id	sid	tid	token	lemma	pos
ejpam-4665	1	1	european	european	PROPN
ejpam-4665	1	2	journal	journal	PROPN
ejpam-4665	1	3	of	of	ADP
ejpam-4665	1	4	pure	pure	ADJ
ejpam-4665	1	5	and	and	CCONJ
ejpam-4665	1	6	applied	apply	VERB
ejpam-4665	1	7	mathematics	mathematic	NOUN
ejpam-4665	1	8	vol	vol	NOUN
ejpam-4665	1	9	.	.	PUNCT
ejpam-4665	2	1	16	16	NUM
ejpam-4665	2	2	,	,	PUNCT
ejpam-4665	2	3	no	no	INTJ
ejpam-4665	2	4	.	.	NOUN
ejpam-4665	2	5	1	1	NUM
ejpam-4665	2	6	,	,	PUNCT
ejpam-4665	2	7	2023	2023	NUM
ejpam-4665	2	8	,	,	PUNCT
ejpam-4665	2	9	286	286	NUM
ejpam-4665	2	10	-	-	SYM
ejpam-4665	2	11	303	303	NUM
ejpam-4665	2	12	issn	issn	PROPN
ejpam-4665	2	13	1307	1307	NUM
ejpam-4665	2	14	-	-	SYM
ejpam-4665	2	15	5543	5543	NUM
ejpam-4665	2	16	–	–	PUNCT
ejpam-4665	2	17	ejpam.com	ejpam.com	X
ejpam-4665	2	18	published	publish	VERB
ejpam-4665	2	19	by	by	ADP
ejpam-4665	2	20	new	new	PROPN
ejpam-4665	2	21	york	york	PROPN
ejpam-4665	2	22	business	business	PROPN
ejpam-4665	2	23	global	global	PROPN
ejpam-4665	2	24	restrained	restrain	VERB
ejpam-4665	2	25	2	2	NUM
ejpam-4665	2	26	-	-	PUNCT
ejpam-4665	2	27	resolving	resolve	VERB
ejpam-4665	2	28	hop	hop	NOUN
ejpam-4665	2	29	domination	domination	NOUN
ejpam-4665	2	30	in	in	ADP
ejpam-4665	2	31	graphs	graph	NOUN
ejpam-4665	2	32	angelica	angelica	PROPN
ejpam-4665	2	33	mae	mae	PROPN
ejpam-4665	2	34	mahistrado1	mahistrado1	PROPN
ejpam-4665	2	35	,	,	PUNCT
ejpam-4665	2	36	helen	helen	PROPN
ejpam-4665	2	37	rara1,∗	rara1,∗	VERB
ejpam-4665	2	38	1	1	NUM
ejpam-4665	2	39	department	department	NOUN
ejpam-4665	2	40	of	of	ADP
ejpam-4665	2	41	mathematics	mathematic	NOUN
ejpam-4665	2	42	and	and	CCONJ
ejpam-4665	2	43	statistics	statistic	NOUN
ejpam-4665	2	44	,	,	PUNCT
ejpam-4665	2	45	college	college	NOUN
ejpam-4665	2	46	of	of	ADP
ejpam-4665	2	47	science	science	NOUN
ejpam-4665	2	48	and	and	CCONJ
ejpam-4665	2	49	mathematics	mathematic	NOUN
ejpam-4665	2	50	,	,	PUNCT
ejpam-4665	2	51	center	center	NOUN
ejpam-4665	2	52	of	of	ADP
ejpam-4665	2	53	graph	graph	NOUN
ejpam-4665	2	54	theory	theory	NOUN
ejpam-4665	2	55	,	,	PUNCT
ejpam-4665	2	56	algebra	algebra	NOUN
ejpam-4665	2	57	,	,	PUNCT
ejpam-4665	2	58	and	and	CCONJ
ejpam-4665	2	59	analysis	analysis	NOUN
ejpam-4665	2	60	-	-	PUNCT
ejpam-4665	2	61	premier	premier	NOUN
ejpam-4665	2	62	research	research	NOUN
ejpam-4665	2	63	institute	institute	PROPN
ejpam-4665	2	64	of	of	ADP
ejpam-4665	2	65	science	science	NOUN
ejpam-4665	2	66	and	and	CCONJ
ejpam-4665	2	67	mathematics	mathematic	NOUN
ejpam-4665	2	68	,	,	PUNCT
ejpam-4665	2	69	mindanao	mindanao	PROPN
ejpam-4665	2	70	state	state	PROPN
ejpam-4665	2	71	university	university	PROPN
ejpam-4665	2	72	-	-	PUNCT
ejpam-4665	2	73	iligan	iligan	PROPN
ejpam-4665	2	74	institute	institute	PROPN
ejpam-4665	2	75	of	of	ADP
ejpam-4665	2	76	technology	technology	PROPN
ejpam-4665	2	77	,	,	PUNCT
ejpam-4665	2	78	9200	9200	NUM
ejpam-4665	2	79	iligan	iligan	ADJ
ejpam-4665	2	80	city	city	NOUN
ejpam-4665	2	81	,	,	PUNCT
ejpam-4665	2	82	philippines	philippine	NOUN
ejpam-4665	2	83	abstract	abstract	ADJ
ejpam-4665	2	84	.	.	PUNCT
ejpam-4665	3	1	letg	letg	NOUN
ejpam-4665	3	2	be	be	VERB
ejpam-4665	3	3	a	a	DET
ejpam-4665	3	4	connected	connected	ADJ
ejpam-4665	3	5	graph	graph	NOUN
ejpam-4665	3	6	.	.	PUNCT
ejpam-4665	4	1	a	a	DET
ejpam-4665	4	2	set	set	NOUN
ejpam-4665	4	3	s	s	NOUN
ejpam-4665	4	4	⊆	⊆	NUM
ejpam-4665	4	5	v	v	NOUN
ejpam-4665	4	6	(	(	PUNCT
ejpam-4665	4	7	g	g	NOUN
ejpam-4665	4	8	)	)	PUNCT
ejpam-4665	4	9	is	be	AUX
ejpam-4665	4	10	a	a	DET
ejpam-4665	4	11	restrained	restrained	ADJ
ejpam-4665	4	12	2	2	NUM
ejpam-4665	4	13	-	-	PUNCT
ejpam-4665	4	14	resolving	resolve	VERB
ejpam-4665	4	15	hop	hop	NOUN
ejpam-4665	4	16	dominating	dominating	NOUN
ejpam-4665	4	17	set	set	NOUN
ejpam-4665	4	18	of	of	ADP
ejpam-4665	4	19	g	g	PROPN
ejpam-4665	4	20	if	if	SCONJ
ejpam-4665	4	21	s	s	VERB
ejpam-4665	4	22	is	be	AUX
ejpam-4665	4	23	a	a	DET
ejpam-4665	4	24	2	2	NUM
ejpam-4665	4	25	-	-	PUNCT
ejpam-4665	4	26	resolving	resolve	VERB
ejpam-4665	4	27	hop	hop	NOUN
ejpam-4665	4	28	dominating	dominating	NOUN
ejpam-4665	4	29	set	set	NOUN
ejpam-4665	4	30	of	of	ADP
ejpam-4665	4	31	g	g	PROPN
ejpam-4665	4	32	and	and	CCONJ
ejpam-4665	4	33	s	s	PART
ejpam-4665	4	34	=	=	SYM
ejpam-4665	4	35	v	v	X
ejpam-4665	4	36	(	(	PUNCT
ejpam-4665	4	37	g	g	NOUN
ejpam-4665	4	38	)	)	PUNCT
ejpam-4665	4	39	or	or	CCONJ
ejpam-4665	4	40	⟨v	⟨v	NUM
ejpam-4665	4	41	(	(	PUNCT
ejpam-4665	4	42	g)\s⟩	g)\s⟩	PROPN
ejpam-4665	4	43	has	have	AUX
ejpam-4665	4	44	no	no	DET
ejpam-4665	4	45	isolated	isolated	ADJ
ejpam-4665	4	46	vertex	vertex	NOUN
ejpam-4665	4	47	.	.	PUNCT
ejpam-4665	5	1	the	the	DET
ejpam-4665	5	2	restrained	restrained	ADJ
ejpam-4665	5	3	2	2	NUM
ejpam-4665	5	4	-	-	PUNCT
ejpam-4665	5	5	resolving	resolve	VERB
ejpam-4665	5	6	hop	hop	NOUN
ejpam-4665	5	7	domination	domination	NOUN
ejpam-4665	5	8	number	number	NOUN
ejpam-4665	5	9	of	of	ADP
ejpam-4665	5	10	g	g	NOUN
ejpam-4665	5	11	,	,	PUNCT
ejpam-4665	5	12	denoted	denote	VERB
ejpam-4665	5	13	by	by	ADP
ejpam-4665	5	14	γr2rh(g	γr2rh(g	NOUN
ejpam-4665	5	15	)	)	PUNCT
ejpam-4665	5	16	is	be	AUX
ejpam-4665	5	17	the	the	DET
ejpam-4665	5	18	smallest	small	ADJ
ejpam-4665	5	19	cardinality	cardinality	NOUN
ejpam-4665	5	20	of	of	ADP
ejpam-4665	5	21	a	a	DET
ejpam-4665	5	22	restrained	restrained	ADJ
ejpam-4665	5	23	2	2	NUM
ejpam-4665	5	24	-	-	PUNCT
ejpam-4665	5	25	resolving	resolve	VERB
ejpam-4665	5	26	hop	hop	NOUN
ejpam-4665	5	27	dominating	dominating	NOUN
ejpam-4665	5	28	set	set	VERB
ejpam-4665	5	29	ofg	ofg	PROPN
ejpam-4665	5	30	.	.	PUNCT
ejpam-4665	6	1	this	this	DET
ejpam-4665	6	2	study	study	NOUN
ejpam-4665	6	3	aims	aim	VERB
ejpam-4665	6	4	to	to	PART
ejpam-4665	6	5	combine	combine	VERB
ejpam-4665	6	6	the	the	DET
ejpam-4665	6	7	concept	concept	NOUN
ejpam-4665	6	8	of	of	ADP
ejpam-4665	6	9	hop	hop	NOUN
ejpam-4665	6	10	domination	domination	NOUN
ejpam-4665	6	11	with	with	ADP
ejpam-4665	6	12	the	the	DET
ejpam-4665	6	13	restrained	restrained	ADJ
ejpam-4665	6	14	2	2	NUM
ejpam-4665	6	15	-	-	PUNCT
ejpam-4665	6	16	resolving	resolve	VERB
ejpam-4665	6	17	sets	set	NOUN
ejpam-4665	6	18	of	of	ADP
ejpam-4665	6	19	graphs	graph	NOUN
ejpam-4665	6	20	.	.	PUNCT
ejpam-4665	7	1	the	the	DET
ejpam-4665	7	2	main	main	ADJ
ejpam-4665	7	3	results	result	NOUN
ejpam-4665	7	4	generated	generate	VERB
ejpam-4665	7	5	in	in	ADP
ejpam-4665	7	6	this	this	DET
ejpam-4665	7	7	study	study	NOUN
ejpam-4665	7	8	include	include	VERB
ejpam-4665	7	9	the	the	DET
ejpam-4665	7	10	characterization	characterization	NOUN
ejpam-4665	7	11	of	of	ADP
ejpam-4665	7	12	restrained	restrained	ADJ
ejpam-4665	7	13	2	2	NUM
ejpam-4665	7	14	-	-	PUNCT
ejpam-4665	7	15	resolving	resolve	VERB
ejpam-4665	7	16	hop	hop	NOUN
ejpam-4665	7	17	dominating	dominating	NOUN
ejpam-4665	7	18	sets	set	NOUN
ejpam-4665	7	19	in	in	ADP
ejpam-4665	7	20	the	the	DET
ejpam-4665	7	21	join	join	NOUN
ejpam-4665	7	22	,	,	PUNCT
ejpam-4665	7	23	corona	corona	PROPN
ejpam-4665	7	24	,	,	PUNCT
ejpam-4665	7	25	edge	edge	NOUN
ejpam-4665	7	26	corona	corona	NOUN
ejpam-4665	7	27	and	and	CCONJ
ejpam-4665	7	28	lexicographic	lexicographic	ADJ
ejpam-4665	7	29	product	product	NOUN
ejpam-4665	7	30	of	of	ADP
ejpam-4665	7	31	graphs	graph	NOUN
ejpam-4665	7	32	,	,	PUNCT
ejpam-4665	7	33	as	as	ADV
ejpam-4665	7	34	well	well	ADV
ejpam-4665	7	35	as	as	ADP
ejpam-4665	7	36	their	their	PRON
ejpam-4665	7	37	corresponding	corresponding	ADJ
ejpam-4665	7	38	bounds	bound	NOUN
ejpam-4665	7	39	or	or	CCONJ
ejpam-4665	7	40	exact	exact	ADJ
ejpam-4665	7	41	values	value	NOUN
ejpam-4665	7	42	.	.	PUNCT
ejpam-4665	8	1	2020	2020	NUM
ejpam-4665	8	2	mathematics	mathematic	NOUN
ejpam-4665	8	3	subject	subject	NOUN
ejpam-4665	8	4	classifications	classification	NOUN
ejpam-4665	8	5	:	:	PUNCT
ejpam-4665	8	6	05c69	05c69	X
ejpam-4665	8	7	key	key	ADJ
ejpam-4665	8	8	words	word	NOUN
ejpam-4665	8	9	and	and	CCONJ
ejpam-4665	8	10	phrases	phrase	NOUN
ejpam-4665	8	11	:	:	PUNCT
ejpam-4665	8	12	restrained	restrain	VERB
ejpam-4665	8	13	2	2	NUM
ejpam-4665	8	14	-	-	PUNCT
ejpam-4665	8	15	resolving	resolve	VERB
ejpam-4665	8	16	hop	hop	NOUN
ejpam-4665	8	17	dominating	dominating	NOUN
ejpam-4665	8	18	set	set	NOUN
ejpam-4665	8	19	,	,	PUNCT
ejpam-4665	8	20	restrained	restrain	VERB
ejpam-4665	8	21	2	2	NUM
ejpam-4665	8	22	-	-	PUNCT
ejpam-4665	8	23	resolving	resolve	VERB
ejpam-4665	8	24	hop	hop	NOUN
ejpam-4665	8	25	domination	domination	NOUN
ejpam-4665	8	26	number	number	NOUN
ejpam-4665	8	27	,	,	PUNCT
ejpam-4665	8	28	join	join	NOUN
ejpam-4665	8	29	,	,	PUNCT
ejpam-4665	8	30	corona	corona	PROPN
ejpam-4665	8	31	,	,	PUNCT
ejpam-4665	8	32	edge	edge	NOUN
ejpam-4665	8	33	corona	corona	NOUN
ejpam-4665	8	34	,	,	PUNCT
ejpam-4665	8	35	lexicographic	lexicographic	ADJ
ejpam-4665	8	36	product	product	NOUN
ejpam-4665	8	37	1	1	NUM
ejpam-4665	8	38	.	.	PUNCT
ejpam-4665	8	39	introduction	introduction	NOUN
ejpam-4665	8	40	the	the	DET
ejpam-4665	8	41	concept	concept	NOUN
ejpam-4665	8	42	of	of	ADP
ejpam-4665	8	43	domination	domination	NOUN
ejpam-4665	8	44	in	in	ADP
ejpam-4665	8	45	graphs	graph	NOUN
ejpam-4665	8	46	is	be	AUX
ejpam-4665	8	47	one	one	NUM
ejpam-4665	8	48	of	of	ADP
ejpam-4665	8	49	the	the	DET
ejpam-4665	8	50	most	most	ADV
ejpam-4665	8	51	studied	study	VERB
ejpam-4665	8	52	problems	problem	NOUN
ejpam-4665	8	53	and	and	CCONJ
ejpam-4665	8	54	one	one	NUM
ejpam-4665	8	55	of	of	ADP
ejpam-4665	8	56	the	the	DET
ejpam-4665	8	57	fastest	fast	ADJ
ejpam-4665	8	58	growing	grow	VERB
ejpam-4665	8	59	areas	area	NOUN
ejpam-4665	8	60	in	in	ADP
ejpam-4665	8	61	graph	graph	NOUN
ejpam-4665	8	62	theory	theory	NOUN
ejpam-4665	8	63	.	.	PUNCT
ejpam-4665	9	1	this	this	PRON
ejpam-4665	9	2	was	be	AUX
ejpam-4665	9	3	formally	formally	ADV
ejpam-4665	9	4	studied	study	VERB
ejpam-4665	9	5	by	by	ADP
ejpam-4665	9	6	claude	claude	PROPN
ejpam-4665	9	7	berge	berge	PROPN
ejpam-4665	10	1	[	[	X
ejpam-4665	10	2	1	1	X
ejpam-4665	10	3	]	]	PUNCT
ejpam-4665	10	4	in	in	ADP
ejpam-4665	10	5	1958	1958	NUM
ejpam-4665	10	6	and	and	CCONJ
ejpam-4665	10	7	oystein	oystein	ADJ
ejpam-4665	10	8	ore	ore	NOUN
ejpam-4665	10	9	in	in	ADP
ejpam-4665	10	10	1962	1962	NUM
ejpam-4665	10	11	.	.	PUNCT
ejpam-4665	11	1	in	in	ADP
ejpam-4665	11	2	2015	2015	NUM
ejpam-4665	11	3	,	,	PUNCT
ejpam-4665	11	4	natarajan	natarajan	PROPN
ejpam-4665	11	5	and	and	CCONJ
ejpam-4665	11	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4665	11	7	introduced	introduce	VERB
ejpam-4665	11	8	and	and	CCONJ
ejpam-4665	11	9	studied	study	VERB
ejpam-4665	11	10	the	the	DET
ejpam-4665	11	11	concept	concept	NOUN
ejpam-4665	11	12	of	of	ADP
ejpam-4665	11	13	hop	hop	NOUN
ejpam-4665	11	14	domination	domination	NOUN
ejpam-4665	11	15	[	[	X
ejpam-4665	11	16	14	14	NUM
ejpam-4665	11	17	]	]	PUNCT
ejpam-4665	11	18	.	.	PUNCT
ejpam-4665	12	1	on	on	ADP
ejpam-4665	12	2	the	the	DET
ejpam-4665	12	3	other	other	ADJ
ejpam-4665	12	4	hand	hand	NOUN
ejpam-4665	12	5	,	,	PUNCT
ejpam-4665	12	6	in	in	ADP
ejpam-4665	12	7	1975	1975	NUM
ejpam-4665	12	8	using	use	VERB
ejpam-4665	12	9	the	the	DET
ejpam-4665	12	10	term	term	NOUN
ejpam-4665	12	11	locating	locate	VERB
ejpam-4665	12	12	set	set	NOUN
ejpam-4665	12	13	,	,	PUNCT
ejpam-4665	12	14	the	the	DET
ejpam-4665	12	15	concept	concept	NOUN
ejpam-4665	12	16	of	of	ADP
ejpam-4665	12	17	resolving	resolve	VERB
ejpam-4665	12	18	sets	set	NOUN
ejpam-4665	12	19	for	for	ADP
ejpam-4665	12	20	a	a	DET
ejpam-4665	12	21	connected	connected	ADJ
ejpam-4665	12	22	graph	graph	NOUN
ejpam-4665	12	23	was	be	AUX
ejpam-4665	12	24	first	first	ADV
ejpam-4665	12	25	introduced	introduce	VERB
ejpam-4665	12	26	by	by	ADP
ejpam-4665	12	27	slater	slater	NOUN
ejpam-4665	12	28	[	[	X
ejpam-4665	12	29	17	17	NUM
ejpam-4665	12	30	]	]	PUNCT
ejpam-4665	12	31	.	.	PUNCT
ejpam-4665	13	1	these	these	DET
ejpam-4665	13	2	concepts	concept	NOUN
ejpam-4665	13	3	were	be	AUX
ejpam-4665	13	4	studied	study	VERB
ejpam-4665	13	5	much	much	ADV
ejpam-4665	13	6	earlier	early	ADV
ejpam-4665	13	7	in	in	ADP
ejpam-4665	13	8	the	the	DET
ejpam-4665	13	9	context	context	NOUN
ejpam-4665	13	10	of	of	ADP
ejpam-4665	13	11	the	the	DET
ejpam-4665	13	12	coin	coin	NOUN
ejpam-4665	13	13	-	-	PUNCT
ejpam-4665	13	14	weighing	weigh	VERB
ejpam-4665	13	15	problem	problem	NOUN
ejpam-4665	13	16	.	.	PUNCT
ejpam-4665	14	1	later	later	ADV
ejpam-4665	14	2	that	that	DET
ejpam-4665	14	3	year	year	NOUN
ejpam-4665	14	4	,	,	PUNCT
ejpam-4665	14	5	harary	harary	NOUN
ejpam-4665	14	6	and	and	CCONJ
ejpam-4665	14	7	melter	melter	NOUN
ejpam-4665	14	8	introduced	introduce	VERB
ejpam-4665	14	9	independently	independently	ADV
ejpam-4665	14	10	these	these	DET
ejpam-4665	14	11	concepts	concept	NOUN
ejpam-4665	14	12	,	,	PUNCT
ejpam-4665	14	13	but	but	CCONJ
ejpam-4665	14	14	with	with	ADP
ejpam-4665	14	15	different	different	ADJ
ejpam-4665	14	16	terminologies	terminology	NOUN
ejpam-4665	14	17	[	[	X
ejpam-4665	14	18	10	10	NUM
ejpam-4665	14	19	]	]	PUNCT
ejpam-4665	14	20	.	.	PUNCT
ejpam-4665	15	1	the	the	DET
ejpam-4665	15	2	term	term	NOUN
ejpam-4665	15	3	metric	metric	ADJ
ejpam-4665	15	4	dimension	dimension	NOUN
ejpam-4665	15	5	was	be	AUX
ejpam-4665	15	6	used	use	VERB
ejpam-4665	15	7	by	by	ADP
ejpam-4665	15	8	harary	harary	NOUN
ejpam-4665	15	9	and	and	CCONJ
ejpam-4665	15	10	melter	melter	NOUN
ejpam-4665	15	11	instead	instead	ADV
ejpam-4665	15	12	of	of	ADP
ejpam-4665	15	13	locating	locate	VERB
ejpam-4665	15	14	number	number	NOUN
ejpam-4665	15	15	.	.	PUNCT
ejpam-4665	16	1	recently	recently	ADV
ejpam-4665	16	2	,	,	PUNCT
ejpam-4665	16	3	2	2	NUM
ejpam-4665	16	4	-	-	PUNCT
ejpam-4665	16	5	resolving	resolve	VERB
ejpam-4665	16	6	hop	hop	NOUN
ejpam-4665	16	7	dominating	dominating	NOUN
ejpam-4665	16	8	sets	set	NOUN
ejpam-4665	16	9	in	in	ADP
ejpam-4665	16	10	graphs	graph	NOUN
ejpam-4665	16	11	was	be	AUX
ejpam-4665	16	12	studied	study	VERB
ejpam-4665	16	13	in	in	ADP
ejpam-4665	16	14	[	[	X
ejpam-4665	16	15	11	11	NUM
ejpam-4665	16	16	]	]	PUNCT
ejpam-4665	16	17	.	.	PUNCT
ejpam-4665	17	1	moreover	moreover	ADV
ejpam-4665	17	2	,	,	PUNCT
ejpam-4665	17	3	other	other	ADJ
ejpam-4665	17	4	variations	variation	NOUN
ejpam-4665	17	5	of	of	ADP
ejpam-4665	17	6	2	2	NUM
ejpam-4665	17	7	-	-	PUNCT
ejpam-4665	17	8	resolving	resolve	VERB
ejpam-4665	17	9	sets	set	NOUN
ejpam-4665	17	10	in	in	ADP
ejpam-4665	17	11	graphs	graph	NOUN
ejpam-4665	17	12	were	be	AUX
ejpam-4665	17	13	also	also	ADV
ejpam-4665	17	14	studied	study	VERB
ejpam-4665	17	15	in	in	ADP
ejpam-4665	17	16	[	[	X
ejpam-4665	17	17	4–6	4–6	NOUN
ejpam-4665	17	18	,	,	PUNCT
ejpam-4665	17	19	8	8	NUM
ejpam-4665	17	20	,	,	PUNCT
ejpam-4665	17	21	12	12	NUM
ejpam-4665	17	22	,	,	PUNCT
ejpam-4665	17	23	13	13	NUM
ejpam-4665	17	24	]	]	PUNCT
ejpam-4665	17	25	,	,	PUNCT
ejpam-4665	17	26	respectively	respectively	ADV
ejpam-4665	17	27	.	.	PUNCT
ejpam-4665	18	1	∗corresponding	∗corresponde	VERB
ejpam-4665	18	2	author	author	NOUN
ejpam-4665	18	3	.	.	PUNCT
ejpam-4665	19	1	doi	doi	NOUN
ejpam-4665	19	2	:	:	PUNCT
ejpam-4665	19	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4665	https://doi.org/10.29020/nybg.ejpam.v16i1.4665	ADJ
ejpam-4665	19	4	email	email	NOUN
ejpam-4665	19	5	addresses	address	NOUN
ejpam-4665	19	6	:	:	PUNCT
ejpam-4665	19	7	angelicamae.mahistrado@g.msuiit.edu.ph	angelicamae.mahistrado@g.msuiit.edu.ph	PROPN
ejpam-4665	19	8	(	(	PUNCT
ejpam-4665	19	9	a.m.	a.m.	NOUN
ejpam-4665	19	10	mahistrado	mahistrado	PROPN
ejpam-4665	19	11	)	)	PUNCT
ejpam-4665	19	12	,	,	PUNCT
ejpam-4665	19	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4665	19	14	(	(	PUNCT
ejpam-4665	19	15	h.	h.	PROPN
ejpam-4665	19	16	rara	rara	PROPN
ejpam-4665	19	17	)	)	PUNCT
ejpam-4665	19	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4665	20	1	286	286	NUM
ejpam-4665	20	2	©	©	ADP
ejpam-4665	20	3	2023	2023	NUM
ejpam-4665	20	4	ejpam	ejpam	NOUN
ejpam-4665	20	5	all	all	DET
ejpam-4665	20	6	rights	right	NOUN
ejpam-4665	20	7	reserved	reserve	VERB
ejpam-4665	20	8	.	.	PUNCT
ejpam-4665	21	1	a.m.	a.m.	PROPN
ejpam-4665	21	2	mahistrado	mahistrado	PROPN
ejpam-4665	21	3	,	,	PUNCT
ejpam-4665	21	4	h.	h.	PROPN
ejpam-4665	21	5	rara	rara	PROPN
ejpam-4665	21	6	/	/	SYM
ejpam-4665	21	7	eur	eur	PROPN
ejpam-4665	21	8	.	.	PUNCT
ejpam-4665	22	1	j.	j.	PROPN
ejpam-4665	22	2	pure	pure	PROPN
ejpam-4665	22	3	appl	appl	PROPN
ejpam-4665	22	4	.	.	PROPN
ejpam-4665	22	5	math	math	PROPN
ejpam-4665	22	6	,	,	PUNCT
ejpam-4665	22	7	16	16	NUM
ejpam-4665	22	8	(	(	PUNCT
ejpam-4665	22	9	1	1	NUM
ejpam-4665	22	10	)	)	PUNCT
ejpam-4665	22	11	(	(	PUNCT
ejpam-4665	22	12	2023	2023	NUM
ejpam-4665	22	13	)	)	PUNCT
ejpam-4665	22	14	,	,	PUNCT
ejpam-4665	22	15	286	286	NUM
ejpam-4665	22	16	-	-	SYM
ejpam-4665	22	17	303	303	NUM
ejpam-4665	22	18	287	287	NUM
ejpam-4665	22	19	2	2	NUM
ejpam-4665	22	20	.	.	PUNCT
ejpam-4665	22	21	terminology	terminology	NOUN
ejpam-4665	22	22	and	and	CCONJ
ejpam-4665	22	23	notation	notation	NOUN
ejpam-4665	22	24	in	in	ADP
ejpam-4665	22	25	this	this	DET
ejpam-4665	22	26	study	study	NOUN
ejpam-4665	22	27	,	,	PUNCT
ejpam-4665	22	28	we	we	PRON
ejpam-4665	22	29	consider	consider	VERB
ejpam-4665	22	30	finite	finite	NOUN
ejpam-4665	22	31	,	,	PUNCT
ejpam-4665	22	32	simple	simple	ADJ
ejpam-4665	22	33	and	and	CCONJ
ejpam-4665	22	34	connected	connected	ADJ
ejpam-4665	22	35	graphs	graph	NOUN
ejpam-4665	22	36	.	.	PUNCT
ejpam-4665	23	1	for	for	ADP
ejpam-4665	23	2	basic	basic	ADJ
ejpam-4665	23	3	graphtheoretic	graphtheoretic	ADJ
ejpam-4665	23	4	concepts	concept	NOUN
ejpam-4665	23	5	,	,	PUNCT
ejpam-4665	23	6	we	we	PRON
ejpam-4665	23	7	then	then	ADV
ejpam-4665	23	8	refer	refer	VERB
ejpam-4665	23	9	readers	reader	NOUN
ejpam-4665	23	10	to	to	ADP
ejpam-4665	23	11	[	[	X
ejpam-4665	23	12	2	2	NUM
ejpam-4665	23	13	]	]	PUNCT
ejpam-4665	23	14	and	and	CCONJ
ejpam-4665	23	15	[	[	X
ejpam-4665	23	16	3	3	NUM
ejpam-4665	23	17	]	]	PUNCT
ejpam-4665	23	18	.	.	PUNCT
ejpam-4665	24	1	the	the	DET
ejpam-4665	24	2	following	follow	VERB
ejpam-4665	24	3	concepts	concept	NOUN
ejpam-4665	24	4	are	be	AUX
ejpam-4665	24	5	found	find	VERB
ejpam-4665	24	6	in	in	ADP
ejpam-4665	24	7	[	[	X
ejpam-4665	24	8	2	2	NUM
ejpam-4665	24	9	]	]	PUNCT
ejpam-4665	24	10	,	,	PUNCT
ejpam-4665	24	11	[	[	X
ejpam-4665	24	12	14	14	NUM
ejpam-4665	24	13	]	]	PUNCT
ejpam-4665	24	14	and	and	CCONJ
ejpam-4665	24	15	[	[	X
ejpam-4665	24	16	16	16	NUM
ejpam-4665	24	17	]	]	PUNCT
ejpam-4665	24	18	.	.	PUNCT
ejpam-4665	25	1	let	let	VERB
ejpam-4665	25	2	g	g	PRON
ejpam-4665	25	3	be	be	AUX
ejpam-4665	25	4	a	a	DET
ejpam-4665	25	5	connected	connected	ADJ
ejpam-4665	25	6	graph	graph	NOUN
ejpam-4665	25	7	.	.	PUNCT
ejpam-4665	26	1	a	a	DET
ejpam-4665	26	2	vertex	vertex	NOUN
ejpam-4665	26	3	v	v	NOUN
ejpam-4665	26	4	in	in	ADP
ejpam-4665	26	5	g	g	PROPN
ejpam-4665	26	6	is	be	AUX
ejpam-4665	26	7	a	a	DET
ejpam-4665	26	8	hop	hop	NOUN
ejpam-4665	26	9	neighbor	neighbor	NOUN
ejpam-4665	26	10	of	of	ADP
ejpam-4665	26	11	vertex	vertex	NOUN
ejpam-4665	26	12	u	u	NOUN
ejpam-4665	26	13	in	in	ADP
ejpam-4665	26	14	g	g	PROPN
ejpam-4665	26	15	if	if	SCONJ
ejpam-4665	26	16	dg(u	dg(u	NOUN
ejpam-4665	26	17	,	,	PUNCT
ejpam-4665	26	18	v	v	NOUN
ejpam-4665	26	19	)	)	PUNCT
ejpam-4665	26	20	=	=	SYM
ejpam-4665	26	21	2	2	X
ejpam-4665	26	22	.	.	X
ejpam-4665	27	1	the	the	DET
ejpam-4665	27	2	set	set	NOUN
ejpam-4665	27	3	ng(u	ng(u	NOUN
ejpam-4665	27	4	,	,	PUNCT
ejpam-4665	27	5	2	2	NUM
ejpam-4665	27	6	)	)	PUNCT
ejpam-4665	27	7	=	=	PRON
ejpam-4665	27	8	{	{	PUNCT
ejpam-4665	27	9	v	v	NUM
ejpam-4665	27	10	∈	∈	NOUN
ejpam-4665	27	11	v	v	NOUN
ejpam-4665	27	12	(	(	PUNCT
ejpam-4665	27	13	g	g	NOUN
ejpam-4665	27	14	)	)	PUNCT
ejpam-4665	27	15	:	:	PUNCT
ejpam-4665	27	16	dg(v	dg(v	X
ejpam-4665	27	17	,	,	PUNCT
ejpam-4665	27	18	u	u	NOUN
ejpam-4665	27	19	)	)	PUNCT
ejpam-4665	27	20	=	=	SYM
ejpam-4665	27	21	2	2	X
ejpam-4665	27	22	}	}	PUNCT
ejpam-4665	27	23	is	be	AUX
ejpam-4665	27	24	called	call	VERB
ejpam-4665	27	25	the	the	DET
ejpam-4665	27	26	open	open	ADJ
ejpam-4665	27	27	hop	hop	NOUN
ejpam-4665	27	28	neighborhood	neighborhood	NOUN
ejpam-4665	27	29	of	of	ADP
ejpam-4665	27	30	u.	u.	PROPN
ejpam-4665	27	31	the	the	DET
ejpam-4665	27	32	closed	closed	ADJ
ejpam-4665	27	33	hop	hop	NOUN
ejpam-4665	27	34	neighborhood	neighborhood	NOUN
ejpam-4665	27	35	of	of	ADP
ejpam-4665	27	36	u	u	PROPN
ejpam-4665	27	37	in	in	ADP
ejpam-4665	27	38	g	g	PROPN
ejpam-4665	27	39	is	be	AUX
ejpam-4665	27	40	given	give	VERB
ejpam-4665	27	41	by	by	ADP
ejpam-4665	27	42	ng[u	ng[u	PROPN
ejpam-4665	27	43	,	,	PUNCT
ejpam-4665	27	44	2	2	NUM
ejpam-4665	27	45	]	]	PUNCT
ejpam-4665	27	46	=	=	SYM
ejpam-4665	27	47	ng(u	ng(u	NOUN
ejpam-4665	27	48	,	,	PUNCT
ejpam-4665	27	49	2)∪{u	2)∪{u	NUM
ejpam-4665	27	50	}	}	PUNCT
ejpam-4665	27	51	.	.	PUNCT
ejpam-4665	28	1	the	the	DET
ejpam-4665	28	2	open	open	ADJ
ejpam-4665	28	3	hop	hop	NOUN
ejpam-4665	28	4	neighborhood	neighborhood	NOUN
ejpam-4665	28	5	ofx	ofx	NOUN
ejpam-4665	28	6	⊆	⊆	NUM
ejpam-4665	28	7	v	v	NOUN
ejpam-4665	28	8	(	(	PUNCT
ejpam-4665	28	9	g	g	NOUN
ejpam-4665	28	10	)	)	PUNCT
ejpam-4665	28	11	is	be	AUX
ejpam-4665	28	12	the	the	DET
ejpam-4665	28	13	set	set	NOUN
ejpam-4665	28	14	ng(x	ng(x	NUM
ejpam-4665	28	15	,	,	PUNCT
ejpam-4665	28	16	2	2	X
ejpam-4665	28	17	)	)	PUNCT
ejpam-4665	28	18	=	=	NOUN
ejpam-4665	28	19	⋃	⋃	NOUN
ejpam-4665	28	20	u∈x	u∈x	ADJ
ejpam-4665	28	21	ng(u	ng(u	NOUN
ejpam-4665	28	22	,	,	PUNCT
ejpam-4665	28	23	2	2	NUM
ejpam-4665	28	24	)	)	PUNCT
ejpam-4665	28	25	.	.	PUNCT
ejpam-4665	29	1	the	the	DET
ejpam-4665	29	2	closed	closed	ADJ
ejpam-4665	29	3	hop	hop	NOUN
ejpam-4665	29	4	neighborhood	neighborhood	NOUN
ejpam-4665	29	5	of	of	ADP
ejpam-4665	29	6	x	x	PUNCT
ejpam-4665	29	7	in	in	ADP
ejpam-4665	29	8	g	g	PROPN
ejpam-4665	29	9	is	be	AUX
ejpam-4665	29	10	the	the	DET
ejpam-4665	29	11	set	set	PROPN
ejpam-4665	29	12	ng[x	ng[x	PROPN
ejpam-4665	29	13	,	,	PUNCT
ejpam-4665	29	14	2	2	NUM
ejpam-4665	29	15	]	]	PUNCT
ejpam-4665	29	16	=	=	SYM
ejpam-4665	29	17	ng(x	ng(x	X
ejpam-4665	29	18	,	,	PUNCT
ejpam-4665	29	19	2	2	NUM
ejpam-4665	29	20	)	)	PUNCT
ejpam-4665	29	21	∪x	∪x	NUM
ejpam-4665	29	22	.	.	PUNCT
ejpam-4665	30	1	a	a	DET
ejpam-4665	30	2	set	set	NOUN
ejpam-4665	30	3	s	s	NOUN
ejpam-4665	30	4	⊆	⊆	NUM
ejpam-4665	30	5	v	v	NOUN
ejpam-4665	30	6	(	(	PUNCT
ejpam-4665	30	7	g	g	NOUN
ejpam-4665	30	8	)	)	PUNCT
ejpam-4665	30	9	is	be	AUX
ejpam-4665	30	10	a	a	DET
ejpam-4665	30	11	hop	hop	NOUN
ejpam-4665	30	12	dominating	dominating	NOUN
ejpam-4665	30	13	set	set	NOUN
ejpam-4665	30	14	of	of	ADP
ejpam-4665	30	15	g	g	PROPN
ejpam-4665	30	16	if	if	SCONJ
ejpam-4665	30	17	ng[s	ng[	NOUN
ejpam-4665	30	18	,	,	PUNCT
ejpam-4665	30	19	2	2	NUM
ejpam-4665	30	20	]	]	PUNCT
ejpam-4665	30	21	=	=	SYM
ejpam-4665	30	22	v	v	NOUN
ejpam-4665	30	23	(	(	PUNCT
ejpam-4665	30	24	g	g	NOUN
ejpam-4665	30	25	)	)	PUNCT
ejpam-4665	30	26	,	,	PUNCT
ejpam-4665	30	27	that	that	ADV
ejpam-4665	30	28	is	is	ADV
ejpam-4665	30	29	,	,	PUNCT
ejpam-4665	30	30	for	for	ADP
ejpam-4665	30	31	every	every	DET
ejpam-4665	30	32	v	v	NUM
ejpam-4665	30	33	∈	∈	NOUN
ejpam-4665	30	34	v	v	NOUN
ejpam-4665	30	35	(	(	PUNCT
ejpam-4665	30	36	g)\s	g)\s	NOUN
ejpam-4665	30	37	,	,	PUNCT
ejpam-4665	30	38	there	there	PRON
ejpam-4665	30	39	exists	exist	VERB
ejpam-4665	30	40	u	u	PROPN
ejpam-4665	30	41	∈	∈	PROPN
ejpam-4665	30	42	s	s	VERB
ejpam-4665	30	43	such	such	ADJ
ejpam-4665	30	44	that	that	DET
ejpam-4665	30	45	dg(u	dg(u	ADJ
ejpam-4665	30	46	,	,	PUNCT
ejpam-4665	30	47	v	v	NOUN
ejpam-4665	30	48	)	)	PUNCT
ejpam-4665	31	1	=	=	SYM
ejpam-4665	31	2	2	2	X
ejpam-4665	31	3	.	.	PUNCT
ejpam-4665	32	1	the	the	DET
ejpam-4665	32	2	minimum	minimum	ADJ
ejpam-4665	32	3	cardinality	cardinality	NOUN
ejpam-4665	32	4	of	of	ADP
ejpam-4665	32	5	a	a	DET
ejpam-4665	32	6	hop	hop	NOUN
ejpam-4665	32	7	dominating	dominating	NOUN
ejpam-4665	32	8	set	set	NOUN
ejpam-4665	32	9	of	of	ADP
ejpam-4665	32	10	g	g	NOUN
ejpam-4665	32	11	,	,	PUNCT
ejpam-4665	32	12	denoted	denote	VERB
ejpam-4665	32	13	by	by	ADP
ejpam-4665	32	14	γh(g	γh(g	NOUN
ejpam-4665	32	15	)	)	PUNCT
ejpam-4665	32	16	,	,	PUNCT
ejpam-4665	32	17	is	be	AUX
ejpam-4665	32	18	called	call	VERB
ejpam-4665	32	19	the	the	DET
ejpam-4665	32	20	hop	hop	NOUN
ejpam-4665	32	21	domination	domination	NOUN
ejpam-4665	32	22	number	number	NOUN
ejpam-4665	32	23	of	of	ADP
ejpam-4665	32	24	g.	g.	PROPN
ejpam-4665	32	25	any	any	DET
ejpam-4665	32	26	hop	hop	NOUN
ejpam-4665	32	27	dominating	dominating	NOUN
ejpam-4665	32	28	set	set	VERB
ejpam-4665	32	29	with	with	ADP
ejpam-4665	32	30	cardinality	cardinality	NOUN
ejpam-4665	32	31	equal	equal	ADJ
ejpam-4665	32	32	to	to	ADP
ejpam-4665	32	33	γh(g	γh(g	NOUN
ejpam-4665	32	34	)	)	PUNCT
ejpam-4665	32	35	is	be	AUX
ejpam-4665	32	36	called	call	VERB
ejpam-4665	32	37	a	a	DET
ejpam-4665	32	38	γh	γh	ADV
ejpam-4665	32	39	-	-	PUNCT
ejpam-4665	32	40	set	set	NOUN
ejpam-4665	32	41	.	.	PUNCT
ejpam-4665	33	1	for	for	ADP
ejpam-4665	33	2	an	an	DET
ejpam-4665	33	3	ordered	order	VERB
ejpam-4665	33	4	set	set	NOUN
ejpam-4665	33	5	of	of	ADP
ejpam-4665	33	6	vertices	vertex	NOUN
ejpam-4665	33	7	w	w	NOUN
ejpam-4665	33	8	=	=	SYM
ejpam-4665	33	9	{	{	PUNCT
ejpam-4665	33	10	w1	w1	NOUN
ejpam-4665	33	11	,	,	PUNCT
ejpam-4665	33	12	w2	w2	NOUN
ejpam-4665	33	13	,	,	PUNCT
ejpam-4665	33	14	...	...	PUNCT
ejpam-4665	33	15	,	,	PUNCT
ejpam-4665	33	16	wk	wk	ADP
ejpam-4665	33	17	}	}	PUNCT
ejpam-4665	33	18	⊆	⊆	NUM
ejpam-4665	33	19	v	v	NOUN
ejpam-4665	33	20	(	(	PUNCT
ejpam-4665	33	21	g	g	NOUN
ejpam-4665	33	22	)	)	PUNCT
ejpam-4665	33	23	and	and	CCONJ
ejpam-4665	33	24	a	a	DET
ejpam-4665	33	25	vertex	vertex	NOUN
ejpam-4665	33	26	v	v	NOUN
ejpam-4665	33	27	in	in	ADP
ejpam-4665	33	28	g	g	NOUN
ejpam-4665	33	29	,	,	PUNCT
ejpam-4665	33	30	we	we	PRON
ejpam-4665	33	31	refer	refer	VERB
ejpam-4665	33	32	to	to	ADP
ejpam-4665	33	33	the	the	DET
ejpam-4665	33	34	k	k	NOUN
ejpam-4665	33	35	-	-	NOUN
ejpam-4665	33	36	vector	vector	NOUN
ejpam-4665	33	37	(	(	PUNCT
ejpam-4665	33	38	ordered	order	VERB
ejpam-4665	33	39	k	k	NOUN
ejpam-4665	33	40	-	-	PUNCT
ejpam-4665	33	41	tuple	tuple	NOUN
ejpam-4665	33	42	)	)	PUNCT
ejpam-4665	33	43	rg(v	rg(v	PROPN
ejpam-4665	33	44	/	/	SYM
ejpam-4665	33	45	w	w	NOUN
ejpam-4665	33	46	)	)	PUNCT
ejpam-4665	34	1	=	=	SYM
ejpam-4665	34	2	(	(	PUNCT
ejpam-4665	34	3	dg(v	dg(v	X
ejpam-4665	34	4	,	,	PUNCT
ejpam-4665	34	5	w1	w1	NOUN
ejpam-4665	34	6	)	)	PUNCT
ejpam-4665	34	7	,	,	PUNCT
ejpam-4665	34	8	dg(v	dg(v	X
ejpam-4665	34	9	,	,	PUNCT
ejpam-4665	34	10	w2	w2	NOUN
ejpam-4665	34	11	)	)	PUNCT
ejpam-4665	34	12	,	,	PUNCT
ejpam-4665	34	13	...	...	PUNCT
ejpam-4665	34	14	,	,	PUNCT
ejpam-4665	34	15	dg(v	dg(v	X
ejpam-4665	34	16	,	,	PUNCT
ejpam-4665	34	17	wk	wk	NOUN
ejpam-4665	34	18	)	)	PUNCT
ejpam-4665	34	19	)	)	PUNCT
ejpam-4665	35	1	as	as	ADP
ejpam-4665	35	2	the	the	DET
ejpam-4665	35	3	(	(	PUNCT
ejpam-4665	35	4	metric	metric	ADJ
ejpam-4665	35	5	)	)	PUNCT
ejpam-4665	35	6	representation	representation	NOUN
ejpam-4665	35	7	of	of	ADP
ejpam-4665	35	8	v	v	NOUN
ejpam-4665	35	9	with	with	ADP
ejpam-4665	35	10	respect	respect	NOUN
ejpam-4665	35	11	to	to	ADP
ejpam-4665	35	12	w	w	PROPN
ejpam-4665	35	13	.	.	PUNCT
ejpam-4665	36	1	the	the	DET
ejpam-4665	36	2	set	set	NOUN
ejpam-4665	36	3	w	w	NOUN
ejpam-4665	36	4	is	be	AUX
ejpam-4665	36	5	called	call	VERB
ejpam-4665	36	6	a	a	DET
ejpam-4665	36	7	resolving	resolving	NOUN
ejpam-4665	36	8	set	set	VERB
ejpam-4665	36	9	for	for	ADP
ejpam-4665	36	10	g	g	PROPN
ejpam-4665	36	11	if	if	SCONJ
ejpam-4665	36	12	distinct	distinct	ADJ
ejpam-4665	36	13	vertices	vertex	NOUN
ejpam-4665	36	14	have	have	VERB
ejpam-4665	36	15	distinct	distinct	ADJ
ejpam-4665	36	16	representations	representation	NOUN
ejpam-4665	36	17	with	with	ADP
ejpam-4665	36	18	respect	respect	NOUN
ejpam-4665	36	19	to	to	ADP
ejpam-4665	36	20	w	w	PROPN
ejpam-4665	36	21	.	.	PUNCT
ejpam-4665	37	1	hence	hence	ADV
ejpam-4665	37	2	,	,	PUNCT
ejpam-4665	37	3	if	if	SCONJ
ejpam-4665	37	4	w	w	NOUN
ejpam-4665	37	5	is	be	AUX
ejpam-4665	37	6	a	a	DET
ejpam-4665	37	7	resolving	resolving	NOUN
ejpam-4665	37	8	set	set	NOUN
ejpam-4665	37	9	of	of	ADP
ejpam-4665	37	10	cardinality	cardinality	PROPN
ejpam-4665	37	11	k	k	PROPN
ejpam-4665	37	12	for	for	ADP
ejpam-4665	37	13	a	a	DET
ejpam-4665	37	14	graph	graph	NOUN
ejpam-4665	37	15	g	g	NOUN
ejpam-4665	37	16	of	of	ADP
ejpam-4665	37	17	order	order	NOUN
ejpam-4665	37	18	n	n	CCONJ
ejpam-4665	37	19	,	,	PUNCT
ejpam-4665	37	20	then	then	ADV
ejpam-4665	37	21	the	the	DET
ejpam-4665	37	22	set	set	NOUN
ejpam-4665	37	23	{	{	PUNCT
ejpam-4665	37	24	rg(v	rg(v	NOUN
ejpam-4665	37	25	/	/	SYM
ejpam-4665	37	26	w	w	NOUN
ejpam-4665	37	27	)	)	PUNCT
ejpam-4665	37	28	:	:	PUNCT
ejpam-4665	37	29	v	v	X
ejpam-4665	37	30	∈	∈	PROPN
ejpam-4665	37	31	v	v	NOUN
ejpam-4665	37	32	(	(	PUNCT
ejpam-4665	37	33	g	g	NOUN
ejpam-4665	37	34	)	)	PUNCT
ejpam-4665	37	35	}	}	PUNCT
ejpam-4665	37	36	consists	consist	VERB
ejpam-4665	37	37	of	of	ADP
ejpam-4665	37	38	n	n	PRON
ejpam-4665	37	39	distinct	distinct	ADJ
ejpam-4665	37	40	k	k	NOUN
ejpam-4665	37	41	-	-	NOUN
ejpam-4665	37	42	vectors	vector	NOUN
ejpam-4665	37	43	.	.	PUNCT
ejpam-4665	38	1	a	a	DET
ejpam-4665	38	2	resolving	resolving	NOUN
ejpam-4665	38	3	set	set	NOUN
ejpam-4665	38	4	of	of	ADP
ejpam-4665	38	5	minimum	minimum	ADJ
ejpam-4665	38	6	cardinality	cardinality	NOUN
ejpam-4665	38	7	is	be	AUX
ejpam-4665	38	8	called	call	VERB
ejpam-4665	38	9	aminimum	aminimum	ADJ
ejpam-4665	38	10	resolving	resolving	NOUN
ejpam-4665	38	11	set	set	VERB
ejpam-4665	38	12	or	or	CCONJ
ejpam-4665	38	13	a	a	DET
ejpam-4665	38	14	basis	basis	NOUN
ejpam-4665	38	15	,	,	PUNCT
ejpam-4665	38	16	and	and	CCONJ
ejpam-4665	38	17	the	the	DET
ejpam-4665	38	18	cardinality	cardinality	NOUN
ejpam-4665	38	19	of	of	ADP
ejpam-4665	38	20	a	a	DET
ejpam-4665	38	21	basis	basis	NOUN
ejpam-4665	38	22	for	for	ADP
ejpam-4665	38	23	g	g	PROPN
ejpam-4665	38	24	is	be	AUX
ejpam-4665	38	25	the	the	DET
ejpam-4665	38	26	dimension	dimension	NOUN
ejpam-4665	38	27	dim(g	dim(g	PROPN
ejpam-4665	38	28	)	)	PUNCT
ejpam-4665	38	29	of	of	ADP
ejpam-4665	38	30	g.	g.	PROPN
ejpam-4665	38	31	an	an	DET
ejpam-4665	38	32	ordered	order	VERB
ejpam-4665	38	33	set	set	NOUN
ejpam-4665	38	34	of	of	ADP
ejpam-4665	38	35	vertices	vertex	NOUN
ejpam-4665	38	36	w	w	NOUN
ejpam-4665	38	37	=	=	SYM
ejpam-4665	38	38	{	{	PUNCT
ejpam-4665	38	39	w1	w1	NOUN
ejpam-4665	38	40	,	,	PUNCT
ejpam-4665	38	41	...	...	PUNCT
ejpam-4665	38	42	,	,	PUNCT
ejpam-4665	38	43	wk	wk	X
ejpam-4665	38	44	}	}	PUNCT
ejpam-4665	38	45	is	be	AUX
ejpam-4665	38	46	a	a	DET
ejpam-4665	38	47	k	k	NOUN
ejpam-4665	38	48	-	-	PUNCT
ejpam-4665	38	49	resolving	resolving	NOUN
ejpam-4665	38	50	set	set	NOUN
ejpam-4665	38	51	for	for	ADP
ejpam-4665	38	52	g	g	PROPN
ejpam-4665	38	53	if	if	SCONJ
ejpam-4665	38	54	,	,	PUNCT
ejpam-4665	38	55	for	for	ADP
ejpam-4665	38	56	any	any	DET
ejpam-4665	38	57	distinct	distinct	ADJ
ejpam-4665	38	58	vertices	vertex	NOUN
ejpam-4665	38	59	u	u	NOUN
ejpam-4665	38	60	,	,	PUNCT
ejpam-4665	38	61	v	v	NOUN
ejpam-4665	38	62	∈	∈	PROPN
ejpam-4665	38	63	v	v	NOUN
ejpam-4665	38	64	(	(	PUNCT
ejpam-4665	38	65	g	g	NOUN
ejpam-4665	38	66	)	)	PUNCT
ejpam-4665	38	67	,	,	PUNCT
ejpam-4665	38	68	the	the	DET
ejpam-4665	38	69	(	(	PUNCT
ejpam-4665	38	70	metric	metric	ADJ
ejpam-4665	38	71	)	)	PUNCT
ejpam-4665	38	72	representations	representation	NOUN
ejpam-4665	38	73	rg(u	rg(u	NOUN
ejpam-4665	38	74	/	/	SYM
ejpam-4665	38	75	w	w	NOUN
ejpam-4665	38	76	)	)	PUNCT
ejpam-4665	38	77	and	and	CCONJ
ejpam-4665	38	78	rg(v	rg(v	PROPN
ejpam-4665	38	79	/	/	SYM
ejpam-4665	38	80	w	w	NOUN
ejpam-4665	38	81	)	)	PUNCT
ejpam-4665	38	82	of	of	ADP
ejpam-4665	38	83	u	u	NOUN
ejpam-4665	38	84	and	and	CCONJ
ejpam-4665	38	85	v	v	NOUN
ejpam-4665	38	86	,	,	PUNCT
ejpam-4665	38	87	respectively	respectively	ADV
ejpam-4665	38	88	,	,	PUNCT
ejpam-4665	38	89	differ	differ	VERB
ejpam-4665	38	90	in	in	ADP
ejpam-4665	38	91	at	at	ADP
ejpam-4665	38	92	least	least	ADJ
ejpam-4665	38	93	k	k	NOUN
ejpam-4665	38	94	positions	position	NOUN
ejpam-4665	38	95	.	.	PUNCT
ejpam-4665	39	1	if	if	SCONJ
ejpam-4665	39	2	k	k	PROPN
ejpam-4665	39	3	=	=	SYM
ejpam-4665	39	4	1	1	NUM
ejpam-4665	39	5	,	,	PUNCT
ejpam-4665	39	6	then	then	ADV
ejpam-4665	39	7	the	the	DET
ejpam-4665	39	8	k	k	NOUN
ejpam-4665	39	9	-	-	PUNCT
ejpam-4665	39	10	resolving	resolving	ADJ
ejpam-4665	39	11	set	set	NOUN
ejpam-4665	39	12	is	be	AUX
ejpam-4665	39	13	called	call	VERB
ejpam-4665	39	14	a	a	DET
ejpam-4665	39	15	resolving	resolving	NOUN
ejpam-4665	39	16	set	set	VERB
ejpam-4665	39	17	for	for	ADP
ejpam-4665	39	18	g.	g.	PROPN
ejpam-4665	39	19	if	if	SCONJ
ejpam-4665	39	20	k	k	PROPN
ejpam-4665	39	21	=	=	SYM
ejpam-4665	39	22	2	2	NUM
ejpam-4665	39	23	,	,	PUNCT
ejpam-4665	39	24	then	then	ADV
ejpam-4665	39	25	the	the	DET
ejpam-4665	39	26	k	k	NOUN
ejpam-4665	39	27	-	-	PUNCT
ejpam-4665	39	28	resolving	resolving	ADJ
ejpam-4665	39	29	set	set	NOUN
ejpam-4665	39	30	is	be	AUX
ejpam-4665	39	31	called	call	VERB
ejpam-4665	39	32	a	a	DET
ejpam-4665	39	33	2	2	NUM
ejpam-4665	39	34	-	-	PUNCT
ejpam-4665	39	35	resolving	resolving	NOUN
ejpam-4665	39	36	set	set	NOUN
ejpam-4665	39	37	for	for	ADP
ejpam-4665	39	38	g.	g.	PROPN
ejpam-4665	39	39	if	if	SCONJ
ejpam-4665	39	40	g	g	PROPN
ejpam-4665	39	41	has	have	VERB
ejpam-4665	39	42	a	a	DET
ejpam-4665	39	43	k	k	ADJ
ejpam-4665	39	44	-	-	ADJ
ejpam-4665	39	45	resolving	resolving	ADJ
ejpam-4665	39	46	set	set	NOUN
ejpam-4665	39	47	,	,	PUNCT
ejpam-4665	39	48	the	the	DET
ejpam-4665	39	49	minimum	minimum	ADJ
ejpam-4665	39	50	cardinality	cardinality	PROPN
ejpam-4665	39	51	dimk(g	dimk(g	PROPN
ejpam-4665	39	52	)	)	PUNCT
ejpam-4665	39	53	of	of	ADP
ejpam-4665	39	54	a	a	DET
ejpam-4665	39	55	k	k	NOUN
ejpam-4665	39	56	-	-	PUNCT
ejpam-4665	39	57	resolving	resolving	ADJ
ejpam-4665	39	58	set	set	NOUN
ejpam-4665	39	59	is	be	AUX
ejpam-4665	39	60	called	call	VERB
ejpam-4665	39	61	the	the	DET
ejpam-4665	39	62	k	k	ADJ
ejpam-4665	39	63	-	-	ADJ
ejpam-4665	39	64	metric	metric	ADJ
ejpam-4665	39	65	dimension	dimension	NOUN
ejpam-4665	39	66	of	of	ADP
ejpam-4665	39	67	g.	g.	PROPN
ejpam-4665	39	68	a	a	DET
ejpam-4665	39	69	set	set	NOUN
ejpam-4665	39	70	s	s	PROPN
ejpam-4665	39	71	⊆	⊆	NUM
ejpam-4665	39	72	v	v	NOUN
ejpam-4665	39	73	(	(	PUNCT
ejpam-4665	39	74	g	g	NOUN
ejpam-4665	39	75	)	)	PUNCT
ejpam-4665	39	76	is	be	AUX
ejpam-4665	39	77	a	a	DET
ejpam-4665	39	78	restrained	restrained	ADJ
ejpam-4665	39	79	2	2	NUM
ejpam-4665	39	80	-	-	PUNCT
ejpam-4665	39	81	resolving	resolve	VERB
ejpam-4665	39	82	hop	hop	NOUN
ejpam-4665	39	83	dominating	dominating	NOUN
ejpam-4665	39	84	set	set	NOUN
ejpam-4665	39	85	of	of	ADP
ejpam-4665	39	86	g	g	PROPN
ejpam-4665	39	87	if	if	SCONJ
ejpam-4665	39	88	s	s	VERB
ejpam-4665	39	89	is	be	AUX
ejpam-4665	39	90	a	a	DET
ejpam-4665	39	91	2resolving	2resolving	NUM
ejpam-4665	39	92	hop	hop	NOUN
ejpam-4665	39	93	dominating	dominating	NOUN
ejpam-4665	39	94	set	set	NOUN
ejpam-4665	39	95	of	of	ADP
ejpam-4665	39	96	g	g	PROPN
ejpam-4665	39	97	and	and	CCONJ
ejpam-4665	39	98	s	s	PART
ejpam-4665	39	99	=	=	SYM
ejpam-4665	39	100	v	v	X
ejpam-4665	39	101	(	(	PUNCT
ejpam-4665	39	102	g	g	NOUN
ejpam-4665	39	103	)	)	PUNCT
ejpam-4665	39	104	or	or	CCONJ
ejpam-4665	39	105	⟨v	⟨v	NUM
ejpam-4665	39	106	(	(	PUNCT
ejpam-4665	39	107	g)\s⟩	g)\s⟩	PROPN
ejpam-4665	39	108	has	have	VERB
ejpam-4665	39	109	no	no	DET
ejpam-4665	39	110	isolated	isolated	ADJ
ejpam-4665	39	111	vertex	vertex	NOUN
ejpam-4665	39	112	.	.	PUNCT
ejpam-4665	40	1	the	the	DET
ejpam-4665	40	2	restrained	restrained	ADJ
ejpam-4665	40	3	2	2	NUM
ejpam-4665	40	4	-	-	PUNCT
ejpam-4665	40	5	resolving	resolve	VERB
ejpam-4665	40	6	hop	hop	NOUN
ejpam-4665	40	7	domination	domination	NOUN
ejpam-4665	40	8	number	number	NOUN
ejpam-4665	40	9	of	of	ADP
ejpam-4665	40	10	g	g	NOUN
ejpam-4665	40	11	,	,	PUNCT
ejpam-4665	40	12	denoted	denote	VERB
ejpam-4665	40	13	by	by	ADP
ejpam-4665	40	14	γr2rh(g	γr2rh(g	NOUN
ejpam-4665	40	15	)	)	PUNCT
ejpam-4665	40	16	is	be	AUX
ejpam-4665	40	17	the	the	DET
ejpam-4665	40	18	smallest	small	ADJ
ejpam-4665	40	19	cardinality	cardinality	NOUN
ejpam-4665	40	20	of	of	ADP
ejpam-4665	40	21	a	a	DET
ejpam-4665	40	22	restrained	restrained	ADJ
ejpam-4665	40	23	2	2	NUM
ejpam-4665	40	24	-	-	PUNCT
ejpam-4665	40	25	resolving	resolve	VERB
ejpam-4665	40	26	hop	hop	NOUN
ejpam-4665	40	27	dominating	dominating	NOUN
ejpam-4665	40	28	set	set	NOUN
ejpam-4665	40	29	of	of	ADP
ejpam-4665	40	30	g.	g.	PROPN
ejpam-4665	40	31	any	any	DET
ejpam-4665	40	32	restrained	restrained	ADJ
ejpam-4665	40	33	2	2	NUM
ejpam-4665	40	34	-	-	PUNCT
ejpam-4665	40	35	resolving	resolve	VERB
ejpam-4665	40	36	hop	hop	NOUN
ejpam-4665	40	37	dominating	dominating	NOUN
ejpam-4665	40	38	set	set	NOUN
ejpam-4665	40	39	of	of	ADP
ejpam-4665	40	40	cardinality	cardinality	NOUN
ejpam-4665	40	41	γr2rh(g	γr2rh(g	NOUN
ejpam-4665	40	42	)	)	PUNCT
ejpam-4665	40	43	is	be	AUX
ejpam-4665	40	44	referred	refer	VERB
ejpam-4665	40	45	to	to	ADP
ejpam-4665	40	46	as	as	ADP
ejpam-4665	40	47	a	a	DET
ejpam-4665	40	48	γr2rh	γr2rh	NUM
ejpam-4665	40	49	-	-	PUNCT
ejpam-4665	40	50	set	set	NOUN
ejpam-4665	40	51	of	of	ADP
ejpam-4665	40	52	g.	g.	PROPN
ejpam-4665	40	53	definition	definition	NOUN
ejpam-4665	40	54	1	1	NUM
ejpam-4665	40	55	.	.	PUNCT
ejpam-4665	41	1	[	[	X
ejpam-4665	41	2	6	6	NUM
ejpam-4665	41	3	]	]	X
ejpam-4665	41	4	letg	letg	NOUN
ejpam-4665	41	5	be	be	VERB
ejpam-4665	41	6	any	any	DET
ejpam-4665	41	7	nontrivial	nontrivial	ADJ
ejpam-4665	41	8	connected	connect	VERB
ejpam-4665	41	9	graph	graph	NOUN
ejpam-4665	41	10	and	and	CCONJ
ejpam-4665	41	11	s	s	VERB
ejpam-4665	41	12	⊆	⊆	NUM
ejpam-4665	41	13	v	v	NOUN
ejpam-4665	41	14	(	(	PUNCT
ejpam-4665	41	15	g	g	NOUN
ejpam-4665	41	16	)	)	PUNCT
ejpam-4665	41	17	.	.	PUNCT
ejpam-4665	42	1	a	a	DET
ejpam-4665	42	2	set	set	NOUN
ejpam-4665	42	3	s	s	PART
ejpam-4665	42	4	⊂	⊂	X
ejpam-4665	42	5	v	v	X
ejpam-4665	42	6	(	(	PUNCT
ejpam-4665	42	7	g	g	NOUN
ejpam-4665	42	8	)	)	PUNCT
ejpam-4665	42	9	is	be	AUX
ejpam-4665	42	10	a	a	DET
ejpam-4665	42	11	2	2	NUM
ejpam-4665	42	12	-	-	PUNCT
ejpam-4665	42	13	locating	locate	VERB
ejpam-4665	42	14	set	set	NOUN
ejpam-4665	42	15	of	of	ADP
ejpam-4665	42	16	g	g	NOUN
ejpam-4665	42	17	if	if	SCONJ
ejpam-4665	42	18	it	it	PRON
ejpam-4665	42	19	satisfies	satisfy	VERB
ejpam-4665	42	20	the	the	DET
ejpam-4665	42	21	following	follow	VERB
ejpam-4665	42	22	conditions	condition	NOUN
ejpam-4665	42	23	:	:	PUNCT
ejpam-4665	42	24	(	(	PUNCT
ejpam-4665	42	25	i	i	NOUN
ejpam-4665	42	26	)	)	PUNCT
ejpam-4665	42	27	∣∣[(ng(x)\ng(y	∣∣[(ng(x)\ng(y	PROPN
ejpam-4665	42	28	)	)	PUNCT
ejpam-4665	42	29	)	)	PUNCT
ejpam-4665	43	1	∩s]∪	∩s]∪	VERB
ejpam-4665	43	2	[	[	PUNCT
ejpam-4665	43	3	(	(	PUNCT
ejpam-4665	43	4	ng(y)\ng(x	ng(y)\ng(x	NOUN
ejpam-4665	43	5	)	)	PUNCT
ejpam-4665	43	6	)	)	PUNCT
ejpam-4665	44	1	∩s	∩s	PROPN
ejpam-4665	44	2	]	]	PUNCT
ejpam-4665	44	3	∣∣	∣∣	NUM
ejpam-4665	44	4	≥	≥	NOUN
ejpam-4665	44	5	2	2	NUM
ejpam-4665	44	6	,	,	PUNCT
ejpam-4665	44	7	for	for	ADP
ejpam-4665	44	8	all	all	DET
ejpam-4665	44	9	x	x	NOUN
ejpam-4665	44	10	,	,	PUNCT
ejpam-4665	44	11	y	y	PROPN
ejpam-4665	44	12	∈	∈	PROPN
ejpam-4665	44	13	v	v	X
ejpam-4665	44	14	(	(	PUNCT
ejpam-4665	44	15	g)\s	g)\s	VERB
ejpam-4665	44	16	with	with	ADP
ejpam-4665	44	17	x	x	PROPN
ejpam-4665	44	18	̸=	̸=	PROPN
ejpam-4665	44	19	y.	y.	PROPN
ejpam-4665	44	20	(	(	PUNCT
ejpam-4665	44	21	ii	ii	PROPN
ejpam-4665	44	22	)	)	PUNCT
ejpam-4665	44	23	(	(	PUNCT
ejpam-4665	44	24	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-4665	44	25	)	)	PUNCT
ejpam-4665	44	26	)	)	PUNCT
ejpam-4665	44	27	∩	∩	PROPN
ejpam-4665	44	28	s	s	PART
ejpam-4665	44	29	̸=	̸=	PROPN
ejpam-4665	44	30	∅	∅	NOUN
ejpam-4665	44	31	or	or	CCONJ
ejpam-4665	44	32	(	(	PUNCT
ejpam-4665	44	33	ng(w)\ng[v	ng(w)\ng[v	PROPN
ejpam-4665	44	34	]	]	PUNCT
ejpam-4665	44	35	)	)	PUNCT
ejpam-4665	44	36	∩	∩	PROPN
ejpam-4665	44	37	s	s	PART
ejpam-4665	44	38	̸=	̸=	PROPN
ejpam-4665	44	39	∅	∅	NOUN
ejpam-4665	44	40	,	,	PUNCT
ejpam-4665	44	41	for	for	ADP
ejpam-4665	44	42	all	all	PRON
ejpam-4665	44	43	v	v	ADP
ejpam-4665	44	44	∈	∈	NOUN
ejpam-4665	44	45	s	s	NOUN
ejpam-4665	44	46	and	and	CCONJ
ejpam-4665	44	47	for	for	ADP
ejpam-4665	44	48	all	all	PRON
ejpam-4665	44	49	w	w	PROPN
ejpam-4665	44	50	∈	∈	PROPN
ejpam-4665	44	51	v	v	NOUN
ejpam-4665	44	52	(	(	PUNCT
ejpam-4665	44	53	g)\s	g)\s	NOUN
ejpam-4665	44	54	.	.	PUNCT
ejpam-4665	45	1	the	the	DET
ejpam-4665	45	2	2	2	NUM
ejpam-4665	45	3	-	-	PUNCT
ejpam-4665	45	4	locating	locate	VERB
ejpam-4665	45	5	number	number	NOUN
ejpam-4665	45	6	of	of	ADP
ejpam-4665	45	7	g	g	NOUN
ejpam-4665	45	8	,	,	PUNCT
ejpam-4665	45	9	denoted	denote	VERB
ejpam-4665	45	10	by	by	ADP
ejpam-4665	45	11	ln2(g	ln2(g	NOUN
ejpam-4665	45	12	)	)	PUNCT
ejpam-4665	45	13	,	,	PUNCT
ejpam-4665	45	14	is	be	AUX
ejpam-4665	45	15	the	the	DET
ejpam-4665	45	16	smallest	small	ADJ
ejpam-4665	45	17	cardinality	cardinality	NOUN
ejpam-4665	45	18	of	of	ADP
ejpam-4665	45	19	a	a	DET
ejpam-4665	45	20	2	2	NUM
ejpam-4665	45	21	-	-	PUNCT
ejpam-4665	45	22	locating	locate	VERB
ejpam-4665	45	23	set	set	NOUN
ejpam-4665	45	24	of	of	ADP
ejpam-4665	45	25	g.	g.	PROPN
ejpam-4665	45	26	a	a	DET
ejpam-4665	45	27	2	2	NUM
ejpam-4665	45	28	-	-	PUNCT
ejpam-4665	45	29	locating	locate	VERB
ejpam-4665	45	30	set	set	NOUN
ejpam-4665	45	31	of	of	ADP
ejpam-4665	45	32	g	g	NOUN
ejpam-4665	45	33	of	of	ADP
ejpam-4665	45	34	cardinality	cardinality	PROPN
ejpam-4665	45	35	ln2(g	ln2(g	PROPN
ejpam-4665	45	36	)	)	PUNCT
ejpam-4665	45	37	is	be	AUX
ejpam-4665	45	38	referred	refer	VERB
ejpam-4665	45	39	to	to	ADP
ejpam-4665	45	40	as	as	ADP
ejpam-4665	45	41	an	an	DET
ejpam-4665	45	42	ln2	ln2	NOUN
ejpam-4665	45	43	-	-	PUNCT
ejpam-4665	45	44	set	set	NOUN
ejpam-4665	45	45	of	of	ADP
ejpam-4665	45	46	g.	g.	PROPN
ejpam-4665	45	47	a.m.	a.m.	PROPN
ejpam-4665	46	1	mahistrado	mahistrado	PROPN
ejpam-4665	46	2	,	,	PUNCT
ejpam-4665	46	3	h.	h.	PROPN
ejpam-4665	46	4	rara	rara	PROPN
ejpam-4665	46	5	/	/	SYM
ejpam-4665	46	6	eur	eur	PROPN
ejpam-4665	46	7	.	.	PUNCT
ejpam-4665	47	1	j.	j.	PROPN
ejpam-4665	47	2	pure	pure	PROPN
ejpam-4665	47	3	appl	appl	PROPN
ejpam-4665	47	4	.	.	PROPN
ejpam-4665	47	5	math	math	PROPN
ejpam-4665	47	6	,	,	PUNCT
ejpam-4665	47	7	16	16	NUM
ejpam-4665	47	8	(	(	PUNCT
ejpam-4665	47	9	1	1	NUM
ejpam-4665	47	10	)	)	PUNCT
ejpam-4665	47	11	(	(	PUNCT
ejpam-4665	47	12	2023	2023	NUM
ejpam-4665	47	13	)	)	PUNCT
ejpam-4665	47	14	,	,	PUNCT
ejpam-4665	47	15	286	286	NUM
ejpam-4665	47	16	-	-	SYM
ejpam-4665	47	17	303	303	NUM
