id	sid	tid	token	lemma	pos
ejpam-3657	1	1	european	european	PROPN
ejpam-3657	1	2	journal	journal	PROPN
ejpam-3657	1	3	of	of	ADP
ejpam-3657	1	4	pure	pure	ADJ
ejpam-3657	1	5	and	and	CCONJ
ejpam-3657	1	6	applied	apply	VERB
ejpam-3657	1	7	mathematics	mathematic	NOUN
ejpam-3657	1	8	vol	vol	NOUN
ejpam-3657	1	9	.	.	PROPN
ejpam-3657	2	1	13	13	NUM
ejpam-3657	2	2	,	,	PUNCT
ejpam-3657	2	3	no	no	INTJ
ejpam-3657	2	4	.	.	NOUN
ejpam-3657	2	5	3	3	NUM
ejpam-3657	2	6	,	,	PUNCT
ejpam-3657	2	7	2020	2020	NUM
ejpam-3657	2	8	,	,	PUNCT
ejpam-3657	2	9	701	701	NUM
ejpam-3657	2	10	-	-	SYM
ejpam-3657	2	11	709	709	NUM
ejpam-3657	2	12	issn	issn	PROPN
ejpam-3657	2	13	1307	1307	NUM
ejpam-3657	2	14	-	-	SYM
ejpam-3657	2	15	5543	5543	NUM
ejpam-3657	2	16	–	–	PUNCT
ejpam-3657	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3657	2	18	published	publish	VERB
ejpam-3657	2	19	by	by	ADP
ejpam-3657	2	20	new	new	PROPN
ejpam-3657	2	21	york	york	PROPN
ejpam-3657	2	22	business	business	PROPN
ejpam-3657	2	23	global	global	PROPN
ejpam-3657	2	24	upper	upper	ADJ
ejpam-3657	2	25	distance	distance	NOUN
ejpam-3657	2	26	kcost	kcost	NOUN
ejpam-3657	2	27	effective	effective	ADJ
ejpam-3657	2	28	numbers	number	NOUN
ejpam-3657	2	29	in	in	ADP
ejpam-3657	2	30	the	the	DET
ejpam-3657	2	31	join	join	NOUN
ejpam-3657	2	32	of	of	ADP
ejpam-3657	2	33	graphs	graph	NOUN
ejpam-3657	2	34	julius	julius	PROPN
ejpam-3657	2	35	g.	g.	PROPN
ejpam-3657	2	36	caadan1,∗	caadan1,∗	PROPN
ejpam-3657	2	37	,	,	PUNCT
ejpam-3657	2	38	rolando	rolando	PROPN
ejpam-3657	2	39	n.	n.	PROPN
ejpam-3657	2	40	paluga2	paluga2	PROPN
ejpam-3657	2	41	,	,	PUNCT
ejpam-3657	3	1	imelda	imelda	PROPN
ejpam-3657	3	2	s.	s.	PROPN
ejpam-3657	3	3	aniversario3	aniversario3	PROPN
ejpam-3657	3	4	1	1	NUM
ejpam-3657	3	5	surigao	surigao	NOUN
ejpam-3657	3	6	state	state	NOUN
ejpam-3657	3	7	college	college	PROPN
ejpam-3657	3	8	of	of	ADP
ejpam-3657	3	9	technology	technology	NOUN
ejpam-3657	3	10	,	,	PUNCT
ejpam-3657	3	11	8400	8400	NUM
ejpam-3657	3	12	surigao	surigao	NOUN
ejpam-3657	3	13	city	city	NOUN
ejpam-3657	3	14	,	,	PUNCT
ejpam-3657	3	15	philippines	philippines	PROPN
ejpam-3657	3	16	2	2	NUM
ejpam-3657	3	17	department	department	NOUN
ejpam-3657	3	18	of	of	ADP
ejpam-3657	3	19	mathematics	mathematic	NOUN
ejpam-3657	3	20	,	,	PUNCT
ejpam-3657	3	21	college	college	NOUN
ejpam-3657	3	22	of	of	ADP
ejpam-3657	3	23	mathematics	mathematic	NOUN
ejpam-3657	3	24	and	and	CCONJ
ejpam-3657	3	25	natural	natural	ADJ
ejpam-3657	3	26	sciences	science	NOUN
ejpam-3657	3	27	,	,	PUNCT
ejpam-3657	3	28	caraga	caraga	PROPN
ejpam-3657	3	29	state	state	PROPN
ejpam-3657	3	30	university	university	PROPN
ejpam-3657	3	31	,	,	PUNCT
ejpam-3657	3	32	8600	8600	NUM
ejpam-3657	3	33	,	,	PUNCT
ejpam-3657	3	34	ampayon	ampayon	NOUN
ejpam-3657	3	35	,	,	PUNCT
ejpam-3657	3	36	butuan	butuan	PROPN
ejpam-3657	3	37	city	city	PROPN
ejpam-3657	3	38	city	city	PROPN
ejpam-3657	3	39	,	,	PUNCT
ejpam-3657	3	40	philippines	philippines	PROPN
ejpam-3657	3	41	3	3	NUM
ejpam-3657	3	42	department	department	NOUN
ejpam-3657	3	43	of	of	ADP
ejpam-3657	3	44	mathematics	mathematic	NOUN
ejpam-3657	3	45	and	and	CCONJ
ejpam-3657	3	46	statistics	statistic	NOUN
ejpam-3657	3	47	,	,	PUNCT
ejpam-3657	3	48	college	college	NOUN
ejpam-3657	3	49	of	of	ADP
ejpam-3657	3	50	science	science	NOUN
ejpam-3657	3	51	and	and	CCONJ
ejpam-3657	3	52	mathematics	mathematic	NOUN
ejpam-3657	3	53	,	,	PUNCT
ejpam-3657	3	54	mindanao	mindanao	PROPN
ejpam-3657	3	55	state	state	PROPN
ejpam-3657	3	56	university	university	PROPN
ejpam-3657	3	57	-	-	PUNCT
ejpam-3657	3	58	iligan	iligan	PROPN
ejpam-3657	3	59	institute	institute	PROPN
ejpam-3657	3	60	of	of	ADP
ejpam-3657	3	61	technology	technology	PROPN
ejpam-3657	3	62	,	,	PUNCT
ejpam-3657	3	63	9200	9200	NUM
ejpam-3657	3	64	iligan	iligan	ADJ
ejpam-3657	3	65	city	city	NOUN
ejpam-3657	3	66	,	,	PUNCT
ejpam-3657	3	67	philippines	philippine	NOUN
ejpam-3657	3	68	abstract	abstract	ADJ
ejpam-3657	3	69	.	.	PUNCT
ejpam-3657	4	1	let	let	VERB
ejpam-3657	4	2	k	k	PRON
ejpam-3657	4	3	be	be	AUX
ejpam-3657	4	4	a	a	DET
ejpam-3657	4	5	positive	positive	ADJ
ejpam-3657	4	6	integer	integer	NOUN
ejpam-3657	4	7	and	and	CCONJ
ejpam-3657	4	8	g	g	PROPN
ejpam-3657	4	9	be	be	AUX
ejpam-3657	4	10	a	a	DET
ejpam-3657	4	11	connected	connected	ADJ
ejpam-3657	4	12	graph	graph	NOUN
ejpam-3657	4	13	.	.	PUNCT
ejpam-3657	5	1	the	the	DET
ejpam-3657	5	2	open	open	ADJ
ejpam-3657	5	3	k	k	ADJ
ejpam-3657	5	4	-	-	ADJ
ejpam-3657	5	5	neighborhood	neighborhood	NOUN
ejpam-3657	5	6	set	set	VERB
ejpam-3657	5	7	nk	nk	PROPN
ejpam-3657	5	8	g(v	g(v	PROPN
ejpam-3657	5	9	)	)	PUNCT
ejpam-3657	5	10	of	of	ADP
ejpam-3657	5	11	v	v	NUM
ejpam-3657	5	12	∈	∈	NOUN
ejpam-3657	5	13	v	v	NOUN
ejpam-3657	5	14	(	(	PUNCT
ejpam-3657	5	15	g	g	NOUN
ejpam-3657	5	16	)	)	PUNCT
ejpam-3657	5	17	is	be	AUX
ejpam-3657	5	18	the	the	DET
ejpam-3657	5	19	set	set	ADJ
ejpam-3657	5	20	nk	nk	PROPN
ejpam-3657	5	21	g(v	g(v	PROPN
ejpam-3657	5	22	)	)	PUNCT
ejpam-3657	6	1	=	=	PRON
ejpam-3657	6	2	{	{	PUNCT
ejpam-3657	6	3	u	u	NOUN
ejpam-3657	6	4	∈	∈	PROPN
ejpam-3657	6	5	v	v	NOUN
ejpam-3657	6	6	(	(	PUNCT
ejpam-3657	6	7	g	g	NOUN
ejpam-3657	6	8	)	)	PUNCT
ejpam-3657	6	9	\	\	NOUN
ejpam-3657	6	10	{	{	PUNCT
ejpam-3657	6	11	v	v	NOUN
ejpam-3657	6	12	}	}	PUNCT
ejpam-3657	6	13	:	:	PUNCT
ejpam-3657	6	14	dg(u	dg(u	X
ejpam-3657	6	15	,	,	PUNCT
ejpam-3657	6	16	v	v	NOUN
ejpam-3657	6	17	)	)	PUNCT
ejpam-3657	6	18	≤	≤	NOUN
ejpam-3657	6	19	k	k	X
ejpam-3657	6	20	}	}	PUNCT
ejpam-3657	6	21	.	.	PUNCT
ejpam-3657	7	1	a	a	DET
ejpam-3657	7	2	set	set	NOUN
ejpam-3657	7	3	s	s	NOUN
ejpam-3657	7	4	of	of	ADP
ejpam-3657	7	5	vertices	vertex	NOUN
ejpam-3657	7	6	of	of	ADP
ejpam-3657	7	7	g	g	PROPN
ejpam-3657	7	8	is	be	AUX
ejpam-3657	7	9	a	a	DET
ejpam-3657	7	10	distance	distance	NOUN
ejpam-3657	7	11	kcost	kcost	NOUN
ejpam-3657	7	12	effective	effective	ADJ
ejpam-3657	7	13	if	if	SCONJ
ejpam-3657	7	14	for	for	ADP
ejpam-3657	7	15	every	every	DET
ejpam-3657	7	16	vertex	vertex	NOUN
ejpam-3657	7	17	u	u	NOUN
ejpam-3657	7	18	in	in	ADP
ejpam-3657	7	19	s	s	PROPN
ejpam-3657	7	20	,	,	PUNCT
ejpam-3657	7	21	|nk	|nk	PRON
ejpam-3657	7	22	g(u	g(u	PROPN
ejpam-3657	7	23	)	)	PUNCT
ejpam-3657	7	24	∩	∩	NOUN
ejpam-3657	7	25	sc|	sc|	PROPN
ejpam-3657	7	26	−	−	PROPN
ejpam-3657	7	27	|nk	|nk	SYM
ejpam-3657	7	28	g(u	g(u	PROPN
ejpam-3657	7	29	)	)	PUNCT
ejpam-3657	7	30	∩	∩	NOUN
ejpam-3657	7	31	s|	s|	VERB
ejpam-3657	7	32	≥	≥	NOUN
ejpam-3657	7	33	0	0	NUM
ejpam-3657	7	34	.	.	PUNCT
ejpam-3657	8	1	the	the	DET
ejpam-3657	8	2	maximum	maximum	ADJ
ejpam-3657	8	3	cardinality	cardinality	NOUN
ejpam-3657	8	4	of	of	ADP
ejpam-3657	8	5	a	a	DET
ejpam-3657	8	6	distance	distance	NOUN
ejpam-3657	8	7	kcost	kcost	NOUN
ejpam-3657	8	8	effective	effective	ADJ
ejpam-3657	8	9	set	set	NOUN
ejpam-3657	8	10	of	of	ADP
ejpam-3657	8	11	g	g	PROPN
ejpam-3657	8	12	is	be	AUX
ejpam-3657	8	13	called	call	VERB
ejpam-3657	8	14	the	the	DET
ejpam-3657	8	15	upper	upper	ADJ
ejpam-3657	8	16	distance	distance	NOUN
ejpam-3657	8	17	kcost	kcost	NOUN
ejpam-3657	8	18	effective	effective	ADJ
ejpam-3657	8	19	number	number	NOUN
ejpam-3657	8	20	of	of	ADP
ejpam-3657	8	21	g.	g.	PROPN
ejpam-3657	8	22	in	in	ADP
ejpam-3657	8	23	this	this	DET
ejpam-3657	8	24	paper	paper	NOUN
ejpam-3657	8	25	,	,	PUNCT
ejpam-3657	8	26	we	we	PRON
ejpam-3657	8	27	characterized	characterize	VERB
ejpam-3657	8	28	a	a	DET
ejpam-3657	8	29	distance	distance	NOUN
ejpam-3657	8	30	kcost	kcost	NOUN
ejpam-3657	8	31	effective	effective	ADJ
ejpam-3657	8	32	set	set	NOUN
ejpam-3657	8	33	in	in	ADP
ejpam-3657	8	34	the	the	DET
ejpam-3657	8	35	join	join	NOUN
ejpam-3657	8	36	of	of	ADP
ejpam-3657	8	37	two	two	NUM
ejpam-3657	8	38	graphs	graph	NOUN
ejpam-3657	8	39	.	.	PUNCT
ejpam-3657	9	1	as	as	ADP
ejpam-3657	9	2	direct	direct	ADJ
ejpam-3657	9	3	consequences	consequence	NOUN
ejpam-3657	9	4	,	,	PUNCT
ejpam-3657	9	5	the	the	DET
ejpam-3657	9	6	bounds	bound	NOUN
ejpam-3657	9	7	or	or	CCONJ
ejpam-3657	9	8	the	the	DET
ejpam-3657	9	9	exact	exact	ADJ
ejpam-3657	9	10	values	value	NOUN
ejpam-3657	9	11	of	of	ADP
ejpam-3657	9	12	the	the	DET
ejpam-3657	9	13	upper	upper	ADJ
ejpam-3657	9	14	distance	distance	NOUN
ejpam-3657	9	15	kcost	kcost	NOUN
ejpam-3657	9	16	effective	effective	ADJ
ejpam-3657	9	17	numbers	number	NOUN
ejpam-3657	9	18	are	be	AUX
ejpam-3657	9	19	determined	determine	VERB
ejpam-3657	9	20	.	.	PUNCT
ejpam-3657	10	1	2020	2020	NUM
ejpam-3657	10	2	mathematics	mathematic	NOUN
ejpam-3657	10	3	subject	subject	NOUN
ejpam-3657	10	4	classifications	classification	NOUN
ejpam-3657	10	5	:	:	PUNCT
ejpam-3657	10	6	05c12	05c12	X
ejpam-3657	10	7	key	key	ADJ
ejpam-3657	10	8	words	word	NOUN
ejpam-3657	10	9	and	and	CCONJ
ejpam-3657	10	10	phrases	phrase	NOUN
ejpam-3657	10	11	:	:	PUNCT
ejpam-3657	10	12	distance	distance	NOUN
ejpam-3657	10	13	k	k	ADJ
ejpam-3657	10	14	-	-	PUNCT
ejpam-3657	10	15	cost	cost	ADJ
ejpam-3657	10	16	effective	effective	ADJ
ejpam-3657	10	17	set	set	NOUN
ejpam-3657	10	18	,	,	PUNCT
ejpam-3657	10	19	upper	upper	ADJ
ejpam-3657	10	20	distance	distance	NOUN
ejpam-3657	10	21	k	k	ADJ
ejpam-3657	10	22	-	-	PUNCT
ejpam-3657	10	23	cost	cost	ADJ
ejpam-3657	10	24	effective	effective	ADJ
ejpam-3657	10	25	number	number	NOUN
ejpam-3657	10	26	,	,	PUNCT
ejpam-3657	10	27	join	join	NOUN
ejpam-3657	10	28	,	,	PUNCT
ejpam-3657	10	29	t	t	NOUN
ejpam-3657	10	30	-	-	PUNCT
ejpam-3657	10	31	fringe	fringe	NOUN
ejpam-3657	10	32	set	set	NOUN
ejpam-3657	10	33	,	,	PUNCT
ejpam-3657	10	34	tincrement	tincrement	NOUN
ejpam-3657	10	35	1	1	NUM
ejpam-3657	10	36	.	.	PUNCT
ejpam-3657	11	1	introduction	introduction	NOUN
ejpam-3657	11	2	we	we	PRON
ejpam-3657	11	3	assume	assume	VERB
ejpam-3657	11	4	that	that	SCONJ
ejpam-3657	11	5	all	all	PRON
ejpam-3657	11	6	graphs	graph	VERB
ejpam-3657	11	7	g	g	NOUN
ejpam-3657	11	8	=	=	SYM
ejpam-3657	11	9	(	(	PUNCT
ejpam-3657	11	10	v	v	NOUN
ejpam-3657	11	11	(	(	PUNCT
ejpam-3657	11	12	g	g	NOUN
ejpam-3657	11	13	)	)	PUNCT
ejpam-3657	11	14	,	,	PUNCT
ejpam-3657	11	15	e(g	e(g	PROPN
ejpam-3657	11	16	)	)	PUNCT
ejpam-3657	11	17	)	)	PUNCT
ejpam-3657	11	18	considered	consider	VERB
ejpam-3657	11	19	throughout	throughout	ADP
ejpam-3657	11	20	this	this	DET
ejpam-3657	11	21	paper	paper	NOUN
ejpam-3657	11	22	are	be	AUX
ejpam-3657	11	23	finite	finite	ADJ
ejpam-3657	11	24	,	,	PUNCT
ejpam-3657	11	25	simple	simple	ADJ
ejpam-3657	11	26	,	,	PUNCT
ejpam-3657	11	27	and	and	CCONJ
ejpam-3657	11	28	undirected	undirected	ADJ
ejpam-3657	11	29	connected	connected	ADJ
ejpam-3657	11	30	graphs	graph	NOUN
ejpam-3657	11	31	.	.	PUNCT
ejpam-3657	12	1	the	the	DET
ejpam-3657	12	2	basic	basic	ADJ
ejpam-3657	12	3	graph	graph	NOUN
ejpam-3657	12	4	theoretic	theoretic	ADJ
ejpam-3657	12	5	concepts	concept	NOUN
ejpam-3657	12	6	are	be	AUX
ejpam-3657	12	7	adapted	adapt	VERB
ejpam-3657	12	8	from	from	ADP
ejpam-3657	12	9	[	[	X
ejpam-3657	12	10	1	1	NUM
ejpam-3657	12	11	]	]	PUNCT
ejpam-3657	12	12	and	and	CCONJ
ejpam-3657	12	13	[	[	X
ejpam-3657	12	14	7	7	NUM
ejpam-3657	12	15	]	]	PUNCT
ejpam-3657	12	16	.	.	PUNCT
ejpam-3657	13	1	the	the	DET
ejpam-3657	13	2	notations	notation	NOUN
ejpam-3657	13	3	v	v	X
ejpam-3657	13	4	(	(	PUNCT
ejpam-3657	13	5	g	g	NOUN
ejpam-3657	13	6	)	)	PUNCT
ejpam-3657	13	7	and	and	CCONJ
ejpam-3657	13	8	e(g	e(g	PROPN
ejpam-3657	13	9	)	)	PUNCT
ejpam-3657	13	10	are	be	AUX
ejpam-3657	13	11	the	the	DET
ejpam-3657	13	12	vertex	vertex	NOUN
ejpam-3657	13	13	set	set	NOUN
ejpam-3657	13	14	and	and	CCONJ
ejpam-3657	13	15	edge	edge	NOUN
ejpam-3657	13	16	set	set	NOUN
ejpam-3657	13	17	,	,	PUNCT
ejpam-3657	13	18	respectively	respectively	ADV
ejpam-3657	13	19	,	,	PUNCT
ejpam-3657	13	20	of	of	ADP
ejpam-3657	13	21	g.	g.	PROPN
ejpam-3657	13	22	the	the	DET
ejpam-3657	13	23	|v	|v	PROPN
ejpam-3657	13	24	(	(	PUNCT
ejpam-3657	13	25	g)|	g)|	NOUN
ejpam-3657	13	26	denotes	denote	VERB
ejpam-3657	13	27	the	the	DET
ejpam-3657	13	28	order	order	NOUN
ejpam-3657	13	29	of	of	ADP
ejpam-3657	13	30	g	g	PROPN
ejpam-3657	13	31	and	and	CCONJ
ejpam-3657	13	32	for	for	ADP
ejpam-3657	13	33	any	any	DET
ejpam-3657	13	34	set	set	NOUN
ejpam-3657	13	35	s	s	PROPN
ejpam-3657	13	36	⊆	⊆	NUM
ejpam-3657	13	37	v	v	NOUN
ejpam-3657	13	38	(	(	PUNCT
ejpam-3657	13	39	g	g	NOUN
ejpam-3657	13	40	)	)	PUNCT
ejpam-3657	13	41	,	,	PUNCT
ejpam-3657	13	42	|s|	|s|	PROPN
ejpam-3657	13	43	is	be	AUX
ejpam-3657	13	44	the	the	DET
ejpam-3657	13	45	cardinality	cardinality	NOUN
ejpam-3657	13	46	of	of	ADP
ejpam-3657	13	47	s.	s.	PROPN
ejpam-3657	13	48	let	let	VERB
ejpam-3657	13	49	g	g	NOUN
ejpam-3657	13	50	be	be	AUX
ejpam-3657	13	51	a	a	DET
ejpam-3657	13	52	connected	connected	ADJ
ejpam-3657	13	53	graph	graph	NOUN
ejpam-3657	13	54	and	and	CCONJ
ejpam-3657	13	55	v	v	ADP
ejpam-3657	13	56	∈	∈	PROPN
ejpam-3657	13	57	v	v	NOUN
ejpam-3657	13	58	(	(	PUNCT
ejpam-3657	13	59	g	g	NOUN
ejpam-3657	13	60	)	)	PUNCT
ejpam-3657	13	61	.	.	PUNCT
ejpam-3657	14	1	the	the	DET
ejpam-3657	14	2	open	open	ADJ
ejpam-3657	14	3	neighborhood	neighborhood	NOUN
ejpam-3657	14	4	of	of	ADP
ejpam-3657	14	5	v	v	NOUN
ejpam-3657	14	6	in	in	ADP
ejpam-3657	14	7	g	g	NOUN
ejpam-3657	14	8	,	,	PUNCT
ejpam-3657	14	9	denoted	denote	VERB
ejpam-3657	14	10	by	by	ADP
ejpam-3657	14	11	ng(v	ng(v	NOUN
ejpam-3657	14	12	)	)	PUNCT
ejpam-3657	14	13	,	,	PUNCT
ejpam-3657	14	14	is	be	AUX
ejpam-3657	14	15	the	the	DET
ejpam-3657	14	16	set	set	NOUN
ejpam-3657	14	17	ng(v	ng(v	PUNCT
ejpam-3657	14	18	)	)	PUNCT
ejpam-3657	14	19	=	=	SYM
ejpam-3657	15	1	{	{	PUNCT
ejpam-3657	15	2	u	u	NOUN
ejpam-3657	15	3	∈	∈	PROPN
ejpam-3657	15	4	v	v	NOUN
ejpam-3657	15	5	(	(	PUNCT
ejpam-3657	15	6	g	g	NOUN
ejpam-3657	15	7	)	)	PUNCT
ejpam-3657	15	8	:	:	PUNCT
ejpam-3657	15	9	uv	uv	PROPN
ejpam-3657	15	10	∈	∈	PROPN
ejpam-3657	15	11	e(g	e(g	PROPN
ejpam-3657	15	12	)	)	PUNCT
ejpam-3657	15	13	}	}	PUNCT
ejpam-3657	15	14	.	.	PUNCT
ejpam-3657	16	1	the	the	DET
ejpam-3657	16	2	degree	degree	NOUN
ejpam-3657	16	3	of	of	ADP
ejpam-3657	16	4	a	a	DET
ejpam-3657	16	5	vertex	vertex	NOUN
ejpam-3657	16	6	v	v	ADP
ejpam-3657	16	7	∈	∈	NOUN
ejpam-3657	16	8	v	v	NOUN
ejpam-3657	16	9	(	(	PUNCT
ejpam-3657	16	10	g	g	NOUN
ejpam-3657	16	11	)	)	PUNCT
ejpam-3657	16	12	,	,	PUNCT
ejpam-3657	16	13	denoted	denote	VERB
ejpam-3657	16	14	by	by	ADP
ejpam-3657	16	15	degg(v	degg(v	PROPN
ejpam-3657	16	16	)	)	PUNCT
ejpam-3657	16	17	,	,	PUNCT
ejpam-3657	16	18	is	be	AUX
ejpam-3657	16	19	the	the	DET
ejpam-3657	16	20	cardinality	cardinality	NOUN
ejpam-3657	16	21	of	of	ADP
ejpam-3657	16	22	ng(v	ng(v	NOUN
ejpam-3657	16	23	)	)	PUNCT
ejpam-3657	16	24	.	.	PUNCT
ejpam-3657	17	1	the	the	DET
ejpam-3657	17	2	minimum	minimum	NOUN
ejpam-3657	17	3	degree	degree	NOUN
ejpam-3657	17	4	of	of	ADP
ejpam-3657	17	5	g	g	PROPN
ejpam-3657	17	6	is	be	AUX
ejpam-3657	17	7	δ(g	δ(g	ADV
ejpam-3657	17	8	)	)	PUNCT
ejpam-3657	17	9	=	=	SYM
ejpam-3657	17	10	min{degg(v	min{degg(v	PROPN
ejpam-3657	17	11	)	)	PUNCT
ejpam-3657	17	12	:	:	PUNCT
ejpam-3657	17	13	v	v	X
ejpam-3657	17	14	∈	∈	PROPN
ejpam-3657	17	15	v	v	NOUN
ejpam-3657	17	16	(	(	PUNCT
ejpam-3657	17	17	g	g	NOUN
ejpam-3657	17	18	)	)	PUNCT
ejpam-3657	17	19	}	}	PUNCT
ejpam-3657	17	20	and	and	CCONJ
ejpam-3657	17	21	the	the	DET
ejpam-3657	17	22	maximum	maximum	ADJ
ejpam-3657	17	23	degree	degree	NOUN
ejpam-3657	17	24	of	of	ADP
ejpam-3657	17	25	g	g	PROPN
ejpam-3657	17	26	is	be	AUX
ejpam-3657	17	27	∆(g	∆(g	NOUN
ejpam-3657	17	28	)	)	PUNCT
ejpam-3657	17	29	=	=	PUNCT
ejpam-3657	17	30	max{degg(v	max{degg(v	NOUN
ejpam-3657	17	31	)	)	PUNCT
ejpam-3657	17	32	:	:	PUNCT
ejpam-3657	17	33	v	v	X
ejpam-3657	17	34	∈	∈	PROPN
ejpam-3657	17	35	v	v	NOUN
ejpam-3657	17	36	(	(	PUNCT
ejpam-3657	17	37	g	g	NOUN
ejpam-3657	17	38	)	)	PUNCT
ejpam-3657	17	39	}	}	PUNCT
ejpam-3657	17	40	.	.	PUNCT
ejpam-3657	18	1	the	the	DET
ejpam-3657	18	2	distance	distance	NOUN
ejpam-3657	18	3	between	between	ADP
ejpam-3657	18	4	vertices	vertex	NOUN
ejpam-3657	18	5	u	u	NOUN
ejpam-3657	18	6	and	and	CCONJ
ejpam-3657	18	7	v	v	NOUN
ejpam-3657	18	8	in	in	ADP
ejpam-3657	18	9	g	g	NOUN
ejpam-3657	18	10	,	,	PUNCT
ejpam-3657	18	11	denoted	denote	VERB
ejpam-3657	18	12	by	by	ADP
ejpam-3657	18	13	∗corresponding	∗corresponde	VERB
ejpam-3657	18	14	author	author	NOUN
ejpam-3657	18	15	.	.	PUNCT
ejpam-3657	19	1	doi	doi	NOUN
ejpam-3657	19	2	:	:	PUNCT
ejpam-3657	19	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3657	https://doi.org/10.29020/nybg.ejpam.v13i3.3657	PRON
ejpam-3657	19	4	email	email	NOUN
ejpam-3657	19	5	addresses	address	NOUN
ejpam-3657	19	6	:	:	PUNCT
ejpam-3657	19	7	juliusgcaadan@gmail.com	juliusgcaadan@gmail.com	X
ejpam-3657	19	8	(	(	PUNCT
ejpam-3657	19	9	j.	j.	PROPN
ejpam-3657	19	10	g.	g.	PROPN
ejpam-3657	19	11	caadan	caadan	PROPN
ejpam-3657	19	12	)	)	PUNCT
ejpam-3657	19	13	,	,	PUNCT
ejpam-3657	19	14	rnpaluga@carsu.edu.ph	rnpaluga@carsu.edu.ph	NOUN
ejpam-3657	19	15	(	(	PUNCT
ejpam-3657	19	16	r.	r.	PROPN
ejpam-3657	19	17	n.	n.	PROPN
ejpam-3657	19	18	paluga	paluga	PROPN
ejpam-3657	19	19	)	)	PUNCT
ejpam-3657	19	20	,	,	PUNCT
ejpam-3657	19	21	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-3657	19	22	(	(	PUNCT
ejpam-3657	19	23	i.	i.	PROPN
ejpam-3657	19	24	s.	s.	PROPN
ejpam-3657	19	25	aniversario	aniversario	PROPN
ejpam-3657	19	26	)	)	PUNCT
ejpam-3657	19	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3657	20	1	701	701	NUM
ejpam-3657	20	2	c	c	NOUN
ejpam-3657	20	3	©	©	PROPN
ejpam-3657	20	4	2020	2020	NUM
ejpam-3657	20	5	ejpam	ejpam	VERB
ejpam-3657	20	6	all	all	DET
ejpam-3657	20	7	rights	right	NOUN
ejpam-3657	20	8	reserved	reserve	VERB
ejpam-3657	20	9	.	.	PUNCT
ejpam-3657	21	1	j.	j.	PROPN
ejpam-3657	21	2	g.	g.	PROPN
ejpam-3657	21	3	caadan	caadan	PROPN
ejpam-3657	21	4	,	,	PUNCT
ejpam-3657	21	5	r.	r.	PROPN
ejpam-3657	21	6	n.	n.	PROPN
ejpam-3657	21	7	paluga	paluga	PROPN
ejpam-3657	21	8	,	,	PUNCT
ejpam-3657	21	9	i.	i.	PROPN
ejpam-3657	21	10	s.	s.	PROPN
ejpam-3657	21	11	aniversario	aniversario	PROPN
