id	sid	tid	token	lemma	pos
ejpam-4771	1	1	european	european	PROPN
ejpam-4771	1	2	journal	journal	PROPN
ejpam-4771	1	3	of	of	ADP
ejpam-4771	1	4	pure	pure	ADJ
ejpam-4771	1	5	and	and	CCONJ
ejpam-4771	1	6	applied	apply	VERB
ejpam-4771	1	7	mathematics	mathematic	NOUN
ejpam-4771	1	8	vol	vol	NOUN
ejpam-4771	1	9	.	.	PUNCT
ejpam-4771	2	1	16	16	NUM
ejpam-4771	2	2	,	,	PUNCT
ejpam-4771	2	3	no	no	INTJ
ejpam-4771	2	4	.	.	NOUN
ejpam-4771	2	5	2	2	NUM
ejpam-4771	2	6	,	,	PUNCT
ejpam-4771	2	7	2023	2023	NUM
ejpam-4771	2	8	,	,	PUNCT
ejpam-4771	2	9	1180	1180	NUM
ejpam-4771	2	10	-	-	SYM
ejpam-4771	2	11	1195	1195	NUM
ejpam-4771	2	12	issn	issn	PROPN
ejpam-4771	2	13	1307	1307	NUM
ejpam-4771	2	14	-	-	SYM
ejpam-4771	2	15	5543	5543	NUM
ejpam-4771	2	16	–	–	PUNCT
ejpam-4771	2	17	ejpam.com	ejpam.com	X
ejpam-4771	2	18	published	publish	VERB
ejpam-4771	2	19	by	by	ADP
ejpam-4771	2	20	new	new	PROPN
ejpam-4771	2	21	york	york	PROPN
ejpam-4771	2	22	business	business	PROPN
ejpam-4771	2	23	global	global	ADJ
ejpam-4771	2	24	outer	outer	ADV
ejpam-4771	2	25	-	-	PUNCT
ejpam-4771	2	26	connected	connect	VERB
ejpam-4771	2	27	2	2	NUM
ejpam-4771	2	28	-	-	PUNCT
ejpam-4771	2	29	resolving	resolve	VERB
ejpam-4771	2	30	hop	hop	NOUN
ejpam-4771	2	31	domination	domination	NOUN
ejpam-4771	2	32	in	in	ADP
ejpam-4771	2	33	graphs	graph	NOUN
ejpam-4771	2	34	angelica	angelica	PROPN
ejpam-4771	2	35	mae	mae	PROPN
ejpam-4771	2	36	mahistrado1,∗	mahistrado1,∗	PROPN
ejpam-4771	2	37	,	,	PUNCT
ejpam-4771	2	38	helen	helen	PROPN
ejpam-4771	2	39	rara1	rara1	PROPN
ejpam-4771	3	1	1	1	NUM
ejpam-4771	3	2	department	department	NOUN
ejpam-4771	3	3	of	of	ADP
ejpam-4771	3	4	mathematics	mathematic	NOUN
ejpam-4771	3	5	and	and	CCONJ
ejpam-4771	3	6	statistics	statistic	NOUN
ejpam-4771	3	7	,	,	PUNCT
ejpam-4771	3	8	college	college	NOUN
ejpam-4771	3	9	of	of	ADP
ejpam-4771	3	10	science	science	NOUN
ejpam-4771	3	11	and	and	CCONJ
ejpam-4771	3	12	mathematics	mathematic	NOUN
ejpam-4771	3	13	,	,	PUNCT
ejpam-4771	3	14	center	center	NOUN
ejpam-4771	3	15	of	of	ADP
ejpam-4771	3	16	graph	graph	NOUN
ejpam-4771	3	17	theory	theory	NOUN
ejpam-4771	3	18	,	,	PUNCT
ejpam-4771	3	19	algebra	algebra	NOUN
ejpam-4771	3	20	,	,	PUNCT
ejpam-4771	3	21	and	and	CCONJ
ejpam-4771	3	22	analysis	analysis	NOUN
ejpam-4771	3	23	-	-	PUNCT
ejpam-4771	3	24	premier	premier	NOUN
ejpam-4771	3	25	research	research	NOUN
ejpam-4771	3	26	institute	institute	PROPN
ejpam-4771	3	27	of	of	ADP
ejpam-4771	3	28	science	science	NOUN
ejpam-4771	3	29	and	and	CCONJ
ejpam-4771	3	30	mathematics	mathematic	NOUN
ejpam-4771	3	31	,	,	PUNCT
ejpam-4771	3	32	mindanao	mindanao	PROPN
ejpam-4771	3	33	state	state	PROPN
ejpam-4771	3	34	university	university	PROPN
ejpam-4771	3	35	-	-	PUNCT
ejpam-4771	3	36	iligan	iligan	PROPN
ejpam-4771	3	37	institute	institute	PROPN
ejpam-4771	3	38	of	of	ADP
ejpam-4771	3	39	technology	technology	PROPN
ejpam-4771	3	40	,	,	PUNCT
ejpam-4771	3	41	9200	9200	NUM
ejpam-4771	3	42	iligan	iligan	ADJ
ejpam-4771	3	43	city	city	NOUN
ejpam-4771	3	44	,	,	PUNCT
ejpam-4771	3	45	philippines	philippine	NOUN
ejpam-4771	3	46	abstract	abstract	ADJ
ejpam-4771	3	47	.	.	PUNCT
ejpam-4771	4	1	let	let	VERB
ejpam-4771	4	2	g	g	PRON
ejpam-4771	4	3	be	be	AUX
ejpam-4771	4	4	a	a	DET
ejpam-4771	4	5	connected	connected	ADJ
ejpam-4771	4	6	graph	graph	NOUN
ejpam-4771	4	7	.	.	PUNCT
ejpam-4771	5	1	a	a	DET
ejpam-4771	5	2	set	set	NOUN
ejpam-4771	5	3	s	s	NOUN
ejpam-4771	5	4	⊆	⊆	NUM
ejpam-4771	5	5	v	v	NOUN
ejpam-4771	5	6	(	(	PUNCT
ejpam-4771	5	7	g	g	NOUN
ejpam-4771	5	8	)	)	PUNCT
ejpam-4771	5	9	is	be	AUX
ejpam-4771	5	10	an	an	DET
ejpam-4771	5	11	outer	outer	ADV
ejpam-4771	5	12	-	-	PUNCT
ejpam-4771	5	13	connected	connect	VERB
ejpam-4771	5	14	2	2	NUM
ejpam-4771	5	15	-	-	PUNCT
ejpam-4771	5	16	resolving	resolve	VERB
ejpam-4771	5	17	hop	hop	NOUN
ejpam-4771	5	18	dominating	dominating	NOUN
ejpam-4771	5	19	set	set	NOUN
ejpam-4771	5	20	of	of	ADP
ejpam-4771	5	21	g	g	PROPN
ejpam-4771	5	22	if	if	SCONJ
ejpam-4771	5	23	s	s	VERB
ejpam-4771	5	24	is	be	AUX
ejpam-4771	5	25	a	a	DET
ejpam-4771	5	26	2	2	NUM
ejpam-4771	5	27	-	-	PUNCT
ejpam-4771	5	28	resolving	resolve	VERB
ejpam-4771	5	29	hop	hop	NOUN
ejpam-4771	5	30	dominating	dominating	NOUN
ejpam-4771	5	31	set	set	NOUN
ejpam-4771	5	32	of	of	ADP
ejpam-4771	5	33	g	g	PROPN
ejpam-4771	5	34	and	and	CCONJ
ejpam-4771	5	35	s	s	PART
ejpam-4771	5	36	=	=	SYM
ejpam-4771	5	37	v	v	X
ejpam-4771	5	38	(	(	PUNCT
ejpam-4771	5	39	g	g	NOUN
ejpam-4771	5	40	)	)	PUNCT
ejpam-4771	5	41	or	or	CCONJ
ejpam-4771	5	42	the	the	DET
ejpam-4771	5	43	subgraph	subgraph	NOUN
ejpam-4771	5	44	⟨v	⟨v	NOUN
ejpam-4771	5	45	(	(	PUNCT
ejpam-4771	5	46	g)\s⟩	g)\s⟩	PROPN
ejpam-4771	5	47	induced	induce	VERB
ejpam-4771	5	48	by	by	ADP
ejpam-4771	5	49	v	v	NOUN
ejpam-4771	5	50	(	(	PUNCT
ejpam-4771	5	51	g)\s	g)\s	NOUN
ejpam-4771	5	52	is	be	AUX
ejpam-4771	5	53	connected	connect	VERB
ejpam-4771	5	54	.	.	PUNCT
ejpam-4771	6	1	the	the	DET
ejpam-4771	6	2	outer	outer	ADV
ejpam-4771	6	3	-	-	PUNCT
ejpam-4771	6	4	connected	connect	VERB
ejpam-4771	6	5	2	2	NUM
ejpam-4771	6	6	-	-	PUNCT
ejpam-4771	6	7	resolving	resolve	VERB
ejpam-4771	6	8	hop	hop	NOUN
ejpam-4771	6	9	domination	domination	NOUN
ejpam-4771	6	10	number	number	NOUN
ejpam-4771	6	11	of	of	ADP
ejpam-4771	6	12	g	g	NOUN
ejpam-4771	6	13	,	,	PUNCT
ejpam-4771	6	14	denoted	denote	VERB
ejpam-4771	6	15	by	by	ADP
ejpam-4771	6	16	γ̃c2rh(g	γ̃c2rh(g	NOUN
ejpam-4771	6	17	)	)	PUNCT
ejpam-4771	6	18	is	be	AUX
ejpam-4771	6	19	the	the	DET
ejpam-4771	6	20	smallest	small	ADJ
ejpam-4771	6	21	cardinality	cardinality	NOUN
ejpam-4771	6	22	of	of	ADP
ejpam-4771	6	23	an	an	DET
ejpam-4771	6	24	outer	outer	ADV
ejpam-4771	6	25	-	-	PUNCT
ejpam-4771	6	26	connected	connect	VERB
ejpam-4771	6	27	2	2	NUM
ejpam-4771	6	28	-	-	PUNCT
ejpam-4771	6	29	resolving	resolve	VERB
ejpam-4771	6	30	hop	hop	NOUN
ejpam-4771	6	31	dominating	dominating	NOUN
ejpam-4771	6	32	set	set	NOUN
ejpam-4771	6	33	of	of	ADP
ejpam-4771	6	34	g.	g.	PROPN
ejpam-4771	6	35	this	this	DET
ejpam-4771	6	36	study	study	NOUN
ejpam-4771	6	37	aims	aim	VERB
ejpam-4771	6	38	to	to	PART
ejpam-4771	6	39	combine	combine	VERB
ejpam-4771	6	40	the	the	DET
ejpam-4771	6	41	concept	concept	NOUN
ejpam-4771	6	42	of	of	ADP
ejpam-4771	6	43	outer	outer	ADV
ejpam-4771	6	44	-	-	PUNCT
ejpam-4771	6	45	connected	connect	VERB
ejpam-4771	6	46	hop	hop	NOUN
ejpam-4771	6	47	domination	domination	NOUN
ejpam-4771	6	48	with	with	ADP
ejpam-4771	6	49	the	the	DET
ejpam-4771	6	50	2	2	NUM
ejpam-4771	6	51	-	-	PUNCT
ejpam-4771	6	52	resolving	resolve	VERB
ejpam-4771	6	53	hop	hop	NOUN
ejpam-4771	6	54	dominating	dominating	NOUN
ejpam-4771	6	55	sets	set	NOUN
ejpam-4771	6	56	of	of	ADP
ejpam-4771	6	57	graphs	graph	NOUN
ejpam-4771	6	58	.	.	PUNCT
ejpam-4771	7	1	the	the	DET
ejpam-4771	7	2	main	main	ADJ
ejpam-4771	7	3	results	result	NOUN
ejpam-4771	7	4	generated	generate	VERB
ejpam-4771	7	5	in	in	ADP
ejpam-4771	7	6	this	this	DET
ejpam-4771	7	7	study	study	NOUN
ejpam-4771	7	8	include	include	VERB
ejpam-4771	7	9	the	the	DET
ejpam-4771	7	10	characterization	characterization	NOUN
ejpam-4771	7	11	of	of	ADP
ejpam-4771	7	12	outer	outer	ADV
ejpam-4771	7	13	-	-	PUNCT
ejpam-4771	7	14	connected	connect	VERB
ejpam-4771	7	15	2	2	NUM
ejpam-4771	7	16	-	-	PUNCT
ejpam-4771	7	17	resolving	resolve	VERB
ejpam-4771	7	18	hop	hop	NOUN
ejpam-4771	7	19	dominating	dominating	NOUN
ejpam-4771	7	20	sets	set	NOUN
ejpam-4771	7	21	in	in	ADP
ejpam-4771	7	22	the	the	DET
ejpam-4771	7	23	join	join	NOUN
ejpam-4771	7	24	,	,	PUNCT
ejpam-4771	7	25	corona	corona	PROPN
ejpam-4771	7	26	,	,	PUNCT
ejpam-4771	7	27	edge	edge	NOUN
ejpam-4771	7	28	corona	corona	NOUN
ejpam-4771	7	29	and	and	CCONJ
ejpam-4771	7	30	lexicographic	lexicographic	ADJ
ejpam-4771	7	31	product	product	NOUN
ejpam-4771	7	32	of	of	ADP
ejpam-4771	7	33	graphs	graph	NOUN
ejpam-4771	7	34	,	,	PUNCT
ejpam-4771	7	35	as	as	ADV
ejpam-4771	7	36	well	well	ADV
ejpam-4771	7	37	as	as	ADP
ejpam-4771	7	38	their	their	PRON
ejpam-4771	7	39	corresponding	corresponding	ADJ
ejpam-4771	7	40	bounds	bound	NOUN
ejpam-4771	7	41	or	or	CCONJ
ejpam-4771	7	42	exact	exact	ADJ
ejpam-4771	7	43	values	value	NOUN
ejpam-4771	7	44	.	.	PUNCT
ejpam-4771	8	1	2020	2020	NUM
ejpam-4771	8	2	mathematics	mathematic	NOUN
ejpam-4771	8	3	subject	subject	NOUN
ejpam-4771	8	4	classifications	classification	NOUN
ejpam-4771	8	5	:	:	PUNCT
ejpam-4771	8	6	05c69	05c69	X
ejpam-4771	8	7	key	key	ADJ
ejpam-4771	8	8	words	word	NOUN
ejpam-4771	8	9	and	and	CCONJ
ejpam-4771	8	10	phrases	phrase	NOUN
ejpam-4771	8	11	:	:	PUNCT
ejpam-4771	8	12	outer	outer	ADJ
ejpam-4771	8	13	-	-	PUNCT
ejpam-4771	8	14	connected	connect	VERB
ejpam-4771	8	15	2	2	NUM
ejpam-4771	8	16	-	-	PUNCT
ejpam-4771	8	17	resolving	resolve	VERB
ejpam-4771	8	18	hop	hop	NOUN
ejpam-4771	8	19	dominating	dominating	NOUN
ejpam-4771	8	20	set	set	NOUN
ejpam-4771	8	21	,	,	PUNCT
ejpam-4771	8	22	outer	outer	ADV
ejpam-4771	8	23	-	-	PUNCT
ejpam-4771	8	24	connected	connect	VERB
ejpam-4771	8	25	2	2	NUM
ejpam-4771	8	26	-	-	PUNCT
ejpam-4771	8	27	resolving	resolve	VERB
ejpam-4771	8	28	hop	hop	NOUN
ejpam-4771	8	29	domination	domination	NOUN
ejpam-4771	8	30	number	number	NOUN
ejpam-4771	8	31	,	,	PUNCT
ejpam-4771	8	32	join	join	NOUN
ejpam-4771	8	33	,	,	PUNCT
ejpam-4771	8	34	corona	corona	PROPN
ejpam-4771	8	35	,	,	PUNCT
ejpam-4771	8	36	edge	edge	NOUN
ejpam-4771	8	37	corona	corona	NOUN
ejpam-4771	8	38	,	,	PUNCT
ejpam-4771	8	39	lexicographic	lexicographic	ADJ
ejpam-4771	8	40	product	product	NOUN
ejpam-4771	8	41	1	1	NUM
ejpam-4771	8	42	.	.	PUNCT
ejpam-4771	8	43	introduction	introduction	NOUN
ejpam-4771	8	44	the	the	DET
ejpam-4771	8	45	concept	concept	NOUN
ejpam-4771	8	46	of	of	ADP
ejpam-4771	8	47	domination	domination	NOUN
ejpam-4771	8	48	in	in	ADP
ejpam-4771	8	49	graphs	graph	NOUN
ejpam-4771	8	50	is	be	AUX
ejpam-4771	8	51	one	one	NUM
ejpam-4771	8	52	of	of	ADP
ejpam-4771	8	53	the	the	DET
ejpam-4771	8	54	most	most	ADV
ejpam-4771	8	55	studied	study	VERB
ejpam-4771	8	56	problems	problem	NOUN
ejpam-4771	8	57	and	and	CCONJ
ejpam-4771	8	58	one	one	NUM
ejpam-4771	8	59	of	of	ADP
ejpam-4771	8	60	the	the	DET
ejpam-4771	8	61	fastest	fast	ADJ
ejpam-4771	8	62	growing	grow	VERB
ejpam-4771	8	63	areas	area	NOUN
ejpam-4771	8	64	in	in	ADP
ejpam-4771	8	65	graph	graph	NOUN
ejpam-4771	8	66	theory	theory	NOUN
ejpam-4771	8	67	.	.	PUNCT
ejpam-4771	9	1	this	this	PRON
ejpam-4771	9	2	was	be	AUX
ejpam-4771	9	3	formally	formally	ADV
ejpam-4771	9	4	studied	study	VERB
ejpam-4771	9	5	by	by	ADP
ejpam-4771	9	6	claude	claude	PROPN
ejpam-4771	9	7	berge	berge	PROPN
ejpam-4771	10	1	[	[	X
ejpam-4771	10	2	1	1	X
ejpam-4771	10	3	]	]	PUNCT
ejpam-4771	10	4	in	in	ADP
ejpam-4771	10	5	1958	1958	NUM
ejpam-4771	10	6	and	and	CCONJ
ejpam-4771	10	7	oystein	oystein	ADJ
ejpam-4771	10	8	ore	ore	NOUN
ejpam-4771	10	9	in	in	ADP
ejpam-4771	10	10	1962	1962	NUM
ejpam-4771	10	11	.	.	PUNCT
ejpam-4771	11	1	in	in	ADP
ejpam-4771	11	2	2007	2007	NUM
ejpam-4771	11	3	,	,	PUNCT
ejpam-4771	11	4	outer	outer	ADV
ejpam-4771	11	5	-	-	PUNCT
ejpam-4771	11	6	connected	connect	VERB
ejpam-4771	11	7	domination	domination	NOUN
ejpam-4771	11	8	,	,	PUNCT
ejpam-4771	11	9	a	a	DET
ejpam-4771	11	10	variation	variation	NOUN
ejpam-4771	11	11	of	of	ADP
ejpam-4771	11	12	domination	domination	NOUN
ejpam-4771	11	13	,	,	PUNCT
ejpam-4771	11	14	was	be	AUX
ejpam-4771	11	15	first	first	ADV
ejpam-4771	11	16	introduced	introduce	VERB
ejpam-4771	11	17	by	by	ADP
ejpam-4771	11	18	cyman	cyman	NOUN
ejpam-4771	11	19	[	[	X
ejpam-4771	11	20	10	10	NUM
ejpam-4771	11	21	]	]	PUNCT
ejpam-4771	11	22	.	.	PUNCT
ejpam-4771	12	1	in	in	ADP
ejpam-4771	12	2	2015	2015	NUM
ejpam-4771	12	3	,	,	PUNCT
ejpam-4771	12	4	natarajan	natarajan	PROPN
ejpam-4771	12	5	and	and	CCONJ
ejpam-4771	12	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4771	12	7	introduced	introduce	VERB
ejpam-4771	12	8	and	and	CCONJ
ejpam-4771	12	9	studied	study	VERB
ejpam-4771	12	10	the	the	DET
ejpam-4771	12	11	concept	concept	NOUN
ejpam-4771	12	12	of	of	ADP
ejpam-4771	12	13	hop	hop	NOUN
ejpam-4771	12	14	domination	domination	NOUN
ejpam-4771	13	1	[	[	X
ejpam-4771	13	2	16	16	NUM
ejpam-4771	13	3	]	]	PUNCT
ejpam-4771	13	4	.	.	PUNCT
ejpam-4771	14	1	in	in	ADP
ejpam-4771	14	2	2022	2022	NUM
ejpam-4771	14	3	,	,	PUNCT
ejpam-4771	14	4	canoy	canoy	ADJ
ejpam-4771	14	5	and	and	CCONJ
ejpam-4771	14	6	saromines	saromine	NOUN
ejpam-4771	14	7	studied	study	VERB
ejpam-4771	14	8	and	and	CCONJ
ejpam-4771	14	9	published	publish	VERB
ejpam-4771	14	10	the	the	DET
ejpam-4771	14	11	outer	outer	ADJ
ejpam-4771	14	12	-	-	PUNCT
ejpam-4771	14	13	connect	connect	ADJ
ejpam-4771	14	14	hop	hop	NOUN
ejpam-4771	14	15	dominating	dominating	NOUN
ejpam-4771	14	16	sets	set	NOUN
ejpam-4771	14	17	in	in	ADP
ejpam-4771	14	18	graphs	graph	NOUN
ejpam-4771	14	19	[	[	X
ejpam-4771	14	20	9	9	NUM
ejpam-4771	14	21	]	]	PUNCT
ejpam-4771	14	22	.	.	PUNCT
ejpam-4771	15	1	on	on	ADP
ejpam-4771	15	2	the	the	DET
ejpam-4771	15	3	other	other	ADJ
ejpam-4771	15	4	hand	hand	NOUN
ejpam-4771	15	5	,	,	PUNCT
ejpam-4771	15	6	in	in	ADP
ejpam-4771	15	7	1975	1975	NUM
ejpam-4771	15	8	the	the	DET
ejpam-4771	15	9	term	term	NOUN
ejpam-4771	15	10	locating	locate	VERB
ejpam-4771	15	11	set	set	NOUN
ejpam-4771	15	12	,	,	PUNCT
ejpam-4771	15	13	the	the	DET
ejpam-4771	15	14	concept	concept	NOUN
ejpam-4771	15	15	of	of	ADP
ejpam-4771	15	16	resolving	resolve	VERB
ejpam-4771	15	17	sets	set	NOUN
ejpam-4771	15	18	for	for	ADP
ejpam-4771	15	19	a	a	DET
ejpam-4771	15	20	connected	connected	ADJ
ejpam-4771	15	21	graph	graph	NOUN
ejpam-4771	15	22	was	be	AUX
ejpam-4771	15	23	first	first	ADV
ejpam-4771	15	24	introduced	introduce	VERB
ejpam-4771	15	25	by	by	ADP
ejpam-4771	15	26	slater	slater	NOUN
ejpam-4771	15	27	[	[	X
ejpam-4771	15	28	19	19	NUM
ejpam-4771	15	29	]	]	PUNCT
ejpam-4771	15	30	.	.	PUNCT
ejpam-4771	16	1	these	these	DET
ejpam-4771	16	2	concepts	concept	NOUN
ejpam-4771	16	3	were	be	AUX
ejpam-4771	16	4	studied	study	VERB
ejpam-4771	16	5	much	much	ADV
ejpam-4771	16	6	earlier	early	ADV
ejpam-4771	16	7	in	in	ADP
ejpam-4771	16	8	the	the	DET
ejpam-4771	16	9	context	context	NOUN
ejpam-4771	16	10	of	of	ADP
ejpam-4771	16	11	the	the	DET
ejpam-4771	16	12	coin	coin	NOUN
ejpam-4771	16	13	-	-	PUNCT
ejpam-4771	16	14	weighing	weigh	VERB
ejpam-4771	16	15	problem	problem	NOUN
ejpam-4771	16	16	.	.	PUNCT
ejpam-4771	17	1	later	later	ADV
ejpam-4771	17	2	that	that	DET
ejpam-4771	17	3	year	year	NOUN
ejpam-4771	17	4	,	,	PUNCT
ejpam-4771	17	5	harary	harary	NOUN
ejpam-4771	17	6	and	and	CCONJ
ejpam-4771	17	7	melter	melter	NOUN
ejpam-4771	17	8	introduced	introduce	VERB
ejpam-4771	17	9	independently	independently	ADV
ejpam-4771	17	10	these	these	DET
ejpam-4771	17	11	concepts	concept	NOUN
ejpam-4771	17	12	,	,	PUNCT
ejpam-4771	17	13	but	but	CCONJ
ejpam-4771	17	14	with	with	ADP
ejpam-4771	17	15	different	different	ADJ
ejpam-4771	17	16	terminologies	terminology	NOUN
ejpam-4771	17	17	[	[	X
ejpam-4771	17	18	11	11	NUM
ejpam-4771	17	19	]	]	PUNCT
ejpam-4771	17	20	.	.	PUNCT
ejpam-4771	18	1	the	the	DET
ejpam-4771	18	2	term	term	NOUN
ejpam-4771	18	3	∗corresponding	∗corresponde	VERB
ejpam-4771	18	4	author	author	NOUN
ejpam-4771	18	5	.	.	PUNCT
ejpam-4771	19	1	doi	doi	NOUN
ejpam-4771	19	2	:	:	PUNCT
ejpam-4771	19	3	https://doi.org/10.29020/nybg.ejpam.v16i2.4771	https://doi.org/10.29020/nybg.ejpam.v16i2.4771	NOUN
ejpam-4771	19	4	email	email	NOUN
ejpam-4771	19	5	addresses	address	NOUN
ejpam-4771	19	6	:	:	PUNCT
ejpam-4771	19	7	angelicamae.mahistrado@g.msuiit.edu.ph	angelicamae.mahistrado@g.msuiit.edu.ph	PROPN
ejpam-4771	19	8	(	(	PUNCT
ejpam-4771	19	9	a.m.	a.m.	NOUN
ejpam-4771	19	10	mahistrado	mahistrado	PROPN
ejpam-4771	19	11	)	)	PUNCT
ejpam-4771	19	12	,	,	PUNCT
ejpam-4771	19	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4771	19	14	(	(	PUNCT
ejpam-4771	19	15	h.	h.	PROPN
ejpam-4771	19	16	rara	rara	PROPN
ejpam-4771	19	17	)	)	PUNCT
ejpam-4771	19	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4771	19	19	1180	1180	NUM
ejpam-4771	20	1	©	©	ADP
ejpam-4771	20	2	2023	2023	NUM
ejpam-4771	20	3	ejpam	ejpam	NOUN
ejpam-4771	20	4	all	all	DET
ejpam-4771	20	5	rights	right	NOUN
ejpam-4771	20	6	reserved	reserve	VERB
ejpam-4771	20	7	.	.	PUNCT
ejpam-4771	21	1	a.m.	a.m.	PROPN
ejpam-4771	21	2	mahistrado	mahistrado	PROPN
ejpam-4771	21	3	,	,	PUNCT
ejpam-4771	21	4	h.	h.	PROPN
ejpam-4771	21	5	rara	rara	PROPN
ejpam-4771	21	6	/	/	SYM
ejpam-4771	21	7	eur	eur	PROPN
ejpam-4771	21	8	.	.	PUNCT
ejpam-4771	22	1	j.	j.	PROPN
ejpam-4771	22	2	pure	pure	PROPN
ejpam-4771	22	3	appl	appl	PROPN
ejpam-4771	22	4	.	.	PROPN
ejpam-4771	22	5	math	math	PROPN
ejpam-4771	22	6	,	,	PUNCT
ejpam-4771	22	7	16	16	NUM
ejpam-4771	22	8	(	(	PUNCT
ejpam-4771	22	9	2	2	NUM
ejpam-4771	22	10	)	)	PUNCT
ejpam-4771	22	11	(	(	PUNCT
ejpam-4771	22	12	2023	2023	NUM
ejpam-4771	22	13	)	)	PUNCT
ejpam-4771	22	14	,	,	PUNCT
ejpam-4771	22	15	1180	1180	NUM
ejpam-4771	22	16	-	-	SYM
ejpam-4771	22	17	1195	1195	NUM
ejpam-4771	22	18	1181	1181	NUM
ejpam-4771	22	19	metric	metric	ADJ
ejpam-4771	22	20	dimension	dimension	NOUN
ejpam-4771	22	21	was	be	AUX
ejpam-4771	22	22	used	use	VERB
ejpam-4771	22	23	by	by	ADP
ejpam-4771	22	24	harary	harary	NOUN
ejpam-4771	22	25	and	and	CCONJ
ejpam-4771	22	26	melter	melter	NOUN
ejpam-4771	22	27	instead	instead	ADV
ejpam-4771	22	28	of	of	ADP
ejpam-4771	22	29	locating	locate	VERB
ejpam-4771	22	30	number	number	NOUN
ejpam-4771	22	31	.	.	PUNCT
ejpam-4771	23	1	recently	recently	ADV
ejpam-4771	23	2	,	,	PUNCT
ejpam-4771	23	3	2	2	NUM
ejpam-4771	23	4	-	-	PUNCT
ejpam-4771	23	5	resolving	resolve	VERB
ejpam-4771	23	6	hop	hop	NOUN
ejpam-4771	23	7	dominating	dominating	NOUN
ejpam-4771	23	8	sets	set	NOUN
ejpam-4771	23	9	in	in	ADP
ejpam-4771	23	10	graphs	graph	NOUN
ejpam-4771	23	11	was	be	AUX
ejpam-4771	23	12	studied	study	VERB
ejpam-4771	23	13	in	in	ADP
ejpam-4771	23	14	[	[	X
ejpam-4771	23	15	12	12	NUM
ejpam-4771	23	16	]	]	PUNCT
ejpam-4771	23	17	.	.	PUNCT
ejpam-4771	24	1	moreover	moreover	ADV
ejpam-4771	24	2	,	,	PUNCT
ejpam-4771	24	3	other	other	ADJ
ejpam-4771	24	4	variations	variation	NOUN
ejpam-4771	24	5	of	of	ADP
ejpam-4771	24	6	resolving	resolve	VERB
ejpam-4771	24	7	sets	set	NOUN
ejpam-4771	24	8	and	and	CCONJ
ejpam-4771	24	9	hop	hop	NOUN
ejpam-4771	24	10	dominating	dominating	NOUN
ejpam-4771	24	11	sets	set	NOUN
ejpam-4771	24	12	in	in	ADP
ejpam-4771	24	13	graphs	graph	NOUN
ejpam-4771	24	14	were	be	AUX
ejpam-4771	24	15	also	also	ADV
ejpam-4771	24	16	studied	study	VERB
ejpam-4771	24	17	in	in	ADP
ejpam-4771	24	18	[	[	X
ejpam-4771	24	19	4–6	4–6	NOUN
ejpam-4771	24	20	,	,	PUNCT
ejpam-4771	24	21	8	8	NUM
ejpam-4771	24	22	,	,	PUNCT
ejpam-4771	24	23	13–15	13–15	NUM
ejpam-4771	24	24	]	]	PUNCT
ejpam-4771	24	25	,	,	PUNCT
ejpam-4771	24	26	respectively	respectively	ADV
ejpam-4771	24	27	.	.	PUNCT
ejpam-4771	25	1	motivated	motivate	VERB
ejpam-4771	25	2	by	by	ADP
ejpam-4771	25	3	the	the	DET
ejpam-4771	25	4	2	2	NUM
ejpam-4771	25	5	-	-	PUNCT
ejpam-4771	25	6	resolving	resolve	VERB
ejpam-4771	25	7	hop	hop	NOUN
ejpam-4771	25	8	domination	domination	NOUN
ejpam-4771	25	9	concept	concept	NOUN
ejpam-4771	25	10	and	and	CCONJ
ejpam-4771	25	11	the	the	DET
ejpam-4771	25	12	introduction	introduction	NOUN
ejpam-4771	25	13	of	of	ADP
ejpam-4771	25	14	the	the	DET
ejpam-4771	25	15	outerconnected	outerconnecte	VERB
ejpam-4771	25	16	hop	hop	NOUN
ejpam-4771	25	17	domination	domination	NOUN
ejpam-4771	25	18	concept	concept	NOUN
ejpam-4771	25	19	by	by	ADP
ejpam-4771	25	20	s.r	s.r	PROPN
ejpam-4771	25	21	.	.	PROPN
ejpam-4771	25	22	canoy	canoy	PROPN
ejpam-4771	25	23	and	and	CCONJ
ejpam-4771	25	24	c.j	c.j	PROPN
ejpam-4771	25	25	.	.	PROPN
ejpam-4771	25	26	saromines	saromines	AUX
ejpam-4771	26	1	[	[	X
ejpam-4771	26	2	9	9	NUM
ejpam-4771	26	3	]	]	PUNCT
ejpam-4771	26	4	,	,	PUNCT
ejpam-4771	26	5	here	here	ADV
ejpam-4771	26	6	authors	author	NOUN
ejpam-4771	26	7	introduced	introduce	VERB
ejpam-4771	26	8	and	and	CCONJ
ejpam-4771	26	9	studied	study	VERB
ejpam-4771	26	10	the	the	DET
ejpam-4771	26	11	concept	concept	NOUN
ejpam-4771	26	12	of	of	ADP
ejpam-4771	26	13	outer	outer	ADV
ejpam-4771	26	14	-	-	PUNCT
ejpam-4771	26	15	connected	connect	VERB
ejpam-4771	26	16	2	2	NUM
ejpam-4771	26	17	-	-	PUNCT
ejpam-4771	26	18	resolving	resolve	VERB
ejpam-4771	26	19	hop	hop	NOUN
ejpam-4771	26	20	domination	domination	NOUN
ejpam-4771	26	21	in	in	ADP
ejpam-4771	26	22	graphs	graph	NOUN
ejpam-4771	26	23	.	.	PUNCT
ejpam-4771	27	1	2	2	X
ejpam-4771	27	2	.	.	X
ejpam-4771	27	3	terminology	terminology	NOUN
ejpam-4771	27	4	and	and	CCONJ
ejpam-4771	27	5	notation	notation	NOUN
ejpam-4771	27	6	in	in	ADP
ejpam-4771	27	7	this	this	DET
ejpam-4771	27	8	study	study	NOUN
ejpam-4771	27	9	,	,	PUNCT
ejpam-4771	27	10	we	we	PRON
ejpam-4771	27	11	consider	consider	VERB
ejpam-4771	27	12	finite	finite	ADJ
ejpam-4771	27	13	,	,	PUNCT
ejpam-4771	27	14	simple	simple	ADJ
ejpam-4771	27	15	,	,	PUNCT
ejpam-4771	27	16	connected	connect	VERB
ejpam-4771	27	17	,	,	PUNCT
ejpam-4771	27	18	undirected	undirected	ADJ
ejpam-4771	27	19	graphs	graph	NOUN
ejpam-4771	27	20	.	.	PUNCT
ejpam-4771	28	1	for	for	ADP
ejpam-4771	28	2	basic	basic	ADJ
ejpam-4771	28	3	graphtheoretic	graphtheoretic	ADJ
ejpam-4771	28	4	concepts	concept	NOUN
ejpam-4771	28	5	,	,	PUNCT
ejpam-4771	28	6	we	we	PRON
ejpam-4771	28	7	then	then	ADV
ejpam-4771	28	8	refer	refer	VERB
ejpam-4771	28	9	readers	reader	NOUN
ejpam-4771	28	10	to	to	ADP
ejpam-4771	28	11	[	[	X
ejpam-4771	28	12	2	2	NUM
ejpam-4771	28	13	]	]	PUNCT
ejpam-4771	28	14	and	and	CCONJ
ejpam-4771	28	15	[	[	X
ejpam-4771	28	16	3	3	NUM
ejpam-4771	28	17	]	]	PUNCT
ejpam-4771	28	18	.	.	PUNCT
ejpam-4771	29	1	the	the	DET
ejpam-4771	29	2	following	follow	VERB
ejpam-4771	29	3	concepts	concept	NOUN
ejpam-4771	29	4	are	be	AUX
ejpam-4771	29	5	found	find	VERB
ejpam-4771	29	6	in	in	ADP
ejpam-4771	29	7	[	[	X
ejpam-4771	29	8	2	2	NUM
ejpam-4771	29	9	]	]	PUNCT
ejpam-4771	29	10	,	,	PUNCT
ejpam-4771	29	11	[	[	X
ejpam-4771	29	12	16	16	NUM
ejpam-4771	29	13	]	]	PUNCT
ejpam-4771	29	14	and	and	CCONJ
ejpam-4771	29	15	[	[	X
ejpam-4771	29	16	18	18	NUM
ejpam-4771	29	17	]	]	PUNCT
ejpam-4771	29	18	.	.	PUNCT
ejpam-4771	30	1	let	let	VERB
ejpam-4771	30	2	g	g	PRON
ejpam-4771	30	3	be	be	AUX
ejpam-4771	30	4	a	a	DET
ejpam-4771	30	5	connected	connected	ADJ
ejpam-4771	30	6	graph	graph	NOUN
ejpam-4771	30	7	.	.	PUNCT
ejpam-4771	31	1	a	a	DET
ejpam-4771	31	2	vertex	vertex	NOUN
ejpam-4771	31	3	v	v	NOUN
ejpam-4771	31	4	in	in	ADP
ejpam-4771	31	5	g	g	PROPN
ejpam-4771	31	6	is	be	AUX
ejpam-4771	31	7	a	a	DET
ejpam-4771	31	8	hop	hop	NOUN
ejpam-4771	31	9	neighbor	neighbor	NOUN
ejpam-4771	31	10	of	of	ADP
ejpam-4771	31	11	vertex	vertex	NOUN
ejpam-4771	31	12	u	u	NOUN
ejpam-4771	31	13	in	in	ADP
ejpam-4771	31	14	g	g	PROPN
ejpam-4771	31	15	if	if	SCONJ
ejpam-4771	31	16	dg(u	dg(u	NOUN
ejpam-4771	31	17	,	,	PUNCT
ejpam-4771	31	18	v	v	NOUN
ejpam-4771	31	19	)	)	PUNCT
ejpam-4771	31	20	=	=	SYM
ejpam-4771	31	21	2	2	X
ejpam-4771	31	22	.	.	X
ejpam-4771	32	1	the	the	DET
ejpam-4771	32	2	set	set	NOUN
ejpam-4771	32	3	ng(u	ng(u	NOUN
ejpam-4771	32	4	,	,	PUNCT
ejpam-4771	32	5	2	2	NUM
ejpam-4771	32	6	)	)	PUNCT
ejpam-4771	32	7	=	=	PRON
ejpam-4771	32	8	{	{	PUNCT
ejpam-4771	32	9	v	v	NUM
ejpam-4771	32	10	∈	∈	NOUN
ejpam-4771	32	11	v	v	NOUN
ejpam-4771	32	12	(	(	PUNCT
ejpam-4771	32	13	g	g	NOUN
ejpam-4771	32	14	)	)	PUNCT
ejpam-4771	32	15	:	:	PUNCT
ejpam-4771	32	16	dg(v	dg(v	X
ejpam-4771	32	17	,	,	PUNCT
ejpam-4771	32	18	u	u	NOUN
ejpam-4771	32	19	)	)	PUNCT
ejpam-4771	32	20	=	=	SYM
ejpam-4771	32	21	2	2	X
ejpam-4771	32	22	}	}	PUNCT
ejpam-4771	32	23	is	be	AUX
ejpam-4771	32	24	called	call	VERB
ejpam-4771	32	25	the	the	DET
ejpam-4771	32	26	open	open	ADJ
ejpam-4771	32	27	hop	hop	NOUN
ejpam-4771	32	28	neighborhood	neighborhood	NOUN
ejpam-4771	32	29	of	of	ADP
ejpam-4771	32	30	u.	u.	PROPN
ejpam-4771	32	31	the	the	DET
ejpam-4771	32	32	closed	closed	ADJ
ejpam-4771	32	33	hop	hop	NOUN
ejpam-4771	32	34	neighborhood	neighborhood	NOUN
ejpam-4771	32	35	of	of	ADP
ejpam-4771	32	36	u	u	PROPN
ejpam-4771	32	37	in	in	ADP
ejpam-4771	32	38	g	g	PROPN
ejpam-4771	32	39	is	be	AUX
ejpam-4771	32	40	given	give	VERB
ejpam-4771	32	41	by	by	ADP
ejpam-4771	32	42	ng[u	ng[u	PROPN
ejpam-4771	32	43	,	,	PUNCT
ejpam-4771	32	44	2	2	NUM
ejpam-4771	32	45	]	]	PUNCT
ejpam-4771	33	1	=	=	SYM
ejpam-4771	33	2	ng(u	ng(u	PROPN
ejpam-4771	33	3	,	,	PUNCT
ejpam-4771	33	4	2)∪	2)∪	NUM
ejpam-4771	33	5	{	{	PUNCT
ejpam-4771	33	6	u	u	NOUN
ejpam-4771	33	7	}	}	PUNCT
ejpam-4771	33	8	.	.	PUNCT
ejpam-4771	34	1	the	the	DET
ejpam-4771	34	2	open	open	ADJ
ejpam-4771	34	3	hop	hop	NOUN
ejpam-4771	34	4	neighborhood	neighborhood	NOUN
ejpam-4771	34	5	of	of	ADP
ejpam-4771	34	6	x	x	PROPN
ejpam-4771	34	7	⊆	⊆	NUM
ejpam-4771	34	8	v	v	ADP
ejpam-4771	34	9	(	(	PUNCT
ejpam-4771	34	10	g	g	NOUN
ejpam-4771	34	11	)	)	PUNCT
ejpam-4771	34	12	is	be	AUX
ejpam-4771	34	13	the	the	DET
ejpam-4771	34	14	set	set	NOUN
ejpam-4771	34	15	ng(x	ng(x	NUM
ejpam-4771	34	16	,	,	PUNCT
ejpam-4771	34	17	2	2	X
ejpam-4771	34	18	)	)	PUNCT
ejpam-4771	34	19	=	=	NOUN
ejpam-4771	34	20	⋃	⋃	NOUN
ejpam-4771	34	21	u∈x	u∈x	ADJ
ejpam-4771	34	22	ng(u	ng(u	NOUN
ejpam-4771	34	23	,	,	PUNCT
ejpam-4771	34	24	2	2	NUM
ejpam-4771	34	25	)	)	PUNCT
ejpam-4771	34	26	.	.	PUNCT
ejpam-4771	35	1	the	the	DET
ejpam-4771	35	2	closed	closed	ADJ
ejpam-4771	35	3	hop	hop	NOUN
ejpam-4771	35	4	neighborhood	neighborhood	NOUN
ejpam-4771	35	5	of	of	ADP
ejpam-4771	35	6	x	x	PUNCT
ejpam-4771	35	7	in	in	ADP
ejpam-4771	35	8	g	g	PROPN
ejpam-4771	35	9	is	be	AUX
ejpam-4771	35	10	the	the	DET
ejpam-4771	35	11	set	set	PROPN
ejpam-4771	35	12	ng[x	ng[x	PROPN
ejpam-4771	35	13	,	,	PUNCT
ejpam-4771	35	14	2	2	NUM
ejpam-4771	35	15	]	]	PUNCT
ejpam-4771	35	16	=	=	SYM
ejpam-4771	35	17	ng(x	ng(x	X
ejpam-4771	35	18	,	,	PUNCT
ejpam-4771	35	19	2	2	NUM
ejpam-4771	35	20	)	)	PUNCT
ejpam-4771	35	21	∪x	∪x	NUM
ejpam-4771	35	22	.	.	PUNCT
ejpam-4771	36	1	a	a	DET
ejpam-4771	36	2	set	set	NOUN
ejpam-4771	36	3	s	s	NOUN
ejpam-4771	36	4	⊆	⊆	NUM
ejpam-4771	36	5	v	v	NOUN
ejpam-4771	36	6	(	(	PUNCT
ejpam-4771	36	7	g	g	NOUN
ejpam-4771	36	8	)	)	PUNCT
ejpam-4771	36	9	is	be	AUX
ejpam-4771	36	10	a	a	DET
ejpam-4771	36	11	hop	hop	NOUN
ejpam-4771	36	12	dominating	dominating	NOUN
ejpam-4771	36	13	set	set	NOUN
ejpam-4771	36	14	of	of	ADP
ejpam-4771	36	15	g	g	PROPN
ejpam-4771	36	16	if	if	SCONJ
ejpam-4771	36	17	ng[s	ng[	NOUN
ejpam-4771	36	18	,	,	PUNCT
ejpam-4771	36	19	2	2	NUM
ejpam-4771	36	20	]	]	PUNCT
ejpam-4771	36	21	=	=	SYM
ejpam-4771	36	22	v	v	NOUN
ejpam-4771	36	23	(	(	PUNCT
ejpam-4771	36	24	g	g	NOUN
ejpam-4771	36	25	)	)	PUNCT
ejpam-4771	36	26	,	,	PUNCT
ejpam-4771	36	27	that	that	ADV
ejpam-4771	36	28	is	is	ADV
ejpam-4771	36	29	,	,	PUNCT
ejpam-4771	36	30	for	for	ADP
ejpam-4771	36	31	every	every	DET
ejpam-4771	36	32	v	v	NUM
ejpam-4771	36	33	∈	∈	NOUN
ejpam-4771	36	34	v	v	NOUN
ejpam-4771	36	35	(	(	PUNCT
ejpam-4771	36	36	g)\s	g)\s	NOUN
ejpam-4771	36	37	,	,	PUNCT
ejpam-4771	36	38	there	there	PRON
ejpam-4771	36	39	exists	exist	VERB
ejpam-4771	36	40	u	u	PROPN
ejpam-4771	36	41	∈	∈	PROPN
ejpam-4771	36	42	s	s	VERB
ejpam-4771	36	43	such	such	ADJ
ejpam-4771	36	44	that	that	DET
ejpam-4771	36	45	dg(u	dg(u	ADJ
ejpam-4771	36	46	,	,	PUNCT
ejpam-4771	36	47	v	v	NOUN
ejpam-4771	36	48	)	)	PUNCT
ejpam-4771	37	1	=	=	SYM
ejpam-4771	37	2	2	2	X
ejpam-4771	37	3	.	.	PUNCT
ejpam-4771	38	1	the	the	DET
ejpam-4771	38	2	minimum	minimum	ADJ
ejpam-4771	38	3	cardinality	cardinality	NOUN
ejpam-4771	38	4	of	of	ADP
ejpam-4771	38	5	a	a	DET
ejpam-4771	38	6	hop	hop	NOUN
ejpam-4771	38	7	dominating	dominating	NOUN
ejpam-4771	38	8	set	set	NOUN
ejpam-4771	38	9	of	of	ADP
ejpam-4771	38	10	g	g	NOUN
ejpam-4771	38	11	,	,	PUNCT
ejpam-4771	38	12	denoted	denote	VERB
ejpam-4771	38	13	by	by	ADP
ejpam-4771	38	14	γh(g	γh(g	NOUN
ejpam-4771	38	15	)	)	PUNCT
ejpam-4771	38	16	,	,	PUNCT
ejpam-4771	38	17	is	be	AUX
ejpam-4771	38	18	called	call	VERB
ejpam-4771	38	19	the	the	DET
ejpam-4771	38	20	hop	hop	NOUN
ejpam-4771	38	21	domination	domination	NOUN
ejpam-4771	38	22	number	number	NOUN
ejpam-4771	38	23	of	of	ADP
ejpam-4771	38	24	g.	g.	PROPN
ejpam-4771	38	25	any	any	DET
ejpam-4771	38	26	hop	hop	NOUN
ejpam-4771	38	27	dominating	dominating	NOUN
ejpam-4771	38	28	set	set	VERB
ejpam-4771	38	29	with	with	ADP
ejpam-4771	38	30	cardinality	cardinality	NOUN
ejpam-4771	38	31	equal	equal	ADJ
ejpam-4771	38	32	to	to	ADP
ejpam-4771	38	33	γh(g	γh(g	NOUN
ejpam-4771	38	34	)	)	PUNCT
ejpam-4771	38	35	is	be	AUX
ejpam-4771	38	36	called	call	VERB
ejpam-4771	38	37	a	a	DET
ejpam-4771	38	38	γh	γh	ADV
ejpam-4771	38	39	-	-	PUNCT
ejpam-4771	38	40	set	set	NOUN
ejpam-4771	38	41	.	.	PUNCT
ejpam-4771	39	1	for	for	ADP
ejpam-4771	39	2	an	an	DET
ejpam-4771	39	3	ordered	order	VERB
ejpam-4771	39	4	set	set	NOUN
ejpam-4771	39	5	of	of	ADP
ejpam-4771	39	6	vertices	vertex	NOUN
ejpam-4771	39	7	w	w	NOUN
ejpam-4771	39	8	=	=	SYM
ejpam-4771	39	9	{	{	PUNCT
ejpam-4771	39	10	w1	w1	NOUN
ejpam-4771	39	11	,	,	PUNCT
ejpam-4771	39	12	w2	w2	NOUN
ejpam-4771	39	13	,	,	PUNCT
ejpam-4771	39	14	...	...	PUNCT
ejpam-4771	39	15	,	,	PUNCT
ejpam-4771	39	16	wk	wk	ADP
ejpam-4771	39	17	}	}	PUNCT
ejpam-4771	39	18	⊆	⊆	NUM
ejpam-4771	39	19	v	v	NOUN
ejpam-4771	39	20	(	(	PUNCT
ejpam-4771	39	21	g	g	NOUN
ejpam-4771	39	22	)	)	PUNCT
ejpam-4771	39	23	and	and	CCONJ
ejpam-4771	39	24	a	a	DET
ejpam-4771	39	25	vertex	vertex	NOUN
ejpam-4771	39	26	v	v	NOUN
ejpam-4771	39	27	in	in	ADP
ejpam-4771	39	28	g	g	NOUN
ejpam-4771	39	29	,	,	PUNCT
ejpam-4771	39	30	we	we	PRON
ejpam-4771	39	31	refer	refer	VERB
ejpam-4771	39	32	to	to	ADP
ejpam-4771	39	33	the	the	DET
ejpam-4771	39	34	k	k	NOUN
ejpam-4771	39	35	-	-	NOUN
ejpam-4771	39	36	vector	vector	NOUN
ejpam-4771	39	37	(	(	PUNCT
ejpam-4771	39	38	ordered	order	VERB
ejpam-4771	39	39	k	k	NOUN
ejpam-4771	39	40	-	-	PUNCT
ejpam-4771	39	41	tuple	tuple	NOUN
ejpam-4771	39	42	)	)	PUNCT
ejpam-4771	39	43	rg(v	rg(v	PROPN
ejpam-4771	39	44	/	/	SYM
ejpam-4771	39	45	w	w	NOUN
ejpam-4771	39	46	)	)	PUNCT
ejpam-4771	40	1	=	=	SYM
ejpam-4771	40	2	(	(	PUNCT
ejpam-4771	40	3	dg(v	dg(v	X
ejpam-4771	40	4	,	,	PUNCT
ejpam-4771	40	5	w1	w1	NOUN
ejpam-4771	40	6	)	)	PUNCT
ejpam-4771	40	7	,	,	PUNCT
ejpam-4771	40	8	dg(v	dg(v	X
ejpam-4771	40	9	,	,	PUNCT
ejpam-4771	40	10	w2	w2	NOUN
ejpam-4771	40	11	)	)	PUNCT
ejpam-4771	40	12	,	,	PUNCT
ejpam-4771	40	13	...	...	PUNCT
ejpam-4771	40	14	,	,	PUNCT
ejpam-4771	40	15	dg(v	dg(v	X
ejpam-4771	40	16	,	,	PUNCT
ejpam-4771	40	17	wk	wk	NOUN
ejpam-4771	40	18	)	)	PUNCT
ejpam-4771	40	19	)	)	PUNCT
ejpam-4771	41	1	as	as	ADP
ejpam-4771	41	2	the	the	DET
ejpam-4771	41	3	(	(	PUNCT
ejpam-4771	41	4	metric	metric	ADJ
ejpam-4771	41	5	)	)	PUNCT
ejpam-4771	41	6	representation	representation	NOUN
ejpam-4771	41	7	of	of	ADP
ejpam-4771	41	8	v	v	NOUN
ejpam-4771	41	9	with	with	ADP
ejpam-4771	41	10	respect	respect	NOUN
ejpam-4771	41	11	to	to	ADP
ejpam-4771	41	12	w	w	PROPN
ejpam-4771	41	13	.	.	PUNCT
ejpam-4771	42	1	the	the	DET
ejpam-4771	42	2	set	set	NOUN
ejpam-4771	42	3	w	w	NOUN
ejpam-4771	42	4	is	be	AUX
ejpam-4771	42	5	called	call	VERB
ejpam-4771	42	6	a	a	DET
ejpam-4771	42	7	resolving	resolving	NOUN
ejpam-4771	42	8	set	set	VERB
ejpam-4771	42	9	for	for	ADP
ejpam-4771	42	10	g	g	PROPN
ejpam-4771	42	11	if	if	SCONJ
ejpam-4771	42	12	distinct	distinct	ADJ
ejpam-4771	42	13	vertices	vertex	NOUN
ejpam-4771	42	14	have	have	VERB
ejpam-4771	42	15	distinct	distinct	ADJ
ejpam-4771	42	16	representations	representation	NOUN
ejpam-4771	42	17	with	with	ADP
ejpam-4771	42	18	respect	respect	NOUN
ejpam-4771	42	19	to	to	ADP
ejpam-4771	42	20	w	w	PROPN
ejpam-4771	42	21	.	.	PUNCT
ejpam-4771	43	1	hence	hence	ADV
ejpam-4771	43	2	,	,	PUNCT
ejpam-4771	43	3	if	if	SCONJ
ejpam-4771	43	4	w	w	NOUN
ejpam-4771	43	5	is	be	AUX
ejpam-4771	43	6	a	a	DET
ejpam-4771	43	7	resolving	resolving	NOUN
ejpam-4771	43	8	set	set	NOUN
ejpam-4771	43	9	of	of	ADP
ejpam-4771	43	10	cardinality	cardinality	PROPN
ejpam-4771	43	11	k	k	PROPN
ejpam-4771	43	12	for	for	ADP
ejpam-4771	43	13	a	a	DET
ejpam-4771	43	14	graph	graph	NOUN
ejpam-4771	43	15	g	g	NOUN
ejpam-4771	43	16	of	of	ADP
ejpam-4771	43	17	order	order	NOUN
ejpam-4771	43	18	n	n	CCONJ
ejpam-4771	43	19	,	,	PUNCT
ejpam-4771	43	20	then	then	ADV
ejpam-4771	43	21	the	the	DET
ejpam-4771	43	22	set	set	NOUN
ejpam-4771	43	23	{	{	PUNCT
ejpam-4771	43	24	rg(v	rg(v	NOUN
ejpam-4771	43	25	/	/	SYM
ejpam-4771	43	26	w	w	NOUN
ejpam-4771	43	27	)	)	PUNCT
ejpam-4771	43	28	:	:	PUNCT
ejpam-4771	43	29	v	v	X
ejpam-4771	43	30	∈	∈	PROPN
ejpam-4771	43	31	v	v	NOUN
ejpam-4771	43	32	(	(	PUNCT
ejpam-4771	43	33	g	g	NOUN
ejpam-4771	43	34	)	)	PUNCT
ejpam-4771	43	35	}	}	PUNCT
ejpam-4771	43	36	consists	consist	VERB
ejpam-4771	43	37	of	of	ADP
ejpam-4771	43	38	n	n	PRON
ejpam-4771	43	39	distinct	distinct	ADJ
ejpam-4771	43	40	k	k	NOUN
ejpam-4771	43	41	-	-	NOUN
ejpam-4771	43	42	vectors	vector	NOUN
ejpam-4771	43	43	.	.	PUNCT
ejpam-4771	44	1	a	a	DET
ejpam-4771	44	2	resolving	resolving	NOUN
ejpam-4771	44	3	set	set	NOUN
ejpam-4771	44	4	of	of	ADP
ejpam-4771	44	5	minimum	minimum	ADJ
ejpam-4771	44	6	cardinality	cardinality	NOUN
ejpam-4771	44	7	is	be	AUX
ejpam-4771	44	8	called	call	VERB
ejpam-4771	44	9	aminimum	aminimum	ADJ
ejpam-4771	44	10	resolving	resolving	NOUN
ejpam-4771	44	11	set	set	VERB
ejpam-4771	44	12	or	or	CCONJ
ejpam-4771	44	13	a	a	DET
ejpam-4771	44	14	basis	basis	NOUN
ejpam-4771	44	15	,	,	PUNCT
ejpam-4771	44	16	and	and	CCONJ
ejpam-4771	44	17	the	the	DET
ejpam-4771	44	18	cardinality	cardinality	NOUN
ejpam-4771	44	19	of	of	ADP
ejpam-4771	44	20	a	a	DET
ejpam-4771	44	21	basis	basis	NOUN
ejpam-4771	44	22	for	for	ADP
ejpam-4771	44	23	g	g	PROPN
ejpam-4771	44	24	is	be	AUX
ejpam-4771	44	25	the	the	DET
ejpam-4771	44	26	dimension	dimension	NOUN
ejpam-4771	44	27	dim(g	dim(g	PROPN
ejpam-4771	44	28	)	)	PUNCT
ejpam-4771	44	29	of	of	ADP
ejpam-4771	44	30	g.	g.	PROPN
ejpam-4771	44	31	an	an	DET
ejpam-4771	44	32	ordered	order	VERB
ejpam-4771	44	33	set	set	NOUN
ejpam-4771	44	34	of	of	ADP
ejpam-4771	44	35	vertices	vertex	NOUN
ejpam-4771	44	36	w	w	NOUN
ejpam-4771	44	37	=	=	SYM
ejpam-4771	44	38	{	{	PUNCT
ejpam-4771	44	39	w1	w1	NOUN
ejpam-4771	44	40	,	,	PUNCT
ejpam-4771	44	41	...	...	PUNCT
ejpam-4771	44	42	,	,	PUNCT
ejpam-4771	44	43	wk	wk	X
ejpam-4771	44	44	}	}	PUNCT
ejpam-4771	44	45	is	be	AUX
ejpam-4771	44	46	a	a	DET
ejpam-4771	44	47	k	k	NOUN
ejpam-4771	44	48	-	-	PUNCT
ejpam-4771	44	49	resolving	resolving	NOUN
ejpam-4771	44	50	set	set	NOUN
ejpam-4771	44	51	for	for	ADP
ejpam-4771	44	52	g	g	PROPN
ejpam-4771	44	53	if	if	SCONJ
ejpam-4771	44	54	,	,	PUNCT
ejpam-4771	44	55	for	for	ADP
ejpam-4771	44	56	any	any	DET
ejpam-4771	44	57	distinct	distinct	ADJ
ejpam-4771	44	58	vertices	vertex	NOUN
ejpam-4771	44	59	u	u	NOUN
ejpam-4771	44	60	,	,	PUNCT
ejpam-4771	44	61	v	v	NOUN
ejpam-4771	44	62	∈	∈	PROPN
ejpam-4771	44	63	v	v	NOUN
ejpam-4771	44	64	(	(	PUNCT
ejpam-4771	44	65	g	g	NOUN
ejpam-4771	44	66	)	)	PUNCT
ejpam-4771	44	67	,	,	PUNCT
ejpam-4771	44	68	the	the	DET
ejpam-4771	44	69	(	(	PUNCT
ejpam-4771	44	70	metric	metric	ADJ
ejpam-4771	44	71	)	)	PUNCT
ejpam-4771	44	72	representations	representation	NOUN
ejpam-4771	44	73	rg(u	rg(u	NOUN
ejpam-4771	44	74	/	/	SYM
ejpam-4771	44	75	w	w	NOUN
ejpam-4771	44	76	)	)	PUNCT
ejpam-4771	44	77	and	and	CCONJ
ejpam-4771	44	78	rg(v	rg(v	PROPN
ejpam-4771	44	79	/	/	SYM
ejpam-4771	44	80	w	w	NOUN
ejpam-4771	44	81	)	)	PUNCT
ejpam-4771	44	82	of	of	ADP
ejpam-4771	44	83	u	u	NOUN
ejpam-4771	44	84	and	and	CCONJ
ejpam-4771	44	85	v	v	NOUN
ejpam-4771	44	86	,	,	PUNCT
ejpam-4771	44	87	respectively	respectively	ADV
ejpam-4771	44	88	,	,	PUNCT
ejpam-4771	44	89	differ	differ	VERB
ejpam-4771	44	90	in	in	ADP
ejpam-4771	44	91	at	at	ADP
ejpam-4771	44	92	least	least	ADJ
ejpam-4771	44	93	k	k	NOUN
ejpam-4771	44	94	positions	position	NOUN
ejpam-4771	44	95	.	.	PUNCT
ejpam-4771	45	1	if	if	SCONJ
ejpam-4771	45	2	k	k	PROPN
ejpam-4771	45	3	=	=	SYM
ejpam-4771	45	4	1	1	NUM
ejpam-4771	45	5	,	,	PUNCT
ejpam-4771	45	6	then	then	ADV
ejpam-4771	45	7	the	the	DET
ejpam-4771	45	8	k	k	NOUN
ejpam-4771	45	9	-	-	PUNCT
ejpam-4771	45	10	resolving	resolving	ADJ
ejpam-4771	45	11	set	set	NOUN
ejpam-4771	45	12	is	be	AUX
ejpam-4771	45	13	called	call	VERB
ejpam-4771	45	14	a	a	DET
ejpam-4771	45	15	resolving	resolving	NOUN
ejpam-4771	45	16	set	set	VERB
ejpam-4771	45	17	for	for	ADP
ejpam-4771	45	18	g.	g.	PROPN
ejpam-4771	45	19	if	if	SCONJ
ejpam-4771	45	20	k	k	PROPN
ejpam-4771	45	21	=	=	SYM
