id	sid	tid	token	lemma	pos
ejpam-4585	1	1	european	european	PROPN
ejpam-4585	1	2	journal	journal	PROPN
ejpam-4585	1	3	of	of	ADP
ejpam-4585	1	4	pure	pure	ADJ
ejpam-4585	1	5	and	and	CCONJ
ejpam-4585	1	6	applied	apply	VERB
ejpam-4585	1	7	mathematics	mathematic	NOUN
ejpam-4585	1	8	vol	vol	NOUN
ejpam-4585	1	9	.	.	PROPN
ejpam-4585	2	1	15	15	NUM
ejpam-4585	2	2	,	,	PUNCT
ejpam-4585	2	3	no	no	INTJ
ejpam-4585	2	4	.	.	NOUN
ejpam-4585	2	5	4	4	NUM
ejpam-4585	2	6	,	,	PUNCT
ejpam-4585	2	7	2022	2022	NUM
ejpam-4585	2	8	,	,	PUNCT
ejpam-4585	2	9	1982	1982	NUM
ejpam-4585	2	10	-	-	SYM
ejpam-4585	2	11	1997	1997	NUM
ejpam-4585	2	12	issn	issn	PROPN
ejpam-4585	2	13	1307	1307	NUM
ejpam-4585	2	14	-	-	SYM
ejpam-4585	2	15	5543	5543	NUM
ejpam-4585	2	16	–	–	PUNCT
ejpam-4585	2	17	ejpam.com	ejpam.com	X
ejpam-4585	2	18	published	publish	VERB
ejpam-4585	2	19	by	by	ADP
ejpam-4585	2	20	new	new	PROPN
ejpam-4585	2	21	york	york	PROPN
ejpam-4585	2	22	business	business	PROPN
ejpam-4585	2	23	global	global	ADJ
ejpam-4585	2	24	on	on	ADP
ejpam-4585	2	25	2	2	NUM
ejpam-4585	2	26	-	-	PUNCT
ejpam-4585	2	27	resolving	resolve	VERB
ejpam-4585	2	28	hop	hop	NOUN
ejpam-4585	2	29	dominating	dominating	NOUN
ejpam-4585	2	30	sets	set	NOUN
ejpam-4585	2	31	in	in	ADP
ejpam-4585	2	32	the	the	DET
ejpam-4585	2	33	join	join	NOUN
ejpam-4585	2	34	,	,	PUNCT
ejpam-4585	2	35	corona	corona	NOUN
ejpam-4585	2	36	and	and	CCONJ
ejpam-4585	2	37	lexicographic	lexicographic	ADJ
ejpam-4585	2	38	product	product	NOUN
ejpam-4585	2	39	of	of	ADP
ejpam-4585	2	40	graphs	graph	NOUN
ejpam-4585	2	41	angelica	angelica	PROPN
ejpam-4585	2	42	mae	mae	PROPN
ejpam-4585	2	43	mahistrado1,∗	mahistrado1,∗	PROPN
ejpam-4585	2	44	,	,	PUNCT
ejpam-4585	2	45	helen	helen	PROPN
ejpam-4585	2	46	rara2	rara2	PROPN
ejpam-4585	2	47	1	1	NUM
ejpam-4585	2	48	department	department	NOUN
ejpam-4585	2	49	of	of	ADP
ejpam-4585	2	50	mathematics	mathematic	NOUN
ejpam-4585	2	51	and	and	CCONJ
ejpam-4585	2	52	statistics	statistic	NOUN
ejpam-4585	2	53	,	,	PUNCT
ejpam-4585	2	54	college	college	NOUN
ejpam-4585	2	55	of	of	ADP
ejpam-4585	2	56	science	science	NOUN
ejpam-4585	2	57	and	and	CCONJ
ejpam-4585	2	58	mathematics	mathematic	NOUN
ejpam-4585	2	59	,	,	PUNCT
ejpam-4585	2	60	mindanao	mindanao	PROPN
ejpam-4585	2	61	state	state	PROPN
ejpam-4585	2	62	university	university	PROPN
ejpam-4585	2	63	-	-	PUNCT
ejpam-4585	2	64	iligan	iligan	PROPN
ejpam-4585	2	65	institute	institute	PROPN
ejpam-4585	2	66	of	of	ADP
ejpam-4585	2	67	technology	technology	PROPN
ejpam-4585	2	68	,	,	PUNCT
ejpam-4585	2	69	9200	9200	NUM
ejpam-4585	2	70	iligan	iligan	ADJ
ejpam-4585	2	71	city	city	NOUN
ejpam-4585	2	72	,	,	PUNCT
ejpam-4585	2	73	philippines	philippines	PROPN
ejpam-4585	2	74	2	2	NUM
ejpam-4585	2	75	department	department	NOUN
ejpam-4585	2	76	of	of	ADP
ejpam-4585	2	77	mathematics	mathematic	NOUN
ejpam-4585	2	78	and	and	CCONJ
ejpam-4585	2	79	statistics	statistic	NOUN
ejpam-4585	2	80	,	,	PUNCT
ejpam-4585	2	81	college	college	NOUN
ejpam-4585	2	82	of	of	ADP
ejpam-4585	2	83	science	science	NOUN
ejpam-4585	2	84	and	and	CCONJ
ejpam-4585	2	85	mathematics	mathematic	NOUN
ejpam-4585	2	86	,	,	PUNCT
ejpam-4585	2	87	center	center	NOUN
ejpam-4585	2	88	of	of	ADP
ejpam-4585	2	89	graph	graph	NOUN
ejpam-4585	2	90	theory	theory	NOUN
ejpam-4585	2	91	,	,	PUNCT
ejpam-4585	2	92	algebra	algebra	NOUN
ejpam-4585	2	93	,	,	PUNCT
ejpam-4585	2	94	and	and	CCONJ
ejpam-4585	2	95	analysis	analysis	NOUN
ejpam-4585	2	96	-	-	PUNCT
ejpam-4585	2	97	premier	premier	NOUN
ejpam-4585	2	98	research	research	NOUN
ejpam-4585	2	99	institute	institute	PROPN
ejpam-4585	2	100	of	of	ADP
ejpam-4585	2	101	science	science	NOUN
ejpam-4585	2	102	and	and	CCONJ
ejpam-4585	2	103	mathematics	mathematic	NOUN
ejpam-4585	2	104	,	,	PUNCT
ejpam-4585	2	105	mindanao	mindanao	PROPN
ejpam-4585	2	106	state	state	PROPN
ejpam-4585	2	107	university	university	PROPN
ejpam-4585	2	108	-	-	PUNCT
ejpam-4585	2	109	iligan	iligan	PROPN
ejpam-4585	2	110	institute	institute	PROPN
ejpam-4585	2	111	of	of	ADP
ejpam-4585	2	112	technology	technology	PROPN
ejpam-4585	2	113	,	,	PUNCT
ejpam-4585	2	114	9200	9200	NUM
ejpam-4585	2	115	iligan	iligan	ADJ
ejpam-4585	2	116	city	city	NOUN
ejpam-4585	2	117	,	,	PUNCT
ejpam-4585	3	1	philippines	philippine	NOUN
ejpam-4585	3	2	abstract	abstract	ADJ
ejpam-4585	3	3	.	.	PUNCT
ejpam-4585	4	1	let	let	VERB
ejpam-4585	4	2	g	g	PRON
ejpam-4585	4	3	be	be	AUX
ejpam-4585	4	4	a	a	DET
ejpam-4585	4	5	connected	connected	ADJ
ejpam-4585	4	6	graph	graph	NOUN
ejpam-4585	4	7	.	.	PUNCT
ejpam-4585	5	1	a	a	DET
ejpam-4585	5	2	set	set	NOUN
ejpam-4585	5	3	s	s	NOUN
ejpam-4585	5	4	of	of	ADP
ejpam-4585	5	5	vertices	vertex	NOUN
ejpam-4585	5	6	in	in	ADP
ejpam-4585	5	7	g	g	PROPN
ejpam-4585	5	8	is	be	AUX
ejpam-4585	5	9	a	a	DET
ejpam-4585	5	10	2	2	NUM
ejpam-4585	5	11	-	-	PUNCT
ejpam-4585	5	12	resolving	resolve	VERB
ejpam-4585	5	13	hop	hop	NOUN
ejpam-4585	5	14	dominating	dominating	NOUN
ejpam-4585	5	15	set	set	NOUN
ejpam-4585	5	16	of	of	ADP
ejpam-4585	5	17	g	g	PROPN
ejpam-4585	5	18	if	if	SCONJ
ejpam-4585	5	19	s	s	VERB
ejpam-4585	5	20	is	be	AUX
ejpam-4585	5	21	a	a	DET
ejpam-4585	5	22	2	2	NUM
ejpam-4585	5	23	-	-	PUNCT
ejpam-4585	5	24	resolving	resolving	NOUN
ejpam-4585	5	25	set	set	NOUN
ejpam-4585	5	26	in	in	ADP
ejpam-4585	5	27	g	g	PROPN
ejpam-4585	5	28	and	and	CCONJ
ejpam-4585	5	29	for	for	ADP
ejpam-4585	5	30	every	every	DET
ejpam-4585	5	31	vertex	vertex	NOUN
ejpam-4585	5	32	x	x	SYM
ejpam-4585	5	33	∈	∈	NOUN
ejpam-4585	5	34	v	v	X
ejpam-4585	5	35	(	(	PUNCT
ejpam-4585	5	36	g)\s	g)\s	NOUN
ejpam-4585	5	37	,	,	PUNCT
ejpam-4585	5	38	there	there	PRON
ejpam-4585	5	39	exists	exist	VERB
ejpam-4585	5	40	y	y	PROPN
ejpam-4585	5	41	∈	∈	PROPN
ejpam-4585	5	42	s	s	VERB
ejpam-4585	5	43	such	such	ADJ
ejpam-4585	5	44	that	that	DET
ejpam-4585	5	45	dg(x	dg(x	NOUN
ejpam-4585	5	46	,	,	PUNCT
ejpam-4585	5	47	y	y	NOUN
ejpam-4585	5	48	)	)	PUNCT
ejpam-4585	5	49	=	=	SYM
ejpam-4585	6	1	2	2	X
ejpam-4585	6	2	.	.	PUNCT
ejpam-4585	6	3	the	the	DET
ejpam-4585	6	4	minimum	minimum	ADJ
ejpam-4585	6	5	cardinality	cardinality	NOUN
ejpam-4585	6	6	of	of	ADP
ejpam-4585	6	7	a	a	DET
ejpam-4585	6	8	set	set	NOUN
ejpam-4585	6	9	s	s	PART
ejpam-4585	6	10	is	be	AUX
ejpam-4585	6	11	called	call	VERB
ejpam-4585	6	12	the	the	DET
ejpam-4585	6	13	2	2	NUM
ejpam-4585	6	14	-	-	PUNCT
ejpam-4585	6	15	resolving	resolve	VERB
ejpam-4585	6	16	hop	hop	NOUN
ejpam-4585	6	17	domination	domination	NOUN
ejpam-4585	6	18	number	number	NOUN
ejpam-4585	6	19	of	of	ADP
ejpam-4585	6	20	g	g	NOUN
ejpam-4585	6	21	and	and	CCONJ
ejpam-4585	6	22	is	be	AUX
ejpam-4585	6	23	denoted	denote	VERB
ejpam-4585	6	24	by	by	ADP
ejpam-4585	6	25	γ2rh(g	γ2rh(g	NOUN
ejpam-4585	6	26	)	)	PUNCT
ejpam-4585	6	27	.	.	PUNCT
ejpam-4585	7	1	this	this	DET
ejpam-4585	7	2	study	study	NOUN
ejpam-4585	7	3	aims	aim	VERB
ejpam-4585	7	4	to	to	PART
ejpam-4585	7	5	combine	combine	VERB
ejpam-4585	7	6	the	the	DET
ejpam-4585	7	7	concept	concept	NOUN
ejpam-4585	7	8	of	of	ADP
ejpam-4585	7	9	hop	hop	NOUN
ejpam-4585	7	10	domination	domination	NOUN
ejpam-4585	7	11	with	with	ADP
ejpam-4585	7	12	the	the	DET
ejpam-4585	7	13	2	2	NUM
ejpam-4585	7	14	-	-	PUNCT
ejpam-4585	7	15	resolving	resolve	VERB
ejpam-4585	7	16	sets	set	NOUN
ejpam-4585	7	17	of	of	ADP
ejpam-4585	7	18	graphs	graph	NOUN
ejpam-4585	7	19	.	.	PUNCT
ejpam-4585	8	1	the	the	DET
ejpam-4585	8	2	main	main	ADJ
ejpam-4585	8	3	results	result	NOUN
ejpam-4585	8	4	generated	generate	VERB
ejpam-4585	8	5	in	in	ADP
ejpam-4585	8	6	this	this	DET
ejpam-4585	8	7	study	study	NOUN
ejpam-4585	8	8	include	include	VERB
ejpam-4585	8	9	the	the	DET
ejpam-4585	8	10	characterization	characterization	NOUN
ejpam-4585	8	11	of	of	ADP
ejpam-4585	8	12	2	2	NUM
ejpam-4585	8	13	-	-	PUNCT
ejpam-4585	8	14	resolving	resolve	VERB
ejpam-4585	8	15	hop	hop	NOUN
ejpam-4585	8	16	dominating	dominating	NOUN
ejpam-4585	8	17	sets	set	NOUN
ejpam-4585	8	18	in	in	ADP
ejpam-4585	8	19	the	the	DET
ejpam-4585	8	20	join	join	NOUN
ejpam-4585	8	21	,	,	PUNCT
ejpam-4585	8	22	corona	corona	NOUN
ejpam-4585	8	23	and	and	CCONJ
ejpam-4585	8	24	lexicographic	lexicographic	ADJ
ejpam-4585	8	25	product	product	NOUN
ejpam-4585	8	26	of	of	ADP
ejpam-4585	8	27	two	two	NUM
ejpam-4585	8	28	graphs	graph	NOUN
ejpam-4585	8	29	,	,	PUNCT
ejpam-4585	8	30	as	as	ADV
ejpam-4585	8	31	well	well	ADV
ejpam-4585	8	32	as	as	ADP
ejpam-4585	8	33	their	their	PRON
ejpam-4585	8	34	corresponding	corresponding	ADJ
ejpam-4585	8	35	bounds	bound	NOUN
ejpam-4585	8	36	or	or	CCONJ
ejpam-4585	8	37	exact	exact	ADJ
ejpam-4585	8	38	values	value	NOUN
ejpam-4585	8	39	.	.	PUNCT
ejpam-4585	9	1	2020	2020	NUM
ejpam-4585	9	2	mathematics	mathematic	NOUN
ejpam-4585	9	3	subject	subject	NOUN
ejpam-4585	9	4	classifications	classification	NOUN
ejpam-4585	9	5	:	:	PUNCT
ejpam-4585	9	6	05c69	05c69	X
ejpam-4585	9	7	key	key	ADJ
ejpam-4585	9	8	words	word	NOUN
ejpam-4585	9	9	and	and	CCONJ
ejpam-4585	9	10	phrases	phrase	NOUN
ejpam-4585	9	11	:	:	PUNCT
ejpam-4585	9	12	2	2	NUM
ejpam-4585	9	13	-	-	PUNCT
ejpam-4585	9	14	resolving	resolve	VERB
ejpam-4585	9	15	hop	hop	NOUN
ejpam-4585	9	16	dominating	dominating	NOUN
ejpam-4585	9	17	set	set	NOUN
ejpam-4585	9	18	,	,	PUNCT
ejpam-4585	9	19	2	2	NUM
ejpam-4585	9	20	-	-	PUNCT
ejpam-4585	9	21	resolving	resolve	VERB
ejpam-4585	9	22	hop	hop	NOUN
ejpam-4585	9	23	domination	domination	NOUN
ejpam-4585	9	24	number	number	NOUN
ejpam-4585	9	25	,	,	PUNCT
ejpam-4585	9	26	join	join	NOUN
ejpam-4585	9	27	,	,	PUNCT
ejpam-4585	9	28	corona	corona	PROPN
ejpam-4585	9	29	,	,	PUNCT
ejpam-4585	9	30	lexicographic	lexicographic	ADJ
ejpam-4585	9	31	product	product	NOUN
ejpam-4585	9	32	1	1	NUM
ejpam-4585	9	33	.	.	PUNCT
ejpam-4585	9	34	introduction	introduction	NOUN
ejpam-4585	9	35	the	the	DET
ejpam-4585	9	36	concept	concept	NOUN
ejpam-4585	9	37	of	of	ADP
ejpam-4585	9	38	domination	domination	NOUN
ejpam-4585	9	39	in	in	ADP
ejpam-4585	9	40	graphs	graph	NOUN
ejpam-4585	9	41	is	be	AUX
ejpam-4585	9	42	one	one	NUM
ejpam-4585	9	43	of	of	ADP
ejpam-4585	9	44	the	the	DET
ejpam-4585	9	45	most	most	ADV
ejpam-4585	9	46	studied	study	VERB
ejpam-4585	9	47	problems	problem	NOUN
ejpam-4585	9	48	and	and	CCONJ
ejpam-4585	9	49	one	one	NUM
ejpam-4585	9	50	of	of	ADP
ejpam-4585	9	51	the	the	DET
ejpam-4585	9	52	fastest	fast	ADJ
ejpam-4585	9	53	growing	grow	VERB
ejpam-4585	9	54	areas	area	NOUN
ejpam-4585	9	55	in	in	ADP
ejpam-4585	9	56	graph	graph	NOUN
ejpam-4585	9	57	theory	theory	NOUN
ejpam-4585	9	58	.	.	PUNCT
ejpam-4585	10	1	this	this	PRON
ejpam-4585	10	2	was	be	AUX
ejpam-4585	10	3	formally	formally	ADV
ejpam-4585	10	4	studied	study	VERB
ejpam-4585	10	5	by	by	ADP
ejpam-4585	10	6	claude	claude	PROPN
ejpam-4585	10	7	berge	berge	PROPN
ejpam-4585	11	1	[	[	X
ejpam-4585	11	2	1	1	X
ejpam-4585	11	3	]	]	PUNCT
ejpam-4585	11	4	in	in	ADP
ejpam-4585	11	5	1958	1958	NUM
ejpam-4585	11	6	and	and	CCONJ
ejpam-4585	11	7	oystein	oystein	ADJ
ejpam-4585	11	8	ore	ore	NOUN
ejpam-4585	11	9	in	in	ADP
ejpam-4585	11	10	1962	1962	NUM
ejpam-4585	11	11	.	.	PUNCT
ejpam-4585	12	1	in	in	ADP
ejpam-4585	12	2	2015	2015	NUM
ejpam-4585	12	3	,	,	PUNCT
ejpam-4585	12	4	natarajan	natarajan	PROPN
ejpam-4585	12	5	and	and	CCONJ
ejpam-4585	12	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4585	12	7	introduced	introduce	VERB
ejpam-4585	12	8	and	and	CCONJ
ejpam-4585	12	9	studied	study	VERB
ejpam-4585	12	10	the	the	DET
ejpam-4585	12	11	concept	concept	NOUN
ejpam-4585	12	12	of	of	ADP
ejpam-4585	12	13	hop	hop	NOUN
ejpam-4585	12	14	domination	domination	NOUN
ejpam-4585	12	15	[	[	X
ejpam-4585	12	16	13	13	NUM
ejpam-4585	12	17	]	]	PUNCT
ejpam-4585	12	18	.	.	PUNCT
ejpam-4585	13	1	on	on	ADP
ejpam-4585	13	2	the	the	DET
ejpam-4585	13	3	other	other	ADJ
ejpam-4585	13	4	hand	hand	NOUN
ejpam-4585	13	5	,	,	PUNCT
ejpam-4585	13	6	in	in	ADP
ejpam-4585	13	7	1975	1975	NUM
ejpam-4585	13	8	using	use	VERB
ejpam-4585	13	9	the	the	DET
ejpam-4585	13	10	term	term	NOUN
ejpam-4585	13	11	locating	locate	VERB
ejpam-4585	13	12	set	set	NOUN
ejpam-4585	13	13	,	,	PUNCT
ejpam-4585	13	14	the	the	DET
ejpam-4585	13	15	concept	concept	NOUN
ejpam-4585	13	16	of	of	ADP
ejpam-4585	13	17	resolving	resolve	VERB
ejpam-4585	13	18	sets	set	NOUN
ejpam-4585	13	19	for	for	ADP
ejpam-4585	13	20	a	a	DET
ejpam-4585	13	21	connected	connected	ADJ
ejpam-4585	13	22	graph	graph	NOUN
ejpam-4585	13	23	was	be	AUX
ejpam-4585	13	24	first	first	ADV
ejpam-4585	13	25	introduced	introduce	VERB
ejpam-4585	13	26	by	by	ADP
ejpam-4585	13	27	slater	slater	NOUN
ejpam-4585	13	28	[	[	X
ejpam-4585	13	29	15	15	NUM
ejpam-4585	13	30	]	]	PUNCT
ejpam-4585	13	31	.	.	PUNCT
ejpam-4585	14	1	these	these	DET
ejpam-4585	14	2	concepts	concept	NOUN
ejpam-4585	14	3	were	be	AUX
ejpam-4585	14	4	studied	study	VERB
ejpam-4585	14	5	much	much	ADV
ejpam-4585	14	6	earlier	early	ADV
ejpam-4585	14	7	in	in	ADP
ejpam-4585	14	8	the	the	DET
ejpam-4585	14	9	context	context	NOUN
ejpam-4585	14	10	of	of	ADP
ejpam-4585	14	11	the	the	DET
ejpam-4585	14	12	coin	coin	NOUN
ejpam-4585	14	13	-	-	PUNCT
ejpam-4585	14	14	weighing	weigh	VERB
ejpam-4585	14	15	problem	problem	NOUN
ejpam-4585	14	16	.	.	PUNCT
ejpam-4585	15	1	later	later	ADV
ejpam-4585	15	2	that	that	DET
ejpam-4585	15	3	year	year	NOUN
ejpam-4585	15	4	,	,	PUNCT
ejpam-4585	15	5	harary	harary	NOUN
ejpam-4585	15	6	and	and	CCONJ
ejpam-4585	15	7	melter	melter	NOUN
ejpam-4585	15	8	introduced	introduce	VERB
ejpam-4585	15	9	independently	independently	ADV
ejpam-4585	15	10	these	these	DET
ejpam-4585	15	11	concepts	concept	NOUN
ejpam-4585	15	12	,	,	PUNCT
ejpam-4585	15	13	but	but	CCONJ
ejpam-4585	15	14	with	with	ADP
ejpam-4585	15	15	different	different	ADJ
ejpam-4585	15	16	terminologies	terminology	NOUN
ejpam-4585	15	17	[	[	X
ejpam-4585	15	18	10	10	NUM
ejpam-4585	15	19	]	]	PUNCT
ejpam-4585	15	20	.	.	PUNCT
ejpam-4585	16	1	the	the	DET
ejpam-4585	16	2	term	term	NOUN
ejpam-4585	16	3	metric	metric	ADJ
ejpam-4585	16	4	dimension	dimension	NOUN
ejpam-4585	16	5	was	be	AUX
ejpam-4585	16	6	used	use	VERB
ejpam-4585	16	7	by	by	ADP
ejpam-4585	16	8	harary	harary	NOUN
ejpam-4585	16	9	and	and	CCONJ
ejpam-4585	16	10	melter	melter	NOUN
ejpam-4585	16	11	instead	instead	ADV
ejpam-4585	16	12	of	of	ADP
ejpam-4585	16	13	locating	locate	VERB
ejpam-4585	16	14	number	number	NOUN
ejpam-4585	16	15	.	.	PUNCT
ejpam-4585	17	1	∗corresponding	∗corresponde	VERB
ejpam-4585	17	2	author	author	NOUN
ejpam-4585	17	3	.	.	PUNCT
ejpam-4585	18	1	doi	doi	NOUN
ejpam-4585	18	2	:	:	PUNCT
ejpam-4585	18	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4585	https://doi.org/10.29020/nybg.ejpam.v15i4.4585	ADJ
ejpam-4585	18	4	email	email	NOUN
ejpam-4585	18	5	addresses	address	NOUN
ejpam-4585	18	6	:	:	PUNCT
ejpam-4585	18	7	angelicamae.mahistrado@g.msuiit.edu.ph	angelicamae.mahistrado@g.msuiit.edu.ph	PROPN
ejpam-4585	18	8	(	(	PUNCT
ejpam-4585	18	9	a.m.	a.m.	NOUN
ejpam-4585	18	10	mahistrado	mahistrado	PROPN
ejpam-4585	18	11	)	)	PUNCT
ejpam-4585	18	12	,	,	PUNCT
ejpam-4585	18	13	helen.rara@g.msuiit.edu.ph	helen.rara@g.msuiit.edu.ph	PROPN
ejpam-4585	18	14	(	(	PUNCT
ejpam-4585	18	15	h.	h.	PROPN
ejpam-4585	18	16	rara	rara	PROPN
ejpam-4585	18	17	)	)	PUNCT
ejpam-4585	18	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4585	18	19	1982	1982	NUM
ejpam-4585	19	1	©	©	PROPN
ejpam-4585	19	2	2022	2022	NUM
ejpam-4585	19	3	ejpam	ejpam	VERB
ejpam-4585	19	4	all	all	DET
ejpam-4585	19	5	rights	right	NOUN
ejpam-4585	19	6	reserved	reserve	VERB
ejpam-4585	19	7	.	.	PUNCT
ejpam-4585	20	1	a.m.	a.m.	PROPN
ejpam-4585	20	2	mahistrado	mahistrado	PROPN
ejpam-4585	20	3	,	,	PUNCT
ejpam-4585	20	4	h.	h.	PROPN
ejpam-4585	20	5	rara	rara	PROPN
ejpam-4585	20	6	/	/	SYM
ejpam-4585	20	7	eur	eur	PROPN
ejpam-4585	20	8	.	.	PUNCT
ejpam-4585	21	1	j.	j.	PROPN
ejpam-4585	21	2	pure	pure	PROPN
ejpam-4585	21	3	appl	appl	PROPN
ejpam-4585	21	4	.	.	PROPN
ejpam-4585	21	5	math	math	PROPN
ejpam-4585	21	6	,	,	PUNCT
ejpam-4585	21	7	15	15	NUM
ejpam-4585	21	8	(	(	PUNCT
ejpam-4585	21	9	4	4	NUM
ejpam-4585	21	10	)	)	PUNCT
ejpam-4585	21	11	(	(	PUNCT
ejpam-4585	21	12	2022	2022	NUM
ejpam-4585	21	13	)	)	PUNCT
ejpam-4585	21	14	,	,	PUNCT
ejpam-4585	21	15	1982	1982	NUM
ejpam-4585	21	16	-	-	SYM
ejpam-4585	21	17	1997	1997	NUM
ejpam-4585	21	18	1983	1983	NUM
ejpam-4585	21	19	moreover	moreover	ADV
ejpam-4585	21	20	,	,	PUNCT
ejpam-4585	21	21	in	in	ADP
ejpam-4585	21	22	the	the	DET
ejpam-4585	21	23	paper	paper	NOUN
ejpam-4585	21	24	of	of	ADP
ejpam-4585	21	25	brigham	brigham	PROPN
ejpam-4585	21	26	et	et	PROPN
ejpam-4585	21	27	al	al	PROPN
ejpam-4585	21	28	.	.	PUNCT
ejpam-4585	22	1	[	[	X
ejpam-4585	22	2	9	9	NUM
ejpam-4585	22	3	]	]	PUNCT
ejpam-4585	22	4	,	,	PUNCT
ejpam-4585	22	5	the	the	DET
ejpam-4585	22	6	concept	concept	NOUN
ejpam-4585	22	7	of	of	ADP
ejpam-4585	22	8	resolving	resolve	VERB
ejpam-4585	22	9	dominating	dominate	VERB
ejpam-4585	22	10	in	in	ADP
ejpam-4585	22	11	graphs	graph	NOUN
ejpam-4585	22	12	was	be	AUX
ejpam-4585	22	13	studied	study	VERB
ejpam-4585	22	14	wherein	wherein	SCONJ
ejpam-4585	22	15	they	they	PRON
ejpam-4585	22	16	defined	define	VERB
ejpam-4585	22	17	it	it	PRON
ejpam-4585	22	18	as	as	ADP
ejpam-4585	22	19	a	a	DET
ejpam-4585	22	20	set	set	NOUN
ejpam-4585	22	21	that	that	PRON
ejpam-4585	22	22	is	be	AUX
ejpam-4585	22	23	both	both	PRON
ejpam-4585	22	24	resolving	resolve	VERB
ejpam-4585	22	25	and	and	CCONJ
ejpam-4585	22	26	dominating	dominating	NOUN
ejpam-4585	22	27	,	,	PUNCT
ejpam-4585	22	28	and	and	CCONJ
ejpam-4585	22	29	determined	determine	VERB
ejpam-4585	22	30	the	the	DET
ejpam-4585	22	31	resolving	resolve	VERB
ejpam-4585	22	32	domination	domination	NOUN
ejpam-4585	22	33	number	number	NOUN
ejpam-4585	22	34	γr(g	γr(g	PROPN
ejpam-4585	22	35	)	)	PUNCT
ejpam-4585	22	36	of	of	ADP
ejpam-4585	22	37	a	a	DET
ejpam-4585	22	38	graph	graph	NOUN
ejpam-4585	22	39	g	g	PROPN
ejpam-4585	22	40	[	[	X
ejpam-4585	22	41	9	9	NUM
ejpam-4585	22	42	]	]	PUNCT
ejpam-4585	22	43	.	.	PUNCT
ejpam-4585	23	1	in	in	ADP
ejpam-4585	23	2	2021	2021	NUM
ejpam-4585	23	3	,	,	PUNCT
ejpam-4585	23	4	the	the	DET
ejpam-4585	23	5	concept	concept	NOUN
ejpam-4585	23	6	of	of	ADP
ejpam-4585	23	7	resolving	resolve	VERB
ejpam-4585	23	8	hop	hop	NOUN
ejpam-4585	23	9	domination	domination	NOUN
ejpam-4585	23	10	in	in	ADP
ejpam-4585	23	11	graphs	graph	NOUN
ejpam-4585	23	12	was	be	AUX
ejpam-4585	23	13	studied	study	VERB
ejpam-4585	23	14	and	and	CCONJ
ejpam-4585	23	15	published	publish	VERB
ejpam-4585	23	16	by	by	ADP
ejpam-4585	23	17	mohamad	mohamad	PROPN
ejpam-4585	23	18	and	and	CCONJ
ejpam-4585	23	19	rara	rara	NOUN
ejpam-4585	24	1	[	[	X
ejpam-4585	24	2	11	11	NUM
ejpam-4585	24	3	]	]	PUNCT
ejpam-4585	24	4	wherein	wherein	SCONJ
ejpam-4585	24	5	they	they	PRON
ejpam-4585	24	6	characterized	characterize	VERB
ejpam-4585	24	7	the	the	DET
ejpam-4585	24	8	resolving	resolve	VERB
ejpam-4585	24	9	hop	hop	NOUN
ejpam-4585	24	10	dominating	dominating	NOUN
ejpam-4585	24	11	sets	set	NOUN
ejpam-4585	24	12	in	in	ADP
ejpam-4585	24	13	some	some	DET
ejpam-4585	24	14	binary	binary	ADJ
ejpam-4585	24	15	operations	operation	NOUN
ejpam-4585	24	16	namely	namely	ADV
ejpam-4585	24	17	,	,	PUNCT
ejpam-4585	24	18	the	the	DET
ejpam-4585	24	19	join	join	NOUN
ejpam-4585	24	20	and	and	CCONJ
ejpam-4585	24	21	corona	corona	NOUN
ejpam-4585	24	22	of	of	ADP
ejpam-4585	24	23	two	two	NUM
ejpam-4585	24	24	graphs	graph	NOUN
ejpam-4585	24	25	and	and	CCONJ
ejpam-4585	24	26	determined	determine	VERB
ejpam-4585	24	27	the	the	DET
ejpam-4585	24	28	bounds	bound	NOUN
ejpam-4585	24	29	or	or	CCONJ
ejpam-4585	24	30	exact	exact	ADJ
ejpam-4585	24	31	values	value	NOUN
ejpam-4585	24	32	of	of	ADP
ejpam-4585	24	33	the	the	DET
ejpam-4585	24	34	resolving	resolve	VERB
ejpam-4585	24	35	hop	hop	NOUN
ejpam-4585	24	36	domination	domination	NOUN
ejpam-4585	24	37	number	number	NOUN
ejpam-4585	24	38	of	of	ADP
ejpam-4585	24	39	these	these	DET
ejpam-4585	24	40	mentioned	mention	VERB
ejpam-4585	24	41	graphs	graph	NOUN
ejpam-4585	24	42	[	[	X
ejpam-4585	24	43	11	11	NUM
ejpam-4585	24	44	]	]	PUNCT
ejpam-4585	24	45	.	.	PUNCT
ejpam-4585	25	1	also	also	ADV
ejpam-4585	25	2	,	,	PUNCT
ejpam-4585	25	3	in	in	ADP
ejpam-4585	25	4	the	the	DET
ejpam-4585	25	5	same	same	ADJ
ejpam-4585	25	6	year	year	NOUN
ejpam-4585	25	7	,	,	PUNCT
ejpam-4585	25	8	cabaro	cabaro	NOUN
ejpam-4585	25	9	and	and	CCONJ
ejpam-4585	25	10	rara	rara	NOUN
ejpam-4585	25	11	published	publish	VERB
ejpam-4585	25	12	the	the	DET
ejpam-4585	25	13	concept	concept	NOUN
ejpam-4585	25	14	of	of	ADP
ejpam-4585	25	15	2	2	NUM
ejpam-4585	25	16	-	-	PUNCT
ejpam-4585	25	17	resolving	resolve	VERB
ejpam-4585	25	18	sets	set	NOUN
ejpam-4585	25	19	in	in	ADP
ejpam-4585	25	20	the	the	DET
ejpam-4585	25	21	join	join	NOUN
ejpam-4585	25	22	and	and	CCONJ
ejpam-4585	25	23	corona	corona	NOUN
ejpam-4585	25	24	of	of	ADP
ejpam-4585	25	25	graphs	graph	NOUN
ejpam-4585	25	26	[	[	X
ejpam-4585	25	27	4	4	NUM
ejpam-4585	25	28	]	]	PUNCT
ejpam-4585	25	29	.	.	PUNCT
ejpam-4585	26	1	their	their	PRON
ejpam-4585	26	2	paper	paper	NOUN
ejpam-4585	26	3	also	also	ADV
ejpam-4585	26	4	presents	present	VERB
ejpam-4585	26	5	some	some	DET
ejpam-4585	26	6	characterizations	characterization	NOUN
ejpam-4585	26	7	involving	involve	VERB
ejpam-4585	26	8	this	this	DET
ejpam-4585	26	9	concept	concept	NOUN
ejpam-4585	26	10	and	and	CCONJ
ejpam-4585	26	11	investigates	investigate	VERB
ejpam-4585	26	12	the	the	DET
ejpam-4585	26	13	2	2	NUM
ejpam-4585	26	14	-	-	PUNCT
ejpam-4585	26	15	resolving	resolve	VERB
ejpam-4585	26	16	dominating	dominating	NOUN
ejpam-4585	26	17	sets	set	NOUN
ejpam-4585	26	18	in	in	ADP
ejpam-4585	26	19	the	the	DET
ejpam-4585	26	20	join	join	NOUN
ejpam-4585	26	21	,	,	PUNCT
ejpam-4585	26	22	corona	corona	NOUN
ejpam-4585	26	23	and	and	CCONJ
ejpam-4585	26	24	lexicorgraphic	lexicorgraphic	ADJ
ejpam-4585	26	25	product	product	NOUN
ejpam-4585	26	26	of	of	ADP
ejpam-4585	26	27	two	two	NUM
ejpam-4585	26	28	graphs	graph	NOUN
ejpam-4585	26	29	[	[	X
ejpam-4585	26	30	7	7	NUM
ejpam-4585	26	31	]	]	PUNCT
ejpam-4585	26	32	.	.	PUNCT
ejpam-4585	27	1	other	other	ADJ
ejpam-4585	27	2	variations	variation	NOUN
ejpam-4585	27	3	of	of	ADP
ejpam-4585	27	4	2	2	NUM
ejpam-4585	27	5	-	-	PUNCT
ejpam-4585	27	6	resolving	resolve	VERB
ejpam-4585	27	7	sets	set	NOUN
ejpam-4585	27	8	in	in	ADP
ejpam-4585	27	9	graphs	graph	NOUN
ejpam-4585	27	10	were	be	AUX
ejpam-4585	27	11	also	also	ADV
ejpam-4585	27	12	studied	study	VERB
ejpam-4585	27	13	in	in	ADP
ejpam-4585	27	14	[	[	X
ejpam-4585	27	15	4–6	4–6	NOUN
ejpam-4585	27	16	,	,	PUNCT
ejpam-4585	27	17	8	8	NUM
ejpam-4585	27	18	]	]	PUNCT
ejpam-4585	27	19	.	.	PUNCT
ejpam-4585	28	1	2	2	X
ejpam-4585	28	2	.	.	X
ejpam-4585	28	3	terminology	terminology	NOUN
ejpam-4585	28	4	and	and	CCONJ
ejpam-4585	28	5	notation	notation	NOUN
ejpam-4585	28	6	in	in	ADP
ejpam-4585	28	7	this	this	DET
ejpam-4585	28	8	study	study	NOUN
ejpam-4585	28	9	,	,	PUNCT
ejpam-4585	28	10	we	we	PRON
ejpam-4585	28	11	consider	consider	VERB
ejpam-4585	28	12	finite	finite	ADJ
ejpam-4585	28	13	,	,	PUNCT
ejpam-4585	28	14	simple	simple	ADJ
ejpam-4585	28	15	,	,	PUNCT
ejpam-4585	28	16	connected	connect	VERB
ejpam-4585	28	17	,	,	PUNCT
ejpam-4585	28	18	undirected	undirected	ADJ
ejpam-4585	28	19	graphs	graph	NOUN
ejpam-4585	28	20	.	.	PUNCT
ejpam-4585	29	1	for	for	ADP
ejpam-4585	29	2	basic	basic	ADJ
ejpam-4585	29	3	graphtheoretic	graphtheoretic	ADJ
ejpam-4585	29	4	concepts	concept	NOUN
ejpam-4585	29	5	,	,	PUNCT
ejpam-4585	29	6	we	we	PRON
ejpam-4585	29	7	then	then	ADV
ejpam-4585	29	8	refer	refer	VERB
ejpam-4585	29	9	readers	reader	NOUN
ejpam-4585	29	10	to	to	ADP
ejpam-4585	29	11	[	[	X
ejpam-4585	29	12	2	2	NUM
ejpam-4585	29	13	]	]	PUNCT
ejpam-4585	29	14	and	and	CCONJ
ejpam-4585	29	15	[	[	X
ejpam-4585	29	16	3	3	NUM
ejpam-4585	29	17	]	]	PUNCT
ejpam-4585	29	18	.	.	PUNCT
ejpam-4585	30	1	the	the	DET
ejpam-4585	30	2	following	follow	VERB
ejpam-4585	30	3	concepts	concept	NOUN
ejpam-4585	30	4	are	be	AUX
ejpam-4585	30	5	found	find	VERB
ejpam-4585	30	6	in	in	ADP
ejpam-4585	30	7	[	[	X
ejpam-4585	30	8	2	2	NUM
ejpam-4585	30	9	]	]	PUNCT
ejpam-4585	30	10	,	,	PUNCT
ejpam-4585	30	11	[	[	X
ejpam-4585	30	12	13	13	NUM
ejpam-4585	30	13	]	]	PUNCT
ejpam-4585	30	14	,	,	PUNCT
ejpam-4585	30	15	and	and	CCONJ
ejpam-4585	30	16	[	[	X
ejpam-4585	30	17	14	14	NUM
ejpam-4585	30	18	]	]	X
ejpam-4585	30	19	,	,	PUNCT
ejpam-4585	30	20	respectively	respectively	ADV
ejpam-4585	30	21	.	.	PUNCT
ejpam-4585	31	1	let	let	VERB
ejpam-4585	31	2	g	g	PRON
ejpam-4585	31	3	be	be	AUX
ejpam-4585	31	4	a	a	DET
ejpam-4585	31	5	connected	connected	ADJ
ejpam-4585	31	6	graph	graph	NOUN
ejpam-4585	31	7	.	.	PUNCT
ejpam-4585	32	1	a	a	DET
ejpam-4585	32	2	vertex	vertex	NOUN
ejpam-4585	32	3	v	v	NOUN
ejpam-4585	32	4	in	in	ADP
ejpam-4585	32	5	g	g	PROPN
ejpam-4585	32	6	is	be	AUX
ejpam-4585	32	7	a	a	DET
ejpam-4585	32	8	hop	hop	NOUN
ejpam-4585	32	9	neighbor	neighbor	NOUN
ejpam-4585	32	10	of	of	ADP
ejpam-4585	32	11	vertex	vertex	NOUN
ejpam-4585	32	12	u	u	NOUN
ejpam-4585	32	13	in	in	ADP
ejpam-4585	32	14	g	g	PROPN
ejpam-4585	32	15	if	if	SCONJ
ejpam-4585	32	16	dg(u	dg(u	NOUN
ejpam-4585	32	17	,	,	PUNCT
ejpam-4585	32	18	v	v	NOUN
ejpam-4585	32	19	)	)	PUNCT
ejpam-4585	32	20	=	=	SYM
ejpam-4585	32	21	2	2	X
ejpam-4585	32	22	.	.	X
ejpam-4585	33	1	the	the	DET
ejpam-4585	33	2	set	set	NOUN
ejpam-4585	33	3	ng(u	ng(u	NOUN
ejpam-4585	33	4	,	,	PUNCT
ejpam-4585	33	5	2	2	NUM
ejpam-4585	33	6	)	)	PUNCT
ejpam-4585	33	7	=	=	PRON
ejpam-4585	33	8	{	{	PUNCT
ejpam-4585	33	9	v	v	NUM
ejpam-4585	33	10	∈	∈	NOUN
ejpam-4585	33	11	v	v	NOUN
ejpam-4585	33	12	(	(	PUNCT
ejpam-4585	33	13	g	g	NOUN
ejpam-4585	33	14	)	)	PUNCT
ejpam-4585	33	15	:	:	PUNCT
ejpam-4585	33	16	dg(v	dg(v	X
ejpam-4585	33	17	,	,	PUNCT
ejpam-4585	33	18	u	u	NOUN
ejpam-4585	33	19	)	)	PUNCT
ejpam-4585	33	20	=	=	SYM
ejpam-4585	33	21	2	2	X
ejpam-4585	33	22	}	}	PUNCT
ejpam-4585	33	23	is	be	AUX
ejpam-4585	33	24	called	call	VERB
ejpam-4585	33	25	the	the	DET
ejpam-4585	33	26	open	open	ADJ
ejpam-4585	33	27	hop	hop	NOUN
ejpam-4585	33	28	neighborhood	neighborhood	NOUN
ejpam-4585	33	29	of	of	ADP
ejpam-4585	33	30	u.	u.	PROPN
ejpam-4585	33	31	the	the	DET
ejpam-4585	33	32	closed	closed	ADJ
ejpam-4585	33	33	hop	hop	NOUN
ejpam-4585	33	34	neighborhood	neighborhood	NOUN
ejpam-4585	33	35	of	of	ADP
ejpam-4585	33	36	u	u	PROPN
ejpam-4585	33	37	in	in	ADP
ejpam-4585	33	38	g	g	PROPN
ejpam-4585	33	39	is	be	AUX
ejpam-4585	33	40	given	give	VERB
ejpam-4585	33	41	by	by	ADP
ejpam-4585	33	42	ng[u	ng[u	PROPN
ejpam-4585	33	43	,	,	PUNCT
ejpam-4585	33	44	2	2	NUM
ejpam-4585	33	45	]	]	PUNCT
ejpam-4585	34	1	=	=	SYM
ejpam-4585	34	2	ng(u	ng(u	PROPN
ejpam-4585	34	3	,	,	PUNCT
ejpam-4585	34	4	2)∪	2)∪	NUM
ejpam-4585	34	5	{	{	PUNCT
ejpam-4585	34	6	u	u	NOUN
ejpam-4585	34	7	}	}	PUNCT
ejpam-4585	34	8	.	.	PUNCT
ejpam-4585	35	1	the	the	DET
ejpam-4585	35	2	open	open	ADJ
ejpam-4585	35	3	hop	hop	NOUN
ejpam-4585	35	4	neighborhood	neighborhood	NOUN
ejpam-4585	35	5	of	of	ADP
ejpam-4585	35	6	x	x	PROPN
ejpam-4585	35	7	⊆	⊆	NUM
ejpam-4585	35	8	v	v	ADP
ejpam-4585	35	9	(	(	PUNCT
ejpam-4585	35	10	g	g	NOUN
ejpam-4585	35	11	)	)	PUNCT
ejpam-4585	35	12	is	be	AUX
ejpam-4585	35	13	the	the	DET
ejpam-4585	35	14	set	set	NOUN
ejpam-4585	35	15	ng(x	ng(x	NUM
ejpam-4585	35	16	,	,	PUNCT
ejpam-4585	35	17	2	2	X
ejpam-4585	35	18	)	)	PUNCT
ejpam-4585	35	19	=	=	NOUN
ejpam-4585	35	20	⋃	⋃	NOUN
ejpam-4585	35	21	u∈x	u∈x	ADJ
ejpam-4585	35	22	ng(u	ng(u	NOUN
ejpam-4585	35	23	,	,	PUNCT
ejpam-4585	35	24	2	2	NUM
ejpam-4585	35	25	)	)	PUNCT
ejpam-4585	35	26	.	.	PUNCT
ejpam-4585	36	1	the	the	DET
ejpam-4585	36	2	closed	closed	ADJ
ejpam-4585	36	3	hop	hop	NOUN
ejpam-4585	36	4	neighborhood	neighborhood	NOUN
ejpam-4585	36	5	of	of	ADP
ejpam-4585	36	6	x	x	PUNCT
ejpam-4585	36	7	in	in	ADP
ejpam-4585	36	8	g	g	PROPN
ejpam-4585	36	9	is	be	AUX
ejpam-4585	36	10	the	the	DET
ejpam-4585	36	11	set	set	PROPN
ejpam-4585	36	12	ng[x	ng[x	PROPN
ejpam-4585	36	13	,	,	PUNCT
ejpam-4585	36	14	2	2	NUM
ejpam-4585	36	15	]	]	PUNCT
ejpam-4585	36	16	=	=	SYM
ejpam-4585	36	17	ng(x	ng(x	X
ejpam-4585	36	18	,	,	PUNCT
ejpam-4585	36	19	2	2	NUM
ejpam-4585	36	20	)	)	PUNCT
ejpam-4585	36	21	∪x	∪x	NUM
ejpam-4585	36	22	.	.	PUNCT
ejpam-4585	37	1	a	a	DET
ejpam-4585	37	2	set	set	NOUN
ejpam-4585	37	3	s	s	NOUN
ejpam-4585	37	4	⊆	⊆	NUM
ejpam-4585	37	5	v	v	NOUN
ejpam-4585	37	6	(	(	PUNCT
ejpam-4585	37	7	g	g	NOUN
ejpam-4585	37	8	)	)	PUNCT
ejpam-4585	37	9	is	be	AUX
ejpam-4585	37	10	a	a	DET
ejpam-4585	37	11	hop	hop	NOUN
ejpam-4585	37	12	dominating	dominating	NOUN
ejpam-4585	37	13	set	set	NOUN
ejpam-4585	37	14	of	of	ADP
ejpam-4585	37	15	g	g	PROPN
ejpam-4585	37	16	if	if	SCONJ
ejpam-4585	37	17	ng[s	ng[	NOUN
ejpam-4585	37	18	,	,	PUNCT
ejpam-4585	37	19	2	2	NUM
ejpam-4585	37	20	]	]	PUNCT
ejpam-4585	37	21	=	=	SYM
ejpam-4585	37	22	v	v	NOUN
ejpam-4585	37	23	(	(	PUNCT
ejpam-4585	37	24	g	g	NOUN
ejpam-4585	37	25	)	)	PUNCT
ejpam-4585	37	26	,	,	PUNCT
ejpam-4585	37	27	that	that	ADV
ejpam-4585	37	28	is	is	ADV
ejpam-4585	37	29	,	,	PUNCT
ejpam-4585	37	30	for	for	ADP
ejpam-4585	37	31	every	every	DET
ejpam-4585	37	32	v	v	NUM
ejpam-4585	37	33	∈	∈	NOUN
ejpam-4585	37	34	v	v	NOUN
ejpam-4585	37	35	(	(	PUNCT
ejpam-4585	37	36	g)\s	g)\s	NOUN
ejpam-4585	37	37	,	,	PUNCT
ejpam-4585	37	38	there	there	PRON
ejpam-4585	37	39	exists	exist	VERB
ejpam-4585	37	40	u	u	PROPN
ejpam-4585	37	41	∈	∈	PROPN
ejpam-4585	37	42	s	s	VERB
ejpam-4585	37	43	such	such	ADJ
ejpam-4585	37	44	that	that	DET
ejpam-4585	37	45	dg(u	dg(u	ADJ
ejpam-4585	37	46	,	,	PUNCT
ejpam-4585	37	47	v	v	NOUN
ejpam-4585	37	48	)	)	PUNCT
ejpam-4585	38	1	=	=	SYM
ejpam-4585	38	2	2	2	X
ejpam-4585	38	3	.	.	PUNCT
ejpam-4585	39	1	the	the	DET
ejpam-4585	39	2	minimum	minimum	ADJ
ejpam-4585	39	3	cardinality	cardinality	NOUN
ejpam-4585	39	4	of	of	ADP
ejpam-4585	39	5	a	a	DET
ejpam-4585	39	6	hop	hop	NOUN
ejpam-4585	39	7	dominating	dominating	NOUN
ejpam-4585	39	8	set	set	NOUN
ejpam-4585	39	9	of	of	ADP
ejpam-4585	39	10	g	g	NOUN
ejpam-4585	39	11	,	,	PUNCT
ejpam-4585	39	12	denoted	denote	VERB
ejpam-4585	39	13	by	by	ADP
ejpam-4585	39	14	γh(g	γh(g	NOUN
ejpam-4585	39	15	)	)	PUNCT
ejpam-4585	39	16	,	,	PUNCT
ejpam-4585	39	17	is	be	AUX
ejpam-4585	39	18	called	call	VERB
ejpam-4585	39	19	the	the	DET
ejpam-4585	39	20	hop	hop	NOUN
ejpam-4585	39	21	domination	domination	NOUN
ejpam-4585	39	22	number	number	NOUN
ejpam-4585	39	23	of	of	ADP
ejpam-4585	39	24	g.	g.	PROPN
ejpam-4585	39	25	any	any	DET
ejpam-4585	39	26	hop	hop	NOUN
ejpam-4585	39	27	dominating	dominating	NOUN
ejpam-4585	39	28	set	set	VERB
ejpam-4585	39	29	with	with	ADP
ejpam-4585	39	30	cardinality	cardinality	NOUN
ejpam-4585	39	31	equal	equal	ADJ
ejpam-4585	39	32	to	to	ADP
ejpam-4585	39	33	γh(g	γh(g	NOUN
ejpam-4585	39	34	)	)	PUNCT
ejpam-4585	39	35	is	be	AUX
ejpam-4585	39	36	called	call	VERB
ejpam-4585	39	37	a	a	DET
ejpam-4585	39	38	γh	γh	ADV
ejpam-4585	39	39	-	-	PUNCT
ejpam-4585	39	40	set	set	NOUN
ejpam-4585	39	41	.	.	PUNCT
ejpam-4585	40	1	for	for	ADP
ejpam-4585	40	2	an	an	DET
ejpam-4585	40	3	ordered	order	VERB
ejpam-4585	40	4	set	set	NOUN
ejpam-4585	40	5	of	of	ADP
ejpam-4585	40	6	vertices	vertex	NOUN
ejpam-4585	40	7	w	w	NOUN
ejpam-4585	40	8	=	=	SYM
ejpam-4585	40	9	{	{	PUNCT
ejpam-4585	40	10	w1	w1	NOUN
ejpam-4585	40	11	,	,	PUNCT
ejpam-4585	40	12	w2	w2	NOUN
ejpam-4585	40	13	,	,	PUNCT
ejpam-4585	40	14	...	...	PUNCT
ejpam-4585	40	15	,	,	PUNCT
ejpam-4585	40	16	wk	wk	ADP
ejpam-4585	40	17	}	}	PUNCT
ejpam-4585	40	18	⊆	⊆	NUM
ejpam-4585	40	19	v	v	NOUN
ejpam-4585	40	20	(	(	PUNCT
ejpam-4585	40	21	g	g	NOUN
ejpam-4585	40	22	)	)	PUNCT
ejpam-4585	40	23	and	and	CCONJ
ejpam-4585	40	24	a	a	DET
ejpam-4585	40	25	vertex	vertex	NOUN
ejpam-4585	40	26	v	v	NOUN
ejpam-4585	40	27	in	in	ADP
ejpam-4585	40	28	g	g	NOUN
ejpam-4585	40	29	,	,	PUNCT
ejpam-4585	40	30	we	we	PRON
ejpam-4585	40	31	refer	refer	VERB
ejpam-4585	40	32	to	to	ADP
ejpam-4585	40	33	the	the	DET
ejpam-4585	40	34	k	k	NOUN
ejpam-4585	40	35	-	-	NOUN
ejpam-4585	40	36	vector	vector	NOUN
ejpam-4585	40	37	(	(	PUNCT
ejpam-4585	40	38	ordered	order	VERB
ejpam-4585	40	39	k	k	NOUN
ejpam-4585	40	40	-	-	PUNCT
ejpam-4585	40	41	tuple	tuple	NOUN
ejpam-4585	40	42	)	)	PUNCT
ejpam-4585	40	43	rg(v	rg(v	PROPN
ejpam-4585	40	44	/	/	SYM
ejpam-4585	40	45	w	w	NOUN
ejpam-4585	40	46	)	)	PUNCT
ejpam-4585	41	1	=	=	SYM
ejpam-4585	41	2	(	(	PUNCT
ejpam-4585	41	3	dg(v	dg(v	X
ejpam-4585	41	4	,	,	PUNCT
ejpam-4585	41	5	w1	w1	NOUN
ejpam-4585	41	6	)	)	PUNCT
ejpam-4585	41	7	,	,	PUNCT
ejpam-4585	41	8	dg(v	dg(v	X
ejpam-4585	41	9	,	,	PUNCT
ejpam-4585	41	10	w2	w2	NOUN
ejpam-4585	41	11	)	)	PUNCT
ejpam-4585	41	12	,	,	PUNCT
ejpam-4585	41	13	...	...	PUNCT
ejpam-4585	41	14	,	,	PUNCT
ejpam-4585	41	15	dg(v	dg(v	X
ejpam-4585	41	16	,	,	PUNCT
ejpam-4585	41	17	wk	wk	NOUN
ejpam-4585	41	18	)	)	PUNCT
ejpam-4585	41	19	)	)	PUNCT
ejpam-4585	42	1	as	as	ADP
ejpam-4585	42	2	the	the	DET
ejpam-4585	42	3	(	(	PUNCT
ejpam-4585	42	4	metric	metric	ADJ
ejpam-4585	42	5	)	)	PUNCT
ejpam-4585	42	6	representation	representation	NOUN
ejpam-4585	42	7	of	of	ADP
ejpam-4585	42	8	v	v	NOUN
ejpam-4585	42	9	with	with	ADP
ejpam-4585	42	10	respect	respect	NOUN
ejpam-4585	42	11	to	to	ADP
ejpam-4585	42	12	w	w	PROPN
ejpam-4585	42	13	.	.	PUNCT
ejpam-4585	43	1	the	the	DET
ejpam-4585	43	2	set	set	NOUN
ejpam-4585	43	3	w	w	NOUN
ejpam-4585	43	4	is	be	AUX
ejpam-4585	43	5	called	call	VERB
ejpam-4585	43	6	a	a	DET
ejpam-4585	43	7	resolving	resolving	NOUN
ejpam-4585	43	8	set	set	VERB
ejpam-4585	43	9	for	for	ADP
ejpam-4585	43	10	g	g	PROPN
ejpam-4585	43	11	if	if	SCONJ
ejpam-4585	43	12	distinct	distinct	ADJ
ejpam-4585	43	13	vertices	vertex	NOUN
ejpam-4585	43	14	have	have	VERB
ejpam-4585	43	15	distinct	distinct	ADJ
ejpam-4585	43	16	representations	representation	NOUN
ejpam-4585	43	17	with	with	ADP
ejpam-4585	43	18	respect	respect	NOUN
ejpam-4585	43	19	to	to	ADP
ejpam-4585	43	20	w	w	PROPN
ejpam-4585	43	21	.	.	PUNCT
ejpam-4585	44	1	hence	hence	ADV
ejpam-4585	44	2	,	,	PUNCT
ejpam-4585	44	3	if	if	SCONJ
ejpam-4585	44	4	w	w	NOUN
ejpam-4585	44	5	is	be	AUX
ejpam-4585	44	6	a	a	DET
ejpam-4585	44	7	resolving	resolving	NOUN
ejpam-4585	44	8	set	set	NOUN
ejpam-4585	44	9	of	of	ADP
ejpam-4585	44	10	cardinality	cardinality	PROPN
ejpam-4585	44	11	k	k	PROPN
ejpam-4585	44	12	for	for	ADP
ejpam-4585	44	13	a	a	DET
ejpam-4585	44	14	graph	graph	NOUN
ejpam-4585	44	15	g	g	NOUN
ejpam-4585	44	16	of	of	ADP
ejpam-4585	44	17	order	order	NOUN
ejpam-4585	44	18	n	n	CCONJ
ejpam-4585	44	19	,	,	PUNCT
ejpam-4585	44	20	then	then	ADV
ejpam-4585	44	21	the	the	DET
ejpam-4585	44	22	set	set	NOUN
ejpam-4585	44	23	{	{	PUNCT
ejpam-4585	44	24	rg(v	rg(v	NOUN
ejpam-4585	44	25	/	/	SYM
ejpam-4585	44	26	w	w	NOUN
ejpam-4585	44	27	)	)	PUNCT
ejpam-4585	44	28	:	:	PUNCT
ejpam-4585	44	29	v	v	X
ejpam-4585	44	30	∈	∈	PROPN
ejpam-4585	44	31	v	v	NOUN
ejpam-4585	44	32	(	(	PUNCT
ejpam-4585	44	33	g	g	NOUN
ejpam-4585	44	34	)	)	PUNCT
ejpam-4585	44	35	}	}	PUNCT
ejpam-4585	44	36	consists	consist	VERB
ejpam-4585	44	37	of	of	ADP
ejpam-4585	44	38	n	n	PRON
ejpam-4585	44	39	distinct	distinct	ADJ
ejpam-4585	44	40	k	k	NOUN
ejpam-4585	44	41	-	-	NOUN
ejpam-4585	44	42	vectors	vector	NOUN
ejpam-4585	44	43	.	.	PUNCT
ejpam-4585	45	1	a	a	DET
ejpam-4585	45	2	resolving	resolving	NOUN
ejpam-4585	45	3	set	set	NOUN
ejpam-4585	45	4	of	of	ADP
ejpam-4585	45	5	minimum	minimum	ADJ
ejpam-4585	45	6	cardinality	cardinality	NOUN
ejpam-4585	45	7	is	be	AUX
ejpam-4585	45	8	called	call	VERB
ejpam-4585	45	9	a	a	DET
ejpam-4585	45	10	minimum	minimum	ADJ
ejpam-4585	45	11	resolving	resolving	NOUN
ejpam-4585	45	12	set	set	VERB
ejpam-4585	45	13	or	or	CCONJ
ejpam-4585	45	14	a	a	DET
ejpam-4585	45	15	basis	basis	NOUN
ejpam-4585	45	16	,	,	PUNCT
ejpam-4585	45	17	and	and	CCONJ
ejpam-4585	45	18	the	the	DET
ejpam-4585	45	19	cardinality	cardinality	NOUN
ejpam-4585	45	20	of	of	ADP
ejpam-4585	45	21	a	a	DET
ejpam-4585	45	22	basis	basis	NOUN
ejpam-4585	45	23	for	for	ADP
ejpam-4585	45	24	g	g	PROPN
ejpam-4585	45	25	is	be	AUX
ejpam-4585	45	26	the	the	DET
ejpam-4585	45	27	dimension	dimension	NOUN
ejpam-4585	45	28	dim(g	dim(g	PROPN
ejpam-4585	45	29	)	)	PUNCT
ejpam-4585	45	30	of	of	ADP
ejpam-4585	45	31	g.	g.	PROPN
ejpam-4585	45	32	an	an	DET
ejpam-4585	45	33	ordered	order	VERB
ejpam-4585	45	34	set	set	NOUN
ejpam-4585	45	35	of	of	ADP
ejpam-4585	45	36	vertices	vertex	NOUN
ejpam-4585	45	37	w	w	NOUN
ejpam-4585	45	38	=	=	SYM
ejpam-4585	45	39	{	{	PUNCT
ejpam-4585	45	40	w1	w1	NOUN
ejpam-4585	45	41	,	,	PUNCT
ejpam-4585	45	42	...	...	PUNCT
ejpam-4585	45	43	,	,	PUNCT
ejpam-4585	45	44	wk	wk	X
ejpam-4585	45	45	}	}	PUNCT
ejpam-4585	45	46	is	be	AUX
ejpam-4585	45	47	a	a	DET
ejpam-4585	45	48	k	k	NOUN
ejpam-4585	45	49	-	-	PUNCT
ejpam-4585	45	50	resolving	resolving	NOUN
ejpam-4585	45	51	set	set	NOUN
