id	sid	tid	token	lemma	pos
ejpam-4506	1	1	european	european	PROPN
ejpam-4506	1	2	journal	journal	PROPN
ejpam-4506	1	3	of	of	ADP
ejpam-4506	1	4	pure	pure	ADJ
ejpam-4506	1	5	and	and	CCONJ
ejpam-4506	1	6	applied	apply	VERB
ejpam-4506	1	7	mathematics	mathematic	NOUN
ejpam-4506	1	8	vol	vol	NOUN
ejpam-4506	1	9	.	.	PUNCT
ejpam-4506	2	1	16	16	NUM
ejpam-4506	2	2	,	,	PUNCT
ejpam-4506	2	3	no	no	INTJ
ejpam-4506	2	4	.	.	NOUN
ejpam-4506	2	5	1	1	NUM
ejpam-4506	2	6	,	,	PUNCT
ejpam-4506	2	7	2023	2023	NUM
ejpam-4506	2	8	,	,	PUNCT
ejpam-4506	2	9	169	169	NUM
ejpam-4506	2	10	-	-	SYM
ejpam-4506	2	11	179	179	NUM
ejpam-4506	2	12	issn	issn	PROPN
ejpam-4506	2	13	1307	1307	NUM
ejpam-4506	2	14	-	-	SYM
ejpam-4506	2	15	5543	5543	NUM
ejpam-4506	2	16	–	–	PUNCT
ejpam-4506	2	17	ejpam.com	ejpam.com	X
ejpam-4506	2	18	published	publish	VERB
ejpam-4506	2	19	by	by	ADP
ejpam-4506	2	20	new	new	PROPN
ejpam-4506	2	21	york	york	PROPN
ejpam-4506	2	22	business	business	PROPN
ejpam-4506	2	23	global	global	ADJ
ejpam-4506	2	24	path	path	NOUN
ejpam-4506	2	25	-	-	PUNCT
ejpam-4506	2	26	induced	induce	VERB
ejpam-4506	2	27	closed	closed	ADJ
ejpam-4506	2	28	geodetic	geodetic	ADJ
ejpam-4506	2	29	domination	domination	NOUN
ejpam-4506	2	30	of	of	ADP
ejpam-4506	2	31	some	some	DET
ejpam-4506	2	32	common	common	ADJ
ejpam-4506	2	33	graphs	graph	NOUN
ejpam-4506	2	34	and	and	CCONJ
ejpam-4506	2	35	edge	edge	NOUN
ejpam-4506	2	36	corona	corona	NOUN
ejpam-4506	2	37	of	of	ADP
ejpam-4506	2	38	graphs	graph	NOUN
ejpam-4506	2	39	jesica	jesica	PROPN
ejpam-4506	2	40	m.	m.	PROPN
ejpam-4506	2	41	anoche1,∗	anoche1,∗	PROPN
ejpam-4506	2	42	,	,	PUNCT
ejpam-4506	2	43	imelda	imelda	PROPN
ejpam-4506	2	44	s.	s.	PROPN
ejpam-4506	2	45	aniversario1	aniversario1	PROPN
ejpam-4506	2	46	,	,	PUNCT
ejpam-4506	2	47	catherine	catherine	PROPN
ejpam-4506	2	48	i.	i.	PROPN
ejpam-4506	2	49	merca1	merca1	PROPN
ejpam-4506	3	1	1	1	NUM
ejpam-4506	3	2	department	department	NOUN
ejpam-4506	3	3	of	of	ADP
ejpam-4506	3	4	mathematics	mathematic	NOUN
ejpam-4506	3	5	and	and	CCONJ
ejpam-4506	3	6	statistics	statistic	NOUN
ejpam-4506	3	7	,	,	PUNCT
ejpam-4506	3	8	college	college	NOUN
ejpam-4506	3	9	of	of	ADP
ejpam-4506	3	10	science	science	NOUN
ejpam-4506	3	11	and	and	CCONJ
ejpam-4506	3	12	mathematics	mathematic	NOUN
ejpam-4506	3	13	,	,	PUNCT
ejpam-4506	3	14	mindanao	mindanao	PROPN
ejpam-4506	3	15	state	state	PROPN
ejpam-4506	3	16	university	university	PROPN
ejpam-4506	3	17	-	-	PUNCT
ejpam-4506	3	18	iligan	iligan	PROPN
ejpam-4506	3	19	institute	institute	PROPN
ejpam-4506	3	20	of	of	ADP
ejpam-4506	3	21	technology	technology	PROPN
ejpam-4506	3	22	,	,	PUNCT
ejpam-4506	3	23	9200	9200	NUM
ejpam-4506	3	24	iligan	iligan	ADJ
ejpam-4506	3	25	city	city	NOUN
ejpam-4506	3	26	,	,	PUNCT
ejpam-4506	3	27	philippines	philippine	NOUN
ejpam-4506	3	28	abstract	abstract	ADJ
ejpam-4506	3	29	.	.	PUNCT
ejpam-4506	4	1	let	let	VERB
ejpam-4506	4	2	g	g	PRON
ejpam-4506	4	3	be	be	AUX
ejpam-4506	4	4	a	a	DET
ejpam-4506	4	5	connected	connected	ADJ
ejpam-4506	4	6	graph	graph	NOUN
ejpam-4506	4	7	of	of	ADP
ejpam-4506	4	8	order	order	NOUN
ejpam-4506	4	9	n	n	NOUN
ejpam-4506	4	10	and	and	CCONJ
ejpam-4506	4	11	s	s	VERB
ejpam-4506	4	12	⊆	⊆	NUM
ejpam-4506	4	13	v	v	NOUN
ejpam-4506	4	14	(	(	PUNCT
ejpam-4506	4	15	g	g	NOUN
ejpam-4506	4	16	)	)	PUNCT
ejpam-4506	4	17	.	.	PUNCT
ejpam-4506	5	1	a	a	DET
ejpam-4506	5	2	closed	closed	ADJ
ejpam-4506	5	3	geodetic	geodetic	ADJ
ejpam-4506	5	4	cover	cover	NOUN
ejpam-4506	5	5	s	s	NOUN
ejpam-4506	5	6	of	of	ADP
ejpam-4506	5	7	g	g	PROPN
ejpam-4506	5	8	is	be	AUX
ejpam-4506	5	9	a	a	DET
ejpam-4506	5	10	path	path	NOUN
ejpam-4506	5	11	-	-	PUNCT
ejpam-4506	5	12	induced	induce	VERB
ejpam-4506	5	13	closed	closed	ADJ
ejpam-4506	5	14	geodetic	geodetic	ADJ
ejpam-4506	5	15	dominating	dominating	NOUN
ejpam-4506	5	16	set	set	NOUN
ejpam-4506	5	17	of	of	ADP
ejpam-4506	5	18	a	a	DET
ejpam-4506	5	19	graph	graph	NOUN
ejpam-4506	5	20	g	g	NOUN
ejpam-4506	5	21	if	if	SCONJ
ejpam-4506	5	22	a	a	DET
ejpam-4506	5	23	subgraph	subgraph	NOUN
ejpam-4506	5	24	⟨s⟩	⟨s⟩	PROPN
ejpam-4506	5	25	has	have	VERB
ejpam-4506	5	26	a	a	DET
ejpam-4506	5	27	hamiltonian	hamiltonian	ADJ
ejpam-4506	5	28	path	path	NOUN
ejpam-4506	5	29	and	and	CCONJ
ejpam-4506	5	30	s	s	VERB
ejpam-4506	5	31	is	be	AUX
ejpam-4506	5	32	a	a	DET
ejpam-4506	5	33	dominating	dominating	NOUN
ejpam-4506	5	34	set	set	NOUN
ejpam-4506	5	35	of	of	ADP
ejpam-4506	5	36	g.	g.	PROPN
ejpam-4506	5	37	the	the	DET
ejpam-4506	5	38	minimum	minimum	ADJ
ejpam-4506	5	39	cardinality	cardinality	NOUN
ejpam-4506	5	40	of	of	ADP
ejpam-4506	5	41	a	a	DET
ejpam-4506	5	42	path	path	NOUN
ejpam-4506	5	43	-	-	PUNCT
ejpam-4506	5	44	induced	induce	VERB
ejpam-4506	5	45	closed	closed	ADJ
ejpam-4506	5	46	geodetic	geodetic	ADJ
ejpam-4506	5	47	dominating	dominating	NOUN
ejpam-4506	5	48	set	set	NOUN
ejpam-4506	5	49	is	be	AUX
ejpam-4506	5	50	called	call	VERB
ejpam-4506	5	51	path	path	NOUN
ejpam-4506	5	52	-	-	PUNCT
ejpam-4506	5	53	induced	induce	VERB
ejpam-4506	5	54	closed	closed	ADJ
ejpam-4506	5	55	geodetic	geodetic	ADJ
ejpam-4506	5	56	domination	domination	NOUN
ejpam-4506	5	57	number	number	NOUN
ejpam-4506	5	58	of	of	ADP
ejpam-4506	5	59	g.	g.	PROPN
ejpam-4506	5	60	this	this	DET
ejpam-4506	5	61	study	study	NOUN
ejpam-4506	5	62	presents	present	VERB
ejpam-4506	5	63	the	the	DET
ejpam-4506	5	64	characterization	characterization	NOUN
ejpam-4506	5	65	of	of	ADP
ejpam-4506	5	66	the	the	DET
ejpam-4506	5	67	path	path	NOUN
ejpam-4506	5	68	-	-	PUNCT
ejpam-4506	5	69	induced	induce	VERB
ejpam-4506	5	70	closed	closed	ADJ
ejpam-4506	5	71	geodetic	geodetic	ADJ
ejpam-4506	5	72	dominating	dominating	NOUN
ejpam-4506	5	73	sets	set	NOUN
ejpam-4506	5	74	of	of	ADP
ejpam-4506	5	75	some	some	DET
ejpam-4506	5	76	common	common	ADJ
ejpam-4506	5	77	graphs	graph	NOUN
ejpam-4506	5	78	and	and	CCONJ
ejpam-4506	5	79	edge	edge	NOUN
ejpam-4506	5	80	corona	corona	NOUN
ejpam-4506	5	81	of	of	ADP
ejpam-4506	5	82	two	two	NUM
ejpam-4506	5	83	graphs	graph	NOUN
ejpam-4506	5	84	.	.	PUNCT
ejpam-4506	6	1	the	the	DET
ejpam-4506	6	2	path	path	NOUN
ejpam-4506	6	3	-	-	PUNCT
ejpam-4506	6	4	induced	induce	VERB
ejpam-4506	6	5	closed	closed	ADJ
ejpam-4506	6	6	geodetic	geodetic	ADJ
ejpam-4506	6	7	domination	domination	NOUN
ejpam-4506	6	8	numbers	number	NOUN
ejpam-4506	6	9	of	of	ADP
ejpam-4506	6	10	these	these	DET
ejpam-4506	6	11	graphs	graph	NOUN
ejpam-4506	6	12	are	be	AUX
ejpam-4506	6	13	also	also	ADV
ejpam-4506	6	14	determined	determine	VERB
ejpam-4506	6	15	.	.	PUNCT
ejpam-4506	7	1	2020	2020	NUM
ejpam-4506	7	2	mathematics	mathematic	NOUN
ejpam-4506	7	3	subject	subject	NOUN
ejpam-4506	7	4	classifications	classification	NOUN
ejpam-4506	7	5	:	:	PUNCT
ejpam-4506	7	6	05c69	05c69	X
ejpam-4506	7	7	key	key	ADJ
ejpam-4506	7	8	words	word	NOUN
ejpam-4506	7	9	and	and	CCONJ
ejpam-4506	7	10	phrases	phrase	NOUN
ejpam-4506	7	11	:	:	PUNCT
ejpam-4506	7	12	geodetic	geodetic	ADJ
ejpam-4506	7	13	set	set	NOUN
ejpam-4506	7	14	,	,	PUNCT
ejpam-4506	7	15	geodetic	geodetic	ADJ
ejpam-4506	7	16	dominating	dominating	NOUN
ejpam-4506	7	17	set	set	NOUN
ejpam-4506	7	18	,	,	PUNCT
ejpam-4506	7	19	path	path	NOUN
ejpam-4506	7	20	-	-	PUNCT
ejpam-4506	7	21	induced	induce	VERB
ejpam-4506	7	22	closed	closed	ADJ
ejpam-4506	7	23	geodetic	geodetic	ADJ
ejpam-4506	7	24	set	set	NOUN
ejpam-4506	7	25	,	,	PUNCT
ejpam-4506	7	26	path	path	NOUN
ejpam-4506	7	27	-	-	PUNCT
ejpam-4506	7	28	induced	induce	VERB
ejpam-4506	7	29	closed	closed	ADJ
ejpam-4506	7	30	geodetic	geodetic	ADJ
ejpam-4506	7	31	dominating	dominating	NOUN
ejpam-4506	7	32	set	set	NOUN
ejpam-4506	7	33	,	,	PUNCT
ejpam-4506	7	34	path	path	NOUN
ejpam-4506	7	35	-	-	PUNCT
ejpam-4506	7	36	induced	induce	VERB
ejpam-4506	7	37	closed	closed	ADJ
ejpam-4506	7	38	geodetic	geodetic	ADJ
ejpam-4506	7	39	domination	domination	NOUN
ejpam-4506	7	40	number	number	NOUN
ejpam-4506	7	41	1	1	NUM
ejpam-4506	7	42	.	.	PUNCT
ejpam-4506	8	1	introduction	introduction	NOUN
ejpam-4506	8	2	domination	domination	NOUN
ejpam-4506	8	3	in	in	ADP
ejpam-4506	8	4	graph	graph	NOUN
ejpam-4506	8	5	is	be	AUX
ejpam-4506	8	6	one	one	NUM
ejpam-4506	8	7	of	of	ADP
ejpam-4506	8	8	the	the	DET
ejpam-4506	8	9	most	most	ADV
ejpam-4506	8	10	studied	study	VERB
ejpam-4506	8	11	concepts	concept	NOUN
ejpam-4506	8	12	in	in	ADP
ejpam-4506	8	13	graph	graph	NOUN
ejpam-4506	8	14	theory	theory	NOUN
ejpam-4506	8	15	.	.	PUNCT
ejpam-4506	9	1	it	it	PRON
ejpam-4506	9	2	was	be	AUX
ejpam-4506	9	3	first	first	ADV
ejpam-4506	9	4	developed	develop	VERB
ejpam-4506	9	5	in	in	ADP
ejpam-4506	9	6	the	the	DET
ejpam-4506	9	7	late	late	ADJ
ejpam-4506	9	8	1950	1950	NUM
ejpam-4506	9	9	’s	’s	NOUN
ejpam-4506	9	10	and	and	CCONJ
ejpam-4506	9	11	1960	1960	NUM
ejpam-4506	9	12	’s	’s	PART
ejpam-4506	9	13	,	,	PUNCT
ejpam-4506	9	14	beginning	begin	VERB
ejpam-4506	9	15	with	with	ADP
ejpam-4506	9	16	c.	c.	PROPN
ejpam-4506	9	17	berge	berge	PROPN
ejpam-4506	9	18	in	in	ADP
ejpam-4506	9	19	1958	1958	NUM
ejpam-4506	9	20	.	.	PUNCT
ejpam-4506	10	1	on	on	ADP
ejpam-4506	10	2	his	his	PRON
ejpam-4506	10	3	study	study	NOUN
ejpam-4506	10	4	,	,	PUNCT
ejpam-4506	10	5	he	he	PRON
ejpam-4506	10	6	referred	refer	VERB
ejpam-4506	10	7	the	the	DET
ejpam-4506	10	8	domination	domination	NOUN
ejpam-4506	10	9	number	number	NOUN
ejpam-4506	10	10	as	as	ADP
ejpam-4506	10	11	the	the	DET
ejpam-4506	10	12	“	"	PUNCT
ejpam-4506	10	13	coefficient	coefficient	NOUN
ejpam-4506	10	14	of	of	ADP
ejpam-4506	10	15	external	external	ADJ
ejpam-4506	10	16	stability	stability	NOUN
ejpam-4506	10	17	”	"	PUNCT
ejpam-4506	10	18	.	.	PUNCT
ejpam-4506	11	1	in	in	ADP
ejpam-4506	11	2	1962	1962	NUM
ejpam-4506	11	3	,	,	PUNCT
ejpam-4506	11	4	o.	o.	NOUN
ejpam-4506	11	5	ore	ore	NOUN
ejpam-4506	11	6	introduced	introduce	VERB
ejpam-4506	11	7	the	the	DET
ejpam-4506	11	8	terms	term	NOUN
ejpam-4506	11	9	“	"	PUNCT
ejpam-4506	11	10	dominating	dominating	NOUN
ejpam-4506	11	11	set	set	NOUN
ejpam-4506	11	12	”	"	PUNCT
ejpam-4506	11	13	and	and	CCONJ
ejpam-4506	11	14	“	"	PUNCT
ejpam-4506	11	15	domination	domination	NOUN
ejpam-4506	11	16	number	number	NOUN
ejpam-4506	11	17	”	"	PUNCT
ejpam-4506	11	18	.	.	PUNCT
ejpam-4506	12	1	years	year	NOUN
ejpam-4506	12	2	later	later	ADV
ejpam-4506	12	3	,	,	PUNCT
ejpam-4506	12	4	a	a	DET
ejpam-4506	12	5	new	new	ADJ
ejpam-4506	12	6	domination	domination	NOUN
ejpam-4506	12	7	parameter	parameter	NOUN
ejpam-4506	12	8	called	call	VERB
ejpam-4506	12	9	geodetic	geodetic	ADJ
ejpam-4506	12	10	domination	domination	NOUN
ejpam-4506	12	11	in	in	ADP
ejpam-4506	12	12	graph	graph	NOUN
ejpam-4506	12	13	was	be	AUX
ejpam-4506	12	14	introduced	introduce	VERB
ejpam-4506	12	15	by	by	ADP
ejpam-4506	12	16	escuadro	escuadro	NOUN
ejpam-4506	12	17	et	et	PROPN
ejpam-4506	12	18	al	al	PROPN
ejpam-4506	12	19	.	.	PROPN
ejpam-4506	13	1	(	(	PUNCT
ejpam-4506	13	2	2011	2011	NUM
ejpam-4506	13	3	)	)	PUNCT
ejpam-4506	14	1	and	and	CCONJ
ejpam-4506	14	2	defined	define	VERB
ejpam-4506	14	3	that	that	SCONJ
ejpam-4506	14	4	a	a	DET
ejpam-4506	14	5	vertex	vertex	NOUN
ejpam-4506	14	6	in	in	ADP
ejpam-4506	14	7	a	a	DET
ejpam-4506	14	8	graph	graph	NOUN
ejpam-4506	14	9	g	g	NOUN
ejpam-4506	14	10	dominates	dominate	VERB
ejpam-4506	14	11	itself	itself	PRON
ejpam-4506	14	12	and	and	CCONJ
ejpam-4506	14	13	its	its	PRON
ejpam-4506	14	14	neighbors	neighbor	NOUN
ejpam-4506	14	15	.	.	PUNCT
ejpam-4506	15	1	on	on	ADP
ejpam-4506	15	2	the	the	DET
ejpam-4506	15	3	other	other	ADJ
ejpam-4506	15	4	hand	hand	NOUN
ejpam-4506	15	5	,	,	PUNCT
ejpam-4506	15	6	o.	o.	NOUN
ejpam-4506	15	7	cauntongan	cauntongan	PROPN
ejpam-4506	15	8	and	and	CCONJ
ejpam-4506	15	9	i.	i.	PROPN
ejpam-4506	15	10	aniversario	aniversario	NOUN
ejpam-4506	16	1	[	[	X
ejpam-4506	16	2	3	3	NUM
ejpam-4506	16	3	]	]	PUNCT
ejpam-4506	16	4	introduced	introduce	VERB
ejpam-4506	16	5	and	and	CCONJ
ejpam-4506	16	6	studied	study	VERB
ejpam-4506	16	7	the	the	DET
ejpam-4506	16	8	concept	concept	NOUN
ejpam-4506	16	9	on	on	ADP
ejpam-4506	16	10	path	path	NOUN
ejpam-4506	16	11	-	-	PUNCT
ejpam-4506	16	12	induced	induce	VERB
ejpam-4506	16	13	closed	closed	ADJ
ejpam-4506	16	14	geodetic	geodetic	ADJ
ejpam-4506	16	15	number	number	NOUN
ejpam-4506	16	16	of	of	ADP
ejpam-4506	16	17	some	some	DET
ejpam-4506	16	18	graphs	graph	NOUN
ejpam-4506	16	19	.	.	PUNCT
ejpam-4506	17	1	this	this	DET
ejpam-4506	17	2	concept	concept	NOUN
ejpam-4506	17	3	follows	follow	VERB
ejpam-4506	17	4	from	from	ADP
ejpam-4506	17	5	the	the	DET
ejpam-4506	17	6	definition	definition	NOUN
ejpam-4506	17	7	of	of	ADP
ejpam-4506	17	8	geodetic	geodetic	ADJ
ejpam-4506	17	9	numbers	number	NOUN
ejpam-4506	17	10	of	of	ADP
ejpam-4506	17	11	graphs	graph	NOUN
ejpam-4506	17	12	introduced	introduce	VERB
ejpam-4506	17	13	by	by	ADP
ejpam-4506	17	14	buckley	buckley	NOUN
ejpam-4506	17	15	and	and	CCONJ
ejpam-4506	17	16	harary	harary	NOUN
ejpam-4506	17	17	in	in	ADP
ejpam-4506	17	18	[	[	X
ejpam-4506	17	19	2	2	NUM
ejpam-4506	17	20	]	]	PUNCT
ejpam-4506	17	21	,	,	PUNCT
ejpam-4506	17	22	closed	close	VERB
ejpam-4506	17	23	geodetic	geodetic	ADJ
ejpam-4506	17	24	numbers	number	NOUN
ejpam-4506	17	25	in	in	ADP
ejpam-4506	17	26	[	[	X
ejpam-4506	17	27	1	1	NUM
ejpam-4506	17	28	]	]	PUNCT
ejpam-4506	17	29	,	,	PUNCT
ejpam-4506	17	30	and	and	CCONJ
ejpam-4506	17	31	path	path	NOUN
ejpam-4506	17	32	-	-	PUNCT
ejpam-4506	17	33	induced	induce	VERB
ejpam-4506	17	34	geodetic	geodetic	ADJ
ejpam-4506	17	35	numbers	number	NOUN
ejpam-4506	17	36	in	in	ADP
ejpam-4506	17	37	[	[	X
ejpam-4506	17	38	7	7	NUM
ejpam-4506	17	39	]	]	PUNCT
ejpam-4506	17	40	.	.	PUNCT
ejpam-4506	18	1	in	in	ADP
ejpam-4506	18	2	their	their	PRON
ejpam-4506	18	3	studies	study	NOUN
ejpam-4506	18	4	,	,	PUNCT
ejpam-4506	18	5	they	they	PRON
ejpam-4506	18	6	were	be	AUX
ejpam-4506	18	7	able	able	ADJ
ejpam-4506	18	8	to	to	PART
ejpam-4506	18	9	present	present	VERB
ejpam-4506	18	10	some	some	DET
ejpam-4506	18	11	properties	property	NOUN
ejpam-4506	18	12	and	and	CCONJ
ejpam-4506	18	13	characterized	characterize	VERB
ejpam-4506	18	14	the	the	DET
ejpam-4506	18	15	path	path	NOUN
ejpam-4506	18	16	-	-	PUNCT
ejpam-4506	18	17	induced	induce	VERB
ejpam-4506	18	18	closed	closed	ADJ
ejpam-4506	18	19	geodetic	geodetic	ADJ
ejpam-4506	18	20	set	set	NOUN
ejpam-4506	18	21	of	of	ADP
ejpam-4506	18	22	some	some	DET
ejpam-4506	18	23	common	common	ADJ
ejpam-4506	18	24	graphs	graph	NOUN
ejpam-4506	18	25	and	and	CCONJ
ejpam-4506	18	26	determined	determine	VERB
ejpam-4506	18	27	the	the	DET
ejpam-4506	18	28	path	path	NOUN
ejpam-4506	18	29	-	-	PUNCT
ejpam-4506	18	30	induced	induce	VERB
ejpam-4506	18	31	closed	closed	ADJ
ejpam-4506	18	32	geodetic	geodetic	ADJ
ejpam-4506	18	33	numbers	number	NOUN
ejpam-4506	18	34	of	of	ADP
ejpam-4506	18	35	those	those	DET
ejpam-4506	18	36	graphs	graph	NOUN
ejpam-4506	18	37	.	.	PUNCT
ejpam-4506	19	1	the	the	DET
ejpam-4506	19	2	researchers	researcher	NOUN
ejpam-4506	19	3	believe	believe	VERB
ejpam-4506	19	4	that	that	SCONJ
ejpam-4506	19	5	the	the	DET
ejpam-4506	19	6	concept	concept	NOUN
ejpam-4506	19	7	of	of	ADP
ejpam-4506	19	8	path	path	NOUN
ejpam-4506	19	9	-	-	PUNCT
ejpam-4506	19	10	induced	induce	VERB
ejpam-4506	19	11	closed	closed	ADJ
ejpam-4506	19	12	∗corresponding	∗corresponde	VERB
ejpam-4506	19	13	author	author	NOUN
ejpam-4506	19	14	.	.	PUNCT
ejpam-4506	20	1	doi	doi	NOUN
ejpam-4506	20	2	:	:	PUNCT
ejpam-4506	20	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4506	https://doi.org/10.29020/nybg.ejpam.v16i1.4506	NUM
ejpam-4506	20	4	email	email	NOUN
ejpam-4506	20	5	addresses	address	NOUN
ejpam-4506	20	6	:	:	PUNCT
ejpam-4506	20	7	jesica.anoche@g.msuiit.edu.ph	jesica.anoche@g.msuiit.edu.ph	PROPN
ejpam-4506	20	8	(	(	PUNCT
ejpam-4506	20	9	j.anoche	j.anoche	NOUN
ejpam-4506	20	10	)	)	PUNCT
ejpam-4506	20	11	,	,	PUNCT
ejpam-4506	20	12	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-4506	20	13	(	(	PUNCT
ejpam-4506	20	14	i.	i.	PROPN
ejpam-4506	20	15	aniversario	aniversario	PROPN
ejpam-4506	20	16	)	)	PUNCT
ejpam-4506	20	17	,	,	PUNCT
ejpam-4506	20	18	catherine.merca@g.msuiit.edu.ph	catherine.merca@g.msuiit.edu.ph	PROPN
ejpam-4506	20	19	(	(	PUNCT
ejpam-4506	20	20	c.	c.	PROPN
ejpam-4506	20	21	merca	merca	PROPN
ejpam-4506	20	22	)	)	PUNCT
ejpam-4506	20	23	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4506	20	24	169	169	NUM
ejpam-4506	21	1	©	©	PROPN
ejpam-4506	21	2	2023	2023	NUM
ejpam-4506	21	3	ejpam	ejpam	NOUN
ejpam-4506	21	4	all	all	DET
ejpam-4506	21	5	rights	right	NOUN
ejpam-4506	21	6	reserved	reserve	VERB
ejpam-4506	21	7	.	.	PUNCT
ejpam-4506	22	1	j.	j.	PROPN
ejpam-4506	22	2	anoche	anoche	PROPN
ejpam-4506	22	3	,	,	PUNCT
ejpam-4506	22	4	i.	i.	PROPN
ejpam-4506	22	5	aniversario	aniversario	PROPN
ejpam-4506	22	6	,	,	PUNCT
ejpam-4506	22	7	c.	c.	PROPN
ejpam-4506	22	8	merca	merca	PROPN
ejpam-4506	22	9	/	/	SYM
ejpam-4506	22	10	eur	eur	PROPN
ejpam-4506	22	11	.	.	PUNCT
ejpam-4506	23	1	j.	j.	PROPN
ejpam-4506	23	2	pure	pure	PROPN
ejpam-4506	23	3	appl	appl	PROPN
ejpam-4506	23	4	.	.	PROPN
ejpam-4506	23	5	math	math	PROPN
ejpam-4506	23	6	,	,	PUNCT
ejpam-4506	23	7	16	16	NUM
ejpam-4506	23	8	(	(	PUNCT
ejpam-4506	23	9	1	1	NUM
ejpam-4506	23	10	)	)	PUNCT
ejpam-4506	23	11	(	(	PUNCT
ejpam-4506	23	12	2023	2023	NUM
ejpam-4506	23	13	)	)	PUNCT
ejpam-4506	23	14	,	,	PUNCT
ejpam-4506	23	15	169	169	NUM
ejpam-4506	23	16	-	-	SYM
ejpam-4506	23	17	179	179	NUM
ejpam-4506	23	18	170	170	NUM
ejpam-4506	23	19	geodetic	geodetic	ADJ
ejpam-4506	23	20	numbers	number	NOUN
ejpam-4506	23	21	of	of	ADP
ejpam-4506	23	22	graphs	graph	NOUN
ejpam-4506	23	23	can	can	AUX
ejpam-4506	23	24	be	be	AUX
ejpam-4506	23	25	applied	apply	VERB
ejpam-4506	23	26	in	in	ADP
ejpam-4506	23	27	travel	travel	NOUN
ejpam-4506	23	28	time	time	NOUN
ejpam-4506	23	29	saving	saving	NOUN
ejpam-4506	23	30	,	,	PUNCT
ejpam-4506	23	31	facility	facility	NOUN
ejpam-4506	23	32	location	location	NOUN
ejpam-4506	23	33	,	,	PUNCT
ejpam-4506	23	34	goods	good	NOUN
ejpam-4506	23	35	distribution	distribution	NOUN
ejpam-4506	23	36	,	,	PUNCT
ejpam-4506	23	37	project	project	NOUN
ejpam-4506	23	38	crashing	crash	VERB
ejpam-4506	23	39	and	and	CCONJ
ejpam-4506	23	40	other	other	ADJ
ejpam-4506	23	41	things	thing	NOUN
ejpam-4506	23	42	in	in	ADP
ejpam-4506	23	43	which	which	PRON
ejpam-4506	23	44	this	this	DET
ejpam-4506	23	45	concept	concept	NOUN
ejpam-4506	23	46	will	will	AUX
ejpam-4506	23	47	be	be	AUX
ejpam-4506	23	48	of	of	ADP
ejpam-4506	23	49	great	great	ADJ
ejpam-4506	23	50	help	help	NOUN
ejpam-4506	23	51	.	.	PUNCT
ejpam-4506	24	1	these	these	DET
ejpam-4506	24	2	previous	previous	ADJ
ejpam-4506	24	3	studies	study	NOUN
ejpam-4506	24	4	motivated	motivate	VERB
ejpam-4506	24	5	the	the	DET
ejpam-4506	24	6	researchers	researcher	NOUN
ejpam-4506	24	7	to	to	PART
ejpam-4506	24	8	combine	combine	VERB
ejpam-4506	24	9	the	the	DET
ejpam-4506	24	10	concepts	concept	NOUN
ejpam-4506	24	11	of	of	ADP
ejpam-4506	24	12	pathinduced	pathinduce	VERB
ejpam-4506	24	13	closed	close	VERB
ejpam-4506	24	14	geodesic	geodesic	ADJ
ejpam-4506	24	15	and	and	CCONJ
ejpam-4506	24	16	dominating	dominating	NOUN
ejpam-4506	24	17	sets	set	NOUN
ejpam-4506	24	18	in	in	ADP
ejpam-4506	24	19	graphs	graph	NOUN
ejpam-4506	24	20	.	.	PUNCT
ejpam-4506	25	1	that	that	PRON
ejpam-4506	25	2	is	is	ADV
ejpam-4506	25	3	,	,	PUNCT
ejpam-4506	25	4	a	a	DET
ejpam-4506	25	5	set	set	NOUN
ejpam-4506	25	6	s	s	NOUN
ejpam-4506	25	7	⊆	⊆	NUM
ejpam-4506	25	8	v	v	NOUN
ejpam-4506	25	9	(	(	PUNCT
ejpam-4506	25	10	g	g	NOUN
ejpam-4506	25	11	)	)	PUNCT
ejpam-4506	25	12	is	be	AUX
ejpam-4506	25	13	both	both	PRON
ejpam-4506	25	14	a	a	DET
ejpam-4506	25	15	path	path	NOUN
ejpam-4506	25	16	-	-	PUNCT
ejpam-4506	25	17	induced	induce	VERB
ejpam-4506	25	18	closed	closed	ADJ
ejpam-4506	25	19	geodetic	geodetic	ADJ
ejpam-4506	25	20	set	set	NOUN
ejpam-4506	25	21	and	and	CCONJ
ejpam-4506	25	22	a	a	DET
ejpam-4506	25	23	dominating	dominating	NOUN
ejpam-4506	25	24	set	set	NOUN
ejpam-4506	25	25	of	of	ADP
ejpam-4506	25	26	g.	g.	PROPN
ejpam-4506	25	27	in	in	ADP
ejpam-4506	25	28	this	this	DET
ejpam-4506	25	29	study	study	NOUN
ejpam-4506	25	30	,	,	PUNCT
ejpam-4506	25	31	we	we	PRON
ejpam-4506	25	32	only	only	ADV
ejpam-4506	25	33	consider	consider	VERB
ejpam-4506	25	34	a	a	DET
ejpam-4506	25	35	connected	connected	ADJ
ejpam-4506	25	36	simple	simple	ADJ
ejpam-4506	25	37	nontrivial	nontrivial	NOUN
ejpam-4506	25	38	graph	graph	NOUN
ejpam-4506	25	39	g.	g.	VERB
ejpam-4506	25	40	the	the	DET
ejpam-4506	25	41	distance	distance	NOUN
ejpam-4506	25	42	between	between	ADP
ejpam-4506	25	43	the	the	DET
ejpam-4506	25	44	vertices	vertex	NOUN
ejpam-4506	25	45	u	u	NOUN
ejpam-4506	25	46	and	and	CCONJ
ejpam-4506	25	47	v	v	NOUN
ejpam-4506	25	48	,	,	PUNCT
ejpam-4506	25	49	denoted	denote	VERB
ejpam-4506	25	50	by	by	ADP
ejpam-4506	25	51	dg(u	dg(u	NOUN
ejpam-4506	25	52	,	,	PUNCT
ejpam-4506	25	53	v	v	NOUN
ejpam-4506	25	54	)	)	PUNCT
ejpam-4506	25	55	,	,	PUNCT
ejpam-4506	25	56	is	be	AUX
ejpam-4506	25	57	the	the	DET
ejpam-4506	25	58	shortest	short	ADJ
ejpam-4506	25	59	length	length	NOUN
ejpam-4506	25	60	of	of	ADP
ejpam-4506	25	61	the	the	DET
ejpam-4506	25	62	u	u	NOUN
ejpam-4506	25	63	-	-	PROPN
ejpam-4506	25	64	v	v	ADJ
ejpam-4506	25	65	path	path	NOUN
ejpam-4506	25	66	in	in	ADP
ejpam-4506	25	67	g.	g.	PROPN
ejpam-4506	25	68	a	a	DET
ejpam-4506	25	69	u	u	NOUN
ejpam-4506	25	70	-	-	NOUN
ejpam-4506	25	71	v	v	ADJ
ejpam-4506	25	72	path	path	NOUN
ejpam-4506	25	73	of	of	ADP
ejpam-4506	25	74	length	length	NOUN
ejpam-4506	25	75	dg(u	dg(u	PROPN
ejpam-4506	25	76	,	,	PUNCT
ejpam-4506	25	77	v	v	NOUN
ejpam-4506	25	78	)	)	PUNCT
ejpam-4506	25	79	is	be	AUX
ejpam-4506	25	80	called	call	VERB
ejpam-4506	25	81	a	a	DET
ejpam-4506	25	82	u	u	NOUN
ejpam-4506	25	83	-	-	NOUN
ejpam-4506	25	84	v	v	ADJ
ejpam-4506	25	85	geodesic	geodesic	NOUN
ejpam-4506	25	86	.	.	PUNCT
ejpam-4506	26	1	for	for	ADP
ejpam-4506	26	2	every	every	DET
ejpam-4506	26	3	two	two	NUM
ejpam-4506	26	4	vertices	vertex	NOUN
ejpam-4506	26	5	u	u	NOUN
ejpam-4506	26	6	and	and	CCONJ
ejpam-4506	26	7	v	v	NOUN
ejpam-4506	26	8	of	of	ADP
ejpam-4506	26	9	g	g	NOUN
ejpam-4506	26	10	,	,	PUNCT
ejpam-4506	26	11	the	the	DET
ejpam-4506	26	12	interval	interval	NOUN
ejpam-4506	26	13	ig	ig	PROPN
ejpam-4506	27	1	[	[	X
ejpam-4506	27	2	u	u	NOUN
ejpam-4506	27	3	,	,	PUNCT
ejpam-4506	27	4	v	v	NOUN
ejpam-4506	27	5	]	]	PUNCT
ejpam-4506	27	6	denotes	denote	VERB
ejpam-4506	27	7	the	the	DET
ejpam-4506	27	8	set	set	NOUN
ejpam-4506	27	9	interval	interval	NOUN
ejpam-4506	27	10	containing	contain	VERB
ejpam-4506	27	11	u	u	NOUN
ejpam-4506	27	12	,	,	PUNCT
ejpam-4506	27	13	v	v	NOUN
ejpam-4506	27	14	and	and	CCONJ
ejpam-4506	27	15	all	all	DET
ejpam-4506	27	16	vertices	vertex	NOUN
ejpam-4506	27	17	lying	lie	VERB
ejpam-4506	27	18	in	in	ADP
ejpam-4506	27	19	some	some	DET
ejpam-4506	27	20	u	u	NOUN
ejpam-4506	27	21	-	-	NOUN
ejpam-4506	27	22	v	v	ADJ
ejpam-4506	27	23	geodesic	geodesic	NOUN
ejpam-4506	27	24	.	.	PUNCT
ejpam-4506	28	1	the	the	DET
ejpam-4506	28	2	geodetic	geodetic	ADJ
ejpam-4506	28	3	closure	closure	NOUN
ejpam-4506	28	4	ig	ig	PROPN
ejpam-4506	29	1	[	[	X
ejpam-4506	29	2	s	s	X
ejpam-4506	29	3	]	]	X
ejpam-4506	29	4	is	be	AUX
ejpam-4506	29	5	the	the	DET
ejpam-4506	29	6	union	union	NOUN
ejpam-4506	29	7	of	of	ADP
ejpam-4506	29	8	intervals	interval	NOUN
ejpam-4506	29	9	between	between	ADP
ejpam-4506	29	10	all	all	DET
ejpam-4506	29	11	pairs	pair	NOUN
ejpam-4506	29	12	of	of	ADP
ejpam-4506	29	13	vertices	vertex	NOUN
ejpam-4506	29	14	from	from	ADP
ejpam-4506	29	15	s	s	PROPN
ejpam-4506	29	16	,	,	PUNCT
ejpam-4506	29	17	that	that	ADV
ejpam-4506	29	18	is	is	ADV
ejpam-4506	29	19	,	,	PUNCT
ejpam-4506	29	20	ig	ig	PROPN
ejpam-4506	30	1	[	[	X
ejpam-4506	30	2	s	s	X
ejpam-4506	30	3	]	]	X
ejpam-4506	30	4	=	=	SYM
ejpam-4506	30	5	⋃	⋃	NOUN
ejpam-4506	30	6	{	{	PUNCT
ejpam-4506	30	7	ig	ig	PROPN
ejpam-4506	30	8	[	[	X
ejpam-4506	30	9	u	u	NOUN
ejpam-4506	30	10	,	,	PUNCT
ejpam-4506	30	11	v	v	NOUN
ejpam-4506	30	12	]	]	X
ejpam-4506	30	13	:	:	PUNCT
ejpam-4506	30	14	u	u	NOUN
ejpam-4506	30	15	,	,	PUNCT
ejpam-4506	30	16	v	v	NOUN
ejpam-4506	30	17	∈	∈	NOUN
ejpam-4506	30	18	s	s	PART
ejpam-4506	30	19	}	}	PUNCT
ejpam-4506	30	20	.	.	PUNCT
ejpam-4506	31	1	a	a	DET
ejpam-4506	31	2	geodetic	geodetic	ADJ
ejpam-4506	31	3	set	set	NOUN
ejpam-4506	31	4	of	of	ADP
ejpam-4506	31	5	g	g	PROPN
ejpam-4506	31	6	is	be	AUX
ejpam-4506	31	7	a	a	DET
ejpam-4506	31	8	set	set	NOUN
ejpam-4506	31	9	s	s	NOUN
ejpam-4506	31	10	with	with	ADP
ejpam-4506	31	11	ig	ig	PROPN
ejpam-4506	32	1	[	[	X
ejpam-4506	32	2	s	s	X
ejpam-4506	32	3	]	]	X
ejpam-4506	32	4	=	=	SYM
ejpam-4506	32	5	v	v	NOUN
ejpam-4506	32	6	(	(	PUNCT
ejpam-4506	32	7	g	g	NOUN
ejpam-4506	32	8	)	)	PUNCT
ejpam-4506	32	9	.	.	PUNCT
ejpam-4506	33	1	the	the	DET
ejpam-4506	33	2	geodetic	geodetic	ADJ
ejpam-4506	33	3	number	number	NOUN
ejpam-4506	33	4	,	,	PUNCT
ejpam-4506	33	5	gn	gn	PROPN
ejpam-4506	33	6	(	(	PUNCT
ejpam-4506	33	7	g	g	NOUN
ejpam-4506	33	8	)	)	PUNCT
ejpam-4506	33	9	of	of	ADP
ejpam-4506	33	10	a	a	DET
ejpam-4506	33	11	graph	graph	NOUN
ejpam-4506	33	12	g	g	NOUN
ejpam-4506	33	13	is	be	AUX
ejpam-4506	33	14	the	the	DET
ejpam-4506	33	15	minimum	minimum	ADJ
ejpam-4506	33	16	cardinality	cardinality	NOUN
ejpam-4506	33	17	among	among	ADP
ejpam-4506	33	18	geodetic	geodetic	ADJ
ejpam-4506	33	19	sets	set	NOUN
ejpam-4506	33	20	of	of	ADP
ejpam-4506	33	21	g.	g.	PROPN
ejpam-4506	33	22	a	a	DET
ejpam-4506	33	23	set	set	NOUN
ejpam-4506	33	24	s	s	PART
ejpam-4506	33	25	is	be	AUX
ejpam-4506	33	26	a	a	DET
ejpam-4506	33	27	closed	closed	ADJ
ejpam-4506	33	28	geodetic	geodetic	ADJ
ejpam-4506	33	29	cover	cover	NOUN
ejpam-4506	33	30	of	of	ADP
ejpam-4506	33	31	g	g	PROPN
ejpam-4506	33	32	if	if	SCONJ
ejpam-4506	33	33	s	s	VERB
ejpam-4506	33	34	=	=	NOUN
ejpam-4506	33	35	{	{	PUNCT
ejpam-4506	33	36	v1	v1	PROPN
ejpam-4506	33	37	,	,	PUNCT
ejpam-4506	33	38	v2	v2	PROPN
ejpam-4506	33	39	,	,	PUNCT
ejpam-4506	33	40	·	·	PUNCT
ejpam-4506	33	41	·	·	PUNCT
ejpam-4506	33	42	·	·	PUNCT
ejpam-4506	33	43	,	,	PUNCT
ejpam-4506	33	44	vk	vk	ADP
ejpam-4506	33	45	}	}	PUNCT
ejpam-4506	33	46	such	such	ADJ
ejpam-4506	33	47	that	that	DET
ejpam-4506	33	48	v1	v1	NOUN
ejpam-4506	33	49	̸=	̸=	PROPN
ejpam-4506	33	50	v2	v2	PROPN
ejpam-4506	33	51	,	,	PUNCT
ejpam-4506	33	52	vi	vi	NOUN
ejpam-4506	33	53	/∈	/∈	PUNCT
ejpam-4506	34	1	ig	ig	PROPN
ejpam-4506	35	1	[	[	X
ejpam-4506	35	2	si−1	si−1	PROPN
ejpam-4506	35	3	]	]	PUNCT
ejpam-4506	35	4	for	for	ADP
ejpam-4506	35	5	3	3	NUM
ejpam-4506	35	6	≤	≤	NUM
ejpam-4506	35	7	i	i	NOUN
ejpam-4506	35	8	≤	≤	ADJ
ejpam-4506	36	1	k	k	PROPN
ejpam-4506	36	2	and	and	CCONJ
ejpam-4506	36	3	ig	ig	PROPN
ejpam-4506	37	1	[	[	X
ejpam-4506	37	2	sk	sk	X
ejpam-4506	37	3	]	]	X
ejpam-4506	37	4	=	=	SYM
ejpam-4506	37	5	v	v	NOUN
ejpam-4506	37	6	(	(	PUNCT
ejpam-4506	37	7	g	g	NOUN
ejpam-4506	37	8	)	)	PUNCT
ejpam-4506	37	9	,	,	PUNCT
ejpam-4506	37	10	where	where	SCONJ
ejpam-4506	37	11	si	si	PROPN
ejpam-4506	37	12	=	=	ADJ