ejpam-4665	47	18	288	288	NUM
ejpam-4665	47	19	definition	definition	NOUN
ejpam-4665	47	20	2	2	NUM
ejpam-4665	47	21	.	.	PUNCT
ejpam-4665	48	1	[	[	X
ejpam-4665	48	2	15	15	NUM
ejpam-4665	48	3	]	]	X
ejpam-4665	48	4	a	a	DET
ejpam-4665	48	5	set	set	NOUN
ejpam-4665	48	6	d	d	NOUN
ejpam-4665	48	7	⊆	⊆	NUM
ejpam-4665	48	8	v	v	ADP
ejpam-4665	48	9	(	(	PUNCT
ejpam-4665	48	10	g	g	NOUN
ejpam-4665	48	11	)	)	PUNCT
ejpam-4665	48	12	is	be	AUX
ejpam-4665	48	13	a	a	DET
ejpam-4665	48	14	point	point	NOUN
ejpam-4665	48	15	-	-	PUNCT
ejpam-4665	48	16	wise	wise	ADJ
ejpam-4665	48	17	non	non	ADJ
ejpam-4665	48	18	-	-	ADJ
ejpam-4665	48	19	dominating	dominating	ADJ
ejpam-4665	48	20	set	set	NOUN
ejpam-4665	48	21	of	of	ADP
ejpam-4665	48	22	g	g	PROPN
ejpam-4665	48	23	if	if	SCONJ
ejpam-4665	48	24	for	for	ADP
ejpam-4665	48	25	each	each	DET
ejpam-4665	48	26	v	v	NUM
ejpam-4665	48	27	∈	∈	PROPN
ejpam-4665	48	28	v	v	NOUN
ejpam-4665	48	29	(	(	PUNCT
ejpam-4665	48	30	g)\d	g)\d	NOUN
ejpam-4665	48	31	,	,	PUNCT
ejpam-4665	48	32	there	there	PRON
ejpam-4665	48	33	exists	exist	VERB
ejpam-4665	48	34	u	u	NOUN
ejpam-4665	48	35	∈	∈	PROPN
ejpam-4665	48	36	d	d	ADP
ejpam-4665	48	37	such	such	ADJ
ejpam-4665	48	38	that	that	DET
ejpam-4665	48	39	v	v	NOUN
ejpam-4665	48	40	/∈	/∈	PUNCT
ejpam-4665	48	41	ng(u	ng(u	NOUN
ejpam-4665	48	42	)	)	PUNCT
ejpam-4665	48	43	.	.	PUNCT
ejpam-4665	49	1	the	the	DET
ejpam-4665	49	2	smallest	small	ADJ
ejpam-4665	49	3	cardinality	cardinality	NOUN
ejpam-4665	49	4	of	of	ADP
ejpam-4665	49	5	a	a	DET
ejpam-4665	49	6	pointwise	pointwise	ADJ
ejpam-4665	49	7	non	non	ADJ
ejpam-4665	49	8	-	-	ADJ
ejpam-4665	49	9	dominating	dominating	ADJ
ejpam-4665	49	10	set	set	NOUN
ejpam-4665	49	11	of	of	ADP
ejpam-4665	49	12	g	g	NOUN
ejpam-4665	49	13	,	,	PUNCT
ejpam-4665	49	14	denoted	denote	VERB
ejpam-4665	49	15	by	by	ADP
ejpam-4665	49	16	pnd(g	pnd(g	PROPN
ejpam-4665	49	17	)	)	PUNCT
ejpam-4665	49	18	,	,	PUNCT
ejpam-4665	49	19	is	be	AUX
ejpam-4665	49	20	called	call	VERB
ejpam-4665	49	21	the	the	DET
ejpam-4665	49	22	point	point	NOUN
ejpam-4665	49	23	-	-	PUNCT
ejpam-4665	49	24	wise	wise	ADJ
ejpam-4665	49	25	non	non	ADJ
ejpam-4665	49	26	-	-	ADJ
ejpam-4665	49	27	domination	domination	ADJ
ejpam-4665	49	28	number	number	NOUN
ejpam-4665	49	29	of	of	ADP
ejpam-4665	49	30	g.	g.	PROPN
ejpam-4665	49	31	any	any	DET
ejpam-4665	49	32	point	point	NOUN
ejpam-4665	49	33	-	-	PUNCT
ejpam-4665	49	34	wise	wise	ADJ
ejpam-4665	49	35	non	non	ADJ
ejpam-4665	49	36	-	-	ADJ
ejpam-4665	49	37	dominating	dominating	ADJ
ejpam-4665	49	38	set	set	NOUN
ejpam-4665	49	39	d	d	NOUN
ejpam-4665	49	40	of	of	ADP
ejpam-4665	49	41	g	g	NOUN
ejpam-4665	49	42	with	with	ADP
ejpam-4665	49	43	|d|	|d|	PROPN
ejpam-4665	49	44	=	=	SYM
ejpam-4665	49	45	pnd(g	pnd(g	PROPN
ejpam-4665	49	46	)	)	PUNCT
ejpam-4665	49	47	,	,	PUNCT
ejpam-4665	49	48	is	be	AUX
ejpam-4665	49	49	called	call	VERB
ejpam-4665	49	50	a	a	DET
ejpam-4665	49	51	pnd	pnd	NOUN
ejpam-4665	49	52	-	-	PUNCT
ejpam-4665	49	53	set	set	NOUN
ejpam-4665	49	54	of	of	ADP
ejpam-4665	49	55	g.	g.	PROPN
ejpam-4665	49	56	definition	definition	NOUN
ejpam-4665	49	57	3	3	NUM
ejpam-4665	49	58	.	.	PUNCT
ejpam-4665	50	1	[	[	X
ejpam-4665	50	2	11	11	NUM
ejpam-4665	50	3	]	]	X
ejpam-4665	50	4	a	a	DET
ejpam-4665	50	5	2	2	NUM
ejpam-4665	50	6	-	-	PUNCT
ejpam-4665	50	7	locating	locate	VERB
ejpam-4665	50	8	set	set	NOUN
ejpam-4665	50	9	s	s	PROPN
ejpam-4665	50	10	⊆	⊆	NUM
ejpam-4665	50	11	v	v	NOUN
ejpam-4665	50	12	(	(	PUNCT
ejpam-4665	50	13	g	g	NOUN
ejpam-4665	50	14	)	)	PUNCT
ejpam-4665	50	15	which	which	PRON
ejpam-4665	50	16	is	be	AUX
ejpam-4665	50	17	point	point	ADV
ejpam-4665	50	18	-	-	PUNCT
ejpam-4665	50	19	wise	wise	ADJ
ejpam-4665	50	20	non	non	ADJ
ejpam-4665	50	21	-	-	ADJ
ejpam-4665	50	22	dominating	dominating	NOUN
ejpam-4665	50	23	is	be	AUX
ejpam-4665	50	24	called	call	VERB
ejpam-4665	50	25	a	a	DET
ejpam-4665	50	26	2	2	NUM
ejpam-4665	50	27	-	-	PUNCT
ejpam-4665	50	28	locating	locate	VERB
ejpam-4665	50	29	point	point	NOUN
ejpam-4665	50	30	-	-	PUNCT
ejpam-4665	50	31	wise	wise	ADJ
ejpam-4665	50	32	non	non	ADJ
ejpam-4665	50	33	-	-	ADJ
ejpam-4665	50	34	dominating	dominating	ADJ
ejpam-4665	50	35	set	set	NOUN
ejpam-4665	50	36	in	in	ADP
ejpam-4665	50	37	g.	g.	PROPN
ejpam-4665	50	38	the	the	DET
ejpam-4665	50	39	minimum	minimum	ADJ
ejpam-4665	50	40	cardinality	cardinality	NOUN
ejpam-4665	50	41	of	of	ADP
ejpam-4665	50	42	a	a	DET
ejpam-4665	50	43	2locating	2locating	NUM
ejpam-4665	50	44	point	point	NOUN
ejpam-4665	50	45	-	-	PUNCT
ejpam-4665	50	46	wise	wise	ADJ
ejpam-4665	50	47	non	non	ADJ
ejpam-4665	50	48	-	-	ADJ
ejpam-4665	50	49	dominating	dominating	ADJ
ejpam-4665	50	50	set	set	NOUN
ejpam-4665	50	51	in	in	ADP
ejpam-4665	50	52	g	g	NOUN
ejpam-4665	50	53	,	,	PUNCT
ejpam-4665	50	54	denoted	denote	VERB
ejpam-4665	50	55	by	by	ADP
ejpam-4665	50	56	lnpnd	lnpnd	ADJ
ejpam-4665	50	57	2	2	NUM
ejpam-4665	50	58	(	(	PUNCT
ejpam-4665	50	59	g	g	NOUN
ejpam-4665	50	60	)	)	PUNCT
ejpam-4665	50	61	is	be	AUX
ejpam-4665	50	62	called	call	VERB
ejpam-4665	50	63	the	the	DET
ejpam-4665	50	64	2	2	NUM
ejpam-4665	50	65	-	-	PUNCT
ejpam-4665	50	66	locating	locate	VERB
ejpam-4665	50	67	point	point	NOUN
ejpam-4665	50	68	-	-	PUNCT
ejpam-4665	50	69	wise	wise	ADJ
ejpam-4665	50	70	non	non	ADJ
ejpam-4665	50	71	-	-	ADJ
ejpam-4665	50	72	domination	domination	ADJ
ejpam-4665	50	73	number	number	NOUN
ejpam-4665	50	74	of	of	ADP
ejpam-4665	50	75	g.	g.	PROPN
ejpam-4665	50	76	any	any	DET
ejpam-4665	50	77	2	2	NUM
ejpam-4665	50	78	-	-	PUNCT
ejpam-4665	50	79	locating	locate	VERB
ejpam-4665	50	80	point	point	NOUN
ejpam-4665	50	81	-	-	PUNCT
ejpam-4665	50	82	wise	wise	ADJ
ejpam-4665	50	83	non	non	ADJ
ejpam-4665	50	84	-	-	ADJ
ejpam-4665	50	85	dominating	dominating	ADJ
ejpam-4665	50	86	set	set	NOUN
ejpam-4665	50	87	of	of	ADP
ejpam-4665	50	88	cardinality	cardinality	PROPN
ejpam-4665	50	89	lnpnd	lnpnd	PROPN
ejpam-4665	50	90	2	2	NUM
ejpam-4665	50	91	(	(	PUNCT
ejpam-4665	50	92	g	g	NOUN
ejpam-4665	50	93	)	)	PUNCT
ejpam-4665	50	94	is	be	AUX
ejpam-4665	50	95	then	then	ADV
ejpam-4665	50	96	referred	refer	VERB
ejpam-4665	50	97	to	to	ADP
ejpam-4665	50	98	as	as	ADP
ejpam-4665	50	99	a	a	DET
ejpam-4665	50	100	lnpnd	lnpnd	ADJ
ejpam-4665	50	101	2	2	NUM
ejpam-4665	50	102	-set	-set	PUNCT
ejpam-4665	50	103	in	in	ADP
ejpam-4665	50	104	g.	g.	PROPN
ejpam-4665	50	105	definition	definition	NOUN
ejpam-4665	50	106	4	4	NUM
ejpam-4665	50	107	.	.	PUNCT
ejpam-4665	51	1	a	a	DET
ejpam-4665	51	2	set	set	NOUN
ejpam-4665	51	3	s	s	NOUN
ejpam-4665	51	4	⊆	⊆	NUM
ejpam-4665	51	5	v	v	NOUN
ejpam-4665	51	6	(	(	PUNCT
ejpam-4665	51	7	g	g	NOUN
ejpam-4665	51	8	)	)	PUNCT
ejpam-4665	51	9	is	be	AUX
ejpam-4665	51	10	a	a	DET
ejpam-4665	51	11	restrained	restrained	ADJ
ejpam-4665	51	12	2	2	NUM
ejpam-4665	51	13	-	-	PUNCT
ejpam-4665	51	14	locating	locate	VERB
ejpam-4665	51	15	point	point	NOUN
ejpam-4665	51	16	-	-	PUNCT
ejpam-4665	51	17	wise	wise	ADJ
ejpam-4665	51	18	non	non	ADJ
ejpam-4665	51	19	-	-	ADJ
ejpam-4665	51	20	dominating	dominating	ADJ
ejpam-4665	51	21	set	set	NOUN
ejpam-4665	51	22	in	in	ADP
ejpam-4665	51	23	g	g	PROPN
ejpam-4665	51	24	if	if	SCONJ
ejpam-4665	51	25	s	s	VERB
ejpam-4665	51	26	is	be	AUX
ejpam-4665	51	27	a	a	DET
ejpam-4665	51	28	2	2	NUM
ejpam-4665	51	29	-	-	PUNCT
ejpam-4665	51	30	locating	locate	VERB
ejpam-4665	51	31	point	point	NOUN
ejpam-4665	51	32	-	-	PUNCT
ejpam-4665	51	33	wise	wise	ADJ
ejpam-4665	51	34	non	non	ADJ
ejpam-4665	51	35	-	-	ADJ
ejpam-4665	51	36	dominating	dominating	ADJ
ejpam-4665	51	37	set	set	NOUN
ejpam-4665	51	38	in	in	ADP
ejpam-4665	51	39	g	g	PROPN
ejpam-4665	51	40	and	and	CCONJ
ejpam-4665	51	41	s	s	PART
ejpam-4665	51	42	=	=	SYM
ejpam-4665	51	43	v	v	X
ejpam-4665	51	44	(	(	PUNCT
ejpam-4665	51	45	g	g	NOUN
ejpam-4665	51	46	)	)	PUNCT
ejpam-4665	51	47	or	or	CCONJ
ejpam-4665	51	48	⟨v	⟨v	NUM
ejpam-4665	51	49	(	(	PUNCT
ejpam-4665	51	50	g)\s⟩	g)\s⟩	PROPN
ejpam-4665	51	51	has	have	AUX
ejpam-4665	51	52	no	no	DET
ejpam-4665	51	53	isolated	isolated	ADJ
ejpam-4665	51	54	vertex	vertex	NOUN
ejpam-4665	51	55	.	.	PUNCT
ejpam-4665	52	1	the	the	DET
ejpam-4665	52	2	restrained	restrained	ADJ
ejpam-4665	52	3	2	2	NUM
ejpam-4665	52	4	-	-	PUNCT
ejpam-4665	52	5	locating	locate	VERB
ejpam-4665	52	6	point	point	NOUN
ejpam-4665	52	7	-	-	PUNCT
ejpam-4665	52	8	wise	wise	ADJ
ejpam-4665	52	9	non	non	ADJ
ejpam-4665	52	10	-	-	ADJ
ejpam-4665	52	11	dominating	dominating	ADJ
ejpam-4665	52	12	number	number	NOUN
ejpam-4665	52	13	of	of	ADP
ejpam-4665	52	14	g	g	NOUN
ejpam-4665	52	15	,	,	PUNCT
ejpam-4665	52	16	denoted	denote	VERB
ejpam-4665	52	17	by	by	ADP
ejpam-4665	52	18	rlnpnd	rlnpnd	NOUN
ejpam-4665	52	19	2	2	NUM
ejpam-4665	52	20	(	(	PUNCT
ejpam-4665	52	21	g	g	NOUN
ejpam-4665	52	22	)	)	PUNCT
ejpam-4665	52	23	,	,	PUNCT
ejpam-4665	52	24	is	be	AUX
ejpam-4665	52	25	the	the	DET
ejpam-4665	52	26	smallest	small	ADJ
ejpam-4665	52	27	cardinality	cardinality	NOUN
ejpam-4665	52	28	of	of	ADP
ejpam-4665	52	29	a	a	DET
ejpam-4665	52	30	restrained	restrained	ADJ
ejpam-4665	52	31	2	2	NUM
ejpam-4665	52	32	-	-	PUNCT
ejpam-4665	52	33	locating	locate	VERB
ejpam-4665	52	34	point	point	NOUN
ejpam-4665	52	35	-	-	PUNCT
ejpam-4665	52	36	wise	wise	ADV
ejpam-4665	52	37	nondominating	nondominate	VERB
ejpam-4665	52	38	set	set	NOUN
ejpam-4665	52	39	in	in	ADP
ejpam-4665	52	40	g.	g.	PROPN
ejpam-4665	52	41	a	a	DET
ejpam-4665	52	42	restrained	restrain	VERB
ejpam-4665	52	43	2	2	NUM
ejpam-4665	52	44	-	-	PUNCT
ejpam-4665	52	45	locating	locate	VERB
ejpam-4665	52	46	point	point	NOUN
ejpam-4665	52	47	-	-	PUNCT
ejpam-4665	52	48	wise	wise	ADJ
ejpam-4665	52	49	non	non	ADJ
ejpam-4665	52	50	-	-	ADJ
ejpam-4665	52	51	dominating	dominating	ADJ
ejpam-4665	52	52	set	set	NOUN
ejpam-4665	52	53	of	of	ADP
ejpam-4665	52	54	cardinality	cardinality	NOUN
ejpam-4665	52	55	rlnpnd	rlnpnd	NOUN
ejpam-4665	52	56	2	2	NUM
ejpam-4665	52	57	(	(	PUNCT
ejpam-4665	52	58	g	g	NOUN
ejpam-4665	52	59	)	)	PUNCT
ejpam-4665	52	60	is	be	AUX
ejpam-4665	52	61	then	then	ADV
ejpam-4665	52	62	referred	refer	VERB
ejpam-4665	52	63	to	to	ADP
ejpam-4665	52	64	as	as	ADP
ejpam-4665	52	65	an	an	DET
ejpam-4665	52	66	rlnpnd	rlnpnd	NOUN
ejpam-4665	52	67	2	2	NUM
ejpam-4665	52	68	-set	-set	PUNCT
ejpam-4665	52	69	in	in	ADP
ejpam-4665	52	70	g.	g.	PROPN
ejpam-4665	52	71	definition	definition	NOUN
ejpam-4665	52	72	5	5	NUM
ejpam-4665	52	73	.	.	PUNCT
ejpam-4665	53	1	[	[	X
ejpam-4665	53	2	6	6	NUM
ejpam-4665	53	3	]	]	PUNCT
ejpam-4665	53	4	let	let	VERB
ejpam-4665	53	5	g	g	NOUN
ejpam-4665	53	6	be	be	AUX
ejpam-4665	53	7	any	any	DET
ejpam-4665	53	8	nontrivial	nontrivial	ADJ
ejpam-4665	53	9	connected	connect	VERB
ejpam-4665	53	10	graph	graph	NOUN
ejpam-4665	53	11	and	and	CCONJ
ejpam-4665	53	12	s	s	VERB
ejpam-4665	53	13	⊆	⊆	NUM
ejpam-4665	53	14	v	v	NOUN
ejpam-4665	53	15	(	(	PUNCT
ejpam-4665	53	16	g	g	NOUN
ejpam-4665	53	17	)	)	PUNCT
ejpam-4665	53	18	.	.	PUNCT
ejpam-4665	54	1	s	s	PART
ejpam-4665	54	2	is	be	AUX
ejpam-4665	54	3	a	a	DET
ejpam-4665	54	4	(	(	PUNCT
ejpam-4665	54	5	2	2	NUM
ejpam-4665	54	6	,	,	PUNCT
ejpam-4665	54	7	2)locating	2)locating	NUM
ejpam-4665	54	8	(	(	PUNCT
ejpam-4665	54	9	(	(	PUNCT
ejpam-4665	54	10	2	2	NUM
ejpam-4665	54	11	,	,	PUNCT
ejpam-4665	54	12	1)-locating	1)-locating	NUM
ejpam-4665	54	13	,	,	PUNCT
ejpam-4665	54	14	respectively	respectively	ADV
ejpam-4665	54	15	)	)	PUNCT
ejpam-4665	54	16	set	set	VERB
ejpam-4665	54	17	in	in	ADP
ejpam-4665	54	18	g	g	PROPN
ejpam-4665	54	19	if	if	SCONJ
ejpam-4665	54	20	s	s	NOUN
ejpam-4665	54	21	is	be	AUX
ejpam-4665	54	22	2	2	NUM
ejpam-4665	54	23	-	-	PUNCT
ejpam-4665	54	24	locating	locate	VERB
ejpam-4665	54	25	and	and	CCONJ
ejpam-4665	54	26	|ng(y)∩	|ng(y)∩	NOUN
ejpam-4665	54	27	s|	s|	VERB
ejpam-4665	54	28	≤	≤	NUM
ejpam-4665	54	29	|s|	|s|	PROPN
ejpam-4665	54	30	−	−	PROPN
ejpam-4665	54	31	2	2	NUM
ejpam-4665	54	32	(	(	PUNCT
ejpam-4665	54	33	|ng(y)∩s|	|ng(y)∩s|	NOUN
ejpam-4665	54	34	≤	≤	X
ejpam-4665	54	35	|s|−	|s|−	NOUN
ejpam-4665	54	36	1	1	NUM
ejpam-4665	54	37	,	,	PUNCT
ejpam-4665	54	38	respectively	respectively	ADV
ejpam-4665	54	39	)	)	PUNCT
ejpam-4665	54	40	,	,	PUNCT
ejpam-4665	54	41	for	for	ADP
ejpam-4665	54	42	all	all	DET
ejpam-4665	54	43	y	y	PROPN
ejpam-4665	54	44	∈	∈	PROPN
ejpam-4665	54	45	v	v	NOUN
ejpam-4665	54	46	(	(	PUNCT
ejpam-4665	54	47	g	g	NOUN
ejpam-4665	54	48	)	)	PUNCT
ejpam-4665	54	49	.	.	PUNCT
ejpam-4665	55	1	the	the	DET
ejpam-4665	55	2	(	(	PUNCT
ejpam-4665	55	3	2	2	NUM
ejpam-4665	55	4	,	,	PUNCT
ejpam-4665	55	5	2)-locating	2)-locating	NUM
ejpam-4665	55	6	(	(	PUNCT
ejpam-4665	55	7	(	(	PUNCT
ejpam-4665	55	8	2	2	NUM
ejpam-4665	55	9	,	,	PUNCT
ejpam-4665	55	10	1)-locating	1)-locating	NUM
ejpam-4665	55	11	,	,	PUNCT
ejpam-4665	55	12	respectively	respectively	ADV
ejpam-4665	55	13	)	)	PUNCT
ejpam-4665	55	14	number	number	NOUN
ejpam-4665	55	15	of	of	ADP
ejpam-4665	55	16	g	g	NOUN
ejpam-4665	55	17	,	,	PUNCT
ejpam-4665	55	18	denoted	denote	VERB
ejpam-4665	55	19	by	by	ADP
ejpam-4665	55	20	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4665	55	21	)	)	PUNCT
ejpam-4665	55	22	(	(	PUNCT
ejpam-4665	55	23	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4665	55	24	)	)	PUNCT
ejpam-4665	55	25	,	,	PUNCT
ejpam-4665	55	26	respectively	respectively	ADV
ejpam-4665	55	27	)	)	PUNCT
ejpam-4665	55	28	,	,	PUNCT
ejpam-4665	55	29	is	be	AUX
ejpam-4665	55	30	the	the	DET
ejpam-4665	55	31	smallest	small	ADJ
ejpam-4665	55	32	cardinality	cardinality	NOUN
ejpam-4665	55	33	of	of	ADP
ejpam-4665	55	34	a	a	DET
ejpam-4665	55	35	(	(	PUNCT
ejpam-4665	55	36	2	2	NUM
ejpam-4665	55	37	,	,	PUNCT
ejpam-4665	55	38	2)-locating	2)-locating	NUM
ejpam-4665	55	39	(	(	PUNCT
ejpam-4665	55	40	(	(	PUNCT
ejpam-4665	55	41	2	2	NUM
ejpam-4665	55	42	,	,	PUNCT
ejpam-4665	55	43	1)-locating	1)-locating	NUM
ejpam-4665	55	44	,	,	PUNCT
ejpam-4665	55	45	respectively	respectively	ADV
ejpam-4665	55	46	)	)	PUNCT
ejpam-4665	55	47	set	set	VERB
ejpam-4665	55	48	in	in	ADP
ejpam-4665	55	49	g.	g.	PROPN
ejpam-4665	55	50	a	a	PRON
ejpam-4665	55	51	(	(	PUNCT
ejpam-4665	55	52	2	2	NUM
ejpam-4665	55	53	,	,	PUNCT
ejpam-4665	55	54	2)-locating	2)-locating	NUM
ejpam-4665	55	55	(	(	PUNCT
ejpam-4665	55	56	(	(	PUNCT
ejpam-4665	55	57	2	2	NUM
ejpam-4665	55	58	,	,	PUNCT
ejpam-4665	55	59	1)-locating	1)-locating	NUM
ejpam-4665	55	60	,	,	PUNCT
ejpam-4665	55	61	respectively	respectively	ADV
ejpam-4665	55	62	)	)	PUNCT
ejpam-4665	55	63	set	set	VERB
ejpam-4665	55	64	in	in	ADP
ejpam-4665	55	65	g	g	NOUN
ejpam-4665	55	66	of	of	ADP
ejpam-4665	55	67	cardinality	cardinality	NOUN
ejpam-4665	55	68	ln(2,2)(g	ln(2,2)(g	PROPN
ejpam-4665	55	69	)	)	PUNCT
ejpam-4665	55	70	(	(	PUNCT
ejpam-4665	55	71	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4665	55	72	)	)	PUNCT
ejpam-4665	55	73	,	,	PUNCT
ejpam-4665	55	74	respectively	respectively	ADV
ejpam-4665	55	75	)	)	PUNCT
ejpam-4665	55	76	is	be	AUX
ejpam-4665	55	77	referred	refer	VERB
ejpam-4665	55	78	to	to	ADP
ejpam-4665	55	79	as	as	ADP
ejpam-4665	55	80	an	an	DET
ejpam-4665	55	81	ln(2,2)-set	ln(2,2)-set	NOUN
ejpam-4665	55	82	(	(	PUNCT
ejpam-4665	55	83	ln(2,1)-set	ln(2,1)-set	PROPN
ejpam-4665	55	84	,	,	PUNCT
ejpam-4665	55	85	respectively	respectively	ADV
ejpam-4665	55	86	)	)	PUNCT
ejpam-4665	55	87	in	in	ADP
ejpam-4665	55	88	g.	g.	PROPN
ejpam-4665	55	89	definition	definition	NOUN
ejpam-4665	55	90	6	6	NUM
ejpam-4665	55	91	.	.	PUNCT
ejpam-4665	56	1	[	[	X
ejpam-4665	56	2	11	11	NUM
ejpam-4665	56	3	]	]	X
ejpam-4665	56	4	a	a	PRON
ejpam-4665	56	5	(	(	PUNCT
ejpam-4665	56	6	2,2)-locating	2,2)-locating	NUM
ejpam-4665	56	7	(	(	PUNCT
ejpam-4665	56	8	(	(	PUNCT
ejpam-4665	56	9	2,1)-locating	2,1)-locating	NUM
ejpam-4665	56	10	,	,	PUNCT
ejpam-4665	56	11	respectively	respectively	ADV
ejpam-4665	56	12	)	)	PUNCT
ejpam-4665	56	13	set	set	VERB
ejpam-4665	56	14	s	s	PROPN
ejpam-4665	56	15	⊆	⊆	NUM
ejpam-4665	56	16	v	v	NOUN
ejpam-4665	56	17	(	(	PUNCT
ejpam-4665	56	18	g	g	NOUN
ejpam-4665	56	19	)	)	PUNCT
ejpam-4665	56	20	which	which	PRON
ejpam-4665	56	21	is	be	AUX
ejpam-4665	56	22	a	a	DET
ejpam-4665	56	23	point	point	NOUN
ejpam-4665	56	24	-	-	PUNCT
ejpam-4665	56	25	wise	wise	ADJ
ejpam-4665	56	26	non	non	ADJ
ejpam-4665	56	27	-	-	ADJ
ejpam-4665	56	28	dominating	dominating	NOUN
ejpam-4665	56	29	is	be	AUX
ejpam-4665	56	30	called	call	VERB
ejpam-4665	56	31	a	a	DET
ejpam-4665	56	32	(	(	PUNCT
ejpam-4665	56	33	2,2)-locating	2,2)-locating	NUM
ejpam-4665	56	34	point	point	ADV
ejpam-4665	56	35	-	-	PUNCT
ejpam-4665	56	36	wise	wise	ADJ
ejpam-4665	56	37	non	non	ADJ
ejpam-4665	56	38	-	-	ADJ
ejpam-4665	56	39	dominating	dominating	ADJ
ejpam-4665	56	40	(	(	PUNCT
ejpam-4665	56	41	(	(	PUNCT
ejpam-4665	56	42	2,1)locating	2,1)locating	NUM
ejpam-4665	56	43	point	point	NOUN
ejpam-4665	56	44	-	-	PUNCT
ejpam-4665	56	45	wise	wise	ADJ
ejpam-4665	56	46	non	non	ADJ
ejpam-4665	56	47	-	-	ADJ
ejpam-4665	56	48	dominating	dominating	ADJ
ejpam-4665	56	49	,	,	PUNCT
ejpam-4665	56	50	respectively	respectively	ADV
ejpam-4665	56	51	)	)	PUNCT
ejpam-4665	56	52	set	set	VERB
ejpam-4665	56	53	in	in	ADP
ejpam-4665	56	54	g.	g.	PROPN
ejpam-4665	56	55	the	the	DET
ejpam-4665	56	56	minimum	minimum	ADJ
ejpam-4665	56	57	cardinality	cardinality	NOUN
ejpam-4665	56	58	of	of	ADP
ejpam-4665	56	59	a	a	DET
ejpam-4665	56	60	(	(	PUNCT
ejpam-4665	56	61	2,2)-locating	2,2)-locating	NUM
ejpam-4665	56	62	point	point	ADV
ejpam-4665	56	63	-	-	PUNCT
ejpam-4665	56	64	wise	wise	ADJ
ejpam-4665	56	65	non	non	ADJ
ejpam-4665	56	66	-	-	ADJ
ejpam-4665	56	67	dominating	dominating	ADJ
ejpam-4665	56	68	(	(	PUNCT
ejpam-4665	56	69	(	(	PUNCT
ejpam-4665	56	70	2,1)-locating	2,1)-locating	NUM
ejpam-4665	56	71	point	point	NOUN
ejpam-4665	56	72	-	-	PUNCT
ejpam-4665	56	73	wise	wise	ADJ
ejpam-4665	56	74	non	non	ADJ
ejpam-4665	56	75	-	-	ADJ
ejpam-4665	56	76	dominating	dominating	ADJ
ejpam-4665	56	77	,	,	PUNCT
ejpam-4665	56	78	respectively	respectively	ADV
ejpam-4665	56	79	)	)	PUNCT
ejpam-4665	56	80	set	set	VERB
ejpam-4665	56	81	in	in	ADP
ejpam-4665	56	82	g	g	NOUN
ejpam-4665	56	83	,	,	PUNCT
ejpam-4665	56	84	denoted	denote	VERB
ejpam-4665	56	85	by	by	ADP
ejpam-4665	56	86	lnpnd	lnpnd	ADJ
ejpam-4665	56	87	(	(	PUNCT
ejpam-4665	56	88	2,2)(g	2,2)(g	NUM
ejpam-4665	56	89	)	)	PUNCT
ejpam-4665	56	90	(	(	PUNCT
ejpam-4665	56	91	lnpnd	lnpnd	ADJ
ejpam-4665	56	92	(	(	PUNCT
ejpam-4665	56	93	2,1)(g),respectively	2,1)(g),respectively	NUM
ejpam-4665	56	94	)	)	PUNCT
ejpam-4665	56	95	is	be	AUX
ejpam-4665	56	96	called	call	VERB
ejpam-4665	56	97	the	the	DET
ejpam-4665	56	98	(	(	PUNCT
ejpam-4665	56	99	2,2)locating	2,2)locating	NUM
ejpam-4665	56	100	point	point	NOUN
ejpam-4665	56	101	-	-	PUNCT
ejpam-4665	56	102	wise	wise	ADJ
ejpam-4665	56	103	non	non	ADJ
ejpam-4665	56	104	-	-	NOUN
ejpam-4665	56	105	domination	domination	ADJ
ejpam-4665	56	106	(	(	PUNCT
ejpam-4665	56	107	(	(	PUNCT
ejpam-4665	56	108	2,1)-locating	2,1)-locating	NUM
ejpam-4665	56	109	point	point	NOUN
ejpam-4665	56	110	-	-	PUNCT
ejpam-4665	56	111	wise	wise	ADJ
ejpam-4665	56	112	non	non	ADJ
ejpam-4665	56	113	-	-	ADJ
ejpam-4665	56	114	domination	domination	ADJ
ejpam-4665	56	115	)	)	PUNCT
ejpam-4665	56	116	number	number	NOUN
ejpam-4665	56	117	of	of	ADP
ejpam-4665	56	118	g.	g.	PROPN
ejpam-4665	56	119	any	any	PRON
ejpam-4665	56	120	(	(	PUNCT
ejpam-4665	56	121	2,2)-locating	2,2)-locating	NUM
ejpam-4665	56	122	point	point	ADV
ejpam-4665	56	123	-	-	PUNCT
ejpam-4665	56	124	wise	wise	ADJ
ejpam-4665	56	125	non	non	ADJ
ejpam-4665	56	126	-	-	ADJ
ejpam-4665	56	127	dominating	dominating	ADJ
ejpam-4665	56	128	(	(	PUNCT
ejpam-4665	56	129	(	(	PUNCT
ejpam-4665	56	130	2,1)-locating	2,1)-locating	NUM
ejpam-4665	56	131	point	point	NOUN
ejpam-4665	56	132	-	-	PUNCT
ejpam-4665	56	133	wise	wise	ADJ
ejpam-4665	56	134	non	non	ADJ
ejpam-4665	56	135	-	-	ADJ
ejpam-4665	56	136	dominating	dominating	ADJ
ejpam-4665	56	137	,	,	PUNCT
ejpam-4665	56	138	respectively	respectively	ADV
ejpam-4665	56	139	)	)	PUNCT
ejpam-4665	56	140	set	set	NOUN
ejpam-4665	56	141	of	of	ADP
ejpam-4665	56	142	cardinality	cardinality	PROPN
ejpam-4665	56	143	lnpnd	lnpnd	ADV
ejpam-4665	56	144	(	(	PUNCT
ejpam-4665	56	145	2,2)(g	2,2)(g	NUM
ejpam-4665	56	146	)	)	PUNCT
ejpam-4665	56	147	(	(	PUNCT
ejpam-4665	56	148	lnpnd	lnpnd	ADJ
ejpam-4665	56	149	(	(	PUNCT
ejpam-4665	56	150	2,1)(g	2,1)(g	NUM
ejpam-4665	56	151	)	)	PUNCT
ejpam-4665	56	152	,	,	PUNCT
ejpam-4665	56	153	respectively	respectively	ADV
ejpam-4665	56	154	)	)	PUNCT
ejpam-4665	56	155	is	be	AUX
ejpam-4665	56	156	then	then	ADV
ejpam-4665	56	157	referred	refer	VERB
ejpam-4665	56	158	to	to	ADP
ejpam-4665	56	159	as	as	ADP
ejpam-4665	56	160	a	a	DET
ejpam-4665	56	161	lnpnd	lnpnd	ADJ
ejpam-4665	56	162	(	(	PUNCT
ejpam-4665	56	163	2,2)-set	2,2)-set	NUM
ejpam-4665	56	164	(	(	PUNCT
ejpam-4665	56	165	ln	ln	ADJ
ejpam-4665	56	166	pnd	pnd	NOUN
ejpam-4665	56	167	(	(	PUNCT
ejpam-4665	56	168	2,1)-set	2,1)-set	NUM
ejpam-4665	56	169	)	)	PUNCT
ejpam-4665	56	170	in	in	ADP
ejpam-4665	56	171	g.	g.	PROPN
ejpam-4665	56	172	definition	definition	NOUN
ejpam-4665	56	173	7	7	NUM
ejpam-4665	56	174	.	.	PUNCT
ejpam-4665	57	1	a	a	DET
ejpam-4665	57	2	set	set	NOUN
ejpam-4665	57	3	s	s	NOUN
ejpam-4665	57	4	⊆	⊆	NUM
ejpam-4665	57	5	v	v	NOUN
ejpam-4665	57	6	(	(	PUNCT
ejpam-4665	57	7	g	g	NOUN
ejpam-4665	57	8	)	)	PUNCT
ejpam-4665	57	9	is	be	AUX
ejpam-4665	57	10	a	a	DET
ejpam-4665	57	11	restrained	restrained	ADJ
ejpam-4665	57	12	(	(	PUNCT
ejpam-4665	57	13	2	2	NUM
ejpam-4665	57	14	,	,	PUNCT
ejpam-4665	57	15	2)-locating	2)-locating	NUM
ejpam-4665	57	16	point	point	NOUN
ejpam-4665	57	17	-	-	PUNCT
ejpam-4665	57	18	wise	wise	ADJ
ejpam-4665	57	19	non	non	ADJ
ejpam-4665	57	20	-	-	ADJ
ejpam-4665	57	21	dominating	dominating	ADJ
ejpam-4665	57	22	(	(	PUNCT
ejpam-4665	57	23	(	(	PUNCT
ejpam-4665	57	24	2	2	NUM
ejpam-4665	57	25	,	,	PUNCT
ejpam-4665	57	26	1)-locating	1)-locating	NUM
ejpam-4665	57	27	point	point	NOUN
ejpam-4665	57	28	-	-	PUNCT
ejpam-4665	57	29	wise	wise	ADJ
ejpam-4665	57	30	non	non	ADJ
ejpam-4665	57	31	-	-	ADJ
ejpam-4665	57	32	dominating	dominating	ADJ
ejpam-4665	57	33	,	,	PUNCT
ejpam-4665	57	34	respectively	respectively	ADV
ejpam-4665	57	35	)	)	PUNCT
ejpam-4665	57	36	in	in	ADP
ejpam-4665	57	37	g	g	PROPN
ejpam-4665	57	38	if	if	SCONJ
ejpam-4665	57	39	s	s	VERB
ejpam-4665	57	40	is	be	AUX
ejpam-4665	57	41	a	a	DET
ejpam-4665	57	42	(	(	PUNCT
ejpam-4665	57	43	2	2	NUM
ejpam-4665	57	44	,	,	PUNCT
ejpam-4665	57	45	2)-locating	2)-locating	NUM
ejpam-4665	57	46	pointwise	pointwise	PROPN
ejpam-4665	57	47	non	non	ADJ
ejpam-4665	57	48	-	-	ADJ
ejpam-4665	57	49	dominating	dominating	ADJ
ejpam-4665	57	50	(	(	PUNCT
ejpam-4665	57	51	(	(	PUNCT
ejpam-4665	57	52	2	2	NUM
ejpam-4665	57	53	,	,	PUNCT
ejpam-4665	57	54	1)-locating	1)-locating	NUM
ejpam-4665	57	55	point	point	NOUN
ejpam-4665	57	56	-	-	PUNCT
ejpam-4665	57	57	wise	wise	ADJ
ejpam-4665	57	58	non	non	ADJ
ejpam-4665	57	59	-	-	ADJ
ejpam-4665	57	60	dominating	dominating	ADJ
ejpam-4665	57	61	,	,	PUNCT
ejpam-4665	57	62	respectively	respectively	ADV
ejpam-4665	57	63	)	)	PUNCT
ejpam-4665	57	64	set	set	VERB
ejpam-4665	57	65	in	in	ADP
ejpam-4665	57	66	g	g	PROPN
ejpam-4665	57	67	and	and	CCONJ
ejpam-4665	57	68	s	s	PART
ejpam-4665	57	69	=	=	SYM
ejpam-4665	57	70	v	v	X
ejpam-4665	57	71	(	(	PUNCT
ejpam-4665	57	72	g	g	NOUN
ejpam-4665	57	73	)	)	PUNCT
ejpam-4665	57	74	or	or	CCONJ
ejpam-4665	57	75	⟨v	⟨v	NUM
ejpam-4665	57	76	(	(	PUNCT
ejpam-4665	57	77	g)\s⟩	g)\s⟩	PROPN
ejpam-4665	57	78	has	have	AUX
ejpam-4665	57	79	no	no	DET
ejpam-4665	57	80	isolated	isolated	ADJ
ejpam-4665	57	81	vertex	vertex	NOUN
ejpam-4665	57	82	.	.	PUNCT
ejpam-4665	58	1	the	the	DET
ejpam-4665	58	2	restrained	restrained	ADJ
ejpam-4665	58	3	(	(	PUNCT
ejpam-4665	58	4	2	2	NUM
ejpam-4665	58	5	,	,	PUNCT
ejpam-4665	58	6	2)-locating	2)-locating	NUM
ejpam-4665	58	7	point	point	NOUN
ejpam-4665	58	8	-	-	PUNCT
ejpam-4665	58	9	wise	wise	ADJ
ejpam-4665	58	10	non	non	ADJ
ejpam-4665	58	11	-	-	NOUN
ejpam-4665	58	12	domination	domination	ADJ
ejpam-4665	58	13	(	(	PUNCT
ejpam-4665	58	14	(	(	PUNCT
ejpam-4665	58	15	2	2	NUM
ejpam-4665	58	16	,	,	PUNCT
ejpam-4665	58	17	1)-locating	1)-locating	NUM
ejpam-4665	58	18	point	point	NOUN
ejpam-4665	58	19	-	-	PUNCT
ejpam-4665	58	20	wise	wise	ADJ
ejpam-4665	58	21	non	non	ADJ
ejpam-4665	58	22	-	-	NOUN
ejpam-4665	58	23	domination	domination	ADJ
ejpam-4665	58	24	,	,	PUNCT
ejpam-4665	58	25	respectively	respectively	ADV
ejpam-4665	58	26	)	)	PUNCT
ejpam-4665	58	27	number	number	NOUN
ejpam-4665	58	28	of	of	ADP
ejpam-4665	58	29	g	g	NOUN
ejpam-4665	58	30	,	,	PUNCT
ejpam-4665	58	31	denoted	denote	VERB
ejpam-4665	58	32	by	by	ADP
ejpam-4665	58	33	rlnpnd	rlnpnd	NOUN
ejpam-4665	58	34	(	(	PUNCT
ejpam-4665	58	35	2,2)(g	2,2)(g	NUM
ejpam-4665	58	36	)	)	PUNCT
ejpam-4665	58	37	(	(	PUNCT
ejpam-4665	58	38	rlnpnd	rlnpnd	NOUN
ejpam-4665	58	39	(	(	PUNCT
ejpam-4665	58	40	2,1)(g	2,1)(g	NUM
ejpam-4665	58	41	)	)	PUNCT
ejpam-4665	58	42	,	,	PUNCT
ejpam-4665	58	43	respectively	respectively	ADV
ejpam-4665	58	44	)	)	PUNCT
ejpam-4665	58	45	,	,	PUNCT
ejpam-4665	58	46	is	be	AUX
ejpam-4665	58	47	the	the	DET
ejpam-4665	58	48	smallest	small	ADJ
ejpam-4665	58	49	cardinality	cardinality	NOUN
ejpam-4665	58	50	of	of	ADP
ejpam-4665	58	51	a	a	DET
ejpam-4665	58	52	restrained	restrain	VERB
ejpam-4665	58	53	(	(	PUNCT
ejpam-4665	58	54	2	2	NUM
ejpam-4665	58	55	,	,	PUNCT
ejpam-4665	58	56	2)-locating	2)-locating	NUM
ejpam-4665	58	57	point	point	NOUN
ejpam-4665	58	58	-	-	PUNCT
ejpam-4665	58	59	wise	wise	ADJ
ejpam-4665	58	60	non	non	ADJ
ejpam-4665	58	61	-	-	ADJ
ejpam-4665	58	62	dominating	dominating	ADJ
ejpam-4665	58	63	(	(	PUNCT
ejpam-4665	58	64	(	(	PUNCT
ejpam-4665	58	65	2	2	NUM
ejpam-4665	58	66	,	,	PUNCT
ejpam-4665	58	67	1)-locating	1)-locating	NUM
ejpam-4665	58	68	point	point	NOUN
ejpam-4665	58	69	-	-	PUNCT
ejpam-4665	58	70	wise	wise	ADJ
ejpam-4665	58	71	non	non	ADJ
ejpam-4665	58	72	-	-	ADJ
ejpam-4665	58	73	dominating	dominating	ADJ
ejpam-4665	58	74	,	,	PUNCT
ejpam-4665	58	75	respectively	respectively	ADV
ejpam-4665	58	76	)	)	PUNCT
ejpam-4665	58	77	set	set	VERB
ejpam-4665	58	78	in	in	ADP
ejpam-4665	58	79	g.	g.	PROPN
ejpam-4665	58	80	a	a	DET
ejpam-4665	58	81	restrained	restrain	VERB
ejpam-4665	58	82	(	(	PUNCT
ejpam-4665	58	83	2	2	NUM
ejpam-4665	58	84	,	,	PUNCT
ejpam-4665	58	85	2)-locating	2)-locating	NUM
ejpam-4665	58	86	point	point	NOUN
ejpam-4665	58	87	-	-	PUNCT
ejpam-4665	58	88	wise	wise	ADJ
ejpam-4665	58	89	non	non	ADJ
ejpam-4665	58	90	-	-	ADJ
ejpam-4665	58	91	dominating	dominating	ADJ
ejpam-4665	58	92	(	(	PUNCT
ejpam-4665	58	93	(	(	PUNCT
ejpam-4665	58	94	2	2	NUM
ejpam-4665	58	95	,	,	PUNCT
ejpam-4665	58	96	1)-locating	1)-locating	NUM
ejpam-4665	58	97	a.m.	a.m.	NOUN
ejpam-4665	58	98	mahistrado	mahistrado	NOUN
ejpam-4665	58	99	,	,	PUNCT
ejpam-4665	58	100	h.	h.	PROPN
ejpam-4665	58	101	rara	rara	PROPN
ejpam-4665	58	102	/	/	SYM
ejpam-4665	58	103	eur	eur	PROPN
ejpam-4665	58	104	.	.	PUNCT
ejpam-4665	59	1	j.	j.	PROPN
ejpam-4665	59	2	pure	pure	PROPN
ejpam-4665	59	3	appl	appl	PROPN
ejpam-4665	59	4	.	.	PROPN
ejpam-4665	59	5	math	math	PROPN
ejpam-4665	59	6	,	,	PUNCT
ejpam-4665	59	7	16	16	NUM
ejpam-4665	59	8	(	(	PUNCT
ejpam-4665	59	9	1	1	NUM
ejpam-4665	59	10	)	)	PUNCT
ejpam-4665	59	11	(	(	PUNCT
ejpam-4665	59	12	2023	2023	NUM
ejpam-4665	59	13	)	)	PUNCT
ejpam-4665	59	14	,	,	PUNCT
ejpam-4665	59	15	286	286	NUM
ejpam-4665	59	16	-	-	SYM
ejpam-4665	59	17	303	303	NUM
ejpam-4665	59	18	289	289	NUM
ejpam-4665	59	19	point	point	NOUN
ejpam-4665	59	20	-	-	PUNCT
ejpam-4665	59	21	wise	wise	ADJ
ejpam-4665	59	22	non	non	ADJ
ejpam-4665	59	23	-	-	ADJ
ejpam-4665	59	24	dominating	dominating	ADJ
ejpam-4665	59	25	,	,	PUNCT
ejpam-4665	59	26	respectively	respectively	ADV
ejpam-4665	59	27	)	)	PUNCT
ejpam-4665	59	28	set	set	NOUN
ejpam-4665	59	29	of	of	ADP
ejpam-4665	59	30	cardinality	cardinality	NOUN
ejpam-4665	59	31	rlnpnd	rlnpnd	NOUN
ejpam-4665	59	32	(	(	PUNCT
ejpam-4665	59	33	2,2)(g	2,2)(g	NUM
ejpam-4665	59	34	)	)	PUNCT
ejpam-4665	59	35	(	(	PUNCT
ejpam-4665	59	36	rlnpnd	rlnpnd	NOUN
ejpam-4665	59	37	(	(	PUNCT
ejpam-4665	59	38	2,1)(g	2,1)(g	NUM
ejpam-4665	59	39	)	)	PUNCT
ejpam-4665	59	40	,	,	PUNCT
ejpam-4665	59	41	respectively	respectively	ADV
ejpam-4665	59	42	)	)	PUNCT
ejpam-4665	59	43	is	be	AUX
ejpam-4665	59	44	then	then	ADV
ejpam-4665	59	45	referred	refer	VERB
ejpam-4665	59	46	to	to	ADP
ejpam-4665	59	47	as	as	ADP
ejpam-4665	59	48	an	an	DET
ejpam-4665	59	49	rlnpnd	rlnpnd	NOUN
ejpam-4665	59	50	(	(	PUNCT
ejpam-4665	59	51	2,2)(g	2,2)(g	NUM
ejpam-4665	59	52	)	)	PUNCT
ejpam-4665	59	53	(	(	PUNCT
ejpam-4665	59	54	rlnpnd	rlnpnd	NOUN
ejpam-4665	59	55	(	(	PUNCT
ejpam-4665	59	56	2,1)(g	2,1)(g	NUM
ejpam-4665	59	57	)	)	PUNCT
ejpam-4665	59	58	,	,	PUNCT
ejpam-4665	59	59	respectively)-set	respectively)-set	VERB
ejpam-4665	59	60	in	in	ADP
ejpam-4665	59	61	g.	g.	PROPN
ejpam-4665	59	62	definition	definition	NOUN
ejpam-4665	59	63	8	8	NUM
ejpam-4665	59	64	.	.	PUNCT
ejpam-4665	60	1	a	a	DET
ejpam-4665	60	2	restrained	restrained	ADJ
ejpam-4665	60	3	2	2	NUM
ejpam-4665	60	4	-	-	PUNCT
ejpam-4665	60	5	resolving	resolve	VERB
ejpam-4665	60	6	set	set	NOUN
ejpam-4665	60	7	s	s	PROPN
ejpam-4665	60	8	⊆	⊆	NUM
ejpam-4665	60	9	v	v	NOUN
ejpam-4665	60	10	(	(	PUNCT
ejpam-4665	60	11	g	g	NOUN
ejpam-4665	60	12	)	)	PUNCT
ejpam-4665	60	13	which	which	PRON
ejpam-4665	60	14	is	be	AUX
ejpam-4665	60	15	point	point	ADV
ejpam-4665	60	16	-	-	PUNCT
ejpam-4665	60	17	wise	wise	ADJ
ejpam-4665	60	18	non	non	ADJ
ejpam-4665	60	19	-	-	ADJ
ejpam-4665	60	20	dominating	dominating	NOUN
ejpam-4665	60	21	is	be	AUX
ejpam-4665	60	22	called	call	VERB
ejpam-4665	60	23	a	a	DET
ejpam-4665	60	24	restrained	restrained	ADJ
ejpam-4665	60	25	2	2	NUM
ejpam-4665	60	26	-	-	PUNCT
ejpam-4665	60	27	resolving	resolve	VERB
ejpam-4665	60	28	point	point	NOUN
ejpam-4665	60	29	-	-	PUNCT
ejpam-4665	60	30	wise	wise	ADJ
ejpam-4665	60	31	non	non	ADJ
ejpam-4665	60	32	-	-	ADJ
ejpam-4665	60	33	dominating	dominating	ADJ
ejpam-4665	60	34	set	set	NOUN
ejpam-4665	60	35	in	in	ADP
ejpam-4665	60	36	g.	g.	PROPN
ejpam-4665	60	37	the	the	DET
ejpam-4665	60	38	minimum	minimum	ADJ
ejpam-4665	60	39	cardinality	cardinality	NOUN
ejpam-4665	60	40	of	of	ADP
ejpam-4665	60	41	a	a	DET
ejpam-4665	60	42	restrained	restrained	ADJ
ejpam-4665	60	43	2	2	NUM
ejpam-4665	60	44	-	-	PUNCT
ejpam-4665	60	45	resolving	resolve	VERB
ejpam-4665	60	46	point	point	NOUN
ejpam-4665	60	47	-	-	PUNCT
ejpam-4665	60	48	wise	wise	ADJ
ejpam-4665	60	49	non	non	ADJ
ejpam-4665	60	50	-	-	ADJ
ejpam-4665	60	51	dominating	dominating	ADJ
ejpam-4665	60	52	set	set	NOUN
ejpam-4665	60	53	in	in	ADP
ejpam-4665	60	54	g	g	NOUN
ejpam-4665	60	55	,	,	PUNCT
ejpam-4665	60	56	denoted	denote	VERB
ejpam-4665	60	57	by	by	ADP
ejpam-4665	60	58	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	60	59	(	(	PUNCT
ejpam-4665	60	60	g	g	NOUN
ejpam-4665	60	61	)	)	PUNCT
ejpam-4665	60	62	is	be	AUX
ejpam-4665	60	63	called	call	VERB
ejpam-4665	60	64	the	the	DET
ejpam-4665	60	65	restrained	restrain	VERB
ejpam-4665	60	66	2	2	NUM
ejpam-4665	60	67	-	-	PUNCT
ejpam-4665	60	68	resolving	resolve	VERB
ejpam-4665	60	69	point	point	NOUN
ejpam-4665	60	70	-	-	PUNCT
ejpam-4665	60	71	wise	wise	ADJ
ejpam-4665	60	72	non	non	ADJ
ejpam-4665	60	73	-	-	ADJ
ejpam-4665	60	74	domination	domination	ADJ
ejpam-4665	60	75	number	number	NOUN
ejpam-4665	60	76	of	of	ADP
ejpam-4665	60	77	g.	g.	PROPN
ejpam-4665	60	78	any	any	DET
ejpam-4665	60	79	r2r	r2r	NOUN
ejpam-4665	60	80	-	-	PUNCT
ejpam-4665	60	81	pointwise	pointwise	VERB
ejpam-4665	60	82	non	non	ADJ
ejpam-4665	60	83	-	-	ADJ
ejpam-4665	60	84	dominating	dominating	ADJ
ejpam-4665	60	85	set	set	NOUN
ejpam-4665	60	86	of	of	ADP
ejpam-4665	60	87	cardinality	cardinality	NOUN
ejpam-4665	60	88	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	60	89	(	(	PUNCT
ejpam-4665	60	90	g	g	NOUN
ejpam-4665	60	91	)	)	PUNCT
ejpam-4665	60	92	is	be	AUX
ejpam-4665	60	93	then	then	ADV
ejpam-4665	60	94	referred	refer	VERB
ejpam-4665	60	95	to	to	ADP
ejpam-4665	60	96	as	as	ADP
ejpam-4665	60	97	a	a	DET
ejpam-4665	60	98	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	60	99	-set	-set	VERB
ejpam-4665	60	100	in	in	ADP
ejpam-4665	60	101	g.	g.	PROPN
ejpam-4665	60	102	proposition	proposition	NOUN
ejpam-4665	60	103	1	1	NUM
ejpam-4665	60	104	.	.	PUNCT
ejpam-4665	61	1	[	[	X
ejpam-4665	61	2	9	9	NUM
ejpam-4665	61	3	]	]	PUNCT
ejpam-4665	61	4	let	let	VERB
ejpam-4665	61	5	g	g	PRON
ejpam-4665	61	6	be	be	AUX
ejpam-4665	61	7	a	a	DET
ejpam-4665	61	8	connected	connected	ADJ
ejpam-4665	61	9	graph	graph	NOUN
ejpam-4665	61	10	of	of	ADP
ejpam-4665	61	11	order	order	NOUN
ejpam-4665	61	12	n	n	PRON
ejpam-4665	61	13	≥	≥	NOUN
ejpam-4665	61	14	2	2	NUM
ejpam-4665	61	15	.	.	PUNCT
ejpam-4665	61	16	then	then	ADV
ejpam-4665	61	17	dim2(g	dim2(g	NOUN
ejpam-4665	61	18	)	)	PUNCT
ejpam-4665	61	19	=	=	SYM
ejpam-4665	61	20	2	2	NUM
ejpam-4665	61	21	if	if	SCONJ
ejpam-4665	61	22	and	and	CCONJ
ejpam-4665	61	23	only	only	ADV
ejpam-4665	61	24	if	if	SCONJ
ejpam-4665	61	25	g	g	PROPN
ejpam-4665	61	26	∼=	∼=	PROPN
ejpam-4665	61	27	pn	pn	PROPN
ejpam-4665	61	28	.	.	PROPN
ejpam-4665	61	29	remark	remark	PROPN
ejpam-4665	61	30	1	1	NUM
ejpam-4665	61	31	.	.	PUNCT
ejpam-4665	62	1	[	[	X
ejpam-4665	62	2	11	11	NUM
ejpam-4665	62	3	]	]	PUNCT
ejpam-4665	62	4	for	for	ADP
ejpam-4665	62	5	a	a	DET
ejpam-4665	62	6	path	path	NOUN
ejpam-4665	62	7	pn	pn	NOUN
ejpam-4665	62	8	on	on	ADP
ejpam-4665	62	9	n	n	PRON
ejpam-4665	62	10	vertices	vertex	NOUN
ejpam-4665	62	11	,	,	PUNCT
ejpam-4665	62	12	lnpnd	lnpnd	ADJ
ejpam-4665	62	13	2	2	NUM
ejpam-4665	62	14	(	(	PUNCT
ejpam-4665	62	15	pn	pn	NOUN
ejpam-4665	62	16	)	)	PUNCT
ejpam-4665	62	17	=	=	PRON
ejpam-4665	62	18	{	{	PUNCT
ejpam-4665	62	19	3	3	NUM
ejpam-4665	62	20	,	,	PUNCT
ejpam-4665	62	21	n	n	NOUN
ejpam-4665	62	22	=	=	SYM
ejpam-4665	62	23	3	3	NUM
ejpam-4665	62	24	⌈n+1	⌈n+1	NOUN
ejpam-4665	62	25	2	2	NUM
ejpam-4665	62	26	⌉	⌉	NOUN
ejpam-4665	62	27	,	,	PUNCT
ejpam-4665	62	28	n	n	PRON
ejpam-4665	62	29	≥	≥	NOUN
ejpam-4665	62	30	4	4	NUM
ejpam-4665	62	31	3	3	NUM
ejpam-4665	62	32	.	.	PUNCT
ejpam-4665	62	33	preliminary	preliminary	ADJ
ejpam-4665	62	34	results	result	NOUN
ejpam-4665	62	35	remark	remark	VERB
ejpam-4665	62	36	2	2	NUM
ejpam-4665	62	37	.	.	PUNCT
ejpam-4665	63	1	every	every	DET
ejpam-4665	63	2	nontrivial	nontrivial	ADJ
ejpam-4665	63	3	connected	connect	VERB
ejpam-4665	63	4	graph	graph	NOUN
ejpam-4665	63	5	g	g	PROPN
ejpam-4665	63	6	admits	admit	VERB
ejpam-4665	63	7	a	a	DET
ejpam-4665	63	8	restrained	restrained	ADJ
ejpam-4665	63	9	2	2	NUM
ejpam-4665	63	10	-	-	PUNCT
ejpam-4665	63	11	resolving	resolve	VERB
ejpam-4665	63	12	hop	hop	NOUN
ejpam-4665	63	13	dominating	dominating	NOUN
ejpam-4665	63	14	set	set	NOUN
ejpam-4665	63	15	.	.	PUNCT
ejpam-4665	64	1	indeed	indeed	ADV
ejpam-4665	64	2	,	,	PUNCT
ejpam-4665	64	3	the	the	DET
ejpam-4665	64	4	vertex	vertex	NOUN
ejpam-4665	64	5	set	set	VERB
ejpam-4665	64	6	v	v	NOUN
ejpam-4665	64	7	(	(	PUNCT
ejpam-4665	64	8	g	g	NOUN
ejpam-4665	64	9	)	)	PUNCT
ejpam-4665	64	10	of	of	ADP
ejpam-4665	64	11	g	g	PROPN
ejpam-4665	64	12	is	be	AUX
ejpam-4665	64	13	a	a	DET
ejpam-4665	64	14	restrained	restrained	ADJ
ejpam-4665	64	15	2	2	NUM
ejpam-4665	64	16	-	-	PUNCT
ejpam-4665	64	17	resolving	resolve	VERB
ejpam-4665	64	18	hop	hop	NOUN
ejpam-4665	64	19	dominating	dominating	NOUN
ejpam-4665	64	20	set	set	NOUN
ejpam-4665	64	21	.	.	PUNCT
ejpam-4665	65	1	theorem	theorem	NOUN
ejpam-4665	65	2	1	1	NUM
ejpam-4665	65	3	.	.	PUNCT
ejpam-4665	66	1	if	if	SCONJ
ejpam-4665	66	2	s	s	VERB
ejpam-4665	66	3	⊆	⊆	NUM
ejpam-4665	66	4	v	v	NOUN
ejpam-4665	66	5	(	(	PUNCT
ejpam-4665	66	6	g	g	NOUN
ejpam-4665	66	7	)	)	PUNCT
ejpam-4665	66	8	is	be	AUX
ejpam-4665	66	9	a	a	DET
ejpam-4665	66	10	restrained	restrained	ADJ
ejpam-4665	66	11	2	2	NUM
ejpam-4665	66	12	-	-	PUNCT
ejpam-4665	66	13	resolving	resolve	VERB
ejpam-4665	66	14	hop	hop	NOUN
ejpam-4665	66	15	dominating	dominating	NOUN
ejpam-4665	66	16	set	set	VERB
ejpam-4665	66	17	in	in	ADP
ejpam-4665	66	18	g	g	PROPN
ejpam-4665	66	19	,	,	PUNCT
ejpam-4665	66	20	then	then	ADV
ejpam-4665	66	21	s	s	VERB
ejpam-4665	66	22	is	be	AUX
ejpam-4665	66	23	a	a	DET
ejpam-4665	66	24	restrained	restrained	ADJ
ejpam-4665	66	25	2	2	NUM
ejpam-4665	66	26	-	-	PUNCT
ejpam-4665	66	27	resolving	resolve	VERB
ejpam-4665	66	28	point	point	NOUN
ejpam-4665	66	29	-	-	PUNCT
ejpam-4665	66	30	wise	wise	ADJ
ejpam-4665	66	31	non	non	ADJ
ejpam-4665	66	32	-	-	ADJ
ejpam-4665	66	33	dominating	dominating	ADJ
ejpam-4665	66	34	set	set	NOUN
ejpam-4665	66	35	in	in	ADP
ejpam-4665	66	36	g.	g.	PROPN
ejpam-4665	66	37	proof	proof	PROPN
ejpam-4665	66	38	.	.	PUNCT
ejpam-4665	67	1	suppose	suppose	VERB
ejpam-4665	67	2	s	s	PRON
ejpam-4665	67	3	is	be	AUX
ejpam-4665	67	4	a	a	DET
ejpam-4665	67	5	restrained	restrained	ADJ
ejpam-4665	67	6	2	2	NUM
ejpam-4665	67	7	-	-	PUNCT
ejpam-4665	67	8	resolving	resolve	VERB
ejpam-4665	67	9	hop	hop	NOUN
ejpam-4665	67	10	dominating	dominating	NOUN
ejpam-4665	67	11	set	set	VERB
ejpam-4665	67	12	in	in	ADP
ejpam-4665	67	13	g.	g.	PROPN
ejpam-4665	67	14	let	let	VERB
ejpam-4665	67	15	v	v	NUM
ejpam-4665	67	16	∈	∈	PROPN
ejpam-4665	67	17	v	v	NOUN
ejpam-4665	67	18	(	(	PUNCT
ejpam-4665	67	19	g)\s	g)\s	NOUN
ejpam-4665	67	20	.	.	PUNCT
ejpam-4665	68	1	since	since	SCONJ
ejpam-4665	68	2	s	s	PROPN
ejpam-4665	68	3	is	be	AUX
ejpam-4665	68	4	hop	hop	NOUN
ejpam-4665	68	5	dominating	dominating	NOUN
ejpam-4665	68	6	set	set	NOUN
ejpam-4665	68	7	,	,	PUNCT
ejpam-4665	68	8	there	there	PRON
ejpam-4665	68	9	exists	exist	VERB
ejpam-4665	68	10	z	z	PROPN
ejpam-4665	68	11	∈	∈	PROPN
ejpam-4665	68	12	s	s	VERB
ejpam-4665	68	13	such	such	ADJ
ejpam-4665	68	14	that	that	PRON
ejpam-4665	68	15	dg(v	dg(v	ADJ
ejpam-4665	68	16	,	,	PUNCT
ejpam-4665	68	17	z	z	NOUN
ejpam-4665	68	18	)	)	PUNCT
ejpam-4665	68	19	=	=	SYM
ejpam-4665	68	20	2	2	X
ejpam-4665	68	21	.	.	X
ejpam-4665	68	22	hence	hence	ADV
ejpam-4665	68	23	,	,	PUNCT
ejpam-4665	68	24	v	v	NOUN
ejpam-4665	68	25	/∈	/∈	PUNCT
ejpam-4665	68	26	ng(z	ng(z	NUM
ejpam-4665	68	27	)	)	PUNCT
ejpam-4665	68	28	.	.	PUNCT
ejpam-4665	69	1	this	this	PRON
ejpam-4665	69	2	shows	show	VERB
ejpam-4665	69	3	that	that	SCONJ
ejpam-4665	69	4	s	s	VERB
ejpam-4665	69	5	is	be	AUX
ejpam-4665	69	6	a	a	DET
ejpam-4665	69	7	point	point	NOUN
ejpam-4665	69	8	-	-	PUNCT
ejpam-4665	69	9	wise	wise	ADJ
ejpam-4665	69	10	non	non	ADJ
ejpam-4665	69	11	-	-	ADJ
ejpam-4665	69	12	dominating	dominating	ADJ
ejpam-4665	69	13	set	set	NOUN
ejpam-4665	69	14	of	of	ADP
ejpam-4665	69	15	g.	g.	PROPN
ejpam-4665	69	16	thus	thus	ADV
ejpam-4665	69	17	,	,	PUNCT
ejpam-4665	69	18	s	s	VERB
ejpam-4665	69	19	is	be	AUX
ejpam-4665	69	20	a	a	DET
ejpam-4665	69	21	restrained	restrained	ADJ
ejpam-4665	69	22	2resolving	2resolving	NUM
ejpam-4665	69	23	point	point	ADV
ejpam-4665	69	24	-	-	PUNCT
ejpam-4665	69	25	wise	wise	ADJ
ejpam-4665	69	26	non	non	ADJ
ejpam-4665	69	27	-	-	ADJ
ejpam-4665	69	28	dominating	dominating	ADJ
ejpam-4665	69	29	set	set	NOUN
ejpam-4665	69	30	in	in	ADP
ejpam-4665	69	31	g.	g.	PROPN
ejpam-4665	69	32	the	the	DET
ejpam-4665	69	33	next	next	ADJ
ejpam-4665	69	34	result	result	NOUN
ejpam-4665	69	35	follows	follow	VERB
ejpam-4665	69	36	from	from	ADP
ejpam-4665	69	37	[	[	X
ejpam-4665	69	38	5	5	NUM
ejpam-4665	69	39	]	]	PUNCT
ejpam-4665	69	40	.	.	PUNCT
ejpam-4665	70	1	remark	remark	PROPN
ejpam-4665	70	2	3	3	NUM
ejpam-4665	70	3	.	.	PUNCT
ejpam-4665	71	1	let	let	VERB
ejpam-4665	71	2	g	g	NOUN
ejpam-4665	71	3	be	be	AUX
ejpam-4665	71	4	any	any	DET
ejpam-4665	71	5	nontrivial	nontrivial	ADJ
ejpam-4665	71	6	connected	connect	VERB
ejpam-4665	71	7	graph	graph	NOUN
ejpam-4665	71	8	.	.	PUNCT
ejpam-4665	72	1	then	then	ADV
ejpam-4665	72	2	2	2	NUM
ejpam-4665	72	3	≤	≤	NOUN
ejpam-4665	72	4	rlnpnd	rlnpnd	NOUN
ejpam-4665	72	5	2	2	NUM
ejpam-4665	72	6	(	(	PUNCT
ejpam-4665	72	7	g	g	NOUN
ejpam-4665	72	8	)	)	PUNCT
ejpam-4665	72	9	≤	≤	NOUN
ejpam-4665	72	10	|v	|v	X
ejpam-4665	72	11	(	(	PUNCT
ejpam-4665	72	12	g)|	g)|	PROPN
ejpam-4665	72	13	.	.	PUNCT
ejpam-4665	73	1	moreover	moreover	ADV
ejpam-4665	73	2	,	,	PUNCT
ejpam-4665	73	3	(	(	PUNCT
ejpam-4665	73	4	i	i	NOUN
ejpam-4665	73	5	)	)	PUNCT
ejpam-4665	73	6	rlnpnd	rlnpnd	NOUN
ejpam-4665	73	7	2	2	NUM
ejpam-4665	73	8	(	(	PUNCT
ejpam-4665	73	9	g	g	NOUN
ejpam-4665	73	10	)	)	PUNCT
ejpam-4665	73	11	=	=	SYM
ejpam-4665	73	12	2	2	NUM
ejpam-4665	73	13	if	if	SCONJ
ejpam-4665	73	14	and	and	CCONJ
ejpam-4665	73	15	only	only	ADV
ejpam-4665	73	16	if	if	SCONJ
ejpam-4665	73	17	g	g	PROPN
ejpam-4665	73	18	=	=	SYM
ejpam-4665	73	19	k2	k2	PROPN
ejpam-4665	73	20	.	.	PUNCT
ejpam-4665	74	1	(	(	PUNCT
ejpam-4665	74	2	ii	ii	NOUN
ejpam-4665	74	3	)	)	PUNCT
ejpam-4665	74	4	if	if	SCONJ
ejpam-4665	74	5	g	g	PROPN
ejpam-4665	74	6	is	be	AUX
ejpam-4665	74	7	a	a	DET
ejpam-4665	74	8	connected	connected	ADJ
ejpam-4665	74	9	graph	graph	NOUN
ejpam-4665	74	10	with	with	ADP
ejpam-4665	74	11	2	2	NUM
ejpam-4665	74	12	≤	≤	NOUN
ejpam-4665	74	13	|v	|v	X
ejpam-4665	74	14	(	(	PUNCT
ejpam-4665	74	15	g)|	g)|	VERB
ejpam-4665	74	16	≤	≤	ADJ
ejpam-4665	74	17	4	4	NUM
ejpam-4665	74	18	,	,	PUNCT
ejpam-4665	74	19	then	then	ADV
ejpam-4665	74	20	rlnpnd	rlnpnd	NOUN
ejpam-4665	74	21	2	2	NUM
ejpam-4665	74	22	(	(	PUNCT
ejpam-4665	74	23	g	g	NOUN
ejpam-4665	74	24	)	)	PUNCT
ejpam-4665	74	25	=	=	SYM
ejpam-4665	75	1	|v	|v	PROPN
ejpam-4665	75	2	(	(	PUNCT
ejpam-4665	75	3	g)|	g)|	PROPN
ejpam-4665	75	4	.	.	PUNCT
ejpam-4665	75	5	a.m.	a.m.	PROPN
ejpam-4665	75	6	mahistrado	mahistrado	PROPN
ejpam-4665	75	7	,	,	PUNCT
ejpam-4665	75	8	h.	h.	PROPN
ejpam-4665	75	9	rara	rara	PROPN
ejpam-4665	75	10	/	/	SYM
ejpam-4665	75	11	eur	eur	PROPN
ejpam-4665	75	12	.	.	PUNCT
ejpam-4665	76	1	j.	j.	PROPN
ejpam-4665	76	2	pure	pure	PROPN
ejpam-4665	76	3	appl	appl	PROPN
ejpam-4665	76	4	.	.	PROPN
ejpam-4665	76	5	math	math	PROPN
ejpam-4665	76	6	,	,	PUNCT
ejpam-4665	76	7	16	16	NUM
ejpam-4665	76	8	(	(	PUNCT
ejpam-4665	76	9	1	1	NUM
ejpam-4665	76	10	)	)	PUNCT
ejpam-4665	76	11	(	(	PUNCT
ejpam-4665	76	12	2023	2023	NUM
ejpam-4665	76	13	)	)	PUNCT
ejpam-4665	76	14	,	,	PUNCT
ejpam-4665	76	15	286	286	NUM
ejpam-4665	76	16	-	-	SYM
ejpam-4665	76	17	303	303	NUM
ejpam-4665	76	18	290	290	NUM
ejpam-4665	76	19	proposition	proposition	NOUN
ejpam-4665	76	20	2	2	NUM
ejpam-4665	76	21	.	.	PUNCT
ejpam-4665	77	1	let	let	VERB
ejpam-4665	77	2	g	g	NOUN
ejpam-4665	77	3	be	be	AUX
ejpam-4665	77	4	any	any	DET
ejpam-4665	77	5	nontrivial	nontrivial	ADJ
ejpam-4665	77	6	connected	connect	VERB
