id	sid	tid	token	lemma	pos
ejpam-4381	1	1	european	european	PROPN
ejpam-4381	1	2	journal	journal	PROPN
ejpam-4381	1	3	of	of	ADP
ejpam-4381	1	4	pure	pure	ADJ
ejpam-4381	1	5	and	and	CCONJ
ejpam-4381	1	6	applied	apply	VERB
ejpam-4381	1	7	mathematics	mathematic	NOUN
ejpam-4381	1	8	vol	vol	NOUN
ejpam-4381	1	9	.	.	PUNCT
ejpam-4381	2	1	16	16	NUM
ejpam-4381	2	2	,	,	PUNCT
ejpam-4381	2	3	no	no	INTJ
ejpam-4381	2	4	.	.	NOUN
ejpam-4381	2	5	1	1	NUM
ejpam-4381	2	6	,	,	PUNCT
ejpam-4381	2	7	2023	2023	NUM
ejpam-4381	2	8	,	,	PUNCT
ejpam-4381	2	9	261	261	NUM
ejpam-4381	2	10	-	-	SYM
ejpam-4381	2	11	270	270	NUM
ejpam-4381	2	12	issn	issn	PROPN
ejpam-4381	2	13	1307	1307	NUM
ejpam-4381	2	14	-	-	SYM
ejpam-4381	2	15	5543	5543	NUM
ejpam-4381	2	16	–	–	PUNCT
ejpam-4381	3	1	ejpam.com	ejpam.com	X
ejpam-4381	3	2	published	publish	VERB
ejpam-4381	3	3	by	by	ADP
ejpam-4381	3	4	new	new	PROPN
ejpam-4381	3	5	york	york	PROPN
ejpam-4381	3	6	business	business	PROPN
ejpam-4381	3	7	global	global	PROPN
ejpam-4381	3	8	distance	distance	NOUN
ejpam-4381	3	9	k	k	ADJ
ejpam-4381	3	10	-	-	PUNCT
ejpam-4381	3	11	cost	cost	ADJ
ejpam-4381	3	12	effective	effective	ADJ
ejpam-4381	3	13	sets	set	NOUN
ejpam-4381	3	14	in	in	ADP
ejpam-4381	3	15	the	the	DET
ejpam-4381	3	16	corona	corona	NOUN
ejpam-4381	3	17	and	and	CCONJ
ejpam-4381	3	18	lexicographic	lexicographic	ADJ
ejpam-4381	3	19	product	product	NOUN
ejpam-4381	3	20	of	of	ADP
ejpam-4381	3	21	graphs	graph	NOUN
ejpam-4381	3	22	julius	julius	PROPN
ejpam-4381	3	23	g.	g.	PROPN
ejpam-4381	3	24	caadan1,∗	caadan1,∗	PROPN
ejpam-4381	3	25	,	,	PUNCT
ejpam-4381	3	26	rolando	rolando	PROPN
ejpam-4381	3	27	n.	n.	PROPN
ejpam-4381	3	28	paluga2	paluga2	PROPN
ejpam-4381	3	29	,	,	PUNCT
ejpam-4381	4	1	imelda	imelda	PROPN
ejpam-4381	4	2	s.	s.	PROPN
ejpam-4381	4	3	aniversario3	aniversario3	PROPN
ejpam-4381	4	4	1	1	NUM
ejpam-4381	4	5	surigao	surigao	NOUN
ejpam-4381	4	6	del	del	PROPN
ejpam-4381	4	7	norte	norte	PROPN
ejpam-4381	4	8	state	state	PROPN
ejpam-4381	4	9	university	university	PROPN
ejpam-4381	4	10	,	,	PUNCT
ejpam-4381	4	11	8400	8400	NUM
ejpam-4381	4	12	surigao	surigao	NOUN
ejpam-4381	4	13	city	city	NOUN
ejpam-4381	4	14	,	,	PUNCT
ejpam-4381	4	15	philippines	philippines	PROPN
ejpam-4381	4	16	2	2	NUM
ejpam-4381	4	17	department	department	NOUN
ejpam-4381	4	18	of	of	ADP
ejpam-4381	4	19	mathematics	mathematic	NOUN
ejpam-4381	4	20	,	,	PUNCT
ejpam-4381	4	21	college	college	NOUN
ejpam-4381	4	22	of	of	ADP
ejpam-4381	4	23	mathematics	mathematic	NOUN
ejpam-4381	4	24	and	and	CCONJ
ejpam-4381	4	25	natural	natural	ADJ
ejpam-4381	4	26	sciences	science	NOUN
ejpam-4381	4	27	,	,	PUNCT
ejpam-4381	4	28	caraga	caraga	PROPN
ejpam-4381	4	29	state	state	PROPN
ejpam-4381	4	30	university	university	PROPN
ejpam-4381	4	31	,	,	PUNCT
ejpam-4381	4	32	8600	8600	NUM
ejpam-4381	4	33	,	,	PUNCT
ejpam-4381	4	34	ampayon	ampayon	NOUN
ejpam-4381	4	35	,	,	PUNCT
ejpam-4381	4	36	butuan	butuan	PROPN
ejpam-4381	4	37	city	city	PROPN
ejpam-4381	4	38	city	city	PROPN
ejpam-4381	4	39	,	,	PUNCT
ejpam-4381	4	40	philippines	philippines	PROPN
ejpam-4381	4	41	3	3	NUM
ejpam-4381	4	42	department	department	NOUN
ejpam-4381	4	43	of	of	ADP
ejpam-4381	4	44	mathematics	mathematic	NOUN
ejpam-4381	4	45	and	and	CCONJ
ejpam-4381	4	46	statistics	statistic	NOUN
ejpam-4381	4	47	,	,	PUNCT
ejpam-4381	4	48	college	college	NOUN
ejpam-4381	4	49	of	of	ADP
ejpam-4381	4	50	science	science	NOUN
ejpam-4381	4	51	and	and	CCONJ
ejpam-4381	4	52	mathematics	mathematic	NOUN
ejpam-4381	4	53	,	,	PUNCT
ejpam-4381	4	54	mindanao	mindanao	PROPN
ejpam-4381	4	55	state	state	PROPN
ejpam-4381	4	56	university	university	PROPN
ejpam-4381	4	57	-	-	PUNCT
ejpam-4381	4	58	iligan	iligan	PROPN
ejpam-4381	4	59	institute	institute	PROPN
ejpam-4381	4	60	of	of	ADP
ejpam-4381	4	61	technology	technology	PROPN
ejpam-4381	4	62	,	,	PUNCT
ejpam-4381	4	63	9200	9200	NUM
ejpam-4381	4	64	iligan	iligan	ADJ
ejpam-4381	4	65	city	city	NOUN
ejpam-4381	4	66	,	,	PUNCT
ejpam-4381	4	67	philippines	philippine	NOUN
ejpam-4381	4	68	abstract	abstract	ADJ
ejpam-4381	4	69	.	.	PUNCT
ejpam-4381	5	1	let	let	VERB
ejpam-4381	5	2	g	g	PRON
ejpam-4381	5	3	be	be	AUX
ejpam-4381	5	4	a	a	DET
ejpam-4381	5	5	connected	connected	ADJ
ejpam-4381	5	6	graph	graph	NOUN
ejpam-4381	5	7	and	and	CCONJ
ejpam-4381	5	8	k	k	PROPN
ejpam-4381	5	9	≥	≥	NUM
ejpam-4381	5	10	1	1	NUM
ejpam-4381	5	11	be	be	AUX
ejpam-4381	5	12	an	an	DET
ejpam-4381	5	13	integer	integer	NOUN
ejpam-4381	5	14	.	.	PUNCT
ejpam-4381	6	1	the	the	DET
ejpam-4381	6	2	open	open	ADJ
ejpam-4381	6	3	k	k	ADJ
ejpam-4381	6	4	-	-	ADJ
ejpam-4381	6	5	neighborhood	neighborhood	NOUN
ejpam-4381	6	6	nk	nk	PROPN
ejpam-4381	6	7	g(v	g(v	PROPN
ejpam-4381	6	8	)	)	PUNCT
ejpam-4381	6	9	of	of	ADP
ejpam-4381	6	10	v	v	NUM
ejpam-4381	6	11	∈	∈	NOUN
ejpam-4381	6	12	v	v	NOUN
ejpam-4381	6	13	(	(	PUNCT
ejpam-4381	6	14	g	g	NOUN
ejpam-4381	6	15	)	)	PUNCT
ejpam-4381	6	16	is	be	AUX
ejpam-4381	6	17	the	the	DET
ejpam-4381	6	18	set	set	ADJ
ejpam-4381	6	19	nk	nk	PROPN
ejpam-4381	6	20	g(v	g(v	PROPN
ejpam-4381	6	21	)	)	PUNCT
ejpam-4381	7	1	=	=	PRON
ejpam-4381	7	2	{	{	PUNCT
ejpam-4381	7	3	u	u	NOUN
ejpam-4381	7	4	∈	∈	PROPN
ejpam-4381	7	5	v	v	NOUN
ejpam-4381	7	6	(	(	PUNCT
ejpam-4381	7	7	g	g	NOUN
ejpam-4381	7	8	)	)	PUNCT
ejpam-4381	7	9	\	\	NOUN
ejpam-4381	7	10	{	{	PUNCT
ejpam-4381	7	11	v	v	NOUN
ejpam-4381	7	12	}	}	PUNCT
ejpam-4381	7	13	:	:	PUNCT
ejpam-4381	7	14	dg(u	dg(u	X
ejpam-4381	7	15	,	,	PUNCT
ejpam-4381	7	16	v	v	NOUN
ejpam-4381	7	17	)	)	PUNCT
ejpam-4381	7	18	≤	≤	NOUN
ejpam-4381	7	19	k	k	X
ejpam-4381	7	20	}	}	PUNCT
ejpam-4381	7	21	.	.	PUNCT
ejpam-4381	8	1	a	a	DET
ejpam-4381	8	2	set	set	NOUN
ejpam-4381	8	3	s	s	NOUN
ejpam-4381	8	4	of	of	ADP
ejpam-4381	8	5	vertices	vertex	NOUN
ejpam-4381	8	6	of	of	ADP
ejpam-4381	8	7	g	g	PROPN
ejpam-4381	8	8	is	be	AUX
ejpam-4381	8	9	called	call	VERB
ejpam-4381	8	10	distance	distance	NOUN
ejpam-4381	8	11	k	k	ADJ
ejpam-4381	8	12	-	-	PUNCT
ejpam-4381	8	13	cost	cost	NOUN
ejpam-4381	8	14	effective	effective	NOUN
ejpam-4381	8	15	of	of	ADP
ejpam-4381	8	16	g	g	PROPN
ejpam-4381	8	17	if	if	SCONJ
ejpam-4381	8	18	for	for	ADP
ejpam-4381	8	19	every	every	DET
ejpam-4381	8	20	vertex	vertex	NOUN
ejpam-4381	8	21	u	u	NOUN
ejpam-4381	8	22	in	in	ADP
ejpam-4381	8	23	s	s	PROPN
ejpam-4381	8	24	,	,	PUNCT
ejpam-4381	8	25	|nk	|nk	PRON
ejpam-4381	8	26	g(u	g(u	PROPN
ejpam-4381	8	27	)	)	PUNCT
ejpam-4381	8	28	∩	∩	NOUN
ejpam-4381	8	29	(	(	PUNCT
ejpam-4381	8	30	v	v	NOUN
ejpam-4381	8	31	(	(	PUNCT
ejpam-4381	8	32	g	g	NOUN
ejpam-4381	8	33	)	)	PUNCT
ejpam-4381	8	34	\	\	PROPN
ejpam-4381	8	35	s)|	s)|	NOUN
ejpam-4381	8	36	−	−	PROPN
ejpam-4381	8	37	|nk	|nk	PROPN
ejpam-4381	8	38	g(u	g(u	PROPN
ejpam-4381	8	39	)	)	PUNCT
ejpam-4381	8	40	∩	∩	NOUN
ejpam-4381	8	41	s|	s|	VERB
ejpam-4381	8	42	≥	≥	NOUN
ejpam-4381	8	43	0	0	NUM
ejpam-4381	8	44	.	.	PUNCT
ejpam-4381	9	1	the	the	DET
ejpam-4381	9	2	maximum	maximum	ADJ
ejpam-4381	9	3	cardinality	cardinality	NOUN
ejpam-4381	9	4	of	of	ADP
ejpam-4381	9	5	a	a	DET
ejpam-4381	9	6	distance	distance	NOUN
ejpam-4381	9	7	k	k	ADJ
ejpam-4381	9	8	-	-	PUNCT
ejpam-4381	9	9	cost	cost	ADJ
ejpam-4381	9	10	effective	effective	ADJ
ejpam-4381	9	11	set	set	NOUN
ejpam-4381	9	12	of	of	ADP
ejpam-4381	9	13	g	g	PROPN
ejpam-4381	9	14	is	be	AUX
ejpam-4381	9	15	called	call	VERB
ejpam-4381	9	16	the	the	DET
ejpam-4381	9	17	upper	upper	ADJ
ejpam-4381	9	18	distance	distance	NOUN
ejpam-4381	9	19	k	k	ADJ
ejpam-4381	9	20	-	-	PUNCT
ejpam-4381	9	21	cost	cost	ADJ
ejpam-4381	9	22	effective	effective	ADJ
ejpam-4381	9	23	number	number	NOUN
ejpam-4381	9	24	of	of	ADP
ejpam-4381	9	25	g.	g.	PROPN
ejpam-4381	9	26	in	in	ADP
ejpam-4381	9	27	this	this	DET
ejpam-4381	9	28	paper	paper	NOUN
ejpam-4381	9	29	,	,	PUNCT
ejpam-4381	9	30	we	we	PRON
ejpam-4381	9	31	characterized	characterize	VERB
ejpam-4381	9	32	the	the	DET
ejpam-4381	9	33	distance	distance	NOUN
ejpam-4381	9	34	k	k	ADJ
ejpam-4381	9	35	-	-	PUNCT
ejpam-4381	9	36	cost	cost	ADJ
ejpam-4381	9	37	effective	effective	ADJ
ejpam-4381	9	38	sets	set	NOUN
ejpam-4381	9	39	in	in	ADP
ejpam-4381	9	40	the	the	DET
ejpam-4381	9	41	corona	corona	NOUN
ejpam-4381	9	42	and	and	CCONJ
ejpam-4381	9	43	lexicographic	lexicographic	ADJ
ejpam-4381	9	44	product	product	NOUN
ejpam-4381	9	45	of	of	ADP
ejpam-4381	9	46	two	two	NUM
ejpam-4381	9	47	graphs	graph	NOUN
ejpam-4381	9	48	.	.	PUNCT
ejpam-4381	10	1	consequently	consequently	ADV
ejpam-4381	10	2	,	,	PUNCT
ejpam-4381	10	3	the	the	DET
ejpam-4381	10	4	bounds	bound	NOUN
ejpam-4381	10	5	or	or	CCONJ
ejpam-4381	10	6	the	the	DET
ejpam-4381	10	7	exact	exact	ADJ
ejpam-4381	10	8	values	value	NOUN
ejpam-4381	10	9	of	of	ADP
ejpam-4381	10	10	the	the	DET
ejpam-4381	10	11	upper	upper	ADJ
ejpam-4381	10	12	distance	distance	NOUN
ejpam-4381	10	13	k	k	ADJ
ejpam-4381	10	14	-	-	PUNCT
ejpam-4381	10	15	cost	cost	ADJ
ejpam-4381	10	16	effective	effective	ADJ
ejpam-4381	10	17	numbers	number	NOUN
ejpam-4381	10	18	of	of	ADP
ejpam-4381	10	19	these	these	DET
ejpam-4381	10	20	graphs	graph	NOUN
ejpam-4381	10	21	are	be	AUX
ejpam-4381	10	22	obtained	obtain	VERB
ejpam-4381	10	23	.	.	PUNCT
ejpam-4381	11	1	2020	2020	NUM
ejpam-4381	11	2	mathematics	mathematic	NOUN
ejpam-4381	11	3	subject	subject	NOUN
ejpam-4381	11	4	classifications	classification	NOUN
ejpam-4381	11	5	:	:	PUNCT
ejpam-4381	11	6	05c76	05c76	NUM
ejpam-4381	11	7	,	,	PUNCT
ejpam-4381	11	8	05c12	05c12	NOUN
ejpam-4381	11	9	key	key	ADJ
ejpam-4381	11	10	words	word	NOUN
ejpam-4381	11	11	and	and	CCONJ
ejpam-4381	11	12	phrases	phrase	NOUN
ejpam-4381	11	13	:	:	PUNCT
ejpam-4381	11	14	distance	distance	NOUN
ejpam-4381	11	15	k	k	ADJ
ejpam-4381	11	16	-	-	PUNCT
ejpam-4381	11	17	cost	cost	ADJ
ejpam-4381	11	18	effective	effective	ADJ
ejpam-4381	11	19	set	set	NOUN
ejpam-4381	11	20	,	,	PUNCT
ejpam-4381	11	21	upper	upper	ADJ
ejpam-4381	11	22	distance	distance	NOUN
ejpam-4381	11	23	k	k	ADJ
ejpam-4381	11	24	-	-	PUNCT
ejpam-4381	11	25	cost	cost	ADJ
ejpam-4381	11	26	effective	effective	ADJ
ejpam-4381	11	27	number	number	NOUN
ejpam-4381	11	28	,	,	PUNCT
ejpam-4381	11	29	distance	distance	NOUN
ejpam-4381	11	30	k	k	ADV
ejpam-4381	11	31	-	-	PUNCT
ejpam-4381	11	32	domonating	domonate	VERB
ejpam-4381	11	33	set	set	NOUN
ejpam-4381	11	34	,	,	PUNCT
ejpam-4381	11	35	very	very	ADV
ejpam-4381	11	36	distance	distance	NOUN
ejpam-4381	11	37	k	k	ADJ
ejpam-4381	11	38	-	-	PUNCT
ejpam-4381	11	39	cost	cost	ADJ
ejpam-4381	11	40	effective	effective	ADJ
ejpam-4381	11	41	set	set	NOUN
ejpam-4381	11	42	,	,	PUNCT
ejpam-4381	11	43	corona	corona	PROPN
ejpam-4381	11	44	,	,	PUNCT
ejpam-4381	11	45	lexicographic	lexicographic	ADJ
ejpam-4381	11	46	product	product	NOUN
ejpam-4381	11	47	1	1	NUM
ejpam-4381	11	48	.	.	PUNCT
ejpam-4381	12	1	introduction	introduction	NOUN
ejpam-4381	12	2	let	let	VERB
ejpam-4381	12	3	g	g	PRON
ejpam-4381	12	4	be	be	AUX
ejpam-4381	12	5	a	a	DET
ejpam-4381	12	6	connected	connected	ADJ
ejpam-4381	12	7	simple	simple	ADJ
ejpam-4381	12	8	graph	graph	NOUN
ejpam-4381	12	9	with	with	ADP
ejpam-4381	12	10	vertex	vertex	NOUN
ejpam-4381	12	11	and	and	CCONJ
ejpam-4381	12	12	edge	edge	NOUN
ejpam-4381	12	13	sets	set	NOUN
ejpam-4381	12	14	v	v	ADP
ejpam-4381	12	15	(	(	PUNCT
ejpam-4381	12	16	g	g	NOUN
ejpam-4381	12	17	)	)	PUNCT
ejpam-4381	12	18	and	and	CCONJ
ejpam-4381	12	19	e(g	e(g	PROPN
ejpam-4381	12	20	)	)	PUNCT
ejpam-4381	12	21	,	,	PUNCT
ejpam-4381	12	22	respectively	respectively	ADV
ejpam-4381	12	23	.	.	PUNCT
ejpam-4381	13	1	the	the	DET
ejpam-4381	13	2	basic	basic	ADJ
ejpam-4381	13	3	concepts	concept	NOUN
ejpam-4381	13	4	of	of	ADP
ejpam-4381	13	5	graph	graph	NOUN
ejpam-4381	13	6	here	here	ADV
ejpam-4381	13	7	are	be	AUX
ejpam-4381	13	8	adapted	adapt	VERB
ejpam-4381	13	9	from	from	ADP
ejpam-4381	13	10	[	[	X
ejpam-4381	13	11	2	2	NUM
ejpam-4381	13	12	]	]	PUNCT
ejpam-4381	13	13	.	.	PUNCT
ejpam-4381	14	1	let	let	VERB
ejpam-4381	14	2	v	v	NUM
ejpam-4381	14	3	∈	∈	PROPN
ejpam-4381	14	4	v	v	NOUN
ejpam-4381	14	5	(	(	PUNCT
ejpam-4381	14	6	g	g	NOUN
ejpam-4381	14	7	)	)	PUNCT
ejpam-4381	14	8	.	.	PUNCT
ejpam-4381	15	1	the	the	DET
ejpam-4381	15	2	open	open	ADJ
ejpam-4381	15	3	neighborhood	neighborhood	NOUN
ejpam-4381	15	4	ng(v	ng(v	NOUN
ejpam-4381	15	5	)	)	PUNCT
ejpam-4381	15	6	of	of	ADP
ejpam-4381	15	7	v	v	NOUN
ejpam-4381	15	8	in	in	ADP
ejpam-4381	15	9	g	g	PROPN
ejpam-4381	15	10	is	be	AUX
ejpam-4381	15	11	the	the	DET
ejpam-4381	15	12	set	set	NOUN
ejpam-4381	15	13	ng(v	ng(v	PUNCT
ejpam-4381	15	14	)	)	PUNCT
ejpam-4381	15	15	=	=	SYM
ejpam-4381	16	1	{	{	PUNCT
ejpam-4381	16	2	u	u	NOUN
ejpam-4381	16	3	∈	∈	PROPN
ejpam-4381	16	4	v	v	NOUN
ejpam-4381	16	5	(	(	PUNCT
ejpam-4381	16	6	g	g	NOUN
ejpam-4381	16	7	)	)	PUNCT
ejpam-4381	16	8	:	:	PUNCT
ejpam-4381	16	9	uv	uv	PROPN
ejpam-4381	16	10	∈	∈	PROPN
ejpam-4381	16	11	e(g	e(g	PROPN
ejpam-4381	16	12	)	)	PUNCT
ejpam-4381	16	13	}	}	PUNCT
ejpam-4381	16	14	.	.	PUNCT
ejpam-4381	17	1	the	the	DET
ejpam-4381	17	2	degree	degree	NOUN
ejpam-4381	17	3	degg(v	degg(v	PROPN
ejpam-4381	17	4	)	)	PUNCT
ejpam-4381	17	5	of	of	ADP
ejpam-4381	17	6	a	a	DET
ejpam-4381	17	7	vertex	vertex	NOUN
ejpam-4381	17	8	v	v	ADP
ejpam-4381	17	9	∈	∈	NOUN
ejpam-4381	17	10	v	v	NOUN
ejpam-4381	17	11	(	(	PUNCT
ejpam-4381	17	12	g	g	NOUN
ejpam-4381	17	13	)	)	PUNCT
ejpam-4381	17	14	is	be	AUX
ejpam-4381	17	15	the	the	DET
ejpam-4381	17	16	cardinality	cardinality	NOUN
ejpam-4381	17	17	of	of	ADP
ejpam-4381	17	18	ng(v	ng(v	NOUN
ejpam-4381	17	19	)	)	PUNCT
ejpam-4381	17	20	.	.	PUNCT
ejpam-4381	18	1	the	the	DET
ejpam-4381	18	2	minimum	minimum	NOUN
ejpam-4381	18	3	degree	degree	NOUN
ejpam-4381	18	4	of	of	ADP
ejpam-4381	18	5	g	g	PROPN
ejpam-4381	18	6	is	be	AUX
ejpam-4381	18	7	δ(g	δ(g	ADV
ejpam-4381	18	8	)	)	PUNCT
ejpam-4381	18	9	=	=	SYM
ejpam-4381	18	10	min{degg(v	min{degg(v	PROPN
ejpam-4381	18	11	)	)	PUNCT
ejpam-4381	18	12	:	:	PUNCT
ejpam-4381	18	13	v	v	X
ejpam-4381	18	14	∈	∈	PROPN
ejpam-4381	18	15	v	v	NOUN
ejpam-4381	18	16	(	(	PUNCT
ejpam-4381	18	17	g	g	NOUN
ejpam-4381	18	18	)	)	PUNCT
ejpam-4381	18	19	}	}	PUNCT
ejpam-4381	18	20	and	and	CCONJ
ejpam-4381	18	21	the	the	DET
ejpam-4381	18	22	maximum	maximum	ADJ
ejpam-4381	18	23	degree	degree	NOUN
ejpam-4381	18	24	of	of	ADP
ejpam-4381	18	25	g	g	PROPN
ejpam-4381	18	26	is	be	AUX
ejpam-4381	18	27	∆(g	∆(g	NOUN
ejpam-4381	18	28	)	)	PUNCT
ejpam-4381	18	29	=	=	PUNCT
ejpam-4381	18	30	max{degg(v	max{degg(v	NOUN
ejpam-4381	18	31	)	)	PUNCT
ejpam-4381	18	32	:	:	PUNCT
ejpam-4381	18	33	v	v	X
ejpam-4381	18	34	∈	∈	PROPN
ejpam-4381	18	35	v	v	NOUN
ejpam-4381	18	36	(	(	PUNCT
ejpam-4381	18	37	g	g	NOUN
ejpam-4381	18	38	)	)	PUNCT
ejpam-4381	18	39	}	}	PUNCT
ejpam-4381	18	40	.	.	PUNCT
ejpam-4381	19	1	the	the	DET
ejpam-4381	19	2	distancce	distancce	NOUN
ejpam-4381	19	3	dg(u	dg(u	X
ejpam-4381	19	4	,	,	PUNCT
ejpam-4381	19	5	v	v	NOUN
ejpam-4381	19	6	)	)	PUNCT
ejpam-4381	19	7	between	between	ADP
ejpam-4381	19	8	vertices	vertex	NOUN
ejpam-4381	19	9	u	u	NOUN
ejpam-4381	19	10	and	and	CCONJ
ejpam-4381	19	11	v	v	NOUN
ejpam-4381	19	12	in	in	ADP
ejpam-4381	19	13	g	g	PROPN
ejpam-4381	19	14	is	be	AUX
ejpam-4381	19	15	the	the	DET
ejpam-4381	19	16	length	length	NOUN
ejpam-4381	19	17	of	of	ADP
ejpam-4381	19	18	the	the	DET
ejpam-4381	19	19	shortest	short	ADJ
ejpam-4381	19	20	path	path	NOUN
ejpam-4381	19	21	from	from	ADP
ejpam-4381	19	22	vertex	vertex	NOUN
ejpam-4381	19	23	u	u	NOUN
ejpam-4381	19	24	to	to	PART
ejpam-4381	19	25	vertex	vertex	VERB
ejpam-4381	19	26	v	v	NOUN
ejpam-4381	19	27	in	in	ADP
ejpam-4381	19	28	g.	g.	PROPN
ejpam-4381	19	29	the	the	DET
ejpam-4381	19	30	diameter	diameter	NOUN
ejpam-4381	19	31	diam(g	diam(g	PROPN
ejpam-4381	19	32	)	)	PUNCT
ejpam-4381	19	33	of	of	ADP
ejpam-4381	19	34	g	g	PROPN
ejpam-4381	19	35	is	be	AUX
ejpam-4381	19	36	the	the	DET
ejpam-4381	19	37	maximum	maximum	ADJ
ejpam-4381	19	38	distance	distance	NOUN
ejpam-4381	19	39	between	between	ADP
ejpam-4381	19	40	any	any	DET
ejpam-4381	19	41	two	two	NUM
ejpam-4381	19	42	vertices	vertex	NOUN
ejpam-4381	19	43	in	in	ADP
ejpam-4381	19	44	g.	g.	PROPN
ejpam-4381	19	45	∗corresponding	∗corresponde	VERB
ejpam-4381	19	46	author	author	NOUN
ejpam-4381	19	47	.	.	PUNCT
ejpam-4381	20	1	doi	doi	NOUN
ejpam-4381	20	2	:	:	PUNCT
ejpam-4381	20	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4381	https://doi.org/10.29020/nybg.ejpam.v16i1.4381	NOUN
ejpam-4381	20	4	email	email	NOUN
ejpam-4381	20	5	addresses	address	VERB
ejpam-4381	20	6	:	:	PUNCT
ejpam-4381	20	7	juliusgcaadan@gmail.com	juliusgcaadan@gmail.com	X
ejpam-4381	20	8	(	(	PUNCT
ejpam-4381	20	9	julius	julius	PROPN
ejpam-4381	20	10	g.	g.	PROPN
ejpam-4381	20	11	caadan	caadan	PROPN
ejpam-4381	20	12	)	)	PUNCT
ejpam-4381	20	13	,	,	PUNCT
ejpam-4381	20	14	rnpaluga@carsu.edu.ph	rnpaluga@carsu.edu.ph	NOUN
ejpam-4381	20	15	(	(	PUNCT
ejpam-4381	20	16	rolando	rolando	PROPN
ejpam-4381	20	17	n.	n.	PROPN
ejpam-4381	20	18	paluga	paluga	PROPN
ejpam-4381	20	19	)	)	PUNCT
ejpam-4381	20	20	,	,	PUNCT
ejpam-4381	20	21	imelda.aniversario@g.msuiit.edu.ph	imelda.aniversario@g.msuiit.edu.ph	PROPN
ejpam-4381	20	22	(	(	PUNCT
ejpam-4381	20	23	imelda	imelda	PROPN
ejpam-4381	20	24	s.	s.	PROPN
ejpam-4381	20	25	aniversario	aniversario	PROPN
ejpam-4381	20	26	)	)	PUNCT
ejpam-4381	20	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4381	21	1	261	261	NUM
ejpam-4381	22	1	©	©	PROPN
ejpam-4381	22	2	2023	2023	NUM
ejpam-4381	22	3	ejpam	ejpam	NOUN
ejpam-4381	22	4	all	all	DET
ejpam-4381	22	5	rights	right	NOUN
ejpam-4381	22	6	reserved	reserve	VERB
ejpam-4381	22	7	.	.	PUNCT
ejpam-4381	23	1	julius	julius	PROPN
ejpam-4381	23	2	g.	g.	PROPN
ejpam-4381	23	3	caadan	caadan	PROPN
ejpam-4381	23	4	,	,	PUNCT
ejpam-4381	23	5	rolando	rolando	PROPN
ejpam-4381	23	6	n.	n.	PROPN
ejpam-4381	23	7	paluga	paluga	PROPN
ejpam-4381	23	8	,	,	PUNCT
ejpam-4381	23	9	imelda	imelda	PROPN
ejpam-4381	23	10	s.	s.	PROPN
ejpam-4381	23	11	aniversario	aniversario	PROPN
ejpam-4381	23	12	/	/	SYM
ejpam-4381	23	13	eur	eur	PROPN
ejpam-4381	23	14	.	.	PUNCT
ejpam-4381	24	1	j.	j.	PROPN
ejpam-4381	24	2	pure	pure	PROPN
ejpam-4381	24	3	appl	appl	PROPN
ejpam-4381	24	4	.	.	PROPN
ejpam-4381	24	5	math	math	PROPN
ejpam-4381	24	6	,	,	PUNCT
ejpam-4381	24	7	16	16	NUM
ejpam-4381	24	8	(	(	PUNCT
ejpam-4381	24	9	1	1	NUM
ejpam-4381	24	10	)	)	PUNCT
ejpam-4381	24	11	(	(	PUNCT
ejpam-4381	24	12	2023	2023	NUM
ejpam-4381	24	13	)	)	PUNCT
ejpam-4381	24	14	,	,	PUNCT
ejpam-4381	24	15	261	261	NUM
ejpam-4381	24	16	-	-	SYM
ejpam-4381	24	17	270	270	NUM
ejpam-4381	24	18	262	262	NUM
ejpam-4381	24	19	let	let	VERB
ejpam-4381	24	20	k	k	PROPN
ejpam-4381	24	21	≥	≥	NUM
ejpam-4381	24	22	1	1	NUM
ejpam-4381	24	23	be	be	AUX
ejpam-4381	24	24	positive	positive	ADJ
ejpam-4381	24	25	integer	integer	NOUN
ejpam-4381	24	26	and	and	CCONJ
ejpam-4381	24	27	v	v	ADP
ejpam-4381	24	28	∈	∈	PROPN
ejpam-4381	24	29	v	v	NOUN
ejpam-4381	24	30	(	(	PUNCT
ejpam-4381	24	31	g	g	NOUN
ejpam-4381	24	32	)	)	PUNCT
ejpam-4381	24	33	.	.	PUNCT
ejpam-4381	25	1	the	the	DET
ejpam-4381	25	2	open	open	ADJ
ejpam-4381	25	3	k	k	ADJ
ejpam-4381	25	4	-	-	ADJ
ejpam-4381	25	5	neighborhood	neighborhood	NOUN
ejpam-4381	25	6	nk	nk	PROPN
ejpam-4381	25	7	g(v	g(v	PROPN
ejpam-4381	25	8	)	)	PUNCT
ejpam-4381	25	9	of	of	ADP
ejpam-4381	25	10	vertex	vertex	NOUN
ejpam-4381	25	11	v	v	NOUN
ejpam-4381	25	12	is	be	AUX
ejpam-4381	25	13	the	the	DET
ejpam-4381	25	14	set	set	NOUN
ejpam-4381	25	15	of	of	ADP
ejpam-4381	25	16	all	all	DET
ejpam-4381	25	17	vertices	vertex	NOUN
ejpam-4381	25	18	u	u	NOUN
ejpam-4381	25	19	of	of	ADP
ejpam-4381	25	20	g	g	NOUN
ejpam-4381	25	21	such	such	ADJ
ejpam-4381	25	22	that	that	SCONJ
ejpam-4381	25	23	0	0	NUM
ejpam-4381	25	24	<	<	X
ejpam-4381	25	25	dg(u	dg(u	X
ejpam-4381	25	26	,	,	PUNCT
ejpam-4381	25	27	v	v	NOUN
ejpam-4381	25	28	)	)	PUNCT
ejpam-4381	25	29	≤	≤	NOUN
ejpam-4381	25	30	k.	k.	NOUN
ejpam-4381	26	1	that	that	PRON
ejpam-4381	26	2	is	be	AUX
ejpam-4381	26	3	,	,	PUNCT
ejpam-4381	26	4	nk	nk	PROPN
ejpam-4381	26	5	g(v	g(v	PROPN
ejpam-4381	26	6	)	)	PUNCT
ejpam-4381	26	7	=	=	PRON
ejpam-4381	27	1	{	{	PUNCT
ejpam-4381	27	2	u	u	NOUN
ejpam-4381	27	3	∈	∈	PROPN
ejpam-4381	27	4	v	v	NOUN
ejpam-4381	27	5	(	(	PUNCT
ejpam-4381	27	6	g	g	NOUN
ejpam-4381	27	7	)	)	PUNCT
ejpam-4381	27	8	:	:	PUNCT
ejpam-4381	27	9	0	0	NUM
ejpam-4381	27	10	<	<	X
ejpam-4381	27	11	dg(u	dg(u	X
ejpam-4381	27	12	,	,	PUNCT
ejpam-4381	27	13	v	v	NOUN
ejpam-4381	27	14	)	)	PUNCT
ejpam-4381	27	15	≤	≤	NOUN
ejpam-4381	28	1	k	k	X
ejpam-4381	28	2	}	}	PUNCT
ejpam-4381	28	3	.	.	PUNCT
ejpam-4381	29	1	the	the	DET
ejpam-4381	29	2	distance	distance	NOUN
ejpam-4381	29	3	k	k	NOUN
ejpam-4381	29	4	-	-	PUNCT
ejpam-4381	29	5	degree	degree	NOUN
ejpam-4381	29	6	of	of	ADP
ejpam-4381	29	7	v	v	NOUN
ejpam-4381	29	8	in	in	ADP
ejpam-4381	29	9	g	g	NOUN
ejpam-4381	29	10	,	,	PUNCT
ejpam-4381	29	11	denoted	denote	VERB
ejpam-4381	29	12	by	by	ADP
ejpam-4381	29	13	degkg(v	degkg(v	PROPN
ejpam-4381	29	14	)	)	PUNCT
ejpam-4381	29	15	,	,	PUNCT
ejpam-4381	29	16	is	be	AUX
ejpam-4381	29	17	the	the	DET
ejpam-4381	29	18	cardinality	cardinality	NOUN
ejpam-4381	29	19	of	of	ADP
