id	sid	tid	token	lemma	pos
ejpam-4658	1	1	european	european	PROPN
ejpam-4658	1	2	journal	journal	PROPN
ejpam-4658	1	3	of	of	ADP
ejpam-4658	1	4	pure	pure	ADJ
ejpam-4658	1	5	and	and	CCONJ
ejpam-4658	1	6	applied	apply	VERB
ejpam-4658	1	7	mathematics	mathematic	NOUN
ejpam-4658	1	8	vol	vol	NOUN
ejpam-4658	1	9	.	.	PUNCT
ejpam-4658	2	1	16	16	NUM
ejpam-4658	2	2	,	,	PUNCT
ejpam-4658	2	3	no	no	INTJ
ejpam-4658	2	4	.	.	NOUN
ejpam-4658	2	5	2	2	NUM
ejpam-4658	2	6	,	,	PUNCT
ejpam-4658	2	7	2023	2023	NUM
ejpam-4658	2	8	,	,	PUNCT
ejpam-4658	2	9	763	763	NUM
ejpam-4658	2	10	-	-	SYM
ejpam-4658	2	11	772	772	NUM
ejpam-4658	2	12	issn	issn	PROPN
ejpam-4658	2	13	1307	1307	NUM
ejpam-4658	2	14	-	-	SYM
ejpam-4658	2	15	5543	5543	NUM
ejpam-4658	2	16	–	–	PUNCT
ejpam-4658	2	17	ejpam.com	ejpam.com	X
ejpam-4658	2	18	published	publish	VERB
ejpam-4658	2	19	by	by	ADP
ejpam-4658	2	20	new	new	PROPN
ejpam-4658	2	21	york	york	PROPN
ejpam-4658	2	22	business	business	PROPN
ejpam-4658	2	23	global	global	ADJ
ejpam-4658	2	24	on	on	ADP
ejpam-4658	2	25	1	1	NUM
ejpam-4658	2	26	-	-	PUNCT
ejpam-4658	2	27	movable	movable	ADJ
ejpam-4658	2	28	strong	strong	ADJ
ejpam-4658	2	29	resolving	resolve	VERB
ejpam-4658	2	30	hop	hop	NOUN
ejpam-4658	2	31	domination	domination	NOUN
ejpam-4658	2	32	in	in	ADP
ejpam-4658	2	33	graphs	graph	NOUN
ejpam-4658	2	34	armalene	armalene	PROPN
ejpam-4658	2	35	h.	h.	PROPN
ejpam-4658	2	36	abragan1,∗	abragan1,∗	PROPN
ejpam-4658	2	37	,	,	PUNCT
ejpam-4658	2	38	helen	helen	PROPN
ejpam-4658	2	39	m.	m.	PROPN
ejpam-4658	2	40	rara2	rara2	PROPN
ejpam-4658	3	1	1	1	NUM
ejpam-4658	3	2	department	department	NOUN
ejpam-4658	3	3	of	of	ADP
ejpam-4658	3	4	mathematics	mathematic	NOUN
ejpam-4658	3	5	and	and	CCONJ
ejpam-4658	3	6	statistics	statistic	NOUN
ejpam-4658	3	7	,	,	PUNCT
ejpam-4658	3	8	college	college	NOUN
ejpam-4658	3	9	of	of	ADP
ejpam-4658	3	10	science	science	NOUN
ejpam-4658	3	11	and	and	CCONJ
ejpam-4658	3	12	mathematics	mathematic	NOUN
ejpam-4658	3	13	,	,	PUNCT
ejpam-4658	3	14	center	center	NOUN
ejpam-4658	3	15	of	of	ADP
ejpam-4658	3	16	graph	graph	NOUN
ejpam-4658	3	17	theory	theory	NOUN
ejpam-4658	3	18	,	,	PUNCT
ejpam-4658	3	19	algebra	algebra	NOUN
ejpam-4658	3	20	,	,	PUNCT
ejpam-4658	3	21	mindanao	mindanao	PROPN
ejpam-4658	3	22	state	state	PROPN
ejpam-4658	3	23	university	university	PROPN
ejpam-4658	3	24	-	-	PUNCT
ejpam-4658	3	25	iligan	iligan	PROPN
ejpam-4658	3	26	institute	institute	PROPN
ejpam-4658	3	27	of	of	ADP
ejpam-4658	3	28	technology	technology	PROPN
ejpam-4658	3	29	,	,	PUNCT
ejpam-4658	3	30	9200	9200	NUM
ejpam-4658	3	31	iligan	iligan	ADJ
ejpam-4658	3	32	city	city	NOUN
ejpam-4658	3	33	,	,	PUNCT
ejpam-4658	3	34	philippines	philippine	VERB
ejpam-4658	3	35	2	2	NUM
ejpam-4658	3	36	analysis	analysis	NOUN
ejpam-4658	3	37	-	-	PUNCT
ejpam-4658	3	38	premier	premier	NOUN
ejpam-4658	3	39	research	research	NOUN
ejpam-4658	3	40	institute	institute	PROPN
ejpam-4658	3	41	of	of	ADP
ejpam-4658	3	42	science	science	NOUN
ejpam-4658	3	43	and	and	CCONJ
ejpam-4658	3	44	mathematics	mathematic	NOUN
ejpam-4658	3	45	,	,	PUNCT
ejpam-4658	3	46	mindanao	mindanao	PROPN
ejpam-4658	3	47	state	state	PROPN
ejpam-4658	3	48	university	university	PROPN
ejpam-4658	3	49	-	-	PUNCT
ejpam-4658	3	50	iligan	iligan	PROPN
ejpam-4658	3	51	institute	institute	PROPN
ejpam-4658	3	52	of	of	ADP
ejpam-4658	3	53	technology	technology	PROPN
ejpam-4658	3	54	,	,	PUNCT
ejpam-4658	3	55	9200	9200	NUM
ejpam-4658	3	56	iligan	iligan	ADJ
ejpam-4658	3	57	city	city	NOUN
ejpam-4658	3	58	,	,	PUNCT
ejpam-4658	3	59	philippines	philippine	NOUN
ejpam-4658	3	60	abstract	abstract	ADJ
ejpam-4658	3	61	.	.	PUNCT
ejpam-4658	4	1	a	a	DET
ejpam-4658	4	2	set	set	NOUN
ejpam-4658	4	3	s	s	PART
ejpam-4658	4	4	is	be	AUX
ejpam-4658	4	5	a	a	DET
ejpam-4658	4	6	1	1	NUM
ejpam-4658	4	7	-	-	PUNCT
ejpam-4658	4	8	movable	movable	ADJ
ejpam-4658	4	9	strong	strong	ADJ
ejpam-4658	4	10	resolving	resolve	VERB
ejpam-4658	4	11	hop	hop	NOUN
ejpam-4658	4	12	dominating	dominating	NOUN
ejpam-4658	4	13	set	set	NOUN
ejpam-4658	4	14	of	of	ADP
ejpam-4658	4	15	g	g	PROPN
ejpam-4658	4	16	if	if	SCONJ
ejpam-4658	4	17	for	for	SCONJ
ejpam-4658	4	18	every	every	DET
ejpam-4658	4	19	v	v	NUM
ejpam-4658	4	20	∈	∈	PROPN
ejpam-4658	4	21	s	s	NOUN
ejpam-4658	4	22	,	,	PUNCT
ejpam-4658	4	23	either	either	CCONJ
ejpam-4658	4	24	s\{v	s\{v	VERB
ejpam-4658	4	25	}	}	PUNCT
ejpam-4658	4	26	is	be	AUX
ejpam-4658	4	27	a	a	DET
ejpam-4658	4	28	strong	strong	ADJ
ejpam-4658	4	29	resolving	resolve	VERB
ejpam-4658	4	30	hop	hop	NOUN
ejpam-4658	4	31	dominating	dominating	NOUN
ejpam-4658	4	32	set	set	NOUN
ejpam-4658	4	33	or	or	CCONJ
ejpam-4658	4	34	there	there	PRON
ejpam-4658	4	35	exists	exist	VERB
ejpam-4658	4	36	a	a	DET
ejpam-4658	4	37	vertex	vertex	NOUN
ejpam-4658	4	38	u	u	NOUN
ejpam-4658	4	39	∈	∈	PROPN
ejpam-4658	4	40	(	(	PUNCT
ejpam-4658	4	41	v	v	NOUN
ejpam-4658	4	42	(	(	PUNCT
ejpam-4658	4	43	g)\s)∩ng(v	g)\s)∩ng(v	NOUN
ejpam-4658	4	44	)	)	PUNCT
ejpam-4658	4	45	such	such	ADJ
ejpam-4658	4	46	that	that	SCONJ
ejpam-4658	4	47	(	(	PUNCT
ejpam-4658	4	48	s	s	NOUN
ejpam-4658	4	49	\	\	X
ejpam-4658	4	50	{	{	PUNCT
ejpam-4658	4	51	v})∩	v})∩	PROPN
ejpam-4658	4	52	{	{	PUNCT
ejpam-4658	4	53	u	u	NOUN
ejpam-4658	4	54	}	}	PUNCT
ejpam-4658	4	55	is	be	AUX
ejpam-4658	4	56	a	a	DET
ejpam-4658	4	57	strong	strong	ADJ
ejpam-4658	4	58	resolving	resolve	VERB
ejpam-4658	4	59	hop	hop	NOUN
ejpam-4658	4	60	dominating	dominating	NOUN
ejpam-4658	4	61	set	set	NOUN
ejpam-4658	4	62	of	of	ADP
ejpam-4658	4	63	g.	g.	PROPN
ejpam-4658	4	64	the	the	DET
ejpam-4658	4	65	minimum	minimum	ADJ
ejpam-4658	4	66	cardinality	cardinality	NOUN
ejpam-4658	4	67	of	of	ADP
ejpam-4658	4	68	a	a	DET
ejpam-4658	4	69	1	1	NUM
ejpam-4658	4	70	-	-	PUNCT
ejpam-4658	4	71	movable	movable	ADJ
ejpam-4658	4	72	strong	strong	ADJ
ejpam-4658	4	73	resolving	resolve	VERB
ejpam-4658	4	74	hop	hop	NOUN
ejpam-4658	4	75	dominating	dominating	NOUN
ejpam-4658	4	76	set	set	NOUN
ejpam-4658	4	77	of	of	ADP
ejpam-4658	4	78	g	g	PROPN
ejpam-4658	4	79	is	be	AUX
ejpam-4658	4	80	denoted	denote	VERB
ejpam-4658	4	81	by	by	ADP
ejpam-4658	4	82	γ1	γ1	PROPN
ejpam-4658	4	83	msrh(g	msrh(g	NOUN
ejpam-4658	4	84	)	)	PUNCT
ejpam-4658	4	85	.	.	PUNCT
ejpam-4658	5	1	in	in	ADP
ejpam-4658	5	2	this	this	DET
ejpam-4658	5	3	paper	paper	NOUN
ejpam-4658	5	4	,	,	PUNCT
ejpam-4658	5	5	we	we	PRON
ejpam-4658	5	6	obtained	obtain	VERB
ejpam-4658	5	7	the	the	DET
ejpam-4658	5	8	corresponding	corresponding	ADJ
ejpam-4658	5	9	parameter	parameter	NOUN
ejpam-4658	5	10	in	in	ADP
ejpam-4658	5	11	graphs	graph	NOUN
ejpam-4658	5	12	resulting	result	VERB
ejpam-4658	5	13	from	from	ADP
ejpam-4658	5	14	the	the	DET
ejpam-4658	5	15	join	join	NOUN
ejpam-4658	5	16	,	,	PUNCT
ejpam-4658	5	17	corona	corona	NOUN
ejpam-4658	5	18	and	and	CCONJ
ejpam-4658	5	19	lexicographic	lexicographic	ADJ
ejpam-4658	5	20	product	product	NOUN
ejpam-4658	5	21	of	of	ADP
ejpam-4658	5	22	two	two	NUM
ejpam-4658	5	23	graphs	graph	NOUN
ejpam-4658	5	24	.	.	PUNCT
ejpam-4658	6	1	specifically	specifically	ADV
ejpam-4658	6	2	,	,	PUNCT
ejpam-4658	6	3	we	we	PRON
ejpam-4658	6	4	characterize	characterize	VERB
ejpam-4658	6	5	the	the	DET
ejpam-4658	6	6	1	1	NUM
ejpam-4658	6	7	-	-	PUNCT
ejpam-4658	6	8	movable	movable	ADJ
ejpam-4658	6	9	strong	strong	ADJ
ejpam-4658	6	10	resolving	resolve	VERB
ejpam-4658	6	11	hop	hop	NOUN
ejpam-4658	6	12	dominating	dominating	NOUN
ejpam-4658	6	13	sets	set	NOUN
ejpam-4658	6	14	in	in	ADP
ejpam-4658	6	15	these	these	DET
ejpam-4658	6	16	types	type	NOUN
ejpam-4658	6	17	of	of	ADP
ejpam-4658	6	18	graphs	graph	NOUN
ejpam-4658	6	19	and	and	CCONJ
ejpam-4658	6	20	determine	determine	VERB
ejpam-4658	6	21	the	the	DET
ejpam-4658	6	22	bounds	bound	NOUN
ejpam-4658	6	23	or	or	CCONJ
ejpam-4658	6	24	exact	exact	ADJ
ejpam-4658	6	25	values	value	NOUN
ejpam-4658	6	26	of	of	ADP
ejpam-4658	6	27	their	their	PRON
ejpam-4658	6	28	1	1	NUM
ejpam-4658	6	29	-	-	PUNCT
ejpam-4658	6	30	movable	movable	ADJ
ejpam-4658	6	31	strong	strong	ADJ
ejpam-4658	6	32	resolving	resolve	VERB
ejpam-4658	6	33	hop	hop	NOUN
ejpam-4658	6	34	domination	domination	NOUN
ejpam-4658	6	35	numbers	number	NOUN
ejpam-4658	6	36	.	.	PUNCT
ejpam-4658	7	1	2020	2020	NUM
ejpam-4658	7	2	mathematics	mathematic	NOUN
ejpam-4658	7	3	subject	subject	NOUN
ejpam-4658	7	4	classifications	classification	NOUN
ejpam-4658	7	5	:	:	PUNCT
ejpam-4658	7	6	05c69	05c69	X
ejpam-4658	7	7	key	key	ADJ
ejpam-4658	7	8	words	word	NOUN
ejpam-4658	7	9	and	and	CCONJ
ejpam-4658	7	10	phrases	phrase	NOUN
ejpam-4658	7	11	:	:	PUNCT
ejpam-4658	7	12	1	1	NUM
ejpam-4658	7	13	-	-	PUNCT
ejpam-4658	7	14	movable	movable	ADJ
ejpam-4658	7	15	strong	strong	ADJ
ejpam-4658	7	16	resolving	resolve	VERB
ejpam-4658	7	17	hop	hop	NOUN
ejpam-4658	7	18	dominating	dominating	NOUN
ejpam-4658	7	19	set	set	NOUN
ejpam-4658	7	20	,	,	PUNCT
ejpam-4658	7	21	1	1	NUM
ejpam-4658	7	22	-	-	PUNCT
ejpam-4658	7	23	movable	movable	ADJ
ejpam-4658	7	24	strong	strong	ADJ
ejpam-4658	7	25	resolving	resolve	VERB
ejpam-4658	7	26	hop	hop	NOUN
ejpam-4658	7	27	domination	domination	NOUN
ejpam-4658	7	28	number	number	NOUN
ejpam-4658	7	29	,	,	PUNCT
ejpam-4658	7	30	join	join	NOUN
ejpam-4658	7	31	,	,	PUNCT
ejpam-4658	7	32	corona	corona	PROPN
ejpam-4658	7	33	,	,	PUNCT
ejpam-4658	7	34	lexicographic	lexicographic	ADJ
ejpam-4658	7	35	product	product	NOUN
ejpam-4658	7	36	1	1	NUM
ejpam-4658	7	37	.	.	PUNCT
ejpam-4658	7	38	introduction	introduction	NOUN
ejpam-4658	7	39	the	the	DET
ejpam-4658	7	40	study	study	NOUN
ejpam-4658	7	41	of	of	ADP
ejpam-4658	7	42	domination	domination	NOUN
ejpam-4658	7	43	can	can	AUX
ejpam-4658	7	44	be	be	AUX
ejpam-4658	7	45	traced	trace	VERB
ejpam-4658	7	46	way	way	NOUN
ejpam-4658	7	47	back	back	ADV
ejpam-4658	7	48	1960	1960	NUM
ejpam-4658	7	49	.	.	PUNCT
ejpam-4658	8	1	since	since	SCONJ
ejpam-4658	8	2	then	then	ADV
ejpam-4658	8	3	numerous	numerous	ADJ
ejpam-4658	8	4	authors	author	NOUN
ejpam-4658	8	5	contribute	contribute	VERB
ejpam-4658	8	6	several	several	ADJ
ejpam-4658	8	7	interesting	interesting	ADJ
ejpam-4658	8	8	domination	domination	NOUN
ejpam-4658	8	9	parameters	parameter	NOUN
ejpam-4658	8	10	to	to	PART
ejpam-4658	8	11	nurture	nurture	VERB
ejpam-4658	8	12	the	the	DET
ejpam-4658	8	13	growth	growth	NOUN
ejpam-4658	8	14	of	of	ADP
ejpam-4658	8	15	this	this	DET
ejpam-4658	8	16	research	research	NOUN
ejpam-4658	8	17	area	area	NOUN
ejpam-4658	8	18	.	.	PUNCT
ejpam-4658	9	1	in	in	ADP
ejpam-4658	9	2	1977	1977	NUM
ejpam-4658	9	3	,	,	PUNCT
ejpam-4658	9	4	e.j	e.j	NOUN
ejpam-4658	9	5	cockayne	cockayne	NOUN
ejpam-4658	9	6	and	and	CCONJ
ejpam-4658	9	7	s.t	s.t	PROPN
ejpam-4658	9	8	hedetniemi	hedetniemi	ADV
ejpam-4658	9	9	introduced	introduce	VERB
ejpam-4658	9	10	the	the	DET
ejpam-4658	9	11	notation	notation	PROPN
ejpam-4658	9	12	γ(g	γ(g	PROPN
ejpam-4658	9	13	)	)	PUNCT
ejpam-4658	9	14	for	for	ADP
ejpam-4658	9	15	the	the	DET
ejpam-4658	9	16	domination	domination	NOUN
ejpam-4658	9	17	number	number	NOUN
ejpam-4658	9	18	of	of	ADP
ejpam-4658	9	19	graph	graph	NOUN
ejpam-4658	9	20	g.	g.	PROPN
ejpam-4658	9	21	until	until	ADP
ejpam-4658	9	22	the	the	DET
ejpam-4658	9	23	initiation	initiation	NOUN
ejpam-4658	9	24	of	of	ADP
ejpam-4658	9	25	the	the	DET
ejpam-4658	9	26	concept	concept	NOUN
ejpam-4658	9	27	of	of	ADP
ejpam-4658	9	28	2	2	NUM
ejpam-4658	9	29	-	-	PUNCT
ejpam-4658	9	30	step	step	NOUN
ejpam-4658	9	31	domination	domination	NOUN
ejpam-4658	9	32	number	number	NOUN
ejpam-4658	9	33	by	by	ADP
ejpam-4658	9	34	chartrand	chartrand	PROPN
ejpam-4658	9	35	et	et	PROPN
ejpam-4658	9	36	al	al	PROPN
ejpam-4658	9	37	.	.	PUNCT
ejpam-4658	10	1	[	[	X
ejpam-4658	10	2	1	1	X
ejpam-4658	10	3	]	]	PUNCT
ejpam-4658	10	4	in	in	ADP
ejpam-4658	10	5	1995	1995	NUM
ejpam-4658	10	6	,	,	PUNCT
ejpam-4658	10	7	which	which	PRON
ejpam-4658	10	8	is	be	AUX
ejpam-4658	10	9	closely	closely	ADV
ejpam-4658	10	10	related	relate	VERB
ejpam-4658	10	11	to	to	ADP
ejpam-4658	10	12	hop	hop	NOUN
ejpam-4658	10	13	domination	domination	NOUN
ejpam-4658	10	14	number	number	NOUN
ejpam-4658	10	15	.	.	PUNCT
ejpam-4658	11	1	subsequently	subsequently	ADV
ejpam-4658	11	2	,	,	PUNCT
ejpam-4658	11	3	natarajan	natarajan	PROPN
ejpam-4658	11	4	and	and	CCONJ
ejpam-4658	11	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4658	11	6	(	(	PUNCT
ejpam-4658	11	7	2015	2015	NUM
ejpam-4658	11	8	)	)	PUNCT
ejpam-4658	11	9	introduced	introduce	VERB
ejpam-4658	11	10	the	the	DET
ejpam-4658	11	11	hop	hop	NOUN
ejpam-4658	11	12	domination	domination	NOUN
ejpam-4658	11	13	concept	concept	NOUN
ejpam-4658	11	14	.	.	PUNCT
ejpam-4658	12	1	some	some	DET
ejpam-4658	12	2	variation	variation	NOUN
ejpam-4658	12	3	of	of	ADP
ejpam-4658	12	4	domination	domination	NOUN
ejpam-4658	12	5	can	can	AUX
ejpam-4658	12	6	be	be	AUX
ejpam-4658	12	7	seen	see	VERB
ejpam-4658	12	8	in	in	ADP
ejpam-4658	12	9	these	these	DET
ejpam-4658	12	10	papers	paper	NOUN
ejpam-4658	12	11	[	[	X
ejpam-4658	12	12	7	7	NUM
ejpam-4658	12	13	]	]	PUNCT
ejpam-4658	12	14	,	,	PUNCT
ejpam-4658	13	1	[	[	X
ejpam-4658	13	2	6	6	NUM
ejpam-4658	13	3	]	]	PUNCT
ejpam-4658	13	4	.	.	PUNCT
ejpam-4658	14	1	blair	blair	PROPN
ejpam-4658	14	2	et	et	PROPN
ejpam-4658	14	3	al	al	PROPN
ejpam-4658	14	4	.	.	PUNCT
ejpam-4658	15	1	[	[	X
ejpam-4658	15	2	3	3	NUM
ejpam-4658	15	3	]	]	PUNCT
ejpam-4658	15	4	introduced	introduce	VERB
ejpam-4658	15	5	and	and	CCONJ
ejpam-4658	15	6	investigated	investigate	VERB
ejpam-4658	15	7	a	a	DET
ejpam-4658	15	8	new	new	ADJ
ejpam-4658	15	9	variant	variant	NOUN
ejpam-4658	15	10	of	of	ADP
ejpam-4658	15	11	the	the	DET
ejpam-4658	15	12	standard	standard	ADJ
ejpam-4658	15	13	domination	domination	NOUN
ejpam-4658	15	14	parameter	parameter	NOUN
ejpam-4658	15	15	called	call	VERB
ejpam-4658	15	16	1	1	NUM
ejpam-4658	15	17	-	-	PUNCT
ejpam-4658	15	18	movable	movable	ADJ
ejpam-4658	15	19	domination	domination	NOUN
ejpam-4658	15	20	.	.	PUNCT
ejpam-4658	16	1	in	in	ADP
ejpam-4658	16	2	2011	2011	NUM
ejpam-4658	16	3	,	,	PUNCT
ejpam-4658	16	4	they	they	PRON
ejpam-4658	16	5	established	establish	VERB
ejpam-4658	16	6	results	result	NOUN
ejpam-4658	16	7	on	on	ADP
ejpam-4658	16	8	the	the	DET
ejpam-4658	16	9	1	1	NUM
ejpam-4658	16	10	-	-	PUNCT
ejpam-4658	16	11	movable	movable	ADJ
ejpam-4658	16	12	∗corresponding	∗corresponding	NOUN
ejpam-4658	16	13	author	author	NOUN
ejpam-4658	16	14	.	.	PUNCT
ejpam-4658	17	1	doi	doi	NOUN
ejpam-4658	17	2	:	:	PUNCT
ejpam-4658	17	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4658	https://doi.org/10.29020/nybg.ejpam.v16i2.4658	ADP
ejpam-4658	17	4	email	email	NOUN
ejpam-4658	17	5	addresses	address	NOUN
ejpam-4658	17	6	:	:	PUNCT
ejpam-4658	17	7	armalene.abragan@g.msuiit.edu.ph	armalene.abragan@g.msuiit.edu.ph	PROPN
ejpam-4658	17	8	(	(	PUNCT
ejpam-4658	17	9	a.	a.	NOUN
ejpam-4658	17	10	abragan	abragan	PROPN
ejpam-4658	17	11	)	)	PUNCT
ejpam-4658	17	12	,	,	PUNCT
ejpam-4658	17	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4658	17	14	(	(	PUNCT
ejpam-4658	17	15	h.	h.	PROPN
ejpam-4658	17	16	m.	m.	PROPN
ejpam-4658	17	17	rara	rara	PROPN
ejpam-4658	17	18	)	)	PUNCT
ejpam-4658	17	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4658	18	1	763	763	NUM
ejpam-4658	19	1	©	©	ADP
ejpam-4658	19	2	2023	2023	NUM
ejpam-4658	19	3	ejpam	ejpam	NOUN
ejpam-4658	19	4	all	all	DET
ejpam-4658	19	5	rights	right	NOUN
ejpam-4658	19	6	reserved	reserve	VERB
ejpam-4658	19	7	.	.	PUNCT
ejpam-4658	20	1	a.	a.	PROPN
ejpam-4658	20	2	h.	h.	PROPN
ejpam-4658	20	3	abragan	abragan	PROPN
ejpam-4658	20	4	,	,	PUNCT
ejpam-4658	20	5	h.	h.	PROPN
ejpam-4658	20	6	m.	m.	PROPN
ejpam-4658	20	7	rara	rara	PROPN
ejpam-4658	20	8	/	/	SYM
ejpam-4658	20	9	eur	eur	PROPN
ejpam-4658	20	10	.	.	PUNCT
ejpam-4658	21	1	j.	j.	PROPN
ejpam-4658	21	2	pure	pure	PROPN
ejpam-4658	21	3	appl	appl	PROPN
ejpam-4658	21	4	.	.	PROPN
ejpam-4658	21	5	math	math	PROPN
ejpam-4658	21	6	,	,	PUNCT
ejpam-4658	21	7	16	16	NUM
ejpam-4658	21	8	(	(	PUNCT
ejpam-4658	21	9	2	2	NUM
ejpam-4658	21	10	)	)	PUNCT
ejpam-4658	21	11	(	(	PUNCT
ejpam-4658	21	12	2023	2023	NUM
ejpam-4658	21	13	)	)	PUNCT
ejpam-4658	21	14	,	,	PUNCT
ejpam-4658	21	15	763	763	NUM
ejpam-4658	21	16	-	-	SYM
ejpam-4658	21	17	772	772	NUM
ejpam-4658	21	18	764	764	NUM
ejpam-4658	21	19	dominating	dominating	NOUN
ejpam-4658	21	20	sets	set	NOUN
ejpam-4658	21	21	of	of	ADP
ejpam-4658	21	22	some	some	DET
ejpam-4658	21	23	graphs	graph	NOUN
ejpam-4658	21	24	and	and	CCONJ
ejpam-4658	21	25	identified	identify	VERB
ejpam-4658	21	26	bounds	bound	NOUN
ejpam-4658	21	27	on	on	ADP
ejpam-4658	21	28	the	the	DET
ejpam-4658	21	29	1	1	NUM
ejpam-4658	21	30	-	-	PUNCT
ejpam-4658	21	31	movable	movable	ADJ
ejpam-4658	21	32	domination	domination	NOUN
ejpam-4658	21	33	number	number	NOUN
ejpam-4658	21	34	for	for	ADP
ejpam-4658	21	35	certain	certain	ADJ
ejpam-4658	21	36	classes	class	NOUN
ejpam-4658	21	37	of	of	ADP
ejpam-4658	21	38	graphs	graph	NOUN
ejpam-4658	21	39	.	.	PUNCT
ejpam-4658	22	1	the	the	DET
ejpam-4658	22	2	concept	concept	NOUN
ejpam-4658	22	3	of	of	ADP
ejpam-4658	22	4	1	1	NUM
ejpam-4658	22	5	-	-	PUNCT
ejpam-4658	22	6	movable	movable	ADJ
ejpam-4658	22	7	dominating	dominating	NOUN
ejpam-4658	22	8	set	set	NOUN
ejpam-4658	22	9	was	be	AUX
ejpam-4658	22	10	discussed	discuss	VERB
ejpam-4658	22	11	in	in	ADP
ejpam-4658	22	12	the	the	DET
ejpam-4658	22	13	paper	paper	NOUN
ejpam-4658	22	14	of	of	ADP
ejpam-4658	22	15	hinampas	hinampas	NOUN
ejpam-4658	22	16	and	and	CCONJ
ejpam-4658	22	17	canoy	canoy	ADJ
ejpam-4658	22	18	[	[	X
ejpam-4658	22	19	4	4	NUM
ejpam-4658	22	20	]	]	PUNCT
ejpam-4658	22	21	.	.	PUNCT
ejpam-4658	23	1	their	their	PRON
ejpam-4658	23	2	paper	paper	NOUN
ejpam-4658	23	3	also	also	ADV
ejpam-4658	23	4	presented	present	VERB
ejpam-4658	23	5	some	some	DET
ejpam-4658	23	6	characterizations	characterization	NOUN
ejpam-4658	23	7	involving	involve	VERB
ejpam-4658	23	8	the	the	DET
ejpam-4658	23	9	concept	concept	NOUN
ejpam-4658	23	10	and	and	CCONJ
ejpam-4658	23	11	investigated	investigate	VERB
ejpam-4658	23	12	the	the	DET
ejpam-4658	23	13	1	1	NUM
ejpam-4658	23	14	-	-	PUNCT
ejpam-4658	23	15	movable	movable	ADJ
ejpam-4658	23	16	dominating	dominating	NOUN
ejpam-4658	23	17	sets	set	NOUN
ejpam-4658	23	18	in	in	ADP
ejpam-4658	23	19	the	the	DET
ejpam-4658	23	20	join	join	NOUN
ejpam-4658	23	21	and	and	CCONJ
ejpam-4658	23	22	corona	corona	NOUN
ejpam-4658	23	23	of	of	ADP
ejpam-4658	23	24	graphs	graph	NOUN
ejpam-4658	23	25	.	.	PUNCT
ejpam-4658	24	1	inspired	inspire	VERB
ejpam-4658	24	2	by	by	ADP
ejpam-4658	24	3	the	the	DET
ejpam-4658	24	4	above	above	ADJ
ejpam-4658	24	5	works	work	NOUN
ejpam-4658	24	6	,	,	PUNCT
ejpam-4658	24	7	this	this	DET
ejpam-4658	24	8	present	present	ADJ
ejpam-4658	24	9	study	study	NOUN
ejpam-4658	24	10	investigates	investigate	VERB
ejpam-4658	24	11	the	the	DET
ejpam-4658	24	12	concepts	concept	NOUN
ejpam-4658	24	13	of	of	ADP
ejpam-4658	24	14	restrained	restrained	ADJ
ejpam-4658	24	15	strong	strong	ADJ
ejpam-4658	24	16	resolving	resolve	VERB
ejpam-4658	24	17	hop	hop	NOUN
ejpam-4658	24	18	dominating	dominating	NOUN
ejpam-4658	24	19	and	and	CCONJ
ejpam-4658	24	20	1movable	1movable	NUM
ejpam-4658	24	21	strong	strong	ADJ
ejpam-4658	24	22	resolving	resolve	VERB
ejpam-4658	24	23	hop	hop	NOUN
ejpam-4658	24	24	dominating	dominating	NOUN
ejpam-4658	24	25	sets	set	NOUN
ejpam-4658	24	26	of	of	ADP
ejpam-4658	24	27	some	some	DET
ejpam-4658	24	28	graphs	graph	NOUN
ejpam-4658	24	29	.	.	PUNCT
ejpam-4658	25	1	in	in	ADP
ejpam-4658	25	2	this	this	DET
ejpam-4658	25	3	study	study	NOUN
ejpam-4658	25	4	,	,	PUNCT
ejpam-4658	25	5	we	we	PRON
ejpam-4658	25	6	only	only	ADV
ejpam-4658	25	7	consider	consider	VERB
ejpam-4658	25	8	graphs	graph	NOUN
ejpam-4658	25	9	that	that	PRON
ejpam-4658	25	10	are	be	AUX
ejpam-4658	25	11	finite	finite	ADJ
ejpam-4658	25	12	,	,	PUNCT
ejpam-4658	25	13	simple	simple	ADJ
ejpam-4658	25	14	,	,	PUNCT
ejpam-4658	25	15	undirected	undirected	ADJ
ejpam-4658	25	16	and	and	CCONJ
ejpam-4658	25	17	connected	connected	ADJ
ejpam-4658	25	18	.	.	PUNCT
ejpam-4658	26	1	readers	reader	NOUN
ejpam-4658	26	2	are	be	AUX
ejpam-4658	26	3	referred	refer	VERB
ejpam-4658	26	4	to	to	ADP
ejpam-4658	26	5	[	[	X
ejpam-4658	26	6	2	2	NUM
ejpam-4658	26	7	]	]	PUNCT
ejpam-4658	26	8	for	for	ADP
ejpam-4658	26	9	elementary	elementary	ADJ
ejpam-4658	26	10	graph	graph	NOUN
ejpam-4658	26	11	theory	theory	NOUN
ejpam-4658	26	12	concepts	concept	NOUN
ejpam-4658	26	13	.	.	PUNCT
ejpam-4658	27	1	let	let	VERB
ejpam-4658	27	2	g	g	PRON
ejpam-4658	27	3	be	be	AUX
ejpam-4658	27	4	a	a	DET
ejpam-4658	27	5	connected	connected	ADJ
ejpam-4658	27	6	graph	graph	NOUN
ejpam-4658	27	7	.	.	PUNCT
ejpam-4658	28	1	a	a	DET
ejpam-4658	28	2	set	set	NOUN
ejpam-4658	28	3	s	s	NOUN
ejpam-4658	28	4	⊆	⊆	NUM
ejpam-4658	28	5	v	v	NOUN
ejpam-4658	28	6	(	(	PUNCT
ejpam-4658	28	7	g	g	NOUN
ejpam-4658	28	8	)	)	PUNCT
ejpam-4658	28	9	is	be	AUX
ejpam-4658	28	10	a	a	DET
ejpam-4658	28	11	hop	hop	NOUN
ejpam-4658	28	12	dominating	dominating	NOUN
ejpam-4658	28	13	set	set	NOUN
ejpam-4658	28	14	of	of	ADP
ejpam-4658	28	15	g	g	PROPN
ejpam-4658	28	16	if	if	SCONJ
ejpam-4658	28	17	for	for	ADP
ejpam-4658	28	18	every	every	DET
ejpam-4658	28	19	v	v	NUM
ejpam-4658	28	20	∈	∈	NOUN
ejpam-4658	28	21	v	v	NOUN
ejpam-4658	28	22	(	(	PUNCT
ejpam-4658	28	23	g)\s	g)\s	NOUN
ejpam-4658	28	24	,	,	PUNCT
ejpam-4658	28	25	there	there	PRON
ejpam-4658	28	26	exists	exist	VERB
ejpam-4658	28	27	u	u	PROPN
ejpam-4658	28	28	∈	∈	PROPN
ejpam-4658	28	29	s	s	VERB
ejpam-4658	28	30	such	such	ADJ
ejpam-4658	28	31	that	that	DET
ejpam-4658	28	32	dg(u	dg(u	ADJ
ejpam-4658	28	33	,	,	PUNCT
ejpam-4658	28	34	v	v	NOUN
ejpam-4658	28	35	)	)	PUNCT
ejpam-4658	29	1	=	=	SYM
ejpam-4658	29	2	2	2	X
ejpam-4658	29	3	.	.	PUNCT
ejpam-4658	30	1	the	the	DET
ejpam-4658	30	2	minimum	minimum	ADJ
ejpam-4658	30	3	cardinality	cardinality	NOUN
ejpam-4658	30	4	of	of	ADP
ejpam-4658	30	5	a	a	DET
ejpam-4658	30	6	hop	hop	NOUN
ejpam-4658	30	7	dominating	dominating	NOUN
ejpam-4658	30	8	set	set	NOUN
ejpam-4658	30	9	of	of	ADP
ejpam-4658	30	10	g	g	NOUN
ejpam-4658	30	11	,	,	PUNCT
ejpam-4658	30	12	denoted	denote	VERB
ejpam-4658	30	13	by	by	ADP
ejpam-4658	30	14	γh(g	γh(g	NOUN
ejpam-4658	30	15	)	)	PUNCT
ejpam-4658	30	16	,	,	PUNCT
ejpam-4658	30	17	is	be	AUX
ejpam-4658	30	18	called	call	VERB
ejpam-4658	30	19	the	the	DET
ejpam-4658	30	20	hop	hop	NOUN
ejpam-4658	30	21	domination	domination	NOUN
ejpam-4658	30	22	number	number	NOUN
ejpam-4658	30	23	of	of	ADP
ejpam-4658	30	24	g.	g.	PROPN
ejpam-4658	30	25	any	any	DET
ejpam-4658	30	26	hop	hop	NOUN
ejpam-4658	30	27	dominating	dominating	NOUN
ejpam-4658	30	28	set	set	VERB
ejpam-4658	30	29	with	with	ADP
ejpam-4658	30	30	cardinality	cardinality	NOUN
ejpam-4658	30	31	equal	equal	ADJ
ejpam-4658	30	32	to	to	ADP
ejpam-4658	30	33	γh(g	γh(g	NOUN
ejpam-4658	30	34	)	)	PUNCT
ejpam-4658	30	35	is	be	AUX
ejpam-4658	30	36	called	call	VERB
ejpam-4658	30	37	a	a	DET
ejpam-4658	30	38	γh	γh	ADV
ejpam-4658	30	39	-	-	PUNCT
ejpam-4658	30	40	set	set	NOUN
ejpam-4658	30	41	.	.	PUNCT
ejpam-4658	31	1	a	a	DET
ejpam-4658	31	2	set	set	NOUN
ejpam-4658	31	3	c	c	NOUN
ejpam-4658	31	4	⊆	⊆	NUM
ejpam-4658	31	5	v	v	NOUN
ejpam-4658	31	6	(	(	PUNCT
ejpam-4658	31	7	g	g	NOUN
ejpam-4658	31	8	)	)	PUNCT
ejpam-4658	31	9	is	be	AUX
ejpam-4658	31	10	called	call	VERB
ejpam-4658	31	11	a	a	DET
ejpam-4658	31	12	superclique	superclique	NOUN
ejpam-4658	31	13	in	in	ADP
ejpam-4658	31	14	g	g	PROPN
ejpam-4658	31	15	if	if	SCONJ
ejpam-4658	31	16	⟨c⟩	⟨c⟩	PROPN
ejpam-4658	31	17	is	be	AUX
ejpam-4658	31	18	a	a	DET
ejpam-4658	31	19	clique	clique	NOUN
ejpam-4658	31	20	and	and	CCONJ
ejpam-4658	31	21	for	for	ADP
ejpam-4658	31	22	every	every	DET
ejpam-4658	31	23	pair	pair	NOUN
ejpam-4658	31	24	of	of	ADP
ejpam-4658	31	25	distinct	distinct	ADJ
ejpam-4658	31	26	vertices	vertex	NOUN
ejpam-4658	31	27	u	u	NOUN
ejpam-4658	31	28	,	,	PUNCT
ejpam-4658	31	29	v	v	NOUN
ejpam-4658	31	30	∈	∈	ADJ
ejpam-4658	31	31	c	c	NOUN
ejpam-4658	31	32	,	,	PUNCT
ejpam-4658	31	33	there	there	PRON
ejpam-4658	31	34	exists	exist	VERB
ejpam-4658	31	35	w	w	PROPN
ejpam-4658	31	36	∈	∈	PROPN
ejpam-4658	31	37	v	v	ADP
ejpam-4658	31	38	(	(	PUNCT
ejpam-4658	31	39	g	g	NOUN
ejpam-4658	31	40	)	)	PUNCT
ejpam-4658	31	41	\	\	PUNCT
ejpam-4658	32	1	c	c	NOUN
ejpam-4658	32	2	such	such	ADJ
ejpam-4658	32	3	that	that	PRON
ejpam-4658	32	4	w	w	PROPN
ejpam-4658	32	5	∈	∈	PROPN
ejpam-4658	32	6	ng(u	ng(u	NOUN
ejpam-4658	32	7	)	)	PUNCT
ejpam-4658	32	8	\	\	NOUN
ejpam-4658	32	9	ng(v	ng(v	PUNCT
ejpam-4658	32	10	)	)	PUNCT
ejpam-4658	32	11	or	or	CCONJ
ejpam-4658	32	12	w	w	PROPN
ejpam-4658	32	13	∈	∈	PROPN
ejpam-4658	32	14	ng(v)\ng(u	ng(v)\ng(u	ADJ
ejpam-4658	32	15	)	)	PUNCT
ejpam-4658	32	16	.	.	PUNCT
ejpam-4658	33	1	a	a	DET
ejpam-4658	33	2	superclique	superclique	NOUN
ejpam-4658	33	3	c	c	NOUN
ejpam-4658	33	4	is	be	AUX
ejpam-4658	33	5	maximum	maximum	ADJ
ejpam-4658	33	6	in	in	ADP
ejpam-4658	33	7	g	g	PROPN
ejpam-4658	33	8	if	if	SCONJ
ejpam-4658	33	9	|c|	|c|	PROPN
ejpam-4658	33	10	≥	≥	NOUN
ejpam-4658	33	11	|c∗|	|c∗|	VERB
ejpam-4658	33	12	for	for	SCONJ
ejpam-4658	33	13	all	all	DET
ejpam-4658	33	14	supercliques	superclique	NOUN
ejpam-4658	33	15	c∗	c∗	PROPN
ejpam-4658	33	16	in	in	ADP
ejpam-4658	33	17	g.	g.	PROPN
ejpam-4658	33	18	the	the	DET
ejpam-4658	33	19	superclique	superclique	ADJ
ejpam-4658	33	20	number	number	NOUN
