id	sid	tid	token	lemma	pos
ejpam-3955	1	1	european	european	PROPN
ejpam-3955	1	2	journal	journal	PROPN
ejpam-3955	1	3	of	of	ADP
ejpam-3955	1	4	pure	pure	ADJ
ejpam-3955	1	5	and	and	CCONJ
ejpam-3955	1	6	applied	apply	VERB
ejpam-3955	1	7	mathematics	mathematic	NOUN
ejpam-3955	1	8	vol	vol	NOUN
ejpam-3955	1	9	.	.	PUNCT
ejpam-3955	2	1	14	14	NUM
ejpam-3955	2	2	,	,	PUNCT
ejpam-3955	2	3	no	no	INTJ
ejpam-3955	2	4	.	.	NOUN
ejpam-3955	2	5	2	2	NUM
ejpam-3955	2	6	,	,	PUNCT
ejpam-3955	2	7	2021	2021	NUM
ejpam-3955	2	8	,	,	PUNCT
ejpam-3955	2	9	537	537	NUM
ejpam-3955	2	10	-	-	SYM
ejpam-3955	2	11	550	550	NUM
ejpam-3955	2	12	issn	issn	PROPN
ejpam-3955	2	13	1307	1307	NUM
ejpam-3955	2	14	-	-	SYM
ejpam-3955	2	15	5543	5543	NUM
ejpam-3955	2	16	–	–	PUNCT
ejpam-3955	2	17	ejpam.com	ejpam.com	X
ejpam-3955	2	18	published	publish	VERB
ejpam-3955	2	19	by	by	ADP
ejpam-3955	2	20	new	new	PROPN
ejpam-3955	2	21	york	york	PROPN
ejpam-3955	2	22	business	business	PROPN
ejpam-3955	2	23	global	global	PROPN
ejpam-3955	2	24	minimal	minimal	ADJ
ejpam-3955	2	25	and	and	CCONJ
ejpam-3955	2	26	upper	upper	ADJ
ejpam-3955	2	27	cost	cost	NOUN
ejpam-3955	2	28	effective	effective	ADJ
ejpam-3955	2	29	domination	domination	NOUN
ejpam-3955	2	30	number	number	NOUN
ejpam-3955	2	31	in	in	ADP
ejpam-3955	2	32	graphs	graph	NOUN
ejpam-3955	2	33	hearty	hearty	ADJ
ejpam-3955	2	34	m.	m.	NOUN
ejpam-3955	2	35	nuenaymaglanque1,∗	nuenaymaglanque1,∗	PROPN
ejpam-3955	2	36	,	,	PUNCT
ejpam-3955	3	1	ferdinand	ferdinand	PROPN
ejpam-3955	3	2	p.	p.	PROPN
ejpam-3955	3	3	jamil2	jamil2	PROPN
ejpam-3955	4	1	1	1	NUM
ejpam-3955	4	2	department	department	NOUN
ejpam-3955	4	3	of	of	ADP
ejpam-3955	4	4	applied	apply	VERB
ejpam-3955	4	5	mathematics	mathematic	NOUN
ejpam-3955	4	6	,	,	PUNCT
ejpam-3955	4	7	college	college	NOUN
ejpam-3955	4	8	of	of	ADP
ejpam-3955	4	9	science	science	NOUN
ejpam-3955	4	10	and	and	CCONJ
ejpam-3955	4	11	mathematics	mathematic	NOUN
ejpam-3955	4	12	,	,	PUNCT
ejpam-3955	4	13	university	university	NOUN
ejpam-3955	4	14	of	of	ADP
ejpam-3955	4	15	science	science	NOUN
ejpam-3955	4	16	and	and	CCONJ
ejpam-3955	4	17	technology	technology	NOUN
ejpam-3955	4	18	of	of	ADP
ejpam-3955	4	19	souther	souther	PROPN
ejpam-3955	4	20	philippines	philippine	NOUN
ejpam-3955	4	21	,	,	PUNCT
ejpam-3955	4	22	9000	9000	NUM
ejpam-3955	4	23	cagayan	cagayan	PROPN
ejpam-3955	4	24	de	de	PROPN
ejpam-3955	4	25	oro	oro	PROPN
ejpam-3955	4	26	city	city	NOUN
ejpam-3955	4	27	,	,	PUNCT
ejpam-3955	4	28	philippines	philippines	PROPN
ejpam-3955	4	29	2	2	NUM
ejpam-3955	4	30	department	department	NOUN
ejpam-3955	4	31	of	of	ADP
ejpam-3955	4	32	mathematics	mathematic	NOUN
ejpam-3955	4	33	and	and	CCONJ
ejpam-3955	4	34	statistics	statistic	NOUN
ejpam-3955	4	35	,	,	PUNCT
ejpam-3955	4	36	college	college	NOUN
ejpam-3955	4	37	of	of	ADP
ejpam-3955	4	38	science	science	NOUN
ejpam-3955	4	39	and	and	CCONJ
ejpam-3955	4	40	mathematics	mathematic	NOUN
ejpam-3955	4	41	,	,	PUNCT
ejpam-3955	4	42	mindanao	mindanao	PROPN
ejpam-3955	4	43	state	state	PROPN
ejpam-3955	4	44	university	university	PROPN
ejpam-3955	4	45	-	-	PUNCT
ejpam-3955	4	46	iligan	iligan	PROPN
ejpam-3955	4	47	institute	institute	PROPN
ejpam-3955	4	48	of	of	ADP
ejpam-3955	4	49	technology	technology	PROPN
ejpam-3955	4	50	,	,	PUNCT
ejpam-3955	4	51	9200	9200	NUM
ejpam-3955	4	52	iligan	iligan	ADJ
ejpam-3955	4	53	city	city	NOUN
ejpam-3955	4	54	,	,	PUNCT
ejpam-3955	4	55	philippines	philippine	NOUN
ejpam-3955	4	56	abstract	abstract	ADJ
ejpam-3955	4	57	.	.	PUNCT
ejpam-3955	5	1	given	give	VERB
ejpam-3955	5	2	a	a	DET
ejpam-3955	5	3	connected	connected	ADJ
ejpam-3955	5	4	graph	graph	NOUN
ejpam-3955	5	5	g	g	NOUN
ejpam-3955	5	6	,	,	PUNCT
ejpam-3955	5	7	we	we	PRON
ejpam-3955	5	8	say	say	VERB
ejpam-3955	5	9	that	that	SCONJ
ejpam-3955	5	10	s	s	VERB
ejpam-3955	5	11	⊆	⊆	NUM
ejpam-3955	5	12	v	v	NOUN
ejpam-3955	5	13	(	(	PUNCT
ejpam-3955	5	14	g	g	NOUN
ejpam-3955	5	15	)	)	PUNCT
ejpam-3955	5	16	is	be	AUX
ejpam-3955	5	17	a	a	DET
ejpam-3955	5	18	cost	cost	NOUN
ejpam-3955	5	19	effective	effective	ADJ
ejpam-3955	5	20	dominating	dominating	NOUN
ejpam-3955	5	21	set	set	VERB
ejpam-3955	5	22	in	in	ADP
ejpam-3955	5	23	g	g	PROPN
ejpam-3955	5	24	if	if	SCONJ
ejpam-3955	5	25	,	,	PUNCT
ejpam-3955	5	26	each	each	DET
ejpam-3955	5	27	vertex	vertex	NOUN
ejpam-3955	5	28	in	in	ADP
ejpam-3955	5	29	s	s	PROPN
ejpam-3955	5	30	is	be	AUX
ejpam-3955	5	31	adjacent	adjacent	ADJ
ejpam-3955	5	32	to	to	ADP
ejpam-3955	5	33	at	at	ADV
ejpam-3955	5	34	least	least	ADJ
ejpam-3955	5	35	as	as	ADP
ejpam-3955	5	36	many	many	ADJ
ejpam-3955	5	37	vertices	vertex	NOUN
ejpam-3955	5	38	outside	outside	ADP
ejpam-3955	5	39	s	s	PRON
ejpam-3955	5	40	as	as	ADP
ejpam-3955	5	41	inside	inside	ADP
ejpam-3955	5	42	s	s	NOUN
ejpam-3955	5	43	and	and	CCONJ
ejpam-3955	5	44	that	that	SCONJ
ejpam-3955	5	45	every	every	DET
ejpam-3955	5	46	vertex	vertex	NOUN
ejpam-3955	5	47	outside	outside	ADP
ejpam-3955	5	48	s	s	PART
ejpam-3955	5	49	is	be	AUX
ejpam-3955	5	50	adjacent	adjacent	ADJ
ejpam-3955	5	51	to	to	ADP
ejpam-3955	5	52	at	at	ADV
ejpam-3955	5	53	least	least	ADV
ejpam-3955	5	54	one	one	NUM
ejpam-3955	5	55	vertex	vertex	NOUN
ejpam-3955	5	56	in	in	ADP
ejpam-3955	5	57	s.	s.	PROPN
ejpam-3955	5	58	the	the	DET
ejpam-3955	5	59	minimum	minimum	ADJ
ejpam-3955	5	60	cardinality	cardinality	NOUN
ejpam-3955	5	61	of	of	ADP
ejpam-3955	5	62	a	a	DET
ejpam-3955	5	63	cost	cost	NOUN
ejpam-3955	5	64	effective	effective	ADJ
ejpam-3955	5	65	dominating	dominating	NOUN
ejpam-3955	5	66	set	set	NOUN
ejpam-3955	5	67	is	be	AUX
ejpam-3955	5	68	the	the	DET
ejpam-3955	5	69	cost	cost	NOUN
ejpam-3955	5	70	effective	effective	ADJ
ejpam-3955	5	71	domination	domination	NOUN
ejpam-3955	5	72	number	number	NOUN
ejpam-3955	5	73	of	of	ADP
ejpam-3955	5	74	g.	g.	PROPN
ejpam-3955	5	75	the	the	DET
ejpam-3955	5	76	maximum	maximum	ADJ
ejpam-3955	5	77	cardinality	cardinality	NOUN
ejpam-3955	5	78	of	of	ADP
ejpam-3955	5	79	a	a	DET
ejpam-3955	5	80	cost	cost	NOUN
ejpam-3955	5	81	effective	effective	ADJ
ejpam-3955	5	82	dominating	dominating	NOUN
ejpam-3955	5	83	set	set	NOUN
ejpam-3955	5	84	is	be	AUX
ejpam-3955	5	85	the	the	DET
ejpam-3955	5	86	upper	upper	ADJ
ejpam-3955	5	87	cost	cost	NOUN
ejpam-3955	5	88	effective	effective	ADJ
ejpam-3955	5	89	domination	domination	NOUN
ejpam-3955	5	90	number	number	NOUN
ejpam-3955	5	91	of	of	ADP
ejpam-3955	5	92	g	g	NOUN
ejpam-3955	5	93	,	,	PUNCT
ejpam-3955	5	94	and	and	CCONJ
ejpam-3955	5	95	is	be	AUX
ejpam-3955	5	96	denoted	denote	VERB
ejpam-3955	5	97	by	by	ADP
ejpam-3955	5	98	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	5	99	)	)	PUNCT
ejpam-3955	5	100	.	.	PUNCT
ejpam-3955	6	1	a	a	DET
ejpam-3955	6	2	cost	cost	NOUN
ejpam-3955	6	3	effective	effective	ADJ
ejpam-3955	6	4	dominating	dominating	NOUN
ejpam-3955	6	5	set	set	NOUN
ejpam-3955	6	6	is	be	AUX
ejpam-3955	6	7	said	say	VERB
ejpam-3955	6	8	to	to	PART
ejpam-3955	6	9	be	be	AUX
ejpam-3955	6	10	minimal	minimal	ADJ
ejpam-3955	6	11	if	if	SCONJ
ejpam-3955	6	12	it	it	PRON
ejpam-3955	6	13	does	do	AUX
ejpam-3955	6	14	not	not	PART
ejpam-3955	6	15	contain	contain	VERB
ejpam-3955	6	16	a	a	DET
ejpam-3955	6	17	proper	proper	ADJ
ejpam-3955	6	18	subset	subset	NOUN