ejpam-4771	45	22	2	2	NUM
ejpam-4771	45	23	,	,	PUNCT
ejpam-4771	45	24	then	then	ADV
ejpam-4771	45	25	the	the	DET
ejpam-4771	45	26	k	k	NOUN
ejpam-4771	45	27	-	-	PUNCT
ejpam-4771	45	28	resolving	resolving	ADJ
ejpam-4771	45	29	set	set	NOUN
ejpam-4771	45	30	is	be	AUX
ejpam-4771	45	31	called	call	VERB
ejpam-4771	45	32	a	a	DET
ejpam-4771	45	33	2	2	NUM
ejpam-4771	45	34	-	-	PUNCT
ejpam-4771	45	35	resolving	resolving	NOUN
ejpam-4771	45	36	set	set	NOUN
ejpam-4771	45	37	for	for	ADP
ejpam-4771	45	38	g.	g.	PROPN
ejpam-4771	45	39	if	if	SCONJ
ejpam-4771	45	40	g	g	PROPN
ejpam-4771	45	41	has	have	VERB
ejpam-4771	45	42	a	a	DET
ejpam-4771	45	43	k	k	ADJ
ejpam-4771	45	44	-	-	ADJ
ejpam-4771	45	45	resolving	resolving	ADJ
ejpam-4771	45	46	set	set	NOUN
ejpam-4771	45	47	,	,	PUNCT
ejpam-4771	45	48	the	the	DET
ejpam-4771	45	49	minimum	minimum	ADJ
ejpam-4771	45	50	cardinality	cardinality	PROPN
ejpam-4771	45	51	dimk(g	dimk(g	PROPN
ejpam-4771	45	52	)	)	PUNCT
ejpam-4771	45	53	of	of	ADP
ejpam-4771	45	54	a	a	DET
ejpam-4771	45	55	k	k	NOUN
ejpam-4771	45	56	-	-	PUNCT
ejpam-4771	45	57	resolving	resolving	ADJ
ejpam-4771	45	58	set	set	NOUN
ejpam-4771	45	59	is	be	AUX
ejpam-4771	45	60	called	call	VERB
ejpam-4771	45	61	the	the	DET
ejpam-4771	45	62	k	k	ADJ
ejpam-4771	45	63	-	-	ADJ
ejpam-4771	45	64	metric	metric	ADJ
ejpam-4771	45	65	dimension	dimension	NOUN
ejpam-4771	45	66	of	of	ADP
ejpam-4771	45	67	g.	g.	PROPN
ejpam-4771	45	68	a	a	DET
ejpam-4771	45	69	set	set	NOUN
ejpam-4771	45	70	s	s	PROPN
ejpam-4771	45	71	⊆	⊆	NUM
ejpam-4771	45	72	v	v	NOUN
ejpam-4771	45	73	(	(	PUNCT
ejpam-4771	45	74	g	g	NOUN
ejpam-4771	45	75	)	)	PUNCT
ejpam-4771	45	76	is	be	AUX
ejpam-4771	45	77	an	an	DET
ejpam-4771	45	78	outer	outer	ADV
ejpam-4771	45	79	-	-	PUNCT
ejpam-4771	45	80	connected	connect	VERB
ejpam-4771	45	81	2	2	NUM
ejpam-4771	45	82	-	-	PUNCT
ejpam-4771	45	83	resolving	resolve	VERB
ejpam-4771	45	84	hop	hop	NOUN
ejpam-4771	45	85	dominating	dominating	NOUN
ejpam-4771	45	86	set	set	NOUN
ejpam-4771	45	87	of	of	ADP
ejpam-4771	45	88	g	g	PROPN
ejpam-4771	45	89	if	if	SCONJ
ejpam-4771	45	90	s	s	VERB
ejpam-4771	45	91	is	be	AUX
ejpam-4771	45	92	a	a	DET
ejpam-4771	45	93	2	2	NUM
ejpam-4771	45	94	-	-	PUNCT
ejpam-4771	45	95	resolving	resolve	VERB
ejpam-4771	45	96	hop	hop	NOUN
ejpam-4771	45	97	dominating	dominating	NOUN
ejpam-4771	45	98	set	set	NOUN
ejpam-4771	45	99	of	of	ADP
ejpam-4771	45	100	g	g	PROPN
ejpam-4771	45	101	and	and	CCONJ
ejpam-4771	45	102	s	s	PART
ejpam-4771	45	103	=	=	SYM
ejpam-4771	45	104	v	v	X
ejpam-4771	45	105	(	(	PUNCT
ejpam-4771	45	106	g	g	NOUN
ejpam-4771	45	107	)	)	PUNCT
ejpam-4771	45	108	or	or	CCONJ
ejpam-4771	45	109	the	the	DET
ejpam-4771	45	110	subgraph	subgraph	NOUN
ejpam-4771	45	111	⟨v	⟨v	NOUN
ejpam-4771	45	112	(	(	PUNCT
ejpam-4771	45	113	g)\s⟩	g)\s⟩	PROPN
ejpam-4771	45	114	induced	induce	VERB
ejpam-4771	45	115	by	by	ADP
ejpam-4771	45	116	v	v	NOUN
ejpam-4771	45	117	(	(	PUNCT
ejpam-4771	45	118	g)\s	g)\s	NOUN
ejpam-4771	45	119	is	be	AUX
ejpam-4771	45	120	connected	connect	VERB
ejpam-4771	45	121	.	.	PUNCT
ejpam-4771	46	1	the	the	DET
ejpam-4771	46	2	outer	outer	ADV
ejpam-4771	46	3	-	-	PUNCT
ejpam-4771	46	4	connected	connect	VERB
ejpam-4771	46	5	2	2	NUM
ejpam-4771	46	6	-	-	PUNCT
ejpam-4771	46	7	resolving	resolve	VERB
ejpam-4771	46	8	hop	hop	NOUN
ejpam-4771	46	9	domination	domination	NOUN
ejpam-4771	46	10	number	number	NOUN
ejpam-4771	46	11	of	of	ADP
ejpam-4771	46	12	g	g	NOUN
ejpam-4771	46	13	,	,	PUNCT
ejpam-4771	46	14	denoted	denote	VERB
ejpam-4771	46	15	by	by	ADP
ejpam-4771	46	16	γ̃c2rh(g	γ̃c2rh(g	NOUN
ejpam-4771	46	17	)	)	PUNCT
ejpam-4771	46	18	is	be	AUX
ejpam-4771	46	19	the	the	DET
ejpam-4771	46	20	smallest	small	ADJ
ejpam-4771	46	21	cardinality	cardinality	NOUN
ejpam-4771	46	22	of	of	ADP
ejpam-4771	46	23	a	a	DET
ejpam-4771	46	24	outer	outer	ADV
ejpam-4771	46	25	-	-	PUNCT
ejpam-4771	46	26	connected	connect	VERB
ejpam-4771	46	27	2	2	NUM
ejpam-4771	46	28	-	-	PUNCT
ejpam-4771	46	29	resolving	resolve	VERB
ejpam-4771	46	30	hop	hop	NOUN
ejpam-4771	46	31	a.m.	a.m.	PROPN
ejpam-4771	46	32	mahistrado	mahistrado	PROPN
ejpam-4771	46	33	,	,	PUNCT
ejpam-4771	46	34	h.	h.	PROPN
ejpam-4771	46	35	rara	rara	PROPN
ejpam-4771	46	36	/	/	SYM
ejpam-4771	46	37	eur	eur	PROPN
ejpam-4771	46	38	.	.	PUNCT
ejpam-4771	47	1	j.	j.	PROPN
ejpam-4771	47	2	pure	pure	PROPN
ejpam-4771	47	3	appl	appl	PROPN
ejpam-4771	47	4	.	.	PROPN
ejpam-4771	47	5	math	math	PROPN
ejpam-4771	47	6	,	,	PUNCT
ejpam-4771	47	7	16	16	NUM
ejpam-4771	47	8	(	(	PUNCT
ejpam-4771	47	9	2	2	NUM
ejpam-4771	47	10	)	)	PUNCT
ejpam-4771	47	11	(	(	PUNCT
ejpam-4771	47	12	2023	2023	NUM
ejpam-4771	47	13	)	)	PUNCT
ejpam-4771	47	14	,	,	PUNCT
ejpam-4771	47	15	1180	1180	NUM
ejpam-4771	47	16	-	-	SYM
ejpam-4771	47	17	1195	1195	NUM
ejpam-4771	47	18	1182	1182	NUM
ejpam-4771	47	19	dominating	dominating	NOUN
ejpam-4771	47	20	set	set	NOUN
ejpam-4771	47	21	of	of	ADP
ejpam-4771	47	22	g.	g.	PROPN
ejpam-4771	47	23	definition	definition	NOUN
ejpam-4771	47	24	1	1	NUM
ejpam-4771	47	25	.	.	PUNCT
ejpam-4771	48	1	[	[	X
ejpam-4771	48	2	6	6	NUM
ejpam-4771	48	3	]	]	X
ejpam-4771	48	4	letg	letg	NOUN
ejpam-4771	48	5	be	be	VERB
ejpam-4771	48	6	any	any	DET
ejpam-4771	48	7	nontrivial	nontrivial	ADJ
ejpam-4771	48	8	connected	connect	VERB
ejpam-4771	48	9	graph	graph	NOUN
ejpam-4771	48	10	and	and	CCONJ
ejpam-4771	48	11	s	s	VERB
ejpam-4771	48	12	⊆	⊆	NUM
ejpam-4771	48	13	v	v	NOUN
ejpam-4771	48	14	(	(	PUNCT
ejpam-4771	48	15	g	g	NOUN
ejpam-4771	48	16	)	)	PUNCT
ejpam-4771	48	17	.	.	PUNCT
ejpam-4771	49	1	a	a	DET
ejpam-4771	49	2	set	set	NOUN
ejpam-4771	49	3	s	s	PART
ejpam-4771	49	4	⊂	⊂	X
ejpam-4771	49	5	v	v	X
ejpam-4771	49	6	(	(	PUNCT
ejpam-4771	49	7	g	g	NOUN
ejpam-4771	49	8	)	)	PUNCT
ejpam-4771	49	9	is	be	AUX
ejpam-4771	49	10	a	a	DET
ejpam-4771	49	11	2	2	NUM
ejpam-4771	49	12	-	-	PUNCT
ejpam-4771	49	13	locating	locate	VERB
ejpam-4771	49	14	set	set	NOUN
ejpam-4771	49	15	of	of	ADP
ejpam-4771	49	16	g	g	NOUN
ejpam-4771	49	17	if	if	SCONJ
ejpam-4771	49	18	it	it	PRON
ejpam-4771	49	19	satisfies	satisfy	VERB
ejpam-4771	49	20	the	the	DET
ejpam-4771	49	21	following	follow	VERB
ejpam-4771	49	22	conditions	condition	NOUN
ejpam-4771	49	23	:	:	PUNCT
ejpam-4771	49	24	(	(	PUNCT
ejpam-4771	49	25	i	i	NOUN
ejpam-4771	49	26	)	)	PUNCT
ejpam-4771	49	27	∣∣[(ng(x)\ng(y	∣∣[(ng(x)\ng(y	PROPN
ejpam-4771	49	28	)	)	PUNCT
ejpam-4771	49	29	)	)	PUNCT
ejpam-4771	50	1	∩s]∪	∩s]∪	VERB
ejpam-4771	50	2	[	[	PUNCT
ejpam-4771	50	3	(	(	PUNCT
ejpam-4771	50	4	ng(y)\ng(x	ng(y)\ng(x	NOUN
ejpam-4771	50	5	)	)	PUNCT
ejpam-4771	50	6	)	)	PUNCT
ejpam-4771	51	1	∩s	∩s	PROPN
ejpam-4771	51	2	]	]	PUNCT
ejpam-4771	51	3	∣∣	∣∣	NUM
ejpam-4771	51	4	≥	≥	NOUN
ejpam-4771	51	5	2	2	NUM
ejpam-4771	51	6	,	,	PUNCT
ejpam-4771	51	7	for	for	ADP
ejpam-4771	51	8	all	all	DET
ejpam-4771	51	9	x	x	NOUN
ejpam-4771	51	10	,	,	PUNCT
ejpam-4771	51	11	y	y	PROPN
ejpam-4771	51	12	∈	∈	PROPN
ejpam-4771	51	13	v	v	X
ejpam-4771	51	14	(	(	PUNCT
ejpam-4771	51	15	g)\s	g)\s	VERB
ejpam-4771	51	16	with	with	ADP
ejpam-4771	51	17	x	x	PROPN
ejpam-4771	51	18	̸=	̸=	PROPN
ejpam-4771	51	19	y.	y.	PROPN
ejpam-4771	51	20	(	(	PUNCT
ejpam-4771	51	21	ii	ii	PROPN
ejpam-4771	51	22	)	)	PUNCT
ejpam-4771	51	23	(	(	PUNCT
ejpam-4771	51	24	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-4771	51	25	)	)	PUNCT
ejpam-4771	51	26	)	)	PUNCT
ejpam-4771	51	27	∩	∩	PROPN
ejpam-4771	51	28	s	s	PART
ejpam-4771	51	29	̸=	̸=	PROPN
ejpam-4771	51	30	∅	∅	NOUN
ejpam-4771	51	31	or	or	CCONJ
ejpam-4771	51	32	(	(	PUNCT
ejpam-4771	51	33	ng(w)\ng[v	ng(w)\ng[v	PROPN
ejpam-4771	51	34	]	]	PUNCT
ejpam-4771	51	35	)	)	PUNCT
ejpam-4771	51	36	∩	∩	PROPN
ejpam-4771	51	37	s	s	PART
ejpam-4771	51	38	̸=	̸=	PROPN
ejpam-4771	51	39	∅	∅	NOUN
ejpam-4771	51	40	,	,	PUNCT
ejpam-4771	51	41	for	for	ADP
ejpam-4771	51	42	all	all	PRON
ejpam-4771	51	43	v	v	ADP
ejpam-4771	51	44	∈	∈	NOUN
ejpam-4771	51	45	s	s	NOUN
ejpam-4771	51	46	and	and	CCONJ
ejpam-4771	51	47	for	for	ADP
ejpam-4771	51	48	all	all	PRON
ejpam-4771	51	49	w	w	PROPN
ejpam-4771	51	50	∈	∈	PROPN
ejpam-4771	51	51	v	v	NOUN
ejpam-4771	51	52	(	(	PUNCT
ejpam-4771	51	53	g)\s	g)\s	NOUN
ejpam-4771	51	54	.	.	PUNCT
ejpam-4771	52	1	the	the	DET
ejpam-4771	52	2	2	2	NUM
ejpam-4771	52	3	-	-	PUNCT
ejpam-4771	52	4	locating	locate	VERB
ejpam-4771	52	5	number	number	NOUN
ejpam-4771	52	6	of	of	ADP
ejpam-4771	52	7	g	g	NOUN
ejpam-4771	52	8	,	,	PUNCT
ejpam-4771	52	9	denoted	denote	VERB
ejpam-4771	52	10	by	by	ADP
ejpam-4771	52	11	ln2(g	ln2(g	NOUN
ejpam-4771	52	12	)	)	PUNCT
ejpam-4771	52	13	,	,	PUNCT
ejpam-4771	52	14	is	be	AUX
ejpam-4771	52	15	the	the	DET
ejpam-4771	52	16	smallest	small	ADJ
ejpam-4771	52	17	cardinality	cardinality	NOUN
ejpam-4771	52	18	of	of	ADP
ejpam-4771	52	19	a	a	DET
ejpam-4771	52	20	2	2	NUM
ejpam-4771	52	21	-	-	PUNCT
ejpam-4771	52	22	locating	locate	VERB
ejpam-4771	52	23	set	set	NOUN
ejpam-4771	52	24	of	of	ADP
ejpam-4771	52	25	g.	g.	PROPN
ejpam-4771	52	26	a	a	DET
ejpam-4771	52	27	2	2	NUM
ejpam-4771	52	28	-	-	PUNCT
ejpam-4771	52	29	locating	locate	VERB
ejpam-4771	52	30	set	set	NOUN
ejpam-4771	52	31	of	of	ADP
ejpam-4771	52	32	g	g	NOUN
ejpam-4771	52	33	of	of	ADP
ejpam-4771	52	34	cardinality	cardinality	PROPN
ejpam-4771	52	35	ln2(g	ln2(g	PROPN
ejpam-4771	52	36	)	)	PUNCT
ejpam-4771	52	37	is	be	AUX
ejpam-4771	52	38	referred	refer	VERB
ejpam-4771	52	39	to	to	ADP
ejpam-4771	52	40	as	as	ADP
ejpam-4771	52	41	an	an	DET
ejpam-4771	52	42	ln2	ln2	NOUN
ejpam-4771	52	43	-	-	PUNCT
ejpam-4771	52	44	set	set	NOUN
ejpam-4771	52	45	of	of	ADP
ejpam-4771	52	46	g.	g.	PROPN
ejpam-4771	52	47	definition	definition	NOUN
ejpam-4771	52	48	2	2	NUM
ejpam-4771	52	49	.	.	PUNCT
ejpam-4771	53	1	[	[	X
ejpam-4771	53	2	17	17	NUM
ejpam-4771	53	3	]	]	PUNCT
ejpam-4771	53	4	a	a	DET
ejpam-4771	53	5	set	set	NOUN
ejpam-4771	53	6	d	d	NOUN
ejpam-4771	53	7	⊆	⊆	NUM
ejpam-4771	53	8	v	v	ADP
ejpam-4771	53	9	(	(	PUNCT
ejpam-4771	53	10	g	g	NOUN
ejpam-4771	53	11	)	)	PUNCT
ejpam-4771	53	12	is	be	AUX
ejpam-4771	53	13	a	a	DET
ejpam-4771	53	14	point	point	NOUN
ejpam-4771	53	15	-	-	PUNCT
ejpam-4771	53	16	wise	wise	ADJ
ejpam-4771	53	17	non	non	ADJ
ejpam-4771	53	18	-	-	ADJ
ejpam-4771	53	19	dominating	dominating	ADJ
ejpam-4771	53	20	set	set	NOUN
ejpam-4771	53	21	of	of	ADP
ejpam-4771	53	22	g	g	PROPN
ejpam-4771	53	23	if	if	SCONJ
ejpam-4771	53	24	for	for	ADP
ejpam-4771	53	25	each	each	DET
ejpam-4771	53	26	v	v	NUM
ejpam-4771	53	27	∈	∈	PROPN
ejpam-4771	53	28	v	v	NOUN
ejpam-4771	53	29	(	(	PUNCT
ejpam-4771	53	30	g)\d	g)\d	NOUN
ejpam-4771	53	31	,	,	PUNCT
ejpam-4771	53	32	there	there	PRON
ejpam-4771	53	33	exists	exist	VERB
ejpam-4771	53	34	u	u	NOUN
ejpam-4771	53	35	∈	∈	PROPN
ejpam-4771	53	36	d	d	ADP
ejpam-4771	53	37	such	such	ADJ
ejpam-4771	53	38	that	that	DET
ejpam-4771	53	39	v	v	NOUN
ejpam-4771	53	40	/∈	/∈	PUNCT
ejpam-4771	53	41	ng(u	ng(u	NOUN
ejpam-4771	53	42	)	)	PUNCT
ejpam-4771	53	43	.	.	PUNCT
ejpam-4771	54	1	the	the	DET
ejpam-4771	54	2	smallest	small	ADJ
ejpam-4771	54	3	cardinality	cardinality	NOUN
ejpam-4771	54	4	of	of	ADP
ejpam-4771	54	5	a	a	DET
ejpam-4771	54	6	point	point	NOUN
ejpam-4771	54	7	-	-	PUNCT
ejpam-4771	54	8	wise	wise	ADJ
ejpam-4771	54	9	non	non	ADJ
ejpam-4771	54	10	-	-	ADJ
ejpam-4771	54	11	dominating	dominating	ADJ
ejpam-4771	54	12	set	set	NOUN
ejpam-4771	54	13	of	of	ADP
ejpam-4771	54	14	g	g	NOUN
ejpam-4771	54	15	,	,	PUNCT
ejpam-4771	54	16	denoted	denote	VERB
ejpam-4771	54	17	by	by	ADP
ejpam-4771	54	18	pnd(g	pnd(g	PROPN
ejpam-4771	54	19	)	)	PUNCT
ejpam-4771	54	20	,	,	PUNCT
ejpam-4771	54	21	is	be	AUX
ejpam-4771	54	22	called	call	VERB
ejpam-4771	54	23	the	the	DET
ejpam-4771	54	24	point	point	NOUN
ejpam-4771	54	25	-	-	PUNCT
ejpam-4771	54	26	wise	wise	ADJ
ejpam-4771	54	27	nondomination	nondomination	NOUN
ejpam-4771	54	28	number	number	NOUN
ejpam-4771	54	29	of	of	ADP
ejpam-4771	54	30	g.	g.	PROPN
ejpam-4771	54	31	any	any	DET
ejpam-4771	54	32	point	point	NOUN
ejpam-4771	54	33	-	-	PUNCT
ejpam-4771	54	34	wise	wise	ADJ
ejpam-4771	54	35	non	non	ADJ
ejpam-4771	54	36	-	-	ADJ
ejpam-4771	54	37	dominating	dominating	ADJ
ejpam-4771	54	38	set	set	NOUN
ejpam-4771	54	39	d	d	NOUN
ejpam-4771	54	40	of	of	ADP
ejpam-4771	54	41	g	g	NOUN
ejpam-4771	54	42	with	with	ADP
ejpam-4771	54	43	|d|	|d|	PROPN
ejpam-4771	54	44	=	=	SYM
ejpam-4771	54	45	pnd(g	pnd(g	PROPN
ejpam-4771	54	46	)	)	PUNCT
ejpam-4771	54	47	,	,	PUNCT
ejpam-4771	54	48	is	be	AUX
ejpam-4771	54	49	called	call	VERB
ejpam-4771	54	50	a	a	DET
ejpam-4771	54	51	pnd	pnd	NOUN
ejpam-4771	54	52	-	-	PUNCT
ejpam-4771	54	53	set	set	VERB
ejpam-4771	54	54	ofg	ofg	NOUN
ejpam-4771	54	55	.	.	PUNCT
ejpam-4771	55	1	a	a	DET
ejpam-4771	55	2	dominating	dominating	NOUN
ejpam-4771	55	3	set	set	NOUN
ejpam-4771	55	4	d	d	NOUN
ejpam-4771	55	5	which	which	PRON
ejpam-4771	55	6	is	be	AUX
ejpam-4771	55	7	also	also	ADV
ejpam-4771	55	8	a	a	DET
ejpam-4771	55	9	point	point	NOUN
ejpam-4771	55	10	-	-	PUNCT
ejpam-4771	55	11	wise	wise	ADJ
ejpam-4771	55	12	non	non	ADJ
ejpam-4771	55	13	-	-	ADJ
ejpam-4771	55	14	dominating	dominating	ADJ
ejpam-4771	55	15	set	set	NOUN
ejpam-4771	55	16	of	of	ADP
ejpam-4771	55	17	g	g	PROPN
ejpam-4771	55	18	is	be	AUX
ejpam-4771	55	19	called	call	VERB
ejpam-4771	55	20	a	a	DET
ejpam-4771	55	21	dominating	dominating	NOUN
ejpam-4771	55	22	pointwise	pointwise	ADV
ejpam-4771	55	23	non	non	ADJ
ejpam-4771	55	24	-	-	ADJ
ejpam-4771	55	25	dominating	dominating	ADJ
ejpam-4771	55	26	set	set	NOUN
ejpam-4771	55	27	of	of	ADP
ejpam-4771	55	28	g.	g.	PROPN
ejpam-4771	55	29	the	the	DET
ejpam-4771	55	30	smallest	small	ADJ
ejpam-4771	55	31	cardinality	cardinality	NOUN
ejpam-4771	55	32	of	of	ADP
ejpam-4771	55	33	a	a	DET
ejpam-4771	55	34	dominating	dominating	NOUN
ejpam-4771	55	35	point	point	NOUN
ejpam-4771	55	36	-	-	PUNCT
ejpam-4771	55	37	wise	wise	ADJ
ejpam-4771	55	38	non	non	ADJ
ejpam-4771	55	39	-	-	ADJ
ejpam-4771	55	40	dominating	dominating	ADJ
ejpam-4771	55	41	set	set	NOUN
ejpam-4771	55	42	of	of	ADP
ejpam-4771	55	43	g	g	NOUN
ejpam-4771	55	44	will	will	AUX
ejpam-4771	55	45	be	be	AUX
ejpam-4771	55	46	denoted	denote	VERB
ejpam-4771	55	47	by	by	ADP
ejpam-4771	55	48	γpnd(g	γpnd(g	PROPN
ejpam-4771	55	49	)	)	PUNCT
ejpam-4771	55	50	.	.	PUNCT
ejpam-4771	56	1	any	any	DET
ejpam-4771	56	2	dominating	dominating	NOUN
ejpam-4771	56	3	point	point	NOUN
ejpam-4771	56	4	-	-	PUNCT
ejpam-4771	56	5	wise	wise	ADJ
ejpam-4771	56	6	non	non	ADJ
ejpam-4771	56	7	-	-	ADJ
ejpam-4771	56	8	dominating	dominating	ADJ
ejpam-4771	56	9	set	set	NOUN
ejpam-4771	56	10	d	d	NOUN
ejpam-4771	56	11	of	of	ADP
ejpam-4771	56	12	g	g	NOUN
ejpam-4771	56	13	with	with	ADP
ejpam-4771	56	14	|d|	|d|	PROPN
ejpam-4771	56	15	=	=	SYM
ejpam-4771	56	16	γpnd(g	γpnd(g	PROPN
ejpam-4771	56	17	)	)	PUNCT
ejpam-4771	56	18	,	,	PUNCT
ejpam-4771	56	19	is	be	AUX
ejpam-4771	56	20	called	call	VERB
ejpam-4771	56	21	a	a	DET
ejpam-4771	56	22	γpnd	γpnd	NOUN
ejpam-4771	56	23	-	-	PUNCT
ejpam-4771	56	24	set	set	NOUN
ejpam-4771	56	25	of	of	ADP
ejpam-4771	56	26	g.	g.	PROPN
ejpam-4771	56	27	definition	definition	NOUN
ejpam-4771	56	28	3	3	NUM
ejpam-4771	56	29	.	.	PUNCT
ejpam-4771	57	1	[	[	X
ejpam-4771	57	2	12	12	NUM
ejpam-4771	57	3	]	]	PUNCT
ejpam-4771	57	4	a	a	DET
ejpam-4771	57	5	2	2	NUM
ejpam-4771	57	6	-	-	PUNCT
ejpam-4771	57	7	locating	locate	VERB
ejpam-4771	57	8	set	set	NOUN
ejpam-4771	57	9	s	s	PROPN
ejpam-4771	57	10	⊆	⊆	NUM
ejpam-4771	57	11	v	v	NOUN
ejpam-4771	57	12	(	(	PUNCT
ejpam-4771	57	13	g	g	NOUN
ejpam-4771	57	14	)	)	PUNCT
ejpam-4771	57	15	which	which	PRON
ejpam-4771	57	16	is	be	AUX
ejpam-4771	57	17	point	point	ADV
ejpam-4771	57	18	-	-	PUNCT
ejpam-4771	57	19	wise	wise	ADJ
ejpam-4771	57	20	non	non	ADJ
ejpam-4771	57	21	-	-	ADJ
ejpam-4771	57	22	dominating	dominating	NOUN
ejpam-4771	57	23	is	be	AUX
ejpam-4771	57	24	called	call	VERB
ejpam-4771	57	25	a	a	DET
ejpam-4771	57	26	2	2	NUM
ejpam-4771	57	27	-	-	PUNCT
ejpam-4771	57	28	locating	locate	VERB
ejpam-4771	57	29	point	point	NOUN
ejpam-4771	57	30	-	-	PUNCT
ejpam-4771	57	31	wise	wise	ADJ
ejpam-4771	57	32	non	non	ADJ
ejpam-4771	57	33	-	-	ADJ
ejpam-4771	57	34	dominating	dominating	ADJ
ejpam-4771	57	35	set	set	NOUN
ejpam-4771	57	36	in	in	ADP
ejpam-4771	57	37	g.	g.	PROPN
ejpam-4771	57	38	the	the	DET
ejpam-4771	57	39	minimum	minimum	ADJ
ejpam-4771	57	40	cardinality	cardinality	NOUN
ejpam-4771	57	41	of	of	ADP
ejpam-4771	57	42	a	a	DET
ejpam-4771	57	43	2locating	2locating	NUM
ejpam-4771	57	44	point	point	NOUN
ejpam-4771	57	45	-	-	PUNCT
ejpam-4771	57	46	wise	wise	ADJ
ejpam-4771	57	47	non	non	ADJ
ejpam-4771	57	48	-	-	ADJ
ejpam-4771	57	49	dominating	dominating	ADJ
ejpam-4771	57	50	set	set	NOUN
ejpam-4771	57	51	in	in	ADP
ejpam-4771	57	52	g	g	NOUN
ejpam-4771	57	53	,	,	PUNCT
ejpam-4771	57	54	denoted	denote	VERB
ejpam-4771	57	55	by	by	ADP
ejpam-4771	57	56	lnpnd	lnpnd	ADJ
ejpam-4771	57	57	2	2	NUM
ejpam-4771	57	58	(	(	PUNCT
ejpam-4771	57	59	g	g	NOUN
ejpam-4771	57	60	)	)	PUNCT
ejpam-4771	57	61	is	be	AUX
ejpam-4771	57	62	called	call	VERB
ejpam-4771	57	63	the	the	DET
ejpam-4771	57	64	2	2	NUM
ejpam-4771	57	65	-	-	PUNCT
ejpam-4771	57	66	locating	locate	VERB
ejpam-4771	57	67	point	point	NOUN
ejpam-4771	57	68	-	-	PUNCT
ejpam-4771	57	69	wise	wise	ADJ
ejpam-4771	57	70	non	non	ADJ
ejpam-4771	57	71	-	-	ADJ
ejpam-4771	57	72	domination	domination	ADJ
ejpam-4771	57	73	number	number	NOUN
ejpam-4771	57	74	of	of	ADP
ejpam-4771	57	75	g.	g.	PROPN
ejpam-4771	57	76	any	any	DET
ejpam-4771	57	77	2	2	NUM
ejpam-4771	57	78	-	-	PUNCT
ejpam-4771	57	79	locating	locate	VERB
ejpam-4771	57	80	point	point	NOUN
ejpam-4771	57	81	-	-	PUNCT
ejpam-4771	57	82	wise	wise	ADJ
ejpam-4771	57	83	non	non	ADJ
ejpam-4771	57	84	-	-	ADJ
ejpam-4771	57	85	dominating	dominating	ADJ
ejpam-4771	57	86	set	set	NOUN
ejpam-4771	57	87	of	of	ADP
ejpam-4771	57	88	cardinality	cardinality	PROPN
ejpam-4771	57	89	lnpnd	lnpnd	PROPN
ejpam-4771	57	90	2	2	NUM
ejpam-4771	57	91	(	(	PUNCT
ejpam-4771	57	92	g	g	NOUN
ejpam-4771	57	93	)	)	PUNCT
ejpam-4771	57	94	is	be	AUX
ejpam-4771	57	95	then	then	ADV
ejpam-4771	57	96	referred	refer	VERB
ejpam-4771	57	97	to	to	ADP
ejpam-4771	57	98	as	as	ADP
ejpam-4771	57	99	a	a	DET
ejpam-4771	57	100	lnpnd	lnpnd	ADJ
ejpam-4771	57	101	2	2	NUM
ejpam-4771	57	102	-set	-set	PUNCT
ejpam-4771	57	103	in	in	ADP
ejpam-4771	57	104	g.	g.	PROPN
ejpam-4771	57	105	definition	definition	NOUN
ejpam-4771	57	106	4	4	NUM
ejpam-4771	57	107	.	.	PUNCT
ejpam-4771	58	1	a	a	DET
ejpam-4771	58	2	set	set	NOUN
ejpam-4771	58	3	s	s	NOUN
ejpam-4771	58	4	⊆	⊆	NUM
ejpam-4771	58	5	v	v	NOUN
ejpam-4771	58	6	(	(	PUNCT
ejpam-4771	58	7	g	g	NOUN
ejpam-4771	58	8	)	)	PUNCT
ejpam-4771	58	9	is	be	AUX
ejpam-4771	58	10	an	an	DET
ejpam-4771	58	11	outer	outer	ADV
ejpam-4771	58	12	-	-	PUNCT
ejpam-4771	58	13	connected	connect	VERB
ejpam-4771	58	14	2	2	NUM
ejpam-4771	58	15	-	-	PUNCT
ejpam-4771	58	16	locating	locate	VERB
ejpam-4771	58	17	point	point	NOUN
ejpam-4771	58	18	-	-	PUNCT
ejpam-4771	58	19	wise	wise	ADJ
ejpam-4771	58	20	non	non	ADJ
ejpam-4771	58	21	-	-	ADJ
ejpam-4771	58	22	dominating	dominating	ADJ
ejpam-4771	58	23	set	set	NOUN
ejpam-4771	58	24	in	in	ADP
ejpam-4771	58	25	g	g	PROPN
ejpam-4771	58	26	if	if	SCONJ
ejpam-4771	58	27	s	s	VERB
ejpam-4771	58	28	is	be	AUX
ejpam-4771	58	29	a	a	DET
ejpam-4771	58	30	2	2	NUM
ejpam-4771	58	31	-	-	PUNCT
ejpam-4771	58	32	locating	locate	VERB
ejpam-4771	58	33	point	point	NOUN
ejpam-4771	58	34	-	-	PUNCT
ejpam-4771	58	35	wise	wise	ADJ
ejpam-4771	58	36	non	non	ADJ
ejpam-4771	58	37	-	-	ADJ
ejpam-4771	58	38	dominating	dominating	ADJ
ejpam-4771	58	39	set	set	NOUN
ejpam-4771	58	40	in	in	ADP
ejpam-4771	58	41	g	g	PROPN
ejpam-4771	58	42	and	and	CCONJ
ejpam-4771	58	43	s	s	PART
ejpam-4771	58	44	=	=	SYM
ejpam-4771	58	45	v	v	X
ejpam-4771	58	46	(	(	PUNCT
ejpam-4771	58	47	g	g	NOUN
ejpam-4771	58	48	)	)	PUNCT
ejpam-4771	58	49	or	or	CCONJ
ejpam-4771	58	50	the	the	DET
ejpam-4771	58	51	subgraph	subgraph	NOUN
ejpam-4771	58	52	⟨v	⟨v	NOUN
ejpam-4771	58	53	(	(	PUNCT
ejpam-4771	58	54	g)\s⟩	g)\s⟩	PROPN
ejpam-4771	58	55	induced	induce	VERB
ejpam-4771	58	56	by	by	ADP
ejpam-4771	58	57	v	v	NOUN
ejpam-4771	58	58	(	(	PUNCT
ejpam-4771	58	59	g)\s	g)\s	NOUN
ejpam-4771	58	60	is	be	AUX
ejpam-4771	58	61	connected	connect	VERB
ejpam-4771	58	62	.	.	PUNCT
ejpam-4771	59	1	the	the	DET
ejpam-4771	59	2	outer	outer	ADV
ejpam-4771	59	3	-	-	PUNCT
ejpam-4771	59	4	connected	connect	VERB
ejpam-4771	59	5	2	2	NUM
ejpam-4771	59	6	-	-	PUNCT
ejpam-4771	59	7	locating	locate	VERB
ejpam-4771	59	8	point	point	NOUN
ejpam-4771	59	9	-	-	PUNCT
ejpam-4771	59	10	wise	wise	ADJ
ejpam-4771	59	11	non	non	ADJ
ejpam-4771	59	12	-	-	ADJ
ejpam-4771	59	13	dominating	dominating	ADJ
ejpam-4771	59	14	number	number	NOUN
ejpam-4771	59	15	of	of	ADP
ejpam-4771	59	16	g	g	NOUN
ejpam-4771	59	17	,	,	PUNCT
ejpam-4771	59	18	denoted	denote	VERB
ejpam-4771	59	19	by	by	ADP
ejpam-4771	59	20	l̃npnd	l̃npnd	NOUN
ejpam-4771	59	21	2	2	NUM
ejpam-4771	59	22	(	(	PUNCT
ejpam-4771	59	23	g	g	NOUN
ejpam-4771	59	24	)	)	PUNCT
ejpam-4771	59	25	,	,	PUNCT
ejpam-4771	59	26	is	be	AUX
ejpam-4771	59	27	the	the	DET
ejpam-4771	59	28	smallest	small	ADJ
ejpam-4771	59	29	cardinality	cardinality	NOUN
ejpam-4771	59	30	of	of	ADP
ejpam-4771	59	31	an	an	DET
ejpam-4771	59	32	outer	outer	ADV
ejpam-4771	59	33	-	-	PUNCT
ejpam-4771	59	34	connected	connect	VERB
ejpam-4771	59	35	2	2	NUM
ejpam-4771	59	36	-	-	PUNCT
ejpam-4771	59	37	locating	locate	VERB
ejpam-4771	59	38	point	point	NOUN
ejpam-4771	59	39	-	-	PUNCT
ejpam-4771	59	40	wise	wise	ADJ
ejpam-4771	59	41	non	non	ADJ
ejpam-4771	59	42	-	-	ADJ
ejpam-4771	59	43	dominating	dominating	ADJ
ejpam-4771	59	44	set	set	NOUN
ejpam-4771	59	45	in	in	ADP
ejpam-4771	59	46	g.	g.	PROPN
ejpam-4771	59	47	an	an	DET
ejpam-4771	59	48	outer	outer	ADV
ejpam-4771	59	49	-	-	PUNCT
ejpam-4771	59	50	connected	connect	VERB
ejpam-4771	59	51	2	2	NUM
ejpam-4771	59	52	-	-	PUNCT
ejpam-4771	59	53	locating	locate	VERB
ejpam-4771	59	54	point	point	NOUN
ejpam-4771	59	55	-	-	PUNCT
ejpam-4771	59	56	wise	wise	ADJ
ejpam-4771	59	57	non	non	ADJ
ejpam-4771	59	58	-	-	ADJ
ejpam-4771	59	59	dominating	dominating	ADJ
ejpam-4771	59	60	set	set	NOUN
ejpam-4771	59	61	of	of	ADP
ejpam-4771	59	62	cardinality	cardinality	NOUN
ejpam-4771	59	63	l̃npnd	l̃npnd	NOUN
ejpam-4771	59	64	2	2	NUM
ejpam-4771	59	65	(	(	PUNCT
ejpam-4771	59	66	g	g	NOUN
ejpam-4771	59	67	)	)	PUNCT
ejpam-4771	59	68	is	be	AUX
ejpam-4771	59	69	then	then	ADV
ejpam-4771	59	70	referred	refer	VERB
ejpam-4771	59	71	to	to	ADP
ejpam-4771	59	72	as	as	ADP
ejpam-4771	59	73	an	an	DET
ejpam-4771	59	74	l̃npnd	l̃npnd	NOUN
ejpam-4771	59	75	2	2	NUM
ejpam-4771	59	76	-set	-set	PUNCT
ejpam-4771	59	77	in	in	ADP
ejpam-4771	59	78	g.	g.	PROPN
ejpam-4771	59	79	definition	definition	NOUN
ejpam-4771	59	80	5	5	NUM
ejpam-4771	59	81	.	.	PUNCT
ejpam-4771	60	1	[	[	X
ejpam-4771	60	2	6	6	NUM
ejpam-4771	60	3	]	]	PUNCT
ejpam-4771	60	4	let	let	VERB
ejpam-4771	60	5	g	g	NOUN
ejpam-4771	60	6	be	be	AUX
ejpam-4771	60	7	any	any	DET
ejpam-4771	60	8	nontrivial	nontrivial	ADJ
ejpam-4771	60	9	connected	connect	VERB
ejpam-4771	60	10	graph	graph	NOUN
ejpam-4771	60	11	and	and	CCONJ
ejpam-4771	60	12	s	s	VERB
ejpam-4771	60	13	⊆	⊆	NUM
ejpam-4771	60	14	v	v	NOUN
ejpam-4771	60	15	(	(	PUNCT
ejpam-4771	60	16	g	g	NOUN
ejpam-4771	60	17	)	)	PUNCT
ejpam-4771	60	18	.	.	PUNCT
ejpam-4771	61	1	s	s	PART
ejpam-4771	61	2	is	be	AUX
ejpam-4771	61	3	a	a	DET
ejpam-4771	61	4	(	(	PUNCT
ejpam-4771	61	5	2	2	NUM
ejpam-4771	61	6	,	,	PUNCT
ejpam-4771	61	7	2)locating	2)locating	NUM
ejpam-4771	61	8	(	(	PUNCT
ejpam-4771	61	9	(	(	PUNCT
ejpam-4771	61	10	2	2	NUM
ejpam-4771	61	11	,	,	PUNCT
ejpam-4771	61	12	1)-locating	1)-locating	NUM
ejpam-4771	61	13	,	,	PUNCT
ejpam-4771	61	14	respectively	respectively	ADV
ejpam-4771	61	15	)	)	PUNCT
ejpam-4771	61	16	set	set	VERB
ejpam-4771	61	17	in	in	ADP
ejpam-4771	61	18	g	g	PROPN
ejpam-4771	61	19	if	if	SCONJ
ejpam-4771	61	20	s	s	NOUN
ejpam-4771	61	21	is	be	AUX
ejpam-4771	61	22	2	2	NUM
ejpam-4771	61	23	-	-	PUNCT
ejpam-4771	61	24	locating	locate	VERB
ejpam-4771	61	25	and	and	CCONJ
ejpam-4771	61	26	|ng(y)∩	|ng(y)∩	NOUN
ejpam-4771	61	27	s|	s|	VERB
ejpam-4771	61	28	≤	≤	NUM
ejpam-4771	61	29	|s|	|s|	PROPN
ejpam-4771	61	30	−	−	PROPN
ejpam-4771	61	31	2	2	NUM
ejpam-4771	61	32	(	(	PUNCT
ejpam-4771	61	33	|ng(y)∩s|	|ng(y)∩s|	NOUN
ejpam-4771	61	34	≤	≤	X
ejpam-4771	61	35	|s|−	|s|−	NOUN
ejpam-4771	61	36	1	1	NUM
ejpam-4771	61	37	,	,	PUNCT
ejpam-4771	61	38	respectively	respectively	ADV
ejpam-4771	61	39	)	)	PUNCT
ejpam-4771	61	40	,	,	PUNCT
ejpam-4771	61	41	for	for	ADP
ejpam-4771	61	42	all	all	DET
ejpam-4771	61	43	y	y	PROPN
ejpam-4771	61	44	∈	∈	PROPN
ejpam-4771	61	45	v	v	NOUN
ejpam-4771	61	46	(	(	PUNCT
ejpam-4771	61	47	g	g	NOUN
ejpam-4771	61	48	)	)	PUNCT
ejpam-4771	61	49	.	.	PUNCT
ejpam-4771	62	1	the	the	DET
ejpam-4771	62	2	(	(	PUNCT
ejpam-4771	62	3	2	2	NUM
ejpam-4771	62	4	,	,	PUNCT
ejpam-4771	62	5	2)-locating	2)-locating	NUM
ejpam-4771	62	6	(	(	PUNCT
ejpam-4771	62	7	(	(	PUNCT
ejpam-4771	62	8	2	2	NUM
ejpam-4771	62	9	,	,	PUNCT
ejpam-4771	62	10	1)-locating	1)-locating	NUM
ejpam-4771	62	11	,	,	PUNCT
ejpam-4771	62	12	respectively	respectively	ADV
ejpam-4771	62	13	)	)	PUNCT
ejpam-4771	62	14	number	number	NOUN
ejpam-4771	62	15	of	of	ADP
ejpam-4771	62	16	g	g	NOUN
ejpam-4771	62	17	,	,	PUNCT
ejpam-4771	62	18	denoted	denote	VERB
ejpam-4771	62	19	by	by	ADP
ejpam-4771	62	20	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4771	62	21	)	)	PUNCT
ejpam-4771	62	22	(	(	PUNCT
ejpam-4771	62	23	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4771	62	24	)	)	PUNCT
ejpam-4771	62	25	,	,	PUNCT
ejpam-4771	62	26	respectively	respectively	ADV
ejpam-4771	62	27	)	)	PUNCT
ejpam-4771	62	28	,	,	PUNCT
ejpam-4771	62	29	is	be	AUX
ejpam-4771	62	30	the	the	DET
ejpam-4771	62	31	smallest	small	ADJ
ejpam-4771	62	32	cardinality	cardinality	NOUN
ejpam-4771	62	33	of	of	ADP
ejpam-4771	62	34	a	a	DET
ejpam-4771	62	35	(	(	PUNCT
ejpam-4771	62	36	2	2	NUM
ejpam-4771	62	37	,	,	PUNCT
ejpam-4771	62	38	2)-locating	2)-locating	NUM
ejpam-4771	62	39	(	(	PUNCT
ejpam-4771	62	40	(	(	PUNCT
ejpam-4771	62	41	2	2	NUM
ejpam-4771	62	42	,	,	PUNCT
ejpam-4771	62	43	1)-locating	1)-locating	NUM
ejpam-4771	62	44	,	,	PUNCT
ejpam-4771	62	45	respectively	respectively	ADV
ejpam-4771	62	46	)	)	PUNCT
ejpam-4771	62	47	set	set	VERB
ejpam-4771	62	48	in	in	ADP
ejpam-4771	62	49	g.	g.	PROPN
ejpam-4771	62	50	a	a	PRON
ejpam-4771	62	51	(	(	PUNCT
ejpam-4771	62	52	2	2	NUM
ejpam-4771	62	53	,	,	PUNCT
ejpam-4771	62	54	2)-locating	2)-locating	NUM
ejpam-4771	62	55	(	(	PUNCT
ejpam-4771	62	56	(	(	PUNCT
ejpam-4771	62	57	2	2	NUM
ejpam-4771	62	58	,	,	PUNCT
ejpam-4771	62	59	1)-locating	1)-locating	NUM
ejpam-4771	62	60	,	,	PUNCT
ejpam-4771	62	61	respectively	respectively	ADV
ejpam-4771	62	62	)	)	PUNCT
ejpam-4771	62	63	set	set	VERB
ejpam-4771	62	64	in	in	ADP
ejpam-4771	62	65	g	g	NOUN
ejpam-4771	62	66	of	of	ADP
ejpam-4771	62	67	cardinality	cardinality	NOUN
ejpam-4771	62	68	ln(2,2)(g	ln(2,2)(g	PROPN
ejpam-4771	62	69	)	)	PUNCT
ejpam-4771	62	70	(	(	PUNCT
ejpam-4771	62	71	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4771	62	72	)	)	PUNCT
ejpam-4771	62	73	,	,	PUNCT
ejpam-4771	62	74	respectively	respectively	ADV
ejpam-4771	62	75	)	)	PUNCT
ejpam-4771	62	76	is	be	AUX
ejpam-4771	62	77	referred	refer	VERB
ejpam-4771	62	78	to	to	ADP
ejpam-4771	62	79	as	as	ADP
ejpam-4771	62	80	an	an	DET
ejpam-4771	62	81	ln(2,2)-set	ln(2,2)-set	NOUN
ejpam-4771	62	82	(	(	PUNCT
ejpam-4771	62	83	ln(2,1)-set	ln(2,1)-set	PROPN
ejpam-4771	62	84	,	,	PUNCT
ejpam-4771	62	85	respectively	respectively	ADV
ejpam-4771	62	86	)	)	PUNCT
ejpam-4771	62	87	in	in	ADP
ejpam-4771	62	88	g.	g.	PROPN
ejpam-4771	62	89	a.m.	a.m.	PROPN
ejpam-4771	62	90	mahistrado	mahistrado	PROPN
ejpam-4771	62	91	,	,	PUNCT
ejpam-4771	62	92	h.	h.	PROPN
ejpam-4771	62	93	rara	rara	PROPN
ejpam-4771	62	94	/	/	SYM
ejpam-4771	62	95	eur	eur	PROPN
ejpam-4771	62	96	.	.	PUNCT
ejpam-4771	63	1	j.	j.	PROPN
ejpam-4771	63	2	pure	pure	PROPN
ejpam-4771	63	3	appl	appl	PROPN
ejpam-4771	63	4	.	.	PROPN
ejpam-4771	63	5	math	math	PROPN
ejpam-4771	63	6	,	,	PUNCT
ejpam-4771	63	7	16	16	NUM
ejpam-4771	63	8	(	(	PUNCT
ejpam-4771	63	9	2	2	NUM
ejpam-4771	63	10	)	)	PUNCT
ejpam-4771	63	11	(	(	PUNCT
ejpam-4771	63	12	2023	2023	NUM
ejpam-4771	63	13	)	)	PUNCT
ejpam-4771	63	14	,	,	PUNCT
ejpam-4771	63	15	1180	1180	NUM
ejpam-4771	63	16	-	-	SYM
ejpam-4771	63	17	1195	1195	NUM
ejpam-4771	63	18	1183	1183	NUM
ejpam-4771	63	19	definition	definition	NOUN
ejpam-4771	63	20	6	6	NUM
ejpam-4771	63	21	.	.	PUNCT
ejpam-4771	64	1	[	[	X
ejpam-4771	64	2	12	12	NUM
ejpam-4771	64	3	]	]	X
ejpam-4771	64	4	a	a	PRON
ejpam-4771	64	5	(	(	PUNCT
ejpam-4771	64	6	2,2)-locating	2,2)-locating	NUM
ejpam-4771	64	7	(	(	PUNCT
ejpam-4771	64	8	(	(	PUNCT
ejpam-4771	64	9	2,1)-locating	2,1)-locating	NUM
ejpam-4771	64	10	,	,	PUNCT
ejpam-4771	64	11	respectively	respectively	ADV
ejpam-4771	64	12	)	)	PUNCT
ejpam-4771	64	13	set	set	VERB
ejpam-4771	64	14	s	s	PROPN
ejpam-4771	64	15	⊆	⊆	NUM
ejpam-4771	64	16	v	v	NOUN
ejpam-4771	64	17	(	(	PUNCT
ejpam-4771	64	18	g	g	NOUN
ejpam-4771	64	19	)	)	PUNCT
ejpam-4771	64	20	which	which	PRON
ejpam-4771	64	21	is	be	AUX
ejpam-4771	64	22	a	a	DET
ejpam-4771	64	23	point	point	NOUN
ejpam-4771	64	24	-	-	PUNCT
ejpam-4771	64	25	wise	wise	ADJ
ejpam-4771	64	26	non	non	ADJ
ejpam-4771	64	27	-	-	ADJ
ejpam-4771	64	28	dominating	dominating	NOUN
ejpam-4771	64	29	is	be	AUX
ejpam-4771	64	30	called	call	VERB
ejpam-4771	64	31	a	a	DET
ejpam-4771	64	32	(	(	PUNCT
ejpam-4771	64	33	2,2)-locating	2,2)-locating	NUM
ejpam-4771	64	34	point	point	ADV
ejpam-4771	64	35	-	-	PUNCT
ejpam-4771	64	36	wise	wise	ADJ
ejpam-4771	64	37	non	non	ADJ
ejpam-4771	64	38	-	-	ADJ
ejpam-4771	64	39	dominating	dominating	ADJ
ejpam-4771	64	40	(	(	PUNCT
ejpam-4771	64	41	(	(	PUNCT
ejpam-4771	64	42	2,1)locating	2,1)locating	NUM
ejpam-4771	64	43	point	point	NOUN
ejpam-4771	64	44	-	-	PUNCT
ejpam-4771	64	45	wise	wise	ADJ
ejpam-4771	64	46	non	non	ADJ
ejpam-4771	64	47	-	-	ADJ
ejpam-4771	64	48	dominating	dominating	ADJ
ejpam-4771	64	49	,	,	PUNCT
ejpam-4771	64	50	respectively	respectively	ADV
ejpam-4771	64	51	)	)	PUNCT
ejpam-4771	64	52	set	set	VERB
ejpam-4771	64	53	in	in	ADP
ejpam-4771	64	54	g.	g.	PROPN
ejpam-4771	64	55	the	the	DET
ejpam-4771	64	56	minimum	minimum	ADJ
ejpam-4771	64	57	cardinality	cardinality	NOUN
ejpam-4771	64	58	of	of	ADP
ejpam-4771	64	59	a	a	DET
ejpam-4771	64	60	(	(	PUNCT
ejpam-4771	64	61	2,2)-locating	2,2)-locating	NUM
ejpam-4771	64	62	point	point	ADV
ejpam-4771	64	63	-	-	PUNCT
ejpam-4771	64	64	wise	wise	ADJ
ejpam-4771	64	65	non	non	ADJ
ejpam-4771	64	66	-	-	ADJ
ejpam-4771	64	67	dominating	dominating	ADJ
ejpam-4771	64	68	(	(	PUNCT
ejpam-4771	64	69	(	(	PUNCT
ejpam-4771	64	70	2,1)-locating	2,1)-locating	NUM
ejpam-4771	64	71	point	point	NOUN
ejpam-4771	64	72	-	-	PUNCT
ejpam-4771	64	73	wise	wise	ADJ
ejpam-4771	64	74	non	non	ADJ
ejpam-4771	64	75	-	-	ADJ
ejpam-4771	64	76	dominating	dominating	ADJ
ejpam-4771	64	77	,	,	PUNCT
ejpam-4771	64	78	respectively	respectively	ADV
ejpam-4771	64	79	)	)	PUNCT
ejpam-4771	64	80	set	set	VERB
ejpam-4771	64	81	in	in	ADP
ejpam-4771	64	82	g	g	NOUN
ejpam-4771	64	83	,	,	PUNCT
ejpam-4771	64	84	denoted	denote	VERB
ejpam-4771	64	85	by	by	ADP
ejpam-4771	64	86	lnpnd	lnpnd	ADJ
ejpam-4771	64	87	(	(	PUNCT
ejpam-4771	64	88	2,2)(g	2,2)(g	NUM
ejpam-4771	64	89	)	)	PUNCT
ejpam-4771	64	90	(	(	PUNCT
ejpam-4771	64	91	lnpnd	lnpnd	ADJ
ejpam-4771	64	92	(	(	PUNCT
ejpam-4771	64	93	2,1)(g),respectively	2,1)(g),respectively	NUM
ejpam-4771	64	94	)	)	PUNCT
ejpam-4771	64	95	is	be	AUX
ejpam-4771	64	96	called	call	VERB
ejpam-4771	64	97	the	the	DET
ejpam-4771	64	98	(	(	PUNCT
ejpam-4771	64	99	2,2)locating	2,2)locating	NUM
ejpam-4771	64	100	point	point	NOUN
ejpam-4771	64	101	-	-	PUNCT
ejpam-4771	64	102	wise	wise	ADJ
ejpam-4771	64	103	non	non	ADJ
ejpam-4771	64	104	-	-	NOUN
ejpam-4771	64	105	domination	domination	ADJ
ejpam-4771	64	106	(	(	PUNCT
ejpam-4771	64	107	(	(	PUNCT
ejpam-4771	64	108	2,1)-locating	2,1)-locating	NUM
ejpam-4771	64	109	point	point	NOUN
ejpam-4771	64	110	-	-	PUNCT
ejpam-4771	64	111	wise	wise	ADJ
ejpam-4771	64	112	non	non	ADJ
ejpam-4771	64	113	-	-	ADJ
ejpam-4771	64	114	domination	domination	ADJ
ejpam-4771	64	115	)	)	PUNCT
ejpam-4771	64	116	number	number	NOUN
ejpam-4771	64	117	of	of	ADP
ejpam-4771	64	118	g.	g.	PROPN
ejpam-4771	64	119	any	any	PRON
ejpam-4771	64	120	(	(	PUNCT
ejpam-4771	64	121	2,2)-locating	2,2)-locating	NUM
ejpam-4771	64	122	point	point	ADV
ejpam-4771	64	123	-	-	PUNCT
ejpam-4771	64	124	wise	wise	ADJ
ejpam-4771	64	125	non	non	ADJ
ejpam-4771	64	126	-	-	ADJ
ejpam-4771	64	127	dominating	dominating	ADJ
ejpam-4771	64	128	(	(	PUNCT
ejpam-4771	64	129	(	(	PUNCT
ejpam-4771	64	130	2,1)-locating	2,1)-locating	NUM
ejpam-4771	64	131	point	point	NOUN
ejpam-4771	64	132	-	-	PUNCT
ejpam-4771	64	133	wise	wise	ADJ
ejpam-4771	64	134	non	non	ADJ
ejpam-4771	64	135	-	-	ADJ
ejpam-4771	64	136	dominating	dominating	ADJ
ejpam-4771	64	137	,	,	PUNCT
ejpam-4771	64	138	respectively	respectively	ADV
ejpam-4771	64	139	)	)	PUNCT
ejpam-4771	64	140	set	set	NOUN
ejpam-4771	64	141	of	of	ADP
ejpam-4771	64	142	cardinality	cardinality	PROPN
ejpam-4771	64	143	lnpnd	lnpnd	ADV
ejpam-4771	64	144	(	(	PUNCT
ejpam-4771	64	145	2,2)(g	2,2)(g	NUM
ejpam-4771	64	146	)	)	PUNCT
ejpam-4771	64	147	(	(	PUNCT
ejpam-4771	64	148	lnpnd	lnpnd	ADJ
ejpam-4771	64	149	(	(	PUNCT
ejpam-4771	64	150	2,1)(g	2,1)(g	NUM
ejpam-4771	64	151	)	)	PUNCT
ejpam-4771	64	152	,	,	PUNCT
ejpam-4771	64	153	respectively	respectively	ADV
ejpam-4771	64	154	)	)	PUNCT
ejpam-4771	64	155	is	be	AUX
ejpam-4771	64	156	then	then	ADV
ejpam-4771	64	157	referred	refer	VERB
ejpam-4771	64	158	to	to	ADP
ejpam-4771	64	159	as	as	ADP
ejpam-4771	64	160	a	a	DET
ejpam-4771	64	161	lnpnd	lnpnd	ADJ
ejpam-4771	64	162	(	(	PUNCT
ejpam-4771	64	163	2,2)-set	2,2)-set	NUM
ejpam-4771	64	164	(	(	PUNCT
ejpam-4771	64	165	ln	ln	ADJ
ejpam-4771	64	166	pnd	pnd	NOUN
ejpam-4771	64	167	(	(	PUNCT
ejpam-4771	64	168	2,1)-set	2,1)-set	NUM
ejpam-4771	64	169	)	)	PUNCT
ejpam-4771	64	170	in	in	ADP
ejpam-4771	64	171	g.	g.	PROPN
ejpam-4771	64	172	definition	definition	NOUN
ejpam-4771	64	173	7	7	NUM
ejpam-4771	64	174	.	.	PUNCT
ejpam-4771	65	1	a	a	DET
ejpam-4771	65	2	set	set	NOUN
ejpam-4771	65	3	s	s	NOUN
ejpam-4771	65	4	⊆	⊆	NUM
ejpam-4771	65	5	v	v	NOUN
ejpam-4771	65	6	(	(	PUNCT
ejpam-4771	65	7	g	g	NOUN
ejpam-4771	65	8	)	)	PUNCT
ejpam-4771	65	9	is	be	AUX
ejpam-4771	65	10	an	an	DET
ejpam-4771	65	11	outer	outer	ADV
ejpam-4771	65	12	-	-	PUNCT
ejpam-4771	65	13	connected	connect	VERB
ejpam-4771	65	14	(	(	PUNCT
ejpam-4771	65	15	2	2	NUM
ejpam-4771	65	16	,	,	PUNCT
ejpam-4771	65	17	2)-locating	2)-locating	NUM
ejpam-4771	65	18	point	point	NOUN
ejpam-4771	65	19	-	-	PUNCT
ejpam-4771	65	20	wise	wise	ADV
ejpam-4771	65	21	nondominating	nondominate	VERB
ejpam-4771	65	22	(	(	PUNCT
ejpam-4771	65	23	(	(	PUNCT
ejpam-4771	65	24	2	2	NUM
ejpam-4771	65	25	,	,	PUNCT
ejpam-4771	65	26	1)-locating	1)-locating	NUM
ejpam-4771	65	27	point	point	NOUN
ejpam-4771	65	28	-	-	PUNCT
ejpam-4771	65	29	wise	wise	ADJ
ejpam-4771	65	30	non	non	ADJ
ejpam-4771	65	31	-	-	ADJ
ejpam-4771	65	32	dominating	dominating	ADJ
ejpam-4771	65	33	,	,	PUNCT
ejpam-4771	65	34	respectively	respectively	ADV
ejpam-4771	65	35	)	)	PUNCT
ejpam-4771	65	36	set	set	VERB
ejpam-4771	65	37	in	in	ADP
ejpam-4771	65	38	g	g	PROPN
ejpam-4771	65	39	if	if	SCONJ
ejpam-4771	65	40	s	s	VERB
ejpam-4771	65	41	is	be	AUX
ejpam-4771	65	42	a	a	DET
ejpam-4771	65	43	(	(	PUNCT
ejpam-4771	65	44	2	2	NUM
ejpam-4771	65	45	,	,	PUNCT
ejpam-4771	65	46	2)-locating	2)-locating	NUM
ejpam-4771	65	47	point	point	NOUN
ejpam-4771	65	48	-	-	PUNCT
ejpam-4771	65	49	wise	wise	ADJ
ejpam-4771	65	50	non	non	ADJ
ejpam-4771	65	51	-	-	ADJ
ejpam-4771	65	52	dominating	dominating	ADJ
ejpam-4771	65	53	(	(	PUNCT
ejpam-4771	65	54	(	(	PUNCT
ejpam-4771	65	55	2	2	NUM
ejpam-4771	65	56	,	,	PUNCT
ejpam-4771	65	57	1)-locating	1)-locating	NUM
ejpam-4771	65	58	point	point	NOUN
ejpam-4771	65	59	-	-	PUNCT
ejpam-4771	65	60	wise	wise	ADJ
ejpam-4771	65	61	non	non	ADJ
ejpam-4771	65	62	-	-	ADJ
ejpam-4771	65	63	dominating	dominating	ADJ
ejpam-4771	65	64	,	,	PUNCT
ejpam-4771	65	65	respectively	respectively	ADV
ejpam-4771	65	66	)	)	PUNCT
ejpam-4771	65	67	set	set	VERB
ejpam-4771	65	68	in	in	ADP
ejpam-4771	65	69	g	g	PROPN
ejpam-4771	65	70	and	and	CCONJ
ejpam-4771	65	71	s	s	PART
ejpam-4771	65	72	=	=	SYM
ejpam-4771	65	73	v	v	X