ejpam-4658	33	21	of	of	ADP
ejpam-4658	33	22	g	g	NOUN
ejpam-4658	33	23	,	,	PUNCT
ejpam-4658	33	24	denoted	denote	VERB
ejpam-4658	33	25	by	by	ADP
ejpam-4658	33	26	ωs(g	ωs(g	NOUN
ejpam-4658	33	27	)	)	PUNCT
ejpam-4658	33	28	,	,	PUNCT
ejpam-4658	33	29	is	be	AUX
ejpam-4658	33	30	the	the	DET
ejpam-4658	33	31	cardinality	cardinality	NOUN
ejpam-4658	33	32	of	of	ADP
ejpam-4658	33	33	a	a	DET
ejpam-4658	33	34	maximum	maximum	ADJ
ejpam-4658	33	35	superclique	superclique	NOUN
ejpam-4658	33	36	in	in	ADP
ejpam-4658	33	37	g.	g.	PROPN
ejpam-4658	33	38	a	a	DET
ejpam-4658	33	39	superclique	superclique	ADJ
ejpam-4658	33	40	c	c	NOUN
ejpam-4658	33	41	in	in	ADP
ejpam-4658	33	42	g	g	PROPN
ejpam-4658	33	43	is	be	AUX
ejpam-4658	33	44	called	call	VERB
ejpam-4658	33	45	a	a	DET
ejpam-4658	33	46	hop	hop	NOUN
ejpam-4658	33	47	dominated	dominate	VERB
ejpam-4658	33	48	superclique	superclique	NOUN
ejpam-4658	33	49	if	if	SCONJ
ejpam-4658	33	50	for	for	ADP
ejpam-4658	33	51	every	every	DET
ejpam-4658	33	52	v	v	NOUN
ejpam-4658	33	53	∈	∈	NOUN
ejpam-4658	33	54	c	c	NOUN
ejpam-4658	33	55	there	there	PRON
ejpam-4658	33	56	exists	exist	VERB
ejpam-4658	33	57	u	u	PROPN
ejpam-4658	33	58	∈	∈	PROPN
ejpam-4658	33	59	v	v	NOUN
ejpam-4658	33	60	(	(	PUNCT
ejpam-4658	33	61	g)\c	g)\c	VERB
ejpam-4658	33	62	such	such	DET
ejpam-4658	33	63	that	that	DET
ejpam-4658	33	64	dg(u	dg(u	ADJ
ejpam-4658	33	65	,	,	PUNCT
ejpam-4658	33	66	v	v	NOUN
ejpam-4658	33	67	)	)	PUNCT
ejpam-4658	33	68	=	=	SYM
ejpam-4658	33	69	2	2	X
ejpam-4658	33	70	.	.	X
ejpam-4658	33	71	a	a	DET
ejpam-4658	33	72	hop	hop	NOUN
ejpam-4658	33	73	dominated	dominate	VERB
ejpam-4658	33	74	superclique	superclique	NOUN
ejpam-4658	33	75	c	c	PROPN
ejpam-4658	33	76	is	be	AUX
ejpam-4658	33	77	maximum	maximum	ADJ
ejpam-4658	33	78	in	in	ADP
ejpam-4658	33	79	g	g	PROPN
ejpam-4658	33	80	if	if	SCONJ
ejpam-4658	33	81	|c|	|c|	PROPN
ejpam-4658	33	82	≥	≥	NOUN
ejpam-4658	33	83	|c∗|	|c∗|	VERB
ejpam-4658	33	84	for	for	ADP
ejpam-4658	33	85	all	all	DET
ejpam-4658	33	86	hop	hop	NOUN
ejpam-4658	33	87	dominated	dominate	VERB
ejpam-4658	33	88	supercliques	superclique	NOUN
ejpam-4658	33	89	c∗	c∗	PROPN
ejpam-4658	33	90	in	in	ADP
ejpam-4658	33	91	g.	g.	PROPN
ejpam-4658	33	92	the	the	DET
ejpam-4658	33	93	hop	hop	NOUN
ejpam-4658	33	94	dominated	dominate	VERB
ejpam-4658	33	95	superclique	superclique	ADJ
ejpam-4658	33	96	number	number	NOUN
ejpam-4658	33	97	denoted	denote	VERB
ejpam-4658	33	98	by	by	ADP
ejpam-4658	33	99	ωhs(g	ωhs(g	PROPN
ejpam-4658	33	100	)	)	PUNCT
ejpam-4658	33	101	,	,	PUNCT
ejpam-4658	33	102	of	of	ADP
ejpam-4658	33	103	g	g	PROPN
ejpam-4658	33	104	is	be	AUX
ejpam-4658	33	105	the	the	DET
ejpam-4658	33	106	cardinality	cardinality	NOUN
ejpam-4658	33	107	of	of	ADP
ejpam-4658	33	108	a	a	DET
ejpam-4658	33	109	maximum	maximum	ADJ
ejpam-4658	33	110	hop	hop	NOUN
ejpam-4658	33	111	dominated	dominate	VERB
ejpam-4658	33	112	superclique	superclique	NOUN
ejpam-4658	33	113	in	in	ADP
ejpam-4658	33	114	g.	g.	PROPN
ejpam-4658	33	115	a	a	DET
ejpam-4658	33	116	superclique	superclique	NOUN
ejpam-4658	33	117	c	c	PROPN
ejpam-4658	33	118	⊆	⊆	NUM
ejpam-4658	33	119	v	v	NOUN
ejpam-4658	33	120	(	(	PUNCT
ejpam-4658	33	121	g	g	NOUN
ejpam-4658	33	122	)	)	PUNCT
ejpam-4658	33	123	is	be	AUX
ejpam-4658	33	124	called	call	VERB
ejpam-4658	33	125	a	a	DET
ejpam-4658	33	126	point	point	NOUN
ejpam-4658	33	127	-	-	PUNCT
ejpam-4658	33	128	wise	wise	ADJ
ejpam-4658	33	129	non	non	ADJ
ejpam-4658	33	130	-	-	ADJ
ejpam-4658	33	131	dominated	dominated	ADJ
ejpam-4658	33	132	superclique	superclique	NOUN
ejpam-4658	33	133	of	of	ADP
ejpam-4658	33	134	g	g	PROPN
ejpam-4658	33	135	if	if	SCONJ
ejpam-4658	33	136	for	for	ADP
ejpam-4658	33	137	every	every	DET
ejpam-4658	33	138	x	x	SYM
ejpam-4658	33	139	∈	∈	PROPN
ejpam-4658	33	140	c	c	NOUN
ejpam-4658	33	141	there	there	PRON
ejpam-4658	33	142	exists	exist	VERB
ejpam-4658	33	143	y	y	PROPN
ejpam-4658	33	144	∈	∈	PROPN
ejpam-4658	33	145	v	v	ADP
ejpam-4658	33	146	(	(	PUNCT
ejpam-4658	33	147	g	g	NOUN
ejpam-4658	33	148	)	)	PUNCT
ejpam-4658	33	149	\c	\c	ADP
ejpam-4658	33	150	such	such	ADJ
ejpam-4658	33	151	that	that	PRON
ejpam-4658	33	152	y	y	PROPN
ejpam-4658	33	153	/∈	/∈	PUNCT
ejpam-4658	33	154	ng(x	ng(x	NUM
ejpam-4658	33	155	)	)	PUNCT
ejpam-4658	33	156	.	.	PUNCT
ejpam-4658	34	1	a	a	DET
ejpam-4658	34	2	maximum	maximum	ADJ
ejpam-4658	34	3	cardinality	cardinality	NOUN
ejpam-4658	34	4	of	of	ADP
ejpam-4658	34	5	a	a	DET
ejpam-4658	34	6	point	point	NOUN
ejpam-4658	34	7	-	-	PUNCT
ejpam-4658	34	8	wise	wise	ADJ
ejpam-4658	34	9	non	non	ADJ
ejpam-4658	34	10	-	-	ADJ
ejpam-4658	34	11	dominated	dominated	ADJ
ejpam-4658	34	12	superclique	superclique	NOUN
ejpam-4658	34	13	in	in	ADP
ejpam-4658	34	14	g	g	PROPN
ejpam-4658	34	15	is	be	AUX
ejpam-4658	34	16	denoted	denote	VERB
ejpam-4658	34	17	by	by	ADP
ejpam-4658	34	18	ωpnds(g	ωpnds(g	NOUN
ejpam-4658	34	19	)	)	PUNCT
ejpam-4658	34	20	.	.	PUNCT
ejpam-4658	35	1	a	a	DET
ejpam-4658	35	2	vertex	vertex	NOUN
ejpam-4658	35	3	u	u	NOUN
ejpam-4658	35	4	of	of	ADP
ejpam-4658	35	5	g	g	PROPN
ejpam-4658	35	6	is	be	AUX
ejpam-4658	35	7	maximally	maximally	ADV
ejpam-4658	35	8	distant	distant	ADJ
ejpam-4658	35	9	from	from	ADP
ejpam-4658	35	10	vertex	vertex	NOUN
ejpam-4658	35	11	v	v	NOUN
ejpam-4658	35	12	of	of	ADP
ejpam-4658	35	13	g	g	NOUN
ejpam-4658	35	14	,	,	PUNCT
ejpam-4658	35	15	u	u	PROPN
ejpam-4658	35	16	̸=	̸=	PROPN
ejpam-4658	35	17	v	v	NOUN
ejpam-4658	35	18	,	,	PUNCT
ejpam-4658	35	19	if	if	SCONJ
ejpam-4658	35	20	for	for	ADP
ejpam-4658	35	21	every	every	DET
ejpam-4658	35	22	vertex	vertex	NOUN
ejpam-4658	35	23	w	w	PROPN
ejpam-4658	35	24	∈	∈	PROPN
ejpam-4658	35	25	ng(u	ng(u	NOUN
ejpam-4658	35	26	)	)	PUNCT
ejpam-4658	35	27	,	,	PUNCT
ejpam-4658	35	28	dg(v	dg(v	X
ejpam-4658	35	29	,	,	PUNCT
ejpam-4658	35	30	w	w	NOUN
ejpam-4658	35	31	)	)	PUNCT
ejpam-4658	35	32	≤	≤	NOUN
ejpam-4658	35	33	dg(u	dg(u	ADJ
ejpam-4658	35	34	,	,	PUNCT
ejpam-4658	35	35	v	v	NOUN
ejpam-4658	35	36	)	)	PUNCT
ejpam-4658	35	37	.	.	PUNCT
ejpam-4658	36	1	if	if	SCONJ
ejpam-4658	36	2	u	u	NOUN
ejpam-4658	36	3	is	be	AUX
ejpam-4658	36	4	maximally	maximally	ADV
ejpam-4658	36	5	distant	distant	ADJ
ejpam-4658	36	6	from	from	ADP
ejpam-4658	36	7	v	v	NOUN
ejpam-4658	36	8	and	and	CCONJ
ejpam-4658	36	9	v	v	NOUN
ejpam-4658	36	10	is	be	AUX
ejpam-4658	36	11	maximally	maximally	ADV
ejpam-4658	36	12	distant	distant	ADJ
ejpam-4658	36	13	from	from	ADP
ejpam-4658	36	14	u	u	NOUN
ejpam-4658	36	15	,	,	PUNCT
ejpam-4658	36	16	then	then	ADV
ejpam-4658	36	17	we	we	PRON
ejpam-4658	36	18	say	say	VERB
ejpam-4658	36	19	that	that	SCONJ
ejpam-4658	36	20	u	u	PROPN
ejpam-4658	36	21	and	and	CCONJ
ejpam-4658	36	22	v	v	NOUN
ejpam-4658	36	23	are	be	AUX
ejpam-4658	36	24	mutually	mutually	ADV
ejpam-4658	36	25	maximally	maximally	ADV
ejpam-4658	36	26	distant	distant	ADJ
ejpam-4658	36	27	,	,	PUNCT
ejpam-4658	36	28	denoted	denote	VERB
ejpam-4658	36	29	by	by	ADP
ejpam-4658	36	30	ummdv	ummdv	NOUN
ejpam-4658	36	31	.	.	PUNCT
ejpam-4658	37	1	a	a	DET
ejpam-4658	37	2	vertex	vertex	NOUN
ejpam-4658	37	3	x	x	X
ejpam-4658	37	4	of	of	ADP
ejpam-4658	37	5	a	a	DET
ejpam-4658	37	6	connected	connected	ADJ
ejpam-4658	37	7	graph	graph	NOUN
ejpam-4658	37	8	g	g	NOUN
ejpam-4658	37	9	is	be	AUX
ejpam-4658	37	10	said	say	VERB
ejpam-4658	37	11	to	to	PART
ejpam-4658	37	12	resolve	resolve	VERB
ejpam-4658	37	13	vertices	vertex	NOUN
ejpam-4658	37	14	u	u	NOUN
ejpam-4658	37	15	and	and	CCONJ
ejpam-4658	37	16	v	v	NOUN
ejpam-4658	37	17	of	of	ADP
ejpam-4658	37	18	g	g	PROPN
ejpam-4658	37	19	if	if	SCONJ
ejpam-4658	37	20	dg(x	dg(x	NUM
ejpam-4658	37	21	,	,	PUNCT
ejpam-4658	37	22	u	u	NOUN
ejpam-4658	37	23	)	)	PUNCT
ejpam-4658	37	24	̸=	̸=	PROPN
ejpam-4658	37	25	dg(x	dg(x	NUM
ejpam-4658	37	26	,	,	PUNCT
ejpam-4658	37	27	v	v	NOUN
ejpam-4658	37	28	)	)	PUNCT
ejpam-4658	37	29	.	.	PUNCT
ejpam-4658	38	1	for	for	ADP
ejpam-4658	38	2	an	an	DET
ejpam-4658	38	3	ordered	order	VERB
ejpam-4658	38	4	set	set	NOUN
ejpam-4658	38	5	w	w	NOUN
ejpam-4658	38	6	=	=	PUNCT
ejpam-4658	38	7	{	{	PUNCT
ejpam-4658	38	8	x1	x1	PROPN
ejpam-4658	38	9	,	,	PUNCT
ejpam-4658	38	10	.	.	PUNCT
ejpam-4658	38	11	.	.	PUNCT
ejpam-4658	38	12	.	.	PUNCT
ejpam-4658	39	1	,	,	PUNCT
ejpam-4658	39	2	xk	xk	ADJ
ejpam-4658	39	3	}	}	PUNCT
ejpam-4658	39	4	⊆	⊆	NUM
ejpam-4658	39	5	v	v	NOUN
ejpam-4658	39	6	(	(	PUNCT
ejpam-4658	39	7	g	g	NOUN
ejpam-4658	39	8	)	)	PUNCT
ejpam-4658	39	9	and	and	CCONJ
ejpam-4658	39	10	a	a	DET
ejpam-4658	39	11	vertex	vertex	NOUN
ejpam-4658	39	12	v	v	NOUN
ejpam-4658	39	13	in	in	ADP
ejpam-4658	39	14	g	g	PROPN
ejpam-4658	39	15	,	,	PUNCT
ejpam-4658	39	16	the	the	DET
ejpam-4658	39	17	k	k	NOUN
ejpam-4658	39	18	-	-	NOUN
ejpam-4658	39	19	vector	vector	NOUN
ejpam-4658	39	20	rg(v	rg(v	NOUN
ejpam-4658	39	21	/	/	SYM
ejpam-4658	39	22	w	w	NOUN
ejpam-4658	39	23	)	)	PUNCT
ejpam-4658	39	24	=	=	SYM
ejpam-4658	39	25	(	(	PUNCT
ejpam-4658	39	26	dg(v	dg(v	X
ejpam-4658	39	27	,	,	PUNCT
ejpam-4658	39	28	x1	x1	PROPN
ejpam-4658	39	29	)	)	PUNCT
ejpam-4658	39	30	,	,	PUNCT
ejpam-4658	39	31	dg(v	dg(v	X
ejpam-4658	39	32	,	,	PUNCT
ejpam-4658	39	33	x2	x2	PROPN
ejpam-4658	39	34	)	)	PUNCT
ejpam-4658	39	35	,	,	PUNCT
ejpam-4658	39	36	.	.	PUNCT
ejpam-4658	39	37	.	.	PUNCT
ejpam-4658	39	38	.	.	PUNCT
ejpam-4658	40	1	dg(v	dg(v	PUNCT
ejpam-4658	40	2	,	,	PUNCT
ejpam-4658	40	3	xk	xk	NOUN
ejpam-4658	40	4	)	)	PUNCT
ejpam-4658	40	5	)	)	PUNCT
ejpam-4658	41	1	is	be	AUX
ejpam-4658	41	2	called	call	VERB
ejpam-4658	41	3	the	the	DET
ejpam-4658	41	4	representation	representation	NOUN
ejpam-4658	41	5	of	of	ADP
ejpam-4658	41	6	v	v	NOUN
ejpam-4658	41	7	with	with	ADP
ejpam-4658	41	8	respect	respect	NOUN
ejpam-4658	41	9	to	to	ADP
ejpam-4658	41	10	w	w	PROPN
ejpam-4658	41	11	.	.	PUNCT
ejpam-4658	42	1	the	the	DET
ejpam-4658	42	2	set	set	NOUN
ejpam-4658	42	3	w	w	NOUN
ejpam-4658	42	4	is	be	AUX
ejpam-4658	42	5	a	a	DET
ejpam-4658	42	6	resolving	resolving	NOUN
ejpam-4658	42	7	set	set	VERB
ejpam-4658	42	8	for	for	ADP
ejpam-4658	42	9	g	g	PROPN
ejpam-4658	42	10	if	if	SCONJ
ejpam-4658	43	1	and	and	CCONJ
ejpam-4658	43	2	only	only	ADV
ejpam-4658	43	3	if	if	SCONJ
ejpam-4658	43	4	no	no	DET
ejpam-4658	43	5	two	two	NUM
ejpam-4658	43	6	vertices	vertex	NOUN
ejpam-4658	43	7	of	of	ADP
ejpam-4658	43	8	g	g	NOUN
ejpam-4658	43	9	have	have	VERB
ejpam-4658	43	10	the	the	DET
ejpam-4658	43	11	same	same	ADJ
ejpam-4658	43	12	representation	representation	NOUN
ejpam-4658	43	13	with	with	ADP
ejpam-4658	43	14	respect	respect	NOUN
ejpam-4658	43	15	to	to	ADP
ejpam-4658	43	16	w	w	PROPN
ejpam-4658	43	17	.	.	PUNCT
ejpam-4658	44	1	the	the	DET
ejpam-4658	44	2	metric	metric	ADJ
ejpam-4658	44	3	dimension	dimension	NOUN
ejpam-4658	44	4	of	of	ADP
ejpam-4658	44	5	g	g	NOUN
ejpam-4658	44	6	,	,	PUNCT
ejpam-4658	44	7	denoted	denote	VERB
ejpam-4658	44	8	by	by	ADP
ejpam-4658	44	9	dim(g	dim(g	PROPN
ejpam-4658	44	10	)	)	PUNCT
ejpam-4658	44	11	,	,	PUNCT
ejpam-4658	44	12	is	be	AUX
ejpam-4658	44	13	the	the	DET
ejpam-4658	44	14	minimum	minimum	ADJ
ejpam-4658	44	15	cardinality	cardinality	NOUN
ejpam-4658	44	16	over	over	ADP
ejpam-4658	44	17	all	all	DET
ejpam-4658	44	18	resolving	resolve	VERB
ejpam-4658	44	19	sets	set	NOUN
ejpam-4658	44	20	of	of	ADP
ejpam-4658	44	21	g.	g.	PROPN
ejpam-4658	44	22	a	a	DET
ejpam-4658	44	23	resolving	resolve	VERB
ejpam-4658	44	24	set	set	NOUN
ejpam-4658	44	25	of	of	ADP
ejpam-4658	44	26	cardinality	cardinality	PROPN
ejpam-4658	44	27	dim(g	dim(g	PROPN
ejpam-4658	44	28	)	)	PUNCT
ejpam-4658	44	29	is	be	AUX
ejpam-4658	44	30	called	call	VERB
ejpam-4658	44	31	a	a	DET
ejpam-4658	44	32	basis	basis	NOUN
ejpam-4658	44	33	.	.	PUNCT
ejpam-4658	45	1	for	for	ADP
ejpam-4658	45	2	two	two	NUM
ejpam-4658	45	3	vertices	vertex	NOUN
ejpam-4658	45	4	u	u	NOUN
ejpam-4658	45	5	,	,	PUNCT
ejpam-4658	45	6	v	v	NOUN
ejpam-4658	45	7	∈	∈	PROPN
ejpam-4658	45	8	v	v	NOUN
ejpam-4658	45	9	(	(	PUNCT
ejpam-4658	45	10	g	g	NOUN
ejpam-4658	45	11	)	)	PUNCT
ejpam-4658	45	12	,	,	PUNCT
ejpam-4658	45	13	the	the	DET
ejpam-4658	45	14	interval	interval	NOUN
ejpam-4658	45	15	ig[u	ig[u	PROPN
ejpam-4658	45	16	,	,	PUNCT
ejpam-4658	45	17	v	v	NOUN
ejpam-4658	45	18	]	]	PUNCT
ejpam-4658	45	19	between	between	ADP
ejpam-4658	45	20	u	u	NOUN
ejpam-4658	45	21	and	and	CCONJ
ejpam-4658	45	22	v	v	NOUN
ejpam-4658	45	23	is	be	AUX
ejpam-4658	45	24	the	the	DET
ejpam-4658	45	25	collection	collection	NOUN
ejpam-4658	45	26	of	of	ADP
ejpam-4658	45	27	all	all	DET
ejpam-4658	45	28	vertices	vertex	NOUN
ejpam-4658	45	29	that	that	PRON
ejpam-4658	45	30	belong	belong	VERB
ejpam-4658	45	31	to	to	ADP
ejpam-4658	45	32	some	some	DET
ejpam-4658	45	33	shortest	short	ADJ
ejpam-4658	45	34	u	u	NOUN
ejpam-4658	45	35	-	-	NOUN
ejpam-4658	45	36	v	v	ADJ
ejpam-4658	45	37	path	path	NOUN
ejpam-4658	45	38	.	.	PUNCT
ejpam-4658	46	1	a	a	DET
ejpam-4658	46	2	vertex	vertex	NOUN
ejpam-4658	46	3	w	w	NOUN
ejpam-4658	46	4	strongly	strongly	ADV
ejpam-4658	46	5	resolves	resolve	VERB
ejpam-4658	46	6	two	two	NUM
ejpam-4658	46	7	vertices	vertex	NOUN
ejpam-4658	46	8	u	u	NOUN
ejpam-4658	46	9	and	and	CCONJ
ejpam-4658	46	10	v	v	NOUN
ejpam-4658	46	11	if	if	SCONJ
ejpam-4658	46	12	v	v	NOUN
ejpam-4658	46	13	∈	∈	PROPN
ejpam-4658	46	14	ig[u	ig[u	PROPN
ejpam-4658	46	15	,	,	PUNCT
ejpam-4658	46	16	w	w	NOUN
ejpam-4658	46	17	]	]	PUNCT
ejpam-4658	46	18	or	or	CCONJ
ejpam-4658	46	19	if	if	SCONJ
ejpam-4658	46	20	u	u	PROPN
ejpam-4658	46	21	∈	∈	PROPN
ejpam-4658	46	22	ig[v	ig[v	PROPN
ejpam-4658	46	23	,	,	PUNCT
ejpam-4658	46	24	w	w	PROPN
ejpam-4658	46	25	]	]	X
ejpam-4658	46	26	.	.	PUNCT
ejpam-4658	47	1	a	a	DET
ejpam-4658	47	2	set	set	NOUN
ejpam-4658	47	3	w	w	NOUN
ejpam-4658	47	4	of	of	ADP
ejpam-4658	47	5	vertices	vertex	NOUN
ejpam-4658	47	6	in	in	ADP
ejpam-4658	47	7	g	g	PROPN
ejpam-4658	47	8	is	be	AUX
ejpam-4658	47	9	a	a	DET
ejpam-4658	47	10	strong	strong	ADJ
ejpam-4658	47	11	a.	a.	NOUN
ejpam-4658	47	12	h.	h.	PROPN
ejpam-4658	47	13	abragan	abragan	PROPN
ejpam-4658	47	14	,	,	PUNCT
ejpam-4658	47	15	h.	h.	PROPN
ejpam-4658	47	16	m.	m.	PROPN
ejpam-4658	47	17	rara	rara	PROPN
ejpam-4658	47	18	/	/	SYM
ejpam-4658	47	19	eur	eur	PROPN
ejpam-4658	47	20	.	.	PUNCT
ejpam-4658	48	1	j.	j.	PROPN
ejpam-4658	48	2	pure	pure	PROPN
ejpam-4658	48	3	appl	appl	PROPN
ejpam-4658	48	4	.	.	PROPN
ejpam-4658	48	5	math	math	PROPN
ejpam-4658	48	6	,	,	PUNCT
ejpam-4658	48	7	16	16	NUM
ejpam-4658	48	8	(	(	PUNCT
ejpam-4658	48	9	2	2	NUM
ejpam-4658	48	10	)	)	PUNCT
ejpam-4658	48	11	(	(	PUNCT
ejpam-4658	48	12	2023	2023	NUM
ejpam-4658	48	13	)	)	PUNCT
ejpam-4658	48	14	,	,	PUNCT
ejpam-4658	48	15	763	763	NUM
ejpam-4658	48	16	-	-	SYM
ejpam-4658	48	17	772	772	NUM
ejpam-4658	48	18	765	765	NUM
ejpam-4658	48	19	resolving	resolve	VERB
ejpam-4658	48	20	set	set	NOUN
ejpam-4658	48	21	of	of	ADP
ejpam-4658	48	22	g	g	NOUN
ejpam-4658	48	23	if	if	SCONJ
ejpam-4658	48	24	every	every	DET
ejpam-4658	48	25	two	two	NUM
ejpam-4658	48	26	vertices	vertex	NOUN
ejpam-4658	48	27	of	of	ADP
ejpam-4658	48	28	g	g	NOUN
ejpam-4658	48	29	are	be	AUX
ejpam-4658	48	30	strongly	strongly	ADV
ejpam-4658	48	31	resolved	resolve	VERB
ejpam-4658	48	32	by	by	ADP
ejpam-4658	48	33	some	some	DET
ejpam-4658	48	34	vertex	vertex	NOUN
ejpam-4658	48	35	of	of	ADP
ejpam-4658	48	36	w	w	PROPN
ejpam-4658	48	37	.	.	PUNCT
ejpam-4658	49	1	the	the	DET
ejpam-4658	49	2	smallest	small	ADJ
ejpam-4658	49	3	cardinality	cardinality	NOUN
ejpam-4658	49	4	of	of	ADP
ejpam-4658	49	5	a	a	DET
ejpam-4658	49	6	strong	strong	ADJ
ejpam-4658	49	7	resolving	resolving	NOUN
ejpam-4658	49	8	set	set	NOUN
ejpam-4658	49	9	of	of	ADP
ejpam-4658	49	10	g	g	PROPN
ejpam-4658	49	11	is	be	AUX
ejpam-4658	49	12	called	call	VERB
ejpam-4658	49	13	the	the	DET
ejpam-4658	49	14	strong	strong	ADJ
ejpam-4658	49	15	metric	metric	ADJ
ejpam-4658	49	16	dimension	dimension	NOUN
ejpam-4658	49	17	of	of	ADP
ejpam-4658	49	18	g	g	NOUN
ejpam-4658	49	19	and	and	CCONJ
ejpam-4658	49	20	is	be	AUX
ejpam-4658	49	21	denoted	denote	VERB
ejpam-4658	49	22	by	by	ADP
ejpam-4658	49	23	sdim(g	sdim(g	PROPN
ejpam-4658	49	24	)	)	PUNCT
ejpam-4658	49	25	.	.	PUNCT
ejpam-4658	50	1	a	a	DET
ejpam-4658	50	2	strong	strong	ADJ
ejpam-4658	50	3	resolving	resolving	NOUN
ejpam-4658	50	4	set	set	NOUN
ejpam-4658	50	5	of	of	ADP
ejpam-4658	50	6	cardinality	cardinality	PROPN
ejpam-4658	50	7	sdim(g	sdim(g	PROPN
ejpam-4658	50	8	)	)	PUNCT
ejpam-4658	50	9	is	be	AUX
ejpam-4658	50	10	called	call	VERB
ejpam-4658	50	11	a	a	DET
ejpam-4658	50	12	strong	strong	ADJ
ejpam-4658	50	13	metric	metric	ADJ
ejpam-4658	50	14	basis	basis	NOUN
ejpam-4658	50	15	of	of	ADP
ejpam-4658	50	16	g.	g.	PROPN
ejpam-4658	50	17	a	a	DET
ejpam-4658	50	18	subset	subset	NOUN
ejpam-4658	50	19	s	s	VERB
ejpam-4658	50	20	⊆	⊆	NUM
ejpam-4658	50	21	v	v	NOUN
ejpam-4658	50	22	(	(	PUNCT
ejpam-4658	50	23	g	g	NOUN
ejpam-4658	50	24	)	)	PUNCT
ejpam-4658	50	25	is	be	AUX
ejpam-4658	50	26	a	a	DET
ejpam-4658	50	27	strong	strong	ADJ
ejpam-4658	50	28	resolving	resolve	VERB
ejpam-4658	50	29	hop	hop	NOUN
ejpam-4658	50	30	dominating	dominating	NOUN
ejpam-4658	50	31	set	set	NOUN
ejpam-4658	50	32	of	of	ADP
ejpam-4658	50	33	g	g	PROPN
ejpam-4658	50	34	if	if	SCONJ
ejpam-4658	50	35	s	s	VERB
ejpam-4658	50	36	is	be	AUX
ejpam-4658	50	37	both	both	CCONJ
ejpam-4658	50	38	a	a	DET
ejpam-4658	50	39	strong	strong	ADJ
ejpam-4658	50	40	resolving	resolving	NOUN
ejpam-4658	50	41	set	set	VERB
ejpam-4658	50	42	and	and	CCONJ
ejpam-4658	50	43	a	a	DET
ejpam-4658	50	44	hop	hop	NOUN
ejpam-4658	50	45	dominating	dominating	NOUN
ejpam-4658	50	46	set	set	NOUN
ejpam-4658	50	47	.	.	PUNCT
ejpam-4658	51	1	the	the	DET
ejpam-4658	51	2	minimum	minimum	ADJ
ejpam-4658	51	3	cardinality	cardinality	NOUN
ejpam-4658	51	4	of	of	ADP
ejpam-4658	51	5	a	a	DET
ejpam-4658	51	6	strong	strong	ADJ
ejpam-4658	51	7	resolving	resolve	VERB
ejpam-4658	51	8	hop	hop	NOUN
ejpam-4658	51	9	dominating	dominating	NOUN
ejpam-4658	51	10	set	set	NOUN
ejpam-4658	51	11	of	of	ADP
ejpam-4658	51	12	g	g	NOUN
ejpam-4658	51	13	,	,	PUNCT
ejpam-4658	51	14	denoted	denote	VERB
ejpam-4658	51	15	by	by	ADP
ejpam-4658	51	16	γsrh(g	γsrh(g	NOUN
ejpam-4658	51	17	)	)	PUNCT
ejpam-4658	51	18	,	,	PUNCT
ejpam-4658	51	19	is	be	AUX
ejpam-4658	51	20	called	call	VERB
ejpam-4658	51	21	the	the	DET
ejpam-4658	51	22	strong	strong	ADJ
ejpam-4658	51	23	resolving	resolve	VERB
ejpam-4658	51	24	hop	hop	NOUN
ejpam-4658	51	25	domination	domination	NOUN
ejpam-4658	51	26	number	number	NOUN
ejpam-4658	51	27	of	of	ADP
ejpam-4658	51	28	g.	g.	PROPN
ejpam-4658	51	29	any	any	PRON
ejpam-4658	51	30	resolving	resolve	VERB
ejpam-4658	51	31	hop	hop	NOUN
ejpam-4658	51	32	dominating	dominating	NOUN
ejpam-4658	51	33	set	set	VERB
ejpam-4658	51	34	with	with	ADP
ejpam-4658	51	35	cardinality	cardinality	NOUN
ejpam-4658	51	36	equal	equal	ADJ
ejpam-4658	51	37	to	to	ADP
ejpam-4658	51	38	γsrh(g	γsrh(g	NOUN
ejpam-4658	51	39	)	)	PUNCT
ejpam-4658	51	40	is	be	AUX
ejpam-4658	51	41	called	call	VERB
ejpam-4658	51	42	a	a	DET
ejpam-4658	51	43	γsrh	γsrh	NOUN
ejpam-4658	51	44	-	-	PUNCT
ejpam-4658	51	45	set	set	NOUN
ejpam-4658	51	46	.	.	PUNCT
ejpam-4658	52	1	a	a	DET
ejpam-4658	52	2	strong	strong	ADJ
ejpam-4658	52	3	resolving	resolve	VERB
ejpam-4658	52	4	hop	hop	NOUN
ejpam-4658	52	5	dominating	dominating	NOUN
ejpam-4658	52	6	set	set	NOUN
ejpam-4658	52	7	s	s	VERB
ejpam-4658	52	8	is	be	AUX
ejpam-4658	52	9	a	a	DET
ejpam-4658	52	10	1	1	NUM
ejpam-4658	52	11	-	-	PUNCT
ejpam-4658	52	12	movable	movable	ADJ
ejpam-4658	52	13	strong	strong	ADJ
ejpam-4658	52	14	resolving	resolve	VERB
ejpam-4658	52	15	hop	hop	NOUN
ejpam-4658	52	16	dominating	dominating	NOUN
ejpam-4658	52	17	set	set	NOUN
ejpam-4658	52	18	of	of	ADP
ejpam-4658	52	19	g	g	PROPN
ejpam-4658	52	20	if	if	SCONJ
ejpam-4658	52	21	for	for	SCONJ
ejpam-4658	52	22	every	every	DET
ejpam-4658	52	23	v	v	NUM
ejpam-4658	52	24	∈	∈	PROPN
ejpam-4658	52	25	s	s	NOUN
ejpam-4658	52	26	,	,	PUNCT
ejpam-4658	52	27	either	either	CCONJ
ejpam-4658	52	28	s	s	VERB
ejpam-4658	52	29	\	\	PROPN
ejpam-4658	52	30	{	{	PUNCT
ejpam-4658	52	31	v	v	NOUN
ejpam-4658	52	32	}	}	PUNCT
ejpam-4658	52	33	is	be	AUX
ejpam-4658	52	34	a	a	DET
ejpam-4658	52	35	strong	strong	ADJ
ejpam-4658	52	36	resolving	resolve	VERB
ejpam-4658	52	37	hop	hop	NOUN
ejpam-4658	52	38	dominating	dominating	NOUN
ejpam-4658	52	39	set	set	NOUN
ejpam-4658	52	40	or	or	CCONJ
ejpam-4658	52	41	there	there	PRON
ejpam-4658	52	42	exists	exist	VERB
ejpam-4658	52	43	a	a	DET
ejpam-4658	52	44	vertex	vertex	NOUN
ejpam-4658	52	45	u	u	NOUN
ejpam-4658	52	46	∈	∈	PROPN
ejpam-4658	52	47	(	(	PUNCT
ejpam-4658	52	48	v	v	NOUN
ejpam-4658	52	49	(	(	PUNCT
ejpam-4658	52	50	g)\s)∩ng(v	g)\s)∩ng(v	NOUN
ejpam-4658	52	51	)	)	PUNCT
ejpam-4658	52	52	such	such	ADJ
ejpam-4658	52	53	that	that	SCONJ
ejpam-4658	52	54	(	(	PUNCT
ejpam-4658	52	55	s	s	AUX
ejpam-4658	52	56	\{v})∩{u	\{v})∩{u	PROPN
ejpam-4658	52	57	}	}	PUNCT
ejpam-4658	52	58	is	be	AUX
ejpam-4658	52	59	a	a	DET
ejpam-4658	52	60	strong	strong	ADJ
ejpam-4658	52	61	resolving	resolve	VERB
ejpam-4658	52	62	hop	hop	NOUN
ejpam-4658	52	63	dominating	dominating	NOUN
ejpam-4658	52	64	set	set	NOUN
ejpam-4658	52	65	of	of	ADP
ejpam-4658	52	66	g.	g.	PROPN
ejpam-4658	52	67	the	the	DET
ejpam-4658	52	68	minimum	minimum	ADJ
ejpam-4658	52	69	cardinality	cardinality	NOUN
ejpam-4658	52	70	of	of	ADP
ejpam-4658	52	71	a	a	DET
ejpam-4658	52	72	1	1	NUM
ejpam-4658	52	73	-	-	PUNCT
ejpam-4658	52	74	movable	movable	ADJ
ejpam-4658	52	75	strong	strong	ADJ
ejpam-4658	52	76	resolving	resolve	VERB
ejpam-4658	52	77	hop	hop	NOUN
ejpam-4658	52	78	dominating	dominating	NOUN
ejpam-4658	52	79	set	set	NOUN
ejpam-4658	52	80	of	of	ADP
ejpam-4658	52	81	g	g	PROPN
ejpam-4658	52	82	is	be	AUX
ejpam-4658	52	83	denoted	denote	VERB
ejpam-4658	52	84	by	by	ADP
ejpam-4658	52	85	γ1msrh(g	γ1msrh(g	NOUN
ejpam-4658	52	86	)	)	PUNCT
ejpam-4658	52	87	.	.	PUNCT
ejpam-4658	53	1	2	2	X
ejpam-4658	53	2	.	.	X
ejpam-4658	53	3	some	some	DET
ejpam-4658	53	4	known	know	VERB
ejpam-4658	53	5	results	result	VERB
ejpam-4658	53	6	the	the	DET
ejpam-4658	53	7	following	follow	VERB
ejpam-4658	53	8	known	know	VERB
ejpam-4658	53	9	results	result	NOUN
ejpam-4658	53	10	are	be	AUX
ejpam-4658	53	11	taken	take	VERB
ejpam-4658	53	12	from	from	ADP
ejpam-4658	53	13	[	[	X
ejpam-4658	53	14	5	5	NUM
ejpam-4658	53	15	]	]	PUNCT
ejpam-4658	53	16	.	.	PUNCT
ejpam-4658	54	1	theorem	theorem	NOUN
ejpam-4658	54	2	1	1	X
ejpam-4658	54	3	.	.	PUNCT
ejpam-4658	55	1	let	let	VERB
ejpam-4658	55	2	g	g	NOUN
ejpam-4658	55	3	and	and	CCONJ
ejpam-4658	55	4	h	h	NOUN
ejpam-4658	55	5	be	be	AUX
ejpam-4658	55	6	nontrivial	nontrivial	ADJ
ejpam-4658	55	7	connected	connect	VERB
ejpam-4658	55	8	graphs	graph	NOUN
ejpam-4658	55	9	of	of	ADP
ejpam-4658	55	10	orders	order	NOUN
ejpam-4658	55	11	m	m	VERB
ejpam-4658	55	12	and	and	CCONJ
ejpam-4658	55	13	n	n	CCONJ
ejpam-4658	55	14	,	,	PUNCT
ejpam-4658	55	15	respectively	respectively	ADV
ejpam-4658	55	16	.	.	PUNCT
ejpam-4658	56	1	a	a	DET
ejpam-4658	56	2	proper	proper	ADJ
ejpam-4658	56	3	subset	subset	NOUN
ejpam-4658	56	4	s	s	NOUN
ejpam-4658	56	5	of	of	ADP
ejpam-4658	56	6	v	v	NOUN
ejpam-4658	56	7	(	(	PUNCT
ejpam-4658	56	8	g	g	PROPN
ejpam-4658	56	9	+	+	NOUN
ejpam-4658	56	10	h	h	NOUN
ejpam-4658	56	11	)	)	PUNCT
ejpam-4658	56	12	is	be	AUX
ejpam-4658	56	13	a	a	DET
ejpam-4658	56	14	strong	strong	ADJ
ejpam-4658	56	15	resolving	resolving	NOUN
ejpam-4658	56	16	set	set	NOUN
ejpam-4658	56	17	of	of	ADP
ejpam-4658	56	18	g	g	PROPN
ejpam-4658	56	19	+	+	PROPN
ejpam-4658	56	20	h	h	NOUN
ejpam-4658	56	21	if	if	SCONJ
ejpam-4658	57	1	and	and	CCONJ
ejpam-4658	57	2	only	only	ADV
ejpam-4658	57	3	if	if	SCONJ
ejpam-4658	57	4	at	at	ADV
ejpam-4658	57	5	least	least	ADJ
ejpam-4658	57	6	one	one	NUM
ejpam-4658	57	7	of	of	ADP
ejpam-4658	57	8	the	the	DET
ejpam-4658	57	9	following	follow	VERB
ejpam-4658	57	10	is	be	AUX
ejpam-4658	57	11	satisfied	satisfied	ADJ
ejpam-4658	57	12	:	:	PUNCT
ejpam-4658	57	13	(	(	PUNCT
ejpam-4658	57	14	i	i	NOUN
ejpam-4658	57	15	)	)	PUNCT
ejpam-4658	57	16	s	s	PART
ejpam-4658	57	17	=	=	SYM
ejpam-4658	57	18	v	v	PROPN
ejpam-4658	57	19	(	(	PUNCT
ejpam-4658	57	20	g+h	g+h	NOUN
ejpam-4658	57	21	)	)	PUNCT
ejpam-4658	57	22	\	\	PROPN
ejpam-4658	58	1	cg	cg	NOUN
ejpam-4658	58	2	where	where	SCONJ
ejpam-4658	58	3	cg	cg	NOUN
ejpam-4658	58	4	is	be	AUX
ejpam-4658	58	5	a	a	DET
ejpam-4658	58	6	superclique	superclique	NOUN
ejpam-4658	58	7	in	in	ADP
ejpam-4658	58	8	g.	g.	PROPN
ejpam-4658	58	9	(	(	PUNCT
ejpam-4658	58	10	ii	ii	PROPN
ejpam-4658	58	11	)	)	PUNCT
ejpam-4658	58	12	s	s	PART
ejpam-4658	58	13	=	=	SYM
ejpam-4658	58	14	v	v	PROPN
ejpam-4658	58	15	(	(	PUNCT
ejpam-4658	58	16	g+h	g+h	NOUN
ejpam-4658	58	17	)	)	PUNCT
ejpam-4658	58	18	\	\	PROPN
ejpam-4658	59	1	ch	ch	NOUN
ejpam-4658	59	2	where	where	SCONJ
ejpam-4658	59	3	ch	ch	NOUN
ejpam-4658	59	4	is	be	AUX
ejpam-4658	59	5	a	a	DET
ejpam-4658	59	6	superclique	superclique	NOUN
ejpam-4658	59	7	in	in	ADP
ejpam-4658	59	8	h.	h.	PROPN
ejpam-4658	59	9	(	(	PUNCT
ejpam-4658	59	10	iii	iii	X
ejpam-4658	59	11	)	)	PUNCT
ejpam-4658	59	12	if	if	SCONJ
ejpam-4658	59	13	γ(g	γ(g	PROPN
ejpam-4658	59	14	)	)	PUNCT
ejpam-4658	59	15	̸=	̸=	PROPN
ejpam-4658	59	16	1	1	NUM
ejpam-4658	59	17	or	or	CCONJ
ejpam-4658	59	18	γ(h	γ(h	NOUN
ejpam-4658	59	19	)	)	PUNCT
ejpam-4658	59	20	̸=	̸=	PROPN
ejpam-4658	59	21	1	1	NUM
ejpam-4658	59	22	,	,	PUNCT
ejpam-4658	59	23	s	s	NOUN
ejpam-4658	59	24	=	=	SYM