ejpam-4585	45	52	for	for	ADP
ejpam-4585	45	53	g	g	PROPN
ejpam-4585	45	54	if	if	SCONJ
ejpam-4585	45	55	,	,	PUNCT
ejpam-4585	45	56	for	for	ADP
ejpam-4585	45	57	any	any	DET
ejpam-4585	45	58	distinct	distinct	ADJ
ejpam-4585	45	59	vertices	vertex	NOUN
ejpam-4585	45	60	u	u	NOUN
ejpam-4585	45	61	,	,	PUNCT
ejpam-4585	45	62	v	v	NOUN
ejpam-4585	45	63	∈	∈	PROPN
ejpam-4585	45	64	v	v	NOUN
ejpam-4585	45	65	(	(	PUNCT
ejpam-4585	45	66	g	g	NOUN
ejpam-4585	45	67	)	)	PUNCT
ejpam-4585	45	68	,	,	PUNCT
ejpam-4585	45	69	the	the	DET
ejpam-4585	45	70	(	(	PUNCT
ejpam-4585	45	71	metric	metric	ADJ
ejpam-4585	45	72	)	)	PUNCT
ejpam-4585	45	73	representations	representation	NOUN
ejpam-4585	45	74	rg(u	rg(u	NOUN
ejpam-4585	45	75	/	/	SYM
ejpam-4585	45	76	w	w	NOUN
ejpam-4585	45	77	)	)	PUNCT
ejpam-4585	45	78	and	and	CCONJ
ejpam-4585	45	79	rg(v	rg(v	PROPN
ejpam-4585	45	80	/	/	SYM
ejpam-4585	45	81	w	w	NOUN
ejpam-4585	45	82	)	)	PUNCT
ejpam-4585	45	83	of	of	ADP
ejpam-4585	45	84	u	u	NOUN
ejpam-4585	45	85	and	and	CCONJ
ejpam-4585	45	86	v	v	NOUN
ejpam-4585	45	87	,	,	PUNCT
ejpam-4585	45	88	respectively	respectively	ADV
ejpam-4585	45	89	,	,	PUNCT
ejpam-4585	45	90	differ	differ	VERB
ejpam-4585	45	91	in	in	ADP
ejpam-4585	45	92	at	at	ADP
ejpam-4585	45	93	least	least	ADJ
ejpam-4585	45	94	k	k	NOUN
ejpam-4585	45	95	positions	position	NOUN
ejpam-4585	45	96	.	.	PUNCT
ejpam-4585	46	1	if	if	SCONJ
ejpam-4585	46	2	k	k	PROPN
ejpam-4585	46	3	=	=	SYM
ejpam-4585	46	4	1	1	NUM
ejpam-4585	46	5	,	,	PUNCT
ejpam-4585	46	6	then	then	ADV
ejpam-4585	46	7	the	the	DET
ejpam-4585	46	8	k	k	NOUN
ejpam-4585	46	9	-	-	PUNCT
ejpam-4585	46	10	resolving	resolving	ADJ
ejpam-4585	46	11	set	set	NOUN
ejpam-4585	46	12	is	be	AUX
ejpam-4585	46	13	called	call	VERB
ejpam-4585	46	14	a	a	DET
ejpam-4585	46	15	resolving	resolving	NOUN
ejpam-4585	46	16	set	set	VERB
ejpam-4585	46	17	for	for	ADP
ejpam-4585	46	18	g.	g.	PROPN
ejpam-4585	46	19	if	if	SCONJ
ejpam-4585	46	20	k	k	PROPN
ejpam-4585	46	21	=	=	SYM
ejpam-4585	46	22	2	2	NUM
ejpam-4585	46	23	,	,	PUNCT
ejpam-4585	46	24	then	then	ADV
ejpam-4585	46	25	the	the	DET
ejpam-4585	46	26	k	k	NOUN
ejpam-4585	46	27	-	-	PUNCT
ejpam-4585	46	28	resolving	resolving	ADJ
ejpam-4585	46	29	set	set	NOUN
ejpam-4585	46	30	is	be	AUX
ejpam-4585	46	31	called	call	VERB
ejpam-4585	46	32	a	a	DET
ejpam-4585	46	33	2	2	NUM
ejpam-4585	46	34	-	-	PUNCT
ejpam-4585	46	35	resolving	resolving	NOUN
ejpam-4585	46	36	set	set	NOUN
ejpam-4585	46	37	for	for	ADP
ejpam-4585	46	38	g.	g.	PROPN
ejpam-4585	46	39	if	if	SCONJ
ejpam-4585	46	40	g	g	PROPN
ejpam-4585	46	41	has	have	VERB
ejpam-4585	46	42	a	a	DET
ejpam-4585	46	43	k	k	ADJ
ejpam-4585	46	44	-	-	ADJ
ejpam-4585	46	45	resolving	resolving	ADJ
ejpam-4585	46	46	set	set	NOUN
ejpam-4585	46	47	,	,	PUNCT
ejpam-4585	46	48	the	the	DET
ejpam-4585	46	49	minimum	minimum	ADJ
ejpam-4585	46	50	cardinality	cardinality	PROPN
ejpam-4585	46	51	dimk(g	dimk(g	PROPN
ejpam-4585	46	52	)	)	PUNCT
ejpam-4585	46	53	of	of	ADP
ejpam-4585	46	54	a	a	DET
ejpam-4585	46	55	k	k	NOUN
ejpam-4585	46	56	-	-	PUNCT
ejpam-4585	46	57	resolving	resolving	ADJ
ejpam-4585	46	58	set	set	NOUN
ejpam-4585	46	59	is	be	AUX
ejpam-4585	46	60	called	call	VERB
ejpam-4585	46	61	the	the	DET
ejpam-4585	46	62	k	k	ADJ
ejpam-4585	46	63	-	-	ADJ
ejpam-4585	46	64	metric	metric	ADJ
ejpam-4585	46	65	dimension	dimension	NOUN
ejpam-4585	46	66	of	of	ADP
ejpam-4585	46	67	g.	g.	PROPN
ejpam-4585	46	68	a.m.	a.m.	PROPN
ejpam-4585	47	1	mahistrado	mahistrado	PROPN
ejpam-4585	47	2	,	,	PUNCT
ejpam-4585	47	3	h.	h.	PROPN
ejpam-4585	47	4	rara	rara	PROPN
ejpam-4585	47	5	/	/	SYM
ejpam-4585	47	6	eur	eur	PROPN
ejpam-4585	47	7	.	.	PUNCT
ejpam-4585	48	1	j.	j.	PROPN
ejpam-4585	48	2	pure	pure	PROPN
ejpam-4585	48	3	appl	appl	PROPN
ejpam-4585	48	4	.	.	PROPN
ejpam-4585	48	5	math	math	PROPN
ejpam-4585	48	6	,	,	PUNCT
ejpam-4585	48	7	15	15	NUM
ejpam-4585	48	8	(	(	PUNCT
ejpam-4585	48	9	4	4	NUM
ejpam-4585	48	10	)	)	PUNCT
ejpam-4585	48	11	(	(	PUNCT
ejpam-4585	48	12	2022	2022	NUM
ejpam-4585	48	13	)	)	PUNCT
ejpam-4585	48	14	,	,	PUNCT
ejpam-4585	48	15	1982	1982	NUM
ejpam-4585	48	16	-	-	SYM
ejpam-4585	48	17	1997	1997	NUM
ejpam-4585	48	18	1984	1984	NUM
ejpam-4585	48	19	a	a	DET
ejpam-4585	48	20	2	2	NUM
ejpam-4585	48	21	-	-	PUNCT
ejpam-4585	48	22	resolving	resolve	VERB
ejpam-4585	48	23	set	set	NOUN
ejpam-4585	48	24	s	s	PROPN
ejpam-4585	48	25	⊆	⊆	NUM
ejpam-4585	48	26	v	v	NOUN
ejpam-4585	48	27	(	(	PUNCT
ejpam-4585	48	28	g	g	NOUN
ejpam-4585	48	29	)	)	PUNCT
ejpam-4585	48	30	which	which	PRON
ejpam-4585	48	31	is	be	AUX
ejpam-4585	48	32	hop	hop	NOUN
ejpam-4585	48	33	dominating	dominating	NOUN
ejpam-4585	48	34	is	be	AUX
ejpam-4585	48	35	called	call	VERB
ejpam-4585	48	36	a	a	DET
ejpam-4585	48	37	2	2	NUM
ejpam-4585	48	38	-	-	PUNCT
ejpam-4585	48	39	resolving	resolve	VERB
ejpam-4585	48	40	hop	hop	NOUN
ejpam-4585	48	41	dominating	dominating	NOUN
ejpam-4585	48	42	set	set	NOUN
ejpam-4585	48	43	or	or	CCONJ
ejpam-4585	48	44	simply	simply	ADV
ejpam-4585	48	45	2r	2r	NUM
ejpam-4585	48	46	-	-	PUNCT
ejpam-4585	48	47	hop	hop	NOUN
ejpam-4585	48	48	dominating	dominating	NOUN
ejpam-4585	48	49	set	set	VERB
ejpam-4585	48	50	ing	ing	NOUN
ejpam-4585	48	51	.	.	PUNCT
ejpam-4585	49	1	the	the	DET
ejpam-4585	49	2	minimum	minimum	ADJ
ejpam-4585	49	3	cardinality	cardinality	NOUN
ejpam-4585	49	4	of	of	ADP
ejpam-4585	49	5	a	a	DET
ejpam-4585	49	6	2	2	NUM
ejpam-4585	49	7	-	-	PUNCT
ejpam-4585	49	8	resolving	resolve	VERB
ejpam-4585	49	9	hop	hop	NOUN
ejpam-4585	49	10	dominating	dominating	NOUN
ejpam-4585	49	11	set	set	VERB
ejpam-4585	49	12	in	in	ADP
ejpam-4585	49	13	g	g	NOUN
ejpam-4585	49	14	,	,	PUNCT
ejpam-4585	49	15	denoted	denote	VERB
ejpam-4585	49	16	by	by	ADP
ejpam-4585	49	17	γ2rh(g	γ2rh(g	NOUN
ejpam-4585	49	18	)	)	PUNCT
ejpam-4585	49	19	,	,	PUNCT
ejpam-4585	49	20	is	be	AUX
ejpam-4585	49	21	called	call	VERB
ejpam-4585	49	22	the	the	DET
ejpam-4585	49	23	2r	2r	NUM
ejpam-4585	49	24	-	-	PUNCT
ejpam-4585	49	25	hop	hop	NOUN
ejpam-4585	49	26	domination	domination	NOUN
ejpam-4585	49	27	number	number	NOUN
ejpam-4585	49	28	of	of	ADP
ejpam-4585	49	29	g.	g.	PROPN
ejpam-4585	49	30	any	any	DET
ejpam-4585	49	31	2r	2r	NUM
ejpam-4585	49	32	-	-	PUNCT
ejpam-4585	49	33	hop	hop	NOUN
ejpam-4585	49	34	dominating	dominating	NOUN
ejpam-4585	49	35	set	set	NOUN
ejpam-4585	49	36	of	of	ADP
ejpam-4585	49	37	cardinality	cardinality	NOUN
ejpam-4585	49	38	γ2rh(g	γ2rh(g	NOUN
ejpam-4585	49	39	)	)	PUNCT
ejpam-4585	49	40	is	be	AUX
ejpam-4585	49	41	then	then	ADV
ejpam-4585	49	42	referred	refer	VERB
ejpam-4585	49	43	to	to	ADP
ejpam-4585	49	44	as	as	ADP
ejpam-4585	49	45	a	a	DET
ejpam-4585	49	46	γ2rh	γ2rh	NOUN
ejpam-4585	49	47	-	-	PUNCT
ejpam-4585	49	48	set	set	ADJ
ejpam-4585	49	49	in	in	ADP
ejpam-4585	49	50	g.	g.	PROPN
ejpam-4585	49	51	3	3	NUM
ejpam-4585	49	52	.	.	PUNCT
ejpam-4585	50	1	preliminary	preliminary	ADJ
ejpam-4585	50	2	results	result	NOUN
ejpam-4585	50	3	definition	definition	NOUN
ejpam-4585	50	4	1	1	NUM
ejpam-4585	50	5	.	.	PUNCT
ejpam-4585	51	1	[	[	X
ejpam-4585	51	2	6	6	NUM
ejpam-4585	51	3	]	]	X
ejpam-4585	51	4	letg	letg	NOUN
ejpam-4585	51	5	be	be	VERB
ejpam-4585	51	6	any	any	DET
ejpam-4585	51	7	nontrivial	nontrivial	ADJ
ejpam-4585	51	8	connected	connect	VERB
ejpam-4585	51	9	graph	graph	NOUN
ejpam-4585	51	10	and	and	CCONJ
ejpam-4585	51	11	s	s	VERB
ejpam-4585	51	12	⊆	⊆	NUM
ejpam-4585	51	13	v	v	NOUN
ejpam-4585	51	14	(	(	PUNCT
ejpam-4585	51	15	g	g	NOUN
ejpam-4585	51	16	)	)	PUNCT
ejpam-4585	51	17	.	.	PUNCT
ejpam-4585	52	1	a	a	DET
ejpam-4585	52	2	set	set	NOUN
ejpam-4585	52	3	s	s	NOUN
ejpam-4585	52	4	⊆	⊆	NUM
ejpam-4585	52	5	v	v	NOUN
ejpam-4585	52	6	(	(	PUNCT
ejpam-4585	52	7	g	g	NOUN
ejpam-4585	52	8	)	)	PUNCT
ejpam-4585	52	9	is	be	AUX
ejpam-4585	52	10	a	a	DET
ejpam-4585	52	11	2	2	NUM
ejpam-4585	52	12	-	-	PUNCT
ejpam-4585	52	13	locating	locate	VERB
ejpam-4585	52	14	set	set	NOUN
ejpam-4585	52	15	of	of	ADP
ejpam-4585	52	16	g	g	NOUN
ejpam-4585	52	17	if	if	SCONJ
ejpam-4585	52	18	it	it	PRON
ejpam-4585	52	19	satisfies	satisfy	VERB
ejpam-4585	52	20	the	the	DET
ejpam-4585	52	21	following	follow	VERB
ejpam-4585	52	22	conditions	condition	NOUN
ejpam-4585	52	23	:	:	PUNCT
ejpam-4585	52	24	(	(	PUNCT
ejpam-4585	52	25	i	i	NOUN
ejpam-4585	52	26	)	)	PUNCT
ejpam-4585	52	27	∣∣[(ng(x)\ng(y	∣∣[(ng(x)\ng(y	PROPN
ejpam-4585	52	28	)	)	PUNCT
ejpam-4585	52	29	)	)	PUNCT
ejpam-4585	53	1	∩s]∪	∩s]∪	VERB
ejpam-4585	53	2	[	[	PUNCT
ejpam-4585	53	3	(	(	PUNCT
ejpam-4585	53	4	ng(y)\ng(x	ng(y)\ng(x	NOUN
ejpam-4585	53	5	)	)	PUNCT
ejpam-4585	53	6	)	)	PUNCT
ejpam-4585	54	1	∩s	∩s	PROPN
ejpam-4585	54	2	]	]	PUNCT
ejpam-4585	54	3	∣∣	∣∣	NUM
ejpam-4585	54	4	≥	≥	NOUN
ejpam-4585	54	5	2	2	NUM
ejpam-4585	54	6	,	,	PUNCT
ejpam-4585	54	7	for	for	ADP
ejpam-4585	54	8	all	all	DET
ejpam-4585	54	9	x	x	NOUN
ejpam-4585	54	10	,	,	PUNCT
ejpam-4585	54	11	y	y	PROPN
ejpam-4585	54	12	∈	∈	PROPN
ejpam-4585	54	13	v	v	X
ejpam-4585	54	14	(	(	PUNCT
ejpam-4585	54	15	g)\s	g)\s	VERB
ejpam-4585	54	16	with	with	ADP
ejpam-4585	54	17	x	x	PROPN
ejpam-4585	54	18	̸=	̸=	PROPN
ejpam-4585	54	19	y.	y.	PROPN
ejpam-4585	54	20	(	(	PUNCT
ejpam-4585	54	21	ii	ii	PROPN
ejpam-4585	54	22	)	)	PUNCT
ejpam-4585	54	23	(	(	PUNCT
ejpam-4585	54	24	ng(v)\ng(w	ng(v)\ng(w	ADJ
ejpam-4585	54	25	)	)	PUNCT
ejpam-4585	54	26	)	)	PUNCT
ejpam-4585	54	27	∩	∩	PROPN
ejpam-4585	54	28	s	s	PART
ejpam-4585	54	29	̸=	̸=	PROPN
ejpam-4585	54	30	∅	∅	NOUN
ejpam-4585	54	31	or	or	CCONJ
ejpam-4585	54	32	(	(	PUNCT
ejpam-4585	54	33	ng(w)\ng[v	ng(w)\ng[v	PROPN
ejpam-4585	54	34	]	]	PUNCT
ejpam-4585	54	35	)	)	PUNCT
ejpam-4585	54	36	∩	∩	PROPN
ejpam-4585	54	37	s	s	PART
ejpam-4585	54	38	̸=	̸=	PROPN
ejpam-4585	54	39	∅	∅	NOUN
ejpam-4585	54	40	,	,	PUNCT
ejpam-4585	54	41	for	for	ADP
ejpam-4585	54	42	all	all	PRON
ejpam-4585	54	43	v	v	ADP
ejpam-4585	54	44	∈	∈	NOUN
ejpam-4585	54	45	s	s	NOUN
ejpam-4585	54	46	and	and	CCONJ
ejpam-4585	54	47	for	for	ADP
ejpam-4585	54	48	all	all	PRON
ejpam-4585	54	49	w	w	PROPN
ejpam-4585	54	50	∈	∈	PROPN
ejpam-4585	54	51	v	v	NOUN
ejpam-4585	54	52	(	(	PUNCT
ejpam-4585	54	53	g)\s	g)\s	NOUN
ejpam-4585	54	54	.	.	PUNCT
ejpam-4585	55	1	the	the	DET
ejpam-4585	55	2	2	2	NUM
ejpam-4585	55	3	-	-	PUNCT
ejpam-4585	55	4	locating	locate	VERB
ejpam-4585	55	5	number	number	NOUN
ejpam-4585	55	6	of	of	ADP
ejpam-4585	55	7	g	g	NOUN
ejpam-4585	55	8	,	,	PUNCT
ejpam-4585	55	9	denoted	denote	VERB
ejpam-4585	55	10	by	by	ADP
ejpam-4585	55	11	ln2(g	ln2(g	NOUN
ejpam-4585	55	12	)	)	PUNCT
ejpam-4585	55	13	,	,	PUNCT
ejpam-4585	55	14	is	be	AUX
ejpam-4585	55	15	the	the	DET
ejpam-4585	55	16	smallest	small	ADJ
ejpam-4585	55	17	cardinality	cardinality	NOUN
ejpam-4585	55	18	of	of	ADP
ejpam-4585	55	19	a	a	DET
ejpam-4585	55	20	2	2	NUM
ejpam-4585	55	21	-	-	PUNCT
ejpam-4585	55	22	locating	locate	VERB
ejpam-4585	55	23	set	set	NOUN
ejpam-4585	55	24	of	of	ADP
ejpam-4585	55	25	g.	g.	PROPN
ejpam-4585	55	26	a	a	DET
ejpam-4585	55	27	2	2	NUM
ejpam-4585	55	28	-	-	PUNCT
ejpam-4585	55	29	locating	locate	VERB
ejpam-4585	55	30	set	set	NOUN
ejpam-4585	55	31	of	of	ADP
ejpam-4585	55	32	g	g	NOUN
ejpam-4585	55	33	of	of	ADP
ejpam-4585	55	34	cardinality	cardinality	PROPN
ejpam-4585	55	35	ln2(g	ln2(g	PROPN
ejpam-4585	55	36	)	)	PUNCT
ejpam-4585	55	37	is	be	AUX
ejpam-4585	55	38	referred	refer	VERB
ejpam-4585	55	39	to	to	ADP
ejpam-4585	55	40	as	as	ADP
ejpam-4585	55	41	an	an	DET
ejpam-4585	55	42	ln2	ln2	NOUN
ejpam-4585	55	43	-	-	PUNCT
ejpam-4585	55	44	set	set	NOUN
ejpam-4585	55	45	of	of	ADP
ejpam-4585	55	46	g.	g.	PROPN
ejpam-4585	55	47	definition	definition	NOUN
ejpam-4585	55	48	2	2	NUM
ejpam-4585	55	49	.	.	PUNCT
ejpam-4585	56	1	[	[	X
ejpam-4585	56	2	12	12	NUM
ejpam-4585	56	3	]	]	PUNCT
ejpam-4585	56	4	a	a	DET
ejpam-4585	56	5	set	set	NOUN
ejpam-4585	56	6	d	d	NOUN
ejpam-4585	56	7	⊆	⊆	NUM
ejpam-4585	56	8	v	v	ADP
ejpam-4585	56	9	(	(	PUNCT
ejpam-4585	56	10	g	g	NOUN
ejpam-4585	56	11	)	)	PUNCT
ejpam-4585	56	12	is	be	AUX
ejpam-4585	56	13	a	a	DET
ejpam-4585	56	14	point	point	NOUN
ejpam-4585	56	15	-	-	PUNCT
ejpam-4585	56	16	wise	wise	ADJ
ejpam-4585	56	17	non	non	ADJ
ejpam-4585	56	18	-	-	ADJ
ejpam-4585	56	19	dominating	dominating	ADJ
ejpam-4585	56	20	set	set	NOUN
ejpam-4585	56	21	of	of	ADP
ejpam-4585	56	22	g	g	PROPN
ejpam-4585	56	23	if	if	SCONJ
ejpam-4585	56	24	for	for	ADP
ejpam-4585	56	25	each	each	DET
ejpam-4585	56	26	v	v	NUM
ejpam-4585	56	27	∈	∈	PROPN
ejpam-4585	56	28	v	v	NOUN
ejpam-4585	56	29	(	(	PUNCT
ejpam-4585	56	30	g)\d	g)\d	NOUN
ejpam-4585	56	31	,	,	PUNCT
ejpam-4585	56	32	there	there	PRON
ejpam-4585	56	33	exists	exist	VERB
ejpam-4585	56	34	u	u	NOUN
ejpam-4585	56	35	∈	∈	PROPN
ejpam-4585	56	36	d	d	ADP
ejpam-4585	56	37	such	such	ADJ
ejpam-4585	56	38	that	that	DET
ejpam-4585	56	39	v	v	NOUN
ejpam-4585	56	40	/∈	/∈	PUNCT
ejpam-4585	56	41	ng(u	ng(u	NOUN
ejpam-4585	56	42	)	)	PUNCT
ejpam-4585	56	43	.	.	PUNCT
ejpam-4585	57	1	the	the	DET
ejpam-4585	57	2	smallest	small	ADJ
ejpam-4585	57	3	cardinality	cardinality	NOUN
ejpam-4585	57	4	of	of	ADP
ejpam-4585	57	5	a	a	DET
ejpam-4585	57	6	point	point	NOUN
ejpam-4585	57	7	-	-	PUNCT
ejpam-4585	57	8	wise	wise	ADJ
ejpam-4585	57	9	non	non	ADJ
ejpam-4585	57	10	-	-	ADJ
ejpam-4585	57	11	dominating	dominating	ADJ
ejpam-4585	57	12	set	set	NOUN
ejpam-4585	57	13	of	of	ADP
ejpam-4585	57	14	g	g	NOUN
ejpam-4585	57	15	,	,	PUNCT
ejpam-4585	57	16	denoted	denote	VERB
ejpam-4585	57	17	by	by	ADP
ejpam-4585	57	18	pnd(g	pnd(g	PROPN
ejpam-4585	57	19	)	)	PUNCT
ejpam-4585	57	20	,	,	PUNCT
ejpam-4585	57	21	is	be	AUX
ejpam-4585	57	22	called	call	VERB
ejpam-4585	57	23	the	the	DET
ejpam-4585	57	24	point	point	NOUN
ejpam-4585	57	25	-	-	PUNCT
ejpam-4585	57	26	wise	wise	ADJ
ejpam-4585	57	27	nondomination	nondomination	NOUN
ejpam-4585	57	28	number	number	NOUN
ejpam-4585	57	29	of	of	ADP
ejpam-4585	57	30	g.	g.	PROPN
ejpam-4585	57	31	any	any	DET
ejpam-4585	57	32	point	point	NOUN
ejpam-4585	57	33	-	-	PUNCT
ejpam-4585	57	34	wise	wise	ADJ
ejpam-4585	57	35	non	non	ADJ
ejpam-4585	57	36	-	-	ADJ
ejpam-4585	57	37	dominating	dominating	ADJ
ejpam-4585	57	38	set	set	NOUN
ejpam-4585	57	39	d	d	NOUN
ejpam-4585	57	40	of	of	ADP
ejpam-4585	57	41	g	g	NOUN
ejpam-4585	57	42	with	with	ADP
ejpam-4585	57	43	|d|	|d|	PROPN
ejpam-4585	57	44	=	=	SYM
ejpam-4585	57	45	pnd(g	pnd(g	PROPN
ejpam-4585	57	46	)	)	PUNCT
ejpam-4585	57	47	,	,	PUNCT
ejpam-4585	57	48	is	be	AUX
ejpam-4585	57	49	called	call	VERB
ejpam-4585	57	50	a	a	DET
ejpam-4585	57	51	pnd	pnd	NOUN
ejpam-4585	57	52	-	-	PUNCT
ejpam-4585	57	53	set	set	VERB
ejpam-4585	57	54	ofg	ofg	NOUN
ejpam-4585	57	55	.	.	PUNCT
ejpam-4585	58	1	a	a	DET
ejpam-4585	58	2	dominating	dominating	NOUN
ejpam-4585	58	3	set	set	NOUN
ejpam-4585	58	4	d	d	NOUN
ejpam-4585	58	5	which	which	PRON
ejpam-4585	58	6	is	be	AUX
ejpam-4585	58	7	also	also	ADV
ejpam-4585	58	8	a	a	DET
ejpam-4585	58	9	point	point	NOUN
ejpam-4585	58	10	-	-	PUNCT
ejpam-4585	58	11	wise	wise	ADJ
ejpam-4585	58	12	non	non	ADJ
ejpam-4585	58	13	-	-	ADJ
ejpam-4585	58	14	dominating	dominating	ADJ
ejpam-4585	58	15	set	set	NOUN
ejpam-4585	58	16	of	of	ADP
ejpam-4585	58	17	g	g	PROPN
ejpam-4585	58	18	is	be	AUX
ejpam-4585	58	19	called	call	VERB
ejpam-4585	58	20	a	a	DET
ejpam-4585	58	21	dominating	dominating	NOUN
ejpam-4585	58	22	point	point	NOUN
ejpam-4585	58	23	-	-	PUNCT
ejpam-4585	58	24	wise	wise	ADJ
ejpam-4585	58	25	non	non	ADJ
ejpam-4585	58	26	-	-	ADJ
ejpam-4585	58	27	dominating	dominating	ADJ
ejpam-4585	58	28	set	set	NOUN
ejpam-4585	58	29	of	of	ADP
ejpam-4585	58	30	g.	g.	PROPN
ejpam-4585	58	31	the	the	DET
ejpam-4585	58	32	smallest	small	ADJ
ejpam-4585	58	33	cardinality	cardinality	NOUN
ejpam-4585	58	34	of	of	ADP
ejpam-4585	58	35	a	a	DET
ejpam-4585	58	36	dominating	dominating	NOUN
ejpam-4585	58	37	point	point	NOUN
ejpam-4585	58	38	-	-	PUNCT
ejpam-4585	58	39	wise	wise	ADJ
ejpam-4585	58	40	non	non	ADJ
ejpam-4585	58	41	-	-	ADJ
ejpam-4585	58	42	dominating	dominating	ADJ
ejpam-4585	58	43	set	set	NOUN
ejpam-4585	58	44	of	of	ADP
ejpam-4585	58	45	g	g	NOUN
ejpam-4585	58	46	will	will	AUX
ejpam-4585	58	47	be	be	AUX
ejpam-4585	58	48	denoted	denote	VERB
ejpam-4585	58	49	by	by	ADP
ejpam-4585	58	50	γpnd(g	γpnd(g	PROPN
ejpam-4585	58	51	)	)	PUNCT
ejpam-4585	58	52	.	.	PUNCT
ejpam-4585	59	1	any	any	DET
ejpam-4585	59	2	dominating	dominating	NOUN
ejpam-4585	59	3	point	point	NOUN
ejpam-4585	59	4	-	-	PUNCT
ejpam-4585	59	5	wise	wise	ADJ
ejpam-4585	59	6	non	non	ADJ
ejpam-4585	59	7	-	-	ADJ
ejpam-4585	59	8	dominating	dominating	ADJ
ejpam-4585	59	9	set	set	NOUN
ejpam-4585	59	10	d	d	NOUN
ejpam-4585	59	11	of	of	ADP
ejpam-4585	59	12	g	g	NOUN
ejpam-4585	59	13	with	with	ADP
ejpam-4585	59	14	|d|	|d|	PROPN
ejpam-4585	59	15	=	=	SYM
ejpam-4585	59	16	γpnd(g	γpnd(g	PROPN
ejpam-4585	59	17	)	)	PUNCT
ejpam-4585	59	18	,	,	PUNCT
ejpam-4585	59	19	is	be	AUX
ejpam-4585	59	20	called	call	VERB
ejpam-4585	59	21	a	a	DET
ejpam-4585	59	22	γpnd	γpnd	NOUN
ejpam-4585	59	23	-	-	PUNCT
ejpam-4585	59	24	set	set	NOUN
ejpam-4585	59	25	of	of	ADP
ejpam-4585	59	26	g.	g.	PROPN
ejpam-4585	59	27	definition	definition	NOUN
ejpam-4585	59	28	3	3	NUM
ejpam-4585	59	29	.	.	PUNCT
ejpam-4585	60	1	a	a	DET
ejpam-4585	60	2	2	2	NUM
ejpam-4585	60	3	-	-	PUNCT
ejpam-4585	60	4	locating	locate	VERB
ejpam-4585	60	5	set	set	NOUN
ejpam-4585	60	6	s	s	PROPN
ejpam-4585	60	7	⊆	⊆	NUM
ejpam-4585	60	8	v	v	NOUN
ejpam-4585	60	9	(	(	PUNCT
ejpam-4585	60	10	g	g	NOUN
ejpam-4585	60	11	)	)	PUNCT
ejpam-4585	60	12	which	which	PRON
ejpam-4585	60	13	is	be	AUX
ejpam-4585	60	14	point	point	ADV
ejpam-4585	60	15	-	-	PUNCT
ejpam-4585	60	16	wise	wise	ADJ
ejpam-4585	60	17	non	non	ADJ
ejpam-4585	60	18	-	-	ADJ
ejpam-4585	60	19	dominating	dominating	NOUN
ejpam-4585	60	20	is	be	AUX
ejpam-4585	60	21	called	call	VERB
ejpam-4585	60	22	a	a	DET
ejpam-4585	60	23	2	2	NUM
ejpam-4585	60	24	-	-	PUNCT
ejpam-4585	60	25	locating	locate	VERB
ejpam-4585	60	26	point	point	NOUN
ejpam-4585	60	27	-	-	PUNCT
ejpam-4585	60	28	wise	wise	ADJ
ejpam-4585	60	29	non	non	ADJ
ejpam-4585	60	30	-	-	ADJ
ejpam-4585	60	31	dominating	dominating	ADJ
ejpam-4585	60	32	set	set	NOUN
ejpam-4585	60	33	in	in	ADP
ejpam-4585	60	34	g.	g.	PROPN
ejpam-4585	60	35	the	the	DET
ejpam-4585	60	36	minimum	minimum	ADJ
ejpam-4585	60	37	cardinality	cardinality	NOUN
ejpam-4585	60	38	of	of	ADP
ejpam-4585	60	39	a	a	DET
ejpam-4585	60	40	2	2	NUM
ejpam-4585	60	41	-	-	PUNCT
ejpam-4585	60	42	locating	locate	VERB
ejpam-4585	60	43	point	point	NOUN
ejpam-4585	60	44	-	-	PUNCT
ejpam-4585	60	45	wise	wise	ADJ
ejpam-4585	60	46	non	non	ADJ
ejpam-4585	60	47	-	-	ADJ
ejpam-4585	60	48	dominating	dominating	ADJ
ejpam-4585	60	49	set	set	NOUN
ejpam-4585	60	50	in	in	ADP
ejpam-4585	60	51	g	g	NOUN
ejpam-4585	60	52	,	,	PUNCT
ejpam-4585	60	53	denoted	denote	VERB
ejpam-4585	60	54	by	by	ADP
ejpam-4585	60	55	lnpnd	lnpnd	ADJ
ejpam-4585	60	56	2	2	NUM
ejpam-4585	60	57	(	(	PUNCT
ejpam-4585	60	58	g	g	NOUN
ejpam-4585	60	59	)	)	PUNCT
ejpam-4585	60	60	is	be	AUX
ejpam-4585	60	61	called	call	VERB
ejpam-4585	60	62	the	the	DET
ejpam-4585	60	63	2	2	NUM
ejpam-4585	60	64	-	-	PUNCT
ejpam-4585	60	65	locating	locate	VERB
ejpam-4585	60	66	point	point	NOUN
ejpam-4585	60	67	-	-	PUNCT
ejpam-4585	60	68	wise	wise	ADJ
ejpam-4585	60	69	non	non	ADJ
ejpam-4585	60	70	-	-	ADJ
ejpam-4585	60	71	domination	domination	ADJ
ejpam-4585	60	72	number	number	NOUN
ejpam-4585	60	73	of	of	ADP
ejpam-4585	60	74	g.	g.	PROPN
ejpam-4585	60	75	any	any	DET
ejpam-4585	60	76	2	2	NUM
ejpam-4585	60	77	-	-	PUNCT
ejpam-4585	60	78	locating	locate	VERB
ejpam-4585	60	79	point	point	NOUN
ejpam-4585	60	80	-	-	PUNCT
ejpam-4585	60	81	wise	wise	ADJ
ejpam-4585	60	82	non	non	ADJ
ejpam-4585	60	83	-	-	ADJ
ejpam-4585	60	84	dominating	dominating	ADJ
ejpam-4585	60	85	set	set	NOUN
ejpam-4585	60	86	of	of	ADP
ejpam-4585	60	87	cardinality	cardinality	PROPN
ejpam-4585	60	88	lnpnd	lnpnd	PROPN
ejpam-4585	60	89	2	2	NUM
ejpam-4585	60	90	(	(	PUNCT
ejpam-4585	60	91	g	g	NOUN
ejpam-4585	60	92	)	)	PUNCT
ejpam-4585	60	93	is	be	AUX
ejpam-4585	60	94	then	then	ADV
ejpam-4585	60	95	referred	refer	VERB
ejpam-4585	60	96	to	to	ADP
ejpam-4585	60	97	as	as	ADP
ejpam-4585	60	98	a	a	DET
ejpam-4585	60	99	lnpnd	lnpnd	ADJ
ejpam-4585	60	100	2	2	NUM
ejpam-4585	60	101	(	(	PUNCT
ejpam-4585	60	102	g)-set	g)-set	VERB
ejpam-4585	60	103	in	in	ADP
ejpam-4585	60	104	g.	g.	PROPN
ejpam-4585	60	105	example	example	NOUN
ejpam-4585	61	1	1	1	NUM
ejpam-4585	61	2	.	.	X
ejpam-4585	62	1	for	for	ADP
ejpam-4585	62	2	any	any	DET
ejpam-4585	62	3	graph	graph	NOUN
ejpam-4585	62	4	g	g	NOUN
ejpam-4585	62	5	,	,	PUNCT
ejpam-4585	62	6	(	(	PUNCT
ejpam-4585	62	7	i	i	NOUN
ejpam-4585	62	8	)	)	PUNCT
ejpam-4585	62	9	lnpnd	lnpnd	ADJ
ejpam-4585	62	10	2	2	NUM
ejpam-4585	62	11	(	(	PUNCT
ejpam-4585	62	12	kn	kn	PROPN
ejpam-4585	62	13	)	)	PUNCT
ejpam-4585	62	14	=	=	SYM
ejpam-4585	62	15	n	n	CCONJ
ejpam-4585	62	16	;	;	PUNCT
ejpam-4585	62	17	(	(	PUNCT
ejpam-4585	62	18	ii	ii	NOUN
ejpam-4585	62	19	)	)	PUNCT
ejpam-4585	62	20	lnpnd	lnpnd	ADJ
ejpam-4585	62	21	2	2	NUM
ejpam-4585	62	22	(	(	PUNCT
ejpam-4585	62	23	k1,n	k1,n	PROPN
ejpam-4585	62	24	)	)	PUNCT
ejpam-4585	62	25	=	=	PUNCT
ejpam-4585	62	26	n+	n+	PUNCT
ejpam-4585	62	27	1	1	NUM
ejpam-4585	62	28	;	;	PUNCT
ejpam-4585	62	29	(	(	PUNCT
ejpam-4585	62	30	iii	iii	X
ejpam-4585	62	31	)	)	PUNCT
ejpam-4585	62	32	lnpnd	lnpnd	ADJ
ejpam-4585	62	33	2	2	NUM
ejpam-4585	62	34	(	(	PUNCT
ejpam-4585	62	35	km	km	NOUN
ejpam-4585	62	36	,	,	PUNCT
ejpam-4585	62	37	n	n	CCONJ
ejpam-4585	62	38	)	)	PUNCT
ejpam-4585	62	39	=	=	SYM
ejpam-4585	62	40	m+	m+	NUM
ejpam-4585	62	41	n	n	CCONJ
ejpam-4585	62	42	;	;	PUNCT
ejpam-4585	62	43	(	(	PUNCT
ejpam-4585	62	44	iv	iv	X
ejpam-4585	62	45	)	)	PUNCT
ejpam-4585	62	46	lnpnd	lnpnd	ADJ
ejpam-4585	62	47	2	2	NUM
ejpam-4585	62	48	(	(	PUNCT
ejpam-4585	62	49	pn	pn	NOUN
ejpam-4585	62	50	)	)	PUNCT
ejpam-4585	62	51	=	=	PRON
ejpam-4585	62	52	{	{	PUNCT
ejpam-4585	62	53	3	3	NUM
ejpam-4585	62	54	,	,	PUNCT
ejpam-4585	62	55	n	n	NOUN
ejpam-4585	62	56	=	=	SYM
ejpam-4585	62	57	3	3	NUM
ejpam-4585	62	58	⌈n+1	⌈n+1	NOUN
ejpam-4585	62	59	2	2	NUM
ejpam-4585	62	60	⌉	⌉	NOUN
ejpam-4585	62	61	,	,	PUNCT
ejpam-4585	62	62	n	n	PRON
ejpam-4585	62	63	≥	≥	NOUN
ejpam-4585	62	64	4	4	NUM
ejpam-4585	62	65	;	;	PUNCT
ejpam-4585	62	66	a.m.	a.m.	PROPN
ejpam-4585	62	67	mahistrado	mahistrado	PROPN
ejpam-4585	62	68	,	,	PUNCT
ejpam-4585	62	69	h.	h.	PROPN
ejpam-4585	62	70	rara	rara	PROPN
ejpam-4585	62	71	/	/	SYM
ejpam-4585	62	72	eur	eur	PROPN
ejpam-4585	62	73	.	.	PUNCT
ejpam-4585	63	1	j.	j.	PROPN
ejpam-4585	63	2	pure	pure	PROPN
ejpam-4585	63	3	appl	appl	PROPN
ejpam-4585	63	4	.	.	PROPN
ejpam-4585	63	5	math	math	PROPN
ejpam-4585	63	6	,	,	PUNCT
ejpam-4585	63	7	15	15	NUM
ejpam-4585	63	8	(	(	PUNCT
ejpam-4585	63	9	4	4	NUM
ejpam-4585	63	10	)	)	PUNCT
ejpam-4585	63	11	(	(	PUNCT
ejpam-4585	63	12	2022	2022	NUM
ejpam-4585	63	13	)	)	PUNCT
ejpam-4585	63	14	,	,	PUNCT
ejpam-4585	63	15	1982	1982	NUM
ejpam-4585	63	16	-	-	SYM
ejpam-4585	63	17	1997	1997	NUM
ejpam-4585	63	18	1985	1985	NUM
ejpam-4585	63	19	(	(	PUNCT
ejpam-4585	63	20	v	v	NOUN
ejpam-4585	63	21	)	)	PUNCT
ejpam-4585	63	22	lnpnd	lnpnd	ADJ
ejpam-4585	63	23	2	2	NUM
ejpam-4585	63	24	(	(	PUNCT
ejpam-4585	63	25	cn	cn	NOUN
ejpam-4585	63	26	)	)	PUNCT
ejpam-4585	63	27	=	=	SYM
ejpam-4585	64	1			NOUN
ejpam-4585	64	2	3	3	NUM
ejpam-4585	64	3	,	,	PUNCT
ejpam-4585	64	4	n	n	NOUN
ejpam-4585	64	5	=	=	SYM
ejpam-4585	64	6	3	3	NUM
ejpam-4585	64	7	4	4	NUM
ejpam-4585	64	8	,	,	PUNCT
ejpam-4585	64	9	n	n	NOUN
ejpam-4585	64	10	=	=	SYM
ejpam-4585	64	11	4	4	NUM
ejpam-4585	64	12	⌈n2	⌈n2	NOUN
ejpam-4585	64	13	⌉	⌉	NOUN
ejpam-4585	64	14	,	,	PUNCT
ejpam-4585	64	15	n	n	PRON
ejpam-4585	64	16	≥	≥	NOUN
ejpam-4585	64	17	5	5	NUM
ejpam-4585	64	18	.	.	PUNCT
ejpam-4585	64	19	remark	remark	NOUN
ejpam-4585	64	20	1	1	NUM
ejpam-4585	64	21	.	.	PUNCT
ejpam-4585	65	1	[	[	X
ejpam-4585	65	2	7	7	X
ejpam-4585	65	3	]	]	X
ejpam-4585	65	4	every	every	DET
ejpam-4585	65	5	2	2	NUM
ejpam-4585	65	6	-	-	PUNCT
ejpam-4585	65	7	locating	locate	VERB
ejpam-4585	65	8	set	set	NOUN
ejpam-4585	65	9	in	in	ADP
ejpam-4585	65	10	g	g	PROPN
ejpam-4585	65	11	is	be	AUX
ejpam-4585	65	12	a	a	DET
ejpam-4585	65	13	2	2	NUM
ejpam-4585	65	14	-	-	PUNCT
ejpam-4585	65	15	resolving	resolving	NOUN
ejpam-4585	65	16	set	set	VERB
ejpam-4585	65	17	in	in	ADP
ejpam-4585	65	18	g.	g.	PROPN
ejpam-4585	65	19	however	however	ADV
ejpam-4585	65	20	,	,	PUNCT
ejpam-4585	65	21	a	a	DET
ejpam-4585	65	22	2	2	NUM
ejpam-4585	65	23	-	-	PUNCT
ejpam-4585	65	24	resolving	resolving	NOUN
ejpam-4585	65	25	set	set	NOUN
ejpam-4585	65	26	in	in	ADP
ejpam-4585	65	27	g	g	NOUN
ejpam-4585	65	28	need	need	AUX
ejpam-4585	65	29	not	not	PART
ejpam-4585	65	30	be	be	AUX
ejpam-4585	65	31	a	a	DET
ejpam-4585	65	32	2	2	NUM
ejpam-4585	65	33	-	-	PUNCT
ejpam-4585	65	34	locating	locate	VERB
ejpam-4585	65	35	set	set	NOUN
ejpam-4585	65	36	in	in	ADP
ejpam-4585	65	37	g.	g.	PROPN
ejpam-4585	65	38	thus	thus	ADV
ejpam-4585	65	39	,	,	PUNCT
ejpam-4585	65	40	dim2(g	dim2(g	NOUN
ejpam-4585	65	41	)	)	PUNCT
ejpam-4585	65	42	≤	≤	NOUN
ejpam-4585	65	43	ln2(g	ln2(g	PROPN
ejpam-4585	65	44	)	)	PUNCT
ejpam-4585	65	45	.	.	PUNCT
ejpam-4585	65	46	example	example	NOUN
ejpam-4585	66	1	2	2	NUM
ejpam-4585	66	2	.	.	X
ejpam-4585	66	3	for	for	ADP
ejpam-4585	66	4	a	a	DET
ejpam-4585	66	5	path	path	NOUN
ejpam-4585	66	6	graph	graph	NOUN
ejpam-4585	66	7	p6	p6	PROPN
ejpam-4585	66	8	,	,	PUNCT
ejpam-4585	66	9	dim2(p6	dim2(p6	PROPN
ejpam-4585	66	10	)	)	PUNCT
ejpam-4585	66	11	=	=	PUNCT
ejpam-4585	66	12	2	2	NUM
ejpam-4585	66	13	<	<	SYM
ejpam-4585	66	14	4	4	NUM
ejpam-4585	66	15	=	=	SYM
ejpam-4585	66	16	ln2(p6	ln2(p6	NUM
ejpam-4585	66	17	)	)	PUNCT
ejpam-4585	66	18	.	.	PUNCT
ejpam-4585	67	1	definition	definition	NOUN
ejpam-4585	67	2	4	4	NUM
ejpam-4585	67	3	.	.	PUNCT
ejpam-4585	68	1	[	[	X
ejpam-4585	68	2	6	6	NUM
ejpam-4585	68	3	]	]	PUNCT
ejpam-4585	68	4	let	let	VERB
ejpam-4585	68	5	g	g	NOUN
ejpam-4585	68	6	be	be	AUX
ejpam-4585	68	7	any	any	DET
ejpam-4585	68	8	nontrivial	nontrivial	ADJ
ejpam-4585	68	9	connected	connect	VERB
ejpam-4585	68	10	graph	graph	NOUN
ejpam-4585	68	11	and	and	CCONJ
ejpam-4585	68	12	s	s	VERB
ejpam-4585	68	13	⊆	⊆	NUM
ejpam-4585	68	14	v	v	NOUN
ejpam-4585	68	15	(	(	PUNCT
ejpam-4585	68	16	g	g	NOUN
ejpam-4585	68	17	)	)	PUNCT
ejpam-4585	68	18	.	.	PUNCT
ejpam-4585	69	1	s	s	PART
ejpam-4585	69	2	is	be	AUX
ejpam-4585	69	3	a	a	DET
ejpam-4585	69	4	(	(	PUNCT
ejpam-4585	69	5	2	2	NUM
ejpam-4585	69	6	,	,	PUNCT
ejpam-4585	69	7	2)locating	2)locating	NUM
ejpam-4585	69	8	(	(	PUNCT
ejpam-4585	69	9	(	(	PUNCT
ejpam-4585	69	10	2	2	NUM
ejpam-4585	69	11	,	,	PUNCT
ejpam-4585	69	12	1)-locating	1)-locating	NUM
ejpam-4585	69	13	,	,	PUNCT
ejpam-4585	69	14	respectively	respectively	ADV
ejpam-4585	69	15	)	)	PUNCT
ejpam-4585	69	16	set	set	VERB
ejpam-4585	69	17	in	in	ADP
ejpam-4585	69	18	g	g	PROPN
ejpam-4585	69	19	if	if	SCONJ
ejpam-4585	69	20	s	s	NOUN
ejpam-4585	69	21	is	be	AUX
ejpam-4585	69	22	2	2	NUM
ejpam-4585	69	23	-	-	PUNCT
ejpam-4585	69	24	locating	locate	VERB
ejpam-4585	69	25	and	and	CCONJ
ejpam-4585	69	26	|ng(y)∩	|ng(y)∩	NOUN
ejpam-4585	69	27	s|	s|	VERB
ejpam-4585	69	28	≤	≤	NUM
ejpam-4585	69	29	|s|	|s|	PROPN
ejpam-4585	69	30	−	−	PROPN
ejpam-4585	69	31	2	2	NUM
ejpam-4585	69	32	(	(	PUNCT
ejpam-4585	69	33	|ng(y)∩s|	|ng(y)∩s|	NOUN
ejpam-4585	69	34	≤	≤	X
ejpam-4585	69	35	|s|−	|s|−	NOUN
ejpam-4585	69	36	1	1	NUM
ejpam-4585	69	37	,	,	PUNCT
ejpam-4585	69	38	respectively	respectively	ADV
ejpam-4585	69	39	)	)	PUNCT
ejpam-4585	69	40	,	,	PUNCT
ejpam-4585	69	41	for	for	ADP
ejpam-4585	69	42	all	all	DET
ejpam-4585	69	43	y	y	PROPN
ejpam-4585	69	44	∈	∈	PROPN
ejpam-4585	69	45	v	v	NOUN
ejpam-4585	69	46	(	(	PUNCT
ejpam-4585	69	47	g	g	NOUN
ejpam-4585	69	48	)	)	PUNCT
ejpam-4585	69	49	.	.	PUNCT
ejpam-4585	70	1	the	the	DET
ejpam-4585	70	2	(	(	PUNCT
ejpam-4585	70	3	2	2	NUM
ejpam-4585	70	4	,	,	PUNCT
ejpam-4585	70	5	2)-locating	2)-locating	NUM
ejpam-4585	70	6	(	(	PUNCT
ejpam-4585	70	7	(	(	PUNCT
ejpam-4585	70	8	2	2	NUM
ejpam-4585	70	9	,	,	PUNCT
ejpam-4585	70	10	1)-locating	1)-locating	NUM
ejpam-4585	70	11	,	,	PUNCT
ejpam-4585	70	12	respectively	respectively	ADV
ejpam-4585	70	13	)	)	PUNCT
ejpam-4585	70	14	number	number	NOUN
ejpam-4585	70	15	of	of	ADP
ejpam-4585	70	16	g	g	NOUN
ejpam-4585	70	17	,	,	PUNCT
ejpam-4585	70	18	denoted	denote	VERB
ejpam-4585	70	19	by	by	ADP
ejpam-4585	70	20	ln(2,2)(g	ln(2,2)(g	NOUN
ejpam-4585	70	21	)	)	PUNCT
ejpam-4585	70	22	(	(	PUNCT
ejpam-4585	70	23	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4585	70	24	)	)	PUNCT
ejpam-4585	70	25	,	,	PUNCT
ejpam-4585	70	26	respectively	respectively	ADV
ejpam-4585	70	27	)	)	PUNCT
ejpam-4585	70	28	,	,	PUNCT
ejpam-4585	70	29	is	be	AUX
ejpam-4585	70	30	the	the	DET
ejpam-4585	70	31	smallest	small	ADJ
ejpam-4585	70	32	cardinality	cardinality	NOUN
ejpam-4585	70	33	of	of	ADP
ejpam-4585	70	34	a	a	DET
ejpam-4585	70	35	(	(	PUNCT
ejpam-4585	70	36	2	2	NUM
ejpam-4585	70	37	,	,	PUNCT
ejpam-4585	70	38	2)-locating	2)-locating	NUM
ejpam-4585	70	39	(	(	PUNCT
ejpam-4585	70	40	(	(	PUNCT
ejpam-4585	70	41	2	2	NUM
ejpam-4585	70	42	,	,	PUNCT
ejpam-4585	70	43	1)-locating	1)-locating	NUM
ejpam-4585	70	44	,	,	PUNCT
ejpam-4585	70	45	respectively	respectively	ADV
ejpam-4585	70	46	)	)	PUNCT
ejpam-4585	70	47	set	set	VERB
ejpam-4585	70	48	in	in	ADP
ejpam-4585	70	49	g.	g.	PROPN
ejpam-4585	70	50	a	a	PRON
ejpam-4585	70	51	(	(	PUNCT
ejpam-4585	70	52	2	2	NUM
ejpam-4585	70	53	,	,	PUNCT
ejpam-4585	70	54	2)-locating	2)-locating	NUM
ejpam-4585	70	55	(	(	PUNCT
ejpam-4585	70	56	(	(	PUNCT
ejpam-4585	70	57	2	2	NUM
ejpam-4585	70	58	,	,	PUNCT
ejpam-4585	70	59	1)-locating	1)-locating	NUM
ejpam-4585	70	60	,	,	PUNCT
ejpam-4585	70	61	respectively	respectively	ADV
ejpam-4585	70	62	)	)	PUNCT
ejpam-4585	70	63	set	set	VERB
ejpam-4585	70	64	in	in	ADP
ejpam-4585	70	65	g	g	NOUN
ejpam-4585	70	66	of	of	ADP
ejpam-4585	70	67	cardinality	cardinality	NOUN
ejpam-4585	70	68	ln(2,2)(g	ln(2,2)(g	PROPN
ejpam-4585	70	69	)	)	PUNCT
ejpam-4585	70	70	(	(	PUNCT
ejpam-4585	70	71	ln(2,1)(g	ln(2,1)(g	NOUN
ejpam-4585	70	72	)	)	PUNCT
ejpam-4585	70	73	,	,	PUNCT
ejpam-4585	70	74	respectively	respectively	ADV
ejpam-4585	70	75	)	)	PUNCT
ejpam-4585	70	76	is	be	AUX
ejpam-4585	70	77	referred	refer	VERB
ejpam-4585	70	78	to	to	ADP
ejpam-4585	70	79	as	as	ADP
ejpam-4585	70	80	an	an	DET
ejpam-4585	70	81	ln(2,2)-set	ln(2,2)-set	NOUN
ejpam-4585	70	82	(	(	PUNCT
ejpam-4585	70	83	ln(2,1)-set	ln(2,1)-set	PROPN
ejpam-4585	70	84	,	,	PUNCT
ejpam-4585	70	85	respectively	respectively	ADV
ejpam-4585	70	86	)	)	PUNCT
ejpam-4585	70	87	in	in	ADP
ejpam-4585	70	88	g.	g.	PROPN
ejpam-4585	70	89	definition	definition	NOUN
ejpam-4585	70	90	5	5	NUM
ejpam-4585	70	91	.	.	PUNCT
ejpam-4585	71	1	a	a	DET
ejpam-4585	71	2	(	(	PUNCT
ejpam-4585	71	3	2,2)-locating	2,2)-locating	NUM
ejpam-4585	71	4	(	(	PUNCT
ejpam-4585	71	5	(	(	PUNCT
ejpam-4585	71	6	2,1)-locating	2,1)-locating	NUM
ejpam-4585	71	7	,	,	PUNCT
ejpam-4585	71	8	respectively	respectively	ADV
ejpam-4585	71	9	)	)	PUNCT
ejpam-4585	71	10	set	set	VERB
ejpam-4585	71	11	s	s	PROPN
ejpam-4585	71	12	⊆	⊆	NUM
ejpam-4585	71	13	v	v	NOUN
ejpam-4585	71	14	(	(	PUNCT
ejpam-4585	71	15	g	g	NOUN
ejpam-4585	71	16	)	)	PUNCT
ejpam-4585	71	17	which	which	PRON
ejpam-4585	71	18	is	be	AUX
ejpam-4585	71	19	a	a	DET
ejpam-4585	71	20	point	point	NOUN
ejpam-4585	71	21	-	-	PUNCT
ejpam-4585	71	22	wise	wise	ADJ
ejpam-4585	71	23	non	non	ADJ
ejpam-4585	71	24	-	-	ADJ
ejpam-4585	71	25	dominating	dominating	NOUN
ejpam-4585	71	26	is	be	AUX
ejpam-4585	71	27	called	call	VERB
ejpam-4585	71	28	a	a	DET
ejpam-4585	71	29	(	(	PUNCT
ejpam-4585	71	30	2,2)-locating	2,2)-locating	NUM
ejpam-4585	71	31	point	point	ADV
ejpam-4585	71	32	-	-	PUNCT
ejpam-4585	71	33	wise	wise	ADJ
ejpam-4585	71	34	non	non	ADJ
ejpam-4585	71	35	-	-	ADJ
ejpam-4585	71	36	dominating	dominating	ADJ
ejpam-4585	71	37	(	(	PUNCT
ejpam-4585	71	38	(	(	PUNCT
ejpam-4585	71	39	2,1)locating	2,1)locating	NUM
ejpam-4585	71	40	point	point	NOUN
ejpam-4585	71	41	-	-	PUNCT
ejpam-4585	71	42	wise	wise	ADJ
ejpam-4585	71	43	non	non	ADJ
ejpam-4585	71	44	-	-	ADJ
ejpam-4585	71	45	dominating	dominating	ADJ
ejpam-4585	71	46	,	,	PUNCT
ejpam-4585	71	47	respectively	respectively	ADV
ejpam-4585	71	48	)	)	PUNCT
ejpam-4585	71	49	set	set	VERB
ejpam-4585	71	50	in	in	ADP
ejpam-4585	71	51	g.	g.	PROPN
ejpam-4585	71	52	the	the	DET
ejpam-4585	71	53	minimum	minimum	ADJ
ejpam-4585	71	54	cardinality	cardinality	NOUN
ejpam-4585	71	55	of	of	ADP
ejpam-4585	71	56	a	a	DET
ejpam-4585	71	57	(	(	PUNCT
ejpam-4585	71	58	2,2)-locating	2,2)-locating	NUM
ejpam-4585	71	59	point	point	ADV
ejpam-4585	71	60	-	-	PUNCT
ejpam-4585	71	61	wise	wise	ADJ
ejpam-4585	71	62	non	non	ADJ
ejpam-4585	71	63	-	-	ADJ
ejpam-4585	71	64	dominating	dominating	ADJ
ejpam-4585	71	65	(	(	PUNCT
ejpam-4585	71	66	(	(	PUNCT
ejpam-4585	71	67	2,1)-locating	2,1)-locating	NUM
ejpam-4585	71	68	point	point	NOUN
ejpam-4585	71	69	-	-	PUNCT
ejpam-4585	71	70	wise	wise	ADJ
ejpam-4585	71	71	non	non	ADJ
ejpam-4585	71	72	-	-	ADJ
ejpam-4585	71	73	dominating	dominating	ADJ
ejpam-4585	71	74	,	,	PUNCT
ejpam-4585	71	75	respectively	respectively	ADV
ejpam-4585	71	76	)	)	PUNCT
ejpam-4585	71	77	set	set	VERB
ejpam-4585	71	78	in	in	ADP
ejpam-4585	71	79	g	g	NOUN
ejpam-4585	71	80	,	,	PUNCT
ejpam-4585	71	81	denoted	denote	VERB
ejpam-4585	71	82	by	by	ADP
ejpam-4585	71	83	lnpnd	lnpnd	ADJ
ejpam-4585	71	84	(	(	PUNCT
ejpam-4585	71	85	2,2)(g	2,2)(g	NUM
ejpam-4585	71	86	)	)	PUNCT
ejpam-4585	71	87	(	(	PUNCT
ejpam-4585	71	88	lnpnd	lnpnd	ADJ
ejpam-4585	71	89	(	(	PUNCT
ejpam-4585	71	90	2,1)(g),respectively	2,1)(g),respectively	NUM
ejpam-4585	71	91	)	)	PUNCT
ejpam-4585	71	92	is	be	AUX
ejpam-4585	71	93	called	call	VERB
ejpam-4585	71	94	the	the	DET
ejpam-4585	71	95	(	(	PUNCT
ejpam-4585	71	96	2,2)locating	2,2)locating	NUM
ejpam-4585	71	97	point	point	NOUN
ejpam-4585	71	98	-	-	PUNCT
ejpam-4585	71	99	wise	wise	ADJ
ejpam-4585	71	100	non	non	ADJ
ejpam-4585	71	101	-	-	NOUN
ejpam-4585	71	102	domination	domination	ADJ
ejpam-4585	71	103	(	(	PUNCT
ejpam-4585	71	104	(	(	PUNCT
ejpam-4585	71	105	2,1)-locating	2,1)-locating	NUM
ejpam-4585	71	106	point	point	NOUN
ejpam-4585	71	107	-	-	PUNCT
ejpam-4585	71	108	wise	wise	ADJ
ejpam-4585	71	109	non	non	ADJ
ejpam-4585	71	110	-	-	ADJ
ejpam-4585	71	111	domination	domination	ADJ
ejpam-4585	71	112	)	)	PUNCT
ejpam-4585	71	113	number	number	NOUN
ejpam-4585	71	114	of	of	ADP
ejpam-4585	71	115	g.	g.	PROPN
ejpam-4585	71	116	any	any	PRON
ejpam-4585	71	117	(	(	PUNCT
ejpam-4585	71	118	2,2)-locating	2,2)-locating	NUM
ejpam-4585	71	119	point	point	ADV
ejpam-4585	71	120	-	-	PUNCT
ejpam-4585	71	121	wise	wise	ADJ
ejpam-4585	71	122	non	non	ADJ
ejpam-4585	71	123	-	-	ADJ
ejpam-4585	71	124	dominating	dominating	ADJ
ejpam-4585	71	125	(	(	PUNCT
ejpam-4585	71	126	(	(	PUNCT
ejpam-4585	71	127	2,1)-locating	2,1)-locating	NUM
ejpam-4585	71	128	point	point	NOUN
ejpam-4585	71	129	-	-	PUNCT
ejpam-4585	71	130	wise	wise	ADJ
ejpam-4585	71	131	non	non	ADJ
ejpam-4585	71	132	-	-	ADJ
ejpam-4585	71	133	dominating	dominating	ADJ
ejpam-4585	71	134	,	,	PUNCT
ejpam-4585	71	135	respectively	respectively	ADV
ejpam-4585	71	136	)	)	PUNCT
ejpam-4585	71	137	set	set	NOUN
ejpam-4585	71	138	of	of	ADP
ejpam-4585	71	139	cardinality	cardinality	PROPN
ejpam-4585	71	140	lnpnd	lnpnd	ADV
ejpam-4585	71	141	(	(	PUNCT
ejpam-4585	71	142	2,2)(g	2,2)(g	NUM
ejpam-4585	71	143	)	)	PUNCT
ejpam-4585	71	144	(	(	PUNCT
ejpam-4585	71	145	lnpnd	lnpnd	ADJ
ejpam-4585	71	146	(	(	PUNCT
ejpam-4585	71	147	2,1)(g	2,1)(g	NUM
ejpam-4585	71	148	)	)	PUNCT
ejpam-4585	71	149	,	,	PUNCT
ejpam-4585	71	150	respectively	respectively	ADV
ejpam-4585	71	151	)	)	PUNCT
ejpam-4585	71	152	is	be	AUX
ejpam-4585	71	153	then	then	ADV
ejpam-4585	71	154	referred	refer	VERB
ejpam-4585	71	155	to	to	ADP
ejpam-4585	71	156	as	as	ADP
ejpam-4585	71	157	a	a	DET
ejpam-4585	71	158	lnpnd	lnpnd	ADJ
ejpam-4585	71	159	(	(	PUNCT
ejpam-4585	71	160	2,2)-set	2,2)-set	NUM
ejpam-4585	71	161	(	(	PUNCT
ejpam-4585	71	162	ln	ln	ADJ
ejpam-4585	71	163	pnd	pnd	NOUN
ejpam-4585	71	164	(	(	PUNCT
ejpam-4585	71	165	2,1)-set	2,1)-set	NUM
ejpam-4585	71	166	)	)	PUNCT
ejpam-4585	71	167	in	in	ADP
ejpam-4585	71	168	g.	g.	PROPN
ejpam-4585	71	169	example	example	NOUN
ejpam-4585	72	1	3	3	X
ejpam-4585	72	2	.	.	PUNCT
ejpam-4585	72	3	(	(	PUNCT
ejpam-4585	72	4	i	i	NOUN
ejpam-4585	72	5	)	)	PUNCT
ejpam-4585	72	6	for	for	ADP
ejpam-4585	72	7	all	all	DET
ejpam-4585	72	8	n	n	PRON
ejpam-4585	72	9	≥	≥	NOUN
ejpam-4585	72	10	5	5	NUM
ejpam-4585	72	11	,	,	PUNCT
ejpam-4585	72	12	lnpnd	lnpnd	ADJ
ejpam-4585	72	13	(	(	PUNCT
ejpam-4585	72	14	2,2)(pn	2,2)(pn	NUM
ejpam-4585	72	15	)	)	PUNCT
ejpam-4585	72	16	=	=	SYM
ejpam-4585	73	1			NOUN
ejpam-4585	73	2	5	5	NUM
ejpam-4585	73	3	,	,	PUNCT