ejpam-4771	65	74	(	(	PUNCT
ejpam-4771	65	75	g	g	NOUN
ejpam-4771	65	76	)	)	PUNCT
ejpam-4771	65	77	or	or	CCONJ
ejpam-4771	65	78	the	the	DET
ejpam-4771	65	79	subgraph	subgraph	NOUN
ejpam-4771	65	80	⟨v	⟨v	NOUN
ejpam-4771	65	81	(	(	PUNCT
ejpam-4771	65	82	g)\s⟩	g)\s⟩	PROPN
ejpam-4771	65	83	induced	induce	VERB
ejpam-4771	65	84	by	by	ADP
ejpam-4771	65	85	v	v	NOUN
ejpam-4771	65	86	(	(	PUNCT
ejpam-4771	65	87	g)\s	g)\s	NOUN
ejpam-4771	65	88	is	be	AUX
ejpam-4771	65	89	connected	connect	VERB
ejpam-4771	65	90	.	.	PUNCT
ejpam-4771	66	1	the	the	DET
ejpam-4771	66	2	outer	outer	ADV
ejpam-4771	66	3	-	-	PUNCT
ejpam-4771	66	4	connected	connect	VERB
ejpam-4771	66	5	(	(	PUNCT
ejpam-4771	66	6	2	2	NUM
ejpam-4771	66	7	,	,	PUNCT
ejpam-4771	66	8	2)-locating	2)-locating	NUM
ejpam-4771	66	9	point	point	NOUN
ejpam-4771	66	10	-	-	PUNCT
ejpam-4771	66	11	wise	wise	ADJ
ejpam-4771	66	12	non	non	ADJ
ejpam-4771	66	13	-	-	NOUN
ejpam-4771	66	14	domination	domination	ADJ
ejpam-4771	66	15	(	(	PUNCT
ejpam-4771	66	16	(	(	PUNCT
ejpam-4771	66	17	2	2	NUM
ejpam-4771	66	18	,	,	PUNCT
ejpam-4771	66	19	1)-locating	1)-locating	NUM
ejpam-4771	66	20	point	point	NOUN
ejpam-4771	66	21	-	-	PUNCT
ejpam-4771	66	22	wise	wise	ADJ
ejpam-4771	66	23	non	non	ADJ
ejpam-4771	66	24	-	-	NOUN
ejpam-4771	66	25	domination	domination	ADJ
ejpam-4771	66	26	,	,	PUNCT
ejpam-4771	66	27	respectively	respectively	ADV
ejpam-4771	66	28	)	)	PUNCT
ejpam-4771	66	29	number	number	NOUN
ejpam-4771	66	30	of	of	ADP
ejpam-4771	66	31	g	g	NOUN
ejpam-4771	66	32	,	,	PUNCT
ejpam-4771	66	33	denoted	denote	VERB
ejpam-4771	66	34	by	by	ADP
ejpam-4771	66	35	l̃npnd	l̃npnd	NOUN
ejpam-4771	66	36	(	(	PUNCT
ejpam-4771	66	37	2,2)(g	2,2)(g	NUM
ejpam-4771	66	38	)	)	PUNCT
ejpam-4771	66	39	(	(	PUNCT
ejpam-4771	66	40	l̃npnd	l̃npnd	NOUN
ejpam-4771	66	41	(	(	PUNCT
ejpam-4771	66	42	2,1)(g	2,1)(g	NUM
ejpam-4771	66	43	)	)	PUNCT
ejpam-4771	66	44	,	,	PUNCT
ejpam-4771	66	45	respectively	respectively	ADV
ejpam-4771	66	46	)	)	PUNCT
ejpam-4771	66	47	,	,	PUNCT
ejpam-4771	66	48	is	be	AUX
ejpam-4771	66	49	the	the	DET
ejpam-4771	66	50	smallest	small	ADJ
ejpam-4771	66	51	cardinality	cardinality	NOUN
ejpam-4771	66	52	of	of	ADP
ejpam-4771	66	53	an	an	DET
ejpam-4771	66	54	outer	outer	ADV
ejpam-4771	66	55	-	-	PUNCT
ejpam-4771	66	56	connected	connect	VERB
ejpam-4771	66	57	(	(	PUNCT
ejpam-4771	66	58	2	2	NUM
ejpam-4771	66	59	,	,	PUNCT
ejpam-4771	66	60	2)-locating	2)-locating	NUM
ejpam-4771	66	61	point	point	NOUN
ejpam-4771	66	62	-	-	PUNCT
ejpam-4771	66	63	wise	wise	ADJ
ejpam-4771	66	64	non	non	ADJ
ejpam-4771	66	65	-	-	ADJ
ejpam-4771	66	66	dominating	dominating	ADJ
ejpam-4771	66	67	(	(	PUNCT
ejpam-4771	66	68	(	(	PUNCT
ejpam-4771	66	69	2	2	NUM
ejpam-4771	66	70	,	,	PUNCT
ejpam-4771	66	71	1)-locating	1)-locating	NUM
ejpam-4771	66	72	point	point	NOUN
ejpam-4771	66	73	-	-	PUNCT
ejpam-4771	66	74	wise	wise	ADJ
ejpam-4771	66	75	non	non	ADJ
ejpam-4771	66	76	-	-	ADJ
ejpam-4771	66	77	dominating	dominating	ADJ
ejpam-4771	66	78	,	,	PUNCT
ejpam-4771	66	79	respectively	respectively	ADV
ejpam-4771	66	80	)	)	PUNCT
ejpam-4771	66	81	set	set	VERB
ejpam-4771	66	82	in	in	ADP
ejpam-4771	66	83	g.	g.	PROPN
ejpam-4771	66	84	an	an	DET
ejpam-4771	66	85	outer	outer	ADV
ejpam-4771	66	86	-	-	PUNCT
ejpam-4771	66	87	connected	connect	VERB
ejpam-4771	66	88	(	(	PUNCT
ejpam-4771	66	89	2	2	NUM
ejpam-4771	66	90	,	,	PUNCT
ejpam-4771	66	91	2)-locating	2)-locating	NUM
ejpam-4771	66	92	point	point	NOUN
ejpam-4771	66	93	-	-	PUNCT
ejpam-4771	66	94	wise	wise	ADJ
ejpam-4771	66	95	non	non	ADJ
ejpam-4771	66	96	-	-	ADJ
ejpam-4771	66	97	dominating	dominating	ADJ
ejpam-4771	66	98	(	(	PUNCT
ejpam-4771	66	99	(	(	PUNCT
ejpam-4771	66	100	2	2	NUM
ejpam-4771	66	101	,	,	PUNCT
ejpam-4771	66	102	1)-locating	1)-locating	NUM
ejpam-4771	66	103	point	point	NOUN
ejpam-4771	66	104	-	-	PUNCT
ejpam-4771	66	105	wise	wise	ADJ
ejpam-4771	66	106	nondominating	nondominating	NOUN
ejpam-4771	66	107	,	,	PUNCT
ejpam-4771	66	108	respectively	respectively	ADV
ejpam-4771	66	109	)	)	PUNCT
ejpam-4771	66	110	set	set	NOUN
ejpam-4771	66	111	of	of	ADP
ejpam-4771	66	112	cardinality	cardinality	NOUN
ejpam-4771	66	113	l̃npnd	l̃npnd	NOUN
ejpam-4771	66	114	(	(	PUNCT
ejpam-4771	66	115	2,2)(g	2,2)(g	NUM
ejpam-4771	66	116	)	)	PUNCT
ejpam-4771	66	117	(	(	PUNCT
ejpam-4771	66	118	l̃npnd	l̃npnd	NOUN
ejpam-4771	66	119	(	(	PUNCT
ejpam-4771	66	120	2,1)(g	2,1)(g	NUM
ejpam-4771	66	121	)	)	PUNCT
ejpam-4771	66	122	,	,	PUNCT
ejpam-4771	66	123	respectively	respectively	ADV
ejpam-4771	66	124	)	)	PUNCT
ejpam-4771	66	125	is	be	AUX
ejpam-4771	66	126	then	then	ADV
ejpam-4771	66	127	referred	refer	VERB
ejpam-4771	66	128	to	to	ADP
ejpam-4771	66	129	as	as	ADP
ejpam-4771	66	130	an	an	DET
ejpam-4771	66	131	l̃npnd	l̃npnd	NOUN
ejpam-4771	66	132	(	(	PUNCT
ejpam-4771	66	133	2,2)-set	2,2)-set	NUM
ejpam-4771	66	134	(	(	PUNCT
ejpam-4771	66	135	l̃n	l̃n	VERB
ejpam-4771	66	136	pnd	pnd	NOUN
ejpam-4771	66	137	(	(	PUNCT
ejpam-4771	66	138	2,1)set	2,1)set	NUM
ejpam-4771	66	139	)	)	PUNCT
ejpam-4771	66	140	in	in	ADP
ejpam-4771	66	141	g.	g.	PROPN
ejpam-4771	66	142	3	3	NUM
ejpam-4771	66	143	.	.	PUNCT
ejpam-4771	66	144	preliminary	preliminary	ADJ
ejpam-4771	66	145	results	result	NOUN
ejpam-4771	66	146	every	every	DET
ejpam-4771	66	147	nontrivial	nontrivial	ADJ
ejpam-4771	66	148	connected	connect	VERB
ejpam-4771	66	149	graph	graph	NOUN
ejpam-4771	66	150	g	g	PROPN
ejpam-4771	66	151	admits	admit	VERB
ejpam-4771	66	152	an	an	DET
ejpam-4771	66	153	outer	outer	ADV
ejpam-4771	66	154	-	-	PUNCT
ejpam-4771	66	155	connected	connect	VERB
ejpam-4771	66	156	2	2	NUM
ejpam-4771	66	157	-	-	PUNCT
ejpam-4771	66	158	resolving	resolve	VERB
ejpam-4771	66	159	hop	hop	NOUN
ejpam-4771	66	160	dominating	dominating	NOUN
ejpam-4771	66	161	set	set	NOUN
ejpam-4771	66	162	.	.	PUNCT
ejpam-4771	67	1	indeed	indeed	ADV
ejpam-4771	67	2	,	,	PUNCT
ejpam-4771	67	3	the	the	DET
ejpam-4771	67	4	vertex	vertex	NOUN
ejpam-4771	67	5	set	set	VERB
ejpam-4771	67	6	v	v	NOUN
ejpam-4771	67	7	(	(	PUNCT
ejpam-4771	67	8	g	g	NOUN
ejpam-4771	67	9	)	)	PUNCT
ejpam-4771	67	10	of	of	ADP
ejpam-4771	67	11	g	g	PROPN
ejpam-4771	67	12	is	be	AUX
ejpam-4771	67	13	an	an	DET
ejpam-4771	67	14	outer	outer	ADV
ejpam-4771	67	15	-	-	PUNCT
ejpam-4771	67	16	connected	connect	VERB
ejpam-4771	67	17	2	2	NUM
ejpam-4771	67	18	-	-	PUNCT
ejpam-4771	67	19	resolving	resolve	VERB
ejpam-4771	67	20	hop	hop	NOUN
ejpam-4771	67	21	dominating	dominating	NOUN
ejpam-4771	67	22	set	set	NOUN
ejpam-4771	67	23	.	.	PUNCT
ejpam-4771	68	1	remark	remark	PROPN
ejpam-4771	68	2	1	1	NUM
ejpam-4771	68	3	.	.	PUNCT
ejpam-4771	69	1	for	for	ADP
ejpam-4771	69	2	any	any	DET
ejpam-4771	69	3	connected	connected	ADJ
ejpam-4771	69	4	graph	graph	NOUN
ejpam-4771	69	5	g	g	NOUN
ejpam-4771	69	6	of	of	ADP
ejpam-4771	69	7	order	order	NOUN
ejpam-4771	69	8	n	n	PRON
ejpam-4771	69	9	≥	≥	NOUN
ejpam-4771	69	10	2	2	NUM
ejpam-4771	69	11	,	,	PUNCT
ejpam-4771	69	12	2	2	NUM
ejpam-4771	69	13	≤	≤	NUM
ejpam-4771	69	14	γ̃c2rh(g	γ̃c2rh(g	NOUN
ejpam-4771	69	15	)	)	PUNCT
ejpam-4771	69	16	≤	≤	NUM
ejpam-4771	69	17	n.	n.	NOUN
ejpam-4771	69	18	moreover	moreover	ADV
ejpam-4771	69	19	,	,	PUNCT
ejpam-4771	69	20	γ̃c2rh(p2	γ̃c2rh(p2	ADJ
ejpam-4771	69	21	)	)	PUNCT
ejpam-4771	69	22	=	=	SYM
ejpam-4771	69	23	2	2	NUM
ejpam-4771	69	24	and	and	CCONJ
ejpam-4771	69	25	γ̃c2rh(kn	γ̃c2rh(kn	NUM
ejpam-4771	69	26	)	)	PUNCT
ejpam-4771	70	1	=	=	PUNCT
ejpam-4771	70	2	n.	n.	NOUN
ejpam-4771	70	3	proposition	proposition	NOUN
ejpam-4771	70	4	1	1	NUM
ejpam-4771	70	5	.	.	PUNCT
ejpam-4771	71	1	(	(	PUNCT
ejpam-4771	71	2	i	i	NOUN
ejpam-4771	71	3	)	)	PUNCT
ejpam-4771	71	4	for	for	ADP
ejpam-4771	71	5	a	a	DET
ejpam-4771	71	6	path	path	NOUN
ejpam-4771	71	7	pn	pn	NOUN
ejpam-4771	71	8	on	on	ADP
ejpam-4771	71	9	n	n	CCONJ
ejpam-4771	71	10	vertices	vertice	VERB
ejpam-4771	71	11	γ̃c2rh(pn	γ̃c2rh(pn	NOUN
ejpam-4771	71	12	)	)	PUNCT
ejpam-4771	71	13	=	=	PUNCT
ejpam-4771	71	14			NOUN
ejpam-4771	71	15	n	n	CCONJ
ejpam-4771	71	16	,	,	PUNCT
ejpam-4771	71	17	if	if	SCONJ
ejpam-4771	71	18	n	n	NOUN
ejpam-4771	71	19	=	=	SYM
ejpam-4771	71	20	2	2	NUM
ejpam-4771	71	21	,	,	PUNCT
ejpam-4771	71	22	3	3	NUM
ejpam-4771	71	23	;	;	PUNCT
ejpam-4771	71	24	n−	n−	NOUN
ejpam-4771	71	25	2	2	NUM
ejpam-4771	71	26	,	,	PUNCT
ejpam-4771	71	27	if	if	SCONJ
ejpam-4771	71	28	n	n	NOUN
ejpam-4771	71	29	=	=	SYM
ejpam-4771	71	30	4	4	NUM
ejpam-4771	71	31	,	,	PUNCT
ejpam-4771	71	32	5	5	NUM
ejpam-4771	71	33	,	,	PUNCT
ejpam-4771	71	34	6	6	NUM
ejpam-4771	71	35	;	;	PUNCT
ejpam-4771	71	36	n−	n−	NOUN
ejpam-4771	71	37	3	3	NUM
ejpam-4771	71	38	,	,	PUNCT
ejpam-4771	71	39	if	if	SCONJ
ejpam-4771	71	40	n	n	NOUN
ejpam-4771	71	41	=	=	SYM
ejpam-4771	71	42	7	7	NUM
ejpam-4771	71	43	;	;	PUNCT
ejpam-4771	71	44	n−	n−	NOUN
ejpam-4771	71	45	4	4	NUM
ejpam-4771	71	46	,	,	PUNCT
ejpam-4771	71	47	if	if	SCONJ
ejpam-4771	71	48	n	n	PRON
ejpam-4771	71	49	≥	≥	NOUN
ejpam-4771	71	50	8	8	NUM
ejpam-4771	71	51	.	.	PUNCT
ejpam-4771	72	1	a.m.	a.m.	PROPN
ejpam-4771	72	2	mahistrado	mahistrado	PROPN
ejpam-4771	72	3	,	,	PUNCT
ejpam-4771	72	4	h.	h.	PROPN
ejpam-4771	72	5	rara	rara	PROPN
ejpam-4771	72	6	/	/	SYM
ejpam-4771	72	7	eur	eur	PROPN
ejpam-4771	72	8	.	.	PUNCT
ejpam-4771	73	1	j.	j.	PROPN
ejpam-4771	73	2	pure	pure	PROPN
ejpam-4771	73	3	appl	appl	PROPN
ejpam-4771	73	4	.	.	PROPN
ejpam-4771	73	5	math	math	PROPN
ejpam-4771	73	6	,	,	PUNCT
ejpam-4771	73	7	16	16	NUM
ejpam-4771	73	8	(	(	PUNCT
ejpam-4771	73	9	2	2	NUM
ejpam-4771	73	10	)	)	PUNCT
ejpam-4771	73	11	(	(	PUNCT
ejpam-4771	73	12	2023	2023	NUM
ejpam-4771	73	13	)	)	PUNCT
ejpam-4771	73	14	,	,	PUNCT
ejpam-4771	73	15	1180	1180	NUM
ejpam-4771	73	16	-	-	SYM
ejpam-4771	73	17	1195	1195	NUM
ejpam-4771	73	18	1184	1184	NUM
ejpam-4771	73	19	(	(	PUNCT
ejpam-4771	73	20	ii	ii	NOUN
ejpam-4771	73	21	)	)	PUNCT
ejpam-4771	73	22	for	for	ADP
ejpam-4771	73	23	a	a	DET
ejpam-4771	73	24	cycle	cycle	NOUN
ejpam-4771	73	25	cn	cn	NOUN
ejpam-4771	73	26	on	on	ADP
ejpam-4771	73	27	n	n	NUM
ejpam-4771	73	28	vertices	vertex	NOUN
ejpam-4771	73	29	γ̃c2rh(cn	γ̃c2rh(cn	NOUN
ejpam-4771	73	30	)	)	PUNCT
ejpam-4771	73	31	=	=	PUNCT
ejpam-4771	73	32			NOUN
ejpam-4771	73	33	n	n	CCONJ
ejpam-4771	73	34	,	,	PUNCT
ejpam-4771	73	35	if	if	SCONJ
ejpam-4771	73	36	n	n	CCONJ
ejpam-4771	73	37	=	=	SYM
ejpam-4771	73	38	3	3	NUM
ejpam-4771	73	39	,	,	PUNCT
ejpam-4771	73	40	4	4	NUM
ejpam-4771	73	41	;	;	PUNCT
ejpam-4771	73	42	n−	n−	NOUN
ejpam-4771	73	43	2	2	NUM
ejpam-4771	73	44	,	,	PUNCT
ejpam-4771	73	45	if	if	SCONJ
ejpam-4771	73	46	n	n	NOUN
ejpam-4771	73	47	=	=	SYM
ejpam-4771	73	48	5	5	NUM
ejpam-4771	73	49	;	;	PUNCT
ejpam-4771	73	50	n−	n−	NOUN
ejpam-4771	73	51	3	3	NUM
ejpam-4771	73	52	,	,	PUNCT
ejpam-4771	73	53	if	if	SCONJ
ejpam-4771	73	54	n	n	NOUN
ejpam-4771	73	55	=	=	SYM
ejpam-4771	73	56	6	6	NUM
ejpam-4771	73	57	;	;	PUNCT
ejpam-4771	73	58	n−	n−	NOUN
ejpam-4771	73	59	4	4	NUM
ejpam-4771	73	60	,	,	PUNCT
ejpam-4771	73	61	if	if	SCONJ
ejpam-4771	73	62	n	n	PRON
ejpam-4771	73	63	≥	≥	NOUN
ejpam-4771	73	64	7	7	NUM
ejpam-4771	73	65	.	.	PUNCT
ejpam-4771	74	1	now	now	ADV
ejpam-4771	74	2	,	,	PUNCT
ejpam-4771	74	3	consider	consider	VERB
ejpam-4771	74	4	the	the	DET
ejpam-4771	74	5	following	follow	VERB
ejpam-4771	74	6	results	result	NOUN
ejpam-4771	74	7	of	of	ADP
ejpam-4771	74	8	outer	outer	ADV
ejpam-4771	74	9	-	-	PUNCT
ejpam-4771	74	10	connected	connect	VERB
ejpam-4771	74	11	2	2	NUM
ejpam-4771	74	12	-	-	PUNCT
ejpam-4771	74	13	locating	locate	VERB
ejpam-4771	74	14	point	point	NOUN
ejpam-4771	74	15	-	-	PUNCT
ejpam-4771	74	16	wise	wise	ADJ
ejpam-4771	74	17	non	non	ADJ
ejpam-4771	74	18	-	-	ADJ
ejpam-4771	74	19	dominating	dominating	ADJ
ejpam-4771	74	20	sets	set	NOUN
ejpam-4771	74	21	which	which	PRON
ejpam-4771	74	22	are	be	AUX
ejpam-4771	74	23	used	use	VERB
ejpam-4771	74	24	in	in	ADP
ejpam-4771	74	25	characterizing	characterize	VERB
ejpam-4771	74	26	the	the	DET
ejpam-4771	74	27	outer	outer	ADV
ejpam-4771	74	28	-	-	PUNCT
ejpam-4771	74	29	connected	connect	VERB
ejpam-4771	74	30	2	2	NUM
ejpam-4771	74	31	-	-	PUNCT
ejpam-4771	74	32	resolving	resolve	VERB
ejpam-4771	74	33	hop	hop	NOUN
ejpam-4771	74	34	dominating	dominating	NOUN
ejpam-4771	74	35	sets	set	NOUN
ejpam-4771	74	36	in	in	ADP
ejpam-4771	74	37	the	the	DET
ejpam-4771	74	38	join	join	NOUN
ejpam-4771	74	39	of	of	ADP
ejpam-4771	74	40	two	two	NUM
ejpam-4771	74	41	graphs	graph	NOUN
ejpam-4771	74	42	.	.	PUNCT
ejpam-4771	75	1	proposition	proposition	NOUN
ejpam-4771	75	2	2	2	NUM
ejpam-4771	75	3	.	.	PUNCT
ejpam-4771	76	1	let	let	VERB
ejpam-4771	76	2	g	g	NOUN
ejpam-4771	76	3	be	be	AUX
ejpam-4771	76	4	any	any	DET
ejpam-4771	76	5	nontrivial	nontrivial	ADJ
ejpam-4771	76	6	connected	connect	VERB
ejpam-4771	76	7	graph	graph	NOUN
ejpam-4771	76	8	.	.	PUNCT
ejpam-4771	77	1	then	then	ADV
ejpam-4771	77	2	for	for	ADP
ejpam-4771	77	3	any	any	DET
ejpam-4771	77	4	positive	positive	ADJ
ejpam-4771	77	5	integers	integer	NOUN
ejpam-4771	77	6	n	n	CCONJ
ejpam-4771	77	7	,	,	PUNCT
ejpam-4771	77	8	we	we	PRON
ejpam-4771	77	9	have	have	VERB
ejpam-4771	77	10	(	(	PUNCT
ejpam-4771	77	11	i	i	NOUN
ejpam-4771	77	12	)	)	PUNCT
ejpam-4771	77	13	l̃npnd	l̃npnd	NOUN
ejpam-4771	77	14	2	2	NUM
ejpam-4771	77	15	(	(	PUNCT
ejpam-4771	77	16	pn	pn	NOUN
ejpam-4771	77	17	)	)	PUNCT
ejpam-4771	77	18	=	=	SYM
ejpam-4771	78	1			PROPN
ejpam-4771	78	2	n	n	CCONJ
ejpam-4771	78	3	,	,	PUNCT
ejpam-4771	78	4	if	if	SCONJ
ejpam-4771	78	5	n	n	NOUN
ejpam-4771	78	6	=	=	SYM
ejpam-4771	78	7	2	2	NUM
ejpam-4771	78	8	,	,	PUNCT
ejpam-4771	78	9	3	3	NUM
ejpam-4771	78	10	;	;	PUNCT
ejpam-4771	78	11	n−	n−	NOUN
ejpam-4771	78	12	1	1	NUM
ejpam-4771	78	13	,	,	PUNCT
ejpam-4771	78	14	if	if	SCONJ
ejpam-4771	78	15	4	4	NUM
ejpam-4771	78	16	≤	≤	NUM
ejpam-4771	78	17	n	n	CCONJ
ejpam-4771	78	18	≤	≤	NOUN
ejpam-4771	78	19	7	7	NUM
ejpam-4771	78	20	;	;	PUNCT
ejpam-4771	78	21	n−	n−	NOUN
ejpam-4771	78	22	2	2	NUM
ejpam-4771	78	23	,	,	PUNCT
ejpam-4771	78	24	if	if	SCONJ
ejpam-4771	78	25	n	n	PRON
ejpam-4771	78	26	≥	≥	NOUN
ejpam-4771	78	27	8	8	NUM
ejpam-4771	78	28	.	.	PUNCT
ejpam-4771	79	1	(	(	PUNCT
ejpam-4771	79	2	ii	ii	NOUN
ejpam-4771	79	3	)	)	PUNCT
ejpam-4771	79	4	l̃npnd	l̃npnd	NOUN
ejpam-4771	79	5	2	2	NUM
ejpam-4771	79	6	(	(	PUNCT
ejpam-4771	79	7	cn	cn	PROPN
ejpam-4771	79	8	)	)	PUNCT
ejpam-4771	79	9	=	=	SYM
ejpam-4771	79	10	{	{	PUNCT
ejpam-4771	79	11	n	n	CCONJ
ejpam-4771	79	12	,	,	PUNCT
ejpam-4771	79	13	if	if	SCONJ
ejpam-4771	79	14	n	n	CCONJ
ejpam-4771	79	15	=	=	SYM
ejpam-4771	79	16	3	3	NUM
ejpam-4771	79	17	,	,	PUNCT
ejpam-4771	79	18	4	4	NUM
ejpam-4771	79	19	;	;	PUNCT
ejpam-4771	79	20	n−	n−	NOUN
ejpam-4771	79	21	2	2	NUM
ejpam-4771	79	22	,	,	PUNCT
ejpam-4771	79	23	if	if	SCONJ
ejpam-4771	79	24	n	n	PRON
ejpam-4771	79	25	≥	≥	NOUN
ejpam-4771	79	26	5	5	NUM
ejpam-4771	79	27	.	.	PUNCT
ejpam-4771	79	28	(	(	PUNCT
ejpam-4771	79	29	iii	iii	NOUN
ejpam-4771	79	30	)	)	PUNCT
ejpam-4771	79	31	for	for	ADP
ejpam-4771	79	32	all	all	DET
ejpam-4771	79	33	n	n	PRON
ejpam-4771	79	34	≥	≥	NUM
ejpam-4771	79	35	5	5	NUM
ejpam-4771	79	36	,	,	PUNCT
ejpam-4771	79	37	l̃npnd	l̃npnd	NOUN
ejpam-4771	79	38	(	(	PUNCT
ejpam-4771	79	39	2,2)(pn	2,2)(pn	NUM
ejpam-4771	79	40	)	)	PUNCT
ejpam-4771	79	41	=	=	PRON
ejpam-4771	79	42	{	{	PUNCT
ejpam-4771	79	43	n−	n−	NOUN
ejpam-4771	79	44	1	1	NUM
ejpam-4771	79	45	,	,	PUNCT
ejpam-4771	79	46	if	if	SCONJ
ejpam-4771	79	47	5	5	NUM
ejpam-4771	79	48	≤	≤	NUM
ejpam-4771	79	49	n	n	PRON
ejpam-4771	79	50	≤	≤	NUM
ejpam-4771	79	51	7	7	NUM
ejpam-4771	79	52	;	;	PUNCT
ejpam-4771	79	53	n−	n−	NOUN
ejpam-4771	79	54	2	2	NUM
ejpam-4771	79	55	,	,	PUNCT
ejpam-4771	79	56	if	if	SCONJ
ejpam-4771	79	57	n	n	PRON
ejpam-4771	79	58	≥	≥	NOUN
ejpam-4771	79	59	8	8	NUM
ejpam-4771	79	60	;	;	PUNCT
ejpam-4771	79	61	for	for	ADP
ejpam-4771	79	62	all	all	PRON
ejpam-4771	79	63	n	n	PRON
ejpam-4771	79	64	≥	≥	NUM
ejpam-4771	79	65	6	6	NUM
ejpam-4771	79	66	,	,	PUNCT
ejpam-4771	79	67	l̃npnd	l̃npnd	NOUN
ejpam-4771	79	68	(	(	PUNCT
ejpam-4771	79	69	2,2)(cn	2,2)(cn	NUM
ejpam-4771	79	70	)	)	PUNCT
ejpam-4771	80	1	=	=	VERB
ejpam-4771	80	2	n−	n−	NOUN
ejpam-4771	80	3	2	2	NUM
ejpam-4771	80	4	.	.	PUNCT
ejpam-4771	80	5	(	(	PUNCT
ejpam-4771	80	6	iv	iv	X
ejpam-4771	80	7	)	)	PUNCT
ejpam-4771	80	8	for	for	ADP
ejpam-4771	80	9	all	all	DET
ejpam-4771	80	10	n	n	PRON
ejpam-4771	80	11	≥	≥	NOUN
ejpam-4771	80	12	4	4	NUM
ejpam-4771	80	13	,	,	PUNCT
ejpam-4771	80	14	l̃npnd	l̃npnd	NOUN
ejpam-4771	80	15	(	(	PUNCT
ejpam-4771	80	16	2,1)(pn	2,1)(pn	NUM
ejpam-4771	80	17	)	)	PUNCT
ejpam-4771	80	18	=	=	PRON
ejpam-4771	80	19	{	{	PUNCT
ejpam-4771	80	20	n−	n−	NOUN
ejpam-4771	80	21	1	1	NUM
ejpam-4771	80	22	,	,	PUNCT
ejpam-4771	80	23	if	if	SCONJ
ejpam-4771	80	24	4	4	NUM
ejpam-4771	80	25	≤	≤	NUM
ejpam-4771	80	26	n	n	CCONJ
ejpam-4771	80	27	≤	≤	NOUN
ejpam-4771	80	28	7	7	NUM
ejpam-4771	80	29	;	;	PUNCT
ejpam-4771	80	30	n−	n−	NOUN
ejpam-4771	80	31	2	2	NUM
ejpam-4771	80	32	,	,	PUNCT
ejpam-4771	80	33	if	if	SCONJ
ejpam-4771	80	34	n	n	PRON
ejpam-4771	80	35	≥	≥	NOUN
ejpam-4771	80	36	8	8	NUM
ejpam-4771	80	37	;	;	PUNCT
ejpam-4771	80	38	for	for	ADP
ejpam-4771	80	39	all	all	PRON
ejpam-4771	80	40	n	n	PRON
ejpam-4771	80	41	≥	≥	NOUN
ejpam-4771	80	42	4	4	NUM
ejpam-4771	80	43	,	,	PUNCT
ejpam-4771	80	44	l̃npnd	l̃npnd	NOUN
ejpam-4771	80	45	(	(	PUNCT
ejpam-4771	80	46	2,1)(cn	2,1)(cn	NUM
ejpam-4771	80	47	)	)	PUNCT
ejpam-4771	80	48	=	=	PRON
ejpam-4771	80	49	{	{	PUNCT
ejpam-4771	80	50	n	n	CCONJ
ejpam-4771	80	51	,	,	PUNCT
ejpam-4771	80	52	if	if	SCONJ
ejpam-4771	80	53	n	n	CCONJ
ejpam-4771	80	54	=	=	SYM
ejpam-4771	80	55	4	4	NUM
ejpam-4771	80	56	;	;	PUNCT
ejpam-4771	80	57	n−	n−	NOUN
ejpam-4771	80	58	2	2	NUM
ejpam-4771	80	59	,	,	PUNCT
ejpam-4771	80	60	if	if	SCONJ
ejpam-4771	80	61	n	n	PRON
ejpam-4771	80	62	≥	≥	NOUN
ejpam-4771	80	63	5	5	NUM
ejpam-4771	80	64	.	.	PUNCT
ejpam-4771	81	1	proof	proof	NOUN
ejpam-4771	81	2	.	.	PUNCT
ejpam-4771	82	1	(	(	PUNCT
ejpam-4771	82	2	i	i	NOUN
ejpam-4771	82	3	)	)	PUNCT
ejpam-4771	82	4	let	let	VERB
ejpam-4771	82	5	pn	pn	NOUN
ejpam-4771	82	6	=	=	PUNCT
ejpam-4771	83	1	[	[	X
ejpam-4771	83	2	v1	v1	NOUN
ejpam-4771	83	3	,	,	PUNCT
ejpam-4771	83	4	v2	v2	PROPN
ejpam-4771	83	5	,	,	PUNCT
ejpam-4771	83	6	v3	v3	PROPN
ejpam-4771	83	7	,	,	PUNCT
ejpam-4771	83	8	.	.	PUNCT
ejpam-4771	83	9	.	.	PUNCT
ejpam-4771	83	10	.	.	PUNCT
ejpam-4771	84	1	,	,	PUNCT
ejpam-4771	84	2	vn	vn	X
ejpam-4771	84	3	]	]	PUNCT
ejpam-4771	84	4	.	.	PUNCT
ejpam-4771	85	1	clearly	clearly	ADV
ejpam-4771	85	2	,	,	PUNCT
ejpam-4771	85	3	l̃n	l̃n	VERB
ejpam-4771	85	4	pnd	pnd	PROPN
ejpam-4771	85	5	2	2	NUM
ejpam-4771	85	6	(	(	PUNCT
ejpam-4771	85	7	pn	pn	NOUN
ejpam-4771	85	8	)	)	PUNCT
ejpam-4771	85	9	=	=	SYM
ejpam-4771	85	10	n	n	PROPN
ejpam-4771	85	11	for	for	ADP
ejpam-4771	85	12	n	n	NOUN
ejpam-4771	85	13	=	=	SYM
ejpam-4771	85	14	2	2	NUM
ejpam-4771	85	15	,	,	PUNCT
ejpam-4771	85	16	3	3	NUM
ejpam-4771	85	17	.	.	PUNCT
ejpam-4771	86	1	let	let	VERB
ejpam-4771	86	2	n	n	PRON
ejpam-4771	86	3	≥	≥	X
ejpam-4771	86	4	4	4	NUM
ejpam-4771	86	5	and	and	CCONJ
ejpam-4771	86	6	let	let	VERB
ejpam-4771	86	7	s	s	PRON
ejpam-4771	86	8	be	be	AUX
ejpam-4771	86	9	an	an	DET
ejpam-4771	86	10	l̃npnd	l̃npnd	NOUN
ejpam-4771	86	11	2	2	NUM
ejpam-4771	86	12	-set	-set	PUNCT
ejpam-4771	86	13	in	in	ADP
ejpam-4771	86	14	pn	pn	PROPN
ejpam-4771	86	15	.	.	PUNCT
ejpam-4771	87	1	since	since	SCONJ
ejpam-4771	87	2	⟨v	⟨v	PROPN
ejpam-4771	87	3	(	(	PUNCT
ejpam-4771	87	4	pn	pn	NOUN
ejpam-4771	87	5	)	)	PUNCT
ejpam-4771	87	6	\	\	PROPN
ejpam-4771	87	7	s⟩	s⟩	PROPN
ejpam-4771	87	8	is	be	AUX
ejpam-4771	87	9	connected	connect	VERB
ejpam-4771	87	10	and	and	CCONJ
ejpam-4771	87	11	s	s	VERB
ejpam-4771	87	12	is	be	AUX
ejpam-4771	87	13	a	a	DET
ejpam-4771	87	14	2	2	NUM
ejpam-4771	87	15	-	-	PUNCT
ejpam-4771	87	16	locating	locate	VERB
ejpam-4771	87	17	point	point	NOUN
ejpam-4771	87	18	-	-	PUNCT
ejpam-4771	87	19	wise	wise	ADJ
ejpam-4771	87	20	non	non	ADJ
ejpam-4771	87	21	-	-	ADJ
ejpam-4771	87	22	dominating	dominating	ADJ
ejpam-4771	87	23	set	set	NOUN
ejpam-4771	87	24	,	,	PUNCT
ejpam-4771	87	25	1	1	NUM
ejpam-4771	87	26	≤	≤	NUM
ejpam-4771	87	27	|v	|v	X
ejpam-4771	87	28	(	(	PUNCT
ejpam-4771	87	29	pn)\s|	pn)\s|	PROPN
ejpam-4771	87	30	≤	≤	NOUN
ejpam-4771	87	31	2	2	NUM
ejpam-4771	87	32	.	.	PUNCT
ejpam-4771	88	1	clearly	clearly	ADV
ejpam-4771	88	2	,	,	PUNCT
ejpam-4771	88	3	at	at	ADV
ejpam-4771	88	4	least	least	ADJ
ejpam-4771	88	5	one	one	NUM
ejpam-4771	88	6	of	of	ADP
ejpam-4771	88	7	v1	v1	NOUN
ejpam-4771	88	8	and	and	CCONJ
ejpam-4771	88	9	vn	vn	PROPN
ejpam-4771	88	10	is	be	AUX
ejpam-4771	88	11	in	in	ADP
ejpam-4771	88	12	s.	s.	PROPN
ejpam-4771	88	13	suppose	suppose	VERB
ejpam-4771	88	14	that	that	SCONJ
ejpam-4771	88	15	v1	v1	PROPN
ejpam-4771	88	16	∈	∈	PROPN
ejpam-4771	88	17	s.	s.	PROPN
ejpam-4771	88	18	suppose	suppose	VERB
ejpam-4771	88	19	further	far	ADV
ejpam-4771	88	20	that	that	SCONJ
ejpam-4771	88	21	|v	|v	PROPN
ejpam-4771	88	22	(	(	PUNCT
ejpam-4771	88	23	pn	pn	NOUN
ejpam-4771	88	24	)	)	PUNCT
ejpam-4771	88	25	\	\	NOUN
ejpam-4771	88	26	s|	s|	NOUN
ejpam-4771	88	27	=	=	SYM
ejpam-4771	89	1	1	1	X
ejpam-4771	89	2	.	.	PUNCT
ejpam-4771	89	3	then	then	ADV
ejpam-4771	89	4	4	4	NUM
ejpam-4771	89	5	≤	≤	NOUN
ejpam-4771	89	6	n	n	PRON
ejpam-4771	89	7	≤	≤	NOUN
ejpam-4771	89	8	7	7	NUM
ejpam-4771	89	9	.	.	PUNCT
ejpam-4771	90	1	hence	hence	ADV
ejpam-4771	90	2	,	,	PUNCT
ejpam-4771	90	3	l̃npnd	l̃npnd	NOUN
ejpam-4771	90	4	2	2	NUM
ejpam-4771	90	5	(	(	PUNCT
ejpam-4771	90	6	pn	pn	NOUN
ejpam-4771	90	7	)	)	PUNCT
ejpam-4771	90	8	=	=	PUNCT
ejpam-4771	90	9	n−	n−	NOUN
ejpam-4771	90	10	1	1	NUM
ejpam-4771	90	11	for	for	ADP
ejpam-4771	90	12	4	4	NUM
ejpam-4771	90	13	≤	≤	NOUN
ejpam-4771	90	14	n	n	PRON
ejpam-4771	90	15	≤	≤	NOUN
ejpam-4771	90	16	7	7	NUM
ejpam-4771	90	17	.	.	PUNCT
ejpam-4771	91	1	next	next	ADV
ejpam-4771	91	2	,	,	PUNCT
ejpam-4771	91	3	suppose	suppose	VERB
ejpam-4771	91	4	that	that	SCONJ
ejpam-4771	91	5	|v	|v	PROPN
ejpam-4771	91	6	(	(	PUNCT
ejpam-4771	91	7	pn	pn	NOUN
ejpam-4771	91	8	)	)	PUNCT
ejpam-4771	91	9	\	\	PROPN
ejpam-4771	91	10	s|	s|	NOUN
ejpam-4771	91	11	=	=	SYM
ejpam-4771	92	1	2	2	X
ejpam-4771	92	2	.	.	X
ejpam-4771	93	1	if	if	SCONJ
ejpam-4771	93	2	p	p	NOUN
ejpam-4771	93	3	is	be	AUX
ejpam-4771	93	4	the	the	DET
ejpam-4771	93	5	smallest	small	ADJ
ejpam-4771	93	6	integer	integer	NOUN
ejpam-4771	93	7	such	such	ADJ
ejpam-4771	93	8	that	that	DET
ejpam-4771	93	9	vp	vp	PROPN
ejpam-4771	93	10	/∈	/∈	PUNCT
ejpam-4771	94	1	s	s	X
ejpam-4771	94	2	,	,	PUNCT
ejpam-4771	94	3	then	then	ADV
ejpam-4771	94	4	p	p	X
ejpam-4771	94	5	/∈	/∈	PUNCT
ejpam-4771	94	6	{	{	PUNCT
ejpam-4771	94	7	1	1	NUM
ejpam-4771	94	8	,	,	PUNCT
ejpam-4771	94	9	2	2	NUM
ejpam-4771	94	10	,	,	PUNCT
ejpam-4771	94	11	3	3	NUM
ejpam-4771	94	12	}	}	PUNCT
ejpam-4771	94	13	.	.	PUNCT
ejpam-4771	95	1	it	it	PRON
ejpam-4771	95	2	follows	follow	VERB
ejpam-4771	95	3	that	that	SCONJ
ejpam-4771	95	4	v1	v1	NOUN
ejpam-4771	95	5	,	,	PUNCT
ejpam-4771	95	6	v2	v2	PROPN
ejpam-4771	95	7	,	,	PUNCT
ejpam-4771	95	8	v3	v3	PROPN
ejpam-4771	95	9	∈	∈	PROPN
ejpam-4771	95	10	s.	s.	PROPN
ejpam-4771	95	11	in	in	ADP
ejpam-4771	95	12	this	this	DET
ejpam-4771	95	13	case	case	NOUN
ejpam-4771	95	14	,	,	PUNCT
ejpam-4771	95	15	for	for	ADP
ejpam-4771	95	16	n	n	PRON
ejpam-4771	95	17	≥	≥	NOUN
ejpam-4771	95	18	8	8	NUM
ejpam-4771	95	19	,	,	PUNCT
ejpam-4771	95	20	the	the	DET
ejpam-4771	95	21	set	set	NOUN
ejpam-4771	95	22	s	s	PART
ejpam-4771	95	23	′	′	NOUN
ejpam-4771	95	24	=	=	SYM
ejpam-4771	95	25	v	v	NOUN
ejpam-4771	95	26	(	(	PUNCT
ejpam-4771	95	27	pn	pn	NOUN
ejpam-4771	95	28	)	)	PUNCT
ejpam-4771	95	29	\	\	NOUN
ejpam-4771	95	30	{	{	PUNCT
ejpam-4771	95	31	v4	v4	NOUN
ejpam-4771	95	32	,	,	PUNCT
ejpam-4771	95	33	v5	v5	PROPN
ejpam-4771	95	34	}	}	PUNCT
ejpam-4771	95	35	is	be	AUX
ejpam-4771	95	36	clearly	clearly	ADV
ejpam-4771	95	37	an	an	DET
ejpam-4771	95	38	outer	outer	ADV
ejpam-4771	95	39	-	-	PUNCT
ejpam-4771	95	40	connected	connect	VERB
ejpam-4771	95	41	2	2	NUM
ejpam-4771	95	42	-	-	PUNCT
ejpam-4771	95	43	locating	locate	VERB
ejpam-4771	95	44	point	point	NOUN
ejpam-4771	95	45	-	-	PUNCT
ejpam-4771	95	46	wise	wise	ADJ
ejpam-4771	95	47	non	non	ADJ
ejpam-4771	95	48	-	-	ADJ
ejpam-4771	95	49	dominating	dominating	ADJ
ejpam-4771	95	50	set	set	NOUN
ejpam-4771	95	51	.	.	PUNCT
ejpam-4771	96	1	thus	thus	ADV
ejpam-4771	96	2	,	,	PUNCT
ejpam-4771	96	3	l̃npnd	l̃npnd	NOUN
ejpam-4771	96	4	2	2	NUM
ejpam-4771	96	5	(	(	PUNCT
ejpam-4771	96	6	pn	pn	NOUN
ejpam-4771	96	7	)	)	PUNCT
ejpam-4771	96	8	=	=	PUNCT
ejpam-4771	96	9	n−	n−	NOUN
ejpam-4771	96	10	2	2	NUM
ejpam-4771	96	11	for	for	ADP
ejpam-4771	96	12	all	all	DET
ejpam-4771	96	13	n	n	PRON
ejpam-4771	96	14	≥	≥	NOUN
ejpam-4771	96	15	8	8	NUM
ejpam-4771	96	16	.	.	PUNCT
ejpam-4771	96	17	(	(	PUNCT
ejpam-4771	96	18	ii	ii	NOUN
ejpam-4771	96	19	)	)	PUNCT
ejpam-4771	96	20	let	let	VERB
ejpam-4771	96	21	cn	cn	PROPN
ejpam-4771	96	22	=	=	PUNCT
ejpam-4771	97	1	[	[	X
ejpam-4771	97	2	v1	v1	NOUN
ejpam-4771	97	3	,	,	PUNCT
ejpam-4771	97	4	v2	v2	PROPN
ejpam-4771	97	5	,	,	PUNCT
ejpam-4771	97	6	v3	v3	PROPN
ejpam-4771	97	7	,	,	PUNCT
ejpam-4771	97	8	.	.	PUNCT
ejpam-4771	97	9	.	.	PUNCT
ejpam-4771	97	10	.	.	PUNCT
ejpam-4771	98	1	,	,	PUNCT
ejpam-4771	98	2	vn	vn	X
ejpam-4771	98	3	]	]	PUNCT
ejpam-4771	98	4	.	.	PUNCT
ejpam-4771	99	1	clearly	clearly	ADV
ejpam-4771	99	2	,	,	PUNCT
ejpam-4771	99	3	l̃n	l̃n	VERB
ejpam-4771	99	4	pnd	pnd	PROPN
ejpam-4771	99	5	2	2	NUM
ejpam-4771	99	6	(	(	PUNCT
ejpam-4771	99	7	cn	cn	PROPN
ejpam-4771	99	8	)	)	PUNCT
ejpam-4771	99	9	=	=	SYM
ejpam-4771	99	10	n	n	PROPN
ejpam-4771	99	11	for	for	ADP
ejpam-4771	99	12	n	n	NOUN
ejpam-4771	99	13	=	=	SYM
ejpam-4771	99	14	3	3	NUM
ejpam-4771	99	15	,	,	PUNCT
ejpam-4771	99	16	4	4	NUM
ejpam-4771	99	17	.	.	PUNCT
ejpam-4771	100	1	let	let	VERB
ejpam-4771	100	2	n	n	PRON
ejpam-4771	100	3	≥	≥	X
ejpam-4771	100	4	5	5	NUM
ejpam-4771	100	5	and	and	CCONJ
ejpam-4771	100	6	let	let	VERB
ejpam-4771	100	7	s	s	PRON
ejpam-4771	100	8	be	be	AUX
ejpam-4771	100	9	an	an	DET
ejpam-4771	100	10	l̃npnd	l̃npnd	NOUN
ejpam-4771	100	11	2	2	NUM
ejpam-4771	100	12	-set	-set	X
ejpam-4771	100	13	of	of	ADP
ejpam-4771	100	14	cn	cn	PROPN
ejpam-4771	100	15	.	.	PUNCT
ejpam-4771	101	1	since	since	SCONJ
ejpam-4771	101	2	⟨v	⟨v	PROPN
ejpam-4771	101	3	(	(	PUNCT
ejpam-4771	101	4	cn	cn	PROPN
ejpam-4771	101	5	)	)	PUNCT
ejpam-4771	101	6	\	\	PROPN
ejpam-4771	101	7	s⟩	s⟩	PROPN
ejpam-4771	101	8	is	be	AUX
ejpam-4771	101	9	connected	connect	VERB
ejpam-4771	101	10	and	and	CCONJ
ejpam-4771	101	11	s	s	VERB
ejpam-4771	101	12	is	be	AUX
ejpam-4771	101	13	a	a	DET
ejpam-4771	101	14	2	2	NUM
ejpam-4771	101	15	-	-	PUNCT
ejpam-4771	101	16	locating	locate	VERB
ejpam-4771	101	17	point	point	NOUN
ejpam-4771	101	18	-	-	PUNCT
ejpam-4771	101	19	wise	wise	ADJ
ejpam-4771	101	20	a.m.	a.m.	PROPN
ejpam-4771	101	21	mahistrado	mahistrado	PROPN
ejpam-4771	101	22	,	,	PUNCT
ejpam-4771	101	23	h.	h.	PROPN
ejpam-4771	101	24	rara	rara	PROPN
ejpam-4771	101	25	/	/	SYM
ejpam-4771	101	26	eur	eur	PROPN
ejpam-4771	101	27	.	.	PUNCT
ejpam-4771	102	1	j.	j.	PROPN
ejpam-4771	102	2	pure	pure	PROPN
ejpam-4771	102	3	appl	appl	PROPN
ejpam-4771	102	4	.	.	PROPN
ejpam-4771	102	5	math	math	PROPN
ejpam-4771	102	6	,	,	PUNCT
ejpam-4771	102	7	16	16	NUM
ejpam-4771	102	8	(	(	PUNCT
ejpam-4771	102	9	2	2	NUM
ejpam-4771	102	10	)	)	PUNCT
ejpam-4771	102	11	(	(	PUNCT
ejpam-4771	102	12	2023	2023	NUM
ejpam-4771	102	13	)	)	PUNCT
ejpam-4771	102	14	,	,	PUNCT
ejpam-4771	102	15	1180	1180	NUM
ejpam-4771	102	16	-	-	SYM
ejpam-4771	102	17	1195	1195	NUM
ejpam-4771	102	18	1185	1185	NUM
ejpam-4771	102	19	non	non	ADJ
ejpam-4771	102	20	-	-	ADJ
ejpam-4771	102	21	dominating	dominating	ADJ
ejpam-4771	102	22	set	set	NOUN
ejpam-4771	102	23	,	,	PUNCT
ejpam-4771	102	24	|v	|v	PROPN
ejpam-4771	102	25	(	(	PUNCT
ejpam-4771	102	26	cn	cn	PROPN
ejpam-4771	102	27	)	)	PUNCT
ejpam-4771	102	28	\	\	PROPN
ejpam-4771	102	29	s|	s|	NOUN
ejpam-4771	102	30	=	=	SYM
ejpam-4771	103	1	2	2	X
ejpam-4771	103	2	.	.	X
ejpam-4771	103	3	therefore	therefore	ADV
ejpam-4771	103	4	,	,	PUNCT
ejpam-4771	103	5	l̃npnd	l̃npnd	NOUN
ejpam-4771	103	6	2	2	NUM
ejpam-4771	103	7	(	(	PUNCT
ejpam-4771	103	8	cn	cn	NOUN
ejpam-4771	103	9	)	)	PUNCT
ejpam-4771	103	10	=	=	PUNCT
ejpam-4771	103	11	n−	n−	NOUN
ejpam-4771	103	12	2	2	NUM
ejpam-4771	103	13	for	for	ADP
ejpam-4771	103	14	all	all	DET
ejpam-4771	103	15	n	n	PRON
ejpam-4771	103	16	≥	≥	NOUN
ejpam-4771	103	17	5	5	NUM
ejpam-4771	103	18	.	.	PUNCT
ejpam-4771	104	1	the	the	DET
ejpam-4771	104	2	proofs	proof	NOUN
ejpam-4771	104	3	of	of	ADP
ejpam-4771	104	4	(	(	PUNCT
ejpam-4771	104	5	iii	iii	NOUN
ejpam-4771	104	6	)	)	PUNCT
ejpam-4771	104	7	and	and	CCONJ
ejpam-4771	104	8	(	(	PUNCT
ejpam-4771	104	9	iv	iv	X
ejpam-4771	104	10	)	)	PUNCT
ejpam-4771	104	11	are	be	AUX
ejpam-4771	104	12	similar	similar	ADJ
ejpam-4771	104	13	to	to	ADP
ejpam-4771	104	14	(	(	PUNCT
ejpam-4771	104	15	i	i	NOUN
ejpam-4771	104	16	)	)	PUNCT
ejpam-4771	104	17	and	and	CCONJ
ejpam-4771	104	18	(	(	PUNCT
ejpam-4771	104	19	ii	ii	NOUN
ejpam-4771	104	20	)	)	PUNCT
ejpam-4771	104	21	.	.	PUNCT
ejpam-4771	105	1	next	next	ADV
ejpam-4771	105	2	,	,	PUNCT
ejpam-4771	105	3	we	we	PRON
ejpam-4771	105	4	show	show	VERB
ejpam-4771	105	5	that	that	SCONJ
ejpam-4771	105	6	every	every	DET
ejpam-4771	105	7	pair	pair	NOUN
ejpam-4771	105	8	of	of	ADP
ejpam-4771	105	9	positive	positive	ADJ
ejpam-4771	105	10	integers	integer	NOUN
ejpam-4771	105	11	are	be	AUX
ejpam-4771	105	12	realizable	realizable	ADJ
ejpam-4771	105	13	as	as	ADP
ejpam-4771	105	14	2	2	NUM
ejpam-4771	105	15	-	-	PUNCT
ejpam-4771	105	16	resolving	resolve	VERB
ejpam-4771	105	17	hop	hop	NOUN
ejpam-4771	105	18	domination	domination	NOUN
ejpam-4771	105	19	number	number	NOUN
ejpam-4771	105	20	and	and	CCONJ
ejpam-4771	105	21	outer	outer	ADV
ejpam-4771	105	22	-	-	PUNCT
ejpam-4771	105	23	connected	connect	VERB
ejpam-4771	105	24	2	2	NUM
ejpam-4771	105	25	-	-	PUNCT
ejpam-4771	105	26	resolving	resolve	VERB
ejpam-4771	105	27	hop	hop	NOUN
ejpam-4771	105	28	domination	domination	NOUN
ejpam-4771	105	29	number	number	NOUN
ejpam-4771	105	30	.	.	PUNCT
ejpam-4771	106	1	remark	remark	NOUN
ejpam-4771	106	2	2	2	NUM
ejpam-4771	106	3	.	.	PUNCT
ejpam-4771	107	1	every	every	DET
ejpam-4771	107	2	outer	outer	ADV
ejpam-4771	107	3	-	-	PUNCT
ejpam-4771	107	4	connected	connect	VERB
ejpam-4771	107	5	2	2	NUM
ejpam-4771	107	6	-	-	PUNCT
ejpam-4771	107	7	resolving	resolve	VERB
ejpam-4771	107	8	hop	hop	NOUN
ejpam-4771	107	9	dominating	dominating	NOUN
ejpam-4771	107	10	set	set	NOUN
ejpam-4771	107	11	of	of	ADP
ejpam-4771	107	12	g	g	PROPN
ejpam-4771	107	13	is	be	AUX
ejpam-4771	107	14	a	a	DET
ejpam-4771	107	15	2	2	NUM
ejpam-4771	107	16	-	-	PUNCT
ejpam-4771	107	17	resolving	resolve	VERB
ejpam-4771	107	18	hop	hop	NOUN
ejpam-4771	107	19	dominating	dominating	NOUN
ejpam-4771	107	20	set	set	NOUN
ejpam-4771	107	21	of	of	ADP
ejpam-4771	107	22	g.	g.	PROPN
ejpam-4771	107	23	thus	thus	ADV
ejpam-4771	107	24	,	,	PUNCT
ejpam-4771	107	25	γ2rh(g	γ2rh(g	NOUN
ejpam-4771	107	26	)	)	PUNCT
ejpam-4771	107	27	≤	≤	NUM
ejpam-4771	107	28	γ̃c2rh(g	γ̃c2rh(g	NOUN
ejpam-4771	107	29	)	)	PUNCT
ejpam-4771	107	30	.	.	PUNCT
ejpam-4771	108	1	theorem	theorem	NOUN
ejpam-4771	108	2	1	1	NUM
ejpam-4771	108	3	.	.	PUNCT
ejpam-4771	109	1	let	let	VERB
ejpam-4771	109	2	a	a	PRON
ejpam-4771	109	3	and	and	CCONJ
ejpam-4771	109	4	b	b	NOUN
ejpam-4771	109	5	be	be	AUX
ejpam-4771	109	6	positive	positive	ADJ
ejpam-4771	109	7	integers	integer	NOUN
ejpam-4771	109	8	such	such	ADJ
ejpam-4771	109	9	that	that	SCONJ
ejpam-4771	109	10	2	2	NUM
ejpam-4771	109	11	≤	≤	NUM
ejpam-4771	109	12	a	a	DET
ejpam-4771	109	13	≤	≤	PROPN
ejpam-4771	109	14	b.	b.	NOUN
ejpam-4771	110	1	then	then	ADV
ejpam-4771	110	2	there	there	PRON
ejpam-4771	110	3	exists	exist	VERB
ejpam-4771	110	4	a	a	DET
ejpam-4771	110	5	nontrivial	nontrivial	ADJ
ejpam-4771	110	6	connected	connect	VERB
ejpam-4771	110	7	graph	graph	NOUN
ejpam-4771	110	8	g	g	ADP
ejpam-4771	110	9	such	such	ADJ
ejpam-4771	110	10	that	that	DET
ejpam-4771	110	11	γ2rh(g	γ2rh(g	NOUN
ejpam-4771	110	12	)	)	PUNCT
ejpam-4771	110	13	=	=	SYM
ejpam-4771	110	14	a	a	PRON
ejpam-4771	110	15	and	and	CCONJ
ejpam-4771	110	16	γ̃c2rh(g	γ̃c2rh(g	NOUN
ejpam-4771	110	17	)	)	PUNCT
ejpam-4771	110	18	=	=	SYM
ejpam-4771	110	19	b.	b.	PROPN
ejpam-4771	110	20	proof	proof	NOUN
ejpam-4771	110	21	.	.	PUNCT
ejpam-4771	111	1	suppose	suppose	VERB
ejpam-4771	111	2	2	2	NUM
ejpam-4771	111	3	≤	≤	NOUN
ejpam-4771	111	4	a	a	DET
ejpam-4771	111	5	=	=	X
ejpam-4771	111	6	b.	b.	PROPN
ejpam-4771	111	7	consider	consider	VERB
ejpam-4771	111	8	figure	figure	NOUN
ejpam-4771	111	9	1	1	NUM
ejpam-4771	111	10	.	.	PUNCT
ejpam-4771	112	1	then	then	ADV
ejpam-4771	112	2	s	s	VERB
ejpam-4771	112	3	=	=	SYM
ejpam-4771	112	4	{	{	PUNCT
ejpam-4771	112	5	u1	u1	NOUN
ejpam-4771	112	6	,	,	PUNCT
ejpam-4771	112	7	u2	u2	NOUN
ejpam-4771	112	8	,	,	PUNCT
ejpam-4771	112	9	u3	u3	NOUN
ejpam-4771	112	10	,	,	PUNCT
ejpam-4771	112	11	u4	u4	PROPN
ejpam-4771	112	12	,	,	PUNCT
ejpam-4771	112	13	.	.	PUNCT
ejpam-4771	112	14	.	.	PUNCT
ejpam-4771	112	15	.	.	PUNCT
ejpam-4771	113	1	un	un	PROPN
ejpam-4771	113	2	}	}	PUNCT
ejpam-4771	113	3	is	be	AUX
ejpam-4771	113	4	both	both	PRON
ejpam-4771	113	5	a	a	DET
ejpam-4771	113	6	γ2rh	γ2rh	NOUN
ejpam-4771	113	7	-	-	ADJ
ejpam-4771	113	8	set	set	ADJ
ejpam-4771	113	9	and	and	CCONJ
ejpam-4771	113	10	γ̃c2rh	γ̃c2rh	NOUN
ejpam-4771	113	11	-	-	PUNCT
ejpam-4771	113	12	set	set	NOUN
ejpam-4771	113	13	of	of	ADP
ejpam-4771	113	14	g1	g1	NOUN
ejpam-4771	113	15	.	.	PUNCT
ejpam-4771	114	1	hence	hence	ADV
ejpam-4771	114	2	,	,	PUNCT
ejpam-4771	114	3	2	2	NUM
ejpam-4771	114	4	≤	≤	NUM
ejpam-4771	114	5	γ2rh(g1	γ2rh(g1	NUM
ejpam-4771	114	6	)	)	PUNCT
ejpam-4771	114	7	=	=	SYM
ejpam-4771	115	1	γ̃c2rh(g1	γ̃c2rh(g1	PROPN
ejpam-4771	115	2	)	)	PUNCT
ejpam-4771	115	3	=	=	SYM
ejpam-4771	115	4	a	a	DET
ejpam-4771	115	5	=	=	X
ejpam-4771	115	6	b.	b.	PROPN
ejpam-4771	115	7	................................................................................................................	................................................................................................................	PROPN
ejpam-4771	115	8	....................................................................................................................................................	....................................................................................................................................................	PUNCT
ejpam-4771	116	1	....................................................................................................................................................	....................................................................................................................................................	PUNCT
ejpam-4771	116	2	....................................	....................................	PUNCT
ejpam-4771	117	1	...............................................................................................................	...............................................................................................................	PUNCT
ejpam-4771	117	2	....................................	....................................	PUNCT
ejpam-4771	118	1	....................................	....................................	PUNCT
ejpam-4771	118	2	......................................................................................................................................................................................	......................................................................................................................................................................................	PUNCT
ejpam-4771	118	3	....................................	....................................	PUNCT
ejpam-4771	119	1	....................................	....................................	PUNCT
ejpam-4771	119	2	............	............	PUNCT
ejpam-4771	119	3	...........	...........	PUNCT
ejpam-4771	119	4	...........	...........	PUNCT
ejpam-4771	119	5	...........	...........	PUNCT
ejpam-4771	119	6	...........	...........	PUNCT
ejpam-4771	119	7	...........	...........	PUNCT
ejpam-4771	119	8	...........	...........	PUNCT
ejpam-4771	119	9	...........	...........	PUNCT
ejpam-4771	119	10	...........	...........	PUNCT
ejpam-4771	119	11	...........	...........	PUNCT