ejpam-4658	59	25	v	v	PROPN
ejpam-4658	59	26	(	(	PUNCT
ejpam-4658	59	27	g+h	g+h	NOUN
ejpam-4658	59	28	)	)	PUNCT
ejpam-4658	59	29	\	\	PUNCT
ejpam-4658	60	1	(	(	PUNCT
ejpam-4658	60	2	cg	cg	NOUN
ejpam-4658	60	3	∪	∪	PROPN
ejpam-4658	60	4	ch	ch	NOUN
ejpam-4658	60	5	)	)	PUNCT
ejpam-4658	60	6	=	=	PUNCT
ejpam-4658	60	7	(	(	PUNCT
ejpam-4658	60	8	v(g	v(g	PROPN
ejpam-4658	60	9	)	)	PUNCT
ejpam-4658	60	10	\	\	PROPN
ejpam-4658	60	11	cg	cg	NOUN
ejpam-4658	60	12	)	)	PUNCT
ejpam-4658	61	1	∪	∪	NOUN
ejpam-4658	61	2	(	(	PUNCT
ejpam-4658	61	3	v	v	NOUN
ejpam-4658	61	4	(	(	PUNCT
ejpam-4658	61	5	h	h	NOUN
ejpam-4658	61	6	)	)	PUNCT
ejpam-4658	61	7	\	\	PROPN
ejpam-4658	61	8	ch	ch	NOUN
ejpam-4658	61	9	)	)	PUNCT
ejpam-4658	61	10	,	,	PUNCT
ejpam-4658	61	11	where	where	SCONJ
ejpam-4658	61	12	cg	cg	NOUN
ejpam-4658	61	13	and	and	CCONJ
ejpam-4658	61	14	ch	ch	NOUN
ejpam-4658	61	15	are	be	AUX
ejpam-4658	61	16	supercliques	superclique	NOUN
ejpam-4658	61	17	in	in	ADP
ejpam-4658	61	18	g	g	PROPN
ejpam-4658	61	19	and	and	CCONJ
ejpam-4658	61	20	h	h	NOUN
ejpam-4658	61	21	respectively	respectively	ADV
ejpam-4658	61	22	.	.	PUNCT
ejpam-4658	62	1	lemma	lemma	PROPN
ejpam-4658	62	2	1	1	X
ejpam-4658	62	3	.	.	PUNCT
ejpam-4658	63	1	let	let	VERB
ejpam-4658	63	2	g	g	PRON
ejpam-4658	63	3	be	be	AUX
ejpam-4658	63	4	a	a	DET
ejpam-4658	63	5	nontrivial	nontrivial	ADJ
ejpam-4658	63	6	connected	connect	VERB
ejpam-4658	63	7	graph	graph	NOUN
ejpam-4658	63	8	with	with	ADP
ejpam-4658	63	9	diam(g	diam(g	NOUN
ejpam-4658	63	10	)	)	PUNCT
ejpam-4658	63	11	≤	≤	NOUN
ejpam-4658	63	12	2	2	NUM
ejpam-4658	63	13	.	.	PUNCT
ejpam-4658	64	1	then	then	ADV
ejpam-4658	64	2	s	s	VERB
ejpam-4658	64	3	=	=	SYM
ejpam-4658	64	4	v	v	NOUN
ejpam-4658	64	5	(	(	PUNCT
ejpam-4658	64	6	g)\c	g)\c	NOUN
ejpam-4658	64	7	is	be	AUX
ejpam-4658	64	8	a	a	DET
ejpam-4658	64	9	strong	strong	ADJ
ejpam-4658	64	10	resolving	resolving	NOUN
ejpam-4658	64	11	set	set	NOUN
ejpam-4658	64	12	of	of	ADP
ejpam-4658	64	13	g	g	PROPN
ejpam-4658	64	14	if	if	SCONJ
ejpam-4658	65	1	and	and	CCONJ
ejpam-4658	65	2	only	only	ADV
ejpam-4658	65	3	if	if	SCONJ
ejpam-4658	65	4	c	c	NOUN
ejpam-4658	65	5	=	=	SYM
ejpam-4658	65	6	∅	∅	NOUN
ejpam-4658	65	7	or	or	CCONJ
ejpam-4658	65	8	c	c	NOUN
ejpam-4658	65	9	is	be	AUX
ejpam-4658	65	10	a	a	DET
ejpam-4658	65	11	superclique	superclique	NOUN
ejpam-4658	65	12	in	in	ADP
ejpam-4658	65	13	g.	g.	PROPN
ejpam-4658	65	14	in	in	ADP
ejpam-4658	65	15	particular	particular	ADJ
ejpam-4658	65	16	,	,	PUNCT
ejpam-4658	65	17	sdim(g	sdim(g	PROPN
ejpam-4658	65	18	)	)	PUNCT
ejpam-4658	65	19	=	=	SYM
ejpam-4658	65	20	|v	|v	PROPN
ejpam-4658	65	21	(	(	PUNCT
ejpam-4658	65	22	g)|	g)|	NOUN
ejpam-4658	65	23	−	−	NOUN
ejpam-4658	65	24	ωs(g	ωs(g	NUM
ejpam-4658	65	25	)	)	PUNCT
ejpam-4658	65	26	.	.	PUNCT
ejpam-4658	66	1	theorem	theorem	NOUN
ejpam-4658	66	2	2	2	NUM
ejpam-4658	66	3	.	.	PUNCT
ejpam-4658	67	1	let	let	VERB
ejpam-4658	67	2	g	g	PRON
ejpam-4658	67	3	be	be	AUX
ejpam-4658	67	4	a	a	DET
ejpam-4658	67	5	nontrivial	nontrivial	ADJ
ejpam-4658	67	6	connected	connect	VERB
ejpam-4658	67	7	graph	graph	NOUN
ejpam-4658	67	8	and	and	CCONJ
ejpam-4658	67	9	h	h	NOUN
ejpam-4658	67	10	a	a	DET
ejpam-4658	67	11	connected	connected	ADJ
ejpam-4658	67	12	graph	graph	NOUN
ejpam-4658	67	13	.	.	PUNCT
ejpam-4658	68	1	a	a	DET
ejpam-4658	68	2	proper	proper	ADJ
ejpam-4658	68	3	subset	subset	NOUN
ejpam-4658	68	4	s	s	NOUN
ejpam-4658	68	5	of	of	ADP
ejpam-4658	68	6	v	v	NOUN
ejpam-4658	68	7	(	(	PUNCT
ejpam-4658	68	8	g	g	PROPN
ejpam-4658	68	9	◦	◦	NOUN
ejpam-4658	68	10	h	h	NOUN
ejpam-4658	68	11	)	)	PUNCT
ejpam-4658	68	12	is	be	AUX
ejpam-4658	68	13	a	a	DET
ejpam-4658	68	14	strong	strong	ADJ
ejpam-4658	68	15	resolving	resolving	NOUN
ejpam-4658	68	16	set	set	NOUN
ejpam-4658	68	17	of	of	ADP
ejpam-4658	68	18	g	g	PROPN
ejpam-4658	68	19	◦	◦	NOUN
ejpam-4658	68	20	h	h	NOUN
ejpam-4658	68	21	if	if	SCONJ
ejpam-4658	69	1	and	and	CCONJ
ejpam-4658	69	2	only	only	ADV
ejpam-4658	69	3	if	if	SCONJ
ejpam-4658	69	4	one	one	NUM
ejpam-4658	69	5	of	of	ADP
ejpam-4658	69	6	the	the	DET
ejpam-4658	69	7	following	follow	VERB
ejpam-4658	69	8	holds	hold	VERB
ejpam-4658	69	9	:	:	PUNCT
ejpam-4658	69	10	(	(	PUNCT
ejpam-4658	69	11	i	i	NOUN
ejpam-4658	69	12	)	)	PUNCT
ejpam-4658	69	13	s	s	PART
ejpam-4658	69	14	=	=	PUNCT
ejpam-4658	69	15	a	a	DET
ejpam-4658	69	16	∪	∪	X
ejpam-4658	69	17	(	(	PUNCT
ejpam-4658	69	18	∪	∪	ADJ
ejpam-4658	69	19	u∈v	u∈v	NOUN
ejpam-4658	69	20	(	(	PUNCT
ejpam-4658	69	21	g	g	NOUN
ejpam-4658	69	22	)	)	PUNCT
ejpam-4658	69	23	v	v	NOUN
ejpam-4658	69	24	(	(	PUNCT
ejpam-4658	69	25	hu	hu	PROPN
ejpam-4658	69	26	)	)	PUNCT
ejpam-4658	69	27	)	)	PUNCT
ejpam-4658	69	28	where	where	SCONJ
ejpam-4658	69	29	a	a	DET
ejpam-4658	69	30	⊆	⊆	NUM
ejpam-4658	69	31	v	v	NOUN
ejpam-4658	69	32	(	(	PUNCT
ejpam-4658	69	33	g	g	NOUN
ejpam-4658	69	34	)	)	PUNCT
ejpam-4658	69	35	.	.	PUNCT
ejpam-4658	70	1	a.	a.	PROPN
ejpam-4658	70	2	h.	h.	PROPN
ejpam-4658	70	3	abragan	abragan	PROPN
ejpam-4658	70	4	,	,	PUNCT
ejpam-4658	70	5	h.	h.	PROPN
ejpam-4658	70	6	m.	m.	PROPN
ejpam-4658	70	7	rara	rara	PROPN
ejpam-4658	70	8	/	/	SYM
ejpam-4658	70	9	eur	eur	PROPN
ejpam-4658	70	10	.	.	PUNCT
ejpam-4658	71	1	j.	j.	PROPN
ejpam-4658	71	2	pure	pure	PROPN
ejpam-4658	71	3	appl	appl	PROPN
ejpam-4658	71	4	.	.	PROPN
ejpam-4658	71	5	math	math	PROPN
ejpam-4658	71	6	,	,	PUNCT
ejpam-4658	71	7	16	16	NUM
ejpam-4658	71	8	(	(	PUNCT
ejpam-4658	71	9	2	2	NUM
ejpam-4658	71	10	)	)	PUNCT
ejpam-4658	71	11	(	(	PUNCT
ejpam-4658	71	12	2023	2023	NUM
ejpam-4658	71	13	)	)	PUNCT
ejpam-4658	71	14	,	,	PUNCT
ejpam-4658	71	15	763	763	NUM
ejpam-4658	71	16	-	-	SYM
ejpam-4658	71	17	772	772	NUM
ejpam-4658	71	18	766	766	NUM
ejpam-4658	71	19	(	(	PUNCT
ejpam-4658	71	20	ii	ii	NOUN
ejpam-4658	71	21	)	)	PUNCT
ejpam-4658	71	22	s	s	PART
ejpam-4658	71	23	=	=	SYM
ejpam-4658	71	24	∪	∪	X
ejpam-4658	71	25	(	(	PUNCT
ejpam-4658	71	26	∪	∪	ADJ
ejpam-4658	71	27	u∈v	u∈v	NOUN
ejpam-4658	71	28	(	(	PUNCT
ejpam-4658	71	29	g)\{v	g)\{v	PROPN
ejpam-4658	71	30	}	}	PUNCT
ejpam-4658	71	31	v	v	PROPN
ejpam-4658	71	32	(	(	PUNCT
ejpam-4658	71	33	hu	hu	PROPN
ejpam-4658	71	34	)	)	PUNCT
ejpam-4658	71	35	)	)	PUNCT
ejpam-4658	71	36	∪bv	∪bv	NOUN
ejpam-4658	71	37	for	for	ADP
ejpam-4658	71	38	a	a	DET
ejpam-4658	71	39	unique	unique	ADJ
ejpam-4658	71	40	v	v	NOUN
ejpam-4658	71	41	in	in	ADP
ejpam-4658	71	42	v	v	NOUN
ejpam-4658	71	43	(	(	PUNCT
ejpam-4658	71	44	g	g	NOUN
ejpam-4658	71	45	)	)	PUNCT
ejpam-4658	71	46	,	,	PUNCT
ejpam-4658	71	47	where	where	SCONJ
ejpam-4658	71	48	a	a	DET
ejpam-4658	71	49	⊆	⊆	NUM
ejpam-4658	71	50	v	v	NOUN
ejpam-4658	71	51	(	(	PUNCT
ejpam-4658	71	52	g	g	NOUN
ejpam-4658	71	53	)	)	PUNCT
ejpam-4658	71	54	and	and	CCONJ
ejpam-4658	71	55	bv	bv	PROPN
ejpam-4658	71	56	is	be	AUX
ejpam-4658	71	57	a	a	DET
ejpam-4658	71	58	strong	strong	ADJ
ejpam-4658	71	59	resolving	resolving	NOUN
ejpam-4658	71	60	set	set	NOUN
ejpam-4658	71	61	of	of	ADP
ejpam-4658	71	62	hv	hv	PROPN
ejpam-4658	71	63	if	if	SCONJ
ejpam-4658	71	64	γ(h	γ(h	NOUN
ejpam-4658	71	65	)	)	PUNCT
ejpam-4658	71	66	=	=	SYM
ejpam-4658	71	67	1	1	NUM
ejpam-4658	71	68	or	or	CCONJ
ejpam-4658	71	69	bv	bv	PROPN
ejpam-4658	71	70	is	be	AUX
ejpam-4658	71	71	a	a	DET
ejpam-4658	71	72	resolving	resolving	NOUN
ejpam-4658	71	73	set	set	NOUN
ejpam-4658	71	74	of	of	ADP
ejpam-4658	71	75	{	{	PUNCT
ejpam-4658	71	76	v}+hv	v}+hv	PRON
ejpam-4658	71	77	if	if	SCONJ
ejpam-4658	71	78	γ(h	γ(h	NOUN
ejpam-4658	71	79	)	)	PUNCT
ejpam-4658	71	80	̸=	̸=	PROPN
ejpam-4658	71	81	1	1	NUM
ejpam-4658	71	82	.	.	PUNCT
ejpam-4658	72	1	remark	remark	NOUN
ejpam-4658	72	2	1	1	NUM
ejpam-4658	72	3	.	.	PUNCT
ejpam-4658	73	1	any	any	DET
ejpam-4658	73	2	superset	superset	NOUN
ejpam-4658	73	3	of	of	ADP
ejpam-4658	73	4	a	a	DET
ejpam-4658	73	5	strong	strong	ADJ
ejpam-4658	73	6	resolving	resolving	NOUN
ejpam-4658	73	7	set	set	NOUN
ejpam-4658	73	8	is	be	AUX
ejpam-4658	73	9	a	a	DET
ejpam-4658	73	10	strong	strong	ADJ
ejpam-4658	73	11	resolving	resolving	NOUN
ejpam-4658	73	12	set	set	NOUN
ejpam-4658	73	13	.	.	PUNCT
ejpam-4658	74	1	theorem	theorem	NOUN
ejpam-4658	74	2	3	3	X
ejpam-4658	74	3	.	.	PUNCT
ejpam-4658	75	1	let	let	VERB
ejpam-4658	75	2	g	g	PROPN
ejpam-4658	75	3	=	=	PROPN
ejpam-4658	75	4	kn	kn	PROPN
ejpam-4658	75	5	for	for	ADP
ejpam-4658	75	6	n	n	PROPN
ejpam-4658	75	7	>	>	SYM
ejpam-4658	75	8	1	1	NUM
ejpam-4658	75	9	and	and	CCONJ
ejpam-4658	75	10	h	h	DET
ejpam-4658	75	11	a	a	DET
ejpam-4658	75	12	nontrivial	nontrivial	ADJ
ejpam-4658	75	13	connected	connect	VERB
ejpam-4658	75	14	graph	graph	NOUN
ejpam-4658	75	15	with	with	ADP
ejpam-4658	75	16	γ(h	γ(h	NOUN
ejpam-4658	75	17	)	)	PUNCT
ejpam-4658	75	18	̸=	̸=	PROPN
ejpam-4658	75	19	1	1	NUM
ejpam-4658	75	20	.	.	PUNCT
ejpam-4658	76	1	a	a	DET
ejpam-4658	76	2	subset	subset	NOUN
ejpam-4658	76	3	s	s	X
ejpam-4658	76	4	of	of	ADP
ejpam-4658	76	5	v	v	NOUN
ejpam-4658	76	6	(	(	PUNCT
ejpam-4658	76	7	g[h	g[h	PROPN
ejpam-4658	76	8	]	]	PUNCT
ejpam-4658	76	9	)	)	PUNCT
ejpam-4658	76	10	is	be	AUX
ejpam-4658	76	11	a	a	DET
ejpam-4658	76	12	strong	strong	ADJ
ejpam-4658	76	13	resolving	resolving	NOUN
ejpam-4658	76	14	set	set	NOUN
ejpam-4658	76	15	of	of	ADP
ejpam-4658	76	16	g[h	g[h	NOUN
ejpam-4658	76	17	]	]	PUNCT
ejpam-4658	76	18	if	if	SCONJ
ejpam-4658	76	19	and	and	CCONJ
ejpam-4658	76	20	only	only	ADV
ejpam-4658	76	21	s	s	PART
ejpam-4658	76	22	=	=	SYM
ejpam-4658	76	23	v	v	PROPN
ejpam-4658	76	24	(	(	PUNCT
ejpam-4658	76	25	g[h])\(a×c	g[h])\(a×c	NOUN
ejpam-4658	76	26	)	)	PUNCT
ejpam-4658	76	27	,	,	PUNCT
ejpam-4658	76	28	where	where	SCONJ
ejpam-4658	76	29	a	a	PRON
ejpam-4658	76	30	is	be	AUX
ejpam-4658	76	31	a	a	DET
ejpam-4658	76	32	subset	subset	NOUN
ejpam-4658	76	33	of	of	ADP
ejpam-4658	76	34	v	v	NOUN
ejpam-4658	76	35	(	(	PUNCT
ejpam-4658	76	36	g	g	NOUN
ejpam-4658	76	37	)	)	PUNCT
ejpam-4658	76	38	and	and	CCONJ
ejpam-4658	76	39	c	c	NOUN
ejpam-4658	76	40	=	=	SYM
ejpam-4658	76	41	∅	∅	NOUN
ejpam-4658	76	42	or	or	CCONJ
ejpam-4658	76	43	c	c	NOUN
ejpam-4658	76	44	is	be	AUX
ejpam-4658	76	45	a	a	DET
ejpam-4658	76	46	superclique	superclique	NOUN
ejpam-4658	76	47	in	in	ADP
ejpam-4658	76	48	h.	h.	PROPN
ejpam-4658	76	49	3	3	NUM
ejpam-4658	76	50	.	.	PUNCT
ejpam-4658	76	51	preliminary	preliminary	ADJ
ejpam-4658	76	52	results	result	NOUN
ejpam-4658	76	53	this	this	DET
ejpam-4658	76	54	section	section	NOUN
ejpam-4658	76	55	introduces	introduce	VERB
ejpam-4658	76	56	the	the	DET
ejpam-4658	76	57	1	1	NUM
ejpam-4658	76	58	-	-	PUNCT
ejpam-4658	76	59	movable	movable	ADJ
ejpam-4658	76	60	strong	strong	ADJ
ejpam-4658	76	61	resolving	resolve	VERB
ejpam-4658	76	62	hop	hop	NOUN
ejpam-4658	76	63	domination	domination	NOUN
ejpam-4658	76	64	in	in	ADP
ejpam-4658	76	65	some	some	DET
ejpam-4658	76	66	graphs	graph	NOUN
ejpam-4658	76	67	.	.	PUNCT
ejpam-4658	77	1	it	it	PRON
ejpam-4658	77	2	also	also	ADV
ejpam-4658	77	3	characterizes	characterize	VERB
ejpam-4658	77	4	some	some	DET
ejpam-4658	77	5	graphs	graph	NOUN
ejpam-4658	77	6	in	in	ADP
ejpam-4658	77	7	terms	term	NOUN
ejpam-4658	77	8	of	of	ADP
ejpam-4658	77	9	its	its	PRON
ejpam-4658	77	10	1	1	NUM
ejpam-4658	77	11	-	-	PUNCT
ejpam-4658	77	12	movable	movable	ADJ
ejpam-4658	77	13	strong	strong	ADJ
ejpam-4658	77	14	resolving	resolve	VERB
ejpam-4658	77	15	hop	hop	NOUN
ejpam-4658	77	16	domination	domination	NOUN
ejpam-4658	77	17	number	number	NOUN
ejpam-4658	77	18	.	.	PUNCT
ejpam-4658	78	1	remark	remark	NOUN
ejpam-4658	78	2	2	2	NUM
ejpam-4658	78	3	.	.	PUNCT
ejpam-4658	79	1	every	every	DET
ejpam-4658	79	2	1	1	NUM
ejpam-4658	79	3	-	-	PUNCT
ejpam-4658	79	4	movable	movable	ADJ
ejpam-4658	79	5	strong	strong	ADJ
ejpam-4658	79	6	resolving	resolve	VERB
ejpam-4658	79	7	hop	hop	NOUN
ejpam-4658	79	8	dominating	dominating	NOUN
ejpam-4658	79	9	set	set	NOUN
ejpam-4658	79	10	of	of	ADP
ejpam-4658	79	11	a	a	DET
ejpam-4658	79	12	connected	connected	ADJ
ejpam-4658	79	13	graph	graph	NOUN
ejpam-4658	79	14	g	g	PROPN
ejpam-4658	79	15	is	be	AUX
ejpam-4658	79	16	a	a	DET
ejpam-4658	79	17	strong	strong	ADJ
ejpam-4658	79	18	resolving	resolve	VERB
ejpam-4658	79	19	hop	hop	NOUN
ejpam-4658	79	20	dominating	dominating	NOUN
ejpam-4658	79	21	set	set	VERB
ejpam-4658	79	22	in	in	ADP
ejpam-4658	79	23	g.	g.	PROPN
ejpam-4658	79	24	hence	hence	ADV
ejpam-4658	79	25	,	,	PUNCT
ejpam-4658	79	26	γsrh(g	γsrh(g	PROPN
ejpam-4658	79	27	)	)	PUNCT
ejpam-4658	79	28	≤	≤	NUM
ejpam-4658	79	29	γ1msrh(g	γ1msrh(g	NOUN
ejpam-4658	79	30	)	)	PUNCT
ejpam-4658	79	31	.	.	PUNCT
ejpam-4658	80	1	remark	remark	PROPN
ejpam-4658	80	2	3	3	NUM
ejpam-4658	80	3	.	.	PUNCT
ejpam-4658	81	1	the	the	DET
ejpam-4658	81	2	converse	converse	NOUN
ejpam-4658	81	3	of	of	ADP
ejpam-4658	81	4	remark	remark	NOUN
ejpam-4658	81	5	2	2	NUM
ejpam-4658	81	6	does	do	AUX
ejpam-4658	81	7	not	not	PART
ejpam-4658	81	8	hold	hold	VERB
ejpam-4658	81	9	.	.	PUNCT
ejpam-4658	82	1	to	to	PART
ejpam-4658	82	2	see	see	VERB
ejpam-4658	82	3	this	this	PRON
ejpam-4658	82	4	,	,	PUNCT
ejpam-4658	82	5	the	the	DET
ejpam-4658	82	6	set	set	NOUN
ejpam-4658	82	7	s	s	PART
ejpam-4658	82	8	=	=	NOUN
ejpam-4658	82	9	{	{	PUNCT
ejpam-4658	82	10	v1	v1	PROPN
ejpam-4658	82	11	,	,	PUNCT
ejpam-4658	82	12	v2	v2	PROPN
ejpam-4658	82	13	,	,	PUNCT
ejpam-4658	82	14	v3	v3	PROPN
ejpam-4658	82	15	}	}	PUNCT
ejpam-4658	82	16	of	of	ADP
ejpam-4658	82	17	the	the	DET
ejpam-4658	82	18	path	path	NOUN
ejpam-4658	82	19	p4	p4	NOUN
ejpam-4658	82	20	=	=	PUNCT
ejpam-4658	83	1	[	[	X
ejpam-4658	83	2	v1	v1	NOUN
ejpam-4658	83	3	,	,	PUNCT
ejpam-4658	83	4	v2	v2	PROPN
ejpam-4658	83	5	,	,	PUNCT
ejpam-4658	83	6	v3	v3	PROPN
ejpam-4658	83	7	,	,	PUNCT
ejpam-4658	83	8	v4	v4	PROPN
ejpam-4658	83	9	]	]	PUNCT
ejpam-4658	83	10	is	be	AUX
ejpam-4658	83	11	a	a	DET
ejpam-4658	83	12	strong	strong	ADJ
ejpam-4658	83	13	resolving	resolving	NOUN
ejpam-4658	83	14	dominating	dominating	NOUN
ejpam-4658	83	15	set	set	NOUN
ejpam-4658	83	16	of	of	ADP
ejpam-4658	83	17	p4	p4	ADJ
ejpam-4658	84	1	but	but	CCONJ
ejpam-4658	84	2	it	it	PRON
ejpam-4658	84	3	is	be	AUX
ejpam-4658	84	4	not	not	PART
ejpam-4658	84	5	a	a	DET
ejpam-4658	84	6	1	1	NUM
ejpam-4658	84	7	-	-	PUNCT
ejpam-4658	84	8	movable	movable	ADJ
ejpam-4658	84	9	strong	strong	ADJ
ejpam-4658	84	10	resolving	resolve	VERB
ejpam-4658	84	11	hop	hop	NOUN
ejpam-4658	84	12	dominating	dominating	NOUN
ejpam-4658	84	13	set	set	NOUN
ejpam-4658	84	14	since	since	SCONJ
ejpam-4658	84	15	s	s	PROPN
ejpam-4658	84	16	\	\	PROPN
ejpam-4658	84	17	{	{	PUNCT
ejpam-4658	84	18	v1	v1	NOUN
ejpam-4658	84	19	}	}	PUNCT
ejpam-4658	84	20	is	be	AUX
ejpam-4658	84	21	not	not	PART
ejpam-4658	84	22	a	a	DET
ejpam-4658	84	23	strong	strong	ADJ
ejpam-4658	84	24	resolving	resolving	NOUN
ejpam-4658	84	25	set	set	NOUN
ejpam-4658	84	26	of	of	ADP
ejpam-4658	84	27	p4	p4	ADJ
ejpam-4658	84	28	.	.	PUNCT
ejpam-4658	85	1	proposition	proposition	NOUN
ejpam-4658	85	2	1	1	NUM
ejpam-4658	85	3	.	.	PUNCT
ejpam-4658	86	1	any	any	DET
ejpam-4658	86	2	superset	superset	NOUN
ejpam-4658	86	3	of	of	ADP
ejpam-4658	86	4	a	a	DET
ejpam-4658	86	5	1	1	NUM
ejpam-4658	86	6	-	-	PUNCT
ejpam-4658	86	7	movable	movable	ADJ
ejpam-4658	86	8	strong	strong	ADJ
ejpam-4658	86	9	resolving	resolve	VERB
ejpam-4658	86	10	hop	hop	NOUN
ejpam-4658	86	11	dominating	dominating	NOUN
ejpam-4658	86	12	set	set	NOUN
ejpam-4658	86	13	is	be	AUX
ejpam-4658	86	14	a	a	DET
ejpam-4658	86	15	1	1	NUM
ejpam-4658	86	16	-	-	PUNCT
ejpam-4658	86	17	movable	movable	ADJ
ejpam-4658	86	18	strong	strong	ADJ
ejpam-4658	86	19	resolving	resolve	VERB
ejpam-4658	86	20	dominating	dominating	NOUN
ejpam-4658	86	21	set	set	NOUN
ejpam-4658	86	22	.	.	PUNCT
ejpam-4658	87	1	proof	proof	NOUN
ejpam-4658	87	2	:	:	PUNCT
ejpam-4658	87	3	let	let	VERB
ejpam-4658	87	4	s	s	PRON
ejpam-4658	87	5	be	be	AUX
ejpam-4658	87	6	a	a	DET
ejpam-4658	87	7	1	1	NUM
ejpam-4658	87	8	-	-	PUNCT
ejpam-4658	87	9	movable	movable	ADJ
ejpam-4658	87	10	strong	strong	ADJ
ejpam-4658	87	11	resolving	resolve	VERB
ejpam-4658	87	12	hop	hop	NOUN
ejpam-4658	87	13	dominating	dominating	NOUN
ejpam-4658	87	14	set	set	NOUN
ejpam-4658	87	15	of	of	ADP
ejpam-4658	87	16	g	g	PROPN
ejpam-4658	87	17	and	and	CCONJ
ejpam-4658	87	18	s	s	NOUN
ejpam-4658	87	19	⊆	⊆	NUM
ejpam-4658	87	20	s′.	s′.	PROPN
ejpam-4658	87	21	then	then	ADV
ejpam-4658	87	22	s	s	VERB
ejpam-4658	87	23	is	be	AUX
ejpam-4658	87	24	a	a	DET
ejpam-4658	87	25	strong	strong	ADJ
ejpam-4658	87	26	resolving	resolving	NOUN
ejpam-4658	87	27	set	set	NOUN
ejpam-4658	87	28	.	.	PUNCT
ejpam-4658	88	1	by	by	ADP
ejpam-4658	88	2	remark	remark	NOUN
ejpam-4658	88	3	1	1	NUM
ejpam-4658	88	4	,	,	PUNCT
ejpam-4658	88	5	s′	s′	ADJ
ejpam-4658	88	6	is	be	AUX
ejpam-4658	88	7	a	a	DET
ejpam-4658	88	8	strong	strong	ADJ
ejpam-4658	88	9	resolving	resolving	NOUN
ejpam-4658	88	10	set	set	NOUN
ejpam-4658	88	11	of	of	ADP
ejpam-4658	88	12	g.	g.	PROPN
ejpam-4658	88	13	we	we	PRON
ejpam-4658	88	14	show	show	VERB
ejpam-4658	88	15	that	that	SCONJ
ejpam-4658	88	16	s′	s′	ADJ
ejpam-4658	88	17	is	be	AUX
ejpam-4658	88	18	a	a	DET
ejpam-4658	88	19	1	1	NUM
ejpam-4658	88	20	-	-	PUNCT
ejpam-4658	88	21	movable	movable	ADJ
ejpam-4658	88	22	strong	strong	ADJ
ejpam-4658	88	23	resolving	resolve	VERB
ejpam-4658	88	24	hop	hop	NOUN
ejpam-4658	88	25	dominating	dominating	NOUN
ejpam-4658	88	26	set	set	NOUN
ejpam-4658	88	27	of	of	ADP
ejpam-4658	88	28	g.	g.	PROPN
ejpam-4658	88	29	let	let	VERB
ejpam-4658	88	30	x	x	SYM
ejpam-4658	88	31	∈	∈	PROPN
ejpam-4658	88	32	s′.	s′.	PROPN
ejpam-4658	89	1	if	if	SCONJ
ejpam-4658	89	2	x	x	PROPN
ejpam-4658	89	3	∈	∈	PROPN
ejpam-4658	89	4	s	s	VERB
ejpam-4658	89	5	then	then	ADV
ejpam-4658	89	6	s	s	VERB
ejpam-4658	89	7	\	\	X
ejpam-4658	89	8	{	{	PUNCT
ejpam-4658	89	9	x	x	NOUN
ejpam-4658	89	10	}	}	PUNCT
ejpam-4658	89	11	⊆	⊆	NUM
ejpam-4658	89	12	s′	s′	ADJ
ejpam-4658	89	13	\	\	NOUN
ejpam-4658	89	14	{	{	PUNCT
ejpam-4658	89	15	x	x	NOUN
ejpam-4658	89	16	}	}	PUNCT
ejpam-4658	89	17	.	.	PUNCT
ejpam-4658	90	1	since	since	SCONJ
ejpam-4658	90	2	s	s	PROPN
ejpam-4658	90	3	is	be	AUX
ejpam-4658	90	4	a	a	DET
ejpam-4658	90	5	1	1	NUM
ejpam-4658	90	6	-	-	PUNCT
ejpam-4658	90	7	movable	movable	ADJ
ejpam-4658	90	8	strong	strong	ADJ
ejpam-4658	90	9	resolving	resolve	VERB
ejpam-4658	90	10	hop	hop	NOUN
ejpam-4658	90	11	dominating	dominating	NOUN
ejpam-4658	90	12	set	set	NOUN
ejpam-4658	90	13	of	of	ADP
ejpam-4658	90	14	g	g	PROPN
ejpam-4658	90	15	either	either	CCONJ
ejpam-4658	90	16	s	s	VERB
ejpam-4658	90	17	\	\	X
ejpam-4658	90	18	{	{	PUNCT
ejpam-4658	90	19	x	x	X
ejpam-4658	90	20	}	}	PUNCT
ejpam-4658	90	21	is	be	AUX
ejpam-4658	90	22	strong	strong	ADJ
ejpam-4658	90	23	resolving	resolve	VERB
ejpam-4658	90	24	hop	hop	NOUN
ejpam-4658	90	25	dominating	dominating	NOUN
ejpam-4658	90	26	set	set	NOUN
ejpam-4658	90	27	of	of	ADP
ejpam-4658	90	28	g	g	PROPN
ejpam-4658	90	29	or	or	CCONJ
ejpam-4658	90	30	∃y	∃y	PROPN
ejpam-4658	90	31	∈	∈	PROPN
ejpam-4658	90	32	(	(	PUNCT
ejpam-4658	90	33	v	v	NOUN
ejpam-4658	90	34	(	(	PUNCT
ejpam-4658	90	35	g	g	NOUN
ejpam-4658	90	36	)	)	PUNCT
ejpam-4658	90	37	\	\	PROPN
ejpam-4658	91	1	s	s	X
ejpam-4658	91	2	)	)	PUNCT
ejpam-4658	91	3	∩ng(x	∩ng(x	NOUN
ejpam-4658	91	4	)	)	PUNCT
ejpam-4658	91	5	such	such	ADJ
ejpam-4658	91	6	that	that	SCONJ
ejpam-4658	91	7	(	(	PUNCT
ejpam-4658	91	8	s	s	NOUN
ejpam-4658	91	9	\	\	X
ejpam-4658	91	10	{	{	PUNCT
ejpam-4658	91	11	x	x	NOUN
ejpam-4658	91	12	}	}	PUNCT
ejpam-4658	91	13	)	)	PUNCT
ejpam-4658	91	14	∪	∪	ADP
ejpam-4658	91	15	{	{	PUNCT
ejpam-4658	91	16	y	y	NOUN
ejpam-4658	91	17	}	}	PUNCT
ejpam-4658	91	18	is	be	AUX
ejpam-4658	91	19	a	a	DET
ejpam-4658	91	20	strong	strong	ADJ
ejpam-4658	91	21	resolving	resolve	VERB
ejpam-4658	91	22	hop	hop	NOUN
ejpam-4658	91	23	dominating	dominating	NOUN
ejpam-4658	91	24	set	set	NOUN
ejpam-4658	91	25	of	of	ADP
ejpam-4658	91	26	g.	g.	PROPN
ejpam-4658	91	27	if	if	SCONJ
ejpam-4658	91	28	s	s	NOUN
ejpam-4658	91	29	\	\	X
ejpam-4658	91	30	{	{	PUNCT
ejpam-4658	91	31	x	x	NOUN
ejpam-4658	91	32	}	}	PUNCT
ejpam-4658	91	33	is	be	AUX
ejpam-4658	91	34	a	a	DET
ejpam-4658	91	35	strong	strong	ADJ
ejpam-4658	91	36	resolving	resolve	VERB
ejpam-4658	91	37	hop	hop	NOUN
ejpam-4658	91	38	dominating	dominating	NOUN
ejpam-4658	91	39	set	set	NOUN
ejpam-4658	91	40	of	of	ADP
ejpam-4658	91	41	g	g	NOUN
ejpam-4658	91	42	,	,	PUNCT
ejpam-4658	91	43	then	then	ADV
ejpam-4658	91	44	s′	s′	ADJ
ejpam-4658	91	45	\	\	PUNCT
ejpam-4658	91	46	{	{	PUNCT
ejpam-4658	91	47	x	x	X
ejpam-4658	91	48	}	}	PUNCT
ejpam-4658	91	49	is	be	AUX
ejpam-4658	91	50	also	also	ADV
ejpam-4658	91	51	a	a	DET
ejpam-4658	91	52	strong	strong	ADJ
ejpam-4658	91	53	resolving	resolving	NOUN
ejpam-4658	91	54	set	set	NOUN
ejpam-4658	91	55	of	of	ADP
ejpam-4658	91	56	g	g	NOUN
ejpam-4658	91	57	by	by	ADP
ejpam-4658	91	58	remark	remark	NOUN
ejpam-4658	91	59	1	1	NUM
ejpam-4658	91	60	.	.	PUNCT
ejpam-4658	92	1	if	if	SCONJ
ejpam-4658	92	2	there	there	PRON
ejpam-4658	92	3	exists	exist	VERB
ejpam-4658	92	4	y	y	PROPN
ejpam-4658	92	5	∈	∈	PROPN
ejpam-4658	92	6	(	(	PUNCT
ejpam-4658	92	7	v	v	NOUN
ejpam-4658	92	8	(	(	PUNCT
ejpam-4658	92	9	g	g	NOUN
ejpam-4658	92	10	)	)	PUNCT
ejpam-4658	92	11	\	\	NOUN
ejpam-4658	93	1	s)∩ng(x	s)∩ng(x	X
ejpam-4658	93	2	)	)	PUNCT
ejpam-4658	93	3	such	such	ADJ
ejpam-4658	93	4	that	that	SCONJ
ejpam-4658	93	5	(	(	PUNCT
ejpam-4658	93	6	s	s	AUX
ejpam-4658	93	7	\	\	X
ejpam-4658	93	8	{	{	PUNCT
ejpam-4658	93	9	x})∪	x})∪	PROPN
ejpam-4658	93	10	{	{	PUNCT
ejpam-4658	93	11	y	y	NOUN
ejpam-4658	93	12	}	}	PUNCT
ejpam-4658	93	13	is	be	AUX
ejpam-4658	93	14	a	a	DET
ejpam-4658	93	15	strong	strong	ADJ
ejpam-4658	93	16	resolving	resolve	VERB
ejpam-4658	93	17	hop	hop	NOUN
ejpam-4658	93	18	dominating	dominating	NOUN
ejpam-4658	93	19	set	set	NOUN
ejpam-4658	93	20	of	of	ADP
ejpam-4658	93	21	g	g	NOUN
ejpam-4658	93	22	,	,	PUNCT
ejpam-4658	93	23	then	then	ADV
ejpam-4658	93	24	(	(	PUNCT
ejpam-4658	93	25	s	s	NOUN
ejpam-4658	93	26	\	\	X
ejpam-4658	93	27	{	{	PUNCT
ejpam-4658	93	28	x	x	NOUN
ejpam-4658	93	29	}	}	PUNCT
ejpam-4658	93	30	)	)	PUNCT
ejpam-4658	93	31	∪	∪	ADP
ejpam-4658	93	32	{	{	PUNCT
ejpam-4658	93	33	y	y	NOUN
ejpam-4658	93	34	}	}	PUNCT
ejpam-4658	93	35	⊆	⊆	NUM
ejpam-4658	93	36	(	(	PUNCT
ejpam-4658	93	37	s′	s′	X
ejpam-4658	93	38	\	\	NOUN
ejpam-4658	93	39	{	{	PUNCT
ejpam-4658	93	40	x	x	NOUN
ejpam-4658	93	41	}	}	PUNCT
ejpam-4658	93	42	)	)	PUNCT
ejpam-4658	93	43	∪	∪	ADP
ejpam-4658	93	44	{	{	PUNCT
ejpam-4658	93	45	y	y	NOUN
ejpam-4658	93	46	}	}	PUNCT
ejpam-4658	93	47	.	.	PUNCT
ejpam-4658	94	1	it	it	PRON
ejpam-4658	94	2	follows	follow	VERB
ejpam-4658	94	3	that	that	SCONJ
ejpam-4658	94	4	(	(	PUNCT
ejpam-4658	94	5	s′	s′	X
ejpam-4658	94	6	\	\	NOUN
ejpam-4658	94	7	{	{	PUNCT
ejpam-4658	94	8	x	x	NOUN
ejpam-4658	94	9	}	}	PUNCT
ejpam-4658	94	10	)	)	PUNCT
ejpam-4658	94	11	∪	∪	SCONJ
ejpam-4658	94	12	{	{	PUNCT
ejpam-4658	94	13	y	y	NOUN
ejpam-4658	94	14	}	}	PUNCT
ejpam-4658	94	15	is	be	AUX
ejpam-4658	94	16	strong	strong	ADJ
ejpam-4658	94	17	resolving	resolve	VERB
ejpam-4658	94	18	set	set	NOUN
ejpam-4658	94	19	of	of	ADP
ejpam-4658	94	20	g.	g.	PROPN
ejpam-4658	95	1	it	it	PRON
ejpam-4658	95	2	can	can	AUX
ejpam-4658	95	3	be	be	AUX
ejpam-4658	95	4	verified	verify	VERB
ejpam-4658	95	5	that	that	SCONJ
ejpam-4658	95	6	every	every	DET
ejpam-4658	95	7	superset	superset	NOUN
ejpam-4658	95	8	of	of	ADP
ejpam-4658	95	9	hop	hop	NOUN
ejpam-4658	95	10	dominating	dominating	NOUN
ejpam-4658	95	11	set	set	NOUN
ejpam-4658	95	12	is	be	AUX
ejpam-4658	95	13	hop	hop	NOUN
ejpam-4658	95	14	dominating	dominating	NOUN
ejpam-4658	95	15	.	.	PUNCT
ejpam-4658	96	1	therefore	therefore	ADV
ejpam-4658	96	2	,	,	PUNCT
ejpam-4658	96	3	s′	s′	PROPN
ejpam-4658	96	4	is	be	AUX
ejpam-4658	96	5	a	a	DET
ejpam-4658	96	6	1	1	NUM
ejpam-4658	96	7	-	-	PUNCT
ejpam-4658	96	8	movable	movable	ADJ
ejpam-4658	96	9	strong	strong	ADJ
ejpam-4658	96	10	resolving	resolve	VERB
ejpam-4658	96	11	hop	hop	NOUN
ejpam-4658	96	12	dominating	dominating	NOUN
ejpam-4658	96	13	set	set	NOUN
ejpam-4658	96	14	of	of	ADP
ejpam-4658	96	15	g.	g.	PROPN
ejpam-4658	96	16	proposition	proposition	PROPN
ejpam-4658	96	17	2	2	X
ejpam-4658	96	18	.	.	PUNCT
ejpam-4658	97	1	let	let	VERB
ejpam-4658	97	2	pn	pn	VERB
ejpam-4658	97	3	=	=	PUNCT
ejpam-4658	98	1	[	[	X
ejpam-4658	98	2	v1	v1	NOUN
ejpam-4658	98	3	,	,	PUNCT
ejpam-4658	98	4	v2	v2	NOUN
ejpam-4658	98	5	,	,	PUNCT
ejpam-4658	98	6	.	.	PUNCT
ejpam-4658	98	7	.	.	PUNCT
ejpam-4658	98	8	.	.	PUNCT
ejpam-4658	99	1	,	,	PUNCT
ejpam-4658	99	2	vn	vn	X
ejpam-4658	99	3	]	]	X
ejpam-4658	100	1	where	where	SCONJ
ejpam-4658	100	2	n	n	PRON
ejpam-4658	100	3	≥	≥	NOUN
ejpam-4658	100	4	1	1	NUM
ejpam-4658	100	5	.	.	PUNCT
ejpam-4658	100	6	if	if	SCONJ
ejpam-4658	100	7	a	a	DET
ejpam-4658	100	8	set	set	NOUN
ejpam-4658	100	9	s	s	VERB
ejpam-4658	100	10	⊆	⊆	NUM
ejpam-4658	100	11	v	v	NOUN
ejpam-4658	100	12	(	(	PUNCT
ejpam-4658	100	13	pn	pn	NOUN
ejpam-4658	100	14	)	)	PUNCT
ejpam-4658	100	15	is	be	AUX
ejpam-4658	100	16	a	a	DET
ejpam-4658	100	17	1	1	NUM
ejpam-4658	100	18	-	-	PUNCT
ejpam-4658	100	19	movable	movable	ADJ
ejpam-4658	100	20	strong	strong	ADJ
ejpam-4658	100	21	resolving	resolve	VERB
ejpam-4658	100	22	hop	hop	NOUN
ejpam-4658	100	23	dominating	dominating	NOUN
ejpam-4658	100	24	set	set	NOUN
ejpam-4658	100	25	of	of	ADP
ejpam-4658	100	26	pn	pn	PROPN
ejpam-4658	100	27	,	,	PUNCT
ejpam-4658	100	28	then	then	ADV
ejpam-4658	100	29	s	s	VERB
ejpam-4658	100	30	contains	contain	VERB
ejpam-4658	100	31	the	the	DET