ejpam-4381	29	20	nk	nk	PROPN
ejpam-4381	29	21	g(v	g(v	PROPN
ejpam-4381	29	22	)	)	PUNCT
ejpam-4381	29	23	.	.	PUNCT
ejpam-4381	30	1	the	the	DET
ejpam-4381	30	2	minimum	minimum	ADJ
ejpam-4381	30	3	distance	distance	NOUN
ejpam-4381	30	4	k	k	NOUN
ejpam-4381	30	5	-	-	PUNCT
ejpam-4381	30	6	degree	degree	NOUN
ejpam-4381	30	7	of	of	ADP
ejpam-4381	30	8	g	g	NOUN
ejpam-4381	30	9	,	,	PUNCT
ejpam-4381	30	10	denoted	denote	VERB
ejpam-4381	30	11	by	by	ADP
ejpam-4381	30	12	δk(g	δk(g	NOUN
ejpam-4381	30	13	)	)	PUNCT
ejpam-4381	30	14	,	,	PUNCT
ejpam-4381	30	15	is	be	AUX
ejpam-4381	30	16	given	give	VERB
ejpam-4381	30	17	by	by	ADP
ejpam-4381	30	18	δk(g	δk(g	NOUN
ejpam-4381	30	19	)	)	PUNCT
ejpam-4381	31	1	=	=	SYM
ejpam-4381	31	2	min{degkg(v	min{degkg(v	X
ejpam-4381	31	3	)	)	PUNCT
ejpam-4381	31	4	:	:	PUNCT
ejpam-4381	31	5	v	v	X
ejpam-4381	31	6	∈	∈	PROPN
ejpam-4381	31	7	v	v	NOUN
ejpam-4381	31	8	(	(	PUNCT
ejpam-4381	31	9	g	g	NOUN
ejpam-4381	31	10	)	)	PUNCT
ejpam-4381	31	11	}	}	PUNCT
ejpam-4381	31	12	and	and	CCONJ
ejpam-4381	31	13	the	the	DET
ejpam-4381	31	14	maximum	maximum	ADJ
ejpam-4381	31	15	distance	distance	NOUN
ejpam-4381	31	16	k	k	NOUN
ejpam-4381	31	17	-	-	PUNCT
ejpam-4381	31	18	degree	degree	NOUN
ejpam-4381	31	19	of	of	ADP
ejpam-4381	31	20	g	g	NOUN
ejpam-4381	31	21	,	,	PUNCT
ejpam-4381	31	22	denoted	denote	VERB
ejpam-4381	31	23	by	by	ADP
ejpam-4381	31	24	∆k(g	∆k(g	NOUN
ejpam-4381	31	25	)	)	PUNCT
ejpam-4381	31	26	,	,	PUNCT
ejpam-4381	31	27	is	be	AUX
ejpam-4381	31	28	given	give	VERB
ejpam-4381	31	29	by	by	ADP
ejpam-4381	31	30	∆k(g	∆k(g	NOUN
ejpam-4381	31	31	)	)	PUNCT
ejpam-4381	31	32	=	=	SYM
ejpam-4381	31	33	max{degkg(v	max{degkg(v	PROPN
ejpam-4381	31	34	)	)	PUNCT
ejpam-4381	31	35	;	;	PUNCT
ejpam-4381	31	36	v	v	X
ejpam-4381	31	37	∈	∈	PROPN
ejpam-4381	31	38	v	v	NOUN
ejpam-4381	31	39	(	(	PUNCT
ejpam-4381	31	40	g	g	NOUN
ejpam-4381	31	41	)	)	PUNCT
ejpam-4381	31	42	}	}	PUNCT
ejpam-4381	31	43	.	.	PUNCT
ejpam-4381	32	1	note	note	VERB
ejpam-4381	32	2	that	that	SCONJ
ejpam-4381	32	3	deg1g(v	deg1g(v	NOUN
ejpam-4381	32	4	)	)	PUNCT
ejpam-4381	32	5	=	=	SYM
ejpam-4381	32	6	degg(v	degg(v	PROPN
ejpam-4381	32	7	)	)	PUNCT
ejpam-4381	32	8	,	,	PUNCT
ejpam-4381	32	9	δ1(g	δ1(g	PROPN
ejpam-4381	32	10	)	)	PUNCT
ejpam-4381	32	11	=	=	PUNCT
ejpam-4381	32	12	δ(g	δ(g	X
ejpam-4381	32	13	)	)	PUNCT
ejpam-4381	32	14	,	,	PUNCT
ejpam-4381	32	15	and	and	CCONJ
ejpam-4381	32	16	∆1(g	∆1(g	NUM
ejpam-4381	32	17	)	)	PUNCT
ejpam-4381	32	18	=	=	SYM
ejpam-4381	32	19	∆(g	∆(g	PROPN
ejpam-4381	32	20	)	)	PUNCT
ejpam-4381	32	21	.	.	PUNCT
ejpam-4381	33	1	let	let	VERB
ejpam-4381	33	2	g	g	PRON
ejpam-4381	33	3	be	be	AUX
ejpam-4381	33	4	a	a	DET
ejpam-4381	33	5	connected	connected	ADJ
ejpam-4381	33	6	graph	graph	NOUN
ejpam-4381	33	7	.	.	PUNCT
ejpam-4381	34	1	haynes	hayne	NOUN
ejpam-4381	34	2	et	et	PROPN
ejpam-4381	35	1	al	al	PROPN
ejpam-4381	35	2	.	.	PUNCT
ejpam-4381	36	1	in	in	ADP
ejpam-4381	36	2	[	[	X
ejpam-4381	36	3	7	7	X
ejpam-4381	36	4	]	]	PUNCT
ejpam-4381	36	5	defined	define	VERB
ejpam-4381	36	6	a	a	DET
ejpam-4381	36	7	vertex	vertex	NOUN
ejpam-4381	36	8	v	v	ADP
ejpam-4381	36	9	∈	∈	NOUN
ejpam-4381	36	10	s	s	PART
ejpam-4381	36	11	⊆	⊆	NUM
ejpam-4381	36	12	v	v	NOUN
ejpam-4381	36	13	(	(	PUNCT
ejpam-4381	36	14	g	g	NOUN
ejpam-4381	36	15	)	)	PUNCT
ejpam-4381	36	16	as	as	SCONJ
ejpam-4381	36	17	cost	cost	NOUN
ejpam-4381	36	18	effective	effective	ADJ
ejpam-4381	36	19	if	if	SCONJ
ejpam-4381	36	20	|ng(v	|ng(v	NOUN
ejpam-4381	36	21	)	)	PUNCT
ejpam-4381	36	22	∩	∩	NOUN
ejpam-4381	36	23	(	(	PUNCT
ejpam-4381	36	24	v	v	NOUN
ejpam-4381	36	25	(	(	PUNCT
ejpam-4381	36	26	g	g	NOUN
ejpam-4381	36	27	)	)	PUNCT
ejpam-4381	36	28	\	\	PROPN
ejpam-4381	36	29	s)|	s)|	NOUN
ejpam-4381	36	30	−	−	NOUN
ejpam-4381	36	31	|ng(v	|ng(v	PART
ejpam-4381	36	32	)	)	PUNCT
ejpam-4381	36	33	∩	∩	NOUN
ejpam-4381	36	34	s|	s|	VERB
ejpam-4381	36	35	≥	≥	NOUN
ejpam-4381	36	36	0	0	NUM
ejpam-4381	36	37	.	.	PUNCT
ejpam-4381	37	1	a	a	DET
ejpam-4381	37	2	set	set	NOUN
ejpam-4381	37	3	s	s	NOUN
ejpam-4381	37	4	⊆	⊆	NUM
ejpam-4381	37	5	v	v	NOUN
ejpam-4381	37	6	(	(	PUNCT
ejpam-4381	37	7	g	g	NOUN
ejpam-4381	37	8	)	)	PUNCT
ejpam-4381	37	9	is	be	AUX
ejpam-4381	37	10	called	call	VERB
ejpam-4381	37	11	cost	cost	NOUN
ejpam-4381	37	12	effective	effective	ADJ
ejpam-4381	37	13	if	if	SCONJ
ejpam-4381	37	14	every	every	DET
ejpam-4381	37	15	vertex	vertex	NOUN
ejpam-4381	37	16	v	v	ADP
ejpam-4381	37	17	∈	∈	NOUN
ejpam-4381	37	18	s	s	VERB
ejpam-4381	37	19	is	be	AUX
ejpam-4381	37	20	a	a	DET
ejpam-4381	37	21	cost	cost	NOUN
ejpam-4381	37	22	effective	effective	ADJ
ejpam-4381	37	23	.	.	PUNCT
ejpam-4381	38	1	paluga	paluga	PROPN
ejpam-4381	38	2	et	et	PROPN
ejpam-4381	38	3	al	al	PROPN
ejpam-4381	38	4	.	.	PUNCT
ejpam-4381	39	1	in	in	ADP
ejpam-4381	39	2	[	[	X
ejpam-4381	39	3	3	3	NUM
ejpam-4381	39	4	]	]	PUNCT
ejpam-4381	39	5	applied	apply	VERB
ejpam-4381	39	6	the	the	DET
ejpam-4381	39	7	distance	distance	NOUN
ejpam-4381	39	8	k	k	PROPN
ejpam-4381	39	9	version	version	NOUN
ejpam-4381	39	10	for	for	ADP
ejpam-4381	39	11	this	this	DET
ejpam-4381	39	12	concept	concept	NOUN
ejpam-4381	39	13	.	.	PUNCT
ejpam-4381	40	1	accordingly	accordingly	ADV
ejpam-4381	40	2	,	,	PUNCT
ejpam-4381	40	3	a	a	DET
ejpam-4381	40	4	nonempty	nonempty	ADJ
ejpam-4381	40	5	set	set	VERB
ejpam-4381	40	6	s	s	PROPN
ejpam-4381	40	7	⊆	⊆	NUM
ejpam-4381	40	8	v	v	NOUN
ejpam-4381	40	9	(	(	PUNCT
ejpam-4381	40	10	g	g	NOUN
ejpam-4381	40	11	)	)	PUNCT
ejpam-4381	40	12	is	be	AUX
ejpam-4381	40	13	a	a	DET
ejpam-4381	40	14	distance	distance	NOUN
ejpam-4381	40	15	k	k	ADJ
ejpam-4381	40	16	-	-	PUNCT
ejpam-4381	40	17	cost	cost	NOUN
ejpam-4381	40	18	effective	effective	ADJ
ejpam-4381	40	19	if	if	SCONJ
ejpam-4381	40	20	for	for	ADP
ejpam-4381	40	21	every	every	DET
ejpam-4381	40	22	v	v	NUM
ejpam-4381	40	23	∈	∈	NOUN
ejpam-4381	40	24	v	v	NOUN
ejpam-4381	40	25	(	(	PUNCT
ejpam-4381	40	26	g	g	NOUN
ejpam-4381	40	27	)	)	PUNCT
ejpam-4381	40	28	,	,	PUNCT
ejpam-4381	40	29	|nk	|nk	ADP
ejpam-4381	40	30	g(v	g(v	PROPN
ejpam-4381	40	31	)	)	PUNCT
ejpam-4381	40	32	∩	∩	NOUN
ejpam-4381	40	33	(	(	PUNCT
ejpam-4381	40	34	v	v	NOUN
ejpam-4381	40	35	(	(	PUNCT
ejpam-4381	40	36	g	g	NOUN
ejpam-4381	40	37	)	)	PUNCT
ejpam-4381	40	38	\	\	PROPN
ejpam-4381	40	39	s)|	s)|	NOUN
ejpam-4381	40	40	−	−	PROPN
ejpam-4381	40	41	|nk	|nk	ADP
ejpam-4381	40	42	g(v	g(v	PROPN
ejpam-4381	40	43	)	)	PUNCT
ejpam-4381	40	44	∩	∩	NOUN
ejpam-4381	40	45	s|	s|	VERB
ejpam-4381	40	46	≥	≥	NOUN
ejpam-4381	40	47	0	0	NUM
ejpam-4381	40	48	.	.	PUNCT
ejpam-4381	41	1	the	the	DET
ejpam-4381	41	2	maximum	maximum	ADJ
ejpam-4381	41	3	cardinality	cardinality	NOUN
ejpam-4381	41	4	of	of	ADP
ejpam-4381	41	5	a	a	DET
ejpam-4381	41	6	distance	distance	NOUN
ejpam-4381	41	7	k	k	ADJ
ejpam-4381	41	8	-	-	PUNCT
ejpam-4381	41	9	cost	cost	ADJ
ejpam-4381	41	10	effective	effective	ADJ
ejpam-4381	41	11	set	set	NOUN
ejpam-4381	41	12	in	in	ADP
ejpam-4381	41	13	g	g	PROPN
ejpam-4381	41	14	is	be	AUX
ejpam-4381	41	15	called	call	VERB
ejpam-4381	41	16	upper	upper	ADJ
ejpam-4381	41	17	distance	distance	NOUN
ejpam-4381	41	18	kcost	kcost	NOUN
ejpam-4381	41	19	effective	effective	ADJ
ejpam-4381	41	20	number	number	NOUN
ejpam-4381	41	21	of	of	ADP
ejpam-4381	41	22	g	g	NOUN
ejpam-4381	41	23	and	and	CCONJ
ejpam-4381	41	24	is	be	AUX
ejpam-4381	41	25	denoted	denote	VERB
ejpam-4381	41	26	by	by	ADP
ejpam-4381	41	27	αk	αk	NOUN
ejpam-4381	41	28	ce(g	ce(g	NOUN
ejpam-4381	41	29	)	)	PUNCT
ejpam-4381	41	30	.	.	PUNCT
ejpam-4381	42	1	a	a	DET
ejpam-4381	42	2	distance	distance	NOUN
ejpam-4381	42	3	k	k	ADJ
ejpam-4381	42	4	-	-	PUNCT
ejpam-4381	42	5	cost	cost	ADJ
ejpam-4381	42	6	effective	effective	ADJ
ejpam-4381	42	7	set	set	NOUN
ejpam-4381	42	8	in	in	ADP
ejpam-4381	42	9	g	g	NOUN
ejpam-4381	42	10	of	of	ADP
ejpam-4381	42	11	cardinality	cardinality	NOUN
ejpam-4381	42	12	αk	αk	PRON
ejpam-4381	42	13	ce(g	ce(g	NUM
ejpam-4381	42	14	)	)	PUNCT
ejpam-4381	42	15	is	be	AUX
ejpam-4381	42	16	called	call	VERB
ejpam-4381	42	17	an	an	DET
ejpam-4381	42	18	upper	upper	ADJ
ejpam-4381	42	19	distance	distance	NOUN
ejpam-4381	42	20	k	k	ADJ
ejpam-4381	42	21	-	-	PUNCT
ejpam-4381	42	22	cost	cost	ADJ
ejpam-4381	42	23	effective	effective	ADJ
ejpam-4381	42	24	set	set	NOUN
ejpam-4381	42	25	and	and	CCONJ
ejpam-4381	42	26	is	be	AUX
ejpam-4381	42	27	simply	simply	ADV
ejpam-4381	42	28	called	call	VERB
ejpam-4381	42	29	αk	αk	ADP
ejpam-4381	42	30	ceset	ceset	NOUN
ejpam-4381	42	31	in	in	ADP
ejpam-4381	42	32	g.	g.	PROPN
ejpam-4381	42	33	for	for	ADP
ejpam-4381	42	34	example	example	NOUN
ejpam-4381	42	35	,	,	PUNCT
ejpam-4381	42	36	for	for	ADP
ejpam-4381	42	37	any	any	DET
ejpam-4381	42	38	integer	integer	NOUN
ejpam-4381	42	39	n	n	PRON
ejpam-4381	42	40	≥	≥	NOUN
ejpam-4381	42	41	3	3	NUM
ejpam-4381	42	42	and	and	CCONJ
ejpam-4381	42	43	if	if	SCONJ
ejpam-4381	42	44	k	k	PROPN
ejpam-4381	42	45	=	=	SYM
ejpam-4381	42	46	2	2	NUM
ejpam-4381	42	47	,	,	PUNCT
ejpam-4381	42	48	s	s	VERB
ejpam-4381	42	49	is	be	AUX
ejpam-4381	42	50	a	a	DET
ejpam-4381	42	51	distance	distance	NOUN
ejpam-4381	42	52	2	2	NUM
ejpam-4381	42	53	-	-	PUNCT
ejpam-4381	42	54	cost	cost	NOUN
ejpam-4381	42	55	effective	effective	ADJ
ejpam-4381	42	56	set	set	NOUN
ejpam-4381	42	57	in	in	ADP
ejpam-4381	42	58	pn	pn	PROPN
ejpam-4381	43	1	if	if	SCONJ
ejpam-4381	43	2	|s|	|s|	NOUN
ejpam-4381	43	3	≤	≤	NUM
ejpam-4381	43	4	⌊2n3	⌊2n3	VERB
ejpam-4381	43	5	⌋.	⌋.	ADV
ejpam-4381	43	6	thus	thus	ADV
ejpam-4381	43	7	,	,	PUNCT
ejpam-4381	43	8	α2	α2	PROPN
ejpam-4381	43	9	ce(pn	ce(pn	PROPN
ejpam-4381	43	10	)	)	PUNCT
ejpam-4381	43	11	=	=	PUNCT
ejpam-4381	43	12	⌊2n3	⌊2n3	NOUN
ejpam-4381	43	13	⌋.	⌋.	NOUN
ejpam-4381	44	1	the	the	DET
ejpam-4381	44	2	concept	concept	NOUN
ejpam-4381	44	3	of	of	ADP
ejpam-4381	44	4	cost	cost	NOUN
ejpam-4381	44	5	effective	effective	ADJ
ejpam-4381	44	6	set	set	NOUN
ejpam-4381	44	7	in	in	ADP
ejpam-4381	44	8	graph	graph	NOUN
ejpam-4381	44	9	was	be	AUX
ejpam-4381	44	10	introduced	introduce	VERB
ejpam-4381	44	11	by	by	ADP
ejpam-4381	44	12	haynes	hayne	NOUN
ejpam-4381	44	13	et	et	PROPN
ejpam-4381	44	14	al	al	PROPN
ejpam-4381	44	15	.	.	PUNCT
ejpam-4381	45	1	in	in	ADP
ejpam-4381	45	2	[	[	X
ejpam-4381	45	3	7	7	NUM
ejpam-4381	45	4	]	]	PUNCT
ejpam-4381	45	5	.	.	PUNCT
ejpam-4381	46	1	in	in	ADP
ejpam-4381	46	2	2018	2018	NUM
ejpam-4381	46	3	,	,	PUNCT
ejpam-4381	46	4	chellali	chellali	PROPN
ejpam-4381	46	5	et	et	PROPN
ejpam-4381	46	6	al	al	PROPN
ejpam-4381	46	7	.	.	PUNCT
ejpam-4381	47	1	in	in	ADP
ejpam-4381	47	2	[	[	X
ejpam-4381	47	3	4	4	X
ejpam-4381	47	4	]	]	PUNCT
ejpam-4381	47	5	established	establish	VERB
ejpam-4381	47	6	a	a	DET
ejpam-4381	47	7	generalization	generalization	NOUN
ejpam-4381	47	8	of	of	ADP
ejpam-4381	47	9	this	this	DET
ejpam-4381	47	10	concept	concept	NOUN
ejpam-4381	47	11	.	.	PUNCT
ejpam-4381	48	1	however	however	ADV
ejpam-4381	48	2	,	,	PUNCT
ejpam-4381	48	3	paluga	paluga	PROPN
ejpam-4381	48	4	et	et	PROPN
ejpam-4381	48	5	al	al	PROPN
ejpam-4381	48	6	.	.	PUNCT
ejpam-4381	49	1	[	[	X
ejpam-4381	49	2	3	3	X
ejpam-4381	49	3	]	]	PUNCT
ejpam-4381	49	4	considered	consider	VERB
ejpam-4381	49	5	distance	distance	NOUN
ejpam-4381	49	6	concept	concept	NOUN
ejpam-4381	49	7	for	for	ADP
ejpam-4381	49	8	the	the	DET
ejpam-4381	49	9	cost	cost	NOUN
ejpam-4381	49	10	effective	effective	ADJ
ejpam-4381	49	11	set	set	NOUN
ejpam-4381	49	12	.	.	PUNCT
ejpam-4381	50	1	for	for	ADP
ejpam-4381	50	2	some	some	DET
ejpam-4381	50	3	investigations	investigation	NOUN
ejpam-4381	50	4	of	of	ADP
ejpam-4381	50	5	the	the	DET
ejpam-4381	50	6	cost	cost	NOUN
ejpam-4381	50	7	effective	effective	ADJ
ejpam-4381	50	8	concept	concept	NOUN
ejpam-4381	50	9	,	,	PUNCT
ejpam-4381	50	10	we	we	PRON
ejpam-4381	50	11	refer	refer	VERB
ejpam-4381	50	12	the	the	DET
ejpam-4381	50	13	readers	reader	NOUN
ejpam-4381	50	14	to	to	PART
ejpam-4381	50	15	see	see	VERB
ejpam-4381	50	16	[	[	X
ejpam-4381	50	17	6	6	NUM
ejpam-4381	50	18	,	,	PUNCT
ejpam-4381	50	19	9	9	NUM
ejpam-4381	50	20	,	,	PUNCT
ejpam-4381	50	21	11	11	NUM
ejpam-4381	50	22	]	]	PUNCT
ejpam-4381	50	23	.	.	PUNCT
ejpam-4381	51	1	for	for	ADP
ejpam-4381	51	2	some	some	DET
ejpam-4381	51	3	practical	practical	ADJ
ejpam-4381	51	4	application	application	NOUN
ejpam-4381	51	5	of	of	ADP
ejpam-4381	51	6	distance	distance	NOUN
ejpam-4381	51	7	concept	concept	NOUN
ejpam-4381	51	8	,	,	PUNCT
ejpam-4381	51	9	we	we	PRON
ejpam-4381	51	10	refer	refer	VERB
ejpam-4381	51	11	the	the	DET
ejpam-4381	51	12	readers	reader	NOUN
ejpam-4381	51	13	to	to	ADP
ejpam-4381	51	14	[	[	X
ejpam-4381	51	15	1	1	NUM
ejpam-4381	51	16	,	,	PUNCT
ejpam-4381	51	17	4	4	NUM
ejpam-4381	51	18	,	,	PUNCT
ejpam-4381	51	19	5	5	NUM
ejpam-4381	51	20	,	,	PUNCT
ejpam-4381	51	21	10	10	NUM
ejpam-4381	51	22	,	,	PUNCT
ejpam-4381	51	23	12	12	NUM
ejpam-4381	51	24	]	]	PUNCT
ejpam-4381	51	25	.	.	PUNCT
ejpam-4381	52	1	in	in	ADP
ejpam-4381	52	2	this	this	DET
ejpam-4381	52	3	paper	paper	NOUN
ejpam-4381	52	4	,	,	PUNCT
ejpam-4381	52	5	we	we	PRON
ejpam-4381	52	6	characterized	characterize	VERB
ejpam-4381	52	7	the	the	DET
ejpam-4381	52	8	distance	distance	NOUN
ejpam-4381	52	9	k	k	ADJ
ejpam-4381	52	10	-	-	PUNCT
ejpam-4381	52	11	cost	cost	ADJ
ejpam-4381	52	12	effective	effective	ADJ
ejpam-4381	52	13	sets	set	NOUN
ejpam-4381	52	14	in	in	ADP
ejpam-4381	52	15	the	the	DET
ejpam-4381	52	16	corona	corona	NOUN
ejpam-4381	52	17	and	and	CCONJ
ejpam-4381	52	18	lexicographic	lexicographic	ADJ
ejpam-4381	52	19	product	product	NOUN
ejpam-4381	52	20	of	of	ADP
ejpam-4381	52	21	two	two	NUM
ejpam-4381	52	22	graphs	graph	NOUN
ejpam-4381	52	23	.	.	PUNCT
ejpam-4381	53	1	as	as	ADP
ejpam-4381	53	2	direct	direct	ADJ
ejpam-4381	53	3	consequences	consequence	NOUN
ejpam-4381	53	4	,	,	PUNCT
ejpam-4381	53	5	we	we	PRON
ejpam-4381	53	6	determined	determine	VERB
ejpam-4381	53	7	the	the	DET
ejpam-4381	53	8	bounds	bound	NOUN
ejpam-4381	53	9	or	or	CCONJ
ejpam-4381	53	10	the	the	DET
ejpam-4381	53	11	exact	exact	ADJ
ejpam-4381	53	12	values	value	NOUN
ejpam-4381	53	13	of	of	ADP
ejpam-4381	53	14	the	the	DET
ejpam-4381	53	15	upper	upper	ADJ
ejpam-4381	53	16	distance	distance	NOUN
ejpam-4381	53	17	k	k	ADJ
ejpam-4381	53	18	-	-	PUNCT
ejpam-4381	53	19	cost	cost	ADJ
ejpam-4381	53	20	effective	effective	ADJ
ejpam-4381	53	21	numbers	number	NOUN
ejpam-4381	53	22	of	of	ADP
ejpam-4381	53	23	these	these	DET
ejpam-4381	53	24	graphs	graph	NOUN
ejpam-4381	53	25	.	.	PUNCT
ejpam-4381	54	1	2	2	X
ejpam-4381	54	2	.	.	X
ejpam-4381	54	3	results	result	VERB
ejpam-4381	54	4	2.1	2.1	NUM
ejpam-4381	54	5	.	.	PUNCT
ejpam-4381	54	6	preliminary	preliminary	ADJ
ejpam-4381	54	7	results	result	NOUN
ejpam-4381	54	8	in	in	ADP
ejpam-4381	54	9	this	this	DET
ejpam-4381	54	10	section	section	NOUN
ejpam-4381	54	11	,	,	PUNCT
ejpam-4381	54	12	we	we	PRON
ejpam-4381	54	13	present	present	VERB
ejpam-4381	54	14	a	a	DET
ejpam-4381	54	15	characterization	characterization	NOUN
ejpam-4381	54	16	of	of	ADP
ejpam-4381	54	17	a	a	DET
ejpam-4381	54	18	distance	distance	NOUN
ejpam-4381	54	19	k	k	ADJ
ejpam-4381	54	20	-	-	PUNCT
ejpam-4381	54	21	cost	cost	NOUN
ejpam-4381	54	22	effective	effective	ADJ
ejpam-4381	54	23	set	set	NOUN
ejpam-4381	54	24	in	in	ADP
ejpam-4381	54	25	g.	g.	PROPN
ejpam-4381	54	26	some	some	DET
ejpam-4381	54	27	examples	example	NOUN
ejpam-4381	54	28	of	of	ADP
ejpam-4381	54	29	the	the	DET
ejpam-4381	54	30	upper	upper	ADJ
ejpam-4381	54	31	distance	distance	NOUN
ejpam-4381	54	32	k	k	ADJ
ejpam-4381	54	33	-	-	PUNCT
ejpam-4381	54	34	cost	cost	ADJ
ejpam-4381	54	35	effective	effective	ADJ
ejpam-4381	54	36	number	number	NOUN
ejpam-4381	54	37	of	of	ADP
ejpam-4381	54	38	simple	simple	ADJ
ejpam-4381	54	39	graphs	graph	NOUN
ejpam-4381	54	40	are	be	AUX
ejpam-4381	54	41	given	give	VERB
ejpam-4381	54	42	.	.	PUNCT
ejpam-4381	55	1	moereover	moereover	PROPN
ejpam-4381	55	2	,	,	PUNCT
ejpam-4381	55	3	we	we	PRON
ejpam-4381	55	4	obtain	obtain	VERB
ejpam-4381	55	5	a	a	DET
ejpam-4381	55	6	relationship	relationship	NOUN
ejpam-4381	55	7	between	between	ADP
ejpam-4381	55	8	upper	upper	ADJ
ejpam-4381	55	9	distance	distance	NOUN
ejpam-4381	55	10	k	k	ADJ
ejpam-4381	55	11	-	-	PUNCT
ejpam-4381	55	12	cost	cost	NOUN
ejpam-4381	55	13	effective	effective	ADJ
ejpam-4381	55	14	set	set	NOUN
ejpam-4381	55	15	and	and	CCONJ
ejpam-4381	55	16	distance	distance	NOUN
ejpam-4381	55	17	k	k	ADV
ejpam-4381	55	18	-	-	PUNCT
ejpam-4381	55	19	dominating	dominating	NOUN
ejpam-4381	55	20	set	set	NOUN
ejpam-4381	55	21	in	in	ADP
ejpam-4381	55	22	g.	g.	PROPN
ejpam-4381	55	23	theorem	theorem	PROPN
ejpam-4381	55	24	1	1	X
ejpam-4381	55	25	.	.	PUNCT
ejpam-4381	56	1	let	let	VERB
ejpam-4381	56	2	g	g	PRON
ejpam-4381	56	3	be	be	AUX
ejpam-4381	56	4	a	a	DET
ejpam-4381	56	5	connected	connected	ADJ
ejpam-4381	56	6	simple	simple	ADJ
ejpam-4381	56	7	graph	graph	NOUN
ejpam-4381	56	8	and	and	CCONJ
ejpam-4381	56	9	k	k	PROPN
ejpam-4381	56	10	≥	≥	NUM
ejpam-4381	56	11	diam(g	diam(g	PROPN
ejpam-4381	56	12	)	)	PUNCT
ejpam-4381	56	13	.	.	PUNCT
ejpam-4381	57	1	then	then	ADV
ejpam-4381	57	2	s	s	VERB
ejpam-4381	57	3	is	be	AUX
ejpam-4381	57	4	a	a	DET
ejpam-4381	57	5	distance	distance	NOUN
ejpam-4381	57	6	k	k	ADJ
ejpam-4381	57	7	-	-	PUNCT
ejpam-4381	57	8	cost	cost	ADJ
ejpam-4381	57	9	effective	effective	ADJ
ejpam-4381	57	10	set	set	NOUN
ejpam-4381	57	11	in	in	ADP
ejpam-4381	57	12	g	g	PROPN
ejpam-4381	57	13	if	if	SCONJ
ejpam-4381	58	1	and	and	CCONJ
ejpam-4381	58	2	only	only	ADV
ejpam-4381	58	3	if	if	SCONJ
ejpam-4381	58	4	|s|	|s|	NOUN
ejpam-4381	58	5	≤	≤	X
ejpam-4381	58	6	⌊	⌊	AUX
ejpam-4381	58	7	|v	|v	PROPN
ejpam-4381	58	8	(	(	PUNCT
ejpam-4381	58	9	g)|+1	g)|+1	NOUN
ejpam-4381	58	10	2	2	NUM
ejpam-4381	58	11	⌋.	⌋.	NOUN
ejpam-4381	58	12	proof	proof	NOUN
ejpam-4381	58	13	:	:	PUNCT
ejpam-4381	58	14	let	let	VERB
ejpam-4381	58	15	g	g	PRON
ejpam-4381	58	16	be	be	AUX
ejpam-4381	58	17	a	a	DET
ejpam-4381	58	18	connected	connected	ADJ
ejpam-4381	58	19	simple	simple	ADJ
ejpam-4381	58	20	graph	graph	NOUN
ejpam-4381	58	21	and	and	CCONJ
ejpam-4381	58	22	k	k	PROPN
ejpam-4381	58	23	≥	≥	NUM
ejpam-4381	58	24	diam(g	diam(g	PROPN
ejpam-4381	58	25	)	)	PUNCT
ejpam-4381	58	26	.	.	PUNCT
ejpam-4381	59	1	suppose	suppose	VERB
ejpam-4381	59	2	s	s	PRON
ejpam-4381	59	3	is	be	AUX
ejpam-4381	59	4	a	a	DET
ejpam-4381	59	5	distance	distance	NOUN
ejpam-4381	59	6	k	k	ADJ
ejpam-4381	59	7	-	-	PUNCT
ejpam-4381	59	8	cost	cost	NOUN
ejpam-4381	59	9	effective	effective	ADJ
ejpam-4381	59	10	set	set	NOUN
ejpam-4381	59	11	in	in	ADP
ejpam-4381	59	12	g.	g.	PROPN
ejpam-4381	59	13	then	then	ADV
ejpam-4381	59	14	for	for	SCONJ
ejpam-4381	59	15	each	each	DET
ejpam-4381	59	16	u	u	PROPN
ejpam-4381	59	17	∈	∈	PROPN
ejpam-4381	59	18	s	s	PROPN
ejpam-4381	59	19	,	,	PUNCT
ejpam-4381	59	20	|nk	|nk	PROPN
ejpam-4381	59	21	g(u	g(u	PROPN
ejpam-4381	59	22	)	)	PUNCT
ejpam-4381	59	23	∩	∩	NOUN
ejpam-4381	59	24	(	(	PUNCT
ejpam-4381	59	25	v	v	NOUN
ejpam-4381	59	26	(	(	PUNCT
ejpam-4381	59	27	g	g	NOUN
ejpam-4381	59	28	)	)	PUNCT
ejpam-4381	59	29	\	\	PROPN
ejpam-4381	59	30	s)|	s)|	NOUN
ejpam-4381	59	31	−	−	PROPN
ejpam-4381	59	32	|nk	|nk	PROPN
ejpam-4381	59	33	g(u	g(u	PROPN
ejpam-4381	59	34	)	)	PUNCT
ejpam-4381	59	35	∩	∩	NOUN
ejpam-4381	59	36	s|	s|	NOUN
ejpam-4381	59	37	=	=	SYM
ejpam-4381	59	38	|	|	ADV
ejpam-4381	59	39	(	(	PUNCT
ejpam-4381	59	40	v	v	NOUN
ejpam-4381	59	41	(	(	PUNCT
ejpam-4381	59	42	g	g	NOUN
ejpam-4381	59	43	)	)	PUNCT
ejpam-4381	59	44	\	\	NOUN
ejpam-4381	59	45	{	{	PUNCT
ejpam-4381	59	46	u	u	NOUN
ejpam-4381	59	47	}	}	PUNCT
ejpam-4381	59	48	)	)	PUNCT
ejpam-4381	59	49	∩	∩	NOUN
ejpam-4381	59	50	(	(	PUNCT
ejpam-4381	59	51	v	v	NOUN
ejpam-4381	59	52	(	(	PUNCT
ejpam-4381	59	53	g	g	NOUN
ejpam-4381	59	54	)	)	PUNCT
ejpam-4381	59	55	\	\	PROPN
ejpam-4381	59	56	s)|	s)|	NOUN
ejpam-4381	60	1	−	−	PROPN
ejpam-4381	61	1	|	|	INTJ
ejpam-4381	61	2	(	(	PUNCT
ejpam-4381	61	3	v	v	NOUN
ejpam-4381	61	4	(	(	PUNCT
ejpam-4381	61	5	g	g	NOUN
ejpam-4381	61	6	)	)	PUNCT
ejpam-4381	61	7	\	\	NOUN
ejpam-4381	61	8	{	{	PUNCT
ejpam-4381	61	9	u	u	NOUN
ejpam-4381	61	10	}	}	PUNCT
ejpam-4381	61	11	)	)	PUNCT
ejpam-4381	61	12	∩	∩	NOUN
ejpam-4381	61	13	s|	s|	NOUN
ejpam-4381	61	14	=	=	SYM
ejpam-4381	61	15	|v	|v	X
ejpam-4381	61	16	(	(	PUNCT
ejpam-4381	61	17	g)|+	g)|+	NOUN
ejpam-4381	61	18	1−	1−	NUM
ejpam-4381	61	19	2|s|	2|s|	NUM
ejpam-4381	61	20	≥	≥	NOUN
ejpam-4381	61	21	0	0	NUM
ejpam-4381	61	22	.	.	PUNCT
ejpam-4381	62	1	julius	julius	PROPN
ejpam-4381	62	2	g.	g.	PROPN
ejpam-4381	62	3	caadan	caadan	PROPN
ejpam-4381	62	4	,	,	PUNCT
ejpam-4381	62	5	rolando	rolando	PROPN
ejpam-4381	62	6	n.	n.	PROPN
ejpam-4381	62	7	paluga	paluga	PROPN
ejpam-4381	62	8	,	,	PUNCT
ejpam-4381	62	9	imelda	imelda	PROPN
ejpam-4381	62	10	s.	s.	PROPN
ejpam-4381	62	11	aniversario	aniversario	PROPN
ejpam-4381	62	12	/	/	SYM
ejpam-4381	62	13	eur	eur	PROPN
ejpam-4381	62	14	.	.	PUNCT
ejpam-4381	63	1	j.	j.	PROPN
ejpam-4381	63	2	pure	pure	PROPN
ejpam-4381	63	3	appl	appl	PROPN
ejpam-4381	63	4	.	.	PROPN
ejpam-4381	63	5	math	math	PROPN
ejpam-4381	63	6	,	,	PUNCT
ejpam-4381	63	7	16	16	NUM
ejpam-4381	63	8	(	(	PUNCT
ejpam-4381	63	9	1	1	NUM
