id	sid	tid	token	lemma	pos
ejpam-4484	1	1	european	european	PROPN
ejpam-4484	1	2	journal	journal	PROPN
ejpam-4484	1	3	of	of	ADP
ejpam-4484	1	4	pure	pure	ADJ
ejpam-4484	1	5	and	and	CCONJ
ejpam-4484	1	6	applied	apply	VERB
ejpam-4484	1	7	mathematics	mathematic	NOUN
ejpam-4484	1	8	vol	vol	NOUN
ejpam-4484	1	9	.	.	PROPN
ejpam-4484	2	1	15	15	NUM
ejpam-4484	2	2	,	,	PUNCT
ejpam-4484	2	3	no	no	INTJ
ejpam-4484	2	4	.	.	NOUN
ejpam-4484	2	5	4	4	NUM
ejpam-4484	2	6	,	,	PUNCT
ejpam-4484	2	7	2022	2022	NUM
ejpam-4484	2	8	,	,	PUNCT
ejpam-4484	2	9	1472	1472	NUM
ejpam-4484	2	10	-	-	SYM
ejpam-4484	2	11	1481	1481	NUM
ejpam-4484	2	12	issn	issn	PROPN
ejpam-4484	2	13	1307	1307	NUM
ejpam-4484	2	14	-	-	SYM
ejpam-4484	2	15	5543	5543	NUM
ejpam-4484	2	16	–	–	PUNCT
ejpam-4484	2	17	ejpam.com	ejpam.com	X
ejpam-4484	2	18	published	publish	VERB
ejpam-4484	2	19	by	by	ADP
ejpam-4484	2	20	new	new	PROPN
ejpam-4484	2	21	york	york	PROPN
ejpam-4484	2	22	business	business	PROPN
ejpam-4484	2	23	global	global	ADJ
ejpam-4484	2	24	restrained	restrain	VERB
ejpam-4484	2	25	strong	strong	ADJ
ejpam-4484	2	26	resolving	resolve	VERB
ejpam-4484	2	27	hop	hop	NOUN
ejpam-4484	2	28	domination	domination	NOUN
ejpam-4484	2	29	in	in	ADP
ejpam-4484	2	30	graphs	graph	NOUN
ejpam-4484	2	31	armalene	armalene	PROPN
ejpam-4484	2	32	h.	h.	PROPN
ejpam-4484	2	33	abragan1,∗	abragan1,∗	PROPN
ejpam-4484	2	34	,	,	PUNCT
ejpam-4484	2	35	helen	helen	PROPN
ejpam-4484	2	36	m.	m.	PROPN
ejpam-4484	2	37	rara2	rara2	PROPN
ejpam-4484	3	1	1	1	NUM
ejpam-4484	3	2	department	department	NOUN
ejpam-4484	3	3	of	of	ADP
ejpam-4484	3	4	mathematics	mathematic	NOUN
ejpam-4484	3	5	and	and	CCONJ
ejpam-4484	3	6	statistics	statistic	NOUN
ejpam-4484	3	7	,	,	PUNCT
ejpam-4484	3	8	college	college	NOUN
ejpam-4484	3	9	of	of	ADP
ejpam-4484	3	10	science	science	NOUN
ejpam-4484	3	11	and	and	CCONJ
ejpam-4484	3	12	mathematics	mathematic	NOUN
ejpam-4484	3	13	,	,	PUNCT
ejpam-4484	3	14	center	center	NOUN
ejpam-4484	3	15	of	of	ADP
ejpam-4484	3	16	graph	graph	NOUN
ejpam-4484	3	17	theory	theory	NOUN
ejpam-4484	3	18	,	,	PUNCT
ejpam-4484	3	19	algebra	algebra	NOUN
ejpam-4484	3	20	,	,	PUNCT
ejpam-4484	3	21	mindanao	mindanao	PROPN
ejpam-4484	3	22	state	state	PROPN
ejpam-4484	3	23	university	university	PROPN
ejpam-4484	3	24	-	-	PUNCT
ejpam-4484	3	25	iligan	iligan	PROPN
ejpam-4484	3	26	institute	institute	PROPN
ejpam-4484	3	27	of	of	ADP
ejpam-4484	3	28	technology	technology	PROPN
ejpam-4484	3	29	,	,	PUNCT
ejpam-4484	3	30	9200	9200	NUM
ejpam-4484	3	31	iligan	iligan	ADJ
ejpam-4484	3	32	city	city	NOUN
ejpam-4484	3	33	,	,	PUNCT
ejpam-4484	3	34	philippines	philippine	VERB
ejpam-4484	3	35	2	2	NUM
ejpam-4484	3	36	analysis	analysis	NOUN
ejpam-4484	3	37	-	-	PUNCT
ejpam-4484	3	38	premier	premier	NOUN
ejpam-4484	3	39	research	research	NOUN
ejpam-4484	3	40	institute	institute	PROPN
ejpam-4484	3	41	of	of	ADP
ejpam-4484	3	42	science	science	NOUN
ejpam-4484	3	43	and	and	CCONJ
ejpam-4484	3	44	mathematics	mathematic	NOUN
ejpam-4484	3	45	,	,	PUNCT
ejpam-4484	3	46	mindanao	mindanao	PROPN
ejpam-4484	3	47	state	state	PROPN
ejpam-4484	3	48	universityiligan	universityiligan	PROPN
ejpam-4484	3	49	institute	institute	PROPN
ejpam-4484	3	50	of	of	ADP
ejpam-4484	3	51	technology	technology	PROPN
ejpam-4484	3	52	,	,	PUNCT
ejpam-4484	3	53	9200	9200	NUM
ejpam-4484	3	54	iligan	iligan	ADJ
ejpam-4484	3	55	city	city	NOUN
ejpam-4484	3	56	,	,	PUNCT
ejpam-4484	3	57	philippines	philippine	NOUN
ejpam-4484	3	58	abstract	abstract	ADJ
ejpam-4484	3	59	.	.	PUNCT
ejpam-4484	4	1	a	a	DET
ejpam-4484	4	2	set	set	NOUN
ejpam-4484	4	3	s	s	NOUN
ejpam-4484	4	4	⊆	⊆	NUM
ejpam-4484	4	5	v	v	NOUN
ejpam-4484	4	6	(	(	PUNCT
ejpam-4484	4	7	g	g	NOUN
ejpam-4484	4	8	)	)	PUNCT
ejpam-4484	4	9	is	be	AUX
ejpam-4484	4	10	a	a	DET
ejpam-4484	4	11	restrained	restrain	VERB
ejpam-4484	4	12	strong	strong	ADJ
ejpam-4484	4	13	resolving	resolve	VERB
ejpam-4484	4	14	hop	hop	NOUN
ejpam-4484	4	15	dominating	dominating	NOUN
ejpam-4484	4	16	set	set	VERB
ejpam-4484	4	17	in	in	ADP
ejpam-4484	4	18	g	g	PROPN
ejpam-4484	4	19	if	if	SCONJ
ejpam-4484	4	20	for	for	ADP
ejpam-4484	4	21	every	every	DET
ejpam-4484	4	22	v	v	NUM
ejpam-4484	4	23	∈	∈	NOUN
ejpam-4484	4	24	v	v	NOUN
ejpam-4484	4	25	(	(	PUNCT
ejpam-4484	4	26	g)\s	g)\s	NOUN
ejpam-4484	4	27	,	,	PUNCT
ejpam-4484	4	28	there	there	PRON
ejpam-4484	4	29	exists	exist	VERB
ejpam-4484	4	30	w	w	PROPN
ejpam-4484	4	31	∈	∈	PROPN
ejpam-4484	4	32	s	s	VERB
ejpam-4484	4	33	such	such	ADJ
ejpam-4484	5	1	that	that	PRON
ejpam-4484	5	2	dg(v	dg(v	ADJ
ejpam-4484	5	3	,	,	PUNCT
ejpam-4484	5	4	w	w	NOUN
ejpam-4484	5	5	)	)	PUNCT
ejpam-4484	5	6	=	=	SYM
ejpam-4484	5	7	2	2	NUM
ejpam-4484	5	8	and	and	CCONJ
ejpam-4484	5	9	s	s	NOUN
ejpam-4484	5	10	=	=	SYM
ejpam-4484	5	11	v	v	X
ejpam-4484	5	12	(	(	PUNCT
ejpam-4484	5	13	g	g	NOUN
ejpam-4484	5	14	)	)	PUNCT
ejpam-4484	5	15	or	or	CCONJ
ejpam-4484	5	16	v	v	NOUN
ejpam-4484	5	17	(	(	PUNCT
ejpam-4484	5	18	g)\s	g)\s	NOUN
ejpam-4484	5	19	has	have	VERB
ejpam-4484	5	20	no	no	DET
ejpam-4484	5	21	isolated	isolated	ADJ
ejpam-4484	5	22	vertex	vertex	NOUN
ejpam-4484	5	23	.	.	PUNCT
ejpam-4484	6	1	the	the	DET
ejpam-4484	6	2	smallest	small	ADJ
ejpam-4484	6	3	cardinality	cardinality	NOUN
ejpam-4484	6	4	of	of	ADP
ejpam-4484	6	5	such	such	DET
ejpam-4484	6	6	a	a	DET
ejpam-4484	6	7	set	set	NOUN
ejpam-4484	6	8	,	,	PUNCT
ejpam-4484	6	9	denoted	denote	VERB
ejpam-4484	6	10	by	by	ADP
ejpam-4484	6	11	γrsrh(g	γrsrh(g	NOUN
ejpam-4484	6	12	)	)	PUNCT
ejpam-4484	6	13	,	,	PUNCT
ejpam-4484	6	14	is	be	AUX
ejpam-4484	6	15	called	call	VERB
ejpam-4484	6	16	the	the	DET
ejpam-4484	6	17	restrained	restrain	VERB
ejpam-4484	6	18	strong	strong	ADJ
ejpam-4484	6	19	resolving	resolve	VERB
ejpam-4484	6	20	hop	hop	NOUN
ejpam-4484	6	21	domination	domination	NOUN
ejpam-4484	6	22	number	number	NOUN
ejpam-4484	6	23	of	of	ADP
ejpam-4484	6	24	g.	g.	PROPN
ejpam-4484	6	25	in	in	ADP
ejpam-4484	6	26	this	this	DET
ejpam-4484	6	27	paper	paper	NOUN
ejpam-4484	6	28	,	,	PUNCT
ejpam-4484	6	29	we	we	PRON
ejpam-4484	6	30	obtained	obtain	VERB
ejpam-4484	6	31	the	the	DET
ejpam-4484	6	32	corresponding	corresponding	ADJ
ejpam-4484	6	33	parameter	parameter	NOUN
ejpam-4484	6	34	in	in	ADP
ejpam-4484	6	35	graphs	graph	NOUN
ejpam-4484	6	36	resulting	result	VERB
ejpam-4484	6	37	from	from	ADP
ejpam-4484	6	38	the	the	DET
ejpam-4484	6	39	join	join	NOUN
ejpam-4484	6	40	,	,	PUNCT
ejpam-4484	6	41	corona	corona	NOUN
ejpam-4484	6	42	and	and	CCONJ
ejpam-4484	6	43	lexicographic	lexicographic	ADJ
ejpam-4484	6	44	product	product	NOUN
ejpam-4484	6	45	of	of	ADP
ejpam-4484	6	46	two	two	NUM
ejpam-4484	6	47	graphs	graph	NOUN
ejpam-4484	6	48	.	.	PUNCT
ejpam-4484	7	1	specifically	specifically	ADV
ejpam-4484	7	2	,	,	PUNCT
ejpam-4484	7	3	we	we	PRON
ejpam-4484	7	4	characterize	characterize	VERB
ejpam-4484	7	5	the	the	DET
ejpam-4484	7	6	restrained	restrain	VERB
ejpam-4484	7	7	strong	strong	ADJ
ejpam-4484	7	8	resolving	resolve	VERB
ejpam-4484	7	9	hop	hop	NOUN
ejpam-4484	7	10	dominating	dominating	NOUN
ejpam-4484	7	11	sets	set	NOUN
ejpam-4484	7	12	in	in	ADP
ejpam-4484	7	13	these	these	DET
ejpam-4484	7	14	types	type	NOUN
ejpam-4484	7	15	of	of	ADP
ejpam-4484	7	16	graphs	graph	NOUN
ejpam-4484	7	17	and	and	CCONJ
ejpam-4484	7	18	determine	determine	VERB
ejpam-4484	7	19	the	the	DET
ejpam-4484	7	20	bounds	bound	NOUN
ejpam-4484	7	21	or	or	CCONJ
ejpam-4484	7	22	exact	exact	ADJ
ejpam-4484	7	23	values	value	NOUN
ejpam-4484	7	24	of	of	ADP
ejpam-4484	7	25	their	their	PRON
ejpam-4484	7	26	restrained	restrain	VERB
ejpam-4484	7	27	strong	strong	ADJ
ejpam-4484	7	28	resolving	resolve	VERB
ejpam-4484	7	29	hop	hop	NOUN
ejpam-4484	7	30	domination	domination	NOUN
ejpam-4484	7	31	numbers	number	NOUN
ejpam-4484	7	32	.	.	PUNCT
ejpam-4484	8	1	2020	2020	NUM
ejpam-4484	8	2	mathematics	mathematic	NOUN
ejpam-4484	8	3	subject	subject	NOUN
ejpam-4484	8	4	classifications	classification	NOUN
ejpam-4484	8	5	:	:	PUNCT
ejpam-4484	8	6	05c69	05c69	X
ejpam-4484	8	7	key	key	ADJ
ejpam-4484	8	8	words	word	NOUN
ejpam-4484	8	9	and	and	CCONJ
ejpam-4484	8	10	phrases	phrase	NOUN
ejpam-4484	8	11	:	:	PUNCT
ejpam-4484	8	12	restrained	restrain	VERB
ejpam-4484	8	13	strong	strong	ADJ
ejpam-4484	8	14	resolving	resolve	VERB
ejpam-4484	8	15	hop	hop	NOUN
ejpam-4484	8	16	dominating	dominating	NOUN
ejpam-4484	8	17	set	set	NOUN
ejpam-4484	8	18	,	,	PUNCT
ejpam-4484	8	19	restrained	restrain	VERB
ejpam-4484	8	20	strong	strong	ADJ
ejpam-4484	8	21	resolving	resolve	VERB
ejpam-4484	8	22	hop	hop	NOUN
ejpam-4484	8	23	domination	domination	NOUN
ejpam-4484	8	24	number	number	NOUN
ejpam-4484	8	25	,	,	PUNCT
ejpam-4484	8	26	join	join	NOUN
ejpam-4484	8	27	,	,	PUNCT
ejpam-4484	8	28	corona	corona	PROPN
ejpam-4484	8	29	,	,	PUNCT
ejpam-4484	8	30	lexicographic	lexicographic	ADJ
ejpam-4484	8	31	product	product	NOUN
ejpam-4484	8	32	1	1	NUM
ejpam-4484	8	33	.	.	PUNCT
ejpam-4484	8	34	introduction	introduction	NOUN
ejpam-4484	8	35	the	the	DET
ejpam-4484	8	36	study	study	NOUN
ejpam-4484	8	37	of	of	ADP
ejpam-4484	8	38	domination	domination	NOUN
ejpam-4484	8	39	can	can	AUX
ejpam-4484	8	40	be	be	AUX
ejpam-4484	8	41	traced	trace	VERB
ejpam-4484	8	42	way	way	NOUN
ejpam-4484	8	43	back	back	ADV
ejpam-4484	8	44	1960	1960	NUM
ejpam-4484	8	45	.	.	PUNCT
ejpam-4484	9	1	since	since	SCONJ
ejpam-4484	9	2	then	then	ADV
ejpam-4484	9	3	numerous	numerous	ADJ
ejpam-4484	9	4	authors	author	NOUN
ejpam-4484	9	5	contribute	contribute	VERB
ejpam-4484	9	6	several	several	ADJ
ejpam-4484	9	7	interesting	interesting	ADJ
ejpam-4484	9	8	domination	domination	NOUN
ejpam-4484	9	9	parameters	parameter	NOUN
ejpam-4484	9	10	to	to	PART
ejpam-4484	9	11	nurture	nurture	VERB
ejpam-4484	9	12	the	the	DET
ejpam-4484	9	13	growth	growth	NOUN
ejpam-4484	9	14	of	of	ADP
ejpam-4484	9	15	this	this	DET
ejpam-4484	9	16	research	research	NOUN
ejpam-4484	9	17	area	area	NOUN
ejpam-4484	9	18	.	.	PUNCT
ejpam-4484	10	1	in	in	ADP
ejpam-4484	10	2	1977	1977	NUM
ejpam-4484	10	3	,	,	PUNCT
ejpam-4484	10	4	e.j	e.j	NOUN
ejpam-4484	10	5	cockayne	cockayne	NOUN
ejpam-4484	10	6	and	and	CCONJ
ejpam-4484	10	7	s.t	s.t	PROPN
ejpam-4484	10	8	hedetniemi	hedetniemi	ADV
ejpam-4484	10	9	introduced	introduce	VERB
ejpam-4484	10	10	the	the	DET
ejpam-4484	10	11	notation	notation	PROPN
ejpam-4484	10	12	γ(g	γ(g	PROPN
ejpam-4484	10	13	)	)	PUNCT
ejpam-4484	10	14	for	for	ADP
ejpam-4484	10	15	the	the	DET
ejpam-4484	10	16	domination	domination	NOUN
ejpam-4484	10	17	number	number	NOUN
ejpam-4484	10	18	of	of	ADP
ejpam-4484	10	19	graph	graph	NOUN
ejpam-4484	10	20	g.	g.	PROPN
ejpam-4484	10	21	until	until	ADP
ejpam-4484	10	22	the	the	DET
ejpam-4484	10	23	initiation	initiation	NOUN
ejpam-4484	10	24	of	of	ADP
ejpam-4484	10	25	the	the	DET
ejpam-4484	10	26	concept	concept	NOUN
ejpam-4484	10	27	of	of	ADP
ejpam-4484	10	28	2	2	NUM
ejpam-4484	10	29	-	-	PUNCT
ejpam-4484	10	30	step	step	NOUN
ejpam-4484	10	31	domination	domination	NOUN
ejpam-4484	10	32	number	number	NOUN
ejpam-4484	10	33	by	by	ADP
ejpam-4484	10	34	chartrand	chartrand	NOUN
ejpam-4484	10	35	et	et	PROPN
ejpam-4484	10	36	al	al	PROPN
ejpam-4484	11	1	[	[	X
ejpam-4484	11	2	3	3	X
ejpam-4484	11	3	]	]	PUNCT
ejpam-4484	11	4	in	in	ADP
ejpam-4484	11	5	1995	1995	NUM
ejpam-4484	11	6	,	,	PUNCT
ejpam-4484	11	7	which	which	PRON
ejpam-4484	11	8	is	be	AUX
ejpam-4484	11	9	closely	closely	ADV
ejpam-4484	11	10	related	relate	VERB
ejpam-4484	11	11	to	to	ADP
ejpam-4484	11	12	hop	hop	NOUN
ejpam-4484	11	13	domination	domination	NOUN
ejpam-4484	11	14	number	number	NOUN
ejpam-4484	11	15	.	.	PUNCT
ejpam-4484	12	1	subsequently	subsequently	ADV
ejpam-4484	12	2	,	,	PUNCT
ejpam-4484	12	3	natarajan	natarajan	PROPN
ejpam-4484	12	4	and	and	CCONJ
ejpam-4484	12	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4484	12	6	(	(	PUNCT
ejpam-4484	12	7	2015	2015	NUM
ejpam-4484	12	8	)	)	PUNCT
ejpam-4484	12	9	introduced	introduce	VERB
ejpam-4484	12	10	the	the	DET
ejpam-4484	12	11	hop	hop	NOUN
ejpam-4484	12	12	domination	domination	NOUN
ejpam-4484	12	13	concept	concept	NOUN
ejpam-4484	12	14	.	.	PUNCT
ejpam-4484	13	1	some	some	DET
ejpam-4484	13	2	variation	variation	NOUN
ejpam-4484	13	3	of	of	ADP
ejpam-4484	13	4	domination	domination	NOUN
ejpam-4484	13	5	can	can	AUX
ejpam-4484	13	6	be	be	AUX
ejpam-4484	13	7	seen	see	VERB
ejpam-4484	13	8	in	in	ADP
ejpam-4484	13	9	these	these	DET
ejpam-4484	13	10	papers	paper	NOUN
ejpam-4484	13	11	[	[	X
ejpam-4484	13	12	2	2	NUM
ejpam-4484	13	13	]	]	PUNCT
ejpam-4484	13	14	,	,	PUNCT
ejpam-4484	13	15	[	[	X
ejpam-4484	13	16	5	5	NUM
ejpam-4484	13	17	]	]	PUNCT
ejpam-4484	13	18	,	,	PUNCT
ejpam-4484	13	19	[	[	X
ejpam-4484	13	20	4	4	NUM
ejpam-4484	13	21	]	]	PUNCT
ejpam-4484	13	22	.	.	PUNCT
ejpam-4484	14	1	in	in	ADP
ejpam-4484	14	2	this	this	DET
ejpam-4484	14	3	study	study	NOUN
ejpam-4484	14	4	,	,	PUNCT
ejpam-4484	14	5	the	the	DET
ejpam-4484	14	6	researcher	researcher	NOUN
ejpam-4484	14	7	defines	define	VERB
ejpam-4484	14	8	and	and	CCONJ
ejpam-4484	14	9	establishes	establish	VERB
ejpam-4484	14	10	a	a	DET
ejpam-4484	14	11	new	new	ADJ
ejpam-4484	14	12	concept	concept	NOUN
ejpam-4484	14	13	of	of	ADP
ejpam-4484	14	14	hop	hop	NOUN
ejpam-4484	14	15	domination	domination	NOUN
ejpam-4484	14	16	called	call	VERB
ejpam-4484	14	17	a	a	DET
ejpam-4484	14	18	restrained	restrained	ADJ
ejpam-4484	14	19	strong	strong	ADJ
ejpam-4484	14	20	resolving	resolve	VERB
ejpam-4484	14	21	hop	hop	NOUN
ejpam-4484	14	22	domination	domination	NOUN
ejpam-4484	14	23	and	and	CCONJ
ejpam-4484	14	24	generates	generate	VERB
ejpam-4484	14	25	some	some	DET
ejpam-4484	14	26	characterizations	characterization	NOUN
ejpam-4484	14	27	∗corresponding	∗corresponde	VERB
ejpam-4484	14	28	author	author	NOUN
ejpam-4484	14	29	.	.	PUNCT
ejpam-4484	15	1	doi	doi	NOUN
ejpam-4484	15	2	:	:	PUNCT
ejpam-4484	15	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4484	https://doi.org/10.29020/nybg.ejpam.v15i4.4484	PRON
ejpam-4484	15	4	email	email	NOUN
ejpam-4484	15	5	addresses	address	NOUN
ejpam-4484	15	6	:	:	PUNCT
ejpam-4484	15	7	armalene.abragan@g.msuiit.edu.ph	armalene.abragan@g.msuiit.edu.ph	PROPN
ejpam-4484	15	8	(	(	PUNCT
ejpam-4484	15	9	a.	a.	NOUN
ejpam-4484	15	10	abragan	abragan	PROPN
ejpam-4484	15	11	)	)	PUNCT
ejpam-4484	15	12	,	,	PUNCT
ejpam-4484	15	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4484	15	14	(	(	PUNCT
ejpam-4484	15	15	h.	h.	PROPN
ejpam-4484	15	16	m.	m.	PROPN
ejpam-4484	15	17	rara	rara	PROPN
ejpam-4484	15	18	)	)	PUNCT
ejpam-4484	15	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4484	15	20	1472	1472	NUM
ejpam-4484	15	21	©	©	ADP
ejpam-4484	15	22	2022	2022	NUM
ejpam-4484	15	23	ejpam	ejpam	VERB
ejpam-4484	15	24	all	all	DET
ejpam-4484	15	25	rights	right	NOUN
ejpam-4484	15	26	reserved	reserve	VERB
ejpam-4484	15	27	.	.	PUNCT
ejpam-4484	16	1	a.	a.	PROPN
ejpam-4484	16	2	h.	h.	PROPN
ejpam-4484	16	3	abragan	abragan	PROPN
ejpam-4484	16	4	,	,	PUNCT
ejpam-4484	16	5	h.	h.	PROPN
ejpam-4484	16	6	m.	m.	PROPN
ejpam-4484	16	7	rara	rara	PROPN
ejpam-4484	16	8	/	/	SYM
ejpam-4484	16	9	eur	eur	PROPN
ejpam-4484	16	10	.	.	PUNCT
ejpam-4484	17	1	j.	j.	PROPN
ejpam-4484	17	2	pure	pure	PROPN
ejpam-4484	17	3	appl	appl	PROPN
ejpam-4484	17	4	.	.	PROPN
ejpam-4484	17	5	math	math	PROPN
ejpam-4484	17	6	,	,	PUNCT
ejpam-4484	17	7	15	15	NUM
ejpam-4484	17	8	(	(	PUNCT
ejpam-4484	17	9	4	4	NUM
ejpam-4484	17	10	)	)	PUNCT
ejpam-4484	17	11	(	(	PUNCT
ejpam-4484	17	12	2022	2022	NUM
ejpam-4484	17	13	)	)	PUNCT
ejpam-4484	17	14	,	,	PUNCT
ejpam-4484	17	15	1472	1472	NUM
ejpam-4484	17	16	-	-	SYM
ejpam-4484	17	17	1481	1481	NUM
ejpam-4484	17	18	1473	1473	NUM
ejpam-4484	17	19	of	of	ADP
ejpam-4484	17	20	restrained	restrained	ADJ
ejpam-4484	17	21	strong	strong	ADJ
ejpam-4484	17	22	resolving	resolve	VERB
ejpam-4484	17	23	hop	hop	NOUN
ejpam-4484	17	24	domination	domination	NOUN
ejpam-4484	17	25	in	in	ADP
ejpam-4484	17	26	graphs	graph	NOUN
ejpam-4484	17	27	.	.	PUNCT
ejpam-4484	18	1	for	for	ADP
ejpam-4484	18	2	an	an	DET
ejpam-4484	18	3	application	application	NOUN
ejpam-4484	18	4	,	,	PUNCT
ejpam-4484	18	5	in	in	ADP
ejpam-4484	18	6	[	[	X
ejpam-4484	18	7	8	8	NUM
ejpam-4484	18	8	]	]	X
ejpam-4484	18	9	haynes	hayne	NOUN
ejpam-4484	18	10	and	and	CCONJ
ejpam-4484	18	11	henning	henning	PROPN
ejpam-4484	18	12	considered	consider	VERB
ejpam-4484	18	13	a	a	DET
ejpam-4484	18	14	factory	factory	NOUN
ejpam-4484	18	15	with	with	ADP
ejpam-4484	18	16	large	large	ADJ
ejpam-4484	18	17	number	number	NOUN
ejpam-4484	18	18	of	of	ADP
ejpam-4484	18	19	employees	employee	NOUN
ejpam-4484	18	20	and	and	CCONJ
ejpam-4484	18	21	a	a	DET
ejpam-4484	18	22	need	need	NOUN
ejpam-4484	18	23	to	to	PART
ejpam-4484	18	24	implement	implement	VERB
ejpam-4484	18	25	a	a	DET
ejpam-4484	18	26	quality	quality	NOUN
ejpam-4484	18	27	assurance	assurance	NOUN
ejpam-4484	18	28	checking	check	VERB
ejpam-4484	18	29	system	system	NOUN
ejpam-4484	18	30	of	of	ADP
ejpam-4484	18	31	their	their	PRON
ejpam-4484	18	32	workers	worker	NOUN
ejpam-4484	18	33	.	.	PUNCT
ejpam-4484	19	1	the	the	DET
ejpam-4484	19	2	factory	factory	NOUN
ejpam-4484	19	3	manager	manager	NOUN
ejpam-4484	19	4	decides	decide	VERB
ejpam-4484	19	5	to	to	PART
ejpam-4484	19	6	designate	designate	VERB
ejpam-4484	19	7	an	an	DET
ejpam-4484	19	8	internal	internal	ADJ
ejpam-4484	19	9	committee	committee	NOUN
ejpam-4484	19	10	to	to	PART
ejpam-4484	19	11	do	do	VERB
ejpam-4484	19	12	this	this	PRON
ejpam-4484	19	13	,	,	PUNCT
ejpam-4484	19	14	i.e	i.e	PRON
ejpam-4484	19	15	,	,	PUNCT
ejpam-4484	19	16	the	the	DET
ejpam-4484	19	17	manager	manager	NOUN
ejpam-4484	19	18	will	will	AUX
ejpam-4484	19	19	select	select	VERB
ejpam-4484	19	20	a	a	DET
ejpam-4484	19	21	subset	subset	NOUN
ejpam-4484	19	22	of	of	ADP
ejpam-4484	19	23	the	the	DET
ejpam-4484	19	24	workers	worker	NOUN
ejpam-4484	19	25	to	to	PART
ejpam-4484	19	26	form	form	VERB
ejpam-4484	19	27	a	a	DET
ejpam-4484	19	28	quality	quality	NOUN
ejpam-4484	19	29	assurance	assurance	NOUN
ejpam-4484	19	30	team	team	NOUN
ejpam-4484	19	31	to	to	PART
ejpam-4484	19	32	inspect	inspect	VERB
ejpam-4484	19	33	the	the	DET
ejpam-4484	19	34	work	work	NOUN
ejpam-4484	19	35	of	of	ADP
ejpam-4484	19	36	their	their	PRON
ejpam-4484	19	37	co	co	NOUN
ejpam-4484	19	38	-	-	NOUN
ejpam-4484	19	39	workers	worker	NOUN
ejpam-4484	19	40	.	.	PUNCT
ejpam-4484	20	1	the	the	DET
ejpam-4484	20	2	manager	manager	NOUN
ejpam-4484	20	3	desires	desire	NOUN
ejpam-4484	20	4	to	to	PART
ejpam-4484	20	5	keep	keep	VERB
ejpam-4484	20	6	this	this	DET
ejpam-4484	20	7	team	team	NOUN
ejpam-4484	20	8	as	as	ADV
ejpam-4484	20	9	small	small	ADJ
ejpam-4484	20	10	as	as	ADP
ejpam-4484	20	11	possible	possible	ADJ
ejpam-4484	20	12	in	in	ADP
ejpam-4484	20	13	order	order	NOUN
ejpam-4484	20	14	to	to	PART
ejpam-4484	20	15	minimize	minimize	VERB
ejpam-4484	20	16	costs	cost	NOUN
ejpam-4484	20	17	(	(	PUNCT
ejpam-4484	20	18	inspectors	inspector	NOUN
ejpam-4484	20	19	’	'	PUNCT
ejpam-4484	20	20	extra	extra	ADJ
ejpam-4484	20	21	pay	pay	NOUN
ejpam-4484	20	22	)	)	PUNCT
ejpam-4484	20	23	and	and	CCONJ
ejpam-4484	20	24	to	to	PART
ejpam-4484	20	25	protect	protect	VERB
ejpam-4484	20	26	privacy	privacy	NOUN
ejpam-4484	20	27	(	(	PUNCT
ejpam-4484	20	28	keeping	keep	VERB
ejpam-4484	20	29	the	the	DET
ejpam-4484	20	30	identity	identity	NOUN
ejpam-4484	20	31	of	of	ADP
ejpam-4484	20	32	inspector	inspector	NOUN
ejpam-4484	20	33	secret).to	secret).to	NOUN
ejpam-4484	20	34	avoid	avoid	VERB
ejpam-4484	20	35	bias	bias	NOUN
ejpam-4484	20	36	,	,	PUNCT
ejpam-4484	20	37	an	an	DET
ejpam-4484	20	38	inspector	inspector	NOUN
ejpam-4484	20	39	should	should	AUX
ejpam-4484	20	40	neither	neither	CCONJ
ejpam-4484	20	41	be	be	AUX
ejpam-4484	20	42	close	close	ADJ
ejpam-4484	20	43	friends	friend	NOUN
ejpam-4484	20	44	nor	nor	CCONJ
ejpam-4484	20	45	enemies	enemy	NOUN
ejpam-4484	20	46	with	with	ADP
ejpam-4484	20	47	any	any	PRON
ejpam-4484	20	48	of	of	ADP
ejpam-4484	20	49	the	the	DET
ejpam-4484	20	50	workers	worker	NOUN
ejpam-4484	21	1	he	he	PRON
ejpam-4484	21	2	/	/	PUNCT
ejpam-4484	22	1	she	she	PRON
ejpam-4484	22	2	is	be	AUX
ejpam-4484	22	3	responsible	responsible	ADJ
ejpam-4484	22	4	for	for	ADP
ejpam-4484	22	5	inspecting	inspect	VERB
ejpam-4484	22	6	.	.	PUNCT
ejpam-4484	23	1	to	to	PART
ejpam-4484	23	2	model	model	VERB
ejpam-4484	23	3	this	this	DET
ejpam-4484	23	4	situation	situation	NOUN
ejpam-4484	23	5	,	,	PUNCT
ejpam-4484	23	6	a	a	DET
ejpam-4484	23	7	social	social	ADJ
ejpam-4484	23	8	network	network	NOUN
ejpam-4484	23	9	graph	graph	NOUN
ejpam-4484	23	10	can	can	AUX
ejpam-4484	23	11	be	be	AUX
ejpam-4484	23	12	constructed	construct	VERB
ejpam-4484	23	13	,	,	PUNCT
ejpam-4484	23	14	where	where	SCONJ
ejpam-4484	23	15	each	each	DET
ejpam-4484	23	16	worker	worker	NOUN
ejpam-4484	23	17	is	be	AUX
ejpam-4484	23	18	represented	represent	VERB
ejpam-4484	23	19	by	by	ADP
ejpam-4484	23	20	a	a	DET
ejpam-4484	23	21	vertex	vertex	NOUN
ejpam-4484	23	22	and	and	CCONJ
ejpam-4484	23	23	an	an	DET
ejpam-4484	23	24	edge	edge	NOUN
ejpam-4484	23	25	between	between	ADP
ejpam-4484	23	26	two	two	NUM
ejpam-4484	23	27	workers	worker	NOUN
ejpam-4484	23	28	represent	represent	VERB
ejpam-4484	23	29	possible	possible	ADJ
ejpam-4484	23	30	bias	bias	NOUN
ejpam-4484	23	31	,	,	PUNCT
ejpam-4484	23	32	i.e	i.e	X
ejpam-4484	23	33	if	if	SCONJ
ejpam-4484	23	34	the	the	DET
ejpam-4484	23	35	two	two	NUM
ejpam-4484	23	36	workers	worker	NOUN
ejpam-4484	23	37	are	be	AUX
ejpam-4484	23	38	either	either	CCONJ
ejpam-4484	23	39	close	close	ADJ
ejpam-4484	23	40	friend	friend	NOUN
ejpam-4484	23	41	or	or	CCONJ
ejpam-4484	23	42	enemies	enemy	NOUN
ejpam-4484	23	43	.	.	PUNCT
ejpam-4484	24	1	ideally	ideally	ADV
ejpam-4484	24	2	,	,	PUNCT
ejpam-4484	24	3	an	an	DET
ejpam-4484	24	4	inspector	inspector	NOUN
ejpam-4484	24	5	should	should	AUX
ejpam-4484	24	6	not	not	PART
ejpam-4484	24	7	be	be	AUX
ejpam-4484	24	8	adjacent	adjacent	ADJ
ejpam-4484	24	9	to	to	ADP
ejpam-4484	24	10	any	any	DET
ejpam-4484	24	11	worker	worker	NOUN
ejpam-4484	24	12	under	under	ADP
ejpam-4484	24	13	his	his	PRON
ejpam-4484	24	14	inspection	inspection	NOUN
ejpam-4484	24	15	.	.	PUNCT
ejpam-4484	25	1	in	in	ADP
ejpam-4484	25	2	hop	hop	PROPN
ejpam-4484	25	3	domination	domination	NOUN
ejpam-4484	25	4	,	,	PUNCT
ejpam-4484	25	5	every	every	DET
ejpam-4484	25	6	worker	worker	NOUN
ejpam-4484	25	7	will	will	AUX
ejpam-4484	25	8	be	be	AUX
ejpam-4484	25	9	inspected	inspect	VERB
ejpam-4484	25	10	by	by	ADP
ejpam-4484	25	11	the	the	DET
ejpam-4484	25	12	nearest	near	ADJ
ejpam-4484	25	13	non	non	ADJ
ejpam-4484	25	14	-	-	ADJ
ejpam-4484	25	15	biased	biased	ADJ
ejpam-4484	25	16	inspector	inspector	NOUN
ejpam-4484	25	17	,	,	PUNCT
ejpam-4484	25	18	that	that	ADV
ejpam-4484	25	19	is	is	ADV
ejpam-4484	25	20	,	,	PUNCT
ejpam-4484	25	21	an	an	DET
ejpam-4484	25	22	inspector	inspector	NOUN
ejpam-4484	25	23	who	who	PRON
ejpam-4484	25	24	is	be	AUX
ejpam-4484	25	25	a	a	DET
ejpam-4484	25	26	close	close	ADJ
ejpam-4484	25	27	friend	friend	NOUN
ejpam-4484	25	28	(	(	PUNCT
ejpam-4484	25	29	or	or	CCONJ
ejpam-4484	25	30	enemy	enemy	NOUN
ejpam-4484	25	31	)	)	PUNCT
ejpam-4484	25	32	of	of	ADP
ejpam-4484	25	33	the	the	DET
ejpam-4484	25	34	worker	worker	NOUN
ejpam-4484	25	35	’s	’s	PART
ejpam-4484	25	36	close	close	ADJ
ejpam-4484	25	37	friend	friend	NOUN
ejpam-4484	25	38	(	(	PUNCT
ejpam-4484	25	39	or	or	CCONJ
ejpam-4484	25	40	enemy	enemy	NOUN
ejpam-4484	25	41	)	)	PUNCT
ejpam-4484	25	42	.	.	PUNCT
ejpam-4484	26	1	this	this	PRON
ejpam-4484	26	2	is	be	AUX
ejpam-4484	26	3	to	to	PART
ejpam-4484	26	4	save	save	VERB
ejpam-4484	26	5	time	time	NOUN
ejpam-4484	26	6	and	and	CCONJ
ejpam-4484	26	7	effort	effort	NOUN
ejpam-4484	26	8	locating	locate	VERB
ejpam-4484	26	9	a	a	DET
ejpam-4484	26	10	particular	particular	ADJ
ejpam-4484	26	11	worker	worker	NOUN
ejpam-4484	26	12	.	.	PUNCT
ejpam-4484	27	1	if	if	SCONJ
ejpam-4484	27	2	we	we	PRON
ejpam-4484	27	3	desire	desire	VERB
ejpam-4484	27	4	a	a	DET
ejpam-4484	27	5	situation	situation	NOUN
ejpam-4484	27	6	where	where	SCONJ
ejpam-4484	27	7	every	every	DET
ejpam-4484	27	8	worker	worker	NOUN
ejpam-4484	27	9	including	include	VERB
ejpam-4484	27	10	the	the	DET
ejpam-4484	27	11	inspector	inspector	NOUN
ejpam-4484	27	12	has	have	VERB
ejpam-4484	27	13	his	his	PRON
ejpam-4484	27	14	/	/	SYM
ejpam-4484	27	15	her	her	PRON
ejpam-4484	27	16	work	work	NOUN
ejpam-4484	27	17	inspected	inspect	VERB