ejpam-4506	37	13	{	{	PUNCT
ejpam-4506	37	14	v1	v1	PROPN
ejpam-4506	37	15	,	,	PUNCT
ejpam-4506	37	16	v2	v2	PROPN
ejpam-4506	37	17	,	,	PUNCT
ejpam-4506	37	18	·	·	PUNCT
ejpam-4506	37	19	·	·	PUNCT
ejpam-4506	37	20	·	·	PUNCT
ejpam-4506	37	21	,	,	PUNCT
ejpam-4506	37	22	vi	vi	X
ejpam-4506	37	23	}	}	PUNCT
ejpam-4506	37	24	for	for	ADP
ejpam-4506	37	25	i	i	PROPN
ejpam-4506	37	26	=	=	NOUN
ejpam-4506	37	27	1	1	NUM
ejpam-4506	37	28	,	,	PUNCT
ejpam-4506	37	29	2	2	NUM
ejpam-4506	37	30	,	,	PUNCT
ejpam-4506	37	31	·	·	PUNCT
ejpam-4506	37	32	·	·	PUNCT
ejpam-4506	37	33	·	·	PUNCT
ejpam-4506	37	34	,	,	PUNCT
ejpam-4506	37	35	k.	k.	PROPN
ejpam-4506	38	1	the	the	DET
ejpam-4506	38	2	closed	closed	ADJ
ejpam-4506	38	3	geodetic	geodetic	ADJ
ejpam-4506	38	4	number	number	NOUN
ejpam-4506	38	5	cgn	cgn	PROPN
ejpam-4506	38	6	(	(	PUNCT
ejpam-4506	38	7	g	g	NOUN
ejpam-4506	38	8	)	)	PUNCT
ejpam-4506	38	9	of	of	ADP
ejpam-4506	38	10	g	g	PROPN
ejpam-4506	38	11	is	be	AUX
ejpam-4506	38	12	the	the	DET
ejpam-4506	38	13	minimum	minimum	ADJ
ejpam-4506	38	14	cardinality	cardinality	NOUN
ejpam-4506	38	15	among	among	ADP
ejpam-4506	38	16	closed	closed	ADJ
ejpam-4506	38	17	geodetic	geodetic	ADJ
ejpam-4506	38	18	covers	cover	NOUN
ejpam-4506	38	19	of	of	ADP
ejpam-4506	38	20	g	g	NOUN
ejpam-4506	38	21	[	[	X
ejpam-4506	38	22	1	1	NUM
ejpam-4506	38	23	]	]	PUNCT
ejpam-4506	38	24	.	.	PUNCT
ejpam-4506	39	1	2	2	X
ejpam-4506	39	2	.	.	X
ejpam-4506	39	3	preliminary	preliminary	ADJ
ejpam-4506	39	4	concepts	concept	NOUN
ejpam-4506	39	5	and	and	CCONJ
ejpam-4506	39	6	results	result	VERB
ejpam-4506	39	7	definition	definition	NOUN
ejpam-4506	39	8	1	1	NUM
ejpam-4506	39	9	.	.	PUNCT
ejpam-4506	40	1	[	[	X
ejpam-4506	40	2	2	2	X
ejpam-4506	40	3	]	]	PUNCT
ejpam-4506	40	4	the	the	DET
ejpam-4506	40	5	removal	removal	NOUN
ejpam-4506	40	6	of	of	ADP
ejpam-4506	40	7	a	a	DET
ejpam-4506	40	8	vertex	vertex	NOUN
ejpam-4506	40	9	v	v	NOUN
ejpam-4506	40	10	from	from	ADP
ejpam-4506	40	11	a	a	DET
ejpam-4506	40	12	graph	graph	NOUN
ejpam-4506	40	13	g	g	NOUN
ejpam-4506	40	14	results	result	NOUN
ejpam-4506	40	15	in	in	ADP
ejpam-4506	40	16	the	the	DET
ejpam-4506	40	17	subgraph	subgraph	NOUN
ejpam-4506	40	18	⟨g∖	⟨g∖	X
ejpam-4506	40	19	{	{	PUNCT
ejpam-4506	40	20	v}⟩	v}⟩	NOUN
ejpam-4506	40	21	with	with	ADP
ejpam-4506	40	22	v	v	NOUN
ejpam-4506	40	23	(	(	PUNCT
ejpam-4506	40	24	g	g	PROPN
ejpam-4506	40	25	∖	∖	PROPN
ejpam-4506	40	26	{	{	PUNCT
ejpam-4506	40	27	v	v	NOUN
ejpam-4506	40	28	}	}	PUNCT
ejpam-4506	40	29	)	)	PUNCT
ejpam-4506	40	30	=	=	SYM
ejpam-4506	40	31	v	v	X
ejpam-4506	40	32	(	(	PUNCT
ejpam-4506	40	33	g	g	NOUN
ejpam-4506	40	34	)	)	PUNCT
ejpam-4506	40	35	∖	∖	NOUN
ejpam-4506	40	36	{	{	PUNCT
ejpam-4506	40	37	v	v	NOUN
ejpam-4506	40	38	}	}	PUNCT
ejpam-4506	40	39	and	and	CCONJ
ejpam-4506	40	40	e(⟨g∖	e(⟨g∖	PROPN
ejpam-4506	40	41	{	{	PUNCT
ejpam-4506	40	42	v}⟩	v}⟩	PROPN
ejpam-4506	40	43	)	)	PUNCT
ejpam-4506	40	44	=	=	PRON
ejpam-4506	40	45	{	{	PUNCT
ejpam-4506	40	46	uw	uw	PROPN
ejpam-4506	40	47	∈	∈	PROPN
ejpam-4506	40	48	e(g	e(g	PROPN
ejpam-4506	40	49	)	)	PUNCT
ejpam-4506	40	50	:	:	PUNCT
ejpam-4506	40	51	u	u	PROPN
ejpam-4506	40	52	̸=	̸=	PROPN
ejpam-4506	40	53	v	v	NUM
ejpam-4506	40	54	and	and	CCONJ
ejpam-4506	40	55	w	w	PROPN
ejpam-4506	40	56	̸=	̸=	PROPN
ejpam-4506	40	57	v	v	NOUN
ejpam-4506	40	58	}	}	PUNCT
ejpam-4506	40	59	.	.	PUNCT
ejpam-4506	41	1	we	we	PRON
ejpam-4506	41	2	may	may	AUX
ejpam-4506	41	3	use	use	VERB
ejpam-4506	41	4	the	the	DET
ejpam-4506	41	5	notation	notation	NOUN
ejpam-4506	41	6	g∖	g∖	PROPN
ejpam-4506	41	7	v	v	NOUN
ejpam-4506	41	8	for	for	ADP
ejpam-4506	41	9	g∖	g∖	PROPN
ejpam-4506	41	10	{	{	PUNCT
ejpam-4506	41	11	v	v	NOUN
ejpam-4506	41	12	}	}	PUNCT
ejpam-4506	41	13	.	.	PUNCT
ejpam-4506	42	1	definition	definition	NOUN
ejpam-4506	42	2	2	2	NUM
ejpam-4506	42	3	.	.	PUNCT
ejpam-4506	43	1	[	[	X
ejpam-4506	43	2	2	2	X
ejpam-4506	43	3	]	]	PUNCT
ejpam-4506	43	4	a	a	DET
ejpam-4506	43	5	vertex	vertex	NOUN
ejpam-4506	43	6	x	x	X
ejpam-4506	43	7	of	of	ADP
ejpam-4506	43	8	a	a	DET
ejpam-4506	43	9	graph	graph	NOUN
ejpam-4506	43	10	g	g	NOUN
ejpam-4506	43	11	is	be	AUX
ejpam-4506	43	12	called	call	VERB
ejpam-4506	43	13	a	a	DET
ejpam-4506	43	14	cut	cut	NOUN
ejpam-4506	43	15	-	-	PUNCT
ejpam-4506	43	16	vertex	vertex	NOUN
ejpam-4506	43	17	if	if	SCONJ
ejpam-4506	43	18	the	the	DET
ejpam-4506	43	19	removal	removal	NOUN
ejpam-4506	43	20	of	of	ADP
ejpam-4506	43	21	x	x	PUNCT
ejpam-4506	43	22	increases	increase	VERB
ejpam-4506	43	23	the	the	DET
ejpam-4506	43	24	number	number	NOUN
ejpam-4506	43	25	of	of	ADP
ejpam-4506	43	26	components	component	NOUN
ejpam-4506	43	27	of	of	ADP
ejpam-4506	43	28	the	the	DET
ejpam-4506	43	29	graph	graph	NOUN
ejpam-4506	43	30	g.	g.	NOUN
ejpam-4506	43	31	we	we	PRON
ejpam-4506	43	32	will	will	AUX
ejpam-4506	43	33	use	use	VERB
ejpam-4506	43	34	ω	ω	PROPN
ejpam-4506	43	35	(	(	PUNCT
ejpam-4506	43	36	g	g	NOUN
ejpam-4506	43	37	)	)	PUNCT
ejpam-4506	43	38	to	to	PART
ejpam-4506	43	39	describe	describe	VERB
ejpam-4506	43	40	the	the	DET
ejpam-4506	43	41	number	number	NOUN
ejpam-4506	43	42	of	of	ADP
ejpam-4506	43	43	components	component	NOUN
ejpam-4506	43	44	a	a	DET
ejpam-4506	43	45	graph	graph	NOUN
ejpam-4506	43	46	g	g	NOUN
ejpam-4506	43	47	has	have	VERB
ejpam-4506	43	48	.	.	PUNCT
ejpam-4506	44	1	definition	definition	NOUN
ejpam-4506	44	2	3	3	NUM
ejpam-4506	44	3	.	.	PUNCT
ejpam-4506	45	1	[	[	X
ejpam-4506	45	2	2	2	X
ejpam-4506	45	3	]	]	PUNCT
ejpam-4506	45	4	in	in	ADP
ejpam-4506	45	5	a	a	DET
ejpam-4506	45	6	graph	graph	NOUN
ejpam-4506	45	7	g	g	NOUN
ejpam-4506	45	8	,	,	PUNCT
ejpam-4506	45	9	the	the	DET
ejpam-4506	45	10	neighborhood	neighborhood	NOUN
ejpam-4506	45	11	ng(u	ng(u	NOUN
ejpam-4506	45	12	)	)	PUNCT
ejpam-4506	45	13	of	of	ADP
ejpam-4506	45	14	a	a	DET
ejpam-4506	45	15	vertex	vertex	NOUN
ejpam-4506	45	16	u	u	NOUN
ejpam-4506	45	17	∈	∈	PROPN
ejpam-4506	45	18	v	v	ADP
ejpam-4506	45	19	(	(	PUNCT
ejpam-4506	45	20	g	g	NOUN
ejpam-4506	45	21	)	)	PUNCT
ejpam-4506	45	22	is	be	AUX
ejpam-4506	45	23	the	the	DET
ejpam-4506	45	24	set	set	NOUN
ejpam-4506	45	25	consisting	consist	VERB
ejpam-4506	45	26	of	of	ADP
ejpam-4506	45	27	all	all	DET
ejpam-4506	45	28	vertices	vertex	NOUN
ejpam-4506	45	29	v	v	NUM
ejpam-4506	45	30	which	which	PRON
ejpam-4506	45	31	are	be	AUX
ejpam-4506	45	32	adjacent	adjacent	ADJ
ejpam-4506	45	33	to	to	ADP
ejpam-4506	45	34	u	u	NOUN
ejpam-4506	45	35	,	,	PUNCT
ejpam-4506	45	36	that	that	ADV
ejpam-4506	45	37	is	is	ADV
ejpam-4506	45	38	,	,	PUNCT
ejpam-4506	45	39	ng(u	ng(u	NOUN
ejpam-4506	45	40	)	)	PUNCT
ejpam-4506	45	41	=	=	PRON
ejpam-4506	45	42	{	{	PUNCT
ejpam-4506	45	43	v	v	NUM
ejpam-4506	45	44	∈	∈	NOUN
ejpam-4506	45	45	v	v	NOUN
ejpam-4506	45	46	(	(	PUNCT
ejpam-4506	45	47	g)|uv	g)|uv	PROPN
ejpam-4506	45	48	∈	∈	PROPN
ejpam-4506	45	49	e(g	e(g	PROPN
ejpam-4506	45	50	)	)	PUNCT
ejpam-4506	45	51	}	}	PUNCT
ejpam-4506	45	52	.	.	PUNCT
ejpam-4506	46	1	a	a	DET
ejpam-4506	46	2	vertex	vertex	NOUN
ejpam-4506	46	3	u	u	NOUN
ejpam-4506	46	4	∈	∈	PROPN
ejpam-4506	46	5	v	v	ADP
ejpam-4506	46	6	(	(	PUNCT
ejpam-4506	46	7	g	g	NOUN
ejpam-4506	46	8	)	)	PUNCT
ejpam-4506	46	9	is	be	AUX
ejpam-4506	46	10	an	an	DET
ejpam-4506	46	11	extreme	extreme	ADJ
ejpam-4506	46	12	vertex	vertex	NOUN
ejpam-4506	46	13	if	if	SCONJ
ejpam-4506	46	14	the	the	DET
ejpam-4506	46	15	neighborhood	neighborhood	NOUN
ejpam-4506	46	16	ng(u	ng(u	NOUN
ejpam-4506	46	17	)	)	PUNCT
ejpam-4506	46	18	of	of	ADP
ejpam-4506	46	19	u	u	PROPN
ejpam-4506	46	20	induces	induce	VERB
ejpam-4506	46	21	a	a	DET
ejpam-4506	46	22	complete	complete	ADJ
ejpam-4506	46	23	subgraph	subgraph	NOUN
ejpam-4506	46	24	of	of	ADP
ejpam-4506	46	25	g.	g.	PROPN
ejpam-4506	46	26	definition	definition	NOUN
ejpam-4506	46	27	4	4	NUM
ejpam-4506	46	28	.	.	PUNCT
ejpam-4506	47	1	[	[	X
ejpam-4506	47	2	2	2	X
ejpam-4506	47	3	]	]	PUNCT
ejpam-4506	47	4	a	a	DET
ejpam-4506	47	5	nontrivial	nontrivial	ADJ
ejpam-4506	47	6	connected	connect	VERB
ejpam-4506	47	7	graph	graph	NOUN
ejpam-4506	47	8	without	without	ADP
ejpam-4506	47	9	cut	cut	NOUN
ejpam-4506	47	10	-	-	PUNCT
ejpam-4506	47	11	vertices	vertex	NOUN
ejpam-4506	47	12	is	be	AUX
ejpam-4506	47	13	called	call	VERB
ejpam-4506	47	14	non	non	ADJ
ejpam-4506	47	15	-	-	ADJ
ejpam-4506	47	16	separable	separable	ADJ
ejpam-4506	47	17	graph	graph	NOUN
ejpam-4506	47	18	.	.	PUNCT
ejpam-4506	48	1	otherwise	otherwise	ADV
ejpam-4506	48	2	,	,	PUNCT
ejpam-4506	48	3	such	such	ADJ
ejpam-4506	48	4	graphs	graph	NOUN
ejpam-4506	48	5	are	be	AUX
ejpam-4506	48	6	separable	separable	ADJ
ejpam-4506	48	7	.	.	PUNCT
ejpam-4506	49	1	definition	definition	NOUN
ejpam-4506	49	2	5	5	NUM
ejpam-4506	49	3	.	.	PUNCT
ejpam-4506	50	1	[	[	X
ejpam-4506	50	2	2	2	X
ejpam-4506	50	3	]	]	PUNCT
ejpam-4506	50	4	let	let	VERB
ejpam-4506	50	5	g	g	PRON
ejpam-4506	50	6	be	be	AUX
ejpam-4506	50	7	a	a	DET
ejpam-4506	50	8	nontrivial	nontrivial	ADJ
ejpam-4506	50	9	connected	connect	VERB
ejpam-4506	50	10	graph	graph	NOUN
ejpam-4506	50	11	.	.	PUNCT
ejpam-4506	51	1	a	a	DET
ejpam-4506	51	2	block	block	NOUN
ejpam-4506	51	3	b	b	NOUN
ejpam-4506	51	4	of	of	ADP
ejpam-4506	51	5	g	g	PROPN
ejpam-4506	51	6	is	be	AUX
ejpam-4506	51	7	a	a	DET
ejpam-4506	51	8	subgraph	subgraph	NOUN
ejpam-4506	51	9	of	of	ADP
ejpam-4506	51	10	g	g	PROPN
ejpam-4506	51	11	that	that	PRON
ejpam-4506	51	12	is	be	AUX
ejpam-4506	51	13	itself	itself	PRON
ejpam-4506	51	14	non	non	ADJ
ejpam-4506	51	15	-	-	ADJ
ejpam-4506	51	16	separable	separable	ADJ
ejpam-4506	51	17	and	and	CCONJ
ejpam-4506	51	18	which	which	PRON
ejpam-4506	51	19	is	be	AUX
ejpam-4506	51	20	maximal	maximal	ADJ
ejpam-4506	51	21	with	with	ADP
ejpam-4506	51	22	respect	respect	NOUN
ejpam-4506	51	23	to	to	ADP
ejpam-4506	51	24	this	this	DET
ejpam-4506	51	25	property	property	NOUN
ejpam-4506	51	26	.	.	PUNCT
ejpam-4506	52	1	definition	definition	NOUN
ejpam-4506	52	2	6	6	NUM
ejpam-4506	52	3	.	.	PUNCT
ejpam-4506	53	1	[	[	X
ejpam-4506	53	2	2	2	X
ejpam-4506	53	3	]	]	PUNCT
ejpam-4506	53	4	a	a	DET
ejpam-4506	53	5	hamiltonian	hamiltonian	ADJ
ejpam-4506	53	6	path	path	NOUN
ejpam-4506	53	7	of	of	ADP
ejpam-4506	53	8	a	a	DET
ejpam-4506	53	9	graph	graph	NOUN
ejpam-4506	53	10	g	g	NOUN
ejpam-4506	53	11	is	be	AUX
ejpam-4506	53	12	a	a	DET
ejpam-4506	53	13	path	path	NOUN
ejpam-4506	53	14	that	that	PRON
ejpam-4506	53	15	contains	contain	VERB
ejpam-4506	53	16	all	all	DET
ejpam-4506	53	17	vertices	vertex	NOUN
ejpam-4506	53	18	of	of	ADP
ejpam-4506	53	19	g	g	NOUN
ejpam-4506	53	20	and	and	CCONJ
ejpam-4506	53	21	passes	pass	VERB
ejpam-4506	53	22	through	through	ADP
ejpam-4506	53	23	each	each	DET
ejpam-4506	53	24	vertex	vertex	NOUN
ejpam-4506	53	25	of	of	ADP
ejpam-4506	53	26	g	g	NOUN
ejpam-4506	53	27	exactly	exactly	ADV
ejpam-4506	53	28	once	once	ADV
ejpam-4506	53	29	.	.	PUNCT
ejpam-4506	54	1	definition	definition	NOUN
ejpam-4506	54	2	7	7	NUM
ejpam-4506	54	3	.	.	PUNCT
ejpam-4506	55	1	[	[	X
ejpam-4506	55	2	6	6	NUM
ejpam-4506	55	3	]	]	PUNCT
ejpam-4506	55	4	the	the	DET
ejpam-4506	55	5	edge	edge	NOUN
ejpam-4506	55	6	corona	corona	PROPN
ejpam-4506	55	7	g	g	PROPN
ejpam-4506	55	8	⋄	⋄	PROPN
ejpam-4506	55	9	h	h	NOUN
ejpam-4506	55	10	of	of	ADP
ejpam-4506	55	11	g	g	PROPN
ejpam-4506	55	12	and	and	CCONJ
ejpam-4506	55	13	h	h	NOUN
ejpam-4506	55	14	is	be	AUX
ejpam-4506	55	15	the	the	DET
ejpam-4506	55	16	graph	graph	NOUN
ejpam-4506	55	17	obtained	obtain	VERB
ejpam-4506	55	18	by	by	ADP
ejpam-4506	55	19	taking	take	VERB
ejpam-4506	55	20	one	one	NUM
ejpam-4506	55	21	copy	copy	NOUN
ejpam-4506	55	22	of	of	ADP
ejpam-4506	55	23	g	g	PROPN
ejpam-4506	55	24	and	and	CCONJ
ejpam-4506	55	25	|e(g)|	|e(g)|	ADJ
ejpam-4506	55	26	copies	copy	NOUN
ejpam-4506	55	27	of	of	ADP
ejpam-4506	55	28	h	h	NOUN
ejpam-4506	55	29	and	and	CCONJ
ejpam-4506	55	30	joining	join	VERB
ejpam-4506	55	31	each	each	PRON
ejpam-4506	55	32	of	of	ADP
ejpam-4506	55	33	the	the	DET
ejpam-4506	55	34	end	end	NOUN
ejpam-4506	55	35	vertices	vertice	VERB
ejpam-4506	55	36	u	u	NOUN
ejpam-4506	55	37	and	and	CCONJ
ejpam-4506	55	38	v	v	NOUN
ejpam-4506	55	39	of	of	ADP
ejpam-4506	55	40	each	each	DET
ejpam-4506	55	41	edge	edge	NOUN
ejpam-4506	55	42	uv	uv	NOUN
ejpam-4506	55	43	of	of	ADP
ejpam-4506	55	44	g	g	NOUN
ejpam-4506	55	45	to	to	ADP
ejpam-4506	55	46	every	every	DET
ejpam-4506	55	47	vertex	vertex	NOUN
ejpam-4506	55	48	of	of	ADP
ejpam-4506	55	49	the	the	DET
ejpam-4506	55	50	copy	copy	NOUN
ejpam-4506	55	51	huv	huv	PROPN
ejpam-4506	55	52	of	of	ADP
ejpam-4506	55	53	h.	h.	PROPN
ejpam-4506	55	54	j.	j.	PROPN
ejpam-4506	55	55	anoche	anoche	PROPN
ejpam-4506	55	56	,	,	PUNCT
ejpam-4506	55	57	i.	i.	PROPN
ejpam-4506	55	58	aniversario	aniversario	PROPN
ejpam-4506	55	59	,	,	PUNCT
ejpam-4506	55	60	c.	c.	PROPN
ejpam-4506	55	61	merca	merca	PROPN
ejpam-4506	55	62	/	/	SYM
ejpam-4506	55	63	eur	eur	PROPN
ejpam-4506	55	64	.	.	PUNCT
ejpam-4506	56	1	j.	j.	PROPN
ejpam-4506	56	2	pure	pure	PROPN
ejpam-4506	56	3	appl	appl	PROPN
ejpam-4506	56	4	.	.	PROPN
ejpam-4506	56	5	math	math	PROPN
ejpam-4506	56	6	,	,	PUNCT
ejpam-4506	56	7	16	16	NUM
ejpam-4506	56	8	(	(	PUNCT
ejpam-4506	56	9	1	1	NUM
ejpam-4506	56	10	)	)	PUNCT
ejpam-4506	56	11	(	(	PUNCT
ejpam-4506	56	12	2023	2023	NUM
ejpam-4506	56	13	)	)	PUNCT
ejpam-4506	56	14	,	,	PUNCT
ejpam-4506	56	15	169	169	NUM
ejpam-4506	56	16	-	-	SYM
ejpam-4506	56	17	179	179	NUM
ejpam-4506	56	18	171	171	NUM
ejpam-4506	56	19	definition	definition	NOUN
ejpam-4506	56	20	8	8	NUM
ejpam-4506	56	21	.	.	PUNCT
ejpam-4506	57	1	[	[	X
ejpam-4506	57	2	4	4	X
ejpam-4506	57	3	]	]	PUNCT
ejpam-4506	57	4	let	let	VERB
ejpam-4506	57	5	g	g	PRON
ejpam-4506	57	6	be	be	AUX
ejpam-4506	57	7	a	a	DET
ejpam-4506	57	8	connected	connected	ADJ
ejpam-4506	57	9	graph	graph	NOUN
ejpam-4506	57	10	and	and	CCONJ
ejpam-4506	57	11	s	s	VERB
ejpam-4506	57	12	⊆	⊆	NUM
ejpam-4506	57	13	v	v	NOUN
ejpam-4506	57	14	(	(	PUNCT
ejpam-4506	57	15	g	g	NOUN
ejpam-4506	57	16	)	)	PUNCT
ejpam-4506	57	17	.	.	PUNCT
ejpam-4506	58	1	the	the	DET
ejpam-4506	58	2	2	2	NUM
ejpam-4506	58	3	-	-	PUNCT
ejpam-4506	58	4	path	path	NOUN
ejpam-4506	58	5	closure	closure	NOUN
ejpam-4506	58	6	p2[s]g	p2[s]g	PROPN
ejpam-4506	58	7	of	of	ADP
ejpam-4506	58	8	set	set	NOUN
ejpam-4506	58	9	s	s	VERB
ejpam-4506	58	10	is	be	AUX
ejpam-4506	58	11	the	the	DET
ejpam-4506	58	12	set	set	NOUN
ejpam-4506	58	13	p2[s]g	p2[s]g	PROPN
ejpam-4506	58	14	=	=	SYM
ejpam-4506	58	15	s	s	X
ejpam-4506	58	16	∪	∪	X
ejpam-4506	58	17	{	{	PUNCT
ejpam-4506	58	18	w	w	NOUN
ejpam-4506	58	19	∈	∈	PROPN
ejpam-4506	58	20	v	v	ADP
ejpam-4506	58	21	(	(	PUNCT
ejpam-4506	58	22	g	g	NOUN
ejpam-4506	58	23	)	)	PUNCT
ejpam-4506	58	24	:	:	PUNCT
ejpam-4506	59	1	w	w	X
ejpam-4506	59	2	∈	∈	PROPN
ejpam-4506	59	3	ig(u	ig(u	NOUN
ejpam-4506	59	4	,	,	PUNCT
ejpam-4506	59	5	v	v	NOUN
ejpam-4506	59	6	)	)	PUNCT
ejpam-4506	59	7	for	for	ADP
ejpam-4506	59	8	some	some	DET
ejpam-4506	59	9	u	u	NOUN
ejpam-4506	59	10	,	,	PUNCT
ejpam-4506	59	11	v	v	PROPN
ejpam-4506	59	12	∈	∈	NOUN
ejpam-4506	59	13	s	s	PART
ejpam-4506	59	14	with	with	ADP
ejpam-4506	59	15	dg(u	dg(u	ADJ
ejpam-4506	59	16	,	,	PUNCT
ejpam-4506	59	17	v	v	NOUN
ejpam-4506	59	18	)	)	PUNCT
ejpam-4506	59	19	=	=	SYM
ejpam-4506	59	20	2	2	X
ejpam-4506	59	21	}	}	PUNCT
ejpam-4506	59	22	.	.	PUNCT
ejpam-4506	60	1	a	a	DET
ejpam-4506	60	2	set	set	NOUN
ejpam-4506	60	3	s	s	PART
ejpam-4506	60	4	is	be	AUX
ejpam-4506	60	5	called	call	VERB
ejpam-4506	60	6	2	2	NUM
ejpam-4506	60	7	-	-	PUNCT
ejpam-4506	60	8	path	path	NOUN
ejpam-4506	60	9	closure	closure	NOUN
ejpam-4506	60	10	absorbing	absorb	VERB
ejpam-4506	60	11	if	if	SCONJ
ejpam-4506	60	12	p2[s]g	p2[s]g	PROPN
ejpam-4506	60	13	=	=	SYM
ejpam-4506	60	14	v	v	PROPN
ejpam-4506	60	15	(	(	PUNCT
ejpam-4506	60	16	g	g	NOUN
ejpam-4506	60	17	)	)	PUNCT
ejpam-4506	60	18	.	.	PUNCT
ejpam-4506	61	1	the	the	DET
ejpam-4506	61	2	minimum	minimum	ADJ
ejpam-4506	61	3	cardinality	cardinality	NOUN
ejpam-4506	61	4	of	of	ADP
ejpam-4506	61	5	a	a	DET
ejpam-4506	61	6	2	2	NUM
ejpam-4506	61	7	-	-	PUNCT
ejpam-4506	61	8	path	path	NOUN
ejpam-4506	61	9	closure	closure	NOUN
ejpam-4506	61	10	absorbing	absorb	VERB
ejpam-4506	61	11	set	set	NOUN
ejpam-4506	61	12	of	of	ADP
ejpam-4506	61	13	g	g	PROPN
ejpam-4506	61	14	is	be	AUX
ejpam-4506	61	15	denoted	denote	VERB
ejpam-4506	61	16	by	by	ADP
ejpam-4506	61	17	φ(g	φ(g	PROPN
ejpam-4506	61	18	)	)	PUNCT
ejpam-4506	61	19	.	.	PUNCT
ejpam-4506	62	1	definition	definition	NOUN
ejpam-4506	62	2	9	9	NUM
ejpam-4506	62	3	.	.	PUNCT
ejpam-4506	63	1	[	[	X
ejpam-4506	63	2	3	3	X
ejpam-4506	63	3	]	]	PUNCT
ejpam-4506	63	4	let	let	VERB
ejpam-4506	63	5	g	g	PRON
ejpam-4506	63	6	be	be	AUX
ejpam-4506	63	7	a	a	DET
ejpam-4506	63	8	connected	connected	ADJ
ejpam-4506	63	9	graph	graph	NOUN
ejpam-4506	63	10	of	of	ADP
ejpam-4506	63	11	order	order	NOUN
ejpam-4506	63	12	n	n	NOUN
ejpam-4506	63	13	and	and	CCONJ
ejpam-4506	63	14	s	s	VERB
ejpam-4506	63	15	⊆	⊆	NUM
ejpam-4506	63	16	v	v	NOUN
ejpam-4506	63	17	(	(	PUNCT
ejpam-4506	63	18	g	g	NOUN
ejpam-4506	63	19	)	)	PUNCT
ejpam-4506	63	20	.	.	PUNCT
ejpam-4506	64	1	a	a	DET
ejpam-4506	64	2	closed	closed	ADJ
ejpam-4506	64	3	geodetic	geodetic	ADJ
ejpam-4506	64	4	cover	cover	NOUN
ejpam-4506	64	5	s	s	NOUN
ejpam-4506	64	6	of	of	ADP
ejpam-4506	64	7	g	g	PROPN
ejpam-4506	64	8	is	be	AUX
ejpam-4506	64	9	called	call	VERB
ejpam-4506	64	10	a	a	DET
ejpam-4506	64	11	path	path	NOUN
ejpam-4506	64	12	-	-	PUNCT
ejpam-4506	64	13	induced	induce	VERB
ejpam-4506	64	14	closed	closed	ADJ
ejpam-4506	64	15	geodetic	geodetic	ADJ
ejpam-4506	64	16	set	set	NOUN
ejpam-4506	64	17	of	of	ADP
ejpam-4506	64	18	a	a	DET
ejpam-4506	64	19	graph	graph	NOUN
ejpam-4506	64	20	g	g	NOUN
ejpam-4506	64	21	,	,	PUNCT
ejpam-4506	64	22	denoted	denote	VERB
ejpam-4506	64	23	by	by	ADP
ejpam-4506	64	24	picgset	picgset	NOUN
ejpam-4506	64	25	,	,	PUNCT
ejpam-4506	64	26	if	if	SCONJ
ejpam-4506	64	27	⟨s⟩	⟨s⟩	PROPN
ejpam-4506	64	28	has	have	VERB
ejpam-4506	64	29	a	a	DET
ejpam-4506	64	30	hamiltonian	hamiltonian	ADJ
ejpam-4506	64	31	path	path	NOUN
ejpam-4506	64	32	.	.	PUNCT
ejpam-4506	65	1	the	the	DET
ejpam-4506	65	2	minimum	minimum	ADJ
ejpam-4506	65	3	cardinality	cardinality	NOUN
ejpam-4506	65	4	of	of	ADP
ejpam-4506	65	5	a	a	DET
ejpam-4506	65	6	path	path	NOUN
ejpam-4506	65	7	-	-	PUNCT
ejpam-4506	65	8	induced	induce	VERB
ejpam-4506	65	9	closed	closed	ADJ
ejpam-4506	65	10	geodetic	geodetic	ADJ
ejpam-4506	65	11	set	set	NOUN
ejpam-4506	65	12	is	be	AUX
ejpam-4506	65	13	called	call	VERB
ejpam-4506	65	14	path	path	NOUN
ejpam-4506	65	15	-	-	PUNCT
ejpam-4506	65	16	induced	induce	VERB
ejpam-4506	65	17	closed	closed	ADJ
ejpam-4506	65	18	geodetic	geodetic	ADJ
ejpam-4506	65	19	number	number	NOUN
ejpam-4506	65	20	of	of	ADP
ejpam-4506	65	21	g	g	NOUN
ejpam-4506	65	22	,	,	PUNCT
ejpam-4506	65	23	denoted	denote	VERB
ejpam-4506	65	24	by	by	ADP
ejpam-4506	65	25	picgn(g	picgn(g	NOUN
ejpam-4506	65	26	)	)	PUNCT
ejpam-4506	65	27	.	.	PUNCT
ejpam-4506	66	1	a	a	DET
ejpam-4506	66	2	path	path	NOUN
ejpam-4506	66	3	-	-	PUNCT
ejpam-4506	66	4	induced	induce	VERB
ejpam-4506	66	5	closed	closed	ADJ
ejpam-4506	66	6	geodetic	geodetic	ADJ
ejpam-4506	66	7	set	set	NOUN
ejpam-4506	66	8	s	s	NOUN
ejpam-4506	66	9	with	with	ADP
ejpam-4506	66	10	|s|	|s|	NOUN
ejpam-4506	66	11	=	=	SYM
ejpam-4506	66	12	picgn(g	picgn(g	NOUN
ejpam-4506	66	13	)	)	PUNCT
ejpam-4506	66	14	is	be	AUX
ejpam-4506	66	15	called	call	VERB
ejpam-4506	66	16	a	a	DET
ejpam-4506	66	17	path	path	NOUN
ejpam-4506	66	18	-	-	PUNCT
ejpam-4506	66	19	induced	induce	VERB
ejpam-4506	66	20	closed	closed	ADJ
ejpam-4506	66	21	geodetic	geodetic	ADJ
ejpam-4506	66	22	basis	basis	NOUN
ejpam-4506	66	23	of	of	ADP
ejpam-4506	66	24	g	g	NOUN
ejpam-4506	66	25	,	,	PUNCT
ejpam-4506	66	26	denoted	denote	VERB
ejpam-4506	66	27	by	by	ADP
ejpam-4506	66	28	picgb(g	picgb(g	NOUN
ejpam-4506	66	29	)	)	PUNCT
ejpam-4506	66	30	.	.	PUNCT
ejpam-4506	67	1	definition	definition	NOUN
ejpam-4506	67	2	10	10	NUM
ejpam-4506	67	3	.	.	PUNCT
ejpam-4506	68	1	let	let	VERB
ejpam-4506	68	2	g	g	PRON
ejpam-4506	68	3	be	be	AUX
ejpam-4506	68	4	a	a	DET
ejpam-4506	68	5	connected	connected	ADJ
ejpam-4506	68	6	graph	graph	NOUN
ejpam-4506	68	7	of	of	ADP
ejpam-4506	68	8	order	order	NOUN
ejpam-4506	68	9	n	n	NOUN
ejpam-4506	68	10	and	and	CCONJ
ejpam-4506	68	11	s	s	VERB
ejpam-4506	68	12	⊆	⊆	NUM
ejpam-4506	68	13	v	v	NOUN
ejpam-4506	68	14	(	(	PUNCT
ejpam-4506	68	15	g	g	NOUN
ejpam-4506	68	16	)	)	PUNCT
ejpam-4506	68	17	.	.	PUNCT
ejpam-4506	69	1	a	a	DET
ejpam-4506	69	2	closed	closed	ADJ
ejpam-4506	69	3	geodetic	geodetic	ADJ
ejpam-4506	69	4	cover	cover	NOUN
ejpam-4506	69	5	s	s	NOUN
ejpam-4506	69	6	of	of	ADP
ejpam-4506	69	7	g	g	PROPN
ejpam-4506	69	8	is	be	AUX
ejpam-4506	69	9	called	call	VERB
ejpam-4506	69	10	a	a	DET
ejpam-4506	69	11	path	path	NOUN
ejpam-4506	69	12	-	-	PUNCT
ejpam-4506	69	13	induced	induce	VERB
ejpam-4506	69	14	closed	closed	ADJ
ejpam-4506	69	15	geodetic	geodetic	ADJ
ejpam-4506	69	16	dominating	dominating	NOUN
ejpam-4506	69	17	set	set	NOUN
ejpam-4506	69	18	of	of	ADP
ejpam-4506	69	19	a	a	DET
ejpam-4506	69	20	graph	graph	NOUN
ejpam-4506	69	21	g	g	NOUN
ejpam-4506	69	22	,	,	PUNCT
ejpam-4506	69	23	denoted	denote	VERB
ejpam-4506	69	24	by	by	ADP
ejpam-4506	69	25	picgd	picgd	ADJ
ejpam-4506	69	26	-	-	PUNCT
ejpam-4506	69	27	set	set	NOUN
ejpam-4506	69	28	,	,	PUNCT
ejpam-4506	69	29	if	if	SCONJ
ejpam-4506	69	30	s	s	VERB
ejpam-4506	69	31	is	be	AUX
ejpam-4506	69	32	both	both	PRON
ejpam-4506	69	33	a	a	DET
ejpam-4506	69	34	path	path	NOUN
ejpam-4506	69	35	-	-	PUNCT
ejpam-4506	69	36	induced	induce	VERB
ejpam-4506	69	37	closed	closed	ADJ
ejpam-4506	69	38	geodetic	geodetic	ADJ
ejpam-4506	69	39	set	set	NOUN
ejpam-4506	69	40	and	and	CCONJ
ejpam-4506	69	41	a	a	DET
ejpam-4506	69	42	dominating	dominating	NOUN
ejpam-4506	69	43	set	set	NOUN
ejpam-4506	69	44	of	of	ADP
ejpam-4506	69	45	g.	g.	PROPN
ejpam-4506	69	46	the	the	DET
ejpam-4506	69	47	minimum	minimum	ADJ
ejpam-4506	69	48	cardinality	cardinality	NOUN
ejpam-4506	69	49	of	of	ADP
ejpam-4506	69	50	a	a	DET
ejpam-4506	69	51	pathinduced	pathinduce	VERB
ejpam-4506	69	52	closed	closed	ADJ
ejpam-4506	69	53	geodetic	geodetic	ADJ
ejpam-4506	69	54	dominating	dominating	NOUN
ejpam-4506	69	55	set	set	NOUN
ejpam-4506	69	56	is	be	AUX
ejpam-4506	69	57	called	call	VERB
ejpam-4506	69	58	pathinduced	pathinduce	VERB
ejpam-4506	69	59	closed	closed	ADJ
ejpam-4506	69	60	geodetic	geodetic	ADJ
ejpam-4506	69	61	domination	domination	NOUN
ejpam-4506	69	62	number	number	NOUN
ejpam-4506	69	63	of	of	ADP
ejpam-4506	69	64	g	g	NOUN
ejpam-4506	69	65	,	,	PUNCT
ejpam-4506	69	66	denoted	denote	VERB
ejpam-4506	69	67	by	by	ADP
ejpam-4506	69	68	γpicg(g	γpicg(g	NOUN
ejpam-4506	69	69	)	)	PUNCT
ejpam-4506	69	70	.	.	PUNCT
ejpam-4506	70	1	a	a	DET
ejpam-4506	70	2	path	path	NOUN
ejpam-4506	70	3	-	-	PUNCT
ejpam-4506	70	4	induced	induce	VERB
ejpam-4506	70	5	closed	closed	ADJ
ejpam-4506	70	6	geodetic	geodetic	ADJ
ejpam-4506	70	7	dominating	dominating	NOUN
ejpam-4506	70	8	set	set	VERB
ejpam-4506	70	9	with	with	ADP
ejpam-4506	70	10	|s|	|s|	PROPN
ejpam-4506	70	11	=	=	PUNCT
ejpam-4506	70	12	γpicg(g	γpicg(g	PROPN
ejpam-4506	70	13	)	)	PUNCT
ejpam-4506	70	14	is	be	AUX
ejpam-4506	70	15	said	say	VERB
ejpam-4506	70	16	to	to	PART
ejpam-4506	70	17	be	be	AUX
ejpam-4506	70	18	a	a	DET
ejpam-4506	70	19	γpicg	γpicg	NOUN
ejpam-4506	70	20	-	-	PUNCT
ejpam-4506	70	21	set	set	NOUN
ejpam-4506	70	22	of	of	ADP
ejpam-4506	70	23	g.	g.	PROPN
ejpam-4506	70	24	........................................................................	........................................................................	PUNCT
ejpam-4506	70	25	........................................................................	........................................................................	PUNCT
ejpam-4506	70	26	........................................................................	........................................................................	PUNCT
ejpam-4506	70	27	.........	.........	PUNCT
ejpam-4506	70	28	........	........	PUNCT
ejpam-4506	70	29	........	........	PUNCT
ejpam-4506	70	30	........	........	PUNCT
ejpam-4506	70	31	........	........	PUNCT
ejpam-4506	70	32	........	........	PUNCT
ejpam-4506	70	33	........	........	PUNCT
ejpam-4506	70	34	........	........	PUNCT
ejpam-4506	70	35	........	........	PUNCT
ejpam-4506	70	36	........	........	PUNCT
ejpam-4506	70	37	........	........	PUNCT
ejpam-4506	70	38	........	........	PUNCT
ejpam-4506	70	39	.......	.......	PUNCT
ejpam-4506	70	40	..............	..............	PUNCT
ejpam-4506	70	41	.............	.............	PUNCT
ejpam-4506	70	42	.............	.............	PUNCT
ejpam-4506	70	43	.............	.............	PUNCT
ejpam-4506	70	44	.............	.............	PUNCT
ejpam-4506	70	45	.............	.............	PUNCT
ejpam-4506	70	46	.............	.............	PUNCT
ejpam-4506	70	47	.............	.............	PUNCT
ejpam-4506	70	48	.............	.............	PUNCT
ejpam-4506	70	49	.............	.............	PUNCT
ejpam-4506	70	50	.............	.............	PUNCT
ejpam-4506	70	51	.............	.............	PUNCT
ejpam-4506	70	52	.............	.............	PUNCT
ejpam-4506	70	53	...	...	PUNCT
ejpam-4506	70	54	...........................................................................................................................................................................................................................................................................................................................	...........................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4506	70	55	........	........	PUNCT
ejpam-4506	70	56	........	........	PUNCT
ejpam-4506	70	57	........	........	PUNCT
ejpam-4506	70	58	........	........	PUNCT
ejpam-4506	70	59	........	........	PUNCT
ejpam-4506	70	60	........	........	PUNCT
ejpam-4506	70	61	........	........	PUNCT
ejpam-4506	70	62	........	........	PUNCT
ejpam-4506	70	63	........	........	PUNCT
ejpam-4506	70	64	........	........	PUNCT
ejpam-4506	70	65	........	........	PUNCT
ejpam-4506	70	66	.......	.......	PUNCT
ejpam-4506	70	67	...........	...........	PUNCT
ejpam-4506	70	68	..........	..........	PUNCT
ejpam-4506	71	1	..........	..........	PUNCT
ejpam-4506	71	2	..........	..........	PUNCT
ejpam-4506	72	1	..........	..........	PUNCT
ejpam-4506	72	2	..........	..........	PUNCT
ejpam-4506	73	1	..........	..........	PUNCT
ejpam-4506	73	2	..........	..........	PUNCT
ejpam-4506	74	1	..........	..........	PUNCT
ejpam-4506	74	2	..........	..........	PUNCT
ejpam-4506	75	1	..........	..........	PUNCT
ejpam-4506	75	2	..........	..........	PUNCT
ejpam-4506	76	1	..........	..........	PUNCT
ejpam-4506	76	2	..........	..........	PUNCT
ejpam-4506	77	1	..........	..........	PUNCT
ejpam-4506	77	2	..........	..........	PUNCT
ejpam-4506	78	1	..........	..........	PUNCT
ejpam-4506	78	2	..........	..........	PUNCT
ejpam-4506	79	1	..........	..........	PUNCT
ejpam-4506	79	2	..........	..........	PUNCT