ejpam-3657	21	12	/	/	SYM
ejpam-3657	21	13	eur	eur	PROPN
ejpam-3657	21	14	.	.	PUNCT
ejpam-3657	22	1	j.	j.	PROPN
ejpam-3657	22	2	pure	pure	PROPN
ejpam-3657	22	3	appl	appl	PROPN
ejpam-3657	22	4	.	.	PROPN
ejpam-3657	22	5	math	math	PROPN
ejpam-3657	22	6	,	,	PUNCT
ejpam-3657	22	7	13	13	NUM
ejpam-3657	22	8	(	(	PUNCT
ejpam-3657	22	9	3	3	NUM
ejpam-3657	22	10	)	)	PUNCT
ejpam-3657	22	11	(	(	PUNCT
ejpam-3657	22	12	2020	2020	NUM
ejpam-3657	22	13	)	)	PUNCT
ejpam-3657	22	14	,	,	PUNCT
ejpam-3657	22	15	701	701	NUM
ejpam-3657	22	16	-	-	SYM
ejpam-3657	22	17	709	709	NUM
ejpam-3657	22	18	702	702	NUM
ejpam-3657	22	19	dg(u	dg(u	NOUN
ejpam-3657	22	20	,	,	PUNCT
ejpam-3657	22	21	v	v	NOUN
ejpam-3657	22	22	)	)	PUNCT
ejpam-3657	22	23	,	,	PUNCT
ejpam-3657	22	24	is	be	AUX
ejpam-3657	22	25	the	the	DET
ejpam-3657	22	26	length	length	NOUN
ejpam-3657	22	27	of	of	ADP
ejpam-3657	22	28	the	the	DET
ejpam-3657	22	29	shortest	short	ADJ
ejpam-3657	22	30	path	path	NOUN
ejpam-3657	22	31	from	from	ADP
ejpam-3657	22	32	vertex	vertex	NOUN
ejpam-3657	22	33	u	u	NOUN
ejpam-3657	22	34	to	to	PART
ejpam-3657	22	35	vertex	vertex	VERB
ejpam-3657	22	36	v	v	NOUN
ejpam-3657	22	37	in	in	ADP
ejpam-3657	22	38	g.	g.	PROPN
ejpam-3657	22	39	thediameter	thediameter	NOUN
ejpam-3657	22	40	of	of	ADP
ejpam-3657	22	41	g	g	PROPN
ejpam-3657	22	42	,	,	PUNCT
ejpam-3657	22	43	denoted	denote	VERB
ejpam-3657	22	44	by	by	ADP
ejpam-3657	22	45	diam(g	diam(g	PROPN
ejpam-3657	22	46	)	)	PUNCT
ejpam-3657	22	47	,	,	PUNCT
ejpam-3657	22	48	is	be	AUX
ejpam-3657	22	49	the	the	DET
ejpam-3657	22	50	maximum	maximum	ADJ
ejpam-3657	22	51	distance	distance	NOUN
ejpam-3657	22	52	between	between	ADP
ejpam-3657	22	53	any	any	DET
ejpam-3657	22	54	two	two	NUM
ejpam-3657	22	55	vertices	vertex	NOUN
ejpam-3657	22	56	in	in	ADP
ejpam-3657	22	57	g.	g.	NOUN
ejpam-3657	22	58	for	for	ADP
ejpam-3657	22	59	any	any	DET
ejpam-3657	22	60	positive	positive	ADJ
ejpam-3657	22	61	integer	integer	NOUN
ejpam-3657	22	62	k	k	PROPN
ejpam-3657	22	63	and	and	CCONJ
ejpam-3657	22	64	v	v	ADP
ejpam-3657	22	65	∈	∈	PROPN
ejpam-3657	22	66	v	v	NOUN
ejpam-3657	22	67	(	(	PUNCT
ejpam-3657	22	68	g	g	NOUN
ejpam-3657	22	69	)	)	PUNCT
ejpam-3657	22	70	,	,	PUNCT
ejpam-3657	22	71	the	the	DET
ejpam-3657	22	72	open	open	ADJ
ejpam-3657	22	73	kneighborhood	kneighborhood	NOUN
ejpam-3657	22	74	set	set	VERB
ejpam-3657	22	75	nk	nk	PROPN
ejpam-3657	22	76	g(v	g(v	PROPN
ejpam-3657	22	77	)	)	PUNCT
ejpam-3657	22	78	of	of	ADP
ejpam-3657	22	79	vertex	vertex	NOUN
ejpam-3657	22	80	v	v	NOUN
ejpam-3657	22	81	is	be	AUX
ejpam-3657	22	82	the	the	DET
ejpam-3657	22	83	set	set	NOUN
ejpam-3657	22	84	of	of	ADP
ejpam-3657	22	85	all	all	DET
ejpam-3657	22	86	vertices	vertex	NOUN
ejpam-3657	22	87	u	u	NOUN
ejpam-3657	22	88	of	of	ADP
ejpam-3657	22	89	g	g	NOUN
ejpam-3657	22	90	such	such	ADJ
ejpam-3657	22	91	that	that	SCONJ
ejpam-3657	22	92	0	0	NUM
ejpam-3657	22	93	<	<	X
ejpam-3657	22	94	dg(u	dg(u	X
ejpam-3657	22	95	,	,	PUNCT
ejpam-3657	22	96	v	v	NOUN
ejpam-3657	22	97	)	)	PUNCT
ejpam-3657	22	98	≤	≤	NOUN
ejpam-3657	22	99	k.	k.	NOUN
ejpam-3657	23	1	that	that	PRON
ejpam-3657	23	2	is	be	AUX
ejpam-3657	23	3	,	,	PUNCT
ejpam-3657	23	4	nk	nk	PROPN
ejpam-3657	23	5	g(v	g(v	PROPN
ejpam-3657	23	6	)	)	PUNCT
ejpam-3657	23	7	=	=	PRON
ejpam-3657	24	1	{	{	PUNCT
ejpam-3657	24	2	u	u	NOUN
ejpam-3657	24	3	∈	∈	PROPN
ejpam-3657	24	4	v	v	NOUN
ejpam-3657	24	5	(	(	PUNCT
ejpam-3657	24	6	g	g	NOUN
ejpam-3657	24	7	)	)	PUNCT
ejpam-3657	24	8	:	:	PUNCT
ejpam-3657	24	9	0	0	NUM
ejpam-3657	24	10	<	<	X
ejpam-3657	24	11	dg(u	dg(u	X
ejpam-3657	24	12	,	,	PUNCT
ejpam-3657	24	13	v	v	NOUN
ejpam-3657	24	14	)	)	PUNCT
ejpam-3657	24	15	≤	≤	NOUN
ejpam-3657	25	1	k	k	X
ejpam-3657	25	2	}	}	PUNCT
ejpam-3657	25	3	.	.	PUNCT
ejpam-3657	26	1	the	the	DET
ejpam-3657	26	2	degree	degree	NOUN
ejpam-3657	26	3	of	of	ADP
ejpam-3657	26	4	v	v	NOUN
ejpam-3657	26	5	in	in	ADP
ejpam-3657	26	6	g	g	NOUN
ejpam-3657	26	7	of	of	ADP
ejpam-3657	26	8	distance	distance	NOUN
ejpam-3657	26	9	k	k	PROPN
ejpam-3657	26	10	,	,	PUNCT
ejpam-3657	26	11	denoted	denote	VERB
ejpam-3657	26	12	by	by	ADP
ejpam-3657	26	13	degkg(v	degkg(v	PROPN
ejpam-3657	26	14	)	)	PUNCT
ejpam-3657	26	15	,	,	PUNCT
ejpam-3657	26	16	is	be	AUX
ejpam-3657	26	17	the	the	DET
ejpam-3657	26	18	cardinality	cardinality	NOUN
ejpam-3657	26	19	of	of	ADP
ejpam-3657	26	20	nk	nk	PROPN
ejpam-3657	26	21	g(v	g(v	PROPN
ejpam-3657	26	22	)	)	PUNCT
ejpam-3657	26	23	.	.	PUNCT
ejpam-3657	27	1	the	the	DET
ejpam-3657	27	2	minimum	minimum	NOUN
ejpam-3657	27	3	degree	degree	NOUN
ejpam-3657	27	4	δk(g	δk(g	NOUN
ejpam-3657	27	5	)	)	PUNCT
ejpam-3657	27	6	of	of	ADP
ejpam-3657	27	7	g	g	NOUN
ejpam-3657	27	8	with	with	ADP
ejpam-3657	27	9	distance	distance	NOUN
ejpam-3657	27	10	k	k	PROPN
ejpam-3657	27	11	is	be	AUX
ejpam-3657	27	12	δk(g	δk(g	NUM
ejpam-3657	27	13	)	)	PUNCT
ejpam-3657	28	1	=	=	SYM
ejpam-3657	28	2	min{degkg(v	min{degkg(v	X
ejpam-3657	28	3	)	)	PUNCT
ejpam-3657	28	4	:	:	PUNCT
ejpam-3657	28	5	v	v	X
ejpam-3657	28	6	∈	∈	PROPN
ejpam-3657	28	7	v	v	NOUN
ejpam-3657	28	8	(	(	PUNCT
ejpam-3657	28	9	g	g	NOUN
ejpam-3657	28	10	)	)	PUNCT
ejpam-3657	28	11	}	}	PUNCT
ejpam-3657	28	12	and	and	CCONJ
ejpam-3657	28	13	the	the	DET
ejpam-3657	28	14	maximum	maximum	ADJ
ejpam-3657	28	15	degree	degree	NOUN
ejpam-3657	28	16	of	of	ADP
ejpam-3657	28	17	g	g	NOUN
ejpam-3657	28	18	with	with	ADP
ejpam-3657	28	19	distance	distance	NOUN
ejpam-3657	28	20	k	k	PROPN
ejpam-3657	28	21	is	be	AUX
ejpam-3657	28	22	∆k(g	∆k(g	NOUN
ejpam-3657	28	23	)	)	PUNCT
ejpam-3657	29	1	=	=	NOUN
ejpam-3657	29	2	max{degkg(v	max{degkg(v	X
ejpam-3657	29	3	)	)	PUNCT
ejpam-3657	29	4	;	;	PUNCT
ejpam-3657	29	5	v	v	X
ejpam-3657	29	6	∈	∈	PROPN
ejpam-3657	29	7	v	v	NOUN
ejpam-3657	29	8	(	(	PUNCT
ejpam-3657	29	9	g	g	NOUN
ejpam-3657	29	10	)	)	PUNCT
ejpam-3657	29	11	}	}	PUNCT
ejpam-3657	29	12	.	.	PUNCT
ejpam-3657	30	1	note	note	VERB
ejpam-3657	30	2	that	that	SCONJ
ejpam-3657	30	3	deg1	deg1	PROPN
ejpam-3657	30	4	g(v	g(v	PROPN
ejpam-3657	30	5	)	)	PUNCT
ejpam-3657	30	6	=	=	SYM
ejpam-3657	30	7	degg(v	degg(v	PROPN
ejpam-3657	30	8	)	)	PUNCT
ejpam-3657	30	9	,	,	PUNCT
ejpam-3657	30	10	δ1(g	δ1(g	PROPN
ejpam-3657	30	11	)	)	PUNCT
ejpam-3657	30	12	=	=	PUNCT
ejpam-3657	30	13	δ(g	δ(g	X
ejpam-3657	30	14	)	)	PUNCT
ejpam-3657	30	15	,	,	PUNCT
ejpam-3657	30	16	and	and	CCONJ
ejpam-3657	30	17	∆1(g	∆1(g	NUM
ejpam-3657	30	18	)	)	PUNCT
ejpam-3657	30	19	=	=	SYM
ejpam-3657	30	20	∆(g	∆(g	PROPN
ejpam-3657	30	21	)	)	PUNCT
ejpam-3657	30	22	.	.	PUNCT
ejpam-3657	31	1	a	a	DET
ejpam-3657	31	2	simple	simple	ADJ
ejpam-3657	31	3	graph	graph	NOUN
ejpam-3657	31	4	g	g	NOUN
ejpam-3657	31	5	is	be	AUX
ejpam-3657	31	6	called	call	VERB
ejpam-3657	31	7	regular	regular	ADJ
ejpam-3657	31	8	if	if	SCONJ
ejpam-3657	31	9	all	all	DET
ejpam-3657	31	10	vertices	vertex	NOUN
ejpam-3657	31	11	of	of	ADP
ejpam-3657	31	12	g	g	PROPN
ejpam-3657	31	13	have	have	VERB
ejpam-3657	31	14	the	the	DET
ejpam-3657	31	15	same	same	ADJ
ejpam-3657	31	16	degree	degree	NOUN
ejpam-3657	31	17	.	.	PUNCT
ejpam-3657	32	1	thus	thus	ADV
ejpam-3657	32	2	,	,	PUNCT
ejpam-3657	32	3	∆(g	∆(g	NOUN
ejpam-3657	32	4	)	)	PUNCT
ejpam-3657	32	5	=	=	PUNCT
ejpam-3657	32	6	δ(g	δ(g	X
ejpam-3657	32	7	)	)	PUNCT
ejpam-3657	32	8	.	.	PUNCT
ejpam-3657	33	1	given	give	VERB
ejpam-3657	33	2	graphs	graph	NOUN
ejpam-3657	33	3	g	g	NOUN
ejpam-3657	33	4	and	and	CCONJ
ejpam-3657	33	5	h	h	NOUN
ejpam-3657	33	6	with	with	ADP
ejpam-3657	33	7	disjoint	disjoint	ADJ
ejpam-3657	33	8	vertex	vertex	NOUN
ejpam-3657	33	9	sets	set	NOUN
ejpam-3657	33	10	,	,	PUNCT
ejpam-3657	33	11	the	the	DET
ejpam-3657	33	12	join	join	NOUN
ejpam-3657	33	13	of	of	ADP
ejpam-3657	33	14	g	g	PROPN
ejpam-3657	33	15	and	and	CCONJ
ejpam-3657	33	16	h	h	NOUN
ejpam-3657	33	17	,	,	PUNCT
ejpam-3657	33	18	denoted	denote	VERB
ejpam-3657	33	19	by	by	ADP
ejpam-3657	33	20	g+h	g+h	PROPN
ejpam-3657	33	21	,	,	PUNCT
ejpam-3657	33	22	is	be	AUX
ejpam-3657	33	23	the	the	DET
ejpam-3657	33	24	graph	graph	NOUN
ejpam-3657	33	25	with	with	ADP
ejpam-3657	33	26	vertex	vertex	NOUN
ejpam-3657	33	27	set	set	VERB
ejpam-3657	33	28	v	v	NOUN
ejpam-3657	33	29	(	(	PUNCT
ejpam-3657	33	30	g+h	g+h	NOUN
ejpam-3657	33	31	)	)	PUNCT
ejpam-3657	33	32	=	=	SYM
ejpam-3657	33	33	v	v	NOUN
ejpam-3657	33	34	(	(	PUNCT
ejpam-3657	33	35	g)∪	g)∪	VERB
ejpam-3657	33	36	v	v	NUM
ejpam-3657	33	37	(	(	PUNCT
ejpam-3657	33	38	h	h	NOUN
ejpam-3657	33	39	)	)	PUNCT
ejpam-3657	33	40	and	and	CCONJ
ejpam-3657	33	41	edge	edge	NOUN
ejpam-3657	33	42	set	set	VERB
ejpam-3657	33	43	e(g+h	e(g+h	NUM
ejpam-3657	33	44	)	)	PUNCT
ejpam-3657	34	1	=	=	SYM
ejpam-3657	34	2	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	X
ejpam-3657	34	3	:	:	PUNCT
ejpam-3657	34	4	u	u	PROPN
ejpam-3657	34	5	∈	∈	PROPN
ejpam-3657	34	6	v	v	NOUN
ejpam-3657	34	7	(	(	PUNCT
ejpam-3657	34	8	g	g	NOUN
ejpam-3657	34	9	)	)	PUNCT
ejpam-3657	34	10	,	,	PUNCT
ejpam-3657	34	11	v	v	X
ejpam-3657	34	12	∈	∈	PROPN
ejpam-3657	34	13	v	v	NOUN
ejpam-3657	34	14	(	(	PUNCT
ejpam-3657	34	15	h	h	NOUN
ejpam-3657	34	16	)	)	PUNCT
ejpam-3657	34	17	}	}	PUNCT
ejpam-3657	34	18	.	.	PUNCT
ejpam-3657	35	1	for	for	ADP
ejpam-3657	35	2	a	a	DET
ejpam-3657	35	3	nonempty	nonempty	ADJ
ejpam-3657	35	4	set	set	VERB
ejpam-3657	35	5	s	s	PROPN
ejpam-3657	35	6	⊆	⊆	NUM
ejpam-3657	35	7	v	v	NOUN
ejpam-3657	35	8	(	(	PUNCT
ejpam-3657	35	9	g	g	NOUN
ejpam-3657	35	10	)	)	PUNCT
ejpam-3657	35	11	,	,	PUNCT
ejpam-3657	35	12	the	the	DET
ejpam-3657	35	13	subgraph	subgraph	NOUN
ejpam-3657	35	14	〈	〈	PROPN
ejpam-3657	35	15	s〉g	s〉g	NOUN
ejpam-3657	35	16	of	of	ADP
ejpam-3657	35	17	g	g	NOUN
ejpam-3657	35	18	induced	induce	VERB
ejpam-3657	35	19	by	by	ADP
ejpam-3657	35	20	s	s	PROPN
ejpam-3657	35	21	is	be	AUX
ejpam-3657	35	22	the	the	DET
ejpam-3657	35	23	maximal	maximal	ADJ
ejpam-3657	35	24	subgraph	subgraph	NOUN
ejpam-3657	35	25	of	of	ADP
ejpam-3657	35	26	g	g	NOUN
ejpam-3657	35	27	with	with	ADP
ejpam-3657	35	28	vertices	vertex	NOUN
ejpam-3657	35	29	in	in	ADP
ejpam-3657	35	30	s.	s.	PROPN
ejpam-3657	35	31	the	the	DET
ejpam-3657	35	32	δ(g	δ(g	PROPN
ejpam-3657	35	33	:	:	PUNCT
ejpam-3657	35	34	s	s	X
ejpam-3657	35	35	)	)	PUNCT
ejpam-3657	35	36	=	=	SYM
ejpam-3657	35	37	min	min	PROPN
ejpam-3657	35	38	{	{	PUNCT
ejpam-3657	35	39	degg(v	degg(v	PROPN
ejpam-3657	35	40	)	)	PUNCT
ejpam-3657	35	41	:	:	PUNCT
ejpam-3657	35	42	v	v	X
ejpam-3657	35	43	∈	∈	PROPN
ejpam-3657	35	44	s	s	PART
ejpam-3657	35	45	}	}	PUNCT
ejpam-3657	35	46	.	.	PUNCT
ejpam-3657	36	1	a	a	DET
ejpam-3657	36	2	vertex	vertex	NOUN
ejpam-3657	36	3	v	v	NOUN
ejpam-3657	36	4	in	in	ADP
ejpam-3657	36	5	a	a	DET
ejpam-3657	36	6	set	set	NOUN
ejpam-3657	36	7	s	s	NOUN
ejpam-3657	36	8	⊆	⊆	NUM
ejpam-3657	36	9	v	v	NOUN
ejpam-3657	36	10	(	(	PUNCT
ejpam-3657	36	11	g	g	NOUN
ejpam-3657	36	12	)	)	PUNCT
ejpam-3657	36	13	is	be	AUX
ejpam-3657	36	14	a	a	DET
ejpam-3657	36	15	cost	cost	NOUN
ejpam-3657	36	16	effective	effective	ADJ
ejpam-3657	36	17	if	if	SCONJ
ejpam-3657	36	18	|ng(v)∩sc|	|ng(v)∩sc|	ADJ
ejpam-3657	36	19	−	−	PROPN
ejpam-3657	36	20	|ng(v)∩s|	|ng(v)∩s|	PROPN
ejpam-3657	36	21	≥	≥	PROPN
ejpam-3657	36	22	0	0	NUM
ejpam-3657	36	23	.	.	PUNCT
ejpam-3657	37	1	a	a	DET
ejpam-3657	37	2	set	set	NOUN
ejpam-3657	37	3	s	s	NOUN
ejpam-3657	37	4	⊆	⊆	NUM
ejpam-3657	37	5	v	v	NOUN
ejpam-3657	37	6	(	(	PUNCT
ejpam-3657	37	7	g	g	NOUN
ejpam-3657	37	8	)	)	PUNCT
ejpam-3657	37	9	is	be	AUX
ejpam-3657	37	10	called	call	VERB
ejpam-3657	37	11	cost	cost	NOUN
ejpam-3657	37	12	effective	effective	ADJ
ejpam-3657	37	13	if	if	SCONJ
ejpam-3657	37	14	every	every	DET
ejpam-3657	37	15	vertex	vertex	NOUN
ejpam-3657	37	16	v	v	ADP
ejpam-3657	37	17	∈	∈	NOUN
ejpam-3657	37	18	s	s	PART
ejpam-3657	37	19	is	be	AUX
ejpam-3657	37	20	cost	cost	NOUN
ejpam-3657	37	21	effective	effective	ADJ
ejpam-3657	37	22	.	.	PUNCT
ejpam-3657	38	1	the	the	DET
ejpam-3657	38	2	concept	concept	NOUN
ejpam-3657	38	3	of	of	ADP
ejpam-3657	38	4	cost	cost	NOUN
ejpam-3657	38	5	effective	effective	ADJ
ejpam-3657	38	6	set	set	NOUN
ejpam-3657	38	7	in	in	ADP
ejpam-3657	38	8	graph	graph	NOUN
ejpam-3657	38	9	was	be	AUX
ejpam-3657	38	10	introduced	introduce	VERB
ejpam-3657	38	11	by	by	ADP
ejpam-3657	38	12	haynes	hayne	NOUN
ejpam-3657	38	13	,	,	PUNCT
ejpam-3657	38	14	et.al	et.al	PROPN
ejpam-3657	38	15	.	.	PUNCT
ejpam-3657	39	1	in	in	ADP
ejpam-3657	39	2	[	[	X
ejpam-3657	39	3	5	5	NUM
ejpam-3657	39	4	]	]	PUNCT
ejpam-3657	39	5	which	which	PRON
ejpam-3657	39	6	was	be	AUX
ejpam-3657	39	7	motivated	motivate	VERB
ejpam-3657	39	8	by	by	ADP
ejpam-3657	39	9	aharoni	aharoni	PROPN
ejpam-3657	39	10	,	,	PUNCT
ejpam-3657	39	11	et	et	NOUN
ejpam-3657	39	12	.	.	PUNCT
ejpam-3657	39	13	al	al	PROPN
ejpam-3657	39	14	.	.	PUNCT
ejpam-3657	40	1	in	in	ADP
ejpam-3657	40	2	[	[	X
ejpam-3657	40	3	8	8	NUM
ejpam-3657	40	4	]	]	PUNCT
ejpam-3657	40	5	.	.	PUNCT
ejpam-3657	41	1	in	in	ADP
ejpam-3657	41	2	2018	2018	NUM
ejpam-3657	41	3	,	,	PUNCT
ejpam-3657	41	4	chellali	chellali	PROPN
ejpam-3657	41	5	,	,	PUNCT
ejpam-3657	41	6	et	et	NOUN
ejpam-3657	41	7	.	.	PUNCT
ejpam-3657	42	1	al	al	PROPN
ejpam-3657	42	2	.	.	PUNCT
ejpam-3657	43	1	in	in	ADP
ejpam-3657	43	2	[	[	X
ejpam-3657	43	3	2	2	NUM
ejpam-3657	43	4	]	]	PUNCT
ejpam-3657	43	5	established	establish	VERB
ejpam-3657	43	6	a	a	DET
ejpam-3657	43	7	generalization	generalization	NOUN
ejpam-3657	43	8	of	of	ADP
ejpam-3657	43	9	this	this	DET
ejpam-3657	43	10	concept	concept	NOUN
ejpam-3657	43	11	.	.	PUNCT
ejpam-3657	44	1	its	its	PRON
ejpam-3657	44	2	application	application	NOUN
ejpam-3657	44	3	in	in	ADP
ejpam-3657	44	4	computer	computer	NOUN
ejpam-3657	44	5	networks	network	NOUN
ejpam-3657	44	6	plays	play	VERB
ejpam-3657	44	7	a	a	DET
ejpam-3657	44	8	vital	vital	ADJ
ejpam-3657	44	9	role	role	NOUN
ejpam-3657	44	10	:	:	PUNCT
ejpam-3657	44	11	in	in	ADP
ejpam-3657	44	12	particular	particular	ADJ
ejpam-3657	44	13	in	in	ADP
ejpam-3657	44	14	maintaining	maintain	VERB
ejpam-3657	44	15	edges	edge	NOUN
ejpam-3657	44	16	in	in	ADP
ejpam-3657	44	17	a	a	DET
ejpam-3657	44	18	network	network	NOUN
ejpam-3657	44	19	that	that	PRON
ejpam-3657	44	20	are	be	AUX
ejpam-3657	44	21	directly	directly	ADV
ejpam-3657	44	22	associated	associate	VERB
ejpam-3657	44	23	with	with	ADP
ejpam-3657	44	24	the	the	DET
ejpam-3657	44	25	cost	cost	NOUN
ejpam-3657	44	26	that	that	PRON
ejpam-3657	44	27	should	should	AUX
ejpam-3657	44	28	be	be	AUX
ejpam-3657	44	29	used	use	VERB
ejpam-3657	44	30	effectively	effectively	ADV
ejpam-3657	44	31	and	and	CCONJ
ejpam-3657	44	32	in	in	ADP
ejpam-3657	44	33	a	a	DET
ejpam-3657	44	34	set	set	NOUN
ejpam-3657	44	35	of	of	ADP
ejpam-3657	44	36	servers	server	NOUN
ejpam-3657	44	37	(	(	PUNCT
ejpam-3657	44	38	vertices	vertex	NOUN
ejpam-3657	44	39	)	)	PUNCT
ejpam-3657	44	40	that	that	SCONJ
ejpam-3657	44	41	each	each	DET
ejpam-3657	44	42	server	server	NOUN
ejpam-3657	44	43	is	be	AUX
ejpam-3657	44	44	serving	serve	VERB
ejpam-3657	44	45	a	a	DET
ejpam-3657	44	46	maximal	maximal	ADJ
ejpam-3657	44	47	number	number	NOUN
ejpam-3657	44	48	of	of	ADP
ejpam-3657	44	49	clients	client	NOUN
ejpam-3657	44	50	(	(	PUNCT
ejpam-3657	44	51	non	non	ADJ
ejpam-3657	44	52	-	-	NOUN
ejpam-3657	44	53	servers	server	NOUN
ejpam-3657	44	54	)	)	PUNCT
ejpam-3657	44	55	.	.	PUNCT
ejpam-3657	45	1	we	we	PRON
ejpam-3657	45	2	refer	refer	VERB
ejpam-3657	45	3	the	the	DET
ejpam-3657	45	4	readers	reader	NOUN
ejpam-3657	45	5	to	to	ADP
ejpam-3657	45	6	[	[	X
ejpam-3657	45	7	2	2	NUM
ejpam-3657	45	8	,	,	PUNCT
ejpam-3657	45	9	4	4	NUM
ejpam-3657	45	10	]	]	PUNCT
ejpam-3657	45	11	for	for	ADP
ejpam-3657	45	12	some	some	PRON
ejpam-3657	45	13	of	of	ADP
ejpam-3657	45	14	its	its	PRON
ejpam-3657	45	15	relevant	relevant	ADJ
ejpam-3657	45	16	applications	application	NOUN
ejpam-3657	45	17	and	and	CCONJ
ejpam-3657	45	18	to	to	ADP
ejpam-3657	45	19	[	[	X
ejpam-3657	45	20	3	3	NUM
ejpam-3657	45	21	,	,	PUNCT
ejpam-3657	45	22	6	6	NUM
ejpam-3657	45	23	,	,	PUNCT
ejpam-3657	45	24	9	9	NUM
ejpam-3657	45	25	]	]	PUNCT
ejpam-3657	45	26	for	for	ADP
ejpam-3657	45	27	some	some	DET
ejpam-3657	45	28	investigations	investigation	NOUN
ejpam-3657	45	29	of	of	ADP
ejpam-3657	45	30	the	the	DET
ejpam-3657	45	31	concepts	concept	NOUN
ejpam-3657	45	32	.	.	PUNCT
ejpam-3657	46	1	in	in	ADP
ejpam-3657	46	2	this	this	DET
ejpam-3657	46	3	paper	paper	NOUN
ejpam-3657	46	4	,	,	PUNCT
ejpam-3657	46	5	we	we	PRON
ejpam-3657	46	6	characterized	characterize	VERB
ejpam-3657	46	7	the	the	DET
ejpam-3657	46	8	distance	distance	NOUN
ejpam-3657	46	9	kcost	kcost	NOUN
ejpam-3657	46	10	effective	effective	ADJ
ejpam-3657	46	11	sets	set	NOUN
ejpam-3657	46	12	in	in	ADP
ejpam-3657	46	13	the	the	DET
ejpam-3657	46	14	join	join	NOUN
ejpam-3657	46	15	of	of	ADP
ejpam-3657	46	16	two	two	NUM
ejpam-3657	46	17	graphs	graph	NOUN
ejpam-3657	46	18	.	.	PUNCT
ejpam-3657	47	1	as	as	ADP
ejpam-3657	47	2	direct	direct	ADJ
ejpam-3657	47	3	consequences	consequence	NOUN
ejpam-3657	47	4	,	,	PUNCT
ejpam-3657	47	5	we	we	PRON
ejpam-3657	47	6	determined	determine	VERB
ejpam-3657	47	7	the	the	DET
ejpam-3657	47	8	bounds	bound	NOUN
ejpam-3657	47	9	or	or	CCONJ
ejpam-3657	47	10	the	the	DET
ejpam-3657	47	11	exact	exact	ADJ
ejpam-3657	47	12	values	value	NOUN
ejpam-3657	47	13	of	of	ADP
ejpam-3657	47	14	the	the	DET
ejpam-3657	47	15	upper	upper	ADJ
ejpam-3657	47	16	distance	distance	NOUN
ejpam-3657	47	17	k	k	ADJ
ejpam-3657	47	18	-	-	PUNCT
ejpam-3657	47	19	cost	cost	ADJ
ejpam-3657	47	20	effective	effective	ADJ
ejpam-3657	47	21	numbers	number	NOUN
ejpam-3657	47	22	of	of	ADP
ejpam-3657	47	23	the	the	DET
ejpam-3657	47	24	join	join	NOUN
ejpam-3657	47	25	of	of	ADP
ejpam-3657	47	26	graphs	graph	NOUN
ejpam-3657	47	27	.	.	PUNCT
ejpam-3657	48	1	2	2	X
ejpam-3657	48	2	.	.	X
ejpam-3657	48	3	results	result	NOUN
ejpam-3657	48	4	remark	remark	VERB
ejpam-3657	48	5	1	1	NUM
ejpam-3657	48	6	.	.	PUNCT
ejpam-3657	49	1	let	let	VERB
ejpam-3657	49	2	g	g	PRON
ejpam-3657	49	3	be	be	AUX