ejpam-3955	6	19	which	which	PRON
ejpam-3955	6	20	is	be	AUX
ejpam-3955	6	21	itself	itself	PRON
ejpam-3955	6	22	a	a	DET
ejpam-3955	6	23	cost	cost	NOUN
ejpam-3955	6	24	effective	effective	ADJ
ejpam-3955	6	25	dominating	dominating	NOUN
ejpam-3955	6	26	in	in	ADP
ejpam-3955	6	27	g.	g.	PROPN
ejpam-3955	6	28	the	the	DET
ejpam-3955	6	29	maximum	maximum	ADJ
ejpam-3955	6	30	cardinality	cardinality	NOUN
ejpam-3955	6	31	of	of	ADP
ejpam-3955	6	32	a	a	DET
ejpam-3955	6	33	minimal	minimal	ADJ
ejpam-3955	6	34	cost	cost	NOUN
ejpam-3955	6	35	effective	effective	ADJ
ejpam-3955	6	36	dominating	dominating	NOUN
ejpam-3955	6	37	set	set	VERB
ejpam-3955	6	38	in	in	ADP
ejpam-3955	6	39	a	a	DET
ejpam-3955	6	40	graph	graph	NOUN
ejpam-3955	6	41	g	g	NOUN
ejpam-3955	6	42	is	be	AUX
ejpam-3955	6	43	the	the	DET
ejpam-3955	6	44	minimal	minimal	ADJ
ejpam-3955	6	45	cost	cost	NOUN
ejpam-3955	6	46	effective	effective	ADJ
ejpam-3955	6	47	domination	domination	NOUN
ejpam-3955	6	48	number	number	NOUN
ejpam-3955	6	49	of	of	ADP
ejpam-3955	6	50	g	g	NOUN
ejpam-3955	6	51	,	,	PUNCT
ejpam-3955	6	52	and	and	CCONJ
ejpam-3955	6	53	is	be	AUX
ejpam-3955	6	54	denoted	denote	VERB
ejpam-3955	6	55	by	by	ADP
ejpam-3955	6	56	γmce(g	γmce(g	PROPN
ejpam-3955	6	57	)	)	PUNCT
ejpam-3955	6	58	.	.	PUNCT
ejpam-3955	7	1	in	in	ADP
ejpam-3955	7	2	this	this	DET
ejpam-3955	7	3	paper	paper	NOUN
ejpam-3955	7	4	we	we	PRON
ejpam-3955	7	5	provide	provide	VERB
ejpam-3955	7	6	bounds	bound	NOUN
ejpam-3955	7	7	on	on	ADP
ejpam-3955	7	8	upper	upper	ADJ
ejpam-3955	7	9	cost	cost	NOUN
ejpam-3955	7	10	effective	effective	ADJ
ejpam-3955	7	11	domination	domination	NOUN
ejpam-3955	7	12	number	number	NOUN
ejpam-3955	7	13	and	and	CCONJ
ejpam-3955	7	14	minimal	minimal	ADJ
ejpam-3955	7	15	cost	cost	NOUN
ejpam-3955	7	16	effective	effective	ADJ
ejpam-3955	7	17	domination	domination	NOUN
ejpam-3955	7	18	number	number	NOUN
ejpam-3955	7	19	of	of	ADP
ejpam-3955	7	20	a	a	DET
ejpam-3955	7	21	connected	connected	ADJ
ejpam-3955	7	22	graph	graph	NOUN
ejpam-3955	7	23	g	g	PROPN
ejpam-3955	7	24	and	and	CCONJ
ejpam-3955	7	25	characterized	characterize	VERB
ejpam-3955	7	26	those	those	DET
ejpam-3955	7	27	graphs	graph	NOUN
ejpam-3955	7	28	whose	whose	DET
ejpam-3955	7	29	upper	upper	ADJ
ejpam-3955	7	30	and	and	CCONJ
ejpam-3955	7	31	minimal	minimal	ADJ
ejpam-3955	7	32	cost	cost	NOUN
ejpam-3955	7	33	effective	effective	ADJ
ejpam-3955	7	34	domination	domination	NOUN
ejpam-3955	7	35	numbers	number	NOUN
ejpam-3955	7	36	are	be	AUX
ejpam-3955	7	37	either	either	PRON
ejpam-3955	7	38	1	1	NUM
ejpam-3955	7	39	,	,	PUNCT
ejpam-3955	7	40	2	2	NUM
ejpam-3955	7	41	or	or	CCONJ
ejpam-3955	7	42	n−	n−	NOUN
ejpam-3955	7	43	1	1	NUM
ejpam-3955	7	44	.	.	PUNCT
ejpam-3955	8	1	we	we	PRON
ejpam-3955	8	2	also	also	ADV
ejpam-3955	8	3	establish	establish	VERB
ejpam-3955	8	4	a	a	DET
ejpam-3955	8	5	nordhaus	nordhaus	NOUN
ejpam-3955	8	6	-	-	PUNCT
ejpam-3955	8	7	gaddum	gaddum	NOUN
ejpam-3955	8	8	type	type	NOUN
ejpam-3955	8	9	result	result	NOUN
ejpam-3955	8	10	for	for	ADP
ejpam-3955	8	11	the	the	DET
ejpam-3955	8	12	introduced	introduce	VERB
ejpam-3955	8	13	parameters	parameter	NOUN
ejpam-3955	8	14	and	and	CCONJ
ejpam-3955	8	15	solve	solve	VERB
ejpam-3955	8	16	some	some	DET
ejpam-3955	8	17	realization	realization	NOUN
ejpam-3955	8	18	problems	problem	NOUN
ejpam-3955	8	19	.	.	PUNCT
ejpam-3955	9	1	2020	2020	NUM
ejpam-3955	9	2	mathematics	mathematic	NOUN
ejpam-3955	9	3	subject	subject	NOUN
ejpam-3955	9	4	classifications	classification	NOUN
ejpam-3955	9	5	:	:	PUNCT
ejpam-3955	9	6	05c69	05c69	X
ejpam-3955	9	7	key	key	ADJ
ejpam-3955	9	8	words	word	NOUN
ejpam-3955	9	9	and	and	CCONJ
ejpam-3955	9	10	phrases	phrase	NOUN
ejpam-3955	9	11	:	:	PUNCT
ejpam-3955	9	12	cost	cost	VERB
ejpam-3955	9	13	effective	effective	ADJ
ejpam-3955	9	14	dominating	dominating	NOUN
ejpam-3955	9	15	set	set	NOUN
ejpam-3955	9	16	,	,	PUNCT
ejpam-3955	9	17	minimal	minimal	ADJ
ejpam-3955	9	18	cost	cost	NOUN
ejpam-3955	9	19	effective	effective	ADJ
ejpam-3955	9	20	dominating	dominating	NOUN
ejpam-3955	9	21	set	set	NOUN
ejpam-3955	9	22	,	,	PUNCT
ejpam-3955	9	23	minimal	minimal	ADJ
ejpam-3955	9	24	cost	cost	NOUN
ejpam-3955	9	25	effective	effective	ADJ
ejpam-3955	9	26	domination	domination	NOUN
ejpam-3955	9	27	number	number	NOUN
ejpam-3955	9	28	,	,	PUNCT
ejpam-3955	9	29	upper	upper	ADJ
ejpam-3955	9	30	cost	cost	NOUN
ejpam-3955	9	31	effective	effective	ADJ
ejpam-3955	9	32	domination	domination	NOUN
ejpam-3955	9	33	number	number	NOUN
ejpam-3955	9	34	1	1	NUM
ejpam-3955	9	35	.	.	PUNCT
ejpam-3955	9	36	introduction	introduction	NOUN
ejpam-3955	9	37	throughout	throughout	ADP
ejpam-3955	9	38	this	this	DET
ejpam-3955	9	39	paper	paper	NOUN
ejpam-3955	9	40	,	,	PUNCT
ejpam-3955	9	41	we	we	PRON
ejpam-3955	9	42	consider	consider	VERB
ejpam-3955	9	43	simple	simple	ADJ
ejpam-3955	9	44	,	,	PUNCT
ejpam-3955	9	45	finite	finite	ADJ
ejpam-3955	9	46	and	and	CCONJ
ejpam-3955	9	47	undirected	undirected	ADJ
ejpam-3955	9	48	graphs	graph	NOUN
ejpam-3955	9	49	g	g	NOUN
ejpam-3955	9	50	=	=	SYM
ejpam-3955	9	51	(	(	PUNCT
ejpam-3955	9	52	v	v	NOUN
ejpam-3955	9	53	(	(	PUNCT
ejpam-3955	9	54	g	g	NOUN
ejpam-3955	9	55	)	)	PUNCT
ejpam-3955	9	56	,	,	PUNCT
ejpam-3955	9	57	e(g	e(g	PROPN
ejpam-3955	9	58	)	)	PUNCT
ejpam-3955	9	59	)	)	PUNCT
ejpam-3955	9	60	.	.	PUNCT
ejpam-3955	10	1	all	all	DET
ejpam-3955	10	2	basic	basic	ADJ
ejpam-3955	10	3	terminologies	terminology	NOUN
ejpam-3955	10	4	used	use	VERB
ejpam-3955	10	5	here	here	ADV
ejpam-3955	10	6	are	be	AUX
ejpam-3955	10	7	taken	take	VERB
ejpam-3955	10	8	from	from	ADP
ejpam-3955	10	9	[	[	X
ejpam-3955	10	10	4	4	NUM
ejpam-3955	10	11	]	]	PUNCT
ejpam-3955	10	12	.	.	PUNCT
ejpam-3955	11	1	for	for	ADP
ejpam-3955	11	2	a	a	DET
ejpam-3955	11	3	subset	subset	NOUN
ejpam-3955	11	4	s	s	VERB
ejpam-3955	11	5	⊆	⊆	NUM
ejpam-3955	11	6	v	v	NOUN
ejpam-3955	11	7	(	(	PUNCT
ejpam-3955	11	8	g	g	NOUN
ejpam-3955	11	9	)	)	PUNCT
ejpam-3955	11	10	,	,	PUNCT
ejpam-3955	11	11	the	the	DET
ejpam-3955	11	12	symbol	symbol	NOUN
ejpam-3955	11	13	|s|	|s|	NOUN
ejpam-3955	11	14	refers	refer	VERB
ejpam-3955	11	15	to	to	ADP
ejpam-3955	11	16	the	the	DET
ejpam-3955	11	17	cardinality	cardinality	NOUN
ejpam-3955	11	18	of	of	ADP
ejpam-3955	11	19	s.	s.	PROPN
ejpam-3955	11	20	in	in	ADP
ejpam-3955	11	21	particular	particular	ADJ
ejpam-3955	11	22	,	,	PUNCT
ejpam-3955	11	23	|v	|v	PROPN
ejpam-3955	11	24	(	(	PUNCT
ejpam-3955	11	25	g)|	g)|	PROPN
ejpam-3955	11	26	is	be	AUX
ejpam-3955	11	27	the	the	DET
ejpam-3955	11	28	order	order	NOUN
ejpam-3955	11	29	of	of	ADP
ejpam-3955	11	30	g.	g.	PROPN
ejpam-3955	11	31	let	let	VERB
ejpam-3955	11	32	g	g	NOUN
ejpam-3955	11	33	be	be	AUX
ejpam-3955	11	34	a	a	DET
ejpam-3955	11	35	connected	connected	ADJ
ejpam-3955	11	36	graph	graph	NOUN
ejpam-3955	11	37	.	.	PUNCT
ejpam-3955	12	1	for	for	ADP
ejpam-3955	12	2	v	v	NUM
ejpam-3955	12	3	∈	∈	PROPN
ejpam-3955	12	4	v	v	NOUN
ejpam-3955	12	5	(	(	PUNCT
ejpam-3955	12	6	g	g	NOUN
ejpam-3955	12	7	)	)	PUNCT
ejpam-3955	12	8	,	,	PUNCT
ejpam-3955	12	9	the	the	DET
ejpam-3955	12	10	closed	closed	ADJ
ejpam-3955	12	11	neighborhood	neighborhood	NOUN
ejpam-3955	12	12	of	of	ADP
ejpam-3955	12	13	v	v	NOUN
ejpam-3955	12	14	is	be	AUX