ejpam-4506	80	1	..........	..........	PUNCT
ejpam-4506	80	2	..........	..........	PUNCT
ejpam-4506	81	1	..........	..........	PUNCT
ejpam-4506	81	2	..........	..........	PUNCT
ejpam-4506	82	1	..........	..........	PUNCT
ejpam-4506	82	2	..........	..........	PUNCT
ejpam-4506	82	3	.	.	PUNCT
ejpam-4506	83	1	..............	..............	PUNCT
ejpam-4506	83	2	.............	.............	PUNCT
ejpam-4506	83	3	.............	.............	PUNCT
ejpam-4506	83	4	.............	.............	PUNCT
ejpam-4506	83	5	.............	.............	PUNCT
ejpam-4506	83	6	.............	.............	PUNCT
ejpam-4506	83	7	.............	.............	PUNCT
ejpam-4506	83	8	.............	.............	PUNCT
ejpam-4506	83	9	.............	.............	PUNCT
ejpam-4506	83	10	.............	.............	PUNCT
ejpam-4506	83	11	.............	.............	PUNCT
ejpam-4506	83	12	.............	.............	PUNCT
ejpam-4506	83	13	.............	.............	PUNCT
ejpam-4506	83	14	...	...	PUNCT
ejpam-4506	84	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4506	84	2	..................................................................................................................................................................................................................................................................................................................	..................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4506	85	1	......................................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................................	PUNCT
ejpam-4506	85	2	.........	.........	PUNCT
ejpam-4506	86	1	........	........	PUNCT
ejpam-4506	86	2	........	........	PUNCT
ejpam-4506	86	3	........	........	PUNCT
ejpam-4506	86	4	........	........	PUNCT
ejpam-4506	86	5	........	........	PUNCT
ejpam-4506	86	6	........	........	PUNCT
ejpam-4506	86	7	........	........	PUNCT
ejpam-4506	86	8	........	........	PUNCT
ejpam-4506	86	9	........	........	PUNCT
ejpam-4506	86	10	........	........	PUNCT
ejpam-4506	86	11	........	........	PUNCT
ejpam-4506	86	12	.......	.......	PUNCT
ejpam-4506	86	13	.........	.........	PUNCT
ejpam-4506	86	14	........	........	PUNCT
ejpam-4506	86	15	........	........	PUNCT
ejpam-4506	86	16	........	........	PUNCT
ejpam-4506	86	17	........	........	PUNCT
ejpam-4506	86	18	........	........	PUNCT
ejpam-4506	86	19	........	........	PUNCT
ejpam-4506	86	20	........	........	PUNCT
ejpam-4506	86	21	........	........	PUNCT
ejpam-4506	86	22	........	........	PUNCT
ejpam-4506	86	23	........	........	PUNCT
ejpam-4506	86	24	........	........	PUNCT
ejpam-4506	86	25	.......	.......	PUNCT
ejpam-4506	87	1	c1	c1	PROPN
ejpam-4506	87	2	c2	c2	PROPN
ejpam-4506	87	3	d1	d1	PROPN
ejpam-4506	87	4	d2	d2	PROPN
ejpam-4506	87	5	e1	e1	PROPN
ejpam-4506	87	6	e2	e2	PROPN
ejpam-4506	87	7	•	•	NUM
ejpam-4506	87	8	•	•	NUM
ejpam-4506	87	9	•	•	NOUN
ejpam-4506	87	10	g	g	NOUN
ejpam-4506	87	11	figure	figure	NOUN
ejpam-4506	87	12	1	1	NUM
ejpam-4506	87	13	:	:	PUNCT
ejpam-4506	87	14	a	a	DET
ejpam-4506	87	15	graph	graph	NOUN
ejpam-4506	87	16	g	g	ADP
ejpam-4506	87	17	example	example	NOUN
ejpam-4506	87	18	1	1	NUM
ejpam-4506	87	19	.	.	X
ejpam-4506	87	20	consider	consider	VERB
ejpam-4506	87	21	the	the	DET
ejpam-4506	87	22	graph	graph	NOUN
ejpam-4506	87	23	g	g	NOUN
ejpam-4506	87	24	in	in	ADP
ejpam-4506	87	25	figure	figure	NOUN
ejpam-4506	87	26	1	1	NUM
ejpam-4506	87	27	.	.	PUNCT
ejpam-4506	88	1	let	let	VERB
ejpam-4506	88	2	s1	s1	PROPN
ejpam-4506	88	3	=	=	SYM
ejpam-4506	88	4	{	{	PUNCT
ejpam-4506	88	5	c1	c1	NOUN
ejpam-4506	88	6	}	}	PUNCT
ejpam-4506	88	7	,	,	PUNCT
ejpam-4506	88	8	s2	s2	X
ejpam-4506	88	9	=	=	SYM
ejpam-4506	88	10	{	{	PUNCT
ejpam-4506	88	11	c1	c1	PROPN
ejpam-4506	88	12	,	,	PUNCT
ejpam-4506	88	13	c2	c2	PROPN
ejpam-4506	88	14	}	}	PUNCT
ejpam-4506	88	15	and	and	CCONJ
ejpam-4506	88	16	s3	s3	PROPN
ejpam-4506	88	17	=	=	SYM
ejpam-4506	88	18	{	{	PUNCT
ejpam-4506	88	19	c1	c1	PROPN
ejpam-4506	88	20	,	,	PUNCT
ejpam-4506	88	21	c2	c2	PROPN
ejpam-4506	88	22	,	,	PUNCT
ejpam-4506	88	23	e1	e1	PROPN
ejpam-4506	88	24	}	}	PUNCT
ejpam-4506	88	25	.	.	PUNCT
ejpam-4506	89	1	then	then	ADV
ejpam-4506	89	2	ig	ig	PROPN
ejpam-4506	89	3	[	[	X
ejpam-4506	89	4	s2	s2	X
ejpam-4506	89	5	]	]	X
ejpam-4506	89	6	=	=	SYM
ejpam-4506	89	7	{	{	PUNCT
ejpam-4506	89	8	c1	c1	PROPN
ejpam-4506	89	9	,	,	PUNCT
ejpam-4506	89	10	c2	c2	PROPN
ejpam-4506	89	11	}	}	PUNCT
ejpam-4506	89	12	and	and	CCONJ
ejpam-4506	89	13	ig	ig	PROPN
ejpam-4506	89	14	[	[	X
ejpam-4506	89	15	s3	s3	PROPN
ejpam-4506	89	16	]	]	X
ejpam-4506	89	17	=	=	SYM
ejpam-4506	89	18	ig[c1	ig[c1	PROPN
ejpam-4506	89	19	,	,	PUNCT
ejpam-4506	89	20	c2	c2	PROPN
ejpam-4506	89	21	]	]	PUNCT
ejpam-4506	89	22	∪	∪	ADP
ejpam-4506	89	23	ig[c1	ig[c1	PROPN
ejpam-4506	89	24	,	,	PUNCT
ejpam-4506	89	25	e1	e1	PROPN
ejpam-4506	89	26	]	]	PUNCT
ejpam-4506	89	27	∪	∪	X
ejpam-4506	89	28	ig[c2	ig[c2	PROPN
ejpam-4506	89	29	,	,	PUNCT
ejpam-4506	89	30	e1	e1	NOUN
ejpam-4506	89	31	]	]	PUNCT
ejpam-4506	89	32	=	=	SYM
ejpam-4506	89	33	{	{	PUNCT
ejpam-4506	89	34	c1	c1	PROPN
ejpam-4506	89	35	,	,	PUNCT
ejpam-4506	89	36	c2	c2	PROPN
ejpam-4506	89	37	}	}	PUNCT
ejpam-4506	89	38	∪	∪	NOUN
ejpam-4506	89	39	{	{	PUNCT
ejpam-4506	89	40	c1	c1	NOUN
ejpam-4506	89	41	,	,	PUNCT
ejpam-4506	89	42	c2	c2	PROPN
ejpam-4506	89	43	,	,	PUNCT
ejpam-4506	89	44	d1	d1	PROPN
ejpam-4506	89	45	,	,	PUNCT
ejpam-4506	89	46	d2	d2	PROPN
ejpam-4506	89	47	,	,	PUNCT
ejpam-4506	89	48	e2	e2	PROPN
ejpam-4506	89	49	,	,	PUNCT
ejpam-4506	89	50	e1	e1	PROPN
ejpam-4506	89	51	}	}	PUNCT
ejpam-4506	89	52	∪	∪	NOUN
ejpam-4506	89	53	{	{	PUNCT
ejpam-4506	89	54	c2	c2	PROPN
ejpam-4506	89	55	,	,	PUNCT
ejpam-4506	89	56	e1	e1	PROPN
ejpam-4506	89	57	}	}	PUNCT
ejpam-4506	89	58	=	=	SYM
ejpam-4506	89	59	{	{	PUNCT
ejpam-4506	89	60	c1	c1	PROPN
ejpam-4506	89	61	,	,	PUNCT
ejpam-4506	89	62	c2	c2	PROPN
ejpam-4506	89	63	,	,	PUNCT
ejpam-4506	89	64	d1	d1	PROPN
ejpam-4506	89	65	,	,	PUNCT
ejpam-4506	89	66	d2	d2	PROPN
ejpam-4506	89	67	,	,	PUNCT
ejpam-4506	89	68	e1	e1	PROPN
ejpam-4506	89	69	,	,	PUNCT
ejpam-4506	89	70	e2	e2	NOUN
ejpam-4506	89	71	}	}	PUNCT
ejpam-4506	89	72	=	=	SYM
ejpam-4506	89	73	v	v	NOUN
ejpam-4506	89	74	(	(	PUNCT
ejpam-4506	89	75	g	g	NOUN
ejpam-4506	89	76	)	)	PUNCT
ejpam-4506	89	77	.	.	PUNCT
ejpam-4506	90	1	let	let	VERB
ejpam-4506	90	2	s	s	PRON
ejpam-4506	90	3	=	=	PUNCT
ejpam-4506	90	4	{	{	PUNCT
ejpam-4506	90	5	c1	c1	PROPN
ejpam-4506	90	6	,	,	PUNCT
ejpam-4506	90	7	c2	c2	PROPN
ejpam-4506	90	8	,	,	PUNCT
ejpam-4506	90	9	e1	e1	PROPN
ejpam-4506	90	10	}	}	PUNCT
ejpam-4506	90	11	=	=	SYM
ejpam-4506	90	12	s3	s3	PROPN
ejpam-4506	90	13	.	.	PUNCT
ejpam-4506	91	1	then	then	ADV
ejpam-4506	91	2	ig	ig	PROPN
ejpam-4506	92	1	[	[	X
ejpam-4506	92	2	s	s	X
ejpam-4506	92	3	]	]	X
ejpam-4506	92	4	=	=	SYM
ejpam-4506	92	5	v	v	NOUN
ejpam-4506	92	6	(	(	PUNCT
ejpam-4506	92	7	g	g	NOUN
ejpam-4506	92	8	)	)	PUNCT
ejpam-4506	92	9	.	.	PUNCT
ejpam-4506	93	1	note	note	VERB
ejpam-4506	93	2	that	that	SCONJ
ejpam-4506	93	3	⟨s⟩	⟨s⟩	PROPN
ejpam-4506	93	4	contains	contain	VERB
ejpam-4506	93	5	a	a	DET
ejpam-4506	93	6	hamiltonian	hamiltonian	ADJ
ejpam-4506	93	7	path	path	NOUN
ejpam-4506	93	8	[	[	X
ejpam-4506	93	9	c1	c1	PROPN
ejpam-4506	93	10	,	,	PUNCT
ejpam-4506	93	11	c2	c2	PROPN
ejpam-4506	93	12	,	,	PUNCT
ejpam-4506	93	13	e1	e1	PROPN
ejpam-4506	93	14	]	]	PUNCT
ejpam-4506	93	15	.	.	PUNCT
ejpam-4506	94	1	thus	thus	ADV
ejpam-4506	94	2	,	,	PUNCT
ejpam-4506	94	3	s	s	VERB
ejpam-4506	94	4	is	be	AUX
ejpam-4506	94	5	a	a	DET
ejpam-4506	94	6	path	path	NOUN
ejpam-4506	94	7	-	-	PUNCT
ejpam-4506	94	8	induced	induce	VERB
ejpam-4506	94	9	closed	closed	ADJ
ejpam-4506	94	10	geodetic	geodetic	ADJ
ejpam-4506	94	11	set	set	VERB
ejpam-4506	94	12	ofg	ofg	PROPN
ejpam-4506	94	13	.	.	PUNCT
ejpam-4506	95	1	observe	observe	VERB
ejpam-4506	95	2	that	that	SCONJ
ejpam-4506	95	3	we	we	PRON
ejpam-4506	95	4	can	can	AUX
ejpam-4506	95	5	not	not	PART
ejpam-4506	95	6	find	find	VERB
ejpam-4506	95	7	a	a	DET
ejpam-4506	95	8	path	path	NOUN
ejpam-4506	95	9	-	-	PUNCT
ejpam-4506	95	10	induced	induce	VERB
ejpam-4506	95	11	closed	closed	ADJ
ejpam-4506	95	12	geodetic	geodetic	ADJ
ejpam-4506	95	13	set	set	NOUN
ejpam-4506	95	14	s	s	PROPN
ejpam-4506	95	15	of	of	ADP
ejpam-4506	95	16	cardinality	cardinality	NOUN
ejpam-4506	95	17	less	less	ADJ
ejpam-4506	95	18	than	than	ADP
ejpam-4506	95	19	3	3	NUM
ejpam-4506	95	20	.	.	PUNCT
ejpam-4506	96	1	thus	thus	ADV
ejpam-4506	96	2	,	,	PUNCT
ejpam-4506	96	3	picgn(g	picgn(g	NOUN
ejpam-4506	96	4	)	)	PUNCT
ejpam-4506	96	5	=	=	SYM
ejpam-4506	97	1	3	3	X
ejpam-4506	97	2	.	.	PUNCT
ejpam-4506	97	3	j.	j.	PROPN
ejpam-4506	97	4	anoche	anoche	PROPN
ejpam-4506	97	5	,	,	PUNCT
ejpam-4506	97	6	i.	i.	PROPN
ejpam-4506	97	7	aniversario	aniversario	PROPN
ejpam-4506	97	8	,	,	PUNCT
ejpam-4506	97	9	c.	c.	PROPN
ejpam-4506	97	10	merca	merca	PROPN
ejpam-4506	97	11	/	/	SYM
ejpam-4506	97	12	eur	eur	PROPN
ejpam-4506	97	13	.	.	PUNCT
ejpam-4506	98	1	j.	j.	PROPN
ejpam-4506	98	2	pure	pure	PROPN
ejpam-4506	98	3	appl	appl	PROPN
ejpam-4506	98	4	.	.	PROPN
ejpam-4506	98	5	math	math	PROPN
ejpam-4506	98	6	,	,	PUNCT
ejpam-4506	98	7	16	16	NUM
ejpam-4506	98	8	(	(	PUNCT
ejpam-4506	98	9	1	1	NUM
ejpam-4506	98	10	)	)	PUNCT
ejpam-4506	98	11	(	(	PUNCT
ejpam-4506	98	12	2023	2023	NUM
ejpam-4506	98	13	)	)	PUNCT
ejpam-4506	98	14	,	,	PUNCT
ejpam-4506	98	15	169	169	NUM
ejpam-4506	98	16	-	-	SYM
ejpam-4506	98	17	179	179	NUM
ejpam-4506	98	18	172	172	NUM
ejpam-4506	98	19	now	now	ADV
ejpam-4506	98	20	,	,	PUNCT
ejpam-4506	98	21	since	since	SCONJ
ejpam-4506	98	22	each	each	DET
ejpam-4506	98	23	vertex	vertex	NOUN
ejpam-4506	98	24	of	of	ADP
ejpam-4506	98	25	v	v	NOUN
ejpam-4506	98	26	(	(	PUNCT
ejpam-4506	98	27	g	g	NOUN
ejpam-4506	98	28	)	)	PUNCT
ejpam-4506	98	29	∖	∖	X
ejpam-4506	99	1	s	s	PART
ejpam-4506	99	2	is	be	AUX
ejpam-4506	99	3	adjacent	adjacent	ADJ
ejpam-4506	99	4	to	to	ADP
ejpam-4506	99	5	at	at	ADV
ejpam-4506	99	6	least	least	ADV
ejpam-4506	99	7	two	two	NUM
ejpam-4506	99	8	vertices	vertex	NOUN
ejpam-4506	99	9	of	of	ADP
ejpam-4506	99	10	s	s	NOUN
ejpam-4506	99	11	,	,	PUNCT
ejpam-4506	99	12	s	s	VERB
ejpam-4506	99	13	is	be	AUX
ejpam-4506	99	14	a	a	DET
ejpam-4506	99	15	dominating	dominating	NOUN
ejpam-4506	99	16	set	set	NOUN
ejpam-4506	99	17	of	of	ADP
ejpam-4506	99	18	g.	g.	PROPN
ejpam-4506	99	19	therefore	therefore	ADV
ejpam-4506	99	20	,	,	PUNCT
ejpam-4506	99	21	s	s	VERB
ejpam-4506	99	22	is	be	AUX
ejpam-4506	99	23	a	a	DET
ejpam-4506	99	24	path	path	NOUN
ejpam-4506	99	25	-	-	PUNCT
ejpam-4506	99	26	induced	induce	VERB
ejpam-4506	99	27	closed	closed	ADJ
ejpam-4506	99	28	geodetic	geodetic	ADJ
ejpam-4506	99	29	dominating	dominating	NOUN
ejpam-4506	99	30	set	set	NOUN
ejpam-4506	99	31	and	and	CCONJ
ejpam-4506	99	32	it	it	PRON
ejpam-4506	99	33	can	can	AUX
ejpam-4506	99	34	be	be	AUX
ejpam-4506	99	35	verified	verify	VERB
ejpam-4506	99	36	that	that	SCONJ
ejpam-4506	99	37	γpicg(g	γpicg(g	NOUN
ejpam-4506	99	38	)	)	PUNCT
ejpam-4506	99	39	=	=	SYM
ejpam-4506	99	40	3	3	X
ejpam-4506	99	41	.	.	NOUN
ejpam-4506	99	42	remark	remark	NOUN
ejpam-4506	99	43	1	1	NUM
ejpam-4506	99	44	.	.	PUNCT
ejpam-4506	100	1	[	[	X
ejpam-4506	100	2	7	7	NUM
ejpam-4506	100	3	]	]	PUNCT
ejpam-4506	100	4	.	.	PUNCT
ejpam-4506	101	1	let	let	VERB
ejpam-4506	101	2	g	g	PRON
ejpam-4506	101	3	be	be	AUX
ejpam-4506	101	4	a	a	DET
ejpam-4506	101	5	connected	connected	ADJ
ejpam-4506	101	6	nontrivial	nontrivial	ADJ
ejpam-4506	101	7	graph	graph	NOUN
ejpam-4506	101	8	of	of	ADP
ejpam-4506	101	9	order	order	NOUN
ejpam-4506	101	10	n.	n.	VERB
ejpam-4506	101	11	if	if	SCONJ
ejpam-4506	101	12	g	g	PROPN
ejpam-4506	101	13	admits	admit	VERB
ejpam-4506	101	14	a	a	DET
ejpam-4506	101	15	pathinduced	pathinduced	ADJ
ejpam-4506	101	16	geodetic	geodetic	ADJ
ejpam-4506	101	17	set	set	NOUN
ejpam-4506	101	18	,	,	PUNCT
ejpam-4506	101	19	then	then	ADV
ejpam-4506	101	20	2	2	NUM
ejpam-4506	101	21	≤	≤	NOUN
ejpam-4506	101	22	gn(g	gn(g	NOUN
ejpam-4506	101	23	)	)	PUNCT
ejpam-4506	101	24	≤	≤	NUM
ejpam-4506	102	1	pign(g	pign(g	NOUN
ejpam-4506	102	2	)	)	PUNCT
ejpam-4506	102	3	≤	≤	PROPN
ejpam-4506	102	4	n.	n.	NOUN
ejpam-4506	102	5	theorem	theorem	NOUN
ejpam-4506	102	6	1	1	NUM
ejpam-4506	102	7	.	.	PUNCT
ejpam-4506	103	1	[	[	X
ejpam-4506	103	2	3	3	NUM
ejpam-4506	103	3	]	]	X
ejpam-4506	103	4	path	path	NOUN
ejpam-4506	103	5	-	-	PUNCT
ejpam-4506	103	6	induced	induce	VERB
ejpam-4506	103	7	closed	closed	ADJ
ejpam-4506	103	8	geodetic	geodetic	ADJ
ejpam-4506	103	9	number	number	NOUN
ejpam-4506	103	10	of	of	ADP
ejpam-4506	103	11	a	a	DET
ejpam-4506	103	12	few	few	ADJ
ejpam-4506	103	13	well	well	ADV
ejpam-4506	103	14	-	-	PUNCT
ejpam-4506	103	15	known	know	VERB
ejpam-4506	103	16	graphs	graph	NOUN
ejpam-4506	103	17	:	:	PUNCT
ejpam-4506	103	18	(	(	PUNCT
ejpam-4506	103	19	i	i	NOUN
ejpam-4506	103	20	)	)	PUNCT
ejpam-4506	103	21	for	for	ADP
ejpam-4506	103	22	a	a	DET
ejpam-4506	103	23	complete	complete	ADJ
ejpam-4506	103	24	graph	graph	NOUN
ejpam-4506	103	25	kn	kn	PROPN
ejpam-4506	103	26	,	,	PUNCT
ejpam-4506	103	27	picgn	picgn	PROPN
ejpam-4506	103	28	(	(	PUNCT
ejpam-4506	103	29	kn	kn	PROPN
ejpam-4506	103	30	)	)	PUNCT
ejpam-4506	103	31	=	=	SYM
ejpam-4506	103	32	n.	n.	NOUN
ejpam-4506	103	33	(	(	PUNCT
ejpam-4506	103	34	ii	ii	PROPN
ejpam-4506	103	35	)	)	PUNCT
ejpam-4506	103	36	for	for	ADP
ejpam-4506	103	37	a	a	DET
ejpam-4506	103	38	path	path	NOUN
ejpam-4506	103	39	pn	pn	NOUN
ejpam-4506	103	40	on	on	ADP
ejpam-4506	103	41	n	n	PRON
ejpam-4506	103	42	vertices	vertex	NOUN
ejpam-4506	103	43	,	,	PUNCT
ejpam-4506	103	44	picgn	picgn	NOUN
ejpam-4506	103	45	(	(	PUNCT
ejpam-4506	103	46	pn	pn	NOUN
ejpam-4506	103	47	)	)	PUNCT
ejpam-4506	104	1	=	=	SYM
ejpam-4506	104	2	n.	n.	NOUN
ejpam-4506	104	3	(	(	PUNCT
ejpam-4506	104	4	iii	iii	NOUN
ejpam-4506	104	5	)	)	PUNCT
ejpam-4506	104	6	for	for	ADP
ejpam-4506	104	7	a	a	DET
ejpam-4506	104	8	cycle	cycle	NOUN
ejpam-4506	104	9	cn	cn	NOUN
ejpam-4506	104	10	of	of	ADP
ejpam-4506	104	11	length	length	NOUN
ejpam-4506	104	12	n	n	CCONJ
ejpam-4506	104	13	,	,	PUNCT
ejpam-4506	104	14	picgn(cn	picgn(cn	NOUN
ejpam-4506	104	15	)	)	PUNCT
ejpam-4506	104	16	=	=	PUNCT
ejpam-4506	104	17	{	{	PUNCT
ejpam-4506	104	18	n	n	ADV
ejpam-4506	104	19	2	2	NUM
ejpam-4506	104	20	+	+	NUM
ejpam-4506	104	21	1	1	NUM
ejpam-4506	104	22	,	,	PUNCT
ejpam-4506	104	23	if	if	SCONJ
ejpam-4506	104	24	n	n	PRON
ejpam-4506	104	25	is	be	AUX
ejpam-4506	104	26	even	even	ADV
ejpam-4506	104	27	;	;	PUNCT
ejpam-4506	104	28	n+1	n+1	PROPN
ejpam-4506	104	29	2	2	NUM
ejpam-4506	104	30	+	+	NUM
ejpam-4506	104	31	1	1	NUM
ejpam-4506	104	32	,	,	PUNCT
ejpam-4506	104	33	if	if	SCONJ
ejpam-4506	104	34	n	n	PRON
ejpam-4506	104	35	is	be	AUX
ejpam-4506	104	36	odd	odd	ADJ
ejpam-4506	104	37	.	.	PUNCT
ejpam-4506	105	1	theorem	theorem	NOUN
ejpam-4506	105	2	2	2	NUM
ejpam-4506	105	3	.	.	PUNCT
ejpam-4506	106	1	[	[	X
ejpam-4506	106	2	3	3	X
ejpam-4506	106	3	]	]	PUNCT
ejpam-4506	106	4	let	let	VERB
ejpam-4506	106	5	g	g	PRON
ejpam-4506	106	6	be	be	AUX
ejpam-4506	106	7	a	a	DET
ejpam-4506	106	8	connected	connected	ADJ
ejpam-4506	106	9	graph	graph	NOUN
ejpam-4506	106	10	with	with	ADP
ejpam-4506	106	11	cut	cut	NOUN
ejpam-4506	106	12	-	-	PUNCT
ejpam-4506	106	13	vertices	vertex	NOUN
ejpam-4506	106	14	.	.	PUNCT
ejpam-4506	107	1	if	if	SCONJ
ejpam-4506	107	2	s	s	VERB
ejpam-4506	107	3	⊆	⊆	NUM
ejpam-4506	107	4	v	v	NOUN
ejpam-4506	107	5	(	(	PUNCT
ejpam-4506	107	6	g	g	NOUN
ejpam-4506	107	7	)	)	PUNCT
ejpam-4506	107	8	is	be	AUX
ejpam-4506	107	9	a	a	DET
ejpam-4506	107	10	path	path	NOUN
ejpam-4506	107	11	-	-	PUNCT
ejpam-4506	107	12	induced	induce	VERB
ejpam-4506	107	13	closed	closed	ADJ
ejpam-4506	107	14	geodetic	geodetic	ADJ
ejpam-4506	107	15	basis	basis	NOUN
ejpam-4506	107	16	of	of	ADP
ejpam-4506	107	17	g	g	PROPN
ejpam-4506	107	18	and	and	CCONJ
ejpam-4506	107	19	x	x	PRON
ejpam-4506	107	20	is	be	AUX
ejpam-4506	107	21	a	a	DET
ejpam-4506	107	22	cut	cut	NOUN
ejpam-4506	107	23	-	-	PUNCT
ejpam-4506	107	24	vertex	vertex	NOUN
ejpam-4506	107	25	of	of	ADP
ejpam-4506	107	26	g	g	NOUN
ejpam-4506	107	27	,	,	PUNCT
ejpam-4506	107	28	then	then	ADV
ejpam-4506	107	29	every	every	DET
ejpam-4506	107	30	component	component	NOUN
ejpam-4506	107	31	of	of	ADP
ejpam-4506	107	32	g∖	g∖	PROPN
ejpam-4506	107	33	x	x	PUNCT
ejpam-4506	107	34	contains	contain	VERB
ejpam-4506	107	35	a	a	DET
ejpam-4506	107	36	vertex	vertex	NOUN
ejpam-4506	107	37	in	in	ADP
ejpam-4506	107	38	s.	s.	PROPN
ejpam-4506	107	39	remark	remark	PROPN
ejpam-4506	107	40	2	2	NUM
ejpam-4506	107	41	.	.	PUNCT
ejpam-4506	108	1	[	[	X
ejpam-4506	108	2	3	3	X
ejpam-4506	108	3	]	]	PUNCT
ejpam-4506	108	4	every	every	DET
ejpam-4506	108	5	cut	cut	NOUN
ejpam-4506	108	6	-	-	PUNCT
ejpam-4506	108	7	vertex	vertex	NOUN
ejpam-4506	108	8	of	of	ADP
ejpam-4506	108	9	a	a	DET
ejpam-4506	108	10	connected	connected	ADJ
ejpam-4506	108	11	graph	graph	NOUN
ejpam-4506	108	12	g	g	PROPN
ejpam-4506	108	13	belongs	belong	VERB
ejpam-4506	108	14	to	to	ADP
ejpam-4506	108	15	every	every	DET
ejpam-4506	108	16	path	path	NOUN
ejpam-4506	108	17	-	-	PUNCT
ejpam-4506	108	18	induced	induce	VERB
ejpam-4506	108	19	closed	closed	ADJ
ejpam-4506	108	20	geodetic	geodetic	ADJ
ejpam-4506	108	21	set	set	NOUN
ejpam-4506	108	22	of	of	ADP
ejpam-4506	108	23	g.	g.	PROPN
ejpam-4506	108	24	theorem	theorem	VERB
ejpam-4506	108	25	3	3	NUM
ejpam-4506	108	26	.	.	PUNCT
ejpam-4506	109	1	[	[	X
ejpam-4506	109	2	3	3	X
ejpam-4506	109	3	]	]	PUNCT
ejpam-4506	109	4	let	let	VERB
ejpam-4506	109	5	g	g	PRON
ejpam-4506	109	6	be	be	AUX
ejpam-4506	109	7	a	a	DET
ejpam-4506	109	8	connected	connected	ADJ
ejpam-4506	109	9	graph	graph	NOUN
ejpam-4506	109	10	with	with	ADP
ejpam-4506	109	11	cut	cut	NOUN
ejpam-4506	109	12	-	-	PUNCT
ejpam-4506	109	13	vertices	vertex	NOUN
ejpam-4506	109	14	.	.	PUNCT
ejpam-4506	110	1	if	if	SCONJ
ejpam-4506	110	2	g	g	PROPN
ejpam-4506	110	3	admits	admit	VERB
ejpam-4506	110	4	path	path	NOUN
ejpam-4506	110	5	-	-	PUNCT
ejpam-4506	110	6	induced	induce	VERB
ejpam-4506	110	7	closed	closed	ADJ
ejpam-4506	110	8	geodetic	geodetic	ADJ
ejpam-4506	110	9	set	set	NOUN
ejpam-4506	110	10	,	,	PUNCT
ejpam-4506	110	11	then	then	ADV
ejpam-4506	110	12	g∖	g∖	PROPN
ejpam-4506	110	13	x	x	PUNCT
ejpam-4506	110	14	has	have	VERB
ejpam-4506	110	15	exactly	exactly	ADV
ejpam-4506	110	16	two	two	NUM
ejpam-4506	110	17	components	component	NOUN
ejpam-4506	110	18	for	for	ADP
ejpam-4506	110	19	each	each	DET
ejpam-4506	110	20	cut	cut	NOUN
ejpam-4506	110	21	-	-	PUNCT
ejpam-4506	110	22	vertex	vertex	NOUN
ejpam-4506	110	23	x	x	X
ejpam-4506	110	24	of	of	ADP
ejpam-4506	110	25	g.	g.	PROPN
ejpam-4506	110	26	theorem	theorem	VERB
ejpam-4506	110	27	4	4	NUM
ejpam-4506	110	28	.	.	PUNCT
ejpam-4506	111	1	[	[	X
ejpam-4506	111	2	3	3	X
ejpam-4506	111	3	]	]	PUNCT
ejpam-4506	111	4	let	let	VERB
ejpam-4506	111	5	g	g	PRON
ejpam-4506	111	6	be	be	AUX
ejpam-4506	111	7	a	a	DET
ejpam-4506	111	8	connected	connected	ADJ
ejpam-4506	111	9	graph	graph	NOUN
ejpam-4506	111	10	with	with	ADP
ejpam-4506	111	11	cut	cut	NOUN
ejpam-4506	111	12	-	-	PUNCT
ejpam-4506	111	13	vertices	vertex	NOUN
ejpam-4506	111	14	.	.	PUNCT
ejpam-4506	112	1	if	if	SCONJ
ejpam-4506	112	2	g	g	PROPN
ejpam-4506	112	3	admits	admit	VERB
ejpam-4506	112	4	a	a	DET
ejpam-4506	112	5	path	path	NOUN
ejpam-4506	112	6	-	-	PUNCT
ejpam-4506	112	7	induced	induce	VERB
ejpam-4506	112	8	closed	closed	ADJ
ejpam-4506	112	9	geodetic	geodetic	ADJ
ejpam-4506	112	10	set	set	NOUN
ejpam-4506	112	11	,	,	PUNCT
ejpam-4506	112	12	then	then	ADV
ejpam-4506	112	13	each	each	DET
ejpam-4506	112	14	block	block	NOUN
ejpam-4506	112	15	of	of	ADP
ejpam-4506	112	16	g	g	PROPN
ejpam-4506	112	17	admits	admit	VERB
ejpam-4506	112	18	at	at	ADP
ejpam-4506	112	19	most	most	ADJ
ejpam-4506	112	20	2	2	NUM
ejpam-4506	112	21	cut	cut	NOUN
ejpam-4506	112	22	-	-	PUNCT
ejpam-4506	112	23	vertices	vertex	NOUN
ejpam-4506	112	24	.	.	PUNCT
ejpam-4506	113	1	theorem	theorem	NOUN
ejpam-4506	113	2	5	5	NUM
ejpam-4506	113	3	.	.	PUNCT
ejpam-4506	114	1	[	[	X
ejpam-4506	114	2	3	3	X
ejpam-4506	114	3	]	]	PUNCT
ejpam-4506	114	4	let	let	VERB
ejpam-4506	114	5	g	g	PRON
ejpam-4506	114	6	be	be	AUX
ejpam-4506	114	7	a	a	DET
ejpam-4506	114	8	connected	connected	ADJ
ejpam-4506	114	9	graph	graph	NOUN
ejpam-4506	114	10	of	of	ADP
ejpam-4506	114	11	orderm	orderm	NOUN
ejpam-4506	114	12	such	such	ADJ
ejpam-4506	114	13	that	that	SCONJ
ejpam-4506	114	14	g	g	PROPN
ejpam-4506	114	15	admits	admit	VERB
ejpam-4506	114	16	a	a	DET
ejpam-4506	114	17	path	path	NOUN
ejpam-4506	114	18	-	-	PUNCT
ejpam-4506	114	19	induced	induce	VERB
ejpam-4506	114	20	closed	closed	ADJ
ejpam-4506	114	21	geodetic	geodetic	ADJ
ejpam-4506	114	22	set	set	NOUN
ejpam-4506	114	23	.	.	PUNCT
ejpam-4506	115	1	if	if	SCONJ
ejpam-4506	115	2	every	every	DET
ejpam-4506	115	3	vertex	vertex	NOUN
ejpam-4506	115	4	of	of	ADP
ejpam-4506	115	5	g	g	PROPN
ejpam-4506	115	6	is	be	AUX
ejpam-4506	115	7	either	either	CCONJ
ejpam-4506	115	8	an	an	DET
ejpam-4506	115	9	extreme	extreme	ADJ
ejpam-4506	115	10	vertex	vertex	NOUN
ejpam-4506	115	11	or	or	CCONJ
ejpam-4506	115	12	a	a	DET
ejpam-4506	115	13	cut	cut	NOUN
ejpam-4506	115	14	-	-	PUNCT
ejpam-4506	115	15	vertex	vertex	NOUN
ejpam-4506	115	16	,	,	PUNCT
ejpam-4506	115	17	then	then	ADV
ejpam-4506	115	18	picgn	picgn	NOUN
ejpam-4506	115	19	(	(	PUNCT
ejpam-4506	115	20	g	g	NOUN
ejpam-4506	115	21	)	)	PUNCT
ejpam-4506	115	22	=	=	SYM
ejpam-4506	115	23	m.	m.	NOUN
ejpam-4506	115	24	theorem	theorem	VERB
ejpam-4506	115	25	6	6	NUM
ejpam-4506	115	26	.	.	PUNCT
ejpam-4506	116	1	[	[	X
ejpam-4506	116	2	3	3	X
ejpam-4506	116	3	]	]	PUNCT
ejpam-4506	116	4	let	let	VERB
ejpam-4506	116	5	t	t	NOUN
ejpam-4506	116	6	be	be	AUX
ejpam-4506	116	7	a	a	DET
ejpam-4506	116	8	tree	tree	NOUN
ejpam-4506	116	9	.	.	PUNCT
ejpam-4506	117	1	then	then	ADV
ejpam-4506	117	2	t	t	PROPN
ejpam-4506	117	3	admits	admit	VERB
ejpam-4506	117	4	a	a	DET
ejpam-4506	117	5	path	path	NOUN
ejpam-4506	117	6	-	-	PUNCT
ejpam-4506	117	7	induced	induce	VERB
ejpam-4506	117	8	closed	closed	ADJ
ejpam-4506	117	9	geodetic	geodetic	ADJ
ejpam-4506	117	10	sets	set	NOUN
ejpam-4506	117	11	if	if	SCONJ
ejpam-4506	118	1	and	and	CCONJ
ejpam-4506	118	2	only	only	ADV
ejpam-4506	118	3	if	if	SCONJ
ejpam-4506	118	4	t	t	PROPN
ejpam-4506	118	5	is	be	AUX
ejpam-4506	118	6	a	a	DET
ejpam-4506	118	7	path	path	NOUN
ejpam-4506	118	8	.	.	PUNCT
ejpam-4506	119	1	3	3	X
ejpam-4506	119	2	.	.	X
ejpam-4506	119	3	path	path	NOUN
ejpam-4506	119	4	-	-	PUNCT
ejpam-4506	119	5	induced	induce	VERB
ejpam-4506	119	6	closed	closed	ADJ
ejpam-4506	119	7	geodetic	geodetic	ADJ
ejpam-4506	119	8	domination	domination	NOUN
ejpam-4506	119	9	numbers	number	NOUN
ejpam-4506	119	10	of	of	ADP
ejpam-4506	119	11	some	some	DET
ejpam-4506	119	12	common	common	ADJ
ejpam-4506	119	13	graphs	graph	NOUN
ejpam-4506	119	14	in	in	ADP
ejpam-4506	119	15	view	view	NOUN
ejpam-4506	119	16	of	of	ADP
ejpam-4506	119	17	definition	definition	NOUN
ejpam-4506	119	18	9	9	NUM
ejpam-4506	119	19	,	,	PUNCT
ejpam-4506	119	20	a	a	DET
ejpam-4506	119	21	picg	picg	NOUN
ejpam-4506	119	22	-	-	PUNCT
ejpam-4506	119	23	set	set	NOUN
ejpam-4506	119	24	s	s	VERB
ejpam-4506	119	25	may	may	AUX
ejpam-4506	119	26	not	not	PART
ejpam-4506	119	27	be	be	AUX
ejpam-4506	119	28	a	a	DET
ejpam-4506	119	29	picgd	picgd	ADJ
ejpam-4506	119	30	-	-	PUNCT
ejpam-4506	119	31	set	set	NOUN
ejpam-4506	119	32	.	.	PUNCT
ejpam-4506	120	1	consider	consider	VERB
ejpam-4506	120	2	the	the	DET
ejpam-4506	120	3	cycle	cycle	NOUN
ejpam-4506	120	4	c8	c8	NOUN
ejpam-4506	120	5	with	with	ADP
ejpam-4506	120	6	vertex	vertex	NOUN
ejpam-4506	120	7	-	-	PUNCT
ejpam-4506	120	8	set	set	VERB
ejpam-4506	120	9	{	{	PUNCT
ejpam-4506	120	10	v1	v1	NOUN
ejpam-4506	120	11	,	,	PUNCT
ejpam-4506	120	12	v2	v2	PROPN
ejpam-4506	120	13	,	,	PUNCT
ejpam-4506	120	14	·	·	PUNCT
ejpam-4506	120	15	·	·	PUNCT
ejpam-4506	120	16	·	·	PUNCT
ejpam-4506	120	17	,	,	PUNCT
ejpam-4506	120	18	v8	v8	PROPN
ejpam-4506	120	19	}	}	PUNCT
ejpam-4506	120	20	in	in	ADP
ejpam-4506	120	21	figure	figure	NOUN
ejpam-4506	120	22	2	2	NUM
ejpam-4506	120	23	.	.	PUNCT
ejpam-4506	121	1	a	a	DET
ejpam-4506	121	2	picgb(c8	picgb(c8	NOUN
ejpam-4506	121	3	)	)	PUNCT
ejpam-4506	121	4	are	be	AUX
ejpam-4506	121	5	s	s	NOUN
ejpam-4506	121	6	=	=	PUNCT
ejpam-4506	121	7	{	{	PUNCT
ejpam-4506	121	8	v1	v1	PROPN
ejpam-4506	121	9	,	,	PUNCT
ejpam-4506	121	10	v2	v2	PROPN
ejpam-4506	121	11	,	,	PUNCT
ejpam-4506	121	12	·	·	PUNCT
ejpam-4506	121	13	·	·	PUNCT
ejpam-4506	121	14	·	·	PUNCT
ejpam-4506	121	15	,	,	PUNCT
ejpam-4506	121	16	v5	v5	PROPN
ejpam-4506	121	17	}	}	PUNCT
ejpam-4506	121	18	and	and	CCONJ
ejpam-4506	121	19	s∗	s∗	PROPN
ejpam-4506	121	20	=	=	SYM
ejpam-4506	121	21	{	{	PUNCT
ejpam-4506	121	22	v1	v1	PROPN
ejpam-4506	121	23	,	,	PUNCT
ejpam-4506	121	24	v8	v8	PROPN
ejpam-4506	121	25	,	,	PUNCT
ejpam-4506	121	26	·	·	PUNCT
ejpam-4506	121	27	·	·	PUNCT
ejpam-4506	121	28	·	·	PUNCT
ejpam-4506	121	29	,	,	PUNCT
ejpam-4506	121	30	v5	v5	PROPN
ejpam-4506	121	31	}	}	PUNCT
ejpam-4506	121	32	but	but	CCONJ
ejpam-4506	121	33	both	both	DET
ejpam-4506	121	34	sets	set	NOUN
ejpam-4506	121	35	are	be	AUX
ejpam-4506	121	36	not	not	PART
ejpam-4506	121	37	dominating	dominate	VERB
ejpam-4506	121	38	sets	set	NOUN
ejpam-4506	121	39	of	of	ADP
ejpam-4506	121	40	c8	c8	PROPN
ejpam-4506	121	41	.	.	PUNCT
ejpam-4506	122	1	however	however	ADV
ejpam-4506	122	2	,	,	PUNCT
ejpam-4506	122	3	a	a	DET
ejpam-4506	122	4	picgd	picgd	ADJ
ejpam-4506	122	5	-	-	PUNCT
ejpam-4506	122	6	set	set	NOUN
ejpam-4506	122	7	s	s	NOUN
ejpam-4506	122	8	of	of	ADP
ejpam-4506	122	9	g	g	PROPN
ejpam-4506	122	10	is	be	AUX
ejpam-4506	122	11	always	always	ADV
ejpam-4506	122	12	a	a	DET
ejpam-4506	122	13	picg	picg	NOUN
ejpam-4506	122	14	-	-	PUNCT
ejpam-4506	122	15	set	set	NOUN
ejpam-4506	122	16	of	of	ADP
ejpam-4506	122	17	g	g	PROPN
ejpam-4506	122	18	and	and	CCONJ
ejpam-4506	122	19	a	a	DET
ejpam-4506	122	20	γpicg	γpicg	NOUN
ejpam-4506	122	21	-	-	PUNCT
ejpam-4506	122	22	set	set	NOUN
ejpam-4506	122	23	of	of	ADP
ejpam-4506	122	24	g	g	PROPN
ejpam-4506	122	25	is	be	AUX
ejpam-4506	122	26	always	always	ADV
ejpam-4506	122	27	a	a	DET
ejpam-4506	122	28	picgb(g	picgb(g	NOUN
ejpam-4506	122	29	)	)	PUNCT
ejpam-4506	122	30	of	of	ADP
ejpam-4506	122	31	g.	g.	PROPN
ejpam-4506	122	32	hence	hence	ADV
ejpam-4506	122	33	,	,	PUNCT
ejpam-4506	122	34	the	the	DET
ejpam-4506	122	35	next	next	ADJ
ejpam-4506	122	36	remarks	remark	NOUN
ejpam-4506	122	37	follow	follow	VERB
ejpam-4506	122	38	.	.	PUNCT
ejpam-4506	123	1	in	in	ADP
ejpam-4506	123	2	general	general	ADJ
ejpam-4506	123	3	,	,	PUNCT
ejpam-4506	123	4	the	the	DET
ejpam-4506	123	5	graph	graph	NOUN
ejpam-4506	123	6	cn	cn	PROPN
ejpam-4506	123	7	does	do	AUX
ejpam-4506	123	8	not	not	PART
ejpam-4506	123	9	have	have	VERB
ejpam-4506	123	10	a	a	DET
ejpam-4506	123	11	path	path	NOUN
ejpam-4506	123	12	-	-	PUNCT
ejpam-4506	123	13	induced	induce	VERB