ejpam-3657	49	4	a	a	DET
ejpam-3657	49	5	connected	connected	ADJ
ejpam-3657	49	6	graph	graph	NOUN
ejpam-3657	49	7	.	.	PUNCT
ejpam-3657	50	1	if	if	SCONJ
ejpam-3657	50	2	s	s	VERB
ejpam-3657	50	3	⊆	⊆	NUM
ejpam-3657	50	4	v	v	NOUN
ejpam-3657	50	5	(	(	PUNCT
ejpam-3657	50	6	g	g	NOUN
ejpam-3657	50	7	)	)	PUNCT
ejpam-3657	50	8	is	be	AUX
ejpam-3657	50	9	a	a	DET
ejpam-3657	50	10	distance	distance	NOUN
ejpam-3657	50	11	kcost	kcost	NOUN
ejpam-3657	50	12	effective	effective	ADJ
ejpam-3657	50	13	then	then	ADV
ejpam-3657	50	14	every	every	DET
ejpam-3657	50	15	subset	subset	NOUN
ejpam-3657	50	16	of	of	ADP
ejpam-3657	50	17	s	s	PROPN
ejpam-3657	50	18	is	be	AUX
ejpam-3657	50	19	also	also	ADV
ejpam-3657	50	20	a	a	DET
ejpam-3657	50	21	distance	distance	NOUN
ejpam-3657	50	22	k	k	ADJ
ejpam-3657	50	23	-	-	PUNCT
ejpam-3657	50	24	cost	cost	NOUN
ejpam-3657	50	25	effective	effective	ADJ
ejpam-3657	50	26	in	in	ADP
ejpam-3657	50	27	g.	g.	PROPN
ejpam-3657	50	28	definition	definition	NOUN
ejpam-3657	50	29	1	1	NUM
ejpam-3657	50	30	.	.	PUNCT
ejpam-3657	51	1	let	let	VERB
ejpam-3657	51	2	g	g	PRON
ejpam-3657	51	3	be	be	AUX
ejpam-3657	51	4	a	a	DET
ejpam-3657	51	5	connected	connected	ADJ
ejpam-3657	51	6	graph	graph	NOUN
ejpam-3657	51	7	and	and	CCONJ
ejpam-3657	51	8	k	k	PROPN
ejpam-3657	51	9	be	be	AUX
ejpam-3657	51	10	a	a	DET
ejpam-3657	51	11	positive	positive	ADJ
ejpam-3657	51	12	integer	integer	NOUN
ejpam-3657	51	13	.	.	PUNCT
ejpam-3657	52	1	a	a	DET
ejpam-3657	52	2	set	set	NOUN
ejpam-3657	52	3	s	s	NOUN
ejpam-3657	52	4	⊆	⊆	NUM
ejpam-3657	52	5	v	v	NOUN
ejpam-3657	52	6	(	(	PUNCT
ejpam-3657	52	7	g	g	NOUN
ejpam-3657	52	8	)	)	PUNCT
ejpam-3657	52	9	is	be	AUX
ejpam-3657	52	10	a	a	DET
ejpam-3657	52	11	distance	distance	NOUN
ejpam-3657	52	12	kcost	kcost	NOUN
ejpam-3657	52	13	effective	effective	ADJ
ejpam-3657	52	14	set	set	NOUN
ejpam-3657	52	15	of	of	ADP
ejpam-3657	52	16	g	g	PROPN
ejpam-3657	52	17	if	if	SCONJ
ejpam-3657	52	18	for	for	ADP
ejpam-3657	52	19	every	every	DET
ejpam-3657	52	20	v	v	NUM
ejpam-3657	52	21	∈	∈	PROPN
ejpam-3657	52	22	s	s	NOUN
ejpam-3657	52	23	,	,	PUNCT
ejpam-3657	52	24	|nk	|nk	X
ejpam-3657	52	25	g(v	g(v	NOUN
ejpam-3657	52	26	)	)	PUNCT
ejpam-3657	52	27	∩	∩	NOUN
ejpam-3657	52	28	sc|	sc|	PROPN
ejpam-3657	52	29	−	−	PROPN
ejpam-3657	52	30	|nk	|nk	ADP
ejpam-3657	52	31	g(v	g(v	PROPN
ejpam-3657	52	32	)	)	PUNCT
ejpam-3657	52	33	∩	∩	NOUN
ejpam-3657	52	34	s|	s|	VERB
ejpam-3657	52	35	≥	≥	NOUN
ejpam-3657	52	36	0	0	NUM
ejpam-3657	52	37	.	.	PUNCT
ejpam-3657	53	1	the	the	DET
ejpam-3657	53	2	upper	upper	ADJ
ejpam-3657	53	3	distance	distance	NOUN
ejpam-3657	53	4	kcost	kcost	NOUN
ejpam-3657	53	5	effective	effective	ADJ
ejpam-3657	53	6	number	number	NOUN
ejpam-3657	53	7	of	of	ADP
ejpam-3657	53	8	a	a	DET
ejpam-3657	53	9	graph	graph	NOUN
ejpam-3657	53	10	g	g	NOUN
ejpam-3657	53	11	,	,	PUNCT
ejpam-3657	53	12	denoted	denote	VERB
ejpam-3657	53	13	by	by	ADP
ejpam-3657	53	14	αkce(g	αkce(g	NOUN
ejpam-3657	53	15	)	)	PUNCT
ejpam-3657	53	16	,	,	PUNCT
ejpam-3657	53	17	is	be	AUX
ejpam-3657	53	18	the	the	DET
ejpam-3657	53	19	maximum	maximum	ADJ
ejpam-3657	53	20	cardinality	cardinality	NOUN
ejpam-3657	53	21	of	of	ADP
ejpam-3657	53	22	a	a	DET
ejpam-3657	53	23	distance	distance	NOUN
ejpam-3657	53	24	k	k	PROPN
ejpam-3657	53	25	cost	cost	VERB
ejpam-3657	53	26	effective	effective	ADJ
ejpam-3657	53	27	set	set	NOUN
ejpam-3657	53	28	in	in	ADP
ejpam-3657	53	29	g.	g.	PROPN
ejpam-3657	53	30	it	it	PRON
ejpam-3657	53	31	is	be	AUX
ejpam-3657	53	32	worth	worth	ADJ
ejpam-3657	53	33	noting	note	VERB
ejpam-3657	53	34	that	that	SCONJ
ejpam-3657	53	35	the	the	DET
ejpam-3657	53	36	concept	concept	NOUN
ejpam-3657	53	37	of	of	ADP
ejpam-3657	53	38	a	a	DET
ejpam-3657	53	39	distance	distance	NOUN
ejpam-3657	53	40	1cost	1cost	NUM
ejpam-3657	53	41	effective	effective	ADJ
ejpam-3657	53	42	set	set	NOUN
ejpam-3657	53	43	in	in	ADP
ejpam-3657	53	44	g	g	PROPN
ejpam-3657	53	45	is	be	AUX
ejpam-3657	53	46	just	just	ADV
ejpam-3657	53	47	equivalent	equivalent	ADJ
ejpam-3657	53	48	to	to	ADP
ejpam-3657	53	49	the	the	DET
ejpam-3657	53	50	concept	concept	NOUN
ejpam-3657	53	51	of	of	ADP
ejpam-3657	53	52	a	a	DET
ejpam-3657	53	53	cost	cost	NOUN
ejpam-3657	53	54	effective	effective	ADJ
ejpam-3657	53	55	set	set	NOUN
ejpam-3657	53	56	in	in	ADP
ejpam-3657	53	57	g.	g.	PROPN
ejpam-3657	53	58	example	example	NOUN
ejpam-3657	54	1	1	1	X
ejpam-3657	54	2	.	.	PUNCT
ejpam-3657	55	1	let	let	VERB
ejpam-3657	55	2	k	k	PROPN
ejpam-3657	55	3	and	and	CCONJ
ejpam-3657	55	4	n	n	CCONJ
ejpam-3657	55	5	be	be	VERB
ejpam-3657	55	6	positive	positive	ADJ
ejpam-3657	55	7	integers	integer	NOUN
ejpam-3657	55	8	.	.	PUNCT
ejpam-3657	56	1	for	for	ADP
ejpam-3657	56	2	any	any	DET
ejpam-3657	56	3	complete	complete	ADJ
ejpam-3657	56	4	graph	graph	NOUN
ejpam-3657	56	5	kn	kn	PROPN
ejpam-3657	56	6	,	,	PUNCT
ejpam-3657	56	7	a	a	DET
ejpam-3657	56	8	set	set	NOUN
ejpam-3657	56	9	s	s	VERB
ejpam-3657	56	10	is	be	AUX
ejpam-3657	56	11	a	a	DET
ejpam-3657	56	12	distance	distance	NOUN
ejpam-3657	56	13	kcost	kcost	NOUN
ejpam-3657	56	14	effective	effective	ADJ
ejpam-3657	56	15	in	in	ADP
ejpam-3657	56	16	kn	kn	PROPN
ejpam-3657	56	17	if	if	SCONJ
ejpam-3657	56	18	and	and	CCONJ
ejpam-3657	56	19	only	only	ADV
ejpam-3657	57	1	if	if	SCONJ
ejpam-3657	57	2	|s|	|s|	NOUN
ejpam-3657	57	3	≤	≤	X
ejpam-3657	57	4	bn+1	bn+1	NUM
ejpam-3657	57	5	2	2	NUM
ejpam-3657	57	6	c.	c.	NOUN
ejpam-3657	57	7	hence	hence	ADV
ejpam-3657	57	8	,	,	PUNCT
ejpam-3657	57	9	αkce(kn	αkce(kn	NOUN
ejpam-3657	57	10	)	)	PUNCT
ejpam-3657	57	11	=	=	SYM
ejpam-3657	57	12	bn+1	bn+1	PROPN
ejpam-3657	57	13	2	2	NUM
ejpam-3657	57	14	c.	c.	NOUN
ejpam-3657	57	15	remark	remark	NOUN
ejpam-3657	57	16	2	2	NUM
ejpam-3657	57	17	.	.	PUNCT
ejpam-3657	58	1	let	let	VERB
ejpam-3657	58	2	g	g	NOUN
ejpam-3657	58	3	and	and	CCONJ
ejpam-3657	58	4	h	h	NOUN
ejpam-3657	58	5	be	be	VERB
ejpam-3657	58	6	any	any	DET
ejpam-3657	58	7	connected	connected	ADJ
ejpam-3657	58	8	graphs	graph	NOUN
ejpam-3657	58	9	and	and	CCONJ
ejpam-3657	58	10	k	k	PROPN
ejpam-3657	58	11	be	be	AUX
ejpam-3657	58	12	any	any	DET
ejpam-3657	58	13	positive	positive	ADJ
ejpam-3657	58	14	integer	integer	NOUN
ejpam-3657	58	15	.	.	PUNCT
ejpam-3657	59	1	j.	j.	PROPN
ejpam-3657	59	2	g.	g.	PROPN
ejpam-3657	59	3	caadan	caadan	PROPN
ejpam-3657	59	4	,	,	PUNCT
ejpam-3657	59	5	r.	r.	PROPN
ejpam-3657	59	6	n.	n.	PROPN
ejpam-3657	59	7	paluga	paluga	PROPN
ejpam-3657	59	8	,	,	PUNCT
ejpam-3657	59	9	i.	i.	PROPN
ejpam-3657	59	10	s.	s.	PROPN
ejpam-3657	59	11	aniversario	aniversario	PROPN
ejpam-3657	59	12	/	/	SYM
ejpam-3657	59	13	eur	eur	PROPN
ejpam-3657	59	14	.	.	PUNCT
ejpam-3657	60	1	j.	j.	PROPN
ejpam-3657	60	2	pure	pure	PROPN
ejpam-3657	60	3	appl	appl	PROPN
ejpam-3657	60	4	.	.	PROPN
ejpam-3657	60	5	math	math	PROPN
ejpam-3657	60	6	,	,	PUNCT
ejpam-3657	60	7	13	13	NUM
ejpam-3657	60	8	(	(	PUNCT
ejpam-3657	60	9	3	3	NUM
ejpam-3657	60	10	)	)	PUNCT
ejpam-3657	60	11	(	(	PUNCT
ejpam-3657	60	12	2020	2020	NUM
ejpam-3657	60	13	)	)	PUNCT
ejpam-3657	60	14	,	,	PUNCT
ejpam-3657	60	15	701	701	NUM
ejpam-3657	60	16	-	-	SYM
ejpam-3657	60	17	709	709	NUM
ejpam-3657	60	18	703	703	NUM
ejpam-3657	60	19	(	(	PUNCT
ejpam-3657	60	20	i	i	NOUN
ejpam-3657	60	21	)	)	PUNCT
ejpam-3657	60	22	if	if	SCONJ
ejpam-3657	60	23	s	s	VERB
ejpam-3657	60	24	⊆	⊆	NUM
ejpam-3657	60	25	v	v	NOUN
ejpam-3657	60	26	(	(	PUNCT
ejpam-3657	60	27	g	g	NOUN
ejpam-3657	60	28	)	)	PUNCT
ejpam-3657	60	29	is	be	AUX
ejpam-3657	60	30	a	a	DET
ejpam-3657	60	31	distance	distance	NOUN
ejpam-3657	60	32	kcost	kcost	NOUN
ejpam-3657	60	33	effective	effective	ADJ
ejpam-3657	60	34	set	set	NOUN
ejpam-3657	60	35	in	in	ADP
ejpam-3657	60	36	g	g	NOUN
ejpam-3657	60	37	,	,	PUNCT
ejpam-3657	60	38	then	then	ADV
ejpam-3657	60	39	s	s	VERB
ejpam-3657	60	40	is	be	AUX
ejpam-3657	60	41	a	a	DET
ejpam-3657	60	42	distance	distance	NOUN
ejpam-3657	60	43	k	k	ADJ
ejpam-3657	60	44	-	-	PUNCT
ejpam-3657	60	45	cost	cost	ADJ
ejpam-3657	60	46	effective	effective	ADJ
ejpam-3657	60	47	set	set	NOUN
ejpam-3657	60	48	in	in	ADP
ejpam-3657	60	49	g+h	g+h	PROPN
ejpam-3657	60	50	.	.	PUNCT
ejpam-3657	61	1	(	(	PUNCT
ejpam-3657	61	2	ii	ii	NOUN
ejpam-3657	61	3	)	)	PUNCT
ejpam-3657	61	4	if	if	SCONJ
ejpam-3657	61	5	s	s	VERB
ejpam-3657	61	6	⊆	⊆	NUM
ejpam-3657	61	7	v	v	NOUN
ejpam-3657	61	8	(	(	PUNCT
ejpam-3657	61	9	h	h	NOUN
ejpam-3657	61	10	)	)	PUNCT
ejpam-3657	61	11	is	be	AUX
ejpam-3657	61	12	a	a	DET
ejpam-3657	61	13	distance	distance	NOUN
ejpam-3657	61	14	kcost	kcost	NOUN
ejpam-3657	61	15	effective	effective	ADJ
ejpam-3657	61	16	set	set	NOUN
ejpam-3657	61	17	in	in	ADP
ejpam-3657	61	18	h	h	NOUN
ejpam-3657	61	19	,	,	PUNCT
ejpam-3657	61	20	then	then	ADV
ejpam-3657	61	21	s	s	VERB
ejpam-3657	61	22	is	be	AUX
ejpam-3657	61	23	a	a	DET
ejpam-3657	61	24	distance	distance	NOUN
ejpam-3657	61	25	kcost	kcost	NOUN
ejpam-3657	61	26	effective	effective	ADJ
ejpam-3657	61	27	set	set	NOUN
ejpam-3657	61	28	in	in	ADP
ejpam-3657	61	29	g+h	g+h	PROPN
ejpam-3657	61	30	.	.	PUNCT
ejpam-3657	62	1	remark	remark	PROPN
ejpam-3657	62	2	3	3	NUM
ejpam-3657	62	3	.	.	PUNCT
ejpam-3657	63	1	let	let	VERB
ejpam-3657	63	2	g	g	NOUN
ejpam-3657	64	1	and	and	CCONJ
ejpam-3657	64	2	h	h	NOUN
ejpam-3657	64	3	be	be	VERB
ejpam-3657	64	4	any	any	DET
ejpam-3657	64	5	connected	connected	ADJ
ejpam-3657	64	6	graphs	graph	NOUN
ejpam-3657	64	7	and	and	CCONJ
ejpam-3657	64	8	k	k	PROPN
ejpam-3657	64	9	be	be	AUX
ejpam-3657	64	10	any	any	DET
ejpam-3657	64	11	positive	positive	ADJ
ejpam-3657	64	12	integer	integer	NOUN
ejpam-3657	64	13	.	.	PUNCT
ejpam-3657	65	1	then	then	ADV
ejpam-3657	65	2	αkce(g+h	αkce(g+h	ADV
ejpam-3657	65	3	)	)	PUNCT
ejpam-3657	65	4	≥	≥	PROPN
ejpam-3657	65	5	max{αkce(g	max{αkce(g	PROPN
ejpam-3657	65	6	)	)	PUNCT
ejpam-3657	65	7	,	,	PUNCT
ejpam-3657	65	8	αkce(h	αkce(h	NOUN
ejpam-3657	65	9	)	)	PUNCT
ejpam-3657	65	10	}	}	PUNCT
ejpam-3657	65	11	.	.	PUNCT
ejpam-3657	66	1	example	example	NOUN
ejpam-3657	67	1	2	2	NUM
ejpam-3657	67	2	.	.	PUNCT
ejpam-3657	67	3	let	let	VERB
ejpam-3657	67	4	g	g	PROPN
ejpam-3657	67	5	=	=	PUNCT
ejpam-3657	67	6	c8	c8	PROPN
ejpam-3657	67	7	and	and	CCONJ
ejpam-3657	67	8	h	h	NOUN
ejpam-3657	67	9	=	=	SYM
ejpam-3657	67	10	k1,9	k1,9	PROPN
ejpam-3657	67	11	.	.	PUNCT
ejpam-3657	68	1	then	then	ADV
ejpam-3657	68	2	α1	α1	PROPN
ejpam-3657	68	3	ce(g	ce(g	PUNCT
ejpam-3657	68	4	+	+	CCONJ
ejpam-3657	68	5	h	h	NOUN
ejpam-3657	68	6	)	)	PUNCT
ejpam-3657	68	7	=	=	SYM
ejpam-3657	68	8	α1	α1	PROPN
ejpam-3657	68	9	ce(h	ce(h	NOUN
ejpam-3657	68	10	)	)	PUNCT
ejpam-3657	68	11	and	and	CCONJ
ejpam-3657	68	12	for	for	ADP
ejpam-3657	68	13	any	any	DET
ejpam-3657	68	14	connected	connected	ADJ
ejpam-3657	68	15	graph	graph	NOUN
ejpam-3657	68	16	g	g	NOUN
ejpam-3657	68	17	and	and	CCONJ
ejpam-3657	68	18	for	for	ADP
ejpam-3657	68	19	all	all	DET
ejpam-3657	68	20	integers	integer	NOUN
ejpam-3657	68	21	k	k	X
ejpam-3657	68	22	≥	≥	NUM
ejpam-3657	68	23	2	2	NUM
ejpam-3657	68	24	,	,	PUNCT
ejpam-3657	68	25	αkce(g+k1	αkce(g+k1	NOUN
ejpam-3657	68	26	)	)	PUNCT
ejpam-3657	68	27	=	=	SYM
ejpam-3657	68	28	αkce(g	αkce(g	PROPN
ejpam-3657	68	29	)	)	PUNCT
ejpam-3657	68	30	.	.	PUNCT
ejpam-3657	69	1	theorem	theorem	NOUN
ejpam-3657	69	2	1	1	NUM
ejpam-3657	69	3	.	.	PUNCT
ejpam-3657	70	1	let	let	VERB
ejpam-3657	70	2	k	k	PRON
ejpam-3657	70	3	be	be	AUX
ejpam-3657	70	4	a	a	DET
ejpam-3657	70	5	positive	positive	ADJ
ejpam-3657	70	6	integer	integer	NOUN
ejpam-3657	70	7	and	and	CCONJ
ejpam-3657	70	8	g	g	PROPN
ejpam-3657	70	9	be	be	AUX
ejpam-3657	70	10	a	a	DET
ejpam-3657	70	11	connected	connected	ADJ
ejpam-3657	70	12	graph	graph	NOUN
ejpam-3657	70	13	such	such	ADJ
ejpam-3657	70	14	that	that	SCONJ
ejpam-3657	70	15	k	k	PROPN
ejpam-3657	70	16	≥	≥	NUM
ejpam-3657	70	17	diam(g	diam(g	PROPN
ejpam-3657	70	18	)	)	PUNCT
ejpam-3657	70	19	.	.	PUNCT
ejpam-3657	71	1	then	then	ADV
ejpam-3657	71	2	s	s	VERB
ejpam-3657	71	3	is	be	AUX
ejpam-3657	71	4	a	a	DET
ejpam-3657	71	5	distance	distance	NOUN
ejpam-3657	71	6	k	k	ADJ
ejpam-3657	71	7	-	-	PUNCT
ejpam-3657	71	8	cost	cost	ADJ
ejpam-3657	71	9	effective	effective	ADJ
ejpam-3657	71	10	set	set	NOUN
ejpam-3657	71	11	in	in	ADP
ejpam-3657	71	12	g	g	PROPN
ejpam-3657	71	13	if	if	SCONJ
ejpam-3657	72	1	and	and	CCONJ
ejpam-3657	72	2	only	only	ADV
ejpam-3657	72	3	if	if	SCONJ
ejpam-3657	72	4	|s|	|s|	NOUN
ejpam-3657	72	5	≤	≤	NUM
ejpam-3657	72	6	b	b	PROPN
ejpam-3657	72	7	|v	|v	X
ejpam-3657	72	8	(	(	PUNCT
ejpam-3657	72	9	g)|+1	g)|+1	PROPN
ejpam-3657	72	10	2	2	NUM
ejpam-3657	72	11	c.	c.	NOUN
ejpam-3657	72	12	proof	proof	NOUN
ejpam-3657	72	13	:	:	PUNCT
ejpam-3657	72	14	let	let	VERB
ejpam-3657	72	15	k	k	PRON
ejpam-3657	72	16	be	be	AUX
ejpam-3657	72	17	a	a	DET
ejpam-3657	72	18	positive	positive	ADJ
ejpam-3657	72	19	integer	integer	NOUN
ejpam-3657	72	20	and	and	CCONJ
ejpam-3657	72	21	g	g	PROPN
ejpam-3657	72	22	be	be	AUX
ejpam-3657	72	23	a	a	DET
ejpam-3657	72	24	connected	connected	ADJ
ejpam-3657	72	25	graph	graph	NOUN
ejpam-3657	72	26	such	such	ADJ
ejpam-3657	72	27	that	that	SCONJ
ejpam-3657	72	28	k	k	PROPN
ejpam-3657	72	29	≥	≥	NUM
ejpam-3657	72	30	diam(g	diam(g	PROPN
ejpam-3657	72	31	)	)	PUNCT
ejpam-3657	72	32	.	.	PUNCT
ejpam-3657	73	1	suppose	suppose	VERB
ejpam-3657	73	2	s	s	PRON
ejpam-3657	73	3	is	be	AUX
ejpam-3657	73	4	a	a	DET
ejpam-3657	73	5	distance	distance	NOUN
ejpam-3657	73	6	k	k	ADJ
ejpam-3657	73	7	-	-	PUNCT
ejpam-3657	73	8	cost	cost	NOUN
ejpam-3657	73	9	effective	effective	ADJ
ejpam-3657	73	10	set	set	NOUN
ejpam-3657	73	11	in	in	ADP
ejpam-3657	73	12	g.	g.	PROPN
ejpam-3657	73	13	then	then	ADV
ejpam-3657	73	14	for	for	ADP
ejpam-3657	73	15	each	each	DET
ejpam-3657	73	16	u	u	PROPN
ejpam-3657	73	17	∈	∈	PROPN
ejpam-3657	73	18	s	s	PROPN
ejpam-3657	73	19	,	,	PUNCT
ejpam-3657	73	20	|nk	|nk	PROPN
ejpam-3657	73	21	g(u	g(u	PROPN
ejpam-3657	73	22	)	)	PUNCT
ejpam-3657	73	23	∩	∩	NOUN
ejpam-3657	74	1	sc|	sc|	PROPN
ejpam-3657	74	2	−	−	PROPN
ejpam-3657	74	3	|nk	|nk	SYM
ejpam-3657	74	4	g(u	g(u	PROPN
ejpam-3657	74	5	)	)	PUNCT
ejpam-3657	74	6	∩	∩	NOUN
ejpam-3657	74	7	s|	s|	NOUN
ejpam-3657	74	8	=	=	SYM
ejpam-3657	75	1	|	|	ADV
ejpam-3657	75	2	(	(	PUNCT
ejpam-3657	75	3	v	v	NOUN
ejpam-3657	75	4	(	(	PUNCT
ejpam-3657	75	5	g	g	NOUN
ejpam-3657	75	6	)	)	PUNCT
ejpam-3657	75	7	\	\	NOUN
ejpam-3657	75	8	{	{	PUNCT
ejpam-3657	75	9	u	u	NOUN
ejpam-3657	75	10	}	}	PUNCT
ejpam-3657	75	11	)	)	PUNCT
ejpam-3657	75	12	∩	∩	PROPN
ejpam-3657	76	1	sc|	sc|	PROPN
ejpam-3657	76	2	−	−	NOUN
ejpam-3657	77	1	|	|	NOUN
ejpam-3657	77	2	(	(	PUNCT
ejpam-3657	77	3	v	v	NOUN
ejpam-3657	77	4	(	(	PUNCT
ejpam-3657	77	5	g	g	NOUN
ejpam-3657	77	6	)	)	PUNCT
ejpam-3657	77	7	\	\	NOUN
ejpam-3657	77	8	{	{	PUNCT
ejpam-3657	77	9	u	u	NOUN
ejpam-3657	77	10	}	}	PUNCT
ejpam-3657	77	11	)	)	PUNCT
ejpam-3657	77	12	∩	∩	NOUN
ejpam-3657	77	13	s|	s|	NOUN
ejpam-3657	77	14	=	=	SYM
ejpam-3657	78	1	|sc|	|sc|	NUM
ejpam-3657	78	2	−	−	PROPN
ejpam-3657	78	3	(	(	PUNCT
ejpam-3657	78	4	|s|	|s|	NOUN
ejpam-3657	78	5	−	−	NOUN
ejpam-3657	78	6	1	1	NUM
ejpam-3657	78	7	)	)	PUNCT
ejpam-3657	78	8	=	=	SYM
ejpam-3657	79	1	|v	|v	PROPN
ejpam-3657	79	2	(	(	PUNCT
ejpam-3657	79	3	g)|	g)|	NOUN
ejpam-3657	79	4	−	−	PROPN
ejpam-3657	79	5	|s|	|s|	NOUN
ejpam-3657	79	6	−	−	PROPN
ejpam-3657	79	7	|s|+	|s|+	PROPN
ejpam-3657	79	8	1	1	NUM
ejpam-3657	79	9	=	=	SYM
ejpam-3657	79	10	|v	|v	X
ejpam-3657	79	11	(	(	PUNCT
ejpam-3657	79	12	g)|+	g)|+	NOUN
ejpam-3657	79	13	1−	1−	NUM
ejpam-3657	79	14	2|s|	2|s|	NUM
ejpam-3657	79	15	≥	≥	NOUN
ejpam-3657	79	16	0	0	NUM
ejpam-3657	79	17	.	.	PUNCT
ejpam-3657	80	1	that	that	PRON
ejpam-3657	80	2	is	is	ADV
ejpam-3657	80	3	,	,	PUNCT
ejpam-3657	80	4	|s|	|s|	NOUN
ejpam-3657	80	5	≤	≤	NUM
ejpam-3657	80	6	|v	|v	X
ejpam-3657	80	7	(	(	PUNCT
ejpam-3657	80	8	g)|+1	g)|+1	NOUN
ejpam-3657	80	9	2	2	NUM
ejpam-3657	80	10	.	.	PUNCT
ejpam-3657	81	1	since	since	SCONJ
ejpam-3657	81	2	|s|	|s|	PROPN
ejpam-3657	81	3	is	be	AUX
ejpam-3657	81	4	an	an	DET
ejpam-3657	81	5	integer	integer	NOUN
ejpam-3657	81	6	,	,	PUNCT
ejpam-3657	81	7	|s|	|s|	VERB
ejpam-3657	81	8	≤	≤	NUM
ejpam-3657	81	9	b	b	PROPN
ejpam-3657	81	10	|v	|v	X
ejpam-3657	81	11	(	(	PUNCT
ejpam-3657	81	12	g)|+1	g)|+1	PROPN
ejpam-3657	81	13	2	2	NUM
ejpam-3657	81	14	c.	c.	NOUN
ejpam-3657	81	15	suppose	suppose	VERB
ejpam-3657	81	16	that	that	SCONJ
ejpam-3657	81	17	|s|	|s|	VERB
ejpam-3657	81	18	≤	≤	PROPN
ejpam-3657	81	19	b	b	PROPN
ejpam-3657	81	20	|v	|v	X
ejpam-3657	81	21	(	(	PUNCT
ejpam-3657	81	22	g)|+1	g)|+1	PROPN
ejpam-3657	81	23	2	2	NUM
ejpam-3657	81	24	c.	c.	NOUN
ejpam-3657	81	25	then	then	ADV
ejpam-3657	81	26	|s|	|s|	VERB
ejpam-3657	81	27	≤	≤	PROPN
ejpam-3657	81	28	|v	|v	X
ejpam-3657	81	29	(	(	PUNCT
ejpam-3657	81	30	g)|+1	g)|+1	PROPN
ejpam-3657	81	31	2	2	NUM
ejpam-3657	81	32	.	.	PUNCT
ejpam-3657	82	1	equivalently	equivalently	ADV
ejpam-3657	82	2	,	,	PUNCT
ejpam-3657	82	3	2|s|	2|s|	NUM
ejpam-3657	82	4	≤	≤	NUM
ejpam-3657	82	5	|v	|v	X
ejpam-3657	82	6	(	(	PUNCT
ejpam-3657	82	7	g)|+	g)|+	NOUN
ejpam-3657	82	8	1	1	NUM
ejpam-3657	82	9	.	.	PUNCT
ejpam-3657	82	10	let	let	VERB
ejpam-3657	82	11	u	u	PRON
ejpam-3657	82	12	∈	∈	PROPN
ejpam-3657	82	13	s.	s.	PROPN
ejpam-3657	82	14	then	then	ADV
ejpam-3657	82	15	|nk	|nk	ADP
ejpam-3657	82	16	g(u	g(u	PROPN
ejpam-3657	82	17	)	)	PUNCT
ejpam-3657	82	18	∩	∩	NOUN
ejpam-3657	82	19	sc|	sc|	PROPN
ejpam-3657	82	20	−	−	PROPN
ejpam-3657	82	21	|nk	|nk	SYM
ejpam-3657	82	22	g(u	g(u	PROPN
ejpam-3657	82	23	)	)	PUNCT
ejpam-3657	82	24	∩	∩	NOUN
ejpam-3657	82	25	s|	s|	NOUN
ejpam-3657	82	26	=	=	SYM
ejpam-3657	82	27	|v	|v	X
ejpam-3657	82	28	(	(	PUNCT
ejpam-3657	82	29	g)|	g)|	NOUN
ejpam-3657	82	30	−	−	PROPN
ejpam-3657	82	31	|s|	|s|	NOUN
ejpam-3657	82	32	−	−	PROPN
ejpam-3657	82	33	|s|+	|s|+	PROPN
ejpam-3657	82	34	1	1	NUM
ejpam-3657	82	35	=	=	SYM
ejpam-3657	82	36	|v	|v	X
ejpam-3657	82	37	(	(	PUNCT
ejpam-3657	82	38	g)|+	g)|+	NOUN
ejpam-3657	82	39	1−	1−	NUM
ejpam-3657	82	40	2|s|	2|s|	NUM
ejpam-3657	82	41	≥	≥	NOUN