ejpam-4484	27	18	,	,	PUNCT
ejpam-4484	27	19	then	then	ADV
ejpam-4484	27	20	restrained	restrain	VERB
ejpam-4484	27	21	strong	strong	ADJ
ejpam-4484	27	22	resolving	resolve	VERB
ejpam-4484	27	23	hop	hop	NOUN
ejpam-4484	27	24	domination	domination	NOUN
ejpam-4484	27	25	numbers	number	NOUN
ejpam-4484	27	26	gives	give	VERB
ejpam-4484	27	27	us	we	PRON
ejpam-4484	27	28	the	the	DET
ejpam-4484	27	29	minimum	minimum	ADJ
ejpam-4484	27	30	number	number	NOUN
ejpam-4484	27	31	of	of	ADP
ejpam-4484	27	32	inspectors	inspector	NOUN
ejpam-4484	27	33	needed	need	VERB
ejpam-4484	27	34	.	.	PUNCT
ejpam-4484	28	1	in	in	ADP
ejpam-4484	28	2	this	this	DET
ejpam-4484	28	3	study	study	NOUN
ejpam-4484	28	4	,	,	PUNCT
ejpam-4484	28	5	we	we	PRON
ejpam-4484	28	6	only	only	ADV
ejpam-4484	28	7	consider	consider	VERB
ejpam-4484	28	8	graphs	graph	NOUN
ejpam-4484	28	9	that	that	PRON
ejpam-4484	28	10	are	be	AUX
ejpam-4484	28	11	finite	finite	ADJ
ejpam-4484	28	12	,	,	PUNCT
ejpam-4484	28	13	simple	simple	ADJ
ejpam-4484	28	14	,	,	PUNCT
ejpam-4484	28	15	undirected	undirected	ADJ
ejpam-4484	28	16	and	and	CCONJ
ejpam-4484	28	17	connected	connected	ADJ
ejpam-4484	28	18	.	.	PUNCT
ejpam-4484	29	1	readers	reader	NOUN
ejpam-4484	29	2	are	be	AUX
ejpam-4484	29	3	referred	refer	VERB
ejpam-4484	29	4	to	to	ADP
ejpam-4484	29	5	[	[	X
ejpam-4484	29	6	6	6	NUM
ejpam-4484	29	7	]	]	PUNCT
ejpam-4484	29	8	for	for	ADP
ejpam-4484	29	9	elementary	elementary	ADJ
ejpam-4484	29	10	graph	graph	NOUN
ejpam-4484	29	11	theory	theory	NOUN
ejpam-4484	29	12	concepts	concept	NOUN
ejpam-4484	29	13	.	.	PUNCT
ejpam-4484	30	1	let	let	VERB
ejpam-4484	30	2	g	g	PRON
ejpam-4484	30	3	be	be	AUX
ejpam-4484	30	4	a	a	DET
ejpam-4484	30	5	connected	connected	ADJ
ejpam-4484	30	6	graph	graph	NOUN
ejpam-4484	30	7	.	.	PUNCT
ejpam-4484	31	1	a	a	DET
ejpam-4484	31	2	set	set	NOUN
ejpam-4484	31	3	s	s	NOUN
ejpam-4484	31	4	⊆	⊆	NUM
ejpam-4484	31	5	v	v	NOUN
ejpam-4484	31	6	(	(	PUNCT
ejpam-4484	31	7	g	g	NOUN
ejpam-4484	31	8	)	)	PUNCT
ejpam-4484	31	9	is	be	AUX
ejpam-4484	31	10	a	a	DET
ejpam-4484	31	11	hop	hop	NOUN
ejpam-4484	31	12	dominating	dominating	NOUN
ejpam-4484	31	13	set	set	NOUN
ejpam-4484	31	14	of	of	ADP
ejpam-4484	31	15	g	g	PROPN
ejpam-4484	31	16	if	if	SCONJ
ejpam-4484	31	17	for	for	ADP
ejpam-4484	31	18	every	every	DET
ejpam-4484	31	19	v	v	NUM
ejpam-4484	31	20	∈	∈	NOUN
ejpam-4484	31	21	v	v	NOUN
ejpam-4484	31	22	(	(	PUNCT
ejpam-4484	31	23	g)\s	g)\s	NOUN
ejpam-4484	31	24	,	,	PUNCT
ejpam-4484	31	25	there	there	PRON
ejpam-4484	31	26	exists	exist	VERB
ejpam-4484	31	27	u	u	PROPN
ejpam-4484	31	28	∈	∈	PROPN
ejpam-4484	31	29	s	s	VERB
ejpam-4484	31	30	such	such	ADJ
ejpam-4484	31	31	that	that	DET
ejpam-4484	31	32	dg(u	dg(u	ADJ
ejpam-4484	31	33	,	,	PUNCT
ejpam-4484	31	34	v	v	NOUN
ejpam-4484	31	35	)	)	PUNCT
ejpam-4484	32	1	=	=	SYM
ejpam-4484	32	2	2	2	X
ejpam-4484	32	3	.	.	PUNCT
ejpam-4484	33	1	the	the	DET
ejpam-4484	33	2	minimum	minimum	ADJ
ejpam-4484	33	3	cardinality	cardinality	NOUN
ejpam-4484	33	4	of	of	ADP
ejpam-4484	33	5	a	a	DET
ejpam-4484	33	6	hop	hop	NOUN
ejpam-4484	33	7	dominating	dominating	NOUN
ejpam-4484	33	8	set	set	NOUN
ejpam-4484	33	9	of	of	ADP
ejpam-4484	33	10	g	g	NOUN
ejpam-4484	33	11	,	,	PUNCT
ejpam-4484	33	12	denoted	denote	VERB
ejpam-4484	33	13	by	by	ADP
ejpam-4484	33	14	γh(g	γh(g	NOUN
ejpam-4484	33	15	)	)	PUNCT
ejpam-4484	33	16	,	,	PUNCT
ejpam-4484	33	17	is	be	AUX
ejpam-4484	33	18	called	call	VERB
ejpam-4484	33	19	the	the	DET
ejpam-4484	33	20	hop	hop	NOUN
ejpam-4484	33	21	domination	domination	NOUN
ejpam-4484	33	22	number	number	NOUN
ejpam-4484	33	23	of	of	ADP
ejpam-4484	33	24	g.	g.	PROPN
ejpam-4484	33	25	any	any	DET
ejpam-4484	33	26	hop	hop	NOUN
ejpam-4484	33	27	dominating	dominating	NOUN
ejpam-4484	33	28	set	set	VERB
ejpam-4484	33	29	with	with	ADP
ejpam-4484	33	30	cardinality	cardinality	NOUN
ejpam-4484	33	31	equal	equal	ADJ
ejpam-4484	33	32	to	to	ADP
ejpam-4484	33	33	γh(g	γh(g	NOUN
ejpam-4484	33	34	)	)	PUNCT
ejpam-4484	33	35	is	be	AUX
ejpam-4484	33	36	called	call	VERB
ejpam-4484	33	37	a	a	DET
ejpam-4484	33	38	γh	γh	ADV
ejpam-4484	33	39	-	-	PUNCT
ejpam-4484	33	40	set	set	NOUN
ejpam-4484	33	41	.	.	PUNCT
ejpam-4484	34	1	a	a	DET
ejpam-4484	34	2	set	set	NOUN
ejpam-4484	34	3	c	c	NOUN
ejpam-4484	34	4	⊆	⊆	NUM
ejpam-4484	34	5	v	v	NOUN
ejpam-4484	34	6	(	(	PUNCT
ejpam-4484	34	7	g	g	NOUN
ejpam-4484	34	8	)	)	PUNCT
ejpam-4484	34	9	is	be	AUX
ejpam-4484	34	10	called	call	VERB
ejpam-4484	34	11	a	a	DET
ejpam-4484	34	12	superclique	superclique	NOUN
ejpam-4484	34	13	in	in	ADP
ejpam-4484	34	14	g	g	PROPN
ejpam-4484	34	15	if	if	SCONJ
ejpam-4484	34	16	⟨c⟩	⟨c⟩	PROPN
ejpam-4484	34	17	is	be	AUX
ejpam-4484	34	18	a	a	DET
ejpam-4484	34	19	clique	clique	NOUN
ejpam-4484	34	20	and	and	CCONJ
ejpam-4484	34	21	for	for	ADP
ejpam-4484	34	22	every	every	DET
ejpam-4484	34	23	pair	pair	NOUN
ejpam-4484	34	24	of	of	ADP
ejpam-4484	34	25	distinct	distinct	ADJ
ejpam-4484	34	26	vertices	vertex	NOUN
ejpam-4484	34	27	u	u	NOUN
ejpam-4484	34	28	,	,	PUNCT
ejpam-4484	34	29	v	v	NOUN
ejpam-4484	34	30	∈	∈	ADJ
ejpam-4484	34	31	c	c	NOUN
ejpam-4484	34	32	,	,	PUNCT
ejpam-4484	34	33	there	there	PRON
ejpam-4484	34	34	exists	exist	VERB
ejpam-4484	34	35	w	w	PROPN
ejpam-4484	34	36	∈	∈	PROPN
ejpam-4484	34	37	v	v	ADP
ejpam-4484	34	38	(	(	PUNCT
ejpam-4484	34	39	g	g	NOUN
ejpam-4484	34	40	)	)	PUNCT
ejpam-4484	34	41	\	\	PUNCT
ejpam-4484	35	1	c	c	NOUN
ejpam-4484	35	2	such	such	ADJ
ejpam-4484	35	3	that	that	PRON
ejpam-4484	35	4	w	w	PROPN
ejpam-4484	35	5	∈	∈	PROPN
ejpam-4484	35	6	ng(u	ng(u	NOUN
ejpam-4484	35	7	)	)	PUNCT
ejpam-4484	35	8	\	\	NOUN
ejpam-4484	35	9	ng(v	ng(v	PUNCT
ejpam-4484	35	10	)	)	PUNCT
ejpam-4484	35	11	or	or	CCONJ
ejpam-4484	35	12	w	w	PROPN
ejpam-4484	35	13	∈	∈	PROPN
ejpam-4484	35	14	ng(v)\ng(u	ng(v)\ng(u	ADJ
ejpam-4484	35	15	)	)	PUNCT
ejpam-4484	35	16	.	.	PUNCT
ejpam-4484	36	1	a	a	DET
ejpam-4484	36	2	superclique	superclique	NOUN
ejpam-4484	36	3	c	c	NOUN
ejpam-4484	36	4	is	be	AUX
ejpam-4484	36	5	maximum	maximum	ADJ
ejpam-4484	36	6	in	in	ADP
ejpam-4484	36	7	g	g	PROPN
ejpam-4484	36	8	if	if	SCONJ
ejpam-4484	36	9	|c|	|c|	PROPN
ejpam-4484	36	10	≥	≥	NOUN
ejpam-4484	36	11	|c∗|	|c∗|	VERB
ejpam-4484	36	12	for	for	SCONJ
ejpam-4484	36	13	all	all	DET
ejpam-4484	36	14	supercliques	superclique	NOUN
ejpam-4484	36	15	c∗	c∗	PROPN
ejpam-4484	36	16	in	in	ADP
ejpam-4484	36	17	g.	g.	PROPN
ejpam-4484	36	18	the	the	DET
ejpam-4484	36	19	superclique	superclique	ADJ
ejpam-4484	36	20	number	number	NOUN
ejpam-4484	36	21	of	of	ADP
ejpam-4484	36	22	g	g	NOUN
ejpam-4484	36	23	,	,	PUNCT
ejpam-4484	36	24	denoted	denote	VERB
ejpam-4484	36	25	by	by	ADP
ejpam-4484	36	26	ωs(g	ωs(g	NOUN
ejpam-4484	36	27	)	)	PUNCT
ejpam-4484	36	28	,	,	PUNCT
ejpam-4484	36	29	is	be	AUX
ejpam-4484	36	30	the	the	DET
ejpam-4484	36	31	cardinality	cardinality	NOUN
ejpam-4484	36	32	of	of	ADP
ejpam-4484	36	33	a	a	DET
ejpam-4484	36	34	maximum	maximum	ADJ
ejpam-4484	36	35	superclique	superclique	NOUN
ejpam-4484	36	36	in	in	ADP
ejpam-4484	36	37	g.	g.	PROPN
ejpam-4484	36	38	a	a	DET
ejpam-4484	36	39	superclique	superclique	ADJ
ejpam-4484	36	40	c	c	NOUN
ejpam-4484	36	41	in	in	ADP
ejpam-4484	36	42	g	g	PROPN
ejpam-4484	36	43	is	be	AUX
ejpam-4484	36	44	called	call	VERB
ejpam-4484	36	45	a	a	DET
ejpam-4484	36	46	hop	hop	NOUN
ejpam-4484	36	47	dominated	dominate	VERB
ejpam-4484	36	48	superclique	superclique	NOUN
ejpam-4484	36	49	if	if	SCONJ
ejpam-4484	36	50	for	for	ADP
ejpam-4484	36	51	every	every	DET
ejpam-4484	36	52	v	v	NOUN
ejpam-4484	36	53	∈	∈	NOUN
ejpam-4484	36	54	c	c	NOUN
ejpam-4484	36	55	there	there	PRON
ejpam-4484	36	56	exists	exist	VERB
ejpam-4484	36	57	u	u	PROPN
ejpam-4484	36	58	∈	∈	PROPN
ejpam-4484	36	59	v	v	NOUN
ejpam-4484	36	60	(	(	PUNCT
ejpam-4484	36	61	g)\c	g)\c	VERB
ejpam-4484	36	62	such	such	DET
ejpam-4484	36	63	that	that	DET
ejpam-4484	36	64	dg(u	dg(u	ADJ
ejpam-4484	36	65	,	,	PUNCT
ejpam-4484	36	66	v	v	NOUN
ejpam-4484	36	67	)	)	PUNCT
ejpam-4484	36	68	=	=	SYM
ejpam-4484	36	69	2	2	X
ejpam-4484	36	70	.	.	X
ejpam-4484	36	71	a	a	DET
ejpam-4484	36	72	hop	hop	NOUN
ejpam-4484	36	73	dominated	dominate	VERB
ejpam-4484	36	74	superclique	superclique	NOUN
ejpam-4484	36	75	c	c	PROPN
ejpam-4484	36	76	is	be	AUX
ejpam-4484	36	77	maximum	maximum	ADJ
ejpam-4484	36	78	in	in	ADP
ejpam-4484	36	79	g	g	PROPN
ejpam-4484	36	80	if	if	SCONJ
ejpam-4484	36	81	|c|	|c|	PROPN
ejpam-4484	36	82	≥	≥	NOUN
ejpam-4484	36	83	|c∗|	|c∗|	VERB
ejpam-4484	36	84	for	for	ADP
ejpam-4484	36	85	all	all	DET
ejpam-4484	36	86	hop	hop	NOUN
ejpam-4484	36	87	dominated	dominate	VERB
ejpam-4484	36	88	supercliques	superclique	NOUN
ejpam-4484	36	89	c∗	c∗	PROPN
ejpam-4484	36	90	in	in	ADP
ejpam-4484	36	91	g.	g.	PROPN
ejpam-4484	36	92	the	the	DET
ejpam-4484	36	93	hop	hop	NOUN
ejpam-4484	36	94	dominated	dominate	VERB
ejpam-4484	36	95	superclique	superclique	ADJ
ejpam-4484	36	96	number	number	NOUN
ejpam-4484	36	97	denoted	denote	VERB
ejpam-4484	36	98	by	by	ADP
ejpam-4484	36	99	ωhs(g	ωhs(g	PROPN
ejpam-4484	36	100	)	)	PUNCT
ejpam-4484	36	101	,	,	PUNCT
ejpam-4484	36	102	of	of	ADP
ejpam-4484	36	103	g	g	PROPN
ejpam-4484	36	104	is	be	AUX
ejpam-4484	36	105	the	the	DET
ejpam-4484	36	106	cardinality	cardinality	NOUN
ejpam-4484	36	107	of	of	ADP
ejpam-4484	36	108	a	a	DET
ejpam-4484	36	109	maximum	maximum	ADJ
ejpam-4484	36	110	hop	hop	NOUN
ejpam-4484	36	111	dominated	dominate	VERB
ejpam-4484	36	112	superclique	superclique	NOUN
ejpam-4484	36	113	in	in	ADP
ejpam-4484	36	114	g.	g.	PROPN
ejpam-4484	36	115	a	a	DET
ejpam-4484	36	116	superclique	superclique	NOUN
ejpam-4484	36	117	c	c	PROPN
ejpam-4484	36	118	⊆	⊆	NUM
ejpam-4484	36	119	v	v	NOUN
ejpam-4484	36	120	(	(	PUNCT
ejpam-4484	36	121	g	g	NOUN
ejpam-4484	36	122	)	)	PUNCT
ejpam-4484	36	123	is	be	AUX
ejpam-4484	36	124	called	call	VERB
ejpam-4484	36	125	a	a	DET
ejpam-4484	36	126	point	point	NOUN
ejpam-4484	36	127	-	-	PUNCT
ejpam-4484	36	128	wise	wise	ADJ
ejpam-4484	36	129	non	non	ADJ
ejpam-4484	36	130	-	-	ADJ
ejpam-4484	36	131	dominated	dominated	ADJ
ejpam-4484	36	132	superclique	superclique	NOUN
ejpam-4484	36	133	of	of	ADP
ejpam-4484	36	134	g	g	PROPN
ejpam-4484	36	135	if	if	SCONJ
ejpam-4484	36	136	for	for	ADP
ejpam-4484	36	137	every	every	DET
ejpam-4484	36	138	x	x	SYM
ejpam-4484	36	139	∈	∈	PROPN
ejpam-4484	36	140	c	c	NOUN
ejpam-4484	36	141	there	there	PRON
ejpam-4484	36	142	exists	exist	VERB
ejpam-4484	36	143	y	y	PROPN
ejpam-4484	36	144	∈	∈	PROPN
ejpam-4484	36	145	v	v	ADP
ejpam-4484	36	146	(	(	PUNCT
ejpam-4484	36	147	g	g	NOUN
ejpam-4484	36	148	)	)	PUNCT
ejpam-4484	36	149	\c	\c	ADP
ejpam-4484	36	150	such	such	ADJ
ejpam-4484	36	151	that	that	PRON
ejpam-4484	36	152	y	y	PROPN
ejpam-4484	36	153	/∈	/∈	PUNCT
ejpam-4484	36	154	ng(x	ng(x	NUM
ejpam-4484	36	155	)	)	PUNCT
ejpam-4484	36	156	.	.	PUNCT
ejpam-4484	37	1	a	a	DET
ejpam-4484	37	2	maximum	maximum	ADJ
ejpam-4484	37	3	cardinality	cardinality	NOUN
ejpam-4484	37	4	of	of	ADP
ejpam-4484	37	5	a	a	DET
ejpam-4484	37	6	point	point	NOUN
ejpam-4484	37	7	-	-	PUNCT
ejpam-4484	37	8	wise	wise	ADJ
ejpam-4484	37	9	non	non	ADJ
ejpam-4484	37	10	-	-	ADJ
ejpam-4484	37	11	dominated	dominated	ADJ
ejpam-4484	37	12	superclique	superclique	NOUN
ejpam-4484	37	13	in	in	ADP
ejpam-4484	37	14	g	g	PROPN
ejpam-4484	37	15	is	be	AUX
ejpam-4484	37	16	denoted	denote	VERB
ejpam-4484	37	17	by	by	ADP
ejpam-4484	37	18	ωpnds(g	ωpnds(g	NOUN
ejpam-4484	37	19	)	)	PUNCT
ejpam-4484	37	20	.	.	PUNCT
ejpam-4484	38	1	a	a	DET
ejpam-4484	38	2	vertex	vertex	NOUN
ejpam-4484	38	3	x	x	X
ejpam-4484	38	4	of	of	ADP
ejpam-4484	38	5	a	a	DET
ejpam-4484	38	6	connected	connected	ADJ
ejpam-4484	38	7	graph	graph	NOUN
ejpam-4484	38	8	g	g	NOUN
ejpam-4484	38	9	is	be	AUX
ejpam-4484	38	10	said	say	VERB
ejpam-4484	38	11	to	to	PART
ejpam-4484	38	12	resolve	resolve	VERB
ejpam-4484	38	13	vertices	vertex	NOUN
ejpam-4484	38	14	u	u	NOUN
ejpam-4484	38	15	and	and	CCONJ
ejpam-4484	38	16	v	v	NOUN
ejpam-4484	38	17	of	of	ADP
ejpam-4484	38	18	g	g	PROPN
ejpam-4484	38	19	if	if	SCONJ
ejpam-4484	38	20	dg(x	dg(x	NUM
ejpam-4484	38	21	,	,	PUNCT
ejpam-4484	38	22	u	u	NOUN
ejpam-4484	38	23	)	)	PUNCT
ejpam-4484	38	24	̸=	̸=	PROPN
ejpam-4484	38	25	dg(x	dg(x	NUM
ejpam-4484	38	26	,	,	PUNCT
ejpam-4484	38	27	v	v	NOUN
ejpam-4484	38	28	)	)	PUNCT
ejpam-4484	38	29	.	.	PUNCT
ejpam-4484	39	1	for	for	ADP
ejpam-4484	39	2	an	an	DET
ejpam-4484	39	3	ordered	order	VERB
ejpam-4484	39	4	set	set	NOUN
ejpam-4484	39	5	w	w	NOUN
ejpam-4484	39	6	=	=	PUNCT
ejpam-4484	39	7	{	{	PUNCT
ejpam-4484	39	8	x1	x1	PROPN
ejpam-4484	39	9	,	,	PUNCT
ejpam-4484	39	10	.	.	PUNCT
ejpam-4484	39	11	.	.	PUNCT
ejpam-4484	39	12	.	.	PUNCT
ejpam-4484	40	1	,	,	PUNCT
ejpam-4484	40	2	xk	xk	ADJ
ejpam-4484	40	3	}	}	PUNCT
ejpam-4484	40	4	⊆	⊆	NUM
ejpam-4484	40	5	v	v	NOUN
ejpam-4484	40	6	(	(	PUNCT
ejpam-4484	40	7	g	g	NOUN
ejpam-4484	40	8	)	)	PUNCT
ejpam-4484	40	9	and	and	CCONJ
ejpam-4484	40	10	a	a	DET
ejpam-4484	40	11	vertex	vertex	NOUN
ejpam-4484	40	12	v	v	NOUN
ejpam-4484	40	13	in	in	ADP
ejpam-4484	40	14	g	g	PROPN
ejpam-4484	40	15	,	,	PUNCT
ejpam-4484	40	16	the	the	DET
ejpam-4484	40	17	k	k	NOUN
ejpam-4484	40	18	-	-	NOUN
ejpam-4484	40	19	vector	vector	NOUN
ejpam-4484	40	20	rg(v	rg(v	NOUN
ejpam-4484	40	21	/	/	SYM
ejpam-4484	40	22	w	w	NOUN
ejpam-4484	40	23	)	)	PUNCT
ejpam-4484	40	24	=	=	SYM
ejpam-4484	40	25	(	(	PUNCT
ejpam-4484	40	26	dg(v	dg(v	X
ejpam-4484	40	27	,	,	PUNCT
ejpam-4484	40	28	x1	x1	PROPN
ejpam-4484	40	29	)	)	PUNCT
ejpam-4484	40	30	,	,	PUNCT
ejpam-4484	40	31	dg(v	dg(v	X
ejpam-4484	40	32	,	,	PUNCT
ejpam-4484	40	33	x2	x2	PROPN
ejpam-4484	40	34	)	)	PUNCT
ejpam-4484	40	35	,	,	PUNCT
ejpam-4484	40	36	.	.	PUNCT
ejpam-4484	40	37	.	.	PUNCT
ejpam-4484	40	38	.	.	PUNCT
ejpam-4484	41	1	dg(v	dg(v	PUNCT
ejpam-4484	41	2	,	,	PUNCT
ejpam-4484	41	3	xk	xk	NOUN
ejpam-4484	41	4	)	)	PUNCT
ejpam-4484	41	5	)	)	PUNCT
ejpam-4484	42	1	is	be	AUX
ejpam-4484	42	2	called	call	VERB
ejpam-4484	42	3	the	the	DET
ejpam-4484	42	4	representation	representation	NOUN
ejpam-4484	42	5	of	of	ADP
ejpam-4484	42	6	v	v	NOUN
ejpam-4484	42	7	with	with	ADP
ejpam-4484	42	8	respect	respect	NOUN
ejpam-4484	42	9	to	to	ADP
ejpam-4484	42	10	w	w	PROPN
ejpam-4484	42	11	.	.	PUNCT
ejpam-4484	43	1	the	the	DET
ejpam-4484	43	2	set	set	NOUN
ejpam-4484	43	3	w	w	NOUN
ejpam-4484	43	4	is	be	AUX
ejpam-4484	43	5	a	a	DET
ejpam-4484	43	6	resolving	resolving	NOUN
ejpam-4484	43	7	set	set	VERB
ejpam-4484	43	8	for	for	ADP
ejpam-4484	43	9	g	g	PROPN
ejpam-4484	43	10	if	if	SCONJ
ejpam-4484	44	1	and	and	CCONJ
ejpam-4484	44	2	only	only	ADV
ejpam-4484	44	3	if	if	SCONJ
ejpam-4484	44	4	no	no	DET
ejpam-4484	44	5	two	two	NUM
ejpam-4484	44	6	vertices	vertex	NOUN
ejpam-4484	44	7	of	of	ADP
ejpam-4484	44	8	g	g	NOUN
ejpam-4484	44	9	have	have	VERB
ejpam-4484	44	10	the	the	DET
ejpam-4484	44	11	same	same	ADJ
ejpam-4484	44	12	representation	representation	NOUN
ejpam-4484	44	13	with	with	ADP
ejpam-4484	44	14	respect	respect	NOUN
ejpam-4484	44	15	to	to	ADP
ejpam-4484	44	16	w	w	PROPN
ejpam-4484	44	17	.	.	PUNCT
ejpam-4484	45	1	the	the	DET
ejpam-4484	45	2	a.	a.	PROPN
ejpam-4484	45	3	h.	h.	PROPN
ejpam-4484	45	4	abragan	abragan	PROPN
ejpam-4484	45	5	,	,	PUNCT
ejpam-4484	45	6	h.	h.	PROPN
ejpam-4484	45	7	m.	m.	PROPN
ejpam-4484	45	8	rara	rara	PROPN
ejpam-4484	45	9	/	/	SYM
ejpam-4484	45	10	eur	eur	PROPN
ejpam-4484	45	11	.	.	PUNCT
ejpam-4484	46	1	j.	j.	PROPN
ejpam-4484	46	2	pure	pure	PROPN
ejpam-4484	46	3	appl	appl	PROPN
ejpam-4484	46	4	.	.	PROPN
ejpam-4484	46	5	math	math	PROPN
ejpam-4484	46	6	,	,	PUNCT
ejpam-4484	46	7	15	15	NUM
ejpam-4484	46	8	(	(	PUNCT
ejpam-4484	46	9	4	4	NUM
ejpam-4484	46	10	)	)	PUNCT
ejpam-4484	46	11	(	(	PUNCT
ejpam-4484	46	12	2022	2022	NUM
ejpam-4484	46	13	)	)	PUNCT
ejpam-4484	46	14	,	,	PUNCT
ejpam-4484	46	15	1472	1472	NUM
ejpam-4484	46	16	-	-	SYM
ejpam-4484	46	17	1481	1481	NUM
ejpam-4484	46	18	1474	1474	NUM
ejpam-4484	46	19	metric	metric	ADJ
ejpam-4484	46	20	dimension	dimension	NOUN
ejpam-4484	46	21	of	of	ADP
ejpam-4484	46	22	g	g	NOUN
ejpam-4484	46	23	,	,	PUNCT
ejpam-4484	46	24	denoted	denote	VERB
ejpam-4484	46	25	by	by	ADP
ejpam-4484	46	26	dim(g	dim(g	PROPN
ejpam-4484	46	27	)	)	PUNCT
ejpam-4484	46	28	,	,	PUNCT
ejpam-4484	46	29	is	be	AUX
ejpam-4484	46	30	the	the	DET
ejpam-4484	46	31	minimum	minimum	ADJ
ejpam-4484	46	32	cardinality	cardinality	NOUN
ejpam-4484	46	33	over	over	ADP
ejpam-4484	46	34	all	all	DET
ejpam-4484	46	35	resolving	resolve	VERB
ejpam-4484	46	36	sets	set	NOUN
ejpam-4484	46	37	of	of	ADP
ejpam-4484	46	38	g.	g.	PROPN
ejpam-4484	46	39	a	a	DET
ejpam-4484	46	40	resolving	resolve	VERB
ejpam-4484	46	41	set	set	NOUN
ejpam-4484	46	42	of	of	ADP
ejpam-4484	46	43	cardinality	cardinality	PROPN
ejpam-4484	46	44	dim(g	dim(g	PROPN
ejpam-4484	46	45	)	)	PUNCT
ejpam-4484	46	46	is	be	AUX
ejpam-4484	46	47	called	call	VERB
ejpam-4484	46	48	a	a	DET
ejpam-4484	46	49	basis	basis	NOUN
ejpam-4484	46	50	.	.	PUNCT
ejpam-4484	47	1	for	for	ADP
ejpam-4484	47	2	two	two	NUM
ejpam-4484	47	3	vertices	vertex	NOUN
ejpam-4484	47	4	u	u	NOUN
ejpam-4484	47	5	,	,	PUNCT
ejpam-4484	47	6	v	v	NOUN
ejpam-4484	47	7	∈	∈	PROPN
ejpam-4484	47	8	v	v	NOUN
ejpam-4484	47	9	(	(	PUNCT
ejpam-4484	47	10	g	g	NOUN
ejpam-4484	47	11	)	)	PUNCT
ejpam-4484	47	12	,	,	PUNCT
ejpam-4484	47	13	the	the	DET
ejpam-4484	47	14	interval	interval	NOUN
ejpam-4484	47	15	ig[u	ig[u	PROPN
ejpam-4484	47	16	,	,	PUNCT
ejpam-4484	47	17	v	v	NOUN
ejpam-4484	47	18	]	]	PUNCT
ejpam-4484	47	19	between	between	ADP
ejpam-4484	47	20	u	u	NOUN
ejpam-4484	47	21	and	and	CCONJ
ejpam-4484	47	22	v	v	NOUN
ejpam-4484	47	23	is	be	AUX
ejpam-4484	47	24	the	the	DET
ejpam-4484	47	25	collection	collection	NOUN
ejpam-4484	47	26	of	of	ADP
ejpam-4484	47	27	all	all	DET
ejpam-4484	47	28	vertices	vertex	NOUN
ejpam-4484	47	29	that	that	PRON
ejpam-4484	47	30	belong	belong	VERB
ejpam-4484	47	31	to	to	ADP
ejpam-4484	47	32	some	some	DET
ejpam-4484	47	33	shortest	short	ADJ
ejpam-4484	47	34	u	u	NOUN
ejpam-4484	47	35	-	-	NOUN
ejpam-4484	47	36	v	v	ADJ
ejpam-4484	47	37	path	path	NOUN
ejpam-4484	47	38	.	.	PUNCT
ejpam-4484	48	1	a	a	DET
ejpam-4484	48	2	vertex	vertex	NOUN
ejpam-4484	48	3	w	w	NOUN
ejpam-4484	48	4	strongly	strongly	ADV
ejpam-4484	48	5	resolves	resolve	VERB
ejpam-4484	48	6	two	two	NUM
ejpam-4484	48	7	vertices	vertex	NOUN
ejpam-4484	48	8	u	u	NOUN
ejpam-4484	48	9	and	and	CCONJ
ejpam-4484	48	10	v	v	NOUN
ejpam-4484	48	11	if	if	SCONJ
ejpam-4484	48	12	v	v	NOUN
ejpam-4484	48	13	∈	∈	PROPN
ejpam-4484	48	14	ig[u	ig[u	PROPN
ejpam-4484	48	15	,	,	PUNCT
ejpam-4484	48	16	w	w	NOUN
ejpam-4484	48	17	]	]	PUNCT
ejpam-4484	48	18	or	or	CCONJ
ejpam-4484	48	19	if	if	SCONJ
ejpam-4484	48	20	u	u	PROPN
ejpam-4484	48	21	∈	∈	PROPN
ejpam-4484	48	22	ig[v	ig[v	PROPN
ejpam-4484	48	23	,	,	PUNCT
ejpam-4484	48	24	w	w	PROPN
ejpam-4484	48	25	]	]	X
ejpam-4484	48	26	.	.	PUNCT
ejpam-4484	49	1	a	a	DET
ejpam-4484	49	2	set	set	NOUN
ejpam-4484	49	3	w	w	NOUN
ejpam-4484	49	4	of	of	ADP
ejpam-4484	49	5	vertices	vertex	NOUN
ejpam-4484	49	6	in	in	ADP
ejpam-4484	49	7	g	g	PROPN
ejpam-4484	49	8	is	be	AUX
ejpam-4484	49	9	a	a	DET
ejpam-4484	49	10	strong	strong	ADJ
ejpam-4484	49	11	resolving	resolving	NOUN
ejpam-4484	49	12	set	set	NOUN
ejpam-4484	49	13	of	of	ADP
ejpam-4484	49	14	g	g	NOUN
ejpam-4484	49	15	if	if	SCONJ
ejpam-4484	49	16	every	every	DET
ejpam-4484	49	17	two	two	NUM
ejpam-4484	49	18	vertices	vertex	NOUN
ejpam-4484	49	19	of	of	ADP
ejpam-4484	49	20	g	g	NOUN
ejpam-4484	49	21	are	be	AUX
ejpam-4484	49	22	strongly	strongly	ADV
ejpam-4484	49	23	resolved	resolve	VERB
ejpam-4484	49	24	by	by	ADP
ejpam-4484	49	25	some	some	DET
ejpam-4484	49	26	vertex	vertex	NOUN
ejpam-4484	49	27	of	of	ADP
ejpam-4484	49	28	w	w	PROPN
ejpam-4484	49	29	.	.	PUNCT
ejpam-4484	50	1	the	the	DET
ejpam-4484	50	2	smallest	small	ADJ
ejpam-4484	50	3	cardinality	cardinality	NOUN
ejpam-4484	50	4	of	of	ADP
ejpam-4484	50	5	a	a	DET
ejpam-4484	50	6	strong	strong	ADJ
ejpam-4484	50	7	resolving	resolving	NOUN
ejpam-4484	50	8	set	set	NOUN
ejpam-4484	50	9	of	of	ADP
ejpam-4484	50	10	g	g	PROPN
ejpam-4484	50	11	is	be	AUX
ejpam-4484	50	12	called	call	VERB
ejpam-4484	50	13	the	the	DET
ejpam-4484	50	14	strong	strong	ADJ
ejpam-4484	50	15	metric	metric	ADJ
ejpam-4484	50	16	dimension	dimension	NOUN
ejpam-4484	50	17	of	of	ADP
ejpam-4484	50	18	g	g	NOUN
ejpam-4484	50	19	and	and	CCONJ
ejpam-4484	50	20	is	be	AUX
ejpam-4484	50	21	denoted	denote	VERB
ejpam-4484	50	22	by	by	ADP
ejpam-4484	50	23	sdim(g	sdim(g	PROPN
ejpam-4484	50	24	)	)	PUNCT
ejpam-4484	50	25	.	.	PUNCT
ejpam-4484	51	1	a	a	DET
ejpam-4484	51	2	strong	strong	ADJ
ejpam-4484	51	3	resolving	resolving	NOUN
ejpam-4484	51	4	set	set	NOUN
ejpam-4484	51	5	of	of	ADP
ejpam-4484	51	6	cardinality	cardinality	PROPN
ejpam-4484	51	7	sdim(g	sdim(g	PROPN
ejpam-4484	51	8	)	)	PUNCT
ejpam-4484	51	9	is	be	AUX
ejpam-4484	51	10	called	call	VERB
ejpam-4484	51	11	a	a	DET
ejpam-4484	51	12	strong	strong	ADJ
ejpam-4484	51	13	metric	metric	ADJ
ejpam-4484	51	14	basis	basis	NOUN
ejpam-4484	51	15	of	of	ADP
ejpam-4484	51	16	g.	g.	PROPN
ejpam-4484	51	17	a	a	DET
ejpam-4484	51	18	subset	subset	NOUN
ejpam-4484	51	19	s	s	VERB
ejpam-4484	51	20	⊆	⊆	NUM
ejpam-4484	51	21	v	v	NOUN
ejpam-4484	51	22	(	(	PUNCT
ejpam-4484	51	23	g	g	NOUN
ejpam-4484	51	24	)	)	PUNCT
ejpam-4484	51	25	is	be	AUX
ejpam-4484	51	26	a	a	DET
ejpam-4484	51	27	strong	strong	ADJ
ejpam-4484	51	28	resolving	resolve	VERB
ejpam-4484	51	29	hop	hop	NOUN
ejpam-4484	51	30	dominating	dominating	NOUN
ejpam-4484	51	31	set	set	NOUN
ejpam-4484	51	32	of	of	ADP
ejpam-4484	51	33	g	g	PROPN
ejpam-4484	51	34	if	if	SCONJ
ejpam-4484	51	35	s	s	VERB
ejpam-4484	51	36	is	be	AUX
ejpam-4484	51	37	both	both	CCONJ
ejpam-4484	51	38	a	a	DET
ejpam-4484	51	39	strong	strong	ADJ
ejpam-4484	51	40	resolving	resolving	NOUN
ejpam-4484	51	41	set	set	VERB
ejpam-4484	51	42	and	and	CCONJ
ejpam-4484	51	43	a	a	DET
ejpam-4484	51	44	hop	hop	NOUN
ejpam-4484	51	45	dominating	dominating	NOUN
ejpam-4484	51	46	set	set	NOUN
ejpam-4484	51	47	.	.	PUNCT
ejpam-4484	52	1	the	the	DET
ejpam-4484	52	2	minimum	minimum	ADJ
ejpam-4484	52	3	cardinality	cardinality	NOUN
ejpam-4484	52	4	of	of	ADP
ejpam-4484	52	5	a	a	DET
ejpam-4484	52	6	strong	strong	ADJ
ejpam-4484	52	7	resolving	resolve	VERB
ejpam-4484	52	8	hop	hop	NOUN
ejpam-4484	52	9	dominating	dominating	NOUN
ejpam-4484	52	10	set	set	NOUN
ejpam-4484	52	11	of	of	ADP
ejpam-4484	52	12	g	g	NOUN
ejpam-4484	52	13	,	,	PUNCT
ejpam-4484	52	14	denoted	denote	VERB
ejpam-4484	52	15	by	by	ADP
ejpam-4484	52	16	γsrh(g	γsrh(g	NOUN
ejpam-4484	52	17	)	)	PUNCT
ejpam-4484	52	18	,	,	PUNCT
ejpam-4484	52	19	is	be	AUX
ejpam-4484	52	20	called	call	VERB
ejpam-4484	52	21	the	the	DET
ejpam-4484	52	22	strong	strong	ADJ
ejpam-4484	52	23	resolving	resolve	VERB
ejpam-4484	52	24	hop	hop	NOUN
ejpam-4484	52	25	domination	domination	NOUN
ejpam-4484	52	26	number	number	NOUN
ejpam-4484	52	27	of	of	ADP
ejpam-4484	52	28	g.	g.	PROPN
ejpam-4484	52	29	any	any	PRON
ejpam-4484	52	30	resolving	resolve	VERB
ejpam-4484	52	31	hop	hop	NOUN
ejpam-4484	52	32	dominating	dominating	NOUN
ejpam-4484	52	33	set	set	VERB
ejpam-4484	52	34	with	with	ADP
ejpam-4484	52	35	cardinality	cardinality	NOUN
ejpam-4484	52	36	equal	equal	ADJ
ejpam-4484	52	37	to	to	ADP
ejpam-4484	52	38	γsrh(g	γsrh(g	NOUN
ejpam-4484	52	39	)	)	PUNCT
ejpam-4484	52	40	is	be	AUX
ejpam-4484	52	41	called	call	VERB
ejpam-4484	52	42	a	a	DET
ejpam-4484	52	43	γsrh	γsrh	NOUN
ejpam-4484	52	44	-	-	PUNCT
ejpam-4484	52	45	set	set	NOUN
ejpam-4484	52	46	.	.	PUNCT
ejpam-4484	53	1	a	a	DET
ejpam-4484	53	2	set	set	NOUN
ejpam-4484	53	3	s	s	NOUN
ejpam-4484	53	4	⊆	⊆	NUM
ejpam-4484	53	5	v	v	NOUN
ejpam-4484	53	6	(	(	PUNCT
ejpam-4484	53	7	g	g	NOUN
ejpam-4484	53	8	)	)	PUNCT
ejpam-4484	53	9	is	be	AUX
ejpam-4484	53	10	a	a	DET
ejpam-4484	53	11	restrained	restrain	VERB
ejpam-4484	53	12	strong	strong	ADJ
ejpam-4484	53	13	resolving	resolve	VERB
ejpam-4484	53	14	hop	hop	NOUN
ejpam-4484	53	15	dominating	dominating	NOUN
ejpam-4484	53	16	set	set	VERB
ejpam-4484	53	17	on	on	ADP
ejpam-4484	53	18	g	g	PROPN
ejpam-4484	53	19	if	if	SCONJ
ejpam-4484	53	20	s	s	VERB
ejpam-4484	53	21	is	be	AUX
ejpam-4484	53	22	a	a	DET
ejpam-4484	53	23	strong	strong	ADJ
ejpam-4484	53	24	resolving	resolve	VERB
ejpam-4484	53	25	hop	hop	NOUN
ejpam-4484	53	26	dominating	dominating	NOUN
ejpam-4484	53	27	set	set	VERB
ejpam-4484	53	28	in	in	ADP
ejpam-4484	53	29	g	g	PROPN
ejpam-4484	53	30	and	and	CCONJ
ejpam-4484	53	31	s	s	PART
ejpam-4484	53	32	=	=	SYM