ejpam-4771	119	12	....................................	....................................	PUNCT
ejpam-4771	119	13	....................................	....................................	PUNCT
ejpam-4771	120	1	..........	..........	PUNCT
ejpam-4771	120	2	.........	.........	PUNCT
ejpam-4771	121	1	.........	.........	PUNCT
ejpam-4771	121	2	.........	.........	PUNCT
ejpam-4771	122	1	.........	.........	PUNCT
ejpam-4771	122	2	.........	.........	PUNCT
ejpam-4771	123	1	.........	.........	PUNCT
ejpam-4771	123	2	.........	.........	PUNCT
ejpam-4771	124	1	.........	.........	PUNCT
ejpam-4771	124	2	.........	.........	PUNCT
ejpam-4771	125	1	.........	.........	PUNCT
ejpam-4771	125	2	.........	.........	PUNCT
ejpam-4771	126	1	.........	.........	PUNCT
ejpam-4771	126	2	.........	.........	PUNCT
ejpam-4771	127	1	.........	.........	PUNCT
ejpam-4771	127	2	.........	.........	PUNCT
ejpam-4771	128	1	.........	.........	PUNCT
ejpam-4771	128	2	.........	.........	PUNCT
ejpam-4771	129	1	.........	.........	PUNCT
ejpam-4771	129	2	.........	.........	PUNCT
ejpam-4771	129	3	.	.	PUNCT
ejpam-4771	130	1	....................................	....................................	PUNCT
ejpam-4771	131	1	....................................	....................................	PUNCT
ejpam-4771	131	2	u1	u1	PROPN
ejpam-4771	131	3	u2	u2	PROPN
ejpam-4771	131	4	u3	u3	PROPN
ejpam-4771	131	5	u4	u4	PROPN
ejpam-4771	131	6	u5	u5	PROPN
ejpam-4771	131	7	un	un	PROPN
ejpam-4771	132	1	•	•	NUM
ejpam-4771	132	2	•	•	NUM
ejpam-4771	132	3	•	•	NUM
ejpam-4771	132	4	•	•	NUM
ejpam-4771	132	5	•	•	NOUN
ejpam-4771	132	6	•	•	NOUN
ejpam-4771	132	7	...	...	PUNCT
ejpam-4771	132	8	g1	g1	NOUN
ejpam-4771	132	9	:	:	PUNCT
ejpam-4771	132	10	figure	figure	NOUN
ejpam-4771	132	11	1	1	NUM
ejpam-4771	132	12	suppose	suppose	VERB
ejpam-4771	132	13	2	2	NUM
ejpam-4771	132	14	<	<	X
ejpam-4771	132	15	a	a	DET
ejpam-4771	132	16	<	<	X
ejpam-4771	132	17	b.	b.	NOUN
ejpam-4771	132	18	consider	consider	VERB
ejpam-4771	132	19	the	the	DET
ejpam-4771	132	20	graph	graph	NOUN
ejpam-4771	132	21	g2	g2	PROPN
ejpam-4771	132	22	in	in	ADP
ejpam-4771	132	23	figure	figure	NOUN
ejpam-4771	132	24	2	2	NUM
ejpam-4771	132	25	.	.	PUNCT
ejpam-4771	133	1	then	then	ADV
ejpam-4771	133	2	s	s	VERB
ejpam-4771	133	3	=	=	PUNCT
ejpam-4771	133	4	{	{	PUNCT
ejpam-4771	133	5	x1	x1	PROPN
ejpam-4771	133	6	,	,	PUNCT
ejpam-4771	133	7	x2	x2	PROPN
ejpam-4771	133	8	,	,	PUNCT
ejpam-4771	133	9	.	.	PUNCT
ejpam-4771	133	10	.	.	PUNCT
ejpam-4771	133	11	.	.	PUNCT
ejpam-4771	134	1	,	,	PUNCT
ejpam-4771	134	2	xa	xa	PROPN
ejpam-4771	134	3	}	}	PUNCT
ejpam-4771	134	4	is	be	AUX
ejpam-4771	134	5	a	a	DET
ejpam-4771	134	6	γ2rh	γ2rh	NOUN
ejpam-4771	134	7	-	-	PUNCT
ejpam-4771	134	8	set	set	NOUN
ejpam-4771	134	9	of	of	ADP
ejpam-4771	134	10	g2	g2	PROPN
ejpam-4771	134	11	and	and	CCONJ
ejpam-4771	134	12	x	x	X
ejpam-4771	134	13	=	=	X
ejpam-4771	134	14	s	s	NOUN
ejpam-4771	134	15	∪	∪	X
ejpam-4771	134	16	{	{	PUNCT
ejpam-4771	134	17	y1	y1	NOUN
ejpam-4771	134	18	,	,	PUNCT
ejpam-4771	134	19	y2	y2	PROPN
ejpam-4771	134	20	,	,	PUNCT
ejpam-4771	134	21	.	.	PUNCT
ejpam-4771	134	22	.	.	PUNCT
ejpam-4771	135	1	.	.	PUNCT
ejpam-4771	136	1	,	,	PUNCT
ejpam-4771	136	2	yb−a	yb−a	PRON
ejpam-4771	136	3	}	}	PUNCT
ejpam-4771	136	4	is	be	AUX
ejpam-4771	136	5	a	a	DET
ejpam-4771	136	6	γ̃c2rh	γ̃c2rh	NOUN
ejpam-4771	136	7	-	-	PUNCT
ejpam-4771	136	8	set	set	NOUN
ejpam-4771	136	9	of	of	ADP
ejpam-4771	136	10	g2	g2	PROPN
ejpam-4771	136	11	.	.	PUNCT
ejpam-4771	137	1	hence	hence	ADV
ejpam-4771	137	2	γ2rh(g2	γ2rh(g2	X
ejpam-4771	137	3	)	)	PUNCT
ejpam-4771	137	4	=	=	SYM
ejpam-4771	137	5	a	a	PROPN
ejpam-4771	137	6	and	and	CCONJ
ejpam-4771	137	7	γ̃c2rh(g2	γ̃c2rh(g2	PROPN
ejpam-4771	137	8	)	)	PUNCT
ejpam-4771	138	1	=	=	SYM
ejpam-4771	138	2	|x|	|x|	PROPN
ejpam-4771	138	3	=	=	SYM
ejpam-4771	138	4	|s|+	|s|+	PROPN
ejpam-4771	138	5	(	(	PUNCT
ejpam-4771	138	6	b−	b−	NOUN
ejpam-4771	138	7	a	a	NOUN
ejpam-4771	138	8	)	)	PUNCT
ejpam-4771	138	9	=	=	NOUN
ejpam-4771	138	10	a+	a+	PUNCT
ejpam-4771	138	11	b−	b−	PROPN
ejpam-4771	138	12	a	a	DET
ejpam-4771	138	13	=	=	X
ejpam-4771	138	14	b.	b.	PROPN
ejpam-4771	138	15	...........	...........	PUNCT
ejpam-4771	138	16	..........	..........	PUNCT
ejpam-4771	138	17	..........	..........	PUNCT
ejpam-4771	139	1	..........	..........	PUNCT
ejpam-4771	139	2	..........	..........	PUNCT
ejpam-4771	140	1	..........	..........	PUNCT
ejpam-4771	140	2	.	.	PUNCT
ejpam-4771	141	1	....................................	....................................	PUNCT
ejpam-4771	141	2	....................................	....................................	PUNCT
ejpam-4771	142	1	...........	...........	PUNCT
ejpam-4771	142	2	..........	..........	PUNCT
ejpam-4771	143	1	..........	..........	PUNCT
ejpam-4771	143	2	..........	..........	PUNCT
ejpam-4771	144	1	..........	..........	PUNCT
ejpam-4771	144	2	..........	..........	PUNCT
ejpam-4771	144	3	.	.	PUNCT
ejpam-4771	145	1	....................................	....................................	PUNCT
ejpam-4771	145	2	....................................	....................................	PUNCT
ejpam-4771	146	1	..............................................................	..............................................................	PUNCT
ejpam-4771	146	2	....................................	....................................	PUNCT
ejpam-4771	147	1	....................................	....................................	PUNCT
ejpam-4771	147	2	..............................................................	..............................................................	PUNCT
ejpam-4771	148	1	....................................	....................................	PUNCT
ejpam-4771	148	2	....................................	....................................	PUNCT
ejpam-4771	148	3	.........	.........	PUNCT
ejpam-4771	149	1	........	........	PUNCT
ejpam-4771	149	2	........	........	PUNCT
ejpam-4771	149	3	........	........	PUNCT
ejpam-4771	149	4	........	........	PUNCT
ejpam-4771	150	1	......	......	PUNCT
ejpam-4771	150	2	....................................	....................................	PUNCT
ejpam-4771	151	1	....................................	....................................	PUNCT
ejpam-4771	151	2	.........	.........	PUNCT
ejpam-4771	151	3	........	........	PUNCT
ejpam-4771	151	4	........	........	PUNCT
ejpam-4771	151	5	........	........	PUNCT
ejpam-4771	151	6	........	........	PUNCT
ejpam-4771	152	1	......	......	PUNCT
ejpam-4771	152	2	....................................	....................................	PUNCT
ejpam-4771	153	1	....................................	....................................	PUNCT
ejpam-4771	153	2	..........................	..........................	PUNCT
ejpam-4771	154	1	.........................	.........................	PUNCT
ejpam-4771	154	2	.........................	.........................	PUNCT
ejpam-4771	155	1	....	....	PUNCT
ejpam-4771	155	2	....................................	....................................	PUNCT
ejpam-4771	156	1	....................................	....................................	PUNCT
ejpam-4771	156	2	....................	....................	PUNCT
ejpam-4771	157	1	...................	...................	PUNCT
ejpam-4771	157	2	..............	..............	PUNCT
ejpam-4771	158	1	....................................	....................................	PUNCT
ejpam-4771	158	2	....................................	....................................	PUNCT
ejpam-4771	158	3	......................................................................................	......................................................................................	PUNCT
ejpam-4771	159	1	....................................	....................................	PUNCT
ejpam-4771	159	2	....................................	....................................	PUNCT
ejpam-4771	160	1	...................................................	...................................................	PUNCT
ejpam-4771	160	2	....................................	....................................	PUNCT
ejpam-4771	161	1	....................................	....................................	PUNCT
ejpam-4771	161	2	............................................................................................................................	............................................................................................................................	PUNCT
ejpam-4771	162	1	........................................................................................................................................................................................................................................	........................................................................................................................................................................................................................................	PUNCT
ejpam-4771	162	2	....................................	....................................	PUNCT
ejpam-4771	163	1	..............................................................	..............................................................	PUNCT
ejpam-4771	163	2	....................................	....................................	PUNCT
ejpam-4771	164	1	....................................	....................................	PUNCT
ejpam-4771	164	2	.....................	.....................	PUNCT
ejpam-4771	164	3	....................	....................	PUNCT
ejpam-4771	164	4	....................	....................	PUNCT
ejpam-4771	164	5	.	.	PUNCT
ejpam-4771	165	1	.......	.......	PUNCT
ejpam-4771	165	2	.............................	.............................	PUNCT
ejpam-4771	166	1	....................................	....................................	PUNCT
ejpam-4771	166	2	...................................................	...................................................	PUNCT
ejpam-4771	167	1	....................................	....................................	PUNCT
ejpam-4771	167	2	.......................................................................................	.......................................................................................	PUNCT
ejpam-4771	168	1	....................................	....................................	PUNCT
ejpam-4771	168	2	.....................................................................................................	.....................................................................................................	PUNCT
ejpam-4771	169	1	....................................	....................................	PUNCT
ejpam-4771	169	2	....................................	....................................	PUNCT
ejpam-4771	169	3	............	............	PUNCT
ejpam-4771	169	4	...........	...........	PUNCT
ejpam-4771	169	5	...........	...........	PUNCT
ejpam-4771	169	6	...........	...........	PUNCT
ejpam-4771	169	7	......	......	PUNCT
ejpam-4771	169	8	.	.	PUNCT
ejpam-4771	170	1	...................................	...................................	PUNCT
ejpam-4771	170	2	....................................	....................................	PUNCT
ejpam-4771	170	3	............	............	PUNCT
ejpam-4771	171	1	...........	...........	PUNCT
ejpam-4771	171	2	...........	...........	PUNCT
ejpam-4771	171	3	...........	...........	PUNCT
ejpam-4771	171	4	......	......	PUNCT
ejpam-4771	171	5	.	.	PUNCT
ejpam-4771	172	1	...................................	...................................	PUNCT
ejpam-4771	172	2	....................................	....................................	PUNCT
ejpam-4771	172	3	............	............	PUNCT
ejpam-4771	172	4	...........	...........	PUNCT
ejpam-4771	172	5	...........	...........	PUNCT
ejpam-4771	172	6	...........	...........	PUNCT
ejpam-4771	172	7	...........	...........	PUNCT
ejpam-4771	172	8	.........	.........	PUNCT
ejpam-4771	173	1	....................................	....................................	PUNCT
ejpam-4771	173	2	....................................	....................................	PUNCT
ejpam-4771	173	3	.........	.........	PUNCT
ejpam-4771	173	4	........	........	PUNCT
ejpam-4771	173	5	........	........	PUNCT
ejpam-4771	173	6	........	........	PUNCT
ejpam-4771	174	1	....................................	....................................	PUNCT
ejpam-4771	174	2	....................................	....................................	PUNCT
ejpam-4771	174	3	.........	.........	PUNCT
ejpam-4771	174	4	........	........	PUNCT
ejpam-4771	174	5	........	........	PUNCT
ejpam-4771	174	6	........	........	PUNCT
ejpam-4771	175	1	....................................	....................................	PUNCT
ejpam-4771	175	2	....................................	....................................	PUNCT
ejpam-4771	175	3	.........	.........	PUNCT
ejpam-4771	175	4	........	........	PUNCT
ejpam-4771	175	5	........	........	PUNCT
ejpam-4771	175	6	........	........	PUNCT
ejpam-4771	176	1	........	........	PUNCT
ejpam-4771	176	2	......	......	PUNCT
ejpam-4771	177	1	....................................	....................................	PUNCT
ejpam-4771	177	2	....................................	....................................	PUNCT
ejpam-4771	178	1	................................................................................	................................................................................	PUNCT
ejpam-4771	178	2	....................................	....................................	PUNCT
ejpam-4771	179	1	..............................................................................	..............................................................................	PUNCT
ejpam-4771	179	2	....................................	....................................	PUNCT
ejpam-4771	179	3	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-4771	180	1	....................................	....................................	PUNCT
ejpam-4771	180	2	....................................	....................................	PUNCT
ejpam-4771	181	1	..........................	..........................	PUNCT
ejpam-4771	181	2	.........................	.........................	PUNCT
ejpam-4771	182	1	.........................	.........................	PUNCT
ejpam-4771	182	2	....	....	PUNCT
ejpam-4771	183	1	....................................	....................................	PUNCT
ejpam-4771	183	2	....................................	....................................	PUNCT
ejpam-4771	183	3	...............	...............	PUNCT
ejpam-4771	184	1	..............	..............	PUNCT
ejpam-4771	184	2	.............	.............	PUNCT
ejpam-4771	185	1	....................................	....................................	PUNCT
ejpam-4771	185	2	....................................	....................................	PUNCT
ejpam-4771	186	1	..............	..............	PUNCT
ejpam-4771	186	2	.............	.............	PUNCT
ejpam-4771	186	3	.............	.............	PUNCT
ejpam-4771	186	4	.............	.............	PUNCT
ejpam-4771	186	5	.............	.............	PUNCT
ejpam-4771	186	6	.............	.............	PUNCT
ejpam-4771	186	7	...	...	PUNCT
ejpam-4771	186	8	...	...	PUNCT
ejpam-4771	186	9	.................................	.................................	PUNCT
ejpam-4771	187	1	....................................	....................................	PUNCT
ejpam-4771	188	1	x1	x1	NUM
ejpam-4771	189	1	x2	x2	NOUN
ejpam-4771	189	2	x3	x3	PROPN
ejpam-4771	189	3	x5	x5	PROPN
ejpam-4771	189	4	x4	x4	PROPN
ejpam-4771	189	5	y1	y1	ADJ
ejpam-4771	189	6	y2	y2	NOUN
ejpam-4771	189	7	y3	y3	NOUN
ejpam-4771	189	8	y4	y4	ADJ
ejpam-4771	189	9	yb−ax6	yb−ax6	NOUN
ejpam-4771	190	1	x7	x7	ADP
ejpam-4771	190	2	x8	x8	PROPN
ejpam-4771	190	3	x9	x9	PROPN
ejpam-4771	190	4	xa	xa	PROPN
ejpam-4771	190	5	xa−1	xa−1	PROPN
ejpam-4771	190	6	•	•	PROPN
ejpam-4771	191	1	•••	•••	ADV
ejpam-4771	191	2	•	•	NOUN
ejpam-4771	191	3	•	•	NOUN
ejpam-4771	191	4	.	.	PUNCT
ejpam-4771	191	5	.	.	PUNCT
ejpam-4771	192	1	.	.	PUNCT
ejpam-4771	193	1	•	•	NUM
ejpam-4771	194	1	•••	•••	ADV
ejpam-4771	194	2	•	•	NUM
ejpam-4771	194	3	•	•	NOUN
ejpam-4771	194	4	••	••	NOUN
ejpam-4771	194	5	•	•	NUM
ejpam-4771	194	6	•	•	NUM
ejpam-4771	194	7	•	•	NOUN
ejpam-4771	194	8	•	•	NOUN
ejpam-4771	194	9	.	.	PUNCT
ejpam-4771	194	10	.	.	PUNCT
ejpam-4771	194	11	.	.	PUNCT
ejpam-4771	194	12	.	.	PUNCT
ejpam-4771	194	13	.	.	PUNCT
ejpam-4771	195	1	.	.	PUNCT
ejpam-4771	196	1	figure	figure	NOUN
ejpam-4771	196	2	2	2	NUM
ejpam-4771	196	3	g2	g2	PROPN
ejpam-4771	196	4	:	:	PUNCT
ejpam-4771	196	5	corollary	corollary	ADJ
ejpam-4771	196	6	1	1	NUM
ejpam-4771	196	7	.	.	PUNCT
ejpam-4771	197	1	for	for	ADP
ejpam-4771	197	2	each	each	DET
ejpam-4771	197	3	positive	positive	ADJ
ejpam-4771	197	4	integer	integer	NOUN
ejpam-4771	197	5	n	n	CCONJ
ejpam-4771	197	6	,	,	PUNCT
ejpam-4771	197	7	there	there	PRON
ejpam-4771	197	8	exists	exist	VERB
ejpam-4771	197	9	a	a	DET
ejpam-4771	197	10	connected	connected	ADJ
ejpam-4771	197	11	graph	graph	NOUN
ejpam-4771	197	12	g	g	ADP
ejpam-4771	197	13	such	such	ADJ
ejpam-4771	197	14	that	that	DET
ejpam-4771	197	15	γ̃c2rh(g)−	γ̃c2rh(g)−	NOUN
ejpam-4771	197	16	γ2rh(g	γ2rh(g	PROPN
ejpam-4771	197	17	)	)	PUNCT
ejpam-4771	197	18	=	=	SYM
ejpam-4771	198	1	n	n	CCONJ
ejpam-4771	198	2	,	,	PUNCT
ejpam-4771	198	3	that	that	ADV
ejpam-4771	198	4	is	is	ADV
ejpam-4771	198	5	,	,	PUNCT
ejpam-4771	198	6	γ̃c2rh	γ̃c2rh	CCONJ
ejpam-4771	198	7	−	−	PROPN
ejpam-4771	198	8	γ2rh	γ2rh	X
ejpam-4771	198	9	can	can	AUX
ejpam-4771	198	10	be	be	AUX
ejpam-4771	198	11	made	make	VERB
ejpam-4771	198	12	arbitrarily	arbitrarily	ADV
ejpam-4771	198	13	large	large	ADJ
ejpam-4771	198	14	.	.	PUNCT
ejpam-4771	199	1	we	we	PRON
ejpam-4771	199	2	now	now	ADV
ejpam-4771	199	3	characterize	characterize	VERB
ejpam-4771	199	4	the	the	DET
ejpam-4771	199	5	outer	outer	ADV
ejpam-4771	199	6	-	-	PUNCT
ejpam-4771	199	7	connected	connect	VERB
ejpam-4771	199	8	2	2	NUM
ejpam-4771	199	9	-	-	PUNCT
ejpam-4771	199	10	resolving	resolve	VERB
ejpam-4771	199	11	hop	hop	NOUN
ejpam-4771	199	12	dominating	dominating	NOUN
ejpam-4771	199	13	sets	set	NOUN
ejpam-4771	199	14	in	in	ADP
ejpam-4771	199	15	some	some	DET
ejpam-4771	199	16	graphs	graph	NOUN
ejpam-4771	199	17	under	under	ADP
ejpam-4771	199	18	some	some	DET
ejpam-4771	199	19	binary	binary	ADJ
ejpam-4771	199	20	operations	operation	NOUN
ejpam-4771	199	21	.	.	PUNCT
ejpam-4771	200	1	a.m.	a.m.	PROPN
ejpam-4771	200	2	mahistrado	mahistrado	PROPN
ejpam-4771	200	3	,	,	PUNCT
ejpam-4771	200	4	h.	h.	PROPN
ejpam-4771	200	5	rara	rara	PROPN
ejpam-4771	200	6	/	/	SYM
ejpam-4771	200	7	eur	eur	PROPN
ejpam-4771	200	8	.	.	PUNCT
ejpam-4771	201	1	j.	j.	PROPN
ejpam-4771	201	2	pure	pure	PROPN
ejpam-4771	201	3	appl	appl	PROPN
ejpam-4771	201	4	.	.	PROPN
ejpam-4771	201	5	math	math	PROPN
ejpam-4771	201	6	,	,	PUNCT
ejpam-4771	201	7	16	16	NUM
ejpam-4771	201	8	(	(	PUNCT
ejpam-4771	201	9	2	2	NUM
ejpam-4771	201	10	)	)	PUNCT
ejpam-4771	201	11	(	(	PUNCT
ejpam-4771	201	12	2023	2023	NUM
ejpam-4771	201	13	)	)	PUNCT
ejpam-4771	201	14	,	,	PUNCT
ejpam-4771	201	15	1180	1180	NUM
ejpam-4771	201	16	-	-	SYM
ejpam-4771	201	17	1195	1195	NUM
ejpam-4771	201	18	1186	1186	NUM
ejpam-4771	201	19	4	4	NUM
ejpam-4771	201	20	.	.	X
ejpam-4771	201	21	join	join	VERB
ejpam-4771	201	22	of	of	ADP
ejpam-4771	201	23	graphs	graph	NOUN
ejpam-4771	201	24	this	this	DET
ejpam-4771	201	25	section	section	NOUN
ejpam-4771	201	26	presents	present	VERB
ejpam-4771	201	27	characterizations	characterization	NOUN
ejpam-4771	201	28	in	in	ADP
ejpam-4771	201	29	the	the	DET
ejpam-4771	201	30	outer	outer	ADV
ejpam-4771	201	31	-	-	PUNCT
ejpam-4771	201	32	connected	connect	VERB
ejpam-4771	201	33	2	2	NUM
ejpam-4771	201	34	-	-	PUNCT
ejpam-4771	201	35	resolving	resolve	VERB
ejpam-4771	201	36	hop	hop	NOUN
ejpam-4771	201	37	dominating	dominating	NOUN
ejpam-4771	201	38	sets	set	NOUN
ejpam-4771	201	39	in	in	ADP
ejpam-4771	201	40	the	the	DET
ejpam-4771	201	41	join	join	NOUN
ejpam-4771	201	42	of	of	ADP
ejpam-4771	201	43	graphs	graph	NOUN
ejpam-4771	201	44	.	.	PUNCT
ejpam-4771	202	1	theorem	theorem	NOUN
ejpam-4771	202	2	2	2	NUM
ejpam-4771	202	3	.	.	PUNCT
ejpam-4771	203	1	[	[	X
ejpam-4771	203	2	12	12	NUM
ejpam-4771	203	3	]	]	PUNCT
ejpam-4771	203	4	let	let	VERB
ejpam-4771	203	5	g	g	PRON
ejpam-4771	203	6	be	be	AUX
ejpam-4771	203	7	a	a	DET
ejpam-4771	203	8	connected	connected	ADJ
ejpam-4771	203	9	graph	graph	NOUN
ejpam-4771	203	10	and	and	CCONJ
ejpam-4771	203	11	let	let	VERB
ejpam-4771	203	12	k1	k1	NOUN
ejpam-4771	203	13	=	=	SYM
ejpam-4771	203	14	{	{	PUNCT
ejpam-4771	203	15	x	x	NOUN
ejpam-4771	203	16	}	}	PUNCT
ejpam-4771	203	17	.	.	PUNCT
ejpam-4771	204	1	then	then	ADV
ejpam-4771	204	2	s	s	VERB
ejpam-4771	204	3	⊆	⊆	NUM
ejpam-4771	204	4	v	v	NOUN
ejpam-4771	204	5	(	(	PUNCT
ejpam-4771	204	6	k1	k1	NOUN
ejpam-4771	204	7	+	+	NOUN
ejpam-4771	204	8	g	g	NOUN
ejpam-4771	204	9	)	)	PUNCT
ejpam-4771	204	10	is	be	AUX
ejpam-4771	204	11	a	a	DET
ejpam-4771	204	12	2	2	NUM
ejpam-4771	204	13	-	-	PUNCT
ejpam-4771	204	14	resolving	resolve	VERB
ejpam-4771	204	15	hop	hop	NOUN
ejpam-4771	204	16	dominating	dominating	NOUN
ejpam-4771	204	17	set	set	VERB
ejpam-4771	204	18	in	in	ADP
ejpam-4771	204	19	k1	k1	NOUN
ejpam-4771	204	20	+	+	CCONJ
ejpam-4771	204	21	g	g	NOUN
ejpam-4771	204	22	if	if	SCONJ
ejpam-4771	205	1	and	and	CCONJ
ejpam-4771	205	2	only	only	ADV
ejpam-4771	205	3	if	if	SCONJ
ejpam-4771	205	4	s	s	AUX
ejpam-4771	205	5	=	=	X
ejpam-4771	205	6	{	{	PUNCT
ejpam-4771	205	7	x	x	NOUN
ejpam-4771	205	8	}	}	PUNCT
ejpam-4771	205	9	∪	∪	ADP
ejpam-4771	205	10	t	t	PROPN
ejpam-4771	205	11	where	where	SCONJ
ejpam-4771	205	12	t	t	PROPN
ejpam-4771	205	13	is	be	AUX
ejpam-4771	205	14	a	a	DET
ejpam-4771	205	15	(	(	PUNCT
ejpam-4771	205	16	2	2	NUM
ejpam-4771	205	17	,	,	PUNCT
ejpam-4771	205	18	1)-locating	1)-locating	NUM
ejpam-4771	205	19	point	point	NOUN
ejpam-4771	205	20	-	-	PUNCT
ejpam-4771	205	21	wise	wise	ADJ
ejpam-4771	205	22	non	non	ADJ
ejpam-4771	205	23	-	-	ADJ
ejpam-4771	205	24	dominating	dominating	ADJ
ejpam-4771	205	25	set	set	NOUN
ejpam-4771	205	26	in	in	ADP
ejpam-4771	205	27	g.	g.	PROPN
ejpam-4771	205	28	theorem	theorem	PROPN
ejpam-4771	205	29	3	3	X
ejpam-4771	205	30	.	.	PUNCT
ejpam-4771	206	1	let	let	VERB
ejpam-4771	206	2	g	g	PRON
ejpam-4771	206	3	be	be	AUX
ejpam-4771	206	4	a	a	DET
ejpam-4771	206	5	connected	connected	ADJ
ejpam-4771	206	6	graph	graph	NOUN
ejpam-4771	206	7	and	and	CCONJ
ejpam-4771	206	8	let	let	VERB
ejpam-4771	206	9	k1	k1	NOUN
ejpam-4771	206	10	=	=	SYM
ejpam-4771	206	11	{	{	PUNCT
ejpam-4771	206	12	x	x	NOUN
ejpam-4771	206	13	}	}	PUNCT
ejpam-4771	206	14	.	.	PUNCT
ejpam-4771	207	1	then	then	ADV
ejpam-4771	207	2	s	s	VERB
ejpam-4771	207	3	⊆	⊆	NUM
ejpam-4771	207	4	v	v	NOUN
ejpam-4771	207	5	(	(	PUNCT
ejpam-4771	207	6	k1	k1	NOUN
ejpam-4771	207	7	+	+	CCONJ
ejpam-4771	207	8	g	g	NOUN
ejpam-4771	207	9	)	)	PUNCT
ejpam-4771	207	10	is	be	AUX
ejpam-4771	207	11	an	an	DET
ejpam-4771	207	12	outer	outer	ADV
ejpam-4771	207	13	-	-	PUNCT
ejpam-4771	207	14	connected	connect	VERB
ejpam-4771	207	15	2	2	NUM
ejpam-4771	207	16	-	-	PUNCT
ejpam-4771	207	17	resolving	resolve	VERB
ejpam-4771	207	18	hop	hop	NOUN
ejpam-4771	207	19	dominating	dominating	NOUN
ejpam-4771	207	20	set	set	VERB
ejpam-4771	207	21	in	in	ADP
ejpam-4771	207	22	k1	k1	NOUN
ejpam-4771	208	1	+	+	ADP
ejpam-4771	208	2	g	g	PROPN
ejpam-4771	208	3	if	if	SCONJ
ejpam-4771	208	4	and	and	CCONJ
ejpam-4771	208	5	only	only	ADV
ejpam-4771	208	6	if	if	SCONJ
ejpam-4771	208	7	s	s	AUX
ejpam-4771	208	8	=	=	X
ejpam-4771	208	9	{	{	PUNCT
ejpam-4771	208	10	x	x	NOUN
ejpam-4771	208	11	}	}	PUNCT
ejpam-4771	208	12	∪	∪	ADP
ejpam-4771	208	13	t	t	PROPN
ejpam-4771	208	14	where	where	SCONJ
ejpam-4771	208	15	t	t	PROPN
ejpam-4771	208	16	is	be	AUX
ejpam-4771	208	17	an	an	DET
ejpam-4771	208	18	outer	outer	ADV
ejpam-4771	208	19	-	-	PUNCT
ejpam-4771	208	20	connected	connect	VERB
ejpam-4771	208	21	(	(	PUNCT
ejpam-4771	208	22	2	2	NUM
ejpam-4771	208	23	,	,	PUNCT
ejpam-4771	208	24	1)-locating	1)-locating	NUM
ejpam-4771	208	25	point	point	NOUN
ejpam-4771	208	26	-	-	PUNCT
ejpam-4771	208	27	wise	wise	ADJ
ejpam-4771	208	28	non	non	ADJ
ejpam-4771	208	29	-	-	ADJ
ejpam-4771	208	30	dominating	dominating	ADJ
ejpam-4771	208	31	set	set	NOUN
ejpam-4771	208	32	in	in	ADP
ejpam-4771	208	33	g.	g.	PROPN
ejpam-4771	208	34	proof	proof	PROPN
ejpam-4771	208	35	.	.	PUNCT
ejpam-4771	209	1	let	let	VERB
ejpam-4771	209	2	s	s	PRON
ejpam-4771	209	3	⊆	⊆	NUM
ejpam-4771	209	4	v	v	NOUN
ejpam-4771	209	5	(	(	PUNCT
ejpam-4771	209	6	k1	k1	NOUN
ejpam-4771	209	7	+	+	CCONJ
ejpam-4771	209	8	g	g	NOUN
ejpam-4771	209	9	)	)	PUNCT
ejpam-4771	209	10	be	be	VERB
ejpam-4771	209	11	an	an	DET
ejpam-4771	209	12	outer	outer	ADV
ejpam-4771	209	13	-	-	PUNCT
ejpam-4771	209	14	connected	connect	VERB
ejpam-4771	209	15	2	2	NUM
ejpam-4771	209	16	-	-	PUNCT
ejpam-4771	209	17	resolving	resolve	VERB
ejpam-4771	209	18	hop	hop	NOUN
ejpam-4771	209	19	dominating	dominating	NOUN
ejpam-4771	209	20	set	set	VERB
ejpam-4771	209	21	in	in	ADP
ejpam-4771	209	22	k1	k1	PROPN
ejpam-4771	209	23	+	+	CCONJ
ejpam-4771	210	1	g.	g.	PROPN
ejpam-4771	211	1	then	then	ADV
ejpam-4771	211	2	s	s	VERB
ejpam-4771	211	3	is	be	AUX
ejpam-4771	211	4	a	a	DET
ejpam-4771	211	5	2	2	NUM
ejpam-4771	211	6	-	-	PUNCT
ejpam-4771	211	7	resolving	resolve	VERB
ejpam-4771	211	8	hop	hop	NOUN
ejpam-4771	211	9	dominating	dominating	NOUN
ejpam-4771	211	10	set	set	VERB
ejpam-4771	211	11	in	in	ADP
ejpam-4771	211	12	k1	k1	PROPN
ejpam-4771	211	13	+	+	CCONJ
ejpam-4771	211	14	g.	g.	PROPN
ejpam-4771	211	15	then	then	ADV
ejpam-4771	211	16	by	by	ADP
ejpam-4771	211	17	theorem	theorem	NOUN
ejpam-4771	211	18	2	2	NUM
ejpam-4771	211	19	,	,	PUNCT
ejpam-4771	211	20	s	s	PART
ejpam-4771	211	21	=	=	PUNCT
ejpam-4771	211	22	{	{	PUNCT
ejpam-4771	211	23	x	x	NOUN
ejpam-4771	211	24	}	}	PUNCT
ejpam-4771	211	25	∪	∪	ADP
ejpam-4771	211	26	t	t	PROPN
ejpam-4771	211	27	where	where	SCONJ
ejpam-4771	211	28	t	t	PROPN
ejpam-4771	211	29	is	be	AUX
ejpam-4771	211	30	a	a	DET
ejpam-4771	211	31	(	(	PUNCT
ejpam-4771	211	32	2,1)-locating	2,1)-locating	NUM
ejpam-4771	211	33	point	point	ADV
ejpam-4771	211	34	-	-	PUNCT
ejpam-4771	211	35	wise	wise	ADJ
ejpam-4771	211	36	non	non	ADJ
ejpam-4771	211	37	-	-	ADJ
ejpam-4771	211	38	dominating	dominating	ADJ
ejpam-4771	211	39	set	set	NOUN
ejpam-4771	211	40	in	in	ADP
ejpam-4771	211	41	g.	g.	PROPN
ejpam-4771	211	42	now	now	ADV
ejpam-4771	211	43	,	,	PUNCT
ejpam-4771	211	44	since	since	SCONJ
ejpam-4771	211	45	s	s	NOUN
ejpam-4771	211	46	is	be	AUX
ejpam-4771	211	47	an	an	DET
ejpam-4771	211	48	outer	outer	ADV
ejpam-4771	211	49	-	-	PUNCT
ejpam-4771	211	50	connected	connect	VERB
ejpam-4771	211	51	2	2	NUM
ejpam-4771	211	52	-	-	PUNCT
ejpam-4771	211	53	resolving	resolve	VERB
ejpam-4771	211	54	hop	hop	NOUN
ejpam-4771	211	55	dominating	dominating	NOUN
ejpam-4771	211	56	set	set	VERB
ejpam-4771	211	57	in	in	ADP
ejpam-4771	211	58	k1	k1	NOUN
ejpam-4771	211	59	+	+	CCONJ
ejpam-4771	211	60	g	g	NOUN
ejpam-4771	211	61	,	,	PUNCT
ejpam-4771	211	62	it	it	PRON
ejpam-4771	211	63	follows	follow	VERB
ejpam-4771	211	64	that	that	PRON
ejpam-4771	211	65	s	s	VERB
ejpam-4771	211	66	=	=	SYM
ejpam-4771	211	67	v	v	PROPN
ejpam-4771	211	68	(	(	PUNCT
ejpam-4771	211	69	k1	k1	NOUN
ejpam-4771	211	70	+	+	CCONJ
ejpam-4771	211	71	g	g	NOUN
ejpam-4771	211	72	)	)	PUNCT
ejpam-4771	211	73	or	or	CCONJ
ejpam-4771	211	74	⟨v	⟨v	NUM
ejpam-4771	211	75	(	(	PUNCT
ejpam-4771	211	76	k1	k1	NOUN
ejpam-4771	211	77	+	+	PROPN
ejpam-4771	211	78	g)\s⟩	g)\s⟩	PROPN
ejpam-4771	211	79	=	=	SYM
ejpam-4771	211	80	⟨v	⟨v	PROPN
ejpam-4771	211	81	(	(	PUNCT
ejpam-4771	211	82	g)\t	g)\t	NOUN
ejpam-4771	211	83	⟩	⟩	NOUN
ejpam-4771	211	84	is	be	AUX
ejpam-4771	211	85	connected	connect	VERB
ejpam-4771	211	86	.	.	PUNCT
ejpam-4771	212	1	thus	thus	ADV
ejpam-4771	212	2	,	,	PUNCT
ejpam-4771	212	3	t	t	PROPN
ejpam-4771	212	4	=	=	SYM
ejpam-4771	212	5	v	v	PROPN
ejpam-4771	212	6	(	(	PUNCT
ejpam-4771	212	7	g	g	NOUN
ejpam-4771	212	8	)	)	PUNCT
ejpam-4771	212	9	or	or	CCONJ
ejpam-4771	212	10	the	the	DET
ejpam-4771	212	11	subgraph	subgraph	NOUN
ejpam-4771	212	12	⟨v	⟨v	NOUN
ejpam-4771	212	13	(	(	PUNCT
ejpam-4771	212	14	g)\t	g)\t	NOUN
ejpam-4771	212	15	⟩	⟩	NOUN
ejpam-4771	212	16	induced	induce	VERB
ejpam-4771	212	17	by	by	ADP
ejpam-4771	212	18	v	v	NOUN
ejpam-4771	212	19	(	(	PUNCT
ejpam-4771	212	20	g)\t	g)\t	NOUN
ejpam-4771	212	21	is	be	AUX
ejpam-4771	212	22	connected	connect	VERB
ejpam-4771	212	23	.	.	PUNCT
ejpam-4771	213	1	therefore	therefore	ADV
ejpam-4771	213	2	,	,	PUNCT
ejpam-4771	213	3	t	t	PROPN
ejpam-4771	213	4	is	be	AUX
ejpam-4771	213	5	an	an	DET
ejpam-4771	213	6	outer	outer	ADV
ejpam-4771	213	7	-	-	PUNCT
ejpam-4771	213	8	connected	connect	VERB
ejpam-4771	213	9	(	(	PUNCT
ejpam-4771	213	10	2	2	NUM
ejpam-4771	213	11	,	,	PUNCT
ejpam-4771	213	12	1)-locating	1)-locating	NUM
ejpam-4771	213	13	point	point	NOUN
ejpam-4771	213	14	-	-	PUNCT
ejpam-4771	213	15	wise	wise	ADJ
ejpam-4771	213	16	non	non	ADJ
ejpam-4771	213	17	-	-	ADJ
ejpam-4771	213	18	dominating	dominating	ADJ
ejpam-4771	213	19	set	set	NOUN
ejpam-4771	213	20	in	in	ADP
ejpam-4771	213	21	g.	g.	NOUN
ejpam-4771	213	22	conversely	conversely	ADV
ejpam-4771	213	23	,	,	PUNCT
ejpam-4771	213	24	assume	assume	VERB
ejpam-4771	213	25	that	that	SCONJ
ejpam-4771	213	26	s	s	VERB
ejpam-4771	213	27	=	=	X
ejpam-4771	213	28	{	{	PUNCT
ejpam-4771	213	29	x	x	NOUN
ejpam-4771	213	30	}	}	PUNCT
ejpam-4771	213	31	∪	∪	ADP
ejpam-4771	213	32	t	t	PROPN
ejpam-4771	213	33	,	,	PUNCT
ejpam-4771	213	34	where	where	SCONJ
ejpam-4771	213	35	t	t	PROPN
ejpam-4771	213	36	is	be	AUX
ejpam-4771	213	37	an	an	DET
ejpam-4771	213	38	outer	outer	ADV
ejpam-4771	213	39	-	-	PUNCT
ejpam-4771	213	40	connected	connect	VERB
ejpam-4771	213	41	(	(	PUNCT
ejpam-4771	213	42	2,1)-locating	2,1)-locating	NUM
ejpam-4771	213	43	point	point	ADV
ejpam-4771	213	44	-	-	PUNCT
ejpam-4771	213	45	wise	wise	ADJ
ejpam-4771	213	46	non	non	ADJ
ejpam-4771	213	47	-	-	ADJ
ejpam-4771	213	48	dominating	dominating	ADJ
ejpam-4771	213	49	set	set	NOUN
ejpam-4771	213	50	in	in	ADP
ejpam-4771	213	51	g.	g.	PROPN
ejpam-4771	213	52	by	by	ADP
ejpam-4771	213	53	theorem	theorem	NOUN
ejpam-4771	213	54	2	2	NUM
ejpam-4771	213	55	,	,	PUNCT
ejpam-4771	213	56	s	s	VERB
ejpam-4771	213	57	is	be	AUX
ejpam-4771	213	58	a	a	DET
ejpam-4771	213	59	2	2	NUM
ejpam-4771	213	60	-	-	PUNCT
ejpam-4771	213	61	resolving	resolve	VERB
ejpam-4771	213	62	hop	hop	NOUN
ejpam-4771	213	63	dominating	dominating	NOUN
ejpam-4771	213	64	set	set	VERB
ejpam-4771	213	65	in	in	ADP
ejpam-4771	213	66	k1	k1	PROPN
ejpam-4771	213	67	+	+	CCONJ
ejpam-4771	213	68	g.	g.	PROPN
ejpam-4771	213	69	next	next	ADV
ejpam-4771	213	70	,	,	PUNCT
ejpam-4771	213	71	since	since	SCONJ
ejpam-4771	213	72	⟨v	⟨v	NOUN
ejpam-4771	213	73	(	(	PUNCT
ejpam-4771	213	74	k1	k1	NOUN
ejpam-4771	213	75	+	+	PROPN
ejpam-4771	213	76	g)\s⟩	g)\s⟩	PROPN
ejpam-4771	213	77	=	=	SYM
ejpam-4771	213	78	⟨v	⟨v	PROPN
ejpam-4771	213	79	(	(	PUNCT
ejpam-4771	213	80	g)\t	g)\t	NOUN
ejpam-4771	213	81	⟩	⟩	NOUN
ejpam-4771	213	82	and	and	CCONJ
ejpam-4771	213	83	t	t	PROPN
ejpam-4771	213	84	is	be	AUX
ejpam-4771	213	85	an	an	DET
ejpam-4771	213	86	outer	outer	ADV
ejpam-4771	213	87	-	-	PUNCT
ejpam-4771	213	88	connected	connect	VERB
ejpam-4771	213	89	(	(	PUNCT
ejpam-4771	213	90	2,1)-locating	2,1)-locating	NUM
ejpam-4771	213	91	point	point	ADV
ejpam-4771	213	92	-	-	PUNCT
ejpam-4771	213	93	wise	wise	ADJ
ejpam-4771	213	94	non	non	ADJ
ejpam-4771	213	95	-	-	ADJ
ejpam-4771	213	96	dominating	dominating	ADJ
ejpam-4771	213	97	set	set	NOUN
ejpam-4771	213	98	in	in	ADP
ejpam-4771	213	99	g	g	PROPN
ejpam-4771	213	100	,	,	PUNCT
ejpam-4771	213	101	it	it	PRON
ejpam-4771	213	102	follows	follow	VERB
ejpam-4771	213	103	that	that	SCONJ
ejpam-4771	213	104	s	s	VERB
ejpam-4771	213	105	is	be	AUX
ejpam-4771	213	106	a	a	DET
ejpam-4771	213	107	outer	outer	ADV
ejpam-4771	213	108	-	-	PUNCT
ejpam-4771	213	109	connected	connect	VERB
ejpam-4771	213	110	2	2	NUM
ejpam-4771	213	111	-	-	PUNCT
ejpam-4771	213	112	resolving	resolve	VERB
ejpam-4771	213	113	hop	hop	NOUN
ejpam-4771	213	114	dominating	dominating	NOUN
ejpam-4771	213	115	set	set	VERB
ejpam-4771	213	116	in	in	ADP
ejpam-4771	213	117	k1	k1	PROPN
ejpam-4771	214	1	+	+	PROPN
ejpam-4771	214	2	g.	g.	PROPN
ejpam-4771	214	3	corollary	corollary	NOUN
ejpam-4771	214	4	2	2	PROPN
ejpam-4771	214	5	.	.	PUNCT
ejpam-4771	215	1	let	let	VERB
ejpam-4771	215	2	g	g	NOUN
ejpam-4771	215	3	be	be	AUX
ejpam-4771	215	4	connected	connect	VERB
ejpam-4771	215	5	nontrivial	nontrivial	ADJ
ejpam-4771	215	6	graph	graph	NOUN
ejpam-4771	215	7	.	.	PUNCT
ejpam-4771	216	1	then	then	ADV
ejpam-4771	216	2	γ̃c2rh(k1+g	γ̃c2rh(k1+g	VERB
ejpam-4771	216	3	)	)	PUNCT
ejpam-4771	217	1	=	=	SYM
ejpam-4771	217	2	l̃npnd	l̃npnd	NOUN
ejpam-4771	217	3	(	(	PUNCT
ejpam-4771	217	4	2,1)(g)+1	2,1)(g)+1	PROPN
ejpam-4771	217	5	.	.	PUNCT
ejpam-4771	217	6	example	example	NOUN
ejpam-4771	218	1	1	1	NUM
ejpam-4771	218	2	.	.	X
ejpam-4771	218	3	for	for	ADP
ejpam-4771	218	4	a	a	DET
ejpam-4771	218	5	fan	fan	NOUN
ejpam-4771	218	6	fn	fn	NOUN
ejpam-4771	218	7	=	=	PUNCT
ejpam-4771	218	8	pn	pn	PROPN
ejpam-4771	218	9	+	+	CCONJ
ejpam-4771	218	10	1	1	NUM
ejpam-4771	218	11	on	on	ADP
ejpam-4771	218	12	n+	n+	ADP
ejpam-4771	218	13	1	1	NUM
ejpam-4771	218	14	vertices	vertex	NOUN
ejpam-4771	218	15	γ̃c2rh(fn	γ̃c2rh(fn	NOUN
ejpam-4771	218	16	)	)	PUNCT
ejpam-4771	219	1	=	=	SYM
ejpam-4771	219	2	l̃npnd	l̃npnd	NOUN
ejpam-4771	219	3	(	(	PUNCT
ejpam-4771	219	4	2,1)(pn	2,1)(pn	NUM
ejpam-4771	219	5	)	)	PUNCT
ejpam-4771	219	6	+	+	CCONJ
ejpam-4771	219	7	1	1	NUM
ejpam-4771	219	8	=	=	SYM
ejpam-4771	219	9	{	{	PUNCT
ejpam-4771	219	10	n	n	CCONJ
ejpam-4771	219	11	,	,	PUNCT
ejpam-4771	219	12	if	if	SCONJ
ejpam-4771	219	13	4	4	NUM
ejpam-4771	219	14	≤	≤	NUM
ejpam-4771	219	15	n	n	CCONJ
ejpam-4771	219	16	≤	≤	NOUN
ejpam-4771	219	17	7	7	NUM
ejpam-4771	219	18	;	;	PUNCT
ejpam-4771	219	19	n−	n−	NOUN
ejpam-4771	219	20	1	1	NUM
ejpam-4771	219	21	,	,	PUNCT
ejpam-4771	219	22	if	if	SCONJ
ejpam-4771	219	23	n	n	PRON
ejpam-4771	219	24	≥	≥	NOUN
ejpam-4771	219	25	8	8	NUM
ejpam-4771	219	26	.	.	PUNCT
ejpam-4771	219	27	example	example	NOUN
ejpam-4771	219	28	2	2	NUM
ejpam-4771	219	29	.	.	X
ejpam-4771	219	30	for	for	ADP
ejpam-4771	219	31	a	a	DET
ejpam-4771	219	32	wheel	wheel	NOUN
ejpam-4771	219	33	wn	wn	NOUN
ejpam-4771	219	34	=	=	SYM
ejpam-4771	219	35	cn	cn	PROPN
ejpam-4771	219	36	+	+	CCONJ
ejpam-4771	219	37	1	1	NUM
ejpam-4771	219	38	on	on	ADP
ejpam-4771	219	39	n+	n+	ADP
ejpam-4771	219	40	1	1	NUM
ejpam-4771	219	41	vertices	vertex	NOUN
ejpam-4771	219	42	γ̃c2rh(wn	γ̃c2rh(wn	NOUN
ejpam-4771	219	43	)	)	PUNCT
ejpam-4771	220	1	=	=	SYM
ejpam-4771	220	2	l̃npnd	l̃npnd	NOUN
ejpam-4771	220	3	(	(	PUNCT
ejpam-4771	220	4	2,1)(cn	2,1)(cn	NUM
ejpam-4771	220	5	)	)	PUNCT
ejpam-4771	220	6	+	+	CCONJ
ejpam-4771	220	7	1	1	NUM
ejpam-4771	220	8	=	=	SYM
ejpam-4771	220	9	{	{	PUNCT
ejpam-4771	220	10	n+	n+	NOUN
ejpam-4771	220	11	1	1	NUM
ejpam-4771	220	12	,	,	PUNCT
ejpam-4771	220	13	if	if	SCONJ
ejpam-4771	220	14	n	n	NOUN
ejpam-4771	220	15	=	=	SYM
ejpam-4771	220	16	4	4	NUM
ejpam-4771	220	17	;	;	PUNCT
ejpam-4771	220	18	n−	n−	NOUN
ejpam-4771	220	19	1	1	NUM
ejpam-4771	220	20	,	,	PUNCT
ejpam-4771	220	21	if	if	SCONJ
ejpam-4771	220	22	n	n	PRON
ejpam-4771	220	23	≥	≥	NOUN
ejpam-4771	220	24	5	5	NUM
ejpam-4771	220	25	.	.	PUNCT
ejpam-4771	220	26	theorem	theorem	VERB
ejpam-4771	220	27	4	4	NUM
ejpam-4771	220	28	.	.	PUNCT
ejpam-4771	221	1	[	[	X
ejpam-4771	221	2	12	12	NUM
ejpam-4771	221	3	]	]	PUNCT
ejpam-4771	221	4	let	let	VERB
ejpam-4771	221	5	g	g	NOUN
ejpam-4771	221	6	and	and	CCONJ
ejpam-4771	221	7	h	h	NOUN
ejpam-4771	221	8	be	be	VERB
ejpam-4771	221	9	any	any	DET
ejpam-4771	221	10	two	two	NUM
ejpam-4771	221	11	graphs	graph	NOUN
ejpam-4771	221	12	.	.	PUNCT
ejpam-4771	222	1	a	a	DET
ejpam-4771	222	2	set	set	NOUN
ejpam-4771	222	3	s	s	NOUN
ejpam-4771	222	4	⊆	⊆	NUM