ejpam-3657	82	42	|v	|v	X
ejpam-3657	82	43	(	(	PUNCT
ejpam-3657	82	44	g)|+	g)|+	NOUN
ejpam-3657	82	45	1−	1−	NUM
ejpam-3657	82	46	[	[	PUNCT
ejpam-3657	82	47	|v	|v	X
ejpam-3657	82	48	(	(	PUNCT
ejpam-3657	82	49	g)|+	g)|+	NOUN
ejpam-3657	82	50	1	1	NUM
ejpam-3657	82	51	]	]	PUNCT
ejpam-3657	82	52	=	=	SYM
ejpam-3657	82	53	0	0	X
ejpam-3657	82	54	.	.	PUNCT
ejpam-3657	83	1	thus	thus	ADV
ejpam-3657	83	2	,	,	PUNCT
ejpam-3657	83	3	s	s	VERB
ejpam-3657	83	4	is	be	AUX
ejpam-3657	83	5	a	a	DET
ejpam-3657	83	6	distance	distance	NOUN
ejpam-3657	83	7	k	k	ADJ
ejpam-3657	83	8	-	-	PUNCT
ejpam-3657	83	9	cost	cost	NOUN
ejpam-3657	83	10	effective	effective	ADJ
ejpam-3657	83	11	set	set	NOUN
ejpam-3657	83	12	in	in	ADP
ejpam-3657	83	13	g.	g.	PROPN
ejpam-3657	83	14	corollary	corollary	NOUN
ejpam-3657	83	15	1	1	NUM
ejpam-3657	83	16	.	.	PUNCT
ejpam-3657	84	1	if	if	SCONJ
ejpam-3657	84	2	k	k	PROPN
ejpam-3657	84	3	≥	≥	NUM
ejpam-3657	84	4	diam(g	diam(g	PROPN
ejpam-3657	84	5	)	)	PUNCT
ejpam-3657	84	6	,	,	PUNCT
ejpam-3657	84	7	then	then	ADV
ejpam-3657	84	8	αkce(g	αkce(g	NOUN
ejpam-3657	84	9	)	)	PUNCT
ejpam-3657	84	10	=	=	SYM
ejpam-3657	84	11	b	b	PROPN
ejpam-3657	84	12	|v	|v	X
ejpam-3657	84	13	(	(	PUNCT
ejpam-3657	84	14	g)|+1	g)|+1	PROPN
ejpam-3657	84	15	2	2	NUM
ejpam-3657	84	16	c.	c.	NOUN
ejpam-3657	84	17	corollary	corollary	NOUN
ejpam-3657	84	18	2	2	PROPN
ejpam-3657	84	19	.	.	PUNCT
ejpam-3657	85	1	let	let	VERB
ejpam-3657	85	2	g	g	NOUN
ejpam-3657	85	3	and	and	CCONJ
ejpam-3657	85	4	h	h	NOUN
ejpam-3657	85	5	be	be	AUX
ejpam-3657	85	6	connected	connect	VERB
ejpam-3657	85	7	graphs	graph	NOUN
ejpam-3657	85	8	and	and	CCONJ
ejpam-3657	85	9	an	an	DET
ejpam-3657	85	10	integer	integer	NOUN
ejpam-3657	85	11	k	k	PROPN
ejpam-3657	85	12	≥	≥	NUM
ejpam-3657	85	13	2	2	NUM
ejpam-3657	85	14	.	.	PUNCT
ejpam-3657	86	1	then	then	ADV
ejpam-3657	86	2	s	s	VERB
ejpam-3657	86	3	is	be	AUX
ejpam-3657	86	4	a	a	DET
ejpam-3657	86	5	distance	distance	NOUN
ejpam-3657	86	6	k	k	ADJ
ejpam-3657	86	7	-	-	PUNCT
ejpam-3657	86	8	cost	cost	ADJ
ejpam-3657	86	9	effective	effective	ADJ
ejpam-3657	86	10	set	set	NOUN
ejpam-3657	86	11	in	in	ADP
ejpam-3657	86	12	g+h	g+h	PROPN
ejpam-3657	87	1	if	if	SCONJ
ejpam-3657	87	2	and	and	CCONJ
ejpam-3657	87	3	only	only	ADV
ejpam-3657	87	4	if	if	SCONJ
ejpam-3657	87	5	|s|	|s|	NOUN
ejpam-3657	87	6	≤	≤	NUM
ejpam-3657	87	7	b	b	PROPN
ejpam-3657	87	8	|v	|v	X
ejpam-3657	87	9	(	(	PUNCT
ejpam-3657	87	10	g)|+|v	g)|+|v	PROPN
ejpam-3657	87	11	(	(	PUNCT
ejpam-3657	87	12	h)|+1	h)|+1	PROPN
ejpam-3657	87	13	2	2	NUM
ejpam-3657	87	14	c.	c.	NOUN
ejpam-3657	87	15	consequently	consequently	ADV
ejpam-3657	87	16	,	,	PUNCT
ejpam-3657	87	17	αkce(g+h	αkce(g+h	ADV
ejpam-3657	87	18	)	)	PUNCT
ejpam-3657	88	1	=	=	SYM
ejpam-3657	88	2	b	b	X
ejpam-3657	88	3	|v	|v	X
ejpam-3657	88	4	(	(	PUNCT
ejpam-3657	88	5	g)|+|v	g)|+|v	PROPN
ejpam-3657	88	6	(	(	PUNCT
ejpam-3657	88	7	h)|+1	h)|+1	PROPN
ejpam-3657	88	8	2	2	NUM
ejpam-3657	88	9	c.	c.	NOUN
ejpam-3657	88	10	proof	proof	NOUN
ejpam-3657	88	11	:	:	PUNCT
ejpam-3657	88	12	follows	follow	VERB
ejpam-3657	88	13	from	from	ADP
ejpam-3657	88	14	theorem	theorem	NOUN
ejpam-3657	88	15	1	1	NUM
ejpam-3657	88	16	since	since	SCONJ
ejpam-3657	88	17	k	k	PROPN
ejpam-3657	88	18	≥	≥	X
ejpam-3657	88	19	diam(g+h	diam(g+h	ADJ
ejpam-3657	88	20	)	)	PUNCT
ejpam-3657	88	21	=	=	SYM
ejpam-3657	88	22	2	2	X
ejpam-3657	88	23	.	.	NOUN
ejpam-3657	88	24	remark	remark	NOUN
ejpam-3657	88	25	4	4	NUM
ejpam-3657	88	26	.	.	PUNCT
ejpam-3657	89	1	for	for	ADP
ejpam-3657	89	2	all	all	DET
ejpam-3657	89	3	positive	positive	ADJ
ejpam-3657	89	4	integer	integer	NOUN
ejpam-3657	89	5	k	k	PROPN
ejpam-3657	89	6	≥	≥	NUM
ejpam-3657	89	7	2	2	NUM
ejpam-3657	89	8	,	,	PUNCT
ejpam-3657	89	9	αkce(g+h	αkce(g+h	ADV
ejpam-3657	89	10	)	)	PUNCT
ejpam-3657	89	11	=	=	PUNCT
ejpam-3657	89	12	α2	α2	VERB
ejpam-3657	89	13	ce(g+h	ce(g+h	NOUN
ejpam-3657	89	14	)	)	PUNCT
ejpam-3657	89	15	.	.	PUNCT
ejpam-3657	90	1	j.	j.	PROPN
ejpam-3657	90	2	g.	g.	PROPN
ejpam-3657	90	3	caadan	caadan	PROPN
ejpam-3657	90	4	,	,	PUNCT
ejpam-3657	90	5	r.	r.	PROPN
ejpam-3657	90	6	n.	n.	PROPN
ejpam-3657	90	7	paluga	paluga	PROPN
ejpam-3657	90	8	,	,	PUNCT
ejpam-3657	90	9	i.	i.	PROPN
ejpam-3657	90	10	s.	s.	PROPN
ejpam-3657	90	11	aniversario	aniversario	PROPN
ejpam-3657	90	12	/	/	SYM
ejpam-3657	90	13	eur	eur	PROPN
ejpam-3657	90	14	.	.	PUNCT
ejpam-3657	91	1	j.	j.	PROPN
ejpam-3657	91	2	pure	pure	PROPN
ejpam-3657	91	3	appl	appl	PROPN
ejpam-3657	91	4	.	.	PROPN
ejpam-3657	91	5	math	math	PROPN
ejpam-3657	91	6	,	,	PUNCT
ejpam-3657	91	7	13	13	NUM
ejpam-3657	91	8	(	(	PUNCT
ejpam-3657	91	9	3	3	NUM
ejpam-3657	91	10	)	)	PUNCT
ejpam-3657	91	11	(	(	PUNCT
ejpam-3657	91	12	2020	2020	NUM
ejpam-3657	91	13	)	)	PUNCT
ejpam-3657	91	14	,	,	PUNCT
ejpam-3657	91	15	701	701	NUM
ejpam-3657	91	16	-	-	SYM
ejpam-3657	91	17	709	709	NUM
ejpam-3657	91	18	704	704	NUM
ejpam-3657	91	19	definition	definition	NOUN
ejpam-3657	91	20	2	2	NUM
ejpam-3657	91	21	.	.	PUNCT
ejpam-3657	92	1	let	let	VERB
ejpam-3657	92	2	g	g	PRON
ejpam-3657	92	3	be	be	AUX
ejpam-3657	92	4	a	a	DET
ejpam-3657	92	5	connected	connected	ADJ
ejpam-3657	92	6	graph	graph	NOUN
ejpam-3657	92	7	and	and	CCONJ
ejpam-3657	92	8	t	t	PROPN
ejpam-3657	92	9	be	be	AUX
ejpam-3657	92	10	a	a	DET
ejpam-3657	92	11	nonnegative	nonnegative	ADJ
ejpam-3657	92	12	integer	integer	NOUN
ejpam-3657	92	13	.	.	PUNCT
ejpam-3657	93	1	a	a	DET
ejpam-3657	93	2	set	set	NOUN
ejpam-3657	93	3	s	s	NOUN
ejpam-3657	93	4	⊆	⊆	NUM
ejpam-3657	93	5	v	v	NOUN
ejpam-3657	93	6	(	(	PUNCT
ejpam-3657	93	7	g	g	NOUN
ejpam-3657	93	8	)	)	PUNCT
ejpam-3657	93	9	is	be	AUX
ejpam-3657	93	10	a	a	DET
ejpam-3657	93	11	tfringe	tfringe	NOUN
ejpam-3657	93	12	subset	subset	NOUN
ejpam-3657	93	13	of	of	ADP
ejpam-3657	93	14	g	g	PROPN
ejpam-3657	93	15	if	if	SCONJ
ejpam-3657	93	16	∆(〈s〉g	∆(〈s〉g	NUM
ejpam-3657	93	17	)	)	PUNCT
ejpam-3657	93	18	≤	≤	NOUN
ejpam-3657	94	1	t.	t.	NOUN
ejpam-3657	94	2	the	the	DET
ejpam-3657	94	3	tfringe	tfringe	NOUN
ejpam-3657	94	4	number	number	NOUN
ejpam-3657	94	5	of	of	ADP
ejpam-3657	94	6	g	g	NOUN
ejpam-3657	94	7	,	,	PUNCT
ejpam-3657	94	8	denoted	denote	VERB
ejpam-3657	94	9	by	by	ADP
ejpam-3657	94	10	τt(g	τt(g	NOUN
ejpam-3657	94	11	)	)	PUNCT
ejpam-3657	94	12	,	,	PUNCT
ejpam-3657	94	13	is	be	AUX
ejpam-3657	94	14	the	the	DET
ejpam-3657	94	15	maximum	maximum	ADJ
ejpam-3657	94	16	cardinality	cardinality	NOUN
ejpam-3657	94	17	of	of	ADP
ejpam-3657	94	18	a	a	DET
ejpam-3657	94	19	tfringe	tfringe	NOUN
ejpam-3657	94	20	subset	subset	NOUN
ejpam-3657	94	21	of	of	ADP
ejpam-3657	94	22	g.	g.	PROPN
ejpam-3657	94	23	example	example	PROPN
ejpam-3657	94	24	3	3	X
ejpam-3657	94	25	.	.	X
ejpam-3657	94	26	consider	consider	VERB
ejpam-3657	94	27	the	the	DET
ejpam-3657	94	28	graph	graph	NOUN
ejpam-3657	94	29	g	g	NOUN
ejpam-3657	94	30	as	as	SCONJ
ejpam-3657	94	31	shown	show	VERB
ejpam-3657	94	32	in	in	ADP
ejpam-3657	94	33	figure	figure	NOUN
ejpam-3657	94	34	1	1	NUM
ejpam-3657	94	35	.	.	PUNCT
ejpam-3657	95	1	let	let	VERB
ejpam-3657	95	2	s1	s1	PROPN
ejpam-3657	95	3	=	=	SYM
ejpam-3657	95	4	{	{	PUNCT
ejpam-3657	95	5	v3	v3	PROPN
ejpam-3657	95	6	,	,	PUNCT
ejpam-3657	95	7	v5	v5	PROPN
ejpam-3657	95	8	,	,	PUNCT
ejpam-3657	95	9	v6	v6	NOUN
ejpam-3657	95	10	,	,	PUNCT
ejpam-3657	95	11	v7	v7	NOUN
ejpam-3657	95	12	}	}	PUNCT
ejpam-3657	95	13	and	and	CCONJ
ejpam-3657	95	14	s2	s2	VERB
ejpam-3657	95	15	=	=	SYM
ejpam-3657	95	16	{	{	PUNCT
ejpam-3657	95	17	v2	v2	PROPN
ejpam-3657	95	18	,	,	PUNCT
ejpam-3657	95	19	v4	v4	NOUN
ejpam-3657	95	20	,	,	PUNCT
ejpam-3657	95	21	v5	v5	NOUN
ejpam-3657	95	22	,	,	PUNCT
ejpam-3657	95	23	v7	v7	NOUN
ejpam-3657	95	24	}	}	PUNCT
ejpam-3657	95	25	.	.	PUNCT
ejpam-3657	96	1	then	then	ADV
ejpam-3657	96	2	∆(〈s1〉g	∆(〈s1〉g	ADV
ejpam-3657	96	3	)	)	PUNCT
ejpam-3657	96	4	=	=	SYM
ejpam-3657	96	5	3	3	NUM
ejpam-3657	96	6	and	and	CCONJ
ejpam-3657	96	7	∆(〈s2〉g	∆(〈s2〉g	PROPN
ejpam-3657	96	8	)	)	PUNCT
ejpam-3657	97	1	=	=	SYM
ejpam-3657	97	2	0	0	X
ejpam-3657	97	3	.	.	PUNCT
ejpam-3657	98	1	thus	thus	ADV
ejpam-3657	98	2	,	,	PUNCT
ejpam-3657	98	3	s1	s1	PROPN
ejpam-3657	98	4	is	be	AUX
ejpam-3657	98	5	t	t	NOUN
ejpam-3657	98	6	-	-	PUNCT
ejpam-3657	98	7	fringe	fringe	NOUN
ejpam-3657	98	8	subset	subset	NOUN
ejpam-3657	98	9	of	of	ADP
ejpam-3657	98	10	g	g	PROPN
ejpam-3657	98	11	if	if	SCONJ
ejpam-3657	98	12	t	t	PROPN
ejpam-3657	98	13	≥	≥	NUM
ejpam-3657	98	14	3	3	NUM
ejpam-3657	98	15	while	while	SCONJ
ejpam-3657	98	16	s2	s2	NOUN
ejpam-3657	98	17	is	be	AUX
ejpam-3657	98	18	a	a	DET
ejpam-3657	98	19	t	t	NOUN
ejpam-3657	98	20	-	-	PUNCT
ejpam-3657	98	21	fringe	fringe	NOUN
ejpam-3657	98	22	subset	subset	NOUN
ejpam-3657	98	23	of	of	ADP
ejpam-3657	98	24	g	g	PROPN
ejpam-3657	99	1	if	if	SCONJ
ejpam-3657	99	2	t	t	PROPN
ejpam-3657	99	3	≥	≥	NOUN
ejpam-3657	99	4	0	0	NUM
ejpam-3657	99	5	.	.	PUNCT
ejpam-3657	99	6	v1	v1	PROPN
ejpam-3657	99	7	v2	v2	PROPN
ejpam-3657	99	8	v3	v3	PROPN
ejpam-3657	99	9	v4	v4	PROPN
ejpam-3657	99	10	v5	v5	PROPN
ejpam-3657	99	11	v6	v6	NOUN
ejpam-3657	99	12	v7	v7	NOUN
ejpam-3657	99	13	figure	figure	NOUN
ejpam-3657	99	14	1	1	NUM
ejpam-3657	99	15	:	:	PUNCT
ejpam-3657	99	16	the	the	DET
ejpam-3657	99	17	graph	graph	NOUN
ejpam-3657	99	18	g	g	NOUN
ejpam-3657	99	19	with	with	ADP
ejpam-3657	99	20	∆(g	∆(g	NOUN
ejpam-3657	99	21	)	)	PUNCT
ejpam-3657	99	22	=	=	SYM
ejpam-3657	99	23	5	5	NUM
ejpam-3657	99	24	theorem	theorem	NOUN
ejpam-3657	99	25	2	2	NUM
ejpam-3657	99	26	.	.	PUNCT
ejpam-3657	99	27	let	let	VERB
ejpam-3657	99	28	g	g	PRON
ejpam-3657	99	29	be	be	AUX
ejpam-3657	99	30	a	a	DET
ejpam-3657	99	31	connected	connected	ADJ
ejpam-3657	99	32	graph	graph	NOUN
ejpam-3657	99	33	,	,	PUNCT
ejpam-3657	99	34	s	s	VERB
ejpam-3657	99	35	⊆	⊆	NUM
ejpam-3657	99	36	v	v	NOUN
ejpam-3657	99	37	(	(	PUNCT
ejpam-3657	99	38	g	g	NOUN
ejpam-3657	99	39	)	)	PUNCT
ejpam-3657	99	40	,	,	PUNCT
ejpam-3657	99	41	and	and	CCONJ
ejpam-3657	99	42	t	t	PROPN
ejpam-3657	99	43	≥	≥	NOUN
ejpam-3657	99	44	b∆(g	b∆(g	X
ejpam-3657	99	45	)	)	PUNCT
ejpam-3657	99	46	2	2	NUM
ejpam-3657	99	47	c.	c.	NOUN
ejpam-3657	99	48	if	if	SCONJ
ejpam-3657	99	49	s	s	VERB
ejpam-3657	99	50	is	be	AUX
ejpam-3657	99	51	a	a	DET
ejpam-3657	99	52	distance	distance	NOUN
ejpam-3657	99	53	1	1	NUM
ejpam-3657	99	54	-	-	PUNCT
ejpam-3657	99	55	cost	cost	NOUN
ejpam-3657	99	56	effective	effective	ADJ
ejpam-3657	99	57	set	set	NOUN
ejpam-3657	99	58	in	in	ADP
ejpam-3657	99	59	g	g	NOUN
ejpam-3657	99	60	,	,	PUNCT
ejpam-3657	99	61	then	then	ADV
ejpam-3657	99	62	s	s	VERB
ejpam-3657	99	63	is	be	AUX
ejpam-3657	99	64	a	a	DET
ejpam-3657	99	65	t	t	NOUN
ejpam-3657	99	66	-	-	PUNCT
ejpam-3657	99	67	fringe	fringe	NOUN
ejpam-3657	99	68	subset	subset	NOUN
ejpam-3657	99	69	of	of	ADP
ejpam-3657	99	70	v	v	NOUN
ejpam-3657	99	71	(	(	PUNCT
ejpam-3657	99	72	g	g	NOUN
ejpam-3657	99	73	)	)	PUNCT
ejpam-3657	99	74	.	.	PUNCT
ejpam-3657	100	1	proof	proof	NOUN
ejpam-3657	100	2	:	:	PUNCT
ejpam-3657	100	3	let	let	VERB
ejpam-3657	100	4	s	s	PRON
ejpam-3657	100	5	⊆	⊆	NUM
ejpam-3657	100	6	v	v	NOUN
ejpam-3657	100	7	(	(	PUNCT
ejpam-3657	100	8	g	g	NOUN
ejpam-3657	100	9	)	)	PUNCT
ejpam-3657	100	10	be	be	AUX
ejpam-3657	100	11	a	a	DET
ejpam-3657	100	12	distance	distance	NOUN
ejpam-3657	100	13	1	1	NUM
ejpam-3657	100	14	-	-	PUNCT
ejpam-3657	100	15	cost	cost	NOUN
ejpam-3657	100	16	effective	effective	ADJ
ejpam-3657	100	17	set	set	NOUN
ejpam-3657	100	18	in	in	ADP
ejpam-3657	100	19	g.	g.	PROPN
ejpam-3657	100	20	then	then	ADV
ejpam-3657	100	21	for	for	SCONJ
ejpam-3657	100	22	u	u	PROPN
ejpam-3657	100	23	∈	∈	PROPN
ejpam-3657	100	24	s	s	PROPN
ejpam-3657	100	25	,	,	PUNCT
ejpam-3657	100	26	|n1	|n1	VERB
ejpam-3657	100	27	g(u	g(u	NOUN
ejpam-3657	100	28	)	)	PUNCT
ejpam-3657	100	29	∩	∩	NOUN
ejpam-3657	100	30	sc|	sc|	PROPN
ejpam-3657	100	31	−	−	NOUN
ejpam-3657	100	32	|n1	|n1	VERB
ejpam-3657	100	33	g(u	g(u	NOUN
ejpam-3657	100	34	)	)	PUNCT
ejpam-3657	101	1	∩	∩	NOUN
ejpam-3657	101	2	s|	s|	NOUN
ejpam-3657	101	3	=	=	SYM
ejpam-3657	101	4	degg(u)−	degg(u)−	PROPN
ejpam-3657	101	5	deg〈s〉g(u)−	deg〈s〉g(u)−	NOUN
ejpam-3657	101	6	deg〈s〉g(u	deg〈s〉g(u	NUM
ejpam-3657	101	7	)	)	PUNCT
ejpam-3657	101	8	=	=	PUNCT
ejpam-3657	101	9	degg(u)−	degg(u)−	PROPN
ejpam-3657	101	10	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	101	11	)	)	PUNCT
ejpam-3657	101	12	≥	≥	NOUN
ejpam-3657	101	13	0	0	NUM
ejpam-3657	101	14	.	.	PUNCT
ejpam-3657	102	1	it	it	PRON
ejpam-3657	102	2	follows	follow	VERB
ejpam-3657	102	3	that	that	PRON
ejpam-3657	102	4	degg(u	degg(u	NOUN
ejpam-3657	102	5	)	)	PUNCT
ejpam-3657	102	6	−	−	PROPN
ejpam-3657	102	7	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	102	8	)	)	PUNCT
ejpam-3657	102	9	≥	≥	NOUN
ejpam-3657	102	10	0	0	NUM
ejpam-3657	102	11	.	.	PUNCT
ejpam-3657	103	1	hence	hence	ADV
ejpam-3657	103	2	,	,	PUNCT
ejpam-3657	103	3	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	103	4	)	)	PUNCT
ejpam-3657	103	5	≤	≤	NOUN
ejpam-3657	103	6	degg(u	degg(u	PROPN
ejpam-3657	103	7	)	)	PUNCT
ejpam-3657	103	8	.	.	PUNCT
ejpam-3657	104	1	since	since	SCONJ
ejpam-3657	104	2	u	u	NOUN
ejpam-3657	104	3	is	be	AUX
ejpam-3657	104	4	arbitrary	arbitrary	ADJ
ejpam-3657	104	5	,	,	PUNCT
ejpam-3657	104	6	2∆(〈s〉g	2∆(〈s〉g	NUM
ejpam-3657	104	7	)	)	PUNCT
ejpam-3657	104	8	≤	≤	NOUN
ejpam-3657	104	9	∆(g	∆(g	NOUN
ejpam-3657	104	10	)	)	PUNCT
ejpam-3657	104	11	.	.	PUNCT
ejpam-3657	105	1	equivalently	equivalently	ADV
ejpam-3657	105	2	,	,	PUNCT
ejpam-3657	105	3	∆(〈s〉g	∆(〈s〉g	NUM
ejpam-3657	105	4	)	)	PUNCT
ejpam-3657	105	5	≤	≤	NOUN
ejpam-3657	105	6	∆(g	∆(g	NOUN
ejpam-3657	105	7	)	)	PUNCT
ejpam-3657	105	8	2	2	NUM
ejpam-3657	105	9	.	.	PUNCT
ejpam-3657	106	1	hence	hence	ADV
ejpam-3657	106	2	,	,	PUNCT
ejpam-3657	106	3	∆(〈s〉g	∆(〈s〉g	NUM
ejpam-3657	106	4	)	)	PUNCT
ejpam-3657	106	5	≤	≤	NOUN
ejpam-3657	106	6	b∆(g	b∆(g	NOUN
ejpam-3657	106	7	)	)	PUNCT
ejpam-3657	106	8	2	2	NUM
ejpam-3657	106	9	c	c	NOUN
ejpam-3657	106	10	≤	≤	NOUN
ejpam-3657	106	11	t.	t.	NOUN
ejpam-3657	106	12	accordingly	accordingly	ADV
ejpam-3657	106	13	,	,	PUNCT
ejpam-3657	106	14	s	s	VERB
ejpam-3657	106	15	is	be	AUX
ejpam-3657	106	16	a	a	DET
ejpam-3657	106	17	t	t	NOUN
ejpam-3657	106	18	-	-	PUNCT
ejpam-3657	106	19	fringe	fringe	NOUN
ejpam-3657	106	20	subset	subset	NOUN
ejpam-3657	106	21	of	of	ADP
ejpam-3657	106	22	v	v	NOUN
ejpam-3657	106	23	(	(	PUNCT
ejpam-3657	106	24	g	g	NOUN
ejpam-3657	106	25	)	)	PUNCT
ejpam-3657	106	26	.	.	PUNCT
ejpam-3657	107	1	theorem	theorem	NOUN
ejpam-3657	107	2	3	3	X
ejpam-3657	107	3	.	.	PUNCT
ejpam-3657	108	1	let	let	VERB
ejpam-3657	108	2	g	g	PRON
ejpam-3657	108	3	be	be	AUX
ejpam-3657	108	4	a	a	DET
ejpam-3657	108	5	connected	connected	ADJ
ejpam-3657	108	6	graph	graph	NOUN
ejpam-3657	108	7	and	and	CCONJ
ejpam-3657	108	8	h	h	NOUN
ejpam-3657	108	9	be	be	AUX
ejpam-3657	108	10	any	any	DET
ejpam-3657	108	11	graph	graph	NOUN
ejpam-3657	108	12	of	of	ADP
ejpam-3657	108	13	order	order	NOUN
ejpam-3657	108	14	n	n	PRON
ejpam-3657	108	15	≥	≥	NOUN
ejpam-3657	108	16	2	2	NUM
ejpam-3657	108	17	,	,	PUNCT
ejpam-3657	108	18	s	s	VERB
ejpam-3657	108	19	⊆	⊆	NUM
ejpam-3657	108	20	v	v	NOUN
ejpam-3657	108	21	(	(	PUNCT
ejpam-3657	108	22	g	g	NOUN
ejpam-3657	108	23	)	)	PUNCT
ejpam-3657	108	24	,	,	PUNCT
ejpam-3657	108	25	and	and	CCONJ
ejpam-3657	108	26	t	t	PROPN
ejpam-3657	108	27	≥	≥	PROPN
ejpam-3657	108	28	bn+∆(g	bn+∆(g	PROPN
ejpam-3657	108	29	)	)	PUNCT
ejpam-3657	108	30	2	2	NUM
ejpam-3657	108	31	c.	c.	NOUN
ejpam-3657	108	32	if	if	SCONJ
ejpam-3657	108	33	s	s	VERB
ejpam-3657	108	34	is	be	AUX
ejpam-3657	108	35	a	a	DET
ejpam-3657	108	36	distance	distance	NOUN
ejpam-3657	108	37	1	1	NUM
ejpam-3657	108	38	-	-	PUNCT
ejpam-3657	108	39	cost	cost	NOUN
ejpam-3657	108	40	effective	effective	ADJ
ejpam-3657	108	41	set	set	NOUN
ejpam-3657	108	42	in	in	ADP
ejpam-3657	108	43	g	g	PROPN
ejpam-3657	109	1	+	+	CCONJ
ejpam-3657	109	2	h	h	NOUN
ejpam-3657	109	3	,	,	PUNCT
ejpam-3657	109	4	then	then	ADV
ejpam-3657	109	5	s	s	VERB
ejpam-3657	109	6	is	be	AUX
ejpam-3657	109	7	a	a	DET
ejpam-3657	109	8	t	t	NOUN
ejpam-3657	109	9	-	-	PUNCT
ejpam-3657	109	10	fringe	fringe	NOUN
ejpam-3657	109	11	subset	subset	NOUN
ejpam-3657	109	12	of	of	ADP
ejpam-3657	109	13	v	v	NOUN
ejpam-3657	109	14	(	(	PUNCT
ejpam-3657	109	15	g	g	NOUN
ejpam-3657	109	16	)	)	PUNCT
ejpam-3657	109	17	.	.	PUNCT
ejpam-3657	110	1	proof	proof	NOUN
ejpam-3657	110	2	:	:	PUNCT
ejpam-3657	110	3	let	let	VERB
ejpam-3657	110	4	u	u	PRON
ejpam-3657	110	5	∈	∈	PROPN
ejpam-3657	110	6	s.	s.	PROPN
ejpam-3657	110	7	then	then	ADV
ejpam-3657	110	8	|n1	|n1	VERB
ejpam-3657	110	9	g+h(u	g+h(u	NOUN
ejpam-3657	110	10	)	)	PUNCT
ejpam-3657	110	11	∩	∩	PROPN
ejpam-3657	110	12	sc|	sc|	PROPN
ejpam-3657	110	13	−	−	NOUN
ejpam-3657	110	14	|n1	|n1	NOUN
ejpam-3657	110	15	g+h(u	g+h(u	NOUN
ejpam-3657	110	16	)	)	PUNCT
ejpam-3657	111	1	∩	∩	NOUN
ejpam-3657	111	2	s|	s|	NOUN
ejpam-3657	111	3	=	=	PUNCT
ejpam-3657	111	4	degg(u)−	degg(u)−	NOUN
ejpam-3657	111	5	deg〈s〉g(u	deg〈s〉g(u	PRON
ejpam-3657	111	6	)	)	PUNCT
ejpam-3657	111	7	+	+	NUM
ejpam-3657	111	8	n−	n−	NOUN
ejpam-3657	111	9	deg〈s〉g(u	deg〈s〉g(u	NUM
ejpam-3657	111	10	)	)	PUNCT
ejpam-3657	111	11	=	=	SYM
ejpam-3657	111	12	degg(u	degg(u	PROPN
ejpam-3657	111	13	)	)	PUNCT
ejpam-3657	112	1	+	+	NUM
ejpam-3657	112	2	n−	n−	NOUN
ejpam-3657	112	3	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	112	4	)	)	PUNCT
ejpam-3657	112	5	since	since	SCONJ
ejpam-3657	112	6	s	s	NOUN
ejpam-3657	112	7	is	be	AUX
ejpam-3657	112	8	a	a	DET
ejpam-3657	112	9	distance	distance	NOUN
ejpam-3657	112	10	1	1	NUM
ejpam-3657	112	11	-	-	PUNCT
ejpam-3657	112	12	cost	cost	NOUN
ejpam-3657	112	13	effective	effective	ADJ
ejpam-3657	112	14	set	set	NOUN
ejpam-3657	112	15	in	in	ADP
ejpam-3657	112	16	g	g	PROPN
ejpam-3657	112	17	+	+	CCONJ
ejpam-3657	112	18	h	h	NOUN
ejpam-3657	112	19	,	,	PUNCT
ejpam-3657	112	20	degg(u	degg(u	PROPN
ejpam-3657	112	21	)	)	PUNCT
ejpam-3657	112	22	+	+	CCONJ