ejpam-4381	63	10	)	)	PUNCT
ejpam-4381	63	11	(	(	PUNCT
ejpam-4381	63	12	2023	2023	NUM
ejpam-4381	63	13	)	)	PUNCT
ejpam-4381	63	14	,	,	PUNCT
ejpam-4381	63	15	261	261	NUM
ejpam-4381	63	16	-	-	SYM
ejpam-4381	63	17	270	270	NUM
ejpam-4381	63	18	263	263	NUM
ejpam-4381	63	19	thus	thus	ADV
ejpam-4381	63	20	,	,	PUNCT
ejpam-4381	63	21	|s|	|s|	NOUN
ejpam-4381	63	22	≤	≤	PROPN
ejpam-4381	63	23	⌊	⌊	AUX
ejpam-4381	63	24	|v	|v	PROPN
ejpam-4381	63	25	(	(	PUNCT
ejpam-4381	63	26	g)|+1	g)|+1	NOUN
ejpam-4381	63	27	2	2	NUM
ejpam-4381	63	28	⌋.	⌋.	ADV
ejpam-4381	63	29	conversely	conversely	ADV
ejpam-4381	63	30	,	,	PUNCT
ejpam-4381	63	31	suppose	suppose	VERB
ejpam-4381	63	32	that	that	SCONJ
ejpam-4381	63	33	|s|	|s|	VERB
ejpam-4381	63	34	≤	≤	X
ejpam-4381	63	35	⌊	⌊	AUX
ejpam-4381	63	36	|v	|v	PROPN
ejpam-4381	63	37	(	(	PUNCT
ejpam-4381	63	38	g)|+1	g)|+1	PROPN
ejpam-4381	63	39	2	2	NUM
ejpam-4381	63	40	⌋.	⌋.	ADV
ejpam-4381	63	41	then	then	ADV
ejpam-4381	63	42	|s|	|s|	VERB
ejpam-4381	63	43	≤	≤	PROPN
ejpam-4381	63	44	|v	|v	X
ejpam-4381	63	45	(	(	PUNCT
ejpam-4381	63	46	g)|+1	g)|+1	NOUN
ejpam-4381	63	47	2	2	NUM
ejpam-4381	63	48	.	.	PUNCT
ejpam-4381	64	1	now	now	ADV
ejpam-4381	64	2	,	,	PUNCT
ejpam-4381	64	3	|nk	|nk	PROPN
ejpam-4381	64	4	g(u	g(u	PROPN
ejpam-4381	64	5	)	)	PUNCT
ejpam-4381	64	6	∩	∩	NOUN
ejpam-4381	64	7	(	(	PUNCT
ejpam-4381	64	8	v	v	NOUN
ejpam-4381	64	9	(	(	PUNCT
ejpam-4381	64	10	g	g	NOUN
ejpam-4381	64	11	)	)	PUNCT
ejpam-4381	64	12	\	\	PROPN
ejpam-4381	64	13	s)|	s)|	NOUN
ejpam-4381	64	14	−	−	PROPN
ejpam-4381	64	15	|nk	|nk	PROPN
ejpam-4381	64	16	g(u	g(u	PROPN
ejpam-4381	64	17	)	)	PUNCT
ejpam-4381	64	18	∩	∩	NOUN
ejpam-4381	64	19	s|	s|	NOUN
ejpam-4381	64	20	=	=	SYM
ejpam-4381	64	21	|v	|v	X
ejpam-4381	64	22	(	(	PUNCT
ejpam-4381	64	23	g)|+	g)|+	NOUN
ejpam-4381	64	24	1−	1−	NUM
ejpam-4381	64	25	2|s|	2|s|	NUM
ejpam-4381	64	26	≥	≥	NOUN
ejpam-4381	64	27	|v	|v	X
ejpam-4381	64	28	(	(	PUNCT
ejpam-4381	64	29	g)|+	g)|+	NOUN
ejpam-4381	64	30	1−	1−	NUM
ejpam-4381	64	31	[	[	PUNCT
ejpam-4381	64	32	|v	|v	X
ejpam-4381	64	33	(	(	PUNCT
ejpam-4381	64	34	g)|+	g)|+	NOUN
ejpam-4381	64	35	1	1	NUM
ejpam-4381	64	36	]	]	PUNCT
ejpam-4381	64	37	=	=	SYM
ejpam-4381	64	38	0	0	X
ejpam-4381	64	39	.	.	PUNCT
ejpam-4381	65	1	thus	thus	ADV
ejpam-4381	65	2	,	,	PUNCT
ejpam-4381	65	3	s	s	VERB
ejpam-4381	65	4	is	be	AUX
ejpam-4381	65	5	a	a	DET
ejpam-4381	65	6	distance	distance	NOUN
ejpam-4381	65	7	k	k	ADJ
ejpam-4381	65	8	-	-	PUNCT
ejpam-4381	65	9	cost	cost	NOUN
ejpam-4381	65	10	effective	effective	ADJ
ejpam-4381	65	11	set	set	NOUN
ejpam-4381	65	12	in	in	ADP
ejpam-4381	65	13	g.	g.	PROPN
ejpam-4381	65	14	corollary	corollary	PROPN
ejpam-4381	65	15	1	1	PROPN
ejpam-4381	65	16	.	.	PUNCT
ejpam-4381	66	1	let	let	VERB
ejpam-4381	66	2	g	g	PRON
ejpam-4381	66	3	be	be	AUX
ejpam-4381	66	4	a	a	DET
ejpam-4381	66	5	connected	connected	ADJ
ejpam-4381	66	6	graph	graph	NOUN
ejpam-4381	66	7	and	and	CCONJ
ejpam-4381	66	8	k	k	PROPN
ejpam-4381	66	9	≥	≥	NUM
ejpam-4381	66	10	diam(g	diam(g	PROPN
ejpam-4381	66	11	)	)	PUNCT
ejpam-4381	66	12	.	.	PUNCT
ejpam-4381	67	1	then	then	ADV
ejpam-4381	67	2	αk	αk	INTJ
ejpam-4381	67	3	ce(g	ce(g	PUNCT
ejpam-4381	67	4	)	)	PUNCT
ejpam-4381	68	1	=	=	SYM
ejpam-4381	68	2	⌊	⌊	VERB
ejpam-4381	68	3	|v	|v	X
ejpam-4381	68	4	(	(	PUNCT
ejpam-4381	68	5	g)|+1	g)|+1	NOUN
ejpam-4381	68	6	2	2	NUM
ejpam-4381	68	7	⌋.	⌋.	ADV
ejpam-4381	68	8	corollary	corollary	ADJ
ejpam-4381	68	9	2	2	X
ejpam-4381	68	10	.	.	PUNCT
ejpam-4381	69	1	let	let	VERB
ejpam-4381	69	2	g	g	PRON
ejpam-4381	69	3	be	be	AUX
ejpam-4381	69	4	a	a	DET
ejpam-4381	69	5	connected	connected	ADJ
ejpam-4381	69	6	graph	graph	NOUN
ejpam-4381	69	7	and	and	CCONJ
ejpam-4381	69	8	k	k	PROPN
ejpam-4381	69	9	≥	≥	NUM
ejpam-4381	69	10	2	2	NUM
ejpam-4381	69	11	be	be	AUX
ejpam-4381	69	12	an	an	DET
ejpam-4381	69	13	integer	integer	NOUN
ejpam-4381	69	14	.	.	PUNCT
ejpam-4381	70	1	then	then	ADV
ejpam-4381	70	2	i.	i.	PROPN
ejpam-4381	70	3	αk	αk	PROPN
ejpam-4381	70	4	ce(kn	ce(kn	PROPN
ejpam-4381	70	5	)	)	PUNCT
ejpam-4381	71	1	=	=	PUNCT
ejpam-4381	71	2	⌊n+1	⌊n+1	NOUN
ejpam-4381	71	3	2	2	NUM
ejpam-4381	71	4	⌋	⌋	NOUN
ejpam-4381	71	5	,	,	PUNCT
ejpam-4381	71	6	for	for	ADP
ejpam-4381	71	7	positive	positive	ADJ
ejpam-4381	71	8	integer	integer	NOUN
ejpam-4381	71	9	n.	n.	PROPN
ejpam-4381	71	10	ii	ii	PROPN
ejpam-4381	71	11	.	.	PUNCT
ejpam-4381	71	12	αk	αk	NOUN
ejpam-4381	71	13	ce(km.n	ce(km.n	NOUN
ejpam-4381	71	14	)	)	PUNCT
ejpam-4381	71	15	=	=	SYM
ejpam-4381	71	16	⌊m+n+1	⌊m+n+1	PROPN
ejpam-4381	71	17	2	2	NUM
ejpam-4381	71	18	⌋	⌋	NOUN
ejpam-4381	71	19	,	,	PUNCT
ejpam-4381	71	20	for	for	ADP
ejpam-4381	71	21	positive	positive	ADJ
ejpam-4381	71	22	integers	integer	NOUN
ejpam-4381	71	23	m	m	VERB
ejpam-4381	71	24	and	and	CCONJ
ejpam-4381	71	25	n.	n.	PROPN
ejpam-4381	71	26	iii	iii	PROPN
ejpam-4381	71	27	.	.	PROPN
ejpam-4381	71	28	αk	αk	ADP
ejpam-4381	71	29	ce(fn	ce(fn	PROPN
ejpam-4381	71	30	)	)	PUNCT
ejpam-4381	71	31	=	=	PRON
ejpam-4381	71	32	⌊n+2	⌊n+2	NUM
ejpam-4381	71	33	2	2	NUM
ejpam-4381	71	34	⌋	⌋	NOUN
ejpam-4381	71	35	,	,	PUNCT
ejpam-4381	71	36	for	for	ADP
ejpam-4381	71	37	integer	integer	NOUN
ejpam-4381	71	38	n	n	PRON
ejpam-4381	71	39	≥	≥	NOUN
ejpam-4381	71	40	3	3	NUM
ejpam-4381	71	41	.	.	NUM
ejpam-4381	71	42	iv	iv	NUM
ejpam-4381	71	43	.	.	PUNCT
ejpam-4381	71	44	αk	αk	NOUN
ejpam-4381	71	45	ce(wn	ce(wn	PROPN
ejpam-4381	71	46	)	)	PUNCT
ejpam-4381	71	47	=	=	PRON
ejpam-4381	71	48	⌊n+2	⌊n+2	NUM
ejpam-4381	71	49	2	2	NUM
ejpam-4381	71	50	⌋	⌋	NOUN
ejpam-4381	71	51	,	,	PUNCT
ejpam-4381	71	52	for	for	ADP
ejpam-4381	71	53	integer	integer	NOUN
ejpam-4381	71	54	n	n	PRON
ejpam-4381	71	55	≥	≥	NOUN
ejpam-4381	71	56	4	4	NUM
ejpam-4381	71	57	.	.	PUNCT
ejpam-4381	72	1	let	let	VERB
ejpam-4381	72	2	g	g	PRON
ejpam-4381	72	3	be	be	AUX
ejpam-4381	72	4	a	a	DET
ejpam-4381	72	5	connected	connected	ADJ
ejpam-4381	72	6	graph	graph	NOUN
ejpam-4381	72	7	and	and	CCONJ
ejpam-4381	72	8	k	k	PROPN
ejpam-4381	72	9	≥	≥	NUM
ejpam-4381	72	10	1	1	NUM
ejpam-4381	72	11	be	be	AUX
ejpam-4381	72	12	an	an	DET
ejpam-4381	72	13	integer	integer	NOUN
ejpam-4381	72	14	.	.	PUNCT
ejpam-4381	73	1	henning	henne	VERB
ejpam-4381	73	2	et	et	PROPN
ejpam-4381	73	3	al	al	PROPN
ejpam-4381	73	4	.	.	PUNCT
ejpam-4381	74	1	in	in	ADP
ejpam-4381	74	2	[	[	X
ejpam-4381	74	3	8	8	NUM
ejpam-4381	74	4	]	]	SYM
ejpam-4381	74	5	defined	define	VERB
ejpam-4381	74	6	distance	distance	NOUN
ejpam-4381	74	7	k	k	X
ejpam-4381	74	8	-	-	PUNCT
ejpam-4381	74	9	dominating	dominating	ADJ
ejpam-4381	74	10	set	set	NOUN
ejpam-4381	74	11	of	of	ADP
ejpam-4381	74	12	g.	g.	PROPN
ejpam-4381	74	13	accordingly	accordingly	ADV
ejpam-4381	74	14	,	,	PUNCT
ejpam-4381	74	15	a	a	DET
ejpam-4381	74	16	set	set	NOUN
ejpam-4381	74	17	s	s	NOUN
ejpam-4381	74	18	⊆	⊆	NUM
ejpam-4381	74	19	v	v	NOUN
ejpam-4381	74	20	(	(	PUNCT
ejpam-4381	74	21	g	g	NOUN
ejpam-4381	74	22	)	)	PUNCT
ejpam-4381	74	23	is	be	AUX
ejpam-4381	74	24	said	say	VERB
ejpam-4381	74	25	to	to	PART
ejpam-4381	74	26	be	be	AUX
ejpam-4381	74	27	a	a	DET
ejpam-4381	74	28	distance	distance	NOUN
ejpam-4381	74	29	kdominating	kdominating	NOUN
ejpam-4381	74	30	set	set	NOUN
ejpam-4381	74	31	of	of	ADP
ejpam-4381	74	32	g	g	PROPN
ejpam-4381	74	33	if	if	SCONJ
ejpam-4381	74	34	for	for	ADP
ejpam-4381	74	35	every	every	DET
ejpam-4381	74	36	v	v	NUM
ejpam-4381	74	37	∈	∈	NOUN
ejpam-4381	74	38	v	v	NOUN
ejpam-4381	74	39	(	(	PUNCT
ejpam-4381	74	40	g	g	NOUN
ejpam-4381	74	41	)	)	PUNCT
ejpam-4381	74	42	\s	\	NOUN
ejpam-4381	74	43	,	,	PUNCT
ejpam-4381	74	44	there	there	PRON
ejpam-4381	74	45	exists	exist	VERB
ejpam-4381	74	46	u	u	PROPN
ejpam-4381	74	47	∈	∈	PROPN
ejpam-4381	74	48	s	s	VERB
ejpam-4381	74	49	such	such	ADJ
ejpam-4381	75	1	that	that	PRON
ejpam-4381	75	2	dg(u	dg(u	ADJ
ejpam-4381	75	3	,	,	PUNCT
ejpam-4381	75	4	v	v	NOUN
ejpam-4381	75	5	)	)	PUNCT
ejpam-4381	75	6	≤	≤	PUNCT
ejpam-4381	75	7	k	k	X
ejpam-4381	75	8	.	.	PUNCT
ejpam-4381	75	9	theorem	theorem	NOUN
ejpam-4381	75	10	2	2	NUM
ejpam-4381	75	11	.	.	PUNCT
ejpam-4381	76	1	every	every	DET
ejpam-4381	76	2	upper	upper	ADJ
ejpam-4381	76	3	distance	distance	NOUN
ejpam-4381	76	4	k	k	ADJ
ejpam-4381	76	5	-	-	PUNCT
ejpam-4381	76	6	cost	cost	NOUN
ejpam-4381	76	7	effective	effective	ADJ
ejpam-4381	76	8	set	set	NOUN
ejpam-4381	76	9	in	in	ADP
ejpam-4381	76	10	a	a	DET
ejpam-4381	76	11	connected	connected	ADJ
ejpam-4381	76	12	graph	graph	NOUN
ejpam-4381	76	13	g	g	PROPN
ejpam-4381	76	14	is	be	AUX
ejpam-4381	76	15	a	a	DET
ejpam-4381	76	16	distance	distance	NOUN
ejpam-4381	76	17	k	k	ADV
ejpam-4381	76	18	-	-	PUNCT
ejpam-4381	76	19	dominating	dominating	NOUN
ejpam-4381	76	20	set	set	NOUN
ejpam-4381	76	21	in	in	ADP
ejpam-4381	76	22	g.	g.	PROPN
ejpam-4381	76	23	proof	proof	PROPN
ejpam-4381	76	24	:	:	PUNCT
ejpam-4381	76	25	suppose	suppose	VERB
ejpam-4381	76	26	s	s	NOUN
ejpam-4381	76	27	is	be	AUX
ejpam-4381	76	28	an	an	DET
ejpam-4381	76	29	upper	upper	ADJ
ejpam-4381	76	30	distance	distance	NOUN
ejpam-4381	76	31	k	k	ADJ
ejpam-4381	76	32	-	-	PUNCT
ejpam-4381	76	33	cost	cost	ADJ
ejpam-4381	76	34	effective	effective	ADJ
ejpam-4381	76	35	set	set	NOUN
ejpam-4381	76	36	in	in	ADP
ejpam-4381	76	37	g	g	PROPN
ejpam-4381	76	38	but	but	CCONJ
ejpam-4381	76	39	not	not	PART
ejpam-4381	76	40	a	a	DET
ejpam-4381	76	41	distance	distance	NOUN
ejpam-4381	76	42	k	k	ADV
ejpam-4381	76	43	-	-	PUNCT
ejpam-4381	76	44	dominating	dominating	NOUN
ejpam-4381	76	45	set	set	NOUN
ejpam-4381	76	46	in	in	ADP
ejpam-4381	76	47	g.	g.	PROPN
ejpam-4381	76	48	then	then	ADV
ejpam-4381	76	49	there	there	PRON
ejpam-4381	76	50	exists	exist	VERB
ejpam-4381	76	51	u	u	PROPN
ejpam-4381	76	52	∈	∈	PROPN
ejpam-4381	76	53	v	v	ADP
ejpam-4381	76	54	(	(	PUNCT
ejpam-4381	76	55	g	g	NOUN
ejpam-4381	76	56	)	)	PUNCT
ejpam-4381	76	57	\	\	PUNCT
ejpam-4381	77	1	s	s	VERB
ejpam-4381	77	2	such	such	ADJ
ejpam-4381	77	3	that	that	DET
ejpam-4381	77	4	dg(u	dg(u	ADJ
ejpam-4381	77	5	,	,	PUNCT
ejpam-4381	77	6	s	s	NOUN
ejpam-4381	77	7	)	)	PUNCT
ejpam-4381	77	8	>	>	X
ejpam-4381	78	1	k	k	X
ejpam-4381	78	2	,	,	PUNCT
ejpam-4381	78	3	for	for	ADP
ejpam-4381	78	4	all	all	DET
ejpam-4381	78	5	s	s	PROPN
ejpam-4381	78	6	∈	∈	PROPN
ejpam-4381	78	7	s.	s.	PROPN
ejpam-4381	78	8	let	let	VERB
ejpam-4381	78	9	a	a	DET
ejpam-4381	78	10	=	=	X
ejpam-4381	78	11	s	s	NOUN
ejpam-4381	78	12	∪	∪	X
ejpam-4381	78	13	{	{	PUNCT
ejpam-4381	78	14	u	u	NOUN
ejpam-4381	78	15	}	}	PUNCT
ejpam-4381	78	16	and	and	CCONJ
ejpam-4381	78	17	x	x	SYM
ejpam-4381	78	18	∈	∈	NOUN
ejpam-4381	78	19	a.	a.	NOUN
ejpam-4381	78	20	suppose	suppose	VERB
ejpam-4381	78	21	x	x	PUNCT
ejpam-4381	78	22	̸=	̸=	PROPN
ejpam-4381	78	23	u	u	NOUN
ejpam-4381	78	24	,	,	PUNCT
ejpam-4381	78	25	i.e.	i.e.	X
ejpam-4381	78	26	,	,	PUNCT
ejpam-4381	78	27	x	x	SYM
ejpam-4381	78	28	∈	∈	PROPN
ejpam-4381	78	29	s.	s.	PROPN
ejpam-4381	78	30	note	note	VERB
ejpam-4381	78	31	that	that	SCONJ
ejpam-4381	78	32	u	u	PROPN
ejpam-4381	78	33	/∈	/∈	PUNCT
ejpam-4381	78	34	nk	nk	PROPN
ejpam-4381	78	35	g(x	g(x	PROPN
ejpam-4381	78	36	)	)	PUNCT
ejpam-4381	78	37	.	.	PUNCT
ejpam-4381	79	1	then	then	ADV
ejpam-4381	79	2	|nk	|nk	ADP
ejpam-4381	79	3	g(x	g(x	NOUN
ejpam-4381	79	4	)	)	PUNCT
ejpam-4381	79	5	∩	∩	NOUN
ejpam-4381	79	6	(	(	PUNCT
ejpam-4381	79	7	v	v	NOUN
ejpam-4381	79	8	(	(	PUNCT
ejpam-4381	79	9	g	g	NOUN
ejpam-4381	79	10	)	)	PUNCT
ejpam-4381	79	11	\	\	PUNCT
ejpam-4381	80	1	a)|	a)|	PUNCT
ejpam-4381	80	2	−	−	NOUN
ejpam-4381	80	3	|nk	|nk	ADP
ejpam-4381	80	4	g(x	g(x	NOUN
ejpam-4381	80	5	)	)	PUNCT
ejpam-4381	80	6	∩	∩	NOUN
ejpam-4381	80	7	a|	a|	PROPN
ejpam-4381	80	8	=	=	PUNCT
ejpam-4381	80	9	|nk	|nk	ADP
ejpam-4381	80	10	g(x	g(x	NOUN
ejpam-4381	80	11	)	)	PUNCT
ejpam-4381	80	12	∩	∩	NOUN
ejpam-4381	80	13	(	(	PUNCT
ejpam-4381	80	14	v	v	NOUN
ejpam-4381	80	15	(	(	PUNCT
ejpam-4381	80	16	g	g	NOUN
ejpam-4381	80	17	)	)	PUNCT
ejpam-4381	80	18	\	\	PROPN
ejpam-4381	80	19	s)|	s)|	NOUN
ejpam-4381	80	20	−	−	PROPN
ejpam-4381	80	21	|nk	|nk	PROPN
ejpam-4381	80	22	g(x	g(x	NOUN
ejpam-4381	80	23	)	)	PUNCT
ejpam-4381	80	24	∩	∩	NOUN
ejpam-4381	80	25	s|	s|	VERB
ejpam-4381	80	26	≥	≥	NOUN
ejpam-4381	80	27	0	0	NUM
ejpam-4381	80	28	.	.	PUNCT
ejpam-4381	81	1	suppose	suppose	VERB
ejpam-4381	81	2	x	x	X
ejpam-4381	82	1	=	=	PUNCT
ejpam-4381	82	2	u.	u.	NOUN
ejpam-4381	82	3	then	then	ADV
ejpam-4381	82	4	|nk	|nk	NUM
ejpam-4381	82	5	g(x)∩(v	g(x)∩(v	PRON
ejpam-4381	82	6	(	(	PUNCT
ejpam-4381	82	7	g)\a)|−|nk	g)\a)|−|nk	PROPN
ejpam-4381	82	8	g(x)∩a|	g(x)∩a|	PRON
ejpam-4381	82	9	≥	≥	NOUN
ejpam-4381	82	10	0	0	NUM
ejpam-4381	82	11	.	.	PUNCT
ejpam-4381	83	1	thus	thus	ADV
ejpam-4381	83	2	,	,	PUNCT
ejpam-4381	83	3	a	a	PRON
ejpam-4381	83	4	is	be	AUX
ejpam-4381	83	5	a	a	DET
ejpam-4381	83	6	distance	distance	NOUN
ejpam-4381	83	7	k	k	ADJ
ejpam-4381	83	8	-	-	PUNCT
ejpam-4381	83	9	cost	cost	NOUN
ejpam-4381	83	10	effective	effective	ADJ
ejpam-4381	83	11	set	set	NOUN
ejpam-4381	83	12	in	in	ADP
ejpam-4381	83	13	g.	g.	PROPN
ejpam-4381	83	14	this	this	PRON
ejpam-4381	83	15	is	be	AUX
ejpam-4381	83	16	a	a	DET
ejpam-4381	83	17	contradiction	contradiction	NOUN
ejpam-4381	83	18	since	since	SCONJ
ejpam-4381	83	19	s	s	NOUN
ejpam-4381	83	20	is	be	AUX
ejpam-4381	83	21	an	an	DET
ejpam-4381	83	22	upper	upper	ADJ
ejpam-4381	83	23	distance	distance	NOUN
ejpam-4381	83	24	k	k	ADJ
ejpam-4381	83	25	-	-	PUNCT
ejpam-4381	83	26	cost	cost	NOUN
ejpam-4381	83	27	effective	effective	ADJ
ejpam-4381	83	28	set	set	NOUN
ejpam-4381	83	29	in	in	ADP
ejpam-4381	83	30	g.	g.	PROPN
ejpam-4381	83	31	therefore	therefore	ADV
ejpam-4381	83	32	,	,	PUNCT
ejpam-4381	83	33	every	every	DET
ejpam-4381	83	34	upper	upper	ADJ
ejpam-4381	83	35	distance	distance	NOUN
ejpam-4381	83	36	k	k	ADJ
ejpam-4381	83	37	-	-	PUNCT
ejpam-4381	83	38	cost	cost	NOUN
ejpam-4381	83	39	effective	effective	ADJ
ejpam-4381	83	40	set	set	NOUN
ejpam-4381	83	41	in	in	ADP
ejpam-4381	83	42	a	a	DET
ejpam-4381	83	43	connected	connected	ADJ
ejpam-4381	83	44	graph	graph	NOUN
ejpam-4381	83	45	g	g	PROPN
ejpam-4381	83	46	is	be	AUX
ejpam-4381	83	47	a	a	DET
ejpam-4381	83	48	distance	distance	NOUN
ejpam-4381	83	49	k	k	ADV
ejpam-4381	83	50	-	-	PUNCT
ejpam-4381	83	51	dominating	dominating	NOUN
ejpam-4381	83	52	set	set	NOUN
ejpam-4381	83	53	in	in	ADP
ejpam-4381	83	54	g.	g.	PROPN
ejpam-4381	83	55	2.2	2.2	NUM
ejpam-4381	83	56	.	.	PUNCT
ejpam-4381	84	1	corona	corona	NOUN
ejpam-4381	84	2	of	of	ADP
ejpam-4381	84	3	graphs	graph	NOUN
ejpam-4381	84	4	this	this	DET
ejpam-4381	84	5	section	section	NOUN
ejpam-4381	84	6	provides	provide	VERB
ejpam-4381	84	7	a	a	DET
ejpam-4381	84	8	neccesary	neccesary	ADJ
ejpam-4381	84	9	condition	condition	NOUN
ejpam-4381	84	10	for	for	ADP
ejpam-4381	84	11	a	a	DET
ejpam-4381	84	12	distance	distance	NOUN
ejpam-4381	84	13	k	k	ADJ
ejpam-4381	84	14	-	-	PUNCT
ejpam-4381	84	15	cost	cost	ADJ
ejpam-4381	84	16	effective	effective	ADJ
ejpam-4381	84	17	set	set	NOUN
ejpam-4381	84	18	in	in	ADP
ejpam-4381	84	19	the	the	DET
ejpam-4381	84	20	corona	corona	NOUN
ejpam-4381	84	21	of	of	ADP
ejpam-4381	84	22	two	two	NUM
ejpam-4381	84	23	graphs	graph	NOUN
ejpam-4381	84	24	.	.	PUNCT
ejpam-4381	85	1	correspondingly	correspondingly	ADV
ejpam-4381	85	2	,	,	PUNCT
ejpam-4381	85	3	a	a	DET
ejpam-4381	85	4	lower	lower	ADV
ejpam-4381	85	5	bound	bind	VERB
ejpam-4381	85	6	for	for	ADP
ejpam-4381	85	7	the	the	DET
ejpam-4381	85	8	upper	upper	ADJ
ejpam-4381	85	9	distance	distance	NOUN
ejpam-4381	85	10	k	k	ADJ
ejpam-4381	85	11	-	-	PUNCT
ejpam-4381	85	12	cost	cost	ADJ
ejpam-4381	85	13	effective	effective	ADJ
ejpam-4381	85	14	number	number	NOUN
ejpam-4381	85	15	of	of	ADP
ejpam-4381	85	16	the	the	DET
ejpam-4381	85	17	corona	corona	NOUN
ejpam-4381	85	18	of	of	ADP
ejpam-4381	85	19	graphs	graph	NOUN
ejpam-4381	85	20	is	be	AUX
ejpam-4381	85	21	determined	determine	VERB
ejpam-4381	85	22	.	.	PUNCT
ejpam-4381	86	1	the	the	DET
ejpam-4381	86	2	corona	corona	NOUN
ejpam-4381	86	3	g	g	PROPN
ejpam-4381	86	4	◦	◦	NOUN
ejpam-4381	86	5	h	h	NOUN
ejpam-4381	86	6	of	of	ADP
ejpam-4381	86	7	two	two	NUM
ejpam-4381	86	8	graphs	graph	NOUN
ejpam-4381	86	9	g	g	NOUN
ejpam-4381	86	10	and	and	CCONJ
ejpam-4381	86	11	h	h	NOUN
ejpam-4381	86	12	is	be	AUX
ejpam-4381	86	13	the	the	DET
ejpam-4381	86	14	graph	graph	NOUN
ejpam-4381	86	15	obtained	obtain	VERB
ejpam-4381	86	16	by	by	ADP
ejpam-4381	86	17	taking	take	VERB
ejpam-4381	86	18	one	one	NUM
ejpam-4381	86	19	copy	copy	NOUN
ejpam-4381	86	20	of	of	ADP
ejpam-4381	86	21	g	g	NOUN
ejpam-4381	86	22	of	of	ADP
ejpam-4381	86	23	order	order	NOUN
ejpam-4381	86	24	n	n	NOUN
ejpam-4381	86	25	and	and	CCONJ
ejpam-4381	86	26	n	n	PRON
ejpam-4381	86	27	copies	copy	NOUN
ejpam-4381	86	28	of	of	ADP
ejpam-4381	86	29	h	h	NOUN
ejpam-4381	86	30	,	,	PUNCT
ejpam-4381	86	31	and	and	CCONJ
ejpam-4381	86	32	then	then	ADV
ejpam-4381	86	33	joining	join	VERB
ejpam-4381	86	34	every	every	DET
ejpam-4381	86	35	vertex	vertex	NOUN
ejpam-4381	86	36	of	of	ADP
ejpam-4381	86	37	the	the	DET
ejpam-4381	86	38	ith	ith	PROPN
ejpam-4381	86	39	copy	copy	NOUN
ejpam-4381	86	40	of	of	ADP
ejpam-4381	86	41	h	h	PROPN
ejpam-4381	86	42	julius	julius	PROPN
ejpam-4381	86	43	g.	g.	PROPN
ejpam-4381	86	44	caadan	caadan	PROPN
ejpam-4381	86	45	,	,	PUNCT
ejpam-4381	86	46	rolando	rolando	PROPN
ejpam-4381	86	47	n.	n.	PROPN
ejpam-4381	86	48	paluga	paluga	PROPN
ejpam-4381	86	49	,	,	PUNCT
ejpam-4381	86	50	imelda	imelda	PROPN
ejpam-4381	86	51	s.	s.	PROPN
ejpam-4381	86	52	aniversario	aniversario	PROPN
ejpam-4381	86	53	/	/	SYM
ejpam-4381	86	54	eur	eur	PROPN
ejpam-4381	86	55	.	.	PUNCT
ejpam-4381	87	1	j.	j.	PROPN
ejpam-4381	87	2	pure	pure	PROPN
ejpam-4381	87	3	appl	appl	PROPN
ejpam-4381	87	4	.	.	PROPN
ejpam-4381	87	5	math	math	PROPN
ejpam-4381	87	6	,	,	PUNCT
ejpam-4381	87	7	16	16	NUM
ejpam-4381	87	8	(	(	PUNCT
ejpam-4381	87	9	1	1	NUM
ejpam-4381	87	10	)	)	PUNCT
ejpam-4381	87	11	(	(	PUNCT
ejpam-4381	87	12	2023	2023	NUM
ejpam-4381	87	13	)	)	PUNCT
ejpam-4381	87	14	,	,	PUNCT
ejpam-4381	87	15	261	261	NUM
ejpam-4381	87	16	-	-	SYM
ejpam-4381	87	17	270	270	NUM
ejpam-4381	87	18	264	264	NUM
ejpam-4381	87	19	to	to	ADP
ejpam-4381	87	20	the	the	DET
ejpam-4381	87	21	ith	ith	PROPN
ejpam-4381	87	22	vertex	vertex	NOUN
ejpam-4381	87	23	of	of	ADP
ejpam-4381	87	24	g.	g.	PROPN
ejpam-4381	87	25	for	for	ADP
ejpam-4381	87	26	every	every	DET
ejpam-4381	87	27	v	v	NUM
ejpam-4381	87	28	∈	∈	PROPN
ejpam-4381	87	29	v	v	NOUN
ejpam-4381	87	30	(	(	PUNCT
ejpam-4381	87	31	g	g	NOUN
ejpam-4381	87	32	)	)	PUNCT
ejpam-4381	87	33	,	,	PUNCT
ejpam-4381	87	34	denote	denote	VERB
ejpam-4381	87	35	hv	hv	PROPN
ejpam-4381	87	36	the	the	DET
ejpam-4381	87	37	copy	copy	NOUN
ejpam-4381	87	38	of	of	ADP
ejpam-4381	87	39	h	h	NOUN
ejpam-4381	87	40	whose	whose	DET
ejpam-4381	87	41	vertices	vertex	NOUN
ejpam-4381	87	42	are	be	AUX
ejpam-4381	87	43	attached	attach	VERB
ejpam-4381	87	44	one	one	NUM
ejpam-4381	87	45	by	by	ADP
ejpam-4381	87	46	one	one	NUM
ejpam-4381	87	47	to	to	ADP
ejpam-4381	87	48	the	the	DET
ejpam-4381	87	49	vertex	vertex	NOUN
ejpam-4381	87	50	v.	v.	ADP
ejpam-4381	87	51	subsequently	subsequently	ADV
ejpam-4381	87	52	,	,	PUNCT
ejpam-4381	87	53	denote	denote	VERB
ejpam-4381	87	54	by	by	ADP
ejpam-4381	87	55	v	v	PRON
ejpam-4381	87	56	+	+	NOUN
ejpam-4381	87	57	hv	hv	NOUN
ejpam-4381	87	58	the	the	DET
ejpam-4381	87	59	subgraph	subgraph	NOUN
ejpam-4381	87	60	of	of	ADP
ejpam-4381	87	61	the	the	DET
ejpam-4381	87	62	corona	corona	NOUN
ejpam-4381	87	63	g	g	PROPN
ejpam-4381	87	64	◦	◦	NOUN
ejpam-4381	87	65	h	h	NOUN
ejpam-4381	87	66	corresponding	correspond	VERB
ejpam-4381	87	67	to	to	ADP
ejpam-4381	87	68	the	the	DET
ejpam-4381	87	69	join	join	NOUN
ejpam-4381	87	70	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4381	87	71	,	,	PUNCT
ejpam-4381	87	72	v	v	PROPN
ejpam-4381	87	73	∈	∈	PROPN
ejpam-4381	87	74	v	v	NOUN
ejpam-4381	87	75	(	(	PUNCT
ejpam-4381	87	76	g	g	NOUN
ejpam-4381	87	77	)	)	PUNCT
ejpam-4381	87	78	.	.	PUNCT
ejpam-4381	88	1	theorem	theorem	NOUN
ejpam-4381	88	2	3	3	X
ejpam-4381	88	3	.	.	PUNCT
ejpam-4381	89	1	let	let	VERB
ejpam-4381	89	2	g	g	NOUN
ejpam-4381	90	1	and	and	CCONJ
ejpam-4381	90	2	h	h	NOUN
ejpam-4381	90	3	be	be	AUX
ejpam-4381	90	4	connected	connect	VERB
ejpam-4381	90	5	graphs	graph	NOUN
ejpam-4381	90	6	and	and	CCONJ
ejpam-4381	90	7	k	k	X
ejpam-4381	90	8	≥	≥	NUM
ejpam-4381	90	9	1	1	NUM
ejpam-4381	90	10	be	be	AUX
ejpam-4381	90	11	an	an	DET
ejpam-4381	90	12	integer	integer	NOUN
ejpam-4381	90	13	.	.	PUNCT
ejpam-4381	91	1	(	(	PUNCT
ejpam-4381	91	2	i	i	NOUN
ejpam-4381	91	3	)	)	PUNCT
ejpam-4381	91	4	if	if	SCONJ
ejpam-4381	91	5	k	k	PROPN
ejpam-4381	91	6	=	=	SYM
ejpam-4381	91	7	1	1	NUM
ejpam-4381	91	8	,	,	PUNCT
ejpam-4381	91	9	2	2	NUM
ejpam-4381	91	10	and	and	CCONJ
ejpam-4381	91	11	sx	sx	PROPN
ejpam-4381	91	12	is	be	AUX
ejpam-4381	91	13	a	a	DET
ejpam-4381	91	14	distance	distance	NOUN
ejpam-4381	91	15	k	k	ADJ
ejpam-4381	91	16	-	-	PUNCT
ejpam-4381	91	17	cost	cost	NOUN
ejpam-4381	91	18	effective	effective	ADJ
ejpam-4381	91	19	set	set	NOUN
ejpam-4381	91	20	in	in	ADP
ejpam-4381	91	21	hx	hx	PROPN
ejpam-4381	91	22	,	,	PUNCT
ejpam-4381	91	23	for	for	ADP