ejpam-4658	100	32	vertices	vertex	NOUN
ejpam-4658	100	33	v1	v1	NOUN
ejpam-4658	100	34	and	and	CCONJ
ejpam-4658	100	35	vn	vn	PROPN
ejpam-4658	100	36	.	.	PUNCT
ejpam-4658	100	37	a.	a.	PROPN
ejpam-4658	100	38	h.	h.	PROPN
ejpam-4658	100	39	abragan	abragan	PROPN
ejpam-4658	100	40	,	,	PUNCT
ejpam-4658	100	41	h.	h.	PROPN
ejpam-4658	100	42	m.	m.	PROPN
ejpam-4658	100	43	rara	rara	PROPN
ejpam-4658	100	44	/	/	SYM
ejpam-4658	100	45	eur	eur	PROPN
ejpam-4658	100	46	.	.	PUNCT
ejpam-4658	101	1	j.	j.	PROPN
ejpam-4658	101	2	pure	pure	PROPN
ejpam-4658	101	3	appl	appl	PROPN
ejpam-4658	101	4	.	.	PROPN
ejpam-4658	101	5	math	math	PROPN
ejpam-4658	101	6	,	,	PUNCT
ejpam-4658	101	7	16	16	NUM
ejpam-4658	101	8	(	(	PUNCT
ejpam-4658	101	9	2	2	NUM
ejpam-4658	101	10	)	)	PUNCT
ejpam-4658	101	11	(	(	PUNCT
ejpam-4658	101	12	2023	2023	NUM
ejpam-4658	101	13	)	)	PUNCT
ejpam-4658	101	14	,	,	PUNCT
ejpam-4658	101	15	763	763	NUM
ejpam-4658	101	16	-	-	SYM
ejpam-4658	101	17	772	772	NUM
ejpam-4658	101	18	767	767	NUM
ejpam-4658	101	19	proof	proof	NOUN
ejpam-4658	101	20	:	:	PUNCT
ejpam-4658	101	21	suppose	suppose	VERB
ejpam-4658	101	22	s	s	NOUN
ejpam-4658	101	23	is	be	AUX
ejpam-4658	101	24	a	a	DET
ejpam-4658	101	25	1	1	NUM
ejpam-4658	101	26	-	-	PUNCT
ejpam-4658	101	27	movable	movable	ADJ
ejpam-4658	101	28	strong	strong	ADJ
ejpam-4658	101	29	resolving	resolve	VERB
ejpam-4658	101	30	hop	hop	NOUN
ejpam-4658	101	31	dominating	dominating	NOUN
ejpam-4658	101	32	set	set	NOUN
ejpam-4658	101	33	of	of	ADP
ejpam-4658	101	34	pn	pn	PROPN
ejpam-4658	101	35	and	and	CCONJ
ejpam-4658	101	36	suppose	suppose	VERB
ejpam-4658	101	37	that	that	SCONJ
ejpam-4658	101	38	s	s	VERB
ejpam-4658	101	39	does	do	AUX
ejpam-4658	101	40	not	not	PART
ejpam-4658	101	41	contain	contain	VERB
ejpam-4658	101	42	v1	v1	NOUN
ejpam-4658	101	43	or	or	CCONJ
ejpam-4658	101	44	vn	vn	NOUN
ejpam-4658	101	45	,	,	PUNCT
ejpam-4658	101	46	say	say	VERB
ejpam-4658	101	47	v1	v1	NOUN
ejpam-4658	101	48	.	.	PUNCT
ejpam-4658	102	1	since	since	SCONJ
ejpam-4658	102	2	v1mmdvn	v1mmdvn	NOUN
ejpam-4658	102	3	,	,	PUNCT
ejpam-4658	102	4	s	s	VERB
ejpam-4658	102	5	∩	∩	NOUN
ejpam-4658	102	6	{	{	PUNCT
ejpam-4658	102	7	v1	v1	NOUN
ejpam-4658	102	8	,	,	PUNCT
ejpam-4658	102	9	vn	vn	PROPN
ejpam-4658	102	10	}	}	PUNCT
ejpam-4658	102	11	̸=	̸=	PROPN
ejpam-4658	102	12	∅.	∅.	PRON
ejpam-4658	102	13	hence	hence	ADV
ejpam-4658	102	14	,	,	PUNCT
ejpam-4658	102	15	vn	vn	PROPN
ejpam-4658	102	16	∈	∈	PROPN
ejpam-4658	102	17	s.	s.	PROPN
ejpam-4658	102	18	this	this	PRON
ejpam-4658	102	19	implies	imply	VERB
ejpam-4658	102	20	that	that	SCONJ
ejpam-4658	102	21	s	s	VERB
ejpam-4658	102	22	\	\	PROPN
ejpam-4658	102	23	{	{	PUNCT
ejpam-4658	102	24	vn	vn	NOUN
ejpam-4658	102	25	}	}	PUNCT
ejpam-4658	102	26	and	and	CCONJ
ejpam-4658	102	27	(	(	PUNCT
ejpam-4658	102	28	s	s	X
ejpam-4658	102	29	\	\	X
ejpam-4658	102	30	{	{	PUNCT
ejpam-4658	102	31	vn	vn	NOUN
ejpam-4658	102	32	}	}	PUNCT
ejpam-4658	102	33	)	)	PUNCT
ejpam-4658	102	34	∪	∪	ADP
ejpam-4658	102	35	{	{	PUNCT
ejpam-4658	102	36	vn−1	vn−1	ADJ
ejpam-4658	102	37	}	}	PUNCT
ejpam-4658	102	38	are	be	AUX
ejpam-4658	102	39	not	not	PART
ejpam-4658	102	40	strong	strong	ADJ
ejpam-4658	102	41	resolving	resolving	NOUN
ejpam-4658	102	42	sets	set	NOUN
ejpam-4658	102	43	of	of	ADP
ejpam-4658	102	44	pn	pn	NOUN
ejpam-4658	102	45	,	,	PUNCT
ejpam-4658	102	46	a	a	DET
ejpam-4658	102	47	contradiction	contradiction	NOUN
ejpam-4658	102	48	.	.	PUNCT
ejpam-4658	103	1	therefore	therefore	ADV
ejpam-4658	103	2	,	,	PUNCT
ejpam-4658	103	3	s	s	PROPN
ejpam-4658	103	4	contains	contain	VERB
ejpam-4658	103	5	v1	v1	NOUN
ejpam-4658	103	6	and	and	CCONJ
ejpam-4658	103	7	vn	vn	NOUN
ejpam-4658	103	8	.	.	PUNCT
ejpam-4658	104	1	proposition	proposition	NOUN
ejpam-4658	104	2	3	3	NUM
ejpam-4658	104	3	.	.	PUNCT
ejpam-4658	105	1	let	let	VERB
ejpam-4658	105	2	g	g	PRON
ejpam-4658	105	3	be	be	AUX
ejpam-4658	105	4	a	a	DET
ejpam-4658	105	5	nontrival	nontrival	ADJ
ejpam-4658	105	6	connected	connected	ADJ
ejpam-4658	105	7	graph	graph	NOUN
ejpam-4658	105	8	with	with	ADP
ejpam-4658	105	9	diam(g	diam(g	NOUN
ejpam-4658	105	10	)	)	PUNCT
ejpam-4658	105	11	≤	≤	NOUN
ejpam-4658	105	12	2	2	NUM
ejpam-4658	105	13	and	and	CCONJ
ejpam-4658	105	14	γ(g	γ(g	PROPN
ejpam-4658	105	15	)	)	PUNCT
ejpam-4658	105	16	̸=	̸=	PROPN
ejpam-4658	105	17	1	1	NUM
ejpam-4658	105	18	.	.	PUNCT
ejpam-4658	106	1	then	then	ADV
ejpam-4658	106	2	s	s	VERB
ejpam-4658	106	3	=	=	SYM
ejpam-4658	106	4	v	v	PROPN
ejpam-4658	106	5	(	(	PUNCT
ejpam-4658	106	6	g	g	NOUN
ejpam-4658	106	7	)	)	PUNCT
ejpam-4658	106	8	\	\	PUNCT
ejpam-4658	107	1	c	c	NOUN
ejpam-4658	107	2	is	be	AUX
ejpam-4658	107	3	a	a	DET
ejpam-4658	107	4	1	1	NUM
ejpam-4658	107	5	-	-	PUNCT
ejpam-4658	107	6	movable	movable	ADJ
ejpam-4658	107	7	strong	strong	ADJ
ejpam-4658	107	8	resolving	resolve	VERB
ejpam-4658	107	9	hop	hop	NOUN
ejpam-4658	107	10	dominating	dominating	NOUN
ejpam-4658	107	11	set	set	NOUN
ejpam-4658	107	12	of	of	ADP
ejpam-4658	107	13	g	g	PROPN
ejpam-4658	107	14	if	if	SCONJ
ejpam-4658	108	1	and	and	CCONJ
ejpam-4658	108	2	only	only	ADV
ejpam-4658	108	3	if	if	SCONJ
ejpam-4658	108	4	c	c	NOUN
ejpam-4658	108	5	=	=	SYM
ejpam-4658	108	6	∅	∅	NOUN
ejpam-4658	108	7	or	or	CCONJ
ejpam-4658	108	8	c	c	NOUN
ejpam-4658	108	9	is	be	AUX
ejpam-4658	108	10	a	a	DET
ejpam-4658	108	11	hop	hop	NOUN
ejpam-4658	108	12	dominated	dominate	VERB
ejpam-4658	108	13	superclique	superclique	NOUN
ejpam-4658	108	14	in	in	ADP
ejpam-4658	108	15	g	g	PROPN
ejpam-4658	108	16	and	and	CCONJ
ejpam-4658	108	17	either	either	ADV
ejpam-4658	108	18	for	for	SCONJ
ejpam-4658	108	19	each	each	DET
ejpam-4658	108	20	x	x	SYM
ejpam-4658	108	21	∈	∈	PROPN
ejpam-4658	108	22	s	s	NOUN
ejpam-4658	108	23	,	,	PUNCT
ejpam-4658	108	24	c	c	PROPN
ejpam-4658	108	25	∪	∪	X
ejpam-4658	108	26	{	{	PUNCT
ejpam-4658	108	27	x	x	NOUN
ejpam-4658	108	28	}	}	PUNCT
ejpam-4658	108	29	is	be	AUX
ejpam-4658	108	30	a	a	DET
ejpam-4658	108	31	hop	hop	NOUN
ejpam-4658	108	32	dominated	dominate	VERB
ejpam-4658	108	33	superclique	superclique	NOUN
ejpam-4658	108	34	or	or	CCONJ
ejpam-4658	108	35	there	there	ADV
ejpam-4658	108	36	exists	exist	VERB
ejpam-4658	108	37	y	y	PROPN
ejpam-4658	108	38	∈	∈	PROPN
ejpam-4658	109	1	[	[	X
ejpam-4658	109	2	c	c	X
ejpam-4658	109	3	∩ng(x	∩ng(x	NOUN
ejpam-4658	109	4	)	)	PUNCT
ejpam-4658	109	5	]	]	PUNCT
ejpam-4658	109	6	such	such	ADJ
ejpam-4658	109	7	that	that	SCONJ
ejpam-4658	109	8	(	(	PUNCT
ejpam-4658	109	9	c	c	NOUN
ejpam-4658	109	10	\	\	PROPN
ejpam-4658	109	11	{	{	PUNCT
ejpam-4658	109	12	y	y	NOUN
ejpam-4658	109	13	}	}	PUNCT
ejpam-4658	109	14	)	)	PUNCT
ejpam-4658	109	15	∪	∪	ADP
ejpam-4658	109	16	{	{	PUNCT
ejpam-4658	109	17	x	x	NOUN
ejpam-4658	109	18	}	}	PUNCT
ejpam-4658	109	19	is	be	AUX
ejpam-4658	109	20	a	a	DET
ejpam-4658	109	21	hop	hop	NOUN
ejpam-4658	109	22	dominated	dominate	VERB
ejpam-4658	109	23	superclique	superclique	NOUN
ejpam-4658	109	24	in	in	ADP
ejpam-4658	109	25	g.	g.	PROPN
ejpam-4658	109	26	proof	proof	NOUN
ejpam-4658	109	27	:	:	PUNCT
ejpam-4658	109	28	suppose	suppose	VERB
ejpam-4658	109	29	s	s	VERB
ejpam-4658	109	30	=	=	SYM
ejpam-4658	109	31	v	v	PROPN
ejpam-4658	109	32	(	(	PUNCT
ejpam-4658	109	33	g	g	NOUN
ejpam-4658	109	34	)	)	PUNCT
ejpam-4658	109	35	\	\	PUNCT
ejpam-4658	110	1	c	c	NOUN
ejpam-4658	110	2	is	be	AUX
ejpam-4658	110	3	a	a	DET
ejpam-4658	110	4	1	1	NUM
ejpam-4658	110	5	-	-	PUNCT
ejpam-4658	110	6	movable	movable	ADJ
ejpam-4658	110	7	strong	strong	ADJ
ejpam-4658	110	8	resolving	resolve	VERB
ejpam-4658	110	9	hop	hop	NOUN
ejpam-4658	110	10	dominating	dominating	NOUN
ejpam-4658	110	11	set	set	NOUN
ejpam-4658	110	12	of	of	ADP
ejpam-4658	110	13	g.	g.	PROPN
ejpam-4658	111	1	then	then	ADV
ejpam-4658	111	2	s	s	VERB
ejpam-4658	111	3	is	be	AUX
ejpam-4658	111	4	strong	strong	ADJ
ejpam-4658	111	5	resolving	resolve	VERB
ejpam-4658	111	6	set	set	VERB
ejpam-4658	111	7	in	in	ADP
ejpam-4658	111	8	g.	g.	PROPN
ejpam-4658	111	9	by	by	ADP
ejpam-4658	111	10	lemma	lemma	PROPN
ejpam-4658	111	11	1	1	NUM
ejpam-4658	111	12	,	,	PUNCT
ejpam-4658	111	13	c	c	NOUN
ejpam-4658	111	14	=	=	SYM
ejpam-4658	111	15	∅	∅	NOUN
ejpam-4658	111	16	or	or	CCONJ
ejpam-4658	111	17	c	c	NOUN
ejpam-4658	111	18	is	be	AUX
ejpam-4658	111	19	a	a	DET
ejpam-4658	111	20	dominated	dominate	VERB
ejpam-4658	111	21	superclique	superclique	NOUN
ejpam-4658	111	22	in	in	ADP
ejpam-4658	111	23	g.	g.	PROPN
ejpam-4658	111	24	we	we	PRON
ejpam-4658	111	25	claim	claim	VERB
ejpam-4658	111	26	that	that	SCONJ
ejpam-4658	111	27	c	c	PROPN
ejpam-4658	111	28	is	be	AUX
ejpam-4658	111	29	a	a	DET
ejpam-4658	111	30	hop	hop	NOUN
ejpam-4658	111	31	dominated	dominate	VERB
ejpam-4658	111	32	superclique	superclique	NOUN
ejpam-4658	111	33	.	.	PUNCT
ejpam-4658	112	1	let	let	VERB
ejpam-4658	112	2	z	z	PROPN
ejpam-4658	112	3	∈	∈	PROPN
ejpam-4658	112	4	c.	c.	NOUN
ejpam-4658	113	1	then	then	ADV
ejpam-4658	113	2	z	z	PROPN
ejpam-4658	113	3	/∈	/∈	PUNCT
ejpam-4658	113	4	s.	s.	PROPN
ejpam-4658	113	5	since	since	SCONJ
ejpam-4658	113	6	s	s	PROPN
ejpam-4658	113	7	is	be	AUX
ejpam-4658	113	8	hop	hop	NOUN
ejpam-4658	113	9	dominating	dominating	NOUN
ejpam-4658	113	10	,	,	PUNCT
ejpam-4658	113	11	there	there	PRON
ejpam-4658	113	12	exists	exist	VERB
ejpam-4658	113	13	y	y	PROPN
ejpam-4658	113	14	∈	∈	PROPN
ejpam-4658	113	15	(	(	PUNCT
ejpam-4658	113	16	s	s	NOUN
ejpam-4658	113	17	\c	\c	NOUN
ejpam-4658	113	18	)	)	PUNCT
ejpam-4658	113	19	such	such	ADJ
ejpam-4658	113	20	that	that	SCONJ
ejpam-4658	113	21	dg(z	dg(z	NOUN
ejpam-4658	113	22	,	,	PUNCT
ejpam-4658	113	23	y	y	NOUN
ejpam-4658	113	24	)	)	PUNCT
ejpam-4658	113	25	=	=	SYM
ejpam-4658	114	1	2	2	X
ejpam-4658	114	2	.	.	X
ejpam-4658	115	1	hence	hence	ADV
ejpam-4658	115	2	,	,	PUNCT
ejpam-4658	115	3	c	c	PROPN
ejpam-4658	115	4	is	be	AUX
ejpam-4658	115	5	a	a	DET
ejpam-4658	115	6	hop	hop	NOUN
ejpam-4658	115	7	dominated	dominate	VERB
ejpam-4658	115	8	superclique	superclique	NOUN
ejpam-4658	115	9	.	.	PUNCT
ejpam-4658	116	1	let	let	VERB
ejpam-4658	116	2	x	x	SYM
ejpam-4658	116	3	∈	∈	PROPN
ejpam-4658	116	4	s.	s.	PROPN
ejpam-4658	116	5	since	since	SCONJ
ejpam-4658	116	6	s	s	PROPN
ejpam-4658	116	7	is	be	AUX
ejpam-4658	116	8	a	a	DET
ejpam-4658	116	9	1	1	NUM
ejpam-4658	116	10	-	-	PUNCT
ejpam-4658	116	11	movable	movable	ADJ
ejpam-4658	116	12	strong	strong	ADJ
ejpam-4658	116	13	resolving	resolve	VERB
ejpam-4658	116	14	hop	hop	NOUN
ejpam-4658	116	15	dominating	dominating	NOUN
ejpam-4658	116	16	set	set	NOUN
ejpam-4658	116	17	,	,	PUNCT
ejpam-4658	116	18	either	either	CCONJ
ejpam-4658	116	19	s	s	VERB
ejpam-4658	116	20	\	\	X
ejpam-4658	116	21	{	{	PUNCT
ejpam-4658	116	22	x	x	X
ejpam-4658	116	23	}	}	PUNCT
ejpam-4658	116	24	is	be	AUX
ejpam-4658	116	25	strong	strong	ADJ
ejpam-4658	116	26	resolving	resolve	VERB
ejpam-4658	116	27	hop	hop	NOUN
ejpam-4658	116	28	dominating	dominating	NOUN
ejpam-4658	116	29	or	or	CCONJ
ejpam-4658	116	30	there	there	ADV
ejpam-4658	116	31	exists	exist	VERB
ejpam-4658	116	32	y	y	PROPN
ejpam-4658	116	33	∈	∈	PROPN
ejpam-4658	117	1	[	[	X
ejpam-4658	117	2	(	(	PUNCT
ejpam-4658	117	3	v	v	NOUN
ejpam-4658	117	4	(	(	PUNCT
ejpam-4658	117	5	g	g	NOUN
ejpam-4658	117	6	)	)	PUNCT
ejpam-4658	117	7	\	\	PROPN
ejpam-4658	117	8	s	s	X
ejpam-4658	117	9	)	)	PUNCT
ejpam-4658	117	10	∩ng(x	∩ng(x	NOUN
ejpam-4658	117	11	)	)	PUNCT
ejpam-4658	117	12	]	]	PUNCT
ejpam-4658	118	1	such	such	ADJ
ejpam-4658	118	2	that	that	SCONJ
ejpam-4658	118	3	(	(	PUNCT
ejpam-4658	118	4	s	s	NOUN
ejpam-4658	118	5	\	\	X
ejpam-4658	118	6	{	{	PUNCT
ejpam-4658	118	7	x	x	NOUN
ejpam-4658	118	8	}	}	PUNCT
ejpam-4658	118	9	)	)	PUNCT
ejpam-4658	118	10	∪	∪	ADP
ejpam-4658	118	11	{	{	PUNCT
ejpam-4658	118	12	y	y	NOUN
ejpam-4658	118	13	}	}	PUNCT
ejpam-4658	118	14	is	be	AUX
ejpam-4658	118	15	a	a	DET
ejpam-4658	118	16	strong	strong	ADJ
ejpam-4658	118	17	resolving	resolve	VERB
ejpam-4658	118	18	hop	hop	NOUN
ejpam-4658	118	19	dominating	dominating	NOUN
ejpam-4658	118	20	set	set	NOUN
ejpam-4658	118	21	of	of	ADP
ejpam-4658	118	22	g.	g.	PROPN
ejpam-4658	118	23	since	since	SCONJ
ejpam-4658	118	24	s	s	PROPN
ejpam-4658	118	25	\	\	X
ejpam-4658	118	26	{	{	PUNCT
ejpam-4658	118	27	x	x	NOUN
ejpam-4658	118	28	}	}	PUNCT
ejpam-4658	118	29	=	=	SYM
ejpam-4658	118	30	v	v	NOUN
ejpam-4658	118	31	(	(	PUNCT
ejpam-4658	118	32	g	g	NOUN
ejpam-4658	118	33	)	)	PUNCT
ejpam-4658	118	34	\	\	PUNCT
ejpam-4658	119	1	(	(	PUNCT
ejpam-4658	119	2	c	c	NOUN
ejpam-4658	119	3	∪	∪	X
ejpam-4658	119	4	{	{	PUNCT
ejpam-4658	119	5	x	x	NOUN
ejpam-4658	119	6	}	}	PUNCT
ejpam-4658	119	7	)	)	PUNCT
ejpam-4658	119	8	and	and	CCONJ
ejpam-4658	119	9	(	(	PUNCT
ejpam-4658	119	10	s	s	NOUN
ejpam-4658	119	11	\	\	X
ejpam-4658	119	12	{	{	PUNCT
ejpam-4658	119	13	x})∪	x})∪	PROPN
ejpam-4658	119	14	{	{	PUNCT
ejpam-4658	119	15	y	y	PROPN
ejpam-4658	119	16	}	}	PUNCT
ejpam-4658	119	17	=	=	PUNCT
ejpam-4658	120	1	[	[	X
ejpam-4658	120	2	v	v	X
ejpam-4658	120	3	(	(	PUNCT
ejpam-4658	120	4	g	g	NOUN
ejpam-4658	120	5	)	)	PUNCT
ejpam-4658	120	6	\c	\c	PROPN
ejpam-4658	120	7	\	\	NOUN
ejpam-4658	120	8	{	{	PUNCT
ejpam-4658	120	9	x}]∪	x}]∪	PROPN
ejpam-4658	120	10	{	{	PUNCT
ejpam-4658	120	11	y	y	NOUN
ejpam-4658	120	12	}	}	PUNCT
ejpam-4658	120	13	,	,	PUNCT
ejpam-4658	120	14	c	c	PROPN
ejpam-4658	120	15	∪	∪	X
ejpam-4658	120	16	{	{	PUNCT
ejpam-4658	120	17	x	x	NOUN
ejpam-4658	120	18	}	}	PUNCT
ejpam-4658	120	19	is	be	AUX
ejpam-4658	120	20	a	a	DET
ejpam-4658	120	21	hop	hop	NOUN
ejpam-4658	120	22	dominated	dominate	VERB
ejpam-4658	120	23	superclique	superclique	NOUN
ejpam-4658	120	24	or	or	CCONJ
ejpam-4658	120	25	(	(	PUNCT
ejpam-4658	120	26	c	c	NOUN
ejpam-4658	120	27	\	\	PROPN
ejpam-4658	120	28	y	y	PROPN
ejpam-4658	120	29	)	)	PUNCT
ejpam-4658	120	30	∪	∪	NOUN
ejpam-4658	120	31	{	{	PUNCT
ejpam-4658	120	32	x	x	NOUN
ejpam-4658	120	33	}	}	PUNCT
ejpam-4658	120	34	is	be	AUX
ejpam-4658	120	35	a	a	DET
ejpam-4658	120	36	hop	hop	NOUN
ejpam-4658	120	37	dominated	dominate	VERB
ejpam-4658	120	38	superclique	superclique	NOUN
ejpam-4658	120	39	in	in	ADP
ejpam-4658	120	40	g.	g.	PROPN
ejpam-4658	120	41	for	for	ADP
ejpam-4658	120	42	the	the	DET
ejpam-4658	120	43	converse	converse	NOUN
ejpam-4658	120	44	,	,	PUNCT
ejpam-4658	120	45	suppose	suppose	VERB
ejpam-4658	120	46	c	c	NOUN
ejpam-4658	120	47	=	=	PUNCT
ejpam-4658	120	48	∅.	∅.	NOUN
ejpam-4658	120	49	then	then	ADV
ejpam-4658	120	50	s	s	PART
ejpam-4658	120	51	=	=	SYM
ejpam-4658	120	52	v	v	PROPN
ejpam-4658	120	53	(	(	PUNCT
ejpam-4658	120	54	g	g	NOUN
ejpam-4658	120	55	)	)	PUNCT
ejpam-4658	120	56	is	be	AUX
ejpam-4658	120	57	a	a	DET
ejpam-4658	120	58	strong	strong	ADJ
ejpam-4658	120	59	resolving	resolve	VERB
ejpam-4658	120	60	hop	hop	NOUN
ejpam-4658	120	61	dominating	dominating	NOUN
ejpam-4658	120	62	set	set	NOUN
ejpam-4658	120	63	of	of	ADP
ejpam-4658	120	64	g.	g.	PROPN
ejpam-4658	120	65	thus	thus	ADV
ejpam-4658	120	66	,	,	PUNCT
ejpam-4658	120	67	s	s	VERB
ejpam-4658	120	68	\	\	X
ejpam-4658	120	69	{	{	PUNCT
ejpam-4658	120	70	x	x	NOUN
ejpam-4658	120	71	}	}	PUNCT
ejpam-4658	120	72	=	=	SYM
ejpam-4658	120	73	v	v	NOUN
ejpam-4658	120	74	(	(	PUNCT
ejpam-4658	120	75	g	g	NOUN
ejpam-4658	120	76	)	)	PUNCT
ejpam-4658	120	77	\	\	NOUN
ejpam-4658	120	78	{	{	PUNCT
ejpam-4658	120	79	x	x	NOUN
ejpam-4658	120	80	}	}	PUNCT
ejpam-4658	120	81	is	be	AUX
ejpam-4658	120	82	a	a	DET
ejpam-4658	120	83	strong	strong	ADJ
ejpam-4658	120	84	resolving	resolve	VERB
ejpam-4658	120	85	hop	hop	NOUN
ejpam-4658	120	86	dominating	dominating	NOUN
ejpam-4658	120	87	since	since	SCONJ
ejpam-4658	120	88	{	{	PUNCT
ejpam-4658	120	89	x	x	X
ejpam-4658	120	90	}	}	PUNCT
ejpam-4658	120	91	is	be	AUX
ejpam-4658	120	92	a	a	DET
ejpam-4658	120	93	superclique	superclique	NOUN
ejpam-4658	120	94	for	for	ADP
ejpam-4658	120	95	each	each	DET
ejpam-4658	120	96	x	x	SYM
ejpam-4658	120	97	∈	∈	PROPN
ejpam-4658	120	98	v	v	NOUN
ejpam-4658	120	99	(	(	PUNCT
ejpam-4658	120	100	g	g	NOUN
ejpam-4658	120	101	)	)	PUNCT
ejpam-4658	120	102	.	.	PUNCT
ejpam-4658	121	1	since	since	SCONJ
ejpam-4658	121	2	γ(g	γ(g	PROPN
ejpam-4658	121	3	)	)	PUNCT
ejpam-4658	121	4	̸=	̸=	PROPN
ejpam-4658	121	5	1	1	NUM
ejpam-4658	121	6	,	,	PUNCT
ejpam-4658	121	7	a	a	DET
ejpam-4658	121	8	vertex	vertex	NOUN
ejpam-4658	121	9	y	y	PROPN
ejpam-4658	121	10	∈	∈	PROPN
ejpam-4658	121	11	s	s	PART
ejpam-4658	121	12	\	\	X
ejpam-4658	121	13	{	{	PUNCT
ejpam-4658	121	14	x	x	NOUN
ejpam-4658	121	15	}	}	PUNCT
ejpam-4658	121	16	exists	exist	VERB
ejpam-4658	121	17	such	such	ADJ
ejpam-4658	121	18	that	that	DET
ejpam-4658	121	19	dg(x	dg(x	PROPN
ejpam-4658	121	20	,	,	PUNCT
ejpam-4658	121	21	y	y	NOUN
ejpam-4658	121	22	)	)	PUNCT
ejpam-4658	122	1	=	=	SYM
ejpam-4658	122	2	2	2	X
ejpam-4658	122	3	.	.	X
ejpam-4658	123	1	hence	hence	ADV
ejpam-4658	123	2	,	,	PUNCT
ejpam-4658	123	3	s	s	VERB
ejpam-4658	123	4	is	be	AUX
ejpam-4658	123	5	a	a	DET
ejpam-4658	123	6	hop	hop	NOUN
ejpam-4658	123	7	dominating	dominating	NOUN
ejpam-4658	123	8	.	.	PUNCT
ejpam-4658	124	1	so	so	ADV
ejpam-4658	124	2	,	,	PUNCT
ejpam-4658	124	3	suppose	suppose	VERB
ejpam-4658	124	4	c	c	NOUN
ejpam-4658	124	5	is	be	AUX
ejpam-4658	124	6	a	a	DET
ejpam-4658	124	7	hop	hop	NOUN
ejpam-4658	124	8	dominated	dominate	VERB
ejpam-4658	124	9	superclique	superclique	NOUN
ejpam-4658	124	10	in	in	ADP
ejpam-4658	124	11	g	g	PROPN
ejpam-4658	124	12	and	and	CCONJ
ejpam-4658	124	13	for	for	SCONJ
ejpam-4658	124	14	each	each	DET
ejpam-4658	124	15	x	x	SYM
ejpam-4658	124	16	∈	∈	PROPN
ejpam-4658	124	17	s	s	VERB
ejpam-4658	124	18	either	either	CCONJ
ejpam-4658	124	19	c	c	PROPN
ejpam-4658	124	20	∪	∪	X
ejpam-4658	124	21	{	{	PUNCT
ejpam-4658	124	22	x	x	NOUN
ejpam-4658	124	23	}	}	PUNCT
ejpam-4658	124	24	is	be	AUX
ejpam-4658	124	25	a	a	DET
ejpam-4658	124	26	hop	hop	NOUN
ejpam-4658	124	27	dominated	dominate	VERB
ejpam-4658	124	28	superclique	superclique	NOUN
ejpam-4658	124	29	or	or	CCONJ
ejpam-4658	124	30	there	there	ADV
ejpam-4658	124	31	exists	exist	VERB
ejpam-4658	124	32	y	y	PROPN
ejpam-4658	124	33	∈	∈	PROPN
ejpam-4658	125	1	[	[	X
ejpam-4658	125	2	c	c	X
ejpam-4658	125	3	∩ng(x	∩ng(x	NOUN
ejpam-4658	125	4	)	)	PUNCT
ejpam-4658	125	5	]	]	PUNCT
ejpam-4658	125	6	such	such	ADJ
ejpam-4658	125	7	that	that	SCONJ
ejpam-4658	125	8	(	(	PUNCT
ejpam-4658	125	9	c	c	NOUN
ejpam-4658	125	10	\{y})∪{x	\{y})∪{x	PROPN
ejpam-4658	125	11	}	}	PUNCT
ejpam-4658	125	12	is	be	AUX
ejpam-4658	125	13	a	a	DET
ejpam-4658	125	14	hop	hop	NOUN
ejpam-4658	125	15	dominated	dominate	VERB
ejpam-4658	125	16	superclique	superclique	NOUN
ejpam-4658	125	17	.	.	PUNCT
ejpam-4658	126	1	hence	hence	ADV
ejpam-4658	126	2	,	,	PUNCT
ejpam-4658	126	3	for	for	ADP
ejpam-4658	126	4	each	each	DET
ejpam-4658	126	5	x	x	PROPN
ejpam-4658	126	6	∈	∈	PROPN
ejpam-4658	126	7	s.	s.	PROPN
ejpam-4658	126	8	(	(	PUNCT
ejpam-4658	126	9	s	s	NOUN
ejpam-4658	126	10	\	\	X
ejpam-4658	126	11	{	{	PUNCT
ejpam-4658	126	12	x	x	NOUN
ejpam-4658	126	13	}	}	PUNCT
ejpam-4658	126	14	)	)	PUNCT
ejpam-4658	126	15	∪	∪	ADP
ejpam-4658	126	16	{	{	PUNCT
ejpam-4658	126	17	y	y	NOUN
ejpam-4658	126	18	}	}	PUNCT
ejpam-4658	126	19	=	=	PUNCT
ejpam-4658	127	1	[	[	X
ejpam-4658	127	2	v	v	X
ejpam-4658	127	3	(	(	PUNCT
ejpam-4658	127	4	g	g	NOUN
ejpam-4658	127	5	)	)	PUNCT
ejpam-4658	127	6	\	\	PUNCT
ejpam-4658	127	7	(	(	PUNCT
ejpam-4658	127	8	c	c	NOUN
ejpam-4658	127	9	\	\	PROPN
ejpam-4658	127	10	{	{	PUNCT
ejpam-4658	127	11	y	y	NOUN
ejpam-4658	127	12	}	}	PUNCT
ejpam-4658	127	13	)	)	PUNCT
ejpam-4658	127	14	]	]	PUNCT
ejpam-4658	127	15	∪	∪	X
ejpam-4658	127	16	{	{	PUNCT
ejpam-4658	127	17	x	x	NOUN
ejpam-4658	127	18	}	}	PUNCT
ejpam-4658	127	19	is	be	AUX
ejpam-4658	127	20	a	a	DET
ejpam-4658	127	21	strong	strong	ADJ
ejpam-4658	127	22	resolving	resolve	VERB
ejpam-4658	127	23	hop	hop	NOUN
ejpam-4658	127	24	dominating	dominating	NOUN
ejpam-4658	127	25	set	set	NOUN
ejpam-4658	127	26	of	of	ADP
ejpam-4658	127	27	g.	g.	PROPN
ejpam-4658	127	28	therefore	therefore	ADV
ejpam-4658	127	29	,	,	PUNCT
ejpam-4658	127	30	s	s	VERB
ejpam-4658	127	31	is	be	AUX
ejpam-4658	127	32	a	a	DET
ejpam-4658	127	33	1	1	NUM
ejpam-4658	127	34	-	-	PUNCT
ejpam-4658	127	35	movable	movable	ADJ
ejpam-4658	127	36	strong	strong	ADJ
ejpam-4658	127	37	resolving	resolve	VERB
ejpam-4658	127	38	hop	hop	NOUN
ejpam-4658	127	39	dominating	dominating	NOUN
ejpam-4658	127	40	set	set	NOUN
ejpam-4658	127	41	of	of	ADP
ejpam-4658	127	42	g.	g.	PROPN
ejpam-4658	127	43	4	4	NUM
ejpam-4658	127	44	.	.	PUNCT
ejpam-4658	128	1	join	join	NOUN
ejpam-4658	128	2	of	of	ADP
ejpam-4658	128	3	graphs	graph	NOUN
ejpam-4658	128	4	theorem	theorem	VERB
ejpam-4658	128	5	4	4	NUM
ejpam-4658	128	6	.	.	PUNCT
ejpam-4658	129	1	let	let	VERB
ejpam-4658	129	2	g	g	PRON
ejpam-4658	129	3	be	be	AUX
ejpam-4658	129	4	a	a	DET
ejpam-4658	129	5	connected	connected	ADJ
ejpam-4658	129	6	graph	graph	NOUN
ejpam-4658	129	7	of	of	ADP
ejpam-4658	129	8	order	order	NOUN
ejpam-4658	129	9	n	n	NOUN
ejpam-4658	129	10	and	and	CCONJ
ejpam-4658	129	11	γ(g	γ(g	PROPN
ejpam-4658	129	12	)	)	PUNCT
ejpam-4658	130	1	=	=	PUNCT
ejpam-4658	130	2	1	1	X
ejpam-4658	130	3	.	.	PUNCT
ejpam-4658	130	4	then	then	ADV
ejpam-4658	130	5	a	a	DET
ejpam-4658	130	6	1	1	NUM
ejpam-4658	130	7	-	-	PUNCT
ejpam-4658	130	8	movable	movable	ADJ
ejpam-4658	130	9	strong	strong	ADJ
ejpam-4658	130	10	resolving	resolve	VERB
ejpam-4658	130	11	hop	hop	NOUN
ejpam-4658	130	12	dominating	dominating	NOUN
ejpam-4658	130	13	set	set	NOUN
ejpam-4658	130	14	of	of	ADP
ejpam-4658	130	15	g	g	PROPN
ejpam-4658	130	16	does	do	AUX
ejpam-4658	130	17	not	not	PART
ejpam-4658	130	18	exist	exist	VERB
ejpam-4658	130	19	.	.	PUNCT
ejpam-4658	131	1	proof	proof	NOUN
ejpam-4658	131	2	:	:	PUNCT
ejpam-4658	131	3	suppose	suppose	VERB
ejpam-4658	131	4	g	g	PROPN
ejpam-4658	131	5	has	have	VERB
ejpam-4658	131	6	a	a	DET
ejpam-4658	131	7	1	1	NUM
ejpam-4658	131	8	-	-	PUNCT
ejpam-4658	131	9	movable	movable	ADJ
ejpam-4658	131	10	strong	strong	ADJ
ejpam-4658	131	11	resolving	resolve	VERB
ejpam-4658	131	12	hop	hop	NOUN
ejpam-4658	131	13	dominating	dominating	NOUN
ejpam-4658	131	14	set	set	NOUN
ejpam-4658	131	15	s.	s.	PROPN
ejpam-4658	131	16	let	let	VERB
ejpam-4658	131	17	d	d	X
ejpam-4658	131	18	=	=	PRON
ejpam-4658	131	19	{	{	PUNCT
ejpam-4658	131	20	x	x	PROPN
ejpam-4658	131	21	∈	∈	PROPN
ejpam-4658	131	22	v	v	NOUN
ejpam-4658	131	23	(	(	PUNCT
ejpam-4658	131	24	g	g	NOUN
ejpam-4658	131	25	)	)	PUNCT
ejpam-4658	131	26	:	:	PUNCT
ejpam-4658	131	27	degg(x	degg(x	X
ejpam-4658	131	28	)	)	PUNCT
ejpam-4658	131	29	=	=	SYM
ejpam-4658	131	30	n	n	CCONJ
ejpam-4658	131	31	−	−	NOUN
ejpam-4658	131	32	1	1	NUM
ejpam-4658	131	33	}	}	PUNCT
ejpam-4658	131	34	.	.	PUNCT
ejpam-4658	132	1	since	since	SCONJ
ejpam-4658	132	2	s	s	PROPN
ejpam-4658	132	3	is	be	AUX
ejpam-4658	132	4	hop	hop	NOUN
ejpam-4658	132	5	dominating	dominating	NOUN
ejpam-4658	132	6	,	,	PUNCT
ejpam-4658	132	7	d	d	PROPN
ejpam-4658	132	8	⊆	⊆	NUM
ejpam-4658	132	9	s.	s.	PROPN
ejpam-4658	132	10	let	let	VERB
ejpam-4658	132	11	x	x	X
ejpam-4658	132	12	∈	∈	PROPN
ejpam-4658	132	13	d.	d.	PROPN
ejpam-4658	132	14	then	then	ADV
ejpam-4658	132	15	s	s	VERB
ejpam-4658	132	16	\{x	\{x	X
ejpam-4658	132	17	}	}	PUNCT
ejpam-4658	132	18	is	be	AUX
ejpam-4658	132	19	not	not	PART
ejpam-4658	132	20	hop	hop	NOUN
ejpam-4658	132	21	dominating	dominating	NOUN
ejpam-4658	132	22	and	and	CCONJ
ejpam-4658	132	23	for	for	ADP
ejpam-4658	132	24	each	each	DET
ejpam-4658	132	25	y	y	PROPN
ejpam-4658	132	26	∈	∈	PROPN
ejpam-4658	132	27	(	(	PUNCT
ejpam-4658	132	28	v	v	NOUN
ejpam-4658	132	29	(	(	PUNCT
ejpam-4658	132	30	g)\s)∩ng(x	g)\s)∩ng(x	NOUN
ejpam-4658	132	31	)	)	PUNCT
ejpam-4658	132	32	,	,	PUNCT
ejpam-4658	132	33	(	(	PUNCT
ejpam-4658	132	34	s	s	NOUN
ejpam-4658	132	35	\{x})∪{y	\{x})∪{y	NOUN
ejpam-4658	132	36	}	}	PUNCT
ejpam-4658	132	37	is	be	AUX
ejpam-4658	132	38	also	also	ADV
ejpam-4658	132	39	not	not	PART
ejpam-4658	132	40	hop	hop	NOUN
ejpam-4658	132	41	dominating	dominating	NOUN
ejpam-4658	132	42	.	.	PUNCT
ejpam-4658	133	1	hence	hence	ADV
ejpam-4658	133	2	,	,	PUNCT
ejpam-4658	133	3	s	s	VERB
ejpam-4658	133	4	is	be	AUX
ejpam-4658	133	5	not	not	PART
ejpam-4658	133	6	a	a	DET
ejpam-4658	133	7	1	1	NUM
ejpam-4658	133	8	-	-	PUNCT
ejpam-4658	133	9	movable	movable	ADJ
ejpam-4658	133	10	strong	strong	ADJ
ejpam-4658	133	11	resolving	resolve	VERB
ejpam-4658	133	12	hop	hop	NOUN
ejpam-4658	133	13	dominating	dominating	NOUN
ejpam-4658	133	14	.	.	PUNCT
ejpam-4658	134	1	as	as	ADP
ejpam-4658	134	2	a	a	DET
ejpam-4658	134	3	consequence	consequence	NOUN
ejpam-4658	134	4	of	of	ADP
ejpam-4658	134	5	theorem	theorem	NOUN
ejpam-4658	134	6	4	4	NUM
ejpam-4658	134	7	the	the	DET
ejpam-4658	134	8	next	next	ADJ
ejpam-4658	134	9	result	result	NOUN
ejpam-4658	134	10	follows	follow	VERB
ejpam-4658	134	11	.	.	PUNCT
ejpam-4658	135	1	a.	a.	PROPN
ejpam-4658	135	2	h.	h.	PROPN
ejpam-4658	135	3	abragan	abragan	PROPN
ejpam-4658	135	4	,	,	PUNCT
ejpam-4658	135	5	h.	h.	PROPN
ejpam-4658	135	6	m.	m.	PROPN
ejpam-4658	135	7	rara	rara	PROPN
ejpam-4658	135	8	/	/	SYM
ejpam-4658	135	9	eur	eur	PROPN
ejpam-4658	135	10	.	.	PUNCT
ejpam-4658	136	1	j.	j.	PROPN
ejpam-4658	136	2	pure	pure	PROPN
ejpam-4658	136	3	appl	appl	PROPN
ejpam-4658	136	4	.	.	PROPN
ejpam-4658	136	5	math	math	PROPN
ejpam-4658	136	6	,	,	PUNCT
ejpam-4658	136	7	16	16	NUM
ejpam-4658	136	8	(	(	PUNCT
ejpam-4658	136	9	2	2	NUM
ejpam-4658	136	10	)	)	PUNCT
ejpam-4658	136	11	(	(	PUNCT