ejpam-3955	12	15	the	the	DET
ejpam-3955	12	16	set	set	NOUN
ejpam-3955	12	17	ng[v	ng[v	NOUN
ejpam-3955	12	18	]	]	PUNCT
ejpam-3955	12	19	consisting	consist	VERB
ejpam-3955	12	20	of	of	ADP
ejpam-3955	12	21	v	v	NOUN
ejpam-3955	12	22	and	and	CCONJ
ejpam-3955	12	23	all	all	DET
ejpam-3955	12	24	vertices	vertex	NOUN
ejpam-3955	12	25	adjacent	adjacent	ADJ
ejpam-3955	12	26	to	to	ADP
ejpam-3955	12	27	v.	v.	ADP
ejpam-3955	12	28	the	the	DET
ejpam-3955	12	29	open	open	ADJ
ejpam-3955	12	30	neighborhood	neighborhood	NOUN
ejpam-3955	12	31	of	of	ADP
ejpam-3955	12	32	v	v	NOUN
ejpam-3955	12	33	is	be	AUX
ejpam-3955	12	34	the	the	DET
ejpam-3955	12	35	set	set	NOUN
ejpam-3955	12	36	∗corresponding	∗corresponde	VERB
ejpam-3955	12	37	author	author	NOUN
ejpam-3955	12	38	.	.	PUNCT
ejpam-3955	13	1	doi	doi	NOUN
ejpam-3955	13	2	:	:	PUNCT
ejpam-3955	13	3	https://doi.org/10.29020/nybg.ejpam.v14i2.3955	https://doi.org/10.29020/nybg.ejpam.v14i2.3955	PROPN
ejpam-3955	13	4	email	email	NOUN
ejpam-3955	13	5	addresses	address	NOUN
ejpam-3955	13	6	:	:	PUNCT
ejpam-3955	13	7	hearty.nuenay@ustp.edu.ph	hearty.nuenay@ustp.edu.ph	PROPN
ejpam-3955	13	8	(	(	PUNCT
ejpam-3955	13	9	h.	h.	PROPN
ejpam-3955	13	10	nuenay	nuenay	PROPN
ejpam-3955	13	11	-	-	PUNCT
ejpam-3955	13	12	maglanque	maglanque	NOUN
ejpam-3955	13	13	)	)	PUNCT
ejpam-3955	13	14	,	,	PUNCT
ejpam-3955	13	15	ferdinand.jamil@gmsuiit.edu.ph	ferdinand.jamil@gmsuiit.edu.ph	PROPN
ejpam-3955	13	16	(	(	PUNCT
ejpam-3955	13	17	f.	f.	PROPN
ejpam-3955	13	18	jamil	jamil	PROPN
ejpam-3955	13	19	)	)	PUNCT
ejpam-3955	13	20	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3955	14	1	537	537	NUM
ejpam-3955	14	2	c	c	X
ejpam-3955	14	3	©	©	PROPN
ejpam-3955	14	4	2021	2021	NUM
ejpam-3955	14	5	ejpam	ejpam	VERB
ejpam-3955	14	6	all	all	DET
ejpam-3955	14	7	rights	right	NOUN
ejpam-3955	14	8	reserved	reserve	VERB
ejpam-3955	14	9	.	.	PUNCT
ejpam-3955	15	1	h.	h.	PROPN
ejpam-3955	15	2	nuenay	nuenay	PROPN
ejpam-3955	15	3	-	-	PUNCT
ejpam-3955	15	4	maglanque	maglanque	ADJ
ejpam-3955	15	5	,	,	PUNCT
ejpam-3955	15	6	f.jamil	f.jamil	PROPN
ejpam-3955	15	7	/	/	SYM
ejpam-3955	15	8	eur	eur	PROPN
ejpam-3955	15	9	.	.	PUNCT
ejpam-3955	16	1	j.	j.	PROPN
ejpam-3955	16	2	pure	pure	PROPN
ejpam-3955	16	3	appl	appl	PROPN
ejpam-3955	16	4	.	.	PROPN
ejpam-3955	16	5	math	math	PROPN
ejpam-3955	16	6	,	,	PUNCT
ejpam-3955	16	7	14	14	NUM
ejpam-3955	16	8	(	(	PUNCT
ejpam-3955	16	9	2	2	NUM
ejpam-3955	16	10	)	)	PUNCT
ejpam-3955	16	11	(	(	PUNCT
ejpam-3955	16	12	2021	2021	NUM
ejpam-3955	16	13	)	)	PUNCT
ejpam-3955	16	14	,	,	PUNCT
ejpam-3955	16	15	537	537	NUM
ejpam-3955	16	16	-	-	SYM
ejpam-3955	16	17	550	550	NUM
ejpam-3955	16	18	538	538	NUM
ejpam-3955	16	19	ng(v	ng(v	PUNCT
ejpam-3955	16	20	)	)	PUNCT
ejpam-3955	16	21	=	=	PUNCT
ejpam-3955	17	1	ng[v	ng[v	X
ejpam-3955	17	2	]	]	PUNCT
ejpam-3955	17	3	\	\	X
ejpam-3955	17	4	{	{	PUNCT
ejpam-3955	17	5	v	v	NOUN
ejpam-3955	17	6	}	}	PUNCT
ejpam-3955	17	7	.	.	PUNCT
ejpam-3955	18	1	for	for	ADP
ejpam-3955	18	2	s	s	PROPN
ejpam-3955	18	3	⊆	⊆	NUM
ejpam-3955	18	4	v	v	NOUN
ejpam-3955	18	5	(	(	PUNCT
ejpam-3955	18	6	g	g	NOUN
ejpam-3955	18	7	)	)	PUNCT
ejpam-3955	18	8	,	,	PUNCT
ejpam-3955	18	9	ng[s	ng[s	PROPN
ejpam-3955	18	10	]	]	PUNCT
ejpam-3955	18	11	=	=	SYM
ejpam-3955	18	12	∪v∈sng[v	∪v∈sng[v	X
ejpam-3955	18	13	]	]	PUNCT
ejpam-3955	18	14	and	and	CCONJ
ejpam-3955	18	15	ng(s	ng(s	NUM
ejpam-3955	18	16	)	)	PUNCT
ejpam-3955	18	17	=	=	SYM
ejpam-3955	18	18	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-3955	18	19	)	)	PUNCT
ejpam-3955	18	20	.	.	PUNCT
ejpam-3955	19	1	s	s	PART
ejpam-3955	19	2	is	be	AUX
ejpam-3955	19	3	said	say	VERB
ejpam-3955	19	4	to	to	PART
ejpam-3955	19	5	be	be	AUX
ejpam-3955	19	6	a	a	DET
ejpam-3955	19	7	dominating	dominating	NOUN
ejpam-3955	19	8	set	set	VERB
ejpam-3955	19	9	in	in	ADP
ejpam-3955	19	10	g	g	PROPN
ejpam-3955	19	11	if	if	SCONJ
ejpam-3955	19	12	ng[s	ng[	NOUN
ejpam-3955	19	13	]	]	PUNCT
ejpam-3955	19	14	=	=	SYM
ejpam-3955	19	15	v	v	NOUN
ejpam-3955	19	16	(	(	PUNCT
ejpam-3955	19	17	g	g	NOUN
ejpam-3955	19	18	)	)	PUNCT
ejpam-3955	19	19	.	.	PUNCT
ejpam-3955	20	1	the	the	DET
ejpam-3955	20	2	minimum	minimum	PROPN
ejpam-3955	20	3	cardinality	cardinality	PROPN
ejpam-3955	20	4	γ(g	γ(g	PROPN
ejpam-3955	20	5	)	)	PUNCT
ejpam-3955	20	6	of	of	ADP
ejpam-3955	20	7	a	a	DET
ejpam-3955	20	8	dominating	dominating	NOUN
ejpam-3955	20	9	set	set	NOUN
ejpam-3955	20	10	is	be	AUX
ejpam-3955	20	11	called	call	VERB
ejpam-3955	20	12	the	the	DET
ejpam-3955	20	13	domination	domination	NOUN
ejpam-3955	20	14	number	number	NOUN
ejpam-3955	20	15	of	of	ADP
ejpam-3955	20	16	g.	g.	PROPN
ejpam-3955	20	17	a	a	DET
ejpam-3955	20	18	dominating	dominating	NOUN
ejpam-3955	20	19	set	set	NOUN
ejpam-3955	20	20	s	s	NOUN
ejpam-3955	20	21	in	in	ADP
ejpam-3955	20	22	g	g	PROPN
ejpam-3955	20	23	is	be	AUX
ejpam-3955	20	24	said	say	VERB
ejpam-3955	20	25	to	to	PART
ejpam-3955	20	26	be	be	AUX
ejpam-3955	20	27	a	a	DET
ejpam-3955	20	28	minimal	minimal	ADJ
ejpam-3955	20	29	dominating	dominating	NOUN
ejpam-3955	20	30	set	set	NOUN
ejpam-3955	20	31	if	if	SCONJ
ejpam-3955	20	32	it	it	PRON
ejpam-3955	20	33	has	have	VERB
ejpam-3955	20	34	no	no	DET
ejpam-3955	20	35	proper	proper	ADJ
ejpam-3955	20	36	subset	subset	NOUN
ejpam-3955	20	37	which	which	PRON
ejpam-3955	20	38	is	be	AUX
ejpam-3955	20	39	itself	itself	PRON
ejpam-3955	20	40	a	a	DET
ejpam-3955	20	41	dominating	dominating	NOUN
ejpam-3955	20	42	set	set	VERB
ejpam-3955	20	43	in	in	ADP
ejpam-3955	20	44	g.	g.	PROPN
ejpam-3955	20	45	the	the	DET
ejpam-3955	20	46	maximum	maximum	ADJ
ejpam-3955	20	47	cardinality	cardinality	NOUN
ejpam-3955	20	48	of	of	ADP
ejpam-3955	20	49	a	a	DET
ejpam-3955	20	50	minimal	minimal	ADJ
ejpam-3955	20	51	domination	domination	NOUN
ejpam-3955	20	52	set	set	VERB
ejpam-3955	20	53	in	in	ADP
ejpam-3955	20	54	g	g	PROPN
ejpam-3955	20	55	is	be	AUX
ejpam-3955	20	56	denoted	denote	VERB
ejpam-3955	20	57	by	by	ADP
ejpam-3955	20	58	γm(g	γm(g	NOUN
ejpam-3955	20	59	)	)	PUNCT
ejpam-3955	20	60	.	.	PUNCT
ejpam-3955	21	1	a	a	DET
ejpam-3955	21	2	subset	subset	NOUN
ejpam-3955	21	3	s	s	VERB
ejpam-3955	21	4	⊆	⊆	NUM
ejpam-3955	21	5	v	v	NOUN
ejpam-3955	21	6	(	(	PUNCT
ejpam-3955	21	7	g	g	NOUN
ejpam-3955	21	8	)	)	PUNCT
ejpam-3955	21	9	is	be	AUX
ejpam-3955	21	10	an	an	DET
ejpam-3955	21	11	independent	independent	ADJ
ejpam-3955	21	12	set	set	NOUN
ejpam-3955	21	13	in	in	ADP
ejpam-3955	21	14	g	g	PROPN
ejpam-3955	21	15	if	if	SCONJ
ejpam-3955	21	16	uv	uv	PROPN
ejpam-3955	21	17	/∈	/∈	PUNCT
ejpam-3955	21	18	e(g	e(g	PROPN
ejpam-3955	21	19	)	)	PUNCT
ejpam-3955	21	20	for	for	ADP
ejpam-3955	21	21	distinct	distinct	ADJ
ejpam-3955	21	22	pairs	pair	NOUN
ejpam-3955	21	23	of	of	ADP
ejpam-3955	21	24	vertices	vertex	NOUN
ejpam-3955	21	25	u	u	NOUN
ejpam-3955	21	26	and	and	CCONJ
ejpam-3955	21	27	v	v	NOUN
ejpam-3955	21	28	in	in	ADP
ejpam-3955	21	29	s.	s.	PROPN
ejpam-3955	21	30	an	an	DET
ejpam-3955	21	31	independent	independent	ADJ
ejpam-3955	21	32	dominating	dominating	NOUN
ejpam-3955	21	33	set	set	VERB
ejpam-3955	21	34	in	in	ADP
ejpam-3955	21	35	g	g	PROPN
ejpam-3955	21	36	is	be	AUX
ejpam-3955	21	37	an	an	DET
ejpam-3955	21	38	independent	independent	ADJ
ejpam-3955	21	39	set	set	NOUN
