id	sid	tid	token	lemma	pos
ejpam-4578	1	1	european	european	PROPN
ejpam-4578	1	2	journal	journal	PROPN
ejpam-4578	1	3	of	of	ADP
ejpam-4578	1	4	pure	pure	ADJ
ejpam-4578	1	5	and	and	CCONJ
ejpam-4578	1	6	applied	apply	VERB
ejpam-4578	1	7	mathematics	mathematic	NOUN
ejpam-4578	1	8	vol	vol	NOUN
ejpam-4578	1	9	.	.	PUNCT
ejpam-4578	2	1	16	16	NUM
ejpam-4578	2	2	,	,	PUNCT
ejpam-4578	2	3	no	no	INTJ
ejpam-4578	2	4	.	.	NOUN
ejpam-4578	2	5	1	1	NUM
ejpam-4578	2	6	,	,	PUNCT
ejpam-4578	2	7	2023	2023	NUM
ejpam-4578	2	8	,	,	PUNCT
ejpam-4578	2	9	131	131	NUM
ejpam-4578	2	10	-	-	SYM
ejpam-4578	2	11	143	143	NUM
ejpam-4578	2	12	issn	issn	PROPN
ejpam-4578	2	13	1307	1307	NUM
ejpam-4578	2	14	-	-	SYM
ejpam-4578	2	15	5543	5543	NUM
ejpam-4578	2	16	–	–	PUNCT
ejpam-4578	2	17	ejpam.com	ejpam.com	X
ejpam-4578	2	18	published	publish	VERB
ejpam-4578	2	19	by	by	ADP
ejpam-4578	2	20	new	new	PROPN
ejpam-4578	2	21	york	york	PROPN
ejpam-4578	2	22	business	business	PROPN
ejpam-4578	2	23	global	global	ADJ
ejpam-4578	2	24	strong	strong	ADJ
ejpam-4578	2	25	resolving	resolve	VERB
ejpam-4578	2	26	hop	hop	NOUN
ejpam-4578	2	27	domination	domination	NOUN
ejpam-4578	2	28	in	in	ADP
ejpam-4578	2	29	graphs	graphs	PROPN
ejpam-4578	2	30	jerson	jerson	PROPN
ejpam-4578	2	31	s.	s.	PROPN
ejpam-4578	2	32	mohamad1	mohamad1	PROPN
ejpam-4578	2	33	,	,	PUNCT
ejpam-4578	2	34	helen	helen	PROPN
ejpam-4578	2	35	m.	m.	PROPN
ejpam-4578	2	36	rara2	rara2	PROPN
ejpam-4578	3	1	1	1	NUM
ejpam-4578	3	2	department	department	NOUN
ejpam-4578	3	3	of	of	ADP
ejpam-4578	3	4	mathematics	mathematic	NOUN
ejpam-4578	3	5	and	and	CCONJ
ejpam-4578	3	6	statistics	statistic	NOUN
ejpam-4578	3	7	,	,	PUNCT
ejpam-4578	3	8	college	college	NOUN
ejpam-4578	3	9	of	of	ADP
ejpam-4578	3	10	science	science	NOUN
ejpam-4578	3	11	and	and	CCONJ
ejpam-4578	3	12	mathematics	mathematic	NOUN
ejpam-4578	3	13	,	,	PUNCT
ejpam-4578	3	14	western	western	ADJ
ejpam-4578	3	15	mindanao	mindanao	PROPN
ejpam-4578	3	16	state	state	PROPN
ejpam-4578	3	17	university	university	PROPN
ejpam-4578	3	18	,	,	PUNCT
ejpam-4578	3	19	7000	7000	NUM
ejpam-4578	3	20	zamboanga	zamboanga	PROPN
ejpam-4578	3	21	city	city	PROPN
ejpam-4578	3	22	,	,	PUNCT
ejpam-4578	3	23	philippines	philippines	PROPN
ejpam-4578	3	24	2	2	NUM
ejpam-4578	3	25	department	department	NOUN
ejpam-4578	3	26	of	of	ADP
ejpam-4578	3	27	mathematics	mathematic	NOUN
ejpam-4578	3	28	and	and	CCONJ
ejpam-4578	3	29	statistics	statistic	NOUN
ejpam-4578	3	30	,	,	PUNCT
ejpam-4578	3	31	college	college	NOUN
ejpam-4578	3	32	of	of	ADP
ejpam-4578	3	33	science	science	NOUN
ejpam-4578	3	34	and	and	CCONJ
ejpam-4578	3	35	mathematics	mathematic	NOUN
ejpam-4578	3	36	,	,	PUNCT
ejpam-4578	3	37	center	center	NOUN
ejpam-4578	3	38	of	of	ADP
ejpam-4578	3	39	graph	graph	NOUN
ejpam-4578	3	40	theory	theory	NOUN
ejpam-4578	3	41	,	,	PUNCT
ejpam-4578	3	42	algebra	algebra	NOUN
ejpam-4578	3	43	,	,	PUNCT
ejpam-4578	3	44	and	and	CCONJ
ejpam-4578	3	45	analysis	analysis	NOUN
ejpam-4578	3	46	-	-	PUNCT
ejpam-4578	3	47	premier	premier	NOUN
ejpam-4578	3	48	research	research	NOUN
ejpam-4578	3	49	institute	institute	PROPN
ejpam-4578	3	50	of	of	ADP
ejpam-4578	3	51	science	science	NOUN
ejpam-4578	3	52	and	and	CCONJ
ejpam-4578	3	53	mathematics	mathematic	NOUN
ejpam-4578	3	54	,	,	PUNCT
ejpam-4578	3	55	mindanao	mindanao	PROPN
ejpam-4578	3	56	state	state	PROPN
ejpam-4578	3	57	university	university	PROPN
ejpam-4578	3	58	-	-	PUNCT
ejpam-4578	3	59	iligan	iligan	PROPN
ejpam-4578	3	60	institute	institute	PROPN
ejpam-4578	3	61	of	of	ADP
ejpam-4578	3	62	technology	technology	PROPN
ejpam-4578	3	63	,	,	PUNCT
ejpam-4578	3	64	9200	9200	NUM
ejpam-4578	3	65	iligan	iligan	ADJ
ejpam-4578	3	66	city	city	NOUN
ejpam-4578	3	67	,	,	PUNCT
ejpam-4578	3	68	philippines	philippine	NOUN
ejpam-4578	3	69	abstract	abstract	ADJ
ejpam-4578	3	70	.	.	PUNCT
ejpam-4578	4	1	a	a	DET
ejpam-4578	4	2	vertex	vertex	NOUN
ejpam-4578	4	3	w	w	NOUN
ejpam-4578	4	4	in	in	ADP
ejpam-4578	4	5	a	a	DET
ejpam-4578	4	6	connected	connected	ADJ
ejpam-4578	4	7	graph	graph	NOUN
ejpam-4578	4	8	g	g	NOUN
ejpam-4578	4	9	strongly	strongly	ADV
ejpam-4578	4	10	resolves	resolve	VERB
ejpam-4578	4	11	two	two	NUM
ejpam-4578	4	12	distinct	distinct	ADJ
ejpam-4578	4	13	vertices	vertex	NOUN
ejpam-4578	4	14	u	u	NOUN
ejpam-4578	4	15	and	and	CCONJ
ejpam-4578	4	16	v	v	NOUN
ejpam-4578	4	17	in	in	ADP
ejpam-4578	4	18	v	v	NOUN
ejpam-4578	4	19	(	(	PUNCT
ejpam-4578	4	20	g	g	NOUN
ejpam-4578	4	21	)	)	PUNCT
ejpam-4578	4	22	if	if	SCONJ
ejpam-4578	4	23	v	v	NOUN
ejpam-4578	4	24	is	be	AUX
ejpam-4578	4	25	in	in	ADP
ejpam-4578	4	26	any	any	DET
ejpam-4578	4	27	shortest	short	ADJ
ejpam-4578	4	28	u	u	NOUN
ejpam-4578	4	29	-	-	NOUN
ejpam-4578	4	30	w	w	NOUN
ejpam-4578	4	31	path	path	NOUN
ejpam-4578	4	32	or	or	CCONJ
ejpam-4578	4	33	if	if	SCONJ
ejpam-4578	4	34	u	u	NOUN
ejpam-4578	4	35	is	be	AUX
ejpam-4578	4	36	in	in	ADP
ejpam-4578	4	37	any	any	DET
ejpam-4578	4	38	shortest	short	ADJ
ejpam-4578	4	39	v	v	NOUN
ejpam-4578	4	40	-	-	PUNCT
ejpam-4578	4	41	w	w	NOUN
ejpam-4578	4	42	path	path	NOUN
ejpam-4578	4	43	.	.	PUNCT
ejpam-4578	5	1	a	a	DET
ejpam-4578	5	2	set	set	NOUN
ejpam-4578	5	3	w	w	NOUN
ejpam-4578	5	4	of	of	ADP
ejpam-4578	5	5	vertices	vertex	NOUN
ejpam-4578	5	6	in	in	ADP
ejpam-4578	5	7	g	g	PROPN
ejpam-4578	5	8	is	be	AUX
ejpam-4578	5	9	a	a	DET
ejpam-4578	5	10	strong	strong	ADJ
ejpam-4578	5	11	resolving	resolving	NOUN
ejpam-4578	5	12	set	set	VERB
ejpam-4578	5	13	g	g	NOUN
ejpam-4578	5	14	if	if	SCONJ
ejpam-4578	5	15	every	every	DET
ejpam-4578	5	16	two	two	NUM
ejpam-4578	5	17	vertices	vertex	NOUN
ejpam-4578	5	18	of	of	ADP
ejpam-4578	5	19	g	g	NOUN
ejpam-4578	5	20	are	be	AUX
ejpam-4578	5	21	strongly	strongly	ADV
ejpam-4578	5	22	resolved	resolve	VERB
ejpam-4578	5	23	by	by	ADP
ejpam-4578	5	24	some	some	DET
ejpam-4578	5	25	vertex	vertex	NOUN
ejpam-4578	5	26	of	of	ADP
ejpam-4578	5	27	w	w	PROPN
ejpam-4578	5	28	.	.	PUNCT
ejpam-4578	6	1	a	a	DET
ejpam-4578	6	2	set	set	NOUN
ejpam-4578	6	3	s	s	NOUN
ejpam-4578	6	4	subset	subset	NOUN
ejpam-4578	6	5	of	of	ADP
ejpam-4578	6	6	v	v	NOUN
ejpam-4578	6	7	(	(	PUNCT
ejpam-4578	6	8	g	g	NOUN
ejpam-4578	6	9	)	)	PUNCT
ejpam-4578	6	10	is	be	AUX
ejpam-4578	6	11	a	a	DET
ejpam-4578	6	12	strong	strong	ADJ
ejpam-4578	6	13	resolving	resolve	VERB
ejpam-4578	6	14	hop	hop	NOUN
ejpam-4578	6	15	dominating	dominating	NOUN
ejpam-4578	6	16	set	set	NOUN
ejpam-4578	6	17	of	of	ADP
ejpam-4578	6	18	g	g	PROPN
ejpam-4578	6	19	if	if	SCONJ
ejpam-4578	6	20	s	s	VERB
ejpam-4578	6	21	is	be	AUX
ejpam-4578	6	22	a	a	DET
ejpam-4578	6	23	strong	strong	ADJ
ejpam-4578	6	24	resolving	resolving	NOUN
ejpam-4578	6	25	set	set	VERB
ejpam-4578	6	26	in	in	ADP
ejpam-4578	6	27	g	g	PROPN
ejpam-4578	6	28	and	and	CCONJ
ejpam-4578	6	29	for	for	ADP
ejpam-4578	6	30	every	every	DET
ejpam-4578	6	31	vertex	vertex	NOUN
ejpam-4578	6	32	v	v	ADP
ejpam-4578	6	33	∈	∈	NOUN
ejpam-4578	6	34	v	v	NOUN
ejpam-4578	6	35	(	(	PUNCT
ejpam-4578	6	36	g	g	NOUN
ejpam-4578	6	37	)	)	PUNCT
ejpam-4578	6	38	\	\	PROPN
ejpam-4578	7	1	s	s	VERB
ejpam-4578	7	2	there	there	PRON
ejpam-4578	7	3	exists	exist	VERB
ejpam-4578	7	4	u	u	PROPN
ejpam-4578	7	5	∈	∈	PROPN
ejpam-4578	7	6	s	s	VERB
ejpam-4578	7	7	such	such	ADJ
ejpam-4578	7	8	that	that	DET
ejpam-4578	7	9	dg(u	dg(u	ADJ
ejpam-4578	7	10	,	,	PUNCT
ejpam-4578	7	11	v	v	NOUN
ejpam-4578	7	12	)	)	PUNCT
ejpam-4578	7	13	=	=	SYM
ejpam-4578	7	14	2	2	X
ejpam-4578	7	15	.	.	X
ejpam-4578	7	16	the	the	DET
ejpam-4578	7	17	smallest	small	ADJ
ejpam-4578	7	18	cardinality	cardinality	NOUN
ejpam-4578	7	19	of	of	ADP
ejpam-4578	7	20	such	such	DET
ejpam-4578	7	21	a	a	DET
ejpam-4578	7	22	set	set	NOUN
ejpam-4578	7	23	s	s	PART
ejpam-4578	7	24	is	be	AUX
ejpam-4578	7	25	called	call	VERB
ejpam-4578	7	26	the	the	DET
ejpam-4578	7	27	strong	strong	ADJ
ejpam-4578	7	28	resolving	resolve	VERB
ejpam-4578	7	29	hop	hop	NOUN
ejpam-4578	7	30	domination	domination	NOUN
ejpam-4578	7	31	number	number	NOUN
ejpam-4578	7	32	of	of	ADP
ejpam-4578	7	33	g.	g.	PROPN
ejpam-4578	7	34	this	this	DET
ejpam-4578	7	35	paper	paper	NOUN
ejpam-4578	7	36	presents	present	VERB
ejpam-4578	7	37	the	the	DET
ejpam-4578	7	38	characterization	characterization	NOUN
ejpam-4578	7	39	of	of	ADP
ejpam-4578	7	40	the	the	DET
ejpam-4578	7	41	strong	strong	ADJ
ejpam-4578	7	42	resolving	resolve	VERB
ejpam-4578	7	43	hop	hop	NOUN
ejpam-4578	7	44	dominating	dominating	NOUN
ejpam-4578	7	45	sets	set	NOUN
ejpam-4578	7	46	in	in	ADP
ejpam-4578	7	47	the	the	DET
ejpam-4578	7	48	join	join	NOUN
ejpam-4578	7	49	,	,	PUNCT
ejpam-4578	7	50	corona	corona	NOUN
ejpam-4578	7	51	and	and	CCONJ
ejpam-4578	7	52	lexicographic	lexicographic	ADJ
ejpam-4578	7	53	product	product	NOUN
ejpam-4578	7	54	of	of	ADP
ejpam-4578	7	55	graphs	graph	NOUN
ejpam-4578	7	56	.	.	PUNCT
ejpam-4578	8	1	furthermore	furthermore	ADV
ejpam-4578	8	2	,	,	PUNCT
ejpam-4578	8	3	this	this	DET
ejpam-4578	8	4	paper	paper	NOUN
ejpam-4578	8	5	determines	determine	VERB
ejpam-4578	8	6	the	the	DET
ejpam-4578	8	7	exact	exact	ADJ
ejpam-4578	8	8	value	value	NOUN
ejpam-4578	8	9	or	or	CCONJ
ejpam-4578	8	10	bounds	bound	NOUN
ejpam-4578	8	11	of	of	ADP
ejpam-4578	8	12	their	their	PRON
ejpam-4578	8	13	corresponding	correspond	VERB
ejpam-4578	8	14	strong	strong	ADJ
ejpam-4578	8	15	resolving	resolve	VERB
ejpam-4578	8	16	hop	hop	NOUN
ejpam-4578	8	17	domination	domination	NOUN
ejpam-4578	8	18	number	number	NOUN
ejpam-4578	8	19	.	.	PUNCT
ejpam-4578	9	1	2020	2020	NUM
ejpam-4578	9	2	mathematics	mathematic	NOUN
ejpam-4578	9	3	subject	subject	NOUN
ejpam-4578	9	4	classifications	classification	NOUN
ejpam-4578	9	5	:	:	PUNCT
ejpam-4578	9	6	05c69	05c69	X
ejpam-4578	9	7	key	key	ADJ
ejpam-4578	9	8	words	word	NOUN
ejpam-4578	9	9	and	and	CCONJ
ejpam-4578	9	10	phrases	phrase	NOUN
ejpam-4578	9	11	:	:	PUNCT
ejpam-4578	9	12	strong	strong	ADJ
ejpam-4578	9	13	resolving	resolve	VERB
ejpam-4578	9	14	hop	hop	NOUN
ejpam-4578	9	15	dominating	dominating	NOUN
ejpam-4578	9	16	set	set	NOUN
ejpam-4578	9	17	,	,	PUNCT
ejpam-4578	9	18	strong	strong	ADJ
ejpam-4578	9	19	resolving	resolve	VERB
ejpam-4578	9	20	hop	hop	NOUN
ejpam-4578	9	21	domination	domination	NOUN
ejpam-4578	9	22	number	number	NOUN
ejpam-4578	9	23	,	,	PUNCT
ejpam-4578	9	24	hop	hop	NOUN
ejpam-4578	9	25	dominated	dominate	VERB
ejpam-4578	9	26	superclique	superclique	NOUN
ejpam-4578	9	27	,	,	PUNCT
ejpam-4578	9	28	join	join	NOUN
ejpam-4578	9	29	,	,	PUNCT
ejpam-4578	9	30	corona	corona	PROPN
ejpam-4578	9	31	,	,	PUNCT
ejpam-4578	9	32	lexicographic	lexicographic	ADJ
ejpam-4578	9	33	product	product	NOUN
ejpam-4578	9	34	1	1	NUM
ejpam-4578	9	35	.	.	PUNCT
ejpam-4578	10	1	introduction	introduction	NOUN
ejpam-4578	10	2	domination	domination	NOUN
ejpam-4578	10	3	in	in	ADP
ejpam-4578	10	4	graphs	graph	NOUN
ejpam-4578	10	5	have	have	AUX
ejpam-4578	10	6	been	be	AUX
ejpam-4578	10	7	widely	widely	ADV
ejpam-4578	10	8	studied	study	VERB
ejpam-4578	10	9	in	in	ADP
ejpam-4578	10	10	graph	graph	NOUN
ejpam-4578	10	11	theory	theory	NOUN
ejpam-4578	10	12	.	.	PUNCT
ejpam-4578	11	1	over	over	ADP
ejpam-4578	11	2	the	the	DET
ejpam-4578	11	3	years	year	NOUN
ejpam-4578	11	4	,	,	PUNCT
ejpam-4578	11	5	many	many	ADJ
ejpam-4578	11	6	variations	variation	NOUN
ejpam-4578	11	7	of	of	ADP
ejpam-4578	11	8	domination	domination	NOUN
ejpam-4578	11	9	have	have	AUX
ejpam-4578	11	10	been	be	AUX
ejpam-4578	11	11	studied	study	VERB
ejpam-4578	11	12	.	.	PUNCT
ejpam-4578	12	1	hop	hop	PROPN
ejpam-4578	12	2	domination	domination	NOUN
ejpam-4578	12	3	in	in	ADP
ejpam-4578	12	4	graphs	graph	NOUN
ejpam-4578	12	5	was	be	AUX
ejpam-4578	12	6	defined	define	VERB
ejpam-4578	12	7	and	and	CCONJ
ejpam-4578	12	8	characterized	characterize	VERB
ejpam-4578	12	9	by	by	ADP
ejpam-4578	12	10	natarajan	natarajan	PROPN
ejpam-4578	12	11	and	and	CCONJ
ejpam-4578	12	12	ayyaswamy	ayyaswamy	ADJ
ejpam-4578	12	13	[	[	X
ejpam-4578	12	14	8	8	NUM
ejpam-4578	12	15	]	]	PUNCT
ejpam-4578	12	16	,	,	PUNCT
ejpam-4578	12	17	they	they	PRON
ejpam-4578	12	18	also	also	ADV
ejpam-4578	12	19	determined	determine	VERB
ejpam-4578	12	20	the	the	DET
ejpam-4578	12	21	hop	hop	NOUN
ejpam-4578	12	22	domination	domination	NOUN
ejpam-4578	12	23	number	number	NOUN
ejpam-4578	12	24	of	of	ADP
ejpam-4578	12	25	some	some	DET
ejpam-4578	12	26	graphs	graph	NOUN
ejpam-4578	12	27	.	.	PUNCT
ejpam-4578	13	1	variations	variation	NOUN
ejpam-4578	13	2	of	of	ADP
ejpam-4578	13	3	the	the	DET
ejpam-4578	13	4	domination	domination	NOUN
ejpam-4578	13	5	and	and	CCONJ
ejpam-4578	13	6	hop	hop	NOUN
ejpam-4578	13	7	domination	domination	NOUN
ejpam-4578	13	8	in	in	ADP
ejpam-4578	13	9	graphs	graph	NOUN
ejpam-4578	13	10	were	be	AUX
ejpam-4578	13	11	studied	study	VERB
ejpam-4578	13	12	in	in	ADP
ejpam-4578	13	13	[	[	X
ejpam-4578	13	14	4	4	NUM
ejpam-4578	13	15	,	,	PUNCT
ejpam-4578	13	16	10	10	NUM
ejpam-4578	13	17	,	,	PUNCT
ejpam-4578	13	18	11	11	NUM
ejpam-4578	13	19	]	]	PUNCT
ejpam-4578	13	20	.	.	PUNCT
ejpam-4578	14	1	resolving	resolve	VERB
ejpam-4578	14	2	sets	set	NOUN
ejpam-4578	14	3	was	be	AUX
ejpam-4578	14	4	studied	study	VERB
ejpam-4578	14	5	by	by	ADP
ejpam-4578	14	6	slater	slater	NOUN
ejpam-4578	14	7	in	in	ADP
ejpam-4578	14	8	[	[	X
ejpam-4578	14	9	12	12	NUM
ejpam-4578	14	10	]	]	PUNCT
ejpam-4578	14	11	.	.	PUNCT
ejpam-4578	15	1	variations	variation	NOUN
ejpam-4578	15	2	of	of	ADP
ejpam-4578	15	3	resolving	resolve	VERB
ejpam-4578	15	4	sets	set	NOUN
ejpam-4578	15	5	and	and	CCONJ
ejpam-4578	15	6	resolving	resolve	VERB
ejpam-4578	15	7	dominating	dominating	NOUN
ejpam-4578	15	8	sets	set	NOUN
ejpam-4578	15	9	were	be	AUX
ejpam-4578	15	10	studied	study	VERB
ejpam-4578	15	11	in	in	ADP
ejpam-4578	15	12	[	[	X
ejpam-4578	15	13	2	2	NUM
ejpam-4578	15	14	,	,	PUNCT
ejpam-4578	15	15	6	6	NUM
ejpam-4578	15	16	,	,	PUNCT
ejpam-4578	15	17	7	7	NUM
ejpam-4578	15	18	]	]	PUNCT
ejpam-4578	15	19	.	.	PUNCT
ejpam-4578	16	1	the	the	DET
ejpam-4578	16	2	strong	strong	ADJ
ejpam-4578	16	3	resolving	resolving	NOUN
ejpam-4578	16	4	sets	set	NOUN
ejpam-4578	16	5	and	and	CCONJ
ejpam-4578	16	6	strong	strong	ADJ
ejpam-4578	16	7	metric	metric	ADJ
ejpam-4578	16	8	dimension	dimension	NOUN
ejpam-4578	16	9	were	be	AUX
ejpam-4578	16	10	introduced	introduce	VERB
ejpam-4578	16	11	and	and	CCONJ
ejpam-4578	16	12	characterized	characterize	VERB
ejpam-4578	16	13	by	by	ADP
ejpam-4578	16	14	oellermann	oellermann	NOUN
ejpam-4578	16	15	and	and	CCONJ
ejpam-4578	16	16	peters	peters	PROPN
ejpam-4578	16	17	-	-	PUNCT
ejpam-4578	16	18	fransen	fransen	PROPN
ejpam-4578	17	1	[	[	X
ejpam-4578	17	2	9	9	NUM
ejpam-4578	17	3	]	]	PUNCT
ejpam-4578	17	4	.	.	PUNCT
ejpam-4578	18	1	resolving	resolve	VERB
ejpam-4578	18	2	hop	hop	NOUN
ejpam-4578	18	3	dominating	dominating	NOUN
ejpam-4578	18	4	sets	set	NOUN
ejpam-4578	18	5	in	in	ADP
ejpam-4578	18	6	graphs	graph	NOUN
ejpam-4578	18	7	was	be	AUX
ejpam-4578	18	8	studied	study	VERB
ejpam-4578	18	9	and	and	CCONJ
ejpam-4578	18	10	presented	present	VERB
ejpam-4578	18	11	with	with	ADP
ejpam-4578	18	12	an	an	DET
ejpam-4578	18	13	example	example	NOUN
ejpam-4578	18	14	of	of	ADP
ejpam-4578	18	15	its	its	PRON
ejpam-4578	18	16	application	application	NOUN
ejpam-4578	18	17	in	in	ADP
ejpam-4578	18	18	minimization	minimization	NOUN
ejpam-4578	18	19	problems	problem	NOUN
ejpam-4578	18	20	in	in	ADP
ejpam-4578	18	21	[	[	X
ejpam-4578	18	22	5	5	NUM
ejpam-4578	18	23	]	]	PUNCT
ejpam-4578	18	24	.	.	PUNCT
ejpam-4578	19	1	this	this	DET
ejpam-4578	19	2	paper	paper	NOUN
ejpam-4578	19	3	introduces	introduce	NOUN
ejpam-4578	19	4	and	and	CCONJ
ejpam-4578	19	5	characterizes	characterize	VERB
ejpam-4578	19	6	the	the	DET
ejpam-4578	19	7	concept	concept	NOUN
ejpam-4578	19	8	of	of	ADP
ejpam-4578	19	9	strong	strong	ADJ
ejpam-4578	19	10	resolving	resolve	VERB
ejpam-4578	19	11	hop	hop	NOUN
ejpam-4578	19	12	domination	domination	NOUN
ejpam-4578	19	13	in	in	ADP
ejpam-4578	19	14	graphs	graph	NOUN
ejpam-4578	19	15	.	.	PUNCT
ejpam-4578	20	1	doi	doi	NOUN
ejpam-4578	20	2	:	:	PUNCT
ejpam-4578	20	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4578	https://doi.org/10.29020/nybg.ejpam.v16i1.4578	PROPN
ejpam-4578	20	4	email	email	NOUN
ejpam-4578	20	5	addresses	address	VERB
ejpam-4578	20	6	:	:	PUNCT
ejpam-4578	21	1	mohamad.jerson@wmsu.edu.ph	mohamad.jerson@wmsu.edu.ph	PROPN
ejpam-4578	21	2	(	(	PUNCT
ejpam-4578	21	3	j.	j.	PROPN
ejpam-4578	21	4	mohamad	mohamad	PROPN
ejpam-4578	21	5	)	)	PUNCT
ejpam-4578	21	6	,	,	PUNCT
ejpam-4578	21	7	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4578	21	8	(	(	PUNCT
ejpam-4578	21	9	h.	h.	PROPN
ejpam-4578	21	10	rara	rara	PROPN
ejpam-4578	21	11	)	)	PUNCT
ejpam-4578	21	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4578	21	13	131	131	NUM
ejpam-4578	22	1	©	©	PROPN
ejpam-4578	22	2	2023	2023	NUM
ejpam-4578	22	3	ejpam	ejpam	NOUN
ejpam-4578	22	4	all	all	DET
ejpam-4578	22	5	rights	right	NOUN
ejpam-4578	22	6	reserved	reserve	VERB
ejpam-4578	22	7	.	.	PUNCT
ejpam-4578	23	1	j.	j.	PROPN
ejpam-4578	23	2	mohamad	mohamad	PROPN
ejpam-4578	23	3	,	,	PUNCT
ejpam-4578	23	4	h.	h.	PROPN
ejpam-4578	23	5	rara	rara	PROPN
ejpam-4578	23	6	/	/	SYM
ejpam-4578	23	7	eur	eur	PROPN
ejpam-4578	23	8	.	.	PUNCT
ejpam-4578	24	1	j.	j.	PROPN
ejpam-4578	24	2	pure	pure	PROPN
ejpam-4578	24	3	appl	appl	PROPN
ejpam-4578	24	4	.	.	PROPN
ejpam-4578	24	5	math	math	PROPN
ejpam-4578	24	6	,	,	PUNCT
ejpam-4578	24	7	16	16	NUM
ejpam-4578	24	8	(	(	PUNCT
ejpam-4578	24	9	1	1	NUM
ejpam-4578	24	10	)	)	PUNCT
ejpam-4578	24	11	(	(	PUNCT
ejpam-4578	24	12	2023	2023	NUM
ejpam-4578	24	13	)	)	PUNCT
ejpam-4578	24	14	,	,	PUNCT
ejpam-4578	24	15	131	131	NUM
ejpam-4578	24	16	-	-	SYM
ejpam-4578	24	17	143	143	NUM
ejpam-4578	24	18	132	132	NUM
ejpam-4578	24	19	we	we	PRON
ejpam-4578	24	20	consider	consider	VERB
ejpam-4578	24	21	connected	connected	ADJ
ejpam-4578	24	22	graphs	graph	NOUN
ejpam-4578	24	23	that	that	PRON
ejpam-4578	24	24	are	be	AUX
ejpam-4578	24	25	finite	finite	ADJ
ejpam-4578	24	26	,	,	PUNCT
ejpam-4578	24	27	simple	simple	ADJ
ejpam-4578	24	28	,	,	PUNCT
ejpam-4578	24	29	and	and	CCONJ
ejpam-4578	24	30	undirected	undirected	ADJ
ejpam-4578	24	31	.	.	PUNCT
ejpam-4578	25	1	for	for	ADP
ejpam-4578	25	2	elementary	elementary	ADJ
ejpam-4578	25	3	graph	graph	NOUN
ejpam-4578	25	4	theory	theory	NOUN
ejpam-4578	25	5	concepts	concept	NOUN
ejpam-4578	25	6	,	,	PUNCT
ejpam-4578	25	7	it	it	PRON
ejpam-4578	25	8	is	be	AUX
ejpam-4578	25	9	recommended	recommend	VERB
ejpam-4578	25	10	that	that	SCONJ
ejpam-4578	25	11	readers	reader	NOUN
ejpam-4578	25	12	refer	refer	VERB
ejpam-4578	25	13	to	to	ADP
ejpam-4578	25	14	[	[	X
ejpam-4578	25	15	3	3	NUM
ejpam-4578	25	16	]	]	PUNCT
ejpam-4578	25	17	.	.	PUNCT
ejpam-4578	26	1	let	let	VERB
ejpam-4578	26	2	g	g	NOUN
ejpam-4578	26	3	=	=	PUNCT
ejpam-4578	26	4	(	(	PUNCT
ejpam-4578	26	5	v	v	NOUN
ejpam-4578	26	6	(	(	PUNCT
ejpam-4578	26	7	g	g	NOUN
ejpam-4578	26	8	)	)	PUNCT
ejpam-4578	26	9	,	,	PUNCT
ejpam-4578	26	10	e(g	e(g	PROPN
ejpam-4578	26	11	)	)	PUNCT
ejpam-4578	26	12	)	)	PUNCT
ejpam-4578	27	1	be	be	AUX
ejpam-4578	27	2	a	a	DET
ejpam-4578	27	3	graph	graph	NOUN
ejpam-4578	27	4	.	.	PUNCT
ejpam-4578	27	5	ng(v	ng(v	PUNCT
ejpam-4578	27	6	)	)	PUNCT
ejpam-4578	28	1	=	=	PRON
ejpam-4578	28	2	{	{	PUNCT
ejpam-4578	28	3	u	u	NOUN
ejpam-4578	28	4	∈	∈	PROPN
ejpam-4578	28	5	v	v	NOUN
ejpam-4578	28	6	(	(	PUNCT
ejpam-4578	28	7	g	g	NOUN
ejpam-4578	28	8	)	)	PUNCT
ejpam-4578	28	9	:	:	PUNCT
ejpam-4578	28	10	uv	uv	PROPN
ejpam-4578	28	11	∈	∈	PROPN
ejpam-4578	28	12	e(g	e(g	PROPN
ejpam-4578	28	13	)	)	PUNCT
ejpam-4578	28	14	}	}	PUNCT
ejpam-4578	28	15	is	be	AUX
ejpam-4578	28	16	a	a	DET
ejpam-4578	28	17	neighborhood	neighborhood	NOUN
ejpam-4578	28	18	of	of	ADP
ejpam-4578	28	19	v.	v.	ADP
ejpam-4578	28	20	an	an	DET
ejpam-4578	28	21	element	element	NOUN
ejpam-4578	28	22	u	u	NOUN
ejpam-4578	28	23	∈	∈	PROPN
ejpam-4578	28	24	ng(v	ng(v	PUNCT
ejpam-4578	28	25	)	)	PUNCT
ejpam-4578	28	26	is	be	AUX
ejpam-4578	28	27	called	call	VERB
ejpam-4578	28	28	a	a	DET
ejpam-4578	28	29	neighbor	neighbor	NOUN
ejpam-4578	28	30	of	of	ADP
ejpam-4578	28	31	v.	v.	CCONJ
ejpam-4578	28	32	ng[v	ng[v	X
ejpam-4578	28	33	]	]	X
ejpam-4578	28	34	=	=	SYM
ejpam-4578	28	35	ng(v	ng(v	X
ejpam-4578	28	36	)	)	PUNCT
ejpam-4578	28	37	∪	∪	ADP
ejpam-4578	28	38	{	{	PUNCT
ejpam-4578	28	39	v	v	NOUN
ejpam-4578	28	40	}	}	PUNCT
ejpam-4578	28	41	is	be	AUX
ejpam-4578	28	42	a	a	DET
ejpam-4578	28	43	closed	closed	ADJ
ejpam-4578	28	44	neighborhood	neighborhood	NOUN
ejpam-4578	28	45	of	of	ADP
ejpam-4578	28	46	v.	v.	ADP
ejpam-4578	28	47	the	the	DET
ejpam-4578	28	48	degree	degree	NOUN
ejpam-4578	28	49	of	of	ADP
ejpam-4578	28	50	v	v	NOUN
ejpam-4578	28	51	,	,	PUNCT
ejpam-4578	28	52	denoted	denote	VERB
ejpam-4578	28	53	by	by	ADP
ejpam-4578	28	54	degg(v	degg(v	PROPN
ejpam-4578	28	55	)	)	PUNCT
ejpam-4578	28	56	,	,	PUNCT
ejpam-4578	28	57	is	be	AUX
ejpam-4578	28	58	equal	equal	ADJ
ejpam-4578	28	59	to	to	ADP
ejpam-4578	28	60	|ng(v)|	|ng(v)|	NOUN
ejpam-4578	28	61	.	.	PUNCT
ejpam-4578	29	1	for	for	ADP
ejpam-4578	29	2	s	s	PROPN
ejpam-4578	29	3	⊆	⊆	NUM
ejpam-4578	29	4	v	v	NOUN
ejpam-4578	29	5	(	(	PUNCT
ejpam-4578	29	6	g	g	NOUN
ejpam-4578	29	7	)	)	PUNCT
ejpam-4578	29	8	,	,	PUNCT
ejpam-4578	29	9	ng(s	ng(s	NUM
ejpam-4578	29	10	)	)	PUNCT
ejpam-4578	29	11	=	=	SYM
ejpam-4578	29	12	⋃	⋃	ADP
ejpam-4578	29	13	v∈s	v∈s	NOUN
ejpam-4578	29	14	ng(v	ng(v	NOUN
ejpam-4578	29	15	)	)	PUNCT
ejpam-4578	29	16	and	and	CCONJ
ejpam-4578	29	17	ng[s	ng[	NOUN
ejpam-4578	29	18	]	]	PUNCT
ejpam-4578	29	19	=	=	PUNCT
ejpam-4578	29	20	⋃	⋃	VERB
ejpam-4578	29	21	v∈s	v∈s	ADJ
ejpam-4578	29	22	ng[v	ng[v	NOUN
ejpam-4578	29	23	]	]	PUNCT
ejpam-4578	29	24	.	.	PUNCT
ejpam-4578	30	1	the	the	DET
ejpam-4578	30	2	distance	distance	NOUN
ejpam-4578	30	3	dg(u	dg(u	NOUN
ejpam-4578	30	4	,	,	PUNCT
ejpam-4578	30	5	v	v	NOUN
ejpam-4578	30	6	)	)	PUNCT
ejpam-4578	30	7	of	of	ADP
ejpam-4578	30	8	two	two	NUM
ejpam-4578	30	9	vertices	vertex	NOUN
ejpam-4578	30	10	u	u	NOUN
ejpam-4578	30	11	,	,	PUNCT
ejpam-4578	30	12	v	v	NOUN
ejpam-4578	30	13	in	in	ADP
ejpam-4578	30	14	g	g	PROPN
ejpam-4578	30	15	is	be	AUX
ejpam-4578	30	16	the	the	DET
ejpam-4578	30	17	length	length	NOUN
ejpam-4578	30	18	of	of	ADP
ejpam-4578	30	19	a	a	DET
ejpam-4578	30	20	shortest	short	ADJ
ejpam-4578	30	21	u	u	NOUN
ejpam-4578	30	22	-	-	NOUN
ejpam-4578	30	23	v	v	ADJ
ejpam-4578	30	24	path	path	NOUN
ejpam-4578	30	25	in	in	ADP
ejpam-4578	30	26	g.	g.	PROPN
ejpam-4578	30	27	the	the	DET
ejpam-4578	30	28	greatest	great	ADJ
ejpam-4578	30	29	distance	distance	NOUN
ejpam-4578	30	30	between	between	ADP
ejpam-4578	30	31	any	any	DET
ejpam-4578	30	32	two	two	NUM
ejpam-4578	30	33	vertices	vertex	NOUN
ejpam-4578	30	34	in	in	ADP
ejpam-4578	30	35	g	g	NOUN
ejpam-4578	30	36	,	,	PUNCT
ejpam-4578	30	37	denoted	denote	VERB
ejpam-4578	30	38	by	by	ADP
ejpam-4578	30	39	diam(g	diam(g	PROPN
ejpam-4578	30	40	)	)	PUNCT
ejpam-4578	30	41	,	,	PUNCT
ejpam-4578	30	42	is	be	AUX
ejpam-4578	30	43	called	call	VERB
ejpam-4578	30	44	the	the	DET
ejpam-4578	30	45	diameter	diameter	NOUN
ejpam-4578	30	46	of	of	ADP
ejpam-4578	30	47	g.	g.	PROPN
ejpam-4578	30	48	a	a	DET
ejpam-4578	30	49	set	set	NOUN
ejpam-4578	30	50	s	s	PROPN
ejpam-4578	30	51	⊆	⊆	NUM
ejpam-4578	30	52	v	v	NOUN
ejpam-4578	30	53	(	(	PUNCT
ejpam-4578	30	54	g	g	NOUN
ejpam-4578	30	55	)	)	PUNCT
ejpam-4578	30	56	of	of	ADP
ejpam-4578	30	57	vertices	vertex	NOUN
ejpam-4578	30	58	of	of	ADP
ejpam-4578	30	59	g	g	PROPN
ejpam-4578	30	60	is	be	AUX
ejpam-4578	30	61	a	a	DET
ejpam-4578	30	62	dominating	dominating	NOUN
ejpam-4578	30	63	set	set	NOUN
ejpam-4578	30	64	if	if	SCONJ
ejpam-4578	30	65	every	every	DET
ejpam-4578	30	66	u	u	PROPN
ejpam-4578	30	67	∈	∈	PROPN
ejpam-4578	30	68	v	v	NOUN
ejpam-4578	30	69	(	(	PUNCT
ejpam-4578	30	70	g	g	NOUN
ejpam-4578	30	71	)	)	PUNCT
ejpam-4578	30	72	\	\	PROPN
ejpam-4578	31	1	s	s	PART
ejpam-4578	31	2	is	be	AUX
ejpam-4578	31	3	adjacent	adjacent	ADJ
ejpam-4578	31	4	to	to	ADP
ejpam-4578	31	5	at	at	ADV
ejpam-4578	31	6	least	least	ADV
ejpam-4578	31	7	one	one	NUM
ejpam-4578	31	8	vertex	vertex	NOUN
ejpam-4578	31	9	v	v	ADP
ejpam-4578	31	10	∈	∈	NOUN
ejpam-4578	31	11	s.	s.	PROPN
ejpam-4578	32	1	the	the	DET
ejpam-4578	32	2	domination	domination	NOUN
ejpam-4578	32	3	number	number	NOUN
ejpam-4578	32	4	of	of	ADP
ejpam-4578	32	5	a	a	DET
ejpam-4578	32	6	graph	graph	NOUN
ejpam-4578	32	7	g	g	NOUN
ejpam-4578	32	8	,	,	PUNCT
ejpam-4578	32	9	denoted	denote	VERB
ejpam-4578	32	10	by	by	ADP
ejpam-4578	32	11	γ(g	γ(g	PROPN
ejpam-4578	32	12	)	)	PUNCT
ejpam-4578	32	13	,	,	PUNCT
ejpam-4578	32	14	is	be	AUX
ejpam-4578	32	15	given	give	VERB
ejpam-4578	32	16	by	by	ADP
ejpam-4578	32	17	γ(g	γ(g	PROPN
ejpam-4578	32	18	)	)	PUNCT
ejpam-4578	33	1	=	=	NOUN
ejpam-4578	33	2	min{|s|	min{|s|	NOUN
ejpam-4578	33	3	:	:	PUNCT
ejpam-4578	33	4	s	s	VERB
ejpam-4578	33	5	is	be	AUX
ejpam-4578	33	6	a	a	DET
ejpam-4578	33	7	dominating	dominating	NOUN
ejpam-4578	33	8	set	set	NOUN
ejpam-4578	33	9	of	of	ADP
ejpam-4578	33	10	g	g	NOUN
ejpam-4578	33	11	}	}	PUNCT
ejpam-4578	33	12	.	.	PUNCT
ejpam-4578	34	1	a	a	DET
ejpam-4578	34	2	set	set	NOUN
ejpam-4578	34	3	s	s	NOUN
ejpam-4578	34	4	⊆	⊆	NUM
ejpam-4578	34	5	v	v	NOUN
ejpam-4578	34	6	(	(	PUNCT
ejpam-4578	34	7	g	g	NOUN
ejpam-4578	34	8	)	)	PUNCT
ejpam-4578	34	9	is	be	AUX
ejpam-4578	34	10	a	a	DET
ejpam-4578	34	11	hop	hop	NOUN
ejpam-4578	34	12	dominating	dominating	NOUN
ejpam-4578	34	13	set	set	NOUN
ejpam-4578	34	14	of	of	ADP
ejpam-4578	34	15	g	g	PROPN
ejpam-4578	34	16	if	if	SCONJ
ejpam-4578	34	17	for	for	ADP
ejpam-4578	34	18	every	every	DET
ejpam-4578	34	19	v	v	NUM
ejpam-4578	34	20	∈	∈	NOUN
ejpam-4578	34	21	v	v	NOUN
ejpam-4578	34	22	(	(	PUNCT
ejpam-4578	34	23	g)\s	g)\s	NOUN
ejpam-4578	34	24	,	,	PUNCT
ejpam-4578	34	25	there	there	PRON
ejpam-4578	34	26	exists	exist	VERB
ejpam-4578	34	27	u	u	PROPN
ejpam-4578	34	28	∈	∈	PROPN
ejpam-4578	34	29	s	s	VERB
ejpam-4578	34	30	such	such	ADJ
ejpam-4578	34	31	that	that	DET
ejpam-4578	34	32	dg(u	dg(u	ADJ
ejpam-4578	34	33	,	,	PUNCT
ejpam-4578	34	34	v	v	NOUN
ejpam-4578	34	35	)	)	PUNCT
ejpam-4578	35	1	=	=	SYM
ejpam-4578	35	2	2	2	X
ejpam-4578	35	3	.	.	PUNCT
ejpam-4578	36	1	the	the	DET
ejpam-4578	36	2	minimum	minimum	ADJ
ejpam-4578	36	3	cardinality	cardinality	NOUN
ejpam-4578	36	4	of	of	ADP
ejpam-4578	36	5	a	a	DET
ejpam-4578	36	6	hop	hop	NOUN
ejpam-4578	36	7	dominating	dominating	NOUN
ejpam-4578	36	8	set	set	NOUN
ejpam-4578	36	9	of	of	ADP
ejpam-4578	36	10	g	g	NOUN
ejpam-4578	36	11	,	,	PUNCT
ejpam-4578	36	12	denoted	denote	VERB
ejpam-4578	36	13	by	by	ADP
ejpam-4578	36	14	γh(g	γh(g	NOUN
ejpam-4578	36	15	)	)	PUNCT
ejpam-4578	36	16	,	,	PUNCT
ejpam-4578	36	17	is	be	AUX
ejpam-4578	36	18	called	call	VERB
ejpam-4578	36	19	the	the	DET
ejpam-4578	36	20	hop	hop	NOUN
ejpam-4578	36	21	domination	domination	NOUN
ejpam-4578	36	22	number	number	NOUN
ejpam-4578	36	23	of	of	ADP
ejpam-4578	36	24	g.	g.	PROPN
ejpam-4578	36	25	any	any	DET
ejpam-4578	36	26	hop	hop	NOUN
ejpam-4578	36	27	dominating	dominating	NOUN
ejpam-4578	36	28	set	set	VERB
ejpam-4578	36	29	with	with	ADP
ejpam-4578	36	30	cardinality	cardinality	NOUN
ejpam-4578	36	31	equal	equal	ADJ
ejpam-4578	36	32	to	to	ADP
ejpam-4578	36	33	γh(g	γh(g	NOUN
ejpam-4578	36	34	)	)	PUNCT
ejpam-4578	36	35	is	be	AUX
ejpam-4578	36	36	called	call	VERB
ejpam-4578	36	37	a	a	DET
ejpam-4578	36	38	γh	γh	ADV
ejpam-4578	36	39	-	-	PUNCT
ejpam-4578	36	40	set	set	NOUN
ejpam-4578	36	41	.	.	PUNCT
ejpam-4578	37	1	the	the	DET
ejpam-4578	37	2	floor	floor	NOUN
ejpam-4578	37	3	function	function	NOUN
ejpam-4578	37	4	of	of	ADP
ejpam-4578	37	5	a	a	DET
ejpam-4578	37	6	real	real	ADJ
ejpam-4578	37	7	number	number	NOUN
ejpam-4578	37	8	x	x	NOUN
ejpam-4578	37	9	,	,	PUNCT
ejpam-4578	37	10	denoted	denote	VERB
ejpam-4578	37	11	by	by	ADP
ejpam-4578	37	12	⌊x⌋	⌊x⌋	NUM
ejpam-4578	37	13	,	,	PUNCT
ejpam-4578	37	14	is	be	AUX
ejpam-4578	37	15	a	a	DET
ejpam-4578	37	16	function	function	NOUN
ejpam-4578	37	17	that	that	PRON
ejpam-4578	37	18	returns	return	VERB
ejpam-4578	37	19	the	the	DET
ejpam-4578	37	20	highest	high	ADJ
ejpam-4578	37	21	integer	integer	NOUN
ejpam-4578	37	22	less	less	ADJ
ejpam-4578	37	23	than	than	ADP
ejpam-4578	37	24	or	or	CCONJ
ejpam-4578	37	25	equal	equal	ADJ
ejpam-4578	37	26	to	to	PART
ejpam-4578	37	27	x.	x.	VERB
ejpam-4578	37	28	formally	formally	ADV
ejpam-4578	37	29	,	,	PUNCT
ejpam-4578	37	30	for	for	ADP
ejpam-4578	37	31	all	all	DET
ejpam-4578	37	32	real	real	ADJ
ejpam-4578	37	33	number	number	NOUN
ejpam-4578	37	34	x	x	NOUN
ejpam-4578	37	35	,	,	PUNCT
ejpam-4578	37	36	⌊x⌋	⌊x⌋	PUNCT
ejpam-4578	37	37	=	=	SYM
ejpam-4578	37	38	max{n	max{n	NUM
ejpam-4578	37	39	∈	∈	PROPN
ejpam-4578	37	40	z	z	NOUN
ejpam-4578	37	41	|n	|n	NOUN
ejpam-4578	37	42	≤	≤	NUM
ejpam-4578	37	43	x	x	NUM
ejpam-4578	37	44	}	}	PUNCT
ejpam-4578	37	45	.	.	PUNCT
ejpam-4578	38	1	a	a	DET
ejpam-4578	38	2	vertex	vertex	NOUN
ejpam-4578	38	3	v	v	NOUN
ejpam-4578	38	4	in	in	ADP
ejpam-4578	38	5	g	g	PROPN
ejpam-4578	38	6	is	be	AUX
ejpam-4578	38	7	a	a	DET
ejpam-4578	38	8	hop	hop	NOUN
ejpam-4578	38	9	neighbor	neighbor	NOUN
ejpam-4578	38	10	of	of	ADP
ejpam-4578	38	11	vertex	vertex	NOUN
ejpam-4578	38	12	u	u	NOUN
ejpam-4578	38	13	in	in	ADP
ejpam-4578	38	14	g	g	PROPN
ejpam-4578	38	15	if	if	SCONJ
ejpam-4578	38	16	dg(u	dg(u	NOUN
ejpam-4578	38	17	,	,	PUNCT
ejpam-4578	38	18	v	v	NOUN
ejpam-4578	38	19	)	)	PUNCT
ejpam-4578	38	20	=	=	SYM
ejpam-4578	38	21	2	2	X
ejpam-4578	38	22	.	.	X
ejpam-4578	39	1	the	the	DET
ejpam-4578	39	2	set	set	NOUN
ejpam-4578	39	3	ng(u	ng(u	NOUN
ejpam-4578	39	4	,	,	PUNCT
ejpam-4578	39	5	2	2	NUM
ejpam-4578	39	6	)	)	PUNCT
ejpam-4578	39	7	=	=	PRON
ejpam-4578	39	8	{	{	PUNCT
ejpam-4578	39	9	v	v	NUM
ejpam-4578	39	10	∈	∈	NOUN
ejpam-4578	39	11	v	v	NOUN
ejpam-4578	39	12	(	(	PUNCT
ejpam-4578	39	13	g	g	NOUN
ejpam-4578	39	14	)	)	PUNCT
ejpam-4578	39	15	:	:	PUNCT
ejpam-4578	39	16	dg(v	dg(v	X
ejpam-4578	39	17	,	,	PUNCT
ejpam-4578	39	18	u	u	NOUN
ejpam-4578	39	19	)	)	PUNCT
ejpam-4578	39	20	=	=	SYM
ejpam-4578	39	21	2	2	X
ejpam-4578	39	22	}	}	PUNCT
ejpam-4578	39	23	is	be	AUX
ejpam-4578	39	24	called	call	VERB
ejpam-4578	39	25	the	the	DET
ejpam-4578	39	26	open	open	ADJ
ejpam-4578	39	27	hop	hop	NOUN
ejpam-4578	39	28	neighborhood	neighborhood	NOUN
ejpam-4578	39	29	of	of	ADP
ejpam-4578	39	30	u.	u.	PROPN
ejpam-4578	39	31	the	the	DET
ejpam-4578	39	32	closed	closed	ADJ
ejpam-4578	39	33	hop	hop	NOUN
ejpam-4578	39	34	neighborhood	neighborhood	NOUN
ejpam-4578	39	35	of	of	ADP
ejpam-4578	39	36	u	u	PROPN
ejpam-4578	39	37	in	in	ADP
ejpam-4578	39	38	g	g	PROPN
ejpam-4578	39	39	is	be	AUX
ejpam-4578	39	40	given	give	VERB
ejpam-4578	39	41	by	by	ADP
ejpam-4578	39	42	ng[u	ng[u	PROPN
ejpam-4578	39	43	,	,	PUNCT
ejpam-4578	39	44	2	2	NUM
ejpam-4578	39	45	]	]	PUNCT
ejpam-4578	39	46	=	=	PUNCT
ejpam-4578	39	47	ng(u	ng(u	NOUN
ejpam-4578	39	48	,	,	PUNCT
ejpam-4578	39	49	2	2	X
ejpam-4578	39	50	)	)	PUNCT
ejpam-4578	39	51	∪	∪	NOUN
ejpam-4578	39	52	{	{	PUNCT
ejpam-4578	39	53	u	u	NOUN
ejpam-4578	39	54	}	}	PUNCT
ejpam-4578	39	55	.	.	PUNCT
ejpam-4578	40	1	the	the	DET
ejpam-4578	40	2	open	open	ADJ
ejpam-4578	40	3	hop	hop	NOUN
ejpam-4578	40	4	neighborhood	neighborhood	NOUN
ejpam-4578	40	5	of	of	ADP
ejpam-4578	40	6	x	x	PROPN
ejpam-4578	40	7	⊆	⊆	NUM
ejpam-4578	40	8	v	v	ADP
ejpam-4578	40	9	(	(	PUNCT
ejpam-4578	40	10	g	g	NOUN
ejpam-4578	40	11	)	)	PUNCT
ejpam-4578	40	12	is	be	AUX
ejpam-4578	40	13	the	the	DET
ejpam-4578	40	14	set	set	NOUN
ejpam-4578	40	15	ng(x	ng(x	NUM
ejpam-4578	40	16	,	,	PUNCT
ejpam-4578	40	17	2	2	X
ejpam-4578	40	18	)	)	PUNCT
ejpam-4578	40	19	=	=	NOUN
ejpam-4578	40	20	⋃	⋃	NOUN
ejpam-4578	40	21	u∈x	u∈x	ADJ
ejpam-4578	40	22	ng(u	ng(u	NOUN
ejpam-4578	40	23	,	,	PUNCT
ejpam-4578	40	24	2	2	NUM
ejpam-4578	40	25	)	)	PUNCT
ejpam-4578	40	26	.	.	PUNCT
ejpam-4578	41	1	the	the	DET
ejpam-4578	41	2	closed	closed	ADJ
ejpam-4578	41	3	hop	hop	NOUN
ejpam-4578	41	4	neighborhood	neighborhood	NOUN
ejpam-4578	41	5	of	of	ADP
ejpam-4578	41	6	x	x	PUNCT
ejpam-4578	41	7	in	in	ADP
ejpam-4578	41	8	g	g	PROPN
ejpam-4578	41	9	is	be	AUX
ejpam-4578	41	10	the	the	DET
ejpam-4578	41	11	set	set	PROPN
ejpam-4578	41	12	ng[x	ng[x	PROPN
ejpam-4578	41	13	,	,	PUNCT
ejpam-4578	41	14	2	2	NUM
ejpam-4578	41	15	]	]	PUNCT
ejpam-4578	41	16	=	=	SYM
ejpam-4578	41	17	ng(x	ng(x	X
ejpam-4578	41	18	,	,	PUNCT
ejpam-4578	41	19	2	2	NUM
ejpam-4578	41	20	)	)	PUNCT
ejpam-4578	41	21	∪x	∪x	NUM
ejpam-4578	41	22	.	.	PUNCT
ejpam-4578	42	1	a	a	DET
ejpam-4578	42	2	vertex	vertex	NOUN