ejpam-4658	136	12	2023	2023	NUM
ejpam-4658	136	13	)	)	PUNCT
ejpam-4658	136	14	,	,	PUNCT
ejpam-4658	136	15	763	763	NUM
ejpam-4658	136	16	-	-	SYM
ejpam-4658	136	17	772	772	NUM
ejpam-4658	136	18	768	768	NUM
ejpam-4658	136	19	corollary	corollary	ADJ
ejpam-4658	136	20	1	1	NUM
ejpam-4658	136	21	.	.	PUNCT
ejpam-4658	137	1	let	let	VERB
ejpam-4658	137	2	g	g	PRON
ejpam-4658	137	3	be	be	AUX
ejpam-4658	137	4	a	a	DET
ejpam-4658	137	5	graph	graph	NOUN
ejpam-4658	137	6	,	,	PUNCT
ejpam-4658	137	7	then	then	ADV
ejpam-4658	137	8	the	the	DET
ejpam-4658	137	9	1	1	NUM
ejpam-4658	137	10	-	-	PUNCT
ejpam-4658	137	11	movable	movable	ADJ
ejpam-4658	137	12	strong	strong	ADJ
ejpam-4658	137	13	resolving	resolve	VERB
ejpam-4658	137	14	hop	hop	NOUN
ejpam-4658	137	15	dominating	dominating	NOUN
ejpam-4658	137	16	set	set	NOUN
ejpam-4658	137	17	of	of	ADP
ejpam-4658	137	18	k1	k1	NOUN
ejpam-4658	138	1	+	+	PROPN
ejpam-4658	138	2	g	g	PROPN
ejpam-4658	138	3	does	do	AUX
ejpam-4658	138	4	not	not	PART
ejpam-4658	138	5	exist	exist	VERB
ejpam-4658	138	6	.	.	PUNCT
ejpam-4658	139	1	theorem	theorem	NOUN
ejpam-4658	139	2	5	5	NUM
ejpam-4658	139	3	.	.	PUNCT
ejpam-4658	140	1	let	let	VERB
ejpam-4658	140	2	g	g	NOUN
ejpam-4658	141	1	and	and	CCONJ
ejpam-4658	141	2	h	h	NOUN
ejpam-4658	141	3	be	be	AUX
ejpam-4658	141	4	graphs	graph	NOUN
ejpam-4658	141	5	where	where	SCONJ
ejpam-4658	141	6	γ(g	γ(g	NOUN
ejpam-4658	141	7	)	)	PUNCT
ejpam-4658	141	8	̸=	̸=	PROPN
ejpam-4658	141	9	1	1	NUM
ejpam-4658	141	10	and	and	CCONJ
ejpam-4658	141	11	γ(h	γ(h	NOUN
ejpam-4658	141	12	)	)	PUNCT
ejpam-4658	141	13	̸=	̸=	PROPN
ejpam-4658	141	14	1	1	NUM
ejpam-4658	141	15	.	.	PUNCT
ejpam-4658	142	1	a	a	DET
ejpam-4658	142	2	proper	proper	ADJ
ejpam-4658	142	3	subset	subset	NOUN
ejpam-4658	142	4	s	s	NOUN
ejpam-4658	142	5	of	of	ADP
ejpam-4658	142	6	v	v	NOUN
ejpam-4658	142	7	(	(	PUNCT
ejpam-4658	142	8	g	g	PROPN
ejpam-4658	142	9	+	+	NOUN
ejpam-4658	142	10	h	h	NOUN
ejpam-4658	142	11	)	)	PUNCT
ejpam-4658	142	12	is	be	AUX
ejpam-4658	142	13	a	a	DET
ejpam-4658	142	14	1	1	NUM
ejpam-4658	142	15	-	-	PUNCT
ejpam-4658	142	16	movable	movable	ADJ
ejpam-4658	142	17	strong	strong	ADJ
ejpam-4658	142	18	resolving	resolve	VERB
ejpam-4658	142	19	hop	hop	NOUN
ejpam-4658	142	20	dominating	dominating	NOUN
ejpam-4658	142	21	set	set	NOUN
ejpam-4658	142	22	of	of	ADP
ejpam-4658	142	23	g	g	PROPN
ejpam-4658	142	24	+	+	PROPN
ejpam-4658	142	25	h	h	NOUN
ejpam-4658	142	26	if	if	SCONJ
ejpam-4658	143	1	and	and	CCONJ
ejpam-4658	143	2	only	only	ADV
ejpam-4658	143	3	if	if	SCONJ
ejpam-4658	143	4	at	at	ADV
ejpam-4658	143	5	least	least	ADJ
ejpam-4658	143	6	one	one	NUM
ejpam-4658	143	7	of	of	ADP
ejpam-4658	143	8	the	the	DET
ejpam-4658	143	9	following	following	NOUN
ejpam-4658	143	10	is	be	AUX
ejpam-4658	143	11	satisfied	satisfied	ADJ
ejpam-4658	143	12	.	.	PUNCT
ejpam-4658	144	1	(	(	PUNCT
ejpam-4658	144	2	i	i	NOUN
ejpam-4658	144	3	)	)	PUNCT
ejpam-4658	144	4	s	s	PART
ejpam-4658	144	5	=	=	SYM
ejpam-4658	144	6	v	v	PROPN
ejpam-4658	144	7	(	(	PUNCT
ejpam-4658	144	8	g+h	g+h	NOUN
ejpam-4658	144	9	)	)	PUNCT
ejpam-4658	144	10	\	\	PROPN
ejpam-4658	145	1	cg	cg	NOUN
ejpam-4658	145	2	where	where	SCONJ
ejpam-4658	145	3	cg	cg	NOUN
ejpam-4658	145	4	and	and	CCONJ
ejpam-4658	145	5	cg	cg	NOUN
ejpam-4658	145	6	∪	∪	X
ejpam-4658	145	7	{	{	PUNCT
ejpam-4658	145	8	x	x	NOUN
ejpam-4658	145	9	}	}	PUNCT
ejpam-4658	145	10	or	or	CCONJ
ejpam-4658	145	11	(	(	PUNCT
ejpam-4658	145	12	cg	cg	NOUN
ejpam-4658	145	13	∪	∪	X
ejpam-4658	145	14	{	{	PUNCT
ejpam-4658	145	15	x	x	NOUN
ejpam-4658	145	16	}	}	PUNCT
ejpam-4658	145	17	)	)	PUNCT
ejpam-4658	145	18	\	\	NOUN
ejpam-4658	145	19	{	{	PUNCT
ejpam-4658	145	20	y	y	NOUN
ejpam-4658	145	21	}	}	PUNCT
ejpam-4658	145	22	are	be	AUX
ejpam-4658	145	23	point	point	ADV
ejpam-4658	145	24	-	-	PUNCT
ejpam-4658	145	25	wise	wise	ADJ
ejpam-4658	145	26	non	non	ADJ
ejpam-4658	145	27	-	-	ADJ
ejpam-4658	145	28	dominated	dominated	ADJ
ejpam-4658	145	29	superclique	superclique	NOUN
ejpam-4658	145	30	in	in	ADP
ejpam-4658	145	31	g	g	NOUN
ejpam-4658	145	32	for	for	ADP
ejpam-4658	145	33	each	each	DET
ejpam-4658	145	34	x	x	PROPN
ejpam-4658	145	35	∈	∈	PROPN
ejpam-4658	145	36	s.	s.	PROPN
ejpam-4658	145	37	(	(	PUNCT
ejpam-4658	145	38	ii	ii	PROPN
ejpam-4658	145	39	)	)	PUNCT
ejpam-4658	145	40	s	s	PART
ejpam-4658	145	41	=	=	SYM
ejpam-4658	145	42	v	v	PROPN
ejpam-4658	145	43	(	(	PUNCT
ejpam-4658	145	44	g+h	g+h	NOUN
ejpam-4658	145	45	)	)	PUNCT
ejpam-4658	145	46	\	\	PROPN
ejpam-4658	146	1	ch	ch	NOUN
ejpam-4658	146	2	where	where	SCONJ
ejpam-4658	146	3	ch	ch	NOUN
ejpam-4658	146	4	and	and	CCONJ
ejpam-4658	146	5	ch	ch	PROPN
ejpam-4658	146	6	∪	∪	X
ejpam-4658	146	7	{	{	PUNCT
ejpam-4658	146	8	z	z	NOUN
ejpam-4658	146	9	}	}	PUNCT
ejpam-4658	146	10	or	or	CCONJ
ejpam-4658	146	11	(	(	PUNCT
ejpam-4658	146	12	ch	ch	NOUN
ejpam-4658	146	13	∪	∪	X
ejpam-4658	146	14	{	{	PUNCT
ejpam-4658	146	15	z	z	NOUN
ejpam-4658	146	16	}	}	PUNCT
ejpam-4658	146	17	)	)	PUNCT
ejpam-4658	146	18	\	\	NOUN
ejpam-4658	147	1	{	{	PUNCT
ejpam-4658	147	2	w	w	NOUN
ejpam-4658	147	3	}	}	PUNCT
ejpam-4658	147	4	are	be	AUX
ejpam-4658	147	5	point	point	ADV
ejpam-4658	147	6	-	-	PUNCT
ejpam-4658	147	7	wise	wise	ADJ
ejpam-4658	147	8	non	non	ADJ
ejpam-4658	147	9	-	-	ADJ
ejpam-4658	147	10	dominated	dominated	ADJ
ejpam-4658	147	11	superclique	superclique	NOUN
ejpam-4658	147	12	in	in	ADP
ejpam-4658	147	13	h	h	NOUN
ejpam-4658	147	14	for	for	ADP
ejpam-4658	147	15	each	each	DET
ejpam-4658	147	16	z	z	NOUN
ejpam-4658	147	17	∈	∈	PROPN
ejpam-4658	147	18	s	s	PART
ejpam-4658	147	19	and	and	CCONJ
ejpam-4658	147	20	w	w	PROPN
ejpam-4658	147	21	∈	∈	PROPN
ejpam-4658	147	22	(	(	PUNCT
ejpam-4658	147	23	v	v	NOUN
ejpam-4658	147	24	(	(	PUNCT
ejpam-4658	147	25	h	h	NOUN
ejpam-4658	147	26	)	)	PUNCT
ejpam-4658	147	27	\	\	PROPN
ejpam-4658	147	28	sh	sh	PROPN
ejpam-4658	147	29	)	)	PUNCT
ejpam-4658	147	30	∩nh(z	∩nh(z	PROPN
ejpam-4658	147	31	)	)	PUNCT
ejpam-4658	147	32	.	.	PUNCT
ejpam-4658	148	1	(	(	PUNCT
ejpam-4658	148	2	iii	iii	X
ejpam-4658	148	3	)	)	PUNCT
ejpam-4658	148	4	s	s	PART
ejpam-4658	148	5	=	=	SYM
ejpam-4658	148	6	v	v	PROPN
ejpam-4658	148	7	(	(	PUNCT
ejpam-4658	148	8	g+h	g+h	NOUN
ejpam-4658	148	9	)	)	PUNCT
ejpam-4658	148	10	\	\	PUNCT
ejpam-4658	149	1	(	(	PUNCT
ejpam-4658	149	2	ch	ch	NOUN
ejpam-4658	149	3	∪	∪	PROPN
ejpam-4658	149	4	cg	cg	NOUN
ejpam-4658	149	5	)	)	PUNCT
ejpam-4658	149	6	where	where	SCONJ
ejpam-4658	149	7	ch	ch	NOUN
ejpam-4658	149	8	,	,	PUNCT
ejpam-4658	149	9	cg	cg	PROPN
ejpam-4658	149	10	,	,	PUNCT
ejpam-4658	149	11	ch	ch	NOUN
ejpam-4658	149	12	∪	∪	NOUN
ejpam-4658	149	13	{	{	PUNCT
ejpam-4658	149	14	x	x	NOUN
ejpam-4658	149	15	}	}	PUNCT
ejpam-4658	149	16	,	,	PUNCT
ejpam-4658	149	17	(	(	PUNCT
ejpam-4658	149	18	ch	ch	NOUN
ejpam-4658	149	19	∪	∪	X
ejpam-4658	149	20	{	{	PUNCT
ejpam-4658	149	21	x	x	NOUN
ejpam-4658	149	22	}	}	PUNCT
ejpam-4658	149	23	)	)	PUNCT
ejpam-4658	149	24	\	\	NOUN
ejpam-4658	150	1	{	{	PUNCT
ejpam-4658	150	2	y	y	NOUN
ejpam-4658	150	3	}	}	PUNCT
ejpam-4658	150	4	,	,	PUNCT
ejpam-4658	150	5	cg	cg	NOUN
ejpam-4658	150	6	∪	∪	NOUN
ejpam-4658	150	7	{	{	PUNCT
ejpam-4658	150	8	z	z	NOUN
ejpam-4658	150	9	}	}	PUNCT
ejpam-4658	150	10	,	,	PUNCT
ejpam-4658	150	11	(	(	PUNCT
ejpam-4658	150	12	cg	cg	NOUN
ejpam-4658	150	13	∪	∪	X
ejpam-4658	150	14	{	{	PUNCT
ejpam-4658	150	15	z	z	NOUN
ejpam-4658	150	16	}	}	PUNCT
ejpam-4658	150	17	)	)	PUNCT
ejpam-4658	150	18	\	\	NOUN
ejpam-4658	150	19	{	{	PUNCT
ejpam-4658	150	20	w	w	NOUN
ejpam-4658	150	21	}	}	PUNCT
ejpam-4658	150	22	are	be	AUX
ejpam-4658	150	23	point	point	ADV
ejpam-4658	150	24	-	-	PUNCT
ejpam-4658	150	25	wise	wise	ADJ
ejpam-4658	150	26	non	non	ADJ
ejpam-4658	150	27	-	-	ADJ
ejpam-4658	150	28	dominated	dominated	ADJ
ejpam-4658	150	29	supercliques	superclique	NOUN
ejpam-4658	150	30	in	in	ADP
ejpam-4658	150	31	h	h	NOUN
ejpam-4658	150	32	and	and	CCONJ
ejpam-4658	150	33	g	g	NOUN
ejpam-4658	150	34	,	,	PUNCT
ejpam-4658	150	35	respectively	respectively	ADV
ejpam-4658	150	36	for	for	ADP
ejpam-4658	150	37	all	all	DET
ejpam-4658	150	38	x	x	SYM
ejpam-4658	150	39	∈	∈	NOUN
ejpam-4658	150	40	sh	sh	INTJ
ejpam-4658	150	41	.	.	PUNCT
ejpam-4658	151	1	proof	proof	NOUN
ejpam-4658	151	2	:	:	PUNCT
ejpam-4658	151	3	suppose	suppose	VERB
ejpam-4658	151	4	s	s	VERB
ejpam-4658	151	5	⊆	⊆	NUM
ejpam-4658	151	6	v	v	NOUN
ejpam-4658	151	7	(	(	PUNCT
ejpam-4658	151	8	g+h	g+h	PROPN
ejpam-4658	151	9	)	)	PUNCT
ejpam-4658	151	10	is	be	AUX
ejpam-4658	151	11	a	a	DET
ejpam-4658	151	12	1	1	NUM
ejpam-4658	151	13	-	-	PUNCT
ejpam-4658	151	14	movable	movable	ADJ
ejpam-4658	151	15	strong	strong	ADJ
ejpam-4658	151	16	resolving	resolve	VERB
ejpam-4658	151	17	hop	hop	NOUN
ejpam-4658	151	18	dominating	dominating	NOUN
ejpam-4658	151	19	set	set	NOUN
ejpam-4658	151	20	of	of	ADP
ejpam-4658	151	21	g.	g.	PROPN
ejpam-4658	152	1	then	then	ADV
ejpam-4658	152	2	s	s	VERB
ejpam-4658	152	3	is	be	AUX
ejpam-4658	152	4	a	a	DET
ejpam-4658	152	5	strong	strong	ADJ
ejpam-4658	152	6	resolving	resolving	NOUN
ejpam-4658	152	7	set	set	NOUN
ejpam-4658	152	8	of	of	ADP
ejpam-4658	152	9	g+h	g+h	PROPN
ejpam-4658	152	10	.	.	PUNCT
ejpam-4658	153	1	by	by	ADP
ejpam-4658	153	2	theorem	theorem	NOUN
ejpam-4658	153	3	1	1	NUM
ejpam-4658	153	4	,	,	PUNCT
ejpam-4658	153	5	at	at	ADV
ejpam-4658	153	6	least	least	ADJ
ejpam-4658	153	7	one	one	NUM
ejpam-4658	153	8	of	of	ADP
ejpam-4658	153	9	the	the	DET
ejpam-4658	153	10	following	follow	VERB
ejpam-4658	153	11	is	be	AUX
ejpam-4658	153	12	satisfied	satisfied	ADJ
ejpam-4658	153	13	:	:	PUNCT
ejpam-4658	154	1	(	(	PUNCT
ejpam-4658	154	2	a	a	X
ejpam-4658	154	3	)	)	PUNCT
ejpam-4658	154	4	s	s	PART
ejpam-4658	154	5	=	=	SYM
ejpam-4658	154	6	v	v	PROPN
ejpam-4658	154	7	(	(	PUNCT
ejpam-4658	154	8	g+h	g+h	NOUN
ejpam-4658	154	9	)	)	PUNCT
ejpam-4658	154	10	\	\	PROPN
ejpam-4658	154	11	cg	cg	NOUN
ejpam-4658	154	12	where	where	SCONJ
ejpam-4658	154	13	cg	cg	NOUN
ejpam-4658	154	14	is	be	AUX
ejpam-4658	154	15	a	a	DET
ejpam-4658	154	16	superclique	superclique	NOUN
ejpam-4658	154	17	in	in	ADP
ejpam-4658	154	18	g.	g.	PROPN
ejpam-4658	154	19	(	(	PUNCT
ejpam-4658	154	20	b	b	X
ejpam-4658	154	21	)	)	PUNCT
ejpam-4658	154	22	s	s	PART
ejpam-4658	154	23	=	=	SYM
ejpam-4658	154	24	v	v	PROPN
ejpam-4658	154	25	(	(	PUNCT
ejpam-4658	154	26	g+h	g+h	NOUN
ejpam-4658	154	27	)	)	PUNCT
ejpam-4658	154	28	\	\	PROPN
ejpam-4658	155	1	ch	ch	NOUN
ejpam-4658	155	2	where	where	SCONJ
ejpam-4658	155	3	ch	ch	NOUN
ejpam-4658	155	4	is	be	AUX
ejpam-4658	155	5	a	a	DET
ejpam-4658	155	6	superclique	superclique	NOUN
ejpam-4658	155	7	in	in	ADP
ejpam-4658	155	8	h.	h.	PROPN
ejpam-4658	155	9	(	(	PUNCT
ejpam-4658	155	10	c	c	X
ejpam-4658	155	11	)	)	PUNCT
ejpam-4658	155	12	if	if	SCONJ
ejpam-4658	155	13	γ(g	γ(g	NOUN
ejpam-4658	155	14	)	)	PUNCT
ejpam-4658	155	15	̸=	̸=	PROPN
ejpam-4658	155	16	1	1	NUM
ejpam-4658	155	17	or	or	CCONJ
ejpam-4658	155	18	γ(h	γ(h	NOUN
ejpam-4658	155	19	)	)	PUNCT
ejpam-4658	155	20	̸=	̸=	PROPN
ejpam-4658	155	21	1	1	NUM
ejpam-4658	155	22	,	,	PUNCT
ejpam-4658	155	23	s	s	NOUN
ejpam-4658	155	24	=	=	SYM
ejpam-4658	155	25	v	v	PROPN
ejpam-4658	155	26	(	(	PUNCT
ejpam-4658	155	27	g+h	g+h	NOUN
ejpam-4658	155	28	)	)	PUNCT
ejpam-4658	155	29	\	\	PUNCT
ejpam-4658	156	1	(	(	PUNCT
ejpam-4658	156	2	cg	cg	NOUN
ejpam-4658	156	3	∪	∪	PROPN
ejpam-4658	156	4	ch	ch	NOUN
ejpam-4658	156	5	)	)	PUNCT
ejpam-4658	156	6	=	=	PUNCT
ejpam-4658	156	7	(	(	PUNCT
ejpam-4658	156	8	v(g	v(g	PROPN
ejpam-4658	156	9	)	)	PUNCT
ejpam-4658	156	10	\	\	PROPN
ejpam-4658	156	11	cg	cg	NOUN
ejpam-4658	156	12	)	)	PUNCT
ejpam-4658	156	13	∪	∪	NOUN
ejpam-4658	156	14	(	(	PUNCT
ejpam-4658	156	15	v	v	NOUN
ejpam-4658	156	16	(	(	PUNCT
ejpam-4658	156	17	h	h	NOUN
ejpam-4658	156	18	)	)	PUNCT
ejpam-4658	156	19	\	\	PROPN
ejpam-4658	156	20	ch	ch	NOUN
ejpam-4658	156	21	)	)	PUNCT
ejpam-4658	156	22	.	.	PUNCT
ejpam-4658	157	1	we	we	PRON
ejpam-4658	157	2	claim	claim	VERB
ejpam-4658	157	3	that	that	SCONJ
ejpam-4658	157	4	cg	cg	NOUN
ejpam-4658	157	5	is	be	AUX
ejpam-4658	157	6	a	a	DET
ejpam-4658	157	7	point	point	NOUN
ejpam-4658	157	8	-	-	PUNCT
ejpam-4658	157	9	wise	wise	ADJ
ejpam-4658	157	10	non	non	ADJ
ejpam-4658	157	11	-	-	ADJ
ejpam-4658	157	12	dominated	dominated	ADJ
ejpam-4658	157	13	set	set	NOUN
ejpam-4658	157	14	of	of	ADP
ejpam-4658	157	15	g.	g.	PROPN
ejpam-4658	157	16	let	let	VERB
ejpam-4658	157	17	x	x	SYM
ejpam-4658	157	18	∈	∈	PROPN
ejpam-4658	157	19	cg	cg	NOUN
ejpam-4658	157	20	.	.	PUNCT
ejpam-4658	158	1	since	since	SCONJ
ejpam-4658	158	2	s	s	PROPN
ejpam-4658	158	3	is	be	AUX
ejpam-4658	158	4	hop	hop	NOUN
ejpam-4658	158	5	dominating	dominating	NOUN
ejpam-4658	158	6	and	and	CCONJ
ejpam-4658	158	7	x	x	SYM
ejpam-4658	158	8	∈	∈	PROPN
ejpam-4658	158	9	v	v	X
ejpam-4658	158	10	(	(	PUNCT
ejpam-4658	158	11	g	g	PROPN
ejpam-4658	158	12	+	+	NOUN
ejpam-4658	158	13	h	h	NOUN
ejpam-4658	158	14	)	)	PUNCT
ejpam-4658	158	15	\	\	PROPN
ejpam-4658	159	1	s	s	X
ejpam-4658	159	2	,	,	PUNCT
ejpam-4658	159	3	there	there	PRON
ejpam-4658	159	4	exists	exist	VERB
ejpam-4658	159	5	y	y	PROPN
ejpam-4658	159	6	∈	∈	PROPN
ejpam-4658	159	7	s	s	VERB
ejpam-4658	159	8	such	such	ADJ
ejpam-4658	159	9	that	that	SCONJ
ejpam-4658	159	10	dg+h(x	dg+h(x	PROPN
ejpam-4658	159	11	,	,	PUNCT
ejpam-4658	159	12	y	y	NOUN
ejpam-4658	159	13	)	)	PUNCT
ejpam-4658	159	14	=	=	SYM
ejpam-4658	160	1	2	2	X
ejpam-4658	160	2	.	.	PUNCT
ejpam-4658	160	3	by	by	ADP
ejpam-4658	160	4	definition	definition	NOUN
ejpam-4658	160	5	of	of	ADP
ejpam-4658	160	6	point	point	NOUN
ejpam-4658	160	7	-	-	PUNCT
ejpam-4658	160	8	wise	wise	ADJ
ejpam-4658	160	9	non	non	ADJ
ejpam-4658	160	10	-	-	ADJ
ejpam-4658	160	11	dominated	dominate	VERB
ejpam-4658	160	12	superclique	superclique	NOUN
ejpam-4658	160	13	,	,	PUNCT
ejpam-4658	160	14	y	y	PROPN
ejpam-4658	160	15	∈	∈	PROPN
ejpam-4658	160	16	v	v	NOUN
ejpam-4658	160	17	(	(	PUNCT
ejpam-4658	160	18	g)\cg	g)\cg	PROPN
ejpam-4658	160	19	and	and	CCONJ
ejpam-4658	160	20	y	y	PROPN
ejpam-4658	160	21	/∈	/∈	PUNCT
ejpam-4658	160	22	ng(x	ng(x	NUM
ejpam-4658	160	23	)	)	PUNCT
ejpam-4658	160	24	.	.	PUNCT
ejpam-4658	161	1	thus	thus	ADV
ejpam-4658	161	2	,	,	PUNCT
ejpam-4658	161	3	cg	cg	NOUN
ejpam-4658	161	4	is	be	AUX
ejpam-4658	161	5	a	a	DET
ejpam-4658	161	6	point	point	NOUN
ejpam-4658	161	7	-	-	PUNCT
ejpam-4658	161	8	wise	wise	ADJ
ejpam-4658	161	9	non	non	ADJ
ejpam-4658	161	10	-	-	ADJ
ejpam-4658	161	11	dominated	dominated	ADJ
ejpam-4658	161	12	superclique	superclique	NOUN
ejpam-4658	161	13	of	of	ADP
ejpam-4658	161	14	g.	g.	PROPN
ejpam-4658	161	15	let	let	VERB
ejpam-4658	161	16	x	x	PROPN
ejpam-4658	161	17	∈	∈	PROPN
ejpam-4658	161	18	s.	s.	PROPN
ejpam-4658	161	19	since	since	SCONJ
ejpam-4658	161	20	s	s	PROPN
ejpam-4658	161	21	is	be	AUX
ejpam-4658	161	22	a	a	DET
ejpam-4658	161	23	1	1	NUM
ejpam-4658	161	24	-	-	PUNCT
ejpam-4658	161	25	movable	movable	ADJ
ejpam-4658	161	26	strong	strong	ADJ
ejpam-4658	161	27	resolving	resolve	VERB
ejpam-4658	161	28	hop	hop	NOUN
ejpam-4658	161	29	dominating	dominating	NOUN
ejpam-4658	161	30	set	set	NOUN
ejpam-4658	161	31	of	of	ADP
ejpam-4658	161	32	g	g	PROPN
ejpam-4658	161	33	+	+	CCONJ
ejpam-4658	161	34	h	h	NOUN
ejpam-4658	161	35	,	,	PUNCT
ejpam-4658	161	36	either	either	CCONJ
ejpam-4658	161	37	s	s	VERB
ejpam-4658	161	38	\	\	X
ejpam-4658	161	39	{	{	PUNCT
ejpam-4658	161	40	x	x	NOUN
ejpam-4658	161	41	}	}	PUNCT
ejpam-4658	161	42	or	or	CCONJ
ejpam-4658	161	43	(	(	PUNCT
ejpam-4658	161	44	s	s	NOUN
ejpam-4658	161	45	\	\	X
ejpam-4658	161	46	{	{	PUNCT
ejpam-4658	161	47	x	x	NOUN
ejpam-4658	161	48	}	}	PUNCT
ejpam-4658	161	49	)	)	PUNCT
ejpam-4658	161	50	∪	∪	SCONJ
ejpam-4658	161	51	{	{	PUNCT
ejpam-4658	161	52	y	y	NOUN
ejpam-4658	161	53	}	}	PUNCT
ejpam-4658	161	54	is	be	AUX
ejpam-4658	161	55	a	a	DET
ejpam-4658	161	56	strong	strong	ADJ
ejpam-4658	161	57	resolving	resolve	VERB
ejpam-4658	161	58	hop	hop	NOUN
ejpam-4658	161	59	dominating	dominating	NOUN
ejpam-4658	161	60	set	set	NOUN
ejpam-4658	161	61	of	of	ADP
ejpam-4658	161	62	g	g	PROPN
ejpam-4658	162	1	+	+	CCONJ
ejpam-4658	162	2	h	h	NOUN
ejpam-4658	163	1	where	where	SCONJ
ejpam-4658	163	2	y	y	PROPN
ejpam-4658	163	3	∈	∈	PROPN
ejpam-4658	164	1	[	[	X
ejpam-4658	164	2	v	v	X
ejpam-4658	164	3	(	(	PUNCT
ejpam-4658	164	4	g	g	NOUN
ejpam-4658	164	5	+	+	NOUN
ejpam-4658	164	6	h	h	NOUN
ejpam-4658	164	7	)	)	PUNCT
ejpam-4658	164	8	\	\	PUNCT
ejpam-4658	165	1	s	s	X
ejpam-4658	165	2	]	]	X
ejpam-4658	165	3	∩	∩	ADJ
ejpam-4658	165	4	ng+h(x	ng+h(x	PROPN
ejpam-4658	165	5	)	)	PUNCT
ejpam-4658	165	6	.	.	PUNCT
ejpam-4658	166	1	since	since	SCONJ
ejpam-4658	166	2	s	s	PART
ejpam-4658	166	3	=	=	SYM
ejpam-4658	166	4	v	v	PROPN
ejpam-4658	166	5	(	(	PUNCT
ejpam-4658	166	6	g	g	PROPN
ejpam-4658	166	7	+	+	NOUN
ejpam-4658	166	8	h	h	NOUN
ejpam-4658	166	9	)	)	PUNCT
ejpam-4658	166	10	\	\	PROPN
ejpam-4658	166	11	cg	cg	NOUN
ejpam-4658	166	12	,	,	PUNCT
ejpam-4658	166	13	s	s	NOUN
ejpam-4658	166	14	\	\	X
ejpam-4658	166	15	{	{	PUNCT
ejpam-4658	166	16	x	x	NOUN
ejpam-4658	166	17	}	}	PUNCT
ejpam-4658	166	18	=	=	SYM
ejpam-4658	166	19	v	v	NOUN
ejpam-4658	166	20	(	(	PUNCT
ejpam-4658	166	21	g	g	PROPN
ejpam-4658	166	22	+	+	NOUN
ejpam-4658	166	23	h	h	NOUN
ejpam-4658	166	24	)	)	PUNCT
ejpam-4658	166	25	\	\	PUNCT
ejpam-4658	167	1	(	(	PUNCT
ejpam-4658	167	2	cg	cg	NOUN
ejpam-4658	167	3	∪	∪	X
ejpam-4658	167	4	{	{	PUNCT
ejpam-4658	167	5	x	x	NOUN
ejpam-4658	167	6	}	}	PUNCT
ejpam-4658	167	7	)	)	PUNCT
ejpam-4658	167	8	and	and	CCONJ
ejpam-4658	167	9	(	(	PUNCT
ejpam-4658	167	10	s	s	NOUN
ejpam-4658	167	11	\	\	X
ejpam-4658	167	12	{	{	PUNCT
ejpam-4658	167	13	x	x	NOUN
ejpam-4658	167	14	}	}	PUNCT
ejpam-4658	167	15	)	)	PUNCT
ejpam-4658	167	16	∪	∪	ADP
ejpam-4658	167	17	{	{	PUNCT
ejpam-4658	167	18	y	y	NOUN
ejpam-4658	167	19	}	}	PUNCT
ejpam-4658	167	20	=	=	PUNCT
ejpam-4658	168	1	[	[	X
ejpam-4658	168	2	v	v	X
ejpam-4658	168	3	(	(	PUNCT
ejpam-4658	168	4	g+h	g+h	PROPN
ejpam-4658	168	5	)	)	PUNCT
ejpam-4658	168	6	]	]	PUNCT
ejpam-4658	168	7	\	\	PUNCT
ejpam-4658	169	1	[	[	X
ejpam-4658	169	2	(	(	PUNCT
ejpam-4658	169	3	cg	cg	NOUN
ejpam-4658	169	4	∪	∪	X
ejpam-4658	169	5	{	{	PUNCT
ejpam-4658	169	6	x	x	NOUN
ejpam-4658	169	7	}	}	PUNCT
ejpam-4658	169	8	)	)	PUNCT
ejpam-4658	169	9	\	\	NOUN
ejpam-4658	169	10	{	{	PUNCT
ejpam-4658	169	11	y	y	NOUN
ejpam-4658	169	12	}	}	PUNCT
ejpam-4658	169	13	]	]	PUNCT
ejpam-4658	169	14	by	by	ADP
ejpam-4658	169	15	lemma	lemma	PROPN
ejpam-4658	169	16	1	1	NUM
ejpam-4658	169	17	,	,	PUNCT
ejpam-4658	169	18	cg	cg	NOUN
ejpam-4658	169	19	∪	∪	NOUN
ejpam-4658	169	20	{	{	PUNCT
ejpam-4658	169	21	x	x	NOUN
ejpam-4658	169	22	}	}	PUNCT
ejpam-4658	169	23	or	or	CCONJ
ejpam-4658	169	24	(	(	PUNCT
ejpam-4658	169	25	cg	cg	NOUN
ejpam-4658	169	26	∪	∪	X
ejpam-4658	169	27	{	{	PUNCT
ejpam-4658	169	28	x	x	NOUN
ejpam-4658	169	29	}	}	PUNCT
ejpam-4658	169	30	)	)	PUNCT
ejpam-4658	169	31	\	\	NOUN
ejpam-4658	169	32	{	{	PUNCT
ejpam-4658	169	33	y	y	NOUN
ejpam-4658	169	34	}	}	PUNCT
ejpam-4658	169	35	is	be	AUX
ejpam-4658	169	36	a	a	DET
ejpam-4658	169	37	superclique	superclique	NOUN
ejpam-4658	169	38	.	.	PUNCT
ejpam-4658	170	1	by	by	ADP
ejpam-4658	170	2	similar	similar	ADJ
ejpam-4658	170	3	argument	argument	NOUN
ejpam-4658	170	4	above	above	ADV
ejpam-4658	170	5	,	,	PUNCT
ejpam-4658	170	6	cg∪{x	cg∪{x	NOUN
ejpam-4658	170	7	}	}	PUNCT
ejpam-4658	170	8	or	or	CCONJ
ejpam-4658	170	9	(	(	PUNCT
ejpam-4658	170	10	cg	cg	NOUN
ejpam-4658	170	11	∪	∪	X
ejpam-4658	170	12	{	{	PUNCT
ejpam-4658	170	13	x})\{y	x})\{y	PROPN
ejpam-4658	170	14	}	}	PUNCT
ejpam-4658	170	15	is	be	AUX
ejpam-4658	170	16	a	a	DET
ejpam-4658	170	17	point	point	NOUN
ejpam-4658	170	18	-	-	PUNCT
ejpam-4658	170	19	wise	wise	ADJ
ejpam-4658	170	20	non	non	ADJ
ejpam-4658	170	21	-	-	ADJ
ejpam-4658	170	22	dominated	dominated	ADJ
ejpam-4658	170	23	superclique	superclique	NOUN
ejpam-4658	170	24	in	in	ADP
ejpam-4658	170	25	g.	g.	PROPN
ejpam-4658	170	26	this	this	PRON
ejpam-4658	170	27	proves	prove	VERB
ejpam-4658	170	28	(	(	PUNCT
ejpam-4658	170	29	i	i	NOUN
ejpam-4658	170	30	)	)	PUNCT
ejpam-4658	170	31	.	.	PUNCT
ejpam-4658	171	1	statements	statement	NOUN
ejpam-4658	171	2	(	(	PUNCT
ejpam-4658	171	3	i	i	NOUN
ejpam-4658	171	4	)	)	PUNCT
ejpam-4658	171	5	and	and	CCONJ
ejpam-4658	171	6	(	(	PUNCT
ejpam-4658	171	7	iii	iii	X
ejpam-4658	171	8	)	)	PUNCT
ejpam-4658	171	9	are	be	AUX
ejpam-4658	171	10	proved	prove	VERB
ejpam-4658	171	11	similarly	similarly	ADV
ejpam-4658	171	12	.	.	PUNCT
ejpam-4658	172	1	for	for	ADP
ejpam-4658	172	2	the	the	DET
ejpam-4658	172	3	converse	converse	NOUN
ejpam-4658	172	4	,	,	PUNCT
ejpam-4658	172	5	suppose	suppose	VERB
ejpam-4658	172	6	(	(	PUNCT
ejpam-4658	172	7	i	i	NOUN
ejpam-4658	172	8	)	)	PUNCT
ejpam-4658	172	9	holds	hold	VERB
ejpam-4658	172	10	.	.	PUNCT
ejpam-4658	173	1	by	by	ADP
ejpam-4658	173	2	theorem	theorem	NOUN
ejpam-4658	173	3	1	1	NUM
ejpam-4658	173	4	,	,	PUNCT
ejpam-4658	173	5	s	s	VERB
ejpam-4658	173	6	is	be	AUX
ejpam-4658	173	7	a	a	DET
ejpam-4658	173	8	strong	strong	ADJ
ejpam-4658	173	9	resolving	resolving	NOUN
ejpam-4658	173	10	set	set	NOUN
ejpam-4658	173	11	.	.	PUNCT
ejpam-4658	174	1	let	let	VERB
ejpam-4658	174	2	u	u	PRON
ejpam-4658	174	3	∈	∈	PROPN
ejpam-4658	174	4	v	v	X
ejpam-4658	174	5	(	(	PUNCT
ejpam-4658	174	6	g+h	g+h	NOUN
ejpam-4658	174	7	)	)	PUNCT
ejpam-4658	174	8	\	\	PUNCT
ejpam-4658	175	1	s.	s.	PROPN
ejpam-4658	175	2	then	then	ADV
ejpam-4658	175	3	u	u	PROPN
ejpam-4658	175	4	∈	∈	PROPN
ejpam-4658	175	5	cg	cg	NOUN
ejpam-4658	175	6	.	.	PUNCT
ejpam-4658	176	1	since	since	SCONJ
ejpam-4658	176	2	cg	cg	NOUN
ejpam-4658	176	3	is	be	AUX
ejpam-4658	176	4	a	a	DET
ejpam-4658	176	5	point	point	NOUN
ejpam-4658	176	6	-	-	PUNCT
ejpam-4658	176	7	wise	wise	ADJ
ejpam-4658	176	8	non	non	ADJ
ejpam-4658	176	9	-	-	ADJ
ejpam-4658	176	10	dominated	dominated	ADJ
ejpam-4658	176	11	superclique	superclique	NOUN
ejpam-4658	176	12	of	of	ADP
ejpam-4658	176	13	g	g	NOUN
ejpam-4658	176	14	,	,	PUNCT
ejpam-4658	176	15	there	there	PRON
ejpam-4658	176	16	exists	exist	VERB
ejpam-4658	176	17	v	v	ADP
ejpam-4658	176	18	∈	∈	PROPN
ejpam-4658	176	19	v	v	NOUN
ejpam-4658	176	20	(	(	PUNCT
ejpam-4658	176	21	g)\cg	g)\cg	VERB
ejpam-4658	176	22	such	such	ADJ
ejpam-4658	176	23	that	that	DET
ejpam-4658	176	24	v	v	NOUN
ejpam-4658	176	25	/∈	/∈	PUNCT
ejpam-4658	176	26	ng(u	ng(u	NOUN
ejpam-4658	176	27	)	)	PUNCT
ejpam-4658	176	28	.	.	PUNCT
ejpam-4658	177	1	hence	hence	ADV
ejpam-4658	177	2	,	,	PUNCT
ejpam-4658	177	3	v	v	ADP
ejpam-4658	177	4	∈	∈	PROPN
ejpam-4658	177	5	s	s	X
ejpam-4658	177	6	and	and	CCONJ
ejpam-4658	177	7	dg+h(u	dg+h(u	PROPN
ejpam-4658	177	8	,	,	PUNCT
ejpam-4658	177	9	v	v	NOUN
ejpam-4658	177	10	)	)	PUNCT
ejpam-4658	177	11	=	=	SYM
ejpam-4658	177	12	2	2	X
ejpam-4658	177	13	.	.	X
ejpam-4658	177	14	let	let	VERB
ejpam-4658	177	15	x	x	PROPN
ejpam-4658	177	16	∈	∈	PROPN
ejpam-4658	177	17	s.	s.	PROPN
ejpam-4658	177	18	since	since	SCONJ
ejpam-4658	177	19	s	s	PROPN
ejpam-4658	177	20	\	\	X
ejpam-4658	177	21	{	{	PUNCT
ejpam-4658	177	22	x	x	NOUN
ejpam-4658	177	23	}	}	PUNCT
ejpam-4658	177	24	=	=	SYM
ejpam-4658	177	25	v	v	NOUN
ejpam-4658	177	26	(	(	PUNCT
ejpam-4658	177	27	g+h	g+h	NOUN
ejpam-4658	177	28	)	)	PUNCT
ejpam-4658	177	29	\	\	PUNCT
ejpam-4658	178	1	(	(	PUNCT
ejpam-4658	178	2	cg	cg	NOUN
ejpam-4658	178	3	∪	∪	X
ejpam-4658	178	4	{	{	PUNCT
ejpam-4658	178	5	x	x	NOUN
ejpam-4658	178	6	}	}	PUNCT
ejpam-4658	178	7	)	)	PUNCT
ejpam-4658	178	8	,	,	PUNCT
ejpam-4658	178	9	by	by	ADP
ejpam-4658	178	10	(	(	PUNCT
ejpam-4658	178	11	i	i	NOUN
ejpam-4658	178	12	)	)	PUNCT
ejpam-4658	178	13	of	of	ADP
ejpam-4658	178	14	theorem	theorem	NOUN
ejpam-4658	178	15	1	1	NUM
ejpam-4658	178	16	and	and	CCONJ
ejpam-4658	178	17	the	the	DET
ejpam-4658	178	18	definition	definition	NOUN
ejpam-4658	178	19	of	of	ADP
ejpam-4658	178	20	point	point	NOUN
ejpam-4658	178	21	-	-	PUNCT
ejpam-4658	178	22	wise	wise	ADJ
ejpam-4658	178	23	non	non	ADJ
ejpam-4658	178	24	-	-	ADJ
ejpam-4658	178	25	dominated	dominate	VERB
ejpam-4658	178	26	superclique	superclique	NOUN
ejpam-4658	178	27	,	,	PUNCT
ejpam-4658	178	28	s	s	PART
ejpam-4658	178	29	is	be	AUX
ejpam-4658	178	30	a	a	DET
ejpam-4658	178	31	1	1	NUM
ejpam-4658	178	32	-	-	PUNCT
ejpam-4658	178	33	movable	movable	ADJ
ejpam-4658	178	34	strong	strong	ADJ
ejpam-4658	178	35	resolving	resolve	VERB
ejpam-4658	178	36	hop	hop	NOUN
ejpam-4658	178	37	dominating	dominating	NOUN
ejpam-4658	178	38	a.	a.	PROPN
ejpam-4658	178	39	h.	h.	PROPN
ejpam-4658	178	40	abragan	abragan	PROPN
ejpam-4658	178	41	,	,	PUNCT
ejpam-4658	178	42	h.	h.	PROPN
ejpam-4658	178	43	m.	m.	PROPN
ejpam-4658	178	44	rara	rara	PROPN
ejpam-4658	178	45	/	/	SYM
ejpam-4658	178	46	eur	eur	PROPN
ejpam-4658	178	47	.	.	PUNCT
ejpam-4658	179	1	j.	j.	PROPN
ejpam-4658	179	2	pure	pure	PROPN
ejpam-4658	179	3	appl	appl	PROPN
ejpam-4658	179	4	.	.	PROPN
ejpam-4658	179	5	math	math	PROPN
ejpam-4658	179	6	,	,	PUNCT
ejpam-4658	179	7	16	16	NUM
ejpam-4658	179	8	(	(	PUNCT
ejpam-4658	179	9	2	2	NUM
ejpam-4658	179	10	)	)	PUNCT
ejpam-4658	179	11	(	(	PUNCT
ejpam-4658	179	12	2023	2023	NUM
ejpam-4658	179	13	)	)	PUNCT
ejpam-4658	179	14	,	,	PUNCT
ejpam-4658	179	15	763	763	NUM
ejpam-4658	179	16	-	-	SYM
ejpam-4658	179	17	772	772	NUM
ejpam-4658	179	18	769	769	NUM
ejpam-4658	179	19	set	set	NOUN
ejpam-4658	179	20	of	of	ADP
ejpam-4658	179	21	g	g	PROPN
ejpam-4658	179	22	+	+	CCONJ
ejpam-4658	179	23	h.	h.	NOUN
ejpam-4658	180	1	similarly	similarly	ADV