ejpam-4506	123	14	closed	closed	ADJ
ejpam-4506	123	15	geodetic	geodetic	ADJ
ejpam-4506	123	16	dominating	dominating	NOUN
ejpam-4506	123	17	set	set	NOUN
ejpam-4506	123	18	,	,	PUNCT
ejpam-4506	123	19	for	for	ADP
ejpam-4506	123	20	all	all	DET
ejpam-4506	123	21	n	n	PRON
ejpam-4506	123	22	≥	≥	NOUN
ejpam-4506	123	23	8	8	NUM
ejpam-4506	123	24	.	.	PUNCT
ejpam-4506	124	1	j.	j.	PROPN
ejpam-4506	124	2	anoche	anoche	PROPN
ejpam-4506	124	3	,	,	PUNCT
ejpam-4506	124	4	i.	i.	PROPN
ejpam-4506	124	5	aniversario	aniversario	PROPN
ejpam-4506	124	6	,	,	PUNCT
ejpam-4506	124	7	c.	c.	PROPN
ejpam-4506	124	8	merca	merca	PROPN
ejpam-4506	124	9	/	/	SYM
ejpam-4506	124	10	eur	eur	PROPN
ejpam-4506	124	11	.	.	PUNCT
ejpam-4506	125	1	j.	j.	PROPN
ejpam-4506	125	2	pure	pure	PROPN
ejpam-4506	125	3	appl	appl	PROPN
ejpam-4506	125	4	.	.	PROPN
ejpam-4506	125	5	math	math	PROPN
ejpam-4506	125	6	,	,	PUNCT
ejpam-4506	125	7	16	16	NUM
ejpam-4506	125	8	(	(	PUNCT
ejpam-4506	125	9	1	1	NUM
ejpam-4506	125	10	)	)	PUNCT
ejpam-4506	125	11	(	(	PUNCT
ejpam-4506	125	12	2023	2023	NUM
ejpam-4506	125	13	)	)	PUNCT
ejpam-4506	125	14	,	,	PUNCT
ejpam-4506	125	15	169	169	NUM
ejpam-4506	125	16	-	-	SYM
ejpam-4506	125	17	179	179	NUM
ejpam-4506	125	18	173	173	NUM
ejpam-4506	125	19	....................................	....................................	PUNCT
ejpam-4506	126	1	....................................................................................................................................................	....................................................................................................................................................	PUNCT
ejpam-4506	126	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4506	127	1	....................................	....................................	PUNCT
ejpam-4506	127	2	............	............	PUNCT
ejpam-4506	127	3	...........	...........	PUNCT
ejpam-4506	127	4	...........	...........	PUNCT
ejpam-4506	127	5	...........	...........	PUNCT
ejpam-4506	127	6	...........	...........	PUNCT
ejpam-4506	127	7	...........	...........	PUNCT
ejpam-4506	127	8	...........	...........	PUNCT
ejpam-4506	127	9	...........	...........	PUNCT
ejpam-4506	127	10	...........	...........	PUNCT
ejpam-4506	127	11	...........	...........	PUNCT
ejpam-4506	127	12	.	.	PUNCT
ejpam-4506	128	1	....	....	PUNCT
ejpam-4506	128	2	................................	................................	PUNCT
ejpam-4506	129	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4506	129	2	....................................	....................................	PUNCT
ejpam-4506	130	1	.........	.........	PUNCT
ejpam-4506	130	2	........	........	PUNCT
ejpam-4506	130	3	........	........	PUNCT
ejpam-4506	130	4	........	........	PUNCT
ejpam-4506	130	5	........	........	PUNCT
ejpam-4506	130	6	........	........	PUNCT
ejpam-4506	130	7	........	........	PUNCT
ejpam-4506	130	8	........	........	PUNCT
ejpam-4506	130	9	........	........	PUNCT
ejpam-4506	130	10	........	........	PUNCT
ejpam-4506	130	11	........	........	PUNCT
ejpam-4506	130	12	........	........	PUNCT
ejpam-4506	130	13	........	........	PUNCT
ejpam-4506	130	14	.......	.......	PUNCT
ejpam-4506	131	1	....................................	....................................	PUNCT
ejpam-4506	131	2	............	............	PUNCT
ejpam-4506	131	3	...........	...........	PUNCT
ejpam-4506	131	4	...........	...........	PUNCT
ejpam-4506	131	5	...........	...........	PUNCT
ejpam-4506	131	6	...........	...........	PUNCT
ejpam-4506	131	7	...........	...........	PUNCT
ejpam-4506	131	8	...........	...........	PUNCT
ejpam-4506	131	9	...........	...........	PUNCT
ejpam-4506	131	10	...........	...........	PUNCT
ejpam-4506	131	11	...........	...........	PUNCT
ejpam-4506	131	12	.	.	PUNCT
ejpam-4506	132	1	....	....	PUNCT
ejpam-4506	132	2	................................	................................	PUNCT
ejpam-4506	133	1	................................................................................................................	................................................................................................................	PUNCT
ejpam-4506	133	2	....................................................................................................................................................	....................................................................................................................................................	PUNCT
ejpam-4506	134	1	c8	c8	PROPN
ejpam-4506	134	2	v8	v8	PROPN
ejpam-4506	134	3	v1	v1	PROPN
ejpam-4506	134	4	v2	v2	PROPN
ejpam-4506	134	5	v3	v3	PROPN
ejpam-4506	134	6	v5v6	v5v6	PROPN
ejpam-4506	134	7	v4	v4	NOUN
ejpam-4506	134	8	v7	v7	VERB
ejpam-4506	134	9	figure	figure	NOUN
ejpam-4506	134	10	2	2	NUM
ejpam-4506	134	11	:	:	PUNCT
ejpam-4506	134	12	the	the	DET
ejpam-4506	134	13	cycle	cycle	NOUN
ejpam-4506	134	14	c8	c8	PROPN
ejpam-4506	134	15	remark	remark	NOUN
ejpam-4506	134	16	3	3	NUM
ejpam-4506	134	17	.	.	PUNCT
ejpam-4506	135	1	every	every	DET
ejpam-4506	135	2	picgd	picgd	ADJ
ejpam-4506	135	3	-	-	PUNCT
ejpam-4506	135	4	set	set	NOUN
ejpam-4506	135	5	of	of	ADP
ejpam-4506	135	6	a	a	DET
ejpam-4506	135	7	graph	graph	NOUN
ejpam-4506	135	8	g	g	NOUN
ejpam-4506	135	9	is	be	AUX
ejpam-4506	135	10	a	a	DET
ejpam-4506	135	11	picg	picg	NOUN
ejpam-4506	135	12	-	-	PUNCT
ejpam-4506	135	13	set	set	NOUN
ejpam-4506	135	14	of	of	ADP
ejpam-4506	135	15	g.	g.	PROPN
ejpam-4506	135	16	remark	remark	PROPN
ejpam-4506	135	17	4	4	NUM
ejpam-4506	135	18	.	.	PUNCT
ejpam-4506	136	1	every	every	DET
ejpam-4506	136	2	γpicg	γpicg	NOUN
ejpam-4506	136	3	-	-	PUNCT
ejpam-4506	136	4	set	set	NOUN
ejpam-4506	136	5	of	of	ADP
ejpam-4506	136	6	a	a	DET
ejpam-4506	136	7	graph	graph	NOUN
ejpam-4506	136	8	g	g	NOUN
ejpam-4506	136	9	is	be	AUX
ejpam-4506	136	10	a	a	DET
ejpam-4506	136	11	picgb(g	picgb(g	NOUN
ejpam-4506	136	12	)	)	PUNCT
ejpam-4506	136	13	of	of	ADP
ejpam-4506	136	14	g.	g.	PROPN
ejpam-4506	136	15	in	in	ADP
ejpam-4506	136	16	view	view	NOUN
ejpam-4506	136	17	of	of	ADP
ejpam-4506	136	18	definition	definition	NOUN
ejpam-4506	136	19	10	10	NUM
ejpam-4506	136	20	,	,	PUNCT
ejpam-4506	136	21	not	not	PART
ejpam-4506	136	22	all	all	DET
ejpam-4506	136	23	connected	connected	ADJ
ejpam-4506	136	24	graphs	graph	NOUN
ejpam-4506	136	25	have	have	VERB
ejpam-4506	136	26	path	path	NOUN
ejpam-4506	136	27	-	-	PUNCT
ejpam-4506	136	28	induced	induce	VERB
ejpam-4506	136	29	closed	closed	ADJ
ejpam-4506	136	30	geodetic	geodetic	ADJ
ejpam-4506	136	31	dominating	dominating	NOUN
ejpam-4506	136	32	set	set	NOUN
ejpam-4506	136	33	.	.	PUNCT
ejpam-4506	137	1	to	to	PART
ejpam-4506	137	2	illustrate	illustrate	VERB
ejpam-4506	137	3	this	this	PRON
ejpam-4506	137	4	,	,	PUNCT
ejpam-4506	137	5	let	let	VERB
ejpam-4506	137	6	us	we	PRON
ejpam-4506	137	7	have	have	VERB
ejpam-4506	137	8	the	the	DET
ejpam-4506	137	9	following	follow	VERB
ejpam-4506	137	10	example	example	NOUN
ejpam-4506	137	11	.	.	PUNCT
ejpam-4506	138	1	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-4506	139	1	....................................	....................................	PUNCT
ejpam-4506	139	2	.........	.........	PUNCT
ejpam-4506	139	3	........	........	PUNCT
ejpam-4506	139	4	........	........	PUNCT
ejpam-4506	139	5	........	........	PUNCT
ejpam-4506	139	6	........	........	PUNCT
ejpam-4506	139	7	........	........	PUNCT
ejpam-4506	139	8	........	........	PUNCT
ejpam-4506	139	9	........	........	PUNCT
ejpam-4506	139	10	........	........	PUNCT
ejpam-4506	139	11	........	........	PUNCT
ejpam-4506	139	12	........	........	PUNCT
ejpam-4506	139	13	........	........	PUNCT
ejpam-4506	139	14	.......	.......	PUNCT
ejpam-4506	140	1	....................................	....................................	PUNCT
ejpam-4506	140	2	....................................	....................................	PUNCT
ejpam-4506	141	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-4506	141	2	..........	..........	PUNCT
ejpam-4506	142	1	.........	.........	PUNCT
ejpam-4506	142	2	.........	.........	PUNCT
ejpam-4506	143	1	.........	.........	PUNCT
ejpam-4506	143	2	.........	.........	PUNCT
ejpam-4506	144	1	.........	.........	PUNCT
ejpam-4506	144	2	.........	.........	PUNCT
ejpam-4506	145	1	.........	.........	PUNCT
ejpam-4506	145	2	.........	.........	PUNCT
ejpam-4506	146	1	.........	.........	PUNCT
ejpam-4506	146	2	.........	.........	PUNCT
ejpam-4506	147	1	.........	.........	PUNCT
ejpam-4506	147	2	.........	.........	PUNCT
ejpam-4506	148	1	....................................	....................................	PUNCT
ejpam-4506	148	2	....................................	....................................	PUNCT
ejpam-4506	148	3	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-4506	149	1	v	v	X
ejpam-4506	149	2	v1	v1	PROPN
ejpam-4506	149	3	v2	v2	PROPN
ejpam-4506	149	4	v3v4	v3v4	NOUN
ejpam-4506	149	5	:	:	PUNCT
ejpam-4506	149	6	v5k1,5	v5k1,5	NOUN
ejpam-4506	149	7	:	:	PUNCT
ejpam-4506	149	8	figure	figure	VERB
ejpam-4506	149	9	3	3	NUM
ejpam-4506	149	10	:	:	PUNCT
ejpam-4506	149	11	a	a	DET
ejpam-4506	149	12	graph	graph	NOUN
ejpam-4506	149	13	without	without	ADP
ejpam-4506	149	14	a	a	DET
ejpam-4506	149	15	picg	picg	NOUN
ejpam-4506	149	16	-	-	PUNCT
ejpam-4506	149	17	set	set	VERB
ejpam-4506	149	18	example	example	NOUN
ejpam-4506	149	19	2	2	NUM
ejpam-4506	149	20	.	.	X
ejpam-4506	149	21	consider	consider	VERB
ejpam-4506	149	22	the	the	DET
ejpam-4506	149	23	star	star	NOUN
ejpam-4506	149	24	k1,5	k1,5	PROPN
ejpam-4506	149	25	in	in	ADP
ejpam-4506	149	26	figure	figure	NOUN
ejpam-4506	149	27	3	3	NUM
ejpam-4506	149	28	.	.	X
ejpam-4506	149	29	observe	observe	VERB
ejpam-4506	149	30	that	that	SCONJ
ejpam-4506	149	31	the	the	DET
ejpam-4506	149	32	only	only	ADJ
ejpam-4506	149	33	geodetic	geodetic	ADJ
ejpam-4506	149	34	covers	cover	NOUN
ejpam-4506	149	35	of	of	ADP
ejpam-4506	149	36	k1,5	k1,5	PROPN
ejpam-4506	149	37	are	be	AUX
ejpam-4506	149	38	sets	set	NOUN
ejpam-4506	149	39	s	s	PART
ejpam-4506	149	40	=	=	PUNCT
ejpam-4506	149	41	{	{	PUNCT
ejpam-4506	149	42	v1	v1	PROPN
ejpam-4506	149	43	,	,	PUNCT
ejpam-4506	149	44	v2	v2	PROPN
ejpam-4506	149	45	,	,	PUNCT
ejpam-4506	149	46	v3	v3	PROPN
ejpam-4506	149	47	,	,	PUNCT
ejpam-4506	149	48	v4	v4	PROPN
ejpam-4506	149	49	,	,	PUNCT
ejpam-4506	149	50	v5	v5	PROPN
ejpam-4506	149	51	}	}	PUNCT
ejpam-4506	149	52	and	and	CCONJ
ejpam-4506	149	53	s∗	s∗	PROPN
ejpam-4506	149	54	=	=	SYM
ejpam-4506	149	55	v	v	PROPN
ejpam-4506	149	56	(	(	PUNCT
ejpam-4506	149	57	k1,5	k1,5	PROPN
ejpam-4506	149	58	)	)	PUNCT
ejpam-4506	149	59	which	which	PRON
ejpam-4506	149	60	are	be	AUX
ejpam-4506	149	61	also	also	ADV
ejpam-4506	149	62	dominating	dominate	VERB
ejpam-4506	149	63	sets	set	NOUN
ejpam-4506	149	64	of	of	ADP
ejpam-4506	149	65	k1,5	k1,5	PROPN
ejpam-4506	149	66	.	.	PUNCT
ejpam-4506	150	1	but	but	CCONJ
ejpam-4506	150	2	⟨s⟩	⟨s⟩	PROPN
ejpam-4506	150	3	and	and	CCONJ
ejpam-4506	150	4	⟨s∗⟩	⟨s∗⟩	NOUN
ejpam-4506	150	5	do	do	AUX
ejpam-4506	150	6	not	not	PART
ejpam-4506	150	7	contain	contain	VERB
ejpam-4506	150	8	a	a	DET
ejpam-4506	150	9	hamiltonian	hamiltonian	ADJ
ejpam-4506	150	10	path	path	NOUN
ejpam-4506	150	11	.	.	PUNCT
ejpam-4506	151	1	therefore	therefore	ADV
ejpam-4506	151	2	,	,	PUNCT
ejpam-4506	151	3	s	s	PART
ejpam-4506	151	4	and	and	CCONJ
ejpam-4506	151	5	s∗	s∗	PROPN
ejpam-4506	151	6	are	be	AUX
ejpam-4506	151	7	not	not	PART
ejpam-4506	151	8	path	path	NOUN
ejpam-4506	151	9	-	-	PUNCT
ejpam-4506	151	10	induced	induce	VERB
ejpam-4506	151	11	closed	closed	ADJ
ejpam-4506	151	12	geodetic	geodetic	ADJ
ejpam-4506	151	13	dominating	dominating	NOUN
ejpam-4506	151	14	sets	set	NOUN
ejpam-4506	151	15	of	of	ADP
ejpam-4506	151	16	k1,5	k1,5	PROPN
ejpam-4506	151	17	.	.	PUNCT
ejpam-4506	152	1	in	in	ADP
ejpam-4506	152	2	general	general	ADJ
ejpam-4506	152	3	,	,	PUNCT
ejpam-4506	152	4	the	the	DET
ejpam-4506	152	5	graph	graph	NOUN
ejpam-4506	152	6	k1,n	k1,n	PROPN
ejpam-4506	152	7	does	do	AUX
ejpam-4506	152	8	not	not	PART
ejpam-4506	152	9	have	have	VERB
ejpam-4506	152	10	a	a	DET
ejpam-4506	152	11	path	path	NOUN
ejpam-4506	152	12	-	-	PUNCT
ejpam-4506	152	13	induced	induce	VERB
ejpam-4506	152	14	closed	closed	ADJ
ejpam-4506	152	15	geodetic	geodetic	ADJ
ejpam-4506	152	16	dominating	dominating	NOUN
ejpam-4506	152	17	set	set	NOUN
ejpam-4506	152	18	,	,	PUNCT
ejpam-4506	152	19	for	for	ADP
ejpam-4506	152	20	all	all	DET
ejpam-4506	152	21	n	n	PRON
ejpam-4506	152	22	≥	≥	NOUN
ejpam-4506	152	23	3	3	NUM
ejpam-4506	152	24	.	.	PUNCT
ejpam-4506	152	25	to	to	ADP
ejpam-4506	152	26	this	this	DET
ejpam-4506	152	27	extent	extent	NOUN
ejpam-4506	152	28	,	,	PUNCT
ejpam-4506	152	29	we	we	PRON
ejpam-4506	152	30	will	will	AUX
ejpam-4506	152	31	examine	examine	VERB
ejpam-4506	152	32	the	the	DET
ejpam-4506	152	33	properties	property	NOUN
ejpam-4506	152	34	of	of	ADP
ejpam-4506	152	35	those	those	DET
ejpam-4506	152	36	graphs	graph	NOUN
ejpam-4506	152	37	which	which	PRON
ejpam-4506	152	38	admit	admit	VERB
ejpam-4506	152	39	pathinduced	pathinduce	VERB
ejpam-4506	152	40	closed	closed	ADJ
ejpam-4506	152	41	geodetic	geodetic	ADJ
ejpam-4506	152	42	dominating	dominating	NOUN
ejpam-4506	152	43	sets	set	NOUN
ejpam-4506	152	44	and	and	CCONJ
ejpam-4506	152	45	provide	provide	VERB
ejpam-4506	152	46	some	some	DET
ejpam-4506	152	47	conditions	condition	NOUN
ejpam-4506	152	48	that	that	PRON
ejpam-4506	152	49	will	will	AUX
ejpam-4506	152	50	help	help	VERB
ejpam-4506	152	51	us	we	PRON
ejpam-4506	152	52	determine	determine	VERB
ejpam-4506	152	53	whether	whether	SCONJ
ejpam-4506	152	54	a	a	DET
ejpam-4506	152	55	graph	graph	NOUN
ejpam-4506	152	56	g	g	PROPN
ejpam-4506	152	57	admits	admit	VERB
ejpam-4506	152	58	a	a	DET
ejpam-4506	152	59	path	path	NOUN
ejpam-4506	152	60	-	-	PUNCT
ejpam-4506	152	61	induced	induce	VERB
ejpam-4506	152	62	closed	closed	ADJ
ejpam-4506	152	63	geodetic	geodetic	ADJ
ejpam-4506	152	64	dominating	dominating	NOUN
ejpam-4506	152	65	set	set	NOUN
ejpam-4506	152	66	or	or	CCONJ
ejpam-4506	152	67	not	not	PART
ejpam-4506	152	68	.	.	PUNCT
ejpam-4506	153	1	let	let	VERB
ejpam-4506	153	2	us	we	PRON
ejpam-4506	153	3	consider	consider	VERB
ejpam-4506	153	4	the	the	DET
ejpam-4506	153	5	following	follow	VERB
ejpam-4506	153	6	theorem	theorem	VERB
ejpam-4506	153	7	.	.	PUNCT
ejpam-4506	153	8	theorem	theorem	PROPN
ejpam-4506	153	9	7	7	NUM
ejpam-4506	153	10	.	.	PUNCT
ejpam-4506	154	1	let	let	VERB
ejpam-4506	154	2	g	g	PRON
ejpam-4506	154	3	be	be	AUX
ejpam-4506	154	4	a	a	DET
ejpam-4506	154	5	connected	connected	ADJ
ejpam-4506	154	6	graph	graph	NOUN
ejpam-4506	154	7	with	with	ADP
ejpam-4506	154	8	cut	cut	NOUN
ejpam-4506	154	9	-	-	PUNCT
ejpam-4506	154	10	vertices	vertex	NOUN
ejpam-4506	154	11	.	.	PUNCT
ejpam-4506	155	1	if	if	SCONJ
ejpam-4506	155	2	s	s	VERB
ejpam-4506	155	3	⊆	⊆	NUM
ejpam-4506	155	4	v	v	NOUN
ejpam-4506	155	5	(	(	PUNCT
ejpam-4506	155	6	g	g	NOUN
ejpam-4506	155	7	)	)	PUNCT
ejpam-4506	155	8	is	be	AUX
ejpam-4506	155	9	a	a	DET
ejpam-4506	155	10	γpicg	γpicg	NOUN
ejpam-4506	155	11	-	-	PUNCT
ejpam-4506	155	12	set	set	NOUN
ejpam-4506	155	13	of	of	ADP
ejpam-4506	155	14	g	g	PROPN
ejpam-4506	155	15	and	and	CCONJ
ejpam-4506	155	16	x	x	PRON
ejpam-4506	155	17	is	be	AUX
ejpam-4506	155	18	a	a	DET
ejpam-4506	155	19	cut	cut	NOUN
ejpam-4506	155	20	-	-	PUNCT
ejpam-4506	155	21	vertex	vertex	NOUN
ejpam-4506	155	22	of	of	ADP
ejpam-4506	155	23	g	g	NOUN
ejpam-4506	155	24	,	,	PUNCT
ejpam-4506	155	25	then	then	ADV
ejpam-4506	155	26	every	every	DET
ejpam-4506	155	27	component	component	NOUN
ejpam-4506	155	28	of	of	ADP
ejpam-4506	155	29	g∖	g∖	PROPN
ejpam-4506	155	30	x	x	PUNCT
ejpam-4506	155	31	contains	contain	VERB
ejpam-4506	155	32	an	an	DET
ejpam-4506	155	33	element	element	NOUN
ejpam-4506	155	34	in	in	ADP
ejpam-4506	155	35	s.	s.	PROPN
ejpam-4506	155	36	j.	j.	PROPN
ejpam-4506	155	37	anoche	anoche	PROPN
ejpam-4506	155	38	,	,	PUNCT
ejpam-4506	155	39	i.	i.	PROPN
ejpam-4506	155	40	aniversario	aniversario	PROPN
ejpam-4506	155	41	,	,	PUNCT
ejpam-4506	155	42	c.	c.	PROPN
ejpam-4506	155	43	merca	merca	PROPN
ejpam-4506	155	44	/	/	SYM
ejpam-4506	155	45	eur	eur	PROPN
ejpam-4506	155	46	.	.	PUNCT
ejpam-4506	156	1	j.	j.	PROPN
ejpam-4506	156	2	pure	pure	PROPN
ejpam-4506	156	3	appl	appl	PROPN
ejpam-4506	156	4	.	.	PROPN
ejpam-4506	156	5	math	math	PROPN
ejpam-4506	156	6	,	,	PUNCT
ejpam-4506	156	7	16	16	NUM
ejpam-4506	156	8	(	(	PUNCT
ejpam-4506	156	9	1	1	NUM
ejpam-4506	156	10	)	)	PUNCT
ejpam-4506	156	11	(	(	PUNCT
ejpam-4506	156	12	2023	2023	NUM
ejpam-4506	156	13	)	)	PUNCT
ejpam-4506	156	14	,	,	PUNCT
ejpam-4506	156	15	169	169	NUM
ejpam-4506	156	16	-	-	SYM
ejpam-4506	156	17	179	179	NUM
ejpam-4506	156	18	174	174	NUM
ejpam-4506	156	19	proof	proof	NOUN
ejpam-4506	156	20	:	:	PUNCT
ejpam-4506	156	21	let	let	VERB
ejpam-4506	156	22	g	g	PRON
ejpam-4506	156	23	be	be	AUX
ejpam-4506	156	24	a	a	DET
ejpam-4506	156	25	connected	connected	ADJ
ejpam-4506	156	26	graph	graph	NOUN
ejpam-4506	156	27	and	and	CCONJ
ejpam-4506	156	28	x	x	SYM
ejpam-4506	156	29	∈	∈	PROPN
ejpam-4506	156	30	v	v	ADP
ejpam-4506	156	31	(	(	PUNCT
ejpam-4506	156	32	g	g	NOUN
ejpam-4506	156	33	)	)	PUNCT
ejpam-4506	156	34	be	be	AUX
ejpam-4506	156	35	a	a	DET
ejpam-4506	156	36	cut	cut	NOUN
ejpam-4506	156	37	-	-	PUNCT
ejpam-4506	156	38	vertex	vertex	NOUN
ejpam-4506	156	39	of	of	ADP
ejpam-4506	156	40	g.	g.	PROPN
ejpam-4506	156	41	let	let	VERB
ejpam-4506	156	42	s	s	PRON
ejpam-4506	156	43	⊆	⊆	NUM
ejpam-4506	156	44	v	v	NOUN
ejpam-4506	156	45	(	(	PUNCT
ejpam-4506	156	46	g	g	NOUN
ejpam-4506	156	47	)	)	PUNCT
ejpam-4506	156	48	be	be	AUX
ejpam-4506	156	49	a	a	DET
ejpam-4506	156	50	γpicg	γpicg	NOUN
ejpam-4506	156	51	-	-	PUNCT
ejpam-4506	156	52	set	set	NOUN
ejpam-4506	156	53	of	of	ADP
ejpam-4506	156	54	g.	g.	PROPN
ejpam-4506	156	55	then	then	ADV
ejpam-4506	156	56	by	by	ADP
ejpam-4506	156	57	remark	remark	NOUN
ejpam-4506	156	58	4	4	NUM
ejpam-4506	156	59	,	,	PUNCT
ejpam-4506	156	60	s	s	VERB
ejpam-4506	156	61	is	be	AUX
ejpam-4506	156	62	a	a	DET
ejpam-4506	156	63	picgb(g	picgb(g	NOUN
ejpam-4506	156	64	)	)	PUNCT
ejpam-4506	156	65	.	.	PUNCT
ejpam-4506	157	1	hence	hence	ADV
ejpam-4506	157	2	,	,	PUNCT
ejpam-4506	157	3	by	by	ADP
ejpam-4506	157	4	theorem	theorem	NOUN
ejpam-4506	157	5	2	2	NUM
ejpam-4506	157	6	,	,	PUNCT
ejpam-4506	157	7	every	every	DET
ejpam-4506	157	8	component	component	NOUN
ejpam-4506	157	9	of	of	ADP
ejpam-4506	157	10	g∖	g∖	PROPN
ejpam-4506	157	11	x	x	PUNCT
ejpam-4506	157	12	contains	contain	VERB
ejpam-4506	157	13	a	a	DET
ejpam-4506	157	14	vertex	vertex	NOUN
ejpam-4506	157	15	in	in	ADP
ejpam-4506	157	16	s.	s.	PROPN
ejpam-4506	157	17	■	■	PUNCT
ejpam-4506	157	18	as	as	ADP
ejpam-4506	157	19	a	a	DET
ejpam-4506	157	20	consequence	consequence	NOUN
ejpam-4506	157	21	of	of	ADP
ejpam-4506	157	22	remark	remark	NOUN
ejpam-4506	157	23	2	2	NUM
ejpam-4506	157	24	,	,	PUNCT
ejpam-4506	157	25	theorem	theorem	VERB
ejpam-4506	157	26	3	3	NUM
ejpam-4506	157	27	and	and	CCONJ
ejpam-4506	157	28	theorem	theorem	VERB
ejpam-4506	157	29	4	4	NUM
ejpam-4506	157	30	,	,	PUNCT
ejpam-4506	157	31	the	the	DET
ejpam-4506	157	32	next	next	ADJ
ejpam-4506	157	33	results	result	NOUN
ejpam-4506	157	34	follow	follow	VERB
ejpam-4506	157	35	.	.	PUNCT
ejpam-4506	158	1	remark	remark	NOUN
ejpam-4506	158	2	5	5	NUM
ejpam-4506	158	3	.	.	PUNCT
ejpam-4506	159	1	every	every	DET
ejpam-4506	159	2	cut	cut	NOUN
ejpam-4506	159	3	-	-	PUNCT
ejpam-4506	159	4	vertex	vertex	NOUN
ejpam-4506	159	5	of	of	ADP
ejpam-4506	159	6	a	a	DET
ejpam-4506	159	7	connected	connected	ADJ
ejpam-4506	159	8	graph	graph	NOUN
ejpam-4506	159	9	g	g	PROPN
ejpam-4506	159	10	belongs	belong	VERB
ejpam-4506	159	11	to	to	ADP
ejpam-4506	159	12	every	every	DET
ejpam-4506	159	13	path	path	NOUN
ejpam-4506	159	14	-	-	PUNCT
ejpam-4506	159	15	induced	induce	VERB
ejpam-4506	159	16	closed	closed	ADJ
ejpam-4506	159	17	geodetic	geodetic	ADJ
ejpam-4506	159	18	dominating	dominating	NOUN
ejpam-4506	159	19	set	set	NOUN
ejpam-4506	159	20	of	of	ADP
ejpam-4506	159	21	g.	g.	PROPN
ejpam-4506	159	22	theorem	theorem	VERB
ejpam-4506	159	23	8	8	NUM
ejpam-4506	159	24	.	.	PUNCT
ejpam-4506	160	1	let	let	VERB
ejpam-4506	160	2	g	g	PRON
ejpam-4506	160	3	be	be	AUX
ejpam-4506	160	4	a	a	DET
ejpam-4506	160	5	connected	connected	ADJ
ejpam-4506	160	6	graph	graph	NOUN
ejpam-4506	160	7	with	with	ADP
ejpam-4506	160	8	cut	cut	NOUN
ejpam-4506	160	9	-	-	PUNCT
ejpam-4506	160	10	vertices	vertex	NOUN
ejpam-4506	160	11	.	.	PUNCT
ejpam-4506	161	1	if	if	SCONJ
ejpam-4506	161	2	g	g	PROPN
ejpam-4506	161	3	has	have	VERB
ejpam-4506	161	4	a	a	DET
ejpam-4506	161	5	path	path	NOUN
ejpam-4506	161	6	-	-	PUNCT
ejpam-4506	161	7	induced	induce	VERB
ejpam-4506	161	8	closed	closed	ADJ
ejpam-4506	161	9	geodetic	geodetic	ADJ
ejpam-4506	161	10	dominating	dominating	NOUN
ejpam-4506	161	11	set	set	NOUN
ejpam-4506	161	12	,	,	PUNCT
ejpam-4506	161	13	then	then	ADV
ejpam-4506	161	14	ω(g−	ω(g−	PROPN
ejpam-4506	161	15	x	x	NOUN
ejpam-4506	161	16	)	)	PUNCT
ejpam-4506	161	17	=	=	SYM
ejpam-4506	161	18	2	2	NUM
ejpam-4506	161	19	for	for	ADP
ejpam-4506	161	20	every	every	DET
ejpam-4506	161	21	cut	cut	NOUN
ejpam-4506	161	22	-	-	PUNCT
ejpam-4506	161	23	vertex	vertex	NOUN
ejpam-4506	161	24	x	x	X
ejpam-4506	161	25	of	of	ADP
ejpam-4506	161	26	g.	g.	PROPN
ejpam-4506	161	27	the	the	DET
ejpam-4506	161	28	contrapositive	contrapositive	NOUN
ejpam-4506	161	29	of	of	ADP
ejpam-4506	161	30	theorem	theorem	ADJ
ejpam-4506	161	31	8	8	NUM
ejpam-4506	161	32	says	say	VERB
ejpam-4506	161	33	that	that	SCONJ
ejpam-4506	161	34	if	if	SCONJ
ejpam-4506	161	35	there	there	PRON
ejpam-4506	161	36	exists	exist	VERB
ejpam-4506	161	37	a	a	DET
ejpam-4506	161	38	cut	cut	NOUN
ejpam-4506	161	39	-	-	PUNCT
ejpam-4506	161	40	vertex	vertex	NOUN
ejpam-4506	161	41	x	x	NOUN
ejpam-4506	161	42	of	of	ADP
ejpam-4506	161	43	g	g	NOUN
ejpam-4506	161	44	with	with	ADP
ejpam-4506	161	45	ω(g−	ω(g−	PROPN
ejpam-4506	161	46	x	x	NOUN
ejpam-4506	161	47	)	)	PUNCT
ejpam-4506	161	48	≥	≥	NOUN
ejpam-4506	161	49	3	3	NUM
ejpam-4506	161	50	,	,	PUNCT
ejpam-4506	161	51	then	then	ADV
ejpam-4506	161	52	g	g	PROPN
ejpam-4506	161	53	has	have	VERB
ejpam-4506	161	54	no	no	DET
ejpam-4506	161	55	path	path	NOUN
ejpam-4506	161	56	-	-	PUNCT
ejpam-4506	161	57	induced	induce	VERB
ejpam-4506	161	58	closed	closed	ADJ
ejpam-4506	161	59	geodetic	geodetic	ADJ
ejpam-4506	161	60	dominating	dominating	NOUN
ejpam-4506	161	61	set	set	NOUN
ejpam-4506	161	62	.	.	PUNCT
ejpam-4506	162	1	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-4506	162	2	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-4506	163	1	....................................	....................................	PUNCT
ejpam-4506	163	2	.........	.........	PUNCT
ejpam-4506	163	3	........	........	PUNCT
ejpam-4506	163	4	........	........	PUNCT
ejpam-4506	163	5	........	........	PUNCT
ejpam-4506	163	6	........	........	PUNCT
ejpam-4506	163	7	........	........	PUNCT
ejpam-4506	163	8	........	........	PUNCT
ejpam-4506	163	9	........	........	PUNCT
ejpam-4506	163	10	........	........	PUNCT
ejpam-4506	163	11	........	........	PUNCT
ejpam-4506	163	12	........	........	PUNCT
ejpam-4506	163	13	........	........	PUNCT
ejpam-4506	163	14	.......	.......	PUNCT
ejpam-4506	164	1	....................................	....................................	PUNCT
ejpam-4506	164	2	............	............	PUNCT
ejpam-4506	164	3	...........	...........	PUNCT
ejpam-4506	164	4	...........	...........	PUNCT
ejpam-4506	164	5	...........	...........	PUNCT
ejpam-4506	164	6	...........	...........	PUNCT
ejpam-4506	164	7	...........	...........	PUNCT
ejpam-4506	164	8	...........	...........	PUNCT
ejpam-4506	164	9	...........	...........	PUNCT
ejpam-4506	164	10	...........	...........	PUNCT
ejpam-4506	164	11	...........	...........	PUNCT
ejpam-4506	164	12	...........	...........	PUNCT
ejpam-4506	164	13	...........	...........	PUNCT
ejpam-4506	164	14	...........	...........	PUNCT
ejpam-4506	164	15	........	........	PUNCT
ejpam-4506	164	16	....................................	....................................	PUNCT
ejpam-4506	164	17	............................................................................................................................................	............................................................................................................................................	PUNCT
ejpam-4506	164	18	........................................................................	........................................................................	PUNCT
ejpam-4506	165	1	..........	..........	PUNCT
ejpam-4506	165	2	.........	.........	PUNCT
ejpam-4506	166	1	.........	.........	PUNCT
ejpam-4506	166	2	.........	.........	PUNCT
ejpam-4506	167	1	.........	.........	PUNCT
ejpam-4506	167	2	.........	.........	PUNCT
ejpam-4506	168	1	.........	.........	PUNCT
ejpam-4506	168	2	.........	.........	PUNCT
ejpam-4506	169	1	.........	.........	PUNCT
ejpam-4506	169	2	.........	.........	PUNCT
ejpam-4506	170	1	.........	.........	PUNCT
ejpam-4506	170	2	.........	.........	PUNCT
ejpam-4506	171	1	.........	.........	PUNCT
ejpam-4506	172	1	........................................................................................................................................................	........................................................................................................................................................	PROPN
ejpam-4506	173	1	v	v	INTJ
ejpam-4506	173	2	•	•	NOUN
ejpam-4506	173	3	g	g	NOUN
ejpam-4506	173	4	:	:	PUNCT
ejpam-4506	173	5	figure	figure	VERB
ejpam-4506	173	6	4	4	NUM
ejpam-4506	173	7	:	:	PUNCT
ejpam-4506	173	8	a	a	DET
ejpam-4506	173	9	graph	graph	NOUN
ejpam-4506	173	10	with	with	ADP
ejpam-4506	173	11	a	a	DET
ejpam-4506	173	12	cut	cut	NOUN
ejpam-4506	173	13	-	-	PUNCT
ejpam-4506	173	14	vertex	vertex	NOUN
ejpam-4506	173	15	and	and	CCONJ
ejpam-4506	173	16	without	without	ADP
ejpam-4506	173	17	a	a	DET
ejpam-4506	173	18	γpicg	γpicg	NOUN
ejpam-4506	173	19	-	-	PUNCT
ejpam-4506	173	20	set	set	VERB
ejpam-4506	173	21	figure	figure	NOUN
ejpam-4506	173	22	4	4	NUM
ejpam-4506	173	23	shows	show	VERB
ejpam-4506	173	24	an	an	DET
ejpam-4506	173	25	illustration	illustration	NOUN
ejpam-4506	173	26	of	of	ADP
ejpam-4506	173	27	the	the	DET
ejpam-4506	173	28	situation	situation	NOUN
ejpam-4506	173	29	described	describe	VERB
ejpam-4506	173	30	in	in	ADP
ejpam-4506	173	31	theorem	theorem	NOUN
ejpam-4506	173	32	8	8	NUM
ejpam-4506	173	33	with	with	ADP
ejpam-4506	173	34	ω(g−x	ω(g−x	NOUN
ejpam-4506	173	35	)	)	PUNCT
ejpam-4506	173	36	=	=	SYM
ejpam-4506	173	37	3	3	NUM
ejpam-4506	173	38	and	and	CCONJ
ejpam-4506	173	39	therefore	therefore	ADV
ejpam-4506	173	40	does	do	AUX
ejpam-4506	173	41	not	not	PART