ejpam-3955	21	40	in	in	ADP
ejpam-3955	21	41	g	g	NOUN
ejpam-3955	21	42	which	which	PRON
ejpam-3955	21	43	is	be	AUX
ejpam-3955	21	44	dominating	dominate	VERB
ejpam-3955	21	45	in	in	ADP
ejpam-3955	21	46	g.	g.	PROPN
ejpam-3955	21	47	the	the	DET
ejpam-3955	21	48	minimum	minimum	ADJ
ejpam-3955	21	49	cardinality	cardinality	NOUN
ejpam-3955	21	50	γi(g	γi(g	NOUN
ejpam-3955	21	51	)	)	PUNCT
ejpam-3955	21	52	of	of	ADP
ejpam-3955	21	53	an	an	DET
ejpam-3955	21	54	independent	independent	ADJ
ejpam-3955	21	55	dominating	dominating	NOUN
ejpam-3955	21	56	set	set	NOUN
ejpam-3955	21	57	in	in	ADP
ejpam-3955	21	58	g	g	PROPN
ejpam-3955	21	59	is	be	AUX
ejpam-3955	21	60	called	call	VERB
ejpam-3955	21	61	independence	independence	NOUN
ejpam-3955	21	62	domination	domination	NOUN
ejpam-3955	21	63	number	number	NOUN
ejpam-3955	21	64	.	.	PUNCT
ejpam-3955	22	1	a	a	DET
ejpam-3955	22	2	subset	subset	NOUN
ejpam-3955	22	3	s	s	VERB
ejpam-3955	22	4	⊆	⊆	NUM
ejpam-3955	22	5	v	v	NOUN
ejpam-3955	22	6	(	(	PUNCT
ejpam-3955	22	7	g	g	NOUN
ejpam-3955	22	8	)	)	PUNCT
ejpam-3955	22	9	is	be	AUX
ejpam-3955	22	10	said	say	VERB
ejpam-3955	22	11	to	to	PART
ejpam-3955	22	12	be	be	AUX
ejpam-3955	22	13	a	a	DET
ejpam-3955	22	14	cost	cost	NOUN
ejpam-3955	22	15	effective	effective	ADJ
ejpam-3955	22	16	set	set	NOUN
ejpam-3955	22	17	in	in	ADP
ejpam-3955	22	18	g	g	PROPN
ejpam-3955	22	19	if	if	SCONJ
ejpam-3955	22	20	for	for	ADP
ejpam-3955	22	21	every	every	DET
ejpam-3955	22	22	v	v	NUM
ejpam-3955	22	23	∈	∈	PROPN
ejpam-3955	22	24	s	s	NOUN
ejpam-3955	22	25	,	,	PUNCT
ejpam-3955	22	26	|ng(v)∩s|	|ng(v)∩s|	PROPN
ejpam-3955	22	27	≤	≤	NUM
ejpam-3955	22	28	|ng(v	|ng(v	NOUN
ejpam-3955	22	29	)	)	PUNCT
ejpam-3955	22	30	\	\	NOUN
ejpam-3955	22	31	s|	s|	PROPN
ejpam-3955	22	32	.	.	PUNCT
ejpam-3955	23	1	a	a	DET
ejpam-3955	23	2	subset	subset	NOUN
ejpam-3955	23	3	s	s	VERB
ejpam-3955	23	4	⊆	⊆	NUM
ejpam-3955	23	5	v	v	NOUN
ejpam-3955	23	6	(	(	PUNCT
ejpam-3955	23	7	g	g	NOUN
ejpam-3955	23	8	)	)	PUNCT
ejpam-3955	23	9	is	be	AUX
ejpam-3955	23	10	said	say	VERB
ejpam-3955	23	11	to	to	PART
ejpam-3955	23	12	be	be	AUX
ejpam-3955	23	13	a	a	DET
ejpam-3955	23	14	very	very	ADV
ejpam-3955	23	15	cost	cost	NOUN
ejpam-3955	23	16	effective	effective	ADJ
ejpam-3955	23	17	set	set	NOUN
ejpam-3955	23	18	in	in	ADP
ejpam-3955	23	19	g	g	PROPN
ejpam-3955	23	20	if	if	SCONJ
ejpam-3955	23	21	for	for	ADP
ejpam-3955	23	22	every	every	DET
ejpam-3955	23	23	v	v	NUM
ejpam-3955	23	24	∈	∈	PROPN
ejpam-3955	23	25	s	s	NOUN
ejpam-3955	23	26	,	,	PUNCT
ejpam-3955	23	27	|ng(v	|ng(v	ADJ
ejpam-3955	23	28	)	)	PUNCT
ejpam-3955	23	29	∩	∩	NOUN
ejpam-3955	23	30	s|	s|	VERB
ejpam-3955	23	31	<	<	X
ejpam-3955	23	32	|ng(v	|ng(v	NOUN
ejpam-3955	23	33	)	)	PUNCT
ejpam-3955	23	34	\	\	NOUN
ejpam-3955	23	35	s|	s|	PROPN
ejpam-3955	23	36	.	.	PUNCT
ejpam-3955	24	1	a	a	DET
ejpam-3955	24	2	subset	subset	NOUN
ejpam-3955	24	3	s	s	VERB
ejpam-3955	24	4	⊆	⊆	NUM
ejpam-3955	24	5	v	v	NOUN
ejpam-3955	24	6	(	(	PUNCT
ejpam-3955	24	7	g	g	NOUN
ejpam-3955	24	8	)	)	PUNCT
ejpam-3955	24	9	is	be	AUX
ejpam-3955	24	10	said	say	VERB
ejpam-3955	24	11	to	to	PART
ejpam-3955	24	12	be	be	AUX
ejpam-3955	24	13	a	a	DET
ejpam-3955	24	14	(	(	PUNCT
ejpam-3955	24	15	very)cost	very)cost	X
ejpam-3955	24	16	effective	effective	ADJ
ejpam-3955	24	17	dominating	dominating	NOUN
ejpam-3955	24	18	set	set	VERB
ejpam-3955	24	19	in	in	ADP
ejpam-3955	24	20	g	g	PROPN
ejpam-3955	24	21	if	if	SCONJ
ejpam-3955	24	22	s	s	VERB
ejpam-3955	24	23	is	be	AUX
ejpam-3955	24	24	both	both	PRON
ejpam-3955	24	25	a	a	DET
ejpam-3955	24	26	(	(	PUNCT
ejpam-3955	24	27	very	very	ADV
ejpam-3955	24	28	)	)	PUNCT
ejpam-3955	24	29	cost	cost	NOUN
ejpam-3955	24	30	effective	effective	ADJ
ejpam-3955	24	31	set	set	NOUN
ejpam-3955	24	32	and	and	CCONJ
ejpam-3955	24	33	a	a	DET
ejpam-3955	24	34	dominating	dominating	NOUN
ejpam-3955	24	35	set	set	VERB
ejpam-3955	24	36	in	in	ADP
ejpam-3955	24	37	g.	g.	PROPN
ejpam-3955	24	38	the	the	DET
ejpam-3955	24	39	minimum	minimum	ADJ
ejpam-3955	24	40	cardinality	cardinality	NOUN
ejpam-3955	24	41	of	of	ADP
ejpam-3955	24	42	a	a	DET
ejpam-3955	24	43	cost	cost	NOUN
ejpam-3955	24	44	effective	effective	ADJ
ejpam-3955	24	45	dominating	dominating	NOUN
ejpam-3955	24	46	set	set	NOUN
ejpam-3955	24	47	of	of	ADP
ejpam-3955	24	48	a	a	DET
ejpam-3955	24	49	graph	graph	NOUN
ejpam-3955	24	50	g	g	NOUN
ejpam-3955	24	51	is	be	AUX
ejpam-3955	24	52	called	call	VERB
ejpam-3955	24	53	the	the	DET
ejpam-3955	24	54	cost	cost	NOUN
ejpam-3955	24	55	effective	effective	ADJ
ejpam-3955	24	56	domination	domination	NOUN
ejpam-3955	24	57	number	number	NOUN
ejpam-3955	24	58	of	of	ADP
ejpam-3955	24	59	g	g	NOUN
ejpam-3955	24	60	,	,	PUNCT
ejpam-3955	24	61	and	and	CCONJ
ejpam-3955	24	62	is	be	AUX
ejpam-3955	24	63	denoted	denote	VERB
ejpam-3955	24	64	by	by	ADP
ejpam-3955	24	65	γce(g	γce(g	PROPN
ejpam-3955	24	66	)	)	PUNCT
ejpam-3955	24	67	.	.	PUNCT
ejpam-3955	25	1	motivated	motivate	VERB
ejpam-3955	25	2	by	by	ADP
ejpam-3955	25	3	[	[	X
ejpam-3955	25	4	8	8	NUM
ejpam-3955	25	5	]	]	PUNCT
ejpam-3955	25	6	,	,	PUNCT
ejpam-3955	25	7	the	the	DET
ejpam-3955	25	8	following	follow	VERB
ejpam-3955	25	9	concepts	concept	NOUN
ejpam-3955	25	10	are	be	AUX
ejpam-3955	25	11	introduced	introduce	VERB
ejpam-3955	25	12	by	by	ADP
ejpam-3955	25	13	the	the	DET
ejpam-3955	25	14	authors	author	NOUN
ejpam-3955	25	15	in	in	ADP
ejpam-3955	25	16	[	[	X
ejpam-3955	25	17	7	7	NUM
ejpam-3955	25	18	]	]	PUNCT
ejpam-3955	25	19	.	.	PUNCT
ejpam-3955	26	1	the	the	DET
ejpam-3955	26	2	maximum	maximum	PROPN
ejpam-3955	26	3	cardinality	cardinality	NOUN
ejpam-3955	26	4	,	,	PUNCT
ejpam-3955	26	5	denoted	denote	VERB
ejpam-3955	26	6	by	by	ADP
ejpam-3955	26	7	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	26	8	)	)	PUNCT
ejpam-3955	26	9	,	,	PUNCT
ejpam-3955	26	10	of	of	ADP
ejpam-3955	26	11	a	a	DET
ejpam-3955	26	12	cost	cost	NOUN
ejpam-3955	26	13	effective	effective	ADJ
ejpam-3955	26	14	dominating	dominating	NOUN
ejpam-3955	26	15	set	set	VERB
ejpam-3955	26	16	in	in	ADP
ejpam-3955	26	17	g	g	PROPN
ejpam-3955	26	18	is	be	AUX
ejpam-3955	26	19	called	call	VERB
ejpam-3955	26	20	an	an	DET
ejpam-3955	26	21	upper	upper	ADJ
ejpam-3955	26	22	cost	cost	NOUN
ejpam-3955	26	23	effective	effective	ADJ
ejpam-3955	26	24	domination	domination	NOUN
ejpam-3955	26	25	number	number	NOUN
ejpam-3955	26	26	of	of	ADP
ejpam-3955	26	27	g.	g.	PROPN
ejpam-3955	26	28	a	a	DET
ejpam-3955	26	29	cost	cost	NOUN
ejpam-3955	26	30	effective	effective	ADJ
ejpam-3955	26	31	dominating	dominating	NOUN
ejpam-3955	26	32	set	set	NOUN
ejpam-3955	26	33	of	of	ADP
ejpam-3955	26	34	cardinality	cardinality	PROPN
ejpam-3955	26	35	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	26	36	)	)	PUNCT
ejpam-3955	26	37	is	be	AUX
ejpam-3955	26	38	called	call	VERB
ejpam-3955	26	39	an	an	DET
ejpam-3955	26	40	upper	upper	ADJ
ejpam-3955	26	41	cost	cost	NOUN
ejpam-3955	26	42	effective	effective	ADJ
ejpam-3955	26	43	dominating	dominating	NOUN
ejpam-3955	26	44	set	set	NOUN
ejpam-3955	26	45	.	.	PUNCT
ejpam-3955	27	1	a	a	DET
ejpam-3955	27	2	cost	cost	NOUN
ejpam-3955	27	3	effective	effective	ADJ
ejpam-3955	27	4	dominating	dominating	NOUN
ejpam-3955	27	5	set	set	NOUN
ejpam-3955	27	6	s	s	PROPN