ejpam-4381	91	24	every	every	DET
ejpam-4381	91	25	x	x	SYM
ejpam-4381	91	26	∈	∈	PROPN
ejpam-4381	91	27	v	v	NOUN
ejpam-4381	91	28	(	(	PUNCT
ejpam-4381	91	29	g	g	NOUN
ejpam-4381	91	30	)	)	PUNCT
ejpam-4381	91	31	,	,	PUNCT
ejpam-4381	91	32	then	then	ADV
ejpam-4381	91	33	s	s	VERB
ejpam-4381	91	34	=	=	PUNCT
ejpam-4381	91	35	⋃	⋃	PROPN
ejpam-4381	91	36	x∈v	x∈v	PROPN
ejpam-4381	91	37	(	(	PUNCT
ejpam-4381	91	38	g	g	NOUN
ejpam-4381	91	39	)	)	PUNCT
ejpam-4381	91	40	sx	sx	PROPN
ejpam-4381	91	41	is	be	AUX
ejpam-4381	91	42	a	a	DET
ejpam-4381	91	43	distance	distance	NOUN
ejpam-4381	91	44	k	k	ADJ
ejpam-4381	91	45	-	-	PUNCT
ejpam-4381	91	46	cost	cost	ADJ
ejpam-4381	91	47	effective	effective	ADJ
ejpam-4381	91	48	set	set	NOUN
ejpam-4381	91	49	in	in	ADP
ejpam-4381	91	50	g	g	PROPN
ejpam-4381	91	51	◦	◦	PROPN
ejpam-4381	91	52	h.	h.	PROPN
ejpam-4381	91	53	(	(	PUNCT
ejpam-4381	91	54	ii	ii	PROPN
ejpam-4381	91	55	)	)	PUNCT
ejpam-4381	91	56	if	if	SCONJ
ejpam-4381	91	57	k	k	PROPN
ejpam-4381	91	58	≥	≥	VERB
ejpam-4381	91	59	3	3	NUM
ejpam-4381	91	60	and	and	CCONJ
ejpam-4381	91	61	|sx|	|sx|	NUM
ejpam-4381	91	62	≤	≤	NUM
ejpam-4381	91	63	|v	|v	X
ejpam-4381	91	64	(	(	PUNCT
ejpam-4381	91	65	h)|	h)|	PROPN
ejpam-4381	91	66	(	(	PUNCT
ejpam-4381	91	67	δk−2(g)+1	δk−2(g)+1	NOUN
ejpam-4381	91	68	)	)	PUNCT
ejpam-4381	92	1	+	+	VERB
ejpam-4381	92	2	δk−1(g)+2	δk−1(g)+2	X
ejpam-4381	92	3	2	2	NUM
ejpam-4381	92	4	(	(	PUNCT
ejpam-4381	92	5	∆k−2(g)+1	∆k−2(g)+1	ADV
ejpam-4381	92	6	)	)	PUNCT
ejpam-4381	92	7	,	,	PUNCT
ejpam-4381	92	8	for	for	ADP
ejpam-4381	92	9	every	every	DET
ejpam-4381	92	10	x	x	SYM
ejpam-4381	92	11	∈	∈	PROPN
ejpam-4381	92	12	v	v	NOUN
ejpam-4381	92	13	(	(	PUNCT
ejpam-4381	92	14	g	g	NOUN
ejpam-4381	92	15	)	)	PUNCT
ejpam-4381	92	16	,	,	PUNCT
ejpam-4381	92	17	then	then	ADV
ejpam-4381	92	18	s	s	VERB
ejpam-4381	92	19	=	=	NOUN
ejpam-4381	92	20	⋃	⋃	PROPN
ejpam-4381	92	21	x∈v	x∈v	PROPN
ejpam-4381	92	22	(	(	PUNCT
ejpam-4381	92	23	g	g	NOUN
ejpam-4381	92	24	)	)	PUNCT
ejpam-4381	92	25	sx	sx	PROPN
ejpam-4381	92	26	is	be	AUX
ejpam-4381	92	27	a	a	DET
ejpam-4381	92	28	distance	distance	NOUN
ejpam-4381	92	29	k	k	ADJ
ejpam-4381	92	30	-	-	PUNCT
ejpam-4381	92	31	cost	cost	ADJ
ejpam-4381	92	32	effective	effective	ADJ
ejpam-4381	92	33	set	set	NOUN
ejpam-4381	92	34	in	in	ADP
ejpam-4381	92	35	g	g	PROPN
ejpam-4381	92	36	◦	◦	NOUN
ejpam-4381	92	37	h.	h.	NOUN
ejpam-4381	92	38	proof	proof	NOUN
ejpam-4381	92	39	:	:	PUNCT
ejpam-4381	92	40	suppose	suppose	VERB
ejpam-4381	92	41	sx	sx	PROPN
ejpam-4381	92	42	is	be	AUX
ejpam-4381	92	43	a	a	DET
ejpam-4381	92	44	distance	distance	NOUN
ejpam-4381	92	45	k	k	ADJ
ejpam-4381	92	46	-	-	PUNCT
ejpam-4381	92	47	cost	cost	NOUN
ejpam-4381	92	48	effective	effective	ADJ
ejpam-4381	92	49	set	set	NOUN
ejpam-4381	92	50	in	in	ADP
ejpam-4381	92	51	hx	hx	PROPN
ejpam-4381	92	52	,	,	PUNCT
ejpam-4381	92	53	for	for	ADP
ejpam-4381	92	54	every	every	DET
ejpam-4381	92	55	x	x	SYM
ejpam-4381	92	56	∈	∈	PROPN
ejpam-4381	92	57	v	v	NOUN
ejpam-4381	92	58	(	(	PUNCT
ejpam-4381	92	59	g	g	NOUN
ejpam-4381	92	60	)	)	PUNCT
ejpam-4381	92	61	.	.	PUNCT
ejpam-4381	93	1	let	let	VERB
ejpam-4381	93	2	s	s	PRON
ejpam-4381	93	3	=	=	VERB
ejpam-4381	93	4	⋃	⋃	PROPN
ejpam-4381	93	5	x∈v	x∈v	PROPN
ejpam-4381	93	6	(	(	PUNCT
ejpam-4381	93	7	g	g	NOUN
ejpam-4381	93	8	)	)	PUNCT
ejpam-4381	93	9	sx	sx	NOUN
ejpam-4381	93	10	and	and	CCONJ
ejpam-4381	93	11	u	u	PROPN
ejpam-4381	93	12	∈	∈	PROPN
ejpam-4381	93	13	s.	s.	PROPN
ejpam-4381	93	14	then	then	ADV
ejpam-4381	93	15	there	there	PRON
ejpam-4381	93	16	exists	exist	VERB
ejpam-4381	93	17	a	a	DET
ejpam-4381	93	18	∈	∈	PROPN
ejpam-4381	93	19	v	v	NOUN
ejpam-4381	93	20	(	(	PUNCT
ejpam-4381	93	21	g	g	NOUN
ejpam-4381	93	22	)	)	PUNCT
ejpam-4381	93	23	such	such	ADJ
ejpam-4381	93	24	that	that	SCONJ
ejpam-4381	93	25	u	u	PROPN
ejpam-4381	93	26	∈	∈	PROPN
ejpam-4381	93	27	sa	sa	PROPN
ejpam-4381	93	28	.	.	PUNCT
ejpam-4381	94	1	since	since	SCONJ
ejpam-4381	94	2	sa	sa	PROPN
ejpam-4381	94	3	is	be	AUX
ejpam-4381	94	4	a	a	DET
ejpam-4381	94	5	distance	distance	NOUN
ejpam-4381	94	6	k	k	ADJ
ejpam-4381	94	7	-	-	PUNCT
ejpam-4381	94	8	cost	cost	NOUN
ejpam-4381	94	9	effective	effective	ADJ
ejpam-4381	94	10	set	set	NOUN
ejpam-4381	94	11	in	in	ADP
ejpam-4381	94	12	ha	ha	INTJ
ejpam-4381	94	13	,	,	PUNCT
ejpam-4381	94	14	for	for	ADP
ejpam-4381	94	15	all	all	DET
ejpam-4381	94	16	a	a	DET
ejpam-4381	94	17	∈	∈	PROPN
ejpam-4381	94	18	v	v	NOUN
ejpam-4381	94	19	(	(	PUNCT
ejpam-4381	94	20	g	g	NOUN
ejpam-4381	94	21	)	)	PUNCT
ejpam-4381	94	22	,	,	PUNCT
ejpam-4381	94	23	|nk	|nk	ADP
ejpam-4381	94	24	ha	ha	INTJ
ejpam-4381	94	25	(	(	PUNCT
ejpam-4381	94	26	u)∩	u)∩	PROPN
ejpam-4381	94	27	(	(	PUNCT
ejpam-4381	94	28	v	v	NOUN
ejpam-4381	94	29	(	(	PUNCT
ejpam-4381	94	30	ha	ha	INTJ
ejpam-4381	94	31	)	)	PUNCT
ejpam-4381	94	32	\	\	PUNCT
ejpam-4381	95	1	sa)|	sa)|	X
ejpam-4381	95	2	−	−	PROPN
ejpam-4381	95	3	|nk	|nk	NUM
ejpam-4381	95	4	ha	ha	INTJ
ejpam-4381	95	5	(	(	PUNCT
ejpam-4381	95	6	u)∩	u)∩	PROPN
ejpam-4381	95	7	sa|	sa|	PROPN
ejpam-4381	95	8	≥	≥	NOUN
ejpam-4381	95	9	0	0	NUM
ejpam-4381	95	10	.	.	PUNCT
ejpam-4381	96	1	if	if	SCONJ
ejpam-4381	96	2	k	k	PROPN
ejpam-4381	96	3	=	=	SYM
ejpam-4381	96	4	1	1	NUM
ejpam-4381	96	5	,	,	PUNCT
ejpam-4381	96	6	we	we	PRON
ejpam-4381	96	7	have	have	AUX
ejpam-4381	96	8	|n1	|n1	VERB
ejpam-4381	96	9	g	g	ADP
ejpam-4381	96	10	◦	◦	NOUN
ejpam-4381	96	11	h(u	h(u	NOUN
ejpam-4381	96	12	)	)	PUNCT
ejpam-4381	97	1	∩	∩	NOUN
ejpam-4381	97	2	(	(	PUNCT
ejpam-4381	97	3	v	v	NOUN
ejpam-4381	97	4	(	(	PUNCT
ejpam-4381	97	5	g	g	PROPN
ejpam-4381	97	6	◦	◦	NOUN
ejpam-4381	97	7	h	h	NOUN
ejpam-4381	97	8	)	)	PUNCT
ejpam-4381	97	9	\	\	PROPN
ejpam-4381	97	10	s	s	PART
ejpam-4381	97	11	)	)	PUNCT
ejpam-4381	98	1	|	|	ADV
ejpam-4381	98	2	=	=	PRON
ejpam-4381	98	3	|n1	|n1	VERB
ejpam-4381	98	4	ha	ha	INTJ
ejpam-4381	98	5	(	(	PUNCT
ejpam-4381	98	6	u	u	NOUN
ejpam-4381	98	7	)	)	PUNCT
ejpam-4381	98	8	(	(	PUNCT
ejpam-4381	98	9	v	v	X
ejpam-4381	98	10	(	(	PUNCT
ejpam-4381	98	11	ha	ha	INTJ
ejpam-4381	98	12	)	)	PUNCT
ejpam-4381	98	13	\	\	PROPN
ejpam-4381	98	14	sa	sa	PROPN
ejpam-4381	98	15	)	)	PUNCT
ejpam-4381	98	16	|+	|+	ADP
ejpam-4381	98	17	1	1	NUM
ejpam-4381	98	18	and	and	CCONJ
ejpam-4381	98	19	|n1	|n1	VERB
ejpam-4381	98	20	g	g	ADP
ejpam-4381	98	21	◦	◦	NOUN
ejpam-4381	98	22	h(u	h(u	NOUN
ejpam-4381	98	23	)	)	PUNCT
ejpam-4381	98	24	∩	∩	NOUN
ejpam-4381	98	25	s|	s|	NOUN
ejpam-4381	98	26	=	=	PUNCT
ejpam-4381	98	27	|n1	|n1	VERB
ejpam-4381	98	28	ha	ha	INTJ
ejpam-4381	98	29	(	(	PUNCT
ejpam-4381	98	30	u	u	NOUN
ejpam-4381	98	31	)	)	PUNCT
ejpam-4381	98	32	∩	∩	NOUN
ejpam-4381	98	33	sa|	sa|	PROPN
ejpam-4381	98	34	thus	thus	ADV
ejpam-4381	98	35	,	,	PUNCT
ejpam-4381	98	36	|n1	|n1	VERB
ejpam-4381	98	37	g	g	ADP
ejpam-4381	98	38	◦	◦	NOUN
ejpam-4381	98	39	h(u	h(u	NOUN
ejpam-4381	98	40	)	)	PUNCT
ejpam-4381	98	41	∩	∩	NOUN
ejpam-4381	98	42	(	(	PUNCT
ejpam-4381	98	43	v	v	NOUN
ejpam-4381	98	44	(	(	PUNCT
ejpam-4381	98	45	g	g	PROPN
ejpam-4381	98	46	◦	◦	NOUN
ejpam-4381	98	47	h	h	NOUN
ejpam-4381	98	48	)	)	PUNCT
ejpam-4381	98	49	\	\	PROPN
ejpam-4381	98	50	s	s	PART
ejpam-4381	98	51	)	)	PUNCT
ejpam-4381	99	1	|	|	ADV
ejpam-4381	99	2	−	−	PROPN
ejpam-4381	99	3	|n1	|n1	VERB
ejpam-4381	99	4	g	g	ADP
ejpam-4381	99	5	◦	◦	NOUN
ejpam-4381	99	6	h(u	h(u	NOUN
ejpam-4381	99	7	)	)	PUNCT
ejpam-4381	99	8	∩	∩	NOUN
ejpam-4381	99	9	s|	s|	VERB
ejpam-4381	99	10	≥	≥	NOUN
ejpam-4381	99	11	0	0	NUM
ejpam-4381	99	12	.	.	PUNCT
ejpam-4381	100	1	hence	hence	ADV
ejpam-4381	100	2	,	,	PUNCT
ejpam-4381	100	3	s	s	VERB
ejpam-4381	100	4	is	be	AUX
ejpam-4381	100	5	a	a	DET
ejpam-4381	100	6	distance	distance	NOUN
ejpam-4381	100	7	1	1	NUM
ejpam-4381	100	8	-	-	PUNCT
ejpam-4381	100	9	cost	cost	NOUN
ejpam-4381	100	10	effective	effective	ADJ
ejpam-4381	100	11	set	set	NOUN
ejpam-4381	100	12	in	in	ADP
ejpam-4381	100	13	g	g	PROPN
ejpam-4381	100	14	◦	◦	NOUN
ejpam-4381	100	15	h.	h.	NOUN
ejpam-4381	100	16	if	if	SCONJ
ejpam-4381	100	17	k	k	PROPN
ejpam-4381	100	18	=	=	SYM
ejpam-4381	100	19	2	2	NUM
ejpam-4381	100	20	,	,	PUNCT
ejpam-4381	100	21	then	then	ADV
ejpam-4381	100	22	|n2	|n2	PROPN
ejpam-4381	100	23	g	g	PROPN
ejpam-4381	100	24	◦	◦	NOUN
ejpam-4381	100	25	h(u	h(u	NOUN
ejpam-4381	100	26	)	)	PUNCT
ejpam-4381	100	27	∩	∩	NOUN
ejpam-4381	100	28	(	(	PUNCT
ejpam-4381	100	29	v	v	NOUN
ejpam-4381	100	30	(	(	PUNCT
ejpam-4381	100	31	g	g	PROPN
ejpam-4381	100	32	◦	◦	NOUN
ejpam-4381	100	33	h	h	NOUN
ejpam-4381	100	34	)	)	PUNCT
ejpam-4381	100	35	\	\	PROPN
ejpam-4381	100	36	s)|	s)|	NOUN
ejpam-4381	100	37	=	=	PUNCT
ejpam-4381	100	38	|n2	|n2	PROPN
ejpam-4381	100	39	ha	ha	INTJ
ejpam-4381	100	40	(	(	PUNCT
ejpam-4381	100	41	u	u	NOUN
ejpam-4381	100	42	)	)	PUNCT
ejpam-4381	100	43	∩	∩	NOUN
ejpam-4381	100	44	(	(	PUNCT
ejpam-4381	100	45	v	v	X
ejpam-4381	100	46	(	(	PUNCT
ejpam-4381	100	47	ha	ha	INTJ
ejpam-4381	100	48	)	)	PUNCT
ejpam-4381	100	49	\	\	PROPN
ejpam-4381	100	50	sa	sa	PROPN
ejpam-4381	100	51	)	)	PUNCT
ejpam-4381	100	52	|+	|+	NOUN
ejpam-4381	101	1	degg(a	degg(a	PROPN
ejpam-4381	101	2	)	)	PUNCT
ejpam-4381	102	1	+	+	CCONJ
ejpam-4381	102	2	1	1	NUM
ejpam-4381	102	3	and	and	CCONJ
ejpam-4381	102	4	|n2	|n2	PROPN
ejpam-4381	102	5	g	g	PROPN
ejpam-4381	102	6	◦	◦	NOUN
ejpam-4381	102	7	h(u	h(u	NOUN
ejpam-4381	102	8	)	)	PUNCT
ejpam-4381	103	1	∩	∩	NOUN
ejpam-4381	103	2	s|	s|	VERB
ejpam-4381	103	3	=	=	PUNCT
ejpam-4381	103	4	|n2	|n2	X
ejpam-4381	103	5	ha	ha	INTJ
ejpam-4381	103	6	(	(	PUNCT
ejpam-4381	103	7	u	u	NOUN
ejpam-4381	103	8	)	)	PUNCT
ejpam-4381	103	9	∩	∩	NOUN
ejpam-4381	103	10	sa|	sa|	PROPN
ejpam-4381	103	11	.	.	PUNCT
ejpam-4381	104	1	thus	thus	ADV
ejpam-4381	104	2	,	,	PUNCT
ejpam-4381	104	3	|n2	|n2	PROPN
ejpam-4381	104	4	g	g	PROPN
ejpam-4381	104	5	◦	◦	NOUN
ejpam-4381	104	6	h(u	h(u	NOUN
ejpam-4381	104	7	)	)	PUNCT
ejpam-4381	104	8	∩	∩	NOUN
ejpam-4381	104	9	(	(	PUNCT
ejpam-4381	104	10	v	v	NOUN
ejpam-4381	104	11	(	(	PUNCT
ejpam-4381	104	12	g	g	PROPN
ejpam-4381	104	13	◦	◦	NOUN
ejpam-4381	104	14	h	h	NOUN
ejpam-4381	104	15	)	)	PUNCT
ejpam-4381	104	16	\	\	PROPN
ejpam-4381	104	17	s)|	s)|	NOUN
ejpam-4381	104	18	−	−	PROPN
ejpam-4381	104	19	|n2	|n2	PROPN
ejpam-4381	104	20	g	g	PROPN
ejpam-4381	104	21	◦	◦	NOUN
ejpam-4381	104	22	h(u	h(u	NOUN
ejpam-4381	104	23	)	)	PUNCT
ejpam-4381	104	24	∩	∩	NOUN
ejpam-4381	104	25	s|	s|	VERB
ejpam-4381	104	26	≥	≥	NOUN
ejpam-4381	104	27	0	0	NUM
ejpam-4381	104	28	.	.	PUNCT
ejpam-4381	105	1	hence	hence	ADV
ejpam-4381	105	2	,	,	PUNCT
ejpam-4381	105	3	s	s	VERB
ejpam-4381	105	4	is	be	AUX
ejpam-4381	105	5	a	a	DET
ejpam-4381	105	6	distance	distance	NOUN
ejpam-4381	105	7	2	2	NUM
ejpam-4381	105	8	-	-	PUNCT
ejpam-4381	105	9	cost	cost	NOUN
ejpam-4381	105	10	effective	effective	ADJ
ejpam-4381	105	11	set	set	NOUN
ejpam-4381	105	12	in	in	ADP
ejpam-4381	105	13	g	g	PROPN
ejpam-4381	105	14	◦	◦	PROPN
ejpam-4381	105	15	h.	h.	PROPN
ejpam-4381	105	16	(	(	PUNCT
ejpam-4381	105	17	ii	ii	NOUN
ejpam-4381	105	18	)	)	PUNCT
ejpam-4381	105	19	let	let	VERB
ejpam-4381	105	20	k	k	PROPN
ejpam-4381	105	21	≥	≥	NUM
ejpam-4381	105	22	3	3	NUM
ejpam-4381	105	23	be	be	AUX
ejpam-4381	105	24	an	an	DET
ejpam-4381	105	25	integer	integer	NOUN
ejpam-4381	105	26	and	and	CCONJ
ejpam-4381	105	27	u	u	NOUN
ejpam-4381	105	28	∈	∈	PROPN
ejpam-4381	105	29	s.	s.	PROPN
ejpam-4381	105	30	then	then	ADV
ejpam-4381	105	31	there	there	PRON
ejpam-4381	105	32	exists	exist	VERB
ejpam-4381	105	33	a	a	DET
ejpam-4381	105	34	∈	∈	PROPN
ejpam-4381	105	35	v	v	NOUN
ejpam-4381	105	36	(	(	PUNCT
ejpam-4381	105	37	g	g	NOUN
ejpam-4381	105	38	)	)	PUNCT
ejpam-4381	105	39	such	such	ADJ
ejpam-4381	105	40	that	that	SCONJ
ejpam-4381	105	41	u	u	PROPN
ejpam-4381	105	42	∈	∈	PROPN
ejpam-4381	105	43	sa	sa	PROPN
ejpam-4381	105	44	.	.	PUNCT
ejpam-4381	106	1	now	now	ADV
ejpam-4381	106	2	,	,	PUNCT
ejpam-4381	106	3	|nk	|nk	ADP
ejpam-4381	106	4	g	g	PROPN
ejpam-4381	106	5	◦	◦	NOUN
ejpam-4381	106	6	h(u	h(u	NOUN
ejpam-4381	106	7	)	)	PUNCT
ejpam-4381	106	8	∩	∩	NOUN
ejpam-4381	106	9	(	(	PUNCT
ejpam-4381	106	10	v	v	NOUN
ejpam-4381	106	11	(	(	PUNCT
ejpam-4381	106	12	g	g	PROPN
ejpam-4381	106	13	◦	◦	NOUN
ejpam-4381	106	14	h	h	NOUN
ejpam-4381	106	15	)	)	PUNCT
ejpam-4381	107	1	\	\	PROPN
ejpam-4381	107	2	s	s	PART
ejpam-4381	107	3	)	)	PUNCT
ejpam-4381	108	1	|	|	ADV
ejpam-4381	108	2	−	−	PROPN
ejpam-4381	109	1	|nk	|nk	ADP
ejpam-4381	109	2	g	g	PROPN
ejpam-4381	109	3	◦	◦	NOUN
ejpam-4381	109	4	h(u	h(u	NOUN
ejpam-4381	109	5	)	)	PUNCT
ejpam-4381	109	6	∩	∩	NOUN
ejpam-4381	109	7	s|	s|	VERB
ejpam-4381	109	8	=	=	PUNCT
ejpam-4381	110	1	[	[	PUNCT
ejpam-4381	110	2	degk−1	degk−1	ADV
ejpam-4381	110	3	g	g	NOUN
ejpam-4381	110	4	(	(	PUNCT
ejpam-4381	110	5	a	a	NOUN
ejpam-4381	110	6	)	)	PUNCT
ejpam-4381	110	7	+	+	CCONJ
ejpam-4381	110	8	1	1	NUM
ejpam-4381	110	9	]	]	PUNCT
ejpam-4381	110	10	+	+	CCONJ
ejpam-4381	110	11	|v	|v	X
ejpam-4381	110	12	(	(	PUNCT
ejpam-4381	110	13	h	h	NOUN
ejpam-4381	110	14	)	)	PUNCT
ejpam-4381	110	15	\	\	PUNCT
ejpam-4381	111	1	sa|	sa|	PROPN
ejpam-4381	111	2	+	+	CCONJ
ejpam-4381	111	3	∑	∑	PROPN
ejpam-4381	111	4	x∈nk−2	x∈nk−2	PROPN
ejpam-4381	111	5	g	g	PROPN
ejpam-4381	111	6	(	(	PUNCT
ejpam-4381	111	7	a	a	PRON
ejpam-4381	111	8	)	)	PUNCT
ejpam-4381	111	9	∣∣∣(v	∣∣∣(v	PROPN
ejpam-4381	111	10	(	(	PUNCT
ejpam-4381	111	11	h	h	NOUN
ejpam-4381	111	12	)	)	PUNCT
ejpam-4381	111	13	\	\	PROPN
ejpam-4381	111	14	sx	sx	PROPN
ejpam-4381	111	15	)	)	PUNCT
ejpam-4381	111	16	∣∣∣−	∣∣∣−	PROPN
ejpam-4381	111	17	∑	∑	PUNCT
ejpam-4381	111	18	x∈nk−2	x∈nk−2	PROPN
ejpam-4381	111	19	g	g	PROPN
ejpam-4381	111	20	(	(	PUNCT
ejpam-4381	111	21	a	a	NOUN
ejpam-4381	111	22	)	)	PUNCT
ejpam-4381	111	23	|sx|	|sx|	NUM
ejpam-4381	111	24	−	−	PROPN
ejpam-4381	111	25	(	(	PUNCT
ejpam-4381	111	26	|sa|	|sa|	NUM
ejpam-4381	111	27	−	−	NOUN
ejpam-4381	111	28	1	1	NUM
ejpam-4381	111	29	)	)	PUNCT
ejpam-4381	111	30	=	=	NOUN
ejpam-4381	112	1	[	[	PUNCT
ejpam-4381	112	2	degk−1	degk−1	ADV
ejpam-4381	112	3	g	g	NOUN
ejpam-4381	112	4	(	(	PUNCT
ejpam-4381	112	5	a	a	NOUN
ejpam-4381	112	6	)	)	PUNCT
ejpam-4381	112	7	+	+	CCONJ
ejpam-4381	112	8	1	1	NUM
ejpam-4381	112	9	]	]	PUNCT
ejpam-4381	112	10	+	+	CCONJ
ejpam-4381	112	11	|v	|v	X
ejpam-4381	112	12	(	(	PUNCT
ejpam-4381	112	13	h)|	h)|	PROPN
ejpam-4381	112	14	−	−	PROPN
ejpam-4381	112	15	|sa|+	|sa|+	VERB
ejpam-4381	112	16	∑	∑	PROPN
ejpam-4381	112	17	x∈nk−2	x∈nk−2	PROPN
ejpam-4381	112	18	g	g	PROPN
ejpam-4381	112	19	(	(	PUNCT
ejpam-4381	112	20	a	a	NOUN
ejpam-4381	112	21	)	)	PUNCT
ejpam-4381	112	22	(	(	PUNCT
ejpam-4381	112	23	|v	|v	PROPN
ejpam-4381	112	24	(	(	PUNCT
ejpam-4381	112	25	h)|	h)|	NOUN
ejpam-4381	112	26	−	−	NOUN
ejpam-4381	112	27	|sx|	|sx|	NUM
ejpam-4381	112	28	)	)	PUNCT
ejpam-4381	112	29	−	−	PROPN
ejpam-4381	113	1	∑	∑	NOUN
ejpam-4381	113	2	x∈nk−2	x∈nk−2	PROPN
ejpam-4381	113	3	g	g	PROPN
ejpam-4381	113	4	(	(	PUNCT
ejpam-4381	113	5	a	a	NOUN
ejpam-4381	113	6	)	)	PUNCT
ejpam-4381	113	7	|sx|	|sx|	ADP
ejpam-4381	113	8	−	−	PROPN
ejpam-4381	113	9	|sa|+	|sa|+	ADP
ejpam-4381	113	10	1	1	NUM
ejpam-4381	113	11	julius	julius	PROPN
ejpam-4381	113	12	g.	g.	PROPN
ejpam-4381	113	13	caadan	caadan	PROPN
ejpam-4381	113	14	,	,	PUNCT
ejpam-4381	113	15	rolando	rolando	PROPN
ejpam-4381	113	16	n.	n.	PROPN
ejpam-4381	113	17	paluga	paluga	PROPN
ejpam-4381	113	18	,	,	PUNCT
ejpam-4381	113	19	imelda	imelda	PROPN
ejpam-4381	113	20	s.	s.	PROPN
ejpam-4381	113	21	aniversario	aniversario	PROPN
ejpam-4381	113	22	/	/	SYM
ejpam-4381	113	23	eur	eur	PROPN
ejpam-4381	113	24	.	.	PUNCT
ejpam-4381	114	1	j.	j.	PROPN
ejpam-4381	114	2	pure	pure	PROPN
ejpam-4381	114	3	appl	appl	PROPN
ejpam-4381	114	4	.	.	PROPN
ejpam-4381	114	5	math	math	PROPN
ejpam-4381	114	6	,	,	PUNCT
ejpam-4381	114	7	16	16	NUM
ejpam-4381	114	8	(	(	PUNCT
ejpam-4381	114	9	1	1	NUM
ejpam-4381	114	10	)	)	PUNCT
ejpam-4381	114	11	(	(	PUNCT
ejpam-4381	114	12	2023	2023	NUM
ejpam-4381	114	13	)	)	PUNCT
ejpam-4381	114	14	,	,	PUNCT
ejpam-4381	114	15	261	261	NUM
ejpam-4381	114	16	-	-	SYM
ejpam-4381	114	17	270	270	NUM
ejpam-4381	114	18	265	265	NUM
ejpam-4381	114	19	=	=	NOUN
ejpam-4381	114	20	degk−1	degk−1	ADJ
ejpam-4381	114	21	g	g	NOUN
ejpam-4381	114	22	(	(	PUNCT
ejpam-4381	114	23	a	a	NOUN
ejpam-4381	114	24	)	)	PUNCT
ejpam-4381	114	25	+	+	CCONJ
ejpam-4381	114	26	2	2	NUM
ejpam-4381	114	27	+	+	CCONJ
ejpam-4381	114	28	|v	|v	X
ejpam-4381	114	29	(	(	PUNCT
ejpam-4381	114	30	h)|	h)|	NOUN
ejpam-4381	114	31	−	−	PROPN
ejpam-4381	114	32	2|sa|+	2|sa|+	PROPN
ejpam-4381	114	33	∑	∑	PROPN
ejpam-4381	114	34	x∈nk−2	x∈nk−2	PROPN
ejpam-4381	114	35	g	g	PROPN
ejpam-4381	114	36	(	(	PUNCT
ejpam-4381	114	37	a	a	NOUN
ejpam-4381	114	38	)	)	PUNCT
ejpam-4381	114	39	(	(	PUNCT
ejpam-4381	114	40	|v	|v	PROPN
ejpam-4381	114	41	(	(	PUNCT
ejpam-4381	114	42	h)|	h)|	NOUN
ejpam-4381	114	43	−	−	PROPN
ejpam-4381	114	44	2|sx|	2|sx|	PROPN
ejpam-4381	114	45	)	)	PUNCT
ejpam-4381	114	46	≥	≥	NOUN
ejpam-4381	114	47	degk−1	degk−1	ADV
ejpam-4381	114	48	g	g	NOUN
ejpam-4381	114	49	(	(	PUNCT
ejpam-4381	114	50	a	a	NOUN
ejpam-4381	114	51	)	)	PUNCT
ejpam-4381	114	52	+	+	CCONJ
ejpam-4381	114	53	2	2	NUM
ejpam-4381	114	54	+	+	CCONJ
ejpam-4381	114	55	|v	|v	X
ejpam-4381	114	56	(	(	PUNCT
ejpam-4381	114	57	h)|	h)|	NOUN
ejpam-4381	114	58	−	−	PROPN
ejpam-4381	114	59	2|sp|+	2|sp|+	PROPN
ejpam-4381	114	60	|nk−2	|nk−2	PROPN
ejpam-4381	114	61	g	g	PROPN
ejpam-4381	114	62	(	(	PUNCT
ejpam-4381	114	63	a)||v	a)||v	PROPN
ejpam-4381	114	64	(	(	PUNCT
ejpam-4381	114	65	h)|	h)|	PROPN
ejpam-4381	114	66	−	−	PROPN
ejpam-4381	114	67	2|nk−2	2|nk−2	PROPN
ejpam-4381	114	68	g	g	PROPN
ejpam-4381	114	69	(	(	PUNCT
ejpam-4381	114	70	a)||sp|,where	a)||sp|,where	NOUN
ejpam-4381	114	71	|sp|	|sp|	NOUN
ejpam-4381	114	72	=	=	PROPN
ejpam-4381	115	1	max{|sx|	max{|sx|	X
ejpam-4381	115	2	:	:	PUNCT
ejpam-4381	115	3	x	x	SYM
ejpam-4381	115	4	∈	∈	NOUN
ejpam-4381	115	5	v	v	NOUN
ejpam-4381	115	6	(	(	PUNCT
ejpam-4381	115	7	g	g	NOUN
ejpam-4381	115	8	)	)	PUNCT
ejpam-4381	115	9	}	}	PUNCT
ejpam-4381	115	10	=	=	PUNCT
ejpam-4381	116	1	degk−1	degk−1	ADJ
ejpam-4381	116	2	g	g	NOUN
ejpam-4381	116	3	(	(	PUNCT
ejpam-4381	116	4	a	a	NOUN
ejpam-4381	116	5	)	)	PUNCT
ejpam-4381	116	6	+	+	CCONJ
ejpam-4381	116	7	2	2	NUM
ejpam-4381	116	8	+	+	CCONJ
ejpam-4381	116	9	|v	|v	X
ejpam-4381	116	10	(	(	PUNCT
ejpam-4381	116	11	h)|+	h)|+	ADJ
ejpam-4381	116	12	degk−2	degk−2	X
ejpam-4381	116	13	g	g	PROPN
ejpam-4381	116	14	(	(	PUNCT
ejpam-4381	116	15	a)|v	a)|v	PROPN
ejpam-4381	116	16	(	(	PUNCT
ejpam-4381	116	17	h)|	h)|	PROPN
ejpam-4381	116	18	−	−	PROPN
ejpam-4381	116	19	2|sp|	2|sp|	PROPN
ejpam-4381	116	20	−	−	PROPN
ejpam-4381	116	21	2degk−2	2degk−2	NUM
ejpam-4381	116	22	g	g	PROPN
ejpam-4381	116	23	(	(	PUNCT
ejpam-4381	116	24	a)||sp|	a)||sp|	PROPN
ejpam-4381	116	25	=	=	PROPN
ejpam-4381	116	26	degk−1	degk−1	PROPN
ejpam-4381	116	27	g	g	NOUN
ejpam-4381	116	28	(	(	PUNCT
ejpam-4381	116	29	a	a	NOUN
ejpam-4381	116	30	)	)	PUNCT
ejpam-4381	116	31	+	+	CCONJ
ejpam-4381	116	32	2	2	NUM
ejpam-4381	116	33	+	+	CCONJ
ejpam-4381	116	34	|v	|v	X
ejpam-4381	116	35	(	(	PUNCT
ejpam-4381	116	36	h)|	h)|	PROPN
ejpam-4381	116	37	(	(	PUNCT
ejpam-4381	116	38	degk−2	degk−2	PROPN
ejpam-4381	116	39	g	g	PROPN
ejpam-4381	116	40	(	(	PUNCT
ejpam-4381	116	41	a	a	NOUN
ejpam-4381	116	42	)	)	PUNCT
ejpam-4381	116	43	+	+	CCONJ
ejpam-4381	116	44	1	1	X
ejpam-4381	116	45	)	)	PUNCT
ejpam-4381	116	46	−	−	NOUN
ejpam-4381	116	47	2	2	NUM
ejpam-4381	116	48	(	(	PUNCT
ejpam-4381	116	49	degk−2	degk−2	X
ejpam-4381	116	50	g	g	PROPN
ejpam-4381	116	51	(	(	PUNCT
ejpam-4381	116	52	a	a	NOUN
ejpam-4381	116	53	)	)	PUNCT
ejpam-4381	116	54	+	+	CCONJ
ejpam-4381	116	55	1	1	X
ejpam-4381	116	56	)	)	PUNCT
ejpam-4381	116	57	|sp|	|sp|	PROPN
ejpam-4381	116	58	≥	≥	PRON
ejpam-4381	116	59	degk−1	degk−1	ADV
ejpam-4381	116	60	g	g	NOUN
ejpam-4381	116	61	(	(	PUNCT
ejpam-4381	116	62	a	a	NOUN
ejpam-4381	116	63	)	)	PUNCT
ejpam-4381	116	64	+	+	CCONJ
ejpam-4381	116	65	2	2	NUM
ejpam-4381	116	66	+	+	CCONJ
ejpam-4381	116	67	|v	|v	X
ejpam-4381	116	68	(	(	PUNCT
ejpam-4381	116	69	h)|	h)|	PROPN
ejpam-4381	116	70	(	(	PUNCT
ejpam-4381	116	71	degk−2	degk−2	PROPN
ejpam-4381	116	72	g	g	PROPN
ejpam-4381	116	73	(	(	PUNCT
ejpam-4381	116	74	a	a	NOUN
ejpam-4381	116	75	)	)	PUNCT
ejpam-4381	117	1	+	+	CCONJ
ejpam-4381	117	2	1	1	X
ejpam-4381	117	3	)	)	PUNCT
ejpam-4381	117	4	−2	−2	NOUN
ejpam-4381	117	5	(	(	PUNCT
ejpam-4381	117	6	degk−2	degk−2	X
ejpam-4381	117	7	g	g	PROPN
ejpam-4381	117	8	(	(	PUNCT
ejpam-4381	117	9	a	a	NOUN
ejpam-4381	117	10	)	)	PUNCT
ejpam-4381	118	1	+	+	NOUN
ejpam-4381	118	2	1	1	X
ejpam-4381	118	3	)	)	PUNCT
ejpam-4381	118	4	[	[	PUNCT
ejpam-4381	118	5	|v	|v	PROPN
ejpam-4381	118	6	(	(	PUNCT
ejpam-4381	118	7	h)|	h)|	PROPN
ejpam-4381	118	8	(	(	PUNCT
ejpam-4381	118	9	δk−2(g	δk−2(g	PROPN
ejpam-4381	118	10	)	)	PUNCT
ejpam-4381	118	11	+	+	CCONJ
ejpam-4381	118	12	1	1	X
ejpam-4381	118	13	)	)	PUNCT
ejpam-4381	118	14	+	+	CCONJ
ejpam-4381	118	15	δk−1(g	δk−1(g	PROPN
ejpam-4381	118	16	)	)	PUNCT
ejpam-4381	119	1	+	+	CCONJ
ejpam-4381	119	2	2	2	NUM
ejpam-4381	119	3	2	2	NUM
ejpam-4381	119	4	(	(	PUNCT
ejpam-4381	119	5	∆k−2(g	∆k−2(g	X