ejpam-4578	42	3	x	x	X
ejpam-4578	42	4	of	of	ADP
ejpam-4578	42	5	a	a	DET
ejpam-4578	42	6	graph	graph	NOUN
ejpam-4578	42	7	g	g	NOUN
ejpam-4578	42	8	is	be	AUX
ejpam-4578	42	9	said	say	VERB
ejpam-4578	42	10	to	to	PART
ejpam-4578	42	11	resolve	resolve	VERB
ejpam-4578	42	12	two	two	NUM
ejpam-4578	42	13	vertices	vertex	NOUN
ejpam-4578	42	14	u	u	NOUN
ejpam-4578	42	15	and	and	CCONJ
ejpam-4578	42	16	v	v	NOUN
ejpam-4578	42	17	of	of	ADP
ejpam-4578	42	18	g	g	PROPN
ejpam-4578	42	19	if	if	SCONJ
ejpam-4578	42	20	dg(x	dg(x	NUM
ejpam-4578	42	21	,	,	PUNCT
ejpam-4578	42	22	u	u	NOUN
ejpam-4578	42	23	)	)	PUNCT
ejpam-4578	42	24	̸=	̸=	PROPN
ejpam-4578	42	25	dg(x	dg(x	NUM
ejpam-4578	42	26	,	,	PUNCT
ejpam-4578	42	27	v	v	NOUN
ejpam-4578	42	28	)	)	PUNCT
ejpam-4578	42	29	.	.	PUNCT
ejpam-4578	43	1	for	for	ADP
ejpam-4578	43	2	an	an	DET
ejpam-4578	43	3	ordered	order	VERB
ejpam-4578	43	4	set	set	NOUN
ejpam-4578	43	5	w	w	NOUN
ejpam-4578	43	6	=	=	PUNCT
ejpam-4578	43	7	{	{	PUNCT
ejpam-4578	43	8	x1	x1	PROPN
ejpam-4578	43	9	,	,	PUNCT
ejpam-4578	43	10	...	...	PUNCT
ejpam-4578	43	11	,	,	PUNCT
ejpam-4578	43	12	xk	xk	ADJ
ejpam-4578	43	13	}	}	PUNCT
ejpam-4578	43	14	⊆	⊆	NUM
ejpam-4578	43	15	v	v	NOUN
ejpam-4578	43	16	(	(	PUNCT
ejpam-4578	43	17	g	g	NOUN
ejpam-4578	43	18	)	)	PUNCT
ejpam-4578	43	19	and	and	CCONJ
ejpam-4578	43	20	a	a	DET
ejpam-4578	43	21	vertex	vertex	NOUN
ejpam-4578	43	22	v	v	NOUN
ejpam-4578	43	23	in	in	ADP
ejpam-4578	43	24	g	g	PROPN
ejpam-4578	43	25	,	,	PUNCT
ejpam-4578	43	26	the	the	DET
ejpam-4578	43	27	k	k	PROPN
ejpam-4578	43	28	−	−	PROPN
ejpam-4578	43	29	vector	vector	NOUN
ejpam-4578	43	30	rg(v	rg(v	NOUN
ejpam-4578	43	31	/	/	SYM
ejpam-4578	43	32	w	w	NOUN
ejpam-4578	43	33	)	)	PUNCT
ejpam-4578	43	34	=	=	SYM
ejpam-4578	43	35	(	(	PUNCT
ejpam-4578	43	36	dg(v	dg(v	X
ejpam-4578	43	37	,	,	PUNCT
ejpam-4578	43	38	x1	x1	PROPN
ejpam-4578	43	39	)	)	PUNCT
ejpam-4578	43	40	,	,	PUNCT
ejpam-4578	43	41	dg(v	dg(v	X
ejpam-4578	43	42	,	,	PUNCT
ejpam-4578	43	43	x2	x2	PROPN
ejpam-4578	43	44	)	)	PUNCT
ejpam-4578	43	45	,	,	PUNCT
ejpam-4578	43	46	·	·	PUNCT
ejpam-4578	43	47	·	·	PUNCT
ejpam-4578	43	48	·	·	PUNCT
ejpam-4578	43	49	,	,	PUNCT
ejpam-4578	43	50	dg(v	dg(v	X
ejpam-4578	43	51	,	,	PUNCT
ejpam-4578	43	52	xk	xk	NOUN
ejpam-4578	43	53	)	)	PUNCT
ejpam-4578	43	54	)	)	PUNCT
ejpam-4578	43	55	is	be	AUX
ejpam-4578	43	56	called	call	VERB
ejpam-4578	43	57	the	the	DET
ejpam-4578	43	58	representation	representation	NOUN
ejpam-4578	43	59	of	of	ADP
ejpam-4578	43	60	v	v	NOUN
ejpam-4578	43	61	with	with	ADP
ejpam-4578	43	62	respect	respect	NOUN
ejpam-4578	43	63	to	to	ADP
ejpam-4578	43	64	w	w	PROPN
ejpam-4578	43	65	.	.	PUNCT
ejpam-4578	44	1	the	the	DET
ejpam-4578	44	2	set	set	NOUN
ejpam-4578	44	3	w	w	NOUN
ejpam-4578	44	4	is	be	AUX
ejpam-4578	44	5	a	a	DET
ejpam-4578	44	6	resolving	resolving	NOUN
ejpam-4578	44	7	set	set	VERB
ejpam-4578	44	8	for	for	ADP
ejpam-4578	44	9	g	g	PROPN
ejpam-4578	44	10	if	if	SCONJ
ejpam-4578	45	1	and	and	CCONJ
ejpam-4578	45	2	only	only	ADV
ejpam-4578	45	3	if	if	SCONJ
ejpam-4578	45	4	no	no	DET
ejpam-4578	45	5	two	two	NUM
ejpam-4578	45	6	vertices	vertex	NOUN
ejpam-4578	45	7	of	of	ADP
ejpam-4578	45	8	g	g	NOUN
ejpam-4578	45	9	have	have	VERB
ejpam-4578	45	10	the	the	DET
ejpam-4578	45	11	same	same	ADJ
ejpam-4578	45	12	representation	representation	NOUN
ejpam-4578	45	13	with	with	ADP
ejpam-4578	45	14	respect	respect	NOUN
ejpam-4578	45	15	to	to	ADP
ejpam-4578	45	16	w	w	PROPN
ejpam-4578	45	17	.	.	PUNCT
ejpam-4578	46	1	the	the	DET
ejpam-4578	46	2	metric	metric	ADJ
ejpam-4578	46	3	dimension	dimension	NOUN
ejpam-4578	46	4	of	of	ADP
ejpam-4578	46	5	g	g	NOUN
ejpam-4578	46	6	,	,	PUNCT
ejpam-4578	46	7	denoted	denote	VERB
ejpam-4578	46	8	by	by	ADP
ejpam-4578	46	9	,	,	PUNCT
ejpam-4578	46	10	dim(g	dim(g	PROPN
ejpam-4578	46	11	)	)	PUNCT
ejpam-4578	46	12	,	,	PUNCT
ejpam-4578	46	13	is	be	AUX
ejpam-4578	46	14	the	the	DET
ejpam-4578	46	15	minimum	minimum	ADJ
ejpam-4578	46	16	cardinality	cardinality	NOUN
ejpam-4578	46	17	over	over	ADP
ejpam-4578	46	18	all	all	DET
ejpam-4578	46	19	resolving	resolve	VERB
ejpam-4578	46	20	sets	set	NOUN
ejpam-4578	46	21	of	of	ADP
ejpam-4578	46	22	g.	g.	PROPN
ejpam-4578	46	23	a	a	DET
ejpam-4578	46	24	resolving	resolve	VERB
ejpam-4578	46	25	set	set	NOUN
ejpam-4578	46	26	of	of	ADP
ejpam-4578	46	27	cardinality	cardinality	PROPN
ejpam-4578	46	28	dim(g	dim(g	PROPN
ejpam-4578	46	29	)	)	PUNCT
ejpam-4578	46	30	is	be	AUX
ejpam-4578	46	31	called	call	VERB
ejpam-4578	46	32	basis	basis	NOUN
ejpam-4578	46	33	.	.	PUNCT
ejpam-4578	47	1	a	a	DET
ejpam-4578	47	2	set	set	NOUN
ejpam-4578	47	3	s	s	NOUN
ejpam-4578	47	4	⊆	⊆	NUM
ejpam-4578	47	5	v	v	NOUN
ejpam-4578	47	6	(	(	PUNCT
ejpam-4578	47	7	g	g	NOUN
ejpam-4578	47	8	)	)	PUNCT
ejpam-4578	47	9	is	be	AUX
ejpam-4578	47	10	a	a	DET
ejpam-4578	47	11	resolving	resolve	VERB
ejpam-4578	47	12	hop	hop	NOUN
ejpam-4578	47	13	dominating	dominating	NOUN
ejpam-4578	47	14	set	set	NOUN
ejpam-4578	47	15	of	of	ADP
ejpam-4578	47	16	g	g	PROPN
ejpam-4578	47	17	if	if	SCONJ
ejpam-4578	47	18	s	s	VERB
ejpam-4578	47	19	is	be	AUX
ejpam-4578	47	20	both	both	PRON
ejpam-4578	47	21	a	a	DET
ejpam-4578	47	22	resolving	resolving	NOUN
ejpam-4578	47	23	set	set	VERB
ejpam-4578	47	24	and	and	CCONJ
ejpam-4578	47	25	a	a	DET
ejpam-4578	47	26	hop	hop	NOUN
ejpam-4578	47	27	dominating	dominating	NOUN
ejpam-4578	47	28	set	set	NOUN
ejpam-4578	47	29	.	.	PUNCT
ejpam-4578	48	1	the	the	DET
ejpam-4578	48	2	minimum	minimum	ADJ
ejpam-4578	48	3	cardinality	cardinality	NOUN
ejpam-4578	48	4	of	of	ADP
ejpam-4578	48	5	a	a	DET
ejpam-4578	48	6	resolving	resolve	VERB
ejpam-4578	48	7	hop	hop	NOUN
ejpam-4578	48	8	dominating	dominating	NOUN
ejpam-4578	48	9	set	set	NOUN
ejpam-4578	48	10	of	of	ADP
ejpam-4578	48	11	g	g	NOUN
ejpam-4578	48	12	,	,	PUNCT
ejpam-4578	48	13	denoted	denote	VERB
ejpam-4578	48	14	by	by	ADP
ejpam-4578	48	15	γrh(g	γrh(g	NOUN
ejpam-4578	48	16	)	)	PUNCT
ejpam-4578	48	17	,	,	PUNCT
ejpam-4578	48	18	is	be	AUX
ejpam-4578	48	19	called	call	VERB
ejpam-4578	48	20	the	the	DET
ejpam-4578	48	21	resolving	resolve	VERB
ejpam-4578	48	22	hop	hop	NOUN
ejpam-4578	48	23	domination	domination	NOUN
ejpam-4578	48	24	number	number	NOUN
ejpam-4578	48	25	of	of	ADP
ejpam-4578	48	26	g.	g.	PROPN
ejpam-4578	48	27	any	any	PRON
ejpam-4578	48	28	resolving	resolve	VERB
ejpam-4578	48	29	hop	hop	NOUN
ejpam-4578	48	30	dominating	dominating	NOUN
ejpam-4578	48	31	set	set	VERB
ejpam-4578	48	32	with	with	ADP
ejpam-4578	48	33	cardinality	cardinality	NOUN
ejpam-4578	48	34	equal	equal	ADJ
ejpam-4578	48	35	to	to	ADP
ejpam-4578	48	36	γrh(g	γrh(g	NOUN
ejpam-4578	48	37	)	)	PUNCT
ejpam-4578	48	38	is	be	AUX
ejpam-4578	48	39	called	call	VERB
ejpam-4578	48	40	a	a	DET
ejpam-4578	48	41	γrh	γrh	NOUN
ejpam-4578	48	42	-	-	PUNCT
ejpam-4578	48	43	set	set	NOUN
ejpam-4578	48	44	.	.	PUNCT
ejpam-4578	49	1	a	a	DET
ejpam-4578	49	2	u	u	NOUN
ejpam-4578	49	3	-	-	NOUN
ejpam-4578	49	4	v	v	ADJ
ejpam-4578	49	5	path	path	NOUN
ejpam-4578	49	6	of	of	ADP
ejpam-4578	49	7	length	length	NOUN
ejpam-4578	49	8	dg(u	dg(u	PROPN
ejpam-4578	49	9	,	,	PUNCT
ejpam-4578	49	10	v	v	NOUN
ejpam-4578	49	11	)	)	PUNCT
ejpam-4578	49	12	is	be	AUX
ejpam-4578	49	13	called	call	VERB
ejpam-4578	49	14	a	a	DET
ejpam-4578	49	15	u	u	NOUN
ejpam-4578	49	16	-	-	NOUN
ejpam-4578	49	17	v	v	ADJ
ejpam-4578	49	18	geodesic	geodesic	NOUN
ejpam-4578	49	19	.	.	PUNCT
ejpam-4578	50	1	the	the	DET
ejpam-4578	50	2	set	set	NOUN
ejpam-4578	50	3	ig[u	ig[u	PROPN
ejpam-4578	50	4	,	,	PUNCT
ejpam-4578	50	5	v	v	NOUN
ejpam-4578	50	6	]	]	PUNCT
ejpam-4578	50	7	is	be	AUX
ejpam-4578	50	8	defined	define	VERB
ejpam-4578	50	9	as	as	ADP
ejpam-4578	50	10	the	the	DET
ejpam-4578	50	11	set	set	NOUN
ejpam-4578	50	12	of	of	ADP
ejpam-4578	50	13	all	all	DET
ejpam-4578	50	14	vertices	vertex	NOUN
ejpam-4578	50	15	of	of	ADP
ejpam-4578	50	16	g	g	NOUN
ejpam-4578	50	17	lying	lie	VERB
ejpam-4578	50	18	on	on	ADP
ejpam-4578	50	19	any	any	DET
ejpam-4578	50	20	u	u	NOUN
ejpam-4578	50	21	-	-	NOUN
ejpam-4578	50	22	v	v	ADJ
ejpam-4578	50	23	geodesic	geodesic	NOUN
ejpam-4578	50	24	.	.	PUNCT
ejpam-4578	51	1	j.	j.	PROPN
ejpam-4578	51	2	mohamad	mohamad	PROPN
ejpam-4578	51	3	,	,	PUNCT
ejpam-4578	51	4	h.	h.	PROPN
ejpam-4578	51	5	rara	rara	PROPN
ejpam-4578	51	6	/	/	SYM
ejpam-4578	51	7	eur	eur	PROPN
ejpam-4578	51	8	.	.	PUNCT
ejpam-4578	52	1	j.	j.	PROPN
ejpam-4578	52	2	pure	pure	PROPN
ejpam-4578	52	3	appl	appl	PROPN
ejpam-4578	52	4	.	.	PROPN
ejpam-4578	52	5	math	math	PROPN
ejpam-4578	52	6	,	,	PUNCT
ejpam-4578	52	7	16	16	NUM
ejpam-4578	52	8	(	(	PUNCT
ejpam-4578	52	9	1	1	NUM
ejpam-4578	52	10	)	)	PUNCT
ejpam-4578	52	11	(	(	PUNCT
ejpam-4578	52	12	2023	2023	NUM
ejpam-4578	52	13	)	)	PUNCT
ejpam-4578	52	14	,	,	PUNCT
ejpam-4578	52	15	131	131	NUM
ejpam-4578	52	16	-	-	SYM
ejpam-4578	52	17	143	143	NUM
ejpam-4578	52	18	133	133	NUM
ejpam-4578	52	19	a	a	DET
ejpam-4578	52	20	vertex	vertex	NOUN
ejpam-4578	52	21	w	w	ADP
ejpam-4578	52	22	∈	∈	PROPN
ejpam-4578	52	23	v	v	ADP
ejpam-4578	52	24	(	(	PUNCT
ejpam-4578	52	25	g	g	NOUN
ejpam-4578	52	26	)	)	PUNCT
ejpam-4578	52	27	strongly	strongly	ADV
ejpam-4578	52	28	resolves	resolve	VERB
ejpam-4578	52	29	two	two	NUM
ejpam-4578	52	30	different	different	ADJ
ejpam-4578	52	31	vertices	vertex	NOUN
ejpam-4578	52	32	u	u	NOUN
ejpam-4578	52	33	,	,	PUNCT
ejpam-4578	52	34	v	v	NOUN
ejpam-4578	52	35	∈	∈	PROPN
ejpam-4578	52	36	v	v	NOUN
ejpam-4578	52	37	(	(	PUNCT
ejpam-4578	52	38	g	g	NOUN
ejpam-4578	52	39	)	)	PUNCT
ejpam-4578	52	40	if	if	SCONJ
ejpam-4578	52	41	v	v	NUM
ejpam-4578	52	42	∈	∈	PROPN
ejpam-4578	52	43	ig[u	ig[u	PROPN
ejpam-4578	52	44	,	,	PUNCT
ejpam-4578	52	45	w	w	NOUN
ejpam-4578	52	46	]	]	PUNCT
ejpam-4578	52	47	or	or	CCONJ
ejpam-4578	52	48	if	if	SCONJ
ejpam-4578	52	49	u	u	PROPN
ejpam-4578	52	50	∈	∈	PROPN
ejpam-4578	52	51	ig[v	ig[v	PROPN
ejpam-4578	52	52	,	,	PUNCT
ejpam-4578	52	53	w	w	PROPN
ejpam-4578	52	54	]	]	X
ejpam-4578	52	55	.	.	PUNCT
ejpam-4578	53	1	a	a	DET
ejpam-4578	53	2	set	set	NOUN
ejpam-4578	53	3	w	w	NOUN
ejpam-4578	53	4	of	of	ADP
ejpam-4578	53	5	vertices	vertex	NOUN
ejpam-4578	53	6	in	in	ADP
ejpam-4578	53	7	g	g	PROPN
ejpam-4578	53	8	is	be	AUX
ejpam-4578	53	9	a	a	DET
ejpam-4578	53	10	strong	strong	ADJ
ejpam-4578	53	11	resolving	resolving	NOUN
ejpam-4578	53	12	set	set	NOUN
ejpam-4578	53	13	of	of	ADP
ejpam-4578	53	14	g	g	NOUN
ejpam-4578	53	15	if	if	SCONJ
ejpam-4578	53	16	every	every	DET
ejpam-4578	53	17	two	two	NUM
ejpam-4578	53	18	vertices	vertex	NOUN
ejpam-4578	53	19	of	of	ADP
ejpam-4578	53	20	g	g	NOUN
ejpam-4578	53	21	are	be	AUX
ejpam-4578	53	22	strongly	strongly	ADV
ejpam-4578	53	23	resolved	resolve	VERB
ejpam-4578	53	24	by	by	ADP
ejpam-4578	53	25	some	some	DET
ejpam-4578	53	26	vertex	vertex	NOUN
ejpam-4578	53	27	of	of	ADP
ejpam-4578	53	28	w	w	PROPN
ejpam-4578	53	29	.	.	PUNCT
ejpam-4578	54	1	the	the	DET
ejpam-4578	54	2	smallest	small	ADJ
ejpam-4578	54	3	cardinality	cardinality	NOUN
ejpam-4578	54	4	of	of	ADP
ejpam-4578	54	5	a	a	DET
ejpam-4578	54	6	strong	strong	ADJ
ejpam-4578	54	7	resolving	resolving	NOUN
ejpam-4578	54	8	set	set	NOUN
ejpam-4578	54	9	of	of	ADP
ejpam-4578	54	10	g	g	PROPN
ejpam-4578	54	11	is	be	AUX
ejpam-4578	54	12	called	call	VERB
ejpam-4578	54	13	the	the	DET
ejpam-4578	54	14	strong	strong	ADJ
ejpam-4578	54	15	metric	metric	ADJ
ejpam-4578	54	16	dimension	dimension	NOUN
ejpam-4578	54	17	of	of	ADP
ejpam-4578	54	18	g	g	NOUN
ejpam-4578	54	19	and	and	CCONJ
ejpam-4578	54	20	is	be	AUX
ejpam-4578	54	21	denoted	denote	VERB
ejpam-4578	54	22	by	by	ADP
ejpam-4578	54	23	sdim(g	sdim(g	PROPN
ejpam-4578	54	24	)	)	PUNCT
ejpam-4578	54	25	.	.	PUNCT
ejpam-4578	55	1	a	a	DET
ejpam-4578	55	2	strong	strong	ADJ
ejpam-4578	55	3	resolving	resolving	NOUN
ejpam-4578	55	4	set	set	NOUN
ejpam-4578	55	5	of	of	ADP
ejpam-4578	55	6	cardinality	cardinality	PROPN
ejpam-4578	55	7	sdim(g	sdim(g	PROPN
ejpam-4578	55	8	)	)	PUNCT
ejpam-4578	55	9	is	be	AUX
ejpam-4578	55	10	called	call	VERB
ejpam-4578	55	11	a	a	DET
ejpam-4578	55	12	strong	strong	ADJ
ejpam-4578	55	13	metric	metric	ADJ
ejpam-4578	55	14	basis	basis	NOUN
ejpam-4578	55	15	of	of	ADP
ejpam-4578	55	16	g.	g.	PROPN
ejpam-4578	55	17	a	a	DET
ejpam-4578	55	18	vertex	vertex	NOUN
ejpam-4578	55	19	u	u	NOUN
ejpam-4578	55	20	of	of	ADP
ejpam-4578	55	21	g	g	PROPN
ejpam-4578	55	22	is	be	AUX
ejpam-4578	55	23	maximally	maximally	ADV
ejpam-4578	55	24	distant	distant	ADJ
ejpam-4578	55	25	from	from	ADP
ejpam-4578	55	26	vertex	vertex	NOUN
ejpam-4578	55	27	v	v	NOUN
ejpam-4578	55	28	of	of	ADP
ejpam-4578	55	29	g	g	NOUN
ejpam-4578	55	30	,	,	PUNCT
ejpam-4578	55	31	u	u	PROPN
ejpam-4578	55	32	̸=	̸=	PROPN
ejpam-4578	55	33	v	v	NOUN
ejpam-4578	55	34	,	,	PUNCT
ejpam-4578	55	35	if	if	SCONJ
ejpam-4578	55	36	for	for	ADP
ejpam-4578	55	37	every	every	DET
ejpam-4578	55	38	vertex	vertex	NOUN
ejpam-4578	55	39	w	w	PROPN
ejpam-4578	55	40	∈	∈	PROPN
ejpam-4578	55	41	ng(u	ng(u	NOUN
ejpam-4578	55	42	)	)	PUNCT
ejpam-4578	55	43	,	,	PUNCT
ejpam-4578	55	44	dg(v	dg(v	X
ejpam-4578	55	45	,	,	PUNCT
ejpam-4578	55	46	w	w	NOUN
ejpam-4578	55	47	)	)	PUNCT
ejpam-4578	55	48	≤	≤	NOUN
ejpam-4578	55	49	dg(u	dg(u	ADJ
ejpam-4578	55	50	,	,	PUNCT
ejpam-4578	55	51	v	v	NOUN
ejpam-4578	55	52	)	)	PUNCT
ejpam-4578	55	53	.	.	PUNCT
ejpam-4578	56	1	if	if	SCONJ
ejpam-4578	56	2	u	u	NOUN
ejpam-4578	56	3	is	be	AUX
ejpam-4578	56	4	maximally	maximally	ADV
ejpam-4578	56	5	distant	distant	ADJ
ejpam-4578	56	6	from	from	ADP
ejpam-4578	56	7	v	v	NUM
ejpam-4578	56	8	,	,	PUNCT
ejpam-4578	56	9	and	and	CCONJ
ejpam-4578	56	10	v	v	NOUN
ejpam-4578	56	11	is	be	AUX
ejpam-4578	56	12	maximally	maximally	ADV
ejpam-4578	56	13	distant	distant	ADJ
ejpam-4578	56	14	from	from	ADP
ejpam-4578	56	15	u	u	NOUN
ejpam-4578	56	16	,	,	PUNCT
ejpam-4578	56	17	then	then	ADV
ejpam-4578	56	18	we	we	PRON
ejpam-4578	56	19	say	say	VERB
ejpam-4578	56	20	that	that	SCONJ
ejpam-4578	56	21	u	u	PROPN
ejpam-4578	56	22	and	and	CCONJ
ejpam-4578	56	23	v	v	NOUN
ejpam-4578	56	24	are	be	AUX
ejpam-4578	56	25	mutually	mutually	ADV
ejpam-4578	56	26	maximally	maximally	ADV
ejpam-4578	56	27	distant	distant	ADJ
ejpam-4578	56	28	,	,	PUNCT
ejpam-4578	56	29	denoted	denote	VERB
ejpam-4578	56	30	by	by	ADP
ejpam-4578	56	31	ummdv	ummdv	NOUN
ejpam-4578	56	32	.	.	PUNCT
ejpam-4578	57	1	the	the	DET
ejpam-4578	57	2	boundary	boundary	NOUN
ejpam-4578	57	3	of	of	ADP
ejpam-4578	57	4	a	a	DET
ejpam-4578	57	5	graph	graph	NOUN
ejpam-4578	57	6	g	g	NOUN
ejpam-4578	57	7	,	,	PUNCT
ejpam-4578	57	8	denoted	denote	VERB
ejpam-4578	57	9	by	by	ADP
ejpam-4578	57	10	∂(g	∂(g	PROPN
ejpam-4578	57	11	)	)	PUNCT
ejpam-4578	57	12	,	,	PUNCT
ejpam-4578	57	13	is	be	AUX
ejpam-4578	57	14	defined	define	VERB
ejpam-4578	57	15	as	as	ADP
ejpam-4578	57	16	∂(g	∂(g	PROPN
ejpam-4578	57	17	)	)	PUNCT
ejpam-4578	58	1	=	=	PUNCT
ejpam-4578	58	2	{	{	PUNCT
ejpam-4578	58	3	u	u	NOUN
ejpam-4578	58	4	∈	∈	PROPN
ejpam-4578	58	5	v	v	NOUN
ejpam-4578	58	6	(	(	PUNCT
ejpam-4578	58	7	g	g	NOUN
ejpam-4578	58	8	)	)	PUNCT
ejpam-4578	58	9	:	:	PUNCT
ejpam-4578	58	10	ummdv	ummdv	VERB
ejpam-4578	58	11	for	for	ADP
ejpam-4578	58	12	some	some	DET
ejpam-4578	58	13	v	v	ADP
ejpam-4578	58	14	∈	∈	PROPN
ejpam-4578	58	15	v	v	NOUN
ejpam-4578	58	16	(	(	PUNCT
ejpam-4578	58	17	g	g	NOUN
ejpam-4578	58	18	)	)	PUNCT
ejpam-4578	58	19	}	}	PUNCT
ejpam-4578	58	20	.	.	PUNCT
ejpam-4578	59	1	a	a	DET
ejpam-4578	59	2	set	set	NOUN
ejpam-4578	59	3	s	s	NOUN
ejpam-4578	59	4	⊆	⊆	NUM
ejpam-4578	59	5	v	v	NOUN
ejpam-4578	59	6	(	(	PUNCT
ejpam-4578	59	7	g	g	NOUN
ejpam-4578	59	8	)	)	PUNCT
ejpam-4578	59	9	is	be	AUX
ejpam-4578	59	10	a	a	DET
ejpam-4578	59	11	strong	strong	ADJ
ejpam-4578	59	12	resolving	resolve	VERB
ejpam-4578	59	13	hop	hop	NOUN
ejpam-4578	59	14	dominating	dominating	NOUN
ejpam-4578	59	15	set	set	NOUN
ejpam-4578	59	16	of	of	ADP
ejpam-4578	59	17	g	g	PROPN
ejpam-4578	59	18	if	if	SCONJ
ejpam-4578	59	19	s	s	VERB
ejpam-4578	59	20	is	be	AUX
ejpam-4578	59	21	both	both	CCONJ
ejpam-4578	59	22	a	a	DET
ejpam-4578	59	23	strong	strong	ADJ
ejpam-4578	59	24	resolving	resolving	NOUN
ejpam-4578	59	25	set	set	VERB
ejpam-4578	59	26	and	and	CCONJ
ejpam-4578	59	27	a	a	DET
ejpam-4578	59	28	hop	hop	NOUN
ejpam-4578	59	29	dominating	dominating	NOUN
ejpam-4578	59	30	set	set	NOUN
ejpam-4578	59	31	.	.	PUNCT
ejpam-4578	60	1	the	the	DET
ejpam-4578	60	2	minimum	minimum	ADJ
ejpam-4578	60	3	cardinality	cardinality	NOUN
ejpam-4578	60	4	of	of	ADP
ejpam-4578	60	5	a	a	DET
ejpam-4578	60	6	strong	strong	ADJ
ejpam-4578	60	7	resolving	resolve	VERB
ejpam-4578	60	8	hop	hop	NOUN
ejpam-4578	60	9	dominating	dominating	NOUN
ejpam-4578	60	10	set	set	NOUN
ejpam-4578	60	11	of	of	ADP
ejpam-4578	60	12	g	g	NOUN
ejpam-4578	60	13	,	,	PUNCT
ejpam-4578	60	14	denoted	denote	VERB
ejpam-4578	60	15	by	by	ADP
ejpam-4578	60	16	γsrh(g	γsrh(g	NOUN
ejpam-4578	60	17	)	)	PUNCT
ejpam-4578	60	18	,	,	PUNCT
ejpam-4578	60	19	is	be	AUX
ejpam-4578	60	20	called	call	VERB
ejpam-4578	60	21	the	the	DET
ejpam-4578	60	22	strong	strong	ADJ
ejpam-4578	60	23	resolving	resolve	VERB
ejpam-4578	60	24	hop	hop	NOUN
ejpam-4578	60	25	domination	domination	NOUN
ejpam-4578	60	26	number	number	NOUN
ejpam-4578	60	27	of	of	ADP
ejpam-4578	60	28	g.	g.	PROPN
ejpam-4578	60	29	any	any	PRON
ejpam-4578	60	30	resolving	resolve	VERB
ejpam-4578	60	31	hop	hop	NOUN
ejpam-4578	60	32	dominating	dominating	NOUN
ejpam-4578	60	33	set	set	VERB
ejpam-4578	60	34	with	with	ADP
ejpam-4578	60	35	cardinality	cardinality	NOUN
ejpam-4578	60	36	equal	equal	ADJ
ejpam-4578	60	37	to	to	ADP
ejpam-4578	60	38	γsrh(g	γsrh(g	NOUN
ejpam-4578	60	39	)	)	PUNCT
ejpam-4578	60	40	is	be	AUX
ejpam-4578	60	41	called	call	VERB
ejpam-4578	60	42	a	a	DET
ejpam-4578	60	43	γsrh	γsrh	NOUN
ejpam-4578	60	44	-	-	PUNCT
ejpam-4578	60	45	set	set	NOUN
ejpam-4578	60	46	.	.	PUNCT
ejpam-4578	61	1	a	a	DET
ejpam-4578	61	2	clique	clique	NOUN
ejpam-4578	61	3	in	in	ADP
ejpam-4578	61	4	a	a	DET
ejpam-4578	61	5	graph	graph	NOUN
ejpam-4578	61	6	g	g	NOUN
ejpam-4578	61	7	is	be	AUX
ejpam-4578	61	8	a	a	DET
ejpam-4578	61	9	complete	complete	ADJ
ejpam-4578	61	10	induced	induce	VERB
ejpam-4578	61	11	subgraph	subgraph	NOUN
ejpam-4578	61	12	of	of	ADP
ejpam-4578	61	13	g.	g.	PROPN
ejpam-4578	61	14	a	a	DET
ejpam-4578	61	15	clique	clique	NOUN
ejpam-4578	61	16	c	c	PROPN
ejpam-4578	61	17	in	in	ADP
ejpam-4578	61	18	a	a	DET
ejpam-4578	61	19	connected	connected	ADJ
ejpam-4578	61	20	graph	graph	NOUN
ejpam-4578	61	21	g	g	NOUN
ejpam-4578	61	22	is	be	AUX
ejpam-4578	61	23	called	call	VERB
ejpam-4578	61	24	a	a	DET
ejpam-4578	61	25	superclique	superclique	NOUN
ejpam-4578	61	26	if	if	SCONJ
ejpam-4578	61	27	for	for	ADP
ejpam-4578	61	28	every	every	DET
ejpam-4578	61	29	pair	pair	NOUN
ejpam-4578	61	30	of	of	ADP
ejpam-4578	61	31	distinct	distinct	ADJ
ejpam-4578	61	32	vertices	vertex	NOUN
ejpam-4578	61	33	u	u	NOUN
ejpam-4578	61	34	,	,	PUNCT
ejpam-4578	61	35	v	v	NOUN
ejpam-4578	61	36	∈	∈	ADJ
ejpam-4578	61	37	c	c	NOUN
ejpam-4578	61	38	,	,	PUNCT
ejpam-4578	61	39	there	there	PRON
ejpam-4578	61	40	exists	exist	VERB
ejpam-4578	61	41	w	w	PROPN
ejpam-4578	61	42	∈	∈	PROPN
ejpam-4578	61	43	v	v	ADP
ejpam-4578	61	44	(	(	PUNCT
ejpam-4578	61	45	g	g	NOUN
ejpam-4578	61	46	)	)	PUNCT
ejpam-4578	61	47	\	\	PUNCT
ejpam-4578	62	1	c	c	NOUN
ejpam-4578	62	2	such	such	ADJ
ejpam-4578	62	3	that	that	PRON
ejpam-4578	62	4	w	w	PROPN
ejpam-4578	62	5	∈	∈	PROPN
ejpam-4578	62	6	ng(u	ng(u	NOUN
ejpam-4578	62	7	)	)	PUNCT
ejpam-4578	62	8	\	\	NOUN
ejpam-4578	62	9	ng(v	ng(v	PUNCT
ejpam-4578	62	10	)	)	PUNCT
ejpam-4578	62	11	or	or	CCONJ
ejpam-4578	62	12	w	w	PROPN
ejpam-4578	62	13	∈	∈	PROPN
ejpam-4578	62	14	ng(v	ng(v	NOUN
ejpam-4578	62	15	)	)	PUNCT
ejpam-4578	62	16	\	\	NOUN
ejpam-4578	62	17	ng(u	ng(u	NOUN
ejpam-4578	62	18	)	)	PUNCT
ejpam-4578	62	19	.	.	PUNCT
ejpam-4578	63	1	a	a	DET
ejpam-4578	63	2	superclique	superclique	NOUN
ejpam-4578	63	3	c	c	NOUN
ejpam-4578	63	4	is	be	AUX
ejpam-4578	63	5	maximum	maximum	ADJ
ejpam-4578	63	6	in	in	ADP
ejpam-4578	63	7	g	g	PROPN
ejpam-4578	63	8	if	if	SCONJ
ejpam-4578	63	9	|c|	|c|	PROPN
ejpam-4578	63	10	≥	≥	NOUN
ejpam-4578	63	11	|c∗|	|c∗|	VERB
ejpam-4578	63	12	for	for	SCONJ
ejpam-4578	63	13	all	all	DET
ejpam-4578	63	14	supercliques	superclique	NOUN
ejpam-4578	63	15	c∗	c∗	PROPN
ejpam-4578	63	16	in	in	ADP
ejpam-4578	63	17	g.	g.	PROPN
ejpam-4578	63	18	the	the	DET
ejpam-4578	63	19	superclique	superclique	ADJ
ejpam-4578	63	20	number	number	NOUN
ejpam-4578	63	21	,	,	PUNCT
ejpam-4578	63	22	ωs(g	ωs(g	NUM
ejpam-4578	63	23	)	)	PUNCT
ejpam-4578	63	24	,	,	PUNCT
ejpam-4578	63	25	of	of	ADP
ejpam-4578	63	26	g	g	PROPN
ejpam-4578	63	27	is	be	AUX
ejpam-4578	63	28	the	the	DET
ejpam-4578	63	29	cardinality	cardinality	NOUN
ejpam-4578	63	30	of	of	ADP
ejpam-4578	63	31	a	a	DET
ejpam-4578	63	32	maximum	maximum	ADJ
ejpam-4578	63	33	superclique	superclique	NOUN
ejpam-4578	63	34	in	in	ADP
ejpam-4578	63	35	g.	g.	PROPN
ejpam-4578	63	36	a	a	DET
ejpam-4578	63	37	superclique	superclique	ADJ
ejpam-4578	63	38	c	c	NOUN
ejpam-4578	63	39	in	in	ADP
ejpam-4578	63	40	g	g	PROPN
ejpam-4578	63	41	is	be	AUX
ejpam-4578	63	42	called	call	VERB
ejpam-4578	63	43	a	a	DET
ejpam-4578	63	44	hop	hop	NOUN
ejpam-4578	63	45	dominated	dominate	VERB
ejpam-4578	63	46	superclique	superclique	NOUN
ejpam-4578	63	47	if	if	SCONJ
ejpam-4578	63	48	for	for	ADP
ejpam-4578	63	49	every	every	DET
ejpam-4578	63	50	v	v	NOUN
ejpam-4578	63	51	∈	∈	NOUN
ejpam-4578	63	52	c	c	NOUN
ejpam-4578	63	53	there	there	PRON
ejpam-4578	63	54	exists	exist	VERB
ejpam-4578	63	55	u	u	PROPN
ejpam-4578	63	56	∈	∈	PROPN
ejpam-4578	63	57	v	v	NOUN
ejpam-4578	63	58	(	(	PUNCT
ejpam-4578	63	59	g)\c	g)\c	VERB
ejpam-4578	63	60	such	such	DET
ejpam-4578	63	61	that	that	DET
ejpam-4578	63	62	dg(u	dg(u	ADJ
ejpam-4578	63	63	,	,	PUNCT
ejpam-4578	63	64	v	v	NOUN
ejpam-4578	63	65	)	)	PUNCT
ejpam-4578	63	66	=	=	SYM
ejpam-4578	63	67	2	2	X
ejpam-4578	63	68	.	.	X
ejpam-4578	63	69	a	a	DET
ejpam-4578	63	70	hop	hop	NOUN
ejpam-4578	63	71	dominated	dominate	VERB
ejpam-4578	63	72	superclique	superclique	NOUN
ejpam-4578	63	73	c	c	PROPN
ejpam-4578	63	74	is	be	AUX
ejpam-4578	63	75	maximum	maximum	ADJ
ejpam-4578	63	76	in	in	ADP
ejpam-4578	63	77	g	g	PROPN
ejpam-4578	63	78	if	if	SCONJ
ejpam-4578	63	79	|c|	|c|	PROPN
ejpam-4578	63	80	≥	≥	NOUN
ejpam-4578	63	81	|c∗|	|c∗|	VERB
ejpam-4578	63	82	for	for	ADP
ejpam-4578	63	83	all	all	DET
ejpam-4578	63	84	hop	hop	NOUN
ejpam-4578	63	85	dominated	dominate	VERB
ejpam-4578	63	86	supercliques	superclique	NOUN
ejpam-4578	63	87	c∗	c∗	PROPN
ejpam-4578	63	88	in	in	ADP
ejpam-4578	63	89	g.	g.	PROPN
ejpam-4578	63	90	the	the	DET
ejpam-4578	63	91	hop	hop	NOUN
ejpam-4578	63	92	dominated	dominate	VERB
ejpam-4578	63	93	superclique	superclique	ADJ
ejpam-4578	63	94	number	number	NOUN
ejpam-4578	63	95	,	,	PUNCT
ejpam-4578	63	96	ωhs(g	ωhs(g	PROPN
ejpam-4578	63	97	)	)	PUNCT
ejpam-4578	63	98	,	,	PUNCT
ejpam-4578	63	99	of	of	ADP
ejpam-4578	63	100	g	g	PROPN
ejpam-4578	63	101	is	be	AUX
ejpam-4578	63	102	the	the	DET
ejpam-4578	63	103	cardinality	cardinality	NOUN
ejpam-4578	63	104	of	of	ADP
ejpam-4578	63	105	a	a	DET
ejpam-4578	63	106	maximum	maximum	ADJ
ejpam-4578	63	107	hop	hop	NOUN
ejpam-4578	63	108	dominated	dominate	VERB
ejpam-4578	63	109	superclique	superclique	NOUN
ejpam-4578	63	110	in	in	ADP
ejpam-4578	63	111	g.	g.	PROPN
ejpam-4578	63	112	2	2	NUM
ejpam-4578	63	113	.	.	PUNCT
ejpam-4578	63	114	preliminary	preliminary	ADJ
ejpam-4578	63	115	results	result	NOUN
ejpam-4578	63	116	remark	remark	VERB
ejpam-4578	63	117	1	1	NUM
ejpam-4578	63	118	.	.	PUNCT
ejpam-4578	64	1	every	every	DET
ejpam-4578	64	2	strong	strong	ADJ
ejpam-4578	64	3	resolving	resolve	VERB
ejpam-4578	64	4	hop	hop	NOUN
ejpam-4578	64	5	dominating	dominating	NOUN
ejpam-4578	64	6	set	set	NOUN
ejpam-4578	64	7	of	of	ADP
ejpam-4578	64	8	g	g	PROPN
ejpam-4578	64	9	is	be	AUX
ejpam-4578	64	10	a	a	DET
ejpam-4578	64	11	resolving	resolve	VERB
ejpam-4578	64	12	hop	hop	NOUN
ejpam-4578	64	13	dominating	dominating	NOUN
ejpam-4578	64	14	set	set	NOUN
ejpam-4578	64	15	.	.	PUNCT
ejpam-4578	65	1	thus	thus	ADV
ejpam-4578	65	2	,	,	PUNCT
ejpam-4578	65	3	2	2	NUM
ejpam-4578	65	4	≤	≤	NUM
ejpam-4578	65	5	γrh(g	γrh(g	NOUN
ejpam-4578	65	6	)	)	PUNCT
ejpam-4578	65	7	≤	≤	NUM
ejpam-4578	65	8	γsrh(g	γsrh(g	NOUN
ejpam-4578	65	9	)	)	PUNCT
ejpam-4578	65	10	.	.	PUNCT
ejpam-4578	66	1	remark	remark	NOUN
ejpam-4578	66	2	2	2	NUM
ejpam-4578	66	3	.	.	PUNCT
ejpam-4578	67	1	every	every	DET
ejpam-4578	67	2	strong	strong	ADJ
ejpam-4578	67	3	resolving	resolve	VERB
ejpam-4578	67	4	hop	hop	NOUN
ejpam-4578	67	5	dominating	dominating	NOUN
ejpam-4578	67	6	set	set	NOUN
ejpam-4578	67	7	of	of	ADP
ejpam-4578	67	8	g	g	PROPN
ejpam-4578	67	9	is	be	AUX
ejpam-4578	67	10	a	a	DET
ejpam-4578	67	11	hop	hop	NOUN
ejpam-4578	67	12	dominating	dominating	NOUN
ejpam-4578	67	13	set	set	NOUN
ejpam-4578	67	14	.	.	PUNCT
ejpam-4578	68	1	thus	thus	ADV
ejpam-4578	68	2	,	,	PUNCT
ejpam-4578	68	3	2	2	NUM
ejpam-4578	68	4	≤	≤	NOUN
ejpam-4578	68	5	γh(g	γh(g	NOUN
ejpam-4578	68	6	)	)	PUNCT
ejpam-4578	68	7	≤	≤	NUM
ejpam-4578	68	8	γsrh(g	γsrh(g	NOUN
ejpam-4578	68	9	)	)	PUNCT
ejpam-4578	68	10	.	.	PUNCT
ejpam-4578	69	1	remark	remark	PROPN
ejpam-4578	69	2	3	3	NUM
ejpam-4578	69	3	.	.	PUNCT
ejpam-4578	70	1	every	every	DET
ejpam-4578	70	2	strong	strong	ADJ
ejpam-4578	70	3	resolving	resolve	VERB
ejpam-4578	70	4	hop	hop	NOUN
ejpam-4578	70	5	dominating	dominating	NOUN
ejpam-4578	70	6	set	set	NOUN
ejpam-4578	70	7	of	of	ADP
ejpam-4578	70	8	g	g	PROPN
ejpam-4578	70	9	is	be	AUX
ejpam-4578	70	10	a	a	DET
ejpam-4578	70	11	resolving	resolving	NOUN
ejpam-4578	70	12	set	set	NOUN
ejpam-4578	70	13	.	.	PUNCT
ejpam-4578	71	1	thus	thus	ADV
ejpam-4578	71	2	,	,	PUNCT
ejpam-4578	71	3	1	1	NUM
ejpam-4578	71	4	≤	≤	NUM
ejpam-4578	71	5	dim(g	dim(g	PROPN
ejpam-4578	71	6	)	)	PUNCT
ejpam-4578	71	7	≤	≤	NUM
ejpam-4578	71	8	γsrh(g	γsrh(g	NOUN
ejpam-4578	71	9	)	)	PUNCT
ejpam-4578	71	10	.	.	PUNCT
ejpam-4578	72	1	remark	remark	PROPN
ejpam-4578	72	2	4	4	NUM
ejpam-4578	72	3	.	.	PUNCT
ejpam-4578	73	1	every	every	DET
ejpam-4578	73	2	strong	strong	ADJ
ejpam-4578	73	3	resolving	resolve	VERB
ejpam-4578	73	4	hop	hop	NOUN
ejpam-4578	73	5	dominating	dominating	NOUN
ejpam-4578	73	6	set	set	NOUN
ejpam-4578	73	7	of	of	ADP
ejpam-4578	73	8	a	a	DET
ejpam-4578	73	9	connected	connected	ADJ
ejpam-4578	73	10	graph	graph	NOUN
ejpam-4578	73	11	g	g	PROPN
ejpam-4578	73	12	is	be	AUX
ejpam-4578	73	13	hop	hop	NOUN
ejpam-4578	73	14	dominating	dominating	NOUN
ejpam-4578	73	15	and	and	CCONJ
ejpam-4578	73	16	every	every	DET
ejpam-4578	73	17	strong	strong	ADJ
ejpam-4578	73	18	resolving	resolve	VERB
ejpam-4578	73	19	hop	hop	NOUN
ejpam-4578	73	20	dominating	dominating	NOUN
ejpam-4578	73	21	set	set	NOUN
ejpam-4578	73	22	of	of	ADP
ejpam-4578	73	23	g	g	PROPN
ejpam-4578	73	24	is	be	AUX
ejpam-4578	73	25	strong	strong	ADJ
ejpam-4578	73	26	resolving	resolving	NOUN
ejpam-4578	73	27	.	.	PUNCT
ejpam-4578	74	1	thus	thus	ADV
ejpam-4578	74	2	,	,	PUNCT
ejpam-4578	74	3	γh(g	γh(g	NOUN
ejpam-4578	74	4	)	)	PUNCT
ejpam-4578	74	5	≤	≤	NUM
ejpam-4578	74	6	γsrh(g	γsrh(g	NOUN
ejpam-4578	74	7	)	)	PUNCT
ejpam-4578	74	8	and	and	CCONJ
ejpam-4578	74	9	sdim(g	sdim(g	PROPN
ejpam-4578	74	10	)	)	PUNCT
ejpam-4578	74	11	≤	≤	NUM
ejpam-4578	74	12	γsrh(g	γsrh(g	NOUN
ejpam-4578	74	13	)	)	PUNCT
ejpam-4578	74	14	.	.	PUNCT
ejpam-4578	75	1	j.	j.	PROPN
ejpam-4578	75	2	mohamad	mohamad	PROPN
ejpam-4578	75	3	,	,	PUNCT
ejpam-4578	75	4	h.	h.	PROPN
ejpam-4578	75	5	rara	rara	PROPN
ejpam-4578	75	6	/	/	SYM
ejpam-4578	75	7	eur	eur	PROPN
ejpam-4578	75	8	.	.	PUNCT
ejpam-4578	76	1	j.	j.	PROPN
ejpam-4578	76	2	pure	pure	PROPN
ejpam-4578	76	3	appl	appl	PROPN
ejpam-4578	76	4	.	.	PROPN
ejpam-4578	76	5	math	math	PROPN
ejpam-4578	76	6	,	,	PUNCT
ejpam-4578	76	7	16	16	NUM
ejpam-4578	76	8	(	(	PUNCT
ejpam-4578	76	9	1	1	NUM
ejpam-4578	76	10	)	)	PUNCT
ejpam-4578	76	11	(	(	PUNCT
ejpam-4578	76	12	2023	2023	NUM
ejpam-4578	76	13	)	)	PUNCT
ejpam-4578	76	14	,	,	PUNCT
ejpam-4578	76	15	131	131	NUM
ejpam-4578	76	16	-	-	SYM
ejpam-4578	76	17	143	143	NUM
ejpam-4578	76	18	134	134	NUM
ejpam-4578	76	19	remark	remark	NOUN
ejpam-4578	76	20	5	5	NUM
ejpam-4578	76	21	.	.	PUNCT
ejpam-4578	77	1	for	for	ADP
ejpam-4578	77	2	any	any	DET
ejpam-4578	77	3	connected	connected	ADJ
ejpam-4578	77	4	graph	graph	NOUN
ejpam-4578	77	5	of	of	ADP
ejpam-4578	77	6	order	order	NOUN
ejpam-4578	77	7	n	n	CCONJ
ejpam-4578	77	8	,	,	PUNCT
ejpam-4578	77	9	2	2	NUM
ejpam-4578	77	10	≤	≤	NUM
ejpam-4578	77	11	γsrh(g	γsrh(g	NOUN
ejpam-4578	77	12	)	)	PUNCT
ejpam-4578	77	13	≤	≤	PROPN
ejpam-4578	77	14	n.	n.	NOUN
ejpam-4578	77	15	moreover	moreover	ADV
ejpam-4578	77	16	,	,	PUNCT
ejpam-4578	77	17	γsrh(g	γsrh(g	PROPN
ejpam-4578	77	18	)	)	PUNCT
ejpam-4578	77	19	=	=	SYM
ejpam-4578	77	20	1	1	NUM
ejpam-4578	77	21	if	if	SCONJ
ejpam-4578	77	22	and	and	CCONJ
ejpam-4578	77	23	only	only	ADV
ejpam-4578	77	24	if	if	SCONJ
ejpam-4578	77	25	g	g	PROPN
ejpam-4578	77	26	is	be	AUX
ejpam-4578	77	27	a	a	DET
ejpam-4578	77	28	trivial	trivial	ADJ
ejpam-4578	77	29	graph	graph	NOUN
ejpam-4578	77	30	and	and	CCONJ
ejpam-4578	77	31	γsrh(g	γsrh(g	NOUN
ejpam-4578	77	32	)	)	PUNCT
ejpam-4578	77	33	=	=	SYM
ejpam-4578	78	1	n	n	NOUN
ejpam-4578	79	1	if	if	SCONJ
ejpam-4578	79	2	g	g	PROPN
ejpam-4578	79	3	=	=	PROPN
ejpam-4578	79	4	kn	kn	PROPN
ejpam-4578	79	5	.	.	PUNCT
ejpam-4578	79	6	proposition	proposition	NOUN
ejpam-4578	79	7	1	1	NUM
ejpam-4578	79	8	.	.	PUNCT
ejpam-4578	80	1	let	let	VERB
ejpam-4578	80	2	s	s	PRON
ejpam-4578	80	3	be	be	AUX
ejpam-4578	80	4	a	a	DET
ejpam-4578	80	5	hop	hop	NOUN
ejpam-4578	80	6	dominating	dominating	NOUN
ejpam-4578	80	7	set	set	NOUN
ejpam-4578	80	8	of	of	ADP
ejpam-4578	80	9	pn	pn	PROPN
ejpam-4578	80	10	for	for	ADP
ejpam-4578	80	11	n	n	X
ejpam-4578	80	12	≥	≥	NUM
ejpam-4578	80	13	3	3	NUM
ejpam-4578	80	14	.	.	PUNCT
ejpam-4578	81	1	then	then	ADV
ejpam-4578	81	2	s	s	VERB
ejpam-4578	81	3	is	be	AUX
ejpam-4578	81	4	a	a	DET
ejpam-4578	81	5	strong	strong	ADJ
ejpam-4578	81	6	resolving	resolve	VERB
ejpam-4578	81	7	hop	hop	NOUN
ejpam-4578	81	8	dominating	dominating	NOUN
ejpam-4578	81	9	set	set	NOUN
ejpam-4578	81	10	of	of	ADP
ejpam-4578	81	11	pn	pn	PROPN
ejpam-4578	81	12	if	if	SCONJ
ejpam-4578	82	1	and	and	CCONJ
ejpam-4578	82	2	only	only	ADV
ejpam-4578	82	3	if	if	SCONJ
ejpam-4578	82	4	there	there	PRON
ejpam-4578	82	5	exists	exist	VERB
ejpam-4578	82	6	u	u	PROPN
ejpam-4578	82	7	∈	∈	PROPN
ejpam-4578	82	8	s	s	PART
ejpam-4578	82	9	with	with	ADP
ejpam-4578	82	10	degpn(u	degpn(u	NOUN
ejpam-4578	82	11	)	)	PUNCT
ejpam-4578	83	1	=	=	SYM
ejpam-4578	83	2	1	1	X
ejpam-4578	83	3	.	.	X
ejpam-4578	84	1	proof	proof	NOUN
ejpam-4578	84	2	:	:	PUNCT
ejpam-4578	84	3	suppose	suppose	VERB
ejpam-4578	84	4	s	s	NOUN
ejpam-4578	84	5	is	be	AUX
ejpam-4578	84	6	a	a	DET
ejpam-4578	84	7	strong	strong	ADJ
ejpam-4578	84	8	resolving	resolve	VERB
ejpam-4578	84	9	hop	hop	NOUN
ejpam-4578	84	10	dominating	dominating	NOUN
ejpam-4578	84	11	set	set	NOUN
ejpam-4578	84	12	of	of	ADP
ejpam-4578	84	13	pn	pn	PROPN
ejpam-4578	84	14	.	.	PUNCT
ejpam-4578	85	1	let	let	VERB
ejpam-4578	85	2	u	u	PRON
ejpam-4578	85	3	and	and	CCONJ
ejpam-4578	85	4	v	v	NOUN
ejpam-4578	85	5	be	be	AUX
ejpam-4578	85	6	distinct	distinct	ADJ
ejpam-4578	85	7	vertices	vertex	NOUN
ejpam-4578	85	8	of	of	ADP
ejpam-4578	85	9	pn	pn	NOUN
ejpam-4578	86	1	such	such	ADJ
ejpam-4578	86	2	that	that	DET
ejpam-4578	86	3	deg(u	deg(u	PROPN
ejpam-4578	86	4	)	)	PUNCT
ejpam-4578	86	5	=	=	SYM
ejpam-4578	86	6	deg(v	deg(v	X
ejpam-4578	86	7	)	)	PUNCT
ejpam-4578	86	8	=	=	SYM
ejpam-4578	87	1	1	1	X
ejpam-4578	87	2	.	.	PUNCT
ejpam-4578	88	1	then	then	ADV
ejpam-4578	88	2	the	the	DET
ejpam-4578	88	3	pair	pair	NOUN
ejpam-4578	88	4	of	of	ADP
ejpam-4578	88	5	vertices	vertex	NOUN
ejpam-4578	88	6	u	u	NOUN
ejpam-4578	88	7	and	and	CCONJ
ejpam-4578	88	8	v	v	NOUN
ejpam-4578	88	9	is	be	AUX
ejpam-4578	88	10	only	only	ADV
ejpam-4578	88	11	strongly	strongly	ADV
ejpam-4578	88	12	resolved	resolve	VERB
ejpam-4578	88	13	by	by	ADP
ejpam-4578	88	14	u	u	NOUN
ejpam-4578	88	15	or	or	CCONJ
ejpam-4578	88	16	by	by	ADP
ejpam-4578	88	17	v	v	NOUN
ejpam-4578	88	18	,	,	PUNCT
ejpam-4578	88	19	since	since	SCONJ
ejpam-4578	88	20	u	u	PROPN
ejpam-4578	88	21	∈	∈	PROPN
ejpam-4578	88	22	i[u	i[u	NOUN
ejpam-4578	88	23	,	,	PUNCT
ejpam-4578	88	24	v	v	NOUN
ejpam-4578	88	25	]	]	PUNCT
ejpam-4578	88	26	or	or	CCONJ
ejpam-4578	88	27	v	v	ADP
ejpam-4578	88	28	∈	∈	PROPN
ejpam-4578	88	29	i[u	i[u	NOUN
ejpam-4578	88	30	,	,	PUNCT