ejpam-4665	77	7	graph	graph	NOUN
ejpam-4665	77	8	.	.	PUNCT
ejpam-4665	78	1	then	then	ADV
ejpam-4665	78	2	for	for	ADP
ejpam-4665	78	3	any	any	DET
ejpam-4665	78	4	positive	positive	ADJ
ejpam-4665	78	5	integers	integer	NOUN
ejpam-4665	78	6	n	n	PRON
ejpam-4665	78	7	and	and	CCONJ
ejpam-4665	78	8	k	k	NOUN
ejpam-4665	78	9	,	,	PUNCT
ejpam-4665	78	10	we	we	PRON
ejpam-4665	78	11	have	have	VERB
ejpam-4665	78	12	(	(	PUNCT
ejpam-4665	78	13	i	i	NOUN
ejpam-4665	78	14	)	)	PUNCT
ejpam-4665	78	15	rlnpnd	rlnpnd	NOUN
ejpam-4665	78	16	2	2	NUM
ejpam-4665	78	17	(	(	PUNCT
ejpam-4665	78	18	pn	pn	NOUN
ejpam-4665	78	19	)	)	PUNCT
ejpam-4665	78	20	=	=	SYM
ejpam-4665	79	1	n	n	ADJ
ejpam-4665	79	2	,	,	PUNCT
ejpam-4665	79	3	if	if	SCONJ
ejpam-4665	79	4	2	2	NUM
ejpam-4665	79	5	≤	≤	NOUN
ejpam-4665	79	6	n	n	CCONJ
ejpam-4665	79	7	≤	≤	NOUN
ejpam-4665	79	8	7	7	NUM
ejpam-4665	79	9	;	;	PUNCT
ejpam-4665	79	10	3n+	3n+	NUM
ejpam-4665	79	11	2k	2k	NUM
ejpam-4665	79	12	5	5	NUM
ejpam-4665	79	13	,	,	PUNCT
ejpam-4665	79	14	if	if	SCONJ
ejpam-4665	79	15	n	n	ADV
ejpam-4665	79	16	=	=	PUNCT
ejpam-4665	79	17	k(mod	k(mod	PROPN
ejpam-4665	79	18	5	5	NUM
ejpam-4665	79	19	)	)	PUNCT
ejpam-4665	79	20	,	,	PUNCT
ejpam-4665	79	21	3	3	NUM
ejpam-4665	79	22	≤	≤	NUM
ejpam-4665	79	23	k	k	X
ejpam-4665	79	24	≤	≤	NUM
ejpam-4665	79	25	7	7	NUM
ejpam-4665	79	26	.	.	PUNCT
ejpam-4665	79	27	(	(	PUNCT
ejpam-4665	79	28	ii	ii	NOUN
ejpam-4665	79	29	)	)	PUNCT
ejpam-4665	79	30	rlnpnd	rlnpnd	NOUN
ejpam-4665	79	31	2	2	NUM
ejpam-4665	79	32	(	(	PUNCT
ejpam-4665	79	33	cn	cn	NOUN
ejpam-4665	79	34	)	)	PUNCT
ejpam-4665	79	35	=	=	SYM
ejpam-4665	79	36	n	n	PROPN
ejpam-4665	79	37	,	,	PUNCT
ejpam-4665	79	38	if	if	SCONJ
ejpam-4665	79	39	n	n	NOUN
ejpam-4665	79	40	=	=	SYM
ejpam-4665	79	41	3	3	NUM
ejpam-4665	79	42	,	,	PUNCT
ejpam-4665	79	43	4	4	NUM
ejpam-4665	79	44	;	;	PUNCT
ejpam-4665	79	45	3n+	3n+	NUM
ejpam-4665	79	46	2k	2k	NUM
ejpam-4665	79	47	5	5	NUM
ejpam-4665	79	48	,	,	PUNCT
ejpam-4665	79	49	if	if	SCONJ
ejpam-4665	79	50	n	n	ADV
ejpam-4665	79	51	=	=	PUNCT
ejpam-4665	79	52	k(mod	k(mod	PROPN
ejpam-4665	79	53	5	5	NUM
ejpam-4665	79	54	)	)	PUNCT
ejpam-4665	79	55	,	,	PUNCT
ejpam-4665	79	56	0	0	NUM
ejpam-4665	79	57	≤	≤	NUM
ejpam-4665	79	58	k	k	X
ejpam-4665	79	59	≤	≤	NUM
ejpam-4665	79	60	4	4	NUM
ejpam-4665	79	61	.	.	PUNCT
ejpam-4665	79	62	(	(	PUNCT
ejpam-4665	79	63	iii	iii	NOUN
ejpam-4665	79	64	)	)	PUNCT
ejpam-4665	79	65	for	for	ADP
ejpam-4665	79	66	all	all	PRON
ejpam-4665	79	67	n	n	PRON
ejpam-4665	79	68	≥	≥	NOUN
ejpam-4665	79	69	4	4	NUM
ejpam-4665	79	70	,	,	PUNCT
ejpam-4665	79	71	rlnpnd	rlnpnd	NOUN
ejpam-4665	79	72	(	(	PUNCT
ejpam-4665	79	73	2,2)(pn	2,2)(pn	NUM
ejpam-4665	79	74	)	)	PUNCT
ejpam-4665	79	75	=	=	SYM
ejpam-4665	80	1	n	n	PROPN
ejpam-4665	80	2	,	,	PUNCT
ejpam-4665	80	3	if	if	SCONJ
ejpam-4665	80	4	4	4	NUM
ejpam-4665	80	5	≤	≤	NUM
ejpam-4665	80	6	n	n	CCONJ
ejpam-4665	80	7	≤	≤	NOUN
ejpam-4665	80	8	7	7	NUM
ejpam-4665	80	9	;	;	PUNCT
ejpam-4665	80	10	3n+	3n+	NUM
ejpam-4665	80	11	2k	2k	NUM
ejpam-4665	80	12	5	5	NUM
ejpam-4665	80	13	,	,	PUNCT
ejpam-4665	80	14	if	if	SCONJ
ejpam-4665	80	15	n	n	ADV
ejpam-4665	80	16	=	=	PUNCT
ejpam-4665	80	17	k(mod	k(mod	PROPN
ejpam-4665	80	18	5	5	NUM
ejpam-4665	80	19	)	)	PUNCT
ejpam-4665	80	20	,	,	PUNCT
ejpam-4665	80	21	3	3	NUM
ejpam-4665	80	22	≤	≤	NUM
ejpam-4665	80	23	k	k	X
ejpam-4665	80	24	≤	≤	NUM
ejpam-4665	80	25	7	7	NUM
ejpam-4665	80	26	.	.	PUNCT
ejpam-4665	81	1	for	for	ADP
ejpam-4665	81	2	all	all	DET
ejpam-4665	81	3	n	n	PRON
ejpam-4665	81	4	≥	≥	NUM
ejpam-4665	81	5	6	6	NUM
ejpam-4665	81	6	,	,	PUNCT
ejpam-4665	81	7	rlnpnd	rlnpnd	NOUN
ejpam-4665	81	8	(	(	PUNCT
ejpam-4665	81	9	2,2)(cn	2,2)(cn	NUM
ejpam-4665	81	10	)	)	PUNCT
ejpam-4665	81	11	=	=	SYM
ejpam-4665	82	1	n	n	ADJ
ejpam-4665	82	2	,	,	PUNCT
ejpam-4665	82	3	if	if	SCONJ
ejpam-4665	82	4	n	n	NOUN
ejpam-4665	82	5	=	=	SYM
ejpam-4665	82	6	4	4	NUM
ejpam-4665	82	7	;	;	PUNCT
ejpam-4665	82	8	3n+	3n+	NUM
ejpam-4665	82	9	2k	2k	NUM
ejpam-4665	82	10	5	5	NUM
ejpam-4665	82	11	,	,	PUNCT
ejpam-4665	82	12	if	if	SCONJ
ejpam-4665	82	13	n	n	ADV
ejpam-4665	82	14	=	=	PUNCT
ejpam-4665	82	15	k(mod	k(mod	PROPN
ejpam-4665	82	16	5	5	NUM
ejpam-4665	82	17	)	)	PUNCT
ejpam-4665	82	18	,	,	PUNCT
ejpam-4665	82	19	0	0	NUM
ejpam-4665	82	20	≤	≤	NUM
ejpam-4665	82	21	k	k	X
ejpam-4665	82	22	≤	≤	NUM
ejpam-4665	82	23	4	4	NUM
ejpam-4665	82	24	.	.	PUNCT
ejpam-4665	82	25	(	(	PUNCT
ejpam-4665	82	26	iv	iv	X
ejpam-4665	82	27	)	)	PUNCT
ejpam-4665	82	28	for	for	ADP
ejpam-4665	82	29	all	all	DET
ejpam-4665	82	30	n	n	PRON
ejpam-4665	82	31	≥	≥	NUM
ejpam-4665	82	32	2	2	NUM
ejpam-4665	82	33	,	,	PUNCT
ejpam-4665	82	34	rlnpnd	rlnpnd	NOUN
ejpam-4665	82	35	(	(	PUNCT
ejpam-4665	82	36	2,1)(pn	2,1)(pn	NUM
ejpam-4665	82	37	)	)	PUNCT
ejpam-4665	82	38	=	=	SYM
ejpam-4665	83	1	n	n	ADJ
ejpam-4665	83	2	,	,	PUNCT
ejpam-4665	83	3	if	if	SCONJ
ejpam-4665	83	4	2	2	NUM
ejpam-4665	83	5	≤	≤	NOUN
ejpam-4665	83	6	n	n	CCONJ
ejpam-4665	83	7	≤	≤	NOUN
ejpam-4665	83	8	7	7	NUM
ejpam-4665	83	9	;	;	PUNCT
ejpam-4665	83	10	3n+	3n+	NUM
ejpam-4665	83	11	2k	2k	NUM
ejpam-4665	83	12	5	5	NUM
ejpam-4665	83	13	,	,	PUNCT
ejpam-4665	83	14	if	if	SCONJ
ejpam-4665	83	15	n	n	ADV
ejpam-4665	83	16	=	=	PUNCT
ejpam-4665	83	17	k(mod	k(mod	PROPN
ejpam-4665	83	18	5	5	NUM
ejpam-4665	83	19	)	)	PUNCT
ejpam-4665	83	20	,	,	PUNCT
ejpam-4665	83	21	3	3	NUM
ejpam-4665	83	22	≤	≤	NUM
ejpam-4665	83	23	k	k	X
ejpam-4665	83	24	≤	≤	NUM
ejpam-4665	83	25	7	7	NUM
ejpam-4665	83	26	.	.	PUNCT
ejpam-4665	84	1	for	for	ADP
ejpam-4665	84	2	all	all	DET
ejpam-4665	84	3	n	n	PRON
ejpam-4665	84	4	≥	≥	NOUN
ejpam-4665	84	5	3	3	NUM
ejpam-4665	84	6	,	,	PUNCT
ejpam-4665	84	7	rlnpnd	rlnpnd	NOUN
ejpam-4665	84	8	(	(	PUNCT
ejpam-4665	84	9	2,1)(cn	2,1)(cn	NUM
ejpam-4665	84	10	)	)	PUNCT
ejpam-4665	84	11	=	=	SYM
ejpam-4665	85	1	n	n	ADJ
ejpam-4665	85	2	,	,	PUNCT
ejpam-4665	85	3	if	if	SCONJ
ejpam-4665	85	4	n	n	NOUN
ejpam-4665	85	5	=	=	SYM
ejpam-4665	85	6	3	3	NUM
ejpam-4665	85	7	,	,	PUNCT
ejpam-4665	85	8	4	4	NUM
ejpam-4665	85	9	;	;	PUNCT
ejpam-4665	85	10	3n+	3n+	NUM
ejpam-4665	85	11	2k	2k	NUM
ejpam-4665	85	12	5	5	NUM
ejpam-4665	85	13	,	,	PUNCT
ejpam-4665	85	14	if	if	SCONJ
ejpam-4665	85	15	n	n	ADV
ejpam-4665	85	16	=	=	PUNCT
ejpam-4665	85	17	k(mod	k(mod	PROPN
ejpam-4665	85	18	5	5	NUM
ejpam-4665	85	19	)	)	PUNCT
ejpam-4665	85	20	,	,	PUNCT
ejpam-4665	85	21	0	0	NUM
ejpam-4665	85	22	≤	≤	NUM
ejpam-4665	85	23	k	k	X
ejpam-4665	85	24	≤	≤	NUM
ejpam-4665	85	25	4	4	NUM
ejpam-4665	85	26	.	.	PUNCT
ejpam-4665	86	1	proof	proof	NOUN
ejpam-4665	86	2	.	.	PUNCT
ejpam-4665	87	1	(	(	PUNCT
ejpam-4665	87	2	i	i	NOUN
ejpam-4665	87	3	)	)	PUNCT
ejpam-4665	87	4	let	let	VERB
ejpam-4665	87	5	pn	pn	NOUN
ejpam-4665	87	6	=	=	PUNCT
ejpam-4665	88	1	[	[	X
ejpam-4665	88	2	v1	v1	NOUN
ejpam-4665	88	3	,	,	PUNCT
ejpam-4665	88	4	v2	v2	NOUN
ejpam-4665	88	5	,	,	PUNCT
ejpam-4665	88	6	.	.	PUNCT
ejpam-4665	88	7	.	.	PUNCT
ejpam-4665	88	8	.	.	PUNCT
ejpam-4665	89	1	,	,	PUNCT
ejpam-4665	89	2	vn	vn	X
ejpam-4665	89	3	]	]	PUNCT
ejpam-4665	89	4	and	and	CCONJ
ejpam-4665	89	5	s	s	AUX
ejpam-4665	89	6	be	be	AUX
ejpam-4665	89	7	an	an	DET
ejpam-4665	89	8	rlnpnd	rlnpnd	NOUN
ejpam-4665	89	9	2	2	NUM
ejpam-4665	89	10	set	set	NOUN
ejpam-4665	89	11	of	of	ADP
ejpam-4665	89	12	pn	pn	PROPN
ejpam-4665	89	13	.	.	PUNCT
ejpam-4665	90	1	the	the	DET
ejpam-4665	90	2	case	case	NOUN
ejpam-4665	90	3	where	where	SCONJ
ejpam-4665	90	4	n	n	X
ejpam-4665	90	5	≤	≤	ADV
ejpam-4665	90	6	7	7	NUM
ejpam-4665	90	7	can	can	AUX
ejpam-4665	90	8	be	be	AUX
ejpam-4665	90	9	easily	easily	ADV
ejpam-4665	90	10	verified	verify	VERB
ejpam-4665	90	11	by	by	ADP
ejpam-4665	90	12	remark	remark	NOUN
ejpam-4665	90	13	1	1	NUM
ejpam-4665	90	14	.	.	PUNCT
ejpam-4665	91	1	next	next	ADV
ejpam-4665	91	2	,	,	PUNCT
ejpam-4665	91	3	let	let	VERB
ejpam-4665	91	4	n	n	PRON
ejpam-4665	91	5	≥	≥	X
ejpam-4665	91	6	8	8	NUM
ejpam-4665	91	7	and	and	CCONJ
ejpam-4665	91	8	n	n	PRON
ejpam-4665	91	9	≡	≡	PROPN
ejpam-4665	91	10	k(mod	k(mod	PROPN
ejpam-4665	91	11	5	5	X
ejpam-4665	91	12	)	)	PUNCT
ejpam-4665	91	13	where	where	SCONJ
ejpam-4665	91	14	3	3	NUM
ejpam-4665	91	15	≤	≤	NUM
ejpam-4665	91	16	k	k	X
ejpam-4665	91	17	≤	≤	NUM
ejpam-4665	91	18	7	7	NUM
ejpam-4665	91	19	.	.	PUNCT
ejpam-4665	92	1	then	then	ADV
ejpam-4665	92	2	n	n	NOUN
ejpam-4665	92	3	=	=	NOUN
ejpam-4665	92	4	5r	5r	NOUN
ejpam-4665	92	5	+	+	CCONJ
ejpam-4665	92	6	k.	k.	PROPN
ejpam-4665	92	7	hence	hence	ADV
ejpam-4665	92	8	,	,	PUNCT
ejpam-4665	92	9	r	r	NOUN
ejpam-4665	92	10	=	=	SYM
ejpam-4665	92	11	n−	n−	NOUN
ejpam-4665	92	12	k	k	NOUN
ejpam-4665	92	13	5	5	NUM
ejpam-4665	92	14	.	.	PUNCT
ejpam-4665	93	1	then	then	ADV
ejpam-4665	93	2	the	the	DET
ejpam-4665	93	3	set	set	NOUN
ejpam-4665	93	4	s	s	PART
ejpam-4665	93	5	=	=	PUNCT
ejpam-4665	93	6	{	{	PUNCT
ejpam-4665	93	7	v1	v1	PROPN
ejpam-4665	93	8	,	,	PUNCT
ejpam-4665	93	9	v2	v2	PROPN
ejpam-4665	93	10	,	,	PUNCT
ejpam-4665	93	11	v3	v3	PROPN
ejpam-4665	93	12	,	,	PUNCT
ejpam-4665	93	13	v6	v6	NOUN
ejpam-4665	93	14	,	,	PUNCT
ejpam-4665	93	15	v7	v7	NUM
ejpam-4665	93	16	,	,	PUNCT
ejpam-4665	93	17	v8	v8	PROPN
ejpam-4665	93	18	,	,	PUNCT
ejpam-4665	93	19	v11	v11	NOUN
ejpam-4665	93	20	,	,	PUNCT
ejpam-4665	93	21	v12	v12	VERB
ejpam-4665	93	22	,	,	PUNCT
ejpam-4665	93	23	v13	v13	NOUN
ejpam-4665	93	24	,	,	PUNCT
ejpam-4665	93	25	.	.	PUNCT
ejpam-4665	93	26	.	.	PUNCT
ejpam-4665	93	27	.	.	PUNCT
ejpam-4665	94	1	,	,	PUNCT
ejpam-4665	94	2	v5r+1	v5r+1	INTJ
ejpam-4665	94	3	,	,	PUNCT
ejpam-4665	94	4	v5r+2	v5r+2	NOUN
ejpam-4665	94	5	,	,	PUNCT
ejpam-4665	94	6	.	.	PUNCT
ejpam-4665	94	7	.	.	PUNCT
ejpam-4665	95	1	.	.	PUNCT
ejpam-4665	96	1	,	,	PUNCT
ejpam-4665	96	2	v5r+k	v5r+k	PROPN
ejpam-4665	96	3	}	}	PUNCT
ejpam-4665	96	4	is	be	AUX
ejpam-4665	96	5	an	an	DET
ejpam-4665	96	6	rlnpnd	rlnpnd	NOUN
ejpam-4665	96	7	2	2	NUM
ejpam-4665	96	8	set	set	NOUN
ejpam-4665	96	9	of	of	ADP
ejpam-4665	96	10	pn	pn	PROPN
ejpam-4665	96	11	.	.	PROPN
ejpam-4665	97	1	therefore	therefore	ADV
ejpam-4665	97	2	,	,	PUNCT
ejpam-4665	97	3	|s|	|s|	PROPN
ejpam-4665	97	4	=	=	NOUN
ejpam-4665	97	5	5r	5r	NOUN
ejpam-4665	98	1	+	+	CCONJ
ejpam-4665	98	2	k	k	X
ejpam-4665	98	3	−	−	X
ejpam-4665	98	4	2r	2r	NUM
ejpam-4665	98	5	=	=	PUNCT
ejpam-4665	98	6	3n+	3n+	NUM
ejpam-4665	98	7	2k	2k	NUM
ejpam-4665	98	8	5	5	NUM
ejpam-4665	98	9	.	.	PUNCT
ejpam-4665	99	1	the	the	DET
ejpam-4665	99	2	proofs	proof	NOUN
ejpam-4665	99	3	of	of	ADP
ejpam-4665	99	4	(	(	PUNCT
ejpam-4665	99	5	ii	ii	NOUN
ejpam-4665	99	6	)	)	PUNCT
ejpam-4665	99	7	,	,	PUNCT
ejpam-4665	99	8	(	(	PUNCT
ejpam-4665	99	9	iii	iii	NOUN
ejpam-4665	99	10	)	)	PUNCT
ejpam-4665	99	11	and	and	CCONJ
ejpam-4665	99	12	(	(	PUNCT
ejpam-4665	99	13	iv	iv	X
ejpam-4665	99	14	)	)	PUNCT
ejpam-4665	99	15	are	be	AUX
ejpam-4665	99	16	similar	similar	ADJ
ejpam-4665	99	17	to	to	ADP
ejpam-4665	99	18	(	(	PUNCT
ejpam-4665	99	19	i	i	NOUN
ejpam-4665	99	20	)	)	PUNCT
ejpam-4665	99	21	.	.	PUNCT
ejpam-4665	100	1	theorem	theorem	NOUN
ejpam-4665	100	2	2	2	NUM
ejpam-4665	100	3	.	.	PUNCT
ejpam-4665	101	1	let	let	VERB
ejpam-4665	101	2	g	g	PRON
ejpam-4665	101	3	be	be	AUX
ejpam-4665	101	4	a	a	DET
ejpam-4665	101	5	connected	connected	ADJ
ejpam-4665	101	6	graph	graph	NOUN
ejpam-4665	101	7	.	.	PUNCT
ejpam-4665	102	1	then	then	ADV
ejpam-4665	102	2	2	2	NUM
ejpam-4665	102	3	≤	≤	NOUN
ejpam-4665	102	4	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	102	5	(	(	PUNCT
ejpam-4665	102	6	g	g	NOUN
ejpam-4665	102	7	)	)	PUNCT
ejpam-4665	102	8	≤	≤	NOUN
ejpam-4665	102	9	|v	|v	X
ejpam-4665	102	10	(	(	PUNCT
ejpam-4665	102	11	g)|	g)|	PROPN
ejpam-4665	102	12	.	.	PUNCT
ejpam-4665	103	1	moreover	moreover	ADV
ejpam-4665	103	2	,	,	PUNCT
ejpam-4665	103	3	(	(	PUNCT
ejpam-4665	103	4	i	i	NOUN
ejpam-4665	103	5	)	)	PUNCT
ejpam-4665	103	6	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	103	7	(	(	PUNCT
ejpam-4665	103	8	g	g	NOUN
ejpam-4665	103	9	)	)	PUNCT
ejpam-4665	103	10	=	=	SYM
ejpam-4665	103	11	2	2	NUM
ejpam-4665	103	12	if	if	SCONJ
ejpam-4665	103	13	and	and	CCONJ
ejpam-4665	103	14	only	only	ADV
ejpam-4665	103	15	if	if	SCONJ
ejpam-4665	103	16	g	g	PROPN
ejpam-4665	103	17	is	be	AUX
ejpam-4665	103	18	a	a	DET
ejpam-4665	103	19	path	path	NOUN
ejpam-4665	103	20	pn	pn	NOUN
ejpam-4665	103	21	except	except	SCONJ
ejpam-4665	103	22	n	n	PROPN
ejpam-4665	103	23	=	=	SYM
ejpam-4665	103	24	3	3	NUM
ejpam-4665	103	25	.	.	PUNCT
ejpam-4665	103	26	(	(	PUNCT
ejpam-4665	103	27	ii	ii	NOUN
ejpam-4665	103	28	)	)	PUNCT
ejpam-4665	103	29	if	if	SCONJ
ejpam-4665	103	30	g	g	PROPN
ejpam-4665	103	31	is	be	AUX
ejpam-4665	103	32	a	a	DET
ejpam-4665	103	33	cycle	cycle	NOUN
ejpam-4665	103	34	cn	cn	NOUN
ejpam-4665	103	35	for	for	ADP
ejpam-4665	103	36	n	n	PROPN
ejpam-4665	103	37	̸=	̸=	PROPN
ejpam-4665	103	38	4	4	NUM
ejpam-4665	103	39	,	,	PUNCT
ejpam-4665	103	40	then	then	ADV
ejpam-4665	103	41	rdim2pnd	rdim2pnd	VERB
ejpam-4665	103	42	(	(	PUNCT
ejpam-4665	103	43	cn	cn	PROPN
ejpam-4665	103	44	)	)	PUNCT
ejpam-4665	103	45	=	=	SYM
ejpam-4665	104	1	3	3	X
ejpam-4665	104	2	.	.	PUNCT
ejpam-4665	104	3	proof	proof	NOUN
ejpam-4665	104	4	.	.	PUNCT
ejpam-4665	105	1	(	(	PUNCT
ejpam-4665	105	2	i	i	NOUN
ejpam-4665	105	3	)	)	PUNCT
ejpam-4665	105	4	suppose	suppose	VERB
ejpam-4665	105	5	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	105	6	(	(	PUNCT
ejpam-4665	105	7	g	g	NOUN
ejpam-4665	105	8	)	)	PUNCT
ejpam-4665	105	9	=	=	SYM
ejpam-4665	106	1	2	2	X
ejpam-4665	106	2	.	.	X
ejpam-4665	106	3	note	note	VERB
ejpam-4665	106	4	that	that	SCONJ
ejpam-4665	106	5	every	every	DET
ejpam-4665	106	6	restrained	restrained	ADJ
ejpam-4665	106	7	2	2	NUM
ejpam-4665	106	8	-	-	PUNCT
ejpam-4665	106	9	resolving	resolve	VERB
ejpam-4665	106	10	pointwise	pointwise	ADP
ejpam-4665	106	11	non	non	ADJ
ejpam-4665	106	12	-	-	ADJ
ejpam-4665	106	13	dominating	dominating	ADJ
ejpam-4665	106	14	set	set	NOUN
ejpam-4665	106	15	is	be	AUX
ejpam-4665	106	16	a	a	DET
ejpam-4665	106	17	2	2	NUM
ejpam-4665	106	18	-	-	PUNCT
ejpam-4665	106	19	resolving	resolve	VERB
ejpam-4665	106	20	point	point	NOUN
ejpam-4665	106	21	-	-	PUNCT
ejpam-4665	106	22	wise	wise	ADJ
ejpam-4665	106	23	non	non	ADJ
ejpam-4665	106	24	-	-	ADJ
ejpam-4665	106	25	dominating	dominating	ADJ
ejpam-4665	106	26	set	set	NOUN
ejpam-4665	106	27	in	in	ADP
ejpam-4665	106	28	g	g	PROPN
ejpam-4665	106	29	,	,	PUNCT
ejpam-4665	106	30	that	that	PRON
ejpam-4665	106	31	is	be	AUX
ejpam-4665	106	32	dim2pnd	dim2pnd	NOUN
ejpam-4665	106	33	(	(	PUNCT
ejpam-4665	106	34	g	g	NOUN
ejpam-4665	106	35	)	)	PUNCT
ejpam-4665	106	36	=	=	SYM
ejpam-4665	107	1	2	2	X
ejpam-4665	107	2	.	.	X
ejpam-4665	107	3	hence	hence	ADV
ejpam-4665	107	4	,	,	PUNCT
ejpam-4665	107	5	by	by	ADP
ejpam-4665	107	6	proposition	proposition	NOUN
ejpam-4665	107	7	1	1	NUM
ejpam-4665	107	8	,	,	PUNCT
ejpam-4665	107	9	g	g	PROPN
ejpam-4665	107	10	=	=	SYM
ejpam-4665	107	11	pn	pn	PROPN
ejpam-4665	107	12	.	.	PROPN
ejpam-4665	108	1	since	since	SCONJ
ejpam-4665	108	2	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	108	3	(	(	PUNCT
ejpam-4665	108	4	p3	p3	PROPN
ejpam-4665	108	5	)	)	PUNCT
ejpam-4665	108	6	=	=	SYM
ejpam-4665	108	7	3	3	NUM
ejpam-4665	108	8	,	,	PUNCT
ejpam-4665	108	9	g	g	PROPN
ejpam-4665	108	10	=	=	PUNCT
ejpam-4665	108	11	pn	pn	PROPN
ejpam-4665	108	12	except	except	SCONJ
ejpam-4665	108	13	n	n	PROPN
ejpam-4665	108	14	=	=	SYM
ejpam-4665	108	15	3	3	X
ejpam-4665	108	16	.	.	PUNCT
ejpam-4665	109	1	conversely	conversely	ADV
ejpam-4665	109	2	,	,	PUNCT
ejpam-4665	109	3	if	if	SCONJ
ejpam-4665	109	4	g	g	PROPN
ejpam-4665	109	5	=	=	PUNCT
ejpam-4665	109	6	pn	pn	PROPN
ejpam-4665	109	7	=	=	PUNCT
ejpam-4665	110	1	[	[	X
ejpam-4665	110	2	v1	v1	NOUN
ejpam-4665	110	3	,	,	PUNCT
ejpam-4665	110	4	v2	v2	NOUN
ejpam-4665	110	5	,	,	PUNCT
ejpam-4665	110	6	.	.	PUNCT
ejpam-4665	110	7	.	.	PUNCT
ejpam-4665	110	8	.	.	PUNCT
ejpam-4665	111	1	,	,	PUNCT
ejpam-4665	111	2	vn	vn	X
ejpam-4665	111	3	]	]	PUNCT
ejpam-4665	111	4	,	,	PUNCT
ejpam-4665	111	5	then	then	ADV
ejpam-4665	111	6	s	s	VERB
ejpam-4665	111	7	=	=	NOUN
ejpam-4665	111	8	{	{	PUNCT
ejpam-4665	111	9	v1	v1	PROPN
ejpam-4665	111	10	,	,	PUNCT
ejpam-4665	111	11	vn	vn	PROPN
ejpam-4665	111	12	}	}	PUNCT
ejpam-4665	111	13	is	be	AUX
ejpam-4665	111	14	a	a	DET
ejpam-4665	111	15	restrained	restrained	ADJ
ejpam-4665	111	16	2	2	NUM
ejpam-4665	111	17	-	-	PUNCT
ejpam-4665	111	18	resolving	resolve	VERB
ejpam-4665	111	19	a.m.	a.m.	PROPN
ejpam-4665	111	20	mahistrado	mahistrado	NOUN
ejpam-4665	111	21	,	,	PUNCT
ejpam-4665	111	22	h.	h.	PROPN
ejpam-4665	111	23	rara	rara	PROPN
ejpam-4665	111	24	/	/	SYM
ejpam-4665	111	25	eur	eur	PROPN
ejpam-4665	111	26	.	.	PUNCT
ejpam-4665	112	1	j.	j.	PROPN
ejpam-4665	112	2	pure	pure	PROPN
ejpam-4665	112	3	appl	appl	PROPN
ejpam-4665	112	4	.	.	PROPN
ejpam-4665	112	5	math	math	PROPN
ejpam-4665	112	6	,	,	PUNCT
ejpam-4665	112	7	16	16	NUM
ejpam-4665	112	8	(	(	PUNCT
ejpam-4665	112	9	1	1	NUM
ejpam-4665	112	10	)	)	PUNCT
ejpam-4665	112	11	(	(	PUNCT
ejpam-4665	112	12	2023	2023	NUM
ejpam-4665	112	13	)	)	PUNCT
ejpam-4665	112	14	,	,	PUNCT
ejpam-4665	112	15	286	286	NUM
ejpam-4665	112	16	-	-	SYM
ejpam-4665	112	17	303	303	NUM
ejpam-4665	112	18	291	291	NUM
ejpam-4665	112	19	point	point	NOUN
ejpam-4665	112	20	-	-	PUNCT
ejpam-4665	112	21	wise	wise	ADJ
ejpam-4665	112	22	non	non	ADJ
ejpam-4665	112	23	-	-	ADJ
ejpam-4665	112	24	dominating	dominating	ADJ
ejpam-4665	112	25	set	set	NOUN
ejpam-4665	112	26	of	of	ADP
ejpam-4665	112	27	g.	g.	PROPN
ejpam-4665	112	28	hence	hence	ADV
ejpam-4665	112	29	,	,	PUNCT
ejpam-4665	112	30	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	112	31	(	(	PUNCT
ejpam-4665	112	32	g	g	NOUN
ejpam-4665	112	33	)	)	PUNCT
ejpam-4665	112	34	=	=	SYM
ejpam-4665	112	35	2	2	X
ejpam-4665	112	36	.	.	PUNCT
ejpam-4665	112	37	(	(	PUNCT
ejpam-4665	112	38	ii	ii	NOUN
ejpam-4665	112	39	)	)	PUNCT
ejpam-4665	112	40	suppose	suppose	VERB
ejpam-4665	112	41	g	g	PROPN
ejpam-4665	112	42	=	=	SYM
ejpam-4665	112	43	cn	cn	PROPN
ejpam-4665	112	44	=	=	PUNCT
ejpam-4665	113	1	[	[	X
ejpam-4665	113	2	v1	v1	NOUN
ejpam-4665	113	3	,	,	PUNCT
ejpam-4665	113	4	v2	v2	NOUN
ejpam-4665	113	5	,	,	PUNCT
ejpam-4665	113	6	.	.	PUNCT
ejpam-4665	113	7	.	.	PUNCT
ejpam-4665	113	8	.	.	PUNCT
ejpam-4665	114	1	,	,	PUNCT
ejpam-4665	114	2	vn	vn	X
ejpam-4665	114	3	]	]	PUNCT
ejpam-4665	114	4	.	.	PUNCT
ejpam-4665	115	1	let	let	VERB
ejpam-4665	115	2	s	s	PRON
ejpam-4665	115	3	be	be	AUX
ejpam-4665	115	4	the	the	DET
ejpam-4665	115	5	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	115	6	-set	-set	X
ejpam-4665	115	7	of	of	ADP
ejpam-4665	115	8	cn	cn	PROPN
ejpam-4665	115	9	.	.	PUNCT
ejpam-4665	116	1	by	by	ADP
ejpam-4665	116	2	(	(	PUNCT
ejpam-4665	116	3	i	i	NOUN
ejpam-4665	116	4	)	)	PUNCT
ejpam-4665	116	5	,	,	PUNCT
ejpam-4665	116	6	rdim2pnd	rdim2pnd	NOUN
ejpam-4665	116	7	(	(	PUNCT
ejpam-4665	116	8	cn	cn	PROPN
ejpam-4665	116	9	)	)	PUNCT
ejpam-4665	116	10	>	>	X
ejpam-4665	116	11	2	2	X
ejpam-4665	116	12	.	.	PUNCT
ejpam-4665	116	13	thus	thus	ADV
ejpam-4665	116	14	,	,	PUNCT
ejpam-4665	116	15	s	s	VERB
ejpam-4665	116	16	=	=	NOUN
ejpam-4665	116	17	{	{	PUNCT
ejpam-4665	116	18	v1	v1	PROPN
ejpam-4665	116	19	,	,	PUNCT
ejpam-4665	116	20	v2	v2	PROPN
ejpam-4665	116	21	,	,	PUNCT
ejpam-4665	116	22	v3	v3	PROPN
ejpam-4665	116	23	}	}	PUNCT
ejpam-4665	116	24	is	be	AUX
ejpam-4665	116	25	a	a	DET
ejpam-4665	116	26	restrained	restrained	ADJ
ejpam-4665	116	27	2	2	NUM
ejpam-4665	116	28	-	-	PUNCT
ejpam-4665	116	29	resolving	resolve	VERB
ejpam-4665	116	30	point	point	NOUN
ejpam-4665	116	31	-	-	PUNCT
ejpam-4665	116	32	wise	wise	ADV
ejpam-4665	116	33	nondominating	nondominate	VERB
ejpam-4665	116	34	set	set	NOUN
ejpam-4665	116	35	of	of	ADP
ejpam-4665	116	36	g.	g.	PROPN
ejpam-4665	116	37	hence	hence	ADV
ejpam-4665	116	38	,	,	PUNCT
ejpam-4665	116	39	rdim2pnd	rdim2pnd	PROPN
ejpam-4665	116	40	(	(	PUNCT
ejpam-4665	116	41	cn	cn	NOUN
ejpam-4665	116	42	)	)	PUNCT
ejpam-4665	116	43	=	=	SYM
ejpam-4665	116	44	3	3	X
ejpam-4665	116	45	.	.	NOUN
ejpam-4665	116	46	remark	remark	NOUN
ejpam-4665	116	47	4	4	NUM
ejpam-4665	116	48	.	.	PUNCT
ejpam-4665	116	49	for	for	ADP
ejpam-4665	116	50	any	any	DET
ejpam-4665	116	51	connected	connected	ADJ
ejpam-4665	116	52	graph	graph	NOUN
ejpam-4665	116	53	g	g	NOUN
ejpam-4665	116	54	of	of	ADP
ejpam-4665	116	55	order	order	NOUN
ejpam-4665	116	56	n	n	PRON
ejpam-4665	116	57	≥	≥	NOUN
ejpam-4665	116	58	2	2	NUM
ejpam-4665	116	59	,	,	PUNCT
ejpam-4665	116	60	2	2	NUM
ejpam-4665	116	61	≤	≤	NUM
ejpam-4665	116	62	γr2rh(g	γr2rh(g	NOUN
ejpam-4665	116	63	)	)	PUNCT
ejpam-4665	116	64	≤	≤	NUM
ejpam-4665	116	65	n.	n.	NOUN
ejpam-4665	116	66	moreover	moreover	ADV
ejpam-4665	116	67	,	,	PUNCT
ejpam-4665	116	68	γr2rh(p2	γr2rh(p2	X
ejpam-4665	116	69	)	)	PUNCT
ejpam-4665	116	70	=	=	SYM
ejpam-4665	116	71	2	2	NUM
ejpam-4665	116	72	and	and	CCONJ
ejpam-4665	116	73	γr2rh(kn	γr2rh(kn	PROPN
ejpam-4665	116	74	)	)	PUNCT
ejpam-4665	117	1	=	=	PUNCT
ejpam-4665	117	2	n.	n.	NOUN
ejpam-4665	117	3	example	example	NOUN
ejpam-4665	118	1	1	1	X
ejpam-4665	118	2	.	.	PUNCT
ejpam-4665	118	3	(	(	PUNCT
ejpam-4665	118	4	i	i	NOUN
ejpam-4665	118	5	)	)	PUNCT
ejpam-4665	118	6	for	for	ADP
ejpam-4665	118	7	complete	complete	ADJ
ejpam-4665	118	8	graph	graph	NOUN
ejpam-4665	118	9	kn	kn	PROPN
ejpam-4665	118	10	on	on	ADP
ejpam-4665	118	11	n	n	PRON
ejpam-4665	118	12	≥	≥	NUM
ejpam-4665	118	13	2	2	NUM
ejpam-4665	118	14	vertices	vertex	NOUN
ejpam-4665	118	15	,	,	PUNCT
ejpam-4665	118	16	γr2rh(kn	γr2rh(kn	PROPN
ejpam-4665	118	17	)	)	PUNCT
ejpam-4665	119	1	=	=	SYM
ejpam-4665	119	2	n.	n.	NOUN
ejpam-4665	119	3	(	(	PUNCT
ejpam-4665	119	4	ii	ii	NOUN
ejpam-4665	119	5	)	)	PUNCT
ejpam-4665	119	6	for	for	ADP
ejpam-4665	119	7	complete	complete	ADJ
ejpam-4665	119	8	bipartite	bipartite	PROPN
ejpam-4665	119	9	graph	graph	NOUN
ejpam-4665	119	10	km	km	PROPN
ejpam-4665	119	11	,	,	PUNCT
ejpam-4665	119	12	n	n	CCONJ
ejpam-4665	119	13	on	on	ADP
ejpam-4665	119	14	m+	m+	NUM
ejpam-4665	119	15	n	n	PRON
ejpam-4665	119	16	vertices	vertex	NOUN
ejpam-4665	119	17	where	where	SCONJ
ejpam-4665	119	18	m	m	VERB
ejpam-4665	119	19	,	,	PUNCT
ejpam-4665	119	20	n	n	PRON
ejpam-4665	119	21	≥	≥	NOUN
ejpam-4665	119	22	1	1	NUM
ejpam-4665	119	23	,	,	PUNCT
ejpam-4665	119	24	γr2rh(km	γr2rh(km	PROPN
ejpam-4665	119	25	,	,	PUNCT
ejpam-4665	119	26	n	n	CCONJ
ejpam-4665	119	27	)	)	PUNCT
ejpam-4665	119	28	=	=	SYM
ejpam-4665	119	29	m+	m+	NUM
ejpam-4665	119	30	n.	n.	NOUN
ejpam-4665	119	31	(	(	PUNCT
ejpam-4665	119	32	iii	iii	NOUN
ejpam-4665	119	33	)	)	PUNCT
ejpam-4665	119	34	for	for	ADP
ejpam-4665	119	35	star	star	NOUN
ejpam-4665	119	36	graph	graph	NOUN
ejpam-4665	119	37	k1,n	k1,n	PROPN
ejpam-4665	119	38	on	on	ADP
ejpam-4665	119	39	n+	n+	ADP
ejpam-4665	119	40	1	1	NUM
ejpam-4665	119	41	vertices	vertex	NOUN
ejpam-4665	119	42	where	where	SCONJ
ejpam-4665	119	43	n	n	NUM
ejpam-4665	119	44	≥	≥	NOUN
ejpam-4665	119	45	1	1	NUM
ejpam-4665	119	46	,	,	PUNCT
ejpam-4665	119	47	γr2rh(k1,n	γr2rh(k1,n	NOUN
ejpam-4665	119	48	)	)	PUNCT
ejpam-4665	119	49	=	=	PUNCT
ejpam-4665	119	50	n+	n+	PUNCT
ejpam-4665	119	51	1	1	X
ejpam-4665	119	52	.	.	PUNCT
ejpam-4665	120	1	the	the	DET
ejpam-4665	120	2	next	next	ADJ
ejpam-4665	120	3	results	result	NOUN
ejpam-4665	120	4	follow	follow	VERB
ejpam-4665	120	5	from	from	ADP
ejpam-4665	120	6	[	[	X
ejpam-4665	120	7	14	14	NUM
ejpam-4665	120	8	]	]	PUNCT
ejpam-4665	120	9	and	and	CCONJ
ejpam-4665	120	10	by	by	ADP
ejpam-4665	120	11	definition	definition	NOUN
ejpam-4665	120	12	of	of	ADP
ejpam-4665	120	13	restrained	restrained	ADJ
ejpam-4665	120	14	2	2	NUM
ejpam-4665	120	15	-	-	PUNCT
ejpam-4665	120	16	resolving	resolve	VERB
ejpam-4665	120	17	hop	hop	NOUN
ejpam-4665	120	18	dominating	dominating	NOUN
ejpam-4665	120	19	set	set	NOUN
ejpam-4665	120	20	.	.	PUNCT
ejpam-4665	121	1	proposition	proposition	NOUN
ejpam-4665	121	2	3	3	NUM
ejpam-4665	121	3	.	.	PUNCT
ejpam-4665	122	1	(	(	PUNCT
ejpam-4665	122	2	i	i	NOUN
ejpam-4665	122	3	)	)	PUNCT
ejpam-4665	122	4	for	for	ADP
ejpam-4665	122	5	a	a	DET
ejpam-4665	122	6	path	path	NOUN
ejpam-4665	122	7	pn	pn	NOUN
ejpam-4665	122	8	on	on	ADP
ejpam-4665	122	9	n	n	CCONJ
ejpam-4665	122	10	vertices	vertex	NOUN
ejpam-4665	122	11	γr2rh(pn	γr2rh(pn	NUM
ejpam-4665	122	12	)	)	PUNCT
ejpam-4665	122	13	=	=	SYM
ejpam-4665	123	1			PROPN
ejpam-4665	123	2	2	2	NUM
ejpam-4665	123	3	,	,	PUNCT
ejpam-4665	123	4	if	if	SCONJ
ejpam-4665	123	5	n	n	NOUN
ejpam-4665	123	6	=	=	SYM
ejpam-4665	123	7	2	2	NUM
ejpam-4665	123	8	,	,	PUNCT
ejpam-4665	123	9	4	4	NUM
ejpam-4665	123	10	;	;	PUNCT
ejpam-4665	123	11	3	3	NUM
ejpam-4665	123	12	,	,	PUNCT
ejpam-4665	123	13	if	if	SCONJ
ejpam-4665	123	14	n	n	NOUN
ejpam-4665	123	15	=	=	SYM
ejpam-4665	123	16	3	3	NUM
ejpam-4665	123	17	,	,	PUNCT
ejpam-4665	123	18	5	5	NUM
ejpam-4665	123	19	;	;	PUNCT
ejpam-4665	123	20	4	4	NUM
ejpam-4665	123	21	,	,	PUNCT
ejpam-4665	123	22	if	if	SCONJ
ejpam-4665	123	23	n	n	NOUN
ejpam-4665	123	24	=	=	SYM
ejpam-4665	123	25	6	6	NUM
ejpam-4665	123	26	;	;	PUNCT
ejpam-4665	123	27	n+	n+	NUM
ejpam-4665	123	28	2s	2s	NUM
ejpam-4665	123	29	3	3	NUM
ejpam-4665	123	30	,	,	PUNCT
ejpam-4665	123	31	if	if	SCONJ
ejpam-4665	123	32	n	n	ADV
ejpam-4665	123	33	≡	≡	PROPN
ejpam-4665	123	34	s(mod	s(mod	ADP
ejpam-4665	123	35	6	6	NUM
ejpam-4665	123	36	)	)	PUNCT
ejpam-4665	123	37	where	where	SCONJ
ejpam-4665	123	38	0	0	NUM
ejpam-4665	123	39	≤	≤	NOUN
ejpam-4665	123	40	s	s	PART
ejpam-4665	123	41	≤	≤	NUM
ejpam-4665	123	42	2	2	NUM
ejpam-4665	123	43	and	and	CCONJ
ejpam-4665	123	44	n	n	NOUN
ejpam-4665	123	45	>	>	SYM
ejpam-4665	123	46	6	6	NUM
ejpam-4665	123	47	;	;	PUNCT
ejpam-4665	123	48	n+	n+	NUM
ejpam-4665	123	49	6−	6−	NUM
ejpam-4665	123	50	s	s	NOUN
ejpam-4665	123	51	3	3	NUM
ejpam-4665	123	52	,	,	PUNCT
ejpam-4665	123	53	if	if	SCONJ
ejpam-4665	123	54	n	n	ADV
ejpam-4665	123	55	≡	≡	PROPN
ejpam-4665	123	56	s(mod	s(mod	ADP
ejpam-4665	123	57	6	6	NUM
ejpam-4665	123	58	)	)	PUNCT
ejpam-4665	123	59	where	where	SCONJ
ejpam-4665	123	60	s	s	NOUN
ejpam-4665	123	61	=	=	SYM
ejpam-4665	123	62	3	3	NUM
ejpam-4665	123	63	,	,	PUNCT
ejpam-4665	123	64	4	4	NUM
ejpam-4665	123	65	and	and	CCONJ
ejpam-4665	123	66	n	n	NOUN
ejpam-4665	123	67	>	>	X
ejpam-4665	123	68	8	8	NUM
ejpam-4665	123	69	;	;	PUNCT
ejpam-4665	123	70	n+	n+	X
ejpam-4665	123	71	4	4	NUM
ejpam-4665	123	72	3	3	NUM
ejpam-4665	123	73	,	,	PUNCT
ejpam-4665	123	74	if	if	SCONJ
ejpam-4665	123	75	n	n	PRON
ejpam-4665	123	76	≡	≡	PROPN
ejpam-4665	123	77	5(mod	5(mod	NOUN
ejpam-4665	123	78	6)where	6)where	NUM
ejpam-4665	123	79	n	n	CCONJ
ejpam-4665	123	80	>	>	X
ejpam-4665	123	81	10	10	NUM
ejpam-4665	123	82	.	.	PUNCT
ejpam-4665	123	83	(	(	PUNCT
ejpam-4665	123	84	ii	ii	NOUN
ejpam-4665	123	85	)	)	PUNCT
ejpam-4665	123	86	for	for	ADP
ejpam-4665	123	87	a	a	DET
ejpam-4665	123	88	cycle	cycle	NOUN
ejpam-4665	123	89	cn	cn	NOUN
ejpam-4665	123	90	on	on	ADP
ejpam-4665	123	91	n	n	CCONJ
ejpam-4665	123	92	vertices	vertex	NOUN
ejpam-4665	123	93	γr2rh(cn	γr2rh(cn	PROPN
ejpam-4665	123	94	)	)	PUNCT
ejpam-4665	124	1	=	=	PUNCT
ejpam-4665	124	2			NUM
ejpam-4665	124	3	3	3	NUM
ejpam-4665	124	4	,	,	PUNCT
ejpam-4665	124	5	if	if	SCONJ
ejpam-4665	124	6	n	n	NOUN
ejpam-4665	124	7	=	=	SYM
ejpam-4665	124	8	3	3	NUM
ejpam-4665	124	9	,	,	PUNCT
ejpam-4665	124	10	5	5	NUM
ejpam-4665	124	11	,	,	PUNCT
ejpam-4665	124	12	6	6	NUM
ejpam-4665	124	13	;	;	PUNCT
ejpam-4665	124	14	4	4	NUM
ejpam-4665	124	15	,	,	PUNCT
ejpam-4665	124	16	if	if	SCONJ
ejpam-4665	124	17	n	n	NOUN
ejpam-4665	124	18	=	=	SYM
ejpam-4665	124	19	4	4	NUM
ejpam-4665	124	20	;	;	PUNCT
ejpam-4665	124	21	n+	n+	NUM
ejpam-4665	125	1	2s	2s	NUM
ejpam-4665	125	2	3	3	NUM
ejpam-4665	125	3	,	,	PUNCT
ejpam-4665	125	4	if	if	SCONJ
ejpam-4665	125	5	n	n	ADV
ejpam-4665	125	6	≡	≡	PROPN
ejpam-4665	125	7	s(mod	s(mod	ADP
ejpam-4665	125	8	6	6	NUM
ejpam-4665	125	9	)	)	PUNCT
ejpam-4665	125	10	where	where	SCONJ
ejpam-4665	125	11	0	0	NUM
ejpam-4665	125	12	≤	≤	NOUN
ejpam-4665	125	13	s	s	PART
ejpam-4665	125	14	≤	≤	NUM
ejpam-4665	125	15	2	2	NUM
ejpam-4665	125	16	and	and	CCONJ
ejpam-4665	125	17	n	n	NOUN
ejpam-4665	125	18	>	>	SYM
ejpam-4665	125	19	6	6	NUM
ejpam-4665	125	20	;	;	PUNCT
ejpam-4665	125	21	n+	n+	NUM
ejpam-4665	125	22	6−	6−	NUM
ejpam-4665	125	23	s	s	NOUN
ejpam-4665	125	24	3	3	NUM
ejpam-4665	125	25	,	,	PUNCT
ejpam-4665	125	26	if	if	SCONJ
ejpam-4665	125	27	n	n	ADV
ejpam-4665	125	28	≡	≡	PROPN
ejpam-4665	125	29	s(mod	s(mod	ADP
ejpam-4665	125	30	6	6	NUM
ejpam-4665	125	31	)	)	PUNCT
ejpam-4665	125	32	where	where	SCONJ
ejpam-4665	125	33	3	3	NUM
ejpam-4665	125	34	≤	≤	NOUN
ejpam-4665	125	35	s	s	PART
ejpam-4665	125	36	≤	≤	NOUN
ejpam-4665	125	37	5	5	NUM
ejpam-4665	125	38	and	and	CCONJ
ejpam-4665	125	39	n	n	NOUN
ejpam-4665	125	40	>	>	X
ejpam-4665	125	41	8	8	NUM
ejpam-4665	125	42	.	.	PUNCT
ejpam-4665	126	1	next	next	ADV
ejpam-4665	126	2	,	,	PUNCT
ejpam-4665	126	3	we	we	PRON
ejpam-4665	126	4	show	show	VERB
ejpam-4665	126	5	that	that	SCONJ
ejpam-4665	126	6	every	every	DET
ejpam-4665	126	7	pair	pair	NOUN
ejpam-4665	126	8	of	of	ADP
ejpam-4665	126	9	positive	positive	ADJ
ejpam-4665	126	10	integers	integer	NOUN
ejpam-4665	126	11	are	be	AUX
ejpam-4665	126	12	realizable	realizable	ADJ
ejpam-4665	126	13	as	as	ADP
ejpam-4665	126	14	2	2	NUM
ejpam-4665	126	15	-	-	PUNCT
ejpam-4665	126	16	resolving	resolve	VERB
ejpam-4665	126	17	hop	hop	NOUN
ejpam-4665	126	18	domination	domination	NOUN
ejpam-4665	126	19	number	number	NOUN
ejpam-4665	126	20	and	and	CCONJ
ejpam-4665	126	21	restrained	restrain	VERB
ejpam-4665	126	22	2	2	NUM
ejpam-4665	126	23	-	-	PUNCT
ejpam-4665	126	24	resolving	resolve	VERB
ejpam-4665	126	25	hop	hop	NOUN
ejpam-4665	126	26	domination	domination	NOUN
ejpam-4665	126	27	number	number	NOUN
ejpam-4665	126	28	.	.	PUNCT
ejpam-4665	127	1	thus	thus	ADV
ejpam-4665	127	2	,	,	PUNCT
ejpam-4665	127	3	as	as	ADP
ejpam-4665	127	4	a	a	DET
ejpam-4665	127	5	consequence	consequence	NOUN
ejpam-4665	127	6	,	,	PUNCT
ejpam-4665	127	7	the	the	DET
ejpam-4665	127	8	difference	difference	NOUN
ejpam-4665	127	9	γr2rh	γr2rh	NUM
ejpam-4665	127	10	−	−	NUM
ejpam-4665	127	11	γ2rh	γ2rh	PUNCT
ejpam-4665	127	12	can	can	AUX
ejpam-4665	127	13	be	be	AUX
ejpam-4665	127	14	made	make	VERB
ejpam-4665	127	15	arbitrarily	arbitrarily	ADV
ejpam-4665	127	16	large	large	ADJ
ejpam-4665	127	17	.	.	PUNCT
ejpam-4665	128	1	remark	remark	NOUN
ejpam-4665	128	2	5	5	NUM
ejpam-4665	128	3	.	.	PUNCT
ejpam-4665	129	1	every	every	DET
ejpam-4665	129	2	restrained	restrain	VERB
ejpam-4665	129	3	2	2	NUM
ejpam-4665	129	4	-	-	PUNCT
ejpam-4665	129	5	resolving	resolve	VERB
ejpam-4665	129	6	hop	hop	NOUN
ejpam-4665	129	7	dominating	dominating	NOUN
ejpam-4665	129	8	set	set	NOUN
ejpam-4665	129	9	of	of	ADP
ejpam-4665	129	10	g	g	PROPN
ejpam-4665	129	11	is	be	AUX
ejpam-4665	129	12	a	a	DET
ejpam-4665	129	13	2	2	NUM
ejpam-4665	129	14	-	-	PUNCT
ejpam-4665	129	15	resolving	resolve	VERB
ejpam-4665	129	16	hop	hop	NOUN
ejpam-4665	129	17	dominating	dominating	NOUN
ejpam-4665	129	18	set	set	NOUN
ejpam-4665	129	19	of	of	ADP
ejpam-4665	129	20	g.	g.	PROPN
ejpam-4665	129	21	thus	thus	ADV
ejpam-4665	129	22	,	,	PUNCT
ejpam-4665	129	23	γ2rh(g	γ2rh(g	NOUN
ejpam-4665	129	24	)	)	PUNCT
ejpam-4665	129	25	≤	≤	NUM
ejpam-4665	129	26	γr2rh(g	γr2rh(g	NOUN
ejpam-4665	129	27	)	)	PUNCT
ejpam-4665	129	28	.	.	PUNCT
ejpam-4665	130	1	a.m.	a.m.	PROPN
ejpam-4665	130	2	mahistrado	mahistrado	PROPN
ejpam-4665	130	3	,	,	PUNCT
ejpam-4665	130	4	h.	h.	PROPN
ejpam-4665	130	5	rara	rara	PROPN
ejpam-4665	130	6	/	/	SYM
ejpam-4665	130	7	eur	eur	PROPN
ejpam-4665	130	8	.	.	PUNCT
ejpam-4665	131	1	j.	j.	PROPN
ejpam-4665	131	2	pure	pure	PROPN
ejpam-4665	131	3	appl	appl	PROPN
ejpam-4665	131	4	.	.	PROPN
ejpam-4665	131	5	math	math	PROPN
ejpam-4665	131	6	,	,	PUNCT
ejpam-4665	131	7	16	16	NUM
ejpam-4665	131	8	(	(	PUNCT
ejpam-4665	131	9	1	1	NUM
ejpam-4665	131	10	)	)	PUNCT
ejpam-4665	131	11	(	(	PUNCT
ejpam-4665	131	12	2023	2023	NUM
ejpam-4665	131	13	)	)	PUNCT
ejpam-4665	131	14	,	,	PUNCT
ejpam-4665	131	15	286	286	NUM
ejpam-4665	131	16	-	-	SYM
ejpam-4665	131	17	303	303	NUM
ejpam-4665	131	18	292	292	NUM
ejpam-4665	131	19	theorem	theorem	NOUN
ejpam-4665	131	20	3	3	X
ejpam-4665	131	21	.	.	PUNCT
ejpam-4665	132	1	let	let	VERB
ejpam-4665	132	2	a	a	PRON
ejpam-4665	132	3	and	and	CCONJ
ejpam-4665	132	4	b	b	NOUN
ejpam-4665	132	5	be	be	AUX
ejpam-4665	132	6	positive	positive	ADJ
ejpam-4665	132	7	integers	integer	NOUN
ejpam-4665	132	8	such	such	ADJ
ejpam-4665	132	9	that	that	SCONJ
ejpam-4665	132	10	2	2	NUM
ejpam-4665	132	11	≤	≤	NUM
ejpam-4665	132	12	a	a	DET
ejpam-4665	132	13	≤	≤	PROPN
ejpam-4665	132	14	b.	b.	NOUN
ejpam-4665	133	1	then	then	ADV
ejpam-4665	133	2	there	there	PRON
ejpam-4665	133	3	exists	exist	VERB
ejpam-4665	133	4	a	a	DET
ejpam-4665	133	5	nontrivial	nontrivial	ADJ
ejpam-4665	133	6	connected	connect	VERB
ejpam-4665	133	7	graph	graph	NOUN
ejpam-4665	133	8	h	h	PRON
ejpam-4665	133	9	such	such	ADJ
ejpam-4665	133	10	that	that	DET
ejpam-4665	133	11	γ2rh(h	γ2rh(h	NOUN
ejpam-4665	133	12	)	)	PUNCT
ejpam-4665	133	13	=	=	PUNCT
ejpam-4665	133	14	a	a	PRON
ejpam-4665	133	15	and	and	CCONJ
ejpam-4665	133	16	γr2rh(h	γr2rh(h	PROPN
ejpam-4665	133	17	)	)	PUNCT
ejpam-4665	133	18	=	=	SYM
ejpam-4665	133	19	b.	b.	NOUN
ejpam-4665	133	20	proof	proof	NOUN
ejpam-4665	133	21	.	.	PUNCT
ejpam-4665	134	1	suppose	suppose	VERB
ejpam-4665	134	2	2	2	NUM
ejpam-4665	134	3	≤	≤	NOUN
ejpam-4665	134	4	a	a	DET
ejpam-4665	134	5	=	=	X
ejpam-4665	134	6	b.	b.	PROPN
ejpam-4665	134	7	consider	consider	VERB
ejpam-4665	134	8	graphh1	graphh1	PROPN
ejpam-4665	134	9	in	in	ADP
ejpam-4665	134	10	figure	figure	NOUN
ejpam-4665	134	11	1	1	NUM
ejpam-4665	134	12	.	.	PUNCT
ejpam-4665	135	1	hence	hence	ADV
ejpam-4665	135	2	,	,	PUNCT
ejpam-4665	135	3	s	s	VERB
ejpam-4665	135	4	=	=	PUNCT
ejpam-4665	135	5	{	{	PUNCT
ejpam-4665	135	6	x1	x1	PROPN
ejpam-4665	135	7	,	,	PUNCT
ejpam-4665	135	8	x2	x2	PROPN
ejpam-4665	135	9	,	,	PUNCT
ejpam-4665	135	10	x3	x3	ADJ
ejpam-4665	135	11	.	.	PUNCT
ejpam-4665	135	12	.	.	PUNCT
ejpam-4665	135	13	.	.	PUNCT
ejpam-4665	136	1	,	,	PUNCT
ejpam-4665	136	2	xa	xa	PROPN
ejpam-4665	136	3	}	}	PUNCT
ejpam-4665	136	4	is	be	AUX
ejpam-4665	136	5	both	both	PRON
ejpam-4665	136	6	γ2rh	γ2rh	PUNCT
ejpam-4665	136	7	and	and	CCONJ
ejpam-4665	136	8	a	a	DET
ejpam-4665	136	9	γr2rh	γr2rh	NOUN
ejpam-4665	136	10	-	-	PUNCT
ejpam-4665	136	11	set	set	NOUN
ejpam-4665	136	12	of	of	ADP
ejpam-4665	136	13	h1	h1	NOUN
ejpam-4665	136	14	.	.	PUNCT
ejpam-4665	137	1	thus	thus	ADV
ejpam-4665	137	2	,	,	PUNCT
ejpam-4665	137	3	2	2	NUM
ejpam-4665	137	4	≤	≤	NUM
ejpam-4665	137	5	γ2rh(h1	γ2rh(h1	NUM
ejpam-4665	137	6	)	)	PUNCT
ejpam-4665	138	1	=	=	PUNCT
ejpam-4665	138	2	a	a	DET
ejpam-4665	138	3	=	=	SYM
ejpam-4665	138	4	b	b	NOUN
ejpam-4665	138	5	=	=	PUNCT
ejpam-4665	138	6	γr2rh(h1	γr2rh(h1	PROPN
ejpam-4665	138	7	)	)	PUNCT
ejpam-4665	138	8	.	.	PUNCT
ejpam-4665	139	1	.........	.........	PUNCT
ejpam-4665	139	2	........	........	PUNCT
ejpam-4665	139	3	........	........	PUNCT
ejpam-4665	139	4	........	........	PUNCT
ejpam-4665	139	5	........	........	PUNCT
ejpam-4665	139	6	........	........	PUNCT
ejpam-4665	139	7	........	........	PUNCT
ejpam-4665	139	8	........	........	PUNCT
ejpam-4665	140	1	........	........	PUNCT
ejpam-4665	140	2	...	...	PUNCT
ejpam-4665	141	1	....................................	....................................	PUNCT
ejpam-4665	141	2	....................................	....................................	PUNCT
ejpam-4665	141	3	.........	.........	PUNCT
ejpam-4665	141	4	........	........	PUNCT
ejpam-4665	141	5	........	........	PUNCT
ejpam-4665	141	6	........	........	PUNCT
ejpam-4665	141	7	........	........	PUNCT
ejpam-4665	141	8	........	........	PUNCT
ejpam-4665	141	9	........	........	PUNCT
ejpam-4665	141	10	........	........	PUNCT
ejpam-4665	141	11	........	........	PUNCT
ejpam-4665	141	12	...	...	PUNCT
ejpam-4665	142	1	....................................	....................................	PUNCT
ejpam-4665	142	2	....................................	....................................	PUNCT
ejpam-4665	142	3	.........	.........	PUNCT
ejpam-4665	142	4	........	........	PUNCT
ejpam-4665	142	5	........	........	PUNCT
ejpam-4665	142	6	........	........	PUNCT
ejpam-4665	142	7	........	........	PUNCT
ejpam-4665	142	8	........	........	PUNCT
ejpam-4665	142	9	........	........	PUNCT
ejpam-4665	142	10	........	........	PUNCT
ejpam-4665	142	11	........	........	PUNCT
ejpam-4665	142	12	...	...	PUNCT
ejpam-4665	143	1	....................................	....................................	PUNCT
ejpam-4665	143	2	....................................	....................................	PUNCT
ejpam-4665	143	3	.........	.........	PUNCT
ejpam-4665	143	4	........	........	PUNCT
ejpam-4665	143	5	........	........	PUNCT
ejpam-4665	143	6	........	........	PUNCT
ejpam-4665	143	7	........	........	PUNCT
ejpam-4665	143	8	........	........	PUNCT
ejpam-4665	143	9	........	........	PUNCT
ejpam-4665	143	10	........	........	PUNCT
ejpam-4665	143	11	........	........	PUNCT
ejpam-4665	143	12	...	...	PUNCT
ejpam-4665	144	1	....................................	....................................	PUNCT
ejpam-4665	144	2	....................................	....................................	PUNCT
ejpam-4665	145	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4665	145	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4665	146	1	....................................	....................................	PUNCT
ejpam-4665	146	2	.........	.........	PUNCT
ejpam-4665	146	3	........	........	PUNCT
ejpam-4665	146	4	........	........	PUNCT
ejpam-4665	146	5	........	........	PUNCT
ejpam-4665	146	6	........	........	PUNCT
ejpam-4665	146	7	........	........	PUNCT
ejpam-4665	146	8	........	........	PUNCT
ejpam-4665	146	9	........	........	PUNCT
ejpam-4665	146	10	........	........	PUNCT
ejpam-4665	146	11	...	...	PUNCT
ejpam-4665	147	1	....................................	....................................	PUNCT
ejpam-4665	147	2	....................................	....................................	PUNCT
ejpam-4665	148	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4665	148	2	....................................	....................................	PUNCT
ejpam-4665	149	1	x1	x1	NUM
ejpam-4665	150	1	x2	x2	NOUN
ejpam-4665	150	2	x3	x3	PROPN
ejpam-4665	150	3	xa−1	xa−1	PROPN
ejpam-4665	150	4	xa	xa	PROPN
ejpam-4665	151	1	=	=	PROPN
ejpam-4665	151	2	b	b	PROPN
ejpam-4665	151	3	•	•	NUM
ejpam-4665	151	4	•	•	NUM
ejpam-4665	151	5	•	•	NUM
ejpam-4665	151	6	•	•	NOUN
ejpam-4665	151	7	•	•	NOUN
ejpam-4665	151	8	.	.	PUNCT
ejpam-4665	151	9	.	.	PUNCT
ejpam-4665	151	10	.	.	PUNCT
ejpam-4665	152	1	h1	h1	PROPN
ejpam-4665	152	2	:	:	PUNCT
ejpam-4665	152	3	figure	figure	VERB
ejpam-4665	152	4	1	1	NUM
ejpam-4665	152	5	suppose	suppose	VERB
ejpam-4665	152	6	2	2	NUM
ejpam-4665	152	7	<	<	X
ejpam-4665	152	8	a	a	DET
ejpam-4665	152	9	<	<	X
ejpam-4665	152	10	b.	b.	NOUN
ejpam-4665	152	11	consider	consider	VERB
ejpam-4665	152	12	the	the	DET
ejpam-4665	152	13	graph	graph	NOUN
ejpam-4665	152	14	h2	h2	NOUN
ejpam-4665	152	15	in	in	ADP
ejpam-4665	152	16	figure	figure	NOUN
ejpam-4665	152	17	2	2	NUM
ejpam-4665	152	18	.	.	PUNCT
ejpam-4665	153	1	then	then	ADV
ejpam-4665	153	2	s	s	VERB
ejpam-4665	153	3	=	=	PUNCT
ejpam-4665	153	4	{	{	PUNCT
ejpam-4665	153	5	x1	x1	PROPN
ejpam-4665	153	6	,	,	PUNCT
ejpam-4665	153	7	x2	x2	PROPN
ejpam-4665	153	8	,	,	PUNCT
ejpam-4665	153	9	.	.	PUNCT
ejpam-4665	153	10	.	.	PUNCT
ejpam-4665	153	11	.	.	PUNCT
ejpam-4665	154	1	,	,	PUNCT
ejpam-4665	154	2	xa	xa	PROPN
ejpam-4665	154	3	}	}	PUNCT
ejpam-4665	154	4	is	be	AUX
ejpam-4665	154	5	a	a	DET
ejpam-4665	154	6	γ2rh	γ2rh	NOUN
ejpam-4665	154	7	-	-	PUNCT
ejpam-4665	154	8	set	set	NOUN
ejpam-4665	154	9	of	of	ADP
ejpam-4665	154	10	h2	h2	NOUN
ejpam-4665	154	11	and	and	CCONJ
ejpam-4665	154	12	x	x	X
ejpam-4665	154	13	=	=	X
ejpam-4665	154	14	s	s	NOUN
ejpam-4665	154	15	∪	∪	X
ejpam-4665	154	16	{	{	PUNCT
ejpam-4665	154	17	y1	y1	NOUN
ejpam-4665	154	18	,	,	PUNCT
ejpam-4665	154	19	y2	y2	PROPN
ejpam-4665	154	20	,	,	PUNCT
ejpam-4665	154	21	.	.	PUNCT
ejpam-4665	154	22	.	.	PUNCT
ejpam-4665	155	1	.	.	PUNCT
ejpam-4665	156	1	,	,	PUNCT
ejpam-4665	156	2	yb−a	yb−a	PRON
ejpam-4665	156	3	}	}	PUNCT
ejpam-4665	156	4	is	be	AUX
ejpam-4665	156	5	a	a	DET
ejpam-4665	156	6	γr2rh	γr2rh	NOUN
ejpam-4665	156	7	-	-	PUNCT
ejpam-4665	156	8	set	set	NOUN
ejpam-4665	156	9	of	of	ADP
ejpam-4665	156	10	h2	h2	NOUN
ejpam-4665	156	11	.	.	PUNCT
ejpam-4665	157	1	hence	hence	ADV
ejpam-4665	157	2	γ2rh(h2	γ2rh(h2	PROPN
ejpam-4665	157	3	)	)	PUNCT
ejpam-4665	157	4	=	=	PUNCT
ejpam-4665	158	1	a	a	PRON
ejpam-4665	158	2	and	and	CCONJ
ejpam-4665	158	3	γr2rh(h2	γr2rh(h2	NOUN
ejpam-4665	158	4	)	)	PUNCT
ejpam-4665	159	1	=	=	SYM
ejpam-4665	159	2	|x|	|x|	PROPN
ejpam-4665	159	3	=	=	SYM
ejpam-4665	159	4	|s|+	|s|+	PROPN
ejpam-4665	159	5	(	(	PUNCT
ejpam-4665	159	6	b−	b−	NOUN
ejpam-4665	159	7	a	a	NOUN
ejpam-4665	159	8	)	)	PUNCT
ejpam-4665	159	9	=	=	NOUN
ejpam-4665	159	10	a+	a+	PUNCT
ejpam-4665	159	11	b−	b−	PROPN
ejpam-4665	159	12	a	a	DET
ejpam-4665	159	13	=	=	X
ejpam-4665	159	14	b.	b.	PROPN
ejpam-4665	159	15	...........	...........	PUNCT
ejpam-4665	159	16	..........	..........	PUNCT
ejpam-4665	159	17	..........	..........	PUNCT
ejpam-4665	160	1	..........	..........	PUNCT
ejpam-4665	160	2	..........	..........	PUNCT
ejpam-4665	161	1	..........	..........	PUNCT
ejpam-4665	161	2	.	.	PUNCT
ejpam-4665	162	1	....................................	....................................	PUNCT
ejpam-4665	162	2	....................................	....................................	PUNCT
ejpam-4665	163	1	...........	...........	PUNCT
ejpam-4665	163	2	..........	..........	PUNCT
ejpam-4665	164	1	..........	..........	PUNCT
ejpam-4665	164	2	..........	..........	PUNCT
ejpam-4665	165	1	..........	..........	PUNCT
ejpam-4665	165	2	..........	..........	PUNCT
ejpam-4665	165	3	.	.	PUNCT
ejpam-4665	166	1	....................................	....................................	PUNCT
ejpam-4665	166	2	....................................	....................................	PUNCT
ejpam-4665	167	1	..............................................................	..............................................................	PUNCT
ejpam-4665	167	2	....................................	....................................	PUNCT
ejpam-4665	168	1	....................................	....................................	PUNCT