ejpam-4381	119	6	)	)	PUNCT
ejpam-4381	119	7	+	+	NUM
ejpam-4381	119	8	1	1	NUM
ejpam-4381	119	9	)	)	PUNCT
ejpam-4381	119	10	]	]	PUNCT
ejpam-4381	120	1	≥	≥	VERB
ejpam-4381	120	2	degk−1	degk−1	ADV
ejpam-4381	120	3	g	g	NOUN
ejpam-4381	120	4	(	(	PUNCT
ejpam-4381	120	5	a	a	NOUN
ejpam-4381	120	6	)	)	PUNCT
ejpam-4381	120	7	+	+	CCONJ
ejpam-4381	120	8	2	2	NUM
ejpam-4381	120	9	+	+	CCONJ
ejpam-4381	120	10	+	+	ADJ
ejpam-4381	120	11	|v	|v	X
ejpam-4381	120	12	(	(	PUNCT
ejpam-4381	120	13	h)|	h)|	PROPN
ejpam-4381	120	14	(	(	PUNCT
ejpam-4381	120	15	degk−2	degk−2	PROPN
ejpam-4381	120	16	g	g	PROPN
ejpam-4381	120	17	(	(	PUNCT
ejpam-4381	120	18	a	a	NOUN
ejpam-4381	120	19	)	)	PUNCT
ejpam-4381	120	20	+	+	CCONJ
ejpam-4381	120	21	1	1	X
ejpam-4381	120	22	)	)	PUNCT
ejpam-4381	120	23	−	−	PROPN
ejpam-4381	121	1	(	(	PUNCT
ejpam-4381	121	2	degk−2	degk−2	X
ejpam-4381	121	3	g	g	PROPN
ejpam-4381	121	4	(	(	PUNCT
ejpam-4381	121	5	a	a	NOUN
ejpam-4381	121	6	)	)	PUNCT
ejpam-4381	121	7	+	+	NOUN
ejpam-4381	121	8	1	1	X
ejpam-4381	121	9	)	)	PUNCT
ejpam-4381	121	10	[	[	PUNCT
ejpam-4381	121	11	|v	|v	PROPN
ejpam-4381	121	12	(	(	PUNCT
ejpam-4381	121	13	h)|	h)|	PROPN
ejpam-4381	121	14	(	(	PUNCT
ejpam-4381	121	15	degk−2	degk−2	PROPN
ejpam-4381	121	16	g	g	PROPN
ejpam-4381	121	17	(	(	PUNCT
ejpam-4381	121	18	a	a	NOUN
ejpam-4381	121	19	)	)	PUNCT
ejpam-4381	121	20	+	+	CCONJ
ejpam-4381	121	21	1	1	X
ejpam-4381	121	22	)	)	PUNCT
ejpam-4381	122	1	+	+	CCONJ
ejpam-4381	122	2	degk−1	degk−1	ADV
ejpam-4381	122	3	g	g	NOUN
ejpam-4381	122	4	(	(	PUNCT
ejpam-4381	122	5	a	a	NOUN
ejpam-4381	122	6	)	)	PUNCT
ejpam-4381	122	7	+	+	NOUN
ejpam-4381	122	8	2	2	NUM
ejpam-4381	122	9	(	(	PUNCT
ejpam-4381	122	10	degk−2	degk−2	NUM
ejpam-4381	122	11	g	g	PROPN
ejpam-4381	122	12	(	(	PUNCT
ejpam-4381	122	13	a	a	NOUN
ejpam-4381	122	14	)	)	PUNCT
ejpam-4381	122	15	+	+	NUM
ejpam-4381	122	16	1	1	NUM
ejpam-4381	122	17	)	)	PUNCT
ejpam-4381	122	18	]	]	PUNCT
ejpam-4381	123	1	=	=	PUNCT
ejpam-4381	123	2	degk−1	degk−1	ADJ
ejpam-4381	123	3	g	g	NOUN
ejpam-4381	123	4	(	(	PUNCT
ejpam-4381	123	5	a	a	NOUN
ejpam-4381	123	6	)	)	PUNCT
ejpam-4381	123	7	+	+	CCONJ
ejpam-4381	123	8	2	2	NUM
ejpam-4381	123	9	+	+	CCONJ
ejpam-4381	123	10	+	+	ADJ
ejpam-4381	123	11	|v	|v	X
ejpam-4381	123	12	(	(	PUNCT
ejpam-4381	123	13	h)|	h)|	PROPN
ejpam-4381	123	14	(	(	PUNCT
ejpam-4381	123	15	degk−2	degk−2	PROPN
ejpam-4381	123	16	g	g	PROPN
ejpam-4381	123	17	(	(	PUNCT
ejpam-4381	123	18	a	a	NOUN
ejpam-4381	123	19	)	)	PUNCT
ejpam-4381	123	20	+	+	CCONJ
ejpam-4381	123	21	1	1	X
ejpam-4381	123	22	)	)	PUNCT
ejpam-4381	123	23	−	−	PROPN
ejpam-4381	123	24	[	[	PUNCT
ejpam-4381	123	25	|v	|v	PROPN
ejpam-4381	123	26	(	(	PUNCT
ejpam-4381	123	27	h)|	h)|	PROPN
ejpam-4381	123	28	(	(	PUNCT
ejpam-4381	123	29	degk−2	degk−2	PROPN
ejpam-4381	123	30	g	g	PROPN
ejpam-4381	123	31	(	(	PUNCT
ejpam-4381	123	32	a	a	NOUN
ejpam-4381	123	33	)	)	PUNCT
ejpam-4381	123	34	+	+	CCONJ
ejpam-4381	123	35	1	1	X
ejpam-4381	123	36	)	)	PUNCT
ejpam-4381	123	37	+	+	CCONJ
ejpam-4381	123	38	degk−1	degk−1	ADV
ejpam-4381	123	39	g	g	NOUN
ejpam-4381	123	40	(	(	PUNCT
ejpam-4381	123	41	a	a	NOUN
ejpam-4381	123	42	)	)	PUNCT
ejpam-4381	123	43	+	+	CCONJ
ejpam-4381	123	44	2	2	X
ejpam-4381	123	45	]	]	PUNCT
ejpam-4381	123	46	=	=	SYM
ejpam-4381	123	47	0	0	X
ejpam-4381	123	48	.	.	PUNCT
ejpam-4381	124	1	thus	thus	ADV
ejpam-4381	124	2	,	,	PUNCT
ejpam-4381	124	3	s	s	VERB
ejpam-4381	124	4	is	be	AUX
ejpam-4381	124	5	a	a	DET
ejpam-4381	124	6	distance	distance	NOUN
ejpam-4381	124	7	k	k	ADJ
ejpam-4381	124	8	-	-	PUNCT
ejpam-4381	124	9	cost	cost	ADJ
ejpam-4381	124	10	effective	effective	ADJ
ejpam-4381	124	11	set	set	NOUN
ejpam-4381	124	12	in	in	ADP
ejpam-4381	124	13	g	g	PROPN
ejpam-4381	124	14	◦	◦	NOUN
ejpam-4381	124	15	h.	h.	NOUN
ejpam-4381	124	16	corollary	corollary	ADJ
ejpam-4381	124	17	3	3	X
ejpam-4381	124	18	.	.	PUNCT
ejpam-4381	125	1	let	let	VERB
ejpam-4381	125	2	g	g	NOUN
ejpam-4381	125	3	and	and	CCONJ
ejpam-4381	125	4	h	h	NOUN
ejpam-4381	125	5	be	be	AUX
ejpam-4381	125	6	connected	connect	VERB
ejpam-4381	125	7	graphs	graph	NOUN
ejpam-4381	125	8	and	and	CCONJ
ejpam-4381	125	9	k	k	X
ejpam-4381	125	10	≥	≥	NUM
ejpam-4381	125	11	1	1	NUM
ejpam-4381	125	12	be	be	AUX
ejpam-4381	125	13	an	an	DET
ejpam-4381	125	14	integer	integer	NOUN
ejpam-4381	125	15	.	.	PUNCT
ejpam-4381	126	1	then	then	ADV
ejpam-4381	126	2	(	(	PUNCT
ejpam-4381	126	3	i	i	NOUN
ejpam-4381	126	4	)	)	PUNCT
ejpam-4381	126	5	αk	αk	NOUN
ejpam-4381	126	6	ce(g	ce(g	NOUN
ejpam-4381	126	7	◦	◦	NOUN
ejpam-4381	126	8	h	h	NOUN
ejpam-4381	126	9	)	)	PUNCT
ejpam-4381	126	10	≥	≥	NOUN
ejpam-4381	126	11	|v	|v	X
ejpam-4381	126	12	(	(	PUNCT
ejpam-4381	126	13	g)|αk	g)|αk	NOUN
ejpam-4381	126	14	ce(h	ce(h	NOUN
ejpam-4381	126	15	)	)	PUNCT
ejpam-4381	126	16	,	,	PUNCT
ejpam-4381	126	17	for	for	ADP
ejpam-4381	126	18	k	k	PROPN
ejpam-4381	126	19	=	=	SYM
ejpam-4381	126	20	1	1	NUM
ejpam-4381	126	21	,	,	PUNCT
ejpam-4381	126	22	2	2	NUM
ejpam-4381	126	23	.	.	PUNCT
ejpam-4381	126	24	(	(	PUNCT
ejpam-4381	126	25	ii	ii	NOUN
ejpam-4381	126	26	)	)	PUNCT
ejpam-4381	126	27	αk	αk	NOUN
ejpam-4381	126	28	ce(g	ce(g	PUNCT
ejpam-4381	126	29	◦	◦	NOUN
ejpam-4381	126	30	h	h	NOUN
ejpam-4381	126	31	)	)	PUNCT
ejpam-4381	126	32	≥	≥	NOUN
ejpam-4381	126	33	|v	|v	PROPN
ejpam-4381	126	34	(	(	PUNCT
ejpam-4381	126	35	g)|	g)|	PROPN
ejpam-4381	126	36	|v	|v	PROPN
ejpam-4381	126	37	(	(	PUNCT
ejpam-4381	126	38	h)|	h)|	PROPN
ejpam-4381	126	39	(	(	PUNCT
ejpam-4381	126	40	δk−2(g)+1	δk−2(g)+1	NOUN
ejpam-4381	126	41	)	)	PUNCT
ejpam-4381	127	1	+	+	VERB
ejpam-4381	127	2	δk−1(g)+2	δk−1(g)+2	X
ejpam-4381	127	3	2	2	NUM
ejpam-4381	127	4	(	(	PUNCT
ejpam-4381	127	5	∆k−2(g)+1	∆k−2(g)+1	ADV
ejpam-4381	127	6	)	)	PUNCT
ejpam-4381	127	7	,	,	PUNCT
ejpam-4381	127	8	for	for	ADP
ejpam-4381	127	9	k	k	PROPN
ejpam-4381	127	10	≥	≥	NUM
ejpam-4381	127	11	3	3	NUM
ejpam-4381	127	12	.	.	PROPN
ejpam-4381	127	13	2.3	2.3	NUM
ejpam-4381	127	14	.	.	PUNCT
ejpam-4381	127	15	lexicographic	lexicographic	ADJ
ejpam-4381	127	16	product	product	NOUN
ejpam-4381	127	17	of	of	ADP
ejpam-4381	127	18	graphs	graph	NOUN
ejpam-4381	127	19	this	this	DET
ejpam-4381	127	20	section	section	NOUN
ejpam-4381	127	21	provides	provide	VERB
ejpam-4381	127	22	a	a	DET
ejpam-4381	127	23	neccesary	neccesary	ADJ
ejpam-4381	127	24	condition	condition	NOUN
ejpam-4381	127	25	for	for	ADP
ejpam-4381	127	26	a	a	DET
ejpam-4381	127	27	distance	distance	NOUN
ejpam-4381	127	28	k	k	ADJ
ejpam-4381	127	29	-	-	PUNCT
ejpam-4381	127	30	cost	cost	ADJ
ejpam-4381	127	31	effective	effective	ADJ
ejpam-4381	127	32	set	set	NOUN
ejpam-4381	127	33	in	in	ADP
ejpam-4381	127	34	the	the	DET
ejpam-4381	127	35	lexicographic	lexicographic	ADJ
ejpam-4381	127	36	product	product	NOUN
ejpam-4381	127	37	of	of	ADP
ejpam-4381	127	38	two	two	NUM
ejpam-4381	127	39	graphs	graph	NOUN
ejpam-4381	127	40	.	.	PUNCT
ejpam-4381	128	1	consequently	consequently	ADV
ejpam-4381	128	2	,	,	PUNCT
ejpam-4381	128	3	a	a	DET
ejpam-4381	128	4	lower	lower	ADV
ejpam-4381	128	5	bound	bind	VERB
ejpam-4381	128	6	for	for	ADP
ejpam-4381	128	7	the	the	DET
ejpam-4381	128	8	upper	upper	ADJ
ejpam-4381	128	9	distance	distance	NOUN
ejpam-4381	128	10	k	k	ADJ
ejpam-4381	128	11	-	-	PUNCT
ejpam-4381	128	12	cost	cost	ADJ
ejpam-4381	128	13	effective	effective	ADJ
ejpam-4381	128	14	number	number	NOUN
ejpam-4381	128	15	of	of	ADP
ejpam-4381	128	16	this	this	DET
ejpam-4381	128	17	graph	graph	NOUN
ejpam-4381	128	18	is	be	AUX
ejpam-4381	128	19	given	give	VERB
ejpam-4381	128	20	.	.	PUNCT
ejpam-4381	129	1	the	the	DET
ejpam-4381	129	2	lexicographic	lexicographic	ADJ
ejpam-4381	129	3	productg[h	productg[h	NOUN
ejpam-4381	129	4	]	]	PUNCT
ejpam-4381	129	5	of	of	ADP
ejpam-4381	129	6	two	two	NUM
ejpam-4381	129	7	graphsg	graphsg	NOUN
ejpam-4381	129	8	andh	andh	NOUN
ejpam-4381	129	9	is	be	AUX
ejpam-4381	129	10	the	the	DET
ejpam-4381	129	11	graph	graph	NOUN
ejpam-4381	129	12	with	with	ADP
ejpam-4381	129	13	v	v	NOUN
ejpam-4381	129	14	(	(	PUNCT
ejpam-4381	129	15	g[h	g[h	PROPN
ejpam-4381	129	16	]	]	PUNCT
ejpam-4381	129	17	)	)	PUNCT
ejpam-4381	129	18	=	=	SYM
ejpam-4381	129	19	v	v	X
ejpam-4381	129	20	(	(	PUNCT
ejpam-4381	129	21	g)×	g)×	NOUN
ejpam-4381	129	22	v	v	NOUN
ejpam-4381	129	23	(	(	PUNCT
ejpam-4381	129	24	h	h	NOUN
ejpam-4381	129	25	)	)	PUNCT
ejpam-4381	129	26	and	and	CCONJ
ejpam-4381	129	27	(	(	PUNCT
ejpam-4381	129	28	u	u	NOUN
ejpam-4381	129	29	,	,	PUNCT
ejpam-4381	129	30	v)(u′	v)(u′	NOUN
ejpam-4381	129	31	,	,	PUNCT
ejpam-4381	129	32	v′	v′	NOUN
ejpam-4381	129	33	)	)	PUNCT
ejpam-4381	129	34	∈	∈	NOUN
ejpam-4381	129	35	e(g[h	e(g[h	NOUN
ejpam-4381	129	36	]	]	PUNCT
ejpam-4381	129	37	)	)	PUNCT
ejpam-4381	130	1	if	if	SCONJ
ejpam-4381	130	2	and	and	CCONJ
ejpam-4381	130	3	only	only	ADV
ejpam-4381	130	4	if	if	SCONJ
ejpam-4381	130	5	either	either	CCONJ
ejpam-4381	130	6	uu′	uu′	PROPN
ejpam-4381	130	7	∈	∈	PROPN
ejpam-4381	130	8	e(g	e(g	PROPN
ejpam-4381	130	9	)	)	PUNCT
ejpam-4381	130	10	or	or	CCONJ
ejpam-4381	130	11	u	u	X
ejpam-4381	130	12	=	=	PUNCT
ejpam-4381	130	13	u′	u′	PROPN
ejpam-4381	130	14	and	and	CCONJ
ejpam-4381	130	15	vv′	vv′	NOUN
ejpam-4381	130	16	∈	∈	PROPN
ejpam-4381	130	17	e(h	e(h	PROPN
ejpam-4381	130	18	)	)	PUNCT
ejpam-4381	130	19	.	.	PUNCT
ejpam-4381	131	1	let	let	VERB
ejpam-4381	131	2	(	(	PUNCT
ejpam-4381	131	3	u	u	NOUN
ejpam-4381	131	4	,	,	PUNCT
ejpam-4381	131	5	v	v	NOUN
ejpam-4381	131	6	)	)	PUNCT
ejpam-4381	131	7	∈	∈	PROPN
ejpam-4381	131	8	s	s	PART
ejpam-4381	131	9	and	and	CCONJ
ejpam-4381	131	10	k	k	PROPN
ejpam-4381	131	11	≥	≥	NUM
ejpam-4381	131	12	1	1	NUM
ejpam-4381	131	13	be	be	AUX
ejpam-4381	131	14	an	an	DET
ejpam-4381	131	15	integer	integer	NOUN
ejpam-4381	131	16	.	.	PUNCT
ejpam-4381	132	1	then	then	ADV
ejpam-4381	132	2	|nk	|nk	ADP
ejpam-4381	132	3	g[h](u	g[h](u	PROPN
ejpam-4381	132	4	,	,	PUNCT
ejpam-4381	132	5	v)∩	v)∩	X
ejpam-4381	132	6	(	(	PUNCT
ejpam-4381	132	7	v	v	NOUN
ejpam-4381	132	8	(	(	PUNCT
ejpam-4381	132	9	g[h	g[h	PROPN
ejpam-4381	132	10	]	]	PUNCT
ejpam-4381	132	11	)	)	PUNCT
ejpam-4381	132	12	\	\	PROPN
ejpam-4381	132	13	s)|	s)|	NOUN
ejpam-4381	132	14	=	=	PUNCT
ejpam-4381	132	15	|nk	|nk	NUM
ejpam-4381	132	16	hu	hu	PROPN
ejpam-4381	132	17	(	(	PUNCT
ejpam-4381	132	18	v)∩	v)∩	X
ejpam-4381	132	19	(	(	PUNCT
ejpam-4381	132	20	v	v	NOUN
ejpam-4381	132	21	(	(	PUNCT
ejpam-4381	132	22	h	h	NOUN
ejpam-4381	132	23	)	)	PUNCT
ejpam-4381	132	24	\	\	NOUN
ejpam-4381	132	25	tu)|+	tu)|+	PROPN
ejpam-4381	133	1	|nk	|nk	NUM
ejpam-4381	133	2	g(u)∩	g(u)∩	PROPN
ejpam-4381	133	3	(	(	PUNCT
ejpam-4381	133	4	v	v	NOUN
ejpam-4381	133	5	(	(	PUNCT
ejpam-4381	133	6	g	g	NOUN
ejpam-4381	133	7	)	)	PUNCT
ejpam-4381	133	8	\a)||v	\a)||v	PUNCT
ejpam-4381	133	9	(	(	PUNCT
ejpam-4381	133	10	h)|	h)|	PROPN
ejpam-4381	133	11	+	+	CCONJ
ejpam-4381	133	12	∑	∑	PROPN
ejpam-4381	133	13	x∈nk	x∈nk	PROPN
ejpam-4381	133	14	g(u)∩a	g(u)∩a	NOUN
ejpam-4381	133	15	|v	|v	PROPN
ejpam-4381	133	16	(	(	PUNCT
ejpam-4381	133	17	h	h	NOUN
ejpam-4381	133	18	)	)	PUNCT
ejpam-4381	133	19	\	\	NOUN
ejpam-4381	133	20	tx|	tx|	PROPN
ejpam-4381	133	21	(	(	PUNCT
ejpam-4381	133	22	1	1	NUM
ejpam-4381	133	23	)	)	PUNCT
ejpam-4381	133	24	julius	julius	PROPN
ejpam-4381	133	25	g.	g.	PROPN
ejpam-4381	133	26	caadan	caadan	PROPN
ejpam-4381	133	27	,	,	PUNCT
ejpam-4381	133	28	rolando	rolando	PROPN
ejpam-4381	133	29	n.	n.	PROPN
ejpam-4381	133	30	paluga	paluga	PROPN
ejpam-4381	133	31	,	,	PUNCT
ejpam-4381	133	32	imelda	imelda	PROPN
ejpam-4381	133	33	s.	s.	PROPN
ejpam-4381	133	34	aniversario	aniversario	PROPN
ejpam-4381	133	35	/	/	SYM
ejpam-4381	133	36	eur	eur	PROPN
ejpam-4381	133	37	.	.	PUNCT
ejpam-4381	134	1	j.	j.	PROPN
ejpam-4381	134	2	pure	pure	PROPN
ejpam-4381	134	3	appl	appl	PROPN
ejpam-4381	134	4	.	.	PROPN
ejpam-4381	134	5	math	math	PROPN
ejpam-4381	134	6	,	,	PUNCT
ejpam-4381	134	7	16	16	NUM
ejpam-4381	134	8	(	(	PUNCT
ejpam-4381	134	9	1	1	NUM
ejpam-4381	134	10	)	)	PUNCT
ejpam-4381	134	11	(	(	PUNCT
ejpam-4381	134	12	2023	2023	NUM
ejpam-4381	134	13	)	)	PUNCT
ejpam-4381	134	14	,	,	PUNCT
ejpam-4381	134	15	261	261	NUM
ejpam-4381	134	16	-	-	SYM
ejpam-4381	134	17	270	270	NUM
ejpam-4381	134	18	266	266	NUM
ejpam-4381	134	19	and	and	CCONJ
ejpam-4381	134	20	|nk	|nk	ADP
ejpam-4381	134	21	g[h](u	g[h](u	PROPN
ejpam-4381	134	22	,	,	PUNCT
ejpam-4381	134	23	v	v	NOUN
ejpam-4381	134	24	)	)	PUNCT
ejpam-4381	134	25	∩	∩	NOUN
ejpam-4381	134	26	s|	s|	NOUN
ejpam-4381	134	27	=	=	SYM
ejpam-4381	134	28	∑	∑	PUNCT
ejpam-4381	134	29	x∈nk	x∈nk	PROPN
ejpam-4381	134	30	g(u)∩a	g(u)∩a	NOUN
ejpam-4381	134	31	|tx|+	|tx|+	X
ejpam-4381	134	32	|nk	|nk	NUM
ejpam-4381	134	33	hu	hu	PROPN
ejpam-4381	134	34	(	(	PUNCT
ejpam-4381	134	35	v	v	NOUN
ejpam-4381	134	36	)	)	PUNCT
ejpam-4381	134	37	∩	∩	NOUN
ejpam-4381	134	38	tu|	tu|	PROPN
ejpam-4381	134	39	.	.	PUNCT
ejpam-4381	134	40	(	(	PUNCT
ejpam-4381	134	41	2	2	X
ejpam-4381	134	42	)	)	PUNCT
ejpam-4381	134	43	theorem	theorem	NOUN
ejpam-4381	134	44	4	4	NUM
ejpam-4381	134	45	.	.	PUNCT
ejpam-4381	135	1	let	let	VERB
ejpam-4381	135	2	g	g	NOUN
ejpam-4381	135	3	and	and	CCONJ
ejpam-4381	135	4	h	h	NOUN
ejpam-4381	135	5	be	be	AUX
ejpam-4381	135	6	connected	connect	VERB
ejpam-4381	135	7	graphs	graph	NOUN
ejpam-4381	135	8	and	and	CCONJ
ejpam-4381	135	9	k	k	X
ejpam-4381	135	10	≥	≥	NUM
ejpam-4381	135	11	2	2	NUM
ejpam-4381	135	12	be	be	AUX
ejpam-4381	135	13	an	an	DET
ejpam-4381	135	14	integer	integer	NOUN
ejpam-4381	135	15	.	.	PUNCT
ejpam-4381	136	1	let	let	VERB
ejpam-4381	136	2	a	a	DET
ejpam-4381	136	3	be	be	AUX
ejpam-4381	136	4	an	an	DET
ejpam-4381	136	5	αk	αk	NOUN
ejpam-4381	136	6	ce	ce	NOUN
ejpam-4381	136	7	-	-	NOUN
ejpam-4381	136	8	set	set	NOUN
ejpam-4381	136	9	in	in	ADP
ejpam-4381	136	10	g.	g.	PROPN
ejpam-4381	136	11	let	let	VERB
ejpam-4381	136	12	s	s	NOUN
ejpam-4381	136	13	=	=	PUNCT
ejpam-4381	136	14	⋃	⋃	NOUN
ejpam-4381	136	15	a∈a({a	a∈a({a	PROPN
ejpam-4381	136	16	}	}	PUNCT
ejpam-4381	136	17	×	×	PROPN
ejpam-4381	136	18	ta	ta	NOUN
ejpam-4381	136	19	)	)	PUNCT
ejpam-4381	136	20	such	such	ADJ
ejpam-4381	136	21	that	that	DET
ejpam-4381	136	22	|{a	|{a	NOUN
ejpam-4381	136	23	}	}	PUNCT
ejpam-4381	136	24	×	×	PROPN
ejpam-4381	136	25	ta|	ta|	PROPN
ejpam-4381	136	26	≤	≤	PROPN
ejpam-4381	136	27	|v	|v	NOUN
ejpam-4381	136	28	(	(	PUNCT
ejpam-4381	136	29	h)|+1	h)|+1	NOUN
ejpam-4381	136	30	2	2	NUM
ejpam-4381	136	31	,	,	PUNCT
ejpam-4381	136	32	for	for	ADP
ejpam-4381	136	33	each	each	DET
ejpam-4381	136	34	a	a	DET
ejpam-4381	136	35	∈	∈	PROPN
ejpam-4381	136	36	a.	a.	NOUN
ejpam-4381	137	1	then	then	ADV
ejpam-4381	137	2	s	s	VERB
ejpam-4381	137	3	is	be	AUX
ejpam-4381	137	4	a	a	DET
ejpam-4381	137	5	distance	distance	NOUN
ejpam-4381	137	6	k	k	ADJ
ejpam-4381	137	7	-	-	PUNCT
ejpam-4381	137	8	cost	cost	NOUN
ejpam-4381	137	9	effective	effective	ADJ
ejpam-4381	137	10	set	set	NOUN
ejpam-4381	137	11	in	in	ADP
ejpam-4381	137	12	g[h	g[h	NOUN
ejpam-4381	137	13	]	]	PUNCT
ejpam-4381	137	14	.	.	PUNCT
ejpam-4381	138	1	proof	proof	NOUN
ejpam-4381	138	2	:	:	PUNCT
ejpam-4381	138	3	let	let	VERB
ejpam-4381	138	4	k	k	PROPN
ejpam-4381	138	5	≥	≥	NUM
ejpam-4381	138	6	2	2	NUM
ejpam-4381	138	7	be	be	AUX
ejpam-4381	138	8	an	an	DET
ejpam-4381	138	9	integer	integer	NOUN
ejpam-4381	138	10	and	and	CCONJ
ejpam-4381	138	11	a	a	DET
ejpam-4381	138	12	be	be	NOUN
ejpam-4381	138	13	an	an	DET
ejpam-4381	138	14	αk	αk	NOUN
ejpam-4381	138	15	ce	ce	NOUN
ejpam-4381	138	16	-	-	NOUN
ejpam-4381	138	17	set	set	NOUN
ejpam-4381	138	18	in	in	ADP
ejpam-4381	138	19	g.	g.	PROPN
ejpam-4381	138	20	let	let	VERB
ejpam-4381	138	21	s	s	NOUN
ejpam-4381	138	22	=	=	PUNCT
ejpam-4381	138	23	⋃	⋃	NOUN
ejpam-4381	138	24	a∈a({a	a∈a({a	PROPN
ejpam-4381	138	25	}	}	PUNCT
ejpam-4381	138	26	×	×	PROPN
ejpam-4381	138	27	ta	ta	NOUN
ejpam-4381	138	28	)	)	PUNCT
ejpam-4381	138	29	such	such	ADJ
ejpam-4381	138	30	that	that	PRON
ejpam-4381	138	31	|{a	|{a	NOUN
ejpam-4381	138	32	}	}	PUNCT
ejpam-4381	138	33	×	×	PROPN
ejpam-4381	138	34	ta|	ta|	PROPN
ejpam-4381	138	35	≤	≤	PROPN
ejpam-4381	138	36	|v	|v	NOUN
ejpam-4381	138	37	(	(	PUNCT
ejpam-4381	138	38	h)|+1	h)|+1	NOUN
ejpam-4381	138	39	2	2	NUM
ejpam-4381	138	40	,	,	PUNCT
ejpam-4381	138	41	for	for	ADP
ejpam-4381	138	42	each	each	DET
ejpam-4381	138	43	a	a	DET
ejpam-4381	138	44	∈	∈	PROPN
ejpam-4381	138	45	a.	a.	NOUN
ejpam-4381	138	46	let	let	NOUN
ejpam-4381	138	47	(	(	PUNCT
ejpam-4381	138	48	u	u	NOUN
ejpam-4381	138	49	,	,	PUNCT
ejpam-4381	138	50	v	v	NOUN
ejpam-4381	138	51	)	)	PUNCT
ejpam-4381	138	52	∈	∈	PROPN
ejpam-4381	138	53	s.	s.	PROPN
ejpam-4381	138	54	then	then	ADV
ejpam-4381	138	55	using	use	VERB
ejpam-4381	138	56	equations	equation	NOUN
ejpam-4381	138	57	(	(	PUNCT
ejpam-4381	138	58	1	1	NUM
ejpam-4381	138	59	)	)	PUNCT
ejpam-4381	138	60	and	and	CCONJ
ejpam-4381	138	61	(	(	PUNCT
ejpam-4381	138	62	2	2	NUM
ejpam-4381	138	63	)	)	PUNCT
ejpam-4381	138	64	,	,	PUNCT
ejpam-4381	138	65	we	we	PRON
ejpam-4381	138	66	have	have	VERB
ejpam-4381	138	67	|nk	|nk	ADP
ejpam-4381	138	68	g[h](u	g[h](u	NOUN
ejpam-4381	138	69	,	,	PUNCT
ejpam-4381	138	70	v	v	NOUN
ejpam-4381	138	71	)	)	PUNCT
ejpam-4381	138	72	∩	∩	NOUN
ejpam-4381	138	73	s|	s|	NOUN
ejpam-4381	138	74	=	=	SYM
ejpam-4381	138	75	∑	∑	PUNCT
ejpam-4381	138	76	x∈nk	x∈nk	PROPN
ejpam-4381	138	77	g(u)∩a	g(u)∩a	NOUN
ejpam-4381	138	78	|tx|+	|tx|+	X
ejpam-4381	138	79	|nk	|nk	NUM
ejpam-4381	138	80	hu	hu	PROPN
ejpam-4381	138	81	(	(	PUNCT
ejpam-4381	138	82	v	v	NOUN
ejpam-4381	138	83	)	)	PUNCT
ejpam-4381	138	84	∩	∩	NOUN
ejpam-4381	138	85	tu|	tu|	ADP
ejpam-4381	138	86	=	=	PUNCT
ejpam-4381	138	87	∑	∑	PROPN
ejpam-4381	138	88	x∈nk	x∈nk	PROPN
ejpam-4381	138	89	g(u)∩a	g(u)∩a	NOUN
ejpam-4381	138	90	|tx|+	|tx|+	NUM
ejpam-4381	138	91	|tu|	|tu|	NOUN
ejpam-4381	138	92	−	−	NOUN
ejpam-4381	138	93	1	1	NUM
ejpam-4381	138	94	.	.	PUNCT
ejpam-4381	138	95	and	and	CCONJ
ejpam-4381	138	96	|nk	|nk	ADP
ejpam-4381	138	97	g[h](u	g[h](u	PROPN
ejpam-4381	138	98	,	,	PUNCT
ejpam-4381	138	99	v	v	NOUN
ejpam-4381	138	100	)	)	PUNCT
ejpam-4381	138	101	∩	∩	NOUN
ejpam-4381	138	102	(	(	PUNCT
ejpam-4381	138	103	v	v	NOUN
ejpam-4381	138	104	(	(	PUNCT
ejpam-4381	138	105	g[h	g[h	PROPN
ejpam-4381	138	106	]	]	PUNCT
ejpam-4381	138	107	)	)	PUNCT
ejpam-4381	138	108	\	\	PROPN
ejpam-4381	138	109	s)|	s)|	NOUN
ejpam-4381	139	1	=	=	PROPN
ejpam-4381	139	2	|nk	|nk	NUM
ejpam-4381	139	3	hu	hu	PROPN
ejpam-4381	139	4	(	(	PUNCT
ejpam-4381	139	5	v	v	NOUN
ejpam-4381	139	6	)	)	PUNCT
ejpam-4381	139	7	∩	∩	NOUN
ejpam-4381	139	8	(	(	PUNCT
ejpam-4381	139	9	v	v	NOUN
ejpam-4381	139	10	(	(	PUNCT
ejpam-4381	139	11	h	h	NOUN
ejpam-4381	139	12	)	)	PUNCT
ejpam-4381	139	13	\	\	NOUN
ejpam-4381	139	14	tu)|+	tu)|+	PROPN
ejpam-4381	139	15	|nk	|nk	ADP
ejpam-4381	139	16	g(u	g(u	PROPN
ejpam-4381	139	17	)	)	PUNCT
ejpam-4381	139	18	∩	∩	NOUN
ejpam-4381	139	19	(	(	PUNCT
ejpam-4381	139	20	v	v	NOUN
ejpam-4381	139	21	(	(	PUNCT
ejpam-4381	139	22	g	g	NOUN
ejpam-4381	139	23	)	)	PUNCT
ejpam-4381	139	24	\a)||v	\a)||v	PUNCT
ejpam-4381	139	25	(	(	PUNCT
ejpam-4381	139	26	h)|	h)|	PROPN
ejpam-4381	139	27	+	+	CCONJ
ejpam-4381	139	28	∑	∑	PROPN
ejpam-4381	139	29	x∈nk	x∈nk	PROPN
ejpam-4381	139	30	g(u)∩a	g(u)∩a	NOUN
ejpam-4381	139	31	|v	|v	PROPN
ejpam-4381	139	32	(	(	PUNCT
ejpam-4381	139	33	h	h	NOUN
ejpam-4381	139	34	)	)	PUNCT
ejpam-4381	139	35	\	\	PUNCT
ejpam-4381	139	36	tx|	tx|	PROPN
ejpam-4381	139	37	=	=	SYM
ejpam-4381	139	38	|v	|v	PROPN
ejpam-4381	139	39	(	(	PUNCT
ejpam-4381	139	40	h)|	h)|	PROPN
ejpam-4381	139	41	−	−	PROPN
ejpam-4381	139	42	|tu|+	|tu|+	NOUN
ejpam-4381	139	43	|nk	|nk	ADP
ejpam-4381	139	44	g(u	g(u	PROPN
ejpam-4381	139	45	)	)	PUNCT
ejpam-4381	139	46	∩	∩	NOUN
ejpam-4381	139	47	(	(	PUNCT
ejpam-4381	139	48	v	v	NOUN
ejpam-4381	139	49	(	(	PUNCT
ejpam-4381	139	50	g	g	NOUN
ejpam-4381	139	51	)	)	PUNCT
ejpam-4381	139	52	\a)||v	\a)||v	PUNCT
ejpam-4381	139	53	(	(	PUNCT
ejpam-4381	139	54	h)|	h)|	PROPN
ejpam-4381	139	55	+	+	CCONJ
ejpam-4381	139	56	∑	∑	PROPN
ejpam-4381	139	57	x∈nk	x∈nk	ADJ
ejpam-4381	139	58	g(u)∩a	g(u)∩a	NOUN
ejpam-4381	139	59	[	[	PUNCT
ejpam-4381	139	60	|v	|v	PROPN
ejpam-4381	139	61	(	(	PUNCT
ejpam-4381	139	62	h)|	h)|	NOUN
ejpam-4381	139	63	−	−	PROPN
ejpam-4381	139	64	|tx|	|tx|	NOUN
ejpam-4381	139	65	]	]	PUNCT
ejpam-4381	139	66	.	.	PUNCT
ejpam-4381	140	1	hence	hence	ADV
ejpam-4381	140	2	,	,	PUNCT
ejpam-4381	140	3	|nk	|nk	ADP
ejpam-4381	140	4	g[h](u	g[h](u	PROPN
ejpam-4381	140	5	,	,	PUNCT
ejpam-4381	140	6	v	v	NOUN
ejpam-4381	140	7	)	)	PUNCT
ejpam-4381	140	8	∩	∩	NOUN
ejpam-4381	140	9	(	(	PUNCT
ejpam-4381	140	10	v	v	NOUN
ejpam-4381	140	11	(	(	PUNCT
ejpam-4381	140	12	g[h	g[h	PROPN
ejpam-4381	140	13	]	]	PUNCT
ejpam-4381	140	14	)	)	PUNCT
ejpam-4381	140	15	\	\	PROPN
ejpam-4381	140	16	s)|	s)|	NOUN
ejpam-4381	140	17	−	−	PROPN
ejpam-4381	140	18	|nk	|nk	ADP
ejpam-4381	140	19	g[h](u	g[h](u	PROPN
ejpam-4381	140	20	,	,	PUNCT
ejpam-4381	140	21	v	v	NOUN
ejpam-4381	140	22	)	)	PUNCT
ejpam-4381	140	23	∩	∩	NOUN
ejpam-4381	140	24	s|	s|	NOUN
ejpam-4381	140	25	=	=	PUNCT
ejpam-4381	140	26	|nk	|nk	PROPN
ejpam-4381	140	27	g(u	g(u	PROPN
ejpam-4381	140	28	)	)	PUNCT
ejpam-4381	140	29	∩	∩	NOUN