ejpam-4578	88	31	v	v	NOUN
ejpam-4578	88	32	]	]	PUNCT
ejpam-4578	88	33	and	and	CCONJ
ejpam-4578	88	34	u	u	PROPN
ejpam-4578	88	35	∈	∈	PROPN
ejpam-4578	88	36	i[v	i[v	PROPN
ejpam-4578	88	37	,	,	PUNCT
ejpam-4578	88	38	u	u	NOUN
ejpam-4578	88	39	]	]	X
ejpam-4578	88	40	or	or	CCONJ
ejpam-4578	88	41	v	v	ADP
ejpam-4578	88	42	∈	∈	PROPN
ejpam-4578	88	43	i[v	i[v	NOUN
ejpam-4578	88	44	,	,	PUNCT
ejpam-4578	88	45	u	u	NOUN
ejpam-4578	88	46	]	]	X
ejpam-4578	88	47	.	.	PUNCT
ejpam-4578	89	1	implying	imply	VERB
ejpam-4578	89	2	that	that	SCONJ
ejpam-4578	89	3	u	u	NOUN
ejpam-4578	89	4	,	,	PUNCT
ejpam-4578	89	5	v	v	PROPN
ejpam-4578	89	6	∈	∈	PROPN
ejpam-4578	89	7	s.	s.	PROPN
ejpam-4578	89	8	for	for	ADP
ejpam-4578	89	9	the	the	DET
ejpam-4578	89	10	converse	converse	NOUN
ejpam-4578	89	11	,	,	PUNCT
ejpam-4578	89	12	let	let	VERB
ejpam-4578	89	13	u	u	PRON
ejpam-4578	89	14	∈	∈	PROPN
ejpam-4578	89	15	s	s	PART
ejpam-4578	89	16	with	with	ADP
ejpam-4578	89	17	degpn(u	degpn(u	NOUN
ejpam-4578	89	18	)	)	PUNCT
ejpam-4578	89	19	=	=	SYM
ejpam-4578	90	1	1	1	X
ejpam-4578	90	2	.	.	PUNCT
ejpam-4578	90	3	then	then	ADV
ejpam-4578	90	4	every	every	DET
ejpam-4578	90	5	pair	pair	NOUN
ejpam-4578	90	6	of	of	ADP
ejpam-4578	90	7	distinct	distinct	ADJ
ejpam-4578	90	8	vertices	vertex	NOUN
ejpam-4578	90	9	x	x	X
ejpam-4578	90	10	,	,	PUNCT
ejpam-4578	90	11	y	y	PROPN
ejpam-4578	90	12	∈	∈	PROPN
ejpam-4578	90	13	v	v	NOUN
ejpam-4578	90	14	(	(	PUNCT
ejpam-4578	90	15	pn	pn	NOUN
ejpam-4578	90	16	)	)	PUNCT
ejpam-4578	90	17	are	be	AUX
ejpam-4578	90	18	strongly	strongly	ADV
ejpam-4578	90	19	resolved	resolve	VERB
ejpam-4578	90	20	by	by	ADP
ejpam-4578	90	21	u	u	NOUN
ejpam-4578	90	22	,	,	PUNCT
ejpam-4578	90	23	since	since	SCONJ
ejpam-4578	90	24	x	x	PROPN
ejpam-4578	90	25	∈	∈	PROPN
ejpam-4578	90	26	i[u	i[u	NOUN
ejpam-4578	90	27	,	,	PUNCT
ejpam-4578	90	28	y	y	NOUN
ejpam-4578	90	29	]	]	PUNCT
ejpam-4578	90	30	or	or	CCONJ
ejpam-4578	90	31	y	y	PROPN
ejpam-4578	90	32	∈	∈	PROPN
ejpam-4578	90	33	i[u	i[u	NOUN
ejpam-4578	90	34	,	,	PUNCT
ejpam-4578	90	35	x	x	X
ejpam-4578	90	36	]	]	X
ejpam-4578	90	37	.	.	PUNCT
ejpam-4578	91	1	hence	hence	ADV
ejpam-4578	91	2	,	,	PUNCT
ejpam-4578	91	3	s	s	VERB
ejpam-4578	91	4	is	be	AUX
ejpam-4578	91	5	a	a	DET
ejpam-4578	91	6	strong	strong	ADJ
ejpam-4578	91	7	resolving	resolving	NOUN
ejpam-4578	91	8	set	set	NOUN
ejpam-4578	91	9	of	of	ADP
ejpam-4578	91	10	pn	pn	PROPN
ejpam-4578	91	11	.	.	PUNCT
ejpam-4578	92	1	since	since	SCONJ
ejpam-4578	92	2	s	s	PROPN
ejpam-4578	92	3	is	be	AUX
ejpam-4578	92	4	hop	hop	NOUN
ejpam-4578	92	5	dominating	dominate	VERB
ejpam-4578	92	6	by	by	ADP
ejpam-4578	92	7	assumption	assumption	NOUN
ejpam-4578	92	8	,	,	PUNCT
ejpam-4578	92	9	s	s	PART
ejpam-4578	92	10	is	be	AUX
ejpam-4578	92	11	a	a	DET
ejpam-4578	92	12	strong	strong	ADJ
ejpam-4578	92	13	resolving	resolve	VERB
ejpam-4578	92	14	hop	hop	NOUN
ejpam-4578	92	15	dominating	dominating	NOUN
ejpam-4578	92	16	set	set	NOUN
ejpam-4578	92	17	of	of	ADP
ejpam-4578	92	18	pn	pn	PROPN
ejpam-4578	92	19	.	.	PROPN
ejpam-4578	92	20	proposition	proposition	PROPN
ejpam-4578	92	21	2	2	NUM
ejpam-4578	92	22	.	.	PUNCT
ejpam-4578	93	1	let	let	VERB
ejpam-4578	93	2	s	s	PRON
ejpam-4578	93	3	be	be	AUX
ejpam-4578	93	4	a	a	DET
ejpam-4578	93	5	hop	hop	NOUN
ejpam-4578	93	6	dominating	dominating	NOUN
ejpam-4578	93	7	set	set	NOUN
ejpam-4578	93	8	of	of	ADP
ejpam-4578	93	9	cn	cn	PROPN
ejpam-4578	93	10	for	for	ADP
ejpam-4578	93	11	n	n	X
ejpam-4578	93	12	≥	≥	NOUN
ejpam-4578	93	13	4	4	NUM
ejpam-4578	93	14	.	.	PUNCT
ejpam-4578	94	1	if	if	SCONJ
ejpam-4578	94	2	dcn(u	dcn(u	PROPN
ejpam-4578	94	3	,	,	PUNCT
ejpam-4578	94	4	v	v	NOUN
ejpam-4578	94	5	)	)	PUNCT
ejpam-4578	94	6	<	<	X
ejpam-4578	94	7	⌊n/2⌋	⌊n/2⌋	X
ejpam-4578	94	8	for	for	ADP
ejpam-4578	94	9	each	each	DET
ejpam-4578	94	10	pair	pair	NOUN
ejpam-4578	94	11	u	u	NOUN
ejpam-4578	94	12	,	,	PUNCT
ejpam-4578	94	13	v	v	NOUN
ejpam-4578	94	14	∈	∈	PROPN
ejpam-4578	94	15	v	v	NOUN
ejpam-4578	94	16	(	(	PUNCT
ejpam-4578	94	17	cn	cn	PROPN
ejpam-4578	94	18	)	)	PUNCT
ejpam-4578	94	19	\	\	PROPN
ejpam-4578	95	1	s	s	X
ejpam-4578	95	2	,	,	PUNCT
ejpam-4578	95	3	then	then	ADV
ejpam-4578	95	4	s	s	VERB
ejpam-4578	95	5	is	be	AUX
ejpam-4578	95	6	a	a	DET
ejpam-4578	95	7	strong	strong	ADJ
ejpam-4578	95	8	resolving	resolve	VERB
ejpam-4578	95	9	hop	hop	NOUN
ejpam-4578	95	10	dominating	dominating	NOUN
ejpam-4578	95	11	set	set	NOUN
ejpam-4578	95	12	of	of	ADP
ejpam-4578	95	13	cn	cn	PROPN
ejpam-4578	95	14	.	.	PUNCT
ejpam-4578	95	15	proof	proof	NOUN
ejpam-4578	95	16	:	:	PUNCT
ejpam-4578	95	17	let	let	VERB
ejpam-4578	95	18	s	s	PRON
ejpam-4578	95	19	be	be	AUX
ejpam-4578	95	20	a	a	DET
ejpam-4578	95	21	hop	hop	NOUN
ejpam-4578	95	22	dominating	dominating	NOUN
ejpam-4578	95	23	set	set	NOUN
ejpam-4578	95	24	of	of	ADP
ejpam-4578	95	25	cn	cn	PROPN
ejpam-4578	95	26	and	and	CCONJ
ejpam-4578	95	27	let	let	VERB
ejpam-4578	95	28	u	u	NOUN
ejpam-4578	95	29	,	,	PUNCT
ejpam-4578	95	30	v	v	PROPN
ejpam-4578	95	31	∈	∈	PROPN
ejpam-4578	95	32	v	v	NOUN
ejpam-4578	95	33	(	(	PUNCT
ejpam-4578	95	34	cn	cn	PROPN
ejpam-4578	95	35	)	)	PUNCT
ejpam-4578	95	36	\	\	PROPN
ejpam-4578	95	37	s	s	VERB
ejpam-4578	95	38	such	such	ADJ
ejpam-4578	95	39	that	that	SCONJ
ejpam-4578	95	40	d(u	d(u	PROPN
ejpam-4578	95	41	,	,	PUNCT
ejpam-4578	95	42	v	v	NOUN
ejpam-4578	95	43	)	)	PUNCT
ejpam-4578	95	44	<	<	X
ejpam-4578	95	45	⌊n/2⌋.	⌊n/2⌋.	X
ejpam-4578	95	46	note	note	VERB
ejpam-4578	95	47	that	that	SCONJ
ejpam-4578	95	48	diam(cn	diam(cn	NOUN
ejpam-4578	95	49	)	)	PUNCT
ejpam-4578	95	50	=	=	PUNCT
ejpam-4578	95	51	⌊n/2⌋.	⌊n/2⌋.	NOUN
ejpam-4578	95	52	then	then	ADV
ejpam-4578	95	53	there	there	PRON
ejpam-4578	95	54	exists	exist	VERB
ejpam-4578	95	55	,	,	PUNCT
ejpam-4578	95	56	s	s	PART
ejpam-4578	95	57	∈	∈	NOUN
ejpam-4578	95	58	s	s	VERB
ejpam-4578	95	59	such	such	ADJ
ejpam-4578	95	60	that	that	SCONJ
ejpam-4578	95	61	dcn(s	dcn(s	PROPN
ejpam-4578	95	62	,	,	PUNCT
ejpam-4578	95	63	u	u	NOUN
ejpam-4578	95	64	)	)	PUNCT
ejpam-4578	95	65	≤	≤	NOUN
ejpam-4578	95	66	dcn(s	dcn(s	PROPN
ejpam-4578	95	67	,	,	PUNCT
ejpam-4578	95	68	v	v	NOUN
ejpam-4578	95	69	)	)	PUNCT
ejpam-4578	95	70	≤	≤	NOUN
ejpam-4578	95	71	⌊n/2⌋	⌊n/2⌋	X
ejpam-4578	95	72	or	or	CCONJ
ejpam-4578	95	73	dcn(s	dcn(s	PROPN
ejpam-4578	95	74	,	,	PUNCT
ejpam-4578	95	75	v	v	NOUN
ejpam-4578	95	76	)	)	PUNCT
ejpam-4578	95	77	≤	≤	NOUN
ejpam-4578	95	78	dcn(s	dcn(s	PROPN
ejpam-4578	95	79	,	,	PUNCT
ejpam-4578	95	80	u	u	NOUN
ejpam-4578	95	81	)	)	PUNCT
ejpam-4578	95	82	≤	≤	NOUN
ejpam-4578	95	83	⌊n/2⌋.	⌊n/2⌋.	NOUN
ejpam-4578	95	84	it	it	PRON
ejpam-4578	95	85	follows	follow	VERB
ejpam-4578	95	86	that	that	SCONJ
ejpam-4578	95	87	u	u	PROPN
ejpam-4578	95	88	∈	∈	PROPN
ejpam-4578	95	89	i[s	i[s	PROPN
ejpam-4578	95	90	,	,	PUNCT
ejpam-4578	95	91	v	v	NOUN
ejpam-4578	95	92	]	]	PUNCT
ejpam-4578	95	93	or	or	CCONJ
ejpam-4578	95	94	v	v	ADP
ejpam-4578	95	95	∈	∈	PROPN
ejpam-4578	95	96	i[s	i[s	PROPN
ejpam-4578	95	97	,	,	PUNCT
ejpam-4578	95	98	u	u	NOUN
ejpam-4578	95	99	]	]	X
ejpam-4578	95	100	.	.	PUNCT
ejpam-4578	96	1	hence	hence	ADV
ejpam-4578	96	2	,	,	PUNCT
ejpam-4578	96	3	s	s	VERB
ejpam-4578	96	4	strongly	strongly	ADV
ejpam-4578	96	5	resolves	resolve	VERB
ejpam-4578	96	6	u	u	NOUN
ejpam-4578	96	7	and	and	CCONJ
ejpam-4578	96	8	v.	v.	ADP
ejpam-4578	96	9	therefore	therefore	ADV
ejpam-4578	96	10	,	,	PUNCT
ejpam-4578	96	11	s	s	VERB
ejpam-4578	96	12	is	be	AUX
ejpam-4578	96	13	a	a	DET
ejpam-4578	96	14	strong	strong	ADJ
ejpam-4578	96	15	resolving	resolve	VERB
ejpam-4578	96	16	hop	hop	NOUN
ejpam-4578	96	17	dominating	dominating	NOUN
ejpam-4578	96	18	set	set	NOUN
ejpam-4578	96	19	of	of	ADP
ejpam-4578	96	20	cn	cn	PROPN
ejpam-4578	96	21	.	.	PROPN
ejpam-4578	96	22	remark	remark	PROPN
ejpam-4578	96	23	6	6	NUM
ejpam-4578	96	24	.	.	PUNCT
ejpam-4578	97	1	every	every	DET
ejpam-4578	97	2	strong	strong	ADJ
ejpam-4578	97	3	resolving	resolve	VERB
ejpam-4578	97	4	hop	hop	NOUN
ejpam-4578	97	5	dominating	dominating	NOUN
ejpam-4578	97	6	set	set	NOUN
ejpam-4578	97	7	of	of	ADP
ejpam-4578	97	8	a	a	DET
ejpam-4578	97	9	connected	connected	ADJ
ejpam-4578	97	10	graph	graph	NOUN
ejpam-4578	97	11	g	g	PROPN
ejpam-4578	97	12	is	be	AUX
ejpam-4578	97	13	a	a	DET
ejpam-4578	97	14	resolving	resolve	VERB
ejpam-4578	97	15	hop	hop	NOUN
ejpam-4578	97	16	dominating	dominating	NOUN
ejpam-4578	97	17	set	set	NOUN
ejpam-4578	97	18	.	.	PUNCT
ejpam-4578	98	1	thus	thus	ADV
ejpam-4578	98	2	,	,	PUNCT
ejpam-4578	98	3	γrh(g	γrh(g	NOUN
ejpam-4578	98	4	)	)	PUNCT
ejpam-4578	98	5	≤	≤	NUM
ejpam-4578	98	6	γsrh(g	γsrh(g	NOUN
ejpam-4578	98	7	)	)	PUNCT
ejpam-4578	98	8	.	.	PUNCT
ejpam-4578	99	1	remark	remark	PROPN
ejpam-4578	99	2	7	7	NUM
ejpam-4578	99	3	.	.	PUNCT
ejpam-4578	100	1	any	any	DET
ejpam-4578	100	2	superset	superset	NOUN
ejpam-4578	100	3	of	of	ADP
ejpam-4578	100	4	a	a	DET
ejpam-4578	100	5	strong	strong	ADJ
ejpam-4578	100	6	resolving	resolve	VERB
ejpam-4578	100	7	hop	hop	NOUN
ejpam-4578	100	8	dominating	dominating	NOUN
ejpam-4578	100	9	set	set	NOUN
ejpam-4578	100	10	is	be	AUX
ejpam-4578	100	11	a	a	DET
ejpam-4578	100	12	strong	strong	ADJ
ejpam-4578	100	13	resolving	resolve	VERB
ejpam-4578	100	14	hop	hop	NOUN
ejpam-4578	100	15	dominating	dominating	NOUN
ejpam-4578	100	16	set	set	NOUN
ejpam-4578	100	17	.	.	PUNCT
ejpam-4578	101	1	proposition	proposition	NOUN
ejpam-4578	101	2	3	3	NUM
ejpam-4578	101	3	.	.	PUNCT
ejpam-4578	102	1	[	[	X
ejpam-4578	102	2	1	1	X
ejpam-4578	102	3	]	]	PUNCT
ejpam-4578	102	4	let	let	VERB
ejpam-4578	102	5	g	g	PRON
ejpam-4578	102	6	be	be	AUX
ejpam-4578	102	7	a	a	DET
ejpam-4578	102	8	connected	connected	ADJ
ejpam-4578	102	9	graph	graph	NOUN
ejpam-4578	102	10	of	of	ADP
ejpam-4578	102	11	order	order	NOUN
ejpam-4578	102	12	n	n	NOUN
ejpam-4578	102	13	and	and	CCONJ
ejpam-4578	102	14	let	let	VERB
ejpam-4578	102	15	a	a	DET
ejpam-4578	102	16	=	=	SYM
ejpam-4578	102	17	{	{	PUNCT
ejpam-4578	102	18	x	x	PROPN
ejpam-4578	102	19	∈	∈	PROPN
ejpam-4578	102	20	v	v	NOUN
ejpam-4578	102	21	(	(	PUNCT
ejpam-4578	102	22	g	g	NOUN
ejpam-4578	102	23	)	)	PUNCT
ejpam-4578	102	24	:	:	PUNCT
ejpam-4578	102	25	degg(x	degg(x	X
ejpam-4578	102	26	)	)	PUNCT
ejpam-4578	102	27	=	=	PUNCT
ejpam-4578	102	28	n−	n−	NOUN
ejpam-4578	102	29	1	1	NUM
ejpam-4578	102	30	}	}	PUNCT
ejpam-4578	102	31	.	.	PUNCT
ejpam-4578	103	1	if	if	SCONJ
ejpam-4578	103	2	a	a	DET
ejpam-4578	103	3	̸=	̸=	PROPN
ejpam-4578	103	4	∅	∅	NOUN
ejpam-4578	103	5	and	and	CCONJ
ejpam-4578	103	6	⟨c⟩	⟨c⟩	PROPN
ejpam-4578	103	7	is	be	AUX
ejpam-4578	103	8	a	a	DET
ejpam-4578	103	9	superclique	superclique	NOUN
ejpam-4578	103	10	in	in	ADP
ejpam-4578	103	11	g	g	NOUN
ejpam-4578	103	12	,	,	PUNCT
ejpam-4578	103	13	then	then	ADV
ejpam-4578	103	14	|c	|c	VERB
ejpam-4578	103	15	∩a|	∩a|	ADP
ejpam-4578	103	16	≤	≤	NUM
ejpam-4578	103	17	1	1	NUM
ejpam-4578	103	18	.	.	PUNCT
ejpam-4578	104	1	moreover	moreover	ADV
ejpam-4578	104	2	,	,	PUNCT
ejpam-4578	104	3	if	if	SCONJ
ejpam-4578	104	4	⟨c⟩	⟨c⟩	PROPN
ejpam-4578	104	5	is	be	AUX
ejpam-4578	104	6	a	a	DET
ejpam-4578	104	7	maximum	maximum	ADJ
ejpam-4578	104	8	superclique	superclique	NOUN
ejpam-4578	104	9	of	of	ADP
ejpam-4578	104	10	g	g	NOUN
ejpam-4578	104	11	,	,	PUNCT
ejpam-4578	104	12	then	then	ADV
ejpam-4578	104	13	|c	|c	VERB
ejpam-4578	104	14	∩a|	∩a|	PUNCT
ejpam-4578	104	15	=	=	SYM
ejpam-4578	104	16	1	1	X
ejpam-4578	104	17	.	.	X
ejpam-4578	104	18	proposition	proposition	NOUN
ejpam-4578	104	19	4	4	NUM
ejpam-4578	104	20	.	.	PUNCT
ejpam-4578	105	1	[	[	X
ejpam-4578	105	2	1	1	X
ejpam-4578	105	3	]	]	PUNCT
ejpam-4578	105	4	let	let	VERB
ejpam-4578	105	5	g	g	PRON
ejpam-4578	105	6	be	be	AUX
ejpam-4578	105	7	a	a	DET
ejpam-4578	105	8	non	non	ADJ
ejpam-4578	105	9	-	-	ADJ
ejpam-4578	105	10	trivial	trivial	ADJ
ejpam-4578	105	11	connected	connected	ADJ
ejpam-4578	105	12	graph	graph	NOUN
ejpam-4578	105	13	with	with	ADP
ejpam-4578	105	14	diam(g	diam(g	NOUN
ejpam-4578	105	15	)	)	PUNCT
ejpam-4578	105	16	≤	≤	NOUN
ejpam-4578	105	17	2	2	NUM
ejpam-4578	105	18	.	.	PUNCT
ejpam-4578	106	1	then	then	ADV
ejpam-4578	106	2	s	s	VERB
ejpam-4578	106	3	=	=	SYM
ejpam-4578	106	4	v	v	PROPN
ejpam-4578	106	5	(	(	PUNCT
ejpam-4578	106	6	g	g	NOUN
ejpam-4578	106	7	)	)	PUNCT
ejpam-4578	106	8	\	\	PUNCT
ejpam-4578	107	1	c	c	NOUN
ejpam-4578	107	2	is	be	AUX
ejpam-4578	107	3	a	a	DET
ejpam-4578	107	4	strong	strong	ADJ
ejpam-4578	107	5	resolving	resolving	NOUN
ejpam-4578	107	6	set	set	NOUN
ejpam-4578	107	7	of	of	ADP
ejpam-4578	107	8	g	g	PROPN
ejpam-4578	107	9	if	if	SCONJ
ejpam-4578	108	1	and	and	CCONJ
ejpam-4578	108	2	only	only	ADV
ejpam-4578	108	3	if	if	SCONJ
ejpam-4578	108	4	c	c	NOUN
ejpam-4578	108	5	=	=	SYM
ejpam-4578	108	6	∅	∅	NOUN
ejpam-4578	108	7	or	or	CCONJ
ejpam-4578	108	8	⟨c⟩	⟨c⟩	PROPN
ejpam-4578	108	9	is	be	AUX
ejpam-4578	108	10	a	a	DET
ejpam-4578	108	11	superclique	superclique	NOUN
ejpam-4578	108	12	in	in	ADP
ejpam-4578	108	13	g.	g.	PROPN
ejpam-4578	108	14	in	in	ADP
ejpam-4578	108	15	particular	particular	ADJ
ejpam-4578	108	16	,	,	PUNCT
ejpam-4578	108	17	sdim(g	sdim(g	PROPN
ejpam-4578	108	18	)	)	PUNCT
ejpam-4578	108	19	=	=	SYM
ejpam-4578	108	20	|v	|v	PROPN
ejpam-4578	108	21	(	(	PUNCT
ejpam-4578	108	22	g)|	g)|	NOUN
ejpam-4578	108	23	−	−	NOUN
ejpam-4578	108	24	ωs(g	ωs(g	PUNCT
ejpam-4578	108	25	)	)	PUNCT
ejpam-4578	108	26	.	.	PUNCT
ejpam-4578	109	1	proposition	proposition	NOUN
ejpam-4578	109	2	5	5	NUM
ejpam-4578	109	3	.	.	PUNCT
ejpam-4578	110	1	let	let	VERB
ejpam-4578	110	2	g	g	PRON
ejpam-4578	110	3	be	be	AUX
ejpam-4578	110	4	a	a	DET
ejpam-4578	110	5	connected	connected	ADJ
ejpam-4578	110	6	graph	graph	NOUN
ejpam-4578	110	7	of	of	ADP
ejpam-4578	110	8	order	order	NOUN
ejpam-4578	110	9	n	n	CCONJ
ejpam-4578	110	10	,	,	PUNCT
ejpam-4578	110	11	and	and	CCONJ
ejpam-4578	110	12	let	let	VERB
ejpam-4578	110	13	a	a	DET
ejpam-4578	110	14	=	=	SYM
ejpam-4578	110	15	{	{	PUNCT
ejpam-4578	110	16	x	x	PROPN
ejpam-4578	110	17	∈	∈	PROPN
ejpam-4578	110	18	v	v	NOUN
ejpam-4578	110	19	(	(	PUNCT
ejpam-4578	110	20	g	g	NOUN
ejpam-4578	110	21	)	)	PUNCT
ejpam-4578	110	22	:	:	PUNCT
ejpam-4578	111	1	degg(x	degg(x	X
ejpam-4578	111	2	)	)	PUNCT
ejpam-4578	111	3	=	=	SYM
ejpam-4578	111	4	n	n	CCONJ
ejpam-4578	111	5	−	−	NOUN
ejpam-4578	111	6	1	1	NUM
ejpam-4578	111	7	}	}	PUNCT
ejpam-4578	111	8	.	.	PUNCT
ejpam-4578	112	1	if	if	SCONJ
ejpam-4578	112	2	a	a	DET
ejpam-4578	112	3	̸=	̸=	PROPN
ejpam-4578	112	4	∅	∅	NOUN
ejpam-4578	112	5	and	and	CCONJ
ejpam-4578	112	6	c	c	NOUN
ejpam-4578	112	7	is	be	AUX
ejpam-4578	112	8	a	a	DET
ejpam-4578	112	9	hop	hop	NOUN
ejpam-4578	112	10	dominated	dominate	VERB
ejpam-4578	112	11	superclique	superclique	NOUN
ejpam-4578	112	12	in	in	ADP
ejpam-4578	112	13	g	g	PROPN
ejpam-4578	112	14	,	,	PUNCT
ejpam-4578	112	15	then	then	ADV
ejpam-4578	112	16	c	c	NOUN
ejpam-4578	112	17	∩a	∩a	PROPN
ejpam-4578	112	18	=	=	PUNCT
ejpam-4578	112	19	∅.	∅.	PRON
ejpam-4578	112	20	proof	proof	NOUN
ejpam-4578	112	21	:	:	PUNCT
ejpam-4578	112	22	suppose	suppose	VERB
ejpam-4578	112	23	c	c	NOUN
ejpam-4578	112	24	is	be	AUX
ejpam-4578	112	25	a	a	DET
ejpam-4578	112	26	hop	hop	NOUN
ejpam-4578	112	27	dominated	dominate	VERB
ejpam-4578	112	28	superclique	superclique	NOUN
ejpam-4578	112	29	in	in	ADP
ejpam-4578	112	30	g.	g.	NOUN
ejpam-4578	112	31	by	by	ADP
ejpam-4578	112	32	proposition	proposition	NOUN
ejpam-4578	112	33	3	3	NUM
ejpam-4578	112	34	,	,	PUNCT
ejpam-4578	112	35	|c	|c	VERB
ejpam-4578	112	36	∩a|	∩a|	ADP
ejpam-4578	112	37	≤	≤	NOUN
ejpam-4578	112	38	1	1	NUM
ejpam-4578	112	39	.	.	PUNCT
ejpam-4578	113	1	if	if	SCONJ
ejpam-4578	113	2	|c	|c	VERB
ejpam-4578	113	3	∩a|	∩a|	ADP
ejpam-4578	113	4	=	=	SYM
ejpam-4578	113	5	1	1	NUM
ejpam-4578	113	6	and	and	CCONJ
ejpam-4578	113	7	x	x	SYM
ejpam-4578	113	8	∈	∈	PROPN
ejpam-4578	114	1	c	c	X
ejpam-4578	114	2	∩a	∩a	PROPN
ejpam-4578	114	3	,	,	PUNCT
ejpam-4578	114	4	then	then	ADV
ejpam-4578	114	5	dg(x	dg(x	NUM
ejpam-4578	114	6	,	,	PUNCT
ejpam-4578	114	7	v	v	NOUN
ejpam-4578	114	8	)	)	PUNCT
ejpam-4578	114	9	=	=	SYM
ejpam-4578	114	10	1	1	NUM
ejpam-4578	114	11	for	for	ADP
ejpam-4578	114	12	each	each	DET
ejpam-4578	114	13	v	v	NUM
ejpam-4578	114	14	∈	∈	PROPN
ejpam-4578	114	15	v	v	NOUN
ejpam-4578	114	16	(	(	PUNCT
ejpam-4578	114	17	g)\{x	g)\{x	PROPN
ejpam-4578	114	18	}	}	PUNCT
ejpam-4578	114	19	since	since	SCONJ
ejpam-4578	114	20	degg(x	degg(x	NUM
ejpam-4578	114	21	)	)	PUNCT
ejpam-4578	114	22	=	=	SYM
ejpam-4578	114	23	n	n	CCONJ
ejpam-4578	114	24	−	−	NOUN
ejpam-4578	114	25	1	1	NUM
ejpam-4578	114	26	.	.	PUNCT
ejpam-4578	115	1	this	this	PRON
ejpam-4578	115	2	is	be	AUX
ejpam-4578	115	3	a	a	DET
ejpam-4578	115	4	contradiction	contradiction	NOUN
ejpam-4578	115	5	to	to	ADP
ejpam-4578	115	6	the	the	DET
ejpam-4578	115	7	definition	definition	NOUN
ejpam-4578	115	8	of	of	ADP
ejpam-4578	115	9	hop	hop	NOUN
ejpam-4578	115	10	dominated	dominate	VERB
ejpam-4578	115	11	superclique	superclique	NOUN
ejpam-4578	115	12	.	.	PUNCT
ejpam-4578	116	1	it	it	PRON
ejpam-4578	116	2	follows	follow	VERB
ejpam-4578	116	3	that	that	SCONJ
ejpam-4578	116	4	|c	|c	VERB
ejpam-4578	116	5	∩a|	∩a|	ADP
ejpam-4578	116	6	=	=	SYM
ejpam-4578	116	7	0	0	X
ejpam-4578	116	8	.	.	PUNCT
ejpam-4578	117	1	therefore	therefore	ADV
ejpam-4578	117	2	c	c	PROPN
ejpam-4578	117	3	∩a	∩a	PROPN
ejpam-4578	118	1	=	=	PUNCT
ejpam-4578	118	2	∅.	∅.	PROPN
ejpam-4578	118	3	j.	j.	PROPN
ejpam-4578	118	4	mohamad	mohamad	PROPN
ejpam-4578	118	5	,	,	PUNCT
ejpam-4578	118	6	h.	h.	PROPN
ejpam-4578	118	7	rara	rara	PROPN
ejpam-4578	118	8	/	/	SYM
ejpam-4578	118	9	eur	eur	PROPN
ejpam-4578	118	10	.	.	PUNCT
ejpam-4578	119	1	j.	j.	PROPN
ejpam-4578	119	2	pure	pure	PROPN
ejpam-4578	119	3	appl	appl	PROPN
ejpam-4578	119	4	.	.	PROPN
ejpam-4578	119	5	math	math	PROPN
ejpam-4578	119	6	,	,	PUNCT
ejpam-4578	119	7	16	16	NUM
ejpam-4578	119	8	(	(	PUNCT
ejpam-4578	119	9	1	1	NUM
ejpam-4578	119	10	)	)	PUNCT
ejpam-4578	119	11	(	(	PUNCT
ejpam-4578	119	12	2023	2023	NUM
ejpam-4578	119	13	)	)	PUNCT
ejpam-4578	119	14	,	,	PUNCT
ejpam-4578	119	15	131	131	NUM
ejpam-4578	119	16	-	-	SYM
ejpam-4578	119	17	143	143	NUM
ejpam-4578	119	18	135	135	NUM
ejpam-4578	119	19	lemma	lemma	PROPN
ejpam-4578	119	20	1	1	NUM
ejpam-4578	119	21	.	.	PUNCT
ejpam-4578	120	1	let	let	VERB
ejpam-4578	120	2	g	g	PRON
ejpam-4578	120	3	be	be	AUX
ejpam-4578	120	4	a	a	DET
ejpam-4578	120	5	nontrivial	nontrivial	ADJ
ejpam-4578	120	6	connected	connect	VERB
ejpam-4578	120	7	graph	graph	NOUN
ejpam-4578	120	8	with	with	ADP
ejpam-4578	120	9	diam(g	diam(g	NOUN
ejpam-4578	120	10	)	)	PUNCT
ejpam-4578	120	11	≤	≤	NOUN
ejpam-4578	120	12	2	2	NUM
ejpam-4578	120	13	.	.	PUNCT
ejpam-4578	121	1	then	then	ADV
ejpam-4578	121	2	s	s	VERB
ejpam-4578	121	3	=	=	SYM
ejpam-4578	121	4	v	v	NOUN
ejpam-4578	121	5	(	(	PUNCT
ejpam-4578	121	6	g)\c	g)\c	NOUN
ejpam-4578	121	7	is	be	AUX
ejpam-4578	121	8	a	a	DET
ejpam-4578	121	9	strong	strong	ADJ
ejpam-4578	121	10	resolving	resolve	VERB
ejpam-4578	121	11	hop	hop	NOUN
ejpam-4578	121	12	dominating	dominating	NOUN
ejpam-4578	121	13	set	set	NOUN
ejpam-4578	121	14	of	of	ADP
ejpam-4578	121	15	g	g	PROPN
ejpam-4578	121	16	if	if	SCONJ
ejpam-4578	122	1	and	and	CCONJ
ejpam-4578	122	2	only	only	ADV
ejpam-4578	122	3	if	if	SCONJ
ejpam-4578	122	4	c	c	NOUN
ejpam-4578	122	5	=	=	SYM
ejpam-4578	122	6	∅	∅	NOUN
ejpam-4578	122	7	or	or	CCONJ
ejpam-4578	122	8	c	c	NOUN
ejpam-4578	122	9	is	be	AUX
ejpam-4578	122	10	a	a	DET
ejpam-4578	122	11	hop	hop	NOUN
ejpam-4578	122	12	dominated	dominate	VERB
ejpam-4578	122	13	superclique	superclique	NOUN
ejpam-4578	122	14	in	in	ADP
ejpam-4578	122	15	g.	g.	PROPN
ejpam-4578	122	16	in	in	ADP
ejpam-4578	122	17	particular	particular	ADJ
ejpam-4578	122	18	,	,	PUNCT
ejpam-4578	122	19	γsrh(g	γsrh(g	PROPN
ejpam-4578	122	20	)	)	PUNCT
ejpam-4578	122	21	=	=	SYM
ejpam-4578	122	22	|v	|v	PROPN
ejpam-4578	122	23	(	(	PUNCT
ejpam-4578	122	24	g)|	g)|	PROPN
ejpam-4578	122	25	−	−	PROPN
ejpam-4578	122	26	ωhs(g	ωhs(g	PROPN
ejpam-4578	122	27	)	)	PUNCT
ejpam-4578	122	28	.	.	PUNCT
ejpam-4578	123	1	proof	proof	NOUN
ejpam-4578	123	2	:	:	PUNCT
ejpam-4578	123	3	suppose	suppose	VERB
ejpam-4578	123	4	that	that	SCONJ
ejpam-4578	123	5	s	s	VERB
ejpam-4578	123	6	=	=	SYM
ejpam-4578	123	7	v	v	X
ejpam-4578	123	8	(	(	PUNCT
ejpam-4578	123	9	g	g	NOUN
ejpam-4578	123	10	)	)	PUNCT
ejpam-4578	123	11	\	\	PUNCT
ejpam-4578	124	1	c	c	NOUN
ejpam-4578	124	2	is	be	AUX
ejpam-4578	124	3	a	a	DET
ejpam-4578	124	4	strong	strong	ADJ
ejpam-4578	124	5	resolving	resolve	VERB
ejpam-4578	124	6	hop	hop	NOUN
ejpam-4578	124	7	dominating	dominating	NOUN
ejpam-4578	124	8	set	set	NOUN
ejpam-4578	124	9	of	of	ADP
ejpam-4578	124	10	g.	g.	PROPN
ejpam-4578	124	11	then	then	ADV
ejpam-4578	124	12	s	s	VERB
ejpam-4578	124	13	is	be	AUX
ejpam-4578	124	14	a	a	DET
ejpam-4578	124	15	strong	strong	ADJ
ejpam-4578	124	16	resolving	resolving	NOUN
ejpam-4578	124	17	set	set	NOUN
ejpam-4578	124	18	.	.	PUNCT
ejpam-4578	125	1	by	by	ADP
ejpam-4578	125	2	proposition	proposition	NOUN
ejpam-4578	125	3	4	4	NUM
ejpam-4578	125	4	,	,	PUNCT
ejpam-4578	125	5	c	c	NOUN
ejpam-4578	125	6	=	=	SYM
ejpam-4578	125	7	∅	∅	NOUN
ejpam-4578	125	8	or	or	CCONJ
ejpam-4578	125	9	c	c	NOUN
ejpam-4578	125	10	is	be	AUX
ejpam-4578	125	11	a	a	DET
ejpam-4578	125	12	superclique	superclique	NOUN
ejpam-4578	125	13	in	in	ADP
ejpam-4578	125	14	g.	g.	PROPN
ejpam-4578	125	15	let	let	VERB
ejpam-4578	125	16	x	x	X
ejpam-4578	125	17	∈	∈	PROPN
ejpam-4578	125	18	c.	c.	NOUN
ejpam-4578	126	1	then	then	ADV
ejpam-4578	126	2	x	x	SYM
ejpam-4578	126	3	∈	∈	PROPN
ejpam-4578	126	4	v	v	ADP
ejpam-4578	126	5	(	(	PUNCT
ejpam-4578	126	6	g	g	NOUN
ejpam-4578	126	7	)	)	PUNCT
ejpam-4578	126	8	\	\	PUNCT
ejpam-4578	127	1	s.	s.	PROPN
ejpam-4578	127	2	since	since	SCONJ
ejpam-4578	127	3	s	s	PROPN
ejpam-4578	127	4	is	be	AUX
ejpam-4578	127	5	hop	hop	NOUN
ejpam-4578	127	6	dominating	dominating	NOUN
ejpam-4578	127	7	,	,	PUNCT
ejpam-4578	127	8	a	a	DET
ejpam-4578	127	9	vertex	vertex	NOUN
ejpam-4578	127	10	y	y	PROPN
ejpam-4578	127	11	∈	∈	PROPN
ejpam-4578	127	12	s	s	PART
ejpam-4578	127	13	∩ng(x	∩ng(x	NOUN
ejpam-4578	127	14	,	,	PUNCT
ejpam-4578	127	15	2	2	NUM
ejpam-4578	127	16	)	)	PUNCT
ejpam-4578	127	17	exists	exist	VERB
ejpam-4578	127	18	.	.	PUNCT
ejpam-4578	128	1	hence	hence	ADV
ejpam-4578	128	2	,	,	PUNCT
ejpam-4578	128	3	y	y	PROPN
ejpam-4578	128	4	∈	∈	PROPN
ejpam-4578	128	5	v	v	ADP
ejpam-4578	128	6	(	(	PUNCT
ejpam-4578	128	7	g	g	NOUN
ejpam-4578	128	8	)	)	PUNCT
ejpam-4578	128	9	\	\	PROPN
ejpam-4578	128	10	c	c	NOUN
ejpam-4578	128	11	and	and	CCONJ
ejpam-4578	128	12	dg(x	dg(x	NUM
ejpam-4578	128	13	,	,	PUNCT
ejpam-4578	128	14	y	y	NOUN
ejpam-4578	128	15	)	)	PUNCT
ejpam-4578	128	16	=	=	SYM
ejpam-4578	128	17	2	2	X
ejpam-4578	128	18	.	.	PUNCT
ejpam-4578	128	19	thus	thus	ADV
ejpam-4578	128	20	,	,	PUNCT
ejpam-4578	128	21	c	c	PROPN
ejpam-4578	128	22	is	be	AUX
ejpam-4578	128	23	a	a	DET
ejpam-4578	128	24	hop	hop	NOUN
ejpam-4578	128	25	dominated	dominate	VERB
ejpam-4578	128	26	superclique	superclique	NOUN
ejpam-4578	128	27	in	in	ADP
ejpam-4578	128	28	g.	g.	PROPN
ejpam-4578	128	29	conversely	conversely	ADV
ejpam-4578	128	30	,	,	PUNCT
ejpam-4578	128	31	suppose	suppose	VERB
ejpam-4578	128	32	c	c	NOUN
ejpam-4578	128	33	=	=	SYM
ejpam-4578	128	34	∅	∅	NOUN
ejpam-4578	128	35	or	or	CCONJ
ejpam-4578	128	36	c	c	NOUN
ejpam-4578	128	37	is	be	AUX
ejpam-4578	128	38	a	a	DET
ejpam-4578	128	39	hop	hop	NOUN
ejpam-4578	128	40	dominated	dominate	VERB
ejpam-4578	128	41	superclique	superclique	NOUN
ejpam-4578	128	42	in	in	ADP
ejpam-4578	128	43	g.	g.	PROPN
ejpam-4578	128	44	then	then	ADV
ejpam-4578	128	45	c	c	PROPN
ejpam-4578	128	46	̸=	̸=	PROPN
ejpam-4578	128	47	∅	∅	NOUN
ejpam-4578	128	48	or	or	CCONJ
ejpam-4578	128	49	c	c	NOUN
ejpam-4578	128	50	is	be	AUX
ejpam-4578	128	51	a	a	DET
ejpam-4578	128	52	superclique	superclique	NOUN
ejpam-4578	128	53	in	in	ADP
ejpam-4578	128	54	g.	g.	NOUN
ejpam-4578	128	55	by	by	ADP
ejpam-4578	128	56	proposition	proposition	NOUN
ejpam-4578	128	57	4	4	NUM
ejpam-4578	128	58	,	,	PUNCT
ejpam-4578	128	59	s	s	PART
ejpam-4578	128	60	=	=	SYM
ejpam-4578	128	61	v	v	X
ejpam-4578	128	62	(	(	PUNCT
ejpam-4578	128	63	g	g	NOUN
ejpam-4578	128	64	)	)	PUNCT
ejpam-4578	128	65	\	\	PUNCT
ejpam-4578	129	1	c	c	NOUN
ejpam-4578	129	2	is	be	AUX
ejpam-4578	129	3	a	a	DET
ejpam-4578	129	4	strong	strong	ADJ
ejpam-4578	129	5	resolving	resolving	NOUN
ejpam-4578	129	6	set	set	NOUN
ejpam-4578	129	7	of	of	ADP
ejpam-4578	129	8	g.	g.	PROPN
ejpam-4578	129	9	let	let	VERB
ejpam-4578	129	10	x	x	SYM
ejpam-4578	129	11	∈	∈	PROPN
ejpam-4578	129	12	v	v	X
ejpam-4578	129	13	(	(	PUNCT
ejpam-4578	129	14	g	g	NOUN
ejpam-4578	129	15	)	)	PUNCT
ejpam-4578	129	16	\	\	PUNCT
ejpam-4578	130	1	s.	s.	PROPN
ejpam-4578	130	2	then	then	ADV
ejpam-4578	130	3	x	x	PROPN
ejpam-4578	130	4	∈	∈	PROPN
ejpam-4578	130	5	c.	c.	NOUN
ejpam-4578	130	6	since	since	SCONJ
ejpam-4578	130	7	c	c	PROPN
ejpam-4578	130	8	is	be	AUX
ejpam-4578	130	9	a	a	DET
ejpam-4578	130	10	hop	hop	NOUN
ejpam-4578	130	11	dominated	dominate	VERB
ejpam-4578	130	12	superclique	superclique	NOUN
ejpam-4578	130	13	,	,	PUNCT
ejpam-4578	130	14	there	there	PRON
ejpam-4578	130	15	exists	exist	VERB
ejpam-4578	130	16	y	y	PROPN
ejpam-4578	130	17	∈	∈	PROPN
ejpam-4578	130	18	v	v	ADP
ejpam-4578	130	19	(	(	PUNCT
ejpam-4578	130	20	g	g	NOUN
ejpam-4578	130	21	)	)	PUNCT
ejpam-4578	130	22	\	\	PROPN
ejpam-4578	131	1	c	c	NOUN
ejpam-4578	131	2	∩	∩	NOUN
ejpam-4578	131	3	ng(x	ng(x	NUM
ejpam-4578	131	4	,	,	PUNCT
ejpam-4578	131	5	2	2	NUM
ejpam-4578	131	6	)	)	PUNCT
ejpam-4578	131	7	.	.	PUNCT
ejpam-4578	132	1	since	since	SCONJ
ejpam-4578	132	2	s	s	PART
ejpam-4578	132	3	=	=	SYM
ejpam-4578	132	4	v	v	PROPN
ejpam-4578	132	5	(	(	PUNCT
ejpam-4578	132	6	g	g	NOUN
ejpam-4578	132	7	)	)	PUNCT
ejpam-4578	132	8	\	\	PUNCT
ejpam-4578	132	9	c	c	X
ejpam-4578	132	10	,	,	PUNCT
ejpam-4578	132	11	y	y	PROPN
ejpam-4578	132	12	∈	∈	PROPN
ejpam-4578	132	13	s	s	PART
ejpam-4578	132	14	∩	∩	NOUN
ejpam-4578	132	15	ng(x	ng(x	NUM
ejpam-4578	132	16	,	,	PUNCT
ejpam-4578	132	17	2	2	NUM
ejpam-4578	132	18	)	)	PUNCT
ejpam-4578	132	19	.	.	PUNCT
ejpam-4578	133	1	therefore	therefore	ADV
ejpam-4578	133	2	,	,	PUNCT
ejpam-4578	133	3	s	s	VERB
ejpam-4578	133	4	is	be	AUX
ejpam-4578	133	5	a	a	DET
ejpam-4578	133	6	hop	hop	NOUN
ejpam-4578	133	7	dominating	dominating	NOUN
ejpam-4578	133	8	set	set	NOUN
ejpam-4578	133	9	of	of	ADP
ejpam-4578	133	10	g.	g.	PROPN
ejpam-4578	133	11	accordingly	accordingly	ADV
ejpam-4578	133	12	,	,	PUNCT
ejpam-4578	133	13	s	s	VERB
ejpam-4578	133	14	is	be	AUX
ejpam-4578	133	15	a	a	DET
ejpam-4578	133	16	strong	strong	ADJ
ejpam-4578	133	17	resolving	resolve	VERB
ejpam-4578	133	18	hop	hop	NOUN
ejpam-4578	133	19	dominating	dominating	NOUN
ejpam-4578	133	20	set	set	NOUN
ejpam-4578	133	21	of	of	ADP
ejpam-4578	133	22	g.	g.	PROPN
ejpam-4578	133	23	suppose	suppose	VERB
ejpam-4578	133	24	s	s	VERB
ejpam-4578	133	25	is	be	AUX
ejpam-4578	133	26	a	a	DET
ejpam-4578	133	27	γsrh	γsrh	NOUN
ejpam-4578	133	28	-	-	PUNCT
ejpam-4578	133	29	set	set	NOUN
ejpam-4578	133	30	of	of	ADP
ejpam-4578	133	31	g.	g.	PROPN
ejpam-4578	133	32	then	then	ADV
ejpam-4578	133	33	s	s	VERB
ejpam-4578	133	34	=	=	SYM
ejpam-4578	133	35	v	v	ADJ
ejpam-4578	133	36	(	(	PUNCT
ejpam-4578	133	37	g	g	NOUN
ejpam-4578	133	38	)	)	PUNCT
ejpam-4578	133	39	\	\	PUNCT
ejpam-4578	134	1	c	c	X
ejpam-4578	134	2	,	,	PUNCT
ejpam-4578	134	3	where	where	SCONJ
ejpam-4578	134	4	c	c	PROPN
ejpam-4578	134	5	is	be	AUX
ejpam-4578	134	6	a	a	DET
ejpam-4578	134	7	hop	hop	NOUN
ejpam-4578	134	8	dominated	dominate	VERB
ejpam-4578	134	9	superclique	superclique	NOUN
ejpam-4578	134	10	in	in	ADP
ejpam-4578	134	11	g	g	PROPN
ejpam-4578	134	12	and	and	CCONJ
ejpam-4578	134	13	|c|	|c|	PROPN
ejpam-4578	134	14	=	=	SYM
ejpam-4578	134	15	ωhs(g	ωhs(g	PROPN
ejpam-4578	134	16	)	)	PUNCT
ejpam-4578	134	17	.	.	PUNCT
ejpam-4578	135	1	hence	hence	ADV
ejpam-4578	135	2	,	,	PUNCT
ejpam-4578	135	3	γsrh(g	γsrh(g	PROPN
ejpam-4578	135	4	)	)	PUNCT
ejpam-4578	135	5	=	=	SYM
ejpam-4578	135	6	|s|	|s|	PROPN
ejpam-4578	135	7	=	=	PUNCT
ejpam-4578	135	8	|v	|v	PROPN
ejpam-4578	135	9	(	(	PUNCT
ejpam-4578	135	10	g)|	g)|	PROPN
ejpam-4578	135	11	−	−	PROPN
ejpam-4578	135	12	|c|	|c|	PROPN
ejpam-4578	135	13	=	=	SYM
ejpam-4578	135	14	|v	|v	PROPN
ejpam-4578	135	15	(	(	PUNCT
ejpam-4578	135	16	g)|	g)|	PROPN
ejpam-4578	135	17	−	−	PROPN
ejpam-4578	135	18	ωhs(g	ωhs(g	PROPN
ejpam-4578	135	19	)	)	PUNCT
ejpam-4578	135	20	.	.	PUNCT
ejpam-4578	136	1	3	3	X
ejpam-4578	136	2	.	.	X
ejpam-4578	136	3	on	on	ADP
ejpam-4578	136	4	strong	strong	ADJ
ejpam-4578	136	5	resolving	resolve	VERB
ejpam-4578	136	6	hop	hop	NOUN
ejpam-4578	136	7	domination	domination	NOUN
ejpam-4578	136	8	in	in	ADP
ejpam-4578	136	9	the	the	DET
ejpam-4578	136	10	join	join	NOUN
ejpam-4578	136	11	of	of	ADP
ejpam-4578	136	12	graphs	graph	NOUN
ejpam-4578	136	13	let	let	VERB
ejpam-4578	136	14	a	a	PRON
ejpam-4578	136	15	and	and	CCONJ
ejpam-4578	136	16	b	b	NOUN
ejpam-4578	136	17	be	be	NOUN
ejpam-4578	136	18	sets	set	NOUN
ejpam-4578	136	19	which	which	PRON
ejpam-4578	136	20	are	be	AUX
ejpam-4578	136	21	not	not	PART
ejpam-4578	136	22	necessarily	necessarily	ADV
ejpam-4578	136	23	disjoint	disjoint	VERB
ejpam-4578	136	24	.	.	PUNCT
ejpam-4578	137	1	the	the	DET
ejpam-4578	137	2	disjoint	disjoint	PROPN
ejpam-4578	137	3	union	union	NOUN
ejpam-4578	137	4	of	of	ADP
ejpam-4578	137	5	a	a	PRON
ejpam-4578	137	6	and	and	CCONJ
ejpam-4578	137	7	b	b	NOUN
ejpam-4578	137	8	,	,	PUNCT
ejpam-4578	137	9	denoted	denote	VERB
ejpam-4578	137	10	by	by	ADP
ejpam-4578	137	11	a	a	DET
ejpam-4578	137	12	•	•	NOUN
ejpam-4578	137	13	∪	∪	NOUN
ejpam-4578	137	14	b	b	NOUN
ejpam-4578	137	15	,	,	PUNCT
ejpam-4578	137	16	is	be	AUX
ejpam-4578	137	17	the	the	DET
ejpam-4578	137	18	set	set	NOUN
ejpam-4578	137	19	obtained	obtain	VERB
ejpam-4578	137	20	by	by	ADP
ejpam-4578	137	21	taking	take	VERB
ejpam-4578	137	22	the	the	DET
ejpam-4578	137	23	union	union	NOUN
ejpam-4578	137	24	of	of	ADP
ejpam-4578	137	25	a	a	PRON
ejpam-4578	137	26	and	and	CCONJ
ejpam-4578	137	27	b	b	NOUN
ejpam-4578	137	28	treating	treat	VERB
ejpam-4578	137	29	each	each	DET
ejpam-4578	137	30	element	element	NOUN
ejpam-4578	137	31	in	in	ADP
ejpam-4578	137	32	a	a	DET
ejpam-4578	137	33	as	as	ADV
ejpam-4578	137	34	distinct	distinct	ADJ
ejpam-4578	137	35	from	from	ADP
ejpam-4578	137	36	each	each	DET
ejpam-4578	137	37	element	element	NOUN
ejpam-4578	137	38	in	in	ADP
ejpam-4578	137	39	b.	b.	PROPN
ejpam-4578	138	1	the	the	DET
ejpam-4578	138	2	union	union	PROPN
ejpam-4578	138	3	g1	g1	PROPN
ejpam-4578	138	4	∪	∪	ADP
ejpam-4578	138	5	g2	g2	PROPN
ejpam-4578	138	6	of	of	ADP
ejpam-4578	138	7	graphs	graph	NOUN
ejpam-4578	138	8	g1	g1	PROPN
ejpam-4578	138	9	and	and	CCONJ
ejpam-4578	138	10	g2	g2	PROPN
ejpam-4578	138	11	with	with	ADP
ejpam-4578	138	12	disjoint	disjoint	PROPN
ejpam-4578	138	13	vertex	vertex	NOUN
ejpam-4578	138	14	-	-	PUNCT
ejpam-4578	138	15	sets	set	NOUN
ejpam-4578	138	16	v	v	NOUN
ejpam-4578	138	17	(	(	PUNCT
ejpam-4578	138	18	g1	g1	PROPN
ejpam-4578	138	19	)	)	PUNCT
ejpam-4578	138	20	and	and	CCONJ
ejpam-4578	138	21	v	v	NOUN
ejpam-4578	138	22	(	(	PUNCT
ejpam-4578	138	23	g2	g2	PROPN
ejpam-4578	138	24	)	)	PUNCT
ejpam-4578	138	25	,	,	PUNCT
ejpam-4578	138	26	respectively	respectively	ADV
ejpam-4578	138	27	,	,	PUNCT
ejpam-4578	138	28	is	be	AUX
ejpam-4578	138	29	the	the	DET
ejpam-4578	138	30	graph	graph	NOUN
ejpam-4578	138	31	g	g	NOUN
ejpam-4578	138	32	with	with	ADP
ejpam-4578	138	33	v	v	NOUN
ejpam-4578	138	34	(	(	PUNCT
ejpam-4578	138	35	g	g	NOUN
ejpam-4578	138	36	)	)	PUNCT
ejpam-4578	139	1	=	=	NOUN
ejpam-4578	139	2	v	v	X
ejpam-4578	139	3	(	(	PUNCT
ejpam-4578	139	4	g1	g1	PROPN
ejpam-4578	139	5	)	)	PUNCT
ejpam-4578	139	6	•	•	ADP
ejpam-4578	139	7	∪	∪	X
ejpam-4578	139	8	v	v	NOUN
ejpam-4578	139	9	(	(	PUNCT
ejpam-4578	139	10	g2	g2	PROPN
ejpam-4578	139	11	)	)	PUNCT
ejpam-4578	139	12	and	and	CCONJ
ejpam-4578	139	13	e(g	e(g	PROPN
ejpam-4578	139	14	)	)	PUNCT
ejpam-4578	139	15	=	=	SYM
ejpam-4578	139	16	e(g1	e(g1	ADJ
ejpam-4578	139	17	)	)	PUNCT
ejpam-4578	139	18	•	•	ADP
ejpam-4578	139	19	∪	∪	ADP
ejpam-4578	139	20	e(g2	e(g2	ADV
ejpam-4578	139	21	)	)	PUNCT
ejpam-4578	139	22	.	.	PUNCT
ejpam-4578	140	1	the	the	DET
ejpam-4578	140	2	join	join	NOUN
ejpam-4578	140	3	of	of	ADP
ejpam-4578	140	4	two	two	NUM
ejpam-4578	140	5	graphs	graph	NOUN
ejpam-4578	140	6	g	g	NOUN
ejpam-4578	140	7	and	and	CCONJ
ejpam-4578	140	8	h	h	NOUN
ejpam-4578	140	9	,	,	PUNCT