ejpam-3955	27	7	⊆	⊆	NUM
ejpam-3955	27	8	v	v	NOUN
ejpam-3955	27	9	(	(	PUNCT
ejpam-3955	27	10	g	g	NOUN
ejpam-3955	27	11	)	)	PUNCT
ejpam-3955	27	12	is	be	AUX
ejpam-3955	27	13	said	say	VERB
ejpam-3955	27	14	to	to	PART
ejpam-3955	27	15	be	be	AUX
ejpam-3955	27	16	minimal	minimal	ADJ
ejpam-3955	27	17	cost	cost	NOUN
ejpam-3955	27	18	effective	effective	ADJ
ejpam-3955	27	19	set	set	NOUN
ejpam-3955	27	20	if	if	SCONJ
ejpam-3955	27	21	s	s	PRON
ejpam-3955	27	22	does	do	AUX
ejpam-3955	27	23	not	not	PART
ejpam-3955	27	24	contain	contain	VERB
ejpam-3955	27	25	a	a	DET
ejpam-3955	27	26	proper	proper	ADJ
ejpam-3955	27	27	subset	subset	NOUN
ejpam-3955	27	28	which	which	PRON
ejpam-3955	27	29	is	be	AUX
ejpam-3955	27	30	itself	itself	PRON
ejpam-3955	27	31	a	a	DET
ejpam-3955	27	32	cost	cost	NOUN
ejpam-3955	27	33	effective	effective	ADJ
ejpam-3955	27	34	dominating	dominating	NOUN
ejpam-3955	27	35	set	set	NOUN
ejpam-3955	27	36	.	.	PUNCT
ejpam-3955	28	1	the	the	DET
ejpam-3955	28	2	symbol	symbol	NOUN
ejpam-3955	28	3	γmce(g	γmce(g	PROPN
ejpam-3955	28	4	)	)	PUNCT
ejpam-3955	28	5	is	be	AUX
ejpam-3955	28	6	used	use	VERB
ejpam-3955	28	7	to	to	PART
ejpam-3955	28	8	denote	denote	VERB
ejpam-3955	28	9	the	the	DET
ejpam-3955	28	10	maximum	maximum	ADJ
ejpam-3955	28	11	cardinality	cardinality	NOUN
ejpam-3955	28	12	of	of	ADP
ejpam-3955	28	13	a	a	DET
ejpam-3955	28	14	minimal	minimal	ADJ
ejpam-3955	28	15	cost	cost	NOUN
ejpam-3955	28	16	effective	effective	ADJ
ejpam-3955	28	17	dominating	dominating	NOUN
ejpam-3955	28	18	set	set	NOUN
ejpam-3955	28	19	of	of	ADP
ejpam-3955	28	20	g.	g.	PROPN
ejpam-3955	28	21	for	for	ADP
ejpam-3955	28	22	convenience	convenience	NOUN
ejpam-3955	28	23	,	,	PUNCT
ejpam-3955	28	24	we	we	PRON
ejpam-3955	28	25	use	use	VERB
ejpam-3955	28	26	the	the	DET
ejpam-3955	28	27	terms	term	NOUN
ejpam-3955	28	28	γce	γce	NOUN
ejpam-3955	28	29	-	-	PUNCT
ejpam-3955	28	30	set	set	VERB
ejpam-3955	28	31	,	,	PUNCT
ejpam-3955	28	32	γ+ce	γ+ce	NOUN
ejpam-3955	28	33	-	-	PUNCT
ejpam-3955	28	34	set	set	VERB
ejpam-3955	28	35	and	and	CCONJ
ejpam-3955	28	36	γmce	γmce	NOUN
ejpam-3955	28	37	-	-	PUNCT
ejpam-3955	28	38	set	set	NOUN
ejpam-3955	28	39	to	to	PART
ejpam-3955	28	40	refer	refer	VERB
ejpam-3955	28	41	to	to	ADP
ejpam-3955	28	42	the	the	DET
ejpam-3955	28	43	cost	cost	NOUN
ejpam-3955	28	44	effective	effective	ADJ
ejpam-3955	28	45	dominating	dominating	NOUN
ejpam-3955	28	46	sets	set	NOUN
ejpam-3955	28	47	with	with	ADP
ejpam-3955	28	48	cardinality	cardinality	PROPN
ejpam-3955	28	49	γce(g	γce(g	PROPN
ejpam-3955	28	50	)	)	PUNCT
ejpam-3955	28	51	,	,	PUNCT
ejpam-3955	28	52	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	28	53	)	)	PUNCT
ejpam-3955	28	54	and	and	CCONJ
ejpam-3955	28	55	γmce(g	γmce(g	PROPN
ejpam-3955	28	56	)	)	PUNCT
ejpam-3955	28	57	,	,	PUNCT
ejpam-3955	28	58	respectively	respectively	ADV
ejpam-3955	28	59	.	.	PUNCT
ejpam-3955	29	1	the	the	DET
ejpam-3955	29	2	following	follow	VERB
ejpam-3955	29	3	results	result	NOUN
ejpam-3955	29	4	are	be	AUX
ejpam-3955	29	5	due	due	ADJ
ejpam-3955	29	6	to	to	ADP
ejpam-3955	29	7	t.w	t.w	PROPN
ejpam-3955	29	8	.	.	PROPN
ejpam-3955	29	9	haynes	haynes	PROPN
ejpam-3955	29	10	et.al	et.al	PROPN
ejpam-3955	29	11	.	.	PUNCT
ejpam-3955	30	1	and	and	CCONJ
ejpam-3955	30	2	f.v	f.v	PROPN
ejpam-3955	30	3	.	.	PROPN
ejpam-3955	30	4	fomin	fomin	PROPN
ejpam-3955	30	5	et.al	et.al	PROPN
ejpam-3955	30	6	.	.	PUNCT
ejpam-3955	30	7	theorem	theorem	NOUN
ejpam-3955	30	8	1	1	NUM
ejpam-3955	30	9	.	.	PUNCT
ejpam-3955	31	1	[	[	X
ejpam-3955	31	2	2	2	NUM
ejpam-3955	31	3	]	]	PUNCT
ejpam-3955	31	4	for	for	ADP
ejpam-3955	31	5	a	a	DET
ejpam-3955	31	6	connected	connected	ADJ
ejpam-3955	31	7	graph	graph	NOUN
ejpam-3955	31	8	g	g	NOUN
ejpam-3955	31	9	of	of	ADP
ejpam-3955	31	10	order	order	NOUN
ejpam-3955	31	11	n	n	PRON
ejpam-3955	31	12	≥	≥	NOUN
ejpam-3955	31	13	2	2	NUM
ejpam-3955	31	14	,	,	PUNCT
ejpam-3955	31	15	γce(g	γce(g	NOUN
ejpam-3955	31	16	)	)	PUNCT
ejpam-3955	31	17	≤	≤	PUNCT
ejpam-3955	31	18	⌊	⌊	VERB
ejpam-3955	31	19	n	n	ADV
ejpam-3955	31	20	2	2	NUM
ejpam-3955	31	21	⌋	⌋	NOUN
ejpam-3955	31	22	.	.	PUNCT
ejpam-3955	32	1	theorem	theorem	VERB
ejpam-3955	32	2	2	2	NUM
ejpam-3955	32	3	.	.	PUNCT
ejpam-3955	33	1	[	[	X
ejpam-3955	33	2	2	2	X
ejpam-3955	33	3	]	]	PUNCT
ejpam-3955	33	4	let	let	VERB
ejpam-3955	33	5	g	g	PRON
ejpam-3955	33	6	be	be	AUX
ejpam-3955	33	7	a	a	DET
ejpam-3955	33	8	connected	connected	ADJ
ejpam-3955	33	9	graph	graph	NOUN
ejpam-3955	33	10	(	(	PUNCT
ejpam-3955	33	11	i	i	NOUN
ejpam-3955	33	12	)	)	PUNCT
ejpam-3955	33	13	if	if	SCONJ
ejpam-3955	33	14	∆(g	∆(g	NOUN
ejpam-3955	33	15	)	)	PUNCT
ejpam-3955	33	16	≤	≤	NOUN
ejpam-3955	33	17	4	4	NUM
ejpam-3955	33	18	,	,	PUNCT
ejpam-3955	33	19	then	then	ADV
ejpam-3955	33	20	γ(g	γ(g	PROPN
ejpam-3955	33	21	)	)	PUNCT
ejpam-3955	33	22	=	=	SYM
ejpam-3955	33	23	γce(g	γce(g	PROPN
ejpam-3955	33	24	)	)	PUNCT
ejpam-3955	33	25	.	.	PUNCT
ejpam-3955	34	1	(	(	PUNCT
ejpam-3955	34	2	ii	ii	NOUN
ejpam-3955	34	3	)	)	PUNCT
ejpam-3955	34	4	if	if	SCONJ
ejpam-3955	34	5	γ(g	γ(g	PROPN
ejpam-3955	34	6	)	)	PUNCT
ejpam-3955	34	7	≤	≤	NOUN
ejpam-3955	34	8	3	3	NUM
ejpam-3955	34	9	,	,	PUNCT
ejpam-3955	34	10	then	then	ADV
ejpam-3955	34	11	γ(g	γ(g	PROPN
ejpam-3955	34	12	)	)	PUNCT
ejpam-3955	34	13	=	=	SYM
ejpam-3955	34	14	γce(g	γce(g	PROPN
ejpam-3955	34	15	)	)	PUNCT
ejpam-3955	34	16	.	.	PUNCT
ejpam-3955	35	1	lemma	lemma	PROPN
ejpam-3955	35	2	1	1	NUM
ejpam-3955	35	3	.	.	PUNCT
ejpam-3955	36	1	[	[	X
ejpam-3955	36	2	2	2	X
ejpam-3955	36	3	]	]	PUNCT
ejpam-3955	36	4	every	every	DET
ejpam-3955	36	5	independent	independent	ADJ
ejpam-3955	36	6	dominating	dominating	NOUN
ejpam-3955	36	7	set	set	VERB
ejpam-3955	36	8	in	in	ADP
ejpam-3955	36	9	an	an	DET
ejpam-3955	36	10	isolate	isolate	NOUN
ejpam-3955	36	11	-	-	PUNCT
ejpam-3955	36	12	free	free	ADJ
ejpam-3955	36	13	graph	graph	NOUN
ejpam-3955	36	14	g	g	PROPN
ejpam-3955	36	15	is	be	AUX
ejpam-3955	36	16	a	a	DET
ejpam-3955	36	17	very	very	ADV
ejpam-3955	36	18	cost	cost	NOUN
ejpam-3955	36	19	effective	effective	ADJ
ejpam-3955	36	20	dominating	dominating	NOUN
ejpam-3955	36	21	set	set	VERB
ejpam-3955	36	22	in	in	ADP
ejpam-3955	36	23	g.	g.	PROPN
ejpam-3955	36	24	theorem	theorem	PROPN
ejpam-3955	36	25	3	3	NUM
ejpam-3955	36	26	.	.	PUNCT
ejpam-3955	37	1	[	[	X
ejpam-3955	37	2	5	5	NUM
ejpam-3955	37	3	]	]	PUNCT
ejpam-3955	37	4	every	every	DET
ejpam-3955	37	5	maximal	maximal	ADJ
ejpam-3955	37	6	independent	independent	ADJ
ejpam-3955	37	7	set	set	NOUN
ejpam-3955	37	8	is	be	AUX
ejpam-3955	37	9	a	a	DET
ejpam-3955	37	10	minimal	minimal	ADJ
ejpam-3955	37	11	dominating	dominating	NOUN
ejpam-3955	37	12	set	set	NOUN
ejpam-3955	37	13	.	.	PUNCT
ejpam-3955	38	1	2	2	X
ejpam-3955	38	2	.	.	X
ejpam-3955	38	3	results	result	NOUN
ejpam-3955	38	4	proposition	proposition	NOUN
ejpam-3955	38	5	1	1	NUM
ejpam-3955	38	6	.	.	PUNCT
ejpam-3955	39	1	let	let	VERB
ejpam-3955	39	2	c1	c1	PROPN
ejpam-3955	39	3	,	,	PUNCT
ejpam-3955	39	4	c2	c2	PROPN
ejpam-3955	39	5	,	,	PUNCT
ejpam-3955	39	6	.	.	PUNCT
ejpam-3955	39	7	.	.	PUNCT
ejpam-3955	40	1	.	.	PUNCT
ejpam-3955	41	1	,	,	PUNCT
ejpam-3955	41	2	cn	cn	PROPN
ejpam-3955	41	3	be	be	AUX
ejpam-3955	41	4	the	the	DET