ejpam-4771	222	5	v	v	NOUN
ejpam-4771	222	6	(	(	PUNCT
ejpam-4771	222	7	g+h	g+h	PROPN
ejpam-4771	222	8	)	)	PUNCT
ejpam-4771	222	9	is	be	AUX
ejpam-4771	222	10	a	a	DET
ejpam-4771	222	11	2	2	NUM
ejpam-4771	222	12	-	-	PUNCT
ejpam-4771	222	13	resolving	resolve	VERB
ejpam-4771	222	14	hop	hop	NOUN
ejpam-4771	222	15	dominating	dominating	NOUN
ejpam-4771	222	16	set	set	VERB
ejpam-4771	222	17	in	in	ADP
ejpam-4771	222	18	g+h	g+h	PROPN
ejpam-4771	222	19	if	if	SCONJ
ejpam-4771	222	20	and	and	CCONJ
ejpam-4771	222	21	only	only	ADV
ejpam-4771	222	22	if	if	SCONJ
ejpam-4771	222	23	s	s	VERB
ejpam-4771	222	24	=	=	PUNCT
ejpam-4771	222	25	sg	sg	X
ejpam-4771	222	26	∪	∪	NOUN
ejpam-4771	222	27	sh	sh	PROPN
ejpam-4771	222	28	where	where	SCONJ
ejpam-4771	222	29	sg	sg	PROPN
ejpam-4771	222	30	=	=	SYM
ejpam-4771	222	31	v	v	PROPN
ejpam-4771	222	32	(	(	PUNCT
ejpam-4771	222	33	g	g	NOUN
ejpam-4771	222	34	)	)	PUNCT
ejpam-4771	222	35	∩	∩	NOUN
ejpam-4771	222	36	s	s	NOUN
ejpam-4771	222	37	and	and	CCONJ
ejpam-4771	222	38	sh	sh	PROPN
ejpam-4771	222	39	=	=	SYM
ejpam-4771	222	40	v	v	PROPN
ejpam-4771	222	41	(	(	PUNCT
ejpam-4771	222	42	h	h	NOUN
ejpam-4771	222	43	)	)	PUNCT
ejpam-4771	222	44	∩	∩	NOUN
ejpam-4771	222	45	s	s	NOUN
ejpam-4771	222	46	are	be	AUX
ejpam-4771	222	47	2	2	NUM
ejpam-4771	222	48	-	-	PUNCT
ejpam-4771	222	49	locating	locate	VERB
ejpam-4771	222	50	point	point	NOUN
ejpam-4771	222	51	-	-	PUNCT
ejpam-4771	222	52	wise	wise	ADJ
ejpam-4771	222	53	non	non	ADJ
ejpam-4771	222	54	-	-	ADJ
ejpam-4771	222	55	dominating	dominating	ADJ
ejpam-4771	222	56	sets	set	NOUN
ejpam-4771	222	57	in	in	ADP
ejpam-4771	222	58	g	g	PROPN
ejpam-4771	222	59	and	and	CCONJ
ejpam-4771	222	60	h	h	NOUN
ejpam-4771	222	61	,	,	PUNCT
ejpam-4771	222	62	respectively	respectively	ADV
ejpam-4771	222	63	,	,	PUNCT
ejpam-4771	222	64	where	where	SCONJ
ejpam-4771	222	65	sg	sg	NOUN
ejpam-4771	222	66	or	or	CCONJ
ejpam-4771	222	67	sh	sh	PROPN
ejpam-4771	222	68	is	be	AUX
ejpam-4771	222	69	a	a	DET
ejpam-4771	222	70	(	(	PUNCT
ejpam-4771	222	71	2	2	NUM
ejpam-4771	222	72	,	,	PUNCT
ejpam-4771	222	73	2)-locating	2)-locating	NUM
ejpam-4771	222	74	point	point	NOUN
ejpam-4771	222	75	-	-	PUNCT
ejpam-4771	222	76	wise	wise	ADJ
ejpam-4771	222	77	non	non	ADJ
ejpam-4771	222	78	-	-	ADJ
ejpam-4771	222	79	dominating	dominating	ADJ
ejpam-4771	222	80	set	set	NOUN
ejpam-4771	222	81	or	or	CCONJ
ejpam-4771	222	82	sg	sg	PROPN
ejpam-4771	222	83	and	and	CCONJ
ejpam-4771	222	84	sh	sh	PROPN
ejpam-4771	222	85	are	be	AUX
ejpam-4771	222	86	(	(	PUNCT
ejpam-4771	222	87	2	2	NUM
ejpam-4771	222	88	,	,	PUNCT
ejpam-4771	222	89	1)-locating	1)-locating	NUM
ejpam-4771	222	90	point	point	NOUN
ejpam-4771	222	91	-	-	PUNCT
ejpam-4771	222	92	wise	wise	ADJ
ejpam-4771	222	93	non	non	ADJ
ejpam-4771	222	94	-	-	ADJ
ejpam-4771	222	95	dominating	dominating	ADJ
ejpam-4771	222	96	sets	set	NOUN
ejpam-4771	222	97	of	of	ADP
ejpam-4771	222	98	g	g	PROPN
ejpam-4771	222	99	and	and	CCONJ
ejpam-4771	222	100	h	h	NOUN
ejpam-4771	222	101	,	,	PUNCT
ejpam-4771	222	102	respectively	respectively	ADV
ejpam-4771	222	103	.	.	PUNCT
ejpam-4771	223	1	a.m.	a.m.	PROPN
ejpam-4771	223	2	mahistrado	mahistrado	PROPN
ejpam-4771	223	3	,	,	PUNCT
ejpam-4771	223	4	h.	h.	PROPN
ejpam-4771	223	5	rara	rara	PROPN
ejpam-4771	223	6	/	/	SYM
ejpam-4771	223	7	eur	eur	PROPN
ejpam-4771	223	8	.	.	PUNCT
ejpam-4771	224	1	j.	j.	PROPN
ejpam-4771	224	2	pure	pure	PROPN
ejpam-4771	224	3	appl	appl	PROPN
ejpam-4771	224	4	.	.	PROPN
ejpam-4771	224	5	math	math	PROPN
ejpam-4771	224	6	,	,	PUNCT
ejpam-4771	224	7	16	16	NUM
ejpam-4771	224	8	(	(	PUNCT
ejpam-4771	224	9	2	2	NUM
ejpam-4771	224	10	)	)	PUNCT
ejpam-4771	224	11	(	(	PUNCT
ejpam-4771	224	12	2023	2023	NUM
ejpam-4771	224	13	)	)	PUNCT
ejpam-4771	224	14	,	,	PUNCT
ejpam-4771	224	15	1180	1180	NUM
ejpam-4771	224	16	-	-	SYM
ejpam-4771	224	17	1195	1195	NUM
ejpam-4771	224	18	1187	1187	NUM
ejpam-4771	224	19	theorem	theorem	NOUN
ejpam-4771	224	20	5	5	NUM
ejpam-4771	224	21	.	.	PUNCT
ejpam-4771	225	1	[	[	X
ejpam-4771	225	2	9	9	NUM
ejpam-4771	225	3	]	]	PUNCT
ejpam-4771	225	4	let	let	VERB
ejpam-4771	225	5	g	g	NOUN
ejpam-4771	225	6	and	and	CCONJ
ejpam-4771	225	7	h	h	NOUN
ejpam-4771	225	8	be	be	VERB
ejpam-4771	225	9	any	any	DET
ejpam-4771	225	10	two	two	NUM
ejpam-4771	225	11	graphs	graph	NOUN
ejpam-4771	225	12	.	.	PUNCT
ejpam-4771	226	1	a	a	DET
ejpam-4771	226	2	set	set	NOUN
ejpam-4771	226	3	s	s	NOUN
ejpam-4771	226	4	⊆	⊆	NUM
ejpam-4771	226	5	v	v	NOUN
ejpam-4771	226	6	(	(	PUNCT
ejpam-4771	226	7	g	g	PROPN
ejpam-4771	226	8	+	+	NOUN
ejpam-4771	226	9	h	h	NOUN
ejpam-4771	226	10	)	)	PUNCT
ejpam-4771	226	11	is	be	AUX
ejpam-4771	226	12	an	an	DET
ejpam-4771	226	13	outerconnected	outerconnected	ADJ
ejpam-4771	226	14	hop	hop	NOUN
ejpam-4771	226	15	dominating	dominating	NOUN
ejpam-4771	226	16	set	set	VERB
ejpam-4771	226	17	in	in	ADP
ejpam-4771	226	18	g+h	g+h	PROPN
ejpam-4771	227	1	if	if	SCONJ
ejpam-4771	227	2	and	and	CCONJ
ejpam-4771	227	3	only	only	ADV
ejpam-4771	227	4	if	if	SCONJ
ejpam-4771	227	5	s	s	NOUN
ejpam-4771	227	6	=	=	PUNCT
ejpam-4771	227	7	sg	sg	PROPN
ejpam-4771	227	8	∪sh	∪sh	NOUN
ejpam-4771	227	9	,	,	PUNCT
ejpam-4771	227	10	where	where	SCONJ
ejpam-4771	227	11	sg	sg	PROPN
ejpam-4771	227	12	and	and	CCONJ
ejpam-4771	227	13	sh	sh	PROPN
ejpam-4771	227	14	are	be	AUX
ejpam-4771	227	15	pointwise	pointwise	PROPN
ejpam-4771	227	16	non	non	ADJ
ejpam-4771	227	17	-	-	ADJ
ejpam-4771	227	18	dominating	dominating	ADJ
ejpam-4771	227	19	subsets	subset	NOUN
ejpam-4771	227	20	of	of	ADP
ejpam-4771	227	21	g	g	PROPN
ejpam-4771	227	22	and	and	CCONJ
ejpam-4771	227	23	h	h	NOUN
ejpam-4771	227	24	,	,	PUNCT
ejpam-4771	227	25	respectively	respectively	ADV
ejpam-4771	227	26	,	,	PUNCT
ejpam-4771	227	27	such	such	ADJ
ejpam-4771	227	28	that	that	SCONJ
ejpam-4771	227	29	(	(	PUNCT
ejpam-4771	227	30	i	i	NOUN
ejpam-4771	227	31	)	)	PUNCT
ejpam-4771	227	32	⟨v	⟨v	CCONJ
ejpam-4771	228	1	(	(	PUNCT
ejpam-4771	228	2	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4771	228	3	is	be	AUX
ejpam-4771	228	4	connected	connect	VERB
ejpam-4771	228	5	whenever	whenever	SCONJ
ejpam-4771	228	6	sh	sh	PROPN
ejpam-4771	228	7	̸=	̸=	PROPN
ejpam-4771	228	8	v	v	ADP
ejpam-4771	228	9	(	(	PUNCT
ejpam-4771	228	10	h	h	NOUN
ejpam-4771	228	11	)	)	PUNCT
ejpam-4771	228	12	and	and	CCONJ
ejpam-4771	228	13	sg	sg	X
ejpam-4771	228	14	=	=	SYM
ejpam-4771	228	15	v	v	PROPN
ejpam-4771	228	16	(	(	PUNCT
ejpam-4771	228	17	g	g	NOUN
ejpam-4771	228	18	)	)	PUNCT
ejpam-4771	228	19	and	and	CCONJ
ejpam-4771	228	20	(	(	PUNCT
ejpam-4771	228	21	ii	ii	NOUN
ejpam-4771	228	22	)	)	PUNCT
ejpam-4771	228	23	⟨v	⟨v	NOUN
ejpam-4771	228	24	(	(	PUNCT
ejpam-4771	228	25	g)\sg⟩	g)\sg⟩	X
ejpam-4771	228	26	is	be	AUX
ejpam-4771	228	27	connected	connect	VERB
ejpam-4771	228	28	whenever	whenever	SCONJ
ejpam-4771	228	29	sg	sg	ADP
ejpam-4771	228	30	̸=	̸=	PROPN
ejpam-4771	228	31	v	v	NOUN
ejpam-4771	228	32	(	(	PUNCT
ejpam-4771	228	33	g	g	NOUN
ejpam-4771	228	34	)	)	PUNCT
ejpam-4771	228	35	and	and	CCONJ
ejpam-4771	228	36	sh	sh	INTJ
ejpam-4771	228	37	=	=	SYM
ejpam-4771	228	38	v	v	PROPN
ejpam-4771	228	39	(	(	PUNCT
ejpam-4771	228	40	h	h	NOUN
ejpam-4771	228	41	)	)	PUNCT
ejpam-4771	228	42	.	.	PUNCT
ejpam-4771	229	1	theorem	theorem	ADJ
ejpam-4771	229	2	6	6	NUM
ejpam-4771	229	3	.	.	PUNCT
ejpam-4771	230	1	let	let	VERB
ejpam-4771	230	2	g	g	NOUN
ejpam-4771	230	3	and	and	CCONJ
ejpam-4771	230	4	h	h	NOUN
ejpam-4771	230	5	be	be	VERB
ejpam-4771	230	6	any	any	DET
ejpam-4771	230	7	two	two	NUM
ejpam-4771	230	8	graphs	graph	NOUN
ejpam-4771	230	9	.	.	PUNCT
ejpam-4771	231	1	a	a	DET
ejpam-4771	231	2	set	set	NOUN
ejpam-4771	231	3	s	s	NOUN
ejpam-4771	231	4	⊆	⊆	NUM
ejpam-4771	231	5	v	v	NOUN
ejpam-4771	231	6	(	(	PUNCT
ejpam-4771	231	7	g	g	PROPN
ejpam-4771	231	8	+	+	NOUN
ejpam-4771	231	9	h	h	NOUN
ejpam-4771	231	10	)	)	PUNCT
ejpam-4771	231	11	is	be	AUX
ejpam-4771	231	12	an	an	DET
ejpam-4771	231	13	outerconnected	outerconnected	ADJ
ejpam-4771	231	14	2	2	NUM
ejpam-4771	231	15	-	-	PUNCT
ejpam-4771	231	16	resolving	resolve	VERB
ejpam-4771	231	17	hop	hop	NOUN
ejpam-4771	231	18	dominating	dominating	NOUN
ejpam-4771	231	19	set	set	VERB
ejpam-4771	231	20	in	in	ADP
ejpam-4771	231	21	g	g	PROPN
ejpam-4771	232	1	+	+	NOUN
ejpam-4771	232	2	h	h	NOUN
ejpam-4771	232	3	if	if	SCONJ
ejpam-4771	232	4	and	and	CCONJ
ejpam-4771	232	5	only	only	ADV
ejpam-4771	232	6	if	if	SCONJ
ejpam-4771	232	7	s	s	VERB
ejpam-4771	232	8	=	=	PUNCT
ejpam-4771	232	9	sg	sg	X
ejpam-4771	232	10	∪	∪	NOUN
ejpam-4771	232	11	sh	sh	PROPN
ejpam-4771	232	12	where	where	SCONJ
ejpam-4771	232	13	sg	sg	PROPN
ejpam-4771	232	14	=	=	SYM
ejpam-4771	232	15	v	v	PROPN
ejpam-4771	232	16	(	(	PUNCT
ejpam-4771	232	17	g	g	NOUN
ejpam-4771	232	18	)	)	PUNCT
ejpam-4771	232	19	∩	∩	NOUN
ejpam-4771	232	20	s	s	NOUN
ejpam-4771	232	21	and	and	CCONJ
ejpam-4771	232	22	sh	sh	PROPN
ejpam-4771	232	23	=	=	SYM
ejpam-4771	232	24	v	v	PROPN
ejpam-4771	232	25	(	(	PUNCT
ejpam-4771	232	26	h	h	NOUN
ejpam-4771	232	27	)	)	PUNCT
ejpam-4771	232	28	∩	∩	NOUN
ejpam-4771	232	29	s	s	NOUN
ejpam-4771	232	30	are	be	AUX
ejpam-4771	232	31	2	2	NUM
ejpam-4771	232	32	-	-	PUNCT
ejpam-4771	232	33	locating	locate	VERB
ejpam-4771	232	34	point	point	NOUN
ejpam-4771	232	35	-	-	PUNCT
ejpam-4771	232	36	wise	wise	ADJ
ejpam-4771	232	37	non	non	ADJ
ejpam-4771	232	38	-	-	ADJ
ejpam-4771	232	39	dominating	dominating	ADJ
ejpam-4771	232	40	sets	set	NOUN
ejpam-4771	232	41	in	in	ADP
ejpam-4771	232	42	g	g	PROPN
ejpam-4771	232	43	and	and	CCONJ
ejpam-4771	232	44	h	h	NOUN
ejpam-4771	232	45	,	,	PUNCT
ejpam-4771	232	46	respectively	respectively	ADV
ejpam-4771	232	47	,	,	PUNCT
ejpam-4771	232	48	where	where	SCONJ
ejpam-4771	232	49	sg	sg	NOUN
ejpam-4771	232	50	or	or	CCONJ
ejpam-4771	232	51	sh	sh	PROPN
ejpam-4771	232	52	is	be	AUX
ejpam-4771	232	53	a	a	DET
ejpam-4771	232	54	(	(	PUNCT
ejpam-4771	232	55	2	2	NUM
ejpam-4771	232	56	,	,	PUNCT
ejpam-4771	232	57	2)-locating	2)-locating	NUM
ejpam-4771	232	58	point	point	NOUN
ejpam-4771	232	59	-	-	PUNCT
ejpam-4771	232	60	wise	wise	ADJ
ejpam-4771	232	61	non	non	ADJ
ejpam-4771	232	62	-	-	ADJ
ejpam-4771	232	63	dominating	dominating	ADJ
ejpam-4771	232	64	set	set	NOUN
ejpam-4771	232	65	or	or	CCONJ
ejpam-4771	232	66	sg	sg	PROPN
ejpam-4771	232	67	and	and	CCONJ
ejpam-4771	232	68	sh	sh	PROPN
ejpam-4771	232	69	are	be	AUX
ejpam-4771	232	70	(	(	PUNCT
ejpam-4771	232	71	2	2	NUM
ejpam-4771	232	72	,	,	PUNCT
ejpam-4771	232	73	1)-locating	1)-locating	NUM
ejpam-4771	232	74	point	point	NOUN
ejpam-4771	232	75	-	-	PUNCT
ejpam-4771	232	76	wise	wise	ADJ
ejpam-4771	232	77	non	non	ADJ
ejpam-4771	232	78	-	-	ADJ
ejpam-4771	232	79	dominating	dominating	ADJ
ejpam-4771	232	80	sets	set	NOUN
ejpam-4771	232	81	of	of	ADP
ejpam-4771	232	82	g	g	PROPN
ejpam-4771	232	83	and	and	CCONJ
ejpam-4771	232	84	h	h	NOUN
ejpam-4771	232	85	,	,	PUNCT
ejpam-4771	232	86	respectively	respectively	ADV
ejpam-4771	232	87	,	,	PUNCT
ejpam-4771	232	88	such	such	ADJ
ejpam-4771	232	89	that	that	SCONJ
ejpam-4771	232	90	(	(	PUNCT
ejpam-4771	232	91	i	i	NOUN
ejpam-4771	232	92	)	)	PUNCT
ejpam-4771	232	93	⟨v	⟨v	CCONJ
ejpam-4771	233	1	(	(	PUNCT
ejpam-4771	233	2	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4771	233	3	is	be	AUX
ejpam-4771	233	4	connected	connect	VERB
ejpam-4771	233	5	whenever	whenever	SCONJ
ejpam-4771	233	6	sh	sh	PROPN
ejpam-4771	233	7	̸=	̸=	PROPN
ejpam-4771	233	8	v	v	ADP
ejpam-4771	233	9	(	(	PUNCT
ejpam-4771	233	10	h	h	NOUN
ejpam-4771	233	11	)	)	PUNCT
ejpam-4771	233	12	and	and	CCONJ
ejpam-4771	233	13	sg	sg	X
ejpam-4771	233	14	=	=	SYM
ejpam-4771	233	15	v	v	PROPN
ejpam-4771	233	16	(	(	PUNCT
ejpam-4771	233	17	g	g	NOUN
ejpam-4771	233	18	)	)	PUNCT
ejpam-4771	233	19	and	and	CCONJ
ejpam-4771	233	20	(	(	PUNCT
ejpam-4771	233	21	ii	ii	NOUN
ejpam-4771	233	22	)	)	PUNCT
ejpam-4771	233	23	⟨v	⟨v	NOUN
ejpam-4771	233	24	(	(	PUNCT
ejpam-4771	233	25	g)\sg⟩	g)\sg⟩	X
ejpam-4771	233	26	is	be	AUX
ejpam-4771	233	27	connected	connect	VERB
ejpam-4771	233	28	whenever	whenever	SCONJ
ejpam-4771	233	29	sg	sg	ADP
ejpam-4771	233	30	̸=	̸=	PROPN
ejpam-4771	233	31	v	v	NOUN
ejpam-4771	233	32	(	(	PUNCT
ejpam-4771	233	33	g	g	NOUN
ejpam-4771	233	34	)	)	PUNCT
ejpam-4771	233	35	and	and	CCONJ
ejpam-4771	233	36	sh	sh	INTJ
ejpam-4771	233	37	=	=	SYM
ejpam-4771	233	38	v	v	PROPN
ejpam-4771	233	39	(	(	PUNCT
ejpam-4771	233	40	h	h	NOUN
ejpam-4771	233	41	)	)	PUNCT
ejpam-4771	233	42	.	.	PUNCT
ejpam-4771	234	1	proof	proof	NOUN
ejpam-4771	234	2	.	.	PUNCT
ejpam-4771	235	1	suppose	suppose	VERB
ejpam-4771	235	2	that	that	SCONJ
ejpam-4771	235	3	s	s	VERB
ejpam-4771	235	4	⊆	⊆	NUM
ejpam-4771	235	5	v	v	NOUN
ejpam-4771	235	6	(	(	PUNCT
ejpam-4771	235	7	g+h	g+h	PROPN
ejpam-4771	235	8	)	)	PUNCT
ejpam-4771	235	9	is	be	AUX
ejpam-4771	235	10	an	an	DET
ejpam-4771	235	11	outer	outer	ADV
ejpam-4771	235	12	-	-	PUNCT
ejpam-4771	235	13	connected	connect	VERB
ejpam-4771	235	14	2	2	NUM
ejpam-4771	235	15	-	-	PUNCT
ejpam-4771	235	16	resolving	resolve	VERB
ejpam-4771	235	17	hop	hop	NOUN
ejpam-4771	235	18	dominating	dominating	NOUN
ejpam-4771	235	19	set	set	VERB
ejpam-4771	235	20	in	in	ADP
ejpam-4771	235	21	g+h	g+h	PROPN
ejpam-4771	235	22	.	.	PUNCT
ejpam-4771	236	1	let	let	VERB
ejpam-4771	236	2	sg	sg	INTJ
ejpam-4771	236	3	=	=	SYM
ejpam-4771	236	4	v	v	PROPN
ejpam-4771	236	5	(	(	PUNCT
ejpam-4771	236	6	g	g	NOUN
ejpam-4771	236	7	)	)	PUNCT
ejpam-4771	236	8	∩	∩	NOUN
ejpam-4771	236	9	s	s	NOUN
ejpam-4771	236	10	and	and	CCONJ
ejpam-4771	236	11	sh	sh	PROPN
ejpam-4771	236	12	=	=	SYM
ejpam-4771	236	13	v	v	PROPN
ejpam-4771	236	14	(	(	PUNCT
ejpam-4771	236	15	h	h	NOUN
ejpam-4771	236	16	)	)	PUNCT
ejpam-4771	236	17	∩	∩	NOUN
ejpam-4771	236	18	s	s	PART
ejpam-4771	236	19	then	then	ADV
ejpam-4771	236	20	s	s	PART
ejpam-4771	236	21	=	=	PUNCT
ejpam-4771	236	22	sg	sg	X
ejpam-4771	236	23	∪	∪	VERB
ejpam-4771	236	24	sh	sh	PROPN
ejpam-4771	236	25	.	.	PUNCT
ejpam-4771	237	1	now	now	ADV
ejpam-4771	237	2	,	,	PUNCT
ejpam-4771	237	3	since	since	SCONJ
ejpam-4771	237	4	s	s	NOUN
ejpam-4771	237	5	is	be	AUX
ejpam-4771	237	6	a	a	DET
ejpam-4771	237	7	2	2	NUM
ejpam-4771	237	8	-	-	PUNCT
ejpam-4771	237	9	resolving	resolve	VERB
ejpam-4771	237	10	hop	hop	NOUN
ejpam-4771	237	11	dominating	dominating	NOUN
ejpam-4771	237	12	set	set	NOUN
ejpam-4771	237	13	,	,	PUNCT
ejpam-4771	237	14	by	by	ADP
ejpam-4771	237	15	theorem	theorem	NOUN
ejpam-4771	237	16	4	4	NUM
ejpam-4771	237	17	,	,	PUNCT
ejpam-4771	237	18	sg	sg	PROPN
ejpam-4771	237	19	and	and	CCONJ
ejpam-4771	237	20	sh	sh	PROPN
ejpam-4771	237	21	are	be	AUX
ejpam-4771	237	22	2	2	NUM
ejpam-4771	237	23	-	-	PUNCT
ejpam-4771	237	24	locating	locate	VERB
ejpam-4771	237	25	point	point	NOUN
ejpam-4771	237	26	-	-	PUNCT
ejpam-4771	237	27	wise	wise	ADJ
ejpam-4771	237	28	non	non	ADJ
ejpam-4771	237	29	-	-	ADJ
ejpam-4771	237	30	dominating	dominating	ADJ
ejpam-4771	237	31	sets	set	NOUN
ejpam-4771	237	32	in	in	ADP
ejpam-4771	237	33	g	g	PROPN
ejpam-4771	237	34	and	and	CCONJ
ejpam-4771	237	35	h	h	NOUN
ejpam-4771	237	36	,	,	PUNCT
ejpam-4771	237	37	respectively	respectively	ADV
ejpam-4771	237	38	,	,	PUNCT
ejpam-4771	237	39	where	where	SCONJ
ejpam-4771	237	40	sg	sg	NOUN
ejpam-4771	237	41	or	or	CCONJ
ejpam-4771	237	42	sh	sh	PROPN
ejpam-4771	237	43	is	be	AUX
ejpam-4771	237	44	a	a	DET
ejpam-4771	237	45	(	(	PUNCT
ejpam-4771	237	46	2	2	NUM
ejpam-4771	237	47	,	,	PUNCT
ejpam-4771	237	48	2)-locating	2)-locating	NUM
ejpam-4771	237	49	pointwise	pointwise	PROPN
ejpam-4771	237	50	non	non	ADJ
ejpam-4771	237	51	-	-	ADJ
ejpam-4771	237	52	dominating	dominating	ADJ
ejpam-4771	237	53	set	set	NOUN
ejpam-4771	237	54	or	or	CCONJ
ejpam-4771	237	55	sg	sg	PROPN
ejpam-4771	237	56	and	and	CCONJ
ejpam-4771	237	57	sh	sh	PROPN
ejpam-4771	237	58	are	be	AUX
ejpam-4771	237	59	(	(	PUNCT
ejpam-4771	237	60	2	2	NUM
ejpam-4771	237	61	,	,	PUNCT
ejpam-4771	237	62	1)-locating	1)-locating	NUM
ejpam-4771	237	63	point	point	NOUN
ejpam-4771	237	64	-	-	PUNCT
ejpam-4771	237	65	wise	wise	ADJ
ejpam-4771	237	66	non	non	ADJ
ejpam-4771	237	67	-	-	ADJ
ejpam-4771	237	68	dominating	dominating	ADJ
ejpam-4771	237	69	sets	set	NOUN
ejpam-4771	237	70	.	.	PUNCT
ejpam-4771	238	1	suppose	suppose	VERB
ejpam-4771	238	2	sg	sg	PROPN
ejpam-4771	238	3	=	=	SYM
ejpam-4771	238	4	v	v	PROPN
ejpam-4771	238	5	(	(	PUNCT
ejpam-4771	238	6	g	g	NOUN
ejpam-4771	238	7	)	)	PUNCT
ejpam-4771	238	8	and	and	CCONJ
ejpam-4771	238	9	sh	sh	INTJ
ejpam-4771	238	10	̸=	̸=	PROPN
ejpam-4771	238	11	v	v	NOUN
ejpam-4771	238	12	(	(	PUNCT
ejpam-4771	238	13	h	h	NOUN
ejpam-4771	238	14	)	)	PUNCT
ejpam-4771	238	15	.	.	PUNCT
ejpam-4771	239	1	since	since	SCONJ
ejpam-4771	239	2	s	s	PROPN
ejpam-4771	239	3	is	be	AUX
ejpam-4771	239	4	an	an	DET
ejpam-4771	239	5	outer	outer	ADV
ejpam-4771	239	6	-	-	PUNCT
ejpam-4771	239	7	connected	connect	VERB
ejpam-4771	239	8	hop	hop	NOUN
ejpam-4771	239	9	dominating	dominating	NOUN
ejpam-4771	239	10	set	set	NOUN
ejpam-4771	239	11	,	,	PUNCT
ejpam-4771	239	12	by	by	ADP
ejpam-4771	239	13	theorem	theorem	NOUN
ejpam-4771	239	14	5	5	NUM
ejpam-4771	239	15	,	,	PUNCT
ejpam-4771	239	16	⟨v	⟨v	NUM
ejpam-4771	239	17	(	(	PUNCT
ejpam-4771	239	18	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4771	239	19	is	be	AUX
ejpam-4771	239	20	connected	connect	VERB
ejpam-4771	239	21	.	.	PUNCT
ejpam-4771	240	1	hence	hence	ADV
ejpam-4771	240	2	,	,	PUNCT
ejpam-4771	240	3	(	(	PUNCT
ejpam-4771	240	4	i	i	NOUN
ejpam-4771	240	5	)	)	PUNCT
ejpam-4771	240	6	holds	hold	VERB
ejpam-4771	240	7	.	.	PUNCT
ejpam-4771	241	1	similarly	similarly	ADV
ejpam-4771	241	2	,	,	PUNCT
ejpam-4771	241	3	suppose	suppose	VERB
ejpam-4771	241	4	that	that	SCONJ
ejpam-4771	241	5	sg	sg	PROPN
ejpam-4771	241	6	̸=	̸=	PROPN
ejpam-4771	241	7	v	v	NOUN
ejpam-4771	241	8	(	(	PUNCT
ejpam-4771	241	9	g	g	NOUN
ejpam-4771	241	10	)	)	PUNCT
ejpam-4771	241	11	and	and	CCONJ
ejpam-4771	241	12	sh	sh	INTJ
ejpam-4771	241	13	=	=	SYM
ejpam-4771	241	14	v	v	PROPN
ejpam-4771	241	15	(	(	PUNCT
ejpam-4771	241	16	h	h	NOUN
ejpam-4771	241	17	)	)	PUNCT
ejpam-4771	241	18	.	.	PUNCT
ejpam-4771	242	1	by	by	ADP
ejpam-4771	242	2	theorem	theorem	NOUN
ejpam-4771	242	3	5	5	NUM
ejpam-4771	242	4	,	,	PUNCT
ejpam-4771	242	5	⟨v	⟨v	NOUN
ejpam-4771	242	6	(	(	PUNCT
ejpam-4771	242	7	g)\sg⟩	g)\sg⟩	X
ejpam-4771	242	8	is	be	AUX
ejpam-4771	242	9	connected	connect	VERB
ejpam-4771	242	10	and	and	CCONJ
ejpam-4771	242	11	so	so	ADV
ejpam-4771	242	12	(	(	PUNCT
ejpam-4771	242	13	ii	ii	NOUN
ejpam-4771	242	14	)	)	PUNCT
ejpam-4771	242	15	holds	hold	VERB
ejpam-4771	242	16	.	.	PUNCT
ejpam-4771	243	1	conversely	conversely	ADV
ejpam-4771	243	2	,	,	PUNCT
ejpam-4771	243	3	suppose	suppose	VERB
ejpam-4771	243	4	that	that	SCONJ
ejpam-4771	243	5	s	s	VERB
ejpam-4771	243	6	=	=	PUNCT
ejpam-4771	243	7	sg	sg	X
ejpam-4771	243	8	∪	∪	NOUN
ejpam-4771	243	9	sh	sh	PROPN
ejpam-4771	243	10	where	where	SCONJ
ejpam-4771	243	11	sg	sg	PROPN
ejpam-4771	243	12	⊆	⊆	NUM
ejpam-4771	243	13	v	v	NOUN
ejpam-4771	243	14	(	(	PUNCT
ejpam-4771	243	15	g	g	NOUN
ejpam-4771	243	16	)	)	PUNCT
ejpam-4771	243	17	and	and	CCONJ
ejpam-4771	243	18	sh	sh	PROPN
ejpam-4771	243	19	⊆	⊆	NUM
ejpam-4771	243	20	v	v	NOUN
ejpam-4771	243	21	(	(	PUNCT
ejpam-4771	243	22	h	h	NOUN
ejpam-4771	243	23	)	)	PUNCT
ejpam-4771	243	24	are	be	AUX
ejpam-4771	243	25	sets	set	NOUN
ejpam-4771	243	26	as	as	SCONJ
ejpam-4771	243	27	described	describe	VERB
ejpam-4771	243	28	and	and	CCONJ
ejpam-4771	243	29	satisfying	satisfy	VERB
ejpam-4771	243	30	(	(	PUNCT
ejpam-4771	243	31	i	i	NOUN
ejpam-4771	243	32	)	)	PUNCT
ejpam-4771	243	33	and	and	CCONJ
ejpam-4771	243	34	(	(	PUNCT
ejpam-4771	243	35	ii	ii	NOUN
ejpam-4771	243	36	)	)	PUNCT
ejpam-4771	243	37	.	.	PUNCT
ejpam-4771	244	1	by	by	ADP
ejpam-4771	244	2	theorem	theorem	NOUN
ejpam-4771	244	3	4	4	NUM
ejpam-4771	244	4	,	,	PUNCT
ejpam-4771	244	5	s	s	VERB
ejpam-4771	244	6	is	be	AUX
ejpam-4771	244	7	a	a	DET
ejpam-4771	244	8	2	2	NUM
ejpam-4771	244	9	-	-	PUNCT
ejpam-4771	244	10	resolving	resolve	VERB
ejpam-4771	244	11	hop	hop	NOUN
ejpam-4771	244	12	dominating	dominating	NOUN
ejpam-4771	244	13	set	set	NOUN
ejpam-4771	244	14	of	of	ADP
ejpam-4771	244	15	g+h	g+h	PROPN
ejpam-4771	244	16	.	.	PUNCT
ejpam-4771	245	1	if	if	SCONJ
ejpam-4771	245	2	sg	sg	PROPN
ejpam-4771	245	3	=	=	SYM
ejpam-4771	245	4	v	v	PROPN
ejpam-4771	245	5	(	(	PUNCT
ejpam-4771	245	6	g	g	NOUN
ejpam-4771	245	7	)	)	PUNCT
ejpam-4771	245	8	and	and	CCONJ
ejpam-4771	245	9	sh	sh	INTJ
ejpam-4771	245	10	=	=	SYM
ejpam-4771	245	11	v	v	PROPN
ejpam-4771	245	12	(	(	PUNCT
ejpam-4771	245	13	h	h	NOUN
ejpam-4771	245	14	)	)	PUNCT
ejpam-4771	245	15	,	,	PUNCT
ejpam-4771	245	16	then	then	ADV
ejpam-4771	245	17	s	s	VERB
ejpam-4771	245	18	=	=	SYM
ejpam-4771	245	19	v	v	PROPN
ejpam-4771	245	20	(	(	PUNCT
ejpam-4771	245	21	g+h	g+h	PROPN
ejpam-4771	245	22	)	)	PUNCT
ejpam-4771	245	23	is	be	AUX
ejpam-4771	245	24	an	an	DET
ejpam-4771	245	25	outer	outer	ADV
ejpam-4771	245	26	-	-	PUNCT
ejpam-4771	245	27	connected	connect	VERB
ejpam-4771	245	28	2	2	NUM
ejpam-4771	245	29	-	-	PUNCT
ejpam-4771	245	30	resolving	resolve	VERB
ejpam-4771	245	31	hop	hop	NOUN
ejpam-4771	245	32	dominating	dominating	NOUN
ejpam-4771	245	33	set	set	NOUN
ejpam-4771	245	34	.	.	PUNCT
ejpam-4771	246	1	suppose	suppose	VERB
ejpam-4771	246	2	,	,	PUNCT
ejpam-4771	246	3	s	s	VERB
ejpam-4771	246	4	̸=	̸=	PROPN
ejpam-4771	246	5	v	v	NOUN
ejpam-4771	246	6	(	(	PUNCT
ejpam-4771	246	7	g+h	g+h	PROPN
ejpam-4771	246	8	)	)	PUNCT
ejpam-4771	246	9	.	.	PUNCT
ejpam-4771	247	1	consider	consider	VERB
ejpam-4771	247	2	the	the	DET
ejpam-4771	247	3	following	follow	VERB
ejpam-4771	247	4	cases	case	NOUN
ejpam-4771	247	5	:	:	PUNCT
ejpam-4771	247	6	case	case	NOUN
ejpam-4771	247	7	1	1	NUM
ejpam-4771	247	8	:	:	PUNCT
ejpam-4771	247	9	sg	sg	ADP
ejpam-4771	247	10	̸=	̸=	PROPN
ejpam-4771	247	11	v	v	NOUN
ejpam-4771	247	12	(	(	PUNCT
ejpam-4771	247	13	g	g	NOUN
ejpam-4771	247	14	)	)	PUNCT
ejpam-4771	247	15	and	and	CCONJ
ejpam-4771	247	16	sh	sh	INTJ
ejpam-4771	247	17	̸=	̸=	PROPN
ejpam-4771	247	18	v	v	NOUN
ejpam-4771	247	19	(	(	PUNCT
ejpam-4771	247	20	h	h	NOUN
ejpam-4771	247	21	)	)	PUNCT
ejpam-4771	247	22	then	then	ADV
ejpam-4771	247	23	⟨v	⟨v	CCONJ
ejpam-4771	247	24	(	(	PUNCT
ejpam-4771	247	25	g+h)\s⟩	g+h)\s⟩	PROPN
ejpam-4771	247	26	=	=	SYM
ejpam-4771	247	27	⟨v	⟨v	PROPN
ejpam-4771	247	28	(	(	PUNCT
ejpam-4771	247	29	g)\sg⟩+	g)\sg⟩+	ADJ
ejpam-4771	247	30	⟨v	⟨v	NUM
ejpam-4771	247	31	(	(	PUNCT
ejpam-4771	247	32	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4771	247	33	is	be	AUX
ejpam-4771	247	34	connected	connect	VERB
ejpam-4771	247	35	.	.	PUNCT
ejpam-4771	248	1	case	case	NOUN
ejpam-4771	248	2	2	2	NUM
ejpam-4771	248	3	:	:	PUNCT
ejpam-4771	248	4	sg	sg	PROPN
ejpam-4771	248	5	=	=	SYM
ejpam-4771	248	6	v	v	PROPN
ejpam-4771	248	7	(	(	PUNCT
ejpam-4771	248	8	g	g	NOUN
ejpam-4771	248	9	)	)	PUNCT
ejpam-4771	248	10	and	and	CCONJ
ejpam-4771	248	11	sh	sh	INTJ
ejpam-4771	248	12	̸=	̸=	PROPN
ejpam-4771	248	13	v	v	NOUN
ejpam-4771	248	14	(	(	PUNCT
ejpam-4771	248	15	h	h	NOUN
ejpam-4771	248	16	)	)	PUNCT
ejpam-4771	248	17	then	then	ADV
ejpam-4771	248	18	⟨v	⟨v	CCONJ
ejpam-4771	248	19	(	(	PUNCT
ejpam-4771	248	20	g+h)\s⟩	g+h)\s⟩	PROPN
ejpam-4771	248	21	=	=	SYM
ejpam-4771	248	22	⟨v	⟨v	PROPN
ejpam-4771	248	23	(	(	PUNCT
ejpam-4771	248	24	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4771	248	25	is	be	AUX
ejpam-4771	248	26	connected	connect	VERB
ejpam-4771	248	27	by	by	ADP
ejpam-4771	248	28	(	(	PUNCT
ejpam-4771	248	29	i	i	NOUN
ejpam-4771	248	30	)	)	PUNCT
ejpam-4771	248	31	.	.	PUNCT
ejpam-4771	249	1	case	case	NOUN
ejpam-4771	249	2	3	3	NUM
ejpam-4771	249	3	:	:	PUNCT
ejpam-4771	249	4	sh	sh	PROPN
ejpam-4771	249	5	=	=	SYM
ejpam-4771	249	6	v	v	PROPN
ejpam-4771	249	7	(	(	PUNCT
ejpam-4771	249	8	h	h	NOUN
ejpam-4771	249	9	)	)	PUNCT
ejpam-4771	249	10	and	and	CCONJ
ejpam-4771	249	11	sg	sg	ADP
ejpam-4771	249	12	̸=	̸=	PROPN
ejpam-4771	249	13	v	v	NOUN
ejpam-4771	249	14	(	(	PUNCT
ejpam-4771	249	15	g	g	NOUN
ejpam-4771	249	16	)	)	PUNCT
ejpam-4771	249	17	then	then	ADV
ejpam-4771	249	18	⟨v	⟨v	CCONJ
ejpam-4771	249	19	(	(	PUNCT
ejpam-4771	249	20	g+h)\s⟩	g+h)\s⟩	PROPN
ejpam-4771	249	21	=	=	SYM
ejpam-4771	249	22	⟨v	⟨v	PROPN
ejpam-4771	249	23	(	(	PUNCT
ejpam-4771	249	24	g)\sg⟩	g)\sg⟩	X
ejpam-4771	249	25	is	be	AUX
ejpam-4771	249	26	connected	connect	VERB
ejpam-4771	249	27	by	by	ADP
ejpam-4771	249	28	(	(	PUNCT
ejpam-4771	249	29	ii	ii	NOUN
ejpam-4771	249	30	)	)	PUNCT
ejpam-4771	249	31	.	.	PUNCT
ejpam-4771	250	1	accordingly	accordingly	ADV
ejpam-4771	250	2	,	,	PUNCT
ejpam-4771	250	3	s	s	VERB
ejpam-4771	250	4	is	be	AUX
ejpam-4771	250	5	an	an	DET
ejpam-4771	250	6	outer	outer	ADV
ejpam-4771	250	7	-	-	PUNCT
ejpam-4771	250	8	connected	connect	VERB
ejpam-4771	250	9	2	2	NUM
ejpam-4771	250	10	-	-	PUNCT
ejpam-4771	250	11	resolving	resolve	VERB
ejpam-4771	250	12	hop	hop	NOUN
ejpam-4771	250	13	dominating	dominating	NOUN
ejpam-4771	250	14	set	set	NOUN
ejpam-4771	250	15	of	of	ADP
ejpam-4771	250	16	g+h	g+h	PROPN
ejpam-4771	250	17	.	.	PUNCT
ejpam-4771	251	1	as	as	ADP
ejpam-4771	251	2	a	a	DET
ejpam-4771	251	3	consequence	consequence	NOUN
ejpam-4771	251	4	of	of	ADP
ejpam-4771	251	5	theorem	theorem	NOUN
ejpam-4771	251	6	6	6	NUM
ejpam-4771	251	7	the	the	DET
ejpam-4771	251	8	next	next	ADJ
ejpam-4771	251	9	result	result	NOUN
ejpam-4771	251	10	follows	follow	VERB
ejpam-4771	251	11	.	.	PUNCT
ejpam-4771	252	1	corollary	corollary	ADJ
ejpam-4771	252	2	3	3	X
ejpam-4771	252	3	.	.	PUNCT
ejpam-4771	253	1	let	let	VERB
ejpam-4771	253	2	g	g	NOUN
ejpam-4771	253	3	and	and	CCONJ
ejpam-4771	253	4	h	h	NOUN
ejpam-4771	253	5	be	be	AUX
ejpam-4771	253	6	nontrivial	nontrivial	ADJ
ejpam-4771	253	7	connected	connected	ADJ
ejpam-4771	253	8	graphs	graph	NOUN
ejpam-4771	253	9	.	.	PUNCT
ejpam-4771	254	1	then	then	ADV
ejpam-4771	254	2	γ̃c2rh(g+h	γ̃c2rh(g+h	NOUN
ejpam-4771	254	3	)	)	PUNCT
ejpam-4771	255	1	=	=	NOUN
ejpam-4771	255	2	min{lnpnd	min{lnpnd	NOUN
ejpam-4771	255	3	(	(	PUNCT
ejpam-4771	255	4	2,2)(g	2,2)(g	NUM
ejpam-4771	255	5	)	)	PUNCT
ejpam-4771	256	1	+	+	CCONJ
ejpam-4771	256	2	lnpnd	lnpnd	ADJ
ejpam-4771	256	3	2	2	NUM
ejpam-4771	256	4	(	(	PUNCT
ejpam-4771	256	5	h	h	NOUN
ejpam-4771	256	6	)	)	PUNCT
ejpam-4771	256	7	,	,	PUNCT
ejpam-4771	256	8	lnpnd	lnpnd	PROPN
ejpam-4771	256	9	2	2	NUM
ejpam-4771	256	10	(	(	PUNCT
ejpam-4771	256	11	g	g	NOUN
ejpam-4771	256	12	)	)	PUNCT
ejpam-4771	256	13	+	+	CCONJ
ejpam-4771	256	14	lnpnd	lnpnd	ADJ
ejpam-4771	256	15	(	(	PUNCT
ejpam-4771	256	16	2,2)(h	2,2)(h	NUM
ejpam-4771	256	17	)	)	PUNCT
ejpam-4771	256	18	,	,	PUNCT
ejpam-4771	256	19	lnpnd	lnpnd	ADJ
ejpam-4771	256	20	(	(	PUNCT
ejpam-4771	256	21	2,1)(g	2,1)(g	NUM
ejpam-4771	256	22	)	)	PUNCT
ejpam-4771	257	1	+	+	CCONJ
ejpam-4771	257	2	lnpnd	lnpnd	ADJ
ejpam-4771	257	3	(	(	PUNCT
ejpam-4771	257	4	2,1)(h	2,1)(h	NUM
ejpam-4771	257	5	)	)	PUNCT
ejpam-4771	257	6	}	}	PUNCT
ejpam-4771	257	7	,	,	PUNCT
ejpam-4771	257	8	a.m.	a.m.	PROPN
ejpam-4771	257	9	mahistrado	mahistrado	PROPN
ejpam-4771	257	10	,	,	PUNCT
ejpam-4771	257	11	h.	h.	PROPN
ejpam-4771	257	12	rara	rara	PROPN
ejpam-4771	257	13	/	/	SYM
ejpam-4771	257	14	eur	eur	PROPN
ejpam-4771	257	15	.	.	PUNCT
ejpam-4771	258	1	j.	j.	PROPN
ejpam-4771	258	2	pure	pure	PROPN
ejpam-4771	258	3	appl	appl	PROPN
ejpam-4771	258	4	.	.	PROPN
ejpam-4771	258	5	math	math	PROPN
ejpam-4771	258	6	,	,	PUNCT
ejpam-4771	258	7	16	16	NUM
ejpam-4771	258	8	(	(	PUNCT
ejpam-4771	258	9	2	2	NUM
ejpam-4771	258	10	)	)	PUNCT
ejpam-4771	258	11	(	(	PUNCT
ejpam-4771	258	12	2023	2023	NUM
ejpam-4771	258	13	)	)	PUNCT
ejpam-4771	258	14	,	,	PUNCT
ejpam-4771	258	15	1180	1180	NUM
ejpam-4771	258	16	-	-	SYM
ejpam-4771	258	17	1195	1195	NUM
ejpam-4771	258	18	1188	1188	NUM
ejpam-4771	258	19	5	5	NUM
ejpam-4771	258	20	.	.	PUNCT
ejpam-4771	259	1	corona	corona	NOUN
ejpam-4771	259	2	of	of	ADP
ejpam-4771	259	3	graphs	graph	NOUN
ejpam-4771	259	4	this	this	DET
ejpam-4771	259	5	section	section	NOUN
ejpam-4771	259	6	presents	present	VERB
ejpam-4771	259	7	characterizations	characterization	NOUN
ejpam-4771	259	8	in	in	ADP
ejpam-4771	259	9	the	the	DET
ejpam-4771	259	10	outer	outer	ADV
ejpam-4771	259	11	-	-	PUNCT
ejpam-4771	259	12	connected	connect	VERB
ejpam-4771	259	13	2	2	NUM
ejpam-4771	259	14	-	-	PUNCT
ejpam-4771	259	15	resolving	resolve	VERB
ejpam-4771	259	16	hop	hop	NOUN
ejpam-4771	259	17	dominating	dominating	NOUN
ejpam-4771	259	18	sets	set	NOUN
ejpam-4771	259	19	in	in	ADP
ejpam-4771	259	20	the	the	DET
ejpam-4771	259	21	corona	corona	NOUN
ejpam-4771	259	22	of	of	ADP
ejpam-4771	259	23	graphs	graph	NOUN
ejpam-4771	259	24	.	.	PUNCT
ejpam-4771	260	1	remark	remark	NOUN
ejpam-4771	260	2	3	3	NUM
ejpam-4771	260	3	.	.	PUNCT
ejpam-4771	261	1	[	[	X
ejpam-4771	261	2	7	7	X
ejpam-4771	261	3	]	]	PUNCT
ejpam-4771	261	4	let	let	VERB
ejpam-4771	261	5	v	v	NUM
ejpam-4771	261	6	∈	∈	PROPN
ejpam-4771	261	7	v	v	NOUN
ejpam-4771	261	8	(	(	PUNCT
ejpam-4771	261	9	g	g	NOUN
ejpam-4771	261	10	)	)	PUNCT
ejpam-4771	261	11	.	.	PUNCT
ejpam-4771	262	1	for	for	ADP
ejpam-4771	262	2	every	every	DET
ejpam-4771	262	3	x	x	PROPN
ejpam-4771	262	4	,	,	PUNCT
ejpam-4771	262	5	y	y	PROPN
ejpam-4771	262	6	∈	∈	PROPN
ejpam-4771	262	7	v	v	PROPN
ejpam-4771	262	8	(	(	PUNCT
ejpam-4771	262	9	hv	hv	PROPN
ejpam-4771	262	10	)	)	PUNCT
ejpam-4771	262	11	,	,	PUNCT
ejpam-4771	262	12	dg	dg	PROPN
ejpam-4771	262	13	◦	◦	NOUN
ejpam-4771	262	14	h(x	h(x	PROPN
ejpam-4771	262	15	,	,	PUNCT
ejpam-4771	262	16	w	w	PROPN
ejpam-4771	262	17	)	)	PUNCT
ejpam-4771	262	18	=	=	SYM
ejpam-4771	262	19	dg	dg	NOUN
ejpam-4771	262	20	◦	◦	NOUN
ejpam-4771	262	21	h(y	h(y	ADV
ejpam-4771	262	22	,	,	PUNCT
ejpam-4771	262	23	w	w	NOUN
ejpam-4771	262	24	)	)	PUNCT
ejpam-4771	262	25	and	and	CCONJ
ejpam-4771	262	26	dg	dg	AUX
ejpam-4771	262	27	◦	◦	NOUN
ejpam-4771	262	28	h(v	h(v	PROPN
ejpam-4771	262	29	,	,	PUNCT
ejpam-4771	262	30	w	w	NOUN
ejpam-4771	262	31	)	)	PUNCT
ejpam-4771	262	32	+	+	CCONJ
ejpam-4771	262	33	1	1	NUM
ejpam-4771	262	34	=	=	SYM
ejpam-4771	262	35	dg	dg	NOUN
ejpam-4771	262	36	◦	◦	NOUN
ejpam-4771	262	37	h(x	h(x	PROPN
ejpam-4771	262	38	,	,	PUNCT
ejpam-4771	262	39	w	w	NOUN
ejpam-4771	262	40	)	)	PUNCT
ejpam-4771	262	41	for	for	ADP
ejpam-4771	262	42	every	every	DET
ejpam-4771	262	43	w	w	PROPN
ejpam-4771	262	44	∈	∈	PROPN
ejpam-4771	262	45	v	v	NOUN
ejpam-4771	262	46	(	(	PUNCT
ejpam-4771	262	47	g	g	PROPN
ejpam-4771	262	48	◦	◦	PROPN
ejpam-4771	262	49	h)\v	h)\v	PROPN
ejpam-4771	262	50	(	(	PUNCT
ejpam-4771	262	51	hv	hv	NOUN
ejpam-4771	262	52	)	)	PUNCT
ejpam-4771	262	53	.	.	PUNCT
ejpam-4771	263	1	theorem	theorem	VERB
ejpam-4771	263	2	7	7	NUM
ejpam-4771	263	3	.	.	PUNCT
ejpam-4771	264	1	[	[	X
ejpam-4771	264	2	12	12	NUM
ejpam-4771	264	3	]	]	PUNCT
ejpam-4771	264	4	let	let	VERB
ejpam-4771	264	5	g	g	NOUN
ejpam-4771	264	6	and	and	CCONJ
ejpam-4771	264	7	h	h	NOUN
ejpam-4771	264	8	be	be	AUX
ejpam-4771	264	9	nontrivial	nontrivial	ADJ
ejpam-4771	264	10	connected	connected	ADJ
ejpam-4771	264	11	graphs	graph	NOUN
ejpam-4771	264	12	.	.	PUNCT
ejpam-4771	265	1	a	a	DET
ejpam-4771	265	2	set	set	NOUN
ejpam-4771	265	3	s	s	NOUN
ejpam-4771	265	4	⊆	⊆	NUM
ejpam-4771	265	5	v	v	NOUN
ejpam-4771	265	6	(	(	PUNCT
ejpam-4771	265	7	g	g	PROPN
ejpam-4771	265	8	◦	◦	NOUN
ejpam-4771	265	9	h	h	NOUN
ejpam-4771	265	10	)	)	PUNCT
ejpam-4771	265	11	is	be	AUX
ejpam-4771	265	12	a	a	DET
ejpam-4771	265	13	2	2	NUM
ejpam-4771	265	14	-	-	PUNCT
ejpam-4771	265	15	resolving	resolve	VERB
ejpam-4771	265	16	hop	hop	NOUN
ejpam-4771	265	17	dominating	dominating	NOUN
ejpam-4771	265	18	set	set	NOUN
ejpam-4771	265	19	of	of	ADP
ejpam-4771	265	20	g	g	PROPN
ejpam-4771	265	21	◦	◦	NOUN
ejpam-4771	265	22	h	h	NOUN
ejpam-4771	265	23	if	if	SCONJ
ejpam-4771	266	1	and	and	CCONJ
ejpam-4771	266	2	only	only	ADV
ejpam-4771	266	3	if	if	SCONJ
ejpam-4771	266	4	s	s	VERB
ejpam-4771	266	5	=	=	NOUN
ejpam-4771	266	6	a	a	PRON
ejpam-4771	266	7	∪	∪	ADJ
ejpam-4771	266	8			PROPN
ejpam-4771	266	9	⋃	⋃	ADJ
ejpam-4771	266	10	v∈v	v∈v	NOUN
ejpam-4771	266	11	(	(	PUNCT
ejpam-4771	266	12	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4771	267	1	)	)	PUNCT
ejpam-4771	267	2	sv	sv	NOUN
ejpam-4771	268	1			PROPN
ejpam-4771	268	2	∪	∪	VERB
ejpam-4771	268	3			PROPN
ejpam-4771	268	4	⋃	⋃	PROPN
ejpam-4771	268	5	w∈v	w∈v	PROPN
ejpam-4771	268	6	(	(	PUNCT
ejpam-4771	268	7	g)\ng(a	g)\ng(a	NOUN
ejpam-4771	268	8	)	)	PUNCT
ejpam-4771	268	9	dw	dw	NOUN
ejpam-4771	268	10			PROPN
ejpam-4771	268	11	where	where	SCONJ
ejpam-4771	268	12	(	(	PUNCT
ejpam-4771	268	13	i	i	NOUN
ejpam-4771	268	14	)	)	PUNCT
ejpam-4771	268	15	a	a	DET
ejpam-4771	268	16	⊆	⊆	NUM
ejpam-4771	268	17	v	v	NOUN
ejpam-4771	268	18	(	(	PUNCT
ejpam-4771	268	19	g	g	NOUN
ejpam-4771	268	20	)	)	PUNCT
ejpam-4771	268	21	such	such	ADJ
ejpam-4771	268	22	that	that	PRON
ejpam-4771	268	23	for	for	ADP
ejpam-4771	268	24	each	each	DET
ejpam-4771	268	25	w	w	PROPN
ejpam-4771	268	26	∈	∈	PROPN
ejpam-4771	268	27	v	v	NOUN
ejpam-4771	268	28	(	(	PUNCT
ejpam-4771	268	29	g)\a	g)\a	NOUN
ejpam-4771	268	30	,	,	PUNCT
ejpam-4771	268	31	there	there	PRON
ejpam-4771	268	32	exists	exist	VERB
ejpam-4771	268	33	x	x	X
ejpam-4771	268	34	∈	∈	PROPN
ejpam-4771	268	35	a	a	PRON
ejpam-4771	268	36	with	with	ADP
ejpam-4771	268	37	dg(w	dg(w	NOUN
ejpam-4771	268	38	,	,	PUNCT
ejpam-4771	268	39	x	x	X
ejpam-4771	268	40	)	)	PUNCT
ejpam-4771	268	41	=	=	SYM
ejpam-4771	268	42	2	2	NUM
ejpam-4771	268	43	or	or	CCONJ
ejpam-4771	268	44	there	there	PRON
ejpam-4771	268	45	exists	exist	VERB
ejpam-4771	268	46	y	y	PROPN
ejpam-4771	268	47	∈	∈	PROPN
ejpam-4771	268	48	v	v	ADP
ejpam-4771	268	49	(	(	PUNCT
ejpam-4771	268	50	g	g	NOUN
ejpam-4771	268	51	)	)	PUNCT
ejpam-4771	268	52	∩ng(w	∩ng(w	PROPN
ejpam-4771	268	53	)	)	PUNCT
ejpam-4771	268	54	with	with	ADP
ejpam-4771	268	55	v	v	NUM
ejpam-4771	268	56	(	(	PUNCT
ejpam-4771	268	57	hy	hy	NOUN
ejpam-4771	268	58	)	)	PUNCT
ejpam-4771	268	59	∩	∩	PROPN
ejpam-4771	268	60	s	s	PART
ejpam-4771	268	61	̸=	̸=	PROPN
ejpam-4771	268	62	∅	∅	NOUN
ejpam-4771	268	63	;	;	PUNCT
ejpam-4771	268	64	(	(	PUNCT
ejpam-4771	268	65	ii	ii	NOUN
ejpam-4771	268	66	)	)	PUNCT
ejpam-4771	268	67	sv	sv	VERB
ejpam-4771	269	1	⊆	⊆	NUM
ejpam-4771	269	2	v	v	ADP
ejpam-4771	269	3	(	(	PUNCT
ejpam-4771	269	4	hv	hv	X
ejpam-4771	269	5	)	)	PUNCT
ejpam-4771	269	6	is	be	AUX
ejpam-4771	269	7	a	a	DET
ejpam-4771	269	8	2	2	NUM
ejpam-4771	269	9	-	-	PUNCT
ejpam-4771	269	10	locating	locate	VERB
ejpam-4771	269	11	set	set	NOUN
ejpam-4771	269	12	of	of	ADP
ejpam-4771	269	13	hv	hv	PROPN
ejpam-4771	269	14	for	for	ADP
ejpam-4771	269	15	all	all	DET
ejpam-4771	269	16	v	v	ADP
ejpam-4771	269	17	∈	∈	NUM
ejpam-4771	269	18	v	v	NOUN
ejpam-4771	269	19	(	(	PUNCT
ejpam-4771	269	20	g	g	NOUN
ejpam-4771	269	21	)	)	PUNCT
ejpam-4771	269	22	∩ng(a	∩ng(a	NOUN
ejpam-4771	269	23	)	)	PUNCT
ejpam-4771	269	24	;	;	PUNCT
ejpam-4771	269	25	and	and	CCONJ
ejpam-4771	269	26	(	(	PUNCT
ejpam-4771	269	27	iii	iii	X
ejpam-4771	269	28	)	)	PUNCT
ejpam-4771	269	29	dw	dw	NOUN
ejpam-4771	269	30	⊆	⊆	NUM
ejpam-4771	269	31	v	v	NOUN
ejpam-4771	269	32	(	(	PUNCT
ejpam-4771	269	33	hw	hw	NOUN
ejpam-4771	269	34	)	)	PUNCT
ejpam-4771	269	35	is	be	AUX
ejpam-4771	269	36	a	a	DET
ejpam-4771	269	37	2	2	NUM
ejpam-4771	269	38	-	-	PUNCT
ejpam-4771	269	39	locating	locate	VERB
ejpam-4771	269	40	point	point	NOUN
ejpam-4771	269	41	-	-	PUNCT
ejpam-4771	269	42	wise	wise	ADJ
ejpam-4771	269	43	non	non	ADJ
ejpam-4771	269	44	-	-	ADJ
ejpam-4771	269	45	dominating	dominating	ADJ
ejpam-4771	269	46	set	set	NOUN
ejpam-4771	269	47	of	of	ADP
ejpam-4771	269	48	hw	hw	PRON
ejpam-4771	269	49	for	for	ADP
ejpam-4771	269	50	all	all	PRON
ejpam-4771	269	51	w	w	PROPN
ejpam-4771	269	52	∈	∈	PROPN
ejpam-4771	269	53	v	v	NOUN
ejpam-4771	269	54	(	(	PUNCT
ejpam-4771	269	55	g)\ng(a	g)\ng(a	NOUN
ejpam-4771	269	56	)	)	PUNCT
ejpam-4771	269	57	.	.	PUNCT
ejpam-4771	270	1	theorem	theorem	VERB
ejpam-4771	270	2	8	8	NUM
ejpam-4771	270	3	.	.	PUNCT
ejpam-4771	271	1	[	[	X
ejpam-4771	271	2	9	9	NUM
ejpam-4771	271	3	]	]	PUNCT
ejpam-4771	271	4	let	let	VERB
ejpam-4771	271	5	g	g	PRON
ejpam-4771	271	6	be	be	AUX
ejpam-4771	271	7	a	a	DET
ejpam-4771	271	8	connected	connected	ADJ
ejpam-4771	271	9	graph	graph	NOUN
ejpam-4771	271	10	and	and	CCONJ
ejpam-4771	271	11	let	let	VERB
ejpam-4771	271	12	h	h	NOUN
ejpam-4771	271	13	be	be	AUX
ejpam-4771	271	14	any	any	DET
ejpam-4771	271	15	graph	graph	NOUN
ejpam-4771	271	16	.	.	PUNCT
ejpam-4771	272	1	then	then	ADV
ejpam-4771	272	2	a	a	DET
ejpam-4771	272	3	subset	subset	NOUN
ejpam-4771	272	4	c	c	NOUN
ejpam-4771	272	5	of	of	ADP
ejpam-4771	272	6	v	v	PROPN
