PUNCT
ejpam-4112	317	25	v	v	NOUN
ejpam-4112	317	26	(	(	PUNCT
ejpam-4112	317	27	kn	kn	PROPN
ejpam-4112	317	28	)	)	PUNCT
ejpam-4112	317	29	\	\	PROPN
ejpam-4112	317	30	{	{	PUNCT
ejpam-4112	317	31	w	w	NOUN
ejpam-4112	317	32	}	}	PUNCT
ejpam-4112	317	33	)	)	PUNCT
ejpam-4112	317	34	∩ng(w	∩ng(w	PROPN
ejpam-4112	317	35	)	)	PUNCT
ejpam-4112	317	36	and	and	CCONJ
ejpam-4112	317	37	(	(	PUNCT
ejpam-4112	317	38	u	u	NOUN
ejpam-4112	317	39	,	,	PUNCT
ejpam-4112	317	40	v	v	NOUN
ejpam-4112	317	41	)	)	PUNCT
ejpam-4112	317	42	/∈	/∈	PUNCT
ejpam-4112	318	1	(	(	PUNCT
ejpam-4112	318	2	a×	a×	NOUN
ejpam-4112	318	3	c	c	X
ejpam-4112	318	4	)	)	PUNCT
ejpam-4112	318	5	for	for	ADP
ejpam-4112	318	6	all	all	PRON
ejpam-4112	318	7	v	v	ADP
ejpam-4112	318	8	∈	∈	NOUN
ejpam-4112	318	9	v	v	NOUN
ejpam-4112	318	10	(	(	PUNCT
ejpam-4112	318	11	h	h	NOUN
ejpam-4112	318	12	)	)	PUNCT
ejpam-4112	318	13	.	.	PUNCT
ejpam-4112	319	1	thus	thus	ADV
ejpam-4112	319	2	,	,	PUNCT
ejpam-4112	319	3	(	(	PUNCT
ejpam-4112	319	4	w	w	NOUN
ejpam-4112	319	5	,	,	PUNCT
ejpam-4112	319	6	p)(u	p)(u	ADJ
ejpam-4112	319	7	,	,	PUNCT
ejpam-4112	319	8	v	v	NOUN
ejpam-4112	319	9	)	)	PUNCT
ejpam-4112	319	10	∈	∈	NOUN
ejpam-4112	319	11	e(g[h	e(g[h	NOUN
ejpam-4112	319	12	]	]	PUNCT
ejpam-4112	319	13	)	)	PUNCT
ejpam-4112	319	14	.	.	PUNCT
ejpam-4112	320	1	therefore	therefore	ADV
ejpam-4112	320	2	a×	a×	PROPN
ejpam-4112	320	3	c	c	PROPN
ejpam-4112	320	4	is	be	AUX
ejpam-4112	320	5	a	a	DET
ejpam-4112	320	6	dominated	dominate	VERB
ejpam-4112	320	7	superclique	superclique	NOUN
ejpam-4112	320	8	in	in	ADP
ejpam-4112	320	9	g[h	g[h	PROPN
ejpam-4112	320	10	]	]	PUNCT
ejpam-4112	320	11	.	.	PUNCT
ejpam-4112	321	1	using	use	VERB
ejpam-4112	321	2	lemma	lemma	PROPN
ejpam-4112	321	3	3	3	NUM
ejpam-4112	321	4	,	,	PUNCT
ejpam-4112	321	5	the	the	DET
ejpam-4112	321	6	proof	proof	NOUN
ejpam-4112	321	7	of	of	ADP
ejpam-4112	321	8	the	the	DET
ejpam-4112	321	9	next	next	ADJ
ejpam-4112	321	10	result	result	NOUN
ejpam-4112	321	11	will	will	AUX
ejpam-4112	321	12	just	just	ADV
ejpam-4112	321	13	be	be	AUX
ejpam-4112	321	14	similar	similar	ADJ
ejpam-4112	321	15	to	to	ADP
ejpam-4112	321	16	that	that	PRON
ejpam-4112	321	17	of	of	ADP
ejpam-4112	321	18	theorem	theorem	ADJ
ejpam-4112	321	19	12	12	NUM
ejpam-4112	321	20	.	.	PUNCT
ejpam-4112	322	1	theorem	theorem	VERB
ejpam-4112	322	2	13	13	NUM
ejpam-4112	322	3	.	.	PUNCT
ejpam-4112	323	1	let	let	VERB
ejpam-4112	323	2	g	g	PROPN
ejpam-4112	323	3	=	=	PROPN
ejpam-4112	323	4	kn	kn	PROPN
ejpam-4112	323	5	for	for	ADP
ejpam-4112	323	6	n	n	PROPN
ejpam-4112	323	7	>	>	SYM
ejpam-4112	323	8	1	1	NUM
ejpam-4112	323	9	and	and	CCONJ
ejpam-4112	323	10	h	h	DET
ejpam-4112	323	11	a	a	DET
ejpam-4112	323	12	nontrivial	nontrivial	ADJ
ejpam-4112	323	13	connected	connect	VERB
ejpam-4112	323	14	graph	graph	NOUN
ejpam-4112	323	15	with	with	ADP
ejpam-4112	323	16	γ(h	γ(h	NOUN
ejpam-4112	323	17	)	)	PUNCT
ejpam-4112	323	18	=	=	SYM
ejpam-4112	324	1	1	1	X
ejpam-4112	324	2	.	.	PUNCT
ejpam-4112	324	3	a	a	DET
ejpam-4112	324	4	subset	subset	NOUN
ejpam-4112	324	5	s	s	X
ejpam-4112	324	6	of	of	ADP
ejpam-4112	324	7	v	v	NOUN
ejpam-4112	324	8	(	(	PUNCT
ejpam-4112	324	9	g[h	g[h	PROPN
ejpam-4112	324	10	]	]	PUNCT
ejpam-4112	324	11	)	)	PUNCT
ejpam-4112	324	12	is	be	AUX
ejpam-4112	324	13	a	a	DET
ejpam-4112	324	14	restrained	restrained	ADJ
ejpam-4112	324	15	strong	strong	ADJ
ejpam-4112	324	16	resolving	resolve	VERB
ejpam-4112	324	17	dominating	dominating	NOUN
ejpam-4112	324	18	set	set	NOUN
ejpam-4112	324	19	of	of	ADP
ejpam-4112	324	20	g[h	g[h	PROPN
ejpam-4112	324	21	]	]	PUNCT
ejpam-4112	324	22	if	if	SCONJ
ejpam-4112	324	23	and	and	CCONJ
ejpam-4112	324	24	only	only	ADV
ejpam-4112	324	25	if	if	SCONJ
ejpam-4112	324	26	s	s	VERB
ejpam-4112	324	27	=	=	SYM
ejpam-4112	324	28	v	v	NOUN
ejpam-4112	324	29	(	(	PUNCT
ejpam-4112	324	30	g[h	g[h	PROPN
ejpam-4112	324	31	]	]	PUNCT
ejpam-4112	324	32	)	)	PUNCT
ejpam-4112	324	33	\	\	PUNCT
ejpam-4112	325	1	(	(	PUNCT
ejpam-4112	325	2	a×	a×	NOUN
ejpam-4112	325	3	c	c	X
ejpam-4112	325	4	)	)	PUNCT
ejpam-4112	325	5	and	and	CCONJ
ejpam-4112	325	6	one	one	NUM
ejpam-4112	325	7	of	of	ADP
ejpam-4112	325	8	the	the	DET
ejpam-4112	325	9	following	follow	VERB
ejpam-4112	325	10	is	be	AUX
ejpam-4112	325	11	satisfied	satisfied	ADJ
ejpam-4112	325	12	:	:	PUNCT
ejpam-4112	325	13	(	(	PUNCT