ejpam-4506	173	42	allow	allow	VERB
ejpam-4506	173	43	g	g	NOUN
ejpam-4506	173	44	to	to	PART
ejpam-4506	173	45	have	have	VERB
ejpam-4506	173	46	a	a	DET
ejpam-4506	173	47	path	path	NOUN
ejpam-4506	173	48	-	-	PUNCT
ejpam-4506	173	49	induced	induce	VERB
ejpam-4506	173	50	closed	closed	ADJ
ejpam-4506	173	51	geodetic	geodetic	ADJ
ejpam-4506	173	52	dominating	dominating	NOUN
ejpam-4506	173	53	set	set	NOUN
ejpam-4506	173	54	.	.	PUNCT
ejpam-4506	174	1	theorem	theorem	VERB
ejpam-4506	174	2	9	9	NUM
ejpam-4506	174	3	.	.	PUNCT
ejpam-4506	175	1	let	let	VERB
ejpam-4506	175	2	g	g	PRON
ejpam-4506	175	3	be	be	AUX
ejpam-4506	175	4	a	a	DET
ejpam-4506	175	5	connected	connected	ADJ
ejpam-4506	175	6	graph	graph	NOUN
ejpam-4506	175	7	with	with	ADP
ejpam-4506	175	8	cut	cut	NOUN
ejpam-4506	175	9	-	-	PUNCT
ejpam-4506	175	10	vertices	vertex	NOUN
ejpam-4506	175	11	.	.	PUNCT
ejpam-4506	176	1	if	if	SCONJ
ejpam-4506	176	2	g	g	PROPN
ejpam-4506	176	3	has	have	VERB
ejpam-4506	176	4	a	a	DET
ejpam-4506	176	5	path	path	NOUN
ejpam-4506	176	6	-	-	PUNCT
ejpam-4506	176	7	induced	induce	VERB
ejpam-4506	176	8	closed	closed	ADJ
ejpam-4506	176	9	geodetic	geodetic	ADJ
ejpam-4506	176	10	dominating	dominating	NOUN
ejpam-4506	176	11	set	set	NOUN
ejpam-4506	176	12	,	,	PUNCT
ejpam-4506	176	13	then	then	ADV
ejpam-4506	176	14	each	each	DET
ejpam-4506	176	15	block	block	NOUN
ejpam-4506	176	16	of	of	ADP
ejpam-4506	176	17	g	g	PROPN
ejpam-4506	176	18	contains	contain	VERB
ejpam-4506	176	19	at	at	ADP
ejpam-4506	176	20	most	most	ADJ
ejpam-4506	176	21	2	2	NUM
ejpam-4506	176	22	cut	cut	NOUN
ejpam-4506	176	23	-	-	PUNCT
ejpam-4506	176	24	vertices	vertex	NOUN
ejpam-4506	176	25	.	.	PUNCT
ejpam-4506	177	1	the	the	DET
ejpam-4506	177	2	contrapositive	contrapositive	NOUN
ejpam-4506	177	3	of	of	ADP
ejpam-4506	177	4	theorem	theorem	ADJ
ejpam-4506	177	5	9	9	NUM
ejpam-4506	177	6	says	say	VERB
ejpam-4506	177	7	that	that	SCONJ
ejpam-4506	177	8	if	if	SCONJ
ejpam-4506	177	9	there	there	PRON
ejpam-4506	177	10	exists	exist	VERB
ejpam-4506	177	11	a	a	DET
ejpam-4506	177	12	block	block	NOUN
ejpam-4506	177	13	of	of	ADP
ejpam-4506	177	14	g	g	NOUN
ejpam-4506	177	15	with	with	ADP
ejpam-4506	177	16	three	three	NUM
ejpam-4506	177	17	or	or	CCONJ
ejpam-4506	177	18	more	more	ADJ
ejpam-4506	177	19	cut	cut	ADJ
ejpam-4506	177	20	-	-	PUNCT
ejpam-4506	177	21	vertices	vertex	NOUN
ejpam-4506	177	22	,	,	PUNCT
ejpam-4506	177	23	then	then	ADV
ejpam-4506	177	24	g	g	PROPN
ejpam-4506	177	25	has	have	VERB
ejpam-4506	177	26	no	no	DET
ejpam-4506	177	27	path	path	NOUN
ejpam-4506	177	28	-	-	PUNCT
ejpam-4506	177	29	induced	induce	VERB
ejpam-4506	177	30	closed	closed	ADJ
ejpam-4506	177	31	geodetic	geodetic	ADJ
ejpam-4506	177	32	dominating	dominating	NOUN
ejpam-4506	177	33	set	set	NOUN
ejpam-4506	177	34	.	.	PUNCT
ejpam-4506	178	1	figure	figure	NOUN
ejpam-4506	178	2	5	5	NUM
ejpam-4506	178	3	shows	show	VERB
ejpam-4506	178	4	an	an	DET
ejpam-4506	178	5	illustration	illustration	NOUN
ejpam-4506	178	6	of	of	ADP
ejpam-4506	178	7	the	the	DET
ejpam-4506	178	8	situation	situation	NOUN
ejpam-4506	178	9	described	describe	VERB
ejpam-4506	178	10	in	in	ADP
ejpam-4506	178	11	theorem	theorem	ADJ
ejpam-4506	178	12	9	9	NUM
ejpam-4506	178	13	.	.	PUNCT
ejpam-4506	178	14	block	block	PROPN
ejpam-4506	178	15	b	b	PROPN
ejpam-4506	178	16	has	have	VERB
ejpam-4506	178	17	three	three	NUM
ejpam-4506	178	18	cut	cut	VERB
ejpam-4506	178	19	-	-	PUNCT
ejpam-4506	178	20	vertices	vertex	NOUN
ejpam-4506	178	21	v1	v1	NOUN
ejpam-4506	178	22	,	,	PUNCT
ejpam-4506	178	23	v2	v2	PROPN
ejpam-4506	178	24	,	,	PUNCT
ejpam-4506	178	25	v3	v3	PROPN
ejpam-4506	178	26	and	and	CCONJ
ejpam-4506	178	27	hence	hence	ADV
ejpam-4506	178	28	g	g	PROPN
ejpam-4506	178	29	has	have	VERB
ejpam-4506	178	30	no	no	DET
ejpam-4506	178	31	path	path	NOUN
ejpam-4506	178	32	-	-	PUNCT
ejpam-4506	178	33	induced	induce	VERB
ejpam-4506	178	34	closed	closed	ADJ
ejpam-4506	178	35	geodetic	geodetic	ADJ
ejpam-4506	178	36	dominating	dominating	NOUN
ejpam-4506	178	37	set	set	NOUN
ejpam-4506	178	38	.	.	PUNCT
ejpam-4506	179	1	j.	j.	PROPN
ejpam-4506	179	2	anoche	anoche	PROPN
ejpam-4506	179	3	,	,	PUNCT
ejpam-4506	179	4	i.	i.	PROPN
ejpam-4506	179	5	aniversario	aniversario	PROPN
ejpam-4506	179	6	,	,	PUNCT
ejpam-4506	179	7	c.	c.	PROPN
ejpam-4506	179	8	merca	merca	PROPN
ejpam-4506	179	9	/	/	SYM
ejpam-4506	179	10	eur	eur	PROPN
ejpam-4506	179	11	.	.	PUNCT
ejpam-4506	180	1	j.	j.	PROPN
ejpam-4506	180	2	pure	pure	PROPN
ejpam-4506	180	3	appl	appl	PROPN
ejpam-4506	180	4	.	.	PROPN
ejpam-4506	180	5	math	math	PROPN
ejpam-4506	180	6	,	,	PUNCT
ejpam-4506	180	7	16	16	NUM
ejpam-4506	180	8	(	(	PUNCT
ejpam-4506	180	9	1	1	NUM
ejpam-4506	180	10	)	)	PUNCT
ejpam-4506	180	11	(	(	PUNCT
ejpam-4506	180	12	2023	2023	NUM
ejpam-4506	180	13	)	)	PUNCT
ejpam-4506	180	14	,	,	PUNCT
ejpam-4506	180	15	169	169	NUM
ejpam-4506	180	16	-	-	SYM
ejpam-4506	180	17	179	179	NUM
ejpam-4506	180	18	175	175	NUM
ejpam-4506	180	19	.........	.........	PUNCT
ejpam-4506	180	20	........	........	PUNCT
ejpam-4506	180	21	........	........	PUNCT
ejpam-4506	180	22	........	........	PUNCT
ejpam-4506	180	23	........	........	PUNCT
ejpam-4506	180	24	........	........	PUNCT
ejpam-4506	180	25	........	........	PUNCT
ejpam-4506	180	26	........	........	PUNCT
ejpam-4506	180	27	........	........	PUNCT
ejpam-4506	180	28	........	........	PUNCT
ejpam-4506	180	29	........	........	PUNCT
ejpam-4506	180	30	........	........	PUNCT
ejpam-4506	180	31	.......	.......	PUNCT
ejpam-4506	180	32	....................................	....................................	PUNCT
ejpam-4506	181	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4506	181	2	....................................	....................................	PUNCT
ejpam-4506	181	3	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-4506	182	1	....................................	....................................	PUNCT
ejpam-4506	182	2	.........	.........	PUNCT
ejpam-4506	182	3	........	........	PUNCT
ejpam-4506	182	4	........	........	PUNCT
ejpam-4506	182	5	........	........	PUNCT
ejpam-4506	182	6	........	........	PUNCT
ejpam-4506	182	7	........	........	PUNCT
ejpam-4506	182	8	........	........	PUNCT
ejpam-4506	182	9	........	........	PUNCT
ejpam-4506	182	10	........	........	PUNCT
ejpam-4506	182	11	........	........	PUNCT
ejpam-4506	182	12	........	........	PUNCT
ejpam-4506	182	13	........	........	PUNCT
ejpam-4506	182	14	.......	.......	PUNCT
ejpam-4506	182	15	....................................	....................................	PUNCT
ejpam-4506	182	16	...............	...............	PUNCT
ejpam-4506	183	1	..............	..............	PUNCT
ejpam-4506	183	2	..............	..............	PUNCT
ejpam-4506	184	1	..............	..............	PUNCT
ejpam-4506	184	2	..............	..............	PUNCT
ejpam-4506	185	1	..............	..............	PUNCT
ejpam-4506	185	2	........	........	PUNCT
ejpam-4506	186	1	....................................	....................................	PUNCT
ejpam-4506	186	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4506	187	1	....................................	....................................	PUNCT
ejpam-4506	187	2	...............	...............	PUNCT
ejpam-4506	187	3	..............	..............	PUNCT
ejpam-4506	188	1	..............	..............	PUNCT
ejpam-4506	188	2	..............	..............	PUNCT
ejpam-4506	189	1	..............	..............	PUNCT
ejpam-4506	189	2	..............	..............	PUNCT
ejpam-4506	189	3	........	........	PUNCT
ejpam-4506	189	4	.	.	PUNCT
ejpam-4506	190	1	...................................	...................................	PUNCT
ejpam-4506	190	2	.............................................................................................	.............................................................................................	PUNCT
ejpam-4506	191	1	....................................	....................................	PUNCT
ejpam-4506	191	2	....................................	....................................	PUNCT
ejpam-4506	192	1	..........	..........	PUNCT
ejpam-4506	192	2	.........	.........	PUNCT
ejpam-4506	193	1	.........	.........	PUNCT
ejpam-4506	193	2	.........	.........	PUNCT
ejpam-4506	194	1	.........	.........	PUNCT
ejpam-4506	194	2	.........	.........	PUNCT
ejpam-4506	195	1	.........	.........	PUNCT
ejpam-4506	195	2	.........	.........	PUNCT
ejpam-4506	196	1	.........	.........	PUNCT
ejpam-4506	196	2	.........	.........	PUNCT
ejpam-4506	197	1	.........	.........	PUNCT
ejpam-4506	197	2	.........	.........	PUNCT
ejpam-4506	198	1	.........	.........	PUNCT
ejpam-4506	198	2	....................................	....................................	PUNCT
ejpam-4506	199	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4506	199	2	........................................................................	........................................................................	PUNCT
ejpam-4506	200	1	........................................................................................................	........................................................................................................	PUNCT
ejpam-4506	201	1	g	g	NOUN
ejpam-4506	201	2	:	:	PUNCT
ejpam-4506	201	3	•	•	NUM
ejpam-4506	201	4	•	•	NOUN
ejpam-4506	201	5	•	•	NOUN
ejpam-4506	201	6	b1	b1	PROPN
ejpam-4506	201	7	bb2	bb2	PROPN
ejpam-4506	201	8	b3	b3	PROPN
ejpam-4506	201	9	v1	v1	PROPN
ejpam-4506	201	10	v2v3	v2v3	NUM
ejpam-4506	201	11	figure	figure	NOUN
ejpam-4506	201	12	5	5	NUM
ejpam-4506	201	13	:	:	PUNCT
ejpam-4506	201	14	a	a	DET
ejpam-4506	201	15	graph	graph	NOUN
ejpam-4506	201	16	with	with	ADP
ejpam-4506	201	17	a	a	DET
ejpam-4506	201	18	cut	cut	NOUN
ejpam-4506	201	19	-	-	PUNCT
ejpam-4506	201	20	vertex	vertex	NOUN
ejpam-4506	201	21	and	and	CCONJ
ejpam-4506	201	22	without	without	ADP
ejpam-4506	201	23	a	a	DET
ejpam-4506	201	24	γpicg	γpicg	NOUN
ejpam-4506	201	25	-	-	PUNCT
ejpam-4506	201	26	set	set	NOUN
ejpam-4506	201	27	the	the	DET
ejpam-4506	201	28	next	next	ADJ
ejpam-4506	201	29	remark	remark	NOUN
ejpam-4506	201	30	is	be	AUX
ejpam-4506	201	31	a	a	DET
ejpam-4506	201	32	restatement	restatement	NOUN
ejpam-4506	201	33	of	of	ADP
ejpam-4506	201	34	remark	remark	NOUN
ejpam-4506	201	35	1	1	NUM
ejpam-4506	201	36	.	.	PUNCT
ejpam-4506	201	37	remark	remark	PROPN
ejpam-4506	201	38	6	6	NUM
ejpam-4506	201	39	.	.	PUNCT
ejpam-4506	202	1	let	let	VERB
ejpam-4506	202	2	g	g	PRON
ejpam-4506	202	3	be	be	AUX
ejpam-4506	202	4	a	a	DET
ejpam-4506	202	5	connected	connected	ADJ
ejpam-4506	202	6	nontrivial	nontrivial	ADJ
ejpam-4506	202	7	graph	graph	NOUN
ejpam-4506	202	8	of	of	ADP
ejpam-4506	202	9	order	order	NOUN
ejpam-4506	202	10	n.	n.	VERB
ejpam-4506	202	11	if	if	SCONJ
ejpam-4506	202	12	g	g	PROPN
ejpam-4506	202	13	admits	admit	VERB
ejpam-4506	202	14	a	a	DET
ejpam-4506	202	15	path	path	NOUN
ejpam-4506	202	16	-	-	PUNCT
ejpam-4506	202	17	induced	induce	VERB
ejpam-4506	202	18	closed	closed	ADJ
ejpam-4506	202	19	geodetic	geodetic	ADJ
ejpam-4506	202	20	dominating	dominating	NOUN
ejpam-4506	202	21	set	set	NOUN
ejpam-4506	202	22	,	,	PUNCT
ejpam-4506	202	23	then	then	ADV
ejpam-4506	202	24	2	2	NUM
ejpam-4506	202	25	≤	≤	NOUN
ejpam-4506	202	26	gn(g	gn(g	NOUN
ejpam-4506	202	27	)	)	PUNCT
ejpam-4506	202	28	≤	≤	NUM
ejpam-4506	202	29	γpicg(g	γpicg(g	NOUN
ejpam-4506	202	30	)	)	PUNCT
ejpam-4506	202	31	≤	≤	NOUN
ejpam-4506	203	1	n.	n.	NOUN
ejpam-4506	203	2	theorem	theorem	VERB
ejpam-4506	203	3	10	10	NUM
ejpam-4506	203	4	.	.	PUNCT
ejpam-4506	204	1	let	let	VERB
ejpam-4506	204	2	g	g	PRON
ejpam-4506	204	3	be	be	AUX
ejpam-4506	204	4	a	a	DET
ejpam-4506	204	5	connected	connected	ADJ
ejpam-4506	204	6	nontrivial	nontrivial	ADJ
ejpam-4506	204	7	graph	graph	NOUN
ejpam-4506	204	8	.	.	PUNCT
ejpam-4506	205	1	then	then	ADV
ejpam-4506	205	2	γpicg(g	γpicg(g	NUM
ejpam-4506	205	3	)	)	PUNCT
ejpam-4506	205	4	=	=	SYM
ejpam-4506	205	5	2	2	NUM
ejpam-4506	205	6	if	if	SCONJ
ejpam-4506	205	7	and	and	CCONJ
ejpam-4506	205	8	only	only	ADV
ejpam-4506	205	9	if	if	SCONJ
ejpam-4506	205	10	g	g	PROPN
ejpam-4506	205	11	=	=	SYM
ejpam-4506	205	12	k2	k2	PROPN
ejpam-4506	205	13	.	.	PUNCT
ejpam-4506	206	1	proof	proof	NOUN
ejpam-4506	206	2	:	:	PUNCT
ejpam-4506	206	3	let	let	VERB
ejpam-4506	206	4	s	s	VERB
ejpam-4506	206	5	=	=	PUNCT
ejpam-4506	206	6	{	{	PUNCT
ejpam-4506	206	7	x	x	PROPN
ejpam-4506	206	8	,	,	PUNCT
ejpam-4506	206	9	y	y	PROPN
ejpam-4506	206	10	}	}	PUNCT
ejpam-4506	206	11	be	be	AUX
ejpam-4506	206	12	a	a	DET
ejpam-4506	206	13	γpicg	γpicg	NOUN
ejpam-4506	206	14	-	-	PUNCT
ejpam-4506	206	15	set	set	NOUN
ejpam-4506	206	16	of	of	ADP
ejpam-4506	206	17	g.	g.	PROPN
ejpam-4506	206	18	then	then	ADV
ejpam-4506	206	19	by	by	ADP
ejpam-4506	206	20	definition	definition	NOUN
ejpam-4506	206	21	10	10	NUM
ejpam-4506	206	22	,	,	PUNCT
ejpam-4506	206	23	s	s	VERB
ejpam-4506	206	24	is	be	AUX
ejpam-4506	206	25	both	both	PRON
ejpam-4506	206	26	a	a	DET
ejpam-4506	206	27	pathinduced	pathinduce	VERB
ejpam-4506	206	28	closed	closed	ADJ
ejpam-4506	206	29	geodetic	geodetic	ADJ
ejpam-4506	206	30	set	set	NOUN
ejpam-4506	206	31	and	and	CCONJ
ejpam-4506	206	32	a	a	DET
ejpam-4506	206	33	dominating	dominating	NOUN
ejpam-4506	206	34	set	set	NOUN
ejpam-4506	206	35	.	.	PUNCT
ejpam-4506	207	1	thus	thus	ADV
ejpam-4506	207	2	,	,	PUNCT
ejpam-4506	207	3	ig[s	ig[s	PROPN
ejpam-4506	207	4	]	]	X
ejpam-4506	207	5	=	=	SYM
ejpam-4506	207	6	v	v	X
ejpam-4506	207	7	(	(	PUNCT
ejpam-4506	207	8	g	g	NOUN
ejpam-4506	207	9	)	)	PUNCT
ejpam-4506	207	10	.	.	PUNCT
ejpam-4506	208	1	but	but	CCONJ
ejpam-4506	208	2	note	note	VERB
ejpam-4506	208	3	that	that	SCONJ
ejpam-4506	208	4	⟨s⟩	⟨s⟩	VERB
ejpam-4506	208	5	=	=	SYM
ejpam-4506	208	6	k2	k2	PROPN
ejpam-4506	208	7	.	.	PUNCT
ejpam-4506	209	1	hence	hence	ADV
ejpam-4506	209	2	,	,	PUNCT
ejpam-4506	209	3	g	g	PROPN
ejpam-4506	209	4	=	=	SYM
ejpam-4506	209	5	k2	k2	PROPN
ejpam-4506	209	6	.	.	PUNCT
ejpam-4506	210	1	conversely	conversely	ADV
ejpam-4506	210	2	,	,	PUNCT
ejpam-4506	210	3	suppose	suppose	VERB
ejpam-4506	210	4	g	g	PROPN
ejpam-4506	210	5	=	=	SYM
ejpam-4506	210	6	k2	k2	PROPN
ejpam-4506	210	7	.	.	PUNCT
ejpam-4506	211	1	then	then	ADV
ejpam-4506	211	2	by	by	ADP
ejpam-4506	211	3	theorem	theorem	NOUN
ejpam-4506	211	4	1	1	NUM
ejpam-4506	211	5	(	(	PUNCT
ejpam-4506	211	6	i	i	NOUN
ejpam-4506	211	7	)	)	PUNCT
ejpam-4506	211	8	,	,	PUNCT
ejpam-4506	211	9	picgn	picgn	NOUN
ejpam-4506	211	10	(	(	PUNCT
ejpam-4506	211	11	k2	k2	NOUN
ejpam-4506	211	12	)	)	PUNCT
ejpam-4506	211	13	=	=	SYM
ejpam-4506	211	14	2	2	X
ejpam-4506	211	15	.	.	PUNCT
ejpam-4506	211	16	thus	thus	ADV
ejpam-4506	211	17	,	,	PUNCT
ejpam-4506	211	18	v	v	INTJ
ejpam-4506	211	19	(	(	PUNCT
ejpam-4506	211	20	g	g	NOUN
ejpam-4506	211	21	)	)	PUNCT
ejpam-4506	211	22	is	be	AUX
ejpam-4506	211	23	a	a	DET
ejpam-4506	211	24	dominating	dominating	NOUN
ejpam-4506	211	25	set	set	NOUN
ejpam-4506	211	26	of	of	ADP
ejpam-4506	211	27	g.	g.	PROPN
ejpam-4506	211	28	therefore	therefore	ADV
ejpam-4506	211	29	,	,	PUNCT
ejpam-4506	211	30	γpicg(g	γpicg(g	NOUN
ejpam-4506	211	31	)	)	PUNCT
ejpam-4506	211	32	=	=	SYM
ejpam-4506	211	33	2	2	X
ejpam-4506	211	34	.	.	PUNCT
ejpam-4506	211	35	■	■	PUNCT
ejpam-4506	211	36	remark	remark	NOUN
ejpam-4506	211	37	7	7	NUM
ejpam-4506	211	38	.	.	PUNCT
ejpam-4506	212	1	every	every	DET
ejpam-4506	212	2	vertex	vertex	NOUN
ejpam-4506	212	3	of	of	ADP
ejpam-4506	212	4	a	a	DET
ejpam-4506	212	5	complete	complete	ADJ
ejpam-4506	212	6	graph	graph	NOUN
ejpam-4506	212	7	km	km	NOUN
ejpam-4506	212	8	is	be	AUX
ejpam-4506	212	9	an	an	DET
ejpam-4506	212	10	extreme	extreme	ADJ
ejpam-4506	212	11	vertex	vertex	NOUN
ejpam-4506	212	12	.	.	PUNCT
ejpam-4506	213	1	in	in	ADP
ejpam-4506	213	2	g.	g.	PROPN
ejpam-4506	213	3	j.	j.	PROPN
ejpam-4506	213	4	changa	changa	PROPN
ejpam-4506	213	5	et	et	PROPN
ejpam-4506	213	6	al	al	PROPN
ejpam-4506	213	7	.	.	PUNCT
ejpam-4506	214	1	[	[	X
ejpam-4506	214	2	5	5	NUM
ejpam-4506	214	3	]	]	PUNCT
ejpam-4506	214	4	,	,	PUNCT
ejpam-4506	214	5	it	it	PRON
ejpam-4506	214	6	is	be	AUX
ejpam-4506	214	7	shown	show	VERB
ejpam-4506	214	8	that	that	SCONJ
ejpam-4506	214	9	every	every	DET
ejpam-4506	214	10	geodetic	geodetic	ADJ
ejpam-4506	214	11	basis	basis	NOUN
ejpam-4506	214	12	of	of	ADP
ejpam-4506	214	13	a	a	DET
ejpam-4506	214	14	graph	graph	NOUN
ejpam-4506	214	15	contains	contain	VERB
ejpam-4506	214	16	its	its	PRON
ejpam-4506	214	17	extreme	extreme	ADJ
ejpam-4506	214	18	vertices	vertex	NOUN
ejpam-4506	214	19	.	.	PUNCT
ejpam-4506	215	1	now	now	ADV
ejpam-4506	215	2	,	,	PUNCT
ejpam-4506	215	3	since	since	SCONJ
ejpam-4506	215	4	every	every	DET
ejpam-4506	215	5	vertex	vertex	NOUN
ejpam-4506	215	6	of	of	ADP
ejpam-4506	215	7	a	a	DET
ejpam-4506	215	8	complete	complete	ADJ
ejpam-4506	215	9	graph	graph	NOUN
ejpam-4506	215	10	km	km	NOUN
ejpam-4506	215	11	is	be	AUX
ejpam-4506	215	12	an	an	DET
ejpam-4506	215	13	extreme	extreme	ADJ
ejpam-4506	215	14	vertex	vertex	NOUN
ejpam-4506	215	15	,	,	PUNCT
ejpam-4506	215	16	then	then	ADV
ejpam-4506	215	17	the	the	DET
ejpam-4506	215	18	next	next	ADJ
ejpam-4506	215	19	result	result	NOUN
ejpam-4506	215	20	follows	follow	VERB
ejpam-4506	215	21	.	.	PUNCT
ejpam-4506	216	1	proposition	proposition	NOUN
ejpam-4506	216	2	1	1	NUM
ejpam-4506	216	3	.	.	PUNCT
ejpam-4506	217	1	for	for	ADP
ejpam-4506	217	2	any	any	DET
ejpam-4506	217	3	natural	natural	ADJ
ejpam-4506	217	4	number	number	NOUN
ejpam-4506	217	5	m	m	NOUN
ejpam-4506	217	6	,	,	PUNCT
ejpam-4506	217	7	γpicg(km	γpicg(km	ADJ
ejpam-4506	217	8	)	)	PUNCT
ejpam-4506	217	9	=	=	VERB
ejpam-4506	217	10	m.	m.	NOUN
ejpam-4506	217	11	the	the	DET
ejpam-4506	217	12	following	follow	VERB
ejpam-4506	217	13	theorem	theorem	NOUN
ejpam-4506	217	14	provides	provide	VERB
ejpam-4506	217	15	some	some	PRON
ejpam-4506	217	16	of	of	ADP
ejpam-4506	217	17	the	the	DET
ejpam-4506	217	18	necessary	necessary	ADJ
ejpam-4506	217	19	conditions	condition	NOUN
ejpam-4506	217	20	for	for	ADP
ejpam-4506	217	21	a	a	DET
ejpam-4506	217	22	graph	graph	NOUN
ejpam-4506	217	23	g	g	NOUN
ejpam-4506	217	24	of	of	ADP
ejpam-4506	217	25	order	order	NOUN
ejpam-4506	217	26	m	m	AUX
ejpam-4506	217	27	to	to	PART
ejpam-4506	217	28	have	have	VERB
ejpam-4506	217	29	γpicg(g	γpicg(g	NOUN
ejpam-4506	217	30	)	)	PUNCT
ejpam-4506	217	31	=	=	SYM
ejpam-4506	217	32	m.	m.	NOUN
ejpam-4506	217	33	theorem	theorem	VERB
ejpam-4506	217	34	11	11	NUM
ejpam-4506	217	35	.	.	PUNCT
ejpam-4506	218	1	let	let	VERB
ejpam-4506	218	2	g	g	PRON
ejpam-4506	218	3	be	be	AUX
ejpam-4506	218	4	a	a	DET
ejpam-4506	218	5	connected	connected	ADJ
ejpam-4506	218	6	graph	graph	NOUN
ejpam-4506	218	7	of	of	ADP
ejpam-4506	218	8	order	order	NOUN
ejpam-4506	218	9	m	m	VERB
ejpam-4506	218	10	such	such	ADJ
ejpam-4506	218	11	that	that	SCONJ
ejpam-4506	218	12	g	g	PROPN
ejpam-4506	218	13	has	have	VERB
ejpam-4506	218	14	a	a	DET
ejpam-4506	218	15	path	path	NOUN
ejpam-4506	218	16	-	-	PUNCT
ejpam-4506	218	17	induced	induce	VERB
ejpam-4506	218	18	closed	closed	ADJ
ejpam-4506	218	19	geodetic	geodetic	ADJ
ejpam-4506	218	20	dominating	dominating	NOUN
ejpam-4506	218	21	set	set	NOUN
ejpam-4506	218	22	.	.	PUNCT
ejpam-4506	219	1	if	if	SCONJ
ejpam-4506	219	2	every	every	DET
ejpam-4506	219	3	vertex	vertex	NOUN
ejpam-4506	219	4	of	of	ADP
ejpam-4506	219	5	g	g	PROPN
ejpam-4506	219	6	is	be	AUX
ejpam-4506	219	7	either	either	CCONJ
ejpam-4506	219	8	an	an	DET
ejpam-4506	219	9	extreme	extreme	ADJ
ejpam-4506	219	10	vertex	vertex	NOUN
ejpam-4506	219	11	or	or	CCONJ
ejpam-4506	219	12	a	a	DET
ejpam-4506	219	13	cut	cut	NOUN
ejpam-4506	219	14	-	-	PUNCT
ejpam-4506	219	15	vertex	vertex	NOUN
ejpam-4506	219	16	,	,	PUNCT
ejpam-4506	219	17	then	then	ADV
ejpam-4506	219	18	γpicg(g	γpicg(g	NOUN
ejpam-4506	219	19	)	)	PUNCT
ejpam-4506	219	20	=	=	VERB
ejpam-4506	219	21	m.	m.	NOUN
ejpam-4506	219	22	proof	proof	NOUN
ejpam-4506	219	23	:	:	PUNCT
ejpam-4506	219	24	let	let	VERB
ejpam-4506	219	25	g	g	PRON
ejpam-4506	219	26	be	be	AUX
ejpam-4506	219	27	a	a	DET
ejpam-4506	219	28	connected	connected	ADJ
ejpam-4506	219	29	graph	graph	NOUN
ejpam-4506	219	30	of	of	ADP
ejpam-4506	219	31	order	order	NOUN
ejpam-4506	219	32	m	m	VERB
ejpam-4506	219	33	and	and	CCONJ
ejpam-4506	219	34	g	g	PROPN
ejpam-4506	219	35	has	have	VERB
ejpam-4506	219	36	a	a	DET
ejpam-4506	219	37	path	path	NOUN
ejpam-4506	219	38	-	-	PUNCT
ejpam-4506	219	39	induced	induce	VERB
ejpam-4506	219	40	closed	closed	ADJ
ejpam-4506	219	41	geodetic	geodetic	ADJ
ejpam-4506	219	42	dominating	dominating	NOUN
ejpam-4506	219	43	set	set	VERB
ejpam-4506	219	44	s.	s.	PROPN
ejpam-4506	219	45	by	by	ADP
ejpam-4506	219	46	remark	remark	NOUN
ejpam-4506	219	47	3	3	NUM
ejpam-4506	219	48	,	,	PUNCT
ejpam-4506	219	49	s	s	VERB
ejpam-4506	219	50	is	be	AUX
ejpam-4506	219	51	a	a	DET
ejpam-4506	219	52	path	path	NOUN
ejpam-4506	219	53	-	-	PUNCT
ejpam-4506	219	54	induced	induce	VERB
ejpam-4506	219	55	closed	closed	ADJ
ejpam-4506	219	56	geodetic	geodetic	ADJ
ejpam-4506	219	57	set	set	NOUN
ejpam-4506	219	58	of	of	ADP
ejpam-4506	219	59	g.	g.	PROPN
ejpam-4506	219	60	let	let	VERB
ejpam-4506	219	61	any	any	DET
ejpam-4506	219	62	v	v	NOUN
ejpam-4506	219	63	∈	∈	NOUN
ejpam-4506	219	64	v	v	NOUN
ejpam-4506	219	65	(	(	PUNCT
ejpam-4506	219	66	g	g	NOUN
ejpam-4506	219	67	)	)	PUNCT
ejpam-4506	219	68	be	be	AUX
ejpam-4506	219	69	either	either	CCONJ
ejpam-4506	219	70	an	an	DET
ejpam-4506	219	71	extreme	extreme	ADJ
ejpam-4506	219	72	vertex	vertex	NOUN
ejpam-4506	219	73	or	or	CCONJ
ejpam-4506	219	74	a	a	DET
ejpam-4506	219	75	cut	cut	NOUN
ejpam-4506	219	76	-	-	PUNCT
ejpam-4506	219	77	vertex	vertex	NOUN
ejpam-4506	219	78	.	.	PUNCT
ejpam-4506	220	1	then	then	ADV
ejpam-4506	220	2	by	by	ADP
ejpam-4506	220	3	theorem	theorem	NOUN
ejpam-4506	220	4	5	5	NUM
ejpam-4506	220	5	,	,	PUNCT
ejpam-4506	220	6	v	v	X
ejpam-4506	220	7	∈	∈	PROPN
ejpam-4506	220	8	s	s	X
ejpam-4506	220	9	and	and	CCONJ
ejpam-4506	220	10	picgn(g	picgn(g	NUM
ejpam-4506	220	11	)	)	PUNCT
ejpam-4506	221	1	=	=	VERB
ejpam-4506	221	2	m.	m.	NOUN
ejpam-4506	221	3	this	this	PRON
ejpam-4506	221	4	means	mean	VERB
ejpam-4506	221	5	that	that	SCONJ
ejpam-4506	221	6	s	s	VERB
ejpam-4506	221	7	=	=	SYM
ejpam-4506	221	8	v	v	ADJ
ejpam-4506	221	9	(	(	PUNCT
ejpam-4506	221	10	g	g	NOUN
ejpam-4506	221	11	)	)	PUNCT
ejpam-4506	221	12	.	.	PUNCT
ejpam-4506	222	1	hence	hence	ADV
ejpam-4506	222	2	,	,	PUNCT
ejpam-4506	222	3	s	s	VERB
ejpam-4506	222	4	is	be	AUX
ejpam-4506	222	5	a	a	DET
ejpam-4506	222	6	dominating	dominating	NOUN
ejpam-4506	222	7	set	set	NOUN
ejpam-4506	222	8	of	of	ADP
ejpam-4506	222	9	g.	g.	PROPN
ejpam-4506	222	10	therefore	therefore	ADV
ejpam-4506	222	11	,	,	PUNCT
ejpam-4506	222	12	γpicg(g	γpicg(g	NOUN
ejpam-4506	222	13	)	)	PUNCT
ejpam-4506	222	14	=	=	SYM
ejpam-4506	222	15	m.	m.	NOUN
ejpam-4506	222	16	■	■	PUNCT
ejpam-4506	222	17	j.	j.	PROPN
ejpam-4506	222	18	anoche	anoche	PROPN
ejpam-4506	222	19	,	,	PUNCT
ejpam-4506	222	20	i.	i.	PROPN
ejpam-4506	222	21	aniversario	aniversario	PROPN
ejpam-4506	222	22	,	,	PUNCT
ejpam-4506	222	23	c.	c.	PROPN
ejpam-4506	222	24	merca	merca	PROPN
ejpam-4506	222	25	/	/	SYM
ejpam-4506	222	26	eur	eur	PROPN
ejpam-4506	222	27	.	.	PUNCT
ejpam-4506	223	1	j.	j.	PROPN
ejpam-4506	223	2	pure	pure	PROPN
ejpam-4506	223	3	appl	appl	PROPN
ejpam-4506	223	4	.	.	PROPN
ejpam-4506	223	5	math	math	PROPN
ejpam-4506	223	6	,	,	PUNCT
ejpam-4506	223	7	16	16	NUM
ejpam-4506	223	8	(	(	PUNCT
ejpam-4506	223	9	1	1	NUM
ejpam-4506	223	10	)	)	PUNCT
ejpam-4506	223	11	(	(	PUNCT
ejpam-4506	223	12	2023	2023	NUM
ejpam-4506	223	13	)	)	PUNCT
ejpam-4506	223	14	,	,	PUNCT
ejpam-4506	223	15	169	169	NUM
ejpam-4506	223	16	-	-	SYM
ejpam-4506	223	17	179	179	NUM
ejpam-4506	223	18	176	176	NUM
ejpam-4506	223	19	remark	remark	NOUN
ejpam-4506	223	20	8	8	NUM
ejpam-4506	223	21	.	.	PUNCT
ejpam-4506	224	1	every	every	DET
ejpam-4506	224	2	end	end	NOUN
ejpam-4506	224	3	-	-	PUNCT
ejpam-4506	224	4	vertex	vertex	NOUN
ejpam-4506	224	5	in	in	ADP
ejpam-4506	224	6	a	a	DET
ejpam-4506	224	7	graph	graph	NOUN
ejpam-4506	224	8	g	g	NOUN
ejpam-4506	224	9	is	be	AUX
ejpam-4506	224	10	an	an	DET
ejpam-4506	224	11	extreme	extreme	ADJ
ejpam-4506	224	12	vertex	vertex	NOUN
ejpam-4506	224	13	.	.	PUNCT
ejpam-4506	225	1	corollary	corollary	ADJ
ejpam-4506	225	2	1	1	NUM
ejpam-4506	225	3	.	.	PUNCT
ejpam-4506	226	1	let	let	VERB
ejpam-4506	226	2	g	g	NOUN
ejpam-4506	226	3	=	=	NOUN
ejpam-4506	226	4	pm	pm	PROPN
ejpam-4506	226	5	.	.	PUNCT
ejpam-4506	227	1	then	then	ADV
ejpam-4506	227	2	γpicg(g	γpicg(g	NUM
ejpam-4506	227	3	)	)	PUNCT
ejpam-4506	228	1	=	=	PRON
ejpam-4506	228	2	m	m	VERB
ejpam-4506	228	3	for	for	ADP
ejpam-4506	228	4	all	all	DET
ejpam-4506	228	5	m	m	PROPN
ejpam-4506	228	6	≥	≥	NOUN
ejpam-4506	228	7	1	1	NUM
ejpam-4506	228	8	.	.	PUNCT
ejpam-4506	229	1	proof	proof	NOUN
ejpam-4506	229	2	:	:	PUNCT
ejpam-4506	229	3	let	let	VERB
ejpam-4506	229	4	g	g	NOUN
ejpam-4506	229	5	=	=	VERB
ejpam-4506	229	6	pm	pm	NOUN
ejpam-4506	229	7	and	and	CCONJ
ejpam-4506	229	8	v	v	NOUN
ejpam-4506	229	9	(	(	PUNCT
ejpam-4506	229	10	g	g	NOUN
ejpam-4506	229	11	)	)	PUNCT
ejpam-4506	229	12	=	=	SYM
ejpam-4506	229	13	{	{	PUNCT
ejpam-4506	229	14	u1	u1	NOUN
ejpam-4506	229	15	,	,	PUNCT
ejpam-4506	229	16	u2	u2	PROPN
ejpam-4506	229	17	,	,	PUNCT
ejpam-4506	229	18	·	·	PUNCT
ejpam-4506	229	19	·	·	PUNCT
ejpam-4506	229	20	·	·	PUNCT
ejpam-4506	229	21	,	,	PUNCT
ejpam-4506	229	22	um	um	INTJ
ejpam-4506	229	23	}	}	PUNCT
ejpam-4506	229	24	.	.	PUNCT
ejpam-4506	230	1	thus	thus	ADV
ejpam-4506	230	2	,	,	PUNCT
ejpam-4506	230	3	by	by	ADP
ejpam-4506	230	4	theorem	theorem	NOUN
ejpam-4506	230	5	1(ii	1(ii	NUM
ejpam-4506	230	6	)	)	PUNCT
ejpam-4506	230	7	,	,	PUNCT
ejpam-4506	230	8	picgn(g	picgn(g	NOUN
ejpam-4506	230	9	)	)	PUNCT
ejpam-4506	230	10	=	=	SYM
ejpam-4506	231	1	m.	m.	NOUN
ejpam-4506	231	2	since	since	SCONJ
ejpam-4506	231	3	v	v	NOUN
ejpam-4506	231	4	(	(	PUNCT
ejpam-4506	231	5	g	g	NOUN
ejpam-4506	231	6	)	)	PUNCT
ejpam-4506	231	7	is	be	AUX
ejpam-4506	231	8	a	a	DET
ejpam-4506	231	9	dominating	dominating	NOUN
ejpam-4506	231	10	set	set	NOUN
ejpam-4506	231	11	of	of	ADP
ejpam-4506	231	12	g	g	NOUN
ejpam-4506	231	13	,	,	PUNCT
ejpam-4506	231	14	then	then	ADV
ejpam-4506	231	15	γpicg(g	γpicg(g	NOUN
ejpam-4506	231	16	)	)	PUNCT
ejpam-4506	231	17	=	=	PUNCT
ejpam-4506	232	1	m.	m.	NOUN
ejpam-4506	232	2	■	■	PUNCT
ejpam-4506	232	3	the	the	DET
ejpam-4506	232	4	next	next	ADJ
ejpam-4506	232	5	theorem	theorem	NOUN
ejpam-4506	232	6	characterizes	characterize	VERB
ejpam-4506	232	7	those	those	DET
ejpam-4506	232	8	trees	tree	NOUN
ejpam-4506	232	9	which	which	PRON
ejpam-4506	232	10	admit	admit	VERB
ejpam-4506	232	11	path	path	NOUN
ejpam-4506	232	12	-	-	PUNCT
ejpam-4506	232	13	induced	induce	VERB
ejpam-4506	232	14	closed	closed	ADJ
ejpam-4506	232	15	geodetic	geodetic	ADJ
ejpam-4506	232	16	dominating	dominating	NOUN
ejpam-4506	232	17	sets	set	NOUN