ejpam-4484	53	33	v	v	X
ejpam-4484	53	34	(	(	PUNCT
ejpam-4484	53	35	g	g	NOUN
ejpam-4484	53	36	)	)	PUNCT
ejpam-4484	53	37	or	or	CCONJ
ejpam-4484	53	38	⟨v	⟨v	NUM
ejpam-4484	53	39	(	(	PUNCT
ejpam-4484	53	40	g	g	NOUN
ejpam-4484	53	41	)	)	PUNCT
ejpam-4484	53	42	\	\	PROPN
ejpam-4484	53	43	s⟩	s⟩	NOUN
ejpam-4484	53	44	has	have	VERB
ejpam-4484	53	45	no	no	DET
ejpam-4484	53	46	isolated	isolated	ADJ
ejpam-4484	53	47	vertex	vertex	NOUN
ejpam-4484	53	48	.	.	PUNCT
ejpam-4484	54	1	the	the	DET
ejpam-4484	54	2	restrained	restrain	VERB
ejpam-4484	54	3	strong	strong	ADJ
ejpam-4484	54	4	resolving	resolve	VERB
ejpam-4484	54	5	hop	hop	NOUN
ejpam-4484	54	6	domination	domination	NOUN
ejpam-4484	54	7	number	number	NOUN
ejpam-4484	54	8	of	of	ADP
ejpam-4484	54	9	g	g	NOUN
ejpam-4484	54	10	,	,	PUNCT
ejpam-4484	54	11	denoted	denote	VERB
ejpam-4484	54	12	by	by	ADP
ejpam-4484	54	13	γrsrh(g	γrsrh(g	NOUN
ejpam-4484	54	14	)	)	PUNCT
ejpam-4484	54	15	,	,	PUNCT
ejpam-4484	54	16	is	be	AUX
ejpam-4484	54	17	the	the	DET
ejpam-4484	54	18	smallest	small	ADJ
ejpam-4484	54	19	cardinality	cardinality	NOUN
ejpam-4484	54	20	of	of	ADP
ejpam-4484	54	21	a	a	DET
ejpam-4484	54	22	restrained	restrain	VERB
ejpam-4484	54	23	strong	strong	ADJ
ejpam-4484	54	24	resolving	resolve	VERB
ejpam-4484	54	25	dominating	dominating	NOUN
ejpam-4484	54	26	set	set	VERB
ejpam-4484	54	27	in	in	ADP
ejpam-4484	54	28	g.	g.	PROPN
ejpam-4484	54	29	a	a	DET
ejpam-4484	54	30	restrained	restrain	VERB
ejpam-4484	54	31	strong	strong	ADJ
ejpam-4484	54	32	resolving	resolve	VERB
ejpam-4484	54	33	hop	hop	NOUN
ejpam-4484	54	34	dominating	dominating	NOUN
ejpam-4484	54	35	set	set	NOUN
ejpam-4484	54	36	of	of	ADP
ejpam-4484	54	37	cardinality	cardinality	PROPN
ejpam-4484	54	38	γrsrh(g	γrsrh(g	PROPN
ejpam-4484	54	39	)	)	PUNCT
ejpam-4484	54	40	is	be	AUX
ejpam-4484	54	41	then	then	ADV
ejpam-4484	54	42	referred	refer	VERB
ejpam-4484	54	43	to	to	ADP
ejpam-4484	54	44	as	as	ADP
ejpam-4484	54	45	γrsrh	γrsrh	NOUN
ejpam-4484	54	46	-	-	PUNCT
ejpam-4484	54	47	set	set	NOUN
ejpam-4484	54	48	of	of	ADP
ejpam-4484	54	49	g.	g.	PROPN
ejpam-4484	54	50	2	2	NUM
ejpam-4484	54	51	.	.	PUNCT
ejpam-4484	54	52	preliminary	preliminary	ADJ
ejpam-4484	54	53	results	result	NOUN
ejpam-4484	54	54	lemma	lemma	PROPN
ejpam-4484	54	55	1	1	X
ejpam-4484	54	56	.	.	PUNCT
ejpam-4484	55	1	[	[	X
ejpam-4484	55	2	7	7	X
ejpam-4484	55	3	]	]	PUNCT
ejpam-4484	55	4	let	let	VERB
ejpam-4484	55	5	g	g	PRON
ejpam-4484	55	6	be	be	AUX
ejpam-4484	55	7	a	a	DET
ejpam-4484	55	8	nontrivial	nontrivial	ADJ
ejpam-4484	55	9	connected	connect	VERB
ejpam-4484	55	10	graph	graph	NOUN
ejpam-4484	55	11	with	with	ADP
ejpam-4484	55	12	diam(g	diam(g	NOUN
ejpam-4484	55	13	)	)	PUNCT
ejpam-4484	55	14	≤	≤	NOUN
ejpam-4484	55	15	2	2	NUM
ejpam-4484	55	16	.	.	PUNCT
ejpam-4484	56	1	then	then	ADV
ejpam-4484	56	2	s	s	VERB
ejpam-4484	56	3	=	=	SYM
ejpam-4484	56	4	v	v	PROPN
ejpam-4484	56	5	(	(	PUNCT
ejpam-4484	56	6	g	g	NOUN
ejpam-4484	56	7	)	)	PUNCT
ejpam-4484	56	8	\c	\c	NOUN
ejpam-4484	56	9	is	be	AUX
ejpam-4484	56	10	a	a	DET
ejpam-4484	56	11	strong	strong	ADJ
ejpam-4484	56	12	resolving	resolving	NOUN
ejpam-4484	56	13	set	set	NOUN
ejpam-4484	56	14	of	of	ADP
ejpam-4484	56	15	g	g	PROPN
ejpam-4484	56	16	if	if	SCONJ
ejpam-4484	56	17	and	and	CCONJ
ejpam-4484	56	18	only	only	ADV
ejpam-4484	56	19	if	if	SCONJ
ejpam-4484	56	20	c	c	NOUN
ejpam-4484	56	21	=	=	SYM
ejpam-4484	56	22	∅	∅	NOUN
ejpam-4484	56	23	or	or	CCONJ
ejpam-4484	56	24	c	c	NOUN
ejpam-4484	56	25	is	be	AUX
ejpam-4484	56	26	a	a	DET
ejpam-4484	56	27	superclique	superclique	NOUN
ejpam-4484	56	28	in	in	ADP
ejpam-4484	56	29	g.	g.	PROPN
ejpam-4484	56	30	in	in	ADP
ejpam-4484	56	31	particular	particular	ADJ
ejpam-4484	56	32	,	,	PUNCT
ejpam-4484	56	33	sdim(g	sdim(g	PROPN
ejpam-4484	56	34	)	)	PUNCT
ejpam-4484	56	35	=	=	SYM
ejpam-4484	56	36	|v	|v	PROPN
ejpam-4484	56	37	(	(	PUNCT
ejpam-4484	56	38	g)|	g)|	NOUN
ejpam-4484	56	39	−	−	NOUN
ejpam-4484	56	40	ωs(g	ωs(g	PUNCT
ejpam-4484	56	41	)	)	PUNCT
ejpam-4484	56	42	.	.	PUNCT
ejpam-4484	57	1	proposition	proposition	NOUN
ejpam-4484	57	2	1	1	NUM
ejpam-4484	57	3	.	.	PUNCT
ejpam-4484	58	1	let	let	VERB
ejpam-4484	58	2	g	g	PRON
ejpam-4484	58	3	be	be	AUX
ejpam-4484	58	4	a	a	DET
ejpam-4484	58	5	connected	connected	ADJ
ejpam-4484	58	6	graph	graph	NOUN
ejpam-4484	58	7	of	of	ADP
ejpam-4484	58	8	order	order	NOUN
ejpam-4484	58	9	n	n	NOUN
ejpam-4484	58	10	and	and	CCONJ
ejpam-4484	58	11	a	a	DET
ejpam-4484	58	12	=	=	X
ejpam-4484	58	13	{	{	PUNCT
ejpam-4484	58	14	x	x	PROPN
ejpam-4484	58	15	∈	∈	PROPN
ejpam-4484	58	16	g	g	NOUN
ejpam-4484	58	17	:	:	PUNCT
ejpam-4484	58	18	degg(x	degg(x	X
ejpam-4484	58	19	)	)	PUNCT
ejpam-4484	58	20	=	=	PUNCT
ejpam-4484	58	21	n−	n−	NOUN
ejpam-4484	58	22	1	1	NUM
ejpam-4484	58	23	}	}	PUNCT
ejpam-4484	58	24	.	.	PUNCT
ejpam-4484	59	1	if	if	SCONJ
ejpam-4484	59	2	a	a	DET
ejpam-4484	59	3	̸=	̸=	PROPN
ejpam-4484	59	4	∅	∅	NOUN
ejpam-4484	59	5	and	and	CCONJ
ejpam-4484	59	6	c	c	NOUN
ejpam-4484	59	7	is	be	AUX
ejpam-4484	59	8	a	a	DET
ejpam-4484	59	9	hop	hop	NOUN
ejpam-4484	59	10	dominated	dominate	VERB
ejpam-4484	59	11	superclique	superclique	NOUN
ejpam-4484	59	12	in	in	ADP
ejpam-4484	59	13	g	g	PROPN
ejpam-4484	59	14	,	,	PUNCT
ejpam-4484	59	15	then	then	ADV
ejpam-4484	59	16	c	c	NOUN
ejpam-4484	59	17	∩a	∩a	PROPN
ejpam-4484	59	18	=	=	PUNCT
ejpam-4484	60	1	∅.	∅.	NOUN
ejpam-4484	60	2	theorem	theorem	VERB
ejpam-4484	60	3	1	1	NUM
ejpam-4484	60	4	.	.	PUNCT
ejpam-4484	61	1	[	[	X
ejpam-4484	61	2	7	7	X
ejpam-4484	61	3	]	]	PUNCT
ejpam-4484	61	4	let	let	VERB
ejpam-4484	61	5	g	g	PRON
ejpam-4484	61	6	be	be	AUX
ejpam-4484	61	7	a	a	DET
ejpam-4484	61	8	nontrivial	nontrivial	ADJ
ejpam-4484	61	9	connected	connect	VERB
ejpam-4484	61	10	graph	graph	NOUN
ejpam-4484	61	11	of	of	ADP
ejpam-4484	61	12	order	order	NOUN
ejpam-4484	61	13	n	n	PRON
ejpam-4484	61	14	with	with	ADP
ejpam-4484	61	15	γ(g	γ(g	PROPN
ejpam-4484	61	16	)	)	PUNCT
ejpam-4484	62	1	̸=	̸=	PROPN
ejpam-4484	62	2	1	1	NUM
ejpam-4484	62	3	and	and	CCONJ
ejpam-4484	62	4	k1	k1	NOUN
ejpam-4484	62	5	=	=	SYM
ejpam-4484	62	6	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4484	62	7	then	then	ADV
ejpam-4484	62	8	s	s	VERB
ejpam-4484	62	9	⊆	⊆	NUM
ejpam-4484	62	10	v	v	NOUN
ejpam-4484	62	11	(	(	PUNCT
ejpam-4484	62	12	k1	k1	NOUN
ejpam-4484	62	13	+	+	CCONJ
ejpam-4484	62	14	g	g	NOUN
ejpam-4484	62	15	)	)	PUNCT
ejpam-4484	62	16	is	be	AUX
ejpam-4484	62	17	a	a	DET
ejpam-4484	62	18	strong	strong	ADJ
ejpam-4484	62	19	resolving	resolving	NOUN
ejpam-4484	62	20	set	set	NOUN
ejpam-4484	62	21	of	of	ADP
ejpam-4484	62	22	k1	k1	NOUN
ejpam-4484	62	23	+	+	CCONJ
ejpam-4484	62	24	g	g	NOUN
ejpam-4484	62	25	if	if	SCONJ
ejpam-4484	63	1	and	and	CCONJ
ejpam-4484	63	2	only	only	ADV
ejpam-4484	63	3	if	if	SCONJ
ejpam-4484	63	4	s	s	VERB
ejpam-4484	63	5	=	=	SYM
ejpam-4484	63	6	v	v	X
ejpam-4484	63	7	(	(	PUNCT
ejpam-4484	63	8	g	g	NOUN
ejpam-4484	63	9	)	)	PUNCT
ejpam-4484	63	10	,	,	PUNCT
ejpam-4484	63	11	s	s	NOUN
ejpam-4484	63	12	=	=	SYM
ejpam-4484	63	13	v	v	X
ejpam-4484	63	14	(	(	PUNCT
ejpam-4484	63	15	g	g	NOUN
ejpam-4484	63	16	)	)	PUNCT
ejpam-4484	63	17	\	\	PUNCT
ejpam-4484	64	1	c	c	X
ejpam-4484	64	2	,	,	PUNCT
ejpam-4484	64	3	or	or	CCONJ
ejpam-4484	64	4	s	s	NOUN
ejpam-4484	64	5	=	=	SYM
ejpam-4484	64	6	v	v	PROPN
ejpam-4484	64	7	(	(	PUNCT
ejpam-4484	64	8	k1	k1	NOUN
ejpam-4484	64	9	+	+	PROPN
ejpam-4484	64	10	g	g	NOUN
ejpam-4484	64	11	)	)	PUNCT
ejpam-4484	64	12	\	\	PUNCT
ejpam-4484	65	1	c	c	NOUN
ejpam-4484	65	2	where	where	SCONJ
ejpam-4484	65	3	c	c	PROPN
ejpam-4484	65	4	is	be	AUX
ejpam-4484	65	5	a	a	DET
ejpam-4484	65	6	superclique	superclique	NOUN
ejpam-4484	65	7	in	in	ADP
ejpam-4484	65	8	g.	g.	PROPN
ejpam-4484	65	9	theorem	theorem	PROPN
ejpam-4484	65	10	2	2	NUM
ejpam-4484	65	11	.	.	PUNCT
ejpam-4484	66	1	[	[	X
ejpam-4484	66	2	7	7	X
ejpam-4484	66	3	]	]	X
ejpam-4484	66	4	let	let	VERB
ejpam-4484	66	5	g	g	NOUN
ejpam-4484	66	6	and	and	CCONJ
ejpam-4484	66	7	h	h	NOUN
ejpam-4484	66	8	be	be	AUX
ejpam-4484	66	9	nontrivial	nontrivial	ADJ
ejpam-4484	66	10	connected	connect	VERB
ejpam-4484	66	11	graphs	graph	NOUN
ejpam-4484	66	12	of	of	ADP
ejpam-4484	66	13	orders	order	NOUN
ejpam-4484	66	14	m	m	VERB
ejpam-4484	66	15	and	and	CCONJ
ejpam-4484	66	16	n	n	CCONJ
ejpam-4484	66	17	,	,	PUNCT
ejpam-4484	66	18	respectively	respectively	ADV
ejpam-4484	66	19	.	.	PUNCT
ejpam-4484	67	1	a	a	DET
ejpam-4484	67	2	proper	proper	ADJ
ejpam-4484	67	3	subset	subset	NOUN
ejpam-4484	67	4	s	s	NOUN
ejpam-4484	67	5	of	of	ADP
ejpam-4484	67	6	v	v	NOUN
ejpam-4484	67	7	(	(	PUNCT
ejpam-4484	67	8	g+h	g+h	PROPN
ejpam-4484	67	9	)	)	PUNCT
ejpam-4484	67	10	is	be	AUX
ejpam-4484	67	11	a	a	DET
ejpam-4484	67	12	strong	strong	ADJ
ejpam-4484	67	13	resolving	resolving	NOUN
ejpam-4484	67	14	set	set	NOUN
ejpam-4484	67	15	of	of	ADP
ejpam-4484	67	16	g+h	g+h	PROPN
ejpam-4484	67	17	if	if	SCONJ
ejpam-4484	67	18	and	and	CCONJ
ejpam-4484	67	19	only	only	ADV
ejpam-4484	67	20	if	if	SCONJ
ejpam-4484	67	21	at	at	ADV
ejpam-4484	67	22	least	least	ADJ
ejpam-4484	67	23	one	one	NUM
ejpam-4484	67	24	of	of	ADP
ejpam-4484	67	25	the	the	DET
ejpam-4484	67	26	following	follow	VERB
ejpam-4484	67	27	is	be	AUX
ejpam-4484	67	28	satisfied	satisfied	ADJ
ejpam-4484	67	29	:	:	PUNCT
ejpam-4484	67	30	(	(	PUNCT
ejpam-4484	67	31	i	i	NOUN
ejpam-4484	67	32	)	)	PUNCT
ejpam-4484	67	33	s	s	PART
ejpam-4484	67	34	=	=	SYM
ejpam-4484	67	35	v	v	PROPN
ejpam-4484	67	36	(	(	PUNCT
ejpam-4484	67	37	g+h	g+h	NOUN
ejpam-4484	67	38	)	)	PUNCT
ejpam-4484	67	39	\	\	PROPN
ejpam-4484	68	1	cg	cg	NOUN
ejpam-4484	68	2	where	where	SCONJ
ejpam-4484	68	3	cg	cg	NOUN
ejpam-4484	68	4	is	be	AUX
ejpam-4484	68	5	a	a	DET
ejpam-4484	68	6	superclique	superclique	NOUN
ejpam-4484	68	7	in	in	ADP
ejpam-4484	68	8	g.	g.	PROPN
ejpam-4484	68	9	(	(	PUNCT
ejpam-4484	68	10	ii	ii	PROPN
ejpam-4484	68	11	)	)	PUNCT
ejpam-4484	68	12	s	s	PART
ejpam-4484	68	13	=	=	SYM
ejpam-4484	68	14	v	v	PROPN
ejpam-4484	68	15	(	(	PUNCT
ejpam-4484	68	16	g+h	g+h	NOUN
ejpam-4484	68	17	)	)	PUNCT
ejpam-4484	68	18	\	\	PROPN
ejpam-4484	69	1	ch	ch	NOUN
ejpam-4484	69	2	where	where	SCONJ
ejpam-4484	69	3	ch	ch	NOUN
ejpam-4484	69	4	is	be	AUX
ejpam-4484	69	5	a	a	DET
ejpam-4484	69	6	superclique	superclique	NOUN
ejpam-4484	69	7	in	in	ADP
ejpam-4484	69	8	h.	h.	PROPN
ejpam-4484	69	9	(	(	PUNCT
ejpam-4484	69	10	iii	iii	X
ejpam-4484	69	11	)	)	PUNCT
ejpam-4484	69	12	if	if	SCONJ
ejpam-4484	69	13	γ(g	γ(g	PROPN
ejpam-4484	69	14	)	)	PUNCT
ejpam-4484	69	15	̸=	̸=	PROPN
ejpam-4484	69	16	1	1	NUM
ejpam-4484	69	17	or	or	CCONJ
ejpam-4484	69	18	γ(h	γ(h	NOUN
ejpam-4484	69	19	)	)	PUNCT
ejpam-4484	69	20	̸=	̸=	PROPN
ejpam-4484	69	21	1	1	NUM
ejpam-4484	69	22	,	,	PUNCT
ejpam-4484	69	23	s	s	NOUN
ejpam-4484	69	24	=	=	SYM
ejpam-4484	69	25	v	v	PROPN
ejpam-4484	69	26	(	(	PUNCT
ejpam-4484	69	27	g+h	g+h	NOUN
ejpam-4484	69	28	)	)	PUNCT
ejpam-4484	69	29	\	\	PUNCT
ejpam-4484	70	1	(	(	PUNCT
ejpam-4484	70	2	cg	cg	NOUN
ejpam-4484	70	3	∪	∪	PROPN
ejpam-4484	70	4	ch	ch	NOUN
ejpam-4484	70	5	)	)	PUNCT
ejpam-4484	70	6	=	=	PUNCT
ejpam-4484	70	7	(	(	PUNCT
ejpam-4484	70	8	v	v	NOUN
ejpam-4484	70	9	(	(	PUNCT
ejpam-4484	70	10	g	g	NOUN
ejpam-4484	70	11	)	)	PUNCT
ejpam-4484	70	12	\	\	PROPN
ejpam-4484	70	13	cg	cg	NOUN
ejpam-4484	70	14	)	)	PUNCT
ejpam-4484	71	1	∪	∪	NOUN
ejpam-4484	71	2	(	(	PUNCT
ejpam-4484	71	3	v	v	NOUN
ejpam-4484	71	4	(	(	PUNCT
ejpam-4484	71	5	h	h	NOUN
ejpam-4484	71	6	)	)	PUNCT
ejpam-4484	71	7	\	\	PROPN
ejpam-4484	71	8	ch	ch	NOUN
ejpam-4484	71	9	)	)	PUNCT
ejpam-4484	71	10	,	,	PUNCT
ejpam-4484	71	11	a.	a.	PROPN
ejpam-4484	71	12	h.	h.	PROPN
ejpam-4484	71	13	abragan	abragan	PROPN
ejpam-4484	71	14	,	,	PUNCT
ejpam-4484	71	15	h.	h.	PROPN
ejpam-4484	71	16	m.	m.	PROPN
ejpam-4484	71	17	rara	rara	PROPN
ejpam-4484	71	18	/	/	SYM
ejpam-4484	71	19	eur	eur	PROPN
ejpam-4484	71	20	.	.	PUNCT
ejpam-4484	72	1	j.	j.	PROPN
ejpam-4484	72	2	pure	pure	PROPN
ejpam-4484	72	3	appl	appl	PROPN
ejpam-4484	72	4	.	.	PROPN
ejpam-4484	72	5	math	math	PROPN
ejpam-4484	72	6	,	,	PUNCT
ejpam-4484	72	7	15	15	NUM
ejpam-4484	72	8	(	(	PUNCT
ejpam-4484	72	9	4	4	NUM
ejpam-4484	72	10	)	)	PUNCT
ejpam-4484	72	11	(	(	PUNCT
ejpam-4484	72	12	2022	2022	NUM
ejpam-4484	72	13	)	)	PUNCT
ejpam-4484	72	14	,	,	PUNCT
ejpam-4484	72	15	1472	1472	NUM
ejpam-4484	72	16	-	-	SYM
ejpam-4484	72	17	1481	1481	NUM
ejpam-4484	72	18	1475	1475	NUM
ejpam-4484	72	19	where	where	SCONJ
ejpam-4484	72	20	cg	cg	NOUN
ejpam-4484	72	21	and	and	CCONJ
ejpam-4484	72	22	ch	ch	NOUN
ejpam-4484	72	23	are	be	AUX
ejpam-4484	72	24	supercliques	superclique	NOUN
ejpam-4484	72	25	in	in	ADP
ejpam-4484	72	26	g	g	PROPN
ejpam-4484	72	27	and	and	CCONJ
ejpam-4484	72	28	h	h	NOUN
ejpam-4484	72	29	,	,	PUNCT
ejpam-4484	72	30	respectively	respectively	ADV
ejpam-4484	72	31	.	.	PUNCT
ejpam-4484	73	1	lemma	lemma	PROPN
ejpam-4484	73	2	2	2	NUM
ejpam-4484	73	3	.	.	PUNCT
ejpam-4484	74	1	[	[	X
ejpam-4484	74	2	1	1	X
ejpam-4484	74	3	]	]	PUNCT
ejpam-4484	74	4	let	let	VERB
ejpam-4484	74	5	g	g	PROPN
ejpam-4484	74	6	=	=	PROPN
ejpam-4484	74	7	kn	kn	PROPN
ejpam-4484	74	8	for	for	ADP
ejpam-4484	74	9	n	n	PROPN
ejpam-4484	74	10	>	>	SYM
ejpam-4484	74	11	1	1	NUM
ejpam-4484	74	12	and	and	CCONJ
ejpam-4484	74	13	h	h	DET
ejpam-4484	74	14	a	a	DET
ejpam-4484	74	15	nontrivial	nontrivial	ADJ
ejpam-4484	74	16	connected	connect	VERB
ejpam-4484	74	17	graph	graph	NOUN
ejpam-4484	74	18	with	with	ADP
ejpam-4484	74	19	γ(h	γ(h	NOUN
ejpam-4484	74	20	)	)	PUNCT
ejpam-4484	74	21	̸=	̸=	PROPN
ejpam-4484	74	22	1	1	NUM
ejpam-4484	74	23	.	.	PUNCT
ejpam-4484	75	1	then	then	ADV
ejpam-4484	75	2	a×c	a×c	PROPN
ejpam-4484	75	3	⊆	⊆	NUM
ejpam-4484	75	4	v	v	NOUN
ejpam-4484	75	5	(	(	PUNCT
ejpam-4484	75	6	g[h	g[h	PROPN
ejpam-4484	75	7	]	]	PUNCT
ejpam-4484	75	8	)	)	PUNCT
ejpam-4484	75	9	is	be	AUX
ejpam-4484	75	10	a	a	DET
ejpam-4484	75	11	superclique	superclique	NOUN
ejpam-4484	75	12	in	in	ADP
ejpam-4484	75	13	g[h	g[h	NOUN
ejpam-4484	75	14	]	]	PUNCT
ejpam-4484	75	15	if	if	SCONJ
ejpam-4484	76	1	and	and	CCONJ
ejpam-4484	76	2	only	only	ADV
ejpam-4484	76	3	if	if	SCONJ
ejpam-4484	76	4	a	a	PRON
ejpam-4484	76	5	is	be	AUX
ejpam-4484	76	6	a	a	DET
ejpam-4484	76	7	nonempty	nonempty	ADJ
ejpam-4484	76	8	subset	subset	NOUN
ejpam-4484	76	9	of	of	ADP
ejpam-4484	76	10	v	v	NOUN
ejpam-4484	76	11	(	(	PUNCT
ejpam-4484	76	12	g	g	NOUN
ejpam-4484	76	13	)	)	PUNCT
ejpam-4484	76	14	and	and	CCONJ
ejpam-4484	76	15	c	c	PROPN
ejpam-4484	76	16	is	be	AUX
ejpam-4484	76	17	a	a	DET
ejpam-4484	76	18	superclique	superclique	NOUN
ejpam-4484	76	19	in	in	ADP
ejpam-4484	76	20	h.	h.	PROPN
ejpam-4484	76	21	theorem	theorem	PROPN
ejpam-4484	76	22	3	3	NUM
ejpam-4484	76	23	.	.	PUNCT
ejpam-4484	77	1	[	[	X
ejpam-4484	77	2	1	1	X
ejpam-4484	77	3	]	]	PUNCT
ejpam-4484	77	4	let	let	VERB
ejpam-4484	77	5	g	g	PROPN
ejpam-4484	77	6	=	=	PROPN
ejpam-4484	77	7	kn	kn	PROPN
ejpam-4484	77	8	for	for	ADP
ejpam-4484	77	9	n	n	PROPN
ejpam-4484	77	10	>	>	SYM
ejpam-4484	77	11	1	1	NUM
ejpam-4484	77	12	and	and	CCONJ
ejpam-4484	77	13	h	h	DET
ejpam-4484	77	14	a	a	DET
ejpam-4484	77	15	nontrivial	nontrivial	ADJ
ejpam-4484	77	16	connected	connect	VERB
ejpam-4484	77	17	graph	graph	NOUN
ejpam-4484	77	18	with	with	ADP
ejpam-4484	77	19	γ(h	γ(h	NOUN
ejpam-4484	77	20	)	)	PUNCT
ejpam-4484	77	21	̸=	̸=	PROPN
ejpam-4484	77	22	1	1	NUM
ejpam-4484	77	23	.	.	PUNCT
ejpam-4484	78	1	a	a	DET
ejpam-4484	78	2	subset	subset	NOUN
ejpam-4484	78	3	s	s	X
ejpam-4484	78	4	of	of	ADP
ejpam-4484	78	5	v	v	NOUN
ejpam-4484	78	6	(	(	PUNCT
ejpam-4484	78	7	g[h	g[h	PROPN
ejpam-4484	78	8	]	]	PUNCT
ejpam-4484	78	9	)	)	PUNCT
ejpam-4484	78	10	is	be	AUX
ejpam-4484	78	11	a	a	DET
ejpam-4484	78	12	strong	strong	ADJ
ejpam-4484	78	13	resolving	resolving	NOUN
ejpam-4484	78	14	set	set	NOUN
ejpam-4484	78	15	of	of	ADP
ejpam-4484	78	16	g[h	g[h	NOUN
ejpam-4484	78	17	]	]	PUNCT
ejpam-4484	78	18	if	if	SCONJ
ejpam-4484	78	19	and	and	CCONJ
ejpam-4484	78	20	only	only	ADV
ejpam-4484	78	21	s	s	PART
ejpam-4484	78	22	=	=	SYM
ejpam-4484	78	23	v	v	PROPN
ejpam-4484	78	24	(	(	PUNCT
ejpam-4484	78	25	g[h])\(a×c	g[h])\(a×c	NOUN
ejpam-4484	78	26	)	)	PUNCT
ejpam-4484	78	27	,	,	PUNCT
ejpam-4484	78	28	where	where	SCONJ
ejpam-4484	78	29	a	a	PRON
ejpam-4484	78	30	is	be	AUX
ejpam-4484	78	31	a	a	DET
ejpam-4484	78	32	subset	subset	NOUN
ejpam-4484	78	33	of	of	ADP
ejpam-4484	78	34	v	v	NOUN
ejpam-4484	78	35	(	(	PUNCT
ejpam-4484	78	36	g	g	NOUN
ejpam-4484	78	37	)	)	PUNCT
ejpam-4484	78	38	and	and	CCONJ
ejpam-4484	78	39	c	c	NOUN
ejpam-4484	78	40	=	=	SYM
ejpam-4484	78	41	∅	∅	NOUN
ejpam-4484	78	42	or	or	CCONJ
ejpam-4484	78	43	c	c	NOUN
ejpam-4484	78	44	is	be	AUX
ejpam-4484	78	45	a	a	DET
ejpam-4484	78	46	superclique	superclique	NOUN
ejpam-4484	78	47	in	in	ADP
ejpam-4484	78	48	h.	h.	PROPN
ejpam-4484	78	49	lemma	lemma	PROPN
ejpam-4484	79	1	3	3	X
ejpam-4484	79	2	.	.	PUNCT
ejpam-4484	80	1	[	[	X
ejpam-4484	80	2	1	1	X
ejpam-4484	80	3	]	]	PUNCT
ejpam-4484	80	4	let	let	VERB
ejpam-4484	80	5	g	g	PROPN
ejpam-4484	80	6	=	=	PROPN
ejpam-4484	80	7	kn	kn	PROPN
ejpam-4484	80	8	for	for	ADP
ejpam-4484	80	9	n	n	PROPN
ejpam-4484	80	10	>	>	SYM
ejpam-4484	80	11	1	1	NUM
ejpam-4484	80	12	and	and	CCONJ
ejpam-4484	80	13	h	h	DET
ejpam-4484	80	14	a	a	DET
ejpam-4484	80	15	nontrivial	nontrivial	ADJ
ejpam-4484	80	16	connected	connect	VERB
ejpam-4484	80	17	graph	graph	NOUN
ejpam-4484	80	18	with	with	ADP
ejpam-4484	80	19	γ(h	γ(h	NOUN
ejpam-4484	80	20	)	)	PUNCT
ejpam-4484	80	21	=	=	SYM
ejpam-4484	81	1	1	1	X
ejpam-4484	81	2	.	.	PUNCT
ejpam-4484	82	1	then	then	ADV
ejpam-4484	82	2	a×c	a×c	PROPN
ejpam-4484	82	3	⊆	⊆	NUM
ejpam-4484	82	4	v	v	NOUN
ejpam-4484	82	5	(	(	PUNCT
ejpam-4484	82	6	g[h	g[h	PROPN
ejpam-4484	82	7	]	]	PUNCT
ejpam-4484	82	8	)	)	PUNCT
ejpam-4484	82	9	is	be	AUX
ejpam-4484	82	10	a	a	DET
ejpam-4484	82	11	superclique	superclique	NOUN
ejpam-4484	82	12	in	in	ADP
ejpam-4484	82	13	g[h	g[h	NOUN
ejpam-4484	82	14	]	]	PUNCT
ejpam-4484	82	15	if	if	SCONJ
ejpam-4484	83	1	and	and	CCONJ
ejpam-4484	83	2	only	only	ADV
ejpam-4484	83	3	if	if	SCONJ
ejpam-4484	83	4	a	a	PRON
ejpam-4484	83	5	is	be	AUX
ejpam-4484	83	6	a	a	DET
ejpam-4484	83	7	nonempty	nonempty	ADJ
ejpam-4484	83	8	subset	subset	NOUN
ejpam-4484	83	9	of	of	ADP
ejpam-4484	83	10	v	v	NOUN
ejpam-4484	83	11	(	(	PUNCT
ejpam-4484	83	12	g	g	NOUN
ejpam-4484	83	13	)	)	PUNCT
ejpam-4484	83	14	and	and	CCONJ
ejpam-4484	83	15	c	c	PROPN
ejpam-4484	83	16	is	be	AUX
ejpam-4484	83	17	a	a	DET
ejpam-4484	83	18	superclique	superclique	NOUN
ejpam-4484	83	19	in	in	ADP
ejpam-4484	83	20	h	h	NOUN
ejpam-4484	83	21	such	such	ADJ
ejpam-4484	83	22	that	that	DET
ejpam-4484	83	23	|a|	|a|	PROPN
ejpam-4484	83	24	=	=	SYM
ejpam-4484	83	25	1	1	NUM
ejpam-4484	83	26	whenever	whenever	SCONJ
ejpam-4484	83	27	c	c	NOUN
ejpam-4484	83	28	∩c∗	∩c∗	SYM
ejpam-4484	83	29	̸=	̸=	PROPN
ejpam-4484	83	30	∅	∅	NOUN
ejpam-4484	83	31	for	for	ADP
ejpam-4484	83	32	some	some	DET
ejpam-4484	83	33	γ	γ	NOUN
ejpam-4484	83	34	-	-	PUNCT
ejpam-4484	83	35	set	set	ADJ
ejpam-4484	83	36	c∗	c∗	NOUN
ejpam-4484	83	37	of	of	ADP
ejpam-4484	83	38	h.	h.	PROPN
ejpam-4484	83	39	theorem	theorem	PROPN
ejpam-4484	83	40	4	4	NUM
ejpam-4484	83	41	.	.	PUNCT
ejpam-4484	84	1	[	[	X
ejpam-4484	84	2	7	7	X
ejpam-4484	84	3	]	]	PUNCT
ejpam-4484	84	4	let	let	VERB
ejpam-4484	84	5	g	g	PRON
ejpam-4484	84	6	be	be	AUX
ejpam-4484	84	7	a	a	DET
ejpam-4484	84	8	nontrivial	nontrivial	ADJ
ejpam-4484	84	9	connected	connect	VERB
ejpam-4484	84	10	graph	graph	NOUN
ejpam-4484	84	11	and	and	CCONJ
ejpam-4484	84	12	h	h	NOUN
ejpam-4484	84	13	a	a	DET
ejpam-4484	84	14	connected	connected	ADJ
ejpam-4484	84	15	graph	graph	NOUN
ejpam-4484	84	16	.	.	PUNCT
ejpam-4484	85	1	a	a	DET
ejpam-4484	85	2	proper	proper	ADJ
ejpam-4484	85	3	subset	subset	NOUN
ejpam-4484	85	4	s	s	NOUN
ejpam-4484	85	5	of	of	ADP
ejpam-4484	85	6	v	v	NOUN
ejpam-4484	85	7	(	(	PUNCT
ejpam-4484	85	8	g	g	PROPN
ejpam-4484	85	9	◦	◦	NOUN
ejpam-4484	85	10	h	h	NOUN
ejpam-4484	85	11	)	)	PUNCT
ejpam-4484	85	12	is	be	AUX
ejpam-4484	85	13	a	a	DET
ejpam-4484	85	14	strong	strong	ADJ
ejpam-4484	85	15	resolving	resolving	NOUN
ejpam-4484	85	16	set	set	NOUN
ejpam-4484	85	17	of	of	ADP
ejpam-4484	85	18	g	g	PROPN
ejpam-4484	85	19	◦	◦	NOUN
ejpam-4484	85	20	h	h	NOUN
ejpam-4484	85	21	if	if	SCONJ
ejpam-4484	86	1	and	and	CCONJ
ejpam-4484	86	2	only	only	ADV
ejpam-4484	86	3	if	if	SCONJ
ejpam-4484	86	4	one	one	NUM
ejpam-4484	86	5	of	of	ADP
ejpam-4484	86	6	the	the	DET
ejpam-4484	86	7	following	follow	VERB
ejpam-4484	86	8	holds	hold	VERB
ejpam-4484	86	9	:	:	PUNCT
ejpam-4484	86	10	(	(	PUNCT
ejpam-4484	86	11	i	i	NOUN
ejpam-4484	86	12	)	)	PUNCT
ejpam-4484	86	13	s	s	PART
ejpam-4484	86	14	=	=	PUNCT
ejpam-4484	86	15	a	a	DET
ejpam-4484	86	16	∪	∪	X
ejpam-4484	86	17	(	(	PUNCT
ejpam-4484	86	18	∪	∪	ADJ
ejpam-4484	86	19	u∈v	u∈v	NOUN
ejpam-4484	86	20	(	(	PUNCT
ejpam-4484	86	21	g	g	NOUN
ejpam-4484	86	22	)	)	PUNCT
ejpam-4484	86	23	v	v	NOUN
ejpam-4484	86	24	(	(	PUNCT
ejpam-4484	86	25	hu	hu	PROPN
ejpam-4484	86	26	)	)	PUNCT
ejpam-4484	86	27	)	)	PUNCT
ejpam-4484	86	28	where	where	SCONJ
ejpam-4484	86	29	a	a	DET
ejpam-4484	86	30	⊆	⊆	NUM
ejpam-4484	86	31	v	v	NOUN
ejpam-4484	86	32	(	(	PUNCT
ejpam-4484	86	33	g	g	NOUN
ejpam-4484	86	34	)	)	PUNCT
ejpam-4484	86	35	.	.	PUNCT
ejpam-4484	87	1	(	(	PUNCT
ejpam-4484	87	2	ii	ii	X
ejpam-4484	87	3	)	)	PUNCT
ejpam-4484	87	4	s	s	PART
ejpam-4484	87	5	=	=	SYM
ejpam-4484	87	6	∪	∪	X
ejpam-4484	87	7	(	(	PUNCT
ejpam-4484	87	8	∪	∪	ADJ
ejpam-4484	87	9	u∈v	u∈v	NOUN
ejpam-4484	87	10	(	(	PUNCT
ejpam-4484	87	11	g)\{v	g)\{v	PROPN
ejpam-4484	87	12	}	}	PUNCT
ejpam-4484	87	13	v	v	PROPN
ejpam-4484	87	14	(	(	PUNCT
ejpam-4484	87	15	hu	hu	PROPN
ejpam-4484	87	16	)	)	PUNCT
ejpam-4484	87	17	)	)	PUNCT
ejpam-4484	88	1	∪bv	∪bv	NOUN
ejpam-4484	88	2	for	for	ADP
ejpam-4484	88	3	a	a	DET
ejpam-4484	88	4	unique	unique	ADJ
ejpam-4484	88	5	v	v	NOUN
ejpam-4484	88	6	in	in	ADP
ejpam-4484	88	7	v	v	NOUN
ejpam-4484	88	8	(	(	PUNCT
ejpam-4484	88	9	g	g	NOUN
ejpam-4484	88	10	)	)	PUNCT
ejpam-4484	88	11	,	,	PUNCT
ejpam-4484	88	12	where	where	SCONJ
ejpam-4484	88	13	a	a	DET
ejpam-4484	88	14	⊆	⊆	NUM
ejpam-4484	88	15	v	v	NOUN
ejpam-4484	88	16	(	(	PUNCT
ejpam-4484	88	17	g	g	NOUN
ejpam-4484	88	18	)	)	PUNCT
ejpam-4484	88	19	and	and	CCONJ
ejpam-4484	88	20	bv	bv	PROPN
ejpam-4484	88	21	is	be	AUX
ejpam-4484	88	22	a	a	DET
ejpam-4484	88	23	strong	strong	ADJ
ejpam-4484	88	24	resolving	resolving	NOUN
ejpam-4484	88	25	set	set	NOUN
ejpam-4484	88	26	of	of	ADP
ejpam-4484	88	27	hv	hv	PROPN
ejpam-4484	88	28	if	if	SCONJ
ejpam-4484	88	29	γ(h	γ(h	NOUN
ejpam-4484	88	30	)	)	PUNCT
ejpam-4484	88	31	=	=	SYM
ejpam-4484	88	32	1	1	NUM
ejpam-4484	88	33	or	or	CCONJ
ejpam-4484	88	34	bv	bv	PROPN
ejpam-4484	88	35	is	be	AUX
ejpam-4484	88	36	a	a	DET
ejpam-4484	88	37	resolving	resolving	NOUN
ejpam-4484	88	38	set	set	NOUN
ejpam-4484	88	39	of	of	ADP
ejpam-4484	88	40	{	{	PUNCT
ejpam-4484	88	41	v}+hv	v}+hv	PRON
ejpam-4484	88	42	if	if	SCONJ
ejpam-4484	88	43	γ(h	γ(h	NOUN
ejpam-4484	88	44	)	)	PUNCT
ejpam-4484	88	45	̸=	̸=	PROPN
ejpam-4484	88	46	1	1	NUM
ejpam-4484	88	47	.	.	PUNCT
ejpam-4484	88	48	remark	remark	NOUN
ejpam-4484	88	49	1	1	NUM
ejpam-4484	88	50	.	.	PUNCT
ejpam-4484	89	1	every	every	DET
ejpam-4484	89	2	restrained	restrain	VERB
ejpam-4484	89	3	strong	strong	ADJ
ejpam-4484	89	4	resolving	resolve	VERB
ejpam-4484	89	5	hop	hop	NOUN
ejpam-4484	89	6	dominating	dominating	NOUN
ejpam-4484	89	7	set	set	NOUN
ejpam-4484	89	8	of	of	ADP
ejpam-4484	89	9	a	a	DET
ejpam-4484	89	10	connected	connected	ADJ
ejpam-4484	89	11	graph	graph	NOUN
ejpam-4484	89	12	g	g	PROPN
ejpam-4484	89	13	is	be	AUX
ejpam-4484	89	14	a	a	DET
ejpam-4484	89	15	strong	strong	ADJ
ejpam-4484	89	16	resolving	resolving	NOUN
ejpam-4484	89	17	set	set	NOUN
ejpam-4484	89	18	.	.	PUNCT
ejpam-4484	90	1	hence	hence	ADV
ejpam-4484	90	2	,	,	PUNCT
ejpam-4484	90	3	sdim(g	sdim(g	PROPN
ejpam-4484	90	4	)	)	PUNCT
ejpam-4484	90	5	≤	≤	NUM
ejpam-4484	90	6	γrsrh(g	γrsrh(g	NOUN
ejpam-4484	90	7	)	)	PUNCT
ejpam-4484	90	8	.	.	PUNCT
ejpam-4484	91	1	also	also	ADV
ejpam-4484	91	2	,	,	PUNCT
ejpam-4484	91	3	every	every	DET
ejpam-4484	91	4	restrained	restrain	VERB
ejpam-4484	91	5	strong	strong	ADJ
ejpam-4484	91	6	resolving	resolve	VERB
ejpam-4484	91	7	hop	hop	NOUN
ejpam-4484	91	8	dominating	dominating	NOUN
ejpam-4484	91	9	set	set	NOUN
ejpam-4484	91	10	of	of	ADP
ejpam-4484	91	11	g	g	PROPN
ejpam-4484	91	12	is	be	AUX
ejpam-4484	91	13	a	a	DET
ejpam-4484	91	14	hop	hop	NOUN
ejpam-4484	91	15	dominating	dominating	NOUN