ejpam-4578	140	10	denoted	denote	VERB
ejpam-4578	140	11	by	by	ADP
ejpam-4578	140	12	g+h	g+h	PROPN
ejpam-4578	140	13	,	,	PUNCT
ejpam-4578	140	14	is	be	AUX
ejpam-4578	140	15	the	the	DET
ejpam-4578	140	16	graph	graph	NOUN
ejpam-4578	140	17	with	with	ADP
ejpam-4578	140	18	vertex	vertex	NOUN
ejpam-4578	140	19	-	-	PUNCT
ejpam-4578	140	20	set	set	VERB
ejpam-4578	140	21	v	v	NOUN
ejpam-4578	140	22	(	(	PUNCT
ejpam-4578	140	23	g+h	g+h	NOUN
ejpam-4578	140	24	)	)	PUNCT
ejpam-4578	140	25	=	=	SYM
ejpam-4578	140	26	v	v	X
ejpam-4578	140	27	(	(	PUNCT
ejpam-4578	140	28	g	g	NOUN
ejpam-4578	140	29	)	)	PUNCT
ejpam-4578	140	30	•	•	ADP
ejpam-4578	140	31	∪	∪	X
ejpam-4578	140	32	v	v	NOUN
ejpam-4578	140	33	(	(	PUNCT
ejpam-4578	140	34	h	h	NOUN
ejpam-4578	140	35	)	)	PUNCT
ejpam-4578	140	36	and	and	CCONJ
ejpam-4578	140	37	edge	edge	NOUN
ejpam-4578	140	38	-	-	PUNCT
ejpam-4578	140	39	set	set	VERB
ejpam-4578	140	40	e(g+h	e(g+h	NUM
ejpam-4578	140	41	)	)	PUNCT
ejpam-4578	140	42	=	=	SYM
ejpam-4578	140	43	e(g	e(g	PROPN
ejpam-4578	140	44	)	)	PUNCT
ejpam-4578	140	45	•	•	ADP
ejpam-4578	140	46	∪	∪	ADP
ejpam-4578	140	47	e(h	e(h	PROPN
ejpam-4578	140	48	)	)	PUNCT
ejpam-4578	140	49	∪	∪	NOUN
ejpam-4578	140	50	{	{	PUNCT
ejpam-4578	140	51	uv	uv	NOUN
ejpam-4578	140	52	:	:	PUNCT
ejpam-4578	140	53	u	u	PROPN
ejpam-4578	140	54	∈	∈	PROPN
ejpam-4578	140	55	v	v	ADP
ejpam-4578	140	56	(	(	PUNCT
ejpam-4578	140	57	g	g	NOUN
ejpam-4578	140	58	)	)	PUNCT
ejpam-4578	140	59	,	,	PUNCT
ejpam-4578	140	60	v	v	X
ejpam-4578	140	61	∈	∈	PROPN
ejpam-4578	140	62	v	v	NOUN
ejpam-4578	140	63	(	(	PUNCT
ejpam-4578	140	64	h	h	NOUN
ejpam-4578	140	65	)	)	PUNCT
ejpam-4578	140	66	}	}	PUNCT
ejpam-4578	140	67	.	.	PUNCT
ejpam-4578	141	1	remark	remark	PROPN
ejpam-4578	141	2	8	8	NUM
ejpam-4578	141	3	.	.	PUNCT
ejpam-4578	142	1	for	for	ADP
ejpam-4578	142	2	the	the	DET
ejpam-4578	142	3	joins	join	NOUN
ejpam-4578	142	4	⟨v⟩+	⟨v⟩+	CCONJ
ejpam-4578	142	5	pn	pn	PROPN
ejpam-4578	142	6	and	and	CCONJ
ejpam-4578	142	7	⟨w⟩+	⟨w⟩+	ADJ
ejpam-4578	142	8	cn	cn	PROPN
ejpam-4578	142	9	,	,	PUNCT
ejpam-4578	142	10	γsrh(⟨v⟩+	γsrh(⟨v⟩+	PROPN
ejpam-4578	142	11	pn	pn	NOUN
ejpam-4578	142	12	)	)	PUNCT
ejpam-4578	143	1	=	=	PUNCT
ejpam-4578	143	2	n−	n−	NOUN
ejpam-4578	143	3	1	1	NUM
ejpam-4578	143	4	for	for	ADP
ejpam-4578	143	5	n	n	PRON
ejpam-4578	143	6	≥	≥	NOUN
ejpam-4578	143	7	3	3	NUM
ejpam-4578	143	8	and	and	CCONJ
ejpam-4578	143	9	γsrh(⟨w⟩+	γsrh(⟨w⟩+	ADP
ejpam-4578	143	10	cn	cn	ADJ
ejpam-4578	143	11	)	)	PUNCT
ejpam-4578	144	1	=	=	PUNCT
ejpam-4578	144	2	n−	n−	NOUN
ejpam-4578	144	3	1	1	NUM
ejpam-4578	144	4	for	for	ADP
ejpam-4578	144	5	n	n	PRON
ejpam-4578	144	6	≥	≥	NUM
ejpam-4578	144	7	4	4	NUM
ejpam-4578	144	8	.	.	PUNCT
ejpam-4578	144	9	theorem	theorem	NOUN
ejpam-4578	144	10	1	1	NUM
ejpam-4578	144	11	.	.	PUNCT
ejpam-4578	145	1	[	[	X
ejpam-4578	145	2	1	1	X
ejpam-4578	145	3	]	]	PUNCT
ejpam-4578	145	4	let	let	VERB
ejpam-4578	145	5	g	g	PRON
ejpam-4578	145	6	be	be	AUX
ejpam-4578	145	7	a	a	DET
ejpam-4578	145	8	non	non	ADJ
ejpam-4578	145	9	-	-	ADJ
ejpam-4578	145	10	trivial	trivial	ADJ
ejpam-4578	145	11	connected	connected	ADJ
ejpam-4578	145	12	graph	graph	NOUN
ejpam-4578	145	13	of	of	ADP
ejpam-4578	145	14	order	order	NOUN
ejpam-4578	145	15	n	n	PRON
ejpam-4578	145	16	with	with	ADP
ejpam-4578	145	17	γ(g	γ(g	PROPN
ejpam-4578	145	18	)	)	PUNCT
ejpam-4578	145	19	̸=	̸=	PROPN
ejpam-4578	145	20	1	1	NUM
ejpam-4578	145	21	and	and	CCONJ
ejpam-4578	145	22	k1	k1	NOUN
ejpam-4578	145	23	=	=	SYM
ejpam-4578	145	24	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4578	145	25	then	then	ADV
ejpam-4578	145	26	s	s	VERB
ejpam-4578	145	27	⊆	⊆	NUM
ejpam-4578	145	28	v	v	NOUN
ejpam-4578	145	29	(	(	PUNCT
ejpam-4578	145	30	k1+g	k1+g	NOUN
ejpam-4578	145	31	)	)	PUNCT
ejpam-4578	145	32	is	be	AUX
ejpam-4578	145	33	a	a	DET
ejpam-4578	145	34	strong	strong	ADJ
ejpam-4578	145	35	resolving	resolving	NOUN
ejpam-4578	145	36	set	set	NOUN
ejpam-4578	145	37	of	of	ADP
ejpam-4578	145	38	k1+g	k1+g	NOUN
ejpam-4578	145	39	if	if	SCONJ
ejpam-4578	145	40	and	and	CCONJ
ejpam-4578	145	41	only	only	ADV
ejpam-4578	145	42	if	if	SCONJ
ejpam-4578	145	43	s	s	VERB
ejpam-4578	145	44	=	=	SYM
ejpam-4578	145	45	v	v	X
ejpam-4578	145	46	(	(	PUNCT
ejpam-4578	145	47	g	g	NOUN
ejpam-4578	145	48	)	)	PUNCT
ejpam-4578	145	49	,	,	PUNCT
ejpam-4578	145	50	or	or	CCONJ
ejpam-4578	145	51	s	s	VERB
ejpam-4578	145	52	=	=	SYM
ejpam-4578	145	53	v	v	PROPN
ejpam-4578	145	54	(	(	PUNCT
ejpam-4578	145	55	g	g	NOUN
ejpam-4578	145	56	)	)	PUNCT
ejpam-4578	145	57	\	\	PUNCT
ejpam-4578	146	1	c	c	X
ejpam-4578	146	2	,	,	PUNCT
ejpam-4578	146	3	or	or	CCONJ
ejpam-4578	146	4	s	s	NOUN
ejpam-4578	146	5	=	=	SYM
ejpam-4578	146	6	v	v	PROPN
ejpam-4578	146	7	(	(	PUNCT
ejpam-4578	146	8	k1	k1	NOUN
ejpam-4578	146	9	+	+	PROPN
ejpam-4578	146	10	g	g	NOUN
ejpam-4578	146	11	)	)	PUNCT
ejpam-4578	146	12	\	\	PUNCT
ejpam-4578	146	13	c	c	NOUN
ejpam-4578	146	14	where	where	SCONJ
ejpam-4578	146	15	⟨c⟩	⟨c⟩	PROPN
ejpam-4578	146	16	is	be	AUX
ejpam-4578	146	17	a	a	DET
ejpam-4578	146	18	superclique	superclique	NOUN
ejpam-4578	146	19	in	in	ADP
ejpam-4578	146	20	g.	g.	PROPN
ejpam-4578	146	21	theorem	theorem	PROPN
ejpam-4578	146	22	2	2	NUM
ejpam-4578	146	23	.	.	PUNCT
ejpam-4578	147	1	[	[	X
ejpam-4578	147	2	1	1	X
ejpam-4578	147	3	]	]	PUNCT
ejpam-4578	147	4	let	let	VERB
ejpam-4578	147	5	g	g	PRON
ejpam-4578	147	6	be	be	AUX
ejpam-4578	147	7	a	a	DET
ejpam-4578	147	8	non	non	ADJ
ejpam-4578	147	9	-	-	ADJ
ejpam-4578	147	10	trivial	trivial	ADJ
ejpam-4578	147	11	connected	connected	ADJ
ejpam-4578	147	12	graph	graph	NOUN
ejpam-4578	147	13	of	of	ADP
ejpam-4578	147	14	order	order	NOUN
ejpam-4578	147	15	n	n	PRON
ejpam-4578	147	16	with	with	ADP
ejpam-4578	147	17	γ(g	γ(g	PROPN
ejpam-4578	147	18	)	)	PUNCT
ejpam-4578	147	19	=	=	SYM
ejpam-4578	147	20	1	1	NUM
ejpam-4578	147	21	and	and	CCONJ
ejpam-4578	147	22	k1	k1	NOUN
ejpam-4578	148	1	=	=	SYM
ejpam-4578	148	2	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4578	148	3	then	then	ADV
ejpam-4578	148	4	s	s	VERB
ejpam-4578	148	5	⊆	⊆	NUM
ejpam-4578	148	6	v	v	NOUN
ejpam-4578	148	7	(	(	PUNCT
ejpam-4578	148	8	k1+g	k1+g	NOUN
ejpam-4578	148	9	)	)	PUNCT
ejpam-4578	148	10	is	be	AUX
ejpam-4578	148	11	a	a	DET
ejpam-4578	148	12	strong	strong	ADJ
ejpam-4578	148	13	resolving	resolving	NOUN
ejpam-4578	148	14	set	set	NOUN
ejpam-4578	148	15	of	of	ADP
ejpam-4578	148	16	k1+g	k1+g	NOUN
ejpam-4578	148	17	if	if	SCONJ
ejpam-4578	148	18	and	and	CCONJ
ejpam-4578	148	19	only	only	ADV
ejpam-4578	148	20	if	if	SCONJ
ejpam-4578	148	21	s	s	VERB
ejpam-4578	148	22	=	=	SYM
ejpam-4578	148	23	v	v	X
ejpam-4578	148	24	(	(	PUNCT
ejpam-4578	148	25	g	g	NOUN
ejpam-4578	148	26	)	)	PUNCT
ejpam-4578	148	27	,	,	PUNCT
ejpam-4578	148	28	or	or	CCONJ
ejpam-4578	148	29	s	s	VERB
ejpam-4578	148	30	=	=	SYM
ejpam-4578	148	31	v	v	PROPN
ejpam-4578	148	32	(	(	PUNCT
ejpam-4578	148	33	k1	k1	NOUN
ejpam-4578	148	34	+	+	PROPN
ejpam-4578	148	35	g	g	NOUN
ejpam-4578	148	36	)	)	PUNCT
ejpam-4578	148	37	\	\	PROPN
ejpam-4578	148	38	c∗	c∗	NOUN
ejpam-4578	148	39	,	,	PUNCT
ejpam-4578	148	40	or	or	CCONJ
ejpam-4578	148	41	s	s	X
ejpam-4578	148	42	=	=	PUNCT
ejpam-4578	148	43	(	(	PUNCT
ejpam-4578	148	44	v	v	NOUN
ejpam-4578	148	45	(	(	PUNCT
ejpam-4578	148	46	g	g	NOUN
ejpam-4578	148	47	)	)	PUNCT
ejpam-4578	148	48	\	\	PROPN
ejpam-4578	148	49	c∗	c∗	PROPN
ejpam-4578	148	50	)	)	PUNCT
ejpam-4578	148	51	∪	∪	NOUN
ejpam-4578	148	52	{	{	PUNCT
ejpam-4578	148	53	x	x	SYM
ejpam-4578	148	54	∈	∈	PROPN
ejpam-4578	148	55	c∗	c∗	NOUN
ejpam-4578	148	56	:	:	PUNCT
ejpam-4578	148	57	degg(x	degg(x	X
ejpam-4578	148	58	)	)	PUNCT
ejpam-4578	148	59	=	=	PUNCT
ejpam-4578	148	60	n−	n−	NOUN
ejpam-4578	148	61	1	1	NUM
ejpam-4578	148	62	}	}	PUNCT
ejpam-4578	148	63	where	where	SCONJ
ejpam-4578	148	64	⟨c∗⟩	⟨c∗⟩	NOUN
ejpam-4578	148	65	is	be	AUX
ejpam-4578	148	66	a	a	DET
ejpam-4578	148	67	superclique	superclique	NOUN
ejpam-4578	148	68	in	in	ADP
ejpam-4578	148	69	g.	g.	PROPN
ejpam-4578	148	70	j.	j.	PROPN
ejpam-4578	148	71	mohamad	mohamad	PROPN
ejpam-4578	148	72	,	,	PUNCT
ejpam-4578	148	73	h.	h.	PROPN
ejpam-4578	148	74	rara	rara	PROPN
ejpam-4578	148	75	/	/	SYM
ejpam-4578	148	76	eur	eur	PROPN
ejpam-4578	148	77	.	.	PUNCT
ejpam-4578	149	1	j.	j.	PROPN
ejpam-4578	149	2	pure	pure	PROPN
ejpam-4578	149	3	appl	appl	PROPN
ejpam-4578	149	4	.	.	PROPN
ejpam-4578	149	5	math	math	PROPN
ejpam-4578	149	6	,	,	PUNCT
ejpam-4578	149	7	16	16	NUM
ejpam-4578	149	8	(	(	PUNCT
ejpam-4578	149	9	1	1	NUM
ejpam-4578	149	10	)	)	PUNCT
ejpam-4578	149	11	(	(	PUNCT
ejpam-4578	149	12	2023	2023	NUM
ejpam-4578	149	13	)	)	PUNCT
ejpam-4578	149	14	,	,	PUNCT
ejpam-4578	149	15	131	131	NUM
ejpam-4578	149	16	-	-	SYM
ejpam-4578	149	17	143	143	NUM
ejpam-4578	149	18	136	136	NUM
ejpam-4578	149	19	theorem	theorem	NOUN
ejpam-4578	149	20	3	3	NUM
ejpam-4578	149	21	.	.	PUNCT
ejpam-4578	150	1	[	[	X
ejpam-4578	150	2	1	1	X
ejpam-4578	150	3	]	]	PUNCT
ejpam-4578	150	4	let	let	VERB
ejpam-4578	150	5	k1	k1	NOUN
ejpam-4578	150	6	=	=	SYM
ejpam-4578	150	7	⟨v⟩	⟨v⟩	PROPN
ejpam-4578	150	8	and	and	CCONJ
ejpam-4578	150	9	g	g	PROPN
ejpam-4578	150	10	be	be	AUX
ejpam-4578	150	11	a	a	DET
ejpam-4578	150	12	disconnected	disconnected	ADJ
ejpam-4578	150	13	graph	graph	NOUN
ejpam-4578	150	14	whose	whose	DET
ejpam-4578	150	15	components	component	NOUN
ejpam-4578	150	16	are	be	AUX
ejpam-4578	150	17	gi	gi	ADJ
ejpam-4578	150	18	for	for	ADP
ejpam-4578	150	19	i	i	PROPN
ejpam-4578	150	20	=	=	NOUN
ejpam-4578	150	21	1	1	NUM
ejpam-4578	150	22	,	,	PUNCT
ejpam-4578	150	23	2	2	NUM
ejpam-4578	150	24	,	,	PUNCT
ejpam-4578	150	25	.	.	PUNCT
ejpam-4578	150	26	.	.	PUNCT
ejpam-4578	150	27	.	.	PUNCT
ejpam-4578	151	1	,	,	PUNCT
ejpam-4578	151	2	m.	m.	NOUN
ejpam-4578	151	3	a	a	DET
ejpam-4578	151	4	proper	proper	ADJ
ejpam-4578	151	5	subset	subset	NOUN
ejpam-4578	151	6	s	s	NOUN
ejpam-4578	151	7	of	of	ADP
ejpam-4578	151	8	v	v	NOUN
ejpam-4578	151	9	(	(	PUNCT
ejpam-4578	151	10	k1	k1	NOUN
ejpam-4578	151	11	+	+	NOUN
ejpam-4578	151	12	g	g	NOUN
ejpam-4578	151	13	)	)	PUNCT
ejpam-4578	151	14	is	be	AUX
ejpam-4578	151	15	a	a	DET
ejpam-4578	151	16	strong	strong	ADJ
ejpam-4578	151	17	resolving	resolving	NOUN
ejpam-4578	151	18	set	set	NOUN
ejpam-4578	151	19	of	of	ADP
ejpam-4578	151	20	k1	k1	NOUN
ejpam-4578	152	1	+	+	ADP
ejpam-4578	152	2	g	g	PROPN
ejpam-4578	152	3	if	if	SCONJ
ejpam-4578	152	4	and	and	CCONJ
ejpam-4578	152	5	only	only	ADV
ejpam-4578	152	6	if	if	SCONJ
ejpam-4578	152	7	s	s	VERB
ejpam-4578	152	8	=	=	SYM
ejpam-4578	152	9	v	v	X
ejpam-4578	152	10	(	(	PUNCT
ejpam-4578	152	11	g	g	NOUN
ejpam-4578	152	12	)	)	PUNCT
ejpam-4578	152	13	or	or	CCONJ
ejpam-4578	152	14	s	s	X
ejpam-4578	152	15	=	=	SYM
ejpam-4578	152	16	v	v	NOUN
ejpam-4578	152	17	(	(	PUNCT
ejpam-4578	152	18	g)\ci	g)\ci	PROPN
ejpam-4578	152	19	or	or	CCONJ
ejpam-4578	152	20	s	s	NOUN
ejpam-4578	152	21	=	=	SYM
ejpam-4578	152	22	v	v	PROPN
ejpam-4578	152	23	(	(	PUNCT
ejpam-4578	152	24	k1+g)\ci	k1+g)\ci	PROPN
ejpam-4578	152	25	where	where	SCONJ
ejpam-4578	152	26	⟨ci⟩	⟨ci⟩	NOUN
ejpam-4578	152	27	is	be	AUX
ejpam-4578	152	28	a	a	DET
ejpam-4578	152	29	superclique	superclique	NOUN
ejpam-4578	152	30	in	in	ADP
ejpam-4578	152	31	gi	gi	NOUN
ejpam-4578	152	32	,	,	PUNCT
ejpam-4578	152	33	for	for	ADP
ejpam-4578	152	34	some	some	DET
ejpam-4578	152	35	i	i	PRON
ejpam-4578	152	36	∈	∈	PROPN
ejpam-4578	152	37	{	{	PUNCT
ejpam-4578	152	38	1	1	NUM
ejpam-4578	152	39	,	,	PUNCT
ejpam-4578	152	40	2	2	NUM
ejpam-4578	152	41	,	,	PUNCT
ejpam-4578	152	42	.	.	PUNCT
ejpam-4578	152	43	.	.	PUNCT
ejpam-4578	152	44	.	.	PUNCT
ejpam-4578	153	1	,	,	PUNCT
ejpam-4578	153	2	m	m	VERB
ejpam-4578	153	3	}	}	PUNCT
ejpam-4578	153	4	.	.	PUNCT
ejpam-4578	154	1	lemma	lemma	PROPN
ejpam-4578	154	2	2	2	X
ejpam-4578	154	3	.	.	PUNCT
ejpam-4578	155	1	let	let	VERB
ejpam-4578	155	2	g	g	PRON
ejpam-4578	155	3	be	be	AUX
ejpam-4578	155	4	a	a	DET
ejpam-4578	155	5	connected	connected	ADJ
ejpam-4578	155	6	graph	graph	NOUN
ejpam-4578	155	7	of	of	ADP
ejpam-4578	155	8	order	order	NOUN
ejpam-4578	155	9	n	n	NOUN
ejpam-4578	155	10	and	and	CCONJ
ejpam-4578	155	11	let	let	VERB
ejpam-4578	155	12	k1	k1	NOUN
ejpam-4578	155	13	=	=	SYM
ejpam-4578	155	14	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4578	155	15	then	then	ADV
ejpam-4578	155	16	c	c	PROPN
ejpam-4578	155	17	⊆	⊆	NUM
ejpam-4578	155	18	v	v	NOUN
ejpam-4578	155	19	(	(	PUNCT
ejpam-4578	155	20	k1+g	k1+g	NOUN
ejpam-4578	155	21	)	)	PUNCT
ejpam-4578	155	22	is	be	AUX
ejpam-4578	155	23	a	a	DET
ejpam-4578	155	24	hop	hop	NOUN
ejpam-4578	155	25	dominated	dominate	VERB
ejpam-4578	155	26	superclique	superclique	NOUN
ejpam-4578	155	27	in	in	ADP
ejpam-4578	155	28	k1	k1	NOUN
ejpam-4578	156	1	+	+	ADP
ejpam-4578	156	2	g	g	PROPN
ejpam-4578	156	3	if	if	SCONJ
ejpam-4578	156	4	and	and	CCONJ
ejpam-4578	156	5	only	only	ADV
ejpam-4578	156	6	if	if	SCONJ
ejpam-4578	156	7	c	c	PROPN
ejpam-4578	156	8	is	be	AUX
ejpam-4578	156	9	a	a	DET
ejpam-4578	156	10	hop	hop	NOUN
ejpam-4578	156	11	dominated	dominate	VERB
ejpam-4578	156	12	superclique	superclique	NOUN
ejpam-4578	156	13	in	in	ADP
ejpam-4578	156	14	g.	g.	PROPN
ejpam-4578	156	15	proof	proof	NOUN
ejpam-4578	156	16	:	:	PUNCT
ejpam-4578	156	17	suppose	suppose	VERB
ejpam-4578	156	18	c	c	NOUN
ejpam-4578	156	19	is	be	AUX
ejpam-4578	156	20	a	a	DET
ejpam-4578	156	21	hop	hop	NOUN
ejpam-4578	156	22	dominated	dominate	VERB
ejpam-4578	156	23	superclique	superclique	NOUN
ejpam-4578	156	24	in	in	ADP
ejpam-4578	156	25	k1	k1	PROPN
ejpam-4578	156	26	+	+	PROPN
ejpam-4578	156	27	g.	g.	PROPN
ejpam-4578	156	28	since	since	SCONJ
ejpam-4578	156	29	degk1+g(v	degk1+g(v	ADV
ejpam-4578	156	30	)	)	PUNCT
ejpam-4578	156	31	=	=	SYM
ejpam-4578	156	32	n	n	CCONJ
ejpam-4578	156	33	,	,	PUNCT
ejpam-4578	156	34	by	by	ADP
ejpam-4578	156	35	proposition	proposition	NOUN
ejpam-4578	156	36	5	5	NUM
ejpam-4578	156	37	,	,	PUNCT
ejpam-4578	156	38	v	v	NOUN
ejpam-4578	156	39	/∈	/∈	PUNCT
ejpam-4578	156	40	c.	c.	PROPN
ejpam-4578	156	41	thus	thus	ADV
ejpam-4578	156	42	,	,	PUNCT
ejpam-4578	156	43	c	c	PROPN
ejpam-4578	156	44	is	be	AUX
ejpam-4578	156	45	a	a	DET
ejpam-4578	156	46	hop	hop	NOUN
ejpam-4578	156	47	dominated	dominate	VERB
ejpam-4578	156	48	superclique	superclique	NOUN
ejpam-4578	156	49	in	in	ADP
ejpam-4578	156	50	g.	g.	PROPN
ejpam-4578	156	51	the	the	DET
ejpam-4578	156	52	converse	converse	NOUN
ejpam-4578	156	53	follows	follow	VERB
ejpam-4578	156	54	immediately	immediately	ADV
ejpam-4578	156	55	from	from	ADP
ejpam-4578	156	56	proposition	proposition	NOUN
ejpam-4578	156	57	5	5	NUM
ejpam-4578	156	58	and	and	CCONJ
ejpam-4578	156	59	definition	definition	NOUN
ejpam-4578	156	60	of	of	ADP
ejpam-4578	156	61	hop	hop	NOUN
ejpam-4578	156	62	dominated	dominate	VERB
ejpam-4578	156	63	superclique	superclique	NOUN
ejpam-4578	156	64	.	.	PUNCT
ejpam-4578	157	1	theorem	theorem	NOUN
ejpam-4578	157	2	4	4	NUM
ejpam-4578	157	3	.	.	PUNCT
ejpam-4578	158	1	let	let	VERB
ejpam-4578	158	2	g	g	PRON
ejpam-4578	158	3	be	be	AUX
ejpam-4578	158	4	a	a	DET
ejpam-4578	158	5	connected	connected	ADJ
ejpam-4578	158	6	graph	graph	NOUN
ejpam-4578	158	7	of	of	ADP
ejpam-4578	158	8	order	order	NOUN
ejpam-4578	158	9	n	n	CCONJ
ejpam-4578	158	10	>	>	X
ejpam-4578	158	11	1	1	NUM
ejpam-4578	158	12	,	,	PUNCT
ejpam-4578	158	13	and	and	CCONJ
ejpam-4578	158	14	let	let	VERB
ejpam-4578	158	15	k1	k1	NOUN
ejpam-4578	158	16	=	=	SYM
ejpam-4578	158	17	⟨v⟩.	⟨v⟩.	PROPN
ejpam-4578	158	18	then	then	ADV
ejpam-4578	158	19	s	s	VERB
ejpam-4578	158	20	⊆	⊆	NUM
ejpam-4578	158	21	v	v	NOUN
ejpam-4578	158	22	(	(	PUNCT
ejpam-4578	158	23	k1	k1	NOUN
ejpam-4578	158	24	+	+	CCONJ
ejpam-4578	158	25	g	g	NOUN
ejpam-4578	158	26	)	)	PUNCT
ejpam-4578	158	27	is	be	AUX
ejpam-4578	158	28	a	a	DET
ejpam-4578	158	29	strong	strong	ADJ
ejpam-4578	158	30	resolving	resolve	VERB
ejpam-4578	158	31	hop	hop	NOUN
ejpam-4578	158	32	dominating	dominating	NOUN
ejpam-4578	158	33	set	set	NOUN
ejpam-4578	158	34	of	of	ADP
ejpam-4578	158	35	k1	k1	NOUN
ejpam-4578	158	36	+	+	CCONJ
ejpam-4578	158	37	g	g	NOUN
ejpam-4578	158	38	if	if	SCONJ
ejpam-4578	159	1	and	and	CCONJ
ejpam-4578	159	2	only	only	ADV
ejpam-4578	159	3	if	if	SCONJ
ejpam-4578	159	4	s	s	VERB
ejpam-4578	159	5	=	=	SYM
ejpam-4578	159	6	v	v	PROPN
ejpam-4578	159	7	(	(	PUNCT
ejpam-4578	159	8	k1	k1	NOUN
ejpam-4578	159	9	+	+	PROPN
ejpam-4578	159	10	g	g	NOUN
ejpam-4578	159	11	)	)	PUNCT
ejpam-4578	159	12	\	\	PUNCT
ejpam-4578	160	1	c	c	NOUN
ejpam-4578	160	2	where	where	SCONJ
ejpam-4578	160	3	c	c	NOUN
ejpam-4578	160	4	=	=	SYM
ejpam-4578	160	5	∅	∅	NOUN
ejpam-4578	160	6	or	or	CCONJ
ejpam-4578	160	7	c	c	NOUN
ejpam-4578	160	8	is	be	AUX
ejpam-4578	160	9	a	a	DET
ejpam-4578	160	10	hop	hop	NOUN
ejpam-4578	160	11	dominated	dominate	VERB
ejpam-4578	160	12	superclique	superclique	NOUN
ejpam-4578	160	13	in	in	ADP
ejpam-4578	160	14	g.	g.	PROPN
ejpam-4578	160	15	proof	proof	NOUN
ejpam-4578	160	16	:	:	PUNCT
ejpam-4578	160	17	suppose	suppose	VERB
ejpam-4578	160	18	s	s	NOUN
ejpam-4578	160	19	is	be	AUX
ejpam-4578	160	20	a	a	DET
ejpam-4578	160	21	strong	strong	ADJ
ejpam-4578	160	22	resolving	resolve	VERB
ejpam-4578	160	23	hop	hop	NOUN
ejpam-4578	160	24	dominating	dominating	NOUN
ejpam-4578	160	25	set	set	NOUN
ejpam-4578	160	26	of	of	ADP
ejpam-4578	160	27	k1	k1	PROPN
ejpam-4578	160	28	+	+	CCONJ
ejpam-4578	160	29	g.	g.	NOUN
ejpam-4578	160	30	by	by	ADP
ejpam-4578	160	31	theorem	theorem	ADJ
ejpam-4578	160	32	1	1	NUM
ejpam-4578	160	33	and	and	CCONJ
ejpam-4578	160	34	theorem	theorem	VERB
ejpam-4578	160	35	2	2	NUM
ejpam-4578	160	36	,	,	PUNCT
ejpam-4578	160	37	s	s	PART
ejpam-4578	160	38	=	=	SYM
ejpam-4578	160	39	v	v	X
ejpam-4578	160	40	(	(	PUNCT
ejpam-4578	160	41	g	g	NOUN
ejpam-4578	160	42	)	)	PUNCT
ejpam-4578	160	43	,	,	PUNCT
ejpam-4578	160	44	or	or	CCONJ
ejpam-4578	160	45	s	s	VERB
ejpam-4578	160	46	=	=	PUNCT
ejpam-4578	160	47	(	(	PUNCT
ejpam-4578	160	48	v	v	NOUN
ejpam-4578	160	49	(	(	PUNCT
ejpam-4578	160	50	g	g	NOUN
ejpam-4578	160	51	)	)	PUNCT
ejpam-4578	160	52	\	\	PUNCT
ejpam-4578	161	1	c	c	X
ejpam-4578	161	2	)	)	PUNCT
ejpam-4578	161	3	∪	∪	NOUN
ejpam-4578	161	4	{	{	PUNCT
ejpam-4578	161	5	x	x	SYM
ejpam-4578	161	6	∈	∈	PROPN
ejpam-4578	161	7	c	c	NOUN
ejpam-4578	161	8	:	:	PUNCT
ejpam-4578	161	9	degg(x	degg(x	X
ejpam-4578	161	10	)	)	PUNCT
ejpam-4578	161	11	=	=	SYM
ejpam-4578	161	12	n	n	CCONJ
ejpam-4578	161	13	−	−	NOUN
ejpam-4578	161	14	1	1	NUM
ejpam-4578	161	15	}	}	PUNCT
ejpam-4578	161	16	,	,	PUNCT
ejpam-4578	161	17	or	or	CCONJ
ejpam-4578	161	18	s	s	VERB
ejpam-4578	161	19	=	=	SYM
ejpam-4578	161	20	v	v	PROPN
ejpam-4578	161	21	(	(	PUNCT
ejpam-4578	161	22	k1	k1	NOUN
ejpam-4578	161	23	+	+	CCONJ
ejpam-4578	161	24	g	g	NOUN
ejpam-4578	161	25	)	)	PUNCT
ejpam-4578	161	26	\	\	PUNCT
ejpam-4578	162	1	c	c	NOUN
ejpam-4578	162	2	where	where	SCONJ
ejpam-4578	162	3	c	c	PROPN
ejpam-4578	162	4	is	be	AUX
ejpam-4578	162	5	a	a	DET
ejpam-4578	162	6	superclique	superclique	NOUN
ejpam-4578	162	7	in	in	ADP
ejpam-4578	162	8	g.	g.	PROPN
ejpam-4578	162	9	since	since	SCONJ
ejpam-4578	162	10	s	s	PROPN
ejpam-4578	162	11	is	be	AUX
ejpam-4578	162	12	a	a	DET
ejpam-4578	162	13	hop	hop	NOUN
ejpam-4578	162	14	dominating	dominating	NOUN
ejpam-4578	162	15	set	set	NOUN
ejpam-4578	162	16	of	of	ADP
ejpam-4578	162	17	k1	k1	NOUN
ejpam-4578	163	1	+	+	PROPN
ejpam-4578	163	2	g	g	NOUN
ejpam-4578	163	3	,	,	PUNCT
ejpam-4578	163	4	v	v	ADP
ejpam-4578	163	5	∈	∈	PROPN
ejpam-4578	163	6	s.	s.	PROPN
ejpam-4578	163	7	thus	thus	ADV
ejpam-4578	163	8	,	,	PUNCT
ejpam-4578	163	9	s	s	VERB
ejpam-4578	163	10	̸=	̸=	PROPN
ejpam-4578	163	11	v	v	NOUN
ejpam-4578	163	12	(	(	PUNCT
ejpam-4578	163	13	g	g	NOUN
ejpam-4578	163	14	)	)	PUNCT
ejpam-4578	163	15	and	and	CCONJ
ejpam-4578	163	16	s	s	VERB
ejpam-4578	163	17	̸=	̸=	PROPN
ejpam-4578	163	18	(	(	PUNCT
ejpam-4578	163	19	v	v	NOUN
ejpam-4578	163	20	(	(	PUNCT
ejpam-4578	163	21	g	g	NOUN
ejpam-4578	163	22	)	)	PUNCT
ejpam-4578	163	23	\	\	PUNCT
ejpam-4578	164	1	c	c	X
ejpam-4578	164	2	)	)	PUNCT
ejpam-4578	164	3	∪	∪	NOUN
ejpam-4578	164	4	{	{	PUNCT
ejpam-4578	164	5	x	x	SYM
ejpam-4578	164	6	∈	∈	PROPN
ejpam-4578	164	7	c	c	NOUN
ejpam-4578	164	8	:	:	PUNCT
ejpam-4578	164	9	degg(x	degg(x	X
ejpam-4578	164	10	)	)	PUNCT
ejpam-4578	164	11	=	=	PUNCT
ejpam-4578	164	12	n−	n−	NOUN
ejpam-4578	164	13	1	1	NUM
ejpam-4578	164	14	}	}	PUNCT
ejpam-4578	164	15	.	.	PUNCT
ejpam-4578	165	1	since	since	SCONJ
ejpam-4578	165	2	diam(k1	diam(k1	PROPN
ejpam-4578	165	3	+	+	PROPN
ejpam-4578	165	4	g	g	NOUN
ejpam-4578	165	5	)	)	PUNCT
ejpam-4578	165	6	≤	≤	NOUN
ejpam-4578	165	7	2	2	NUM
ejpam-4578	165	8	,	,	PUNCT
ejpam-4578	165	9	by	by	ADP
ejpam-4578	165	10	lemma	lemma	PROPN
ejpam-4578	165	11	1	1	NUM
ejpam-4578	165	12	and	and	CCONJ
ejpam-4578	165	13	proposition	proposition	NOUN
ejpam-4578	165	14	5	5	NUM
ejpam-4578	165	15	,	,	PUNCT
ejpam-4578	165	16	s	s	PART
ejpam-4578	165	17	=	=	SYM
ejpam-4578	165	18	v	v	PROPN
ejpam-4578	165	19	(	(	PUNCT
ejpam-4578	165	20	k1	k1	NOUN
ejpam-4578	165	21	+	+	PROPN
ejpam-4578	165	22	g	g	NOUN
ejpam-4578	165	23	)	)	PUNCT
ejpam-4578	165	24	\	\	PUNCT
ejpam-4578	166	1	c	c	NOUN
ejpam-4578	166	2	where	where	SCONJ
ejpam-4578	166	3	c	c	NOUN
ejpam-4578	166	4	=	=	SYM
ejpam-4578	166	5	∅	∅	NOUN
ejpam-4578	166	6	or	or	CCONJ
ejpam-4578	166	7	c	c	NOUN
ejpam-4578	166	8	is	be	AUX
ejpam-4578	166	9	a	a	DET
ejpam-4578	166	10	hop	hop	NOUN
ejpam-4578	166	11	dominated	dominate	VERB
ejpam-4578	166	12	superclique	superclique	NOUN
ejpam-4578	166	13	in	in	ADP
ejpam-4578	166	14	g.	g.	PROPN
ejpam-4578	166	15	the	the	DET
ejpam-4578	166	16	converse	converse	NOUN
ejpam-4578	166	17	follows	follow	VERB
ejpam-4578	166	18	immediately	immediately	ADV
ejpam-4578	166	19	from	from	ADP
ejpam-4578	166	20	lemma	lemma	PROPN
ejpam-4578	166	21	1	1	NUM
ejpam-4578	166	22	and	and	CCONJ
ejpam-4578	166	23	proposition	proposition	NOUN
ejpam-4578	166	24	5	5	NUM
ejpam-4578	166	25	.	.	PUNCT
ejpam-4578	167	1	the	the	DET
ejpam-4578	167	2	next	next	ADJ
ejpam-4578	167	3	result	result	NOUN
ejpam-4578	167	4	is	be	AUX
ejpam-4578	167	5	a	a	DET
ejpam-4578	167	6	consequence	consequence	NOUN
ejpam-4578	167	7	of	of	ADP
ejpam-4578	167	8	theorem	theorem	ADJ
ejpam-4578	167	9	4	4	NUM
ejpam-4578	167	10	.	.	PUNCT
ejpam-4578	167	11	corollary	corollary	ADJ
ejpam-4578	167	12	1	1	NUM
ejpam-4578	167	13	.	.	PUNCT
ejpam-4578	168	1	let	let	VERB
ejpam-4578	168	2	g	g	PRON
ejpam-4578	168	3	be	be	AUX
ejpam-4578	168	4	a	a	DET
ejpam-4578	168	5	connected	connected	ADJ
ejpam-4578	168	6	graph	graph	NOUN
ejpam-4578	168	7	of	of	ADP
ejpam-4578	168	8	order	order	NOUN
ejpam-4578	168	9	n.	n.	NOUN
ejpam-4578	168	10	then	then	ADV
ejpam-4578	168	11	γsrh(k1	γsrh(k1	VERB
ejpam-4578	168	12	+	+	ADV
ejpam-4578	168	13	g	g	NOUN
ejpam-4578	168	14	)	)	PUNCT
ejpam-4578	168	15	=	=	SYM
ejpam-4578	168	16	n+	n+	X
ejpam-4578	168	17	1−	1−	NUM
ejpam-4578	168	18	ωhs(g	ωhs(g	NUM
ejpam-4578	168	19	)	)	PUNCT
ejpam-4578	168	20	.	.	PUNCT
ejpam-4578	169	1	the	the	DET
ejpam-4578	169	2	next	next	ADJ
ejpam-4578	169	3	result	result	NOUN
ejpam-4578	169	4	follows	follow	VERB
ejpam-4578	169	5	immediately	immediately	ADV
ejpam-4578	169	6	from	from	ADP
ejpam-4578	169	7	theorem	theorem	ADJ
ejpam-4578	169	8	3	3	NUM
ejpam-4578	169	9	,	,	PUNCT
ejpam-4578	169	10	and	and	CCONJ
ejpam-4578	169	11	definitions	definition	NOUN
ejpam-4578	169	12	of	of	ADP
ejpam-4578	169	13	strong	strong	ADJ
ejpam-4578	169	14	resolving	resolve	VERB
ejpam-4578	169	15	hop	hop	NOUN
ejpam-4578	169	16	domination	domination	NOUN
ejpam-4578	169	17	and	and	CCONJ
ejpam-4578	169	18	k1	k1	PROPN
ejpam-4578	169	19	+	+	PROPN
ejpam-4578	169	20	g.	g.	PROPN
ejpam-4578	169	21	theorem	theorem	VERB
ejpam-4578	169	22	5	5	NUM
ejpam-4578	169	23	.	.	PUNCT
ejpam-4578	170	1	let	let	VERB
ejpam-4578	170	2	k1	k1	NOUN
ejpam-4578	170	3	=	=	PROPN
ejpam-4578	170	4	⟨v⟩	⟨v⟩	PROPN
ejpam-4578	170	5	and	and	CCONJ
ejpam-4578	170	6	g	g	PROPN
ejpam-4578	170	7	be	be	AUX
ejpam-4578	170	8	a	a	DET
ejpam-4578	170	9	disconnected	disconnected	ADJ
ejpam-4578	170	10	graph	graph	NOUN
ejpam-4578	170	11	whose	whose	DET
ejpam-4578	170	12	components	component	NOUN
ejpam-4578	170	13	are	be	AUX
ejpam-4578	170	14	gi	gi	ADJ
ejpam-4578	170	15	for	for	ADP
ejpam-4578	170	16	i	i	PROPN
ejpam-4578	170	17	=	=	NOUN
ejpam-4578	170	18	1	1	NUM
ejpam-4578	170	19	,	,	PUNCT
ejpam-4578	170	20	2	2	NUM
ejpam-4578	170	21	,	,	PUNCT
ejpam-4578	170	22	·	·	PUNCT
ejpam-4578	170	23	·	·	PUNCT
ejpam-4578	170	24	·	·	PUNCT
ejpam-4578	170	25	,	,	PUNCT
ejpam-4578	170	26	m.	m.	NOUN
ejpam-4578	170	27	a	a	DET
ejpam-4578	170	28	proper	proper	ADJ
ejpam-4578	170	29	subset	subset	NOUN
ejpam-4578	170	30	s	s	NOUN
ejpam-4578	170	31	of	of	ADP
ejpam-4578	170	32	v	v	NOUN
ejpam-4578	170	33	(	(	PUNCT
ejpam-4578	170	34	k1	k1	NOUN
ejpam-4578	170	35	+	+	NOUN
ejpam-4578	170	36	g	g	NOUN
ejpam-4578	170	37	)	)	PUNCT
ejpam-4578	170	38	is	be	AUX
ejpam-4578	170	39	a	a	DET
ejpam-4578	170	40	strong	strong	ADJ
ejpam-4578	170	41	resolving	resolve	VERB
ejpam-4578	170	42	hop	hop	NOUN
ejpam-4578	170	43	dominating	dominating	NOUN
ejpam-4578	170	44	set	set	NOUN
ejpam-4578	170	45	of	of	ADP
ejpam-4578	170	46	k1	k1	NOUN
ejpam-4578	170	47	+	+	CCONJ
ejpam-4578	170	48	g	g	NOUN
ejpam-4578	170	49	if	if	SCONJ
ejpam-4578	171	1	and	and	CCONJ
ejpam-4578	171	2	only	only	ADV
ejpam-4578	171	3	if	if	SCONJ
ejpam-4578	171	4	s	s	VERB
ejpam-4578	171	5	=	=	SYM
ejpam-4578	171	6	v	v	PROPN
ejpam-4578	171	7	(	(	PUNCT
ejpam-4578	171	8	k1	k1	NOUN
ejpam-4578	171	9	+	+	CCONJ
ejpam-4578	171	10	g	g	NOUN
ejpam-4578	171	11	)	)	PUNCT
ejpam-4578	171	12	\	\	PROPN
ejpam-4578	171	13	ci	ci	PROPN
ejpam-4578	171	14	where	where	SCONJ
ejpam-4578	171	15	ci	ci	PROPN
ejpam-4578	171	16	is	be	AUX
ejpam-4578	171	17	a	a	DET
ejpam-4578	171	18	superclique	superclique	NOUN
ejpam-4578	171	19	in	in	ADP
ejpam-4578	171	20	gi	gi	NOUN
ejpam-4578	171	21	for	for	ADP
ejpam-4578	171	22	some	some	DET
ejpam-4578	171	23	i	i	PRON
ejpam-4578	171	24	∈	∈	PROPN
ejpam-4578	171	25	{	{	PUNCT
ejpam-4578	171	26	1	1	NUM
ejpam-4578	171	27	,	,	PUNCT
ejpam-4578	171	28	2	2	NUM
ejpam-4578	171	29	,	,	PUNCT
ejpam-4578	171	30	·	·	PUNCT
ejpam-4578	171	31	·	·	PUNCT
ejpam-4578	171	32	·	·	PUNCT
ejpam-4578	171	33	,	,	PUNCT
ejpam-4578	171	34	m	m	NOUN
ejpam-4578	171	35	}	}	PUNCT
ejpam-4578	171	36	.	.	PUNCT
ejpam-4578	172	1	proof	proof	NOUN
ejpam-4578	172	2	:	:	PUNCT
ejpam-4578	172	3	suppose	suppose	VERB
ejpam-4578	172	4	s	s	NOUN
ejpam-4578	172	5	is	be	AUX
ejpam-4578	172	6	a	a	DET
ejpam-4578	172	7	strong	strong	ADJ
ejpam-4578	172	8	resolving	resolve	VERB
ejpam-4578	172	9	hop	hop	NOUN
ejpam-4578	172	10	dominating	dominate	VERB
ejpam-4578	172	11	proper	proper	ADJ
ejpam-4578	172	12	subset	subset	NOUN
ejpam-4578	172	13	of	of	ADP
ejpam-4578	172	14	k1	k1	PROPN
ejpam-4578	172	15	+	+	CCONJ
ejpam-4578	172	16	g.	g.	PROPN
ejpam-4578	172	17	by	by	ADP
ejpam-4578	172	18	theorem	theorem	NOUN
ejpam-4578	172	19	3	3	NUM
ejpam-4578	172	20	,	,	PUNCT
ejpam-4578	172	21	s	s	PART
ejpam-4578	172	22	=	=	SYM
ejpam-4578	172	23	v	v	X
ejpam-4578	172	24	(	(	PUNCT
ejpam-4578	172	25	g	g	NOUN
ejpam-4578	172	26	)	)	PUNCT
ejpam-4578	172	27	,	,	PUNCT
ejpam-4578	172	28	or	or	CCONJ
ejpam-4578	172	29	s	s	VERB
ejpam-4578	172	30	=	=	SYM
ejpam-4578	172	31	v	v	PROPN
ejpam-4578	172	32	(	(	PUNCT
ejpam-4578	172	33	g	g	NOUN
ejpam-4578	172	34	)	)	PUNCT
ejpam-4578	172	35	\ci	\ci	PROPN
ejpam-4578	172	36	or	or	CCONJ
ejpam-4578	172	37	s	s	NOUN
ejpam-4578	172	38	=	=	SYM
ejpam-4578	172	39	v	v	PROPN
ejpam-4578	172	40	(	(	PUNCT
ejpam-4578	172	41	k1+g	k1+g	NOUN
ejpam-4578	172	42	)	)	PUNCT
ejpam-4578	172	43	\ci	\ci	PROPN
ejpam-4578	172	44	where	where	SCONJ
ejpam-4578	172	45	ci	ci	PROPN
ejpam-4578	172	46	is	be	AUX
ejpam-4578	172	47	a	a	DET
ejpam-4578	172	48	superclique	superclique	NOUN
ejpam-4578	172	49	in	in	ADP
ejpam-4578	172	50	gi	gi	NOUN
ejpam-4578	172	51	for	for	ADP
ejpam-4578	172	52	some	some	DET
ejpam-4578	172	53	i	i	PRON
ejpam-4578	172	54	∈	∈	PROPN
ejpam-4578	172	55	{	{	PUNCT
ejpam-4578	172	56	1	1	NUM
ejpam-4578	172	57	,	,	PUNCT
ejpam-4578	172	58	2	2	NUM
ejpam-4578	172	59	,	,	PUNCT
ejpam-4578	172	60	·	·	PUNCT
ejpam-4578	172	61	·	·	PUNCT
ejpam-4578	172	62	·	·	PUNCT
ejpam-4578	172	63	,	,	PUNCT
ejpam-4578	172	64	m	m	NOUN
ejpam-4578	172	65	}	}	PUNCT
ejpam-4578	172	66	.	.	PUNCT
ejpam-4578	173	1	by	by	ADP
ejpam-4578	173	2	definition	definition	NOUN
ejpam-4578	173	3	of	of	ADP
ejpam-4578	173	4	strong	strong	ADJ
ejpam-4578	173	5	resolving	resolve	VERB
ejpam-4578	173	6	hop	hop	NOUN
ejpam-4578	173	7	domination	domination	NOUN
ejpam-4578	173	8	,	,	PUNCT
ejpam-4578	173	9	v	v	ADP
ejpam-4578	173	10	∈	∈	NOUN
ejpam-4578	173	11	s.	s.	PROPN
ejpam-4578	173	12	hence	hence	ADV
ejpam-4578	173	13	,	,	PUNCT
ejpam-4578	173	14	s	s	VERB
ejpam-4578	173	15	̸=	̸=	PROPN
ejpam-4578	173	16	v	v	NOUN
ejpam-4578	173	17	(	(	PUNCT
ejpam-4578	173	18	g	g	NOUN
ejpam-4578	173	19	)	)	PUNCT
ejpam-4578	173	20	and	and	CCONJ
ejpam-4578	173	21	s	s	VERB
ejpam-4578	173	22	̸=	̸=	PROPN
ejpam-4578	173	23	v	v	NOUN
ejpam-4578	173	24	(	(	PUNCT
ejpam-4578	173	25	g)\ci	g)\ci	PROPN
ejpam-4578	173	26	.	.	PUNCT
ejpam-4578	174	1	thus	thus	ADV
ejpam-4578	174	2	,	,	PUNCT
ejpam-4578	174	3	s	s	VERB
ejpam-4578	174	4	=	=	SYM
ejpam-4578	174	5	v	v	PROPN
ejpam-4578	174	6	(	(	PUNCT
ejpam-4578	174	7	k1+g)\ci	k1+g)\ci	PROPN
ejpam-4578	174	8	where	where	SCONJ
ejpam-4578	174	9	ci	ci	PROPN
ejpam-4578	174	10	is	be	AUX
ejpam-4578	174	11	a	a	DET
ejpam-4578	174	12	superclique	superclique	NOUN
ejpam-4578	174	13	in	in	ADP
ejpam-4578	174	14	gi	gi	NOUN
ejpam-4578	174	15	for	for	ADP
ejpam-4578	174	16	some	some	DET
ejpam-4578	174	17	i	i	PRON
ejpam-4578	174	18	∈	∈	PROPN
ejpam-4578	174	19	{	{	PUNCT
ejpam-4578	174	20	1	1	NUM
ejpam-4578	174	21	,	,	PUNCT
ejpam-4578	174	22	2	2	NUM
ejpam-4578	174	23	,	,	PUNCT
ejpam-4578	174	24	·	·	PUNCT
ejpam-4578	174	25	·	·	PUNCT
ejpam-4578	174	26	·	·	PUNCT
ejpam-4578	174	27	,	,	PUNCT
ejpam-4578	174	28	m	m	NOUN
ejpam-4578	174	29	}	}	PUNCT
ejpam-4578	174	30	.	.	PUNCT
ejpam-4578	175	1	conversely	conversely	ADV
ejpam-4578	175	2	,	,	PUNCT
ejpam-4578	175	3	suppose	suppose	VERB
ejpam-4578	175	4	s	s	VERB
ejpam-4578	175	5	=	=	SYM
ejpam-4578	175	6	v	v	PROPN
ejpam-4578	175	7	(	(	PUNCT
ejpam-4578	175	8	k1	k1	NOUN
ejpam-4578	175	9	+	+	CCONJ
ejpam-4578	175	10	g	g	NOUN
ejpam-4578	175	11	)	)	PUNCT
ejpam-4578	175	12	\	\	PROPN
ejpam-4578	175	13	ci	ci	PROPN
ejpam-4578	175	14	where	where	SCONJ
ejpam-4578	175	15	ci	ci	PROPN
ejpam-4578	175	16	is	be	AUX
ejpam-4578	175	17	a	a	DET
ejpam-4578	175	18	superclique	superclique	NOUN
ejpam-4578	175	19	in	in	ADP
ejpam-4578	175	20	gi	gi	NOUN
ejpam-4578	175	21	for	for	ADP
ejpam-4578	175	22	some	some	DET
ejpam-4578	175	23	i	i	PRON
ejpam-4578	175	24	∈	∈	PROPN
ejpam-4578	175	25	{	{	PUNCT
ejpam-4578	175	26	1	1	NUM
ejpam-4578	175	27	,	,	PUNCT
ejpam-4578	175	28	2	2	NUM
ejpam-4578	175	29	,	,	PUNCT
ejpam-4578	175	30	·	·	PUNCT
ejpam-4578	175	31	·	·	PUNCT
ejpam-4578	175	32	·	·	PUNCT
ejpam-4578	175	33	,	,	PUNCT
ejpam-4578	175	34	m	m	NOUN
ejpam-4578	175	35	}	}	PUNCT
ejpam-4578	175	36	.	.	PUNCT
ejpam-4578	176	1	let	let	VERB
ejpam-4578	176	2	x	x	SYM
ejpam-4578	176	3	∈	∈	PROPN
ejpam-4578	176	4	v	v	X
ejpam-4578	176	5	(	(	PUNCT
ejpam-4578	176	6	k1	k1	NOUN
ejpam-4578	176	7	+	+	CCONJ
ejpam-4578	176	8	g	g	NOUN
ejpam-4578	176	9	)	)	PUNCT
ejpam-4578	176	10	\	\	PUNCT
ejpam-4578	177	1	s.	s.	PROPN
ejpam-4578	177	2	then	then	ADV
ejpam-4578	177	3	x	x	PROPN
ejpam-4578	177	4	∈	∈	PROPN
ejpam-4578	177	5	ci	ci	NOUN
ejpam-4578	177	6	for	for	ADP
ejpam-4578	177	7	some	some	DET
ejpam-4578	177	8	i	i	PRON
ejpam-4578	177	9	∈	∈	PROPN
ejpam-4578	177	10	{	{	PUNCT
ejpam-4578	177	11	1	1	NUM
ejpam-4578	177	12	,	,	PUNCT
ejpam-4578	177	13	2	2	NUM
ejpam-4578	177	14	,	,	PUNCT
ejpam-4578	177	15	·	·	PUNCT
ejpam-4578	177	16	·	·	PUNCT
ejpam-4578	177	17	·	·	PUNCT
ejpam-4578	177	18	,	,	PUNCT
ejpam-4578	177	19	m	m	NOUN
ejpam-4578	177	20	}	}	PUNCT
ejpam-4578	177	21	.	.	PUNCT
ejpam-4578	178	1	since	since	SCONJ
ejpam-4578	178	2	m	m	PROPN
ejpam-4578	178	3	≥	≥	NUM
ejpam-4578	178	4	2	2	NUM
ejpam-4578	178	5	,	,	PUNCT
ejpam-4578	178	6	there	there	PRON
ejpam-4578	178	7	exists	exist	VERB
ejpam-4578	178	8	gj	gj	NOUN
ejpam-4578	178	9	,	,	PUNCT
ejpam-4578	178	10	j	j	PROPN
ejpam-4578	178	11	̸=	̸=	PROPN
ejpam-4578	178	12	i	i	PRON
ejpam-4578	178	13	and	and	CCONJ
ejpam-4578	178	14	vertex	vertex	NOUN
ejpam-4578	178	15	y	y	PROPN
ejpam-4578	178	16	∈	∈	PROPN
ejpam-4578	178	17	v	v	PROPN