ejpam-4506	232	18	.	.	PUNCT
ejpam-4506	233	1	theorem	theorem	NOUN
ejpam-4506	233	2	12	12	NUM
ejpam-4506	233	3	.	.	PUNCT
ejpam-4506	234	1	let	let	VERB
ejpam-4506	234	2	t	t	NOUN
ejpam-4506	234	3	be	be	AUX
ejpam-4506	234	4	a	a	DET
ejpam-4506	234	5	tree	tree	NOUN
ejpam-4506	234	6	.	.	PUNCT
ejpam-4506	235	1	then	then	ADV
ejpam-4506	235	2	t	t	PROPN
ejpam-4506	235	3	admits	admit	VERB
ejpam-4506	235	4	a	a	DET
ejpam-4506	235	5	path	path	NOUN
ejpam-4506	235	6	-	-	PUNCT
ejpam-4506	235	7	induced	induce	VERB
ejpam-4506	235	8	closed	closed	ADJ
ejpam-4506	235	9	geodetic	geodetic	ADJ
ejpam-4506	235	10	dominating	dominating	NOUN
ejpam-4506	235	11	set	set	VERB
ejpam-4506	235	12	if	if	SCONJ
ejpam-4506	235	13	and	and	CCONJ
ejpam-4506	235	14	only	only	ADV
ejpam-4506	235	15	if	if	SCONJ
ejpam-4506	235	16	t	t	PROPN
ejpam-4506	235	17	is	be	AUX
ejpam-4506	235	18	a	a	DET
ejpam-4506	235	19	path	path	NOUN
ejpam-4506	235	20	.	.	PUNCT
ejpam-4506	236	1	proof	proof	NOUN
ejpam-4506	236	2	:	:	PUNCT
ejpam-4506	236	3	suppose	suppose	VERB
ejpam-4506	236	4	t	t	PROPN
ejpam-4506	236	5	is	be	AUX
ejpam-4506	236	6	a	a	DET
ejpam-4506	236	7	tree	tree	NOUN
ejpam-4506	236	8	that	that	PRON
ejpam-4506	236	9	admits	admit	VERB
ejpam-4506	236	10	a	a	DET
ejpam-4506	236	11	path	path	NOUN
ejpam-4506	236	12	-	-	PUNCT
ejpam-4506	236	13	induced	induce	VERB
ejpam-4506	236	14	closed	closed	ADJ
ejpam-4506	236	15	geodetic	geodetic	ADJ
ejpam-4506	236	16	dominating	dominating	NOUN
ejpam-4506	236	17	set	set	NOUN
ejpam-4506	236	18	.	.	PUNCT
ejpam-4506	237	1	then	then	ADV
ejpam-4506	237	2	by	by	ADP
ejpam-4506	237	3	definition	definition	NOUN
ejpam-4506	237	4	10	10	NUM
ejpam-4506	237	5	,	,	PUNCT
ejpam-4506	237	6	t	t	PROPN
ejpam-4506	237	7	admits	admit	VERB
ejpam-4506	237	8	a	a	DET
ejpam-4506	237	9	path	path	NOUN
ejpam-4506	237	10	-	-	PUNCT
ejpam-4506	237	11	induced	induce	VERB
ejpam-4506	237	12	closed	closed	ADJ
ejpam-4506	237	13	geodetic	geodetic	ADJ
ejpam-4506	237	14	set	set	NOUN
ejpam-4506	237	15	.	.	PUNCT
ejpam-4506	238	1	thus	thus	ADV
ejpam-4506	238	2	,	,	PUNCT
ejpam-4506	238	3	by	by	ADP
ejpam-4506	238	4	theorem	theorem	NOUN
ejpam-4506	238	5	6	6	NUM
ejpam-4506	238	6	,	,	PUNCT
ejpam-4506	238	7	t	t	PROPN
ejpam-4506	238	8	is	be	AUX
ejpam-4506	238	9	a	a	DET
ejpam-4506	238	10	path	path	NOUN
ejpam-4506	238	11	.	.	PUNCT
ejpam-4506	239	1	conversely	conversely	ADV
ejpam-4506	239	2	,	,	PUNCT
ejpam-4506	239	3	suppose	suppose	VERB
ejpam-4506	239	4	t	t	PROPN
ejpam-4506	239	5	is	be	AUX
ejpam-4506	239	6	a	a	DET
ejpam-4506	239	7	path	path	NOUN
ejpam-4506	239	8	.	.	PUNCT
ejpam-4506	240	1	then	then	ADV
ejpam-4506	240	2	,	,	PUNCT
ejpam-4506	240	3	by	by	ADP
ejpam-4506	240	4	corollary	corollary	ADJ
ejpam-4506	240	5	1	1	NUM
ejpam-4506	240	6	,	,	PUNCT
ejpam-4506	240	7	t	t	PROPN
ejpam-4506	240	8	admits	admit	VERB
ejpam-4506	240	9	a	a	DET
ejpam-4506	240	10	path	path	NOUN
ejpam-4506	240	11	-	-	PUNCT
ejpam-4506	240	12	induced	induce	VERB
ejpam-4506	240	13	closed	closed	ADJ
ejpam-4506	240	14	geodetic	geodetic	ADJ
ejpam-4506	240	15	dominating	dominating	NOUN
ejpam-4506	240	16	set	set	NOUN
ejpam-4506	240	17	.	.	PUNCT
ejpam-4506	241	1	■	■	PUNCT
ejpam-4506	241	2	4	4	X
ejpam-4506	241	3	.	.	X
ejpam-4506	241	4	path	path	NOUN
ejpam-4506	241	5	-	-	PUNCT
ejpam-4506	241	6	induced	induce	VERB
ejpam-4506	241	7	closed	closed	ADJ
ejpam-4506	241	8	geodetic	geodetic	ADJ
ejpam-4506	241	9	domination	domination	NOUN
ejpam-4506	241	10	numbers	number	NOUN
ejpam-4506	241	11	of	of	ADP
ejpam-4506	241	12	the	the	DET
ejpam-4506	241	13	edge	edge	NOUN
ejpam-4506	241	14	corona	corona	NOUN
ejpam-4506	241	15	of	of	ADP
ejpam-4506	241	16	graphs	graph	NOUN
ejpam-4506	241	17	in	in	ADP
ejpam-4506	241	18	this	this	DET
ejpam-4506	241	19	section	section	NOUN
ejpam-4506	241	20	,	,	PUNCT
ejpam-4506	241	21	we	we	PRON
ejpam-4506	241	22	discuss	discuss	VERB
ejpam-4506	241	23	the	the	DET
ejpam-4506	241	24	path	path	NOUN
ejpam-4506	241	25	-	-	PUNCT
ejpam-4506	241	26	induced	induce	VERB
ejpam-4506	241	27	closed	closed	ADJ
ejpam-4506	241	28	geodetic	geodetic	ADJ
ejpam-4506	241	29	domination	domination	NOUN
ejpam-4506	241	30	number	number	NOUN
ejpam-4506	241	31	of	of	ADP
ejpam-4506	241	32	a	a	DET
ejpam-4506	241	33	graph	graph	NOUN
ejpam-4506	241	34	obtained	obtain	VERB
ejpam-4506	241	35	from	from	ADP
ejpam-4506	241	36	the	the	DET
ejpam-4506	241	37	edge	edge	NOUN
ejpam-4506	241	38	corona	corona	NOUN
ejpam-4506	241	39	of	of	ADP
ejpam-4506	241	40	two	two	NUM
ejpam-4506	241	41	graphs	graph	NOUN
ejpam-4506	241	42	.	.	PUNCT
ejpam-4506	242	1	we	we	PRON
ejpam-4506	242	2	remark	remark	VERB
ejpam-4506	242	3	that	that	SCONJ
ejpam-4506	242	4	not	not	PART
ejpam-4506	242	5	all	all	DET
ejpam-4506	242	6	edge	edge	NOUN
ejpam-4506	242	7	corona	corona	NOUN
ejpam-4506	242	8	of	of	ADP
ejpam-4506	242	9	two	two	NUM
ejpam-4506	242	10	graphs	graph	NOUN
ejpam-4506	242	11	admit	admit	VERB
ejpam-4506	242	12	path	path	NOUN
ejpam-4506	242	13	-	-	PUNCT
ejpam-4506	242	14	induced	induce	VERB
ejpam-4506	242	15	closed	closed	ADJ
ejpam-4506	242	16	geodetic	geodetic	ADJ
ejpam-4506	242	17	dominating	dominating	NOUN
ejpam-4506	242	18	sets	set	NOUN
ejpam-4506	242	19	.	.	PUNCT
ejpam-4506	243	1	consider	consider	VERB
ejpam-4506	243	2	the	the	DET
ejpam-4506	243	3	edge	edge	NOUN
ejpam-4506	243	4	corona	corona	NOUN
ejpam-4506	243	5	g	g	PROPN
ejpam-4506	243	6	=	=	PROPN
ejpam-4506	243	7	c6	c6	PROPN
ejpam-4506	243	8	⋄	⋄	PROPN
ejpam-4506	243	9	p2	p2	PROPN
ejpam-4506	243	10	shown	show	VERB
ejpam-4506	243	11	in	in	ADP
ejpam-4506	243	12	figure	figure	NOUN
ejpam-4506	243	13	6	6	NUM
ejpam-4506	243	14	.	.	PUNCT
ejpam-4506	243	15	observe	observe	VERB
ejpam-4506	243	16	that	that	SCONJ
ejpam-4506	243	17	the	the	DET
ejpam-4506	243	18	only	only	ADV
ejpam-4506	243	19	connected	connected	ADJ
ejpam-4506	243	20	geodetic	geodetic	ADJ
ejpam-4506	243	21	sets	set	NOUN
ejpam-4506	243	22	in	in	ADP
ejpam-4506	243	23	g	g	PROPN
ejpam-4506	243	24	are	be	AUX
ejpam-4506	243	25	v	v	ADP
ejpam-4506	243	26	(	(	PUNCT
ejpam-4506	243	27	g	g	NOUN
ejpam-4506	243	28	)	)	PUNCT
ejpam-4506	243	29	,	,	PUNCT
ejpam-4506	243	30	v	v	X
ejpam-4506	243	31	(	(	PUNCT
ejpam-4506	243	32	g)∖	g)∖	PROPN
ejpam-4506	243	33	v6	v6	PROPN
ejpam-4506	243	34	,	,	PUNCT
ejpam-4506	243	35	and	and	CCONJ
ejpam-4506	243	36	v	v	NOUN
ejpam-4506	243	37	(	(	PUNCT
ejpam-4506	243	38	g)∖	g)∖	PROPN
ejpam-4506	243	39	v2	v2	PROPN
ejpam-4506	243	40	.	.	PUNCT
ejpam-4506	244	1	but	but	CCONJ
ejpam-4506	244	2	these	these	DET
ejpam-4506	244	3	sets	set	NOUN
ejpam-4506	244	4	are	be	AUX
ejpam-4506	244	5	not	not	PART
ejpam-4506	244	6	closed	close	VERB
ejpam-4506	244	7	geodetic	geodetic	ADJ
ejpam-4506	244	8	sets	set	NOUN
ejpam-4506	244	9	of	of	ADP
ejpam-4506	244	10	g.	g.	PROPN
ejpam-4506	244	11	hence	hence	ADV
ejpam-4506	244	12	,	,	PUNCT
ejpam-4506	244	13	g	g	PROPN
ejpam-4506	244	14	does	do	AUX
ejpam-4506	244	15	not	not	PART
ejpam-4506	244	16	admit	admit	VERB
ejpam-4506	244	17	path	path	NOUN
ejpam-4506	244	18	-	-	PUNCT
ejpam-4506	244	19	induced	induce	VERB
ejpam-4506	244	20	closed	closed	ADJ
ejpam-4506	244	21	geodetic	geodetic	ADJ
ejpam-4506	244	22	dominating	dominating	NOUN
ejpam-4506	244	23	set	set	NOUN
ejpam-4506	244	24	.	.	PUNCT
ejpam-4506	244	25	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PROPN
ejpam-4506	244	26	............	............	PUNCT
ejpam-4506	245	1	...........	...........	PUNCT
ejpam-4506	245	2	...........	...........	PUNCT
ejpam-4506	245	3	...........	...........	PUNCT
ejpam-4506	245	4	...........	...........	PUNCT
ejpam-4506	245	5	...........	...........	PUNCT
ejpam-4506	245	6	...........	...........	PUNCT
ejpam-4506	245	7	...........	...........	PUNCT
ejpam-4506	245	8	...........	...........	PUNCT
ejpam-4506	245	9	...........	...........	PUNCT
ejpam-4506	245	10	...........	...........	PUNCT
ejpam-4506	245	11	...........	...........	PUNCT
ejpam-4506	245	12	...........	...........	PUNCT
ejpam-4506	245	13	...........	...........	PUNCT
ejpam-4506	245	14	...........	...........	PUNCT
ejpam-4506	245	15	...........	...........	PUNCT
ejpam-4506	245	16	...........	...........	PUNCT
ejpam-4506	246	1	.....	.....	PUNCT
ejpam-4506	246	2	...............................................................................................................................................................................................	...............................................................................................................................................................................................	PUNCT
ejpam-4506	246	3	.................................................................................................................................................................................................	.................................................................................................................................................................................................	PUNCT
ejpam-4506	246	4	............	............	PUNCT
ejpam-4506	246	5	...........	...........	PUNCT
ejpam-4506	246	6	...........	...........	PUNCT
ejpam-4506	246	7	...........	...........	PUNCT
ejpam-4506	246	8	...........	...........	PUNCT
ejpam-4506	246	9	...........	...........	PUNCT
ejpam-4506	246	10	...........	...........	PUNCT
ejpam-4506	246	11	...........	...........	PUNCT
ejpam-4506	246	12	...........	...........	PUNCT
ejpam-4506	246	13	...........	...........	PUNCT
ejpam-4506	246	14	...........	...........	PUNCT
ejpam-4506	246	15	...........	...........	PUNCT
ejpam-4506	246	16	...........	...........	PUNCT
ejpam-4506	246	17	...........	...........	PUNCT
ejpam-4506	246	18	...........	...........	PUNCT
ejpam-4506	246	19	...........	...........	PUNCT
ejpam-4506	246	20	...........	...........	PUNCT
ejpam-4506	246	21	.....	.....	PUNCT
ejpam-4506	246	22	...............................................................................................................................................................................................	...............................................................................................................................................................................................	PUNCT
ejpam-4506	246	23	.........	.........	PUNCT
ejpam-4506	246	24	........	........	PUNCT
ejpam-4506	246	25	........	........	PUNCT
ejpam-4506	246	26	........	........	PUNCT
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ejpam-4506	246	30	........	........	PUNCT
ejpam-4506	246	31	........	........	PUNCT
ejpam-4506	246	32	........	........	PUNCT
ejpam-4506	246	33	........	........	PUNCT
ejpam-4506	246	34	........	........	PUNCT
ejpam-4506	246	35	.......	.......	PUNCT
ejpam-4506	247	1	.................	.................	PUNCT
ejpam-4506	247	2	................	................	PUNCT
ejpam-4506	248	1	................	................	PUNCT
ejpam-4506	248	2	................	................	PUNCT
ejpam-4506	249	1	................	................	PUNCT
ejpam-4506	249	2	................	................	PUNCT
ejpam-4506	250	1	................	................	PUNCT
ejpam-4506	250	2	................	................	PUNCT
ejpam-4506	251	1	................	................	PUNCT
ejpam-4506	251	2	................	................	PUNCT
ejpam-4506	252	1	................	................	PUNCT
ejpam-4506	252	2	................	................	PUNCT
ejpam-4506	253	1	................	................	PUNCT
ejpam-4506	253	2	............	............	PUNCT
ejpam-4506	253	3	...............................................................................................................................................................................................	...............................................................................................................................................................................................	PUNCT
ejpam-4506	253	4	....	....	PUNCT
ejpam-4506	253	5	........	........	PUNCT
ejpam-4506	253	6	........	........	PUNCT
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ejpam-4506	253	12	........	........	PUNCT
ejpam-4506	253	13	........	........	PUNCT
ejpam-4506	253	14	........	........	PUNCT
ejpam-4506	253	15	........	........	PUNCT
ejpam-4506	253	16	........	........	PUNCT
ejpam-4506	253	17	.................................................................................................................................................................................................................................	.................................................................................................................................................................................................................................	PUNCT
ejpam-4506	253	18	.........	.........	PUNCT
ejpam-4506	253	19	........	........	PUNCT
ejpam-4506	253	20	........	........	PUNCT
ejpam-4506	253	21	........	........	PUNCT
ejpam-4506	253	22	........	........	PUNCT
ejpam-4506	253	23	........	........	PUNCT
ejpam-4506	253	24	........	........	PUNCT
ejpam-4506	253	25	........	........	PUNCT
ejpam-4506	253	26	........	........	PUNCT
ejpam-4506	253	27	........	........	PUNCT
ejpam-4506	253	28	........	........	PUNCT
ejpam-4506	253	29	........	........	PUNCT
ejpam-4506	253	30	.......	.......	PUNCT
ejpam-4506	254	1	.............................................................................................................................................................................................................................	.............................................................................................................................................................................................................................	PUNCT
ejpam-4506	254	2	...............................................................................................................................................................................................	...............................................................................................................................................................................................	PUNCT
ejpam-4506	255	1	.................	.................	PUNCT
ejpam-4506	255	2	................	................	PUNCT
ejpam-4506	256	1	................	................	PUNCT
ejpam-4506	256	2	................	................	PUNCT
ejpam-4506	257	1	................	................	PUNCT
ejpam-4506	257	2	................	................	PUNCT
ejpam-4506	258	1	................	................	PUNCT
ejpam-4506	258	2	................	................	PUNCT
ejpam-4506	259	1	................	................	PUNCT
ejpam-4506	259	2	................	................	PUNCT
ejpam-4506	260	1	................	................	PUNCT
ejpam-4506	260	2	................	................	PUNCT
ejpam-4506	260	3	................	................	PUNCT
ejpam-4506	260	4	............	............	PUNCT
ejpam-4506	260	5	.........	.........	PUNCT
ejpam-4506	260	6	........	........	PUNCT
ejpam-4506	260	7	........	........	PUNCT
ejpam-4506	260	8	........	........	PUNCT
ejpam-4506	260	9	........	........	PUNCT
ejpam-4506	260	10	........	........	PUNCT
ejpam-4506	260	11	........	........	PUNCT
ejpam-4506	260	12	........	........	PUNCT
ejpam-4506	260	13	........	........	PUNCT
ejpam-4506	260	14	........	........	PUNCT
ejpam-4506	260	15	........	........	PUNCT
ejpam-4506	260	16	........	........	PUNCT
ejpam-4506	260	17	.......	.......	PUNCT
ejpam-4506	261	1	..............................................................................................................................................................................................................	..............................................................................................................................................................................................................	PUNCT
ejpam-4506	261	2	................	................	PUNCT
ejpam-4506	261	3	...............	...............	PUNCT
ejpam-4506	261	4	...............	...............	PUNCT
ejpam-4506	261	5	...............	...............	PUNCT
ejpam-4506	261	6	...............	...............	PUNCT
ejpam-4506	261	7	...............	...............	PUNCT
ejpam-4506	261	8	...............	...............	PUNCT
ejpam-4506	261	9	...............	...............	PUNCT
ejpam-4506	262	1	....	....	PUNCT
ejpam-4506	262	2	.......................................................................................................................................................................................	.......................................................................................................................................................................................	PUNCT
ejpam-4506	263	1	....................................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................................	PUNCT
ejpam-4506	263	2	...............	...............	PUNCT
ejpam-4506	263	3	..............	..............	PUNCT
ejpam-4506	264	1	..............	..............	PUNCT
ejpam-4506	264	2	..............	..............	PUNCT
ejpam-4506	265	1	..............	..............	PUNCT
ejpam-4506	265	2	..............	..............	PUNCT
ejpam-4506	266	1	..............	..............	PUNCT
ejpam-4506	266	2	..............	..............	PUNCT
ejpam-4506	267	1	.............................................................................................................................	.............................................................................................................................	PUNCT
ejpam-4506	267	2	.........	.........	PUNCT
ejpam-4506	267	3	........	........	PUNCT
ejpam-4506	267	4	........	........	PUNCT
ejpam-4506	267	5	........	........	PUNCT
ejpam-4506	267	6	........	........	PUNCT
ejpam-4506	267	7	........	........	PUNCT
ejpam-4506	267	8	........	........	PUNCT
ejpam-4506	267	9	........	........	PUNCT
ejpam-4506	267	10	........	........	PUNCT
ejpam-4506	267	11	........	........	PUNCT
ejpam-4506	267	12	........	........	PUNCT
ejpam-4506	267	13	........	........	PUNCT
ejpam-4506	267	14	........	........	PUNCT
ejpam-4506	267	15	........	........	PUNCT
ejpam-4506	267	16	........	........	PUNCT
ejpam-4506	267	17	........	........	PUNCT
ejpam-4506	267	18	........	........	PUNCT
ejpam-4506	267	19	........	........	PUNCT
ejpam-4506	267	20	........	........	PUNCT
ejpam-4506	267	21	........	........	PUNCT
ejpam-4506	267	22	........	........	PUNCT
ejpam-4506	267	23	........	........	PUNCT
ejpam-4506	267	24	........	........	PUNCT
ejpam-4506	267	25	........	........	PUNCT
ejpam-4506	267	26	........	........	PUNCT
ejpam-4506	268	1	.....	.....	PUNCT
ejpam-4506	268	2	............	............	PUNCT
ejpam-4506	268	3	...........	...........	PUNCT
ejpam-4506	268	4	...........	...........	PUNCT
ejpam-4506	268	5	...........	...........	PUNCT
ejpam-4506	268	6	...........	...........	PUNCT
ejpam-4506	268	7	...........	...........	PUNCT
ejpam-4506	268	8	...........	...........	PUNCT
ejpam-4506	268	9	...........	...........	PUNCT
ejpam-4506	268	10	...........	...........	PUNCT
ejpam-4506	268	11	...........	...........	PUNCT
ejpam-4506	268	12	...........	...........	PUNCT
ejpam-4506	268	13	...........	...........	PUNCT
ejpam-4506	268	14	...........	...........	PUNCT
ejpam-4506	268	15	...........	...........	PUNCT
ejpam-4506	268	16	...........	...........	PUNCT
ejpam-4506	268	17	...........	...........	PUNCT
ejpam-4506	268	18	......	......	PUNCT
ejpam-4506	268	19	.............................	.............................	PUNCT
ejpam-4506	269	1	............................	............................	PUNCT
ejpam-4506	269	2	............................	............................	PUNCT
ejpam-4506	269	3	............................	............................	PUNCT
ejpam-4506	269	4	............................	............................	PUNCT
ejpam-4506	269	5	............................	............................	PUNCT
ejpam-4506	269	6	............................	............................	PUNCT
ejpam-4506	269	7	............................	............................	PUNCT
ejpam-4506	269	8	...................	...................	PUNCT
ejpam-4506	269	9	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4506	270	1	.........	.........	PUNCT
ejpam-4506	270	2	........	........	PUNCT
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ejpam-4506	270	5	........	........	PUNCT
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ejpam-4506	270	10	........	........	PUNCT
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ejpam-4506	270	12	........	........	PUNCT
ejpam-4506	270	13	........	........	PUNCT
ejpam-4506	270	14	........	........	PUNCT
ejpam-4506	270	15	........	........	PUNCT
ejpam-4506	270	16	........	........	PUNCT
ejpam-4506	270	17	........	........	PUNCT
ejpam-4506	270	18	........	........	PUNCT
ejpam-4506	270	19	........	........	PUNCT
ejpam-4506	270	20	........	........	PUNCT
ejpam-4506	270	21	........	........	PUNCT
ejpam-4506	270	22	........	........	PUNCT
ejpam-4506	270	23	........	........	PUNCT
ejpam-4506	271	1	........	........	PUNCT
ejpam-4506	271	2	........	........	PUNCT
ejpam-4506	272	1	.....	.....	PUNCT
ejpam-4506	272	2	.............................................................................................................................	.............................................................................................................................	PUNCT
ejpam-4506	272	3	...........	...........	PUNCT
ejpam-4506	272	4	...........	...........	PUNCT
ejpam-4506	272	5	...........	...........	PUNCT
ejpam-4506	272	6	...........	...........	PUNCT
ejpam-4506	272	7	...........	...........	PUNCT
ejpam-4506	272	8	...........	...........	PUNCT
ejpam-4506	272	9	...........	...........	PUNCT
ejpam-4506	272	10	...........	...........	PUNCT
ejpam-4506	272	11	...........	...........	PUNCT
ejpam-4506	272	12	...........	...........	PUNCT
ejpam-4506	272	13	...........	...........	PUNCT
ejpam-4506	272	14	...........	...........	PUNCT
ejpam-4506	272	15	...........	...........	PUNCT
ejpam-4506	272	16	...........	...........	PUNCT
ejpam-4506	272	17	...........	...........	PUNCT
ejpam-4506	272	18	...........	...........	PUNCT
ejpam-4506	272	19	.......	.......	PUNCT
ejpam-4506	272	20	.................................................................................................................	.................................................................................................................	PUNCT
ejpam-4506	272	21	.............................	.............................	PUNCT
ejpam-4506	273	1	............................	............................	PUNCT
ejpam-4506	273	2	............................	............................	PUNCT
ejpam-4506	273	3	............................	............................	PUNCT
ejpam-4506	273	4	............................	............................	PUNCT
ejpam-4506	273	5	............................	............................	PUNCT
ejpam-4506	273	6	............................	............................	PUNCT
ejpam-4506	273	7	............................	............................	PUNCT
ejpam-4506	273	8	...................	...................	PUNCT
ejpam-4506	274	1	................	................	PUNCT
ejpam-4506	274	2	...............	...............	PUNCT
ejpam-4506	274	3	...............	...............	PUNCT
ejpam-4506	274	4	...............	...............	PUNCT
ejpam-4506	274	5	...............	...............	PUNCT
ejpam-4506	274	6	...............	...............	PUNCT
ejpam-4506	274	7	...............	...............	PUNCT
ejpam-4506	274	8	...............	...............	PUNCT
ejpam-4506	275	1	....	....	PUNCT
ejpam-4506	275	2	.......................................................................................................................................................................................	.......................................................................................................................................................................................	PUNCT
ejpam-4506	276	1	..............................................................................................................................................................................................................	..............................................................................................................................................................................................................	PUNCT
ejpam-4506	276	2	....................................................................................................................................................................................................................................................	....................................................................................................................................................................................................................................................	PUNCT
ejpam-4506	276	3	...............	...............	PUNCT
ejpam-4506	276	4	..............	..............	PUNCT
ejpam-4506	276	5	..............	..............	PUNCT
ejpam-4506	277	1	..............	..............	PUNCT
ejpam-4506	277	2	..............	..............	PUNCT
ejpam-4506	278	1	..............	..............	PUNCT
ejpam-4506	278	2	..............	..............	PUNCT
ejpam-4506	279	1	..............	..............	PUNCT
ejpam-4506	279	2	....................................	....................................	PUNCT
ejpam-4506	280	1	....................................	....................................	PUNCT
ejpam-4506	280	2	....................................	....................................	PUNCT
ejpam-4506	281	1	....................................	....................................	PUNCT
ejpam-4506	281	2	....................................	....................................	PUNCT
ejpam-4506	282	1	....................................	....................................	PUNCT
ejpam-4506	282	2	....................................	....................................	PUNCT
ejpam-4506	283	1	....................................	....................................	PUNCT
ejpam-4506	283	2	....................................	....................................	PUNCT
ejpam-4506	284	1	....................................	....................................	PUNCT