ejpam-4771	272	7	(	(	PUNCT
ejpam-4771	272	8	g	g	PROPN
ejpam-4771	272	9	◦	◦	NOUN
ejpam-4771	272	10	h	h	NOUN
ejpam-4771	272	11	)	)	PUNCT
ejpam-4771	272	12	is	be	AUX
ejpam-4771	272	13	an	an	DET
ejpam-4771	272	14	outer	outer	ADV
ejpam-4771	272	15	-	-	PUNCT
ejpam-4771	272	16	connected	connect	VERB
ejpam-4771	272	17	hop	hop	NOUN
ejpam-4771	272	18	dominating	dominating	NOUN
ejpam-4771	272	19	set	set	NOUN
ejpam-4771	272	20	of	of	ADP
ejpam-4771	272	21	g	g	PROPN
ejpam-4771	272	22	◦	◦	NOUN
ejpam-4771	272	23	h	h	NOUN
ejpam-4771	272	24	if	if	SCONJ
ejpam-4771	273	1	and	and	CCONJ
ejpam-4771	273	2	only	only	ADV
ejpam-4771	273	3	if	if	SCONJ
ejpam-4771	273	4	c	c	X
ejpam-4771	273	5	=	=	PUNCT
ejpam-4771	273	6	a	a	PRON
ejpam-4771	273	7	∪	∪	ADJ
ejpam-4771	273	8			PROPN
ejpam-4771	273	9	⋃	⋃	ADJ
ejpam-4771	273	10	v∈v	v∈v	NOUN
ejpam-4771	273	11	(	(	PUNCT
ejpam-4771	273	12	g	g	NOUN
ejpam-4771	273	13	)	)	PUNCT
ejpam-4771	273	14	sv	sv	INTJ
ejpam-4771	274	1			PROPN
ejpam-4771	274	2	where	where	SCONJ
ejpam-4771	274	3	sv	sv	PROPN
ejpam-4771	274	4	⊆	⊆	NUM
ejpam-4771	274	5	v	v	PROPN
ejpam-4771	274	6	(	(	PUNCT
ejpam-4771	274	7	hv	hv	PROPN
ejpam-4771	274	8	)	)	PUNCT
ejpam-4771	274	9	for	for	ADP
ejpam-4771	274	10	each	each	DET
ejpam-4771	274	11	v	v	NUM
ejpam-4771	274	12	∈	∈	PROPN
ejpam-4771	274	13	v	v	NOUN
ejpam-4771	274	14	(	(	PUNCT
ejpam-4771	274	15	g	g	NOUN
ejpam-4771	274	16	)	)	PUNCT
ejpam-4771	274	17	and	and	CCONJ
ejpam-4771	274	18	satisfies	satisfy	VERB
ejpam-4771	274	19	each	each	PRON
ejpam-4771	274	20	of	of	ADP
ejpam-4771	274	21	the	the	DET
ejpam-4771	274	22	following	following	ADJ
ejpam-4771	274	23	statements	statement	NOUN
ejpam-4771	274	24	:	:	PUNCT
ejpam-4771	274	25	(	(	PUNCT
ejpam-4771	274	26	i	i	NOUN
ejpam-4771	274	27	)	)	PUNCT
ejpam-4771	274	28	a	a	PRON
ejpam-4771	274	29	=	=	SYM
ejpam-4771	274	30	v	v	NOUN
ejpam-4771	274	31	(	(	PUNCT
ejpam-4771	274	32	g	g	NOUN
ejpam-4771	274	33	)	)	PUNCT
ejpam-4771	274	34	or	or	CCONJ
ejpam-4771	274	35	⟨v	⟨v	NUM
ejpam-4771	274	36	(	(	PUNCT
ejpam-4771	274	37	g)\a⟩	g)\a⟩	PROPN
ejpam-4771	274	38	is	be	AUX
ejpam-4771	274	39	connected	connect	VERB
ejpam-4771	274	40	;	;	PUNCT
ejpam-4771	274	41	(	(	PUNCT
ejpam-4771	274	42	ii	ii	NOUN
ejpam-4771	274	43	)	)	PUNCT
ejpam-4771	274	44	if	if	SCONJ
ejpam-4771	274	45	a	a	DET
ejpam-4771	274	46	=	=	X
ejpam-4771	274	47	v	v	NOUN
ejpam-4771	274	48	(	(	PUNCT
ejpam-4771	274	49	g	g	NOUN
ejpam-4771	274	50	)	)	PUNCT
ejpam-4771	274	51	,	,	PUNCT
ejpam-4771	274	52	then	then	ADV
ejpam-4771	274	53	⟨v	⟨v	CCONJ
ejpam-4771	274	54	(	(	PUNCT
ejpam-4771	274	55	hv)\sv⟩	hv)\sv⟩	NOUN
ejpam-4771	274	56	is	be	AUX
ejpam-4771	274	57	a	a	DET
ejpam-4771	274	58	connected	connect	VERB
ejpam-4771	274	59	proper	proper	ADJ
ejpam-4771	274	60	subgraph	subgraph	NOUN
ejpam-4771	274	61	of	of	ADP
ejpam-4771	274	62	hv	hv	PROPN
ejpam-4771	274	63	for	for	ADP
ejpam-4771	274	64	at	at	ADP
ejpam-4771	274	65	most	most	ADV
ejpam-4771	274	66	one	one	NUM
ejpam-4771	274	67	vertex	vertex	NOUN
ejpam-4771	274	68	v	v	ADP
ejpam-4771	274	69	∈	∈	PROPN
ejpam-4771	274	70	a.	a.	NOUN
ejpam-4771	274	71	otherwise	otherwise	ADV
ejpam-4771	274	72	,	,	PUNCT
ejpam-4771	274	73	sv	sv	PROPN
ejpam-4771	274	74	=	=	SYM
ejpam-4771	274	75	v	v	PROPN
ejpam-4771	274	76	(	(	PUNCT
ejpam-4771	274	77	hv	hv	PROPN
ejpam-4771	274	78	)	)	PUNCT
ejpam-4771	274	79	for	for	ADP
ejpam-4771	274	80	all	all	DET
ejpam-4771	274	81	v	v	NOUN
ejpam-4771	274	82	∈	∈	NOUN
ejpam-4771	274	83	a.	a.	NOUN
ejpam-4771	274	84	(	(	PUNCT
ejpam-4771	274	85	iii	iii	NOUN
ejpam-4771	274	86	)	)	PUNCT
ejpam-4771	274	87	for	for	ADP
ejpam-4771	274	88	all	all	PRON
ejpam-4771	274	89	v	v	NOUN
ejpam-4771	274	90	∈	∈	NOUN
ejpam-4771	274	91	(	(	PUNCT
ejpam-4771	274	92	v	v	NOUN
ejpam-4771	274	93	(	(	PUNCT
ejpam-4771	274	94	g)\ng[a	g)\ng[a	PROPN
ejpam-4771	274	95	,	,	PUNCT
ejpam-4771	274	96	2	2	NUM
ejpam-4771	274	97	]	]	PUNCT
ejpam-4771	274	98	,	,	PUNCT
ejpam-4771	274	99	there	there	PRON
ejpam-4771	274	100	exists	exist	VERB
ejpam-4771	274	101	w	w	PROPN
ejpam-4771	274	102	∈	∈	PROPN
ejpam-4771	274	103	ng(v	ng(v	PUNCT
ejpam-4771	274	104	)	)	PUNCT
ejpam-4771	274	105	such	such	ADJ
ejpam-4771	274	106	that	that	SCONJ
ejpam-4771	274	107	sw	sw	PROPN
ejpam-4771	274	108	̸=	̸=	PROPN
ejpam-4771	274	109	∅	∅	NOUN
ejpam-4771	274	110	;	;	PUNCT
ejpam-4771	274	111	(	(	PUNCT
ejpam-4771	274	112	iv	iv	X
ejpam-4771	274	113	)	)	PUNCT
ejpam-4771	274	114	sv	sv	PROPN
ejpam-4771	274	115	is	be	AUX
ejpam-4771	274	116	a	a	DET
ejpam-4771	274	117	point	point	NOUN
ejpam-4771	274	118	-	-	PUNCT
ejpam-4771	274	119	wise	wise	ADJ
ejpam-4771	274	120	non	non	ADJ
ejpam-4771	274	121	-	-	ADJ
ejpam-4771	274	122	dominating	dominating	ADJ
ejpam-4771	274	123	set	set	NOUN
ejpam-4771	274	124	of	of	ADP
ejpam-4771	274	125	hv	hv	PROPN
ejpam-4771	274	126	for	for	ADP
ejpam-4771	274	127	all	all	PRON
ejpam-4771	274	128	v	v	ADP
ejpam-4771	274	129	∈	∈	NOUN
ejpam-4771	274	130	(	(	PUNCT
ejpam-4771	274	131	v	v	NOUN
ejpam-4771	274	132	(	(	PUNCT
ejpam-4771	274	133	g)\ng[a	g)\ng[a	PROPN
ejpam-4771	274	134	]	]	PUNCT
ejpam-4771	274	135	)	)	PUNCT
ejpam-4771	274	136	.	.	PUNCT
ejpam-4771	275	1	theorem	theorem	NOUN
ejpam-4771	275	2	9	9	NUM
ejpam-4771	275	3	.	.	PUNCT
ejpam-4771	276	1	let	let	VERB
ejpam-4771	276	2	g	g	NOUN
ejpam-4771	276	3	and	and	CCONJ
ejpam-4771	276	4	h	h	NOUN
ejpam-4771	276	5	be	be	AUX
ejpam-4771	276	6	nontrivial	nontrivial	ADJ
ejpam-4771	276	7	connected	connected	ADJ
ejpam-4771	276	8	graphs	graph	NOUN
ejpam-4771	276	9	.	.	PUNCT
ejpam-4771	277	1	a	a	DET
ejpam-4771	277	2	set	set	NOUN
ejpam-4771	277	3	s	s	NOUN
ejpam-4771	277	4	⊆	⊆	NUM
ejpam-4771	277	5	v	v	NOUN
ejpam-4771	277	6	(	(	PUNCT
ejpam-4771	277	7	g	g	PROPN
ejpam-4771	277	8	◦	◦	NOUN
ejpam-4771	277	9	h	h	NOUN
ejpam-4771	277	10	)	)	PUNCT
ejpam-4771	277	11	is	be	AUX
ejpam-4771	277	12	an	an	DET
ejpam-4771	277	13	outer	outer	ADV
ejpam-4771	277	14	-	-	PUNCT
ejpam-4771	277	15	connected	connect	VERB
ejpam-4771	277	16	2	2	NUM
ejpam-4771	277	17	-	-	PUNCT
ejpam-4771	277	18	resolving	resolve	VERB
ejpam-4771	277	19	hop	hop	NOUN
ejpam-4771	277	20	dominating	dominating	NOUN
ejpam-4771	277	21	set	set	NOUN
ejpam-4771	277	22	of	of	ADP
ejpam-4771	277	23	g	g	PROPN
ejpam-4771	277	24	◦	◦	NOUN
ejpam-4771	277	25	h	h	NOUN
ejpam-4771	277	26	if	if	SCONJ
ejpam-4771	278	1	and	and	CCONJ
ejpam-4771	278	2	only	only	ADV
ejpam-4771	278	3	if	if	SCONJ
ejpam-4771	278	4	s	s	VERB
ejpam-4771	278	5	=	=	NOUN
ejpam-4771	278	6	a	a	PRON
ejpam-4771	278	7	∪	∪	ADJ
ejpam-4771	278	8			PROPN
ejpam-4771	278	9	⋃	⋃	ADJ
ejpam-4771	278	10	v∈v	v∈v	NOUN
ejpam-4771	278	11	(	(	PUNCT
ejpam-4771	278	12	g	g	NOUN
ejpam-4771	278	13	)	)	PUNCT
ejpam-4771	278	14	sv	sv	INTJ
ejpam-4771	279	1			PROPN
ejpam-4771	279	2	a.m.	a.m.	PROPN
ejpam-4771	279	3	mahistrado	mahistrado	PROPN
ejpam-4771	279	4	,	,	PUNCT
ejpam-4771	279	5	h.	h.	PROPN
ejpam-4771	279	6	rara	rara	PROPN
ejpam-4771	279	7	/	/	SYM
ejpam-4771	279	8	eur	eur	PROPN
ejpam-4771	279	9	.	.	PUNCT
ejpam-4771	280	1	j.	j.	PROPN
ejpam-4771	280	2	pure	pure	PROPN
ejpam-4771	280	3	appl	appl	PROPN
ejpam-4771	280	4	.	.	PROPN
ejpam-4771	280	5	math	math	PROPN
ejpam-4771	280	6	,	,	PUNCT
ejpam-4771	280	7	16	16	NUM
ejpam-4771	280	8	(	(	PUNCT
ejpam-4771	280	9	2	2	NUM
ejpam-4771	280	10	)	)	PUNCT
ejpam-4771	280	11	(	(	PUNCT
ejpam-4771	280	12	2023	2023	NUM
ejpam-4771	280	13	)	)	PUNCT
ejpam-4771	280	14	,	,	PUNCT
ejpam-4771	280	15	1180	1180	NUM
ejpam-4771	280	16	-	-	SYM
ejpam-4771	280	17	1195	1195	NUM
ejpam-4771	280	18	1189	1189	NUM
ejpam-4771	280	19	where	where	SCONJ
ejpam-4771	280	20	sv	sv	PROPN
ejpam-4771	280	21	⊆	⊆	NUM
ejpam-4771	280	22	v	v	PROPN
ejpam-4771	280	23	(	(	PUNCT
ejpam-4771	280	24	hv	hv	PROPN
ejpam-4771	280	25	)	)	PUNCT
ejpam-4771	280	26	for	for	ADP
ejpam-4771	280	27	each	each	DET
ejpam-4771	280	28	v	v	NUM
ejpam-4771	280	29	∈	∈	PROPN
ejpam-4771	280	30	v	v	NOUN
ejpam-4771	280	31	(	(	PUNCT
ejpam-4771	280	32	g	g	NOUN
ejpam-4771	280	33	)	)	PUNCT
ejpam-4771	280	34	and	and	CCONJ
ejpam-4771	280	35	satisfies	satisfy	VERB
ejpam-4771	280	36	each	each	PRON
ejpam-4771	280	37	of	of	ADP
ejpam-4771	280	38	the	the	DET
ejpam-4771	280	39	following	following	ADJ
ejpam-4771	280	40	statements	statement	NOUN
ejpam-4771	280	41	:	:	PUNCT
ejpam-4771	280	42	(	(	PUNCT
ejpam-4771	280	43	i	i	NOUN
ejpam-4771	280	44	)	)	PUNCT
ejpam-4771	280	45	a	a	PRON
ejpam-4771	280	46	=	=	SYM
ejpam-4771	280	47	v	v	NOUN
ejpam-4771	280	48	(	(	PUNCT
ejpam-4771	280	49	g	g	NOUN
ejpam-4771	280	50	)	)	PUNCT
ejpam-4771	280	51	or	or	CCONJ
ejpam-4771	280	52	⟨v	⟨v	NUM
ejpam-4771	280	53	(	(	PUNCT
ejpam-4771	280	54	g)\a⟩	g)\a⟩	PROPN
ejpam-4771	280	55	is	be	AUX
ejpam-4771	280	56	connected	connect	VERB
ejpam-4771	280	57	;	;	PUNCT
ejpam-4771	280	58	(	(	PUNCT
ejpam-4771	280	59	ii	ii	NOUN
ejpam-4771	280	60	)	)	PUNCT
ejpam-4771	280	61	if	if	SCONJ
ejpam-4771	280	62	a	a	DET
ejpam-4771	280	63	=	=	X
ejpam-4771	280	64	v	v	NOUN
ejpam-4771	280	65	(	(	PUNCT
ejpam-4771	280	66	g	g	NOUN
ejpam-4771	280	67	)	)	PUNCT
ejpam-4771	280	68	,	,	PUNCT
ejpam-4771	280	69	then	then	ADV
ejpam-4771	280	70	⟨v	⟨v	CCONJ
ejpam-4771	280	71	(	(	PUNCT
ejpam-4771	280	72	hv)\sv⟩	hv)\sv⟩	NOUN
ejpam-4771	280	73	is	be	AUX
ejpam-4771	280	74	a	a	DET
ejpam-4771	280	75	connected	connect	VERB
ejpam-4771	280	76	proper	proper	ADJ
ejpam-4771	280	77	subgraph	subgraph	NOUN
ejpam-4771	280	78	of	of	ADP
ejpam-4771	280	79	hv	hv	PROPN
ejpam-4771	280	80	for	for	ADP
ejpam-4771	280	81	at	at	ADP
ejpam-4771	280	82	most	most	ADV
ejpam-4771	280	83	one	one	NUM
ejpam-4771	280	84	vertex	vertex	NOUN
ejpam-4771	280	85	v	v	ADP
ejpam-4771	280	86	∈	∈	PROPN
ejpam-4771	280	87	a.	a.	NOUN
ejpam-4771	280	88	otherwise	otherwise	ADV
ejpam-4771	280	89	,	,	PUNCT
ejpam-4771	280	90	sv	sv	PROPN
ejpam-4771	280	91	=	=	SYM
ejpam-4771	280	92	v	v	PROPN
ejpam-4771	280	93	(	(	PUNCT
ejpam-4771	280	94	hv	hv	PROPN
ejpam-4771	280	95	)	)	PUNCT
ejpam-4771	280	96	for	for	ADP
ejpam-4771	280	97	all	all	PRON
ejpam-4771	280	98	v	v	ADP
ejpam-4771	280	99	∈	∈	PRON
ejpam-4771	280	100	a	a	PRON
ejpam-4771	280	101	;	;	PUNCT
ejpam-4771	280	102	(	(	PUNCT
ejpam-4771	280	103	iii	iii	X
ejpam-4771	280	104	)	)	PUNCT
ejpam-4771	280	105	sv	sv	PROPN
ejpam-4771	280	106	is	be	AUX
ejpam-4771	280	107	a	a	DET
ejpam-4771	280	108	2	2	NUM
ejpam-4771	280	109	-	-	PUNCT
ejpam-4771	280	110	locating	locate	VERB
ejpam-4771	280	111	set	set	NOUN
ejpam-4771	280	112	for	for	ADP
ejpam-4771	280	113	all	all	DET
ejpam-4771	280	114	v	v	ADP
ejpam-4771	280	115	∈	∈	NOUN
ejpam-4771	280	116	v	v	NOUN
ejpam-4771	280	117	(	(	PUNCT
ejpam-4771	280	118	g	g	NOUN
ejpam-4771	280	119	)	)	PUNCT
ejpam-4771	280	120	where	where	SCONJ
ejpam-4771	280	121	sv	sv	PROPN
ejpam-4771	280	122	is	be	AUX
ejpam-4771	280	123	a	a	DET
ejpam-4771	280	124	(	(	PUNCT
ejpam-4771	280	125	2	2	NUM
ejpam-4771	280	126	-	-	PUNCT
ejpam-4771	280	127	locating	locate	VERB
ejpam-4771	280	128	)	)	PUNCT
ejpam-4771	280	129	point	point	NOUN
ejpam-4771	280	130	-	-	PUNCT
ejpam-4771	280	131	wise	wise	ADJ
ejpam-4771	280	132	non	non	ADJ
ejpam-4771	280	133	-	-	ADJ
ejpam-4771	280	134	dominating	dominating	ADJ
ejpam-4771	280	135	set	set	NOUN
ejpam-4771	280	136	of	of	ADP
ejpam-4771	280	137	hv	hv	PROPN
ejpam-4771	280	138	if	if	SCONJ
ejpam-4771	280	139	v	v	ADP
ejpam-4771	280	140	∈	∈	PROPN
ejpam-4771	280	141	(	(	PUNCT
ejpam-4771	280	142	v	v	NOUN
ejpam-4771	280	143	(	(	PUNCT
ejpam-4771	280	144	g)\ng[a	g)\ng[a	PROPN
ejpam-4771	280	145	]	]	PUNCT
ejpam-4771	280	146	)	)	PUNCT
ejpam-4771	280	147	.	.	PUNCT
ejpam-4771	281	1	proof	proof	NOUN
ejpam-4771	281	2	.	.	PUNCT
ejpam-4771	282	1	suppose	suppose	VERB
ejpam-4771	282	2	s	s	VERB
ejpam-4771	282	3	⊆	⊆	NUM
ejpam-4771	282	4	v	v	NOUN
ejpam-4771	282	5	(	(	PUNCT
ejpam-4771	282	6	g	g	PROPN
ejpam-4771	282	7	◦	◦	NOUN
ejpam-4771	282	8	h	h	NOUN
ejpam-4771	282	9	)	)	PUNCT
ejpam-4771	282	10	is	be	AUX
ejpam-4771	282	11	an	an	DET
ejpam-4771	282	12	outer	outer	ADV
ejpam-4771	282	13	-	-	PUNCT
ejpam-4771	282	14	connected	connect	VERB
ejpam-4771	282	15	2	2	NUM
ejpam-4771	282	16	-	-	PUNCT
ejpam-4771	282	17	resolving	resolve	VERB
ejpam-4771	282	18	hop	hop	NOUN
ejpam-4771	282	19	dominating	dominating	NOUN
ejpam-4771	282	20	set	set	NOUN
ejpam-4771	282	21	of	of	ADP
ejpam-4771	282	22	g	g	PROPN
ejpam-4771	282	23	◦	◦	NOUN
ejpam-4771	282	24	h.	h.	NOUN
ejpam-4771	282	25	let	let	VERB
ejpam-4771	282	26	a	a	DET
ejpam-4771	282	27	=	=	PUNCT
ejpam-4771	282	28	s∩v	s∩v	NOUN
ejpam-4771	282	29	(	(	PUNCT
ejpam-4771	282	30	g	g	NOUN
ejpam-4771	282	31	)	)	PUNCT
ejpam-4771	282	32	,	,	PUNCT
ejpam-4771	283	1	sv	sv	INTJ
ejpam-4771	284	1	=	=	SYM
ejpam-4771	284	2	s∩v	s∩v	PROPN
ejpam-4771	284	3	(	(	PUNCT
ejpam-4771	284	4	hv	hv	PROPN
ejpam-4771	284	5	)	)	PUNCT
ejpam-4771	284	6	for	for	ADP
ejpam-4771	284	7	each	each	DET
ejpam-4771	284	8	v	v	NUM
ejpam-4771	284	9	∈	∈	PROPN
ejpam-4771	284	10	v	v	NOUN
ejpam-4771	284	11	(	(	PUNCT
ejpam-4771	284	12	g	g	NOUN
ejpam-4771	284	13	)	)	PUNCT
ejpam-4771	284	14	.	.	PUNCT
ejpam-4771	285	1	then	then	ADV
ejpam-4771	285	2	s	s	VERB
ejpam-4771	285	3	=	=	SYM
ejpam-4771	285	4	a∪	a∪	PROPN
ejpam-4771	285	5	(	(	PUNCT
ejpam-4771	285	6	⋃	⋃	NOUN
ejpam-4771	285	7	v∈v	v∈v	NOUN
ejpam-4771	285	8	(	(	PUNCT
ejpam-4771	285	9	g	g	NOUN
ejpam-4771	285	10	)	)	PUNCT
ejpam-4771	285	11	sv	sv	NOUN
ejpam-4771	285	12	)	)	PUNCT
ejpam-4771	286	1	since	since	SCONJ
ejpam-4771	286	2	s	s	NOUN
ejpam-4771	286	3	is	be	AUX
ejpam-4771	286	4	an	an	DET
ejpam-4771	286	5	outer	outer	ADV
ejpam-4771	286	6	-	-	PUNCT
ejpam-4771	286	7	connected	connect	VERB
ejpam-4771	286	8	hop	hop	NOUN
ejpam-4771	286	9	dominating	dominating	NOUN
ejpam-4771	286	10	set	set	NOUN
ejpam-4771	286	11	,	,	PUNCT
ejpam-4771	286	12	(	(	PUNCT
ejpam-4771	286	13	i	i	NOUN
ejpam-4771	286	14	)	)	PUNCT
ejpam-4771	286	15	and	and	CCONJ
ejpam-4771	286	16	(	(	PUNCT
ejpam-4771	286	17	ii	ii	NOUN
ejpam-4771	286	18	)	)	PUNCT
ejpam-4771	286	19	follow	follow	VERB
ejpam-4771	286	20	immediately	immediately	ADV
ejpam-4771	286	21	from	from	ADP
ejpam-4771	286	22	theorem	theorem	ADJ
ejpam-4771	286	23	8	8	NUM
ejpam-4771	286	24	.	.	PUNCT
ejpam-4771	287	1	now	now	ADV
ejpam-4771	287	2	,	,	PUNCT
ejpam-4771	287	3	since	since	SCONJ
ejpam-4771	287	4	s	s	NOUN
ejpam-4771	287	5	is	be	AUX
ejpam-4771	287	6	a	a	DET
ejpam-4771	287	7	2	2	NUM
ejpam-4771	287	8	-	-	PUNCT
ejpam-4771	287	9	resolving	resolve	VERB
ejpam-4771	287	10	hop	hop	NOUN
ejpam-4771	287	11	dominating	dominating	NOUN
ejpam-4771	287	12	set	set	NOUN
ejpam-4771	287	13	,	,	PUNCT
ejpam-4771	287	14	by	by	ADP
ejpam-4771	287	15	theorem	theorem	NOUN
ejpam-4771	287	16	7	7	NUM
ejpam-4771	287	17	,	,	PUNCT
ejpam-4771	287	18	(	(	PUNCT
ejpam-4771	287	19	iii	iii	NOUN
ejpam-4771	287	20	)	)	PUNCT
ejpam-4771	287	21	holds	hold	VERB
ejpam-4771	287	22	.	.	PUNCT
ejpam-4771	288	1	conversely	conversely	ADV
ejpam-4771	288	2	,	,	PUNCT
ejpam-4771	288	3	let	let	VERB
ejpam-4771	288	4	s	s	PRON
ejpam-4771	288	5	be	be	AUX
ejpam-4771	288	6	the	the	DET
ejpam-4771	288	7	set	set	NOUN
ejpam-4771	288	8	as	as	SCONJ
ejpam-4771	288	9	described	describe	VERB
ejpam-4771	288	10	and	and	CCONJ
ejpam-4771	288	11	satisfies	satisfy	VERB
ejpam-4771	288	12	the	the	DET
ejpam-4771	288	13	given	give	VERB
ejpam-4771	288	14	conditions	condition	NOUN
ejpam-4771	288	15	.	.	PUNCT
ejpam-4771	289	1	by	by	ADP
ejpam-4771	289	2	theorem	theorem	NOUN
ejpam-4771	289	3	7	7	NUM
ejpam-4771	289	4	,	,	PUNCT
ejpam-4771	289	5	s	s	X
ejpam-4771	289	6	is	be	AUX
ejpam-4771	289	7	2	2	NUM
ejpam-4771	289	8	-	-	PUNCT
ejpam-4771	289	9	resolving	resolve	VERB
ejpam-4771	289	10	hop	hop	NOUN
ejpam-4771	289	11	dominating	dominating	NOUN
ejpam-4771	289	12	set	set	NOUN
ejpam-4771	289	13	.	.	PUNCT
ejpam-4771	290	1	furthermore	furthermore	ADV
ejpam-4771	290	2	,	,	PUNCT
ejpam-4771	290	3	because	because	SCONJ
ejpam-4771	290	4	(	(	PUNCT
ejpam-4771	290	5	i	i	NOUN
ejpam-4771	290	6	)	)	PUNCT
ejpam-4771	290	7	and	and	CCONJ
ejpam-4771	290	8	(	(	PUNCT
ejpam-4771	290	9	ii	ii	NOUN
ejpam-4771	290	10	)	)	PUNCT
ejpam-4771	290	11	hold	hold	VERB
ejpam-4771	290	12	,	,	PUNCT
ejpam-4771	290	13	s	s	VERB
ejpam-4771	290	14	is	be	AUX
ejpam-4771	290	15	an	an	DET
ejpam-4771	290	16	outer	outer	ADV
ejpam-4771	290	17	-	-	PUNCT
ejpam-4771	290	18	connected	connect	VERB
ejpam-4771	290	19	hop	hop	NOUN
ejpam-4771	290	20	dominating	dominating	NOUN
ejpam-4771	290	21	set	set	NOUN
ejpam-4771	290	22	.	.	PUNCT
ejpam-4771	291	1	accordingly	accordingly	ADV
ejpam-4771	291	2	,	,	PUNCT
ejpam-4771	291	3	s	s	VERB
ejpam-4771	291	4	is	be	AUX
ejpam-4771	291	5	an	an	DET
ejpam-4771	291	6	outer	outer	ADV
ejpam-4771	291	7	-	-	PUNCT
ejpam-4771	291	8	connected	connect	VERB
ejpam-4771	291	9	2	2	NUM
ejpam-4771	291	10	-	-	PUNCT
ejpam-4771	291	11	resolving	resolve	VERB
ejpam-4771	291	12	hop	hop	NOUN
ejpam-4771	291	13	dominating	dominating	NOUN
ejpam-4771	291	14	set	set	VERB
ejpam-4771	291	15	in	in	ADP
ejpam-4771	291	16	g	g	PROPN
ejpam-4771	291	17	◦	◦	NOUN
ejpam-4771	291	18	h.	h.	NOUN
ejpam-4771	291	19	corollary	corollary	ADJ
ejpam-4771	291	20	4	4	NUM
ejpam-4771	291	21	.	.	PUNCT
ejpam-4771	292	1	let	let	VERB
ejpam-4771	292	2	g	g	NOUN
ejpam-4771	292	3	and	and	CCONJ
ejpam-4771	292	4	h	h	NOUN
ejpam-4771	292	5	be	be	AUX
ejpam-4771	292	6	connected	connect	VERB
ejpam-4771	292	7	graphs	graph	NOUN
ejpam-4771	292	8	of	of	ADP
ejpam-4771	292	9	orders	order	NOUN
ejpam-4771	292	10	n	n	PRON
ejpam-4771	292	11	and	and	CCONJ
ejpam-4771	292	12	m	m	PROPN
ejpam-4771	292	13	,	,	PUNCT
ejpam-4771	292	14	respectively	respectively	ADV
ejpam-4771	292	15	.	.	PUNCT
ejpam-4771	293	1	then	then	ADV
ejpam-4771	293	2	γ̃c2rh(g	γ̃c2rh(g	PROPN
ejpam-4771	293	3	◦	◦	NOUN
ejpam-4771	293	4	h	h	NOUN
ejpam-4771	293	5	)	)	PUNCT
ejpam-4771	293	6	≤	≤	NUM
ejpam-4771	293	7	min{γ̃c(g)(m+	min{γ̃c(g)(m+	NOUN
ejpam-4771	293	8	1	1	NUM
ejpam-4771	293	9	)	)	PUNCT
ejpam-4771	293	10	+	+	CCONJ
ejpam-4771	293	11	(	(	PUNCT
ejpam-4771	293	12	n−	n−	NOUN
ejpam-4771	293	13	γ̃c(g))ln2(h	γ̃c(g))ln2(h	NOUN
ejpam-4771	293	14	)	)	PUNCT
ejpam-4771	293	15	,	,	PUNCT
ejpam-4771	293	16	nlnpnd	nlnpnd	NOUN
ejpam-4771	293	17	2	2	NUM
ejpam-4771	293	18	}	}	PUNCT
ejpam-4771	293	19	.	.	PUNCT
ejpam-4771	294	1	proof	proof	NOUN
ejpam-4771	294	2	.	.	PUNCT
ejpam-4771	295	1	let	let	VERB
ejpam-4771	295	2	a	a	PRON
ejpam-4771	295	3	be	be	AUX
ejpam-4771	295	4	a	a	DET
ejpam-4771	295	5	γ̃c	γ̃c	NUM
ejpam-4771	295	6	-	-	PUNCT
ejpam-4771	295	7	set	set	NOUN
ejpam-4771	295	8	of	of	ADP
ejpam-4771	295	9	g	g	PROPN
ejpam-4771	295	10	and	and	CCONJ
ejpam-4771	295	11	sv	sv	PROPN
ejpam-4771	295	12	be	be	AUX
ejpam-4771	295	13	an	an	DET
ejpam-4771	295	14	ln2	ln2	NOUN
ejpam-4771	295	15	-	-	PUNCT
ejpam-4771	295	16	set	set	NOUN
ejpam-4771	295	17	of	of	ADP
ejpam-4771	295	18	hv	hv	PROPN
ejpam-4771	295	19	for	for	ADP
ejpam-4771	295	20	each	each	PRON
ejpam-4771	295	21	v	v	NUM
ejpam-4771	295	22	∈	∈	PROPN
ejpam-4771	295	23	v	v	NOUN
ejpam-4771	295	24	(	(	PUNCT
ejpam-4771	295	25	g	g	NOUN
ejpam-4771	295	26	)	)	PUNCT
ejpam-4771	295	27	\	\	NOUN
ejpam-4771	295	28	a.	a.	NOUN
ejpam-4771	295	29	thus	thus	ADV
ejpam-4771	295	30	,	,	PUNCT
ejpam-4771	295	31	by	by	ADP
ejpam-4771	295	32	theorem	theorem	NOUN
ejpam-4771	295	33	9	9	NUM
ejpam-4771	295	34	s	s	NOUN
ejpam-4771	295	35	=	=	PUNCT
ejpam-4771	295	36	a	a	DET
ejpam-4771	295	37	∪	∪	X
ejpam-4771	295	38	(	(	PUNCT
ejpam-4771	295	39	⋃	⋃	NOUN
ejpam-4771	295	40	v∈v	v∈v	NOUN
ejpam-4771	295	41	(	(	PUNCT
ejpam-4771	295	42	g	g	NOUN
ejpam-4771	295	43	)	)	PUNCT
ejpam-4771	295	44	v	v	NOUN
ejpam-4771	295	45	(	(	PUNCT
ejpam-4771	295	46	hv	hv	NOUN
ejpam-4771	295	47	)	)	PUNCT
ejpam-4771	295	48	)	)	PUNCT
ejpam-4771	295	49	∪	∪	ADP
ejpam-4771	295	50	(	(	PUNCT
ejpam-4771	295	51	⋃	⋃	NOUN
ejpam-4771	295	52	v∈v	v∈v	NOUN
ejpam-4771	295	53	(	(	PUNCT
ejpam-4771	295	54	g)\a	g)\a	NOUN
ejpam-4771	295	55	sv	sv	PROPN
ejpam-4771	295	56	)	)	PUNCT
ejpam-4771	295	57	is	be	AUX
ejpam-4771	295	58	an	an	DET
ejpam-4771	295	59	outer	outer	ADV
ejpam-4771	295	60	-	-	PUNCT
ejpam-4771	295	61	connected	connect	VERB
ejpam-4771	295	62	2	2	NUM
ejpam-4771	295	63	-	-	PUNCT
ejpam-4771	295	64	resolving	resolve	VERB
ejpam-4771	295	65	hop	hop	NOUN
ejpam-4771	295	66	dominating	dominating	NOUN
ejpam-4771	295	67	set	set	NOUN
ejpam-4771	295	68	.	.	PUNCT
ejpam-4771	296	1	hence	hence	ADV
ejpam-4771	296	2	,	,	PUNCT
ejpam-4771	296	3	γ̃c2rh(g	γ̃c2rh(g	PROPN
ejpam-4771	296	4	◦	◦	NOUN
ejpam-4771	296	5	h	h	NOUN
ejpam-4771	296	6	)	)	PUNCT
ejpam-4771	296	7	≤	≤	NUM
ejpam-4771	296	8	|s|	|s|	NOUN
ejpam-4771	296	9	=	=	SYM
ejpam-4771	296	10	|a|+	|a|+	NOUN
ejpam-4771	296	11	∑	∑	PUNCT
ejpam-4771	296	12	v∈v	v∈v	NOUN
ejpam-4771	296	13	(	(	PUNCT
ejpam-4771	296	14	g	g	NOUN
ejpam-4771	296	15	)	)	PUNCT
ejpam-4771	296	16	|v	|v	PROPN
ejpam-4771	296	17	(	(	PUNCT
ejpam-4771	296	18	hv)|+	hv)|+	PROPN
ejpam-4771	296	19	∑	∑	PUNCT
ejpam-4771	296	20	v∈v	v∈v	NOUN
ejpam-4771	296	21	(	(	PUNCT
ejpam-4771	296	22	g)\a	g)\a	NOUN
ejpam-4771	296	23	|sv|	|sv|	NOUN
ejpam-4771	296	24	=	=	NOUN
ejpam-4771	296	25	γ̃c(g)(m+	γ̃c(g)(m+	X
ejpam-4771	296	26	1	1	NUM
ejpam-4771	296	27	)	)	PUNCT
ejpam-4771	296	28	+	+	CCONJ
ejpam-4771	296	29	(	(	PUNCT
ejpam-4771	296	30	n−	n−	NOUN
ejpam-4771	296	31	γ̃c(g))ln2(h	γ̃c(g))ln2(h	NOUN
ejpam-4771	296	32	)	)	PUNCT
ejpam-4771	296	33	.	.	PUNCT
ejpam-4771	297	1	let	let	VERB
ejpam-4771	297	2	a	a	DET
ejpam-4771	297	3	=	=	NOUN
ejpam-4771	297	4	∅	∅	NOUN
ejpam-4771	297	5	,	,	PUNCT
ejpam-4771	297	6	sw	sw	PROPN
ejpam-4771	297	7	be	be	AUX
ejpam-4771	297	8	a	a	DET
ejpam-4771	297	9	lnpnd	lnpnd	ADJ
ejpam-4771	297	10	2	2	NUM
ejpam-4771	297	11	-set	-set	PUNCT
ejpam-4771	297	12	of	of	ADP
ejpam-4771	297	13	hw	hw	PRON
ejpam-4771	297	14	.	.	PUNCT
ejpam-4771	298	1	then	then	ADV
ejpam-4771	298	2	s	s	VERB
ejpam-4771	298	3	=	=	PUNCT
ejpam-4771	298	4	a	a	DET
ejpam-4771	298	5	∪	∪	X
ejpam-4771	298	6	(	(	PUNCT
ejpam-4771	298	7	⋃	⋃	PROPN
ejpam-4771	298	8	w∈v	w∈v	PROPN
ejpam-4771	298	9	(	(	PUNCT
ejpam-4771	298	10	g	g	NOUN
ejpam-4771	298	11	)	)	PUNCT
ejpam-4771	298	12	sw	sw	PROPN
ejpam-4771	298	13	)	)	PUNCT
ejpam-4771	298	14	is	be	AUX
ejpam-4771	298	15	an	an	DET
ejpam-4771	298	16	outer	outer	ADV
ejpam-4771	298	17	-	-	PUNCT
ejpam-4771	298	18	connected	connect	VERB
ejpam-4771	298	19	2	2	NUM
ejpam-4771	298	20	-	-	PUNCT
ejpam-4771	298	21	resolving	resolve	VERB
ejpam-4771	298	22	hop	hop	NOUN
ejpam-4771	298	23	dominating	dominating	NOUN
ejpam-4771	298	24	set	set	VERB
ejpam-4771	298	25	in	in	ADP
ejpam-4771	298	26	g	g	PROPN
ejpam-4771	298	27	◦	◦	NOUN
ejpam-4771	298	28	h	h	NOUN
ejpam-4771	298	29	by	by	ADP
ejpam-4771	298	30	theorem	theorem	NOUN
ejpam-4771	298	31	9	9	NUM
ejpam-4771	298	32	.	.	PUNCT
ejpam-4771	299	1	hence	hence	ADV
ejpam-4771	299	2	,	,	PUNCT
ejpam-4771	299	3	γ̃c2rh(g	γ̃c2rh(g	PROPN
ejpam-4771	299	4	◦	◦	NOUN
ejpam-4771	299	5	h	h	NOUN
ejpam-4771	299	6	)	)	PUNCT
ejpam-4771	299	7	≤	≤	NUM
ejpam-4771	299	8	|s|	|s|	NOUN
ejpam-4771	299	9	=	=	SYM
ejpam-4771	299	10	|a|+	|a|+	VERB
ejpam-4771	299	11	∑	∑	PUNCT
ejpam-4771	299	12	w∈v	w∈v	PROPN
ejpam-4771	299	13	(	(	PUNCT
ejpam-4771	299	14	g	g	NOUN
ejpam-4771	299	15	)	)	PUNCT
ejpam-4771	299	16	|sw|	|sw|	PROPN
ejpam-4771	299	17	=	=	SYM
ejpam-4771	299	18	|v	|v	PROPN
ejpam-4771	299	19	(	(	PUNCT
ejpam-4771	299	20	g)|	g)|	PROPN
ejpam-4771	299	21	·	·	PUNCT
ejpam-4771	299	22	|sw|	|sw|	NOUN
ejpam-4771	299	23	=	=	PUNCT
ejpam-4771	299	24	n(lnpnd	n(lnpnd	NOUN
ejpam-4771	299	25	2	2	NUM
ejpam-4771	299	26	(	(	PUNCT
ejpam-4771	299	27	h	h	NOUN
ejpam-4771	299	28	)	)	PUNCT
ejpam-4771	299	29	)	)	PUNCT
ejpam-4771	299	30	.	.	PUNCT
ejpam-4771	300	1	accordingly	accordingly	ADV
ejpam-4771	300	2	,	,	PUNCT
ejpam-4771	300	3	γ̃c2rh(g	γ̃c2rh(g	PROPN
ejpam-4771	300	4	◦	◦	NOUN
ejpam-4771	300	5	h	h	NOUN
ejpam-4771	300	6	)	)	PUNCT
ejpam-4771	300	7	≤	≤	NUM
ejpam-4771	300	8	min{γ̃c(g)(m+	min{γ̃c(g)(m+	NOUN
ejpam-4771	300	9	1	1	NUM
ejpam-4771	300	10	)	)	PUNCT
ejpam-4771	300	11	+	+	CCONJ
ejpam-4771	300	12	(	(	PUNCT
ejpam-4771	300	13	n−	n−	NOUN
ejpam-4771	300	14	γ̃c(g))ln2(h	γ̃c(g))ln2(h	NOUN
ejpam-4771	300	15	)	)	PUNCT
ejpam-4771	300	16	,	,	PUNCT
ejpam-4771	300	17	nlnpnd	nlnpnd	NOUN
ejpam-4771	300	18	2	2	NUM
ejpam-4771	300	19	}	}	PUNCT
ejpam-4771	300	20	.	.	PUNCT
ejpam-4771	301	1	a.m.	a.m.	PROPN
ejpam-4771	301	2	mahistrado	mahistrado	PROPN
ejpam-4771	301	3	,	,	PUNCT
ejpam-4771	301	4	h.	h.	PROPN
ejpam-4771	301	5	rara	rara	PROPN
ejpam-4771	301	6	/	/	SYM
ejpam-4771	301	7	eur	eur	PROPN
ejpam-4771	301	8	.	.	PUNCT
ejpam-4771	302	1	j.	j.	PROPN
ejpam-4771	302	2	pure	pure	PROPN
ejpam-4771	302	3	appl	appl	PROPN
ejpam-4771	302	4	.	.	PROPN
ejpam-4771	302	5	math	math	PROPN
ejpam-4771	302	6	,	,	PUNCT
ejpam-4771	302	7	16	16	NUM
ejpam-4771	302	8	(	(	PUNCT
ejpam-4771	302	9	2	2	NUM
ejpam-4771	302	10	)	)	PUNCT
ejpam-4771	302	11	(	(	PUNCT
ejpam-4771	302	12	2023	2023	NUM
ejpam-4771	302	13	)	)	PUNCT
ejpam-4771	302	14	,	,	PUNCT
ejpam-4771	302	15	1180	1180	NUM
ejpam-4771	302	16	-	-	SYM
ejpam-4771	302	17	1195	1195	NUM
ejpam-4771	302	18	1190	1190	NUM
ejpam-4771	302	19	6	6	NUM
ejpam-4771	302	20	.	.	PUNCT
ejpam-4771	302	21	edge	edge	NOUN
ejpam-4771	302	22	corona	corona	NOUN
ejpam-4771	302	23	of	of	ADP
ejpam-4771	302	24	graphs	graph	NOUN
ejpam-4771	302	25	this	this	DET
ejpam-4771	302	26	section	section	NOUN
ejpam-4771	302	27	presents	present	VERB
ejpam-4771	302	28	characterizations	characterization	NOUN
ejpam-4771	302	29	in	in	ADP
ejpam-4771	302	30	the	the	DET
ejpam-4771	302	31	outer	outer	ADV
ejpam-4771	302	32	-	-	PUNCT
ejpam-4771	302	33	connected	connect	VERB
ejpam-4771	302	34	2	2	NUM
ejpam-4771	302	35	-	-	PUNCT
ejpam-4771	302	36	resolving	resolve	VERB
ejpam-4771	302	37	hop	hop	NOUN
ejpam-4771	302	38	dominating	dominating	NOUN
ejpam-4771	302	39	sets	set	NOUN
ejpam-4771	302	40	in	in	ADP
ejpam-4771	302	41	the	the	DET
ejpam-4771	302	42	edge	edge	NOUN
ejpam-4771	302	43	corona	corona	NOUN
ejpam-4771	302	44	of	of	ADP
ejpam-4771	302	45	graphs	graph	NOUN
ejpam-4771	302	46	.	.	PUNCT
ejpam-4771	303	1	remark	remark	NOUN
ejpam-4771	303	2	4	4	NUM
ejpam-4771	303	3	.	.	PUNCT
ejpam-4771	304	1	[	[	X
ejpam-4771	304	2	12	12	NUM
ejpam-4771	304	3	]	]	PUNCT
ejpam-4771	304	4	let	let	VERB
ejpam-4771	304	5	uv	uv	NOUN
ejpam-4771	304	6	∈	∈	PROPN
ejpam-4771	304	7	e(g	e(g	PROPN
ejpam-4771	304	8	)	)	PUNCT
ejpam-4771	304	9	.	.	PUNCT
ejpam-4771	305	1	for	for	ADP
ejpam-4771	305	2	every	every	DET
ejpam-4771	305	3	x	x	PROPN
ejpam-4771	305	4	,	,	PUNCT
ejpam-4771	305	5	y	y	PROPN
ejpam-4771	305	6	∈	∈	PROPN
ejpam-4771	305	7	v	v	PROPN
ejpam-4771	305	8	(	(	PUNCT
ejpam-4771	305	9	huv	huv	PROPN
ejpam-4771	305	10	)	)	PUNCT
ejpam-4771	305	11	,	,	PUNCT
ejpam-4771	305	12	dg⋄h(x	dg⋄h(x	PROPN
ejpam-4771	305	13	,	,	PUNCT
ejpam-4771	305	14	w	w	PROPN
ejpam-4771	305	15	)	)	PUNCT
ejpam-4771	305	16	=	=	SYM
ejpam-4771	306	1	dg⋄h(y	dg⋄h(y	PROPN
ejpam-4771	306	2	,	,	PUNCT
ejpam-4771	306	3	w	w	NOUN
ejpam-4771	306	4	)	)	PUNCT
ejpam-4771	306	5	,	,	PUNCT
ejpam-4771	306	6	dg⋄h(u	dg⋄h(u	X
ejpam-4771	306	7	,	,	PUNCT
ejpam-4771	306	8	w	w	NOUN
ejpam-4771	306	9	)	)	PUNCT
ejpam-4771	306	10	=	=	SYM
ejpam-4771	307	1	dg⋄h(x	dg⋄h(x	PROPN
ejpam-4771	307	2	,	,	PUNCT
ejpam-4771	307	3	w	w	PROPN
ejpam-4771	307	4	)	)	PUNCT
ejpam-4771	307	5	,	,	PUNCT
ejpam-4771	307	6	and	and	CCONJ
ejpam-4771	307	7	dg⋄h(v	dg⋄h(v	PROPN
ejpam-4771	307	8	,	,	PUNCT
ejpam-4771	307	9	w)+1	w)+1	X
ejpam-4771	307	10	=	=	SYM
ejpam-4771	307	11	dg⋄h(x	dg⋄h(x	PROPN
ejpam-4771	307	12	,	,	PUNCT
ejpam-4771	307	13	w	w	PROPN
ejpam-4771	307	14	)	)	PUNCT
ejpam-4771	307	15	for	for	ADP
ejpam-4771	307	16	every	every	DET
ejpam-4771	307	17	w	w	PROPN
ejpam-4771	307	18	∈	∈	PROPN
ejpam-4771	307	19	v	v	NOUN
ejpam-4771	307	20	(	(	PUNCT
ejpam-4771	307	21	g⋄h)\v	g⋄h)\v	PROPN
ejpam-4771	307	22	(	(	PUNCT
ejpam-4771	307	23	huv	huv	PROPN
ejpam-4771	307	24	)	)	PUNCT
ejpam-4771	307	25	.	.	PUNCT
ejpam-4771	308	1	remark	remark	NOUN
ejpam-4771	308	2	5	5	NUM
ejpam-4771	308	3	.	.	PUNCT
ejpam-4771	309	1	[	[	X
ejpam-4771	309	2	12	12	NUM
ejpam-4771	309	3	]	]	PUNCT
ejpam-4771	309	4	let	let	VERB
ejpam-4771	309	5	g	g	NOUN
ejpam-4771	309	6	and	and	CCONJ
ejpam-4771	309	7	h	h	NOUN
ejpam-4771	309	8	be	be	AUX
ejpam-4771	309	9	nontrivial	nontrivial	ADJ
ejpam-4771	309	10	connected	connected	ADJ
ejpam-4771	309	11	graphs	graph	NOUN
ejpam-4771	309	12	,	,	PUNCT
ejpam-4771	309	13	c	c	PROPN
ejpam-4771	309	14	⊆	⊆	NUM
ejpam-4771	309	15	v	v	NOUN
ejpam-4771	309	16	(	(	PUNCT
ejpam-4771	309	17	g	g	PROPN
ejpam-4771	309	18	⋄h	⋄h	PROPN
ejpam-4771	309	19	)	)	PUNCT
ejpam-4771	309	20	and	and	CCONJ
ejpam-4771	309	21	suv	suv	PROPN
ejpam-4771	309	22	=	=	SYM
ejpam-4771	309	23	v	v	PROPN
ejpam-4771	309	24	(	(	PUNCT
ejpam-4771	309	25	huv	huv	PROPN
ejpam-4771	309	26	)	)	PUNCT
ejpam-4771	309	27	∩	∩	NOUN
ejpam-4771	309	28	c	c	X
ejpam-4771	309	29	where	where	SCONJ
ejpam-4771	309	30	uv	uv	NOUN
ejpam-4771	309	31	∈	∈	PROPN
ejpam-4771	309	32	e(g	e(g	PROPN
ejpam-4771	309	33	)	)	PUNCT
ejpam-4771	309	34	.	.	PUNCT
ejpam-4771	310	1	for	for	ADP
ejpam-4771	310	2	each	each	DET
ejpam-4771	310	3	x	x	SYM
ejpam-4771	310	4	∈	∈	PROPN
ejpam-4771	310	5	v	v	NOUN
ejpam-4771	310	6	(	(	PUNCT
ejpam-4771	310	7	huv)\suv	huv)\suv	PROPN
ejpam-4771	310	8	and	and	CCONJ
ejpam-4771	310	9	z	z	PROPN
ejpam-4771	310	10	∈	∈	PROPN
ejpam-4771	310	11	suv	suv	PROPN
ejpam-4771	310	12	,	,	PUNCT
ejpam-4771	310	13	dg⋄h(x	dg⋄h(x	PROPN
ejpam-4771	310	14	,	,	PUNCT
ejpam-4771	310	15	z	z	NOUN
ejpam-4771	310	16	)	)	PUNCT
ejpam-4771	310	17	=	=	PRON
ejpam-4771	310	18	{	{	PUNCT
ejpam-4771	310	19	1	1	NUM
ejpam-4771	310	20	if	if	SCONJ
ejpam-4771	310	21	z	z	PROPN
ejpam-4771	310	22	∈	∈	PROPN
ejpam-4771	310	23	nhuv(x	nhuv(x	NOUN
ejpam-4771	310	24	)	)	PUNCT
ejpam-4771	310	25	2	2	NUM
ejpam-4771	310	26	otherwise	otherwise	ADV
ejpam-4771	310	27	.	.	PUNCT
ejpam-4771	311	1	definition	definition	NOUN
ejpam-4771	311	2	8	8	NUM
ejpam-4771	311	3	.	.	PUNCT
ejpam-4771	312	1	a	a	DET
ejpam-4771	312	2	leaf	leaf	NOUN
ejpam-4771	312	3	l(g	l(g	NOUN
ejpam-4771	312	4	)	)	PUNCT
ejpam-4771	312	5	of	of	ADP
ejpam-4771	312	6	a	a	DET
ejpam-4771	312	7	graph	graph	NOUN
ejpam-4771	312	8	g	g	NOUN
ejpam-4771	312	9	is	be	AUX
ejpam-4771	312	10	a	a	DET
ejpam-4771	312	11	set	set	NOUN
ejpam-4771	312	12	of	of	ADP
ejpam-4771	312	13	vertices	vertex	NOUN
ejpam-4771	312	14	v	v	NOUN
ejpam-4771	312	15	in	in	ADP
ejpam-4771	312	16	g	g	NOUN
ejpam-4771	312	17	with	with	ADP
ejpam-4771	312	18	degg(v	degg(v	PROPN
ejpam-4771	312	19	)	)	PUNCT
ejpam-4771	312	20	=	=	SYM
ejpam-4771	312	21	1	1	X
ejpam-4771	312	22	.	.	PUNCT
ejpam-4771	312	23	theorem	theorem	VERB
ejpam-4771	312	24	10	10	NUM
ejpam-4771	312	25	.	.	PUNCT
ejpam-4771	313	1	[	[	X
ejpam-4771	313	2	12	12	NUM
ejpam-4771	313	3	]	]	PUNCT
ejpam-4771	313	4	let	let	VERB
ejpam-4771	313	5	γ(g	γ(g	PRON
ejpam-4771	313	6	)	)	PUNCT
ejpam-4771	314	1	̸=	̸=	PROPN
ejpam-4771	314	2	1	1	NUM
ejpam-4771	314	3	and	and	CCONJ
ejpam-4771	314	4	h	h	NOUN
ejpam-4771	314	5	be	be	VERB
ejpam-4771	314	6	any	any	DET
ejpam-4771	314	7	nontrivial	nontrivial	ADJ
ejpam-4771	314	8	connected	connect	VERB
ejpam-4771	314	9	graphs	graph	NOUN
ejpam-4771	314	10	.	.	PUNCT
ejpam-4771	315	1	a	a	DET
ejpam-4771	315	2	set	set	NOUN
ejpam-4771	315	3	c	c	NOUN
ejpam-4771	315	4	⊆	⊆	NUM
ejpam-4771	315	5	v	v	NOUN
ejpam-4771	315	6	(	(	PUNCT
ejpam-4771	315	7	g	g	PROPN
ejpam-4771	315	8	⋄h	⋄h	PROPN
ejpam-4771	315	9	)	)	PUNCT
ejpam-4771	315	10	is	be	AUX
ejpam-4771	315	11	a	a	DET
ejpam-4771	315	12	2	2	NUM
ejpam-4771	315	13	-	-	PUNCT
ejpam-4771	315	14	resolving	resolve	VERB
ejpam-4771	315	15	hop	hop	NOUN
ejpam-4771	315	16	dominating	dominating	NOUN
ejpam-4771	315	17	set	set	NOUN
ejpam-4771	315	18	of	of	ADP
ejpam-4771	315	19	g	g	PROPN
ejpam-4771	315	20	⋄h	⋄h	X
ejpam-4771	315	21	if	if	SCONJ
ejpam-4771	316	1	and	and	CCONJ
ejpam-4771	316	2	only	only	ADV
ejpam-4771	316	3	if	if	SCONJ
ejpam-4771	316	4	c	c	X
ejpam-4771	316	5	=	=	PUNCT
ejpam-4771	316	6	a	a	DET
ejpam-4771	316	7	∪	∪	ADJ
ejpam-4771	316	8			PROPN
ejpam-4771	316	9	⋃	⋃	ADJ
ejpam-4771	316	10	uv∈e(g	uv∈e(g	NOUN
ejpam-4771	316	11	)	)	PUNCT
ejpam-4771	316	12	suv	suv	NOUN
ejpam-4771	316	13			PROPN
ejpam-4771	317	1	where	where	SCONJ
ejpam-4771	317	2	(	(	PUNCT
ejpam-4771	317	3	i	i	NOUN
ejpam-4771	317	4	)	)	PUNCT
ejpam-4771	317	5	a	a	DET
ejpam-4771	317	6	⊆	⊆	NUM
ejpam-4771	317	7	v	v	NOUN
ejpam-4771	317	8	(	(	PUNCT
ejpam-4771	317	9	g	g	NOUN
ejpam-4771	317	10	)	)	PUNCT
ejpam-4771	317	11	;	;	PUNCT
ejpam-4771	317	12	(	(	PUNCT
ejpam-4771	317	13	ii	ii	X
ejpam-4771	317	14	)	)	PUNCT
ejpam-4771	317	15	suv	suv	PROPN
ejpam-4771	317	16	⊆	⊆	NUM
ejpam-4771	317	17	v	v	NOUN
ejpam-4771	317	18	(	(	PUNCT
ejpam-4771	317	19	huv	huv	PROPN
ejpam-4771	317	20	)	)	PUNCT
ejpam-4771	317	21	is	be	AUX
ejpam-4771	317	22	a	a	DET
ejpam-4771	317	23	2	2	NUM
ejpam-4771	317	24	-	-	PUNCT
ejpam-4771	317	25	locating	locate	VERB
ejpam-4771	317	26	set	set	NOUN
ejpam-4771	317	27	of	of	ADP
ejpam-4771	317	28	huv	huv	PROPN
ejpam-4771	317	29	for	for	ADP
ejpam-4771	317	30	all	all	DET
ejpam-4771	317	31	uv	uv	PROPN
ejpam-4771	317	32	∈	∈	PROPN
ejpam-4771	317	33	e(g	e(g	PROPN
ejpam-4771	317	34	)	)	PUNCT
ejpam-4771	317	35	or	or	CCONJ
ejpam-4771	317	36	if	if	SCONJ
ejpam-4771	317	37	uv	uv	NOUN
ejpam-4771	317	38	is	be	AUX
ejpam-4771	317	39	a	a	DET
ejpam-4771	317	40	pendant	pendant	ADJ
ejpam-4771	317	41	edge	edge	NOUN
ejpam-4771	317	42	,	,	PUNCT
ejpam-4771	317	43	then	then	ADV
ejpam-4771	317	44	suv	suv	PROPN
ejpam-4771	317	45	is	be	AUX
ejpam-4771	317	46	a	a	DET
ejpam-4771	317	47	(	(	PUNCT
ejpam-4771	317	48	2	2	NUM
ejpam-4771	317	49	,	,	PUNCT
ejpam-4771	317	50	1)-locating	1)-locating	NUM
ejpam-4771	317	51	set	set	NOUN
ejpam-4771	317	52	of	of	ADP
ejpam-4771	317	53	huv	huv	PROPN
ejpam-4771	317	54	whenever	whenever	SCONJ
ejpam-4771	317	55	l(⟨{u	l(⟨{u	PROPN
ejpam-4771	317	56	,	,	PUNCT
ejpam-4771	317	57	v}⟩	v}⟩	PROPN
ejpam-4771	317	58	)	)	PUNCT
ejpam-4771	317	59	⊆	⊆	NUM
ejpam-4771	317	60	a	a	PRON
ejpam-4771	317	61	and	and	CCONJ
ejpam-4771	317	62	suv	suv	PROPN
ejpam-4771	317	63	is	be	AUX
ejpam-4771	317	64	a	a	DET
ejpam-4771	317	65	(	(	PUNCT
ejpam-4771	317	66	2	2	NUM
ejpam-4771	317	67	,	,	PUNCT
ejpam-4771	317	68	2)-locating	2)-locating	NUM
ejpam-4771	317	69	set	set	NOUN
ejpam-4771	317	70	of	of	ADP
ejpam-4771	317	71	huv	huv	PROPN
ejpam-4771	317	72	otherwise	otherwise	ADV
ejpam-4771	317	73	.	.	PUNCT
ejpam-4771	318	1	theorem	theorem	VERB
ejpam-4771	318	2	11	11	NUM
ejpam-4771	318	3	.	.	PUNCT
ejpam-4771	319	1	let	let	VERB
ejpam-4771	319	2	γ(g	γ(g	PRON
ejpam-4771	319	3	)	)	PUNCT
ejpam-4771	320	1	̸=	̸=	PROPN
ejpam-4771	320	2	1	1	NUM
ejpam-4771	320	3	and	and	CCONJ
ejpam-4771	320	4	h	h	NOUN
ejpam-4771	320	5	be	be	VERB
ejpam-4771	320	6	any	any	DET
ejpam-4771	320	7	nontrivial	nontrivial	ADJ
ejpam-4771	320	8	connected	connect	VERB
ejpam-4771	320	9	graphs	graph	NOUN
ejpam-4771	320	10	.	.	PUNCT
ejpam-4771	321	1	a	a	DET
ejpam-4771	321	2	set	set	NOUN
ejpam-4771	321	3	s	s	NOUN
ejpam-4771	321	4	⊆	⊆	NUM
ejpam-4771	321	5	v	v	NOUN
ejpam-4771	321	6	(	(	PUNCT
ejpam-4771	321	7	g	g	PROPN
ejpam-4771	321	8	⋄h	⋄h	PROPN
ejpam-4771	321	9	)	)	PUNCT
ejpam-4771	321	10	is	be	AUX
ejpam-4771	321	11	an	an	DET
ejpam-4771	321	12	outer	outer	ADV
ejpam-4771	321	13	-	-	PUNCT
ejpam-4771	321	14	connected	connect	VERB
ejpam-4771	321	15	2	2	NUM
ejpam-4771	321	16	-	-	PUNCT
ejpam-4771	321	17	resolving	resolve	VERB
ejpam-4771	321	18	hop	hop	NOUN
ejpam-4771	321	19	dominating	dominating	NOUN
ejpam-4771	321	20	set	set	NOUN
ejpam-4771	321	21	of	of	ADP
ejpam-4771	321	22	g	g	PROPN
ejpam-4771	321	23	⋄h	⋄h	X
ejpam-4771	321	24	if	if	SCONJ
ejpam-4771	322	1	and	and	CCONJ
ejpam-4771	322	2	only	only	ADV
ejpam-4771	322	3	if	if	SCONJ
ejpam-4771	322	4	c	c	X
ejpam-4771	322	5	=	=	PUNCT
ejpam-4771	322	6	a	a	DET
ejpam-4771	322	7	∪	∪	ADJ
ejpam-4771	322	8			PROPN
ejpam-4771	322	9	⋃	⋃	ADJ
ejpam-4771	322	10	uv∈e(g	uv∈e(g	NOUN
ejpam-4771	322	11	)	)	PUNCT
ejpam-4771	322	12	suv	suv	NOUN
ejpam-4771	322	13			PROPN
ejpam-4771	322	14	where	where	SCONJ
ejpam-4771	322	15	suv	suv	PROPN
ejpam-4771	322	16	⊆	⊆	PROPN
ejpam-4771	322	17	v	v	NOUN
ejpam-4771	322	18	(	(	PUNCT
ejpam-4771	322	19	huv	huv	PROPN
ejpam-4771	322	20	)	)	PUNCT
ejpam-4771	322	21	for	for	ADP
ejpam-4771	322	22	each	each	DET
ejpam-4771	322	23	uv	uv	PROPN
ejpam-4771	322	24	∈	∈	PROPN
ejpam-4771	322	25	e(g	e(g	PROPN
ejpam-4771	322	26	)	)	PUNCT
ejpam-4771	322	27	and	and	CCONJ
ejpam-4771	322	28	satisfies	satisfy	VERB
ejpam-4771	322	29	each	each	PRON
ejpam-4771	322	30	of	of	ADP