ejpam-4112	325	14	i	i	NOUN
ejpam-4112	325	15	)	)	PUNCT
ejpam-4112	325	16	a	a	DET
ejpam-4112	325	17	⊆	⊆	NUM
ejpam-4112	325	18	v	v	NOUN
ejpam-4112	325	19	(	(	PUNCT
ejpam-4112	325	20	g	g	NOUN
ejpam-4112	325	21	)	)	PUNCT
ejpam-4112	325	22	and	and	CCONJ
ejpam-4112	325	23	c	c	NOUN
ejpam-4112	325	24	=	=	SYM
ejpam-4112	325	25	∅	∅	NOUN
ejpam-4112	325	26	(	(	PUNCT
ejpam-4112	325	27	ii	ii	NOUN
ejpam-4112	325	28	)	)	PUNCT
ejpam-4112	325	29	a	a	PRON
ejpam-4112	325	30	is	be	AUX
ejpam-4112	325	31	nonempty	nonempty	ADJ
ejpam-4112	325	32	nonsingleton	nonsingleton	NOUN
ejpam-4112	325	33	subset	subset	NOUN
ejpam-4112	325	34	of	of	ADP
ejpam-4112	325	35	v	v	NOUN
ejpam-4112	325	36	(	(	PUNCT
ejpam-4112	325	37	g	g	NOUN
ejpam-4112	325	38	)	)	PUNCT
ejpam-4112	325	39	and	and	CCONJ
ejpam-4112	325	40	c	c	PROPN
ejpam-4112	325	41	is	be	AUX
ejpam-4112	325	42	a	a	DET
ejpam-4112	325	43	superclique	superclique	NOUN
ejpam-4112	325	44	in	in	ADP
ejpam-4112	325	45	h	h	NOUN
ejpam-4112	325	46	if	if	SCONJ
ejpam-4112	325	47	c∩c∗	c∩c∗	NUM
ejpam-4112	325	48	=	=	NOUN
ejpam-4112	325	49	∅	∅	NOUN
ejpam-4112	325	50	for	for	ADP
ejpam-4112	325	51	all	all	DET
ejpam-4112	325	52	γ	γ	PROPN
ejpam-4112	325	53	-	-	PUNCT
ejpam-4112	325	54	set	set	ADJ
ejpam-4112	325	55	c∗	c∗	NOUN
ejpam-4112	325	56	in	in	ADP
ejpam-4112	325	57	h.	h.	PROPN
ejpam-4112	325	58	references	reference	NOUN
ejpam-4112	325	59	1377	1377	NUM
ejpam-4112	325	60	(	(	PUNCT
ejpam-4112	325	61	iii	iii	NOUN
ejpam-4112	325	62	)	)	PUNCT
ejpam-4112	325	63	a	a	PRON
ejpam-4112	325	64	is	be	AUX
ejpam-4112	325	65	a	a	DET
ejpam-4112	325	66	singleton	singleton	NOUN
ejpam-4112	325	67	subset	subset	NOUN
ejpam-4112	325	68	of	of	ADP
ejpam-4112	325	69	v	v	PROPN
ejpam-4112	325	70	(	(	PUNCT
ejpam-4112	325	71	g	g	NOUN
ejpam-4112	325	72	)	)	PUNCT
ejpam-4112	325	73	and	and	CCONJ
ejpam-4112	325	74	c	c	PROPN
ejpam-4112	325	75	is	be	AUX
ejpam-4112	325	76	a	a	DET
ejpam-4112	325	77	nonsingleton	nonsingleton	NOUN
ejpam-4112	325	78	superclique	superclique	NOUN
ejpam-4112	325	79	inh	inh	NOUN
ejpam-4112	325	80	if	if	SCONJ
ejpam-4112	325	81	c∩c∗	c∩c∗	PROPN
ejpam-4112	325	82	̸=	̸=	PROPN
ejpam-4112	325	83	∅	∅	NOUN
ejpam-4112	325	84	for	for	ADP
ejpam-4112	325	85	some	some	DET
ejpam-4112	325	86	γ	γ	NOUN
ejpam-4112	325	87	-	-	PUNCT
ejpam-4112	325	88	set	set	ADJ
ejpam-4112	325	89	c∗	c∗	NOUN
ejpam-4112	325	90	of	of	ADP
ejpam-4112	325	91	h.	h.	PROPN
ejpam-4112	325	92	corollary	corollary	PROPN
ejpam-4112	325	93	7	7	PROPN
ejpam-4112	325	94	.	.	PUNCT
ejpam-4112	326	1	let	let	VERB
ejpam-4112	326	2	g	g	PROPN
ejpam-4112	326	3	=	=	PROPN
ejpam-4112	326	4	kn	kn	PROPN
ejpam-4112	326	5	for	for	ADP
ejpam-4112	326	6	n	n	PROPN
ejpam-4112	326	7	>	>	SYM
ejpam-4112	326	8	1	1	NUM
ejpam-4112	326	9	and	and	CCONJ
ejpam-4112	326	10	h	h	DET
ejpam-4112	326	11	a	a	DET
ejpam-4112	326	12	non	non	ADJ
ejpam-4112	326	13	-	-	ADJ
ejpam-4112	326	14	trivial	trivial	ADJ
ejpam-4112	326	15	connected	connected	ADJ
ejpam-4112	326	16	graph	graph	NOUN
ejpam-4112	326	17	of	of	ADP
ejpam-4112	326	18	order	order	NOUN
ejpam-4112	326	19	m.	m.	NOUN
ejpam-4112	326	20	then	then	ADV
ejpam-4112	326	21	γrsr(g[h	γrsr(g[h	VERB
ejpam-4112	326	22	]	]	PUNCT
ejpam-4112	326	23	)	)	PUNCT
ejpam-4112	326	24	=	=	SYM
ejpam-4112	327	1	mn−	mn−	NOUN
ejpam-4112	327	2	ωds(g[h	ωds(g[h	NUM
ejpam-4112	327	3	]	]	NUM
ejpam-4112	327	4	)	)	PUNCT
ejpam-4112	327	5	.	.	PUNCT
ejpam-4112	328	1	proof	proof	NOUN
ejpam-4112	328	2	:	:	PUNCT
ejpam-4112	328	3	let	let	VERB
ejpam-4112	328	4	s	s	PRON
ejpam-4112	328	5	be	be	AUX
ejpam-4112	328	6	a	a	DET
ejpam-4112	328	7	γrsr	γrsr	NOUN
ejpam-4112	328	8	-	-	PUNCT
ejpam-4112	328	9	set	set	NOUN
ejpam-4112	328	10	of	of	ADP
ejpam-4112	328	11	g[h	g[h	NOUN
ejpam-4112	328	12	]	]	PUNCT
ejpam-4112	328	13	.	.	PUNCT
ejpam-4112	329	1	then	then	ADV
ejpam-4112	329	2	s	s	VERB
ejpam-4112	329	3	is	be	AUX
ejpam-4112	329	4	a	a	DET
ejpam-4112	329	5	restrained	restrain	VERB
ejpam-4112	329	6	strong	strong	ADJ
ejpam-4112	329	7	resolving	resolve	VERB
ejpam-4112	329	8	dominating	dominating	NOUN
ejpam-4112	329	9	set	set	NOUN
ejpam-4112	329	10	of	of	ADP
ejpam-4112	329	11	g[h	g[h	NOUN
ejpam-4112	329	12	]	]	PUNCT
ejpam-4112	329	13	.	.	PUNCT
ejpam-4112	330	1	by	by	ADP
ejpam-4112	330	2	theorem	theorem	ADJ
ejpam-4112	330	3	12	12	NUM
ejpam-4112	330	4	or	or	CCONJ