ejpam-4506	284	2	....................................	....................................	PUNCT
ejpam-4506	285	1	....................................	....................................	PUNCT
ejpam-4506	285	2	....................................	....................................	PUNCT
ejpam-4506	286	1	....................................	....................................	PUNCT
ejpam-4506	286	2	....................................	....................................	PUNCT
ejpam-4506	287	1	....................................	....................................	PUNCT
ejpam-4506	287	2	....................................	....................................	PUNCT
ejpam-4506	288	1	....................................	....................................	PUNCT
ejpam-4506	289	1	v6v1	v6v1	X
ejpam-4506	289	2	v2	v2	VERB
ejpam-4506	289	3	v3	v3	PROPN
ejpam-4506	289	4	v4	v4	NOUN
ejpam-4506	289	5	:	:	PUNCT
ejpam-4506	289	6	v5	v5	PROPN
ejpam-4506	289	7	figure	figure	NOUN
ejpam-4506	289	8	6	6	NUM
ejpam-4506	289	9	:	:	PUNCT
ejpam-4506	289	10	g	g	PROPN
ejpam-4506	289	11	=	=	PROPN
ejpam-4506	289	12	c6	c6	PROPN
ejpam-4506	289	13	⋄	⋄	PROPN
ejpam-4506	289	14	p2	p2	PROPN
ejpam-4506	289	15	in	in	ADP
ejpam-4506	289	16	general	general	ADJ
ejpam-4506	289	17	,	,	PUNCT
ejpam-4506	289	18	the	the	DET
ejpam-4506	289	19	graph	graph	NOUN
ejpam-4506	289	20	cn	cn	PROPN
ejpam-4506	289	21	⋄h	⋄h	NOUN
ejpam-4506	289	22	does	do	AUX
ejpam-4506	289	23	not	not	PART
ejpam-4506	289	24	admit	admit	VERB
ejpam-4506	289	25	path	path	NOUN
ejpam-4506	289	26	-	-	PUNCT
ejpam-4506	289	27	induced	induce	VERB
ejpam-4506	289	28	closed	closed	ADJ
ejpam-4506	289	29	geodetic	geodetic	ADJ
ejpam-4506	289	30	dominating	dominating	NOUN
ejpam-4506	289	31	set	set	NOUN
ejpam-4506	289	32	,	,	PUNCT
ejpam-4506	289	33	for	for	ADP
ejpam-4506	289	34	all	all	DET
ejpam-4506	289	35	n	n	PRON
ejpam-4506	289	36	≥	≥	NOUN
ejpam-4506	289	37	6	6	NUM
ejpam-4506	289	38	.	.	PUNCT
ejpam-4506	289	39	j.	j.	PROPN
ejpam-4506	289	40	anoche	anoche	PROPN
ejpam-4506	289	41	,	,	PUNCT
ejpam-4506	289	42	i.	i.	PROPN
ejpam-4506	289	43	aniversario	aniversario	PROPN
ejpam-4506	289	44	,	,	PUNCT
ejpam-4506	289	45	c.	c.	PROPN
ejpam-4506	289	46	merca	merca	PROPN
ejpam-4506	289	47	/	/	SYM
ejpam-4506	289	48	eur	eur	PROPN
ejpam-4506	289	49	.	.	PUNCT
ejpam-4506	290	1	j.	j.	PROPN
ejpam-4506	290	2	pure	pure	PROPN
ejpam-4506	290	3	appl	appl	PROPN
ejpam-4506	290	4	.	.	PROPN
ejpam-4506	290	5	math	math	PROPN
ejpam-4506	290	6	,	,	PUNCT
ejpam-4506	290	7	16	16	NUM
ejpam-4506	290	8	(	(	PUNCT
ejpam-4506	290	9	1	1	NUM
ejpam-4506	290	10	)	)	PUNCT
ejpam-4506	290	11	(	(	PUNCT
ejpam-4506	290	12	2023	2023	NUM
ejpam-4506	290	13	)	)	PUNCT
ejpam-4506	290	14	,	,	PUNCT
ejpam-4506	290	15	169	169	NUM
ejpam-4506	290	16	-	-	SYM
ejpam-4506	290	17	179	179	NUM
ejpam-4506	290	18	177	177	NUM
ejpam-4506	290	19	to	to	ADP
ejpam-4506	290	20	this	this	DET
ejpam-4506	290	21	extent	extent	NOUN
ejpam-4506	291	1	,	,	PUNCT
ejpam-4506	291	2	we	we	PRON
ejpam-4506	291	3	will	will	AUX
ejpam-4506	291	4	give	give	VERB
ejpam-4506	291	5	necessary	necessary	ADJ
ejpam-4506	291	6	conditions	condition	NOUN
ejpam-4506	291	7	for	for	ADP
ejpam-4506	291	8	those	those	DET
ejpam-4506	291	9	graphs	graph	NOUN
ejpam-4506	291	10	whose	whose	DET
ejpam-4506	291	11	edge	edge	NOUN
ejpam-4506	291	12	corona	corona	NOUN
ejpam-4506	291	13	admits	admit	VERB
ejpam-4506	291	14	a	a	DET
ejpam-4506	291	15	path	path	NOUN
ejpam-4506	291	16	-	-	PUNCT
ejpam-4506	291	17	induced	induce	VERB
ejpam-4506	291	18	closed	closed	ADJ
ejpam-4506	291	19	geodetic	geodetic	ADJ
ejpam-4506	291	20	dominating	dominating	NOUN
ejpam-4506	291	21	set	set	NOUN
ejpam-4506	291	22	.	.	PUNCT
ejpam-4506	292	1	first	first	ADV
ejpam-4506	292	2	,	,	PUNCT
ejpam-4506	292	3	let	let	VERB
ejpam-4506	292	4	us	we	PRON
ejpam-4506	292	5	consider	consider	VERB
ejpam-4506	292	6	the	the	DET
ejpam-4506	292	7	following	follow	VERB
ejpam-4506	292	8	theorem	theorem	VERB
ejpam-4506	292	9	.	.	PUNCT
ejpam-4506	293	1	here	here	ADV
ejpam-4506	293	2	,	,	PUNCT
ejpam-4506	293	3	we	we	PRON
ejpam-4506	293	4	let	let	VERB
ejpam-4506	293	5	g	g	PROPN
ejpam-4506	293	6	=	=	PROPN
ejpam-4506	293	7	k	k	PROPN
ejpam-4506	293	8	⋄h	⋄h	PROPN
ejpam-4506	293	9	,	,	PUNCT
ejpam-4506	293	10	ωg	ωg	ADP
ejpam-4506	293	11	=	=	NOUN
ejpam-4506	293	12	{	{	PUNCT
ejpam-4506	293	13	s	s	PROPN
ejpam-4506	293	14	⊆	⊆	NUM
ejpam-4506	293	15	v	v	NOUN
ejpam-4506	293	16	(	(	PUNCT
ejpam-4506	293	17	g	g	NOUN
ejpam-4506	293	18	)	)	PUNCT
ejpam-4506	293	19	:	:	PUNCT
ejpam-4506	293	20	p2[s]g	p2[s]g	PROPN
ejpam-4506	293	21	=	=	SYM
ejpam-4506	293	22	v	v	PROPN
ejpam-4506	293	23	(	(	PUNCT
ejpam-4506	293	24	g	g	NOUN
ejpam-4506	293	25	)	)	PUNCT
ejpam-4506	293	26	and	and	CCONJ
ejpam-4506	293	27	⟨s⟩	⟨s⟩	PROPN
ejpam-4506	293	28	has	have	VERB
ejpam-4506	293	29	a	a	DET
ejpam-4506	293	30	hamiltonian	hamiltonian	ADJ
ejpam-4506	293	31	path	path	NOUN
ejpam-4506	293	32	}	}	PUNCT
ejpam-4506	293	33	and	and	CCONJ
ejpam-4506	293	34	let	let	VERB
ejpam-4506	293	35	huv	huv	PROPN
ejpam-4506	293	36	be	be	AUX
ejpam-4506	293	37	the	the	DET
ejpam-4506	293	38	copy	copy	NOUN
ejpam-4506	293	39	of	of	ADP
ejpam-4506	293	40	the	the	DET
ejpam-4506	293	41	graph	graph	NOUN
ejpam-4506	293	42	h	h	NOUN
ejpam-4506	293	43	for	for	ADP
ejpam-4506	293	44	each	each	DET
ejpam-4506	293	45	uv	uv	NOUN
ejpam-4506	293	46	∈	∈	PROPN
ejpam-4506	293	47	e(k	e(k	NOUN
ejpam-4506	293	48	)	)	PUNCT
ejpam-4506	293	49	.	.	PUNCT
ejpam-4506	294	1	remark	remark	NOUN
ejpam-4506	294	2	9	9	NUM
ejpam-4506	294	3	.	.	PUNCT
ejpam-4506	295	1	if	if	SCONJ
ejpam-4506	295	2	k	k	PROPN
ejpam-4506	295	3	is	be	AUX
ejpam-4506	295	4	a	a	DET
ejpam-4506	295	5	connected	connected	ADJ
ejpam-4506	295	6	graph	graph	NOUN
ejpam-4506	295	7	of	of	ADP
ejpam-4506	295	8	order	order	NOUN
ejpam-4506	295	9	2	2	NUM
ejpam-4506	295	10	and	and	CCONJ
ejpam-4506	295	11	h	h	NOUN
ejpam-4506	295	12	is	be	AUX
ejpam-4506	295	13	any	any	DET
ejpam-4506	295	14	graph	graph	NOUN
ejpam-4506	295	15	,	,	PUNCT
ejpam-4506	295	16	then	then	ADV
ejpam-4506	295	17	g	g	PROPN
ejpam-4506	295	18	=	=	PROPN
ejpam-4506	295	19	k	k	PROPN
ejpam-4506	295	20	⋄h	⋄h	NOUN
ejpam-4506	296	1	=	=	PUNCT
ejpam-4506	296	2	k	k	PROPN
ejpam-4506	297	1	+	+	PROPN
ejpam-4506	297	2	h.	h.	PROPN
ejpam-4506	297	3	theorem	theorem	VERB
ejpam-4506	297	4	13	13	NUM
ejpam-4506	297	5	.	.	PUNCT
ejpam-4506	298	1	let	let	VERB
ejpam-4506	298	2	h	h	NOUN
ejpam-4506	298	3	be	be	AUX
ejpam-4506	298	4	any	any	DET
ejpam-4506	298	5	graph	graph	NOUN
ejpam-4506	298	6	and	and	CCONJ
ejpam-4506	298	7	k	k	PROPN
ejpam-4506	298	8	be	be	AUX
ejpam-4506	298	9	a	a	DET
ejpam-4506	298	10	connected	connected	ADJ
ejpam-4506	298	11	noncomplete	noncomplete	ADJ
ejpam-4506	298	12	graph	graph	NOUN
ejpam-4506	298	13	of	of	ADP
ejpam-4506	298	14	order	order	NOUN
ejpam-4506	298	15	n	n	PRON
ejpam-4506	298	16	≥	≥	NOUN
ejpam-4506	298	17	3	3	NUM
ejpam-4506	298	18	and	and	CCONJ
ejpam-4506	298	19	bothk	bothk	ADJ
ejpam-4506	298	20	andh	andh	NOUN
ejpam-4506	298	21	admit	admit	VERB
ejpam-4506	298	22	sk	sk	ADP
ejpam-4506	298	23	∈	∈	PROPN
ejpam-4506	298	24	ωk	ωk	ADP
ejpam-4506	298	25	and	and	CCONJ
ejpam-4506	298	26	sh	sh	INTJ
ejpam-4506	298	27	∈	∈	PROPN
ejpam-4506	298	28	ωh	ωh	NUM
ejpam-4506	298	29	,	,	PUNCT
ejpam-4506	298	30	respectively	respectively	ADV
ejpam-4506	298	31	.	.	PUNCT
ejpam-4506	299	1	then	then	ADV
ejpam-4506	299	2	g	g	PROPN
ejpam-4506	299	3	=	=	PUNCT
ejpam-4506	299	4	k⋄h	k⋄h	PROPN
ejpam-4506	299	5	admits	admit	VERB
ejpam-4506	299	6	a	a	DET
ejpam-4506	299	7	path	path	NOUN
ejpam-4506	299	8	-	-	PUNCT
ejpam-4506	299	9	induced	induce	VERB
ejpam-4506	299	10	closed	closed	ADJ
ejpam-4506	299	11	geodetic	geodetic	ADJ
ejpam-4506	299	12	dominating	dominating	NOUN
ejpam-4506	299	13	set	set	NOUN
ejpam-4506	299	14	s	s	VERB
ejpam-4506	299	15	if	if	SCONJ
ejpam-4506	300	1	and	and	CCONJ
ejpam-4506	300	2	only	only	ADV
ejpam-4506	300	3	if	if	SCONJ
ejpam-4506	300	4	s	s	VERB
ejpam-4506	300	5	=	=	X
ejpam-4506	300	6	(	(	PUNCT
ejpam-4506	300	7	⋃	⋃	NOUN
ejpam-4506	300	8	uv∈e(k	uv∈e(k	NOUN
ejpam-4506	300	9	)	)	PUNCT
ejpam-4506	300	10	suv	suv	NOUN
ejpam-4506	300	11	)	)	PUNCT
ejpam-4506	300	12	∪a	∪a	NUM
ejpam-4506	300	13	where	where	SCONJ
ejpam-4506	300	14	the	the	DET
ejpam-4506	300	15	following	follow	VERB
ejpam-4506	300	16	holds	hold	VERB
ejpam-4506	300	17	:	:	PUNCT
ejpam-4506	300	18	(	(	PUNCT
ejpam-4506	300	19	i	i	NOUN
ejpam-4506	300	20	)	)	PUNCT
ejpam-4506	300	21	a	a	DET
ejpam-4506	300	22	⊆	⊆	NUM
ejpam-4506	300	23	v	v	NOUN
ejpam-4506	300	24	(	(	PUNCT
ejpam-4506	300	25	k	k	NOUN
ejpam-4506	300	26	)	)	PUNCT
ejpam-4506	300	27	and	and	CCONJ
ejpam-4506	300	28	a	a	DET
ejpam-4506	300	29	∈	∈	NOUN
ejpam-4506	300	30	ωk	ωk	ADP
ejpam-4506	300	31	;	;	PUNCT
ejpam-4506	300	32	and	and	CCONJ
ejpam-4506	300	33	(	(	PUNCT
ejpam-4506	300	34	ii	ii	NOUN
ejpam-4506	300	35	)	)	PUNCT
ejpam-4506	300	36	for	for	ADP
ejpam-4506	300	37	all	all	DET
ejpam-4506	300	38	suv	suv	PROPN
ejpam-4506	300	39	⊆	⊆	NUM
ejpam-4506	300	40	v	v	NOUN
ejpam-4506	300	41	(	(	PUNCT
ejpam-4506	300	42	huv	huv	PROPN
ejpam-4506	300	43	)	)	PUNCT
ejpam-4506	300	44	,	,	PUNCT
ejpam-4506	300	45	suv	suv	PROPN
ejpam-4506	300	46	∈	∈	PROPN
ejpam-4506	300	47	ωhuv	ωhuv	NOUN
ejpam-4506	300	48	for	for	ADP
ejpam-4506	300	49	each	each	DET
ejpam-4506	300	50	uv	uv	NOUN
ejpam-4506	300	51	∈	∈	PROPN
ejpam-4506	300	52	e(k	e(k	NOUN
ejpam-4506	300	53	)	)	PUNCT
ejpam-4506	300	54	.	.	PUNCT
ejpam-4506	301	1	proof	proof	NOUN
ejpam-4506	301	2	:	:	PUNCT
ejpam-4506	301	3	let	let	VERB
ejpam-4506	301	4	g	g	PROPN
ejpam-4506	301	5	=	=	SYM
ejpam-4506	301	6	k	k	PROPN
ejpam-4506	301	7	⋄	⋄	PROPN
ejpam-4506	301	8	h	h	NOUN
ejpam-4506	301	9	admits	admit	VERB
ejpam-4506	301	10	a	a	DET
ejpam-4506	301	11	path	path	NOUN
ejpam-4506	301	12	-	-	PUNCT
ejpam-4506	301	13	induced	induce	VERB
ejpam-4506	301	14	closed	closed	ADJ
ejpam-4506	301	15	geodetic	geodetic	ADJ
ejpam-4506	301	16	dominating	dominating	NOUN
ejpam-4506	301	17	set	set	NOUN
ejpam-4506	301	18	s	s	PRON
ejpam-4506	301	19	and	and	CCONJ
ejpam-4506	301	20	let	let	VERB
ejpam-4506	301	21	a	a	DET
ejpam-4506	301	22	=	=	X
ejpam-4506	301	23	s	s	NOUN
ejpam-4506	301	24	∩	∩	ADJ
ejpam-4506	301	25	v	v	X
ejpam-4506	301	26	(	(	PUNCT
ejpam-4506	301	27	k	k	NOUN
ejpam-4506	301	28	)	)	PUNCT
ejpam-4506	301	29	and	and	CCONJ
ejpam-4506	301	30	suv	suv	PROPN
ejpam-4506	301	31	=	=	PROPN
ejpam-4506	301	32	s	s	PROPN
ejpam-4506	301	33	∩	∩	ADJ
ejpam-4506	301	34	v	v	X
ejpam-4506	301	35	(	(	PUNCT
ejpam-4506	301	36	huv	huv	PROPN
ejpam-4506	301	37	)	)	PUNCT
ejpam-4506	301	38	for	for	ADP
ejpam-4506	301	39	each	each	DET
ejpam-4506	301	40	uv	uv	PROPN
ejpam-4506	301	41	∈	∈	PROPN
ejpam-4506	301	42	e(k	e(k	NOUN
ejpam-4506	301	43	)	)	PUNCT
ejpam-4506	301	44	.	.	PUNCT
ejpam-4506	302	1	then	then	ADV
ejpam-4506	302	2	a	a	DET
ejpam-4506	302	3	⊆	⊆	NUM
ejpam-4506	302	4	v	v	NOUN
ejpam-4506	302	5	(	(	PUNCT
ejpam-4506	302	6	k	k	NOUN
ejpam-4506	302	7	)	)	PUNCT
ejpam-4506	302	8	and	and	CCONJ
ejpam-4506	302	9	suv	suv	PROPN
ejpam-4506	302	10	⊆	⊆	NUM
ejpam-4506	302	11	v	v	NOUN
ejpam-4506	302	12	(	(	PUNCT
ejpam-4506	302	13	huv	huv	PROPN
ejpam-4506	302	14	)	)	PUNCT
ejpam-4506	302	15	.	.	PUNCT
ejpam-4506	303	1	note	note	VERB
ejpam-4506	303	2	that	that	SCONJ
ejpam-4506	303	3	ig[s	ig[	NOUN
ejpam-4506	303	4	]	]	X
ejpam-4506	303	5	=	=	SYM
ejpam-4506	303	6	v	v	X
ejpam-4506	303	7	(	(	PUNCT
ejpam-4506	303	8	g	g	NOUN
ejpam-4506	303	9	)	)	PUNCT
ejpam-4506	303	10	and	and	CCONJ
ejpam-4506	303	11	so	so	ADV
ejpam-4506	303	12	s	s	PART
ejpam-4506	303	13	=	=	PUNCT
ejpam-4506	303	14	(	(	PUNCT
ejpam-4506	303	15	⋃	⋃	NOUN
ejpam-4506	303	16	uv∈e(k	uv∈e(k	NOUN
ejpam-4506	303	17	)	)	PUNCT
ejpam-4506	303	18	suv	suv	NOUN
ejpam-4506	303	19	)	)	PUNCT
ejpam-4506	303	20	∪	∪	ADP
ejpam-4506	303	21	a.	a.	NOUN
ejpam-4506	303	22	by	by	ADP
ejpam-4506	303	23	definition	definition	NOUN
ejpam-4506	303	24	7	7	NUM
ejpam-4506	303	25	,	,	PUNCT
ejpam-4506	303	26	for	for	ADP
ejpam-4506	303	27	each	each	DET
ejpam-4506	303	28	uv	uv	NOUN
ejpam-4506	303	29	∈	∈	PROPN
ejpam-4506	303	30	e(k	e(k	NOUN
ejpam-4506	303	31	)	)	PUNCT
ejpam-4506	303	32	there	there	PRON
ejpam-4506	303	33	exists	exist	VERB
ejpam-4506	303	34	huv	huv	PROPN
ejpam-4506	303	35	copy	copy	NOUN
ejpam-4506	303	36	of	of	ADP
ejpam-4506	303	37	h.	h.	PROPN
ejpam-4506	303	38	note	note	PROPN
ejpam-4506	303	39	that	that	SCONJ
ejpam-4506	303	40	h	h	NOUN
ejpam-4506	303	41	admits	admit	VERB
ejpam-4506	303	42	sh	sh	PROPN
ejpam-4506	303	43	∈	∈	PROPN
ejpam-4506	303	44	ωh	ωh	X
ejpam-4506	304	1	and	and	CCONJ
ejpam-4506	304	2	so	so	ADV
ejpam-4506	304	3	for	for	ADP
ejpam-4506	304	4	any	any	DET
ejpam-4506	304	5	huv	huv	PROPN
ejpam-4506	304	6	copy	copy	NOUN
ejpam-4506	304	7	of	of	ADP
ejpam-4506	304	8	h	h	NOUN
ejpam-4506	304	9	,	,	PUNCT
ejpam-4506	304	10	huv	huv	PROPN
ejpam-4506	304	11	admits	admit	VERB
ejpam-4506	304	12	an	an	DET
ejpam-4506	304	13	element	element	NOUN
ejpam-4506	304	14	in	in	ADP
ejpam-4506	304	15	ωhuv	ωhuv	NOUN
ejpam-4506	304	16	.	.	PUNCT
ejpam-4506	305	1	since	since	SCONJ
ejpam-4506	305	2	s	s	PROPN
ejpam-4506	305	3	is	be	AUX
ejpam-4506	305	4	a	a	DET
ejpam-4506	305	5	path	path	NOUN
ejpam-4506	305	6	-	-	PUNCT
ejpam-4506	305	7	induced	induce	VERB
ejpam-4506	305	8	closed	closed	ADJ
ejpam-4506	305	9	geodetic	geodetic	ADJ
ejpam-4506	305	10	dominating	dominating	NOUN
ejpam-4506	305	11	set	set	NOUN
ejpam-4506	305	12	of	of	ADP
ejpam-4506	305	13	g	g	PROPN
ejpam-4506	305	14	,	,	PUNCT
ejpam-4506	305	15	a	a	PRON
ejpam-4506	305	16	and	and	CCONJ
ejpam-4506	305	17	suv	suv	PROPN
ejpam-4506	305	18	must	must	AUX
ejpam-4506	305	19	be	be	AUX
ejpam-4506	305	20	elements	element	NOUN
ejpam-4506	305	21	of	of	ADP
ejpam-4506	305	22	ωk	ωk	ADV
ejpam-4506	305	23	and	and	CCONJ
ejpam-4506	305	24	ωhuv	ωhuv	VERB
ejpam-4506	305	25	,	,	PUNCT
ejpam-4506	305	26	respectively	respectively	ADV
ejpam-4506	305	27	.	.	PUNCT
ejpam-4506	306	1	otherwise	otherwise	ADV
ejpam-4506	306	2	,	,	PUNCT
ejpam-4506	306	3	ig[s	ig[s	PROPN
ejpam-4506	306	4	]	]	PUNCT
ejpam-4506	306	5	̸=	̸=	PROPN
ejpam-4506	306	6	v	v	NOUN
ejpam-4506	306	7	(	(	PUNCT
ejpam-4506	306	8	g	g	NOUN
ejpam-4506	306	9	)	)	PUNCT
ejpam-4506	306	10	or	or	CCONJ
ejpam-4506	306	11	⟨s⟩	⟨s⟩	PROPN
ejpam-4506	306	12	can	can	AUX
ejpam-4506	306	13	not	not	PART
ejpam-4506	306	14	contain	contain	VERB
ejpam-4506	306	15	a	a	DET
ejpam-4506	306	16	hamiltonian	hamiltonian	ADJ
ejpam-4506	306	17	path	path	NOUN
ejpam-4506	306	18	or	or	CCONJ
ejpam-4506	306	19	s	s	NOUN
ejpam-4506	306	20	is	be	AUX
ejpam-4506	306	21	not	not	PART
ejpam-4506	306	22	a	a	DET
ejpam-4506	306	23	dominating	dominating	NOUN
ejpam-4506	306	24	set	set	NOUN
ejpam-4506	306	25	of	of	ADP
ejpam-4506	306	26	g	g	NOUN
ejpam-4506	306	27	,	,	PUNCT
ejpam-4506	306	28	which	which	PRON
ejpam-4506	306	29	is	be	AUX
ejpam-4506	306	30	a	a	DET
ejpam-4506	306	31	contradiction	contradiction	NOUN
ejpam-4506	306	32	.	.	PUNCT
ejpam-4506	307	1	conversely	conversely	ADV
ejpam-4506	307	2	,	,	PUNCT
ejpam-4506	307	3	suppose	suppose	VERB
ejpam-4506	307	4	s	s	VERB
ejpam-4506	307	5	=	=	PUNCT
ejpam-4506	307	6	(	(	PUNCT
ejpam-4506	307	7	⋃	⋃	NOUN
ejpam-4506	307	8	uv∈e(k	uv∈e(k	NOUN
ejpam-4506	307	9	)	)	PUNCT
ejpam-4506	307	10	suv	suv	NOUN
ejpam-4506	307	11	)	)	PUNCT
ejpam-4506	307	12	∪a	∪a	X
ejpam-4506	307	13	and	and	CCONJ
ejpam-4506	307	14	(	(	PUNCT
ejpam-4506	307	15	i	i	NOUN
ejpam-4506	307	16	)	)	PUNCT
ejpam-4506	307	17	and	and	CCONJ
ejpam-4506	307	18	(	(	PUNCT
ejpam-4506	307	19	ii	ii	NOUN
ejpam-4506	307	20	)	)	PUNCT
ejpam-4506	307	21	hold	hold	VERB
ejpam-4506	307	22	.	.	PUNCT
ejpam-4506	308	1	since	since	SCONJ
ejpam-4506	308	2	a	a	PRON
ejpam-4506	308	3	and	and	CCONJ
ejpam-4506	308	4	suv	suv	PROPN
ejpam-4506	308	5	are	be	AUX
ejpam-4506	308	6	2	2	NUM
ejpam-4506	308	7	-	-	PUNCT
ejpam-4506	308	8	path	path	NOUN
ejpam-4506	308	9	closure	closure	NOUN
ejpam-4506	308	10	absorbing	absorbing	NOUN
ejpam-4506	308	11	of	of	ADP
ejpam-4506	308	12	k	k	PROPN
ejpam-4506	308	13	and	and	CCONJ
ejpam-4506	308	14	huv	huv	PROPN
ejpam-4506	308	15	for	for	ADP
ejpam-4506	308	16	each	each	DET
ejpam-4506	308	17	uv	uv	PROPN
ejpam-4506	308	18	∈	∈	PROPN
ejpam-4506	308	19	e(k	e(k	NOUN
ejpam-4506	308	20	)	)	PUNCT
ejpam-4506	308	21	,	,	PUNCT
ejpam-4506	308	22	respectively	respectively	ADV
ejpam-4506	308	23	,	,	PUNCT
ejpam-4506	308	24	it	it	PRON
ejpam-4506	308	25	follows	follow	VERB
ejpam-4506	308	26	that	that	SCONJ
ejpam-4506	308	27	ig[s	ig[	NOUN
ejpam-4506	308	28	]	]	X
ejpam-4506	308	29	=	=	SYM
ejpam-4506	308	30	v	v	X
ejpam-4506	308	31	(	(	PUNCT
ejpam-4506	308	32	g	g	NOUN
ejpam-4506	308	33	)	)	PUNCT
ejpam-4506	308	34	.	.	PUNCT
ejpam-4506	309	1	note	note	VERB
ejpam-4506	309	2	that	that	SCONJ
ejpam-4506	309	3	each	each	PRON
ejpam-4506	309	4	of	of	ADP
ejpam-4506	309	5	⟨suv⟩	⟨suv⟩	PROPN
ejpam-4506	309	6	and	and	CCONJ
ejpam-4506	309	7	⟨a⟩	⟨a⟩	PROPN
ejpam-4506	309	8	contains	contain	VERB
ejpam-4506	309	9	a	a	DET
ejpam-4506	309	10	hamiltonian	hamiltonian	ADJ
ejpam-4506	309	11	path	path	NOUN
ejpam-4506	309	12	.	.	PUNCT
ejpam-4506	310	1	thus	thus	ADV
ejpam-4506	310	2	,	,	PUNCT
ejpam-4506	310	3	by	by	ADP
ejpam-4506	310	4	definition	definition	NOUN
ejpam-4506	310	5	7	7	NUM
ejpam-4506	310	6	,	,	PUNCT
ejpam-4506	310	7	⟨s⟩	⟨s⟩	PROPN
ejpam-4506	310	8	contains	contain	VERB
ejpam-4506	310	9	a	a	DET
ejpam-4506	310	10	hamiltonian	hamiltonian	ADJ
ejpam-4506	310	11	path	path	NOUN
ejpam-4506	310	12	.	.	PUNCT
ejpam-4506	311	1	since	since	SCONJ
ejpam-4506	311	2	a	a	PRON
ejpam-4506	311	3	is	be	AUX
ejpam-4506	311	4	a	a	DET
ejpam-4506	311	5	2	2	NUM
ejpam-4506	311	6	-	-	PUNCT
ejpam-4506	311	7	path	path	NOUN
ejpam-4506	311	8	closure	closure	NOUN
ejpam-4506	311	9	absorbing	absorbing	NOUN
ejpam-4506	311	10	of	of	ADP
ejpam-4506	311	11	k	k	PROPN
ejpam-4506	311	12	,	,	PUNCT
ejpam-4506	311	13	for	for	ADP
ejpam-4506	311	14	any	any	DET
ejpam-4506	311	15	wk	wk	ADP
ejpam-4506	311	16	∈	∈	PROPN
ejpam-4506	311	17	v	v	PROPN
ejpam-4506	311	18	(	(	PUNCT
ejpam-4506	311	19	k)∖a	k)∖a	PROPN
ejpam-4506	311	20	,	,	PUNCT
ejpam-4506	311	21	wk	wk	X
ejpam-4506	311	22	is	be	AUX
ejpam-4506	311	23	adjacent	adjacent	ADJ
ejpam-4506	311	24	to	to	ADP
ejpam-4506	311	25	at	at	ADV
ejpam-4506	311	26	least	least	ADV
ejpam-4506	311	27	two	two	NUM
ejpam-4506	311	28	vertices	vertex	NOUN
ejpam-4506	311	29	of	of	ADP
ejpam-4506	311	30	a.	a.	NOUN
ejpam-4506	311	31	this	this	PRON
ejpam-4506	311	32	means	mean	VERB
ejpam-4506	311	33	that	that	SCONJ
ejpam-4506	311	34	a	a	PRON
ejpam-4506	311	35	is	be	AUX
ejpam-4506	311	36	a	a	DET
ejpam-4506	311	37	dominating	dominating	NOUN
ejpam-4506	311	38	set	set	NOUN
ejpam-4506	311	39	of	of	ADP
ejpam-4506	311	40	k.	k.	PROPN
ejpam-4506	311	41	thus	thus	ADV
ejpam-4506	311	42	,	,	PUNCT
ejpam-4506	311	43	by	by	ADP
ejpam-4506	311	44	definition	definition	NOUN
ejpam-4506	311	45	7	7	NUM
ejpam-4506	311	46	,	,	PUNCT
ejpam-4506	311	47	a	a	PRON
ejpam-4506	311	48	is	be	AUX
ejpam-4506	311	49	a	a	DET
ejpam-4506	311	50	dominating	dominating	NOUN
ejpam-4506	311	51	set	set	NOUN
ejpam-4506	311	52	of	of	ADP
ejpam-4506	311	53	g	g	PROPN
ejpam-4506	311	54	and	and	CCONJ
ejpam-4506	311	55	so	so	ADV
ejpam-4506	311	56	s	s	VERB
ejpam-4506	311	57	is	be	AUX
ejpam-4506	311	58	a	a	DET
ejpam-4506	311	59	dominating	dominating	NOUN
ejpam-4506	311	60	set	set	NOUN
ejpam-4506	311	61	of	of	ADP
ejpam-4506	311	62	g.	g.	PROPN
ejpam-4506	311	63	therefore	therefore	ADV
ejpam-4506	311	64	,	,	PUNCT
ejpam-4506	311	65	s	s	VERB
ejpam-4506	311	66	is	be	AUX
ejpam-4506	311	67	a	a	DET
ejpam-4506	311	68	path	path	NOUN
ejpam-4506	311	69	-	-	PUNCT
ejpam-4506	311	70	induced	induce	VERB
ejpam-4506	311	71	closed	closed	ADJ
ejpam-4506	311	72	geodetic	geodetic	ADJ
ejpam-4506	311	73	dominating	dominating	NOUN
ejpam-4506	311	74	set	set	NOUN
ejpam-4506	311	75	of	of	ADP
ejpam-4506	311	76	g.	g.	PROPN
ejpam-4506	311	77	■	■	PUNCT
ejpam-4506	311	78	theorem	theorem	VERB
ejpam-4506	311	79	14	14	NUM
ejpam-4506	311	80	.	.	PUNCT
ejpam-4506	312	1	let	let	VERB
ejpam-4506	312	2	h	h	NOUN
ejpam-4506	312	3	be	be	AUX
ejpam-4506	312	4	any	any	DET
ejpam-4506	312	5	graph	graph	NOUN
ejpam-4506	312	6	and	and	CCONJ
ejpam-4506	312	7	k	k	PROPN
ejpam-4506	312	8	be	be	AUX
ejpam-4506	312	9	a	a	DET
ejpam-4506	312	10	connected	connected	ADJ
ejpam-4506	312	11	noncomplete	noncomplete	ADJ
ejpam-4506	312	12	graph	graph	NOUN
ejpam-4506	312	13	with	with	ADP
ejpam-4506	312	14	|v	|v	PROPN
ejpam-4506	312	15	(	(	PUNCT
ejpam-4506	312	16	k)|	k)|	NOUN
ejpam-4506	312	17	=	=	PUNCT
ejpam-4506	312	18	m	m	VERB
ejpam-4506	312	19	≥	≥	NOUN
ejpam-4506	312	20	3	3	NUM
ejpam-4506	312	21	,	,	PUNCT
ejpam-4506	312	22	|e(k)|	|e(k)|	NOUN
ejpam-4506	312	23	=	=	SYM
ejpam-4506	312	24	n	n	NOUN
ejpam-4506	312	25	and	and	CCONJ
ejpam-4506	312	26	both	both	DET
ejpam-4506	312	27	k	k	PROPN
ejpam-4506	312	28	and	and	CCONJ
ejpam-4506	312	29	h	h	PROPN
ejpam-4506	312	30	admit	admit	VERB
ejpam-4506	312	31	sk	sk	ADP
ejpam-4506	312	32	∈	∈	PROPN
ejpam-4506	312	33	ωk	ωk	ADP
ejpam-4506	312	34	and	and	CCONJ
ejpam-4506	312	35	sh	sh	INTJ
ejpam-4506	312	36	∈	∈	PROPN
ejpam-4506	312	37	ωh	ωh	NUM
ejpam-4506	312	38	,	,	PUNCT
ejpam-4506	312	39	respectively	respectively	ADV
ejpam-4506	312	40	.	.	PUNCT
ejpam-4506	313	1	let	let	VERB
ejpam-4506	313	2	g	g	PROPN
ejpam-4506	313	3	=	=	PROPN
ejpam-4506	313	4	k	k	PROPN
ejpam-4506	313	5	⋄h	⋄h	PROPN
ejpam-4506	313	6	.	.	PUNCT
ejpam-4506	314	1	then	then	ADV
ejpam-4506	314	2	γpicg(g	γpicg(g	NUM
ejpam-4506	314	3	)	)	PUNCT
ejpam-4506	314	4	=	=	SYM
ejpam-4506	315	1	n	n	PROPN
ejpam-4506	315	2	·	·	PUNCT
ejpam-4506	315	3	min{|sh	min{|sh	ADJ
ejpam-4506	316	1	|	|	ADV
ejpam-4506	316	2	:	:	PUNCT
ejpam-4506	316	3	sh	sh	PROPN
ejpam-4506	316	4	∈	∈	PROPN
ejpam-4506	316	5	ωh}+min{|sk	ωh}+min{|sk	NOUN
ejpam-4506	317	1	|	|	ADV
ejpam-4506	317	2	:	:	PUNCT
ejpam-4506	317	3	sk	sk	ADP
ejpam-4506	317	4	∈	∈	PROPN
ejpam-4506	317	5	ωh	ωh	PART
ejpam-4506	317	6	}	}	PUNCT
ejpam-4506	317	7	.	.	PUNCT
ejpam-4506	318	1	j.	j.	PROPN
ejpam-4506	318	2	anoche	anoche	PROPN
ejpam-4506	318	3	,	,	PUNCT
ejpam-4506	318	4	i.	i.	PROPN
ejpam-4506	318	5	aniversario	aniversario	PROPN
ejpam-4506	318	6	,	,	PUNCT
ejpam-4506	318	7	c.	c.	PROPN
ejpam-4506	318	8	merca	merca	PROPN
ejpam-4506	318	9	/	/	SYM
ejpam-4506	318	10	eur	eur	PROPN
ejpam-4506	318	11	.	.	PUNCT
ejpam-4506	319	1	j.	j.	PROPN
ejpam-4506	319	2	pure	pure	PROPN
ejpam-4506	319	3	appl	appl	PROPN
ejpam-4506	319	4	.	.	PROPN
ejpam-4506	319	5	math	math	PROPN
ejpam-4506	319	6	,	,	PUNCT
ejpam-4506	319	7	16	16	NUM
ejpam-4506	319	8	(	(	PUNCT
ejpam-4506	319	9	1	1	NUM
ejpam-4506	319	10	)	)	PUNCT
ejpam-4506	319	11	(	(	PUNCT
ejpam-4506	319	12	2023	2023	NUM
ejpam-4506	319	13	)	)	PUNCT
ejpam-4506	319	14	,	,	PUNCT
ejpam-4506	319	15	169	169	NUM
ejpam-4506	319	16	-	-	SYM
ejpam-4506	319	17	179	179	NUM
ejpam-4506	319	18	178	178	NUM
ejpam-4506	319	19	proof	proof	NOUN
ejpam-4506	319	20	:	:	PUNCT
ejpam-4506	319	21	let	let	VERB
ejpam-4506	319	22	k	k	NOUN
ejpam-4506	319	23	and	and	CCONJ
ejpam-4506	319	24	h	h	PROPN
ejpam-4506	319	25	admit	admit	VERB
ejpam-4506	319	26	sk	sk	ADP
ejpam-4506	319	27	∈	∈	PROPN
ejpam-4506	319	28	ωk	ωk	ADP
ejpam-4506	319	29	and	and	CCONJ
ejpam-4506	319	30	sh	sh	INTJ
ejpam-4506	319	31	∈	∈	PROPN
ejpam-4506	319	32	ωh	ωh	NUM
ejpam-4506	319	33	,	,	PUNCT
ejpam-4506	319	34	respectively	respectively	ADV
ejpam-4506	319	35	.	.	PUNCT
ejpam-4506	320	1	let	let	VERB
ejpam-4506	320	2	g	g	PROPN
ejpam-4506	320	3	=	=	PUNCT
ejpam-4506	320	4	k	k	PROPN
ejpam-4506	320	5	⋄	⋄	PROPN
ejpam-4506	320	6	h	h	NOUN
ejpam-4506	320	7	where	where	SCONJ
ejpam-4506	320	8	|v	|v	PROPN
ejpam-4506	320	9	(	(	PUNCT
ejpam-4506	320	10	k)|	k)|	INTJ
ejpam-4506	320	11	=	=	PUNCT
ejpam-4506	320	12	m	m	VERB
ejpam-4506	320	13	≥	≥	NOUN
ejpam-4506	320	14	3	3	NUM
ejpam-4506	320	15	and	and	CCONJ
ejpam-4506	320	16	|e(k)|	|e(k)|	PROPN
ejpam-4506	320	17	=	=	SYM
ejpam-4506	320	18	n.	n.	NOUN
ejpam-4506	320	19	then	then	ADV
ejpam-4506	320	20	by	by	ADP
ejpam-4506	320	21	definition	definition	NOUN
ejpam-4506	320	22	7	7	NUM
ejpam-4506	320	23	,	,	PUNCT
ejpam-4506	320	24	there	there	PRON
ejpam-4506	320	25	are	be	VERB
ejpam-4506	320	26	n	n	ADV
ejpam-4506	320	27	copies	copy	NOUN
ejpam-4506	320	28	of	of	ADP
ejpam-4506	320	29	h	h	NOUN
ejpam-4506	320	30	in	in	ADP
ejpam-4506	320	31	g.	g.	PROPN
ejpam-4506	320	32	thus	thus	ADV
ejpam-4506	320	33	,	,	PUNCT
ejpam-4506	320	34	by	by	ADP
ejpam-4506	320	35	theorem	theorem	NOUN
ejpam-4506	320	36	13	13	NUM
ejpam-4506	320	37	,	,	PUNCT
ejpam-4506	320	38	the	the	DET
ejpam-4506	320	39	path	path	NOUN
ejpam-4506	320	40	-	-	PUNCT
ejpam-4506	320	41	induced	induce	VERB
ejpam-4506	320	42	closed	closed	ADJ
ejpam-4506	320	43	geodetic	geodetic	ADJ
ejpam-4506	320	44	dominating	dominating	NOUN
ejpam-4506	320	45	sets	set	NOUN
ejpam-4506	320	46	of	of	ADP
ejpam-4506	320	47	g	g	PROPN
ejpam-4506	320	48	are	be	AUX
ejpam-4506	320	49	of	of	ADP
ejpam-4506	320	50	the	the	DET
ejpam-4506	320	51	form	form	NOUN
ejpam-4506	320	52	s	s	PART
ejpam-4506	320	53	=	=	PUNCT
ejpam-4506	320	54	(	(	PUNCT
ejpam-4506	320	55	⋃	⋃	NOUN
ejpam-4506	320	56	uv∈e(k	uv∈e(k	NOUN
ejpam-4506	320	57	)	)	PUNCT
ejpam-4506	320	58	suv	suv	NOUN
ejpam-4506	320	59	)	)	PUNCT
ejpam-4506	320	60	∪a	∪a	NUM
ejpam-4506	320	61	where	where	SCONJ
ejpam-4506	320	62	a	a	DET
ejpam-4506	320	63	⊆	⊆	NUM
ejpam-4506	320	64	v	v	NOUN
ejpam-4506	320	65	(	(	PUNCT
ejpam-4506	320	66	k	k	NOUN
ejpam-4506	320	67	)	)	PUNCT
ejpam-4506	320	68	and	and	CCONJ
ejpam-4506	320	69	a	a	DET
ejpam-4506	320	70	∈	∈	NOUN
ejpam-4506	320	71	ωk	ωk	ADP
ejpam-4506	320	72	and	and	CCONJ
ejpam-4506	320	73	for	for	ADP
ejpam-4506	320	74	all	all	DET
ejpam-4506	320	75	suv	suv	PROPN
ejpam-4506	320	76	⊆	⊆	NUM
ejpam-4506	320	77	v	v	NOUN
ejpam-4506	320	78	(	(	PUNCT
ejpam-4506	320	79	huv	huv	PROPN
ejpam-4506	320	80	)	)	PUNCT
ejpam-4506	320	81	,	,	PUNCT
ejpam-4506	320	82	suv	suv	PROPN
ejpam-4506	320	83	∈	∈	PROPN
ejpam-4506	320	84	ωhuv	ωhuv	NOUN
ejpam-4506	320	85	for	for	ADP
ejpam-4506	320	86	each	each	DET
ejpam-4506	320	87	uv	uv	NOUN
ejpam-4506	320	88	∈	∈	PROPN
ejpam-4506	320	89	e(k	e(k	NOUN
ejpam-4506	320	90	)	)	PUNCT
ejpam-4506	320	91	.	.	PUNCT
ejpam-4506	321	1	note	note	VERB
ejpam-4506	321	2	that	that	SCONJ
ejpam-4506	321	3	the	the	DET
ejpam-4506	321	4	minimum	minimum	ADJ
ejpam-4506	321	5	cardinality	cardinality	NOUN
ejpam-4506	321	6	of	of	ADP
ejpam-4506	321	7	s	s	PROPN
ejpam-4506	321	8	is	be	AUX
ejpam-4506	321	9	obtained	obtain	VERB
ejpam-4506	321	10	when	when	SCONJ
ejpam-4506	321	11	each	each	DET
ejpam-4506	321	12	|suv|	|suv|	PROPN
ejpam-4506	321	13	and	and	CCONJ
ejpam-4506	321	14	|sk	|sk	NUM
ejpam-4506	321	15	|	|	ADV
ejpam-4506	321	16	are	be	AUX
ejpam-4506	321	17	minimum	minimum	ADJ
ejpam-4506	321	18	in	in	ADP
ejpam-4506	321	19	ωhuv	ωhuv	NOUN
ejpam-4506	321	20	and	and	CCONJ
ejpam-4506	321	21	ωk	ωk	ADP
ejpam-4506	321	22	,	,	PUNCT