ejpam-4484	91	16	set	set	NOUN
ejpam-4484	91	17	.	.	PUNCT
ejpam-4484	92	1	thus	thus	ADV
ejpam-4484	92	2	,	,	PUNCT
ejpam-4484	92	3	γh(g	γh(g	NOUN
ejpam-4484	92	4	)	)	PUNCT
ejpam-4484	92	5	≤	≤	NUM
ejpam-4484	92	6	γrsrh(g	γrsrh(g	NOUN
ejpam-4484	92	7	)	)	PUNCT
ejpam-4484	92	8	.	.	PUNCT
ejpam-4484	93	1	remark	remark	PROPN
ejpam-4484	93	2	2	2	NUM
ejpam-4484	93	3	.	.	PUNCT
ejpam-4484	94	1	for	for	ADP
ejpam-4484	94	2	any	any	DET
ejpam-4484	94	3	connected	connected	ADJ
ejpam-4484	94	4	graph	graph	NOUN
ejpam-4484	94	5	g	g	NOUN
ejpam-4484	94	6	of	of	ADP
ejpam-4484	94	7	order	order	NOUN
ejpam-4484	94	8	n	n	CCONJ
ejpam-4484	94	9	,	,	PUNCT
ejpam-4484	94	10	1	1	NUM
ejpam-4484	94	11	≤	≤	NUM
ejpam-4484	94	12	γrsrh(g	γrsrh(g	PROPN
ejpam-4484	94	13	)	)	PUNCT
ejpam-4484	94	14	≤	≤	NOUN
ejpam-4484	94	15	n.	n.	NOUN
ejpam-4484	94	16	moreover	moreover	ADV
ejpam-4484	94	17	,	,	PUNCT
ejpam-4484	94	18	γrsrh(g	γrsrh(g	NOUN
ejpam-4484	94	19	)	)	PUNCT
ejpam-4484	94	20	=	=	SYM
ejpam-4484	94	21	1	1	NUM
ejpam-4484	94	22	if	if	SCONJ
ejpam-4484	94	23	g	g	PROPN
ejpam-4484	94	24	is	be	AUX
ejpam-4484	94	25	a	a	DET
ejpam-4484	94	26	trivial	trivial	ADJ
ejpam-4484	94	27	graph	graph	NOUN
ejpam-4484	94	28	and	and	CCONJ
ejpam-4484	94	29	γrsrh(kn	γrsrh(kn	NOUN
ejpam-4484	94	30	)	)	PUNCT
ejpam-4484	94	31	=	=	SYM
ejpam-4484	94	32	n	n	PROPN
ejpam-4484	94	33	for	for	ADP
ejpam-4484	94	34	n	n	PRON
ejpam-4484	94	35	≥	≥	NUM
ejpam-4484	94	36	1	1	NUM
ejpam-4484	94	37	.	.	PUNCT
ejpam-4484	95	1	the	the	DET
ejpam-4484	95	2	next	next	ADJ
ejpam-4484	95	3	result	result	NOUN
ejpam-4484	95	4	follows	follow	VERB
ejpam-4484	95	5	immediately	immediately	ADV
ejpam-4484	95	6	from	from	ADP
ejpam-4484	95	7	lemma	lemma	PROPN
ejpam-4484	95	8	1	1	NUM
ejpam-4484	95	9	.	.	PUNCT
ejpam-4484	95	10	proposition	proposition	NOUN
ejpam-4484	95	11	2	2	NUM
ejpam-4484	95	12	.	.	PUNCT
ejpam-4484	96	1	let	let	VERB
ejpam-4484	96	2	g	g	PRON
ejpam-4484	96	3	be	be	AUX
ejpam-4484	96	4	a	a	DET
ejpam-4484	96	5	nontrivial	nontrivial	ADJ
ejpam-4484	96	6	connected	connect	VERB
ejpam-4484	96	7	graph	graph	NOUN
ejpam-4484	96	8	with	with	ADP
ejpam-4484	96	9	diam(g	diam(g	NOUN
ejpam-4484	96	10	)	)	PUNCT
ejpam-4484	96	11	≤	≤	NOUN
ejpam-4484	96	12	2	2	NUM
ejpam-4484	96	13	.	.	PUNCT
ejpam-4484	97	1	then	then	ADV
ejpam-4484	97	2	s	s	VERB
ejpam-4484	97	3	⊆	⊆	NUM
ejpam-4484	97	4	v	v	NOUN
ejpam-4484	97	5	(	(	PUNCT
ejpam-4484	97	6	g	g	NOUN
ejpam-4484	97	7	)	)	PUNCT
ejpam-4484	97	8	is	be	AUX
ejpam-4484	97	9	a	a	DET
ejpam-4484	97	10	restrained	restrain	VERB
ejpam-4484	97	11	strong	strong	ADJ
ejpam-4484	97	12	resolving	resolve	VERB
ejpam-4484	97	13	hop	hop	NOUN
ejpam-4484	97	14	dominating	dominating	NOUN
ejpam-4484	97	15	set	set	NOUN
ejpam-4484	97	16	of	of	ADP
ejpam-4484	97	17	g	g	PROPN
ejpam-4484	97	18	if	if	SCONJ
ejpam-4484	98	1	and	and	CCONJ
ejpam-4484	98	2	only	only	ADV
ejpam-4484	98	3	if	if	SCONJ
ejpam-4484	98	4	s	s	VERB
ejpam-4484	98	5	=	=	SYM
ejpam-4484	98	6	v	v	X
ejpam-4484	98	7	(	(	PUNCT
ejpam-4484	98	8	g	g	NOUN
ejpam-4484	98	9	)	)	PUNCT
ejpam-4484	98	10	\	\	PUNCT
ejpam-4484	99	1	c	c	NOUN
ejpam-4484	99	2	where	where	SCONJ
ejpam-4484	99	3	c	c	NOUN
ejpam-4484	99	4	=	=	SYM
ejpam-4484	99	5	∅	∅	NOUN
ejpam-4484	99	6	or	or	CCONJ
ejpam-4484	99	7	c	c	NOUN
ejpam-4484	99	8	is	be	AUX
ejpam-4484	99	9	a	a	DET
ejpam-4484	99	10	nonsingleton	nonsingleton	NOUN
ejpam-4484	99	11	hop	hop	NOUN
ejpam-4484	99	12	dominated	dominate	VERB
ejpam-4484	99	13	superclique	superclique	NOUN
ejpam-4484	99	14	in	in	ADP
ejpam-4484	99	15	g.	g.	PROPN
ejpam-4484	99	16	in	in	ADP
ejpam-4484	99	17	particular	particular	ADJ
ejpam-4484	99	18	,	,	PUNCT
ejpam-4484	99	19	γrsrh(g	γrsrh(g	NOUN
ejpam-4484	99	20	)	)	PUNCT
ejpam-4484	99	21	=	=	SYM
ejpam-4484	99	22	|v	|v	PROPN
ejpam-4484	99	23	(	(	PUNCT
ejpam-4484	99	24	g)|	g)|	PROPN
ejpam-4484	99	25	−	−	PROPN
ejpam-4484	99	26	ωhs(g	ωhs(g	PROPN
ejpam-4484	99	27	)	)	PUNCT
ejpam-4484	99	28	.	.	PUNCT
ejpam-4484	100	1	3	3	X
ejpam-4484	100	2	.	.	X
ejpam-4484	100	3	join	join	VERB
ejpam-4484	100	4	of	of	ADP
ejpam-4484	100	5	graphs	graph	NOUN
ejpam-4484	100	6	definition	definition	NOUN
ejpam-4484	100	7	1	1	NUM
ejpam-4484	100	8	.	.	PUNCT
ejpam-4484	101	1	[	[	X
ejpam-4484	101	2	6	6	NUM
ejpam-4484	101	3	]	]	PUNCT
ejpam-4484	101	4	the	the	DET
ejpam-4484	101	5	join	join	NOUN
ejpam-4484	101	6	g+h	g+h	PROPN
ejpam-4484	101	7	of	of	ADP
ejpam-4484	101	8	graphs	graph	NOUN
ejpam-4484	101	9	g	g	PROPN
ejpam-4484	101	10	and	and	CCONJ
ejpam-4484	101	11	h	h	NOUN
ejpam-4484	101	12	,	,	PUNCT
ejpam-4484	101	13	is	be	AUX
ejpam-4484	101	14	the	the	DET
ejpam-4484	101	15	graph	graph	NOUN
ejpam-4484	101	16	with	with	ADP
ejpam-4484	101	17	vertex	vertex	NOUN
ejpam-4484	101	18	set	set	VERB
ejpam-4484	101	19	v	v	NOUN
ejpam-4484	101	20	(	(	PUNCT
ejpam-4484	101	21	g+h	g+h	NOUN
ejpam-4484	101	22	)	)	PUNCT
ejpam-4484	101	23	=	=	SYM
ejpam-4484	101	24	v	v	X
ejpam-4484	101	25	(	(	PUNCT
ejpam-4484	101	26	g	g	NOUN
ejpam-4484	101	27	)	)	PUNCT
ejpam-4484	101	28	∪̇	∪̇	PROPN
ejpam-4484	101	29	v	v	X
ejpam-4484	101	30	(	(	PUNCT
ejpam-4484	101	31	h	h	NOUN
ejpam-4484	101	32	)	)	PUNCT
ejpam-4484	101	33	and	and	CCONJ
ejpam-4484	101	34	edge	edge	NOUN
ejpam-4484	101	35	-	-	PUNCT
ejpam-4484	101	36	set	set	VERB
ejpam-4484	101	37	e(g+h	e(g+h	NUM
ejpam-4484	101	38	)	)	PUNCT
ejpam-4484	101	39	=	=	SYM
ejpam-4484	101	40	e(g	e(g	PROPN
ejpam-4484	101	41	)	)	PUNCT
ejpam-4484	101	42	∪̇	∪̇	PROPN
ejpam-4484	101	43	e(h	e(h	PROPN
ejpam-4484	101	44	)	)	PUNCT
ejpam-4484	101	45	∪	∪	NOUN
ejpam-4484	101	46	{	{	PUNCT
ejpam-4484	101	47	uv	uv	NOUN
ejpam-4484	101	48	:	:	PUNCT
ejpam-4484	101	49	u	u	PROPN
ejpam-4484	101	50	∈	∈	PROPN
ejpam-4484	101	51	v	v	ADP
ejpam-4484	101	52	(	(	PUNCT
ejpam-4484	101	53	g	g	NOUN
ejpam-4484	101	54	)	)	PUNCT
ejpam-4484	101	55	and	and	CCONJ
ejpam-4484	101	56	v	v	ADP
ejpam-4484	101	57	∈	∈	PROPN
ejpam-4484	101	58	v	v	NOUN
ejpam-4484	101	59	(	(	PUNCT
ejpam-4484	101	60	h	h	NOUN
ejpam-4484	101	61	)	)	PUNCT
ejpam-4484	101	62	}	}	PUNCT
ejpam-4484	101	63	.	.	PUNCT
ejpam-4484	102	1	a.	a.	PROPN
ejpam-4484	102	2	h.	h.	PROPN
ejpam-4484	102	3	abragan	abragan	PROPN
ejpam-4484	102	4	,	,	PUNCT
ejpam-4484	102	5	h.	h.	PROPN
ejpam-4484	102	6	m.	m.	PROPN
ejpam-4484	102	7	rara	rara	PROPN
ejpam-4484	102	8	/	/	SYM
ejpam-4484	102	9	eur	eur	PROPN
ejpam-4484	102	10	.	.	PUNCT
ejpam-4484	103	1	j.	j.	PROPN
ejpam-4484	103	2	pure	pure	PROPN
ejpam-4484	103	3	appl	appl	PROPN
ejpam-4484	103	4	.	.	PROPN
ejpam-4484	103	5	math	math	PROPN
ejpam-4484	103	6	,	,	PUNCT
ejpam-4484	103	7	15	15	NUM
ejpam-4484	103	8	(	(	PUNCT
ejpam-4484	103	9	4	4	NUM
ejpam-4484	103	10	)	)	PUNCT
ejpam-4484	103	11	(	(	PUNCT
ejpam-4484	103	12	2022	2022	NUM
ejpam-4484	103	13	)	)	PUNCT
ejpam-4484	103	14	,	,	PUNCT
ejpam-4484	103	15	1472	1472	NUM
ejpam-4484	103	16	-	-	SYM
ejpam-4484	103	17	1481	1481	NUM
ejpam-4484	103	18	1476	1476	NUM
ejpam-4484	103	19	theorem	theorem	NOUN
ejpam-4484	103	20	5	5	NUM
ejpam-4484	103	21	.	.	PUNCT
ejpam-4484	104	1	let	let	VERB
ejpam-4484	104	2	g	g	PRON
ejpam-4484	104	3	be	be	AUX
ejpam-4484	104	4	a	a	DET
ejpam-4484	104	5	nontrivial	nontrivial	ADJ
ejpam-4484	104	6	connected	connect	VERB
ejpam-4484	104	7	graph	graph	NOUN
ejpam-4484	104	8	of	of	ADP
ejpam-4484	104	9	order	order	NOUN
ejpam-4484	104	10	n	n	PRON
ejpam-4484	104	11	with	with	ADP
ejpam-4484	104	12	γ(g	γ(g	PROPN
ejpam-4484	104	13	)	)	PUNCT
ejpam-4484	105	1	̸=	̸=	PROPN
ejpam-4484	105	2	1	1	NUM
ejpam-4484	105	3	and	and	CCONJ
ejpam-4484	105	4	k1	k1	NOUN
ejpam-4484	105	5	=	=	SYM
ejpam-4484	105	6	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4484	105	7	then	then	ADV
ejpam-4484	105	8	s	s	VERB
ejpam-4484	105	9	⊆	⊆	NUM
ejpam-4484	105	10	v	v	NOUN
ejpam-4484	105	11	(	(	PUNCT
ejpam-4484	105	12	k1+g	k1+g	NOUN
ejpam-4484	105	13	)	)	PUNCT
ejpam-4484	105	14	is	be	AUX
ejpam-4484	105	15	a	a	DET
ejpam-4484	105	16	restrained	restrain	VERB
ejpam-4484	105	17	strong	strong	ADJ
ejpam-4484	105	18	resolving	resolve	VERB
ejpam-4484	105	19	hop	hop	NOUN
ejpam-4484	105	20	dominating	dominating	NOUN
ejpam-4484	105	21	set	set	NOUN
ejpam-4484	105	22	of	of	ADP
ejpam-4484	105	23	k1+g	k1+g	NOUN
ejpam-4484	105	24	if	if	SCONJ
ejpam-4484	105	25	and	and	CCONJ
ejpam-4484	105	26	only	only	ADV
ejpam-4484	105	27	if	if	SCONJ
ejpam-4484	105	28	s	s	VERB
ejpam-4484	105	29	=	=	SYM
ejpam-4484	105	30	v	v	PROPN
ejpam-4484	105	31	(	(	PUNCT
ejpam-4484	105	32	k1	k1	NOUN
ejpam-4484	105	33	+	+	PROPN
ejpam-4484	105	34	g	g	NOUN
ejpam-4484	105	35	)	)	PUNCT
ejpam-4484	105	36	\	\	PUNCT
ejpam-4484	106	1	c	c	NOUN
ejpam-4484	106	2	where	where	SCONJ
ejpam-4484	106	3	c	c	NOUN
ejpam-4484	106	4	=	=	SYM
ejpam-4484	106	5	∅	∅	NOUN
ejpam-4484	106	6	or	or	CCONJ
ejpam-4484	106	7	c	c	NOUN
ejpam-4484	106	8	is	be	AUX
ejpam-4484	106	9	a	a	DET
ejpam-4484	106	10	hop	hop	NOUN
ejpam-4484	106	11	dominated	dominate	VERB
ejpam-4484	106	12	superclique	superclique	NOUN
ejpam-4484	106	13	of	of	ADP
ejpam-4484	106	14	g.	g.	PROPN
ejpam-4484	106	15	proof	proof	NOUN
ejpam-4484	106	16	:	:	PUNCT
ejpam-4484	106	17	let	let	VERB
ejpam-4484	106	18	s	s	PRON
ejpam-4484	106	19	be	be	AUX
ejpam-4484	106	20	a	a	DET
ejpam-4484	106	21	restrained	restrain	VERB
ejpam-4484	106	22	strong	strong	ADJ
ejpam-4484	106	23	resolving	resolving	NOUN
ejpam-4484	106	24	set	set	NOUN
ejpam-4484	106	25	of	of	ADP
ejpam-4484	106	26	k1+g	k1+g	NOUN
ejpam-4484	106	27	.	.	PUNCT
ejpam-4484	107	1	since	since	SCONJ
ejpam-4484	107	2	s	s	NOUN
ejpam-4484	107	3	is	be	AUX
ejpam-4484	107	4	strong	strong	ADJ
ejpam-4484	107	5	resolving	resolving	NOUN
ejpam-4484	107	6	,	,	PUNCT
ejpam-4484	107	7	by	by	ADP
ejpam-4484	107	8	theorem	theorem	NOUN
ejpam-4484	107	9	1	1	NUM
ejpam-4484	107	10	,	,	PUNCT
ejpam-4484	107	11	s	s	PART
ejpam-4484	107	12	=	=	SYM
ejpam-4484	107	13	v	v	X
ejpam-4484	107	14	(	(	PUNCT
ejpam-4484	107	15	g	g	NOUN
ejpam-4484	107	16	)	)	PUNCT
ejpam-4484	107	17	or	or	CCONJ
ejpam-4484	107	18	s	s	X
ejpam-4484	107	19	=	=	SYM
ejpam-4484	107	20	v	v	PROPN
ejpam-4484	107	21	(	(	PUNCT
ejpam-4484	107	22	g)\c∗	g)\c∗	PROPN
ejpam-4484	107	23	or	or	CCONJ
ejpam-4484	107	24	s	s	PROPN
ejpam-4484	107	25	=	=	SYM
ejpam-4484	107	26	v	v	PROPN
ejpam-4484	107	27	(	(	PUNCT
ejpam-4484	107	28	k1+g)\c∗	k1+g)\c∗	PROPN
ejpam-4484	107	29	where	where	SCONJ
ejpam-4484	107	30	c∗	c∗	PROPN
ejpam-4484	107	31	is	be	AUX
ejpam-4484	107	32	a	a	DET
ejpam-4484	107	33	superclique	superclique	NOUN
ejpam-4484	107	34	in	in	ADP
ejpam-4484	107	35	g.	g.	PROPN
ejpam-4484	107	36	since	since	SCONJ
ejpam-4484	107	37	s	s	PROPN
ejpam-4484	107	38	is	be	AUX
ejpam-4484	107	39	restrained	restrain	VERB
ejpam-4484	107	40	hop	hop	NOUN
ejpam-4484	107	41	dominating	dominating	NOUN
ejpam-4484	107	42	set	set	VERB
ejpam-4484	107	43	in	in	ADP
ejpam-4484	107	44	k1	k1	NOUN
ejpam-4484	107	45	+	+	PROPN
ejpam-4484	107	46	g	g	NOUN
ejpam-4484	107	47	,	,	PUNCT
ejpam-4484	107	48	so	so	PRON
ejpam-4484	107	49	s	s	PART
ejpam-4484	107	50	=	=	SYM
ejpam-4484	107	51	v	v	PROPN
ejpam-4484	107	52	(	(	PUNCT
ejpam-4484	107	53	g+k1	g+k1	NOUN
ejpam-4484	107	54	)	)	PUNCT
ejpam-4484	107	55	or	or	CCONJ
ejpam-4484	107	56	⟨v	⟨v	NUM
ejpam-4484	107	57	(	(	PUNCT
ejpam-4484	107	58	g+k1	g+k1	NOUN
ejpam-4484	107	59	)	)	PUNCT
ejpam-4484	108	1	\s⟩	\s⟩	PROPN
ejpam-4484	108	2	has	have	VERB
ejpam-4484	108	3	no	no	DET
ejpam-4484	108	4	isolated	isolated	ADJ
ejpam-4484	108	5	vertex	vertex	NOUN
ejpam-4484	108	6	and	and	CCONJ
ejpam-4484	108	7	v	v	ADP
ejpam-4484	108	8	∈	∈	NOUN
ejpam-4484	108	9	s.	s.	PROPN
ejpam-4484	108	10	hence	hence	ADV
ejpam-4484	108	11	,	,	PUNCT
ejpam-4484	108	12	s	s	VERB
ejpam-4484	108	13	̸=	̸=	PROPN
ejpam-4484	108	14	v	v	NOUN
ejpam-4484	108	15	(	(	PUNCT
ejpam-4484	108	16	g	g	NOUN
ejpam-4484	108	17	)	)	PUNCT
ejpam-4484	108	18	and	and	CCONJ
ejpam-4484	108	19	s	s	VERB
ejpam-4484	108	20	=	=	SYM
ejpam-4484	108	21	v	v	X
ejpam-4484	108	22	(	(	PUNCT
ejpam-4484	108	23	g	g	NOUN
ejpam-4484	108	24	)	)	PUNCT
ejpam-4484	108	25	\c∗.	\c∗.	PROPN
ejpam-4484	108	26	hence	hence	ADV
ejpam-4484	108	27	,	,	PUNCT
ejpam-4484	108	28	s	s	NOUN
ejpam-4484	108	29	=	=	SYM
ejpam-4484	108	30	v	v	PROPN
ejpam-4484	108	31	(	(	PUNCT
ejpam-4484	108	32	k1	k1	NOUN
ejpam-4484	108	33	+	+	CCONJ
ejpam-4484	108	34	g	g	NOUN
ejpam-4484	108	35	)	)	PUNCT
ejpam-4484	108	36	\	\	PROPN
ejpam-4484	108	37	c∗	c∗	PROPN
ejpam-4484	108	38	where	where	SCONJ
ejpam-4484	108	39	c∗	c∗	NOUN
ejpam-4484	108	40	=	=	SYM
ejpam-4484	108	41	∅	∅	NOUN
ejpam-4484	108	42	or	or	CCONJ
ejpam-4484	108	43	c∗	c∗	NOUN
ejpam-4484	108	44	is	be	AUX
ejpam-4484	108	45	a	a	DET
ejpam-4484	108	46	nonsingleton	nonsingleton	NOUN
ejpam-4484	108	47	hop	hop	NOUN
ejpam-4484	108	48	dominated	dominate	VERB
ejpam-4484	108	49	superclique	superclique	NOUN
ejpam-4484	108	50	of	of	ADP
ejpam-4484	108	51	g.	g.	PROPN
ejpam-4484	108	52	the	the	DET
ejpam-4484	108	53	converse	converse	NOUN
ejpam-4484	108	54	follows	follow	VERB
ejpam-4484	108	55	immediately	immediately	ADV
ejpam-4484	108	56	from	from	ADP
ejpam-4484	108	57	theorem	theorem	ADJ
ejpam-4484	108	58	1	1	NUM
ejpam-4484	108	59	.	.	PUNCT
ejpam-4484	108	60	theorem	theorem	NOUN
ejpam-4484	108	61	6	6	NUM
ejpam-4484	108	62	.	.	PUNCT
ejpam-4484	109	1	let	let	VERB
ejpam-4484	109	2	g	g	PRON
ejpam-4484	109	3	be	be	AUX
ejpam-4484	109	4	a	a	DET
ejpam-4484	109	5	nontrivial	nontrivial	ADJ
ejpam-4484	109	6	connected	connect	VERB
ejpam-4484	109	7	graph	graph	NOUN
ejpam-4484	109	8	of	of	ADP
ejpam-4484	109	9	order	order	NOUN
ejpam-4484	109	10	n	n	PRON
ejpam-4484	109	11	with	with	ADP
ejpam-4484	109	12	γ(g	γ(g	PROPN
ejpam-4484	109	13	)	)	PUNCT
ejpam-4484	109	14	=	=	SYM
ejpam-4484	109	15	1	1	NUM
ejpam-4484	109	16	and	and	CCONJ
ejpam-4484	109	17	k1	k1	NOUN
ejpam-4484	110	1	=	=	SYM
ejpam-4484	110	2	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4484	110	3	then	then	ADV
ejpam-4484	110	4	s	s	VERB
ejpam-4484	110	5	⊆	⊆	NUM
ejpam-4484	110	6	v	v	NOUN
ejpam-4484	110	7	(	(	PUNCT
ejpam-4484	110	8	k1+g	k1+g	NOUN
ejpam-4484	110	9	)	)	PUNCT
ejpam-4484	110	10	is	be	AUX
ejpam-4484	110	11	a	a	DET
ejpam-4484	110	12	restrained	restrain	VERB
ejpam-4484	110	13	strong	strong	ADJ
ejpam-4484	110	14	resolving	resolve	VERB
ejpam-4484	110	15	hop	hop	NOUN
ejpam-4484	110	16	dominating	dominating	NOUN
ejpam-4484	110	17	set	set	NOUN
ejpam-4484	110	18	of	of	ADP
ejpam-4484	110	19	k1+g	k1+g	NOUN
ejpam-4484	110	20	if	if	SCONJ
ejpam-4484	110	21	and	and	CCONJ
ejpam-4484	110	22	only	only	ADV
ejpam-4484	110	23	if	if	SCONJ
ejpam-4484	110	24	s	s	VERB
ejpam-4484	110	25	=	=	X
ejpam-4484	110	26	(	(	PUNCT
ejpam-4484	110	27	v	v	NOUN
ejpam-4484	110	28	(	(	PUNCT
ejpam-4484	110	29	k1	k1	NOUN
ejpam-4484	110	30	+	+	CCONJ
ejpam-4484	110	31	g	g	NOUN
ejpam-4484	110	32	)	)	PUNCT
ejpam-4484	110	33	\	\	PUNCT
ejpam-4484	111	1	c	c	X
ejpam-4484	111	2	)	)	PUNCT
ejpam-4484	111	3	∪	∪	NOUN
ejpam-4484	111	4	{	{	PUNCT
ejpam-4484	111	5	x	x	SYM
ejpam-4484	111	6	∈	∈	PROPN
ejpam-4484	111	7	c	c	NOUN
ejpam-4484	111	8	:	:	PUNCT
ejpam-4484	111	9	degg(x	degg(x	X
ejpam-4484	111	10	)	)	PUNCT
ejpam-4484	111	11	=	=	SYM
ejpam-4484	111	12	n	n	CCONJ
ejpam-4484	111	13	−	−	NOUN
ejpam-4484	111	14	1	1	NUM
ejpam-4484	111	15	}	}	PUNCT
ejpam-4484	111	16	where	where	SCONJ
ejpam-4484	111	17	c	c	NOUN
ejpam-4484	111	18	=	=	SYM
ejpam-4484	111	19	∅	∅	NOUN
ejpam-4484	111	20	or	or	CCONJ
ejpam-4484	111	21	c	c	NOUN
ejpam-4484	111	22	is	be	AUX
ejpam-4484	111	23	a	a	DET
ejpam-4484	111	24	hop	hop	NOUN
ejpam-4484	111	25	dominated	dominate	VERB
ejpam-4484	111	26	superclique	superclique	NOUN
ejpam-4484	111	27	in	in	ADP
ejpam-4484	111	28	g.	g.	PROPN
ejpam-4484	111	29	proof	proof	NOUN
ejpam-4484	111	30	:	:	PUNCT
ejpam-4484	111	31	let	let	VERB
ejpam-4484	111	32	s	s	PRON
ejpam-4484	111	33	be	be	AUX
ejpam-4484	111	34	a	a	DET
ejpam-4484	111	35	restrained	restrain	VERB
ejpam-4484	111	36	strong	strong	ADJ
ejpam-4484	111	37	resolving	resolve	VERB
ejpam-4484	111	38	hop	hop	NOUN
ejpam-4484	111	39	dominating	dominating	NOUN
ejpam-4484	111	40	set	set	NOUN
ejpam-4484	111	41	of	of	ADP
ejpam-4484	111	42	k1	k1	PROPN
ejpam-4484	111	43	+	+	CCONJ
ejpam-4484	111	44	g.	g.	PROPN
ejpam-4484	111	45	then	then	ADV
ejpam-4484	111	46	by	by	ADP
ejpam-4484	111	47	theorem	theorem	NOUN
ejpam-4484	111	48	1	1	NUM
ejpam-4484	111	49	,	,	PUNCT
ejpam-4484	111	50	s	s	PART
ejpam-4484	111	51	=	=	SYM
ejpam-4484	111	52	v	v	NOUN
ejpam-4484	111	53	(	(	PUNCT
ejpam-4484	111	54	g)ors	g)or	NOUN
ejpam-4484	111	55	=	=	SYM
ejpam-4484	111	56	v	v	X
ejpam-4484	111	57	(	(	PUNCT
ejpam-4484	111	58	k1	k1	NOUN
ejpam-4484	111	59	+	+	PROPN
ejpam-4484	111	60	g	g	NOUN
ejpam-4484	111	61	)	)	PUNCT
ejpam-4484	111	62	\	\	PUNCT
ejpam-4484	112	1	c∗ors	c∗ors	PROPN
ejpam-4484	112	2	=	=	SYM
ejpam-4484	112	3	(	(	PUNCT
ejpam-4484	112	4	v	v	NOUN
ejpam-4484	112	5	(	(	PUNCT
ejpam-4484	112	6	g	g	NOUN
ejpam-4484	112	7	)	)	PUNCT
ejpam-4484	112	8	\	\	PROPN
ejpam-4484	112	9	c∗	c∗	PROPN
ejpam-4484	112	10	)	)	PUNCT
ejpam-4484	112	11	∪	∪	NOUN
ejpam-4484	112	12	{	{	PUNCT
ejpam-4484	112	13	x	x	SYM
ejpam-4484	112	14	∈	∈	PROPN
ejpam-4484	112	15	c∗	c∗	NOUN
ejpam-4484	112	16	:	:	PUNCT
ejpam-4484	112	17	degg(x	degg(x	X
ejpam-4484	112	18	)	)	PUNCT
ejpam-4484	112	19	=	=	PUNCT
ejpam-4484	112	20	n−	n−	NOUN
ejpam-4484	112	21	1	1	NUM
ejpam-4484	112	22	}	}	PUNCT
ejpam-4484	112	23	where	where	SCONJ
ejpam-4484	112	24	c∗	c∗	NOUN
ejpam-4484	112	25	is	be	AUX
ejpam-4484	112	26	a	a	DET
ejpam-4484	112	27	superclique	superclique	NOUN
ejpam-4484	112	28	of	of	ADP
ejpam-4484	112	29	g.	g.	PROPN
ejpam-4484	112	30	since	since	SCONJ
ejpam-4484	112	31	s	s	PROPN
ejpam-4484	112	32	is	be	AUX
ejpam-4484	112	33	a	a	DET
ejpam-4484	112	34	restrained	restrained	ADJ
ejpam-4484	112	35	hop	hop	NOUN
ejpam-4484	112	36	dominating	dominating	NOUN
ejpam-4484	112	37	set	set	NOUN
ejpam-4484	112	38	,	,	PUNCT
ejpam-4484	112	39	s	s	PART
ejpam-4484	112	40	=	=	SYM
ejpam-4484	112	41	v	v	PROPN
ejpam-4484	112	42	(	(	PUNCT
ejpam-4484	112	43	k1+g	k1+g	NOUN
ejpam-4484	112	44	)	)	PUNCT
ejpam-4484	112	45	or	or	CCONJ
ejpam-4484	112	46	⟨v	⟨v	NUM
ejpam-4484	112	47	(	(	PUNCT
ejpam-4484	112	48	k1	k1	NOUN
ejpam-4484	112	49	+	+	CCONJ
ejpam-4484	112	50	g	g	NOUN
ejpam-4484	112	51	)	)	PUNCT
ejpam-4484	112	52	\	\	PROPN
ejpam-4484	112	53	s⟩	s⟩	NOUN
ejpam-4484	112	54	has	have	VERB
ejpam-4484	112	55	no	no	DET
ejpam-4484	112	56	isolated	isolated	ADJ
ejpam-4484	112	57	vertex	vertex	NOUN
ejpam-4484	112	58	and	and	CCONJ
ejpam-4484	112	59	v	v	NOUN
ejpam-4484	112	60	,	,	PUNCT
ejpam-4484	112	61	x	x	SYM
ejpam-4484	112	62	∈	∈	PROPN
ejpam-4484	112	63	s	s	VERB
ejpam-4484	112	64	where	where	SCONJ
ejpam-4484	112	65	degg(x	degg(x	NOUN
ejpam-4484	112	66	)	)	PUNCT
ejpam-4484	112	67	=	=	SYM
ejpam-4484	113	1	n	n	CCONJ
ejpam-4484	114	1	−	−	NOUN
ejpam-4484	114	2	1	1	NUM
ejpam-4484	114	3	.	.	PUNCT
ejpam-4484	115	1	thus	thus	ADV
ejpam-4484	115	2	,	,	PUNCT
ejpam-4484	115	3	s	s	VERB
ejpam-4484	115	4	=	=	PUNCT
ejpam-4484	115	5	(	(	PUNCT
ejpam-4484	115	6	v	v	NOUN
ejpam-4484	115	7	(	(	PUNCT
ejpam-4484	115	8	g	g	NOUN
ejpam-4484	115	9	)	)	PUNCT
ejpam-4484	115	10	\	\	PROPN
ejpam-4484	115	11	c∗	c∗	PROPN
ejpam-4484	115	12	)	)	PUNCT
ejpam-4484	115	13	∪	∪	NOUN
ejpam-4484	115	14	{	{	PUNCT
ejpam-4484	115	15	x	x	SYM
ejpam-4484	115	16	∈	∈	PROPN
ejpam-4484	115	17	c∗	c∗	NOUN
ejpam-4484	115	18	:	:	PUNCT
ejpam-4484	115	19	degg(x	degg(x	X
ejpam-4484	115	20	)	)	PUNCT
ejpam-4484	115	21	=	=	PUNCT
ejpam-4484	115	22	n−	n−	NOUN
ejpam-4484	115	23	1	1	NUM
ejpam-4484	115	24	}	}	PUNCT
ejpam-4484	115	25	where	where	SCONJ
ejpam-4484	115	26	c∗	c∗	NOUN
ejpam-4484	115	27	=	=	SYM
ejpam-4484	115	28	∅	∅	NOUN
ejpam-4484	115	29	or	or	CCONJ
ejpam-4484	115	30	c∗	c∗	NOUN
ejpam-4484	115	31	is	be	AUX
ejpam-4484	115	32	nonsingleton	nonsingleton	PROPN
ejpam-4484	115	33	hop	hop	NOUN
ejpam-4484	115	34	dominated	dominate	VERB
ejpam-4484	115	35	superclique	superclique	NOUN
ejpam-4484	115	36	of	of	ADP
ejpam-4484	115	37	g.	g.	PROPN
ejpam-4484	115	38	the	the	DET
ejpam-4484	115	39	converse	converse	NOUN
ejpam-4484	115	40	follows	follow	VERB
ejpam-4484	115	41	immediately	immediately	ADV
ejpam-4484	115	42	from	from	ADP
ejpam-4484	115	43	theorem	theorem	ADJ
ejpam-4484	115	44	1	1	NUM
ejpam-4484	115	45	.	.	PUNCT
ejpam-4484	115	46	corollary	corollary	ADJ
ejpam-4484	115	47	1	1	NUM
ejpam-4484	115	48	.	.	PUNCT
ejpam-4484	116	1	let	let	VERB
ejpam-4484	116	2	g	g	PRON
ejpam-4484	116	3	be	be	AUX
ejpam-4484	116	4	a	a	DET
ejpam-4484	116	5	nontrivial	nontrivial	ADJ
ejpam-4484	116	6	connected	connect	VERB
ejpam-4484	116	7	graph	graph	NOUN
ejpam-4484	116	8	of	of	ADP
ejpam-4484	116	9	order	order	NOUN
ejpam-4484	116	10	n.	n.	PROPN
ejpam-4484	116	11	then	then	ADV
ejpam-4484	116	12	γrsrh(k1	γrsrh(k1	VERB
ejpam-4484	116	13	+	+	ADV
ejpam-4484	116	14	g	g	NOUN
ejpam-4484	116	15	)	)	PUNCT
ejpam-4484	117	1	=	=	SYM
ejpam-4484	117	2	n−	n−	NOUN
ejpam-4484	117	3	ωhs(g	ωhs(g	X
ejpam-4484	117	4	)	)	PUNCT
ejpam-4484	117	5	+	+	NUM
ejpam-4484	117	6	1	1	X
ejpam-4484	117	7	.	.	X
ejpam-4484	117	8	corollary	corollary	ADJ
ejpam-4484	117	9	2	2	NUM
ejpam-4484	117	10	.	.	PUNCT
ejpam-4484	118	1	let	let	VERB
ejpam-4484	118	2	pn	pn	VERB
ejpam-4484	118	3	=	=	PUNCT
ejpam-4484	119	1	[	[	X
ejpam-4484	119	2	v1	v1	NOUN
ejpam-4484	119	3	,	,	PUNCT
ejpam-4484	119	4	v2	v2	NOUN
ejpam-4484	119	5	,	,	PUNCT
ejpam-4484	119	6	.	.	PUNCT
ejpam-4484	119	7	.	.	PUNCT
ejpam-4484	119	8	.	.	PUNCT
ejpam-4484	120	1	,	,	PUNCT
ejpam-4484	120	2	vn	vn	X
ejpam-4484	120	3	]	]	PUNCT
ejpam-4484	120	4	and	and	CCONJ
ejpam-4484	120	5	cm	cm	NOUN
ejpam-4484	120	6	=	=	PUNCT
ejpam-4484	121	1	[	[	X
ejpam-4484	121	2	c1	c1	PROPN
ejpam-4484	121	3	,	,	PUNCT
ejpam-4484	121	4	c2	c2	PROPN
ejpam-4484	121	5	,	,	PUNCT
ejpam-4484	121	6	.	.	PUNCT
ejpam-4484	121	7	.	.	PUNCT
ejpam-4484	121	8	.	.	PUNCT
ejpam-4484	122	1	cm	cm	NOUN
ejpam-4484	122	2	,	,	PUNCT
ejpam-4484	122	3	c1	c1	NOUN
ejpam-4484	122	4	]	]	PUNCT
ejpam-4484	122	5	where	where	SCONJ
ejpam-4484	122	6	n	n	X
ejpam-4484	122	7	,	,	PUNCT
ejpam-4484	122	8	m	m	VERB
ejpam-4484	122	9	≥	≥	NOUN
ejpam-4484	122	10	4	4	NUM
ejpam-4484	122	11	.	.	PUNCT
ejpam-4484	123	1	(	(	PUNCT
ejpam-4484	123	2	i	i	NOUN
ejpam-4484	123	3	)	)	PUNCT
ejpam-4484	123	4	the	the	DET
ejpam-4484	123	5	set	set	NOUN
ejpam-4484	123	6	[	[	PUNCT
ejpam-4484	123	7	v	v	NOUN
ejpam-4484	123	8	(	(	PUNCT
ejpam-4484	123	9	pn	pn	NOUN
ejpam-4484	123	10	)	)	PUNCT
ejpam-4484	123	11	∪	∪	NOUN
ejpam-4484	123	12	{	{	PUNCT
ejpam-4484	123	13	v	v	NOUN
ejpam-4484	123	14	}	}	PUNCT
ejpam-4484	123	15	]	]	PUNCT
ejpam-4484	123	16	\	\	NOUN
ejpam-4484	123	17	{	{	PUNCT
ejpam-4484	123	18	vk	vk	PROPN
ejpam-4484	123	19	,	,	PUNCT
ejpam-4484	123	20	vk+1	vk+1	VERB
ejpam-4484	123	21	}	}	PUNCT
ejpam-4484	123	22	for	for	ADP
ejpam-4484	123	23	k	k	PROPN
ejpam-4484	123	24	=	=	SYM
ejpam-4484	123	25	1	1	NUM
ejpam-4484	123	26	,	,	PUNCT
ejpam-4484	123	27	2	2	NUM
ejpam-4484	123	28	,	,	PUNCT
ejpam-4484	123	29	.	.	PUNCT
ejpam-4484	123	30	.	.	PUNCT
ejpam-4484	123	31	.	.	PUNCT
ejpam-4484	124	1	,	,	PUNCT
ejpam-4484	124	2	n−	n−	NOUN
ejpam-4484	124	3	1	1	NUM
ejpam-4484	124	4	are	be	AUX
ejpam-4484	124	5	the	the	DET
ejpam-4484	124	6	restrained	restrain	VERB
ejpam-4484	124	7	strong	strong	ADJ
ejpam-4484	124	8	resolving	resolve	VERB
ejpam-4484	124	9	hop	hop	NOUN
ejpam-4484	124	10	dominating	dominating	NOUN
ejpam-4484	124	11	sets	set	NOUN
ejpam-4484	124	12	of	of	ADP
ejpam-4484	124	13	⟨v⟩+	⟨v⟩+	INTJ
ejpam-4484	124	14	pn	pn	PROPN
ejpam-4484	124	15	.	.	PROPN
ejpam-4484	124	16	(	(	PUNCT
ejpam-4484	124	17	ii	ii	NOUN
ejpam-4484	124	18	)	)	PUNCT
ejpam-4484	124	19	the	the	DET
ejpam-4484	124	20	sets	set	NOUN
ejpam-4484	124	21	[	[	X
ejpam-4484	124	22	(	(	PUNCT
ejpam-4484	124	23	v	v	INTJ
ejpam-4484	124	24	(	(	PUNCT
ejpam-4484	124	25	cm)∪{v})\{ci	cm)∪{v})\{ci	ADJ
ejpam-4484	124	26	,	,	PUNCT
ejpam-4484	124	27	ci+1	ci+1	ADJ
ejpam-4484	124	28	}	}	PUNCT
ejpam-4484	124	29	]	]	PUNCT
ejpam-4484	124	30	and	and	CCONJ
ejpam-4484	124	31	(	(	PUNCT
ejpam-4484	124	32	v	v	NOUN
ejpam-4484	124	33	(	(	PUNCT
ejpam-4484	124	34	cm)∪{v}\{c1	cm)∪{v}\{c1	PROPN
ejpam-4484	124	35	,	,	PUNCT
ejpam-4484	124	36	cm	cm	NOUN
ejpam-4484	124	37	}	}	PUNCT
ejpam-4484	124	38	)	)	PUNCT
ejpam-4484	124	39	for	for	ADP
ejpam-4484	124	40	i	i	PROPN
ejpam-4484	124	41	=	=	SYM
ejpam-4484	124	42	1	1	NUM
ejpam-4484	124	43	,	,	PUNCT
ejpam-4484	124	44	2	2	NUM
ejpam-4484	124	45	,	,	PUNCT
ejpam-4484	124	46	.	.	PUNCT
ejpam-4484	124	47	.	.	PUNCT
ejpam-4484	124	48	.	.	PUNCT