ejpam-4381	140	30	(	(	PUNCT
ejpam-4381	140	31	v	v	NOUN
ejpam-4381	140	32	(	(	PUNCT
ejpam-4381	140	33	g	g	NOUN
ejpam-4381	140	34	)	)	PUNCT
ejpam-4381	140	35	\a)||v	\a)||v	PUNCT
ejpam-4381	140	36	(	(	PUNCT
ejpam-4381	140	37	h)|	h)|	PROPN
ejpam-4381	140	38	+	+	CCONJ
ejpam-4381	140	39	∑	∑	PROPN
ejpam-4381	140	40	x∈nk	x∈nk	ADJ
ejpam-4381	140	41	g(u)∩a	g(u)∩a	NOUN
ejpam-4381	140	42	[	[	PUNCT
ejpam-4381	140	43	|v	|v	PROPN
ejpam-4381	140	44	(	(	PUNCT
ejpam-4381	140	45	h)|	h)|	NOUN
ejpam-4381	140	46	−	−	PROPN
ejpam-4381	140	47	2|tx|	2|tx|	PROPN
ejpam-4381	140	48	]	]	PUNCT
ejpam-4381	140	49	+	+	CCONJ
ejpam-4381	140	50	|v	|v	X
ejpam-4381	140	51	(	(	PUNCT
ejpam-4381	140	52	h)|	h)|	NOUN
ejpam-4381	140	53	−	−	PROPN
ejpam-4381	140	54	2|tu|+	2|tu|+	NOUN
ejpam-4381	140	55	1	1	NUM
ejpam-4381	140	56	≥	≥	NOUN
ejpam-4381	140	57	|nk	|nk	ADP
ejpam-4381	140	58	g(u	g(u	PROPN
ejpam-4381	140	59	)	)	PUNCT
ejpam-4381	140	60	∩	∩	NOUN
ejpam-4381	140	61	(	(	PUNCT
ejpam-4381	140	62	v	v	NOUN
ejpam-4381	140	63	(	(	PUNCT
ejpam-4381	140	64	g	g	NOUN
ejpam-4381	140	65	)	)	PUNCT
ejpam-4381	140	66	\a)||v	\a)||v	NOUN
ejpam-4381	140	67	(	(	PUNCT
ejpam-4381	140	68	h)|+	h)|+	ADJ
ejpam-4381	140	69	∑	∑	PUNCT
ejpam-4381	140	70	x∈nk	x∈nk	ADJ
ejpam-4381	140	71	g(u)∩a	g(u)∩a	NOUN
ejpam-4381	140	72	[	[	PUNCT
ejpam-4381	140	73	|v	|v	PROPN
ejpam-4381	140	74	(	(	PUNCT
ejpam-4381	140	75	h)|	h)|	PROPN
ejpam-4381	140	76	−	−	PROPN
ejpam-4381	140	77	2|v	2|v	PROPN
ejpam-4381	140	78	(	(	PUNCT
ejpam-4381	140	79	h)|	h)|	X
ejpam-4381	140	80	]	]	PUNCT
ejpam-4381	140	81	+	+	CCONJ
ejpam-4381	140	82	|v	|v	X
ejpam-4381	140	83	(	(	PUNCT
ejpam-4381	140	84	h)|	h)|	NOUN
ejpam-4381	140	85	−	−	PROPN
ejpam-4381	140	86	2|tu|+	2|tu|+	NOUN
ejpam-4381	140	87	1	1	X
ejpam-4381	140	88	=	=	SYM
ejpam-4381	140	89	|nk	|nk	PROPN
ejpam-4381	140	90	g(u	g(u	PROPN
ejpam-4381	140	91	)	)	PUNCT
ejpam-4381	140	92	∩	∩	NOUN
ejpam-4381	140	93	(	(	PUNCT
ejpam-4381	140	94	v	v	NOUN
ejpam-4381	140	95	(	(	PUNCT
ejpam-4381	140	96	g	g	NOUN
ejpam-4381	140	97	)	)	PUNCT
ejpam-4381	140	98	\a)||v	\a)||v	PUNCT
ejpam-4381	140	99	(	(	PUNCT
ejpam-4381	140	100	h)|	h)|	NOUN
ejpam-4381	140	101	−	−	PROPN
ejpam-4381	140	102	|nk	|nk	ADP
ejpam-4381	140	103	g(u	g(u	PROPN
ejpam-4381	140	104	)	)	PUNCT
ejpam-4381	140	105	∩a)||v	∩a)||v	PROPN
ejpam-4381	140	106	(	(	PUNCT
ejpam-4381	140	107	h)|	h)|	PROPN
ejpam-4381	140	108	+	+	CCONJ
ejpam-4381	140	109	|v	|v	PROPN
ejpam-4381	140	110	(	(	PUNCT
ejpam-4381	140	111	h)|	h)|	NOUN
ejpam-4381	140	112	−	−	PROPN
ejpam-4381	140	113	2|tu|+	2|tu|+	NOUN
ejpam-4381	140	114	1	1	X
ejpam-4381	141	1	=	=	PUNCT
ejpam-4381	141	2	[	[	PUNCT
ejpam-4381	141	3	|nk	|nk	NUM
ejpam-4381	141	4	g(u	g(u	PROPN
ejpam-4381	141	5	)	)	PUNCT
ejpam-4381	141	6	∩	∩	NOUN
ejpam-4381	141	7	(	(	PUNCT
ejpam-4381	141	8	v	v	NOUN
ejpam-4381	141	9	(	(	PUNCT
ejpam-4381	141	10	g	g	NOUN
ejpam-4381	141	11	)	)	PUNCT
ejpam-4381	141	12	\a)|	\a)|	X
ejpam-4381	141	13	−	−	PROPN
ejpam-4381	141	14	|nk	|nk	PROPN
ejpam-4381	141	15	g(u	g(u	PROPN
ejpam-4381	141	16	)	)	PUNCT
ejpam-4381	141	17	∩a|	∩a|	PUNCT
ejpam-4381	141	18	]	]	PUNCT
ejpam-4381	141	19	|v	|v	PROPN
ejpam-4381	141	20	(	(	PUNCT
ejpam-4381	141	21	h)|+	h)|+	ADJ
ejpam-4381	141	22	|v	|v	NOUN
ejpam-4381	141	23	(	(	PUNCT
ejpam-4381	141	24	h)|	h)|	NOUN
ejpam-4381	141	25	−	−	PROPN
ejpam-4381	141	26	2|tu|+	2|tu|+	NOUN
ejpam-4381	141	27	1	1	NUM
ejpam-4381	141	28	≥	≥	NOUN
ejpam-4381	141	29	[	[	PUNCT
ejpam-4381	141	30	|nk	|nk	NUM
ejpam-4381	141	31	g(u	g(u	PROPN
ejpam-4381	141	32	)	)	PUNCT
ejpam-4381	141	33	∩	∩	NOUN
ejpam-4381	141	34	(	(	PUNCT
ejpam-4381	141	35	v	v	NOUN
ejpam-4381	141	36	(	(	PUNCT
ejpam-4381	141	37	g	g	NOUN
ejpam-4381	141	38	)	)	PUNCT
ejpam-4381	141	39	\a)|	\a)|	X
ejpam-4381	141	40	−	−	PROPN
ejpam-4381	141	41	|nk	|nk	PROPN
ejpam-4381	141	42	g(u	g(u	PROPN
ejpam-4381	141	43	)	)	PUNCT
ejpam-4381	141	44	∩a|	∩a|	PUNCT
ejpam-4381	141	45	]	]	PUNCT
ejpam-4381	141	46	|v	|v	PROPN
ejpam-4381	141	47	(	(	PUNCT
ejpam-4381	141	48	h)|+	h)|+	ADJ
ejpam-4381	141	49	|v	|v	NOUN
ejpam-4381	141	50	(	(	PUNCT
ejpam-4381	141	51	h)|	h)|	PROPN
ejpam-4381	141	52	julius	julius	PROPN
ejpam-4381	141	53	g.	g.	PROPN
ejpam-4381	141	54	caadan	caadan	PROPN
ejpam-4381	141	55	,	,	PUNCT
ejpam-4381	141	56	rolando	rolando	PROPN
ejpam-4381	141	57	n.	n.	PROPN
ejpam-4381	141	58	paluga	paluga	PROPN
ejpam-4381	141	59	,	,	PUNCT
ejpam-4381	141	60	imelda	imelda	PROPN
ejpam-4381	141	61	s.	s.	PROPN
ejpam-4381	141	62	aniversario	aniversario	PROPN
ejpam-4381	141	63	/	/	SYM
ejpam-4381	141	64	eur	eur	PROPN
ejpam-4381	141	65	.	.	PUNCT
ejpam-4381	142	1	j.	j.	PROPN
ejpam-4381	142	2	pure	pure	PROPN
ejpam-4381	142	3	appl	appl	PROPN
ejpam-4381	142	4	.	.	PROPN
ejpam-4381	142	5	math	math	PROPN
ejpam-4381	142	6	,	,	PUNCT
ejpam-4381	142	7	16	16	NUM
ejpam-4381	142	8	(	(	PUNCT
ejpam-4381	142	9	1	1	NUM
ejpam-4381	142	10	)	)	PUNCT
ejpam-4381	142	11	(	(	PUNCT
ejpam-4381	142	12	2023	2023	NUM
ejpam-4381	142	13	)	)	PUNCT
ejpam-4381	142	14	,	,	PUNCT
ejpam-4381	142	15	261	261	NUM
ejpam-4381	142	16	-	-	SYM
ejpam-4381	142	17	270	270	NUM
ejpam-4381	142	18	267	267	NUM
ejpam-4381	142	19	−	−	NOUN
ejpam-4381	142	20	[	[	PUNCT
ejpam-4381	142	21	|v	|v	X
ejpam-4381	142	22	(	(	PUNCT
ejpam-4381	142	23	h)|+	h)|+	NOUN
ejpam-4381	142	24	1	1	NUM
ejpam-4381	142	25	]	]	PUNCT
ejpam-4381	143	1	+	+	CCONJ
ejpam-4381	143	2	1	1	X
ejpam-4381	143	3	=	=	SYM
ejpam-4381	143	4	[	[	PUNCT
ejpam-4381	143	5	|nk	|nk	NUM
ejpam-4381	143	6	g(u	g(u	PROPN
ejpam-4381	143	7	)	)	PUNCT
ejpam-4381	143	8	∩	∩	NOUN
ejpam-4381	143	9	(	(	PUNCT
ejpam-4381	143	10	v	v	NOUN
ejpam-4381	143	11	(	(	PUNCT
ejpam-4381	143	12	g	g	NOUN
ejpam-4381	143	13	)	)	PUNCT
ejpam-4381	143	14	\a)|	\a)|	X
ejpam-4381	143	15	−	−	PROPN
ejpam-4381	143	16	|nk	|nk	PROPN
ejpam-4381	143	17	g(u	g(u	PROPN
ejpam-4381	143	18	)	)	PUNCT
ejpam-4381	143	19	∩a|	∩a|	PUNCT
ejpam-4381	143	20	]	]	PUNCT
ejpam-4381	143	21	|v	|v	PROPN
ejpam-4381	143	22	(	(	PUNCT
ejpam-4381	143	23	h)|	h)|	PROPN
ejpam-4381	143	24	.	.	PUNCT
ejpam-4381	144	1	since	since	SCONJ
ejpam-4381	144	2	a	a	PRON
ejpam-4381	144	3	is	be	AUX
ejpam-4381	144	4	an	an	DET
ejpam-4381	144	5	αk	αk	NOUN
ejpam-4381	144	6	ce	ce	NOUN
ejpam-4381	144	7	-	-	NOUN
ejpam-4381	144	8	set	set	NOUN
ejpam-4381	144	9	in	in	ADP
ejpam-4381	144	10	g	g	NOUN
ejpam-4381	144	11	,	,	PUNCT
ejpam-4381	144	12	[	[	PUNCT
ejpam-4381	144	13	|nk	|nk	ADP
ejpam-4381	144	14	g(u	g(u	PROPN
ejpam-4381	144	15	)	)	PUNCT
ejpam-4381	144	16	∩	∩	NOUN
ejpam-4381	144	17	(	(	PUNCT
ejpam-4381	144	18	v	v	NOUN
ejpam-4381	144	19	(	(	PUNCT
ejpam-4381	144	20	g	g	NOUN
ejpam-4381	144	21	)	)	PUNCT
ejpam-4381	144	22	\	\	PUNCT
ejpam-4381	145	1	a)|	a)|	PUNCT
ejpam-4381	145	2	−	−	NOUN
ejpam-4381	145	3	|nk	|nk	NUM
ejpam-4381	145	4	g(u	g(u	PROPN
ejpam-4381	145	5	)	)	PUNCT
ejpam-4381	145	6	∩	∩	NOUN
ejpam-4381	145	7	a|	a|	PROPN
ejpam-4381	145	8	]	]	PUNCT
ejpam-4381	145	9	|v	|v	PROPN
ejpam-4381	145	10	(	(	PUNCT
ejpam-4381	145	11	h)|	h)|	PROPN
ejpam-4381	145	12	≥	≥	NOUN
ejpam-4381	145	13	0	0	NUM
ejpam-4381	145	14	.	.	PUNCT
ejpam-4381	146	1	thus	thus	ADV
ejpam-4381	146	2	,	,	PUNCT
ejpam-4381	146	3	|nk	|nk	ADP
ejpam-4381	146	4	g[h](u	g[h](u	PROPN
ejpam-4381	146	5	,	,	PUNCT
ejpam-4381	146	6	v	v	NOUN
ejpam-4381	146	7	)	)	PUNCT
ejpam-4381	146	8	∩	∩	NOUN
ejpam-4381	146	9	(	(	PUNCT
ejpam-4381	146	10	v	v	NOUN
ejpam-4381	146	11	(	(	PUNCT
ejpam-4381	146	12	g[h	g[h	PROPN
ejpam-4381	146	13	]	]	PUNCT
ejpam-4381	146	14	)	)	PUNCT
ejpam-4381	146	15	\	\	PROPN
ejpam-4381	146	16	s)|	s)|	NOUN
ejpam-4381	146	17	−	−	PROPN
ejpam-4381	146	18	|nk	|nk	ADP
ejpam-4381	146	19	g[h](u	g[h](u	PROPN
ejpam-4381	146	20	,	,	PUNCT
ejpam-4381	146	21	v	v	NOUN
ejpam-4381	146	22	)	)	PUNCT
ejpam-4381	146	23	∩	∩	NOUN
ejpam-4381	146	24	s|	s|	VERB
ejpam-4381	146	25	≥	≥	NOUN
ejpam-4381	146	26	0	0	NUM
ejpam-4381	146	27	.	.	PUNCT
ejpam-4381	147	1	therefore	therefore	ADV
ejpam-4381	147	2	,	,	PUNCT
ejpam-4381	147	3	s	s	VERB
ejpam-4381	147	4	is	be	AUX
ejpam-4381	147	5	a	a	DET
ejpam-4381	147	6	distance	distance	NOUN
ejpam-4381	147	7	k	k	ADJ
ejpam-4381	147	8	-	-	PUNCT
ejpam-4381	147	9	cost	cost	NOUN
ejpam-4381	147	10	effective	effective	ADJ
ejpam-4381	147	11	set	set	NOUN
ejpam-4381	147	12	in	in	ADP
ejpam-4381	147	13	g[h	g[h	PROPN
ejpam-4381	147	14	]	]	PUNCT
ejpam-4381	147	15	.	.	PUNCT
ejpam-4381	148	1	corollary	corollary	ADJ
ejpam-4381	148	2	4	4	NUM
ejpam-4381	148	3	.	.	PUNCT
ejpam-4381	149	1	let	let	VERB
ejpam-4381	149	2	g	g	NOUN
ejpam-4381	149	3	and	and	CCONJ
ejpam-4381	149	4	h	h	NOUN
ejpam-4381	149	5	be	be	AUX
ejpam-4381	149	6	connected	connect	VERB
ejpam-4381	149	7	graphs	graph	NOUN
ejpam-4381	149	8	and	and	CCONJ
ejpam-4381	149	9	k	k	X
ejpam-4381	149	10	≥	≥	NUM
ejpam-4381	149	11	2	2	NUM
ejpam-4381	149	12	be	be	AUX
ejpam-4381	149	13	an	an	DET
ejpam-4381	149	14	integer	integer	NOUN
ejpam-4381	149	15	.	.	PUNCT
ejpam-4381	150	1	then	then	ADV
ejpam-4381	150	2	αk	αk	ADP
ejpam-4381	150	3	ce(g[h	ce(g[h	NOUN
ejpam-4381	150	4	]	]	X
ejpam-4381	150	5	)	)	PUNCT
ejpam-4381	150	6	≥	≥	NOUN
ejpam-4381	150	7	|v	|v	NOUN
ejpam-4381	150	8	(	(	PUNCT
ejpam-4381	150	9	h)|+1	h)|+1	NOUN
ejpam-4381	150	10	2	2	NUM
ejpam-4381	150	11	αk	αk	NOUN
ejpam-4381	150	12	ce(g	ce(g	NOUN
ejpam-4381	150	13	)	)	PUNCT
ejpam-4381	150	14	.	.	PUNCT
ejpam-4381	151	1	theorem	theorem	ADJ
ejpam-4381	151	2	5	5	NUM
ejpam-4381	151	3	.	.	PUNCT
ejpam-4381	152	1	let	let	VERB
ejpam-4381	152	2	g	g	NOUN
ejpam-4381	152	3	and	and	CCONJ
ejpam-4381	152	4	h	h	NOUN
ejpam-4381	152	5	be	be	AUX
ejpam-4381	152	6	connected	connect	VERB
ejpam-4381	152	7	graphs	graph	NOUN
ejpam-4381	152	8	.	.	PUNCT
ejpam-4381	153	1	let	let	VERB
ejpam-4381	153	2	a	a	DET
ejpam-4381	153	3	be	be	AUX
ejpam-4381	153	4	an	an	DET
ejpam-4381	153	5	α1	α1	PROPN
ejpam-4381	153	6	ce	ce	NOUN
ejpam-4381	153	7	-	-	NOUN
ejpam-4381	153	8	set	set	NOUN
ejpam-4381	153	9	in	in	ADP
ejpam-4381	153	10	g	g	NOUN
ejpam-4381	153	11	,	,	PUNCT
ejpam-4381	153	12	ta	ta	PART
ejpam-4381	153	13	be	be	AUX
ejpam-4381	153	14	an	an	DET
ejpam-4381	153	15	α1	α1	PROPN
ejpam-4381	153	16	ce	ce	PROPN
ejpam-4381	153	17	-	-	ADJ
ejpam-4381	153	18	set	set	NOUN
ejpam-4381	153	19	in	in	ADP
ejpam-4381	153	20	h	h	NOUN
ejpam-4381	153	21	,	,	PUNCT
ejpam-4381	153	22	for	for	ADP
ejpam-4381	153	23	each	each	DET
ejpam-4381	153	24	a	a	DET
ejpam-4381	153	25	∈	∈	PROPN
ejpam-4381	153	26	a	a	PRON
ejpam-4381	153	27	,	,	PUNCT
ejpam-4381	153	28	and	and	CCONJ
ejpam-4381	153	29	s	s	AUX
ejpam-4381	153	30	=	=	PUNCT
ejpam-4381	153	31	⋃	⋃	NOUN
ejpam-4381	153	32	a∈a({a	a∈a({a	PROPN
ejpam-4381	153	33	}	}	PUNCT
ejpam-4381	153	34	×	×	PROPN
ejpam-4381	153	35	ta	ta	PROPN
ejpam-4381	153	36	)	)	PUNCT
ejpam-4381	153	37	.	.	PUNCT
ejpam-4381	154	1	then	then	ADV
ejpam-4381	154	2	s	s	VERB
ejpam-4381	154	3	is	be	AUX
ejpam-4381	154	4	a	a	DET
ejpam-4381	154	5	distance	distance	NOUN
ejpam-4381	154	6	1	1	NUM
ejpam-4381	154	7	-	-	PUNCT
ejpam-4381	154	8	cost	cost	NOUN
ejpam-4381	154	9	effective	effective	ADJ
ejpam-4381	154	10	set	set	NOUN
ejpam-4381	154	11	in	in	ADP
ejpam-4381	154	12	g[h	g[h	NOUN
ejpam-4381	154	13	]	]	PUNCT
ejpam-4381	154	14	.	.	PUNCT
ejpam-4381	155	1	proof	proof	NOUN
ejpam-4381	155	2	:	:	PUNCT
ejpam-4381	155	3	let	let	VERB
ejpam-4381	155	4	a	a	PRON
ejpam-4381	155	5	be	be	AUX
ejpam-4381	155	6	an	an	DET
ejpam-4381	155	7	α1	α1	PROPN
ejpam-4381	155	8	ce	ce	NOUN
ejpam-4381	155	9	-	-	NOUN
ejpam-4381	155	10	set	set	NOUN
ejpam-4381	155	11	in	in	ADP
ejpam-4381	155	12	g	g	NOUN
ejpam-4381	155	13	,	,	PUNCT
ejpam-4381	155	14	ta	ta	PART
ejpam-4381	155	15	be	be	AUX
ejpam-4381	155	16	an	an	DET
ejpam-4381	155	17	α1	α1	PROPN
ejpam-4381	155	18	ce	ce	PROPN
ejpam-4381	155	19	-	-	ADJ
ejpam-4381	155	20	set	set	NOUN
ejpam-4381	155	21	in	in	ADP
ejpam-4381	155	22	h	h	NOUN
ejpam-4381	155	23	,	,	PUNCT
ejpam-4381	155	24	for	for	ADP
ejpam-4381	155	25	each	each	DET
ejpam-4381	155	26	a	a	DET
ejpam-4381	155	27	∈	∈	PROPN
ejpam-4381	155	28	a	a	PRON
ejpam-4381	155	29	,	,	PUNCT
ejpam-4381	155	30	and	and	CCONJ
ejpam-4381	155	31	s	s	VERB
ejpam-4381	155	32	=	=	NOUN
ejpam-4381	155	33	⋃	⋃	NOUN
ejpam-4381	155	34	a∈a({a}×ta	a∈a({a}×ta	NOUN
ejpam-4381	155	35	)	)	PUNCT
ejpam-4381	155	36	.	.	PUNCT
ejpam-4381	156	1	let	let	VERB
ejpam-4381	156	2	(	(	PUNCT
ejpam-4381	156	3	u	u	NOUN
ejpam-4381	156	4	,	,	PUNCT
ejpam-4381	156	5	v	v	NOUN
ejpam-4381	156	6	)	)	PUNCT
ejpam-4381	156	7	∈	∈	PROPN
ejpam-4381	156	8	s.	s.	PROPN
ejpam-4381	156	9	then	then	ADV
ejpam-4381	156	10	|n1	|n1	VERB
ejpam-4381	156	11	g[h](u	g[h](u	PROPN
ejpam-4381	156	12	,	,	PUNCT
ejpam-4381	156	13	v)∩s|	v)∩s|	NOUN
ejpam-4381	156	14	=	=	PUNCT
ejpam-4381	156	15	|n1	|n1	VERB
ejpam-4381	156	16	hu	hu	PROPN
ejpam-4381	157	1	(	(	PUNCT
ejpam-4381	157	2	v)∩tu|+	v)∩tu|+	PROPN
ejpam-4381	157	3	|n1	|n1	VERB
ejpam-4381	157	4	g(u)∩a||tu|	g(u)∩a||tu|	NOUN
ejpam-4381	157	5	and	and	CCONJ
ejpam-4381	157	6	|n1	|n1	VERB
ejpam-4381	157	7	g[h](u	g[h](u	PROPN
ejpam-4381	157	8	,	,	PUNCT
ejpam-4381	157	9	v)∩(v	v)∩(v	PROPN
ejpam-4381	157	10	(	(	PUNCT
ejpam-4381	157	11	g[h	g[h	NOUN
ejpam-4381	157	12	]	]	PUNCT
ejpam-4381	157	13	)	)	PUNCT
ejpam-4381	157	14	\	\	PROPN
ejpam-4381	157	15	s)|	s)|	NOUN
ejpam-4381	158	1	=	=	PUNCT
ejpam-4381	158	2	|n1	|n1	VERB
ejpam-4381	158	3	hu	hu	PROPN
ejpam-4381	158	4	(	(	PUNCT
ejpam-4381	158	5	v	v	NOUN
ejpam-4381	158	6	)	)	PUNCT
ejpam-4381	158	7	∩	∩	NOUN
ejpam-4381	158	8	(	(	PUNCT
ejpam-4381	158	9	v	v	NOUN
ejpam-4381	158	10	(	(	PUNCT
ejpam-4381	158	11	h	h	NOUN
ejpam-4381	158	12	)	)	PUNCT
ejpam-4381	158	13	\	\	NOUN
ejpam-4381	158	14	tu)|+	tu)|+	PROPN
ejpam-4381	158	15	|n1	|n1	VERB
ejpam-4381	158	16	g(u	g(u	NOUN
ejpam-4381	158	17	)	)	PUNCT
ejpam-4381	158	18	∩	∩	NOUN
ejpam-4381	158	19	(	(	PUNCT
ejpam-4381	158	20	v	v	NOUN
ejpam-4381	158	21	(	(	PUNCT
ejpam-4381	158	22	g	g	NOUN
ejpam-4381	158	23	)	)	PUNCT
ejpam-4381	158	24	\a)||v	\a)||v	PUNCT
ejpam-4381	158	25	(	(	PUNCT
ejpam-4381	158	26	h)|	h)|	NOUN
ejpam-4381	158	27	+	+	CCONJ
ejpam-4381	158	28	|n1	|n1	VERB
ejpam-4381	159	1	g(u	g(u	PROPN
ejpam-4381	159	2	)	)	PUNCT
ejpam-4381	159	3	∩a||v	∩a||v	PROPN
ejpam-4381	159	4	(	(	PUNCT
ejpam-4381	159	5	h	h	NOUN
ejpam-4381	159	6	)	)	PUNCT
ejpam-4381	159	7	\	\	NOUN
ejpam-4381	159	8	tu|	tu|	PROPN
ejpam-4381	159	9	.	.	PUNCT
ejpam-4381	159	10	hence	hence	ADV
ejpam-4381	159	11	,	,	PUNCT
ejpam-4381	159	12	|n1	|n1	VERB
ejpam-4381	159	13	g[h](u	g[h](u	PROPN
ejpam-4381	159	14	,	,	PUNCT
ejpam-4381	159	15	v	v	NOUN
ejpam-4381	159	16	)	)	PUNCT
ejpam-4381	159	17	∩	∩	NOUN
ejpam-4381	159	18	(	(	PUNCT
ejpam-4381	159	19	v	v	NOUN
ejpam-4381	159	20	(	(	PUNCT
ejpam-4381	159	21	g[h	g[h	PROPN
ejpam-4381	159	22	]	]	PUNCT
ejpam-4381	159	23	)	)	PUNCT
ejpam-4381	159	24	\	\	PROPN
ejpam-4381	159	25	s)|	s)|	PROPN
ejpam-4381	159	26	−	−	PROPN
ejpam-4381	159	27	|n1	|n1	VERB
ejpam-4381	159	28	g[h](u	g[h](u	PROPN
ejpam-4381	159	29	,	,	PUNCT
ejpam-4381	159	30	v	v	NOUN
ejpam-4381	159	31	)	)	PUNCT
ejpam-4381	160	1	∩	∩	NOUN
ejpam-4381	160	2	s|	s|	NOUN
ejpam-4381	160	3	=	=	PUNCT
ejpam-4381	160	4	|n1	|n1	VERB
ejpam-4381	160	5	hu	hu	PROPN
ejpam-4381	160	6	(	(	PUNCT
ejpam-4381	160	7	v	v	NOUN
ejpam-4381	160	8	)	)	PUNCT
ejpam-4381	160	9	∩	∩	NOUN
ejpam-4381	160	10	(	(	PUNCT
ejpam-4381	160	11	v	v	NOUN
ejpam-4381	160	12	(	(	PUNCT
ejpam-4381	160	13	h	h	NOUN
ejpam-4381	160	14	)	)	PUNCT
ejpam-4381	160	15	\	\	PROPN
ejpam-4381	160	16	tu)|	tu)|	PROPN
ejpam-4381	160	17	−	−	PROPN
ejpam-4381	160	18	|n1	|n1	VERB
ejpam-4381	160	19	hu	hu	PROPN
ejpam-4381	160	20	(	(	PUNCT
ejpam-4381	160	21	v	v	NOUN
ejpam-4381	160	22	)	)	PUNCT
ejpam-4381	161	1	∩	∩	NOUN
ejpam-4381	161	2	tu|+	tu|+	PROPN
ejpam-4381	161	3	|n1	|n1	VERB
ejpam-4381	161	4	g(u	g(u	NOUN
ejpam-4381	161	5	)	)	PUNCT
ejpam-4381	161	6	∩	∩	NOUN
ejpam-4381	161	7	(	(	PUNCT
ejpam-4381	161	8	v	v	NOUN
ejpam-4381	161	9	(	(	PUNCT
ejpam-4381	161	10	g	g	NOUN
ejpam-4381	161	11	)	)	PUNCT
ejpam-4381	161	12	\a)||v	\a)||v	PUNCT
ejpam-4381	161	13	(	(	PUNCT
ejpam-4381	161	14	h)|	h)|	PROPN
ejpam-4381	161	15	−	−	PROPN
ejpam-4381	161	16	|n1	|n1	VERB
ejpam-4381	161	17	g(u	g(u	PROPN
ejpam-4381	161	18	)	)	PUNCT
ejpam-4381	161	19	∩a||tu|+	∩a||tu|+	X
ejpam-4381	161	20	|n1	|n1	VERB
ejpam-4381	162	1	g(u	g(u	PROPN
ejpam-4381	162	2	)	)	PUNCT
ejpam-4381	162	3	∩a||v	∩a||v	PROPN
ejpam-4381	162	4	(	(	PUNCT
ejpam-4381	162	5	h	h	NOUN
ejpam-4381	162	6	)	)	PUNCT
ejpam-4381	162	7	\	\	PUNCT
ejpam-4381	163	1	tu|	tu|	ADP
ejpam-4381	163	2	≥	≥	PROPN
ejpam-4381	163	3	|n1	|n1	VERB
ejpam-4381	163	4	hu	hu	PROPN
ejpam-4381	163	5	(	(	PUNCT
ejpam-4381	163	6	v	v	NOUN
ejpam-4381	163	7	)	)	PUNCT
ejpam-4381	163	8	∩	∩	NOUN
ejpam-4381	163	9	(	(	PUNCT
ejpam-4381	163	10	v	v	NOUN
ejpam-4381	163	11	(	(	PUNCT
ejpam-4381	163	12	h	h	NOUN
ejpam-4381	163	13	)	)	PUNCT
ejpam-4381	163	14	\	\	PROPN
ejpam-4381	163	15	tu)|	tu)|	PROPN
ejpam-4381	163	16	−	−	PROPN
ejpam-4381	163	17	|n1	|n1	VERB
ejpam-4381	163	18	hu	hu	PROPN
ejpam-4381	163	19	(	(	PUNCT
ejpam-4381	163	20	v	v	NOUN
ejpam-4381	163	21	)	)	PUNCT
ejpam-4381	163	22	∩	∩	NOUN
ejpam-4381	163	23	tu|+	tu|+	PROPN
ejpam-4381	163	24	|n1	|n1	VERB
ejpam-4381	163	25	g(u	g(u	NOUN
ejpam-4381	163	26	)	)	PUNCT
ejpam-4381	163	27	∩	∩	NOUN
ejpam-4381	163	28	(	(	PUNCT
ejpam-4381	163	29	v	v	NOUN
ejpam-4381	163	30	(	(	PUNCT
ejpam-4381	163	31	g	g	NOUN
ejpam-4381	163	32	)	)	PUNCT
ejpam-4381	163	33	\a)||v	\a)||v	PUNCT
ejpam-4381	163	34	(	(	PUNCT
ejpam-4381	163	35	h)|	h)|	PROPN
ejpam-4381	163	36	−	−	PROPN
ejpam-4381	163	37	|n1	|n1	VERB
ejpam-4381	163	38	g(u	g(u	NOUN
ejpam-4381	163	39	)	)	PUNCT
ejpam-4381	163	40	∩a||v	∩a||v	PROPN
ejpam-4381	163	41	(	(	PUNCT
ejpam-4381	163	42	h)|	h)|	PROPN
ejpam-4381	163	43	+	+	NOUN
ejpam-4381	163	44	|n1	|n1	VERB
ejpam-4381	163	45	g(u	g(u	NOUN
ejpam-4381	163	46	)	)	PUNCT
ejpam-4381	163	47	∩a||v	∩a||v	PROPN
ejpam-4381	163	48	(	(	PUNCT
ejpam-4381	163	49	h)|	h)|	NOUN
ejpam-4381	163	50	−	−	PROPN
ejpam-4381	163	51	|n1	|n1	VERB
ejpam-4381	163	52	g(u	g(u	NOUN
ejpam-4381	163	53	)	)	PUNCT
ejpam-4381	163	54	∩a||v	∩a||v	PROPN
ejpam-4381	163	55	(	(	PUNCT
ejpam-4381	163	56	h)|	h)|	NOUN
ejpam-4381	163	57	=	=	PUNCT
ejpam-4381	163	58	|n1	|n1	VERB
ejpam-4381	163	59	h(v	h(v	NOUN
ejpam-4381	163	60	)	)	PUNCT
ejpam-4381	163	61	∩	∩	NOUN
ejpam-4381	163	62	(	(	PUNCT
ejpam-4381	163	63	v	v	X
ejpam-4381	163	64	(	(	PUNCT
ejpam-4381	163	65	hu	hu	PROPN
ejpam-4381	163	66	)	)	PUNCT
ejpam-4381	163	67	\	\	PROPN
ejpam-4381	164	1	tu)|	tu)|	PROPN
ejpam-4381	164	2	−	−	PROPN
ejpam-4381	164	3	|n1	|n1	VERB
ejpam-4381	164	4	hu	hu	PROPN
ejpam-4381	164	5	(	(	PUNCT
ejpam-4381	164	6	v	v	NOUN
ejpam-4381	164	7	)	)	PUNCT
ejpam-4381	164	8	∩	∩	NOUN
ejpam-4381	164	9	tu|	tu|	ADP
ejpam-4381	164	10	+	+	CCONJ
ejpam-4381	164	11	[	[	PUNCT
ejpam-4381	164	12	|n1	|n1	X
ejpam-4381	164	13	g(u	g(u	NOUN
ejpam-4381	164	14	)	)	PUNCT
ejpam-4381	164	15	∩	∩	NOUN
ejpam-4381	164	16	(	(	PUNCT
ejpam-4381	164	17	v	v	NOUN
ejpam-4381	164	18	(	(	PUNCT
ejpam-4381	164	19	g	g	NOUN
ejpam-4381	164	20	)	)	PUNCT
ejpam-4381	164	21	\a)|	\a)|	PROPN
ejpam-4381	164	22	−	−	NOUN
ejpam-4381	164	23	|n1	|n1	VERB
ejpam-4381	164	24	g(u	g(u	PROPN
ejpam-4381	164	25	)	)	PUNCT
ejpam-4381	164	26	∩a|	∩a|	PUNCT
ejpam-4381	164	27	]	]	PUNCT
ejpam-4381	164	28	|v	|v	PROPN
ejpam-4381	164	29	(	(	PUNCT
ejpam-4381	164	30	h)|	h)|	PROPN
ejpam-4381	164	31	.	.	PUNCT
ejpam-4381	165	1	since	since	SCONJ
ejpam-4381	165	2	tu	tu	PROPN
ejpam-4381	165	3	is	be	AUX
ejpam-4381	165	4	an	an	DET
ejpam-4381	165	5	α1	α1	PROPN
ejpam-4381	165	6	ce	ce	PROPN
ejpam-4381	165	7	-	-	ADJ
ejpam-4381	165	8	set	set	NOUN
ejpam-4381	165	9	in	in	ADP
ejpam-4381	165	10	hu,∀	hu,∀	NOUN
ejpam-4381	165	11	u	u	PROPN
ejpam-4381	165	12	∈	∈	PROPN
ejpam-4381	165	13	a	a	DET
ejpam-4381	165	14	,	,	PUNCT
ejpam-4381	165	15	|n1	|n1	VERB
ejpam-4381	165	16	hu	hu	PROPN
ejpam-4381	165	17	(	(	PUNCT
ejpam-4381	165	18	v	v	NOUN
ejpam-4381	165	19	)	)	PUNCT
ejpam-4381	165	20	∩	∩	NOUN
ejpam-4381	165	21	(	(	PUNCT
ejpam-4381	165	22	v	v	NOUN
ejpam-4381	165	23	(	(	PUNCT
ejpam-4381	165	24	h	h	NOUN
ejpam-4381	165	25	)	)	PUNCT
ejpam-4381	165	26	\	\	PROPN
ejpam-4381	165	27	tu)|	tu)|	PROPN
ejpam-4381	165	28	−	−	PROPN
ejpam-4381	165	29	|n1	|n1	VERB
ejpam-4381	165	30	hu	hu	PROPN
ejpam-4381	165	31	(	(	PUNCT
ejpam-4381	165	32	v	v	NOUN
ejpam-4381	165	33	)	)	PUNCT
ejpam-4381	165	34	∩	∩	NOUN
ejpam-4381	165	35	tu|	tu|	ADP
ejpam-4381	165	36	≥	≥	NOUN
ejpam-4381	165	37	0	0	NUM
ejpam-4381	165	38	.	.	PUNCT
ejpam-4381	166	1	also	also	ADV
ejpam-4381	166	2	,	,	PUNCT
ejpam-4381	166	3	since	since	SCONJ
ejpam-4381	166	4	a	a	PRON
ejpam-4381	166	5	is	be	AUX
ejpam-4381	166	6	an	an	DET
ejpam-4381	166	7	α1	α1	PROPN
ejpam-4381	166	8	ce	ce	NOUN
ejpam-4381	166	9	-	-	NOUN
ejpam-4381	166	10	set	set	NOUN
ejpam-4381	166	11	in	in	ADP
ejpam-4381	166	12	g	g	NOUN
ejpam-4381	166	13	,	,	PUNCT
ejpam-4381	166	14	|n1	|n1	VERB
ejpam-4381	166	15	g(u	g(u	NOUN
ejpam-4381	166	16	)	)	PUNCT
ejpam-4381	166	17	∩	∩	NOUN
ejpam-4381	166	18	(	(	PUNCT
ejpam-4381	166	19	v	v	NOUN
ejpam-4381	166	20	(	(	PUNCT
ejpam-4381	166	21	g	g	NOUN
ejpam-4381	166	22	)	)	PUNCT
ejpam-4381	166	23	\a)|	\a)|	PROPN
ejpam-4381	167	1	−	−	NOUN