ejpam-4506	321	23	respectively	respectively	ADV
ejpam-4506	321	24	.	.	PUNCT
ejpam-4506	322	1	that	that	PRON
ejpam-4506	322	2	is	be	AUX
ejpam-4506	322	3	,	,	PUNCT
ejpam-4506	322	4	γpicg(g	γpicg(g	NOUN
ejpam-4506	322	5	)	)	PUNCT
ejpam-4506	322	6	=	=	SYM
ejpam-4506	322	7	⋃	⋃	NOUN
ejpam-4506	322	8	uv∈e(k	uv∈e(k	NOUN
ejpam-4506	322	9	)	)	PUNCT
ejpam-4506	322	10	min{|suv|	min{|suv|	NOUN
ejpam-4506	322	11	:	:	PUNCT
ejpam-4506	322	12	suv	suv	PROPN
ejpam-4506	322	13	∈	∈	PROPN
ejpam-4506	323	1	ωhuv}+min{|sk	ωhuv}+min{|sk	PROPN
ejpam-4506	323	2	|	|	ADV
ejpam-4506	323	3	:	:	PUNCT
ejpam-4506	323	4	sk	sk	VERB
ejpam-4506	323	5	∈	∈	PROPN
ejpam-4506	323	6	ωk	ωk	ADP
ejpam-4506	323	7	}	}	PUNCT
ejpam-4506	323	8	.	.	PUNCT
ejpam-4506	324	1	since	since	SCONJ
ejpam-4506	324	2	all	all	DET
ejpam-4506	324	3	⟨suv⟩	⟨suv⟩	NOUN
ejpam-4506	324	4	are	be	AUX
ejpam-4506	324	5	just	just	ADV
ejpam-4506	324	6	copies	copy	NOUN
ejpam-4506	324	7	of	of	ADP
ejpam-4506	324	8	the	the	DET
ejpam-4506	324	9	graph	graph	NOUN
ejpam-4506	324	10	h	h	NOUN
ejpam-4506	324	11	,	,	PUNCT
ejpam-4506	324	12	it	it	PRON
ejpam-4506	324	13	follows	follow	VERB
ejpam-4506	324	14	that	that	SCONJ
ejpam-4506	324	15	min{|suv|	min{|suv|	PROPN
ejpam-4506	324	16	:	:	PUNCT
ejpam-4506	324	17	suv	suv	PROPN
ejpam-4506	324	18	∈	∈	PROPN
ejpam-4506	324	19	ωhuv	ωhuv	PROPN
ejpam-4506	324	20	}	}	PUNCT
ejpam-4506	324	21	=	=	SYM
ejpam-4506	324	22	min{|sh	min{|sh	ADJ
ejpam-4506	325	1	|	|	ADV
ejpam-4506	325	2	:	:	PUNCT
ejpam-4506	325	3	sh	sh	PROPN
ejpam-4506	325	4	∈	∈	PROPN
ejpam-4506	325	5	ωh	ωh	PROPN
ejpam-4506	325	6	}	}	PUNCT
ejpam-4506	325	7	.	.	PUNCT
ejpam-4506	326	1	therefore	therefore	ADV
ejpam-4506	326	2	,	,	PUNCT
ejpam-4506	326	3	γpicg(g	γpicg(g	NOUN
ejpam-4506	326	4	)	)	PUNCT
ejpam-4506	326	5	=	=	SYM
ejpam-4506	326	6	n	n	PROPN
ejpam-4506	326	7	·	·	PUNCT
ejpam-4506	326	8	min{|sh	min{|sh	ADJ
ejpam-4506	327	1	|	|	ADV
ejpam-4506	327	2	:	:	PUNCT
ejpam-4506	327	3	sh	sh	PROPN
ejpam-4506	327	4	∈	∈	PROPN
ejpam-4506	327	5	ωh}+min{|sk	ωh}+min{|sk	NOUN
ejpam-4506	328	1	|	|	ADV
ejpam-4506	328	2	:	:	PUNCT
ejpam-4506	328	3	sk	sk	VERB
ejpam-4506	328	4	∈	∈	PROPN
ejpam-4506	328	5	ωk	ωk	ADP
ejpam-4506	328	6	}	}	PUNCT
ejpam-4506	328	7	.	.	PUNCT
ejpam-4506	329	1	■	■	PUNCT
ejpam-4506	329	2	corollary	corollary	ADJ
ejpam-4506	329	3	2	2	NUM
ejpam-4506	329	4	.	.	PUNCT
ejpam-4506	330	1	let	let	VERB
ejpam-4506	330	2	m	m	PRON
ejpam-4506	330	3	,	,	PUNCT
ejpam-4506	330	4	n	n	PRON
ejpam-4506	330	5	≥	≥	NOUN
ejpam-4506	330	6	3	3	NUM
ejpam-4506	330	7	be	be	AUX
ejpam-4506	330	8	natural	natural	ADJ
ejpam-4506	330	9	numbers	number	NOUN
ejpam-4506	330	10	.	.	PUNCT
ejpam-4506	331	1	then	then	ADV
ejpam-4506	331	2	γpicg(pn	γpicg(pn	ADJ
ejpam-4506	331	3	⋄km	⋄km	NOUN
ejpam-4506	331	4	)	)	PUNCT
ejpam-4506	331	5	=	=	PUNCT
ejpam-4506	332	1	(	(	PUNCT
ejpam-4506	332	2	n−	n−	NOUN
ejpam-4506	332	3	1)m+	1)m+	NUM
ejpam-4506	332	4	n.	n.	NOUN
ejpam-4506	332	5	proof	proof	NOUN
ejpam-4506	332	6	:	:	PUNCT
ejpam-4506	332	7	note	note	VERB
ejpam-4506	332	8	that	that	SCONJ
ejpam-4506	332	9	ωpn	ωpn	VERB
ejpam-4506	332	10	=	=	SYM
ejpam-4506	332	11	{	{	PUNCT
ejpam-4506	332	12	v	v	NOUN
ejpam-4506	332	13	(	(	PUNCT
ejpam-4506	332	14	pn	pn	NOUN
ejpam-4506	332	15	)	)	PUNCT
ejpam-4506	332	16	}	}	PUNCT
ejpam-4506	332	17	,	,	PUNCT
ejpam-4506	332	18	|e(pn)|	|e(pn)|	VERB
ejpam-4506	332	19	=	=	SYM
ejpam-4506	332	20	n	n	CCONJ
ejpam-4506	332	21	−	−	PROPN
ejpam-4506	332	22	1	1	NUM
ejpam-4506	332	23	and	and	CCONJ
ejpam-4506	332	24	ωkm	ωkm	NOUN
ejpam-4506	332	25	=	=	SYM
ejpam-4506	332	26	{	{	PUNCT
ejpam-4506	332	27	v	v	NOUN
ejpam-4506	332	28	(	(	PUNCT
ejpam-4506	332	29	km	km	NOUN
ejpam-4506	332	30	)	)	PUNCT
ejpam-4506	332	31	}	}	PUNCT
ejpam-4506	332	32	for	for	ADP
ejpam-4506	332	33	all	all	DET
ejpam-4506	332	34	m	m	PROPN
ejpam-4506	332	35	,	,	PUNCT
ejpam-4506	332	36	n	n	PRON
ejpam-4506	332	37	≥	≥	NOUN
ejpam-4506	332	38	1	1	NUM
ejpam-4506	332	39	.	.	PUNCT
ejpam-4506	332	40	then	then	ADV
ejpam-4506	332	41	by	by	ADP
ejpam-4506	332	42	theorem	theorem	NOUN
ejpam-4506	332	43	14	14	NUM
ejpam-4506	332	44	,	,	PUNCT
ejpam-4506	332	45	γpicg(pn	γpicg(pn	ADJ
ejpam-4506	332	46	⋄km	⋄km	NOUN
ejpam-4506	332	47	)	)	PUNCT
ejpam-4506	332	48	=	=	PRON
ejpam-4506	332	49	|e(pn)|	|e(pn)|	X
ejpam-4506	332	50	·	·	PUNCT
ejpam-4506	332	51	min{|skm	min{|skm	VERB
ejpam-4506	332	52	|	|	ADV
ejpam-4506	332	53	:	:	PUNCT
ejpam-4506	332	54	skm	skm	PROPN
ejpam-4506	332	55	∈	∈	PROPN
ejpam-4506	332	56	ωkm}+min{|spn	ωkm}+min{|spn	NUM
ejpam-4506	332	57	|	|	ADV
ejpam-4506	332	58	:	:	PUNCT
ejpam-4506	332	59	spn	spn	PROPN
ejpam-4506	332	60	∈	∈	PROPN
ejpam-4506	332	61	ωpn	ωpn	NOUN
ejpam-4506	332	62	}	}	PUNCT
ejpam-4506	332	63	=	=	SYM
ejpam-4506	332	64	(	(	PUNCT
ejpam-4506	332	65	n−	n−	NOUN
ejpam-4506	332	66	1	1	NUM
ejpam-4506	332	67	)	)	PUNCT
ejpam-4506	332	68	·	·	PUNCT
ejpam-4506	332	69	min{|skm	min{|skm	VERB
ejpam-4506	332	70	|	|	ADV
ejpam-4506	332	71	:	:	PUNCT
ejpam-4506	332	72	s	s	AUX
ejpam-4506	332	73	∈	∈	NOUN
ejpam-4506	332	74	ωkm}+	ωkm}+	PROPN
ejpam-4506	332	75	n	n	NOUN
ejpam-4506	332	76	=	=	PUNCT
ejpam-4506	332	77	(	(	PUNCT
ejpam-4506	332	78	n−	n−	NOUN
ejpam-4506	332	79	1	1	NUM
ejpam-4506	332	80	)	)	PUNCT
ejpam-4506	332	81	·	·	PUNCT
ejpam-4506	332	82	m+	m+	NUM
ejpam-4506	332	83	n.	n.	NOUN
ejpam-4506	332	84	■	■	PUNCT
ejpam-4506	332	85	theorem	theorem	ADJ
ejpam-4506	332	86	15	15	NUM
ejpam-4506	332	87	.	.	PUNCT
ejpam-4506	333	1	let	let	VERB
ejpam-4506	333	2	g	g	PROPN
ejpam-4506	333	3	=	=	SYM
ejpam-4506	333	4	k2	k2	PROPN
ejpam-4506	333	5	⋄	⋄	PROPN
ejpam-4506	333	6	h	h	NOUN
ejpam-4506	333	7	where	where	SCONJ
ejpam-4506	333	8	h	h	NOUN
ejpam-4506	333	9	is	be	AUX
ejpam-4506	333	10	any	any	DET
ejpam-4506	333	11	graph	graph	NOUN
ejpam-4506	333	12	that	that	PRON
ejpam-4506	333	13	admits	admit	VERB
ejpam-4506	333	14	s	s	PROPN
ejpam-4506	333	15	∈	∈	NOUN
ejpam-4506	333	16	ωh	ωh	ADP
ejpam-4506	333	17	with	with	ADP
ejpam-4506	333	18	|v	|v	PROPN
ejpam-4506	333	19	(	(	PUNCT
ejpam-4506	333	20	h)|	h)|	NOUN
ejpam-4506	333	21	=	=	SYM
ejpam-4506	333	22	n	n	NOUN
ejpam-4506	333	23	≥	≥	NOUN
ejpam-4506	333	24	3	3	NUM
ejpam-4506	333	25	and	and	CCONJ
ejpam-4506	333	26	diam(h	diam(h	ADJ
ejpam-4506	333	27	)	)	PUNCT
ejpam-4506	333	28	≥	≥	NOUN
ejpam-4506	333	29	2	2	NUM
ejpam-4506	333	30	.	.	PUNCT
ejpam-4506	334	1	then	then	ADV
ejpam-4506	334	2	γpicg(g	γpicg(g	NUM
ejpam-4506	334	3	)	)	PUNCT
ejpam-4506	334	4	=	=	SYM
ejpam-4506	334	5	γpicg(h	γpicg(h	NUM
ejpam-4506	334	6	)	)	PUNCT
ejpam-4506	334	7	.	.	PUNCT
ejpam-4506	335	1	proof	proof	NOUN
ejpam-4506	335	2	:	:	PUNCT
ejpam-4506	335	3	let	let	VERB
ejpam-4506	335	4	g	g	NOUN
ejpam-4506	335	5	=	=	VERB
ejpam-4506	335	6	k2⋄h	k2⋄h	NOUN
ejpam-4506	335	7	where	where	SCONJ
ejpam-4506	335	8	h	h	NOUN
ejpam-4506	335	9	is	be	AUX
ejpam-4506	335	10	any	any	DET
ejpam-4506	335	11	graph	graph	NOUN
ejpam-4506	335	12	that	that	PRON
ejpam-4506	335	13	admits	admit	VERB
ejpam-4506	335	14	s	s	PROPN
ejpam-4506	335	15	∈	∈	NOUN
ejpam-4506	335	16	ωh	ωh	ADP
ejpam-4506	335	17	with	with	ADP
ejpam-4506	335	18	|v	|v	PROPN
ejpam-4506	335	19	(	(	PUNCT
ejpam-4506	335	20	h)|	h)|	NOUN
ejpam-4506	335	21	=	=	SYM
ejpam-4506	335	22	n	n	NOUN
ejpam-4506	335	23	≥	≥	NOUN
ejpam-4506	335	24	3	3	NUM
ejpam-4506	335	25	and	and	CCONJ
ejpam-4506	335	26	diam(h	diam(h	ADJ
ejpam-4506	335	27	)	)	PUNCT
ejpam-4506	335	28	≥	≥	NOUN
ejpam-4506	335	29	2	2	NUM
ejpam-4506	335	30	.	.	PUNCT
ejpam-4506	336	1	then	then	ADV
ejpam-4506	336	2	,	,	PUNCT
ejpam-4506	336	3	by	by	ADP
ejpam-4506	336	4	remark	remark	NOUN
ejpam-4506	336	5	9	9	NUM
ejpam-4506	336	6	,	,	PUNCT
ejpam-4506	336	7	g	g	PROPN
ejpam-4506	336	8	=	=	SYM
ejpam-4506	336	9	k2	k2	NOUN
ejpam-4506	336	10	⋄h	⋄h	NOUN
ejpam-4506	336	11	=	=	PUNCT
ejpam-4506	336	12	k2+h	k2+h	PROPN
ejpam-4506	336	13	.	.	PUNCT
ejpam-4506	336	14	now	now	ADV
ejpam-4506	336	15	,	,	PUNCT
ejpam-4506	336	16	we	we	PRON
ejpam-4506	336	17	let	let	VERB
ejpam-4506	336	18	u	u	PRON
ejpam-4506	336	19	,	,	PUNCT
ejpam-4506	336	20	v	v	PROPN
ejpam-4506	336	21	∈	∈	PROPN
ejpam-4506	336	22	v	v	NOUN
ejpam-4506	336	23	(	(	PUNCT
ejpam-4506	336	24	k2	k2	NOUN
ejpam-4506	336	25	)	)	PUNCT
ejpam-4506	336	26	.	.	PUNCT
ejpam-4506	337	1	by	by	ADP
ejpam-4506	337	2	definition	definition	NOUN
ejpam-4506	337	3	7	7	NUM
ejpam-4506	337	4	,	,	PUNCT
ejpam-4506	337	5	all	all	DET
ejpam-4506	337	6	vertices	vertex	NOUN
ejpam-4506	337	7	of	of	ADP
ejpam-4506	337	8	h	h	NOUN
ejpam-4506	337	9	are	be	AUX
ejpam-4506	337	10	joined	join	VERB
ejpam-4506	337	11	to	to	ADP
ejpam-4506	337	12	u	u	PROPN
ejpam-4506	337	13	and	and	CCONJ
ejpam-4506	337	14	v.	v.	ADP
ejpam-4506	337	15	since	since	SCONJ
ejpam-4506	337	16	diam(h	diam(h	PROPN
ejpam-4506	337	17	)	)	PUNCT
ejpam-4506	337	18	≥	≥	NOUN
ejpam-4506	337	19	2	2	NUM
ejpam-4506	337	20	,	,	PUNCT
ejpam-4506	337	21	for	for	SCONJ
ejpam-4506	337	22	any	any	DET
ejpam-4506	337	23	non	non	ADJ
ejpam-4506	337	24	adjacent	adjacent	NOUN
ejpam-4506	337	25	x	x	NOUN
ejpam-4506	337	26	,	,	PUNCT
ejpam-4506	337	27	y	y	PROPN
ejpam-4506	337	28	∈	∈	PROPN
ejpam-4506	337	29	s	s	PROPN
ejpam-4506	337	30	,	,	PUNCT
ejpam-4506	337	31	u	u	NOUN
ejpam-4506	337	32	and	and	CCONJ
ejpam-4506	337	33	v	v	NUM
ejpam-4506	337	34	lie	lie	NOUN
ejpam-4506	337	35	in	in	ADP
ejpam-4506	337	36	some	some	DET
ejpam-4506	337	37	x	x	NOUN
ejpam-4506	337	38	-	-	NOUN
ejpam-4506	337	39	y	y	ADJ
ejpam-4506	337	40	geodesic	geodesic	NOUN
ejpam-4506	337	41	.	.	PUNCT
ejpam-4506	338	1	hence	hence	ADV
ejpam-4506	338	2	,	,	PUNCT
ejpam-4506	338	3	ig[s	ig[s	PROPN
ejpam-4506	338	4	]	]	PUNCT
ejpam-4506	338	5	=	=	SYM
ejpam-4506	338	6	v	v	X
ejpam-4506	338	7	(	(	PUNCT
ejpam-4506	338	8	g	g	NOUN
ejpam-4506	338	9	)	)	PUNCT
ejpam-4506	338	10	.	.	PUNCT
ejpam-4506	339	1	note	note	VERB
ejpam-4506	339	2	that	that	SCONJ
ejpam-4506	339	3	s	s	VERB
ejpam-4506	339	4	∈	∈	NOUN
ejpam-4506	340	1	ωh	ωh	X
ejpam-4506	341	1	and	and	CCONJ
ejpam-4506	341	2	so	so	ADV
ejpam-4506	341	3	⟨s⟩	⟨s⟩	PROPN
ejpam-4506	341	4	contains	contain	VERB
ejpam-4506	341	5	a	a	DET
ejpam-4506	341	6	hamiltonian	hamiltonian	ADJ
ejpam-4506	341	7	path	path	NOUN
ejpam-4506	341	8	and	and	CCONJ
ejpam-4506	341	9	s	s	VERB
ejpam-4506	341	10	is	be	AUX
ejpam-4506	341	11	a	a	DET
ejpam-4506	341	12	2	2	NUM
ejpam-4506	341	13	-	-	PUNCT
ejpam-4506	341	14	path	path	NOUN
ejpam-4506	341	15	closure	closure	NOUN
ejpam-4506	341	16	absorbing	absorbing	NOUN
ejpam-4506	341	17	of	of	ADP
ejpam-4506	341	18	h.	h.	PROPN
ejpam-4506	341	19	hence	hence	ADV
ejpam-4506	341	20	,	,	PUNCT
ejpam-4506	341	21	by	by	ADP
ejpam-4506	341	22	definition	definition	NOUN
ejpam-4506	341	23	8	8	NUM
ejpam-4506	341	24	,	,	PUNCT
ejpam-4506	341	25	for	for	ADP
ejpam-4506	341	26	any	any	DET
ejpam-4506	341	27	a	a	DET
ejpam-4506	341	28	∈	∈	PROPN
ejpam-4506	341	29	v	v	NOUN
ejpam-4506	341	30	(	(	PUNCT
ejpam-4506	341	31	h)∖	h)∖	PROPN
ejpam-4506	341	32	s	s	PROPN
ejpam-4506	341	33	,	,	PUNCT
ejpam-4506	341	34	a	a	PRON
ejpam-4506	341	35	is	be	AUX
ejpam-4506	341	36	adjacent	adjacent	ADJ
ejpam-4506	341	37	to	to	ADP
ejpam-4506	341	38	at	at	ADV
ejpam-4506	341	39	least	least	ADV
ejpam-4506	341	40	two	two	NUM
ejpam-4506	341	41	vertices	vertex	NOUN
ejpam-4506	341	42	of	of	ADP
ejpam-4506	341	43	s.	s.	PROPN
ejpam-4506	341	44	it	it	PRON
ejpam-4506	341	45	follows	follow	VERB
ejpam-4506	341	46	that	that	SCONJ
ejpam-4506	341	47	s	s	VERB
ejpam-4506	341	48	is	be	AUX
ejpam-4506	341	49	a	a	DET
ejpam-4506	341	50	dominating	dominating	NOUN
ejpam-4506	341	51	set	set	NOUN
ejpam-4506	341	52	of	of	ADP
ejpam-4506	341	53	h	h	NOUN
ejpam-4506	342	1	and	and	CCONJ
ejpam-4506	342	2	so	so	ADV
ejpam-4506	342	3	s	s	VERB
ejpam-4506	342	4	is	be	AUX
ejpam-4506	342	5	a	a	DET
ejpam-4506	342	6	dominating	dominating	NOUN
ejpam-4506	342	7	set	set	NOUN
ejpam-4506	342	8	of	of	ADP
ejpam-4506	342	9	g.	g.	PROPN
ejpam-4506	342	10	therefore	therefore	ADV
ejpam-4506	342	11	,	,	PUNCT
ejpam-4506	342	12	γpicg(g	γpicg(g	NOUN
ejpam-4506	342	13	)	)	PUNCT
ejpam-4506	342	14	=	=	SYM
ejpam-4506	342	15	s	s	PART
ejpam-4506	342	16	=	=	SYM
ejpam-4506	342	17	γpicg(h	γpicg(h	NOUN
ejpam-4506	342	18	)	)	PUNCT
ejpam-4506	342	19	.	.	PUNCT
ejpam-4506	343	1	■	■	PUNCT
ejpam-4506	343	2	corollary	corollary	ADJ
ejpam-4506	343	3	3	3	X
ejpam-4506	343	4	.	.	PUNCT
ejpam-4506	343	5	for	for	ADP
ejpam-4506	343	6	all	all	DET
ejpam-4506	343	7	integers	integer	NOUN
ejpam-4506	343	8	n	n	PRON
ejpam-4506	343	9	≥	≥	NUM
ejpam-4506	343	10	3	3	NUM
ejpam-4506	343	11	,	,	PUNCT
ejpam-4506	343	12	γpicg(k2	γpicg(k2	VERB
ejpam-4506	343	13	⋄	⋄	PROPN
ejpam-4506	343	14	pn	pn	PROPN
ejpam-4506	343	15	)	)	PUNCT
ejpam-4506	344	1	=	=	VERB
ejpam-4506	344	2	n.	n.	NOUN
ejpam-4506	344	3	references	reference	VERB
ejpam-4506	344	4	179	179	NUM
ejpam-4506	344	5	proof	proof	NOUN
ejpam-4506	344	6	:	:	PUNCT
ejpam-4506	344	7	note	note	VERB
ejpam-4506	344	8	that	that	SCONJ
ejpam-4506	344	9	ωpn	ωpn	VERB
ejpam-4506	344	10	=	=	SYM
ejpam-4506	344	11	{	{	PUNCT
ejpam-4506	344	12	v	v	NOUN
ejpam-4506	344	13	(	(	PUNCT
ejpam-4506	344	14	pn	pn	NOUN
ejpam-4506	344	15	)	)	PUNCT
ejpam-4506	344	16	}	}	PUNCT
ejpam-4506	344	17	,	,	PUNCT
ejpam-4506	344	18	for	for	ADP
ejpam-4506	344	19	all	all	DET
ejpam-4506	344	20	integers	integer	NOUN
ejpam-4506	344	21	n	n	PRON
ejpam-4506	344	22	≥	≥	NOUN
ejpam-4506	344	23	1	1	NUM
ejpam-4506	344	24	.	.	PUNCT
ejpam-4506	344	25	hence	hence	ADV
ejpam-4506	344	26	,	,	PUNCT
ejpam-4506	344	27	by	by	ADP
ejpam-4506	344	28	theorem	theorem	NOUN
ejpam-4506	344	29	15	15	NUM
ejpam-4506	344	30	,	,	PUNCT
ejpam-4506	344	31	γpicg(k2	γpicg(k2	VERB
ejpam-4506	344	32	⋄	⋄	PROPN
ejpam-4506	344	33	pn	pn	PROPN
ejpam-4506	344	34	)	)	PUNCT
ejpam-4506	345	1	=	=	NOUN
ejpam-4506	345	2	γpicg(pn	γpicg(pn	ADJ
ejpam-4506	345	3	)	)	PUNCT
ejpam-4506	345	4	=	=	NOUN
ejpam-4506	345	5	|v	|v	X
ejpam-4506	345	6	(	(	PUNCT
ejpam-4506	345	7	pn)|	pn)|	PROPN
ejpam-4506	345	8	=	=	PROPN
ejpam-4506	345	9	n.	n.	NOUN
ejpam-4506	345	10	■	■	PUNCT
ejpam-4506	345	11	corollary	corollary	ADJ
ejpam-4506	345	12	4	4	NUM
ejpam-4506	345	13	.	.	PUNCT
ejpam-4506	346	1	let	let	VERB
ejpam-4506	346	2	h	h	PRON
ejpam-4506	346	3	be	be	AUX
ejpam-4506	346	4	a	a	DET
ejpam-4506	346	5	graph	graph	NOUN
ejpam-4506	346	6	that	that	PRON
ejpam-4506	346	7	has	have	VERB
ejpam-4506	346	8	a	a	DET
ejpam-4506	346	9	path	path	NOUN
ejpam-4506	346	10	-	-	PUNCT
ejpam-4506	346	11	induced	induce	VERB
ejpam-4506	346	12	closed	closed	ADJ
ejpam-4506	346	13	geodetic	geodetic	ADJ
ejpam-4506	346	14	dominating	dominating	NOUN
ejpam-4506	346	15	set	set	NOUN
ejpam-4506	346	16	.	.	PUNCT
ejpam-4506	347	1	if	if	SCONJ
ejpam-4506	347	2	diam(h	diam(h	ADJ
ejpam-4506	347	3	)	)	PUNCT
ejpam-4506	347	4	=	=	SYM
ejpam-4506	347	5	2	2	NUM
ejpam-4506	347	6	,	,	PUNCT
ejpam-4506	347	7	then	then	ADV
ejpam-4506	347	8	γpicg(k2	γpicg(k2	VERB
ejpam-4506	347	9	⋄h	⋄h	PROPN
ejpam-4506	347	10	)	)	PUNCT
ejpam-4506	348	1	=	=	PUNCT
ejpam-4506	348	2	γpicg(h	γpicg(h	NOUN
ejpam-4506	348	3	)	)	PUNCT
ejpam-4506	348	4	.	.	PUNCT
ejpam-4506	349	1	proof	proof	NOUN
ejpam-4506	349	2	:	:	PUNCT
ejpam-4506	349	3	let	let	VERB
ejpam-4506	349	4	s	s	PRON
ejpam-4506	349	5	be	be	AUX
ejpam-4506	349	6	a	a	DET
ejpam-4506	349	7	path	path	NOUN
ejpam-4506	349	8	-	-	PUNCT
ejpam-4506	349	9	induced	induce	VERB
ejpam-4506	349	10	closed	closed	ADJ
ejpam-4506	349	11	geodetic	geodetic	ADJ
ejpam-4506	349	12	dominating	dominating	NOUN
ejpam-4506	349	13	set	set	NOUN
ejpam-4506	349	14	of	of	ADP
ejpam-4506	349	15	h	h	PRON
ejpam-4506	349	16	where	where	SCONJ
ejpam-4506	349	17	diam(h	diam(h	ADJ
ejpam-4506	349	18	)	)	PUNCT
ejpam-4506	349	19	=	=	SYM
ejpam-4506	349	20	2	2	X
ejpam-4506	349	21	.	.	X
ejpam-4506	349	22	that	that	PRON
ejpam-4506	349	23	is	be	AUX
ejpam-4506	349	24	,	,	PUNCT
ejpam-4506	349	25	for	for	ADP
ejpam-4506	349	26	every	every	DET
ejpam-4506	349	27	u	u	NOUN
ejpam-4506	349	28	,	,	PUNCT
ejpam-4506	349	29	v	v	PROPN
ejpam-4506	349	30	∈	∈	PROPN
ejpam-4506	349	31	v	v	NOUN
ejpam-4506	349	32	(	(	PUNCT
ejpam-4506	349	33	h	h	NOUN
ejpam-4506	349	34	)	)	PUNCT
ejpam-4506	349	35	,	,	PUNCT
ejpam-4506	349	36	dh(u	dh(u	PROPN
ejpam-4506	349	37	,	,	PUNCT
ejpam-4506	349	38	v	v	NOUN
ejpam-4506	349	39	)	)	PUNCT
ejpam-4506	349	40	≤	≤	NOUN
ejpam-4506	349	41	2	2	NUM
ejpam-4506	349	42	.	.	PUNCT
ejpam-4506	350	1	thus	thus	ADV
ejpam-4506	350	2	,	,	PUNCT
ejpam-4506	350	3	p2[s]h	p2[s]h	PROPN
ejpam-4506	350	4	=	=	PUNCT
ejpam-4506	350	5	v	v	PROPN
ejpam-4506	350	6	(	(	PUNCT
ejpam-4506	350	7	h	h	NOUN
ejpam-4506	350	8	)	)	PUNCT
ejpam-4506	350	9	.	.	PUNCT
ejpam-4506	351	1	this	this	PRON
ejpam-4506	351	2	means	mean	VERB
ejpam-4506	351	3	that	that	SCONJ
ejpam-4506	351	4	s	s	VERB
ejpam-4506	351	5	∈	∈	NOUN
ejpam-4506	351	6	ωh	ωh	X
ejpam-4506	351	7	is	be	AUX
ejpam-4506	351	8	with	with	ADP
ejpam-4506	351	9	minimum	minimum	ADJ
ejpam-4506	351	10	cardinality	cardinality	NOUN
ejpam-4506	351	11	.	.	PUNCT
ejpam-4506	352	1	therefore	therefore	ADV
ejpam-4506	352	2	,	,	PUNCT
ejpam-4506	352	3	by	by	ADP
ejpam-4506	352	4	theorem	theorem	NOUN
ejpam-4506	352	5	15	15	NUM
ejpam-4506	352	6	,	,	PUNCT
ejpam-4506	352	7	γpicg(k2	γpicg(k2	VERB
ejpam-4506	352	8	⋄h	⋄h	PROPN
ejpam-4506	352	9	)	)	PUNCT
ejpam-4506	352	10	=	=	SYM
ejpam-4506	352	11	|s|	|s|	PROPN
ejpam-4506	352	12	=	=	PUNCT
ejpam-4506	352	13	γpicg(h	γpicg(h	NOUN
ejpam-4506	352	14	)	)	PUNCT
ejpam-4506	352	15	.	.	PUNCT
ejpam-4506	353	1	■	■	PUNCT
ejpam-4506	353	2	example	example	NOUN
ejpam-4506	354	1	3	3	X
ejpam-4506	354	2	.	.	PUNCT
ejpam-4506	355	1	since	since	SCONJ
ejpam-4506	355	2	diam(fn	diam(fn	NOUN
ejpam-4506	355	3	)	)	PUNCT
ejpam-4506	355	4	=	=	SYM
ejpam-4506	355	5	2	2	NUM
ejpam-4506	355	6	for	for	ADP
ejpam-4506	355	7	all	all	DET
ejpam-4506	355	8	n	n	PRON
ejpam-4506	355	9	≥	≥	NOUN
ejpam-4506	355	10	3	3	NUM
ejpam-4506	355	11	and	and	CCONJ
ejpam-4506	355	12	diam(wm	diam(wm	NOUN
ejpam-4506	355	13	)	)	PUNCT
ejpam-4506	355	14	=	=	SYM
ejpam-4506	355	15	2	2	NUM
ejpam-4506	355	16	for	for	ADP
ejpam-4506	355	17	all	all	DET
ejpam-4506	355	18	m	m	PROPN
ejpam-4506	355	19	≥	≥	NOUN
ejpam-4506	355	20	4	4	NUM
ejpam-4506	355	21	,	,	PUNCT
ejpam-4506	355	22	by	by	ADP
ejpam-4506	355	23	corollary	corollary	ADJ
ejpam-4506	355	24	4	4	NUM
ejpam-4506	355	25	,	,	PUNCT
ejpam-4506	355	26	we	we	PRON
ejpam-4506	355	27	have	have	VERB
ejpam-4506	355	28	the	the	DET
ejpam-4506	355	29	following	following	NOUN
ejpam-4506	355	30	:	:	PUNCT
ejpam-4506	355	31	(	(	PUNCT
ejpam-4506	355	32	i	i	NOUN
ejpam-4506	355	33	)	)	PUNCT
ejpam-4506	355	34	γpicg(k2	γpicg(k2	VERB
ejpam-4506	355	35	⋄	⋄	PROPN
ejpam-4506	355	36	fn	fn	NOUN
ejpam-4506	355	37	)	)	PUNCT
ejpam-4506	355	38	=	=	SYM
ejpam-4506	355	39	n	n	CCONJ
ejpam-4506	355	40	,	,	PUNCT
ejpam-4506	355	41	for	for	ADP
ejpam-4506	355	42	all	all	DET
ejpam-4506	355	43	n	n	PRON
ejpam-4506	355	44	≥	≥	NOUN
ejpam-4506	355	45	3	3	NUM
ejpam-4506	355	46	.	.	PUNCT
ejpam-4506	355	47	(	(	PUNCT
ejpam-4506	355	48	ii	ii	NOUN
ejpam-4506	355	49	)	)	PUNCT
ejpam-4506	355	50	γpicg(k2	γpicg(k2	VERB
ejpam-4506	355	51	⋄wm	⋄wm	PRON
ejpam-4506	355	52	)	)	PUNCT
ejpam-4506	356	1	=	=	SYM
ejpam-4506	356	2	m	m	PROPN
ejpam-4506	356	3	,	,	PUNCT
ejpam-4506	356	4	for	for	ADP
ejpam-4506	356	5	all	all	DET
ejpam-4506	356	6	m	m	PROPN
ejpam-4506	356	7	≥	≥	NOUN
ejpam-4506	356	8	4	4	NUM
ejpam-4506	356	9	.	.	PUNCT
ejpam-4506	356	10	acknowledgements	acknowledgement	NOUN
ejpam-4506	356	11	this	this	DET
ejpam-4506	356	12	research	research	NOUN
ejpam-4506	356	13	is	be	AUX
ejpam-4506	356	14	funded	fund	VERB
ejpam-4506	356	15	by	by	ADP
ejpam-4506	356	16	the	the	DET
ejpam-4506	356	17	department	department	PROPN
ejpam-4506	356	18	of	of	ADP
ejpam-4506	356	19	science	science	NOUN
ejpam-4506	356	20	and	and	CCONJ
ejpam-4506	356	21	technology	technology	NOUN
ejpam-4506	356	22	accelerated	accelerate	VERB
ejpam-4506	356	23	science	science	NOUN
ejpam-4506	356	24	and	and	CCONJ
ejpam-4506	356	25	technology	technology	NOUN
ejpam-4506	356	26	human	human	ADJ
ejpam-4506	356	27	resource	resource	NOUN
ejpam-4506	356	28	development	development	NOUN
ejpam-4506	356	29	program	program	NOUN
ejpam-4506	356	30	(	(	PUNCT
ejpam-4506	356	31	dost	dost	NOUN
ejpam-4506	356	32	-	-	PUNCT
ejpam-4506	356	33	asthrdp	asthrdp	NOUN
ejpam-4506	356	34	)	)	PUNCT
ejpam-4506	356	35	,	,	PUNCT
ejpam-4506	356	36	philippines	philippine	NOUN
ejpam-4506	356	37	.	.	PUNCT
ejpam-4506	357	1	references	reference	NOUN
ejpam-4506	357	2	[	[	X
ejpam-4506	357	3	1	1	NUM
ejpam-4506	357	4	]	]	PUNCT
ejpam-4506	357	5	i.	i.	PROPN
ejpam-4506	357	6	s.	s.	PROPN
ejpam-4506	357	7	aniversario	aniversario	PROPN
ejpam-4506	357	8	,	,	PUNCT
ejpam-4506	357	9	f.	f.	PROPN
ejpam-4506	357	10	p.	p.	PROPN
ejpam-4506	357	11	jamil	jamil	PROPN
ejpam-4506	357	12	,	,	PUNCT
ejpam-4506	357	13	and	and	CCONJ
ejpam-4506	357	14	s.	s.	PROPN
ejpam-4506	357	15	r.	r.	PROPN
ejpam-4506	357	16	canoy	canoy	PROPN
ejpam-4506	357	17	jr	jr	PROPN
ejpam-4506	357	18	.	.	PUNCT
ejpam-4506	358	1	the	the	DET
ejpam-4506	358	2	closed	closed	ADJ
ejpam-4506	358	3	geodetic	geodetic	ADJ
ejpam-4506	358	4	numbers	number	NOUN
ejpam-4506	358	5	of	of	ADP
ejpam-4506	358	6	graphs	graph	NOUN
ejpam-4506	358	7	.	.	PUNCT
ejpam-4506	359	1	utilitas	utilitas	PROPN
ejpam-4506	359	2	mathematica	mathematica	PROPN
ejpam-4506	359	3	,	,	PUNCT
ejpam-4506	359	4	74:3–18	74:3–18	NUM
ejpam-4506	359	5	,	,	PUNCT
ejpam-4506	359	6	2007	2007	NUM
ejpam-4506	359	7	.	.	PUNCT
ejpam-4506	360	1	[	[	X
ejpam-4506	360	2	2	2	NUM
ejpam-4506	360	3	]	]	X
ejpam-4506	360	4	f.	f.	PROPN
ejpam-4506	360	5	buckley	buckley	PROPN
ejpam-4506	360	6	and	and	CCONJ
ejpam-4506	360	7	f.	f.	PROPN
ejpam-4506	360	8	harary	harary	PROPN
ejpam-4506	360	9	.	.	PUNCT
ejpam-4506	361	1	distance	distance	NOUN
ejpam-4506	361	2	in	in	ADP
ejpam-4506	361	3	graphs	graph	NOUN
ejpam-4506	361	4	.	.	PUNCT
ejpam-4506	362	1	redwood	redwood	NOUN
ejpam-4506	362	2	city	city	NOUN
ejpam-4506	362	3	,	,	PUNCT
ejpam-4506	362	4	ca	ca	PROPN
ejpam-4506	362	5	:	:	PUNCT
ejpam-4506	362	6	addison	addison	PROPN
ejpam-4506	362	7	-	-	PUNCT
ejpam-4506	362	8	wesley	wesley	PROPN
ejpam-4506	362	9	,	,	PUNCT
ejpam-4506	362	10	1990	1990	NUM
ejpam-4506	362	11	.	.	PUNCT
ejpam-4506	363	1	[	[	X
ejpam-4506	363	2	3	3	X
ejpam-4506	363	3	]	]	X
ejpam-4506	363	4	o.	o.	PROPN
ejpam-4506	363	5	i.	i.	PROPN
ejpam-4506	363	6	cauntongan	cauntongan	PROPN
ejpam-4506	363	7	and	and	CCONJ
ejpam-4506	363	8	i.	i.	PROPN
ejpam-4506	363	9	s.	s.	PROPN
ejpam-4506	363	10	aniversario	aniversario	PROPN
ejpam-4506	363	11	.	.	PUNCT
ejpam-4506	364	1	path	path	NOUN
ejpam-4506	364	2	-	-	PUNCT
ejpam-4506	364	3	induced	induce	VERB
ejpam-4506	364	4	closed	closed	ADJ
ejpam-4506	364	5	geodetic	geodetic	ADJ
ejpam-4506	364	6	numbers	number	NOUN
ejpam-4506	364	7	of	of	ADP
ejpam-4506	364	8	some	some	DET
ejpam-4506	364	9	graphs	graph	NOUN
ejpam-4506	364	10	.	.	PUNCT
ejpam-4506	365	1	advances	advance	NOUN
ejpam-4506	365	2	and	and	CCONJ
ejpam-4506	365	3	applications	application	NOUN
ejpam-4506	365	4	in	in	ADP
ejpam-4506	365	5	discrete	discrete	ADJ
ejpam-4506	365	6	mathematics	mathematic	NOUN
ejpam-4506	365	7	.	.	PUNCT
ejpam-4506	365	8	,	,	PUNCT
ejpam-4506	365	9	22(1):41–53	22(1):41–53	NUM
ejpam-4506	365	10	,	,	PUNCT
ejpam-4506	365	11	2019	2019	NUM
ejpam-4506	365	12	.	.	PUNCT
ejpam-4506	366	1	[	[	X
ejpam-4506	366	2	4	4	X
ejpam-4506	366	3	]	]	PUNCT
ejpam-4506	366	4	m.	m.	NOUN
ejpam-4506	366	5	p.	p.	PROPN
ejpam-4506	366	6	laurente	laurente	PROPN
ejpam-4506	366	7	f.p	f.p	PROPN
ejpam-4506	366	8	.	.	PROPN
ejpam-4506	366	9	jamil	jamil	PROPN
ejpam-4506	366	10	and	and	CCONJ
ejpam-4506	366	11	m.	m.	PROPN
ejpam-4506	366	12	b.	b.	PROPN
ejpam-4506	366	13	macababat	macababat	PROPN
ejpam-4506	366	14	.	.	PUNCT
ejpam-4506	367	1	strongly	strongly	ADV
ejpam-4506	367	2	closed	close	VERB
ejpam-4506	367	3	geodetic	geodetic	ADJ
ejpam-4506	367	4	numbers	number	NOUN
ejpam-4506	367	5	of	of	ADP
ejpam-4506	367	6	graphs	graph	NOUN
ejpam-4506	367	7	.	.	PUNCT
ejpam-4506	368	1	international	international	ADJ
ejpam-4506	368	2	mathematical	mathematical	PROPN
ejpam-4506	368	3	forum	forum	PROPN
ejpam-4506	368	4	,	,	PUNCT
ejpam-4506	368	5	26:1277–1290	26:1277–1290	NUM
ejpam-4506	368	6	,	,	PUNCT
ejpam-4506	368	7	2010	2010	NUM
ejpam-4506	368	8	.	.	PUNCT
ejpam-4506	369	1	[	[	X
ejpam-4506	369	2	5	5	NUM
ejpam-4506	369	3	]	]	X
ejpam-4506	369	4	l.d	l.d	PROPN
ejpam-4506	369	5	.	.	PUNCT
ejpam-4506	369	6	tong	tong	PROPN
ejpam-4506	369	7	g.	g.	PROPN
ejpam-4506	369	8	j.	j.	PROPN
ejpam-4506	369	9	changa	changa	PROPN
ejpam-4506	369	10	and	and	CCONJ
ejpam-4506	369	11	h.h	h.h	PROPN
ejpam-4506	369	12	.	.	PROPN
ejpam-4506	369	13	wang	wang	PROPN
ejpam-4506	369	14	.	.	PUNCT
ejpam-4506	370	1	geodetic	geodetic	ADJ
ejpam-4506	370	2	spectra	spectra	NOUN
ejpam-4506	370	3	of	of	ADP
ejpam-4506	370	4	graphs	graph	NOUN
ejpam-4506	370	5	,	,	PUNCT
ejpam-4506	370	6	volume	volume	NOUN
ejpam-4506	370	7	25	25	NUM
ejpam-4506	370	8	.	.	PUNCT
ejpam-4506	370	9	2004	2004	NUM
ejpam-4506	370	10	.	.	PUNCT
ejpam-4506	371	1	[	[	X
ejpam-4506	371	2	6	6	NUM
ejpam-4506	371	3	]	]	X
ejpam-4506	371	4	y.	y.	PROPN
ejpam-4506	371	5	pabilona	pabilona	PROPN
ejpam-4506	371	6	and	and	CCONJ
ejpam-4506	371	7	h.	h.	PROPN
ejpam-4506	371	8	rara	rara	PROPN
ejpam-4506	371	9	.	.	PUNCT
ejpam-4506	372	1	total	total	ADJ
ejpam-4506	372	2	hop	hop	NOUN
ejpam-4506	372	3	dominating	dominating	NOUN
ejpam-4506	372	4	sets	set	NOUN
ejpam-4506	372	5	in	in	ADP
ejpam-4506	372	6	the	the	DET
ejpam-4506	372	7	join	join	NOUN
ejpam-4506	372	8	,	,	PUNCT
ejpam-4506	372	9	corona	corona	PROPN
ejpam-4506	372	10	,	,	PUNCT
ejpam-4506	372	11	and	and	CCONJ
ejpam-4506	372	12	lexicographic	lexicographic	ADJ
ejpam-4506	372	13	product	product	NOUN
ejpam-4506	372	14	of	of	ADP
ejpam-4506	372	15	graphs	graph	NOUN
ejpam-4506	372	16	.	.	PUNCT
ejpam-4506	373	1	journal	journal	NOUN
ejpam-4506	373	2	of	of	ADP
ejpam-4506	373	3	algebra	algebra	PROPN
ejpam-4506	373	4	and	and	CCONJ
ejpam-4506	373	5	applied	apply	VERB
ejpam-4506	373	6	mathematics	mathematic	NOUN
ejpam-4506	373	7	,	,	PUNCT
ejpam-4506	373	8	2017	2017	NUM
ejpam-4506	373	9	.	.	PUNCT
ejpam-4506	374	1	[	[	X
ejpam-4506	374	2	7	7	X
ejpam-4506	374	3	]	]	X
ejpam-4506	374	4	r.	r.	PROPN
ejpam-4506	374	5	n.	n.	PROPN
ejpam-4506	374	6	villarante	villarante	PROPN
ejpam-4506	374	7	and	and	CCONJ
ejpam-4506	374	8	i.	i.	PROPN
ejpam-4506	374	9	s.	s.	PROPN
ejpam-4506	374	10	aniversario	aniversario	PROPN
ejpam-4506	374	11	.	.	PUNCT
ejpam-4506	375	1	path	path	NOUN
ejpam-4506	375	2	-	-	PUNCT
ejpam-4506	375	3	induced	induce	VERB
ejpam-4506	375	4	geodetic	geodetic	ADJ
ejpam-4506	375	5	numbers	number	NOUN
ejpam-4506	375	6	of	of	ADP
ejpam-4506	375	7	some	some	DET
ejpam-4506	375	8	graphs	graph	NOUN
ejpam-4506	375	9	.	.	PUNCT
ejpam-4506	375	10	,	,	PUNCT
ejpam-4506	375	11	volume	volume	NOUN
ejpam-4506	375	12	29(5	29(5	NUM
ejpam-4506	375	13	)	)	PUNCT
ejpam-4506	375	14	.	.	PUNCT
ejpam-4506	376	1	2017	2017	NUM
ejpam-4506	376	2	.	.	PUNCT