ejpam-4112	330	5	theorem	theorem	VERB
ejpam-4112	330	6	13	13	NUM
ejpam-4112	330	7	,	,	PUNCT
ejpam-4112	330	8	s	s	PART
ejpam-4112	330	9	=	=	SYM
ejpam-4112	330	10	v	v	NOUN
ejpam-4112	330	11	(	(	PUNCT
ejpam-4112	330	12	g[h	g[h	PROPN
ejpam-4112	330	13	]	]	PUNCT
ejpam-4112	330	14	)	)	PUNCT
ejpam-4112	330	15	\	\	PUNCT
ejpam-4112	330	16	(	(	PUNCT
ejpam-4112	330	17	a	a	DET
ejpam-4112	330	18	×	×	NOUN
ejpam-4112	330	19	c	c	NOUN
ejpam-4112	330	20	)	)	PUNCT
ejpam-4112	330	21	where	where	SCONJ
ejpam-4112	330	22	a	a	DET
ejpam-4112	330	23	×	×	NOUN
ejpam-4112	330	24	c	c	NOUN
ejpam-4112	330	25	is	be	AUX
ejpam-4112	330	26	a	a	DET
ejpam-4112	330	27	dominated	dominate	VERB
ejpam-4112	330	28	superclique	superclique	NOUN
ejpam-4112	330	29	in	in	ADP
ejpam-4112	330	30	g[h	g[h	NOUN
ejpam-4112	330	31	]	]	PUNCT
ejpam-4112	330	32	.	.	PUNCT
ejpam-4112	331	1	since	since	SCONJ
ejpam-4112	331	2	s	s	PROPN
ejpam-4112	331	3	is	be	AUX
ejpam-4112	331	4	a	a	DET
ejpam-4112	331	5	γrsr	γrsr	ADJ
ejpam-4112	331	6	-	-	PUNCT
ejpam-4112	331	7	set	set	NOUN
ejpam-4112	331	8	,	,	PUNCT
ejpam-4112	331	9	a	a	DET
ejpam-4112	331	10	×	×	NOUN
ejpam-4112	331	11	c	c	NOUN
ejpam-4112	331	12	is	be	AUX
ejpam-4112	331	13	a	a	DET
ejpam-4112	331	14	maximum	maximum	ADV
ejpam-4112	331	15	dominated	dominate	VERB
ejpam-4112	331	16	superclique	superclique	NOUN
ejpam-4112	331	17	of	of	ADP
ejpam-4112	331	18	g[h	g[h	NOUN
ejpam-4112	331	19	]	]	PUNCT
ejpam-4112	331	20	.	.	PUNCT
ejpam-4112	332	1	hence	hence	ADV
ejpam-4112	332	2	,	,	PUNCT
ejpam-4112	332	3	γrsr(g[h	γrsr(g[h	ADP
ejpam-4112	332	4	]	]	PUNCT
ejpam-4112	332	5	)	)	PUNCT
ejpam-4112	332	6	=	=	SYM
ejpam-4112	333	1	|s|	|s|	PROPN
ejpam-4112	333	2	=	=	SYM
ejpam-4112	333	3	|v	|v	PROPN
ejpam-4112	333	4	(	(	PUNCT
ejpam-4112	333	5	g[h])|	g[h])|	PROPN
ejpam-4112	333	6	−	−	PROPN
ejpam-4112	333	7	|a×	|a×	ADJ
ejpam-4112	333	8	c|	c|	PROPN
ejpam-4112	333	9	=	=	SYM
ejpam-4112	333	10	mn−	mn−	NOUN
ejpam-4112	333	11	ωds(g[h	ωds(g[h	NUM
ejpam-4112	333	12	]	]	NUM
ejpam-4112	333	13	)	)	PUNCT
ejpam-4112	333	14	.	.	PUNCT
ejpam-4112	334	1	by	by	ADP
ejpam-4112	334	2	lemma	lemma	PROPN
ejpam-4112	334	3	2	2	PROPN
ejpam-4112	334	4	and	and	CCONJ
ejpam-4112	334	5	lemma	lemma	PROPN
ejpam-4112	334	6	3	3	NUM
ejpam-4112	334	7	,	,	PUNCT
ejpam-4112	334	8	the	the	DET
ejpam-4112	334	9	dominated	dominate	VERB
ejpam-4112	334	10	superclique	superclique	NOUN
ejpam-4112	334	11	a×	a×	PROPN
ejpam-4112	334	12	c	c	NOUN
ejpam-4112	334	13	of	of	ADP
ejpam-4112	334	14	kn[h	kn[h	PROPN
ejpam-4112	334	15	]	]	PUNCT
ejpam-4112	334	16	is	be	AUX
ejpam-4112	334	17	maximum	maximum	ADJ
ejpam-4112	334	18	if	if	SCONJ
ejpam-4112	334	19	a	a	DET
ejpam-4112	334	20	=	=	X
ejpam-4112	334	21	v	v	X
ejpam-4112	334	22	(	(	PUNCT
ejpam-4112	334	23	g	g	NOUN
ejpam-4112	334	24	)	)	PUNCT
ejpam-4112	334	25	and	and	CCONJ
ejpam-4112	334	26	c	c	PROPN
ejpam-4112	334	27	is	be	AUX
ejpam-4112	334	28	a	a	DET
ejpam-4112	334	29	maximum	maximum	ADJ
ejpam-4112	334	30	superclique	superclique	NOUN
ejpam-4112	334	31	in	in	ADP
ejpam-4112	334	32	h.	h.	PROPN
ejpam-4112	334	33	thus	thus	ADV
ejpam-4112	334	34	,	,	PUNCT
ejpam-4112	334	35	the	the	DET
ejpam-4112	334	36	next	next	ADJ
ejpam-4112	334	37	result	result	NOUN
ejpam-4112	334	38	follows	follow	VERB
ejpam-4112	334	39	.	.	PUNCT
ejpam-4112	335	1	corollary	corollary	ADJ
ejpam-4112	335	2	8	8	NUM
ejpam-4112	335	3	.	.	PUNCT
ejpam-4112	336	1	let	let	VERB
ejpam-4112	336	2	g	g	PROPN
ejpam-4112	336	3	=	=	PROPN
ejpam-4112	336	4	kn	kn	PROPN
ejpam-4112	336	5	for	for	ADP
ejpam-4112	336	6	n	n	PROPN
ejpam-4112	336	7	>	>	SYM
ejpam-4112	336	8	1	1	NUM
ejpam-4112	336	9	and	and	CCONJ
ejpam-4112	336	10	h	h	NOUN
ejpam-4112	336	11	be	be	VERB
ejpam-4112	336	12	a	a	DET
ejpam-4112	336	13	connected	connected	ADJ
ejpam-4112	336	14	graph	graph	NOUN
ejpam-4112	336	15	of	of	ADP
ejpam-4112	336	16	order	order	NOUN
ejpam-4112	336	17	m	m	VERB
ejpam-4112	336	18	>	>	X
ejpam-4112	336	19	1	1	NUM
ejpam-4112	336	20	.	.	PUNCT
ejpam-4112	336	21	then	then	ADV
ejpam-4112	336	22	γrsr(g[h	γrsr(g[h	VERB
ejpam-4112	336	23	]	]	PUNCT
ejpam-4112	336	24	)	)	PUNCT
ejpam-4112	337	1	=	=	SYM
ejpam-4112	337	2	n(m−	n(m−	PROPN
ejpam-4112	337	3	ωs(h	ωs(h	NUM
ejpam-4112	337	4	)	)	PUNCT
ejpam-4112	337	5	)	)	PUNCT
ejpam-4112	337	6	.	.	PUNCT
ejpam-4112	338	1	acknowledgements	acknowledgement	NOUN