ejpam-4381	167	2	|n1	|n1	VERB
ejpam-4381	167	3	g(u	g(u	PROPN
ejpam-4381	167	4	)	)	PUNCT
ejpam-4381	167	5	∩a|	∩a|	ADP
ejpam-4381	167	6	≥	≥	NOUN
ejpam-4381	167	7	0	0	NUM
ejpam-4381	167	8	.	.	PUNCT
ejpam-4381	168	1	thus	thus	ADV
ejpam-4381	168	2	,	,	PUNCT
ejpam-4381	168	3	|n1	|n1	VERB
ejpam-4381	168	4	g[h](u	g[h](u	PROPN
ejpam-4381	168	5	,	,	PUNCT
ejpam-4381	168	6	v	v	NOUN
ejpam-4381	168	7	)	)	PUNCT
ejpam-4381	168	8	∩	∩	NOUN
ejpam-4381	168	9	(	(	PUNCT
ejpam-4381	168	10	v	v	NOUN
ejpam-4381	168	11	(	(	PUNCT
ejpam-4381	168	12	g[h	g[h	PROPN
ejpam-4381	168	13	]	]	PUNCT
ejpam-4381	168	14	)	)	PUNCT
ejpam-4381	168	15	\	\	PROPN
ejpam-4381	168	16	s)|	s)|	PROPN
ejpam-4381	168	17	−	−	PROPN
ejpam-4381	168	18	|n1	|n1	VERB
ejpam-4381	168	19	g[h](u	g[h](u	PROPN
ejpam-4381	168	20	,	,	PUNCT
ejpam-4381	168	21	v	v	NOUN
ejpam-4381	168	22	)	)	PUNCT
ejpam-4381	168	23	∩	∩	NOUN
ejpam-4381	168	24	s|	s|	VERB
ejpam-4381	168	25	≥	≥	NOUN
ejpam-4381	168	26	0	0	NUM
ejpam-4381	168	27	.	.	PUNCT
ejpam-4381	169	1	therefore	therefore	ADV
ejpam-4381	169	2	,	,	PUNCT
ejpam-4381	169	3	s	s	VERB
ejpam-4381	169	4	is	be	AUX
ejpam-4381	169	5	a	a	DET
ejpam-4381	169	6	distance	distance	NOUN
ejpam-4381	169	7	1	1	NUM
ejpam-4381	169	8	-	-	PUNCT
ejpam-4381	169	9	cost	cost	NOUN
ejpam-4381	169	10	effective	effective	ADJ
ejpam-4381	169	11	in	in	ADP
ejpam-4381	169	12	g[h	g[h	NOUN
ejpam-4381	169	13	]	]	PUNCT
ejpam-4381	169	14	.	.	PUNCT
ejpam-4381	170	1	corollary	corollary	ADJ
ejpam-4381	170	2	5	5	NUM
ejpam-4381	170	3	.	.	PUNCT
ejpam-4381	171	1	let	let	VERB
ejpam-4381	171	2	g	g	NOUN
ejpam-4381	171	3	and	and	CCONJ
ejpam-4381	171	4	h	h	NOUN
ejpam-4381	171	5	be	be	AUX
ejpam-4381	171	6	connected	connect	VERB
ejpam-4381	171	7	graphs	graph	NOUN
ejpam-4381	171	8	.	.	PUNCT
ejpam-4381	172	1	then	then	ADV
ejpam-4381	172	2	α1	α1	PROPN
ejpam-4381	172	3	ce(g[h	ce(g[h	NOUN
ejpam-4381	172	4	]	]	X
ejpam-4381	172	5	)	)	PUNCT
ejpam-4381	172	6	≥	≥	PROPN
ejpam-4381	172	7	α1	α1	PROPN
ejpam-4381	172	8	ce(g)α1	ce(g)α1	PROPN
ejpam-4381	172	9	ce(h	ce(h	NOUN
ejpam-4381	172	10	)	)	PUNCT
ejpam-4381	172	11	.	.	PUNCT
ejpam-4381	173	1	julius	julius	PROPN
ejpam-4381	173	2	g.	g.	PROPN
ejpam-4381	173	3	caadan	caadan	PROPN
ejpam-4381	173	4	,	,	PUNCT
ejpam-4381	173	5	rolando	rolando	PROPN
ejpam-4381	173	6	n.	n.	PROPN
ejpam-4381	173	7	paluga	paluga	PROPN
ejpam-4381	173	8	,	,	PUNCT
ejpam-4381	173	9	imelda	imelda	PROPN
ejpam-4381	173	10	s.	s.	PROPN
ejpam-4381	173	11	aniversario	aniversario	PROPN
ejpam-4381	173	12	/	/	SYM
ejpam-4381	173	13	eur	eur	PROPN
ejpam-4381	173	14	.	.	PUNCT
ejpam-4381	174	1	j.	j.	PROPN
ejpam-4381	174	2	pure	pure	PROPN
ejpam-4381	174	3	appl	appl	PROPN
ejpam-4381	174	4	.	.	PROPN
ejpam-4381	174	5	math	math	PROPN
ejpam-4381	174	6	,	,	PUNCT
ejpam-4381	174	7	16	16	NUM
ejpam-4381	174	8	(	(	PUNCT
ejpam-4381	174	9	1	1	NUM
ejpam-4381	174	10	)	)	PUNCT
ejpam-4381	174	11	(	(	PUNCT
ejpam-4381	174	12	2023	2023	NUM
ejpam-4381	174	13	)	)	PUNCT
ejpam-4381	174	14	,	,	PUNCT
ejpam-4381	174	15	261	261	NUM
ejpam-4381	174	16	-	-	SYM
ejpam-4381	174	17	270	270	NUM
ejpam-4381	174	18	268	268	NUM
ejpam-4381	174	19	corollary	corollary	NOUN
ejpam-4381	174	20	6	6	NUM
ejpam-4381	174	21	.	.	PUNCT
ejpam-4381	175	1	let	let	VERB
ejpam-4381	175	2	g	g	NOUN
ejpam-4381	175	3	and	and	CCONJ
ejpam-4381	175	4	h	h	NOUN
ejpam-4381	175	5	be	be	AUX
ejpam-4381	175	6	connected	connect	VERB
ejpam-4381	175	7	graphs	graph	NOUN
ejpam-4381	175	8	.	.	PUNCT
ejpam-4381	176	1	let	let	VERB
ejpam-4381	176	2	a	a	PRON
ejpam-4381	176	3	and	and	CCONJ
ejpam-4381	176	4	b	b	NOUN
ejpam-4381	176	5	be	be	PROPN
ejpam-4381	176	6	α1	α1	PROPN
ejpam-4381	176	7	ce	ce	NOUN
ejpam-4381	176	8	-	-	NOUN
ejpam-4381	176	9	sets	set	NOUN
ejpam-4381	176	10	in	in	ADP
ejpam-4381	176	11	g	g	PROPN
ejpam-4381	176	12	and	and	CCONJ
ejpam-4381	176	13	h	h	NOUN
ejpam-4381	176	14	,	,	PUNCT
ejpam-4381	176	15	respectively	respectively	ADV
ejpam-4381	176	16	.	.	PUNCT
ejpam-4381	177	1	then	then	ADV
ejpam-4381	177	2	a×b	a×b	PROPN
ejpam-4381	177	3	is	be	AUX
ejpam-4381	177	4	a	a	DET
ejpam-4381	177	5	distance	distance	NOUN
ejpam-4381	177	6	1	1	NUM
ejpam-4381	177	7	-	-	PUNCT
ejpam-4381	177	8	cost	cost	NOUN
ejpam-4381	177	9	effective	effective	ADJ
ejpam-4381	177	10	set	set	NOUN
ejpam-4381	177	11	in	in	ADP
ejpam-4381	177	12	g[h	g[h	PROPN
ejpam-4381	177	13	]	]	PUNCT
ejpam-4381	177	14	.	.	PUNCT
ejpam-4381	178	1	definition	definition	NOUN
ejpam-4381	178	2	1	1	NUM
ejpam-4381	178	3	.	.	PUNCT
ejpam-4381	178	4	letg	letg	PROPN
ejpam-4381	178	5	be	be	VERB
ejpam-4381	178	6	a	a	DET
ejpam-4381	178	7	nontrivial	nontrivial	ADJ
ejpam-4381	178	8	connected	connect	VERB
ejpam-4381	178	9	graph	graph	NOUN
ejpam-4381	178	10	and	and	CCONJ
ejpam-4381	178	11	k	k	PROPN
ejpam-4381	178	12	≥	≥	NUM
ejpam-4381	178	13	1	1	NUM
ejpam-4381	178	14	be	be	AUX
ejpam-4381	178	15	an	an	DET
ejpam-4381	178	16	integer	integer	NOUN
ejpam-4381	178	17	.	.	PUNCT
ejpam-4381	179	1	a	a	DET
ejpam-4381	179	2	nonempty	nonempty	ADV
ejpam-4381	179	3	set	set	VERB
ejpam-4381	179	4	s	s	PROPN
ejpam-4381	179	5	⊆	⊆	NUM
ejpam-4381	179	6	v	v	NOUN
ejpam-4381	179	7	(	(	PUNCT
ejpam-4381	179	8	g	g	NOUN
ejpam-4381	179	9	)	)	PUNCT
ejpam-4381	179	10	is	be	AUX
ejpam-4381	179	11	said	say	VERB
ejpam-4381	179	12	to	to	PART
ejpam-4381	179	13	be	be	AUX
ejpam-4381	179	14	a	a	DET
ejpam-4381	179	15	very	very	ADJ
ejpam-4381	179	16	distance	distance	NOUN
ejpam-4381	179	17	k	k	ADJ
ejpam-4381	179	18	-	-	PUNCT
ejpam-4381	179	19	cost	cost	ADJ
ejpam-4381	179	20	effective	effective	ADJ
ejpam-4381	179	21	set	set	NOUN
ejpam-4381	179	22	in	in	ADP
ejpam-4381	179	23	g	g	PROPN
ejpam-4381	179	24	if	if	SCONJ
ejpam-4381	179	25	for	for	SCONJ
ejpam-4381	179	26	every	every	DET
ejpam-4381	179	27	u	u	PROPN
ejpam-4381	179	28	∈	∈	PROPN
ejpam-4381	179	29	s	s	NOUN
ejpam-4381	179	30	,	,	PUNCT
ejpam-4381	179	31	|nk	|nk	PROPN
ejpam-4381	179	32	g(u	g(u	PROPN
ejpam-4381	179	33	)	)	PUNCT
ejpam-4381	179	34	∩	∩	NOUN
ejpam-4381	179	35	sc|	sc|	PROPN
ejpam-4381	179	36	−	−	PROPN
ejpam-4381	179	37	|nk	|nk	SYM
ejpam-4381	179	38	g(u	g(u	PROPN
ejpam-4381	179	39	)	)	PUNCT
ejpam-4381	179	40	∩	∩	NOUN
ejpam-4381	179	41	s|	s|	VERB
ejpam-4381	179	42	>	>	X
ejpam-4381	179	43	0	0	X
ejpam-4381	179	44	.	.	PUNCT
ejpam-4381	179	45	example	example	NOUN
ejpam-4381	180	1	1	1	NUM
ejpam-4381	180	2	.	.	X
ejpam-4381	180	3	consider	consider	VERB
ejpam-4381	180	4	the	the	DET
ejpam-4381	180	5	graph	graph	NOUN
ejpam-4381	180	6	g	g	NOUN
ejpam-4381	180	7	as	as	SCONJ
ejpam-4381	180	8	shown	show	VERB
ejpam-4381	180	9	in	in	ADP
ejpam-4381	180	10	figure	figure	NOUN
ejpam-4381	180	11	1	1	NUM
ejpam-4381	180	12	.	.	PUNCT
ejpam-4381	181	1	for	for	ADP
ejpam-4381	181	2	each	each	DET
ejpam-4381	181	3	v	v	NOUN
ejpam-4381	181	4	∈	∈	NOUN
ejpam-4381	181	5	s	s	PART
ejpam-4381	181	6	=	=	PUNCT
ejpam-4381	181	7	{	{	PUNCT
ejpam-4381	181	8	v2	v2	PROPN
ejpam-4381	181	9	,	,	PUNCT
ejpam-4381	181	10	v3	v3	PROPN
ejpam-4381	181	11	,	,	PUNCT
ejpam-4381	181	12	v4	v4	PROPN
ejpam-4381	181	13	,	,	PUNCT
ejpam-4381	181	14	v5	v5	PROPN
ejpam-4381	181	15	}	}	PUNCT
ejpam-4381	181	16	|n2	|n2	PROPN
ejpam-4381	181	17	g(v	g(v	PROPN
ejpam-4381	181	18	)	)	PUNCT
ejpam-4381	181	19	∩	∩	NOUN
ejpam-4381	181	20	(	(	PUNCT
ejpam-4381	181	21	v	v	NOUN
ejpam-4381	181	22	(	(	PUNCT
ejpam-4381	181	23	g	g	NOUN
ejpam-4381	181	24	)	)	PUNCT
ejpam-4381	181	25	\	\	PROPN
ejpam-4381	181	26	s)|	s)|	NOUN
ejpam-4381	181	27	−	−	PROPN
ejpam-4381	181	28	|n2	|n2	PROPN
ejpam-4381	181	29	g(v	g(v	PROPN
ejpam-4381	181	30	)	)	PUNCT
ejpam-4381	181	31	∩	∩	NOUN
ejpam-4381	181	32	s|	s|	VERB
ejpam-4381	181	33	>	>	X
ejpam-4381	181	34	0	0	X
ejpam-4381	181	35	.	.	PUNCT
ejpam-4381	182	1	thus	thus	ADV
ejpam-4381	182	2	,	,	PUNCT
ejpam-4381	182	3	s	s	VERB
ejpam-4381	182	4	is	be	AUX
ejpam-4381	182	5	a	a	DET
ejpam-4381	182	6	very	very	ADJ
ejpam-4381	182	7	distance	distance	NOUN
ejpam-4381	182	8	2	2	NUM
ejpam-4381	182	9	-	-	PUNCT
ejpam-4381	182	10	cost	cost	NOUN
ejpam-4381	182	11	effective	effective	ADJ
ejpam-4381	182	12	set	set	NOUN
ejpam-4381	182	13	in	in	ADP
ejpam-4381	182	14	g.	g.	PROPN
ejpam-4381	182	15	v1	v1	PROPN
ejpam-4381	182	16	v2	v2	PROPN
ejpam-4381	182	17	v5	v5	PROPN
ejpam-4381	182	18	v3	v3	PROPN
ejpam-4381	182	19	v4	v4	PROPN
ejpam-4381	182	20	v7	v7	VERB
ejpam-4381	182	21	v8	v8	PROPN
ejpam-4381	182	22	v6	v6	NOUN
ejpam-4381	182	23	figure	figure	NOUN
ejpam-4381	182	24	1	1	NUM
ejpam-4381	182	25	:	:	PUNCT
ejpam-4381	182	26	the	the	DET
ejpam-4381	182	27	graph	graph	NOUN
ejpam-4381	182	28	g	g	NOUN
ejpam-4381	182	29	with	with	ADP
ejpam-4381	182	30	a	a	DET
ejpam-4381	182	31	very	very	ADJ
ejpam-4381	182	32	distance	distance	NOUN
ejpam-4381	182	33	2	2	NUM
ejpam-4381	182	34	-	-	PUNCT
ejpam-4381	182	35	cost	cost	NOUN
ejpam-4381	182	36	effective	effective	ADJ
ejpam-4381	182	37	set	set	NOUN
ejpam-4381	182	38	in	in	ADP
ejpam-4381	182	39	g	g	PROPN
ejpam-4381	182	40	theorem	theorem	NOUN
ejpam-4381	182	41	6	6	NUM
ejpam-4381	182	42	.	.	PUNCT
ejpam-4381	183	1	let	let	VERB
ejpam-4381	183	2	g	g	NOUN
ejpam-4381	183	3	and	and	CCONJ
ejpam-4381	183	4	h	h	NOUN
ejpam-4381	183	5	be	be	AUX
ejpam-4381	183	6	connected	connect	VERB
ejpam-4381	183	7	graphs	graph	NOUN
ejpam-4381	183	8	and	and	CCONJ
ejpam-4381	183	9	k	k	X
ejpam-4381	183	10	≥	≥	NUM
ejpam-4381	183	11	1	1	NUM
ejpam-4381	183	12	be	be	AUX
ejpam-4381	183	13	an	an	DET
ejpam-4381	183	14	integer	integer	NOUN
ejpam-4381	183	15	.	.	PUNCT
ejpam-4381	184	1	if	if	SCONJ
ejpam-4381	184	2	a	a	PRON
ejpam-4381	184	3	is	be	AUX
ejpam-4381	184	4	a	a	DET
ejpam-4381	184	5	very	very	ADJ
ejpam-4381	184	6	distance	distance	NOUN
ejpam-4381	184	7	k	k	ADJ
ejpam-4381	184	8	-	-	PUNCT
ejpam-4381	184	9	cost	cost	ADJ
ejpam-4381	184	10	effective	effective	ADJ
ejpam-4381	184	11	set	set	NOUN
ejpam-4381	184	12	in	in	ADP
ejpam-4381	184	13	g	g	NOUN
ejpam-4381	184	14	,	,	PUNCT
ejpam-4381	184	15	then	then	ADV
ejpam-4381	184	16	a×v	a×v	PROPN
ejpam-4381	184	17	(	(	PUNCT
ejpam-4381	184	18	h	h	NOUN
ejpam-4381	184	19	)	)	PUNCT
ejpam-4381	184	20	is	be	AUX
ejpam-4381	184	21	a	a	DET
ejpam-4381	184	22	distance	distance	NOUN
ejpam-4381	184	23	k	k	ADJ
ejpam-4381	184	24	-	-	PUNCT
ejpam-4381	184	25	cost	cost	NOUN
ejpam-4381	184	26	effective	effective	ADJ
ejpam-4381	184	27	set	set	NOUN
ejpam-4381	184	28	in	in	ADP
ejpam-4381	184	29	g[h	g[h	NOUN
ejpam-4381	184	30	]	]	PUNCT
ejpam-4381	184	31	.	.	PUNCT
ejpam-4381	185	1	proof	proof	NOUN
ejpam-4381	185	2	:	:	PUNCT
ejpam-4381	185	3	let	let	VERB
ejpam-4381	185	4	a	a	PRON
ejpam-4381	185	5	be	be	AUX
ejpam-4381	185	6	a	a	DET
ejpam-4381	185	7	very	very	ADJ
ejpam-4381	185	8	distance	distance	NOUN
ejpam-4381	185	9	k	k	ADJ
ejpam-4381	185	10	-	-	PUNCT
ejpam-4381	185	11	cost	cost	ADJ
ejpam-4381	185	12	effective	effective	ADJ
ejpam-4381	185	13	set	set	NOUN
ejpam-4381	185	14	in	in	ADP
ejpam-4381	185	15	g	g	PROPN
ejpam-4381	185	16	and	and	CCONJ
ejpam-4381	185	17	k	k	PROPN
ejpam-4381	185	18	≥	≥	NUM
ejpam-4381	185	19	2	2	NUM
ejpam-4381	185	20	be	be	AUX
ejpam-4381	185	21	a	a	DET
ejpam-4381	185	22	positive	positive	ADJ
ejpam-4381	185	23	integer	integer	NOUN
ejpam-4381	185	24	.	.	PUNCT
ejpam-4381	186	1	let	let	VERB
ejpam-4381	186	2	(	(	PUNCT
ejpam-4381	186	3	u	u	NOUN
ejpam-4381	186	4	,	,	PUNCT
ejpam-4381	186	5	v	v	NOUN
ejpam-4381	186	6	)	)	PUNCT
ejpam-4381	186	7	∈	∈	PROPN
ejpam-4381	186	8	a×	a×	PUNCT
ejpam-4381	186	9	v	v	NOUN
ejpam-4381	186	10	(	(	PUNCT
ejpam-4381	186	11	h	h	NOUN
ejpam-4381	186	12	)	)	PUNCT
ejpam-4381	186	13	.	.	PUNCT
ejpam-4381	187	1	then∣∣nk	then∣∣nk	VERB
ejpam-4381	187	2	g[h](u	g[h](u	NOUN
ejpam-4381	187	3	,	,	PUNCT
ejpam-4381	187	4	v	v	NOUN
ejpam-4381	187	5	)	)	PUNCT
ejpam-4381	187	6	∩	∩	NOUN
ejpam-4381	187	7	(	(	PUNCT
ejpam-4381	187	8	a×	a×	NOUN
ejpam-4381	187	9	v	v	X
ejpam-4381	187	10	(	(	PUNCT
ejpam-4381	187	11	h	h	NOUN
ejpam-4381	187	12	)	)	PUNCT
ejpam-4381	187	13	)	)	PUNCT
ejpam-4381	187	14	∣∣	∣∣	X
ejpam-4381	188	1	=	=	PUNCT
ejpam-4381	188	2	|nk	|nk	NUM
ejpam-4381	188	3	h(v)|+	h(v)|+	PROPN
ejpam-4381	188	4	|nk	|nk	PROPN
ejpam-4381	188	5	g(u	g(u	PROPN
ejpam-4381	188	6	)	)	PUNCT
ejpam-4381	188	7	∩a||v	∩a||v	PROPN
ejpam-4381	188	8	(	(	PUNCT
ejpam-4381	188	9	h)|	h)|	NOUN
ejpam-4381	188	10	=	=	PUNCT
ejpam-4381	188	11	|nk	|nk	PROPN
ejpam-4381	188	12	g(u	g(u	PROPN
ejpam-4381	188	13	)	)	PUNCT
ejpam-4381	188	14	∩a||v	∩a||v	PROPN
ejpam-4381	188	15	(	(	PUNCT
ejpam-4381	188	16	h)|+	h)|+	ADJ
ejpam-4381	188	17	|v	|v	PROPN
ejpam-4381	188	18	(	(	PUNCT
ejpam-4381	188	19	h)|	h)|	PROPN
ejpam-4381	188	20	.	.	PUNCT
ejpam-4381	188	21	and	and	CCONJ
ejpam-4381	188	22	∣∣∣nk	∣∣∣nk	PUNCT
ejpam-4381	188	23	g[h](u	g[h](u	PROPN
ejpam-4381	188	24	,	,	PUNCT
ejpam-4381	188	25	v	v	NOUN
ejpam-4381	188	26	)	)	PUNCT
ejpam-4381	188	27	∩	∩	NOUN
ejpam-4381	188	28	(	(	PUNCT
ejpam-4381	188	29	v	v	NOUN
ejpam-4381	188	30	(	(	PUNCT
ejpam-4381	188	31	g[h	g[h	NOUN
ejpam-4381	188	32	]	]	PUNCT
ejpam-4381	188	33	)	)	PUNCT
ejpam-4381	188	34	\	\	PUNCT
ejpam-4381	189	1	(	(	PUNCT
ejpam-4381	189	2	a×	a×	NOUN
ejpam-4381	189	3	v	v	X
ejpam-4381	189	4	(	(	PUNCT
ejpam-4381	189	5	h	h	NOUN
ejpam-4381	189	6	)	)	PUNCT
ejpam-4381	189	7	)	)	PUNCT
ejpam-4381	189	8	)	)	PUNCT
ejpam-4381	189	9	∣∣∣	∣∣∣	NOUN
ejpam-4381	189	10	=	=	PUNCT
ejpam-4381	189	11	|nk	|nk	PROPN
ejpam-4381	189	12	g(u	g(u	PROPN
ejpam-4381	189	13	)	)	PUNCT
ejpam-4381	189	14	∩	∩	NOUN
ejpam-4381	189	15	(	(	PUNCT
ejpam-4381	189	16	v	v	NOUN
ejpam-4381	189	17	(	(	PUNCT
ejpam-4381	189	18	g	g	NOUN
ejpam-4381	189	19	)	)	PUNCT
ejpam-4381	189	20	\a)||v	\a)||v	X
ejpam-4381	189	21	(	(	PUNCT
ejpam-4381	189	22	h)|	h)|	PROPN
ejpam-4381	189	23	.	.	PUNCT
ejpam-4381	189	24	hence	hence	ADV
ejpam-4381	189	25	,	,	PUNCT
ejpam-4381	189	26	|nk	|nk	ADP
ejpam-4381	189	27	g[h](u	g[h](u	PROPN
ejpam-4381	189	28	,	,	PUNCT
ejpam-4381	189	29	v	v	NOUN
ejpam-4381	189	30	)	)	PUNCT
ejpam-4381	189	31	∩	∩	NOUN
ejpam-4381	189	32	(	(	PUNCT
ejpam-4381	189	33	v	v	NOUN
ejpam-4381	189	34	(	(	PUNCT
ejpam-4381	189	35	g[h])\(a×	g[h])\(a×	PROPN
ejpam-4381	189	36	v	v	NOUN
ejpam-4381	189	37	(	(	PUNCT
ejpam-4381	189	38	h)))|	h)))|	X
ejpam-4381	189	39	−	−	PROPN
ejpam-4381	189	40	|nk	|nk	ADP
ejpam-4381	189	41	g[h](u	g[h](u	PROPN
ejpam-4381	189	42	,	,	PUNCT
ejpam-4381	189	43	v	v	NOUN
ejpam-4381	189	44	)	)	PUNCT
ejpam-4381	189	45	∩	∩	NOUN
ejpam-4381	189	46	(	(	PUNCT
ejpam-4381	189	47	a×	a×	NOUN
ejpam-4381	189	48	v	v	X
ejpam-4381	189	49	(	(	PUNCT
ejpam-4381	189	50	h))|	h))|	PROPN
ejpam-4381	189	51	=	=	PUNCT
ejpam-4381	189	52	|nk	|nk	PROPN
ejpam-4381	189	53	g(u	g(u	PROPN
ejpam-4381	189	54	)	)	PUNCT
ejpam-4381	189	55	∩	∩	NOUN
ejpam-4381	189	56	(	(	PUNCT
ejpam-4381	189	57	v	v	NOUN
ejpam-4381	189	58	(	(	PUNCT
ejpam-4381	189	59	g	g	NOUN
ejpam-4381	189	60	)	)	PUNCT
ejpam-4381	189	61	\a)||v	\a)||v	PUNCT
ejpam-4381	189	62	(	(	PUNCT
ejpam-4381	189	63	h)|	h)|	NOUN
ejpam-4381	189	64	−	−	PROPN
ejpam-4381	189	65	|nk	|nk	ADP
ejpam-4381	189	66	g(u	g(u	PROPN
ejpam-4381	189	67	)	)	PUNCT
ejpam-4381	189	68	∩a||v	∩a||v	PROPN
ejpam-4381	189	69	(	(	PUNCT
ejpam-4381	189	70	h)|	h)|	PROPN
ejpam-4381	189	71	−	−	PROPN
ejpam-4381	189	72	|v	|v	PROPN
ejpam-4381	189	73	(	(	PUNCT
ejpam-4381	189	74	h)|	h)|	NOUN
ejpam-4381	189	75	=	=	SYM
ejpam-4381	189	76	(	(	PUNCT
ejpam-4381	189	77	|nk	|nk	ADP
ejpam-4381	189	78	g(u	g(u	PROPN
ejpam-4381	189	79	)	)	PUNCT
ejpam-4381	189	80	∩	∩	NOUN
ejpam-4381	189	81	(	(	PUNCT
ejpam-4381	189	82	v	v	NOUN
ejpam-4381	189	83	(	(	PUNCT
ejpam-4381	189	84	g	g	NOUN
ejpam-4381	189	85	)	)	PUNCT
ejpam-4381	189	86	\a)|	\a)|	X
ejpam-4381	189	87	−	−	PROPN
ejpam-4381	189	88	|nk	|nk	PROPN
ejpam-4381	189	89	g(u	g(u	PROPN
ejpam-4381	189	90	)	)	PUNCT
ejpam-4381	189	91	∩a|	∩a|	ADP
ejpam-4381	189	92	−	−	NOUN
ejpam-4381	189	93	1	1	NUM
ejpam-4381	189	94	)	)	PUNCT
ejpam-4381	189	95	|v	|v	PROPN
ejpam-4381	189	96	(	(	PUNCT
ejpam-4381	189	97	h)|	h)|	PROPN
ejpam-4381	189	98	.	.	PUNCT
ejpam-4381	190	1	since	since	SCONJ
ejpam-4381	190	2	a	a	PRON
ejpam-4381	190	3	is	be	AUX
ejpam-4381	190	4	a	a	DET
ejpam-4381	190	5	very	very	ADJ
ejpam-4381	190	6	distance	distance	NOUN
ejpam-4381	190	7	k	k	ADJ
ejpam-4381	190	8	-	-	PUNCT
ejpam-4381	190	9	cost	cost	ADJ
ejpam-4381	190	10	effective	effective	ADJ
ejpam-4381	190	11	set	set	NOUN
ejpam-4381	190	12	in	in	ADP
ejpam-4381	190	13	g	g	NOUN
ejpam-4381	190	14	,	,	PUNCT
ejpam-4381	190	15	|nk	|nk	NUM
ejpam-4381	190	16	g(u)∩(v	g(u)∩(v	X
ejpam-4381	190	17	(	(	PUNCT
ejpam-4381	190	18	g)\a)|−|nk	g)\a)|−|nk	NOUN
ejpam-4381	190	19	g(u)∩a|	g(u)∩a|	PROPN
ejpam-4381	190	20	>	>	X
ejpam-4381	190	21	0	0	NUM
ejpam-4381	190	22	.	.	PUNCT
ejpam-4381	191	1	thus	thus	ADV
ejpam-4381	191	2	,	,	PUNCT
ejpam-4381	191	3	∣∣nk	∣∣nk	PROPN
ejpam-4381	191	4	g[h](u	g[h](u	PROPN
ejpam-4381	191	5	,	,	PUNCT
ejpam-4381	191	6	v)∩	v)∩	X
ejpam-4381	191	7	(	(	PUNCT
ejpam-4381	191	8	v	v	X
ejpam-4381	191	9	(	(	PUNCT
ejpam-4381	191	10	g[h])\(a×v	g[h])\(a×v	PROPN
ejpam-4381	191	11	(	(	PUNCT
ejpam-4381	191	12	h	h	NOUN
ejpam-4381	191	13	)	)	PUNCT
ejpam-4381	191	14	)	)	PUNCT
ejpam-4381	191	15	)	)	PUNCT
ejpam-4381	191	16	∣∣−|nk	∣∣−|nk	X
ejpam-4381	192	1	g[h](u	g[h](u	X
ejpam-4381	192	2	,	,	PUNCT
ejpam-4381	192	3	v)∩(a×v	v)∩(a×v	PROPN
ejpam-4381	192	4	(	(	PUNCT
ejpam-4381	192	5	h))|	h))|	PROPN
ejpam-4381	192	6	≥	≥	NUM
ejpam-4381	192	7	0	0	NUM
ejpam-4381	192	8	.	.	PUNCT
ejpam-4381	192	9	accordingly	accordingly	ADV
ejpam-4381	192	10	,	,	PUNCT
ejpam-4381	192	11	a×	a×	PROPN
ejpam-4381	192	12	v	v	X
ejpam-4381	192	13	(	(	PUNCT
ejpam-4381	192	14	h	h	NOUN
ejpam-4381	192	15	)	)	PUNCT
ejpam-4381	192	16	is	be	AUX
ejpam-4381	192	17	a	a	DET
ejpam-4381	192	18	distance	distance	NOUN
ejpam-4381	192	19	k	k	ADJ
ejpam-4381	192	20	-	-	PUNCT
ejpam-4381	192	21	cost	cost	NOUN
ejpam-4381	192	22	effective	effective	ADJ
ejpam-4381	192	23	set	set	NOUN
ejpam-4381	192	24	in	in	ADP
ejpam-4381	192	25	g[h	g[h	PROPN
ejpam-4381	192	26	]	]	PUNCT
ejpam-4381	192	27	.	.	PUNCT
ejpam-4381	193	1	references	reference	NOUN
ejpam-4381	193	2	269	269	NUM
ejpam-4381	193	3	now	now	ADV
ejpam-4381	193	4	for	for	ADP
ejpam-4381	193	5	k	k	PROPN
ejpam-4381	193	6	=	=	SYM
ejpam-4381	193	7	1	1	NUM
ejpam-4381	193	8	,	,	PUNCT
ejpam-4381	193	9	let	let	VERB
ejpam-4381	193	10	a	a	PRON
ejpam-4381	193	11	be	be	AUX
ejpam-4381	193	12	a	a	DET
ejpam-4381	193	13	very	very	ADJ
ejpam-4381	193	14	distance	distance	NOUN
ejpam-4381	193	15	1	1	NUM
ejpam-4381	193	16	-	-	PUNCT
ejpam-4381	193	17	cost	cost	NOUN
ejpam-4381	193	18	effective	effective	ADJ
ejpam-4381	193	19	set	set	NOUN
ejpam-4381	193	20	in	in	ADP
ejpam-4381	193	21	g.	g.	PROPN
ejpam-4381	193	22	then	then	ADV
ejpam-4381	193	23	for	for	ADP
ejpam-4381	193	24	each	each	DET
ejpam-4381	193	25	(	(	PUNCT
ejpam-4381	193	26	u	u	NOUN
ejpam-4381	193	27	,	,	PUNCT
ejpam-4381	193	28	v	v	NOUN
ejpam-4381	193	29	)	)	PUNCT
ejpam-4381	193	30	∈	∈	PROPN
ejpam-4381	193	31	a×	a×	PUNCT
ejpam-4381	193	32	v	v	NOUN
ejpam-4381	193	33	(	(	PUNCT
ejpam-4381	193	34	h	h	NOUN
ejpam-4381	193	35	)	)	PUNCT
ejpam-4381	193	36	,	,	PUNCT
ejpam-4381	193	37	we	we	PRON
ejpam-4381	193	38	have	have	AUX
ejpam-4381	193	39	|n1	|n1	VERB
ejpam-4381	193	40	g[h](u	g[h](u	PROPN
ejpam-4381	193	41	,	,	PUNCT
ejpam-4381	193	42	v	v	NOUN
ejpam-4381	193	43	)	)	PUNCT
ejpam-4381	194	1	∩	∩	NOUN
ejpam-4381	194	2	(	(	PUNCT
ejpam-4381	194	3	v	v	NOUN
ejpam-4381	194	4	(	(	PUNCT
ejpam-4381	194	5	g[h])\(a×	g[h])\(a×	PROPN
ejpam-4381	194	6	v	v	NOUN
ejpam-4381	194	7	(	(	PUNCT
ejpam-4381	194	8	h)))|	h)))|	PROPN
ejpam-4381	194	9	−	−	PROPN
ejpam-4381	194	10	|n1	|n1	VERB
ejpam-4381	194	11	g[h](u	g[h](u	PROPN
ejpam-4381	194	12	,	,	PUNCT
ejpam-4381	194	13	v	v	NOUN
ejpam-4381	194	14	)	)	PUNCT
ejpam-4381	194	15	∩	∩	NOUN
ejpam-4381	194	16	(	(	PUNCT
ejpam-4381	194	17	a×	a×	NOUN
ejpam-4381	194	18	v	v	X
ejpam-4381	194	19	(	(	PUNCT
ejpam-4381	194	20	h))|	h))|	PROPN
ejpam-4381	194	21	=	=	PUNCT
ejpam-4381	194	22	|n1	|n1	VERB
ejpam-4381	194	23	g(u	g(u	NOUN
ejpam-4381	194	24	)	)	PUNCT
ejpam-4381	194	25	∩	∩	NOUN
ejpam-4381	194	26	(	(	PUNCT
ejpam-4381	194	27	v	v	NOUN
ejpam-4381	194	28	(	(	PUNCT
ejpam-4381	194	29	g	g	NOUN
ejpam-4381	194	30	)	)	PUNCT
ejpam-4381	194	31	\a)||v	\a)||v	PUNCT
ejpam-4381	194	32	(	(	PUNCT
ejpam-4381	194	33	h)|	h)|	PROPN
ejpam-4381	194	34	−	−	PROPN
ejpam-4381	194	35	|n1	|n1	VERB
ejpam-4381	194	36	g(u	g(u	NOUN
ejpam-4381	194	37	)	)	PUNCT
ejpam-4381	194	38	∩a||v	∩a||v	PROPN
ejpam-4381	194	39	(	(	PUNCT
ejpam-4381	194	40	h)|	h)|	PROPN
ejpam-4381	194	41	−	−	PROPN
ejpam-4381	194	42	|n1	|n1	VERB
ejpam-4381	194	43	h(v)|	h(v)|	NOUN
ejpam-4381	194	44	=	=	PUNCT
ejpam-4381	194	45	(	(	PUNCT
ejpam-4381	194	46	|n1	|n1	X
ejpam-4381	194	47	g(u	g(u	NOUN
ejpam-4381	194	48	)	)	PUNCT
ejpam-4381	195	1	∩	∩	NOUN
ejpam-4381	195	2	(	(	PUNCT
ejpam-4381	195	3	v	v	NOUN
ejpam-4381	195	4	(	(	PUNCT
ejpam-4381	195	5	g	g	NOUN
ejpam-4381	195	6	)	)	PUNCT
ejpam-4381	195	7	\a)|	\a)|	PROPN
ejpam-4381	195	8	−	−	NOUN
ejpam-4381	195	9	|n1	|n1	VERB
ejpam-4381	195	10	g(u	g(u	PROPN
ejpam-4381	195	11	)	)	PUNCT
ejpam-4381	195	12	∩a|	∩a|	PROPN
ejpam-4381	195	13	)	)	PUNCT
ejpam-4381	195	14	|v	|v	PROPN