ejpam-4484	125	1	,	,	PUNCT
ejpam-4484	125	2	m−1	m−1	PROPN
ejpam-4484	125	3	,	,	PUNCT
ejpam-4484	125	4	are	be	AUX
ejpam-4484	125	5	the	the	DET
ejpam-4484	125	6	restrained	restrain	VERB
ejpam-4484	125	7	strong	strong	ADJ
ejpam-4484	125	8	resolving	resolve	VERB
ejpam-4484	125	9	hop	hop	NOUN
ejpam-4484	125	10	dominating	dominating	NOUN
ejpam-4484	125	11	sets	set	NOUN
ejpam-4484	125	12	of	of	ADP
ejpam-4484	125	13	⟨v⟩+	⟨v⟩+	INTJ
ejpam-4484	125	14	cn	cn	PROPN
ejpam-4484	125	15	.	.	PUNCT
ejpam-4484	125	16	theorem	theorem	PROPN
ejpam-4484	125	17	7	7	NUM
ejpam-4484	125	18	.	.	PUNCT
ejpam-4484	126	1	let	let	VERB
ejpam-4484	126	2	g	g	PRON
ejpam-4484	126	3	be	be	AUX
ejpam-4484	126	4	a	a	DET
ejpam-4484	126	5	disconnected	disconnected	ADJ
ejpam-4484	126	6	graph	graph	NOUN
ejpam-4484	126	7	whose	whose	DET
ejpam-4484	126	8	components	component	NOUN
ejpam-4484	126	9	are	be	AUX
ejpam-4484	126	10	gi	gi	ADJ
ejpam-4484	126	11	for	for	ADP
ejpam-4484	126	12	i	i	PROPN
ejpam-4484	126	13	=	=	NOUN
ejpam-4484	126	14	1	1	NUM
ejpam-4484	126	15	,	,	PUNCT
ejpam-4484	126	16	2	2	NUM
ejpam-4484	126	17	,	,	PUNCT
ejpam-4484	126	18	.	.	PUNCT
ejpam-4484	126	19	.	.	PUNCT
ejpam-4484	127	1	.	.	PUNCT
ejpam-4484	128	1	,	,	PUNCT
ejpam-4484	128	2	n.	n.	PROPN
ejpam-4484	128	3	a	a	DET
ejpam-4484	128	4	subset	subset	NOUN
ejpam-4484	128	5	s	s	NOUN
ejpam-4484	128	6	of	of	ADP
ejpam-4484	128	7	v	v	NOUN
ejpam-4484	128	8	(	(	PUNCT
ejpam-4484	128	9	k1+g	k1+g	NOUN
ejpam-4484	128	10	)	)	PUNCT
ejpam-4484	128	11	is	be	AUX
ejpam-4484	128	12	a	a	DET
ejpam-4484	128	13	restrained	restrain	VERB
ejpam-4484	128	14	strong	strong	ADJ
ejpam-4484	128	15	resolving	resolve	VERB
ejpam-4484	128	16	hop	hop	NOUN
ejpam-4484	128	17	dominating	dominating	NOUN
ejpam-4484	128	18	set	set	NOUN
ejpam-4484	128	19	of	of	ADP
ejpam-4484	128	20	k1+g	k1+g	NOUN
ejpam-4484	128	21	if	if	SCONJ
ejpam-4484	128	22	and	and	CCONJ
ejpam-4484	128	23	only	only	ADV
ejpam-4484	128	24	if	if	SCONJ
ejpam-4484	128	25	s	s	VERB
ejpam-4484	128	26	=	=	SYM
ejpam-4484	128	27	v	v	PROPN
ejpam-4484	128	28	(	(	PUNCT
ejpam-4484	128	29	k1	k1	NOUN
ejpam-4484	128	30	+	+	PROPN
ejpam-4484	128	31	g	g	NOUN
ejpam-4484	128	32	)	)	PUNCT
ejpam-4484	128	33	\	\	PROPN
ejpam-4484	128	34	ci	ci	PROPN
ejpam-4484	128	35	where	where	SCONJ
ejpam-4484	128	36	ci	ci	NOUN
ejpam-4484	128	37	=	=	NOUN
ejpam-4484	128	38	∅	∅	NOUN
ejpam-4484	128	39	or	or	CCONJ
ejpam-4484	128	40	ci	ci	NOUN
ejpam-4484	128	41	is	be	AUX
ejpam-4484	128	42	a	a	DET
ejpam-4484	128	43	nonsingleton	nonsingleton	NOUN
ejpam-4484	128	44	superclique	superclique	NOUN
ejpam-4484	128	45	of	of	ADP
ejpam-4484	128	46	gi	gi	NOUN
ejpam-4484	128	47	.	.	PUNCT
ejpam-4484	129	1	proof	proof	NOUN
ejpam-4484	129	2	:	:	PUNCT
ejpam-4484	129	3	let	let	VERB
ejpam-4484	129	4	s	s	PRON
ejpam-4484	129	5	be	be	AUX
ejpam-4484	129	6	a	a	DET
ejpam-4484	129	7	restrained	restrain	VERB
ejpam-4484	129	8	strong	strong	ADJ
ejpam-4484	129	9	resolving	resolve	VERB
ejpam-4484	129	10	hop	hop	NOUN
ejpam-4484	129	11	dominating	dominating	NOUN
ejpam-4484	129	12	set	set	NOUN
ejpam-4484	129	13	of	of	ADP
ejpam-4484	129	14	k1	k1	PROPN
ejpam-4484	129	15	+	+	CCONJ
ejpam-4484	129	16	g.	g.	PROPN
ejpam-4484	129	17	then	then	ADV
ejpam-4484	129	18	by	by	ADP
ejpam-4484	129	19	theorem	theorem	NOUN
ejpam-4484	129	20	1	1	NUM
ejpam-4484	129	21	,	,	PUNCT
ejpam-4484	129	22	s	s	PART
ejpam-4484	129	23	=	=	SYM
ejpam-4484	129	24	v	v	X
ejpam-4484	129	25	(	(	PUNCT
ejpam-4484	129	26	g	g	NOUN
ejpam-4484	129	27	)	)	PUNCT
ejpam-4484	129	28	or	or	CCONJ
ejpam-4484	129	29	s	s	X
ejpam-4484	129	30	=	=	SYM
ejpam-4484	129	31	v	v	PROPN
ejpam-4484	129	32	(	(	PUNCT
ejpam-4484	129	33	g)\c∗	g)\c∗	PROPN
ejpam-4484	129	34	i	i	PRON
ejpam-4484	129	35	or	or	CCONJ
ejpam-4484	129	36	s	s	VERB
ejpam-4484	129	37	=	=	SYM
ejpam-4484	129	38	v	v	PROPN
ejpam-4484	129	39	(	(	PUNCT
ejpam-4484	129	40	k1+g)\c∗	k1+g)\c∗	PROPN
ejpam-4484	129	41	i	i	PRON
ejpam-4484	129	42	where	where	SCONJ
ejpam-4484	129	43	c∗	c∗	PROPN
ejpam-4484	129	44	i	i	PROPN
ejpam-4484	129	45	a.	a.	PROPN
ejpam-4484	129	46	h.	h.	PROPN
ejpam-4484	129	47	abragan	abragan	PROPN
ejpam-4484	129	48	,	,	PUNCT
ejpam-4484	129	49	h.	h.	PROPN
ejpam-4484	129	50	m.	m.	PROPN
ejpam-4484	129	51	rara	rara	PROPN
ejpam-4484	129	52	/	/	SYM
ejpam-4484	129	53	eur	eur	PROPN
ejpam-4484	129	54	.	.	PUNCT
ejpam-4484	130	1	j.	j.	PROPN
ejpam-4484	130	2	pure	pure	PROPN
ejpam-4484	130	3	appl	appl	PROPN
ejpam-4484	130	4	.	.	PROPN
ejpam-4484	130	5	math	math	PROPN
ejpam-4484	130	6	,	,	PUNCT
ejpam-4484	130	7	15	15	NUM
ejpam-4484	130	8	(	(	PUNCT
ejpam-4484	130	9	4	4	NUM
ejpam-4484	130	10	)	)	PUNCT
ejpam-4484	130	11	(	(	PUNCT
ejpam-4484	130	12	2022	2022	NUM
ejpam-4484	130	13	)	)	PUNCT
ejpam-4484	130	14	,	,	PUNCT
ejpam-4484	130	15	1472	1472	NUM
ejpam-4484	130	16	-	-	SYM
ejpam-4484	130	17	1481	1481	NUM
ejpam-4484	130	18	1477	1477	NUM
ejpam-4484	130	19	is	be	AUX
ejpam-4484	130	20	a	a	DET
ejpam-4484	130	21	superclique	superclique	NOUN
ejpam-4484	130	22	of	of	ADP
ejpam-4484	130	23	gi	gi	NOUN
ejpam-4484	130	24	and	and	CCONJ
ejpam-4484	130	25	c∗	c∗	PROPN
ejpam-4484	131	1	i	i	NOUN
ejpam-4484	131	2	=	=	NOUN
ejpam-4484	131	3	∅	∅	NOUN
ejpam-4484	131	4	or	or	CCONJ
ejpam-4484	131	5	c∗	c∗	NOUN
ejpam-4484	131	6	i	i	PRON
ejpam-4484	131	7	is	be	AUX
ejpam-4484	131	8	a	a	DET
ejpam-4484	131	9	nonsingleton	nonsingleton	NOUN
ejpam-4484	131	10	superclique	superclique	NOUN
ejpam-4484	131	11	in	in	ADP
ejpam-4484	131	12	gi	gi	NOUN
ejpam-4484	131	13	.	.	PUNCT
ejpam-4484	132	1	since	since	SCONJ
ejpam-4484	132	2	s	s	PROPN
ejpam-4484	132	3	is	be	AUX
ejpam-4484	132	4	a	a	DET
ejpam-4484	132	5	restrained	restrained	ADJ
ejpam-4484	132	6	and	and	CCONJ
ejpam-4484	132	7	hop	hop	NOUN
ejpam-4484	132	8	dominating	dominating	NOUN
ejpam-4484	132	9	,	,	PUNCT
ejpam-4484	132	10	s	s	PART
ejpam-4484	132	11	=	=	SYM
ejpam-4484	132	12	v	v	PROPN
ejpam-4484	132	13	(	(	PUNCT
ejpam-4484	132	14	k1+g	k1+g	NOUN
ejpam-4484	132	15	)	)	PUNCT
ejpam-4484	132	16	or	or	CCONJ
ejpam-4484	132	17	⟨v	⟨v	NUM
ejpam-4484	132	18	(	(	PUNCT
ejpam-4484	132	19	k1+g)\s⟩	k1+g)\s⟩	NOUN
ejpam-4484	132	20	has	have	VERB
ejpam-4484	132	21	no	no	DET
ejpam-4484	132	22	isolated	isolated	ADJ
ejpam-4484	132	23	vertex	vertex	NOUN
ejpam-4484	132	24	.	.	PUNCT
ejpam-4484	133	1	hence	hence	ADV
ejpam-4484	133	2	,	,	PUNCT
ejpam-4484	133	3	s	s	VERB
ejpam-4484	133	4	̸=	̸=	PROPN
ejpam-4484	133	5	v	v	NOUN
ejpam-4484	133	6	(	(	PUNCT
ejpam-4484	133	7	g	g	NOUN
ejpam-4484	133	8	)	)	PUNCT
ejpam-4484	133	9	and	and	CCONJ
ejpam-4484	133	10	s	s	VERB
ejpam-4484	133	11	̸=	̸=	PROPN
ejpam-4484	133	12	v	v	NOUN
ejpam-4484	133	13	(	(	PUNCT
ejpam-4484	133	14	g	g	NOUN
ejpam-4484	133	15	)	)	PUNCT
ejpam-4484	133	16	\	\	PROPN
ejpam-4484	133	17	c∗	c∗	PROPN
ejpam-4484	133	18	i	i	PRON
ejpam-4484	133	19	where	where	SCONJ
ejpam-4484	133	20	c∗	c∗	ADJ
ejpam-4484	133	21	i	i	NOUN
ejpam-4484	133	22	=	=	NOUN
ejpam-4484	133	23	∅	∅	NOUN
ejpam-4484	133	24	or	or	CCONJ
ejpam-4484	133	25	c∗	c∗	NOUN
ejpam-4484	133	26	i	i	PRON
ejpam-4484	133	27	is	be	AUX
ejpam-4484	133	28	a	a	DET
ejpam-4484	133	29	nonsingleton	nonsingleton	NOUN
ejpam-4484	133	30	superclique	superclique	NOUN
ejpam-4484	133	31	in	in	ADP
ejpam-4484	133	32	gi	gi	NOUN
ejpam-4484	133	33	.	.	PUNCT
ejpam-4484	134	1	the	the	DET
ejpam-4484	134	2	converse	converse	NOUN
ejpam-4484	134	3	follows	follow	VERB
ejpam-4484	134	4	immediately	immediately	ADV
ejpam-4484	134	5	from	from	ADP
ejpam-4484	134	6	theorem	theorem	ADJ
ejpam-4484	134	7	1	1	NUM
ejpam-4484	134	8	.	.	PUNCT
ejpam-4484	134	9	corollary	corollary	ADJ
ejpam-4484	134	10	3	3	X
ejpam-4484	134	11	.	.	PUNCT
ejpam-4484	135	1	let	let	VERB
ejpam-4484	135	2	gi	gi	PART
ejpam-4484	135	3	be	be	AUX
ejpam-4484	135	4	connected	connect	VERB
ejpam-4484	135	5	graphs	graph	NOUN
ejpam-4484	135	6	of	of	ADP
ejpam-4484	135	7	order	order	NOUN
ejpam-4484	135	8	ni	ni	PROPN
ejpam-4484	135	9	and	and	CCONJ
ejpam-4484	135	10	g	g	PROPN
ejpam-4484	135	11	be	be	VERB
ejpam-4484	135	12	a	a	DET
ejpam-4484	135	13	disconnected	disconnected	ADJ
ejpam-4484	135	14	graph	graph	NOUN
ejpam-4484	135	15	whose	whose	DET
ejpam-4484	135	16	components	component	NOUN
ejpam-4484	135	17	are	be	AUX
ejpam-4484	135	18	gi	gi	ADJ
ejpam-4484	135	19	for	for	ADP
ejpam-4484	135	20	i	i	PROPN
ejpam-4484	135	21	=	=	NOUN
ejpam-4484	135	22	1	1	NUM
ejpam-4484	135	23	,	,	PUNCT
ejpam-4484	135	24	2	2	NUM
ejpam-4484	135	25	,	,	PUNCT
ejpam-4484	135	26	.	.	PUNCT
ejpam-4484	135	27	.	.	PUNCT
ejpam-4484	136	1	.	.	PUNCT
ejpam-4484	137	1	,	,	PUNCT
ejpam-4484	137	2	m.	m.	NOUN
ejpam-4484	137	3	then	then	ADV
ejpam-4484	137	4	,	,	PUNCT
ejpam-4484	137	5	γrsrh(k1	γrsrh(k1	VERB
ejpam-4484	137	6	+	+	ADV
ejpam-4484	137	7	g	g	NOUN
ejpam-4484	137	8	)	)	PUNCT
ejpam-4484	137	9	=	=	PUNCT
ejpam-4484	138	1	m∑	m∑	CCONJ
ejpam-4484	138	2	i=1	i=1	PROPN
ejpam-4484	138	3	ni	ni	PROPN
ejpam-4484	138	4	−max{ωs(gi	−max{ωs(gi	PROPN
ejpam-4484	138	5	)	)	PUNCT
ejpam-4484	139	1	:	:	PUNCT
ejpam-4484	139	2	i	i	NOUN
ejpam-4484	139	3	=	=	NOUN
ejpam-4484	139	4	1	1	NUM
ejpam-4484	139	5	,	,	PUNCT
ejpam-4484	139	6	·	·	PUNCT
ejpam-4484	139	7	·	·	PUNCT
ejpam-4484	139	8	·	·	PUNCT
ejpam-4484	139	9	,	,	PUNCT
ejpam-4484	139	10	m	m	NOUN
ejpam-4484	139	11	}	}	PUNCT
ejpam-4484	139	12	.	.	PUNCT
ejpam-4484	140	1	in	in	ADP
ejpam-4484	140	2	the	the	DET
ejpam-4484	140	3	join	join	NOUN
ejpam-4484	140	4	of	of	ADP
ejpam-4484	140	5	two	two	NUM
ejpam-4484	140	6	graphs	graph	NOUN
ejpam-4484	140	7	g	g	NOUN
ejpam-4484	140	8	and	and	CCONJ
ejpam-4484	140	9	h	h	NOUN
ejpam-4484	140	10	,	,	PUNCT
ejpam-4484	140	11	the	the	DET
ejpam-4484	140	12	results	result	NOUN
ejpam-4484	140	13	of	of	ADP
ejpam-4484	140	14	theorem	theorem	ADJ
ejpam-4484	140	15	5	5	NUM
ejpam-4484	140	16	and	and	CCONJ
ejpam-4484	140	17	theorem	theorem	VERB
ejpam-4484	140	18	6	6	NUM
ejpam-4484	140	19	have	have	AUX
ejpam-4484	140	20	already	already	ADV
ejpam-4484	140	21	considered	consider	VERB
ejpam-4484	140	22	the	the	DET
ejpam-4484	140	23	case	case	NOUN
ejpam-4484	140	24	when	when	SCONJ
ejpam-4484	140	25	g	g	PROPN
ejpam-4484	140	26	or	or	CCONJ
ejpam-4484	140	27	h	h	NOUN
ejpam-4484	140	28	is	be	AUX
ejpam-4484	140	29	trivial	trivial	ADJ
ejpam-4484	140	30	.	.	PUNCT
ejpam-4484	141	1	hence	hence	ADV
ejpam-4484	141	2	,	,	PUNCT
ejpam-4484	141	3	the	the	DET
ejpam-4484	141	4	next	next	ADJ
ejpam-4484	141	5	result	result	NOUN
ejpam-4484	141	6	considers	consider	VERB
ejpam-4484	141	7	the	the	DET
ejpam-4484	141	8	characterizations	characterization	NOUN
ejpam-4484	141	9	of	of	ADP
ejpam-4484	141	10	the	the	DET
ejpam-4484	141	11	restrained	restrain	VERB
ejpam-4484	141	12	strong	strong	ADJ
ejpam-4484	141	13	resolving	resolve	VERB
ejpam-4484	141	14	hop	hop	NOUN
ejpam-4484	141	15	dominating	dominating	NOUN
ejpam-4484	141	16	sets	set	NOUN
ejpam-4484	141	17	of	of	ADP
ejpam-4484	141	18	nontrivial	nontrivial	ADJ
ejpam-4484	141	19	connected	connect	VERB
ejpam-4484	141	20	graphs	graph	NOUN
ejpam-4484	141	21	g	g	PROPN
ejpam-4484	141	22	and	and	CCONJ
ejpam-4484	141	23	h.	h.	PROPN
ejpam-4484	141	24	the	the	DET
ejpam-4484	141	25	next	next	ADJ
ejpam-4484	141	26	result	result	NOUN
ejpam-4484	141	27	follows	follow	VERB
ejpam-4484	141	28	from	from	ADP
ejpam-4484	141	29	theorem	theorem	ADJ
ejpam-4484	141	30	2	2	NUM
ejpam-4484	141	31	.	.	PUNCT
ejpam-4484	141	32	theorem	theorem	NOUN
ejpam-4484	141	33	8	8	NUM
ejpam-4484	141	34	.	.	PUNCT
ejpam-4484	142	1	let	let	VERB
ejpam-4484	142	2	g	g	NOUN
ejpam-4484	142	3	and	and	CCONJ
ejpam-4484	142	4	h	h	NOUN
ejpam-4484	142	5	be	be	AUX
ejpam-4484	142	6	nontrivial	nontrivial	ADJ
ejpam-4484	142	7	connected	connect	VERB
ejpam-4484	142	8	graphs	graph	NOUN
ejpam-4484	142	9	of	of	ADP
ejpam-4484	142	10	orders	order	NOUN
ejpam-4484	142	11	m	m	VERB
ejpam-4484	142	12	and	and	CCONJ
ejpam-4484	142	13	n	n	CCONJ
ejpam-4484	142	14	,	,	PUNCT
ejpam-4484	142	15	respectively	respectively	ADV
ejpam-4484	142	16	.	.	PUNCT
ejpam-4484	143	1	a	a	DET
ejpam-4484	143	2	subset	subset	NOUN
ejpam-4484	143	3	s	s	X
ejpam-4484	143	4	of	of	ADP
ejpam-4484	143	5	v	v	NOUN
ejpam-4484	143	6	(	(	PUNCT
ejpam-4484	143	7	g	g	PROPN
ejpam-4484	143	8	+	+	NOUN
ejpam-4484	143	9	h	h	NOUN
ejpam-4484	143	10	)	)	PUNCT
ejpam-4484	143	11	is	be	AUX
ejpam-4484	143	12	a	a	DET
ejpam-4484	143	13	restrained	restrain	VERB
ejpam-4484	143	14	strong	strong	ADJ
ejpam-4484	143	15	resolving	resolve	VERB
ejpam-4484	143	16	hop	hop	NOUN
ejpam-4484	143	17	dominating	dominating	NOUN
ejpam-4484	143	18	set	set	NOUN
ejpam-4484	143	19	of	of	ADP
ejpam-4484	143	20	g	g	PROPN
ejpam-4484	143	21	+	+	PROPN
ejpam-4484	143	22	h	h	NOUN
ejpam-4484	143	23	if	if	SCONJ
ejpam-4484	144	1	and	and	CCONJ
ejpam-4484	144	2	only	only	ADV
ejpam-4484	144	3	if	if	SCONJ
ejpam-4484	144	4	at	at	ADV
ejpam-4484	144	5	least	least	ADJ
ejpam-4484	144	6	one	one	NUM
ejpam-4484	144	7	of	of	ADP
ejpam-4484	144	8	the	the	DET
ejpam-4484	144	9	following	follow	VERB
ejpam-4484	144	10	is	be	AUX
ejpam-4484	144	11	satisfied	satisfied	ADJ
ejpam-4484	144	12	:	:	PUNCT
ejpam-4484	144	13	(	(	PUNCT
ejpam-4484	144	14	i	i	NOUN
ejpam-4484	144	15	)	)	PUNCT
ejpam-4484	144	16	s	s	PART
ejpam-4484	144	17	=	=	SYM
ejpam-4484	144	18	v	v	PROPN
ejpam-4484	144	19	(	(	PUNCT
ejpam-4484	144	20	g+h	g+h	NOUN
ejpam-4484	144	21	)	)	PUNCT
ejpam-4484	144	22	\	\	PROPN
ejpam-4484	145	1	cg	cg	NOUN
ejpam-4484	145	2	where	where	SCONJ
ejpam-4484	145	3	cg	cg	NOUN
ejpam-4484	145	4	is	be	AUX
ejpam-4484	145	5	a	a	DET
ejpam-4484	145	6	nonsingleton	nonsingleton	NOUN
ejpam-4484	145	7	hop	hop	NOUN
ejpam-4484	145	8	dominated	dominate	VERB
ejpam-4484	145	9	superclique	superclique	NOUN
ejpam-4484	145	10	of	of	ADP
ejpam-4484	145	11	g.	g.	PROPN
ejpam-4484	145	12	(	(	PUNCT
ejpam-4484	145	13	ii	ii	PROPN
ejpam-4484	145	14	)	)	PUNCT
ejpam-4484	145	15	s	s	PART
ejpam-4484	145	16	=	=	SYM
ejpam-4484	145	17	v	v	PROPN
ejpam-4484	145	18	(	(	PUNCT
ejpam-4484	145	19	g+h	g+h	NOUN
ejpam-4484	145	20	)	)	PUNCT
ejpam-4484	145	21	\	\	PROPN
ejpam-4484	146	1	ch	ch	NOUN
ejpam-4484	146	2	where	where	SCONJ
ejpam-4484	146	3	ch	ch	NOUN
ejpam-4484	146	4	is	be	AUX
ejpam-4484	146	5	a	a	DET
ejpam-4484	146	6	nonsingleton	nonsingleton	NOUN
ejpam-4484	146	7	hop	hop	NOUN
ejpam-4484	146	8	dominated	dominate	VERB
ejpam-4484	146	9	superclique	superclique	NOUN
ejpam-4484	146	10	of	of	ADP
ejpam-4484	146	11	h.	h.	PROPN
ejpam-4484	146	12	(	(	PUNCT
ejpam-4484	146	13	iii	iii	NOUN
ejpam-4484	146	14	)	)	PUNCT
ejpam-4484	146	15	if	if	SCONJ
ejpam-4484	146	16	γ(g	γ(g	PROPN
ejpam-4484	146	17	)	)	PUNCT
ejpam-4484	146	18	=	=	SYM
ejpam-4484	146	19	1	1	NUM
ejpam-4484	146	20	and	and	CCONJ
ejpam-4484	146	21	γ(h	γ(h	NOUN
ejpam-4484	146	22	)	)	PUNCT
ejpam-4484	146	23	=	=	SYM
ejpam-4484	146	24	1	1	NUM
ejpam-4484	146	25	,	,	PUNCT
ejpam-4484	146	26	s	s	PART
ejpam-4484	146	27	=	=	PUNCT
ejpam-4484	147	1	[	[	X
ejpam-4484	147	2	v	v	X
ejpam-4484	147	3	(	(	PUNCT
ejpam-4484	147	4	g+h)\(cg∪ch)]∪{z	g+h)\(cg∪ch)]∪{z	NOUN
ejpam-4484	147	5	∈	∈	PROPN
ejpam-4484	147	6	cg	cg	NOUN
ejpam-4484	147	7	:	:	PUNCT
ejpam-4484	147	8	degg(z	degg(z	NOUN
ejpam-4484	147	9	)	)	PUNCT
ejpam-4484	147	10	=	=	SYM
ejpam-4484	147	11	m−1	m−1	PROPN
ejpam-4484	147	12	}	}	PUNCT
ejpam-4484	147	13	∪{w	∪{w	PROPN
ejpam-4484	147	14	∈	∈	PROPN
ejpam-4484	147	15	ch	ch	NOUN
ejpam-4484	147	16	:	:	PUNCT
ejpam-4484	147	17	degh(w	degh(w	PROPN
ejpam-4484	147	18	)	)	PUNCT
ejpam-4484	147	19	=	=	SYM
ejpam-4484	147	20	n−1	n−1	PROPN
ejpam-4484	147	21	}	}	PUNCT
ejpam-4484	147	22	where	where	SCONJ
ejpam-4484	147	23	cg	cg	NOUN
ejpam-4484	147	24	and	and	CCONJ
ejpam-4484	147	25	ch	ch	NOUN
ejpam-4484	147	26	are	be	AUX
ejpam-4484	147	27	hop	hop	ADV
ejpam-4484	147	28	dominated	dominate	VERB
ejpam-4484	147	29	supercliques	superclique	NOUN
ejpam-4484	147	30	in	in	ADP
ejpam-4484	147	31	g	g	PROPN
ejpam-4484	147	32	and	and	CCONJ
ejpam-4484	147	33	h	h	NOUN
ejpam-4484	147	34	,	,	PUNCT
ejpam-4484	147	35	respectively	respectively	ADV
ejpam-4484	147	36	.	.	PUNCT
ejpam-4484	148	1	(	(	PUNCT
ejpam-4484	148	2	iv	iv	X
ejpam-4484	148	3	)	)	PUNCT
ejpam-4484	148	4	if	if	SCONJ
ejpam-4484	148	5	γ(g	γ(g	PROPN
ejpam-4484	148	6	)	)	PUNCT
ejpam-4484	148	7	̸=	̸=	PROPN
ejpam-4484	148	8	1	1	NUM
ejpam-4484	148	9	and	and	CCONJ
ejpam-4484	148	10	γ(h	γ(h	NOUN
ejpam-4484	148	11	)	)	PUNCT
ejpam-4484	148	12	̸=	̸=	PROPN
ejpam-4484	148	13	1	1	NUM
ejpam-4484	148	14	,	,	PUNCT
ejpam-4484	148	15	s	s	VERB
ejpam-4484	148	16	=	=	PUNCT
ejpam-4484	149	1	[	[	X
ejpam-4484	149	2	v	v	X
ejpam-4484	149	3	(	(	PUNCT
ejpam-4484	149	4	g+h	g+h	NOUN
ejpam-4484	149	5	)	)	PUNCT
ejpam-4484	149	6	\	\	PUNCT
ejpam-4484	150	1	(	(	PUNCT
ejpam-4484	150	2	cg	cg	NOUN
ejpam-4484	150	3	∪	∪	PROPN
ejpam-4484	150	4	ch	ch	NOUN
ejpam-4484	150	5	)	)	PUNCT
ejpam-4484	150	6	]	]	PUNCT
ejpam-4484	151	1	=	=	PUNCT
ejpam-4484	151	2	(	(	PUNCT
ejpam-4484	151	3	v	v	NOUN
ejpam-4484	151	4	(	(	PUNCT
ejpam-4484	151	5	g	g	NOUN
ejpam-4484	151	6	)	)	PUNCT
ejpam-4484	151	7	\	\	PROPN
ejpam-4484	151	8	cg	cg	NOUN
ejpam-4484	151	9	)	)	PUNCT
ejpam-4484	151	10	∪	∪	NOUN
ejpam-4484	151	11	(	(	PUNCT
ejpam-4484	151	12	v	v	NOUN
ejpam-4484	151	13	(	(	PUNCT
ejpam-4484	151	14	h	h	NOUN
ejpam-4484	151	15	)	)	PUNCT
ejpam-4484	151	16	\	\	PROPN
ejpam-4484	151	17	ch	ch	NOUN
ejpam-4484	151	18	)	)	PUNCT
ejpam-4484	151	19	where	where	SCONJ
ejpam-4484	151	20	cg	cg	NOUN
ejpam-4484	151	21	and	and	CCONJ
ejpam-4484	151	22	ch	ch	NOUN
ejpam-4484	151	23	are	be	AUX
ejpam-4484	151	24	hop	hop	ADV
ejpam-4484	151	25	dominated	dominate	VERB
ejpam-4484	151	26	supercliques	superclique	NOUN
ejpam-4484	151	27	in	in	ADP
ejpam-4484	151	28	g	g	PROPN
ejpam-4484	151	29	and	and	CCONJ
ejpam-4484	151	30	h	h	NOUN
ejpam-4484	151	31	,	,	PUNCT
ejpam-4484	151	32	respectively	respectively	ADV
ejpam-4484	151	33	.	.	PUNCT
ejpam-4484	152	1	corollary	corollary	ADJ
ejpam-4484	152	2	4	4	NUM
ejpam-4484	152	3	.	.	PUNCT
ejpam-4484	153	1	let	let	VERB
ejpam-4484	153	2	g	g	NOUN
ejpam-4484	153	3	and	and	CCONJ
ejpam-4484	153	4	h	h	NOUN
ejpam-4484	153	5	be	be	AUX
ejpam-4484	153	6	nontrivial	nontrivial	ADJ
ejpam-4484	153	7	connected	connect	VERB
ejpam-4484	153	8	graphs	graph	NOUN
ejpam-4484	153	9	of	of	ADP
ejpam-4484	153	10	orders	order	NOUN
ejpam-4484	153	11	m	m	VERB
ejpam-4484	153	12	and	and	CCONJ
ejpam-4484	153	13	n	n	CCONJ
ejpam-4484	153	14	,	,	PUNCT
ejpam-4484	153	15	respectively	respectively	ADV
ejpam-4484	153	16	.	.	PUNCT
ejpam-4484	154	1	then	then	ADV
ejpam-4484	154	2	γsrrh(g+h	γsrrh(g+h	PROPN
ejpam-4484	154	3	)	)	PUNCT
ejpam-4484	155	1	=	=	PRON
ejpam-4484	155	2	{	{	PUNCT
ejpam-4484	155	3	(	(	PUNCT
ejpam-4484	155	4	m−	m−	PROPN
ejpam-4484	155	5	ωhs(g	ωhs(g	NUM
ejpam-4484	155	6	)	)	PUNCT
ejpam-4484	155	7	)	)	PUNCT
ejpam-4484	156	1	+	+	CCONJ
ejpam-4484	156	2	(	(	PUNCT
ejpam-4484	156	3	n−	n−	NOUN
ejpam-4484	156	4	ωhs(h	ωhs(h	PROPN
ejpam-4484	156	5	)	)	PUNCT
ejpam-4484	156	6	)	)	PUNCT
ejpam-4484	157	1	+	+	CCONJ
ejpam-4484	157	2	1	1	NUM
ejpam-4484	157	3	,	,	PUNCT
ejpam-4484	157	4	if	if	SCONJ
ejpam-4484	157	5	γ(g	γ(g	PROPN
ejpam-4484	157	6	)	)	PUNCT
ejpam-4484	157	7	=	=	SYM
ejpam-4484	157	8	1	1	NUM
ejpam-4484	157	9	or	or	CCONJ
ejpam-4484	157	10	γ(h	γ(h	NOUN
ejpam-4484	157	11	)	)	PUNCT
ejpam-4484	157	12	=	=	SYM
ejpam-4484	157	13	1	1	X
ejpam-4484	157	14	(	(	PUNCT
ejpam-4484	157	15	m−	m−	PROPN
ejpam-4484	157	16	ωhs(g	ωhs(g	NUM
ejpam-4484	157	17	)	)	PUNCT
ejpam-4484	157	18	)	)	PUNCT
ejpam-4484	158	1	+	+	CCONJ
ejpam-4484	158	2	(	(	PUNCT
ejpam-4484	158	3	n−	n−	NOUN
ejpam-4484	158	4	ωhs(h	ωhs(h	PROPN
ejpam-4484	158	5	)	)	PUNCT
ejpam-4484	158	6	)	)	PUNCT
ejpam-4484	158	7	,	,	PUNCT
ejpam-4484	158	8	if	if	SCONJ
ejpam-4484	158	9	γ(g	γ(g	NOUN
ejpam-4484	158	10	)	)	PUNCT
ejpam-4484	158	11	̸=	̸=	PROPN
ejpam-4484	158	12	1	1	NUM
ejpam-4484	158	13	and	and	CCONJ
ejpam-4484	158	14	γ(h	γ(h	NOUN
ejpam-4484	158	15	)	)	PUNCT
ejpam-4484	158	16	̸=	̸=	PROPN
ejpam-4484	158	17	1	1	NUM
ejpam-4484	158	18	.	.	PUNCT
ejpam-4484	158	19	example	example	NOUN
ejpam-4484	159	1	1	1	NUM
ejpam-4484	159	2	.	.	X
ejpam-4484	160	1	consider	consider	VERB
ejpam-4484	160	2	the	the	DET
ejpam-4484	160	3	graphs	graph	NOUN
ejpam-4484	160	4	⟨w⟩+	⟨w⟩+	NOUN
ejpam-4484	160	5	c4	c4	VERB
ejpam-4484	160	6	.	.	PUNCT
ejpam-4484	161	1	then	then	ADV
ejpam-4484	161	2	γrsrh(⟨w⟩+	γrsrh(⟨w⟩+	PROPN
ejpam-4484	161	3	c6	c6	PROPN
ejpam-4484	161	4	)	)	PUNCT
ejpam-4484	162	1	=	=	SYM
ejpam-4484	162	2	3	3	X
ejpam-4484	162	3	.	.	PUNCT
ejpam-4484	162	4	a.	a.	PROPN
ejpam-4484	162	5	h.	h.	PROPN
ejpam-4484	162	6	abragan	abragan	PROPN
ejpam-4484	162	7	,	,	PUNCT
ejpam-4484	162	8	h.	h.	PROPN
ejpam-4484	162	9	m.	m.	PROPN
ejpam-4484	162	10	rara	rara	PROPN
ejpam-4484	162	11	/	/	SYM
ejpam-4484	162	12	eur	eur	PROPN
ejpam-4484	162	13	.	.	PUNCT
ejpam-4484	163	1	j.	j.	PROPN
ejpam-4484	163	2	pure	pure	PROPN
ejpam-4484	163	3	appl	appl	PROPN
ejpam-4484	163	4	.	.	PROPN
ejpam-4484	163	5	math	math	PROPN
ejpam-4484	163	6	,	,	PUNCT
ejpam-4484	163	7	15	15	NUM
ejpam-4484	163	8	(	(	PUNCT
ejpam-4484	163	9	4	4	NUM
ejpam-4484	163	10	)	)	PUNCT
ejpam-4484	163	11	(	(	PUNCT
ejpam-4484	163	12	2022	2022	NUM
ejpam-4484	163	13	)	)	PUNCT
ejpam-4484	163	14	,	,	PUNCT
ejpam-4484	163	15	1472	1472	NUM
ejpam-4484	163	16	-	-	SYM
ejpam-4484	163	17	1481	1481	NUM
ejpam-4484	163	18	1478	1478	NUM
ejpam-4484	163	19	4	4	NUM
ejpam-4484	163	20	.	.	PUNCT
ejpam-4484	164	1	corona	corona	NOUN
ejpam-4484	164	2	of	of	ADP
ejpam-4484	164	3	graphs	graph	NOUN
ejpam-4484	164	4	definition	definition	NOUN
ejpam-4484	164	5	2	2	NUM
ejpam-4484	164	6	.	.	PUNCT
ejpam-4484	165	1	[	[	X
ejpam-4484	165	2	8	8	NUM
ejpam-4484	165	3	]	]	PUNCT
ejpam-4484	165	4	the	the	DET
ejpam-4484	165	5	corona	corona	NOUN
ejpam-4484	165	6	g	g	PROPN
ejpam-4484	165	7	◦	◦	NOUN
ejpam-4484	165	8	h	h	NOUN
ejpam-4484	165	9	of	of	ADP
ejpam-4484	165	10	graphs	graph	NOUN
ejpam-4484	165	11	g	g	PROPN
ejpam-4484	165	12	and	and	CCONJ
ejpam-4484	165	13	h	h	NOUN
ejpam-4484	165	14	,	,	PUNCT
ejpam-4484	165	15	is	be	AUX
ejpam-4484	165	16	the	the	DET
ejpam-4484	165	17	graph	graph	NOUN
ejpam-4484	165	18	obtained	obtain	VERB
ejpam-4484	165	19	by	by	ADP
ejpam-4484	165	20	taking	take	VERB
ejpam-4484	165	21	one	one	NUM
ejpam-4484	165	22	copy	copy	NOUN
ejpam-4484	165	23	of	of	ADP
ejpam-4484	165	24	g	g	NOUN
ejpam-4484	165	25	of	of	ADP
ejpam-4484	165	26	order	order	NOUN
ejpam-4484	165	27	n	n	NOUN
ejpam-4484	165	28	and	and	CCONJ
ejpam-4484	165	29	n	n	PRON
ejpam-4484	165	30	copies	copy	NOUN
ejpam-4484	165	31	of	of	ADP
ejpam-4484	165	32	h	h	NOUN
ejpam-4484	165	33	,	,	PUNCT
ejpam-4484	165	34	and	and	CCONJ
ejpam-4484	165	35	then	then	ADV
ejpam-4484	165	36	joining	join	VERB
ejpam-4484	165	37	the	the	DET
ejpam-4484	165	38	ith	ith	PROPN
ejpam-4484	165	39	vertex	vertex	NOUN
ejpam-4484	165	40	of	of	ADP
ejpam-4484	165	41	g	g	NOUN
ejpam-4484	165	42	to	to	ADP
ejpam-4484	165	43	every	every	DET
ejpam-4484	165	44	vertex	vertex	NOUN
ejpam-4484	165	45	of	of	ADP
ejpam-4484	165	46	the	the	DET
ejpam-4484	165	47	ith	ith	PROPN
ejpam-4484	165	48	copy	copy	NOUN
ejpam-4484	165	49	of	of	ADP
ejpam-4484	165	50	h.	h.	PROPN
ejpam-4484	165	51	for	for	ADP
ejpam-4484	165	52	every	every	DET
ejpam-4484	165	53	v	v	NUM
ejpam-4484	165	54	∈	∈	PROPN
ejpam-4484	165	55	v	v	NOUN
ejpam-4484	165	56	(	(	PUNCT
ejpam-4484	165	57	g	g	NOUN
ejpam-4484	165	58	)	)	PUNCT
ejpam-4484	165	59	,	,	PUNCT
ejpam-4484	165	60	denote	denote	VERB
ejpam-4484	165	61	by	by	ADP
ejpam-4484	165	62	hv	hv	PROPN
ejpam-4484	165	63	the	the	DET
ejpam-4484	165	64	copy	copy	NOUN
ejpam-4484	165	65	of	of	ADP
ejpam-4484	165	66	h	h	NOUN
ejpam-4484	165	67	whose	whose	DET
ejpam-4484	165	68	vertices	vertex	NOUN
ejpam-4484	165	69	are	be	AUX
ejpam-4484	165	70	attached	attach	VERB
ejpam-4484	165	71	one	one	NUM
ejpam-4484	165	72	by	by	ADP
ejpam-4484	165	73	one	one	NUM
ejpam-4484	165	74	to	to	ADP
ejpam-4484	165	75	the	the	DET
ejpam-4484	165	76	vertex	vertex	NOUN
ejpam-4484	165	77	v.	v.	ADP
ejpam-4484	165	78	subsequently	subsequently	ADV
ejpam-4484	165	79	,	,	PUNCT
ejpam-4484	165	80	denote	denote	VERB
ejpam-4484	165	81	by	by	ADP
ejpam-4484	165	82	v	v	PRON
ejpam-4484	165	83	+	+	CCONJ
ejpam-4484	165	84	hv	hv	NOUN
ejpam-4484	165	85	the	the	DET
ejpam-4484	165	86	subgraph	subgraph	NOUN
ejpam-4484	165	87	of	of	ADP
ejpam-4484	165	88	the	the	DET
ejpam-4484	165	89	corona	corona	NOUN
ejpam-4484	165	90	g	g	PROPN
ejpam-4484	165	91	◦	◦	NOUN
ejpam-4484	165	92	h	h	NOUN
ejpam-4484	165	93	corresponding	correspond	VERB