ejpam-4112	338	2	this	this	DET
ejpam-4112	338	3	research	research	NOUN
ejpam-4112	338	4	is	be	AUX
ejpam-4112	338	5	funded	fund	VERB
ejpam-4112	338	6	by	by	ADP
ejpam-4112	338	7	the	the	DET
ejpam-4112	338	8	department	department	PROPN
ejpam-4112	338	9	of	of	ADP
ejpam-4112	338	10	science	science	NOUN
ejpam-4112	338	11	and	and	CCONJ
ejpam-4112	338	12	technology	technology	NOUN
ejpam-4112	338	13	accelerated	accelerate	VERB
ejpam-4112	338	14	science	science	NOUN
ejpam-4112	338	15	and	and	CCONJ
ejpam-4112	338	16	technology	technology	NOUN
ejpam-4112	338	17	human	human	ADJ
ejpam-4112	338	18	resource	resource	NOUN
ejpam-4112	338	19	development	development	NOUN
ejpam-4112	338	20	program	program	NOUN
ejpam-4112	338	21	(	(	PUNCT
ejpam-4112	338	22	dost	dost	NOUN
ejpam-4112	338	23	-	-	PUNCT
ejpam-4112	338	24	asthrdp	asthrdp	NOUN
ejpam-4112	338	25	)	)	PUNCT
ejpam-4112	338	26	,	,	PUNCT
ejpam-4112	338	27	philippines	philippine	NOUN
ejpam-4112	338	28	.	.	PUNCT
ejpam-4112	339	1	references	reference	NOUN
ejpam-4112	339	2	[	[	X
ejpam-4112	339	3	1	1	NUM
ejpam-4112	339	4	]	]	PUNCT
ejpam-4112	339	5	c.	c.	PROPN
ejpam-4112	339	6	berge	berge	PROPN
ejpam-4112	339	7	.	.	PUNCT
ejpam-4112	340	1	theorie	theorie	PROPN
ejpam-4112	340	2	des	des	PROPN
ejpam-4112	340	3	graphes	graphes	PROPN
ejpam-4112	340	4	et	et	PROPN
ejpam-4112	340	5	ses	ses	PROPN
ejpam-4112	340	6	applications	application	NOUN
ejpam-4112	340	7	.	.	PUNCT
ejpam-4112	341	1	metheun	metheun	NOUN
ejpam-4112	341	2	and	and	CCONJ
ejpam-4112	341	3	wiley	wiley	PROPN
ejpam-4112	341	4	,	,	PUNCT
ejpam-4112	341	5	london	london	PROPN
ejpam-4112	341	6	and	and	CCONJ
ejpam-4112	341	7	new	new	PROPN
ejpam-4112	341	8	york	york	PROPN
ejpam-4112	341	9	,	,	PUNCT
ejpam-4112	341	10	1962	1962	NUM
ejpam-4112	341	11	.	.	PUNCT
ejpam-4112	342	1	[	[	X
ejpam-4112	342	2	2	2	NUM
ejpam-4112	342	3	]	]	X
ejpam-4112	342	4	acal	acal	PROPN
ejpam-4112	342	5	p.l	p.l	PROPN
ejpam-4112	342	6	.	.	PROPN
ejpam-4112	343	1	and	and	CCONJ
ejpam-4112	343	2	rara	rara	PROPN
ejpam-4112	343	3	h.m	h.m	PROPN
ejpam-4112	343	4	.	.	PUNCT
ejpam-4112	344	1	the	the	DET
ejpam-4112	344	2	strong	strong	ADJ
ejpam-4112	344	3	connected	connected	ADJ
ejpam-4112	344	4	metric	metric	ADJ
ejpam-4112	344	5	dimension	dimension	NOUN
ejpam-4112	344	6	in	in	ADP
ejpam-4112	344	7	the	the	DET
ejpam-4112	344	8	join	join	NOUN
ejpam-4112	344	9	and	and	CCONJ
ejpam-4112	344	10	corona	corona	NOUN
ejpam-4112	344	11	of	of	ADP
ejpam-4112	344	12	graphs	graph	NOUN
ejpam-4112	344	13	.	.	PUNCT
ejpam-4112	345	1	advances	advance	NOUN
ejpam-4112	345	2	and	and	CCONJ
ejpam-4112	345	3	applications	application	NOUN
ejpam-4112	345	4	in	in	ADP
ejpam-4112	345	5	discrete	discrete	ADJ
ejpam-4112	345	6	mathematics	mathematic	NOUN
ejpam-4112	345	7	,	,	PUNCT
ejpam-4112	345	8	vol	vol	NOUN
ejpam-4112	345	9	21	21	NUM
ejpam-4112	345	10	(	(	PUNCT
ejpam-4112	345	11	2019	2019	NUM
ejpam-4112	345	12	)	)	PUNCT
ejpam-4112	345	13	,	,	PUNCT
ejpam-4112	345	14	no	no	INTJ
ejpam-4112	345	15	.	.	NOUN
ejpam-4112	345	16	1	1	NUM
ejpam-4112	345	17	,	,	PUNCT
ejpam-4112	345	18	91	91	NUM
ejpam-4112	345	19	-	-	SYM
ejpam-4112	345	20	101	101	NUM
ejpam-4112	345	21	.	.	PUNCT
ejpam-4112	346	1	doi.org/10.17654/dm021010091	doi.org/10.17654/dm021010091	NOUN
ejpam-4112	346	2	.	.	PUNCT
ejpam-4112	347	1	[	[	X
ejpam-4112	347	2	3	3	NUM
ejpam-4112	347	3	]	]	X
ejpam-4112	347	4	acal	acal	PROPN
ejpam-4112	347	5	p.l	p.l	PROPN
ejpam-4112	347	6	.	.	PROPN
ejpam-4112	347	7	,	,	PUNCT
ejpam-4112	347	8	monsanto	monsanto	PROPN
ejpam-4112	347	9	,	,	PUNCT
ejpam-4112	347	10	g.b	g.b	PROPN
ejpam-4112	347	11	.	.	PROPN
ejpam-4112	347	12	,	,	PUNCT
ejpam-4112	347	13	and	and	CCONJ
ejpam-4112	347	14	rara	rara	PROPN
ejpam-4112	347	15	h.m	h.m	PROPN
ejpam-4112	347	16	.	.	PROPN
ejpam-4112	347	17	on	on	ADP
ejpam-4112	347	18	strong	strong	ADJ
ejpam-4112	347	19	resolving	resolving	NOUN
ejpam-4112	347	20	domination	domination	NOUN
ejpam-4112	347	21	in	in	ADP
ejpam-4112	347	22	the	the	DET
ejpam-4112	347	23	join	join	NOUN
ejpam-4112	347	24	and	and	CCONJ
ejpam-4112	347	25	corona	corona	NOUN
ejpam-4112	347	26	of	of	ADP
ejpam-4112	347	27	graphs	graph	NOUN
ejpam-4112	347	28	european	european	ADJ
ejpam-4112	347	29	journal	journal	PROPN
ejpam-4112	347	30	of	of	ADP
ejpam-4112	347	31	pure	pure	ADJ
ejpam-4112	347	32	and	and	CCONJ