ejpam-3955	41	5	components	component	NOUN
ejpam-3955	41	6	of	of	ADP
ejpam-3955	41	7	a	a	DET
ejpam-3955	41	8	graph	graph	NOUN
ejpam-3955	41	9	g	g	NOUN
ejpam-3955	41	10	,	,	PUNCT
ejpam-3955	41	11	and	and	CCONJ
ejpam-3955	41	12	let	let	VERB
ejpam-3955	41	13	s	s	PRON
ejpam-3955	41	14	⊆	⊆	NUM
ejpam-3955	41	15	v	v	NOUN
ejpam-3955	41	16	(	(	PUNCT
ejpam-3955	41	17	g	g	NOUN
ejpam-3955	41	18	)	)	PUNCT
ejpam-3955	41	19	.	.	PUNCT
ejpam-3955	42	1	then	then	ADV
ejpam-3955	42	2	s	s	VERB
ejpam-3955	42	3	is	be	AUX
ejpam-3955	42	4	a	a	DET
ejpam-3955	42	5	cost	cost	NOUN
ejpam-3955	42	6	effective	effective	ADJ
ejpam-3955	42	7	dominating	dominating	NOUN
ejpam-3955	42	8	set	set	VERB
ejpam-3955	42	9	in	in	ADP
ejpam-3955	42	10	g	g	PROPN
ejpam-3955	42	11	if	if	SCONJ
ejpam-3955	43	1	and	and	CCONJ
ejpam-3955	43	2	only	only	ADV
ejpam-3955	43	3	if	if	SCONJ
ejpam-3955	43	4	sk	sk	ADP
ejpam-3955	43	5	=	=	SYM
ejpam-3955	43	6	s	s	NOUN
ejpam-3955	43	7	∩	∩	ADJ
ejpam-3955	43	8	v	v	NOUN
ejpam-3955	43	9	(	(	PUNCT
ejpam-3955	43	10	ck	ck	NOUN
ejpam-3955	43	11	)	)	PUNCT
ejpam-3955	43	12	is	be	AUX
ejpam-3955	43	13	a	a	DET
ejpam-3955	43	14	cost	cost	NOUN
ejpam-3955	43	15	effective	effective	ADJ
ejpam-3955	43	16	dominating	dominating	NOUN
ejpam-3955	43	17	set	set	VERB
ejpam-3955	43	18	in	in	ADP
ejpam-3955	43	19	ck	ck	PROPN
ejpam-3955	43	20	for	for	ADP
ejpam-3955	43	21	k	k	PROPN
ejpam-3955	43	22	=	=	SYM
ejpam-3955	43	23	1	1	NUM
ejpam-3955	43	24	,	,	PUNCT
ejpam-3955	43	25	2	2	NUM
ejpam-3955	43	26	,	,	PUNCT
ejpam-3955	43	27	.	.	PUNCT
ejpam-3955	43	28	.	.	PUNCT
ejpam-3955	44	1	.	.	PUNCT
ejpam-3955	45	1	,	,	PUNCT
ejpam-3955	45	2	n.	n.	PROPN
ejpam-3955	45	3	h.	h.	PROPN
ejpam-3955	45	4	nuenay	nuenay	PROPN
ejpam-3955	45	5	-	-	PUNCT
ejpam-3955	45	6	maglanque	maglanque	ADJ
ejpam-3955	45	7	,	,	PUNCT
ejpam-3955	45	8	f.jamil	f.jamil	PROPN
ejpam-3955	45	9	/	/	SYM
ejpam-3955	45	10	eur	eur	PROPN
ejpam-3955	45	11	.	.	PUNCT
ejpam-3955	46	1	j.	j.	PROPN
ejpam-3955	46	2	pure	pure	PROPN
ejpam-3955	46	3	appl	appl	PROPN
ejpam-3955	46	4	.	.	PROPN
ejpam-3955	46	5	math	math	PROPN
ejpam-3955	46	6	,	,	PUNCT
ejpam-3955	46	7	14	14	NUM
ejpam-3955	46	8	(	(	PUNCT
ejpam-3955	46	9	2	2	NUM
ejpam-3955	46	10	)	)	PUNCT
ejpam-3955	46	11	(	(	PUNCT
ejpam-3955	46	12	2021	2021	NUM
ejpam-3955	46	13	)	)	PUNCT
ejpam-3955	46	14	,	,	PUNCT
ejpam-3955	46	15	537	537	NUM
ejpam-3955	46	16	-	-	SYM
ejpam-3955	46	17	550	550	NUM
ejpam-3955	46	18	539	539	NUM
ejpam-3955	46	19	proof	proof	NOUN
ejpam-3955	46	20	.	.	PUNCT
ejpam-3955	47	1	it	it	PRON
ejpam-3955	47	2	is	be	AUX
ejpam-3955	47	3	clear	clear	ADJ
ejpam-3955	47	4	that	that	SCONJ
ejpam-3955	47	5	s	s	VERB
ejpam-3955	47	6	is	be	AUX
ejpam-3955	47	7	a	a	DET
ejpam-3955	47	8	dominating	dominating	NOUN
ejpam-3955	47	9	set	set	VERB
ejpam-3955	47	10	in	in	ADP
ejpam-3955	47	11	g	g	PROPN
ejpam-3955	47	12	if	if	SCONJ
ejpam-3955	48	1	and	and	CCONJ
ejpam-3955	48	2	only	only	ADV
ejpam-3955	48	3	if	if	SCONJ
ejpam-3955	48	4	sk	sk	INTJ
ejpam-3955	48	5	is	be	AUX
ejpam-3955	48	6	a	a	DET
ejpam-3955	48	7	dominating	dominating	NOUN
ejpam-3955	48	8	set	set	VERB
ejpam-3955	48	9	in	in	ADP
ejpam-3955	48	10	ck	ck	PROPN
ejpam-3955	48	11	for	for	ADP
ejpam-3955	48	12	each	each	PRON
ejpam-3955	48	13	k	k	NOUN
ejpam-3955	48	14	=	=	SYM
ejpam-3955	48	15	1	1	NUM
ejpam-3955	48	16	,	,	PUNCT
ejpam-3955	48	17	2	2	NUM
ejpam-3955	48	18	,	,	PUNCT
ejpam-3955	48	19	.	.	PUNCT
ejpam-3955	48	20	.	.	PUNCT
ejpam-3955	49	1	.	.	PUNCT
ejpam-3955	50	1	,	,	PUNCT
ejpam-3955	50	2	n.	n.	PROPN
ejpam-3955	50	3	moreover	moreover	ADV
ejpam-3955	50	4	,	,	PUNCT
ejpam-3955	50	5	since	since	SCONJ
ejpam-3955	50	6	for	for	ADP
ejpam-3955	50	7	v	v	NOUN
ejpam-3955	50	8	∈	∈	PROPN
ejpam-3955	50	9	sk	sk	NOUN
ejpam-3955	50	10	,	,	PUNCT
ejpam-3955	50	11	we	we	PRON
ejpam-3955	50	12	have	have	VERB
ejpam-3955	50	13	ng(v	ng(v	NOUN
ejpam-3955	50	14	)	)	PUNCT
ejpam-3955	50	15	∩	∩	NOUN
ejpam-3955	50	16	s	s	PART
ejpam-3955	50	17	=	=	NOUN
ejpam-3955	50	18	nck	nck	NOUN
ejpam-3955	50	19	∩	∩	NOUN
ejpam-3955	50	20	sk	sk	NOUN
ejpam-3955	50	21	and	and	CCONJ
ejpam-3955	50	22	ng(v	ng(v	NUM
ejpam-3955	50	23	)	)	PUNCT
ejpam-3955	50	24	\	\	PART
ejpam-3955	51	1	s	s	PART
ejpam-3955	51	2	=	=	X
ejpam-3955	51	3	nck	nck	NOUN
ejpam-3955	51	4	(	(	PUNCT
ejpam-3955	51	5	v	v	NOUN
ejpam-3955	51	6	)	)	PUNCT
ejpam-3955	51	7	\	\	NOUN
ejpam-3955	51	8	sk	sk	X
ejpam-3955	51	9	,	,	PUNCT
ejpam-3955	51	10	s	s	PART
ejpam-3955	51	11	is	be	AUX
ejpam-3955	51	12	a	a	DET
ejpam-3955	51	13	cost	cost	NOUN
ejpam-3955	51	14	effective	effective	ADJ
ejpam-3955	51	15	set	set	NOUN
ejpam-3955	51	16	in	in	ADP
ejpam-3955	51	17	g	g	PROPN
ejpam-3955	51	18	if	if	SCONJ
ejpam-3955	51	19	and	and	CCONJ
ejpam-3955	51	20	only	only	ADV
ejpam-3955	51	21	if	if	SCONJ
ejpam-3955	51	22	sk	sk	INTJ
ejpam-3955	51	23	is	be	AUX
ejpam-3955	51	24	a	a	DET
ejpam-3955	51	25	cost	cost	NOUN
ejpam-3955	51	26	effective	effective	ADJ
ejpam-3955	51	27	set	set	NOUN
ejpam-3955	51	28	in	in	ADP
ejpam-3955	51	29	ck	ck	PROPN
ejpam-3955	51	30	for	for	ADP
ejpam-3955	51	31	each	each	PRON
ejpam-3955	51	32	k	k	NOUN
ejpam-3955	51	33	=	=	SYM
ejpam-3955	51	34	1	1	NUM
ejpam-3955	51	35	,	,	PUNCT
ejpam-3955	51	36	2	2	NUM
ejpam-3955	51	37	,	,	PUNCT
ejpam-3955	51	38	.	.	PUNCT
ejpam-3955	51	39	.	.	PUNCT
ejpam-3955	52	1	.	.	PUNCT
ejpam-3955	53	1	,	,	PUNCT
ejpam-3955	53	2	n.	n.	PROPN
ejpam-3955	53	3	corollary	corollary	NOUN
ejpam-3955	53	4	1	1	X
ejpam-3955	53	5	.	.	PUNCT
ejpam-3955	54	1	let	let	VERB
ejpam-3955	54	2	g	g	PRON
ejpam-3955	54	3	be	be	AUX
ejpam-3955	54	4	a	a	DET
ejpam-3955	54	5	graph	graph	NOUN
ejpam-3955	54	6	of	of	ADP
ejpam-3955	54	7	order	order	NOUN
ejpam-3955	54	8	n.	n.	NOUN
ejpam-3955	54	9	then	then	ADV
ejpam-3955	54	10	γce(g	γce(g	NOUN
ejpam-3955	54	11	)	)	PUNCT
ejpam-3955	55	1	=	=	SYM
ejpam-3955	56	1	n	n	NOUN
ejpam-3955	56	2	if	if	SCONJ
ejpam-3955	57	1	and	and	CCONJ
ejpam-3955	57	2	only	only	ADV
ejpam-3955	57	3	if	if	SCONJ
ejpam-3955	57	4	g	g	PROPN
ejpam-3955	57	5	=	=	PROPN
ejpam-3955	57	6	kn	kn	PROPN
ejpam-3955	57	7	.	.	PUNCT
ejpam-3955	57	8	proof	proof	PROPN
ejpam-3955	57	9	.	.	PUNCT
ejpam-3955	58	1	suppose	suppose	VERB
ejpam-3955	58	2	that	that	SCONJ
ejpam-3955	58	3	γce(g	γce(g	PROPN
ejpam-3955	58	4	)	)	PUNCT
ejpam-3955	59	1	=	=	VERB
ejpam-3955	59	2	n.	n.	NOUN
ejpam-3955	59	3	then	then	ADV
ejpam-3955	59	4	s	s	VERB
ejpam-3955	59	5	=	=	SYM
ejpam-3955	59	6	v	v	PROPN
ejpam-3955	59	7	(	(	PUNCT
ejpam-3955	59	8	g	g	NOUN
ejpam-3955	59	9	)	)	PUNCT
ejpam-3955	59	10	is	be	AUX
ejpam-3955	59	11	the	the	DET
ejpam-3955	59	12	only	only	ADJ
ejpam-3955	59	13	cost	cost	NOUN
ejpam-3955	59	14	effective	effective	ADJ
ejpam-3955	59	15	set	set	NOUN
ejpam-3955	59	16	in	in	ADP
ejpam-3955	59	17	g.	g.	PROPN
ejpam-3955	59	18	let	let	VERB
ejpam-3955	59	19	u	u	NOUN
ejpam-3955	59	20	,	,	PUNCT
ejpam-3955	59	21	v	v	PROPN
ejpam-3955	59	22	∈	∈	PROPN
ejpam-3955	59	23	v	v	NOUN
ejpam-3955	59	24	(	(	PUNCT
ejpam-3955	59	25	g	g	NOUN
ejpam-3955	59	26	)	)	PUNCT
ejpam-3955	59	27	with	with	ADP
ejpam-3955	59	28	u	u	PROPN
ejpam-3955	59	29	6=	6=	PROPN
ejpam-3955	59	30	v.	v.	ADP
ejpam-3955	59	31	since	since	SCONJ
ejpam-3955	59	32	ng(v	ng(v	NOUN
ejpam-3955	59	33	)	)	PUNCT
ejpam-3955	59	34	\	\	PART