ejpam-4578	178	18	(	(	PUNCT
ejpam-4578	178	19	gj	gj	NOUN
ejpam-4578	178	20	)	)	PUNCT
ejpam-4578	178	21	∩	∩	PROPN
ejpam-4578	178	22	nk1+g(x	nk1+g(x	NOUN
ejpam-4578	178	23	,	,	PUNCT
ejpam-4578	178	24	2	2	NUM
ejpam-4578	178	25	)	)	PUNCT
ejpam-4578	178	26	.	.	PUNCT
ejpam-4578	179	1	since	since	SCONJ
ejpam-4578	179	2	j.	j.	PROPN
ejpam-4578	179	3	mohamad	mohamad	PROPN
ejpam-4578	179	4	,	,	PUNCT
ejpam-4578	179	5	h.	h.	PROPN
ejpam-4578	179	6	rara	rara	PROPN
ejpam-4578	179	7	/	/	SYM
ejpam-4578	179	8	eur	eur	PROPN
ejpam-4578	179	9	.	.	PUNCT
ejpam-4578	180	1	j.	j.	PROPN
ejpam-4578	180	2	pure	pure	PROPN
ejpam-4578	180	3	appl	appl	PROPN
ejpam-4578	180	4	.	.	PROPN
ejpam-4578	180	5	math	math	PROPN
ejpam-4578	180	6	,	,	PUNCT
ejpam-4578	180	7	16	16	NUM
ejpam-4578	180	8	(	(	PUNCT
ejpam-4578	180	9	1	1	NUM
ejpam-4578	180	10	)	)	PUNCT
ejpam-4578	180	11	(	(	PUNCT
ejpam-4578	180	12	2023	2023	NUM
ejpam-4578	180	13	)	)	PUNCT
ejpam-4578	180	14	,	,	PUNCT
ejpam-4578	180	15	131	131	NUM
ejpam-4578	180	16	-	-	SYM
ejpam-4578	180	17	143	143	NUM
ejpam-4578	180	18	137	137	NUM
ejpam-4578	180	19	s	s	NOUN
ejpam-4578	180	20	=	=	X
ejpam-4578	180	21	v	v	PROPN
ejpam-4578	180	22	(	(	PUNCT
ejpam-4578	180	23	k1	k1	NOUN
ejpam-4578	180	24	+	+	CCONJ
ejpam-4578	180	25	g	g	NOUN
ejpam-4578	180	26	)	)	PUNCT
ejpam-4578	180	27	\	\	PROPN
ejpam-4578	180	28	ci	ci	PROPN
ejpam-4578	180	29	,	,	PUNCT
ejpam-4578	180	30	y	y	PROPN
ejpam-4578	180	31	∈	∈	PROPN
ejpam-4578	180	32	s	s	PART
ejpam-4578	180	33	∩	∩	NOUN
ejpam-4578	180	34	nk1+g(x	nk1+g(x	NOUN
ejpam-4578	180	35	,	,	PUNCT
ejpam-4578	180	36	2	2	NUM
ejpam-4578	180	37	)	)	PUNCT
ejpam-4578	180	38	.	.	PUNCT
ejpam-4578	181	1	therefore	therefore	ADV
ejpam-4578	181	2	,	,	PUNCT
ejpam-4578	181	3	s	s	VERB
ejpam-4578	181	4	is	be	AUX
ejpam-4578	181	5	a	a	DET
ejpam-4578	181	6	hop	hop	NOUN
ejpam-4578	181	7	dominating	dominating	NOUN
ejpam-4578	181	8	set	set	NOUN
ejpam-4578	181	9	of	of	ADP
ejpam-4578	181	10	k1	k1	PROPN
ejpam-4578	181	11	+	+	PROPN
ejpam-4578	181	12	g.	g.	PROPN
ejpam-4578	181	13	as	as	ADP
ejpam-4578	181	14	a	a	DET
ejpam-4578	181	15	consequence	consequence	NOUN
ejpam-4578	181	16	of	of	ADP
ejpam-4578	181	17	theorem	theorem	NOUN
ejpam-4578	181	18	5	5	NUM
ejpam-4578	181	19	,	,	PUNCT
ejpam-4578	181	20	the	the	DET
ejpam-4578	181	21	next	next	ADJ
ejpam-4578	181	22	result	result	NOUN
ejpam-4578	181	23	follows	follow	VERB
ejpam-4578	181	24	.	.	PUNCT
ejpam-4578	182	1	corollary	corollary	ADJ
ejpam-4578	182	2	2	2	NUM
ejpam-4578	182	3	.	.	PUNCT
ejpam-4578	183	1	let	let	VERB
ejpam-4578	183	2	gi	gi	PART
ejpam-4578	183	3	be	be	AUX
ejpam-4578	183	4	connected	connect	VERB
ejpam-4578	183	5	graphs	graph	NOUN
ejpam-4578	183	6	of	of	ADP
ejpam-4578	183	7	orders	order	NOUN
ejpam-4578	183	8	ni	ni	PROPN
ejpam-4578	183	9	and	and	CCONJ
ejpam-4578	183	10	g	g	PROPN
ejpam-4578	183	11	be	be	VERB
ejpam-4578	183	12	a	a	DET
ejpam-4578	183	13	disconnected	disconnected	ADJ
ejpam-4578	183	14	graph	graph	NOUN
ejpam-4578	183	15	whose	whose	DET
ejpam-4578	183	16	components	component	NOUN
ejpam-4578	183	17	are	be	AUX
ejpam-4578	183	18	gi	gi	ADJ
ejpam-4578	183	19	for	for	ADP
ejpam-4578	183	20	i	i	PROPN
ejpam-4578	183	21	=	=	NOUN
ejpam-4578	183	22	1	1	NUM
ejpam-4578	183	23	,	,	PUNCT
ejpam-4578	183	24	2	2	NUM
ejpam-4578	183	25	,	,	PUNCT
ejpam-4578	183	26	·	·	PUNCT
ejpam-4578	183	27	·	·	PUNCT
ejpam-4578	183	28	·	·	PUNCT
ejpam-4578	183	29	,	,	PUNCT
ejpam-4578	183	30	m.	m.	NOUN
ejpam-4578	183	31	then	then	ADV
ejpam-4578	183	32	γsrh(k1	γsrh(k1	VERB
ejpam-4578	183	33	+	+	ADV
ejpam-4578	183	34	g	g	NOUN
ejpam-4578	183	35	)	)	PUNCT
ejpam-4578	184	1	=	=	PUNCT
ejpam-4578	184	2	m∑	m∑	CCONJ
ejpam-4578	184	3	i=1	i=1	PROPN
ejpam-4578	184	4	ni	ni	PROPN
ejpam-4578	184	5	−max	−max	PRON
ejpam-4578	184	6	{	{	PUNCT
ejpam-4578	184	7	ωhs(gi)(i	ωhs(gi)(i	NOUN
ejpam-4578	184	8	=	=	SYM
ejpam-4578	184	9	1	1	NUM
ejpam-4578	184	10	,	,	PUNCT
ejpam-4578	184	11	2	2	NUM
ejpam-4578	184	12	,	,	PUNCT
ejpam-4578	184	13	·	·	PUNCT
ejpam-4578	184	14	·	·	PUNCT
ejpam-4578	184	15	·	·	PUNCT
ejpam-4578	184	16	,	,	PUNCT
ejpam-4578	184	17	m	m	NOUN
ejpam-4578	184	18	)	)	PUNCT
ejpam-4578	184	19	}	}	PUNCT
ejpam-4578	184	20	.	.	PUNCT
ejpam-4578	185	1	theorem	theorem	NOUN
ejpam-4578	185	2	6	6	NUM
ejpam-4578	185	3	.	.	PUNCT
ejpam-4578	186	1	let	let	VERB
ejpam-4578	186	2	g	g	NOUN
ejpam-4578	186	3	and	and	CCONJ
ejpam-4578	186	4	h	h	NOUN
ejpam-4578	186	5	be	be	AUX
ejpam-4578	186	6	nontrivial	nontrivial	ADJ
ejpam-4578	186	7	connected	connected	ADJ
ejpam-4578	186	8	graphs	graph	NOUN
ejpam-4578	186	9	.	.	PUNCT
ejpam-4578	187	1	a	a	DET
ejpam-4578	187	2	proper	proper	ADJ
ejpam-4578	187	3	subset	subset	NOUN
ejpam-4578	187	4	s	s	NOUN
ejpam-4578	187	5	of	of	ADP
ejpam-4578	187	6	v	v	NOUN
ejpam-4578	187	7	(	(	PUNCT
ejpam-4578	187	8	g+h	g+h	PROPN
ejpam-4578	187	9	)	)	PUNCT
ejpam-4578	187	10	is	be	AUX
ejpam-4578	187	11	a	a	DET
ejpam-4578	187	12	strong	strong	ADJ
ejpam-4578	187	13	resolving	resolve	VERB
ejpam-4578	187	14	hop	hop	NOUN
ejpam-4578	187	15	dominating	dominating	NOUN
ejpam-4578	187	16	set	set	NOUN
ejpam-4578	187	17	of	of	ADP
ejpam-4578	187	18	g+h	g+h	PROPN
ejpam-4578	187	19	if	if	SCONJ
ejpam-4578	187	20	and	and	CCONJ
ejpam-4578	187	21	only	only	ADV
ejpam-4578	187	22	if	if	SCONJ
ejpam-4578	187	23	at	at	ADV
ejpam-4578	187	24	least	least	ADJ
ejpam-4578	187	25	one	one	NUM
ejpam-4578	187	26	of	of	ADP
ejpam-4578	187	27	the	the	DET
ejpam-4578	187	28	following	follow	VERB
ejpam-4578	187	29	is	be	AUX
ejpam-4578	187	30	satisfied	satisfied	ADJ
ejpam-4578	187	31	:	:	PUNCT
ejpam-4578	187	32	(	(	PUNCT
ejpam-4578	187	33	i	i	NOUN
ejpam-4578	187	34	)	)	PUNCT
ejpam-4578	187	35	s	s	PART
ejpam-4578	187	36	=	=	SYM
ejpam-4578	187	37	v	v	PROPN
ejpam-4578	187	38	(	(	PUNCT
ejpam-4578	187	39	g+h	g+h	NOUN
ejpam-4578	187	40	)	)	PUNCT
ejpam-4578	187	41	\	\	PROPN
ejpam-4578	188	1	cg	cg	NOUN
ejpam-4578	188	2	where	where	SCONJ
ejpam-4578	188	3	cg	cg	NOUN
ejpam-4578	188	4	is	be	AUX
ejpam-4578	188	5	a	a	DET
ejpam-4578	188	6	hop	hop	NOUN
ejpam-4578	188	7	dominated	dominate	VERB
ejpam-4578	188	8	superclique	superclique	NOUN
ejpam-4578	188	9	in	in	ADP
ejpam-4578	188	10	g.	g.	PROPN
ejpam-4578	188	11	(	(	PUNCT
ejpam-4578	188	12	ii	ii	PROPN
ejpam-4578	188	13	)	)	PUNCT
ejpam-4578	188	14	s	s	PART
ejpam-4578	188	15	=	=	SYM
ejpam-4578	188	16	v	v	PROPN
ejpam-4578	188	17	(	(	PUNCT
ejpam-4578	188	18	g+h	g+h	NOUN
ejpam-4578	188	19	)	)	PUNCT
ejpam-4578	188	20	\	\	PROPN
ejpam-4578	189	1	ch	ch	NOUN
ejpam-4578	189	2	where	where	SCONJ
ejpam-4578	189	3	ch	ch	NOUN
ejpam-4578	189	4	is	be	AUX
ejpam-4578	189	5	a	a	DET
ejpam-4578	189	6	hop	hop	NOUN
ejpam-4578	189	7	dominated	dominate	VERB
ejpam-4578	189	8	superclique	superclique	NOUN
ejpam-4578	189	9	in	in	ADP
ejpam-4578	189	10	h.	h.	PROPN
ejpam-4578	189	11	(	(	PUNCT
ejpam-4578	189	12	iii	iii	NOUN
ejpam-4578	189	13	)	)	PUNCT
ejpam-4578	189	14	s	s	PART
ejpam-4578	189	15	=	=	SYM
ejpam-4578	189	16	v	v	PROPN
ejpam-4578	189	17	(	(	PUNCT
ejpam-4578	189	18	g+h	g+h	NOUN
ejpam-4578	189	19	)	)	PUNCT
ejpam-4578	189	20	\	\	PUNCT
ejpam-4578	190	1	(	(	PUNCT
ejpam-4578	190	2	cg	cg	NOUN
ejpam-4578	190	3	∪ch	∪ch	PROPN
ejpam-4578	190	4	)	)	PUNCT
ejpam-4578	190	5	where	where	SCONJ
ejpam-4578	190	6	cg	cg	NOUN
ejpam-4578	190	7	and	and	CCONJ
ejpam-4578	190	8	ch	ch	NOUN
ejpam-4578	190	9	are	be	AUX
ejpam-4578	190	10	hop	hop	ADV
ejpam-4578	190	11	dominated	dominate	VERB
ejpam-4578	190	12	supercliques	superclique	NOUN
ejpam-4578	190	13	of	of	ADP
ejpam-4578	190	14	g	g	PROPN
ejpam-4578	190	15	and	and	CCONJ
ejpam-4578	190	16	h	h	NOUN
ejpam-4578	190	17	,	,	PUNCT
ejpam-4578	190	18	respectively	respectively	ADV
ejpam-4578	190	19	.	.	PUNCT
ejpam-4578	191	1	proof	proof	NOUN
ejpam-4578	191	2	:	:	PUNCT
ejpam-4578	191	3	note	note	VERB
ejpam-4578	191	4	that	that	SCONJ
ejpam-4578	191	5	diam(g	diam(g	PROPN
ejpam-4578	191	6	+	+	NOUN
ejpam-4578	191	7	h	h	NOUN
ejpam-4578	191	8	)	)	PUNCT
ejpam-4578	191	9	≤	≤	NUM
ejpam-4578	191	10	2	2	NUM
ejpam-4578	191	11	and	and	CCONJ
ejpam-4578	191	12	cg	cg	NOUN
ejpam-4578	191	13	,	,	PUNCT
ejpam-4578	191	14	ch	ch	NOUN
ejpam-4578	191	15	,	,	PUNCT
ejpam-4578	191	16	and	and	CCONJ
ejpam-4578	191	17	(	(	PUNCT
ejpam-4578	191	18	cg	cg	NOUN
ejpam-4578	191	19	∪	∪	PROPN
ejpam-4578	191	20	ch	ch	NOUN
ejpam-4578	191	21	)	)	PUNCT
ejpam-4578	191	22	are	be	AUX
ejpam-4578	191	23	hop	hop	ADV
ejpam-4578	191	24	dominated	dominate	VERB
ejpam-4578	191	25	supercliques	superclique	NOUN
ejpam-4578	191	26	in	in	ADP
ejpam-4578	191	27	g+h	g+h	PROPN
ejpam-4578	191	28	.	.	PUNCT
ejpam-4578	192	1	then	then	ADV
ejpam-4578	192	2	by	by	ADP
ejpam-4578	192	3	lemma	lemma	PROPN
ejpam-4578	192	4	1	1	NUM
ejpam-4578	192	5	,	,	PUNCT
ejpam-4578	192	6	the	the	DET
ejpam-4578	192	7	theorem	theorem	NOUN
ejpam-4578	192	8	holds	hold	VERB
ejpam-4578	192	9	.	.	PUNCT
ejpam-4578	193	1	the	the	DET
ejpam-4578	193	2	next	next	ADJ
ejpam-4578	193	3	result	result	NOUN
ejpam-4578	193	4	is	be	AUX
ejpam-4578	193	5	a	a	DET
ejpam-4578	193	6	consequence	consequence	NOUN
ejpam-4578	193	7	of	of	ADP
ejpam-4578	193	8	theorem	theorem	ADJ
ejpam-4578	193	9	6	6	NUM
ejpam-4578	193	10	.	.	PUNCT
ejpam-4578	193	11	corollary	corollary	ADJ
ejpam-4578	193	12	3	3	X
ejpam-4578	193	13	.	.	PUNCT
ejpam-4578	194	1	let	let	VERB
ejpam-4578	194	2	g	g	NOUN
ejpam-4578	194	3	and	and	CCONJ
ejpam-4578	194	4	h	h	NOUN
ejpam-4578	194	5	be	be	AUX
ejpam-4578	194	6	nontrivial	nontrivial	ADJ
ejpam-4578	194	7	connected	connect	VERB
ejpam-4578	194	8	graphs	graph	NOUN
ejpam-4578	194	9	of	of	ADP
ejpam-4578	194	10	orders	order	NOUN
ejpam-4578	194	11	m	m	VERB
ejpam-4578	194	12	and	and	CCONJ
ejpam-4578	194	13	n	n	CCONJ
ejpam-4578	194	14	,	,	PUNCT
ejpam-4578	194	15	respectively	respectively	ADV
ejpam-4578	194	16	.	.	PUNCT
ejpam-4578	195	1	then	then	ADV
ejpam-4578	195	2	γsrh(g+h	γsrh(g+h	PROPN
ejpam-4578	195	3	)	)	PUNCT
ejpam-4578	196	1	=	=	SYM
ejpam-4578	197	1	m+	m+	NUM
ejpam-4578	197	2	n−	n−	PROPN
ejpam-4578	197	3	(	(	PUNCT
ejpam-4578	197	4	ωhs(g	ωhs(g	PROPN
ejpam-4578	197	5	)	)	PUNCT
ejpam-4578	197	6	+	+	CCONJ
ejpam-4578	197	7	ωhs(h	ωhs(h	PROPN
ejpam-4578	197	8	)	)	PUNCT
ejpam-4578	197	9	)	)	PUNCT
ejpam-4578	197	10	.	.	PUNCT
ejpam-4578	198	1	4	4	X
ejpam-4578	198	2	.	.	X
ejpam-4578	198	3	on	on	ADP
ejpam-4578	198	4	strong	strong	ADJ
ejpam-4578	198	5	resolving	resolve	VERB
ejpam-4578	198	6	hop	hop	NOUN
ejpam-4578	198	7	domination	domination	NOUN
ejpam-4578	198	8	in	in	ADP
ejpam-4578	198	9	the	the	DET
ejpam-4578	198	10	corona	corona	NOUN
ejpam-4578	198	11	of	of	ADP
ejpam-4578	198	12	graphs	graph	NOUN
ejpam-4578	198	13	the	the	DET
ejpam-4578	198	14	corona	corona	NOUN
ejpam-4578	198	15	of	of	ADP
ejpam-4578	198	16	two	two	NUM
ejpam-4578	198	17	graphs	graph	NOUN
ejpam-4578	198	18	g	g	NOUN
ejpam-4578	198	19	and	and	CCONJ
ejpam-4578	198	20	h	h	NOUN
ejpam-4578	198	21	,	,	PUNCT
ejpam-4578	198	22	denoted	denote	VERB
ejpam-4578	198	23	by	by	ADP
ejpam-4578	198	24	g	g	PROPN
ejpam-4578	198	25	◦	◦	NOUN
ejpam-4578	198	26	h	h	NOUN
ejpam-4578	198	27	,	,	PUNCT
ejpam-4578	198	28	is	be	AUX
ejpam-4578	198	29	the	the	DET
ejpam-4578	198	30	graph	graph	NOUN
ejpam-4578	198	31	obtained	obtain	VERB
ejpam-4578	198	32	by	by	ADP
ejpam-4578	198	33	taking	take	VERB
ejpam-4578	198	34	one	one	NUM
ejpam-4578	198	35	copy	copy	NOUN
ejpam-4578	198	36	of	of	ADP
ejpam-4578	198	37	g	g	NOUN
ejpam-4578	198	38	of	of	ADP
ejpam-4578	198	39	order	order	NOUN
ejpam-4578	198	40	n	n	NOUN
ejpam-4578	198	41	and	and	CCONJ
ejpam-4578	198	42	n	n	PRON
ejpam-4578	198	43	copies	copy	NOUN
ejpam-4578	198	44	of	of	ADP
ejpam-4578	198	45	h	h	NOUN
ejpam-4578	198	46	,	,	PUNCT
ejpam-4578	198	47	and	and	CCONJ
ejpam-4578	198	48	then	then	ADV
ejpam-4578	198	49	joining	join	VERB
ejpam-4578	198	50	every	every	DET
ejpam-4578	198	51	vertex	vertex	NOUN
ejpam-4578	198	52	of	of	ADP
ejpam-4578	198	53	the	the	DET
ejpam-4578	198	54	ith	ith	PROPN
ejpam-4578	198	55	copy	copy	NOUN
ejpam-4578	198	56	of	of	ADP
ejpam-4578	198	57	h	h	NOUN
ejpam-4578	198	58	to	to	ADP
ejpam-4578	198	59	the	the	DET
ejpam-4578	198	60	ith	ith	PROPN
ejpam-4578	198	61	vertex	vertex	NOUN
ejpam-4578	198	62	of	of	ADP
ejpam-4578	198	63	g.	g.	PROPN
ejpam-4578	198	64	for	for	ADP
ejpam-4578	198	65	v	v	NOUN
ejpam-4578	198	66	∈	∈	PROPN
ejpam-4578	198	67	v	v	NOUN
ejpam-4578	198	68	(	(	PUNCT
ejpam-4578	198	69	g	g	NOUN
ejpam-4578	198	70	)	)	PUNCT
ejpam-4578	198	71	,	,	PUNCT
ejpam-4578	198	72	denote	denote	VERB
ejpam-4578	198	73	by	by	ADP
ejpam-4578	198	74	hv	hv	PROPN
ejpam-4578	198	75	the	the	DET
ejpam-4578	198	76	copy	copy	NOUN
ejpam-4578	198	77	of	of	ADP
ejpam-4578	198	78	h	h	NOUN
ejpam-4578	198	79	whose	whose	DET
ejpam-4578	198	80	vertices	vertex	NOUN
ejpam-4578	198	81	are	be	AUX
ejpam-4578	198	82	attached	attach	VERB
ejpam-4578	198	83	one	one	NUM
ejpam-4578	198	84	by	by	ADP
ejpam-4578	198	85	one	one	NUM
ejpam-4578	198	86	to	to	ADP
ejpam-4578	198	87	the	the	DET
ejpam-4578	198	88	vertex	vertex	NOUN
ejpam-4578	198	89	v.	v.	ADP
ejpam-4578	198	90	subsequently	subsequently	ADV
ejpam-4578	198	91	,	,	PUNCT
ejpam-4578	198	92	denote	denote	VERB
ejpam-4578	198	93	by	by	ADP
ejpam-4578	198	94	v+hv	v+hv	NOUN
ejpam-4578	198	95	the	the	DET
ejpam-4578	198	96	subgraph	subgraph	NOUN
ejpam-4578	198	97	of	of	ADP
ejpam-4578	198	98	the	the	DET
ejpam-4578	198	99	corona	corona	NOUN
ejpam-4578	198	100	g	g	PROPN
ejpam-4578	198	101	◦	◦	NOUN
ejpam-4578	198	102	h	h	NOUN
ejpam-4578	198	103	corresponding	correspond	VERB
ejpam-4578	198	104	to	to	ADP
ejpam-4578	198	105	the	the	DET
ejpam-4578	198	106	join	join	NOUN
ejpam-4578	198	107	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4578	198	108	,	,	PUNCT
ejpam-4578	198	109	v	v	PROPN
ejpam-4578	198	110	∈	∈	PROPN
ejpam-4578	198	111	v	v	NOUN
ejpam-4578	198	112	(	(	PUNCT
ejpam-4578	198	113	g	g	NOUN
ejpam-4578	198	114	)	)	PUNCT
ejpam-4578	198	115	.	.	PUNCT
ejpam-4578	199	1	theorem	theorem	VERB
ejpam-4578	199	2	7	7	NUM
ejpam-4578	199	3	.	.	PUNCT
ejpam-4578	200	1	[	[	X
ejpam-4578	200	2	1	1	X
ejpam-4578	200	3	]	]	PUNCT
ejpam-4578	200	4	let	let	VERB
ejpam-4578	200	5	g	g	PRON
ejpam-4578	200	6	be	be	AUX
ejpam-4578	200	7	a	a	DET
ejpam-4578	200	8	non	non	ADJ
ejpam-4578	200	9	-	-	ADJ
ejpam-4578	200	10	trivial	trivial	ADJ
ejpam-4578	200	11	connected	connected	ADJ
ejpam-4578	200	12	graph	graph	NOUN
ejpam-4578	200	13	and	and	CCONJ
ejpam-4578	200	14	h	h	NOUN
ejpam-4578	200	15	a	a	DET
ejpam-4578	200	16	connected	connected	ADJ
ejpam-4578	200	17	graph	graph	NOUN
ejpam-4578	200	18	.	.	PUNCT
ejpam-4578	201	1	a	a	DET
ejpam-4578	201	2	proper	proper	ADJ
ejpam-4578	201	3	subset	subset	NOUN
ejpam-4578	201	4	s	s	NOUN
ejpam-4578	201	5	of	of	ADP
ejpam-4578	201	6	v	v	NOUN
ejpam-4578	201	7	(	(	PUNCT
ejpam-4578	201	8	g	g	PROPN
ejpam-4578	201	9	◦	◦	NOUN
ejpam-4578	201	10	h	h	NOUN
ejpam-4578	201	11	)	)	PUNCT
ejpam-4578	201	12	is	be	AUX
ejpam-4578	201	13	a	a	DET
ejpam-4578	201	14	strong	strong	ADJ
ejpam-4578	201	15	resolving	resolving	NOUN
ejpam-4578	201	16	dominating	dominating	NOUN
ejpam-4578	201	17	set	set	NOUN
ejpam-4578	201	18	of	of	ADP
ejpam-4578	201	19	g	g	PROPN
ejpam-4578	201	20	◦	◦	NOUN
ejpam-4578	201	21	h	h	NOUN
ejpam-4578	201	22	if	if	SCONJ
ejpam-4578	202	1	and	and	CCONJ
ejpam-4578	202	2	only	only	ADV
ejpam-4578	202	3	if	if	SCONJ
ejpam-4578	202	4	one	one	NUM
ejpam-4578	202	5	of	of	ADP
ejpam-4578	202	6	the	the	DET
ejpam-4578	202	7	following	follow	VERB
ejpam-4578	202	8	holds	hold	VERB
ejpam-4578	202	9	:	:	PUNCT
ejpam-4578	202	10	(	(	PUNCT
ejpam-4578	202	11	i	i	NOUN
ejpam-4578	202	12	)	)	PUNCT
ejpam-4578	202	13	s	s	PART
ejpam-4578	202	14	=	=	NOUN
ejpam-4578	202	15	a	a	DET
ejpam-4578	202	16	⋃	⋃	PROPN
ejpam-4578	202	17	(	(	PUNCT
ejpam-4578	202	18	⋃	⋃	NOUN
ejpam-4578	202	19	u∈v	u∈v	NOUN
ejpam-4578	202	20	(	(	PUNCT
ejpam-4578	202	21	g	g	NOUN
ejpam-4578	202	22	)	)	PUNCT
ejpam-4578	202	23	v	v	NOUN
ejpam-4578	202	24	(	(	PUNCT
ejpam-4578	202	25	hu	hu	PROPN
ejpam-4578	202	26	)	)	PUNCT
ejpam-4578	202	27	)	)	PUNCT
ejpam-4578	202	28	where	where	SCONJ
ejpam-4578	202	29	a	a	DET
ejpam-4578	202	30	⊆	⊆	NUM
ejpam-4578	202	31	v	v	NOUN
ejpam-4578	202	32	(	(	PUNCT
ejpam-4578	202	33	g	g	NOUN
ejpam-4578	202	34	)	)	PUNCT
ejpam-4578	202	35	;	;	PUNCT
ejpam-4578	202	36	(	(	PUNCT
ejpam-4578	202	37	ii	ii	NOUN
ejpam-4578	202	38	)	)	PUNCT
ejpam-4578	202	39	s	s	PART
ejpam-4578	202	40	=	=	PUNCT
ejpam-4578	202	41	a	a	DET
ejpam-4578	202	42	⋃	⋃	PROPN
ejpam-4578	202	43	(	(	PUNCT
ejpam-4578	202	44	⋃	⋃	NOUN
ejpam-4578	202	45	u∈v	u∈v	NOUN
ejpam-4578	202	46	(	(	PUNCT
ejpam-4578	202	47	g)\{v	g)\{v	PROPN
ejpam-4578	202	48	}	}	PUNCT
ejpam-4578	202	49	v	v	PROPN
ejpam-4578	202	50	(	(	PUNCT
ejpam-4578	202	51	hu	hu	PROPN
ejpam-4578	202	52	)	)	PUNCT
ejpam-4578	202	53	)	)	PUNCT
ejpam-4578	203	1	⋃	⋃	PUNCT
ejpam-4578	203	2	bv	bv	PROPN
ejpam-4578	203	3	for	for	ADP
ejpam-4578	203	4	a	a	DET
ejpam-4578	203	5	unique	unique	ADJ
ejpam-4578	203	6	vertex	vertex	NOUN
ejpam-4578	203	7	v	v	NOUN
ejpam-4578	203	8	in	in	ADP
ejpam-4578	203	9	g	g	PROPN
ejpam-4578	203	10	,	,	PUNCT
ejpam-4578	203	11	where	where	SCONJ
ejpam-4578	203	12	a	a	DET
ejpam-4578	203	13	⊆	⊆	NUM
ejpam-4578	203	14	v	v	NOUN
ejpam-4578	203	15	(	(	PUNCT
ejpam-4578	203	16	g	g	NOUN
ejpam-4578	203	17	)	)	PUNCT
ejpam-4578	203	18	and	and	CCONJ
ejpam-4578	203	19	bv	bv	PROPN
ejpam-4578	203	20	is	be	AUX
ejpam-4578	203	21	a	a	DET
ejpam-4578	203	22	strong	strong	ADJ
ejpam-4578	203	23	resolving	resolving	NOUN
ejpam-4578	203	24	set	set	NOUN
ejpam-4578	203	25	of	of	ADP
ejpam-4578	203	26	hv	hv	PROPN
ejpam-4578	203	27	if	if	SCONJ
ejpam-4578	203	28	γ(h	γ(h	NOUN
ejpam-4578	203	29	)	)	PUNCT
ejpam-4578	203	30	=	=	SYM
ejpam-4578	203	31	1	1	NUM
ejpam-4578	203	32	or	or	CCONJ
ejpam-4578	203	33	bv	bv	PROPN
ejpam-4578	203	34	is	be	AUX
ejpam-4578	203	35	a	a	DET
ejpam-4578	203	36	resolving	resolving	NOUN
ejpam-4578	203	37	set	set	NOUN
ejpam-4578	203	38	of	of	ADP
ejpam-4578	203	39	⟨v⟩	⟨v⟩	PROPN
ejpam-4578	204	1	+	+	PROPN
ejpam-4578	204	2	hv	hv	PROPN
ejpam-4578	204	3	if	if	SCONJ
ejpam-4578	204	4	γ(h	γ(h	NOUN
ejpam-4578	204	5	)	)	PUNCT
ejpam-4578	204	6	̸=	̸=	PROPN
ejpam-4578	204	7	1	1	NUM
ejpam-4578	204	8	.	.	PUNCT
ejpam-4578	204	9	j.	j.	PROPN
ejpam-4578	204	10	mohamad	mohamad	PROPN
ejpam-4578	204	11	,	,	PUNCT
ejpam-4578	204	12	h.	h.	PROPN
ejpam-4578	204	13	rara	rara	PROPN
ejpam-4578	204	14	/	/	SYM
ejpam-4578	204	15	eur	eur	PROPN
ejpam-4578	204	16	.	.	PUNCT
ejpam-4578	205	1	j.	j.	PROPN
ejpam-4578	205	2	pure	pure	PROPN
ejpam-4578	205	3	appl	appl	PROPN
ejpam-4578	205	4	.	.	PROPN
ejpam-4578	205	5	math	math	PROPN
ejpam-4578	205	6	,	,	PUNCT
ejpam-4578	205	7	16	16	NUM
ejpam-4578	205	8	(	(	PUNCT
ejpam-4578	205	9	1	1	NUM
ejpam-4578	205	10	)	)	PUNCT
ejpam-4578	205	11	(	(	PUNCT
ejpam-4578	205	12	2023	2023	NUM
ejpam-4578	205	13	)	)	PUNCT
ejpam-4578	205	14	,	,	PUNCT
ejpam-4578	205	15	131	131	NUM
ejpam-4578	205	16	-	-	SYM
ejpam-4578	205	17	143	143	NUM
ejpam-4578	205	18	138	138	NUM
ejpam-4578	205	19	theorem	theorem	NOUN
ejpam-4578	205	20	8	8	NUM
ejpam-4578	205	21	.	.	PUNCT
ejpam-4578	206	1	let	let	VERB
ejpam-4578	206	2	g	g	PRON
ejpam-4578	206	3	be	be	AUX
ejpam-4578	206	4	a	a	DET
ejpam-4578	206	5	nontrivial	nontrivial	ADJ
ejpam-4578	206	6	connected	connect	VERB
ejpam-4578	206	7	graph	graph	NOUN
ejpam-4578	206	8	and	and	CCONJ
ejpam-4578	206	9	h	h	NOUN
ejpam-4578	206	10	a	a	DET
ejpam-4578	206	11	connected	connected	ADJ
ejpam-4578	206	12	graph	graph	NOUN
ejpam-4578	206	13	.	.	PUNCT
ejpam-4578	207	1	a	a	DET
ejpam-4578	207	2	proper	proper	ADJ
ejpam-4578	207	3	subset	subset	NOUN
ejpam-4578	207	4	s	s	NOUN
ejpam-4578	207	5	of	of	ADP
ejpam-4578	207	6	v	v	NOUN
ejpam-4578	207	7	(	(	PUNCT
ejpam-4578	207	8	g	g	PROPN
ejpam-4578	207	9	◦	◦	NOUN
ejpam-4578	207	10	h	h	NOUN
ejpam-4578	207	11	)	)	PUNCT
ejpam-4578	207	12	is	be	AUX
ejpam-4578	207	13	a	a	DET
ejpam-4578	207	14	strong	strong	ADJ
ejpam-4578	207	15	resolving	resolve	VERB
ejpam-4578	207	16	hop	hop	NOUN
ejpam-4578	207	17	dominating	dominating	NOUN
ejpam-4578	207	18	set	set	NOUN
ejpam-4578	207	19	of	of	ADP
ejpam-4578	207	20	g	g	PROPN
ejpam-4578	207	21	◦	◦	NOUN
ejpam-4578	207	22	h	h	NOUN
ejpam-4578	207	23	if	if	SCONJ
ejpam-4578	208	1	and	and	CCONJ
ejpam-4578	208	2	only	only	ADV
ejpam-4578	208	3	if	if	SCONJ
ejpam-4578	208	4	one	one	NUM
ejpam-4578	208	5	of	of	ADP
ejpam-4578	208	6	the	the	DET
ejpam-4578	208	7	following	follow	VERB
ejpam-4578	208	8	holds	hold	VERB
ejpam-4578	208	9	:	:	PUNCT
ejpam-4578	208	10	(	(	PUNCT
ejpam-4578	208	11	i	i	NOUN
ejpam-4578	208	12	)	)	PUNCT
ejpam-4578	208	13	s	s	AUX
ejpam-4578	208	14	=	=	PUNCT
ejpam-4578	208	15	a	a	PRON
ejpam-4578	208	16	∪	∪	ADJ
ejpam-4578	208	17			PROPN
ejpam-4578	208	18	⋃	⋃	ADJ
ejpam-4578	208	19	v∈v	v∈v	NOUN
ejpam-4578	208	20	(	(	PUNCT
ejpam-4578	208	21	g	g	NOUN
ejpam-4578	208	22	)	)	PUNCT
ejpam-4578	208	23	v	v	NOUN
ejpam-4578	208	24	(	(	PUNCT
ejpam-4578	208	25	hv	hv	PROPN
ejpam-4578	208	26	)	)	PUNCT
ejpam-4578	208	27			PROPN
ejpam-4578	208	28	where	where	SCONJ
ejpam-4578	208	29	a	a	DET
ejpam-4578	208	30	⊆	⊆	NUM
ejpam-4578	208	31	v	v	NOUN
ejpam-4578	208	32	(	(	PUNCT
ejpam-4578	208	33	g	g	NOUN
ejpam-4578	208	34	)	)	PUNCT
ejpam-4578	208	35	;	;	PUNCT
ejpam-4578	208	36	(	(	PUNCT
ejpam-4578	208	37	ii	ii	NOUN
ejpam-4578	208	38	)	)	PUNCT
ejpam-4578	208	39	s	s	PART
ejpam-4578	208	40	=	=	PUNCT
ejpam-4578	208	41	a	a	PRON
ejpam-4578	208	42	∪	∪	ADJ
ejpam-4578	208	43			PROPN
ejpam-4578	208	44	⋃	⋃	ADJ
ejpam-4578	208	45	v∈v	v∈v	NOUN
ejpam-4578	208	46	(	(	PUNCT
ejpam-4578	208	47	g)\{u	g)\{u	PROPN
ejpam-4578	208	48	}	}	PUNCT
ejpam-4578	208	49	v	v	PROPN
ejpam-4578	208	50	(	(	PUNCT
ejpam-4578	208	51	hv	hv	NOUN
ejpam-4578	208	52	)	)	PUNCT
ejpam-4578	208	53			PROPN
ejpam-4578	208	54	∪	∪	VERB
ejpam-4578	208	55	bu	bu	ADV
ejpam-4578	208	56	for	for	ADP
ejpam-4578	208	57	a	a	DET
ejpam-4578	208	58	unique	unique	ADJ
ejpam-4578	208	59	vertex	vertex	NOUN
ejpam-4578	208	60	u	u	NOUN
ejpam-4578	208	61	in	in	ADP
ejpam-4578	208	62	g	g	PROPN
ejpam-4578	208	63	,	,	PUNCT
ejpam-4578	208	64	where	where	SCONJ
ejpam-4578	208	65	a	a	DET
ejpam-4578	208	66	⊆	⊆	NUM
ejpam-4578	208	67	v	v	NOUN
ejpam-4578	208	68	(	(	PUNCT
ejpam-4578	208	69	g	g	NOUN
ejpam-4578	208	70	)	)	PUNCT
ejpam-4578	208	71	,	,	PUNCT
ejpam-4578	208	72	bu	bu	PROPN
ejpam-4578	208	73	is	be	AUX
ejpam-4578	208	74	a	a	DET
ejpam-4578	208	75	strong	strong	ADJ
ejpam-4578	208	76	resolving	resolving	NOUN
ejpam-4578	208	77	set	set	NOUN
ejpam-4578	208	78	of	of	ADP
ejpam-4578	208	79	hu	hu	PROPN
ejpam-4578	208	80	and	and	CCONJ
ejpam-4578	208	81	bu	bu	PROPN
ejpam-4578	208	82	is	be	AUX
ejpam-4578	208	83	strong	strong	ADJ
ejpam-4578	208	84	resolving	resolve	VERB
ejpam-4578	208	85	hop	hop	NOUN
ejpam-4578	208	86	dominating	dominating	NOUN
ejpam-4578	208	87	of	of	ADP
ejpam-4578	208	88	hu	hu	PROPN
ejpam-4578	208	89	if	if	SCONJ
ejpam-4578	208	90	ng(u	ng(u	NOUN
ejpam-4578	208	91	)	)	PUNCT
ejpam-4578	208	92	∩a	∩a	NOUN
ejpam-4578	209	1	=	=	PUNCT
ejpam-4578	209	2	∅.	∅.	PRON
ejpam-4578	209	3	proof	proof	NOUN
ejpam-4578	209	4	:	:	PUNCT
ejpam-4578	209	5	suppose	suppose	VERB
ejpam-4578	209	6	s	s	NOUN
ejpam-4578	209	7	is	be	AUX
ejpam-4578	209	8	a	a	DET
ejpam-4578	209	9	strong	strong	ADJ
ejpam-4578	209	10	resolving	resolve	VERB
ejpam-4578	209	11	hop	hop	NOUN
ejpam-4578	209	12	dominating	dominating	NOUN
ejpam-4578	209	13	set	set	NOUN
ejpam-4578	209	14	of	of	ADP
ejpam-4578	209	15	g	g	PROPN
ejpam-4578	209	16	◦	◦	NOUN
ejpam-4578	209	17	h.	h.	NOUN
ejpam-4578	209	18	by	by	ADP
ejpam-4578	209	19	theorem	theorem	NOUN
ejpam-4578	209	20	7	7	NUM
ejpam-4578	209	21	,	,	PUNCT
ejpam-4578	209	22	(	(	PUNCT
ejpam-4578	209	23	i	i	NOUN
ejpam-4578	209	24	)	)	PUNCT
ejpam-4578	209	25	holds	hold	VERB
ejpam-4578	209	26	or	or	CCONJ
ejpam-4578	209	27	s	s	X
ejpam-4578	209	28	=	=	PUNCT
ejpam-4578	209	29	a∪	a∪	PROPN
ejpam-4578	210	1			PROPN
ejpam-4578	210	2	⋃	⋃	PROPN
ejpam-4578	210	3	v∈v	v∈v	NOUN
ejpam-4578	210	4	(	(	PUNCT
ejpam-4578	210	5	g)\{u	g)\{u	PROPN
ejpam-4578	210	6	}	}	PUNCT
ejpam-4578	210	7	v	v	PROPN
ejpam-4578	210	8	(	(	PUNCT
ejpam-4578	210	9	hv	hv	NOUN
ejpam-4578	210	10	)	)	PUNCT
ejpam-4578	210	11	∪bu	∪bu	PROPN
ejpam-4578	210	12	for	for	ADP
ejpam-4578	210	13	a	a	DET
ejpam-4578	210	14	unique	unique	ADJ
ejpam-4578	210	15	vertex	vertex	NOUN
ejpam-4578	210	16	u	u	NOUN
ejpam-4578	210	17	in	in	ADP
ejpam-4578	210	18	g	g	PROPN
ejpam-4578	210	19	,	,	PUNCT
ejpam-4578	210	20	where	where	SCONJ
ejpam-4578	210	21	a	a	DET
ejpam-4578	210	22	⊆	⊆	NUM
ejpam-4578	210	23	v	v	NOUN
ejpam-4578	210	24	(	(	PUNCT
ejpam-4578	210	25	g	g	NOUN
ejpam-4578	210	26	)	)	PUNCT
ejpam-4578	210	27	,	,	PUNCT
ejpam-4578	210	28	bu	bu	PROPN
ejpam-4578	210	29	is	be	AUX
ejpam-4578	210	30	a	a	DET
ejpam-4578	210	31	strong	strong	ADJ
ejpam-4578	210	32	resolving	resolving	NOUN
ejpam-4578	210	33	set	set	NOUN
ejpam-4578	210	34	of	of	ADP
ejpam-4578	210	35	hu	hu	PROPN
ejpam-4578	210	36	if	if	SCONJ
ejpam-4578	210	37	γ(h	γ(h	NOUN
ejpam-4578	210	38	)	)	PUNCT
ejpam-4578	210	39	=	=	SYM
ejpam-4578	210	40	1	1	NUM
ejpam-4578	210	41	or	or	CCONJ
ejpam-4578	210	42	bu	bu	PROPN
ejpam-4578	210	43	is	be	AUX
ejpam-4578	210	44	a	a	DET
ejpam-4578	210	45	strong	strong	ADJ
ejpam-4578	210	46	resolving	resolving	NOUN
ejpam-4578	210	47	set	set	NOUN
ejpam-4578	210	48	of	of	ADP
ejpam-4578	210	49	{	{	PUNCT
ejpam-4578	210	50	u}+hu	u}+hu	NOUN
ejpam-4578	210	51	if	if	SCONJ
ejpam-4578	210	52	γ(h	γ(h	NOUN
ejpam-4578	210	53	)	)	PUNCT
ejpam-4578	210	54	̸=	̸=	PROPN
ejpam-4578	210	55	1	1	NUM
ejpam-4578	210	56	.	.	PUNCT
ejpam-4578	211	1	let	let	VERB
ejpam-4578	211	2	ng(u	ng(u	NOUN
ejpam-4578	211	3	)	)	PUNCT
ejpam-4578	211	4	∩	∩	NOUN
ejpam-4578	211	5	a	a	DET
ejpam-4578	211	6	=	=	NOUN
ejpam-4578	211	7	∅	∅	NOUN
ejpam-4578	211	8	and	and	CCONJ
ejpam-4578	211	9	x	x	SYM
ejpam-4578	211	10	∈	∈	NOUN
ejpam-4578	211	11	v	v	X
ejpam-4578	211	12	(	(	PUNCT
ejpam-4578	211	13	hu	hu	PROPN
ejpam-4578	211	14	)	)	PUNCT
ejpam-4578	211	15	\	\	PROPN
ejpam-4578	212	1	bu	bu	PROPN
ejpam-4578	212	2	.	.	PUNCT
ejpam-4578	213	1	since	since	SCONJ
ejpam-4578	213	2	s	s	PROPN
ejpam-4578	213	3	is	be	AUX
ejpam-4578	213	4	hop	hop	NOUN
ejpam-4578	213	5	dominating	dominating	NOUN
ejpam-4578	213	6	and	and	CCONJ
ejpam-4578	213	7	x	x	SYM
ejpam-4578	213	8	∈	∈	PROPN
ejpam-4578	213	9	v	v	NOUN
ejpam-4578	213	10	(	(	PUNCT
ejpam-4578	213	11	g	g	PROPN
ejpam-4578	213	12	◦	◦	NOUN
ejpam-4578	213	13	h	h	NOUN
ejpam-4578	213	14	)	)	PUNCT
ejpam-4578	213	15	\	\	PROPN
ejpam-4578	214	1	s	s	X
ejpam-4578	214	2	,	,	PUNCT
ejpam-4578	214	3	there	there	PRON
ejpam-4578	214	4	exists	exist	VERB
ejpam-4578	214	5	y	y	PROPN
ejpam-4578	214	6	∈	∈	PROPN
ejpam-4578	214	7	ng	ng	PROPN
ejpam-4578	214	8	◦	◦	PROPN
ejpam-4578	214	9	h(x	h(x	PROPN
ejpam-4578	214	10	,	,	PUNCT
ejpam-4578	214	11	2	2	NUM
ejpam-4578	214	12	)	)	PUNCT
ejpam-4578	214	13	∩	∩	NOUN
ejpam-4578	214	14	s.	s.	PROPN
ejpam-4578	214	15	thus	thus	ADV
ejpam-4578	214	16	,	,	PUNCT
ejpam-4578	214	17	y	y	PROPN
ejpam-4578	214	18	∈	∈	PROPN
ejpam-4578	214	19	nhu(x	nhu(x	PROPN
ejpam-4578	214	20	,	,	PUNCT
ejpam-4578	214	21	2	2	NUM
ejpam-4578	214	22	)	)	PUNCT
ejpam-4578	214	23	∩	∩	NOUN
ejpam-4578	214	24	bu	bu	PROPN
ejpam-4578	214	25	.	.	PUNCT
ejpam-4578	215	1	it	it	PRON
ejpam-4578	215	2	follows	follow	VERB
ejpam-4578	215	3	that	that	SCONJ
ejpam-4578	215	4	bu	bu	PROPN
ejpam-4578	215	5	is	be	AUX
ejpam-4578	215	6	strong	strong	ADJ
ejpam-4578	215	7	resolving	resolve	VERB
ejpam-4578	215	8	hop	hop	NOUN
ejpam-4578	215	9	dominating	dominating	NOUN
ejpam-4578	215	10	set	set	NOUN
ejpam-4578	215	11	of	of	ADP
ejpam-4578	215	12	hu	hu	PROPN
ejpam-4578	215	13	.	.	PUNCT
ejpam-4578	216	1	hence	hence	ADV
ejpam-4578	216	2	,	,	PUNCT
ejpam-4578	216	3	(	(	PUNCT
ejpam-4578	216	4	ii	ii	NOUN
ejpam-4578	216	5	)	)	PUNCT
ejpam-4578	216	6	holds	hold	VERB
ejpam-4578	216	7	.	.	PUNCT
ejpam-4578	217	1	for	for	ADP
ejpam-4578	217	2	the	the	DET
ejpam-4578	217	3	converse	converse	NOUN
ejpam-4578	217	4	,	,	PUNCT
ejpam-4578	217	5	suppose	suppose	VERB
ejpam-4578	217	6	(	(	PUNCT
ejpam-4578	217	7	i	i	NOUN
ejpam-4578	217	8	)	)	PUNCT
ejpam-4578	217	9	and	and	CCONJ
ejpam-4578	217	10	(	(	PUNCT
ejpam-4578	217	11	ii	ii	NOUN
ejpam-4578	217	12	)	)	PUNCT
ejpam-4578	217	13	hold	hold	VERB
ejpam-4578	217	14	.	.	PUNCT
ejpam-4578	218	1	then	then	ADV
ejpam-4578	218	2	by	by	ADP
ejpam-4578	218	3	theorem	theorem	NOUN
ejpam-4578	218	4	7	7	NUM
ejpam-4578	218	5	,	,	PUNCT
ejpam-4578	218	6	s	s	VERB
ejpam-4578	218	7	is	be	AUX
ejpam-4578	218	8	a	a	DET
ejpam-4578	218	9	strong	strong	ADJ
ejpam-4578	218	10	resolving	resolving	NOUN
ejpam-4578	218	11	set	set	NOUN
ejpam-4578	218	12	of	of	ADP
ejpam-4578	218	13	g	g	PROPN
ejpam-4578	218	14	◦	◦	NOUN
ejpam-4578	218	15	h.	h.	NOUN
ejpam-4578	218	16	let	let	VERB
ejpam-4578	218	17	x	x	SYM
ejpam-4578	218	18	∈	∈	PROPN
ejpam-4578	218	19	v	v	X
ejpam-4578	218	20	(	(	PUNCT
ejpam-4578	218	21	g	g	PROPN
ejpam-4578	218	22	◦	◦	NOUN
ejpam-4578	218	23	h	h	NOUN
ejpam-4578	218	24	)	)	PUNCT
ejpam-4578	218	25	\	\	PUNCT
ejpam-4578	219	1	s.	s.	PROPN
ejpam-4578	219	2	consider	consider	VERB
ejpam-4578	219	3	the	the	DET
ejpam-4578	219	4	following	follow	VERB
ejpam-4578	219	5	cases	case	NOUN
ejpam-4578	219	6	:	:	PUNCT
ejpam-4578	219	7	case	case	NOUN
ejpam-4578	219	8	1	1	NUM
ejpam-4578	219	9	.	.	PUNCT
ejpam-4578	219	10	x	x	SYM
ejpam-4578	219	11	∈	∈	NOUN
ejpam-4578	219	12	v	v	ADP
ejpam-4578	219	13	(	(	PUNCT
ejpam-4578	219	14	g	g	NOUN
ejpam-4578	219	15	)	)	PUNCT
ejpam-4578	219	16	\a	\a	VERB
ejpam-4578	219	17	since	since	SCONJ
ejpam-4578	219	18	g	g	PROPN
ejpam-4578	219	19	is	be	AUX
ejpam-4578	219	20	nontrivial	nontrivial	ADJ
ejpam-4578	219	21	connected	connect	VERB
ejpam-4578	219	22	,	,	PUNCT
ejpam-4578	219	23	there	there	PRON
ejpam-4578	219	24	exists	exist	VERB
ejpam-4578	219	25	a	a	DET
ejpam-4578	219	26	vertex	vertex	NOUN
ejpam-4578	219	27	y	y	PROPN
ejpam-4578	219	28	∈	∈	PROPN
ejpam-4578	219	29	v	v	PROPN
ejpam-4578	219	30	(	(	PUNCT
ejpam-4578	219	31	g)∩ng(x	g)∩ng(x	PROPN
ejpam-4578	219	32	)	)	PUNCT
ejpam-4578	219	33	.	.	PUNCT
ejpam-4578	220	1	by	by	ADP
ejpam-4578	220	2	(	(	PUNCT
ejpam-4578	220	3	i	i	NOUN
ejpam-4578	220	4	)	)	PUNCT
ejpam-4578	220	5	or	or	CCONJ
ejpam-4578	220	6	(	(	PUNCT
ejpam-4578	220	7	ii	ii	NOUN
ejpam-4578	220	8	)	)	PUNCT
ejpam-4578	220	9	,	,	PUNCT
ejpam-4578	220	10	vertex	vertex	NOUN
ejpam-4578	220	11	z	z	PROPN
ejpam-4578	220	12	∈	∈	PROPN
ejpam-4578	220	13	ng	ng	PROPN
ejpam-4578	220	14	◦	◦	PROPN
ejpam-4578	220	15	h(x	h(x	PROPN
ejpam-4578	220	16	,	,	PUNCT
ejpam-4578	220	17	2	2	NUM
ejpam-4578	220	18	)	)	PUNCT
ejpam-4578	220	19	∩	∩	ADJ
ejpam-4578	220	20	v	v	X
ejpam-4578	220	21	(	(	PUNCT
ejpam-4578	220	22	hy	hy	NOUN
ejpam-4578	220	23	)	)	PUNCT
ejpam-4578	220	24	or	or	CCONJ
ejpam-4578	220	25	z	z	PROPN
ejpam-4578	220	26	∈	∈	PROPN
ejpam-4578	220	27	ng	ng	PROPN
ejpam-4578	220	28	◦	◦	PROPN
ejpam-4578	220	29	h(x	h(x	PROPN
ejpam-4578	220	30	,	,	PUNCT
ejpam-4578	220	31	2	2	NUM
ejpam-4578	220	32	)	)	PUNCT
ejpam-4578	220	33	∩by	∩by	NOUN
ejpam-4578	220	34	exists	exist	VERB
ejpam-4578	220	35	.	.	PUNCT
ejpam-4578	221	1	case	case	NOUN
ejpam-4578	221	2	2	2	NUM
ejpam-4578	221	3	.	.	PUNCT
ejpam-4578	221	4	x	x	SYM
ejpam-4578	221	5	∈	∈	PROPN
ejpam-4578	221	6	v	v	ADP
ejpam-4578	221	7	(	(	PUNCT
ejpam-4578	221	8	hu	hu	PROPN
ejpam-4578	221	9	)	)	PUNCT
ejpam-4578	221	10	\bu	\bu	PROPN
ejpam-4578	221	11	for	for	ADP
ejpam-4578	221	12	a	a	DET
ejpam-4578	221	13	unique	unique	ADJ
ejpam-4578	221	14	vertex	vertex	NOUN
ejpam-4578	221	15	u	u	NOUN
ejpam-4578	221	16	in	in	ADP
ejpam-4578	221	17	g.	g.	PROPN
ejpam-4578	221	18	if	if	SCONJ
ejpam-4578	221	19	ng(u	ng(u	NOUN
ejpam-4578	221	20	)	)	PUNCT
ejpam-4578	221	21	∩	∩	NOUN
ejpam-4578	221	22	a	a	DET
ejpam-4578	221	23	̸=	̸=	PROPN
ejpam-4578	221	24	∅	∅	NOUN
ejpam-4578	221	25	,	,	PUNCT
ejpam-4578	221	26	then	then	ADV
ejpam-4578	221	27	w	w	PROPN
ejpam-4578	221	28	∈	∈	PROPN
ejpam-4578	221	29	(	(	PUNCT
ejpam-4578	221	30	(	(	PUNCT
ejpam-4578	221	31	ng(u	ng(u	NOUN
ejpam-4578	221	32	)	)	PUNCT
ejpam-4578	221	33	∩	∩	NOUN
ejpam-4578	221	34	a	a	PRON
ejpam-4578	221	35	)	)	PUNCT
ejpam-4578	221	36	∩ng	∩ng	VERB
ejpam-4578	221	37	◦	◦	NOUN
ejpam-4578	221	38	h(x	h(x	PROPN
ejpam-4578	221	39	,	,	PUNCT
ejpam-4578	221	40	2	2	NUM
ejpam-4578	221	41	)	)	PUNCT
ejpam-4578	221	42	exists	exist	VERB
ejpam-4578	221	43	.	.	PUNCT
ejpam-4578	222	1	on	on	ADP
ejpam-4578	222	2	the	the	DET
ejpam-4578	222	3	other	other	ADJ