ejpam-4112	347	33	applied	applied	ADJ
ejpam-4112	347	34	mathematics	mathematic	NOUN
ejpam-4112	347	35	,	,	PUNCT
ejpam-4112	347	36	vol	vol	NOUN
ejpam-4112	347	37	13	13	NUM
ejpam-4112	347	38	(	(	PUNCT
ejpam-4112	347	39	2020	2020	NUM
ejpam-4112	347	40	)	)	PUNCT
ejpam-4112	347	41	,	,	PUNCT
ejpam-4112	347	42	no	no	INTJ
ejpam-4112	347	43	.	.	NOUN
ejpam-4112	347	44	1	1	NUM
ejpam-4112	347	45	,	,	PUNCT
ejpam-4112	347	46	170	170	NUM
ejpam-4112	347	47	-	-	SYM
ejpam-4112	347	48	179	179	NUM
ejpam-4112	347	49	.	.	PUNCT
ejpam-4112	348	1	[	[	X
ejpam-4112	348	2	4	4	X
ejpam-4112	348	3	]	]	X
ejpam-4112	348	4	ibrahim	ibrahim	PROPN
ejpam-4112	348	5	t.	t.	PROPN
ejpam-4112	348	6	a.	a.	PROPN
ejpam-4112	348	7	,	,	PUNCT
ejpam-4112	348	8	and	and	CCONJ
ejpam-4112	348	9	omran	omran	ADJ
ejpam-4112	348	10	a.	a.	NOUN
ejpam-4112	348	11	a.	a.	PROPN
ejpam-4112	348	12	restrained	restrain	VERB
ejpam-4112	348	13	whole	whole	ADJ
ejpam-4112	348	14	domination	domination	NOUN
ejpam-4112	348	15	in	in	ADP
ejpam-4112	348	16	graphs	graph	NOUN
ejpam-4112	348	17	european	european	ADJ
ejpam-4112	348	18	journal	journal	PROPN
ejpam-4112	348	19	of	of	ADP
ejpam-4112	348	20	pure	pure	ADJ
ejpam-4112	348	21	and	and	CCONJ
ejpam-4112	348	22	applied	applied	ADJ
ejpam-4112	348	23	mathematics	mathematic	NOUN
ejpam-4112	348	24	,	,	PUNCT
ejpam-4112	348	25	1879	1879	NUM
ejpam-4112	348	26	(	(	PUNCT
ejpam-4112	348	27	2021	2021	NUM
ejpam-4112	348	28	)	)	PUNCT
ejpam-4112	348	29	032029	032029	NUM
ejpam-4112	349	1	[	[	X
ejpam-4112	349	2	5	5	X
ejpam-4112	349	3	]	]	X
ejpam-4112	349	4	knor	knor	NOUN
ejpam-4112	349	5	m.	m.	NOUN
ejpam-4112	349	6	,	,	PUNCT
ejpam-4112	349	7	tepeh	tepeh	PROPN
ejpam-4112	349	8	h.	h.	PROPN
ejpam-4112	349	9	,	,	PUNCT
ejpam-4112	349	10	and	and	CCONJ
ejpam-4112	349	11	skrekovski	skrekovski	PROPN
ejpam-4112	349	12	r.	r.	PROPN
ejpam-4112	349	13	domination	domination	PROPN
ejpam-4112	349	14	versus	versus	ADP
ejpam-4112	349	15	independent	independent	ADJ
ejpam-4112	349	16	domination	domination	NOUN
ejpam-4112	349	17	in	in	ADP
ejpam-4112	349	18	regular	regular	ADJ
ejpam-4112	349	19	graphs	graph	NOUN
ejpam-4112	349	20	european	european	ADJ
ejpam-4112	349	21	journal	journal	PROPN
ejpam-4112	349	22	of	of	ADP
ejpam-4112	349	23	pure	pure	ADJ
ejpam-4112	349	24	and	and	CCONJ
ejpam-4112	349	25	applied	apply	VERB
ejpam-4112	349	26	(	(	PUNCT
ejpam-4112	349	27	2021	2021	NUM
ejpam-4112	349	28	)	)	PUNCT
ejpam-4112	349	29	.	.	PUNCT
ejpam-4112	350	1	references	reference	NOUN
ejpam-4112	350	2	1378	1378	NUM
ejpam-4112	350	3	[	[	SYM
ejpam-4112	350	4	6	6	NUM
ejpam-4112	350	5	]	]	PUNCT
ejpam-4112	350	6	oellermann	oellermann	NOUN
ejpam-4112	350	7	,	,	PUNCT
ejpam-4112	350	8	o.	o.	PROPN
ejpam-4112	350	9	r.	r.	PROPN
ejpam-4112	350	10	,	,	PUNCT
ejpam-4112	350	11	and	and	CCONJ
ejpam-4112	350	12	peters	peters	PROPN
ejpam-4112	350	13	-	-	PUNCT
ejpam-4112	350	14	fransen	fransen	PROPN
ejpam-4112	350	15	,	,	PUNCT
ejpam-4112	350	16	j.	j.	PROPN
ejpam-4112	350	17	(	(	PUNCT
ejpam-4112	350	18	2007	2007	NUM
ejpam-4112	350	19	)	)	PUNCT
ejpam-4112	350	20	.	.	PUNCT
ejpam-4112	351	1	the	the	DET
ejpam-4112	351	2	strong	strong	ADJ
ejpam-4112	351	3	metric	metric	ADJ
ejpam-4112	351	4	dimension	dimension	NOUN
ejpam-4112	351	5	of	of	ADP
ejpam-4112	351	6	graphs	graph	NOUN
ejpam-4112	351	7	and	and	CCONJ
ejpam-4112	351	8	digraphs	digraph	NOUN
ejpam-4112	351	9	.	.	PUNCT
ejpam-4112	352	1	discrete	discrete	ADJ
ejpam-4112	352	2	applied	apply	VERB
ejpam-4112	352	3	mathematics	mathematic	NOUN
ejpam-4112	352	4	,	,	PUNCT
ejpam-4112	352	5	155(3	155(3	NUM
ejpam-4112	352	6	)	)	PUNCT
ejpam-4112	352	7	,	,	PUNCT
ejpam-4112	352	8	356	356	NUM
ejpam-4112	352	9	-	-	SYM
ejpam-4112	352	10	364	364	NUM
ejpam-4112	352	11	.	.	PUNCT
ejpam-4112	353	1	[	[	X
ejpam-4112	353	2	7	7	NUM
ejpam-4112	353	3	]	]	SYM
ejpam-4112	353	4	domke	domke	NOUN
ejpam-4112	353	5	,	,	PUNCT
ejpam-4112	353	6	g.s	g.s	PROPN
ejpam-4112	353	7	.	.	PROPN
ejpam-4112	353	8	,	,	PUNCT
ejpam-4112	353	9	hattingh	hattingh	PROPN
ejpam-4112	353	10	,	,	PUNCT
ejpam-4112	353	11	j.s	j.s	PROPN
ejpam-4112	353	12	,	,	PUNCT
ejpam-4112	353	13	hedetniemi	hedetniemi	PROPN
ejpam-4112	353	14	,	,	PUNCT
ejpam-4112	353	15	s.t	s.t	PROPN
ejpam-4112	353	16	.	.	PROPN
ejpam-4112	353	17	,	,	PUNCT
ejpam-4112	353	18	laskar	laskar	PROPN