ejpam-3955	60	1	s	s	PART
ejpam-3955	60	2	=	=	SYM
ejpam-3955	60	3	∅	∅	NOUN
ejpam-3955	60	4	,	,	PUNCT
ejpam-3955	60	5	|ng(v	|ng(v	ADJ
ejpam-3955	60	6	)	)	PUNCT
ejpam-3955	60	7	∩	∩	NOUN
ejpam-3955	60	8	s|	s|	VERB
ejpam-3955	60	9	≤	≤	NUM
ejpam-3955	60	10	|ng(v	|ng(v	NOUN
ejpam-3955	60	11	)	)	PUNCT
ejpam-3955	60	12	\	\	NOUN
ejpam-3955	60	13	s|	s|	NOUN
ejpam-3955	60	14	=	=	SYM
ejpam-3955	61	1	0	0	X
ejpam-3955	61	2	.	.	PUNCT
ejpam-3955	62	1	consequently	consequently	ADV
ejpam-3955	62	2	,	,	PUNCT
ejpam-3955	62	3	|ng(v)∩s|	|ng(v)∩s|	PROPN
ejpam-3955	62	4	=	=	SYM
ejpam-3955	62	5	0	0	PROPN
ejpam-3955	62	6	,	,	PUNCT
ejpam-3955	62	7	that	that	ADV
ejpam-3955	62	8	is	is	ADV
ejpam-3955	62	9	,	,	PUNCT
ejpam-3955	62	10	ng(v)∩s	ng(v)∩s	PROPN
ejpam-3955	62	11	=	=	PROPN
ejpam-3955	62	12	∅.	∅.	VERB
ejpam-3955	62	13	thus	thus	ADV
ejpam-3955	62	14	,	,	PUNCT
ejpam-3955	62	15	u	u	NOUN
ejpam-3955	62	16	/∈	/∈	PUNCT
ejpam-3955	62	17	ng(v	ng(v	PUNCT
ejpam-3955	62	18	)	)	PUNCT
ejpam-3955	62	19	so	so	SCONJ
ejpam-3955	62	20	that	that	SCONJ
ejpam-3955	62	21	uv	uv	PROPN
ejpam-3955	62	22	/∈	/∈	PUNCT
ejpam-3955	62	23	e(g	e(g	PROPN
ejpam-3955	62	24	)	)	PUNCT
ejpam-3955	62	25	.	.	PUNCT
ejpam-3955	63	1	since	since	SCONJ
ejpam-3955	63	2	u	u	PROPN
ejpam-3955	63	3	and	and	CCONJ
ejpam-3955	63	4	v	v	NOUN
ejpam-3955	63	5	are	be	AUX
ejpam-3955	63	6	arbitrary	arbitrary	ADJ
ejpam-3955	63	7	,	,	PUNCT
ejpam-3955	63	8	g	g	PROPN
ejpam-3955	63	9	=	=	SYM
ejpam-3955	63	10	kn	kn	PROPN
ejpam-3955	63	11	.	.	PUNCT
ejpam-3955	64	1	the	the	DET
ejpam-3955	64	2	converse	converse	NOUN
ejpam-3955	64	3	follows	follow	VERB
ejpam-3955	64	4	immediately	immediately	ADV
ejpam-3955	64	5	from	from	ADP
ejpam-3955	64	6	proposition	proposition	NOUN
ejpam-3955	64	7	1	1	NUM
ejpam-3955	64	8	.	.	PUNCT
ejpam-3955	65	1	lemma	lemma	PROPN
ejpam-3955	65	2	2	2	X
ejpam-3955	65	3	.	.	PUNCT
ejpam-3955	66	1	let	let	VERB
ejpam-3955	66	2	g	g	PRON
ejpam-3955	66	3	be	be	AUX
ejpam-3955	66	4	a	a	DET
ejpam-3955	66	5	nontrivial	nontrivial	ADJ
ejpam-3955	66	6	connected	connect	VERB
ejpam-3955	66	7	graph	graph	NOUN
ejpam-3955	66	8	,	,	PUNCT
ejpam-3955	66	9	and	and	CCONJ
ejpam-3955	66	10	s	s	VERB
ejpam-3955	66	11	⊆	⊆	NUM
ejpam-3955	66	12	v	v	NOUN
ejpam-3955	66	13	(	(	PUNCT
ejpam-3955	66	14	g	g	NOUN
ejpam-3955	66	15	)	)	PUNCT
ejpam-3955	66	16	.	.	PUNCT
ejpam-3955	67	1	if	if	SCONJ
ejpam-3955	67	2	s	s	NOUN
ejpam-3955	67	3	is	be	AUX
ejpam-3955	67	4	a	a	DET
ejpam-3955	67	5	cost	cost	NOUN
ejpam-3955	67	6	effective	effective	ADJ
ejpam-3955	67	7	set	set	NOUN
ejpam-3955	67	8	in	in	ADP
ejpam-3955	67	9	g	g	NOUN
ejpam-3955	67	10	,	,	PUNCT
ejpam-3955	67	11	then	then	ADV
ejpam-3955	67	12	every	every	DET
ejpam-3955	67	13	subset	subset	NOUN
ejpam-3955	67	14	of	of	ADP
ejpam-3955	67	15	s	s	PROPN
ejpam-3955	67	16	is	be	AUX
ejpam-3955	67	17	also	also	ADV
ejpam-3955	67	18	a	a	DET
ejpam-3955	67	19	cost	cost	NOUN
ejpam-3955	67	20	effective	effective	ADJ
ejpam-3955	67	21	set	set	NOUN
ejpam-3955	67	22	in	in	ADP
ejpam-3955	67	23	g.	g.	PROPN
ejpam-3955	67	24	proof	proof	NOUN
ejpam-3955	67	25	.	.	PUNCT
ejpam-3955	68	1	if	if	SCONJ
ejpam-3955	68	2	s	s	PRON
ejpam-3955	68	3	=	=	NOUN
ejpam-3955	68	4	∅	∅	NOUN
ejpam-3955	68	5	,	,	PUNCT
ejpam-3955	68	6	then	then	ADV
ejpam-3955	68	7	the	the	DET
ejpam-3955	68	8	conclusion	conclusion	NOUN
ejpam-3955	68	9	is	be	AUX
ejpam-3955	68	10	trivial	trivial	ADJ
ejpam-3955	68	11	.	.	PUNCT
ejpam-3955	69	1	suppose	suppose	VERB
ejpam-3955	69	2	that	that	SCONJ
ejpam-3955	69	3	s	s	VERB
ejpam-3955	69	4	⊆	⊆	NUM
ejpam-3955	69	5	v	v	NOUN
ejpam-3955	69	6	(	(	PUNCT
ejpam-3955	69	7	g	g	NOUN
ejpam-3955	69	8	)	)	PUNCT
ejpam-3955	69	9	is	be	AUX
ejpam-3955	69	10	a	a	DET
ejpam-3955	69	11	nonempty	nonempty	ADJ
ejpam-3955	69	12	cost	cost	NOUN
ejpam-3955	69	13	effective	effective	ADJ
ejpam-3955	69	14	set	set	NOUN
ejpam-3955	69	15	in	in	ADP
ejpam-3955	69	16	g.	g.	PROPN
ejpam-3955	69	17	let	let	VERB
ejpam-3955	69	18	u	u	PRON
ejpam-3955	69	19	∈	∈	PROPN
ejpam-3955	69	20	s	s	PART
ejpam-3955	69	21	and	and	CCONJ
ejpam-3955	69	22	put	put	VERB
ejpam-3955	69	23	s∗	s∗	PROPN
ejpam-3955	69	24	=	=	SYM
ejpam-3955	69	25	s	s	PART
ejpam-3955	69	26	\	\	X
ejpam-3955	69	27	{	{	PUNCT
ejpam-3955	69	28	u	u	NOUN
ejpam-3955	69	29	}	}	PUNCT
ejpam-3955	69	30	.	.	PUNCT
ejpam-3955	70	1	let	let	VERB
ejpam-3955	70	2	v	v	X
ejpam-3955	70	3	∈	∈	VERB
ejpam-3955	70	4	s∗.	s∗.	ADJ
ejpam-3955	70	5	if	if	SCONJ
ejpam-3955	70	6	u	u	PROPN
ejpam-3955	70	7	∈	∈	PROPN
ejpam-3955	70	8	ng(v	ng(v	NOUN
ejpam-3955	70	9	)	)	PUNCT
ejpam-3955	70	10	,	,	PUNCT
ejpam-3955	70	11	then	then	ADV
ejpam-3955	70	12	ng(v	ng(v	PUNCT
ejpam-3955	70	13	)	)	PUNCT
ejpam-3955	70	14	∩	∩	NOUN
ejpam-3955	70	15	s∗	s∗	PROPN
ejpam-3955	70	16	=	=	SYM
ejpam-3955	70	17	(	(	PUNCT
ejpam-3955	70	18	ng(v	ng(v	NOUN
ejpam-3955	70	19	)	)	PUNCT
ejpam-3955	70	20	∩	∩	NOUN
ejpam-3955	70	21	s	s	NOUN
ejpam-3955	70	22	)	)	PUNCT
ejpam-3955	70	23	\	\	NOUN
ejpam-3955	70	24	{	{	PUNCT
ejpam-3955	70	25	u	u	NOUN
ejpam-3955	70	26	}	}	PUNCT
ejpam-3955	70	27	and	and	CCONJ
ejpam-3955	70	28	ng(v	ng(v	NUM
ejpam-3955	70	29	)	)	PUNCT
ejpam-3955	70	30	\	\	PART
ejpam-3955	70	31	s	s	PART
ejpam-3955	70	32	=	=	PUNCT
ejpam-3955	70	33	(	(	PUNCT
ejpam-3955	70	34	ng(v	ng(v	NOUN
ejpam-3955	70	35	)	)	PUNCT
ejpam-3955	70	36	\	\	PROPN
ejpam-3955	70	37	s∗	s∗	PROPN
ejpam-3955	70	38	)	)	PUNCT
ejpam-3955	70	39	\	\	PUNCT
ejpam-3955	71	1	{	{	PUNCT
ejpam-3955	71	2	u	u	NOUN
ejpam-3955	71	3	}	}	PUNCT
ejpam-3955	71	4	so	so	SCONJ
ejpam-3955	71	5	that	that	SCONJ
ejpam-3955	71	6	|ng(v	|ng(v	ADP
ejpam-3955	71	7	)	)	PUNCT
ejpam-3955	71	8	∩	∩	NOUN
ejpam-3955	71	9	s∗|	s∗|	PROPN
ejpam-3955	71	10	<	<	X
ejpam-3955	71	11	|ng(v	|ng(v	NOUN
ejpam-3955	71	12	)	)	PUNCT
ejpam-3955	71	13	∩	∩	NOUN
ejpam-3955	71	14	s|	s|	VERB
ejpam-3955	71	15	≤	≤	NUM
ejpam-3955	71	16	|ng(v	|ng(v	NOUN
ejpam-3955	71	17	)	)	PUNCT
ejpam-3955	71	18	\	\	NOUN
ejpam-3955	71	19	s|	s|	VERB
ejpam-3955	71	20	<	<	X
ejpam-3955	71	21	|ng(v	|ng(v	NOUN
ejpam-3955	71	22	)	)	PUNCT
ejpam-3955	71	23	\	\	NOUN
ejpam-3955	71	24	s∗|	s∗|	PROPN
ejpam-3955	71	25	.	.	PUNCT
ejpam-3955	72	1	if	if	SCONJ
ejpam-3955	72	2	u	u	PROPN
ejpam-3955	72	3	/∈	/∈	PUNCT
ejpam-3955	72	4	ng(v	ng(v	NUM
ejpam-3955	72	5	)	)	PUNCT
ejpam-3955	72	6	,	,	PUNCT
ejpam-3955	72	7	then	then	ADV
ejpam-3955	72	8	ng(v	ng(v	PUNCT
ejpam-3955	72	9	)	)	PUNCT
ejpam-3955	72	10	∩	∩	NOUN
ejpam-3955	72	11	s∗	s∗	PROPN
ejpam-3955	72	12	=	=	SYM
ejpam-3955	72	13	ng(v	ng(v	X
ejpam-3955	72	14	)	)	PUNCT
ejpam-3955	72	15	∩	∩	NOUN
ejpam-3955	72	16	s	s	PART
ejpam-3955	72	17	and	and	CCONJ
ejpam-3955	72	18	ng(v	ng(v	NUM
ejpam-3955	72	19	)	)	PUNCT
ejpam-3955	72	20	\	\	PROPN
ejpam-3955	72	21	s∗	s∗	PROPN
ejpam-3955	72	22	=	=	PUNCT
ejpam-3955	72	23	ng(v	ng(v	X
ejpam-3955	72	24	)	)	PUNCT
ejpam-3955	72	25	\	\	NOUN
ejpam-3955	73	1	s	s	VERB
ejpam-3955	73	2	so	so	SCONJ
ejpam-3955	73	3	that	that	SCONJ
ejpam-3955	73	4	|ng(v	|ng(v	ADP
ejpam-3955	73	5	)	)	PUNCT
ejpam-3955	73	6	∩	∩	NOUN
ejpam-3955	73	7	s∗|	s∗|	VERB
ejpam-3955	73	8	≤	≤	NUM
ejpam-3955	73	9	|ng(v	|ng(v	NOUN
ejpam-3955	73	10	)	)	PUNCT
ejpam-3955	73	11	\	\	NOUN
ejpam-3955	73	12	s∗|	s∗|	PROPN
ejpam-3955	73	13	.	.	PUNCT
ejpam-3955	74	1	this	this	PRON