ejpam-3657	113	1	n	n	CCONJ
ejpam-3657	113	2	−	−	PROPN
ejpam-3657	113	3	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	113	4	)	)	PUNCT
ejpam-3657	113	5	≥	≥	NOUN
ejpam-3657	113	6	0	0	NUM
ejpam-3657	113	7	.	.	PUNCT
ejpam-3657	114	1	hence	hence	ADV
ejpam-3657	114	2	,	,	PUNCT
ejpam-3657	114	3	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	114	4	)	)	PUNCT
ejpam-3657	114	5	≤	≤	NOUN
ejpam-3657	114	6	degg(u	degg(u	PROPN
ejpam-3657	114	7	)	)	PUNCT
ejpam-3657	115	1	+	+	CCONJ
ejpam-3657	115	2	n.	n.	NOUN
ejpam-3657	115	3	it	it	PRON
ejpam-3657	115	4	follows	follow	VERB
ejpam-3657	115	5	that	that	SCONJ
ejpam-3657	115	6	2deg〈s〉g(u	2deg〈s〉g(u	X
ejpam-3657	115	7	)	)	PUNCT
ejpam-3657	115	8	≤	≤	NUM
ejpam-3657	115	9	∆(g	∆(g	NOUN
ejpam-3657	115	10	)	)	PUNCT
ejpam-3657	115	11	+	+	NUM
ejpam-3657	115	12	n	n	CCONJ
ejpam-3657	115	13	,	,	PUNCT
ejpam-3657	116	1	∀	∀	VERB
ejpam-3657	116	2	u	u	NOUN
ejpam-3657	116	3	∈	∈	PROPN
ejpam-3657	116	4	s.	s.	PROPN
ejpam-3657	116	5	since	since	SCONJ
ejpam-3657	116	6	u	u	NOUN
ejpam-3657	116	7	is	be	AUX
ejpam-3657	116	8	arbitrary	arbitrary	ADJ
ejpam-3657	116	9	,	,	PUNCT
ejpam-3657	116	10	2∆(〈s〉g	2∆(〈s〉g	NUM
ejpam-3657	116	11	)	)	PUNCT
ejpam-3657	116	12	≤	≤	NOUN
ejpam-3657	116	13	∆(g	∆(g	NOUN
ejpam-3657	116	14	)	)	PUNCT
ejpam-3657	116	15	+	+	CCONJ
ejpam-3657	116	16	n.	n.	PROPN
ejpam-3657	116	17	equivalently	equivalently	ADV
ejpam-3657	116	18	,	,	PUNCT
ejpam-3657	116	19	∆(〈s〉g	∆(〈s〉g	NUM
ejpam-3657	116	20	)	)	PUNCT
ejpam-3657	116	21	≤	≤	NUM
ejpam-3657	116	22	∆(g)+n	∆(g)+n	PROPN
ejpam-3657	116	23	2	2	NUM
ejpam-3657	116	24	.	.	PUNCT
ejpam-3657	117	1	hence	hence	ADV
ejpam-3657	117	2	,	,	PUNCT
ejpam-3657	117	3	∆(〈s〉g	∆(〈s〉g	NUM
ejpam-3657	117	4	)	)	PUNCT
ejpam-3657	117	5	≤	≤	NUM
ejpam-3657	117	6	b∆(g)+n	b∆(g)+n	NOUN
ejpam-3657	117	7	2	2	NUM
ejpam-3657	117	8	c	c	NOUN
ejpam-3657	117	9	≤	≤	NUM
ejpam-3657	117	10	t.	t.	NOUN
ejpam-3657	117	11	accordingly	accordingly	ADV
ejpam-3657	117	12	,	,	PUNCT
ejpam-3657	117	13	s	s	VERB
ejpam-3657	117	14	is	be	AUX
ejpam-3657	117	15	a	a	DET
ejpam-3657	117	16	t	t	NOUN
ejpam-3657	117	17	-	-	PUNCT
ejpam-3657	117	18	fringe	fringe	NOUN
ejpam-3657	117	19	subset	subset	NOUN
ejpam-3657	117	20	of	of	ADP
ejpam-3657	117	21	v	v	NOUN
ejpam-3657	117	22	(	(	PUNCT
ejpam-3657	117	23	g	g	NOUN
ejpam-3657	117	24	)	)	PUNCT
ejpam-3657	117	25	.	.	PUNCT
ejpam-3657	118	1	j.	j.	PROPN
ejpam-3657	118	2	g.	g.	PROPN
ejpam-3657	118	3	caadan	caadan	PROPN
ejpam-3657	118	4	,	,	PUNCT
ejpam-3657	118	5	r.	r.	PROPN
ejpam-3657	118	6	n.	n.	PROPN
ejpam-3657	118	7	paluga	paluga	PROPN
ejpam-3657	118	8	,	,	PUNCT
ejpam-3657	118	9	i.	i.	PROPN
ejpam-3657	118	10	s.	s.	PROPN
ejpam-3657	118	11	aniversario	aniversario	PROPN
ejpam-3657	118	12	/	/	SYM
ejpam-3657	118	13	eur	eur	PROPN
ejpam-3657	118	14	.	.	PUNCT
ejpam-3657	119	1	j.	j.	PROPN
ejpam-3657	119	2	pure	pure	PROPN
ejpam-3657	119	3	appl	appl	PROPN
ejpam-3657	119	4	.	.	PROPN
ejpam-3657	119	5	math	math	PROPN
ejpam-3657	119	6	,	,	PUNCT
ejpam-3657	119	7	13	13	NUM
ejpam-3657	119	8	(	(	PUNCT
ejpam-3657	119	9	3	3	NUM
ejpam-3657	119	10	)	)	PUNCT
ejpam-3657	119	11	(	(	PUNCT
ejpam-3657	119	12	2020	2020	NUM
ejpam-3657	119	13	)	)	PUNCT
ejpam-3657	119	14	,	,	PUNCT
ejpam-3657	119	15	701	701	NUM
ejpam-3657	119	16	-	-	SYM
ejpam-3657	119	17	709	709	NUM
ejpam-3657	119	18	705	705	NUM
ejpam-3657	119	19	corollary	corollary	NOUN
ejpam-3657	119	20	3	3	NUM
ejpam-3657	119	21	.	.	PUNCT
ejpam-3657	120	1	let	let	VERB
ejpam-3657	120	2	g	g	PRON
ejpam-3657	120	3	be	be	AUX
ejpam-3657	120	4	a	a	DET
ejpam-3657	120	5	connected	connected	ADJ
ejpam-3657	120	6	graph	graph	NOUN
ejpam-3657	120	7	,	,	PUNCT
ejpam-3657	120	8	h	h	NOUN
ejpam-3657	120	9	be	be	VERB
ejpam-3657	120	10	any	any	DET
ejpam-3657	120	11	graph	graph	NOUN
ejpam-3657	120	12	of	of	ADP
ejpam-3657	120	13	order	order	NOUN
ejpam-3657	120	14	n	n	PRON
ejpam-3657	120	15	≥	≥	NOUN
ejpam-3657	120	16	2	2	NUM
ejpam-3657	120	17	and	and	CCONJ
ejpam-3657	120	18	t	t	PROPN
ejpam-3657	120	19	≥	≥	PROPN
ejpam-3657	120	20	bn+∆(g	bn+∆(g	PROPN
ejpam-3657	120	21	)	)	PUNCT
ejpam-3657	120	22	2	2	NUM
ejpam-3657	120	23	c.	c.	NOUN
ejpam-3657	120	24	then	then	ADV
ejpam-3657	120	25	α1	α1	PROPN
ejpam-3657	120	26	ce(g+h	ce(g+h	PROPN
ejpam-3657	120	27	)	)	PUNCT
ejpam-3657	120	28	≤	≤	NOUN
ejpam-3657	120	29	τt(g	τt(g	PUNCT
ejpam-3657	120	30	)	)	PUNCT
ejpam-3657	120	31	.	.	PUNCT
ejpam-3657	121	1	theorem	theorem	ADJ
ejpam-3657	121	2	4	4	NUM
ejpam-3657	121	3	.	.	PUNCT
ejpam-3657	122	1	let	let	VERB
ejpam-3657	122	2	g	g	PRON
ejpam-3657	122	3	be	be	AUX
ejpam-3657	122	4	a	a	DET
ejpam-3657	122	5	connected	connected	ADJ
ejpam-3657	122	6	graph	graph	NOUN
ejpam-3657	122	7	and	and	CCONJ
ejpam-3657	122	8	h	h	NOUN
ejpam-3657	122	9	be	be	AUX
ejpam-3657	122	10	any	any	DET
ejpam-3657	122	11	graph	graph	NOUN
ejpam-3657	122	12	of	of	ADP
ejpam-3657	122	13	order	order	NOUN
ejpam-3657	122	14	n	n	PRON
ejpam-3657	122	15	≥	≥	NOUN
ejpam-3657	122	16	2	2	NUM
ejpam-3657	122	17	,	,	PUNCT
ejpam-3657	122	18	s	s	VERB
ejpam-3657	122	19	⊆	⊆	NUM
ejpam-3657	122	20	v	v	NOUN
ejpam-3657	122	21	(	(	PUNCT
ejpam-3657	122	22	g	g	NOUN
ejpam-3657	122	23	)	)	PUNCT
ejpam-3657	122	24	,	,	PUNCT
ejpam-3657	122	25	and	and	CCONJ
ejpam-3657	122	26	t	t	X
ejpam-3657	122	27	≤	≤	NUM
ejpam-3657	123	1	bn+δ(g	bn+δ(g	PROPN
ejpam-3657	123	2	)	)	PUNCT
ejpam-3657	123	3	2	2	NUM
ejpam-3657	123	4	c.	c.	NOUN
ejpam-3657	123	5	if	if	SCONJ
ejpam-3657	123	6	s	s	VERB
ejpam-3657	123	7	is	be	AUX
ejpam-3657	123	8	a	a	DET
ejpam-3657	123	9	t	t	NOUN
ejpam-3657	123	10	-	-	PUNCT
ejpam-3657	123	11	fringe	fringe	NOUN
ejpam-3657	123	12	subset	subset	NOUN
ejpam-3657	123	13	of	of	ADP
ejpam-3657	123	14	v	v	NOUN
ejpam-3657	123	15	(	(	PUNCT
ejpam-3657	123	16	g	g	NOUN
ejpam-3657	123	17	)	)	PUNCT
ejpam-3657	123	18	,	,	PUNCT
ejpam-3657	123	19	then	then	ADV
ejpam-3657	123	20	s	s	VERB
ejpam-3657	123	21	is	be	AUX
ejpam-3657	123	22	a	a	DET
ejpam-3657	123	23	distance	distance	NOUN
ejpam-3657	123	24	1	1	NUM
ejpam-3657	123	25	-	-	PUNCT
ejpam-3657	123	26	cost	cost	NOUN
ejpam-3657	123	27	effective	effective	ADJ
ejpam-3657	123	28	set	set	NOUN
ejpam-3657	123	29	in	in	ADP
ejpam-3657	123	30	g+h	g+h	PROPN
ejpam-3657	123	31	.	.	PUNCT
ejpam-3657	124	1	proof	proof	NOUN
ejpam-3657	124	2	:	:	PUNCT
ejpam-3657	124	3	since	since	SCONJ
ejpam-3657	124	4	s	s	NOUN
ejpam-3657	124	5	is	be	AUX
ejpam-3657	124	6	a	a	DET
ejpam-3657	124	7	t	t	NOUN
ejpam-3657	124	8	-	-	PUNCT
ejpam-3657	124	9	fringe	fringe	NOUN
ejpam-3657	124	10	subset	subset	NOUN
ejpam-3657	124	11	of	of	ADP
ejpam-3657	124	12	v	v	NOUN
ejpam-3657	124	13	(	(	PUNCT
ejpam-3657	124	14	g	g	NOUN
ejpam-3657	124	15	)	)	PUNCT
ejpam-3657	124	16	,	,	PUNCT
ejpam-3657	124	17	then	then	ADV
ejpam-3657	124	18	∆(〈s〉g	∆(〈s〉g	NUM
ejpam-3657	124	19	)	)	PUNCT
ejpam-3657	124	20	≤	≤	NOUN
ejpam-3657	124	21	t	t	PROPN
ejpam-3657	124	22	≤	≤	NUM
ejpam-3657	124	23	bn+δ(g	bn+δ(g	VERB
ejpam-3657	124	24	)	)	PUNCT
ejpam-3657	124	25	2	2	NUM
ejpam-3657	124	26	c	c	NOUN
ejpam-3657	124	27	≤	≤	NUM
ejpam-3657	124	28	n+δ(g	n+δ(g	CCONJ
ejpam-3657	124	29	)	)	PUNCT
ejpam-3657	124	30	2	2	NUM
ejpam-3657	124	31	.	.	PUNCT
ejpam-3657	125	1	it	it	PRON
ejpam-3657	125	2	follows	follow	VERB
ejpam-3657	125	3	that	that	SCONJ
ejpam-3657	125	4	2∆(〈s〉g	2∆(〈s〉g	NUM
ejpam-3657	125	5	)	)	PUNCT
ejpam-3657	125	6	≤	≤	NOUN
ejpam-3657	125	7	δ(g	δ(g	PUNCT
ejpam-3657	125	8	)	)	PUNCT
ejpam-3657	126	1	+	+	CCONJ
ejpam-3657	126	2	n.	n.	NOUN
ejpam-3657	126	3	let	let	VERB
ejpam-3657	126	4	u	u	PRON
ejpam-3657	126	5	∈	∈	PROPN
ejpam-3657	126	6	s.	s.	PROPN
ejpam-3657	126	7	then	then	ADV
ejpam-3657	126	8	|n1	|n1	VERB
ejpam-3657	126	9	g+h(u	g+h(u	NOUN
ejpam-3657	126	10	)	)	PUNCT
ejpam-3657	126	11	∩	∩	PROPN
ejpam-3657	127	1	sc|	sc|	PROPN
ejpam-3657	127	2	−	−	NOUN
ejpam-3657	127	3	|n1	|n1	NOUN
ejpam-3657	127	4	g+h(u	g+h(u	NOUN
ejpam-3657	127	5	)	)	PUNCT
ejpam-3657	127	6	∩	∩	NOUN
ejpam-3657	127	7	s|	s|	NOUN
ejpam-3657	127	8	=	=	PUNCT
ejpam-3657	127	9	degg(u)−	degg(u)−	NOUN
ejpam-3657	127	10	deg〈s〉g(u	deg〈s〉g(u	PRON
ejpam-3657	127	11	)	)	PUNCT
ejpam-3657	127	12	+	+	NUM
ejpam-3657	127	13	n−	n−	NOUN
ejpam-3657	127	14	deg〈s〉g(u	deg〈s〉g(u	NUM
ejpam-3657	127	15	)	)	PUNCT
ejpam-3657	127	16	=	=	SYM
ejpam-3657	127	17	degg(u	degg(u	PROPN
ejpam-3657	127	18	)	)	PUNCT
ejpam-3657	128	1	+	+	NUM
ejpam-3657	128	2	n−	n−	NOUN
ejpam-3657	128	3	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	128	4	)	)	PUNCT
ejpam-3657	128	5	≥	≥	NOUN
ejpam-3657	128	6	degg(u	degg(u	PROPN
ejpam-3657	128	7	)	)	PUNCT
ejpam-3657	128	8	+	+	NUM
ejpam-3657	128	9	n−	n−	NOUN
ejpam-3657	128	10	2∆(〈s〉g	2∆(〈s〉g	NUM
ejpam-3657	128	11	)	)	PUNCT
ejpam-3657	128	12	≥	≥	NOUN
ejpam-3657	128	13	degg(u	degg(u	PROPN
ejpam-3657	128	14	)	)	PUNCT
ejpam-3657	129	1	+	+	NUM
ejpam-3657	129	2	n−	n−	NOUN
ejpam-3657	129	3	(	(	PUNCT
ejpam-3657	129	4	n+	n+	X
ejpam-3657	129	5	δ(g	δ(g	X
ejpam-3657	129	6	)	)	PUNCT
ejpam-3657	129	7	=	=	SYM
ejpam-3657	129	8	degg(u)−	degg(u)−	PROPN
ejpam-3657	129	9	δ(g	δ(g	PROPN
ejpam-3657	129	10	)	)	PUNCT
ejpam-3657	129	11	≥	≥	NOUN
ejpam-3657	129	12	0	0	NUM
ejpam-3657	129	13	.	.	PUNCT
ejpam-3657	130	1	thus	thus	ADV
ejpam-3657	130	2	,	,	PUNCT
ejpam-3657	130	3	s	s	VERB
ejpam-3657	130	4	is	be	AUX
ejpam-3657	130	5	a	a	DET
ejpam-3657	130	6	distance	distance	NOUN
ejpam-3657	130	7	1	1	NUM
ejpam-3657	130	8	-	-	PUNCT
ejpam-3657	130	9	cost	cost	NOUN
ejpam-3657	130	10	effective	effective	ADJ
ejpam-3657	130	11	set	set	NOUN
ejpam-3657	130	12	in	in	ADP
ejpam-3657	130	13	g+h	g+h	PROPN
ejpam-3657	130	14	.	.	PUNCT
ejpam-3657	131	1	corollary	corollary	ADJ
ejpam-3657	131	2	4	4	NUM
ejpam-3657	131	3	.	.	PUNCT
ejpam-3657	132	1	let	let	VERB
ejpam-3657	132	2	g	g	PRON
ejpam-3657	132	3	be	be	AUX
ejpam-3657	132	4	a	a	DET
ejpam-3657	132	5	connected	connected	ADJ
ejpam-3657	132	6	graph	graph	NOUN
ejpam-3657	132	7	,	,	PUNCT
ejpam-3657	132	8	h	h	NOUN
ejpam-3657	132	9	be	be	VERB
ejpam-3657	132	10	any	any	DET
ejpam-3657	132	11	graph	graph	NOUN
ejpam-3657	132	12	of	of	ADP
ejpam-3657	132	13	order	order	NOUN
ejpam-3657	132	14	n	n	PRON
ejpam-3657	132	15	≥	≥	NOUN
ejpam-3657	132	16	2	2	NUM
ejpam-3657	132	17	,	,	PUNCT
ejpam-3657	132	18	and	and	CCONJ
ejpam-3657	132	19	t	t	X
ejpam-3657	132	20	≤	≤	NUM
ejpam-3657	132	21	bn+δ(g	bn+δ(g	VERB
ejpam-3657	132	22	)	)	PUNCT
ejpam-3657	132	23	2	2	NUM
ejpam-3657	132	24	c.	c.	NOUN
ejpam-3657	132	25	then	then	ADV
ejpam-3657	132	26	α1	α1	PROPN
ejpam-3657	132	27	ce(g+h	ce(g+h	PROPN
ejpam-3657	132	28	)	)	PUNCT
ejpam-3657	132	29	≥	≥	NOUN
ejpam-3657	132	30	τt(g	τt(g	PUNCT
ejpam-3657	132	31	)	)	PUNCT
ejpam-3657	132	32	.	.	PUNCT
ejpam-3657	133	1	the	the	DET
ejpam-3657	133	2	next	next	ADJ
ejpam-3657	133	3	theorem	theorem	NOUN
ejpam-3657	133	4	is	be	AUX
ejpam-3657	133	5	an	an	DET
ejpam-3657	133	6	immediate	immediate	ADJ
ejpam-3657	133	7	consequence	consequence	NOUN
ejpam-3657	133	8	of	of	ADP
ejpam-3657	133	9	theorems	theorem	NOUN
ejpam-3657	133	10	3	3	NUM
ejpam-3657	133	11	and	and	CCONJ
ejpam-3657	133	12	4	4	NUM
ejpam-3657	133	13	.	.	X
ejpam-3657	133	14	theorem	theorem	NOUN
ejpam-3657	133	15	5	5	NUM
ejpam-3657	133	16	.	.	PUNCT
ejpam-3657	133	17	letg	letg	PROPN
ejpam-3657	133	18	be	be	AUX
ejpam-3657	133	19	any	any	DET
ejpam-3657	133	20	regular	regular	ADJ
ejpam-3657	133	21	graph	graph	NOUN
ejpam-3657	133	22	,	,	PUNCT
ejpam-3657	133	23	h	h	NOUN
ejpam-3657	133	24	be	be	VERB
ejpam-3657	133	25	any	any	DET
ejpam-3657	133	26	graph	graph	NOUN
ejpam-3657	133	27	of	of	ADP
ejpam-3657	133	28	order	order	NOUN
ejpam-3657	133	29	n	n	PRON
ejpam-3657	133	30	≥	≥	NOUN
ejpam-3657	133	31	2	2	NUM
ejpam-3657	133	32	and	and	CCONJ
ejpam-3657	133	33	t	t	NOUN
ejpam-3657	133	34	=	=	SYM
ejpam-3657	133	35	bn+∆(g	bn+∆(g	PROPN
ejpam-3657	133	36	)	)	PUNCT
ejpam-3657	133	37	2	2	NUM
ejpam-3657	133	38	c.	c.	NOUN
ejpam-3657	133	39	then	then	ADV
ejpam-3657	133	40	α1	α1	PROPN
ejpam-3657	133	41	ce(g+h	ce(g+h	PROPN
ejpam-3657	133	42	)	)	PUNCT
ejpam-3657	133	43	=	=	PUNCT
ejpam-3657	133	44	τt(g	τt(g	NUM
ejpam-3657	133	45	)	)	PUNCT
ejpam-3657	133	46	.	.	PUNCT
ejpam-3657	134	1	definition	definition	NOUN
ejpam-3657	134	2	3	3	X
ejpam-3657	134	3	.	.	PUNCT
ejpam-3657	135	1	let	let	VERB
ejpam-3657	135	2	g	g	PRON
ejpam-3657	135	3	be	be	AUX
ejpam-3657	135	4	a	a	DET
ejpam-3657	135	5	connected	connected	ADJ
ejpam-3657	135	6	graph	graph	NOUN
ejpam-3657	135	7	,	,	PUNCT
ejpam-3657	135	8	s	s	VERB
ejpam-3657	135	9	⊆	⊆	NUM
ejpam-3657	135	10	v	v	NOUN
ejpam-3657	135	11	(	(	PUNCT
ejpam-3657	135	12	g	g	NOUN
ejpam-3657	135	13	)	)	PUNCT
ejpam-3657	135	14	and	and	CCONJ
ejpam-3657	135	15	t	t	PROPN
ejpam-3657	135	16	be	be	AUX
ejpam-3657	135	17	any	any	DET
ejpam-3657	135	18	integer	integer	NOUN
ejpam-3657	135	19	.	.	PUNCT
ejpam-3657	136	1	the	the	DET
ejpam-3657	136	2	π(g	π(g	PROPN
ejpam-3657	136	3	:	:	PUNCT
ejpam-3657	136	4	s	s	X
ejpam-3657	136	5	)	)	PUNCT
ejpam-3657	136	6	is	be	AUX
ejpam-3657	136	7	defined	define	VERB
ejpam-3657	136	8	as	as	ADP
ejpam-3657	136	9	π(g	π(g	PROPN
ejpam-3657	136	10	:	:	PUNCT
ejpam-3657	136	11	s	s	X
ejpam-3657	136	12	)	)	PUNCT
ejpam-3657	136	13	=	=	SYM
ejpam-3657	136	14	max{2deg〈s〉g(v)−degg(v	max{2deg〈s〉g(v)−degg(v	PROPN
ejpam-3657	136	15	)	)	PUNCT
ejpam-3657	136	16	:	:	PUNCT
ejpam-3657	137	1	v	v	X
ejpam-3657	137	2	∈	∈	PROPN
ejpam-3657	137	3	s	s	PART
ejpam-3657	137	4	}	}	PUNCT
ejpam-3657	137	5	.	.	PUNCT
ejpam-3657	138	1	a	a	DET
ejpam-3657	138	2	set	set	NOUN
ejpam-3657	138	3	s	s	NOUN
ejpam-3657	138	4	is	be	AUX
ejpam-3657	138	5	tincrement	tincrement	ADJ
ejpam-3657	138	6	subset	subset	NOUN
ejpam-3657	138	7	of	of	ADP
ejpam-3657	138	8	g	g	PROPN
ejpam-3657	138	9	if	if	SCONJ
ejpam-3657	138	10	π(g	π(g	NOUN
ejpam-3657	138	11	:	:	PUNCT
ejpam-3657	138	12	s	s	X
ejpam-3657	138	13	)	)	PUNCT
ejpam-3657	138	14	≤	≤	NOUN
ejpam-3657	138	15	t.	t.	ADJ
ejpam-3657	138	16	example	example	NOUN
ejpam-3657	138	17	4	4	X
ejpam-3657	138	18	.	.	X
ejpam-3657	138	19	consider	consider	VERB
ejpam-3657	138	20	the	the	DET
ejpam-3657	138	21	graph	graph	NOUN
ejpam-3657	138	22	g	g	NOUN
ejpam-3657	138	23	as	as	SCONJ
ejpam-3657	138	24	shown	show	VERB
ejpam-3657	138	25	in	in	ADP
ejpam-3657	138	26	figure	figure	NOUN
ejpam-3657	138	27	1	1	NUM
ejpam-3657	138	28	.	.	PUNCT
ejpam-3657	139	1	let	let	VERB
ejpam-3657	139	2	s1	s1	PROPN
ejpam-3657	139	3	=	=	PUNCT
ejpam-3657	139	4	{	{	PUNCT
ejpam-3657	139	5	v2	v2	PROPN
ejpam-3657	139	6	,	,	PUNCT
ejpam-3657	139	7	v4	v4	PROPN
ejpam-3657	139	8	,	,	PUNCT
ejpam-3657	139	9	v6	v6	NOUN
ejpam-3657	139	10	,	,	PUNCT
ejpam-3657	139	11	v7	v7	NOUN
ejpam-3657	139	12	}	}	PUNCT
ejpam-3657	139	13	,	,	PUNCT
ejpam-3657	139	14	s2	s2	X
ejpam-3657	139	15	=	=	SYM
ejpam-3657	139	16	{	{	PUNCT
ejpam-3657	139	17	v1	v1	PROPN
ejpam-3657	139	18	,	,	PUNCT
ejpam-3657	139	19	v2	v2	PROPN
ejpam-3657	139	20	,	,	PUNCT
ejpam-3657	139	21	v5	v5	PROPN
ejpam-3657	139	22	,	,	PUNCT
ejpam-3657	139	23	v6	v6	NOUN
ejpam-3657	139	24	}	}	PUNCT
ejpam-3657	139	25	,	,	PUNCT
ejpam-3657	139	26	and	and	CCONJ
ejpam-3657	139	27	s3	s3	PROPN
ejpam-3657	139	28	=	=	SYM
ejpam-3657	139	29	{	{	PUNCT
ejpam-3657	139	30	v2	v2	PROPN
ejpam-3657	139	31	,	,	PUNCT
ejpam-3657	139	32	v3	v3	PROPN
ejpam-3657	139	33	,	,	PUNCT
ejpam-3657	139	34	v5	v5	NOUN
ejpam-3657	139	35	,	,	PUNCT
ejpam-3657	139	36	v7	v7	NOUN
ejpam-3657	139	37	}	}	PUNCT
ejpam-3657	139	38	.	.	PUNCT
ejpam-3657	140	1	then	then	ADV
ejpam-3657	140	2	π(g	π(g	PRON
ejpam-3657	140	3	:	:	PUNCT
ejpam-3657	140	4	s1	s1	NOUN
ejpam-3657	140	5	)	)	PUNCT
ejpam-3657	140	6	=	=	PUNCT
ejpam-3657	140	7	max{2deg〈s1〉g(u)−	max{2deg〈s1〉g(u)−	NOUN
ejpam-3657	140	8	degg(u	degg(u	PROPN
ejpam-3657	140	9	)	)	PUNCT
ejpam-3657	140	10	:	:	PUNCT
ejpam-3657	140	11	u	u	PROPN
ejpam-3657	140	12	∈	∈	NOUN
ejpam-3657	140	13	s1	s1	NOUN
ejpam-3657	140	14	}	}	PUNCT
ejpam-3657	140	15	=	=	NOUN
ejpam-3657	140	16	−	−	PROPN
ejpam-3657	140	17	1	1	NUM
ejpam-3657	140	18	π(g	π(g	PRON
ejpam-3657	140	19	:	:	PUNCT
ejpam-3657	140	20	s2	s2	PROPN
ejpam-3657	140	21	)	)	PUNCT
ejpam-3657	140	22	=	=	SYM
ejpam-3657	140	23	max{2deg〈s2〉g(u)−	max{2deg〈s2〉g(u)−	NOUN
ejpam-3657	140	24	degg(u	degg(u	PROPN
ejpam-3657	140	25	)	)	PUNCT
ejpam-3657	140	26	:	:	PUNCT
ejpam-3657	141	1	u	u	PROPN
ejpam-3657	141	2	∈	∈	PROPN
ejpam-3657	141	3	s2	s2	PROPN
ejpam-3657	141	4	}	}	PUNCT
ejpam-3657	141	5	=	=	PUNCT
ejpam-3657	141	6	0	0	PUNCT
ejpam-3657	141	7	π(g	π(g	PRON
ejpam-3657	141	8	:	:	PUNCT
ejpam-3657	141	9	s3	s3	PROPN
ejpam-3657	141	10	)	)	PUNCT
ejpam-3657	141	11	=	=	SYM
ejpam-3657	141	12	max{2deg〈s3〉g(u)−	max{2deg〈s3〉g(u)−	NOUN
ejpam-3657	141	13	degg(u	degg(u	NUM
ejpam-3657	141	14	)	)	PUNCT
ejpam-3657	141	15	:	:	PUNCT
ejpam-3657	141	16	u	u	PROPN
ejpam-3657	141	17	∈	∈	PROPN
ejpam-3657	141	18	s3	s3	PROPN
ejpam-3657	141	19	}	}	PUNCT
ejpam-3657	141	20	=	=	SYM
ejpam-3657	141	21	1	1	NUM
ejpam-3657	141	22	thus	thus	ADV
ejpam-3657	141	23	,	,	PUNCT
ejpam-3657	141	24	s1	s1	PROPN
ejpam-3657	141	25	is	be	AUX
ejpam-3657	141	26	−1	−1	NOUN
ejpam-3657	141	27	-	-	PUNCT
ejpam-3657	141	28	increment	increment	NOUN
ejpam-3657	141	29	,	,	PUNCT
ejpam-3657	141	30	s2	s2	PROPN
ejpam-3657	141	31	is	be	AUX
ejpam-3657	141	32	0	0	NUM
ejpam-3657	141	33	-	-	PUNCT
ejpam-3657	141	34	increment	increment	NOUN
ejpam-3657	141	35	,	,	PUNCT
ejpam-3657	141	36	and	and	CCONJ
ejpam-3657	141	37	s3	s3	PROPN
ejpam-3657	141	38	is	be	AUX
ejpam-3657	141	39	1	1	NUM
ejpam-3657	141	40	-	-	PUNCT
ejpam-3657	141	41	increment	increment	NOUN
ejpam-3657	141	42	subsets	subset	NOUN
ejpam-3657	141	43	of	of	ADP
ejpam-3657	141	44	v	v	NOUN
ejpam-3657	141	45	(	(	PUNCT
ejpam-3657	141	46	g	g	NOUN
ejpam-3657	141	47	)	)	PUNCT
ejpam-3657	141	48	.	.	PUNCT
ejpam-3657	142	1	remark	remark	PROPN
ejpam-3657	142	2	5	5	NUM
ejpam-3657	142	3	.	.	PUNCT
ejpam-3657	143	1	let	let	VERB
ejpam-3657	143	2	g	g	PRON
ejpam-3657	143	3	be	be	AUX
ejpam-3657	143	4	a	a	DET
ejpam-3657	143	5	connected	connected	ADJ
ejpam-3657	143	6	graph	graph	NOUN