ejpam-4112	353	19	,	,	PUNCT
ejpam-4112	353	20	r.c	r.c	PROPN
ejpam-4112	353	21	.	.	PROPN
ejpam-4112	353	22	,	,	PUNCT
ejpam-4112	353	23	and	and	CCONJ
ejpam-4112	353	24	markus	marku	NOUN
ejpam-4112	353	25	,	,	PUNCT
ejpam-4112	353	26	l.r	l.r	PROPN
ejpam-4112	353	27	.	.	PROPN
ejpam-4112	353	28	restrained	restrained	ADJ
ejpam-4112	353	29	domination	domination	NOUN
ejpam-4112	353	30	in	in	ADP
ejpam-4112	353	31	graphs	graph	NOUN
ejpam-4112	353	32	.	.	PUNCT
ejpam-4112	354	1	discrete	discrete	ADJ
ejpam-4112	354	2	mathematics	mathematic	NOUN
ejpam-4112	354	3	203(1999	203(1999	NUM
ejpam-4112	354	4	)	)	PUNCT
ejpam-4112	354	5	61	61	NUM
ejpam-4112	354	6	-	-	SYM
ejpam-4112	354	7	69	69	NUM
ejpam-4112	354	8	.	.	PUNCT
ejpam-4112	355	1	[	[	X
ejpam-4112	355	2	8	8	NUM
ejpam-4112	355	3	]	]	X
ejpam-4112	355	4	p.	p.	NOUN
ejpam-4112	355	5	slater	slater	PROPN
ejpam-4112	355	6	.	.	PUNCT
ejpam-4112	356	1	dominating	dominating	NOUN
ejpam-4112	356	2	and	and	CCONJ
ejpam-4112	356	3	reference	reference	NOUN
ejpam-4112	356	4	sets	set	NOUN
ejpam-4112	356	5	in	in	ADP
ejpam-4112	356	6	a	a	DET
ejpam-4112	356	7	graph	graph	NOUN
ejpam-4112	356	8	.	.	PUNCT
ejpam-4112	357	1	journal	journal	NOUN
ejpam-4112	357	2	of	of	ADP
ejpam-4112	357	3	mathematics	mathematic	NOUN
ejpam-4112	357	4	and	and	CCONJ
ejpam-4112	357	5	physical	physical	ADJ
ejpam-4112	357	6	science	science	NOUN
ejpam-4112	357	7	,	,	PUNCT
ejpam-4112	357	8	33(4):445	33(4):445	PROPN
ejpam-4112	357	9	-	-	SYM
ejpam-4112	357	10	455	455	NUM
ejpam-4112	357	11	,	,	PUNCT
ejpam-4112	357	12	1988	1988	NUM
ejpam-4112	357	13	.	.	PUNCT
ejpam-4112	358	1	[	[	X
ejpam-4112	358	2	9	9	NUM
ejpam-4112	358	3	]	]	SYM
ejpam-4112	358	4	harary	harary	NOUN
ejpam-4112	358	5	,	,	PUNCT
ejpam-4112	358	6	f.	f.	PROPN
ejpam-4112	358	7	(	(	PUNCT
ejpam-4112	358	8	1969	1969	NUM
ejpam-4112	358	9	)	)	PUNCT
ejpam-4112	358	10	.	.	PUNCT
ejpam-4112	359	1	graph	graph	NOUN
ejpam-4112	359	2	theory	theory	NOUN
ejpam-4112	359	3	.	.	PUNCT
ejpam-4112	360	1	michigan	michigan	PROPN
ejpam-4112	360	2	university	university	PROPN
ejpam-4112	360	3	ann	ann	PROPN
ejpam-4112	360	4	arbor	arbor	PROPN
ejpam-4112	360	5	department	department	PROPN
ejpam-4112	360	6	of	of	ADP
ejpam-4112	360	7	mathematics	mathematic	NOUN
ejpam-4112	360	8	.	.	PUNCT
ejpam-4112	361	1	[	[	X
ejpam-4112	361	2	10	10	NUM
ejpam-4112	361	3	]	]	X
ejpam-4112	361	4	johnson	johnson	PROPN
ejpam-4112	361	5	,	,	PUNCT
ejpam-4112	361	6	m.	m.	NOUN
ejpam-4112	361	7	a.	a.	NOUN
ejpam-4112	361	8	”	"	PUNCT
ejpam-4112	361	9	browsable	browsable	ADJ
ejpam-4112	361	10	structure	structure	NOUN
ejpam-4112	361	11	-	-	PUNCT
ejpam-4112	361	12	activity	activity	NOUN
ejpam-4112	361	13	datasets	dataset	NOUN
ejpam-4112	361	14	.	.	PUNCT
ejpam-4112	361	15	”	"	PUNCT
ejpam-4112	362	1	advances	advance	NOUN
ejpam-4112	362	2	in	in	ADP
ejpam-4112	362	3	molecular	molecular	ADJ
ejpam-4112	362	4	similarity	similarity	NOUN
ejpam-4112	362	5	2	2	NUM
ejpam-4112	362	6	(	(	PUNCT
ejpam-4112	362	7	1998	1998	NUM
ejpam-4112	362	8	):	):	PUNCT
ejpam-4112	362	9	153	153	NUM
ejpam-4112	362	10	-	-	SYM
ejpam-4112	362	11	170	170	NUM
ejpam-4112	362	12	.	.	PUNCT
ejpam-4112	363	1	[	[	X
ejpam-4112	363	2	11	11	NUM
ejpam-4112	363	3	]	]	SYM
ejpam-4112	363	4	khuller	khuller	NOUN
ejpam-4112	363	5	,	,	PUNCT
ejpam-4112	363	6	samir	samir	PROPN
ejpam-4112	363	7	,	,	PUNCT
ejpam-4112	363	8	balaji	balaji	PROPN
ejpam-4112	363	9	raghavachari	raghavachari	PROPN
ejpam-4112	363	10	,	,	PUNCT
ejpam-4112	363	11	and	and	CCONJ
ejpam-4112	363	12	azriel	azriel	PROPN
ejpam-4112	363	13	rosenfeld	rosenfeld	PROPN
ejpam-4112	363	14	.	.	PUNCT
ejpam-4112	364	1	landmarks	landmark	NOUN
ejpam-4112	364	2	in	in	ADP
ejpam-4112	364	3	graphs	graph	NOUN
ejpam-4112	364	4	.	.	PUNCT
ejpam-4112	365	1	discrete	discrete	ADJ
ejpam-4112	365	2	applied	apply	VERB
ejpam-4112	365	3	mathematics	mathematic	NOUN
ejpam-4112	365	4	70.3	70.3	NUM
ejpam-4112	365	5	(	(	PUNCT
ejpam-4112	365	6	1996	1996	NUM
ejpam-4112	365	7	):	):	PUNCT
ejpam-4112	365	8	217	217	NUM
ejpam-4112	365	9	-	-	SYM
ejpam-4112	365	10	229	229	NUM
ejpam-4112	365	11	.	.	PUNCT
ejpam-4112	366	1	[	[	X
ejpam-4112	366	2	12	12	NUM
ejpam-4112	366	3	]	]	X
ejpam-4112	366	4	liu	liu	PROPN
ejpam-4112	366	5	k.	k.	PROPN
ejpam-4112	366	6	,	,	PUNCT
ejpam-4112	366	7	abu	abu	PROPN
ejpam-4112	366	8	-	-	PUNCT