ejpam-4484	165	94	to	to	ADP
ejpam-4484	165	95	the	the	DET
ejpam-4484	165	96	join	join	NOUN
ejpam-4484	165	97	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4484	165	98	,	,	PUNCT
ejpam-4484	165	99	v	v	PROPN
ejpam-4484	165	100	∈	∈	PROPN
ejpam-4484	165	101	v	v	NOUN
ejpam-4484	165	102	(	(	PUNCT
ejpam-4484	165	103	g	g	NOUN
ejpam-4484	165	104	)	)	PUNCT
ejpam-4484	165	105	.	.	PUNCT
ejpam-4484	166	1	theorem	theorem	ADJ
ejpam-4484	166	2	9	9	NUM
ejpam-4484	166	3	.	.	PUNCT
ejpam-4484	167	1	let	let	VERB
ejpam-4484	167	2	g	g	PRON
ejpam-4484	167	3	be	be	AUX
ejpam-4484	167	4	a	a	DET
ejpam-4484	167	5	nontrivial	nontrivial	ADJ
ejpam-4484	167	6	connected	connect	VERB
ejpam-4484	167	7	graph	graph	NOUN
ejpam-4484	167	8	and	and	CCONJ
ejpam-4484	167	9	h	h	NOUN
ejpam-4484	167	10	a	a	DET
ejpam-4484	167	11	connected	connected	ADJ
ejpam-4484	167	12	graph	graph	NOUN
ejpam-4484	167	13	.	.	PUNCT
ejpam-4484	168	1	a	a	DET
ejpam-4484	168	2	proper	proper	ADJ
ejpam-4484	168	3	subset	subset	NOUN
ejpam-4484	168	4	s	s	VERB
ejpam-4484	168	5	⊆	⊆	NUM
ejpam-4484	168	6	v	v	NOUN
ejpam-4484	168	7	(	(	PUNCT
ejpam-4484	168	8	g	g	PROPN
ejpam-4484	168	9	◦	◦	NOUN
ejpam-4484	168	10	h	h	NOUN
ejpam-4484	168	11	)	)	PUNCT
ejpam-4484	168	12	is	be	AUX
ejpam-4484	168	13	a	a	DET
ejpam-4484	168	14	restrained	restrain	VERB
ejpam-4484	168	15	strong	strong	ADJ
ejpam-4484	168	16	resolving	resolve	VERB
ejpam-4484	168	17	hop	hop	NOUN
ejpam-4484	168	18	dominating	dominating	NOUN
ejpam-4484	168	19	set	set	NOUN
ejpam-4484	168	20	of	of	ADP
ejpam-4484	168	21	g	g	PROPN
ejpam-4484	168	22	◦	◦	NOUN
ejpam-4484	168	23	h	h	NOUN
ejpam-4484	168	24	if	if	SCONJ
ejpam-4484	169	1	and	and	CCONJ
ejpam-4484	169	2	only	only	ADV
ejpam-4484	169	3	if	if	SCONJ
ejpam-4484	169	4	one	one	NUM
ejpam-4484	169	5	of	of	ADP
ejpam-4484	169	6	the	the	DET
ejpam-4484	169	7	following	follow	VERB
ejpam-4484	169	8	holds	hold	VERB
ejpam-4484	169	9	:	:	PUNCT
ejpam-4484	169	10	(	(	PUNCT
ejpam-4484	169	11	i	i	NOUN
ejpam-4484	169	12	)	)	PUNCT
ejpam-4484	169	13	s	s	PART
ejpam-4484	169	14	=	=	PUNCT
ejpam-4484	169	15	a	a	DET
ejpam-4484	169	16	∪	∪	X
ejpam-4484	169	17	(	(	PUNCT
ejpam-4484	169	18	⋃	⋃	NOUN
ejpam-4484	169	19	u∈v	u∈v	NOUN
ejpam-4484	169	20	(	(	PUNCT
ejpam-4484	169	21	g	g	NOUN
ejpam-4484	169	22	)	)	PUNCT
ejpam-4484	169	23	v	v	NOUN
ejpam-4484	169	24	(	(	PUNCT
ejpam-4484	169	25	hu	hu	PROPN
ejpam-4484	169	26	)	)	PUNCT
ejpam-4484	169	27	)	)	PUNCT
ejpam-4484	169	28	where	where	SCONJ
ejpam-4484	169	29	a	a	DET
ejpam-4484	169	30	⊆	⊆	NUM
ejpam-4484	169	31	v	v	NOUN
ejpam-4484	169	32	(	(	PUNCT
ejpam-4484	169	33	g	g	NOUN
ejpam-4484	169	34	)	)	PUNCT
ejpam-4484	169	35	and	and	CCONJ
ejpam-4484	169	36	⟨v	⟨v	NUM
ejpam-4484	169	37	(	(	PUNCT
ejpam-4484	169	38	g	g	NOUN
ejpam-4484	169	39	)	)	PUNCT
ejpam-4484	169	40	\a⟩	\a⟩	PROPN
ejpam-4484	169	41	has	have	VERB
ejpam-4484	169	42	no	no	DET
ejpam-4484	169	43	isolated	isolated	ADJ
ejpam-4484	169	44	vertex	vertex	NOUN
ejpam-4484	169	45	.	.	PUNCT
ejpam-4484	170	1	(	(	PUNCT
ejpam-4484	170	2	ii	ii	NOUN
ejpam-4484	170	3	)	)	PUNCT
ejpam-4484	170	4	s	s	PART
ejpam-4484	170	5	=	=	PUNCT
ejpam-4484	170	6	a∪	a∪	PROPN
ejpam-4484	170	7	(	(	PUNCT
ejpam-4484	170	8	⋃	⋃	NOUN
ejpam-4484	170	9	u∈v	u∈v	NOUN
ejpam-4484	170	10	(	(	PUNCT
ejpam-4484	170	11	g)\{v	g)\{v	PROPN
ejpam-4484	170	12	}	}	PUNCT
ejpam-4484	170	13	v	v	PROPN
ejpam-4484	170	14	(	(	PUNCT
ejpam-4484	170	15	hu	hu	PROPN
ejpam-4484	170	16	)	)	PUNCT
ejpam-4484	170	17	)	)	PUNCT
ejpam-4484	170	18	∪bv	∪bv	NOUN
ejpam-4484	170	19	for	for	ADP
ejpam-4484	170	20	a	a	DET
ejpam-4484	170	21	unique	unique	ADJ
ejpam-4484	170	22	vertex	vertex	NOUN
ejpam-4484	170	23	v	v	NOUN
ejpam-4484	170	24	in	in	ADP
ejpam-4484	170	25	g	g	PROPN
ejpam-4484	170	26	,	,	PUNCT
ejpam-4484	170	27	where	where	SCONJ
ejpam-4484	170	28	a	a	DET
ejpam-4484	170	29	=	=	SYM
ejpam-4484	170	30	v	v	X
ejpam-4484	170	31	(	(	PUNCT
ejpam-4484	170	32	g	g	NOUN
ejpam-4484	170	33	)	)	PUNCT
ejpam-4484	170	34	\	\	NOUN
ejpam-4484	170	35	{	{	PUNCT
ejpam-4484	170	36	v	v	NOUN
ejpam-4484	170	37	}	}	PUNCT
ejpam-4484	170	38	or	or	CCONJ
ejpam-4484	170	39	⟨v	⟨v	NUM
ejpam-4484	170	40	(	(	PUNCT
ejpam-4484	170	41	g	g	NOUN
ejpam-4484	170	42	)	)	PUNCT
ejpam-4484	170	43	\	\	PUNCT
ejpam-4484	171	1	(	(	PUNCT
ejpam-4484	171	2	a∪{v})⟩	a∪{v})⟩	PROPN
ejpam-4484	171	3	has	have	VERB
ejpam-4484	171	4	no	no	DET
ejpam-4484	171	5	isolated	isolated	ADJ
ejpam-4484	171	6	vertex	vertex	NOUN
ejpam-4484	171	7	and	and	CCONJ
ejpam-4484	171	8	bv	bv	PROPN
ejpam-4484	171	9	is	be	AUX
ejpam-4484	171	10	a	a	DET
ejpam-4484	171	11	strong	strong	ADJ
ejpam-4484	171	12	resolving	resolve	VERB
ejpam-4484	171	13	hop	hop	NOUN
ejpam-4484	171	14	dominating	dominating	NOUN
ejpam-4484	171	15	set	set	NOUN
ejpam-4484	171	16	of	of	ADP
ejpam-4484	171	17	hv	hv	PROPN
ejpam-4484	171	18	+	+	X
ejpam-4484	171	19	⟨v⟩	⟨v⟩	PROPN
ejpam-4484	171	20	if	if	SCONJ
ejpam-4484	171	21	ng(v	ng(v	NOUN
ejpam-4484	171	22	)	)	PUNCT
ejpam-4484	171	23	∩	∩	NOUN
ejpam-4484	171	24	a	a	DET
ejpam-4484	171	25	=	=	SYM
ejpam-4484	171	26	∅	∅	NOUN
ejpam-4484	171	27	and	and	CCONJ
ejpam-4484	171	28	bv	bv	PROPN
ejpam-4484	171	29	is	be	AUX
ejpam-4484	171	30	a	a	DET
ejpam-4484	171	31	strong	strong	ADJ
ejpam-4484	171	32	resolving	resolving	NOUN
ejpam-4484	171	33	set	set	VERB
ejpam-4484	171	34	where	where	SCONJ
ejpam-4484	171	35	⟨v	⟨v	NOUN
ejpam-4484	171	36	(	(	PUNCT
ejpam-4484	171	37	hv	hv	NOUN
ejpam-4484	171	38	)	)	PUNCT
ejpam-4484	171	39	\	\	NOUN
ejpam-4484	171	40	bv⟩	bv⟩	PROPN
ejpam-4484	171	41	has	have	VERB
ejpam-4484	171	42	no	no	DET
ejpam-4484	171	43	isolated	isolated	ADJ
ejpam-4484	171	44	vertex	vertex	NOUN
ejpam-4484	171	45	if	if	SCONJ
ejpam-4484	171	46	v	v	NOUN
ejpam-4484	171	47	∈	∈	PROPN
ejpam-4484	171	48	a	a	PRON
ejpam-4484	171	49	and	and	CCONJ
ejpam-4484	171	50	ng(v	ng(v	NUM
ejpam-4484	171	51	)	)	PUNCT
ejpam-4484	172	1	∩a	∩a	PROPN
ejpam-4484	172	2	̸=	̸=	PROPN
ejpam-4484	172	3	∅.	∅.	PRON
ejpam-4484	172	4	proof	proof	NOUN
ejpam-4484	172	5	:	:	PUNCT
ejpam-4484	172	6	suppose	suppose	VERB
ejpam-4484	172	7	s	s	NOUN
ejpam-4484	172	8	is	be	AUX
ejpam-4484	172	9	a	a	DET
ejpam-4484	172	10	restrained	restrained	ADJ
ejpam-4484	172	11	resolving	resolve	VERB
ejpam-4484	172	12	hop	hop	NOUN
ejpam-4484	172	13	dominating	dominating	NOUN
ejpam-4484	172	14	set	set	NOUN
ejpam-4484	172	15	of	of	ADP
ejpam-4484	172	16	g	g	PROPN
ejpam-4484	172	17	◦	◦	PROPN
ejpam-4484	172	18	h.	h.	PROPN
ejpam-4484	173	1	then	then	ADV
ejpam-4484	173	2	s	s	VERB
ejpam-4484	173	3	is	be	AUX
ejpam-4484	173	4	a	a	DET
ejpam-4484	173	5	strong	strong	ADJ
ejpam-4484	173	6	resolving	resolve	VERB
ejpam-4484	173	7	hop	hop	NOUN
ejpam-4484	173	8	dominating	dominating	NOUN
ejpam-4484	173	9	set	set	NOUN
ejpam-4484	173	10	and	and	CCONJ
ejpam-4484	173	11	by	by	ADP
ejpam-4484	173	12	theorem	theorem	NOUN
ejpam-4484	173	13	4	4	NUM
ejpam-4484	173	14	,	,	PUNCT
ejpam-4484	173	15	one	one	NUM
ejpam-4484	173	16	of	of	ADP
ejpam-4484	173	17	the	the	DET
ejpam-4484	173	18	following	following	NOUN
ejpam-4484	173	19	holds	hold	VERB
ejpam-4484	173	20	:	:	PUNCT
ejpam-4484	173	21	(	(	PUNCT
ejpam-4484	173	22	a	a	X
ejpam-4484	173	23	)	)	PUNCT
ejpam-4484	173	24	s	s	NOUN
ejpam-4484	173	25	=	=	PUNCT
ejpam-4484	173	26	a	a	DET
ejpam-4484	173	27	∪	∪	X
ejpam-4484	173	28	(	(	PUNCT
ejpam-4484	173	29	⋃	⋃	NOUN
ejpam-4484	173	30	u∈v	u∈v	NOUN
ejpam-4484	173	31	(	(	PUNCT
ejpam-4484	173	32	g	g	NOUN
ejpam-4484	173	33	)	)	PUNCT
ejpam-4484	173	34	v	v	NOUN
ejpam-4484	173	35	(	(	PUNCT
ejpam-4484	173	36	hu	hu	PROPN
ejpam-4484	173	37	)	)	PUNCT
ejpam-4484	173	38	)	)	PUNCT
ejpam-4484	173	39	,	,	PUNCT
ejpam-4484	174	1	where	where	SCONJ
ejpam-4484	174	2	a	a	DET
ejpam-4484	174	3	⊆	⊆	NUM
ejpam-4484	174	4	v	v	NOUN
ejpam-4484	174	5	(	(	PUNCT
ejpam-4484	174	6	g	g	NOUN
ejpam-4484	174	7	)	)	PUNCT
ejpam-4484	174	8	;	;	PUNCT
ejpam-4484	174	9	(	(	PUNCT
ejpam-4484	174	10	b	b	X
ejpam-4484	174	11	)	)	PUNCT
ejpam-4484	174	12	s	s	PART
ejpam-4484	174	13	=	=	PUNCT
ejpam-4484	174	14	a∪	a∪	PROPN
ejpam-4484	174	15	(	(	PUNCT
ejpam-4484	174	16	⋃	⋃	NOUN
ejpam-4484	174	17	u∈v	u∈v	NOUN
ejpam-4484	174	18	(	(	PUNCT
ejpam-4484	174	19	g)\{v	g)\{v	PROPN
ejpam-4484	174	20	}	}	PUNCT
ejpam-4484	174	21	v	v	PROPN
ejpam-4484	174	22	(	(	PUNCT
ejpam-4484	174	23	hu	hu	PROPN
ejpam-4484	174	24	)	)	PUNCT
ejpam-4484	174	25	)	)	PUNCT
ejpam-4484	174	26	∪bv	∪bv	NOUN
ejpam-4484	174	27	for	for	ADP
ejpam-4484	174	28	a	a	DET
ejpam-4484	174	29	unique	unique	ADJ
ejpam-4484	174	30	vertex	vertex	NOUN
ejpam-4484	174	31	v	v	NOUN
ejpam-4484	174	32	in	in	ADP
ejpam-4484	174	33	g	g	PROPN
ejpam-4484	174	34	,	,	PUNCT
ejpam-4484	174	35	where	where	SCONJ
ejpam-4484	174	36	a	a	DET
ejpam-4484	174	37	⊆	⊆	NUM
ejpam-4484	174	38	v	v	NOUN
ejpam-4484	174	39	(	(	PUNCT
ejpam-4484	174	40	g)\{v	g)\{v	PROPN
ejpam-4484	174	41	}	}	PUNCT
ejpam-4484	174	42	and	and	CCONJ
ejpam-4484	174	43	bv	bv	PROPN
ejpam-4484	174	44	is	be	AUX
ejpam-4484	174	45	a	a	DET
ejpam-4484	174	46	strong	strong	ADJ
ejpam-4484	174	47	resolving	resolving	NOUN
ejpam-4484	174	48	set	set	NOUN
ejpam-4484	174	49	of	of	ADP
ejpam-4484	174	50	hv	hv	PROPN
ejpam-4484	174	51	if	if	SCONJ
ejpam-4484	174	52	γ(h	γ(h	NOUN
ejpam-4484	174	53	)	)	PUNCT
ejpam-4484	174	54	=	=	SYM
ejpam-4484	174	55	1	1	NUM
ejpam-4484	174	56	or	or	CCONJ
ejpam-4484	174	57	bv	bv	PROPN
ejpam-4484	174	58	is	be	AUX
ejpam-4484	174	59	a	a	DET
ejpam-4484	174	60	strong	strong	ADJ
ejpam-4484	174	61	resolving	resolving	NOUN
ejpam-4484	174	62	set	set	NOUN
ejpam-4484	174	63	of	of	ADP
ejpam-4484	174	64	⟨v⟩+hv	⟨v⟩+hv	NOUN
ejpam-4484	174	65	if	if	SCONJ
ejpam-4484	174	66	γ(h	γ(h	NOUN
ejpam-4484	174	67	)	)	PUNCT
ejpam-4484	174	68	̸=	̸=	PROPN
ejpam-4484	174	69	1	1	NUM
ejpam-4484	174	70	.	.	PUNCT
ejpam-4484	175	1	suppose	suppose	VERB
ejpam-4484	175	2	(	(	PUNCT
ejpam-4484	175	3	a	a	PRON
ejpam-4484	175	4	)	)	PUNCT
ejpam-4484	175	5	holds	hold	NOUN
ejpam-4484	175	6	.	.	PUNCT
ejpam-4484	176	1	since	since	SCONJ
ejpam-4484	176	2	s	s	PROPN
ejpam-4484	176	3	is	be	AUX
ejpam-4484	176	4	a	a	DET
ejpam-4484	176	5	proper	proper	ADJ
ejpam-4484	176	6	restrained	restrained	ADJ
ejpam-4484	176	7	hop	hop	NOUN
ejpam-4484	176	8	dominating	dominating	NOUN
ejpam-4484	176	9	subset	subset	NOUN
ejpam-4484	176	10	of	of	ADP
ejpam-4484	176	11	g	g	PROPN
ejpam-4484	176	12	◦	◦	NOUN
ejpam-4484	176	13	h	h	NOUN
ejpam-4484	176	14	,	,	PUNCT
ejpam-4484	176	15	⟨v	⟨v	PROPN
ejpam-4484	176	16	(	(	PUNCT
ejpam-4484	176	17	g	g	PROPN
ejpam-4484	176	18	◦	◦	NOUN
ejpam-4484	176	19	h	h	NOUN
ejpam-4484	176	20	)	)	PUNCT
ejpam-4484	176	21	\	\	PROPN
ejpam-4484	176	22	s	s	PART
ejpam-4484	176	23	=	=	SYM
ejpam-4484	176	24	v	v	NOUN
ejpam-4484	176	25	(	(	PUNCT
ejpam-4484	176	26	g	g	NOUN
ejpam-4484	176	27	)	)	PUNCT
ejpam-4484	176	28	\a⟩	\a⟩	PROPN
ejpam-4484	176	29	has	have	VERB
ejpam-4484	176	30	no	no	DET
ejpam-4484	176	31	isolated	isolated	ADJ
ejpam-4484	176	32	vertex	vertex	NOUN
ejpam-4484	176	33	.	.	PUNCT
ejpam-4484	177	1	thus	thus	ADV
ejpam-4484	177	2	,	,	PUNCT
ejpam-4484	177	3	(	(	PUNCT
ejpam-4484	177	4	i	i	NOUN
ejpam-4484	177	5	)	)	PUNCT
ejpam-4484	177	6	holds	hold	VERB
ejpam-4484	177	7	.	.	PUNCT
ejpam-4484	178	1	on	on	ADP
ejpam-4484	178	2	the	the	DET
ejpam-4484	178	3	other	other	ADJ
ejpam-4484	178	4	hand	hand	NOUN
ejpam-4484	178	5	,	,	PUNCT
ejpam-4484	178	6	suppose	suppose	VERB
ejpam-4484	178	7	(	(	PUNCT
ejpam-4484	178	8	b	b	NOUN
ejpam-4484	178	9	)	)	PUNCT
ejpam-4484	178	10	holds	hold	VERB
ejpam-4484	178	11	.	.	PUNCT
ejpam-4484	179	1	since	since	SCONJ
ejpam-4484	179	2	s	s	PROPN
ejpam-4484	179	3	is	be	AUX
ejpam-4484	179	4	a	a	DET
ejpam-4484	179	5	restrained	restrained	ADJ
ejpam-4484	179	6	hop	hop	NOUN
ejpam-4484	179	7	dominating	dominating	NOUN
ejpam-4484	179	8	set	set	NOUN
ejpam-4484	179	9	of	of	ADP
ejpam-4484	179	10	g	g	PROPN
ejpam-4484	179	11	◦	◦	NOUN
ejpam-4484	179	12	h	h	NOUN
ejpam-4484	179	13	,	,	PUNCT
ejpam-4484	179	14	s	s	PART
ejpam-4484	179	15	=	=	PUNCT
ejpam-4484	179	16	a	a	DET
ejpam-4484	179	17	∪	∪	X
ejpam-4484	179	18	(	(	PUNCT
ejpam-4484	179	19	⋃	⋃	NOUN
ejpam-4484	179	20	u∈v	u∈v	NOUN
ejpam-4484	179	21	(	(	PUNCT
ejpam-4484	179	22	g)\{v	g)\{v	PROPN
ejpam-4484	179	23	}	}	PUNCT
ejpam-4484	179	24	v	v	PROPN
ejpam-4484	179	25	(	(	PUNCT
ejpam-4484	179	26	hu	hu	PROPN
ejpam-4484	179	27	)	)	PUNCT
ejpam-4484	179	28	)	)	PUNCT
ejpam-4484	180	1	∪	∪	ADP
ejpam-4484	180	2	bv	bv	PROPN
ejpam-4484	180	3	for	for	ADP
ejpam-4484	180	4	a	a	DET
ejpam-4484	180	5	unique	unique	ADJ
ejpam-4484	180	6	vertex	vertex	NOUN
ejpam-4484	180	7	v	v	ADP
ejpam-4484	180	8	∈	∈	NOUN
ejpam-4484	180	9	v	v	NOUN
ejpam-4484	180	10	(	(	PUNCT
ejpam-4484	180	11	g	g	NOUN
ejpam-4484	180	12	)	)	PUNCT
ejpam-4484	180	13	,	,	PUNCT
ejpam-4484	180	14	where	where	SCONJ
ejpam-4484	180	15	a	a	DET
ejpam-4484	180	16	=	=	SYM
ejpam-4484	180	17	v	v	X
ejpam-4484	180	18	(	(	PUNCT
ejpam-4484	180	19	g	g	NOUN
ejpam-4484	180	20	)	)	PUNCT
ejpam-4484	180	21	\	\	NOUN
ejpam-4484	180	22	{	{	PUNCT
ejpam-4484	180	23	v	v	NOUN
ejpam-4484	180	24	}	}	PUNCT
ejpam-4484	180	25	or	or	CCONJ
ejpam-4484	180	26	⟨v	⟨v	NUM
ejpam-4484	180	27	(	(	PUNCT
ejpam-4484	180	28	g	g	NOUN
ejpam-4484	180	29	)	)	PUNCT
ejpam-4484	180	30	\	\	PUNCT
ejpam-4484	181	1	(	(	PUNCT
ejpam-4484	181	2	a	a	DET
ejpam-4484	181	3	∪	∪	X
ejpam-4484	181	4	{	{	PUNCT
ejpam-4484	181	5	v})⟩	v})⟩	PROPN
ejpam-4484	181	6	has	have	VERB
ejpam-4484	181	7	no	no	DET
ejpam-4484	181	8	isolated	isolated	ADJ
ejpam-4484	181	9	vertex	vertex	NOUN
ejpam-4484	181	10	and	and	CCONJ
ejpam-4484	181	11	bv	bv	PROPN
ejpam-4484	181	12	is	be	AUX
ejpam-4484	181	13	a	a	DET
ejpam-4484	181	14	strong	strong	ADJ
ejpam-4484	181	15	resolving	resolve	VERB
ejpam-4484	181	16	hop	hop	NOUN
ejpam-4484	181	17	dominating	dominating	NOUN
ejpam-4484	181	18	set	set	NOUN
ejpam-4484	181	19	of	of	ADP
ejpam-4484	181	20	hv	hv	PROPN
ejpam-4484	181	21	+	+	X
ejpam-4484	181	22	⟨v⟩	⟨v⟩	PROPN
ejpam-4484	181	23	if	if	SCONJ
ejpam-4484	181	24	ng(v	ng(v	NOUN
ejpam-4484	181	25	)	)	PUNCT
ejpam-4484	182	1	∩a	∩a	NOUN
ejpam-4484	182	2	=	=	PUNCT
ejpam-4484	182	3	∅	∅	NOUN
ejpam-4484	182	4	and	and	CCONJ
ejpam-4484	182	5	bv	bv	PROPN
ejpam-4484	182	6	is	be	AUX
ejpam-4484	182	7	a	a	DET
ejpam-4484	182	8	strong	strong	ADJ
ejpam-4484	182	9	resolving	resolving	NOUN
ejpam-4484	182	10	set	set	NOUN
ejpam-4484	182	11	,	,	PUNCT
ejpam-4484	182	12	where	where	SCONJ
ejpam-4484	182	13	⟨v	⟨v	NOUN
ejpam-4484	182	14	(	(	PUNCT
ejpam-4484	182	15	hv)\bv⟩	hv)\bv⟩	NOUN
ejpam-4484	182	16	has	have	VERB
ejpam-4484	182	17	no	no	DET
ejpam-4484	182	18	isolated	isolated	ADJ
ejpam-4484	182	19	vertex	vertex	NOUN
ejpam-4484	182	20	if	if	SCONJ
ejpam-4484	182	21	v	v	NOUN
ejpam-4484	182	22	∈	∈	PROPN
ejpam-4484	182	23	a	a	DET
ejpam-4484	182	24	and	and	CCONJ
ejpam-4484	182	25	ng(v)∩a	ng(v)∩a	PROPN
ejpam-4484	182	26	̸=	̸=	PROPN
ejpam-4484	182	27	∅.	∅.	NOUN
ejpam-4484	182	28	since	since	SCONJ
ejpam-4484	182	29	v	v	NUM
ejpam-4484	182	30	∈	∈	NOUN
ejpam-4484	182	31	s	s	NOUN
ejpam-4484	182	32	,	,	PUNCT
ejpam-4484	182	33	⟨v	⟨v	PROPN
ejpam-4484	182	34	(	(	PUNCT
ejpam-4484	182	35	hv)\bv⟩	hv)\bv⟩	NOUN
ejpam-4484	182	36	has	have	VERB
ejpam-4484	182	37	no	no	DET
ejpam-4484	182	38	isolated	isolated	ADJ
ejpam-4484	182	39	vertex	vertex	NOUN
ejpam-4484	182	40	and	and	CCONJ
ejpam-4484	182	41	bv	bv	PROPN
ejpam-4484	182	42	is	be	AUX
ejpam-4484	182	43	a	a	DET
ejpam-4484	182	44	strong	strong	ADJ
ejpam-4484	182	45	hop	hop	NOUN
ejpam-4484	182	46	dominating	dominating	NOUN
ejpam-4484	182	47	set	set	NOUN
ejpam-4484	182	48	of	of	ADP
ejpam-4484	182	49	hv	hv	PROPN
ejpam-4484	182	50	+	+	PROPN
ejpam-4484	182	51	⟨v⟩	⟨v⟩	PROPN
ejpam-4484	182	52	,	,	PUNCT
ejpam-4484	182	53	if	if	SCONJ
ejpam-4484	182	54	v	v	NUM
ejpam-4484	182	55	∈	∈	PROPN
ejpam-4484	182	56	s	s	NOUN
ejpam-4484	182	57	and	and	CCONJ
ejpam-4484	182	58	bv	bv	PROPN
ejpam-4484	182	59	is	be	AUX
ejpam-4484	182	60	strong	strong	ADJ
ejpam-4484	182	61	resolving	resolve	VERB
ejpam-4484	182	62	set	set	NOUN
ejpam-4484	182	63	of	of	ADP
ejpam-4484	182	64	hv	hv	PROPN
ejpam-4484	182	65	and	and	CCONJ
ejpam-4484	182	66	⟨v	⟨v	PROPN
ejpam-4484	182	67	(	(	PUNCT
ejpam-4484	182	68	hv	hv	NOUN
ejpam-4484	182	69	)	)	PUNCT
ejpam-4484	182	70	\	\	NOUN
ejpam-4484	182	71	bv⟩	bv⟩	PROPN
ejpam-4484	182	72	has	have	VERB
ejpam-4484	182	73	no	no	DET
ejpam-4484	182	74	isolated	isolated	ADJ
ejpam-4484	182	75	vertex	vertex	NOUN
ejpam-4484	182	76	if	if	SCONJ
ejpam-4484	182	77	v	v	NOUN
ejpam-4484	182	78	∈	∈	PROPN
ejpam-4484	182	79	s.	s.	PROPN
ejpam-4484	182	80	thus	thus	ADV
ejpam-4484	182	81	(	(	PUNCT
ejpam-4484	182	82	ii	ii	NOUN
ejpam-4484	182	83	)	)	PUNCT
ejpam-4484	182	84	holds	hold	VERB
ejpam-4484	182	85	.	.	PUNCT
ejpam-4484	183	1	conversely	conversely	ADV
ejpam-4484	183	2	,	,	PUNCT
ejpam-4484	183	3	suppose	suppose	VERB
ejpam-4484	183	4	(	(	PUNCT
ejpam-4484	183	5	i	i	NOUN
ejpam-4484	183	6	)	)	PUNCT
ejpam-4484	183	7	and	and	CCONJ
ejpam-4484	183	8	(	(	PUNCT
ejpam-4484	183	9	ii	ii	NOUN
ejpam-4484	183	10	)	)	PUNCT
ejpam-4484	183	11	hold	hold	NOUN
ejpam-4484	183	12	.	.	PUNCT
ejpam-4484	184	1	by	by	ADP
ejpam-4484	184	2	theorem	theorem	NOUN
ejpam-4484	184	3	4	4	NUM
ejpam-4484	184	4	,	,	PUNCT
ejpam-4484	184	5	s	s	VERB
ejpam-4484	184	6	is	be	AUX
ejpam-4484	184	7	a	a	DET
ejpam-4484	184	8	strong	strong	ADJ
ejpam-4484	184	9	resolving	resolving	NOUN
ejpam-4484	184	10	set	set	NOUN
ejpam-4484	184	11	of	of	ADP
ejpam-4484	184	12	g	g	PROPN
ejpam-4484	184	13	◦	◦	NOUN
ejpam-4484	184	14	h.	h.	NOUN
ejpam-4484	184	15	if	if	SCONJ
ejpam-4484	184	16	(	(	PUNCT
ejpam-4484	184	17	i	i	NOUN
ejpam-4484	184	18	)	)	PUNCT
ejpam-4484	184	19	holds	hold	VERB
ejpam-4484	184	20	,	,	PUNCT
ejpam-4484	184	21	then	then	ADV
ejpam-4484	184	22	⟨v	⟨v	NUM
ejpam-4484	184	23	(	(	PUNCT
ejpam-4484	184	24	g	g	PROPN
ejpam-4484	184	25	◦	◦	NOUN
ejpam-4484	184	26	h	h	NOUN
ejpam-4484	184	27	)	)	PUNCT
ejpam-4484	184	28	\	\	PROPN
ejpam-4484	184	29	s	s	PART
ejpam-4484	184	30	=	=	SYM
ejpam-4484	184	31	v	v	NOUN
ejpam-4484	184	32	(	(	PUNCT
ejpam-4484	184	33	g	g	NOUN
ejpam-4484	184	34	)	)	PUNCT
ejpam-4484	184	35	\	\	NOUN
ejpam-4484	185	1	a⟩	a⟩	PUNCT
ejpam-4484	185	2	has	have	VERB
ejpam-4484	185	3	no	no	DET
ejpam-4484	185	4	isolated	isolated	ADJ
ejpam-4484	185	5	vertex	vertex	NOUN
ejpam-4484	185	6	.	.	PUNCT
ejpam-4484	186	1	if	if	SCONJ
ejpam-4484	186	2	(	(	PUNCT
ejpam-4484	186	3	ii	ii	NOUN
ejpam-4484	186	4	)	)	PUNCT
ejpam-4484	186	5	holds	hold	VERB
ejpam-4484	186	6	a.	a.	PROPN
ejpam-4484	186	7	h.	h.	PROPN
ejpam-4484	186	8	abragan	abragan	PROPN
ejpam-4484	186	9	,	,	PUNCT
ejpam-4484	186	10	h.	h.	PROPN
ejpam-4484	186	11	m.	m.	PROPN
ejpam-4484	186	12	rara	rara	PROPN
ejpam-4484	186	13	/	/	SYM
ejpam-4484	186	14	eur	eur	PROPN
ejpam-4484	186	15	.	.	PUNCT
ejpam-4484	187	1	j.	j.	PROPN
ejpam-4484	187	2	pure	pure	PROPN
ejpam-4484	187	3	appl	appl	PROPN
ejpam-4484	187	4	.	.	PROPN
ejpam-4484	187	5	math	math	PROPN
ejpam-4484	187	6	,	,	PUNCT
ejpam-4484	187	7	15	15	NUM
ejpam-4484	187	8	(	(	PUNCT
ejpam-4484	187	9	4	4	NUM
ejpam-4484	187	10	)	)	PUNCT
ejpam-4484	187	11	(	(	PUNCT
ejpam-4484	187	12	2022	2022	NUM
ejpam-4484	187	13	)	)	PUNCT
ejpam-4484	187	14	,	,	PUNCT
ejpam-4484	187	15	1472	1472	NUM
ejpam-4484	187	16	-	-	SYM
ejpam-4484	187	17	1481	1481	NUM
ejpam-4484	187	18	1479	1479	NUM
ejpam-4484	187	19	then	then	ADV
ejpam-4484	187	20	v	v	X
ejpam-4484	187	21	(	(	PUNCT
ejpam-4484	187	22	g	g	PROPN
ejpam-4484	187	23	◦	◦	NOUN
ejpam-4484	187	24	h	h	NOUN
ejpam-4484	187	25	)	)	PUNCT
ejpam-4484	187	26	\	\	PROPN
ejpam-4484	188	1	s	s	PART
ejpam-4484	188	2	=	=	SYM
ejpam-4484	188	3	(	(	PUNCT
ejpam-4484	188	4	v	v	NOUN
ejpam-4484	188	5	(	(	PUNCT
ejpam-4484	188	6	g	g	NOUN
ejpam-4484	188	7	)	)	PUNCT
ejpam-4484	188	8	\a	\a	NUM
ejpam-4484	188	9	)	)	PUNCT
ejpam-4484	188	10	∪	∪	NOUN
ejpam-4484	188	11	(	(	PUNCT
ejpam-4484	188	12	v	v	NOUN
ejpam-4484	188	13	(	(	PUNCT
ejpam-4484	188	14	hv	hv	PROPN
ejpam-4484	188	15	+	+	PROPN
ejpam-4484	188	16	⟨v⟩	⟨v⟩	PROPN
ejpam-4484	188	17	)	)	PUNCT
ejpam-4484	188	18	\bv	\bv	NOUN
ejpam-4484	188	19	)	)	PUNCT
ejpam-4484	188	20	.	.	PUNCT
ejpam-4484	189	1	since	since	SCONJ
ejpam-4484	189	2	a	a	DET
ejpam-4484	189	3	=	=	SYM
ejpam-4484	189	4	v	v	NOUN
ejpam-4484	189	5	(	(	PUNCT
ejpam-4484	189	6	g	g	NOUN
ejpam-4484	189	7	)	)	PUNCT
ejpam-4484	189	8	\	\	NOUN
ejpam-4484	189	9	{	{	PUNCT
ejpam-4484	189	10	v	v	NOUN
ejpam-4484	189	11	}	}	PUNCT
ejpam-4484	189	12	or	or	CCONJ
ejpam-4484	189	13	⟨v	⟨v	NUM
ejpam-4484	189	14	(	(	PUNCT
ejpam-4484	189	15	g	g	NOUN
ejpam-4484	189	16	)	)	PUNCT
ejpam-4484	189	17	\	\	PUNCT
ejpam-4484	189	18	(	(	PUNCT
ejpam-4484	189	19	a	a	DET
ejpam-4484	189	20	∪	∪	X
ejpam-4484	189	21	{	{	PUNCT
ejpam-4484	189	22	v})⟩	v})⟩	PROPN
ejpam-4484	189	23	has	have	VERB
ejpam-4484	189	24	no	no	DET
ejpam-4484	189	25	isolated	isolated	ADJ
ejpam-4484	189	26	vertex	vertex	NOUN
ejpam-4484	189	27	,	,	PUNCT
ejpam-4484	189	28	⟨v	⟨v	NOUN
ejpam-4484	189	29	(	(	PUNCT
ejpam-4484	189	30	g	g	PROPN
ejpam-4484	189	31	+	+	NOUN
ejpam-4484	189	32	h	h	NOUN
ejpam-4484	189	33	)	)	PUNCT
ejpam-4484	189	34	\	\	PROPN
ejpam-4484	189	35	s⟩	s⟩	NOUN
ejpam-4484	189	36	has	have	VERB
ejpam-4484	189	37	no	no	DET
ejpam-4484	189	38	isolated	isolated	ADJ
ejpam-4484	189	39	vertex	vertex	NOUN
ejpam-4484	189	40	.	.	PUNCT
ejpam-4484	190	1	in	in	ADP
ejpam-4484	190	2	either	either	DET
ejpam-4484	190	3	case	case	NOUN
ejpam-4484	190	4	,	,	PUNCT
ejpam-4484	190	5	⟨v	⟨v	NOUN
ejpam-4484	190	6	(	(	PUNCT
ejpam-4484	190	7	g	g	PROPN
ejpam-4484	190	8	◦	◦	NOUN
ejpam-4484	190	9	h	h	NOUN
ejpam-4484	190	10	)	)	PUNCT
ejpam-4484	190	11	\	\	PROPN
ejpam-4484	190	12	s⟩	s⟩	NOUN
ejpam-4484	190	13	has	have	VERB
ejpam-4484	190	14	no	no	DET
ejpam-4484	190	15	isolated	isolated	ADJ
ejpam-4484	190	16	vertex	vertex	NOUN
ejpam-4484	190	17	.	.	PUNCT
ejpam-4484	191	1	therefore	therefore	ADV
ejpam-4484	191	2	,	,	PUNCT
ejpam-4484	191	3	s	s	VERB
ejpam-4484	191	4	is	be	AUX
ejpam-4484	191	5	a	a	DET
ejpam-4484	191	6	restrained	restrain	VERB
ejpam-4484	191	7	strong	strong	ADJ
ejpam-4484	191	8	resolving	resolve	VERB
ejpam-4484	191	9	hop	hop	NOUN
ejpam-4484	191	10	dominating	dominating	NOUN
ejpam-4484	191	11	set	set	NOUN
ejpam-4484	191	12	of	of	ADP
ejpam-4484	191	13	g	g	PROPN
ejpam-4484	191	14	◦	◦	NOUN
ejpam-4484	191	15	h.	h.	NOUN
ejpam-4484	191	16	corollary	corollary	ADJ
ejpam-4484	191	17	5	5	PROPN
ejpam-4484	191	18	.	.	PUNCT
ejpam-4484	192	1	let	let	VERB
ejpam-4484	192	2	g	g	NOUN
ejpam-4484	192	3	andh	andh	NOUN
ejpam-4484	192	4	be	be	AUX
ejpam-4484	192	5	nontrivial	nontrivial	ADJ
ejpam-4484	192	6	connected	connect	VERB
ejpam-4484	192	7	graphs	graph	NOUN
ejpam-4484	192	8	of	of	ADP
ejpam-4484	192	9	ordersm	ordersm	NOUN
ejpam-4484	192	10	and	and	CCONJ
ejpam-4484	192	11	n	n	CCONJ
ejpam-4484	192	12	,	,	PUNCT
ejpam-4484	192	13	respectively	respectively	ADV
ejpam-4484	192	14	.	.	PUNCT
ejpam-4484	193	1	then	then	ADV
ejpam-4484	193	2	,	,	PUNCT
ejpam-4484	193	3	γrsrh(g	γrsrh(g	ADP
ejpam-4484	193	4	◦	◦	NOUN
ejpam-4484	193	5	h	h	NOUN
ejpam-4484	193	6	)	)	PUNCT
ejpam-4484	193	7	=	=	PUNCT
ejpam-4484	194	1	(	(	PUNCT
ejpam-4484	194	2	m−	m−	PROPN
ejpam-4484	194	3	1)n+	1)n+	NUM
ejpam-4484	194	4	γsr(h	γsr(h	PROPN
ejpam-4484	194	5	+	+	NOUN
ejpam-4484	194	6	k1	k1	NOUN
ejpam-4484	194	7	)	)	PUNCT
ejpam-4484	194	8	.	.	PUNCT
ejpam-4484	195	1	proof	proof	NOUN
ejpam-4484	195	2	:	:	PUNCT
ejpam-4484	195	3	let	let	VERB
ejpam-4484	195	4	s	s	PRON
ejpam-4484	195	5	be	be	AUX
ejpam-4484	195	6	a	a	DET
ejpam-4484	195	7	γrsrh	γrsrh	NOUN
ejpam-4484	195	8	-	-	PUNCT
ejpam-4484	195	9	set	set	NOUN
ejpam-4484	195	10	of	of	ADP
ejpam-4484	195	11	g	g	PROPN
ejpam-4484	195	12	◦	◦	NOUN
ejpam-4484	195	13	h.	h.	NOUN
ejpam-4484	195	14	then	then	ADV
ejpam-4484	195	15	by	by	ADP
ejpam-4484	195	16	theorem	theorem	ADJ
ejpam-4484	195	17	9	9	NUM
ejpam-4484	195	18	(	(	PUNCT
ejpam-4484	195	19	ii	ii	NOUN
ejpam-4484	195	20	)	)	PUNCT
ejpam-4484	195	21	,	,	PUNCT
ejpam-4484	195	22	s	s	VERB
ejpam-4484	195	23	=	=	PUNCT
ejpam-4484	195	24	a	a	DET
ejpam-4484	195	25	⋃	⋃	NOUN
ejpam-4484	195	26	u∈v	u∈v	NOUN
ejpam-4484	195	27	(	(	PUNCT
ejpam-4484	195	28	g)\{v	g)\{v	PROPN
ejpam-4484	195	29	}	}	PUNCT
ejpam-4484	195	30	v	v	PROPN
ejpam-4484	195	31	(	(	PUNCT
ejpam-4484	195	32	hu	hu	PROPN
ejpam-4484	195	33	)	)	PUNCT
ejpam-4484	196	1	⋃	⋃	PUNCT
ejpam-4484	196	2	bv	bv	PROPN
ejpam-4484	196	3	for	for	ADP
ejpam-4484	196	4	a	a	DET
ejpam-4484	196	5	unique	unique	ADJ
ejpam-4484	196	6	vertex	vertex	NOUN