ejpam-4665	168	2	..............................................................	..............................................................	PUNCT
ejpam-4665	169	1	....................................	....................................	PUNCT
ejpam-4665	169	2	....................................	....................................	PUNCT
ejpam-4665	169	3	.........	.........	PUNCT
ejpam-4665	170	1	........	........	PUNCT
ejpam-4665	170	2	........	........	PUNCT
ejpam-4665	170	3	........	........	PUNCT
ejpam-4665	170	4	........	........	PUNCT
ejpam-4665	171	1	......	......	PUNCT
ejpam-4665	171	2	....................................	....................................	PUNCT
ejpam-4665	172	1	....................................	....................................	PUNCT
ejpam-4665	172	2	.........	.........	PUNCT
ejpam-4665	172	3	........	........	PUNCT
ejpam-4665	172	4	........	........	PUNCT
ejpam-4665	172	5	........	........	PUNCT
ejpam-4665	172	6	........	........	PUNCT
ejpam-4665	173	1	......	......	PUNCT
ejpam-4665	173	2	....................................	....................................	PUNCT
ejpam-4665	174	1	....................................	....................................	PUNCT
ejpam-4665	174	2	..........................	..........................	PUNCT
ejpam-4665	175	1	.........................	.........................	PUNCT
ejpam-4665	175	2	.........................	.........................	PUNCT
ejpam-4665	176	1	....	....	PUNCT
ejpam-4665	176	2	....................................	....................................	PUNCT
ejpam-4665	177	1	....................................	....................................	PUNCT
ejpam-4665	177	2	....................	....................	PUNCT
ejpam-4665	178	1	...................	...................	PUNCT
ejpam-4665	178	2	..............	..............	PUNCT
ejpam-4665	179	1	....................................	....................................	PUNCT
ejpam-4665	179	2	....................................	....................................	PUNCT
ejpam-4665	179	3	......................................................................................	......................................................................................	PUNCT
ejpam-4665	180	1	....................................	....................................	PUNCT
ejpam-4665	180	2	....................................	....................................	PUNCT
ejpam-4665	181	1	...................................................	...................................................	PUNCT
ejpam-4665	181	2	....................................	....................................	PUNCT
ejpam-4665	182	1	....................................	....................................	PUNCT
ejpam-4665	182	2	...................................................	...................................................	PUNCT
ejpam-4665	183	1	....................................	....................................	PUNCT
ejpam-4665	183	2	.......................................................................................	.......................................................................................	PUNCT
ejpam-4665	184	1	....................................	....................................	PUNCT
ejpam-4665	184	2	.....................................................................................................	.....................................................................................................	PUNCT
ejpam-4665	185	1	....................................	....................................	PUNCT
ejpam-4665	185	2	....................................	....................................	PUNCT
ejpam-4665	185	3	............	............	PUNCT
ejpam-4665	185	4	...........	...........	PUNCT
ejpam-4665	185	5	...........	...........	PUNCT
ejpam-4665	185	6	...........	...........	PUNCT
ejpam-4665	185	7	......	......	PUNCT
ejpam-4665	185	8	.	.	PUNCT
ejpam-4665	186	1	...................................	...................................	PUNCT
ejpam-4665	186	2	....................................	....................................	PUNCT
ejpam-4665	186	3	............	............	PUNCT
ejpam-4665	187	1	...........	...........	PUNCT
ejpam-4665	187	2	...........	...........	PUNCT
ejpam-4665	187	3	...........	...........	PUNCT
ejpam-4665	187	4	......	......	PUNCT
ejpam-4665	187	5	.	.	PUNCT
ejpam-4665	188	1	...................................	...................................	PUNCT
ejpam-4665	188	2	....................................	....................................	PUNCT
ejpam-4665	188	3	............	............	PUNCT
ejpam-4665	188	4	...........	...........	PUNCT
ejpam-4665	188	5	...........	...........	PUNCT
ejpam-4665	188	6	...........	...........	PUNCT
ejpam-4665	188	7	...........	...........	PUNCT
ejpam-4665	188	8	.........	.........	PUNCT
ejpam-4665	189	1	....................................	....................................	PUNCT
ejpam-4665	189	2	....................................	....................................	PUNCT
ejpam-4665	189	3	.........	.........	PUNCT
ejpam-4665	189	4	........	........	PUNCT
ejpam-4665	189	5	........	........	PUNCT
ejpam-4665	189	6	........	........	PUNCT
ejpam-4665	190	1	....................................	....................................	PUNCT
ejpam-4665	190	2	....................................	....................................	PUNCT
ejpam-4665	190	3	.........	.........	PUNCT
ejpam-4665	190	4	........	........	PUNCT
ejpam-4665	190	5	........	........	PUNCT
ejpam-4665	190	6	........	........	PUNCT
ejpam-4665	191	1	....................................	....................................	PUNCT
ejpam-4665	191	2	....................................	....................................	PUNCT
ejpam-4665	191	3	.........	.........	PUNCT
ejpam-4665	191	4	........	........	PUNCT
ejpam-4665	191	5	........	........	PUNCT
ejpam-4665	191	6	........	........	PUNCT
ejpam-4665	192	1	........	........	PUNCT
ejpam-4665	192	2	......	......	PUNCT
ejpam-4665	193	1	....................................	....................................	PUNCT
ejpam-4665	193	2	....................................	....................................	PUNCT
ejpam-4665	194	1	................................................................................	................................................................................	PUNCT
ejpam-4665	194	2	....................................	....................................	PUNCT
ejpam-4665	195	1	..............................................................................	..............................................................................	PUNCT
ejpam-4665	195	2	....................................	....................................	PUNCT
ejpam-4665	195	3	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-4665	196	1	....................................	....................................	PUNCT
ejpam-4665	196	2	....................................	....................................	PUNCT
ejpam-4665	197	1	..........................	..........................	PUNCT
ejpam-4665	197	2	.........................	.........................	PUNCT
ejpam-4665	198	1	.........................	.........................	PUNCT
ejpam-4665	198	2	....	....	PUNCT
ejpam-4665	199	1	....................................	....................................	PUNCT
ejpam-4665	199	2	....................................	....................................	PUNCT
ejpam-4665	199	3	...............	...............	PUNCT
ejpam-4665	200	1	..............	..............	PUNCT
ejpam-4665	200	2	.............	.............	PUNCT
ejpam-4665	201	1	....................................	....................................	PUNCT
ejpam-4665	201	2	....................................	....................................	PUNCT
ejpam-4665	202	1	..............	..............	PUNCT
ejpam-4665	202	2	.............	.............	PUNCT
ejpam-4665	202	3	.............	.............	PUNCT
ejpam-4665	202	4	.............	.............	PUNCT
ejpam-4665	202	5	.............	.............	PUNCT
ejpam-4665	202	6	.............	.............	PUNCT
ejpam-4665	202	7	...	...	PUNCT
ejpam-4665	202	8	...	...	PUNCT
ejpam-4665	202	9	.................................	.................................	PUNCT
ejpam-4665	203	1	....................................	....................................	PUNCT
ejpam-4665	204	1	x1	x1	NUM
ejpam-4665	205	1	x2	x2	NOUN
ejpam-4665	205	2	x3	x3	PROPN
ejpam-4665	205	3	x5	x5	PROPN
ejpam-4665	205	4	x4	x4	PROPN
ejpam-4665	205	5	y1	y1	ADJ
ejpam-4665	205	6	y2	y2	NOUN
ejpam-4665	205	7	y3	y3	NOUN
ejpam-4665	205	8	y4	y4	ADJ
ejpam-4665	205	9	yb−ax6	yb−ax6	NOUN
ejpam-4665	206	1	x7	x7	ADP
ejpam-4665	206	2	x8	x8	PROPN
ejpam-4665	206	3	x9	x9	PROPN
ejpam-4665	206	4	xa	xa	PROPN
ejpam-4665	206	5	xa−1	xa−1	PROPN
ejpam-4665	206	6	•	•	PROPN
ejpam-4665	207	1	•••	•••	ADV
ejpam-4665	207	2	•	•	NOUN
ejpam-4665	207	3	•	•	NOUN
ejpam-4665	207	4	.	.	PUNCT
ejpam-4665	207	5	.	.	PUNCT
ejpam-4665	208	1	.	.	PUNCT
ejpam-4665	209	1	•	•	NUM
ejpam-4665	210	1	•••	•••	ADV
ejpam-4665	210	2	•	•	NUM
ejpam-4665	210	3	•	•	NOUN
ejpam-4665	210	4	••	••	NOUN
ejpam-4665	210	5	•	•	NUM
ejpam-4665	210	6	•	•	NUM
ejpam-4665	210	7	•	•	NOUN
ejpam-4665	210	8	•	•	NOUN
ejpam-4665	210	9	.	.	PUNCT
ejpam-4665	210	10	.	.	PUNCT
ejpam-4665	210	11	.	.	PUNCT
ejpam-4665	210	12	.	.	PUNCT
ejpam-4665	210	13	.	.	PUNCT
ejpam-4665	211	1	.	.	PUNCT
ejpam-4665	212	1	figure	figure	NOUN
ejpam-4665	212	2	2	2	NUM
ejpam-4665	212	3	h2	h2	NOUN
ejpam-4665	212	4	:	:	PUNCT
ejpam-4665	212	5	we	we	PRON
ejpam-4665	212	6	now	now	ADV
ejpam-4665	212	7	characterize	characterize	VERB
ejpam-4665	212	8	the	the	DET
ejpam-4665	212	9	restrained	restrained	ADJ
ejpam-4665	212	10	2	2	NUM
ejpam-4665	212	11	-	-	PUNCT
ejpam-4665	212	12	resolving	resolve	VERB
ejpam-4665	212	13	hop	hop	NOUN
ejpam-4665	212	14	dominating	dominating	NOUN
ejpam-4665	212	15	sets	set	NOUN
ejpam-4665	212	16	in	in	ADP
ejpam-4665	212	17	some	some	DET
ejpam-4665	212	18	graphs	graph	NOUN
ejpam-4665	212	19	under	under	ADP
ejpam-4665	212	20	some	some	DET
ejpam-4665	212	21	binary	binary	ADJ
ejpam-4665	212	22	operations	operation	NOUN
ejpam-4665	212	23	.	.	PUNCT
ejpam-4665	213	1	4	4	X
ejpam-4665	213	2	.	.	X
ejpam-4665	213	3	restrained	restrain	VERB
ejpam-4665	213	4	2	2	NUM
ejpam-4665	213	5	-	-	PUNCT
ejpam-4665	213	6	resolving	resolve	VERB
ejpam-4665	213	7	hop	hop	NOUN
ejpam-4665	213	8	dominating	dominating	NOUN
ejpam-4665	213	9	sets	set	NOUN
ejpam-4665	213	10	in	in	ADP
ejpam-4665	213	11	the	the	DET
ejpam-4665	213	12	join	join	NOUN
ejpam-4665	213	13	of	of	ADP
ejpam-4665	213	14	graphs	graph	NOUN
ejpam-4665	213	15	this	this	DET
ejpam-4665	213	16	section	section	NOUN
ejpam-4665	213	17	presents	present	VERB
ejpam-4665	213	18	characterizations	characterization	NOUN
ejpam-4665	213	19	on	on	ADP
ejpam-4665	213	20	the	the	DET
ejpam-4665	213	21	restrained	restrained	ADJ
ejpam-4665	213	22	2	2	NUM
ejpam-4665	213	23	-	-	PUNCT
ejpam-4665	213	24	resolving	resolve	VERB
ejpam-4665	213	25	hop	hop	NOUN
ejpam-4665	213	26	dominating	dominating	NOUN
ejpam-4665	213	27	sets	set	NOUN
ejpam-4665	213	28	in	in	ADP
ejpam-4665	213	29	the	the	DET
ejpam-4665	213	30	join	join	NOUN
ejpam-4665	213	31	of	of	ADP
ejpam-4665	213	32	graphs	graph	NOUN
ejpam-4665	213	33	.	.	PUNCT
ejpam-4665	214	1	theorem	theorem	ADJ
ejpam-4665	214	2	4	4	NUM
ejpam-4665	214	3	.	.	PUNCT
ejpam-4665	215	1	[	[	X
ejpam-4665	215	2	7	7	X
ejpam-4665	215	3	]	]	PUNCT
ejpam-4665	215	4	let	let	VERB
ejpam-4665	215	5	g	g	PRON
ejpam-4665	215	6	be	be	AUX
ejpam-4665	215	7	a	a	DET
ejpam-4665	215	8	connected	connected	ADJ
ejpam-4665	215	9	graph	graph	NOUN
ejpam-4665	215	10	of	of	ADP
ejpam-4665	215	11	order	order	NOUN
ejpam-4665	215	12	greater	great	ADJ
ejpam-4665	215	13	than	than	ADP
ejpam-4665	215	14	3	3	NUM
ejpam-4665	215	15	and	and	CCONJ
ejpam-4665	215	16	let	let	VERB
ejpam-4665	215	17	k1	k1	NOUN
ejpam-4665	215	18	=	=	SYM
ejpam-4665	215	19	{	{	PUNCT
ejpam-4665	215	20	v	v	NOUN
ejpam-4665	215	21	}	}	PUNCT
ejpam-4665	215	22	.	.	PUNCT
ejpam-4665	216	1	then	then	ADV
ejpam-4665	216	2	s	s	VERB
ejpam-4665	216	3	⊆	⊆	NUM
ejpam-4665	216	4	v	v	NOUN
ejpam-4665	216	5	(	(	PUNCT
ejpam-4665	216	6	k1	k1	NOUN
ejpam-4665	216	7	+	+	NOUN
ejpam-4665	216	8	g	g	NOUN
ejpam-4665	216	9	)	)	PUNCT
ejpam-4665	216	10	is	be	AUX
ejpam-4665	216	11	a	a	DET
ejpam-4665	216	12	2	2	NUM
ejpam-4665	216	13	-	-	PUNCT
ejpam-4665	216	14	resolving	resolving	NOUN
ejpam-4665	216	15	set	set	VERB
ejpam-4665	216	16	in	in	ADP
ejpam-4665	216	17	k1	k1	NOUN
ejpam-4665	216	18	+	+	ADP
ejpam-4665	216	19	g	g	PROPN
ejpam-4665	216	20	if	if	SCONJ
ejpam-4665	217	1	and	and	CCONJ
ejpam-4665	217	2	only	only	ADV
ejpam-4665	217	3	if	if	SCONJ
ejpam-4665	217	4	either	either	PRON
ejpam-4665	217	5	v	v	NOUN
ejpam-4665	217	6	/∈	/∈	PUNCT
ejpam-4665	217	7	s	s	PART
ejpam-4665	217	8	and	and	CCONJ
ejpam-4665	217	9	s	s	VERB
ejpam-4665	217	10	is	be	AUX
ejpam-4665	217	11	a	a	DET
ejpam-4665	217	12	(	(	PUNCT
ejpam-4665	217	13	2	2	NUM
ejpam-4665	217	14	,	,	PUNCT
ejpam-4665	217	15	2)-locating	2)-locating	NUM
ejpam-4665	217	16	set	set	VERB
ejpam-4665	217	17	in	in	ADP
ejpam-4665	217	18	g	g	PROPN
ejpam-4665	217	19	or	or	CCONJ
ejpam-4665	217	20	s	s	NOUN
ejpam-4665	217	21	=	=	PUNCT
ejpam-4665	217	22	{	{	PUNCT
ejpam-4665	217	23	v	v	NOUN
ejpam-4665	217	24	}	}	PUNCT
ejpam-4665	217	25	∪	∪	ADP
ejpam-4665	217	26	t	t	PROPN
ejpam-4665	217	27	where	where	SCONJ
ejpam-4665	217	28	t	t	PROPN
ejpam-4665	217	29	is	be	AUX
ejpam-4665	217	30	a	a	DET
ejpam-4665	217	31	(	(	PUNCT
ejpam-4665	217	32	2	2	NUM
ejpam-4665	217	33	,	,	PUNCT
ejpam-4665	217	34	1)-locating	1)-locating	NUM
ejpam-4665	217	35	set	set	VERB
ejpam-4665	217	36	in	in	ADP
ejpam-4665	217	37	g.	g.	PROPN
ejpam-4665	217	38	theorem	theorem	VERB
ejpam-4665	217	39	5	5	NUM
ejpam-4665	217	40	.	.	PUNCT
ejpam-4665	218	1	[	[	X
ejpam-4665	218	2	11	11	NUM
ejpam-4665	218	3	]	]	PUNCT
ejpam-4665	218	4	let	let	VERB
ejpam-4665	218	5	g	g	PRON
ejpam-4665	218	6	be	be	AUX
ejpam-4665	218	7	a	a	DET
ejpam-4665	218	8	connected	connected	ADJ
ejpam-4665	218	9	graph	graph	NOUN
ejpam-4665	218	10	and	and	CCONJ
ejpam-4665	218	11	let	let	VERB
ejpam-4665	218	12	k1	k1	NOUN
ejpam-4665	218	13	=	=	SYM
ejpam-4665	218	14	{	{	PUNCT
ejpam-4665	218	15	x	x	NOUN
ejpam-4665	218	16	}	}	PUNCT
ejpam-4665	218	17	.	.	PUNCT
ejpam-4665	219	1	then	then	ADV
ejpam-4665	219	2	s	s	VERB
ejpam-4665	219	3	⊆	⊆	NUM
ejpam-4665	219	4	v	v	NOUN
ejpam-4665	219	5	(	(	PUNCT
ejpam-4665	219	6	k1	k1	NOUN
ejpam-4665	219	7	+	+	NOUN
ejpam-4665	219	8	g	g	NOUN
ejpam-4665	219	9	)	)	PUNCT
ejpam-4665	219	10	is	be	AUX
ejpam-4665	219	11	a	a	DET
ejpam-4665	219	12	2	2	NUM
ejpam-4665	219	13	-	-	PUNCT
ejpam-4665	219	14	resolving	resolve	VERB
ejpam-4665	219	15	hop	hop	NOUN
ejpam-4665	219	16	dominating	dominating	NOUN
ejpam-4665	219	17	set	set	VERB
ejpam-4665	219	18	in	in	ADP
ejpam-4665	219	19	k1	k1	NOUN
ejpam-4665	219	20	+	+	CCONJ
ejpam-4665	219	21	g	g	NOUN
ejpam-4665	219	22	if	if	SCONJ
ejpam-4665	220	1	and	and	CCONJ
ejpam-4665	220	2	only	only	ADV
ejpam-4665	220	3	if	if	SCONJ
ejpam-4665	220	4	s	s	AUX
ejpam-4665	220	5	=	=	X
ejpam-4665	220	6	{	{	PUNCT
ejpam-4665	220	7	x	x	NOUN
ejpam-4665	220	8	}	}	PUNCT
ejpam-4665	220	9	∪	∪	ADP
ejpam-4665	220	10	t	t	PROPN
ejpam-4665	220	11	where	where	SCONJ
ejpam-4665	220	12	t	t	PROPN
ejpam-4665	220	13	is	be	AUX
ejpam-4665	220	14	a	a	DET
ejpam-4665	220	15	(	(	PUNCT
ejpam-4665	220	16	2	2	NUM
ejpam-4665	220	17	,	,	PUNCT
ejpam-4665	220	18	1)-locating	1)-locating	NUM
ejpam-4665	220	19	point	point	NOUN
ejpam-4665	220	20	-	-	PUNCT
ejpam-4665	220	21	wise	wise	ADJ
ejpam-4665	220	22	non	non	ADJ
ejpam-4665	220	23	-	-	ADJ
ejpam-4665	220	24	dominating	dominating	ADJ
ejpam-4665	220	25	set	set	NOUN
ejpam-4665	220	26	in	in	ADP
ejpam-4665	220	27	g.	g.	PROPN
ejpam-4665	220	28	theorem	theorem	VERB
ejpam-4665	220	29	6	6	NUM
ejpam-4665	220	30	.	.	PUNCT
ejpam-4665	221	1	let	let	VERB
ejpam-4665	221	2	g	g	PRON
ejpam-4665	221	3	be	be	AUX
ejpam-4665	221	4	a	a	DET
ejpam-4665	221	5	connected	connected	ADJ
ejpam-4665	221	6	graph	graph	NOUN
ejpam-4665	221	7	and	and	CCONJ
ejpam-4665	221	8	let	let	VERB
ejpam-4665	221	9	k1	k1	NOUN
ejpam-4665	221	10	=	=	SYM
ejpam-4665	221	11	{	{	PUNCT
ejpam-4665	221	12	x	x	NOUN
ejpam-4665	221	13	}	}	PUNCT
ejpam-4665	221	14	.	.	PUNCT
ejpam-4665	222	1	then	then	ADV
ejpam-4665	222	2	s	s	VERB
ejpam-4665	222	3	⊆	⊆	NUM
ejpam-4665	222	4	v	v	NOUN
ejpam-4665	222	5	(	(	PUNCT
ejpam-4665	222	6	k1	k1	NOUN
ejpam-4665	222	7	+	+	CCONJ
ejpam-4665	222	8	g	g	NOUN
ejpam-4665	222	9	)	)	PUNCT
ejpam-4665	222	10	is	be	AUX
ejpam-4665	222	11	a	a	DET
ejpam-4665	222	12	restrained	restrained	ADJ
ejpam-4665	222	13	2	2	NUM
ejpam-4665	222	14	-	-	PUNCT
ejpam-4665	222	15	resolving	resolve	VERB
ejpam-4665	222	16	hop	hop	NOUN
ejpam-4665	222	17	dominating	dominating	NOUN
ejpam-4665	222	18	set	set	VERB
ejpam-4665	222	19	in	in	ADP
ejpam-4665	222	20	k1	k1	NOUN
ejpam-4665	223	1	+	+	ADP
ejpam-4665	223	2	g	g	PROPN
ejpam-4665	223	3	if	if	SCONJ
ejpam-4665	223	4	and	and	CCONJ
ejpam-4665	223	5	only	only	ADV
ejpam-4665	223	6	if	if	SCONJ
ejpam-4665	223	7	s	s	VERB
ejpam-4665	223	8	=	=	X
ejpam-4665	223	9	{	{	PUNCT
ejpam-4665	223	10	x	x	NOUN
ejpam-4665	223	11	}	}	PUNCT
ejpam-4665	223	12	∪	∪	ADP
ejpam-4665	223	13	t	t	PROPN
ejpam-4665	223	14	where	where	SCONJ
ejpam-4665	223	15	t	t	PROPN
ejpam-4665	223	16	is	be	AUX
ejpam-4665	223	17	a	a	DET
ejpam-4665	223	18	restrained	restrained	ADJ
ejpam-4665	223	19	(	(	PUNCT
ejpam-4665	223	20	2	2	NUM
ejpam-4665	223	21	,	,	PUNCT
ejpam-4665	223	22	1)-locating	1)-locating	NUM
ejpam-4665	223	23	point	point	NOUN
ejpam-4665	223	24	-	-	PUNCT
ejpam-4665	223	25	wise	wise	ADJ
ejpam-4665	223	26	non	non	ADJ
ejpam-4665	223	27	-	-	ADJ
ejpam-4665	223	28	dominating	dominating	ADJ
ejpam-4665	223	29	set	set	NOUN
ejpam-4665	223	30	in	in	ADP
ejpam-4665	223	31	g.	g.	PROPN
ejpam-4665	223	32	a.m.	a.m.	PROPN
ejpam-4665	224	1	mahistrado	mahistrado	PROPN
ejpam-4665	224	2	,	,	PUNCT
ejpam-4665	224	3	h.	h.	PROPN
ejpam-4665	224	4	rara	rara	PROPN
ejpam-4665	224	5	/	/	SYM
ejpam-4665	224	6	eur	eur	PROPN
ejpam-4665	224	7	.	.	PUNCT
ejpam-4665	225	1	j.	j.	PROPN
ejpam-4665	225	2	pure	pure	PROPN
ejpam-4665	225	3	appl	appl	PROPN
ejpam-4665	225	4	.	.	PROPN
ejpam-4665	225	5	math	math	PROPN
ejpam-4665	225	6	,	,	PUNCT
ejpam-4665	225	7	16	16	NUM
ejpam-4665	225	8	(	(	PUNCT
ejpam-4665	225	9	1	1	NUM
ejpam-4665	225	10	)	)	PUNCT
ejpam-4665	225	11	(	(	PUNCT
ejpam-4665	225	12	2023	2023	NUM
ejpam-4665	225	13	)	)	PUNCT
ejpam-4665	225	14	,	,	PUNCT
ejpam-4665	225	15	286	286	NUM
ejpam-4665	225	16	-	-	SYM
ejpam-4665	225	17	303	303	NUM
ejpam-4665	225	18	293	293	NUM
ejpam-4665	225	19	proof	proof	NOUN
ejpam-4665	225	20	.	.	PUNCT
ejpam-4665	226	1	let	let	VERB
ejpam-4665	226	2	s	s	PRON
ejpam-4665	226	3	⊆	⊆	NUM
ejpam-4665	226	4	v	v	NOUN
ejpam-4665	226	5	(	(	PUNCT
ejpam-4665	226	6	k1	k1	NOUN
ejpam-4665	226	7	+	+	NOUN
ejpam-4665	226	8	g	g	NOUN
ejpam-4665	226	9	)	)	PUNCT
ejpam-4665	226	10	be	be	VERB
ejpam-4665	226	11	a	a	DET
ejpam-4665	226	12	restrained	restrained	ADJ
ejpam-4665	226	13	2	2	NUM
ejpam-4665	226	14	-	-	PUNCT
ejpam-4665	226	15	resolving	resolve	VERB
ejpam-4665	226	16	hop	hop	NOUN
ejpam-4665	226	17	dominating	dominating	NOUN
ejpam-4665	226	18	set	set	VERB
ejpam-4665	226	19	in	in	ADP
ejpam-4665	226	20	k1	k1	PROPN
ejpam-4665	227	1	+	+	PROPN
ejpam-4665	227	2	g.	g.	PROPN
ejpam-4665	227	3	then	then	ADV
ejpam-4665	227	4	s	s	VERB
ejpam-4665	227	5	is	be	AUX
ejpam-4665	227	6	a	a	DET
ejpam-4665	227	7	restrained	restrained	ADJ
ejpam-4665	227	8	2	2	NUM
ejpam-4665	227	9	-	-	PUNCT
ejpam-4665	227	10	resolving	resolving	NOUN
ejpam-4665	227	11	set	set	VERB
ejpam-4665	227	12	in	in	ADP
ejpam-4665	227	13	k1	k1	PROPN
ejpam-4665	227	14	+	+	PROPN
ejpam-4665	227	15	g.	g.	PROPN
ejpam-4665	227	16	since	since	SCONJ
ejpam-4665	227	17	s	s	PROPN
ejpam-4665	227	18	is	be	AUX
ejpam-4665	227	19	a	a	DET
ejpam-4665	227	20	hop	hop	NOUN
ejpam-4665	227	21	dominating	dominating	NOUN
ejpam-4665	227	22	set	set	NOUN
ejpam-4665	227	23	,	,	PUNCT
ejpam-4665	227	24	x	x	PROPN
ejpam-4665	227	25	∈	∈	PROPN
ejpam-4665	227	26	s.	s.	PROPN
ejpam-4665	227	27	hence	hence	ADV
ejpam-4665	227	28	,	,	PUNCT
ejpam-4665	227	29	s	s	VERB
ejpam-4665	227	30	=	=	PUNCT
ejpam-4665	227	31	{	{	PUNCT
ejpam-4665	227	32	x	x	NOUN
ejpam-4665	227	33	}	}	PUNCT
ejpam-4665	227	34	∪	∪	ADP
ejpam-4665	227	35	t	t	PROPN
ejpam-4665	227	36	for	for	ADP
ejpam-4665	227	37	t	t	PROPN
ejpam-4665	227	38	⊆	⊆	NUM
ejpam-4665	227	39	v	v	NOUN
ejpam-4665	227	40	(	(	PUNCT
ejpam-4665	227	41	g	g	NOUN
ejpam-4665	227	42	)	)	PUNCT
ejpam-4665	227	43	.	.	PUNCT
ejpam-4665	228	1	then	then	ADV
ejpam-4665	228	2	by	by	ADP
ejpam-4665	228	3	theorem	theorem	NOUN
ejpam-4665	228	4	5	5	NUM
ejpam-4665	228	5	,	,	PUNCT
ejpam-4665	228	6	t	t	PROPN
ejpam-4665	228	7	is	be	AUX
ejpam-4665	228	8	a	a	DET
ejpam-4665	228	9	(	(	PUNCT
ejpam-4665	228	10	2,1)-locating	2,1)-locating	NUM
ejpam-4665	228	11	point	point	ADV
ejpam-4665	228	12	-	-	PUNCT
ejpam-4665	228	13	wise	wise	ADJ
ejpam-4665	228	14	non	non	ADJ
ejpam-4665	228	15	-	-	ADJ
ejpam-4665	228	16	dominating	dominating	ADJ
ejpam-4665	228	17	set	set	NOUN
ejpam-4665	228	18	in	in	ADP
ejpam-4665	228	19	g.	g.	PROPN
ejpam-4665	228	20	now	now	ADV
ejpam-4665	228	21	,	,	PUNCT
ejpam-4665	228	22	since	since	SCONJ
ejpam-4665	228	23	⟨v	⟨v	NOUN
ejpam-4665	228	24	(	(	PUNCT
ejpam-4665	228	25	k1	k1	NOUN
ejpam-4665	228	26	+	+	PROPN
ejpam-4665	228	27	g)\s⟩	g)\s⟩	PROPN
ejpam-4665	228	28	=	=	SYM
ejpam-4665	228	29	⟨v	⟨v	PROPN
ejpam-4665	228	30	(	(	PUNCT
ejpam-4665	228	31	g)\t	g)\t	NOUN
ejpam-4665	228	32	⟩	⟩	NOUN
ejpam-4665	228	33	,	,	PUNCT
ejpam-4665	228	34	and	and	CCONJ
ejpam-4665	228	35	s	s	VERB
ejpam-4665	228	36	is	be	AUX
ejpam-4665	228	37	a	a	DET
ejpam-4665	228	38	restrained	restrained	ADJ
ejpam-4665	228	39	2	2	NUM
ejpam-4665	228	40	-	-	PUNCT
ejpam-4665	228	41	resolving	resolve	VERB
ejpam-4665	228	42	hop	hop	NOUN
ejpam-4665	228	43	dominating	dominating	NOUN
ejpam-4665	228	44	set	set	VERB
ejpam-4665	228	45	in	in	ADP
ejpam-4665	228	46	k1+g	k1+g	NOUN
ejpam-4665	228	47	,	,	PUNCT
ejpam-4665	228	48	then	then	ADV
ejpam-4665	228	49	it	it	PRON
ejpam-4665	228	50	follows	follow	VERB
ejpam-4665	228	51	that	that	SCONJ
ejpam-4665	228	52	t	t	NOUN
ejpam-4665	228	53	=	=	SYM
ejpam-4665	228	54	v	v	PROPN
ejpam-4665	228	55	(	(	PUNCT
ejpam-4665	228	56	g	g	NOUN
ejpam-4665	228	57	)	)	PUNCT
ejpam-4665	228	58	or	or	CCONJ
ejpam-4665	228	59	⟨v	⟨v	NUM
ejpam-4665	228	60	(	(	PUNCT
ejpam-4665	228	61	g)\t	g)\t	NOUN
ejpam-4665	228	62	⟩	⟩	NOUN
ejpam-4665	228	63	has	have	AUX
ejpam-4665	228	64	no	no	DET
ejpam-4665	228	65	isolated	isolated	ADJ
ejpam-4665	228	66	vertex	vertex	NOUN
ejpam-4665	228	67	.	.	PUNCT
ejpam-4665	229	1	therefore	therefore	ADV
ejpam-4665	229	2	,	,	PUNCT
ejpam-4665	229	3	t	t	PROPN
ejpam-4665	229	4	is	be	AUX
ejpam-4665	229	5	a	a	DET
ejpam-4665	229	6	restrained	restrained	ADJ
ejpam-4665	229	7	(	(	PUNCT
ejpam-4665	229	8	2	2	NUM
ejpam-4665	229	9	,	,	PUNCT
ejpam-4665	229	10	1)-locating	1)-locating	NUM
ejpam-4665	229	11	point	point	NOUN
ejpam-4665	229	12	-	-	PUNCT
ejpam-4665	229	13	wise	wise	ADJ
ejpam-4665	229	14	non	non	ADJ
ejpam-4665	229	15	-	-	ADJ
ejpam-4665	229	16	dominating	dominating	ADJ
ejpam-4665	229	17	set	set	NOUN
ejpam-4665	229	18	in	in	ADP
ejpam-4665	229	19	g.	g.	NOUN
ejpam-4665	229	20	conversely	conversely	ADV
ejpam-4665	229	21	,	,	PUNCT
ejpam-4665	229	22	assume	assume	VERB
ejpam-4665	229	23	that	that	SCONJ
ejpam-4665	229	24	s	s	VERB
ejpam-4665	229	25	=	=	X
ejpam-4665	229	26	{	{	PUNCT
ejpam-4665	229	27	x}∪t	x}∪t	PROPN
ejpam-4665	229	28	,	,	PUNCT
ejpam-4665	229	29	where	where	SCONJ
ejpam-4665	229	30	t	t	PROPN
ejpam-4665	229	31	is	be	AUX
ejpam-4665	229	32	a	a	DET
ejpam-4665	229	33	restrained	restrained	ADJ
ejpam-4665	229	34	(	(	PUNCT
ejpam-4665	229	35	2,1)-locating	2,1)-locating	NUM
ejpam-4665	229	36	point	point	ADV
ejpam-4665	229	37	-	-	PUNCT
ejpam-4665	229	38	wise	wise	ADJ
ejpam-4665	229	39	non	non	ADJ
ejpam-4665	229	40	-	-	ADJ
ejpam-4665	229	41	dominating	dominating	ADJ
ejpam-4665	229	42	set	set	NOUN
ejpam-4665	229	43	in	in	ADP
ejpam-4665	229	44	g.	g.	PROPN
ejpam-4665	229	45	by	by	ADP
ejpam-4665	229	46	theorem	theorem	NOUN
ejpam-4665	229	47	5	5	NUM
ejpam-4665	229	48	,	,	PUNCT
ejpam-4665	229	49	s	s	VERB
ejpam-4665	229	50	is	be	AUX
ejpam-4665	229	51	a	a	DET
ejpam-4665	229	52	2	2	NUM
ejpam-4665	229	53	-	-	PUNCT
ejpam-4665	229	54	resolving	resolve	VERB
ejpam-4665	229	55	hop	hop	NOUN
ejpam-4665	229	56	dominating	dominating	NOUN
ejpam-4665	229	57	set	set	VERB
ejpam-4665	229	58	in	in	ADP
ejpam-4665	229	59	k1+g	k1+g	PROPN
ejpam-4665	229	60	.	.	PUNCT
ejpam-4665	230	1	next	next	ADV
ejpam-4665	230	2	,	,	PUNCT
ejpam-4665	230	3	since	since	SCONJ
ejpam-4665	230	4	⟨v	⟨v	NOUN
ejpam-4665	230	5	(	(	PUNCT
ejpam-4665	230	6	k1	k1	NOUN
ejpam-4665	230	7	+	+	PROPN
ejpam-4665	230	8	g)\s⟩	g)\s⟩	PROPN
ejpam-4665	230	9	=	=	SYM
ejpam-4665	230	10	⟨v	⟨v	PROPN
ejpam-4665	230	11	(	(	PUNCT
ejpam-4665	230	12	g)\t	g)\t	NOUN
ejpam-4665	230	13	⟩	⟩	NOUN
ejpam-4665	230	14	and	and	CCONJ
ejpam-4665	230	15	t	t	PROPN
ejpam-4665	230	16	is	be	AUX
ejpam-4665	230	17	a	a	DET
ejpam-4665	230	18	restrained	restrained	ADJ
ejpam-4665	230	19	(	(	PUNCT
ejpam-4665	230	20	2,1)-locating	2,1)-locating	NUM
ejpam-4665	230	21	point	point	ADV
ejpam-4665	230	22	-	-	PUNCT
ejpam-4665	230	23	wise	wise	ADJ
ejpam-4665	230	24	non	non	ADJ
ejpam-4665	230	25	-	-	ADJ
ejpam-4665	230	26	dominating	dominating	ADJ
ejpam-4665	230	27	set	set	NOUN
ejpam-4665	230	28	in	in	ADP
ejpam-4665	230	29	g	g	PROPN
ejpam-4665	230	30	,	,	PUNCT
ejpam-4665	230	31	it	it	PRON
ejpam-4665	230	32	follows	follow	VERB
ejpam-4665	230	33	that	that	SCONJ
ejpam-4665	230	34	s	s	VERB
ejpam-4665	230	35	is	be	AUX
ejpam-4665	230	36	a	a	DET
ejpam-4665	230	37	restrained	restrained	ADJ
ejpam-4665	230	38	2	2	NUM
ejpam-4665	230	39	-	-	PUNCT
ejpam-4665	230	40	resolving	resolve	VERB
ejpam-4665	230	41	hop	hop	NOUN
ejpam-4665	230	42	dominating	dominating	NOUN
ejpam-4665	230	43	set	set	VERB
ejpam-4665	230	44	in	in	ADP
ejpam-4665	230	45	k1	k1	PROPN
ejpam-4665	230	46	+	+	PROPN
ejpam-4665	230	47	g.	g.	PROPN
ejpam-4665	230	48	as	as	ADP
ejpam-4665	230	49	a	a	DET
ejpam-4665	230	50	consequence	consequence	NOUN
ejpam-4665	230	51	of	of	ADP
ejpam-4665	230	52	theorem	theorem	NOUN
ejpam-4665	230	53	6	6	NUM
ejpam-4665	230	54	the	the	DET
ejpam-4665	230	55	next	next	ADJ
ejpam-4665	230	56	result	result	NOUN
ejpam-4665	230	57	follows	follow	VERB
ejpam-4665	230	58	.	.	PUNCT
ejpam-4665	231	1	corollary	corollary	ADJ
ejpam-4665	231	2	1	1	NUM
ejpam-4665	231	3	.	.	PUNCT
ejpam-4665	232	1	let	let	VERB
ejpam-4665	232	2	g	g	NOUN
ejpam-4665	232	3	be	be	AUX
ejpam-4665	232	4	connected	connect	VERB
ejpam-4665	232	5	nontrivial	nontrivial	ADJ
ejpam-4665	232	6	graph	graph	NOUN
ejpam-4665	232	7	.	.	PUNCT
ejpam-4665	233	1	then	then	ADV
ejpam-4665	233	2	γr2rh(k1+g	γr2rh(k1+g	X
ejpam-4665	233	3	)	)	PUNCT
ejpam-4665	234	1	=	=	SYM
ejpam-4665	234	2	rlnpnd	rlnpnd	NOUN
ejpam-4665	234	3	(	(	PUNCT
ejpam-4665	234	4	2,1)(g)+1	2,1)(g)+1	PROPN
ejpam-4665	234	5	.	.	PUNCT
ejpam-4665	234	6	example	example	NOUN
ejpam-4665	235	1	2	2	NUM
ejpam-4665	235	2	.	.	X
ejpam-4665	235	3	for	for	ADP
ejpam-4665	235	4	a	a	DET
ejpam-4665	235	5	fan	fan	NOUN
ejpam-4665	235	6	fn	fn	NOUN
ejpam-4665	235	7	=	=	PUNCT
ejpam-4665	235	8	pn	pn	PROPN
ejpam-4665	235	9	+	+	NOUN
ejpam-4665	235	10	k1	k1	NOUN
ejpam-4665	235	11	on	on	ADP
ejpam-4665	235	12	n+	n+	ADP
ejpam-4665	235	13	1	1	NUM
ejpam-4665	235	14	vertices	vertex	NOUN
ejpam-4665	235	15	γr2rh(fn	γr2rh(fn	PROPN
ejpam-4665	235	16	)	)	PUNCT
ejpam-4665	236	1	=	=	SYM
ejpam-4665	236	2	rlnpnd	rlnpnd	NOUN
ejpam-4665	236	3	(	(	PUNCT
ejpam-4665	236	4	2,1)(pn	2,1)(pn	NUM
ejpam-4665	236	5	)	)	PUNCT
ejpam-4665	236	6	+	+	CCONJ
ejpam-4665	236	7	1	1	NUM
ejpam-4665	236	8	=	=	SYM
ejpam-4665	236	9	n+	n+	NUM
ejpam-4665	236	10	1	1	NUM
ejpam-4665	236	11	,	,	PUNCT
ejpam-4665	236	12	if	if	SCONJ
ejpam-4665	236	13	2	2	NUM
ejpam-4665	236	14	≤	≤	NOUN
ejpam-4665	236	15	n	n	CCONJ
ejpam-4665	236	16	≤	≤	NOUN
ejpam-4665	236	17	7	7	NUM
ejpam-4665	236	18	;	;	PUNCT
ejpam-4665	236	19	3n+	3n+	NUM
ejpam-4665	236	20	2k	2k	NOUN
ejpam-4665	236	21	5	5	NUM
ejpam-4665	236	22	+	+	CCONJ
ejpam-4665	236	23	1	1	NUM
ejpam-4665	236	24	,	,	PUNCT
ejpam-4665	236	25	if	if	SCONJ
ejpam-4665	236	26	n	n	ADV
ejpam-4665	236	27	=	=	PUNCT
ejpam-4665	236	28	k(mod	k(mod	PROPN
ejpam-4665	236	29	5	5	NUM
ejpam-4665	236	30	)	)	PUNCT
ejpam-4665	236	31	,	,	PUNCT
ejpam-4665	236	32	3	3	NUM
ejpam-4665	236	33	≤	≤	NUM
ejpam-4665	236	34	k	k	X
ejpam-4665	236	35	≤	≤	NUM
ejpam-4665	236	36	7	7	NUM
ejpam-4665	236	37	.	.	PUNCT
ejpam-4665	236	38	example	example	NOUN
ejpam-4665	237	1	3	3	NUM
ejpam-4665	237	2	.	.	X
ejpam-4665	238	1	for	for	ADP
ejpam-4665	238	2	a	a	DET
ejpam-4665	238	3	wheel	wheel	NOUN
ejpam-4665	238	4	wn	wn	NOUN
ejpam-4665	238	5	=	=	SYM
ejpam-4665	238	6	cn	cn	PROPN
ejpam-4665	238	7	+	+	CCONJ
ejpam-4665	238	8	1	1	NUM
ejpam-4665	238	9	on	on	ADP
ejpam-4665	238	10	n+	n+	ADP
ejpam-4665	238	11	1	1	NUM
ejpam-4665	238	12	vertices	vertex	NOUN
ejpam-4665	238	13	γr2rh(wn	γr2rh(wn	X
ejpam-4665	238	14	)	)	PUNCT
ejpam-4665	239	1	=	=	SYM
ejpam-4665	239	2	rlnpnd	rlnpnd	NOUN
ejpam-4665	239	3	(	(	PUNCT
ejpam-4665	239	4	2,1)(cn	2,1)(cn	NUM
ejpam-4665	239	5	)	)	PUNCT
ejpam-4665	240	1	+	+	CCONJ
ejpam-4665	240	2	1	1	NUM
ejpam-4665	240	3	=	=	SYM
ejpam-4665	240	4	n+	n+	NUM
ejpam-4665	240	5	1	1	NUM
ejpam-4665	240	6	,	,	PUNCT
ejpam-4665	240	7	if	if	SCONJ
ejpam-4665	240	8	n	n	NOUN
ejpam-4665	240	9	=	=	SYM
ejpam-4665	240	10	3	3	NUM
ejpam-4665	240	11	,	,	PUNCT
ejpam-4665	240	12	4	4	NUM
ejpam-4665	240	13	;	;	PUNCT
ejpam-4665	240	14	3n+	3n+	NUM
ejpam-4665	240	15	2k	2k	NOUN
ejpam-4665	240	16	5	5	NUM
ejpam-4665	240	17	+	+	CCONJ
ejpam-4665	240	18	1	1	NUM
ejpam-4665	240	19	,	,	PUNCT
ejpam-4665	240	20	if	if	SCONJ
ejpam-4665	240	21	n	n	ADV
ejpam-4665	240	22	=	=	PUNCT
ejpam-4665	240	23	k(mod	k(mod	PROPN
ejpam-4665	240	24	5	5	NUM
ejpam-4665	240	25	)	)	PUNCT
ejpam-4665	240	26	,	,	PUNCT
ejpam-4665	240	27	0	0	NUM
ejpam-4665	240	28	≤	≤	NUM
ejpam-4665	241	1	k	k	X
ejpam-4665	241	2	≤	≤	NUM
ejpam-4665	241	3	4	4	NUM
ejpam-4665	241	4	.	.	PUNCT
ejpam-4665	241	5	theorem	theorem	VERB
ejpam-4665	241	6	7	7	NUM
ejpam-4665	241	7	.	.	PUNCT
ejpam-4665	242	1	[	[	X
ejpam-4665	242	2	11	11	NUM
ejpam-4665	242	3	]	]	PUNCT
ejpam-4665	242	4	let	let	VERB
ejpam-4665	242	5	g	g	NOUN
ejpam-4665	242	6	and	and	CCONJ
ejpam-4665	242	7	h	h	NOUN
ejpam-4665	242	8	be	be	VERB
ejpam-4665	242	9	any	any	DET
ejpam-4665	242	10	two	two	NUM
ejpam-4665	242	11	graphs	graph	NOUN
ejpam-4665	242	12	.	.	PUNCT
ejpam-4665	243	1	a	a	DET
ejpam-4665	243	2	set	set	NOUN
ejpam-4665	243	3	s	s	NOUN
ejpam-4665	243	4	⊆	⊆	NUM
ejpam-4665	243	5	v	v	NOUN
ejpam-4665	243	6	(	(	PUNCT
ejpam-4665	243	7	g+h	g+h	PROPN
ejpam-4665	243	8	)	)	PUNCT
ejpam-4665	243	9	is	be	AUX
ejpam-4665	243	10	a	a	DET
ejpam-4665	243	11	2	2	NUM
ejpam-4665	243	12	-	-	PUNCT
ejpam-4665	243	13	resolving	resolve	VERB
ejpam-4665	243	14	hop	hop	NOUN
ejpam-4665	243	15	dominating	dominating	NOUN
ejpam-4665	243	16	set	set	VERB
ejpam-4665	243	17	in	in	ADP
ejpam-4665	243	18	g+h	g+h	PROPN
ejpam-4665	243	19	if	if	SCONJ
ejpam-4665	243	20	and	and	CCONJ
ejpam-4665	243	21	only	only	ADV
ejpam-4665	243	22	if	if	SCONJ
ejpam-4665	243	23	s	s	VERB
ejpam-4665	243	24	=	=	PUNCT
ejpam-4665	243	25	sg	sg	X
ejpam-4665	243	26	∪	∪	NOUN
ejpam-4665	243	27	sh	sh	PROPN
ejpam-4665	243	28	where	where	SCONJ
ejpam-4665	243	29	sg	sg	PROPN
ejpam-4665	243	30	=	=	SYM
ejpam-4665	243	31	v	v	PROPN
ejpam-4665	243	32	(	(	PUNCT
ejpam-4665	243	33	g	g	NOUN
ejpam-4665	243	34	)	)	PUNCT
ejpam-4665	243	35	∩	∩	NOUN
ejpam-4665	243	36	s	s	NOUN
ejpam-4665	243	37	and	and	CCONJ
ejpam-4665	243	38	sh	sh	PROPN
ejpam-4665	243	39	=	=	SYM
ejpam-4665	243	40	v	v	PROPN
ejpam-4665	243	41	(	(	PUNCT
ejpam-4665	243	42	h	h	NOUN
ejpam-4665	243	43	)	)	PUNCT
ejpam-4665	243	44	∩	∩	NOUN
ejpam-4665	243	45	s	s	NOUN
ejpam-4665	243	46	are	be	AUX
ejpam-4665	243	47	2	2	NUM
ejpam-4665	243	48	-	-	PUNCT
ejpam-4665	243	49	locating	locate	VERB
ejpam-4665	243	50	point	point	NOUN
ejpam-4665	243	51	-	-	PUNCT
ejpam-4665	243	52	wise	wise	ADJ
ejpam-4665	243	53	non	non	ADJ
ejpam-4665	243	54	-	-	ADJ
ejpam-4665	243	55	dominating	dominating	ADJ
ejpam-4665	243	56	sets	set	NOUN
ejpam-4665	243	57	in	in	ADP
ejpam-4665	243	58	g	g	PROPN
ejpam-4665	243	59	and	and	CCONJ
ejpam-4665	243	60	h	h	NOUN
ejpam-4665	243	61	,	,	PUNCT
ejpam-4665	243	62	respectively	respectively	ADV
ejpam-4665	243	63	,	,	PUNCT
ejpam-4665	243	64	where	where	SCONJ
ejpam-4665	243	65	sg	sg	NOUN
ejpam-4665	243	66	or	or	CCONJ
ejpam-4665	243	67	sh	sh	PROPN
ejpam-4665	243	68	is	be	AUX
ejpam-4665	243	69	a	a	DET
ejpam-4665	243	70	(	(	PUNCT
ejpam-4665	243	71	2	2	NUM
ejpam-4665	243	72	,	,	PUNCT
ejpam-4665	243	73	2)-locating	2)-locating	NUM
ejpam-4665	243	74	point	point	NOUN
ejpam-4665	243	75	-	-	PUNCT
ejpam-4665	243	76	wise	wise	ADJ
ejpam-4665	243	77	non	non	ADJ
ejpam-4665	243	78	-	-	ADJ
ejpam-4665	243	79	dominating	dominating	ADJ
ejpam-4665	243	80	set	set	NOUN
ejpam-4665	243	81	or	or	CCONJ
ejpam-4665	243	82	sg	sg	PROPN
ejpam-4665	243	83	and	and	CCONJ
ejpam-4665	243	84	sh	sh	PROPN
ejpam-4665	243	85	are	be	AUX
ejpam-4665	243	86	(	(	PUNCT
ejpam-4665	243	87	2	2	NUM
ejpam-4665	243	88	,	,	PUNCT
ejpam-4665	243	89	1)-locating	1)-locating	NUM
ejpam-4665	243	90	point	point	NOUN
ejpam-4665	243	91	-	-	PUNCT
ejpam-4665	243	92	wise	wise	ADJ
ejpam-4665	243	93	non	non	ADJ
ejpam-4665	243	94	-	-	ADJ
ejpam-4665	243	95	dominating	dominating	ADJ
ejpam-4665	243	96	sets	set	NOUN
ejpam-4665	243	97	of	of	ADP
ejpam-4665	243	98	g	g	PROPN
ejpam-4665	243	99	and	and	CCONJ
ejpam-4665	243	100	h	h	NOUN
ejpam-4665	243	101	,	,	PUNCT
ejpam-4665	243	102	respectively	respectively	ADV
ejpam-4665	243	103	.	.	PUNCT
ejpam-4665	244	1	theorem	theorem	VERB
ejpam-4665	244	2	8	8	NUM
ejpam-4665	244	3	.	.	PUNCT
ejpam-4665	245	1	[	[	X
ejpam-4665	245	2	8	8	NUM
ejpam-4665	245	3	]	]	PUNCT
ejpam-4665	245	4	let	let	VERB
ejpam-4665	245	5	g	g	NOUN
ejpam-4665	245	6	and	and	CCONJ
ejpam-4665	245	7	h	h	NOUN
ejpam-4665	245	8	be	be	VERB
ejpam-4665	245	9	any	any	DET
ejpam-4665	245	10	two	two	NUM
ejpam-4665	245	11	graphs	graph	NOUN
ejpam-4665	245	12	.	.	PUNCT
ejpam-4665	246	1	a	a	DET
ejpam-4665	246	2	set	set	NOUN
ejpam-4665	246	3	s	s	NOUN
ejpam-4665	246	4	⊆	⊆	NUM
ejpam-4665	246	5	v	v	NOUN
ejpam-4665	246	6	(	(	PUNCT
ejpam-4665	246	7	g+h	g+h	PROPN
ejpam-4665	246	8	)	)	PUNCT
ejpam-4665	246	9	is	be	AUX
ejpam-4665	246	10	a	a	DET
ejpam-4665	246	11	restrained	restrain	VERB
ejpam-4665	246	12	2resolving	2resolving	NUM
ejpam-4665	246	13	set	set	VERB
ejpam-4665	246	14	in	in	ADP
ejpam-4665	246	15	g+h	g+h	PROPN
ejpam-4665	246	16	if	if	SCONJ
ejpam-4665	246	17	and	and	CCONJ
ejpam-4665	246	18	only	only	ADV
ejpam-4665	246	19	if	if	SCONJ
ejpam-4665	246	20	sg	sg	PROPN
ejpam-4665	246	21	=	=	SYM
ejpam-4665	246	22	v	v	NOUN
ejpam-4665	246	23	(	(	PUNCT
ejpam-4665	246	24	g)∩s	g)∩s	PROPN
ejpam-4665	246	25	and	and	CCONJ
ejpam-4665	246	26	sh	sh	PROPN
ejpam-4665	246	27	=	=	SYM
ejpam-4665	246	28	v	v	PROPN
ejpam-4665	246	29	(	(	PUNCT
ejpam-4665	246	30	h)∩s	h)∩s	NOUN
ejpam-4665	246	31	where	where	SCONJ
ejpam-4665	246	32	s	s	VERB
ejpam-4665	246	33	=	=	SYM
ejpam-4665	246	34	sg∪sh	sg∪sh	PROPN
ejpam-4665	246	35	are	be	AUX
ejpam-4665	246	36	2	2	NUM
ejpam-4665	246	37	-	-	PUNCT
ejpam-4665	246	38	locating	locate	VERB
ejpam-4665	246	39	set	set	NOUN
ejpam-4665	246	40	in	in	ADP
ejpam-4665	246	41	g	g	PROPN
ejpam-4665	246	42	and	and	CCONJ
ejpam-4665	246	43	h	h	NOUN
ejpam-4665	246	44	,	,	PUNCT
ejpam-4665	246	45	respectively	respectively	ADV
ejpam-4665	246	46	where	where	SCONJ
ejpam-4665	246	47	sg	sg	PROPN
ejpam-4665	246	48	or	or	CCONJ
ejpam-4665	246	49	sh	sh	PROPN
ejpam-4665	246	50	is	be	AUX
ejpam-4665	246	51	a	a	DET
ejpam-4665	246	52	(	(	PUNCT
ejpam-4665	246	53	2	2	NUM
ejpam-4665	246	54	,	,	PUNCT
ejpam-4665	246	55	2)-locating	2)-locating	NUM
ejpam-4665	246	56	or	or	CCONJ
ejpam-4665	246	57	sg	sg	PROPN
ejpam-4665	246	58	and	and	CCONJ
ejpam-4665	246	59	sh	sh	PROPN
ejpam-4665	246	60	are	be	AUX
ejpam-4665	246	61	(	(	PUNCT
ejpam-4665	246	62	2	2	NUM
ejpam-4665	246	63	,	,	PUNCT
ejpam-4665	246	64	1)-locating	1)-locating	NUM
ejpam-4665	246	65	sets	set	NOUN
ejpam-4665	246	66	and	and	CCONJ
ejpam-4665	246	67	one	one	NUM
ejpam-4665	246	68	of	of	ADP
ejpam-4665	246	69	the	the	DET
ejpam-4665	246	70	following	follow	VERB
ejpam-4665	246	71	holds	hold	VERB
ejpam-4665	246	72	:	:	PUNCT
ejpam-4665	246	73	(	(	PUNCT
ejpam-4665	246	74	i	i	NOUN
ejpam-4665	246	75	)	)	PUNCT
ejpam-4665	246	76	sg	sg	PROPN
ejpam-4665	246	77	=	=	SYM
ejpam-4665	246	78	v	v	PROPN
ejpam-4665	246	79	(	(	PUNCT
ejpam-4665	246	80	g	g	NOUN
ejpam-4665	246	81	)	)	PUNCT
ejpam-4665	246	82	and	and	CCONJ
ejpam-4665	246	83	sh	sh	PROPN
ejpam-4665	246	84	is	be	AUX
ejpam-4665	246	85	a	a	DET
ejpam-4665	246	86	restrained	restrained	ADJ
ejpam-4665	246	87	2	2	NUM
ejpam-4665	246	88	-	-	PUNCT
ejpam-4665	246	89	locating	locate	VERB
ejpam-4665	246	90	set	set	NOUN
ejpam-4665	246	91	in	in	ADP
ejpam-4665	246	92	h	h	NOUN
ejpam-4665	246	93	;	;	PUNCT
ejpam-4665	246	94	(	(	PUNCT
ejpam-4665	246	95	ii	ii	NOUN
ejpam-4665	246	96	)	)	PUNCT
ejpam-4665	246	97	sh	sh	PROPN
ejpam-4665	246	98	=	=	SYM
ejpam-4665	246	99	v	v	PROPN
ejpam-4665	246	100	(	(	PUNCT
ejpam-4665	246	101	h	h	NOUN
ejpam-4665	246	102	)	)	PUNCT
ejpam-4665	246	103	and	and	CCONJ
ejpam-4665	246	104	sg	sg	PROPN
ejpam-4665	246	105	is	be	AUX
ejpam-4665	246	106	a	a	DET
ejpam-4665	246	107	restrained	restrained	ADJ
ejpam-4665	246	108	2	2	NUM
ejpam-4665	246	109	-	-	PUNCT
ejpam-4665	246	110	locating	locate	VERB
ejpam-4665	246	111	set	set	NOUN
ejpam-4665	246	112	in	in	ADP
ejpam-4665	246	113	g	g	NOUN
ejpam-4665	246	114	;	;	PUNCT
ejpam-4665	246	115	(	(	PUNCT
ejpam-4665	246	116	iii	iii	X
ejpam-4665	246	117	)	)	PUNCT
ejpam-4665	246	118	sg	sg	ADP
ejpam-4665	246	119	̸=	̸=	PROPN
ejpam-4665	246	120	v	v	NOUN
ejpam-4665	246	121	(	(	PUNCT
ejpam-4665	246	122	g	g	NOUN
ejpam-4665	246	123	)	)	PUNCT
ejpam-4665	246	124	and	and	CCONJ
ejpam-4665	246	125	sh	sh	INTJ
ejpam-4665	246	126	̸=	̸=	PROPN
ejpam-4665	246	127	v	v	NOUN
ejpam-4665	246	128	(	(	PUNCT
ejpam-4665	246	129	h	h	NOUN
ejpam-4665	246	130	)	)	PUNCT
ejpam-4665	246	131	.	.	PUNCT
ejpam-4665	247	1	theorem	theorem	NOUN
ejpam-4665	247	2	9	9	NUM
ejpam-4665	247	3	.	.	PUNCT
ejpam-4665	248	1	let	let	VERB
ejpam-4665	248	2	g	g	NOUN
ejpam-4665	248	3	and	and	CCONJ
ejpam-4665	248	4	h	h	NOUN
ejpam-4665	248	5	be	be	VERB
ejpam-4665	248	6	any	any	DET
ejpam-4665	248	7	two	two	NUM
ejpam-4665	248	8	graphs	graph	NOUN
ejpam-4665	248	9	.	.	PUNCT
ejpam-4665	249	1	a	a	DET
ejpam-4665	249	2	set	set	NOUN
ejpam-4665	249	3	s	s	NOUN
ejpam-4665	249	4	⊆	⊆	NUM
ejpam-4665	249	5	v	v	NOUN
ejpam-4665	249	6	(	(	PUNCT
ejpam-4665	249	7	g	g	PROPN
ejpam-4665	249	8	+	+	NOUN
ejpam-4665	249	9	h	h	NOUN
ejpam-4665	249	10	)	)	PUNCT
ejpam-4665	249	11	is	be	AUX
ejpam-4665	249	12	a	a	DET
ejpam-4665	249	13	restrained	restrained	ADJ
ejpam-4665	249	14	2	2	NUM
ejpam-4665	249	15	-	-	PUNCT
ejpam-4665	249	16	resolving	resolve	VERB
ejpam-4665	249	17	hop	hop	NOUN
ejpam-4665	249	18	dominating	dominating	NOUN
ejpam-4665	249	19	set	set	VERB
ejpam-4665	249	20	in	in	ADP
ejpam-4665	249	21	g+h	g+h	PROPN
ejpam-4665	250	1	if	if	SCONJ
ejpam-4665	250	2	and	and	CCONJ
ejpam-4665	250	3	only	only	ADV
ejpam-4665	250	4	if	if	SCONJ
ejpam-4665	250	5	sg	sg	PROPN
ejpam-4665	250	6	=	=	SYM
ejpam-4665	250	7	v	v	NOUN
ejpam-4665	250	8	(	(	PUNCT
ejpam-4665	250	9	g)∩s	g)∩s	PROPN
ejpam-4665	250	10	and	and	CCONJ
ejpam-4665	250	11	sh	sh	PROPN
ejpam-4665	250	12	=	=	SYM
ejpam-4665	250	13	v	v	PROPN
ejpam-4665	250	14	(	(	PUNCT
ejpam-4665	250	15	h)∩s	h)∩s	PROPN
ejpam-4665	250	16	a.m.	a.m.	PROPN
ejpam-4665	250	17	mahistrado	mahistrado	PROPN
ejpam-4665	250	18	,	,	PUNCT
ejpam-4665	250	19	h.	h.	PROPN
ejpam-4665	250	20	rara	rara	PROPN
ejpam-4665	250	21	/	/	SYM
ejpam-4665	250	22	eur	eur	PROPN
ejpam-4665	250	23	.	.	PUNCT
ejpam-4665	251	1	j.	j.	PROPN
ejpam-4665	251	2	pure	pure	PROPN
ejpam-4665	251	3	appl	appl	PROPN
ejpam-4665	251	4	.	.	PROPN
ejpam-4665	251	5	math	math	PROPN
ejpam-4665	251	6	,	,	PUNCT
ejpam-4665	251	7	16	16	NUM
ejpam-4665	251	8	(	(	PUNCT
ejpam-4665	251	9	1	1	NUM
ejpam-4665	251	10	)	)	PUNCT
ejpam-4665	251	11	(	(	PUNCT
ejpam-4665	251	12	2023	2023	NUM
ejpam-4665	251	13	)	)	PUNCT
ejpam-4665	251	14	,	,	PUNCT
ejpam-4665	251	15	286	286	NUM
ejpam-4665	251	16	-	-	SYM
ejpam-4665	251	17	303	303	NUM
ejpam-4665	251	18	294	294	NUM
ejpam-4665	251	19	are	be	AUX
ejpam-4665	251	20	2	2	NUM
ejpam-4665	251	21	-	-	PUNCT
ejpam-4665	251	22	locating	locate	VERB
ejpam-4665	251	23	pointwise	pointwise	ADJ
ejpam-4665	251	24	non	non	ADJ
ejpam-4665	251	25	-	-	ADJ
ejpam-4665	251	26	dominating	dominating	ADJ
ejpam-4665	251	27	sets	set	NOUN
ejpam-4665	251	28	in	in	ADP
ejpam-4665	251	29	g	g	PROPN
ejpam-4665	251	30	and	and	CCONJ
ejpam-4665	251	31	h	h	NOUN
ejpam-4665	251	32	,	,	PUNCT
ejpam-4665	251	33	respectively	respectively	ADV
ejpam-4665	251	34	where	where	SCONJ
ejpam-4665	251	35	sg	sg	PROPN
ejpam-4665	251	36	or	or	CCONJ
ejpam-4665	251	37	sh	sh	PROPN
ejpam-4665	251	38	is	be	AUX
ejpam-4665	251	39	a	a	DET
ejpam-4665	251	40	(	(	PUNCT
ejpam-4665	251	41	2	2	NUM
ejpam-4665	251	42	,	,	PUNCT
ejpam-4665	251	43	2)-locating	2)-locating	NUM
ejpam-4665	251	44	point	point	NOUN
ejpam-4665	251	45	-	-	PUNCT
ejpam-4665	251	46	wise	wise	ADJ
ejpam-4665	251	47	non	non	ADJ
ejpam-4665	251	48	-	-	ADJ
ejpam-4665	251	49	dominating	dominating	ADJ
ejpam-4665	251	50	set	set	NOUN
ejpam-4665	251	51	or	or	CCONJ
ejpam-4665	251	52	sg	sg	PROPN
ejpam-4665	251	53	and	and	CCONJ
ejpam-4665	251	54	sh	sh	PROPN
ejpam-4665	251	55	are	be	AUX
ejpam-4665	251	56	(	(	PUNCT
ejpam-4665	251	57	2	2	NUM
ejpam-4665	251	58	,	,	PUNCT
ejpam-4665	251	59	1)-locating	1)-locating	NUM
ejpam-4665	251	60	point	point	NOUN
ejpam-4665	251	61	-	-	PUNCT
ejpam-4665	251	62	wise	wise	ADJ
ejpam-4665	251	63	non	non	ADJ
ejpam-4665	251	64	-	-	ADJ