ejpam-4112	366	9	ghazaleh	ghazaleh	PROPN
ejpam-4112	366	10	n.	n.	PROPN
ejpam-4112	366	11	virtual	virtual	ADJ
ejpam-4112	366	12	coordinate	coordinate	NOUN
ejpam-4112	366	13	backtracking	backtrack	VERB
ejpam-4112	366	14	for	for	ADP
ejpam-4112	366	15	void	void	ADJ
ejpam-4112	366	16	traversal	traversal	NOUN
ejpam-4112	366	17	in	in	ADP
ejpam-4112	366	18	geographic	geographic	ADJ
ejpam-4112	366	19	routing	routing	NOUN
ejpam-4112	366	20	.	.	PUNCT
ejpam-4112	367	1	lecture	lecture	NOUN
ejpam-4112	367	2	notes	note	NOUN
ejpam-4112	367	3	in	in	ADP
ejpam-4112	367	4	comput	comput	NOUN
ejpam-4112	367	5	.	.	PUNCT
ejpam-4112	368	1	sci	sci	PROPN
ejpam-4112	368	2	.	.	PROPN
ejpam-4112	368	3	,	,	PUNCT
ejpam-4112	368	4	4104	4104	NUM
ejpam-4112	368	5	(	(	PUNCT
ejpam-4112	368	6	2006	2006	NUM
ejpam-4112	368	7	)	)	PUNCT
ejpam-4112	368	8	,	,	PUNCT
ejpam-4112	368	9	46âas59	46âas59	NOUN
ejpam-4112	368	10	.	.	PUNCT
ejpam-4112	369	1	[	[	X
ejpam-4112	369	2	13	13	NUM
ejpam-4112	369	3	]	]	PUNCT
ejpam-4112	369	4	sebo	sebo	NOUN
ejpam-4112	369	5	,	,	PUNCT
ejpam-4112	369	6	andrás	andrás	NOUN
ejpam-4112	369	7	and	and	CCONJ
ejpam-4112	369	8	tannier	tannier	NOUN
ejpam-4112	369	9	,	,	PUNCT
ejpam-4112	369	10	eric	eric	PROPN
ejpam-4112	369	11	a.	a.	PROPN
ejpam-4112	369	12	on	on	ADP
ejpam-4112	369	13	metric	metric	ADJ
ejpam-4112	369	14	generators	generator	NOUN
ejpam-4112	369	15	of	of	ADP
ejpam-4112	369	16	graphs	graph	NOUN
ejpam-4112	369	17	.	.	PUNCT
ejpam-4112	370	1	mathematics	mathematic	NOUN
ejpam-4112	370	2	of	of	ADP
ejpam-4112	370	3	operations	operation	NOUN
ejpam-4112	370	4	research	research	NOUN
ejpam-4112	370	5	,	,	PUNCT
ejpam-4112	370	6	29(2	29(2	NUM
ejpam-4112	370	7	)	)	PUNCT
ejpam-4112	370	8	,	,	PUNCT
ejpam-4112	370	9	383	383	NUM
ejpam-4112	370	10	-	-	SYM
ejpam-4112	370	11	393	393	NUM
ejpam-4112	370	12	.	.	PUNCT
ejpam-4112	371	1	[	[	X
ejpam-4112	371	2	14	14	NUM
ejpam-4112	371	3	]	]	X
ejpam-4112	371	4	bailey	bailey	NOUN
ejpam-4112	371	5	,	,	PUNCT
ejpam-4112	371	6	robert	robert	PROPN
ejpam-4112	371	7	f.	f.	PROPN
ejpam-4112	371	8	,	,	PUNCT
ejpam-4112	371	9	cameron	cameron	PROPN
ejpam-4112	371	10	,	,	PUNCT
ejpam-4112	371	11	peter	peter	PROPN
ejpam-4112	371	12	j.	j.	PROPN
ejpam-4112	371	13	base	base	PROPN
ejpam-4112	371	14	size	size	NOUN
ejpam-4112	371	15	,	,	PUNCT
ejpam-4112	371	16	metric	metric	ADJ
ejpam-4112	371	17	dimension	dimension	NOUN
ejpam-4112	371	18	and	and	CCONJ
ejpam-4112	371	19	other	other	ADJ
ejpam-4112	371	20	invariants	invariant	NOUN
ejpam-4112	371	21	of	of	ADP
ejpam-4112	371	22	groups	group	NOUN
ejpam-4112	371	23	and	and	CCONJ
ejpam-4112	371	24	graphs	graph	NOUN
ejpam-4112	371	25	.	.	PUNCT
ejpam-4112	372	1	base	base	NOUN
ejpam-4112	372	2	size	size	NOUN
ejpam-4112	372	3	,	,	PUNCT
ejpam-4112	372	4	metric	metric	ADJ
ejpam-4112	372	5	dimension	dimension	NOUN
ejpam-4112	372	6	and	and	CCONJ
ejpam-4112	372	7	other	other	ADJ
ejpam-4112	372	8	invariants	invariant	NOUN
ejpam-4112	372	9	of	of	ADP
ejpam-4112	372	10	groups	group	NOUN
ejpam-4112	372	11	and	and	CCONJ
ejpam-4112	372	12	graphs	graph	NOUN
ejpam-4112	372	13	,	,	PUNCT
ejpam-4112	372	14	43(2	43(2	NUM
ejpam-4112	372	15	):	):	PUNCT
ejpam-4112	372	16	209	209	NUM
ejpam-4112	372	17	-	-	SYM
ejpam-4112	372	18	242,2011	242,2011	NUM
ejpam-4112	372	19	.	.	PUNCT
ejpam-4112	373	1	[	[	X
ejpam-4112	373	2	15	15	NUM
ejpam-4112	373	3	]	]	X
ejpam-4112	373	4	chartrand	chartrand	NOUN
ejpam-4112	373	5	,	,	PUNCT
ejpam-4112	373	6	g.	g.	PROPN
ejpam-4112	373	7	,	,	PUNCT
ejpam-4112	373	8	eroh	eroh	PROPN
ejpam-4112	373	9	,	,	PUNCT
ejpam-4112	373	10	l.	l.	PROPN
ejpam-4112	373	11	,	,	PUNCT
ejpam-4112	373	12	johnson	johnson	PROPN
ejpam-4112	373	13	,	,	PUNCT
ejpam-4112	373	14	m.	m.	NOUN
ejpam-4112	373	15	a.	a.	PROPN
ejpam-4112	373	16	,	,	PUNCT
ejpam-4112	373	17	and	and	CCONJ
ejpam-4112	373	18	oellermann	oellermann	NOUN
ejpam-4112	373	19	,	,	PUNCT
ejpam-4112	373	20	o.	o.	PROPN
ejpam-4112	373	21	r.	r.	PROPN
ejpam-4112	373	22	(	(	PUNCT
ejpam-4112	373	23	2000	2000	NUM
ejpam-4112	373	24	)	)	PUNCT
ejpam-4112	373	25	.	.	PUNCT
ejpam-4112	374	1	resolvability	resolvability	NOUN
ejpam-4112	374	2	in	in	ADP
ejpam-4112	374	3	graphs	graph	NOUN
ejpam-4112	374	4	and	and	CCONJ
ejpam-4112	374	5	the	the	DET
ejpam-4112	374	6	metric	metric	ADJ
ejpam-4112	374	7	dimension	dimension	NOUN