ejpam-4585	73	4	n	n	NOUN
ejpam-4585	73	5	=	=	SYM
ejpam-4585	73	6	5	5	NUM
ejpam-4585	73	7	n	n	DET
ejpam-4585	73	8	2	2	NUM
ejpam-4585	73	9	+	+	NUM
ejpam-4585	73	10	1	1	NUM
ejpam-4585	73	11	,	,	PUNCT
ejpam-4585	73	12	n	n	PRON
ejpam-4585	73	13	is	be	AUX
ejpam-4585	73	14	even	even	ADV
ejpam-4585	73	15	⌈n2	⌈n2	ADJ
ejpam-4585	73	16	⌉	⌉	NOUN
ejpam-4585	73	17	,	,	PUNCT
ejpam-4585	73	18	n	n	PRON
ejpam-4585	73	19	is	be	AUX
ejpam-4585	73	20	odd	odd	ADJ
ejpam-4585	73	21	.	.	PUNCT
ejpam-4585	74	1	(	(	PUNCT
ejpam-4585	74	2	ii	ii	NOUN
ejpam-4585	74	3	)	)	PUNCT
ejpam-4585	74	4	for	for	ADP
ejpam-4585	74	5	all	all	DET
ejpam-4585	74	6	n	n	PRON
ejpam-4585	74	7	≥	≥	NOUN
ejpam-4585	74	8	7	7	NUM
ejpam-4585	74	9	,	,	PUNCT
ejpam-4585	74	10	lnpnd	lnpnd	ADJ
ejpam-4585	74	11	(	(	PUNCT
ejpam-4585	74	12	2,2)(cn	2,2)(cn	NUM
ejpam-4585	74	13	)	)	PUNCT
ejpam-4585	74	14	=	=	PRON
ejpam-4585	74	15	{	{	PUNCT
ejpam-4585	75	1	n	n	ADV
ejpam-4585	75	2	2	2	NUM
ejpam-4585	75	3	,	,	PUNCT
ejpam-4585	75	4	n	n	X
ejpam-4585	75	5	is	be	AUX
ejpam-4585	75	6	even	even	ADV
ejpam-4585	75	7	⌈n2	⌈n2	ADJ
ejpam-4585	75	8	⌉	⌉	NOUN
ejpam-4585	75	9	,	,	PUNCT
ejpam-4585	75	10	n	n	PRON
ejpam-4585	75	11	is	be	AUX
ejpam-4585	75	12	odd	odd	ADJ
ejpam-4585	75	13	.	.	PUNCT
ejpam-4585	75	14	example	example	NOUN
ejpam-4585	76	1	4	4	NUM
ejpam-4585	76	2	.	.	PUNCT
ejpam-4585	76	3	(	(	PUNCT
ejpam-4585	76	4	i	i	NOUN
ejpam-4585	76	5	)	)	PUNCT
ejpam-4585	76	6	for	for	ADP
ejpam-4585	76	7	all	all	DET
ejpam-4585	76	8	n	n	PRON
ejpam-4585	76	9	≥	≥	NOUN
ejpam-4585	76	10	4	4	NUM
ejpam-4585	76	11	,	,	PUNCT
ejpam-4585	76	12	lnpnd	lnpnd	ADJ
ejpam-4585	76	13	(	(	PUNCT
ejpam-4585	76	14	2,1)(pn	2,1)(pn	NUM
ejpam-4585	76	15	)	)	PUNCT
ejpam-4585	76	16	=	=	NOUN
ejpam-4585	76	17	{	{	PUNCT
ejpam-4585	76	18	n	n	ADV
ejpam-4585	76	19	2	2	NUM
ejpam-4585	76	20	+	+	NUM
ejpam-4585	76	21	1	1	NUM
ejpam-4585	76	22	,	,	PUNCT
ejpam-4585	76	23	n	n	PRON
ejpam-4585	76	24	is	be	AUX
ejpam-4585	76	25	even	even	ADV
ejpam-4585	76	26	⌈n2	⌈n2	ADJ
ejpam-4585	76	27	⌉	⌉	NOUN
ejpam-4585	76	28	,	,	PUNCT
ejpam-4585	76	29	n	n	PRON
ejpam-4585	76	30	is	be	AUX
ejpam-4585	76	31	odd	odd	ADJ
ejpam-4585	76	32	.	.	PUNCT
ejpam-4585	77	1	(	(	PUNCT
ejpam-4585	77	2	ii	ii	NOUN
ejpam-4585	77	3	)	)	PUNCT
ejpam-4585	77	4	for	for	ADP
ejpam-4585	77	5	all	all	DET
ejpam-4585	77	6	n	n	PRON
ejpam-4585	77	7	≥	≥	NOUN
ejpam-4585	77	8	5	5	NUM
ejpam-4585	77	9	,	,	PUNCT
ejpam-4585	77	10	lnpnd	lnpnd	ADJ
ejpam-4585	77	11	(	(	PUNCT
ejpam-4585	77	12	2,1)(cn	2,1)(cn	NUM
ejpam-4585	77	13	)	)	PUNCT
ejpam-4585	78	1	=	=	PRON
ejpam-4585	78	2	{	{	PUNCT
ejpam-4585	78	3	n	n	ADV
ejpam-4585	78	4	2	2	NUM
ejpam-4585	78	5	,	,	PUNCT
ejpam-4585	78	6	n	n	X
ejpam-4585	78	7	is	be	AUX
ejpam-4585	78	8	even	even	ADV
ejpam-4585	78	9	⌈n2	⌈n2	ADJ
ejpam-4585	78	10	⌉	⌉	NOUN
ejpam-4585	78	11	,	,	PUNCT
ejpam-4585	78	12	n	n	PRON
ejpam-4585	78	13	is	be	AUX
ejpam-4585	78	14	odd	odd	ADJ
ejpam-4585	78	15	.	.	PUNCT
ejpam-4585	79	1	definition	definition	NOUN
ejpam-4585	79	2	6	6	NUM
ejpam-4585	79	3	.	.	PUNCT
ejpam-4585	80	1	a	a	DET
ejpam-4585	80	2	2	2	NUM
ejpam-4585	80	3	-	-	PUNCT
ejpam-4585	80	4	resolving	resolve	VERB
ejpam-4585	80	5	set	set	NOUN
ejpam-4585	80	6	s	s	PROPN
ejpam-4585	80	7	⊆	⊆	NUM
ejpam-4585	80	8	v	v	NOUN
ejpam-4585	80	9	(	(	PUNCT
ejpam-4585	80	10	g	g	NOUN
ejpam-4585	80	11	)	)	PUNCT
ejpam-4585	80	12	which	which	PRON
ejpam-4585	80	13	is	be	AUX
ejpam-4585	80	14	point	point	ADV
ejpam-4585	80	15	-	-	PUNCT
ejpam-4585	80	16	wise	wise	ADJ
ejpam-4585	80	17	non	non	ADJ
ejpam-4585	80	18	-	-	ADJ
ejpam-4585	80	19	dominating	dominating	NOUN
ejpam-4585	80	20	is	be	AUX
ejpam-4585	80	21	called	call	VERB
ejpam-4585	80	22	a	a	DET
ejpam-4585	80	23	2	2	NUM
ejpam-4585	80	24	-	-	PUNCT
ejpam-4585	80	25	resolving	resolve	VERB
ejpam-4585	80	26	point	point	NOUN
ejpam-4585	80	27	-	-	PUNCT
ejpam-4585	80	28	wise	wise	ADJ
ejpam-4585	80	29	non	non	ADJ
ejpam-4585	80	30	-	-	ADJ
ejpam-4585	80	31	dominating	dominating	ADJ
ejpam-4585	80	32	set	set	NOUN
ejpam-4585	80	33	in	in	ADP
ejpam-4585	80	34	g.	g.	PROPN
ejpam-4585	80	35	the	the	DET
ejpam-4585	80	36	minimum	minimum	ADJ
ejpam-4585	80	37	cardinality	cardinality	NOUN
ejpam-4585	80	38	of	of	ADP
ejpam-4585	80	39	a	a	DET
ejpam-4585	80	40	2	2	NUM
ejpam-4585	80	41	-	-	PUNCT
ejpam-4585	80	42	resolving	resolve	VERB
ejpam-4585	80	43	a.m.	a.m.	PROPN
ejpam-4585	80	44	mahistrado	mahistrado	NOUN
ejpam-4585	80	45	,	,	PUNCT
ejpam-4585	80	46	h.	h.	PROPN
ejpam-4585	80	47	rara	rara	PROPN
ejpam-4585	80	48	/	/	SYM
ejpam-4585	80	49	eur	eur	PROPN
ejpam-4585	80	50	.	.	PUNCT
ejpam-4585	81	1	j.	j.	PROPN
ejpam-4585	81	2	pure	pure	PROPN
ejpam-4585	81	3	appl	appl	PROPN
ejpam-4585	81	4	.	.	PROPN
ejpam-4585	81	5	math	math	PROPN
ejpam-4585	81	6	,	,	PUNCT
ejpam-4585	81	7	15	15	NUM
ejpam-4585	81	8	(	(	PUNCT
ejpam-4585	81	9	4	4	NUM
ejpam-4585	81	10	)	)	PUNCT
ejpam-4585	81	11	(	(	PUNCT
ejpam-4585	81	12	2022	2022	NUM
ejpam-4585	81	13	)	)	PUNCT
ejpam-4585	81	14	,	,	PUNCT
ejpam-4585	81	15	1982	1982	NUM
ejpam-4585	81	16	-	-	SYM
ejpam-4585	81	17	1997	1997	NUM
ejpam-4585	81	18	1986	1986	NUM
ejpam-4585	81	19	point	point	NOUN
ejpam-4585	81	20	-	-	PUNCT
ejpam-4585	81	21	wise	wise	ADJ
ejpam-4585	81	22	non	non	ADJ
ejpam-4585	81	23	-	-	ADJ
ejpam-4585	81	24	dominating	dominating	ADJ
ejpam-4585	81	25	set	set	NOUN
ejpam-4585	81	26	in	in	ADP
ejpam-4585	81	27	g	g	NOUN
ejpam-4585	81	28	,	,	PUNCT
ejpam-4585	81	29	denoted	denote	VERB
ejpam-4585	81	30	by	by	ADP
ejpam-4585	81	31	dim2pnd	dim2pnd	NOUN
ejpam-4585	81	32	(	(	PUNCT
ejpam-4585	81	33	g	g	NOUN
ejpam-4585	81	34	)	)	PUNCT
ejpam-4585	81	35	is	be	AUX
ejpam-4585	81	36	called	call	VERB
ejpam-4585	81	37	the	the	DET
ejpam-4585	81	38	2	2	NUM
ejpam-4585	81	39	-	-	PUNCT
ejpam-4585	81	40	resolving	resolve	VERB
ejpam-4585	81	41	pointwise	pointwise	ADP
ejpam-4585	81	42	non	non	ADJ
ejpam-4585	81	43	-	-	ADJ
ejpam-4585	81	44	domination	domination	ADJ
ejpam-4585	81	45	number	number	NOUN
ejpam-4585	81	46	of	of	ADP
ejpam-4585	81	47	g.	g.	PROPN
ejpam-4585	81	48	any	any	DET
ejpam-4585	81	49	2r	2r	NUM
ejpam-4585	81	50	-	-	PUNCT
ejpam-4585	81	51	point	point	NOUN
ejpam-4585	81	52	-	-	PUNCT
ejpam-4585	81	53	wise	wise	ADJ
ejpam-4585	81	54	non	non	ADJ
ejpam-4585	81	55	-	-	ADJ
ejpam-4585	81	56	dominating	dominating	ADJ
ejpam-4585	81	57	set	set	NOUN
ejpam-4585	81	58	of	of	ADP
ejpam-4585	81	59	cardinality	cardinality	NOUN
ejpam-4585	81	60	dim2pnd	dim2pnd	NOUN
ejpam-4585	81	61	(	(	PUNCT
ejpam-4585	81	62	g	g	NOUN
ejpam-4585	81	63	)	)	PUNCT
ejpam-4585	81	64	is	be	AUX
ejpam-4585	81	65	then	then	ADV
ejpam-4585	81	66	referred	refer	VERB
ejpam-4585	81	67	to	to	ADP
ejpam-4585	81	68	as	as	ADP
ejpam-4585	81	69	a	a	DET
ejpam-4585	81	70	dim2pnd	dim2pnd	NOUN
ejpam-4585	81	71	(	(	PUNCT
ejpam-4585	81	72	g)-set	g)-set	VERB
ejpam-4585	81	73	in	in	ADP
ejpam-4585	81	74	g.	g.	PROPN
ejpam-4585	81	75	example	example	NOUN
ejpam-4585	81	76	5	5	NUM
ejpam-4585	81	77	.	.	X
ejpam-4585	81	78	for	for	ADP
ejpam-4585	81	79	any	any	DET
ejpam-4585	81	80	graph	graph	NOUN
ejpam-4585	81	81	g	g	NOUN
ejpam-4585	81	82	,	,	PUNCT
ejpam-4585	81	83	(	(	PUNCT
ejpam-4585	81	84	i	i	NOUN
ejpam-4585	81	85	)	)	PUNCT
ejpam-4585	81	86	dim2pnd	dim2pnd	NOUN
ejpam-4585	81	87	(	(	PUNCT
ejpam-4585	81	88	kn	kn	PROPN
ejpam-4585	81	89	)	)	PUNCT
ejpam-4585	81	90	=	=	SYM
ejpam-4585	82	1	n	n	CCONJ
ejpam-4585	82	2	;	;	PUNCT
ejpam-4585	82	3	(	(	PUNCT
ejpam-4585	82	4	ii	ii	NOUN
ejpam-4585	82	5	)	)	PUNCT
ejpam-4585	82	6	dim2pnd	dim2pnd	NOUN
ejpam-4585	82	7	(	(	PUNCT
ejpam-4585	82	8	km	km	PROPN
ejpam-4585	82	9	,	,	PUNCT
ejpam-4585	82	10	n	n	CCONJ
ejpam-4585	82	11	)	)	PUNCT
ejpam-4585	82	12	=	=	SYM
ejpam-4585	83	1	m+	m+	NUM
ejpam-4585	83	2	n	n	PROPN
ejpam-4585	83	3	where	where	SCONJ
ejpam-4585	83	4	m	m	VERB
ejpam-4585	83	5	,	,	PUNCT
ejpam-4585	83	6	n	n	PRON
ejpam-4585	83	7	≥	≥	NOUN
ejpam-4585	83	8	1	1	NUM
ejpam-4585	83	9	;	;	PUNCT
ejpam-4585	83	10	(	(	PUNCT
ejpam-4585	83	11	iii	iii	X
ejpam-4585	83	12	)	)	PUNCT
ejpam-4585	83	13	dim2pnd	dim2pnd	NOUN
ejpam-4585	83	14	(	(	PUNCT
ejpam-4585	83	15	pn	pn	NOUN
ejpam-4585	83	16	)	)	PUNCT
ejpam-4585	83	17	=	=	NOUN
ejpam-4585	83	18	{	{	PUNCT
ejpam-4585	83	19	3	3	NUM
ejpam-4585	83	20	,	,	PUNCT
ejpam-4585	83	21	n	n	NOUN
ejpam-4585	83	22	=	=	SYM
ejpam-4585	83	23	3	3	NUM
ejpam-4585	83	24	2	2	NUM
ejpam-4585	83	25	,	,	PUNCT
ejpam-4585	83	26	n	n	PRON
ejpam-4585	83	27	≥	≥	NOUN
ejpam-4585	83	28	4	4	NUM
ejpam-4585	83	29	.	.	PUNCT
ejpam-4585	83	30	remark	remark	NOUN
ejpam-4585	83	31	2	2	NUM
ejpam-4585	83	32	.	.	PUNCT
ejpam-4585	84	1	every	every	DET
ejpam-4585	84	2	(	(	PUNCT
ejpam-4585	84	3	2	2	NUM
ejpam-4585	84	4	,	,	PUNCT
ejpam-4585	84	5	1)-locating	1)-locating	NUM
ejpam-4585	84	6	point	point	NOUN
ejpam-4585	84	7	-	-	PUNCT
ejpam-4585	84	8	wise	wise	ADJ
ejpam-4585	84	9	non	non	ADJ
ejpam-4585	84	10	-	-	ADJ
ejpam-4585	84	11	dominating	dominating	ADJ
ejpam-4585	84	12	set	set	NOUN
ejpam-4585	84	13	in	in	ADP
ejpam-4585	84	14	g	g	PROPN
ejpam-4585	84	15	is	be	AUX
ejpam-4585	84	16	a	a	DET
ejpam-4585	84	17	2	2	NUM
ejpam-4585	84	18	-	-	PUNCT
ejpam-4585	84	19	resolving	resolve	VERB
ejpam-4585	84	20	point	point	NOUN
ejpam-4585	84	21	-	-	PUNCT
ejpam-4585	84	22	wise	wise	ADJ
ejpam-4585	84	23	non	non	ADJ
ejpam-4585	84	24	-	-	ADJ
ejpam-4585	84	25	dominating	dominating	ADJ
ejpam-4585	84	26	set	set	NOUN
ejpam-4585	84	27	in	in	ADP
ejpam-4585	84	28	g.	g.	PROPN
ejpam-4585	84	29	however	however	ADV
ejpam-4585	84	30	,	,	PUNCT
ejpam-4585	84	31	a	a	DET
ejpam-4585	84	32	2	2	NUM
ejpam-4585	84	33	-	-	PUNCT
ejpam-4585	84	34	resolving	resolve	VERB
ejpam-4585	84	35	point	point	NOUN
ejpam-4585	84	36	-	-	PUNCT
ejpam-4585	84	37	wise	wise	ADJ
ejpam-4585	84	38	non	non	ADJ
ejpam-4585	84	39	-	-	ADJ
ejpam-4585	84	40	dominating	dominating	ADJ
ejpam-4585	84	41	set	set	NOUN
ejpam-4585	84	42	in	in	ADP
ejpam-4585	84	43	g	g	NOUN
ejpam-4585	84	44	need	need	AUX
ejpam-4585	84	45	not	not	PART
ejpam-4585	84	46	be	be	AUX
ejpam-4585	84	47	a	a	DET
ejpam-4585	84	48	(	(	PUNCT
ejpam-4585	84	49	2	2	NUM
ejpam-4585	84	50	,	,	PUNCT
ejpam-4585	84	51	1)-locating	1)-locating	NUM
ejpam-4585	84	52	point	point	NOUN
ejpam-4585	84	53	-	-	PUNCT
ejpam-4585	84	54	wise	wise	ADJ
ejpam-4585	84	55	non	non	ADJ
ejpam-4585	84	56	-	-	ADJ
ejpam-4585	84	57	dominating	dominating	ADJ
ejpam-4585	84	58	set	set	NOUN
ejpam-4585	84	59	in	in	ADP
ejpam-4585	84	60	g.	g.	PROPN
ejpam-4585	84	61	thus	thus	ADV
ejpam-4585	84	62	,	,	PUNCT
ejpam-4585	84	63	dim2pnd	dim2pnd	NOUN
ejpam-4585	84	64	(	(	PUNCT
ejpam-4585	84	65	g	g	NOUN
ejpam-4585	84	66	)	)	PUNCT
ejpam-4585	84	67	≤	≤	NOUN
ejpam-4585	84	68	lnpnd	lnpnd	ADJ
ejpam-4585	84	69	(	(	PUNCT
ejpam-4585	84	70	2,1)(g	2,1)(g	NUM
ejpam-4585	84	71	)	)	PUNCT
ejpam-4585	84	72	.	.	PUNCT
ejpam-4585	85	1	example	example	NOUN
ejpam-4585	86	1	6	6	NUM
ejpam-4585	86	2	.	.	X
ejpam-4585	87	1	for	for	ADP
ejpam-4585	87	2	a	a	DET
ejpam-4585	87	3	path	path	NOUN
ejpam-4585	87	4	graph	graph	NOUN
ejpam-4585	87	5	p4	p4	ADJ
ejpam-4585	87	6	,	,	PUNCT
ejpam-4585	87	7	dim2pnd	dim2pnd	NOUN
ejpam-4585	87	8	(	(	PUNCT
ejpam-4585	87	9	p4	p4	ADJ
ejpam-4585	87	10	)	)	PUNCT
ejpam-4585	87	11	=	=	SYM
ejpam-4585	87	12	2	2	NUM
ejpam-4585	87	13	<	<	SYM
ejpam-4585	87	14	3	3	NUM
ejpam-4585	87	15	=	=	SYM
ejpam-4585	87	16	lnpnd	lnpnd	ADJ
ejpam-4585	87	17	(	(	PUNCT
ejpam-4585	87	18	2,1)(p4	2,1)(p4	NUM
ejpam-4585	87	19	)	)	PUNCT
ejpam-4585	87	20	.	.	PUNCT
ejpam-4585	88	1	remark	remark	PROPN
ejpam-4585	88	2	3	3	NUM
ejpam-4585	88	3	.	.	PUNCT
ejpam-4585	89	1	every	every	DET
ejpam-4585	89	2	nontrivial	nontrivial	ADJ
ejpam-4585	89	3	connected	connect	VERB
ejpam-4585	89	4	graph	graph	NOUN
ejpam-4585	89	5	g	g	PROPN
ejpam-4585	89	6	admits	admit	VERB
ejpam-4585	89	7	a	a	DET
ejpam-4585	89	8	2	2	NUM
ejpam-4585	89	9	-	-	PUNCT
ejpam-4585	89	10	resolving	resolve	VERB
ejpam-4585	89	11	hop	hop	NOUN
ejpam-4585	89	12	dominating	dominating	NOUN
ejpam-4585	89	13	set	set	NOUN
ejpam-4585	89	14	.	.	PUNCT
ejpam-4585	90	1	indeed	indeed	ADV
ejpam-4585	90	2	,	,	PUNCT
ejpam-4585	90	3	the	the	DET
ejpam-4585	90	4	vertex	vertex	NOUN
ejpam-4585	90	5	set	set	VERB
ejpam-4585	90	6	v	v	NOUN
ejpam-4585	90	7	(	(	PUNCT
ejpam-4585	90	8	g	g	NOUN
ejpam-4585	90	9	)	)	PUNCT
ejpam-4585	90	10	of	of	ADP
ejpam-4585	90	11	g	g	PROPN
ejpam-4585	90	12	is	be	AUX
ejpam-4585	90	13	a	a	DET
ejpam-4585	90	14	2	2	NUM
ejpam-4585	90	15	-	-	PUNCT
ejpam-4585	90	16	resolving	resolve	VERB
ejpam-4585	90	17	hop	hop	NOUN
ejpam-4585	90	18	dominating	dominating	NOUN
ejpam-4585	90	19	set	set	NOUN
ejpam-4585	90	20	.	.	PUNCT
ejpam-4585	91	1	remark	remark	PROPN
ejpam-4585	91	2	4	4	NUM
ejpam-4585	91	3	.	.	PUNCT
ejpam-4585	92	1	[	[	X
ejpam-4585	92	2	4	4	X
ejpam-4585	92	3	]	]	PUNCT
ejpam-4585	92	4	let	let	VERB
ejpam-4585	92	5	s	s	PRON
ejpam-4585	92	6	⊆	⊆	NUM
ejpam-4585	92	7	g.	g.	NOUN
ejpam-4585	92	8	since	since	SCONJ
ejpam-4585	92	9	any	any	DET
ejpam-4585	92	10	pair	pair	NOUN
ejpam-4585	92	11	of	of	ADP
ejpam-4585	92	12	vertices	vertex	NOUN
ejpam-4585	92	13	u	u	NOUN
ejpam-4585	92	14	and	and	CCONJ
ejpam-4585	92	15	v	v	ADP
ejpam-4585	92	16	where	where	SCONJ
ejpam-4585	92	17	u	u	NOUN
ejpam-4585	92	18	and	and	CCONJ
ejpam-4585	92	19	v	v	NOUN
ejpam-4585	92	20	are	be	AUX
ejpam-4585	92	21	in	in	ADP
ejpam-4585	92	22	the	the	DET
ejpam-4585	92	23	2	2	NUM
ejpam-4585	92	24	-	-	PUNCT
ejpam-4585	92	25	resolving	resolve	VERB
ejpam-4585	92	26	set	set	NOUN
ejpam-4585	92	27	s	s	PRON
ejpam-4585	92	28	of	of	ADP
ejpam-4585	92	29	a	a	DET
ejpam-4585	92	30	graph	graph	NOUN
ejpam-4585	92	31	g	g	NOUN
ejpam-4585	92	32	,	,	PUNCT
ejpam-4585	92	33	rg(u	rg(u	X
ejpam-4585	92	34	/	/	SYM
ejpam-4585	92	35	s	s	PART
ejpam-4585	92	36	)	)	PUNCT
ejpam-4585	92	37	and	and	CCONJ
ejpam-4585	92	38	rg(v	rg(v	PROPN
ejpam-4585	92	39	/	/	SYM
ejpam-4585	92	40	s	s	X
ejpam-4585	92	41	)	)	PUNCT
ejpam-4585	92	42	differ	differ	VERB
ejpam-4585	92	43	in	in	ADP
ejpam-4585	92	44	at	at	ADV
ejpam-4585	92	45	least	least	ADJ
ejpam-4585	92	46	2	2	NUM
ejpam-4585	92	47	positions	position	NOUN
ejpam-4585	92	48	.	.	PUNCT
ejpam-4585	93	1	hence	hence	ADV
ejpam-4585	93	2	,	,	PUNCT
ejpam-4585	93	3	to	to	PART
ejpam-4585	93	4	show	show	VERB
ejpam-4585	93	5	that	that	SCONJ
ejpam-4585	93	6	s	s	VERB
ejpam-4585	93	7	is	be	AUX
ejpam-4585	93	8	a	a	DET
ejpam-4585	93	9	2	2	NUM
ejpam-4585	93	10	-	-	PUNCT
ejpam-4585	93	11	resolving	resolve	VERB
ejpam-4585	93	12	set	set	NOUN
ejpam-4585	93	13	of	of	ADP
ejpam-4585	93	14	g	g	NOUN
ejpam-4585	93	15	,	,	PUNCT
ejpam-4585	93	16	we	we	PRON
ejpam-4585	93	17	only	only	ADV
ejpam-4585	93	18	need	need	VERB
ejpam-4585	93	19	to	to	PART
ejpam-4585	93	20	show	show	VERB
ejpam-4585	93	21	that	that	SCONJ
ejpam-4585	93	22	every	every	DET
ejpam-4585	93	23	pair	pair	NOUN
ejpam-4585	93	24	u	u	NOUN
ejpam-4585	93	25	,	,	PUNCT
ejpam-4585	93	26	v	v	NOUN
ejpam-4585	93	27	of	of	ADP
ejpam-4585	93	28	distinct	distinct	ADJ
ejpam-4585	93	29	vertices	vertex	NOUN
ejpam-4585	93	30	in	in	ADP
ejpam-4585	93	31	v	v	NOUN
ejpam-4585	93	32	(	(	PUNCT
ejpam-4585	93	33	g)\s	g)\s	NOUN
ejpam-4585	93	34	or	or	CCONJ
ejpam-4585	93	35	u	u	NOUN
ejpam-4585	93	36	∈	∈	PROPN
ejpam-4585	93	37	s	s	X
ejpam-4585	93	38	and	and	CCONJ
ejpam-4585	93	39	v	v	ADP
ejpam-4585	93	40	∈	∈	NOUN
ejpam-4585	93	41	v	v	NOUN
ejpam-4585	93	42	(	(	PUNCT
ejpam-4585	93	43	g)\s	g)\s	NOUN
ejpam-4585	93	44	,	,	PUNCT
ejpam-4585	93	45	rg(u	rg(u	X
ejpam-4585	93	46	/	/	SYM
ejpam-4585	93	47	s	s	PART
ejpam-4585	93	48	)	)	PUNCT
ejpam-4585	93	49	and	and	CCONJ
ejpam-4585	93	50	rg(v	rg(v	PROPN
ejpam-4585	93	51	/	/	SYM
ejpam-4585	93	52	s	s	X
ejpam-4585	93	53	)	)	PUNCT
ejpam-4585	93	54	differ	differ	VERB
ejpam-4585	93	55	in	in	ADP
ejpam-4585	93	56	at	at	ADV
ejpam-4585	93	57	least	least	ADJ
ejpam-4585	93	58	2	2	NUM
ejpam-4585	93	59	positions	position	NOUN
ejpam-4585	93	60	.	.	PUNCT
ejpam-4585	94	1	theorem	theorem	NOUN
ejpam-4585	94	2	1	1	NUM
ejpam-4585	94	3	.	.	PUNCT
ejpam-4585	95	1	let	let	VERB
ejpam-4585	95	2	g	g	NOUN
ejpam-4585	95	3	be	be	AUX
ejpam-4585	95	4	any	any	DET
ejpam-4585	95	5	nontrivial	nontrivial	ADJ
ejpam-4585	95	6	connected	connect	VERB
ejpam-4585	95	7	graph	graph	NOUN
ejpam-4585	95	8	.	.	PUNCT
ejpam-4585	96	1	then	then	ADV
ejpam-4585	96	2	s	s	VERB
ejpam-4585	96	3	⊆	⊆	NUM
ejpam-4585	96	4	v	v	NOUN
ejpam-4585	96	5	(	(	PUNCT
ejpam-4585	96	6	g	g	NOUN
ejpam-4585	96	7	)	)	PUNCT
ejpam-4585	96	8	is	be	AUX
ejpam-4585	96	9	a	a	DET
ejpam-4585	96	10	2	2	NUM
ejpam-4585	96	11	-	-	PUNCT
ejpam-4585	96	12	resolving	resolve	VERB
ejpam-4585	96	13	hop	hop	NOUN
ejpam-4585	96	14	dominating	dominating	NOUN
ejpam-4585	96	15	set	set	VERB
ejpam-4585	96	16	in	in	ADP
ejpam-4585	96	17	g	g	PROPN
ejpam-4585	96	18	if	if	SCONJ
ejpam-4585	96	19	it	it	PRON
ejpam-4585	96	20	satisfies	satisfy	VERB
ejpam-4585	96	21	the	the	DET
ejpam-4585	96	22	following	follow	VERB
ejpam-4585	96	23	conditions	condition	NOUN
ejpam-4585	96	24	:	:	PUNCT
ejpam-4585	96	25	(	(	PUNCT
ejpam-4585	96	26	i	i	NOUN
ejpam-4585	96	27	)	)	PUNCT
ejpam-4585	96	28	for	for	ADP
ejpam-4585	96	29	every	every	DET
ejpam-4585	96	30	pair	pair	NOUN
ejpam-4585	96	31	of	of	ADP
ejpam-4585	96	32	vertices	vertex	NOUN
ejpam-4585	96	33	x	x	X
ejpam-4585	96	34	,	,	PUNCT
ejpam-4585	96	35	y	y	PROPN
ejpam-4585	96	36	∈	∈	PROPN
ejpam-4585	96	37	v	v	ADP
ejpam-4585	96	38	(	(	PUNCT
ejpam-4585	96	39	g	g	NOUN
ejpam-4585	96	40	)	)	PUNCT
ejpam-4585	96	41	where	where	SCONJ
ejpam-4585	96	42	x	x	PUNCT
ejpam-4585	96	43	∈	∈	PROPN
ejpam-4585	96	44	s	s	X
ejpam-4585	96	45	and	and	CCONJ
ejpam-4585	96	46	y	y	PROPN
ejpam-4585	96	47	∈	∈	PROPN
ejpam-4585	96	48	v	v	X
ejpam-4585	96	49	(	(	PUNCT
ejpam-4585	96	50	g)\s	g)\s	NOUN
ejpam-4585	96	51	or	or	CCONJ
ejpam-4585	96	52	both	both	DET
ejpam-4585	96	53	x	x	NOUN
ejpam-4585	96	54	,	,	PUNCT
ejpam-4585	96	55	y	y	PROPN
ejpam-4585	96	56	∈	∈	PROPN
ejpam-4585	96	57	v	v	X
ejpam-4585	96	58	(	(	PUNCT
ejpam-4585	96	59	g)\s	g)\s	NOUN
ejpam-4585	96	60	,	,	PUNCT
ejpam-4585	96	61	rg(x	rg(x	X
ejpam-4585	96	62	/	/	SYM
ejpam-4585	96	63	s	s	NOUN
ejpam-4585	96	64	)	)	PUNCT
ejpam-4585	96	65	and	and	CCONJ
ejpam-4585	96	66	rg(y	rg(y	NOUN
ejpam-4585	96	67	/	/	SYM
ejpam-4585	96	68	s	s	PART
ejpam-4585	96	69	)	)	PUNCT
ejpam-4585	96	70	differ	differ	VERB
ejpam-4585	96	71	in	in	ADP
ejpam-4585	96	72	at	at	ADV
ejpam-4585	96	73	least	least	ADJ
ejpam-4585	96	74	2	2	NUM
ejpam-4585	96	75	positions	position	NOUN
ejpam-4585	96	76	;	;	PUNCT
ejpam-4585	96	77	(	(	PUNCT
ejpam-4585	96	78	ii	ii	NOUN
ejpam-4585	96	79	)	)	PUNCT
ejpam-4585	96	80	s	s	VERB
ejpam-4585	96	81	is	be	AUX
ejpam-4585	96	82	a	a	DET
ejpam-4585	96	83	point	point	NOUN
ejpam-4585	96	84	-	-	PUNCT
ejpam-4585	96	85	wise	wise	ADJ
ejpam-4585	96	86	non	non	ADJ
ejpam-4585	96	87	-	-	ADJ
ejpam-4585	96	88	dominating	dominating	ADJ
ejpam-4585	96	89	set	set	NOUN
ejpam-4585	96	90	in	in	ADP
ejpam-4585	96	91	g.	g.	PROPN
ejpam-4585	96	92	proof	proof	PROPN
ejpam-4585	96	93	.	.	PUNCT
ejpam-4585	97	1	suppose	suppose	VERB
ejpam-4585	97	2	s	s	VERB
ejpam-4585	97	3	⊆	⊆	NUM
ejpam-4585	97	4	v	v	NOUN
ejpam-4585	97	5	(	(	PUNCT
ejpam-4585	97	6	g	g	NOUN
ejpam-4585	97	7	)	)	PUNCT
ejpam-4585	97	8	is	be	AUX
ejpam-4585	97	9	a	a	DET
ejpam-4585	97	10	2	2	NUM
ejpam-4585	97	11	-	-	PUNCT
ejpam-4585	97	12	resolving	resolve	VERB
ejpam-4585	97	13	hop	hop	NOUN
ejpam-4585	97	14	dominating	dominating	NOUN
ejpam-4585	97	15	set	set	VERB
ejpam-4585	97	16	in	in	ADP
ejpam-4585	97	17	g.	g.	PROPN
ejpam-4585	97	18	then	then	ADV
ejpam-4585	97	19	by	by	ADP
ejpam-4585	97	20	remark	remark	NOUN
ejpam-4585	97	21	4	4	NUM
ejpam-4585	97	22	,	,	PUNCT
ejpam-4585	97	23	(	(	PUNCT
ejpam-4585	97	24	i	i	NOUN
ejpam-4585	97	25	)	)	PUNCT
ejpam-4585	97	26	holds	hold	VERB
ejpam-4585	97	27	.	.	PUNCT
ejpam-4585	98	1	to	to	PART
ejpam-4585	98	2	prove	prove	VERB
ejpam-4585	98	3	(	(	PUNCT
ejpam-4585	98	4	ii	ii	NOUN
ejpam-4585	98	5	)	)	PUNCT
ejpam-4585	98	6	,	,	PUNCT
ejpam-4585	98	7	let	let	VERB
ejpam-4585	98	8	v	v	NUM
ejpam-4585	98	9	∈	∈	NOUN
ejpam-4585	98	10	v	v	NOUN
ejpam-4585	98	11	(	(	PUNCT
ejpam-4585	98	12	g)\s	g)\s	NOUN
ejpam-4585	98	13	.	.	PUNCT
ejpam-4585	99	1	since	since	SCONJ
ejpam-4585	99	2	s	s	PROPN
ejpam-4585	99	3	is	be	AUX
ejpam-4585	99	4	a	a	DET
ejpam-4585	99	5	hop	hop	NOUN
ejpam-4585	99	6	dominating	dominating	NOUN
ejpam-4585	99	7	set	set	NOUN
ejpam-4585	99	8	,	,	PUNCT
ejpam-4585	99	9	there	there	PRON
ejpam-4585	99	10	exists	exist	VERB
ejpam-4585	99	11	z	z	PROPN
ejpam-4585	99	12	∈	∈	PROPN
ejpam-4585	99	13	s	s	VERB
ejpam-4585	99	14	such	such	ADJ
ejpam-4585	99	15	that	that	PRON
ejpam-4585	99	16	dg(v	dg(v	ADJ
ejpam-4585	99	17	,	,	PUNCT
ejpam-4585	99	18	z	z	NOUN
ejpam-4585	99	19	)	)	PUNCT
ejpam-4585	99	20	=	=	SYM
ejpam-4585	99	21	2	2	X
ejpam-4585	99	22	.	.	X
ejpam-4585	99	23	hence	hence	ADV
ejpam-4585	99	24	,	,	PUNCT
ejpam-4585	99	25	v	v	NOUN
ejpam-4585	99	26	/∈	/∈	PUNCT
ejpam-4585	99	27	ng(z	ng(z	NUM
ejpam-4585	99	28	)	)	PUNCT
ejpam-4585	99	29	.	.	PUNCT
ejpam-4585	100	1	this	this	PRON
ejpam-4585	100	2	shows	show	VERB
ejpam-4585	100	3	that	that	SCONJ
ejpam-4585	100	4	s	s	VERB
ejpam-4585	100	5	is	be	AUX
ejpam-4585	100	6	a	a	DET
ejpam-4585	100	7	point	point	NOUN
ejpam-4585	100	8	-	-	PUNCT
ejpam-4585	100	9	wise	wise	ADJ
ejpam-4585	100	10	non	non	ADJ
ejpam-4585	100	11	-	-	ADJ
ejpam-4585	100	12	dominating	dominating	ADJ
ejpam-4585	100	13	set	set	NOUN
ejpam-4585	100	14	of	of	ADP
ejpam-4585	100	15	g.	g.	PROPN
ejpam-4585	100	16	thus	thus	ADV
ejpam-4585	100	17	,	,	PUNCT
ejpam-4585	100	18	(	(	PUNCT
ejpam-4585	100	19	ii	ii	NOUN
ejpam-4585	100	20	)	)	PUNCT
ejpam-4585	100	21	holds	hold	VERB
ejpam-4585	100	22	.	.	PUNCT
ejpam-4585	101	1	a.m.	a.m.	PROPN
ejpam-4585	101	2	mahistrado	mahistrado	PROPN
ejpam-4585	101	3	,	,	PUNCT
ejpam-4585	101	4	h.	h.	PROPN
ejpam-4585	101	5	rara	rara	PROPN
ejpam-4585	101	6	/	/	SYM
ejpam-4585	101	7	eur	eur	PROPN
ejpam-4585	101	8	.	.	PUNCT
ejpam-4585	102	1	j.	j.	PROPN
ejpam-4585	102	2	pure	pure	PROPN
ejpam-4585	102	3	appl	appl	PROPN
ejpam-4585	102	4	.	.	PROPN
ejpam-4585	102	5	math	math	PROPN
ejpam-4585	102	6	,	,	PUNCT
ejpam-4585	102	7	15	15	NUM
ejpam-4585	102	8	(	(	PUNCT
ejpam-4585	102	9	4	4	NUM
ejpam-4585	102	10	)	)	PUNCT
ejpam-4585	102	11	(	(	PUNCT
ejpam-4585	102	12	2022	2022	NUM
ejpam-4585	102	13	)	)	PUNCT
ejpam-4585	102	14	,	,	PUNCT
ejpam-4585	102	15	1982	1982	NUM
ejpam-4585	102	16	-	-	SYM
ejpam-4585	102	17	1997	1997	NUM
ejpam-4585	102	18	1987	1987	NUM
ejpam-4585	102	19	remark	remark	NOUN
ejpam-4585	102	20	5	5	NUM
ejpam-4585	102	21	.	.	PUNCT
ejpam-4585	103	1	every	every	DET
ejpam-4585	103	2	2	2	NUM
ejpam-4585	103	3	-	-	PUNCT
ejpam-4585	103	4	resolving	resolve	VERB
ejpam-4585	103	5	hop	hop	NOUN
ejpam-4585	103	6	dominating	dominating	NOUN
ejpam-4585	103	7	set	set	NOUN
ejpam-4585	103	8	in	in	ADP
ejpam-4585	103	9	g	g	PROPN
ejpam-4585	103	10	is	be	AUX
ejpam-4585	103	11	a	a	DET
ejpam-4585	103	12	2	2	NUM
ejpam-4585	103	13	-	-	PUNCT
ejpam-4585	103	14	resolving	resolve	VERB
ejpam-4585	103	15	point	point	NOUN
ejpam-4585	103	16	-	-	PUNCT
ejpam-4585	103	17	wise	wise	ADV
ejpam-4585	103	18	nondominating	nondominate	VERB
ejpam-4585	103	19	set	set	NOUN
ejpam-4585	103	20	in	in	ADP
ejpam-4585	103	21	g.	g.	PROPN
ejpam-4585	103	22	however	however	ADV
ejpam-4585	103	23	,	,	PUNCT
ejpam-4585	103	24	a	a	DET
ejpam-4585	103	25	2	2	NUM
ejpam-4585	103	26	-	-	PUNCT
ejpam-4585	103	27	resolving	resolve	VERB
ejpam-4585	103	28	point	point	NOUN
ejpam-4585	103	29	-	-	PUNCT
ejpam-4585	103	30	wise	wise	ADJ
ejpam-4585	103	31	non	non	ADJ
ejpam-4585	103	32	-	-	ADJ
ejpam-4585	103	33	dominating	dominating	ADJ
ejpam-4585	103	34	set	set	NOUN
ejpam-4585	103	35	in	in	ADP
ejpam-4585	103	36	g	g	NOUN
ejpam-4585	103	37	need	need	AUX
ejpam-4585	103	38	not	not	PART
ejpam-4585	103	39	be	be	AUX
ejpam-4585	103	40	a	a	DET
ejpam-4585	103	41	2	2	NUM
ejpam-4585	103	42	-	-	PUNCT
ejpam-4585	103	43	resolving	resolve	VERB
ejpam-4585	103	44	hop	hop	NOUN
ejpam-4585	103	45	dominating	dominating	NOUN
ejpam-4585	103	46	set	set	VERB
ejpam-4585	103	47	in	in	ADP
ejpam-4585	103	48	g.	g.	PROPN
ejpam-4585	103	49	thus	thus	ADV
ejpam-4585	103	50	,	,	PUNCT
ejpam-4585	103	51	dim2pnd	dim2pnd	NOUN
ejpam-4585	103	52	(	(	PUNCT
ejpam-4585	103	53	g	g	NOUN
ejpam-4585	103	54	)	)	PUNCT
ejpam-4585	103	55	≤	≤	NUM
ejpam-4585	103	56	γ2rh(g	γ2rh(g	NOUN
ejpam-4585	103	57	)	)	PUNCT
ejpam-4585	103	58	.	.	PUNCT
ejpam-4585	104	1	remark	remark	PROPN
ejpam-4585	104	2	6	6	NUM
ejpam-4585	104	3	.	.	PUNCT
ejpam-4585	105	1	let	let	VERB
ejpam-4585	105	2	g	g	PRON
ejpam-4585	105	3	be	be	AUX
ejpam-4585	105	4	a	a	DET
ejpam-4585	105	5	connected	connected	ADJ
ejpam-4585	105	6	graph	graph	NOUN
ejpam-4585	105	7	.	.	PUNCT
ejpam-4585	106	1	then	then	ADV
ejpam-4585	106	2	every	every	DET
ejpam-4585	106	3	2	2	NUM
ejpam-4585	106	4	-	-	PUNCT
ejpam-4585	106	5	resolving	resolve	VERB
ejpam-4585	106	6	hop	hop	NOUN
ejpam-4585	106	7	dominating	dominating	NOUN
ejpam-4585	106	8	set	set	NOUN
ejpam-4585	106	9	in	in	ADP
ejpam-4585	106	10	g	g	PROPN
ejpam-4585	106	11	is	be	AUX
ejpam-4585	106	12	a	a	DET
ejpam-4585	106	13	2	2	NUM
ejpam-4585	106	14	-	-	PUNCT
ejpam-4585	106	15	resolving	resolving	NOUN
ejpam-4585	106	16	set	set	VERB
ejpam-4585	106	17	in	in	ADP
ejpam-4585	106	18	g.	g.	PROPN
ejpam-4585	106	19	however	however	ADV
ejpam-4585	106	20	,	,	PUNCT
ejpam-4585	106	21	a	a	DET
ejpam-4585	106	22	2	2	NUM
ejpam-4585	106	23	-	-	PUNCT
ejpam-4585	106	24	resolving	resolving	NOUN
ejpam-4585	106	25	set	set	NOUN
ejpam-4585	106	26	in	in	ADP
ejpam-4585	106	27	g	g	NOUN
ejpam-4585	106	28	need	need	AUX
ejpam-4585	106	29	not	not	PART
ejpam-4585	106	30	be	be	AUX
ejpam-4585	106	31	a	a	DET
ejpam-4585	106	32	2	2	NUM
ejpam-4585	106	33	-	-	PUNCT
ejpam-4585	106	34	resolving	resolve	VERB
ejpam-4585	106	35	hop	hop	NOUN
ejpam-4585	106	36	dominating	dominating	NOUN
ejpam-4585	106	37	set	set	VERB
ejpam-4585	106	38	in	in	ADP
ejpam-4585	106	39	g.	g.	PROPN
ejpam-4585	106	40	thus	thus	ADV
ejpam-4585	106	41	,	,	PUNCT
ejpam-4585	106	42	dim2(g	dim2(g	NOUN
ejpam-4585	106	43	)	)	PUNCT
ejpam-4585	106	44	≤	≤	NUM
ejpam-4585	106	45	γ2rh(g	γ2rh(g	NOUN
ejpam-4585	106	46	)	)	PUNCT
ejpam-4585	106	47	.	.	PUNCT
ejpam-4585	107	1	proposition	proposition	NOUN
ejpam-4585	107	2	1	1	NUM
ejpam-4585	107	3	.	.	PUNCT
ejpam-4585	108	1	for	for	ADP
ejpam-4585	108	2	a	a	DET
ejpam-4585	108	3	path	path	NOUN
ejpam-4585	108	4	pn	pn	NOUN
ejpam-4585	108	5	on	on	ADP
ejpam-4585	109	1	n	n	PRON
ejpam-4585	109	2	vertices	vertex	NOUN
ejpam-4585	109	3	γ2rh(pn	γ2rh(pn	NUM
ejpam-4585	109	4	)	)	PUNCT
ejpam-4585	109	5	=	=	PUNCT
ejpam-4585	110	1			NUM
ejpam-4585	110	2	2	2	NUM
ejpam-4585	110	3	,	,	PUNCT
ejpam-4585	110	4	if	if	SCONJ
ejpam-4585	110	5	n	n	NOUN
ejpam-4585	110	6	=	=	SYM
ejpam-4585	110	7	2	2	NUM
ejpam-4585	110	8	,	,	PUNCT
ejpam-4585	110	9	4	4	NUM
ejpam-4585	110	10	;	;	PUNCT
ejpam-4585	110	11	3	3	NUM
ejpam-4585	110	12	,	,	PUNCT
ejpam-4585	110	13	if	if	SCONJ
ejpam-4585	110	14	n	n	NOUN
ejpam-4585	110	15	=	=	SYM
ejpam-4585	110	16	3	3	NUM
ejpam-4585	110	17	,	,	PUNCT
ejpam-4585	110	18	5	5	NUM
ejpam-4585	110	19	,	,	PUNCT
ejpam-4585	110	20	6	6	NUM
ejpam-4585	110	21	;	;	PUNCT
ejpam-4585	110	22	2s	2s	NUM
ejpam-4585	110	23	,	,	PUNCT
ejpam-4585	110	24	if	if	SCONJ
ejpam-4585	110	25	n	n	NOUN
ejpam-4585	110	26	=	=	SYM
ejpam-4585	110	27	6s	6s	NUM
ejpam-4585	110	28	,	,	PUNCT
ejpam-4585	110	29	s	s	X
ejpam-4585	110	30	≥	≥	NOUN
ejpam-4585	110	31	2	2	NUM
ejpam-4585	110	32	;	;	PUNCT
ejpam-4585	110	33	2s+	2s+	NUM
ejpam-4585	110	34	1	1	NUM
ejpam-4585	110	35	,	,	PUNCT
ejpam-4585	110	36	if	if	SCONJ
ejpam-4585	110	37	n	n	ADV
ejpam-4585	110	38	=	=	SYM
ejpam-4585	110	39	6s+	6s+	NUM
ejpam-4585	110	40	1	1	NUM
ejpam-4585	110	41	,	,	PUNCT
ejpam-4585	110	42	s	s	VERB
ejpam-4585	110	43	≥	≥	NOUN
ejpam-4585	110	44	1	1	NUM
ejpam-4585	110	45	;	;	PUNCT
ejpam-4585	110	46	2s+	2s+	NUM
ejpam-4585	110	47	2	2	NUM
ejpam-4585	110	48	,	,	PUNCT
ejpam-4585	110	49	if	if	SCONJ
ejpam-4585	110	50	n	n	ADV
ejpam-4585	110	51	=	=	SYM
ejpam-4585	110	52	6s+	6s+	NUM
ejpam-4585	110	53	x	x	SYM
ejpam-4585	110	54	;	;	PUNCT
ejpam-4585	110	55	2	2	NUM
ejpam-4585	110	56	≤	≤	NUM
ejpam-4585	110	57	x	x	PUNCT
ejpam-4585	110	58	≤	≤	NUM
ejpam-4585	110	59	5	5	NUM
ejpam-4585	110	60	,	,	PUNCT
ejpam-4585	110	61	s	s	VERB
ejpam-4585	110	62	≥	≥	NOUN
ejpam-4585	110	63	1	1	NUM
ejpam-4585	110	64	.	.	PUNCT
ejpam-4585	110	65	proposition	proposition	NOUN
ejpam-4585	110	66	2	2	NUM
ejpam-4585	110	67	.	.	X
ejpam-4585	111	1	for	for	ADP
ejpam-4585	111	2	a	a	DET
ejpam-4585	111	3	cycle	cycle	NOUN
ejpam-4585	111	4	cn	cn	NOUN
ejpam-4585	111	5	on	on	ADP
ejpam-4585	111	6	n	n	CCONJ
ejpam-4585	111	7	vertices	vertex	NOUN
ejpam-4585	111	8	γ2rh(cn	γ2rh(cn	X
ejpam-4585	111	9	)	)	PUNCT
ejpam-4585	111	10	=	=	PUNCT
ejpam-4585	112	1			NOUN
ejpam-4585	112	2	3	3	NUM
ejpam-4585	112	3	,	,	PUNCT
ejpam-4585	112	4	if	if	SCONJ
ejpam-4585	112	5	n	n	NOUN
ejpam-4585	112	6	=	=	SYM
ejpam-4585	112	7	3	3	NUM
ejpam-4585	112	8	,	,	PUNCT
ejpam-4585	112	9	5	5	NUM
ejpam-4585	112	10	,	,	PUNCT
ejpam-4585	112	11	6	6	NUM
ejpam-4585	112	12	;	;	PUNCT
ejpam-4585	112	13	2s	2s	NUM
ejpam-4585	112	14	if	if	SCONJ
ejpam-4585	112	15	n	n	NOUN
ejpam-4585	112	16	=	=	SYM
ejpam-4585	112	17	6s	6s	NUM
ejpam-4585	112	18	,	,	PUNCT
ejpam-4585	112	19	s	s	X
ejpam-4585	112	20	≥	≥	NOUN
ejpam-4585	112	21	2	2	NUM
ejpam-4585	112	22	;	;	PUNCT
ejpam-4585	112	23	2s+	2s+	NUM
ejpam-4585	112	24	1	1	NUM
ejpam-4585	112	25	,	,	PUNCT
ejpam-4585	112	26	if	if	SCONJ
ejpam-4585	112	27	n	n	ADV
ejpam-4585	112	28	=	=	SYM
ejpam-4585	112	29	6s+	6s+	NUM
ejpam-4585	112	30	1	1	NUM
ejpam-4585	112	31	,	,	PUNCT
ejpam-4585	112	32	s	s	VERB
ejpam-4585	112	33	≥	≥	NOUN
ejpam-4585	112	34	1	1	NUM
ejpam-4585	112	35	;	;	PUNCT
ejpam-4585	112	36	2s+	2s+	NUM
ejpam-4585	112	37	2	2	NUM
ejpam-4585	112	38	,	,	PUNCT
ejpam-4585	112	39	if	if	SCONJ
ejpam-4585	112	40	n	n	ADV
ejpam-4585	112	41	=	=	SYM
ejpam-4585	112	42	6s+	6s+	NUM
ejpam-4585	112	43	x	x	SYM
ejpam-4585	112	44	;	;	PUNCT
ejpam-4585	112	45	2	2	NUM
ejpam-4585	112	46	≤	≤	NUM
ejpam-4585	112	47	x	x	PUNCT
ejpam-4585	112	48	≤	≤	NUM
ejpam-4585	112	49	5	5	NUM
ejpam-4585	112	50	,	,	PUNCT
ejpam-4585	112	51	s	s	VERB
ejpam-4585	112	52	≥	≥	NOUN
ejpam-4585	112	53	1	1	NUM
ejpam-4585	112	54	.	.	PUNCT
ejpam-4585	112	55	proposition	proposition	NOUN
ejpam-4585	112	56	3	3	X
ejpam-4585	112	57	.	.	PUNCT
ejpam-4585	113	1	let	let	VERB
ejpam-4585	113	2	g	g	PRON
ejpam-4585	113	3	be	be	AUX
ejpam-4585	113	4	a	a	DET
ejpam-4585	113	5	connected	connected	ADJ
ejpam-4585	113	6	graph	graph	NOUN
ejpam-4585	113	7	of	of	ADP
ejpam-4585	113	8	order	order	NOUN
ejpam-4585	113	9	4	4	NUM
ejpam-4585	113	10	.	.	PUNCT
ejpam-4585	114	1	then	then	ADV
ejpam-4585	114	2	γ2rh(p4	γ2rh(p4	X
ejpam-4585	114	3	)	)	PUNCT
ejpam-4585	114	4	=	=	SYM
ejpam-4585	114	5	2	2	NUM
ejpam-4585	114	6	and	and	CCONJ
ejpam-4585	114	7	γ2rh(c4	γ2rh(c4	NOUN
ejpam-4585	114	8	)	)	PUNCT
ejpam-4585	115	1	=	=	SYM
ejpam-4585	115	2	4	4	NUM
ejpam-4585	115	3	,	,	PUNCT
ejpam-4585	115	4	respectively	respectively	ADV
ejpam-4585	115	5	.	.	PUNCT
ejpam-4585	116	1	theorem	theorem	NOUN
ejpam-4585	116	2	2	2	NUM
ejpam-4585	116	3	.	.	X
ejpam-4585	116	4	for	for	ADP
ejpam-4585	116	5	a	a	DET
ejpam-4585	116	6	complete	complete	ADJ
ejpam-4585	116	7	graph	graph	NOUN
ejpam-4585	116	8	kn	kn	PROPN
ejpam-4585	116	9	on	on	ADP
ejpam-4585	116	10	n	n	PRON
ejpam-4585	116	11	vertices	vertex	NOUN
ejpam-4585	116	12	,	,	PUNCT
ejpam-4585	116	13	γ2rh(kn	γ2rh(kn	NUM
ejpam-4585	116	14	)	)	PUNCT
ejpam-4585	117	1	=	=	SYM
ejpam-4585	117	2	n.	n.	NOUN
ejpam-4585	117	3	proof	proof	NOUN
ejpam-4585	117	4	.	.	PUNCT
ejpam-4585	118	1	suppose	suppose	VERB
ejpam-4585	118	2	that	that	SCONJ
ejpam-4585	118	3	γ2rh(kn	γ2rh(kn	PROPN
ejpam-4585	118	4	)	)	PUNCT
ejpam-4585	118	5	<	<	X
ejpam-4585	118	6	n.	n.	NOUN
ejpam-4585	118	7	let	let	VERB
ejpam-4585	118	8	s	s	PRON
ejpam-4585	118	9	be	be	AUX
ejpam-4585	118	10	the	the	DET
ejpam-4585	118	11	minimum	minimum	ADJ
ejpam-4585	118	12	2	2	NUM
ejpam-4585	118	13	-	-	PUNCT
ejpam-4585	118	14	resolving	resolve	VERB
ejpam-4585	118	15	hop	hop	NOUN
ejpam-4585	118	16	dominating	dominating	NOUN
ejpam-4585	118	17	set	set	NOUN
ejpam-4585	118	18	of	of	ADP
ejpam-4585	118	19	kn	kn	PROPN
ejpam-4585	118	20	.	.	PUNCT
ejpam-4585	119	1	let	let	VERB
ejpam-4585	119	2	x	x	SYM
ejpam-4585	119	3	∈	∈	PROPN
ejpam-4585	119	4	v	v	NOUN
ejpam-4585	119	5	(	(	PUNCT
ejpam-4585	119	6	kn)\s	kn)\s	NOUN
ejpam-4585	119	7	and	and	CCONJ
ejpam-4585	119	8	y	y	PROPN
ejpam-4585	119	9	∈	∈	PROPN
ejpam-4585	119	10	s.	s.	PROPN
ejpam-4585	120	1	then	then	ADV
ejpam-4585	120	2	x	x	X
ejpam-4585	120	3	and	and	CCONJ
ejpam-4585	120	4	y	y	PROPN
ejpam-4585	120	5	differ	differ	VERB
ejpam-4585	120	6	at	at	ADP
ejpam-4585	120	7	exactly	exactly	ADV
ejpam-4585	120	8	one	one	NUM
ejpam-4585	120	9	position	position	NOUN
ejpam-4585	120	10	,	,	PUNCT
ejpam-4585	120	11	that	that	PRON
ejpam-4585	120	12	is	be	AUX
ejpam-4585	120	13	a	a	DET
ejpam-4585	120	14	contradiction	contradiction	NOUN
ejpam-4585	120	15	to	to	ADP
ejpam-4585	120	16	the	the	DET
ejpam-4585	120	17	assumption	assumption	NOUN
ejpam-4585	120	18	that	that	SCONJ
ejpam-4585	120	19	s	s	VERB
ejpam-4585	120	20	is	be	AUX
ejpam-4585	120	21	a	a	DET
ejpam-4585	120	22	2	2	NUM
ejpam-4585	120	23	-	-	PUNCT
ejpam-4585	120	24	resolving	resolve	VERB
ejpam-4585	120	25	hop	hop	NOUN
ejpam-4585	120	26	dominating	dominating	NOUN
ejpam-4585	120	27	set	set	NOUN
ejpam-4585	120	28	of	of	ADP
ejpam-4585	120	29	kn	kn	PROPN
ejpam-4585	120	30	.	.	PUNCT
ejpam-4585	121	1	therefore	therefore	ADV
ejpam-4585	121	2	,	,	PUNCT
ejpam-4585	121	3	γ2rh(kn	γ2rh(kn	PROPN
ejpam-4585	121	4	)	)	PUNCT
ejpam-4585	122	1	=	=	SYM
ejpam-4585	122	2	n.	n.	NOUN
ejpam-4585	122	3	theorem	theorem	VERB
ejpam-4585	122	4	3	3	NUM
ejpam-4585	122	5	.	.	PUNCT
ejpam-4585	123	1	a	a	DET
ejpam-4585	123	2	set	set	NOUN
ejpam-4585	123	3	s	s	NOUN
ejpam-4585	123	4	⊆	⊆	NUM
ejpam-4585	123	5	v	v	NOUN
ejpam-4585	123	6	(	(	PUNCT
ejpam-4585	123	7	km	km	PROPN
ejpam-4585	123	8	,	,	PUNCT
ejpam-4585	123	9	n	n	CCONJ
ejpam-4585	123	10	)	)	PUNCT
ejpam-4585	123	11	is	be	AUX
ejpam-4585	123	12	a	a	DET
ejpam-4585	123	13	2	2	NUM
ejpam-4585	123	14	-	-	PUNCT
ejpam-4585	123	15	resolving	resolve	VERB
ejpam-4585	123	16	hop	hop	NOUN
ejpam-4585	123	17	dominating	dominating	NOUN
ejpam-4585	123	18	set	set	VERB
ejpam-4585	123	19	in	in	ADP
ejpam-4585	123	20	km	km	PROPN
ejpam-4585	123	21	,	,	PUNCT
ejpam-4585	123	22	n	n	CCONJ
ejpam-4585	123	23	if	if	SCONJ
ejpam-4585	123	24	and	and	CCONJ
ejpam-4585	123	25	only	only	ADV
ejpam-4585	123	26	if	if	SCONJ
ejpam-4585	123	27	s	s	VERB
ejpam-4585	123	28	=	=	SYM
ejpam-4585	123	29	v	v	PROPN
ejpam-4585	123	30	(	(	PUNCT
ejpam-4585	123	31	km	km	PROPN
ejpam-4585	123	32	,	,	PUNCT
ejpam-4585	123	33	n	n	CCONJ
ejpam-4585	123	34	)	)	PUNCT
ejpam-4585	123	35	.	.	PUNCT
ejpam-4585	124	1	proof	proof	NOUN
ejpam-4585	124	2	.	.	PUNCT
ejpam-4585	125	1	let	let	VERB
ejpam-4585	125	2	s	s	PRON
ejpam-4585	125	3	be	be	AUX
ejpam-4585	125	4	a	a	DET
ejpam-4585	125	5	subset	subset	NOUN
ejpam-4585	125	6	of	of	ADP
ejpam-4585	125	7	v	v	NOUN
ejpam-4585	125	8	(	(	PUNCT
ejpam-4585	125	9	km	km	PROPN
ejpam-4585	125	10	,	,	PUNCT
ejpam-4585	125	11	n	n	CCONJ
ejpam-4585	125	12	)	)	PUNCT
ejpam-4585	125	13	.	.	PUNCT
ejpam-4585	126	1	let	let	VERB
ejpam-4585	126	2	u	u	PRON
ejpam-4585	126	3	and	and	CCONJ
ejpam-4585	126	4	v	v	NOUN
ejpam-4585	126	5	be	be	AUX
ejpam-4585	126	6	partite	partite	ADJ
ejpam-4585	126	7	sets	set	NOUN
ejpam-4585	126	8	with	with	ADP
ejpam-4585	126	9	|u	|u	ADJ
ejpam-4585	127	1	|	|	NOUN
ejpam-4585	127	2	=	=	NOUN
ejpam-4585	127	3	m	m	NOUN
ejpam-4585	127	4	and	and	CCONJ
ejpam-4585	127	5	|v	|v	VERB
ejpam-4585	127	6	|	|	ADV
ejpam-4585	127	7	=	=	SYM
ejpam-4585	127	8	n	n	CCONJ
ejpam-4585	127	9	;	;	PUNCT
ejpam-4585	127	10	m	m	PROPN
ejpam-4585	127	11	,	,	PUNCT
ejpam-4585	127	12	n	n	PRON
ejpam-4585	127	13	≥	≥	NOUN
ejpam-4585	127	14	1	1	NUM
ejpam-4585	127	15	.	.	PUNCT
ejpam-4585	128	1	let	let	VERB
ejpam-4585	128	2	u	u	PRON
ejpam-4585	128	3	=	=	NOUN
ejpam-4585	128	4	{	{	PUNCT
ejpam-4585	128	5	u1	u1	NOUN
ejpam-4585	128	6	,	,	PUNCT
ejpam-4585	128	7	u2	u2	NOUN
ejpam-4585	128	8	,	,	PUNCT
ejpam-4585	128	9	.	.	PUNCT
ejpam-4585	128	10	.	.	PUNCT
ejpam-4585	128	11	.	.	PUNCT
ejpam-4585	129	1	um	um	INTJ
ejpam-4585	129	2	}	}	PUNCT
ejpam-4585	129	3	and	and	CCONJ
ejpam-4585	129	4	v	v	NOUN
ejpam-4585	129	5	=	=	SYM
ejpam-4585	129	6	{	{	PUNCT
ejpam-4585	129	7	v1	v1	PROPN
ejpam-4585	129	8	,	,	PUNCT
ejpam-4585	129	9	v2	v2	PROPN
ejpam-4585	129	10	,	,	PUNCT
ejpam-4585	129	11	.	.	PUNCT
ejpam-4585	129	12	.	.	PUNCT
ejpam-4585	129	13	.	.	PUNCT
ejpam-4585	130	1	vn	vn	X
ejpam-4585	130	2	}	}	PUNCT
ejpam-4585	130	3	.	.	PUNCT
ejpam-4585	131	1	suppose	suppose	VERB