ejpam-4665	251	65	dominating	dominating	ADJ
ejpam-4665	251	66	sets	set	NOUN
ejpam-4665	251	67	and	and	CCONJ
ejpam-4665	251	68	one	one	NUM
ejpam-4665	251	69	of	of	ADP
ejpam-4665	251	70	the	the	DET
ejpam-4665	251	71	following	follow	VERB
ejpam-4665	251	72	holds	hold	VERB
ejpam-4665	251	73	:	:	PUNCT
ejpam-4665	251	74	(	(	PUNCT
ejpam-4665	251	75	i	i	NOUN
ejpam-4665	251	76	)	)	PUNCT
ejpam-4665	251	77	sg	sg	PROPN
ejpam-4665	251	78	=	=	SYM
ejpam-4665	251	79	v	v	PROPN
ejpam-4665	251	80	(	(	PUNCT
ejpam-4665	251	81	g	g	NOUN
ejpam-4665	251	82	)	)	PUNCT
ejpam-4665	251	83	and	and	CCONJ
ejpam-4665	251	84	sh	sh	PROPN
ejpam-4665	251	85	is	be	AUX
ejpam-4665	251	86	a	a	DET
ejpam-4665	251	87	restrained	restrained	ADJ
ejpam-4665	251	88	2	2	NUM
ejpam-4665	251	89	-	-	PUNCT
ejpam-4665	251	90	locating	locate	VERB
ejpam-4665	251	91	point	point	NOUN
ejpam-4665	251	92	-	-	PUNCT
ejpam-4665	251	93	wise	wise	ADJ
ejpam-4665	251	94	non	non	ADJ
ejpam-4665	251	95	-	-	ADJ
ejpam-4665	251	96	dominating	dominating	ADJ
ejpam-4665	251	97	set	set	NOUN
ejpam-4665	251	98	in	in	ADP
ejpam-4665	251	99	h	h	NOUN
ejpam-4665	251	100	;	;	PUNCT
ejpam-4665	251	101	(	(	PUNCT
ejpam-4665	251	102	ii	ii	NOUN
ejpam-4665	251	103	)	)	PUNCT
ejpam-4665	251	104	sh	sh	PROPN
ejpam-4665	251	105	=	=	SYM
ejpam-4665	251	106	v	v	PROPN
ejpam-4665	251	107	(	(	PUNCT
ejpam-4665	251	108	h	h	NOUN
ejpam-4665	251	109	)	)	PUNCT
ejpam-4665	251	110	and	and	CCONJ
ejpam-4665	251	111	sg	sg	PROPN
ejpam-4665	251	112	is	be	AUX
ejpam-4665	251	113	a	a	DET
ejpam-4665	251	114	restrained	restrained	ADJ
ejpam-4665	251	115	2	2	NUM
ejpam-4665	251	116	-	-	PUNCT
ejpam-4665	251	117	locating	locate	VERB
ejpam-4665	251	118	point	point	NOUN
ejpam-4665	251	119	-	-	PUNCT
ejpam-4665	251	120	wise	wise	ADJ
ejpam-4665	251	121	non	non	ADJ
ejpam-4665	251	122	-	-	ADJ
ejpam-4665	251	123	dominating	dominating	ADJ
ejpam-4665	251	124	set	set	NOUN
ejpam-4665	251	125	in	in	ADP
ejpam-4665	251	126	g	g	NOUN
ejpam-4665	251	127	;	;	PUNCT
ejpam-4665	251	128	and	and	CCONJ
ejpam-4665	251	129	(	(	PUNCT
ejpam-4665	251	130	iii	iii	X
ejpam-4665	251	131	)	)	PUNCT
ejpam-4665	251	132	sg	sg	ADP
ejpam-4665	251	133	̸=	̸=	PROPN
ejpam-4665	251	134	v	v	NOUN
ejpam-4665	251	135	(	(	PUNCT
ejpam-4665	251	136	g	g	NOUN
ejpam-4665	251	137	)	)	PUNCT
ejpam-4665	251	138	and	and	CCONJ
ejpam-4665	251	139	sh	sh	INTJ
ejpam-4665	251	140	̸=	̸=	PROPN
ejpam-4665	251	141	v	v	NOUN
ejpam-4665	251	142	(	(	PUNCT
ejpam-4665	251	143	h	h	NOUN
ejpam-4665	251	144	)	)	PUNCT
ejpam-4665	251	145	.	.	PUNCT
ejpam-4665	252	1	proof	proof	NOUN
ejpam-4665	252	2	.	.	PUNCT
ejpam-4665	253	1	suppose	suppose	VERB
ejpam-4665	253	2	that	that	SCONJ
ejpam-4665	253	3	s	s	VERB
ejpam-4665	253	4	⊆	⊆	NUM
ejpam-4665	253	5	v	v	NOUN
ejpam-4665	253	6	(	(	PUNCT
ejpam-4665	253	7	g+h	g+h	PROPN
ejpam-4665	253	8	)	)	PUNCT
ejpam-4665	253	9	is	be	AUX
ejpam-4665	253	10	a	a	DET
ejpam-4665	253	11	restrained	restrained	ADJ
ejpam-4665	253	12	2	2	NUM
ejpam-4665	253	13	-	-	PUNCT
ejpam-4665	253	14	resolving	resolve	VERB
ejpam-4665	253	15	hop	hop	NOUN
ejpam-4665	253	16	dominating	dominating	NOUN
ejpam-4665	253	17	set	set	VERB
ejpam-4665	253	18	in	in	ADP
ejpam-4665	253	19	g+h	g+h	PROPN
ejpam-4665	253	20	.	.	PUNCT
ejpam-4665	254	1	let	let	VERB
ejpam-4665	254	2	sg	sg	INTJ
ejpam-4665	254	3	=	=	SYM
ejpam-4665	254	4	v	v	PROPN
ejpam-4665	254	5	(	(	PUNCT
ejpam-4665	254	6	g	g	NOUN
ejpam-4665	254	7	)	)	PUNCT
ejpam-4665	254	8	∩	∩	NOUN
ejpam-4665	254	9	s	s	NOUN
ejpam-4665	254	10	and	and	CCONJ
ejpam-4665	254	11	sh	sh	PROPN
ejpam-4665	254	12	=	=	SYM
ejpam-4665	254	13	v	v	PROPN
ejpam-4665	254	14	(	(	PUNCT
ejpam-4665	254	15	h	h	NOUN
ejpam-4665	254	16	)	)	PUNCT
ejpam-4665	254	17	∩	∩	NOUN
ejpam-4665	254	18	s	s	VERB
ejpam-4665	254	19	where	where	SCONJ
ejpam-4665	254	20	s	s	VERB
ejpam-4665	254	21	=	=	PUNCT
ejpam-4665	254	22	sg	sg	X
ejpam-4665	254	23	∪	∪	VERB
ejpam-4665	254	24	sh	sh	PROPN
ejpam-4665	254	25	.	.	PUNCT
ejpam-4665	255	1	now	now	ADV
ejpam-4665	255	2	,	,	PUNCT
ejpam-4665	255	3	since	since	SCONJ
ejpam-4665	255	4	s	s	NOUN
ejpam-4665	255	5	is	be	AUX
ejpam-4665	255	6	a	a	DET
ejpam-4665	255	7	2	2	NUM
ejpam-4665	255	8	-	-	PUNCT
ejpam-4665	255	9	resolving	resolve	VERB
ejpam-4665	255	10	hop	hop	NOUN
ejpam-4665	255	11	dominating	dominating	NOUN
ejpam-4665	255	12	set	set	VERB
ejpam-4665	255	13	by	by	ADP
ejpam-4665	255	14	theorem	theorem	NOUN
ejpam-4665	255	15	7	7	NUM
ejpam-4665	255	16	,	,	PUNCT
ejpam-4665	255	17	sg	sg	PROPN
ejpam-4665	255	18	and	and	CCONJ
ejpam-4665	255	19	sh	sh	PROPN
ejpam-4665	255	20	are	be	AUX
ejpam-4665	255	21	2	2	NUM
ejpam-4665	255	22	-	-	PUNCT
ejpam-4665	255	23	locating	locate	VERB
ejpam-4665	255	24	point	point	NOUN
ejpam-4665	255	25	-	-	PUNCT
ejpam-4665	255	26	wise	wise	ADJ
ejpam-4665	255	27	nondominating	nondominate	VERB
ejpam-4665	255	28	sets	set	NOUN
ejpam-4665	255	29	in	in	ADP
ejpam-4665	255	30	g	g	PROPN
ejpam-4665	255	31	and	and	CCONJ
ejpam-4665	255	32	h	h	NOUN
ejpam-4665	255	33	,	,	PUNCT
ejpam-4665	255	34	respectively	respectively	ADV
ejpam-4665	255	35	,	,	PUNCT
ejpam-4665	255	36	where	where	SCONJ
ejpam-4665	255	37	sg	sg	NOUN
ejpam-4665	255	38	or	or	CCONJ
ejpam-4665	255	39	sh	sh	PROPN
ejpam-4665	255	40	is	be	AUX
ejpam-4665	255	41	a	a	DET
ejpam-4665	255	42	(	(	PUNCT
ejpam-4665	255	43	2	2	NUM
ejpam-4665	255	44	,	,	PUNCT
ejpam-4665	255	45	2)-locating	2)-locating	NUM
ejpam-4665	255	46	point	point	NOUN
ejpam-4665	255	47	-	-	PUNCT
ejpam-4665	255	48	wise	wise	ADJ
ejpam-4665	255	49	non	non	ADJ
ejpam-4665	255	50	-	-	ADJ
ejpam-4665	255	51	dominating	dominating	ADJ
ejpam-4665	255	52	set	set	NOUN
ejpam-4665	255	53	or	or	CCONJ
ejpam-4665	255	54	sg	sg	PROPN
ejpam-4665	256	1	and	and	CCONJ
ejpam-4665	256	2	sh	sh	INTJ
ejpam-4665	256	3	(	(	PUNCT
ejpam-4665	256	4	2	2	NUM
ejpam-4665	256	5	,	,	PUNCT
ejpam-4665	256	6	1)-locating	1)-locating	NUM
ejpam-4665	256	7	point	point	NOUN
ejpam-4665	256	8	-	-	PUNCT
ejpam-4665	256	9	wise	wise	ADJ
ejpam-4665	256	10	non	non	ADJ
ejpam-4665	256	11	-	-	ADJ
ejpam-4665	256	12	dominating	dominating	ADJ
ejpam-4665	256	13	sets	set	NOUN
ejpam-4665	256	14	of	of	ADP
ejpam-4665	256	15	g	g	PROPN
ejpam-4665	256	16	and	and	CCONJ
ejpam-4665	256	17	h	h	NOUN
ejpam-4665	256	18	,	,	PUNCT
ejpam-4665	256	19	respectively	respectively	ADV
ejpam-4665	256	20	.	.	PUNCT
ejpam-4665	257	1	suppose	suppose	VERB
ejpam-4665	257	2	sg	sg	PROPN
ejpam-4665	257	3	=	=	SYM
ejpam-4665	257	4	v	v	PROPN
ejpam-4665	257	5	(	(	PUNCT
ejpam-4665	257	6	g	g	NOUN
ejpam-4665	257	7	)	)	PUNCT
ejpam-4665	257	8	.	.	PUNCT
ejpam-4665	258	1	let	let	VERB
ejpam-4665	258	2	sh	sh	PRON
ejpam-4665	258	3	̸=	̸=	PROPN
ejpam-4665	258	4	v	v	NOUN
ejpam-4665	258	5	(	(	PUNCT
ejpam-4665	258	6	h	h	NOUN
ejpam-4665	258	7	)	)	PUNCT
ejpam-4665	258	8	.	.	PUNCT
ejpam-4665	259	1	since	since	SCONJ
ejpam-4665	259	2	s	s	NOUN
ejpam-4665	259	3	is	be	AUX
ejpam-4665	259	4	restrained	restrain	VERB
ejpam-4665	259	5	2	2	NUM
ejpam-4665	259	6	-	-	PUNCT
ejpam-4665	259	7	resolving	resolve	VERB
ejpam-4665	259	8	hop	hop	NOUN
ejpam-4665	259	9	dominating	dominating	NOUN
ejpam-4665	259	10	,	,	PUNCT
ejpam-4665	259	11	s	s	PART
ejpam-4665	259	12	=	=	SYM
ejpam-4665	259	13	v	v	NOUN
ejpam-4665	259	14	(	(	PUNCT
ejpam-4665	259	15	g	g	PROPN
ejpam-4665	259	16	+	+	NOUN
ejpam-4665	259	17	h	h	NOUN
ejpam-4665	259	18	)	)	PUNCT
ejpam-4665	259	19	or	or	CCONJ
ejpam-4665	259	20	⟨v	⟨v	NUM
ejpam-4665	259	21	(	(	PUNCT
ejpam-4665	259	22	g+h)\s⟩	g+h)\s⟩	PROPN
ejpam-4665	259	23	=	=	SYM
ejpam-4665	259	24	⟨v	⟨v	PROPN
ejpam-4665	259	25	(	(	PUNCT
ejpam-4665	259	26	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4665	259	27	has	have	AUX
ejpam-4665	259	28	no	no	DET
ejpam-4665	259	29	isolated	isolated	ADJ
ejpam-4665	259	30	vertex	vertex	NOUN
ejpam-4665	259	31	.	.	PUNCT
ejpam-4665	260	1	hence	hence	ADV
ejpam-4665	260	2	,	,	PUNCT
ejpam-4665	260	3	sh	sh	PROPN
ejpam-4665	260	4	=	=	SYM
ejpam-4665	260	5	v	v	PROPN
ejpam-4665	260	6	(	(	PUNCT
ejpam-4665	260	7	h	h	NOUN
ejpam-4665	260	8	)	)	PUNCT
ejpam-4665	260	9	or	or	CCONJ
ejpam-4665	260	10	⟨v	⟨v	NUM
ejpam-4665	260	11	(	(	PUNCT
ejpam-4665	260	12	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4665	260	13	has	have	AUX
ejpam-4665	260	14	no	no	DET
ejpam-4665	260	15	isolated	isolated	ADJ
ejpam-4665	260	16	vertex	vertex	NOUN
ejpam-4665	260	17	.	.	PUNCT
ejpam-4665	261	1	thus	thus	ADV
ejpam-4665	261	2	,	,	PUNCT
ejpam-4665	261	3	it	it	PRON
ejpam-4665	261	4	follows	follow	VERB
ejpam-4665	261	5	that	that	SCONJ
ejpam-4665	261	6	sh	sh	PROPN
ejpam-4665	261	7	is	be	AUX
ejpam-4665	261	8	a	a	DET
ejpam-4665	261	9	restrained	restrained	ADJ
ejpam-4665	261	10	2	2	NUM
ejpam-4665	261	11	-	-	PUNCT
ejpam-4665	261	12	locating	locate	VERB
ejpam-4665	261	13	point	point	NOUN
ejpam-4665	261	14	-	-	PUNCT
ejpam-4665	261	15	wise	wise	ADJ
ejpam-4665	261	16	non	non	ADJ
ejpam-4665	261	17	-	-	ADJ
ejpam-4665	261	18	dominating	dominating	ADJ
ejpam-4665	261	19	set	set	NOUN
ejpam-4665	261	20	of	of	ADP
ejpam-4665	261	21	h	h	NOUN
ejpam-4665	262	1	and	and	CCONJ
ejpam-4665	262	2	so	so	ADV
ejpam-4665	262	3	(	(	PUNCT
ejpam-4665	262	4	i	i	NOUN
ejpam-4665	262	5	)	)	PUNCT
ejpam-4665	262	6	holds	hold	VERB
ejpam-4665	262	7	.	.	PUNCT
ejpam-4665	263	1	next	next	ADV
ejpam-4665	263	2	,	,	PUNCT
ejpam-4665	263	3	suppose	suppose	VERB
ejpam-4665	263	4	that	that	SCONJ
ejpam-4665	263	5	sg	sg	PROPN
ejpam-4665	263	6	̸=	̸=	PROPN
ejpam-4665	263	7	v	v	NOUN
ejpam-4665	263	8	(	(	PUNCT
ejpam-4665	263	9	g	g	NOUN
ejpam-4665	263	10	)	)	PUNCT
ejpam-4665	263	11	.	.	PUNCT
ejpam-4665	264	1	if	if	SCONJ
ejpam-4665	264	2	sh	sh	PROPN
ejpam-4665	264	3	̸=	̸=	PROPN
ejpam-4665	264	4	v	v	NOUN
ejpam-4665	264	5	(	(	PUNCT
ejpam-4665	264	6	h	h	NOUN
ejpam-4665	264	7	)	)	PUNCT
ejpam-4665	264	8	,	,	PUNCT
ejpam-4665	264	9	then	then	ADV
ejpam-4665	264	10	(	(	PUNCT
ejpam-4665	264	11	iii	iii	NOUN
ejpam-4665	264	12	)	)	PUNCT
ejpam-4665	264	13	holds	hold	VERB
ejpam-4665	264	14	.	.	PUNCT
ejpam-4665	265	1	on	on	ADP
ejpam-4665	265	2	the	the	DET
ejpam-4665	265	3	other	other	ADJ
ejpam-4665	265	4	hand	hand	NOUN
ejpam-4665	265	5	,	,	PUNCT
ejpam-4665	265	6	if	if	SCONJ
ejpam-4665	265	7	sh	sh	PROPN
ejpam-4665	265	8	=	=	SYM
ejpam-4665	265	9	v	v	PROPN
ejpam-4665	265	10	(	(	PUNCT
ejpam-4665	265	11	h	h	NOUN
ejpam-4665	265	12	)	)	PUNCT
ejpam-4665	265	13	,	,	PUNCT
ejpam-4665	265	14	then	then	ADV
ejpam-4665	265	15	⟨v	⟨v	CCONJ
ejpam-4665	265	16	(	(	PUNCT
ejpam-4665	265	17	g)\sg⟩	g)\sg⟩	X
ejpam-4665	265	18	has	have	VERB
ejpam-4665	265	19	no	no	DET
ejpam-4665	265	20	isolated	isolated	ADJ
ejpam-4665	265	21	vertex	vertex	NOUN
ejpam-4665	265	22	and	and	CCONJ
ejpam-4665	265	23	so	so	ADV
ejpam-4665	265	24	(	(	PUNCT
ejpam-4665	265	25	ii	ii	NOUN
ejpam-4665	265	26	)	)	PUNCT
ejpam-4665	265	27	holds	hold	VERB
ejpam-4665	265	28	.	.	PUNCT
ejpam-4665	266	1	conversely	conversely	ADV
ejpam-4665	266	2	,	,	PUNCT
ejpam-4665	266	3	suppose	suppose	VERB
ejpam-4665	266	4	that	that	SCONJ
ejpam-4665	266	5	s	s	VERB
ejpam-4665	266	6	=	=	PUNCT
ejpam-4665	266	7	sg	sg	X
ejpam-4665	266	8	∪	∪	NOUN
ejpam-4665	266	9	sh	sh	PROPN
ejpam-4665	266	10	where	where	SCONJ
ejpam-4665	266	11	sg	sg	PROPN
ejpam-4665	266	12	⊆	⊆	NUM
ejpam-4665	266	13	v	v	NOUN
ejpam-4665	266	14	(	(	PUNCT
ejpam-4665	266	15	g	g	NOUN
ejpam-4665	266	16	)	)	PUNCT
ejpam-4665	266	17	and	and	CCONJ
ejpam-4665	266	18	sh	sh	PROPN
ejpam-4665	266	19	⊆	⊆	NUM
ejpam-4665	266	20	v	v	NOUN
ejpam-4665	266	21	(	(	PUNCT
ejpam-4665	266	22	h	h	NOUN
ejpam-4665	266	23	)	)	PUNCT
ejpam-4665	266	24	are	be	AUX
ejpam-4665	266	25	2locating	2locating	NUM
ejpam-4665	266	26	point	point	NOUN
ejpam-4665	266	27	-	-	PUNCT
ejpam-4665	266	28	wise	wise	ADJ
ejpam-4665	266	29	non	non	ADJ
ejpam-4665	266	30	-	-	ADJ
ejpam-4665	266	31	dominating	dominating	ADJ
ejpam-4665	266	32	sets	set	NOUN
ejpam-4665	266	33	of	of	ADP
ejpam-4665	266	34	g	g	PROPN
ejpam-4665	266	35	and	and	CCONJ
ejpam-4665	266	36	h	h	NOUN
ejpam-4665	266	37	,	,	PUNCT
ejpam-4665	266	38	respectively	respectively	ADV
ejpam-4665	266	39	,	,	PUNCT
ejpam-4665	266	40	and	and	CCONJ
ejpam-4665	266	41	(	(	PUNCT
ejpam-4665	266	42	i	i	NOUN
ejpam-4665	266	43	)	)	PUNCT
ejpam-4665	266	44	,	,	PUNCT
ejpam-4665	266	45	(	(	PUNCT
ejpam-4665	266	46	ii	ii	NOUN
ejpam-4665	266	47	)	)	PUNCT
ejpam-4665	266	48	and	and	CCONJ
ejpam-4665	266	49	(	(	PUNCT
ejpam-4665	266	50	iii	iii	NOUN
ejpam-4665	266	51	)	)	PUNCT
ejpam-4665	266	52	hold	hold	NOUN
ejpam-4665	266	53	.	.	PUNCT
ejpam-4665	267	1	by	by	ADP
ejpam-4665	267	2	theorem	theorem	NOUN
ejpam-4665	267	3	7	7	NUM
ejpam-4665	267	4	,	,	PUNCT
ejpam-4665	267	5	s	s	VERB
ejpam-4665	267	6	is	be	AUX
ejpam-4665	267	7	a	a	DET
ejpam-4665	267	8	2	2	NUM
ejpam-4665	267	9	-	-	PUNCT
ejpam-4665	267	10	resolving	resolve	VERB
ejpam-4665	267	11	hop	hop	NOUN
ejpam-4665	267	12	dominating	dominating	NOUN
ejpam-4665	267	13	set	set	NOUN
ejpam-4665	267	14	of	of	ADP
ejpam-4665	267	15	g	g	PROPN
ejpam-4665	267	16	+	+	CCONJ
ejpam-4665	267	17	h.	h.	NOUN
ejpam-4665	268	1	if	if	SCONJ
ejpam-4665	268	2	(	(	PUNCT
ejpam-4665	268	3	i	i	NOUN
ejpam-4665	268	4	)	)	PUNCT
ejpam-4665	268	5	holds	hold	VERB
ejpam-4665	268	6	,	,	PUNCT
ejpam-4665	268	7	then	then	ADV
ejpam-4665	268	8	s	s	VERB
ejpam-4665	268	9	=	=	SYM
ejpam-4665	268	10	v	v	NOUN
ejpam-4665	268	11	(	(	PUNCT
ejpam-4665	268	12	g	g	PROPN
ejpam-4665	268	13	+	+	NOUN
ejpam-4665	268	14	h	h	NOUN
ejpam-4665	268	15	)	)	PUNCT
ejpam-4665	268	16	or	or	CCONJ
ejpam-4665	268	17	⟨v	⟨v	NUM
ejpam-4665	268	18	(	(	PUNCT
ejpam-4665	268	19	g+h)\s⟩	g+h)\s⟩	PROPN
ejpam-4665	268	20	=	=	SYM
ejpam-4665	268	21	⟨v	⟨v	PROPN
ejpam-4665	268	22	(	(	PUNCT
ejpam-4665	268	23	h)\sh⟩	h)\sh⟩	NOUN
ejpam-4665	268	24	has	have	AUX
ejpam-4665	268	25	no	no	DET
ejpam-4665	268	26	isolated	isolated	ADJ
ejpam-4665	268	27	vertex	vertex	NOUN
ejpam-4665	268	28	since	since	SCONJ
ejpam-4665	268	29	sh	sh	PROPN
ejpam-4665	268	30	is	be	AUX
ejpam-4665	268	31	restrained	restrain	VERB
ejpam-4665	268	32	2	2	NUM
ejpam-4665	268	33	-	-	PUNCT
ejpam-4665	268	34	resolving	resolve	VERB
ejpam-4665	268	35	hop	hop	NOUN
ejpam-4665	268	36	dominating	dominating	NOUN
ejpam-4665	268	37	.	.	PUNCT
ejpam-4665	269	1	similarly	similarly	ADV
ejpam-4665	269	2	,	,	PUNCT
ejpam-4665	269	3	if	if	SCONJ
ejpam-4665	269	4	(	(	PUNCT
ejpam-4665	269	5	ii	ii	NOUN
ejpam-4665	269	6	)	)	PUNCT
ejpam-4665	269	7	holds	hold	VERB
ejpam-4665	269	8	,	,	PUNCT
ejpam-4665	269	9	then	then	ADV
ejpam-4665	269	10	s	s	VERB
ejpam-4665	269	11	=	=	SYM
ejpam-4665	269	12	v	v	PROPN
ejpam-4665	269	13	(	(	PUNCT
ejpam-4665	269	14	g	g	PROPN
ejpam-4665	269	15	+	+	NOUN
ejpam-4665	269	16	h	h	NOUN
ejpam-4665	269	17	)	)	PUNCT
ejpam-4665	269	18	or	or	CCONJ
ejpam-4665	269	19	⟨v	⟨v	NUM
ejpam-4665	269	20	(	(	PUNCT
ejpam-4665	269	21	g+h)\s⟩	g+h)\s⟩	PROPN
ejpam-4665	269	22	=	=	SYM
ejpam-4665	269	23	⟨v	⟨v	PROPN
ejpam-4665	269	24	(	(	PUNCT
ejpam-4665	269	25	g)\sg⟩	g)\sg⟩	X
ejpam-4665	269	26	has	have	VERB
ejpam-4665	269	27	no	no	DET
ejpam-4665	269	28	isolated	isolated	ADJ
ejpam-4665	269	29	vertex	vertex	NOUN
ejpam-4665	269	30	since	since	SCONJ
ejpam-4665	269	31	sg	sg	PROPN
ejpam-4665	269	32	is	be	AUX
ejpam-4665	269	33	restrained	restrain	VERB
ejpam-4665	269	34	2	2	NUM
ejpam-4665	269	35	-	-	PUNCT
ejpam-4665	269	36	resolving	resolve	VERB
ejpam-4665	269	37	hop	hop	NOUN
ejpam-4665	269	38	dominating	dominating	NOUN
ejpam-4665	269	39	set	set	NOUN
ejpam-4665	269	40	.	.	PUNCT
ejpam-4665	270	1	therefore	therefore	ADV
ejpam-4665	270	2	,	,	PUNCT
ejpam-4665	270	3	it	it	PRON
ejpam-4665	270	4	follows	follow	VERB
ejpam-4665	270	5	that	that	SCONJ
ejpam-4665	270	6	s	s	VERB
ejpam-4665	270	7	is	be	AUX
ejpam-4665	270	8	a	a	DET
ejpam-4665	270	9	restrained	restrained	ADJ
ejpam-4665	270	10	2	2	NUM
ejpam-4665	270	11	-	-	PUNCT
ejpam-4665	270	12	resolving	resolve	VERB
ejpam-4665	270	13	hop	hop	NOUN
ejpam-4665	270	14	dominating	dominating	NOUN
ejpam-4665	270	15	set	set	NOUN
ejpam-4665	270	16	of	of	ADP
ejpam-4665	270	17	g+h	g+h	PROPN
ejpam-4665	270	18	.	.	PUNCT
ejpam-4665	271	1	as	as	ADP
ejpam-4665	271	2	a	a	DET
ejpam-4665	271	3	consequence	consequence	NOUN
ejpam-4665	271	4	of	of	ADP
ejpam-4665	271	5	theorem	theorem	NOUN
ejpam-4665	271	6	9	9	NUM
ejpam-4665	271	7	the	the	DET
ejpam-4665	271	8	next	next	ADJ
ejpam-4665	271	9	result	result	NOUN
ejpam-4665	271	10	follows	follow	VERB
ejpam-4665	271	11	.	.	PUNCT
ejpam-4665	272	1	corollary	corollary	ADJ
ejpam-4665	272	2	2	2	NUM
ejpam-4665	272	3	.	.	PUNCT
ejpam-4665	273	1	let	let	VERB
ejpam-4665	273	2	g	g	NOUN
ejpam-4665	273	3	and	and	CCONJ
ejpam-4665	273	4	h	h	NOUN
ejpam-4665	273	5	be	be	AUX
ejpam-4665	273	6	nontrivial	nontrivial	ADJ
ejpam-4665	273	7	connected	connected	ADJ
ejpam-4665	273	8	graphs	graph	NOUN
ejpam-4665	273	9	.	.	PUNCT
ejpam-4665	274	1	then	then	ADV
ejpam-4665	274	2	γr2rh(g+h	γr2rh(g+h	NUM
ejpam-4665	274	3	)	)	PUNCT
ejpam-4665	274	4	=	=	SYM
ejpam-4665	274	5			NUM
ejpam-4665	275	1	m+	m+	NUM
ejpam-4665	275	2	n	n	CCONJ
ejpam-4665	275	3	,	,	PUNCT
ejpam-4665	275	4	if	if	SCONJ
ejpam-4665	275	5	rlnpnd	rlnpnd	NOUN
ejpam-4665	275	6	2	2	NUM
ejpam-4665	275	7	(	(	PUNCT
ejpam-4665	275	8	g	g	NOUN
ejpam-4665	275	9	)	)	PUNCT
ejpam-4665	275	10	=	=	NOUN
ejpam-4665	276	1	m	m	NOUN
ejpam-4665	276	2	and	and	CCONJ
ejpam-4665	276	3	rlnpnd	rlnpnd	NOUN
ejpam-4665	276	4	2	2	NUM
ejpam-4665	276	5	(	(	PUNCT
ejpam-4665	276	6	h	h	NOUN
ejpam-4665	276	7	)	)	PUNCT
ejpam-4665	276	8	=	=	SYM
ejpam-4665	276	9	n	n	PRON
ejpam-4665	276	10	min{lnpnd	min{lnpnd	NOUN
ejpam-4665	276	11	(	(	PUNCT
ejpam-4665	276	12	2,2)(g	2,2)(g	NUM
ejpam-4665	276	13	)	)	PUNCT
ejpam-4665	277	1	+	+	CCONJ
ejpam-4665	277	2	lnpnd	lnpnd	ADJ
ejpam-4665	277	3	2	2	NUM
ejpam-4665	277	4	(	(	PUNCT
ejpam-4665	277	5	h	h	NOUN
ejpam-4665	277	6	)	)	PUNCT
ejpam-4665	277	7	,	,	PUNCT
ejpam-4665	277	8	lnpnd	lnpnd	PROPN
ejpam-4665	277	9	2	2	NUM
ejpam-4665	277	10	(	(	PUNCT
ejpam-4665	277	11	g	g	NOUN
ejpam-4665	277	12	)	)	PUNCT
ejpam-4665	277	13	+	+	CCONJ
ejpam-4665	277	14	lnpnd	lnpnd	ADJ
ejpam-4665	277	15	(	(	PUNCT
ejpam-4665	277	16	2,2)(h	2,2)(h	NUM
ejpam-4665	277	17	)	)	PUNCT
ejpam-4665	277	18	,	,	PUNCT
ejpam-4665	277	19	lnpnd	lnpnd	ADJ
ejpam-4665	277	20	(	(	PUNCT
ejpam-4665	277	21	2,1)(g	2,1)(g	NUM
ejpam-4665	277	22	)	)	PUNCT
ejpam-4665	278	1	+	+	CCONJ
ejpam-4665	278	2	lnpnd	lnpnd	ADJ
ejpam-4665	278	3	(	(	PUNCT
ejpam-4665	278	4	2,1)(h	2,1)(h	NUM
ejpam-4665	278	5	)	)	PUNCT
ejpam-4665	278	6	}	}	PUNCT
ejpam-4665	278	7	,	,	PUNCT
ejpam-4665	278	8	otherwise	otherwise	ADV
ejpam-4665	278	9	.	.	PUNCT
ejpam-4665	278	10	example	example	NOUN
ejpam-4665	279	1	4	4	NUM
ejpam-4665	279	2	.	.	X
ejpam-4665	280	1	for	for	ADP
ejpam-4665	280	2	any	any	DET
ejpam-4665	280	3	nontrivial	nontrivial	ADJ
ejpam-4665	280	4	connected	connect	VERB
ejpam-4665	280	5	graph	graph	NOUN
ejpam-4665	280	6	g	g	NOUN
ejpam-4665	280	7	and	and	CCONJ
ejpam-4665	280	8	h	h	NOUN
ejpam-4665	280	9	of	of	ADP
ejpam-4665	280	10	order	order	NOUN
ejpam-4665	280	11	n	n	NOUN
ejpam-4665	280	12	and	and	CCONJ
ejpam-4665	280	13	m	m	PROPN
ejpam-4665	280	14	,	,	PUNCT
ejpam-4665	280	15	respectively	respectively	ADV
ejpam-4665	280	16	;	;	PUNCT
ejpam-4665	280	17	(	(	PUNCT
ejpam-4665	280	18	i	i	NOUN
ejpam-4665	280	19	)	)	PUNCT
ejpam-4665	280	20	γr2rh(g+h	γr2rh(g+h	NUM
ejpam-4665	280	21	)	)	PUNCT
ejpam-4665	281	1	=	=	SYM
ejpam-4665	282	1	m+	m+	NUM
ejpam-4665	282	2	n	n	NOUN
ejpam-4665	282	3	if	if	SCONJ
ejpam-4665	282	4	g	g	PROPN
ejpam-4665	282	5	and	and	CCONJ
ejpam-4665	282	6	h	h	NOUN
ejpam-4665	282	7	are	be	AUX
ejpam-4665	282	8	complete	complete	ADJ
ejpam-4665	282	9	;	;	PUNCT
ejpam-4665	282	10	a.m.	a.m.	PROPN
ejpam-4665	282	11	mahistrado	mahistrado	PROPN
ejpam-4665	282	12	,	,	PUNCT
ejpam-4665	282	13	h.	h.	PROPN
ejpam-4665	282	14	rara	rara	PROPN
ejpam-4665	282	15	/	/	SYM
ejpam-4665	282	16	eur	eur	PROPN
ejpam-4665	282	17	.	.	PUNCT
ejpam-4665	283	1	j.	j.	PROPN
ejpam-4665	283	2	pure	pure	PROPN
ejpam-4665	283	3	appl	appl	PROPN
ejpam-4665	283	4	.	.	PROPN
ejpam-4665	283	5	math	math	PROPN
ejpam-4665	283	6	,	,	PUNCT
ejpam-4665	283	7	16	16	NUM
ejpam-4665	283	8	(	(	PUNCT
ejpam-4665	283	9	1	1	NUM
ejpam-4665	283	10	)	)	PUNCT
ejpam-4665	283	11	(	(	PUNCT
ejpam-4665	283	12	2023	2023	NUM
ejpam-4665	283	13	)	)	PUNCT
ejpam-4665	283	14	,	,	PUNCT
ejpam-4665	283	15	286	286	NUM
ejpam-4665	283	16	-	-	SYM
ejpam-4665	283	17	303	303	NUM
ejpam-4665	283	18	295	295	NUM
ejpam-4665	283	19	(	(	PUNCT
ejpam-4665	283	20	ii	ii	NOUN
ejpam-4665	283	21	)	)	PUNCT
ejpam-4665	283	22	γr2rh(g+h	γr2rh(g+h	NUM
ejpam-4665	283	23	)	)	PUNCT
ejpam-4665	284	1	=	=	PUNCT
ejpam-4665	284	2			NOUN
ejpam-4665	284	3	(	(	PUNCT
ejpam-4665	284	4	n	n	ADV
ejpam-4665	284	5	2	2	NUM
ejpam-4665	284	6	+	+	NUM
ejpam-4665	284	7	1	1	NUM
ejpam-4665	284	8	)	)	PUNCT
ejpam-4665	284	9	+	+	CCONJ
ejpam-4665	284	10	(	(	PUNCT
ejpam-4665	284	11	m	m	VERB
ejpam-4665	284	12	2	2	NUM
ejpam-4665	284	13	+	+	NUM
ejpam-4665	284	14	1	1	NUM
ejpam-4665	284	15	)	)	PUNCT
ejpam-4665	284	16	,	,	PUNCT
ejpam-4665	284	17	if	if	SCONJ
ejpam-4665	284	18	n	n	CCONJ
ejpam-4665	284	19	,	,	PUNCT
ejpam-4665	284	20	m	m	VERB
ejpam-4665	284	21	are	be	AUX
ejpam-4665	284	22	even	even	ADV
ejpam-4665	284	23	(	(	PUNCT
ejpam-4665	284	24	n	n	ADV
ejpam-4665	284	25	2	2	NUM
ejpam-4665	284	26	+	+	NUM
ejpam-4665	284	27	1	1	NUM
ejpam-4665	284	28	)	)	PUNCT
ejpam-4665	284	29	+	+	CCONJ
ejpam-4665	284	30	⌈m2	⌈m2	PROPN
ejpam-4665	284	31	⌉	⌉	NOUN
ejpam-4665	284	32	,	,	PUNCT
ejpam-4665	284	33	if	if	SCONJ
ejpam-4665	284	34	n	n	PRON
ejpam-4665	284	35	is	be	AUX
ejpam-4665	284	36	even	even	ADV
ejpam-4665	284	37	,	,	PUNCT
ejpam-4665	284	38	m	m	VERB
ejpam-4665	284	39	is	be	AUX
ejpam-4665	284	40	odd	odd	ADJ
ejpam-4665	284	41	⌈n2	⌈n2	NOUN
ejpam-4665	284	42	⌉+	⌉+	X
ejpam-4665	285	1	(	(	PUNCT
ejpam-4665	285	2	m	m	NOUN
ejpam-4665	285	3	2	2	NUM
ejpam-4665	285	4	+	+	NUM
ejpam-4665	285	5	1	1	NUM
ejpam-4665	285	6	)	)	PUNCT
ejpam-4665	285	7	,	,	PUNCT
ejpam-4665	285	8	if	if	SCONJ
ejpam-4665	285	9	n	n	PRON
ejpam-4665	285	10	is	be	AUX
ejpam-4665	285	11	odd	odd	ADJ
ejpam-4665	285	12	,	,	PUNCT
ejpam-4665	285	13	m	m	VERB
ejpam-4665	285	14	is	be	AUX
ejpam-4665	285	15	even	even	ADV
ejpam-4665	285	16	⌈n2	⌈n2	ADJ
ejpam-4665	286	1	⌉+	⌉+	PROPN
ejpam-4665	286	2	⌈m2	⌈m2	PROPN
ejpam-4665	286	3	⌉	⌉	NOUN
ejpam-4665	286	4	,	,	PUNCT
ejpam-4665	286	5	if	if	SCONJ
ejpam-4665	286	6	n	n	CCONJ
ejpam-4665	286	7	,	,	PUNCT
ejpam-4665	286	8	m	m	VERB
ejpam-4665	286	9	are	be	AUX
ejpam-4665	286	10	odd	odd	ADJ
ejpam-4665	286	11	.	.	PUNCT
ejpam-4665	287	1	where	where	SCONJ
ejpam-4665	287	2	g	g	NOUN
ejpam-4665	287	3	=	=	SYM
ejpam-4665	287	4	pn	pn	PROPN
ejpam-4665	287	5	and	and	CCONJ
ejpam-4665	287	6	h	h	NOUN
ejpam-4665	287	7	=	=	NOUN
ejpam-4665	287	8	pm	pm	NOUN
ejpam-4665	287	9	and	and	CCONJ
ejpam-4665	287	10	n	n	CCONJ
ejpam-4665	287	11	,	,	PUNCT
ejpam-4665	287	12	m	m	VERB
ejpam-4665	287	13	≥	≥	NOUN
ejpam-4665	287	14	4	4	NUM
ejpam-4665	287	15	.	.	PUNCT
ejpam-4665	288	1	(	(	PUNCT
ejpam-4665	288	2	iii	iii	NOUN
ejpam-4665	288	3	)	)	PUNCT
ejpam-4665	288	4	γr2rh(g+h	γr2rh(g+h	ADJ
ejpam-4665	288	5	)	)	PUNCT
ejpam-4665	289	1	=	=	PUNCT
ejpam-4665	289	2			NOUN
ejpam-4665	289	3	(	(	PUNCT
ejpam-4665	289	4	n	n	ADV
ejpam-4665	289	5	2	2	NUM
ejpam-4665	289	6	)	)	PUNCT
ejpam-4665	289	7	+	+	CCONJ
ejpam-4665	289	8	(	(	PUNCT
ejpam-4665	289	9	m	m	PROPN
ejpam-4665	289	10	2	2	NUM
ejpam-4665	289	11	)	)	PUNCT
ejpam-4665	289	12	,	,	PUNCT
ejpam-4665	289	13	if	if	SCONJ
ejpam-4665	289	14	n	n	CCONJ
ejpam-4665	289	15	,	,	PUNCT
ejpam-4665	289	16	m	m	VERB
ejpam-4665	289	17	are	be	AUX
ejpam-4665	289	18	even	even	ADV
ejpam-4665	289	19	(	(	PUNCT
ejpam-4665	289	20	n	n	ADV
ejpam-4665	289	21	2	2	NUM
ejpam-4665	289	22	)	)	PUNCT
ejpam-4665	290	1	+	+	CCONJ
ejpam-4665	290	2	⌈m2	⌈m2	PROPN
ejpam-4665	290	3	⌉	⌉	NOUN
ejpam-4665	290	4	,	,	PUNCT
ejpam-4665	290	5	if	if	SCONJ
ejpam-4665	290	6	n	n	PRON
ejpam-4665	290	7	is	be	AUX
ejpam-4665	290	8	even	even	ADV
ejpam-4665	290	9	,	,	PUNCT
ejpam-4665	290	10	m	m	VERB
ejpam-4665	290	11	is	be	AUX
ejpam-4665	290	12	odd	odd	ADJ
ejpam-4665	290	13	⌈n2	⌈n2	NOUN
ejpam-4665	290	14	⌉+	⌉+	X
ejpam-4665	290	15	(	(	PUNCT
ejpam-4665	290	16	m	m	NOUN
ejpam-4665	290	17	2	2	NUM
ejpam-4665	290	18	)	)	PUNCT
ejpam-4665	290	19	,	,	PUNCT
ejpam-4665	290	20	if	if	SCONJ
ejpam-4665	290	21	n	n	PRON
ejpam-4665	290	22	is	be	AUX
ejpam-4665	290	23	odd	odd	ADJ
ejpam-4665	290	24	,	,	PUNCT
ejpam-4665	290	25	m	m	VERB
ejpam-4665	290	26	is	be	AUX
ejpam-4665	290	27	even	even	ADV
ejpam-4665	290	28	⌈n2	⌈n2	ADJ
ejpam-4665	291	1	⌉+	⌉+	PROPN
ejpam-4665	291	2	⌈m2	⌈m2	PROPN
ejpam-4665	291	3	⌉	⌉	NOUN
ejpam-4665	291	4	,	,	PUNCT
ejpam-4665	291	5	if	if	SCONJ
ejpam-4665	291	6	n	n	CCONJ
ejpam-4665	291	7	,	,	PUNCT
ejpam-4665	291	8	m	m	VERB
ejpam-4665	291	9	are	be	AUX
ejpam-4665	291	10	odd	odd	ADJ
ejpam-4665	291	11	.	.	PUNCT
ejpam-4665	292	1	where	where	SCONJ
ejpam-4665	292	2	g	g	NOUN
ejpam-4665	292	3	=	=	SYM
ejpam-4665	292	4	cn	cn	PROPN
ejpam-4665	292	5	and	and	CCONJ
ejpam-4665	292	6	h	h	NOUN
ejpam-4665	292	7	=	=	NOUN
ejpam-4665	292	8	cm	cm	NOUN
ejpam-4665	292	9	and	and	CCONJ
ejpam-4665	292	10	n	n	CCONJ
ejpam-4665	292	11	,	,	PUNCT
ejpam-4665	292	12	m	m	VERB
ejpam-4665	292	13	≥	≥	NOUN
ejpam-4665	292	14	5	5	NUM
ejpam-4665	292	15	.	.	NOUN
ejpam-4665	292	16	5	5	NUM
ejpam-4665	292	17	.	.	PUNCT
ejpam-4665	293	1	restrained	restrain	VERB
ejpam-4665	293	2	2	2	NUM
ejpam-4665	293	3	-	-	PUNCT
ejpam-4665	293	4	resolving	resolve	VERB
ejpam-4665	293	5	hop	hop	NOUN
ejpam-4665	293	6	dominating	dominating	NOUN
ejpam-4665	293	7	sets	set	NOUN
ejpam-4665	293	8	in	in	ADP
ejpam-4665	293	9	the	the	DET
ejpam-4665	293	10	corona	corona	NOUN
ejpam-4665	293	11	of	of	ADP
ejpam-4665	293	12	graphs	graph	NOUN
ejpam-4665	293	13	this	this	DET
ejpam-4665	293	14	section	section	NOUN
ejpam-4665	293	15	presents	present	VERB
ejpam-4665	293	16	characterizations	characterization	NOUN
ejpam-4665	293	17	on	on	ADP
ejpam-4665	293	18	the	the	DET
ejpam-4665	293	19	restrained	restrained	ADJ
ejpam-4665	293	20	2	2	NUM
ejpam-4665	293	21	-	-	PUNCT
ejpam-4665	293	22	resolving	resolve	VERB
ejpam-4665	293	23	hop	hop	NOUN
ejpam-4665	293	24	dominating	dominating	NOUN
ejpam-4665	293	25	sets	set	NOUN
ejpam-4665	293	26	in	in	ADP
ejpam-4665	293	27	the	the	DET
ejpam-4665	293	28	corona	corona	NOUN
ejpam-4665	293	29	of	of	ADP
ejpam-4665	293	30	graphs	graph	NOUN
ejpam-4665	293	31	.	.	PUNCT
ejpam-4665	294	1	remark	remark	NOUN
ejpam-4665	294	2	6	6	NUM
ejpam-4665	294	3	.	.	PUNCT
ejpam-4665	295	1	[	[	X
ejpam-4665	295	2	7	7	X
ejpam-4665	295	3	]	]	PUNCT
ejpam-4665	295	4	let	let	VERB
ejpam-4665	295	5	v	v	NUM
ejpam-4665	295	6	∈	∈	PROPN
ejpam-4665	295	7	v	v	NOUN
ejpam-4665	295	8	(	(	PUNCT
ejpam-4665	295	9	g	g	NOUN
ejpam-4665	295	10	)	)	PUNCT
ejpam-4665	295	11	.	.	PUNCT
ejpam-4665	296	1	for	for	ADP
ejpam-4665	296	2	every	every	DET
ejpam-4665	296	3	x	x	PROPN
ejpam-4665	296	4	,	,	PUNCT
ejpam-4665	296	5	y	y	PROPN
ejpam-4665	296	6	∈	∈	PROPN
ejpam-4665	296	7	v	v	PROPN
ejpam-4665	296	8	(	(	PUNCT
ejpam-4665	296	9	hv	hv	PROPN
ejpam-4665	296	10	)	)	PUNCT
ejpam-4665	296	11	,	,	PUNCT
ejpam-4665	296	12	dg	dg	PROPN
ejpam-4665	296	13	◦	◦	NOUN
ejpam-4665	296	14	h(x	h(x	PROPN
ejpam-4665	296	15	,	,	PUNCT
ejpam-4665	296	16	w	w	PROPN
ejpam-4665	296	17	)	)	PUNCT
ejpam-4665	296	18	=	=	SYM
ejpam-4665	296	19	dg	dg	NOUN
ejpam-4665	296	20	◦	◦	NOUN
ejpam-4665	296	21	h(y	h(y	ADV
ejpam-4665	296	22	,	,	PUNCT
ejpam-4665	296	23	w	w	NOUN
ejpam-4665	296	24	)	)	PUNCT
ejpam-4665	296	25	and	and	CCONJ
ejpam-4665	296	26	dg	dg	AUX
ejpam-4665	296	27	◦	◦	NOUN
ejpam-4665	296	28	h(v	h(v	PROPN
ejpam-4665	296	29	,	,	PUNCT
ejpam-4665	296	30	w	w	NOUN
ejpam-4665	296	31	)	)	PUNCT
ejpam-4665	296	32	+	+	CCONJ
ejpam-4665	296	33	1	1	NUM
ejpam-4665	296	34	=	=	SYM
ejpam-4665	296	35	dg	dg	NOUN
ejpam-4665	296	36	◦	◦	NOUN
ejpam-4665	296	37	h(x	h(x	PROPN
ejpam-4665	296	38	,	,	PUNCT
ejpam-4665	296	39	w	w	NOUN
ejpam-4665	296	40	)	)	PUNCT
ejpam-4665	296	41	for	for	ADP
ejpam-4665	296	42	every	every	DET
ejpam-4665	296	43	w	w	PROPN
ejpam-4665	296	44	∈	∈	PROPN
ejpam-4665	296	45	v	v	NOUN
ejpam-4665	296	46	(	(	PUNCT
ejpam-4665	296	47	g	g	PROPN
ejpam-4665	296	48	◦	◦	PROPN
ejpam-4665	296	49	h)\v	h)\v	PROPN
ejpam-4665	296	50	(	(	PUNCT
ejpam-4665	296	51	hv	hv	NOUN
ejpam-4665	296	52	)	)	PUNCT
ejpam-4665	296	53	.	.	PUNCT
ejpam-4665	297	1	theorem	theorem	VERB
ejpam-4665	297	2	10	10	NUM
ejpam-4665	297	3	.	.	PUNCT
ejpam-4665	298	1	[	[	X
ejpam-4665	298	2	11	11	NUM
ejpam-4665	298	3	]	]	PUNCT
ejpam-4665	298	4	let	let	VERB
ejpam-4665	298	5	g	g	NOUN
ejpam-4665	298	6	and	and	CCONJ
ejpam-4665	298	7	h	h	NOUN
ejpam-4665	298	8	be	be	AUX
ejpam-4665	298	9	nontrivial	nontrivial	ADJ
ejpam-4665	298	10	connected	connected	ADJ
ejpam-4665	298	11	graphs	graph	NOUN
ejpam-4665	298	12	.	.	PUNCT
ejpam-4665	299	1	a	a	DET
ejpam-4665	299	2	set	set	NOUN
ejpam-4665	299	3	s	s	NOUN
ejpam-4665	299	4	⊆	⊆	NUM
ejpam-4665	299	5	v	v	NOUN
ejpam-4665	299	6	(	(	PUNCT
ejpam-4665	299	7	g	g	PROPN
ejpam-4665	299	8	◦	◦	NOUN
ejpam-4665	299	9	h	h	NOUN
ejpam-4665	299	10	)	)	PUNCT
ejpam-4665	299	11	is	be	AUX
ejpam-4665	299	12	a	a	DET
ejpam-4665	299	13	2	2	NUM
ejpam-4665	299	14	-	-	PUNCT
ejpam-4665	299	15	resolving	resolve	VERB
ejpam-4665	299	16	hop	hop	NOUN
ejpam-4665	299	17	dominating	dominating	NOUN
ejpam-4665	299	18	set	set	NOUN
ejpam-4665	299	19	of	of	ADP
ejpam-4665	299	20	g	g	PROPN
ejpam-4665	299	21	◦	◦	NOUN
ejpam-4665	299	22	h	h	NOUN
ejpam-4665	299	23	if	if	SCONJ
ejpam-4665	300	1	and	and	CCONJ
ejpam-4665	300	2	only	only	ADV
ejpam-4665	300	3	if	if	SCONJ
ejpam-4665	300	4	s	s	VERB
ejpam-4665	300	5	=	=	NOUN
ejpam-4665	300	6	a	a	PRON
ejpam-4665	300	7	∪	∪	ADJ
ejpam-4665	300	8			PROPN
ejpam-4665	300	9	⋃	⋃	ADJ
ejpam-4665	300	10	v∈v	v∈v	NOUN
ejpam-4665	300	11	(	(	PUNCT
ejpam-4665	300	12	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4665	301	1	)	)	PUNCT
ejpam-4665	301	2	sv	sv	NOUN
ejpam-4665	302	1			PROPN
ejpam-4665	302	2	∪	∪	VERB
ejpam-4665	302	3			PROPN
ejpam-4665	302	4	⋃	⋃	PROPN
ejpam-4665	302	5	w∈v	w∈v	PROPN
ejpam-4665	302	6	(	(	PUNCT
ejpam-4665	302	7	g)\ng(a	g)\ng(a	NOUN
ejpam-4665	302	8	)	)	PUNCT
ejpam-4665	302	9	dw	dw	NOUN
ejpam-4665	302	10			PROPN
ejpam-4665	302	11	where	where	SCONJ
ejpam-4665	302	12	(	(	PUNCT
ejpam-4665	302	13	i	i	NOUN
ejpam-4665	302	14	)	)	PUNCT
ejpam-4665	302	15	a	a	DET
ejpam-4665	302	16	⊆	⊆	NUM
ejpam-4665	302	17	v	v	NOUN
ejpam-4665	302	18	(	(	PUNCT
ejpam-4665	302	19	g	g	NOUN
ejpam-4665	302	20	)	)	PUNCT
ejpam-4665	302	21	such	such	ADJ
ejpam-4665	302	22	that	that	PRON
ejpam-4665	302	23	for	for	ADP
ejpam-4665	302	24	each	each	DET
ejpam-4665	302	25	w	w	PROPN
ejpam-4665	302	26	∈	∈	PROPN
ejpam-4665	302	27	v	v	NOUN
ejpam-4665	302	28	(	(	PUNCT
ejpam-4665	302	29	g)\a	g)\a	NOUN
ejpam-4665	302	30	,	,	PUNCT
ejpam-4665	302	31	there	there	PRON
ejpam-4665	302	32	exists	exist	VERB
ejpam-4665	302	33	x	x	X
ejpam-4665	302	34	∈	∈	PROPN
ejpam-4665	302	35	a	a	PRON
ejpam-4665	302	36	with	with	ADP
ejpam-4665	302	37	dg(w	dg(w	NOUN
ejpam-4665	302	38	,	,	PUNCT
ejpam-4665	302	39	x	x	X
ejpam-4665	302	40	)	)	PUNCT
ejpam-4665	302	41	=	=	SYM
ejpam-4665	302	42	2	2	NUM
ejpam-4665	302	43	or	or	CCONJ
ejpam-4665	302	44	there	there	PRON
ejpam-4665	302	45	exists	exist	VERB
ejpam-4665	302	46	y	y	PROPN
ejpam-4665	302	47	∈	∈	PROPN
ejpam-4665	302	48	v	v	ADP
ejpam-4665	302	49	(	(	PUNCT
ejpam-4665	302	50	g	g	NOUN
ejpam-4665	302	51	)	)	PUNCT
ejpam-4665	302	52	∩ng(w	∩ng(w	PROPN
ejpam-4665	302	53	)	)	PUNCT
ejpam-4665	302	54	with	with	ADP
ejpam-4665	302	55	v	v	NUM
ejpam-4665	302	56	(	(	PUNCT
ejpam-4665	302	57	hy	hy	NOUN
ejpam-4665	302	58	)	)	PUNCT
ejpam-4665	302	59	∩	∩	PROPN
ejpam-4665	302	60	s	s	PART
ejpam-4665	302	61	̸=	̸=	PROPN
ejpam-4665	302	62	∅	∅	NOUN
ejpam-4665	302	63	;	;	PUNCT
ejpam-4665	302	64	(	(	PUNCT
ejpam-4665	302	65	ii	ii	NOUN
ejpam-4665	302	66	)	)	PUNCT
ejpam-4665	302	67	sv	sv	VERB
ejpam-4665	303	1	⊆	⊆	NUM
ejpam-4665	303	2	v	v	ADP
ejpam-4665	303	3	(	(	PUNCT
ejpam-4665	303	4	hv	hv	X
ejpam-4665	303	5	)	)	PUNCT
ejpam-4665	303	6	is	be	AUX
ejpam-4665	303	7	a	a	DET
ejpam-4665	303	8	2	2	NUM
ejpam-4665	303	9	-	-	PUNCT
ejpam-4665	303	10	locating	locate	VERB
ejpam-4665	303	11	set	set	NOUN
ejpam-4665	303	12	of	of	ADP
ejpam-4665	303	13	hv	hv	PROPN
ejpam-4665	303	14	for	for	ADP
ejpam-4665	303	15	all	all	DET
ejpam-4665	303	16	v	v	ADP
ejpam-4665	303	17	∈	∈	NUM
ejpam-4665	303	18	v	v	NOUN
ejpam-4665	303	19	(	(	PUNCT
ejpam-4665	303	20	g	g	NOUN
ejpam-4665	303	21	)	)	PUNCT
ejpam-4665	303	22	∩ng(a	∩ng(a	NOUN
ejpam-4665	303	23	)	)	PUNCT
ejpam-4665	303	24	;	;	PUNCT
ejpam-4665	303	25	and	and	CCONJ
ejpam-4665	303	26	(	(	PUNCT
ejpam-4665	303	27	iii	iii	X
ejpam-4665	303	28	)	)	PUNCT
ejpam-4665	303	29	dw	dw	NOUN
ejpam-4665	303	30	⊆	⊆	NUM
ejpam-4665	303	31	v	v	NOUN
ejpam-4665	303	32	(	(	PUNCT
ejpam-4665	303	33	hw	hw	NOUN
ejpam-4665	303	34	)	)	PUNCT
ejpam-4665	303	35	is	be	AUX
ejpam-4665	303	36	a	a	DET
ejpam-4665	303	37	2	2	NUM
ejpam-4665	303	38	-	-	PUNCT
ejpam-4665	303	39	locating	locate	VERB
ejpam-4665	303	40	point	point	NOUN
ejpam-4665	303	41	-	-	PUNCT
ejpam-4665	303	42	wise	wise	ADJ
ejpam-4665	303	43	non	non	ADJ
ejpam-4665	303	44	-	-	ADJ
ejpam-4665	303	45	dominating	dominating	ADJ
ejpam-4665	303	46	set	set	NOUN
ejpam-4665	303	47	of	of	ADP
ejpam-4665	303	48	hw	hw	PRON
ejpam-4665	303	49	for	for	ADP
ejpam-4665	303	50	all	all	PRON
ejpam-4665	303	51	w	w	PROPN
ejpam-4665	303	52	∈	∈	PROPN
ejpam-4665	303	53	v	v	NOUN
ejpam-4665	303	54	(	(	PUNCT
ejpam-4665	303	55	g)\ng(a	g)\ng(a	NOUN
ejpam-4665	303	56	)	)	PUNCT
ejpam-4665	303	57	.	.	PUNCT
ejpam-4665	304	1	a.m.	a.m.	PROPN
ejpam-4665	304	2	mahistrado	mahistrado	PROPN
ejpam-4665	304	3	,	,	PUNCT
ejpam-4665	304	4	h.	h.	PROPN
ejpam-4665	304	5	rara	rara	PROPN
ejpam-4665	304	6	/	/	SYM
ejpam-4665	304	7	eur	eur	PROPN
ejpam-4665	304	8	.	.	PUNCT
ejpam-4665	305	1	j.	j.	PROPN
ejpam-4665	305	2	pure	pure	PROPN
ejpam-4665	305	3	appl	appl	PROPN
ejpam-4665	305	4	.	.	PROPN
ejpam-4665	305	5	math	math	PROPN
ejpam-4665	305	6	,	,	PUNCT
ejpam-4665	305	7	16	16	NUM
ejpam-4665	305	8	(	(	PUNCT
ejpam-4665	305	9	1	1	NUM
ejpam-4665	305	10	)	)	PUNCT
ejpam-4665	305	11	(	(	PUNCT
ejpam-4665	305	12	2023	2023	NUM
ejpam-4665	305	13	)	)	PUNCT
ejpam-4665	305	14	,	,	PUNCT
ejpam-4665	305	15	286	286	NUM
ejpam-4665	305	16	-	-	SYM
ejpam-4665	305	17	303	303	NUM
ejpam-4665	305	18	296	296	NUM
ejpam-4665	305	19	theorem	theorem	VERB
ejpam-4665	305	20	11	11	NUM
ejpam-4665	305	21	.	.	PUNCT
ejpam-4665	306	1	let	let	VERB
ejpam-4665	306	2	g	g	NOUN
ejpam-4665	306	3	and	and	CCONJ
ejpam-4665	306	4	h	h	NOUN
ejpam-4665	306	5	be	be	AUX
ejpam-4665	306	6	nontrivial	nontrivial	ADJ
ejpam-4665	306	7	connected	connected	ADJ
ejpam-4665	306	8	graphs	graph	NOUN
ejpam-4665	306	9	.	.	PUNCT
ejpam-4665	307	1	a	a	DET
ejpam-4665	307	2	set	set	NOUN
ejpam-4665	307	3	s	s	NOUN
ejpam-4665	307	4	⊆	⊆	NUM
ejpam-4665	307	5	v	v	NOUN
ejpam-4665	307	6	(	(	PUNCT
ejpam-4665	307	7	g	g	PROPN
ejpam-4665	307	8	◦	◦	NOUN
ejpam-4665	307	9	h	h	NOUN
ejpam-4665	307	10	)	)	PUNCT
ejpam-4665	307	11	is	be	AUX
ejpam-4665	307	12	a	a	DET
ejpam-4665	307	13	restrained	restrained	ADJ
ejpam-4665	307	14	2	2	NUM
ejpam-4665	307	15	-	-	PUNCT
ejpam-4665	307	16	resolving	resolve	VERB
ejpam-4665	307	17	hop	hop	NOUN
ejpam-4665	307	18	dominating	dominating	NOUN
ejpam-4665	307	19	set	set	NOUN
ejpam-4665	307	20	of	of	ADP
ejpam-4665	307	21	g	g	PROPN
ejpam-4665	307	22	◦	◦	NOUN
ejpam-4665	307	23	h	h	NOUN
ejpam-4665	307	24	if	if	SCONJ
ejpam-4665	308	1	and	and	CCONJ
ejpam-4665	308	2	only	only	ADV
ejpam-4665	308	3	if	if	SCONJ
ejpam-4665	308	4	s	s	VERB
ejpam-4665	308	5	=	=	PUNCT
ejpam-4665	308	6	a∪	a∪	NOUN
ejpam-4665	309	1			PROPN
ejpam-4665	309	2	⋃	⋃	PROPN
ejpam-4665	309	3	v∈(v	v∈(v	NOUN
ejpam-4665	309	4	(	(	PUNCT
ejpam-4665	309	5	g)\a)∩ng(a	g)\a)∩ng(a	PROPN
ejpam-4665	309	6	)	)	PUNCT
ejpam-4665	309	7	sv	sv	NOUN
ejpam-4665	309	8	∪	∪	PROPN
ejpam-4665	310	1			PROPN
ejpam-4665	310	2	⋃	⋃	PROPN
ejpam-4665	310	3	w∈(v	w∈(v	NOUN
ejpam-4665	310	4	(	(	PUNCT
ejpam-4665	310	5	g)\a)\ng(a	g)\a)\ng(a	NOUN
ejpam-4665	310	6	)	)	PUNCT
ejpam-4665	310	7	dw	dw	NOUN
ejpam-4665	310	8	∪	∪	PROPN
ejpam-4665	311	1			PROPN
ejpam-4665	311	2	⋃	⋃	NOUN
ejpam-4665	311	3	u∈a∩ng(a	u∈a∩ng(a	NOUN
ejpam-4665	311	4	)	)	PUNCT
ejpam-4665	311	5	eu	eu	PROPN
ejpam-4665	312	1	∪	∪	PROPN
ejpam-4665	313	1			PROPN
ejpam-4665	313	2	⋃	⋃	PROPN
ejpam-4665	313	3	j∈a\ng(a	j∈a\ng(a	PROPN
ejpam-4665	313	4	)	)	PUNCT
ejpam-4665	314	1	fj	fj	PROPN
ejpam-4665	314	2			PROPN
ejpam-4665	314	3	where	where	SCONJ
ejpam-4665	314	4	(	(	PUNCT
ejpam-4665	314	5	i	i	NOUN
ejpam-4665	314	6	)	)	PUNCT
ejpam-4665	314	7	a	a	DET
ejpam-4665	314	8	⊆	⊆	NUM
ejpam-4665	314	9	v	v	NOUN
ejpam-4665	314	10	(	(	PUNCT
ejpam-4665	314	11	g	g	NOUN
ejpam-4665	314	12	)	)	PUNCT
ejpam-4665	314	13	such	such	ADJ
ejpam-4665	314	14	that	that	PRON
ejpam-4665	314	15	for	for	ADP
ejpam-4665	314	16	each	each	DET
ejpam-4665	314	17	w	w	PROPN
ejpam-4665	314	18	∈	∈	PROPN
ejpam-4665	314	19	v	v	NOUN
ejpam-4665	314	20	(	(	PUNCT
ejpam-4665	314	21	g)\a	g)\a	NOUN
ejpam-4665	314	22	,	,	PUNCT
ejpam-4665	314	23	there	there	PRON
ejpam-4665	314	24	exists	exist	VERB
ejpam-4665	314	25	x	x	X
ejpam-4665	314	26	∈	∈	PROPN
ejpam-4665	314	27	a	a	PRON
ejpam-4665	314	28	with	with	ADP
ejpam-4665	314	29	dg(w	dg(w	NOUN
ejpam-4665	314	30	,	,	PUNCT
ejpam-4665	314	31	x	x	X
ejpam-4665	314	32	)	)	PUNCT
ejpam-4665	314	33	=	=	SYM
ejpam-4665	314	34	2	2	NUM
ejpam-4665	314	35	or	or	CCONJ
ejpam-4665	314	36	there	there	PRON
ejpam-4665	314	37	exists	exist	VERB
ejpam-4665	314	38	y	y	PROPN
ejpam-4665	314	39	∈	∈	PROPN
ejpam-4665	314	40	v	v	ADP
ejpam-4665	314	41	(	(	PUNCT
ejpam-4665	314	42	g	g	NOUN
ejpam-4665	314	43	)	)	PUNCT
ejpam-4665	314	44	∩ng(w	∩ng(w	PROPN
ejpam-4665	314	45	)	)	PUNCT
ejpam-4665	314	46	with	with	ADP
ejpam-4665	314	47	v	v	NUM
ejpam-4665	314	48	(	(	PUNCT
ejpam-4665	314	49	hy	hy	NOUN
ejpam-4665	314	50	)	)	PUNCT
ejpam-4665	314	51	∩	∩	PROPN
ejpam-4665	314	52	s	s	PART
ejpam-4665	314	53	̸=	̸=	PROPN
ejpam-4665	314	54	∅	∅	NOUN
ejpam-4665	314	55	;	;	PUNCT
ejpam-4665	314	56	(	(	PUNCT
ejpam-4665	314	57	ii	ii	NOUN
ejpam-4665	314	58	)	)	PUNCT
ejpam-4665	315	1	sv	sv	PROPN
ejpam-4665	315	2	is	be	AUX
ejpam-4665	315	3	a	a	DET
ejpam-4665	315	4	2	2	NUM
ejpam-4665	315	5	-	-	PUNCT
ejpam-4665	315	6	locating	locate	VERB
ejpam-4665	315	7	set	set	NOUN
ejpam-4665	315	8	of	of	ADP
ejpam-4665	315	9	hv	hv	PROPN
ejpam-4665	315	10	for	for	ADP
ejpam-4665	315	11	all	all	DET
ejpam-4665	315	12	v	v	ADP
ejpam-4665	315	13	∈	∈	NOUN
ejpam-4665	315	14	(	(	PUNCT
ejpam-4665	315	15	v	v	NOUN
ejpam-4665	315	16	(	(	PUNCT
ejpam-4665	315	17	g)\a	g)\a	NOUN
ejpam-4665	315	18	)	)	PUNCT
ejpam-4665	315	19	∩ng(a	∩ng(a	PROPN
ejpam-4665	315	20	)	)	PUNCT
ejpam-4665	315	21	;	;	PUNCT
ejpam-4665	315	22	(	(	PUNCT
ejpam-4665	315	23	iii	iii	X
ejpam-4665	315	24	)	)	PUNCT
ejpam-4665	315	25	dw	dw	PROPN
ejpam-4665	315	26	is	be	AUX
ejpam-4665	315	27	a	a	DET
ejpam-4665	315	28	2	2	NUM
ejpam-4665	315	29	-	-	PUNCT
ejpam-4665	315	30	locating	locate	VERB
ejpam-4665	315	31	point	point	NOUN
ejpam-4665	315	32	-	-	PUNCT
ejpam-4665	315	33	wise	wise	ADV
ejpam-4665	315	34	nondominating	nondominate	VERB
ejpam-4665	315	35	set	set	VERB
ejpam-4665	315	36	ofhw	ofhw	NOUN
ejpam-4665	315	37	for	for	ADP
ejpam-4665	315	38	all	all	DET
ejpam-4665	315	39	w	w	PROPN
ejpam-4665	315	40	∈	∈	NOUN
ejpam-4665	315	41	(	(	PUNCT
ejpam-4665	315	42	v	v	NOUN
ejpam-4665	315	43	(	(	PUNCT
ejpam-4665	315	44	g)\a)\ng(a	g)\a)\ng(a	NOUN
ejpam-4665	315	45	)	)	PUNCT
ejpam-4665	315	46	;	;	PUNCT
ejpam-4665	315	47	(	(	PUNCT
ejpam-4665	315	48	iv	iv	X
ejpam-4665	315	49	)	)	PUNCT
ejpam-4665	315	50	eu	eu	PROPN
ejpam-4665	315	51	is	be	AUX
ejpam-4665	315	52	a	a	DET
ejpam-4665	315	53	restrained	restrained	ADJ
ejpam-4665	315	54	2	2	NUM
ejpam-4665	315	55	-	-	PUNCT
ejpam-4665	315	56	locating	locate	VERB
ejpam-4665	315	57	set	set	NOUN
ejpam-4665	315	58	of	of	ADP
ejpam-4665	315	59	hu	hu	PROPN
ejpam-4665	315	60	for	for	ADP
ejpam-4665	315	61	all	all	PRON
ejpam-4665	315	62	u	u	PROPN
ejpam-4665	315	63	∈	∈	PROPN
ejpam-4665	315	64	a	a	DET
ejpam-4665	315	65	∩ng(a	∩ng(a	NOUN
ejpam-4665	315	66	)	)	PUNCT
ejpam-4665	315	67	;	;	PUNCT
ejpam-4665	315	68	(	(	PUNCT
ejpam-4665	315	69	v	v	NOUN
ejpam-4665	315	70	)	)	PUNCT
ejpam-4665	315	71	fj	fj	PROPN
ejpam-4665	315	72	is	be	AUX
ejpam-4665	315	73	a	a	DET
ejpam-4665	315	74	restrained	restrained	ADJ
ejpam-4665	315	75	2	2	NUM
ejpam-4665	315	76	-	-	PUNCT
ejpam-4665	315	77	locating	locate	VERB
ejpam-4665	315	78	point	point	NOUN
ejpam-4665	315	79	-	-	PUNCT
ejpam-4665	315	80	wise	wise	ADJ
ejpam-4665	315	81	non	non	ADJ
ejpam-4665	315	82	-	-	ADJ
ejpam-4665	315	83	dominating	dominating	ADJ
ejpam-4665	315	84	set	set	VERB
ejpam-4665	315	85	ofhj	ofhj	NOUN
ejpam-4665	315	86	for	for	ADP
ejpam-4665	315	87	all	all	DET
ejpam-4665	315	88	j	j	PROPN
ejpam-4665	315	89	∈	∈	PROPN
ejpam-4665	315	90	a\ng(a	a\ng(a	PROPN
ejpam-4665	315	91	)	)	PUNCT
ejpam-4665	315	92	.	.	PUNCT
ejpam-4665	316	1	proof	proof	NOUN
ejpam-4665	316	2	.	.	PUNCT
ejpam-4665	317	1	suppose	suppose	VERB
ejpam-4665	317	2	s	s	VERB
ejpam-4665	317	3	⊆	⊆	NUM
ejpam-4665	317	4	v	v	NOUN
ejpam-4665	317	5	(	(	PUNCT
ejpam-4665	317	6	g	g	PROPN
ejpam-4665	317	7	◦	◦	NOUN
ejpam-4665	317	8	h	h	NOUN
ejpam-4665	317	9	)	)	PUNCT
ejpam-4665	317	10	be	be	VERB
ejpam-4665	317	11	a	a	DET
ejpam-4665	317	12	restrained	restrained	ADJ
ejpam-4665	317	13	2	2	NUM
ejpam-4665	317	14	-	-	PUNCT
ejpam-4665	317	15	resolving	resolve	VERB
ejpam-4665	317	16	hop	hop	NOUN
ejpam-4665	317	17	dominating	dominating	NOUN
ejpam-4665	317	18	set	set	NOUN
ejpam-4665	317	19	of	of	ADP
ejpam-4665	317	20	g	g	PROPN
ejpam-4665	317	21	◦	◦	NOUN
ejpam-4665	317	22	h.	h.	NOUN
ejpam-4665	317	23	let	let	VERB
ejpam-4665	317	24	a	a	DET
ejpam-4665	317	25	=	=	PUNCT
ejpam-4665	317	26	s∩v	s∩v	NOUN
ejpam-4665	317	27	(	(	PUNCT
ejpam-4665	317	28	g	g	NOUN
ejpam-4665	317	29	)	)	PUNCT
ejpam-4665	317	30	,	,	PUNCT
ejpam-4665	317	31	sv	sv	INTJ
ejpam-4665	318	1	=	=	SYM
ejpam-4665	318	2	s∩v	s∩v	PROPN
ejpam-4665	318	3	(	(	PUNCT
ejpam-4665	318	4	hv	hv	PROPN
ejpam-4665	318	5	)	)	PUNCT
ejpam-4665	318	6	for	for	ADP
ejpam-4665	318	7	each	each	DET
ejpam-4665	318	8	v	v	X
ejpam-4665	318	9	∈	∈	NOUN
ejpam-4665	318	10	(	(	PUNCT
ejpam-4665	318	11	v	v	NOUN
ejpam-4665	318	12	(	(	PUNCT
ejpam-4665	318	13	g)\a)∩ng(a	g)\a)∩ng(a	PROPN
ejpam-4665	318	14	)	)	PUNCT
ejpam-4665	318	15	,	,	PUNCT
ejpam-4665	318	16	dw	dw	NOUN
ejpam-4665	318	17	=	=	SYM