ejpam-4578	222	4	hand	hand	NOUN
ejpam-4578	222	5	,	,	PUNCT
ejpam-4578	222	6	if	if	SCONJ
ejpam-4578	222	7	ng(u	ng(u	NOUN
ejpam-4578	222	8	)	)	PUNCT
ejpam-4578	222	9	∩a	∩a	NOUN
ejpam-4578	222	10	=	=	NOUN
ejpam-4578	222	11	∅	∅	NOUN
ejpam-4578	222	12	,	,	PUNCT
ejpam-4578	222	13	by	by	ADP
ejpam-4578	222	14	(	(	PUNCT
ejpam-4578	222	15	ii	ii	NOUN
ejpam-4578	222	16	)	)	PUNCT
ejpam-4578	222	17	,	,	PUNCT
ejpam-4578	222	18	bu	bu	PROPN
ejpam-4578	222	19	is	be	AUX
ejpam-4578	222	20	a	a	DET
ejpam-4578	222	21	strong	strong	ADJ
ejpam-4578	222	22	resolving	resolve	VERB
ejpam-4578	222	23	hop	hop	NOUN
ejpam-4578	222	24	dominating	dominating	NOUN
ejpam-4578	222	25	set	set	NOUN
ejpam-4578	222	26	of	of	ADP
ejpam-4578	222	27	hu	hu	PROPN
ejpam-4578	222	28	.	.	PUNCT
ejpam-4578	223	1	hence	hence	ADV
ejpam-4578	223	2	,	,	PUNCT
ejpam-4578	223	3	there	there	PRON
ejpam-4578	223	4	exists	exist	VERB
ejpam-4578	223	5	p	p	PROPN
ejpam-4578	223	6	∈	∈	PROPN
ejpam-4578	223	7	nhu(x	nhu(x	NOUN
ejpam-4578	223	8	,	,	PUNCT
ejpam-4578	223	9	2	2	NUM
ejpam-4578	223	10	)	)	PUNCT
ejpam-4578	223	11	∩bu	∩bu	NOUN
ejpam-4578	223	12	.	.	PUNCT
ejpam-4578	224	1	this	this	PRON
ejpam-4578	224	2	implies	imply	VERB
ejpam-4578	224	3	that	that	SCONJ
ejpam-4578	224	4	p	p	PROPN
ejpam-4578	224	5	∈	∈	PROPN
ejpam-4578	224	6	ng	ng	PROPN
ejpam-4578	224	7	◦	◦	PROPN
ejpam-4578	224	8	h(x	h(x	PROPN
ejpam-4578	224	9	,	,	PUNCT
ejpam-4578	224	10	2	2	NUM
ejpam-4578	224	11	)	)	PUNCT
ejpam-4578	224	12	∩	∩	NOUN
ejpam-4578	224	13	s.	s.	PROPN
ejpam-4578	224	14	in	in	ADP
ejpam-4578	224	15	any	any	DET
ejpam-4578	224	16	case	case	NOUN
ejpam-4578	224	17	,	,	PUNCT
ejpam-4578	224	18	s	s	VERB
ejpam-4578	224	19	is	be	AUX
ejpam-4578	224	20	a	a	DET
ejpam-4578	224	21	hop	hop	NOUN
ejpam-4578	224	22	dominating	dominating	NOUN
ejpam-4578	224	23	set	set	NOUN
ejpam-4578	224	24	of	of	ADP
ejpam-4578	224	25	g	g	PROPN
ejpam-4578	224	26	◦	◦	NOUN
ejpam-4578	224	27	h.	h.	NOUN
ejpam-4578	224	28	accordingly	accordingly	ADV
ejpam-4578	224	29	,	,	PUNCT
ejpam-4578	224	30	s	s	VERB
ejpam-4578	224	31	is	be	AUX
ejpam-4578	224	32	a	a	DET
ejpam-4578	224	33	strong	strong	ADJ
ejpam-4578	224	34	resolving	resolve	VERB
ejpam-4578	224	35	hop	hop	NOUN
ejpam-4578	224	36	dominating	dominating	NOUN
ejpam-4578	224	37	set	set	NOUN
ejpam-4578	224	38	of	of	ADP
ejpam-4578	224	39	g	g	PROPN
ejpam-4578	224	40	◦	◦	NOUN
ejpam-4578	224	41	h.	h.	NOUN
ejpam-4578	224	42	corollary	corollary	ADJ
ejpam-4578	224	43	4	4	NUM
ejpam-4578	224	44	.	.	PUNCT
ejpam-4578	225	1	let	let	VERB
ejpam-4578	225	2	g	g	NOUN
ejpam-4578	225	3	and	and	CCONJ
ejpam-4578	225	4	h	h	NOUN
ejpam-4578	225	5	be	be	AUX
ejpam-4578	225	6	connected	connect	VERB
ejpam-4578	225	7	graphs	graph	NOUN
ejpam-4578	225	8	of	of	ADP
ejpam-4578	225	9	orders	order	NOUN
ejpam-4578	225	10	m	m	VERB
ejpam-4578	225	11	>	>	X
ejpam-4578	225	12	1	1	NUM
ejpam-4578	225	13	and	and	CCONJ
ejpam-4578	225	14	n	n	CCONJ
ejpam-4578	225	15	,	,	PUNCT
ejpam-4578	225	16	respectively	respectively	ADV
ejpam-4578	225	17	.	.	PUNCT
ejpam-4578	226	1	then	then	ADV
ejpam-4578	226	2	γsrh(g	γsrh(g	ADP
ejpam-4578	226	3	◦	◦	NOUN
ejpam-4578	226	4	h	h	NOUN
ejpam-4578	226	5	)	)	PUNCT
ejpam-4578	226	6	=	=	PUNCT
ejpam-4578	227	1	(	(	PUNCT
ejpam-4578	227	2	m−	m−	PROPN
ejpam-4578	227	3	1)n+	1)n+	NUM
ejpam-4578	227	4	γsrh(h	γsrh(h	PROPN
ejpam-4578	227	5	)	)	PUNCT
ejpam-4578	227	6	.	.	PUNCT
ejpam-4578	228	1	moreover	moreover	ADV
ejpam-4578	228	2	,	,	PUNCT
ejpam-4578	228	3	if	if	SCONJ
ejpam-4578	228	4	diam(h	diam(h	ADJ
ejpam-4578	228	5	)	)	PUNCT
ejpam-4578	228	6	≤	≤	NOUN
ejpam-4578	228	7	2	2	NUM
ejpam-4578	228	8	,	,	PUNCT
ejpam-4578	228	9	then	then	ADV
ejpam-4578	228	10	γsrh(g	γsrh(g	ADP
ejpam-4578	228	11	◦	◦	NOUN
ejpam-4578	228	12	h	h	NOUN
ejpam-4578	228	13	)	)	PUNCT
ejpam-4578	228	14	=	=	PUNCT
ejpam-4578	228	15	(	(	PUNCT
ejpam-4578	228	16	m−	m−	PROPN
ejpam-4578	228	17	1)n+	1)n+	NUM
ejpam-4578	228	18	|v	|v	PROPN
ejpam-4578	228	19	(	(	PUNCT
ejpam-4578	228	20	h)|	h)|	NOUN
ejpam-4578	228	21	−	−	PROPN
ejpam-4578	228	22	ωhs(h	ωhs(h	PROPN
ejpam-4578	228	23	)	)	PUNCT
ejpam-4578	228	24	=	=	PUNCT
ejpam-4578	228	25	mn−	mn−	NUM
ejpam-4578	228	26	ωhs(h	ωhs(h	PROPN
ejpam-4578	228	27	)	)	PUNCT
ejpam-4578	228	28	.	.	PUNCT
ejpam-4578	229	1	proof	proof	NOUN
ejpam-4578	229	2	:	:	PUNCT
ejpam-4578	229	3	let	let	VERB
ejpam-4578	229	4	s	s	PRON
ejpam-4578	229	5	be	be	AUX
ejpam-4578	229	6	a	a	DET
ejpam-4578	229	7	γsrh	γsrh	NOUN
ejpam-4578	229	8	-	-	PUNCT
ejpam-4578	229	9	set	set	NOUN
ejpam-4578	229	10	of	of	ADP
ejpam-4578	229	11	g	g	PROPN
ejpam-4578	229	12	◦	◦	NOUN
ejpam-4578	229	13	h.	h.	NOUN
ejpam-4578	229	14	then	then	ADV
ejpam-4578	229	15	,	,	PUNCT
ejpam-4578	229	16	s	s	VERB
ejpam-4578	229	17	=	=	PUNCT
ejpam-4578	229	18	a	a	PRON
ejpam-4578	229	19	∪	∪	ADJ
ejpam-4578	229	20			PROPN
ejpam-4578	229	21	⋃	⋃	ADJ
ejpam-4578	229	22	v∈v	v∈v	NOUN
ejpam-4578	229	23	(	(	PUNCT
ejpam-4578	229	24	g)\{u	g)\{u	PROPN
ejpam-4578	229	25	}	}	PUNCT
ejpam-4578	229	26	v	v	PROPN
ejpam-4578	229	27	(	(	PUNCT
ejpam-4578	229	28	hv	hv	NOUN
ejpam-4578	229	29	)	)	PUNCT
ejpam-4578	229	30			PROPN
ejpam-4578	229	31	∪	∪	VERB
ejpam-4578	229	32	bu	bu	ADV
ejpam-4578	229	33	for	for	ADP
ejpam-4578	229	34	a	a	DET
ejpam-4578	229	35	unique	unique	ADJ
ejpam-4578	229	36	vertex	vertex	NOUN
ejpam-4578	229	37	u	u	NOUN
ejpam-4578	229	38	in	in	ADP
ejpam-4578	229	39	g	g	PROPN
ejpam-4578	229	40	,	,	PUNCT
ejpam-4578	229	41	where	where	SCONJ
ejpam-4578	229	42	a	a	DET
ejpam-4578	229	43	⊆	⊆	NUM
ejpam-4578	229	44	v	v	NOUN
ejpam-4578	229	45	(	(	PUNCT
ejpam-4578	229	46	g	g	NOUN
ejpam-4578	229	47	)	)	PUNCT
ejpam-4578	229	48	,	,	PUNCT
ejpam-4578	229	49	and	and	CCONJ
ejpam-4578	229	50	bu	bu	VERB
ejpam-4578	229	51	satisfies	satisfie	NOUN
ejpam-4578	229	52	(	(	PUNCT
ejpam-4578	229	53	ii	ii	NOUN
ejpam-4578	229	54	)	)	PUNCT
ejpam-4578	229	55	of	of	ADP
ejpam-4578	229	56	theorem	theorem	NOUN
ejpam-4578	229	57	8	8	NUM
ejpam-4578	229	58	.	.	PUNCT
ejpam-4578	230	1	let	let	VERB
ejpam-4578	230	2	a	a	DET
ejpam-4578	230	3	=	=	PUNCT
ejpam-4578	230	4	∅	∅	NOUN
ejpam-4578	230	5	j.	j.	PROPN
ejpam-4578	230	6	mohamad	mohamad	PROPN
ejpam-4578	230	7	,	,	PUNCT
ejpam-4578	230	8	h.	h.	PROPN
ejpam-4578	230	9	rara	rara	PROPN
ejpam-4578	230	10	/	/	SYM
ejpam-4578	230	11	eur	eur	PROPN
ejpam-4578	230	12	.	.	PUNCT
ejpam-4578	231	1	j.	j.	PROPN
ejpam-4578	231	2	pure	pure	PROPN
ejpam-4578	231	3	appl	appl	PROPN
ejpam-4578	231	4	.	.	PROPN
ejpam-4578	231	5	math	math	PROPN
ejpam-4578	231	6	,	,	PUNCT
ejpam-4578	231	7	16	16	NUM
ejpam-4578	231	8	(	(	PUNCT
ejpam-4578	231	9	1	1	NUM
ejpam-4578	231	10	)	)	PUNCT
ejpam-4578	231	11	(	(	PUNCT
ejpam-4578	231	12	2023	2023	NUM
ejpam-4578	231	13	)	)	PUNCT
ejpam-4578	231	14	,	,	PUNCT
ejpam-4578	231	15	131	131	NUM
ejpam-4578	231	16	-	-	SYM
ejpam-4578	231	17	143	143	NUM
ejpam-4578	231	18	139	139	NUM
ejpam-4578	231	19	and	and	CCONJ
ejpam-4578	231	20	bu	bu	PROPN
ejpam-4578	231	21	be	be	AUX
ejpam-4578	231	22	γsrh	γsrh	NOUN
ejpam-4578	231	23	-	-	PUNCT
ejpam-4578	231	24	set	set	NOUN
ejpam-4578	231	25	of	of	ADP
ejpam-4578	231	26	h	h	NOUN
ejpam-4578	231	27	u.	u.	PROPN
ejpam-4578	231	28	then	then	ADV
ejpam-4578	231	29	γsrh(g	γsrh(g	ADP
ejpam-4578	231	30	◦	◦	NOUN
ejpam-4578	231	31	h	h	NOUN
ejpam-4578	231	32	)	)	PUNCT
ejpam-4578	232	1	=	=	NOUN
ejpam-4578	232	2	|s|	|s|	NOUN
ejpam-4578	232	3	=	=	NOUN
ejpam-4578	232	4	|a|+	|a|+	NOUN
ejpam-4578	232	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4578	232	6	⋃	⋃	NOUN
ejpam-4578	232	7	v∈v	v∈v	NOUN
ejpam-4578	232	8	(	(	PUNCT
ejpam-4578	232	9	g)\{u	g)\{u	PROPN
ejpam-4578	232	10	}	}	PUNCT
ejpam-4578	232	11	v	v	PROPN
ejpam-4578	232	12	(	(	PUNCT
ejpam-4578	232	13	hv	hv	PROPN
ejpam-4578	232	14	)	)	PUNCT
ejpam-4578	232	15	∣∣∣∣∣∣+	∣∣∣∣∣∣+	PROPN
ejpam-4578	232	16	|bu|	|bu|	NOUN
ejpam-4578	233	1	=	=	NOUN
ejpam-4578	233	2	0	0	PROPN
ejpam-4578	234	1	+	+	CCONJ
ejpam-4578	234	2	(	(	PUNCT
ejpam-4578	234	3	m−	m−	PROPN
ejpam-4578	234	4	1)n+	1)n+	NUM
ejpam-4578	234	5	γsrh(h	γsrh(h	PROPN
ejpam-4578	234	6	)	)	PUNCT
ejpam-4578	234	7	=(	=(	NOUN
ejpam-4578	234	8	m−	m−	PROPN
ejpam-4578	234	9	1)n+	1)n+	NUM
ejpam-4578	234	10	γsrh(h	γsrh(h	PROPN
ejpam-4578	234	11	)	)	PUNCT
ejpam-4578	234	12	.	.	PUNCT
ejpam-4578	235	1	suppose	suppose	VERB
ejpam-4578	235	2	that	that	SCONJ
ejpam-4578	235	3	diam(h	diam(h	NOUN
ejpam-4578	235	4	)	)	PUNCT
ejpam-4578	235	5	≤	≤	NOUN
ejpam-4578	235	6	2	2	NUM
ejpam-4578	235	7	.	.	PUNCT
ejpam-4578	236	1	then	then	ADV
ejpam-4578	236	2	by	by	ADP
ejpam-4578	236	3	lemma	lemma	PROPN
ejpam-4578	236	4	1	1	NUM
ejpam-4578	236	5	,	,	PUNCT
ejpam-4578	236	6	γsrh(h	γsrh(h	PROPN
ejpam-4578	236	7	)	)	PUNCT
ejpam-4578	237	1	=	=	SYM
ejpam-4578	237	2	|v	|v	PROPN
ejpam-4578	237	3	(	(	PUNCT
ejpam-4578	237	4	h)|	h)|	NOUN
ejpam-4578	237	5	−	−	PROPN
ejpam-4578	237	6	ωhs(h	ωhs(h	PROPN
ejpam-4578	237	7	)	)	PUNCT
ejpam-4578	237	8	=	=	PUNCT
ejpam-4578	237	9	n−	n−	PROPN
ejpam-4578	237	10	ωhs(h	ωhs(h	PROPN
ejpam-4578	237	11	)	)	PUNCT
ejpam-4578	237	12	.	.	PUNCT
ejpam-4578	238	1	hence	hence	ADV
ejpam-4578	238	2	,	,	PUNCT
ejpam-4578	238	3	γsrh(g	γsrh(g	ADP
ejpam-4578	238	4	◦	◦	NOUN
ejpam-4578	238	5	h	h	NOUN
ejpam-4578	238	6	)	)	PUNCT
ejpam-4578	238	7	=(	=(	NOUN
ejpam-4578	238	8	m−	m−	PROPN
ejpam-4578	238	9	1)n+	1)n+	NUM
ejpam-4578	238	10	n−	n−	NOUN
ejpam-4578	238	11	ωhs(h	ωhs(h	PROPN
ejpam-4578	238	12	)	)	PUNCT
ejpam-4578	238	13	=	=	NOUN
ejpam-4578	238	14	mn−	mn−	PROPN
ejpam-4578	238	15	n+	n+	NUM
ejpam-4578	238	16	n−	n−	NOUN
ejpam-4578	238	17	ωhs(h	ωhs(h	PROPN
ejpam-4578	238	18	)	)	PUNCT
ejpam-4578	238	19	=	=	NOUN
ejpam-4578	238	20	mn−	mn−	NOUN
ejpam-4578	238	21	ωhs(h	ωhs(h	PROPN
ejpam-4578	238	22	)	)	PUNCT
ejpam-4578	238	23	.	.	PUNCT
ejpam-4578	239	1	therefore	therefore	ADV
ejpam-4578	239	2	,	,	PUNCT
ejpam-4578	239	3	γsrh(g	γsrh(g	ADP
ejpam-4578	239	4	◦	◦	NOUN
ejpam-4578	239	5	h	h	NOUN
ejpam-4578	239	6	)	)	PUNCT
ejpam-4578	239	7	=	=	PUNCT
ejpam-4578	239	8	(	(	PUNCT
ejpam-4578	239	9	m−	m−	PROPN
ejpam-4578	239	10	1)n+	1)n+	NUM
ejpam-4578	239	11	|v	|v	PROPN
ejpam-4578	239	12	(	(	PUNCT
ejpam-4578	239	13	h)|	h)|	NOUN
ejpam-4578	239	14	−	−	PROPN
ejpam-4578	239	15	ωhs(h	ωhs(h	PROPN
ejpam-4578	239	16	)	)	PUNCT
ejpam-4578	239	17	=	=	PUNCT
ejpam-4578	239	18	mn−	mn−	NUM
ejpam-4578	239	19	ωhs(h	ωhs(h	PROPN
ejpam-4578	239	20	)	)	PUNCT
ejpam-4578	239	21	.	.	PUNCT
ejpam-4578	240	1	5	5	X
ejpam-4578	240	2	.	.	X
ejpam-4578	240	3	on	on	ADP
ejpam-4578	240	4	strong	strong	ADJ
ejpam-4578	240	5	resolving	resolve	VERB
ejpam-4578	240	6	hop	hop	NOUN
ejpam-4578	240	7	domination	domination	NOUN
ejpam-4578	240	8	in	in	ADP
ejpam-4578	240	9	the	the	DET
ejpam-4578	240	10	lexicographic	lexicographic	ADJ
ejpam-4578	240	11	product	product	NOUN
ejpam-4578	240	12	of	of	ADP
ejpam-4578	240	13	graphs	graph	NOUN
ejpam-4578	240	14	the	the	DET
ejpam-4578	240	15	lexicographic	lexicographic	ADJ
ejpam-4578	240	16	product	product	NOUN
ejpam-4578	240	17	of	of	ADP
ejpam-4578	240	18	two	two	NUM
ejpam-4578	240	19	graphs	graph	NOUN
ejpam-4578	240	20	g	g	NOUN
ejpam-4578	240	21	and	and	CCONJ
ejpam-4578	240	22	h	h	NOUN
ejpam-4578	240	23	,	,	PUNCT
ejpam-4578	240	24	denoted	denote	VERB
ejpam-4578	240	25	by	by	ADP
ejpam-4578	240	26	g[h	g[h	NOUN
ejpam-4578	240	27	]	]	PUNCT
ejpam-4578	240	28	,	,	PUNCT
ejpam-4578	240	29	is	be	AUX
ejpam-4578	240	30	the	the	DET
ejpam-4578	240	31	graph	graph	NOUN
ejpam-4578	240	32	with	with	ADP
ejpam-4578	240	33	vertex	vertex	NOUN
ejpam-4578	240	34	-	-	PUNCT
ejpam-4578	240	35	set	set	VERB
ejpam-4578	240	36	v	v	NOUN
ejpam-4578	240	37	(	(	PUNCT
ejpam-4578	240	38	g[h	g[h	PROPN
ejpam-4578	240	39	]	]	PUNCT
ejpam-4578	240	40	)	)	PUNCT
ejpam-4578	240	41	=	=	SYM
ejpam-4578	240	42	v	v	X
ejpam-4578	240	43	(	(	PUNCT
ejpam-4578	240	44	g	g	NOUN
ejpam-4578	240	45	)	)	PUNCT
ejpam-4578	240	46	×	×	NOUN
ejpam-4578	240	47	v	v	NOUN
ejpam-4578	240	48	(	(	PUNCT
ejpam-4578	240	49	h	h	NOUN
ejpam-4578	240	50	)	)	PUNCT
ejpam-4578	240	51	such	such	ADJ
ejpam-4578	240	52	that	that	SCONJ
ejpam-4578	240	53	(	(	PUNCT
ejpam-4578	240	54	u1	u1	NOUN
ejpam-4578	240	55	,	,	PUNCT
ejpam-4578	240	56	u2)(v1	u2)(v1	NOUN
ejpam-4578	240	57	,	,	PUNCT
ejpam-4578	240	58	v2	v2	NOUN
ejpam-4578	240	59	)	)	PUNCT
ejpam-4578	240	60	∈	∈	NOUN
ejpam-4578	240	61	e(g[h	e(g[h	NOUN
ejpam-4578	240	62	]	]	PUNCT
ejpam-4578	240	63	)	)	PUNCT
ejpam-4578	240	64	if	if	SCONJ
ejpam-4578	240	65	either	either	CCONJ
ejpam-4578	240	66	u1v1	u1v1	PROPN
ejpam-4578	240	67	∈	∈	PROPN
ejpam-4578	240	68	e(g	e(g	PROPN
ejpam-4578	240	69	)	)	PUNCT
ejpam-4578	240	70	or	or	CCONJ
ejpam-4578	240	71	u1	u1	NOUN
ejpam-4578	240	72	=	=	SYM
ejpam-4578	240	73	v1	v1	NOUN
ejpam-4578	240	74	and	and	CCONJ
ejpam-4578	240	75	u2v2	u2v2	ADJ
ejpam-4578	240	76	∈	∈	PROPN
ejpam-4578	240	77	e(h	e(h	PROPN
ejpam-4578	240	78	)	)	PUNCT
ejpam-4578	240	79	.	.	PUNCT
ejpam-4578	241	1	lemma	lemma	PROPN
ejpam-4578	241	2	3	3	X
ejpam-4578	241	3	.	.	PUNCT
ejpam-4578	242	1	[	[	X
ejpam-4578	242	2	1	1	X
ejpam-4578	242	3	]	]	PUNCT
ejpam-4578	242	4	let	let	VERB
ejpam-4578	242	5	g	g	PROPN
ejpam-4578	242	6	=	=	PROPN
ejpam-4578	242	7	kn	kn	PROPN
ejpam-4578	242	8	for	for	ADP
ejpam-4578	242	9	n	n	PROPN
ejpam-4578	242	10	>	>	SYM
ejpam-4578	242	11	1	1	NUM
ejpam-4578	242	12	and	and	CCONJ
ejpam-4578	242	13	h	h	DET
ejpam-4578	242	14	a	a	DET
ejpam-4578	242	15	non	non	ADJ
ejpam-4578	242	16	-	-	ADJ
ejpam-4578	242	17	trivial	trivial	ADJ
ejpam-4578	242	18	connected	connected	ADJ
ejpam-4578	242	19	graph	graph	NOUN
ejpam-4578	242	20	with	with	ADP
ejpam-4578	242	21	γ(h	γ(h	NOUN
ejpam-4578	242	22	)	)	PUNCT
ejpam-4578	242	23	̸=	̸=	PROPN
ejpam-4578	242	24	1	1	NUM
ejpam-4578	242	25	.	.	PUNCT
ejpam-4578	243	1	then	then	ADV
ejpam-4578	243	2	a	a	DET
ejpam-4578	243	3	×	×	NOUN
ejpam-4578	243	4	c	c	NOUN
ejpam-4578	243	5	⊆	⊆	NUM
ejpam-4578	243	6	v	v	NOUN
ejpam-4578	243	7	(	(	PUNCT
ejpam-4578	243	8	g[h	g[h	PROPN
ejpam-4578	243	9	]	]	PUNCT
ejpam-4578	243	10	)	)	PUNCT
ejpam-4578	243	11	induces	induce	VERB
ejpam-4578	243	12	a	a	DET
ejpam-4578	243	13	superclique	superclique	NOUN
ejpam-4578	243	14	in	in	ADP
ejpam-4578	243	15	g[h	g[h	NOUN
ejpam-4578	243	16	]	]	PUNCT
ejpam-4578	243	17	if	if	SCONJ
ejpam-4578	243	18	and	and	CCONJ
ejpam-4578	243	19	only	only	ADV
ejpam-4578	243	20	if	if	SCONJ
ejpam-4578	243	21	a	a	PRON
ejpam-4578	243	22	is	be	AUX
ejpam-4578	243	23	a	a	DET
ejpam-4578	243	24	nonempty	nonempty	ADJ
ejpam-4578	243	25	subset	subset	NOUN
ejpam-4578	243	26	of	of	ADP
ejpam-4578	243	27	v	v	NOUN
ejpam-4578	243	28	(	(	PUNCT
ejpam-4578	243	29	g	g	NOUN
ejpam-4578	243	30	)	)	PUNCT
ejpam-4578	243	31	and	and	CCONJ
ejpam-4578	243	32	⟨c⟩	⟨c⟩	PROPN
ejpam-4578	243	33	is	be	AUX
ejpam-4578	243	34	a	a	DET
ejpam-4578	243	35	superclique	superclique	NOUN
ejpam-4578	243	36	in	in	ADP
ejpam-4578	243	37	h.	h.	PROPN
ejpam-4578	243	38	lemma	lemma	PROPN
ejpam-4578	243	39	4	4	X
ejpam-4578	243	40	.	.	PUNCT
ejpam-4578	244	1	[	[	X
ejpam-4578	244	2	1	1	X
ejpam-4578	244	3	]	]	PUNCT
ejpam-4578	244	4	let	let	VERB
ejpam-4578	244	5	g	g	PROPN
ejpam-4578	244	6	=	=	PROPN
ejpam-4578	244	7	kn	kn	PROPN
ejpam-4578	244	8	for	for	ADP
ejpam-4578	244	9	n	n	PROPN
ejpam-4578	244	10	>	>	SYM
ejpam-4578	244	11	1	1	NUM
ejpam-4578	244	12	and	and	CCONJ
ejpam-4578	244	13	h	h	DET
ejpam-4578	244	14	a	a	DET
ejpam-4578	244	15	non	non	ADJ
ejpam-4578	244	16	-	-	ADJ
ejpam-4578	244	17	trivial	trivial	ADJ
ejpam-4578	244	18	connected	connected	ADJ
ejpam-4578	244	19	graph	graph	NOUN
ejpam-4578	244	20	with	with	ADP
ejpam-4578	244	21	γ(h	γ(h	NOUN
ejpam-4578	244	22	)	)	PUNCT
ejpam-4578	244	23	=	=	SYM
ejpam-4578	245	1	1	1	X
ejpam-4578	245	2	.	.	PUNCT
ejpam-4578	246	1	then	then	ADV
ejpam-4578	246	2	a×c	a×c	PROPN
ejpam-4578	246	3	⊆	⊆	NUM
ejpam-4578	246	4	v	v	NOUN
ejpam-4578	246	5	(	(	PUNCT
ejpam-4578	246	6	g[h	g[h	PROPN
ejpam-4578	246	7	]	]	PUNCT
ejpam-4578	246	8	)	)	PUNCT
ejpam-4578	246	9	is	be	AUX
ejpam-4578	246	10	a	a	DET
ejpam-4578	246	11	superclique	superclique	NOUN
ejpam-4578	246	12	in	in	ADP
ejpam-4578	246	13	g[h	g[h	NOUN
ejpam-4578	246	14	]	]	PUNCT
ejpam-4578	246	15	if	if	SCONJ
ejpam-4578	247	1	and	and	CCONJ
ejpam-4578	247	2	only	only	ADV
ejpam-4578	247	3	if	if	SCONJ
ejpam-4578	247	4	a	a	PRON
ejpam-4578	247	5	is	be	AUX
ejpam-4578	247	6	a	a	DET
ejpam-4578	247	7	nonempty	nonempty	ADJ
ejpam-4578	247	8	subset	subset	NOUN
ejpam-4578	247	9	of	of	ADP
ejpam-4578	247	10	v	v	NOUN
ejpam-4578	247	11	(	(	PUNCT
ejpam-4578	247	12	g	g	NOUN
ejpam-4578	247	13	)	)	PUNCT
ejpam-4578	247	14	and	and	CCONJ
ejpam-4578	247	15	c	c	PROPN
ejpam-4578	247	16	is	be	AUX
ejpam-4578	247	17	a	a	DET
ejpam-4578	247	18	superclique	superclique	NOUN
ejpam-4578	247	19	in	in	ADP
ejpam-4578	247	20	h	h	NOUN
ejpam-4578	247	21	such	such	ADJ
ejpam-4578	247	22	that	that	DET
ejpam-4578	247	23	|a|	|a|	PROPN
ejpam-4578	247	24	=	=	SYM
ejpam-4578	247	25	1	1	NUM
ejpam-4578	247	26	whenever	whenever	SCONJ
ejpam-4578	247	27	c	c	NOUN
ejpam-4578	247	28	∩c∗	∩c∗	SYM
ejpam-4578	247	29	̸=	̸=	PROPN
ejpam-4578	247	30	∅	∅	NOUN
ejpam-4578	247	31	for	for	ADP
ejpam-4578	247	32	some	some	DET
ejpam-4578	247	33	γ	γ	NOUN
ejpam-4578	247	34	-	-	PUNCT
ejpam-4578	247	35	set	set	NOUN
ejpam-4578	247	36	of	of	ADP
ejpam-4578	247	37	h.	h.	PROPN
ejpam-4578	247	38	lemma	lemma	PROPN
ejpam-4578	247	39	5	5	X
ejpam-4578	247	40	.	.	PUNCT
ejpam-4578	248	1	let	let	VERB
ejpam-4578	248	2	g	g	PROPN
ejpam-4578	248	3	=	=	PROPN
ejpam-4578	248	4	kn	kn	PROPN
ejpam-4578	248	5	for	for	ADP
ejpam-4578	248	6	n	n	PROPN
ejpam-4578	248	7	>	>	SYM
ejpam-4578	248	8	1	1	NUM
ejpam-4578	248	9	and	and	CCONJ
ejpam-4578	248	10	h	h	DET
ejpam-4578	248	11	a	a	DET
ejpam-4578	248	12	connected	connected	ADJ
ejpam-4578	248	13	graph	graph	NOUN
ejpam-4578	248	14	with	with	ADP
ejpam-4578	248	15	|v	|v	PROPN
ejpam-4578	248	16	(	(	PUNCT
ejpam-4578	248	17	h)|	h)|	PROPN
ejpam-4578	248	18	≥	≥	NUM
ejpam-4578	248	19	3	3	NUM
ejpam-4578	248	20	.	.	PUNCT
ejpam-4578	249	1	then	then	ADV
ejpam-4578	249	2	a×c	a×c	PROPN
ejpam-4578	249	3	⊆	⊆	NUM
ejpam-4578	249	4	v	v	NOUN
ejpam-4578	249	5	(	(	PUNCT
ejpam-4578	249	6	g[h	g[h	PROPN
ejpam-4578	249	7	]	]	PUNCT
ejpam-4578	249	8	)	)	PUNCT
ejpam-4578	249	9	is	be	AUX
ejpam-4578	249	10	a	a	DET
ejpam-4578	249	11	hop	hop	NOUN
ejpam-4578	249	12	dominated	dominate	VERB
ejpam-4578	249	13	superclique	superclique	NOUN
ejpam-4578	249	14	in	in	ADP
ejpam-4578	249	15	g[h	g[h	NOUN
ejpam-4578	249	16	]	]	PUNCT
ejpam-4578	249	17	if	if	SCONJ
ejpam-4578	250	1	and	and	CCONJ
ejpam-4578	250	2	only	only	ADV
ejpam-4578	250	3	if	if	SCONJ
ejpam-4578	250	4	a	a	PRON
ejpam-4578	250	5	is	be	AUX
ejpam-4578	250	6	a	a	DET
ejpam-4578	250	7	nonempty	nonempty	ADJ
ejpam-4578	250	8	subset	subset	NOUN
ejpam-4578	250	9	of	of	ADP
ejpam-4578	250	10	v	v	NOUN
ejpam-4578	250	11	(	(	PUNCT
ejpam-4578	250	12	g	g	NOUN
ejpam-4578	250	13	)	)	PUNCT
ejpam-4578	250	14	and	and	CCONJ
ejpam-4578	250	15	c	c	PROPN
ejpam-4578	250	16	is	be	AUX
ejpam-4578	250	17	a	a	DET
ejpam-4578	250	18	hop	hop	NOUN
ejpam-4578	250	19	dominated	dominate	VERB
ejpam-4578	250	20	superclique	superclique	NOUN
ejpam-4578	250	21	in	in	ADP
ejpam-4578	250	22	h.	h.	PROPN
ejpam-4578	250	23	j.	j.	PROPN
ejpam-4578	250	24	mohamad	mohamad	PROPN
ejpam-4578	250	25	,	,	PUNCT
ejpam-4578	250	26	h.	h.	PROPN
ejpam-4578	250	27	rara	rara	PROPN
ejpam-4578	250	28	/	/	SYM
ejpam-4578	250	29	eur	eur	PROPN
ejpam-4578	250	30	.	.	PUNCT
ejpam-4578	251	1	j.	j.	PROPN
ejpam-4578	251	2	pure	pure	PROPN
ejpam-4578	251	3	appl	appl	PROPN
ejpam-4578	251	4	.	.	PROPN
ejpam-4578	251	5	math	math	PROPN
ejpam-4578	251	6	,	,	PUNCT
ejpam-4578	251	7	16	16	NUM
ejpam-4578	251	8	(	(	PUNCT
ejpam-4578	251	9	1	1	NUM
ejpam-4578	251	10	)	)	PUNCT
ejpam-4578	251	11	(	(	PUNCT
ejpam-4578	251	12	2023	2023	NUM
ejpam-4578	251	13	)	)	PUNCT
ejpam-4578	251	14	,	,	PUNCT
ejpam-4578	251	15	131	131	NUM
ejpam-4578	251	16	-	-	SYM
ejpam-4578	251	17	143	143	NUM
ejpam-4578	251	18	140	140	NUM
ejpam-4578	251	19	proof	proof	NOUN
ejpam-4578	251	20	:	:	PUNCT
ejpam-4578	251	21	suppose	suppose	VERB
ejpam-4578	251	22	that	that	SCONJ
ejpam-4578	251	23	a	a	DET
ejpam-4578	251	24	×	×	NOUN
ejpam-4578	251	25	c	c	NOUN
ejpam-4578	251	26	⊆	⊆	NUM
ejpam-4578	251	27	v	v	NOUN
ejpam-4578	251	28	(	(	PUNCT
ejpam-4578	251	29	g[h	g[h	PROPN
ejpam-4578	251	30	]	]	PUNCT
ejpam-4578	251	31	)	)	PUNCT
ejpam-4578	251	32	is	be	AUX
ejpam-4578	251	33	a	a	DET
ejpam-4578	251	34	hop	hop	NOUN
ejpam-4578	251	35	dominated	dominate	VERB
ejpam-4578	251	36	superclique	superclique	NOUN
ejpam-4578	251	37	in	in	ADP
ejpam-4578	251	38	g[h	g[h	NOUN
ejpam-4578	251	39	]	]	PUNCT
ejpam-4578	251	40	.	.	PUNCT
ejpam-4578	252	1	by	by	ADP
ejpam-4578	252	2	lemma	lemma	PROPN
ejpam-4578	252	3	3	3	PROPN
ejpam-4578	252	4	and	and	CCONJ
ejpam-4578	252	5	lemma	lemma	PROPN
ejpam-4578	252	6	4	4	NUM
ejpam-4578	252	7	,	,	PUNCT
ejpam-4578	252	8	a	a	PRON
ejpam-4578	252	9	is	be	AUX
ejpam-4578	252	10	a	a	DET
ejpam-4578	252	11	nonempty	nonempty	ADJ
ejpam-4578	252	12	subset	subset	NOUN
ejpam-4578	252	13	of	of	ADP
ejpam-4578	252	14	v	v	NOUN
ejpam-4578	252	15	(	(	PUNCT
ejpam-4578	252	16	g	g	NOUN
ejpam-4578	252	17	)	)	PUNCT
ejpam-4578	252	18	and	and	CCONJ
ejpam-4578	252	19	c	c	PROPN
ejpam-4578	252	20	is	be	AUX
ejpam-4578	252	21	a	a	DET
ejpam-4578	252	22	superclique	superclique	NOUN
ejpam-4578	252	23	in	in	ADP
ejpam-4578	252	24	h.	h.	NOUN
ejpam-4578	252	25	let	let	VERB
ejpam-4578	252	26	x	x	SYM
ejpam-4578	252	27	∈	∈	PROPN
ejpam-4578	252	28	c.	c.	NOUN
ejpam-4578	252	29	then	then	ADV
ejpam-4578	252	30	(	(	PUNCT
ejpam-4578	252	31	a	a	PRON
ejpam-4578	252	32	,	,	PUNCT
ejpam-4578	252	33	x	x	NOUN
ejpam-4578	252	34	)	)	PUNCT
ejpam-4578	252	35	∈	∈	PROPN
ejpam-4578	252	36	a×	a×	PUNCT
ejpam-4578	252	37	c	c	NOUN
ejpam-4578	252	38	for	for	ADP
ejpam-4578	252	39	any	any	DET
ejpam-4578	252	40	a	a	DET
ejpam-4578	252	41	∈	∈	NOUN
ejpam-4578	252	42	a.	a.	NOUN
ejpam-4578	252	43	since	since	SCONJ
ejpam-4578	252	44	a×	a×	PROPN
ejpam-4578	252	45	c	c	PROPN
ejpam-4578	252	46	is	be	AUX
ejpam-4578	252	47	a	a	DET
ejpam-4578	252	48	hop	hop	NOUN
ejpam-4578	252	49	dominated	dominate	VERB
ejpam-4578	252	50	superclique	superclique	NOUN
ejpam-4578	252	51	,	,	PUNCT
ejpam-4578	252	52	there	there	PRON
ejpam-4578	252	53	exists	exist	VERB
ejpam-4578	252	54	(	(	PUNCT
ejpam-4578	252	55	b	b	X
ejpam-4578	252	56	,	,	PUNCT
ejpam-4578	252	57	y	y	NOUN
ejpam-4578	252	58	)	)	PUNCT
ejpam-4578	252	59	∈	∈	PROPN
ejpam-4578	253	1	[	[	X
ejpam-4578	253	2	v	v	X
ejpam-4578	253	3	(	(	PUNCT
ejpam-4578	253	4	g[h	g[h	PROPN
ejpam-4578	253	5	]	]	PUNCT
ejpam-4578	253	6	)	)	PUNCT
ejpam-4578	253	7	\	\	PUNCT
ejpam-4578	254	1	(	(	PUNCT
ejpam-4578	254	2	a	a	DET
ejpam-4578	254	3	×	×	NOUN
ejpam-4578	254	4	c	c	NOUN
ejpam-4578	254	5	)	)	PUNCT
ejpam-4578	254	6	]	]	PUNCT
ejpam-4578	254	7	∩	∩	NOUN
ejpam-4578	254	8	ng[h]((a	ng[h]((a	SYM
ejpam-4578	254	9	,	,	PUNCT
ejpam-4578	254	10	x	x	X
ejpam-4578	254	11	)	)	PUNCT
ejpam-4578	254	12	,	,	PUNCT
ejpam-4578	254	13	2	2	NUM
ejpam-4578	254	14	)	)	PUNCT
ejpam-4578	254	15	.	.	PUNCT
ejpam-4578	255	1	suppose	suppose	VERB
ejpam-4578	256	1	γ(h	γ(h	NOUN
ejpam-4578	256	2	)	)	PUNCT
ejpam-4578	256	3	̸=	̸=	PROPN
ejpam-4578	256	4	1	1	NUM
ejpam-4578	256	5	.	.	PUNCT
ejpam-4578	257	1	since	since	SCONJ
ejpam-4578	257	2	g	g	PROPN
ejpam-4578	257	3	=	=	PROPN
ejpam-4578	257	4	kn	kn	PROPN
ejpam-4578	257	5	for	for	ADP
ejpam-4578	257	6	n	n	PROPN
ejpam-4578	257	7	>	>	X
ejpam-4578	257	8	1	1	NUM
ejpam-4578	257	9	,	,	PUNCT
ejpam-4578	257	10	a	a	DET
ejpam-4578	257	11	=	=	SYM
ejpam-4578	257	12	b	b	PROPN
ejpam-4578	257	13	and	and	CCONJ
ejpam-4578	257	14	y	y	PROPN
ejpam-4578	257	15	∈	∈	PROPN
ejpam-4578	257	16	(	(	PUNCT
ejpam-4578	257	17	v	v	NOUN
ejpam-4578	257	18	(	(	PUNCT
ejpam-4578	257	19	h)\c)∩nh(x	h)\c)∩nh(x	PROPN
ejpam-4578	257	20	,	,	PUNCT
ejpam-4578	257	21	2	2	NUM
ejpam-4578	257	22	)	)	PUNCT
ejpam-4578	257	23	.	.	PUNCT
ejpam-4578	258	1	if	if	SCONJ
ejpam-4578	258	2	γ(h	γ(h	NOUN
ejpam-4578	258	3	)	)	PUNCT
ejpam-4578	258	4	=	=	SYM
ejpam-4578	258	5	1	1	NUM
ejpam-4578	258	6	,	,	PUNCT
ejpam-4578	258	7	then	then	ADV
ejpam-4578	258	8	by	by	ADP
ejpam-4578	258	9	proposition	proposition	NOUN
ejpam-4578	258	10	5	5	NUM
ejpam-4578	258	11	,	,	PUNCT
ejpam-4578	258	12	c	c	PROPN
ejpam-4578	258	13	∩	∩	ADJ
ejpam-4578	258	14	c∗	c∗	NOUN
ejpam-4578	258	15	=	=	NOUN
ejpam-4578	258	16	∅	∅	NOUN
ejpam-4578	258	17	for	for	ADP
ejpam-4578	258	18	all	all	DET
ejpam-4578	258	19	γ	γ	NOUN
ejpam-4578	258	20	-	-	PUNCT
ejpam-4578	258	21	sets	set	NOUN
ejpam-4578	258	22	c∗	c∗	NOUN
ejpam-4578	258	23	of	of	ADP
ejpam-4578	258	24	h.	h.	PROPN
ejpam-4578	258	25	thus	thus	ADV
ejpam-4578	258	26	,	,	PUNCT
ejpam-4578	258	27	x	x	PUNCT
ejpam-4578	258	28	∈	∈	PROPN
ejpam-4578	258	29	c	c	NOUN
ejpam-4578	258	30	\	\	PROPN
ejpam-4578	258	31	c∗	c∗	PROPN
ejpam-4578	258	32	and	and	CCONJ
ejpam-4578	258	33	y	y	PROPN
ejpam-4578	258	34	∈	∈	PROPN
ejpam-4578	258	35	nh(x	nh(x	PUNCT
ejpam-4578	258	36	,	,	PUNCT
ejpam-4578	258	37	2	2	X
ejpam-4578	258	38	)	)	PUNCT
ejpam-4578	258	39	exists	exist	VERB
ejpam-4578	258	40	.	.	PUNCT
ejpam-4578	259	1	hence	hence	ADV
ejpam-4578	259	2	,	,	PUNCT
ejpam-4578	259	3	c	c	PROPN
ejpam-4578	259	4	is	be	AUX
ejpam-4578	259	5	a	a	DET
ejpam-4578	259	6	hop	hop	NOUN
ejpam-4578	259	7	dominated	dominate	VERB
ejpam-4578	259	8	superclique	superclique	NOUN
ejpam-4578	259	9	in	in	ADP
ejpam-4578	259	10	h.	h.	PROPN
ejpam-4578	259	11	for	for	ADP
ejpam-4578	259	12	the	the	DET
ejpam-4578	259	13	converse	converse	NOUN
ejpam-4578	259	14	,	,	PUNCT
ejpam-4578	259	15	suppose	suppose	VERB
ejpam-4578	259	16	that	that	SCONJ
ejpam-4578	259	17	a	a	PRON
ejpam-4578	259	18	is	be	AUX
ejpam-4578	259	19	a	a	DET
ejpam-4578	259	20	nonempty	nonempty	ADJ
ejpam-4578	259	21	subset	subset	NOUN
ejpam-4578	259	22	of	of	ADP
ejpam-4578	259	23	v	v	NOUN
ejpam-4578	259	24	(	(	PUNCT
ejpam-4578	259	25	g	g	NOUN
ejpam-4578	259	26	)	)	PUNCT
ejpam-4578	259	27	and	and	CCONJ
ejpam-4578	259	28	c	c	PROPN
ejpam-4578	259	29	is	be	AUX
ejpam-4578	259	30	a	a	DET
ejpam-4578	259	31	hop	hop	NOUN
ejpam-4578	259	32	dominated	dominate	VERB
ejpam-4578	259	33	superclique	superclique	NOUN
ejpam-4578	259	34	in	in	ADP
ejpam-4578	259	35	h.	h.	PROPN
ejpam-4578	259	36	by	by	ADP
ejpam-4578	259	37	lemma	lemma	PROPN
ejpam-4578	259	38	3	3	NUM
ejpam-4578	259	39	,	,	PUNCT
ejpam-4578	259	40	lemma	lemma	PROPN
ejpam-4578	259	41	4	4	NUM
ejpam-4578	259	42	and	and	CCONJ
ejpam-4578	259	43	proposition	proposition	NOUN
ejpam-4578	259	44	5	5	NUM
ejpam-4578	259	45	,	,	PUNCT
ejpam-4578	259	46	a	a	DET
ejpam-4578	259	47	×	×	NOUN
ejpam-4578	259	48	c	c	NOUN
ejpam-4578	259	49	is	be	AUX
ejpam-4578	259	50	a	a	DET
ejpam-4578	259	51	superclique	superclique	NOUN
ejpam-4578	259	52	in	in	ADP
ejpam-4578	259	53	g[h	g[h	NOUN
ejpam-4578	259	54	]	]	PUNCT
ejpam-4578	259	55	.	.	PUNCT
ejpam-4578	260	1	let	let	AUX
ejpam-4578	260	2	(	(	PUNCT
ejpam-4578	260	3	a	a	PRON
ejpam-4578	260	4	,	,	PUNCT
ejpam-4578	260	5	x	x	X
ejpam-4578	260	6	)	)	PUNCT
ejpam-4578	260	7	∈	∈	PROPN
ejpam-4578	260	8	a	a	DET
ejpam-4578	260	9	×	×	NOUN
ejpam-4578	260	10	c	c	NOUN
ejpam-4578	260	11	and	and	CCONJ
ejpam-4578	260	12	γ(h	γ(h	NOUN
ejpam-4578	260	13	)	)	PUNCT
ejpam-4578	260	14	̸=	̸=	PROPN
ejpam-4578	260	15	1	1	NUM
ejpam-4578	260	16	.	.	PUNCT
ejpam-4578	261	1	since	since	SCONJ
ejpam-4578	261	2	c	c	PROPN
ejpam-4578	261	3	is	be	AUX
ejpam-4578	261	4	a	a	DET
ejpam-4578	261	5	hop	hop	NOUN
ejpam-4578	261	6	dominated	dominate	VERB
ejpam-4578	261	7	superclique	superclique	NOUN
ejpam-4578	261	8	in	in	ADP
ejpam-4578	261	9	h	h	NOUN
ejpam-4578	261	10	,	,	PUNCT
ejpam-4578	261	11	there	there	PRON
ejpam-4578	261	12	exists	exist	VERB
ejpam-4578	261	13	y	y	PROPN
ejpam-4578	261	14	∈	∈	PROPN
ejpam-4578	261	15	(	(	PUNCT
ejpam-4578	261	16	v	v	NOUN
ejpam-4578	261	17	(	(	PUNCT
ejpam-4578	261	18	h	h	NOUN
ejpam-4578	261	19	)	)	PUNCT
ejpam-4578	261	20	\	\	NOUN
ejpam-4578	262	1	c	c	X
ejpam-4578	262	2	)	)	PUNCT
ejpam-4578	262	3	∩nh(x	∩nh(x	PROPN
ejpam-4578	262	4	,	,	PUNCT
ejpam-4578	262	5	2	2	NUM
ejpam-4578	262	6	)	)	PUNCT
ejpam-4578	262	7	.	.	PUNCT
ejpam-4578	263	1	hence	hence	ADV
ejpam-4578	263	2	,	,	PUNCT
ejpam-4578	263	3	(	(	PUNCT
ejpam-4578	263	4	a	a	PRON
ejpam-4578	263	5	,	,	PUNCT
ejpam-4578	263	6	y	y	NOUN
ejpam-4578	263	7	)	)	PUNCT
ejpam-4578	263	8	∈	∈	PROPN
ejpam-4578	264	1	[	[	X
ejpam-4578	264	2	v	v	X
ejpam-4578	264	3	(	(	PUNCT
ejpam-4578	264	4	g[h	g[h	PROPN
ejpam-4578	264	5	]	]	PUNCT
ejpam-4578	264	6	)	)	PUNCT
ejpam-4578	264	7	\	\	PUNCT
ejpam-4578	265	1	(	(	PUNCT
ejpam-4578	265	2	a×	a×	NOUN
ejpam-4578	265	3	c	c	NOUN
ejpam-4578	265	4	)	)	PUNCT
ejpam-4578	265	5	]	]	PUNCT
ejpam-4578	266	1	∩ng[h]((a	∩ng[h]((a	PROPN
ejpam-4578	266	2	,	,	PUNCT
ejpam-4578	266	3	x	x	NOUN
ejpam-4578	266	4	)	)	PUNCT
ejpam-4578	266	5	,	,	PUNCT
ejpam-4578	266	6	2	2	NUM
ejpam-4578	266	7	)	)	PUNCT
ejpam-4578	266	8	.	.	PUNCT
ejpam-4578	267	1	suppose	suppose	VERB
ejpam-4578	267	2	γ(h	γ(h	NOUN
ejpam-4578	267	3	)	)	PUNCT
ejpam-4578	267	4	=	=	SYM
ejpam-4578	268	1	1	1	X
ejpam-4578	268	2	.	.	PUNCT
ejpam-4578	268	3	then	then	ADV
ejpam-4578	268	4	by	by	ADP
ejpam-4578	268	5	proposition	proposition	NOUN
ejpam-4578	268	6	5	5	NUM
ejpam-4578	268	7	,	,	PUNCT
ejpam-4578	268	8	c	c	PROPN
ejpam-4578	268	9	∩	∩	ADJ
ejpam-4578	268	10	c∗	c∗	NOUN
ejpam-4578	268	11	=	=	NOUN
ejpam-4578	268	12	∅	∅	NOUN
ejpam-4578	268	13	for	for	ADP
ejpam-4578	268	14	all	all	DET
ejpam-4578	268	15	γ	γ	NOUN
ejpam-4578	268	16	-	-	PUNCT
ejpam-4578	268	17	sets	set	NOUN
ejpam-4578	268	18	c∗	c∗	NOUN
ejpam-4578	268	19	of	of	ADP
ejpam-4578	268	20	h.	h.	PROPN
ejpam-4578	268	21	thus	thus	ADV
ejpam-4578	268	22	,	,	PUNCT
ejpam-4578	268	23	x	x	PUNCT
ejpam-4578	268	24	∈	∈	PROPN
ejpam-4578	268	25	c	c	NOUN
ejpam-4578	268	26	\	\	X
ejpam-4578	268	27	c∗.	c∗.	NOUN
ejpam-4578	268	28	this	this	PRON
ejpam-4578	268	29	implies	imply	VERB
ejpam-4578	268	30	that	that	SCONJ
ejpam-4578	268	31	a	a	DET
ejpam-4578	268	32	vertex	vertex	NOUN
ejpam-4578	268	33	z	z	NOUN
ejpam-4578	268	34	∈	∈	PROPN
ejpam-4578	268	35	nh(x	nh(x	NUM
ejpam-4578	268	36	,	,	PUNCT
ejpam-4578	268	37	2	2	X
ejpam-4578	268	38	)	)	PUNCT
ejpam-4578	268	39	exists	exist	VERB
ejpam-4578	268	40	.	.	PUNCT
ejpam-4578	269	1	since	since	SCONJ
ejpam-4578	269	2	c	c	PROPN
ejpam-4578	269	3	is	be	AUX
ejpam-4578	269	4	a	a	DET
ejpam-4578	269	5	superclique	superclique	NOUN
ejpam-4578	269	6	,	,	PUNCT
ejpam-4578	269	7	z	z	PROPN
ejpam-4578	269	8	∈	∈	PROPN
ejpam-4578	269	9	v	v	ADP
ejpam-4578	269	10	(	(	PUNCT
ejpam-4578	269	11	h	h	NOUN
ejpam-4578	269	12	)	)	PUNCT
ejpam-4578	269	13	\	\	PROPN
ejpam-4578	269	14	c.	c.	PROPN
ejpam-4578	269	15	hence	hence	ADV
ejpam-4578	269	16	,	,	PUNCT
ejpam-4578	269	17	(	(	PUNCT
ejpam-4578	269	18	a	a	PRON
ejpam-4578	269	19	,	,	PUNCT
ejpam-4578	269	20	z	z	NOUN
ejpam-4578	269	21	)	)	PUNCT
ejpam-4578	269	22	∈	∈	PROPN
ejpam-4578	270	1	[	[	X
ejpam-4578	270	2	v	v	X
ejpam-4578	270	3	(	(	PUNCT
ejpam-4578	270	4	g[h	g[h	PROPN
ejpam-4578	270	5	]	]	PUNCT
ejpam-4578	270	6	)	)	PUNCT
ejpam-4578	270	7	\	\	PUNCT
ejpam-4578	271	1	(	(	PUNCT
ejpam-4578	271	2	a×	a×	NOUN
ejpam-4578	271	3	c	c	NOUN
ejpam-4578	271	4	)	)	PUNCT
ejpam-4578	271	5	]	]	PUNCT
ejpam-4578	272	1	∩ng[h]((a	∩ng[h]((a	PROPN
ejpam-4578	272	2	,	,	PUNCT
ejpam-4578	272	3	x	x	NOUN
ejpam-4578	272	4	)	)	PUNCT
ejpam-4578	272	5	,	,	PUNCT
ejpam-4578	272	6	2	2	NUM
ejpam-4578	272	7	)	)	PUNCT
ejpam-4578	272	8	.	.	PUNCT
ejpam-4578	273	1	therefore	therefore	ADV
ejpam-4578	273	2	a×	a×	PROPN
ejpam-4578	273	3	c	c	PROPN
ejpam-4578	273	4	is	be	AUX
ejpam-4578	273	5	a	a	DET
ejpam-4578	273	6	hop	hop	NOUN
ejpam-4578	273	7	dominated	dominate	VERB
ejpam-4578	273	8	superclique	superclique	NOUN
ejpam-4578	273	9	in	in	ADP
ejpam-4578	273	10	g[h	g[h	NOUN
ejpam-4578	273	11	]	]	PUNCT
ejpam-4578	273	12	.	.	PUNCT
ejpam-4578	274	1	theorem	theorem	NOUN
ejpam-4578	274	2	9	9	NUM
ejpam-4578	274	3	.	.	PUNCT
ejpam-4578	275	1	let	let	VERB
ejpam-4578	275	2	g	g	PROPN
ejpam-4578	275	3	=	=	PROPN
ejpam-4578	275	4	kn	kn	PROPN
ejpam-4578	275	5	for	for	ADP
ejpam-4578	275	6	n	n	PROPN
ejpam-4578	275	7	>	>	SYM
ejpam-4578	275	8	1	1	NUM
ejpam-4578	275	9	and	and	CCONJ
ejpam-4578	275	10	h	h	DET
ejpam-4578	275	11	a	a	DET
ejpam-4578	275	12	connected	connected	ADJ
ejpam-4578	275	13	graph	graph	NOUN
ejpam-4578	275	14	with	with	ADP
ejpam-4578	275	15	|v	|v	PROPN
ejpam-4578	275	16	(	(	PUNCT
ejpam-4578	275	17	h)|	h)|	PROPN
ejpam-4578	275	18	≥	≥	NOUN
ejpam-4578	275	19	3	3	NUM