ejpam-4585	131	2	there	there	PRON
ejpam-4585	131	3	exists	exist	VERB
ejpam-4585	131	4	uk	uk	PROPN
ejpam-4585	131	5	∈	∈	PROPN
ejpam-4585	131	6	u\s	u\s	PROPN
ejpam-4585	131	7	.	.	PUNCT
ejpam-4585	132	1	then	then	ADV
ejpam-4585	132	2	∀	∀	PUNCT
ejpam-4585	132	3	i	i	PRON
ejpam-4585	132	4	∈	∈	PROPN
ejpam-4585	132	5	{	{	PUNCT
ejpam-4585	132	6	1	1	NUM
ejpam-4585	132	7	,	,	PUNCT
ejpam-4585	132	8	.	.	PUNCT
ejpam-4585	132	9	.	.	PUNCT
ejpam-4585	132	10	.	.	PUNCT
ejpam-4585	133	1	,	,	PUNCT
ejpam-4585	133	2	m}\{k	m}\{k	PROPN
ejpam-4585	133	3	}	}	PUNCT
ejpam-4585	133	4	,	,	PUNCT
ejpam-4585	133	5	rkm	rkm	PROPN
ejpam-4585	133	6	,	,	PUNCT
ejpam-4585	133	7	n(ui	n(ui	PROPN
ejpam-4585	133	8	/	/	SYM
ejpam-4585	133	9	s	s	NOUN
ejpam-4585	133	10	)	)	PUNCT
ejpam-4585	133	11	and	and	CCONJ
ejpam-4585	133	12	rkm	rkm	PROPN
ejpam-4585	133	13	,	,	PUNCT
ejpam-4585	133	14	n(uk	n(uk	PROPN
ejpam-4585	133	15	/	/	SYM
ejpam-4585	133	16	s	s	PART
ejpam-4585	133	17	)	)	PUNCT
ejpam-4585	133	18	differ	differ	VERB
ejpam-4585	133	19	in	in	ADP
ejpam-4585	133	20	at	at	ADP
ejpam-4585	133	21	most	most	ADV
ejpam-4585	133	22	one	one	NUM
ejpam-4585	133	23	position	position	NOUN
ejpam-4585	133	24	.	.	PUNCT
ejpam-4585	134	1	similarly	similarly	ADV
ejpam-4585	134	2	,	,	PUNCT
ejpam-4585	134	3	suppose	suppose	VERB
ejpam-4585	134	4	there	there	PRON
ejpam-4585	134	5	exists	exist	VERB
ejpam-4585	134	6	vk	vk	ADP
ejpam-4585	134	7	∈	∈	PROPN
ejpam-4585	134	8	v	v	ADP
ejpam-4585	134	9	\s	\s	NOUN
ejpam-4585	134	10	∀	∀	PUNCT
ejpam-4585	135	1	j	j	PROPN
ejpam-4585	135	2	∈	∈	PROPN
ejpam-4585	135	3	{	{	PUNCT
ejpam-4585	135	4	1	1	NUM
ejpam-4585	135	5	,	,	PUNCT
ejpam-4585	135	6	.	.	PUNCT
ejpam-4585	135	7	.	.	PUNCT
ejpam-4585	135	8	.	.	PUNCT
ejpam-4585	135	9	,	,	PUNCT
ejpam-4585	135	10	n}\{k	n}\{k	ADV
ejpam-4585	135	11	}	}	PUNCT
ejpam-4585	135	12	,	,	PUNCT
ejpam-4585	135	13	rkm	rkm	PROPN
ejpam-4585	135	14	,	,	PUNCT
ejpam-4585	135	15	n(vj	n(vj	PROPN
ejpam-4585	135	16	/	/	SYM
ejpam-4585	135	17	s	s	NOUN
ejpam-4585	135	18	)	)	PUNCT
ejpam-4585	135	19	and	and	CCONJ
ejpam-4585	135	20	rkm	rkm	PROPN
ejpam-4585	135	21	,	,	PUNCT
ejpam-4585	135	22	n(vk	n(vk	PROPN
ejpam-4585	135	23	/	/	SYM
ejpam-4585	135	24	s	s	PART
ejpam-4585	135	25	)	)	PUNCT
ejpam-4585	135	26	differ	differ	VERB
ejpam-4585	135	27	in	in	ADP
ejpam-4585	135	28	at	at	ADP
ejpam-4585	135	29	most	most	ADV
ejpam-4585	135	30	one	one	NUM
ejpam-4585	135	31	position	position	NOUN
ejpam-4585	135	32	.	.	PUNCT
ejpam-4585	136	1	thus	thus	ADV
ejpam-4585	136	2	,	,	PUNCT
ejpam-4585	136	3	it	it	PRON
ejpam-4585	136	4	follows	follow	VERB
ejpam-4585	136	5	that	that	PRON
ejpam-4585	136	6	s	s	VERB
ejpam-4585	136	7	=	=	SYM
ejpam-4585	136	8	v	v	PROPN
ejpam-4585	136	9	(	(	PUNCT
ejpam-4585	136	10	km	km	PROPN
ejpam-4585	136	11	,	,	PUNCT
ejpam-4585	136	12	n	n	CCONJ
ejpam-4585	136	13	)	)	PUNCT
ejpam-4585	136	14	.	.	PUNCT
ejpam-4585	137	1	the	the	DET
ejpam-4585	137	2	converse	converse	NOUN
ejpam-4585	137	3	is	be	AUX
ejpam-4585	137	4	clear	clear	ADJ
ejpam-4585	137	5	.	.	PUNCT
ejpam-4585	138	1	corollary	corollary	ADJ
ejpam-4585	138	2	1	1	NUM
ejpam-4585	138	3	.	.	PUNCT
ejpam-4585	139	1	a	a	DET
ejpam-4585	139	2	set	set	NOUN
ejpam-4585	139	3	s	s	NOUN
ejpam-4585	139	4	⊆	⊆	NUM
ejpam-4585	139	5	v	v	NOUN
ejpam-4585	139	6	(	(	PUNCT
ejpam-4585	139	7	k1,n	k1,n	PROPN
ejpam-4585	139	8	)	)	PUNCT
ejpam-4585	139	9	is	be	AUX
ejpam-4585	139	10	a	a	DET
ejpam-4585	139	11	2	2	NUM
ejpam-4585	139	12	-	-	PUNCT
ejpam-4585	139	13	resolving	resolve	VERB
ejpam-4585	139	14	hop	hop	NOUN
ejpam-4585	139	15	dominating	dominating	NOUN
ejpam-4585	139	16	set	set	VERB
ejpam-4585	139	17	in	in	ADP
ejpam-4585	139	18	k1,n	k1,n	PROPN
ejpam-4585	139	19	if	if	SCONJ
ejpam-4585	139	20	and	and	CCONJ
ejpam-4585	139	21	only	only	ADV
ejpam-4585	139	22	if	if	SCONJ
ejpam-4585	139	23	s	s	VERB
ejpam-4585	139	24	=	=	SYM
ejpam-4585	139	25	v	v	PROPN
ejpam-4585	139	26	(	(	PUNCT
ejpam-4585	139	27	k1,n	k1,n	PROPN
ejpam-4585	139	28	)	)	PUNCT
ejpam-4585	139	29	.	.	PUNCT
ejpam-4585	140	1	corollary	corollary	ADJ
ejpam-4585	140	2	2	2	NUM
ejpam-4585	140	3	.	.	PUNCT
ejpam-4585	141	1	for	for	ADP
ejpam-4585	141	2	a	a	DET
ejpam-4585	141	3	complete	complete	ADJ
ejpam-4585	141	4	bipartite	bipartite	NOUN
ejpam-4585	141	5	graph	graph	NOUN
ejpam-4585	141	6	km	km	PROPN
ejpam-4585	141	7	,	,	PUNCT
ejpam-4585	141	8	n	n	CCONJ
ejpam-4585	141	9	,	,	PUNCT
ejpam-4585	141	10	γ2rh(km	γ2rh(km	ADJ
ejpam-4585	141	11	,	,	PUNCT
ejpam-4585	141	12	n	n	CCONJ
ejpam-4585	141	13	)	)	PUNCT
ejpam-4585	142	1	=	=	SYM
ejpam-4585	142	2	m+	m+	NUM
ejpam-4585	142	3	n.	n.	PROPN
ejpam-4585	142	4	a.m.	a.m.	PROPN
ejpam-4585	143	1	mahistrado	mahistrado	PROPN
ejpam-4585	143	2	,	,	PUNCT
ejpam-4585	143	3	h.	h.	PROPN
ejpam-4585	143	4	rara	rara	PROPN
ejpam-4585	143	5	/	/	SYM
ejpam-4585	143	6	eur	eur	PROPN
ejpam-4585	143	7	.	.	PUNCT
ejpam-4585	144	1	j.	j.	PROPN
ejpam-4585	144	2	pure	pure	PROPN
ejpam-4585	144	3	appl	appl	PROPN
ejpam-4585	144	4	.	.	PROPN
ejpam-4585	144	5	math	math	PROPN
ejpam-4585	144	6	,	,	PUNCT
ejpam-4585	144	7	15	15	NUM
ejpam-4585	144	8	(	(	PUNCT
ejpam-4585	144	9	4	4	NUM
ejpam-4585	144	10	)	)	PUNCT
ejpam-4585	144	11	(	(	PUNCT
ejpam-4585	144	12	2022	2022	NUM
ejpam-4585	144	13	)	)	PUNCT
ejpam-4585	144	14	,	,	PUNCT
ejpam-4585	144	15	1982	1982	NUM
ejpam-4585	144	16	-	-	SYM
ejpam-4585	144	17	1997	1997	NUM
ejpam-4585	144	18	1988	1988	NUM
ejpam-4585	144	19	4	4	NUM
ejpam-4585	144	20	.	.	SYM
ejpam-4585	144	21	2	2	NUM
ejpam-4585	144	22	-	-	PUNCT
ejpam-4585	144	23	resolving	resolve	VERB
ejpam-4585	144	24	hop	hop	NOUN
ejpam-4585	144	25	dominating	dominating	NOUN
ejpam-4585	144	26	sets	set	NOUN
ejpam-4585	144	27	in	in	ADP
ejpam-4585	144	28	the	the	DET
ejpam-4585	144	29	join	join	NOUN
ejpam-4585	144	30	of	of	ADP
ejpam-4585	144	31	graphs	graph	NOUN
ejpam-4585	144	32	definition	definition	NOUN
ejpam-4585	144	33	7	7	NUM
ejpam-4585	144	34	.	.	PUNCT
ejpam-4585	145	1	[	[	X
ejpam-4585	145	2	2	2	X
ejpam-4585	145	3	]	]	PUNCT
ejpam-4585	145	4	the	the	DET
ejpam-4585	145	5	join	join	NOUN
ejpam-4585	145	6	g	g	PROPN
ejpam-4585	145	7	+	+	CCONJ
ejpam-4585	145	8	h	h	NOUN
ejpam-4585	145	9	of	of	ADP
ejpam-4585	145	10	two	two	NUM
ejpam-4585	145	11	graphs	graph	NOUN
ejpam-4585	145	12	g	g	NOUN
ejpam-4585	145	13	and	and	CCONJ
ejpam-4585	145	14	h	h	NOUN
ejpam-4585	145	15	is	be	AUX
ejpam-4585	145	16	the	the	DET
ejpam-4585	145	17	graph	graph	NOUN
ejpam-4585	145	18	with	with	ADP
ejpam-4585	145	19	vertex	vertex	NOUN
ejpam-4585	145	20	set	set	VERB
ejpam-4585	145	21	v	v	NOUN
ejpam-4585	145	22	(	(	PUNCT
ejpam-4585	145	23	g+h	g+h	NOUN
ejpam-4585	145	24	)	)	PUNCT
ejpam-4585	145	25	=	=	SYM
ejpam-4585	145	26	v	v	X
ejpam-4585	145	27	(	(	PUNCT
ejpam-4585	145	28	g)∪̇v	g)∪̇v	X
ejpam-4585	145	29	(	(	PUNCT
ejpam-4585	145	30	h	h	NOUN
ejpam-4585	145	31	)	)	PUNCT
ejpam-4585	145	32	and	and	CCONJ
ejpam-4585	145	33	edge	edge	NOUN
ejpam-4585	145	34	set	set	VERB
ejpam-4585	145	35	e(g+h	e(g+h	NUM
ejpam-4585	145	36	)	)	PUNCT
ejpam-4585	145	37	=	=	SYM
ejpam-4585	145	38	e(g)∪̇e(h	e(g)∪̇e(h	NOUN
ejpam-4585	145	39	)	)	PUNCT
ejpam-4585	145	40	∪	∪	NOUN
ejpam-4585	145	41	{	{	PUNCT
ejpam-4585	145	42	uv	uv	NOUN
ejpam-4585	145	43	:	:	PUNCT
ejpam-4585	145	44	u	u	PROPN
ejpam-4585	145	45	∈	∈	PROPN
ejpam-4585	145	46	v	v	ADP
ejpam-4585	145	47	(	(	PUNCT
ejpam-4585	145	48	g	g	NOUN
ejpam-4585	145	49	)	)	PUNCT
ejpam-4585	145	50	,	,	PUNCT
ejpam-4585	145	51	v	v	X
ejpam-4585	145	52	∈	∈	PROPN
ejpam-4585	145	53	v	v	NOUN
ejpam-4585	145	54	(	(	PUNCT
ejpam-4585	145	55	h	h	NOUN
ejpam-4585	145	56	)	)	PUNCT
ejpam-4585	145	57	}	}	PUNCT
ejpam-4585	145	58	.	.	PUNCT
ejpam-4585	146	1	note	note	VERB
ejpam-4585	146	2	that	that	SCONJ
ejpam-4585	146	3	the	the	DET
ejpam-4585	146	4	star	star	NOUN
ejpam-4585	146	5	k1,n	k1,n	PROPN
ejpam-4585	146	6	can	can	AUX
ejpam-4585	146	7	be	be	AUX
ejpam-4585	146	8	expressed	express	VERB
ejpam-4585	146	9	as	as	ADP
ejpam-4585	146	10	the	the	DET
ejpam-4585	146	11	join	join	NOUN
ejpam-4585	146	12	of	of	ADP
ejpam-4585	146	13	the	the	DET
ejpam-4585	146	14	trivial	trivial	ADJ
ejpam-4585	146	15	graph	graph	NOUN
ejpam-4585	146	16	k1	k1	NOUN
ejpam-4585	146	17	and	and	CCONJ
ejpam-4585	146	18	the	the	DET
ejpam-4585	146	19	empty	empty	ADJ
ejpam-4585	146	20	graph	graph	NOUN
ejpam-4585	146	21	kn	kn	PROPN
ejpam-4585	146	22	of	of	ADP
ejpam-4585	146	23	order	order	NOUN
ejpam-4585	146	24	n	n	CCONJ
ejpam-4585	146	25	,	,	PUNCT
ejpam-4585	146	26	that	that	ADV
ejpam-4585	146	27	is	is	ADV
ejpam-4585	146	28	,	,	PUNCT
ejpam-4585	146	29	k1,n	k1,n	PROPN
ejpam-4585	146	30	=	=	PROPN
ejpam-4585	146	31	k1	k1	PROPN
ejpam-4585	146	32	+	+	X
ejpam-4585	146	33	kn	kn	PROPN
ejpam-4585	146	34	.	.	PUNCT
ejpam-4585	147	1	the	the	DET
ejpam-4585	147	2	graphs	graph	NOUN
ejpam-4585	147	3	fn	fn	NOUN
ejpam-4585	147	4	=	=	SYM
ejpam-4585	147	5	k1	k1	PROPN
ejpam-4585	147	6	+	+	CCONJ
ejpam-4585	147	7	pn	pn	PROPN
ejpam-4585	147	8	and	and	CCONJ
ejpam-4585	147	9	wn	wn	PROPN
ejpam-4585	147	10	=	=	PROPN
ejpam-4585	147	11	k1	k1	PROPN
ejpam-4585	148	1	+	+	CCONJ
ejpam-4585	148	2	cn	cn	NOUN
ejpam-4585	148	3	of	of	ADP
ejpam-4585	148	4	orders	order	NOUN
ejpam-4585	148	5	n+	n+	PUNCT
ejpam-4585	148	6	1	1	NUM
ejpam-4585	148	7	are	be	AUX
ejpam-4585	148	8	called	call	VERB
ejpam-4585	148	9	fan	fan	NOUN
ejpam-4585	148	10	and	and	CCONJ
ejpam-4585	148	11	wheel	wheel	NOUN
ejpam-4585	148	12	,	,	PUNCT
ejpam-4585	148	13	respectively	respectively	ADV
ejpam-4585	148	14	.	.	PUNCT
ejpam-4585	149	1	theorem	theorem	VERB
ejpam-4585	149	2	4	4	NUM
ejpam-4585	149	3	.	.	PUNCT
ejpam-4585	150	1	[	[	X
ejpam-4585	150	2	4	4	X
ejpam-4585	150	3	]	]	PUNCT
ejpam-4585	150	4	let	let	VERB
ejpam-4585	150	5	g	g	PRON
ejpam-4585	150	6	be	be	AUX
ejpam-4585	150	7	a	a	DET
ejpam-4585	150	8	connected	connected	ADJ
ejpam-4585	150	9	graph	graph	NOUN
ejpam-4585	150	10	of	of	ADP
ejpam-4585	150	11	order	order	NOUN
ejpam-4585	150	12	greater	great	ADJ
ejpam-4585	150	13	than	than	ADP
ejpam-4585	150	14	3	3	NUM
ejpam-4585	150	15	and	and	CCONJ
ejpam-4585	150	16	let	let	VERB
ejpam-4585	150	17	k1	k1	NOUN
ejpam-4585	150	18	=	=	SYM
ejpam-4585	150	19	{	{	PUNCT
ejpam-4585	150	20	v	v	NOUN
ejpam-4585	150	21	}	}	PUNCT
ejpam-4585	150	22	.	.	PUNCT
ejpam-4585	151	1	then	then	ADV
ejpam-4585	151	2	s	s	VERB
ejpam-4585	151	3	⊆	⊆	NUM
ejpam-4585	151	4	v	v	NOUN
ejpam-4585	151	5	(	(	PUNCT
ejpam-4585	151	6	k1	k1	NOUN
ejpam-4585	151	7	+	+	NOUN
ejpam-4585	151	8	g	g	NOUN
ejpam-4585	151	9	)	)	PUNCT
ejpam-4585	151	10	is	be	AUX
ejpam-4585	151	11	a	a	DET
ejpam-4585	151	12	2	2	NUM
ejpam-4585	151	13	-	-	PUNCT
ejpam-4585	151	14	resolving	resolving	NOUN
ejpam-4585	151	15	set	set	VERB
ejpam-4585	151	16	in	in	ADP
ejpam-4585	151	17	k1	k1	NOUN
ejpam-4585	151	18	+	+	ADP
ejpam-4585	151	19	g	g	PROPN
ejpam-4585	151	20	if	if	SCONJ
ejpam-4585	152	1	and	and	CCONJ
ejpam-4585	152	2	only	only	ADV
ejpam-4585	152	3	if	if	SCONJ
ejpam-4585	152	4	either	either	PRON
ejpam-4585	152	5	v	v	NOUN
ejpam-4585	152	6	/∈	/∈	PUNCT
ejpam-4585	152	7	s	s	PART
ejpam-4585	152	8	and	and	CCONJ
ejpam-4585	152	9	s	s	VERB
ejpam-4585	152	10	is	be	AUX
ejpam-4585	152	11	a	a	DET
ejpam-4585	152	12	(	(	PUNCT
ejpam-4585	152	13	2	2	NUM
ejpam-4585	152	14	,	,	PUNCT
ejpam-4585	152	15	2)-locating	2)-locating	NUM
ejpam-4585	152	16	set	set	VERB
ejpam-4585	152	17	in	in	ADP
ejpam-4585	152	18	g	g	PROPN
ejpam-4585	152	19	or	or	CCONJ
ejpam-4585	152	20	s	s	NOUN
ejpam-4585	152	21	=	=	PUNCT
ejpam-4585	152	22	{	{	PUNCT
ejpam-4585	152	23	v	v	NOUN
ejpam-4585	152	24	}	}	PUNCT
ejpam-4585	152	25	∪	∪	ADP
ejpam-4585	152	26	t	t	PROPN
ejpam-4585	152	27	where	where	SCONJ
ejpam-4585	152	28	t	t	PROPN
ejpam-4585	152	29	is	be	AUX
ejpam-4585	152	30	a	a	DET
ejpam-4585	152	31	(	(	PUNCT
ejpam-4585	152	32	2	2	NUM
ejpam-4585	152	33	,	,	PUNCT
ejpam-4585	152	34	1)-locating	1)-locating	NUM
ejpam-4585	152	35	set	set	VERB
ejpam-4585	152	36	in	in	ADP
ejpam-4585	152	37	g.	g.	PROPN
ejpam-4585	152	38	theorem	theorem	VERB
ejpam-4585	152	39	5	5	X
ejpam-4585	152	40	.	.	PUNCT
ejpam-4585	153	1	let	let	VERB
ejpam-4585	153	2	g	g	PRON
ejpam-4585	153	3	be	be	AUX
ejpam-4585	153	4	a	a	DET
ejpam-4585	153	5	connected	connected	ADJ
ejpam-4585	153	6	graph	graph	NOUN
ejpam-4585	153	7	and	and	CCONJ
ejpam-4585	153	8	let	let	VERB
ejpam-4585	153	9	k1	k1	NOUN
ejpam-4585	153	10	=	=	SYM
ejpam-4585	153	11	{	{	PUNCT
ejpam-4585	153	12	x	x	NOUN
ejpam-4585	153	13	}	}	PUNCT
ejpam-4585	153	14	.	.	PUNCT
ejpam-4585	154	1	then	then	ADV
ejpam-4585	154	2	s	s	VERB
ejpam-4585	154	3	⊆	⊆	NUM
ejpam-4585	154	4	v	v	NOUN
ejpam-4585	154	5	(	(	PUNCT
ejpam-4585	154	6	k1	k1	NOUN
ejpam-4585	154	7	+	+	CCONJ
ejpam-4585	154	8	g	g	NOUN
ejpam-4585	154	9	)	)	PUNCT
ejpam-4585	154	10	is	be	AUX
ejpam-4585	154	11	a	a	DET
ejpam-4585	154	12	2	2	NUM
ejpam-4585	154	13	-	-	PUNCT
ejpam-4585	154	14	resolving	resolve	VERB
ejpam-4585	154	15	hop	hop	NOUN
ejpam-4585	154	16	dominating	dominating	NOUN
ejpam-4585	154	17	set	set	VERB
ejpam-4585	154	18	in	in	ADP
ejpam-4585	154	19	k1	k1	NOUN
ejpam-4585	154	20	+	+	CCONJ
ejpam-4585	154	21	g	g	NOUN
ejpam-4585	154	22	if	if	SCONJ
ejpam-4585	155	1	and	and	CCONJ
ejpam-4585	155	2	only	only	ADV
ejpam-4585	155	3	if	if	SCONJ
ejpam-4585	155	4	s	s	VERB
ejpam-4585	155	5	=	=	X
ejpam-4585	155	6	{	{	PUNCT
ejpam-4585	155	7	x	x	NOUN
ejpam-4585	155	8	}	}	PUNCT
ejpam-4585	155	9	∪	∪	ADP
ejpam-4585	155	10	t	t	PROPN
ejpam-4585	155	11	where	where	SCONJ
ejpam-4585	155	12	t	t	PROPN
ejpam-4585	155	13	is	be	AUX
ejpam-4585	155	14	a	a	DET
ejpam-4585	155	15	(	(	PUNCT
ejpam-4585	155	16	2	2	NUM
ejpam-4585	155	17	,	,	PUNCT
ejpam-4585	155	18	1)-locating	1)-locating	NUM
ejpam-4585	155	19	point	point	NOUN
ejpam-4585	155	20	-	-	PUNCT
ejpam-4585	155	21	wise	wise	ADJ
ejpam-4585	155	22	non	non	ADJ
ejpam-4585	155	23	-	-	ADJ
ejpam-4585	155	24	dominating	dominating	ADJ
ejpam-4585	155	25	set	set	NOUN
ejpam-4585	155	26	in	in	ADP
ejpam-4585	155	27	g.	g.	PROPN
ejpam-4585	155	28	proof	proof	PROPN
ejpam-4585	155	29	.	.	PUNCT
ejpam-4585	156	1	let	let	VERB
ejpam-4585	156	2	s	s	PRON
ejpam-4585	156	3	⊆	⊆	NUM
ejpam-4585	156	4	v	v	NOUN
ejpam-4585	156	5	(	(	PUNCT
ejpam-4585	156	6	k1	k1	NOUN
ejpam-4585	156	7	+	+	NOUN
ejpam-4585	156	8	g	g	NOUN
ejpam-4585	156	9	)	)	PUNCT
ejpam-4585	156	10	be	be	VERB
ejpam-4585	156	11	a	a	DET
ejpam-4585	156	12	2	2	NUM
ejpam-4585	156	13	-	-	PUNCT
ejpam-4585	156	14	resolving	resolve	VERB
ejpam-4585	156	15	hop	hop	NOUN
ejpam-4585	156	16	dominating	dominating	NOUN
ejpam-4585	156	17	set	set	VERB
ejpam-4585	156	18	in	in	ADP
ejpam-4585	156	19	k1	k1	PROPN
ejpam-4585	157	1	+	+	PROPN
ejpam-4585	158	1	g.	g.	PROPN
ejpam-4585	158	2	since	since	SCONJ
ejpam-4585	158	3	s	s	PROPN
ejpam-4585	158	4	is	be	AUX
ejpam-4585	158	5	a	a	DET
ejpam-4585	158	6	hop	hop	NOUN
ejpam-4585	158	7	dominating	dominating	NOUN
ejpam-4585	158	8	set	set	NOUN
ejpam-4585	158	9	,	,	PUNCT
ejpam-4585	158	10	x	x	PROPN
ejpam-4585	158	11	∈	∈	PROPN
ejpam-4585	158	12	s.	s.	PROPN
ejpam-4585	158	13	hence	hence	ADV
ejpam-4585	158	14	,	,	PUNCT
ejpam-4585	158	15	s	s	VERB
ejpam-4585	158	16	=	=	PUNCT
ejpam-4585	158	17	{	{	PUNCT
ejpam-4585	158	18	x	x	NOUN
ejpam-4585	158	19	}	}	PUNCT
ejpam-4585	158	20	∪	∪	ADP
ejpam-4585	158	21	t	t	PROPN
ejpam-4585	158	22	for	for	ADP
ejpam-4585	158	23	t	t	PROPN
ejpam-4585	158	24	⊆	⊆	NUM
ejpam-4585	158	25	v	v	NOUN
ejpam-4585	158	26	(	(	PUNCT
ejpam-4585	158	27	g	g	NOUN
ejpam-4585	158	28	)	)	PUNCT
ejpam-4585	158	29	.	.	PUNCT
ejpam-4585	159	1	by	by	ADP
ejpam-4585	159	2	theorem	theorem	NOUN
ejpam-4585	159	3	4	4	NUM
ejpam-4585	159	4	,	,	PUNCT
ejpam-4585	159	5	t	t	PROPN
ejpam-4585	159	6	is	be	AUX
ejpam-4585	159	7	a	a	DET
ejpam-4585	159	8	(	(	PUNCT
ejpam-4585	159	9	2	2	NUM
ejpam-4585	159	10	,	,	PUNCT
ejpam-4585	159	11	1)-locating	1)-locating	NUM
ejpam-4585	159	12	set	set	VERB
ejpam-4585	159	13	in	in	ADP
ejpam-4585	159	14	g.	g.	PROPN
ejpam-4585	159	15	now	now	ADV
ejpam-4585	159	16	,	,	PUNCT
ejpam-4585	159	17	since	since	SCONJ
ejpam-4585	159	18	s	s	NOUN
ejpam-4585	159	19	is	be	AUX
ejpam-4585	159	20	a	a	DET
ejpam-4585	159	21	hop	hop	NOUN
ejpam-4585	159	22	dominating	dominating	NOUN
ejpam-4585	159	23	set	set	NOUN
ejpam-4585	159	24	∀	∀	NOUN
ejpam-4585	159	25	v	v	ADP
ejpam-4585	159	26	∈	∈	PROPN
ejpam-4585	159	27	v	v	NOUN
ejpam-4585	159	28	(	(	PUNCT
ejpam-4585	159	29	g)\t	g)\t	PROPN
ejpam-4585	159	30	,	,	PUNCT
ejpam-4585	159	31	there	there	PRON
ejpam-4585	159	32	exists	exist	VERB
ejpam-4585	159	33	z	z	PROPN
ejpam-4585	159	34	∈	∈	PROPN
ejpam-4585	159	35	t	t	NOUN
ejpam-4585	159	36	such	such	ADJ
ejpam-4585	159	37	that	that	PRON
ejpam-4585	159	38	dk1+g(v	dk1+g(v	NOUN
ejpam-4585	159	39	,	,	PUNCT
ejpam-4585	159	40	z	z	NOUN
ejpam-4585	159	41	)	)	PUNCT
ejpam-4585	159	42	=	=	SYM
ejpam-4585	160	1	2	2	X
ejpam-4585	160	2	.	.	PUNCT
ejpam-4585	160	3	this	this	PRON
ejpam-4585	160	4	follows	follow	VERB
ejpam-4585	160	5	that	that	PRON
ejpam-4585	160	6	v	v	ADP
ejpam-4585	160	7	/∈	/∈	PUNCT
ejpam-4585	160	8	ng(z	ng(z	NUM
ejpam-4585	160	9	)	)	PUNCT
ejpam-4585	160	10	.	.	PUNCT
ejpam-4585	161	1	thus	thus	ADV
ejpam-4585	161	2	,	,	PUNCT
ejpam-4585	161	3	t	t	PROPN
ejpam-4585	161	4	is	be	AUX
ejpam-4585	161	5	a	a	DET
ejpam-4585	161	6	point	point	NOUN
ejpam-4585	161	7	-	-	PUNCT
ejpam-4585	161	8	wise	wise	ADJ
ejpam-4585	161	9	non	non	ADJ
ejpam-4585	161	10	-	-	ADJ
ejpam-4585	161	11	dominating	dominating	ADJ
ejpam-4585	161	12	set	set	NOUN
ejpam-4585	161	13	in	in	ADP
ejpam-4585	161	14	g.	g.	PROPN
ejpam-4585	161	15	therefore	therefore	ADV
ejpam-4585	161	16	,	,	PUNCT
ejpam-4585	161	17	t	t	PROPN
ejpam-4585	161	18	is	be	AUX
ejpam-4585	161	19	a	a	DET
ejpam-4585	161	20	(	(	PUNCT
ejpam-4585	161	21	2	2	NUM
ejpam-4585	161	22	,	,	PUNCT
ejpam-4585	161	23	1)-locating	1)-locating	NUM
ejpam-4585	161	24	point	point	NOUN
ejpam-4585	161	25	-	-	PUNCT
ejpam-4585	161	26	wise	wise	ADJ
ejpam-4585	161	27	non	non	ADJ
ejpam-4585	161	28	-	-	ADJ
ejpam-4585	161	29	dominating	dominating	ADJ
ejpam-4585	161	30	set	set	NOUN
ejpam-4585	161	31	in	in	ADP
ejpam-4585	161	32	g.	g.	PROPN
ejpam-4585	161	33	conversely	conversely	ADV
ejpam-4585	161	34	,	,	PUNCT
ejpam-4585	161	35	suppose	suppose	VERB
ejpam-4585	161	36	s	s	VERB
ejpam-4585	161	37	=	=	PUNCT
ejpam-4585	161	38	{	{	PUNCT
ejpam-4585	161	39	x}∪t	x}∪t	PROPN
ejpam-4585	161	40	where	where	SCONJ
ejpam-4585	161	41	t	t	PROPN
ejpam-4585	161	42	is	be	AUX
ejpam-4585	161	43	a	a	DET
ejpam-4585	161	44	(	(	PUNCT
ejpam-4585	161	45	2	2	NUM
ejpam-4585	161	46	,	,	PUNCT
ejpam-4585	161	47	1)-locating	1)-locating	NUM
ejpam-4585	161	48	point	point	NOUN
ejpam-4585	161	49	-	-	PUNCT
ejpam-4585	161	50	wise	wise	ADJ
ejpam-4585	161	51	non	non	ADJ
ejpam-4585	161	52	-	-	ADJ
ejpam-4585	161	53	dominating	dominating	ADJ
ejpam-4585	161	54	set	set	NOUN
ejpam-4585	161	55	in	in	ADP
ejpam-4585	161	56	g.	g.	PROPN
ejpam-4585	161	57	then	then	ADV
ejpam-4585	161	58	by	by	ADP
ejpam-4585	161	59	theorem	theorem	NOUN
ejpam-4585	161	60	4	4	NUM
ejpam-4585	161	61	,	,	PUNCT
ejpam-4585	161	62	s	s	VERB
ejpam-4585	161	63	is	be	AUX
ejpam-4585	161	64	a	a	DET
ejpam-4585	161	65	2	2	NUM
ejpam-4585	161	66	-	-	PUNCT
ejpam-4585	161	67	resolving	resolving	NOUN
ejpam-4585	161	68	set	set	VERB
ejpam-4585	161	69	in	in	ADP
ejpam-4585	161	70	k1+g	k1+g	NOUN
ejpam-4585	161	71	.	.	PUNCT
ejpam-4585	162	1	since	since	SCONJ
ejpam-4585	162	2	t	t	PROPN
ejpam-4585	162	3	is	be	AUX
ejpam-4585	162	4	a	a	DET
ejpam-4585	162	5	point	point	NOUN
ejpam-4585	162	6	-	-	PUNCT
ejpam-4585	162	7	wise	wise	ADV
ejpam-4585	162	8	nondominating	nondominate	VERB
ejpam-4585	162	9	set	set	NOUN
ejpam-4585	162	10	in	in	ADP
ejpam-4585	162	11	g	g	NOUN
ejpam-4585	162	12	,	,	PUNCT
ejpam-4585	162	13	∀	∀	VERB
ejpam-4585	162	14	y	y	PROPN
ejpam-4585	162	15	∈	∈	PROPN
ejpam-4585	162	16	v	v	X
ejpam-4585	162	17	(	(	PUNCT
ejpam-4585	162	18	g)\t	g)\t	PROPN
ejpam-4585	162	19	,	,	PUNCT
ejpam-4585	162	20	there	there	PRON
ejpam-4585	162	21	exists	exist	VERB
ejpam-4585	162	22	v	v	ADP
ejpam-4585	162	23	∈	∈	PROPN
ejpam-4585	162	24	t	t	NOUN
ejpam-4585	162	25	such	such	ADJ
ejpam-4585	162	26	that	that	PRON
ejpam-4585	162	27	vy	vy	PROPN
ejpam-4585	162	28	/∈	/∈	PUNCT
ejpam-4585	162	29	e(g	e(g	PROPN
ejpam-4585	162	30	)	)	PUNCT
ejpam-4585	162	31	.	.	PUNCT
ejpam-4585	163	1	this	this	PRON
ejpam-4585	163	2	follows	follow	VERB
ejpam-4585	163	3	that	that	SCONJ
ejpam-4585	163	4	dk1+g(v	dk1+g(v	ADP
ejpam-4585	163	5	,	,	PUNCT
ejpam-4585	163	6	y	y	NOUN
ejpam-4585	163	7	)	)	PUNCT
ejpam-4585	163	8	=	=	SYM
ejpam-4585	163	9	2	2	X
ejpam-4585	163	10	.	.	PUNCT
ejpam-4585	163	11	thus	thus	ADV
ejpam-4585	163	12	,	,	PUNCT
ejpam-4585	163	13	s	s	VERB
ejpam-4585	163	14	is	be	AUX
ejpam-4585	163	15	a	a	DET
ejpam-4585	163	16	hop	hop	NOUN
ejpam-4585	163	17	dominating	dominating	NOUN
ejpam-4585	163	18	set	set	NOUN
ejpam-4585	163	19	.	.	PUNCT
ejpam-4585	164	1	therefore	therefore	ADV
ejpam-4585	164	2	,	,	PUNCT
ejpam-4585	164	3	s	s	VERB
ejpam-4585	164	4	is	be	AUX
ejpam-4585	164	5	a	a	DET
ejpam-4585	164	6	2	2	NUM
ejpam-4585	164	7	-	-	PUNCT
ejpam-4585	164	8	resolving	resolve	VERB
ejpam-4585	164	9	hop	hop	NOUN
ejpam-4585	164	10	dominating	dominating	NOUN
ejpam-4585	164	11	set	set	VERB
ejpam-4585	164	12	in	in	ADP
ejpam-4585	164	13	k1	k1	PROPN
ejpam-4585	164	14	+	+	PROPN
ejpam-4585	164	15	g.	g.	PROPN
ejpam-4585	164	16	corollary	corollary	NOUN
ejpam-4585	164	17	3	3	X
ejpam-4585	164	18	.	.	PUNCT
ejpam-4585	165	1	let	let	VERB
ejpam-4585	165	2	g	g	NOUN
ejpam-4585	165	3	be	be	AUX
ejpam-4585	165	4	connected	connect	VERB
ejpam-4585	165	5	nontrivial	nontrivial	ADJ
ejpam-4585	165	6	graph	graph	NOUN
ejpam-4585	165	7	.	.	PUNCT
ejpam-4585	166	1	then	then	ADV
ejpam-4585	166	2	γ2rh(k1	γ2rh(k1	VERB
ejpam-4585	167	1	+	+	NOUN
ejpam-4585	167	2	g	g	NOUN
ejpam-4585	167	3	)	)	PUNCT
ejpam-4585	167	4	=	=	VERB
ejpam-4585	168	1	lnpnd	lnpnd	ADJ
ejpam-4585	168	2	(	(	PUNCT
ejpam-4585	168	3	2,1)(g	2,1)(g	NUM
ejpam-4585	168	4	)	)	PUNCT
ejpam-4585	169	1	+	+	NOUN
ejpam-4585	169	2	1	1	X
ejpam-4585	169	3	.	.	X
ejpam-4585	169	4	proof	proof	NOUN
ejpam-4585	169	5	.	.	PUNCT
ejpam-4585	170	1	suppose	suppose	VERB
ejpam-4585	170	2	s	s	PRON
ejpam-4585	170	3	is	be	AUX
ejpam-4585	170	4	a	a	DET
ejpam-4585	170	5	γ2rh	γ2rh	NOUN
ejpam-4585	170	6	-	-	PUNCT
ejpam-4585	170	7	set	set	ADJ
ejpam-4585	170	8	in	in	ADP
ejpam-4585	170	9	k1	k1	PROPN
ejpam-4585	170	10	+	+	PROPN
ejpam-4585	170	11	g.	g.	PROPN
ejpam-4585	170	12	then	then	ADV
ejpam-4585	170	13	by	by	ADP
ejpam-4585	170	14	theorem	theorem	NOUN
ejpam-4585	170	15	5	5	NUM
ejpam-4585	170	16	,	,	PUNCT
ejpam-4585	170	17	s	s	PART
ejpam-4585	170	18	=	=	PUNCT
ejpam-4585	170	19	{	{	PUNCT
ejpam-4585	170	20	x	x	NOUN
ejpam-4585	170	21	}	}	PUNCT
ejpam-4585	170	22	∪	∪	ADP
ejpam-4585	170	23	t	t	PROPN
ejpam-4585	170	24	where	where	SCONJ
ejpam-4585	170	25	t	t	PROPN
ejpam-4585	170	26	is	be	AUX
ejpam-4585	170	27	a	a	DET
ejpam-4585	170	28	(	(	PUNCT
ejpam-4585	170	29	2	2	NUM
ejpam-4585	170	30	,	,	PUNCT
ejpam-4585	170	31	1)locating	1)locating	NUM
ejpam-4585	170	32	point	point	ADV
ejpam-4585	170	33	-	-	PUNCT
ejpam-4585	170	34	wise	wise	ADJ
ejpam-4585	170	35	non	non	ADJ
ejpam-4585	170	36	-	-	ADJ
ejpam-4585	170	37	dominating	dominating	ADJ
ejpam-4585	170	38	set	set	NOUN
ejpam-4585	170	39	in	in	ADP
ejpam-4585	170	40	g.	g.	PROPN
ejpam-4585	170	41	thus	thus	ADV
ejpam-4585	170	42	,	,	PUNCT
ejpam-4585	170	43	γ2rh(k1	γ2rh(k1	PUNCT
ejpam-4585	171	1	+	+	NOUN
ejpam-4585	171	2	g	g	NOUN
ejpam-4585	171	3	)	)	PUNCT
ejpam-4585	171	4	=	=	SYM
ejpam-4585	171	5	|s|	|s|	PROPN
ejpam-4585	171	6	=	=	PUNCT
ejpam-4585	171	7	|t	|t	NOUN
ejpam-4585	171	8	|+	|+	NOUN
ejpam-4585	171	9	1	1	NUM
ejpam-4585	171	10	≥	≥	NOUN
ejpam-4585	171	11	lnpnd	lnpnd	ADV
ejpam-4585	171	12	(	(	PUNCT
ejpam-4585	171	13	2,1)(g	2,1)(g	NUM
ejpam-4585	171	14	)	)	PUNCT
ejpam-4585	172	1	+	+	CCONJ
ejpam-4585	172	2	1	1	X
ejpam-4585	172	3	.	.	X
ejpam-4585	172	4	on	on	ADP
ejpam-4585	172	5	the	the	DET
ejpam-4585	172	6	other	other	ADJ
ejpam-4585	172	7	hand	hand	NOUN
ejpam-4585	172	8	,	,	PUNCT
ejpam-4585	172	9	let	let	VERB
ejpam-4585	172	10	t	t	PROPN
ejpam-4585	172	11	′	′	NOUN
ejpam-4585	172	12	be	be	AUX
ejpam-4585	172	13	a	a	DET
ejpam-4585	172	14	lnpnd	lnpnd	ADJ
ejpam-4585	172	15	(	(	PUNCT
ejpam-4585	172	16	2,1)-set	2,1)-set	NUM
ejpam-4585	172	17	of	of	ADP
ejpam-4585	172	18	g.	g.	PROPN
ejpam-4585	172	19	then	then	ADV
ejpam-4585	172	20	by	by	ADP
ejpam-4585	172	21	theorem	theorem	NOUN
ejpam-4585	172	22	5	5	NUM
ejpam-4585	172	23	,	,	PUNCT
ejpam-4585	172	24	s	s	PART
ejpam-4585	172	25	=	=	PUNCT
ejpam-4585	172	26	{	{	PUNCT
ejpam-4585	172	27	x	x	NOUN
ejpam-4585	172	28	}	}	PUNCT
ejpam-4585	172	29	∪	∪	ADP
ejpam-4585	172	30	t	t	PROPN
ejpam-4585	172	31	′	′	NUM
ejpam-4585	172	32	is	be	AUX
ejpam-4585	172	33	a	a	DET
ejpam-4585	172	34	2	2	NUM
ejpam-4585	172	35	-	-	PUNCT
ejpam-4585	172	36	resolving	resolve	VERB
ejpam-4585	172	37	hop	hop	NOUN
ejpam-4585	172	38	dominating	dominating	NOUN
ejpam-4585	172	39	set	set	NOUN
ejpam-4585	172	40	of	of	ADP
ejpam-4585	172	41	k1	k1	PROPN
ejpam-4585	173	1	+	+	PROPN
ejpam-4585	173	2	g.	g.	PROPN
ejpam-4585	173	3	thus	thus	ADV
ejpam-4585	173	4	,	,	PUNCT
ejpam-4585	174	1	γ2rh(k1	γ2rh(k1	PUNCT
ejpam-4585	174	2	+	+	NOUN
ejpam-4585	174	3	g	g	NOUN
ejpam-4585	174	4	)	)	PUNCT
ejpam-4585	174	5	≤	≤	NUM
ejpam-4585	174	6	|s|	|s|	PROPN
ejpam-4585	174	7	=	=	PUNCT
ejpam-4585	174	8	|t	|t	NOUN
ejpam-4585	175	1	′	′	NUM
ejpam-4585	175	2	|+	|+	NOUN
ejpam-4585	176	1	1	1	NUM
ejpam-4585	176	2	=	=	SYM
ejpam-4585	176	3	lnpnd	lnpnd	ADJ
ejpam-4585	176	4	(	(	PUNCT
ejpam-4585	176	5	2,1)(g	2,1)(g	NUM
ejpam-4585	176	6	)	)	PUNCT
ejpam-4585	177	1	+	+	CCONJ
ejpam-4585	177	2	1	1	X
ejpam-4585	177	3	.	.	X
ejpam-4585	177	4	therefore	therefore	ADV
ejpam-4585	177	5	,	,	PUNCT
ejpam-4585	177	6	γ2rh(k1	γ2rh(k1	PUNCT
ejpam-4585	178	1	+	+	NOUN
ejpam-4585	178	2	g	g	NOUN
ejpam-4585	178	3	)	)	PUNCT
ejpam-4585	178	4	=	=	VERB
ejpam-4585	179	1	lnpnd	lnpnd	ADJ
ejpam-4585	179	2	(	(	PUNCT
ejpam-4585	179	3	2,1)(g	2,1)(g	NUM
ejpam-4585	179	4	)	)	PUNCT
ejpam-4585	180	1	+	+	CCONJ
ejpam-4585	180	2	1	1	X
ejpam-4585	180	3	.	.	X
ejpam-4585	180	4	a.m.	a.m.	PROPN
ejpam-4585	180	5	mahistrado	mahistrado	PROPN
ejpam-4585	180	6	,	,	PUNCT
ejpam-4585	180	7	h.	h.	PROPN
ejpam-4585	180	8	rara	rara	PROPN
ejpam-4585	180	9	/	/	SYM
ejpam-4585	180	10	eur	eur	PROPN
ejpam-4585	180	11	.	.	PUNCT
ejpam-4585	181	1	j.	j.	PROPN
ejpam-4585	181	2	pure	pure	PROPN
ejpam-4585	181	3	appl	appl	PROPN
ejpam-4585	181	4	.	.	PROPN
ejpam-4585	181	5	math	math	PROPN
ejpam-4585	181	6	,	,	PUNCT
ejpam-4585	181	7	15	15	NUM
ejpam-4585	181	8	(	(	PUNCT
ejpam-4585	181	9	4	4	NUM
ejpam-4585	181	10	)	)	PUNCT
ejpam-4585	181	11	(	(	PUNCT
ejpam-4585	181	12	2022	2022	NUM
ejpam-4585	181	13	)	)	PUNCT
ejpam-4585	181	14	,	,	PUNCT
ejpam-4585	181	15	1982	1982	NUM
ejpam-4585	181	16	-	-	SYM
ejpam-4585	181	17	1997	1997	NUM
ejpam-4585	181	18	1989	1989	NUM
ejpam-4585	181	19	example	example	NOUN
ejpam-4585	181	20	7	7	NUM
ejpam-4585	181	21	.	.	X
ejpam-4585	182	1	for	for	ADP
ejpam-4585	182	2	a	a	DET
ejpam-4585	182	3	fan	fan	NOUN
ejpam-4585	182	4	fn	fn	NOUN
ejpam-4585	182	5	=	=	PUNCT
ejpam-4585	182	6	pn	pn	PROPN
ejpam-4585	182	7	+	+	NOUN
ejpam-4585	182	8	k1	k1	NOUN
ejpam-4585	182	9	on	on	ADP
ejpam-4585	182	10	n+	n+	ADP
ejpam-4585	182	11	1	1	NUM
ejpam-4585	182	12	(	(	PUNCT
ejpam-4585	182	13	n	n	CCONJ
ejpam-4585	182	14	≥	≥	NOUN
ejpam-4585	182	15	3	3	NUM
ejpam-4585	182	16	)	)	PUNCT
ejpam-4585	182	17	vertices	vertice	VERB
ejpam-4585	182	18	γ2rh(fn	γ2rh(fn	PROPN
ejpam-4585	182	19	)	)	PUNCT
ejpam-4585	182	20	=	=	SYM
ejpam-4585	183	1	lnpnd	lnpnd	ADJ
ejpam-4585	183	2	(	(	PUNCT
ejpam-4585	183	3	2,1)(pn	2,1)(pn	NUM
ejpam-4585	183	4	)	)	PUNCT
ejpam-4585	183	5	+	+	CCONJ
ejpam-4585	183	6	1	1	X
ejpam-4585	183	7	=	=	SYM
ejpam-4585	183	8			NOUN
ejpam-4585	183	9	4	4	NUM
ejpam-4585	183	10	,	,	PUNCT
ejpam-4585	183	11	if	if	SCONJ
ejpam-4585	183	12	n	n	CCONJ
ejpam-4585	183	13	=	=	SYM
ejpam-4585	183	14	3	3	NUM
ejpam-4585	183	15	n	n	NUM
ejpam-4585	183	16	2	2	NUM
ejpam-4585	183	17	+	+	NUM
ejpam-4585	183	18	2	2	NUM
ejpam-4585	183	19	,	,	PUNCT
ejpam-4585	183	20	if	if	SCONJ
ejpam-4585	183	21	n	n	PRON
ejpam-4585	183	22	is	be	AUX
ejpam-4585	183	23	even	even	ADV
ejpam-4585	183	24	⌈n2	⌈n2	ADJ
ejpam-4585	183	25	⌉+	⌉+	X
ejpam-4585	183	26	1	1	NUM
ejpam-4585	183	27	,	,	PUNCT
ejpam-4585	183	28	if	if	SCONJ
ejpam-4585	183	29	n	n	PRON
ejpam-4585	183	30	is	be	AUX
ejpam-4585	183	31	odd	odd	ADJ
ejpam-4585	183	32	.	.	PUNCT
ejpam-4585	183	33	example	example	NOUN
ejpam-4585	183	34	8	8	NUM
ejpam-4585	183	35	.	.	PUNCT
ejpam-4585	184	1	for	for	ADP
ejpam-4585	184	2	a	a	DET
ejpam-4585	184	3	wheel	wheel	NOUN
ejpam-4585	184	4	wn	wn	NOUN
ejpam-4585	184	5	=	=	SYM
ejpam-4585	184	6	cn	cn	PROPN
ejpam-4585	184	7	+	+	CCONJ
ejpam-4585	184	8	1	1	NUM
ejpam-4585	184	9	on	on	ADP
ejpam-4585	184	10	n+	n+	ADP
ejpam-4585	184	11	1	1	NUM
ejpam-4585	184	12	(	(	PUNCT
ejpam-4585	184	13	n	n	CCONJ
ejpam-4585	184	14	≥	≥	NOUN
ejpam-4585	184	15	3	3	NUM
ejpam-4585	184	16	)	)	PUNCT
ejpam-4585	184	17	vertices	vertex	NOUN
ejpam-4585	184	18	γ2rh(wn	γ2rh(wn	NOUN
ejpam-4585	184	19	)	)	PUNCT
ejpam-4585	184	20	=	=	SYM
ejpam-4585	184	21	lnpnd	lnpnd	ADJ
ejpam-4585	184	22	(	(	PUNCT
ejpam-4585	184	23	2,1)(cn	2,1)(cn	NUM
ejpam-4585	184	24	)	)	PUNCT
ejpam-4585	185	1	+	+	CCONJ
ejpam-4585	185	2	1	1	X
ejpam-4585	185	3	=	=	SYM
ejpam-4585	185	4			NOUN
ejpam-4585	185	5	4	4	NUM
ejpam-4585	185	6	,	,	PUNCT
ejpam-4585	185	7	if	if	SCONJ
ejpam-4585	185	8	n	n	NOUN
ejpam-4585	185	9	=	=	SYM
ejpam-4585	185	10	3	3	NUM
ejpam-4585	185	11	5	5	NUM
ejpam-4585	185	12	,	,	PUNCT
ejpam-4585	185	13	if	if	SCONJ
ejpam-4585	185	14	n	n	NOUN
ejpam-4585	185	15	=	=	SYM
ejpam-4585	185	16	4	4	NUM
ejpam-4585	185	17	n	n	DET
ejpam-4585	185	18	2	2	NUM
ejpam-4585	185	19	+	+	NUM
ejpam-4585	185	20	1	1	NUM
ejpam-4585	185	21	,	,	PUNCT
ejpam-4585	185	22	if	if	SCONJ
ejpam-4585	185	23	n	n	PRON
ejpam-4585	185	24	is	be	AUX
ejpam-4585	185	25	even	even	ADV
ejpam-4585	185	26	⌈n2	⌈n2	ADJ
ejpam-4585	185	27	⌉+	⌉+	X
ejpam-4585	185	28	1	1	NUM
ejpam-4585	185	29	,	,	PUNCT
ejpam-4585	185	30	if	if	SCONJ
ejpam-4585	185	31	n	n	PRON
ejpam-4585	185	32	is	be	AUX
ejpam-4585	185	33	odd	odd	ADJ
ejpam-4585	185	34	.	.	PUNCT
ejpam-4585	186	1	theorem	theorem	ADJ
ejpam-4585	186	2	6	6	NUM
ejpam-4585	186	3	.	.	PUNCT
ejpam-4585	187	1	[	[	X
ejpam-4585	187	2	4	4	X
ejpam-4585	187	3	]	]	PUNCT
ejpam-4585	187	4	let	let	VERB
ejpam-4585	187	5	g	g	NOUN
ejpam-4585	187	6	and	and	CCONJ
ejpam-4585	187	7	h	h	NOUN
ejpam-4585	187	8	be	be	AUX
ejpam-4585	187	9	nontrivial	nontrivial	ADJ
ejpam-4585	187	10	connected	connected	ADJ
ejpam-4585	187	11	graphs	graph	NOUN
ejpam-4585	187	12	.	.	PUNCT
ejpam-4585	188	1	a	a	DET
ejpam-4585	188	2	proper	proper	ADJ
ejpam-4585	188	3	subset	subset	NOUN
ejpam-4585	188	4	s	s	NOUN
ejpam-4585	188	5	of	of	ADP
ejpam-4585	188	6	v	v	NOUN
ejpam-4585	188	7	(	(	PUNCT
ejpam-4585	188	8	g+h	g+h	PROPN
ejpam-4585	188	9	)	)	PUNCT
ejpam-4585	188	10	is	be	AUX
ejpam-4585	188	11	a	a	DET
ejpam-4585	188	12	2	2	NUM
ejpam-4585	188	13	-	-	PUNCT
ejpam-4585	188	14	resolving	resolving	NOUN
ejpam-4585	188	15	set	set	NOUN
ejpam-4585	188	16	in	in	ADP
ejpam-4585	188	17	g+h	g+h	PROPN
ejpam-4585	188	18	if	if	SCONJ
ejpam-4585	188	19	and	and	CCONJ
ejpam-4585	188	20	only	only	ADV
ejpam-4585	188	21	if	if	SCONJ
ejpam-4585	188	22	sg	sg	PROPN
ejpam-4585	188	23	=	=	SYM
ejpam-4585	188	24	v	v	NOUN
ejpam-4585	188	25	(	(	PUNCT
ejpam-4585	188	26	g)∩s	g)∩s	PROPN
ejpam-4585	188	27	and	and	CCONJ
ejpam-4585	188	28	sh	sh	PROPN
ejpam-4585	188	29	=	=	SYM
ejpam-4585	188	30	v	v	PROPN
ejpam-4585	188	31	(	(	PUNCT
ejpam-4585	188	32	h)∩s	h)∩s	PROPN
ejpam-4585	188	33	are	be	AUX
ejpam-4585	188	34	2	2	NUM
ejpam-4585	188	35	-	-	PUNCT
ejpam-4585	188	36	locating	locate	VERB
ejpam-4585	188	37	sets	set	NOUN
ejpam-4585	188	38	in	in	ADP
ejpam-4585	188	39	g	g	PROPN
ejpam-4585	188	40	and	and	CCONJ
ejpam-4585	188	41	h	h	NOUN
ejpam-4585	188	42	,	,	PUNCT
ejpam-4585	188	43	respectively	respectively	ADV
ejpam-4585	188	44	,	,	PUNCT
ejpam-4585	188	45	where	where	SCONJ
ejpam-4585	188	46	sg	sg	NOUN
ejpam-4585	188	47	or	or	CCONJ
ejpam-4585	188	48	sh	sh	PROPN
ejpam-4585	188	49	is	be	AUX
ejpam-4585	188	50	a	a	DET
ejpam-4585	188	51	(	(	PUNCT
ejpam-4585	188	52	2	2	NUM
ejpam-4585	188	53	,	,	PUNCT
ejpam-4585	188	54	2)-locating	2)-locating	NUM
ejpam-4585	188	55	set	set	NOUN
ejpam-4585	188	56	or	or	CCONJ
ejpam-4585	188	57	sg	sg	PROPN
ejpam-4585	188	58	and	and	CCONJ
ejpam-4585	188	59	sh	sh	PROPN
ejpam-4585	188	60	are	be	AUX
ejpam-4585	188	61	(	(	PUNCT
ejpam-4585	188	62	2	2	NUM
ejpam-4585	188	63	,	,	PUNCT
ejpam-4585	188	64	1)-locating	1)-locating	NUM
ejpam-4585	188	65	sets	set	NOUN
ejpam-4585	188	66	.	.	PUNCT
ejpam-4585	189	1	theorem	theorem	VERB
ejpam-4585	189	2	7	7	NUM
ejpam-4585	189	3	.	.	PUNCT
ejpam-4585	190	1	[	[	X
ejpam-4585	190	2	12	12	NUM
ejpam-4585	190	3	]	]	PUNCT
ejpam-4585	190	4	let	let	VERB
ejpam-4585	190	5	g	g	NOUN
ejpam-4585	190	6	and	and	CCONJ
ejpam-4585	190	7	h	h	NOUN
ejpam-4585	190	8	be	be	VERB
ejpam-4585	190	9	any	any	DET
ejpam-4585	190	10	two	two	NUM
ejpam-4585	190	11	graphs	graph	NOUN
ejpam-4585	190	12	.	.	PUNCT
ejpam-4585	191	1	a	a	DET
ejpam-4585	191	2	set	set	NOUN
ejpam-4585	191	3	s	s	NOUN
ejpam-4585	191	4	⊆	⊆	NUM
ejpam-4585	191	5	v	v	NOUN
ejpam-4585	191	6	(	(	PUNCT
ejpam-4585	191	7	g	g	PROPN
ejpam-4585	191	8	+	+	NOUN
ejpam-4585	191	9	h	h	NOUN
ejpam-4585	191	10	)	)	PUNCT
ejpam-4585	191	11	is	be	AUX
ejpam-4585	191	12	a	a	DET
ejpam-4585	191	13	hop	hop	NOUN
ejpam-4585	191	14	dominating	dominating	NOUN
ejpam-4585	191	15	set	set	NOUN
ejpam-4585	191	16	of	of	ADP
ejpam-4585	191	17	g	g	PROPN
ejpam-4585	192	1	+	+	CCONJ
ejpam-4585	192	2	h	h	NOUN
ejpam-4585	192	3	if	if	SCONJ
ejpam-4585	192	4	and	and	CCONJ
ejpam-4585	192	5	only	only	ADV
ejpam-4585	192	6	if	if	SCONJ
ejpam-4585	192	7	s	s	VERB
ejpam-4585	192	8	=	=	PUNCT
ejpam-4585	192	9	sg	sg	X
ejpam-4585	192	10	∪	∪	ADJ
ejpam-4585	192	11	sh	sh	PROPN
ejpam-4585	192	12	,	,	PUNCT
ejpam-4585	192	13	where	where	SCONJ
ejpam-4585	192	14	sg	sg	PROPN
ejpam-4585	192	15	and	and	CCONJ
ejpam-4585	192	16	sh	sh	PROPN
ejpam-4585	192	17	are	be	AUX
ejpam-4585	192	18	point	point	ADV
ejpam-4585	192	19	-	-	PUNCT
ejpam-4585	192	20	wise	wise	ADJ
ejpam-4585	192	21	non	non	ADJ
ejpam-4585	192	22	-	-	ADJ
ejpam-4585	192	23	dominating	dominating	ADJ
ejpam-4585	192	24	sets	set	NOUN
ejpam-4585	192	25	of	of	ADP
ejpam-4585	192	26	g	g	PROPN
ejpam-4585	192	27	and	and	CCONJ
ejpam-4585	192	28	h	h	NOUN
ejpam-4585	192	29	,	,	PUNCT
ejpam-4585	192	30	respectively	respectively	ADV
ejpam-4585	192	31	.	.	PUNCT
ejpam-4585	193	1	theorem	theorem	VERB
ejpam-4585	193	2	8	8	NUM
ejpam-4585	193	3	.	.	PUNCT
ejpam-4585	194	1	let	let	VERB
ejpam-4585	194	2	g	g	NOUN
ejpam-4585	194	3	and	and	CCONJ
ejpam-4585	194	4	h	h	NOUN
ejpam-4585	194	5	be	be	VERB
ejpam-4585	194	6	any	any	DET
ejpam-4585	194	7	two	two	NUM
ejpam-4585	194	8	graphs	graph	NOUN
ejpam-4585	194	9	.	.	PUNCT
ejpam-4585	195	1	a	a	DET
ejpam-4585	195	2	set	set	NOUN
ejpam-4585	195	3	s	s	NOUN
ejpam-4585	195	4	⊆	⊆	NUM
ejpam-4585	195	5	v	v	NOUN
ejpam-4585	195	6	(	(	PUNCT
ejpam-4585	195	7	g+h	g+h	PROPN
ejpam-4585	195	8	)	)	PUNCT
ejpam-4585	195	9	is	be	AUX
ejpam-4585	195	10	a	a	DET
ejpam-4585	195	11	2	2	NUM
ejpam-4585	195	12	-	-	PUNCT
ejpam-4585	195	13	resolving	resolve	VERB
ejpam-4585	195	14	hop	hop	NOUN
ejpam-4585	195	15	dominating	dominating	NOUN
ejpam-4585	195	16	set	set	VERB
ejpam-4585	195	17	in	in	ADP
ejpam-4585	195	18	g+h	g+h	PROPN
ejpam-4585	195	19	if	if	SCONJ
ejpam-4585	195	20	and	and	CCONJ
ejpam-4585	195	21	only	only	ADV
ejpam-4585	195	22	if	if	SCONJ
ejpam-4585	195	23	s	s	VERB
ejpam-4585	195	24	=	=	PUNCT
ejpam-4585	195	25	sg	sg	X
ejpam-4585	195	26	∪	∪	NOUN
ejpam-4585	195	27	sh	sh	PROPN
ejpam-4585	195	28	where	where	SCONJ
ejpam-4585	195	29	sg	sg	PROPN
ejpam-4585	195	30	=	=	SYM
ejpam-4585	195	31	v	v	PROPN
ejpam-4585	195	32	(	(	PUNCT
ejpam-4585	195	33	g	g	NOUN
ejpam-4585	195	34	)	)	PUNCT
ejpam-4585	195	35	∩	∩	NOUN
ejpam-4585	195	36	s	s	NOUN
ejpam-4585	195	37	and	and	CCONJ
ejpam-4585	195	38	sh	sh	PROPN
ejpam-4585	195	39	=	=	SYM
ejpam-4585	195	40	v	v	PROPN
ejpam-4585	195	41	(	(	PUNCT
ejpam-4585	195	42	h	h	NOUN
ejpam-4585	195	43	)	)	PUNCT
ejpam-4585	195	44	∩	∩	NOUN
ejpam-4585	195	45	s	s	NOUN
ejpam-4585	195	46	are	be	AUX
ejpam-4585	195	47	2	2	NUM
ejpam-4585	195	48	-	-	PUNCT
ejpam-4585	195	49	locating	locate	VERB
ejpam-4585	195	50	point	point	NOUN
ejpam-4585	195	51	-	-	PUNCT
ejpam-4585	195	52	wise	wise	ADJ
ejpam-4585	195	53	non	non	ADJ
ejpam-4585	195	54	-	-	ADJ
ejpam-4585	195	55	dominating	dominating	ADJ
ejpam-4585	195	56	sets	set	NOUN
ejpam-4585	195	57	in	in	ADP
ejpam-4585	195	58	g	g	PROPN