ejpam-4665	318	18	s∩v	s∩v	PROPN
ejpam-4665	318	19	(	(	PUNCT
ejpam-4665	318	20	hw	hw	NOUN
ejpam-4665	318	21	)	)	PUNCT
ejpam-4665	318	22	for	for	ADP
ejpam-4665	318	23	each	each	DET
ejpam-4665	318	24	w	w	PROPN
ejpam-4665	318	25	∈	∈	PROPN
ejpam-4665	318	26	(	(	PUNCT
ejpam-4665	318	27	v	v	NOUN
ejpam-4665	318	28	(	(	PUNCT
ejpam-4665	318	29	g)\a)\ng(a	g)\a)\ng(a	NOUN
ejpam-4665	318	30	)	)	PUNCT
ejpam-4665	318	31	,	,	PUNCT
ejpam-4665	318	32	eu	eu	PROPN
ejpam-4665	318	33	=	=	PUNCT
ejpam-4665	318	34	s∩v	s∩v	PROPN
ejpam-4665	318	35	(	(	PUNCT
ejpam-4665	318	36	hu	hu	PROPN
ejpam-4665	318	37	)	)	PUNCT
ejpam-4665	318	38	for	for	ADP
ejpam-4665	318	39	each	each	DET
ejpam-4665	318	40	u	u	PROPN
ejpam-4665	318	41	∈	∈	PROPN
ejpam-4665	318	42	a∩ng(a	a∩ng(a	PROPN
ejpam-4665	318	43	)	)	PUNCT
ejpam-4665	318	44	and	and	CCONJ
ejpam-4665	318	45	fj	fj	PROPN
ejpam-4665	318	46	=	=	PUNCT
ejpam-4665	318	47	s∩v	s∩v	PROPN
ejpam-4665	318	48	(	(	PUNCT
ejpam-4665	318	49	hj	hj	PROPN
ejpam-4665	318	50	)	)	PUNCT
ejpam-4665	318	51	for	for	ADP
ejpam-4665	318	52	each	each	DET
ejpam-4665	318	53	j	j	PROPN
ejpam-4665	318	54	∈	∈	PROPN
ejpam-4665	318	55	a\ng(a	a\ng(a	PROPN
ejpam-4665	318	56	)	)	PUNCT
ejpam-4665	318	57	.	.	PUNCT
ejpam-4665	319	1	then	then	ADV
ejpam-4665	319	2	s	s	VERB
ejpam-4665	319	3	=	=	PUNCT
ejpam-4665	319	4	a∪	a∪	NOUN
ejpam-4665	320	1			PROPN
ejpam-4665	320	2	⋃	⋃	PROPN
ejpam-4665	320	3	v∈(v	v∈(v	NOUN
ejpam-4665	320	4	(	(	PUNCT
ejpam-4665	320	5	g)\a)∩ng(a	g)\a)∩ng(a	PROPN
ejpam-4665	320	6	)	)	PUNCT
ejpam-4665	320	7	sv	sv	NOUN
ejpam-4665	320	8	∪	∪	PROPN
ejpam-4665	321	1			PROPN
ejpam-4665	321	2	⋃	⋃	PROPN
ejpam-4665	321	3	w∈(v	w∈(v	NOUN
ejpam-4665	321	4	(	(	PUNCT
ejpam-4665	321	5	g)\a)\ng(a	g)\a)\ng(a	NOUN
ejpam-4665	321	6	)	)	PUNCT
ejpam-4665	321	7	dw	dw	NOUN
ejpam-4665	321	8	∪	∪	PROPN
ejpam-4665	322	1			PROPN
ejpam-4665	322	2	⋃	⋃	NOUN
ejpam-4665	322	3	u∈a∩ng(a	u∈a∩ng(a	NOUN
ejpam-4665	322	4	)	)	PUNCT
ejpam-4665	322	5	eu	eu	PROPN
ejpam-4665	323	1	∪	∪	PROPN
ejpam-4665	324	1			PROPN
ejpam-4665	324	2	⋃	⋃	PROPN
ejpam-4665	324	3	j∈a\ng(a	j∈a\ng(a	PROPN
ejpam-4665	324	4	)	)	PUNCT
ejpam-4665	324	5	fj	fj	PROPN
ejpam-4665	324	6			PROPN
ejpam-4665	324	7	.	.	PUNCT
ejpam-4665	325	1	since	since	SCONJ
ejpam-4665	325	2	s	s	PROPN
ejpam-4665	325	3	is	be	AUX
ejpam-4665	325	4	a	a	DET
ejpam-4665	325	5	2	2	NUM
ejpam-4665	325	6	-	-	PUNCT
ejpam-4665	325	7	resolving	resolve	VERB
ejpam-4665	325	8	hop	hop	NOUN
ejpam-4665	325	9	dominating	dominating	NOUN
ejpam-4665	325	10	set	set	NOUN
ejpam-4665	325	11	,	,	PUNCT
ejpam-4665	325	12	(	(	PUNCT
ejpam-4665	325	13	i	i	NOUN
ejpam-4665	325	14	)	)	PUNCT
ejpam-4665	325	15	,	,	PUNCT
ejpam-4665	325	16	(	(	PUNCT
ejpam-4665	325	17	ii	ii	NOUN
ejpam-4665	325	18	)	)	PUNCT
ejpam-4665	325	19	and	and	CCONJ
ejpam-4665	325	20	(	(	PUNCT
ejpam-4665	325	21	iii	iii	X
ejpam-4665	325	22	)	)	PUNCT
ejpam-4665	325	23	follow	follow	VERB
ejpam-4665	325	24	immediately	immediately	ADV
ejpam-4665	325	25	from	from	ADP
ejpam-4665	325	26	theorem	theorem	ADJ
ejpam-4665	325	27	10	10	NUM
ejpam-4665	325	28	.	.	PUNCT
ejpam-4665	326	1	next	next	ADV
ejpam-4665	326	2	,	,	PUNCT
ejpam-4665	326	3	let	let	VERB
ejpam-4665	326	4	u	u	PRON
ejpam-4665	326	5	∈	∈	PROPN
ejpam-4665	326	6	a∩ng(a	a∩ng(a	PROPN
ejpam-4665	326	7	)	)	PUNCT
ejpam-4665	326	8	.	.	PUNCT
ejpam-4665	327	1	if	if	SCONJ
ejpam-4665	327	2	eu	eu	PROPN
ejpam-4665	327	3	=	=	PROPN
ejpam-4665	327	4	v	v	PROPN
ejpam-4665	327	5	(	(	PUNCT
ejpam-4665	327	6	hu	hu	PROPN
ejpam-4665	327	7	)	)	PUNCT
ejpam-4665	327	8	,	,	PUNCT
ejpam-4665	327	9	then	then	ADV
ejpam-4665	327	10	eu	eu	PROPN
ejpam-4665	327	11	is	be	AUX
ejpam-4665	327	12	a	a	DET
ejpam-4665	327	13	restrained	restrained	ADJ
ejpam-4665	327	14	2	2	NUM
ejpam-4665	327	15	-	-	PUNCT
ejpam-4665	327	16	locating	locating	NOUN
ejpam-4665	327	17	.	.	PUNCT
ejpam-4665	328	1	suppose	suppose	VERB
ejpam-4665	328	2	that	that	SCONJ
ejpam-4665	328	3	eu	eu	PROPN
ejpam-4665	328	4	̸=	̸=	PROPN
ejpam-4665	328	5	v	v	PROPN
ejpam-4665	328	6	(	(	PUNCT
ejpam-4665	328	7	hu	hu	PROPN
ejpam-4665	328	8	)	)	PUNCT
ejpam-4665	328	9	.	.	PUNCT
ejpam-4665	329	1	then	then	ADV
ejpam-4665	329	2	v	v	X
ejpam-4665	329	3	(	(	PUNCT
ejpam-4665	329	4	g	g	PROPN
ejpam-4665	329	5	◦	◦	NOUN
ejpam-4665	329	6	h	h	NOUN
ejpam-4665	329	7	)	)	PUNCT
ejpam-4665	329	8	̸=	̸=	PROPN
ejpam-4665	329	9	s.	s.	PROPN
ejpam-4665	329	10	now	now	ADV
ejpam-4665	329	11	,	,	PUNCT
ejpam-4665	329	12	since	since	SCONJ
ejpam-4665	329	13	v	v	NOUN
ejpam-4665	329	14	(	(	PUNCT
ejpam-4665	329	15	hu)\eu	hu)\eu	PROPN
ejpam-4665	329	16	⊆	⊆	NUM
ejpam-4665	329	17	v	v	NOUN
ejpam-4665	329	18	(	(	PUNCT
ejpam-4665	329	19	g	g	NOUN
ejpam-4665	329	20	◦	◦	NOUN
ejpam-4665	329	21	h)\s	h)\s	NOUN
ejpam-4665	329	22	and	and	CCONJ
ejpam-4665	329	23	s	s	VERB
ejpam-4665	329	24	is	be	AUX
ejpam-4665	329	25	a	a	DET
ejpam-4665	329	26	restrained	restrained	ADJ
ejpam-4665	329	27	2	2	NUM
ejpam-4665	329	28	-	-	PUNCT
ejpam-4665	329	29	resolving	resolving	NOUN
ejpam-4665	329	30	,	,	PUNCT
ejpam-4665	329	31	it	it	PRON
ejpam-4665	329	32	follows	follow	VERB
ejpam-4665	329	33	that	that	PRON
ejpam-4665	329	34	⟨v	⟨v	PROPN
ejpam-4665	329	35	(	(	PUNCT
ejpam-4665	329	36	hu)\eu⟩	hu)\eu⟩	NOUN
ejpam-4665	329	37	has	have	VERB
ejpam-4665	329	38	no	no	DET
ejpam-4665	329	39	isolated	isolated	ADJ
ejpam-4665	329	40	vertex	vertex	NOUN
ejpam-4665	329	41	.	.	PUNCT
ejpam-4665	330	1	thus	thus	ADV
ejpam-4665	330	2	,	,	PUNCT
ejpam-4665	330	3	eu	eu	PROPN
ejpam-4665	330	4	is	be	AUX
ejpam-4665	330	5	a	a	DET
ejpam-4665	330	6	restrained	restrained	ADJ
ejpam-4665	330	7	2	2	NUM
ejpam-4665	330	8	-	-	PUNCT
ejpam-4665	330	9	locating	locate	VERB
ejpam-4665	330	10	set	set	NOUN
ejpam-4665	330	11	of	of	ADP
ejpam-4665	330	12	hu	hu	PROPN
ejpam-4665	330	13	.	.	PUNCT
ejpam-4665	331	1	hence	hence	ADV
ejpam-4665	331	2	,	,	PUNCT
ejpam-4665	331	3	(	(	PUNCT
ejpam-4665	331	4	iv	iv	X
ejpam-4665	331	5	)	)	PUNCT
ejpam-4665	331	6	follows	follow	VERB
ejpam-4665	331	7	.	.	PUNCT
ejpam-4665	332	1	finally	finally	ADV
ejpam-4665	332	2	,	,	PUNCT
ejpam-4665	332	3	suppose	suppose	VERB
ejpam-4665	332	4	j	j	PROPN
ejpam-4665	332	5	∈	∈	PROPN
ejpam-4665	332	6	a\ng(a	a\ng(a	PROPN
ejpam-4665	332	7	)	)	PUNCT
ejpam-4665	332	8	.	.	PUNCT
ejpam-4665	333	1	since	since	SCONJ
ejpam-4665	333	2	s	s	PROPN
ejpam-4665	333	3	is	be	AUX
ejpam-4665	333	4	a	a	DET
ejpam-4665	333	5	restrained	restrained	ADJ
ejpam-4665	333	6	2	2	NUM
ejpam-4665	333	7	-	-	PUNCT
ejpam-4665	333	8	resolving	resolve	VERB
ejpam-4665	333	9	hop	hop	NOUN
ejpam-4665	333	10	dominating	dominating	NOUN
ejpam-4665	333	11	set	set	NOUN
ejpam-4665	333	12	and	and	CCONJ
ejpam-4665	333	13	fj	fj	PROPN
ejpam-4665	333	14	⊆	⊆	NUM
ejpam-4665	333	15	s	s	NOUN
ejpam-4665	333	16	,	,	PUNCT
ejpam-4665	333	17	fj	fj	PROPN
ejpam-4665	333	18	is	be	AUX
ejpam-4665	333	19	a	a	DET
ejpam-4665	333	20	restrained	restrained	ADJ
ejpam-4665	333	21	2	2	NUM
ejpam-4665	333	22	-	-	PUNCT
ejpam-4665	333	23	locating	locate	VERB
ejpam-4665	333	24	point	point	NOUN
ejpam-4665	333	25	-	-	PUNCT
ejpam-4665	333	26	wise	wise	ADJ
ejpam-4665	333	27	non	non	ADJ
ejpam-4665	333	28	-	-	ADJ
ejpam-4665	333	29	dominating	dominating	ADJ
ejpam-4665	333	30	set	set	NOUN
ejpam-4665	333	31	of	of	ADP
ejpam-4665	333	32	hj	hj	PROPN
ejpam-4665	333	33	.	.	PUNCT
ejpam-4665	334	1	thus	thus	ADV
ejpam-4665	334	2	,	,	PUNCT
ejpam-4665	334	3	(	(	PUNCT
ejpam-4665	334	4	v	v	NOUN
ejpam-4665	334	5	)	)	PUNCT
ejpam-4665	334	6	follows	follow	VERB
ejpam-4665	334	7	.	.	PUNCT
ejpam-4665	335	1	conversely	conversely	ADV
ejpam-4665	335	2	,	,	PUNCT
ejpam-4665	335	3	let	let	VERB
ejpam-4665	335	4	s	s	PRON
ejpam-4665	335	5	be	be	AUX
ejpam-4665	335	6	the	the	DET
ejpam-4665	335	7	set	set	NOUN
ejpam-4665	335	8	as	as	SCONJ
ejpam-4665	335	9	described	describe	VERB
ejpam-4665	335	10	and	and	CCONJ
ejpam-4665	335	11	satisfies	satisfy	VERB
ejpam-4665	335	12	the	the	DET
ejpam-4665	335	13	given	give	VERB
ejpam-4665	335	14	conditions	condition	NOUN
ejpam-4665	335	15	.	.	PUNCT
ejpam-4665	336	1	by	by	ADP
ejpam-4665	336	2	theorem	theorem	NOUN
ejpam-4665	336	3	10	10	NUM
ejpam-4665	336	4	,	,	PUNCT
ejpam-4665	336	5	s	s	X
ejpam-4665	336	6	is	be	AUX
ejpam-4665	336	7	2	2	NUM
ejpam-4665	336	8	-	-	PUNCT
ejpam-4665	336	9	resolving	resolve	VERB
ejpam-4665	336	10	hop	hop	NOUN
ejpam-4665	336	11	dominating	dominating	NOUN
ejpam-4665	336	12	set	set	NOUN
ejpam-4665	336	13	.	.	PUNCT
ejpam-4665	337	1	furthermore	furthermore	ADV
ejpam-4665	337	2	,	,	PUNCT
ejpam-4665	337	3	because	because	SCONJ
ejpam-4665	337	4	(	(	PUNCT
ejpam-4665	337	5	i	i	NOUN
ejpam-4665	337	6	)	)	PUNCT
ejpam-4665	337	7	,	,	PUNCT
ejpam-4665	337	8	(	(	PUNCT
ejpam-4665	337	9	ii	ii	NOUN
ejpam-4665	337	10	)	)	PUNCT
ejpam-4665	337	11	,	,	PUNCT
ejpam-4665	337	12	(	(	PUNCT
ejpam-4665	337	13	iii	iii	NOUN
ejpam-4665	337	14	)	)	PUNCT
ejpam-4665	337	15	,	,	PUNCT
ejpam-4665	337	16	(	(	PUNCT
ejpam-4665	337	17	iv	iv	X
ejpam-4665	337	18	)	)	PUNCT
ejpam-4665	337	19	and	and	CCONJ
ejpam-4665	337	20	(	(	PUNCT
ejpam-4665	337	21	v	v	NOUN
ejpam-4665	337	22	)	)	PUNCT
ejpam-4665	337	23	hold	hold	NOUN
ejpam-4665	337	24	,	,	PUNCT
ejpam-4665	337	25	s	s	VERB
ejpam-4665	337	26	is	be	AUX
ejpam-4665	337	27	a	a	DET
ejpam-4665	337	28	restrained	restrained	ADJ
ejpam-4665	337	29	2	2	NUM
ejpam-4665	337	30	-	-	PUNCT
ejpam-4665	337	31	resolving	resolve	VERB
ejpam-4665	337	32	hop	hop	NOUN
ejpam-4665	337	33	dominating	dominating	NOUN
ejpam-4665	337	34	set	set	VERB
ejpam-4665	337	35	in	in	ADP
ejpam-4665	337	36	g	g	PROPN
ejpam-4665	337	37	◦	◦	NOUN
ejpam-4665	337	38	h.	h.	PROPN
ejpam-4665	337	39	as	as	ADP
ejpam-4665	337	40	a	a	DET
ejpam-4665	337	41	consequence	consequence	NOUN
ejpam-4665	337	42	of	of	ADP
ejpam-4665	337	43	theorem	theorem	NOUN
ejpam-4665	337	44	11	11	NUM
ejpam-4665	337	45	the	the	DET
ejpam-4665	337	46	next	next	ADJ
ejpam-4665	337	47	results	result	NOUN
ejpam-4665	337	48	follow	follow	VERB
ejpam-4665	337	49	.	.	PUNCT
ejpam-4665	338	1	corollary	corollary	ADJ
ejpam-4665	338	2	3	3	X
ejpam-4665	338	3	.	.	PUNCT
ejpam-4665	339	1	let	let	VERB
ejpam-4665	339	2	g	g	NOUN
ejpam-4665	339	3	and	and	CCONJ
ejpam-4665	339	4	h	h	NOUN
ejpam-4665	339	5	be	be	AUX
ejpam-4665	339	6	nontrivial	nontrivial	ADJ
ejpam-4665	339	7	connected	connect	VERB
ejpam-4665	339	8	graphs	graph	NOUN
ejpam-4665	339	9	and	and	CCONJ
ejpam-4665	339	10	|v	|v	PROPN
ejpam-4665	339	11	(	(	PUNCT
ejpam-4665	339	12	g)|	g)|	NOUN
ejpam-4665	339	13	=	=	NOUN
ejpam-4665	339	14	n.	n.	NOUN
ejpam-4665	340	1	then	then	ADV
ejpam-4665	340	2	(	(	PUNCT
ejpam-4665	340	3	i	i	NOUN
ejpam-4665	340	4	)	)	PUNCT
ejpam-4665	340	5	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	340	6	◦	◦	NOUN
ejpam-4665	340	7	h	h	NOUN
ejpam-4665	340	8	)	)	PUNCT
ejpam-4665	340	9	≤	≤	NUM
ejpam-4665	340	10	n(1	n(1	NOUN
ejpam-4665	340	11	+	+	CCONJ
ejpam-4665	340	12	rln2(h	rln2(h	NOUN
ejpam-4665	340	13	)	)	PUNCT
ejpam-4665	340	14	)	)	PUNCT
ejpam-4665	340	15	.	.	PUNCT
ejpam-4665	341	1	a.m.	a.m.	PROPN
ejpam-4665	341	2	mahistrado	mahistrado	PROPN
ejpam-4665	341	3	,	,	PUNCT
ejpam-4665	341	4	h.	h.	PROPN
ejpam-4665	341	5	rara	rara	PROPN
ejpam-4665	341	6	/	/	SYM
ejpam-4665	341	7	eur	eur	PROPN
ejpam-4665	341	8	.	.	PUNCT
ejpam-4665	342	1	j.	j.	PROPN
ejpam-4665	342	2	pure	pure	PROPN
ejpam-4665	342	3	appl	appl	PROPN
ejpam-4665	342	4	.	.	PROPN
ejpam-4665	342	5	math	math	PROPN
ejpam-4665	342	6	,	,	PUNCT
ejpam-4665	342	7	16	16	NUM
ejpam-4665	342	8	(	(	PUNCT
ejpam-4665	342	9	1	1	NUM
ejpam-4665	342	10	)	)	PUNCT
ejpam-4665	342	11	(	(	PUNCT
ejpam-4665	342	12	2023	2023	NUM
ejpam-4665	342	13	)	)	PUNCT
ejpam-4665	342	14	,	,	PUNCT
ejpam-4665	342	15	286	286	NUM
ejpam-4665	342	16	-	-	SYM
ejpam-4665	342	17	303	303	NUM
ejpam-4665	342	18	297	297	NUM
ejpam-4665	342	19	(	(	PUNCT
ejpam-4665	342	20	ii	ii	NOUN
ejpam-4665	342	21	)	)	PUNCT
ejpam-4665	342	22	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	342	23	◦	◦	NOUN
ejpam-4665	342	24	h	h	NOUN
ejpam-4665	342	25	)	)	PUNCT
ejpam-4665	342	26	≤	≤	NUM
ejpam-4665	342	27	n(lnpnd	n(lnpnd	NOUN
ejpam-4665	342	28	2	2	NUM
ejpam-4665	342	29	(	(	PUNCT
ejpam-4665	342	30	h	h	NOUN
ejpam-4665	342	31	)	)	PUNCT
ejpam-4665	342	32	)	)	PUNCT
ejpam-4665	342	33	.	.	PUNCT
ejpam-4665	343	1	proof	proof	NOUN
ejpam-4665	343	2	.	.	PUNCT
ejpam-4665	344	1	(	(	PUNCT
ejpam-4665	344	2	i	i	NOUN
ejpam-4665	344	3	)	)	PUNCT
ejpam-4665	344	4	let	let	VERB
ejpam-4665	344	5	a	a	DET
ejpam-4665	344	6	=	=	X
ejpam-4665	344	7	v	v	NOUN
ejpam-4665	344	8	(	(	PUNCT
ejpam-4665	344	9	g	g	NOUN
ejpam-4665	344	10	)	)	PUNCT
ejpam-4665	344	11	,	,	PUNCT
ejpam-4665	344	12	e	e	X
ejpam-4665	344	13	be	be	AUX
ejpam-4665	344	14	an	an	DET
ejpam-4665	344	15	rln2	rln2	NOUN
ejpam-4665	344	16	-	-	PUNCT
ejpam-4665	344	17	set	set	NOUN
ejpam-4665	344	18	of	of	ADP
ejpam-4665	344	19	h	h	NOUN
ejpam-4665	344	20	and	and	CCONJ
ejpam-4665	344	21	eu	eu	PROPN
ejpam-4665	344	22	⊆	⊆	NUM
ejpam-4665	344	23	v	v	NOUN
ejpam-4665	344	24	(	(	PUNCT
ejpam-4665	344	25	hu	hu	PROPN
ejpam-4665	344	26	)	)	PUNCT
ejpam-4665	344	27	be	be	AUX
ejpam-4665	344	28	an	an	DET
ejpam-4665	344	29	rln2	rln2	NOUN
ejpam-4665	344	30	-	-	PUNCT
ejpam-4665	344	31	set	set	NOUN
ejpam-4665	344	32	of	of	ADP
ejpam-4665	344	33	hu	hu	PROPN
ejpam-4665	344	34	with	with	ADP
ejpam-4665	344	35	⟨eu⟩	⟨eu⟩	X
ejpam-4665	344	36	∼=	∼=	PROPN
ejpam-4665	344	37	⟨e⟩	⟨e⟩	PROPN
ejpam-4665	344	38	for	for	ADP
ejpam-4665	344	39	each	each	DET
ejpam-4665	344	40	u	u	PROPN
ejpam-4665	344	41	∈	∈	PROPN
ejpam-4665	344	42	v	v	NOUN
ejpam-4665	344	43	(	(	PUNCT
ejpam-4665	344	44	g	g	NOUN
ejpam-4665	344	45	)	)	PUNCT
ejpam-4665	344	46	.	.	PUNCT
ejpam-4665	345	1	then	then	ADV
ejpam-4665	345	2	s	s	VERB
ejpam-4665	345	3	=	=	PUNCT
ejpam-4665	345	4	a	a	DET
ejpam-4665	345	5	∪	∪	X
ejpam-4665	345	6	(	(	PUNCT
ejpam-4665	345	7	⋃	⋃	NOUN
ejpam-4665	345	8	u∈v	u∈v	NOUN
ejpam-4665	345	9	(	(	PUNCT
ejpam-4665	345	10	g	g	NOUN
ejpam-4665	345	11	)	)	PUNCT
ejpam-4665	345	12	ew	ew	NOUN
ejpam-4665	345	13	)	)	PUNCT
ejpam-4665	345	14	is	be	AUX
ejpam-4665	345	15	a	a	DET
ejpam-4665	345	16	restrained	restrained	ADJ
ejpam-4665	345	17	2	2	NUM
ejpam-4665	345	18	-	-	PUNCT
ejpam-4665	345	19	resolving	resolve	VERB
ejpam-4665	345	20	hop	hop	NOUN
ejpam-4665	345	21	dominating	dominating	NOUN
ejpam-4665	345	22	set	set	NOUN
ejpam-4665	345	23	of	of	ADP
ejpam-4665	345	24	g	g	PROPN
ejpam-4665	345	25	◦	◦	NOUN
ejpam-4665	345	26	h	h	NOUN
ejpam-4665	345	27	by	by	ADP
ejpam-4665	345	28	theorem	theorem	NOUN
ejpam-4665	345	29	11	11	NUM
ejpam-4665	345	30	.	.	PUNCT
ejpam-4665	346	1	hence	hence	ADV
ejpam-4665	346	2	,	,	PUNCT
ejpam-4665	346	3	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	346	4	◦	◦	NOUN
ejpam-4665	346	5	h	h	NOUN
ejpam-4665	346	6	)	)	PUNCT
ejpam-4665	346	7	≤	≤	NUM
ejpam-4665	346	8	|s|	|s|	PROPN
ejpam-4665	346	9	=	=	SYM
ejpam-4665	346	10	|v	|v	X
ejpam-4665	346	11	(	(	PUNCT
ejpam-4665	346	12	g)|+	g)|+	PROPN
ejpam-4665	346	13	∑	∑	PROPN
ejpam-4665	346	14	w∈v	w∈v	PROPN
ejpam-4665	346	15	(	(	PUNCT
ejpam-4665	346	16	g	g	NOUN
ejpam-4665	346	17	)	)	PUNCT
ejpam-4665	346	18	|eu|	|eu|	PROPN
ejpam-4665	346	19	=	=	SYM
ejpam-4665	346	20	|v	|v	PROPN
ejpam-4665	346	21	(	(	PUNCT
ejpam-4665	346	22	g)|+	g)|+	PROPN
ejpam-4665	346	23	|v	|v	PROPN
ejpam-4665	346	24	(	(	PUNCT
ejpam-4665	346	25	g)|	g)|	NOUN
ejpam-4665	346	26	·	·	PUNCT
ejpam-4665	346	27	|e|	|e|	ADJ
ejpam-4665	346	28	=	=	SYM
ejpam-4665	346	29	n(1	n(1	NOUN
ejpam-4665	346	30	+	+	NUM
ejpam-4665	346	31	rln2(h	rln2(h	NOUN
ejpam-4665	346	32	)	)	PUNCT
ejpam-4665	346	33	)	)	PUNCT
ejpam-4665	346	34	.	.	PUNCT
ejpam-4665	347	1	(	(	PUNCT
ejpam-4665	347	2	ii	ii	NOUN
ejpam-4665	347	3	)	)	PUNCT
ejpam-4665	347	4	let	let	VERB
ejpam-4665	347	5	a	a	DET
ejpam-4665	347	6	=	=	NOUN
ejpam-4665	347	7	∅	∅	NOUN
ejpam-4665	347	8	,	,	PUNCT
ejpam-4665	347	9	d	d	X
ejpam-4665	347	10	be	be	AUX
ejpam-4665	347	11	a	a	DET
ejpam-4665	347	12	lnpnd	lnpnd	ADJ
ejpam-4665	347	13	2	2	NUM
ejpam-4665	347	14	-set	-set	PUNCT
ejpam-4665	347	15	of	of	ADP
ejpam-4665	347	16	h	h	NOUN
ejpam-4665	347	17	and	and	CCONJ
ejpam-4665	347	18	dw	dw	PROPN
ejpam-4665	347	19	⊆	⊆	NUM
ejpam-4665	347	20	v	v	NOUN
ejpam-4665	347	21	(	(	PUNCT
ejpam-4665	347	22	hw	hw	NOUN
ejpam-4665	347	23	)	)	PUNCT
ejpam-4665	347	24	be	be	AUX
ejpam-4665	347	25	a	a	DET
ejpam-4665	347	26	lnpnd	lnpnd	ADJ
ejpam-4665	347	27	2	2	NUM
ejpam-4665	347	28	-set	-set	PUNCT
ejpam-4665	347	29	of	of	ADP
ejpam-4665	347	30	hw	hw	PRON
ejpam-4665	347	31	with	with	ADP
ejpam-4665	347	32	⟨dw⟩	⟨dw⟩	NOUN
ejpam-4665	347	33	∼=	∼=	PROPN
ejpam-4665	347	34	⟨d⟩	⟨d⟩	PROPN
ejpam-4665	347	35	for	for	ADP
ejpam-4665	347	36	each	each	DET
ejpam-4665	347	37	w	w	PROPN
ejpam-4665	347	38	∈	∈	PROPN
ejpam-4665	347	39	v	v	ADP
ejpam-4665	347	40	(	(	PUNCT
ejpam-4665	347	41	g	g	NOUN
ejpam-4665	347	42	)	)	PUNCT
ejpam-4665	347	43	.	.	PUNCT
ejpam-4665	348	1	then	then	ADV
ejpam-4665	348	2	s	s	VERB
ejpam-4665	348	3	=	=	PUNCT
ejpam-4665	348	4	a	a	DET
ejpam-4665	348	5	∪	∪	X
ejpam-4665	348	6	(	(	PUNCT
ejpam-4665	348	7	⋃	⋃	PROPN
ejpam-4665	348	8	w∈v	w∈v	PROPN
ejpam-4665	348	9	(	(	PUNCT
ejpam-4665	348	10	g	g	NOUN
ejpam-4665	348	11	)	)	PUNCT
ejpam-4665	348	12	dw	dw	PROPN
ejpam-4665	348	13	)	)	PUNCT
ejpam-4665	348	14	is	be	AUX
ejpam-4665	348	15	a	a	DET
ejpam-4665	348	16	restrained	restrained	ADJ
ejpam-4665	348	17	2	2	NUM
ejpam-4665	348	18	-	-	PUNCT
ejpam-4665	348	19	resolving	resolve	VERB
ejpam-4665	348	20	hop	hop	NOUN
ejpam-4665	348	21	dominating	dominating	NOUN
ejpam-4665	348	22	set	set	NOUN
ejpam-4665	348	23	of	of	ADP
ejpam-4665	348	24	g	g	PROPN
ejpam-4665	348	25	◦	◦	NOUN
ejpam-4665	348	26	h	h	NOUN
ejpam-4665	348	27	by	by	ADP
ejpam-4665	348	28	theorem	theorem	NOUN
ejpam-4665	348	29	11	11	NUM
ejpam-4665	348	30	.	.	PUNCT
ejpam-4665	349	1	hence	hence	ADV
ejpam-4665	349	2	,	,	PUNCT
ejpam-4665	349	3	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	349	4	◦	◦	NOUN
ejpam-4665	349	5	h	h	NOUN
ejpam-4665	349	6	)	)	PUNCT
ejpam-4665	349	7	≤	≤	NUM
ejpam-4665	349	8	|s|	|s|	NOUN
ejpam-4665	349	9	=	=	SYM
ejpam-4665	349	10	|a|+	|a|+	VERB
ejpam-4665	349	11	∑	∑	PUNCT
ejpam-4665	349	12	w∈v	w∈v	PROPN
ejpam-4665	349	13	(	(	PUNCT
ejpam-4665	349	14	g	g	NOUN
ejpam-4665	349	15	)	)	PUNCT
ejpam-4665	349	16	|dw|	|dw|	NOUN
ejpam-4665	349	17	=	=	SYM
ejpam-4665	349	18	|v	|v	PROPN
ejpam-4665	349	19	(	(	PUNCT
ejpam-4665	349	20	g)|	g)|	PROPN
ejpam-4665	349	21	·	·	PUNCT
ejpam-4665	349	22	|d|	|d|	PROPN
ejpam-4665	349	23	=	=	SYM
ejpam-4665	349	24	n(lnpnd	n(lnpnd	NOUN
ejpam-4665	349	25	2	2	NUM
ejpam-4665	349	26	(	(	PUNCT
ejpam-4665	349	27	h	h	NOUN
ejpam-4665	349	28	)	)	PUNCT
ejpam-4665	349	29	)	)	PUNCT
ejpam-4665	349	30	.	.	PUNCT
ejpam-4665	350	1	corollary	corollary	ADJ
ejpam-4665	350	2	4	4	NUM
ejpam-4665	350	3	.	.	PUNCT
ejpam-4665	351	1	let	let	VERB
ejpam-4665	351	2	g	g	NOUN
ejpam-4665	351	3	and	and	CCONJ
ejpam-4665	351	4	h	h	NOUN
ejpam-4665	351	5	be	be	AUX
ejpam-4665	351	6	nontrivial	nontrivial	ADJ
ejpam-4665	351	7	connected	connect	VERB
ejpam-4665	351	8	graphs	graph	NOUN
ejpam-4665	351	9	where	where	SCONJ
ejpam-4665	351	10	|v	|v	PROPN
ejpam-4665	351	11	(	(	PUNCT
ejpam-4665	351	12	g)|	g)|	NOUN
ejpam-4665	351	13	=	=	PUNCT
ejpam-4665	351	14	n	n	NOUN
ejpam-4665	351	15	and	and	CCONJ
ejpam-4665	351	16	lnpnd	lnpnd	ADJ
ejpam-4665	351	17	2	2	NUM
ejpam-4665	351	18	(	(	PUNCT
ejpam-4665	351	19	h	h	NOUN
ejpam-4665	351	20	)	)	PUNCT
ejpam-4665	351	21	=	=	SYM
ejpam-4665	351	22	ln2(h	ln2(h	PROPN
ejpam-4665	351	23	)	)	PUNCT
ejpam-4665	351	24	.	.	PUNCT
ejpam-4665	352	1	then	then	ADV
ejpam-4665	352	2	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	352	3	◦	◦	NOUN
ejpam-4665	352	4	h	h	NOUN
ejpam-4665	352	5	)	)	PUNCT
ejpam-4665	353	1	=	=	SYM
ejpam-4665	353	2	n(lnpnd	n(lnpnd	NOUN
ejpam-4665	353	3	2	2	NUM
ejpam-4665	353	4	(	(	PUNCT
ejpam-4665	353	5	h	h	NOUN
ejpam-4665	353	6	)	)	PUNCT
ejpam-4665	353	7	)	)	PUNCT
ejpam-4665	353	8	.	.	PUNCT
ejpam-4665	354	1	proof	proof	NOUN
ejpam-4665	354	2	.	.	PUNCT
ejpam-4665	355	1	we	we	PRON
ejpam-4665	355	2	have	have	VERB
ejpam-4665	355	3	γr2rh(g	γr2rh(g	NOUN
ejpam-4665	355	4	◦	◦	VERB
ejpam-4665	355	5	h	h	NOUN
ejpam-4665	355	6	)	)	PUNCT
ejpam-4665	355	7	≤	≤	NUM
ejpam-4665	355	8	n(lnpnd	n(lnpnd	NOUN
ejpam-4665	355	9	2	2	NUM
ejpam-4665	355	10	(	(	PUNCT
ejpam-4665	355	11	h	h	NOUN
ejpam-4665	355	12	)	)	PUNCT
ejpam-4665	355	13	)	)	PUNCT
ejpam-4665	355	14	by	by	ADP
ejpam-4665	355	15	corollary	corollary	ADJ
ejpam-4665	355	16	3	3	NUM
ejpam-4665	355	17	(	(	PUNCT
ejpam-4665	355	18	ii	ii	NOUN
ejpam-4665	355	19	)	)	PUNCT
ejpam-4665	355	20	.	.	PUNCT
ejpam-4665	356	1	since	since	SCONJ
ejpam-4665	356	2	lnpnd	lnpnd	ADJ
ejpam-4665	356	3	2	2	NUM
ejpam-4665	356	4	(	(	PUNCT
ejpam-4665	356	5	h	h	NOUN
ejpam-4665	356	6	)	)	PUNCT
ejpam-4665	356	7	=	=	SYM
ejpam-4665	356	8	ln2(h	ln2(h	PROPN
ejpam-4665	356	9	)	)	PUNCT
ejpam-4665	356	10	,	,	PUNCT
ejpam-4665	356	11	then	then	ADV
ejpam-4665	356	12	by	by	ADP
ejpam-4665	356	13	remark	remark	NOUN
ejpam-4665	356	14	5	5	NUM
ejpam-4665	356	15	and	and	CCONJ
ejpam-4665	356	16	corollary	corollary	ADJ
ejpam-4665	356	17	5	5	NUM
ejpam-4665	356	18	in	in	ADP
ejpam-4665	356	19	[	[	PUNCT
ejpam-4665	356	20	11	11	NUM
ejpam-4665	356	21	]	]	PUNCT
ejpam-4665	356	22	,	,	PUNCT
ejpam-4665	356	23	we	we	PRON
ejpam-4665	356	24	have	have	VERB
ejpam-4665	356	25	γr2rh(g	γr2rh(g	NOUN
ejpam-4665	356	26	◦	◦	NOUN
ejpam-4665	356	27	h	h	NOUN
ejpam-4665	356	28	)	)	PUNCT
ejpam-4665	356	29	≥	≥	NOUN
ejpam-4665	356	30	γ2rh(g	γ2rh(g	NOUN
ejpam-4665	356	31	◦	◦	NOUN
ejpam-4665	356	32	h	h	NOUN
ejpam-4665	356	33	)	)	PUNCT
ejpam-4665	356	34	=	=	SYM
ejpam-4665	356	35	n(lnpnd	n(lnpnd	NOUN
ejpam-4665	356	36	2	2	NUM
ejpam-4665	356	37	(	(	PUNCT
ejpam-4665	356	38	h	h	NOUN
ejpam-4665	356	39	)	)	PUNCT
ejpam-4665	356	40	)	)	PUNCT
ejpam-4665	356	41	.	.	PUNCT
ejpam-4665	357	1	therefore	therefore	ADV
ejpam-4665	357	2	,	,	PUNCT
ejpam-4665	357	3	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	357	4	◦	◦	NOUN
ejpam-4665	357	5	h	h	NOUN
ejpam-4665	357	6	)	)	PUNCT
ejpam-4665	358	1	=	=	SYM
ejpam-4665	358	2	n(lnpnd	n(lnpnd	NOUN
ejpam-4665	358	3	2	2	NUM
ejpam-4665	358	4	(	(	PUNCT
ejpam-4665	358	5	h	h	NOUN
ejpam-4665	358	6	)	)	PUNCT
ejpam-4665	358	7	)	)	PUNCT
ejpam-4665	358	8	.	.	PUNCT
ejpam-4665	359	1	example	example	NOUN
ejpam-4665	360	1	5	5	NUM
ejpam-4665	360	2	.	.	X
ejpam-4665	360	3	for	for	ADP
ejpam-4665	360	4	any	any	DET
ejpam-4665	360	5	nontrivial	nontrivial	ADJ
ejpam-4665	360	6	connected	connect	VERB
ejpam-4665	360	7	graph	graph	NOUN
ejpam-4665	360	8	g	g	NOUN
ejpam-4665	360	9	of	of	ADP
ejpam-4665	360	10	order	order	NOUN
ejpam-4665	360	11	n	n	CCONJ
ejpam-4665	360	12	,	,	PUNCT
ejpam-4665	360	13	(	(	PUNCT
ejpam-4665	360	14	i	i	NOUN
ejpam-4665	360	15	)	)	PUNCT
ejpam-4665	360	16	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	360	17	◦	◦	NOUN
ejpam-4665	360	18	h	h	NOUN
ejpam-4665	360	19	)	)	PUNCT
ejpam-4665	360	20	≤	≤	NOUN
ejpam-4665	360	21	4n	4n	NOUN
ejpam-4665	360	22	if	if	SCONJ
ejpam-4665	360	23	h	h	NOUN
ejpam-4665	360	24	=	=	SYM
ejpam-4665	360	25	p3	p3	PROPN
ejpam-4665	360	26	;	;	PUNCT
ejpam-4665	360	27	(	(	PUNCT
ejpam-4665	360	28	ii	ii	NOUN
ejpam-4665	360	29	)	)	PUNCT
ejpam-4665	360	30	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	360	31	◦	◦	NOUN
ejpam-4665	360	32	h	h	NOUN
ejpam-4665	360	33	)	)	PUNCT
ejpam-4665	360	34	=	=	SYM
ejpam-4665	360	35	n	n	NOUN
ejpam-4665	360	36	·	·	PUNCT
ejpam-4665	360	37	(	(	PUNCT
ejpam-4665	360	38	⌈	⌈	NOUN
ejpam-4665	360	39	m+1	m+1	NUM
ejpam-4665	360	40	2	2	NUM
ejpam-4665	360	41	⌉	⌉	NOUN
ejpam-4665	360	42	)	)	PUNCT
ejpam-4665	360	43	if	if	SCONJ
ejpam-4665	360	44	h	h	NOUN
ejpam-4665	360	45	=	=	VERB
ejpam-4665	360	46	pm	pm	NOUN
ejpam-4665	360	47	and	and	CCONJ
ejpam-4665	360	48	m	m	PRON
ejpam-4665	360	49	≥	≥	NOUN
ejpam-4665	360	50	4	4	NUM
ejpam-4665	360	51	;	;	PUNCT
ejpam-4665	360	52	(	(	PUNCT
ejpam-4665	360	53	iiii	iiii	PROPN
ejpam-4665	360	54	)	)	PUNCT
ejpam-4665	360	55	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	360	56	◦	◦	NOUN
ejpam-4665	360	57	h	h	NOUN
ejpam-4665	360	58	)	)	PUNCT
ejpam-4665	360	59	=	=	SYM
ejpam-4665	361	1	n	n	NOUN
ejpam-4665	361	2	·	·	PUNCT
ejpam-4665	361	3	(	(	PUNCT
ejpam-4665	361	4	⌈	⌈	SYM
ejpam-4665	361	5	m	m	PROPN
ejpam-4665	361	6	2	2	NUM
ejpam-4665	361	7	⌉	⌉	NOUN
ejpam-4665	361	8	)	)	PUNCT
ejpam-4665	361	9	if	if	SCONJ
ejpam-4665	361	10	h	h	NOUN
ejpam-4665	361	11	=	=	SYM
ejpam-4665	361	12	cm	cm	PROPN
ejpam-4665	361	13	and	and	CCONJ
ejpam-4665	361	14	m	m	PRON
ejpam-4665	361	15	≥	≥	NOUN
ejpam-4665	361	16	5	5	NUM
ejpam-4665	361	17	.	.	NOUN
ejpam-4665	361	18	6	6	NUM
ejpam-4665	361	19	.	.	PUNCT
ejpam-4665	362	1	restrained	restrain	VERB
ejpam-4665	362	2	2	2	NUM
ejpam-4665	362	3	-	-	PUNCT
ejpam-4665	362	4	resolving	resolve	VERB
ejpam-4665	362	5	hop	hop	NOUN
ejpam-4665	362	6	dominating	dominating	NOUN
ejpam-4665	362	7	sets	set	NOUN
ejpam-4665	362	8	in	in	ADP
ejpam-4665	362	9	the	the	DET
ejpam-4665	362	10	edge	edge	NOUN
ejpam-4665	362	11	corona	corona	NOUN
ejpam-4665	362	12	of	of	ADP
ejpam-4665	362	13	graphs	graph	NOUN
ejpam-4665	362	14	this	this	DET
ejpam-4665	362	15	section	section	NOUN
ejpam-4665	362	16	presents	present	VERB
ejpam-4665	362	17	characterizations	characterization	NOUN
ejpam-4665	362	18	on	on	ADP
ejpam-4665	362	19	the	the	DET
ejpam-4665	362	20	2	2	NUM
ejpam-4665	362	21	-	-	PUNCT
ejpam-4665	362	22	resolving	resolve	VERB
ejpam-4665	362	23	hop	hop	NOUN
ejpam-4665	362	24	dominating	dominating	NOUN
ejpam-4665	362	25	sets	set	NOUN
ejpam-4665	362	26	and	and	CCONJ
ejpam-4665	362	27	restrained	restrain	VERB
ejpam-4665	362	28	2	2	NUM
ejpam-4665	362	29	-	-	PUNCT
ejpam-4665	362	30	resolving	resolve	VERB
ejpam-4665	362	31	hop	hop	NOUN
ejpam-4665	362	32	dominating	dominating	NOUN
ejpam-4665	362	33	sets	set	NOUN
ejpam-4665	362	34	in	in	ADP
ejpam-4665	362	35	the	the	DET
ejpam-4665	362	36	edge	edge	NOUN
ejpam-4665	362	37	corona	corona	NOUN
ejpam-4665	362	38	of	of	ADP
ejpam-4665	362	39	graphs	graph	NOUN
ejpam-4665	362	40	.	.	PUNCT
ejpam-4665	363	1	remark	remark	PROPN
ejpam-4665	363	2	7	7	NUM
ejpam-4665	363	3	.	.	PUNCT
ejpam-4665	364	1	let	let	VERB
ejpam-4665	364	2	uv	uv	PRON
ejpam-4665	364	3	∈	∈	PROPN
ejpam-4665	364	4	e(g	e(g	PROPN
ejpam-4665	364	5	)	)	PUNCT
ejpam-4665	364	6	.	.	PUNCT
ejpam-4665	365	1	for	for	ADP
ejpam-4665	365	2	every	every	DET
ejpam-4665	365	3	x	x	PROPN
ejpam-4665	365	4	,	,	PUNCT
ejpam-4665	365	5	y	y	PROPN
ejpam-4665	365	6	∈	∈	PROPN
ejpam-4665	365	7	v	v	PROPN
ejpam-4665	365	8	(	(	PUNCT
ejpam-4665	365	9	huv	huv	PROPN
ejpam-4665	365	10	)	)	PUNCT
ejpam-4665	365	11	,	,	PUNCT
ejpam-4665	365	12	dg⋄h(x	dg⋄h(x	PROPN
ejpam-4665	365	13	,	,	PUNCT
ejpam-4665	365	14	w	w	PROPN
ejpam-4665	365	15	)	)	PUNCT
ejpam-4665	365	16	=	=	SYM
ejpam-4665	366	1	dg⋄h(y	dg⋄h(y	PROPN
ejpam-4665	366	2	,	,	PUNCT
ejpam-4665	366	3	w	w	NOUN
ejpam-4665	366	4	)	)	PUNCT
ejpam-4665	366	5	,	,	PUNCT
ejpam-4665	366	6	dg⋄h(u	dg⋄h(u	X
ejpam-4665	366	7	,	,	PUNCT
ejpam-4665	366	8	w	w	NOUN
ejpam-4665	366	9	)	)	PUNCT
ejpam-4665	366	10	=	=	SYM
ejpam-4665	367	1	dg⋄h(x	dg⋄h(x	PROPN
ejpam-4665	367	2	,	,	PUNCT
ejpam-4665	367	3	w	w	PROPN
ejpam-4665	367	4	)	)	PUNCT
ejpam-4665	367	5	,	,	PUNCT
ejpam-4665	367	6	and	and	CCONJ
ejpam-4665	367	7	dg⋄h(v	dg⋄h(v	PROPN
ejpam-4665	367	8	,	,	PUNCT
ejpam-4665	367	9	w)+1	w)+1	X
ejpam-4665	367	10	=	=	SYM
ejpam-4665	367	11	dg⋄h(x	dg⋄h(x	PROPN
ejpam-4665	367	12	,	,	PUNCT
ejpam-4665	367	13	w	w	PROPN
ejpam-4665	367	14	)	)	PUNCT
ejpam-4665	367	15	for	for	ADP
ejpam-4665	367	16	every	every	DET
ejpam-4665	367	17	w	w	PROPN
ejpam-4665	367	18	∈	∈	PROPN
ejpam-4665	367	19	v	v	NOUN
ejpam-4665	367	20	(	(	PUNCT
ejpam-4665	367	21	g⋄h)\v	g⋄h)\v	PROPN
ejpam-4665	367	22	(	(	PUNCT
ejpam-4665	367	23	huv	huv	PROPN
ejpam-4665	367	24	)	)	PUNCT
ejpam-4665	367	25	.	.	PUNCT
ejpam-4665	368	1	a.m.	a.m.	PROPN
ejpam-4665	368	2	mahistrado	mahistrado	PROPN
ejpam-4665	368	3	,	,	PUNCT
ejpam-4665	368	4	h.	h.	PROPN
ejpam-4665	368	5	rara	rara	PROPN
ejpam-4665	368	6	/	/	SYM
ejpam-4665	368	7	eur	eur	PROPN
ejpam-4665	368	8	.	.	PUNCT
ejpam-4665	369	1	j.	j.	PROPN
ejpam-4665	369	2	pure	pure	PROPN
ejpam-4665	369	3	appl	appl	PROPN
ejpam-4665	369	4	.	.	PROPN
ejpam-4665	369	5	math	math	PROPN
ejpam-4665	369	6	,	,	PUNCT
ejpam-4665	369	7	16	16	NUM
ejpam-4665	369	8	(	(	PUNCT
ejpam-4665	369	9	1	1	NUM
ejpam-4665	369	10	)	)	PUNCT
ejpam-4665	369	11	(	(	PUNCT
ejpam-4665	369	12	2023	2023	NUM
ejpam-4665	369	13	)	)	PUNCT
ejpam-4665	369	14	,	,	PUNCT
ejpam-4665	369	15	286	286	NUM
ejpam-4665	369	16	-	-	SYM
ejpam-4665	369	17	303	303	NUM
ejpam-4665	369	18	298	298	NUM
ejpam-4665	369	19	remark	remark	NOUN
ejpam-4665	369	20	8	8	NUM
ejpam-4665	369	21	.	.	PUNCT
ejpam-4665	370	1	let	let	VERB
ejpam-4665	370	2	g	g	NOUN
ejpam-4665	370	3	and	and	CCONJ
ejpam-4665	370	4	h	h	NOUN
ejpam-4665	370	5	be	be	AUX
ejpam-4665	370	6	nontrivial	nontrivial	ADJ
ejpam-4665	370	7	connected	connected	ADJ
ejpam-4665	370	8	graphs	graph	NOUN
ejpam-4665	370	9	,	,	PUNCT
ejpam-4665	370	10	c	c	PROPN
ejpam-4665	370	11	⊆	⊆	NUM
ejpam-4665	370	12	v	v	NOUN
ejpam-4665	370	13	(	(	PUNCT
ejpam-4665	370	14	g	g	PROPN
ejpam-4665	370	15	⋄	⋄	PROPN
ejpam-4665	370	16	h	h	NOUN
ejpam-4665	370	17	)	)	PUNCT
ejpam-4665	370	18	and	and	CCONJ
ejpam-4665	370	19	suv	suv	PROPN
ejpam-4665	370	20	=	=	SYM
ejpam-4665	370	21	v	v	PROPN
ejpam-4665	370	22	(	(	PUNCT
ejpam-4665	370	23	huv	huv	PROPN
ejpam-4665	370	24	)	)	PUNCT
ejpam-4665	370	25	∩	∩	NOUN
ejpam-4665	370	26	c	c	X
ejpam-4665	370	27	where	where	SCONJ
ejpam-4665	370	28	uv	uv	NOUN
ejpam-4665	370	29	∈	∈	PROPN
ejpam-4665	370	30	e(g	e(g	PROPN
ejpam-4665	370	31	)	)	PUNCT
ejpam-4665	370	32	.	.	PUNCT
ejpam-4665	371	1	for	for	ADP
ejpam-4665	371	2	each	each	DET
ejpam-4665	371	3	x	x	SYM
ejpam-4665	371	4	∈	∈	PROPN
ejpam-4665	371	5	v	v	NOUN
ejpam-4665	371	6	(	(	PUNCT
ejpam-4665	371	7	huv)\suv	huv)\suv	PROPN
ejpam-4665	371	8	and	and	CCONJ
ejpam-4665	371	9	z	z	PROPN
ejpam-4665	371	10	∈	∈	PROPN
ejpam-4665	371	11	suv	suv	PROPN
ejpam-4665	371	12	,	,	PUNCT
ejpam-4665	371	13	dg⋄h(x	dg⋄h(x	PROPN
ejpam-4665	371	14	,	,	PUNCT
ejpam-4665	371	15	z	z	NOUN
ejpam-4665	371	16	)	)	PUNCT
ejpam-4665	371	17	=	=	PRON
ejpam-4665	371	18	{	{	PUNCT
ejpam-4665	371	19	1	1	NUM
ejpam-4665	371	20	if	if	SCONJ
ejpam-4665	371	21	z	z	PROPN
ejpam-4665	371	22	∈	∈	PROPN
ejpam-4665	371	23	nhuv(x	nhuv(x	NOUN
ejpam-4665	371	24	)	)	PUNCT
ejpam-4665	371	25	2	2	NUM
ejpam-4665	371	26	otherwise	otherwise	ADV
ejpam-4665	371	27	.	.	PUNCT
ejpam-4665	372	1	definition	definition	NOUN
ejpam-4665	372	2	9	9	NUM
ejpam-4665	372	3	.	.	PUNCT
ejpam-4665	373	1	a	a	DET
ejpam-4665	373	2	leaf	leaf	NOUN
ejpam-4665	373	3	l(g	l(g	NOUN
ejpam-4665	373	4	)	)	PUNCT
ejpam-4665	373	5	of	of	ADP
ejpam-4665	373	6	a	a	DET
ejpam-4665	373	7	graph	graph	NOUN
ejpam-4665	373	8	g	g	NOUN
ejpam-4665	373	9	is	be	AUX
ejpam-4665	373	10	a	a	DET
ejpam-4665	373	11	set	set	NOUN
ejpam-4665	373	12	of	of	ADP
ejpam-4665	373	13	vertices	vertex	NOUN
ejpam-4665	373	14	v	v	NOUN
ejpam-4665	373	15	in	in	ADP
ejpam-4665	373	16	g	g	NOUN
ejpam-4665	373	17	with	with	ADP
ejpam-4665	373	18	degg(v	degg(v	PROPN
ejpam-4665	373	19	)	)	PUNCT
ejpam-4665	373	20	=	=	SYM
ejpam-4665	373	21	1	1	X
ejpam-4665	373	22	.	.	PUNCT
ejpam-4665	373	23	theorem	theorem	NOUN
ejpam-4665	373	24	12	12	NUM
ejpam-4665	373	25	.	.	PUNCT
ejpam-4665	374	1	let	let	VERB
ejpam-4665	374	2	g	g	PROPN
ejpam-4665	374	3	̸=	̸=	PROPN
ejpam-4665	374	4	p2	p2	PROPN
ejpam-4665	374	5	and	and	CCONJ
ejpam-4665	374	6	h	h	NOUN
ejpam-4665	374	7	be	be	VERB
ejpam-4665	374	8	any	any	DET
ejpam-4665	374	9	nontrivial	nontrivial	ADJ
ejpam-4665	374	10	connected	connect	VERB
ejpam-4665	374	11	graphs	graph	NOUN
ejpam-4665	374	12	.	.	PUNCT
ejpam-4665	375	1	a	a	DET
ejpam-4665	375	2	set	set	NOUN
ejpam-4665	375	3	c	c	NOUN
ejpam-4665	375	4	⊆	⊆	NUM
ejpam-4665	375	5	v	v	NOUN
ejpam-4665	375	6	(	(	PUNCT
ejpam-4665	375	7	g	g	PROPN
ejpam-4665	375	8	⋄h	⋄h	PROPN
ejpam-4665	375	9	)	)	PUNCT
ejpam-4665	375	10	is	be	AUX
ejpam-4665	375	11	a	a	DET
ejpam-4665	375	12	2	2	NUM
ejpam-4665	375	13	-	-	PUNCT
ejpam-4665	375	14	resolving	resolve	VERB
ejpam-4665	375	15	hop	hop	NOUN
ejpam-4665	375	16	dominating	dominating	NOUN
ejpam-4665	375	17	set	set	NOUN
ejpam-4665	375	18	of	of	ADP
ejpam-4665	375	19	g	g	PROPN
ejpam-4665	375	20	⋄h	⋄h	X
ejpam-4665	375	21	if	if	SCONJ
ejpam-4665	376	1	and	and	CCONJ
ejpam-4665	376	2	only	only	ADV
ejpam-4665	376	3	if	if	SCONJ
ejpam-4665	376	4	c	c	X
ejpam-4665	376	5	=	=	PUNCT
ejpam-4665	376	6	a	a	DET
ejpam-4665	376	7	∪	∪	ADJ
ejpam-4665	376	8			PROPN
ejpam-4665	376	9	⋃	⋃	ADJ
ejpam-4665	376	10	uv∈e(g	uv∈e(g	NOUN
ejpam-4665	376	11	)	)	PUNCT
ejpam-4665	376	12	suv	suv	NOUN
ejpam-4665	376	13			PROPN
ejpam-4665	377	1	where	where	SCONJ
ejpam-4665	377	2	(	(	PUNCT
ejpam-4665	377	3	i	i	NOUN
ejpam-4665	377	4	)	)	PUNCT
ejpam-4665	377	5	a	a	DET
ejpam-4665	377	6	⊆	⊆	NUM
ejpam-4665	377	7	v	v	NOUN
ejpam-4665	377	8	(	(	PUNCT
ejpam-4665	377	9	g	g	NOUN
ejpam-4665	377	10	)	)	PUNCT
ejpam-4665	377	11	;	;	PUNCT
ejpam-4665	377	12	(	(	PUNCT
ejpam-4665	377	13	ii	ii	X
ejpam-4665	377	14	)	)	PUNCT
ejpam-4665	377	15	suv	suv	PROPN
ejpam-4665	377	16	⊆	⊆	NUM
ejpam-4665	377	17	v	v	NOUN
ejpam-4665	377	18	(	(	PUNCT
ejpam-4665	377	19	huv	huv	PROPN
ejpam-4665	377	20	)	)	PUNCT
ejpam-4665	377	21	is	be	AUX
ejpam-4665	377	22	a	a	DET
ejpam-4665	377	23	2	2	NUM
ejpam-4665	377	24	-	-	PUNCT
ejpam-4665	377	25	locating	locate	VERB
ejpam-4665	377	26	set	set	NOUN
ejpam-4665	377	27	of	of	ADP
ejpam-4665	377	28	huv	huv	PROPN
ejpam-4665	377	29	for	for	ADP
ejpam-4665	377	30	all	all	DET
ejpam-4665	377	31	uv	uv	PROPN
ejpam-4665	377	32	∈	∈	PROPN
ejpam-4665	377	33	e(g	e(g	PROPN
ejpam-4665	377	34	)	)	PUNCT
ejpam-4665	377	35	or	or	CCONJ
ejpam-4665	377	36	if	if	SCONJ
ejpam-4665	377	37	uv	uv	NOUN
ejpam-4665	377	38	is	be	AUX
ejpam-4665	377	39	a	a	DET
ejpam-4665	377	40	pendant	pendant	ADJ
ejpam-4665	377	41	edge	edge	NOUN
ejpam-4665	377	42	,	,	PUNCT
ejpam-4665	377	43	then	then	ADV
ejpam-4665	377	44	suv	suv	PROPN
ejpam-4665	377	45	is	be	AUX
ejpam-4665	377	46	a	a	DET
ejpam-4665	377	47	(	(	PUNCT
ejpam-4665	377	48	2	2	NUM
ejpam-4665	377	49	,	,	PUNCT
ejpam-4665	377	50	1)-locating	1)-locating	NUM
ejpam-4665	377	51	set	set	NOUN
ejpam-4665	377	52	of	of	ADP
ejpam-4665	377	53	huv	huv	PROPN
ejpam-4665	377	54	whenever	whenever	SCONJ
ejpam-4665	377	55	l(⟨{u	l(⟨{u	PROPN
ejpam-4665	377	56	,	,	PUNCT
ejpam-4665	377	57	v}⟩	v}⟩	PROPN
ejpam-4665	377	58	)	)	PUNCT
ejpam-4665	377	59	⊆	⊆	NUM
ejpam-4665	377	60	a	a	PRON
ejpam-4665	377	61	and	and	CCONJ
ejpam-4665	377	62	suv	suv	PROPN
ejpam-4665	377	63	is	be	AUX
ejpam-4665	377	64	a	a	DET
ejpam-4665	377	65	(	(	PUNCT
ejpam-4665	377	66	2	2	NUM
ejpam-4665	377	67	,	,	PUNCT
ejpam-4665	377	68	2)-locating	2)-locating	NUM
ejpam-4665	377	69	set	set	NOUN
ejpam-4665	377	70	of	of	ADP
ejpam-4665	377	71	huv	huv	PROPN
ejpam-4665	377	72	otherwise	otherwise	ADV
ejpam-4665	377	73	.	.	PUNCT
ejpam-4665	378	1	proof	proof	NOUN
ejpam-4665	378	2	.	.	PUNCT
ejpam-4665	379	1	suppose	suppose	VERB
ejpam-4665	379	2	that	that	SCONJ
ejpam-4665	379	3	c	c	PROPN
ejpam-4665	379	4	⊆	⊆	NUM
ejpam-4665	379	5	v	v	NOUN
ejpam-4665	379	6	(	(	PUNCT
ejpam-4665	379	7	g	g	PROPN
ejpam-4665	379	8	⋄h	⋄h	PROPN
ejpam-4665	379	9	)	)	PUNCT
ejpam-4665	379	10	is	be	AUX
ejpam-4665	379	11	a	a	DET
ejpam-4665	379	12	2	2	NUM
ejpam-4665	379	13	-	-	PUNCT
ejpam-4665	379	14	resolving	resolve	VERB
ejpam-4665	379	15	hop	hop	NOUN
ejpam-4665	379	16	dominating	dominating	NOUN
ejpam-4665	379	17	set	set	NOUN
ejpam-4665	379	18	of	of	ADP
ejpam-4665	379	19	g	g	PROPN
ejpam-4665	379	20	⋄h	⋄h	PROPN
ejpam-4665	379	21	.	.	PUNCT
ejpam-4665	380	1	let	let	VERB
ejpam-4665	380	2	a	a	DET
ejpam-4665	380	3	=	=	X
ejpam-4665	380	4	v	v	X
ejpam-4665	380	5	(	(	PUNCT
ejpam-4665	380	6	g	g	NOUN
ejpam-4665	380	7	)	)	PUNCT
ejpam-4665	380	8	∩	∩	NOUN
ejpam-4665	380	9	c	c	PROPN
ejpam-4665	380	10	and	and	CCONJ
ejpam-4665	380	11	suv	suv	PROPN
ejpam-4665	380	12	=	=	PROPN
ejpam-4665	380	13	c	c	PROPN
ejpam-4665	380	14	∩	∩	X
ejpam-4665	380	15	v	v	X
ejpam-4665	380	16	(	(	PUNCT
ejpam-4665	380	17	huv	huv	PROPN
ejpam-4665	380	18	)	)	PUNCT
ejpam-4665	380	19	for	for	ADP
ejpam-4665	380	20	all	all	DET
ejpam-4665	380	21	uv	uv	PROPN
ejpam-4665	380	22	∈	∈	PROPN
ejpam-4665	380	23	e(g	e(g	PROPN
ejpam-4665	380	24	)	)	PUNCT
ejpam-4665	380	25	.	.	PUNCT
ejpam-4665	381	1	then	then	ADV
ejpam-4665	381	2	c	c	X
ejpam-4665	381	3	=	=	PUNCT
ejpam-4665	381	4	a	a	DET
ejpam-4665	381	5	∪	∪	X
ejpam-4665	381	6	(	(	PUNCT
ejpam-4665	381	7	⋃	⋃	NOUN
ejpam-4665	381	8	uv∈e(g	uv∈e(g	NOUN
ejpam-4665	381	9	)	)	PUNCT
ejpam-4665	381	10	suv	suv	PROPN
ejpam-4665	381	11	)	)	PUNCT
ejpam-4665	381	12	where	where	SCONJ
ejpam-4665	381	13	a	a	DET
ejpam-4665	381	14	⊆	⊆	NUM
ejpam-4665	381	15	v	v	NOUN
ejpam-4665	381	16	(	(	PUNCT
ejpam-4665	381	17	g	g	NOUN
ejpam-4665	381	18	)	)	PUNCT
ejpam-4665	381	19	and	and	CCONJ
ejpam-4665	381	20	suv	suv	PROPN
ejpam-4665	381	21	⊆	⊆	NUM
ejpam-4665	381	22	v	v	NOUN
ejpam-4665	381	23	(	(	PUNCT
ejpam-4665	381	24	huv	huv	PROPN
ejpam-4665	381	25	)	)	PUNCT
ejpam-4665	381	26	.	.	PUNCT
ejpam-4665	382	1	now	now	ADV
ejpam-4665	382	2	,	,	PUNCT
ejpam-4665	382	3	suppose	suppose	VERB
ejpam-4665	382	4	that	that	SCONJ
ejpam-4665	382	5	suv	suv	PROPN
ejpam-4665	382	6	=	=	NOUN
ejpam-4665	382	7	∅	∅	NOUN
ejpam-4665	382	8	for	for	ADP
ejpam-4665	382	9	some	some	DET
ejpam-4665	382	10	uv	uv	PROPN
ejpam-4665	382	11	∈	∈	PROPN
ejpam-4665	382	12	e(g	e(g	PROPN
ejpam-4665	382	13	)	)	PUNCT
ejpam-4665	382	14	where	where	SCONJ
ejpam-4665	382	15	v	v	X
ejpam-4665	382	16	∈	∈	PROPN
ejpam-4665	382	17	v	v	NOUN
ejpam-4665	382	18	(	(	PUNCT
ejpam-4665	382	19	g	g	NOUN
ejpam-4665	382	20	)	)	PUNCT
ejpam-4665	382	21	∩ng(a	∩ng(a	NOUN
ejpam-4665	382	22	)	)	PUNCT
ejpam-4665	382	23	or	or	CCONJ
ejpam-4665	382	24	u	u	PROPN
ejpam-4665	382	25	∈	∈	PROPN
ejpam-4665	382	26	v	v	ADP
ejpam-4665	382	27	(	(	PUNCT
ejpam-4665	382	28	g	g	NOUN
ejpam-4665	382	29	)	)	PUNCT
ejpam-4665	382	30	∩ng(a	∩ng(a	NOUN
ejpam-4665	382	31	)	)	PUNCT
ejpam-4665	382	32	.	.	PUNCT
ejpam-4665	383	1	let	let	VERB
ejpam-4665	383	2	x	x	PRON
ejpam-4665	383	3	,	,	PUNCT
ejpam-4665	383	4	y	y	PROPN
ejpam-4665	383	5	∈	∈	PROPN
ejpam-4665	383	6	v	v	PROPN
ejpam-4665	383	7	(	(	PUNCT
ejpam-4665	383	8	huv	huv	PROPN
ejpam-4665	383	9	)	)	PUNCT
ejpam-4665	383	10	.	.	PUNCT
ejpam-4665	384	1	then	then	ADV
ejpam-4665	384	2	rg⋄h(x	rg⋄h(x	PROPN
ejpam-4665	384	3	/	/	SYM
ejpam-4665	384	4	c	c	NOUN
ejpam-4665	384	5	)	)	PUNCT
ejpam-4665	385	1	=	=	SYM
ejpam-4665	386	1	rg⋄h(y	rg⋄h(y	ADJ
ejpam-4665	386	2	/	/	SYM
ejpam-4665	386	3	c	c	NOUN
ejpam-4665	386	4	)	)	PUNCT
ejpam-4665	386	5	which	which	PRON
ejpam-4665	386	6	is	be	AUX
ejpam-4665	386	7	a	a	DET
ejpam-4665	386	8	contradiction	contradiction	NOUN
ejpam-4665	386	9	to	to	ADP
ejpam-4665	386	10	the	the	DET
ejpam-4665	386	11	assumption	assumption	NOUN
ejpam-4665	386	12	of	of	ADP
ejpam-4665	386	13	c.	c.	PROPN
ejpam-4665	386	14	thus	thus	ADV
ejpam-4665	386	15	,	,	PUNCT
ejpam-4665	386	16	suv	suv	PROPN
ejpam-4665	386	17	̸=	̸=	PROPN
ejpam-4665	386	18	∅.	∅.	ADP
ejpam-4665	386	19	next	next	ADV
ejpam-4665	386	20	,	,	PUNCT
ejpam-4665	386	21	we	we	PRON
ejpam-4665	386	22	claim	claim	VERB
ejpam-4665	386	23	that	that	SCONJ
ejpam-4665	386	24	suv	suv	PROPN
ejpam-4665	386	25	is	be	AUX
ejpam-4665	386	26	a	a	DET
ejpam-4665	386	27	2	2	NUM
ejpam-4665	386	28	-	-	PUNCT
ejpam-4665	386	29	locating	locate	VERB
ejpam-4665	386	30	set	set	NOUN
ejpam-4665	386	31	in	in	ADP
ejpam-4665	386	32	huv	huv	PROPN
ejpam-4665	386	33	for	for	ADP
ejpam-4665	386	34	each	each	DET
ejpam-4665	386	35	uv	uv	PROPN
ejpam-4665	386	36	∈	∈	PROPN
ejpam-4665	386	37	e(g	e(g	PROPN
ejpam-4665	386	38	)	)	PUNCT
ejpam-4665	386	39	.	.	PUNCT
ejpam-4665	387	1	let	let	VERB
ejpam-4665	387	2	a	a	DET
ejpam-4665	387	3	,	,	PUNCT
ejpam-4665	387	4	b	b	PROPN
ejpam-4665	387	5	∈	∈	PROPN
ejpam-4665	387	6	v	v	NOUN
ejpam-4665	387	7	(	(	PUNCT
ejpam-4665	387	8	huv)\suv	huv)\suv	X
ejpam-4665	387	9	where	where	SCONJ
ejpam-4665	387	10	a	a	DET
ejpam-4665	387	11	̸=	̸=	PROPN
ejpam-4665	387	12	b	b	PROPN
ejpam-4665	387	13	or	or	CCONJ
ejpam-4665	387	14	[	[	X
ejpam-4665	387	15	a	a	DET
ejpam-4665	387	16	∈	∈	PROPN
ejpam-4665	387	17	suv	suv	NOUN
ejpam-4665	387	18	and	and	CCONJ
ejpam-4665	387	19	b	b	PROPN
ejpam-4665	387	20	/∈	/∈	PUNCT
ejpam-4665	387	21	suv	suv	PROPN
ejpam-4665	387	22	]	]	PUNCT
ejpam-4665	387	23	.	.	PUNCT
ejpam-4665	388	1	since	since	SCONJ
ejpam-4665	388	2	c	c	PROPN
ejpam-4665	388	3	is	be	AUX
ejpam-4665	388	4	a	a	DET
ejpam-4665	388	5	2	2	NUM
ejpam-4665	388	6	-	-	PUNCT
ejpam-4665	388	7	resolving	resolving	NOUN
ejpam-4665	388	8	set	set	NOUN
ejpam-4665	388	9	in	in	ADP
ejpam-4665	388	10	g	g	PROPN
ejpam-4665	388	11	⋄	⋄	PROPN
ejpam-4665	388	12	h	h	NOUN
ejpam-4665	388	13	,	,	PUNCT
ejpam-4665	388	14	rg⋄h(a	rg⋄h(a	NOUN
ejpam-4665	388	15	/	/	SYM
ejpam-4665	388	16	c	c	NOUN
ejpam-4665	388	17	)	)	PUNCT
ejpam-4665	388	18	and	and	CCONJ
ejpam-4665	388	19	rg⋄h(b	rg⋄h(b	PROPN
ejpam-4665	388	20	/	/	SYM
ejpam-4665	388	21	c	c	NOUN
ejpam-4665	388	22	)	)	PUNCT
ejpam-4665	388	23	differ	differ	VERB
ejpam-4665	388	24	in	in	ADP
ejpam-4665	388	25	at	at	ADV
ejpam-4665	388	26	least	least	ADJ
ejpam-4665	388	27	2	2	NUM
ejpam-4665	388	28	positions	position	NOUN
ejpam-4665	388	29	.	.	PUNCT
ejpam-4665	389	1	by	by	ADP
ejpam-4665	389	2	remark	remark	NOUN
ejpam-4665	389	3	7	7	NUM
ejpam-4665	389	4	,	,	PUNCT
ejpam-4665	389	5	rhuv(a	rhuv(a	NOUN
ejpam-4665	389	6	/	/	SYM
ejpam-4665	389	7	suv	suv	NOUN
ejpam-4665	389	8	)	)	PUNCT
ejpam-4665	389	9	and	and	CCONJ
ejpam-4665	389	10	rhuv(b	rhuv(b	PROPN
ejpam-4665	389	11	/	/	SYM
ejpam-4665	389	12	suv	suv	PROPN
ejpam-4665	389	13	)	)	PUNCT
ejpam-4665	389	14	must	must	AUX
ejpam-4665	389	15	differ	differ	VERB
ejpam-4665	389	16	in	in	ADP
ejpam-4665	389	17	at	at	ADV
ejpam-4665	389	18	least	least	ADJ
ejpam-4665	389	19	2	2	NUM
ejpam-4665	389	20	positions	position	NOUN
ejpam-4665	389	21	.	.	PUNCT
ejpam-4665	390	1	by	by	ADP
ejpam-4665	390	2	definition	definition	NOUN
ejpam-4665	390	3	of	of	ADP
ejpam-4665	390	4	g	g	PROPN
ejpam-4665	390	5	⋄h	⋄h	PROPN
ejpam-4665	390	6	,	,	PUNCT
ejpam-4665	390	7	there	there	PRON
ejpam-4665	390	8	exists	exist	VERB
ejpam-4665	390	9	at	at	ADP
ejpam-4665	390	10	least	least	ADV
ejpam-4665	390	11	two	two	NUM
ejpam-4665	390	12	vertices	vertex	NOUN
ejpam-4665	390	13	say	say	VERB
ejpam-4665	390	14	p	p	NOUN
ejpam-4665	390	15	,	,	PUNCT