ejpam-4112	374	8	of	of	ADP
ejpam-4112	374	9	a	a	DET
ejpam-4112	374	10	graph	graph	NOUN
ejpam-4112	374	11	.	.	PUNCT
ejpam-4112	375	1	discrete	discrete	ADJ
ejpam-4112	375	2	applied	apply	VERB
ejpam-4112	375	3	mathematics	mathematic	NOUN
ejpam-4112	375	4	,	,	PUNCT
ejpam-4112	375	5	105(13	105(13	NUM
ejpam-4112	375	6	)	)	PUNCT
ejpam-4112	375	7	,	,	PUNCT
ejpam-4112	375	8	99	99	NUM
ejpam-4112	375	9	-	-	SYM
ejpam-4112	375	10	113	113	NUM
ejpam-4112	375	11	.	.	PUNCT
ejpam-4112	376	1	[	[	X
ejpam-4112	376	2	16	16	NUM
ejpam-4112	376	3	]	]	X
ejpam-4112	376	4	chappell	chappell	NOUN
ejpam-4112	376	5	,	,	PUNCT
ejpam-4112	376	6	g.	g.	PROPN
ejpam-4112	376	7	g.	g.	PROPN
ejpam-4112	376	8	,	,	PUNCT
ejpam-4112	376	9	gimbel	gimbel	NOUN
ejpam-4112	376	10	,	,	PUNCT
ejpam-4112	376	11	j.	j.	PROPN
ejpam-4112	376	12	,	,	PUNCT
ejpam-4112	376	13	and	and	CCONJ
ejpam-4112	376	14	hartman	hartman	PROPN
ejpam-4112	376	15	,	,	PUNCT
ejpam-4112	376	16	c.	c.	PROPN
ejpam-4112	376	17	(	(	PUNCT
ejpam-4112	376	18	2008	2008	NUM
ejpam-4112	376	19	)	)	PUNCT
ejpam-4112	376	20	.	.	PUNCT
ejpam-4112	377	1	bounds	bound	VERB
ejpam-4112	377	2	on	on	ADP
ejpam-4112	377	3	the	the	DET
ejpam-4112	377	4	metric	metric	ADJ
ejpam-4112	377	5	and	and	CCONJ
ejpam-4112	377	6	partition	partition	NOUN
ejpam-4112	377	7	dimensions	dimension	NOUN
ejpam-4112	377	8	of	of	ADP
ejpam-4112	377	9	a	a	DET
ejpam-4112	377	10	graph	graph	NOUN
ejpam-4112	377	11	.	.	PUNCT
ejpam-4112	378	1	ars	ars	PROPN
ejpam-4112	378	2	combinatoria	combinatoria	PROPN
ejpam-4112	378	3	,	,	PUNCT
ejpam-4112	378	4	88	88	NUM
ejpam-4112	378	5	,	,	PUNCT
ejpam-4112	378	6	349	349	NUM
ejpam-4112	378	7	-	-	SYM
ejpam-4112	378	8	366	366	NUM
ejpam-4112	378	9	.	.	PUNCT
ejpam-4112	379	1	[	[	X
ejpam-4112	379	2	17	17	NUM
ejpam-4112	379	3	]	]	X
ejpam-4112	379	4	kuziak	kuziak	PROPN
ejpam-4112	379	5	d.	d.	PROPN
ejpam-4112	379	6	,	,	PUNCT
ejpam-4112	379	7	yero	yero	PROPN
ejpam-4112	379	8	i.g	i.g	PROPN
ejpam-4112	379	9	.	.	PROPN
ejpam-4112	379	10	and	and	CCONJ
ejpam-4112	379	11	rodriguez	rodriguez	PROPN
ejpam-4112	379	12	-	-	PUNCT
ejpam-4112	379	13	velasquez	velasquez	PROPN
ejpam-4112	379	14	j.a	j.a	PROPN
ejpam-4112	379	15	.	.	PROPN
ejpam-4112	379	16	closed	close	VERB
ejpam-4112	379	17	formuale	formuale	NOUN
ejpam-4112	379	18	for	for	ADP
ejpam-4112	379	19	the	the	DET
ejpam-4112	379	20	strong	strong	ADJ
ejpam-4112	379	21	metric	metric	ADJ
ejpam-4112	379	22	dimension	dimension	NOUN
ejpam-4112	379	23	of	of	ADP
ejpam-4112	379	24	lexicographic	lexicographic	ADJ
ejpam-4112	379	25	product	product	NOUN
ejpam-4112	379	26	graphs	graph	NOUN
ejpam-4112	379	27	.	.	PUNCT
ejpam-4112	380	1	discussiones	discussione	NOUN
ejpam-4112	380	2	mathematicae	mathematicae	PROPN
ejpam-4112	380	3	graph	graph	NOUN
ejpam-4112	380	4	theory	theory	NOUN
ejpam-4112	380	5	36(2016	36(2016	PROPN
ejpam-4112	380	6	)	)	PUNCT
ejpam-4112	380	7	1051	1051	NUM
ejpam-4112	380	8	-	-	SYM
ejpam-4112	380	9	1064	1064	NUM
ejpam-4112	380	10	.	.	PUNCT
ejpam-4112	381	1	doi:10.7151	doi:10.7151	NOUN
ejpam-4112	381	2	/	/	SYM
ejpam-4112	381	3	dmgt.1911	dmgt.1911	PROPN
ejpam-4112	381	4	.	.	PUNCT
ejpam-4112	382	1	[	[	X
ejpam-4112	382	2	18	18	NUM
ejpam-4112	382	3	]	]	X
ejpam-4112	382	4	brigham	brigham	PROPN
ejpam-4112	382	5	,	,	PUNCT
ejpam-4112	382	6	r.c	r.c	PROPN
ejpam-4112	382	7	.	.	PROPN
ejpam-4112	382	8	,	,	PUNCT
ejpam-4112	382	9	chartrand	chartrand	PROPN
ejpam-4112	382	10	g.	g.	PROPN
ejpam-4112	382	11	,	,	PUNCT
ejpam-4112	382	12	dutton	dutton	PROPN
ejpam-4112	382	13	,	,	PUNCT
ejpam-4112	382	14	r.d	r.d	PROPN
ejpam-4112	382	15	.	.	PROPN
ejpam-4112	382	16	,	,	PUNCT
ejpam-4112	382	17	and	and	CCONJ
ejpam-4112	382	18	zhang	zhang	PROPN
ejpam-4112	382	19	p.	p.	PROPN
ejpam-4112	382	20	resolving	resolve	VERB
ejpam-4112	382	21	domination	domination	NOUN
ejpam-4112	382	22	in	in	ADP
ejpam-4112	382	23	graphs	graph	NOUN
ejpam-4112	382	24	.	.	PUNCT
ejpam-4112	383	1	mathematica	mathematica	PROPN
ejpam-4112	383	2	bohemica	bohemica	PROPN
ejpam-4112	383	3	,	,	PUNCT
ejpam-4112	383	4	vol	vol	NOUN
ejpam-4112	383	5	.	.	PROPN
ejpam-4112	383	6	1	1	NUM
ejpam-4112	383	7	(	(	PUNCT
ejpam-4112	383	8	2003	2003	NUM
ejpam-4112	383	9	)	)	PUNCT
ejpam-4112	383	10	,	,	PUNCT
ejpam-4112	383	11	25	25	NUM
ejpam-4112	383	12	-	-	SYM
ejpam-4112	383	13	36	36	NUM
ejpam-4112	383	14	.	.	PUNCT