ejpam-4585	195	59	and	and	CCONJ
ejpam-4585	195	60	h	h	NOUN
ejpam-4585	195	61	,	,	PUNCT
ejpam-4585	195	62	respectively	respectively	ADV
ejpam-4585	195	63	,	,	PUNCT
ejpam-4585	195	64	where	where	SCONJ
ejpam-4585	195	65	sg	sg	NOUN
ejpam-4585	195	66	or	or	CCONJ
ejpam-4585	195	67	sh	sh	PROPN
ejpam-4585	195	68	is	be	AUX
ejpam-4585	195	69	a	a	DET
ejpam-4585	195	70	(	(	PUNCT
ejpam-4585	195	71	2	2	NUM
ejpam-4585	195	72	,	,	PUNCT
ejpam-4585	195	73	2)-locating	2)-locating	NUM
ejpam-4585	195	74	point	point	NOUN
ejpam-4585	195	75	-	-	PUNCT
ejpam-4585	195	76	wise	wise	ADJ
ejpam-4585	195	77	non	non	ADJ
ejpam-4585	195	78	-	-	ADJ
ejpam-4585	195	79	dominating	dominating	ADJ
ejpam-4585	195	80	set	set	NOUN
ejpam-4585	195	81	or	or	CCONJ
ejpam-4585	195	82	sg	sg	PROPN
ejpam-4585	195	83	and	and	CCONJ
ejpam-4585	195	84	sh	sh	INTJ
ejpam-4585	195	85	(	(	PUNCT
ejpam-4585	195	86	2	2	NUM
ejpam-4585	195	87	,	,	PUNCT
ejpam-4585	195	88	1)locating	1)locating	NUM
ejpam-4585	195	89	point	point	ADV
ejpam-4585	195	90	-	-	PUNCT
ejpam-4585	195	91	wise	wise	ADJ
ejpam-4585	195	92	non	non	ADJ
ejpam-4585	195	93	-	-	ADJ
ejpam-4585	195	94	dominating	dominating	ADJ
ejpam-4585	195	95	sets	set	NOUN
ejpam-4585	195	96	.	.	PUNCT
ejpam-4585	196	1	proof	proof	NOUN
ejpam-4585	196	2	.	.	PUNCT
ejpam-4585	197	1	suppose	suppose	VERB
ejpam-4585	197	2	that	that	SCONJ
ejpam-4585	197	3	s	s	VERB
ejpam-4585	197	4	is	be	AUX
ejpam-4585	197	5	a	a	DET
ejpam-4585	197	6	2	2	NUM
ejpam-4585	197	7	-	-	PUNCT
ejpam-4585	197	8	resolving	resolve	VERB
ejpam-4585	197	9	hop	hop	NOUN
ejpam-4585	197	10	dominating	dominating	NOUN
ejpam-4585	197	11	set	set	NOUN
ejpam-4585	197	12	of	of	ADP
ejpam-4585	197	13	g	g	PROPN
ejpam-4585	197	14	+	+	CCONJ
ejpam-4585	197	15	h.	h.	PROPN
ejpam-4585	197	16	then	then	ADV
ejpam-4585	197	17	s	s	VERB
ejpam-4585	197	18	is	be	AUX
ejpam-4585	197	19	a	a	DET
ejpam-4585	197	20	2	2	NUM
ejpam-4585	197	21	-	-	PUNCT
ejpam-4585	197	22	resolving	resolve	VERB
ejpam-4585	197	23	set	set	NOUN
ejpam-4585	197	24	of	of	ADP
ejpam-4585	197	25	g	g	PROPN
ejpam-4585	197	26	+	+	CCONJ
ejpam-4585	197	27	h.	h.	PROPN
ejpam-4585	197	28	by	by	ADP
ejpam-4585	197	29	theorem	theorem	NOUN
ejpam-4585	197	30	6	6	NUM
ejpam-4585	197	31	,	,	PUNCT
ejpam-4585	197	32	s	s	PART
ejpam-4585	197	33	=	=	PUNCT
ejpam-4585	197	34	sg	sg	X
ejpam-4585	197	35	∪	∪	NOUN
ejpam-4585	197	36	sh	sh	PROPN
ejpam-4585	197	37	where	where	SCONJ
ejpam-4585	197	38	sg	sg	PROPN
ejpam-4585	197	39	=	=	SYM
ejpam-4585	197	40	v	v	PROPN
ejpam-4585	197	41	(	(	PUNCT
ejpam-4585	197	42	g	g	NOUN
ejpam-4585	197	43	)	)	PUNCT
ejpam-4585	197	44	∩	∩	NOUN
ejpam-4585	197	45	s	s	NOUN
ejpam-4585	197	46	and	and	CCONJ
ejpam-4585	197	47	sh	sh	PROPN
ejpam-4585	197	48	=	=	SYM
ejpam-4585	197	49	v	v	PROPN
ejpam-4585	197	50	(	(	PUNCT
ejpam-4585	197	51	h	h	NOUN
ejpam-4585	197	52	)	)	PUNCT
ejpam-4585	197	53	∩	∩	NOUN
ejpam-4585	197	54	s	s	NOUN
ejpam-4585	197	55	are	be	AUX
ejpam-4585	197	56	2	2	NUM
ejpam-4585	197	57	-	-	PUNCT
ejpam-4585	197	58	locating	locate	VERB
ejpam-4585	197	59	sets	set	NOUN
ejpam-4585	197	60	in	in	ADP
ejpam-4585	197	61	g	g	PROPN
ejpam-4585	197	62	and	and	CCONJ
ejpam-4585	197	63	h	h	NOUN
ejpam-4585	197	64	,	,	PUNCT
ejpam-4585	197	65	respectively	respectively	ADV
ejpam-4585	197	66	where	where	SCONJ
ejpam-4585	197	67	sg	sg	PROPN
ejpam-4585	197	68	or	or	CCONJ
ejpam-4585	197	69	sh	sh	PROPN
ejpam-4585	197	70	is	be	AUX
ejpam-4585	197	71	a	a	DET
ejpam-4585	197	72	(	(	PUNCT
ejpam-4585	197	73	2	2	NUM
ejpam-4585	197	74	,	,	PUNCT
ejpam-4585	197	75	2)locating	2)locating	NUM
ejpam-4585	197	76	set	set	NOUN
ejpam-4585	197	77	or	or	CCONJ
ejpam-4585	197	78	sg	sg	PROPN
ejpam-4585	197	79	and	and	CCONJ
ejpam-4585	197	80	sh	sh	PROPN
ejpam-4585	197	81	are	be	AUX
ejpam-4585	197	82	(	(	PUNCT
ejpam-4585	197	83	2	2	NUM
ejpam-4585	197	84	,	,	PUNCT
ejpam-4585	197	85	1)-locating	1)-locating	NUM
ejpam-4585	197	86	sets	set	NOUN
ejpam-4585	197	87	.	.	PUNCT
ejpam-4585	198	1	also	also	ADV
ejpam-4585	198	2	,	,	PUNCT
ejpam-4585	198	3	since	since	SCONJ
ejpam-4585	198	4	s	s	NOUN
ejpam-4585	198	5	is	be	AUX
ejpam-4585	198	6	a	a	DET
ejpam-4585	198	7	hop	hop	NOUN
ejpam-4585	198	8	dominating	dominating	NOUN
ejpam-4585	198	9	set	set	VERB
ejpam-4585	198	10	in	in	ADP
ejpam-4585	198	11	g+h	g+h	PROPN
ejpam-4585	198	12	,	,	PUNCT
ejpam-4585	198	13	it	it	PRON
ejpam-4585	198	14	follows	follow	VERB
ejpam-4585	198	15	by	by	ADP
ejpam-4585	198	16	theorem	theorem	NOUN
ejpam-4585	198	17	7	7	NUM
ejpam-4585	198	18	that	that	PRON
ejpam-4585	198	19	sg	sg	VERB
ejpam-4585	199	1	and	and	CCONJ
ejpam-4585	199	2	sh	sh	PROPN
ejpam-4585	199	3	are	be	AUX
ejpam-4585	199	4	point	point	ADV
ejpam-4585	199	5	-	-	PUNCT
ejpam-4585	199	6	wise	wise	ADJ
ejpam-4585	199	7	non	non	ADJ
ejpam-4585	199	8	-	-	ADJ
ejpam-4585	199	9	dominating	dominating	ADJ
ejpam-4585	199	10	sets	set	NOUN
ejpam-4585	199	11	of	of	ADP
ejpam-4585	199	12	g	g	PROPN
ejpam-4585	199	13	and	and	CCONJ
ejpam-4585	199	14	h	h	NOUN
ejpam-4585	199	15	,	,	PUNCT
ejpam-4585	199	16	respectively	respectively	ADV
ejpam-4585	199	17	.	.	PUNCT
ejpam-4585	200	1	therefore	therefore	ADV
ejpam-4585	200	2	,	,	PUNCT
ejpam-4585	200	3	sg	sg	PROPN
ejpam-4585	200	4	or	or	CCONJ
ejpam-4585	200	5	sh	sh	PROPN
ejpam-4585	200	6	is	be	AUX
ejpam-4585	200	7	a	a	DET
ejpam-4585	200	8	(	(	PUNCT
ejpam-4585	200	9	2	2	NUM
ejpam-4585	200	10	,	,	PUNCT
ejpam-4585	200	11	2)-locating	2)-locating	NUM
ejpam-4585	200	12	point	point	NOUN
ejpam-4585	200	13	-	-	PUNCT
ejpam-4585	200	14	wise	wise	ADJ
ejpam-4585	200	15	non	non	ADJ
ejpam-4585	200	16	-	-	ADJ
ejpam-4585	200	17	dominating	dominating	ADJ
ejpam-4585	200	18	set	set	NOUN
ejpam-4585	200	19	or	or	CCONJ
ejpam-4585	200	20	sg	sg	PROPN
ejpam-4585	200	21	and	and	CCONJ
ejpam-4585	200	22	sh	sh	PROPN
ejpam-4585	200	23	are	be	AUX
ejpam-4585	200	24	(	(	PUNCT
ejpam-4585	200	25	2	2	NUM
ejpam-4585	200	26	,	,	PUNCT
ejpam-4585	200	27	1)-locating	1)-locating	NUM
ejpam-4585	200	28	point	point	NOUN
ejpam-4585	200	29	-	-	PUNCT
ejpam-4585	200	30	wise	wise	ADJ
ejpam-4585	200	31	non	non	ADJ
ejpam-4585	200	32	-	-	ADJ
ejpam-4585	200	33	dominating	dominating	ADJ
ejpam-4585	200	34	sets	set	NOUN
ejpam-4585	200	35	of	of	ADP
ejpam-4585	200	36	g	g	PROPN
ejpam-4585	200	37	and	and	CCONJ
ejpam-4585	200	38	h.	h.	PROPN
ejpam-4585	200	39	conversely	conversely	ADV
ejpam-4585	200	40	,	,	PUNCT
ejpam-4585	200	41	suppose	suppose	VERB
ejpam-4585	200	42	sg	sg	PROPN
ejpam-4585	200	43	or	or	CCONJ
ejpam-4585	200	44	sh	sh	PROPN
ejpam-4585	200	45	is	be	AUX
ejpam-4585	200	46	a	a	DET
ejpam-4585	200	47	(	(	PUNCT
ejpam-4585	200	48	2	2	NUM
ejpam-4585	200	49	,	,	PUNCT
ejpam-4585	200	50	2)-locating	2)-locating	NUM
ejpam-4585	200	51	point	point	NOUN
ejpam-4585	200	52	-	-	PUNCT
ejpam-4585	200	53	wise	wise	ADJ
ejpam-4585	200	54	non	non	ADJ
ejpam-4585	200	55	-	-	ADJ
ejpam-4585	200	56	dominating	dominating	ADJ
ejpam-4585	200	57	set	set	NOUN
ejpam-4585	200	58	or	or	CCONJ
ejpam-4585	200	59	sg	sg	PROPN
ejpam-4585	200	60	and	and	CCONJ
ejpam-4585	200	61	sh	sh	PROPN
ejpam-4585	200	62	are	be	AUX
ejpam-4585	200	63	(	(	PUNCT
ejpam-4585	200	64	2	2	NUM
ejpam-4585	200	65	,	,	PUNCT
ejpam-4585	200	66	1)-locating	1)-locating	NUM
ejpam-4585	200	67	point	point	NOUN
ejpam-4585	200	68	-	-	PUNCT
ejpam-4585	200	69	wise	wise	ADJ
ejpam-4585	200	70	non	non	ADJ
ejpam-4585	200	71	-	-	ADJ
ejpam-4585	200	72	dominating	dominating	ADJ
ejpam-4585	200	73	sets	set	NOUN
ejpam-4585	200	74	of	of	ADP
ejpam-4585	200	75	g	g	PROPN
ejpam-4585	200	76	and	and	CCONJ
ejpam-4585	200	77	h	h	NOUN
ejpam-4585	200	78	,	,	PUNCT
ejpam-4585	200	79	respectively	respectively	ADV
ejpam-4585	200	80	.	.	PUNCT
ejpam-4585	201	1	then	then	ADV
ejpam-4585	201	2	by	by	ADP
ejpam-4585	201	3	theorem	theorem	NOUN
ejpam-4585	201	4	6	6	NUM
ejpam-4585	201	5	,	,	PUNCT
ejpam-4585	201	6	s	s	VERB
ejpam-4585	201	7	is	be	AUX
ejpam-4585	201	8	a	a	DET
ejpam-4585	201	9	2	2	NUM
ejpam-4585	201	10	-	-	PUNCT
ejpam-4585	201	11	resolving	resolving	NOUN
ejpam-4585	201	12	set	set	NOUN
ejpam-4585	201	13	in	in	ADP
ejpam-4585	201	14	g	g	PROPN
ejpam-4585	201	15	+	+	CCONJ
ejpam-4585	201	16	h.	h.	PROPN
ejpam-4585	201	17	similarly	similarly	ADV
ejpam-4585	201	18	,	,	PUNCT
ejpam-4585	201	19	by	by	ADP
ejpam-4585	201	20	theorem	theorem	NOUN
ejpam-4585	201	21	7	7	NUM
ejpam-4585	201	22	it	it	PRON
ejpam-4585	201	23	follows	follow	VERB
ejpam-4585	201	24	that	that	SCONJ
ejpam-4585	201	25	s	s	VERB
ejpam-4585	201	26	is	be	AUX
ejpam-4585	201	27	a	a	DET
ejpam-4585	201	28	hop	hop	NOUN
ejpam-4585	201	29	dominating	dominating	NOUN
ejpam-4585	201	30	set	set	NOUN
ejpam-4585	201	31	of	of	ADP
ejpam-4585	201	32	g+h	g+h	PROPN
ejpam-4585	201	33	.	.	PUNCT
ejpam-4585	202	1	therefore	therefore	ADV
ejpam-4585	202	2	,	,	PUNCT
ejpam-4585	202	3	s	s	VERB
ejpam-4585	202	4	is	be	AUX
ejpam-4585	202	5	a	a	DET
ejpam-4585	202	6	2	2	NUM
ejpam-4585	202	7	-	-	PUNCT
ejpam-4585	202	8	resolving	resolve	VERB
ejpam-4585	202	9	hop	hop	NOUN
ejpam-4585	202	10	dominating	dominating	NOUN
ejpam-4585	202	11	set	set	VERB
ejpam-4585	202	12	in	in	ADP
ejpam-4585	202	13	g+h	g+h	PROPN
ejpam-4585	202	14	.	.	PUNCT
ejpam-4585	203	1	corollary	corollary	ADJ
ejpam-4585	203	2	4	4	NUM
ejpam-4585	203	3	.	.	PUNCT
ejpam-4585	204	1	let	let	VERB
ejpam-4585	204	2	g	g	NOUN
ejpam-4585	204	3	and	and	CCONJ
ejpam-4585	204	4	h	h	NOUN
ejpam-4585	204	5	be	be	AUX
ejpam-4585	204	6	connected	connect	VERB
ejpam-4585	204	7	nontrivial	nontrivial	ADJ
ejpam-4585	204	8	graphs	graph	NOUN
ejpam-4585	204	9	.	.	PUNCT
ejpam-4585	205	1	then	then	ADV
ejpam-4585	205	2	,	,	PUNCT
ejpam-4585	205	3	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	205	4	)	)	PUNCT
ejpam-4585	206	1	=	=	VERB
ejpam-4585	206	2	min{lnpnd	min{lnpnd	NOUN
ejpam-4585	206	3	(	(	PUNCT
ejpam-4585	206	4	2,2)(g	2,2)(g	NUM
ejpam-4585	206	5	)	)	PUNCT
ejpam-4585	207	1	+	+	CCONJ
ejpam-4585	207	2	lnpnd	lnpnd	ADJ
ejpam-4585	207	3	(	(	PUNCT
ejpam-4585	207	4	2	2	NUM
ejpam-4585	207	5	)	)	PUNCT
ejpam-4585	207	6	(	(	PUNCT
ejpam-4585	207	7	h	h	NOUN
ejpam-4585	207	8	)	)	PUNCT
ejpam-4585	207	9	,	,	PUNCT
ejpam-4585	207	10	lnpnd	lnpnd	ADJ
ejpam-4585	207	11	(	(	PUNCT
ejpam-4585	207	12	2	2	NUM
ejpam-4585	207	13	)	)	PUNCT
ejpam-4585	207	14	(	(	PUNCT
ejpam-4585	207	15	g)lnpnd	g)lnpnd	X
ejpam-4585	207	16	(	(	PUNCT
ejpam-4585	207	17	2,2)(h	2,2)(h	NUM
ejpam-4585	207	18	)	)	PUNCT
ejpam-4585	207	19	,	,	PUNCT
ejpam-4585	207	20	lnpnd	lnpnd	ADJ
ejpam-4585	207	21	(	(	PUNCT
ejpam-4585	207	22	2,1)(g	2,1)(g	NUM
ejpam-4585	207	23	)	)	PUNCT
ejpam-4585	207	24	+	+	CCONJ
ejpam-4585	207	25	lnpnd	lnpnd	ADJ
ejpam-4585	207	26	(	(	PUNCT
ejpam-4585	207	27	2,1)(h	2,1)(h	NUM
ejpam-4585	207	28	)	)	PUNCT
ejpam-4585	207	29	}	}	PUNCT
ejpam-4585	207	30	.	.	PUNCT
ejpam-4585	208	1	a.m.	a.m.	PROPN
ejpam-4585	208	2	mahistrado	mahistrado	PROPN
ejpam-4585	208	3	,	,	PUNCT
ejpam-4585	208	4	h.	h.	PROPN
ejpam-4585	208	5	rara	rara	PROPN
ejpam-4585	208	6	/	/	SYM
ejpam-4585	208	7	eur	eur	PROPN
ejpam-4585	208	8	.	.	PUNCT
ejpam-4585	209	1	j.	j.	PROPN
ejpam-4585	209	2	pure	pure	PROPN
ejpam-4585	209	3	appl	appl	PROPN
ejpam-4585	209	4	.	.	PROPN
ejpam-4585	209	5	math	math	PROPN
ejpam-4585	209	6	,	,	PUNCT
ejpam-4585	209	7	15	15	NUM
ejpam-4585	209	8	(	(	PUNCT
ejpam-4585	209	9	4	4	NUM
ejpam-4585	209	10	)	)	PUNCT
ejpam-4585	209	11	(	(	PUNCT
ejpam-4585	209	12	2022	2022	NUM
ejpam-4585	209	13	)	)	PUNCT
ejpam-4585	209	14	,	,	PUNCT
ejpam-4585	209	15	1982	1982	NUM
ejpam-4585	209	16	-	-	SYM
ejpam-4585	209	17	1997	1997	NUM
ejpam-4585	209	18	1990	1990	NUM
ejpam-4585	209	19	proof	proof	NOUN
ejpam-4585	209	20	.	.	PUNCT
ejpam-4585	210	1	let	let	VERB
ejpam-4585	210	2	s	s	PRON
ejpam-4585	210	3	be	be	AUX
ejpam-4585	210	4	a	a	DET
ejpam-4585	210	5	minimum	minimum	ADJ
ejpam-4585	210	6	2	2	NUM
ejpam-4585	210	7	-	-	PUNCT
ejpam-4585	210	8	resolving	resolve	VERB
ejpam-4585	210	9	hop	hop	NOUN
ejpam-4585	210	10	dominating	dominating	NOUN
ejpam-4585	210	11	set	set	NOUN
ejpam-4585	210	12	ing+h	ing+h	PROPN
ejpam-4585	210	13	.	.	PUNCT
ejpam-4585	211	1	since	since	SCONJ
ejpam-4585	211	2	s	s	PART
ejpam-4585	211	3	=	=	PUNCT
ejpam-4585	211	4	sg∪sh	sg∪sh	PROPN
ejpam-4585	211	5	where	where	SCONJ
ejpam-4585	211	6	sg	sg	PROPN
ejpam-4585	211	7	=	=	SYM
ejpam-4585	211	8	v	v	PROPN
ejpam-4585	211	9	(	(	PUNCT
ejpam-4585	211	10	g)∩s	g)∩s	PROPN
ejpam-4585	211	11	and	and	CCONJ
ejpam-4585	211	12	sh	sh	PROPN
ejpam-4585	211	13	=	=	SYM
ejpam-4585	211	14	v	v	PROPN
ejpam-4585	211	15	(	(	PUNCT
ejpam-4585	211	16	h)∩s	h)∩s	PROPN
ejpam-4585	211	17	.	.	PUNCT
ejpam-4585	212	1	by	by	ADP
ejpam-4585	212	2	theorem	theorem	NOUN
ejpam-4585	212	3	8	8	NUM
ejpam-4585	212	4	,	,	PUNCT
ejpam-4585	212	5	sg	sg	PROPN
ejpam-4585	212	6	and	and	CCONJ
ejpam-4585	212	7	sh	sh	PROPN
ejpam-4585	212	8	are	be	AUX
ejpam-4585	212	9	2	2	NUM
ejpam-4585	212	10	-	-	PUNCT
ejpam-4585	212	11	locating	locate	VERB
ejpam-4585	212	12	pointwise	pointwise	ADJ
ejpam-4585	212	13	non	non	ADJ
ejpam-4585	212	14	-	-	ADJ
ejpam-4585	212	15	dominating	dominating	ADJ
ejpam-4585	212	16	sets	set	NOUN
ejpam-4585	212	17	in	in	ADP
ejpam-4585	212	18	g	g	PROPN
ejpam-4585	212	19	and	and	CCONJ
ejpam-4585	212	20	h	h	NOUN
ejpam-4585	212	21	,	,	PUNCT
ejpam-4585	212	22	respectively	respectively	ADV
ejpam-4585	212	23	,	,	PUNCT
ejpam-4585	212	24	where	where	SCONJ
ejpam-4585	212	25	sg	sg	NOUN
ejpam-4585	212	26	or	or	CCONJ
ejpam-4585	212	27	sh	sh	PROPN
ejpam-4585	212	28	is	be	AUX
ejpam-4585	212	29	a	a	DET
ejpam-4585	212	30	(	(	PUNCT
ejpam-4585	212	31	2	2	NUM
ejpam-4585	212	32	,	,	PUNCT
ejpam-4585	212	33	2)-locating	2)-locating	NUM
ejpam-4585	212	34	point	point	NOUN
ejpam-4585	212	35	-	-	PUNCT
ejpam-4585	212	36	wise	wise	ADJ
ejpam-4585	212	37	non	non	ADJ
ejpam-4585	212	38	-	-	ADJ
ejpam-4585	212	39	dominating	dominating	ADJ
ejpam-4585	212	40	set	set	NOUN
ejpam-4585	212	41	or	or	CCONJ
ejpam-4585	212	42	sg	sg	PROPN
ejpam-4585	213	1	and	and	CCONJ
ejpam-4585	213	2	sh	sh	PROPN
ejpam-4585	213	3	are	be	AUX
ejpam-4585	213	4	(	(	PUNCT
ejpam-4585	213	5	2	2	NUM
ejpam-4585	213	6	,	,	PUNCT
ejpam-4585	213	7	1)-locating	1)-locating	NUM
ejpam-4585	213	8	point	point	NOUN
ejpam-4585	213	9	-	-	PUNCT
ejpam-4585	213	10	wise	wise	ADJ
ejpam-4585	213	11	non	non	ADJ
ejpam-4585	213	12	-	-	ADJ
ejpam-4585	213	13	dominating	dominating	ADJ
ejpam-4585	213	14	sets	set	NOUN
ejpam-4585	213	15	.	.	PUNCT
ejpam-4585	214	1	if	if	SCONJ
ejpam-4585	214	2	sg	sg	PROPN
ejpam-4585	214	3	is	be	AUX
ejpam-4585	214	4	(	(	PUNCT
ejpam-4585	214	5	2	2	NUM
ejpam-4585	214	6	,	,	PUNCT
ejpam-4585	214	7	2)-locating	2)-locating	NUM
ejpam-4585	214	8	point	point	NOUN
ejpam-4585	214	9	-	-	PUNCT
ejpam-4585	214	10	wise	wise	ADJ
ejpam-4585	214	11	non	non	ADJ
ejpam-4585	214	12	-	-	ADJ
ejpam-4585	214	13	dominating	dominating	ADJ
ejpam-4585	214	14	set	set	NOUN
ejpam-4585	214	15	in	in	ADP
ejpam-4585	214	16	g	g	NOUN
ejpam-4585	214	17	,	,	PUNCT
ejpam-4585	214	18	then	then	ADV
ejpam-4585	214	19	lnpnd	lnpnd	ADJ
ejpam-4585	214	20	(	(	PUNCT
ejpam-4585	214	21	2,2)(g	2,2)(g	NUM
ejpam-4585	214	22	)	)	PUNCT
ejpam-4585	215	1	+	+	CCONJ
ejpam-4585	215	2	lnpnd	lnpnd	ADJ
ejpam-4585	215	3	2	2	NUM
ejpam-4585	215	4	(	(	PUNCT
ejpam-4585	215	5	h	h	NOUN
ejpam-4585	215	6	)	)	PUNCT
ejpam-4585	215	7	≤	≤	NOUN
ejpam-4585	215	8	|sg|+	|sg|+	ADP
ejpam-4585	215	9	|sh	|sh	ADP
ejpam-4585	215	10	|	|	ADV
ejpam-4585	215	11	=	=	SYM
ejpam-4585	215	12	|s|	|s|	PROPN
ejpam-4585	215	13	=	=	PUNCT
ejpam-4585	215	14	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	215	15	)	)	PUNCT
ejpam-4585	215	16	.	.	PUNCT
ejpam-4585	216	1	if	if	SCONJ
ejpam-4585	216	2	sh	sh	PROPN
ejpam-4585	216	3	is	be	AUX
ejpam-4585	216	4	a	a	DET
ejpam-4585	216	5	(	(	PUNCT
ejpam-4585	216	6	2	2	NUM
ejpam-4585	216	7	,	,	PUNCT
ejpam-4585	216	8	2)-locating	2)-locating	NUM
ejpam-4585	216	9	point	point	NOUN
ejpam-4585	216	10	-	-	PUNCT
ejpam-4585	216	11	wise	wise	ADJ
ejpam-4585	216	12	non	non	ADJ
ejpam-4585	216	13	-	-	ADJ
ejpam-4585	216	14	dominating	dominating	ADJ
ejpam-4585	216	15	set	set	NOUN
ejpam-4585	216	16	in	in	ADP
ejpam-4585	216	17	h	h	NOUN
ejpam-4585	216	18	,	,	PUNCT
ejpam-4585	216	19	then	then	ADV
ejpam-4585	216	20	lnpnd	lnpnd	ADJ
ejpam-4585	216	21	(	(	PUNCT
ejpam-4585	216	22	2,2)(h	2,2)(h	NUM
ejpam-4585	216	23	)	)	PUNCT
ejpam-4585	217	1	+	+	CCONJ
ejpam-4585	217	2	lnpnd	lnpnd	ADJ
ejpam-4585	217	3	2	2	NUM
ejpam-4585	217	4	(	(	PUNCT
ejpam-4585	217	5	g	g	NOUN
ejpam-4585	217	6	)	)	PUNCT
ejpam-4585	217	7	≤	≤	NUM
ejpam-4585	217	8	|sh	|sh	ADP
ejpam-4585	217	9	|+	|+	X
ejpam-4585	217	10	|sg|	|sg|	PROPN
ejpam-4585	217	11	=	=	SYM
ejpam-4585	217	12	|s|	|s|	PROPN
ejpam-4585	217	13	=	=	PUNCT
ejpam-4585	217	14	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	217	15	)	)	PUNCT
ejpam-4585	217	16	.	.	PUNCT
ejpam-4585	218	1	if	if	SCONJ
ejpam-4585	218	2	sg	sg	PROPN
ejpam-4585	218	3	and	and	CCONJ
ejpam-4585	218	4	sh	sh	PROPN
ejpam-4585	218	5	are	be	AUX
ejpam-4585	218	6	both	both	PRON
ejpam-4585	218	7	(	(	PUNCT
ejpam-4585	218	8	2	2	NUM
ejpam-4585	218	9	,	,	PUNCT
ejpam-4585	218	10	1)-locating	1)-locating	NUM
ejpam-4585	218	11	point	point	NOUN
ejpam-4585	218	12	-	-	PUNCT
ejpam-4585	218	13	wise	wise	ADJ
ejpam-4585	218	14	non	non	ADJ
ejpam-4585	218	15	-	-	ADJ
ejpam-4585	218	16	dominating	dominating	ADJ
ejpam-4585	218	17	sets	set	NOUN
ejpam-4585	218	18	,	,	PUNCT
ejpam-4585	218	19	then	then	ADV
ejpam-4585	218	20	lnpnd	lnpnd	ADJ
ejpam-4585	218	21	(	(	PUNCT
ejpam-4585	218	22	2,1)(g	2,1)(g	NUM
ejpam-4585	218	23	)	)	PUNCT
ejpam-4585	219	1	+	+	CCONJ
ejpam-4585	219	2	lnpnd	lnpnd	ADJ
ejpam-4585	219	3	(	(	PUNCT
ejpam-4585	219	4	2,1)(h	2,1)(h	NUM
ejpam-4585	219	5	)	)	PUNCT
ejpam-4585	219	6	≤	≤	NOUN
ejpam-4585	219	7	|sg|+	|sg|+	ADP
ejpam-4585	219	8	|sh	|sh	ADP
ejpam-4585	219	9	|	|	ADV
ejpam-4585	219	10	=	=	SYM
ejpam-4585	219	11	|s|	|s|	PROPN
ejpam-4585	219	12	=	=	PUNCT
ejpam-4585	219	13	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	219	14	)	)	PUNCT
ejpam-4585	219	15	.	.	PUNCT
ejpam-4585	220	1	thus	thus	ADV
ejpam-4585	220	2	,	,	PUNCT
ejpam-4585	220	3	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	220	4	)	)	PUNCT
ejpam-4585	220	5	≥	≥	NOUN
ejpam-4585	220	6	min{lnpnd	min{lnpnd	NOUN
ejpam-4585	220	7	(	(	PUNCT
ejpam-4585	220	8	2,2)(g	2,2)(g	NUM
ejpam-4585	220	9	)	)	PUNCT
ejpam-4585	221	1	+	+	CCONJ
ejpam-4585	221	2	lnpnd	lnpnd	ADJ
ejpam-4585	221	3	(	(	PUNCT
ejpam-4585	221	4	2	2	NUM
ejpam-4585	221	5	)	)	PUNCT
ejpam-4585	221	6	(	(	PUNCT
ejpam-4585	221	7	h	h	NOUN
ejpam-4585	221	8	)	)	PUNCT
ejpam-4585	221	9	,	,	PUNCT
ejpam-4585	221	10	lnpnd	lnpnd	ADJ
ejpam-4585	221	11	(	(	PUNCT
ejpam-4585	221	12	2	2	NUM
ejpam-4585	221	13	)	)	PUNCT
ejpam-4585	221	14	(	(	PUNCT
ejpam-4585	221	15	g)lnpnd	g)lnpnd	X
ejpam-4585	221	16	(	(	PUNCT
ejpam-4585	221	17	2,2)(h	2,2)(h	NUM
ejpam-4585	221	18	)	)	PUNCT
ejpam-4585	221	19	,	,	PUNCT
ejpam-4585	221	20	lnpnd	lnpnd	ADJ
ejpam-4585	221	21	(	(	PUNCT
ejpam-4585	221	22	2,1)(g	2,1)(g	NUM
ejpam-4585	221	23	)	)	PUNCT
ejpam-4585	221	24	+	+	CCONJ
ejpam-4585	221	25	lnpnd	lnpnd	ADJ
ejpam-4585	221	26	(	(	PUNCT
ejpam-4585	221	27	2,1)(h	2,1)(h	NUM
ejpam-4585	221	28	)	)	PUNCT
ejpam-4585	221	29	}	}	PUNCT
ejpam-4585	221	30	.	.	PUNCT
ejpam-4585	222	1	next	next	ADV
ejpam-4585	222	2	,	,	PUNCT
ejpam-4585	222	3	suppose	suppose	VERB
ejpam-4585	222	4	that	that	SCONJ
ejpam-4585	222	5	lnpnd	lnpnd	ADJ
ejpam-4585	222	6	(	(	PUNCT
ejpam-4585	222	7	2,1)(g	2,1)(g	NUM
ejpam-4585	222	8	)	)	PUNCT
ejpam-4585	223	1	+	+	CCONJ
ejpam-4585	223	2	lnpnd	lnpnd	ADJ
ejpam-4585	223	3	(	(	PUNCT
ejpam-4585	223	4	2,1)(h	2,1)(h	NUM
ejpam-4585	223	5	)	)	PUNCT
ejpam-4585	223	6	≤	≤	NOUN
ejpam-4585	223	7	lnpnd	lnpnd	ADJ
ejpam-4585	223	8	(	(	PUNCT
ejpam-4585	223	9	2,2)(g	2,2)(g	NUM
ejpam-4585	223	10	)	)	PUNCT
ejpam-4585	224	1	+	+	CCONJ
ejpam-4585	224	2	lnpnd	lnpnd	ADJ
ejpam-4585	224	3	2	2	NUM
ejpam-4585	224	4	(	(	PUNCT
ejpam-4585	224	5	h	h	NOUN
ejpam-4585	224	6	)	)	PUNCT
ejpam-4585	224	7	and	and	CCONJ
ejpam-4585	224	8	lnpnd	lnpnd	PROPN
ejpam-4585	224	9	2,1	2,1	NUM
ejpam-4585	224	10	(	(	PUNCT
ejpam-4585	224	11	g	g	NOUN
ejpam-4585	224	12	)	)	PUNCT
ejpam-4585	224	13	+	+	CCONJ
ejpam-4585	224	14	lnpnd	lnpnd	ADJ
ejpam-4585	224	15	(	(	PUNCT
ejpam-4585	224	16	2,1)(h	2,1)(h	NUM
ejpam-4585	224	17	)	)	PUNCT
ejpam-4585	224	18	≤	≤	NOUN
ejpam-4585	224	19	lnpnd	lnpnd	ADJ
ejpam-4585	224	20	2	2	NUM
ejpam-4585	224	21	(	(	PUNCT
ejpam-4585	224	22	g	g	NOUN
ejpam-4585	224	23	)	)	PUNCT
ejpam-4585	224	24	+	+	CCONJ
ejpam-4585	224	25	lnpnd	lnpnd	ADJ
ejpam-4585	224	26	(	(	PUNCT
ejpam-4585	224	27	2,2)(h	2,2)(h	NUM
ejpam-4585	224	28	)	)	PUNCT
ejpam-4585	224	29	.	.	PUNCT
ejpam-4585	225	1	let	let	VERB
ejpam-4585	225	2	sg	sg	PART
ejpam-4585	225	3	be	be	AUX
ejpam-4585	225	4	a	a	DET
ejpam-4585	225	5	minimum	minimum	NOUN
ejpam-4585	225	6	(	(	PUNCT
ejpam-4585	225	7	2	2	NUM
ejpam-4585	225	8	,	,	PUNCT
ejpam-4585	225	9	1)-locating	1)-locating	NUM
ejpam-4585	225	10	point	point	NOUN
ejpam-4585	225	11	-	-	PUNCT
ejpam-4585	225	12	wise	wise	ADJ
ejpam-4585	225	13	non	non	ADJ
ejpam-4585	225	14	-	-	ADJ
ejpam-4585	225	15	dominating	dominating	ADJ
ejpam-4585	225	16	set	set	NOUN
ejpam-4585	225	17	in	in	ADP
ejpam-4585	225	18	g	g	PROPN
ejpam-4585	226	1	and	and	CCONJ
ejpam-4585	226	2	sh	sh	PROPN
ejpam-4585	226	3	be	be	AUX
ejpam-4585	226	4	a	a	DET
ejpam-4585	226	5	minimum	minimum	NOUN
ejpam-4585	226	6	(	(	PUNCT
ejpam-4585	226	7	2	2	NUM
ejpam-4585	226	8	,	,	PUNCT
ejpam-4585	226	9	1)-locating	1)-locating	NUM
ejpam-4585	226	10	point	point	NOUN
ejpam-4585	226	11	-	-	PUNCT
ejpam-4585	226	12	wise	wise	ADV
ejpam-4585	226	13	nondominating	nondominate	VERB
ejpam-4585	226	14	set	set	NOUN
ejpam-4585	226	15	in	in	ADP
ejpam-4585	226	16	h.	h.	PROPN
ejpam-4585	226	17	then	then	ADV
ejpam-4585	226	18	s	s	VERB
ejpam-4585	226	19	=	=	SYM
ejpam-4585	226	20	sg∪sh	sg∪sh	PROPN
ejpam-4585	226	21	is	be	AUX
ejpam-4585	226	22	a	a	DET
ejpam-4585	226	23	2	2	NUM
ejpam-4585	226	24	-	-	PUNCT
ejpam-4585	226	25	resolving	resolve	VERB
ejpam-4585	226	26	hop	hop	NOUN
ejpam-4585	226	27	dominating	dominating	NOUN
ejpam-4585	226	28	set	set	VERB
ejpam-4585	226	29	in	in	ADP
ejpam-4585	226	30	g+h	g+h	PROPN
ejpam-4585	226	31	,	,	PUNCT
ejpam-4585	226	32	by	by	ADP
ejpam-4585	226	33	theorem	theorem	NOUN
ejpam-4585	226	34	8	8	NUM
ejpam-4585	226	35	.	.	PUNCT
ejpam-4585	227	1	hence	hence	ADV
ejpam-4585	227	2	,	,	PUNCT
ejpam-4585	227	3	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	227	4	)	)	PUNCT
ejpam-4585	227	5	≤	≤	NUM
ejpam-4585	227	6	|s|	|s|	PROPN
ejpam-4585	227	7	=	=	PROPN
ejpam-4585	227	8	|sg|+	|sg|+	ADP
ejpam-4585	227	9	|sh	|sh	ADP
ejpam-4585	227	10	|	|	ADV
ejpam-4585	227	11	=	=	SYM
ejpam-4585	227	12	lnpnd	lnpnd	ADJ
ejpam-4585	227	13	(	(	PUNCT
ejpam-4585	227	14	2,1)(g)+	2,1)(g)+	NUM
ejpam-4585	227	15	lnpnd	lnpnd	ADJ
ejpam-4585	227	16	(	(	PUNCT
ejpam-4585	227	17	2,1)(h	2,1)(h	NUM
ejpam-4585	227	18	)	)	PUNCT
ejpam-4585	227	19	.	.	PUNCT
ejpam-4585	228	1	therefore	therefore	ADV
ejpam-4585	228	2	,	,	PUNCT
ejpam-4585	228	3	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	228	4	)	)	PUNCT
ejpam-4585	228	5	≤	≤	NOUN
ejpam-4585	228	6	lnpnd	lnpnd	ADJ
ejpam-4585	228	7	(	(	PUNCT
ejpam-4585	228	8	2,1)(g	2,1)(g	NUM
ejpam-4585	228	9	)	)	PUNCT
ejpam-4585	229	1	+	+	CCONJ
ejpam-4585	229	2	lnpnd	lnpnd	ADJ
ejpam-4585	229	3	(	(	PUNCT
ejpam-4585	229	4	2,1)(h	2,1)(h	NUM
ejpam-4585	229	5	)	)	PUNCT
ejpam-4585	229	6	.	.	PUNCT
ejpam-4585	230	1	similarly	similarly	ADV
ejpam-4585	230	2	,	,	PUNCT
ejpam-4585	230	3	if	if	SCONJ
ejpam-4585	230	4	lnpnd	lnpnd	ADJ
ejpam-4585	230	5	(	(	PUNCT
ejpam-4585	230	6	2,2)(g	2,2)(g	NUM
ejpam-4585	230	7	)	)	PUNCT
ejpam-4585	231	1	+	+	CCONJ
ejpam-4585	231	2	lnpnd	lnpnd	ADJ
ejpam-4585	231	3	2	2	NUM
ejpam-4585	231	4	(	(	PUNCT
ejpam-4585	231	5	h	h	NOUN
ejpam-4585	231	6	)	)	PUNCT
ejpam-4585	231	7	≤	≤	NOUN
ejpam-4585	231	8	lnpnd	lnpnd	ADJ
ejpam-4585	231	9	(	(	PUNCT
ejpam-4585	231	10	2,1)(g	2,1)(g	NUM
ejpam-4585	231	11	)	)	PUNCT
ejpam-4585	232	1	+	+	CCONJ
ejpam-4585	232	2	lnpnd	lnpnd	ADJ
ejpam-4585	232	3	(	(	PUNCT
ejpam-4585	232	4	2,1)(h	2,1)(h	NUM
ejpam-4585	232	5	)	)	PUNCT
ejpam-4585	232	6	and	and	CCONJ
ejpam-4585	232	7	lnpnd	lnpnd	ADJ
ejpam-4585	232	8	(	(	PUNCT
ejpam-4585	232	9	2,2)(g	2,2)(g	NUM
ejpam-4585	232	10	)	)	PUNCT
ejpam-4585	233	1	+	+	CCONJ
ejpam-4585	233	2	lnpnd	lnpnd	ADJ
ejpam-4585	233	3	2	2	NUM
ejpam-4585	233	4	(	(	PUNCT
ejpam-4585	233	5	h	h	NOUN
ejpam-4585	233	6	)	)	PUNCT
ejpam-4585	233	7	≤	≤	NOUN
ejpam-4585	233	8	lnpnd	lnpnd	ADJ
ejpam-4585	233	9	2	2	NUM
ejpam-4585	233	10	(	(	PUNCT
ejpam-4585	233	11	g	g	NOUN
ejpam-4585	233	12	)	)	PUNCT
ejpam-4585	233	13	+	+	CCONJ
ejpam-4585	233	14	lnpnd	lnpnd	ADJ
ejpam-4585	233	15	(	(	PUNCT
ejpam-4585	233	16	2,2)(h	2,2)(h	NUM
ejpam-4585	233	17	)	)	PUNCT
ejpam-4585	233	18	,	,	PUNCT
ejpam-4585	233	19	then	then	ADV
ejpam-4585	233	20	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	233	21	)	)	PUNCT
ejpam-4585	233	22	≤	≤	NOUN
ejpam-4585	233	23	lnpnd	lnpnd	ADJ
ejpam-4585	233	24	(	(	PUNCT
ejpam-4585	233	25	2,2)(g	2,2)(g	NUM
ejpam-4585	233	26	)	)	PUNCT
ejpam-4585	234	1	+	+	CCONJ
ejpam-4585	234	2	lnpnd	lnpnd	ADJ
ejpam-4585	234	3	2	2	NUM
ejpam-4585	234	4	(	(	PUNCT
ejpam-4585	234	5	h	h	NOUN
ejpam-4585	234	6	)	)	PUNCT
ejpam-4585	234	7	.	.	PUNCT
ejpam-4585	235	1	also	also	ADV
ejpam-4585	235	2	,	,	PUNCT
ejpam-4585	235	3	if	if	SCONJ
ejpam-4585	235	4	lnpnd	lnpnd	ADJ
ejpam-4585	235	5	2	2	NUM
ejpam-4585	235	6	(	(	PUNCT
ejpam-4585	235	7	g	g	NOUN
ejpam-4585	235	8	)	)	PUNCT
ejpam-4585	236	1	+	+	CCONJ
ejpam-4585	236	2	lnpnd	lnpnd	ADJ
ejpam-4585	236	3	(	(	PUNCT
ejpam-4585	236	4	2,2)(h	2,2)(h	NUM
ejpam-4585	236	5	)	)	PUNCT
ejpam-4585	236	6	≤	≤	NUM
ejpam-4585	236	7	ln(2,2	ln(2,2	PROPN
ejpam-4585	236	8	)	)	PUNCT
ejpam-4585	236	9	(	(	PUNCT
ejpam-4585	236	10	pndg	pndg	NOUN
ejpam-4585	236	11	)	)	PUNCT
ejpam-4585	237	1	+	+	CCONJ
ejpam-4585	237	2	lnpnd	lnpnd	ADJ
ejpam-4585	237	3	2	2	NUM
ejpam-4585	237	4	(	(	PUNCT
ejpam-4585	237	5	h	h	NOUN
ejpam-4585	237	6	)	)	PUNCT
ejpam-4585	237	7	and	and	CCONJ
ejpam-4585	237	8	lnpnd	lnpnd	ADJ
ejpam-4585	237	9	2	2	NUM
ejpam-4585	237	10	(	(	PUNCT
ejpam-4585	237	11	g	g	NOUN
ejpam-4585	237	12	)	)	PUNCT
ejpam-4585	237	13	+	+	CCONJ
ejpam-4585	237	14	lnpnd	lnpnd	ADJ
ejpam-4585	237	15	(	(	PUNCT
ejpam-4585	237	16	2,2)(h	2,2)(h	NUM
ejpam-4585	237	17	)	)	PUNCT
ejpam-4585	237	18	≤	≤	NOUN
ejpam-4585	237	19	lnpnd	lnpnd	ADJ
ejpam-4585	237	20	(	(	PUNCT
ejpam-4585	237	21	2,1)(g	2,1)(g	NUM
ejpam-4585	237	22	)	)	PUNCT
ejpam-4585	238	1	+	+	CCONJ
ejpam-4585	238	2	lnpnd	lnpnd	ADJ
ejpam-4585	238	3	(	(	PUNCT
ejpam-4585	238	4	2,1)(h	2,1)(h	NUM
ejpam-4585	238	5	)	)	PUNCT
ejpam-4585	238	6	,	,	PUNCT
ejpam-4585	238	7	then	then	ADV
ejpam-4585	238	8	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	238	9	)	)	PUNCT
ejpam-4585	238	10	≤	≤	NOUN
ejpam-4585	238	11	lnpnd	lnpnd	ADJ
ejpam-4585	238	12	2	2	NUM
ejpam-4585	238	13	(	(	PUNCT
ejpam-4585	238	14	g	g	NOUN
ejpam-4585	238	15	)	)	PUNCT
ejpam-4585	238	16	+	+	CCONJ
ejpam-4585	238	17	lnpnd	lnpnd	ADJ
ejpam-4585	238	18	(	(	PUNCT
ejpam-4585	238	19	2,2)(h	2,2)(h	NUM
ejpam-4585	238	20	)	)	PUNCT
ejpam-4585	238	21	.	.	PUNCT
ejpam-4585	239	1	thus	thus	ADV
ejpam-4585	239	2	,	,	PUNCT
ejpam-4585	239	3	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	239	4	)	)	PUNCT
ejpam-4585	239	5	≤	≤	NUM
ejpam-4585	239	6	min{lnpnd	min{lnpnd	NOUN
ejpam-4585	239	7	(	(	PUNCT
ejpam-4585	239	8	2,2)(g	2,2)(g	NUM
ejpam-4585	239	9	)	)	PUNCT
ejpam-4585	240	1	+	+	CCONJ
ejpam-4585	240	2	lnpnd	lnpnd	ADJ
ejpam-4585	240	3	(	(	PUNCT
ejpam-4585	240	4	2	2	NUM
ejpam-4585	240	5	)	)	PUNCT
ejpam-4585	240	6	(	(	PUNCT
ejpam-4585	240	7	h	h	NOUN
ejpam-4585	240	8	)	)	PUNCT
ejpam-4585	240	9	,	,	PUNCT
ejpam-4585	240	10	lnpnd	lnpnd	ADJ
ejpam-4585	240	11	(	(	PUNCT
ejpam-4585	240	12	2	2	NUM
ejpam-4585	240	13	)	)	PUNCT
ejpam-4585	240	14	(	(	PUNCT
ejpam-4585	240	15	g)lnpnd	g)lnpnd	X
ejpam-4585	240	16	(	(	PUNCT
ejpam-4585	240	17	2,2)(h	2,2)(h	NUM
ejpam-4585	240	18	)	)	PUNCT
ejpam-4585	240	19	,	,	PUNCT
ejpam-4585	240	20	lnpnd	lnpnd	ADJ
ejpam-4585	240	21	(	(	PUNCT
ejpam-4585	240	22	2,1)(g	2,1)(g	NUM
ejpam-4585	240	23	)	)	PUNCT
ejpam-4585	240	24	+	+	CCONJ
ejpam-4585	240	25	lnpnd	lnpnd	ADJ
ejpam-4585	240	26	(	(	PUNCT
ejpam-4585	240	27	2,1)(h	2,1)(h	NUM
ejpam-4585	240	28	)	)	PUNCT
ejpam-4585	240	29	}	}	PUNCT
ejpam-4585	240	30	.	.	PUNCT
ejpam-4585	241	1	a.m.	a.m.	PROPN
ejpam-4585	241	2	mahistrado	mahistrado	PROPN
ejpam-4585	241	3	,	,	PUNCT
ejpam-4585	241	4	h.	h.	PROPN
ejpam-4585	241	5	rara	rara	PROPN
ejpam-4585	241	6	/	/	SYM
ejpam-4585	241	7	eur	eur	PROPN
ejpam-4585	241	8	.	.	PUNCT
ejpam-4585	242	1	j.	j.	PROPN
ejpam-4585	242	2	pure	pure	PROPN
ejpam-4585	242	3	appl	appl	PROPN
ejpam-4585	242	4	.	.	PROPN
ejpam-4585	242	5	math	math	PROPN
ejpam-4585	242	6	,	,	PUNCT
ejpam-4585	242	7	15	15	NUM
ejpam-4585	242	8	(	(	PUNCT
ejpam-4585	242	9	4	4	NUM
ejpam-4585	242	10	)	)	PUNCT
ejpam-4585	242	11	(	(	PUNCT
ejpam-4585	242	12	2022	2022	NUM
ejpam-4585	242	13	)	)	PUNCT
ejpam-4585	242	14	,	,	PUNCT
ejpam-4585	242	15	1982	1982	NUM
ejpam-4585	242	16	-	-	SYM
ejpam-4585	242	17	1997	1997	NUM
ejpam-4585	242	18	1991	1991	NUM
ejpam-4585	242	19	therefore	therefore	ADV
ejpam-4585	242	20	,	,	PUNCT
ejpam-4585	242	21	γ2rh(g+h	γ2rh(g+h	NOUN
ejpam-4585	242	22	)	)	PUNCT
ejpam-4585	242	23	=	=	SYM
ejpam-4585	242	24	min	min	NOUN
ejpam-4585	242	25	{	{	PUNCT
ejpam-4585	242	26	lnpnd	lnpnd	ADV
ejpam-4585	242	27	(	(	PUNCT
ejpam-4585	242	28	2,2)(g	2,2)(g	NUM
ejpam-4585	242	29	)	)	PUNCT
ejpam-4585	243	1	+	+	CCONJ
ejpam-4585	243	2	lnpnd	lnpnd	ADJ
ejpam-4585	243	3	2	2	NUM
ejpam-4585	243	4	(	(	PUNCT
ejpam-4585	243	5	h	h	NOUN
ejpam-4585	243	6	)	)	PUNCT
ejpam-4585	243	7	,	,	PUNCT
ejpam-4585	243	8	lnpnd	lnpnd	PROPN
ejpam-4585	243	9	2	2	NUM
ejpam-4585	243	10	(	(	PUNCT
ejpam-4585	243	11	g	g	NOUN
ejpam-4585	243	12	)	)	PUNCT
ejpam-4585	243	13	+	+	CCONJ
ejpam-4585	243	14	lnpnd	lnpnd	ADJ
ejpam-4585	243	15	(	(	PUNCT
ejpam-4585	243	16	2,2)(h	2,2)(h	NUM
ejpam-4585	243	17	)	)	PUNCT
ejpam-4585	243	18	,	,	PUNCT
ejpam-4585	243	19	lnpnd	lnpnd	ADJ
ejpam-4585	243	20	(	(	PUNCT
ejpam-4585	243	21	2,1)(g	2,1)(g	NUM
ejpam-4585	243	22	)	)	PUNCT
ejpam-4585	244	1	+	+	CCONJ
ejpam-4585	244	2	lnpnd	lnpnd	ADJ
ejpam-4585	244	3	(	(	PUNCT
ejpam-4585	244	4	2,1)(h	2,1)(h	NUM
ejpam-4585	244	5	)	)	PUNCT
ejpam-4585	244	6	}	}	PUNCT
ejpam-4585	244	7	.	.	PUNCT
ejpam-4585	245	1	example	example	NOUN
ejpam-4585	245	2	9	9	NUM
ejpam-4585	245	3	.	.	X
ejpam-4585	246	1	for	for	ADP
ejpam-4585	246	2	paths	path	NOUN
ejpam-4585	246	3	pn	pn	VERB
ejpam-4585	246	4	and	and	CCONJ
ejpam-4585	246	5	pm	pm	VERB
ejpam-4585	246	6	on	on	ADP
ejpam-4585	246	7	n	n	PRON
ejpam-4585	246	8	and	and	CCONJ
ejpam-4585	246	9	m	m	PROPN
ejpam-4585	246	10	vertices	vertex	NOUN
ejpam-4585	246	11	(	(	PUNCT
ejpam-4585	246	12	n	n	CCONJ
ejpam-4585	246	13	,	,	PUNCT
ejpam-4585	246	14	m	m	VERB
ejpam-4585	246	15	≥	≥	NOUN
ejpam-4585	246	16	4	4	NUM
ejpam-4585	246	17	)	)	PUNCT
ejpam-4585	246	18	,	,	PUNCT
ejpam-4585	246	19	we	we	PRON
ejpam-4585	246	20	have	have	VERB
ejpam-4585	246	21	γ2rh(pn	γ2rh(pn	PROPN
ejpam-4585	246	22	+	+	CCONJ
ejpam-4585	246	23	pm	pm	NOUN
ejpam-4585	246	24	)	)	PUNCT
ejpam-4585	246	25	=	=	PUNCT
ejpam-4585	247	1			NOUN
ejpam-4585	247	2	(	(	PUNCT
ejpam-4585	247	3	n	n	ADV
ejpam-4585	247	4	2	2	NUM
ejpam-4585	247	5	+	+	NUM
ejpam-4585	247	6	1	1	NUM
ejpam-4585	247	7	)	)	PUNCT
ejpam-4585	247	8	+	+	CCONJ
ejpam-4585	247	9	(	(	PUNCT
ejpam-4585	247	10	m	m	VERB
ejpam-4585	247	11	2	2	NUM
ejpam-4585	247	12	+	+	NUM
ejpam-4585	247	13	1	1	NUM
ejpam-4585	247	14	)	)	PUNCT
ejpam-4585	247	15	,	,	PUNCT
ejpam-4585	247	16	if	if	SCONJ
ejpam-4585	247	17	n	n	CCONJ
ejpam-4585	247	18	,	,	PUNCT
ejpam-4585	247	19	m	m	VERB
ejpam-4585	247	20	are	be	AUX
ejpam-4585	247	21	even	even	ADV
ejpam-4585	247	22	(	(	PUNCT
ejpam-4585	247	23	n	n	ADV
ejpam-4585	247	24	2	2	NUM
ejpam-4585	247	25	+	+	NUM
ejpam-4585	247	26	1	1	NUM
ejpam-4585	247	27	)	)	PUNCT
ejpam-4585	247	28	+	+	CCONJ
ejpam-4585	247	29	⌈m2	⌈m2	PROPN
ejpam-4585	247	30	⌉	⌉	NOUN
ejpam-4585	247	31	,	,	PUNCT
ejpam-4585	247	32	if	if	SCONJ
ejpam-4585	247	33	n	n	PRON
ejpam-4585	247	34	is	be	AUX
ejpam-4585	247	35	even	even	ADV
ejpam-4585	247	36	,	,	PUNCT
ejpam-4585	247	37	m	m	VERB
ejpam-4585	247	38	is	be	AUX
ejpam-4585	247	39	odd	odd	ADJ
ejpam-4585	247	40	⌈n2	⌈n2	NOUN
ejpam-4585	247	41	⌉+	⌉+	X
ejpam-4585	248	1	(	(	PUNCT
ejpam-4585	248	2	m	m	NOUN
ejpam-4585	248	3	2	2	NUM
ejpam-4585	248	4	+	+	NUM
ejpam-4585	248	5	1	1	NUM
ejpam-4585	248	6	)	)	PUNCT
ejpam-4585	248	7	,	,	PUNCT
ejpam-4585	248	8	if	if	SCONJ
ejpam-4585	248	9	n	n	PRON
ejpam-4585	248	10	is	be	AUX
ejpam-4585	248	11	odd	odd	ADJ
ejpam-4585	248	12	,	,	PUNCT
ejpam-4585	248	13	m	m	VERB
ejpam-4585	248	14	is	be	AUX
ejpam-4585	248	15	even	even	ADV
ejpam-4585	248	16	⌈n2	⌈n2	ADJ
ejpam-4585	249	1	⌉+	⌉+	PROPN
ejpam-4585	249	2	⌈m2	⌈m2	PROPN
ejpam-4585	249	3	⌉	⌉	NOUN
ejpam-4585	249	4	,	,	PUNCT
ejpam-4585	249	5	if	if	SCONJ
ejpam-4585	249	6	n	n	CCONJ
ejpam-4585	249	7	,	,	PUNCT
ejpam-4585	249	8	m	m	VERB
ejpam-4585	249	9	are	be	AUX
ejpam-4585	249	10	odd	odd	ADJ
ejpam-4585	249	11	.	.	PUNCT
ejpam-4585	250	1	in	in	ADP
ejpam-4585	250	2	particular	particular	ADJ
ejpam-4585	250	3	,	,	PUNCT
ejpam-4585	250	4	for	for	ADP
ejpam-4585	250	5	n	n	CCONJ
ejpam-4585	250	6	,	,	PUNCT
ejpam-4585	250	7	m	m	VERB
ejpam-4585	250	8	=	=	NOUN
ejpam-4585	250	9	2	2	NUM
ejpam-4585	250	10	,	,	PUNCT
ejpam-4585	250	11	3	3	NUM
ejpam-4585	250	12	,	,	PUNCT
ejpam-4585	250	13	γ2rh(pn	γ2rh(pn	PROPN
ejpam-4585	250	14	+	+	CCONJ
ejpam-4585	250	15	pm	pm	NOUN
ejpam-4585	250	16	)	)	PUNCT
ejpam-4585	250	17	=	=	SYM
ejpam-4585	250	18	n+m	n+m	PROPN
ejpam-4585	250	19	.	.	PUNCT
ejpam-4585	250	20	4.1	4.1	NUM
ejpam-4585	250	21	.	.	NOUN
ejpam-4585	250	22	2	2	NUM
ejpam-4585	250	23	-	-	PUNCT
ejpam-4585	250	24	resolving	resolve	VERB
ejpam-4585	250	25	hop	hop	NOUN
ejpam-4585	250	26	dominating	dominating	NOUN
ejpam-4585	250	27	sets	set	NOUN
ejpam-4585	250	28	in	in	ADP
ejpam-4585	250	29	the	the	DET
ejpam-4585	250	30	corona	corona	NOUN
ejpam-4585	250	31	of	of	ADP
ejpam-4585	250	32	graphs	graph	NOUN
ejpam-4585	250	33	let	let	VERB
ejpam-4585	250	34	the	the	DET
ejpam-4585	250	35	following	follow	VERB
ejpam-4585	250	36	notations	notation	NOUN
ejpam-4585	250	37	be	be	AUX
ejpam-4585	250	38	described	describe	VERB
ejpam-4585	250	39	as	as	SCONJ
ejpam-4585	250	40	follows	follow	VERB
ejpam-4585	250	41	:	:	PUNCT
ejpam-4585	250	42	for	for	ADP
ejpam-4585	250	43	k	k	PROPN
ejpam-4585	250	44	∈	∈	PROPN
ejpam-4585	250	45	v	v	PROPN
ejpam-4585	250	46	(	(	PUNCT
ejpam-4585	250	47	g	g	PROPN
ejpam-4585	250	48	◦	◦	NOUN
ejpam-4585	250	49	h	h	NOUN
ejpam-4585	250	50	)	)	PUNCT
ejpam-4585	250	51	,	,	PUNCT
ejpam-4585	250	52	v	v	X
ejpam-4585	250	53	∈	∈	PROPN
ejpam-4585	250	54	v	v	NOUN
ejpam-4585	250	55	(	(	PUNCT
ejpam-4585	250	56	g	g	NOUN
ejpam-4585	250	57	)	)	PUNCT
ejpam-4585	250	58	and	and	CCONJ
ejpam-4585	250	59	sv	sv	X
ejpam-4585	250	60	⊂	⊂	PROPN
ejpam-4585	250	61	v	v	X
ejpam-4585	250	62	(	(	PUNCT
ejpam-4585	250	63	hv	hv	PROPN
ejpam-4585	250	64	)	)	PUNCT
ejpam-4585	250	65	.	.	PUNCT
ejpam-4585	251	1	v	v	X
ejpam-4585	251	2	k	k	PROPN
ejpam-4585	251	3	sv	sv	PROPN
ejpam-4585	251	4	is	be	AUX
ejpam-4585	251	5	a	a	DET
ejpam-4585	251	6	vector	vector	NOUN
ejpam-4585	251	7	whose	whose	DET
ejpam-4585	251	8	components	component	NOUN
ejpam-4585	251	9	are	be	AUX
ejpam-4585	251	10	the	the	DET
ejpam-4585	251	11	distances	distance	NOUN
ejpam-4585	251	12	of	of	ADP
ejpam-4585	251	13	k	k	PROPN
ejpam-4585	251	14	from	from	ADP
ejpam-4585	251	15	the	the	DET
ejpam-4585	251	16	elements	element	NOUN
ejpam-4585	251	17	of	of	ADP
ejpam-4585	251	18	sv	sv	PROPN
ejpam-4585	251	19	.	.	PUNCT
ejpam-4585	251	20	definition	definition	NOUN
ejpam-4585	251	21	8	8	NUM
ejpam-4585	251	22	.	.	PUNCT
ejpam-4585	252	1	[	[	X
ejpam-4585	252	2	2	2	X
ejpam-4585	252	3	]	]	PUNCT
ejpam-4585	252	4	the	the	DET
ejpam-4585	252	5	corona	corona	NOUN
ejpam-4585	252	6	g	g	PROPN
ejpam-4585	252	7	◦	◦	NOUN
ejpam-4585	252	8	h	h	NOUN
ejpam-4585	252	9	of	of	ADP
ejpam-4585	252	10	two	two	NUM
ejpam-4585	252	11	graphs	graph	NOUN
ejpam-4585	252	12	g	g	NOUN
ejpam-4585	252	13	and	and	CCONJ
ejpam-4585	252	14	h	h	NOUN
ejpam-4585	252	15	is	be	AUX
ejpam-4585	252	16	the	the	DET
ejpam-4585	252	17	graph	graph	NOUN
ejpam-4585	252	18	obtained	obtain	VERB
ejpam-4585	252	19	by	by	ADP
ejpam-4585	252	20	taking	take	VERB
ejpam-4585	252	21	one	one	NUM
ejpam-4585	252	22	copy	copy	NOUN
ejpam-4585	252	23	of	of	ADP
ejpam-4585	252	24	g	g	NOUN
ejpam-4585	252	25	of	of	ADP
ejpam-4585	252	26	order	order	NOUN
ejpam-4585	252	27	n	n	NOUN
ejpam-4585	252	28	and	and	CCONJ
ejpam-4585	252	29	n	n	PRON
ejpam-4585	252	30	copies	copy	NOUN