ejpam-4484	196	7	v	v	NOUN
ejpam-4484	196	8	in	in	ADP
ejpam-4484	196	9	g	g	PROPN
ejpam-4484	196	10	and	and	CCONJ
ejpam-4484	196	11	bv	bv	PROPN
ejpam-4484	196	12	is	be	AUX
ejpam-4484	196	13	a	a	DET
ejpam-4484	196	14	strong	strong	ADJ
ejpam-4484	196	15	resolving	resolve	VERB
ejpam-4484	196	16	hop	hop	NOUN
ejpam-4484	196	17	dominating	dominating	NOUN
ejpam-4484	196	18	set	set	NOUN
ejpam-4484	196	19	of	of	ADP
ejpam-4484	196	20	hv	hv	PROPN
ejpam-4484	196	21	.	.	PUNCT
ejpam-4484	197	1	hence	hence	ADV
ejpam-4484	197	2	,	,	PUNCT
ejpam-4484	197	3	γrsrh(g	γrsrh(g	ADP
ejpam-4484	197	4	◦	◦	NOUN
ejpam-4484	197	5	h	h	NOUN
ejpam-4484	197	6	)	)	PUNCT
ejpam-4484	197	7	=	=	SYM
ejpam-4484	197	8	|s|	|s|	PROPN
ejpam-4484	197	9	=	=	PUNCT
ejpam-4484	197	10	|v	|v	X
ejpam-4484	197	11	(	(	PUNCT
ejpam-4484	197	12	h)||v	h)||v	PROPN
ejpam-4484	197	13	(	(	PUNCT
ejpam-4484	197	14	g	g	NOUN
ejpam-4484	197	15	)	)	PUNCT
ejpam-4484	197	16	\	\	NOUN
ejpam-4484	197	17	{	{	PUNCT
ejpam-4484	197	18	v}|+	v}|+	PROPN
ejpam-4484	197	19	|bv|	|bv|	PROPN
ejpam-4484	197	20	≥	≥	NUM
ejpam-4484	197	21	(	(	PUNCT
ejpam-4484	197	22	m−	m−	PROPN
ejpam-4484	197	23	1)n+	1)n+	NUM
ejpam-4484	197	24	γsrh(h	γsrh(h	PROPN
ejpam-4484	197	25	)	)	PUNCT
ejpam-4484	197	26	.	.	PUNCT
ejpam-4484	198	1	let	let	VERB
ejpam-4484	198	2	cv	cv	PROPN
ejpam-4484	198	3	be	be	AUX
ejpam-4484	198	4	a	a	DET
ejpam-4484	198	5	minimum	minimum	ADJ
ejpam-4484	198	6	strong	strong	ADJ
ejpam-4484	198	7	resolving	resolve	VERB
ejpam-4484	198	8	hop	hop	NOUN
ejpam-4484	198	9	dominating	dominating	NOUN
ejpam-4484	198	10	set	set	PROPN
ejpam-4484	198	11	ofk1+hv	ofk1+hv	PROPN
ejpam-4484	198	12	.	.	PUNCT
ejpam-4484	199	1	for	for	ADP
ejpam-4484	199	2	a	a	DET
ejpam-4484	199	3	unique	unique	ADJ
ejpam-4484	199	4	vertex	vertex	NOUN
ejpam-4484	199	5	v	v	ADP
ejpam-4484	199	6	∈	∈	NOUN
ejpam-4484	199	7	v	v	NOUN
ejpam-4484	199	8	(	(	PUNCT
ejpam-4484	199	9	g	g	NOUN
ejpam-4484	199	10	)	)	PUNCT
ejpam-4484	199	11	,	,	PUNCT
ejpam-4484	199	12	let	let	VERB
ejpam-4484	199	13	⟨bv⟩	⟨bv⟩	VERB
ejpam-4484	199	14	∼=	∼=	PROPN
ejpam-4484	199	15	⟨cv⟩.	⟨cv⟩.	PUNCT
ejpam-4484	199	16	then	then	ADV
ejpam-4484	199	17	by	by	ADP
ejpam-4484	199	18	theorem	theorem	NOUN
ejpam-4484	199	19	9	9	NUM
ejpam-4484	199	20	,	,	PUNCT
ejpam-4484	199	21	s	s	VERB
ejpam-4484	199	22	=	=	NOUN
ejpam-4484	199	23	a	a	DET
ejpam-4484	199	24	⋃	⋃	PROPN
ejpam-4484	199	25	(	(	PUNCT
ejpam-4484	199	26	⋃	⋃	NOUN
ejpam-4484	199	27	u∈v	u∈v	NOUN
ejpam-4484	199	28	(	(	PUNCT
ejpam-4484	199	29	g)\{v	g)\{v	PROPN
ejpam-4484	199	30	}	}	PUNCT
ejpam-4484	199	31	v	v	PROPN
ejpam-4484	199	32	(	(	PUNCT
ejpam-4484	199	33	hu	hu	PROPN
ejpam-4484	199	34	)	)	PUNCT
ejpam-4484	199	35	)	)	PUNCT
ejpam-4484	200	1	⋃	⋃	ADP
ejpam-4484	200	2	bv	bv	PROPN
ejpam-4484	200	3	is	be	AUX
ejpam-4484	200	4	a	a	DET
ejpam-4484	200	5	restrained	restrained	ADJ
ejpam-4484	200	6	strong	strong	ADJ
ejpam-4484	200	7	resolving	resolve	VERB
ejpam-4484	200	8	hop	hop	NOUN
ejpam-4484	200	9	dominating	dominating	NOUN
ejpam-4484	200	10	set	set	NOUN
ejpam-4484	200	11	of	of	ADP
ejpam-4484	200	12	g	g	PROPN
ejpam-4484	200	13	◦	◦	NOUN
ejpam-4484	200	14	h.	h.	PROPN
ejpam-4484	200	15	thus	thus	ADV
ejpam-4484	200	16	,	,	PUNCT
ejpam-4484	200	17	γrsrh(g	γrsrh(g	ADP
ejpam-4484	200	18	◦	◦	NOUN
ejpam-4484	200	19	h	h	NOUN
ejpam-4484	200	20	)	)	PUNCT
ejpam-4484	200	21	≤	≤	NUM
ejpam-4484	200	22	|s|	|s|	PROPN
ejpam-4484	200	23	=	=	PUNCT
ejpam-4484	200	24	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4484	200	25	⋃	⋃	NOUN
ejpam-4484	200	26	u∈v	u∈v	NOUN
ejpam-4484	200	27	(	(	PUNCT
ejpam-4484	200	28	g)\{v	g)\{v	PROPN
ejpam-4484	200	29	}	}	PUNCT
ejpam-4484	200	30	v	v	PROPN
ejpam-4484	200	31	(	(	PUNCT
ejpam-4484	200	32	hu	hu	PROPN
ejpam-4484	200	33	)	)	PUNCT
ejpam-4484	200	34	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-4484	200	35	|bv|	|bv|	PROPN
ejpam-4484	200	36	=	=	PUNCT
ejpam-4484	200	37	(	(	PUNCT
ejpam-4484	200	38	m−	m−	PROPN
ejpam-4484	200	39	1)(n	1)(n	NUM
ejpam-4484	200	40	)	)	PUNCT
ejpam-4484	200	41	+	+	NUM
ejpam-4484	200	42	|cv|	|cv|	NOUN
ejpam-4484	200	43	=	=	SYM
ejpam-4484	200	44	(	(	PUNCT
ejpam-4484	200	45	m−	m−	PROPN
ejpam-4484	200	46	1)(n	1)(n	NUM
ejpam-4484	200	47	)	)	PUNCT
ejpam-4484	200	48	+	+	NUM
ejpam-4484	200	49	γsrh(k1	γsrh(k1	NOUN
ejpam-4484	200	50	+	+	NOUN
ejpam-4484	200	51	h	h	NOUN
ejpam-4484	200	52	)	)	PUNCT
ejpam-4484	200	53	.	.	PUNCT
ejpam-4484	201	1	therefore	therefore	ADV
ejpam-4484	201	2	,	,	PUNCT
ejpam-4484	201	3	γrsrh(g	γrsrh(g	ADP
ejpam-4484	201	4	◦	◦	NOUN
ejpam-4484	201	5	h	h	NOUN
ejpam-4484	201	6	)	)	PUNCT
ejpam-4484	201	7	=	=	PUNCT
ejpam-4484	202	1	(	(	PUNCT
ejpam-4484	202	2	m−	m−	PROPN
ejpam-4484	202	3	1)n+	1)n+	NUM
ejpam-4484	202	4	γsrh(k1	γsrh(k1	NOUN
ejpam-4484	202	5	+	+	NOUN
ejpam-4484	202	6	h	h	NOUN
ejpam-4484	202	7	)	)	PUNCT
ejpam-4484	202	8	.	.	PUNCT
ejpam-4484	203	1	example	example	NOUN
ejpam-4484	204	1	2	2	NUM
ejpam-4484	204	2	.	.	X
ejpam-4484	204	3	consider	consider	VERB
ejpam-4484	204	4	the	the	DET
ejpam-4484	204	5	graph	graph	NOUN
ejpam-4484	204	6	p3	p3	PROPN
ejpam-4484	204	7	◦	◦	PROPN
ejpam-4484	204	8	p3	p3	PROPN
ejpam-4484	204	9	.	.	PUNCT
ejpam-4484	205	1	then	then	ADV
ejpam-4484	205	2	the	the	DET
ejpam-4484	205	3	minimum	minimum	NOUN
ejpam-4484	205	4	restrained	restrain	VERB
ejpam-4484	205	5	strong	strong	ADJ
ejpam-4484	205	6	resolving	resolve	VERB
ejpam-4484	205	7	hop	hop	NOUN
ejpam-4484	205	8	dominating	dominating	NOUN
ejpam-4484	205	9	set	set	NOUN
ejpam-4484	205	10	is	be	AUX
ejpam-4484	205	11	γrsrh(p3	γrsrh(p3	ADJ
ejpam-4484	205	12	◦	◦	PROPN
ejpam-4484	205	13	p3	p3	PROPN
ejpam-4484	205	14	)	)	PUNCT
ejpam-4484	206	1	=	=	SYM
ejpam-4484	206	2	8	8	NUM
ejpam-4484	206	3	.	.	NOUN
ejpam-4484	207	1	5	5	NUM
ejpam-4484	207	2	.	.	NOUN
ejpam-4484	207	3	lexicographic	lexicographic	ADJ
ejpam-4484	207	4	of	of	ADP
ejpam-4484	207	5	graphs	graph	NOUN
ejpam-4484	207	6	definition	definition	NOUN
ejpam-4484	207	7	3	3	NUM
ejpam-4484	207	8	.	.	PUNCT
ejpam-4484	208	1	[	[	X
ejpam-4484	208	2	6	6	NUM
ejpam-4484	208	3	]	]	PUNCT
ejpam-4484	208	4	the	the	DET
ejpam-4484	208	5	lexicographic	lexicographic	ADJ
ejpam-4484	208	6	product	product	NOUN
ejpam-4484	208	7	of	of	ADP
ejpam-4484	208	8	graphs	graph	NOUN
ejpam-4484	208	9	g	g	PROPN
ejpam-4484	208	10	and	and	CCONJ
ejpam-4484	208	11	h	h	NOUN
ejpam-4484	208	12	,	,	PUNCT
ejpam-4484	208	13	denoted	denote	VERB
ejpam-4484	208	14	by	by	ADP
ejpam-4484	208	15	g[h	g[h	NOUN
ejpam-4484	208	16	]	]	PUNCT
ejpam-4484	208	17	,	,	PUNCT
ejpam-4484	208	18	is	be	AUX
ejpam-4484	208	19	the	the	DET
ejpam-4484	208	20	graph	graph	NOUN
ejpam-4484	208	21	with	with	ADP
ejpam-4484	208	22	vertex	vertex	NOUN
ejpam-4484	208	23	-	-	PUNCT
ejpam-4484	208	24	set	set	VERB
ejpam-4484	208	25	v	v	NOUN
ejpam-4484	208	26	(	(	PUNCT
ejpam-4484	208	27	g[h	g[h	PROPN
ejpam-4484	208	28	]	]	PUNCT
ejpam-4484	208	29	)	)	PUNCT
ejpam-4484	208	30	=	=	SYM
ejpam-4484	208	31	v	v	X
ejpam-4484	208	32	(	(	PUNCT
ejpam-4484	208	33	g)×	g)×	NOUN
ejpam-4484	208	34	v	v	NOUN
ejpam-4484	208	35	(	(	PUNCT
ejpam-4484	208	36	h	h	NOUN
ejpam-4484	208	37	)	)	PUNCT
ejpam-4484	208	38	and	and	CCONJ
ejpam-4484	208	39	edge	edge	NOUN
ejpam-4484	208	40	-	-	PUNCT
ejpam-4484	208	41	set	set	VERB
ejpam-4484	208	42	e(g[h	e(g[h	NOUN
ejpam-4484	208	43	]	]	PUNCT
ejpam-4484	208	44	)	)	PUNCT
ejpam-4484	208	45	satisfying	satisfy	VERB
ejpam-4484	208	46	the	the	DET
ejpam-4484	208	47	following	follow	VERB
ejpam-4484	208	48	conditions	condition	NOUN
ejpam-4484	208	49	:	:	PUNCT
ejpam-4484	208	50	(	(	PUNCT
ejpam-4484	208	51	u1	u1	PROPN
ejpam-4484	208	52	,	,	PUNCT
ejpam-4484	208	53	v1)(u2	v1)(u2	PROPN
ejpam-4484	208	54	,	,	PUNCT
ejpam-4484	208	55	v2	v2	PROPN
ejpam-4484	208	56	)	)	PUNCT
ejpam-4484	208	57	∈	∈	NOUN
ejpam-4484	208	58	e(g[h	e(g[h	NOUN
ejpam-4484	208	59	]	]	PUNCT
ejpam-4484	208	60	)	)	PUNCT
ejpam-4484	209	1	if	if	SCONJ
ejpam-4484	209	2	and	and	CCONJ
ejpam-4484	209	3	only	only	ADV
ejpam-4484	209	4	if	if	SCONJ
ejpam-4484	209	5	either	either	PRON
ejpam-4484	209	6	u1u2	u1u2	PROPN
ejpam-4484	209	7	∈	∈	PROPN
ejpam-4484	209	8	e(g	e(g	PROPN
ejpam-4484	209	9	)	)	PUNCT
ejpam-4484	209	10	or	or	CCONJ
ejpam-4484	209	11	u1	u1	NOUN
ejpam-4484	209	12	=	=	SYM
ejpam-4484	209	13	u2	u2	PROPN
ejpam-4484	209	14	and	and	CCONJ
ejpam-4484	209	15	v1v2	v1v2	PUNCT
ejpam-4484	209	16	∈	∈	PROPN
ejpam-4484	209	17	e(h	e(h	PROPN
ejpam-4484	209	18	)	)	PUNCT
ejpam-4484	209	19	.	.	PUNCT
ejpam-4484	210	1	lemma	lemma	PROPN
ejpam-4484	210	2	4	4	X
ejpam-4484	210	3	.	.	PUNCT
ejpam-4484	211	1	let	let	VERB
ejpam-4484	211	2	g	g	PROPN
ejpam-4484	211	3	=	=	PROPN
ejpam-4484	211	4	kn	kn	PROPN
ejpam-4484	211	5	for	for	ADP
ejpam-4484	211	6	n	n	PROPN
ejpam-4484	211	7	>	>	SYM
ejpam-4484	211	8	1	1	NUM
ejpam-4484	211	9	and	and	CCONJ
ejpam-4484	211	10	h	h	DET
ejpam-4484	211	11	a	a	DET
ejpam-4484	211	12	nontrivial	nontrivial	ADJ
ejpam-4484	211	13	connected	connect	VERB
ejpam-4484	211	14	graph	graph	NOUN
ejpam-4484	211	15	with	with	ADP
ejpam-4484	211	16	γ(h	γ(h	NOUN
ejpam-4484	211	17	)	)	PUNCT
ejpam-4484	211	18	̸=	̸=	PROPN
ejpam-4484	211	19	1	1	NUM
ejpam-4484	211	20	.	.	PUNCT
ejpam-4484	212	1	then	then	ADV
ejpam-4484	212	2	a	a	DET
ejpam-4484	212	3	×	×	NOUN
ejpam-4484	212	4	c	c	NOUN
ejpam-4484	212	5	⊆	⊆	NUM
ejpam-4484	212	6	v	v	NOUN
ejpam-4484	212	7	(	(	PUNCT
ejpam-4484	212	8	g[h	g[h	PROPN
ejpam-4484	212	9	]	]	PUNCT
ejpam-4484	212	10	)	)	PUNCT
ejpam-4484	212	11	is	be	AUX
ejpam-4484	212	12	a	a	DET
ejpam-4484	212	13	hop	hop	NOUN
ejpam-4484	212	14	dominated	dominate	VERB
ejpam-4484	212	15	superclique	superclique	NOUN
ejpam-4484	212	16	in	in	ADP
ejpam-4484	212	17	g[h	g[h	NOUN
ejpam-4484	212	18	]	]	PUNCT
ejpam-4484	213	1	if	if	SCONJ
ejpam-4484	214	1	and	and	CCONJ
ejpam-4484	214	2	only	only	ADV
ejpam-4484	214	3	if	if	SCONJ
ejpam-4484	214	4	a	a	PRON
ejpam-4484	214	5	is	be	AUX
ejpam-4484	214	6	a	a	DET
ejpam-4484	214	7	nonempty	nonempty	ADJ
ejpam-4484	214	8	subset	subset	NOUN
ejpam-4484	214	9	of	of	ADP
ejpam-4484	214	10	v	v	NOUN
ejpam-4484	214	11	(	(	PUNCT
ejpam-4484	214	12	g	g	NOUN
ejpam-4484	214	13	)	)	PUNCT
ejpam-4484	214	14	and	and	CCONJ
ejpam-4484	214	15	c	c	PROPN
ejpam-4484	214	16	is	be	AUX
ejpam-4484	214	17	a	a	DET
ejpam-4484	214	18	superclique	superclique	NOUN
ejpam-4484	214	19	in	in	ADP
ejpam-4484	214	20	h.	h.	PROPN
ejpam-4484	214	21	a.	a.	PROPN
ejpam-4484	214	22	h.	h.	PROPN
ejpam-4484	214	23	abragan	abragan	PROPN
ejpam-4484	214	24	,	,	PUNCT
ejpam-4484	214	25	h.	h.	PROPN
ejpam-4484	214	26	m.	m.	PROPN
ejpam-4484	214	27	rara	rara	PROPN
ejpam-4484	214	28	/	/	SYM
ejpam-4484	214	29	eur	eur	PROPN
ejpam-4484	214	30	.	.	PUNCT
ejpam-4484	215	1	j.	j.	PROPN
ejpam-4484	215	2	pure	pure	PROPN
ejpam-4484	215	3	appl	appl	PROPN
ejpam-4484	215	4	.	.	PROPN
ejpam-4484	215	5	math	math	PROPN
ejpam-4484	215	6	,	,	PUNCT
ejpam-4484	215	7	15	15	NUM
ejpam-4484	215	8	(	(	PUNCT
ejpam-4484	215	9	4	4	NUM
ejpam-4484	215	10	)	)	PUNCT
ejpam-4484	215	11	(	(	PUNCT
ejpam-4484	215	12	2022	2022	NUM
ejpam-4484	215	13	)	)	PUNCT
ejpam-4484	215	14	,	,	PUNCT
ejpam-4484	215	15	1472	1472	NUM
ejpam-4484	215	16	-	-	SYM
ejpam-4484	215	17	1481	1481	NUM
ejpam-4484	215	18	1480	1480	NUM
ejpam-4484	215	19	proof	proof	NOUN
ejpam-4484	215	20	:	:	PUNCT
ejpam-4484	215	21	suppose	suppose	VERB
ejpam-4484	215	22	that	that	SCONJ
ejpam-4484	215	23	a	a	DET
ejpam-4484	215	24	×	×	NOUN
ejpam-4484	215	25	c	c	NOUN
ejpam-4484	215	26	⊆	⊆	NUM
ejpam-4484	215	27	v	v	NOUN
ejpam-4484	215	28	(	(	PUNCT
ejpam-4484	215	29	g[h	g[h	PROPN
ejpam-4484	215	30	]	]	PUNCT
ejpam-4484	215	31	)	)	PUNCT
ejpam-4484	215	32	is	be	AUX
ejpam-4484	215	33	a	a	DET
ejpam-4484	215	34	hop	hop	NOUN
ejpam-4484	215	35	dominated	dominate	VERB
ejpam-4484	215	36	superclique	superclique	NOUN
ejpam-4484	215	37	in	in	ADP
ejpam-4484	215	38	g[h	g[h	NOUN
ejpam-4484	215	39	]	]	PUNCT
ejpam-4484	215	40	.	.	PUNCT
ejpam-4484	216	1	by	by	ADP
ejpam-4484	216	2	lemma	lemma	PROPN
ejpam-4484	216	3	2	2	PROPN
ejpam-4484	216	4	and	and	CCONJ
ejpam-4484	216	5	lemma	lemma	PROPN
ejpam-4484	216	6	3	3	NUM
ejpam-4484	216	7	,	,	PUNCT
ejpam-4484	216	8	a	a	PRON
ejpam-4484	216	9	is	be	AUX
ejpam-4484	216	10	a	a	DET
ejpam-4484	216	11	nonempty	nonempty	ADJ
ejpam-4484	216	12	subset	subset	NOUN
ejpam-4484	216	13	of	of	ADP
ejpam-4484	216	14	v	v	NOUN
ejpam-4484	216	15	(	(	PUNCT
ejpam-4484	216	16	g	g	NOUN
ejpam-4484	216	17	)	)	PUNCT
ejpam-4484	216	18	and	and	CCONJ
ejpam-4484	216	19	c	c	PROPN
ejpam-4484	216	20	is	be	AUX
ejpam-4484	216	21	a	a	DET
ejpam-4484	216	22	superclique	superclique	NOUN
ejpam-4484	216	23	in	in	ADP
ejpam-4484	216	24	h.	h.	NOUN
ejpam-4484	216	25	let	let	VERB
ejpam-4484	216	26	x	x	SYM
ejpam-4484	216	27	∈	∈	PROPN
ejpam-4484	216	28	c.	c.	NOUN
ejpam-4484	216	29	then	then	ADV
ejpam-4484	216	30	(	(	PUNCT
ejpam-4484	216	31	a	a	PRON
ejpam-4484	216	32	,	,	PUNCT
ejpam-4484	216	33	x	x	NOUN
ejpam-4484	216	34	)	)	PUNCT
ejpam-4484	216	35	∈	∈	PROPN
ejpam-4484	217	1	a×c	a×c	PROPN
ejpam-4484	217	2	for	for	ADP
ejpam-4484	217	3	any	any	DET
ejpam-4484	217	4	a	a	DET
ejpam-4484	217	5	∈	∈	NOUN
ejpam-4484	217	6	a.	a.	NOUN
ejpam-4484	217	7	since	since	SCONJ
ejpam-4484	217	8	a×c	a×c	PROPN
ejpam-4484	217	9	is	be	AUX
ejpam-4484	217	10	hop	hop	ADV
ejpam-4484	217	11	dominated	dominate	VERB
ejpam-4484	217	12	superclique	superclique	NOUN
ejpam-4484	217	13	,	,	PUNCT
ejpam-4484	217	14	there	there	PRON
ejpam-4484	217	15	exists	exist	VERB
ejpam-4484	217	16	(	(	PUNCT
ejpam-4484	217	17	b	b	X
ejpam-4484	217	18	,	,	PUNCT
ejpam-4484	217	19	y	y	NOUN
ejpam-4484	217	20	)	)	PUNCT
ejpam-4484	217	21	∈	∈	PROPN
ejpam-4484	218	1	[	[	X
ejpam-4484	218	2	v	v	X
ejpam-4484	218	3	(	(	PUNCT
ejpam-4484	218	4	g[h	g[h	PROPN
ejpam-4484	218	5	]	]	PUNCT
ejpam-4484	218	6	)	)	PUNCT
ejpam-4484	218	7	\	\	PUNCT
ejpam-4484	219	1	(	(	PUNCT
ejpam-4484	219	2	a	a	DET
ejpam-4484	219	3	×	×	NOUN
ejpam-4484	219	4	c	c	NOUN
ejpam-4484	219	5	)	)	PUNCT
ejpam-4484	219	6	]	]	PUNCT
ejpam-4484	220	1	∩ng[h]((a	∩ng[h]((a	PROPN
ejpam-4484	220	2	,	,	PUNCT
ejpam-4484	220	3	x	x	NOUN
ejpam-4484	220	4	)	)	PUNCT
ejpam-4484	220	5	,	,	PUNCT
ejpam-4484	220	6	2	2	NUM
ejpam-4484	220	7	)	)	PUNCT
ejpam-4484	220	8	.	.	PUNCT
ejpam-4484	221	1	suppose	suppose	VERB
ejpam-4484	221	2	γ(h	γ(h	NOUN
ejpam-4484	221	3	)	)	PUNCT
ejpam-4484	221	4	=	=	PUNCT
ejpam-4484	222	1	1	1	X
ejpam-4484	222	2	.	.	PUNCT
ejpam-4484	222	3	since	since	SCONJ
ejpam-4484	222	4	g	g	PROPN
ejpam-4484	222	5	=	=	PROPN
ejpam-4484	222	6	kn	kn	PROPN
ejpam-4484	222	7	for	for	ADP
ejpam-4484	222	8	n	n	PROPN
ejpam-4484	222	9	>	>	X
ejpam-4484	222	10	1	1	NUM
ejpam-4484	222	11	,	,	PUNCT
ejpam-4484	222	12	a	a	DET
ejpam-4484	222	13	=	=	SYM
ejpam-4484	222	14	b	b	PROPN
ejpam-4484	222	15	and	and	CCONJ
ejpam-4484	222	16	y	y	PROPN
ejpam-4484	222	17	∈	∈	PROPN
ejpam-4484	223	1	[	[	X
ejpam-4484	223	2	(	(	PUNCT
ejpam-4484	223	3	v	v	NOUN
ejpam-4484	223	4	(	(	PUNCT
ejpam-4484	223	5	h	h	NOUN
ejpam-4484	223	6	)	)	PUNCT
ejpam-4484	223	7	\	\	NOUN
ejpam-4484	223	8	c	c	X
ejpam-4484	223	9	)	)	PUNCT
ejpam-4484	223	10	∩	∩	NOUN
ejpam-4484	223	11	nh(x	nh(x	NUM
ejpam-4484	223	12	,	,	PUNCT
ejpam-4484	223	13	2	2	NUM
ejpam-4484	223	14	)	)	PUNCT
ejpam-4484	223	15	]	]	PUNCT
ejpam-4484	223	16	.	.	PUNCT
ejpam-4484	224	1	if	if	SCONJ
ejpam-4484	224	2	γ(h	γ(h	NOUN
ejpam-4484	224	3	)	)	PUNCT
ejpam-4484	224	4	=	=	SYM
ejpam-4484	224	5	1	1	NUM
ejpam-4484	224	6	,	,	PUNCT
ejpam-4484	224	7	then	then	ADV
ejpam-4484	224	8	by	by	ADP
ejpam-4484	224	9	proposition	proposition	NOUN
ejpam-4484	224	10	1	1	NUM
ejpam-4484	224	11	,	,	PUNCT
ejpam-4484	224	12	c	c	PROPN
ejpam-4484	224	13	∩	∩	ADJ
ejpam-4484	224	14	c∗	c∗	NOUN
ejpam-4484	224	15	=	=	NOUN
ejpam-4484	224	16	∅	∅	NOUN
ejpam-4484	224	17	for	for	ADP
ejpam-4484	224	18	all	all	DET
ejpam-4484	224	19	γ	γ	NOUN
ejpam-4484	224	20	-	-	PUNCT
ejpam-4484	224	21	sets	set	NOUN
ejpam-4484	224	22	c∗	c∗	NOUN
ejpam-4484	224	23	of	of	ADP
ejpam-4484	224	24	h.	h.	PROPN
ejpam-4484	224	25	thus	thus	ADV
ejpam-4484	224	26	,	,	PUNCT
ejpam-4484	224	27	x	x	PUNCT
ejpam-4484	224	28	∈	∈	PROPN
ejpam-4484	224	29	c	c	NOUN
ejpam-4484	224	30	\	\	PROPN
ejpam-4484	224	31	c∗	c∗	PROPN
ejpam-4484	224	32	and	and	CCONJ
ejpam-4484	224	33	y	y	PROPN
ejpam-4484	224	34	∈	∈	PROPN
ejpam-4484	224	35	nh(x	nh(x	PUNCT
ejpam-4484	224	36	,	,	PUNCT
ejpam-4484	224	37	2	2	X
ejpam-4484	224	38	)	)	PUNCT
ejpam-4484	224	39	exists	exist	VERB
ejpam-4484	224	40	.	.	PUNCT
ejpam-4484	225	1	hence	hence	ADV
ejpam-4484	225	2	,	,	PUNCT
ejpam-4484	225	3	c	c	PROPN
ejpam-4484	225	4	is	be	AUX
ejpam-4484	225	5	a	a	DET
ejpam-4484	225	6	hop	hop	NOUN
ejpam-4484	225	7	dominated	dominate	VERB
ejpam-4484	225	8	superclique	superclique	NOUN
ejpam-4484	225	9	in	in	ADP
ejpam-4484	225	10	h.	h.	PROPN
ejpam-4484	225	11	for	for	ADP
ejpam-4484	225	12	the	the	DET
ejpam-4484	225	13	converse	converse	NOUN
ejpam-4484	225	14	,	,	PUNCT
ejpam-4484	225	15	suppose	suppose	VERB
ejpam-4484	225	16	that	that	SCONJ
ejpam-4484	225	17	a	a	PRON
ejpam-4484	225	18	is	be	AUX
ejpam-4484	225	19	a	a	DET
ejpam-4484	225	20	nonempty	nonempty	ADJ
ejpam-4484	225	21	subset	subset	NOUN
ejpam-4484	225	22	of	of	ADP
ejpam-4484	225	23	v	v	NOUN
ejpam-4484	225	24	(	(	PUNCT
ejpam-4484	225	25	g	g	NOUN
ejpam-4484	225	26	)	)	PUNCT
ejpam-4484	225	27	and	and	CCONJ
ejpam-4484	225	28	c	c	PROPN
ejpam-4484	225	29	is	be	AUX
ejpam-4484	225	30	a	a	DET
ejpam-4484	225	31	hop	hop	NOUN
ejpam-4484	225	32	dominated	dominate	VERB
ejpam-4484	225	33	superclique	superclique	NOUN
ejpam-4484	225	34	in	in	ADP
ejpam-4484	225	35	h.	h.	PROPN
ejpam-4484	225	36	by	by	ADP
ejpam-4484	225	37	lemma	lemma	PROPN
ejpam-4484	225	38	2	2	NUM
ejpam-4484	225	39	,	,	PUNCT
ejpam-4484	225	40	lemma	lemma	PROPN
ejpam-4484	225	41	3	3	NUM
ejpam-4484	225	42	and	and	CCONJ
ejpam-4484	225	43	proposition	proposition	NOUN
ejpam-4484	225	44	1	1	NUM
ejpam-4484	225	45	,	,	PUNCT
ejpam-4484	225	46	a	a	DET
ejpam-4484	225	47	×	×	NOUN
ejpam-4484	225	48	c	c	NOUN
ejpam-4484	225	49	is	be	AUX
ejpam-4484	225	50	a	a	DET
ejpam-4484	225	51	superclique	superclique	NOUN
ejpam-4484	225	52	in	in	ADP
ejpam-4484	225	53	g[h	g[h	NOUN
ejpam-4484	225	54	]	]	PUNCT
ejpam-4484	225	55	.	.	PUNCT
ejpam-4484	226	1	let	let	VERB
ejpam-4484	226	2	(	(	PUNCT
ejpam-4484	226	3	a	a	PRON
ejpam-4484	226	4	,	,	PUNCT
ejpam-4484	226	5	x	x	NOUN
ejpam-4484	226	6	)	)	PUNCT
ejpam-4484	226	7	∈	∈	PROPN
ejpam-4484	226	8	a×c	a×c	PROPN
ejpam-4484	226	9	and	and	CCONJ
ejpam-4484	226	10	γ(h	γ(h	NOUN
ejpam-4484	226	11	)	)	PUNCT
ejpam-4484	226	12	̸=	̸=	PROPN
ejpam-4484	226	13	1	1	NUM
ejpam-4484	226	14	.	.	PUNCT
ejpam-4484	227	1	since	since	SCONJ
ejpam-4484	227	2	c	c	PROPN
ejpam-4484	227	3	is	be	AUX
ejpam-4484	227	4	a	a	DET
ejpam-4484	227	5	hop	hop	NOUN
ejpam-4484	227	6	dominated	dominate	VERB
ejpam-4484	227	7	superclique	superclique	NOUN
ejpam-4484	227	8	in	in	ADP
ejpam-4484	227	9	h	h	NOUN
ejpam-4484	227	10	,	,	PUNCT
ejpam-4484	227	11	there	there	PRON
ejpam-4484	227	12	exists	exist	VERB
ejpam-4484	227	13	y	y	PROPN
ejpam-4484	227	14	∈	∈	PROPN
ejpam-4484	228	1	[	[	X
ejpam-4484	228	2	⟨(v	⟨(v	NOUN
ejpam-4484	228	3	(	(	PUNCT
ejpam-4484	228	4	h)\c)⟩∩nh(x	h)\c)⟩∩nh(x	PROPN
ejpam-4484	228	5	,	,	PUNCT
ejpam-4484	228	6	2	2	NUM
ejpam-4484	228	7	)	)	PUNCT
ejpam-4484	228	8	]	]	PUNCT
ejpam-4484	228	9	.	.	PUNCT
ejpam-4484	229	1	hence	hence	ADV
ejpam-4484	229	2	,	,	PUNCT
ejpam-4484	229	3	(	(	PUNCT
ejpam-4484	229	4	a	a	PRON
ejpam-4484	229	5	,	,	PUNCT
ejpam-4484	229	6	y	y	NOUN
ejpam-4484	229	7	)	)	PUNCT
ejpam-4484	229	8	∈	∈	PROPN
ejpam-4484	230	1	[	[	X
ejpam-4484	230	2	v	v	X
ejpam-4484	230	3	(	(	PUNCT
ejpam-4484	230	4	g[h])\	g[h])\	X
ejpam-4484	230	5	(	(	PUNCT
ejpam-4484	230	6	a×c)]∩ng[h]((a	a×c)]∩ng[h]((a	PROPN
ejpam-4484	230	7	,	,	PUNCT
ejpam-4484	230	8	x	x	NOUN
ejpam-4484	230	9	)	)	PUNCT
ejpam-4484	230	10	,	,	PUNCT
ejpam-4484	230	11	2	2	NUM
ejpam-4484	230	12	)	)	PUNCT
ejpam-4484	230	13	.	.	PUNCT
ejpam-4484	231	1	suppose	suppose	VERB
ejpam-4484	231	2	γ(h	γ(h	NOUN
ejpam-4484	231	3	)	)	PUNCT
ejpam-4484	231	4	=	=	SYM
ejpam-4484	232	1	1	1	X
ejpam-4484	232	2	.	.	PUNCT
ejpam-4484	232	3	then	then	ADV
ejpam-4484	232	4	by	by	ADP
ejpam-4484	232	5	proposition	proposition	NOUN
ejpam-4484	232	6	1	1	NUM
ejpam-4484	232	7	,	,	PUNCT
ejpam-4484	232	8	c	c	PROPN
ejpam-4484	232	9	∩	∩	ADJ
ejpam-4484	232	10	c∗	c∗	NOUN
ejpam-4484	232	11	=	=	NOUN
ejpam-4484	232	12	∅	∅	NOUN
ejpam-4484	232	13	for	for	ADP
ejpam-4484	232	14	all	all	DET
ejpam-4484	232	15	γ	γ	NOUN
ejpam-4484	232	16	-	-	PUNCT
ejpam-4484	232	17	sets	set	NOUN
ejpam-4484	232	18	c∗	c∗	NOUN
ejpam-4484	232	19	of	of	ADP
ejpam-4484	232	20	h.	h.	PROPN
ejpam-4484	232	21	thus	thus	ADV
ejpam-4484	232	22	,	,	PUNCT
ejpam-4484	232	23	x	x	PUNCT
ejpam-4484	232	24	∈	∈	PROPN
ejpam-4484	232	25	c	c	NOUN
ejpam-4484	232	26	\	\	X
ejpam-4484	232	27	c∗.	c∗.	NOUN
ejpam-4484	232	28	this	this	PRON
ejpam-4484	232	29	implies	imply	VERB
ejpam-4484	232	30	that	that	SCONJ
ejpam-4484	232	31	a	a	DET
ejpam-4484	232	32	vertex	vertex	NOUN
ejpam-4484	232	33	z	z	NOUN
ejpam-4484	232	34	∈	∈	PROPN
ejpam-4484	232	35	nh(x	nh(x	NUM
ejpam-4484	232	36	,	,	PUNCT
ejpam-4484	232	37	2	2	X
ejpam-4484	232	38	)	)	PUNCT
ejpam-4484	232	39	exists	exist	VERB
ejpam-4484	232	40	.	.	PUNCT
ejpam-4484	233	1	since	since	SCONJ
ejpam-4484	233	2	c	c	PROPN
ejpam-4484	233	3	is	be	AUX
ejpam-4484	233	4	a	a	DET
ejpam-4484	233	5	superclique	superclique	NOUN
ejpam-4484	233	6	,	,	PUNCT
ejpam-4484	233	7	z	z	NOUN
ejpam-4484	233	8	∈	∈	PROPN
ejpam-4484	233	9	⟨v	⟨v	PUNCT
ejpam-4484	233	10	(	(	PUNCT
ejpam-4484	233	11	h	h	NOUN
ejpam-4484	233	12	)	)	PUNCT
ejpam-4484	233	13	\	\	PROPN
ejpam-4484	233	14	c⟩.	c⟩.	PROPN
ejpam-4484	233	15	hence	hence	ADV
ejpam-4484	233	16	,	,	PUNCT
ejpam-4484	233	17	(	(	PUNCT
ejpam-4484	233	18	a	a	PRON
ejpam-4484	233	19	,	,	PUNCT
ejpam-4484	233	20	z	z	NOUN
ejpam-4484	233	21	)	)	PUNCT
ejpam-4484	233	22	∈	∈	PROPN
ejpam-4484	234	1	[	[	X
ejpam-4484	234	2	v	v	X
ejpam-4484	234	3	(	(	PUNCT
ejpam-4484	234	4	g[h	g[h	PROPN
ejpam-4484	234	5	]	]	PUNCT
ejpam-4484	234	6	)	)	PUNCT
ejpam-4484	234	7	\	\	PUNCT
ejpam-4484	235	1	(	(	PUNCT
ejpam-4484	235	2	a×	a×	NOUN
ejpam-4484	235	3	c	c	NOUN
ejpam-4484	235	4	)	)	PUNCT
ejpam-4484	235	5	∩ng[h]((a	∩ng[h]((a	PROPN
ejpam-4484	235	6	,	,	PUNCT
ejpam-4484	235	7	x	x	NOUN
ejpam-4484	235	8	)	)	PUNCT
ejpam-4484	235	9	,	,	PUNCT
ejpam-4484	235	10	2	2	NUM
ejpam-4484	235	11	)	)	PUNCT
ejpam-4484	235	12	]	]	PUNCT
ejpam-4484	235	13	.	.	PUNCT
ejpam-4484	236	1	therefore	therefore	ADV
ejpam-4484	236	2	,	,	PUNCT
ejpam-4484	236	3	a×	a×	PROPN
ejpam-4484	236	4	c	c	PROPN
ejpam-4484	236	5	is	be	AUX
ejpam-4484	236	6	a	a	DET
ejpam-4484	236	7	hop	hop	NOUN
ejpam-4484	236	8	dominated	dominate	VERB
ejpam-4484	236	9	superclique	superclique	NOUN
ejpam-4484	236	10	in	in	ADP
ejpam-4484	236	11	g[h	g[h	NOUN
ejpam-4484	236	12	]	]	PUNCT
ejpam-4484	236	13	.	.	PUNCT
ejpam-4484	237	1	theorem	theorem	ADJ
ejpam-4484	237	2	10	10	NUM
ejpam-4484	237	3	.	.	PUNCT
ejpam-4484	238	1	let	let	VERB
ejpam-4484	238	2	g	g	PROPN
ejpam-4484	238	3	=	=	PROPN
ejpam-4484	238	4	kn	kn	PROPN
ejpam-4484	238	5	for	for	ADP
ejpam-4484	238	6	n	n	PROPN
ejpam-4484	238	7	>	>	SYM
ejpam-4484	238	8	1	1	NUM
ejpam-4484	238	9	and	and	CCONJ
ejpam-4484	238	10	h	h	DET
ejpam-4484	238	11	a	a	DET
ejpam-4484	238	12	nontrivial	nontrivial	ADJ
ejpam-4484	238	13	connected	connect	VERB
ejpam-4484	238	14	graph	graph	NOUN
ejpam-4484	238	15	with	with	ADP
ejpam-4484	238	16	γ(h	γ(h	NOUN
ejpam-4484	238	17	)	)	PUNCT
ejpam-4484	238	18	̸=	̸=	PROPN
ejpam-4484	238	19	1	1	NUM
ejpam-4484	238	20	.	.	PUNCT
ejpam-4484	239	1	a	a	DET
ejpam-4484	239	2	subset	subset	NOUN
ejpam-4484	239	3	s	s	X
ejpam-4484	239	4	of	of	ADP
ejpam-4484	239	5	v	v	NOUN
ejpam-4484	239	6	(	(	PUNCT
ejpam-4484	239	7	g[h	g[h	PROPN
ejpam-4484	239	8	]	]	PUNCT
ejpam-4484	239	9	)	)	PUNCT
ejpam-4484	239	10	is	be	AUX
ejpam-4484	239	11	a	a	DET
ejpam-4484	239	12	restrained	restrained	ADJ
ejpam-4484	239	13	strong	strong	ADJ
ejpam-4484	239	14	resolving	resolve	VERB
ejpam-4484	239	15	dominating	dominating	NOUN
ejpam-4484	239	16	set	set	NOUN
ejpam-4484	239	17	of	of	ADP
ejpam-4484	239	18	g[h	g[h	PROPN
ejpam-4484	239	19	]	]	PUNCT
ejpam-4484	239	20	if	if	SCONJ
ejpam-4484	239	21	and	and	CCONJ
ejpam-4484	239	22	only	only	ADV
ejpam-4484	239	23	if	if	SCONJ
ejpam-4484	239	24	s	s	VERB
ejpam-4484	239	25	=	=	SYM
ejpam-4484	239	26	v	v	NOUN
ejpam-4484	239	27	(	(	PUNCT
ejpam-4484	239	28	g[h	g[h	PROPN