ejpam-3657	143	7	.	.	PUNCT
ejpam-3657	144	1	if	if	SCONJ
ejpam-3657	144	2	s	s	VERB
ejpam-3657	144	3	=	=	SYM
ejpam-3657	144	4	v	v	X
ejpam-3657	144	5	(	(	PUNCT
ejpam-3657	144	6	g	g	NOUN
ejpam-3657	144	7	)	)	PUNCT
ejpam-3657	144	8	,	,	PUNCT
ejpam-3657	144	9	then	then	ADV
ejpam-3657	144	10	π(g	π(g	X
ejpam-3657	144	11	:	:	PUNCT
ejpam-3657	144	12	s	s	X
ejpam-3657	144	13	)	)	PUNCT
ejpam-3657	144	14	=	=	SYM
ejpam-3657	144	15	∆(g	∆(g	PROPN
ejpam-3657	144	16	)	)	PUNCT
ejpam-3657	144	17	.	.	PUNCT
ejpam-3657	145	1	definition	definition	NOUN
ejpam-3657	145	2	4	4	NUM
ejpam-3657	145	3	.	.	PUNCT
ejpam-3657	146	1	let	let	VERB
ejpam-3657	146	2	t	t	NOUN
ejpam-3657	146	3	be	be	AUX
ejpam-3657	146	4	any	any	DET
ejpam-3657	146	5	integer	integer	NOUN
ejpam-3657	146	6	.	.	PUNCT
ejpam-3657	147	1	the	the	DET
ejpam-3657	147	2	t	t	NOUN
ejpam-3657	147	3	-	-	PUNCT
ejpam-3657	147	4	increment	increment	NOUN
ejpam-3657	147	5	number	number	NOUN
ejpam-3657	147	6	of	of	ADP
ejpam-3657	147	7	g	g	NOUN
ejpam-3657	147	8	,	,	PUNCT
ejpam-3657	147	9	denoted	denote	VERB
ejpam-3657	147	10	by	by	ADP
ejpam-3657	147	11	ρt(g	ρt(g	NOUN
ejpam-3657	147	12	)	)	PUNCT
ejpam-3657	147	13	,	,	PUNCT
ejpam-3657	147	14	is	be	AUX
ejpam-3657	147	15	the	the	DET
ejpam-3657	147	16	maximum	maximum	ADJ
ejpam-3657	147	17	cardinality	cardinality	NOUN
ejpam-3657	147	18	of	of	ADP
ejpam-3657	147	19	a	a	DET
ejpam-3657	147	20	t	t	NOUN
ejpam-3657	147	21	-	-	PUNCT
ejpam-3657	147	22	increment	increment	NOUN
ejpam-3657	147	23	.	.	PUNCT
ejpam-3657	148	1	j.	j.	PROPN
ejpam-3657	148	2	g.	g.	PROPN
ejpam-3657	148	3	caadan	caadan	PROPN
ejpam-3657	148	4	,	,	PUNCT
ejpam-3657	148	5	r.	r.	PROPN
ejpam-3657	148	6	n.	n.	PROPN
ejpam-3657	148	7	paluga	paluga	PROPN
ejpam-3657	148	8	,	,	PUNCT
ejpam-3657	148	9	i.	i.	PROPN
ejpam-3657	148	10	s.	s.	PROPN
ejpam-3657	148	11	aniversario	aniversario	PROPN
ejpam-3657	148	12	/	/	SYM
ejpam-3657	148	13	eur	eur	PROPN
ejpam-3657	148	14	.	.	PUNCT
ejpam-3657	149	1	j.	j.	PROPN
ejpam-3657	149	2	pure	pure	PROPN
ejpam-3657	149	3	appl	appl	PROPN
ejpam-3657	149	4	.	.	PROPN
ejpam-3657	149	5	math	math	PROPN
ejpam-3657	149	6	,	,	PUNCT
ejpam-3657	149	7	13	13	NUM
ejpam-3657	149	8	(	(	PUNCT
ejpam-3657	149	9	3	3	NUM
ejpam-3657	149	10	)	)	PUNCT
ejpam-3657	149	11	(	(	PUNCT
ejpam-3657	149	12	2020	2020	NUM
ejpam-3657	149	13	)	)	PUNCT
ejpam-3657	149	14	,	,	PUNCT
ejpam-3657	149	15	701	701	NUM
ejpam-3657	149	16	-	-	SYM
ejpam-3657	149	17	709	709	NUM
ejpam-3657	149	18	706	706	NUM
ejpam-3657	149	19	example	example	NOUN
ejpam-3657	149	20	5	5	NUM
ejpam-3657	149	21	.	.	PUNCT
ejpam-3657	149	22	consider	consider	VERB
ejpam-3657	149	23	the	the	DET
ejpam-3657	149	24	graph	graph	NOUN
ejpam-3657	149	25	g	g	NOUN
ejpam-3657	149	26	as	as	SCONJ
ejpam-3657	149	27	shown	show	VERB
ejpam-3657	149	28	in	in	ADP
ejpam-3657	149	29	figure	figure	NOUN
ejpam-3657	149	30	1	1	NUM
ejpam-3657	149	31	.	.	PUNCT
ejpam-3657	149	32	observe	observe	VERB
ejpam-3657	149	33	that	that	SCONJ
ejpam-3657	149	34	the	the	DET
ejpam-3657	149	35	sets	set	NOUN
ejpam-3657	149	36	{	{	PUNCT
ejpam-3657	149	37	v3	v3	PROPN
ejpam-3657	149	38	,	,	PUNCT
ejpam-3657	149	39	v5	v5	PROPN
ejpam-3657	149	40	,	,	PUNCT
ejpam-3657	149	41	v6	v6	NOUN
ejpam-3657	149	42	}	}	PUNCT
ejpam-3657	149	43	,	,	PUNCT
ejpam-3657	149	44	{	{	PUNCT
ejpam-3657	149	45	v1	v1	NOUN
ejpam-3657	149	46	,	,	PUNCT
ejpam-3657	149	47	v3	v3	PROPN
ejpam-3657	149	48	,	,	PUNCT
ejpam-3657	149	49	v5	v5	PROPN
ejpam-3657	149	50	,	,	PUNCT
ejpam-3657	149	51	v6	v6	NOUN
ejpam-3657	149	52	}	}	PUNCT
ejpam-3657	149	53	,	,	PUNCT
ejpam-3657	149	54	{	{	PUNCT
ejpam-3657	149	55	v1	v1	NOUN
ejpam-3657	149	56	,	,	PUNCT
ejpam-3657	149	57	v2	v2	PROPN
ejpam-3657	149	58	,	,	PUNCT
ejpam-3657	149	59	v3	v3	PROPN
ejpam-3657	149	60	,	,	PUNCT
ejpam-3657	149	61	v5	v5	PROPN
ejpam-3657	149	62	,	,	PUNCT
ejpam-3657	149	63	v7	v7	NOUN
ejpam-3657	149	64	}	}	PUNCT
ejpam-3657	149	65	and	and	CCONJ
ejpam-3657	149	66	{	{	PUNCT
ejpam-3657	149	67	v1	v1	NOUN
ejpam-3657	149	68	,	,	PUNCT
ejpam-3657	149	69	v2	v2	PROPN
ejpam-3657	149	70	,	,	PUNCT
ejpam-3657	149	71	v4	v4	NOUN
ejpam-3657	149	72	,	,	PUNCT
ejpam-3657	149	73	v5	v5	PROPN
ejpam-3657	149	74	,	,	PUNCT
ejpam-3657	149	75	v6	v6	NOUN
ejpam-3657	149	76	,	,	PUNCT
ejpam-3657	149	77	v7	v7	VERB
ejpam-3657	149	78	}	}	PUNCT
ejpam-3657	149	79	are	be	AUX
ejpam-3657	149	80	2	2	NUM
ejpam-3657	149	81	-	-	PUNCT
ejpam-3657	149	82	increment	increment	NOUN
ejpam-3657	149	83	subsets	subset	NOUN
ejpam-3657	149	84	of	of	ADP
ejpam-3657	149	85	g	g	NOUN
ejpam-3657	149	86	while	while	SCONJ
ejpam-3657	149	87	s4	s4	NOUN
ejpam-3657	149	88	=	=	SYM
ejpam-3657	149	89	v	v	PROPN
ejpam-3657	149	90	(	(	PUNCT
ejpam-3657	149	91	g	g	NOUN
ejpam-3657	149	92	)	)	PUNCT
ejpam-3657	149	93	is	be	AUX
ejpam-3657	149	94	not	not	PART
ejpam-3657	149	95	a	a	DET
ejpam-3657	149	96	2	2	NUM
ejpam-3657	149	97	-	-	PUNCT
ejpam-3657	149	98	increment	increment	NOUN
ejpam-3657	149	99	subset	subset	NOUN
ejpam-3657	149	100	of	of	ADP
ejpam-3657	149	101	g	g	PROPN
ejpam-3657	149	102	since	since	SCONJ
ejpam-3657	149	103	π(g	π(g	PROPN
ejpam-3657	149	104	:	:	PUNCT
ejpam-3657	149	105	s4	s4	PROPN
ejpam-3657	149	106	)	)	PUNCT
ejpam-3657	150	1	=	=	SYM
ejpam-3657	150	2	5	5	X
ejpam-3657	150	3	.	.	PUNCT
ejpam-3657	150	4	thus	thus	ADV
ejpam-3657	150	5	,	,	PUNCT
ejpam-3657	150	6	ρ2(g	ρ2(g	NUM
ejpam-3657	150	7	)	)	PUNCT
ejpam-3657	150	8	=	=	SYM
ejpam-3657	150	9	6	6	X
ejpam-3657	150	10	.	.	PUNCT
ejpam-3657	150	11	remark	remark	NOUN
ejpam-3657	150	12	6	6	NUM
ejpam-3657	150	13	.	.	PUNCT
ejpam-3657	151	1	let	let	VERB
ejpam-3657	151	2	g	g	PRON
ejpam-3657	151	3	be	be	AUX
ejpam-3657	151	4	a	a	DET
ejpam-3657	151	5	connected	connected	ADJ
ejpam-3657	151	6	graph	graph	NOUN
ejpam-3657	151	7	and	and	CCONJ
ejpam-3657	151	8	t1	t1	NOUN
ejpam-3657	151	9	≤	≤	ADJ
ejpam-3657	151	10	t2	t2	NOUN
ejpam-3657	151	11	.	.	PUNCT
ejpam-3657	152	1	if	if	SCONJ
ejpam-3657	152	2	s	s	VERB
ejpam-3657	152	3	⊆	⊆	NUM
ejpam-3657	152	4	v	v	NOUN
ejpam-3657	152	5	(	(	PUNCT
ejpam-3657	152	6	g	g	NOUN
ejpam-3657	152	7	)	)	PUNCT
ejpam-3657	152	8	is	be	AUX
ejpam-3657	152	9	a	a	DET
ejpam-3657	152	10	t1increment	t1increment	NOUN
ejpam-3657	152	11	,	,	PUNCT
ejpam-3657	152	12	then	then	ADV
ejpam-3657	152	13	s	s	VERB
ejpam-3657	152	14	is	be	AUX
ejpam-3657	152	15	a	a	DET
ejpam-3657	152	16	t2increment	t2increment	NOUN
ejpam-3657	152	17	.	.	PUNCT
ejpam-3657	153	1	hence	hence	ADV
ejpam-3657	153	2	,	,	PUNCT
ejpam-3657	153	3	ρt1(g	ρt1(g	PROPN
ejpam-3657	153	4	)	)	PUNCT
ejpam-3657	153	5	≤	≤	NOUN
ejpam-3657	153	6	ρt2(g	ρt2(g	NOUN
ejpam-3657	153	7	)	)	PUNCT
ejpam-3657	153	8	.	.	PUNCT
ejpam-3657	154	1	theorem	theorem	VERB
ejpam-3657	154	2	6	6	NUM
ejpam-3657	154	3	.	.	PUNCT
ejpam-3657	155	1	let	let	VERB
ejpam-3657	155	2	g	g	NOUN
ejpam-3657	155	3	and	and	CCONJ
ejpam-3657	155	4	h	h	NOUN
ejpam-3657	155	5	be	be	AUX
ejpam-3657	155	6	connected	connect	VERB
ejpam-3657	155	7	graphs	graph	NOUN
ejpam-3657	155	8	of	of	ADP
ejpam-3657	155	9	order	order	NOUN
ejpam-3657	155	10	m	m	VERB
ejpam-3657	155	11	and	and	CCONJ
ejpam-3657	155	12	n	n	CCONJ
ejpam-3657	155	13	,	,	PUNCT
ejpam-3657	155	14	respectively	respectively	ADV
ejpam-3657	155	15	.	.	PUNCT
ejpam-3657	156	1	then	then	ADV
ejpam-3657	156	2	s	s	VERB
ejpam-3657	156	3	is	be	AUX
ejpam-3657	156	4	a	a	DET
ejpam-3657	156	5	distance	distance	NOUN
ejpam-3657	156	6	1	1	NUM
ejpam-3657	156	7	-	-	PUNCT
ejpam-3657	156	8	cost	cost	NOUN
ejpam-3657	156	9	effective	effective	ADJ
ejpam-3657	156	10	set	set	NOUN
ejpam-3657	156	11	in	in	ADP
ejpam-3657	156	12	g+h	g+h	PROPN
ejpam-3657	156	13	if	if	SCONJ
ejpam-3657	156	14	and	and	CCONJ
ejpam-3657	156	15	only	only	ADV
ejpam-3657	156	16	if	if	SCONJ
ejpam-3657	156	17	any	any	PRON
ejpam-3657	156	18	of	of	ADP
ejpam-3657	156	19	the	the	DET
ejpam-3657	156	20	following	following	NOUN
ejpam-3657	156	21	holds	hold	VERB
ejpam-3657	156	22	:	:	PUNCT
ejpam-3657	156	23	(	(	PUNCT
ejpam-3657	156	24	i	i	NOUN
ejpam-3657	156	25	)	)	PUNCT
ejpam-3657	156	26	s	s	VERB
ejpam-3657	156	27	⊆	⊆	NUM
ejpam-3657	156	28	v	v	NOUN
ejpam-3657	156	29	(	(	PUNCT
ejpam-3657	156	30	g	g	NOUN
ejpam-3657	156	31	)	)	PUNCT
ejpam-3657	156	32	is	be	AUX
ejpam-3657	156	33	n	n	CCONJ
ejpam-3657	156	34	-	-	PUNCT
ejpam-3657	156	35	increment	increment	NOUN
ejpam-3657	156	36	of	of	ADP
ejpam-3657	156	37	g.	g.	PROPN
ejpam-3657	156	38	(	(	PUNCT
ejpam-3657	156	39	ii	ii	PROPN
ejpam-3657	156	40	)	)	PUNCT
ejpam-3657	156	41	s	s	PART
ejpam-3657	156	42	⊆	⊆	NUM
ejpam-3657	156	43	v	v	NOUN
ejpam-3657	156	44	(	(	PUNCT
ejpam-3657	156	45	h	h	NOUN
ejpam-3657	156	46	)	)	PUNCT
ejpam-3657	156	47	is	be	AUX
ejpam-3657	156	48	m	m	NOUN
ejpam-3657	156	49	-	-	NOUN
ejpam-3657	156	50	increment	increment	NOUN
ejpam-3657	156	51	of	of	ADP
ejpam-3657	156	52	h.	h.	PROPN
ejpam-3657	156	53	(	(	PUNCT
ejpam-3657	156	54	iii	iii	NOUN
ejpam-3657	156	55	)	)	PUNCT
ejpam-3657	156	56	v	v	NOUN
ejpam-3657	156	57	(	(	PUNCT
ejpam-3657	156	58	g)∩s	g)∩s	PROPN
ejpam-3657	156	59	is	be	AUX
ejpam-3657	156	60	(	(	PUNCT
ejpam-3657	156	61	n−2q)-increment	n−2q)-increment	NOUN
ejpam-3657	156	62	and	and	CCONJ
ejpam-3657	156	63	v	v	NOUN
ejpam-3657	156	64	(	(	PUNCT
ejpam-3657	156	65	h)∩s	h)∩s	PROPN
ejpam-3657	156	66	is	be	AUX
ejpam-3657	156	67	(	(	PUNCT
ejpam-3657	156	68	m−2p)-increment	m−2p)-increment	NOUN
ejpam-3657	156	69	,	,	PUNCT
ejpam-3657	156	70	where	where	SCONJ
ejpam-3657	156	71	|v	|v	PROPN
ejpam-3657	156	72	(	(	PUNCT
ejpam-3657	156	73	g)∩s|	g)∩s|	PROPN
ejpam-3657	156	74	=	=	SYM
ejpam-3657	156	75	p	p	PROPN
ejpam-3657	156	76	and	and	CCONJ
ejpam-3657	156	77	|v	|v	PROPN
ejpam-3657	156	78	(	(	PUNCT
ejpam-3657	156	79	h	h	NOUN
ejpam-3657	156	80	)	)	PUNCT
ejpam-3657	156	81	∩	∩	NOUN
ejpam-3657	156	82	s|	s|	NOUN
ejpam-3657	156	83	=	=	PUNCT
ejpam-3657	156	84	q.	q.	NOUN
ejpam-3657	156	85	proof	proof	NOUN
ejpam-3657	156	86	:	:	PUNCT
ejpam-3657	156	87	suppose	suppose	VERB
ejpam-3657	156	88	s	s	NOUN
ejpam-3657	156	89	is	be	AUX
ejpam-3657	156	90	a	a	DET
ejpam-3657	156	91	distance	distance	NOUN
ejpam-3657	156	92	1	1	NUM
ejpam-3657	156	93	-	-	PUNCT
ejpam-3657	156	94	cost	cost	NOUN
ejpam-3657	156	95	effective	effective	ADJ
ejpam-3657	156	96	set	set	NOUN
ejpam-3657	156	97	in	in	ADP
ejpam-3657	156	98	g	g	PROPN
ejpam-3657	156	99	+	+	CCONJ
ejpam-3657	156	100	h.	h.	PROPN
ejpam-3657	156	101	consider	consider	VERB
ejpam-3657	156	102	the	the	DET
ejpam-3657	156	103	following	follow	VERB
ejpam-3657	156	104	cases	case	NOUN
ejpam-3657	156	105	:	:	PUNCT
ejpam-3657	156	106	case	case	NOUN
ejpam-3657	156	107	1	1	NUM
ejpam-3657	156	108	:	:	PUNCT
ejpam-3657	156	109	s	s	VERB
ejpam-3657	156	110	⊆	⊆	NUM
ejpam-3657	156	111	v	v	NOUN
ejpam-3657	156	112	(	(	PUNCT
ejpam-3657	156	113	g	g	NOUN
ejpam-3657	156	114	)	)	PUNCT
ejpam-3657	156	115	let	let	VERB
ejpam-3657	156	116	u	u	PRON
ejpam-3657	156	117	∈	∈	PROPN
ejpam-3657	156	118	s.	s.	PROPN
ejpam-3657	156	119	then	then	ADV
ejpam-3657	156	120	|n1	|n1	VERB
ejpam-3657	156	121	g+h(u	g+h(u	NOUN
ejpam-3657	156	122	)	)	PUNCT
ejpam-3657	156	123	∩	∩	PROPN
ejpam-3657	157	1	sc|	sc|	PROPN
ejpam-3657	157	2	−	−	NOUN
ejpam-3657	157	3	|n1	|n1	NOUN
ejpam-3657	157	4	g+h(u	g+h(u	NOUN
ejpam-3657	157	5	)	)	PUNCT
ejpam-3657	157	6	∩	∩	NOUN
ejpam-3657	157	7	s|	s|	NOUN
ejpam-3657	157	8	=	=	PUNCT
ejpam-3657	157	9	degg(u)−	degg(u)−	NOUN
ejpam-3657	157	10	deg〈s〉g(u	deg〈s〉g(u	PRON
ejpam-3657	157	11	)	)	PUNCT
ejpam-3657	157	12	+	+	NUM
ejpam-3657	157	13	n−	n−	NOUN
ejpam-3657	157	14	deg〈s〉g(u	deg〈s〉g(u	NUM
ejpam-3657	157	15	)	)	PUNCT
ejpam-3657	157	16	=	=	SYM
ejpam-3657	157	17	degg(u	degg(u	PROPN
ejpam-3657	157	18	)	)	PUNCT
ejpam-3657	158	1	+	+	NUM
ejpam-3657	158	2	n−	n−	NOUN
ejpam-3657	158	3	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	158	4	)	)	PUNCT
ejpam-3657	159	1	=	=	SYM
ejpam-3657	159	2	n−	n−	NOUN
ejpam-3657	159	3	(	(	PUNCT
ejpam-3657	159	4	2deg〈s〉g(u)−	2deg〈s〉g(u)−	NUM
ejpam-3657	159	5	degg(u	degg(u	PROPN
ejpam-3657	159	6	)	)	PUNCT
ejpam-3657	159	7	)	)	PUNCT
ejpam-3657	159	8	≥	≥	NOUN
ejpam-3657	159	9	0	0	NUM
ejpam-3657	159	10	.	.	PUNCT
ejpam-3657	160	1	thus	thus	ADV
ejpam-3657	160	2	,	,	PUNCT
ejpam-3657	160	3	n	n	CCONJ
ejpam-3657	160	4	−	−	PROPN
ejpam-3657	160	5	(	(	PUNCT
ejpam-3657	160	6	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	160	7	)	)	PUNCT
ejpam-3657	160	8	−	−	PROPN
ejpam-3657	160	9	degg(u	degg(u	PROPN
ejpam-3657	160	10	)	)	PUNCT
ejpam-3657	160	11	)	)	PUNCT
ejpam-3657	160	12	≥	≥	NOUN
ejpam-3657	160	13	0	0	NUM
ejpam-3657	160	14	,	,	PUNCT
ejpam-3657	160	15	for	for	ADP
ejpam-3657	160	16	each	each	DET
ejpam-3657	160	17	u	u	PROPN
ejpam-3657	160	18	∈	∈	PROPN
ejpam-3657	160	19	s.	s.	PROPN
ejpam-3657	160	20	equivalently	equivalently	PROPN
ejpam-3657	160	21	,	,	PUNCT
ejpam-3657	160	22	for	for	ADP
ejpam-3657	160	23	each	each	DET
ejpam-3657	160	24	u	u	PROPN
ejpam-3657	160	25	∈	∈	PROPN
ejpam-3657	160	26	s	s	PROPN
ejpam-3657	160	27	,	,	PUNCT
ejpam-3657	160	28	2deg〈s〉g(u)−	2deg〈s〉g(u)−	NUM
ejpam-3657	160	29	degg(u	degg(u	PROPN
ejpam-3657	160	30	)	)	PUNCT
ejpam-3657	160	31	≤	≤	NOUN
ejpam-3657	160	32	n.	n.	NOUN
ejpam-3657	160	33	hence	hence	ADV
ejpam-3657	160	34	,	,	PUNCT
ejpam-3657	160	35	π(g	π(g	PROPN
ejpam-3657	160	36	:	:	PUNCT
ejpam-3657	160	37	s	s	X
ejpam-3657	160	38	)	)	PUNCT
ejpam-3657	160	39	≤	≤	NUM
ejpam-3657	160	40	n.	n.	NOUN
ejpam-3657	160	41	thus	thus	ADV
ejpam-3657	160	42	,	,	PUNCT
ejpam-3657	160	43	(	(	PUNCT
ejpam-3657	160	44	i	i	NOUN
ejpam-3657	160	45	)	)	PUNCT
ejpam-3657	160	46	holds	hold	VERB
ejpam-3657	160	47	.	.	PUNCT
ejpam-3657	161	1	case	case	NOUN
ejpam-3657	161	2	2	2	NUM
ejpam-3657	161	3	:	:	PUNCT
ejpam-3657	161	4	s	s	VERB
ejpam-3657	161	5	⊆	⊆	NUM
ejpam-3657	161	6	v	v	NOUN
ejpam-3657	161	7	(	(	PUNCT
ejpam-3657	161	8	h	h	NOUN
ejpam-3657	161	9	)	)	PUNCT
ejpam-3657	161	10	by	by	ADP
ejpam-3657	161	11	similar	similar	ADJ
ejpam-3657	161	12	argument	argument	NOUN
ejpam-3657	161	13	to	to	PART
ejpam-3657	161	14	case	case	VERB
ejpam-3657	161	15	1	1	NUM
ejpam-3657	161	16	,	,	PUNCT
ejpam-3657	161	17	(	(	PUNCT
ejpam-3657	161	18	ii	ii	NOUN
ejpam-3657	161	19	)	)	PUNCT
ejpam-3657	161	20	holds	hold	VERB
ejpam-3657	161	21	.	.	PUNCT
ejpam-3657	162	1	case	case	NOUN
ejpam-3657	162	2	3	3	NUM
ejpam-3657	162	3	:	:	SYM
ejpam-3657	162	4	v	v	NOUN
ejpam-3657	162	5	(	(	PUNCT
ejpam-3657	162	6	g	g	NOUN
ejpam-3657	162	7	)	)	PUNCT
ejpam-3657	162	8	∩	∩	PROPN
ejpam-3657	162	9	s	s	PART
ejpam-3657	162	10	6=	6=	NOUN
ejpam-3657	162	11	∅	∅	NOUN
ejpam-3657	162	12	and	and	CCONJ
ejpam-3657	162	13	v	v	NOUN
ejpam-3657	162	14	(	(	PUNCT
ejpam-3657	162	15	h	h	NOUN
ejpam-3657	162	16	)	)	PUNCT
ejpam-3657	162	17	∩	∩	X
ejpam-3657	162	18	s	s	PART
ejpam-3657	162	19	6=	6=	PROPN
ejpam-3657	162	20	∅	∅	NOUN
ejpam-3657	162	21	let	let	VERB
ejpam-3657	162	22	u	u	PRON
ejpam-3657	162	23	∈	∈	PROPN
ejpam-3657	162	24	v	v	ADP
ejpam-3657	162	25	(	(	PUNCT
ejpam-3657	162	26	g	g	NOUN
ejpam-3657	162	27	)	)	PUNCT
ejpam-3657	162	28	∩	∩	NOUN
ejpam-3657	162	29	s.	s.	PROPN
ejpam-3657	162	30	suppose	suppose	VERB
ejpam-3657	162	31	|v	|v	PROPN
ejpam-3657	162	32	(	(	PUNCT
ejpam-3657	162	33	g	g	NOUN
ejpam-3657	162	34	)	)	PUNCT
ejpam-3657	162	35	∩	∩	NOUN
ejpam-3657	162	36	s|	s|	VERB
ejpam-3657	162	37	=	=	SYM
ejpam-3657	163	1	p	p	NOUN
ejpam-3657	163	2	,	,	PUNCT
ejpam-3657	163	3	where	where	SCONJ
ejpam-3657	163	4	1	1	NUM
ejpam-3657	163	5	≤	≤	NOUN
ejpam-3657	163	6	p	p	NOUN
ejpam-3657	163	7	≤	≤	ADJ
ejpam-3657	163	8	m.	m.	NOUN
ejpam-3657	163	9	then	then	ADV
ejpam-3657	163	10	for	for	ADP
ejpam-3657	163	11	each	each	DET
ejpam-3657	163	12	u	u	PROPN
ejpam-3657	163	13	∈	∈	PROPN
ejpam-3657	163	14	s	s	PROPN
ejpam-3657	163	15	,	,	PUNCT
ejpam-3657	163	16	|n1	|n1	VERB
ejpam-3657	163	17	g+h(u	g+h(u	NOUN
ejpam-3657	163	18	)	)	PUNCT
ejpam-3657	163	19	∩	∩	PROPN
ejpam-3657	163	20	sc|	sc|	PROPN
ejpam-3657	163	21	−	−	NOUN
ejpam-3657	163	22	|n1	|n1	NOUN
ejpam-3657	163	23	g+h(u	g+h(u	NOUN
ejpam-3657	163	24	)	)	PUNCT
ejpam-3657	163	25	∩	∩	NOUN
ejpam-3657	163	26	s|	s|	NOUN
ejpam-3657	163	27	=	=	PUNCT
ejpam-3657	163	28	degg(u)−	degg(u)−	NOUN
ejpam-3657	163	29	deg〈v	deg〈v	PROPN
ejpam-3657	163	30	(	(	PUNCT
ejpam-3657	163	31	g)∩s〉(u	g)∩s〉(u	NOUN
ejpam-3657	163	32	)	)	PUNCT
ejpam-3657	164	1	+	+	CCONJ
ejpam-3657	164	2	n−	n−	NOUN
ejpam-3657	164	3	q	q	NOUN
ejpam-3657	164	4	−	−	X
ejpam-3657	165	1	deg〈v	deg〈v	PROPN
ejpam-3657	165	2	(	(	PUNCT
ejpam-3657	165	3	g)∩s〉(u)−	g)∩s〉(u)−	PROPN
ejpam-3657	165	4	q	q	NOUN
ejpam-3657	165	5	=	=	PUNCT
ejpam-3657	165	6	degg(u)−	degg(u)−	PROPN
ejpam-3657	165	7	2deg〈v	2deg〈v	PROPN
ejpam-3657	165	8	(	(	PUNCT
ejpam-3657	165	9	g)∩s〉(u	g)∩s〉(u	NOUN
ejpam-3657	165	10	)	)	PUNCT
ejpam-3657	166	1	+	+	NUM
ejpam-3657	166	2	n−	n−	NOUN
ejpam-3657	166	3	2q	2q	NOUN
ejpam-3657	166	4	.	.	PUNCT
ejpam-3657	167	1	since	since	SCONJ
ejpam-3657	167	2	s	s	PROPN
ejpam-3657	167	3	is	be	AUX
ejpam-3657	167	4	a	a	DET
ejpam-3657	167	5	distance	distance	NOUN
ejpam-3657	167	6	1	1	NUM
ejpam-3657	167	7	-	-	PUNCT
ejpam-3657	167	8	cost	cost	NOUN
ejpam-3657	167	9	effective	effective	ADJ
ejpam-3657	167	10	,	,	PUNCT
ejpam-3657	167	11	degg(u	degg(u	PROPN
ejpam-3657	167	12	)	)	PUNCT
ejpam-3657	167	13	−	−	PROPN
ejpam-3657	168	1	2deg〈v	2deg〈v	PROPN
ejpam-3657	168	2	(	(	PUNCT
ejpam-3657	168	3	g)∩s〉(u	g)∩s〉(u	NOUN
ejpam-3657	168	4	)	)	PUNCT
ejpam-3657	169	1	+	+	CCONJ
ejpam-3657	169	2	n	n	CCONJ
ejpam-3657	169	3	−	−	PROPN
ejpam-3657	169	4	2q	2q	NUM
ejpam-3657	169	5	≥	≥	NOUN
ejpam-3657	169	6	0	0	NUM
ejpam-3657	169	7	,	,	PUNCT
ejpam-3657	169	8	∀	∀	VERB
ejpam-3657	170	1	u	u	NOUN
ejpam-3657	170	2	∈	∈	PROPN
ejpam-3657	170	3	s.	s.	PROPN
ejpam-3657	170	4	thus	thus	ADV
ejpam-3657	170	5	,	,	PUNCT
ejpam-3657	170	6	2deg〈v	2deg〈v	PROPN
ejpam-3657	170	7	(	(	PUNCT
ejpam-3657	170	8	g)∩s〉(u)−degg(u	g)∩s〉(u)−degg(u	NOUN
ejpam-3657	170	9	)	)	PUNCT
ejpam-3657	170	10	≤	≤	NOUN
ejpam-3657	170	11	n−2q	n−2q	NOUN
ejpam-3657	170	12	.	.	PUNCT