ejpam-4585	252	31	of	of	ADP
ejpam-4585	252	32	h	h	NOUN
ejpam-4585	252	33	,	,	PUNCT
ejpam-4585	252	34	and	and	CCONJ
ejpam-4585	252	35	then	then	ADV
ejpam-4585	252	36	joining	join	VERB
ejpam-4585	252	37	the	the	DET
ejpam-4585	252	38	ith	ith	PROPN
ejpam-4585	252	39	vertex	vertex	NOUN
ejpam-4585	252	40	of	of	ADP
ejpam-4585	252	41	g	g	NOUN
ejpam-4585	252	42	to	to	ADP
ejpam-4585	252	43	every	every	DET
ejpam-4585	252	44	vertex	vertex	NOUN
ejpam-4585	252	45	in	in	ADP
ejpam-4585	252	46	the	the	DET
ejpam-4585	252	47	ith	ith	PROPN
ejpam-4585	252	48	copy	copy	NOUN
ejpam-4585	252	49	of	of	ADP
ejpam-4585	252	50	h.	h.	PROPN
ejpam-4585	252	51	for	for	ADP
ejpam-4585	252	52	every	every	DET
ejpam-4585	252	53	v	v	NUM
ejpam-4585	252	54	∈	∈	PROPN
ejpam-4585	252	55	v	v	NOUN
ejpam-4585	252	56	(	(	PUNCT
ejpam-4585	252	57	g	g	NOUN
ejpam-4585	252	58	)	)	PUNCT
ejpam-4585	252	59	,	,	PUNCT
ejpam-4585	252	60	denote	denote	VERB
ejpam-4585	252	61	by	by	ADP
ejpam-4585	252	62	hv	hv	PROPN
ejpam-4585	252	63	the	the	DET
ejpam-4585	252	64	copy	copy	NOUN
ejpam-4585	252	65	of	of	ADP
ejpam-4585	252	66	h	h	NOUN
ejpam-4585	252	67	whose	whose	DET
ejpam-4585	252	68	vertices	vertex	NOUN
ejpam-4585	252	69	are	be	AUX
ejpam-4585	252	70	attached	attach	VERB
ejpam-4585	252	71	one	one	NUM
ejpam-4585	252	72	by	by	ADP
ejpam-4585	252	73	one	one	NUM
ejpam-4585	252	74	to	to	ADP
ejpam-4585	252	75	the	the	DET
ejpam-4585	252	76	vertex	vertex	NOUN
ejpam-4585	252	77	v.	v.	ADP
ejpam-4585	252	78	subsequently	subsequently	ADV
ejpam-4585	252	79	,	,	PUNCT
ejpam-4585	252	80	denote	denote	VERB
ejpam-4585	252	81	by	by	ADP
ejpam-4585	252	82	v	v	PRON
ejpam-4585	252	83	+	+	NOUN
ejpam-4585	252	84	hv	hv	NOUN
ejpam-4585	252	85	the	the	DET
ejpam-4585	252	86	subgraph	subgraph	NOUN
ejpam-4585	252	87	of	of	ADP
ejpam-4585	252	88	the	the	DET
ejpam-4585	252	89	corona	corona	NOUN
ejpam-4585	252	90	g	g	PROPN
ejpam-4585	252	91	◦	◦	NOUN
ejpam-4585	252	92	h	h	NOUN
ejpam-4585	252	93	corresponding	correspond	VERB
ejpam-4585	252	94	to	to	ADP
ejpam-4585	252	95	the	the	DET
ejpam-4585	252	96	join	join	NOUN
ejpam-4585	252	97	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4585	252	98	,	,	PUNCT
ejpam-4585	252	99	v	v	PROPN
ejpam-4585	252	100	∈	∈	PROPN
ejpam-4585	252	101	v	v	NOUN
ejpam-4585	252	102	(	(	PUNCT
ejpam-4585	252	103	g	g	NOUN
ejpam-4585	252	104	)	)	PUNCT
ejpam-4585	252	105	.	.	PUNCT
ejpam-4585	253	1	remark	remark	PROPN
ejpam-4585	253	2	7	7	NUM
ejpam-4585	253	3	.	.	PUNCT
ejpam-4585	254	1	[	[	X
ejpam-4585	254	2	4	4	X
ejpam-4585	254	3	]	]	PUNCT
ejpam-4585	254	4	let	let	VERB
ejpam-4585	254	5	v	v	NUM
ejpam-4585	254	6	∈	∈	PROPN
ejpam-4585	254	7	v	v	NOUN
ejpam-4585	254	8	(	(	PUNCT
ejpam-4585	254	9	g	g	NOUN
ejpam-4585	254	10	)	)	PUNCT
ejpam-4585	254	11	.	.	PUNCT
ejpam-4585	255	1	for	for	ADP
ejpam-4585	255	2	every	every	DET
ejpam-4585	255	3	x	x	PROPN
ejpam-4585	255	4	,	,	PUNCT
ejpam-4585	255	5	y	y	PROPN
ejpam-4585	255	6	∈	∈	PROPN
ejpam-4585	255	7	v	v	PROPN
ejpam-4585	255	8	(	(	PUNCT
ejpam-4585	255	9	hv	hv	PROPN
ejpam-4585	255	10	)	)	PUNCT
ejpam-4585	255	11	,	,	PUNCT
ejpam-4585	255	12	dg	dg	PROPN
ejpam-4585	255	13	◦	◦	NOUN
ejpam-4585	255	14	h(x	h(x	PROPN
ejpam-4585	255	15	,	,	PUNCT
ejpam-4585	255	16	w	w	PROPN
ejpam-4585	255	17	)	)	PUNCT
ejpam-4585	255	18	=	=	SYM
ejpam-4585	255	19	dg	dg	NOUN
ejpam-4585	255	20	◦	◦	NOUN
ejpam-4585	255	21	h(y	h(y	ADV
ejpam-4585	255	22	,	,	PUNCT
ejpam-4585	255	23	w	w	NOUN
ejpam-4585	255	24	)	)	PUNCT
ejpam-4585	255	25	and	and	CCONJ
ejpam-4585	255	26	dg	dg	AUX
ejpam-4585	255	27	◦	◦	NOUN
ejpam-4585	255	28	h(v	h(v	PROPN
ejpam-4585	255	29	,	,	PUNCT
ejpam-4585	255	30	w	w	NOUN
ejpam-4585	255	31	)	)	PUNCT
ejpam-4585	255	32	+	+	CCONJ
ejpam-4585	255	33	1	1	NUM
ejpam-4585	255	34	=	=	SYM
ejpam-4585	255	35	dg	dg	NOUN
ejpam-4585	255	36	◦	◦	NOUN
ejpam-4585	255	37	h(x	h(x	PROPN
ejpam-4585	255	38	,	,	PUNCT
ejpam-4585	255	39	w	w	NOUN
ejpam-4585	255	40	)	)	PUNCT
ejpam-4585	255	41	for	for	ADP
ejpam-4585	255	42	every	every	DET
ejpam-4585	255	43	w	w	PROPN
ejpam-4585	255	44	∈	∈	PROPN
ejpam-4585	255	45	v	v	NOUN
ejpam-4585	255	46	(	(	PUNCT
ejpam-4585	255	47	g	g	PROPN
ejpam-4585	255	48	◦	◦	PROPN
ejpam-4585	255	49	h)\v	h)\v	PROPN
ejpam-4585	255	50	(	(	PUNCT
ejpam-4585	255	51	hv	hv	NOUN
ejpam-4585	255	52	)	)	PUNCT
ejpam-4585	255	53	.	.	PUNCT
ejpam-4585	256	1	theorem	theorem	VERB
ejpam-4585	256	2	9	9	NUM
ejpam-4585	256	3	.	.	PUNCT
ejpam-4585	257	1	[	[	X
ejpam-4585	257	2	12	12	NUM
ejpam-4585	257	3	]	]	PUNCT
ejpam-4585	257	4	let	let	VERB
ejpam-4585	257	5	g	g	NOUN
ejpam-4585	257	6	and	and	CCONJ
ejpam-4585	257	7	h	h	NOUN
ejpam-4585	257	8	be	be	VERB
ejpam-4585	257	9	any	any	DET
ejpam-4585	257	10	two	two	NUM
ejpam-4585	257	11	graphs	graph	NOUN
ejpam-4585	257	12	.	.	PUNCT
ejpam-4585	258	1	a	a	DET
ejpam-4585	258	2	set	set	NOUN
ejpam-4585	258	3	c	c	NOUN
ejpam-4585	258	4	⊆	⊆	NUM
ejpam-4585	258	5	v	v	NOUN
ejpam-4585	258	6	(	(	PUNCT
ejpam-4585	258	7	g	g	PROPN
ejpam-4585	258	8	◦	◦	NOUN
ejpam-4585	258	9	h	h	NOUN
ejpam-4585	258	10	)	)	PUNCT
ejpam-4585	258	11	is	be	AUX
ejpam-4585	258	12	a	a	DET
ejpam-4585	258	13	hop	hop	NOUN
ejpam-4585	258	14	dominating	dominating	NOUN
ejpam-4585	258	15	set	set	NOUN
ejpam-4585	258	16	of	of	ADP
ejpam-4585	258	17	g	g	PROPN
ejpam-4585	258	18	◦	◦	NOUN
ejpam-4585	258	19	h	h	NOUN
ejpam-4585	258	20	if	if	SCONJ
ejpam-4585	259	1	and	and	CCONJ
ejpam-4585	259	2	only	only	ADV
ejpam-4585	259	3	if	if	SCONJ
ejpam-4585	259	4	c	c	X
ejpam-4585	259	5	=	=	PUNCT
ejpam-4585	259	6	a	a	PRON
ejpam-4585	259	7	∪	∪	ADJ
ejpam-4585	259	8			PROPN
ejpam-4585	259	9	⋃	⋃	ADJ
ejpam-4585	259	10	v∈v	v∈v	NOUN
ejpam-4585	259	11	(	(	PUNCT
ejpam-4585	259	12	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4585	259	13	)	)	PUNCT
ejpam-4585	259	14	sv	sv	NOUN
ejpam-4585	260	1			PROPN
ejpam-4585	260	2	∪	∪	VERB
ejpam-4585	260	3			PROPN
ejpam-4585	260	4	⋃	⋃	PROPN
ejpam-4585	260	5	w∈v	w∈v	PROPN
ejpam-4585	260	6	(	(	PUNCT
ejpam-4585	260	7	g)\ng(a	g)\ng(a	NOUN
ejpam-4585	260	8	)	)	PUNCT
ejpam-4585	260	9	ew	ew	VERB
ejpam-4585	260	10			PROPN
ejpam-4585	260	11	where	where	SCONJ
ejpam-4585	260	12	(	(	PUNCT
ejpam-4585	260	13	i	i	NOUN
ejpam-4585	260	14	)	)	PUNCT
ejpam-4585	260	15	a	a	DET
ejpam-4585	260	16	⊆	⊆	NUM
ejpam-4585	260	17	v	v	NOUN
ejpam-4585	260	18	(	(	PUNCT
ejpam-4585	260	19	g	g	NOUN
ejpam-4585	260	20	)	)	PUNCT
ejpam-4585	260	21	such	such	ADJ
ejpam-4585	260	22	that	that	PRON
ejpam-4585	260	23	for	for	ADP
ejpam-4585	260	24	each	each	DET
ejpam-4585	260	25	w	w	PROPN
ejpam-4585	260	26	∈	∈	PROPN
ejpam-4585	260	27	v	v	NOUN
ejpam-4585	260	28	(	(	PUNCT
ejpam-4585	260	29	g)\a	g)\a	NOUN
ejpam-4585	260	30	,	,	PUNCT
ejpam-4585	260	31	there	there	PRON
ejpam-4585	260	32	exists	exist	VERB
ejpam-4585	260	33	x	x	X
ejpam-4585	260	34	∈	∈	PROPN
ejpam-4585	260	35	a	a	PRON
ejpam-4585	260	36	with	with	ADP
ejpam-4585	260	37	dg(w	dg(w	NOUN
ejpam-4585	260	38	,	,	PUNCT
ejpam-4585	260	39	x	x	X
ejpam-4585	260	40	)	)	PUNCT
ejpam-4585	260	41	=	=	SYM
ejpam-4585	260	42	2	2	NUM
ejpam-4585	260	43	or	or	CCONJ
ejpam-4585	260	44	there	there	PRON
ejpam-4585	260	45	exists	exist	VERB
ejpam-4585	260	46	y	y	PROPN
ejpam-4585	260	47	∈	∈	PROPN
ejpam-4585	260	48	v	v	ADP
ejpam-4585	260	49	(	(	PUNCT
ejpam-4585	260	50	g	g	NOUN
ejpam-4585	260	51	)	)	PUNCT
ejpam-4585	260	52	∩ng(w	∩ng(w	PROPN
ejpam-4585	260	53	)	)	PUNCT
ejpam-4585	260	54	with	with	ADP
ejpam-4585	260	55	v	v	NUM
ejpam-4585	260	56	(	(	PUNCT
ejpam-4585	260	57	hy	hy	NOUN
ejpam-4585	260	58	)	)	PUNCT
ejpam-4585	260	59	∩	∩	NOUN
ejpam-4585	260	60	c	c	PROPN
ejpam-4585	260	61	̸=	̸=	PROPN
ejpam-4585	260	62	∅	∅	NOUN
ejpam-4585	260	63	,	,	PUNCT
ejpam-4585	260	64	(	(	PUNCT
ejpam-4585	260	65	ii	ii	NOUN
ejpam-4585	260	66	)	)	PUNCT
ejpam-4585	260	67	sv	sv	VERB
ejpam-4585	261	1	⊆	⊆	NUM
ejpam-4585	261	2	v	v	X
ejpam-4585	261	3	(	(	PUNCT
ejpam-4585	261	4	hv	hv	PROPN
ejpam-4585	261	5	)	)	PUNCT
ejpam-4585	261	6	for	for	ADP
ejpam-4585	261	7	each	each	DET
ejpam-4585	261	8	v	v	NUM
ejpam-4585	261	9	∈	∈	PROPN
ejpam-4585	261	10	v	v	NOUN
ejpam-4585	261	11	(	(	PUNCT
ejpam-4585	261	12	g	g	NOUN
ejpam-4585	261	13	)	)	PUNCT
ejpam-4585	261	14	∩ng(a	∩ng(a	NOUN
ejpam-4585	261	15	)	)	PUNCT
ejpam-4585	261	16	,	,	PUNCT
ejpam-4585	261	17	and	and	CCONJ
ejpam-4585	261	18	(	(	PUNCT
ejpam-4585	261	19	iii	iii	NOUN
ejpam-4585	261	20	)	)	PUNCT
ejpam-4585	261	21	ew	ew	NOUN
ejpam-4585	261	22	⊆	⊆	NUM
ejpam-4585	261	23	v	v	NOUN
ejpam-4585	261	24	(	(	PUNCT
ejpam-4585	261	25	hw	hw	NOUN
ejpam-4585	261	26	)	)	PUNCT
ejpam-4585	261	27	is	be	AUX
ejpam-4585	261	28	a	a	DET
ejpam-4585	261	29	point	point	NOUN
ejpam-4585	261	30	-	-	PUNCT
ejpam-4585	261	31	wise	wise	ADJ
ejpam-4585	261	32	non	non	ADJ
ejpam-4585	261	33	-	-	ADJ
ejpam-4585	261	34	dominating	dominating	ADJ
ejpam-4585	261	35	set	set	NOUN
ejpam-4585	261	36	of	of	ADP
ejpam-4585	261	37	hw	hw	PRON
ejpam-4585	261	38	for	for	ADP
ejpam-4585	261	39	each	each	DET
ejpam-4585	261	40	w	w	PROPN
ejpam-4585	261	41	∈	∈	PROPN
ejpam-4585	261	42	v	v	NOUN
ejpam-4585	261	43	(	(	PUNCT
ejpam-4585	261	44	g)\ng(a	g)\ng(a	NOUN
ejpam-4585	261	45	)	)	PUNCT
ejpam-4585	261	46	.	.	PUNCT
ejpam-4585	262	1	a.m.	a.m.	PROPN
ejpam-4585	262	2	mahistrado	mahistrado	PROPN
ejpam-4585	262	3	,	,	PUNCT
ejpam-4585	262	4	h.	h.	PROPN
ejpam-4585	262	5	rara	rara	PROPN
ejpam-4585	262	6	/	/	SYM
ejpam-4585	262	7	eur	eur	PROPN
ejpam-4585	262	8	.	.	PUNCT
ejpam-4585	263	1	j.	j.	PROPN
ejpam-4585	263	2	pure	pure	PROPN
ejpam-4585	263	3	appl	appl	PROPN
ejpam-4585	263	4	.	.	PROPN
ejpam-4585	263	5	math	math	PROPN
ejpam-4585	263	6	,	,	PUNCT
ejpam-4585	263	7	15	15	NUM
ejpam-4585	263	8	(	(	PUNCT
ejpam-4585	263	9	4	4	NUM
ejpam-4585	263	10	)	)	PUNCT
ejpam-4585	263	11	(	(	PUNCT
ejpam-4585	263	12	2022	2022	NUM
ejpam-4585	263	13	)	)	PUNCT
ejpam-4585	263	14	,	,	PUNCT
ejpam-4585	263	15	1982	1982	NUM
ejpam-4585	263	16	-	-	SYM
ejpam-4585	263	17	1997	1997	NUM
ejpam-4585	263	18	1992	1992	NUM
ejpam-4585	263	19	theorem	theorem	VERB
ejpam-4585	263	20	10	10	NUM
ejpam-4585	263	21	.	.	PUNCT
ejpam-4585	264	1	let	let	VERB
ejpam-4585	264	2	g	g	NOUN
ejpam-4585	264	3	and	and	CCONJ
ejpam-4585	264	4	h	h	NOUN
ejpam-4585	264	5	be	be	AUX
ejpam-4585	264	6	nontrivial	nontrivial	ADJ
ejpam-4585	264	7	connected	connected	ADJ
ejpam-4585	264	8	graphs	graph	NOUN
ejpam-4585	264	9	.	.	PUNCT
ejpam-4585	265	1	a	a	DET
ejpam-4585	265	2	set	set	NOUN
ejpam-4585	265	3	s	s	NOUN
ejpam-4585	265	4	⊆	⊆	NUM
ejpam-4585	265	5	v	v	NOUN
ejpam-4585	265	6	(	(	PUNCT
ejpam-4585	265	7	g	g	PROPN
ejpam-4585	265	8	◦	◦	NOUN
ejpam-4585	265	9	h	h	NOUN
ejpam-4585	265	10	)	)	PUNCT
ejpam-4585	265	11	is	be	AUX
ejpam-4585	265	12	a	a	DET
ejpam-4585	265	13	2	2	NUM
ejpam-4585	265	14	-	-	PUNCT
ejpam-4585	265	15	resolving	resolve	VERB
ejpam-4585	265	16	hop	hop	NOUN
ejpam-4585	265	17	dominating	dominating	NOUN
ejpam-4585	265	18	set	set	NOUN
ejpam-4585	265	19	of	of	ADP
ejpam-4585	265	20	g	g	PROPN
ejpam-4585	265	21	◦	◦	NOUN
ejpam-4585	265	22	h	h	NOUN
ejpam-4585	265	23	if	if	SCONJ
ejpam-4585	266	1	and	and	CCONJ
ejpam-4585	266	2	only	only	ADV
ejpam-4585	266	3	if	if	SCONJ
ejpam-4585	266	4	s	s	VERB
ejpam-4585	266	5	=	=	NOUN
ejpam-4585	266	6	a	a	PRON
ejpam-4585	266	7	∪	∪	ADJ
ejpam-4585	266	8			PROPN
ejpam-4585	266	9	⋃	⋃	ADJ
ejpam-4585	266	10	v∈v	v∈v	NOUN
ejpam-4585	266	11	(	(	PUNCT
ejpam-4585	266	12	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4585	267	1	)	)	PUNCT
ejpam-4585	267	2	sv	sv	NOUN
ejpam-4585	268	1			PROPN
ejpam-4585	268	2	∪	∪	VERB
ejpam-4585	268	3			PROPN
ejpam-4585	268	4	⋃	⋃	PROPN
ejpam-4585	268	5	w∈v	w∈v	PROPN
ejpam-4585	268	6	(	(	PUNCT
ejpam-4585	268	7	g)\ng(a	g)\ng(a	NOUN
ejpam-4585	268	8	)	)	PUNCT
ejpam-4585	268	9	dw	dw	NOUN
ejpam-4585	268	10			PROPN
ejpam-4585	268	11	where	where	SCONJ
ejpam-4585	268	12	(	(	PUNCT
ejpam-4585	268	13	i	i	NOUN
ejpam-4585	268	14	)	)	PUNCT
ejpam-4585	268	15	a	a	DET
ejpam-4585	268	16	⊆	⊆	NUM
ejpam-4585	268	17	v	v	NOUN
ejpam-4585	268	18	(	(	PUNCT
ejpam-4585	268	19	g	g	NOUN
ejpam-4585	268	20	)	)	PUNCT
ejpam-4585	268	21	such	such	ADJ
ejpam-4585	268	22	that	that	PRON
ejpam-4585	268	23	for	for	ADP
ejpam-4585	268	24	each	each	DET
ejpam-4585	268	25	w	w	PROPN
ejpam-4585	268	26	∈	∈	PROPN
ejpam-4585	268	27	v	v	NOUN
ejpam-4585	268	28	(	(	PUNCT
ejpam-4585	268	29	g)\a	g)\a	NOUN
ejpam-4585	268	30	,	,	PUNCT
ejpam-4585	268	31	there	there	PRON
ejpam-4585	268	32	exists	exist	VERB
ejpam-4585	268	33	x	x	X
ejpam-4585	268	34	∈	∈	PROPN
ejpam-4585	268	35	a	a	PRON
ejpam-4585	268	36	with	with	ADP
ejpam-4585	268	37	dg(w	dg(w	NOUN
ejpam-4585	268	38	,	,	PUNCT
ejpam-4585	268	39	x	x	X
ejpam-4585	268	40	)	)	PUNCT
ejpam-4585	268	41	=	=	SYM
ejpam-4585	268	42	2	2	NUM
ejpam-4585	268	43	or	or	CCONJ
ejpam-4585	268	44	there	there	PRON
ejpam-4585	268	45	exists	exist	VERB
ejpam-4585	268	46	y	y	PROPN
ejpam-4585	268	47	∈	∈	PROPN
ejpam-4585	268	48	v	v	ADP
ejpam-4585	268	49	(	(	PUNCT
ejpam-4585	268	50	g	g	NOUN
ejpam-4585	268	51	)	)	PUNCT
ejpam-4585	268	52	∩ng(w	∩ng(w	PROPN
ejpam-4585	268	53	)	)	PUNCT
ejpam-4585	268	54	with	with	ADP
ejpam-4585	268	55	v	v	NUM
ejpam-4585	268	56	(	(	PUNCT
ejpam-4585	268	57	hy	hy	NOUN
ejpam-4585	268	58	)	)	PUNCT
ejpam-4585	268	59	∩	∩	PROPN
ejpam-4585	268	60	s	s	PART
ejpam-4585	268	61	̸=	̸=	PROPN
ejpam-4585	268	62	∅	∅	NOUN
ejpam-4585	268	63	;	;	PUNCT
ejpam-4585	268	64	(	(	PUNCT
ejpam-4585	268	65	ii	ii	NOUN
ejpam-4585	268	66	)	)	PUNCT
ejpam-4585	268	67	sv	sv	VERB
ejpam-4585	269	1	⊆	⊆	NUM
ejpam-4585	269	2	v	v	ADP
ejpam-4585	269	3	(	(	PUNCT
ejpam-4585	269	4	hv	hv	X
ejpam-4585	269	5	)	)	PUNCT
ejpam-4585	269	6	is	be	AUX
ejpam-4585	269	7	a	a	DET
ejpam-4585	269	8	2	2	NUM
ejpam-4585	269	9	-	-	PUNCT
ejpam-4585	269	10	locating	locate	VERB
ejpam-4585	269	11	set	set	NOUN
ejpam-4585	269	12	of	of	ADP
ejpam-4585	269	13	hv	hv	PROPN
ejpam-4585	269	14	for	for	ADP
ejpam-4585	269	15	all	all	DET
ejpam-4585	269	16	v	v	ADP
ejpam-4585	269	17	∈	∈	NUM
ejpam-4585	269	18	v	v	NOUN
ejpam-4585	269	19	(	(	PUNCT
ejpam-4585	269	20	g	g	NOUN
ejpam-4585	269	21	)	)	PUNCT
ejpam-4585	269	22	∩ng(a	∩ng(a	NOUN
ejpam-4585	269	23	)	)	PUNCT
ejpam-4585	269	24	;	;	PUNCT
ejpam-4585	269	25	and	and	CCONJ
ejpam-4585	269	26	(	(	PUNCT
ejpam-4585	269	27	iii	iii	X
ejpam-4585	269	28	)	)	PUNCT
ejpam-4585	269	29	dw	dw	NOUN
ejpam-4585	269	30	⊆	⊆	NUM
ejpam-4585	269	31	v	v	NOUN
ejpam-4585	269	32	(	(	PUNCT
ejpam-4585	269	33	hw	hw	NOUN
ejpam-4585	269	34	)	)	PUNCT
ejpam-4585	269	35	is	be	AUX
ejpam-4585	269	36	a	a	DET
ejpam-4585	269	37	2	2	NUM
ejpam-4585	269	38	-	-	PUNCT
ejpam-4585	269	39	locating	locate	VERB
ejpam-4585	269	40	point	point	NOUN
ejpam-4585	269	41	-	-	PUNCT
ejpam-4585	269	42	wise	wise	ADJ
ejpam-4585	269	43	non	non	ADJ
ejpam-4585	269	44	-	-	ADJ
ejpam-4585	269	45	dominating	dominating	ADJ
ejpam-4585	269	46	set	set	NOUN
ejpam-4585	269	47	of	of	ADP
ejpam-4585	269	48	hw	hw	PRON
ejpam-4585	269	49	for	for	ADP
ejpam-4585	269	50	all	all	DET
ejpam-4585	269	51	w	w	PROPN
ejpam-4585	269	52	∈	∈	PROPN
ejpam-4585	269	53	v	v	NOUN
ejpam-4585	269	54	(	(	PUNCT
ejpam-4585	269	55	g)\ng(a	g)\ng(a	NOUN
ejpam-4585	269	56	)	)	PUNCT
ejpam-4585	269	57	.	.	PUNCT
ejpam-4585	270	1	proof	proof	NOUN
ejpam-4585	270	2	.	.	PUNCT
ejpam-4585	271	1	suppose	suppose	VERB
ejpam-4585	271	2	that	that	SCONJ
ejpam-4585	271	3	s	s	VERB
ejpam-4585	271	4	⊆	⊆	NUM
ejpam-4585	271	5	v	v	NOUN
ejpam-4585	271	6	(	(	PUNCT
ejpam-4585	271	7	g	g	PROPN
ejpam-4585	271	8	◦	◦	NOUN
ejpam-4585	271	9	h	h	NOUN
ejpam-4585	271	10	)	)	PUNCT
ejpam-4585	271	11	is	be	AUX
ejpam-4585	271	12	a	a	DET
ejpam-4585	271	13	2	2	NUM
ejpam-4585	271	14	-	-	PUNCT
ejpam-4585	271	15	resolving	resolve	VERB
ejpam-4585	271	16	hop	hop	NOUN
ejpam-4585	271	17	dominating	dominating	NOUN
ejpam-4585	271	18	set	set	NOUN
ejpam-4585	271	19	of	of	ADP
ejpam-4585	271	20	g	g	PROPN
ejpam-4585	271	21	◦	◦	NOUN
ejpam-4585	271	22	h.	h.	NOUN
ejpam-4585	271	23	let	let	VERB
ejpam-4585	271	24	a	a	PRON
ejpam-4585	271	25	=	=	X
ejpam-4585	271	26	v	v	X
ejpam-4585	271	27	(	(	PUNCT
ejpam-4585	271	28	g	g	NOUN
ejpam-4585	271	29	)	)	PUNCT
ejpam-4585	271	30	∩	∩	PROPN
ejpam-4585	271	31	s	s	NOUN
ejpam-4585	271	32	,	,	PUNCT
ejpam-4585	271	33	sv	sv	INTJ
ejpam-4585	271	34	=	=	SYM
ejpam-4585	271	35	s	s	PROPN
ejpam-4585	271	36	∩	∩	ADJ
ejpam-4585	271	37	v	v	X
ejpam-4585	271	38	(	(	PUNCT
ejpam-4585	271	39	hv	hv	PROPN
ejpam-4585	271	40	)	)	PUNCT
ejpam-4585	271	41	for	for	ADP
ejpam-4585	271	42	all	all	DET
ejpam-4585	271	43	v	v	ADP
ejpam-4585	271	44	∈	∈	NOUN
ejpam-4585	271	45	v	v	NOUN
ejpam-4585	271	46	(	(	PUNCT
ejpam-4585	271	47	g	g	NOUN
ejpam-4585	271	48	)	)	PUNCT
ejpam-4585	271	49	∩ng(a	∩ng(a	NOUN
ejpam-4585	271	50	)	)	PUNCT
ejpam-4585	271	51	and	and	CCONJ
ejpam-4585	271	52	dw	dw	X
ejpam-4585	271	53	=	=	SYM
ejpam-4585	271	54	s	s	PROPN
ejpam-4585	271	55	∩	∩	ADJ
ejpam-4585	271	56	v	v	X
ejpam-4585	271	57	(	(	PUNCT
ejpam-4585	271	58	hw	hw	NOUN
ejpam-4585	271	59	)	)	PUNCT
ejpam-4585	271	60	for	for	ADP
ejpam-4585	271	61	all	all	PRON
ejpam-4585	271	62	w	w	PROPN
ejpam-4585	271	63	∈	∈	PROPN
ejpam-4585	271	64	v	v	NOUN
ejpam-4585	271	65	(	(	PUNCT
ejpam-4585	271	66	g)\ng(a	g)\ng(a	NOUN
ejpam-4585	271	67	)	)	PUNCT
ejpam-4585	271	68	.	.	PUNCT
ejpam-4585	272	1	then	then	ADV
ejpam-4585	272	2	s	s	VERB
ejpam-4585	272	3	=	=	PUNCT
ejpam-4585	272	4	a	a	PRON
ejpam-4585	272	5	∪	∪	ADJ
ejpam-4585	272	6			PROPN
ejpam-4585	272	7	⋃	⋃	ADJ
ejpam-4585	272	8	v∈v	v∈v	NOUN
ejpam-4585	272	9	(	(	PUNCT
ejpam-4585	272	10	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4585	272	11	)	)	PUNCT
ejpam-4585	272	12	sv	sv	NOUN
ejpam-4585	273	1			PROPN
ejpam-4585	273	2	∪	∪	VERB
ejpam-4585	273	3			PROPN
ejpam-4585	273	4	⋃	⋃	PROPN
ejpam-4585	273	5	w∈v	w∈v	PROPN
ejpam-4585	273	6	(	(	PUNCT
ejpam-4585	273	7	g)\ng(a	g)\ng(a	NOUN
ejpam-4585	273	8	)	)	PUNCT
ejpam-4585	273	9	dw	dw	NOUN
ejpam-4585	273	10			PROPN
ejpam-4585	273	11	where	where	SCONJ
ejpam-4585	273	12	a	a	DET
ejpam-4585	273	13	⊆	⊆	NUM
ejpam-4585	273	14	v	v	NOUN
ejpam-4585	273	15	(	(	PUNCT
ejpam-4585	273	16	g	g	NOUN
ejpam-4585	273	17	)	)	PUNCT
ejpam-4585	273	18	,	,	PUNCT
ejpam-4585	273	19	sv	sv	PROPN
ejpam-4585	273	20	⊆	⊆	NUM
ejpam-4585	273	21	v	v	X
ejpam-4585	273	22	(	(	PUNCT
ejpam-4585	273	23	hv	hv	PROPN
ejpam-4585	273	24	)	)	PUNCT
ejpam-4585	273	25	and	and	CCONJ
ejpam-4585	273	26	dw	dw	VERB
ejpam-4585	273	27	⊆	⊆	NUM
ejpam-4585	273	28	v	v	NOUN
ejpam-4585	273	29	(	(	PUNCT
ejpam-4585	273	30	hw	hw	NOUN
ejpam-4585	273	31	)	)	PUNCT
ejpam-4585	273	32	.	.	PUNCT
ejpam-4585	274	1	now	now	ADV
ejpam-4585	274	2	,	,	PUNCT
ejpam-4585	274	3	since	since	SCONJ
ejpam-4585	274	4	s	s	PROPN
ejpam-4585	274	5	is	be	AUX
ejpam-4585	274	6	2	2	NUM
ejpam-4585	274	7	-	-	PUNCT
ejpam-4585	274	8	resolving	resolve	VERB
ejpam-4585	274	9	hop	hop	NOUN
ejpam-4585	274	10	dominating	dominating	NOUN
ejpam-4585	274	11	set	set	NOUN
ejpam-4585	274	12	of	of	ADP
ejpam-4585	274	13	g	g	PROPN
ejpam-4585	274	14	◦	◦	PROPN
ejpam-4585	274	15	h.	h.	PROPN
ejpam-4585	274	16	by	by	ADP
ejpam-4585	274	17	theorem	theorem	NOUN
ejpam-4585	274	18	9	9	NUM
ejpam-4585	274	19	,	,	PUNCT
ejpam-4585	274	20	(	(	PUNCT
ejpam-4585	274	21	i	i	NOUN
ejpam-4585	274	22	)	)	PUNCT
ejpam-4585	274	23	holds	hold	VERB
ejpam-4585	274	24	.	.	PUNCT
ejpam-4585	275	1	next	next	ADV
ejpam-4585	275	2	,	,	PUNCT
ejpam-4585	275	3	suppose	suppose	VERB
ejpam-4585	275	4	that	that	SCONJ
ejpam-4585	275	5	sv	sv	PROPN
ejpam-4585	275	6	=	=	NOUN
ejpam-4585	275	7	∅	∅	NOUN
ejpam-4585	275	8	for	for	ADP
ejpam-4585	275	9	some	some	DET
ejpam-4585	275	10	v	v	ADP
ejpam-4585	275	11	∈	∈	NOUN
ejpam-4585	275	12	v	v	NOUN
ejpam-4585	275	13	(	(	PUNCT
ejpam-4585	275	14	g	g	NOUN
ejpam-4585	275	15	)	)	PUNCT
ejpam-4585	275	16	∩	∩	NOUN
ejpam-4585	275	17	ng(a	ng(a	NOUN
ejpam-4585	275	18	)	)	PUNCT
ejpam-4585	275	19	.	.	PUNCT
ejpam-4585	276	1	let	let	VERB
ejpam-4585	276	2	x	x	PRON
ejpam-4585	276	3	,	,	PUNCT
ejpam-4585	276	4	y	y	PROPN
ejpam-4585	276	5	∈	∈	PROPN
ejpam-4585	276	6	v	v	PROPN
ejpam-4585	276	7	(	(	PUNCT
ejpam-4585	276	8	hv	hv	PROPN
ejpam-4585	276	9	)	)	PUNCT
ejpam-4585	276	10	.	.	PUNCT
ejpam-4585	277	1	then	then	ADV
ejpam-4585	277	2	rg	rg	PROPN
ejpam-4585	277	3	◦	◦	PROPN
ejpam-4585	277	4	h(x	h(x	PROPN
ejpam-4585	277	5	/	/	SYM
ejpam-4585	277	6	s	s	PROPN
ejpam-4585	277	7	)	)	PUNCT
ejpam-4585	277	8	=	=	SYM
ejpam-4585	278	1	rg	rg	VERB
ejpam-4585	278	2	◦	◦	NOUN
ejpam-4585	278	3	h(y	h(y	ADV
ejpam-4585	278	4	/	/	SYM
ejpam-4585	278	5	s	s	NOUN
ejpam-4585	278	6	)	)	PUNCT
ejpam-4585	278	7	which	which	PRON
ejpam-4585	278	8	is	be	AUX
ejpam-4585	278	9	a	a	DET
ejpam-4585	278	10	contradiction	contradiction	NOUN
ejpam-4585	278	11	to	to	ADP
ejpam-4585	278	12	the	the	DET
ejpam-4585	278	13	assumption	assumption	NOUN
ejpam-4585	278	14	of	of	ADP
ejpam-4585	278	15	s.	s.	PROPN
ejpam-4585	278	16	thus	thus	ADV
ejpam-4585	278	17	,	,	PUNCT
ejpam-4585	278	18	sv	sv	PROPN
ejpam-4585	278	19	̸=	̸=	PROPN
ejpam-4585	278	20	∅.	∅.	PRON
ejpam-4585	278	21	similarly	similarly	ADV
ejpam-4585	278	22	,	,	PUNCT
ejpam-4585	278	23	dw	dw	PROPN
ejpam-4585	278	24	̸=	̸=	PROPN
ejpam-4585	278	25	∅	∅	NOUN
ejpam-4585	278	26	for	for	ADP
ejpam-4585	278	27	some	some	DET
ejpam-4585	278	28	w	w	PROPN
ejpam-4585	278	29	∈	∈	PROPN
ejpam-4585	278	30	v	v	NOUN
ejpam-4585	278	31	(	(	PUNCT
ejpam-4585	278	32	g)\ng(a	g)\ng(a	NOUN
ejpam-4585	278	33	)	)	PUNCT
ejpam-4585	278	34	.	.	PUNCT
ejpam-4585	279	1	next	next	ADJ
ejpam-4585	279	2	,	,	PUNCT
ejpam-4585	279	3	claim	claim	VERB
ejpam-4585	279	4	that	that	SCONJ
ejpam-4585	279	5	sv	sv	PROPN
ejpam-4585	279	6	is	be	AUX
ejpam-4585	279	7	a	a	DET
ejpam-4585	279	8	2	2	NUM
ejpam-4585	279	9	-	-	PUNCT
ejpam-4585	279	10	locating	locate	VERB
ejpam-4585	279	11	set	set	VERB
ejpam-4585	279	12	inhv	inhv	NOUN
ejpam-4585	279	13	for	for	ADP
ejpam-4585	279	14	each	each	DET
ejpam-4585	279	15	v	v	NUM
ejpam-4585	279	16	∈	∈	PROPN
ejpam-4585	279	17	v	v	NOUN
ejpam-4585	279	18	(	(	PUNCT
ejpam-4585	279	19	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4585	279	20	)	)	PUNCT
ejpam-4585	279	21	.	.	PUNCT
ejpam-4585	280	1	let	let	VERB
ejpam-4585	280	2	p	p	PRON
ejpam-4585	280	3	,	,	PUNCT
ejpam-4585	280	4	q	q	PROPN
ejpam-4585	280	5	∈	∈	PROPN
ejpam-4585	280	6	v	v	NOUN
ejpam-4585	280	7	(	(	PUNCT
ejpam-4585	280	8	hv)\sv	hv)\sv	ADP
ejpam-4585	280	9	where	where	SCONJ
ejpam-4585	280	10	p	p	PROPN
ejpam-4585	280	11	̸=	̸=	PROPN
ejpam-4585	280	12	q.	q.	NOUN
ejpam-4585	280	13	since	since	SCONJ
ejpam-4585	280	14	s	s	PROPN
ejpam-4585	280	15	is	be	AUX
ejpam-4585	280	16	a	a	DET
ejpam-4585	280	17	2	2	NUM
ejpam-4585	280	18	-	-	PUNCT
ejpam-4585	280	19	resolving	resolving	NOUN
ejpam-4585	280	20	set	set	NOUN
ejpam-4585	280	21	in	in	ADP
ejpam-4585	280	22	g	g	PROPN
ejpam-4585	280	23	◦	◦	NOUN
ejpam-4585	280	24	h	h	NOUN
ejpam-4585	280	25	,	,	PUNCT
ejpam-4585	280	26	rg	rg	NOUN
ejpam-4585	280	27	◦	◦	NOUN
ejpam-4585	280	28	h(p	h(p	NOUN
ejpam-4585	280	29	/	/	SYM
ejpam-4585	280	30	s	s	NOUN
ejpam-4585	280	31	)	)	PUNCT
ejpam-4585	280	32	and	and	CCONJ
ejpam-4585	280	33	rg	rg	NOUN
ejpam-4585	280	34	◦	◦	NOUN
ejpam-4585	280	35	h(q	h(q	ADV
ejpam-4585	280	36	/	/	SYM
ejpam-4585	280	37	s	s	X
ejpam-4585	280	38	)	)	PUNCT
ejpam-4585	280	39	differ	differ	VERB
ejpam-4585	280	40	in	in	ADP
ejpam-4585	280	41	at	at	ADV
ejpam-4585	280	42	least	least	ADJ
ejpam-4585	280	43	2	2	NUM
ejpam-4585	280	44	positions	position	NOUN
ejpam-4585	280	45	and	and	CCONJ
ejpam-4585	280	46	by	by	ADP
ejpam-4585	280	47	remark	remark	NOUN
ejpam-4585	280	48	7	7	NUM
ejpam-4585	280	49	,	,	PUNCT
ejpam-4585	280	50	rhv(p	rhv(p	PROPN
ejpam-4585	280	51	/	/	SYM
ejpam-4585	280	52	sv	sv	NOUN
ejpam-4585	280	53	)	)	PUNCT
ejpam-4585	280	54	and	and	CCONJ
ejpam-4585	280	55	rhv(q	rhv(q	PROPN
ejpam-4585	280	56	/	/	SYM
ejpam-4585	280	57	sv	sv	NOUN
ejpam-4585	280	58	)	)	PUNCT
ejpam-4585	280	59	must	must	AUX
ejpam-4585	280	60	differ	differ	VERB
ejpam-4585	280	61	in	in	ADP
ejpam-4585	280	62	at	at	ADV
ejpam-4585	280	63	least	least	ADJ
ejpam-4585	280	64	2	2	NUM
ejpam-4585	280	65	positions	position	NOUN
ejpam-4585	280	66	.	.	PUNCT
ejpam-4585	281	1	thus	thus	ADV
ejpam-4585	281	2	,	,	PUNCT
ejpam-4585	281	3	it	it	PRON
ejpam-4585	281	4	follows	follow	VERB
ejpam-4585	281	5	that	that	SCONJ
ejpam-4585	281	6	sv	sv	PROPN
ejpam-4585	281	7	is	be	AUX
ejpam-4585	281	8	a	a	DET
ejpam-4585	281	9	2	2	NUM
ejpam-4585	281	10	-	-	PUNCT
ejpam-4585	281	11	locating	locate	VERB
ejpam-4585	281	12	set	set	NOUN
ejpam-4585	281	13	of	of	ADP
ejpam-4585	281	14	hv	hv	PROPN
ejpam-4585	281	15	and	and	CCONJ
ejpam-4585	281	16	so	so	ADV
ejpam-4585	281	17	(	(	PUNCT
ejpam-4585	281	18	ii	ii	NOUN
ejpam-4585	281	19	)	)	PUNCT
ejpam-4585	281	20	holds	hold	VERB
ejpam-4585	281	21	.	.	PUNCT
ejpam-4585	282	1	similarly	similarly	ADV
ejpam-4585	282	2	,	,	PUNCT
ejpam-4585	282	3	dw	dw	PROPN
ejpam-4585	282	4	is	be	AUX
ejpam-4585	282	5	a	a	DET
ejpam-4585	282	6	2	2	NUM
ejpam-4585	282	7	-	-	PUNCT
ejpam-4585	282	8	locating	locate	VERB
ejpam-4585	282	9	set	set	NOUN
ejpam-4585	282	10	of	of	ADP
ejpam-4585	282	11	hw	hw	PRON
ejpam-4585	282	12	.	.	PUNCT
ejpam-4585	283	1	now	now	ADV
ejpam-4585	283	2	,	,	PUNCT
ejpam-4585	283	3	since	since	SCONJ
ejpam-4585	283	4	s	s	NOUN
ejpam-4585	283	5	is	be	AUX
ejpam-4585	283	6	a	a	DET
ejpam-4585	283	7	hop	hop	NOUN
ejpam-4585	283	8	dominating	dominating	NOUN
ejpam-4585	283	9	set	set	NOUN
ejpam-4585	283	10	of	of	ADP
ejpam-4585	283	11	g	g	PROPN
ejpam-4585	283	12	◦	◦	NOUN
ejpam-4585	283	13	h	h	NOUN
ejpam-4585	283	14	,	,	PUNCT
ejpam-4585	283	15	theorem	theorem	ADJ
ejpam-4585	283	16	9	9	NUM
ejpam-4585	283	17	follows	follow	VERB
ejpam-4585	283	18	,	,	PUNCT
ejpam-4585	283	19	showing	show	VERB
ejpam-4585	283	20	dw	dw	NOUN
ejpam-4585	283	21	is	be	AUX
ejpam-4585	283	22	a	a	DET
ejpam-4585	283	23	point	point	NOUN
ejpam-4585	283	24	-	-	PUNCT
ejpam-4585	283	25	wise	wise	ADJ
ejpam-4585	283	26	non	non	ADJ
ejpam-4585	283	27	-	-	ADJ
ejpam-4585	283	28	dominating	dominating	ADJ
ejpam-4585	283	29	set	set	NOUN
ejpam-4585	283	30	of	of	ADP
ejpam-4585	283	31	hw	hw	PRON
ejpam-4585	283	32	that	that	PRON
ejpam-4585	283	33	is	is	ADV
ejpam-4585	283	34	(	(	PUNCT
ejpam-4585	283	35	iii	iii	NOUN
ejpam-4585	283	36	)	)	PUNCT
ejpam-4585	283	37	holds	hold	VERB
ejpam-4585	283	38	.	.	PUNCT
ejpam-4585	284	1	conversely	conversely	ADV
ejpam-4585	284	2	,	,	PUNCT
ejpam-4585	284	3	let	let	VERB
ejpam-4585	284	4	s	s	VERB
ejpam-4585	284	5	=	=	NOUN
ejpam-4585	284	6	a	a	DET
ejpam-4585	284	7	∪	∪	X
ejpam-4585	284	8	(	(	PUNCT
ejpam-4585	284	9	⋃	⋃	NOUN
ejpam-4585	284	10	v∈v	v∈v	NOUN
ejpam-4585	284	11	(	(	PUNCT
ejpam-4585	284	12	g)∩ng(a	g)∩ng(a	PROPN
ejpam-4585	284	13	)	)	PUNCT
ejpam-4585	284	14	sv	sv	NOUN
ejpam-4585	284	15	)	)	PUNCT
ejpam-4585	284	16	∪	∪	PROPN
ejpam-4585	284	17	(	(	PUNCT
ejpam-4585	284	18	⋃	⋃	PROPN
ejpam-4585	284	19	w∈v	w∈v	PROPN
ejpam-4585	284	20	(	(	PUNCT
ejpam-4585	284	21	g)\ng(a	g)\ng(a	NOUN
ejpam-4585	284	22	)	)	PUNCT
ejpam-4585	284	23	dw	dw	NOUN
ejpam-4585	284	24	)	)	PUNCT
ejpam-4585	284	25	where	where	SCONJ
ejpam-4585	284	26	a	a	DET
ejpam-4585	284	27	⊆	⊆	NUM
ejpam-4585	284	28	v	v	NOUN
ejpam-4585	284	29	(	(	PUNCT
ejpam-4585	284	30	g	g	NOUN
ejpam-4585	284	31	)	)	PUNCT
ejpam-4585	284	32	,	,	PUNCT
ejpam-4585	284	33	sv	sv	PROPN
ejpam-4585	284	34	⊆	⊆	NUM
ejpam-4585	284	35	v	v	X
ejpam-4585	284	36	(	(	PUNCT
ejpam-4585	284	37	hv	hv	PROPN
ejpam-4585	284	38	)	)	PUNCT
ejpam-4585	284	39	and	and	CCONJ
ejpam-4585	284	40	dw	dw	VERB
ejpam-4585	284	41	⊆	⊆	NUM
ejpam-4585	284	42	v	v	NOUN
ejpam-4585	284	43	(	(	PUNCT
ejpam-4585	284	44	hw	hw	NOUN
ejpam-4585	284	45	)	)	PUNCT
ejpam-4585	284	46	satisfying	satisfy	VERB
ejpam-4585	284	47	the	the	DET
ejpam-4585	284	48	given	give	VERB
ejpam-4585	284	49	conditions	condition	NOUN
ejpam-4585	284	50	.	.	PUNCT
ejpam-4585	285	1	let	let	VERB
ejpam-4585	285	2	x	x	SYM
ejpam-4585	285	3	∈	∈	PROPN
ejpam-4585	285	4	v	v	X
ejpam-4585	285	5	(	(	PUNCT
ejpam-4585	285	6	g	g	PROPN
ejpam-4585	285	7	◦	◦	NOUN
ejpam-4585	285	8	h)\s	h)\s	NOUN
ejpam-4585	285	9	and	and	CCONJ
ejpam-4585	285	10	let	let	VERB
ejpam-4585	285	11	v	v	NUM
ejpam-4585	285	12	∈	∈	PROPN
ejpam-4585	285	13	v	v	NOUN
ejpam-4585	285	14	(	(	PUNCT
ejpam-4585	285	15	g	g	NOUN
ejpam-4585	285	16	)	)	PUNCT
ejpam-4585	285	17	such	such	ADJ
ejpam-4585	285	18	that	that	SCONJ
ejpam-4585	285	19	x	x	SYM
ejpam-4585	285	20	∈	∈	PROPN
ejpam-4585	285	21	v	v	NOUN
ejpam-4585	285	22	(	(	PUNCT
ejpam-4585	285	23	v+hv	v+hv	NOUN
ejpam-4585	285	24	)	)	PUNCT
ejpam-4585	285	25	.	.	PUNCT
ejpam-4585	286	1	suppose	suppose	VERB
ejpam-4585	286	2	x	x	PUNCT
ejpam-4585	287	1	=	=	PUNCT
ejpam-4585	287	2	v.	v.	CCONJ
ejpam-4585	287	3	then	then	ADV
ejpam-4585	287	4	x	x	X
ejpam-4585	287	5	/∈	/∈	PUNCT
ejpam-4585	287	6	a.	a.	NOUN
ejpam-4585	287	7	from	from	ADP
ejpam-4585	287	8	the	the	DET
ejpam-4585	287	9	assumption	assumption	NOUN
ejpam-4585	287	10	that	that	SCONJ
ejpam-4585	287	11	(	(	PUNCT
ejpam-4585	287	12	i	i	NOUN
ejpam-4585	287	13	)	)	PUNCT
ejpam-4585	287	14	holds	hold	VERB
ejpam-4585	287	15	,	,	PUNCT
ejpam-4585	287	16	it	it	PRON
ejpam-4585	287	17	follows	follow	VERB
ejpam-4585	287	18	that	that	SCONJ
ejpam-4585	287	19	there	there	PRON
ejpam-4585	287	20	exists	exist	VERB
ejpam-4585	287	21	y	y	PROPN
ejpam-4585	287	22	∈	∈	PROPN
ejpam-4585	287	23	s	s	VERB
ejpam-4585	287	24	such	such	ADJ
ejpam-4585	287	25	that	that	SCONJ
ejpam-4585	288	1	dg	dg	AUX
ejpam-4585	288	2	◦	◦	NOUN
ejpam-4585	288	3	h(x	h(x	PROPN
ejpam-4585	288	4	,	,	PUNCT
ejpam-4585	288	5	y	y	PROPN
ejpam-4585	288	6	)	)	PUNCT
ejpam-4585	289	1	=	=	SYM
ejpam-4585	289	2	2	2	X
ejpam-4585	289	3	.	.	PUNCT
ejpam-4585	290	1	next	next	ADV
ejpam-4585	290	2	,	,	PUNCT
ejpam-4585	290	3	suppose	suppose	VERB
ejpam-4585	290	4	x	x	PUNCT
ejpam-4585	290	5	̸=	̸=	PROPN
ejpam-4585	290	6	v.	v.	ADV
ejpam-4585	290	7	if	if	SCONJ
ejpam-4585	290	8	v	v	NOUN
ejpam-4585	290	9	∈	∈	PROPN
ejpam-4585	290	10	ng(a	ng(a	NOUN
ejpam-4585	290	11	)	)	PUNCT
ejpam-4585	290	12	,	,	PUNCT
ejpam-4585	290	13	then	then	ADV
ejpam-4585	290	14	there	there	PRON
ejpam-4585	290	15	exists	exist	VERB
ejpam-4585	290	16	a	a	DET
ejpam-4585	290	17	vertex	vertex	NOUN
ejpam-4585	290	18	say	say	VERB
ejpam-4585	290	19	z	z	NOUN
ejpam-4585	290	20	∈	∈	PROPN
ejpam-4585	290	21	a	a	DET
ejpam-4585	290	22	∩	∩	NOUN
ejpam-4585	290	23	ng(v	ng(v	NOUN
ejpam-4585	290	24	)	)	PUNCT
ejpam-4585	290	25	such	such	ADJ
ejpam-4585	290	26	that	that	SCONJ
ejpam-4585	290	27	z	z	PROPN
ejpam-4585	290	28	∈	∈	PROPN
ejpam-4585	290	29	s	s	PART
ejpam-4585	290	30	and	and	CCONJ
ejpam-4585	290	31	dg	dg	NOUN
ejpam-4585	290	32	◦	◦	NOUN
ejpam-4585	290	33	h(x	h(x	PROPN
ejpam-4585	290	34	,	,	PUNCT
ejpam-4585	290	35	z	z	NOUN
ejpam-4585	290	36	)	)	PUNCT
ejpam-4585	290	37	=	=	SYM
ejpam-4585	290	38	2	2	X
ejpam-4585	290	39	.	.	PUNCT
ejpam-4585	290	40	suppose	suppose	VERB
ejpam-4585	290	41	v	v	X
ejpam-4585	290	42	/∈	/∈	PUNCT
ejpam-4585	290	43	ng(a	ng(a	NUM
ejpam-4585	290	44	)	)	PUNCT
ejpam-4585	290	45	.	.	PUNCT
ejpam-4585	291	1	then	then	ADV
ejpam-4585	291	2	x	x	SYM
ejpam-4585	291	3	∈	∈	PROPN
ejpam-4585	291	4	v	v	X
ejpam-4585	291	5	(	(	PUNCT
ejpam-4585	291	6	hv)\dv	hv)\dv	NOUN
ejpam-4585	291	7	.	.	PUNCT
ejpam-4585	292	1	since	since	SCONJ
ejpam-4585	292	2	dv	dv	PROPN
ejpam-4585	292	3	is	be	AUX
ejpam-4585	292	4	point	point	ADV
ejpam-4585	292	5	-	-	PUNCT
ejpam-4585	292	6	wise	wise	ADJ
ejpam-4585	292	7	non	non	ADJ
ejpam-4585	292	8	-	-	ADJ
ejpam-4585	292	9	dominating	dominating	NOUN
ejpam-4585	292	10	by	by	ADP
ejpam-4585	292	11	theorem	theorem	NOUN
ejpam-4585	292	12	9	9	NUM
ejpam-4585	292	13	,	,	PUNCT
ejpam-4585	292	14	it	it	PRON
ejpam-4585	292	15	follows	follow	VERB
ejpam-4585	292	16	that	that	SCONJ
ejpam-4585	292	17	there	there	PRON
ejpam-4585	292	18	exists	exist	VERB
ejpam-4585	292	19	y	y	PROPN
ejpam-4585	292	20	∈	∈	PROPN
ejpam-4585	292	21	dv	dv	PROPN
ejpam-4585	292	22	,	,	PUNCT
ejpam-4585	292	23	that	that	PRON
ejpam-4585	292	24	is	be	AUX
ejpam-4585	292	25	y	y	PROPN
ejpam-4585	292	26	∈	∈	PROPN
ejpam-4585	292	27	s	s	VERB
ejpam-4585	292	28	such	such	ADJ
ejpam-4585	292	29	that	that	SCONJ
ejpam-4585	293	1	dg	dg	AUX
ejpam-4585	293	2	◦	◦	NOUN
ejpam-4585	293	3	h(x	h(x	PROPN
ejpam-4585	293	4	,	,	PUNCT
ejpam-4585	293	5	y	y	PROPN
ejpam-4585	293	6	)	)	PUNCT
ejpam-4585	294	1	=	=	SYM
ejpam-4585	294	2	2	2	X
ejpam-4585	294	3	.	.	PUNCT
ejpam-4585	295	1	this	this	PRON
ejpam-4585	295	2	shows	show	VERB
ejpam-4585	295	3	that	that	SCONJ
ejpam-4585	295	4	s	s	VERB
ejpam-4585	295	5	is	be	AUX
ejpam-4585	295	6	a	a	DET
ejpam-4585	295	7	hop	hop	NOUN
ejpam-4585	295	8	dominating	dominating	NOUN
ejpam-4585	295	9	set	set	NOUN
ejpam-4585	295	10	of	of	ADP
ejpam-4585	295	11	g	g	PROPN
ejpam-4585	295	12	◦	◦	NOUN
ejpam-4585	295	13	h.	h.	PROPN
ejpam-4585	295	14	since	since	SCONJ
ejpam-4585	295	15	sv	sv	PROPN
ejpam-4585	295	16	or	or	CCONJ
ejpam-4585	295	17	dv	dv	PROPN
ejpam-4585	295	18	is	be	AUX
ejpam-4585	295	19	a	a	DET
ejpam-4585	295	20	a.m.	a.m.	NOUN
ejpam-4585	295	21	mahistrado	mahistrado	NOUN
ejpam-4585	295	22	,	,	PUNCT
ejpam-4585	295	23	h.	h.	PROPN
ejpam-4585	295	24	rara	rara	PROPN
ejpam-4585	295	25	/	/	SYM
ejpam-4585	295	26	eur	eur	PROPN
ejpam-4585	295	27	.	.	PUNCT
ejpam-4585	296	1	j.	j.	PROPN
ejpam-4585	296	2	pure	pure	PROPN
ejpam-4585	296	3	appl	appl	PROPN
ejpam-4585	296	4	.	.	PROPN
ejpam-4585	296	5	math	math	PROPN
ejpam-4585	296	6	,	,	PUNCT
ejpam-4585	296	7	15	15	NUM
ejpam-4585	296	8	(	(	PUNCT
ejpam-4585	296	9	4	4	NUM
ejpam-4585	296	10	)	)	PUNCT
ejpam-4585	296	11	(	(	PUNCT
ejpam-4585	296	12	2022	2022	NUM
ejpam-4585	296	13	)	)	PUNCT
ejpam-4585	296	14	,	,	PUNCT
ejpam-4585	296	15	1982	1982	NUM
ejpam-4585	296	16	-	-	SYM
ejpam-4585	296	17	1997	1997	NUM
ejpam-4585	296	18	1993	1993	NUM
ejpam-4585	296	19	2	2	NUM
ejpam-4585	296	20	-	-	PUNCT
ejpam-4585	296	21	locating	locate	VERB
ejpam-4585	296	22	set	set	NOUN
ejpam-4585	296	23	of	of	ADP
ejpam-4585	296	24	g	g	PROPN
ejpam-4585	296	25	◦	◦	NOUN
ejpam-4585	296	26	h	h	NOUN
ejpam-4585	296	27	,	,	PUNCT
ejpam-4585	296	28	by	by	ADP
ejpam-4585	296	29	our	our	PRON
ejpam-4585	296	30	assumption	assumption	NOUN
ejpam-4585	296	31	.	.	PUNCT
ejpam-4585	297	1	by	by	ADP
ejpam-4585	297	2	remark	remark	NOUN
ejpam-4585	297	3	1	1	NUM
ejpam-4585	297	4	,	,	PUNCT
ejpam-4585	297	5	it	it	PRON
ejpam-4585	297	6	then	then	ADV
ejpam-4585	297	7	follows	follow	VERB
ejpam-4585	297	8	that	that	SCONJ
ejpam-4585	297	9	sv	sv	PROPN
ejpam-4585	297	10	or	or	CCONJ
ejpam-4585	297	11	dv	dv	PROPN
ejpam-4585	297	12	is	be	AUX
ejpam-4585	297	13	a	a	DET
ejpam-4585	297	14	2	2	NUM
ejpam-4585	297	15	-	-	PUNCT
ejpam-4585	297	16	resolving	resolve	VERB
ejpam-4585	297	17	set	set	NOUN
ejpam-4585	297	18	of	of	ADP
ejpam-4585	297	19	g	g	PROPN
ejpam-4585	297	20	◦	◦	NOUN
ejpam-4585	297	21	h.	h.	NOUN
ejpam-4585	297	22	accordingly	accordingly	ADV
ejpam-4585	297	23	,	,	PUNCT
ejpam-4585	297	24	s	s	VERB
ejpam-4585	297	25	is	be	AUX
ejpam-4585	297	26	a	a	DET
ejpam-4585	297	27	2	2	NUM
ejpam-4585	297	28	-	-	PUNCT
ejpam-4585	297	29	resolving	resolve	VERB
ejpam-4585	297	30	hop	hop	NOUN
ejpam-4585	297	31	dominating	dominating	NOUN
ejpam-4585	297	32	set	set	NOUN
ejpam-4585	297	33	of	of	ADP
ejpam-4585	297	34	g	g	PROPN
ejpam-4585	297	35	◦	◦	NOUN
ejpam-4585	297	36	h.	h.	NOUN
ejpam-4585	297	37	corollary	corollary	ADJ
ejpam-4585	297	38	5	5	PROPN
ejpam-4585	297	39	.	.	PUNCT
ejpam-4585	298	1	let	let	VERB
ejpam-4585	298	2	g	g	PRON
ejpam-4585	298	3	be	be	AUX
ejpam-4585	298	4	a	a	DET
ejpam-4585	298	5	nontrivial	nontrivial	ADJ
ejpam-4585	298	6	graph	graph	NOUN
ejpam-4585	298	7	of	of	ADP
ejpam-4585	298	8	order	order	NOUN
ejpam-4585	298	9	n	n	NOUN
ejpam-4585	299	1	and	and	CCONJ
ejpam-4585	299	2	h	h	NOUN
ejpam-4585	299	3	be	be	AUX
ejpam-4585	299	4	any	any	DET
ejpam-4585	299	5	graph	graph	NOUN
ejpam-4585	299	6	.	.	PUNCT
ejpam-4585	300	1	then	then	ADV
ejpam-4585	300	2	the	the	DET
ejpam-4585	300	3	following	follow	VERB
ejpam-4585	300	4	statements	statement	NOUN
ejpam-4585	300	5	hold	hold	VERB
ejpam-4585	300	6	.	.	PUNCT
ejpam-4585	301	1	(	(	PUNCT
ejpam-4585	301	2	i	i	NOUN
ejpam-4585	301	3	)	)	PUNCT
ejpam-4585	301	4	γ2rh(g	γ2rh(g	VERB
ejpam-4585	301	5	◦	◦	NOUN
ejpam-4585	301	6	h	h	NOUN
ejpam-4585	301	7	)	)	PUNCT
ejpam-4585	301	8	≤	≤	NUM
ejpam-4585	301	9	n(1	n(1	NOUN
ejpam-4585	301	10	+	+	CCONJ
ejpam-4585	301	11	ln2(h	ln2(h	PROPN
ejpam-4585	301	12	)	)	PUNCT
ejpam-4585	301	13	)	)	PUNCT
ejpam-4585	301	14	.	.	PUNCT
ejpam-4585	302	1	(	(	PUNCT
ejpam-4585	302	2	ii	ii	NOUN
ejpam-4585	302	3	)	)	PUNCT
ejpam-4585	302	4	if	if	SCONJ
ejpam-4585	302	5	lnpnd	lnpnd	ADJ
ejpam-4585	302	6	2	2	NUM
ejpam-4585	302	7	(	(	PUNCT
ejpam-4585	302	8	h	h	NOUN
ejpam-4585	302	9	)	)	PUNCT
ejpam-4585	302	10	=	=	SYM
ejpam-4585	302	11	ln2(h	ln2(h	PROPN
ejpam-4585	302	12	)	)	PUNCT
ejpam-4585	302	13	,	,	PUNCT
ejpam-4585	302	14	then	then	ADV