ejpam-4578	275	20	.	.	PUNCT
ejpam-4578	276	1	a	a	DET
ejpam-4578	276	2	subset	subset	NOUN
ejpam-4578	276	3	s	s	X
ejpam-4578	276	4	of	of	ADP
ejpam-4578	276	5	v	v	NOUN
ejpam-4578	276	6	(	(	PUNCT
ejpam-4578	276	7	g[h	g[h	PROPN
ejpam-4578	276	8	]	]	PUNCT
ejpam-4578	276	9	)	)	PUNCT
ejpam-4578	276	10	is	be	AUX
ejpam-4578	276	11	a	a	DET
ejpam-4578	276	12	strong	strong	ADJ
ejpam-4578	276	13	resolving	resolve	VERB
ejpam-4578	276	14	hop	hop	NOUN
ejpam-4578	276	15	dominating	dominating	NOUN
ejpam-4578	276	16	set	set	NOUN
ejpam-4578	276	17	of	of	ADP
ejpam-4578	276	18	g[h	g[h	PROPN
ejpam-4578	276	19	]	]	PUNCT
ejpam-4578	276	20	if	if	SCONJ
ejpam-4578	276	21	and	and	CCONJ
ejpam-4578	276	22	only	only	ADV
ejpam-4578	276	23	if	if	SCONJ
ejpam-4578	276	24	s	s	VERB
ejpam-4578	276	25	=	=	SYM
ejpam-4578	276	26	v	v	NOUN
ejpam-4578	276	27	(	(	PUNCT
ejpam-4578	276	28	g[h	g[h	PROPN
ejpam-4578	276	29	]	]	PUNCT
ejpam-4578	276	30	)	)	PUNCT
ejpam-4578	276	31	\	\	PUNCT
ejpam-4578	277	1	(	(	PUNCT
ejpam-4578	277	2	a	a	DET
ejpam-4578	277	3	×	×	NOUN
ejpam-4578	277	4	c	c	NOUN
ejpam-4578	277	5	)	)	PUNCT
ejpam-4578	277	6	,	,	PUNCT
ejpam-4578	277	7	where	where	SCONJ
ejpam-4578	277	8	a	a	PRON
ejpam-4578	277	9	is	be	AUX
ejpam-4578	277	10	a	a	DET
ejpam-4578	277	11	subset	subset	NOUN
ejpam-4578	277	12	of	of	ADP
ejpam-4578	277	13	v	v	NOUN
ejpam-4578	277	14	(	(	PUNCT
ejpam-4578	277	15	g	g	NOUN
ejpam-4578	277	16	)	)	PUNCT
ejpam-4578	277	17	and	and	CCONJ
ejpam-4578	277	18	c	c	NOUN
ejpam-4578	277	19	=	=	SYM
ejpam-4578	277	20	∅	∅	NOUN
ejpam-4578	277	21	or	or	CCONJ
ejpam-4578	277	22	a	a	PRON
ejpam-4578	277	23	is	be	AUX
ejpam-4578	277	24	a	a	DET
ejpam-4578	277	25	nonempty	nonempty	ADJ
ejpam-4578	277	26	subset	subset	NOUN
ejpam-4578	277	27	of	of	ADP
ejpam-4578	277	28	v	v	NOUN
ejpam-4578	277	29	(	(	PUNCT
ejpam-4578	277	30	g	g	NOUN
ejpam-4578	277	31	)	)	PUNCT
ejpam-4578	277	32	and	and	CCONJ
ejpam-4578	277	33	c	c	PROPN
ejpam-4578	277	34	is	be	AUX
ejpam-4578	277	35	a	a	DET
ejpam-4578	277	36	hop	hop	NOUN
ejpam-4578	277	37	dominated	dominate	VERB
ejpam-4578	277	38	superclique	superclique	NOUN
ejpam-4578	277	39	in	in	ADP
ejpam-4578	277	40	h.	h.	PROPN
ejpam-4578	277	41	proof	proof	NOUN
ejpam-4578	277	42	:	:	PUNCT
ejpam-4578	277	43	let	let	VERB
ejpam-4578	277	44	s	s	PRON
ejpam-4578	277	45	be	be	AUX
ejpam-4578	277	46	a	a	DET
ejpam-4578	277	47	strong	strong	ADJ
ejpam-4578	277	48	resolving	resolve	VERB
ejpam-4578	277	49	hop	hop	NOUN
ejpam-4578	277	50	dominating	dominating	NOUN
ejpam-4578	277	51	set	set	NOUN
ejpam-4578	277	52	of	of	ADP
ejpam-4578	277	53	g[h	g[h	NOUN
ejpam-4578	277	54	]	]	PUNCT
ejpam-4578	277	55	.	.	PUNCT
ejpam-4578	278	1	since	since	SCONJ
ejpam-4578	278	2	diam(g[h	diam(g[h	PROPN
ejpam-4578	278	3	]	]	PUNCT
ejpam-4578	278	4	)	)	PUNCT
ejpam-4578	278	5	=	=	SYM
ejpam-4578	278	6	2	2	X
ejpam-4578	278	7	,	,	PUNCT
ejpam-4578	278	8	by	by	ADP
ejpam-4578	278	9	lemma	lemma	PROPN
ejpam-4578	278	10	1	1	NUM
ejpam-4578	278	11	,	,	PUNCT
ejpam-4578	278	12	s	s	PART
ejpam-4578	278	13	=	=	SYM
ejpam-4578	278	14	v	v	NOUN
ejpam-4578	278	15	(	(	PUNCT
ejpam-4578	278	16	g[h	g[h	PROPN
ejpam-4578	278	17	]	]	PUNCT
ejpam-4578	278	18	)	)	PUNCT
ejpam-4578	278	19	\	\	PUNCT
ejpam-4578	279	1	(	(	PUNCT
ejpam-4578	279	2	a	a	DET
ejpam-4578	279	3	×	×	NOUN
ejpam-4578	279	4	c	c	NOUN
ejpam-4578	279	5	)	)	PUNCT
ejpam-4578	279	6	where	where	SCONJ
ejpam-4578	279	7	a	a	DET
ejpam-4578	279	8	×	×	NOUN
ejpam-4578	279	9	c	c	NOUN
ejpam-4578	279	10	=	=	NOUN
ejpam-4578	279	11	∅	∅	NOUN
ejpam-4578	279	12	or	or	CCONJ
ejpam-4578	279	13	a	a	DET
ejpam-4578	279	14	×	×	NOUN
ejpam-4578	279	15	c	c	NOUN
ejpam-4578	279	16	is	be	AUX
ejpam-4578	279	17	a	a	DET
ejpam-4578	279	18	hop	hop	NOUN
ejpam-4578	279	19	dominated	dominate	VERB
ejpam-4578	279	20	superclique	superclique	NOUN
ejpam-4578	279	21	in	in	ADP
ejpam-4578	279	22	g[h	g[h	NOUN
ejpam-4578	279	23	]	]	PUNCT
ejpam-4578	279	24	.	.	PUNCT
ejpam-4578	280	1	if	if	SCONJ
ejpam-4578	280	2	a×	a×	PROPN
ejpam-4578	280	3	c	c	NOUN
ejpam-4578	280	4	=	=	SYM
ejpam-4578	280	5	∅	∅	NOUN
ejpam-4578	280	6	,	,	PUNCT
ejpam-4578	280	7	then	then	ADV
ejpam-4578	280	8	a	a	DET
ejpam-4578	280	9	=	=	NOUN
ejpam-4578	280	10	∅	∅	NOUN
ejpam-4578	280	11	or	or	CCONJ
ejpam-4578	280	12	c	c	NOUN
ejpam-4578	280	13	=	=	PUNCT
ejpam-4578	280	14	∅.	∅.	NOUN
ejpam-4578	280	15	on	on	ADP
ejpam-4578	280	16	the	the	DET
ejpam-4578	280	17	other	other	ADJ
ejpam-4578	280	18	hand	hand	NOUN
ejpam-4578	280	19	,	,	PUNCT
ejpam-4578	280	20	if	if	SCONJ
ejpam-4578	280	21	a×	a×	PROPN
ejpam-4578	280	22	c	c	NOUN
ejpam-4578	280	23	is	be	AUX
ejpam-4578	280	24	a	a	DET
ejpam-4578	280	25	hop	hop	NOUN
ejpam-4578	280	26	dominated	dominate	VERB
ejpam-4578	280	27	superclique	superclique	NOUN
ejpam-4578	280	28	in	in	ADP
ejpam-4578	280	29	g[h	g[h	PROPN
ejpam-4578	280	30	]	]	PUNCT
ejpam-4578	280	31	,	,	PUNCT
ejpam-4578	280	32	a	a	PRON
ejpam-4578	280	33	is	be	AUX
ejpam-4578	280	34	a	a	DET
ejpam-4578	280	35	nonempty	nonempty	ADJ
ejpam-4578	280	36	subset	subset	NOUN
ejpam-4578	280	37	of	of	ADP
ejpam-4578	280	38	v	v	NOUN
ejpam-4578	280	39	(	(	PUNCT
ejpam-4578	280	40	g	g	NOUN
ejpam-4578	280	41	)	)	PUNCT
ejpam-4578	280	42	and	and	CCONJ
ejpam-4578	280	43	c	c	PROPN
ejpam-4578	280	44	is	be	AUX
ejpam-4578	280	45	a	a	DET
ejpam-4578	280	46	hop	hop	NOUN
ejpam-4578	280	47	dominated	dominate	VERB
ejpam-4578	280	48	superclique	superclique	NOUN
ejpam-4578	280	49	in	in	ADP
ejpam-4578	280	50	h	h	NOUN
ejpam-4578	280	51	,	,	PUNCT
ejpam-4578	280	52	by	by	ADP
ejpam-4578	280	53	lemma	lemma	PROPN
ejpam-4578	280	54	5	5	NUM
ejpam-4578	280	55	.	.	PUNCT
ejpam-4578	281	1	for	for	ADP
ejpam-4578	281	2	the	the	DET
ejpam-4578	281	3	converse	converse	NOUN
ejpam-4578	281	4	,	,	PUNCT
ejpam-4578	281	5	suppose	suppose	VERB
ejpam-4578	281	6	s	s	VERB
ejpam-4578	281	7	=	=	SYM
ejpam-4578	281	8	v	v	PROPN
ejpam-4578	281	9	(	(	PUNCT
ejpam-4578	281	10	g[h	g[h	PROPN
ejpam-4578	281	11	]	]	PUNCT
ejpam-4578	281	12	)	)	PUNCT
ejpam-4578	281	13	\	\	PUNCT
ejpam-4578	282	1	(	(	PUNCT
ejpam-4578	282	2	a×	a×	NOUN
ejpam-4578	282	3	c	c	X
ejpam-4578	282	4	)	)	PUNCT
ejpam-4578	282	5	,	,	PUNCT
ejpam-4578	282	6	where	where	SCONJ
ejpam-4578	282	7	a	a	DET
ejpam-4578	282	8	⊆	⊆	NUM
ejpam-4578	282	9	v	v	NOUN
ejpam-4578	282	10	(	(	PUNCT
ejpam-4578	282	11	g	g	NOUN
ejpam-4578	282	12	)	)	PUNCT
ejpam-4578	282	13	and	and	CCONJ
ejpam-4578	282	14	c	c	NOUN
ejpam-4578	282	15	=	=	SYM
ejpam-4578	282	16	∅	∅	NOUN
ejpam-4578	282	17	or	or	CCONJ
ejpam-4578	282	18	a	a	PRON
ejpam-4578	282	19	is	be	AUX
ejpam-4578	282	20	a	a	DET
ejpam-4578	282	21	nonempty	nonempty	ADJ
ejpam-4578	282	22	subset	subset	NOUN
ejpam-4578	282	23	of	of	ADP
ejpam-4578	282	24	v	v	NOUN
ejpam-4578	282	25	(	(	PUNCT
ejpam-4578	282	26	g	g	NOUN
ejpam-4578	282	27	)	)	PUNCT
ejpam-4578	282	28	and	and	CCONJ
ejpam-4578	282	29	c	c	PROPN
ejpam-4578	282	30	is	be	AUX
ejpam-4578	282	31	a	a	DET
ejpam-4578	282	32	hop	hop	NOUN
ejpam-4578	282	33	dominated	dominate	VERB
ejpam-4578	282	34	superclique	superclique	NOUN
ejpam-4578	282	35	in	in	ADP
ejpam-4578	282	36	h.	h.	PROPN
ejpam-4578	282	37	if	if	SCONJ
ejpam-4578	282	38	c	c	NOUN
ejpam-4578	282	39	=	=	SYM
ejpam-4578	282	40	∅	∅	NOUN
ejpam-4578	282	41	,	,	PUNCT
ejpam-4578	282	42	then	then	ADV
ejpam-4578	282	43	a	a	DET
ejpam-4578	282	44	×	×	NOUN
ejpam-4578	282	45	c	c	NOUN
ejpam-4578	282	46	=	=	NOUN
ejpam-4578	282	47	∅	∅	NOUN
ejpam-4578	282	48	and	and	CCONJ
ejpam-4578	282	49	s	s	NOUN
ejpam-4578	282	50	=	=	SYM
ejpam-4578	282	51	v	v	PROPN
ejpam-4578	282	52	(	(	PUNCT
ejpam-4578	282	53	g[h	g[h	PROPN
ejpam-4578	282	54	]	]	PUNCT
ejpam-4578	282	55	)	)	PUNCT
ejpam-4578	282	56	is	be	AUX
ejpam-4578	282	57	a	a	DET
ejpam-4578	282	58	strong	strong	ADJ
ejpam-4578	282	59	resolving	resolve	VERB
ejpam-4578	282	60	hop	hop	NOUN
ejpam-4578	282	61	dominating	dominating	NOUN
ejpam-4578	282	62	set	set	NOUN
ejpam-4578	282	63	of	of	ADP
ejpam-4578	282	64	g[h	g[h	NOUN
ejpam-4578	282	65	]	]	PUNCT
ejpam-4578	282	66	.	.	PUNCT
ejpam-4578	283	1	on	on	ADP
ejpam-4578	283	2	the	the	DET
ejpam-4578	283	3	other	other	ADJ
ejpam-4578	283	4	hand	hand	NOUN
ejpam-4578	283	5	,	,	PUNCT
ejpam-4578	283	6	if	if	SCONJ
ejpam-4578	283	7	a	a	PRON
ejpam-4578	283	8	is	be	AUX
ejpam-4578	283	9	a	a	DET
ejpam-4578	283	10	nonempty	nonempty	ADJ
ejpam-4578	283	11	subset	subset	NOUN
ejpam-4578	283	12	of	of	ADP
ejpam-4578	283	13	v	v	NOUN
ejpam-4578	283	14	(	(	PUNCT
ejpam-4578	283	15	g	g	NOUN
ejpam-4578	283	16	)	)	PUNCT
ejpam-4578	283	17	and	and	CCONJ
ejpam-4578	283	18	c	c	PROPN
ejpam-4578	283	19	is	be	AUX
ejpam-4578	283	20	a	a	DET
ejpam-4578	283	21	hop	hop	NOUN
ejpam-4578	283	22	dominated	dominate	VERB
ejpam-4578	283	23	superclique	superclique	NOUN
ejpam-4578	283	24	in	in	ADP
ejpam-4578	283	25	h	h	NOUN
ejpam-4578	283	26	,	,	PUNCT
ejpam-4578	283	27	then	then	ADV
ejpam-4578	283	28	by	by	ADP
ejpam-4578	283	29	lemma	lemma	PROPN
ejpam-4578	283	30	5	5	NUM
ejpam-4578	283	31	and	and	CCONJ
ejpam-4578	283	32	lemma	lemma	PROPN
ejpam-4578	283	33	1	1	NUM
ejpam-4578	283	34	,	,	PUNCT
ejpam-4578	283	35	s	s	VERB
ejpam-4578	283	36	is	be	AUX
ejpam-4578	283	37	a	a	DET
ejpam-4578	283	38	strong	strong	ADJ
ejpam-4578	283	39	resolving	resolve	VERB
ejpam-4578	283	40	hop	hop	NOUN
ejpam-4578	283	41	dominating	dominating	NOUN
ejpam-4578	283	42	set	set	NOUN
ejpam-4578	283	43	of	of	ADP
ejpam-4578	283	44	g[h	g[h	PROPN
ejpam-4578	283	45	]	]	PUNCT
ejpam-4578	283	46	.	.	PUNCT
ejpam-4578	284	1	corollary	corollary	ADJ
ejpam-4578	284	2	5	5	NUM
ejpam-4578	284	3	.	.	PUNCT
ejpam-4578	285	1	let	let	VERB
ejpam-4578	285	2	g	g	PROPN
ejpam-4578	285	3	=	=	PROPN
ejpam-4578	285	4	kn	kn	PROPN
ejpam-4578	285	5	for	for	ADP
ejpam-4578	285	6	n	n	PROPN
ejpam-4578	285	7	>	>	SYM
ejpam-4578	285	8	1	1	NUM
ejpam-4578	285	9	and	and	CCONJ
ejpam-4578	285	10	h	h	DET
ejpam-4578	285	11	a	a	DET
ejpam-4578	285	12	connected	connected	ADJ
ejpam-4578	285	13	graph	graph	NOUN
ejpam-4578	285	14	of	of	ADP
ejpam-4578	285	15	order	order	NOUN
ejpam-4578	285	16	m	m	VERB
ejpam-4578	285	17	≥	≥	NOUN
ejpam-4578	285	18	3	3	NUM
ejpam-4578	285	19	.	.	PUNCT
ejpam-4578	286	1	then	then	ADV
ejpam-4578	286	2	γsrh(g[h	γsrh(g[h	NOUN
ejpam-4578	286	3	]	]	X
ejpam-4578	286	4	)	)	PUNCT
ejpam-4578	286	5	=	=	SYM
ejpam-4578	287	1	mn−	mn−	NOUN
ejpam-4578	287	2	ωhs(g[h	ωhs(g[h	NUM
ejpam-4578	287	3	]	]	NUM
ejpam-4578	287	4	)	)	PUNCT
ejpam-4578	287	5	.	.	PUNCT
ejpam-4578	288	1	proof	proof	NOUN
ejpam-4578	288	2	:	:	PUNCT
ejpam-4578	288	3	let	let	VERB
ejpam-4578	288	4	s	s	PRON
ejpam-4578	288	5	be	be	AUX
ejpam-4578	288	6	a	a	DET
ejpam-4578	288	7	γsrh	γsrh	NOUN
ejpam-4578	288	8	-	-	PUNCT
ejpam-4578	288	9	set	set	NOUN
ejpam-4578	288	10	of	of	ADP
ejpam-4578	288	11	g[h	g[h	NOUN
ejpam-4578	288	12	]	]	PUNCT
ejpam-4578	288	13	.	.	PUNCT
ejpam-4578	289	1	then	then	ADV
ejpam-4578	289	2	by	by	ADP
ejpam-4578	289	3	theorem	theorem	NOUN
ejpam-4578	289	4	9	9	NUM
ejpam-4578	289	5	,	,	PUNCT
ejpam-4578	289	6	s	s	PART
ejpam-4578	289	7	=	=	SYM
ejpam-4578	289	8	v	v	PROPN
ejpam-4578	289	9	(	(	PUNCT
ejpam-4578	289	10	g[h])\(a×c	g[h])\(a×c	NOUN
ejpam-4578	289	11	)	)	PUNCT
ejpam-4578	289	12	where	where	SCONJ
ejpam-4578	289	13	a	a	DET
ejpam-4578	289	14	×	×	NOUN
ejpam-4578	289	15	c	c	NOUN
ejpam-4578	289	16	is	be	AUX
ejpam-4578	289	17	a	a	DET
ejpam-4578	289	18	hop	hop	NOUN
ejpam-4578	289	19	dominated	dominate	VERB
ejpam-4578	289	20	superclique	superclique	NOUN
ejpam-4578	289	21	in	in	ADP
ejpam-4578	289	22	g[h	g[h	NOUN
ejpam-4578	289	23	]	]	PUNCT
ejpam-4578	289	24	.	.	PUNCT
ejpam-4578	290	1	since	since	SCONJ
ejpam-4578	290	2	s	s	PROPN
ejpam-4578	290	3	is	be	AUX
ejpam-4578	290	4	a	a	DET
ejpam-4578	290	5	minimum	minimum	ADJ
ejpam-4578	290	6	strong	strong	ADJ
ejpam-4578	290	7	resolving	resolve	VERB
ejpam-4578	290	8	hop	hop	NOUN
ejpam-4578	290	9	dominating	dominating	NOUN
ejpam-4578	290	10	set	set	NOUN
ejpam-4578	290	11	of	of	ADP
ejpam-4578	290	12	g[h	g[h	NOUN
ejpam-4578	290	13	]	]	PUNCT
ejpam-4578	290	14	.	.	PUNCT
ejpam-4578	291	1	hence	hence	ADV
ejpam-4578	291	2	,	,	PUNCT
ejpam-4578	291	3	γsrh(g[h	γsrh(g[h	PROPN
ejpam-4578	291	4	]	]	X
ejpam-4578	291	5	)	)	PUNCT
ejpam-4578	291	6	=	=	SYM
ejpam-4578	291	7	|s|	|s|	PROPN
ejpam-4578	291	8	=	=	SYM
ejpam-4578	291	9	|v	|v	PROPN
ejpam-4578	291	10	(	(	PUNCT
ejpam-4578	291	11	g[h])|	g[h])|	PROPN
ejpam-4578	291	12	−	−	PROPN
ejpam-4578	291	13	|a×	|a×	ADJ
ejpam-4578	291	14	c|	c|	PROPN
ejpam-4578	291	15	=	=	SYM
ejpam-4578	291	16	mn−	mn−	NOUN
ejpam-4578	291	17	ωhs(g[h	ωhs(g[h	NUM
ejpam-4578	291	18	]	]	NUM
ejpam-4578	291	19	)	)	PUNCT
ejpam-4578	291	20	.	.	PUNCT
ejpam-4578	292	1	by	by	ADP
ejpam-4578	292	2	lemma	lemma	PROPN
ejpam-4578	292	3	5	5	NUM
ejpam-4578	292	4	and	and	CCONJ
ejpam-4578	292	5	corollary	corollary	ADJ
ejpam-4578	292	6	5	5	NUM
ejpam-4578	292	7	the	the	DET
ejpam-4578	292	8	next	next	ADJ
ejpam-4578	292	9	result	result	NOUN
ejpam-4578	292	10	follows	follow	VERB
ejpam-4578	292	11	.	.	PUNCT
ejpam-4578	293	1	j.	j.	PROPN
ejpam-4578	293	2	mohamad	mohamad	PROPN
ejpam-4578	293	3	,	,	PUNCT
ejpam-4578	293	4	h.	h.	PROPN
ejpam-4578	293	5	rara	rara	PROPN
ejpam-4578	293	6	/	/	SYM
ejpam-4578	293	7	eur	eur	PROPN
ejpam-4578	293	8	.	.	PUNCT
ejpam-4578	294	1	j.	j.	PROPN
ejpam-4578	294	2	pure	pure	PROPN
ejpam-4578	294	3	appl	appl	PROPN
ejpam-4578	294	4	.	.	PROPN
ejpam-4578	294	5	math	math	PROPN
ejpam-4578	294	6	,	,	PUNCT
ejpam-4578	294	7	16	16	NUM
ejpam-4578	294	8	(	(	PUNCT
ejpam-4578	294	9	1	1	NUM
ejpam-4578	294	10	)	)	PUNCT
ejpam-4578	294	11	(	(	PUNCT
ejpam-4578	294	12	2023	2023	NUM
ejpam-4578	294	13	)	)	PUNCT
ejpam-4578	294	14	,	,	PUNCT
ejpam-4578	294	15	131	131	NUM
ejpam-4578	294	16	-	-	SYM
ejpam-4578	294	17	143	143	NUM
ejpam-4578	294	18	141	141	NUM
ejpam-4578	294	19	corollary	corollary	NOUN
ejpam-4578	294	20	6	6	NUM
ejpam-4578	294	21	.	.	PUNCT
ejpam-4578	295	1	let	let	VERB
ejpam-4578	295	2	g	g	PROPN
ejpam-4578	295	3	=	=	PROPN
ejpam-4578	295	4	kn	kn	PROPN
ejpam-4578	295	5	for	for	ADP
ejpam-4578	295	6	n	n	PROPN
ejpam-4578	295	7	>	>	SYM
ejpam-4578	295	8	1	1	NUM
ejpam-4578	295	9	and	and	CCONJ
ejpam-4578	295	10	h	h	DET
ejpam-4578	295	11	a	a	DET
ejpam-4578	295	12	connected	connected	ADJ
ejpam-4578	295	13	graph	graph	NOUN
ejpam-4578	295	14	of	of	ADP
ejpam-4578	295	15	order	order	NOUN
ejpam-4578	295	16	m.	m.	NOUN
ejpam-4578	295	17	then	then	ADV
ejpam-4578	295	18	γsrh(g[h	γsrh(g[h	PROPN
ejpam-4578	295	19	]	]	PUNCT
ejpam-4578	295	20	)	)	PUNCT
ejpam-4578	295	21	=	=	SYM
ejpam-4578	295	22	n(m−	n(m−	PROPN
ejpam-4578	295	23	ωhs(h	ωhs(h	PROPN
ejpam-4578	295	24	)	)	PUNCT
ejpam-4578	295	25	)	)	PUNCT
ejpam-4578	295	26	.	.	PUNCT
ejpam-4578	296	1	theorem	theorem	ADJ
ejpam-4578	296	2	10	10	NUM
ejpam-4578	296	3	.	.	PUNCT
ejpam-4578	297	1	[	[	X
ejpam-4578	297	2	1	1	X
ejpam-4578	297	3	]	]	PUNCT
ejpam-4578	297	4	let	let	VERB
ejpam-4578	297	5	g	g	PRON
ejpam-4578	297	6	be	be	AUX
ejpam-4578	297	7	a	a	DET
ejpam-4578	297	8	non	non	ADJ
ejpam-4578	297	9	-	-	ADJ
ejpam-4578	297	10	trivial	trivial	ADJ
ejpam-4578	297	11	connected	connected	ADJ
ejpam-4578	297	12	graph	graph	NOUN
ejpam-4578	297	13	and	and	CCONJ
ejpam-4578	297	14	h	h	NOUN
ejpam-4578	297	15	be	be	AUX
ejpam-4578	297	16	non	non	ADJ
ejpam-4578	297	17	-	-	ADJ
ejpam-4578	297	18	trivial	trivial	ADJ
ejpam-4578	297	19	complete	complete	ADJ
ejpam-4578	297	20	graph	graph	NOUN
ejpam-4578	297	21	.	.	PUNCT
ejpam-4578	298	1	a	a	DET
ejpam-4578	298	2	subset	subset	NOUN
ejpam-4578	298	3	c	c	NOUN
ejpam-4578	298	4	=	=	SYM
ejpam-4578	298	5	(	(	PUNCT
ejpam-4578	298	6	⋃	⋃	PROPN
ejpam-4578	298	7	x∈s	x∈s	X
ejpam-4578	298	8	{	{	PUNCT
ejpam-4578	298	9	{	{	PUNCT
ejpam-4578	298	10	x	x	NOUN
ejpam-4578	298	11	}	}	PUNCT
ejpam-4578	298	12	×	×	NOUN
ejpam-4578	298	13	tx	tx	PROPN
ejpam-4578	298	14	}	}	PUNCT
ejpam-4578	298	15	)	)	PUNCT
ejpam-4578	298	16	⋃	⋃	NOUN
ejpam-4578	298	17	⋃	⋃	PROPN
ejpam-4578	298	18	x∈wg	x∈wg	NOUN
ejpam-4578	298	19	{	{	PUNCT
ejpam-4578	298	20	{	{	PUNCT
ejpam-4578	298	21	x	x	NOUN
ejpam-4578	298	22	}	}	PUNCT
ejpam-4578	298	23	×	×	NOUN
ejpam-4578	298	24	(	(	PUNCT
ejpam-4578	298	25	v	v	NOUN
ejpam-4578	298	26	(	(	PUNCT
ejpam-4578	298	27	h	h	NOUN
ejpam-4578	298	28	)	)	PUNCT
ejpam-4578	298	29	\	\	PUNCT
ejpam-4578	298	30	tx	tx	PROPN
ejpam-4578	298	31	)	)	PUNCT
ejpam-4578	298	32	}	}	PUNCT
ejpam-4578	298	33			PROPN
ejpam-4578	298	34	of	of	ADP
ejpam-4578	298	35	v	v	NOUN
ejpam-4578	298	36	(	(	PUNCT
ejpam-4578	298	37	g[h	g[h	PROPN
ejpam-4578	298	38	]	]	PUNCT
ejpam-4578	298	39	)	)	PUNCT
ejpam-4578	298	40	where	where	SCONJ
ejpam-4578	298	41	wg	wg	VERB
ejpam-4578	298	42	⊆	⊆	NUM
ejpam-4578	298	43	s	s	NOUN
ejpam-4578	298	44	and	and	CCONJ
ejpam-4578	298	45	tx	tx	VERB
ejpam-4578	298	46	⊆	⊆	NUM
ejpam-4578	298	47	v	v	NOUN
ejpam-4578	298	48	(	(	PUNCT
ejpam-4578	298	49	h	h	NOUN
ejpam-4578	298	50	)	)	PUNCT
ejpam-4578	298	51	,	,	PUNCT
ejpam-4578	298	52	∀x	∀x	VERB
ejpam-4578	298	53	∈	∈	PROPN
ejpam-4578	298	54	s	s	NOUN
ejpam-4578	298	55	,	,	PUNCT
ejpam-4578	298	56	is	be	AUX
ejpam-4578	298	57	a	a	DET
ejpam-4578	298	58	strong	strong	ADJ
ejpam-4578	298	59	resolving	resolving	NOUN
ejpam-4578	298	60	set	set	NOUN
ejpam-4578	298	61	of	of	ADP
ejpam-4578	298	62	g[h	g[h	NOUN
ejpam-4578	298	63	]	]	PUNCT
ejpam-4578	298	64	if	if	SCONJ
ejpam-4578	298	65	and	and	CCONJ
ejpam-4578	298	66	only	only	ADV
ejpam-4578	298	67	if	if	SCONJ
ejpam-4578	298	68	(	(	PUNCT
ejpam-4578	298	69	i	i	NOUN
ejpam-4578	298	70	)	)	PUNCT
ejpam-4578	298	71	s	s	PART
ejpam-4578	298	72	=	=	SYM
ejpam-4578	298	73	v	v	NOUN
ejpam-4578	298	74	(	(	PUNCT
ejpam-4578	298	75	g	g	NOUN
ejpam-4578	298	76	)	)	PUNCT
ejpam-4578	298	77	.	.	PUNCT
ejpam-4578	299	1	(	(	PUNCT
ejpam-4578	299	2	ii	ii	NOUN
ejpam-4578	299	3	)	)	PUNCT
ejpam-4578	299	4	v	v	NOUN
ejpam-4578	299	5	(	(	PUNCT
ejpam-4578	299	6	h	h	NOUN
ejpam-4578	299	7	)	)	PUNCT
ejpam-4578	299	8	\	\	PROPN
ejpam-4578	300	1	tx	tx	PROPN
ejpam-4578	300	2	is	be	AUX
ejpam-4578	300	3	a	a	DET
ejpam-4578	300	4	superclique	superclique	NOUN
ejpam-4578	300	5	of	of	ADP
ejpam-4578	300	6	h.	h.	PROPN
ejpam-4578	300	7	(	(	PUNCT
ejpam-4578	300	8	iii	iii	X
ejpam-4578	300	9	)	)	PUNCT
ejpam-4578	300	10	wg	wg	PROPN
ejpam-4578	300	11	is	be	AUX
ejpam-4578	300	12	a	a	DET
ejpam-4578	300	13	strong	strong	ADJ
ejpam-4578	300	14	resolving	resolving	NOUN
ejpam-4578	300	15	set	set	NOUN
ejpam-4578	300	16	of	of	ADP
ejpam-4578	300	17	g.	g.	PROPN
ejpam-4578	300	18	theorem	theorem	VERB
ejpam-4578	300	19	11	11	NUM
ejpam-4578	300	20	.	.	PUNCT
ejpam-4578	301	1	let	let	VERB
ejpam-4578	301	2	g	g	PRON
ejpam-4578	301	3	be	be	AUX
ejpam-4578	301	4	a	a	DET
ejpam-4578	301	5	nontrivial	nontrivial	ADJ
ejpam-4578	301	6	connected	connect	VERB
ejpam-4578	301	7	graph	graph	NOUN
ejpam-4578	301	8	and	and	CCONJ
ejpam-4578	301	9	h	h	NOUN
ejpam-4578	301	10	be	be	AUX
ejpam-4578	301	11	a	a	DET
ejpam-4578	301	12	nontrivial	nontrivial	ADJ
ejpam-4578	301	13	complete	complete	ADJ
ejpam-4578	301	14	graph	graph	NOUN
ejpam-4578	301	15	.	.	PUNCT
ejpam-4578	302	1	a	a	DET
ejpam-4578	302	2	subset	subset	NOUN
ejpam-4578	302	3	c	c	NOUN
ejpam-4578	302	4	=	=	PUNCT
ejpam-4578	302	5	⋃	⋃	PROPN
ejpam-4578	302	6	x∈s	x∈s	NOUN
ejpam-4578	302	7	(	(	PUNCT
ejpam-4578	302	8	{	{	PUNCT
ejpam-4578	302	9	x}×tx	x}×tx	NUM
ejpam-4578	302	10	)	)	PUNCT
ejpam-4578	302	11	of	of	ADP
ejpam-4578	302	12	v	v	NOUN
ejpam-4578	302	13	(	(	PUNCT
ejpam-4578	302	14	g[h	g[h	PROPN
ejpam-4578	302	15	]	]	PUNCT
ejpam-4578	302	16	)	)	PUNCT
ejpam-4578	302	17	where	where	SCONJ
ejpam-4578	302	18	s	s	VERB
ejpam-4578	302	19	⊂	⊂	PROPN
ejpam-4578	302	20	v	v	X
ejpam-4578	302	21	(	(	PUNCT
ejpam-4578	302	22	g	g	NOUN
ejpam-4578	302	23	)	)	PUNCT
ejpam-4578	302	24	and	and	CCONJ
ejpam-4578	302	25	tx	tx	VERB
ejpam-4578	302	26	⊆	⊆	NUM
ejpam-4578	302	27	v	v	NOUN
ejpam-4578	302	28	(	(	PUNCT
ejpam-4578	302	29	h	h	NOUN
ejpam-4578	302	30	)	)	PUNCT
ejpam-4578	302	31	for	for	ADP
ejpam-4578	302	32	each	each	DET
ejpam-4578	302	33	x	x	SYM
ejpam-4578	302	34	∈	∈	PROPN
ejpam-4578	302	35	s	s	NOUN
ejpam-4578	302	36	,	,	PUNCT
ejpam-4578	302	37	is	be	AUX
ejpam-4578	302	38	a	a	DET
ejpam-4578	302	39	strong	strong	ADJ
ejpam-4578	302	40	resolving	resolve	VERB
ejpam-4578	302	41	hop	hop	NOUN
ejpam-4578	302	42	dominating	dominating	NOUN
ejpam-4578	302	43	set	set	NOUN
ejpam-4578	302	44	of	of	ADP
ejpam-4578	302	45	g[h	g[h	PROPN
ejpam-4578	302	46	]	]	PUNCT
ejpam-4578	302	47	if	if	SCONJ
ejpam-4578	302	48	and	and	CCONJ
ejpam-4578	302	49	only	only	ADV
ejpam-4578	302	50	if	if	SCONJ
ejpam-4578	302	51	(	(	PUNCT
ejpam-4578	302	52	i	i	NOUN
ejpam-4578	302	53	)	)	PUNCT
ejpam-4578	302	54	s	s	PART
ejpam-4578	302	55	=	=	SYM
ejpam-4578	302	56	v	v	NOUN
ejpam-4578	302	57	(	(	PUNCT
ejpam-4578	302	58	g	g	NOUN
ejpam-4578	302	59	)	)	PUNCT
ejpam-4578	302	60	;	;	PUNCT
ejpam-4578	302	61	(	(	PUNCT
ejpam-4578	302	62	ii	ii	NOUN
ejpam-4578	302	63	)	)	PUNCT
ejpam-4578	302	64	0	0	NUM
ejpam-4578	303	1	≤	≤	NUM
ejpam-4578	303	2	|v	|v	X
ejpam-4578	303	3	(	(	PUNCT
ejpam-4578	303	4	h	h	NOUN
ejpam-4578	303	5	)	)	PUNCT
ejpam-4578	303	6	\	\	PUNCT
ejpam-4578	303	7	tx|	tx|	PROPN
ejpam-4578	303	8	≤	≤	NUM
ejpam-4578	303	9	1	1	NUM
ejpam-4578	303	10	for	for	ADP
ejpam-4578	303	11	every	every	DET
ejpam-4578	303	12	x	x	SYM
ejpam-4578	303	13	∈	∈	PROPN
ejpam-4578	303	14	s	s	PART
ejpam-4578	303	15	;	;	PUNCT
ejpam-4578	303	16	(	(	PUNCT
ejpam-4578	303	17	iii	iii	X
ejpam-4578	303	18	)	)	PUNCT
ejpam-4578	303	19	tx	tx	PROPN
ejpam-4578	303	20	=	=	SYM
ejpam-4578	303	21	v	v	PROPN
ejpam-4578	303	22	(	(	PUNCT
ejpam-4578	303	23	h	h	NOUN
ejpam-4578	303	24	)	)	PUNCT
ejpam-4578	303	25	or	or	CCONJ
ejpam-4578	303	26	ty	ty	INTJ
ejpam-4578	303	27	=	=	NOUN
ejpam-4578	303	28	v	v	NOUN
ejpam-4578	303	29	(	(	PUNCT
ejpam-4578	303	30	h	h	NOUN
ejpam-4578	303	31	)	)	PUNCT
ejpam-4578	303	32	for	for	ADP
ejpam-4578	303	33	every	every	DET
ejpam-4578	303	34	pair	pair	NOUN
ejpam-4578	303	35	of	of	ADP
ejpam-4578	303	36	vertices	vertex	NOUN
ejpam-4578	303	37	x	x	X
ejpam-4578	303	38	,	,	PUNCT
ejpam-4578	303	39	y	y	PROPN
ejpam-4578	303	40	∈	∈	PROPN
ejpam-4578	303	41	v	v	ADP
ejpam-4578	303	42	(	(	PUNCT
ejpam-4578	303	43	g	g	NOUN
ejpam-4578	303	44	)	)	PUNCT
ejpam-4578	303	45	such	such	ADJ
ejpam-4578	303	46	that	that	SCONJ
ejpam-4578	303	47	x	x	SYM
ejpam-4578	303	48	∈	∈	PROPN
ejpam-4578	303	49	wg	wg	INTJ
ejpam-4578	303	50	where	where	SCONJ
ejpam-4578	303	51	wg	wg	PROPN
ejpam-4578	303	52	is	be	AUX
ejpam-4578	303	53	a	a	DET
ejpam-4578	303	54	strong	strong	ADJ
ejpam-4578	303	55	resolving	resolving	NOUN
ejpam-4578	303	56	set	set	NOUN
ejpam-4578	303	57	of	of	ADP
ejpam-4578	303	58	g	g	NOUN
ejpam-4578	303	59	;	;	PUNCT
ejpam-4578	303	60	(	(	PUNCT
ejpam-4578	303	61	iv	iv	X
ejpam-4578	303	62	)	)	PUNCT
ejpam-4578	303	63	tx	tx	PROPN
ejpam-4578	303	64	=	=	SYM
ejpam-4578	303	65	v	v	PROPN
ejpam-4578	303	66	(	(	PUNCT
ejpam-4578	303	67	h	h	NOUN
ejpam-4578	303	68	)	)	PUNCT
ejpam-4578	303	69	for	for	ADP
ejpam-4578	303	70	every	every	DET
ejpam-4578	303	71	x	x	SYM
ejpam-4578	303	72	∈	∈	PROPN
ejpam-4578	303	73	s	s	X
ejpam-4578	303	74	with	with	ADP
ejpam-4578	303	75	degg(x	degg(x	NOUN
ejpam-4578	303	76	)	)	PUNCT
ejpam-4578	303	77	=	=	SYM
ejpam-4578	303	78	|v	|v	PROPN
ejpam-4578	303	79	(	(	PUNCT
ejpam-4578	303	80	g)|	g)|	INTJ
ejpam-4578	303	81	−	−	NOUN
ejpam-4578	303	82	1	1	NUM
ejpam-4578	303	83	.	.	PUNCT
ejpam-4578	304	1	proof	proof	NOUN
ejpam-4578	304	2	:	:	PUNCT
ejpam-4578	304	3	suppose	suppose	VERB
ejpam-4578	304	4	c	c	NOUN
ejpam-4578	304	5	is	be	AUX
ejpam-4578	304	6	a	a	DET
ejpam-4578	304	7	strong	strong	ADJ
ejpam-4578	304	8	resolving	resolve	VERB
ejpam-4578	304	9	hop	hop	NOUN
ejpam-4578	304	10	dominating	dominating	NOUN
ejpam-4578	304	11	set	set	NOUN
ejpam-4578	304	12	of	of	ADP
ejpam-4578	304	13	g[h	g[h	NOUN
ejpam-4578	304	14	]	]	PUNCT
ejpam-4578	304	15	.	.	PUNCT
ejpam-4578	305	1	by	by	ADP
ejpam-4578	305	2	theorem	theorem	NOUN
ejpam-4578	305	3	10	10	NUM
ejpam-4578	305	4	(	(	PUNCT
ejpam-4578	305	5	i	i	NOUN
ejpam-4578	305	6	)	)	PUNCT
ejpam-4578	305	7	and	and	CCONJ
ejpam-4578	305	8	(	(	PUNCT
ejpam-4578	305	9	ii	ii	NOUN
ejpam-4578	305	10	)	)	PUNCT
ejpam-4578	305	11	hold	hold	VERB
ejpam-4578	305	12	.	.	PUNCT
ejpam-4578	306	1	now	now	ADV
ejpam-4578	306	2	,	,	PUNCT
ejpam-4578	306	3	let	let	VERB
ejpam-4578	306	4	x	x	PUNCT
ejpam-4578	306	5	∈	∈	NOUN
ejpam-4578	306	6	s	s	X
ejpam-4578	306	7	with	with	ADP
ejpam-4578	306	8	degg(x	degg(x	NOUN
ejpam-4578	306	9	)	)	PUNCT
ejpam-4578	306	10	=	=	SYM
ejpam-4578	306	11	|v	|v	PROPN
ejpam-4578	306	12	(	(	PUNCT
ejpam-4578	306	13	g)|	g)|	INTJ
ejpam-4578	306	14	−	−	NOUN
ejpam-4578	306	15	1	1	NUM
ejpam-4578	306	16	.	.	PUNCT
ejpam-4578	306	17	suppose	suppose	VERB
ejpam-4578	306	18	tx	tx	PROPN
ejpam-4578	306	19	̸=	̸=	PROPN
ejpam-4578	306	20	v	v	PROPN
ejpam-4578	306	21	(	(	PUNCT
ejpam-4578	306	22	h	h	NOUN
ejpam-4578	306	23	)	)	PUNCT
ejpam-4578	306	24	.	.	PUNCT
ejpam-4578	307	1	let	let	VERB
ejpam-4578	308	1	a	a	DET
ejpam-4578	308	2	∈	∈	PROPN
ejpam-4578	308	3	v	v	NOUN
ejpam-4578	308	4	(	(	PUNCT
ejpam-4578	308	5	h	h	NOUN
ejpam-4578	308	6	)	)	PUNCT
ejpam-4578	308	7	\	\	PROPN
ejpam-4578	308	8	tx	tx	PROPN
ejpam-4578	308	9	.	.	PUNCT
ejpam-4578	309	1	then	then	ADV
ejpam-4578	309	2	(	(	PUNCT
ejpam-4578	309	3	x	x	X
ejpam-4578	309	4	,	,	PUNCT
ejpam-4578	309	5	a	a	PRON
ejpam-4578	309	6	)	)	PUNCT
ejpam-4578	309	7	/∈	/∈	PUNCT
ejpam-4578	309	8	c.	c.	NOUN
ejpam-4578	309	9	since	since	SCONJ
ejpam-4578	309	10	c	c	PROPN
ejpam-4578	309	11	is	be	AUX
ejpam-4578	309	12	a	a	DET
ejpam-4578	309	13	hop	hop	NOUN
ejpam-4578	309	14	dominating	dominating	NOUN
ejpam-4578	309	15	set	set	NOUN
ejpam-4578	309	16	of	of	ADP
ejpam-4578	309	17	g[h	g[h	PROPN
ejpam-4578	309	18	]	]	PUNCT
ejpam-4578	309	19	,	,	PUNCT
ejpam-4578	309	20	there	there	PRON
ejpam-4578	309	21	exists	exist	VERB
ejpam-4578	309	22	(	(	PUNCT
ejpam-4578	309	23	y	y	PROPN
ejpam-4578	309	24	,	,	PUNCT
ejpam-4578	309	25	b	b	NOUN
ejpam-4578	309	26	)	)	PUNCT
ejpam-4578	309	27	∈	∈	PROPN
ejpam-4578	309	28	c	c	NOUN
ejpam-4578	309	29	∩	∩	X
ejpam-4578	309	30	ng[h]((x	ng[h]((x	NOUN
ejpam-4578	309	31	,	,	PUNCT
ejpam-4578	309	32	a	a	PRON
ejpam-4578	309	33	)	)	PUNCT
ejpam-4578	309	34	,	,	PUNCT
ejpam-4578	309	35	2	2	NUM
ejpam-4578	309	36	)	)	PUNCT
ejpam-4578	309	37	.	.	PUNCT
ejpam-4578	310	1	since	since	SCONJ
ejpam-4578	310	2	h	h	NOUN
ejpam-4578	310	3	is	be	AUX
ejpam-4578	310	4	complete	complete	ADJ
ejpam-4578	310	5	,	,	PUNCT
ejpam-4578	310	6	y	y	PROPN
ejpam-4578	310	7	∈	∈	PROPN
ejpam-4578	310	8	s	s	PART
ejpam-4578	310	9	∩	∩	NOUN
ejpam-4578	310	10	ng(x	ng(x	NUM
ejpam-4578	310	11	,	,	PUNCT
ejpam-4578	310	12	2	2	NUM
ejpam-4578	310	13	)	)	PUNCT
ejpam-4578	310	14	.	.	PUNCT
ejpam-4578	311	1	this	this	PRON
ejpam-4578	311	2	implies	imply	VERB
ejpam-4578	311	3	that	that	SCONJ
ejpam-4578	311	4	y	y	PROPN
ejpam-4578	311	5	∈	∈	PROPN
ejpam-4578	311	6	(	(	PUNCT
ejpam-4578	311	7	v	v	NOUN
ejpam-4578	311	8	(	(	PUNCT
ejpam-4578	311	9	g	g	NOUN
ejpam-4578	311	10	)	)	PUNCT
ejpam-4578	311	11	\	\	NOUN
ejpam-4578	311	12	{	{	PUNCT
ejpam-4578	311	13	x	x	NOUN
ejpam-4578	311	14	}	}	PUNCT
ejpam-4578	311	15	)	)	PUNCT
ejpam-4578	311	16	\	\	NOUN
ejpam-4578	311	17	ng(x	ng(x	NUM
ejpam-4578	311	18	)	)	PUNCT
ejpam-4578	311	19	,	,	PUNCT
ejpam-4578	311	20	showing	show	VERB
ejpam-4578	311	21	that	that	PRON
ejpam-4578	311	22	degg(x	degg(x	NOUN
ejpam-4578	311	23	)	)	PUNCT
ejpam-4578	311	24	<	<	X
ejpam-4578	311	25	|v	|v	X
ejpam-4578	311	26	(	(	PUNCT
ejpam-4578	311	27	g)|	g)|	INTJ
ejpam-4578	311	28	−	−	PROPN
ejpam-4578	311	29	1	1	NUM
ejpam-4578	311	30	,	,	PUNCT
ejpam-4578	311	31	a	a	DET
ejpam-4578	311	32	contradiction	contradiction	NOUN
ejpam-4578	311	33	.	.	PUNCT
ejpam-4578	312	1	hence	hence	ADV
ejpam-4578	312	2	,	,	PUNCT
ejpam-4578	312	3	tx	tx	PROPN
ejpam-4578	312	4	=	=	SYM
ejpam-4578	312	5	v	v	PROPN
ejpam-4578	312	6	(	(	PUNCT
ejpam-4578	312	7	h	h	NOUN
ejpam-4578	312	8	)	)	PUNCT
ejpam-4578	312	9	and	and	CCONJ
ejpam-4578	312	10	(	(	PUNCT
ejpam-4578	312	11	iv	iv	X
ejpam-4578	312	12	)	)	PUNCT
ejpam-4578	312	13	is	be	AUX
ejpam-4578	312	14	true	true	ADJ
ejpam-4578	312	15	.	.	PUNCT
ejpam-4578	313	1	for	for	ADP
ejpam-4578	313	2	(	(	PUNCT
ejpam-4578	313	3	iii	iii	NOUN
ejpam-4578	313	4	)	)	PUNCT
ejpam-4578	313	5	,	,	PUNCT
ejpam-4578	313	6	let	let	VERB
ejpam-4578	313	7	x	x	PRON
ejpam-4578	313	8	,	,	PUNCT
ejpam-4578	313	9	y	y	PROPN
ejpam-4578	313	10	∈	∈	PROPN
ejpam-4578	313	11	v	v	ADP
ejpam-4578	313	12	(	(	PUNCT
ejpam-4578	313	13	g	g	NOUN
ejpam-4578	313	14	)	)	PUNCT
ejpam-4578	313	15	such	such	ADJ
ejpam-4578	313	16	that	that	PRON
ejpam-4578	313	17	xmmdy	xmmdy	PROPN
ejpam-4578	313	18	.	.	PUNCT
ejpam-4578	314	1	suppose	suppose	VERB
ejpam-4578	314	2	tx	tx	PROPN
ejpam-4578	314	3	̸=	̸=	PROPN
ejpam-4578	314	4	v	v	PROPN
ejpam-4578	314	5	(	(	PUNCT
ejpam-4578	314	6	h	h	NOUN
ejpam-4578	314	7	)	)	PUNCT
ejpam-4578	314	8	and	and	CCONJ
ejpam-4578	314	9	ty	ty	INTJ
ejpam-4578	314	10	̸=	̸=	PROPN
ejpam-4578	314	11	v	v	NOUN
ejpam-4578	314	12	(	(	PUNCT
ejpam-4578	314	13	h	h	NOUN
ejpam-4578	314	14	)	)	PUNCT
ejpam-4578	314	15	.	.	PUNCT
ejpam-4578	315	1	let	let	VERB
ejpam-4578	315	2	p	p	PRON
ejpam-4578	315	3	∈	∈	PROPN
ejpam-4578	315	4	v	v	ADP
ejpam-4578	315	5	(	(	PUNCT
ejpam-4578	315	6	h	h	NOUN
ejpam-4578	315	7	)	)	PUNCT
ejpam-4578	315	8	\	\	PROPN
ejpam-4578	315	9	tx	tx	PROPN
ejpam-4578	315	10	and	and	CCONJ
ejpam-4578	315	11	q	q	PROPN
ejpam-4578	315	12	∈	∈	PROPN
ejpam-4578	315	13	v	v	ADP
ejpam-4578	315	14	(	(	PUNCT
ejpam-4578	315	15	h	h	NOUN
ejpam-4578	315	16	)	)	PUNCT
ejpam-4578	315	17	\	\	PROPN
ejpam-4578	316	1	ty	ty	X
ejpam-4578	316	2	.	.	PUNCT
ejpam-4578	317	1	then	then	ADV
ejpam-4578	317	2	(	(	PUNCT
ejpam-4578	317	3	x	x	X
ejpam-4578	317	4	,	,	PUNCT
ejpam-4578	317	5	p	p	NOUN
ejpam-4578	317	6	)	)	PUNCT
ejpam-4578	317	7	,	,	PUNCT
ejpam-4578	317	8	(	(	PUNCT
ejpam-4578	317	9	y	y	NOUN
ejpam-4578	317	10	,	,	PUNCT
ejpam-4578	317	11	q	q	NOUN
ejpam-4578	317	12	)	)	PUNCT
ejpam-4578	317	13	/∈	/∈	PUNCT
ejpam-4578	317	14	c.	c.	NOUN
ejpam-4578	317	15	since	since	SCONJ
ejpam-4578	317	16	c	c	PROPN
ejpam-4578	317	17	is	be	AUX
ejpam-4578	317	18	a	a	DET
ejpam-4578	317	19	strong	strong	ADJ
ejpam-4578	317	20	resolving	resolving	NOUN
ejpam-4578	317	21	set	set	NOUN
ejpam-4578	317	22	of	of	ADP
ejpam-4578	317	23	g[h	g[h	PROPN
ejpam-4578	317	24	]	]	PUNCT
ejpam-4578	317	25	,	,	PUNCT
ejpam-4578	317	26	there	there	PRON
ejpam-4578	317	27	exists	exist	VERB
ejpam-4578	317	28	(	(	PUNCT
ejpam-4578	317	29	z	z	NOUN
ejpam-4578	317	30	,	,	PUNCT
ejpam-4578	317	31	w	w	NOUN
ejpam-4578	317	32	)	)	PUNCT
ejpam-4578	317	33	∈	∈	PROPN
ejpam-4578	317	34	c	c	NOUN
ejpam-4578	317	35	such	such	ADJ
ejpam-4578	317	36	that	that	PRON
ejpam-4578	317	37	(	(	PUNCT
ejpam-4578	317	38	z	z	NOUN
ejpam-4578	317	39	,	,	PUNCT
ejpam-4578	317	40	w	w	NOUN
ejpam-4578	317	41	)	)	PUNCT
ejpam-4578	317	42	strongly	strongly	ADV
ejpam-4578	317	43	resolves	resolve	NOUN
ejpam-4578	317	44	(	(	PUNCT
ejpam-4578	317	45	x	x	X
ejpam-4578	317	46	,	,	PUNCT
ejpam-4578	317	47	p	p	NOUN
ejpam-4578	317	48	)	)	PUNCT
ejpam-4578	317	49	and	and	CCONJ
ejpam-4578	317	50	(	(	PUNCT
ejpam-4578	317	51	y	y	PROPN
ejpam-4578	317	52	,	,	PUNCT
ejpam-4578	317	53	q	q	NOUN
ejpam-4578	317	54	)	)	PUNCT
ejpam-4578	317	55	.	.	PUNCT
ejpam-4578	318	1	suppose	suppose	VERB
ejpam-4578	318	2	(	(	PUNCT
ejpam-4578	318	3	x	x	X
ejpam-4578	318	4	,	,	PUNCT
ejpam-4578	318	5	p	p	NOUN
ejpam-4578	318	6	)	)	PUNCT
ejpam-4578	318	7	∈	∈	PROPN
ejpam-4578	318	8	ig[h][(y	ig[h][(y	PROPN
ejpam-4578	318	9	,	,	PUNCT
ejpam-4578	318	10	q	q	NOUN
ejpam-4578	318	11	)	)	PUNCT
ejpam-4578	318	12	,	,	PUNCT
ejpam-4578	318	13	(	(	PUNCT
ejpam-4578	318	14	z	z	X
ejpam-4578	318	15	,	,	PUNCT
ejpam-4578	318	16	w	w	PROPN
ejpam-4578	318	17	)	)	PUNCT
ejpam-4578	318	18	]	]	PUNCT
ejpam-4578	318	19	.	.	PUNCT
ejpam-4578	319	1	then	then	ADV
ejpam-4578	319	2	dg[h]((z	dg[h]((z	VERB
ejpam-4578	319	3	,	,	PUNCT
ejpam-4578	319	4	w	w	PROPN
ejpam-4578	319	5	)	)	PUNCT
ejpam-4578	319	6	,	,	PUNCT
ejpam-4578	319	7	(	(	PUNCT
ejpam-4578	319	8	x	x	X
ejpam-4578	319	9	,	,	PUNCT
ejpam-4578	319	10	p	p	NOUN
ejpam-4578	319	11	)	)	PUNCT
ejpam-4578	319	12	)	)	PUNCT
ejpam-4578	320	1	+	+	CCONJ
ejpam-4578	320	2	dg[h]((x	dg[h]((x	X
ejpam-4578	320	3	,	,	PUNCT
ejpam-4578	320	4	p	p	NOUN
ejpam-4578	320	5	)	)	PUNCT
ejpam-4578	320	6	,	,	PUNCT
ejpam-4578	320	7	(	(	PUNCT
ejpam-4578	320	8	y	y	NOUN
ejpam-4578	320	9	,	,	PUNCT
ejpam-4578	320	10	q	q	NOUN
ejpam-4578	320	11	)	)	PUNCT