ejpam-4484	239	29	]	]	PUNCT
ejpam-4484	239	30	)	)	PUNCT
ejpam-4484	239	31	\	\	PUNCT
ejpam-4484	240	1	(	(	PUNCT
ejpam-4484	240	2	a×	a×	NOUN
ejpam-4484	240	3	c	c	X
ejpam-4484	240	4	)	)	PUNCT
ejpam-4484	240	5	and	and	CCONJ
ejpam-4484	240	6	one	one	NUM
ejpam-4484	240	7	of	of	ADP
ejpam-4484	240	8	the	the	DET
ejpam-4484	240	9	following	follow	VERB
ejpam-4484	240	10	is	be	AUX
ejpam-4484	240	11	satisfied	satisfied	ADJ
ejpam-4484	240	12	:	:	PUNCT
ejpam-4484	240	13	(	(	PUNCT
ejpam-4484	240	14	i	i	NOUN
ejpam-4484	240	15	)	)	PUNCT
ejpam-4484	240	16	a	a	DET
ejpam-4484	240	17	⊆	⊆	NUM
ejpam-4484	240	18	v	v	NOUN
ejpam-4484	240	19	(	(	PUNCT
ejpam-4484	240	20	g	g	NOUN
ejpam-4484	240	21	)	)	PUNCT
ejpam-4484	240	22	and	and	CCONJ
ejpam-4484	240	23	c	c	NOUN
ejpam-4484	240	24	=	=	SYM
ejpam-4484	240	25	∅.	∅.	X
ejpam-4484	240	26	(	(	PUNCT
ejpam-4484	240	27	ii	ii	NOUN
ejpam-4484	240	28	)	)	PUNCT
ejpam-4484	240	29	a	a	PRON
ejpam-4484	240	30	is	be	AUX
ejpam-4484	240	31	a	a	DET
ejpam-4484	240	32	singleton	singleton	NOUN
ejpam-4484	240	33	subset	subset	NOUN
ejpam-4484	240	34	of	of	ADP
ejpam-4484	240	35	v	v	PROPN
ejpam-4484	240	36	(	(	PUNCT
ejpam-4484	240	37	g	g	NOUN
ejpam-4484	240	38	)	)	PUNCT
ejpam-4484	240	39	and	and	CCONJ
ejpam-4484	240	40	c	c	PROPN
ejpam-4484	240	41	is	be	AUX
ejpam-4484	240	42	a	a	DET
ejpam-4484	240	43	nonsingleton	nonsingleton	NOUN
ejpam-4484	240	44	superclique	superclique	NOUN
ejpam-4484	240	45	in	in	ADP
ejpam-4484	240	46	h.	h.	PROPN
ejpam-4484	240	47	(	(	PUNCT
ejpam-4484	240	48	iii	iii	X
ejpam-4484	240	49	)	)	PUNCT
ejpam-4484	240	50	a	a	PRON
ejpam-4484	240	51	is	be	AUX
ejpam-4484	240	52	a	a	DET
ejpam-4484	240	53	nonempty	nonempty	ADJ
ejpam-4484	240	54	nonsingleton	nonsingleton	NOUN
ejpam-4484	240	55	subset	subset	NOUN
ejpam-4484	240	56	of	of	ADP
ejpam-4484	240	57	v	v	NOUN
ejpam-4484	240	58	(	(	PUNCT
ejpam-4484	240	59	g	g	NOUN
ejpam-4484	240	60	)	)	PUNCT
ejpam-4484	240	61	and	and	CCONJ
ejpam-4484	240	62	c	c	PROPN
ejpam-4484	240	63	is	be	AUX
ejpam-4484	240	64	a	a	DET
ejpam-4484	240	65	hop	hop	NOUN
ejpam-4484	240	66	dominated	dominate	VERB
ejpam-4484	240	67	superclique	superclique	NOUN
ejpam-4484	240	68	in	in	ADP
ejpam-4484	240	69	h.	h.	PROPN
ejpam-4484	240	70	proof	proof	NOUN
ejpam-4484	240	71	:	:	PUNCT
ejpam-4484	240	72	let	let	VERB
ejpam-4484	240	73	s	s	PRON
ejpam-4484	240	74	be	be	AUX
ejpam-4484	240	75	a	a	DET
ejpam-4484	240	76	restrained	restrain	VERB
ejpam-4484	240	77	strong	strong	ADJ
ejpam-4484	240	78	resolving	resolve	VERB
ejpam-4484	240	79	hop	hop	NOUN
ejpam-4484	240	80	dominating	dominating	NOUN
ejpam-4484	240	81	set	set	NOUN
ejpam-4484	240	82	of	of	ADP
ejpam-4484	240	83	g[h	g[h	NOUN
ejpam-4484	240	84	]	]	PUNCT
ejpam-4484	240	85	.	.	PUNCT
ejpam-4484	241	1	by	by	ADP
ejpam-4484	241	2	theorem	theorem	NOUN
ejpam-4484	241	3	3	3	NUM
ejpam-4484	241	4	,	,	PUNCT
ejpam-4484	241	5	s	s	PART
ejpam-4484	241	6	=	=	SYM
ejpam-4484	241	7	v	v	NOUN
ejpam-4484	241	8	(	(	PUNCT
ejpam-4484	241	9	g[h	g[h	PROPN
ejpam-4484	241	10	]	]	PUNCT
ejpam-4484	241	11	)	)	PUNCT
ejpam-4484	241	12	\	\	PUNCT
ejpam-4484	242	1	(	(	PUNCT
ejpam-4484	242	2	a×	a×	NOUN
ejpam-4484	242	3	c	c	X
ejpam-4484	242	4	)	)	PUNCT
ejpam-4484	242	5	where	where	SCONJ
ejpam-4484	242	6	a	a	PRON
ejpam-4484	242	7	is	be	AUX
ejpam-4484	242	8	a	a	DET
ejpam-4484	242	9	subset	subset	NOUN
ejpam-4484	242	10	of	of	ADP
ejpam-4484	242	11	v	v	NOUN
ejpam-4484	242	12	(	(	PUNCT
ejpam-4484	242	13	g	g	NOUN
ejpam-4484	242	14	)	)	PUNCT
ejpam-4484	242	15	and	and	CCONJ
ejpam-4484	242	16	c	c	NOUN
ejpam-4484	242	17	=	=	SYM
ejpam-4484	242	18	∅	∅	NOUN
ejpam-4484	242	19	or	or	CCONJ
ejpam-4484	242	20	c	c	NOUN
ejpam-4484	242	21	is	be	AUX
ejpam-4484	242	22	a	a	DET
ejpam-4484	242	23	superclique	superclique	NOUN
ejpam-4484	242	24	in	in	ADP
ejpam-4484	242	25	h.	h.	NOUN
ejpam-4484	242	26	since	since	SCONJ
ejpam-4484	242	27	s	s	PROPN
ejpam-4484	242	28	is	be	AUX
ejpam-4484	242	29	a	a	DET
ejpam-4484	242	30	restrained	restrain	VERB
ejpam-4484	242	31	strong	strong	ADJ
ejpam-4484	242	32	resolving	resolving	NOUN
ejpam-4484	242	33	set	set	NOUN
ejpam-4484	242	34	,	,	PUNCT
ejpam-4484	242	35	s	s	PART
ejpam-4484	242	36	=	=	SYM
ejpam-4484	242	37	v	v	NOUN
ejpam-4484	242	38	(	(	PUNCT
ejpam-4484	242	39	g[h	g[h	PROPN
ejpam-4484	242	40	]	]	PUNCT
ejpam-4484	242	41	)	)	PUNCT
ejpam-4484	242	42	or	or	CCONJ
ejpam-4484	242	43	⟨v	⟨v	NUM
ejpam-4484	242	44	(	(	PUNCT
ejpam-4484	242	45	g[h	g[h	NOUN
ejpam-4484	242	46	]	]	PUNCT
ejpam-4484	242	47	)	)	PUNCT
ejpam-4484	242	48	\	\	PROPN
ejpam-4484	242	49	s⟩	s⟩	PROPN
ejpam-4484	242	50	has	have	VERB
ejpam-4484	242	51	no	no	DET
ejpam-4484	242	52	isolated	isolated	ADJ
ejpam-4484	242	53	vertex	vertex	NOUN
ejpam-4484	242	54	.	.	PUNCT
ejpam-4484	243	1	if	if	SCONJ
ejpam-4484	243	2	s	s	VERB
ejpam-4484	243	3	=	=	SYM
ejpam-4484	243	4	v	v	NOUN
ejpam-4484	243	5	(	(	PUNCT
ejpam-4484	243	6	g[h	g[h	PROPN
ejpam-4484	243	7	]	]	PUNCT
ejpam-4484	243	8	)	)	PUNCT
ejpam-4484	243	9	then	then	ADV
ejpam-4484	243	10	a	a	DET
ejpam-4484	243	11	×	×	NOUN
ejpam-4484	243	12	c	c	NOUN
ejpam-4484	243	13	=	=	SYM
ejpam-4484	243	14	∅	∅	NOUN
ejpam-4484	243	15	,	,	PUNCT
ejpam-4484	243	16	showing	show	VERB
ejpam-4484	243	17	that	that	SCONJ
ejpam-4484	243	18	a	a	DET
ejpam-4484	243	19	⊆	⊆	NUM
ejpam-4484	243	20	v	v	NOUN
ejpam-4484	243	21	(	(	PUNCT
ejpam-4484	243	22	g	g	NOUN
ejpam-4484	243	23	)	)	PUNCT
ejpam-4484	243	24	and	and	CCONJ
ejpam-4484	243	25	c	c	NOUN
ejpam-4484	243	26	=	=	PUNCT
ejpam-4484	243	27	∅.	∅.	VERB
ejpam-4484	243	28	thus	thus	ADV
ejpam-4484	243	29	,	,	PUNCT
ejpam-4484	243	30	(	(	PUNCT
ejpam-4484	243	31	i	i	NOUN
ejpam-4484	243	32	)	)	PUNCT
ejpam-4484	243	33	holds	hold	VERB
ejpam-4484	243	34	.	.	PUNCT
ejpam-4484	244	1	if	if	SCONJ
ejpam-4484	244	2	⟨v	⟨v	NOUN
ejpam-4484	244	3	(	(	PUNCT
ejpam-4484	244	4	g[h	g[h	NOUN
ejpam-4484	244	5	]	]	PUNCT
ejpam-4484	244	6	)	)	PUNCT
ejpam-4484	245	1	\s⟩	\s⟩	PROPN
ejpam-4484	245	2	has	have	VERB
ejpam-4484	245	3	no	no	DET
ejpam-4484	245	4	isolated	isolated	ADJ
ejpam-4484	245	5	vertex	vertex	NOUN
ejpam-4484	245	6	,	,	PUNCT
ejpam-4484	245	7	then	then	ADV
ejpam-4484	245	8	a×c	a×c	PRON
ejpam-4484	245	9	is	be	AUX
ejpam-4484	245	10	a	a	DET
ejpam-4484	245	11	nonsingleton	nonsingleton	NOUN
ejpam-4484	245	12	hop	hop	NOUN
ejpam-4484	245	13	dominated	dominate	VERB
ejpam-4484	245	14	superclique	superclique	NOUN
ejpam-4484	245	15	in	in	ADP
ejpam-4484	245	16	g[h	g[h	NOUN
ejpam-4484	245	17	]	]	PUNCT
ejpam-4484	245	18	.	.	PUNCT
ejpam-4484	246	1	this	this	PRON
ejpam-4484	246	2	implies	imply	VERB
ejpam-4484	246	3	that	that	SCONJ
ejpam-4484	246	4	a	a	PRON
ejpam-4484	246	5	is	be	AUX
ejpam-4484	246	6	a	a	DET
ejpam-4484	246	7	singleton	singleton	NOUN
ejpam-4484	246	8	subset	subset	NOUN
ejpam-4484	246	9	of	of	ADP
ejpam-4484	246	10	v	v	PROPN
ejpam-4484	246	11	(	(	PUNCT
ejpam-4484	246	12	g	g	NOUN
ejpam-4484	246	13	)	)	PUNCT
ejpam-4484	246	14	and	and	CCONJ
ejpam-4484	246	15	c	c	PROPN
ejpam-4484	246	16	is	be	AUX
ejpam-4484	246	17	a	a	DET
ejpam-4484	246	18	nonsingleton	nonsingleton	NOUN
ejpam-4484	246	19	superclique	superclique	NOUN
ejpam-4484	246	20	in	in	ADP
ejpam-4484	246	21	h	h	NOUN
ejpam-4484	246	22	or	or	CCONJ
ejpam-4484	246	23	a	a	PRON
ejpam-4484	246	24	is	be	AUX
ejpam-4484	246	25	nonempty	nonempty	ADJ
ejpam-4484	246	26	nonsingleton	nonsingleton	NOUN
ejpam-4484	246	27	subset	subset	NOUN
ejpam-4484	246	28	of	of	ADP
ejpam-4484	246	29	v	v	NOUN
ejpam-4484	246	30	(	(	PUNCT
ejpam-4484	246	31	g	g	NOUN
ejpam-4484	246	32	)	)	PUNCT
ejpam-4484	246	33	and	and	CCONJ
ejpam-4484	246	34	c	c	PROPN
ejpam-4484	246	35	is	be	AUX
ejpam-4484	246	36	hop	hop	ADV
ejpam-4484	246	37	dominated	dominate	VERB
ejpam-4484	246	38	superclique	superclique	NOUN
ejpam-4484	246	39	in	in	ADP
ejpam-4484	246	40	h.	h.	PROPN
ejpam-4484	246	41	hence	hence	ADV
ejpam-4484	246	42	(	(	PUNCT
ejpam-4484	246	43	ii	ii	NOUN
ejpam-4484	246	44	)	)	PUNCT
ejpam-4484	246	45	or	or	CCONJ
ejpam-4484	246	46	(	(	PUNCT
ejpam-4484	246	47	iii	iii	NOUN
ejpam-4484	246	48	)	)	PUNCT
ejpam-4484	246	49	holds	hold	VERB
ejpam-4484	246	50	.	.	PUNCT
ejpam-4484	247	1	for	for	ADP
ejpam-4484	247	2	the	the	DET
ejpam-4484	247	3	converse	converse	NOUN
ejpam-4484	247	4	,	,	PUNCT
ejpam-4484	247	5	suppose	suppose	VERB
ejpam-4484	247	6	s	s	VERB
ejpam-4484	247	7	=	=	SYM
ejpam-4484	247	8	v	v	PROPN
ejpam-4484	247	9	(	(	PUNCT
ejpam-4484	247	10	g[h	g[h	PROPN
ejpam-4484	247	11	]	]	PUNCT
ejpam-4484	247	12	)	)	PUNCT
ejpam-4484	247	13	\	\	PUNCT
ejpam-4484	248	1	(	(	PUNCT
ejpam-4484	248	2	a	a	DET
ejpam-4484	248	3	×	×	NOUN
ejpam-4484	248	4	c	c	NOUN
ejpam-4484	248	5	)	)	PUNCT
ejpam-4484	248	6	,	,	PUNCT
ejpam-4484	248	7	where	where	SCONJ
ejpam-4484	248	8	a	a	PRON
ejpam-4484	248	9	and	and	CCONJ
ejpam-4484	248	10	c	c	NOUN
ejpam-4484	248	11	satisfy	satisfy	NOUN
ejpam-4484	248	12	(	(	PUNCT
ejpam-4484	248	13	i),(ii	i),(ii	PROPN
ejpam-4484	248	14	)	)	PUNCT
ejpam-4484	248	15	or	or	CCONJ
ejpam-4484	248	16	(	(	PUNCT
ejpam-4484	248	17	iii	iii	NOUN
ejpam-4484	248	18	)	)	PUNCT
ejpam-4484	248	19	.	.	PUNCT
ejpam-4484	249	1	then	then	ADV
ejpam-4484	249	2	,	,	PUNCT
ejpam-4484	249	3	either	either	CCONJ
ejpam-4484	249	4	a	a	DET
ejpam-4484	249	5	×	×	NOUN
ejpam-4484	249	6	c	c	NOUN
ejpam-4484	249	7	=	=	NOUN
ejpam-4484	249	8	∅	∅	NOUN
ejpam-4484	249	9	or	or	CCONJ
ejpam-4484	249	10	by	by	ADP
ejpam-4484	249	11	lemma	lemma	PROPN
ejpam-4484	249	12	4	4	NUM
ejpam-4484	249	13	,	,	PUNCT
ejpam-4484	249	14	a	a	DET
ejpam-4484	249	15	×	×	NOUN
ejpam-4484	249	16	c	c	NOUN
ejpam-4484	249	17	is	be	AUX
ejpam-4484	249	18	a	a	DET
ejpam-4484	249	19	nonsingleton	nonsingleton	NOUN
ejpam-4484	249	20	hop	hop	NOUN
ejpam-4484	249	21	dominated	dominate	VERB
ejpam-4484	249	22	superclique	superclique	NOUN
ejpam-4484	249	23	in	in	ADP
ejpam-4484	249	24	g[h	g[h	NOUN
ejpam-4484	249	25	]	]	PUNCT
ejpam-4484	249	26	.	.	PUNCT
ejpam-4484	250	1	by	by	ADP
ejpam-4484	250	2	theorem	theorem	NOUN
ejpam-4484	250	3	3	3	NUM
ejpam-4484	250	4	,	,	PUNCT
ejpam-4484	250	5	s	s	VERB
ejpam-4484	250	6	is	be	AUX
ejpam-4484	250	7	a	a	DET
ejpam-4484	250	8	strong	strong	ADJ
ejpam-4484	250	9	resolving	resolving	NOUN
ejpam-4484	250	10	set	set	VERB
ejpam-4484	250	11	in	in	ADP
ejpam-4484	250	12	g[h	g[h	NOUN
ejpam-4484	250	13	]	]	PUNCT
ejpam-4484	250	14	.	.	PUNCT
ejpam-4484	251	1	since	since	SCONJ
ejpam-4484	251	2	a	a	DET
ejpam-4484	251	3	×	×	NOUN
ejpam-4484	251	4	c	c	NOUN
ejpam-4484	251	5	is	be	AUX
ejpam-4484	251	6	hop	hop	ADV
ejpam-4484	251	7	dominated	dominate	VERB
ejpam-4484	251	8	superclique	superclique	NOUN
ejpam-4484	251	9	,	,	PUNCT
ejpam-4484	251	10	s	s	PART
ejpam-4484	251	11	is	be	AUX
ejpam-4484	251	12	a	a	DET
ejpam-4484	251	13	strong	strong	ADJ
ejpam-4484	251	14	resolving	resolve	VERB
ejpam-4484	251	15	hop	hop	NOUN
ejpam-4484	251	16	dominating	dominating	NOUN
ejpam-4484	251	17	set	set	NOUN
ejpam-4484	251	18	of	of	ADP
ejpam-4484	251	19	g[h	g[h	NOUN
ejpam-4484	251	20	]	]	PUNCT
ejpam-4484	251	21	.	.	PUNCT
ejpam-4484	252	1	if	if	SCONJ
ejpam-4484	252	2	(	(	PUNCT
ejpam-4484	252	3	i	i	NOUN
ejpam-4484	252	4	)	)	PUNCT
ejpam-4484	252	5	is	be	AUX
ejpam-4484	252	6	true	true	ADJ
ejpam-4484	252	7	,	,	PUNCT
ejpam-4484	252	8	then	then	ADV
ejpam-4484	252	9	a	a	DET
ejpam-4484	252	10	⊆	⊆	NUM
ejpam-4484	252	11	v	v	NOUN
ejpam-4484	252	12	(	(	PUNCT
ejpam-4484	252	13	g	g	NOUN
ejpam-4484	252	14	)	)	PUNCT
ejpam-4484	252	15	and	and	CCONJ
ejpam-4484	252	16	c	c	NOUN
ejpam-4484	252	17	=	=	SYM
ejpam-4484	252	18	∅	∅	NOUN
ejpam-4484	252	19	,	,	PUNCT
ejpam-4484	252	20	that	that	ADV
ejpam-4484	252	21	is	is	ADV
ejpam-4484	252	22	,	,	PUNCT
ejpam-4484	252	23	a×	a×	PROPN
ejpam-4484	252	24	c	c	NOUN
ejpam-4484	252	25	=	=	NOUN
ejpam-4484	252	26	∅	∅	NOUN
ejpam-4484	252	27	and	and	CCONJ
ejpam-4484	252	28	s	s	NOUN
ejpam-4484	252	29	=	=	SYM
ejpam-4484	252	30	v	v	PROPN
ejpam-4484	252	31	(	(	PUNCT
ejpam-4484	252	32	g[h	g[h	PROPN
ejpam-4484	252	33	]	]	PUNCT
ejpam-4484	252	34	)	)	PUNCT
ejpam-4484	252	35	.	.	PUNCT
ejpam-4484	253	1	if	if	SCONJ
ejpam-4484	253	2	(	(	PUNCT
ejpam-4484	253	3	ii	ii	NOUN
ejpam-4484	253	4	)	)	PUNCT
ejpam-4484	253	5	or	or	CCONJ
ejpam-4484	253	6	(	(	PUNCT
ejpam-4484	253	7	iii	iii	X
ejpam-4484	253	8	)	)	PUNCT
ejpam-4484	253	9	is	be	AUX
ejpam-4484	253	10	satisfied	satisfied	ADJ
ejpam-4484	253	11	,	,	PUNCT
ejpam-4484	253	12	then	then	ADV
ejpam-4484	253	13	⟨v	⟨v	NOUN
ejpam-4484	253	14	(	(	PUNCT
ejpam-4484	253	15	g[h	g[h	NOUN
ejpam-4484	253	16	]	]	PUNCT
ejpam-4484	253	17	)	)	PUNCT
ejpam-4484	253	18	\	\	PROPN
ejpam-4484	253	19	s⟩	s⟩	PROPN
ejpam-4484	253	20	has	have	VERB
ejpam-4484	253	21	no	no	DET
ejpam-4484	253	22	isolated	isolated	ADJ
ejpam-4484	253	23	vertex	vertex	NOUN
ejpam-4484	253	24	.	.	PUNCT
ejpam-4484	254	1	therefore	therefore	ADV
ejpam-4484	254	2	,	,	PUNCT
ejpam-4484	254	3	s	s	VERB
ejpam-4484	254	4	is	be	AUX
ejpam-4484	254	5	a	a	DET
ejpam-4484	254	6	restrained	restrain	VERB
ejpam-4484	254	7	strong	strong	ADJ
ejpam-4484	254	8	resolving	resolve	VERB
ejpam-4484	254	9	hop	hop	NOUN
ejpam-4484	254	10	dominating	dominate	VERB
ejpam-4484	254	11	set	set	NOUN
ejpam-4484	254	12	g[h	g[h	PROPN
ejpam-4484	254	13	]	]	PUNCT
ejpam-4484	254	14	.	.	PUNCT
ejpam-4484	255	1	example	example	NOUN
ejpam-4484	256	1	3	3	X
ejpam-4484	256	2	.	.	X
ejpam-4484	256	3	consider	consider	VERB
ejpam-4484	256	4	the	the	DET
ejpam-4484	256	5	graph	graph	NOUN
ejpam-4484	256	6	of	of	ADP
ejpam-4484	256	7	k3[p5	k3[p5	NOUN
ejpam-4484	256	8	]	]	PUNCT
ejpam-4484	256	9	then	then	ADV
ejpam-4484	256	10	the	the	DET
ejpam-4484	256	11	γrsrh(k3[p5	γrsrh(k3[p5	NOUN
ejpam-4484	256	12	]	]	X
ejpam-4484	256	13	)	)	PUNCT
ejpam-4484	256	14	=	=	SYM
ejpam-4484	256	15	13	13	NUM
ejpam-4484	256	16	.	.	PUNCT
ejpam-4484	257	1	references	reference	NOUN
ejpam-4484	257	2	1481	1481	NUM
ejpam-4484	257	3	acknowledgments	acknowledgment	NOUN
ejpam-4484	257	4	the	the	DET
ejpam-4484	257	5	authors	author	NOUN
ejpam-4484	257	6	would	would	AUX
ejpam-4484	257	7	like	like	VERB
ejpam-4484	257	8	to	to	PART
ejpam-4484	257	9	thank	thank	VERB
ejpam-4484	257	10	the	the	DET
ejpam-4484	257	11	department	department	NOUN
ejpam-4484	257	12	of	of	ADP
ejpam-4484	257	13	science	science	NOUN
ejpam-4484	257	14	and	and	CCONJ
ejpam-4484	257	15	technology	technology	NOUN
ejpam-4484	257	16	accelerated	accelerate	VERB
ejpam-4484	257	17	science	science	NOUN
ejpam-4484	257	18	and	and	CCONJ
ejpam-4484	257	19	technology	technology	NOUN
ejpam-4484	257	20	human	human	ADJ
ejpam-4484	257	21	resource	resource	NOUN
ejpam-4484	257	22	development	development	NOUN
ejpam-4484	257	23	program	program	NOUN
ejpam-4484	257	24	(	(	PUNCT
ejpam-4484	257	25	dost	dost	NOUN
ejpam-4484	257	26	-	-	PUNCT
ejpam-4484	257	27	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4484	257	28	,	,	PUNCT
ejpam-4484	257	29	and	and	CCONJ
ejpam-4484	257	30	msu	msu	PROPN
ejpam-4484	257	31	-	-	PUNCT
ejpam-4484	257	32	iligan	iligan	PROPN
ejpam-4484	257	33	institute	institute	PROPN
ejpam-4484	257	34	of	of	ADP
ejpam-4484	257	35	technology	technology	NOUN
ejpam-4484	257	36	for	for	ADP
ejpam-4484	257	37	funding	fund	VERB
ejpam-4484	257	38	this	this	DET
ejpam-4484	257	39	research	research	NOUN
ejpam-4484	257	40	.	.	PUNCT
ejpam-4484	258	1	references	reference	NOUN
ejpam-4484	258	2	[	[	X
ejpam-4484	258	3	1	1	NUM
ejpam-4484	258	4	]	]	PUNCT
ejpam-4484	258	5	p.	p.	NOUN
ejpam-4484	258	6	acal	acal	ADJ
ejpam-4484	258	7	and	and	CCONJ
ejpam-4484	258	8	h.	h.	PROPN
ejpam-4484	258	9	rara	rara	PROPN
ejpam-4484	258	10	.	.	PUNCT
ejpam-4484	259	1	the	the	DET
ejpam-4484	259	2	strong	strong	ADJ
ejpam-4484	259	3	connected	connected	ADJ
ejpam-4484	259	4	metric	metric	ADJ
ejpam-4484	259	5	dimension	dimension	NOUN
ejpam-4484	259	6	in	in	ADP
ejpam-4484	259	7	the	the	DET
ejpam-4484	259	8	join	join	NOUN
ejpam-4484	259	9	and	and	CCONJ
ejpam-4484	259	10	corona	corona	NOUN
ejpam-4484	259	11	of	of	ADP
ejpam-4484	259	12	graphs	graph	NOUN
ejpam-4484	259	13	.	.	PUNCT
ejpam-4484	260	1	advances	advance	NOUN
ejpam-4484	260	2	and	and	CCONJ
ejpam-4484	260	3	applications	application	NOUN
ejpam-4484	260	4	in	in	ADP
ejpam-4484	260	5	discrete	discrete	ADJ
ejpam-4484	260	6	mathematics	mathematic	NOUN
ejpam-4484	260	7	,	,	PUNCT
ejpam-4484	260	8	21(1):91–101	21(1):91–101	NUM
ejpam-4484	260	9	,	,	PUNCT
ejpam-4484	260	10	2019	2019	NUM
ejpam-4484	260	11	.	.	PUNCT
ejpam-4484	261	1	[	[	X
ejpam-4484	261	2	2	2	NUM
ejpam-4484	261	3	]	]	PUNCT
ejpam-4484	261	4	sergio	sergio	PROPN
ejpam-4484	261	5	canoy	canoy	PROPN
ejpam-4484	261	6	,	,	PUNCT
ejpam-4484	261	7	jr	jr	PROPN
ejpam-4484	261	8	,	,	PUNCT
ejpam-4484	261	9	reynaldo	reynaldo	PROPN
ejpam-4484	261	10	villarobe	villarobe	PROPN
ejpam-4484	261	11	mollejon	mollejon	NOUN
ejpam-4484	261	12	,	,	PUNCT
ejpam-4484	261	13	and	and	CCONJ
ejpam-4484	261	14	john	john	PROPN
ejpam-4484	261	15	gabriel	gabriel	PROPN
ejpam-4484	261	16	e.	e.	PROPN
ejpam-4484	261	17	canoy	canoy	PROPN
ejpam-4484	261	18	.	.	PUNCT
ejpam-4484	262	1	hop	hop	PROPN
ejpam-4484	262	2	dominating	dominating	NOUN
ejpam-4484	262	3	sets	set	NOUN
ejpam-4484	262	4	in	in	ADP
ejpam-4484	262	5	graphs	graph	NOUN
ejpam-4484	262	6	under	under	ADP
ejpam-4484	262	7	binary	binary	ADJ
ejpam-4484	262	8	operations	operation	NOUN
ejpam-4484	262	9	.	.	PUNCT
ejpam-4484	263	1	european	european	ADJ
ejpam-4484	263	2	journal	journal	PROPN
ejpam-4484	263	3	of	of	ADP
ejpam-4484	263	4	pure	pure	ADJ
ejpam-4484	263	5	and	and	CCONJ
ejpam-4484	263	6	applied	applied	ADJ
ejpam-4484	263	7	mathematics	mathematic	NOUN
ejpam-4484	263	8	,	,	PUNCT
ejpam-4484	263	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4484	263	10	,	,	PUNCT
ejpam-4484	263	11	oct	oct	PROPN
ejpam-4484	263	12	.	.	PROPN
ejpam-4484	263	13	2019	2019	NUM
ejpam-4484	263	14	.	.	PUNCT
ejpam-4484	264	1	[	[	X
ejpam-4484	264	2	3	3	X
ejpam-4484	264	3	]	]	X
ejpam-4484	264	4	g.	g.	PROPN
ejpam-4484	264	5	chartrand	chartrand	PROPN
ejpam-4484	264	6	,	,	PUNCT
ejpam-4484	264	7	l.	l.	PROPN
ejpam-4484	264	8	eroh	eroh	PROPN
ejpam-4484	264	9	,	,	PUNCT
ejpam-4484	264	10	m.	m.	NOUN
ejpam-4484	264	11	johnson	johnson	PROPN
ejpam-4484	264	12	,	,	PUNCT
ejpam-4484	264	13	and	and	CCONJ
ejpam-4484	264	14	o.r	o.r	PROPN
ejpam-4484	264	15	.	.	PROPN
ejpam-4484	264	16	oellermann	oellermann	PROPN
ejpam-4484	264	17	.	.	PUNCT
ejpam-4484	265	1	resolvability	resolvability	NOUN
ejpam-4484	265	2	in	in	ADP
ejpam-4484	265	3	graphs	graph	NOUN
ejpam-4484	265	4	and	and	CCONJ
ejpam-4484	265	5	the	the	DET
ejpam-4484	265	6	metric	metric	ADJ
ejpam-4484	265	7	dimension	dimension	NOUN
ejpam-4484	265	8	of	of	ADP
ejpam-4484	265	9	a	a	DET
ejpam-4484	265	10	graph	graph	NOUN
ejpam-4484	265	11	the	the	DET
ejpam-4484	265	12	metric	metric	ADJ
ejpam-4484	265	13	dimension	dimension	NOUN
ejpam-4484	265	14	of	of	ADP
ejpam-4484	265	15	a	a	DET
ejpam-4484	265	16	graph	graph	NOUN
ejpam-4484	265	17	.	.	PUNCT
ejpam-4484	266	1	discrete	discrete	ADJ
ejpam-4484	266	2	applied	apply	VERB
ejpam-4484	266	3	mathematics	mathematic	NOUN
ejpam-4484	266	4	,	,	PUNCT
ejpam-4484	266	5	105:99–113	105:99–113	NUM
ejpam-4484	266	6	,	,	PUNCT
ejpam-4484	266	7	2000	2000	NUM
ejpam-4484	266	8	.	.	PUNCT
ejpam-4484	267	1	[	[	X
ejpam-4484	267	2	4	4	NUM
ejpam-4484	267	3	]	]	PUNCT
ejpam-4484	267	4	natarajan	natarajan	PROPN
ejpam-4484	267	5	chidambaram	chidambaram	PROPN
ejpam-4484	267	6	and	and	CCONJ
ejpam-4484	267	7	s.k	s.k	PROPN
ejpam-4484	267	8	.	.	PROPN
ejpam-4484	267	9	ayyaswamy	ayyaswamy	PROPN
ejpam-4484	267	10	.	.	PUNCT
ejpam-4484	268	1	hop	hop	PROPN
ejpam-4484	268	2	domination	domination	NOUN
ejpam-4484	268	3	in	in	ADP
ejpam-4484	268	4	graphs	graph	NOUN
ejpam-4484	268	5	-	-	PUNCT
ejpam-4484	268	6	ii	ii	NOUN
ejpam-4484	268	7	.	.	PUNCT
ejpam-4484	269	1	analele	analele	ADP
ejpam-4484	269	2	stiintifice	stiintifice	PROPN
ejpam-4484	269	3	ale	ale	PROPN
ejpam-4484	269	4	universitatii	universitatii	PROPN
ejpam-4484	269	5	ovidius	ovidius	PROPN
ejpam-4484	269	6	constanta	constanta	PROPN
ejpam-4484	269	7	,	,	PUNCT
ejpam-4484	269	8	seria	seria	PROPN
ejpam-4484	269	9	matematica	matematica	PROPN
ejpam-4484	269	10	,	,	PUNCT
ejpam-4484	269	11	23:187–199	23:187–199	PROPN
ejpam-4484	269	12	,	,	PUNCT
ejpam-4484	269	13	06	06	NUM
ejpam-4484	269	14	2015	2015	NUM
ejpam-4484	269	15	.	.	PUNCT
ejpam-4484	270	1	[	[	X
ejpam-4484	270	2	5	5	NUM
ejpam-4484	270	3	]	]	PUNCT
ejpam-4484	270	4	sumaoy	sumaoy	NOUN
ejpam-4484	270	5	h.	h.	PROPN
ejpam-4484	270	6	and	and	CCONJ
ejpam-4484	270	7	h.	h.	PROPN
ejpam-4484	270	8	rara	rara	PROPN
ejpam-4484	270	9	.	.	PUNCT
ejpam-4484	271	1	on	on	ADP
ejpam-4484	271	2	restrained	restrained	ADJ
ejpam-4484	271	3	strong	strong	ADJ
ejpam-4484	271	4	resolving	resolving	NOUN
ejpam-4484	271	5	domination	domination	NOUN
ejpam-4484	271	6	in	in	ADP
ejpam-4484	271	7	graphs	graph	NOUN
ejpam-4484	271	8	.	.	PUNCT
ejpam-4484	272	1	european	european	ADJ
ejpam-4484	272	2	journal	journal	PROPN
ejpam-4484	272	3	of	of	ADP
ejpam-4484	272	4	pure	pure	ADJ
ejpam-4484	272	5	and	and	CCONJ
ejpam-4484	272	6	applied	applied	ADJ
ejpam-4484	272	7	mathematics	mathematic	NOUN
ejpam-4484	272	8	,	,	PUNCT
ejpam-4484	272	9	14(4):1367–1378	14(4):1367–1378	NUM
ejpam-4484	272	10	,	,	PUNCT
ejpam-4484	272	11	2021	2021	NUM
ejpam-4484	272	12	.	.	PUNCT
ejpam-4484	273	1	[	[	X
ejpam-4484	273	2	6	6	NUM
ejpam-4484	273	3	]	]	PUNCT
ejpam-4484	273	4	f.	f.	PROPN
ejpam-4484	273	5	harary	harary	PROPN
ejpam-4484	273	6	and	and	CCONJ
ejpam-4484	273	7	r.a	r.a	PROPN
ejpam-4484	273	8	.	.	PROPN
ejpam-4484	273	9	melter	melter	NOUN
ejpam-4484	273	10	.	.	PUNCT
ejpam-4484	274	1	on	on	ADP
ejpam-4484	274	2	the	the	DET
ejpam-4484	274	3	metric	metric	ADJ
ejpam-4484	274	4	dimension	dimension	NOUN
ejpam-4484	274	5	of	of	ADP
ejpam-4484	274	6	a	a	DET
ejpam-4484	274	7	graph	graph	NOUN
ejpam-4484	274	8	.	.	PUNCT
ejpam-4484	274	9	ars	ars	PROPN
ejpam-4484	274	10	combinatoria	combinatoria	NOUN
ejpam-4484	274	11	,	,	PUNCT
ejpam-4484	274	12	2:191–195	2:191–195	NUM
ejpam-4484	274	13	,	,	PUNCT
ejpam-4484	274	14	1976	1976	NUM
ejpam-4484	274	15	.	.	PUNCT
ejpam-4484	275	1	[	[	X
ejpam-4484	275	2	7	7	X
ejpam-4484	275	3	]	]	X
ejpam-4484	275	4	gerald	gerald	PROPN
ejpam-4484	275	5	bacon	bacon	PROPN
ejpam-4484	275	6	monsanto	monsanto	PROPN
ejpam-4484	275	7	,	,	PUNCT
ejpam-4484	275	8	penelyn	penelyn	NOUN
ejpam-4484	275	9	l.	l.	PROPN
ejpam-4484	275	10	acal	acal	PROPN
ejpam-4484	275	11	,	,	PUNCT
ejpam-4484	275	12	and	and	CCONJ
ejpam-4484	275	13	helen	helen	PROPN
ejpam-4484	275	14	m.	m.	PROPN
ejpam-4484	275	15	rara	rara	PROPN
ejpam-4484	275	16	.	.	PUNCT
ejpam-4484	276	1	on	on	ADP
ejpam-4484	276	2	strong	strong	ADJ
ejpam-4484	276	3	resolving	resolving	NOUN
ejpam-4484	276	4	domination	domination	NOUN
ejpam-4484	276	5	in	in	ADP
ejpam-4484	276	6	the	the	DET
ejpam-4484	276	7	join	join	NOUN
ejpam-4484	276	8	and	and	CCONJ
ejpam-4484	276	9	corona	corona	NOUN
ejpam-4484	276	10	of	of	ADP
ejpam-4484	276	11	graphs	graph	NOUN
ejpam-4484	276	12	.	.	PUNCT
ejpam-4484	277	1	european	european	ADJ
ejpam-4484	277	2	journal	journal	PROPN
ejpam-4484	277	3	of	of	ADP
ejpam-4484	277	4	pure	pure	ADJ
ejpam-4484	277	5	and	and	CCONJ
ejpam-4484	277	6	applied	applied	ADJ
ejpam-4484	277	7	mathematics	mathematic	NOUN
ejpam-4484	277	8	,	,	PUNCT
ejpam-4484	277	9	13(1):170–179	13(1):170–179	NUM
ejpam-4484	277	10	,	,	PUNCT
ejpam-4484	277	11	jan	jan	PROPN
ejpam-4484	277	12	.	.	PROPN
ejpam-4484	277	13	2020	2020	NUM
ejpam-4484	277	14	.	.	PUNCT
ejpam-4484	278	1	[	[	X
ejpam-4484	278	2	8	8	NUM
ejpam-4484	278	3	]	]	X
ejpam-4484	278	4	haynes	haynes	PROPN
ejpam-4484	278	5	t.w	t.w	PROPN
ejpam-4484	278	6	.	.	PROPN
ejpam-4484	278	7	,	,	PUNCT
ejpam-4484	278	8	hedetniemi	hedetniemi	ADP
ejpam-4484	278	9	s.	s.	PROPN
ejpam-4484	278	10	,	,	PUNCT
ejpam-4484	278	11	and	and	CCONJ
ejpam-4484	278	12	p.	p.	PROPN
ejpam-4484	278	13	slater	slater	PROPN
ejpam-4484	278	14	.	.	PUNCT
ejpam-4484	279	1	(	(	PUNCT
ejpam-4484	279	2	fundamentals	fundamental	NOUN
ejpam-4484	279	3	of	of	ADP
ejpam-4484	279	4	domination	domination	NOUN
ejpam-4484	279	5	in	in	ADP
ejpam-4484	279	6	graphs	graph	NOUN
ejpam-4484	279	7	(	(	PUNCT
ejpam-4484	279	8	1st	1st	ADJ
ejpam-4484	279	9	ed	ed	NOUN
ejpam-4484	279	10	.	.	PUNCT
ejpam-4484	279	11	)	)	PUNCT
ejpam-4484	279	12	)	)	PUNCT
ejpam-4484	279	13	.	.	PUNCT
ejpam-4484	280	1	crc	crc	PROPN
ejpam-4484	280	2	press	press	PROPN
ejpam-4484	280	3	,	,	PUNCT
ejpam-4484	280	4	1998	1998	NUM
ejpam-4484	280	5	.	.	PUNCT