ejpam-4771	322	31	the	the	DET
ejpam-4771	322	32	following	following	ADJ
ejpam-4771	322	33	statements	statement	NOUN
ejpam-4771	322	34	:	:	PUNCT
ejpam-4771	322	35	(	(	PUNCT
ejpam-4771	322	36	i	i	NOUN
ejpam-4771	322	37	)	)	PUNCT
ejpam-4771	322	38	suv	suv	PROPN
ejpam-4771	322	39	⊆	⊆	PROPN
ejpam-4771	322	40	v	v	NOUN
ejpam-4771	322	41	(	(	PUNCT
ejpam-4771	322	42	huv	huv	PROPN
ejpam-4771	322	43	)	)	PUNCT
ejpam-4771	322	44	is	be	AUX
ejpam-4771	322	45	a	a	DET
ejpam-4771	322	46	2	2	NUM
ejpam-4771	322	47	-	-	PUNCT
ejpam-4771	322	48	locating	locate	VERB
ejpam-4771	322	49	set	set	NOUN
ejpam-4771	322	50	of	of	ADP
ejpam-4771	322	51	huv	huv	PROPN
ejpam-4771	322	52	for	for	ADP
ejpam-4771	322	53	all	all	DET
ejpam-4771	322	54	uv	uv	PROPN
ejpam-4771	322	55	∈	∈	PROPN
ejpam-4771	322	56	e(g	e(g	PROPN
ejpam-4771	322	57	)	)	PUNCT
ejpam-4771	322	58	or	or	CCONJ
ejpam-4771	322	59	if	if	SCONJ
ejpam-4771	322	60	uv	uv	NOUN
ejpam-4771	322	61	is	be	AUX
ejpam-4771	322	62	a	a	DET
ejpam-4771	322	63	pendant	pendant	ADJ
ejpam-4771	322	64	edge	edge	NOUN
ejpam-4771	322	65	,	,	PUNCT
ejpam-4771	322	66	then	then	ADV
ejpam-4771	322	67	suv	suv	PROPN
ejpam-4771	322	68	is	be	AUX
ejpam-4771	322	69	a	a	DET
ejpam-4771	322	70	(	(	PUNCT
ejpam-4771	322	71	2	2	NUM
ejpam-4771	322	72	,	,	PUNCT
ejpam-4771	322	73	1)-locating	1)-locating	NUM
ejpam-4771	322	74	set	set	NOUN
ejpam-4771	322	75	of	of	ADP
ejpam-4771	322	76	huv	huv	PROPN
ejpam-4771	322	77	whenever	whenever	SCONJ
ejpam-4771	322	78	l(⟨{u	l(⟨{u	PROPN
ejpam-4771	322	79	,	,	PUNCT
ejpam-4771	322	80	v}⟩	v}⟩	PROPN
ejpam-4771	322	81	)	)	PUNCT
ejpam-4771	322	82	⊆	⊆	NUM
ejpam-4771	322	83	a	a	PRON
ejpam-4771	322	84	and	and	CCONJ
ejpam-4771	322	85	suv	suv	PROPN
ejpam-4771	322	86	is	be	AUX
ejpam-4771	322	87	a	a	DET
ejpam-4771	322	88	(	(	PUNCT
ejpam-4771	322	89	2	2	NUM
ejpam-4771	322	90	,	,	PUNCT
ejpam-4771	322	91	2)-locating	2)-locating	NUM
ejpam-4771	322	92	set	set	NOUN
ejpam-4771	322	93	of	of	ADP
ejpam-4771	322	94	huv	huv	PROPN
ejpam-4771	322	95	otherwise	otherwise	ADV
ejpam-4771	322	96	.	.	PUNCT
ejpam-4771	323	1	(	(	PUNCT
ejpam-4771	323	2	ii	ii	NOUN
ejpam-4771	323	3	)	)	PUNCT
ejpam-4771	323	4	a	a	PRON
ejpam-4771	323	5	=	=	SYM
ejpam-4771	323	6	v	v	NOUN
ejpam-4771	323	7	(	(	PUNCT
ejpam-4771	323	8	g	g	NOUN
ejpam-4771	323	9	)	)	PUNCT
ejpam-4771	323	10	or	or	CCONJ
ejpam-4771	323	11	⟨v	⟨v	NUM
ejpam-4771	323	12	(	(	PUNCT
ejpam-4771	323	13	g)\a⟩	g)\a⟩	PROPN
ejpam-4771	323	14	is	be	AUX
ejpam-4771	323	15	connected	connect	VERB
ejpam-4771	323	16	;	;	PUNCT
ejpam-4771	323	17	(	(	PUNCT
ejpam-4771	323	18	iii	iii	X
ejpam-4771	323	19	)	)	PUNCT
ejpam-4771	323	20	if	if	SCONJ
ejpam-4771	323	21	a	a	DET
ejpam-4771	323	22	=	=	SYM
ejpam-4771	323	23	v	v	NOUN
ejpam-4771	323	24	(	(	PUNCT
ejpam-4771	323	25	g	g	NOUN
ejpam-4771	323	26	)	)	PUNCT
ejpam-4771	323	27	,	,	PUNCT
ejpam-4771	323	28	then	then	ADV
ejpam-4771	323	29	⟨v	⟨v	CCONJ
ejpam-4771	323	30	(	(	PUNCT
ejpam-4771	323	31	huv)\suv⟩	huv)\suv⟩	PROPN
ejpam-4771	323	32	is	be	AUX
ejpam-4771	323	33	a	a	DET
ejpam-4771	323	34	connected	connect	VERB
ejpam-4771	323	35	proper	proper	ADJ
ejpam-4771	323	36	subgraph	subgraph	NOUN
ejpam-4771	323	37	of	of	ADP
ejpam-4771	323	38	huv	huv	PROPN
ejpam-4771	323	39	for	for	ADP
ejpam-4771	323	40	at	at	ADP
ejpam-4771	323	41	most	most	ADV
ejpam-4771	323	42	one	one	NUM
ejpam-4771	323	43	edge	edge	NOUN
ejpam-4771	323	44	uv	uv	PROPN
ejpam-4771	323	45	∈	∈	PROPN
ejpam-4771	323	46	e(g	e(g	PROPN
ejpam-4771	323	47	)	)	PUNCT
ejpam-4771	323	48	.	.	PUNCT
ejpam-4771	324	1	otherwise	otherwise	ADV
ejpam-4771	324	2	,	,	PUNCT
ejpam-4771	324	3	suv	suv	PROPN
ejpam-4771	324	4	=	=	SYM
ejpam-4771	324	5	v	v	PROPN
ejpam-4771	324	6	(	(	PUNCT
ejpam-4771	324	7	huv	huv	PROPN
ejpam-4771	324	8	)	)	PUNCT
ejpam-4771	324	9	for	for	ADP
ejpam-4771	324	10	all	all	DET
ejpam-4771	324	11	uv	uv	PROPN
ejpam-4771	324	12	∈	∈	PROPN
ejpam-4771	324	13	e(g	e(g	PROPN
ejpam-4771	324	14	)	)	PUNCT
ejpam-4771	324	15	;	;	PUNCT
ejpam-4771	324	16	a.m.	a.m.	PROPN
ejpam-4771	324	17	mahistrado	mahistrado	PROPN
ejpam-4771	324	18	,	,	PUNCT
ejpam-4771	324	19	h.	h.	PROPN
ejpam-4771	324	20	rara	rara	PROPN
ejpam-4771	324	21	/	/	SYM
ejpam-4771	324	22	eur	eur	PROPN
ejpam-4771	324	23	.	.	PUNCT
ejpam-4771	325	1	j.	j.	PROPN
ejpam-4771	325	2	pure	pure	PROPN
ejpam-4771	325	3	appl	appl	PROPN
ejpam-4771	325	4	.	.	PROPN
ejpam-4771	325	5	math	math	PROPN
ejpam-4771	325	6	,	,	PUNCT
ejpam-4771	325	7	16	16	NUM
ejpam-4771	325	8	(	(	PUNCT
ejpam-4771	325	9	2	2	NUM
ejpam-4771	325	10	)	)	PUNCT
ejpam-4771	325	11	(	(	PUNCT
ejpam-4771	325	12	2023	2023	NUM
ejpam-4771	325	13	)	)	PUNCT
ejpam-4771	325	14	,	,	PUNCT
ejpam-4771	325	15	1180	1180	NUM
ejpam-4771	325	16	-	-	SYM
ejpam-4771	325	17	1195	1195	NUM
ejpam-4771	325	18	1191	1191	NUM
ejpam-4771	325	19	proof	proof	NOUN
ejpam-4771	325	20	.	.	PUNCT
ejpam-4771	326	1	suppose	suppose	VERB
ejpam-4771	326	2	c	c	NOUN
ejpam-4771	326	3	is	be	AUX
ejpam-4771	326	4	an	an	DET
ejpam-4771	326	5	outer	outer	ADV
ejpam-4771	326	6	-	-	PUNCT
ejpam-4771	326	7	connected	connect	VERB
ejpam-4771	326	8	2	2	NUM
ejpam-4771	326	9	-	-	PUNCT
ejpam-4771	326	10	resolving	resolve	VERB
ejpam-4771	326	11	hop	hop	NOUN
ejpam-4771	326	12	dominating	dominating	NOUN
ejpam-4771	326	13	set	set	VERB
ejpam-4771	326	14	in	in	ADP
ejpam-4771	326	15	g	g	PROPN
ejpam-4771	326	16	⋄h	⋄h	PROPN
ejpam-4771	326	17	.	.	PUNCT
ejpam-4771	327	1	let	let	VERB
ejpam-4771	327	2	a	a	DET
ejpam-4771	327	3	=	=	X
ejpam-4771	327	4	v	v	X
ejpam-4771	327	5	(	(	PUNCT
ejpam-4771	327	6	g	g	NOUN
ejpam-4771	327	7	)	)	PUNCT
ejpam-4771	327	8	∩	∩	NOUN
ejpam-4771	327	9	c	c	PROPN
ejpam-4771	327	10	and	and	CCONJ
ejpam-4771	327	11	suv	suv	PROPN
ejpam-4771	327	12	=	=	PROPN
ejpam-4771	327	13	c	c	PROPN
ejpam-4771	327	14	∩	∩	X
ejpam-4771	327	15	v	v	X
ejpam-4771	327	16	(	(	PUNCT
ejpam-4771	327	17	huv	huv	PROPN
ejpam-4771	327	18	)	)	PUNCT
ejpam-4771	327	19	for	for	ADP
ejpam-4771	327	20	all	all	DET
ejpam-4771	327	21	uv	uv	PROPN
ejpam-4771	327	22	∈	∈	PROPN
ejpam-4771	327	23	e(g	e(g	PROPN
ejpam-4771	327	24	)	)	PUNCT
ejpam-4771	327	25	.	.	PUNCT
ejpam-4771	328	1	then	then	ADV
ejpam-4771	328	2	c	c	X
ejpam-4771	328	3	=	=	PUNCT
ejpam-4771	328	4	a	a	DET
ejpam-4771	328	5	∪	∪	X
ejpam-4771	328	6	(	(	PUNCT
ejpam-4771	328	7	⋃	⋃	NOUN
ejpam-4771	328	8	uv∈e(g	uv∈e(g	NOUN
ejpam-4771	328	9	)	)	PUNCT
ejpam-4771	328	10	suv	suv	PROPN
ejpam-4771	328	11	)	)	PUNCT
ejpam-4771	328	12	where	where	SCONJ
ejpam-4771	328	13	a	a	DET
ejpam-4771	328	14	⊆	⊆	NUM
ejpam-4771	328	15	v	v	NOUN
ejpam-4771	328	16	(	(	PUNCT
ejpam-4771	328	17	g	g	NOUN
ejpam-4771	328	18	)	)	PUNCT
ejpam-4771	328	19	and	and	CCONJ
ejpam-4771	328	20	suv	suv	PROPN
ejpam-4771	328	21	⊆	⊆	NUM
ejpam-4771	328	22	v	v	NOUN
ejpam-4771	328	23	(	(	PUNCT
ejpam-4771	328	24	huv	huv	PROPN
ejpam-4771	328	25	)	)	PUNCT
ejpam-4771	328	26	for	for	ADP
ejpam-4771	328	27	each	each	DET
ejpam-4771	328	28	uv	uv	PROPN
ejpam-4771	328	29	∈	∈	PROPN
ejpam-4771	328	30	e(g	e(g	PROPN
ejpam-4771	328	31	)	)	PUNCT
ejpam-4771	328	32	.	.	PUNCT
ejpam-4771	329	1	then	then	ADV
ejpam-4771	329	2	c	c	PROPN
ejpam-4771	329	3	is	be	AUX
ejpam-4771	329	4	a	a	DET
ejpam-4771	329	5	2	2	NUM
ejpam-4771	329	6	-	-	PUNCT
ejpam-4771	329	7	resolving	resolve	VERB
ejpam-4771	329	8	hop	hop	NOUN
ejpam-4771	329	9	dominating	dominating	NOUN
ejpam-4771	329	10	set	set	VERB
ejpam-4771	329	11	in	in	ADP
ejpam-4771	329	12	g	g	PROPN
ejpam-4771	329	13	⋄	⋄	PROPN
ejpam-4771	329	14	h.	h.	PROPN
ejpam-4771	329	15	by	by	ADP
ejpam-4771	329	16	theorem	theorem	NOUN
ejpam-4771	329	17	10	10	NUM
ejpam-4771	329	18	,	,	PUNCT
ejpam-4771	329	19	(	(	PUNCT
ejpam-4771	329	20	i	i	NOUN
ejpam-4771	329	21	)	)	PUNCT
ejpam-4771	329	22	holds	hold	VERB
ejpam-4771	329	23	.	.	PUNCT
ejpam-4771	330	1	now	now	ADV
ejpam-4771	330	2	,	,	PUNCT
ejpam-4771	330	3	suppose	suppose	VERB
ejpam-4771	330	4	a	a	DET
ejpam-4771	330	5	̸=	̸=	PROPN
ejpam-4771	330	6	v	v	NOUN
ejpam-4771	330	7	(	(	PUNCT
ejpam-4771	330	8	g	g	NOUN
ejpam-4771	330	9	)	)	PUNCT
ejpam-4771	330	10	.	.	PUNCT
ejpam-4771	331	1	then	then	ADV
ejpam-4771	331	2	c	c	PROPN
ejpam-4771	331	3	̸=	̸=	PROPN
ejpam-4771	331	4	v	v	NOUN
ejpam-4771	331	5	(	(	PUNCT
ejpam-4771	331	6	g	g	PROPN
ejpam-4771	331	7	⋄h	⋄h	PROPN
ejpam-4771	331	8	)	)	PUNCT
ejpam-4771	331	9	.	.	PUNCT
ejpam-4771	332	1	since	since	SCONJ
ejpam-4771	332	2	c	c	PROPN
ejpam-4771	332	3	is	be	AUX
ejpam-4771	332	4	an	an	DET
ejpam-4771	332	5	outer	outer	ADV
ejpam-4771	332	6	-	-	PUNCT
ejpam-4771	332	7	connected	connect	VERB
ejpam-4771	332	8	2	2	NUM
ejpam-4771	332	9	-	-	PUNCT
ejpam-4771	332	10	resolving	resolve	VERB
ejpam-4771	332	11	hop	hop	NOUN
ejpam-4771	332	12	dominating	dominating	NOUN
ejpam-4771	332	13	set	set	NOUN
ejpam-4771	332	14	,	,	PUNCT
ejpam-4771	332	15	it	it	PRON
ejpam-4771	332	16	follows	follow	VERB
ejpam-4771	332	17	that	that	PRON
ejpam-4771	332	18	⟨v	⟨v	NOUN
ejpam-4771	332	19	(	(	PUNCT
ejpam-4771	332	20	g	g	NOUN
ejpam-4771	332	21	⋄h)\c⟩	⋄h)\c⟩	NOUN
ejpam-4771	332	22	=	=	PUNCT
ejpam-4771	332	23	⟨v	⟨v	PUNCT
ejpam-4771	332	24	(	(	PUNCT
ejpam-4771	332	25	huv)\suv⟩	huv)\suv⟩	PROPN
ejpam-4771	332	26	∪	∪	ADV
ejpam-4771	332	27	⟨v	⟨v	NOUN
ejpam-4771	332	28	(	(	PUNCT
ejpam-4771	332	29	g)\a⟩	g)\a⟩	PROPN
ejpam-4771	332	30	is	be	AUX
ejpam-4771	332	31	connected	connect	VERB
ejpam-4771	332	32	.	.	PUNCT
ejpam-4771	333	1	hence	hence	ADV
ejpam-4771	333	2	,	,	PUNCT
ejpam-4771	333	3	⟨v	⟨v	PROPN
ejpam-4771	333	4	(	(	PUNCT
ejpam-4771	333	5	g)\a⟩	g)\a⟩	PROPN
ejpam-4771	333	6	is	be	AUX
ejpam-4771	333	7	connected	connect	VERB
ejpam-4771	333	8	.	.	PUNCT
ejpam-4771	334	1	hence	hence	ADV
ejpam-4771	334	2	,	,	PUNCT
ejpam-4771	334	3	(	(	PUNCT
ejpam-4771	334	4	ii	ii	NOUN
ejpam-4771	334	5	)	)	PUNCT
ejpam-4771	334	6	holds	hold	VERB
ejpam-4771	334	7	.	.	PUNCT
ejpam-4771	335	1	suppose	suppose	VERB
ejpam-4771	335	2	a	a	DET
ejpam-4771	335	3	=	=	SYM
ejpam-4771	335	4	v	v	NOUN
ejpam-4771	335	5	(	(	PUNCT
ejpam-4771	335	6	g	g	NOUN
ejpam-4771	335	7	)	)	PUNCT
ejpam-4771	335	8	.	.	PUNCT
ejpam-4771	336	1	if	if	SCONJ
ejpam-4771	336	2	v	v	INTJ
ejpam-4771	336	3	(	(	PUNCT
ejpam-4771	336	4	g	g	PROPN
ejpam-4771	336	5	⋄	⋄	PROPN
ejpam-4771	336	6	h	h	NOUN
ejpam-4771	336	7	)	)	PUNCT
ejpam-4771	336	8	̸=	̸=	PROPN
ejpam-4771	336	9	c	c	NOUN
ejpam-4771	336	10	,	,	PUNCT
ejpam-4771	336	11	then	then	ADV
ejpam-4771	336	12	⟨v	⟨v	CCONJ
ejpam-4771	336	13	(	(	PUNCT
ejpam-4771	336	14	g	g	PROPN
ejpam-4771	336	15	⋄	⋄	PROPN
ejpam-4771	336	16	h)\c⟩	h)\c⟩	PROPN
ejpam-4771	336	17	=	=	SYM
ejpam-4771	336	18	⟨v	⟨v	PROPN
ejpam-4771	336	19	(	(	PUNCT
ejpam-4771	336	20	huv)\suv⟩.	huv)\suv⟩.	NOUN
ejpam-4771	336	21	since	since	SCONJ
ejpam-4771	336	22	c	c	PROPN
ejpam-4771	336	23	is	be	AUX
ejpam-4771	336	24	outer	outer	ADV
ejpam-4771	336	25	-	-	PUNCT
ejpam-4771	336	26	connected	connect	VERB
ejpam-4771	336	27	2resolving	2resolving	NUM
ejpam-4771	336	28	hop	hop	NOUN
ejpam-4771	336	29	dominating	dominating	NOUN
ejpam-4771	336	30	set	set	NOUN
ejpam-4771	336	31	,	,	PUNCT
ejpam-4771	336	32	⟨v	⟨v	PROPN
ejpam-4771	336	33	(	(	PUNCT
ejpam-4771	336	34	huv)\suv⟩	huv)\suv⟩	PROPN
ejpam-4771	336	35	is	be	AUX
ejpam-4771	336	36	a	a	DET
ejpam-4771	336	37	connected	connect	VERB
ejpam-4771	336	38	proper	proper	ADJ
ejpam-4771	336	39	subgraph	subgraph	NOUN
ejpam-4771	336	40	of	of	ADP
ejpam-4771	336	41	huv	huv	PROPN
ejpam-4771	336	42	for	for	ADP
ejpam-4771	336	43	at	at	ADP
ejpam-4771	336	44	most	most	ADV
ejpam-4771	336	45	one	one	NUM
ejpam-4771	336	46	edge	edge	NOUN
ejpam-4771	336	47	uv	uv	PROPN
ejpam-4771	336	48	∈	∈	PROPN
ejpam-4771	336	49	e(g	e(g	PROPN
ejpam-4771	336	50	)	)	PUNCT
ejpam-4771	336	51	.	.	PUNCT
ejpam-4771	337	1	otherwise	otherwise	ADV
ejpam-4771	337	2	,	,	PUNCT
ejpam-4771	337	3	if	if	SCONJ
ejpam-4771	337	4	v	v	INTJ
ejpam-4771	337	5	(	(	PUNCT
ejpam-4771	337	6	g	g	PROPN
ejpam-4771	337	7	⋄	⋄	PROPN
ejpam-4771	337	8	h	h	NOUN
ejpam-4771	337	9	)	)	PUNCT
ejpam-4771	337	10	=	=	SYM
ejpam-4771	338	1	c	c	X
ejpam-4771	338	2	,	,	PUNCT
ejpam-4771	338	3	then	then	ADV
ejpam-4771	338	4	suv	suv	PROPN
ejpam-4771	338	5	=	=	SYM
ejpam-4771	338	6	v	v	PROPN
ejpam-4771	338	7	(	(	PUNCT
ejpam-4771	338	8	huv	huv	PROPN
ejpam-4771	338	9	)	)	PUNCT
ejpam-4771	338	10	for	for	ADP
ejpam-4771	338	11	all	all	DET
ejpam-4771	338	12	uv	uv	PROPN
ejpam-4771	338	13	∈	∈	PROPN
ejpam-4771	338	14	e(g	e(g	PROPN
ejpam-4771	338	15	)	)	PUNCT
ejpam-4771	338	16	.	.	PUNCT
ejpam-4771	339	1	hence	hence	ADV
ejpam-4771	339	2	,	,	PUNCT
ejpam-4771	339	3	(	(	PUNCT
ejpam-4771	339	4	iii	iii	NOUN
ejpam-4771	339	5	)	)	PUNCT
ejpam-4771	339	6	holds	hold	VERB
ejpam-4771	339	7	.	.	PUNCT
ejpam-4771	340	1	conversely	conversely	ADV
ejpam-4771	340	2	,	,	PUNCT
ejpam-4771	340	3	let	let	VERB
ejpam-4771	340	4	c	c	PRON
ejpam-4771	340	5	be	be	AUX
ejpam-4771	340	6	a	a	DET
ejpam-4771	340	7	set	set	NOUN
ejpam-4771	340	8	as	as	SCONJ
ejpam-4771	340	9	described	describe	VERB
ejpam-4771	340	10	and	and	CCONJ
ejpam-4771	340	11	satisfies	satisfy	VERB
ejpam-4771	340	12	the	the	DET
ejpam-4771	340	13	given	give	VERB
ejpam-4771	340	14	conditions	condition	NOUN
ejpam-4771	340	15	.	.	PUNCT
ejpam-4771	341	1	by	by	ADP
ejpam-4771	341	2	(	(	PUNCT
ejpam-4771	341	3	i	i	NOUN
ejpam-4771	341	4	)	)	PUNCT
ejpam-4771	341	5	,	,	PUNCT
ejpam-4771	341	6	c	c	PROPN
ejpam-4771	341	7	is	be	AUX
ejpam-4771	341	8	a	a	DET
ejpam-4771	341	9	2	2	NUM
ejpam-4771	341	10	-	-	PUNCT
ejpam-4771	341	11	resolving	resolve	VERB
ejpam-4771	341	12	hop	hop	NOUN
ejpam-4771	341	13	dominating	dominating	NOUN
ejpam-4771	341	14	set	set	NOUN
ejpam-4771	341	15	.	.	PUNCT
ejpam-4771	342	1	if	if	SCONJ
ejpam-4771	342	2	v	v	X
ejpam-4771	342	3	(	(	PUNCT
ejpam-4771	342	4	g⋄h	g⋄h	X
ejpam-4771	342	5	)	)	PUNCT
ejpam-4771	343	1	=	=	SYM
ejpam-4771	343	2	c	c	X
ejpam-4771	343	3	,	,	PUNCT
ejpam-4771	343	4	then	then	ADV
ejpam-4771	343	5	we	we	PRON
ejpam-4771	343	6	are	be	AUX
ejpam-4771	343	7	done	do	VERB
ejpam-4771	343	8	.	.	PUNCT
ejpam-4771	344	1	now	now	ADV
ejpam-4771	344	2	,	,	PUNCT
ejpam-4771	344	3	if	if	SCONJ
ejpam-4771	344	4	v	v	X
ejpam-4771	344	5	(	(	PUNCT
ejpam-4771	344	6	g⋄h	g⋄h	X
ejpam-4771	344	7	)	)	PUNCT
ejpam-4771	344	8	̸=	̸=	PROPN
ejpam-4771	344	9	c.	c.	NOUN
ejpam-4771	344	10	consider	consider	VERB
ejpam-4771	344	11	the	the	DET
ejpam-4771	344	12	following	follow	VERB
ejpam-4771	344	13	cases	case	NOUN
ejpam-4771	344	14	:	:	PUNCT
ejpam-4771	344	15	case	case	NOUN
ejpam-4771	344	16	1	1	NUM
ejpam-4771	344	17	:	:	PUNCT
ejpam-4771	344	18	a	a	DET
ejpam-4771	344	19	=	=	SYM
ejpam-4771	344	20	v	v	X
ejpam-4771	344	21	(	(	PUNCT
ejpam-4771	344	22	g	g	NOUN
ejpam-4771	344	23	)	)	PUNCT
ejpam-4771	344	24	then	then	ADV
ejpam-4771	344	25	⟨v	⟨v	X
ejpam-4771	344	26	(	(	PUNCT
ejpam-4771	344	27	g	g	PROPN
ejpam-4771	344	28	⋄	⋄	PROPN
ejpam-4771	344	29	h)\c⟩	h)\c⟩	PROPN
ejpam-4771	344	30	=	=	PUNCT
ejpam-4771	344	31	⟨v	⟨v	PUNCT
ejpam-4771	344	32	(	(	PUNCT
ejpam-4771	344	33	huv)\suv⟩	huv)\suv⟩	PROPN
ejpam-4771	344	34	and	and	CCONJ
ejpam-4771	344	35	by	by	ADP
ejpam-4771	344	36	(	(	PUNCT
ejpam-4771	344	37	iii	iii	NOUN
ejpam-4771	344	38	)	)	PUNCT
ejpam-4771	344	39	,	,	PUNCT
ejpam-4771	344	40	⟨v	⟨v	PROPN
ejpam-4771	344	41	(	(	PUNCT
ejpam-4771	344	42	huv)\suv⟩	huv)\suv⟩	PROPN
ejpam-4771	344	43	is	be	AUX
ejpam-4771	344	44	a	a	DET
ejpam-4771	344	45	connected	connect	VERB
ejpam-4771	344	46	proper	proper	ADJ
ejpam-4771	344	47	subgraph	subgraph	NOUN
ejpam-4771	344	48	of	of	ADP
ejpam-4771	344	49	huv	huv	PROPN
ejpam-4771	344	50	for	for	ADP
ejpam-4771	344	51	at	at	ADP
ejpam-4771	344	52	most	most	ADV
ejpam-4771	344	53	one	one	NUM
ejpam-4771	344	54	edge	edge	NOUN
ejpam-4771	344	55	uv	uv	PROPN
ejpam-4771	344	56	∈	∈	PROPN
ejpam-4771	344	57	e(g	e(g	PROPN
ejpam-4771	344	58	)	)	PUNCT
ejpam-4771	344	59	.	.	PUNCT
ejpam-4771	345	1	thus	thus	ADV
ejpam-4771	345	2	,	,	PUNCT
ejpam-4771	345	3	⟨v	⟨v	PROPN
ejpam-4771	345	4	(	(	PUNCT
ejpam-4771	345	5	g	g	PROPN
ejpam-4771	345	6	⋄	⋄	PROPN
ejpam-4771	345	7	h)\c⟩	h)\c⟩	PROPN
ejpam-4771	345	8	is	be	AUX
ejpam-4771	345	9	connected	connect	VERB
ejpam-4771	345	10	.	.	PUNCT
ejpam-4771	346	1	case	case	NOUN
ejpam-4771	346	2	2	2	NUM
ejpam-4771	346	3	:	:	PUNCT
ejpam-4771	346	4	a	a	DET
ejpam-4771	346	5	̸=	̸=	PROPN
ejpam-4771	346	6	v	v	NOUN
ejpam-4771	346	7	(	(	PUNCT
ejpam-4771	346	8	g	g	NOUN
ejpam-4771	346	9	)	)	PUNCT
ejpam-4771	346	10	then	then	ADV
ejpam-4771	346	11	v	v	X
ejpam-4771	346	12	(	(	PUNCT
ejpam-4771	346	13	huv	huv	PROPN
ejpam-4771	346	14	)	)	PUNCT
ejpam-4771	346	15	=	=	SYM
ejpam-4771	346	16	suv	suv	PROPN
ejpam-4771	346	17	for	for	ADP
ejpam-4771	346	18	all	all	DET
ejpam-4771	346	19	uv	uv	PROPN
ejpam-4771	346	20	∈	∈	PROPN
ejpam-4771	346	21	e(g	e(g	PROPN
ejpam-4771	346	22	)	)	PUNCT
ejpam-4771	346	23	.	.	PUNCT
ejpam-4771	347	1	hence	hence	ADV
ejpam-4771	347	2	,	,	PUNCT
ejpam-4771	347	3	⟨v	⟨v	PROPN
ejpam-4771	347	4	(	(	PUNCT
ejpam-4771	347	5	g	g	NOUN
ejpam-4771	347	6	⋄h)\c⟩	⋄h)\c⟩	NOUN
ejpam-4771	347	7	=	=	PUNCT
ejpam-4771	347	8	⟨v	⟨v	PUNCT
ejpam-4771	347	9	(	(	PUNCT
ejpam-4771	347	10	huv)\suv⟩	huv)\suv⟩	PROPN
ejpam-4771	347	11	∪	∪	ADV
ejpam-4771	347	12	⟨v	⟨v	PROPN
ejpam-4771	347	13	(	(	PUNCT
ejpam-4771	347	14	g)\a⟩	g)\a⟩	PROPN
ejpam-4771	347	15	=	=	SYM
ejpam-4771	347	16	⟨v	⟨v	PROPN
ejpam-4771	347	17	(	(	PUNCT
ejpam-4771	347	18	g)\a⟩.	g)\a⟩.	PROPN
ejpam-4771	347	19	thus	thus	ADV
ejpam-4771	347	20	,	,	PUNCT
ejpam-4771	347	21	⟨v	⟨v	PROPN
ejpam-4771	347	22	(	(	PUNCT
ejpam-4771	347	23	g	g	PROPN
ejpam-4771	347	24	⋄h)\c⟩	⋄h)\c⟩	PROPN
ejpam-4771	347	25	is	be	AUX
ejpam-4771	347	26	connected	connect	VERB
ejpam-4771	347	27	since	since	SCONJ
ejpam-4771	347	28	⟨v	⟨v	PROPN
ejpam-4771	347	29	(	(	PUNCT
ejpam-4771	347	30	g)\a⟩	g)\a⟩	PROPN
ejpam-4771	347	31	is	be	AUX
ejpam-4771	347	32	connected	connect	VERB
ejpam-4771	347	33	by	by	ADP
ejpam-4771	347	34	(	(	PUNCT
ejpam-4771	347	35	ii	ii	NOUN
ejpam-4771	347	36	)	)	PUNCT
ejpam-4771	347	37	.	.	PUNCT
ejpam-4771	348	1	accordingly	accordingly	ADV
ejpam-4771	348	2	,	,	PUNCT
ejpam-4771	348	3	c	c	PROPN
ejpam-4771	348	4	is	be	AUX
ejpam-4771	348	5	an	an	DET
ejpam-4771	348	6	outer	outer	ADV
ejpam-4771	348	7	-	-	PUNCT
ejpam-4771	348	8	connected	connect	VERB
ejpam-4771	348	9	2	2	NUM
ejpam-4771	348	10	-	-	PUNCT
ejpam-4771	348	11	resolving	resolve	VERB
ejpam-4771	348	12	hop	hop	NOUN
ejpam-4771	348	13	dominating	dominating	NOUN
ejpam-4771	348	14	set	set	VERB
ejpam-4771	348	15	in	in	ADP
ejpam-4771	348	16	g	g	PROPN
ejpam-4771	348	17	⋄h	⋄h	PROPN
ejpam-4771	348	18	.	.	PUNCT
ejpam-4771	349	1	corollary	corollary	ADJ
ejpam-4771	349	2	5	5	NUM
ejpam-4771	349	3	.	.	PUNCT
ejpam-4771	350	1	let	let	VERB
ejpam-4771	350	2	γ(g	γ(g	PRON
ejpam-4771	350	3	)	)	PUNCT
ejpam-4771	351	1	̸=	̸=	PROPN
ejpam-4771	351	2	1	1	NUM
ejpam-4771	351	3	be	be	AUX
ejpam-4771	351	4	any	any	DET
ejpam-4771	351	5	nontrivial	nontrivial	ADJ
ejpam-4771	351	6	connected	connect	VERB
ejpam-4771	351	7	graph	graph	NOUN
ejpam-4771	351	8	of	of	ADP
ejpam-4771	351	9	sizem	sizem	NOUN
ejpam-4771	351	10	andh	andh	NOUN
ejpam-4771	351	11	a	a	DET
ejpam-4771	351	12	nontrivial	nontrivial	ADJ
ejpam-4771	351	13	connected	connect	VERB
ejpam-4771	351	14	graph	graph	NOUN
ejpam-4771	351	15	.	.	PUNCT
ejpam-4771	352	1	then	then	ADV
ejpam-4771	352	2	the	the	DET
ejpam-4771	352	3	following	follow	VERB
ejpam-4771	352	4	statements	statement	NOUN
ejpam-4771	352	5	hold	hold	VERB
ejpam-4771	352	6	.	.	PUNCT
ejpam-4771	353	1	(	(	PUNCT
ejpam-4771	353	2	i	i	NOUN
ejpam-4771	353	3	)	)	PUNCT
ejpam-4771	353	4	if	if	SCONJ
ejpam-4771	353	5	g	g	PROPN
ejpam-4771	353	6	is	be	AUX
ejpam-4771	353	7	a	a	DET
ejpam-4771	353	8	graph	graph	NOUN
ejpam-4771	353	9	with	with	ADP
ejpam-4771	353	10	no	no	DET
ejpam-4771	353	11	pendant	pendant	ADJ
ejpam-4771	353	12	edges	edge	NOUN
ejpam-4771	353	13	,	,	PUNCT
ejpam-4771	353	14	then	then	ADV
ejpam-4771	353	15	γ̃c2rh(g	γ̃c2rh(g	PROPN
ejpam-4771	353	16	⋄h	⋄h	PROPN
ejpam-4771	353	17	)	)	PUNCT
ejpam-4771	353	18	=	=	PUNCT
ejpam-4771	353	19	m	m	PUNCT
ejpam-4771	353	20	·	·	PUNCT
ejpam-4771	353	21	ln2(h	ln2(h	PROPN
ejpam-4771	353	22	)	)	PUNCT
ejpam-4771	353	23	.	.	PUNCT
ejpam-4771	354	1	(	(	PUNCT
ejpam-4771	354	2	ii	ii	NOUN
ejpam-4771	354	3	)	)	PUNCT
ejpam-4771	354	4	if	if	SCONJ
ejpam-4771	354	5	g	g	PROPN
ejpam-4771	354	6	is	be	AUX
ejpam-4771	354	7	a	a	DET
ejpam-4771	354	8	graph	graph	NOUN
ejpam-4771	354	9	with	with	ADP
ejpam-4771	354	10	k	k	PROPN
ejpam-4771	354	11	≥	≥	NUM
ejpam-4771	354	12	1	1	NUM
ejpam-4771	354	13	pendant	pendant	ADJ
ejpam-4771	354	14	edges	edge	NOUN
ejpam-4771	354	15	,	,	PUNCT
ejpam-4771	354	16	then	then	ADV
ejpam-4771	354	17	γ̃c2rh(g⋄h	γ̃c2rh(g⋄h	PRON
ejpam-4771	354	18	)	)	PUNCT
ejpam-4771	354	19	=	=	SYM
ejpam-4771	354	20	min	min	NOUN
ejpam-4771	354	21	{	{	PUNCT
ejpam-4771	354	22	(	(	PUNCT
ejpam-4771	354	23	m−k	m−k	NOUN
ejpam-4771	354	24	)	)	PUNCT
ejpam-4771	354	25	ln2(h)+k	ln2(h)+k	PROPN
ejpam-4771	354	26	·	·	PUNCT
ejpam-4771	354	27	ln(2,1)(h)+k	ln(2,1)(h)+k	ADJ
ejpam-4771	354	28	,	,	PUNCT
ejpam-4771	354	29	(	(	PUNCT
ejpam-4771	354	30	m−k	m−k	NOUN
ejpam-4771	354	31	)	)	PUNCT
ejpam-4771	354	32	ln2(h)+k	ln2(h)+k	PROPN
ejpam-4771	354	33	·	·	PUNCT
ejpam-4771	354	34	ln(2,2)(h	ln(2,2)(h	PROPN
ejpam-4771	354	35	)	)	PUNCT
ejpam-4771	354	36	}	}	PUNCT
ejpam-4771	354	37	and	and	CCONJ
ejpam-4771	354	38	γ̃c2rh(g	γ̃c2rh(g	PROPN
ejpam-4771	354	39	⋄h	⋄h	PROPN
ejpam-4771	354	40	)	)	PUNCT
ejpam-4771	354	41	=	=	PRON
ejpam-4771	354	42	(	(	PUNCT
ejpam-4771	354	43	m−	m−	PROPN
ejpam-4771	354	44	k	k	PROPN
ejpam-4771	354	45	)	)	PUNCT
ejpam-4771	354	46	ln2(g)+	ln2(g)+	PROPN
ejpam-4771	355	1	k	k	X
ejpam-4771	355	2	·	·	PUNCT
ejpam-4771	355	3	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4771	355	4	)	)	PUNCT
ejpam-4771	355	5	whenever	whenever	SCONJ
ejpam-4771	355	6	ln(2,2)(h	ln(2,2)(h	ADV
ejpam-4771	355	7	)	)	PUNCT
ejpam-4771	355	8	=	=	PUNCT
ejpam-4771	355	9	ln(2,1)(h	ln(2,1)(h	NOUN
ejpam-4771	355	10	)	)	PUNCT
ejpam-4771	355	11	.	.	PUNCT
ejpam-4771	356	1	7	7	X
ejpam-4771	356	2	.	.	NOUN
ejpam-4771	356	3	lexicographic	lexicographic	ADJ
ejpam-4771	356	4	product	product	NOUN
ejpam-4771	356	5	of	of	ADP
ejpam-4771	356	6	graphs	graph	NOUN
ejpam-4771	356	7	this	this	DET
ejpam-4771	356	8	section	section	NOUN
ejpam-4771	356	9	presents	present	VERB
ejpam-4771	356	10	characterizations	characterization	NOUN
ejpam-4771	356	11	on	on	ADP
ejpam-4771	356	12	the	the	DET
ejpam-4771	356	13	outer	outer	ADV
ejpam-4771	356	14	-	-	PUNCT
ejpam-4771	356	15	connected	connect	VERB
ejpam-4771	356	16	2	2	NUM
ejpam-4771	356	17	-	-	PUNCT
ejpam-4771	356	18	resolving	resolve	VERB
ejpam-4771	356	19	hop	hop	NOUN
ejpam-4771	356	20	dominating	dominating	NOUN
ejpam-4771	356	21	sets	set	NOUN
ejpam-4771	356	22	in	in	ADP
ejpam-4771	356	23	the	the	DET
ejpam-4771	356	24	lexicographic	lexicographic	ADJ
ejpam-4771	356	25	product	product	NOUN
ejpam-4771	356	26	of	of	ADP
ejpam-4771	356	27	graphs	graph	NOUN
ejpam-4771	356	28	.	.	PUNCT
ejpam-4771	357	1	a.m.	a.m.	PROPN
ejpam-4771	357	2	mahistrado	mahistrado	PROPN
ejpam-4771	357	3	,	,	PUNCT
ejpam-4771	357	4	h.	h.	PROPN
ejpam-4771	357	5	rara	rara	PROPN
ejpam-4771	357	6	/	/	SYM
ejpam-4771	357	7	eur	eur	PROPN
ejpam-4771	357	8	.	.	PUNCT
ejpam-4771	358	1	j.	j.	PROPN
ejpam-4771	358	2	pure	pure	PROPN
ejpam-4771	358	3	appl	appl	PROPN
ejpam-4771	358	4	.	.	PROPN
ejpam-4771	358	5	math	math	PROPN
ejpam-4771	358	6	,	,	PUNCT
ejpam-4771	358	7	16	16	NUM
ejpam-4771	358	8	(	(	PUNCT
ejpam-4771	358	9	2	2	NUM
ejpam-4771	358	10	)	)	PUNCT
ejpam-4771	358	11	(	(	PUNCT
ejpam-4771	358	12	2023	2023	NUM
ejpam-4771	358	13	)	)	PUNCT
ejpam-4771	358	14	,	,	PUNCT
ejpam-4771	358	15	1180	1180	NUM
ejpam-4771	358	16	-	-	SYM
ejpam-4771	358	17	1195	1195	NUM
ejpam-4771	358	18	1192	1192	NUM
ejpam-4771	358	19	theorem	theorem	NOUN
ejpam-4771	358	20	12	12	NUM
ejpam-4771	358	21	.	.	PUNCT
ejpam-4771	359	1	[	[	X
ejpam-4771	359	2	12	12	NUM
ejpam-4771	359	3	]	]	PUNCT
ejpam-4771	359	4	let	let	VERB
ejpam-4771	359	5	g	g	NOUN
ejpam-4771	359	6	and	and	CCONJ
ejpam-4771	359	7	h	h	NOUN
ejpam-4771	359	8	be	be	AUX
ejpam-4771	359	9	nontrivial	nontrivial	ADJ
ejpam-4771	359	10	connected	connected	ADJ
ejpam-4771	359	11	graphs	graph	NOUN
ejpam-4771	359	12	.	.	PUNCT
ejpam-4771	360	1	then	then	ADV
ejpam-4771	360	2	w	w	NOUN
ejpam-4771	360	3	=	=	PUNCT
ejpam-4771	360	4	⋃	⋃	PROPN
ejpam-4771	360	5	x∈s	x∈s	NOUN
ejpam-4771	361	1	[	[	X
ejpam-4771	361	2	{	{	PUNCT
ejpam-4771	361	3	x	x	NOUN
ejpam-4771	361	4	}	}	PUNCT
ejpam-4771	361	5	×	×	PROPN
ejpam-4771	361	6	tx	tx	PROPN
ejpam-4771	361	7	]	]	X
ejpam-4771	361	8	,	,	PUNCT
ejpam-4771	361	9	where	where	SCONJ
ejpam-4771	361	10	s	s	VERB
ejpam-4771	361	11	⊆	⊆	NUM
ejpam-4771	361	12	v	v	NOUN
ejpam-4771	361	13	(	(	PUNCT
ejpam-4771	361	14	g	g	NOUN
ejpam-4771	361	15	)	)	PUNCT
ejpam-4771	361	16	and	and	CCONJ
ejpam-4771	361	17	tx	tx	VERB
ejpam-4771	361	18	⊆	⊆	NUM
ejpam-4771	361	19	v	v	NOUN
ejpam-4771	361	20	(	(	PUNCT
ejpam-4771	361	21	h	h	NOUN
ejpam-4771	361	22	)	)	PUNCT
ejpam-4771	361	23	for	for	ADP
ejpam-4771	361	24	each	each	DET
ejpam-4771	361	25	x	x	SYM
ejpam-4771	361	26	∈	∈	PROPN
ejpam-4771	361	27	s	s	NOUN
ejpam-4771	361	28	,	,	PUNCT
ejpam-4771	361	29	is	be	AUX
ejpam-4771	361	30	a	a	DET
ejpam-4771	361	31	2	2	NUM
ejpam-4771	361	32	-	-	PUNCT
ejpam-4771	361	33	resolving	resolve	VERB
ejpam-4771	361	34	hop	hop	NOUN
ejpam-4771	361	35	dominating	dominating	NOUN
ejpam-4771	361	36	set	set	VERB
ejpam-4771	361	37	in	in	ADP
ejpam-4771	361	38	g[h	g[h	PROPN
ejpam-4771	361	39	]	]	PUNCT
ejpam-4771	361	40	if	if	SCONJ
ejpam-4771	361	41	and	and	CCONJ
ejpam-4771	361	42	only	only	ADV
ejpam-4771	361	43	if	if	SCONJ
ejpam-4771	361	44	(	(	PUNCT
ejpam-4771	361	45	i	i	NOUN
ejpam-4771	361	46	)	)	PUNCT
ejpam-4771	361	47	s	s	PART
ejpam-4771	361	48	=	=	SYM
ejpam-4771	361	49	v	v	NOUN
ejpam-4771	361	50	(	(	PUNCT
ejpam-4771	361	51	g	g	NOUN
ejpam-4771	361	52	)	)	PUNCT
ejpam-4771	361	53	;	;	PUNCT
ejpam-4771	361	54	(	(	PUNCT
ejpam-4771	361	55	ii	ii	NOUN
ejpam-4771	361	56	)	)	PUNCT
ejpam-4771	361	57	tx	tx	PROPN
ejpam-4771	361	58	is	be	AUX
ejpam-4771	361	59	a	a	DET
ejpam-4771	361	60	2	2	NUM
ejpam-4771	361	61	-	-	PUNCT
ejpam-4771	361	62	locating	locate	VERB
ejpam-4771	361	63	set	set	NOUN
ejpam-4771	361	64	in	in	ADP
ejpam-4771	361	65	h	h	NOUN
ejpam-4771	361	66	for	for	ADP
ejpam-4771	361	67	every	every	DET
ejpam-4771	361	68	x	x	SYM
ejpam-4771	361	69	∈	∈	PROPN
ejpam-4771	361	70	v	v	ADP
ejpam-4771	361	71	(	(	PUNCT
ejpam-4771	361	72	g	g	NOUN
ejpam-4771	361	73	)	)	PUNCT
ejpam-4771	361	74	;	;	PUNCT
ejpam-4771	361	75	(	(	PUNCT
ejpam-4771	361	76	iii	iii	X
ejpam-4771	361	77	)	)	PUNCT
ejpam-4771	361	78	tx	tx	NOUN
ejpam-4771	362	1	or	or	CCONJ
ejpam-4771	362	2	ty	ty	INTJ
ejpam-4771	362	3	is	be	AUX
ejpam-4771	362	4	a	a	DET
ejpam-4771	362	5	(	(	PUNCT
ejpam-4771	362	6	2	2	NUM
ejpam-4771	362	7	,	,	PUNCT
ejpam-4771	362	8	1)-locating	1)-locating	NUM
ejpam-4771	362	9	set	set	NOUN
ejpam-4771	362	10	or	or	CCONJ
ejpam-4771	362	11	one	one	NUM
ejpam-4771	362	12	of	of	ADP
ejpam-4771	362	13	tx	tx	PROPN
ejpam-4771	362	14	and	and	CCONJ
ejpam-4771	362	15	ty	ty	PRON
ejpam-4771	362	16	is	be	AUX
ejpam-4771	362	17	a	a	DET
ejpam-4771	362	18	(	(	PUNCT
ejpam-4771	362	19	2	2	NUM
ejpam-4771	362	20	,	,	PUNCT
ejpam-4771	362	21	2)-locating	2)-locating	NUM
ejpam-4771	362	22	set	set	VERB
ejpam-4771	362	23	in	in	ADP
ejpam-4771	362	24	h	h	NOUN
ejpam-4771	362	25	whenever	whenever	SCONJ
ejpam-4771	362	26	x	x	X
ejpam-4771	362	27	,	,	PUNCT
ejpam-4771	362	28	y	y	PROPN
ejpam-4771	362	29	∈	∈	PROPN
ejpam-4771	362	30	eq1(g	eq1(g	PROPN
ejpam-4771	362	31	)	)	PUNCT
ejpam-4771	362	32	;	;	PUNCT
ejpam-4771	362	33	(	(	PUNCT
ejpam-4771	362	34	iv	iv	X
ejpam-4771	362	35	)	)	PUNCT
ejpam-4771	362	36	tx	tx	PROPN
ejpam-4771	363	1	and	and	CCONJ
ejpam-4771	363	2	ty	ty	INTJ
ejpam-4771	363	3	are	be	AUX
ejpam-4771	363	4	(	(	PUNCT
ejpam-4771	363	5	2	2	NUM
ejpam-4771	363	6	−	−	NOUN
ejpam-4771	363	7	locating	locating	NOUN
ejpam-4771	363	8	)	)	PUNCT
ejpam-4771	363	9	dominating	dominating	NOUN
ejpam-4771	363	10	sets	set	NOUN
ejpam-4771	363	11	in	in	ADP
ejpam-4771	363	12	h	h	NOUN
ejpam-4771	363	13	or	or	CCONJ
ejpam-4771	363	14	one	one	NUM
ejpam-4771	363	15	of	of	ADP
ejpam-4771	363	16	tx	tx	PROPN
ejpam-4771	364	1	and	and	CCONJ
ejpam-4771	364	2	ty	ty	INTJ
ejpam-4771	364	3	is	be	AUX
ejpam-4771	364	4	a	a	DET
ejpam-4771	364	5	2dominating	2dominating	NUM
ejpam-4771	364	6	set	set	NOUN
ejpam-4771	364	7	whenever	whenever	SCONJ
ejpam-4771	364	8	x	x	X
ejpam-4771	364	9	,	,	PUNCT
ejpam-4771	364	10	y	y	PROPN
ejpam-4771	364	11	∈	∈	PROPN
ejpam-4771	364	12	eq2(g	eq2(g	VERB
ejpam-4771	364	13	)	)	PUNCT
ejpam-4771	364	14	.	.	PUNCT
ejpam-4771	365	1	(	(	PUNCT
ejpam-4771	365	2	v	v	NOUN
ejpam-4771	365	3	)	)	PUNCT
ejpam-4771	365	4	tx	tx	PROPN
ejpam-4771	365	5	is	be	AUX
ejpam-4771	365	6	a	a	DET
ejpam-4771	365	7	2	2	NUM
ejpam-4771	365	8	-	-	PUNCT
ejpam-4771	365	9	locating	locate	VERB
ejpam-4771	365	10	point	point	NOUN
ejpam-4771	365	11	-	-	PUNCT
ejpam-4771	365	12	wise	wise	ADJ
ejpam-4771	365	13	non	non	ADJ
ejpam-4771	365	14	-	-	ADJ
ejpam-4771	365	15	dominating	dominating	ADJ
ejpam-4771	365	16	set	set	VERB
ejpam-4771	365	17	inh	inh	NOUN
ejpam-4771	365	18	for	for	ADP
ejpam-4771	365	19	every	every	DET
ejpam-4771	365	20	x	x	SYM
ejpam-4771	365	21	∈	∈	PROPN
ejpam-4771	365	22	s	s	VERB
ejpam-4771	365	23	with	with	ADP
ejpam-4771	365	24	|ng(x	|ng(x	ADP
ejpam-4771	365	25	,	,	PUNCT
ejpam-4771	365	26	2)∩	2)∩	ADJ
ejpam-4771	365	27	s|	s|	NOUN
ejpam-4771	365	28	=	=	SYM
ejpam-4771	365	29	0	0	X
ejpam-4771	365	30	.	.	PUNCT
ejpam-4771	365	31	theorem	theorem	VERB
ejpam-4771	365	32	13	13	NUM
ejpam-4771	365	33	.	.	PUNCT
ejpam-4771	366	1	[	[	X
ejpam-4771	366	2	9	9	NUM
ejpam-4771	366	3	]	]	PUNCT
ejpam-4771	366	4	let	let	VERB
ejpam-4771	366	5	g	g	NOUN
ejpam-4771	366	6	and	and	CCONJ
ejpam-4771	366	7	h	h	NOUN
ejpam-4771	366	8	be	be	AUX
ejpam-4771	366	9	connected	connect	VERB
ejpam-4771	366	10	nontrivial	nontrivial	ADJ
ejpam-4771	366	11	graphs	graph	NOUN
ejpam-4771	366	12	.	.	PUNCT
ejpam-4771	367	1	a	a	DET
ejpam-4771	367	2	subset	subset	NOUN
ejpam-4771	367	3	c	c	NOUN
ejpam-4771	367	4	=	=	PUNCT
ejpam-4771	367	5	⋃	⋃	PROPN
ejpam-4771	367	6	x∈s	x∈s	NOUN
ejpam-4771	367	7	[	[	X
ejpam-4771	367	8	{	{	PUNCT
ejpam-4771	367	9	x}×	x}×	PROPN
ejpam-4771	367	10	tx	tx	PROPN
ejpam-4771	367	11	]	]	PUNCT
ejpam-4771	367	12	of	of	ADP
ejpam-4771	367	13	v	v	NOUN
ejpam-4771	367	14	(	(	PUNCT
ejpam-4771	367	15	g[h	g[h	PROPN
ejpam-4771	367	16	]	]	PUNCT
ejpam-4771	367	17	)	)	PUNCT
ejpam-4771	367	18	is	be	AUX
ejpam-4771	367	19	an	an	DET
ejpam-4771	367	20	outer	outer	ADV
ejpam-4771	367	21	-	-	PUNCT
ejpam-4771	367	22	connected	connect	VERB
ejpam-4771	367	23	hop	hop	NOUN
ejpam-4771	367	24	dominating	dominating	NOUN
ejpam-4771	367	25	set	set	NOUN
ejpam-4771	367	26	of	of	ADP
ejpam-4771	367	27	g[h	g[h	PROPN
ejpam-4771	367	28	]	]	PUNCT
ejpam-4771	367	29	if	if	SCONJ
ejpam-4771	367	30	and	and	CCONJ
ejpam-4771	367	31	only	only	ADV
ejpam-4771	367	32	if	if	SCONJ
ejpam-4771	367	33	(	(	PUNCT
ejpam-4771	367	34	i	i	NOUN
ejpam-4771	367	35	)	)	PUNCT
ejpam-4771	367	36	s	s	VERB
ejpam-4771	367	37	is	be	AUX
ejpam-4771	367	38	a	a	DET
ejpam-4771	367	39	hop	hop	NOUN
ejpam-4771	367	40	dominating	dominating	NOUN
ejpam-4771	367	41	set	set	NOUN
ejpam-4771	367	42	of	of	ADP
ejpam-4771	367	43	g	g	NOUN
ejpam-4771	367	44	;	;	PUNCT
ejpam-4771	367	45	and	and	CCONJ
ejpam-4771	367	46	(	(	PUNCT
ejpam-4771	367	47	ii	ii	NOUN
ejpam-4771	367	48	)	)	PUNCT
ejpam-4771	367	49	tx	tx	PROPN
ejpam-4771	367	50	is	be	AUX
ejpam-4771	367	51	a	a	DET
ejpam-4771	367	52	point	point	NOUN
ejpam-4771	367	53	-	-	PUNCT
ejpam-4771	367	54	wise	wise	ADJ
ejpam-4771	367	55	non	non	ADJ
ejpam-4771	367	56	-	-	ADJ
ejpam-4771	367	57	dominating	dominating	ADJ
ejpam-4771	367	58	set	set	NOUN
ejpam-4771	367	59	of	of	ADP
ejpam-4771	367	60	h	h	NOUN
ejpam-4771	367	61	for	for	ADP
ejpam-4771	367	62	every	every	DET
ejpam-4771	367	63	x	x	SYM
ejpam-4771	367	64	∈	∈	PROPN
ejpam-4771	367	65	s	s	VERB
ejpam-4771	367	66	with	with	ADP
ejpam-4771	367	67	|ng(x	|ng(x	ADP
ejpam-4771	367	68	,	,	PUNCT
ejpam-4771	367	69	2	2	X
ejpam-4771	367	70	)	)	PUNCT
ejpam-4771	367	71	∩	∩	NOUN
ejpam-4771	367	72	s|	s|	NOUN
ejpam-4771	367	73	=	=	SYM
ejpam-4771	367	74	0	0	NUM
ejpam-4771	367	75	;	;	PUNCT
ejpam-4771	367	76	(	(	PUNCT
ejpam-4771	367	77	iii	iii	X
ejpam-4771	367	78	)	)	PUNCT
ejpam-4771	367	79	⟨(v	⟨(v	NOUN
ejpam-4771	367	80	(	(	PUNCT
ejpam-4771	367	81	g)\s	g)\s	NOUN
ejpam-4771	367	82	)	)	PUNCT
ejpam-4771	367	83	∪	∪	NOUN
ejpam-4771	367	84	{	{	PUNCT
ejpam-4771	367	85	v	v	NOUN
ejpam-4771	367	86	∈	∈	NOUN
ejpam-4771	367	87	s	s	PART
ejpam-4771	367	88	:	:	PUNCT
ejpam-4771	367	89	tv	tv	NOUN
ejpam-4771	367	90	̸=	̸=	PROPN
ejpam-4771	367	91	v	v	NOUN
ejpam-4771	367	92	(	(	PUNCT
ejpam-4771	367	93	h)}⟩	h)}⟩	NUM
ejpam-4771	367	94	is	be	AUX
ejpam-4771	367	95	a	a	DET
ejpam-4771	367	96	connected	connected	ADJ
ejpam-4771	367	97	graph	graph	NOUN
ejpam-4771	367	98	in	in	ADP
ejpam-4771	367	99	g.	g.	PROPN
ejpam-4771	367	100	theorem	theorem	PROPN
ejpam-4771	367	101	14	14	NUM
ejpam-4771	367	102	.	.	PUNCT
ejpam-4771	368	1	let	let	VERB
ejpam-4771	368	2	g	g	NOUN
ejpam-4771	368	3	and	and	CCONJ
ejpam-4771	368	4	h	h	NOUN
ejpam-4771	368	5	be	be	AUX
ejpam-4771	368	6	nontrivial	nontrivial	ADJ
ejpam-4771	368	7	connected	connect	VERB
ejpam-4771	368	8	graphs	graph	NOUN
ejpam-4771	368	9	with	with	ADP
ejpam-4771	368	10	∆(h	∆(h	NOUN
ejpam-4771	368	11	)	)	PUNCT
ejpam-4771	368	12	≤	≤	NOUN
ejpam-4771	368	13	|v	|v	X
ejpam-4771	368	14	(	(	PUNCT
ejpam-4771	368	15	h)|	h)|	NOUN
ejpam-4771	368	16	−	−	PROPN
ejpam-4771	368	17	3	3	NUM
ejpam-4771	368	18	.	.	PUNCT
ejpam-4771	369	1	then	then	ADV
ejpam-4771	369	2	w	w	PROPN
ejpam-4771	369	3	=	=	PUNCT
ejpam-4771	369	4	⋃	⋃	PROPN
ejpam-4771	369	5	x∈s	x∈s	NOUN
ejpam-4771	370	1	[	[	X
ejpam-4771	370	2	{	{	PUNCT
ejpam-4771	370	3	x	x	NOUN
ejpam-4771	370	4	}	}	PUNCT
ejpam-4771	370	5	×	×	PROPN
ejpam-4771	370	6	tx	tx	PROPN
ejpam-4771	370	7	]	]	X
ejpam-4771	370	8	,	,	PUNCT
ejpam-4771	370	9	where	where	SCONJ
ejpam-4771	370	10	s	s	VERB
ejpam-4771	370	11	⊆	⊆	NUM
ejpam-4771	370	12	v	v	NOUN
ejpam-4771	370	13	(	(	PUNCT
ejpam-4771	370	14	g	g	NOUN
ejpam-4771	370	15	)	)	PUNCT
ejpam-4771	370	16	and	and	CCONJ
ejpam-4771	370	17	tx	tx	VERB
ejpam-4771	370	18	⊆	⊆	NUM
ejpam-4771	370	19	v	v	NOUN
ejpam-4771	370	20	(	(	PUNCT
ejpam-4771	370	21	h	h	NOUN
ejpam-4771	370	22	)	)	PUNCT
ejpam-4771	370	23	for	for	ADP
ejpam-4771	370	24	each	each	DET
ejpam-4771	370	25	x	x	SYM
ejpam-4771	370	26	∈	∈	PROPN
ejpam-4771	370	27	s	s	NOUN
ejpam-4771	370	28	,	,	PUNCT
ejpam-4771	370	29	is	be	AUX
ejpam-4771	370	30	an	an	DET
ejpam-4771	370	31	outer	outer	ADV
ejpam-4771	370	32	-	-	PUNCT
ejpam-4771	370	33	connected	connect	VERB
ejpam-4771	370	34	2	2	NUM
ejpam-4771	370	35	-	-	PUNCT
ejpam-4771	370	36	resolving	resolve	VERB
ejpam-4771	370	37	hop	hop	NOUN
ejpam-4771	370	38	dominating	dominating	NOUN
ejpam-4771	370	39	set	set	VERB
ejpam-4771	370	40	in	in	ADP
ejpam-4771	370	41	g[h	g[h	PROPN
ejpam-4771	370	42	]	]	PUNCT
ejpam-4771	370	43	if	if	SCONJ
ejpam-4771	370	44	and	and	CCONJ
ejpam-4771	370	45	only	only	ADV
ejpam-4771	370	46	if	if	SCONJ
ejpam-4771	370	47	(	(	PUNCT
ejpam-4771	370	48	i	i	NOUN
ejpam-4771	370	49	)	)	PUNCT
ejpam-4771	370	50	s	s	PART
ejpam-4771	370	51	=	=	SYM
ejpam-4771	370	52	v	v	NOUN
ejpam-4771	370	53	(	(	PUNCT
ejpam-4771	370	54	g	g	NOUN
ejpam-4771	370	55	)	)	PUNCT
ejpam-4771	370	56	;	;	PUNCT
ejpam-4771	370	57	(	(	PUNCT
ejpam-4771	370	58	ii	ii	NOUN
ejpam-4771	370	59	)	)	PUNCT
ejpam-4771	370	60	tx	tx	PROPN
ejpam-4771	370	61	is	be	AUX
ejpam-4771	370	62	a	a	DET
ejpam-4771	370	63	2	2	NUM
ejpam-4771	370	64	-	-	PUNCT
ejpam-4771	370	65	locating	locate	VERB
ejpam-4771	370	66	set	set	NOUN
ejpam-4771	370	67	of	of	ADP
ejpam-4771	370	68	h	h	NOUN
ejpam-4771	370	69	for	for	ADP
ejpam-4771	370	70	every	every	DET
ejpam-4771	370	71	x	x	SYM
ejpam-4771	370	72	∈	∈	PROPN
ejpam-4771	370	73	v	v	ADP
ejpam-4771	370	74	(	(	PUNCT
ejpam-4771	370	75	g	g	NOUN
ejpam-4771	370	76	)	)	PUNCT
ejpam-4771	370	77	;	;	PUNCT
ejpam-4771	370	78	(	(	PUNCT
ejpam-4771	370	79	iii	iii	X
ejpam-4771	370	80	)	)	PUNCT
ejpam-4771	370	81	tx	tx	NOUN
ejpam-4771	371	1	and	and	CCONJ
ejpam-4771	371	2	ty	ty	INTJ
ejpam-4771	371	3	are	be	AUX
ejpam-4771	371	4	(	(	PUNCT
ejpam-4771	371	5	2	2	NUM
ejpam-4771	371	6	,	,	PUNCT
ejpam-4771	371	7	1)-locating	1)-locating	NUM
ejpam-4771	371	8	set	set	NOUN
ejpam-4771	371	9	or	or	CCONJ