ejpam-4658	180	2	if	if	SCONJ
ejpam-4658	180	3	(	(	PUNCT
ejpam-4658	180	4	ii	ii	NOUN
ejpam-4658	180	5	)	)	PUNCT
ejpam-4658	180	6	and	and	CCONJ
ejpam-4658	180	7	(	(	PUNCT
ejpam-4658	180	8	iii	iii	NOUN
ejpam-4658	180	9	)	)	PUNCT
ejpam-4658	180	10	holds	hold	VERB
ejpam-4658	180	11	,	,	PUNCT
ejpam-4658	180	12	s	s	VERB
ejpam-4658	180	13	is	be	AUX
ejpam-4658	180	14	a	a	DET
ejpam-4658	180	15	1	1	NUM
ejpam-4658	180	16	-	-	PUNCT
ejpam-4658	180	17	movable	movable	ADJ
ejpam-4658	180	18	strong	strong	ADJ
ejpam-4658	180	19	resolving	resolve	VERB
ejpam-4658	180	20	hop	hop	NOUN
ejpam-4658	180	21	dominating	dominating	NOUN
ejpam-4658	180	22	set	set	NOUN
ejpam-4658	180	23	of	of	ADP
ejpam-4658	180	24	g+h	g+h	PROPN
ejpam-4658	180	25	.	.	PUNCT
ejpam-4658	181	1	the	the	DET
ejpam-4658	181	2	next	next	ADJ
ejpam-4658	181	3	result	result	NOUN
ejpam-4658	181	4	follows	follow	VERB
ejpam-4658	181	5	from	from	ADP
ejpam-4658	181	6	theorem	theorem	ADJ
ejpam-4658	181	7	5	5	NUM
ejpam-4658	181	8	.	.	PUNCT
ejpam-4658	181	9	corollary	corollary	ADJ
ejpam-4658	181	10	2	2	NUM
ejpam-4658	181	11	.	.	PUNCT
ejpam-4658	182	1	let	let	VERB
ejpam-4658	182	2	g	g	NOUN
ejpam-4658	182	3	andh	andh	NOUN
ejpam-4658	182	4	be	be	AUX
ejpam-4658	182	5	nontrivial	nontrivial	ADJ
ejpam-4658	182	6	connected	connect	VERB
ejpam-4658	182	7	graphs	graph	NOUN
ejpam-4658	182	8	of	of	ADP
ejpam-4658	182	9	ordersm	ordersm	NOUN
ejpam-4658	182	10	and	and	CCONJ
ejpam-4658	182	11	n	n	CCONJ
ejpam-4658	182	12	,	,	PUNCT
ejpam-4658	182	13	respectively	respectively	ADV
ejpam-4658	182	14	.	.	PUNCT
ejpam-4658	183	1	then	then	ADV
ejpam-4658	183	2	,	,	PUNCT
ejpam-4658	183	3	γ1msrh(g+h	γ1msrh(g+h	PROPN
ejpam-4658	183	4	)	)	PUNCT
ejpam-4658	184	1	=	=	PROPN
ejpam-4658	184	2	m−	m−	PROPN
ejpam-4658	184	3	ωpnds}(g	ωpnds}(g	NUM
ejpam-4658	184	4	)	)	PUNCT
ejpam-4658	185	1	+	+	NUM
ejpam-4658	185	2	n−	n−	NOUN
ejpam-4658	185	3	ωpnds(h	ωpnds(h	NOUN
ejpam-4658	185	4	)	)	PUNCT
ejpam-4658	185	5	.	.	PUNCT
ejpam-4658	186	1	5	5	X
ejpam-4658	186	2	.	.	X
ejpam-4658	186	3	corona	corona	NOUN
ejpam-4658	186	4	of	of	ADP
ejpam-4658	186	5	graphs	graph	NOUN
ejpam-4658	186	6	this	this	DET
ejpam-4658	186	7	section	section	NOUN
ejpam-4658	186	8	gives	give	VERB
ejpam-4658	186	9	characterization	characterization	NOUN
ejpam-4658	186	10	of	of	ADP
ejpam-4658	186	11	the	the	DET
ejpam-4658	186	12	1	1	NUM
ejpam-4658	186	13	-	-	PUNCT
ejpam-4658	186	14	movable	movable	ADJ
ejpam-4658	186	15	strong	strong	ADJ
ejpam-4658	186	16	resolving	resolve	VERB
ejpam-4658	186	17	hop	hop	NOUN
ejpam-4658	186	18	dominating	dominating	NOUN
ejpam-4658	186	19	sets	set	NOUN
ejpam-4658	186	20	in	in	ADP
ejpam-4658	186	21	the	the	DET
ejpam-4658	186	22	corona	corona	NOUN
ejpam-4658	186	23	of	of	ADP
ejpam-4658	186	24	graphs	graph	NOUN
ejpam-4658	186	25	as	as	ADV
ejpam-4658	186	26	well	well	ADV
ejpam-4658	186	27	as	as	ADP
ejpam-4658	186	28	its	its	PRON
ejpam-4658	186	29	1	1	NUM
ejpam-4658	186	30	-	-	PUNCT
ejpam-4658	186	31	movable	movable	ADJ
ejpam-4658	186	32	strong	strong	ADJ
ejpam-4658	186	33	resolving	resolve	VERB
ejpam-4658	186	34	hop	hop	NOUN
ejpam-4658	186	35	domination	domination	NOUN
ejpam-4658	186	36	number	number	NOUN
ejpam-4658	186	37	.	.	PUNCT
ejpam-4658	187	1	theorem	theorem	VERB
ejpam-4658	187	2	6	6	NUM
ejpam-4658	187	3	.	.	PUNCT
ejpam-4658	188	1	let	let	VERB
ejpam-4658	188	2	g	g	PRON
ejpam-4658	188	3	be	be	AUX
ejpam-4658	188	4	a	a	DET
ejpam-4658	188	5	nontrivial	nontrivial	ADJ
ejpam-4658	188	6	connected	connect	VERB
ejpam-4658	188	7	graph	graph	NOUN
ejpam-4658	188	8	and	and	CCONJ
ejpam-4658	188	9	h	h	NOUN
ejpam-4658	188	10	a	a	DET
ejpam-4658	188	11	connected	connected	ADJ
ejpam-4658	188	12	graph	graph	NOUN
ejpam-4658	188	13	with	with	ADP
ejpam-4658	188	14	γ(h	γ(h	NOUN
ejpam-4658	188	15	)	)	PUNCT
ejpam-4658	188	16	̸=	̸=	PROPN
ejpam-4658	188	17	1	1	NUM
ejpam-4658	188	18	.	.	PUNCT
ejpam-4658	189	1	a	a	DET
ejpam-4658	189	2	proper	proper	ADJ
ejpam-4658	189	3	subset	subset	NOUN
ejpam-4658	189	4	s	s	NOUN
ejpam-4658	189	5	of	of	ADP
ejpam-4658	189	6	v	v	NOUN
ejpam-4658	189	7	(	(	PUNCT
ejpam-4658	189	8	g	g	PROPN
ejpam-4658	189	9	◦	◦	NOUN
ejpam-4658	189	10	h	h	NOUN
ejpam-4658	189	11	)	)	PUNCT
ejpam-4658	189	12	is	be	AUX
ejpam-4658	189	13	a	a	DET
ejpam-4658	189	14	1	1	NUM
ejpam-4658	189	15	-	-	PUNCT
ejpam-4658	189	16	movable	movable	ADJ
ejpam-4658	189	17	strong	strong	ADJ
ejpam-4658	189	18	resolving	resolve	VERB
ejpam-4658	189	19	hop	hop	NOUN
ejpam-4658	189	20	dominating	dominating	NOUN
ejpam-4658	189	21	set	set	NOUN
ejpam-4658	189	22	of	of	ADP
ejpam-4658	189	23	g	g	PROPN
ejpam-4658	189	24	◦	◦	NOUN
ejpam-4658	189	25	h	h	NOUN
ejpam-4658	189	26	if	if	SCONJ
ejpam-4658	190	1	and	and	CCONJ
ejpam-4658	190	2	only	only	ADV
ejpam-4658	190	3	if	if	SCONJ
ejpam-4658	190	4	s	s	VERB
ejpam-4658	190	5	=	=	NOUN
ejpam-4658	190	6	a	a	DET
ejpam-4658	190	7	⋃	⋃	PROPN
ejpam-4658	190	8	(	(	PUNCT
ejpam-4658	190	9	⋃	⋃	NOUN
ejpam-4658	190	10	u∈v	u∈v	NOUN
ejpam-4658	190	11	(	(	PUNCT
ejpam-4658	190	12	g	g	NOUN
ejpam-4658	190	13	)	)	PUNCT
ejpam-4658	190	14	v	v	NOUN
ejpam-4658	190	15	(	(	PUNCT
ejpam-4658	190	16	hu	hu	PROPN
ejpam-4658	190	17	)	)	PUNCT
ejpam-4658	190	18	)	)	PUNCT
ejpam-4658	190	19	where	where	SCONJ
ejpam-4658	190	20	a	a	DET
ejpam-4658	190	21	⊆	⊆	NUM
ejpam-4658	190	22	v	v	NOUN
ejpam-4658	190	23	(	(	PUNCT
ejpam-4658	190	24	g	g	NOUN
ejpam-4658	190	25	)	)	PUNCT
ejpam-4658	190	26	.	.	PUNCT
ejpam-4658	191	1	proof	proof	NOUN
ejpam-4658	191	2	:	:	PUNCT
ejpam-4658	191	3	suppose	suppose	VERB
ejpam-4658	191	4	that	that	SCONJ
ejpam-4658	191	5	a	a	DET
ejpam-4658	191	6	proper	proper	ADJ
ejpam-4658	191	7	subset	subset	NOUN
ejpam-4658	191	8	s	s	NOUN
ejpam-4658	191	9	of	of	ADP
ejpam-4658	191	10	v	v	NOUN
ejpam-4658	191	11	(	(	PUNCT
ejpam-4658	191	12	g	g	PROPN
ejpam-4658	191	13	◦	◦	NOUN
ejpam-4658	191	14	h	h	NOUN
ejpam-4658	191	15	)	)	PUNCT
ejpam-4658	191	16	is	be	AUX
ejpam-4658	191	17	a	a	DET
ejpam-4658	191	18	1	1	NUM
ejpam-4658	191	19	-	-	PUNCT
ejpam-4658	191	20	movable	movable	ADJ
ejpam-4658	191	21	strong	strong	ADJ
ejpam-4658	191	22	resolving	resolve	VERB
ejpam-4658	191	23	hop	hop	NOUN
ejpam-4658	191	24	dominating	dominating	NOUN
ejpam-4658	191	25	set	set	NOUN
ejpam-4658	191	26	of	of	ADP
ejpam-4658	191	27	g	g	PROPN
ejpam-4658	191	28	◦	◦	NOUN
ejpam-4658	191	29	h.	h.	PROPN
ejpam-4658	191	30	since	since	SCONJ
ejpam-4658	191	31	s	s	PROPN
ejpam-4658	191	32	is	be	AUX
ejpam-4658	191	33	strong	strong	ADJ
ejpam-4658	191	34	resolving	resolve	VERB
ejpam-4658	191	35	set	set	NOUN
ejpam-4658	191	36	of	of	ADP
ejpam-4658	191	37	g	g	PROPN
ejpam-4658	191	38	◦	◦	NOUN
ejpam-4658	191	39	h	h	NOUN
ejpam-4658	191	40	,	,	PUNCT
ejpam-4658	191	41	(	(	PUNCT
ejpam-4658	191	42	i	i	NOUN
ejpam-4658	191	43	)	)	PUNCT
ejpam-4658	191	44	or	or	CCONJ
ejpam-4658	191	45	(	(	PUNCT
ejpam-4658	191	46	ii	ii	NOUN
ejpam-4658	191	47	)	)	PUNCT
ejpam-4658	191	48	of	of	ADP
ejpam-4658	191	49	theorem	theorem	ADJ
ejpam-4658	191	50	2	2	NUM
ejpam-4658	191	51	holds	hold	NOUN
ejpam-4658	191	52	.	.	PUNCT
ejpam-4658	192	1	if	if	SCONJ
ejpam-4658	192	2	(	(	PUNCT
ejpam-4658	192	3	i	i	NOUN
ejpam-4658	192	4	)	)	PUNCT
ejpam-4658	192	5	holds	hold	VERB
ejpam-4658	192	6	,	,	PUNCT
ejpam-4658	192	7	then	then	ADV
ejpam-4658	192	8	s	s	VERB
ejpam-4658	192	9	=	=	NOUN
ejpam-4658	192	10	a	a	DET
ejpam-4658	192	11	⋃	⋃	PROPN
ejpam-4658	192	12	(	(	PUNCT
ejpam-4658	192	13	⋃	⋃	NOUN
ejpam-4658	192	14	u∈v	u∈v	NOUN
ejpam-4658	192	15	(	(	PUNCT
ejpam-4658	192	16	g	g	NOUN
ejpam-4658	192	17	)	)	PUNCT
ejpam-4658	192	18	v	v	NOUN
ejpam-4658	192	19	(	(	PUNCT
ejpam-4658	192	20	hu	hu	PROPN
ejpam-4658	192	21	)	)	PUNCT
ejpam-4658	192	22	)	)	PUNCT
ejpam-4658	192	23	,	,	PUNCT
ejpam-4658	192	24	where	where	SCONJ
ejpam-4658	192	25	a	a	DET
ejpam-4658	192	26	⊆	⊆	NUM
ejpam-4658	192	27	v	v	NOUN
ejpam-4658	192	28	(	(	PUNCT
ejpam-4658	192	29	g	g	NOUN
ejpam-4658	192	30	)	)	PUNCT
ejpam-4658	192	31	.	.	PUNCT
ejpam-4658	193	1	suppose	suppose	VERB
ejpam-4658	193	2	(	(	PUNCT
ejpam-4658	193	3	ii	ii	NOUN
ejpam-4658	193	4	)	)	PUNCT
ejpam-4658	193	5	holds	hold	VERB
ejpam-4658	193	6	.	.	PUNCT
ejpam-4658	194	1	let	let	VERB
ejpam-4658	194	2	x	x	SYM
ejpam-4658	194	3	∈	∈	PROPN
ejpam-4658	194	4	v	v	NOUN
ejpam-4658	194	5	(	(	PUNCT
ejpam-4658	194	6	hw	hw	NOUN
ejpam-4658	194	7	)	)	PUNCT
ejpam-4658	194	8	for	for	ADP
ejpam-4658	194	9	some	some	DET
ejpam-4658	194	10	w	w	PROPN
ejpam-4658	194	11	∈	∈	PROPN
ejpam-4658	194	12	v	v	ADP
ejpam-4658	194	13	(	(	PUNCT
ejpam-4658	194	14	g	g	NOUN
ejpam-4658	194	15	)	)	PUNCT
ejpam-4658	194	16	with	with	ADP
ejpam-4658	194	17	w	w	PROPN
ejpam-4658	194	18	̸=	̸=	PROPN
ejpam-4658	194	19	v.	v.	CCONJ
ejpam-4658	194	20	then	then	ADV
ejpam-4658	194	21	s	s	VERB
ejpam-4658	194	22	\	\	PROPN
ejpam-4658	194	23	{	{	PUNCT
ejpam-4658	194	24	x	x	NOUN
ejpam-4658	194	25	}	}	PUNCT
ejpam-4658	194	26	=	=	PUNCT
ejpam-4658	194	27	a	a	DET
ejpam-4658	194	28	⋃	⋃	PROPN
ejpam-4658	194	29	(	(	PUNCT
ejpam-4658	194	30	⋃	⋃	NOUN
ejpam-4658	194	31	u∈v	u∈v	NOUN
ejpam-4658	194	32	(	(	PUNCT
ejpam-4658	194	33	g)\{w	g)\{w	NOUN
ejpam-4658	194	34	,	,	PUNCT
ejpam-4658	194	35	v	v	NOUN
ejpam-4658	194	36	}	}	SYM
ejpam-4658	194	37	v	v	PROPN
ejpam-4658	194	38	(	(	PUNCT
ejpam-4658	194	39	hu	hu	PROPN
ejpam-4658	194	40	)	)	PUNCT
ejpam-4658	194	41	)	)	PUNCT
ejpam-4658	195	1	⋃	⋃	PROPN
ejpam-4658	195	2	(	(	PUNCT
ejpam-4658	195	3	v	v	NOUN
ejpam-4658	195	4	(	(	PUNCT
ejpam-4658	195	5	hw	hw	NOUN
ejpam-4658	195	6	)	)	PUNCT
ejpam-4658	195	7	\	\	AUX
ejpam-4658	195	8	{	{	PUNCT
ejpam-4658	195	9	x	x	NOUN
ejpam-4658	195	10	}	}	PUNCT
ejpam-4658	195	11	)	)	PUNCT
ejpam-4658	195	12	⋃	⋃	PUNCT
ejpam-4658	195	13	bv	bv	PROPN
ejpam-4658	195	14	is	be	AUX
ejpam-4658	195	15	not	not	PART
ejpam-4658	195	16	a	a	DET
ejpam-4658	195	17	strong	strong	ADJ
ejpam-4658	195	18	resolving	resolving	NOUN
ejpam-4658	195	19	set	set	VERB
ejpam-4658	195	20	by	by	ADP
ejpam-4658	195	21	theorem	theorem	NOUN
ejpam-4658	195	22	2	2	NUM
ejpam-4658	195	23	.	.	PUNCT
ejpam-4658	195	24	hence	hence	ADV
ejpam-4658	195	25	,	,	PUNCT
ejpam-4658	195	26	s	s	VERB
ejpam-4658	195	27	=	=	NOUN
ejpam-4658	195	28	a	a	DET
ejpam-4658	195	29	⋃	⋃	PROPN
ejpam-4658	195	30	(	(	PUNCT
ejpam-4658	195	31	⋃	⋃	NOUN
ejpam-4658	195	32	u∈v	u∈v	NOUN
ejpam-4658	195	33	(	(	PUNCT
ejpam-4658	195	34	g	g	NOUN
ejpam-4658	195	35	)	)	PUNCT
ejpam-4658	195	36	v	v	NOUN
ejpam-4658	195	37	(	(	PUNCT
ejpam-4658	195	38	hu	hu	PROPN
ejpam-4658	195	39	)	)	PUNCT
ejpam-4658	195	40	)	)	PUNCT
ejpam-4658	195	41	where	where	SCONJ
ejpam-4658	195	42	a	a	DET
ejpam-4658	195	43	⊆	⊆	NUM
ejpam-4658	195	44	v	v	NOUN
ejpam-4658	195	45	(	(	PUNCT
ejpam-4658	195	46	g	g	NOUN
ejpam-4658	195	47	)	)	PUNCT
ejpam-4658	195	48	.	.	PUNCT
ejpam-4658	196	1	for	for	ADP
ejpam-4658	196	2	the	the	DET
ejpam-4658	196	3	converse	converse	NOUN
ejpam-4658	196	4	,	,	PUNCT
ejpam-4658	196	5	suppose	suppose	VERB
ejpam-4658	196	6	s	s	VERB
ejpam-4658	196	7	=	=	NOUN
ejpam-4658	196	8	a	a	DET
ejpam-4658	196	9	⋃	⋃	PROPN
ejpam-4658	196	10	(	(	PUNCT
ejpam-4658	196	11	⋃	⋃	NOUN
ejpam-4658	196	12	u∈v	u∈v	NOUN
ejpam-4658	196	13	(	(	PUNCT
ejpam-4658	196	14	g	g	NOUN
ejpam-4658	196	15	)	)	PUNCT
ejpam-4658	196	16	v	v	NOUN
ejpam-4658	196	17	(	(	PUNCT
ejpam-4658	196	18	hu	hu	PROPN
ejpam-4658	196	19	)	)	PUNCT
ejpam-4658	196	20	)	)	PUNCT
ejpam-4658	196	21	where	where	SCONJ
ejpam-4658	196	22	a	a	DET
ejpam-4658	196	23	⊆	⊆	NUM
ejpam-4658	196	24	v	v	NOUN
ejpam-4658	196	25	(	(	PUNCT
ejpam-4658	196	26	g	g	NOUN
ejpam-4658	196	27	)	)	PUNCT
ejpam-4658	196	28	.	.	PUNCT
ejpam-4658	197	1	by	by	ADP
ejpam-4658	197	2	theorem	theorem	NOUN
ejpam-4658	197	3	2	2	NUM
ejpam-4658	197	4	,	,	PUNCT
ejpam-4658	197	5	s	s	VERB
ejpam-4658	197	6	is	be	AUX
ejpam-4658	197	7	a	a	DET
ejpam-4658	197	8	strong	strong	ADJ
ejpam-4658	197	9	resolving	resolving	NOUN
ejpam-4658	197	10	set	set	NOUN
ejpam-4658	197	11	of	of	ADP
ejpam-4658	197	12	g	g	PROPN
ejpam-4658	197	13	◦	◦	NOUN
ejpam-4658	197	14	h.	h.	NOUN
ejpam-4658	197	15	it	it	PRON
ejpam-4658	197	16	can	can	AUX
ejpam-4658	197	17	be	be	AUX
ejpam-4658	197	18	seen	see	VERB
ejpam-4658	197	19	that	that	SCONJ
ejpam-4658	197	20	s	s	VERB
ejpam-4658	197	21	is	be	AUX
ejpam-4658	197	22	a	a	DET
ejpam-4658	197	23	hop	hop	NOUN
ejpam-4658	197	24	dominating	dominating	NOUN
ejpam-4658	197	25	set	set	NOUN
ejpam-4658	197	26	also	also	ADV
ejpam-4658	197	27	.	.	PUNCT
ejpam-4658	198	1	let	let	VERB
ejpam-4658	198	2	p	p	PRON
ejpam-4658	198	3	∈	∈	PROPN
ejpam-4658	198	4	s.	s.	PROPN
ejpam-4658	198	5	if	if	SCONJ
ejpam-4658	198	6	p	p	PROPN
ejpam-4658	198	7	∈	∈	PROPN
ejpam-4658	198	8	a	a	PRON
ejpam-4658	198	9	,	,	PUNCT
ejpam-4658	198	10	then	then	ADV
ejpam-4658	198	11	s	s	VERB
ejpam-4658	198	12	\	\	X
ejpam-4658	198	13	{	{	PUNCT
ejpam-4658	198	14	p	p	X
ejpam-4658	198	15	}	}	PUNCT
ejpam-4658	198	16	=	=	SYM
ejpam-4658	198	17	(	(	PUNCT
ejpam-4658	198	18	a	a	DET
ejpam-4658	198	19	\	\	X
ejpam-4658	198	20	{	{	PUNCT
ejpam-4658	198	21	p	p	NOUN
ejpam-4658	198	22	}	}	PUNCT
ejpam-4658	198	23	)	)	PUNCT
ejpam-4658	198	24	∪	∪	ADP
ejpam-4658	198	25	(	(	PUNCT
ejpam-4658	198	26	⋃	⋃	NOUN
ejpam-4658	198	27	u∈v	u∈v	NOUN
ejpam-4658	198	28	(	(	PUNCT
ejpam-4658	198	29	g	g	NOUN
ejpam-4658	198	30	)	)	PUNCT
ejpam-4658	198	31	v	v	NOUN
ejpam-4658	198	32	(	(	PUNCT
ejpam-4658	198	33	hu	hu	PROPN
ejpam-4658	198	34	)	)	PUNCT
ejpam-4658	198	35	)	)	PUNCT
ejpam-4658	198	36	is	be	AUX
ejpam-4658	198	37	a	a	DET
ejpam-4658	198	38	strong	strong	ADJ
ejpam-4658	198	39	resolving	resolve	VERB
ejpam-4658	198	40	hop	hop	NOUN
ejpam-4658	198	41	dominating	dominating	NOUN
ejpam-4658	198	42	set	set	NOUN
ejpam-4658	198	43	.	.	PUNCT
ejpam-4658	199	1	if	if	SCONJ
ejpam-4658	199	2	p	p	PROPN
ejpam-4658	199	3	∈	∈	PROPN
ejpam-4658	199	4	v	v	ADP
ejpam-4658	199	5	(	(	PUNCT
ejpam-4658	199	6	hu	hu	PROPN
ejpam-4658	199	7	)	)	PUNCT
ejpam-4658	199	8	for	for	ADP
ejpam-4658	199	9	each	each	DET
ejpam-4658	199	10	u	u	PROPN
ejpam-4658	199	11	∈	∈	PROPN
ejpam-4658	199	12	v	v	NOUN
ejpam-4658	199	13	(	(	PUNCT
ejpam-4658	199	14	g	g	NOUN
ejpam-4658	199	15	)	)	PUNCT
ejpam-4658	199	16	,	,	PUNCT
ejpam-4658	199	17	then	then	ADV
ejpam-4658	199	18	s	s	VERB
ejpam-4658	199	19	\	\	X
ejpam-4658	199	20	{	{	PUNCT
ejpam-4658	199	21	p	p	X
ejpam-4658	199	22	}	}	PUNCT
ejpam-4658	199	23	=	=	PUNCT
ejpam-4658	199	24	a∪	a∪	NOUN
ejpam-4658	199	25	(	(	PUNCT
ejpam-4658	199	26	⋃	⋃	NOUN
ejpam-4658	199	27	u∈v	u∈v	NOUN
ejpam-4658	199	28	(	(	PUNCT
ejpam-4658	199	29	g	g	NOUN
ejpam-4658	199	30	)	)	PUNCT
ejpam-4658	199	31	v	v	NOUN
ejpam-4658	199	32	(	(	PUNCT
ejpam-4658	199	33	hu)\{p	hu)\{p	PROPN
ejpam-4658	199	34	}	}	PUNCT
ejpam-4658	199	35	)	)	PUNCT
ejpam-4658	199	36	∪	∪	ADP
ejpam-4658	199	37	(	(	PUNCT
ejpam-4658	199	38	⋃	⋃	NOUN
ejpam-4658	199	39	v∈v	v∈v	NOUN
ejpam-4658	199	40	(	(	PUNCT
ejpam-4658	199	41	g)\{u	g)\{u	PROPN
ejpam-4658	199	42	}	}	PUNCT
ejpam-4658	199	43	v	v	PROPN
ejpam-4658	199	44	(	(	PUNCT
ejpam-4658	199	45	hv	hv	PROPN
ejpam-4658	199	46	)	)	PUNCT
ejpam-4658	199	47	)	)	PUNCT
ejpam-4658	199	48	is	be	AUX
ejpam-4658	199	49	a	a	DET
ejpam-4658	199	50	strong	strong	ADJ
ejpam-4658	199	51	resolving	resolving	NOUN
ejpam-4658	199	52	set	set	VERB
ejpam-4658	199	53	by	by	ADP
ejpam-4658	199	54	theorem	theorem	ADJ
ejpam-4658	199	55	2	2	NUM
ejpam-4658	199	56	and	and	CCONJ
ejpam-4658	199	57	hop	hop	NOUN
ejpam-4658	199	58	dominating	dominating	NOUN
ejpam-4658	199	59	since	since	SCONJ
ejpam-4658	199	60	γ(h	γ(h	NOUN
ejpam-4658	199	61	)	)	PUNCT
ejpam-4658	199	62	̸=	̸=	PROPN
ejpam-4658	199	63	1	1	NUM
ejpam-4658	199	64	.	.	PUNCT
ejpam-4658	199	65	a.	a.	PROPN
ejpam-4658	199	66	h.	h.	PROPN
ejpam-4658	199	67	abragan	abragan	PROPN
ejpam-4658	199	68	,	,	PUNCT
ejpam-4658	199	69	h.	h.	PROPN
ejpam-4658	199	70	m.	m.	PROPN
ejpam-4658	199	71	rara	rara	PROPN
ejpam-4658	199	72	/	/	SYM
ejpam-4658	199	73	eur	eur	PROPN
ejpam-4658	199	74	.	.	PUNCT
ejpam-4658	200	1	j.	j.	PROPN
ejpam-4658	200	2	pure	pure	PROPN
ejpam-4658	200	3	appl	appl	PROPN
ejpam-4658	200	4	.	.	PROPN
ejpam-4658	200	5	math	math	PROPN
ejpam-4658	200	6	,	,	PUNCT
ejpam-4658	200	7	16	16	NUM
ejpam-4658	200	8	(	(	PUNCT
ejpam-4658	200	9	2	2	NUM
ejpam-4658	200	10	)	)	PUNCT
ejpam-4658	200	11	(	(	PUNCT
ejpam-4658	200	12	2023	2023	NUM
ejpam-4658	200	13	)	)	PUNCT
ejpam-4658	200	14	,	,	PUNCT
ejpam-4658	200	15	763	763	NUM
ejpam-4658	200	16	-	-	SYM
ejpam-4658	200	17	772	772	NUM
ejpam-4658	200	18	770	770	NUM
ejpam-4658	200	19	accordingly	accordingly	ADV
ejpam-4658	200	20	s	s	PART
ejpam-4658	200	21	is	be	AUX
ejpam-4658	200	22	a	a	DET
ejpam-4658	200	23	1	1	NUM
ejpam-4658	200	24	-	-	PUNCT
ejpam-4658	200	25	movable	movable	ADJ
ejpam-4658	200	26	strong	strong	ADJ
ejpam-4658	200	27	resolving	resolve	VERB
ejpam-4658	200	28	hop	hop	NOUN
ejpam-4658	200	29	dominating	dominating	NOUN
ejpam-4658	200	30	set	set	VERB
ejpam-4658	200	31	in	in	ADP
ejpam-4658	200	32	g	g	PROPN
ejpam-4658	200	33	◦	◦	NOUN
ejpam-4658	200	34	h.	h.	NOUN
ejpam-4658	200	35	corollary	corollary	ADJ
ejpam-4658	200	36	3	3	X
ejpam-4658	200	37	.	.	PUNCT
ejpam-4658	201	1	let	let	VERB
ejpam-4658	201	2	g	g	PRON
ejpam-4658	201	3	be	be	AUX
ejpam-4658	201	4	a	a	DET
ejpam-4658	201	5	connected	connected	ADJ
ejpam-4658	201	6	graph	graph	NOUN
ejpam-4658	201	7	of	of	ADP
ejpam-4658	201	8	order	order	NOUN
ejpam-4658	201	9	m	m	VERB
ejpam-4658	201	10	>	>	X
ejpam-4658	201	11	1	1	NUM
ejpam-4658	201	12	and	and	CCONJ
ejpam-4658	201	13	h	h	NOUN
ejpam-4658	201	14	be	be	VERB
ejpam-4658	201	15	any	any	DET
ejpam-4658	201	16	graph	graph	NOUN
ejpam-4658	201	17	of	of	ADP
ejpam-4658	201	18	order	order	NOUN
ejpam-4658	201	19	n	n	PRON
ejpam-4658	201	20	with	with	ADP
ejpam-4658	201	21	γ(h	γ(h	NOUN
ejpam-4658	201	22	)	)	PUNCT
ejpam-4658	201	23	̸=	̸=	PROPN
ejpam-4658	201	24	1	1	NUM
ejpam-4658	201	25	.	.	PUNCT
ejpam-4658	202	1	then	then	ADV
ejpam-4658	202	2	γ1msrh(g	γ1msrh(g	VERB
ejpam-4658	202	3	◦	◦	NOUN
ejpam-4658	202	4	h	h	NOUN
ejpam-4658	202	5	)	)	PUNCT
ejpam-4658	202	6	=	=	SYM
ejpam-4658	202	7	mn	mn	PROPN
ejpam-4658	202	8	.	.	PUNCT
ejpam-4658	202	9	proof	proof	NOUN
ejpam-4658	202	10	:	:	PUNCT
ejpam-4658	202	11	let	let	VERB
ejpam-4658	202	12	s	s	PRON
ejpam-4658	202	13	be	be	AUX
ejpam-4658	202	14	a	a	DET
ejpam-4658	202	15	γ1msrh	γ1msrh	NOUN
ejpam-4658	202	16	-	-	PUNCT
ejpam-4658	202	17	set	set	NOUN
ejpam-4658	202	18	of	of	ADP
ejpam-4658	202	19	g	g	PROPN
ejpam-4658	202	20	◦	◦	NOUN
ejpam-4658	202	21	h.	h.	NOUN
ejpam-4658	202	22	then	then	ADV
ejpam-4658	202	23	by	by	ADP
ejpam-4658	202	24	theorem	theorem	NOUN
ejpam-4658	202	25	6	6	NUM
ejpam-4658	202	26	,	,	PUNCT
ejpam-4658	202	27	s	s	PART
ejpam-4658	202	28	=	=	NOUN
ejpam-4658	202	29	a	a	DET
ejpam-4658	202	30	⋃	⋃	PROPN
ejpam-4658	202	31	(	(	PUNCT
ejpam-4658	202	32	⋃	⋃	NOUN
ejpam-4658	202	33	u∈v	u∈v	NOUN
ejpam-4658	202	34	(	(	PUNCT
ejpam-4658	202	35	g	g	NOUN
ejpam-4658	202	36	)	)	PUNCT
ejpam-4658	202	37	v	v	NOUN
ejpam-4658	202	38	(	(	PUNCT
ejpam-4658	202	39	hu	hu	PROPN
ejpam-4658	202	40	)	)	PUNCT
ejpam-4658	202	41	)	)	PUNCT
ejpam-4658	202	42	where	where	SCONJ
ejpam-4658	202	43	a	a	DET
ejpam-4658	202	44	⊆	⊆	NUM
ejpam-4658	202	45	v	v	NOUN
ejpam-4658	202	46	(	(	PUNCT
ejpam-4658	202	47	g	g	NOUN
ejpam-4658	202	48	)	)	PUNCT
ejpam-4658	202	49	.	.	PUNCT
ejpam-4658	203	1	thus	thus	ADV
ejpam-4658	203	2	,	,	PUNCT
ejpam-4658	203	3	γ1msrh(g	γ1msrh(g	VERB
ejpam-4658	203	4	◦	◦	NOUN
ejpam-4658	203	5	h	h	NOUN
ejpam-4658	203	6	)	)	PUNCT
ejpam-4658	203	7	=	=	PUNCT
ejpam-4658	203	8	|s|	|s|	NOUN
ejpam-4658	203	9	=	=	SYM
ejpam-4658	204	1	|a|+	|a|+	NOUN
ejpam-4658	204	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4658	204	3	⋃	⋃	NOUN
ejpam-4658	204	4	u∈v	u∈v	NOUN
ejpam-4658	204	5	(	(	PUNCT
ejpam-4658	204	6	g	g	NOUN
ejpam-4658	204	7	)	)	PUNCT
ejpam-4658	204	8	v	v	NOUN
ejpam-4658	204	9	(	(	PUNCT
ejpam-4658	204	10	hu	hu	PROPN
ejpam-4658	204	11	)	)	PUNCT
ejpam-4658	204	12	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4658	204	13	≥	≥	NUM
ejpam-4658	204	14	|v	|v	NOUN
ejpam-4658	204	15	(	(	PUNCT
ejpam-4658	204	16	g)||v	g)||v	PROPN
ejpam-4658	204	17	(	(	PUNCT
ejpam-4658	204	18	h)|	h)|	PROPN
ejpam-4658	204	19	=	=	SYM
ejpam-4658	204	20	mn	mn	PROPN
ejpam-4658	204	21	.	.	PROPN
ejpam-4658	204	22	let	let	VERB
ejpam-4658	204	23	a	a	DET
ejpam-4658	204	24	=	=	PUNCT
ejpam-4658	204	25	∅.	∅.	NOUN
ejpam-4658	204	26	then	then	ADV
ejpam-4658	204	27	s∗	s∗	PROPN
ejpam-4658	204	28	=	=	PUNCT
ejpam-4658	204	29	a	a	DET
ejpam-4658	204	30	⋃	⋃	PROPN
ejpam-4658	204	31	(	(	PUNCT
ejpam-4658	204	32	⋃	⋃	NOUN
ejpam-4658	204	33	u∈v	u∈v	NOUN
ejpam-4658	204	34	(	(	PUNCT
ejpam-4658	204	35	g	g	NOUN
ejpam-4658	204	36	)	)	PUNCT
ejpam-4658	204	37	v	v	NOUN
ejpam-4658	204	38	(	(	PUNCT
ejpam-4658	204	39	hu	hu	PROPN
ejpam-4658	204	40	)	)	PUNCT
ejpam-4658	204	41	)	)	PUNCT
ejpam-4658	204	42	is	be	AUX
ejpam-4658	204	43	a	a	DET
ejpam-4658	204	44	1	1	NUM
ejpam-4658	204	45	-	-	PUNCT
ejpam-4658	204	46	movable	movable	ADJ
ejpam-4658	204	47	strong	strong	ADJ
ejpam-4658	204	48	resolving	resolve	VERB
ejpam-4658	204	49	hop	hop	NOUN
ejpam-4658	204	50	dominating	dominating	NOUN
ejpam-4658	204	51	set	set	NOUN
ejpam-4658	204	52	of	of	ADP
ejpam-4658	204	53	g	g	PROPN
ejpam-4658	204	54	◦	◦	NOUN
ejpam-4658	204	55	h	h	NOUN
ejpam-4658	204	56	by	by	ADP
ejpam-4658	204	57	theorem	theorem	NOUN
ejpam-4658	204	58	6	6	NUM
ejpam-4658	204	59	.	.	PUNCT
ejpam-4658	205	1	hence	hence	ADV
ejpam-4658	205	2	,	,	PUNCT
ejpam-4658	205	3	γ1msrh(g	γ1msrh(g	X
ejpam-4658	205	4	◦	◦	NOUN
ejpam-4658	205	5	h	h	NOUN
ejpam-4658	205	6	)	)	PUNCT
ejpam-4658	205	7	≤	≤	NOUN
ejpam-4658	205	8	|s∗|	|s∗|	PUNCT
ejpam-4658	205	9	=	=	SYM
ejpam-4658	205	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4658	205	11	⋃	⋃	NOUN
ejpam-4658	205	12	u∈v	u∈v	NOUN
ejpam-4658	205	13	(	(	PUNCT
ejpam-4658	205	14	g	g	NOUN
ejpam-4658	205	15	)	)	PUNCT
ejpam-4658	205	16	v	v	NOUN
ejpam-4658	205	17	(	(	PUNCT
ejpam-4658	205	18	hu	hu	NOUN
ejpam-4658	205	19	)	)	PUNCT
ejpam-4658	205	20	∣∣∣∣	∣∣∣∣	PROPN
ejpam-4658	205	21	=	=	SYM
ejpam-4658	205	22	mn	mn	PROPN
ejpam-4658	205	23	.	.	PUNCT
ejpam-4658	206	1	therefore	therefore	ADV
ejpam-4658	206	2	,	,	PUNCT
ejpam-4658	206	3	γ1msrh(g	γ1msrh(g	X
ejpam-4658	206	4	◦	◦	NOUN
ejpam-4658	206	5	h	h	NOUN
ejpam-4658	206	6	)	)	PUNCT
ejpam-4658	206	7	=	=	SYM
ejpam-4658	206	8	mn	mn	PROPN
ejpam-4658	206	9	.	.	PROPN
ejpam-4658	206	10	example	example	NOUN
ejpam-4658	207	1	1	1	NUM
ejpam-4658	207	2	.	.	X
ejpam-4658	207	3	for	for	ADP
ejpam-4658	207	4	the	the	DET
ejpam-4658	207	5	graph	graph	NOUN
ejpam-4658	207	6	of	of	ADP
ejpam-4658	207	7	p3	p3	PROPN
ejpam-4658	207	8	◦	◦	NOUN
ejpam-4658	207	9	p4	p4	ADJ
ejpam-4658	207	10	,	,	PUNCT
ejpam-4658	207	11	the	the	DET
ejpam-4658	207	12	minimum	minimum	ADJ
ejpam-4658	207	13	1	1	NUM
ejpam-4658	207	14	-	-	PUNCT
ejpam-4658	207	15	movable	movable	ADJ
ejpam-4658	207	16	strong	strong	ADJ
ejpam-4658	207	17	resolving	resolve	VERB
ejpam-4658	207	18	hop	hop	NOUN
ejpam-4658	207	19	dominating	dominating	NOUN
ejpam-4658	207	20	set	set	NOUN
ejpam-4658	207	21	is	be	AUX
ejpam-4658	207	22	γ1msrh(p3	γ1msrh(p3	PROPN
ejpam-4658	207	23	◦	◦	NOUN
ejpam-4658	207	24	p4	p4	ADJ
ejpam-4658	207	25	)	)	PUNCT
ejpam-4658	207	26	=	=	SYM
ejpam-4658	207	27	3(4	3(4	NUM
ejpam-4658	207	28	)	)	PUNCT
ejpam-4658	207	29	=	=	PUNCT
ejpam-4658	208	1	12	12	NUM
ejpam-4658	208	2	.	.	NOUN
ejpam-4658	209	1	6	6	NUM
ejpam-4658	209	2	.	.	NOUN
ejpam-4658	209	3	lexicographic	lexicographic	ADJ
ejpam-4658	209	4	of	of	ADP
ejpam-4658	209	5	graphs	graph	NOUN
ejpam-4658	209	6	this	this	DET
ejpam-4658	209	7	section	section	NOUN
ejpam-4658	209	8	gives	give	VERB
ejpam-4658	209	9	characterization	characterization	NOUN
ejpam-4658	209	10	of	of	ADP
ejpam-4658	209	11	a	a	DET
ejpam-4658	209	12	1	1	NUM
ejpam-4658	209	13	-	-	PUNCT
ejpam-4658	209	14	movable	movable	ADJ
ejpam-4658	209	15	strong	strong	ADJ
ejpam-4658	209	16	resolving	resolve	VERB
ejpam-4658	209	17	hop	hop	NOUN
ejpam-4658	209	18	dominating	dominating	NOUN
ejpam-4658	209	19	sets	set	NOUN
ejpam-4658	209	20	in	in	ADP
ejpam-4658	209	21	the	the	DET
ejpam-4658	209	22	lexicographic	lexicographic	ADJ
ejpam-4658	209	23	product	product	NOUN
ejpam-4658	209	24	of	of	ADP
ejpam-4658	209	25	graphs	graph	NOUN
ejpam-4658	209	26	as	as	ADV
ejpam-4658	209	27	well	well	ADV
ejpam-4658	209	28	as	as	ADP
ejpam-4658	209	29	its	its	PRON
ejpam-4658	209	30	1	1	NUM
ejpam-4658	209	31	-	-	PUNCT
ejpam-4658	209	32	movable	movable	ADJ
ejpam-4658	209	33	strong	strong	ADJ
ejpam-4658	209	34	resolving	resolve	VERB
ejpam-4658	209	35	hop	hop	NOUN
ejpam-4658	209	36	domination	domination	NOUN
ejpam-4658	209	37	number	number	NOUN
ejpam-4658	209	38	.	.	PUNCT
ejpam-4658	210	1	theorem	theorem	VERB
ejpam-4658	210	2	7	7	NUM
ejpam-4658	210	3	.	.	PUNCT
ejpam-4658	211	1	let	let	VERB
ejpam-4658	211	2	g	g	PROPN
ejpam-4658	211	3	=	=	PROPN
ejpam-4658	211	4	kn	kn	PROPN
ejpam-4658	211	5	for	for	ADP
ejpam-4658	211	6	n	n	PROPN
ejpam-4658	211	7	>	>	SYM
ejpam-4658	211	8	1	1	NUM
ejpam-4658	211	9	and	and	CCONJ
ejpam-4658	211	10	h	h	NOUN
ejpam-4658	211	11	is	be	AUX
ejpam-4658	211	12	a	a	DET
ejpam-4658	211	13	connected	connected	ADJ
ejpam-4658	211	14	graph	graph	NOUN
ejpam-4658	211	15	with	with	ADP
ejpam-4658	211	16	γ(h	γ(h	NOUN
ejpam-4658	211	17	)	)	PUNCT
ejpam-4658	211	18	̸=	̸=	PROPN
ejpam-4658	211	19	1	1	NUM
ejpam-4658	211	20	.	.	PUNCT