ejpam-4665	390	16	q	q	PROPN
ejpam-4665	390	17	∈	∈	PROPN
ejpam-4665	390	18	v	v	NOUN
ejpam-4665	390	19	(	(	PUNCT
ejpam-4665	390	20	huv	huv	PROPN
ejpam-4665	390	21	)	)	PUNCT
ejpam-4665	390	22	∩	∩	PROPN
ejpam-4665	390	23	suv	suv	NOUN
ejpam-4665	390	24	such	such	ADJ
ejpam-4665	390	25	that	that	SCONJ
ejpam-4665	390	26	either	either	CCONJ
ejpam-4665	390	27	p	p	X
ejpam-4665	390	28	,	,	PUNCT
ejpam-4665	390	29	q	q	PROPN
ejpam-4665	390	30	∈	∈	PROPN
ejpam-4665	390	31	nhuv(a)\nhuv(b	nhuv(a)\nhuv(b	PROPN
ejpam-4665	390	32	)	)	PUNCT
ejpam-4665	390	33	or	or	CCONJ
ejpam-4665	390	34	p	p	X
ejpam-4665	390	35	,	,	PUNCT
ejpam-4665	390	36	q	q	PROPN
ejpam-4665	390	37	∈	∈	PROPN
ejpam-4665	390	38	nhuv(b)\nhuv(a	nhuv(b)\nhuv(a	NUM
ejpam-4665	390	39	)	)	PUNCT
ejpam-4665	390	40	or	or	CCONJ
ejpam-4665	390	41	p	p	NOUN
ejpam-4665	390	42	∈	∈	PROPN
ejpam-4665	390	43	nhuv(a)\nhuv(b	nhuv(a)\nhuv(b	PROPN
ejpam-4665	390	44	)	)	PUNCT
ejpam-4665	390	45	and	and	CCONJ
ejpam-4665	390	46	q	q	PROPN
ejpam-4665	390	47	∈	∈	PROPN
ejpam-4665	390	48	nhuv(b)\nhuv(a	nhuv(b)\nhuv(a	NUM
ejpam-4665	390	49	)	)	PUNCT
ejpam-4665	390	50	.	.	PUNCT
ejpam-4665	391	1	similarly	similarly	ADV
ejpam-4665	391	2	,	,	PUNCT
ejpam-4665	391	3	if	if	SCONJ
ejpam-4665	391	4	a	a	DET
ejpam-4665	391	5	∈	∈	PROPN
ejpam-4665	391	6	suv	suv	NOUN
ejpam-4665	391	7	and	and	CCONJ
ejpam-4665	391	8	b	b	PROPN
ejpam-4665	391	9	∈	∈	PROPN
ejpam-4665	391	10	v	v	NOUN
ejpam-4665	391	11	(	(	PUNCT
ejpam-4665	391	12	huv)\suv	huv)\suv	PROPN
ejpam-4665	391	13	,	,	PUNCT
ejpam-4665	391	14	then	then	ADV
ejpam-4665	391	15	there	there	PRON
ejpam-4665	391	16	exists	exist	VERB
ejpam-4665	391	17	a	a	DET
ejpam-4665	391	18	vertex	vertex	NOUN
ejpam-4665	391	19	s	s	NOUN
ejpam-4665	391	20	∈	∈	NOUN
ejpam-4665	391	21	v	v	NOUN
ejpam-4665	391	22	(	(	PUNCT
ejpam-4665	391	23	huv)∩suv	huv)∩suv	X
ejpam-4665	391	24	such	such	ADJ
ejpam-4665	391	25	that	that	DET
ejpam-4665	391	26	s	s	PART
ejpam-4665	391	27	∈	∈	PROPN
ejpam-4665	391	28	nhuv(a)\nhuv(b	nhuv(a)\nhuv(b	PROPN
ejpam-4665	391	29	)	)	PUNCT
ejpam-4665	391	30	or	or	CCONJ
ejpam-4665	391	31	s	s	NOUN
ejpam-4665	391	32	∈	∈	NOUN
ejpam-4665	391	33	nhuv(b)\nhuv(a	nhuv(b)\nhuv(a	NUM
ejpam-4665	391	34	)	)	PUNCT
ejpam-4665	391	35	.	.	PUNCT
ejpam-4665	392	1	thus	thus	ADV
ejpam-4665	392	2	,	,	PUNCT
ejpam-4665	392	3	it	it	PRON
ejpam-4665	392	4	follows	follow	VERB
ejpam-4665	392	5	that	that	SCONJ
ejpam-4665	392	6	suv	suv	PROPN
ejpam-4665	392	7	is	be	AUX
ejpam-4665	392	8	a	a	DET
ejpam-4665	392	9	2	2	NUM
ejpam-4665	392	10	-	-	PUNCT
ejpam-4665	392	11	locating	locate	VERB
ejpam-4665	392	12	set	set	NOUN
ejpam-4665	392	13	of	of	ADP
ejpam-4665	392	14	huv	huv	PROPN
ejpam-4665	392	15	.	.	PUNCT
ejpam-4665	393	1	next	next	ADV
ejpam-4665	393	2	,	,	PUNCT
ejpam-4665	393	3	suppose	suppose	VERB
ejpam-4665	393	4	that	that	SCONJ
ejpam-4665	393	5	uv	uv	NOUN
ejpam-4665	393	6	is	be	AUX
ejpam-4665	393	7	a	a	DET
ejpam-4665	393	8	pendant	pendant	ADJ
ejpam-4665	393	9	edge	edge	NOUN
ejpam-4665	393	10	and	and	CCONJ
ejpam-4665	393	11	suppose	suppose	VERB
ejpam-4665	393	12	u	u	PRON
ejpam-4665	393	13	is	be	AUX
ejpam-4665	393	14	an	an	DET
ejpam-4665	393	15	end	end	NOUN
ejpam-4665	393	16	-	-	PUNCT
ejpam-4665	393	17	vertex	vertex	NOUN
ejpam-4665	393	18	.	.	PUNCT
ejpam-4665	394	1	then	then	ADV
ejpam-4665	394	2	⟨v⟩	⟨v⟩	X
ejpam-4665	395	1	+	+	CCONJ
ejpam-4665	395	2	huv	huv	PROPN
ejpam-4665	395	3	is	be	AUX
ejpam-4665	395	4	a	a	DET
ejpam-4665	395	5	subgraph	subgraph	NOUN
ejpam-4665	395	6	g	g	PROPN
ejpam-4665	395	7	⋄	⋄	PROPN
ejpam-4665	395	8	h.	h.	PROPN
ejpam-4665	395	9	since	since	SCONJ
ejpam-4665	395	10	suv	suv	PROPN
ejpam-4665	395	11	=	=	PROPN
ejpam-4665	395	12	c	c	PROPN
ejpam-4665	395	13	∩	∩	X
ejpam-4665	395	14	v	v	X
ejpam-4665	395	15	(	(	PUNCT
ejpam-4665	395	16	huv	huv	PROPN
ejpam-4665	395	17	)	)	PUNCT
ejpam-4665	395	18	⊆	⊆	NUM
ejpam-4665	395	19	c	c	NOUN
ejpam-4665	395	20	and	and	CCONJ
ejpam-4665	395	21	c	c	PROPN
ejpam-4665	395	22	is	be	AUX
ejpam-4665	395	23	a	a	DET
ejpam-4665	395	24	2	2	NUM
ejpam-4665	395	25	-	-	PUNCT
ejpam-4665	395	26	resolving	resolving	NOUN
ejpam-4665	395	27	set	set	NOUN
ejpam-4665	395	28	it	it	PRON
ejpam-4665	395	29	follows	follow	VERB
ejpam-4665	395	30	by	by	ADP
ejpam-4665	395	31	theorem	theorem	ADJ
ejpam-4665	395	32	4	4	NUM
ejpam-4665	395	33	,	,	PUNCT
ejpam-4665	395	34	suv	suv	PROPN
ejpam-4665	395	35	is	be	AUX
ejpam-4665	395	36	a	a	DET
ejpam-4665	395	37	(	(	PUNCT
ejpam-4665	395	38	2	2	NUM
ejpam-4665	395	39	,	,	PUNCT
ejpam-4665	395	40	1)-locating	1)-locating	NUM
ejpam-4665	395	41	set	set	NOUN
ejpam-4665	395	42	of	of	ADP
ejpam-4665	395	43	huv	huv	PROPN
ejpam-4665	395	44	whenever	whenever	SCONJ
ejpam-4665	395	45	u	u	PROPN
ejpam-4665	395	46	∈	∈	PROPN
ejpam-4665	395	47	c	c	PROPN
ejpam-4665	395	48	and	and	CCONJ
ejpam-4665	395	49	suv	suv	PROPN
ejpam-4665	395	50	is	be	AUX
ejpam-4665	395	51	a	a	DET
ejpam-4665	395	52	(	(	PUNCT
ejpam-4665	395	53	2	2	NUM
ejpam-4665	395	54	,	,	PUNCT
ejpam-4665	395	55	2)-locating	2)-locating	NUM
ejpam-4665	395	56	set	set	NOUN
ejpam-4665	395	57	of	of	ADP
ejpam-4665	395	58	huv	huv	PROPN
ejpam-4665	395	59	otherwise	otherwise	ADV
ejpam-4665	395	60	.	.	PUNCT
ejpam-4665	396	1	conversely	conversely	ADV
ejpam-4665	396	2	,	,	PUNCT
ejpam-4665	396	3	let	let	VERB
ejpam-4665	396	4	c	c	PRON
ejpam-4665	396	5	be	be	AUX
ejpam-4665	396	6	the	the	DET
ejpam-4665	396	7	set	set	NOUN
ejpam-4665	396	8	as	as	SCONJ
ejpam-4665	396	9	described	describe	VERB
ejpam-4665	396	10	and	and	CCONJ
ejpam-4665	396	11	satisfies	satisfy	VERB
ejpam-4665	396	12	the	the	DET
ejpam-4665	396	13	given	give	VERB
ejpam-4665	396	14	conditions	condition	NOUN
ejpam-4665	396	15	.	.	PUNCT
ejpam-4665	397	1	let	let	VERB
ejpam-4665	397	2	x	x	PRON
ejpam-4665	397	3	,	,	PUNCT
ejpam-4665	397	4	y	y	PROPN
ejpam-4665	397	5	∈	∈	PROPN
ejpam-4665	397	6	v	v	NOUN
ejpam-4665	397	7	(	(	PUNCT
ejpam-4665	397	8	g	g	PROPN
ejpam-4665	397	9	⋄h	⋄h	PROPN
ejpam-4665	397	10	)	)	PUNCT
ejpam-4665	397	11	with	with	ADP
ejpam-4665	397	12	x	x	SYM
ejpam-4665	397	13	̸=	̸=	PROPN
ejpam-4665	397	14	y.	y.	NOUN
ejpam-4665	397	15	then	then	ADV
ejpam-4665	397	16	it	it	PRON
ejpam-4665	397	17	can	can	AUX
ejpam-4665	397	18	be	be	AUX
ejpam-4665	397	19	easily	easily	ADV
ejpam-4665	397	20	verify	verify	VERB
ejpam-4665	397	21	that	that	SCONJ
ejpam-4665	397	22	rg⋄h(x	rg⋄h(x	NUM
ejpam-4665	397	23	/	/	SYM
ejpam-4665	397	24	c	c	NOUN
ejpam-4665	397	25	)	)	PUNCT
ejpam-4665	397	26	and	and	CCONJ
ejpam-4665	397	27	rg⋄h(y	rg⋄h(y	ADJ
ejpam-4665	397	28	/	/	SYM
ejpam-4665	397	29	c	c	NOUN
ejpam-4665	397	30	)	)	PUNCT
ejpam-4665	397	31	differ	differ	VERB
ejpam-4665	397	32	in	in	ADP
ejpam-4665	397	33	at	at	ADV
ejpam-4665	397	34	least	least	ADV
ejpam-4665	397	35	two	two	NUM
ejpam-4665	397	36	positions	position	NOUN
ejpam-4665	397	37	for	for	ADP
ejpam-4665	397	38	all	all	DET
ejpam-4665	397	39	x	x	NOUN
ejpam-4665	397	40	,	,	PUNCT
ejpam-4665	397	41	y	y	PROPN
ejpam-4665	397	42	∈	∈	PROPN
ejpam-4665	397	43	v	v	ADP
ejpam-4665	397	44	(	(	PUNCT
ejpam-4665	397	45	g	g	NOUN
ejpam-4665	397	46	)	)	PUNCT
ejpam-4665	397	47	or	or	CCONJ
ejpam-4665	397	48	x	x	PUNCT
ejpam-4665	397	49	∈	∈	NOUN
ejpam-4665	397	50	v	v	X
ejpam-4665	397	51	(	(	PUNCT
ejpam-4665	397	52	huv	huv	PROPN
ejpam-4665	397	53	)	)	PUNCT
ejpam-4665	397	54	and	and	CCONJ
ejpam-4665	397	55	y	y	PROPN
ejpam-4665	397	56	∈	∈	PROPN
ejpam-4665	397	57	v	v	ADP
ejpam-4665	397	58	(	(	PUNCT
ejpam-4665	397	59	g	g	NOUN
ejpam-4665	397	60	)	)	PUNCT
ejpam-4665	397	61	for	for	ADP
ejpam-4665	397	62	all	all	DET
ejpam-4665	397	63	edge	edge	NOUN
ejpam-4665	397	64	uv	uv	PROPN
ejpam-4665	397	65	∈	∈	PROPN
ejpam-4665	397	66	e(g	e(g	PROPN
ejpam-4665	397	67	)	)	PUNCT
ejpam-4665	397	68	or	or	CCONJ
ejpam-4665	397	69	x	x	PUNCT
ejpam-4665	397	70	∈	∈	NOUN
ejpam-4665	397	71	v	v	PROPN
ejpam-4665	397	72	(	(	PUNCT
ejpam-4665	397	73	hpq	hpq	PROPN
ejpam-4665	397	74	)	)	PUNCT
ejpam-4665	397	75	and	and	CCONJ
ejpam-4665	397	76	y	y	PROPN
ejpam-4665	397	77	∈	∈	PROPN
ejpam-4665	397	78	v	v	ADP
ejpam-4665	397	79	(	(	PUNCT
ejpam-4665	397	80	hab	hab	NOUN
ejpam-4665	397	81	)	)	PUNCT
ejpam-4665	397	82	such	such	ADJ
ejpam-4665	397	83	that	that	DET
ejpam-4665	397	84	pq	pq	NOUN
ejpam-4665	397	85	̸=	̸=	PROPN
ejpam-4665	397	86	ab	ab	NOUN
ejpam-4665	397	87	for	for	ADP
ejpam-4665	397	88	some	some	DET
ejpam-4665	397	89	pq	pq	NOUN
ejpam-4665	397	90	,	,	PUNCT
ejpam-4665	397	91	ab	ab	PROPN
ejpam-4665	397	92	∈	∈	PROPN
ejpam-4665	397	93	e(g	e(g	PROPN
ejpam-4665	397	94	)	)	PUNCT
ejpam-4665	397	95	.	.	PUNCT
ejpam-4665	398	1	a.m.	a.m.	PROPN
ejpam-4665	398	2	mahistrado	mahistrado	PROPN
ejpam-4665	398	3	,	,	PUNCT
ejpam-4665	398	4	h.	h.	PROPN
ejpam-4665	398	5	rara	rara	PROPN
ejpam-4665	398	6	/	/	SYM
ejpam-4665	398	7	eur	eur	PROPN
ejpam-4665	398	8	.	.	PUNCT
ejpam-4665	399	1	j.	j.	PROPN
ejpam-4665	399	2	pure	pure	PROPN
ejpam-4665	399	3	appl	appl	PROPN
ejpam-4665	399	4	.	.	PROPN
ejpam-4665	399	5	math	math	PROPN
ejpam-4665	399	6	,	,	PUNCT
ejpam-4665	399	7	16	16	NUM
ejpam-4665	399	8	(	(	PUNCT
ejpam-4665	399	9	1	1	NUM
ejpam-4665	399	10	)	)	PUNCT
ejpam-4665	399	11	(	(	PUNCT
ejpam-4665	399	12	2023	2023	NUM
ejpam-4665	399	13	)	)	PUNCT
ejpam-4665	399	14	,	,	PUNCT
ejpam-4665	399	15	286	286	NUM
ejpam-4665	399	16	-	-	SYM
ejpam-4665	399	17	303	303	NUM
ejpam-4665	399	18	299	299	NUM
ejpam-4665	399	19	hence	hence	ADV
ejpam-4665	399	20	,	,	PUNCT
ejpam-4665	399	21	consider	consider	VERB
ejpam-4665	399	22	only	only	ADV
ejpam-4665	399	23	the	the	DET
ejpam-4665	399	24	following	follow	VERB
ejpam-4665	399	25	cases	case	NOUN
ejpam-4665	399	26	:	:	PUNCT
ejpam-4665	399	27	case	case	NOUN
ejpam-4665	399	28	1	1	NUM
ejpam-4665	399	29	:	:	PUNCT
ejpam-4665	399	30	x	x	X
ejpam-4665	399	31	,	,	PUNCT
ejpam-4665	399	32	y	y	PROPN
ejpam-4665	399	33	∈	∈	PROPN
ejpam-4665	399	34	v	v	PROPN
ejpam-4665	399	35	(	(	PUNCT
ejpam-4665	399	36	huv)\suv	huv)\suv	PROPN
ejpam-4665	399	37	or	or	CCONJ
ejpam-4665	399	38	x	x	PART
ejpam-4665	399	39	∈	∈	PROPN
ejpam-4665	399	40	v	v	NOUN
ejpam-4665	399	41	(	(	PUNCT
ejpam-4665	399	42	huv)\suv	huv)\suv	PROPN
ejpam-4665	399	43	and	and	CCONJ
ejpam-4665	399	44	y	y	PROPN
ejpam-4665	399	45	∈	∈	PROPN
ejpam-4665	399	46	suv	suv	PROPN
ejpam-4665	399	47	for	for	ADP
ejpam-4665	399	48	some	some	DET
ejpam-4665	399	49	edge	edge	NOUN
ejpam-4665	399	50	uv	uv	PROPN
ejpam-4665	399	51	∈	∈	PROPN
ejpam-4665	399	52	e(g	e(g	PROPN
ejpam-4665	399	53	)	)	PUNCT
ejpam-4665	399	54	.	.	PUNCT
ejpam-4665	400	1	now	now	ADV
ejpam-4665	400	2	,	,	PUNCT
ejpam-4665	400	3	since	since	SCONJ
ejpam-4665	400	4	suv	suv	PROPN
ejpam-4665	400	5	is	be	AUX
ejpam-4665	400	6	a	a	DET
ejpam-4665	400	7	2	2	NUM
ejpam-4665	400	8	-	-	PUNCT
ejpam-4665	400	9	locating	locate	VERB
ejpam-4665	400	10	set	set	NOUN
ejpam-4665	400	11	,	,	PUNCT
ejpam-4665	400	12	rhuv(x	rhuv(x	PROPN
ejpam-4665	400	13	/	/	SYM
ejpam-4665	400	14	suv	suv	NOUN
ejpam-4665	400	15	)	)	PUNCT
ejpam-4665	400	16	and	and	CCONJ
ejpam-4665	400	17	rhuv(y	rhuv(y	PROPN
ejpam-4665	400	18	/	/	SYM
ejpam-4665	400	19	suv	suv	NOUN
ejpam-4665	400	20	)	)	PUNCT
ejpam-4665	400	21	differ	differ	VERB
ejpam-4665	400	22	in	in	ADP
ejpam-4665	400	23	at	at	ADV
ejpam-4665	400	24	least	least	ADV
ejpam-4665	400	25	two	two	NUM
ejpam-4665	400	26	positions	position	NOUN
ejpam-4665	400	27	.	.	PUNCT
ejpam-4665	401	1	then	then	ADV
ejpam-4665	401	2	by	by	ADP
ejpam-4665	401	3	definition	definition	NOUN
ejpam-4665	401	4	of	of	ADP
ejpam-4665	401	5	g	g	PROPN
ejpam-4665	401	6	⋄h	⋄h	PROPN
ejpam-4665	401	7	,	,	PUNCT
ejpam-4665	401	8	rg⋄h(x	rg⋄h(x	PROPN
ejpam-4665	401	9	/	/	SYM
ejpam-4665	401	10	c	c	NOUN
ejpam-4665	401	11	)	)	PUNCT
ejpam-4665	401	12	and	and	CCONJ
ejpam-4665	401	13	rg⋄h(y	rg⋄h(y	ADJ
ejpam-4665	401	14	/	/	SYM
ejpam-4665	401	15	c	c	NOUN
ejpam-4665	401	16	)	)	PUNCT
ejpam-4665	401	17	differ	differ	VERB
ejpam-4665	401	18	in	in	ADP
ejpam-4665	401	19	at	at	ADV
ejpam-4665	401	20	least	least	ADV
ejpam-4665	401	21	two	two	NUM
ejpam-4665	401	22	positions	position	NOUN
ejpam-4665	401	23	.	.	PUNCT
ejpam-4665	402	1	case	case	NOUN
ejpam-4665	402	2	2	2	NUM
ejpam-4665	402	3	:	:	PUNCT
ejpam-4665	402	4	x	x	SYM
ejpam-4665	402	5	∈	∈	NOUN
ejpam-4665	402	6	v	v	NOUN
ejpam-4665	402	7	(	(	PUNCT
ejpam-4665	402	8	huv)\suv	huv)\suv	PROPN
ejpam-4665	402	9	or	or	CCONJ
ejpam-4665	402	10	x	x	PROPN
ejpam-4665	402	11	∈	∈	PROPN
ejpam-4665	402	12	suv	suv	PROPN
ejpam-4665	402	13	and	and	CCONJ
ejpam-4665	402	14	y	y	PROPN
ejpam-4665	402	15	=	=	PROPN
ejpam-4665	402	16	u	u	PROPN
ejpam-4665	402	17	for	for	ADP
ejpam-4665	402	18	some	some	DET
ejpam-4665	402	19	pendant	pendant	ADJ
ejpam-4665	402	20	edge	edge	NOUN
ejpam-4665	402	21	uv	uv	PROPN
ejpam-4665	402	22	∈	∈	PROPN
ejpam-4665	402	23	e(g	e(g	PROPN
ejpam-4665	402	24	)	)	PUNCT
ejpam-4665	402	25	and	and	CCONJ
ejpam-4665	402	26	u	u	NOUN
ejpam-4665	402	27	is	be	AUX
ejpam-4665	402	28	an	an	DET
ejpam-4665	402	29	end	end	NOUN
ejpam-4665	402	30	-	-	PUNCT
ejpam-4665	402	31	vertex	vertex	NOUN
ejpam-4665	402	32	since	since	SCONJ
ejpam-4665	402	33	suv	suv	PROPN
ejpam-4665	402	34	is	be	AUX
ejpam-4665	402	35	a	a	DET
ejpam-4665	402	36	(	(	PUNCT
ejpam-4665	402	37	2	2	NUM
ejpam-4665	402	38	,	,	PUNCT
ejpam-4665	402	39	2)-locating	2)-locating	NUM
ejpam-4665	402	40	set	set	NOUN
ejpam-4665	402	41	,	,	PUNCT
ejpam-4665	402	42	there	there	PRON
ejpam-4665	402	43	exists	exist	VERB
ejpam-4665	402	44	a	a	DET
ejpam-4665	402	45	,	,	PUNCT
ejpam-4665	402	46	b	b	X
ejpam-4665	402	47	∈	∈	PROPN
ejpam-4665	402	48	suv\nhuv(x	suv\nhuv(x	VERB
ejpam-4665	402	49	)	)	PUNCT
ejpam-4665	402	50	but	but	CCONJ
ejpam-4665	402	51	a	a	PRON
ejpam-4665	402	52	,	,	PUNCT
ejpam-4665	402	53	b	b	PROPN
ejpam-4665	402	54	∈	∈	PROPN
ejpam-4665	402	55	ng⋄h(y	ng⋄h(y	NOUN
ejpam-4665	402	56	)	)	PUNCT
ejpam-4665	402	57	.	.	PUNCT
ejpam-4665	403	1	thus	thus	ADV
ejpam-4665	403	2	,	,	PUNCT
ejpam-4665	403	3	it	it	PRON
ejpam-4665	403	4	follows	follow	VERB
ejpam-4665	403	5	that	that	SCONJ
ejpam-4665	403	6	rg⋄h(x	rg⋄h(x	PROPN
ejpam-4665	403	7	/	/	SYM
ejpam-4665	403	8	c	c	NOUN
ejpam-4665	403	9	)	)	PUNCT
ejpam-4665	403	10	and	and	CCONJ
ejpam-4665	403	11	rg⋄h(y	rg⋄h(y	ADJ
ejpam-4665	403	12	/	/	SYM
ejpam-4665	403	13	c	c	NOUN
ejpam-4665	403	14	)	)	PUNCT
ejpam-4665	403	15	differ	differ	VERB
ejpam-4665	403	16	in	in	ADP
ejpam-4665	403	17	ath	ath	NOUN
ejpam-4665	403	18	and	and	CCONJ
ejpam-4665	403	19	bth	bth	PROPN
ejpam-4665	403	20	positions	position	NOUN
ejpam-4665	403	21	.	.	PUNCT
ejpam-4665	404	1	therefore	therefore	ADV
ejpam-4665	404	2	,	,	PUNCT
ejpam-4665	404	3	c	c	PROPN
ejpam-4665	404	4	is	be	AUX
ejpam-4665	404	5	a	a	DET
ejpam-4665	404	6	2	2	NUM
ejpam-4665	404	7	-	-	PUNCT
ejpam-4665	404	8	resolving	resolving	NOUN
ejpam-4665	404	9	set	set	NOUN
ejpam-4665	404	10	in	in	ADP
ejpam-4665	404	11	g	g	PROPN
ejpam-4665	404	12	⋄h	⋄h	PROPN
ejpam-4665	404	13	.	.	PUNCT
ejpam-4665	405	1	next	next	ADV
ejpam-4665	405	2	,	,	PUNCT
ejpam-4665	405	3	we	we	PRON
ejpam-4665	405	4	claim	claim	VERB
ejpam-4665	405	5	that	that	SCONJ
ejpam-4665	405	6	c	c	PROPN
ejpam-4665	405	7	is	be	AUX
ejpam-4665	405	8	a	a	DET
ejpam-4665	405	9	hop	hop	NOUN
ejpam-4665	405	10	dominating	dominating	NOUN
ejpam-4665	405	11	set	set	NOUN
ejpam-4665	405	12	.	.	PUNCT
ejpam-4665	406	1	let	let	VERB
ejpam-4665	406	2	x	x	SYM
ejpam-4665	406	3	∈	∈	PROPN
ejpam-4665	406	4	v	v	NOUN
ejpam-4665	406	5	(	(	PUNCT
ejpam-4665	406	6	g)\a	g)\a	NOUN
ejpam-4665	406	7	.	.	PUNCT
ejpam-4665	407	1	since	since	SCONJ
ejpam-4665	407	2	g	g	PROPN
ejpam-4665	407	3	is	be	AUX
ejpam-4665	407	4	a	a	DET
ejpam-4665	407	5	connected	connected	ADJ
ejpam-4665	407	6	graph	graph	NOUN
ejpam-4665	407	7	and	and	CCONJ
ejpam-4665	407	8	g	g	PROPN
ejpam-4665	407	9	̸=	̸=	PROPN
ejpam-4665	407	10	p2	p2	NOUN
ejpam-4665	407	11	,	,	PUNCT
ejpam-4665	407	12	there	there	PRON
ejpam-4665	407	13	exist	exist	VERB
ejpam-4665	407	14	y	y	PROPN
ejpam-4665	407	15	,	,	PUNCT
ejpam-4665	407	16	q	q	PROPN
ejpam-4665	407	17	∈	∈	PROPN
ejpam-4665	407	18	v	v	ADP
ejpam-4665	407	19	(	(	PUNCT
ejpam-4665	407	20	g	g	NOUN
ejpam-4665	407	21	)	)	PUNCT
ejpam-4665	407	22	such	such	ADJ
ejpam-4665	407	23	that	that	SCONJ
ejpam-4665	407	24	y	y	PROPN
ejpam-4665	407	25	∈	∈	PROPN
ejpam-4665	407	26	ng(x	ng(x	NUM
ejpam-4665	407	27	)	)	PUNCT
ejpam-4665	407	28	∩	∩	NOUN
ejpam-4665	407	29	ng(q	ng(q	NOUN
ejpam-4665	407	30	)	)	PUNCT
ejpam-4665	407	31	.	.	PUNCT
ejpam-4665	408	1	now	now	ADV
ejpam-4665	408	2	,	,	PUNCT
ejpam-4665	408	3	since	since	SCONJ
ejpam-4665	408	4	syq	syq	NOUN
ejpam-4665	408	5	̸=	̸=	PROPN
ejpam-4665	408	6	∅	∅	NOUN
ejpam-4665	408	7	,	,	PUNCT
ejpam-4665	408	8	a	a	DET
ejpam-4665	408	9	vertex	vertex	NOUN
ejpam-4665	408	10	z	z	NOUN
ejpam-4665	408	11	∈	∈	PROPN
ejpam-4665	408	12	syq∩ng⋄h(x	syq∩ng⋄h(x	PROPN
ejpam-4665	408	13	,	,	PUNCT
ejpam-4665	408	14	2	2	NUM
ejpam-4665	408	15	)	)	PUNCT
ejpam-4665	408	16	exists	exist	VERB
ejpam-4665	408	17	.	.	PUNCT
ejpam-4665	409	1	on	on	ADP
ejpam-4665	409	2	the	the	DET
ejpam-4665	409	3	other	other	ADJ
ejpam-4665	409	4	hand	hand	NOUN
ejpam-4665	409	5	,	,	PUNCT
ejpam-4665	409	6	if	if	SCONJ
ejpam-4665	409	7	x	x	PROPN
ejpam-4665	409	8	∈	∈	PROPN
ejpam-4665	409	9	v	v	NOUN
ejpam-4665	409	10	(	(	PUNCT
ejpam-4665	409	11	huv)\suv	huv)\suv	PROPN
ejpam-4665	409	12	,	,	PUNCT
ejpam-4665	409	13	then	then	ADV
ejpam-4665	409	14	there	there	PRON
ejpam-4665	409	15	exists	exist	VERB
ejpam-4665	409	16	y	y	PROPN
ejpam-4665	409	17	∈	∈	PROPN
ejpam-4665	409	18	ng(u)∪ng(v	ng(u)∪ng(v	PROPN
ejpam-4665	409	19	)	)	PUNCT
ejpam-4665	409	20	such	such	ADJ
ejpam-4665	409	21	that	that	SCONJ
ejpam-4665	409	22	ng⋄h(x	ng⋄h(x	PROPN
ejpam-4665	409	23	,	,	PUNCT
ejpam-4665	409	24	2)∩svy	2)∩svy	NUM
ejpam-4665	409	25	̸=	̸=	PROPN
ejpam-4665	409	26	∅	∅	NOUN
ejpam-4665	409	27	or	or	CCONJ
ejpam-4665	409	28	ng⋄h(x	ng⋄h(x	PROPN
ejpam-4665	409	29	,	,	PUNCT
ejpam-4665	409	30	2)∩suy	2)∩suy	PROPN
ejpam-4665	409	31	̸=	̸=	PROPN
ejpam-4665	409	32	∅.	∅.	ADV
ejpam-4665	409	33	thus	thus	ADV
ejpam-4665	409	34	,	,	PUNCT
ejpam-4665	409	35	c	c	PROPN
ejpam-4665	409	36	is	be	AUX
ejpam-4665	409	37	a	a	DET
ejpam-4665	409	38	hop	hop	NOUN
ejpam-4665	409	39	dominating	dominating	NOUN
ejpam-4665	409	40	set	set	VERB
ejpam-4665	409	41	in	in	ADP
ejpam-4665	409	42	g	g	PROPN
ejpam-4665	409	43	⋄h	⋄h	PROPN
ejpam-4665	409	44	.	.	PUNCT
ejpam-4665	410	1	accordingly	accordingly	ADV
ejpam-4665	410	2	,	,	PUNCT
ejpam-4665	410	3	c	c	PROPN
ejpam-4665	410	4	is	be	AUX
ejpam-4665	410	5	a	a	DET
ejpam-4665	410	6	2	2	NUM
ejpam-4665	410	7	-	-	PUNCT
ejpam-4665	410	8	resolving	resolve	VERB
ejpam-4665	410	9	hop	hop	NOUN
ejpam-4665	410	10	dominating	dominating	NOUN
ejpam-4665	410	11	set	set	VERB
ejpam-4665	410	12	in	in	ADP
ejpam-4665	410	13	g	g	PROPN
ejpam-4665	410	14	⋄h	⋄h	PROPN
ejpam-4665	410	15	.	.	PUNCT
ejpam-4665	411	1	as	as	ADP
ejpam-4665	411	2	a	a	DET
ejpam-4665	411	3	consequence	consequence	NOUN
ejpam-4665	411	4	of	of	ADP
ejpam-4665	411	5	theorem	theorem	NOUN
ejpam-4665	411	6	12	12	NUM
ejpam-4665	411	7	the	the	DET
ejpam-4665	411	8	next	next	ADJ
ejpam-4665	411	9	result	result	NOUN
ejpam-4665	411	10	follows	follow	VERB
ejpam-4665	411	11	.	.	PUNCT
ejpam-4665	412	1	corollary	corollary	ADJ
ejpam-4665	412	2	5	5	NUM
ejpam-4665	412	3	.	.	PUNCT
ejpam-4665	413	1	let	let	VERB
ejpam-4665	413	2	g	g	PROPN
ejpam-4665	413	3	̸=	̸=	PROPN
ejpam-4665	413	4	p2	p2	PROPN
ejpam-4665	413	5	be	be	VERB
ejpam-4665	413	6	any	any	DET
ejpam-4665	413	7	nontrivial	nontrivial	ADJ
ejpam-4665	413	8	connected	connect	VERB
ejpam-4665	413	9	graph	graph	NOUN
ejpam-4665	413	10	of	of	ADP
ejpam-4665	413	11	size	size	NOUN
ejpam-4665	413	12	m	m	PROPN
ejpam-4665	413	13	and	and	CCONJ
ejpam-4665	413	14	h	h	DET
ejpam-4665	413	15	a	a	DET
ejpam-4665	413	16	nontrivial	nontrivial	ADJ
ejpam-4665	413	17	connected	connect	VERB
ejpam-4665	413	18	graph	graph	NOUN
ejpam-4665	413	19	.	.	PUNCT
ejpam-4665	414	1	then	then	ADV
ejpam-4665	414	2	the	the	DET
ejpam-4665	414	3	following	follow	VERB
ejpam-4665	414	4	statements	statement	NOUN
ejpam-4665	414	5	hold	hold	VERB
ejpam-4665	414	6	.	.	PUNCT
ejpam-4665	415	1	(	(	PUNCT
ejpam-4665	415	2	i	i	NOUN
ejpam-4665	415	3	)	)	PUNCT
ejpam-4665	415	4	if	if	SCONJ
ejpam-4665	415	5	g	g	PROPN
ejpam-4665	415	6	is	be	AUX
ejpam-4665	415	7	a	a	DET
ejpam-4665	415	8	graph	graph	NOUN
ejpam-4665	415	9	with	with	ADP
ejpam-4665	415	10	no	no	DET
ejpam-4665	415	11	pendant	pendant	ADJ
ejpam-4665	415	12	edges	edge	NOUN
ejpam-4665	415	13	,	,	PUNCT
ejpam-4665	415	14	then	then	ADV
ejpam-4665	415	15	γ2rh(g	γ2rh(g	VERB
ejpam-4665	415	16	⋄h	⋄h	NOUN
ejpam-4665	415	17	)	)	PUNCT
ejpam-4665	415	18	=	=	PUNCT
ejpam-4665	415	19	m	m	PUNCT
ejpam-4665	415	20	·	·	PUNCT
ejpam-4665	415	21	ln2(h	ln2(h	PROPN
ejpam-4665	415	22	)	)	PUNCT
ejpam-4665	415	23	.	.	PUNCT
ejpam-4665	416	1	(	(	PUNCT
ejpam-4665	416	2	ii	ii	NOUN
ejpam-4665	416	3	)	)	PUNCT
ejpam-4665	416	4	if	if	SCONJ
ejpam-4665	416	5	g	g	PROPN
ejpam-4665	416	6	is	be	AUX
ejpam-4665	416	7	a	a	DET
ejpam-4665	416	8	graph	graph	NOUN
ejpam-4665	416	9	with	with	ADP
ejpam-4665	416	10	k	k	PROPN
ejpam-4665	416	11	≥	≥	NUM
ejpam-4665	416	12	1	1	NUM
ejpam-4665	416	13	pendant	pendant	ADJ
ejpam-4665	416	14	edges	edge	NOUN
ejpam-4665	416	15	,	,	PUNCT
ejpam-4665	416	16	then	then	ADV
ejpam-4665	416	17	γ2rh(g⋄h	γ2rh(g⋄h	PUNCT
ejpam-4665	416	18	)	)	PUNCT
ejpam-4665	417	1	=	=	SYM
ejpam-4665	417	2	min	min	NOUN
ejpam-4665	417	3	{	{	PUNCT
ejpam-4665	417	4	(	(	PUNCT
ejpam-4665	417	5	m−k	m−k	NOUN
ejpam-4665	417	6	)	)	PUNCT
ejpam-4665	417	7	ln2(h)+k	ln2(h)+k	PROPN
ejpam-4665	417	8	·	·	PUNCT
ejpam-4665	417	9	ln(2,1)(h)+k	ln(2,1)(h)+k	VERB
ejpam-4665	417	10	,	,	PUNCT
ejpam-4665	417	11	(	(	PUNCT
ejpam-4665	417	12	m−k	m−k	NOUN
ejpam-4665	417	13	)	)	PUNCT
ejpam-4665	417	14	ln2(h)+k	ln2(h)+k	PROPN
ejpam-4665	417	15	·	·	PUNCT
ejpam-4665	417	16	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4665	417	17	)	)	PUNCT
ejpam-4665	417	18	}	}	PUNCT
ejpam-4665	417	19	and	and	CCONJ
ejpam-4665	417	20	γ2rh(g	γ2rh(g	VERB
ejpam-4665	417	21	⋄h	⋄h	NOUN
ejpam-4665	417	22	)	)	PUNCT
ejpam-4665	417	23	=	=	PUNCT
ejpam-4665	417	24	(	(	PUNCT
ejpam-4665	417	25	m−	m−	PROPN
ejpam-4665	417	26	k	k	PROPN
ejpam-4665	417	27	)	)	PUNCT
ejpam-4665	417	28	ln2(h	ln2(h	PROPN
ejpam-4665	417	29	)	)	PUNCT
ejpam-4665	418	1	+	+	CCONJ
ejpam-4665	418	2	k	k	PROPN
ejpam-4665	418	3	·	·	PUNCT
ejpam-4665	418	4	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4665	418	5	)	)	PUNCT
ejpam-4665	418	6	whenever	whenever	SCONJ
ejpam-4665	418	7	ln(2,2)(h	ln(2,2)(h	ADJ
ejpam-4665	418	8	)	)	PUNCT
ejpam-4665	418	9	=	=	PUNCT
ejpam-4665	418	10	ln(2,1)(h	ln(2,1)(h	PRON
ejpam-4665	418	11	)	)	PUNCT
ejpam-4665	418	12	.	.	PUNCT
ejpam-4665	419	1	theorem	theorem	NOUN
ejpam-4665	419	2	13	13	NUM
ejpam-4665	419	3	.	.	PUNCT
ejpam-4665	420	1	let	let	VERB
ejpam-4665	420	2	g	g	PROPN
ejpam-4665	420	3	̸=	̸=	PROPN
ejpam-4665	420	4	p2	p2	PROPN
ejpam-4665	420	5	and	and	CCONJ
ejpam-4665	420	6	h	h	NOUN
ejpam-4665	420	7	be	be	VERB
ejpam-4665	420	8	any	any	DET
ejpam-4665	420	9	nontrivial	nontrivial	ADJ
ejpam-4665	420	10	connected	connect	VERB
ejpam-4665	420	11	graphs	graph	NOUN
ejpam-4665	420	12	.	.	PUNCT
ejpam-4665	421	1	a	a	DET
ejpam-4665	421	2	set	set	NOUN
ejpam-4665	421	3	s	s	NOUN
ejpam-4665	421	4	⊆	⊆	NUM
ejpam-4665	421	5	v	v	NOUN
ejpam-4665	421	6	(	(	PUNCT
ejpam-4665	421	7	g⋄h	g⋄h	X
ejpam-4665	421	8	)	)	PUNCT
ejpam-4665	421	9	is	be	AUX
ejpam-4665	421	10	a	a	DET
ejpam-4665	421	11	restrained	restrained	ADJ
ejpam-4665	421	12	2	2	NUM
ejpam-4665	421	13	-	-	PUNCT
ejpam-4665	421	14	resolving	resolve	VERB
ejpam-4665	421	15	hop	hop	NOUN
ejpam-4665	421	16	dominating	dominating	NOUN
ejpam-4665	421	17	set	set	NOUN
ejpam-4665	421	18	of	of	ADP
ejpam-4665	421	19	g	g	PROPN
ejpam-4665	421	20	⋄h	⋄h	X
ejpam-4665	421	21	if	if	SCONJ
ejpam-4665	422	1	and	and	CCONJ
ejpam-4665	422	2	only	only	ADV
ejpam-4665	422	3	if	if	SCONJ
ejpam-4665	422	4	c	c	X
ejpam-4665	422	5	=	=	PUNCT
ejpam-4665	422	6	a	a	PRON
ejpam-4665	422	7	∪	∪	ADJ
ejpam-4665	422	8			PROPN
ejpam-4665	422	9	⋃	⋃	ADJ
ejpam-4665	422	10	uv∈e(g	uv∈e(g	NOUN
ejpam-4665	422	11	)	)	PUNCT
ejpam-4665	422	12	suv	suv	PROPN
ejpam-4665	423	1			PROPN
ejpam-4665	423	2	is	be	AUX
ejpam-4665	423	3	a	a	DET
ejpam-4665	423	4	2	2	NUM
ejpam-4665	423	5	-	-	PUNCT
ejpam-4665	423	6	resolving	resolve	VERB
ejpam-4665	423	7	hop	hop	NOUN
ejpam-4665	423	8	dominating	dominating	NOUN
ejpam-4665	423	9	set	set	NOUN
ejpam-4665	423	10	and	and	CCONJ
ejpam-4665	423	11	(	(	PUNCT
ejpam-4665	423	12	i	i	NOUN
ejpam-4665	423	13	)	)	PUNCT
ejpam-4665	423	14	⟨v	⟨v	CCONJ
ejpam-4665	424	1	(	(	PUNCT
ejpam-4665	424	2	g)\a⟩	g)\a⟩	PROPN
ejpam-4665	424	3	has	have	VERB
ejpam-4665	424	4	no	no	DET
ejpam-4665	424	5	isolated	isolated	ADJ
ejpam-4665	424	6	vertex	vertex	NOUN
ejpam-4665	424	7	whenever	whenever	SCONJ
ejpam-4665	424	8	suv	suv	PROPN
ejpam-4665	424	9	=	=	SYM
ejpam-4665	424	10	v	v	PROPN
ejpam-4665	424	11	(	(	PUNCT
ejpam-4665	424	12	huv	huv	PROPN
ejpam-4665	424	13	)	)	PUNCT
ejpam-4665	424	14	;	;	PUNCT
ejpam-4665	424	15	and	and	CCONJ
ejpam-4665	424	16	(	(	PUNCT
ejpam-4665	424	17	ii	ii	NOUN
ejpam-4665	424	18	)	)	PUNCT
ejpam-4665	424	19	suv	suv	PROPN
ejpam-4665	424	20	is	be	AUX
ejpam-4665	424	21	a	a	DET
ejpam-4665	424	22	restrained	restrained	ADJ
ejpam-4665	424	23	2	2	NUM
ejpam-4665	424	24	-	-	PUNCT
ejpam-4665	424	25	locating	locate	VERB
ejpam-4665	424	26	set	set	NOUN
ejpam-4665	424	27	of	of	ADP
ejpam-4665	424	28	huv	huv	PROPN
ejpam-4665	424	29	for	for	ADP
ejpam-4665	424	30	all	all	DET
ejpam-4665	424	31	uv	uv	PROPN
ejpam-4665	424	32	∈	∈	PROPN
ejpam-4665	424	33	e(g	e(g	PROPN
ejpam-4665	424	34	)	)	PUNCT
ejpam-4665	424	35	if	if	SCONJ
ejpam-4665	424	36	u	u	PROPN
ejpam-4665	424	37	∈	∈	VERB
ejpam-4665	424	38	a	a	DET
ejpam-4665	424	39	and	and	CCONJ
ejpam-4665	424	40	v	v	ADP
ejpam-4665	424	41	∈	∈	NOUN
ejpam-4665	424	42	a.	a.	NOUN
ejpam-4665	424	43	proof	proof	NOUN
ejpam-4665	424	44	.	.	PUNCT
ejpam-4665	425	1	suppose	suppose	VERB
ejpam-4665	425	2	c	c	NOUN
ejpam-4665	425	3	is	be	AUX
ejpam-4665	425	4	a	a	DET
ejpam-4665	425	5	restrained	restrained	ADJ
ejpam-4665	425	6	2	2	NUM
ejpam-4665	425	7	-	-	PUNCT
ejpam-4665	425	8	resolving	resolve	VERB
ejpam-4665	425	9	hop	hop	NOUN
ejpam-4665	425	10	dominating	dominating	NOUN
ejpam-4665	425	11	set	set	VERB
ejpam-4665	425	12	in	in	ADP
ejpam-4665	425	13	g	g	PROPN
ejpam-4665	425	14	⋄	⋄	PROPN
ejpam-4665	425	15	h.	h.	NOUN
ejpam-4665	426	1	then	then	ADV
ejpam-4665	426	2	c	c	PROPN
ejpam-4665	426	3	is	be	AUX
ejpam-4665	426	4	a	a	DET
ejpam-4665	426	5	2	2	NUM
ejpam-4665	426	6	-	-	PUNCT
ejpam-4665	426	7	resolving	resolve	VERB
ejpam-4665	426	8	hop	hop	NOUN
ejpam-4665	426	9	dominating	dominating	NOUN
ejpam-4665	426	10	set	set	VERB
ejpam-4665	426	11	in	in	ADP
ejpam-4665	426	12	g	g	PROPN
ejpam-4665	426	13	⋄h	⋄h	PROPN
ejpam-4665	426	14	.	.	PUNCT
ejpam-4665	427	1	by	by	ADP
ejpam-4665	427	2	theorem	theorem	NOUN
ejpam-4665	427	3	12	12	NUM
ejpam-4665	427	4	,	,	PUNCT
ejpam-4665	427	5	suv	suv	PROPN
ejpam-4665	427	6	is	be	AUX
ejpam-4665	427	7	a	a	DET
ejpam-4665	427	8	2	2	NUM
ejpam-4665	427	9	-	-	PUNCT
ejpam-4665	427	10	locating	locate	VERB
ejpam-4665	427	11	set	set	NOUN
ejpam-4665	427	12	in	in	ADP
ejpam-4665	427	13	huv	huv	PROPN
ejpam-4665	427	14	for	for	ADP
ejpam-4665	427	15	all	all	DET
ejpam-4665	427	16	uv	uv	PROPN
ejpam-4665	427	17	∈	∈	PROPN
ejpam-4665	427	18	e(g	e(g	PROPN
ejpam-4665	427	19	)	)	PUNCT
ejpam-4665	427	20	.	.	PUNCT
ejpam-4665	428	1	let	let	VERB
ejpam-4665	428	2	a	a	DET
ejpam-4665	428	3	=	=	X
ejpam-4665	428	4	v	v	X
ejpam-4665	428	5	(	(	PUNCT
ejpam-4665	428	6	g	g	NOUN
ejpam-4665	428	7	)	)	PUNCT
ejpam-4665	428	8	∩	∩	NOUN
ejpam-4665	428	9	c	c	PROPN
ejpam-4665	428	10	and	and	CCONJ
ejpam-4665	428	11	suv	suv	PROPN
ejpam-4665	428	12	=	=	PROPN
ejpam-4665	428	13	c	c	PROPN
ejpam-4665	428	14	∩	∩	X
ejpam-4665	428	15	v	v	X
ejpam-4665	428	16	(	(	PUNCT
ejpam-4665	428	17	huv	huv	PROPN
ejpam-4665	428	18	)	)	PUNCT
ejpam-4665	428	19	for	for	ADP
ejpam-4665	428	20	all	all	DET
ejpam-4665	428	21	uv	uv	PROPN
ejpam-4665	428	22	∈	∈	PROPN
ejpam-4665	428	23	e(g	e(g	PROPN
ejpam-4665	428	24	)	)	PUNCT
ejpam-4665	428	25	.	.	PUNCT
ejpam-4665	429	1	then	then	ADV
ejpam-4665	429	2	c	c	X
ejpam-4665	429	3	=	=	PUNCT
ejpam-4665	429	4	a	a	DET
ejpam-4665	429	5	∪	∪	X
ejpam-4665	429	6	(	(	PUNCT
ejpam-4665	429	7	⋃	⋃	NOUN
ejpam-4665	429	8	uv∈e(g	uv∈e(g	NOUN
ejpam-4665	429	9	)	)	PUNCT
ejpam-4665	429	10	suv	suv	PROPN
ejpam-4665	429	11	)	)	PUNCT
ejpam-4665	429	12	where	where	SCONJ
ejpam-4665	429	13	a	a	DET
ejpam-4665	429	14	⊆	⊆	NUM
ejpam-4665	429	15	v	v	NOUN
ejpam-4665	429	16	(	(	PUNCT
ejpam-4665	429	17	g	g	NOUN
ejpam-4665	429	18	)	)	PUNCT
ejpam-4665	429	19	and	and	CCONJ
ejpam-4665	429	20	suv	suv	PROPN
ejpam-4665	429	21	⊆	⊆	NUM
ejpam-4665	429	22	v	v	NOUN
ejpam-4665	429	23	(	(	PUNCT
ejpam-4665	429	24	huv	huv	PROPN
ejpam-4665	429	25	)	)	PUNCT
ejpam-4665	429	26	for	for	ADP
ejpam-4665	429	27	each	each	DET
ejpam-4665	429	28	uv	uv	PROPN
ejpam-4665	429	29	∈	∈	PROPN
ejpam-4665	429	30	e(g	e(g	PROPN
ejpam-4665	429	31	)	)	PUNCT
ejpam-4665	429	32	.	.	PUNCT
ejpam-4665	430	1	a.m.	a.m.	PROPN
ejpam-4665	430	2	mahistrado	mahistrado	PROPN
ejpam-4665	430	3	,	,	PUNCT
ejpam-4665	430	4	h.	h.	PROPN
ejpam-4665	430	5	rara	rara	PROPN
ejpam-4665	430	6	/	/	SYM
ejpam-4665	430	7	eur	eur	PROPN
ejpam-4665	430	8	.	.	PUNCT
ejpam-4665	431	1	j.	j.	PROPN
ejpam-4665	431	2	pure	pure	PROPN
ejpam-4665	431	3	appl	appl	PROPN
ejpam-4665	431	4	.	.	PROPN
ejpam-4665	431	5	math	math	PROPN
ejpam-4665	431	6	,	,	PUNCT
ejpam-4665	431	7	16	16	NUM
ejpam-4665	431	8	(	(	PUNCT
ejpam-4665	431	9	1	1	NUM
ejpam-4665	431	10	)	)	PUNCT
ejpam-4665	431	11	(	(	PUNCT
ejpam-4665	431	12	2023	2023	NUM
ejpam-4665	431	13	)	)	PUNCT
ejpam-4665	431	14	,	,	PUNCT
ejpam-4665	431	15	286	286	NUM
ejpam-4665	431	16	-	-	SYM
ejpam-4665	431	17	303	303	NUM
ejpam-4665	431	18	300	300	NUM
ejpam-4665	431	19	now	now	ADV
ejpam-4665	431	20	,	,	PUNCT
ejpam-4665	431	21	suppose	suppose	VERB
ejpam-4665	431	22	suv	suv	PROPN
ejpam-4665	431	23	=	=	SYM
ejpam-4665	431	24	v	v	PROPN
ejpam-4665	431	25	(	(	PUNCT
ejpam-4665	431	26	huv	huv	PROPN
ejpam-4665	431	27	)	)	PUNCT
ejpam-4665	431	28	.	.	PUNCT
ejpam-4665	432	1	since	since	SCONJ
ejpam-4665	432	2	c	c	PROPN
ejpam-4665	432	3	is	be	AUX
ejpam-4665	432	4	a	a	DET
ejpam-4665	432	5	restrained	restrained	ADJ
ejpam-4665	432	6	2	2	NUM
ejpam-4665	432	7	-	-	PUNCT
ejpam-4665	432	8	resolving	resolve	VERB
ejpam-4665	432	9	hop	hop	NOUN
ejpam-4665	432	10	dominating	dominating	NOUN
ejpam-4665	432	11	set	set	NOUN
ejpam-4665	432	12	,	,	PUNCT
ejpam-4665	432	13	then	then	ADV
ejpam-4665	432	14	⟨v	⟨v	CCONJ
ejpam-4665	432	15	(	(	PUNCT
ejpam-4665	432	16	g)\a⟩	g)\a⟩	PROPN
ejpam-4665	432	17	must	must	AUX
ejpam-4665	432	18	contain	contain	VERB
ejpam-4665	432	19	no	no	DET
ejpam-4665	432	20	isolated	isolated	ADJ
ejpam-4665	432	21	vertex	vertex	NOUN
ejpam-4665	432	22	.	.	PUNCT
ejpam-4665	433	1	thus	thus	ADV
ejpam-4665	433	2	,	,	PUNCT
ejpam-4665	433	3	(	(	PUNCT
ejpam-4665	433	4	i	i	NOUN
ejpam-4665	433	5	)	)	PUNCT
ejpam-4665	433	6	holds	hold	VERB
ejpam-4665	433	7	.	.	PUNCT
ejpam-4665	434	1	next	next	ADV
ejpam-4665	434	2	,	,	PUNCT
ejpam-4665	434	3	let	let	VERB
ejpam-4665	434	4	u	u	NOUN
ejpam-4665	434	5	,	,	PUNCT
ejpam-4665	434	6	v	v	PROPN
ejpam-4665	434	7	∈	∈	NOUN
ejpam-4665	434	8	a.	a.	NOUN
ejpam-4665	434	9	if	if	SCONJ
ejpam-4665	434	10	suv	suv	PROPN
ejpam-4665	434	11	=	=	SYM
ejpam-4665	434	12	v	v	PROPN
ejpam-4665	434	13	(	(	PUNCT
ejpam-4665	434	14	huv	huv	PROPN
ejpam-4665	434	15	)	)	PUNCT
ejpam-4665	434	16	,	,	PUNCT
ejpam-4665	434	17	then	then	ADV
ejpam-4665	434	18	suv	suv	PROPN
ejpam-4665	434	19	is	be	AUX
ejpam-4665	434	20	a	a	DET
ejpam-4665	434	21	restrained	restrained	ADJ
ejpam-4665	434	22	2	2	NUM
ejpam-4665	434	23	-	-	PUNCT
ejpam-4665	434	24	locating	locate	VERB
ejpam-4665	434	25	set	set	NOUN
ejpam-4665	434	26	of	of	ADP
ejpam-4665	434	27	huv	huv	PROPN
ejpam-4665	434	28	.	.	PUNCT
ejpam-4665	435	1	suppose	suppose	VERB
ejpam-4665	435	2	suv	suv	PROPN
ejpam-4665	435	3	̸=	̸=	PROPN
ejpam-4665	435	4	v	v	PROPN
ejpam-4665	435	5	(	(	PUNCT
ejpam-4665	435	6	huv	huv	PROPN
ejpam-4665	435	7	)	)	PUNCT
ejpam-4665	435	8	.	.	PUNCT
ejpam-4665	436	1	since	since	SCONJ
ejpam-4665	436	2	v	v	NOUN
ejpam-4665	436	3	(	(	PUNCT
ejpam-4665	436	4	huv)\suv	huv)\suv	PROPN
ejpam-4665	436	5	⊆	⊆	NUM
ejpam-4665	436	6	v	v	NOUN
ejpam-4665	436	7	(	(	PUNCT
ejpam-4665	436	8	g	g	NOUN
ejpam-4665	436	9	⋄h)\c	⋄h)\c	PROPN
ejpam-4665	436	10	and	and	CCONJ
ejpam-4665	436	11	c	c	NOUN
ejpam-4665	436	12	is	be	AUX
ejpam-4665	436	13	a	a	DET
ejpam-4665	436	14	restrained	restrain	VERB
ejpam-4665	436	15	2resolving	2resolving	NUM
ejpam-4665	436	16	hop	hop	NOUN
ejpam-4665	436	17	dominating	dominating	NOUN
ejpam-4665	436	18	set	set	VERB
ejpam-4665	436	19	in	in	ADP
ejpam-4665	436	20	g⋄h	g⋄h	PROPN
ejpam-4665	436	21	,	,	PUNCT
ejpam-4665	436	22	it	it	PRON
ejpam-4665	436	23	follows	follow	VERB
ejpam-4665	436	24	⟨v	⟨v	NOUN
ejpam-4665	436	25	(	(	PUNCT
ejpam-4665	436	26	huv)\suv⟩	huv)\suv⟩	PROPN
ejpam-4665	436	27	must	must	AUX
ejpam-4665	436	28	have	have	VERB
ejpam-4665	436	29	no	no	DET
ejpam-4665	436	30	isolated	isolate	VERB
ejpam-4665	436	31	vertex	vertex	NOUN
ejpam-4665	436	32	.	.	PUNCT
ejpam-4665	437	1	hence	hence	ADV
ejpam-4665	437	2	,	,	PUNCT
ejpam-4665	437	3	suv	suv	PROPN
ejpam-4665	437	4	is	be	AUX
ejpam-4665	437	5	a	a	DET
ejpam-4665	437	6	restrained	restrained	ADJ
ejpam-4665	437	7	2	2	NUM
ejpam-4665	437	8	-	-	PUNCT
ejpam-4665	437	9	locating	locate	VERB
ejpam-4665	437	10	set	set	NOUN
ejpam-4665	437	11	in	in	ADP
ejpam-4665	437	12	huv	huv	PROPN
ejpam-4665	437	13	.	.	PUNCT
ejpam-4665	438	1	hence	hence	ADV
ejpam-4665	438	2	,	,	PUNCT
ejpam-4665	438	3	(	(	PUNCT
ejpam-4665	438	4	ii	ii	NOUN
ejpam-4665	438	5	)	)	PUNCT
ejpam-4665	438	6	holds	hold	VERB
ejpam-4665	438	7	.	.	PUNCT
ejpam-4665	439	1	conversely	conversely	ADV
ejpam-4665	439	2	,	,	PUNCT
ejpam-4665	439	3	let	let	VERB
ejpam-4665	439	4	c	c	PRON
ejpam-4665	439	5	be	be	AUX
ejpam-4665	439	6	a	a	DET
ejpam-4665	439	7	2	2	NUM
ejpam-4665	439	8	-	-	PUNCT
ejpam-4665	439	9	resolving	resolve	VERB
ejpam-4665	439	10	hop	hop	NOUN
ejpam-4665	439	11	dominating	dominating	NOUN
ejpam-4665	439	12	set	set	VERB
ejpam-4665	439	13	as	as	SCONJ
ejpam-4665	439	14	described	describe	VERB
ejpam-4665	439	15	and	and	CCONJ
ejpam-4665	439	16	satisfies	satisfy	VERB
ejpam-4665	439	17	the	the	DET
ejpam-4665	439	18	given	give	VERB
ejpam-4665	439	19	conditions	condition	NOUN
ejpam-4665	439	20	.	.	PUNCT
ejpam-4665	440	1	suppose	suppose	VERB
ejpam-4665	440	2	v	v	X
ejpam-4665	440	3	(	(	PUNCT
ejpam-4665	440	4	huv	huv	PROPN
ejpam-4665	440	5	)	)	PUNCT
ejpam-4665	440	6	=	=	SYM
ejpam-4665	440	7	suv	suv	PROPN
ejpam-4665	440	8	for	for	ADP
ejpam-4665	440	9	all	all	DET
ejpam-4665	440	10	uv	uv	PROPN
ejpam-4665	440	11	∈	∈	PROPN
ejpam-4665	440	12	e(g	e(g	PROPN
ejpam-4665	440	13	)	)	PUNCT
ejpam-4665	440	14	.	.	PUNCT
ejpam-4665	441	1	then	then	ADV
ejpam-4665	441	2	⟨v	⟨v	X
ejpam-4665	441	3	(	(	PUNCT
ejpam-4665	441	4	g	g	PROPN
ejpam-4665	441	5	⋄	⋄	PROPN
ejpam-4665	441	6	h)\c⟩	h)\c⟩	PROPN
ejpam-4665	441	7	=	=	SYM
ejpam-4665	441	8	⟨v	⟨v	PROPN
ejpam-4665	441	9	(	(	PUNCT
ejpam-4665	441	10	g)\a⟩.	g)\a⟩.	PROPN
ejpam-4665	441	11	by	by	ADP
ejpam-4665	441	12	(	(	PUNCT
ejpam-4665	441	13	i	i	NOUN
ejpam-4665	441	14	)	)	PUNCT
ejpam-4665	441	15	,	,	PUNCT
ejpam-4665	441	16	⟨v	⟨v	PROPN
ejpam-4665	441	17	(	(	PUNCT
ejpam-4665	441	18	g⋄h)\c⟩	g⋄h)\c⟩	NOUN
ejpam-4665	441	19	has	have	VERB
ejpam-4665	441	20	no	no	DET
ejpam-4665	441	21	isolated	isolated	ADJ
ejpam-4665	441	22	vertex	vertex	NOUN
ejpam-4665	441	23	.	.	PUNCT
ejpam-4665	442	1	next	next	ADV
ejpam-4665	442	2	,	,	PUNCT
ejpam-4665	442	3	suppose	suppose	VERB
ejpam-4665	442	4	v	v	X
ejpam-4665	442	5	(	(	PUNCT
ejpam-4665	442	6	huv	huv	PROPN
ejpam-4665	442	7	)	)	PUNCT
ejpam-4665	442	8	̸=	̸=	PROPN
ejpam-4665	442	9	suv	suv	NOUN
ejpam-4665	442	10	for	for	ADP
ejpam-4665	442	11	some	some	DET
ejpam-4665	442	12	uv	uv	PROPN
ejpam-4665	442	13	∈	∈	PROPN
ejpam-4665	442	14	e(g	e(g	PROPN
ejpam-4665	442	15	)	)	PUNCT
ejpam-4665	442	16	.	.	PUNCT
ejpam-4665	443	1	if	if	SCONJ
ejpam-4665	443	2	u	u	NOUN
ejpam-4665	443	3	or	or	CCONJ
ejpam-4665	443	4	v	v	NOUN
ejpam-4665	443	5	is	be	AUX
ejpam-4665	443	6	not	not	PART
ejpam-4665	443	7	an	an	DET
ejpam-4665	443	8	element	element	NOUN
ejpam-4665	443	9	of	of	ADP
ejpam-4665	443	10	a	a	PRON
ejpam-4665	443	11	,	,	PUNCT
ejpam-4665	443	12	then	then	ADV
ejpam-4665	443	13	⟨v	⟨v	NUM
ejpam-4665	443	14	(	(	PUNCT
ejpam-4665	443	15	huv)\suv⟩	huv)\suv⟩	PROPN
ejpam-4665	443	16	+	+	NUM
ejpam-4665	443	17	⟨{u	⟨{u	PROPN
ejpam-4665	443	18	,	,	PUNCT
ejpam-4665	443	19	v}⟩	v}⟩	PROPN
ejpam-4665	443	20	has	have	VERB
ejpam-4665	443	21	no	no	DET
ejpam-4665	443	22	isolated	isolated	ADJ
ejpam-4665	443	23	vertex	vertex	NOUN
ejpam-4665	443	24	.	.	PUNCT
ejpam-4665	444	1	on	on	ADP
ejpam-4665	444	2	the	the	DET
ejpam-4665	444	3	other	other	ADJ
ejpam-4665	444	4	hand	hand	NOUN
ejpam-4665	444	5	,	,	PUNCT
ejpam-4665	444	6	if	if	SCONJ
ejpam-4665	444	7	u	u	NOUN
ejpam-4665	444	8	,	,	PUNCT
ejpam-4665	444	9	v	v	ADP
ejpam-4665	444	10	∈	∈	PROPN
ejpam-4665	444	11	a	a	DET
ejpam-4665	444	12	,	,	PUNCT
ejpam-4665	444	13	then	then	ADV
ejpam-4665	444	14	v	v	X
ejpam-4665	444	15	(	(	PUNCT
ejpam-4665	444	16	huv)\suv	huv)\suv	PROPN
ejpam-4665	444	17	has	have	VERB
ejpam-4665	444	18	no	no	DET
ejpam-4665	444	19	isolated	isolated	ADJ
ejpam-4665	444	20	vertex	vertex	NOUN
ejpam-4665	444	21	by	by	ADP
ejpam-4665	444	22	(	(	PUNCT
ejpam-4665	444	23	ii	ii	NOUN
ejpam-4665	444	24	)	)	PUNCT
ejpam-4665	444	25	.	.	PUNCT
ejpam-4665	445	1	thus	thus	ADV
ejpam-4665	445	2	,	,	PUNCT
ejpam-4665	445	3	it	it	PRON
ejpam-4665	445	4	follows	follow	VERB
ejpam-4665	445	5	that	that	PRON
ejpam-4665	445	6	⟨v	⟨v	NOUN
ejpam-4665	445	7	(	(	PUNCT
ejpam-4665	445	8	g	g	PROPN
ejpam-4665	445	9	⋄	⋄	PROPN
ejpam-4665	445	10	h)\c⟩	h)\c⟩	PROPN
ejpam-4665	445	11	has	have	VERB
ejpam-4665	445	12	no	no	DET
ejpam-4665	445	13	isolated	isolated	ADJ
ejpam-4665	445	14	vertex	vertex	NOUN
ejpam-4665	445	15	.	.	PUNCT
ejpam-4665	446	1	therefore	therefore	ADV
ejpam-4665	446	2	,	,	PUNCT
ejpam-4665	446	3	c	c	PROPN
ejpam-4665	446	4	is	be	AUX
ejpam-4665	446	5	a	a	DET
ejpam-4665	446	6	restrained	restrained	ADJ
ejpam-4665	446	7	2	2	NUM
ejpam-4665	446	8	-	-	PUNCT
ejpam-4665	446	9	resolving	resolve	VERB
ejpam-4665	446	10	hop	hop	NOUN
ejpam-4665	446	11	dominating	dominating	NOUN
ejpam-4665	446	12	set	set	VERB
ejpam-4665	446	13	in	in	ADP
ejpam-4665	446	14	g	g	PROPN
ejpam-4665	446	15	⋄h	⋄h	PROPN
ejpam-4665	446	16	.	.	PUNCT
ejpam-4665	447	1	corollary	corollary	NOUN
ejpam-4665	447	2	6	6	NUM
ejpam-4665	447	3	.	.	PUNCT
ejpam-4665	448	1	let	let	VERB
ejpam-4665	448	2	g	g	NOUN
ejpam-4665	449	1	and	and	CCONJ
ejpam-4665	449	2	h	h	NOUN
ejpam-4665	449	3	be	be	VERB
ejpam-4665	449	4	a	a	DET
ejpam-4665	449	5	nontrivial	nontrivial	ADJ
ejpam-4665	449	6	connected	connect	VERB
ejpam-4665	449	7	graph	graph	NOUN
ejpam-4665	449	8	.	.	PUNCT
ejpam-4665	450	1	then	then	ADV
ejpam-4665	450	2	γr2rh(g	γr2rh(g	PROPN
ejpam-4665	450	3	⋄h	⋄h	PROPN
ejpam-4665	450	4	)	)	PUNCT
ejpam-4665	450	5	=	=	PUNCT
ejpam-4665	450	6	γ2rh(g	γ2rh(g	PROPN
ejpam-4665	450	7	⋄h	⋄h	NOUN
ejpam-4665	450	8	)	)	PUNCT
ejpam-4665	450	9	.	.	PUNCT
ejpam-4665	451	1	7	7	X
ejpam-4665	451	2	.	.	X
ejpam-4665	451	3	restrained	restrain	VERB
ejpam-4665	451	4	2	2	NUM
ejpam-4665	451	5	-	-	PUNCT
ejpam-4665	451	6	resolving	resolve	VERB
ejpam-4665	451	7	hop	hop	NOUN
ejpam-4665	451	8	dominating	dominating	NOUN
ejpam-4665	451	9	sets	set	NOUN
ejpam-4665	451	10	in	in	ADP
ejpam-4665	451	11	the	the	DET
ejpam-4665	451	12	lexicographic	lexicographic	ADJ
ejpam-4665	451	13	product	product	NOUN
ejpam-4665	451	14	of	of	ADP
ejpam-4665	451	15	graphs	graph	NOUN
ejpam-4665	451	16	this	this	DET
ejpam-4665	451	17	section	section	NOUN
ejpam-4665	451	18	presents	present	VERB
ejpam-4665	451	19	characterizations	characterization	NOUN
ejpam-4665	451	20	on	on	ADP
ejpam-4665	451	21	the	the	DET
ejpam-4665	451	22	restrained	restrained	ADJ
ejpam-4665	451	23	2	2	NUM
ejpam-4665	451	24	-	-	PUNCT
ejpam-4665	451	25	resolving	resolve	VERB
ejpam-4665	451	26	hop	hop	NOUN
ejpam-4665	451	27	dominating	dominating	NOUN
ejpam-4665	451	28	sets	set	NOUN
ejpam-4665	451	29	in	in	ADP
ejpam-4665	451	30	the	the	DET
ejpam-4665	451	31	lexicographic	lexicographic	ADJ
ejpam-4665	451	32	product	product	NOUN
ejpam-4665	451	33	of	of	ADP
ejpam-4665	451	34	graphs	graph	NOUN
ejpam-4665	451	35	.	.	PUNCT
ejpam-4665	452	1	theorem	theorem	VERB
ejpam-4665	452	2	14	14	NUM
ejpam-4665	452	3	.	.	PUNCT
ejpam-4665	453	1	[	[	X
ejpam-4665	453	2	11	11	NUM
ejpam-4665	453	3	]	]	PUNCT
ejpam-4665	453	4	let	let	VERB
ejpam-4665	453	5	g	g	NOUN
ejpam-4665	453	6	and	and	CCONJ
ejpam-4665	453	7	h	h	NOUN
ejpam-4665	453	8	be	be	AUX
ejpam-4665	453	9	nontrivial	nontrivial	ADJ
ejpam-4665	453	10	connected	connected	ADJ
ejpam-4665	453	11	graphs	graph	NOUN
ejpam-4665	453	12	.	.	PUNCT
ejpam-4665	454	1	then	then	ADV
ejpam-4665	454	2	w	w	NOUN
ejpam-4665	454	3	=	=	PUNCT
ejpam-4665	454	4	⋃	⋃	PROPN
ejpam-4665	454	5	x∈s	x∈s	NOUN
ejpam-4665	455	1	[	[	X
ejpam-4665	455	2	{	{	PUNCT
ejpam-4665	455	3	x	x	NOUN
ejpam-4665	455	4	}	}	PUNCT
ejpam-4665	455	5	×	×	PROPN
ejpam-4665	455	6	tx	tx	PROPN
ejpam-4665	455	7	]	]	X
ejpam-4665	455	8	,	,	PUNCT
ejpam-4665	455	9	where	where	SCONJ
ejpam-4665	455	10	s	s	VERB
ejpam-4665	455	11	⊆	⊆	NUM
ejpam-4665	455	12	v	v	NOUN
ejpam-4665	455	13	(	(	PUNCT
ejpam-4665	455	14	g	g	NOUN
ejpam-4665	455	15	)	)	PUNCT
ejpam-4665	455	16	and	and	CCONJ
ejpam-4665	455	17	tx	tx	VERB
ejpam-4665	455	18	⊆	⊆	NUM
ejpam-4665	455	19	v	v	NOUN
ejpam-4665	455	20	(	(	PUNCT
ejpam-4665	455	21	h	h	NOUN
ejpam-4665	455	22	)	)	PUNCT
ejpam-4665	455	23	for	for	ADP
ejpam-4665	455	24	each	each	DET
ejpam-4665	455	25	x	x	SYM
ejpam-4665	455	26	∈	∈	PROPN
ejpam-4665	455	27	s	s	NOUN
ejpam-4665	455	28	,	,	PUNCT
ejpam-4665	455	29	is	be	AUX
ejpam-4665	455	30	a	a	DET
ejpam-4665	455	31	2	2	NUM
ejpam-4665	455	32	-	-	PUNCT
ejpam-4665	455	33	resolving	resolve	VERB
ejpam-4665	455	34	hop	hop	NOUN
ejpam-4665	455	35	dominating	dominating	NOUN
ejpam-4665	455	36	set	set	VERB
ejpam-4665	455	37	in	in	ADP
ejpam-4665	455	38	g[h	g[h	PROPN
ejpam-4665	455	39	]	]	PUNCT
ejpam-4665	455	40	if	if	SCONJ
ejpam-4665	455	41	and	and	CCONJ
ejpam-4665	455	42	only	only	ADV