ejpam-4585	302	15	γ2rh(g	γ2rh(g	VERB
ejpam-4585	302	16	◦	◦	NOUN
ejpam-4585	302	17	h	h	NOUN
ejpam-4585	302	18	)	)	PUNCT
ejpam-4585	302	19	=	=	SYM
ejpam-4585	302	20	n(lnpnd	n(lnpnd	NOUN
ejpam-4585	302	21	2	2	NUM
ejpam-4585	302	22	(	(	PUNCT
ejpam-4585	302	23	h	h	NOUN
ejpam-4585	302	24	)	)	PUNCT
ejpam-4585	302	25	)	)	PUNCT
ejpam-4585	302	26	.	.	PUNCT
ejpam-4585	303	1	proof	proof	NOUN
ejpam-4585	303	2	.	.	PUNCT
ejpam-4585	304	1	(	(	PUNCT
ejpam-4585	304	2	i	i	NOUN
ejpam-4585	304	3	)	)	PUNCT
ejpam-4585	304	4	let	let	VERB
ejpam-4585	304	5	a	a	DET
ejpam-4585	304	6	=	=	X
ejpam-4585	304	7	v	v	X
ejpam-4585	304	8	(	(	PUNCT
ejpam-4585	304	9	g	g	NOUN
ejpam-4585	304	10	)	)	PUNCT
ejpam-4585	304	11	and	and	CCONJ
ejpam-4585	304	12	let	let	VERB
ejpam-4585	304	13	sv	sv	INTJ
ejpam-4585	304	14	be	be	AUX
ejpam-4585	304	15	a	a	DET
ejpam-4585	304	16	2	2	NUM
ejpam-4585	304	17	-	-	PUNCT
ejpam-4585	304	18	locating	locate	VERB
ejpam-4585	304	19	set	set	NOUN
ejpam-4585	304	20	of	of	ADP
ejpam-4585	304	21	hv	hv	PROPN
ejpam-4585	304	22	for	for	ADP
ejpam-4585	304	23	all	all	DET
ejpam-4585	304	24	v	v	ADP
ejpam-4585	304	25	∈	∈	NUM
ejpam-4585	304	26	v	v	NOUN
ejpam-4585	304	27	(	(	PUNCT
ejpam-4585	304	28	g	g	NOUN
ejpam-4585	304	29	)	)	PUNCT
ejpam-4585	304	30	.	.	PUNCT
ejpam-4585	305	1	then	then	ADV
ejpam-4585	305	2	s	s	VERB
ejpam-4585	305	3	=	=	SYM
ejpam-4585	305	4	a∪	a∪	PROPN
ejpam-4585	305	5	(	(	PUNCT
ejpam-4585	305	6	⋃	⋃	NOUN
ejpam-4585	305	7	v∈v	v∈v	NOUN
ejpam-4585	305	8	(	(	PUNCT
ejpam-4585	305	9	g	g	NOUN
ejpam-4585	305	10	)	)	PUNCT
ejpam-4585	305	11	sv	sv	NOUN
ejpam-4585	305	12	)	)	PUNCT
ejpam-4585	305	13	is	be	AUX
ejpam-4585	305	14	a	a	DET
ejpam-4585	305	15	2	2	NUM
ejpam-4585	305	16	-	-	PUNCT
ejpam-4585	305	17	resolving	resolve	VERB
ejpam-4585	305	18	hop	hop	NOUN
ejpam-4585	305	19	dominating	dominating	NOUN
ejpam-4585	305	20	set	set	NOUN
ejpam-4585	305	21	of	of	ADP
ejpam-4585	305	22	g	g	PROPN
ejpam-4585	305	23	◦	◦	NOUN
ejpam-4585	305	24	h	h	NOUN
ejpam-4585	305	25	by	by	ADP
ejpam-4585	305	26	theorem	theorem	NOUN
ejpam-4585	305	27	10	10	NUM
ejpam-4585	305	28	.	.	PUNCT
ejpam-4585	306	1	hence	hence	ADV
ejpam-4585	306	2	,	,	PUNCT
ejpam-4585	306	3	γ2rh(g	γ2rh(g	VERB
ejpam-4585	306	4	◦	◦	NOUN
ejpam-4585	306	5	h	h	NOUN
ejpam-4585	306	6	)	)	PUNCT
ejpam-4585	306	7	≤	≤	NUM
ejpam-4585	306	8	|s|	|s|	PROPN
ejpam-4585	306	9	=	=	SYM
ejpam-4585	306	10	|v	|v	X
ejpam-4585	306	11	(	(	PUNCT
ejpam-4585	306	12	g)|+	g)|+	PROPN
ejpam-4585	306	13	|v	|v	PROPN
ejpam-4585	306	14	(	(	PUNCT
ejpam-4585	306	15	g)||sv|	g)||sv|	NOUN
ejpam-4585	306	16	=	=	SYM
ejpam-4585	306	17	n(1	n(1	PROPN
ejpam-4585	306	18	+	+	CCONJ
ejpam-4585	306	19	ln2(h	ln2(h	PROPN
ejpam-4585	306	20	)	)	PUNCT
ejpam-4585	306	21	)	)	PUNCT
ejpam-4585	306	22	.	.	PUNCT
ejpam-4585	307	1	(	(	PUNCT
ejpam-4585	307	2	ii	ii	NOUN
ejpam-4585	307	3	)	)	PUNCT
ejpam-4585	307	4	suppose	suppose	VERB
ejpam-4585	307	5	that	that	SCONJ
ejpam-4585	307	6	lnpnd	lnpnd	ADJ
ejpam-4585	307	7	2	2	NUM
ejpam-4585	307	8	(	(	PUNCT
ejpam-4585	307	9	h	h	NOUN
ejpam-4585	307	10	)	)	PUNCT
ejpam-4585	307	11	=	=	SYM
ejpam-4585	307	12	ln2(h	ln2(h	PROPN
ejpam-4585	307	13	)	)	PUNCT
ejpam-4585	307	14	.	.	PUNCT
ejpam-4585	308	1	now	now	ADV
ejpam-4585	308	2	,	,	PUNCT
ejpam-4585	308	3	set	set	VERB
ejpam-4585	308	4	a	a	DET
ejpam-4585	308	5	=	=	NOUN
ejpam-4585	308	6	∅	∅	NOUN
ejpam-4585	308	7	and	and	CCONJ
ejpam-4585	308	8	let	let	VERB
ejpam-4585	308	9	dw	dw	PART
ejpam-4585	308	10	be	be	AUX
ejpam-4585	308	11	a	a	DET
ejpam-4585	308	12	2	2	NUM
ejpam-4585	308	13	-	-	PUNCT
ejpam-4585	308	14	locating	locate	VERB
ejpam-4585	308	15	point	point	NOUN
ejpam-4585	308	16	-	-	PUNCT
ejpam-4585	308	17	wise	wise	ADJ
ejpam-4585	308	18	non	non	ADJ
ejpam-4585	308	19	-	-	ADJ
ejpam-4585	308	20	dominating	dominating	ADJ
ejpam-4585	308	21	set	set	NOUN
ejpam-4585	308	22	of	of	ADP
ejpam-4585	308	23	hw	hw	PRON
ejpam-4585	308	24	for	for	ADP
ejpam-4585	308	25	all	all	DET
ejpam-4585	308	26	w	w	PROPN
ejpam-4585	308	27	∈	∈	PROPN
ejpam-4585	308	28	v	v	ADP
ejpam-4585	308	29	(	(	PUNCT
ejpam-4585	308	30	g	g	NOUN
ejpam-4585	308	31	)	)	PUNCT
ejpam-4585	308	32	.	.	PUNCT
ejpam-4585	309	1	then	then	ADV
ejpam-4585	309	2	s	s	VERB
ejpam-4585	309	3	=	=	PUNCT
ejpam-4585	309	4	a	a	DET
ejpam-4585	309	5	∪	∪	X
ejpam-4585	309	6	(	(	PUNCT
ejpam-4585	309	7	⋃	⋃	PROPN
ejpam-4585	309	8	w∈v	w∈v	PROPN
ejpam-4585	309	9	(	(	PUNCT
ejpam-4585	309	10	g	g	NOUN
ejpam-4585	309	11	)	)	PUNCT
ejpam-4585	309	12	dw	dw	PROPN
ejpam-4585	309	13	)	)	PUNCT
ejpam-4585	309	14	is	be	AUX
ejpam-4585	309	15	a	a	DET
ejpam-4585	309	16	2	2	NUM
ejpam-4585	309	17	-	-	PUNCT
ejpam-4585	309	18	resolving	resolve	VERB
ejpam-4585	309	19	hop	hop	NOUN
ejpam-4585	309	20	dominating	dominating	NOUN
ejpam-4585	309	21	set	set	VERB
ejpam-4585	309	22	by	by	ADP
ejpam-4585	309	23	theorem	theorem	NOUN
ejpam-4585	309	24	10	10	NUM
ejpam-4585	309	25	.	.	PUNCT
ejpam-4585	310	1	hence	hence	ADV
ejpam-4585	310	2	,	,	PUNCT
ejpam-4585	310	3	γ2rh(g	γ2rh(g	VERB
ejpam-4585	310	4	◦	◦	NOUN
ejpam-4585	310	5	h	h	NOUN
ejpam-4585	310	6	)	)	PUNCT
ejpam-4585	310	7	≤	≤	NUM
ejpam-4585	310	8	|s|	|s|	NOUN
ejpam-4585	310	9	=	=	SYM
ejpam-4585	310	10	|a|+	|a|+	NOUN
ejpam-4585	310	11	|v	|v	X
ejpam-4585	310	12	(	(	PUNCT
ejpam-4585	310	13	g)||dw|	g)||dw|	NOUN
ejpam-4585	310	14	=	=	PUNCT
ejpam-4585	310	15	n(lnpnd	n(lnpnd	NOUN
ejpam-4585	310	16	2	2	NUM
ejpam-4585	310	17	(	(	PUNCT
ejpam-4585	310	18	h	h	NOUN
ejpam-4585	310	19	)	)	PUNCT
ejpam-4585	310	20	)	)	PUNCT
ejpam-4585	310	21	.	.	PUNCT
ejpam-4585	311	1	next	next	ADV
ejpam-4585	311	2	,	,	PUNCT
ejpam-4585	311	3	let	let	VERB
ejpam-4585	311	4	s0	s0	PROPN
ejpam-4585	311	5	=	=	SYM
ejpam-4585	311	6	a0	a0	PROPN
ejpam-4585	311	7	∪	∪	X
ejpam-4585	311	8	(	(	PUNCT
ejpam-4585	311	9	⋃	⋃	ADJ
ejpam-4585	311	10	v∈v	v∈v	NOUN
ejpam-4585	311	11	(	(	PUNCT
ejpam-4585	311	12	g)\c0	g)\c0	PROPN
ejpam-4585	311	13	sv	sv	PROPN
ejpam-4585	311	14	)	)	PUNCT
ejpam-4585	311	15	∪	∪	ADV
ejpam-4585	311	16	(	(	PUNCT
ejpam-4585	311	17	⋃	⋃	PROPN
ejpam-4585	311	18	w∈c0	w∈c0	NOUN
ejpam-4585	311	19	dw	dw	PROPN
ejpam-4585	311	20	)	)	PUNCT
ejpam-4585	311	21	be	be	AUX
ejpam-4585	311	22	a	a	DET
ejpam-4585	311	23	2	2	NUM
ejpam-4585	311	24	-	-	PUNCT
ejpam-4585	311	25	resolving	resolve	VERB
ejpam-4585	311	26	hop	hop	NOUN
ejpam-4585	311	27	dominating	dominating	NOUN
ejpam-4585	311	28	set	set	NOUN
ejpam-4585	311	29	of	of	ADP
ejpam-4585	311	30	g	g	PROPN
ejpam-4585	311	31	◦	◦	PROPN
ejpam-4585	311	32	h.	h.	PROPN
ejpam-4585	311	33	by	by	ADP
ejpam-4585	311	34	theorem	theorem	NOUN
ejpam-4585	311	35	10	10	NUM
ejpam-4585	311	36	,	,	PUNCT
ejpam-4585	311	37	a0	a0	NOUN
ejpam-4585	311	38	⊆	⊆	NUM
ejpam-4585	311	39	v	v	NOUN
ejpam-4585	311	40	(	(	PUNCT
ejpam-4585	311	41	g	g	NOUN
ejpam-4585	311	42	)	)	PUNCT
ejpam-4585	311	43	where	where	SCONJ
ejpam-4585	311	44	c0	c0	NOUN
ejpam-4585	311	45	=	=	PUNCT
ejpam-4585	311	46	{	{	PUNCT
ejpam-4585	311	47	x	x	PROPN
ejpam-4585	311	48	∈	∈	PROPN
ejpam-4585	311	49	v	v	NOUN
ejpam-4585	311	50	(	(	PUNCT
ejpam-4585	311	51	g	g	NOUN
ejpam-4585	311	52	)	)	PUNCT
ejpam-4585	311	53	:	:	PUNCT
ejpam-4585	312	1	x	x	X
ejpam-4585	312	2	/∈	/∈	PUNCT
ejpam-4585	312	3	ng(a0	ng(a0	NOUN
ejpam-4585	312	4	)	)	PUNCT
ejpam-4585	312	5	}	}	PUNCT
ejpam-4585	312	6	,	,	PUNCT
ejpam-4585	312	7	sv	sv	PROPN
ejpam-4585	312	8	is	be	AUX
ejpam-4585	312	9	a	a	DET
ejpam-4585	312	10	2locating	2locating	NUM
ejpam-4585	312	11	set	set	NOUN
ejpam-4585	312	12	of	of	ADP
ejpam-4585	312	13	hv	hv	NOUN
ejpam-4585	312	14	for	for	ADP
ejpam-4585	312	15	all	all	DET
ejpam-4585	312	16	v	v	ADP
ejpam-4585	312	17	∈	∈	NOUN
ejpam-4585	312	18	v	v	NOUN
ejpam-4585	312	19	(	(	PUNCT
ejpam-4585	312	20	g)\c0	g)\c0	PROPN
ejpam-4585	312	21	and	and	CCONJ
ejpam-4585	312	22	dw	dw	PROPN
ejpam-4585	312	23	is	be	AUX
ejpam-4585	312	24	a	a	DET
ejpam-4585	312	25	2	2	NUM
ejpam-4585	312	26	-	-	PUNCT
ejpam-4585	312	27	locating	locate	VERB
ejpam-4585	312	28	point	point	NOUN
ejpam-4585	312	29	-	-	PUNCT
ejpam-4585	312	30	wise	wise	ADJ
ejpam-4585	312	31	non	non	ADJ
ejpam-4585	312	32	-	-	ADJ
ejpam-4585	312	33	dominating	dominating	ADJ
ejpam-4585	312	34	set	set	NOUN
ejpam-4585	312	35	of	of	ADP
ejpam-4585	312	36	hw	hw	PRON
ejpam-4585	312	37	for	for	ADP
ejpam-4585	312	38	all	all	DET
ejpam-4585	312	39	w	w	PROPN
ejpam-4585	312	40	∈	∈	PROPN
ejpam-4585	312	41	c0	c0	NOUN
ejpam-4585	312	42	.	.	PUNCT
ejpam-4585	313	1	thus	thus	ADV
ejpam-4585	313	2	,	,	PUNCT
ejpam-4585	313	3	we	we	PRON
ejpam-4585	313	4	can	can	AUX
ejpam-4585	313	5	write	write	VERB
ejpam-4585	313	6	this	this	PRON
ejpam-4585	313	7	as	as	ADP
ejpam-4585	313	8	γ2rh(g	γ2rh(g	NOUN
ejpam-4585	313	9	◦	◦	NOUN
ejpam-4585	313	10	h	h	NOUN
ejpam-4585	313	11	)	)	PUNCT
ejpam-4585	313	12	=	=	PUNCT
ejpam-4585	313	13	|s|	|s|	NOUN
ejpam-4585	313	14	(	(	PUNCT
ejpam-4585	313	15	1	1	NUM
ejpam-4585	313	16	)	)	PUNCT
ejpam-4585	313	17	=	=	PUNCT
ejpam-4585	314	1	|a|+	|a|+	VERB
ejpam-4585	314	2	|v	|v	X
ejpam-4585	314	3	(	(	PUNCT
ejpam-4585	314	4	g)\c0||sv|+	g)\c0||sv|+	PROPN
ejpam-4585	314	5	|c0||dw|	|c0||dw|	VERB
ejpam-4585	314	6	≥	≥	NUM
ejpam-4585	314	7	|v	|v	X
ejpam-4585	314	8	(	(	PUNCT
ejpam-4585	314	9	g)\c0|ln2(h	g)\c0|ln2(h	PROPN
ejpam-4585	314	10	)	)	PUNCT
ejpam-4585	314	11	+	+	CCONJ
ejpam-4585	314	12	|c0|lnpnd2	|c0|lnpnd2	PROPN
ejpam-4585	314	13	(	(	PUNCT
ejpam-4585	314	14	h	h	NOUN
ejpam-4585	314	15	)	)	PUNCT
ejpam-4585	314	16	=	=	SYM
ejpam-4585	314	17	(	(	PUNCT
ejpam-4585	314	18	|v	|v	X
ejpam-4585	314	19	(	(	PUNCT
ejpam-4585	314	20	g)|	g)|	NOUN
ejpam-4585	314	21	−	−	PROPN
ejpam-4585	314	22	|c0|)ln2(h	|c0|)ln2(h	NOUN
ejpam-4585	314	23	)	)	PUNCT
ejpam-4585	314	24	+	+	CCONJ
ejpam-4585	314	25	|c0|lnpnd2	|c0|lnpnd2	PROPN
ejpam-4585	314	26	(	(	PUNCT
ejpam-4585	314	27	h	h	NOUN
ejpam-4585	314	28	)	)	PUNCT
ejpam-4585	314	29	=	=	SYM
ejpam-4585	314	30	(	(	PUNCT
ejpam-4585	314	31	|v	|v	X
ejpam-4585	314	32	(	(	PUNCT
ejpam-4585	314	33	g)|	g)|	PROPN
ejpam-4585	314	34	−	−	PROPN
ejpam-4585	314	35	|c0|)lnpnd2	|c0|)lnpnd2	NOUN
ejpam-4585	314	36	(	(	PUNCT
ejpam-4585	314	37	h	h	NOUN
ejpam-4585	314	38	)	)	PUNCT
ejpam-4585	314	39	+	+	CCONJ
ejpam-4585	314	40	|c0|lnpnd2	|c0|lnpnd2	PROPN
ejpam-4585	314	41	(	(	PUNCT
ejpam-4585	314	42	h	h	NOUN
ejpam-4585	314	43	)	)	PUNCT
ejpam-4585	314	44	=	=	SYM
ejpam-4585	314	45	n	n	PROPN
ejpam-4585	314	46	·	·	PUNCT
ejpam-4585	314	47	lnpnd2	lnpnd2	X
ejpam-4585	314	48	(	(	PUNCT
ejpam-4585	314	49	h	h	NOUN
ejpam-4585	314	50	)	)	PUNCT
ejpam-4585	314	51	therefore	therefore	ADV
ejpam-4585	314	52	,	,	PUNCT
ejpam-4585	314	53	γ2rh(g	γ2rh(g	VERB
ejpam-4585	314	54	◦	◦	NOUN
ejpam-4585	314	55	h	h	NOUN
ejpam-4585	314	56	)	)	PUNCT
ejpam-4585	314	57	=	=	SYM
ejpam-4585	314	58	n(lnpnd	n(lnpnd	NOUN
ejpam-4585	314	59	2	2	NUM
ejpam-4585	314	60	(	(	PUNCT
ejpam-4585	314	61	h	h	NOUN
ejpam-4585	314	62	)	)	PUNCT
ejpam-4585	314	63	)	)	PUNCT
ejpam-4585	314	64	.	.	PUNCT
ejpam-4585	315	1	example	example	NOUN
ejpam-4585	316	1	10	10	NUM
ejpam-4585	316	2	.	.	PUNCT
ejpam-4585	317	1	(	(	PUNCT
ejpam-4585	317	2	i	i	NOUN
ejpam-4585	317	3	)	)	PUNCT
ejpam-4585	317	4	for	for	ADP
ejpam-4585	317	5	n	n	NOUN
ejpam-4585	317	6	=	=	SYM
ejpam-4585	317	7	4	4	NUM
ejpam-4585	317	8	and	and	CCONJ
ejpam-4585	317	9	m	m	PROPN
ejpam-4585	317	10	=	=	SYM
ejpam-4585	317	11	3	3	NUM
ejpam-4585	317	12	,	,	PUNCT
ejpam-4585	317	13	γ2rh(p4	γ2rh(p4	PROPN
ejpam-4585	317	14	◦	◦	PROPN
ejpam-4585	317	15	p3	p3	PROPN
ejpam-4585	317	16	)	)	PUNCT
ejpam-4585	317	17	=	=	PUNCT
ejpam-4585	318	1	10	10	NUM
ejpam-4585	318	2	<	<	SYM
ejpam-4585	318	3	12	12	NUM
ejpam-4585	318	4	=	=	SYM
ejpam-4585	318	5	4(1	4(1	NOUN
ejpam-4585	318	6	+	+	CCONJ
ejpam-4585	318	7	2	2	NUM
ejpam-4585	318	8	)	)	PUNCT
ejpam-4585	318	9	.	.	PUNCT
ejpam-4585	319	1	a.m.	a.m.	PROPN
ejpam-4585	319	2	mahistrado	mahistrado	PROPN
ejpam-4585	319	3	,	,	PUNCT
ejpam-4585	319	4	h.	h.	PROPN
ejpam-4585	319	5	rara	rara	PROPN
ejpam-4585	319	6	/	/	SYM
ejpam-4585	319	7	eur	eur	PROPN
ejpam-4585	319	8	.	.	PUNCT
ejpam-4585	320	1	j.	j.	PROPN
ejpam-4585	320	2	pure	pure	PROPN
ejpam-4585	320	3	appl	appl	PROPN
ejpam-4585	320	4	.	.	PROPN
ejpam-4585	320	5	math	math	PROPN
ejpam-4585	320	6	,	,	PUNCT
ejpam-4585	320	7	15	15	NUM
ejpam-4585	320	8	(	(	PUNCT
ejpam-4585	320	9	4	4	NUM
ejpam-4585	320	10	)	)	PUNCT
ejpam-4585	320	11	(	(	PUNCT
ejpam-4585	320	12	2022	2022	NUM
ejpam-4585	320	13	)	)	PUNCT
ejpam-4585	320	14	,	,	PUNCT
ejpam-4585	320	15	1982	1982	NUM
ejpam-4585	320	16	-	-	SYM
ejpam-4585	320	17	1997	1997	NUM
ejpam-4585	320	18	1994	1994	NUM
ejpam-4585	320	19	(	(	PUNCT
ejpam-4585	320	20	ii	ii	NOUN
ejpam-4585	320	21	)	)	PUNCT
ejpam-4585	320	22	for	for	ADP
ejpam-4585	320	23	any	any	DET
ejpam-4585	320	24	integer	integer	NOUN
ejpam-4585	320	25	n	n	PRON
ejpam-4585	320	26	≥	≥	NOUN
ejpam-4585	320	27	2	2	NUM
ejpam-4585	320	28	and	and	CCONJ
ejpam-4585	320	29	m	m	PROPN
ejpam-4585	320	30	≥	≥	NOUN
ejpam-4585	320	31	4	4	NUM
ejpam-4585	320	32	,	,	PUNCT
ejpam-4585	320	33	γ2rh(g	γ2rh(g	VERB
ejpam-4585	320	34	◦	◦	NOUN
ejpam-4585	320	35	pm	pm	NOUN
ejpam-4585	320	36	)	)	PUNCT
ejpam-4585	320	37	=	=	SYM
ejpam-4585	320	38	n	n	CCONJ
ejpam-4585	320	39	·	·	PUNCT
ejpam-4585	320	40	lnpnd	lnpnd	ADJ
ejpam-4585	320	41	2	2	NUM
ejpam-4585	320	42	(	(	PUNCT
ejpam-4585	320	43	pm	pm	NOUN
ejpam-4585	320	44	)	)	PUNCT
ejpam-4585	320	45	=	=	SYM
ejpam-4585	321	1	n	n	CCONJ
ejpam-4585	321	2	(	(	PUNCT
ejpam-4585	321	3	⌈m+	⌈m+	ADP
ejpam-4585	321	4	1	1	NUM
ejpam-4585	321	5	2	2	NUM
ejpam-4585	321	6	⌉	⌉	NOUN
ejpam-4585	321	7	)	)	PUNCT
ejpam-4585	321	8	.	.	PUNCT
ejpam-4585	322	1	example	example	NOUN
ejpam-4585	323	1	11	11	NUM
ejpam-4585	323	2	.	.	PUNCT
ejpam-4585	324	1	for	for	ADP
ejpam-4585	324	2	any	any	DET
ejpam-4585	324	3	integer	integer	NOUN
ejpam-4585	324	4	n	n	PRON
ejpam-4585	324	5	≥	≥	NOUN
ejpam-4585	324	6	2	2	NUM
ejpam-4585	324	7	and	and	CCONJ
ejpam-4585	324	8	m	m	PROPN
ejpam-4585	324	9	≥	≥	NOUN
ejpam-4585	324	10	5	5	NUM
ejpam-4585	324	11	,	,	PUNCT
ejpam-4585	324	12	γ2rh(g	γ2rh(g	VERB
ejpam-4585	324	13	◦	◦	NOUN
ejpam-4585	324	14	cm	cm	NOUN
ejpam-4585	324	15	)	)	PUNCT
ejpam-4585	325	1	=	=	SYM
ejpam-4585	326	1	n	n	CCONJ
ejpam-4585	326	2	·	·	PUNCT
ejpam-4585	326	3	lnpnd	lnpnd	ADJ
ejpam-4585	326	4	2	2	NUM
ejpam-4585	326	5	(	(	PUNCT
ejpam-4585	326	6	cm	cm	NOUN
ejpam-4585	326	7	)	)	PUNCT
ejpam-4585	326	8	=	=	SYM
ejpam-4585	327	1	n	n	PROPN
ejpam-4585	327	2	(	(	PUNCT
ejpam-4585	327	3	⌈m	⌈m	NOUN
ejpam-4585	327	4	2	2	NUM
ejpam-4585	327	5	⌉	⌉	NOUN
ejpam-4585	327	6	)	)	PUNCT
ejpam-4585	327	7	.	.	PUNCT
ejpam-4585	328	1	4.2	4.2	NUM
ejpam-4585	328	2	.	.	X
ejpam-4585	328	3	2	2	NUM
ejpam-4585	328	4	-	-	PUNCT
ejpam-4585	328	5	resolving	resolve	VERB
ejpam-4585	328	6	hop	hop	NOUN
ejpam-4585	328	7	dominating	dominating	NOUN
ejpam-4585	328	8	sets	set	NOUN
ejpam-4585	328	9	in	in	ADP
ejpam-4585	328	10	the	the	DET
ejpam-4585	328	11	lexicographic	lexicographic	ADJ
ejpam-4585	328	12	product	product	NOUN
ejpam-4585	328	13	of	of	ADP
ejpam-4585	328	14	graphs	graph	NOUN
ejpam-4585	328	15	definition	definition	NOUN
ejpam-4585	328	16	9	9	NUM
ejpam-4585	328	17	.	.	PUNCT
ejpam-4585	329	1	[	[	X
ejpam-4585	329	2	2	2	X
ejpam-4585	329	3	]	]	PUNCT
ejpam-4585	329	4	the	the	DET
ejpam-4585	329	5	lexicographic	lexicographic	ADJ
ejpam-4585	329	6	product	product	NOUN
ejpam-4585	329	7	of	of	ADP
ejpam-4585	329	8	graphs	graph	NOUN
ejpam-4585	329	9	g	g	PROPN
ejpam-4585	329	10	and	and	CCONJ
ejpam-4585	329	11	h	h	NOUN
ejpam-4585	329	12	,	,	PUNCT
ejpam-4585	329	13	denoted	denote	VERB
ejpam-4585	329	14	by	by	ADP
ejpam-4585	329	15	g[h	g[h	NOUN
ejpam-4585	329	16	]	]	PUNCT
ejpam-4585	329	17	,	,	PUNCT
ejpam-4585	329	18	is	be	AUX
ejpam-4585	329	19	the	the	DET
ejpam-4585	329	20	graph	graph	NOUN
ejpam-4585	329	21	with	with	ADP
ejpam-4585	329	22	vertex	vertex	NOUN
ejpam-4585	329	23	set	set	VERB
ejpam-4585	329	24	v	v	NOUN
ejpam-4585	329	25	(	(	PUNCT
ejpam-4585	329	26	g[h	g[h	PROPN
ejpam-4585	329	27	]	]	PUNCT
ejpam-4585	329	28	)	)	PUNCT
ejpam-4585	329	29	=	=	SYM
ejpam-4585	329	30	v	v	X
ejpam-4585	329	31	(	(	PUNCT
ejpam-4585	329	32	g	g	NOUN
ejpam-4585	329	33	)	)	PUNCT
ejpam-4585	329	34	×	×	NOUN
ejpam-4585	329	35	v	v	NOUN
ejpam-4585	329	36	(	(	PUNCT
ejpam-4585	329	37	h	h	NOUN
ejpam-4585	329	38	)	)	PUNCT
ejpam-4585	329	39	such	such	ADJ
ejpam-4585	329	40	that	that	SCONJ
ejpam-4585	329	41	(	(	PUNCT
ejpam-4585	329	42	v	v	NOUN
ejpam-4585	329	43	,	,	PUNCT
ejpam-4585	329	44	a)(u	a)(u	ADJ
ejpam-4585	329	45	,	,	PUNCT
ejpam-4585	329	46	b	b	X
ejpam-4585	329	47	)	)	PUNCT
ejpam-4585	329	48	∈	∈	NOUN
ejpam-4585	329	49	e(g[h	e(g[h	NOUN
ejpam-4585	329	50	]	]	PUNCT
ejpam-4585	329	51	)	)	PUNCT
ejpam-4585	329	52	if	if	SCONJ
ejpam-4585	329	53	and	and	CCONJ
ejpam-4585	329	54	only	only	ADV
ejpam-4585	329	55	if	if	SCONJ
ejpam-4585	329	56	either	either	DET
ejpam-4585	329	57	uv	uv	PROPN
ejpam-4585	329	58	∈	∈	PROPN
ejpam-4585	329	59	e(g	e(g	PROPN
ejpam-4585	329	60	)	)	PUNCT
ejpam-4585	329	61	or	or	CCONJ
ejpam-4585	329	62	u	u	X
ejpam-4585	329	63	=	=	PROPN
ejpam-4585	329	64	v	v	PROPN
ejpam-4585	329	65	and	and	CCONJ
ejpam-4585	329	66	ab	ab	PROPN
ejpam-4585	329	67	∈	∈	PROPN
ejpam-4585	329	68	e(h	e(h	PROPN
ejpam-4585	329	69	)	)	PUNCT
ejpam-4585	329	70	.	.	PUNCT
ejpam-4585	330	1	note	note	VERB
ejpam-4585	330	2	that	that	SCONJ
ejpam-4585	330	3	every	every	DET
ejpam-4585	330	4	non	non	ADJ
ejpam-4585	330	5	-	-	ADJ
ejpam-4585	330	6	empty	empty	ADJ
ejpam-4585	330	7	subset	subset	NOUN
ejpam-4585	330	8	c	c	NOUN
ejpam-4585	330	9	of	of	ADP
ejpam-4585	330	10	v	v	PROPN
ejpam-4585	330	11	(	(	PUNCT
ejpam-4585	330	12	g)×v	g)×v	PROPN
ejpam-4585	330	13	(	(	PUNCT
ejpam-4585	330	14	h	h	NOUN
ejpam-4585	330	15	)	)	PUNCT
ejpam-4585	330	16	can	can	AUX
ejpam-4585	330	17	be	be	AUX
ejpam-4585	330	18	expressed	express	VERB
ejpam-4585	330	19	as	as	ADP
ejpam-4585	330	20	c	c	NOUN
ejpam-4585	330	21	=	=	PUNCT
ejpam-4585	330	22	⋃	⋃	PROPN
ejpam-4585	330	23	x∈s	x∈s	NOUN
ejpam-4585	331	1	[	[	X
ejpam-4585	331	2	{	{	PUNCT
ejpam-4585	331	3	x}×tx	x}×tx	X
ejpam-4585	331	4	]	]	X
ejpam-4585	331	5	,	,	PUNCT
ejpam-4585	331	6	where	where	SCONJ
ejpam-4585	331	7	s	s	VERB
ejpam-4585	331	8	⊆	⊆	NUM
ejpam-4585	331	9	v	v	NOUN
ejpam-4585	331	10	(	(	PUNCT
ejpam-4585	331	11	g	g	NOUN
ejpam-4585	331	12	)	)	PUNCT
ejpam-4585	331	13	and	and	CCONJ
ejpam-4585	331	14	tx	tx	VERB
ejpam-4585	331	15	⊆	⊆	NUM
ejpam-4585	331	16	v	v	NOUN
ejpam-4585	331	17	(	(	PUNCT
ejpam-4585	331	18	h	h	NOUN
ejpam-4585	331	19	)	)	PUNCT
ejpam-4585	331	20	.	.	PUNCT
ejpam-4585	332	1	definition	definition	NOUN
ejpam-4585	332	2	10	10	NUM
ejpam-4585	332	3	.	.	PUNCT
ejpam-4585	333	1	[	[	X
ejpam-4585	333	2	7	7	X
ejpam-4585	333	3	]	]	X
ejpam-4585	333	4	a	a	DET
ejpam-4585	333	5	vertex	vertex	NOUN
ejpam-4585	333	6	x	x	PRON
ejpam-4585	333	7	is	be	AUX
ejpam-4585	333	8	said	say	VERB
ejpam-4585	333	9	to	to	PART
ejpam-4585	333	10	be	be	AUX
ejpam-4585	333	11	1	1	NUM
ejpam-4585	333	12	-	-	PUNCT
ejpam-4585	333	13	equidistant	equidistant	NOUN
ejpam-4585	333	14	to	to	ADP
ejpam-4585	333	15	y	y	PRON
ejpam-4585	333	16	if	if	SCONJ
ejpam-4585	333	17	xy	xy	PROPN
ejpam-4585	333	18	∈	∈	PROPN
ejpam-4585	333	19	e(g	e(g	PROPN
ejpam-4585	333	20	)	)	PUNCT
ejpam-4585	333	21	and	and	CCONJ
ejpam-4585	333	22	dg(x	dg(x	NUM
ejpam-4585	333	23	,	,	PUNCT
ejpam-4585	333	24	z	z	NOUN
ejpam-4585	333	25	)	)	PUNCT
ejpam-4585	333	26	=	=	SYM
ejpam-4585	333	27	dg(y	dg(y	ADJ
ejpam-4585	333	28	,	,	PUNCT
ejpam-4585	333	29	z	z	NOUN
ejpam-4585	333	30	)	)	PUNCT
ejpam-4585	333	31	,	,	PUNCT
ejpam-4585	333	32	for	for	ADP
ejpam-4585	333	33	all	all	DET
ejpam-4585	333	34	z	z	NOUN
ejpam-4585	333	35	∈	∈	PROPN
ejpam-4585	333	36	v	v	NOUN
ejpam-4585	333	37	(	(	PUNCT
ejpam-4585	333	38	g)\{x	g)\{x	PROPN
ejpam-4585	333	39	,	,	PUNCT
ejpam-4585	333	40	y	y	NOUN
ejpam-4585	333	41	}	}	PUNCT
ejpam-4585	333	42	and	and	CCONJ
ejpam-4585	333	43	it	it	PRON
ejpam-4585	333	44	is	be	AUX
ejpam-4585	333	45	2	2	NUM
ejpam-4585	333	46	-	-	PUNCT
ejpam-4585	333	47	equidistant	equidistant	NOUN
ejpam-4585	333	48	to	to	ADP
ejpam-4585	333	49	y	y	PRON
ejpam-4585	333	50	if	if	SCONJ
ejpam-4585	333	51	dg(x	dg(x	NUM
ejpam-4585	333	52	,	,	PUNCT
ejpam-4585	333	53	y	y	NOUN
ejpam-4585	333	54	)	)	PUNCT
ejpam-4585	333	55	=	=	SYM
ejpam-4585	333	56	2	2	NUM
ejpam-4585	333	57	and	and	CCONJ
ejpam-4585	333	58	dg(x	dg(x	NUM
ejpam-4585	333	59	,	,	PUNCT
ejpam-4585	333	60	z	z	NOUN
ejpam-4585	333	61	)	)	PUNCT
ejpam-4585	333	62	=	=	SYM
ejpam-4585	333	63	dg(y	dg(y	ADJ
ejpam-4585	333	64	,	,	PUNCT
ejpam-4585	333	65	z	z	NOUN
ejpam-4585	333	66	)	)	PUNCT
ejpam-4585	333	67	,	,	PUNCT
ejpam-4585	333	68	for	for	ADP
ejpam-4585	333	69	all	all	DET
ejpam-4585	333	70	z	z	NOUN
ejpam-4585	333	71	∈	∈	PROPN
ejpam-4585	333	72	v	v	NOUN
ejpam-4585	333	73	(	(	PUNCT
ejpam-4585	333	74	g)\{x	g)\{x	PROPN
ejpam-4585	333	75	,	,	PUNCT
ejpam-4585	333	76	y	y	PROPN
ejpam-4585	333	77	}	}	PUNCT
ejpam-4585	333	78	.	.	PUNCT
ejpam-4585	334	1	a	a	DET
ejpam-4585	334	2	vertex	vertex	NOUN
ejpam-4585	334	3	is	be	AUX
ejpam-4585	334	4	called	call	VERB
ejpam-4585	334	5	a	a	DET
ejpam-4585	334	6	free	free	ADJ
ejpam-4585	334	7	-	-	PUNCT
ejpam-4585	334	8	vertex	vertex	NOUN
ejpam-4585	334	9	in	in	ADP
ejpam-4585	334	10	g	g	PROPN
ejpam-4585	334	11	if	if	SCONJ
ejpam-4585	334	12	it	it	PRON
ejpam-4585	334	13	is	be	AUX
ejpam-4585	334	14	neither	neither	PRON
ejpam-4585	334	15	1	1	NUM
ejpam-4585	334	16	-	-	PUNCT
ejpam-4585	334	17	equidistant	equidistant	ADJ
ejpam-4585	334	18	nor	nor	CCONJ
ejpam-4585	334	19	2	2	NUM
ejpam-4585	334	20	-	-	PUNCT
ejpam-4585	334	21	equidistant	equidistant	NOUN
ejpam-4585	334	22	to	to	ADP
ejpam-4585	334	23	any	any	DET
ejpam-4585	334	24	vertex	vertex	NOUN
ejpam-4585	334	25	.	.	PUNCT
ejpam-4585	335	1	the	the	DET
ejpam-4585	335	2	set	set	NOUN
ejpam-4585	335	3	containing	contain	VERB
ejpam-4585	335	4	all	all	DET
ejpam-4585	335	5	1equidistant	1equidistant	NUM
ejpam-4585	335	6	,	,	PUNCT
ejpam-4585	335	7	2	2	NUM
ejpam-4585	335	8	-	-	PUNCT
ejpam-4585	335	9	equidistant	equidistant	ADJ
ejpam-4585	335	10	,	,	PUNCT
ejpam-4585	335	11	and	and	CCONJ
ejpam-4585	335	12	free	free	ADJ
ejpam-4585	335	13	-	-	PUNCT
ejpam-4585	335	14	vertices	vertex	NOUN
ejpam-4585	335	15	in	in	ADP
ejpam-4585	335	16	g	g	PROPN
ejpam-4585	335	17	are	be	AUX
ejpam-4585	335	18	denoted	denote	VERB
ejpam-4585	335	19	by	by	ADP
ejpam-4585	335	20	eq1(g	eq1(g	PROPN
ejpam-4585	335	21	)	)	PUNCT
ejpam-4585	335	22	,	,	PUNCT
ejpam-4585	335	23	eq2(g	eq2(g	PROPN
ejpam-4585	335	24	)	)	PUNCT
ejpam-4585	335	25	and	and	CCONJ
ejpam-4585	335	26	fr(g	fr(g	NUM
ejpam-4585	335	27	)	)	PUNCT
ejpam-4585	335	28	,	,	PUNCT
ejpam-4585	335	29	respectively	respectively	ADV
ejpam-4585	335	30	.	.	PUNCT
ejpam-4585	336	1	definition	definition	NOUN
ejpam-4585	336	2	11	11	NUM
ejpam-4585	336	3	.	.	PUNCT
ejpam-4585	337	1	[	[	X
ejpam-4585	337	2	7	7	X
ejpam-4585	337	3	]	]	X
ejpam-4585	337	4	a	a	DET
ejpam-4585	337	5	graph	graph	NOUN
ejpam-4585	337	6	is	be	AUX
ejpam-4585	337	7	called	call	VERB
ejpam-4585	337	8	free	free	ADJ
ejpam-4585	337	9	-	-	PUNCT
ejpam-4585	337	10	equidistant	equidistant	NOUN
ejpam-4585	337	11	if	if	SCONJ
ejpam-4585	337	12	all	all	PRON
ejpam-4585	337	13	of	of	ADP
ejpam-4585	337	14	its	its	PRON
ejpam-4585	337	15	vertices	vertex	NOUN
ejpam-4585	337	16	are	be	AUX
ejpam-4585	337	17	free	free	ADJ
ejpam-4585	337	18	-	-	PUNCT
ejpam-4585	337	19	vertices	vertex	NOUN
ejpam-4585	337	20	.	.	PUNCT
ejpam-4585	338	1	remark	remark	NOUN
ejpam-4585	338	2	8	8	NUM
ejpam-4585	338	3	.	.	PUNCT
ejpam-4585	339	1	[	[	X
ejpam-4585	339	2	16	16	NUM
ejpam-4585	339	3	]	]	PUNCT
ejpam-4585	339	4	let	let	VERB
ejpam-4585	339	5	g	g	NOUN
ejpam-4585	339	6	and	and	CCONJ
ejpam-4585	339	7	h	h	NOUN
ejpam-4585	339	8	be	be	VERB
ejpam-4585	339	9	two	two	NUM
ejpam-4585	339	10	nontrivial	nontrivial	ADJ
ejpam-4585	339	11	graphs	graph	NOUN
ejpam-4585	339	12	such	such	ADJ
ejpam-4585	339	13	that	that	SCONJ
ejpam-4585	339	14	g	g	PROPN
ejpam-4585	339	15	is	be	AUX
ejpam-4585	339	16	connected	connect	VERB
ejpam-4585	339	17	.	.	PUNCT
ejpam-4585	340	1	then	then	ADV
ejpam-4585	340	2	the	the	DET
ejpam-4585	340	3	following	follow	VERB
ejpam-4585	340	4	assertions	assertion	NOUN
ejpam-4585	340	5	hold	hold	VERB
ejpam-4585	340	6	for	for	ADP
ejpam-4585	340	7	any	any	DET
ejpam-4585	340	8	a	a	NOUN
ejpam-4585	340	9	,	,	PUNCT
ejpam-4585	340	10	c	c	PROPN
ejpam-4585	340	11	∈	∈	PROPN
ejpam-4585	340	12	v	v	ADP
ejpam-4585	340	13	(	(	PUNCT
ejpam-4585	340	14	g	g	NOUN
ejpam-4585	340	15	)	)	PUNCT
ejpam-4585	340	16	and	and	CCONJ
ejpam-4585	340	17	b	b	X
ejpam-4585	340	18	,	,	PUNCT
ejpam-4585	340	19	d	d	PROPN
ejpam-4585	340	20	∈	∈	PROPN
ejpam-4585	340	21	v	v	ADP
ejpam-4585	340	22	(	(	PUNCT
ejpam-4585	340	23	h	h	NOUN
ejpam-4585	340	24	)	)	PUNCT
ejpam-4585	340	25	such	such	ADJ
ejpam-4585	340	26	that	that	SCONJ
ejpam-4585	340	27	a	a	DET
ejpam-4585	340	28	̸=	̸=	PROPN
ejpam-4585	340	29	c.	c.	NOUN
ejpam-4585	340	30	(	(	PUNCT
ejpam-4585	340	31	i	i	NOUN
ejpam-4585	340	32	)	)	PUNCT
ejpam-4585	340	33	ng[h](a	ng[h](a	PROPN
ejpam-4585	340	34	,	,	PUNCT
ejpam-4585	340	35	b	b	NOUN
ejpam-4585	340	36	)	)	PUNCT
ejpam-4585	340	37	=	=	SYM
ejpam-4585	340	38	(	(	PUNCT
ejpam-4585	340	39	{	{	PUNCT
ejpam-4585	340	40	a	a	PRON
ejpam-4585	340	41	}	}	PUNCT
ejpam-4585	340	42	×nh{b	×nh{b	PROPN
ejpam-4585	340	43	}	}	PUNCT
ejpam-4585	340	44	)	)	PUNCT
ejpam-4585	340	45	∪	∪	ADP
ejpam-4585	340	46	{	{	PUNCT
ejpam-4585	340	47	ng{a	ng{a	NOUN
ejpam-4585	340	48	}	}	PUNCT
ejpam-4585	340	49	×	×	NOUN
ejpam-4585	340	50	v	v	NOUN
ejpam-4585	340	51	(	(	PUNCT
ejpam-4585	340	52	h	h	NOUN
ejpam-4585	340	53	)	)	PUNCT
ejpam-4585	340	54	}	}	PUNCT
ejpam-4585	340	55	(	(	PUNCT
ejpam-4585	340	56	ii	ii	NOUN
ejpam-4585	340	57	)	)	PUNCT
ejpam-4585	340	58	dg[h]((a	dg[h]((a	PROPN
ejpam-4585	340	59	,	,	PUNCT
ejpam-4585	340	60	b	b	NOUN
ejpam-4585	340	61	)	)	PUNCT
ejpam-4585	340	62	,	,	PUNCT
ejpam-4585	340	63	(	(	PUNCT
ejpam-4585	340	64	c	c	X
ejpam-4585	340	65	,	,	PUNCT
ejpam-4585	340	66	d	d	NOUN
ejpam-4585	340	67	)	)	PUNCT
ejpam-4585	340	68	)	)	PUNCT
ejpam-4585	340	69	=	=	SYM
ejpam-4585	340	70	dg(a	dg(a	X
ejpam-4585	340	71	,	,	PUNCT
ejpam-4585	340	72	c	c	NOUN
ejpam-4585	340	73	)	)	PUNCT
ejpam-4585	340	74	(	(	PUNCT
ejpam-4585	340	75	iii	iii	NOUN
ejpam-4585	340	76	)	)	PUNCT
ejpam-4585	340	77	dg[h]((a	dg[h]((a	PROPN
ejpam-4585	340	78	,	,	PUNCT
ejpam-4585	340	79	b	b	NOUN
ejpam-4585	340	80	)	)	PUNCT
ejpam-4585	340	81	,	,	PUNCT
ejpam-4585	340	82	(	(	PUNCT
ejpam-4585	340	83	a	a	DET
ejpam-4585	340	84	,	,	PUNCT
ejpam-4585	340	85	d	d	NOUN
ejpam-4585	340	86	)	)	PUNCT
ejpam-4585	340	87	)	)	PUNCT
ejpam-4585	341	1	=	=	SYM
ejpam-4585	341	2	min{dh(b	min{dh(b	PROPN
ejpam-4585	341	3	,	,	PUNCT
ejpam-4585	341	4	d	d	NOUN
ejpam-4585	341	5	)	)	PUNCT
ejpam-4585	341	6	,	,	PUNCT
ejpam-4585	341	7	2	2	NUM
ejpam-4585	341	8	}	}	PUNCT
ejpam-4585	341	9	.	.	PUNCT
ejpam-4585	342	1	theorem	theorem	VERB
ejpam-4585	342	2	11	11	NUM
ejpam-4585	342	3	.	.	PUNCT
ejpam-4585	343	1	[	[	X
ejpam-4585	343	2	7	7	X
ejpam-4585	343	3	]	]	X
ejpam-4585	343	4	let	let	VERB
ejpam-4585	343	5	g	g	NOUN
ejpam-4585	343	6	and	and	CCONJ
ejpam-4585	343	7	h	h	NOUN
ejpam-4585	343	8	be	be	AUX
ejpam-4585	343	9	nontrivial	nontrivial	ADJ
ejpam-4585	343	10	connected	connected	ADJ
ejpam-4585	343	11	graphs	graph	NOUN
ejpam-4585	343	12	.	.	PUNCT
ejpam-4585	344	1	then	then	ADV
ejpam-4585	344	2	w	w	NOUN
ejpam-4585	344	3	=	=	PUNCT
ejpam-4585	344	4	⋃	⋃	PROPN
ejpam-4585	344	5	x∈s	x∈s	NOUN
ejpam-4585	345	1	[	[	X
ejpam-4585	345	2	{	{	PUNCT
ejpam-4585	345	3	x	x	NOUN
ejpam-4585	345	4	}	}	PUNCT
ejpam-4585	345	5	×	×	PROPN
ejpam-4585	345	6	tx	tx	PROPN
ejpam-4585	345	7	]	]	X
ejpam-4585	345	8	,	,	PUNCT
ejpam-4585	345	9	where	where	SCONJ
ejpam-4585	345	10	s	s	VERB
ejpam-4585	345	11	⊆	⊆	NUM
ejpam-4585	345	12	v	v	NOUN
ejpam-4585	345	13	(	(	PUNCT
ejpam-4585	345	14	g	g	NOUN
ejpam-4585	345	15	)	)	PUNCT
ejpam-4585	345	16	and	and	CCONJ
ejpam-4585	345	17	tx	tx	VERB
ejpam-4585	345	18	⊆	⊆	NUM
ejpam-4585	345	19	v	v	NOUN
ejpam-4585	345	20	(	(	PUNCT
ejpam-4585	345	21	h	h	NOUN
ejpam-4585	345	22	)	)	PUNCT
ejpam-4585	345	23	for	for	ADP
ejpam-4585	345	24	each	each	DET
ejpam-4585	345	25	x	x	SYM
ejpam-4585	345	26	∈	∈	PROPN
ejpam-4585	345	27	s	s	NOUN
ejpam-4585	345	28	,	,	PUNCT
ejpam-4585	345	29	is	be	AUX
ejpam-4585	345	30	a	a	DET
ejpam-4585	345	31	2	2	NUM
ejpam-4585	345	32	-	-	PUNCT
ejpam-4585	345	33	resolving	resolve	VERB
ejpam-4585	345	34	hop	hop	NOUN
ejpam-4585	345	35	dominating	dominating	NOUN
ejpam-4585	345	36	set	set	VERB
ejpam-4585	345	37	in	in	ADP
ejpam-4585	345	38	g[h	g[h	PROPN
ejpam-4585	345	39	]	]	PUNCT
ejpam-4585	345	40	if	if	SCONJ
ejpam-4585	345	41	and	and	CCONJ
ejpam-4585	345	42	only	only	ADV
ejpam-4585	345	43	if	if	SCONJ
ejpam-4585	345	44	(	(	PUNCT
ejpam-4585	345	45	i	i	NOUN
ejpam-4585	345	46	)	)	PUNCT
ejpam-4585	345	47	s	s	PART
ejpam-4585	345	48	=	=	SYM
ejpam-4585	345	49	v	v	NOUN
ejpam-4585	345	50	(	(	PUNCT
ejpam-4585	345	51	g	g	NOUN
ejpam-4585	345	52	)	)	PUNCT
ejpam-4585	345	53	;	;	PUNCT
ejpam-4585	345	54	(	(	PUNCT
ejpam-4585	345	55	ii	ii	NOUN
ejpam-4585	345	56	)	)	PUNCT
ejpam-4585	345	57	tx	tx	PROPN
ejpam-4585	345	58	is	be	AUX
ejpam-4585	345	59	a	a	DET
ejpam-4585	345	60	2	2	NUM
ejpam-4585	345	61	-	-	PUNCT
ejpam-4585	345	62	locating	locate	VERB
ejpam-4585	345	63	set	set	NOUN
ejpam-4585	345	64	in	in	ADP
ejpam-4585	345	65	h	h	NOUN
ejpam-4585	345	66	for	for	ADP
ejpam-4585	345	67	every	every	DET
ejpam-4585	345	68	x	x	SYM
ejpam-4585	345	69	∈	∈	PROPN
ejpam-4585	345	70	v	v	NOUN
ejpam-4585	345	71	(	(	PUNCT
ejpam-4585	345	72	g	g	NOUN
ejpam-4585	345	73	)	)	PUNCT
ejpam-4585	345	74	;	;	PUNCT
ejpam-4585	345	75	(	(	PUNCT
ejpam-4585	345	76	iii	iii	X
ejpam-4585	345	77	)	)	PUNCT
ejpam-4585	345	78	tx	tx	NOUN
ejpam-4585	346	1	or	or	CCONJ
ejpam-4585	346	2	ty	ty	INTJ
ejpam-4585	346	3	is	be	AUX
ejpam-4585	346	4	a	a	DET
ejpam-4585	346	5	(	(	PUNCT
ejpam-4585	346	6	2	2	NUM
ejpam-4585	346	7	,	,	PUNCT
ejpam-4585	346	8	1)-locating	1)-locating	NUM
ejpam-4585	346	9	set	set	NOUN
ejpam-4585	346	10	or	or	CCONJ
ejpam-4585	346	11	one	one	NUM
ejpam-4585	346	12	of	of	ADP
ejpam-4585	346	13	tx	tx	PROPN
ejpam-4585	346	14	and	and	CCONJ
ejpam-4585	346	15	ty	ty	PRON
ejpam-4585	346	16	is	be	AUX
ejpam-4585	346	17	a	a	DET
ejpam-4585	346	18	(	(	PUNCT
ejpam-4585	346	19	2	2	NUM
ejpam-4585	346	20	,	,	PUNCT
ejpam-4585	346	21	2)-locating	2)-locating	NUM
ejpam-4585	346	22	set	set	VERB
ejpam-4585	346	23	in	in	ADP
ejpam-4585	346	24	h	h	NOUN
ejpam-4585	346	25	whenever	whenever	SCONJ
ejpam-4585	346	26	x	x	X
ejpam-4585	346	27	,	,	PUNCT
ejpam-4585	346	28	y	y	PROPN
ejpam-4585	346	29	∈	∈	PROPN
ejpam-4585	346	30	eq1(g	eq1(g	PROPN
ejpam-4585	346	31	)	)	PUNCT
ejpam-4585	346	32	;	;	PUNCT
ejpam-4585	346	33	and	and	CCONJ
ejpam-4585	346	34	(	(	PUNCT
ejpam-4585	346	35	iv	iv	X
ejpam-4585	346	36	)	)	PUNCT
ejpam-4585	346	37	tx	tx	PROPN
ejpam-4585	347	1	and	and	CCONJ
ejpam-4585	347	2	ty	ty	INTJ
ejpam-4585	347	3	are	be	AUX
ejpam-4585	347	4	(	(	PUNCT
ejpam-4585	347	5	2	2	NUM
ejpam-4585	347	6	−	−	NOUN
ejpam-4585	347	7	locating	locating	NOUN
ejpam-4585	347	8	)	)	PUNCT
ejpam-4585	347	9	dominating	dominating	NOUN
ejpam-4585	347	10	sets	set	NOUN
ejpam-4585	347	11	in	in	ADP
ejpam-4585	347	12	h	h	NOUN
ejpam-4585	347	13	or	or	CCONJ
ejpam-4585	347	14	one	one	NUM
ejpam-4585	347	15	of	of	ADP
ejpam-4585	347	16	tx	tx	PROPN
ejpam-4585	348	1	and	and	CCONJ
ejpam-4585	348	2	ty	ty	INTJ
ejpam-4585	348	3	is	be	AUX
ejpam-4585	348	4	a	a	DET
ejpam-4585	348	5	2dominating	2dominating	NUM
ejpam-4585	348	6	set	set	NOUN
ejpam-4585	348	7	whenever	whenever	SCONJ
ejpam-4585	348	8	x	x	X
ejpam-4585	348	9	,	,	PUNCT
ejpam-4585	348	10	y	y	PROPN
ejpam-4585	348	11	∈	∈	PROPN
ejpam-4585	348	12	eq2(g	eq2(g	VERB
ejpam-4585	348	13	)	)	PUNCT
ejpam-4585	348	14	.	.	PUNCT
ejpam-4585	349	1	a.m.	a.m.	PROPN
ejpam-4585	349	2	mahistrado	mahistrado	PROPN
ejpam-4585	349	3	,	,	PUNCT
ejpam-4585	349	4	h.	h.	PROPN
ejpam-4585	349	5	rara	rara	PROPN
ejpam-4585	349	6	/	/	SYM
ejpam-4585	349	7	eur	eur	PROPN
ejpam-4585	349	8	.	.	PUNCT
ejpam-4585	350	1	j.	j.	PROPN
ejpam-4585	350	2	pure	pure	PROPN
ejpam-4585	350	3	appl	appl	PROPN
ejpam-4585	350	4	.	.	PROPN
ejpam-4585	350	5	math	math	PROPN
ejpam-4585	350	6	,	,	PUNCT
ejpam-4585	350	7	15	15	NUM
ejpam-4585	350	8	(	(	PUNCT
ejpam-4585	350	9	4	4	NUM
ejpam-4585	350	10	)	)	PUNCT
ejpam-4585	350	11	(	(	PUNCT
ejpam-4585	350	12	2022	2022	NUM
ejpam-4585	350	13	)	)	PUNCT
ejpam-4585	350	14	,	,	PUNCT
ejpam-4585	350	15	1982	1982	NUM
ejpam-4585	350	16	-	-	SYM
ejpam-4585	350	17	1997	1997	NUM
ejpam-4585	350	18	1995	1995	NUM
ejpam-4585	350	19	theorem	theorem	NOUN
ejpam-4585	350	20	12	12	NUM
ejpam-4585	350	21	.	.	PUNCT
ejpam-4585	351	1	[	[	X
ejpam-4585	351	2	12	12	NUM
ejpam-4585	351	3	]	]	PUNCT
ejpam-4585	351	4	let	let	VERB
ejpam-4585	351	5	g	g	NOUN
ejpam-4585	351	6	and	and	CCONJ
ejpam-4585	351	7	h	h	NOUN
ejpam-4585	351	8	be	be	AUX
ejpam-4585	351	9	nontrivial	nontrivial	ADJ
ejpam-4585	351	10	connected	connected	ADJ
ejpam-4585	351	11	graphs	graph	NOUN
ejpam-4585	351	12	.	.	PUNCT
ejpam-4585	352	1	a	a	DET
ejpam-4585	352	2	subset	subset	NOUN
ejpam-4585	352	3	c	c	NOUN
ejpam-4585	352	4	=	=	PUNCT
ejpam-4585	352	5	⋃	⋃	PROPN
ejpam-4585	352	6	x∈s	x∈s	NOUN
ejpam-4585	353	1	[	[	X
ejpam-4585	353	2	{	{	PUNCT
ejpam-4585	353	3	x}×tx	x}×tx	X
ejpam-4585	353	4	]	]	X
ejpam-4585	353	5	of	of	ADP
ejpam-4585	353	6	v	v	NOUN
ejpam-4585	353	7	(	(	PUNCT
ejpam-4585	353	8	g[h	g[h	PROPN
ejpam-4585	353	9	]	]	PUNCT
ejpam-4585	353	10	)	)	PUNCT
ejpam-4585	353	11	is	be	AUX
ejpam-4585	353	12	a	a	DET
ejpam-4585	353	13	hop	hop	NOUN
ejpam-4585	353	14	dominating	dominating	NOUN
ejpam-4585	353	15	set	set	NOUN
ejpam-4585	353	16	of	of	ADP
ejpam-4585	353	17	g[h	g[h	PROPN
ejpam-4585	353	18	]	]	PUNCT
ejpam-4585	353	19	if	if	SCONJ
ejpam-4585	353	20	and	and	CCONJ
ejpam-4585	353	21	only	only	ADV
ejpam-4585	353	22	if	if	SCONJ
ejpam-4585	353	23	the	the	DET
ejpam-4585	353	24	following	follow	VERB
ejpam-4585	353	25	conditions	condition	NOUN
ejpam-4585	353	26	hold	hold	VERB
ejpam-4585	353	27	:	:	PUNCT
ejpam-4585	353	28	(	(	PUNCT
ejpam-4585	353	29	i	i	NOUN
ejpam-4585	353	30	)	)	PUNCT
ejpam-4585	353	31	s	s	AUX
ejpam-4585	353	32	is	be	AUX
ejpam-4585	353	33	a	a	DET
ejpam-4585	353	34	hop	hop	NOUN
ejpam-4585	353	35	dominating	dominating	NOUN
ejpam-4585	353	36	set	set	NOUN
ejpam-4585	353	37	of	of	ADP
ejpam-4585	353	38	g	g	NOUN
ejpam-4585	353	39	;	;	PUNCT
ejpam-4585	353	40	(	(	PUNCT
ejpam-4585	353	41	ii	ii	NOUN
ejpam-4585	353	42	)	)	PUNCT
ejpam-4585	353	43	tx	tx	PROPN
ejpam-4585	353	44	is	be	AUX
ejpam-4585	353	45	a	a	DET
ejpam-4585	353	46	point	point	NOUN
ejpam-4585	353	47	-	-	PUNCT
ejpam-4585	353	48	wise	wise	ADJ
ejpam-4585	353	49	non	non	ADJ
ejpam-4585	353	50	-	-	ADJ
ejpam-4585	353	51	dominating	dominating	ADJ
ejpam-4585	353	52	set	set	NOUN
ejpam-4585	353	53	of	of	ADP
ejpam-4585	353	54	h	h	NOUN
ejpam-4585	353	55	for	for	ADP
ejpam-4585	353	56	each	each	DET
ejpam-4585	353	57	x	x	SYM
ejpam-4585	353	58	∈	∈	PROPN
ejpam-4585	353	59	s	s	VERB
ejpam-4585	353	60	with	with	ADP
ejpam-4585	353	61	|ng(x	|ng(x	ADP
ejpam-4585	353	62	,	,	PUNCT
ejpam-4585	353	63	2	2	X
ejpam-4585	353	64	)	)	PUNCT
ejpam-4585	353	65	∩	∩	NOUN
ejpam-4585	353	66	s|	s|	VERB
ejpam-4585	353	67	=	=	SYM
ejpam-4585	353	68	0	0	X
ejpam-4585	353	69	.	.	PUNCT
ejpam-4585	353	70	theorem	theorem	VERB
ejpam-4585	353	71	13	13	NUM
ejpam-4585	353	72	.	.	PUNCT
ejpam-4585	354	1	let	let	VERB
ejpam-4585	354	2	g	g	NOUN
ejpam-4585	354	3	and	and	CCONJ
ejpam-4585	354	4	h	h	NOUN
ejpam-4585	354	5	be	be	AUX
ejpam-4585	354	6	nontrivial	nontrivial	ADJ
ejpam-4585	354	7	connected	connected	ADJ
ejpam-4585	354	8	graphs	graph	NOUN
ejpam-4585	354	9	.	.	PUNCT
ejpam-4585	355	1	then	then	ADV
ejpam-4585	355	2	w	w	NOUN
ejpam-4585	355	3	=	=	PUNCT
ejpam-4585	355	4	⋃	⋃	PROPN
ejpam-4585	355	5	x∈s	x∈s	NOUN
ejpam-4585	356	1	[	[	X
ejpam-4585	356	2	{	{	PUNCT
ejpam-4585	356	3	x	x	NOUN
ejpam-4585	356	4	}	}	PUNCT
ejpam-4585	356	5	×	×	PROPN
ejpam-4585	356	6	tx	tx	PROPN
ejpam-4585	356	7	]	]	X
ejpam-4585	356	8	,	,	PUNCT
ejpam-4585	356	9	where	where	SCONJ
ejpam-4585	356	10	s	s	VERB
ejpam-4585	356	11	⊆	⊆	NUM
ejpam-4585	356	12	v	v	NOUN
ejpam-4585	356	13	(	(	PUNCT
ejpam-4585	356	14	g	g	NOUN
ejpam-4585	356	15	)	)	PUNCT
ejpam-4585	356	16	and	and	CCONJ
ejpam-4585	356	17	tx	tx	VERB
ejpam-4585	356	18	⊆	⊆	NUM
ejpam-4585	356	19	v	v	NOUN
ejpam-4585	356	20	(	(	PUNCT
ejpam-4585	356	21	h	h	NOUN
ejpam-4585	356	22	)	)	PUNCT
ejpam-4585	356	23	for	for	ADP
ejpam-4585	356	24	each	each	DET
ejpam-4585	356	25	x	x	SYM
ejpam-4585	356	26	∈	∈	PROPN
ejpam-4585	356	27	s	s	NOUN
ejpam-4585	356	28	,	,	PUNCT
ejpam-4585	356	29	is	be	AUX
ejpam-4585	356	30	a	a	DET
ejpam-4585	356	31	2	2	NUM