ejpam-4658	212	1	a	a	DET
ejpam-4658	212	2	subset	subset	NOUN
ejpam-4658	212	3	s	s	X
ejpam-4658	212	4	of	of	ADP
ejpam-4658	212	5	v	v	NOUN
ejpam-4658	212	6	(	(	PUNCT
ejpam-4658	212	7	g[h	g[h	PROPN
ejpam-4658	212	8	]	]	PUNCT
ejpam-4658	212	9	)	)	PUNCT
ejpam-4658	212	10	is	be	AUX
ejpam-4658	212	11	a	a	DET
ejpam-4658	212	12	1	1	NUM
ejpam-4658	212	13	-	-	PUNCT
ejpam-4658	212	14	movable	movable	ADJ
ejpam-4658	212	15	strong	strong	ADJ
ejpam-4658	212	16	resolving	resolve	VERB
ejpam-4658	212	17	hop	hop	NOUN
ejpam-4658	212	18	dominating	dominating	NOUN
ejpam-4658	212	19	set	set	NOUN
ejpam-4658	212	20	of	of	ADP
ejpam-4658	212	21	g[h	g[h	PROPN
ejpam-4658	212	22	]	]	PUNCT
ejpam-4658	212	23	if	if	SCONJ
ejpam-4658	212	24	and	and	CCONJ
ejpam-4658	212	25	only	only	ADV
ejpam-4658	212	26	if	if	SCONJ
ejpam-4658	212	27	s	s	VERB
ejpam-4658	212	28	=	=	SYM
ejpam-4658	212	29	v	v	NOUN
ejpam-4658	212	30	(	(	PUNCT
ejpam-4658	212	31	g[h	g[h	PROPN
ejpam-4658	212	32	]	]	PUNCT
ejpam-4658	212	33	)	)	PUNCT
ejpam-4658	212	34	\	\	PUNCT
ejpam-4658	213	1	(	(	PUNCT
ejpam-4658	213	2	a×	a×	NOUN
ejpam-4658	213	3	c	c	X
ejpam-4658	213	4	)	)	PUNCT
ejpam-4658	213	5	,	,	PUNCT
ejpam-4658	213	6	where	where	SCONJ
ejpam-4658	213	7	a	a	PRON
ejpam-4658	213	8	is	be	AUX
ejpam-4658	213	9	a	a	DET
ejpam-4658	213	10	subset	subset	NOUN
ejpam-4658	213	11	of	of	ADP
ejpam-4658	213	12	v	v	NOUN
ejpam-4658	213	13	(	(	PUNCT
ejpam-4658	213	14	g	g	NOUN
ejpam-4658	213	15	)	)	PUNCT
ejpam-4658	213	16	and	and	CCONJ
ejpam-4658	213	17	c	c	AUX
ejpam-4658	213	18	=	=	PUNCT
ejpam-4658	213	19	∅.	∅.	NOUN
ejpam-4658	213	20	references	reference	NOUN
ejpam-4658	213	21	771	771	NUM
ejpam-4658	213	22	proof	proof	NOUN
ejpam-4658	213	23	:	:	PUNCT
ejpam-4658	213	24	suppose	suppose	VERB
ejpam-4658	213	25	s	s	NOUN
ejpam-4658	213	26	is	be	AUX
ejpam-4658	213	27	a	a	DET
ejpam-4658	213	28	1	1	NUM
ejpam-4658	213	29	-	-	PUNCT
ejpam-4658	213	30	movable	movable	ADJ
ejpam-4658	213	31	strong	strong	ADJ
ejpam-4658	213	32	resolving	resolve	VERB
ejpam-4658	213	33	hop	hop	NOUN
ejpam-4658	213	34	dominating	dominate	VERB
ejpam-4658	213	35	set	set	NOUN
ejpam-4658	213	36	g[h	g[h	PROPN
ejpam-4658	213	37	]	]	PUNCT
ejpam-4658	213	38	.	.	PUNCT
ejpam-4658	214	1	by	by	ADP
ejpam-4658	214	2	theorem	theorem	NOUN
ejpam-4658	214	3	3	3	NUM
ejpam-4658	214	4	,	,	PUNCT
ejpam-4658	214	5	s	s	PART
ejpam-4658	214	6	=	=	SYM
ejpam-4658	214	7	v	v	NOUN
ejpam-4658	214	8	(	(	PUNCT
ejpam-4658	214	9	g[h	g[h	PROPN
ejpam-4658	214	10	]	]	PUNCT
ejpam-4658	214	11	)	)	PUNCT
ejpam-4658	214	12	\	\	PUNCT
ejpam-4658	215	1	(	(	PUNCT
ejpam-4658	215	2	a	a	DET
ejpam-4658	215	3	×	×	NOUN
ejpam-4658	215	4	c	c	NOUN
ejpam-4658	215	5	)	)	PUNCT
ejpam-4658	215	6	where	where	SCONJ
ejpam-4658	215	7	a	a	DET
ejpam-4658	215	8	⊆	⊆	NUM
ejpam-4658	215	9	v	v	NOUN
ejpam-4658	215	10	(	(	PUNCT
ejpam-4658	215	11	g	g	NOUN
ejpam-4658	215	12	)	)	PUNCT
ejpam-4658	215	13	and	and	CCONJ
ejpam-4658	215	14	c	c	NOUN
ejpam-4658	215	15	=	=	SYM
ejpam-4658	215	16	∅	∅	NOUN
ejpam-4658	215	17	or	or	CCONJ
ejpam-4658	215	18	c	c	NOUN
ejpam-4658	215	19	is	be	AUX
ejpam-4658	215	20	a	a	DET
ejpam-4658	215	21	superclique	superclique	NOUN
ejpam-4658	215	22	in	in	ADP
ejpam-4658	215	23	h.	h.	PROPN
ejpam-4658	215	24	suppose	suppose	VERB
ejpam-4658	215	25	c	c	AUX
ejpam-4658	215	26	̸=	̸=	PROPN
ejpam-4658	215	27	∅	∅	NOUN
ejpam-4658	215	28	and	and	CCONJ
ejpam-4658	215	29	c	c	NOUN
ejpam-4658	215	30	is	be	AUX
ejpam-4658	215	31	a	a	DET
ejpam-4658	215	32	superclique	superclique	NOUN
ejpam-4658	215	33	in	in	ADP
ejpam-4658	215	34	h.	h.	PROPN
ejpam-4658	215	35	let	let	VERB
ejpam-4658	215	36	(	(	PUNCT
ejpam-4658	215	37	x	x	NOUN
ejpam-4658	215	38	,	,	PUNCT
ejpam-4658	215	39	y	y	PROPN
ejpam-4658	215	40	)	)	PUNCT
ejpam-4658	215	41	∈	∈	PROPN
ejpam-4658	215	42	s.	s.	PROPN
ejpam-4658	216	1	then	then	ADV
ejpam-4658	216	2	y	y	PROPN
ejpam-4658	216	3	/∈	/∈	PUNCT
ejpam-4658	216	4	c.	c.	PROPN
ejpam-4658	216	5	hence	hence	ADV
ejpam-4658	216	6	,	,	PUNCT
ejpam-4658	216	7	s	s	NOUN
ejpam-4658	216	8	\	\	X
ejpam-4658	216	9	{	{	PUNCT
ejpam-4658	216	10	x	x	NOUN
ejpam-4658	216	11	,	,	PUNCT
ejpam-4658	216	12	y	y	PROPN
ejpam-4658	216	13	}	}	PUNCT
ejpam-4658	216	14	=	=	SYM
ejpam-4658	216	15	v	v	NOUN
ejpam-4658	216	16	(	(	PUNCT
ejpam-4658	216	17	g[h	g[h	PROPN
ejpam-4658	216	18	]	]	PUNCT
ejpam-4658	216	19	)	)	PUNCT
ejpam-4658	216	20	\	\	PUNCT
ejpam-4658	217	1	(	(	PUNCT
ejpam-4658	217	2	(	(	PUNCT
ejpam-4658	217	3	a	a	DET
ejpam-4658	217	4	×	×	NOUN
ejpam-4658	217	5	c	c	NOUN
ejpam-4658	217	6	)	)	PUNCT
ejpam-4658	217	7	∪	∪	X
ejpam-4658	217	8	{	{	PUNCT
ejpam-4658	217	9	x	x	NOUN
ejpam-4658	217	10	,	,	PUNCT
ejpam-4658	217	11	y	y	NOUN
ejpam-4658	217	12	}	}	PUNCT
ejpam-4658	217	13	)	)	PUNCT
ejpam-4658	217	14	.	.	PUNCT
ejpam-4658	218	1	since	since	SCONJ
ejpam-4658	218	2	γ(h	γ(h	NOUN
ejpam-4658	218	3	)	)	PUNCT
ejpam-4658	218	4	̸=	̸=	PROPN
ejpam-4658	218	5	1	1	NUM
ejpam-4658	218	6	,	,	PUNCT
ejpam-4658	218	7	c	c	NOUN
ejpam-4658	218	8	∪	∪	X
ejpam-4658	218	9	{	{	PUNCT
ejpam-4658	218	10	y	y	NOUN
ejpam-4658	218	11	}	}	PUNCT
ejpam-4658	218	12	is	be	AUX
ejpam-4658	218	13	not	not	PART
ejpam-4658	218	14	a	a	DET
ejpam-4658	218	15	superclique	superclique	NOUN
ejpam-4658	218	16	in	in	ADP
ejpam-4658	218	17	h.	h.	PROPN
ejpam-4658	218	18	therefore	therefore	ADV
ejpam-4658	218	19	a	a	DET
ejpam-4658	218	20	⊆	⊆	NUM
ejpam-4658	218	21	v	v	NOUN
ejpam-4658	218	22	(	(	PUNCT
ejpam-4658	218	23	g)and	g)and	NOUN
ejpam-4658	218	24	c	c	NOUN
ejpam-4658	218	25	=	=	PUNCT
ejpam-4658	218	26	∅.	∅.	PRON
ejpam-4658	218	27	the	the	DET
ejpam-4658	218	28	converse	converse	NOUN
ejpam-4658	218	29	follows	follow	VERB
ejpam-4658	218	30	immediately	immediately	ADV
ejpam-4658	218	31	from	from	ADP
ejpam-4658	218	32	theorem	theorem	ADJ
ejpam-4658	218	33	3	3	NUM
ejpam-4658	218	34	.	.	PUNCT
ejpam-4658	218	35	as	as	ADP
ejpam-4658	218	36	a	a	DET
ejpam-4658	218	37	consequence	consequence	NOUN
ejpam-4658	218	38	of	of	ADP
ejpam-4658	218	39	theorem	theorem	NOUN
ejpam-4658	218	40	7	7	NUM
ejpam-4658	218	41	the	the	DET
ejpam-4658	218	42	next	next	ADJ
ejpam-4658	218	43	result	result	NOUN
ejpam-4658	218	44	follows	follow	VERB
ejpam-4658	218	45	.	.	PUNCT
ejpam-4658	219	1	corollary	corollary	ADJ
ejpam-4658	219	2	4	4	NUM
ejpam-4658	219	3	.	.	PUNCT
ejpam-4658	220	1	let	let	VERB
ejpam-4658	220	2	g	g	PROPN
ejpam-4658	220	3	=	=	PROPN
ejpam-4658	220	4	kn	kn	PROPN
ejpam-4658	220	5	for	for	ADP
ejpam-4658	220	6	n	n	PROPN
ejpam-4658	220	7	>	>	SYM
ejpam-4658	220	8	1	1	NUM
ejpam-4658	220	9	and	and	CCONJ
ejpam-4658	220	10	h	h	NOUN
ejpam-4658	220	11	is	be	AUX
ejpam-4658	220	12	a	a	DET
ejpam-4658	220	13	connected	connected	ADJ
ejpam-4658	220	14	graph	graph	NOUN
ejpam-4658	220	15	of	of	ADP
ejpam-4658	220	16	order	order	NOUN
ejpam-4658	220	17	m	m	VERB
ejpam-4658	220	18	and	and	CCONJ
ejpam-4658	220	19	γ(h	γ(h	NOUN
ejpam-4658	220	20	)	)	PUNCT
ejpam-4658	220	21	̸=	̸=	PROPN
ejpam-4658	220	22	1	1	NUM
ejpam-4658	220	23	.	.	PUNCT
ejpam-4658	221	1	then	then	ADV
ejpam-4658	221	2	γ1msrh(g[h	γ1msrh(g[h	VERB
ejpam-4658	221	3	]	]	PUNCT
ejpam-4658	221	4	)	)	PUNCT
ejpam-4658	221	5	=	=	SYM
ejpam-4658	221	6	mn	mn	PROPN
ejpam-4658	221	7	.	.	PROPN
ejpam-4658	221	8	example	example	NOUN
ejpam-4658	222	1	2	2	NUM
ejpam-4658	222	2	.	.	PUNCT
ejpam-4658	222	3	the	the	DET
ejpam-4658	222	4	sets	set	NOUN
ejpam-4658	222	5	of	of	ADP
ejpam-4658	222	6	shaded	shaded	ADJ
ejpam-4658	222	7	vertices	vertex	NOUN
ejpam-4658	222	8	in	in	ADP
ejpam-4658	222	9	k4[p4	k4[p4	PROPN
ejpam-4658	222	10	]	]	PUNCT
ejpam-4658	222	11	and	and	CCONJ
ejpam-4658	222	12	k4[p3	k4[p3	NOUN
ejpam-4658	222	13	]	]	X
ejpam-4658	222	14	in	in	ADP
ejpam-4658	222	15	figure	figure	NOUN
ejpam-4658	222	16	1	1	NUM
ejpam-4658	222	17	represent	represent	VERB
ejpam-4658	222	18	1movable	1movable	NUM
ejpam-4658	222	19	strong	strong	ADJ
ejpam-4658	222	20	resolving	resolve	VERB
ejpam-4658	222	21	hop	hop	NOUN
ejpam-4658	222	22	dominating	dominating	NOUN
ejpam-4658	222	23	sets	set	NOUN
ejpam-4658	222	24	.	.	PUNCT
ejpam-4658	222	25	.........	.........	PUNCT
ejpam-4658	223	1	........	........	PUNCT
ejpam-4658	223	2	........	........	PUNCT
ejpam-4658	223	3	........	........	PUNCT
ejpam-4658	223	4	........	........	PUNCT
ejpam-4658	223	5	........	........	PUNCT
ejpam-4658	224	1	........	........	PUNCT
ejpam-4658	224	2	.....	.....	PUNCT
ejpam-4658	224	3	............	............	PUNCT
ejpam-4658	224	4	...........	...........	PUNCT
ejpam-4658	224	5	...........	...........	PUNCT
ejpam-4658	224	6	...........	...........	PUNCT
ejpam-4658	224	7	...........	...........	PUNCT
ejpam-4658	224	8	...........	...........	PUNCT
ejpam-4658	224	9	...........	...........	PUNCT
ejpam-4658	224	10	...........	...........	PUNCT
ejpam-4658	224	11	..	..	PUNCT
ejpam-4658	224	12	...................	...................	PUNCT
ejpam-4658	225	1	..................	..................	PUNCT
ejpam-4658	225	2	..................	..................	PUNCT
ejpam-4658	226	1	..................	..................	PUNCT
ejpam-4658	226	2	..................	..................	PUNCT
ejpam-4658	227	1	..................	..................	PUNCT
ejpam-4658	227	2	..................	..................	PUNCT
ejpam-4658	228	1	..................	..................	PUNCT
ejpam-4658	228	2	........................................................................................................	........................................................................................................	PUNCT
ejpam-4658	228	3	........	........	PUNCT
ejpam-4658	229	1	........	........	PUNCT
ejpam-4658	229	2	........	........	PUNCT
ejpam-4658	229	3	........	........	PUNCT
ejpam-4658	229	4	........	........	PUNCT
ejpam-4658	229	5	........	........	PUNCT
ejpam-4658	230	1	......	......	PUNCT
ejpam-4658	230	2	............	............	PUNCT
ejpam-4658	230	3	...........	...........	PUNCT
ejpam-4658	230	4	...........	...........	PUNCT
ejpam-4658	230	5	...........	...........	PUNCT
ejpam-4658	230	6	...........	...........	PUNCT
ejpam-4658	230	7	...........	...........	PUNCT
ejpam-4658	230	8	...........	...........	PUNCT
ejpam-4658	230	9	...........	...........	PUNCT
ejpam-4658	230	10	........................................................................................................................................................	........................................................................................................................................................	PUNCT
ejpam-4658	230	11	...........................................................................................	...........................................................................................	PUNCT
ejpam-4658	230	12	...........................................................................................	...........................................................................................	PUNCT
ejpam-4658	230	13	.........................................................................................................................................................................................................................	.........................................................................................................................................................................................................................	PUNCT
ejpam-4658	230	14	...............................................................................................................................................................	...............................................................................................................................................................	PUNCT
ejpam-4658	230	15	........	........	PUNCT
ejpam-4658	230	16	........	........	PUNCT
ejpam-4658	230	17	........	........	PUNCT
ejpam-4658	230	18	........	........	PUNCT
ejpam-4658	230	19	........	........	PUNCT
ejpam-4658	230	20	........	........	PUNCT
ejpam-4658	231	1	.....	.....	PUNCT
ejpam-4658	231	2	..........................	..........................	PUNCT
ejpam-4658	232	1	.........................	.........................	PUNCT
ejpam-4658	232	2	.........................	.........................	PUNCT
ejpam-4658	232	3	.........................	.........................	PUNCT
ejpam-4658	232	4	.........................	.........................	PUNCT
ejpam-4658	232	5	.........................	.........................	PUNCT
ejpam-4658	232	6	.........................	.........................	PUNCT
ejpam-4658	232	7	.........................	.........................	PUNCT
ejpam-4658	233	1	................	................	PUNCT
ejpam-4658	233	2	...................	...................	PUNCT
ejpam-4658	233	3	..................	..................	PUNCT
ejpam-4658	234	1	..................	..................	PUNCT
ejpam-4658	234	2	..................	..................	PUNCT
ejpam-4658	235	1	..................	..................	PUNCT
ejpam-4658	235	2	..................	..................	PUNCT
ejpam-4658	236	1	..................	..................	PUNCT
ejpam-4658	236	2	..................	..................	PUNCT
ejpam-4658	237	1	.....	.....	PUNCT
ejpam-4658	237	2	............	............	PUNCT
ejpam-4658	237	3	...........	...........	PUNCT
ejpam-4658	237	4	...........	...........	PUNCT
ejpam-4658	237	5	...........	...........	PUNCT
ejpam-4658	237	6	...........	...........	PUNCT
ejpam-4658	237	7	...........	...........	PUNCT
ejpam-4658	237	8	...........	...........	PUNCT
ejpam-4658	237	9	...........	...........	PUNCT
ejpam-4658	237	10	..	..	PUNCT
ejpam-4658	237	11	.........	.........	PUNCT
ejpam-4658	237	12	........	........	PUNCT
ejpam-4658	237	13	........	........	PUNCT
ejpam-4658	237	14	........	........	PUNCT
ejpam-4658	237	15	........	........	PUNCT
ejpam-4658	237	16	........	........	PUNCT
ejpam-4658	237	17	........	........	PUNCT
ejpam-4658	238	1	.....	.....	PUNCT
ejpam-4658	238	2	..........................	..........................	PUNCT
ejpam-4658	239	1	.........................	.........................	PUNCT
ejpam-4658	239	2	.........................	.........................	PUNCT
ejpam-4658	239	3	.........................	.........................	PUNCT
ejpam-4658	239	4	.........................	.........................	PUNCT
ejpam-4658	239	5	.........................	.........................	PUNCT
ejpam-4658	239	6	.........................	.........................	PUNCT
ejpam-4658	239	7	.........................	.........................	PUNCT
ejpam-4658	240	1	................	................	PUNCT
ejpam-4658	240	2	...................	...................	PUNCT
ejpam-4658	240	3	..................	..................	PUNCT
ejpam-4658	241	1	..................	..................	PUNCT
ejpam-4658	241	2	..................	..................	PUNCT
ejpam-4658	242	1	..................	..................	PUNCT
ejpam-4658	242	2	..................	..................	PUNCT
ejpam-4658	243	1	..................	..................	PUNCT
ejpam-4658	243	2	..................	..................	PUNCT
ejpam-4658	244	1	.....	.....	PUNCT
ejpam-4658	244	2	............	............	PUNCT
ejpam-4658	244	3	...........	...........	PUNCT
ejpam-4658	244	4	...........	...........	PUNCT
ejpam-4658	244	5	...........	...........	PUNCT
ejpam-4658	244	6	...........	...........	PUNCT
ejpam-4658	244	7	...........	...........	PUNCT
ejpam-4658	244	8	...........	...........	PUNCT
ejpam-4658	244	9	...........	...........	PUNCT
ejpam-4658	244	10	..	..	PUNCT
ejpam-4658	244	11	...................	...................	PUNCT
ejpam-4658	244	12	..................	..................	PUNCT
ejpam-4658	244	13	..................	..................	PUNCT
ejpam-4658	244	14	..................	..................	PUNCT
ejpam-4658	244	15	..................	..................	PUNCT
ejpam-4658	244	16	..................	..................	PUNCT
ejpam-4658	244	17	..................	..................	PUNCT
ejpam-4658	245	1	..................	..................	PUNCT
ejpam-4658	245	2	.....	.....	PUNCT
ejpam-4658	245	3	.........	.........	PUNCT
ejpam-4658	245	4	........	........	PUNCT
ejpam-4658	245	5	........	........	PUNCT
ejpam-4658	245	6	........	........	PUNCT
ejpam-4658	245	7	........	........	PUNCT
ejpam-4658	245	8	........	........	PUNCT
ejpam-4658	246	1	........	........	PUNCT
ejpam-4658	246	2	.....	.....	PUNCT
ejpam-4658	246	3	.........	.........	PUNCT
ejpam-4658	246	4	........	........	PUNCT
ejpam-4658	246	5	........	........	PUNCT
ejpam-4658	246	6	........	........	PUNCT
ejpam-4658	246	7	........	........	PUNCT
ejpam-4658	246	8	........	........	PUNCT
ejpam-4658	247	1	........	........	PUNCT
ejpam-4658	247	2	.....	.....	PUNCT
ejpam-4658	247	3	.........	.........	PUNCT
ejpam-4658	247	4	........	........	PUNCT
ejpam-4658	247	5	........	........	PUNCT
ejpam-4658	247	6	........	........	PUNCT
ejpam-4658	247	7	........	........	PUNCT
ejpam-4658	247	8	........	........	PUNCT
ejpam-4658	248	1	........	........	PUNCT
ejpam-4658	248	2	............................................................................................................	............................................................................................................	PUNCT
ejpam-4658	249	1	...........	...........	PUNCT
ejpam-4658	249	2	...........	...........	PUNCT
ejpam-4658	249	3	...........	...........	PUNCT
ejpam-4658	249	4	...........	...........	PUNCT
ejpam-4658	249	5	...........	...........	PUNCT
ejpam-4658	249	6	...........	...........	PUNCT
ejpam-4658	249	7	...........	...........	PUNCT
ejpam-4658	249	8	......................................................................................................................................................................................................................	......................................................................................................................................................................................................................	PUNCT
ejpam-4658	249	9	..............................................................	..............................................................	PUNCT
ejpam-4658	249	10	.........	.........	PUNCT
ejpam-4658	249	11	........	........	PUNCT
ejpam-4658	249	12	........	........	PUNCT
ejpam-4658	249	13	........	........	PUNCT
ejpam-4658	249	14	........	........	PUNCT
ejpam-4658	249	15	........	........	PUNCT
ejpam-4658	249	16	........	........	PUNCT
ejpam-4658	250	1	.....	.....	PUNCT
ejpam-4658	250	2	..............................................................	..............................................................	PUNCT
ejpam-4658	250	3	...........................................................................................	...........................................................................................	PUNCT
ejpam-4658	251	1	.........................................................................................................................................................	.........................................................................................................................................................	PUNCT
ejpam-4658	251	2	......................................................................................................................................................	......................................................................................................................................................	NUM
ejpam-4658	251	3	..............................................................	..............................................................	PUNCT
ejpam-4658	251	4	.........................................................................................................................................................................................................................	.........................................................................................................................................................................................................................	PUNCT
ejpam-4658	251	5	..............................................................	..............................................................	PUNCT
ejpam-4658	251	6	..............................................................	..............................................................	PUNCT
ejpam-4658	251	7	..............................................................	..............................................................	PUNCT
ejpam-4658	251	8	..............................................................	..............................................................	PUNCT
ejpam-4658	251	9	.........	.........	PUNCT
ejpam-4658	251	10	........	........	PUNCT
ejpam-4658	251	11	........	........	PUNCT
ejpam-4658	251	12	........	........	PUNCT
ejpam-4658	251	13	........	........	PUNCT
ejpam-4658	251	14	........	........	PUNCT
ejpam-4658	251	15	........	........	PUNCT
ejpam-4658	252	1	.....	.....	PUNCT
ejpam-4658	252	2	.........	.........	PUNCT
ejpam-4658	252	3	........	........	PUNCT
ejpam-4658	252	4	........	........	PUNCT
ejpam-4658	252	5	........	........	PUNCT
ejpam-4658	252	6	........	........	PUNCT
ejpam-4658	252	7	........	........	PUNCT
ejpam-4658	252	8	........	........	PUNCT
ejpam-4658	253	1	.....	.....	PUNCT
ejpam-4658	253	2	.........	.........	PUNCT
ejpam-4658	253	3	........	........	PUNCT
ejpam-4658	253	4	........	........	PUNCT
ejpam-4658	253	5	........	........	PUNCT
ejpam-4658	253	6	........	........	PUNCT
ejpam-4658	253	7	........	........	PUNCT
ejpam-4658	253	8	........	........	PUNCT
ejpam-4658	254	1	.....	.....	PUNCT
ejpam-4658	254	2	.........	.........	PUNCT
ejpam-4658	254	3	........	........	PUNCT
ejpam-4658	254	4	........	........	PUNCT
ejpam-4658	254	5	........	........	PUNCT
ejpam-4658	254	6	........	........	PUNCT
ejpam-4658	254	7	........	........	PUNCT
ejpam-4658	254	8	........	........	PUNCT
ejpam-4658	255	1	.....	.....	PUNCT
ejpam-4658	255	2	..............................................................	..............................................................	PUNCT
ejpam-4658	255	3	..............................................................	..............................................................	PUNCT
ejpam-4658	256	1	..............................................................	..............................................................	PUNCT
ejpam-4658	256	2	............	............	PUNCT
ejpam-4658	256	3	...........	...........	PUNCT
ejpam-4658	256	4	...........	...........	PUNCT
ejpam-4658	256	5	...........	...........	PUNCT
ejpam-4658	256	6	...........	...........	PUNCT
ejpam-4658	256	7	...........	...........	PUNCT
ejpam-4658	256	8	...........	...........	PUNCT
ejpam-4658	256	9	...........	...........	PUNCT
ejpam-4658	256	10	..	..	PUNCT
ejpam-4658	256	11	...........................................................................................	...........................................................................................	PUNCT
ejpam-4658	257	1	......................................................................................................................................................	......................................................................................................................................................	PUNCT
ejpam-4658	257	2	.....................................................................................................................................................................................................................................	.....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	257	3	...........	...........	PUNCT
ejpam-4658	257	4	...........	...........	PUNCT
ejpam-4658	257	5	...........	...........	PUNCT
ejpam-4658	257	6	...........	...........	PUNCT
ejpam-4658	257	7	...........	...........	PUNCT
ejpam-4658	257	8	...........	...........	PUNCT
ejpam-4658	257	9	...........	...........	PUNCT
ejpam-4658	257	10	..	..	PUNCT
ejpam-4658	257	11	...........................................................................................	...........................................................................................	PUNCT
ejpam-4658	258	1	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-4658	258	2	..................	..................	PUNCT
ejpam-4658	258	3	..................	..................	PUNCT
ejpam-4658	258	4	..................	..................	PUNCT
ejpam-4658	258	5	..................	..................	PUNCT
ejpam-4658	259	1	..................	..................	PUNCT
ejpam-4658	259	2	..................	..................	PUNCT
ejpam-4658	260	1	..................	..................	PUNCT
ejpam-4658	260	2	.....	.....	PUNCT
ejpam-4658	260	3	............	............	PUNCT
ejpam-4658	260	4	...........	...........	PUNCT
ejpam-4658	260	5	...........	...........	PUNCT
ejpam-4658	260	6	...........	...........	PUNCT