ejpam-4665	455	43	if	if	SCONJ
ejpam-4665	455	44	(	(	PUNCT
ejpam-4665	455	45	i	i	NOUN
ejpam-4665	455	46	)	)	PUNCT
ejpam-4665	455	47	s	s	PART
ejpam-4665	455	48	=	=	SYM
ejpam-4665	455	49	v	v	NOUN
ejpam-4665	455	50	(	(	PUNCT
ejpam-4665	455	51	g	g	NOUN
ejpam-4665	455	52	)	)	PUNCT
ejpam-4665	455	53	;	;	PUNCT
ejpam-4665	455	54	(	(	PUNCT
ejpam-4665	455	55	ii	ii	NOUN
ejpam-4665	455	56	)	)	PUNCT
ejpam-4665	455	57	tx	tx	PROPN
ejpam-4665	455	58	is	be	AUX
ejpam-4665	455	59	a	a	DET
ejpam-4665	455	60	2	2	NUM
ejpam-4665	455	61	-	-	PUNCT
ejpam-4665	455	62	locating	locate	VERB
ejpam-4665	455	63	set	set	NOUN
ejpam-4665	455	64	in	in	ADP
ejpam-4665	455	65	h	h	NOUN
ejpam-4665	455	66	for	for	ADP
ejpam-4665	455	67	every	every	DET
ejpam-4665	455	68	x	x	SYM
ejpam-4665	455	69	∈	∈	PROPN
ejpam-4665	455	70	v	v	ADP
ejpam-4665	455	71	(	(	PUNCT
ejpam-4665	455	72	g	g	NOUN
ejpam-4665	455	73	)	)	PUNCT
ejpam-4665	455	74	;	;	PUNCT
ejpam-4665	455	75	(	(	PUNCT
ejpam-4665	455	76	iii	iii	X
ejpam-4665	455	77	)	)	PUNCT
ejpam-4665	455	78	tx	tx	NOUN
ejpam-4665	456	1	or	or	CCONJ
ejpam-4665	456	2	ty	ty	INTJ
ejpam-4665	456	3	is	be	AUX
ejpam-4665	456	4	a	a	DET
ejpam-4665	456	5	(	(	PUNCT
ejpam-4665	456	6	2	2	NUM
ejpam-4665	456	7	,	,	PUNCT
ejpam-4665	456	8	1)-locating	1)-locating	NUM
ejpam-4665	456	9	set	set	NOUN
ejpam-4665	456	10	or	or	CCONJ
ejpam-4665	456	11	one	one	NUM
ejpam-4665	456	12	of	of	ADP
ejpam-4665	456	13	tx	tx	PROPN
ejpam-4665	456	14	and	and	CCONJ
ejpam-4665	456	15	ty	ty	PRON
ejpam-4665	456	16	is	be	AUX
ejpam-4665	456	17	a	a	DET
ejpam-4665	456	18	(	(	PUNCT
ejpam-4665	456	19	2	2	NUM
ejpam-4665	456	20	,	,	PUNCT
ejpam-4665	456	21	2)-locating	2)-locating	NUM
ejpam-4665	456	22	set	set	VERB
ejpam-4665	456	23	in	in	ADP
ejpam-4665	456	24	h	h	NOUN
ejpam-4665	456	25	whenever	whenever	SCONJ
ejpam-4665	456	26	x	x	X
ejpam-4665	456	27	,	,	PUNCT
ejpam-4665	456	28	y	y	PROPN
ejpam-4665	456	29	∈	∈	PROPN
ejpam-4665	456	30	eq1(g	eq1(g	PROPN
ejpam-4665	456	31	)	)	PUNCT
ejpam-4665	456	32	;	;	PUNCT
ejpam-4665	456	33	(	(	PUNCT
ejpam-4665	456	34	iv	iv	X
ejpam-4665	456	35	)	)	PUNCT
ejpam-4665	456	36	tx	tx	PROPN
ejpam-4665	457	1	and	and	CCONJ
ejpam-4665	457	2	ty	ty	INTJ
ejpam-4665	457	3	are	be	AUX
ejpam-4665	457	4	(	(	PUNCT
ejpam-4665	457	5	2	2	NUM
ejpam-4665	457	6	−	−	NOUN
ejpam-4665	457	7	locating	locating	NOUN
ejpam-4665	457	8	)	)	PUNCT
ejpam-4665	457	9	dominating	dominating	NOUN
ejpam-4665	457	10	sets	set	NOUN
ejpam-4665	457	11	in	in	ADP
ejpam-4665	457	12	h	h	NOUN
ejpam-4665	457	13	or	or	CCONJ
ejpam-4665	457	14	one	one	NUM
ejpam-4665	457	15	of	of	ADP
ejpam-4665	457	16	tx	tx	PROPN
ejpam-4665	458	1	and	and	CCONJ
ejpam-4665	458	2	ty	ty	INTJ
ejpam-4665	458	3	is	be	AUX
ejpam-4665	458	4	a	a	DET
ejpam-4665	458	5	2dominating	2dominating	NUM
ejpam-4665	458	6	set	set	NOUN
ejpam-4665	458	7	whenever	whenever	SCONJ
ejpam-4665	458	8	x	x	X
ejpam-4665	458	9	,	,	PUNCT
ejpam-4665	458	10	y	y	PROPN
ejpam-4665	458	11	∈	∈	PROPN
ejpam-4665	458	12	eq2(g	eq2(g	VERB
ejpam-4665	458	13	)	)	PUNCT
ejpam-4665	458	14	.	.	PUNCT
ejpam-4665	459	1	(	(	PUNCT
ejpam-4665	459	2	v	v	NOUN
ejpam-4665	459	3	)	)	PUNCT
ejpam-4665	459	4	tx	tx	PROPN
ejpam-4665	459	5	is	be	AUX
ejpam-4665	459	6	a	a	DET
ejpam-4665	459	7	2	2	NUM
ejpam-4665	459	8	-	-	PUNCT
ejpam-4665	459	9	locating	locate	VERB
ejpam-4665	459	10	point	point	NOUN
ejpam-4665	459	11	-	-	PUNCT
ejpam-4665	459	12	wise	wise	ADJ
ejpam-4665	459	13	non	non	ADJ
ejpam-4665	459	14	-	-	ADJ
ejpam-4665	459	15	dominating	dominating	ADJ
ejpam-4665	459	16	set	set	VERB
ejpam-4665	459	17	inh	inh	NOUN
ejpam-4665	459	18	for	for	ADP
ejpam-4665	459	19	every	every	DET
ejpam-4665	459	20	x	x	SYM
ejpam-4665	459	21	∈	∈	PROPN
ejpam-4665	459	22	s	s	VERB
ejpam-4665	459	23	with	with	ADP
ejpam-4665	459	24	|ng(x	|ng(x	ADP
ejpam-4665	459	25	,	,	PUNCT
ejpam-4665	459	26	2)∩	2)∩	ADJ
ejpam-4665	459	27	s|	s|	NOUN
ejpam-4665	459	28	=	=	SYM
ejpam-4665	459	29	0	0	X
ejpam-4665	459	30	.	.	PUNCT
ejpam-4665	459	31	theorem	theorem	NOUN
ejpam-4665	459	32	15	15	NUM
ejpam-4665	459	33	.	.	PUNCT
ejpam-4665	460	1	let	let	VERB
ejpam-4665	460	2	g	g	NOUN
ejpam-4665	460	3	and	and	CCONJ
ejpam-4665	460	4	h	h	NOUN
ejpam-4665	460	5	be	be	AUX
ejpam-4665	460	6	nontrivial	nontrivial	ADJ
ejpam-4665	460	7	connected	connected	ADJ
ejpam-4665	460	8	graphs	graph	NOUN
ejpam-4665	460	9	.	.	PUNCT
ejpam-4665	461	1	then	then	ADV
ejpam-4665	461	2	w	w	NOUN
ejpam-4665	461	3	=	=	PUNCT
ejpam-4665	461	4	⋃	⋃	PROPN
ejpam-4665	461	5	x∈s	x∈s	NOUN
ejpam-4665	462	1	[	[	X
ejpam-4665	462	2	{	{	PUNCT
ejpam-4665	462	3	x	x	NOUN
ejpam-4665	462	4	}	}	PUNCT
ejpam-4665	462	5	×	×	PROPN
ejpam-4665	462	6	tx	tx	PROPN
ejpam-4665	462	7	]	]	X
ejpam-4665	462	8	,	,	PUNCT
ejpam-4665	462	9	where	where	SCONJ
ejpam-4665	462	10	s	s	VERB
ejpam-4665	462	11	⊆	⊆	NUM
ejpam-4665	462	12	v	v	NOUN
ejpam-4665	462	13	(	(	PUNCT
ejpam-4665	462	14	g	g	NOUN
ejpam-4665	462	15	)	)	PUNCT
ejpam-4665	462	16	and	and	CCONJ
ejpam-4665	462	17	tx	tx	VERB
ejpam-4665	462	18	⊆	⊆	NUM
ejpam-4665	462	19	v	v	NOUN
ejpam-4665	462	20	(	(	PUNCT
ejpam-4665	462	21	h	h	NOUN
ejpam-4665	462	22	)	)	PUNCT
ejpam-4665	462	23	for	for	ADP
ejpam-4665	462	24	each	each	DET
ejpam-4665	462	25	x	x	SYM
ejpam-4665	462	26	∈	∈	PROPN
ejpam-4665	462	27	s	s	NOUN
ejpam-4665	462	28	,	,	PUNCT
ejpam-4665	462	29	is	be	AUX
ejpam-4665	462	30	a	a	DET
ejpam-4665	462	31	restrained	restrained	ADJ
ejpam-4665	462	32	2	2	NUM
ejpam-4665	462	33	-	-	PUNCT
ejpam-4665	462	34	resolving	resolve	VERB
ejpam-4665	462	35	hop	hop	NOUN
ejpam-4665	462	36	dominating	dominating	NOUN
ejpam-4665	462	37	set	set	VERB
ejpam-4665	462	38	in	in	ADP
ejpam-4665	462	39	g[h	g[h	PROPN
ejpam-4665	462	40	]	]	PUNCT
ejpam-4665	462	41	if	if	SCONJ
ejpam-4665	462	42	and	and	CCONJ
ejpam-4665	462	43	only	only	ADV
ejpam-4665	462	44	if	if	SCONJ
ejpam-4665	462	45	it	it	PRON
ejpam-4665	462	46	is	be	AUX
ejpam-4665	462	47	a	a	DET
ejpam-4665	462	48	2	2	NUM
ejpam-4665	462	49	-	-	PUNCT
ejpam-4665	462	50	resolving	resolve	VERB
ejpam-4665	462	51	hop	hop	NOUN
ejpam-4665	462	52	dominating	dominating	NOUN
ejpam-4665	462	53	set	set	NOUN
ejpam-4665	462	54	and	and	CCONJ
ejpam-4665	462	55	tx	tx	PROPN
ejpam-4665	462	56	is	be	AUX
ejpam-4665	462	57	a	a	DET
ejpam-4665	462	58	restrained	restrained	ADJ
ejpam-4665	462	59	2	2	NUM
ejpam-4665	462	60	-	-	PUNCT
ejpam-4665	462	61	locating	locate	VERB
ejpam-4665	462	62	point	point	NOUN
ejpam-4665	462	63	-	-	PUNCT
ejpam-4665	462	64	wise	wise	ADJ
ejpam-4665	462	65	non	non	ADJ
ejpam-4665	462	66	-	-	ADJ
ejpam-4665	462	67	dominating	dominating	ADJ
ejpam-4665	462	68	set	set	NOUN
ejpam-4665	462	69	for	for	ADP
ejpam-4665	462	70	each	each	PRON
ejpam-4665	462	71	x	x	PUNCT
ejpam-4665	462	72	with	with	ADP
ejpam-4665	462	73	ty	ty	NOUN
ejpam-4665	462	74	=	=	SYM
ejpam-4665	462	75	v	v	NOUN
ejpam-4665	462	76	(	(	PUNCT
ejpam-4665	462	77	h	h	NOUN
ejpam-4665	462	78	)	)	PUNCT
ejpam-4665	462	79	for	for	ADP
ejpam-4665	462	80	all	all	DET
ejpam-4665	462	81	y	y	PROPN
ejpam-4665	462	82	∈	∈	PROPN
ejpam-4665	462	83	ng(x	ng(x	NUM
ejpam-4665	462	84	)	)	PUNCT
ejpam-4665	462	85	.	.	PUNCT
ejpam-4665	463	1	a.m.	a.m.	PROPN
ejpam-4665	463	2	mahistrado	mahistrado	PROPN
ejpam-4665	463	3	,	,	PUNCT
ejpam-4665	463	4	h.	h.	PROPN
ejpam-4665	463	5	rara	rara	PROPN
ejpam-4665	463	6	/	/	SYM
ejpam-4665	463	7	eur	eur	PROPN
ejpam-4665	463	8	.	.	PUNCT
ejpam-4665	464	1	j.	j.	PROPN
ejpam-4665	464	2	pure	pure	PROPN
ejpam-4665	464	3	appl	appl	PROPN
ejpam-4665	464	4	.	.	PROPN
ejpam-4665	464	5	math	math	PROPN
ejpam-4665	464	6	,	,	PUNCT
ejpam-4665	464	7	16	16	NUM
ejpam-4665	464	8	(	(	PUNCT
ejpam-4665	464	9	1	1	NUM
ejpam-4665	464	10	)	)	PUNCT
ejpam-4665	464	11	(	(	PUNCT
ejpam-4665	464	12	2023	2023	NUM
ejpam-4665	464	13	)	)	PUNCT
ejpam-4665	464	14	,	,	PUNCT
ejpam-4665	464	15	286	286	NUM
ejpam-4665	464	16	-	-	SYM
ejpam-4665	464	17	303	303	NUM
ejpam-4665	464	18	301	301	NUM
ejpam-4665	464	19	proof	proof	NOUN
ejpam-4665	464	20	.	.	PUNCT
ejpam-4665	465	1	let	let	VERB
ejpam-4665	465	2	w	w	NOUN
ejpam-4665	465	3	=	=	PUNCT
ejpam-4665	465	4	⋃	⋃	PROPN
ejpam-4665	465	5	x∈s	x∈s	NOUN
ejpam-4665	466	1	[	[	X
ejpam-4665	466	2	{	{	PUNCT
ejpam-4665	466	3	x	x	NOUN
ejpam-4665	466	4	}	}	PUNCT
ejpam-4665	466	5	×	×	PROPN
ejpam-4665	466	6	tx	tx	PROPN
ejpam-4665	466	7	]	]	X
ejpam-4665	466	8	,	,	PUNCT
ejpam-4665	466	9	where	where	SCONJ
ejpam-4665	466	10	s	s	VERB
ejpam-4665	466	11	⊆	⊆	NUM
ejpam-4665	466	12	v	v	NOUN
ejpam-4665	466	13	(	(	PUNCT
ejpam-4665	466	14	g	g	NOUN
ejpam-4665	466	15	)	)	PUNCT
ejpam-4665	466	16	and	and	CCONJ
ejpam-4665	466	17	tx	tx	VERB
ejpam-4665	466	18	⊆	⊆	NUM
ejpam-4665	466	19	v	v	NOUN
ejpam-4665	466	20	(	(	PUNCT
ejpam-4665	466	21	h	h	NOUN
ejpam-4665	466	22	)	)	PUNCT
ejpam-4665	466	23	for	for	ADP
ejpam-4665	466	24	each	each	DET
ejpam-4665	466	25	x	x	SYM
ejpam-4665	466	26	∈	∈	PROPN
ejpam-4665	466	27	s	s	AUX
ejpam-4665	466	28	,	,	PUNCT
ejpam-4665	466	29	be	be	AUX
ejpam-4665	466	30	a	a	DET
ejpam-4665	466	31	restrained	restrained	ADJ
ejpam-4665	466	32	2	2	NUM
ejpam-4665	466	33	-	-	PUNCT
ejpam-4665	466	34	resolving	resolve	VERB
ejpam-4665	466	35	hop	hop	NOUN
ejpam-4665	466	36	dominating	dominating	NOUN
ejpam-4665	466	37	set	set	VERB
ejpam-4665	466	38	in	in	ADP
ejpam-4665	466	39	g[h	g[h	PROPN
ejpam-4665	466	40	]	]	PUNCT
ejpam-4665	466	41	.	.	PUNCT
ejpam-4665	467	1	then	then	ADV
ejpam-4665	467	2	w	w	PROPN
ejpam-4665	467	3	is	be	AUX
ejpam-4665	467	4	a	a	DET
ejpam-4665	467	5	2	2	NUM
ejpam-4665	467	6	-	-	PUNCT
ejpam-4665	467	7	resolving	resolve	VERB
ejpam-4665	467	8	hop	hop	NOUN
ejpam-4665	467	9	dominating	dominating	NOUN
ejpam-4665	467	10	set	set	VERB
ejpam-4665	467	11	in	in	ADP
ejpam-4665	467	12	g[h	g[h	PROPN
ejpam-4665	467	13	]	]	PUNCT
ejpam-4665	467	14	.	.	PUNCT
ejpam-4665	468	1	by	by	ADP
ejpam-4665	468	2	theorem	theorem	NOUN
ejpam-4665	468	3	14	14	NUM
ejpam-4665	468	4	,	,	PUNCT
ejpam-4665	468	5	(	(	PUNCT
ejpam-4665	468	6	i)-(iv	i)-(iv	X
ejpam-4665	468	7	)	)	PUNCT
ejpam-4665	468	8	hold	hold	VERB
ejpam-4665	468	9	and	and	CCONJ
ejpam-4665	468	10	tx	tx	PROPN
ejpam-4665	468	11	is	be	AUX
ejpam-4665	468	12	a	a	DET
ejpam-4665	468	13	2	2	NUM
ejpam-4665	468	14	-	-	PUNCT
ejpam-4665	468	15	locating	locate	VERB
ejpam-4665	468	16	point	point	NOUN
ejpam-4665	468	17	-	-	PUNCT
ejpam-4665	468	18	wise	wise	ADV
ejpam-4665	468	19	nondominating	nondominate	VERB
ejpam-4665	468	20	set	set	VERB
ejpam-4665	468	21	inh	inh	NOUN
ejpam-4665	468	22	for	for	ADP
ejpam-4665	468	23	every	every	DET
ejpam-4665	468	24	x	x	SYM
ejpam-4665	468	25	∈	∈	PROPN
ejpam-4665	468	26	s	s	VERB
ejpam-4665	468	27	with	with	ADP
ejpam-4665	468	28	|ng(x	|ng(x	PUNCT
ejpam-4665	468	29	,	,	PUNCT
ejpam-4665	468	30	2)∩s|	2)∩s|	NUM
ejpam-4665	468	31	=	=	SYM
ejpam-4665	468	32	0	0	X
ejpam-4665	468	33	.	.	PUNCT
ejpam-4665	469	1	since	since	SCONJ
ejpam-4665	469	2	v	v	NOUN
ejpam-4665	469	3	(	(	PUNCT
ejpam-4665	469	4	h)\tx	h)\tx	NOUN
ejpam-4665	469	5	⊆	⊆	NUM
ejpam-4665	469	6	v	v	NOUN
ejpam-4665	469	7	(	(	PUNCT
ejpam-4665	469	8	g[h])\w	g[h])\w	NOUN
ejpam-4665	469	9	and	and	CCONJ
ejpam-4665	469	10	w	w	PROPN
ejpam-4665	469	11	is	be	AUX
ejpam-4665	469	12	a	a	DET
ejpam-4665	469	13	restrained	restrained	ADJ
ejpam-4665	469	14	2	2	NUM
ejpam-4665	469	15	-	-	PUNCT
ejpam-4665	469	16	resolving	resolve	VERB
ejpam-4665	469	17	hop	hop	NOUN
ejpam-4665	469	18	dominating	dominating	NOUN
ejpam-4665	469	19	set	set	NOUN
ejpam-4665	469	20	,	,	PUNCT
ejpam-4665	469	21	it	it	PRON
ejpam-4665	469	22	follows	follow	VERB
ejpam-4665	469	23	that	that	PRON
ejpam-4665	469	24	⟨v	⟨v	NOUN
ejpam-4665	469	25	(	(	PUNCT
ejpam-4665	469	26	h)\tx⟩	h)\tx⟩	PRON
ejpam-4665	469	27	has	have	VERB
ejpam-4665	469	28	no	no	DET
ejpam-4665	469	29	isolated	isolated	ADJ
ejpam-4665	469	30	vertex	vertex	NOUN
ejpam-4665	469	31	.	.	PUNCT
ejpam-4665	470	1	hence	hence	ADV
ejpam-4665	470	2	,	,	PUNCT
ejpam-4665	470	3	tx	tx	PROPN
ejpam-4665	470	4	is	be	AUX
ejpam-4665	470	5	a	a	DET
ejpam-4665	470	6	restrained	restrained	ADJ
ejpam-4665	470	7	2	2	NUM
ejpam-4665	470	8	-	-	PUNCT
ejpam-4665	470	9	locating	locate	VERB
ejpam-4665	470	10	point	point	NOUN
ejpam-4665	470	11	-	-	PUNCT
ejpam-4665	470	12	wise	wise	ADJ
ejpam-4665	470	13	non	non	ADJ
ejpam-4665	470	14	-	-	ADJ
ejpam-4665	470	15	dominating	dominating	ADJ
ejpam-4665	470	16	set	set	NOUN
ejpam-4665	470	17	of	of	ADP
ejpam-4665	470	18	h.	h.	PROPN
ejpam-4665	470	19	for	for	ADP
ejpam-4665	470	20	the	the	DET
ejpam-4665	470	21	converse	converse	NOUN
ejpam-4665	470	22	,	,	PUNCT
ejpam-4665	470	23	let	let	VERB
ejpam-4665	470	24	w	w	NOUN
ejpam-4665	470	25	be	be	AUX
ejpam-4665	470	26	a	a	DET
ejpam-4665	470	27	2	2	NUM
ejpam-4665	470	28	-	-	PUNCT
ejpam-4665	470	29	resolving	resolve	VERB
ejpam-4665	470	30	hop	hop	NOUN
ejpam-4665	470	31	dominating	dominating	NOUN
ejpam-4665	470	32	set	set	VERB
ejpam-4665	470	33	as	as	SCONJ
ejpam-4665	470	34	described	describe	VERB
ejpam-4665	470	35	and	and	CCONJ
ejpam-4665	470	36	satisfies	satisfy	VERB
ejpam-4665	470	37	the	the	DET
ejpam-4665	470	38	given	give	VERB
ejpam-4665	470	39	conditions	condition	NOUN
ejpam-4665	470	40	.	.	PUNCT
ejpam-4665	471	1	suppose	suppose	VERB
ejpam-4665	471	2	that	that	SCONJ
ejpam-4665	471	3	v	v	X
ejpam-4665	471	4	(	(	PUNCT
ejpam-4665	471	5	g[h	g[h	PROPN
ejpam-4665	471	6	]	]	PUNCT
ejpam-4665	471	7	)	)	PUNCT
ejpam-4665	472	1	=	=	SYM
ejpam-4665	472	2	w	w	X
ejpam-4665	472	3	.	.	PUNCT
ejpam-4665	473	1	then	then	ADV
ejpam-4665	473	2	w	w	PROPN
ejpam-4665	473	3	is	be	AUX
ejpam-4665	473	4	a	a	DET
ejpam-4665	473	5	restrained	restrained	ADJ
ejpam-4665	473	6	2	2	NUM
ejpam-4665	473	7	-	-	PUNCT
ejpam-4665	473	8	resolving	resolve	VERB
ejpam-4665	473	9	hop	hop	NOUN
ejpam-4665	473	10	dominating	dominating	NOUN
ejpam-4665	473	11	set	set	NOUN
ejpam-4665	473	12	of	of	ADP
ejpam-4665	473	13	g[h	g[h	PROPN
ejpam-4665	473	14	]	]	PUNCT
ejpam-4665	473	15	.	.	PUNCT
ejpam-4665	474	1	suppose	suppose	VERB
ejpam-4665	474	2	that	that	SCONJ
ejpam-4665	474	3	v	v	X
ejpam-4665	474	4	(	(	PUNCT
ejpam-4665	474	5	g[h	g[h	PROPN
ejpam-4665	474	6	]	]	PUNCT
ejpam-4665	474	7	)	)	PUNCT
ejpam-4665	474	8	̸=	̸=	PROPN
ejpam-4665	474	9	w	w	NOUN
ejpam-4665	474	10	.	.	PUNCT
ejpam-4665	475	1	let	let	VERB
ejpam-4665	475	2	(	(	PUNCT
ejpam-4665	475	3	x	x	NOUN
ejpam-4665	475	4	,	,	PUNCT
ejpam-4665	475	5	v	v	NOUN
ejpam-4665	475	6	)	)	PUNCT
ejpam-4665	475	7	∈	∈	NOUN
ejpam-4665	475	8	v	v	NOUN
ejpam-4665	475	9	(	(	PUNCT
ejpam-4665	475	10	g[h])\w	g[h])\w	INTJ
ejpam-4665	475	11	.	.	PUNCT
ejpam-4665	476	1	if	if	SCONJ
ejpam-4665	476	2	ty	ty	NUM
ejpam-4665	476	3	̸=	̸=	PROPN
ejpam-4665	476	4	v	v	NOUN
ejpam-4665	476	5	(	(	PUNCT
ejpam-4665	476	6	h	h	NOUN
ejpam-4665	476	7	)	)	PUNCT
ejpam-4665	476	8	,	,	PUNCT
ejpam-4665	476	9	for	for	ADP
ejpam-4665	476	10	all	all	DET
ejpam-4665	476	11	y	y	PROPN
ejpam-4665	476	12	∈	∈	PROPN
ejpam-4665	476	13	ng(x	ng(x	NUM
ejpam-4665	476	14	)	)	PUNCT
ejpam-4665	476	15	,	,	PUNCT
ejpam-4665	476	16	then	then	ADV
ejpam-4665	476	17	⟨v	⟨v	NUM
ejpam-4665	476	18	(	(	PUNCT
ejpam-4665	476	19	g[h])\w	g[h])\w	INTJ
ejpam-4665	476	20	⟩	⟩	PROPN
ejpam-4665	476	21	has	have	VERB
ejpam-4665	476	22	no	no	DET
ejpam-4665	476	23	isolated	isolated	ADJ
ejpam-4665	476	24	vertex	vertex	NOUN
ejpam-4665	476	25	.	.	PUNCT
ejpam-4665	477	1	if	if	SCONJ
ejpam-4665	477	2	ty	ty	PRON
ejpam-4665	477	3	=	=	SYM
ejpam-4665	477	4	v	v	NOUN
ejpam-4665	477	5	(	(	PUNCT
ejpam-4665	477	6	h	h	NOUN
ejpam-4665	477	7	)	)	PUNCT
ejpam-4665	477	8	,	,	PUNCT
ejpam-4665	477	9	for	for	ADP
ejpam-4665	477	10	some	some	DET
ejpam-4665	477	11	y	y	PROPN
ejpam-4665	477	12	∈	∈	PROPN
ejpam-4665	477	13	ng(x	ng(x	NUM
ejpam-4665	477	14	)	)	PUNCT
ejpam-4665	477	15	,	,	PUNCT
ejpam-4665	477	16	then	then	ADV
ejpam-4665	477	17	tx	tx	PROPN
ejpam-4665	477	18	is	be	AUX
ejpam-4665	477	19	a	a	DET
ejpam-4665	477	20	restrained	restrained	ADJ
ejpam-4665	477	21	2	2	NUM
ejpam-4665	477	22	-	-	PUNCT
ejpam-4665	477	23	locating	locate	VERB
ejpam-4665	477	24	point	point	NOUN
ejpam-4665	477	25	-	-	PUNCT
ejpam-4665	477	26	wise	wise	ADJ
ejpam-4665	477	27	non	non	ADJ
ejpam-4665	477	28	-	-	ADJ
ejpam-4665	477	29	dominating	dominating	ADJ
ejpam-4665	477	30	set	set	NOUN
ejpam-4665	477	31	.	.	PUNCT
ejpam-4665	478	1	thus	thus	ADV
ejpam-4665	478	2	,	,	PUNCT
ejpam-4665	478	3	⟨v	⟨v	X
ejpam-4665	478	4	(	(	PUNCT
ejpam-4665	478	5	h)\tx⟩	h)\tx⟩	PRON
ejpam-4665	478	6	has	have	VERB
ejpam-4665	478	7	no	no	DET
ejpam-4665	478	8	isolated	isolated	ADJ
ejpam-4665	478	9	vertex	vertex	NOUN
ejpam-4665	478	10	.	.	PUNCT
ejpam-4665	479	1	hence	hence	ADV
ejpam-4665	479	2	,	,	PUNCT
ejpam-4665	479	3	⟨v	⟨v	PROPN
ejpam-4665	479	4	(	(	PUNCT
ejpam-4665	479	5	g[h])\w	g[h])\w	INTJ
ejpam-4665	479	6	⟩	⟩	PROPN
ejpam-4665	479	7	has	have	VERB
ejpam-4665	479	8	no	no	DET
ejpam-4665	479	9	isolated	isolated	ADJ
ejpam-4665	479	10	vertex	vertex	NOUN
ejpam-4665	479	11	.	.	PUNCT
ejpam-4665	480	1	therefore	therefore	ADV
ejpam-4665	480	2	,	,	PUNCT
ejpam-4665	480	3	w	w	PROPN
ejpam-4665	480	4	is	be	AUX
ejpam-4665	480	5	a	a	DET
ejpam-4665	480	6	restrained	restrained	ADJ
ejpam-4665	480	7	2	2	NUM
ejpam-4665	480	8	-	-	PUNCT
ejpam-4665	480	9	resolving	resolve	VERB
ejpam-4665	480	10	hop	hop	NOUN
ejpam-4665	480	11	dominating	dominating	NOUN
ejpam-4665	480	12	set	set	VERB
ejpam-4665	480	13	in	in	ADP
ejpam-4665	480	14	g[h	g[h	PROPN
ejpam-4665	480	15	]	]	PUNCT
ejpam-4665	480	16	.	.	PUNCT
ejpam-4665	481	1	the	the	DET
ejpam-4665	481	2	following	follow	VERB
ejpam-4665	481	3	results	result	NOUN
ejpam-4665	481	4	follow	follow	VERB
ejpam-4665	481	5	from	from	ADP
ejpam-4665	481	6	theorem	theorem	ADJ
ejpam-4665	481	7	15	15	NUM
ejpam-4665	481	8	.	.	PUNCT
ejpam-4665	482	1	corollary	corollary	ADJ
ejpam-4665	482	2	7	7	NUM
ejpam-4665	482	3	.	.	PUNCT
ejpam-4665	483	1	let	let	VERB
ejpam-4665	483	2	g	g	NOUN
ejpam-4665	483	3	and	and	CCONJ
ejpam-4665	483	4	h	h	NOUN
ejpam-4665	483	5	be	be	AUX
ejpam-4665	483	6	nontrivial	nontrivial	ADJ
ejpam-4665	483	7	connected	connect	VERB
ejpam-4665	483	8	graphs	graph	NOUN
ejpam-4665	483	9	such	such	ADJ
ejpam-4665	483	10	that	that	SCONJ
ejpam-4665	483	11	g	g	PROPN
ejpam-4665	483	12	is	be	AUX
ejpam-4665	483	13	not	not	PART
ejpam-4665	483	14	freeequidistant	freeequidistant	ADJ
ejpam-4665	483	15	..	..	PUNCT
ejpam-4665	483	16	then	then	ADV
ejpam-4665	483	17	,	,	PUNCT
ejpam-4665	483	18	γr2rh(g[h	γr2rh(g[h	ADJ
ejpam-4665	483	19	]	]	X
ejpam-4665	483	20	)	)	PUNCT
ejpam-4665	483	21	≤	≤	NOUN
ejpam-4665	484	1	n	n	CCONJ
ejpam-4665	484	2	·	·	PUNCT
ejpam-4665	484	3	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4665	484	4	)	)	PUNCT
ejpam-4665	485	1	+	+	NOUN
ejpam-4665	485	2	m	m	NOUN
ejpam-4665	485	3	·	·	PUNCT
ejpam-4665	485	4	γ2l(h	γ2l(h	PROPN
ejpam-4665	485	5	)	)	PUNCT
ejpam-4665	486	1	+	+	CCONJ
ejpam-4665	486	2	p	p	X
ejpam-4665	486	3	·	·	PUNCT
ejpam-4665	486	4	rlnpnd	rlnpnd	NOUN
ejpam-4665	486	5	2	2	NUM
ejpam-4665	486	6	(	(	PUNCT
ejpam-4665	486	7	h	h	NOUN
ejpam-4665	486	8	)	)	PUNCT
ejpam-4665	486	9	,	,	PUNCT
ejpam-4665	486	10	where	where	SCONJ
ejpam-4665	486	11	n+m+	n+m+	VERB
ejpam-4665	486	12	p	p	X
ejpam-4665	486	13	=	=	X
ejpam-4665	486	14	|v	|v	X
ejpam-4665	486	15	(	(	PUNCT
ejpam-4665	486	16	g)|	g)|	NOUN
ejpam-4665	486	17	with	with	ADP
ejpam-4665	486	18	|eq1(g)|	|eq1(g)|	NOUN
ejpam-4665	486	19	=	=	SYM
ejpam-4665	486	20	n	n	CCONJ
ejpam-4665	486	21	,	,	PUNCT
ejpam-4665	486	22	|eq2(g)|	|eq2(g)|	X
ejpam-4665	486	23	=	=	PUNCT
ejpam-4665	486	24	m	m	VERB
ejpam-4665	486	25	and	and	CCONJ
ejpam-4665	486	26	|fr(g)|	|fr(g)|	NOUN
ejpam-4665	486	27	=	=	SYM
ejpam-4665	487	1	p.	p.	NOUN
ejpam-4665	487	2	corollary	corollary	NOUN
ejpam-4665	487	3	8	8	NUM
ejpam-4665	487	4	.	.	PUNCT
ejpam-4665	488	1	let	let	VERB
ejpam-4665	488	2	g	g	NOUN
ejpam-4665	488	3	and	and	CCONJ
ejpam-4665	488	4	h	h	NOUN
ejpam-4665	488	5	be	be	VERB
ejpam-4665	488	6	any	any	DET
ejpam-4665	488	7	nontrivial	nontrivial	ADJ
ejpam-4665	488	8	connected	connect	VERB
ejpam-4665	488	9	graph	graph	NOUN
ejpam-4665	488	10	and	and	CCONJ
ejpam-4665	488	11	g	g	NOUN
ejpam-4665	488	12	is	be	AUX
ejpam-4665	488	13	a	a	DET
ejpam-4665	488	14	free	free	ADJ
ejpam-4665	488	15	-	-	PUNCT
ejpam-4665	488	16	equidistant	equidistant	NOUN
ejpam-4665	488	17	.	.	PUNCT
ejpam-4665	489	1	then	then	ADV
ejpam-4665	489	2	γr2rh(g[h	γr2rh(g[h	ADJ
ejpam-4665	489	3	]	]	X
ejpam-4665	489	4	)	)	PUNCT
ejpam-4665	489	5	=	=	PRON
ejpam-4665	489	6	{	{	PUNCT
ejpam-4665	489	7	|v	|v	PROPN
ejpam-4665	489	8	(	(	PUNCT
ejpam-4665	489	9	g)|	g)|	NOUN
ejpam-4665	489	10	·	·	PUNCT
ejpam-4665	489	11	lnpnd	lnpnd	ADJ
ejpam-4665	489	12	2	2	NUM
ejpam-4665	489	13	(	(	PUNCT
ejpam-4665	489	14	h	h	NOUN
ejpam-4665	489	15	)	)	PUNCT
ejpam-4665	489	16	,	,	PUNCT
ejpam-4665	489	17	if	if	SCONJ
ejpam-4665	489	18	lnpnd	lnpnd	ADJ
ejpam-4665	489	19	2	2	NUM
ejpam-4665	489	20	(	(	PUNCT
ejpam-4665	489	21	h	h	NOUN
ejpam-4665	489	22	)	)	PUNCT
ejpam-4665	489	23	̸=	̸=	PROPN
ejpam-4665	489	24	v	v	NOUN
ejpam-4665	489	25	(	(	PUNCT
ejpam-4665	489	26	h	h	NOUN
ejpam-4665	489	27	)	)	PUNCT
ejpam-4665	489	28	|v	|v	PROPN
ejpam-4665	489	29	(	(	PUNCT
ejpam-4665	489	30	g)|	g)|	NOUN
ejpam-4665	489	31	·	·	PUNCT
ejpam-4665	489	32	rlnpnd	rlnpnd	NOUN
ejpam-4665	489	33	2	2	NUM
ejpam-4665	489	34	(	(	PUNCT
ejpam-4665	489	35	h	h	NOUN
ejpam-4665	489	36	)	)	PUNCT
ejpam-4665	489	37	,	,	PUNCT
ejpam-4665	489	38	otherwise	otherwise	ADV
ejpam-4665	489	39	.	.	PUNCT
ejpam-4665	490	1	example	example	NOUN
ejpam-4665	491	1	6	6	NUM
ejpam-4665	491	2	.	.	X
ejpam-4665	492	1	for	for	ADP
ejpam-4665	492	2	any	any	DET
ejpam-4665	492	3	nontrivial	nontrivial	ADJ
ejpam-4665	492	4	connected	connect	VERB
ejpam-4665	492	5	graph	graph	NOUN
ejpam-4665	492	6	g	g	NOUN
ejpam-4665	492	7	of	of	ADP
ejpam-4665	492	8	order	order	NOUN
ejpam-4665	492	9	n	n	PRON
ejpam-4665	492	10	≥	≥	NOUN
ejpam-4665	492	11	3	3	NUM
ejpam-4665	492	12	,	,	PUNCT
ejpam-4665	492	13	(	(	PUNCT
ejpam-4665	492	14	i	i	NOUN
ejpam-4665	492	15	)	)	PUNCT
ejpam-4665	492	16	γr2rh(g[h	γr2rh(g[h	NOUN
ejpam-4665	492	17	]	]	X
ejpam-4665	492	18	)	)	PUNCT
ejpam-4665	492	19	=	=	SYM
ejpam-4665	492	20	n	n	X
ejpam-4665	492	21	·	·	PUNCT
ejpam-4665	492	22	(	(	PUNCT
ejpam-4665	492	23	⌈	⌈	NOUN
ejpam-4665	492	24	m+1	m+1	NUM
ejpam-4665	492	25	2	2	NUM
ejpam-4665	492	26	⌉	⌉	NOUN
ejpam-4665	492	27	)	)	PUNCT
ejpam-4665	492	28	if	if	SCONJ
ejpam-4665	492	29	h	h	NOUN
ejpam-4665	492	30	=	=	VERB
ejpam-4665	492	31	pm	pm	NOUN
ejpam-4665	492	32	;	;	PUNCT
ejpam-4665	492	33	(	(	PUNCT
ejpam-4665	492	34	ii	ii	NOUN
ejpam-4665	492	35	)	)	PUNCT
ejpam-4665	492	36	γr2rh(g[h	γr2rh(g[h	NOUN
ejpam-4665	492	37	]	]	X
ejpam-4665	492	38	)	)	PUNCT
ejpam-4665	492	39	=	=	SYM
ejpam-4665	492	40	n	n	X
ejpam-4665	492	41	·	·	PUNCT
ejpam-4665	492	42	(	(	PUNCT
ejpam-4665	492	43	⌈	⌈	SYM
ejpam-4665	492	44	m	m	PROPN
ejpam-4665	492	45	2	2	NUM
ejpam-4665	492	46	⌉	⌉	NOUN
ejpam-4665	492	47	)	)	PUNCT
ejpam-4665	492	48	if	if	SCONJ
ejpam-4665	492	49	h	h	NOUN
ejpam-4665	492	50	=	=	NOUN
ejpam-4665	492	51	cm	cm	NOUN
ejpam-4665	492	52	.	.	PUNCT
ejpam-4665	493	1	(	(	PUNCT
ejpam-4665	493	2	iii	iii	NOUN
ejpam-4665	493	3	)	)	PUNCT
ejpam-4665	493	4	γr2rh(g[h	γr2rh(g[h	NOUN
ejpam-4665	493	5	]	]	X
ejpam-4665	493	6	)	)	PUNCT
ejpam-4665	493	7	=	=	SYM
ejpam-4665	493	8	n	n	PROPN
ejpam-4665	493	9	·	·	PUNCT
ejpam-4665	493	10	lnpnd2	lnpnd2	X
ejpam-4665	493	11	(	(	PUNCT
ejpam-4665	493	12	h	h	NOUN
ejpam-4665	493	13	)	)	PUNCT
ejpam-4665	493	14	if	if	SCONJ
ejpam-4665	493	15	g	g	PROPN
ejpam-4665	493	16	=	=	PROPN
ejpam-4665	493	17	kn	kn	PROPN
ejpam-4665	493	18	.	.	PUNCT
ejpam-4665	494	1	acknowledgements	acknowledgement	VERB
ejpam-4665	494	2	the	the	DET
ejpam-4665	494	3	authors	author	NOUN
ejpam-4665	494	4	would	would	AUX
ejpam-4665	494	5	like	like	VERB
ejpam-4665	494	6	to	to	PART
ejpam-4665	494	7	thank	thank	VERB
ejpam-4665	494	8	the	the	DET
ejpam-4665	494	9	department	department	NOUN
ejpam-4665	494	10	of	of	ADP
ejpam-4665	494	11	science	science	NOUN
ejpam-4665	494	12	and	and	CCONJ
ejpam-4665	494	13	technology	technology	NOUN
ejpam-4665	494	14	accelerated	accelerate	VERB
ejpam-4665	494	15	science	science	NOUN
ejpam-4665	494	16	and	and	CCONJ
ejpam-4665	494	17	technology	technology	NOUN
ejpam-4665	494	18	human	human	ADJ
ejpam-4665	494	19	resource	resource	NOUN
ejpam-4665	494	20	development	development	NOUN
ejpam-4665	494	21	program	program	NOUN
ejpam-4665	494	22	(	(	PUNCT
ejpam-4665	494	23	dost	dost	NOUN
ejpam-4665	494	24	-	-	PUNCT
ejpam-4665	494	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4665	494	26	and	and	CCONJ
ejpam-4665	494	27	msu	msu	PROPN
ejpam-4665	494	28	-	-	PUNCT
ejpam-4665	494	29	iligan	iligan	PROPN
ejpam-4665	494	30	institute	institute	PROPN
ejpam-4665	494	31	of	of	ADP
ejpam-4665	494	32	technology	technology	PROPN
ejpam-4665	494	33	,	,	PUNCT
ejpam-4665	494	34	iligan	iligan	PROPN
ejpam-4665	494	35	city	city	PROPN
ejpam-4665	494	36	,	,	PUNCT
ejpam-4665	494	37	philippines	philippine	NOUN
ejpam-4665	494	38	for	for	ADP
ejpam-4665	494	39	funding	fund	VERB
ejpam-4665	494	40	this	this	DET
ejpam-4665	494	41	research	research	NOUN
ejpam-4665	494	42	.	.	PUNCT
ejpam-4665	495	1	references	reference	NOUN
ejpam-4665	495	2	302	302	NUM
ejpam-4665	495	3	references	reference	NOUN
ejpam-4665	495	4	[	[	X
ejpam-4665	495	5	1	1	NUM
ejpam-4665	495	6	]	]	PUNCT
ejpam-4665	495	7	c.	c.	PROPN
ejpam-4665	495	8	berge	berge	PROPN
ejpam-4665	495	9	.	.	PUNCT
ejpam-4665	496	1	theorie	theorie	PROPN
ejpam-4665	496	2	des	des	PROPN
ejpam-4665	496	3	graphes	graphes	PROPN
ejpam-4665	496	4	et	et	PROPN
ejpam-4665	496	5	ses	ses	PROPN
ejpam-4665	496	6	applications	application	NOUN
ejpam-4665	496	7	.	.	PUNCT
ejpam-4665	497	1	methuen	methuen	PROPN
ejpam-4665	497	2	(	(	PUNCT
ejpam-4665	497	3	london	london	PROPN
ejpam-4665	497	4	)	)	PUNCT
ejpam-4665	497	5	and	and	CCONJ
ejpam-4665	497	6	wiley	wiley	PROPN
ejpam-4665	497	7	(	(	PUNCT
ejpam-4665	497	8	new	new	PROPN
ejpam-4665	497	9	york	york	PROPN
ejpam-4665	497	10	)	)	PUNCT
ejpam-4665	497	11	,	,	PUNCT
ejpam-4665	497	12	1962	1962	NUM
ejpam-4665	497	13	.	.	PUNCT
ejpam-4665	498	1	[	[	X
ejpam-4665	498	2	2	2	X
ejpam-4665	498	3	]	]	PUNCT
ejpam-4665	498	4	j.	j.	PROPN
ejpam-4665	498	5	a.	a.	PROPN
ejpam-4665	498	6	bondy	bondy	PROPN
ejpam-4665	498	7	and	and	CCONJ
ejpam-4665	498	8	u.	u.	PROPN
ejpam-4665	498	9	s.	s.	PROPN
ejpam-4665	498	10	r.	r.	PROPN
ejpam-4665	498	11	murty	murty	PROPN
ejpam-4665	498	12	.	.	PUNCT
ejpam-4665	499	1	graph	graph	NOUN
ejpam-4665	499	2	theory	theory	NOUN
ejpam-4665	499	3	.	.	PUNCT
ejpam-4665	500	1	springer	springer	NOUN
ejpam-4665	500	2	,	,	PUNCT
ejpam-4665	500	3	2008	2008	NUM
ejpam-4665	500	4	.	.	PUNCT
ejpam-4665	501	1	[	[	X
ejpam-4665	501	2	3	3	NUM
ejpam-4665	501	3	]	]	X
ejpam-4665	501	4	f.	f.	PROPN
ejpam-4665	501	5	buckley	buckley	PROPN
ejpam-4665	501	6	and	and	CCONJ
ejpam-4665	501	7	f.	f.	PROPN
ejpam-4665	501	8	harary	harary	PROPN
ejpam-4665	501	9	.	.	PUNCT
ejpam-4665	502	1	distance	distance	NOUN
ejpam-4665	502	2	in	in	ADP
ejpam-4665	502	3	graphs	graph	NOUN
ejpam-4665	502	4	.	.	PUNCT
ejpam-4665	503	1	addison	addison	PROPN
ejpam-4665	503	2	-	-	PUNCT
ejpam-4665	503	3	wesley	wesley	PROPN
ejpam-4665	503	4	,	,	PUNCT
ejpam-4665	503	5	redwood	redwood	NOUN
ejpam-4665	503	6	city	city	NOUN
ejpam-4665	503	7	,	,	PUNCT
ejpam-4665	503	8	ca	ca	NOUN
ejpam-4665	503	9	,	,	PUNCT
ejpam-4665	503	10	1990	1990	NUM
ejpam-4665	503	11	.	.	PUNCT
ejpam-4665	504	1	[	[	X
ejpam-4665	504	2	4	4	X
ejpam-4665	504	3	]	]	X
ejpam-4665	504	4	j.	j.	PROPN
ejpam-4665	504	5	cabaro	cabaro	PROPN
ejpam-4665	504	6	and	and	CCONJ
ejpam-4665	504	7	h.	h.	PROPN
ejpam-4665	504	8	rara	rara	PROPN
ejpam-4665	504	9	.	.	PUNCT
ejpam-4665	505	1	restrained	restrain	VERB
ejpam-4665	505	2	2	2	NUM
ejpam-4665	505	3	-	-	PUNCT
ejpam-4665	505	4	resolving	resolve	VERB
ejpam-4665	505	5	dominating	dominating	NOUN
ejpam-4665	505	6	sets	set	NOUN
ejpam-4665	505	7	in	in	ADP
ejpam-4665	505	8	the	the	DET
ejpam-4665	505	9	join	join	NOUN
ejpam-4665	505	10	and	and	CCONJ
ejpam-4665	505	11	corona	corona	PROPN
ejpam-4665	505	12	and	and	CCONJ
ejpam-4665	505	13	lexicographic	lexicographic	ADJ
ejpam-4665	505	14	product	product	NOUN
ejpam-4665	505	15	of	of	ADP
ejpam-4665	505	16	two	two	NUM
ejpam-4665	505	17	graphs	graph	NOUN
ejpam-4665	505	18	.	.	PUNCT
ejpam-4665	506	1	european	european	ADJ
ejpam-4665	506	2	journal	journal	PROPN
ejpam-4665	506	3	of	of	ADP
ejpam-4665	506	4	pure	pure	ADJ
ejpam-4665	506	5	and	and	CCONJ
ejpam-4665	506	6	applied	applied	ADJ
ejpam-4665	506	7	mathematics	mathematic	NOUN
ejpam-4665	506	8	,	,	PUNCT
ejpam-4665	506	9	15(3):1047–1053	15(3):1047–1053	NUM
ejpam-4665	506	10	,	,	PUNCT
ejpam-4665	506	11	2022	2022	NUM
ejpam-4665	506	12	.	.	PUNCT
ejpam-4665	507	1	[	[	X
ejpam-4665	507	2	5	5	X
ejpam-4665	507	3	]	]	PUNCT
ejpam-4665	507	4	j.	j.	PROPN
ejpam-4665	507	5	cabaro	cabaro	PROPN
ejpam-4665	507	6	and	and	CCONJ
ejpam-4665	507	7	h.	h.	PROPN
ejpam-4665	507	8	rara	rara	PROPN
ejpam-4665	507	9	.	.	PUNCT
ejpam-4665	508	1	2	2	NUM
ejpam-4665	508	2	-	-	PUNCT
ejpam-4665	508	3	resolving	resolve	VERB
ejpam-4665	508	4	sets	set	NOUN
ejpam-4665	508	5	in	in	ADP
ejpam-4665	508	6	the	the	DET
ejpam-4665	508	7	join	join	NOUN
ejpam-4665	508	8	,	,	PUNCT
ejpam-4665	508	9	and	and	CCONJ
ejpam-4665	508	10	corona	corona	NOUN
ejpam-4665	508	11	of	of	ADP
ejpam-4665	508	12	two	two	NUM
ejpam-4665	508	13	graphs	graph	NOUN
ejpam-4665	508	14	.	.	PUNCT
ejpam-4665	509	1	european	european	ADJ
ejpam-4665	509	2	journal	journal	PROPN
ejpam-4665	509	3	of	of	ADP
ejpam-4665	509	4	pure	pure	ADJ
ejpam-4665	509	5	and	and	CCONJ
ejpam-4665	509	6	applied	applied	ADJ
ejpam-4665	509	7	mathematics	mathematic	NOUN
ejpam-4665	509	8	,	,	PUNCT
ejpam-4665	509	9	14(3):773–782	14(3):773–782	PROPN
ejpam-4665	509	10	,	,	PUNCT
ejpam-4665	509	11	2022	2022	NUM
ejpam-4665	509	12	.	.	PUNCT
ejpam-4665	510	1	[	[	X
ejpam-4665	510	2	6	6	NUM
ejpam-4665	510	3	]	]	PUNCT
ejpam-4665	510	4	j.	j.	PROPN
ejpam-4665	510	5	cabaro	cabaro	PROPN
ejpam-4665	510	6	and	and	CCONJ
ejpam-4665	510	7	h.	h.	PROPN
ejpam-4665	510	8	rara	rara	PROPN
ejpam-4665	510	9	.	.	PUNCT
ejpam-4665	511	1	on	on	ADP
ejpam-4665	511	2	2	2	NUM
ejpam-4665	511	3	-	-	PUNCT
ejpam-4665	511	4	resolving	resolve	VERB
ejpam-4665	511	5	dominating	dominating	NOUN
ejpam-4665	511	6	sets	set	NOUN
ejpam-4665	511	7	in	in	ADP
ejpam-4665	511	8	the	the	DET
ejpam-4665	511	9	join	join	NOUN
ejpam-4665	511	10	and	and	CCONJ
ejpam-4665	511	11	corona	corona	PROPN
ejpam-4665	511	12	and	and	CCONJ
ejpam-4665	511	13	lexicographic	lexicographic	ADJ
ejpam-4665	511	14	product	product	NOUN
ejpam-4665	511	15	of	of	ADP
ejpam-4665	511	16	graphs	graph	NOUN
ejpam-4665	511	17	.	.	PUNCT
ejpam-4665	512	1	european	european	ADJ
ejpam-4665	512	2	journal	journal	PROPN
ejpam-4665	512	3	of	of	ADP
ejpam-4665	512	4	pure	pure	ADJ
ejpam-4665	512	5	and	and	CCONJ
ejpam-4665	512	6	applied	applied	ADJ
ejpam-4665	512	7	mathematics	mathematic	NOUN
ejpam-4665	512	8	,	,	PUNCT
ejpam-4665	512	9	15(3):1417–1425	15(3):1417–1425	NUM
ejpam-4665	512	10	,	,	PUNCT
ejpam-4665	512	11	2022	2022	NUM
ejpam-4665	512	12	.	.	PUNCT
ejpam-4665	513	1	[	[	X
ejpam-4665	513	2	7	7	X
ejpam-4665	513	3	]	]	X
ejpam-4665	513	4	j.	j.	PROPN
ejpam-4665	513	5	cabaro	cabaro	PROPN
ejpam-4665	513	6	and	and	CCONJ
ejpam-4665	513	7	h.	h.	PROPN
ejpam-4665	513	8	rara	rara	PROPN
ejpam-4665	513	9	.	.	PUNCT
ejpam-4665	514	1	on	on	ADP
ejpam-4665	514	2	variations	variation	NOUN
ejpam-4665	514	3	of	of	ADP
ejpam-4665	514	4	2	2	NUM
ejpam-4665	514	5	-	-	PUNCT
ejpam-4665	514	6	resolving	resolve	VERB
ejpam-4665	514	7	sets	set	NOUN
ejpam-4665	514	8	in	in	ADP
ejpam-4665	514	9	graphs	graph	NOUN
ejpam-4665	514	10	.	.	PUNCT
ejpam-4665	515	1	phd	phd	NOUN
ejpam-4665	515	2	thesis	thesis	PROPN
ejpam-4665	515	3	,	,	PUNCT
ejpam-4665	515	4	mindanao	mindanao	PROPN
ejpam-4665	515	5	state	state	PROPN
ejpam-4665	515	6	universityiligan	universityiligan	PROPN
ejpam-4665	515	7	institute	institute	PROPN
ejpam-4665	515	8	of	of	ADP
ejpam-4665	515	9	technology	technology	NOUN
ejpam-4665	515	10	,	,	PUNCT
ejpam-4665	515	11	2022	2022	NUM
ejpam-4665	515	12	.	.	PUNCT
ejpam-4665	516	1	[	[	X
ejpam-4665	516	2	8	8	X
ejpam-4665	516	3	]	]	X
ejpam-4665	516	4	j.	j.	PROPN
ejpam-4665	516	5	cabaro	cabaro	PROPN
ejpam-4665	516	6	and	and	CCONJ
ejpam-4665	516	7	h.	h.	PROPN
ejpam-4665	516	8	rara	rara	PROPN
ejpam-4665	516	9	.	.	PUNCT
ejpam-4665	517	1	restrained	restrain	VERB
ejpam-4665	517	2	2	2	NUM
ejpam-4665	517	3	-	-	PUNCT
ejpam-4665	517	4	resolving	resolve	VERB
ejpam-4665	517	5	sets	set	NOUN
ejpam-4665	517	6	in	in	ADP
ejpam-4665	517	7	the	the	DET
ejpam-4665	517	8	join	join	NOUN
ejpam-4665	517	9	and	and	CCONJ
ejpam-4665	517	10	corona	corona	PROPN
ejpam-4665	517	11	and	and	CCONJ
ejpam-4665	517	12	lexicographic	lexicographic	ADJ
ejpam-4665	517	13	product	product	NOUN
ejpam-4665	517	14	of	of	ADP
ejpam-4665	517	15	graphs	graph	NOUN
ejpam-4665	517	16	.	.	PUNCT
ejpam-4665	518	1	european	european	ADJ
ejpam-4665	518	2	journal	journal	PROPN
ejpam-4665	518	3	of	of	ADP
ejpam-4665	518	4	pure	pure	ADJ
ejpam-4665	518	5	and	and	CCONJ
ejpam-4665	518	6	applied	applied	ADJ
ejpam-4665	518	7	mathematics	mathematic	NOUN
ejpam-4665	518	8	,	,	PUNCT
ejpam-4665	518	9	15(3):1229–1236	15(3):1229–1236	NUM
ejpam-4665	518	10	,	,	PUNCT
ejpam-4665	518	11	2022	2022	NUM
ejpam-4665	518	12	.	.	PUNCT
ejpam-4665	519	1	[	[	X
ejpam-4665	519	2	9	9	NUM
ejpam-4665	519	3	]	]	PUNCT
ejpam-4665	519	4	a.	a.	NOUN
ejpam-4665	519	5	estrada	estrada	PROPN
ejpam-4665	519	6	-	-	PUNCT
ejpam-4665	519	7	moreno	moreno	PROPN
ejpam-4665	519	8	,	,	PUNCT
ejpam-4665	519	9	j.a	j.a	PROPN
ejpam-4665	519	10	.	.	PROPN
ejpam-4665	519	11	rodriguez	rodriguez	PROPN
ejpam-4665	519	12	-	-	PUNCT
ejpam-4665	519	13	velasquez	velasquez	PROPN
ejpam-4665	519	14	,	,	PUNCT
ejpam-4665	519	15	and	and	CCONJ
ejpam-4665	519	16	i.g	i.g	PROPN
ejpam-4665	519	17	yero	yero	NOUN
ejpam-4665	519	18	.	.	PUNCT
ejpam-4665	520	1	the	the	DET
ejpam-4665	520	2	kmetric	kmetric	ADJ
ejpam-4665	520	3	dimension	dimension	NOUN
ejpam-4665	520	4	of	of	ADP
ejpam-4665	520	5	a	a	DET
ejpam-4665	520	6	graph	graph	NOUN
ejpam-4665	520	7	.	.	PUNCT
ejpam-4665	521	1	appl	appl	PROPN
ejpam-4665	521	2	.	.	PROPN
ejpam-4665	522	1	math	math	PROPN
ejpam-4665	522	2	.	.	PUNCT
ejpam-4665	523	1	inf	inf	PROPN
ejpam-4665	523	2	.	.	PUNCT
ejpam-4665	524	1	sci	sci	PROPN
ejpam-4665	524	2	.	.	PROPN
ejpam-4665	524	3	,	,	PUNCT
ejpam-4665	524	4	9:2829–2840	9:2829–2840	NUM
ejpam-4665	524	5	,	,	PUNCT
ejpam-4665	524	6	2015	2015	NUM
ejpam-4665	524	7	.	.	PUNCT
ejpam-4665	525	1	[	[	X
ejpam-4665	525	2	10	10	NUM
ejpam-4665	525	3	]	]	X
ejpam-4665	525	4	f.	f.	PROPN
ejpam-4665	525	5	harary	harary	PROPN
ejpam-4665	525	6	and	and	CCONJ
ejpam-4665	525	7	r.	r.	PROPN
ejpam-4665	525	8	melter	melter	NOUN
ejpam-4665	525	9	.	.	PUNCT
ejpam-4665	526	1	on	on	ADP
ejpam-4665	526	2	the	the	DET
ejpam-4665	526	3	metric	metric	ADJ
ejpam-4665	526	4	dimension	dimension	NOUN
ejpam-4665	526	5	of	of	ADP
ejpam-4665	526	6	a	a	DET
ejpam-4665	526	7	graph	graph	NOUN
ejpam-4665	526	8	.	.	PUNCT
ejpam-4665	526	9	ars	ars	PROPN
ejpam-4665	526	10	combinatoria	combinatoria	NOUN
ejpam-4665	526	11	,	,	PUNCT
ejpam-4665	526	12	2:191–195	2:191–195	NUM
ejpam-4665	526	13	,	,	PUNCT
ejpam-4665	526	14	1976	1976	NUM
ejpam-4665	526	15	.	.	PUNCT
ejpam-4665	527	1	[	[	X
ejpam-4665	527	2	11	11	NUM
ejpam-4665	527	3	]	]	PUNCT
ejpam-4665	527	4	a.	a.	NOUN
ejpam-4665	527	5	mahistrado	mahistrado	NOUN
ejpam-4665	527	6	and	and	CCONJ
ejpam-4665	527	7	h.	h.	PROPN
ejpam-4665	527	8	rara	rara	PROPN
ejpam-4665	527	9	.	.	PUNCT
ejpam-4665	528	1	on	on	ADP
ejpam-4665	528	2	2	2	NUM
ejpam-4665	528	3	-	-	PUNCT
ejpam-4665	528	4	resolving	resolve	VERB
ejpam-4665	528	5	hop	hop	NOUN
ejpam-4665	528	6	dominating	dominating	NOUN
ejpam-4665	528	7	sets	set	NOUN
ejpam-4665	528	8	in	in	ADP
ejpam-4665	528	9	the	the	DET
ejpam-4665	528	10	join	join	NOUN
ejpam-4665	528	11	and	and	CCONJ
ejpam-4665	528	12	corona	corona	PROPN
ejpam-4665	528	13	and	and	CCONJ
ejpam-4665	528	14	lexicographic	lexicographic	ADJ
ejpam-4665	528	15	product	product	NOUN
ejpam-4665	528	16	of	of	ADP
ejpam-4665	528	17	graphs	graph	NOUN
ejpam-4665	528	18	.	.	PUNCT
ejpam-4665	529	1	european	european	ADJ
ejpam-4665	529	2	journal	journal	PROPN
ejpam-4665	529	3	of	of	ADP
ejpam-4665	529	4	pure	pure	ADJ
ejpam-4665	529	5	and	and	CCONJ
ejpam-4665	529	6	applied	applied	ADJ
ejpam-4665	529	7	mathematics	mathematic	NOUN
ejpam-4665	529	8	,	,	PUNCT
ejpam-4665	529	9	15(4):1982–1997	15(4):1982–1997	NUM
ejpam-4665	529	10	,	,	PUNCT
ejpam-4665	529	11	2022	2022	NUM
ejpam-4665	529	12	.	.	PUNCT
ejpam-4665	530	1	[	[	X
ejpam-4665	530	2	12	12	NUM
ejpam-4665	530	3	]	]	X
ejpam-4665	530	4	j.s	j.s	PROPN
ejpam-4665	530	5	.	.	PROPN
ejpam-4665	530	6	mohamad	mohamad	PROPN
ejpam-4665	530	7	and	and	CCONJ
ejpam-4665	530	8	h.m	h.m	PROPN
ejpam-4665	530	9	.	.	PROPN
ejpam-4665	530	10	rara	rara	PROPN
ejpam-4665	530	11	.	.	PUNCT
ejpam-4665	530	12	resolving	resolve	VERB
ejpam-4665	530	13	hop	hop	NOUN
ejpam-4665	530	14	domination	domination	NOUN
ejpam-4665	530	15	in	in	ADP
ejpam-4665	530	16	graphs	graph	NOUN
ejpam-4665	530	17	.	.	PUNCT
ejpam-4665	531	1	european	european	ADJ
ejpam-4665	531	2	journal	journal	PROPN
ejpam-4665	531	3	of	of	ADP
ejpam-4665	531	4	pure	pure	ADJ
ejpam-4665	531	5	and	and	CCONJ
ejpam-4665	531	6	applied	applied	ADJ
ejpam-4665	531	7	mathematics	mathematic	NOUN
ejpam-4665	531	8	,	,	PUNCT
ejpam-4665	531	9	14(3):1015–1023	14(3):1015–1023	NUM
ejpam-4665	531	10	,	,	PUNCT
ejpam-4665	531	11	2021	2021	NUM
ejpam-4665	531	12	.	.	PUNCT
ejpam-4665	532	1	[	[	X
ejpam-4665	532	2	13	13	NUM
ejpam-4665	532	3	]	]	PUNCT
ejpam-4665	532	4	.b	.b	PROPN
ejpam-4665	532	5	.	.	PUNCT
ejpam-4665	533	1	monsanto	monsanto	PROPN
ejpam-4665	533	2	and	and	CCONJ
ejpam-4665	533	3	h.m	h.m	PROPN
ejpam-4665	533	4	.	.	PROPN
ejpam-4665	533	5	rara	rara	PROPN
ejpam-4665	533	6	.	.	PUNCT
ejpam-4665	534	1	resolving	resolve	VERB
ejpam-4665	534	2	restrained	restrained	ADJ
ejpam-4665	534	3	domination	domination	NOUN
ejpam-4665	534	4	in	in	ADP
ejpam-4665	534	5	graphs	graph	NOUN
ejpam-4665	534	6	.	.	PUNCT
ejpam-4665	535	1	european	european	ADJ
ejpam-4665	535	2	journal	journal	PROPN
ejpam-4665	535	3	of	of	ADP
ejpam-4665	535	4	pure	pure	ADJ
ejpam-4665	535	5	and	and	CCONJ
ejpam-4665	535	6	applied	applied	ADJ
ejpam-4665	535	7	mathematics	mathematic	NOUN
ejpam-4665	535	8	.	.	PUNCT
ejpam-4665	536	1	european	european	PROPN
ejpam-4665	536	2	journal	journal	PROPN
ejpam-4665	536	3	of	of	ADP
ejpam-4665	536	4	pure	pure	ADJ
ejpam-4665	536	5	and	and	CCONJ
ejpam-4665	536	6	applied	applied	ADJ
ejpam-4665	536	7	mathematics	mathematic	NOUN
ejpam-4665	536	8	,	,	PUNCT
ejpam-4665	536	9	14(3):829–841	14(3):829–841	PROPN
ejpam-4665	536	10	,	,	PUNCT
ejpam-4665	536	11	2021	2021	NUM
ejpam-4665	536	12	.	.	PUNCT
ejpam-4665	537	1	[	[	X
ejpam-4665	537	2	14	14	NUM
ejpam-4665	537	3	]	]	X
ejpam-4665	537	4	c.	c.	PROPN
ejpam-4665	537	5	natarajan	natarajan	PROPN
ejpam-4665	537	6	and	and	CCONJ
ejpam-4665	537	7	s.k	s.k	PROPN
ejpam-4665	537	8	.	.	PROPN
ejpam-4665	537	9	ayyaswamy	ayyaswamy	PROPN
ejpam-4665	537	10	.	.	PUNCT
ejpam-4665	538	1	hop	hop	PROPN
ejpam-4665	538	2	domination	domination	NOUN
ejpam-4665	538	3	in	in	ADP
ejpam-4665	538	4	graphs	graph	NOUN
ejpam-4665	538	5	-	-	PUNCT
ejpam-4665	538	6	ii	ii	NOUN
ejpam-4665	538	7	.	.	PUNCT
ejpam-4665	538	8	versita	versita	PROPN
ejpam-4665	538	9	,	,	PUNCT
ejpam-4665	538	10	23(2):187	23(2):187	NUM
ejpam-4665	538	11	–	–	PUNCT
ejpam-4665	538	12	199	199	NUM
ejpam-4665	538	13	,	,	PUNCT
ejpam-4665	538	14	2015	2015	NUM
ejpam-4665	538	15	.	.	PUNCT
ejpam-4665	539	1	references	reference	NOUN
ejpam-4665	539	2	303	303	NUM
ejpam-4665	539	3	[	[	X
ejpam-4665	539	4	15	15	NUM
ejpam-4665	539	5	]	]	X
ejpam-4665	539	6	jr	jr	PROPN
ejpam-4665	539	7	.	.	PROPN
ejpam-4665	539	8	r.	r.	PROPN
ejpam-4665	539	9	mollejon	mollejon	PROPN
ejpam-4665	539	10	s.	s.	PROPN
ejpam-4665	539	11	canoy	canoy	PROPN
ejpam-4665	539	12	and	and	CCONJ
ejpam-4665	539	13	j.g.canoy	j.g.canoy	PROPN
ejpam-4665	539	14	.	.	PUNCT
ejpam-4665	540	1	hop	hop	PROPN
ejpam-4665	540	2	dominating	dominating	NOUN
ejpam-4665	540	3	sets	set	NOUN
ejpam-4665	540	4	in	in	ADP
ejpam-4665	540	5	graphs	graph	NOUN
ejpam-4665	540	6	under	under	ADP
ejpam-4665	540	7	binary	binary	ADJ
ejpam-4665	540	8	operations	operation	NOUN
ejpam-4665	540	9	.	.	PUNCT
ejpam-4665	541	1	european	european	ADJ
ejpam-4665	541	2	journal	journal	PROPN
ejpam-4665	541	3	of	of	ADP
ejpam-4665	541	4	pure	pure	ADJ
ejpam-4665	541	5	and	and	CCONJ
ejpam-4665	541	6	applied	applied	ADJ
ejpam-4665	541	7	mathematics	mathematic	NOUN
ejpam-4665	541	8	,	,	PUNCT
ejpam-4665	541	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4665	541	10	,	,	PUNCT
ejpam-4665	541	11	2019	2019	NUM
ejpam-4665	541	12	.	.	PUNCT
ejpam-4665	542	1	[	[	X
ejpam-4665	542	2	16	16	X
ejpam-4665	542	3	]	]	X
ejpam-4665	542	4	v.	v.	ADP
ejpam-4665	542	5	saenpholphat	saenpholphat	PROPN
ejpam-4665	542	6	and	and	CCONJ
ejpam-4665	542	7	p.	p.	PROPN
ejpam-4665	542	8	zhang	zhang	PROPN
ejpam-4665	542	9	.	.	PUNCT
ejpam-4665	543	1	on	on	ADP
ejpam-4665	543	2	connected	connected	ADJ
ejpam-4665	543	3	resolvability	resolvability	NOUN
ejpam-4665	543	4	of	of	ADP
ejpam-4665	543	5	graphs	graph	NOUN
ejpam-4665	543	6	.	.	PUNCT
ejpam-4665	544	1	australian	australian	ADJ
ejpam-4665	544	2	journal	journal	NOUN
ejpam-4665	544	3	of	of	ADP
ejpam-4665	544	4	combinatorics	combinatoric	NOUN
ejpam-4665	544	5	,	,	PUNCT
ejpam-4665	544	6	28:26–37	28:26–37	NUM
ejpam-4665	544	7	,	,	PUNCT
ejpam-4665	544	8	2003	2003	NUM
ejpam-4665	544	9	.	.	PUNCT
ejpam-4665	545	1	[	[	X
ejpam-4665	545	2	17	17	NUM
ejpam-4665	545	3	]	]	PUNCT
ejpam-4665	545	4	p.	p.	PROPN
ejpam-4665	545	5	j.	j.	PROPN
ejpam-4665	545	6	slater	slater	PROPN
ejpam-4665	545	7	.	.	PUNCT
ejpam-4665	546	1	dominating	dominating	NOUN
ejpam-4665	546	2	and	and	CCONJ
ejpam-4665	546	3	reference	reference	NOUN
ejpam-4665	546	4	sets	set	NOUN
ejpam-4665	546	5	in	in	ADP
ejpam-4665	546	6	a	a	DET
ejpam-4665	546	7	graph	graph	NOUN
ejpam-4665	546	8	.	.	PUNCT
ejpam-4665	547	1	journal	journal	NOUN
ejpam-4665	547	2	of	of	ADP
ejpam-4665	547	3	mathematics	mathematic	NOUN
ejpam-4665	547	4	and	and	CCONJ
ejpam-4665	547	5	physical	physical	ADJ
ejpam-4665	547	6	science	science	NOUN
ejpam-4665	547	7	,	,	PUNCT
ejpam-4665	547	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4665	547	9	.	.	PUNCT