ejpam-4585	356	32	-	-	PUNCT
ejpam-4585	356	33	resolving	resolve	VERB
ejpam-4585	356	34	hop	hop	NOUN
ejpam-4585	356	35	dominating	dominating	NOUN
ejpam-4585	356	36	set	set	VERB
ejpam-4585	356	37	in	in	ADP
ejpam-4585	356	38	g[h	g[h	PROPN
ejpam-4585	356	39	]	]	PUNCT
ejpam-4585	356	40	if	if	SCONJ
ejpam-4585	356	41	and	and	CCONJ
ejpam-4585	356	42	only	only	ADV
ejpam-4585	356	43	if	if	SCONJ
ejpam-4585	356	44	(	(	PUNCT
ejpam-4585	356	45	i	i	NOUN
ejpam-4585	356	46	)	)	PUNCT
ejpam-4585	356	47	s	s	VERB
ejpam-4585	356	48	is	be	AUX
ejpam-4585	356	49	a	a	DET
ejpam-4585	356	50	hop	hop	NOUN
ejpam-4585	356	51	dominating	dominating	NOUN
ejpam-4585	356	52	set	set	NOUN
ejpam-4585	356	53	of	of	ADP
ejpam-4585	356	54	g	g	NOUN
ejpam-4585	356	55	,	,	PUNCT
ejpam-4585	356	56	that	that	PRON
ejpam-4585	356	57	is	be	AUX
ejpam-4585	356	58	s	s	NOUN
ejpam-4585	356	59	=	=	X
ejpam-4585	356	60	v	v	NOUN
ejpam-4585	356	61	(	(	PUNCT
ejpam-4585	356	62	g	g	NOUN
ejpam-4585	356	63	)	)	PUNCT
ejpam-4585	356	64	;	;	PUNCT
ejpam-4585	356	65	(	(	PUNCT
ejpam-4585	356	66	ii	ii	NOUN
ejpam-4585	356	67	)	)	PUNCT
ejpam-4585	356	68	tx	tx	PROPN
ejpam-4585	356	69	is	be	AUX
ejpam-4585	356	70	a	a	DET
ejpam-4585	356	71	2	2	NUM
ejpam-4585	356	72	-	-	PUNCT
ejpam-4585	356	73	locating	locate	VERB
ejpam-4585	356	74	set	set	NOUN
ejpam-4585	356	75	in	in	ADP
ejpam-4585	356	76	h	h	NOUN
ejpam-4585	356	77	for	for	ADP
ejpam-4585	356	78	every	every	DET
ejpam-4585	356	79	x	x	SYM
ejpam-4585	356	80	∈	∈	PROPN
ejpam-4585	356	81	v	v	NOUN
ejpam-4585	356	82	(	(	PUNCT
ejpam-4585	356	83	g	g	NOUN
ejpam-4585	356	84	)	)	PUNCT
ejpam-4585	356	85	;	;	PUNCT
ejpam-4585	356	86	(	(	PUNCT
ejpam-4585	356	87	iii	iii	X
ejpam-4585	356	88	)	)	PUNCT
ejpam-4585	356	89	tx	tx	NOUN
ejpam-4585	357	1	or	or	CCONJ
ejpam-4585	357	2	ty	ty	INTJ
ejpam-4585	357	3	is	be	AUX
ejpam-4585	357	4	a	a	DET
ejpam-4585	357	5	(	(	PUNCT
ejpam-4585	357	6	2	2	NUM
ejpam-4585	357	7	,	,	PUNCT
ejpam-4585	357	8	1)-locating	1)-locating	NUM
ejpam-4585	357	9	set	set	NOUN
ejpam-4585	357	10	or	or	CCONJ
ejpam-4585	357	11	one	one	NUM
ejpam-4585	357	12	of	of	ADP
ejpam-4585	357	13	tx	tx	PROPN
ejpam-4585	357	14	and	and	CCONJ
ejpam-4585	357	15	ty	ty	PRON
ejpam-4585	357	16	is	be	AUX
ejpam-4585	357	17	a	a	DET
ejpam-4585	357	18	(	(	PUNCT
ejpam-4585	357	19	2	2	NUM
ejpam-4585	357	20	,	,	PUNCT
ejpam-4585	357	21	2)-locating	2)-locating	NUM
ejpam-4585	357	22	set	set	VERB
ejpam-4585	357	23	in	in	ADP
ejpam-4585	357	24	h	h	NOUN
ejpam-4585	357	25	whenever	whenever	SCONJ
ejpam-4585	357	26	x	x	X
ejpam-4585	357	27	,	,	PUNCT
ejpam-4585	357	28	y	y	PROPN
ejpam-4585	357	29	∈	∈	PROPN
ejpam-4585	357	30	eq1(g	eq1(g	PROPN
ejpam-4585	357	31	)	)	PUNCT
ejpam-4585	357	32	;	;	PUNCT
ejpam-4585	357	33	(	(	PUNCT
ejpam-4585	357	34	iv	iv	X
ejpam-4585	357	35	)	)	PUNCT
ejpam-4585	357	36	tx	tx	PROPN
ejpam-4585	358	1	and	and	CCONJ
ejpam-4585	358	2	ty	ty	INTJ
ejpam-4585	358	3	are	be	AUX
ejpam-4585	358	4	(	(	PUNCT
ejpam-4585	358	5	2	2	NUM
ejpam-4585	358	6	−	−	NOUN
ejpam-4585	358	7	locating	locating	NOUN
ejpam-4585	358	8	)	)	PUNCT
ejpam-4585	358	9	dominating	dominating	NOUN
ejpam-4585	358	10	sets	set	NOUN
ejpam-4585	358	11	in	in	ADP
ejpam-4585	358	12	h	h	NOUN
ejpam-4585	358	13	or	or	CCONJ
ejpam-4585	358	14	one	one	NUM
ejpam-4585	358	15	of	of	ADP
ejpam-4585	358	16	tx	tx	PROPN
ejpam-4585	359	1	and	and	CCONJ
ejpam-4585	359	2	ty	ty	INTJ
ejpam-4585	359	3	is	be	AUX
ejpam-4585	359	4	a	a	DET
ejpam-4585	359	5	2dominating	2dominating	NUM
ejpam-4585	359	6	set	set	NOUN
ejpam-4585	359	7	whenever	whenever	SCONJ
ejpam-4585	359	8	x	x	X
ejpam-4585	359	9	,	,	PUNCT
ejpam-4585	359	10	y	y	PROPN
ejpam-4585	359	11	∈	∈	PROPN
ejpam-4585	359	12	eq2(g	eq2(g	VERB
ejpam-4585	359	13	)	)	PUNCT
ejpam-4585	359	14	;	;	PUNCT
ejpam-4585	359	15	and	and	CCONJ
ejpam-4585	359	16	(	(	PUNCT
ejpam-4585	359	17	v	v	NOUN
ejpam-4585	359	18	)	)	PUNCT
ejpam-4585	359	19	tx	tx	PROPN
ejpam-4585	359	20	is	be	AUX
ejpam-4585	359	21	a	a	DET
ejpam-4585	359	22	2	2	NUM
ejpam-4585	359	23	-	-	PUNCT
ejpam-4585	359	24	locating	locate	VERB
ejpam-4585	359	25	point	point	NOUN
ejpam-4585	359	26	-	-	PUNCT
ejpam-4585	359	27	wise	wise	ADJ
ejpam-4585	359	28	non	non	ADJ
ejpam-4585	359	29	-	-	ADJ
ejpam-4585	359	30	dominating	dominating	ADJ
ejpam-4585	359	31	set	set	VERB
ejpam-4585	359	32	inh	inh	NOUN
ejpam-4585	359	33	for	for	ADP
ejpam-4585	359	34	every	every	DET
ejpam-4585	359	35	x	x	SYM
ejpam-4585	359	36	∈	∈	PROPN
ejpam-4585	359	37	s	s	VERB
ejpam-4585	359	38	with	with	ADP
ejpam-4585	359	39	|ng(x	|ng(x	ADP
ejpam-4585	359	40	,	,	PUNCT
ejpam-4585	359	41	2)∩	2)∩	ADJ
ejpam-4585	359	42	s|	s|	NOUN
ejpam-4585	359	43	=	=	SYM
ejpam-4585	360	1	0	0	X
ejpam-4585	360	2	.	.	PUNCT
ejpam-4585	360	3	proof	proof	NOUN
ejpam-4585	360	4	.	.	PUNCT
ejpam-4585	361	1	supposew	supposew	PROPN
ejpam-4585	362	1	=	=	PUNCT
ejpam-4585	362	2	⋃	⋃	PROPN
ejpam-4585	362	3	x∈s	x∈s	NOUN
ejpam-4585	363	1	[	[	X
ejpam-4585	363	2	{	{	PUNCT
ejpam-4585	363	3	x}×tx	x}×tx	X
ejpam-4585	363	4	]	]	X
ejpam-4585	363	5	is	be	AUX
ejpam-4585	363	6	a	a	DET
ejpam-4585	363	7	2	2	NUM
ejpam-4585	363	8	-	-	PUNCT
ejpam-4585	363	9	resolving	resolve	VERB
ejpam-4585	363	10	hop	hop	NOUN
ejpam-4585	363	11	dominating	dominating	NOUN
ejpam-4585	363	12	set	set	NOUN
ejpam-4585	363	13	of	of	ADP
ejpam-4585	363	14	g[h	g[h	PROPN
ejpam-4585	363	15	]	]	PUNCT
ejpam-4585	363	16	.	.	PUNCT
ejpam-4585	364	1	then	then	ADV
ejpam-4585	364	2	w	w	PROPN
ejpam-4585	364	3	is	be	AUX
ejpam-4585	364	4	a	a	DET
ejpam-4585	364	5	2	2	NUM
ejpam-4585	364	6	-	-	PUNCT
ejpam-4585	364	7	resolving	resolve	VERB
ejpam-4585	364	8	set	set	NOUN
ejpam-4585	364	9	.	.	PUNCT
ejpam-4585	365	1	by	by	ADP
ejpam-4585	365	2	theorem	theorem	NOUN
ejpam-4585	365	3	11	11	NUM
ejpam-4585	365	4	,	,	PUNCT
ejpam-4585	365	5	(	(	PUNCT
ejpam-4585	365	6	i	i	NOUN
ejpam-4585	365	7	)	)	PUNCT
ejpam-4585	365	8	to	to	PART
ejpam-4585	365	9	(	(	PUNCT
ejpam-4585	365	10	iv	iv	X
ejpam-4585	365	11	)	)	PUNCT
ejpam-4585	365	12	hold	hold	NOUN
ejpam-4585	365	13	.	.	PUNCT
ejpam-4585	366	1	since	since	SCONJ
ejpam-4585	366	2	w	w	PROPN
ejpam-4585	366	3	is	be	AUX
ejpam-4585	366	4	a	a	DET
ejpam-4585	366	5	hop	hop	NOUN
ejpam-4585	366	6	dominating	dominating	NOUN
ejpam-4585	366	7	set	set	NOUN
ejpam-4585	366	8	then	then	ADV
ejpam-4585	366	9	by	by	ADP
ejpam-4585	366	10	theorem	theorem	NOUN
ejpam-4585	366	11	12	12	NUM
ejpam-4585	366	12	,	,	PUNCT
ejpam-4585	366	13	it	it	PRON
ejpam-4585	366	14	follows	follow	VERB
ejpam-4585	366	15	that	that	SCONJ
ejpam-4585	366	16	(	(	PUNCT
ejpam-4585	366	17	i	i	NOUN
ejpam-4585	366	18	)	)	PUNCT
ejpam-4585	366	19	and	and	CCONJ
ejpam-4585	366	20	(	(	PUNCT
ejpam-4585	366	21	v	v	NOUN
ejpam-4585	366	22	)	)	PUNCT
ejpam-4585	366	23	hold	hold	NOUN
ejpam-4585	366	24	.	.	PUNCT
ejpam-4585	367	1	now	now	ADV
ejpam-4585	367	2	,	,	PUNCT
ejpam-4585	367	3	let	let	VERB
ejpam-4585	367	4	x	x	PUNCT
ejpam-4585	367	5	∈	∈	PROPN
ejpam-4585	367	6	v	v	X
ejpam-4585	367	7	(	(	PUNCT
ejpam-4585	367	8	g	g	NOUN
ejpam-4585	367	9	)	)	PUNCT
ejpam-4585	367	10	and	and	CCONJ
ejpam-4585	367	11	p	p	X
ejpam-4585	367	12	,	,	PUNCT
ejpam-4585	367	13	q	q	PROPN
ejpam-4585	367	14	∈	∈	PROPN
ejpam-4585	367	15	s\ng(s	s\ng(s	NOUN
ejpam-4585	367	16	,	,	PUNCT
ejpam-4585	367	17	2	2	NUM
ejpam-4585	367	18	)	)	PUNCT
ejpam-4585	367	19	where	where	SCONJ
ejpam-4585	367	20	p	p	PROPN
ejpam-4585	367	21	̸=	̸=	PROPN
ejpam-4585	367	22	q.	q.	NOUN
ejpam-4585	367	23	then	then	ADV
ejpam-4585	367	24	(	(	PUNCT
ejpam-4585	367	25	x	x	X
ejpam-4585	367	26	,	,	PUNCT
ejpam-4585	367	27	p	p	NOUN
ejpam-4585	367	28	)	)	PUNCT
ejpam-4585	367	29	̸=	̸=	PROPN
ejpam-4585	367	30	(	(	PUNCT
ejpam-4585	367	31	x	x	X
ejpam-4585	367	32	,	,	PUNCT
ejpam-4585	367	33	q	q	NOUN
ejpam-4585	367	34	)	)	PUNCT
ejpam-4585	367	35	.	.	PUNCT
ejpam-4585	368	1	if	if	SCONJ
ejpam-4585	368	2	p	p	X
ejpam-4585	368	3	,	,	PUNCT
ejpam-4585	368	4	q	q	NOUN
ejpam-4585	368	5	/∈	/∈	PUNCT
ejpam-4585	369	1	tx	tx	INTJ
ejpam-4585	369	2	or	or	CCONJ
ejpam-4585	369	3	[	[	X
ejpam-4585	369	4	p	p	X
ejpam-4585	369	5	∈	∈	PROPN
ejpam-4585	369	6	tx	tx	NOUN
ejpam-4585	369	7	and	and	CCONJ
ejpam-4585	369	8	q	q	NOUN
ejpam-4585	369	9	/∈	/∈	PUNCT
ejpam-4585	370	1	tx	tx	PROPN
ejpam-4585	370	2	]	]	PUNCT
ejpam-4585	370	3	,	,	PUNCT
ejpam-4585	370	4	then	then	ADV
ejpam-4585	370	5	(	(	PUNCT
ejpam-4585	370	6	x	x	X
ejpam-4585	370	7	,	,	PUNCT
ejpam-4585	370	8	p	p	NOUN
ejpam-4585	370	9	)	)	PUNCT
ejpam-4585	370	10	,	,	PUNCT
ejpam-4585	370	11	(	(	PUNCT
ejpam-4585	370	12	x	x	X
ejpam-4585	370	13	,	,	PUNCT
ejpam-4585	370	14	q	q	NOUN
ejpam-4585	370	15	)	)	PUNCT
ejpam-4585	370	16	/∈	/∈	PUNCT
ejpam-4585	371	1	w	w	NOUN
ejpam-4585	371	2	or	or	CCONJ
ejpam-4585	371	3	[	[	X
ejpam-4585	371	4	(	(	PUNCT
ejpam-4585	371	5	x	x	X
ejpam-4585	371	6	,	,	PUNCT
ejpam-4585	371	7	p	p	NOUN
ejpam-4585	371	8	)	)	PUNCT
ejpam-4585	371	9	∈	∈	PROPN
ejpam-4585	371	10	w	w	NOUN
ejpam-4585	371	11	and	and	CCONJ
ejpam-4585	371	12	(	(	PUNCT
ejpam-4585	371	13	x	x	NOUN
ejpam-4585	371	14	,	,	PUNCT
ejpam-4585	371	15	q	q	NOUN
ejpam-4585	371	16	)	)	PUNCT
ejpam-4585	371	17	/∈	/∈	PUNCT
ejpam-4585	372	1	w	w	NOUN
ejpam-4585	372	2	]	]	X
ejpam-4585	372	3	.	.	PUNCT
ejpam-4585	373	1	since	since	SCONJ
ejpam-4585	373	2	w	w	PROPN
ejpam-4585	373	3	is	be	AUX
ejpam-4585	373	4	a	a	DET
ejpam-4585	373	5	2	2	NUM
ejpam-4585	373	6	-	-	PUNCT
ejpam-4585	373	7	resolving	resolve	VERB
ejpam-4585	373	8	hop	hop	NOUN
ejpam-4585	373	9	dominating	dominating	NOUN
ejpam-4585	373	10	set	set	VERB
ejpam-4585	373	11	in	in	ADP
ejpam-4585	373	12	g[h	g[h	PROPN
ejpam-4585	373	13	]	]	PUNCT
ejpam-4585	373	14	,	,	PUNCT
ejpam-4585	373	15	rg[h]((x	rg[h]((x	NOUN
ejpam-4585	373	16	,	,	PUNCT
ejpam-4585	373	17	p)/w	p)/w	PROPN
ejpam-4585	373	18	)	)	PUNCT
ejpam-4585	373	19	and	and	CCONJ
ejpam-4585	373	20	rg[h]((x	rg[h]((x	NOUN
ejpam-4585	373	21	,	,	PUNCT
ejpam-4585	373	22	q)/w	q)/w	PROPN
ejpam-4585	373	23	)	)	PUNCT
ejpam-4585	373	24	differ	differ	VERB
ejpam-4585	373	25	in	in	ADP
ejpam-4585	373	26	at	at	ADV
ejpam-4585	373	27	least	least	ADJ
ejpam-4585	373	28	2	2	NUM
ejpam-4585	373	29	positions	position	NOUN
ejpam-4585	373	30	.	.	PUNCT
ejpam-4585	374	1	hence	hence	ADV
ejpam-4585	374	2	,	,	PUNCT
ejpam-4585	374	3	by	by	ADP
ejpam-4585	374	4	remark	remark	NOUN
ejpam-4585	374	5	8	8	NUM
ejpam-4585	374	6	and	and	CCONJ
ejpam-4585	374	7	definition	definition	NOUN
ejpam-4585	374	8	1	1	NUM
ejpam-4585	374	9	,	,	PUNCT
ejpam-4585	374	10	tx	tx	PROPN
ejpam-4585	374	11	is	be	AUX
ejpam-4585	374	12	a	a	DET
ejpam-4585	374	13	2	2	NUM
ejpam-4585	374	14	-	-	PUNCT
ejpam-4585	374	15	locating	locate	VERB
ejpam-4585	374	16	set	set	NOUN
ejpam-4585	374	17	in	in	ADP
ejpam-4585	374	18	h.	h.	PROPN
ejpam-4585	374	19	thus	thus	ADV
ejpam-4585	374	20	,	,	PUNCT
ejpam-4585	374	21	(	(	PUNCT
ejpam-4585	374	22	v	v	NOUN
ejpam-4585	374	23	)	)	PUNCT
ejpam-4585	374	24	holds	hold	VERB
ejpam-4585	374	25	.	.	PUNCT
ejpam-4585	375	1	conversely	conversely	ADV
ejpam-4585	375	2	,	,	PUNCT
ejpam-4585	375	3	suppose	suppose	VERB
ejpam-4585	375	4	(	(	PUNCT
ejpam-4585	375	5	i	i	NOUN
ejpam-4585	375	6	)	)	PUNCT
ejpam-4585	375	7	to	to	PART
ejpam-4585	375	8	(	(	PUNCT
ejpam-4585	375	9	iv	iv	X
ejpam-4585	375	10	)	)	PUNCT
ejpam-4585	375	11	hold	hold	NOUN
ejpam-4585	375	12	.	.	PUNCT
ejpam-4585	376	1	by	by	ADP
ejpam-4585	376	2	theorem	theorem	NOUN
ejpam-4585	376	3	11	11	NUM
ejpam-4585	376	4	,	,	PUNCT
ejpam-4585	376	5	w	w	NOUN
ejpam-4585	376	6	is	be	AUX
ejpam-4585	376	7	a	a	DET
ejpam-4585	376	8	2	2	NUM
ejpam-4585	376	9	-	-	PUNCT
ejpam-4585	376	10	resolving	resolve	VERB
ejpam-4585	376	11	set	set	NOUN
ejpam-4585	376	12	.	.	PUNCT
ejpam-4585	377	1	also	also	ADV
ejpam-4585	377	2	,	,	PUNCT
ejpam-4585	377	3	since	since	SCONJ
ejpam-4585	377	4	(	(	PUNCT
ejpam-4585	377	5	i	i	NOUN
ejpam-4585	377	6	)	)	PUNCT
ejpam-4585	377	7	and	and	CCONJ
ejpam-4585	377	8	(	(	PUNCT
ejpam-4585	377	9	v	v	NOUN
ejpam-4585	377	10	)	)	PUNCT
ejpam-4585	377	11	hold	hold	NOUN
ejpam-4585	377	12	.	.	PUNCT
ejpam-4585	378	1	by	by	ADP
ejpam-4585	378	2	theorem	theorem	NOUN
ejpam-4585	378	3	12	12	NUM
ejpam-4585	378	4	,	,	PUNCT
ejpam-4585	378	5	w	w	NOUN
ejpam-4585	378	6	is	be	AUX
ejpam-4585	378	7	a	a	DET
ejpam-4585	378	8	hop	hop	NOUN
ejpam-4585	378	9	dominating	dominating	NOUN
ejpam-4585	378	10	set	set	NOUN
ejpam-4585	378	11	.	.	PUNCT
ejpam-4585	379	1	accordingly	accordingly	ADV
ejpam-4585	379	2	,	,	PUNCT
ejpam-4585	379	3	w	w	PROPN
ejpam-4585	379	4	is	be	AUX
ejpam-4585	379	5	2	2	NUM
ejpam-4585	379	6	-	-	PUNCT
ejpam-4585	379	7	resolving	resolve	VERB
ejpam-4585	379	8	hop	hop	NOUN
ejpam-4585	379	9	dominating	dominating	NOUN
ejpam-4585	379	10	set	set	NOUN
ejpam-4585	379	11	of	of	ADP
ejpam-4585	379	12	g[h	g[h	PROPN
ejpam-4585	379	13	]	]	PUNCT
ejpam-4585	379	14	.	.	PUNCT
ejpam-4585	380	1	the	the	DET
ejpam-4585	380	2	following	follow	VERB
ejpam-4585	380	3	corollaries	corollary	NOUN
ejpam-4585	380	4	are	be	AUX
ejpam-4585	380	5	the	the	DET
ejpam-4585	380	6	direct	direct	ADJ
ejpam-4585	380	7	consequences	consequence	NOUN
ejpam-4585	380	8	of	of	ADP
ejpam-4585	380	9	theorem	theorem	ADJ
ejpam-4585	380	10	13	13	NUM
ejpam-4585	380	11	.	.	PUNCT
ejpam-4585	380	12	corollary	corollary	ADJ
ejpam-4585	380	13	6	6	NUM
ejpam-4585	380	14	.	.	PUNCT
ejpam-4585	381	1	let	let	VERB
ejpam-4585	381	2	g	g	NOUN
ejpam-4585	381	3	and	and	CCONJ
ejpam-4585	381	4	h	h	NOUN
ejpam-4585	381	5	be	be	AUX
ejpam-4585	381	6	nontrivial	nontrivial	ADJ
ejpam-4585	381	7	connected	connected	ADJ
ejpam-4585	381	8	graphs	graph	NOUN
ejpam-4585	381	9	.	.	PUNCT
ejpam-4585	382	1	then	then	ADV
ejpam-4585	382	2	,	,	PUNCT
ejpam-4585	382	3	γ2rh(g[h	γ2rh(g[h	PROPN
ejpam-4585	382	4	]	]	PUNCT
ejpam-4585	382	5	)	)	PUNCT
ejpam-4585	382	6	≤	≤	NOUN
ejpam-4585	383	1	n	n	CCONJ
ejpam-4585	383	2	·	·	PUNCT
ejpam-4585	383	3	ln(2,1)(h	ln(2,1)(h	NUM
ejpam-4585	383	4	)	)	PUNCT
ejpam-4585	384	1	+	+	NOUN
ejpam-4585	384	2	m	m	NOUN
ejpam-4585	384	3	·	·	PUNCT
ejpam-4585	384	4	γ2l(h	γ2l(h	PROPN
ejpam-4585	384	5	)	)	PUNCT
ejpam-4585	385	1	+	+	CCONJ
ejpam-4585	385	2	p	p	X
ejpam-4585	385	3	·	·	PUNCT
ejpam-4585	385	4	lnpnd	lnpnd	ADJ
ejpam-4585	385	5	2	2	NUM
ejpam-4585	385	6	(	(	PUNCT
ejpam-4585	385	7	h	h	NOUN
ejpam-4585	385	8	)	)	PUNCT
ejpam-4585	385	9	,	,	PUNCT
ejpam-4585	385	10	where	where	SCONJ
ejpam-4585	385	11	n	n	X
ejpam-4585	385	12	+	+	NOUN
ejpam-4585	385	13	m	m	VERB
ejpam-4585	385	14	+	+	NOUN
ejpam-4585	385	15	p	p	X
ejpam-4585	385	16	=	=	X
ejpam-4585	385	17	|v	|v	X
ejpam-4585	385	18	(	(	PUNCT
ejpam-4585	385	19	g)|	g)|	NOUN
ejpam-4585	385	20	with	with	ADP
ejpam-4585	385	21	|eq1(g)|	|eq1(g)|	NOUN
ejpam-4585	385	22	=	=	SYM
ejpam-4585	385	23	n	n	CCONJ
ejpam-4585	385	24	,	,	PUNCT
ejpam-4585	385	25	|eq2(g)|	|eq2(g)|	X
ejpam-4585	385	26	=	=	PUNCT
ejpam-4585	385	27	m	m	VERB
ejpam-4585	385	28	and	and	CCONJ
ejpam-4585	385	29	|fr(g)|	|fr(g)|	NOUN
ejpam-4585	385	30	=	=	SYM
ejpam-4585	386	1	p.	p.	NOUN
ejpam-4585	386	2	in	in	ADP
ejpam-4585	386	3	particular	particular	ADJ
ejpam-4585	386	4	,	,	PUNCT
ejpam-4585	386	5	if	if	SCONJ
ejpam-4585	386	6	n	n	NOUN
ejpam-4585	386	7	=	=	NOUN
ejpam-4585	386	8	m	m	NOUN
ejpam-4585	386	9	=	=	SYM
ejpam-4585	386	10	0	0	NUM
ejpam-4585	386	11	,	,	PUNCT
ejpam-4585	386	12	then	then	ADV
ejpam-4585	386	13	γ2rh(g[h	γ2rh(g[h	PROPN
ejpam-4585	386	14	]	]	PUNCT
ejpam-4585	386	15	)	)	PUNCT
ejpam-4585	387	1	=	=	SYM
ejpam-4585	387	2	|v	|v	PROPN
ejpam-4585	387	3	(	(	PUNCT
ejpam-4585	387	4	g)|	g)|	NOUN
ejpam-4585	387	5	·	·	PUNCT
ejpam-4585	387	6	lnpnd	lnpnd	ADJ
ejpam-4585	387	7	2	2	NUM
ejpam-4585	387	8	(	(	PUNCT
ejpam-4585	387	9	h	h	NOUN
ejpam-4585	387	10	)	)	PUNCT
ejpam-4585	387	11	.	.	PUNCT
ejpam-4585	388	1	corollary	corollary	ADJ
ejpam-4585	388	2	7	7	NUM
ejpam-4585	388	3	follows	follow	VERB
ejpam-4585	388	4	from	from	ADP
ejpam-4585	388	5	theorem	theorem	ADJ
ejpam-4585	388	6	13	13	NUM
ejpam-4585	388	7	.	.	PUNCT
ejpam-4585	389	1	corollary	corollary	ADJ
ejpam-4585	389	2	7	7	NUM
ejpam-4585	389	3	.	.	PUNCT
ejpam-4585	390	1	let	let	VERB
ejpam-4585	390	2	g	g	NOUN
ejpam-4585	390	3	and	and	CCONJ
ejpam-4585	390	4	h	h	NOUN
ejpam-4585	390	5	be	be	AUX
ejpam-4585	390	6	nontrivial	nontrivial	ADJ
ejpam-4585	390	7	connected	connect	VERB
ejpam-4585	390	8	graphs	graph	NOUN
ejpam-4585	390	9	such	such	ADJ
ejpam-4585	390	10	that	that	SCONJ
ejpam-4585	390	11	g	g	PROPN
ejpam-4585	390	12	is	be	AUX
ejpam-4585	390	13	free	free	ADJ
ejpam-4585	390	14	-	-	PUNCT
ejpam-4585	390	15	equidistant	equidistant	NOUN
ejpam-4585	390	16	.	.	PUNCT
ejpam-4585	391	1	then	then	ADV
ejpam-4585	391	2	γ2rh(g[h	γ2rh(g[h	PROPN
ejpam-4585	391	3	]	]	PUNCT
ejpam-4585	391	4	)	)	PUNCT
ejpam-4585	392	1	=	=	SYM
ejpam-4585	392	2	|v	|v	PROPN
ejpam-4585	392	3	(	(	PUNCT
ejpam-4585	392	4	g)|	g)|	NOUN
ejpam-4585	392	5	·	·	PUNCT
ejpam-4585	392	6	lnpnd	lnpnd	ADJ
ejpam-4585	392	7	2	2	NUM
ejpam-4585	392	8	(	(	PUNCT
ejpam-4585	392	9	h	h	NOUN
ejpam-4585	392	10	)	)	PUNCT
ejpam-4585	392	11	.	.	PUNCT
ejpam-4585	393	1	references	reference	NOUN
ejpam-4585	393	2	1996	1996	NUM
ejpam-4585	393	3	proof	proof	NOUN
ejpam-4585	393	4	.	.	PUNCT
ejpam-4585	394	1	since	since	SCONJ
ejpam-4585	394	2	g	g	PROPN
ejpam-4585	394	3	is	be	AUX
ejpam-4585	394	4	free	free	ADJ
ejpam-4585	394	5	-	-	PUNCT
ejpam-4585	394	6	equidistant	equidistant	ADJ
ejpam-4585	394	7	,	,	PUNCT
ejpam-4585	394	8	then	then	ADV
ejpam-4585	394	9	|eq1(g)|	|eq1(g)|	NOUN
ejpam-4585	394	10	=	=	SYM
ejpam-4585	394	11	|eq2(g)|	|eq2(g)|	NOUN
ejpam-4585	394	12	=	=	NOUN
ejpam-4585	394	13	0	0	X
ejpam-4585	394	14	.	.	PUNCT
ejpam-4585	395	1	therefore	therefore	ADV
ejpam-4585	395	2	,	,	PUNCT
ejpam-4585	395	3	γ2rh(g[h	γ2rh(g[h	PROPN
ejpam-4585	395	4	]	]	X
ejpam-4585	395	5	)	)	PUNCT
ejpam-4585	396	1	=	=	SYM
ejpam-4585	396	2	|v	|v	PROPN
ejpam-4585	396	3	(	(	PUNCT
ejpam-4585	396	4	g)|	g)|	NOUN
ejpam-4585	396	5	·	·	PUNCT
ejpam-4585	396	6	lnpnd	lnpnd	ADJ
ejpam-4585	396	7	2	2	NUM
ejpam-4585	396	8	(	(	PUNCT
ejpam-4585	396	9	h	h	NOUN
ejpam-4585	396	10	)	)	PUNCT
ejpam-4585	396	11	.	.	PUNCT
ejpam-4585	397	1	example	example	NOUN
ejpam-4585	398	1	12	12	NUM
ejpam-4585	398	2	.	.	PUNCT
ejpam-4585	399	1	for	for	ADP
ejpam-4585	399	2	any	any	DET
ejpam-4585	399	3	integer	integer	NOUN
ejpam-4585	399	4	n	n	PRON
ejpam-4585	399	5	≥	≥	NOUN
ejpam-4585	399	6	2	2	NUM
ejpam-4585	399	7	and	and	CCONJ
ejpam-4585	399	8	m	m	PROPN
ejpam-4585	399	9	≥	≥	NOUN
ejpam-4585	399	10	4	4	NUM
ejpam-4585	399	11	,	,	PUNCT
ejpam-4585	399	12	γ2rh(g[pm	γ2rh(g[pm	NOUN
ejpam-4585	399	13	]	]	PUNCT
ejpam-4585	399	14	)	)	PUNCT
ejpam-4585	399	15	=	=	SYM
ejpam-4585	399	16	n	n	CCONJ
ejpam-4585	399	17	·	·	PUNCT
ejpam-4585	399	18	lnpnd	lnpnd	ADJ
ejpam-4585	399	19	2	2	NUM
ejpam-4585	399	20	(	(	PUNCT
ejpam-4585	399	21	pm	pm	NOUN
ejpam-4585	399	22	)	)	PUNCT
ejpam-4585	399	23	=	=	SYM
ejpam-4585	399	24	n	n	CCONJ
ejpam-4585	399	25	(	(	PUNCT
ejpam-4585	399	26	⌈m+	⌈m+	ADP
ejpam-4585	399	27	1	1	NUM
ejpam-4585	399	28	2	2	NUM
ejpam-4585	399	29	⌉	⌉	NOUN
ejpam-4585	399	30	)	)	PUNCT
ejpam-4585	399	31	.	.	PUNCT
ejpam-4585	399	32	example	example	NOUN
ejpam-4585	400	1	13	13	NUM
ejpam-4585	400	2	.	.	PUNCT
ejpam-4585	401	1	for	for	ADP
ejpam-4585	401	2	any	any	DET
ejpam-4585	401	3	integer	integer	NOUN
ejpam-4585	401	4	n	n	PRON
ejpam-4585	401	5	≥	≥	NOUN
ejpam-4585	401	6	2	2	NUM
ejpam-4585	401	7	and	and	CCONJ
ejpam-4585	401	8	m	m	PROPN
ejpam-4585	401	9	≥	≥	NOUN
ejpam-4585	401	10	5	5	NUM
ejpam-4585	401	11	,	,	PUNCT
ejpam-4585	401	12	γ2rh(g[cm	γ2rh(g[cm	NUM
ejpam-4585	401	13	]	]	PUNCT
ejpam-4585	401	14	)	)	PUNCT
ejpam-4585	401	15	=	=	SYM
ejpam-4585	401	16	n	n	CCONJ
ejpam-4585	401	17	·	·	PUNCT
ejpam-4585	401	18	lnpnd	lnpnd	ADJ
ejpam-4585	401	19	2	2	NUM
ejpam-4585	401	20	(	(	PUNCT
ejpam-4585	401	21	cm	cm	NOUN
ejpam-4585	401	22	)	)	PUNCT
ejpam-4585	401	23	=	=	SYM
ejpam-4585	401	24	n	n	PROPN
ejpam-4585	401	25	(	(	PUNCT
ejpam-4585	401	26	⌈m	⌈m	NOUN
ejpam-4585	401	27	2	2	NUM
ejpam-4585	401	28	⌉	⌉	NOUN
ejpam-4585	401	29	)	)	PUNCT
ejpam-4585	401	30	.	.	PUNCT
ejpam-4585	402	1	acknowledgements	acknowledgement	NOUN
ejpam-4585	402	2	the	the	DET
ejpam-4585	402	3	authors	author	NOUN
ejpam-4585	402	4	would	would	AUX
ejpam-4585	402	5	like	like	VERB
ejpam-4585	402	6	to	to	PART
ejpam-4585	402	7	thank	thank	VERB
ejpam-4585	402	8	the	the	DET
ejpam-4585	402	9	department	department	NOUN
ejpam-4585	402	10	of	of	ADP
ejpam-4585	402	11	science	science	NOUN
ejpam-4585	402	12	and	and	CCONJ
ejpam-4585	402	13	technology	technology	NOUN
ejpam-4585	402	14	accelerated	accelerate	VERB
ejpam-4585	402	15	science	science	NOUN
ejpam-4585	402	16	and	and	CCONJ
ejpam-4585	402	17	technology	technology	NOUN
ejpam-4585	402	18	human	human	ADJ
ejpam-4585	402	19	resource	resource	NOUN
ejpam-4585	402	20	development	development	NOUN
ejpam-4585	402	21	program	program	NOUN
ejpam-4585	402	22	(	(	PUNCT
ejpam-4585	402	23	dost	dost	NOUN
ejpam-4585	402	24	-	-	PUNCT
ejpam-4585	402	25	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4585	402	26	,	,	PUNCT
ejpam-4585	402	27	msu	msu	PROPN
ejpam-4585	402	28	-	-	PUNCT
ejpam-4585	402	29	iligan	iligan	PROPN
ejpam-4585	402	30	institute	institute	PROPN
ejpam-4585	402	31	of	of	ADP
ejpam-4585	402	32	technology	technology	PROPN
ejpam-4585	402	33	.	.	PUNCT
ejpam-4585	403	1	references	reference	NOUN
ejpam-4585	403	2	[	[	X
ejpam-4585	403	3	1	1	NUM
ejpam-4585	403	4	]	]	PUNCT
ejpam-4585	403	5	c.	c.	PROPN
ejpam-4585	403	6	berge	berge	PROPN
ejpam-4585	403	7	.	.	PUNCT
ejpam-4585	404	1	theorie	theorie	PROPN
ejpam-4585	404	2	des	des	PROPN
ejpam-4585	404	3	graphes	graphes	PROPN
ejpam-4585	404	4	et	et	PROPN
ejpam-4585	404	5	ses	ses	PROPN
ejpam-4585	404	6	applications	application	NOUN
ejpam-4585	404	7	.	.	PUNCT
ejpam-4585	405	1	methuen	methuen	PROPN
ejpam-4585	405	2	(	(	PUNCT
ejpam-4585	405	3	london	london	PROPN
ejpam-4585	405	4	)	)	PUNCT
ejpam-4585	405	5	and	and	CCONJ
ejpam-4585	405	6	wiley	wiley	PROPN
ejpam-4585	405	7	(	(	PUNCT
ejpam-4585	405	8	new	new	PROPN
ejpam-4585	405	9	york	york	PROPN
ejpam-4585	405	10	)	)	PUNCT
ejpam-4585	405	11	,	,	PUNCT
ejpam-4585	405	12	1962	1962	NUM
ejpam-4585	405	13	.	.	PUNCT
ejpam-4585	406	1	[	[	X
ejpam-4585	406	2	2	2	X
ejpam-4585	406	3	]	]	PUNCT
ejpam-4585	406	4	j.	j.	PROPN
ejpam-4585	406	5	a.	a.	PROPN
ejpam-4585	406	6	bondy	bondy	PROPN
ejpam-4585	406	7	and	and	CCONJ
ejpam-4585	406	8	u.	u.	PROPN
ejpam-4585	406	9	s.	s.	PROPN
ejpam-4585	406	10	r.	r.	PROPN
ejpam-4585	406	11	murty	murty	PROPN
ejpam-4585	406	12	.	.	PUNCT
ejpam-4585	407	1	graph	graph	NOUN
ejpam-4585	407	2	theory	theory	NOUN
ejpam-4585	407	3	.	.	PUNCT
ejpam-4585	408	1	springer	springer	NOUN
ejpam-4585	408	2	,	,	PUNCT
ejpam-4585	408	3	2008	2008	NUM
ejpam-4585	408	4	.	.	PUNCT
ejpam-4585	409	1	[	[	X
ejpam-4585	409	2	3	3	NUM
ejpam-4585	409	3	]	]	X
ejpam-4585	409	4	f.	f.	PROPN
ejpam-4585	409	5	buckley	buckley	PROPN
ejpam-4585	409	6	and	and	CCONJ
ejpam-4585	409	7	f.	f.	PROPN
ejpam-4585	409	8	harary	harary	PROPN
ejpam-4585	409	9	.	.	PUNCT
ejpam-4585	410	1	distance	distance	NOUN
ejpam-4585	410	2	in	in	ADP
ejpam-4585	410	3	graphs	graph	NOUN
ejpam-4585	410	4	.	.	PUNCT
ejpam-4585	411	1	addison	addison	PROPN
ejpam-4585	411	2	-	-	PUNCT
ejpam-4585	411	3	wesley	wesley	PROPN
ejpam-4585	411	4	,	,	PUNCT
ejpam-4585	411	5	redwood	redwood	NOUN
ejpam-4585	411	6	city	city	NOUN
ejpam-4585	411	7	,	,	PUNCT
ejpam-4585	411	8	ca	ca	NOUN
ejpam-4585	411	9	,	,	PUNCT
ejpam-4585	411	10	1990	1990	NUM
ejpam-4585	411	11	.	.	PUNCT
ejpam-4585	412	1	[	[	X
ejpam-4585	412	2	4	4	X
ejpam-4585	412	3	]	]	X
ejpam-4585	412	4	j.	j.	PROPN
ejpam-4585	412	5	cabaro	cabaro	PROPN
ejpam-4585	412	6	and	and	CCONJ
ejpam-4585	412	7	h.	h.	PROPN
ejpam-4585	412	8	rara	rara	PROPN
ejpam-4585	412	9	.	.	PUNCT
ejpam-4585	413	1	on	on	ADP
ejpam-4585	413	2	2	2	NUM
ejpam-4585	413	3	-	-	PUNCT
ejpam-4585	413	4	resolving	resolve	VERB
ejpam-4585	413	5	sets	set	NOUN
ejpam-4585	413	6	in	in	ADP
ejpam-4585	413	7	the	the	DET
ejpam-4585	413	8	join	join	NOUN
ejpam-4585	413	9	and	and	CCONJ
ejpam-4585	413	10	corona	corona	NOUN
ejpam-4585	413	11	of	of	ADP
ejpam-4585	413	12	graphs	graph	NOUN
ejpam-4585	413	13	.	.	PUNCT
ejpam-4585	414	1	european	european	ADJ
ejpam-4585	414	2	journal	journal	PROPN
ejpam-4585	414	3	of	of	ADP
ejpam-4585	414	4	pure	pure	ADJ
ejpam-4585	414	5	and	and	CCONJ
ejpam-4585	414	6	applied	applied	ADJ
ejpam-4585	414	7	mathematics	mathematic	NOUN
ejpam-4585	414	8	,	,	PUNCT
ejpam-4585	414	9	14(3):773–782	14(3):773–782	PROPN
ejpam-4585	414	10	,	,	PUNCT
ejpam-4585	414	11	2021	2021	NUM
ejpam-4585	414	12	.	.	PUNCT
ejpam-4585	415	1	[	[	X
ejpam-4585	415	2	5	5	X
ejpam-4585	415	3	]	]	PUNCT
ejpam-4585	415	4	j.	j.	PROPN
ejpam-4585	415	5	cabaro	cabaro	PROPN
ejpam-4585	415	6	and	and	CCONJ
ejpam-4585	415	7	h.	h.	PROPN
ejpam-4585	415	8	rara	rara	PROPN
ejpam-4585	415	9	.	.	PUNCT
ejpam-4585	416	1	restrained	restrain	VERB
ejpam-4585	416	2	2	2	NUM
ejpam-4585	416	3	-	-	PUNCT
ejpam-4585	416	4	resolving	resolve	VERB
ejpam-4585	416	5	dominating	dominating	NOUN
ejpam-4585	416	6	sets	set	NOUN
ejpam-4585	416	7	in	in	ADP
ejpam-4585	416	8	the	the	DET
ejpam-4585	416	9	join	join	NOUN
ejpam-4585	416	10	and	and	CCONJ
ejpam-4585	416	11	corona	corona	PROPN
ejpam-4585	416	12	and	and	CCONJ
ejpam-4585	416	13	lexicographic	lexicographic	ADJ
ejpam-4585	416	14	product	product	NOUN
ejpam-4585	416	15	of	of	ADP
ejpam-4585	416	16	two	two	NUM
ejpam-4585	416	17	graphs	graph	NOUN
ejpam-4585	416	18	.	.	PUNCT
ejpam-4585	417	1	european	european	ADJ
ejpam-4585	417	2	journal	journal	PROPN
ejpam-4585	417	3	of	of	ADP
ejpam-4585	417	4	pure	pure	ADJ
ejpam-4585	417	5	and	and	CCONJ
ejpam-4585	417	6	applied	applied	ADJ
ejpam-4585	417	7	mathematics	mathematic	NOUN
ejpam-4585	417	8	,	,	PUNCT
ejpam-4585	417	9	15(3):1047–1053	15(3):1047–1053	NUM
ejpam-4585	417	10	,	,	PUNCT
ejpam-4585	417	11	2022	2022	NUM
ejpam-4585	417	12	.	.	PUNCT
ejpam-4585	418	1	[	[	X
ejpam-4585	418	2	6	6	NUM
ejpam-4585	418	3	]	]	PUNCT
ejpam-4585	418	4	j.	j.	PROPN
ejpam-4585	418	5	cabaro	cabaro	PROPN
ejpam-4585	418	6	and	and	CCONJ
ejpam-4585	418	7	h.	h.	PROPN
ejpam-4585	418	8	rara	rara	PROPN
ejpam-4585	418	9	.	.	PUNCT
ejpam-4585	419	1	on	on	ADP
ejpam-4585	419	2	2	2	NUM
ejpam-4585	419	3	-	-	PUNCT
ejpam-4585	419	4	resolving	resolve	VERB
ejpam-4585	419	5	dominating	dominating	NOUN
ejpam-4585	419	6	sets	set	NOUN
ejpam-4585	419	7	in	in	ADP
ejpam-4585	419	8	the	the	DET
ejpam-4585	419	9	join	join	NOUN
ejpam-4585	419	10	and	and	CCONJ
ejpam-4585	419	11	corona	corona	PROPN
ejpam-4585	419	12	and	and	CCONJ
ejpam-4585	419	13	lexicographic	lexicographic	ADJ
ejpam-4585	419	14	product	product	NOUN
ejpam-4585	419	15	of	of	ADP
ejpam-4585	419	16	graphs	graph	NOUN
ejpam-4585	419	17	.	.	PUNCT
ejpam-4585	420	1	european	european	ADJ
ejpam-4585	420	2	journal	journal	PROPN
ejpam-4585	420	3	of	of	ADP
ejpam-4585	420	4	pure	pure	ADJ
ejpam-4585	420	5	and	and	CCONJ
ejpam-4585	420	6	applied	applied	ADJ
ejpam-4585	420	7	mathematics	mathematic	NOUN
ejpam-4585	420	8	,	,	PUNCT
ejpam-4585	420	9	15(3):1417–1425	15(3):1417–1425	NUM
ejpam-4585	420	10	,	,	PUNCT
ejpam-4585	420	11	2022	2022	NUM
ejpam-4585	420	12	.	.	PUNCT
ejpam-4585	421	1	[	[	X
ejpam-4585	421	2	7	7	X
ejpam-4585	421	3	]	]	X
ejpam-4585	421	4	j.	j.	PROPN
ejpam-4585	421	5	cabaro	cabaro	PROPN
ejpam-4585	421	6	and	and	CCONJ
ejpam-4585	421	7	h.	h.	PROPN
ejpam-4585	421	8	rara	rara	PROPN
ejpam-4585	421	9	.	.	PUNCT
ejpam-4585	422	1	on	on	ADP
ejpam-4585	422	2	variations	variation	NOUN
ejpam-4585	422	3	of	of	ADP
ejpam-4585	422	4	2	2	NUM
ejpam-4585	422	5	-	-	PUNCT
ejpam-4585	422	6	resolving	resolve	VERB
ejpam-4585	422	7	sets	set	NOUN
ejpam-4585	422	8	in	in	ADP
ejpam-4585	422	9	graphs	graph	NOUN
ejpam-4585	422	10	.	.	PUNCT
ejpam-4585	423	1	phd	phd	NOUN
ejpam-4585	423	2	thesis	thesis	PROPN
ejpam-4585	423	3	,	,	PUNCT
ejpam-4585	423	4	mindanao	mindanao	PROPN
ejpam-4585	423	5	state	state	PROPN
ejpam-4585	423	6	universityiligan	universityiligan	PROPN
ejpam-4585	423	7	institute	institute	PROPN
ejpam-4585	423	8	of	of	ADP
ejpam-4585	423	9	technology	technology	NOUN
ejpam-4585	423	10	,	,	PUNCT
ejpam-4585	423	11	2022	2022	NUM
ejpam-4585	423	12	.	.	PUNCT
ejpam-4585	424	1	[	[	X
ejpam-4585	424	2	8	8	X
ejpam-4585	424	3	]	]	X
ejpam-4585	424	4	j.	j.	PROPN
ejpam-4585	424	5	cabaro	cabaro	PROPN
ejpam-4585	424	6	and	and	CCONJ
ejpam-4585	424	7	h.	h.	PROPN
ejpam-4585	424	8	rara	rara	PROPN
ejpam-4585	424	9	.	.	PUNCT
ejpam-4585	425	1	restrained	restrain	VERB
ejpam-4585	425	2	2	2	NUM
ejpam-4585	425	3	-	-	PUNCT
ejpam-4585	425	4	resolving	resolve	VERB
ejpam-4585	425	5	sets	set	NOUN
ejpam-4585	425	6	in	in	ADP
ejpam-4585	425	7	the	the	DET
ejpam-4585	425	8	join	join	NOUN
ejpam-4585	425	9	and	and	CCONJ
ejpam-4585	425	10	corona	corona	PROPN
ejpam-4585	425	11	and	and	CCONJ
ejpam-4585	425	12	lexicographic	lexicographic	ADJ
ejpam-4585	425	13	product	product	NOUN
ejpam-4585	425	14	of	of	ADP
ejpam-4585	425	15	graphs	graph	NOUN
ejpam-4585	425	16	.	.	PUNCT
ejpam-4585	426	1	european	european	ADJ
ejpam-4585	426	2	journal	journal	PROPN
ejpam-4585	426	3	of	of	ADP
ejpam-4585	426	4	pure	pure	ADJ
ejpam-4585	426	5	and	and	CCONJ
ejpam-4585	426	6	applied	applied	ADJ
ejpam-4585	426	7	mathematics	mathematic	NOUN
ejpam-4585	426	8	,	,	PUNCT
ejpam-4585	426	9	15(3):1229–1236	15(3):1229–1236	NUM
ejpam-4585	426	10	,	,	PUNCT
ejpam-4585	426	11	2022	2022	NUM
ejpam-4585	426	12	.	.	PUNCT
ejpam-4585	427	1	references	reference	NOUN
ejpam-4585	427	2	1997	1997	NUM
ejpam-4585	427	3	[	[	X
ejpam-4585	427	4	9	9	NUM
ejpam-4585	427	5	]	]	SYM
ejpam-4585	427	6	r.	r.	PROPN
ejpam-4585	427	7	c.	c.	PROPN
ejpam-4585	427	8	brigham	brigham	PROPN
ejpam-4585	427	9	g.	g.	PROPN
ejpam-4585	427	10	chartrand	chartrand	PROPN
ejpam-4585	427	11	d.	d.	PROPN
ejpam-4585	427	12	dutton	dutton	PROPN
ejpam-4585	427	13	and	and	CCONJ
ejpam-4585	427	14	p.	p.	PROPN
ejpam-4585	427	15	zhang	zhang	PROPN
ejpam-4585	427	16	.	.	PUNCT
ejpam-4585	428	1	resolving	resolve	VERB
ejpam-4585	428	2	domination	domination	NOUN
ejpam-4585	428	3	in	in	ADP
ejpam-4585	428	4	graph	graph	NOUN
ejpam-4585	428	5	.	.	PUNCT
ejpam-4585	429	1	mathematica	mathematica	PROPN
ejpam-4585	429	2	bohemica	bohemica	PROPN
ejpam-4585	429	3	,	,	PUNCT
ejpam-4585	429	4	128(2003):25–36	128(2003):25–36	NOUN
ejpam-4585	429	5	.	.	PUNCT
ejpam-4585	430	1	[	[	X
ejpam-4585	430	2	10	10	NUM
ejpam-4585	430	3	]	]	X
ejpam-4585	430	4	f.	f.	PROPN
ejpam-4585	430	5	harary	harary	PROPN
ejpam-4585	430	6	and	and	CCONJ
ejpam-4585	430	7	r.	r.	PROPN
ejpam-4585	430	8	melter	melter	NOUN
ejpam-4585	430	9	.	.	PUNCT
ejpam-4585	431	1	on	on	ADP
ejpam-4585	431	2	the	the	DET
ejpam-4585	431	3	metric	metric	ADJ
ejpam-4585	431	4	dimension	dimension	NOUN
ejpam-4585	431	5	of	of	ADP
ejpam-4585	431	6	a	a	DET
ejpam-4585	431	7	graph	graph	NOUN
ejpam-4585	431	8	.	.	PUNCT
ejpam-4585	431	9	ars	ars	PROPN
ejpam-4585	431	10	combinatoria	combinatoria	NOUN
ejpam-4585	431	11	,	,	PUNCT
ejpam-4585	431	12	2:191–195	2:191–195	NUM
ejpam-4585	431	13	,	,	PUNCT
ejpam-4585	431	14	1976	1976	NUM
ejpam-4585	431	15	.	.	PUNCT
ejpam-4585	432	1	[	[	X
ejpam-4585	432	2	11	11	NUM
ejpam-4585	432	3	]	]	PUNCT
ejpam-4585	432	4	j.	j.	PROPN
ejpam-4585	432	5	mohamad	mohamad	PROPN
ejpam-4585	432	6	and	and	CCONJ
ejpam-4585	432	7	h.	h.	PROPN
ejpam-4585	432	8	rara	rara	PROPN
ejpam-4585	432	9	.	.	PUNCT
ejpam-4585	433	1	on	on	ADP
ejpam-4585	433	2	resolving	resolve	VERB
ejpam-4585	433	3	hop	hop	NOUN
ejpam-4585	433	4	domination	domination	NOUN
ejpam-4585	433	5	in	in	ADP
ejpam-4585	433	6	graphs	graph	NOUN
ejpam-4585	433	7	.	.	PUNCT
ejpam-4585	434	1	european	european	ADJ
ejpam-4585	434	2	journal	journal	PROPN
ejpam-4585	434	3	of	of	ADP
ejpam-4585	434	4	pure	pure	ADJ
ejpam-4585	434	5	and	and	CCONJ
ejpam-4585	434	6	applied	applied	ADJ
ejpam-4585	434	7	mathematics	mathematic	NOUN
ejpam-4585	434	8	,	,	PUNCT
ejpam-4585	434	9	14(3):1015–1023	14(3):1015–1023	NUM
ejpam-4585	434	10	,	,	PUNCT
ejpam-4585	434	11	2021	2021	NUM
ejpam-4585	434	12	.	.	PUNCT
ejpam-4585	435	1	[	[	X
ejpam-4585	435	2	12	12	NUM
ejpam-4585	435	3	]	]	PUNCT
ejpam-4585	435	4	j.g.canoy	j.g.canoy	PROPN
ejpam-4585	435	5	r.	r.	PROPN
ejpam-4585	435	6	mollejon	mollejon	NOUN
ejpam-4585	435	7	and	and	CCONJ
ejpam-4585	435	8	s.	s.	PROPN
ejpam-4585	435	9	canoy	canoy	PROPN
ejpam-4585	435	10	jr	jr	PROPN
ejpam-4585	435	11	.	.	PROPN
ejpam-4585	435	12	hop	hop	PROPN
ejpam-4585	435	13	dominating	dominating	NOUN
ejpam-4585	435	14	sets	set	NOUN
ejpam-4585	435	15	in	in	ADP
ejpam-4585	435	16	graphs	graph	NOUN
ejpam-4585	435	17	under	under	ADP
ejpam-4585	435	18	binary	binary	ADJ
ejpam-4585	435	19	operations	operation	NOUN
ejpam-4585	435	20	.	.	PUNCT
ejpam-4585	436	1	european	european	ADJ
ejpam-4585	436	2	journal	journal	PROPN
ejpam-4585	436	3	of	of	ADP
ejpam-4585	436	4	pure	pure	ADJ
ejpam-4585	436	5	and	and	CCONJ
ejpam-4585	436	6	applied	applied	ADJ
ejpam-4585	436	7	mathematics	mathematic	NOUN
ejpam-4585	436	8	,	,	PUNCT
ejpam-4585	436	9	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4585	436	10	,	,	PUNCT
ejpam-4585	436	11	2019	2019	NUM
ejpam-4585	436	12	.	.	PUNCT
ejpam-4585	437	1	[	[	X
ejpam-4585	437	2	13	13	NUM
ejpam-4585	437	3	]	]	X
ejpam-4585	437	4	c.	c.	PROPN
ejpam-4585	437	5	natarajan	natarajan	PROPN
ejpam-4585	437	6	and	and	CCONJ
ejpam-4585	437	7	s.k	s.k	PROPN
ejpam-4585	437	8	.	.	PROPN
ejpam-4585	437	9	ayyaswamy	ayyaswamy	PROPN
ejpam-4585	437	10	.	.	PUNCT
ejpam-4585	438	1	hop	hop	PROPN
ejpam-4585	438	2	domination	domination	NOUN
ejpam-4585	438	3	in	in	ADP
ejpam-4585	438	4	graphs	graph	NOUN
ejpam-4585	438	5	-	-	PUNCT
ejpam-4585	438	6	ii	ii	NOUN
ejpam-4585	438	7	.	.	PUNCT
ejpam-4585	438	8	versita	versita	PROPN
ejpam-4585	438	9	,	,	PUNCT
ejpam-4585	438	10	23(2):187	23(2):187	NUM
ejpam-4585	438	11	–	–	PUNCT
ejpam-4585	438	12	199	199	NUM
ejpam-4585	438	13	,	,	PUNCT
ejpam-4585	438	14	2015	2015	NUM
ejpam-4585	438	15	.	.	PUNCT
ejpam-4585	439	1	[	[	X
ejpam-4585	439	2	14	14	NUM
ejpam-4585	439	3	]	]	X
ejpam-4585	439	4	v.	v.	ADP
ejpam-4585	439	5	saenpholphat	saenpholphat	PROPN
ejpam-4585	439	6	and	and	CCONJ
ejpam-4585	439	7	p.	p.	PROPN
ejpam-4585	439	8	zhang	zhang	PROPN
ejpam-4585	439	9	.	.	PUNCT
ejpam-4585	440	1	on	on	ADP
ejpam-4585	440	2	connected	connected	ADJ
ejpam-4585	440	3	resolvability	resolvability	NOUN
ejpam-4585	440	4	of	of	ADP
ejpam-4585	440	5	graphs	graph	NOUN
ejpam-4585	440	6	.	.	PUNCT
ejpam-4585	441	1	australian	australian	ADJ
ejpam-4585	441	2	journal	journal	NOUN
ejpam-4585	441	3	of	of	ADP
ejpam-4585	441	4	combinatorics	combinatoric	NOUN
ejpam-4585	441	5	,	,	PUNCT
ejpam-4585	441	6	28:26–37	28:26–37	NUM
ejpam-4585	441	7	,	,	PUNCT
ejpam-4585	441	8	2003	2003	NUM
ejpam-4585	441	9	.	.	PUNCT
ejpam-4585	442	1	[	[	X
ejpam-4585	442	2	15	15	NUM
ejpam-4585	442	3	]	]	X
ejpam-4585	442	4	p.	p.	PROPN
ejpam-4585	442	5	j.	j.	PROPN
ejpam-4585	442	6	slater	slater	PROPN
ejpam-4585	442	7	.	.	PUNCT
ejpam-4585	443	1	dominating	dominating	NOUN
ejpam-4585	443	2	and	and	CCONJ
ejpam-4585	443	3	reference	reference	NOUN
ejpam-4585	443	4	sets	set	NOUN
ejpam-4585	443	5	in	in	ADP
ejpam-4585	443	6	a	a	DET
ejpam-4585	443	7	graph	graph	NOUN
ejpam-4585	443	8	.	.	PUNCT
ejpam-4585	444	1	journal	journal	NOUN
ejpam-4585	444	2	of	of	ADP
ejpam-4585	444	3	mathematics	mathematic	NOUN
ejpam-4585	444	4	and	and	CCONJ
ejpam-4585	444	5	physical	physical	ADJ
ejpam-4585	444	6	science	science	NOUN
ejpam-4585	444	7	,	,	PUNCT
ejpam-4585	444	8	22(4):445–455	22(4):445–455	PROPN
ejpam-4585	444	9	.	.	PUNCT
ejpam-4585	445	1	[	[	X
ejpam-4585	445	2	16	16	NUM
ejpam-4585	445	3	]	]	X
ejpam-4585	445	4	d.	d.	PROPN
ejpam-4585	445	5	kuziak	kuziak	PROPN
ejpam-4585	445	6	i.g	i.g	PROPN
ejpam-4585	445	7	.	.	PROPN
ejpam-4585	445	8	yero	yero	PROPN
ejpam-4585	445	9	and	and	CCONJ
ejpam-4585	445	10	j.a	j.a	PROPN
ejpam-4585	445	11	.	.	PROPN
ejpam-4585	445	12	rodriguez	rodriguez	PROPN
ejpam-4585	445	13	-	-	PUNCT
ejpam-4585	445	14	velasquez	velasquez	PROPN
ejpam-4585	445	15	.	.	PROPN
ejpam-4585	445	16	closed	close	VERB
ejpam-4585	445	17	formulae	formulae	ADJ
ejpam-4585	445	18	for	for	ADP
ejpam-4585	445	19	the	the	DET
ejpam-4585	445	20	strong	strong	ADJ
ejpam-4585	445	21	metric	metric	ADJ
ejpam-4585	445	22	dimension	dimension	NOUN
ejpam-4585	445	23	of	of	ADP
ejpam-4585	445	24	lexicographic	lexicographic	ADJ
ejpam-4585	445	25	product	product	NOUN
ejpam-4585	445	26	of	of	ADP
ejpam-4585	445	27	graphs	graph	NOUN
ejpam-4585	445	28	.	.	PUNCT
ejpam-4585	446	1	discussiones	discussione	NOUN
ejpam-4585	446	2	mathematicae	mathematicae	PROPN
ejpam-4585	446	3	graph	graph	NOUN
ejpam-4585	446	4	theory	theory	NOUN
ejpam-4585	446	5	,	,	PUNCT
ejpam-4585	446	6	36:1051–1064	36:1051–1064	NUM
ejpam-4585	446	7	,	,	PUNCT
ejpam-4585	446	8	2016	2016	NUM
ejpam-4585	446	9	.	.	PUNCT