ejpam-4578	320	12	)	)	PUNCT
ejpam-4578	320	13	=	=	SYM
ejpam-4578	320	14	dg[h]((z	dg[h]((z	X
ejpam-4578	320	15	,	,	PUNCT
ejpam-4578	320	16	w	w	NOUN
ejpam-4578	320	17	)	)	PUNCT
ejpam-4578	320	18	,	,	PUNCT
ejpam-4578	320	19	(	(	PUNCT
ejpam-4578	320	20	y	y	NOUN
ejpam-4578	320	21	,	,	PUNCT
ejpam-4578	320	22	q	q	NOUN
ejpam-4578	320	23	)	)	PUNCT
ejpam-4578	320	24	)	)	PUNCT
ejpam-4578	320	25	.	.	PUNCT
ejpam-4578	321	1	if	if	SCONJ
ejpam-4578	321	2	z	z	NOUN
ejpam-4578	321	3	=	=	SYM
ejpam-4578	321	4	x	x	NOUN
ejpam-4578	321	5	,	,	PUNCT
ejpam-4578	321	6	then	then	ADV
ejpam-4578	321	7	w	w	PROPN
ejpam-4578	321	8	∈	∈	PROPN
ejpam-4578	321	9	tx	tx	PROPN
ejpam-4578	321	10	and	and	CCONJ
ejpam-4578	321	11	dg[h]((z	dg[h]((z	PROPN
ejpam-4578	321	12	,	,	PUNCT
ejpam-4578	321	13	w	w	NOUN
ejpam-4578	321	14	)	)	PUNCT
ejpam-4578	321	15	,	,	PUNCT
ejpam-4578	321	16	(	(	PUNCT
ejpam-4578	321	17	x	x	X
ejpam-4578	321	18	,	,	PUNCT
ejpam-4578	321	19	p	p	NOUN
ejpam-4578	321	20	)	)	PUNCT
ejpam-4578	321	21	)	)	PUNCT
ejpam-4578	322	1	=	=	SYM
ejpam-4578	322	2	1	1	X
ejpam-4578	322	3	.	.	PUNCT
ejpam-4578	322	4	thus	thus	ADV
ejpam-4578	322	5	1	1	NUM
ejpam-4578	322	6	+	+	CCONJ
ejpam-4578	322	7	dg[h]((x	dg[h]((x	ADJ
ejpam-4578	322	8	,	,	PUNCT
ejpam-4578	322	9	p	p	NOUN
ejpam-4578	322	10	)	)	PUNCT
ejpam-4578	322	11	,	,	PUNCT
ejpam-4578	322	12	(	(	PUNCT
ejpam-4578	322	13	y	y	NOUN
ejpam-4578	322	14	,	,	PUNCT
ejpam-4578	322	15	q	q	NOUN
ejpam-4578	322	16	)	)	PUNCT
ejpam-4578	322	17	)	)	PUNCT
ejpam-4578	322	18	=	=	SYM
ejpam-4578	323	1	dg[h]((z	dg[h]((z	X
ejpam-4578	323	2	,	,	PUNCT
ejpam-4578	323	3	w	w	NOUN
ejpam-4578	323	4	)	)	PUNCT
ejpam-4578	323	5	,	,	PUNCT
ejpam-4578	323	6	(	(	PUNCT
ejpam-4578	323	7	y	y	NOUN
ejpam-4578	323	8	,	,	PUNCT
ejpam-4578	323	9	q	q	NOUN
ejpam-4578	323	10	)	)	PUNCT
ejpam-4578	323	11	)	)	PUNCT
ejpam-4578	323	12	,	,	PUNCT
ejpam-4578	323	13	j.	j.	PROPN
ejpam-4578	323	14	mohamad	mohamad	PROPN
ejpam-4578	323	15	,	,	PUNCT
ejpam-4578	323	16	h.	h.	PROPN
ejpam-4578	323	17	rara	rara	PROPN
ejpam-4578	323	18	/	/	SYM
ejpam-4578	323	19	eur	eur	PROPN
ejpam-4578	323	20	.	.	PUNCT
ejpam-4578	324	1	j.	j.	PROPN
ejpam-4578	324	2	pure	pure	PROPN
ejpam-4578	324	3	appl	appl	PROPN
ejpam-4578	324	4	.	.	PROPN
ejpam-4578	324	5	math	math	PROPN
ejpam-4578	324	6	,	,	PUNCT
ejpam-4578	324	7	16	16	NUM
ejpam-4578	324	8	(	(	PUNCT
ejpam-4578	324	9	1	1	NUM
ejpam-4578	324	10	)	)	PUNCT
ejpam-4578	324	11	(	(	PUNCT
ejpam-4578	324	12	2023	2023	NUM
ejpam-4578	324	13	)	)	PUNCT
ejpam-4578	324	14	,	,	PUNCT
ejpam-4578	324	15	131	131	NUM
ejpam-4578	324	16	-	-	SYM
ejpam-4578	324	17	143	143	NUM
ejpam-4578	324	18	142	142	NUM
ejpam-4578	324	19	that	that	PRON
ejpam-4578	324	20	is	be	AUX
ejpam-4578	324	21	,	,	PUNCT
ejpam-4578	324	22	1	1	NUM
ejpam-4578	324	23	+	+	CCONJ
ejpam-4578	324	24	dg[h]((z	dg[h]((z	X
ejpam-4578	324	25	,	,	PUNCT
ejpam-4578	324	26	p	p	NOUN
ejpam-4578	324	27	)	)	PUNCT
ejpam-4578	324	28	,	,	PUNCT
ejpam-4578	324	29	(	(	PUNCT
ejpam-4578	324	30	y	y	NOUN
ejpam-4578	324	31	,	,	PUNCT
ejpam-4578	324	32	q	q	NOUN
ejpam-4578	324	33	)	)	PUNCT
ejpam-4578	324	34	)	)	PUNCT
ejpam-4578	325	1	=	=	SYM
ejpam-4578	325	2	dg[h]((z	dg[h]((z	X
ejpam-4578	325	3	,	,	PUNCT
ejpam-4578	325	4	w	w	NOUN
ejpam-4578	325	5	)	)	PUNCT
ejpam-4578	325	6	,	,	PUNCT
ejpam-4578	325	7	(	(	PUNCT
ejpam-4578	325	8	y	y	NOUN
ejpam-4578	325	9	,	,	PUNCT
ejpam-4578	325	10	q	q	NOUN
ejpam-4578	325	11	)	)	PUNCT
ejpam-4578	325	12	)	)	PUNCT
ejpam-4578	325	13	or	or	CCONJ
ejpam-4578	325	14	1	1	NUM
ejpam-4578	325	15	+	+	CCONJ
ejpam-4578	325	16	dg(z	dg(z	NUM
ejpam-4578	325	17	,	,	PUNCT
ejpam-4578	325	18	y	y	NOUN
ejpam-4578	325	19	)	)	PUNCT
ejpam-4578	325	20	=	=	SYM
ejpam-4578	326	1	dg(z	dg(z	NUM
ejpam-4578	326	2	,	,	PUNCT
ejpam-4578	326	3	y	y	NOUN
ejpam-4578	326	4	)	)	PUNCT
ejpam-4578	326	5	,	,	PUNCT
ejpam-4578	326	6	which	which	PRON
ejpam-4578	326	7	is	be	AUX
ejpam-4578	326	8	a	a	DET
ejpam-4578	326	9	contradiction	contradiction	NOUN
ejpam-4578	326	10	.	.	PUNCT
ejpam-4578	327	1	thus	thus	ADV
ejpam-4578	327	2	,	,	PUNCT
ejpam-4578	327	3	z	z	PROPN
ejpam-4578	327	4	̸=	̸=	PROPN
ejpam-4578	327	5	x.	x.	PUNCT
ejpam-4578	327	6	consequently	consequently	ADV
ejpam-4578	327	7	,	,	PUNCT
ejpam-4578	327	8	dg(z	dg(z	NUM
ejpam-4578	327	9	,	,	PUNCT
ejpam-4578	327	10	x	x	X
ejpam-4578	327	11	)	)	PUNCT
ejpam-4578	328	1	+	+	CCONJ
ejpam-4578	328	2	dg(x	dg(x	X
ejpam-4578	328	3	,	,	PUNCT
ejpam-4578	328	4	y	y	NOUN
ejpam-4578	328	5	)	)	PUNCT
ejpam-4578	328	6	=	=	SYM
ejpam-4578	328	7	dg(z	dg(z	NUM
ejpam-4578	328	8	,	,	PUNCT
ejpam-4578	328	9	y	y	NOUN
ejpam-4578	328	10	)	)	PUNCT
ejpam-4578	328	11	implying	imply	VERB
ejpam-4578	328	12	that	that	SCONJ
ejpam-4578	328	13	x	x	SYM
ejpam-4578	328	14	∈	∈	PROPN
ejpam-4578	328	15	ig[z	ig[z	PROPN
ejpam-4578	328	16	,	,	PUNCT
ejpam-4578	328	17	y	y	NOUN
ejpam-4578	328	18	]	]	PUNCT
ejpam-4578	328	19	.	.	PUNCT
ejpam-4578	329	1	this	this	PRON
ejpam-4578	329	2	is	be	AUX
ejpam-4578	329	3	a	a	DET
ejpam-4578	329	4	contradiction	contradiction	NOUN
ejpam-4578	329	5	to	to	ADP
ejpam-4578	329	6	the	the	DET
ejpam-4578	329	7	assumption	assumption	NOUN
ejpam-4578	329	8	that	that	SCONJ
ejpam-4578	329	9	xmmdy	xmmdy	PROPN
ejpam-4578	329	10	.	.	PUNCT
ejpam-4578	330	1	similarly	similarly	ADV
ejpam-4578	330	2	,	,	PUNCT
ejpam-4578	330	3	if	if	SCONJ
ejpam-4578	330	4	(	(	PUNCT
ejpam-4578	330	5	y	y	NOUN
ejpam-4578	330	6	,	,	PUNCT
ejpam-4578	330	7	q	q	NOUN
ejpam-4578	330	8	)	)	PUNCT
ejpam-4578	330	9	∈	∈	PROPN
ejpam-4578	330	10	ig[h][(x	ig[h][(x	PROPN
ejpam-4578	330	11	,	,	PUNCT
ejpam-4578	330	12	p	p	NOUN
ejpam-4578	330	13	)	)	PUNCT
ejpam-4578	330	14	,	,	PUNCT
ejpam-4578	330	15	(	(	PUNCT
ejpam-4578	330	16	z	z	X
ejpam-4578	330	17	,	,	PUNCT
ejpam-4578	330	18	w	w	PROPN
ejpam-4578	330	19	)	)	PUNCT
ejpam-4578	330	20	]	]	PUNCT
ejpam-4578	330	21	,	,	PUNCT
ejpam-4578	330	22	then	then	ADV
ejpam-4578	330	23	a	a	DET
ejpam-4578	330	24	contradiction	contradiction	NOUN
ejpam-4578	330	25	can	can	AUX
ejpam-4578	330	26	be	be	AUX
ejpam-4578	330	27	obtained	obtain	VERB
ejpam-4578	330	28	.	.	PUNCT
ejpam-4578	331	1	hence	hence	ADV
ejpam-4578	331	2	tx	tx	PROPN
ejpam-4578	331	3	=	=	SYM
ejpam-4578	331	4	v	v	PROPN
ejpam-4578	331	5	(	(	PUNCT
ejpam-4578	331	6	h	h	NOUN
ejpam-4578	331	7	)	)	PUNCT
ejpam-4578	331	8	or	or	CCONJ
ejpam-4578	331	9	ty	ty	INTJ
ejpam-4578	331	10	=	=	NOUN
ejpam-4578	331	11	v	v	NOUN
ejpam-4578	331	12	(	(	PUNCT
ejpam-4578	331	13	h	h	NOUN
ejpam-4578	331	14	)	)	PUNCT
ejpam-4578	331	15	.	.	PUNCT
ejpam-4578	332	1	for	for	ADP
ejpam-4578	332	2	the	the	DET
ejpam-4578	332	3	converse	converse	NOUN
ejpam-4578	332	4	,	,	PUNCT
ejpam-4578	332	5	suppose	suppose	VERB
ejpam-4578	332	6	c	c	NOUN
ejpam-4578	332	7	satisfies	satisfie	NOUN
ejpam-4578	332	8	conditions	condition	NOUN
ejpam-4578	332	9	(	(	PUNCT
ejpam-4578	332	10	i	i	NOUN
ejpam-4578	332	11	)	)	PUNCT
ejpam-4578	332	12	to	to	ADP
ejpam-4578	332	13	(	(	PUNCT
ejpam-4578	332	14	iv	iv	X
ejpam-4578	332	15	)	)	PUNCT
ejpam-4578	332	16	.	.	PUNCT
ejpam-4578	333	1	let	let	VERB
ejpam-4578	333	2	(	(	PUNCT
ejpam-4578	333	3	(	(	PUNCT
ejpam-4578	333	4	x1	x1	PROPN
ejpam-4578	333	5	,	,	PUNCT
ejpam-4578	333	6	y1	y1	PROPN
ejpam-4578	333	7	)	)	PUNCT
ejpam-4578	333	8	,	,	PUNCT
ejpam-4578	333	9	(	(	PUNCT
ejpam-4578	333	10	x2	x2	PROPN
ejpam-4578	333	11	,	,	PUNCT
ejpam-4578	333	12	y2	y2	PROPN
ejpam-4578	333	13	)	)	PUNCT
ejpam-4578	333	14	)	)	PUNCT
ejpam-4578	333	15	/∈	/∈	PUNCT
ejpam-4578	334	1	c	c	NOUN
ejpam-4578	334	2	with	with	ADP
ejpam-4578	334	3	(	(	PUNCT
ejpam-4578	334	4	x1	x1	PROPN
ejpam-4578	334	5	,	,	PUNCT
ejpam-4578	334	6	y1	y1	ADJ
ejpam-4578	334	7	)	)	PUNCT
ejpam-4578	334	8	̸=	̸=	PROPN
ejpam-4578	334	9	(	(	PUNCT
ejpam-4578	334	10	x2	x2	PROPN
ejpam-4578	334	11	,	,	PUNCT
ejpam-4578	334	12	y2	y2	PROPN
ejpam-4578	334	13	)	)	PUNCT
ejpam-4578	334	14	.	.	PUNCT
ejpam-4578	335	1	then	then	ADV
ejpam-4578	335	2	y1	y1	PROPN
ejpam-4578	335	3	/∈	/∈	PUNCT
ejpam-4578	335	4	tx1	tx1	NOUN
ejpam-4578	335	5	and	and	CCONJ
ejpam-4578	335	6	y2	y2	INTJ
ejpam-4578	335	7	/∈	/∈	PUNCT
ejpam-4578	336	1	tx2	tx2	INTJ
ejpam-4578	336	2	.	.	PUNCT
ejpam-4578	337	1	hence	hence	ADV
ejpam-4578	337	2	,	,	PUNCT
ejpam-4578	337	3	x1	x1	PROPN
ejpam-4578	337	4	is	be	AUX
ejpam-4578	337	5	not	not	PART
ejpam-4578	337	6	mutually	mutually	ADV
ejpam-4578	337	7	maximally	maximally	ADV
ejpam-4578	337	8	distant	distant	ADJ
ejpam-4578	337	9	with	with	ADP
ejpam-4578	337	10	x2	x2	PROPN
ejpam-4578	337	11	.	.	PUNCT
ejpam-4578	338	1	thus	thus	ADV
ejpam-4578	338	2	,	,	PUNCT
ejpam-4578	338	3	there	there	PRON
ejpam-4578	338	4	exists	exist	VERB
ejpam-4578	338	5	u	u	PROPN
ejpam-4578	338	6	∈	∈	PROPN
ejpam-4578	338	7	ng(x1	ng(x1	NOUN
ejpam-4578	338	8	)	)	PUNCT
ejpam-4578	338	9	such	such	ADJ
ejpam-4578	338	10	that	that	DET
ejpam-4578	338	11	dg(u	dg(u	ADJ
ejpam-4578	338	12	,	,	PUNCT
ejpam-4578	338	13	x2	x2	PROPN
ejpam-4578	338	14	)	)	PUNCT
ejpam-4578	338	15	>	>	X
ejpam-4578	338	16	dg(x1	dg(x1	PROPN
ejpam-4578	338	17	,	,	PUNCT
ejpam-4578	338	18	x2	x2	PROPN
ejpam-4578	338	19	)	)	PUNCT
ejpam-4578	338	20	,	,	PUNCT
ejpam-4578	338	21	that	that	ADV
ejpam-4578	338	22	is	is	ADV
ejpam-4578	338	23	,	,	PUNCT
ejpam-4578	338	24	x1	x1	PROPN
ejpam-4578	338	25	∈	∈	PROPN
ejpam-4578	338	26	ig[x2	ig[x2	PROPN
ejpam-4578	338	27	,	,	PUNCT
ejpam-4578	338	28	u	u	NOUN
ejpam-4578	338	29	]	]	X
ejpam-4578	338	30	.	.	PUNCT
ejpam-4578	339	1	let	let	VERB
ejpam-4578	339	2	v	v	X
ejpam-4578	339	3	∈	∈	PROPN
ejpam-4578	339	4	tu	tu	PROPN
ejpam-4578	339	5	.	.	PUNCT
ejpam-4578	340	1	then	then	ADV
ejpam-4578	340	2	(	(	PUNCT
ejpam-4578	340	3	u	u	NOUN
ejpam-4578	340	4	,	,	PUNCT
ejpam-4578	340	5	v	v	NOUN
ejpam-4578	340	6	)	)	PUNCT
ejpam-4578	340	7	∈	∈	PROPN
ejpam-4578	340	8	c	c	NOUN
ejpam-4578	340	9	strongly	strongly	ADV
ejpam-4578	340	10	resolves	resolve	NOUN
ejpam-4578	340	11	(	(	PUNCT
ejpam-4578	340	12	x1	x1	PROPN
ejpam-4578	340	13	,	,	PUNCT
ejpam-4578	340	14	y1	y1	PROPN
ejpam-4578	340	15	)	)	PUNCT
ejpam-4578	340	16	and	and	CCONJ
ejpam-4578	340	17	(	(	PUNCT
ejpam-4578	340	18	x2	x2	PROPN
ejpam-4578	340	19	,	,	PUNCT
ejpam-4578	340	20	y2	y2	PROPN
ejpam-4578	340	21	)	)	PUNCT
ejpam-4578	340	22	.	.	PUNCT
ejpam-4578	341	1	hence	hence	ADV
ejpam-4578	341	2	,	,	PUNCT
ejpam-4578	341	3	c	c	PROPN
ejpam-4578	341	4	is	be	AUX
ejpam-4578	341	5	a	a	DET
ejpam-4578	341	6	strong	strong	ADJ
ejpam-4578	341	7	resolving	resolving	NOUN
ejpam-4578	341	8	set	set	NOUN
ejpam-4578	341	9	of	of	ADP
ejpam-4578	341	10	g[h	g[h	NOUN
ejpam-4578	341	11	]	]	PUNCT
ejpam-4578	341	12	.	.	PUNCT
ejpam-4578	342	1	now	now	ADV
ejpam-4578	342	2	,	,	PUNCT
ejpam-4578	342	3	we	we	PRON
ejpam-4578	342	4	show	show	VERB
ejpam-4578	342	5	that	that	SCONJ
ejpam-4578	342	6	c	c	PROPN
ejpam-4578	342	7	is	be	AUX
ejpam-4578	342	8	a	a	DET
ejpam-4578	342	9	hop	hop	NOUN
ejpam-4578	342	10	dominating	dominating	NOUN
ejpam-4578	342	11	set	set	NOUN
ejpam-4578	342	12	of	of	ADP
ejpam-4578	342	13	g[h	g[h	PROPN
ejpam-4578	342	14	]	]	PUNCT
ejpam-4578	342	15	.	.	PUNCT
ejpam-4578	343	1	let	let	VERB
ejpam-4578	343	2	(	(	PUNCT
ejpam-4578	343	3	x	x	NOUN
ejpam-4578	343	4	,	,	PUNCT
ejpam-4578	343	5	y	y	NOUN
ejpam-4578	343	6	)	)	PUNCT
ejpam-4578	343	7	∈	∈	PROPN
ejpam-4578	343	8	c.	c.	NOUN
ejpam-4578	344	1	then	then	ADV
ejpam-4578	344	2	y	y	PROPN
ejpam-4578	344	3	∈	∈	PROPN
ejpam-4578	344	4	v	v	ADP
ejpam-4578	344	5	(	(	PUNCT
ejpam-4578	344	6	h	h	NOUN
ejpam-4578	344	7	)	)	PUNCT
ejpam-4578	344	8	\	\	PROPN
ejpam-4578	344	9	tx	tx	PROPN
ejpam-4578	344	10	.	.	PUNCT
ejpam-4578	345	1	by	by	ADP
ejpam-4578	345	2	(	(	PUNCT
ejpam-4578	345	3	iv	iv	NOUN
ejpam-4578	345	4	)	)	PUNCT
ejpam-4578	345	5	,	,	PUNCT
ejpam-4578	345	6	degg(x	degg(x	NOUN
ejpam-4578	345	7	)	)	PUNCT
ejpam-4578	345	8	<	<	X
ejpam-4578	345	9	|v	|v	X
ejpam-4578	345	10	(	(	PUNCT
ejpam-4578	345	11	g)|	g)|	INTJ
ejpam-4578	345	12	−	−	NOUN
ejpam-4578	345	13	1	1	NUM
ejpam-4578	345	14	.	.	PUNCT
ejpam-4578	346	1	thus	thus	ADV
ejpam-4578	346	2	,	,	PUNCT
ejpam-4578	346	3	there	there	PRON
ejpam-4578	346	4	exists	exist	VERB
ejpam-4578	346	5	z	z	PROPN
ejpam-4578	346	6	∈	∈	PROPN
ejpam-4578	346	7	v	v	NOUN
ejpam-4578	346	8	(	(	PUNCT
ejpam-4578	346	9	g\{x})\ng(x	g\{x})\ng(x	NUM
ejpam-4578	346	10	)	)	PUNCT
ejpam-4578	346	11	.	.	PUNCT
ejpam-4578	347	1	let	let	VERB
ejpam-4578	347	2	z	z	PROPN
ejpam-4578	347	3	∈	∈	PROPN
ejpam-4578	347	4	ng(x	ng(x	NUM
ejpam-4578	347	5	,	,	PUNCT
ejpam-4578	347	6	2	2	NUM
ejpam-4578	347	7	)	)	PUNCT
ejpam-4578	347	8	and	and	CCONJ
ejpam-4578	347	9	w	w	PROPN
ejpam-4578	347	10	∈	∈	PROPN
ejpam-4578	347	11	tz	tz	NOUN
ejpam-4578	347	12	.	.	PUNCT
ejpam-4578	348	1	then	then	ADV
ejpam-4578	348	2	,	,	PUNCT
ejpam-4578	348	3	(	(	PUNCT
ejpam-4578	348	4	z	z	X
ejpam-4578	348	5	,	,	PUNCT
ejpam-4578	348	6	w	w	NOUN
ejpam-4578	348	7	)	)	PUNCT
ejpam-4578	348	8	∈	∈	PROPN
ejpam-4578	348	9	c	c	NOUN
ejpam-4578	348	10	∩ng[h]((x	∩ng[h]((x	NOUN
ejpam-4578	348	11	,	,	PUNCT
ejpam-4578	348	12	y	y	PROPN
ejpam-4578	348	13	)	)	PUNCT
ejpam-4578	348	14	,	,	PUNCT
ejpam-4578	348	15	2	2	NUM
ejpam-4578	348	16	)	)	PUNCT
ejpam-4578	348	17	.	.	PUNCT
ejpam-4578	349	1	this	this	PRON
ejpam-4578	349	2	shows	show	VERB
ejpam-4578	349	3	that	that	SCONJ
ejpam-4578	349	4	c	c	PROPN
ejpam-4578	349	5	is	be	AUX
ejpam-4578	349	6	a	a	DET
ejpam-4578	349	7	hop	hop	NOUN
ejpam-4578	349	8	dominating	dominating	NOUN
ejpam-4578	349	9	set	set	NOUN
ejpam-4578	349	10	of	of	ADP
ejpam-4578	349	11	g[h	g[h	PROPN
ejpam-4578	349	12	]	]	PUNCT
ejpam-4578	349	13	.	.	PUNCT
ejpam-4578	350	1	accordingly	accordingly	ADV
ejpam-4578	350	2	,	,	PUNCT
ejpam-4578	350	3	c	c	PROPN
ejpam-4578	350	4	is	be	AUX
ejpam-4578	350	5	a	a	DET
ejpam-4578	350	6	strong	strong	ADJ
ejpam-4578	350	7	resolving	resolve	VERB
ejpam-4578	350	8	hop	hop	NOUN
ejpam-4578	350	9	dominating	dominating	NOUN
ejpam-4578	350	10	set	set	NOUN
ejpam-4578	350	11	of	of	ADP
ejpam-4578	350	12	g[h	g[h	PROPN
ejpam-4578	350	13	]	]	PUNCT
ejpam-4578	350	14	.	.	PUNCT
ejpam-4578	351	1	corollary	corollary	ADJ
ejpam-4578	351	2	7	7	NUM
ejpam-4578	351	3	.	.	PUNCT
ejpam-4578	352	1	let	let	VERB
ejpam-4578	352	2	g	g	PRON
ejpam-4578	352	3	be	be	AUX
ejpam-4578	352	4	a	a	DET
ejpam-4578	352	5	connected	connected	ADJ
ejpam-4578	352	6	graph	graph	NOUN
ejpam-4578	352	7	of	of	ADP
ejpam-4578	352	8	order	order	NOUN
ejpam-4578	352	9	m	m	VERB
ejpam-4578	352	10	>	>	X
ejpam-4578	352	11	1	1	NUM
ejpam-4578	352	12	and	and	CCONJ
ejpam-4578	352	13	γ(g	γ(g	PROPN
ejpam-4578	352	14	)	)	PUNCT
ejpam-4578	352	15	̸=	̸=	PROPN
ejpam-4578	352	16	1	1	NUM
ejpam-4578	352	17	and	and	CCONJ
ejpam-4578	352	18	h	h	NOUN
ejpam-4578	352	19	=	=	SYM
ejpam-4578	352	20	kn	kn	PROPN
ejpam-4578	352	21	for	for	ADP
ejpam-4578	352	22	n	n	PROPN
ejpam-4578	352	23	>	>	X
ejpam-4578	352	24	1	1	NUM
ejpam-4578	352	25	.	.	PUNCT
ejpam-4578	353	1	then	then	ADV
ejpam-4578	353	2	γsrh(g[h	γsrh(g[h	NOUN
ejpam-4578	353	3	]	]	PUNCT
ejpam-4578	353	4	)	)	PUNCT
ejpam-4578	353	5	=	=	SYM
ejpam-4578	353	6	m(n−	m(n−	NOUN
ejpam-4578	353	7	1	1	NUM
ejpam-4578	353	8	)	)	PUNCT
ejpam-4578	353	9	+	+	CCONJ
ejpam-4578	353	10	|∂(g)|	|∂(g)|	NOUN
ejpam-4578	353	11	−	−	PROPN
ejpam-4578	353	12	1	1	X
ejpam-4578	353	13	.	.	PUNCT
ejpam-4578	354	1	proof	proof	NOUN
ejpam-4578	354	2	:	:	PUNCT
ejpam-4578	354	3	let	let	VERB
ejpam-4578	354	4	c	c	PART
ejpam-4578	354	5	be	be	AUX
ejpam-4578	354	6	a	a	DET
ejpam-4578	354	7	γsrh	γsrh	NOUN
ejpam-4578	354	8	-	-	PUNCT
ejpam-4578	354	9	set	set	NOUN
ejpam-4578	354	10	of	of	ADP
ejpam-4578	354	11	g[h	g[h	NOUN
ejpam-4578	354	12	]	]	PUNCT
ejpam-4578	354	13	.	.	PUNCT
ejpam-4578	355	1	then	then	ADV
ejpam-4578	355	2	c	c	X
ejpam-4578	355	3	=	=	PUNCT
ejpam-4578	355	4	⋃	⋃	PROPN
ejpam-4578	355	5	x∈s	x∈s	NOUN
ejpam-4578	355	6	(	(	PUNCT
ejpam-4578	355	7	{	{	PUNCT
ejpam-4578	355	8	x	x	NOUN
ejpam-4578	355	9	}	}	PUNCT
ejpam-4578	355	10	×	×	PROPN
ejpam-4578	355	11	tx	tx	PROPN
ejpam-4578	355	12	)	)	PUNCT
ejpam-4578	355	13	satisfying	satisfy	VERB
ejpam-4578	355	14	conditions	condition	NOUN
ejpam-4578	355	15	of	of	ADP
ejpam-4578	355	16	theorem	theorem	NOUN
ejpam-4578	355	17	11	11	NUM
ejpam-4578	355	18	.	.	PUNCT
ejpam-4578	356	1	thus	thus	ADV
ejpam-4578	356	2	,	,	PUNCT
ejpam-4578	356	3	s	s	VERB
ejpam-4578	356	4	=	=	SYM
ejpam-4578	356	5	v	v	X
ejpam-4578	356	6	(	(	PUNCT
ejpam-4578	356	7	g	g	NOUN
ejpam-4578	356	8	)	)	PUNCT
ejpam-4578	356	9	=	=	PUNCT
ejpam-4578	357	1	[	[	X
ejpam-4578	357	2	v	v	X
ejpam-4578	357	3	(	(	PUNCT
ejpam-4578	357	4	g	g	NOUN
ejpam-4578	357	5	)	)	PUNCT
ejpam-4578	357	6	\	\	NOUN
ejpam-4578	357	7	∂(g	∂(g	PROPN
ejpam-4578	357	8	)	)	PUNCT
ejpam-4578	357	9	]	]	PUNCT
ejpam-4578	357	10	∪	∪	X
ejpam-4578	357	11	(	(	PUNCT
ejpam-4578	357	12	∂(g	∂(g	PROPN
ejpam-4578	357	13	)	)	PUNCT
ejpam-4578	357	14	)	)	PUNCT
ejpam-4578	357	15	.	.	PUNCT
ejpam-4578	358	1	hence	hence	ADV
ejpam-4578	358	2	,	,	PUNCT
ejpam-4578	358	3	γsrh(g[h	γsrh(g[h	PROPN
ejpam-4578	358	4	]	]	X
ejpam-4578	358	5	)	)	PUNCT
ejpam-4578	358	6	=	=	NOUN
ejpam-4578	358	7	|c|	|c|	NOUN
ejpam-4578	358	8	=	=	SYM
ejpam-4578	358	9	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4578	358	10	⋃	⋃	PROPN
ejpam-4578	358	11	x∈v	x∈v	PROPN
ejpam-4578	358	12	(	(	PUNCT
ejpam-4578	358	13	g)\∂(g	g)\∂(g	PROPN
ejpam-4578	358	14	)	)	PUNCT
ejpam-4578	358	15	(	(	PUNCT
ejpam-4578	358	16	{	{	PUNCT
ejpam-4578	358	17	x	x	NOUN
ejpam-4578	358	18	}	}	PUNCT
ejpam-4578	358	19	×	×	PROPN
ejpam-4578	358	20	tx	tx	PROPN
ejpam-4578	358	21	)	)	PUNCT
ejpam-4578	358	22	∣∣∣∣∣∣+	∣∣∣∣∣∣+	PROPN
ejpam-4578	358	23	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4578	358	24	⋃	⋃	PROPN
ejpam-4578	358	25	y∈∂(g	y∈∂(g	PROPN
ejpam-4578	358	26	)	)	PUNCT
ejpam-4578	358	27	(	(	PUNCT
ejpam-4578	358	28	{	{	PUNCT
ejpam-4578	358	29	y	y	NOUN
ejpam-4578	358	30	}	}	PUNCT
ejpam-4578	358	31	×	×	NOUN
ejpam-4578	358	32	ty	ty	INTJ
ejpam-4578	358	33	)	)	PUNCT
ejpam-4578	358	34	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-4578	359	1	=	=	SYM
ejpam-4578	359	2	|v	|v	X
ejpam-4578	359	3	(	(	PUNCT
ejpam-4578	359	4	g	g	NOUN
ejpam-4578	359	5	)	)	PUNCT
ejpam-4578	359	6	\	\	NOUN
ejpam-4578	359	7	∂(g)||tx|+	∂(g)||tx|+	NOUN
ejpam-4578	359	8	|∂(g)−	|∂(g)−	PUNCT
ejpam-4578	359	9	1||ty|+	1||ty|+	NUM
ejpam-4578	359	10	n−	n−	NOUN
ejpam-4578	359	11	1	1	NUM
ejpam-4578	359	12	=(	=(	NOUN
ejpam-4578	359	13	m−	m−	PROPN
ejpam-4578	359	14	|∂(g)|)(n−	|∂(g)|)(n−	NUM
ejpam-4578	359	15	1	1	NUM
ejpam-4578	359	16	)	)	PUNCT
ejpam-4578	360	1	+	+	CCONJ
ejpam-4578	360	2	|∂(g)−	|∂(g)−	PUNCT
ejpam-4578	360	3	1|n+	1|n+	NUM
ejpam-4578	360	4	n−	n−	NOUN
ejpam-4578	360	5	1	1	NUM
ejpam-4578	360	6	=	=	NOUN
ejpam-4578	360	7	m(n−	m(n−	NOUN
ejpam-4578	360	8	1)−	1)−	PROPN
ejpam-4578	360	9	|∂(g)|n+	|∂(g)|n+	PROPN
ejpam-4578	360	10	|∂(g)|+	|∂(g)|+	PROPN
ejpam-4578	360	11	|∂(g)|n−	|∂(g)|n−	NUM
ejpam-4578	360	12	n+	n+	NUM
ejpam-4578	360	13	n−	n−	NOUN
ejpam-4578	360	14	1	1	NUM
ejpam-4578	360	15	=	=	NOUN
ejpam-4578	360	16	m(n−	m(n−	NOUN
ejpam-4578	360	17	1	1	NUM
ejpam-4578	360	18	)	)	PUNCT
ejpam-4578	360	19	+	+	CCONJ
ejpam-4578	360	20	|∂(g)|	|∂(g)|	NOUN
ejpam-4578	360	21	−	−	PROPN
ejpam-4578	360	22	1	1	X
ejpam-4578	360	23	.	.	PUNCT
ejpam-4578	360	24	therefore	therefore	ADV
ejpam-4578	360	25	,	,	PUNCT
ejpam-4578	360	26	γsrh(g[h	γsrh(g[h	PROPN
ejpam-4578	360	27	]	]	PUNCT
ejpam-4578	360	28	)	)	PUNCT
ejpam-4578	360	29	=	=	SYM
ejpam-4578	360	30	m(n−	m(n−	NOUN
ejpam-4578	360	31	1	1	NUM
ejpam-4578	360	32	)	)	PUNCT
ejpam-4578	360	33	+	+	CCONJ
ejpam-4578	360	34	|∂(g)|	|∂(g)|	NOUN
ejpam-4578	360	35	−	−	PROPN
ejpam-4578	360	36	1	1	X
ejpam-4578	360	37	.	.	PUNCT
ejpam-4578	360	38	acknowledgements	acknowledgement	NOUN
ejpam-4578	360	39	this	this	DET
ejpam-4578	360	40	research	research	NOUN
ejpam-4578	360	41	is	be	AUX
ejpam-4578	360	42	funded	fund	VERB
ejpam-4578	360	43	by	by	ADP
ejpam-4578	360	44	the	the	DET
ejpam-4578	360	45	department	department	PROPN
ejpam-4578	360	46	of	of	ADP
ejpam-4578	360	47	science	science	NOUN
ejpam-4578	360	48	and	and	CCONJ
ejpam-4578	360	49	technology	technology	NOUN
ejpam-4578	360	50	accelerated	accelerate	VERB
ejpam-4578	360	51	science	science	NOUN
ejpam-4578	360	52	and	and	CCONJ
ejpam-4578	360	53	technology	technology	NOUN
ejpam-4578	360	54	human	human	ADJ
ejpam-4578	360	55	resource	resource	NOUN
ejpam-4578	360	56	development	development	NOUN
ejpam-4578	360	57	program	program	NOUN
ejpam-4578	360	58	(	(	PUNCT
ejpam-4578	360	59	dost	dost	NOUN
ejpam-4578	360	60	-	-	PUNCT
ejpam-4578	360	61	asthrdp	asthrdp	NOUN
ejpam-4578	360	62	)	)	PUNCT
ejpam-4578	360	63	,	,	PUNCT
ejpam-4578	360	64	mindanao	mindanao	PROPN
ejpam-4578	360	65	state	state	PROPN
ejpam-4578	360	66	university	university	PROPN
ejpam-4578	360	67	iligan	iligan	PROPN
ejpam-4578	360	68	institute	institute	PROPN
ejpam-4578	360	69	of	of	ADP
ejpam-4578	360	70	technology	technology	NOUN
ejpam-4578	360	71	,	,	PUNCT
ejpam-4578	360	72	and	and	CCONJ
ejpam-4578	360	73	western	western	ADJ
ejpam-4578	360	74	mindanao	mindanao	PROPN
ejpam-4578	360	75	state	state	PROPN
ejpam-4578	360	76	university	university	PROPN
ejpam-4578	360	77	,	,	PUNCT
ejpam-4578	360	78	philippines	philippine	NOUN
ejpam-4578	360	79	.	.	PUNCT
ejpam-4578	361	1	references	reference	NOUN
ejpam-4578	361	2	143	143	NUM
ejpam-4578	361	3	references	reference	NOUN
ejpam-4578	361	4	[	[	X
ejpam-4578	361	5	1	1	NUM
ejpam-4578	361	6	]	]	X
ejpam-4578	361	7	g.	g.	PROPN
ejpam-4578	361	8	monsanto	monsanto	PROPN
ejpam-4578	361	9	,	,	PUNCT
ejpam-4578	361	10	p.	p.	NOUN
ejpam-4578	361	11	acal	acal	ADJ
ejpam-4578	361	12	and	and	CCONJ
ejpam-4578	361	13	h.	h.	PROPN
ejpam-4578	361	14	rara	rara	PROPN
ejpam-4578	361	15	.	.	PUNCT
ejpam-4578	362	1	on	on	ADP
ejpam-4578	362	2	strong	strong	ADJ
ejpam-4578	362	3	resolving	resolving	NOUN
ejpam-4578	362	4	domination	domination	NOUN
ejpam-4578	362	5	in	in	ADP
ejpam-4578	362	6	the	the	DET
ejpam-4578	362	7	join	join	NOUN
ejpam-4578	362	8	and	and	CCONJ
ejpam-4578	362	9	corona	corona	NOUN
ejpam-4578	362	10	of	of	ADP
ejpam-4578	362	11	graphs	graph	NOUN
ejpam-4578	362	12	.	.	PUNCT
ejpam-4578	363	1	european	european	ADJ
ejpam-4578	363	2	journal	journal	PROPN
ejpam-4578	363	3	of	of	ADP
ejpam-4578	363	4	pure	pure	ADJ
ejpam-4578	363	5	and	and	CCONJ
ejpam-4578	363	6	applied	applied	ADJ
ejpam-4578	363	7	mathematics	mathematic	NOUN
ejpam-4578	363	8	,	,	PUNCT
ejpam-4578	363	9	13(1):170	13(1):170	NUM
ejpam-4578	363	10	–	–	PUNCT
ejpam-4578	363	11	179	179	NUM
ejpam-4578	363	12	,	,	PUNCT
ejpam-4578	363	13	2020	2020	NUM
ejpam-4578	363	14	.	.	PUNCT
ejpam-4578	364	1	[	[	X
ejpam-4578	364	2	2	2	X
ejpam-4578	364	3	]	]	PUNCT
ejpam-4578	364	4	p.	p.	NOUN
ejpam-4578	364	5	acal	acal	ADJ
ejpam-4578	364	6	and	and	CCONJ
ejpam-4578	364	7	h.	h.	PROPN
ejpam-4578	364	8	rara	rara	PROPN
ejpam-4578	364	9	.	.	PUNCT
ejpam-4578	365	1	the	the	DET
ejpam-4578	365	2	strong	strong	ADJ
ejpam-4578	365	3	connected	connected	ADJ
ejpam-4578	365	4	metric	metric	ADJ
ejpam-4578	365	5	dimension	dimension	NOUN
ejpam-4578	365	6	in	in	ADP
ejpam-4578	365	7	the	the	DET
ejpam-4578	365	8	join	join	NOUN
ejpam-4578	365	9	and	and	CCONJ
ejpam-4578	365	10	corona	corona	NOUN
ejpam-4578	365	11	of	of	ADP
ejpam-4578	365	12	graphs	graph	NOUN
ejpam-4578	365	13	.	.	PUNCT
ejpam-4578	366	1	advances	advance	NOUN
ejpam-4578	366	2	and	and	CCONJ
ejpam-4578	366	3	applications	application	NOUN
ejpam-4578	366	4	in	in	ADP
ejpam-4578	366	5	discrete	discrete	ADJ
ejpam-4578	366	6	mathematics	mathematic	NOUN
ejpam-4578	366	7	,	,	PUNCT
ejpam-4578	366	8	21(1):91–101	21(1):91–101	NUM
ejpam-4578	366	9	,	,	PUNCT
ejpam-4578	366	10	2019	2019	NUM
ejpam-4578	366	11	.	.	PUNCT
ejpam-4578	367	1	[	[	X
ejpam-4578	367	2	3	3	X
ejpam-4578	367	3	]	]	X
ejpam-4578	367	4	f.	f.	PROPN
ejpam-4578	367	5	harary	harary	PROPN
ejpam-4578	367	6	.	.	PUNCT
ejpam-4578	368	1	graph	graph	NOUN
ejpam-4578	368	2	theory	theory	NOUN
ejpam-4578	368	3	.	.	PUNCT
ejpam-4578	369	1	addison	addison	PROPN
ejpam-4578	369	2	-	-	PUNCT
ejpam-4578	369	3	wesley	wesley	PROPN
ejpam-4578	369	4	publishing	publishing	PROPN
ejpam-4578	369	5	company	company	NOUN
ejpam-4578	369	6	,	,	PUNCT
ejpam-4578	369	7	usa	usa	PROPN
ejpam-4578	369	8	,	,	PUNCT
ejpam-4578	369	9	1969	1969	NUM
ejpam-4578	369	10	.	.	PUNCT
ejpam-4578	370	1	[	[	X
ejpam-4578	370	2	4	4	X
ejpam-4578	370	3	]	]	X
ejpam-4578	370	4	g.	g.	PROPN
ejpam-4578	370	5	malacas	malacas	PROPN
ejpam-4578	370	6	,	,	PUNCT
ejpam-4578	370	7	e.	e.	PROPN
ejpam-4578	370	8	ahmad	ahmad	PROPN
ejpam-4578	370	9	,	,	PUNCT
ejpam-4578	370	10	and	and	CCONJ
ejpam-4578	370	11	s.	s.	PROPN
ejpam-4578	370	12	canoy	canoy	PROPN
ejpam-4578	370	13	jr	jr	PROPN
ejpam-4578	370	14	.	.	PROPN
ejpam-4578	370	15	stable	stable	ADJ
ejpam-4578	370	16	locating	locating	NOUN
ejpam-4578	370	17	-	-	PUNCT
ejpam-4578	370	18	dominating	dominating	NOUN
ejpam-4578	370	19	sets	set	NOUN
ejpam-4578	370	20	in	in	ADP
ejpam-4578	370	21	graphs	graph	NOUN
ejpam-4578	370	22	.	.	PUNCT
ejpam-4578	371	1	european	european	ADJ
ejpam-4578	371	2	journal	journal	PROPN
ejpam-4578	371	3	of	of	ADP
ejpam-4578	371	4	pure	pure	ADJ
ejpam-4578	371	5	and	and	CCONJ
ejpam-4578	371	6	applied	applied	ADJ
ejpam-4578	371	7	mathematics	mathematic	NOUN
ejpam-4578	371	8	,	,	PUNCT
ejpam-4578	371	9	14(3):638–649	14(3):638–649	NOUN
ejpam-4578	371	10	,	,	PUNCT
ejpam-4578	371	11	2021	2021	NUM
ejpam-4578	371	12	.	.	PUNCT
ejpam-4578	372	1	[	[	X
ejpam-4578	372	2	5	5	X
ejpam-4578	372	3	]	]	PUNCT
ejpam-4578	372	4	j.	j.	PROPN
ejpam-4578	372	5	mohamad	mohamad	PROPN
ejpam-4578	372	6	and	and	CCONJ
ejpam-4578	372	7	h.	h.	PROPN
ejpam-4578	372	8	rara	rara	PROPN
ejpam-4578	372	9	.	.	PUNCT
ejpam-4578	373	1	on	on	ADP
ejpam-4578	373	2	resolving	resolve	VERB
ejpam-4578	373	3	hop	hop	NOUN
ejpam-4578	373	4	domination	domination	NOUN
ejpam-4578	373	5	in	in	ADP
ejpam-4578	373	6	graphs	graph	NOUN
ejpam-4578	373	7	.	.	PUNCT
ejpam-4578	374	1	european	european	ADJ
ejpam-4578	374	2	journal	journal	PROPN
ejpam-4578	374	3	of	of	ADP
ejpam-4578	374	4	pure	pure	ADJ
ejpam-4578	374	5	and	and	CCONJ
ejpam-4578	374	6	applied	applied	ADJ
ejpam-4578	374	7	mathematics	mathematic	NOUN
ejpam-4578	374	8	,	,	PUNCT
ejpam-4578	374	9	14(3):1015–1023	14(3):1015–1023	NUM
ejpam-4578	374	10	,	,	PUNCT
ejpam-4578	374	11	2021	2021	NUM
ejpam-4578	374	12	.	.	PUNCT
ejpam-4578	375	1	[	[	X
ejpam-4578	375	2	6	6	NUM
ejpam-4578	375	3	]	]	PUNCT
ejpam-4578	375	4	g.	g.	PROPN
ejpam-4578	375	5	monsanto	monsanto	PROPN
ejpam-4578	375	6	and	and	CCONJ
ejpam-4578	375	7	h.	h.	PROPN
ejpam-4578	375	8	rara	rara	PROPN
ejpam-4578	375	9	.	.	PUNCT
ejpam-4578	376	1	resolving	resolve	VERB
ejpam-4578	376	2	sets	set	NOUN
ejpam-4578	376	3	in	in	ADP
ejpam-4578	376	4	graphs	graph	NOUN
ejpam-4578	376	5	.	.	PUNCT
ejpam-4578	377	1	international	international	ADJ
ejpam-4578	377	2	journal	journal	NOUN
ejpam-4578	377	3	of	of	ADP
ejpam-4578	377	4	pure	pure	ADJ
ejpam-4578	377	5	and	and	CCONJ
ejpam-4578	377	6	applied	applied	ADJ
ejpam-4578	377	7	mathematics	mathematic	NOUN
ejpam-4578	377	8	,	,	PUNCT
ejpam-4578	377	9	accepted	accept	VERB
ejpam-4578	377	10	article	article	NOUN
ejpam-4578	377	11	2020	2020	NUM
ejpam-4578	377	12	.	.	PUNCT
ejpam-4578	378	1	[	[	X
ejpam-4578	378	2	7	7	X
ejpam-4578	378	3	]	]	X
ejpam-4578	378	4	g.	g.	PROPN
ejpam-4578	378	5	monsanto	monsanto	PROPN
ejpam-4578	378	6	and	and	CCONJ
ejpam-4578	378	7	h.	h.	PROPN
ejpam-4578	378	8	rara	rara	PROPN
ejpam-4578	378	9	.	.	PUNCT
ejpam-4578	379	1	resolving	resolve	VERB
ejpam-4578	379	2	restrained	restrained	ADJ
ejpam-4578	379	3	domination	domination	NOUN
ejpam-4578	379	4	in	in	ADP
ejpam-4578	379	5	graphs	graph	NOUN
ejpam-4578	379	6	.	.	PUNCT
ejpam-4578	380	1	european	european	ADJ
ejpam-4578	380	2	journal	journal	PROPN
ejpam-4578	380	3	of	of	ADP
ejpam-4578	380	4	pure	pure	ADJ
ejpam-4578	380	5	and	and	CCONJ
ejpam-4578	380	6	applied	applied	ADJ
ejpam-4578	380	7	mathematics	mathematic	NOUN
ejpam-4578	380	8	,	,	PUNCT
ejpam-4578	380	9	accepted	accept	VERB
ejpam-4578	380	10	article	article	NOUN
ejpam-4578	380	11	2021	2021	NUM
ejpam-4578	380	12	.	.	PUNCT
ejpam-4578	381	1	[	[	X
ejpam-4578	381	2	8	8	NUM
ejpam-4578	381	3	]	]	X
ejpam-4578	381	4	c.	c.	PROPN
ejpam-4578	381	5	natarajan	natarajan	PROPN
ejpam-4578	381	6	and	and	CCONJ
ejpam-4578	381	7	s.	s.	PROPN
ejpam-4578	381	8	ayyaswamy	ayyaswamy	PROPN
ejpam-4578	381	9	.	.	PUNCT
ejpam-4578	382	1	hop	hop	PROPN
ejpam-4578	382	2	domination	domination	NOUN
ejpam-4578	382	3	in	in	ADP
ejpam-4578	382	4	graphs	graph	NOUN
ejpam-4578	382	5	-	-	PUNCT
ejpam-4578	382	6	ii	ii	NOUN
ejpam-4578	382	7	.	.	PUNCT
ejpam-4578	382	8	versita	versita	PROPN
ejpam-4578	382	9	,	,	PUNCT
ejpam-4578	382	10	23(2):187	23(2):187	NUM
ejpam-4578	382	11	–	–	PUNCT
ejpam-4578	382	12	199	199	NUM
ejpam-4578	382	13	,	,	PUNCT
ejpam-4578	382	14	2015	2015	NUM
ejpam-4578	382	15	.	.	PUNCT
ejpam-4578	383	1	[	[	X
ejpam-4578	383	2	9	9	NUM
ejpam-4578	383	3	]	]	X
ejpam-4578	383	4	o.r	o.r	PROPN
ejpam-4578	383	5	.	.	PROPN
ejpam-4578	383	6	oellermann	oellermann	PROPN
ejpam-4578	383	7	and	and	CCONJ
ejpam-4578	383	8	j.	j.	PROPN
ejpam-4578	383	9	peters	peters	PROPN
ejpam-4578	383	10	-	-	PUNCT
ejpam-4578	383	11	fransen	fransen	PROPN
ejpam-4578	383	12	.	.	PUNCT
ejpam-4578	384	1	the	the	DET
ejpam-4578	384	2	strong	strong	ADJ
ejpam-4578	384	3	metric	metric	ADJ
ejpam-4578	384	4	dimension	dimension	NOUN
ejpam-4578	384	5	of	of	ADP
ejpam-4578	384	6	graphs	graph	NOUN
ejpam-4578	384	7	and	and	CCONJ
ejpam-4578	384	8	digraphs	digraph	NOUN
ejpam-4578	384	9	.	.	PUNCT
ejpam-4578	385	1	discrete	discrete	ADJ
ejpam-4578	385	2	applied	apply	VERB
ejpam-4578	385	3	mathematics	mathematic	NOUN
ejpam-4578	385	4	,	,	PUNCT
ejpam-4578	385	5	155(3):356–364	155(3):356–364	NUM
ejpam-4578	385	6	,	,	PUNCT
ejpam-4578	385	7	2007	2007	NUM
ejpam-4578	385	8	.	.	PUNCT
ejpam-4578	386	1	[	[	X
ejpam-4578	386	2	10	10	NUM
ejpam-4578	386	3	]	]	PUNCT
ejpam-4578	386	4	m.	m.	NOUN
ejpam-4578	386	5	n.	n.	PROPN
ejpam-4578	386	6	paspasan	paspasan	NOUN
ejpam-4578	386	7	and	and	CCONJ
ejpam-4578	386	8	s.	s.	PROPN
ejpam-4578	386	9	canoy	canoy	PROPN
ejpam-4578	386	10	jr	jr	PROPN
ejpam-4578	386	11	.	.	PROPN
ejpam-4578	386	12	restrained	restrained	ADJ
ejpam-4578	386	13	total	total	ADJ
ejpam-4578	386	14	edge	edge	NOUN
ejpam-4578	386	15	domination	domination	NOUN
ejpam-4578	386	16	in	in	ADP
ejpam-4578	386	17	graphs	graph	NOUN
ejpam-4578	386	18	.	.	PUNCT
ejpam-4578	387	1	applied	apply	VERB
ejpam-4578	387	2	mathematical	mathematical	ADJ
ejpam-4578	387	3	sciences	science	NOUN
ejpam-4578	387	4	,	,	PUNCT
ejpam-4578	387	5	9:7139–7148	9:7139–7148	NUM
ejpam-4578	387	6	,	,	PUNCT
ejpam-4578	387	7	2015	2015	NUM
ejpam-4578	387	8	.	.	PUNCT
ejpam-4578	388	1	[	[	X
ejpam-4578	388	2	11	11	NUM
ejpam-4578	388	3	]	]	X
ejpam-4578	388	4	g.	g.	NOUN
ejpam-4578	388	5	salasalan	salasalan	NOUN
ejpam-4578	388	6	and	and	CCONJ
ejpam-4578	388	7	s.	s.	PROPN
ejpam-4578	388	8	canoy	canoy	PROPN
ejpam-4578	388	9	jr	jr	PROPN
ejpam-4578	388	10	.	.	PROPN
ejpam-4578	388	11	global	global	PROPN
ejpam-4578	388	12	hop	hop	PROPN
ejpam-4578	388	13	domination	domination	NOUN
ejpam-4578	388	14	number	number	NOUN
ejpam-4578	388	15	of	of	ADP
ejpam-4578	388	16	graphs	graph	NOUN
ejpam-4578	388	17	.	.	PUNCT
ejpam-4578	389	1	european	european	ADJ
ejpam-4578	389	2	journal	journal	PROPN
ejpam-4578	389	3	of	of	ADP
ejpam-4578	389	4	pure	pure	ADJ
ejpam-4578	389	5	and	and	CCONJ
ejpam-4578	389	6	applied	applied	ADJ
ejpam-4578	389	7	mathematics	mathematic	NOUN
ejpam-4578	389	8	,	,	PUNCT
ejpam-4578	389	9	14(1):112–125	14(1):112–125	NUM
ejpam-4578	389	10	,	,	PUNCT
ejpam-4578	389	11	2021	2021	NUM
ejpam-4578	389	12	.	.	PUNCT
ejpam-4578	390	1	[	[	X
ejpam-4578	390	2	12	12	NUM
ejpam-4578	390	3	]	]	X
ejpam-4578	390	4	p.	p.	NOUN
ejpam-4578	390	5	slater	slater	PROPN
ejpam-4578	390	6	.	.	PUNCT
ejpam-4578	391	1	dominating	dominating	NOUN
ejpam-4578	391	2	and	and	CCONJ
ejpam-4578	391	3	reference	reference	NOUN
ejpam-4578	391	4	sets	set	NOUN
ejpam-4578	391	5	in	in	ADP
ejpam-4578	391	6	a	a	DET
ejpam-4578	391	7	graph	graph	NOUN
ejpam-4578	391	8	.	.	PUNCT
ejpam-4578	392	1	journal	journal	NOUN
ejpam-4578	392	2	of	of	ADP
ejpam-4578	392	3	mathematics	mathematic	NOUN
ejpam-4578	392	4	and	and	CCONJ
ejpam-4578	392	5	physical	physical	ADJ
ejpam-4578	392	6	science	science	NOUN
ejpam-4578	392	7	,	,	PUNCT
ejpam-4578	392	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4578	392	9	,	,	PUNCT
ejpam-4578	392	10	1988	1988	NUM
ejpam-4578	392	11	.	.	PUNCT