ejpam-4658	260	7	...........	...........	PUNCT
ejpam-4658	260	8	...........	...........	PUNCT
ejpam-4658	260	9	...........	...........	PUNCT
ejpam-4658	260	10	...........	...........	PUNCT
ejpam-4658	260	11	..	..	PUNCT
ejpam-4658	260	12	.....................................................................................................................	.....................................................................................................................	PUNCT
ejpam-4658	260	13	.........................	.........................	PUNCT
ejpam-4658	261	1	.........................	.........................	PUNCT
ejpam-4658	261	2	.........................	.........................	PUNCT
ejpam-4658	261	3	.........................	.........................	PUNCT
ejpam-4658	261	4	.........................	.........................	PUNCT
ejpam-4658	261	5	.........................	.........................	PUNCT
ejpam-4658	261	6	.........................	.........................	PUNCT
ejpam-4658	262	1	................	................	PUNCT
ejpam-4658	262	2	...................	...................	PUNCT
ejpam-4658	262	3	..................	..................	PUNCT
ejpam-4658	263	1	..................	..................	PUNCT
ejpam-4658	263	2	..................	..................	PUNCT
ejpam-4658	264	1	..................	..................	PUNCT
ejpam-4658	264	2	..................	..................	PUNCT
ejpam-4658	265	1	..................	..................	PUNCT
ejpam-4658	265	2	..................	..................	PUNCT
ejpam-4658	266	1	.....	.....	PUNCT
ejpam-4658	266	2	............	............	PUNCT
ejpam-4658	266	3	...........	...........	PUNCT
ejpam-4658	266	4	...........	...........	PUNCT
ejpam-4658	266	5	...........	...........	PUNCT
ejpam-4658	266	6	...........	...........	PUNCT
ejpam-4658	266	7	...........	...........	PUNCT
ejpam-4658	266	8	...........	...........	PUNCT
ejpam-4658	266	9	...........	...........	PUNCT
ejpam-4658	266	10	..	..	PUNCT
ejpam-4658	266	11	....................................	....................................	PUNCT
ejpam-4658	266	12	....................................	....................................	PUNCT
ejpam-4658	267	1	....................................	....................................	PUNCT
ejpam-4658	267	2	........................................................................	........................................................................	PUNCT
ejpam-4658	268	1	....................................	....................................	PUNCT
ejpam-4658	268	2	....................................	....................................	PUNCT
ejpam-4658	269	1	....................................	....................................	PUNCT
ejpam-4658	269	2	....................................	....................................	PUNCT
ejpam-4658	270	1	....................................	....................................	PUNCT
ejpam-4658	270	2	....................................	....................................	PUNCT
ejpam-4658	271	1	....................................	....................................	PUNCT
ejpam-4658	271	2	....................................	....................................	PUNCT
ejpam-4658	272	1	....................................	....................................	PUNCT
ejpam-4658	272	2	....................................	....................................	PUNCT
ejpam-4658	273	1	....................................	....................................	PUNCT
ejpam-4658	274	1	•	•	NUM
ejpam-4658	274	2	•	•	NUM
ejpam-4658	274	3	••	••	NOUN
ejpam-4658	274	4	•	•	NUM
ejpam-4658	274	5	•	•	NOUN
ejpam-4658	274	6	••	••	NOUN
ejpam-4658	274	7	•	•	NUM
ejpam-4658	274	8	•	•	NUM
ejpam-4658	274	9	•	•	NUM
ejpam-4658	274	10	•	•	NUM
ejpam-4658	274	11	•	•	NUM
ejpam-4658	274	12	•	•	NOUN
ejpam-4658	274	13	•	•	NOUN
ejpam-4658	274	14	•	•	NOUN
ejpam-4658	274	15	....................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	274	16	....................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	274	17	.................................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................................	PUNCT
ejpam-4658	274	18	....................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	275	1	k4[p4	k4[p4	NOUN
ejpam-4658	275	2	]	]	X
ejpam-4658	275	3	....................................	....................................	PUNCT
ejpam-4658	275	4	....................................	....................................	PUNCT
ejpam-4658	275	5	....................................	....................................	PUNCT
ejpam-4658	275	6	....................................	....................................	PUNCT
ejpam-4658	275	7	....................................	....................................	PUNCT
ejpam-4658	275	8	....................................	....................................	PUNCT
ejpam-4658	275	9	....................................	....................................	PUNCT
ejpam-4658	275	10	....................................	....................................	PUNCT
ejpam-4658	275	11	....................................	....................................	PUNCT
ejpam-4658	275	12	....................................	....................................	PUNCT
ejpam-4658	275	13	....................................	....................................	PUNCT
ejpam-4658	275	14	....................................	....................................	PUNCT
ejpam-4658	275	15	.........	.........	PUNCT
ejpam-4658	275	16	........	........	PUNCT
ejpam-4658	275	17	........	........	PUNCT
ejpam-4658	275	18	........	........	PUNCT
ejpam-4658	275	19	........	........	PUNCT
ejpam-4658	275	20	........	........	PUNCT
ejpam-4658	275	21	........	........	PUNCT
ejpam-4658	276	1	.....	.....	PUNCT
ejpam-4658	276	2	.........	.........	PUNCT
ejpam-4658	276	3	........	........	PUNCT
ejpam-4658	276	4	........	........	PUNCT
ejpam-4658	276	5	........	........	PUNCT
ejpam-4658	276	6	........	........	PUNCT
ejpam-4658	276	7	........	........	PUNCT
ejpam-4658	276	8	........	........	PUNCT
ejpam-4658	277	1	.....	.....	PUNCT
ejpam-4658	277	2	.........	.........	PUNCT
ejpam-4658	277	3	........	........	PUNCT
ejpam-4658	277	4	........	........	PUNCT
ejpam-4658	277	5	........	........	PUNCT
ejpam-4658	277	6	........	........	PUNCT
ejpam-4658	277	7	........	........	PUNCT
ejpam-4658	277	8	........	........	PUNCT
ejpam-4658	278	1	.....	.....	PUNCT
ejpam-4658	278	2	.........	.........	PUNCT
ejpam-4658	278	3	........	........	PUNCT
ejpam-4658	278	4	........	........	PUNCT
ejpam-4658	278	5	........	........	PUNCT
ejpam-4658	278	6	........	........	PUNCT
ejpam-4658	278	7	........	........	PUNCT
ejpam-4658	278	8	........	........	PUNCT
ejpam-4658	279	1	.....	.....	PUNCT
ejpam-4658	279	2	.........	.........	PUNCT
ejpam-4658	279	3	........	........	PUNCT
ejpam-4658	279	4	........	........	PUNCT
ejpam-4658	279	5	........	........	PUNCT
ejpam-4658	279	6	........	........	PUNCT
ejpam-4658	279	7	........	........	PUNCT
ejpam-4658	279	8	........	........	PUNCT
ejpam-4658	280	1	.....	.....	PUNCT
ejpam-4658	280	2	.........	.........	PUNCT
ejpam-4658	280	3	........	........	PUNCT
ejpam-4658	280	4	........	........	PUNCT
ejpam-4658	280	5	........	........	PUNCT
ejpam-4658	280	6	........	........	PUNCT
ejpam-4658	280	7	........	........	PUNCT
ejpam-4658	280	8	........	........	PUNCT
ejpam-4658	281	1	.....	.....	PUNCT
ejpam-4658	281	2	.........	.........	PUNCT
ejpam-4658	281	3	........	........	PUNCT
ejpam-4658	281	4	........	........	PUNCT
ejpam-4658	281	5	........	........	PUNCT
ejpam-4658	281	6	........	........	PUNCT
ejpam-4658	281	7	........	........	PUNCT
ejpam-4658	281	8	........	........	PUNCT
ejpam-4658	282	1	.....	.....	PUNCT
ejpam-4658	282	2	.........	.........	PUNCT
ejpam-4658	282	3	........	........	PUNCT
ejpam-4658	282	4	........	........	PUNCT
ejpam-4658	282	5	........	........	PUNCT
ejpam-4658	282	6	........	........	PUNCT
ejpam-4658	282	7	........	........	PUNCT
ejpam-4658	282	8	........	........	PUNCT
ejpam-4658	283	1	.....	.....	PUNCT
ejpam-4658	283	2	.........	.........	PUNCT
ejpam-4658	283	3	........	........	PUNCT
ejpam-4658	283	4	........	........	PUNCT
ejpam-4658	283	5	........	........	PUNCT
ejpam-4658	283	6	........	........	PUNCT
ejpam-4658	283	7	........	........	PUNCT
ejpam-4658	283	8	........	........	PUNCT
ejpam-4658	284	1	.....	.....	PUNCT
ejpam-4658	284	2	..............................................................	..............................................................	PUNCT
ejpam-4658	284	3	..............................................................	..............................................................	PUNCT
ejpam-4658	284	4	..............................................................	..............................................................	PUNCT
ejpam-4658	284	5	..............................................................	..............................................................	PUNCT
ejpam-4658	284	6	..............................................................	..............................................................	PUNCT
ejpam-4658	284	7	..............................................................	..............................................................	PUNCT
ejpam-4658	284	8	..............................................................	..............................................................	PUNCT
ejpam-4658	284	9	..............................................................	..............................................................	PUNCT
ejpam-4658	284	10	...........................................................................................	...........................................................................................	PUNCT
ejpam-4658	285	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4658	285	2	...........	...........	PUNCT
ejpam-4658	285	3	...........	...........	PUNCT
ejpam-4658	285	4	...........	...........	PUNCT
ejpam-4658	285	5	...........	...........	PUNCT
ejpam-4658	285	6	...........	...........	PUNCT
ejpam-4658	285	7	...........	...........	PUNCT
ejpam-4658	285	8	...........	...........	PUNCT
ejpam-4658	285	9	..	..	PUNCT
ejpam-4658	285	10	..............................................................................................................	..............................................................................................................	PUNCT
ejpam-4658	285	11	..................	..................	PUNCT
ejpam-4658	286	1	..................	..................	PUNCT
ejpam-4658	286	2	..................	..................	PUNCT
ejpam-4658	287	1	..................	..................	PUNCT
ejpam-4658	287	2	..................	..................	PUNCT
ejpam-4658	288	1	..................	..................	PUNCT
ejpam-4658	288	2	..................	..................	PUNCT
ejpam-4658	289	1	.....	.....	PUNCT
ejpam-4658	289	2	............	............	PUNCT
ejpam-4658	289	3	...........	...........	PUNCT
ejpam-4658	289	4	...........	...........	PUNCT
ejpam-4658	289	5	...........	...........	PUNCT
ejpam-4658	289	6	...........	...........	PUNCT
ejpam-4658	289	7	...........	...........	PUNCT
ejpam-4658	289	8	...........	...........	PUNCT
ejpam-4658	289	9	...........	...........	PUNCT
ejpam-4658	289	10	..	..	PUNCT
ejpam-4658	289	11	...........................................................................................	...........................................................................................	PUNCT
ejpam-4658	290	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4658	290	2	...........	...........	PUNCT
ejpam-4658	290	3	...........	...........	PUNCT
ejpam-4658	290	4	...........	...........	PUNCT
ejpam-4658	290	5	...........	...........	PUNCT
ejpam-4658	290	6	...........	...........	PUNCT
ejpam-4658	290	7	...........	...........	PUNCT
ejpam-4658	290	8	...........	...........	PUNCT
ejpam-4658	290	9	..	..	PUNCT
ejpam-4658	290	10	..............................................................................................................	..............................................................................................................	PUNCT
ejpam-4658	290	11	..................	..................	PUNCT
ejpam-4658	291	1	..................	..................	PUNCT
ejpam-4658	291	2	..................	..................	PUNCT
ejpam-4658	292	1	..................	..................	PUNCT
ejpam-4658	292	2	..................	..................	PUNCT
ejpam-4658	293	1	..................	..................	PUNCT
ejpam-4658	293	2	..................	..................	PUNCT
ejpam-4658	294	1	.....	.....	PUNCT
ejpam-4658	294	2	............	............	PUNCT
ejpam-4658	294	3	...........	...........	PUNCT
ejpam-4658	294	4	...........	...........	PUNCT
ejpam-4658	294	5	...........	...........	PUNCT
ejpam-4658	294	6	...........	...........	PUNCT
ejpam-4658	294	7	...........	...........	PUNCT
ejpam-4658	294	8	...........	...........	PUNCT
ejpam-4658	294	9	...........	...........	PUNCT
ejpam-4658	294	10	..	..	PUNCT
ejpam-4658	294	11	...........................................................................................	...........................................................................................	PUNCT
ejpam-4658	295	1	..................................................................................................................................................................	..................................................................................................................................................................	PUNCT
ejpam-4658	295	2	...........	...........	PUNCT
ejpam-4658	295	3	...........	...........	PUNCT
ejpam-4658	295	4	...........	...........	PUNCT
ejpam-4658	295	5	...........	...........	PUNCT
ejpam-4658	295	6	...........	...........	PUNCT
ejpam-4658	295	7	...........	...........	PUNCT
ejpam-4658	295	8	...........	...........	PUNCT
ejpam-4658	295	9	..	..	PUNCT
ejpam-4658	295	10	..............................................................................................................	..............................................................................................................	PUNCT
ejpam-4658	295	11	..................	..................	PUNCT
ejpam-4658	296	1	..................	..................	PUNCT
ejpam-4658	296	2	..................	..................	PUNCT
ejpam-4658	297	1	..................	..................	PUNCT
ejpam-4658	297	2	..................	..................	PUNCT
ejpam-4658	298	1	..................	..................	PUNCT
ejpam-4658	298	2	..................	..................	PUNCT
ejpam-4658	299	1	.....	.....	PUNCT
ejpam-4658	299	2	............	............	PUNCT
ejpam-4658	299	3	...........	...........	PUNCT
ejpam-4658	299	4	...........	...........	PUNCT
ejpam-4658	299	5	...........	...........	PUNCT
ejpam-4658	299	6	...........	...........	PUNCT
ejpam-4658	299	7	...........	...........	PUNCT
ejpam-4658	299	8	...........	...........	PUNCT
ejpam-4658	299	9	...........	...........	PUNCT
ejpam-4658	299	10	..	..	PUNCT
ejpam-4658	299	11	....................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	300	1	....................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	300	2	....................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	301	1	....................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	301	2	....................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	302	1	.................................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................................	PUNCT
ejpam-4658	303	1	....................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................	PUNCT
ejpam-4658	304	1	•	•	NUM
ejpam-4658	305	1	•	•	NUM
ejpam-4658	305	2	•	•	NUM
ejpam-4658	305	3	•	•	NUM
ejpam-4658	305	4	•	•	NUM
ejpam-4658	305	5	•	•	NUM
ejpam-4658	305	6	•	•	NUM
ejpam-4658	305	7	•	•	NUM
ejpam-4658	305	8	•	•	NUM
ejpam-4658	305	9	•	•	NOUN
ejpam-4658	305	10	•	•	NUM
ejpam-4658	305	11	k4[p3	k4[p3	PROPN
ejpam-4658	305	12	]	]	PUNCT
ejpam-4658	305	13	figure	figure	NOUN
ejpam-4658	305	14	1	1	NUM
ejpam-4658	305	15	:	:	PUNCT
ejpam-4658	305	16	a	a	DET
ejpam-4658	305	17	1	1	NUM
ejpam-4658	305	18	-	-	PUNCT
ejpam-4658	305	19	movable	movable	ADJ
ejpam-4658	305	20	strong	strong	ADJ
ejpam-4658	305	21	resolving	resolve	VERB
ejpam-4658	305	22	hop	hop	NOUN
ejpam-4658	305	23	dominating	dominating	NOUN
ejpam-4658	305	24	sets	set	NOUN
ejpam-4658	305	25	of	of	ADP
ejpam-4658	305	26	k4[p4	k4[p4	PROPN
ejpam-4658	305	27	]	]	PUNCT
ejpam-4658	305	28	and	and	CCONJ
ejpam-4658	305	29	k4[p3	k4[p3	PROPN
ejpam-4658	305	30	]	]	X
ejpam-4658	305	31	references	reference	NOUN
ejpam-4658	305	32	[	[	X
ejpam-4658	305	33	1	1	NUM
ejpam-4658	305	34	]	]	PUNCT
ejpam-4658	305	35	g.	g.	PROPN
ejpam-4658	305	36	chartrand	chartrand	PROPN
ejpam-4658	305	37	,	,	PUNCT
ejpam-4658	305	38	l.	l.	PROPN
ejpam-4658	305	39	eroh	eroh	PROPN
ejpam-4658	305	40	,	,	PUNCT
ejpam-4658	305	41	m.	m.	NOUN
ejpam-4658	305	42	johnson	johnson	PROPN
ejpam-4658	305	43	,	,	PUNCT
ejpam-4658	305	44	and	and	CCONJ
ejpam-4658	305	45	o.r	o.r	PROPN
ejpam-4658	305	46	.	.	PROPN
ejpam-4658	305	47	oellermann	oellermann	PROPN
ejpam-4658	305	48	.	.	PUNCT
ejpam-4658	306	1	resolvability	resolvability	NOUN
ejpam-4658	306	2	in	in	ADP
ejpam-4658	306	3	graphs	graph	NOUN
ejpam-4658	306	4	and	and	CCONJ
ejpam-4658	306	5	the	the	DET
ejpam-4658	306	6	metric	metric	ADJ
ejpam-4658	306	7	dimension	dimension	NOUN
ejpam-4658	306	8	of	of	ADP
ejpam-4658	306	9	a	a	DET
ejpam-4658	306	10	graph	graph	NOUN
ejpam-4658	306	11	the	the	DET
ejpam-4658	306	12	metric	metric	ADJ
ejpam-4658	306	13	dimension	dimension	NOUN
ejpam-4658	306	14	of	of	ADP
ejpam-4658	306	15	a	a	DET
ejpam-4658	306	16	graph	graph	NOUN
ejpam-4658	306	17	.	.	PUNCT
ejpam-4658	307	1	discrete	discrete	ADJ
ejpam-4658	307	2	applied	apply	VERB
ejpam-4658	307	3	mathematics	mathematic	NOUN
ejpam-4658	307	4	,	,	PUNCT
ejpam-4658	307	5	105:99–113	105:99–113	NUM
ejpam-4658	307	6	,	,	PUNCT
ejpam-4658	307	7	2000	2000	NUM
ejpam-4658	307	8	.	.	PUNCT
ejpam-4658	308	1	[	[	X
ejpam-4658	308	2	2	2	NUM
ejpam-4658	308	3	]	]	PUNCT
ejpam-4658	308	4	f.	f.	PROPN
ejpam-4658	308	5	harary	harary	PROPN
ejpam-4658	308	6	and	and	CCONJ
ejpam-4658	308	7	r.a	r.a	PROPN
ejpam-4658	308	8	.	.	PROPN
ejpam-4658	308	9	melter	melter	NOUN
ejpam-4658	308	10	.	.	PUNCT
ejpam-4658	309	1	on	on	ADP
ejpam-4658	309	2	the	the	DET
ejpam-4658	309	3	metric	metric	ADJ
ejpam-4658	309	4	dimension	dimension	NOUN
ejpam-4658	309	5	of	of	ADP
ejpam-4658	309	6	a	a	DET
ejpam-4658	309	7	graph	graph	NOUN
ejpam-4658	309	8	.	.	PUNCT
ejpam-4658	309	9	ars	ars	PROPN
ejpam-4658	309	10	combinatoria	combinatoria	NOUN
ejpam-4658	309	11	,	,	PUNCT
ejpam-4658	309	12	2:191–195	2:191–195	NUM
ejpam-4658	309	13	,	,	PUNCT
ejpam-4658	309	14	1976	1976	NUM
ejpam-4658	309	15	.	.	PUNCT
ejpam-4658	310	1	[	[	X
ejpam-4658	310	2	3	3	X
ejpam-4658	310	3	]	]	X
ejpam-4658	310	4	blair	blair	PROPN
ejpam-4658	310	5	j.	j.	PROPN
ejpam-4658	310	6	,	,	PUNCT
ejpam-4658	310	7	gera	gera	PROPN
ejpam-4658	310	8	r.	r.	PROPN
ejpam-4658	310	9	,	,	PUNCT
ejpam-4658	310	10	and	and	CCONJ
ejpam-4658	310	11	horton	horton	PROPN
ejpam-4658	310	12	s.	s.	PROPN
ejpam-4658	310	13	movable	movable	ADJ
ejpam-4658	310	14	dominating	dominating	NOUN
ejpam-4658	310	15	sets	set	NOUN
ejpam-4658	310	16	in	in	ADP
ejpam-4658	310	17	networks	network	NOUN
ejpam-4658	310	18	.	.	PUNCT
ejpam-4658	311	1	journal	journal	NOUN
ejpam-4658	311	2	of	of	ADP
ejpam-4658	311	3	combinatorial	combinatorial	ADJ
ejpam-4658	311	4	mathematics	mathematic	NOUN
ejpam-4658	311	5	and	and	CCONJ
ejpam-4658	311	6	combinatorial	combinatorial	ADJ
ejpam-4658	311	7	computing	computing	NOUN
ejpam-4658	311	8	,	,	PUNCT
ejpam-4658	311	9	(	(	PUNCT
ejpam-4658	311	10	77):102–123	77):102–123	NOUN
ejpam-4658	311	11	,	,	PUNCT
ejpam-4658	311	12	2011	2011	NUM
ejpam-4658	311	13	.	.	PUNCT
ejpam-4658	312	1	[	[	X
ejpam-4658	312	2	4	4	X
ejpam-4658	312	3	]	]	PUNCT
ejpam-4658	312	4	renario	renario	PROPN
ejpam-4658	312	5	g.	g.	PROPN
ejpam-4658	312	6	hinampas	hinampas	PROPN
ejpam-4658	312	7	jr	jr	PROPN
ejpam-4658	312	8	.	.	PROPN
ejpam-4658	312	9	and	and	CCONJ
ejpam-4658	312	10	sergio	sergio	PROPN
ejpam-4658	312	11	r.	r.	PROPN
ejpam-4658	312	12	canoy	canoy	PROPN
ejpam-4658	312	13	jr	jr	PROPN
ejpam-4658	312	14	.	.	PROPN
ejpam-4658	312	15	1	1	NUM
ejpam-4658	312	16	-	-	PUNCT
ejpam-4658	312	17	movable	movable	ADJ
ejpam-4658	312	18	domination	domination	NOUN
ejpam-4658	312	19	in	in	ADP
ejpam-4658	312	20	graphs	graph	NOUN
ejpam-4658	312	21	.	.	PUNCT
ejpam-4658	313	1	applied	apply	VERB
ejpam-4658	313	2	mathematical	mathematical	ADJ
ejpam-4658	313	3	sciences	science	NOUN
ejpam-4658	313	4	,	,	PUNCT
ejpam-4658	313	5	8(172):8565	8(172):8565	NUM
ejpam-4658	313	6	–	–	PUNCT
ejpam-4658	313	7	8571	8571	NUM
ejpam-4658	313	8	,	,	PUNCT
ejpam-4658	313	9	2014	2014	NUM
ejpam-4658	313	10	.	.	PUNCT
ejpam-4658	314	1	[	[	X
ejpam-4658	314	2	5	5	X
ejpam-4658	314	3	]	]	X
ejpam-4658	314	4	gerald	gerald	PROPN
ejpam-4658	314	5	bacon	bacon	PROPN
ejpam-4658	314	6	monsanto	monsanto	PROPN
ejpam-4658	314	7	,	,	PUNCT
ejpam-4658	314	8	penelyn	penelyn	NOUN
ejpam-4658	314	9	l.	l.	PROPN
ejpam-4658	314	10	acal	acal	PROPN
ejpam-4658	314	11	,	,	PUNCT
ejpam-4658	314	12	and	and	CCONJ
ejpam-4658	314	13	helen	helen	PROPN
ejpam-4658	314	14	m.	m.	PROPN
ejpam-4658	314	15	rara	rara	PROPN
ejpam-4658	314	16	.	.	PUNCT
ejpam-4658	315	1	on	on	ADP
ejpam-4658	315	2	strong	strong	ADJ
ejpam-4658	315	3	resolving	resolving	NOUN
ejpam-4658	315	4	domination	domination	NOUN
ejpam-4658	315	5	in	in	ADP
ejpam-4658	315	6	the	the	DET
ejpam-4658	315	7	join	join	NOUN
ejpam-4658	315	8	and	and	CCONJ
ejpam-4658	315	9	corona	corona	NOUN
ejpam-4658	315	10	of	of	ADP
ejpam-4658	315	11	graphs	graph	NOUN
ejpam-4658	315	12	.	.	PUNCT
ejpam-4658	316	1	european	european	ADJ
ejpam-4658	316	2	journal	journal	PROPN
ejpam-4658	316	3	of	of	ADP
ejpam-4658	316	4	pure	pure	ADJ
ejpam-4658	316	5	and	and	CCONJ
ejpam-4658	316	6	applied	applied	ADJ
ejpam-4658	316	7	mathematics	mathematic	NOUN
ejpam-4658	316	8	,	,	PUNCT
ejpam-4658	316	9	13(1):170–179	13(1):170–179	NUM
ejpam-4658	316	10	,	,	PUNCT
ejpam-4658	316	11	jan	jan	PROPN
ejpam-4658	316	12	.	.	PROPN
ejpam-4658	316	13	2020	2020	NUM
ejpam-4658	316	14	.	.	PUNCT
ejpam-4658	317	1	references	reference	NOUN
ejpam-4658	317	2	772	772	NUM
ejpam-4658	317	3	[	[	X
ejpam-4658	317	4	6	6	NUM
ejpam-4658	317	5	]	]	X
ejpam-4658	317	6	chidambaram	chidambaram	PROPN
ejpam-4658	317	7	natarajan	natarajan	PROPN
ejpam-4658	317	8	and	and	CCONJ
ejpam-4658	317	9	ayyaswamy	ayyaswamy	PROPN
ejpam-4658	317	10	s.k	s.k	PROPN
ejpam-4658	317	11	.	.	PROPN
ejpam-4658	317	12	hop	hop	PROPN
ejpam-4658	317	13	domination	domination	NOUN
ejpam-4658	317	14	in	in	ADP
ejpam-4658	317	15	graphs	graph	NOUN
ejpam-4658	317	16	-	-	PUNCT
ejpam-4658	317	17	ii	ii	NOUN
ejpam-4658	317	18	.	.	PUNCT
ejpam-4658	318	1	analele	analele	ADP
ejpam-4658	318	2	stiintifice	stiintifice	PROPN
ejpam-4658	318	3	ale	ale	PROPN
ejpam-4658	318	4	universitatii	universitatii	PROPN
ejpam-4658	318	5	ovidius	ovidius	PROPN
ejpam-4658	318	6	constanta	constanta	PROPN
ejpam-4658	318	7	,	,	PUNCT
ejpam-4658	318	8	seria	seria	PROPN
ejpam-4658	318	9	matematica	matematica	PROPN
ejpam-4658	318	10	,	,	PUNCT
ejpam-4658	318	11	23:187–199	23:187–199	PROPN
ejpam-4658	318	12	,	,	PUNCT
ejpam-4658	318	13	06	06	NUM
ejpam-4658	318	14	2015	2015	NUM
ejpam-4658	318	15	.	.	PUNCT
ejpam-4658	319	1	[	[	X
ejpam-4658	319	2	7	7	X
ejpam-4658	319	3	]	]	PUNCT
ejpam-4658	319	4	canoy	canoy	PROPN
ejpam-4658	319	5	jr	jr	PROPN
ejpam-4658	319	6	sergio	sergio	PROPN
ejpam-4658	319	7	,	,	PUNCT
ejpam-4658	319	8	mollejon	mollejon	ADJ
ejpam-4658	319	9	reynaldo	reynaldo	PROPN
ejpam-4658	319	10	villarobe	villarobe	NOUN
ejpam-4658	319	11	,	,	PUNCT
ejpam-4658	319	12	and	and	CCONJ
ejpam-4658	319	13	canoy	canoy	PROPN
ejpam-4658	319	14	john	john	PROPN
ejpam-4658	319	15	gabriel	gabriel	PROPN
ejpam-4658	319	16	e.	e.	PROPN
ejpam-4658	319	17	hop	hop	PROPN
ejpam-4658	319	18	dominating	dominating	NOUN
ejpam-4658	319	19	sets	set	NOUN
ejpam-4658	319	20	in	in	ADP
ejpam-4658	319	21	graphs	graph	NOUN
ejpam-4658	319	22	under	under	ADP
ejpam-4658	319	23	binary	binary	ADJ
ejpam-4658	319	24	operations	operation	NOUN
ejpam-4658	319	25	.	.	PUNCT
ejpam-4658	320	1	european	european	ADJ
ejpam-4658	320	2	journal	journal	PROPN
ejpam-4658	320	3	of	of	ADP
ejpam-4658	320	4	pure	pure	ADJ
ejpam-4658	320	5	and	and	CCONJ
ejpam-4658	320	6	applied	applied	ADJ
ejpam-4658	320	7	mathematics	mathematic	NOUN
ejpam-4658	320	8	,	,	PUNCT
ejpam-4658	320	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4658	320	10	,	,	PUNCT
ejpam-4658	320	11	oct	oct	PROPN
ejpam-4658	320	12	.	.	PROPN
ejpam-4658	320	13	2019	2019	NUM
ejpam-4658	320	14	.	.	PUNCT