ejpam-4771	371	10	one	one	NUM
ejpam-4771	371	11	of	of	ADP
ejpam-4771	371	12	tx	tx	PROPN
ejpam-4771	372	1	and	and	CCONJ
ejpam-4771	372	2	ty	ty	PRON
ejpam-4771	372	3	is	be	AUX
ejpam-4771	372	4	a	a	DET
ejpam-4771	372	5	(	(	PUNCT
ejpam-4771	372	6	2	2	NUM
ejpam-4771	372	7	,	,	PUNCT
ejpam-4771	372	8	2)-locating	2)-locating	NUM
ejpam-4771	372	9	set	set	NOUN
ejpam-4771	372	10	of	of	ADP
ejpam-4771	372	11	h	h	NOUN
ejpam-4771	372	12	whenever	whenever	SCONJ
ejpam-4771	372	13	x	x	X
ejpam-4771	372	14	,	,	PUNCT
ejpam-4771	372	15	y	y	PROPN
ejpam-4771	372	16	∈	∈	PROPN
ejpam-4771	372	17	eq1(g	eq1(g	PROPN
ejpam-4771	372	18	)	)	PUNCT
ejpam-4771	372	19	;	;	PUNCT
ejpam-4771	372	20	(	(	PUNCT
ejpam-4771	372	21	iv	iv	X
ejpam-4771	372	22	)	)	PUNCT
ejpam-4771	372	23	tx	tx	PROPN
ejpam-4771	373	1	and	and	CCONJ
ejpam-4771	373	2	ty	ty	INTJ
ejpam-4771	373	3	are	be	AUX
ejpam-4771	373	4	(	(	PUNCT
ejpam-4771	373	5	2	2	NUM
ejpam-4771	373	6	−	−	NOUN
ejpam-4771	373	7	locating	locating	NOUN
ejpam-4771	373	8	)	)	PUNCT
ejpam-4771	373	9	dominating	dominating	NOUN
ejpam-4771	373	10	sets	set	NOUN
ejpam-4771	373	11	in	in	ADP
ejpam-4771	373	12	h	h	NOUN
ejpam-4771	373	13	or	or	CCONJ
ejpam-4771	373	14	one	one	NUM
ejpam-4771	373	15	of	of	ADP
ejpam-4771	373	16	tx	tx	PROPN
ejpam-4771	374	1	and	and	CCONJ
ejpam-4771	374	2	ty	ty	INTJ
ejpam-4771	374	3	is	be	AUX
ejpam-4771	374	4	a	a	DET
ejpam-4771	374	5	2dominating	2dominating	NUM
ejpam-4771	374	6	set	set	NOUN
ejpam-4771	374	7	whenever	whenever	SCONJ
ejpam-4771	374	8	x	x	X
ejpam-4771	374	9	,	,	PUNCT
ejpam-4771	374	10	y	y	PROPN
ejpam-4771	374	11	∈	∈	PROPN
ejpam-4771	374	12	eq2(g	eq2(g	VERB
ejpam-4771	374	13	)	)	PUNCT
ejpam-4771	374	14	.	.	PUNCT
ejpam-4771	375	1	(	(	PUNCT
ejpam-4771	375	2	v	v	NOUN
ejpam-4771	375	3	)	)	PUNCT
ejpam-4771	375	4	tx	tx	PROPN
ejpam-4771	375	5	is	be	AUX
ejpam-4771	375	6	a	a	DET
ejpam-4771	375	7	2	2	NUM
ejpam-4771	375	8	-	-	PUNCT
ejpam-4771	375	9	locating	locate	VERB
ejpam-4771	375	10	point	point	NOUN
ejpam-4771	375	11	-	-	PUNCT
ejpam-4771	375	12	wise	wise	ADJ
ejpam-4771	375	13	non	non	ADJ
ejpam-4771	375	14	-	-	ADJ
ejpam-4771	375	15	dominating	dominating	ADJ
ejpam-4771	375	16	set	set	NOUN
ejpam-4771	375	17	of	of	ADP
ejpam-4771	375	18	h	h	NOUN
ejpam-4771	375	19	for	for	ADP
ejpam-4771	375	20	every	every	DET
ejpam-4771	375	21	x	x	SYM
ejpam-4771	375	22	∈	∈	PROPN
ejpam-4771	375	23	s	s	VERB
ejpam-4771	375	24	with	with	ADP
ejpam-4771	375	25	|ng(x	|ng(x	ADP
ejpam-4771	375	26	,	,	PUNCT
ejpam-4771	375	27	2	2	X
ejpam-4771	375	28	)	)	PUNCT
ejpam-4771	375	29	∩	∩	NOUN
ejpam-4771	375	30	s|	s|	NOUN
ejpam-4771	375	31	=	=	SYM
ejpam-4771	376	1	0	0	X
ejpam-4771	376	2	.	.	PUNCT
ejpam-4771	376	3	(	(	PUNCT
ejpam-4771	376	4	vi	vi	NOUN
ejpam-4771	376	5	)	)	PUNCT
ejpam-4771	376	6	⟨∪{v	⟨∪{v	NOUN
ejpam-4771	377	1	∈	∈	PROPN
ejpam-4771	377	2	v	v	ADP
ejpam-4771	377	3	(	(	PUNCT
ejpam-4771	377	4	g	g	NOUN
ejpam-4771	377	5	)	)	PUNCT
ejpam-4771	377	6	:	:	PUNCT
ejpam-4771	377	7	tv	tv	NOUN
ejpam-4771	377	8	̸=	̸=	PROPN
ejpam-4771	377	9	v	v	NOUN
ejpam-4771	377	10	(	(	PUNCT
ejpam-4771	377	11	h)}⟩	h)}⟩	NUM
ejpam-4771	377	12	is	be	AUX
ejpam-4771	377	13	a	a	DET
ejpam-4771	377	14	connected	connected	ADJ
ejpam-4771	377	15	graph	graph	NOUN
ejpam-4771	377	16	in	in	ADP
ejpam-4771	377	17	g.	g.	PROPN
ejpam-4771	377	18	references	reference	NOUN
ejpam-4771	377	19	1193	1193	NUM
ejpam-4771	377	20	proof	proof	NOUN
ejpam-4771	377	21	.	.	PUNCT
ejpam-4771	378	1	let	let	VERB
ejpam-4771	378	2	w	w	NOUN
ejpam-4771	378	3	=	=	PUNCT
ejpam-4771	378	4	⋃	⋃	PROPN
ejpam-4771	378	5	x∈s	x∈s	NOUN
ejpam-4771	379	1	[	[	X
ejpam-4771	379	2	{	{	PUNCT
ejpam-4771	379	3	x	x	NOUN
ejpam-4771	379	4	}	}	PUNCT
ejpam-4771	379	5	×	×	PROPN
ejpam-4771	379	6	tx	tx	PROPN
ejpam-4771	379	7	]	]	X
ejpam-4771	379	8	,	,	PUNCT
ejpam-4771	379	9	where	where	SCONJ
ejpam-4771	379	10	s	s	VERB
ejpam-4771	379	11	⊆	⊆	NUM
ejpam-4771	379	12	v	v	NOUN
ejpam-4771	379	13	(	(	PUNCT
ejpam-4771	379	14	g	g	NOUN
ejpam-4771	379	15	)	)	PUNCT
ejpam-4771	379	16	and	and	CCONJ
ejpam-4771	379	17	tx	tx	VERB
ejpam-4771	379	18	⊆	⊆	NUM
ejpam-4771	379	19	v	v	NOUN
ejpam-4771	379	20	(	(	PUNCT
ejpam-4771	379	21	h	h	NOUN
ejpam-4771	379	22	)	)	PUNCT
ejpam-4771	379	23	for	for	ADP
ejpam-4771	379	24	each	each	DET
ejpam-4771	379	25	x	x	SYM
ejpam-4771	379	26	∈	∈	PROPN
ejpam-4771	379	27	s	s	AUX
ejpam-4771	379	28	,	,	PUNCT
ejpam-4771	379	29	be	be	AUX
ejpam-4771	379	30	an	an	DET
ejpam-4771	379	31	outer	outer	ADV
ejpam-4771	379	32	-	-	PUNCT
ejpam-4771	379	33	connected	connect	VERB
ejpam-4771	379	34	2	2	NUM
ejpam-4771	379	35	-	-	PUNCT
ejpam-4771	379	36	resolving	resolve	VERB
ejpam-4771	379	37	hop	hop	NOUN
ejpam-4771	379	38	dominating	dominating	NOUN
ejpam-4771	379	39	set	set	VERB
ejpam-4771	379	40	in	in	ADP
ejpam-4771	379	41	g[h	g[h	PROPN
ejpam-4771	379	42	]	]	PUNCT
ejpam-4771	379	43	.	.	PUNCT
ejpam-4771	380	1	then	then	ADV
ejpam-4771	380	2	w	w	PROPN
ejpam-4771	380	3	is	be	AUX
ejpam-4771	380	4	a	a	DET
ejpam-4771	380	5	2	2	NUM
ejpam-4771	380	6	-	-	PUNCT
ejpam-4771	380	7	resolving	resolve	VERB
ejpam-4771	380	8	hop	hop	NOUN
ejpam-4771	380	9	dominating	dominating	NOUN
ejpam-4771	380	10	set	set	VERB
ejpam-4771	380	11	in	in	ADP
ejpam-4771	380	12	g[h	g[h	PROPN
ejpam-4771	380	13	]	]	PUNCT
ejpam-4771	380	14	.	.	PUNCT
ejpam-4771	381	1	since	since	SCONJ
ejpam-4771	381	2	w	w	PROPN
ejpam-4771	381	3	is	be	AUX
ejpam-4771	381	4	an	an	DET
ejpam-4771	381	5	outer	outer	ADV
ejpam-4771	381	6	-	-	PUNCT
ejpam-4771	381	7	connected	connect	VERB
ejpam-4771	381	8	hop	hop	NOUN
ejpam-4771	381	9	dominating	dominating	NOUN
ejpam-4771	381	10	set	set	NOUN
ejpam-4771	381	11	and	and	CCONJ
ejpam-4771	381	12	s	s	NOUN
ejpam-4771	381	13	=	=	SYM
ejpam-4771	381	14	v	v	X
ejpam-4771	381	15	(	(	PUNCT
ejpam-4771	381	16	g	g	NOUN
ejpam-4771	381	17	)	)	PUNCT
ejpam-4771	381	18	,	,	PUNCT
ejpam-4771	381	19	by	by	ADP
ejpam-4771	381	20	theorem	theorem	VERB
ejpam-4771	381	21	13	13	NUM
ejpam-4771	381	22	(	(	PUNCT
ejpam-4771	381	23	iii	iii	NOUN
ejpam-4771	381	24	)	)	PUNCT
ejpam-4771	381	25	,	,	PUNCT
ejpam-4771	381	26	⟨	⟨	VERB
ejpam-4771	381	27	⋃	⋃	PROPN
ejpam-4771	381	28	{	{	PUNCT
ejpam-4771	381	29	v	v	NOUN
ejpam-4771	381	30	∈	∈	NUM
ejpam-4771	381	31	v	v	NOUN
ejpam-4771	381	32	(	(	PUNCT
ejpam-4771	381	33	g	g	NOUN
ejpam-4771	381	34	)	)	PUNCT
ejpam-4771	381	35	:	:	PUNCT
ejpam-4771	381	36	tv	tv	NOUN
ejpam-4771	381	37	̸=	̸=	PROPN
ejpam-4771	381	38	v	v	NOUN
ejpam-4771	381	39	(	(	PUNCT
ejpam-4771	381	40	h)}⟩	h)}⟩	NUM
ejpam-4771	381	41	is	be	AUX
ejpam-4771	381	42	a	a	DET
ejpam-4771	381	43	connected	connected	ADJ
ejpam-4771	381	44	graph	graph	NOUN
ejpam-4771	381	45	in	in	ADP
ejpam-4771	381	46	g.	g.	PROPN
ejpam-4771	381	47	for	for	ADP
ejpam-4771	381	48	the	the	DET
ejpam-4771	381	49	converse	converse	NOUN
ejpam-4771	381	50	,	,	PUNCT
ejpam-4771	381	51	let	let	VERB
ejpam-4771	381	52	w	w	NOUN
ejpam-4771	381	53	be	be	AUX
ejpam-4771	381	54	a	a	DET
ejpam-4771	381	55	2	2	NUM
ejpam-4771	381	56	-	-	PUNCT
ejpam-4771	381	57	resolving	resolve	VERB
ejpam-4771	381	58	hop	hop	NOUN
ejpam-4771	381	59	dominating	dominating	NOUN
ejpam-4771	381	60	set	set	NOUN
ejpam-4771	381	61	and	and	CCONJ
ejpam-4771	381	62	satisfies	satisfy	VERB
ejpam-4771	381	63	the	the	DET
ejpam-4771	381	64	given	give	VERB
ejpam-4771	381	65	condition	condition	NOUN
ejpam-4771	381	66	.	.	PUNCT
ejpam-4771	382	1	if	if	SCONJ
ejpam-4771	382	2	v	v	X
ejpam-4771	382	3	(	(	PUNCT
ejpam-4771	382	4	g[h	g[h	PROPN
ejpam-4771	382	5	]	]	PUNCT
ejpam-4771	382	6	)	)	PUNCT
ejpam-4771	383	1	=	=	SYM
ejpam-4771	383	2	w	w	PROPN
ejpam-4771	383	3	,	,	PUNCT
ejpam-4771	383	4	then	then	ADV
ejpam-4771	383	5	we	we	PRON
ejpam-4771	383	6	are	be	AUX
ejpam-4771	383	7	done	do	VERB
ejpam-4771	383	8	.	.	PUNCT
ejpam-4771	384	1	on	on	ADP
ejpam-4771	384	2	the	the	DET
ejpam-4771	384	3	other	other	ADJ
ejpam-4771	384	4	hand	hand	NOUN
ejpam-4771	384	5	,	,	PUNCT
ejpam-4771	384	6	suppose	suppose	VERB
ejpam-4771	384	7	v	v	X
ejpam-4771	384	8	(	(	PUNCT
ejpam-4771	384	9	g[h	g[h	PROPN
ejpam-4771	384	10	]	]	PUNCT
ejpam-4771	384	11	)	)	PUNCT
ejpam-4771	384	12	̸=	̸=	PROPN
ejpam-4771	384	13	w	w	NOUN
ejpam-4771	384	14	.	.	PUNCT
ejpam-4771	385	1	since	since	SCONJ
ejpam-4771	385	2	s	s	PART
ejpam-4771	385	3	=	=	SYM
ejpam-4771	385	4	v	v	PROPN
ejpam-4771	385	5	(	(	PUNCT
ejpam-4771	385	6	g	g	NOUN
ejpam-4771	385	7	)	)	PUNCT
ejpam-4771	385	8	,	,	PUNCT
ejpam-4771	385	9	⟨(v	⟨(v	PROPN
ejpam-4771	385	10	(	(	PUNCT
ejpam-4771	385	11	g)\s	g)\s	NOUN
ejpam-4771	385	12	)	)	PUNCT
ejpam-4771	385	13	∪	∪	NOUN
ejpam-4771	385	14	{	{	PUNCT
ejpam-4771	385	15	v	v	NOUN
ejpam-4771	385	16	∈	∈	NOUN
ejpam-4771	385	17	s	s	PART
ejpam-4771	385	18	:	:	PUNCT
ejpam-4771	385	19	tv	tv	NOUN
ejpam-4771	385	20	̸=	̸=	PROPN
ejpam-4771	385	21	v	v	NOUN
ejpam-4771	385	22	(	(	PUNCT
ejpam-4771	385	23	h)}⟩	h)}⟩	NUM
ejpam-4771	385	24	=	=	PUNCT
ejpam-4771	385	25	⟨∪{v	⟨∪{v	NOUN
ejpam-4771	385	26	∈	∈	PROPN
ejpam-4771	385	27	v	v	ADP
ejpam-4771	385	28	(	(	PUNCT
ejpam-4771	385	29	g	g	NOUN
ejpam-4771	385	30	)	)	PUNCT
ejpam-4771	385	31	:	:	PUNCT
ejpam-4771	385	32	tv	tv	NOUN
ejpam-4771	385	33	̸=	̸=	PROPN
ejpam-4771	385	34	v	v	NOUN
ejpam-4771	385	35	(	(	PUNCT
ejpam-4771	385	36	h)}⟩	h)}⟩	NUM
ejpam-4771	385	37	which	which	PRON
ejpam-4771	385	38	is	be	AUX
ejpam-4771	385	39	connected	connect	VERB
ejpam-4771	385	40	.	.	PUNCT
ejpam-4771	386	1	by	by	ADP
ejpam-4771	386	2	theorem	theorem	ADJ
ejpam-4771	386	3	13	13	NUM
ejpam-4771	386	4	,	,	PUNCT
ejpam-4771	386	5	theorem	theorem	VERB
ejpam-4771	386	6	12(i	12(i	NUM
ejpam-4771	386	7	)	)	PUNCT
ejpam-4771	386	8	,	,	PUNCT
ejpam-4771	386	9	and	and	CCONJ
ejpam-4771	386	10	by	by	ADP
ejpam-4771	386	11	theorem	theorem	NOUN
ejpam-4771	386	12	12	12	NUM
ejpam-4771	386	13	(	(	PUNCT
ejpam-4771	386	14	iii	iii	NOUN
ejpam-4771	386	15	)	)	PUNCT
ejpam-4771	386	16	therefore	therefore	ADV
ejpam-4771	386	17	,	,	PUNCT
ejpam-4771	386	18	w	w	PROPN
ejpam-4771	386	19	is	be	AUX
ejpam-4771	386	20	an	an	DET
ejpam-4771	386	21	outer	outer	ADV
ejpam-4771	386	22	-	-	PUNCT
ejpam-4771	386	23	connected	connect	VERB
ejpam-4771	386	24	hop	hop	NOUN
ejpam-4771	386	25	dominating	dominating	NOUN
ejpam-4771	386	26	set	set	VERB
ejpam-4771	386	27	in	in	ADP
ejpam-4771	386	28	g[h	g[h	PROPN
ejpam-4771	386	29	]	]	PUNCT
ejpam-4771	386	30	.	.	PUNCT
ejpam-4771	387	1	accordingly	accordingly	ADV
ejpam-4771	387	2	,	,	PUNCT
ejpam-4771	387	3	w	w	PROPN
ejpam-4771	387	4	is	be	AUX
ejpam-4771	387	5	an	an	DET
ejpam-4771	387	6	outer	outer	ADV
ejpam-4771	387	7	-	-	PUNCT
ejpam-4771	387	8	connected	connect	VERB
ejpam-4771	387	9	2	2	NUM
ejpam-4771	387	10	-	-	PUNCT
ejpam-4771	387	11	resolving	resolve	VERB
ejpam-4771	387	12	hop	hop	NOUN
ejpam-4771	387	13	dominating	dominating	NOUN
ejpam-4771	387	14	set	set	VERB
ejpam-4771	387	15	in	in	ADP
ejpam-4771	387	16	g[h	g[h	PROPN
ejpam-4771	387	17	]	]	PUNCT
ejpam-4771	387	18	.	.	PUNCT
ejpam-4771	388	1	corollary	corollary	ADJ
ejpam-4771	388	2	6	6	NUM
ejpam-4771	388	3	.	.	PUNCT
ejpam-4771	389	1	let	let	VERB
ejpam-4771	389	2	g	g	NOUN
ejpam-4771	390	1	and	and	CCONJ
ejpam-4771	390	2	h	h	NOUN
ejpam-4771	390	3	be	be	VERB
ejpam-4771	390	4	any	any	DET
ejpam-4771	390	5	nontrivial	nontrivial	ADJ
ejpam-4771	390	6	connected	connect	VERB
ejpam-4771	390	7	graph	graph	NOUN
ejpam-4771	390	8	with	with	ADP
ejpam-4771	390	9	γ(g	γ(g	PROPN
ejpam-4771	390	10	)	)	PUNCT
ejpam-4771	390	11	̸=	̸=	PROPN
ejpam-4771	390	12	1	1	NUM
ejpam-4771	390	13	and	and	CCONJ
ejpam-4771	390	14	g	g	PROPN
ejpam-4771	390	15	is	be	AUX
ejpam-4771	390	16	a	a	DET
ejpam-4771	390	17	free	free	ADJ
ejpam-4771	390	18	-	-	PUNCT
ejpam-4771	390	19	equidistant	equidistant	NOUN
ejpam-4771	390	20	.	.	PUNCT
ejpam-4771	391	1	then	then	ADV
ejpam-4771	391	2	γ̃c2rh(g[h	γ̃c2rh(g[h	PROPN
ejpam-4771	391	3	]	]	PUNCT
ejpam-4771	391	4	)	)	PUNCT
ejpam-4771	392	1	=	=	SYM
ejpam-4771	392	2	|v	|v	PROPN
ejpam-4771	392	3	(	(	PUNCT
ejpam-4771	392	4	g)|	g)|	PROPN
ejpam-4771	392	5	·	·	SYM
ejpam-4771	392	6	ln2(h	ln2(h	PROPN
ejpam-4771	392	7	)	)	PUNCT
ejpam-4771	392	8	.	.	PUNCT
ejpam-4771	393	1	proof	proof	NOUN
ejpam-4771	393	2	.	.	PUNCT
ejpam-4771	394	1	let	let	VERB
ejpam-4771	394	2	s	s	PRON
ejpam-4771	394	3	=	=	X
ejpam-4771	394	4	v	v	ADJ
ejpam-4771	394	5	(	(	PUNCT
ejpam-4771	394	6	g	g	NOUN
ejpam-4771	394	7	)	)	PUNCT
ejpam-4771	394	8	and	and	CCONJ
ejpam-4771	394	9	let	let	VERB
ejpam-4771	394	10	rx	rx	AUX
ejpam-4771	394	11	be	be	AUX
ejpam-4771	394	12	an	an	DET
ejpam-4771	394	13	ln2	ln2	NOUN
ejpam-4771	394	14	-	-	PUNCT
ejpam-4771	394	15	set	set	NOUN
ejpam-4771	394	16	of	of	ADP
ejpam-4771	394	17	h	h	NOUN
ejpam-4771	394	18	for	for	ADP
ejpam-4771	394	19	each	each	DET
ejpam-4771	394	20	x	x	SYM
ejpam-4771	394	21	∈	∈	PROPN
ejpam-4771	394	22	s.	s.	PROPN
ejpam-4771	394	23	by	by	ADP
ejpam-4771	394	24	theorem	theorem	PROPN
ejpam-4771	394	25	14	14	NUM
ejpam-4771	394	26	,	,	PUNCT
ejpam-4771	394	27	w	w	NOUN
ejpam-4771	394	28	=	=	PUNCT
ejpam-4771	394	29	⋃	⋃	PROPN
ejpam-4771	394	30	x∈s	x∈s	NOUN
ejpam-4771	395	1	[	[	X
ejpam-4771	395	2	{	{	PUNCT
ejpam-4771	395	3	x	x	NOUN
ejpam-4771	395	4	}	}	PUNCT
ejpam-4771	395	5	×	×	NOUN
ejpam-4771	395	6	rx	rx	NOUN
ejpam-4771	395	7	]	]	PUNCT
ejpam-4771	395	8	is	be	AUX
ejpam-4771	395	9	an	an	DET
ejpam-4771	395	10	outer	outer	ADV
ejpam-4771	395	11	-	-	PUNCT
ejpam-4771	395	12	connected	connect	VERB
ejpam-4771	395	13	2	2	NUM
ejpam-4771	395	14	-	-	PUNCT
ejpam-4771	395	15	resolving	resolve	VERB
ejpam-4771	395	16	hop	hop	NOUN
ejpam-4771	395	17	dominating	dominating	NOUN
ejpam-4771	395	18	set	set	VERB
ejpam-4771	395	19	in	in	ADP
ejpam-4771	395	20	g[h	g[h	PROPN
ejpam-4771	395	21	]	]	PUNCT
ejpam-4771	395	22	.	.	PUNCT
ejpam-4771	396	1	thus	thus	ADV
ejpam-4771	396	2	,	,	PUNCT
ejpam-4771	396	3	γ̃c2rh(g[h	γ̃c2rh(g[h	PROPN
ejpam-4771	396	4	]	]	X
ejpam-4771	396	5	)	)	PUNCT
ejpam-4771	396	6	≤	≤	NUM
ejpam-4771	396	7	|w	|w	NOUN
ejpam-4771	396	8	|	|	NOUN
ejpam-4771	396	9	=	=	SYM
ejpam-4771	396	10	|v	|v	PROPN
ejpam-4771	396	11	(	(	PUNCT
ejpam-4771	396	12	g)||rx|	g)||rx|	PROPN
ejpam-4771	396	13	=	=	SYM
ejpam-4771	396	14	|v	|v	X
ejpam-4771	396	15	(	(	PUNCT
ejpam-4771	396	16	g)|ln2(h	g)|ln2(h	NOUN
ejpam-4771	396	17	)	)	PUNCT
ejpam-4771	396	18	.	.	PUNCT
ejpam-4771	397	1	if	if	SCONJ
ejpam-4771	397	2	w0	w0	PROPN
ejpam-4771	397	3	=	=	PUNCT
ejpam-4771	397	4	⋃	⋃	PROPN
ejpam-4771	397	5	x∈s({x}×t	x∈s({x}×t	PROPN
ejpam-4771	397	6	)	)	PUNCT
ejpam-4771	397	7	is	be	AUX
ejpam-4771	397	8	a	a	DET
ejpam-4771	397	9	γ̃c2rh	γ̃c2rh	NOUN
ejpam-4771	397	10	-set	-set	ADJ
ejpam-4771	397	11	of	of	ADP
ejpam-4771	397	12	g[h	g[h	PROPN
ejpam-4771	397	13	]	]	PUNCT
ejpam-4771	397	14	,	,	PUNCT
ejpam-4771	397	15	then	then	ADV
ejpam-4771	397	16	s0	s0	PROPN
ejpam-4771	397	17	=	=	SYM
ejpam-4771	397	18	v	v	PROPN
ejpam-4771	397	19	(	(	PUNCT
ejpam-4771	397	20	g	g	NOUN
ejpam-4771	397	21	)	)	PUNCT
ejpam-4771	397	22	and	and	CCONJ
ejpam-4771	397	23	tx	tx	PROPN
ejpam-4771	397	24	is	be	AUX
ejpam-4771	397	25	a	a	DET
ejpam-4771	397	26	2	2	NUM
ejpam-4771	397	27	-	-	PUNCT
ejpam-4771	397	28	locating	locate	VERB
ejpam-4771	397	29	set	set	NOUN
ejpam-4771	397	30	in	in	ADP
ejpam-4771	397	31	h	h	NOUN
ejpam-4771	397	32	for	for	ADP
ejpam-4771	397	33	each	each	DET
ejpam-4771	397	34	x	x	SYM
ejpam-4771	397	35	∈	∈	PROPN
ejpam-4771	397	36	v	v	ADP
ejpam-4771	397	37	(	(	PUNCT
ejpam-4771	397	38	g	g	NOUN
ejpam-4771	397	39	)	)	PUNCT
ejpam-4771	397	40	by	by	ADP
ejpam-4771	397	41	theorem	theorem	NOUN
ejpam-4771	397	42	14	14	NUM
ejpam-4771	397	43	.	.	PUNCT
ejpam-4771	398	1	hence	hence	ADV
ejpam-4771	398	2	,	,	PUNCT
ejpam-4771	398	3	γ̃c2rh(g[h	γ̃c2rh(g[h	PROPN
ejpam-4771	398	4	]	]	PUNCT
ejpam-4771	398	5	)	)	PUNCT
ejpam-4771	398	6	=	=	VERB
ejpam-4771	398	7	|w0|	|w0|	X
ejpam-4771	398	8	=	=	SYM
ejpam-4771	398	9	|v	|v	X
ejpam-4771	398	10	(	(	PUNCT
ejpam-4771	398	11	g)||tx|	g)||tx|	PROPN
ejpam-4771	398	12	≥	≥	NUM
ejpam-4771	398	13	|v	|v	PROPN
ejpam-4771	398	14	(	(	PUNCT
ejpam-4771	398	15	g)|	g)|	PROPN
ejpam-4771	398	16	·	·	SYM
ejpam-4771	398	17	ln2(h	ln2(h	PROPN
ejpam-4771	398	18	)	)	PUNCT
ejpam-4771	398	19	.	.	PUNCT
ejpam-4771	399	1	therefore	therefore	ADV
ejpam-4771	399	2	,	,	PUNCT
ejpam-4771	399	3	γ̃c2rh(g[h	γ̃c2rh(g[h	PROPN
ejpam-4771	399	4	]	]	PUNCT
ejpam-4771	399	5	)	)	PUNCT
ejpam-4771	399	6	=	=	SYM
ejpam-4771	400	1	n	n	PROPN
ejpam-4771	400	2	·	·	PUNCT
ejpam-4771	400	3	ln2(h	ln2(h	PROPN
ejpam-4771	400	4	)	)	PUNCT
ejpam-4771	400	5	.	.	PUNCT
ejpam-4771	401	1	acknowledgements	acknowledgement	VERB
ejpam-4771	401	2	the	the	DET
ejpam-4771	401	3	authors	author	NOUN
ejpam-4771	401	4	would	would	AUX
ejpam-4771	401	5	like	like	VERB
ejpam-4771	401	6	to	to	PART
ejpam-4771	401	7	thank	thank	VERB
ejpam-4771	401	8	the	the	DET
ejpam-4771	401	9	department	department	NOUN
ejpam-4771	401	10	of	of	ADP
ejpam-4771	401	11	science	science	NOUN
ejpam-4771	401	12	and	and	CCONJ
ejpam-4771	401	13	technology	technology	NOUN
ejpam-4771	401	14	accelerated	accelerate	VERB
ejpam-4771	401	15	science	science	NOUN
ejpam-4771	401	16	and	and	CCONJ
ejpam-4771	401	17	technology	technology	NOUN
ejpam-4771	401	18	human	human	ADJ
ejpam-4771	401	19	resource	resource	NOUN
ejpam-4771	401	20	development	development	NOUN
ejpam-4771	401	21	program	program	NOUN
ejpam-4771	401	22	(	(	PUNCT
ejpam-4771	401	23	dostasthrdp)-philippines	dostasthrdp)-philippines	PROPN
ejpam-4771	401	24	,	,	PUNCT
ejpam-4771	401	25	msu	msu	PROPN
ejpam-4771	401	26	-	-	PUNCT
ejpam-4771	401	27	iligan	iligan	PROPN
ejpam-4771	401	28	institute	institute	PROPN
ejpam-4771	401	29	of	of	ADP
ejpam-4771	401	30	technology	technology	PROPN
ejpam-4771	401	31	,	,	PUNCT
ejpam-4771	401	32	iligan	iligan	PROPN
ejpam-4771	401	33	city	city	PROPN
ejpam-4771	401	34	,	,	PUNCT
ejpam-4771	401	35	philippines	philippine	NOUN
ejpam-4771	401	36	.	.	PUNCT
ejpam-4771	402	1	references	reference	NOUN
ejpam-4771	402	2	[	[	X
ejpam-4771	402	3	1	1	NUM
ejpam-4771	402	4	]	]	PUNCT
ejpam-4771	402	5	c.	c.	PROPN
ejpam-4771	402	6	berge	berge	PROPN
ejpam-4771	402	7	.	.	PUNCT
ejpam-4771	403	1	theorie	theorie	PROPN
ejpam-4771	403	2	des	des	PROPN
ejpam-4771	403	3	graphes	graphes	PROPN
ejpam-4771	403	4	et	et	PROPN
ejpam-4771	403	5	ses	ses	PROPN
ejpam-4771	403	6	applications	application	NOUN
ejpam-4771	403	7	.	.	PUNCT
ejpam-4771	404	1	methuen	methuen	PROPN
ejpam-4771	404	2	(	(	PUNCT
ejpam-4771	404	3	london	london	PROPN
ejpam-4771	404	4	)	)	PUNCT
ejpam-4771	404	5	and	and	CCONJ
ejpam-4771	404	6	wiley	wiley	PROPN
ejpam-4771	404	7	(	(	PUNCT
ejpam-4771	404	8	new	new	PROPN
ejpam-4771	404	9	york	york	PROPN
ejpam-4771	404	10	)	)	PUNCT
ejpam-4771	404	11	,	,	PUNCT
ejpam-4771	404	12	1962	1962	NUM
ejpam-4771	404	13	.	.	PUNCT
ejpam-4771	405	1	[	[	X
ejpam-4771	405	2	2	2	X
ejpam-4771	405	3	]	]	PUNCT
ejpam-4771	405	4	j.	j.	PROPN
ejpam-4771	405	5	a.	a.	PROPN
ejpam-4771	405	6	bondy	bondy	PROPN
ejpam-4771	405	7	and	and	CCONJ
ejpam-4771	405	8	u.	u.	PROPN
ejpam-4771	405	9	s.	s.	PROPN
ejpam-4771	405	10	r.	r.	PROPN
ejpam-4771	405	11	murty	murty	PROPN
ejpam-4771	405	12	.	.	PUNCT
ejpam-4771	406	1	graph	graph	NOUN
ejpam-4771	406	2	theory	theory	NOUN
ejpam-4771	406	3	.	.	PUNCT
ejpam-4771	407	1	springer	springer	NOUN
ejpam-4771	407	2	,	,	PUNCT
ejpam-4771	407	3	2008	2008	NUM
ejpam-4771	407	4	.	.	PUNCT
ejpam-4771	408	1	[	[	X
ejpam-4771	408	2	3	3	NUM
ejpam-4771	408	3	]	]	X
ejpam-4771	408	4	f.	f.	PROPN
ejpam-4771	408	5	buckley	buckley	PROPN
ejpam-4771	408	6	and	and	CCONJ
ejpam-4771	408	7	f.	f.	PROPN
ejpam-4771	408	8	harary	harary	PROPN
ejpam-4771	408	9	.	.	PUNCT
ejpam-4771	409	1	distance	distance	NOUN
ejpam-4771	409	2	in	in	ADP
ejpam-4771	409	3	graphs	graph	NOUN
ejpam-4771	409	4	.	.	PUNCT
ejpam-4771	410	1	addison	addison	PROPN
ejpam-4771	410	2	-	-	PUNCT
ejpam-4771	410	3	wesley	wesley	PROPN
ejpam-4771	410	4	,	,	PUNCT
ejpam-4771	410	5	redwood	redwood	NOUN
ejpam-4771	410	6	city	city	NOUN
ejpam-4771	410	7	,	,	PUNCT
ejpam-4771	410	8	ca	ca	NOUN
ejpam-4771	410	9	,	,	PUNCT
ejpam-4771	410	10	1990	1990	NUM
ejpam-4771	410	11	.	.	PUNCT
ejpam-4771	411	1	references	reference	NOUN
ejpam-4771	411	2	1194	1194	NUM
ejpam-4771	411	3	[	[	X
ejpam-4771	411	4	4	4	X
ejpam-4771	411	5	]	]	X
ejpam-4771	411	6	j.	j.	PROPN
ejpam-4771	411	7	cabaro	cabaro	PROPN
ejpam-4771	411	8	and	and	CCONJ
ejpam-4771	411	9	h.	h.	PROPN
ejpam-4771	411	10	rara	rara	PROPN
ejpam-4771	411	11	.	.	PUNCT
ejpam-4771	412	1	restrained	restrain	VERB
ejpam-4771	412	2	2	2	NUM
ejpam-4771	412	3	-	-	PUNCT
ejpam-4771	412	4	resolving	resolve	VERB
ejpam-4771	412	5	dominating	dominating	NOUN
ejpam-4771	412	6	sets	set	NOUN
ejpam-4771	412	7	in	in	ADP
ejpam-4771	412	8	the	the	DET
ejpam-4771	412	9	join	join	NOUN
ejpam-4771	412	10	and	and	CCONJ
ejpam-4771	412	11	corona	corona	PROPN
ejpam-4771	412	12	and	and	CCONJ
ejpam-4771	412	13	lexicographic	lexicographic	ADJ
ejpam-4771	412	14	product	product	NOUN
ejpam-4771	412	15	of	of	ADP
ejpam-4771	412	16	two	two	NUM
ejpam-4771	412	17	graphs	graph	NOUN
ejpam-4771	412	18	.	.	PUNCT
ejpam-4771	413	1	european	european	ADJ
ejpam-4771	413	2	journal	journal	PROPN
ejpam-4771	413	3	of	of	ADP
ejpam-4771	413	4	pure	pure	ADJ
ejpam-4771	413	5	and	and	CCONJ
ejpam-4771	413	6	applied	applied	ADJ
ejpam-4771	413	7	mathematics	mathematic	NOUN
ejpam-4771	413	8	,	,	PUNCT
ejpam-4771	413	9	15(3):1047–1053	15(3):1047–1053	NUM
ejpam-4771	413	10	,	,	PUNCT
ejpam-4771	413	11	2022	2022	NUM
ejpam-4771	413	12	.	.	PUNCT
ejpam-4771	414	1	[	[	X
ejpam-4771	414	2	5	5	X
ejpam-4771	414	3	]	]	PUNCT
ejpam-4771	414	4	j.	j.	PROPN
ejpam-4771	414	5	cabaro	cabaro	PROPN
ejpam-4771	414	6	and	and	CCONJ
ejpam-4771	414	7	h.	h.	PROPN
ejpam-4771	414	8	rara	rara	PROPN
ejpam-4771	414	9	.	.	PUNCT
ejpam-4771	415	1	2	2	NUM
ejpam-4771	415	2	-	-	PUNCT
ejpam-4771	415	3	resolving	resolve	VERB
ejpam-4771	415	4	sets	set	NOUN
ejpam-4771	415	5	in	in	ADP
ejpam-4771	415	6	the	the	DET
ejpam-4771	415	7	join	join	NOUN
ejpam-4771	415	8	,	,	PUNCT
ejpam-4771	415	9	and	and	CCONJ
ejpam-4771	415	10	corona	corona	NOUN
ejpam-4771	415	11	of	of	ADP
ejpam-4771	415	12	two	two	NUM
ejpam-4771	415	13	graphs	graph	NOUN
ejpam-4771	415	14	.	.	PUNCT
ejpam-4771	416	1	european	european	ADJ
ejpam-4771	416	2	journal	journal	PROPN
ejpam-4771	416	3	of	of	ADP
ejpam-4771	416	4	pure	pure	ADJ
ejpam-4771	416	5	and	and	CCONJ
ejpam-4771	416	6	applied	applied	ADJ
ejpam-4771	416	7	mathematics	mathematic	NOUN
ejpam-4771	416	8	,	,	PUNCT
ejpam-4771	416	9	14(3):773–782	14(3):773–782	PROPN
ejpam-4771	416	10	,	,	PUNCT
ejpam-4771	416	11	2022	2022	NUM
ejpam-4771	416	12	.	.	PUNCT
ejpam-4771	417	1	[	[	X
ejpam-4771	417	2	6	6	NUM
ejpam-4771	417	3	]	]	PUNCT
ejpam-4771	417	4	j.	j.	PROPN
ejpam-4771	417	5	cabaro	cabaro	PROPN
ejpam-4771	417	6	and	and	CCONJ
ejpam-4771	417	7	h.	h.	PROPN
ejpam-4771	417	8	rara	rara	PROPN
ejpam-4771	417	9	.	.	PUNCT
ejpam-4771	418	1	on	on	ADP
ejpam-4771	418	2	2	2	NUM
ejpam-4771	418	3	-	-	PUNCT
ejpam-4771	418	4	resolving	resolve	VERB
ejpam-4771	418	5	dominating	dominating	NOUN
ejpam-4771	418	6	sets	set	NOUN
ejpam-4771	418	7	in	in	ADP
ejpam-4771	418	8	the	the	DET
ejpam-4771	418	9	join	join	NOUN
ejpam-4771	418	10	and	and	CCONJ
ejpam-4771	418	11	corona	corona	PROPN
ejpam-4771	418	12	and	and	CCONJ
ejpam-4771	418	13	lexicographic	lexicographic	ADJ
ejpam-4771	418	14	product	product	NOUN
ejpam-4771	418	15	of	of	ADP
ejpam-4771	418	16	graphs	graph	NOUN
ejpam-4771	418	17	.	.	PUNCT
ejpam-4771	419	1	european	european	ADJ
ejpam-4771	419	2	journal	journal	PROPN
ejpam-4771	419	3	of	of	ADP
ejpam-4771	419	4	pure	pure	ADJ
ejpam-4771	419	5	and	and	CCONJ
ejpam-4771	419	6	applied	applied	ADJ
ejpam-4771	419	7	mathematics	mathematic	NOUN
ejpam-4771	419	8	,	,	PUNCT
ejpam-4771	419	9	15(3):1417–1425	15(3):1417–1425	NUM
ejpam-4771	419	10	,	,	PUNCT
ejpam-4771	419	11	2022	2022	NUM
ejpam-4771	419	12	.	.	PUNCT
ejpam-4771	420	1	[	[	X
ejpam-4771	420	2	7	7	X
ejpam-4771	420	3	]	]	X
ejpam-4771	420	4	j.	j.	PROPN
ejpam-4771	420	5	cabaro	cabaro	PROPN
ejpam-4771	420	6	and	and	CCONJ
ejpam-4771	420	7	h.	h.	PROPN
ejpam-4771	420	8	rara	rara	PROPN
ejpam-4771	420	9	.	.	PUNCT
ejpam-4771	421	1	on	on	ADP
ejpam-4771	421	2	variations	variation	NOUN
ejpam-4771	421	3	of	of	ADP
ejpam-4771	421	4	2	2	NUM
ejpam-4771	421	5	-	-	PUNCT
ejpam-4771	421	6	resolving	resolve	VERB
ejpam-4771	421	7	sets	set	NOUN
ejpam-4771	421	8	in	in	ADP
ejpam-4771	421	9	graphs	graph	NOUN
ejpam-4771	421	10	.	.	PUNCT
ejpam-4771	422	1	phd	phd	NOUN
ejpam-4771	422	2	thesis	thesis	PROPN
ejpam-4771	422	3	,	,	PUNCT
ejpam-4771	422	4	mindanao	mindanao	PROPN
ejpam-4771	422	5	state	state	PROPN
ejpam-4771	422	6	universityiligan	universityiligan	PROPN
ejpam-4771	422	7	institute	institute	PROPN
ejpam-4771	422	8	of	of	ADP
ejpam-4771	422	9	technology	technology	NOUN
ejpam-4771	422	10	,	,	PUNCT
ejpam-4771	422	11	2022	2022	NUM
ejpam-4771	422	12	.	.	PUNCT
ejpam-4771	423	1	[	[	X
ejpam-4771	423	2	8	8	X
ejpam-4771	423	3	]	]	X
ejpam-4771	423	4	j.	j.	PROPN
ejpam-4771	423	5	cabaro	cabaro	PROPN
ejpam-4771	423	6	and	and	CCONJ
ejpam-4771	423	7	h.	h.	PROPN
ejpam-4771	423	8	rara	rara	PROPN
ejpam-4771	423	9	.	.	PUNCT
ejpam-4771	424	1	restrained	restrain	VERB
ejpam-4771	424	2	2	2	NUM
ejpam-4771	424	3	-	-	PUNCT
ejpam-4771	424	4	resolving	resolve	VERB
ejpam-4771	424	5	sets	set	NOUN
ejpam-4771	424	6	in	in	ADP
ejpam-4771	424	7	the	the	DET
ejpam-4771	424	8	join	join	NOUN
ejpam-4771	424	9	and	and	CCONJ
ejpam-4771	424	10	corona	corona	PROPN
ejpam-4771	424	11	and	and	CCONJ
ejpam-4771	424	12	lexicographic	lexicographic	ADJ
ejpam-4771	424	13	product	product	NOUN
ejpam-4771	424	14	of	of	ADP
ejpam-4771	424	15	graphs	graph	NOUN
ejpam-4771	424	16	.	.	PUNCT
ejpam-4771	425	1	european	european	ADJ
ejpam-4771	425	2	journal	journal	PROPN
ejpam-4771	425	3	of	of	ADP
ejpam-4771	425	4	pure	pure	ADJ
ejpam-4771	425	5	and	and	CCONJ
ejpam-4771	425	6	applied	applied	ADJ
ejpam-4771	425	7	mathematics	mathematic	NOUN
ejpam-4771	425	8	,	,	PUNCT
ejpam-4771	425	9	15(3):1229–1236	15(3):1229–1236	NUM
ejpam-4771	425	10	,	,	PUNCT
ejpam-4771	425	11	2022	2022	NUM
ejpam-4771	425	12	.	.	PUNCT
ejpam-4771	426	1	[	[	X
ejpam-4771	426	2	9	9	NUM
ejpam-4771	426	3	]	]	X
ejpam-4771	426	4	s.r	s.r	PROPN
ejpam-4771	426	5	.	.	PROPN
ejpam-4771	426	6	canoy	canoy	PROPN
ejpam-4771	426	7	and	and	CCONJ
ejpam-4771	426	8	c.j	c.j	PROPN
ejpam-4771	426	9	.	.	PROPN
ejpam-4771	426	10	saromines	saromine	NOUN
ejpam-4771	426	11	.	.	PUNCT
ejpam-4771	427	1	outer	outer	ADV
ejpam-4771	427	2	-	-	PUNCT
ejpam-4771	427	3	connected	connect	VERB
ejpam-4771	427	4	hop	hop	NOUN
ejpam-4771	427	5	dominating	dominating	NOUN
ejpam-4771	427	6	sets	set	NOUN
ejpam-4771	427	7	in	in	ADP
ejpam-4771	427	8	graphs	graph	NOUN
ejpam-4771	427	9	.	.	PUNCT
ejpam-4771	428	1	european	european	ADJ
ejpam-4771	428	2	journal	journal	PROPN
ejpam-4771	428	3	of	of	ADP
ejpam-4771	428	4	pure	pure	ADJ
ejpam-4771	428	5	and	and	CCONJ
ejpam-4771	428	6	applied	applied	ADJ
ejpam-4771	428	7	mathematics	mathematic	NOUN
ejpam-4771	428	8	,	,	PUNCT
ejpam-4771	428	9	15(4):1966–1981	15(4):1966–1981	NUM
ejpam-4771	428	10	,	,	PUNCT
ejpam-4771	428	11	2022	2022	NUM
ejpam-4771	428	12	.	.	PUNCT
ejpam-4771	429	1	[	[	X
ejpam-4771	429	2	10	10	NUM
ejpam-4771	429	3	]	]	X
ejpam-4771	429	4	j.	j.	PROPN
ejpam-4771	429	5	cyman	cyman	PROPN
ejpam-4771	429	6	.	.	PUNCT
ejpam-4771	430	1	the	the	DET
ejpam-4771	430	2	outer	outer	ADV
ejpam-4771	430	3	-	-	PUNCT
ejpam-4771	430	4	conected	conecte	VERB
ejpam-4771	430	5	domination	domination	NOUN
ejpam-4771	430	6	numbers	number	NOUN
ejpam-4771	430	7	of	of	ADP
ejpam-4771	430	8	graphs	graph	NOUN
ejpam-4771	430	9	.	.	PUNCT
ejpam-4771	431	1	australasian	australasian	ADJ
ejpam-4771	431	2	journal	journal	NOUN
ejpam-4771	431	3	of	of	ADP
ejpam-4771	431	4	combinatorics	combinatoric	NOUN
ejpam-4771	431	5	,	,	PUNCT
ejpam-4771	431	6	38(1):35–46	38(1):35–46	NUM
ejpam-4771	431	7	,	,	PUNCT
ejpam-4771	431	8	2007	2007	NUM
ejpam-4771	431	9	.	.	PUNCT
ejpam-4771	432	1	[	[	X
ejpam-4771	432	2	11	11	NUM
ejpam-4771	432	3	]	]	X
ejpam-4771	432	4	f.	f.	PROPN
ejpam-4771	432	5	harary	harary	PROPN
ejpam-4771	432	6	and	and	CCONJ
ejpam-4771	432	7	r.	r.	PROPN
ejpam-4771	432	8	melter	melter	NOUN
ejpam-4771	432	9	.	.	PUNCT
ejpam-4771	433	1	on	on	ADP
ejpam-4771	433	2	the	the	DET
ejpam-4771	433	3	metric	metric	ADJ
ejpam-4771	433	4	dimension	dimension	NOUN
ejpam-4771	433	5	of	of	ADP
ejpam-4771	433	6	a	a	DET
ejpam-4771	433	7	graph	graph	NOUN
ejpam-4771	433	8	.	.	PUNCT
ejpam-4771	433	9	ars	ars	PROPN
ejpam-4771	433	10	combinatoria	combinatoria	NOUN
ejpam-4771	433	11	,	,	PUNCT
ejpam-4771	433	12	2:191–195	2:191–195	NUM
ejpam-4771	433	13	,	,	PUNCT
ejpam-4771	433	14	1976	1976	NUM
ejpam-4771	433	15	.	.	PUNCT
ejpam-4771	434	1	[	[	X
ejpam-4771	434	2	12	12	NUM
ejpam-4771	434	3	]	]	PUNCT
ejpam-4771	434	4	a.	a.	NOUN
ejpam-4771	434	5	mahistrado	mahistrado	NOUN
ejpam-4771	434	6	and	and	CCONJ
ejpam-4771	434	7	h.	h.	PROPN
ejpam-4771	434	8	rara	rara	PROPN
ejpam-4771	434	9	.	.	PUNCT
ejpam-4771	435	1	on	on	ADP
ejpam-4771	435	2	2	2	NUM
ejpam-4771	435	3	-	-	PUNCT
ejpam-4771	435	4	resolving	resolve	VERB
ejpam-4771	435	5	hop	hop	NOUN
ejpam-4771	435	6	dominating	dominating	NOUN
ejpam-4771	435	7	sets	set	NOUN
ejpam-4771	435	8	in	in	ADP
ejpam-4771	435	9	the	the	DET
ejpam-4771	435	10	join	join	NOUN
ejpam-4771	435	11	and	and	CCONJ
ejpam-4771	435	12	corona	corona	PROPN
ejpam-4771	435	13	and	and	CCONJ
ejpam-4771	435	14	lexicographic	lexicographic	ADJ
ejpam-4771	435	15	product	product	NOUN
ejpam-4771	435	16	of	of	ADP
ejpam-4771	435	17	graphs	graph	NOUN
ejpam-4771	435	18	.	.	PUNCT
ejpam-4771	436	1	european	european	ADJ
ejpam-4771	436	2	journal	journal	PROPN
ejpam-4771	436	3	of	of	ADP
ejpam-4771	436	4	pure	pure	ADJ
ejpam-4771	436	5	and	and	CCONJ
ejpam-4771	436	6	applied	applied	ADJ
ejpam-4771	436	7	mathematics	mathematic	NOUN
ejpam-4771	436	8	,	,	PUNCT
ejpam-4771	436	9	15(4):1982–1997	15(4):1982–1997	NUM
ejpam-4771	436	10	,	,	PUNCT
ejpam-4771	436	11	2022	2022	NUM
ejpam-4771	436	12	.	.	PUNCT
ejpam-4771	437	1	[	[	X
ejpam-4771	437	2	13	13	NUM
ejpam-4771	437	3	]	]	PUNCT
ejpam-4771	437	4	a.	a.	NOUN
ejpam-4771	437	5	mahistrado	mahistrado	NOUN
ejpam-4771	437	6	and	and	CCONJ
ejpam-4771	437	7	h.	h.	PROPN
ejpam-4771	437	8	rara	rara	PROPN
ejpam-4771	437	9	.	.	PUNCT
ejpam-4771	438	1	restrained	restrain	VERB
ejpam-4771	438	2	2	2	NUM
ejpam-4771	438	3	-	-	PUNCT
ejpam-4771	438	4	resolving	resolve	VERB
ejpam-4771	438	5	hop	hop	NOUN
ejpam-4771	438	6	domination	domination	NOUN
ejpam-4771	438	7	in	in	ADP
ejpam-4771	438	8	graphs	graph	NOUN
ejpam-4771	438	9	.	.	PUNCT
ejpam-4771	439	1	european	european	ADJ
ejpam-4771	439	2	journal	journal	PROPN
ejpam-4771	439	3	of	of	ADP
ejpam-4771	439	4	pure	pure	ADJ
ejpam-4771	439	5	and	and	CCONJ
ejpam-4771	439	6	applied	applied	ADJ
ejpam-4771	439	7	mathematics	mathematic	NOUN
ejpam-4771	439	8	,	,	PUNCT
ejpam-4771	439	9	16(1):286–303	16(1):286–303	NUM
ejpam-4771	439	10	,	,	PUNCT
ejpam-4771	439	11	2023	2023	NUM
ejpam-4771	439	12	.	.	PUNCT
ejpam-4771	440	1	[	[	X
ejpam-4771	440	2	14	14	NUM
ejpam-4771	440	3	]	]	X
ejpam-4771	440	4	j.	j.	PROPN
ejpam-4771	440	5	mohamad	mohamad	PROPN
ejpam-4771	440	6	and	and	CCONJ
ejpam-4771	440	7	h.	h.	PROPN
ejpam-4771	440	8	rara	rara	PROPN
ejpam-4771	440	9	.	.	PUNCT
ejpam-4771	441	1	on	on	ADP
ejpam-4771	441	2	resolving	resolve	VERB
ejpam-4771	441	3	hop	hop	NOUN
ejpam-4771	441	4	domination	domination	NOUN
ejpam-4771	441	5	in	in	ADP
ejpam-4771	441	6	graphs	graph	NOUN
ejpam-4771	441	7	.	.	PUNCT
ejpam-4771	442	1	european	european	ADJ
ejpam-4771	442	2	journal	journal	PROPN
ejpam-4771	442	3	of	of	ADP
ejpam-4771	442	4	pure	pure	ADJ
ejpam-4771	442	5	and	and	CCONJ
ejpam-4771	442	6	applied	applied	ADJ
ejpam-4771	442	7	mathematics	mathematic	NOUN
ejpam-4771	442	8	,	,	PUNCT
ejpam-4771	442	9	14(3):1015–1023	14(3):1015–1023	NUM
ejpam-4771	442	10	,	,	PUNCT
ejpam-4771	442	11	2021	2021	NUM
ejpam-4771	442	12	.	.	PUNCT
ejpam-4771	443	1	[	[	X
ejpam-4771	443	2	15	15	NUM
ejpam-4771	443	3	]	]	X
ejpam-4771	443	4	g.	g.	PROPN
ejpam-4771	443	5	monsanto	monsanto	PROPN
ejpam-4771	443	6	and	and	CCONJ
ejpam-4771	443	7	h.	h.	PROPN
ejpam-4771	443	8	rara	rara	PROPN
ejpam-4771	443	9	.	.	PUNCT
ejpam-4771	444	1	resolving	resolve	VERB
ejpam-4771	444	2	restrained	restrained	ADJ
ejpam-4771	444	3	domination	domination	NOUN
ejpam-4771	444	4	in	in	ADP
ejpam-4771	444	5	graphs	graph	NOUN
ejpam-4771	444	6	.	.	PUNCT
ejpam-4771	445	1	european	european	ADJ
ejpam-4771	445	2	journal	journal	PROPN
ejpam-4771	445	3	of	of	ADP
ejpam-4771	445	4	pure	pure	ADJ
ejpam-4771	445	5	and	and	CCONJ
ejpam-4771	445	6	applied	applied	ADJ
ejpam-4771	445	7	mathematics	mathematic	NOUN
ejpam-4771	445	8	,	,	PUNCT
ejpam-4771	445	9	4(3):829–841	4(3):829–841	NOUN
ejpam-4771	445	10	,	,	PUNCT
ejpam-4771	445	11	2021	2021	NUM
ejpam-4771	445	12	.	.	PUNCT
ejpam-4771	446	1	[	[	X
ejpam-4771	446	2	16	16	NUM
ejpam-4771	446	3	]	]	X
ejpam-4771	446	4	c.	c.	PROPN
ejpam-4771	446	5	natarajan	natarajan	PROPN
ejpam-4771	446	6	and	and	CCONJ
ejpam-4771	446	7	s.k	s.k	PROPN
ejpam-4771	446	8	.	.	PROPN
ejpam-4771	446	9	ayyaswamy	ayyaswamy	PROPN
ejpam-4771	446	10	.	.	PUNCT
ejpam-4771	447	1	hop	hop	PROPN
ejpam-4771	447	2	domination	domination	NOUN
ejpam-4771	447	3	in	in	ADP
ejpam-4771	447	4	graphs	graph	NOUN
ejpam-4771	447	5	-	-	PUNCT
ejpam-4771	447	6	ii	ii	NOUN
ejpam-4771	447	7	.	.	PUNCT
ejpam-4771	447	8	versita	versita	PROPN
ejpam-4771	447	9	,	,	PUNCT
ejpam-4771	447	10	23(2):187	23(2):187	NUM
ejpam-4771	447	11	–	–	PUNCT
ejpam-4771	447	12	199	199	NUM
ejpam-4771	447	13	,	,	PUNCT
ejpam-4771	447	14	2015	2015	NUM
ejpam-4771	447	15	.	.	PUNCT
ejpam-4771	448	1	[	[	X
ejpam-4771	448	2	17	17	NUM
ejpam-4771	448	3	]	]	X
ejpam-4771	448	4	jr	jr	PROPN
ejpam-4771	448	5	.	.	PROPN
ejpam-4771	448	6	r.	r.	PROPN
ejpam-4771	448	7	mollejon	mollejon	PROPN
ejpam-4771	448	8	s.	s.	PROPN
ejpam-4771	448	9	canoy	canoy	PROPN
ejpam-4771	448	10	and	and	CCONJ
ejpam-4771	448	11	j.g.canoy	j.g.canoy	PROPN
ejpam-4771	448	12	.	.	PUNCT
ejpam-4771	449	1	hop	hop	PROPN
ejpam-4771	449	2	dominating	dominating	NOUN
ejpam-4771	449	3	sets	set	NOUN
ejpam-4771	449	4	in	in	ADP
ejpam-4771	449	5	graphs	graph	NOUN
ejpam-4771	449	6	under	under	ADP
ejpam-4771	449	7	binary	binary	ADJ
ejpam-4771	449	8	operations	operation	NOUN
ejpam-4771	449	9	.	.	PUNCT
ejpam-4771	450	1	european	european	ADJ
ejpam-4771	450	2	journal	journal	PROPN
ejpam-4771	450	3	of	of	ADP
ejpam-4771	450	4	pure	pure	ADJ
ejpam-4771	450	5	and	and	CCONJ
ejpam-4771	450	6	applied	applied	ADJ
ejpam-4771	450	7	mathematics	mathematic	NOUN
ejpam-4771	450	8	,	,	PUNCT
ejpam-4771	450	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4771	450	10	,	,	PUNCT
ejpam-4771	450	11	2019	2019	NUM
ejpam-4771	450	12	.	.	PUNCT
ejpam-4771	451	1	references	reference	NOUN
ejpam-4771	451	2	1195	1195	NUM
ejpam-4771	451	3	[	[	X
ejpam-4771	451	4	18	18	NUM
ejpam-4771	451	5	]	]	X
ejpam-4771	451	6	v.	v.	ADP
ejpam-4771	451	7	saenpholphat	saenpholphat	PROPN
ejpam-4771	451	8	and	and	CCONJ
ejpam-4771	451	9	p.	p.	PROPN
ejpam-4771	451	10	zhang	zhang	PROPN
ejpam-4771	451	11	.	.	PUNCT
ejpam-4771	452	1	on	on	ADP
ejpam-4771	452	2	connected	connected	ADJ
ejpam-4771	452	3	resolvability	resolvability	NOUN
ejpam-4771	452	4	of	of	ADP
ejpam-4771	452	5	graphs	graph	NOUN
ejpam-4771	452	6	.	.	PUNCT
ejpam-4771	453	1	australian	australian	ADJ
ejpam-4771	453	2	journal	journal	NOUN
ejpam-4771	453	3	of	of	ADP
ejpam-4771	453	4	combinatorics	combinatoric	NOUN
ejpam-4771	453	5	,	,	PUNCT
ejpam-4771	453	6	28:26–37	28:26–37	NUM
ejpam-4771	453	7	,	,	PUNCT
ejpam-4771	453	8	2003	2003	NUM
ejpam-4771	453	9	.	.	PUNCT
ejpam-4771	454	1	[	[	X
ejpam-4771	454	2	19	19	NUM
ejpam-4771	454	3	]	]	PUNCT
ejpam-4771	454	4	p.	p.	PROPN
ejpam-4771	454	5	j.	j.	PROPN
ejpam-4771	454	6	slater	slater	PROPN
ejpam-4771	454	7	.	.	PUNCT
ejpam-4771	455	1	dominating	dominating	NOUN
ejpam-4771	455	2	and	and	CCONJ
ejpam-4771	455	3	reference	reference	NOUN
ejpam-4771	455	4	sets	set	NOUN
ejpam-4771	455	5	in	in	ADP
ejpam-4771	455	6	a	a	DET
ejpam-4771	455	7	graph	graph	NOUN
ejpam-4771	455	8	.	.	PUNCT
ejpam-4771	456	1	journal	journal	NOUN
ejpam-4771	456	2	of	of	ADP
ejpam-4771	456	3	mathematics	mathematic	NOUN
ejpam-4771	456	4	and	and	CCONJ
ejpam-4771	456	5	physical	physical	ADJ
ejpam-4771	456	6	science	science	NOUN
ejpam-4771	456	7	,	,	PUNCT
ejpam-4771	456	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4771	456	9	.	.	PUNCT