ejpam-4381	195	15	(	(	PUNCT
ejpam-4381	195	16	h)|	h)|	NOUN
ejpam-4381	195	17	−	−	PROPN
ejpam-4381	195	18	|n1	|n1	VERB
ejpam-4381	195	19	h(v)|	h(v)|	NOUN
ejpam-4381	195	20	≥	≥	X
ejpam-4381	195	21	(	(	PUNCT
ejpam-4381	195	22	|n1	|n1	VERB
ejpam-4381	195	23	g(u	g(u	NOUN
ejpam-4381	195	24	)	)	PUNCT
ejpam-4381	195	25	∩	∩	NOUN
ejpam-4381	195	26	(	(	PUNCT
ejpam-4381	195	27	v	v	NOUN
ejpam-4381	195	28	(	(	PUNCT
ejpam-4381	195	29	g	g	NOUN
ejpam-4381	195	30	)	)	PUNCT
ejpam-4381	195	31	\a)|	\a)|	PROPN
ejpam-4381	195	32	−	−	NOUN
ejpam-4381	195	33	|n1	|n1	VERB
ejpam-4381	195	34	g(u	g(u	PROPN
ejpam-4381	195	35	)	)	PUNCT
ejpam-4381	195	36	∩a|	∩a|	PROPN
ejpam-4381	195	37	)	)	PUNCT
ejpam-4381	196	1	|v	|v	PROPN
ejpam-4381	196	2	(	(	PUNCT
ejpam-4381	196	3	h)|	h)|	PROPN
ejpam-4381	196	4	−	−	PROPN
ejpam-4381	196	5	|v	|v	PROPN
ejpam-4381	196	6	(	(	PUNCT
ejpam-4381	196	7	h)|	h)|	NOUN
ejpam-4381	196	8	=	=	PUNCT
ejpam-4381	196	9	(	(	PUNCT
ejpam-4381	196	10	|n1	|n1	X
ejpam-4381	196	11	g(u	g(u	NOUN
ejpam-4381	196	12	)	)	PUNCT
ejpam-4381	196	13	∩	∩	NOUN
ejpam-4381	196	14	(	(	PUNCT
ejpam-4381	196	15	v	v	NOUN
ejpam-4381	196	16	(	(	PUNCT
ejpam-4381	196	17	g	g	NOUN
ejpam-4381	196	18	)	)	PUNCT
ejpam-4381	196	19	\a)|	\a)|	PROPN
ejpam-4381	196	20	−	−	NOUN
ejpam-4381	196	21	|n1	|n1	VERB
ejpam-4381	196	22	g(u	g(u	PROPN
ejpam-4381	196	23	)	)	PUNCT
ejpam-4381	196	24	∩a|	∩a|	ADP
ejpam-4381	196	25	−	−	NOUN
ejpam-4381	196	26	1	1	NUM
ejpam-4381	196	27	)	)	PUNCT
ejpam-4381	196	28	|v	|v	PROPN
ejpam-4381	196	29	(	(	PUNCT
ejpam-4381	196	30	h)|	h)|	PROPN
ejpam-4381	196	31	.	.	PUNCT
ejpam-4381	197	1	since	since	SCONJ
ejpam-4381	197	2	a	a	PRON
ejpam-4381	197	3	is	be	AUX
ejpam-4381	197	4	a	a	DET
ejpam-4381	197	5	very	very	ADJ
ejpam-4381	197	6	distance	distance	NOUN
ejpam-4381	197	7	1	1	NUM
ejpam-4381	197	8	-	-	PUNCT
ejpam-4381	197	9	cost	cost	NOUN
ejpam-4381	197	10	effective	effective	ADJ
ejpam-4381	197	11	set	set	NOUN
ejpam-4381	197	12	in	in	ADP
ejpam-4381	197	13	g	g	NOUN
ejpam-4381	197	14	,	,	PUNCT
ejpam-4381	197	15	|n1	|n1	VERB
ejpam-4381	197	16	g(u)∩	g(u)∩	PROPN
ejpam-4381	197	17	(	(	PUNCT
ejpam-4381	197	18	v	v	NOUN
ejpam-4381	197	19	(	(	PUNCT
ejpam-4381	197	20	g)\a)|−|n1	g)\a)|−|n1	NOUN
ejpam-4381	197	21	g(u)∩a|	g(u)∩a|	PROPN
ejpam-4381	197	22	>	>	X
ejpam-4381	197	23	0	0	NUM
ejpam-4381	197	24	.	.	PUNCT
ejpam-4381	198	1	thus	thus	ADV
ejpam-4381	198	2	,	,	PUNCT
ejpam-4381	198	3	|n1	|n1	VERB
ejpam-4381	198	4	g[h](u	g[h](u	PROPN
ejpam-4381	198	5	,	,	PUNCT
ejpam-4381	198	6	v	v	NOUN
ejpam-4381	198	7	)	)	PUNCT
ejpam-4381	198	8	∩	∩	NOUN
ejpam-4381	198	9	(	(	PUNCT
ejpam-4381	198	10	v	v	NOUN
ejpam-4381	198	11	(	(	PUNCT
ejpam-4381	198	12	g[h	g[h	NOUN
ejpam-4381	198	13	]	]	PUNCT
ejpam-4381	198	14	)	)	PUNCT
ejpam-4381	198	15	\	\	PUNCT
ejpam-4381	199	1	(	(	PUNCT
ejpam-4381	199	2	a×	a×	NOUN
ejpam-4381	199	3	v	v	X
ejpam-4381	199	4	(	(	PUNCT
ejpam-4381	199	5	h	h	NOUN
ejpam-4381	199	6	)	)	PUNCT
ejpam-4381	199	7	)	)	PUNCT
ejpam-4381	199	8	)	)	PUNCT
ejpam-4381	200	1	|	|	ADV
ejpam-4381	200	2	−	−	NOUN
ejpam-4381	200	3	|n1	|n1	VERB
ejpam-4381	200	4	g[h](u	g[h](u	PROPN
ejpam-4381	200	5	,	,	PUNCT
ejpam-4381	200	6	v	v	NOUN
ejpam-4381	200	7	)	)	PUNCT
ejpam-4381	200	8	∩	∩	NOUN
ejpam-4381	200	9	(	(	PUNCT
ejpam-4381	200	10	a×	a×	PROPN
ejpam-4381	200	11	v	v	X
ejpam-4381	200	12	(	(	PUNCT
ejpam-4381	200	13	h))|	h))|	PROPN
ejpam-4381	200	14	≥	≥	NOUN
ejpam-4381	200	15	0	0	NUM
ejpam-4381	200	16	.	.	PUNCT
ejpam-4381	201	1	hence	hence	ADV
ejpam-4381	201	2	,	,	PUNCT
ejpam-4381	201	3	a	a	DET
ejpam-4381	201	4	×	×	NOUN
ejpam-4381	201	5	v	v	NOUN
ejpam-4381	201	6	(	(	PUNCT
ejpam-4381	201	7	h	h	NOUN
ejpam-4381	201	8	)	)	PUNCT
ejpam-4381	201	9	is	be	AUX
ejpam-4381	201	10	a	a	DET
ejpam-4381	201	11	distance	distance	NOUN
ejpam-4381	201	12	1	1	NUM
ejpam-4381	201	13	-	-	PUNCT
ejpam-4381	201	14	cost	cost	NOUN
ejpam-4381	201	15	effective	effective	ADJ
ejpam-4381	201	16	set	set	NOUN
ejpam-4381	201	17	in	in	ADP
ejpam-4381	201	18	g[h	g[h	PROPN
ejpam-4381	201	19	]	]	PUNCT
ejpam-4381	201	20	.	.	PUNCT
ejpam-4381	202	1	therefore	therefore	ADV
ejpam-4381	202	2	,	,	PUNCT
ejpam-4381	202	3	a	a	DET
ejpam-4381	202	4	×	×	NOUN
ejpam-4381	202	5	v	v	NOUN
ejpam-4381	202	6	(	(	PUNCT
ejpam-4381	202	7	h	h	NOUN
ejpam-4381	202	8	)	)	PUNCT
ejpam-4381	202	9	is	be	AUX
ejpam-4381	202	10	a	a	DET
ejpam-4381	202	11	distance	distance	NOUN
ejpam-4381	202	12	k	k	ADJ
ejpam-4381	202	13	-	-	PUNCT
ejpam-4381	202	14	cost	cost	NOUN
ejpam-4381	202	15	effective	effective	ADJ
ejpam-4381	202	16	set	set	NOUN
ejpam-4381	202	17	in	in	ADP
ejpam-4381	202	18	g[h	g[h	PROPN
ejpam-4381	202	19	]	]	PUNCT
ejpam-4381	202	20	.	.	PUNCT
ejpam-4381	203	1	corollary	corollary	ADJ
ejpam-4381	203	2	7	7	NUM
ejpam-4381	203	3	.	.	PUNCT
ejpam-4381	204	1	let	let	VERB
ejpam-4381	204	2	g	g	NOUN
ejpam-4381	204	3	and	and	CCONJ
ejpam-4381	204	4	h	h	NOUN
ejpam-4381	204	5	be	be	AUX
ejpam-4381	204	6	connected	connect	VERB
ejpam-4381	204	7	graphs	graph	NOUN
ejpam-4381	204	8	and	and	CCONJ
ejpam-4381	204	9	k	k	X
ejpam-4381	204	10	≥	≥	NUM
ejpam-4381	204	11	1	1	NUM
ejpam-4381	204	12	be	be	AUX
ejpam-4381	204	13	an	an	DET
ejpam-4381	204	14	integer	integer	NOUN
ejpam-4381	204	15	.	.	PUNCT
ejpam-4381	205	1	then	then	ADV
ejpam-4381	205	2	αk	αk	ADP
ejpam-4381	205	3	ce(g[h	ce(g[h	NOUN
ejpam-4381	205	4	]	]	X
ejpam-4381	205	5	)	)	PUNCT
ejpam-4381	205	6	≥	≥	NOUN
ejpam-4381	206	1	αk	αk	X
ejpam-4381	206	2	ce(g)|v	ce(g)|v	PROPN
ejpam-4381	206	3	(	(	PUNCT
ejpam-4381	206	4	h)|	h)|	PROPN
ejpam-4381	206	5	.	.	PUNCT
ejpam-4381	206	6	acknowledgements	acknowledgement	NOUN
ejpam-4381	206	7	this	this	DET
ejpam-4381	206	8	research	research	NOUN
ejpam-4381	206	9	is	be	AUX
ejpam-4381	206	10	funded	fund	VERB
ejpam-4381	206	11	by	by	ADP
ejpam-4381	206	12	the	the	DET
ejpam-4381	206	13	commission	commission	NOUN
ejpam-4381	206	14	on	on	ADP
ejpam-4381	206	15	higher	high	ADJ
ejpam-4381	206	16	education	education	NOUN
ejpam-4381	206	17	(	(	PUNCT
ejpam-4381	206	18	ched	che	VERB
ejpam-4381	206	19	)	)	PUNCT
ejpam-4381	206	20	and	and	CCONJ
ejpam-4381	206	21	mindanao	mindanao	PROPN
ejpam-4381	206	22	state	state	PROPN
ejpam-4381	206	23	university	university	PROPN
ejpam-4381	206	24	-	-	PUNCT
ejpam-4381	206	25	iligan	iligan	PROPN
ejpam-4381	206	26	institute	institute	PROPN
ejpam-4381	206	27	of	of	ADP
ejpam-4381	206	28	technology	technology	PROPN
ejpam-4381	206	29	.	.	PUNCT
ejpam-4381	207	1	references	reference	NOUN
ejpam-4381	207	2	[	[	X
ejpam-4381	207	3	1	1	X
ejpam-4381	207	4	]	]	PUNCT
ejpam-4381	207	5	k.	k.	PROPN
ejpam-4381	207	6	a.	a.	PROPN
ejpam-4381	207	7	bibi	bibi	PROPN
ejpam-4381	207	8	,	,	PUNCT
ejpam-4381	207	9	a.	a.	NOUN
ejpam-4381	207	10	lakshmi	lakshmi	PROPN
ejpam-4381	207	11	,	,	PUNCT
ejpam-4381	207	12	and	and	CCONJ
ejpam-4381	207	13	r.	r.	PROPN
ejpam-4381	207	14	jothilakshmi	jothilakshmi	PROPN
ejpam-4381	207	15	.	.	PUNCT
ejpam-4381	208	1	applications	application	NOUN
ejpam-4381	208	2	of	of	ADP
ejpam-4381	208	3	distance-2	distance-2	PRON
ejpam-4381	208	4	dominating	dominating	NOUN
ejpam-4381	208	5	sets	set	NOUN
ejpam-4381	208	6	of	of	ADP
ejpam-4381	208	7	graph	graph	NOUN
ejpam-4381	208	8	in	in	ADP
ejpam-4381	208	9	networks	network	NOUN
ejpam-4381	208	10	.	.	PUNCT
ejpam-4381	209	1	advances	advance	NOUN
ejpam-4381	209	2	in	in	ADP
ejpam-4381	209	3	computational	computational	ADJ
ejpam-4381	209	4	sciences	science	NOUN
ejpam-4381	209	5	and	and	CCONJ
ejpam-4381	209	6	technology	technology	NOUN
ejpam-4381	209	7	,	,	PUNCT
ejpam-4381	209	8	10(9):2801–2810	10(9):2801–2810	NUM
ejpam-4381	209	9	,	,	PUNCT
ejpam-4381	209	10	2017	2017	NUM
ejpam-4381	209	11	.	.	PUNCT
ejpam-4381	210	1	[	[	X
ejpam-4381	210	2	2	2	NUM
ejpam-4381	210	3	]	]	X
ejpam-4381	210	4	f.	f.	PROPN
ejpam-4381	210	5	buckley	buckley	PROPN
ejpam-4381	210	6	and	and	CCONJ
ejpam-4381	210	7	f.	f.	PROPN
ejpam-4381	210	8	harary	harary	PROPN
ejpam-4381	210	9	.	.	PUNCT
ejpam-4381	211	1	distance	distance	NOUN
ejpam-4381	211	2	in	in	ADP
ejpam-4381	211	3	graphs	graph	NOUN
ejpam-4381	211	4	.	.	PUNCT
ejpam-4381	212	1	addison	addison	PROPN
ejpam-4381	212	2	-	-	PUNCT
ejpam-4381	212	3	wesley	wesley	PROPN
ejpam-4381	212	4	,	,	PUNCT
ejpam-4381	212	5	redwood	redwood	NOUN
ejpam-4381	212	6	city	city	NOUN
ejpam-4381	212	7	,	,	PUNCT
ejpam-4381	212	8	ca	ca	NOUN
ejpam-4381	212	9	,	,	PUNCT
ejpam-4381	212	10	1990	1990	NUM
ejpam-4381	212	11	.	.	PUNCT
ejpam-4381	213	1	[	[	X
ejpam-4381	213	2	3	3	X
ejpam-4381	213	3	]	]	X
ejpam-4381	213	4	j.	j.	PROPN
ejpam-4381	213	5	caadan	caadan	PROPN
ejpam-4381	213	6	,	,	PUNCT
ejpam-4381	213	7	r.	r.	PROPN
ejpam-4381	213	8	paluga	paluga	PROPN
ejpam-4381	213	9	,	,	PUNCT
ejpam-4381	213	10	and	and	CCONJ
ejpam-4381	213	11	i.	i.	PROPN
ejpam-4381	213	12	aniversario	aniversario	PROPN
ejpam-4381	213	13	.	.	PUNCT
ejpam-4381	214	1	upper	upper	ADJ
ejpam-4381	214	2	distance	distance	NOUN
ejpam-4381	214	3	k	k	ADJ
ejpam-4381	214	4	-	-	PUNCT
ejpam-4381	214	5	cost	cost	ADJ
ejpam-4381	214	6	effective	effective	ADJ
ejpam-4381	214	7	numbers	number	NOUN
ejpam-4381	214	8	in	in	ADP
ejpam-4381	214	9	the	the	DET
ejpam-4381	214	10	join	join	NOUN
ejpam-4381	214	11	of	of	ADP
ejpam-4381	214	12	graphs	graph	NOUN
ejpam-4381	214	13	.	.	PUNCT
ejpam-4381	215	1	european	european	ADJ
ejpam-4381	215	2	journal	journal	PROPN
ejpam-4381	215	3	of	of	ADP
ejpam-4381	215	4	pure	pure	ADJ
ejpam-4381	215	5	and	and	CCONJ
ejpam-4381	215	6	applied	applied	ADJ
ejpam-4381	215	7	mathematics	mathematic	NOUN
ejpam-4381	215	8	,	,	PUNCT
ejpam-4381	215	9	13(3):701	13(3):701	NUM
ejpam-4381	215	10	–	–	PUNCT
ejpam-4381	215	11	709	709	NUM
ejpam-4381	215	12	,	,	PUNCT
ejpam-4381	215	13	2020	2020	NUM
ejpam-4381	215	14	.	.	PUNCT
ejpam-4381	216	1	[	[	X
ejpam-4381	216	2	4	4	X
ejpam-4381	216	3	]	]	X
ejpam-4381	216	4	t.w	t.w	PROPN
ejpam-4381	216	5	.	.	PROPN
ejpam-4381	216	6	haynes	haynes	PROPN
ejpam-4381	216	7	,	,	PUNCT
ejpam-4381	216	8	m.	m.	NOUN
ejpam-4381	216	9	chellali	chellali	PROPN
ejpam-4381	216	10	,	,	PUNCT
ejpam-4381	216	11	and	and	CCONJ
ejpam-4381	216	12	s.t	s.t	PROPN
ejpam-4381	216	13	.	.	PROPN
ejpam-4381	216	14	hedetniem	hedetniem	PROPN
ejpam-4381	216	15	.	.	PUNCT
ejpam-4381	216	16	client	client	NOUN
ejpam-4381	216	17	-	-	PUNCT
ejpam-4381	216	18	server	server	NOUN
ejpam-4381	216	19	and	and	CCONJ
ejpam-4381	216	20	cost	cost	VERB
ejpam-4381	216	21	effective	effective	ADJ
ejpam-4381	216	22	sets	set	NOUN
ejpam-4381	216	23	in	in	ADP
ejpam-4381	216	24	graphs	graph	NOUN
ejpam-4381	216	25	.	.	PUNCT
ejpam-4381	217	1	akce	akce	PROPN
ejpam-4381	217	2	international	international	PROPN
ejpam-4381	217	3	journal	journal	NOUN
ejpam-4381	217	4	of	of	ADP
ejpam-4381	217	5	graphs	graph	NOUN
ejpam-4381	217	6	and	and	CCONJ
ejpam-4381	217	7	combinatorics	combinatoric	NOUN
ejpam-4381	217	8	,	,	PUNCT
ejpam-4381	217	9	15:211–218	15:211–218	NUM
ejpam-4381	217	10	,	,	PUNCT
ejpam-4381	217	11	2018	2018	NUM
ejpam-4381	217	12	.	.	PUNCT
ejpam-4381	218	1	[	[	X
ejpam-4381	218	2	5	5	X
ejpam-4381	218	3	]	]	X
ejpam-4381	218	4	t.w	t.w	PROPN
ejpam-4381	218	5	.	.	PROPN
ejpam-4381	218	6	haynes	haynes	PROPN
ejpam-4381	218	7	,	,	PUNCT
ejpam-4381	218	8	m.	m.	NOUN
ejpam-4381	218	9	henning	henning	PROPN
ejpam-4381	218	10	,	,	PUNCT
ejpam-4381	218	11	and	and	CCONJ
ejpam-4381	218	12	s.t	s.t	PROPN
ejpam-4381	218	13	.	.	PROPN
ejpam-4381	218	14	hedetniemi	hedetniemi	PROPN
ejpam-4381	218	15	.	.	PUNCT
ejpam-4381	219	1	domination	domination	NOUN
ejpam-4381	219	2	in	in	ADP
ejpam-4381	219	3	graphs	graph	NOUN
ejpam-4381	219	4	applied	apply	VERB
ejpam-4381	219	5	to	to	ADP
ejpam-4381	219	6	electrical	electrical	ADJ
ejpam-4381	219	7	power	power	NOUN
ejpam-4381	219	8	networks	network	NOUN
ejpam-4381	219	9	.	.	PUNCT
ejpam-4381	220	1	j.	j.	PROPN
ejpam-4381	220	2	discrete	discrete	PROPN
ejpam-4381	220	3	math	math	PROPN
ejpam-4381	220	4	,	,	PUNCT
ejpam-4381	220	5	15(4	15(4	NUM
ejpam-4381	220	6	)	)	PUNCT
ejpam-4381	220	7	,	,	PUNCT
ejpam-4381	220	8	2000	2000	NUM
ejpam-4381	220	9	.	.	PUNCT
ejpam-4381	221	1	references	reference	NOUN
ejpam-4381	221	2	270	270	NUM
ejpam-4381	221	3	[	[	X
ejpam-4381	221	4	6	6	NUM
ejpam-4381	221	5	]	]	X
ejpam-4381	221	6	t.w	t.w	PROPN
ejpam-4381	221	7	.	.	PROPN
ejpam-4381	221	8	haynes	haynes	PROPN
ejpam-4381	221	9	,	,	PUNCT
ejpam-4381	221	10	i.	i.	PROPN
ejpam-4381	221	11	vasylieva	vasylieva	PROPN
ejpam-4381	221	12	,	,	PUNCT
ejpam-4381	221	13	and	and	CCONJ
ejpam-4381	221	14	s.t	s.t	PROPN
ejpam-4381	221	15	.	.	PROPN
ejpam-4381	221	16	hedetniemi	hedetniemi	PROPN
ejpam-4381	221	17	.	.	PUNCT
ejpam-4381	222	1	very	very	ADV
ejpam-4381	222	2	cost	cost	VERB
ejpam-4381	222	3	effective	effective	ADJ
ejpam-4381	222	4	bipartitions	bipartition	NOUN
ejpam-4381	222	5	in	in	ADP
ejpam-4381	222	6	graphs	graph	NOUN
ejpam-4381	222	7	.	.	PUNCT
ejpam-4381	223	1	akce	akce	PROPN
ejpam-4381	223	2	international	international	PROPN
ejpam-4381	223	3	journal	journal	NOUN
ejpam-4381	223	4	of	of	ADP
ejpam-4381	223	5	graphs	graph	NOUN
ejpam-4381	223	6	and	and	CCONJ
ejpam-4381	223	7	combinatorics	combinatoric	NOUN
ejpam-4381	223	8	,	,	PUNCT
ejpam-4381	223	9	12:155–160	12:155–160	NUM
ejpam-4381	223	10	,	,	PUNCT
ejpam-4381	223	11	2015	2015	NUM
ejpam-4381	223	12	.	.	PUNCT
ejpam-4381	224	1	[	[	X
ejpam-4381	224	2	7	7	NUM
ejpam-4381	224	3	]	]	X
ejpam-4381	224	4	s.m	s.m	PROPN
ejpam-4381	224	5	.	.	PROPN
ejpam-4381	224	6	hedetniemi	hedetniemi	PROPN
ejpam-4381	224	7	,	,	PUNCT
ejpam-4381	224	8	t.w	t.w	PROPN
ejpam-4381	224	9	.	.	PROPN
ejpam-4381	224	10	haynes	haynes	PROPN
ejpam-4381	224	11	,	,	PUNCT
ejpam-4381	224	12	s.t	s.t	PROPN
ejpam-4381	224	13	.	.	PROPN
ejpam-4381	224	14	hedetniemi	hedetniemi	PROPN
ejpam-4381	224	15	,	,	PUNCT
ejpam-4381	224	16	t.l	t.l	PROPN
ejpam-4381	224	17	.	.	PROPN
ejpam-4381	224	18	mccoy	mccoy	PROPN
ejpam-4381	224	19	,	,	PUNCT
ejpam-4381	224	20	and	and	CCONJ
ejpam-4381	224	21	i.	i.	PROPN
ejpam-4381	224	22	vasylieva	vasylieva	PROPN
ejpam-4381	224	23	.	.	PUNCT
ejpam-4381	225	1	cost	cost	VERB
ejpam-4381	225	2	effective	effective	ADJ
ejpam-4381	225	3	domination	domination	NOUN
ejpam-4381	225	4	in	in	ADP
ejpam-4381	225	5	graphs	graph	NOUN
ejpam-4381	225	6	.	.	PUNCT
ejpam-4381	226	1	congr	congr	NOUN
ejpam-4381	226	2	.	.	PUNCT
ejpam-4381	227	1	numer	numer	PROPN
ejpam-4381	227	2	.	.	PROPN
ejpam-4381	227	3	,	,	PUNCT
ejpam-4381	227	4	211:197–209	211:197–209	NUM
ejpam-4381	227	5	,	,	PUNCT
ejpam-4381	227	6	2012	2012	NUM
ejpam-4381	227	7	.	.	PUNCT
ejpam-4381	228	1	[	[	X
ejpam-4381	228	2	8	8	NUM
ejpam-4381	228	3	]	]	X
ejpam-4381	228	4	m.	m.	NOUN
ejpam-4381	228	5	a.	a.	PROPN
ejpam-4381	228	6	henning	henning	PROPN
ejpam-4381	228	7	,	,	PUNCT
ejpam-4381	228	8	o.	o.	PROPN
ejpam-4381	228	9	r.	r.	PROPN
ejpam-4381	228	10	swart	swart	PROPN
ejpam-4381	228	11	,	,	PUNCT
ejpam-4381	228	12	and	and	CCONJ
ejpam-4381	228	13	h.	h.	PROPN
ejpam-4381	228	14	c	c	PROPN
ejpam-4381	228	15	swart	swart	PROPN
ejpam-4381	228	16	.	.	PUNCT
ejpam-4381	229	1	bounds	bound	VERB
ejpam-4381	229	2	on	on	ADP
ejpam-4381	229	3	distance	distance	NOUN
ejpam-4381	229	4	domination	domination	NOUN
ejpam-4381	229	5	parameters	parameter	NOUN
ejpam-4381	229	6	.	.	PUNCT
ejpam-4381	230	1	journal	journal	PROPN
ejpam-4381	230	2	of	of	ADP
ejpam-4381	230	3	combinatorics	combinatoric	NOUN
ejpam-4381	230	4	,	,	PUNCT
ejpam-4381	230	5	information	information	NOUN
ejpam-4381	230	6	and	and	CCONJ
ejpam-4381	230	7	system	system	NOUN
ejpam-4381	230	8	sciences	science	NOUN
ejpam-4381	230	9	,	,	PUNCT
ejpam-4381	230	10	16:11–18	16:11–18	NUM
ejpam-4381	230	11	,	,	PUNCT
ejpam-4381	230	12	1991	1991	NUM
ejpam-4381	230	13	.	.	PUNCT
ejpam-4381	231	1	[	[	X
ejpam-4381	231	2	9	9	NUM
ejpam-4381	231	3	]	]	X
ejpam-4381	231	4	f.	f.	PROPN
ejpam-4381	231	5	jamil	jamil	PROPN
ejpam-4381	231	6	and	and	CCONJ
ejpam-4381	231	7	h.	h.	PROPN
ejpam-4381	231	8	nuenay	nuenay	PROPN
ejpam-4381	231	9	-	-	PUNCT
ejpam-4381	231	10	maglanque	maglanque	ADJ
ejpam-4381	231	11	.	.	PUNCT
ejpam-4381	232	1	cost	cost	NOUN
ejpam-4381	232	2	effective	effective	ADJ
ejpam-4381	232	3	domination	domination	NOUN
ejpam-4381	232	4	in	in	ADP
ejpam-4381	232	5	the	the	DET
ejpam-4381	232	6	join	join	NOUN
ejpam-4381	232	7	,	,	PUNCT
ejpam-4381	232	8	corona	corona	NOUN
ejpam-4381	232	9	and	and	CCONJ
ejpam-4381	232	10	composition	composition	NOUN
ejpam-4381	232	11	of	of	ADP
ejpam-4381	232	12	graphs	graph	NOUN
ejpam-4381	232	13	.	.	PUNCT
ejpam-4381	233	1	european	european	ADJ
ejpam-4381	233	2	journal	journal	PROPN
ejpam-4381	233	3	of	of	ADP
ejpam-4381	233	4	pure	pure	ADJ
ejpam-4381	233	5	and	and	CCONJ
ejpam-4381	233	6	applied	applied	ADJ
ejpam-4381	233	7	mathematics	mathematic	NOUN
ejpam-4381	233	8	,	,	PUNCT
ejpam-4381	233	9	12(3):978–998	12(3):978–998	NUM
ejpam-4381	233	10	,	,	PUNCT
ejpam-4381	233	11	2019	2019	NUM
ejpam-4381	233	12	.	.	PUNCT
ejpam-4381	234	1	[	[	X
ejpam-4381	234	2	10	10	NUM
ejpam-4381	234	3	]	]	PUNCT
ejpam-4381	234	4	a.	a.	NOUN
ejpam-4381	234	5	h.	h.	PROPN
ejpam-4381	234	6	karbasi	karbasi	PROPN
ejpam-4381	234	7	and	and	CCONJ
ejpam-4381	234	8	r.	r.	PROPN
ejpam-4381	234	9	e.	e.	PROPN
ejpam-4381	234	10	atani	atani	PROPN
ejpam-4381	234	11	.	.	PUNCT
ejpam-4381	235	1	application	application	NOUN
ejpam-4381	235	2	of	of	ADP
ejpam-4381	235	3	dominating	dominating	NOUN
ejpam-4381	235	4	sets	set	NOUN
ejpam-4381	235	5	in	in	ADP
ejpam-4381	235	6	wireless	wireless	ADJ
ejpam-4381	235	7	sensor	sensor	NOUN
ejpam-4381	235	8	networks	network	NOUN
ejpam-4381	235	9	.	.	PUNCT
ejpam-4381	236	1	int	int	NOUN
ejpam-4381	236	2	.	.	PUNCT
ejpam-4381	237	1	j.	j.	PROPN
ejpam-4381	237	2	secur	secur	PROPN
ejpam-4381	237	3	.	.	PUNCT
ejpam-4381	238	1	its	its	PRON
ejpam-4381	238	2	appl	appl	NOUN
ejpam-4381	238	3	,	,	PUNCT
ejpam-4381	238	4	7:185–202	7:185–202	PROPN
ejpam-4381	238	5	,	,	PUNCT
ejpam-4381	238	6	2013	2013	NUM
ejpam-4381	238	7	.	.	PUNCT
ejpam-4381	239	1	[	[	X
ejpam-4381	239	2	11	11	NUM
ejpam-4381	239	3	]	]	PUNCT
ejpam-4381	239	4	j.	j.	PROPN
ejpam-4381	239	5	palco	palco	PROPN
ejpam-4381	239	6	,	,	PUNCT
ejpam-4381	239	7	r.	r.	PROPN
ejpam-4381	239	8	paluga	paluga	PROPN
ejpam-4381	239	9	,	,	PUNCT
ejpam-4381	239	10	and	and	CCONJ
ejpam-4381	239	11	g.	g.	PROPN
ejpam-4381	239	12	malacas	malacas	PROPN
ejpam-4381	239	13	.	.	PUNCT
ejpam-4381	240	1	on	on	ADP
ejpam-4381	240	2	k	k	ADJ
ejpam-4381	240	3	-	-	PUNCT
ejpam-4381	240	4	cost	cost	ADJ
ejpam-4381	240	5	effective	effective	ADJ
ejpam-4381	240	6	domination	domination	NOUN
ejpam-4381	240	7	number	number	NOUN
ejpam-4381	240	8	,	,	PUNCT
ejpam-4381	240	9	cost	cost	VERB
ejpam-4381	240	10	effective	effective	ADJ
ejpam-4381	240	11	domination	domination	NOUN
ejpam-4381	240	12	index	index	NOUN
ejpam-4381	240	13	,	,	PUNCT
ejpam-4381	240	14	and	and	CCONJ
ejpam-4381	240	15	maximal	maximal	ADJ
ejpam-4381	240	16	cost	cost	NOUN
ejpam-4381	240	17	effective	effective	ADJ
ejpam-4381	240	18	domination	domination	NOUN
ejpam-4381	240	19	number	number	NOUN
ejpam-4381	240	20	of	of	ADP
ejpam-4381	240	21	simple	simple	ADJ
ejpam-4381	240	22	graphs	graph	NOUN
ejpam-4381	240	23	.	.	PUNCT
ejpam-4381	241	1	far	far	ADV
ejpam-4381	241	2	east	east	PROPN
ejpam-4381	241	3	journal	journal	PROPN
ejpam-4381	241	4	of	of	ADP
ejpam-4381	241	5	mathematical	mathematical	ADJ
ejpam-4381	241	6	sciences	science	NOUN
ejpam-4381	241	7	,	,	PUNCT
ejpam-4381	241	8	114(1):55–68	114(1):55–68	NUM
ejpam-4381	241	9	,	,	PUNCT
ejpam-4381	241	10	2019	2019	NUM
ejpam-4381	241	11	.	.	PUNCT
ejpam-4381	242	1	[	[	X
ejpam-4381	242	2	12	12	NUM
ejpam-4381	242	3	]	]	PUNCT
ejpam-4381	242	4	m.	m.	PROPN
ejpam-4381	242	5	saravanan	saravanan	PROPN
ejpam-4381	242	6	,	,	PUNCT
ejpam-4381	242	7	r.	r.	PROPN
ejpam-4381	242	8	sujatha	sujatha	PROPN
ejpam-4381	242	9	,	,	PUNCT
ejpam-4381	242	10	r.	r.	PROPN
ejpam-4381	242	11	sundareswaran	sundareswaran	PROPN
ejpam-4381	242	12	,	,	PUNCT
ejpam-4381	242	13	and	and	CCONJ
ejpam-4381	242	14	m.	m.	PROPN
ejpam-4381	242	15	s.	s.	PROPN
ejpam-4381	242	16	balasubramanian	balasubramanian	PROPN
ejpam-4381	242	17	.	.	PUNCT
ejpam-4381	243	1	application	application	NOUN
ejpam-4381	243	2	of	of	ADP
ejpam-4381	243	3	domination	domination	NOUN
ejpam-4381	243	4	integrity	integrity	NOUN
ejpam-4381	243	5	of	of	ADP
ejpam-4381	243	6	graphs	graph	NOUN
ejpam-4381	243	7	in	in	ADP
ejpam-4381	243	8	pmu	pmu	ADJ
ejpam-4381	243	9	placement	placement	NOUN
ejpam-4381	243	10	in	in	ADP
ejpam-4381	243	11	electric	electric	ADJ
ejpam-4381	243	12	power	power	NOUN
ejpam-4381	243	13	networks	network	NOUN
ejpam-4381	243	14	.	.	PUNCT
ejpam-4381	244	1	turkish	turkish	ADJ
ejpam-4381	244	2	journal	journal	NOUN
ejpam-4381	244	3	of	of	ADP
ejpam-4381	244	4	electrical	electrical	ADJ
ejpam-4381	244	5	engineering	engineering	NOUN
ejpam-4381	244	6	and	and	CCONJ
ejpam-4381	244	7	computer	computer	NOUN
ejpam-4381	244	8	sciences	science	NOUN
ejpam-4381	244	9	,	,	PUNCT
ejpam-4381	244	10	26(4):2066	26(4):2066	NUM
ejpam-4381	244	11	–	–	PUNCT
ejpam-4381	244	12	2076	2076	NUM
ejpam-4381	244	13	,	,	PUNCT
ejpam-4381	244	14	2018	2018	NUM
ejpam-4381	244	15	.	.	PUNCT