ejpam-3657	171	1	this	this	PRON
ejpam-3657	171	2	implies	imply	VERB
ejpam-3657	171	3	that	that	SCONJ
ejpam-3657	171	4	v	v	X
ejpam-3657	171	5	(	(	PUNCT
ejpam-3657	171	6	g)∩s	g)∩s	PROPN
ejpam-3657	171	7	is	be	AUX
ejpam-3657	171	8	(	(	PUNCT
ejpam-3657	171	9	n−2q)-increment	n−2q)-increment	NOUN
ejpam-3657	171	10	of	of	ADP
ejpam-3657	171	11	g.	g.	NOUN
ejpam-3657	171	12	similarly	similarly	ADV
ejpam-3657	171	13	,	,	PUNCT
ejpam-3657	171	14	let	let	VERB
ejpam-3657	171	15	u	u	PRON
ejpam-3657	171	16	∈	∈	PROPN
ejpam-3657	171	17	v	v	ADP
ejpam-3657	171	18	(	(	PUNCT
ejpam-3657	171	19	h	h	NOUN
ejpam-3657	171	20	)	)	PUNCT
ejpam-3657	171	21	∩	∩	PROPN
ejpam-3657	171	22	s.	s.	PROPN
ejpam-3657	171	23	then	then	ADV
ejpam-3657	171	24	for	for	ADP
ejpam-3657	171	25	each	each	DET
ejpam-3657	171	26	u	u	PROPN
ejpam-3657	171	27	∈	∈	PROPN
ejpam-3657	171	28	s	s	PROPN
ejpam-3657	171	29	,	,	PUNCT
ejpam-3657	171	30	|n1	|n1	VERB
ejpam-3657	171	31	g+h(u	g+h(u	NOUN
ejpam-3657	171	32	)	)	PUNCT
ejpam-3657	171	33	∩	∩	PROPN
ejpam-3657	171	34	sc|	sc|	PROPN
ejpam-3657	171	35	−	−	NOUN
ejpam-3657	171	36	|n1	|n1	NOUN
ejpam-3657	171	37	g+h(u	g+h(u	NOUN
ejpam-3657	171	38	)	)	PUNCT
ejpam-3657	171	39	∩	∩	NOUN
ejpam-3657	171	40	s|	s|	NOUN
ejpam-3657	171	41	=	=	PUNCT
ejpam-3657	172	1	m−	m−	PROPN
ejpam-3657	172	2	p+	p+	VERB
ejpam-3657	172	3	degh(u)−	degh(u)−	PROPN
ejpam-3657	172	4	deg〈v	deg〈v	PROPN
ejpam-3657	172	5	(	(	PUNCT
ejpam-3657	172	6	h)∩s〉(u)−	h)∩s〉(u)−	PROPN
ejpam-3657	172	7	p−	p−	NOUN
ejpam-3657	172	8	deg〈v	deg〈v	NOUN
ejpam-3657	172	9	(	(	PUNCT
ejpam-3657	172	10	h)∩s〉(u)−	h)∩s〉(u)−	PROPN
ejpam-3657	172	11	q	q	PROPN
ejpam-3657	172	12	j.	j.	PROPN
ejpam-3657	172	13	g.	g.	PROPN
ejpam-3657	172	14	caadan	caadan	PROPN
ejpam-3657	172	15	,	,	PUNCT
ejpam-3657	172	16	r.	r.	PROPN
ejpam-3657	172	17	n.	n.	PROPN
ejpam-3657	172	18	paluga	paluga	PROPN
ejpam-3657	172	19	,	,	PUNCT
ejpam-3657	172	20	i.	i.	PROPN
ejpam-3657	172	21	s.	s.	PROPN
ejpam-3657	172	22	aniversario	aniversario	PROPN
ejpam-3657	172	23	/	/	SYM
ejpam-3657	172	24	eur	eur	PROPN
ejpam-3657	172	25	.	.	PUNCT
ejpam-3657	173	1	j.	j.	PROPN
ejpam-3657	173	2	pure	pure	PROPN
ejpam-3657	173	3	appl	appl	PROPN
ejpam-3657	173	4	.	.	PROPN
ejpam-3657	173	5	math	math	PROPN
ejpam-3657	173	6	,	,	PUNCT
ejpam-3657	173	7	13	13	NUM
ejpam-3657	173	8	(	(	PUNCT
ejpam-3657	173	9	3	3	NUM
ejpam-3657	173	10	)	)	PUNCT
ejpam-3657	173	11	(	(	PUNCT
ejpam-3657	173	12	2020	2020	NUM
ejpam-3657	173	13	)	)	PUNCT
ejpam-3657	173	14	,	,	PUNCT
ejpam-3657	173	15	701	701	NUM
ejpam-3657	173	16	-	-	SYM
ejpam-3657	173	17	709	709	NUM
ejpam-3657	173	18	707	707	NUM
ejpam-3657	173	19	=	=	SYM
ejpam-3657	173	20	m−	m−	PROPN
ejpam-3657	173	21	2p+	2p+	NUM
ejpam-3657	174	1	degh(u)−	degh(u)−	INTJ
ejpam-3657	174	2	2deg〈v	2deg〈v	PROPN
ejpam-3657	174	3	(	(	PUNCT
ejpam-3657	174	4	h)∩s〉(u	h)∩s〉(u	PROPN
ejpam-3657	174	5	)	)	PUNCT
ejpam-3657	174	6	≥	≥	PROPN
ejpam-3657	174	7	0	0	NUM
ejpam-3657	174	8	.	.	PUNCT
ejpam-3657	175	1	it	it	PRON
ejpam-3657	175	2	follows	follow	VERB
ejpam-3657	175	3	that	that	SCONJ
ejpam-3657	175	4	2deg〈v	2deg〈v	PROPN
ejpam-3657	175	5	(	(	PUNCT
ejpam-3657	175	6	h)∩s〉(u	h)∩s〉(u	NOUN
ejpam-3657	175	7	)	)	PUNCT
ejpam-3657	175	8	−	−	PROPN
ejpam-3657	175	9	degh(u	degh(u	PROPN
ejpam-3657	175	10	)	)	PUNCT
ejpam-3657	175	11	≤	≤	NOUN
ejpam-3657	175	12	m	m	VERB
ejpam-3657	175	13	−	−	NOUN
ejpam-3657	175	14	2p	2p	NOUN
ejpam-3657	175	15	.	.	PUNCT
ejpam-3657	176	1	this	this	PRON
ejpam-3657	176	2	implies	imply	VERB
ejpam-3657	176	3	that	that	SCONJ
ejpam-3657	176	4	v	v	X
ejpam-3657	176	5	(	(	PUNCT
ejpam-3657	176	6	h	h	NOUN
ejpam-3657	176	7	)	)	PUNCT
ejpam-3657	176	8	∩	∩	NOUN
ejpam-3657	176	9	s	s	PART
ejpam-3657	176	10	is	be	AUX
ejpam-3657	176	11	(	(	PUNCT
ejpam-3657	176	12	m−	m−	PROPN
ejpam-3657	176	13	2p)-increment	2p)-increment	NUM
ejpam-3657	176	14	of	of	ADP
ejpam-3657	176	15	h.	h.	PROPN
ejpam-3657	176	16	thus	thus	ADV
ejpam-3657	176	17	,	,	PUNCT
ejpam-3657	176	18	(	(	PUNCT
ejpam-3657	176	19	iii	iii	NOUN
ejpam-3657	176	20	)	)	PUNCT
ejpam-3657	176	21	holds	hold	VERB
ejpam-3657	176	22	.	.	PUNCT
ejpam-3657	177	1	conversely	conversely	ADV
ejpam-3657	177	2	,	,	PUNCT
ejpam-3657	177	3	if	if	SCONJ
ejpam-3657	177	4	(	(	PUNCT
ejpam-3657	177	5	i	i	NOUN
ejpam-3657	177	6	)	)	PUNCT
ejpam-3657	177	7	holds	hold	VERB
ejpam-3657	177	8	then	then	ADV
ejpam-3657	177	9	π(g	π(g	PRON
ejpam-3657	177	10	:	:	PUNCT
ejpam-3657	177	11	s	s	X
ejpam-3657	177	12	)	)	PUNCT
ejpam-3657	177	13	≤	≤	NOUN
ejpam-3657	177	14	n.	n.	NOUN
ejpam-3657	177	15	let	let	VERB
ejpam-3657	177	16	u	u	PRON
ejpam-3657	177	17	∈	∈	PROPN
ejpam-3657	177	18	s.	s.	PROPN
ejpam-3657	177	19	then	then	ADV
ejpam-3657	177	20	|n1	|n1	VERB
ejpam-3657	177	21	g+h(u	g+h(u	NOUN
ejpam-3657	177	22	)	)	PUNCT
ejpam-3657	177	23	∩	∩	PROPN
ejpam-3657	178	1	sc|	sc|	PROPN
ejpam-3657	178	2	−	−	NOUN
ejpam-3657	178	3	|n1	|n1	NOUN
ejpam-3657	178	4	g+h(u	g+h(u	NOUN
ejpam-3657	178	5	)	)	PUNCT
ejpam-3657	178	6	∩	∩	NOUN
ejpam-3657	178	7	s|	s|	NOUN
ejpam-3657	178	8	=	=	SYM
ejpam-3657	178	9	degg(u	degg(u	PROPN
ejpam-3657	178	10	)	)	PUNCT
ejpam-3657	179	1	+	+	NUM
ejpam-3657	179	2	n−	n−	NOUN
ejpam-3657	179	3	2deg〈s〉g(u	2deg〈s〉g(u	NUM
ejpam-3657	179	4	)	)	PUNCT
ejpam-3657	180	1	=	=	SYM
ejpam-3657	180	2	n−	n−	NOUN
ejpam-3657	180	3	(	(	PUNCT
ejpam-3657	180	4	2deg〈s〉g(u)−	2deg〈s〉g(u)−	NUM
ejpam-3657	180	5	degg(u	degg(u	PROPN
ejpam-3657	180	6	)	)	PUNCT
ejpam-3657	180	7	)	)	PUNCT
ejpam-3657	181	1	=	=	PUNCT
ejpam-3657	181	2	n−	n−	NOUN
ejpam-3657	181	3	π(g	π(g	NOUN
ejpam-3657	181	4	:	:	PUNCT
ejpam-3657	181	5	s	s	X
ejpam-3657	181	6	)	)	PUNCT
ejpam-3657	181	7	≥	≥	NOUN
ejpam-3657	181	8	n−	n−	NOUN
ejpam-3657	181	9	n	n	NOUN
ejpam-3657	181	10	=	=	SYM
ejpam-3657	181	11	0	0	NUM
ejpam-3657	181	12	.	.	PUNCT
ejpam-3657	182	1	thus	thus	ADV
ejpam-3657	182	2	,	,	PUNCT
ejpam-3657	182	3	s	s	VERB
ejpam-3657	182	4	is	be	AUX
ejpam-3657	182	5	a	a	DET
ejpam-3657	182	6	distance	distance	NOUN
ejpam-3657	182	7	1	1	NUM
ejpam-3657	182	8	-	-	PUNCT
ejpam-3657	182	9	cost	cost	NOUN
ejpam-3657	182	10	effective	effective	ADJ
ejpam-3657	182	11	set	set	NOUN
ejpam-3657	182	12	in	in	ADP
ejpam-3657	182	13	g+h	g+h	PROPN
ejpam-3657	182	14	.	.	PUNCT
ejpam-3657	183	1	suppose	suppose	VERB
ejpam-3657	183	2	(	(	PUNCT
ejpam-3657	183	3	ii	ii	NOUN
ejpam-3657	183	4	)	)	PUNCT
ejpam-3657	183	5	holds	hold	VERB
ejpam-3657	183	6	.	.	PUNCT
ejpam-3657	184	1	let	let	VERB
ejpam-3657	184	2	u	u	PRON
ejpam-3657	184	3	∈	∈	PROPN
ejpam-3657	184	4	s.	s.	PROPN
ejpam-3657	184	5	then	then	ADV
ejpam-3657	184	6	by	by	ADP
ejpam-3657	184	7	similar	similar	ADJ
ejpam-3657	184	8	argument	argument	NOUN
ejpam-3657	184	9	,	,	PUNCT
ejpam-3657	184	10	s	s	PART
ejpam-3657	184	11	is	be	AUX
ejpam-3657	184	12	a	a	DET
ejpam-3657	184	13	distance	distance	NOUN
ejpam-3657	184	14	1	1	NUM
ejpam-3657	184	15	-	-	PUNCT
ejpam-3657	184	16	cost	cost	NOUN
ejpam-3657	184	17	effective	effective	ADJ
ejpam-3657	184	18	set	set	NOUN
ejpam-3657	184	19	in	in	ADP
ejpam-3657	184	20	g+h	g+h	PROPN
ejpam-3657	184	21	.	.	PUNCT
ejpam-3657	185	1	suppose	suppose	VERB
ejpam-3657	185	2	(	(	PUNCT
ejpam-3657	185	3	iii	iii	NOUN
ejpam-3657	185	4	)	)	PUNCT
ejpam-3657	185	5	holds	hold	VERB
ejpam-3657	185	6	.	.	PUNCT
ejpam-3657	186	1	then	then	ADV
ejpam-3657	186	2	π(g	π(g	PRON
ejpam-3657	186	3	:	:	PUNCT
ejpam-3657	186	4	v	v	NOUN
ejpam-3657	186	5	(	(	PUNCT
ejpam-3657	186	6	g	g	NOUN
ejpam-3657	186	7	)	)	PUNCT
ejpam-3657	186	8	∩	∩	NOUN
ejpam-3657	186	9	s	s	X
ejpam-3657	186	10	)	)	PUNCT
ejpam-3657	186	11	≤	≤	NUM
ejpam-3657	186	12	n−	n−	PROPN
ejpam-3657	186	13	2q	2q	NOUN
ejpam-3657	186	14	and	and	CCONJ
ejpam-3657	186	15	π(h	π(h	PROPN
ejpam-3657	186	16	:	:	PUNCT
ejpam-3657	186	17	v	v	X
ejpam-3657	186	18	(	(	PUNCT
ejpam-3657	186	19	h	h	NOUN
ejpam-3657	186	20	)	)	PUNCT
ejpam-3657	186	21	∩	∩	NOUN
ejpam-3657	186	22	s	s	PART
ejpam-3657	186	23	)	)	PUNCT
ejpam-3657	186	24	≤	≤	NUM
ejpam-3657	186	25	m−	m−	PROPN
ejpam-3657	186	26	2p	2p	NUM
ejpam-3657	186	27	.	.	PUNCT
ejpam-3657	187	1	let	let	VERB
ejpam-3657	187	2	u	u	PRON
ejpam-3657	187	3	∈	∈	PROPN
ejpam-3657	187	4	v	v	ADP
ejpam-3657	187	5	(	(	PUNCT
ejpam-3657	187	6	g	g	NOUN
ejpam-3657	187	7	)	)	PUNCT
ejpam-3657	187	8	∩	∩	PROPN
ejpam-3657	187	9	s.	s.	PROPN
ejpam-3657	187	10	then	then	ADV
ejpam-3657	187	11	for	for	SCONJ
ejpam-3657	187	12	each	each	DET
ejpam-3657	187	13	u	u	PROPN
ejpam-3657	187	14	∈	∈	PROPN
ejpam-3657	187	15	s	s	PROPN
ejpam-3657	187	16	,	,	PUNCT
ejpam-3657	187	17	|n1	|n1	VERB
ejpam-3657	187	18	g+h(u	g+h(u	NOUN
ejpam-3657	187	19	)	)	PUNCT
ejpam-3657	187	20	∩	∩	PROPN
ejpam-3657	187	21	sc|	sc|	PROPN
ejpam-3657	187	22	−	−	NOUN
ejpam-3657	187	23	|n1	|n1	NOUN
ejpam-3657	187	24	g+h(u	g+h(u	NOUN
ejpam-3657	187	25	)	)	PUNCT
ejpam-3657	187	26	∩	∩	NOUN
ejpam-3657	187	27	s|	s|	NOUN
ejpam-3657	188	1	=	=	PUNCT
ejpam-3657	188	2	degg(u)−	degg(u)−	PROPN
ejpam-3657	188	3	2deg〈v	2deg〈v	PROPN
ejpam-3657	188	4	(	(	PUNCT
ejpam-3657	188	5	g)∩s〉(u	g)∩s〉(u	NOUN
ejpam-3657	188	6	)	)	PUNCT
ejpam-3657	189	1	+	+	NUM
ejpam-3657	189	2	n−	n−	NOUN
ejpam-3657	189	3	2q	2q	X
ejpam-3657	189	4	=	=	PUNCT
ejpam-3657	189	5	n−	n−	NOUN
ejpam-3657	189	6	2q	2q	NOUN
ejpam-3657	189	7	−	−	PROPN
ejpam-3657	189	8	(	(	PUNCT
ejpam-3657	189	9	2deg〈v	2deg〈v	PROPN
ejpam-3657	189	10	(	(	PUNCT
ejpam-3657	189	11	g)∩s〉(u)−	g)∩s〉(u)−	PROPN
ejpam-3657	189	12	degg(u	degg(u	PROPN
ejpam-3657	189	13	)	)	PUNCT
ejpam-3657	189	14	)	)	PUNCT
ejpam-3657	190	1	=	=	PUNCT
ejpam-3657	190	2	n−	n−	NOUN
ejpam-3657	190	3	2q	2q	NOUN
ejpam-3657	190	4	−	−	PROPN
ejpam-3657	191	1	π(g	π(g	X
ejpam-3657	191	2	:	:	PUNCT
ejpam-3657	191	3	v	v	NOUN
ejpam-3657	191	4	(	(	PUNCT
ejpam-3657	191	5	g	g	NOUN
ejpam-3657	191	6	)	)	PUNCT
ejpam-3657	191	7	∩	∩	NOUN
ejpam-3657	191	8	s	s	PART
ejpam-3657	191	9	)	)	PUNCT
ejpam-3657	191	10	≥	≥	NOUN
ejpam-3657	191	11	n−	n−	NOUN
ejpam-3657	191	12	2q	2q	NOUN
ejpam-3657	191	13	−	−	PROPN
ejpam-3657	191	14	(	(	PUNCT
ejpam-3657	191	15	n−	n−	NOUN
ejpam-3657	191	16	2q	2q	NUM
ejpam-3657	191	17	)	)	PUNCT
ejpam-3657	191	18	=	=	SYM
ejpam-3657	192	1	0	0	X
ejpam-3657	192	2	.	.	PUNCT
ejpam-3657	193	1	thus	thus	ADV
ejpam-3657	193	2	,	,	PUNCT
ejpam-3657	193	3	s	s	VERB
ejpam-3657	193	4	is	be	AUX
ejpam-3657	193	5	a	a	DET
ejpam-3657	193	6	distance	distance	NOUN
ejpam-3657	193	7	1	1	NUM
ejpam-3657	193	8	-	-	PUNCT
ejpam-3657	193	9	cost	cost	NOUN
ejpam-3657	193	10	effective	effective	ADJ
ejpam-3657	193	11	set	set	NOUN
ejpam-3657	193	12	in	in	ADP
ejpam-3657	193	13	g+h	g+h	PROPN
ejpam-3657	193	14	.	.	PUNCT
ejpam-3657	194	1	similarly	similarly	ADV
ejpam-3657	194	2	,	,	PUNCT
ejpam-3657	194	3	let	let	VERB
ejpam-3657	194	4	u	u	PRON
ejpam-3657	194	5	∈	∈	PROPN
ejpam-3657	194	6	v	v	ADP
ejpam-3657	194	7	(	(	PUNCT
ejpam-3657	194	8	h	h	NOUN
ejpam-3657	194	9	)	)	PUNCT
ejpam-3657	194	10	∩	∩	PROPN
ejpam-3657	194	11	s.	s.	PROPN
ejpam-3657	194	12	then	then	ADV
ejpam-3657	194	13	for	for	ADP
ejpam-3657	194	14	each	each	DET
ejpam-3657	194	15	u	u	PROPN
ejpam-3657	194	16	∈	∈	PROPN
ejpam-3657	194	17	s	s	PROPN
ejpam-3657	194	18	,	,	PUNCT
ejpam-3657	194	19	|n1	|n1	VERB
ejpam-3657	194	20	g+h(u	g+h(u	NOUN
ejpam-3657	194	21	)	)	PUNCT
ejpam-3657	194	22	∩	∩	PROPN
ejpam-3657	194	23	sc|	sc|	PROPN
ejpam-3657	194	24	−	−	NOUN
ejpam-3657	194	25	|n1	|n1	NOUN
ejpam-3657	194	26	g+h(u	g+h(u	NOUN
ejpam-3657	194	27	)	)	PUNCT
ejpam-3657	194	28	∩	∩	NOUN
ejpam-3657	194	29	s|	s|	NOUN
ejpam-3657	194	30	=	=	PUNCT
ejpam-3657	195	1	m−	m−	PROPN
ejpam-3657	195	2	2p+	2p+	NUM
ejpam-3657	196	1	degh(u)−	degh(u)−	INTJ
ejpam-3657	196	2	2deg〈v	2deg〈v	PROPN
ejpam-3657	196	3	(	(	PUNCT
ejpam-3657	196	4	h)∩s〉(u	h)∩s〉(u	NOUN
ejpam-3657	196	5	)	)	PUNCT
ejpam-3657	197	1	=	=	SYM
ejpam-3657	198	1	m−	m−	PROPN
ejpam-3657	198	2	2p−	2p−	PROPN
ejpam-3657	198	3	(	(	PUNCT
ejpam-3657	198	4	2deg〈v	2deg〈v	PROPN
ejpam-3657	198	5	(	(	PUNCT
ejpam-3657	198	6	h)∩s〉(u)−	h)∩s〉(u)−	PROPN
ejpam-3657	198	7	degh(u	degh(u	PROPN
ejpam-3657	198	8	)	)	PUNCT
ejpam-3657	198	9	)	)	PUNCT
ejpam-3657	199	1	=	=	PUNCT
ejpam-3657	200	1	m−	m−	PROPN
ejpam-3657	200	2	2p−	2p−	NUM
ejpam-3657	200	3	π(h	π(h	PROPN
ejpam-3657	200	4	:	:	PUNCT
ejpam-3657	200	5	v	v	X
ejpam-3657	200	6	(	(	PUNCT
ejpam-3657	200	7	h	h	NOUN
ejpam-3657	200	8	)	)	PUNCT
ejpam-3657	200	9	∩	∩	NOUN
ejpam-3657	200	10	s	s	PART
ejpam-3657	200	11	)	)	PUNCT
ejpam-3657	200	12	≥	≥	NOUN
ejpam-3657	200	13	m−	m−	PROPN
ejpam-3657	200	14	2p−	2p−	PROPN
ejpam-3657	200	15	(	(	PUNCT
ejpam-3657	200	16	m−	m−	PROPN
ejpam-3657	200	17	2p	2p	NUM
ejpam-3657	200	18	)	)	PUNCT
ejpam-3657	201	1	=	=	SYM
ejpam-3657	201	2	0	0	X
ejpam-3657	201	3	.	.	PUNCT
ejpam-3657	202	1	thus	thus	ADV
ejpam-3657	202	2	,	,	PUNCT
ejpam-3657	202	3	s	s	VERB
ejpam-3657	202	4	is	be	AUX
ejpam-3657	202	5	a	a	DET
ejpam-3657	202	6	distance	distance	NOUN
ejpam-3657	202	7	1	1	NUM
ejpam-3657	202	8	-	-	PUNCT
ejpam-3657	202	9	cost	cost	NOUN
ejpam-3657	202	10	effective	effective	ADJ
ejpam-3657	202	11	set	set	NOUN
ejpam-3657	202	12	in	in	ADP
ejpam-3657	202	13	g+h	g+h	PROPN
ejpam-3657	202	14	.	.	PUNCT
ejpam-3657	203	1	corollary	corollary	ADJ
ejpam-3657	203	2	5	5	NUM
ejpam-3657	203	3	.	.	PUNCT
ejpam-3657	204	1	let	let	VERB
ejpam-3657	204	2	g	g	PRON
ejpam-3657	204	3	be	be	AUX
ejpam-3657	204	4	a	a	DET
ejpam-3657	204	5	connected	connected	ADJ
ejpam-3657	204	6	graph	graph	NOUN
ejpam-3657	204	7	,	,	PUNCT
ejpam-3657	204	8	s	s	VERB
ejpam-3657	204	9	⊆	⊆	NUM
ejpam-3657	204	10	v	v	NOUN
ejpam-3657	204	11	(	(	PUNCT
ejpam-3657	204	12	g	g	NOUN
ejpam-3657	204	13	)	)	PUNCT
ejpam-3657	204	14	and	and	CCONJ
ejpam-3657	204	15	n	n	PRON
ejpam-3657	204	16	≥	≥	NOUN
ejpam-3657	204	17	2	2	NUM
ejpam-3657	204	18	.	.	PUNCT
ejpam-3657	205	1	then	then	ADV
ejpam-3657	205	2	s	s	VERB
ejpam-3657	205	3	is	be	AUX
ejpam-3657	205	4	a	a	DET
ejpam-3657	205	5	distance	distance	NOUN
ejpam-3657	205	6	1	1	NUM
ejpam-3657	205	7	-	-	PUNCT
ejpam-3657	205	8	cost	cost	NOUN
ejpam-3657	205	9	effective	effective	ADJ
ejpam-3657	205	10	set	set	NOUN
ejpam-3657	205	11	in	in	ADP
ejpam-3657	205	12	g+kn	g+kn	NOUN
ejpam-3657	205	13	if	if	SCONJ
ejpam-3657	205	14	and	and	CCONJ
ejpam-3657	205	15	only	only	ADV
ejpam-3657	205	16	if	if	SCONJ
ejpam-3657	205	17	s	s	NOUN
ejpam-3657	205	18	is	be	AUX
ejpam-3657	205	19	n	n	PRON
ejpam-3657	205	20	-	-	PUNCT
ejpam-3657	205	21	increment	increment	NOUN
ejpam-3657	205	22	.	.	PUNCT
ejpam-3657	206	1	corollary	corollary	ADJ
ejpam-3657	206	2	6	6	NUM
ejpam-3657	206	3	.	.	PUNCT
ejpam-3657	207	1	let	let	VERB
ejpam-3657	207	2	g	g	PRON
ejpam-3657	207	3	be	be	AUX
ejpam-3657	207	4	a	a	DET
ejpam-3657	207	5	connected	connected	ADJ
ejpam-3657	207	6	graph	graph	NOUN
ejpam-3657	207	7	and	and	CCONJ
ejpam-3657	207	8	n	n	PRON
ejpam-3657	207	9	≥	≥	NOUN
ejpam-3657	207	10	2	2	NUM
ejpam-3657	207	11	.	.	PUNCT
ejpam-3657	208	1	a	a	DET
ejpam-3657	208	2	set	set	NOUN
ejpam-3657	208	3	s	s	NOUN
ejpam-3657	208	4	⊆	⊆	NUM
ejpam-3657	208	5	v	v	NOUN
ejpam-3657	208	6	(	(	PUNCT
ejpam-3657	208	7	kn	kn	PROPN
ejpam-3657	208	8	)	)	PUNCT
ejpam-3657	208	9	is	be	AUX
ejpam-3657	208	10	a	a	DET
ejpam-3657	208	11	distance	distance	NOUN
ejpam-3657	208	12	1	1	NUM
ejpam-3657	208	13	-	-	PUNCT
ejpam-3657	208	14	cost	cost	NOUN
ejpam-3657	208	15	effective	effective	ADJ
ejpam-3657	208	16	in	in	ADP
ejpam-3657	208	17	g+kn	g+kn	ADJ
ejpam-3657	208	18	if	if	SCONJ
ejpam-3657	208	19	and	and	CCONJ
ejpam-3657	208	20	only	only	ADV
ejpam-3657	208	21	if	if	SCONJ
ejpam-3657	208	22	|s|	|s|	NOUN
ejpam-3657	208	23	≤	≤	NUM
ejpam-3657	208	24	b	b	PROPN
ejpam-3657	208	25	|v	|v	X
ejpam-3657	208	26	(	(	PUNCT
ejpam-3657	208	27	g)|+n+1	g)|+n+1	NOUN
ejpam-3657	208	28	2	2	NUM
ejpam-3657	208	29	c.	c.	NOUN
ejpam-3657	208	30	references	reference	VERB
ejpam-3657	208	31	708	708	NUM
ejpam-3657	208	32	corollary	corollary	NOUN
ejpam-3657	208	33	7	7	NUM
ejpam-3657	208	34	.	.	PUNCT
ejpam-3657	209	1	let	let	VERB
ejpam-3657	209	2	g	g	PRON
ejpam-3657	209	3	be	be	AUX
ejpam-3657	209	4	a	a	DET
ejpam-3657	209	5	graph	graph	NOUN
ejpam-3657	209	6	,	,	PUNCT
ejpam-3657	209	7	n	n	CCONJ
ejpam-3657	209	8	≥	≥	NOUN
ejpam-3657	209	9	2	2	NUM
ejpam-3657	209	10	and	and	CCONJ
ejpam-3657	209	11	s	s	PRON
ejpam-3657	209	12	⊆	⊆	NUM
ejpam-3657	209	13	(	(	PUNCT
ejpam-3657	209	14	g	g	PROPN
ejpam-3657	209	15	+	+	PROPN
ejpam-3657	209	16	kn	kn	PROPN
ejpam-3657	209	17	)	)	PUNCT
ejpam-3657	209	18	such	such	ADJ
ejpam-3657	209	19	that	that	DET
ejpam-3657	209	20	v	v	NOUN
ejpam-3657	209	21	(	(	PUNCT
ejpam-3657	209	22	g	g	NOUN
ejpam-3657	209	23	)	)	PUNCT
ejpam-3657	209	24	∩	∩	PROPN
ejpam-3657	209	25	s	s	PART
ejpam-3657	209	26	6=	6=	NOUN
ejpam-3657	209	27	∅	∅	NOUN
ejpam-3657	209	28	and	and	CCONJ
ejpam-3657	209	29	v	v	NOUN
ejpam-3657	209	30	(	(	PUNCT
ejpam-3657	209	31	kn	kn	NOUN
ejpam-3657	209	32	)	)	PUNCT
ejpam-3657	209	33	∩	∩	PROPN
ejpam-3657	209	34	s	s	PART
ejpam-3657	209	35	6=	6=	NUM
ejpam-3657	209	36	∅.	∅.	NOUN
ejpam-3657	209	37	then	then	ADV
ejpam-3657	209	38	s	s	VERB
ejpam-3657	209	39	is	be	AUX
ejpam-3657	209	40	a	a	DET
ejpam-3657	209	41	distance	distance	NOUN
ejpam-3657	209	42	1	1	NUM
ejpam-3657	209	43	-	-	PUNCT
ejpam-3657	209	44	cost	cost	NOUN
ejpam-3657	209	45	effective	effective	ADJ
ejpam-3657	209	46	set	set	NOUN
ejpam-3657	209	47	in	in	ADP
ejpam-3657	209	48	g	g	PROPN
ejpam-3657	210	1	+	+	CCONJ
ejpam-3657	210	2	kn	kn	PROPN
ejpam-3657	210	3	if	if	SCONJ
ejpam-3657	210	4	and	and	CCONJ
ejpam-3657	210	5	only	only	ADV
ejpam-3657	210	6	if	if	SCONJ
ejpam-3657	210	7	the	the	DET
ejpam-3657	210	8	following	follow	VERB
ejpam-3657	210	9	hold	hold	NOUN
ejpam-3657	210	10	:	:	PUNCT
ejpam-3657	210	11	(	(	PUNCT
ejpam-3657	210	12	i	i	NOUN
ejpam-3657	210	13	)	)	PUNCT
ejpam-3657	210	14	|s|	|s|	VERB
ejpam-3657	210	15	≤	≤	NUM
ejpam-3657	210	16	b	b	PROPN
ejpam-3657	210	17	|v	|v	X
ejpam-3657	210	18	(	(	PUNCT
ejpam-3657	210	19	g)|+n+1	g)|+n+1	NOUN
ejpam-3657	210	20	2	2	NUM
ejpam-3657	210	21	c	c	NOUN
ejpam-3657	210	22	;	;	PUNCT
ejpam-3657	210	23	and	and	CCONJ
ejpam-3657	210	24	(	(	PUNCT
ejpam-3657	210	25	ii	ii	NOUN
ejpam-3657	210	26	)	)	PUNCT
ejpam-3657	210	27	v	v	NOUN
ejpam-3657	210	28	(	(	PUNCT
ejpam-3657	210	29	g	g	NOUN
ejpam-3657	210	30	)	)	PUNCT
ejpam-3657	210	31	∩	∩	NOUN
ejpam-3657	210	32	s	s	PART
ejpam-3657	210	33	is	be	AUX
ejpam-3657	210	34	(	(	PUNCT
ejpam-3657	210	35	n−	n−	NOUN
ejpam-3657	210	36	2p)-increment	2p)-increment	NUM
ejpam-3657	210	37	,	,	PUNCT
ejpam-3657	210	38	where	where	SCONJ
ejpam-3657	210	39	p	p	NOUN
ejpam-3657	210	40	=	=	X
ejpam-3657	210	41	|v	|v	X
ejpam-3657	210	42	(	(	PUNCT
ejpam-3657	210	43	kn	kn	NOUN
ejpam-3657	210	44	)	)	PUNCT
ejpam-3657	210	45	∩	∩	NOUN
ejpam-3657	210	46	s|	s|	NOUN
ejpam-3657	210	47	and	and	CCONJ
ejpam-3657	210	48	1	1	NUM
ejpam-3657	210	49	≤	≤	NOUN
ejpam-3657	210	50	p	p	PROPN
ejpam-3657	210	51	≤	≤	PROPN
ejpam-3657	210	52	n.	n.	NOUN
ejpam-3657	210	53	theorem	theorem	VERB
ejpam-3657	210	54	7	7	NUM
ejpam-3657	210	55	.	.	PUNCT
ejpam-3657	211	1	let	let	VERB
ejpam-3657	211	2	g	g	NOUN
ejpam-3657	212	1	and	and	CCONJ
ejpam-3657	212	2	h	h	NOUN
ejpam-3657	212	3	be	be	AUX
ejpam-3657	212	4	connected	connect	VERB
ejpam-3657	212	5	graphs	graph	NOUN
ejpam-3657	212	6	of	of	ADP
ejpam-3657	212	7	order	order	NOUN
ejpam-3657	212	8	m	m	VERB
ejpam-3657	212	9	and	and	CCONJ
ejpam-3657	212	10	n	n	CCONJ
ejpam-3657	212	11	,	,	PUNCT
ejpam-3657	212	12	respectively	respectively	ADV
ejpam-3657	212	13	.	.	PUNCT
ejpam-3657	213	1	then	then	ADV
ejpam-3657	213	2	α1	α1	PROPN
ejpam-3657	213	3	ce(g+h	ce(g+h	PROPN
ejpam-3657	213	4	)	)	PUNCT
ejpam-3657	213	5	=	=	SYM
ejpam-3657	214	1	max{ρn(g	max{ρn(g	X
ejpam-3657	214	2	)	)	PUNCT
ejpam-3657	214	3	,	,	PUNCT
ejpam-3657	214	4	ρm(h	ρm(h	NUM
ejpam-3657	214	5	)	)	PUNCT
ejpam-3657	214	6	,	,	PUNCT
ejpam-3657	214	7	ρn−2q(g	ρn−2q(g	NUM
ejpam-3657	214	8	)	)	PUNCT
ejpam-3657	215	1	+	+	CCONJ
ejpam-3657	215	2	ρm−2p(h	ρm−2p(h	NOUN
ejpam-3657	215	3	)	)	PUNCT
ejpam-3657	215	4	,	,	PUNCT
ejpam-3657	215	5	1	1	NUM
ejpam-3657	215	6	≤	≤	NOUN
ejpam-3657	215	7	p	p	X
ejpam-3657	215	8	≤	≤	NUM
ejpam-3657	215	9	m	m	NOUN
ejpam-3657	215	10	,	,	PUNCT
ejpam-3657	215	11	1	1	NUM
ejpam-3657	215	12	≤	≤	NUM
ejpam-3657	215	13	q	q	PROPN
ejpam-3657	215	14	≤	≤	NOUN
ejpam-3657	215	15	n	n	CCONJ
ejpam-3657	215	16	}	}	PUNCT
ejpam-3657	215	17	.	.	PUNCT
ejpam-3657	216	1	proof	proof	NOUN
ejpam-3657	216	2	:	:	PUNCT
ejpam-3657	216	3	let	let	VERB
ejpam-3657	216	4	s	s	PRON
ejpam-3657	216	5	be	be	AUX
ejpam-3657	216	6	an	an	DET
ejpam-3657	216	7	upper	upper	ADJ
ejpam-3657	216	8	distance	distance	NOUN
ejpam-3657	216	9	1	1	NUM
ejpam-3657	216	10	-	-	PUNCT
ejpam-3657	216	11	cost	cost	NOUN
ejpam-3657	216	12	effective	effective	ADJ
ejpam-3657	216	13	set	set	NOUN
ejpam-3657	216	14	in	in	ADP
ejpam-3657	216	15	g+h	g+h	PROPN
ejpam-3657	216	16	.	.	PUNCT
ejpam-3657	217	1	suppose	suppose	VERB
ejpam-3657	217	2	s	s	VERB
ejpam-3657	217	3	⊆	⊆	NUM
ejpam-3657	217	4	v	v	NOUN
ejpam-3657	217	5	(	(	PUNCT
ejpam-3657	217	6	g	g	NOUN
ejpam-3657	217	7	)	)	PUNCT
ejpam-3657	217	8	.	.	PUNCT
ejpam-3657	218	1	then	then	ADV
ejpam-3657	218	2	by	by	ADP
ejpam-3657	218	3	theorem	theorem	NOUN
ejpam-3657	218	4	6(i	6(i	NUM
ejpam-3657	218	5	)	)	PUNCT
ejpam-3657	218	6	,	,	PUNCT
ejpam-3657	218	7	|s|	|s|	PROPN
ejpam-3657	218	8	=	=	SYM
ejpam-3657	218	9	ρn(g	ρn(g	NUM
ejpam-3657	218	10	)	)	PUNCT
ejpam-3657	218	11	.	.	PUNCT
ejpam-3657	219	1	suppose	suppose	VERB
ejpam-3657	219	2	s	s	VERB
ejpam-3657	219	3	⊆	⊆	NUM
ejpam-3657	219	4	v	v	NOUN
ejpam-3657	219	5	(	(	PUNCT
ejpam-3657	219	6	h	h	NOUN
ejpam-3657	219	7	)	)	PUNCT
ejpam-3657	219	8	.	.	PUNCT
ejpam-3657	220	1	then	then	ADV
ejpam-3657	220	2	by	by	ADP
ejpam-3657	220	3	theorem	theorem	PROPN
ejpam-3657	220	4	6(ii	6(ii	PROPN
ejpam-3657	220	5	)	)	PUNCT
ejpam-3657	220	6	,	,	PUNCT
ejpam-3657	220	7	|s|	|s|	PROPN
ejpam-3657	220	8	=	=	SYM
ejpam-3657	220	9	ρm(h	ρm(h	NUM
ejpam-3657	220	10	)	)	PUNCT
ejpam-3657	220	11	.	.	PUNCT
ejpam-3657	221	1	suppose	suppose	VERB
ejpam-3657	221	2	v	v	X
ejpam-3657	221	3	(	(	PUNCT
ejpam-3657	221	4	g	g	NOUN
ejpam-3657	221	5	)	)	PUNCT
ejpam-3657	221	6	∩	∩	PROPN
ejpam-3657	221	7	s	s	PART
ejpam-3657	221	8	6=	6=	NOUN
ejpam-3657	221	9	∅	∅	NOUN
ejpam-3657	221	10	and	and	CCONJ
ejpam-3657	221	11	v	v	NOUN
ejpam-3657	221	12	(	(	PUNCT
ejpam-3657	221	13	h	h	NOUN
ejpam-3657	221	14	)	)	PUNCT
ejpam-3657	221	15	∩	∩	X
ejpam-3657	221	16	s	s	PART
ejpam-3657	221	17	6=	6=	NUM
ejpam-3657	221	18	∅.	∅.	NOUN
ejpam-3657	221	19	then	then	ADV
ejpam-3657	221	20	by	by	ADP
ejpam-3657	221	21	theorem	theorem	ADJ
ejpam-3657	221	22	6(iii	6(iii	NOUN
ejpam-3657	221	23	)	)	PUNCT
ejpam-3657	221	24	,	,	PUNCT
ejpam-3657	221	25	|s|	|s|	PROPN
ejpam-3657	221	26	=	=	PUNCT
ejpam-3657	221	27	ρn−2q(g	ρn−2q(g	NOUN
ejpam-3657	221	28	)	)	PUNCT
ejpam-3657	221	29	+	+	CCONJ
ejpam-3657	221	30	ρm−2p(h	ρm−2p(h	NOUN
ejpam-3657	221	31	)	)	PUNCT
ejpam-3657	221	32	.	.	PUNCT
ejpam-3657	222	1	therefore	therefore	ADV
ejpam-3657	222	2	,	,	PUNCT
ejpam-3657	222	3	α1	α1	PROPN
ejpam-3657	222	4	ce(g+h	ce(g+h	PROPN
ejpam-3657	222	5	)	)	PUNCT
ejpam-3657	222	6	=	=	SYM
ejpam-3657	222	7	max{ρn(g	max{ρn(g	X
ejpam-3657	222	8	)	)	PUNCT
ejpam-3657	222	9	,	,	PUNCT
ejpam-3657	222	10	ρm(h	ρm(h	NUM
ejpam-3657	222	11	)	)	PUNCT
ejpam-3657	222	12	,	,	PUNCT
ejpam-3657	222	13	ρn−2q(g	ρn−2q(g	NUM
ejpam-3657	222	14	)	)	PUNCT
ejpam-3657	222	15	+	+	CCONJ
ejpam-3657	222	16	ρm−2p(h	ρm−2p(h	NOUN
ejpam-3657	222	17	)	)	PUNCT
ejpam-3657	222	18	,	,	PUNCT
ejpam-3657	222	19	1	1	NUM
ejpam-3657	222	20	≤	≤	NOUN
ejpam-3657	222	21	p	p	X
ejpam-3657	222	22	≤	≤	NUM
ejpam-3657	222	23	m	m	NOUN
ejpam-3657	222	24	,	,	PUNCT
ejpam-3657	222	25	1	1	NUM
ejpam-3657	222	26	≤	≤	NUM
ejpam-3657	222	27	q	q	PROPN
ejpam-3657	222	28	≤	≤	NOUN
ejpam-3657	222	29	n	n	CCONJ
ejpam-3657	222	30	}	}	PUNCT
ejpam-3657	222	31	.	.	PUNCT
ejpam-3657	223	1	corollary	corollary	ADJ
ejpam-3657	223	2	8	8	NUM
ejpam-3657	223	3	.	.	PUNCT
ejpam-3657	224	1	let	let	VERB
ejpam-3657	224	2	g	g	PRON
ejpam-3657	224	3	be	be	AUX
ejpam-3657	224	4	a	a	DET
ejpam-3657	224	5	graph	graph	NOUN
ejpam-3657	224	6	and	and	CCONJ
ejpam-3657	224	7	n	n	PRON
ejpam-3657	224	8	≥	≥	NOUN
ejpam-3657	224	9	2	2	NUM
ejpam-3657	224	10	.	.	PUNCT
ejpam-3657	225	1	then	then	ADV
ejpam-3657	225	2	α1	α1	PROPN
ejpam-3657	225	3	ce(g+kn	ce(g+kn	PROPN
ejpam-3657	225	4	)	)	PUNCT
ejpam-3657	226	1	=	=	VERB
ejpam-3657	226	2	max{b	max{b	PROPN
ejpam-3657	226	3	|v	|v	PROPN
ejpam-3657	226	4	(	(	PUNCT
ejpam-3657	226	5	g)|+n+1	g)|+n+1	NOUN
ejpam-3657	226	6	2	2	NUM
ejpam-3657	226	7	c	c	NOUN
ejpam-3657	226	8	,	,	PUNCT
ejpam-3657	226	9	ρn(g	ρn(g	NUM
ejpam-3657	226	10	)	)	PUNCT
ejpam-3657	226	11	}	}	PUNCT
ejpam-3657	226	12	.	.	PUNCT
ejpam-3657	227	1	acknowledgements	acknowledgement	NOUN
ejpam-3657	227	2	this	this	DET
ejpam-3657	227	3	research	research	NOUN
ejpam-3657	227	4	is	be	AUX
ejpam-3657	227	5	funded	fund	VERB
ejpam-3657	227	6	by	by	ADP
ejpam-3657	227	7	the	the	DET
ejpam-3657	227	8	commission	commission	NOUN
ejpam-3657	227	9	of	of	ADP
ejpam-3657	227	10	higher	high	ADJ
ejpam-3657	227	11	education	education	NOUN
ejpam-3657	227	12	(	(	PUNCT
ejpam-3657	227	13	ched	che	VERB
ejpam-3657	227	14	)	)	PUNCT
ejpam-3657	227	15	and	and	CCONJ
ejpam-3657	227	16	mindanao	mindanao	PROPN
ejpam-3657	227	17	state	state	PROPN
ejpam-3657	227	18	university	university	PROPN
ejpam-3657	227	19	-	-	PUNCT
ejpam-3657	227	20	iligan	iligan	PROPN
ejpam-3657	227	21	institute	institute	PROPN
ejpam-3657	227	22	of	of	ADP
ejpam-3657	227	23	technology	technology	PROPN
ejpam-3657	227	24	.	.	PUNCT
ejpam-3657	228	1	references	reference	NOUN
ejpam-3657	228	2	[	[	X
ejpam-3657	228	3	1	1	NUM
ejpam-3657	228	4	]	]	X
ejpam-3657	228	5	f.	f.	PROPN
ejpam-3657	228	6	buckley	buckley	PROPN
ejpam-3657	228	7	and	and	CCONJ
ejpam-3657	228	8	f.	f.	PROPN
ejpam-3657	228	9	harary	harary	PROPN
ejpam-3657	228	10	.	.	PUNCT
ejpam-3657	229	1	distance	distance	NOUN
ejpam-3657	229	2	in	in	ADP
ejpam-3657	229	3	graphs	graph	NOUN
ejpam-3657	229	4	.	.	PUNCT
ejpam-3657	230	1	addison	addison	PROPN
ejpam-3657	230	2	-	-	PUNCT
ejpam-3657	230	3	wesley	wesley	PROPN
ejpam-3657	230	4	,	,	PUNCT
ejpam-3657	230	5	redwood	redwood	NOUN
ejpam-3657	230	6	city	city	NOUN
ejpam-3657	230	7	,	,	PUNCT
ejpam-3657	230	8	ca	ca	NOUN
ejpam-3657	230	9	,	,	PUNCT
ejpam-3657	230	10	1990	1990	NUM
ejpam-3657	230	11	.	.	PUNCT
ejpam-3657	231	1	[	[	X
ejpam-3657	231	2	2	2	X
ejpam-3657	231	3	]	]	X
ejpam-3657	231	4	t.w	t.w	PROPN
ejpam-3657	231	5	.	.	PROPN
ejpam-3657	231	6	haynes	haynes	PROPN
ejpam-3657	231	7	,	,	PUNCT
ejpam-3657	231	8	m.	m.	NOUN
ejpam-3657	231	9	chellali	chellali	PROPN
ejpam-3657	231	10	,	,	PUNCT
ejpam-3657	231	11	and	and	CCONJ
ejpam-3657	231	12	s.t	s.t	PROPN
ejpam-3657	231	13	.	.	PROPN
ejpam-3657	231	14	hedetniem	hedetniem	PROPN
ejpam-3657	231	15	.	.	PUNCT
ejpam-3657	232	1	client	client	NOUN
ejpam-3657	232	2	-	-	PUNCT
ejpam-3657	232	3	server	server	NOUN
ejpam-3657	232	4	and	and	CCONJ
ejpam-3657	232	5	cost	cost	VERB
ejpam-3657	232	6	effective	effective	ADJ
ejpam-3657	232	7	sets	set	NOUN
ejpam-3657	232	8	in	in	ADP
ejpam-3657	232	9	graphs	graph	NOUN
ejpam-3657	232	10	.	.	PUNCT
ejpam-3657	233	1	akce	akce	PROPN
ejpam-3657	233	2	international	international	PROPN
ejpam-3657	233	3	journal	journal	NOUN
ejpam-3657	233	4	of	of	ADP
ejpam-3657	233	5	graphs	graph	NOUN
ejpam-3657	233	6	and	and	CCONJ
ejpam-3657	233	7	combinatorics	combinatoric	NOUN
ejpam-3657	233	8	,	,	PUNCT
ejpam-3657	233	9	15:211–218	15:211–218	NUM
ejpam-3657	233	10	,	,	PUNCT
ejpam-3657	233	11	2018	2018	NUM
ejpam-3657	233	12	.	.	PUNCT
ejpam-3657	234	1	[	[	X
ejpam-3657	234	2	3	3	X
ejpam-3657	234	3	]	]	X
ejpam-3657	234	4	t.w	t.w	PROPN
ejpam-3657	234	5	.	.	PROPN
ejpam-3657	234	6	haynes	haynes	PROPN
ejpam-3657	234	7	,	,	PUNCT
ejpam-3657	234	8	i.	i.	PROPN
ejpam-3657	234	9	vasylieva	vasylieva	PROPN
ejpam-3657	234	10	,	,	PUNCT
ejpam-3657	234	11	and	and	CCONJ
ejpam-3657	234	12	s.t	s.t	PROPN
ejpam-3657	234	13	.	.	PROPN
ejpam-3657	234	14	hedetniemi	hedetniemi	PROPN
ejpam-3657	234	15	.	.	PUNCT
ejpam-3657	235	1	very	very	ADV
ejpam-3657	235	2	cost	cost	VERB
ejpam-3657	235	3	effective	effective	ADJ
ejpam-3657	235	4	bipartitions	bipartition	NOUN
ejpam-3657	235	5	in	in	ADP
ejpam-3657	235	6	graphs	graph	NOUN
ejpam-3657	235	7	.	.	PUNCT
ejpam-3657	236	1	akce	akce	PROPN
ejpam-3657	236	2	international	international	PROPN
ejpam-3657	236	3	journal	journal	NOUN
ejpam-3657	236	4	of	of	ADP
ejpam-3657	236	5	graphs	graph	NOUN
ejpam-3657	236	6	and	and	CCONJ
ejpam-3657	236	7	combinatorics	combinatoric	NOUN
ejpam-3657	236	8	,	,	PUNCT
ejpam-3657	236	9	12:155–160	12:155–160	NUM
ejpam-3657	236	10	,	,	PUNCT
ejpam-3657	236	11	2015	2015	NUM
ejpam-3657	236	12	.	.	PUNCT
ejpam-3657	237	1	[	[	X
ejpam-3657	237	2	4	4	X
ejpam-3657	237	3	]	]	X
ejpam-3657	237	4	t.w	t.w	PROPN
ejpam-3657	237	5	.	.	PROPN
ejpam-3657	237	6	hayness	hayness	PROPN
ejpam-3657	237	7	,	,	PUNCT
ejpam-3657	237	8	m.	m.	NOUN
ejpam-3657	237	9	henning	henning	PROPN
ejpam-3657	237	10	,	,	PUNCT
ejpam-3657	237	11	and	and	CCONJ
ejpam-3657	237	12	s.t	s.t	PROPN
ejpam-3657	237	13	.	.	PROPN
ejpam-3657	237	14	hedetniemi	hedetniemi	PROPN
ejpam-3657	237	15	.	.	PUNCT
ejpam-3657	238	1	domination	domination	NOUN
ejpam-3657	238	2	in	in	ADP
ejpam-3657	238	3	graphs	graph	NOUN
ejpam-3657	238	4	applied	apply	VERB
ejpam-3657	238	5	to	to	ADP
ejpam-3657	238	6	electrical	electrical	ADJ
ejpam-3657	238	7	power	power	NOUN
ejpam-3657	238	8	networks	network	NOUN
ejpam-3657	238	9	.	.	PUNCT
ejpam-3657	239	1	j.	j.	PROPN
ejpam-3657	239	2	discrete	discrete	PROPN
ejpam-3657	239	3	math	math	PROPN
ejpam-3657	239	4	,	,	PUNCT
ejpam-3657	239	5	15(4	15(4	NUM
ejpam-3657	239	6	)	)	PUNCT
ejpam-3657	239	7	,	,	PUNCT
ejpam-3657	239	8	2000	2000	NUM
ejpam-3657	239	9	.	.	PUNCT
ejpam-3657	240	1	[	[	X
ejpam-3657	240	2	5	5	NUM
ejpam-3657	240	3	]	]	X
ejpam-3657	240	4	s.m	s.m	PROPN
ejpam-3657	240	5	.	.	PROPN
ejpam-3657	240	6	hedetniemi	hedetniemi	PROPN
ejpam-3657	240	7	,	,	PUNCT
ejpam-3657	240	8	t.w	t.w	PROPN
ejpam-3657	240	9	.	.	PROPN
ejpam-3657	240	10	haynes	haynes	PROPN
ejpam-3657	240	11	,	,	PUNCT
ejpam-3657	240	12	s.t	s.t	PROPN
ejpam-3657	240	13	.	.	PROPN
ejpam-3657	240	14	hedetniemi	hedetniemi	PROPN
ejpam-3657	240	15	,	,	PUNCT
ejpam-3657	240	16	t.l	t.l	PROPN
ejpam-3657	240	17	.	.	PROPN
ejpam-3657	240	18	mccoy	mccoy	PROPN
ejpam-3657	240	19	,	,	PUNCT
ejpam-3657	240	20	and	and	CCONJ
ejpam-3657	240	21	i.	i.	PROPN
ejpam-3657	240	22	vasylieva	vasylieva	PROPN
ejpam-3657	240	23	.	.	PUNCT
ejpam-3657	241	1	cost	cost	VERB
ejpam-3657	241	2	effective	effective	ADJ
ejpam-3657	241	3	domination	domination	NOUN
ejpam-3657	241	4	in	in	ADP
ejpam-3657	241	5	graphs	graph	NOUN
ejpam-3657	241	6	.	.	PUNCT
ejpam-3657	242	1	congr	congr	NOUN
ejpam-3657	242	2	.	.	PUNCT
ejpam-3657	243	1	numer	numer	PROPN
ejpam-3657	243	2	.	.	PROPN
ejpam-3657	243	3	,	,	PUNCT
ejpam-3657	243	4	211:197–209	211:197–209	NUM
ejpam-3657	243	5	,	,	PUNCT
ejpam-3657	243	6	2012	2012	NUM
ejpam-3657	243	7	.	.	PUNCT
ejpam-3657	244	1	references	reference	NOUN
ejpam-3657	244	2	709	709	NUM
ejpam-3657	245	1	[	[	X
ejpam-3657	245	2	6	6	NUM
ejpam-3657	245	3	]	]	X
ejpam-3657	245	4	f.	f.	PROPN
ejpam-3657	245	5	jamil	jamil	PROPN
ejpam-3657	245	6	and	and	CCONJ
ejpam-3657	245	7	h.	h.	PROPN
ejpam-3657	245	8	nuenay	nuenay	PROPN
ejpam-3657	245	9	-	-	PUNCT
ejpam-3657	245	10	maglanque	maglanque	ADJ
ejpam-3657	245	11	.	.	PUNCT
ejpam-3657	246	1	cost	cost	NOUN
ejpam-3657	246	2	effective	effective	ADJ
ejpam-3657	246	3	domination	domination	NOUN
ejpam-3657	246	4	in	in	ADP
ejpam-3657	246	5	the	the	DET
ejpam-3657	246	6	join	join	NOUN
ejpam-3657	246	7	,	,	PUNCT
ejpam-3657	246	8	corona	corona	NOUN
ejpam-3657	246	9	and	and	CCONJ
ejpam-3657	246	10	composition	composition	NOUN
ejpam-3657	246	11	of	of	ADP
ejpam-3657	246	12	graphs	graph	NOUN
ejpam-3657	246	13	.	.	PUNCT
ejpam-3657	247	1	european	european	ADJ
ejpam-3657	247	2	journal	journal	PROPN
ejpam-3657	247	3	of	of	ADP
ejpam-3657	247	4	pure	pure	ADJ
ejpam-3657	247	5	and	and	CCONJ
ejpam-3657	247	6	applied	applied	ADJ
ejpam-3657	247	7	mathematics	mathematic	NOUN
ejpam-3657	247	8	,	,	PUNCT
ejpam-3657	247	9	12(3):978–998	12(3):978–998	NUM
ejpam-3657	247	10	,	,	PUNCT
ejpam-3657	247	11	2019	2019	NUM
ejpam-3657	247	12	.	.	PUNCT
ejpam-3657	248	1	[	[	X
ejpam-3657	248	2	7	7	X
ejpam-3657	248	3	]	]	X
ejpam-3657	248	4	l.	l.	PROPN
ejpam-3657	248	5	lesniaks	lesniaks	PROPN
ejpam-3657	248	6	,	,	PUNCT
ejpam-3657	248	7	g.	g.	PROPN
ejpam-3657	248	8	chartrand	chartrand	PROPN
ejpam-3657	248	9	,	,	PUNCT
ejpam-3657	248	10	and	and	CCONJ
ejpam-3657	248	11	p.	p.	PROPN
ejpam-3657	248	12	zhang	zhang	PROPN
ejpam-3657	248	13	.	.	PUNCT
ejpam-3657	248	14	graphs	graph	NOUN
ejpam-3657	248	15	and	and	CCONJ
ejpam-3657	248	16	digraphs	digraphs	ADJ
ejpam-3657	248	17	(	(	PUNCT
ejpam-3657	248	18	6th	6th	ADJ
ejpam-3657	248	19	ed	ed	NOUN
ejpam-3657	248	20	)	)	PUNCT
ejpam-3657	248	21	.	.	PUNCT
ejpam-3657	249	1	taylor	taylor	PROPN
ejpam-3657	249	2	and	and	CCONJ
ejpam-3657	249	3	francis	francis	PROPN
ejpam-3657	249	4	group	group	PROPN
ejpam-3657	249	5	,	,	PUNCT
ejpam-3657	249	6	llc	llc	PROPN
ejpam-3657	249	7	crc	crc	PROPN
ejpam-3657	249	8	press	press	PROPN
ejpam-3657	249	9	,	,	PUNCT
ejpam-3657	249	10	2016	2016	NUM
ejpam-3657	249	11	.	.	PUNCT
ejpam-3657	250	1	[	[	X
ejpam-3657	250	2	8	8	NUM
ejpam-3657	250	3	]	]	X
ejpam-3657	250	4	e.c	e.c	PROPN
ejpam-3657	250	5	.	.	PROPN
ejpam-3657	250	6	milners	milner	NOUN
ejpam-3657	250	7	,	,	PUNCT
ejpam-3657	250	8	r.aharoni	r.aharoni	NOUN
ejpam-3657	250	9	,	,	PUNCT
ejpam-3657	250	10	and	and	CCONJ
ejpam-3657	250	11	k.	k.	PROPN
ejpam-3657	250	12	prikry	prikry	PROPN
ejpam-3657	250	13	.	.	PUNCT
ejpam-3657	251	1	unfriendly	unfriendly	ADJ
ejpam-3657	251	2	partitions	partition	NOUN
ejpam-3657	251	3	of	of	ADP
ejpam-3657	251	4	a	a	DET
ejpam-3657	251	5	graph	graph	NOUN
ejpam-3657	251	6	.	.	PUNCT
ejpam-3657	252	1	j.	j.	PROPN
ejpam-3657	252	2	combin	combin	PROPN
ejpam-3657	252	3	.	.	PUNCT
ejpam-3657	253	1	theory	theory	NOUN
ejpam-3657	253	2	,	,	PUNCT
ejpam-3657	253	3	ser	ser	PROPN
ejpam-3657	253	4	b	b	PROPN
ejpam-3657	254	1	50(1):1–10	50(1):1–10	NUM
ejpam-3657	254	2	,	,	PUNCT
ejpam-3657	254	3	1990	1990	NUM
ejpam-3657	254	4	.	.	PUNCT
ejpam-3657	255	1	[	[	X
ejpam-3657	255	2	9	9	NUM
ejpam-3657	255	3	]	]	X
ejpam-3657	255	4	j.	j.	PROPN
ejpam-3657	255	5	palco	palco	PROPN
ejpam-3657	255	6	,	,	PUNCT
ejpam-3657	255	7	r.	r.	PROPN
ejpam-3657	255	8	paluga	paluga	PROPN
ejpam-3657	255	9	,	,	PUNCT
ejpam-3657	255	10	and	and	CCONJ
ejpam-3657	255	11	g.	g.	PROPN
ejpam-3657	255	12	malacas	malacas	PROPN
ejpam-3657	255	13	.	.	PUNCT
ejpam-3657	256	1	on	on	ADP
ejpam-3657	256	2	k	k	ADJ
ejpam-3657	256	3	-	-	PUNCT
ejpam-3657	256	4	cost	cost	ADJ
ejpam-3657	256	5	effective	effective	ADJ
ejpam-3657	256	6	domination	domination	NOUN
ejpam-3657	256	7	number	number	NOUN
ejpam-3657	256	8	,	,	PUNCT
ejpam-3657	256	9	cost	cost	VERB
ejpam-3657	256	10	effective	effective	ADJ
ejpam-3657	256	11	domination	domination	NOUN
ejpam-3657	256	12	index	index	NOUN
ejpam-3657	256	13	,	,	PUNCT
ejpam-3657	256	14	and	and	CCONJ
ejpam-3657	256	15	maximal	maximal	ADJ
ejpam-3657	256	16	cost	cost	NOUN
ejpam-3657	256	17	effective	effective	ADJ
ejpam-3657	256	18	domination	domination	NOUN
ejpam-3657	256	19	number	number	NOUN
ejpam-3657	256	20	of	of	ADP
ejpam-3657	256	21	simple	simple	ADJ
ejpam-3657	256	22	graphs	graph	NOUN
ejpam-3657	256	23	.	.	PUNCT
ejpam-3657	257	1	far	far	ADV
ejpam-3657	257	2	east	east	PROPN
ejpam-3657	257	3	journal	journal	PROPN
ejpam-3657	257	4	of	of	ADP
ejpam-3657	257	5	mathematical	mathematical	ADJ
ejpam-3657	257	6	sciences	science	NOUN
ejpam-3657	257	7	,	,	PUNCT
ejpam-3657	257	8	114(1):55–68	114(1):55–68	NUM
ejpam-3657	257	9	,	,	PUNCT
ejpam-3657	257	10	2019	2019	NUM
ejpam-3657	257	11	.	.	PUNCT