ejpam-3955	74	2	shows	show	VERB
ejpam-3955	74	3	that	that	SCONJ
ejpam-3955	74	4	s∗	s∗	PROPN
ejpam-3955	74	5	is	be	AUX
ejpam-3955	74	6	a	a	DET
ejpam-3955	74	7	cost	cost	NOUN
ejpam-3955	74	8	effective	effective	ADJ
ejpam-3955	74	9	set	set	NOUN
ejpam-3955	74	10	.	.	PUNCT
ejpam-3955	75	1	if	if	SCONJ
ejpam-3955	75	2	a	a	DET
ejpam-3955	75	3	(	(	PUNCT
ejpam-3955	75	4	s	s	PROPN
ejpam-3955	75	5	,	,	PUNCT
ejpam-3955	75	6	then	then	ADV
ejpam-3955	75	7	a	a	PRON
ejpam-3955	75	8	can	can	AUX
ejpam-3955	75	9	be	be	AUX
ejpam-3955	75	10	obtained	obtain	VERB
ejpam-3955	75	11	from	from	ADP
ejpam-3955	75	12	s	s	PRON
ejpam-3955	75	13	by	by	ADP
ejpam-3955	75	14	removing	remove	VERB
ejpam-3955	75	15	one	one	NUM
ejpam-3955	75	16	vertex	vertex	NOUN
ejpam-3955	75	17	at	at	ADP
ejpam-3955	75	18	a	a	DET
ejpam-3955	75	19	time	time	NOUN
ejpam-3955	75	20	.	.	PUNCT
ejpam-3955	76	1	as	as	SCONJ
ejpam-3955	76	2	shown	show	VERB
ejpam-3955	76	3	above	above	ADP
ejpam-3955	76	4	,	,	PUNCT
ejpam-3955	76	5	removal	removal	NOUN
ejpam-3955	76	6	of	of	ADP
ejpam-3955	76	7	a	a	DET
ejpam-3955	76	8	vertex	vertex	NOUN
ejpam-3955	76	9	from	from	ADP
ejpam-3955	76	10	a	a	DET
ejpam-3955	76	11	cost	cost	NOUN
ejpam-3955	76	12	effective	effective	ADJ
ejpam-3955	76	13	set	set	NOUN
ejpam-3955	76	14	results	result	NOUN
ejpam-3955	76	15	to	to	ADP
ejpam-3955	76	16	a	a	DET
ejpam-3955	76	17	cost	cost	NOUN
ejpam-3955	76	18	effective	effective	ADJ
ejpam-3955	76	19	set	set	NOUN
ejpam-3955	76	20	.	.	PUNCT
ejpam-3955	77	1	thus	thus	ADV
ejpam-3955	77	2	,	,	PUNCT
ejpam-3955	77	3	a	a	PRON
ejpam-3955	77	4	is	be	AUX
ejpam-3955	77	5	a	a	DET
ejpam-3955	77	6	cost	cost	NOUN
ejpam-3955	77	7	effective	effective	ADJ
ejpam-3955	77	8	set	set	NOUN
ejpam-3955	77	9	in	in	ADP
ejpam-3955	77	10	g.	g.	PROPN
ejpam-3955	77	11	corollary	corollary	PROPN
ejpam-3955	77	12	2	2	PROPN
ejpam-3955	77	13	.	.	PUNCT
ejpam-3955	78	1	let	let	VERB
ejpam-3955	78	2	g	g	PRON
ejpam-3955	78	3	be	be	AUX
ejpam-3955	78	4	a	a	DET
ejpam-3955	78	5	nontrivial	nontrivial	ADJ
ejpam-3955	78	6	connected	connect	VERB
ejpam-3955	78	7	graph	graph	NOUN
ejpam-3955	78	8	.	.	PUNCT
ejpam-3955	79	1	then	then	ADV
ejpam-3955	79	2	every	every	DET
ejpam-3955	79	3	minimal	minimal	ADJ
ejpam-3955	79	4	cost	cost	NOUN
ejpam-3955	79	5	effective	effective	ADJ
ejpam-3955	79	6	dominating	dominating	NOUN
ejpam-3955	79	7	set	set	VERB
ejpam-3955	79	8	in	in	ADP
ejpam-3955	79	9	g	g	PROPN
ejpam-3955	79	10	is	be	AUX
ejpam-3955	79	11	a	a	DET
ejpam-3955	79	12	minimal	minimal	ADJ
ejpam-3955	79	13	dominating	dominating	NOUN
ejpam-3955	79	14	set	set	NOUN
ejpam-3955	79	15	.	.	PUNCT
ejpam-3955	80	1	consequently	consequently	ADV
ejpam-3955	80	2	,	,	PUNCT
ejpam-3955	80	3	γmce(g	γmce(g	PROPN
ejpam-3955	80	4	)	)	PUNCT
ejpam-3955	80	5	≤	≤	NOUN
ejpam-3955	80	6	γm(g	γm(g	NUM
ejpam-3955	80	7	)	)	PUNCT
ejpam-3955	80	8	.	.	PUNCT
ejpam-3955	81	1	h.	h.	PROPN
ejpam-3955	81	2	nuenay	nuenay	PROPN
ejpam-3955	81	3	-	-	PUNCT
ejpam-3955	81	4	maglanque	maglanque	ADJ
ejpam-3955	81	5	,	,	PUNCT
ejpam-3955	81	6	f.jamil	f.jamil	PROPN
ejpam-3955	81	7	/	/	SYM
ejpam-3955	81	8	eur	eur	PROPN
ejpam-3955	81	9	.	.	PUNCT
ejpam-3955	82	1	j.	j.	PROPN
ejpam-3955	82	2	pure	pure	PROPN
ejpam-3955	82	3	appl	appl	PROPN
ejpam-3955	82	4	.	.	PROPN
ejpam-3955	82	5	math	math	PROPN
ejpam-3955	82	6	,	,	PUNCT
ejpam-3955	82	7	14	14	NUM
ejpam-3955	82	8	(	(	PUNCT
ejpam-3955	82	9	2	2	NUM
ejpam-3955	82	10	)	)	PUNCT
ejpam-3955	82	11	(	(	PUNCT
ejpam-3955	82	12	2021	2021	NUM
ejpam-3955	82	13	)	)	PUNCT
ejpam-3955	82	14	,	,	PUNCT
ejpam-3955	82	15	537	537	NUM
ejpam-3955	82	16	-	-	SYM
ejpam-3955	82	17	550	550	NUM
ejpam-3955	82	18	540	540	NUM
ejpam-3955	82	19	remark	remark	NOUN
ejpam-3955	82	20	1	1	NUM
ejpam-3955	82	21	.	.	PUNCT
ejpam-3955	83	1	a	a	DET
ejpam-3955	83	2	minimal	minimal	ADJ
ejpam-3955	83	3	dominating	dominating	NOUN
ejpam-3955	83	4	set	set	NOUN
ejpam-3955	83	5	need	need	AUX
ejpam-3955	83	6	not	not	PART
ejpam-3955	83	7	be	be	AUX
ejpam-3955	83	8	a	a	DET
ejpam-3955	83	9	minimal	minimal	ADJ
ejpam-3955	83	10	cost	cost	NOUN
ejpam-3955	83	11	effective	effective	ADJ
ejpam-3955	83	12	dominating	dominating	NOUN
ejpam-3955	83	13	set	set	NOUN
ejpam-3955	83	14	.	.	PUNCT
ejpam-3955	84	1	remark	remark	PROPN
ejpam-3955	84	2	2	2	NUM
ejpam-3955	84	3	.	.	PUNCT
ejpam-3955	85	1	any	any	DET
ejpam-3955	85	2	independent	independent	ADJ
ejpam-3955	85	3	dominating	dominating	NOUN
ejpam-3955	85	4	set	set	VERB
ejpam-3955	85	5	in	in	ADP
ejpam-3955	85	6	a	a	DET
ejpam-3955	85	7	connected	connected	ADJ
ejpam-3955	85	8	nontrivial	nontrivial	ADJ
ejpam-3955	85	9	graph	graph	NOUN
ejpam-3955	85	10	is	be	AUX
ejpam-3955	85	11	a	a	DET
ejpam-3955	85	12	minimal	minimal	ADJ
ejpam-3955	85	13	cost	cost	NOUN
ejpam-3955	85	14	effective	effective	ADJ
ejpam-3955	85	15	dominating	dominating	NOUN
ejpam-3955	85	16	set	set	VERB
ejpam-3955	85	17	in	in	ADP
ejpam-3955	85	18	g.	g.	PROPN
ejpam-3955	85	19	corollary	corollary	PROPN
ejpam-3955	85	20	3	3	X
ejpam-3955	85	21	.	.	PUNCT
ejpam-3955	86	1	let	let	VERB
ejpam-3955	86	2	g	g	PRON
ejpam-3955	86	3	be	be	AUX
ejpam-3955	86	4	a	a	DET
ejpam-3955	86	5	nontrivial	nontrivial	ADJ
ejpam-3955	86	6	connected	connect	VERB
ejpam-3955	86	7	graph	graph	NOUN
ejpam-3955	86	8	.	.	PUNCT
ejpam-3955	87	1	then	then	ADV
ejpam-3955	87	2	i(g	i(g	NOUN
ejpam-3955	87	3	)	)	PUNCT
ejpam-3955	88	1	≤	≤	PROPN
ejpam-3955	88	2	γmce(g	γmce(g	PROPN
ejpam-3955	88	3	)	)	PUNCT
ejpam-3955	88	4	≤	≤	NOUN
ejpam-3955	88	5	γm(g	γm(g	NUM
ejpam-3955	88	6	)	)	PUNCT
ejpam-3955	88	7	.	.	PUNCT
ejpam-3955	89	1	proof	proof	NOUN
ejpam-3955	89	2	.	.	PUNCT
ejpam-3955	90	1	this	this	PRON
ejpam-3955	90	2	follows	follow	VERB
ejpam-3955	90	3	from	from	ADP
ejpam-3955	90	4	remark	remark	NOUN
ejpam-3955	90	5	2	2	NUM
ejpam-3955	90	6	and	and	CCONJ
ejpam-3955	90	7	corollary	corollary	ADJ
ejpam-3955	90	8	2	2	NUM
ejpam-3955	90	9	.	.	PUNCT
ejpam-3955	90	10	remark	remark	NOUN
ejpam-3955	90	11	3	3	NUM
ejpam-3955	90	12	.	.	PUNCT
ejpam-3955	91	1	for	for	ADP
ejpam-3955	91	2	any	any	DET
ejpam-3955	91	3	nontrivial	nontrivial	ADJ
ejpam-3955	91	4	connected	connect	VERB
ejpam-3955	91	5	graph	graph	NOUN
ejpam-3955	91	6	g	g	PROPN
ejpam-3955	91	7	,	,	PUNCT
ejpam-3955	91	8	γce(g	γce(g	PROPN
ejpam-3955	91	9	)	)	PUNCT
ejpam-3955	91	10	≤	≤	NOUN
ejpam-3955	91	11	γmce(g	γmce(g	PROPN
ejpam-3955	91	12	)	)	PUNCT
ejpam-3955	91	13	≤	≤	NUM
ejpam-3955	91	14	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	91	15	)	)	PUNCT
ejpam-3955	91	16	.	.	PUNCT
ejpam-3955	92	1	theorem	theorem	ADJ
ejpam-3955	92	2	4	4	NUM
ejpam-3955	92	3	.	.	X
ejpam-3955	93	1	for	for	ADP
ejpam-3955	93	2	any	any	DET
ejpam-3955	93	3	connected	connected	ADJ
ejpam-3955	93	4	graph	graph	NOUN
ejpam-3955	93	5	g	g	NOUN
ejpam-3955	93	6	of	of	ADP
ejpam-3955	93	7	order	order	NOUN
ejpam-3955	93	8	n	n	PRON
ejpam-3955	93	9	≥	≥	NOUN
ejpam-3955	93	10	2	2	NUM
ejpam-3955	93	11	,	,	PUNCT
ejpam-3955	93	12	if	if	SCONJ
ejpam-3955	93	13	g	g	PROPN
ejpam-3955	93	14	is	be	AUX
ejpam-3955	93	15	not	not	PART
ejpam-3955	93	16	complete	complete	ADJ
ejpam-3955	93	17	,	,	PUNCT
ejpam-3955	93	18	then	then	ADV
ejpam-3955	93	19	γmce(g	γmce(g	PROPN
ejpam-3955	93	20	)	)	PUNCT
ejpam-3955	93	21	≥	≥	NOUN
ejpam-3955	93	22	2	2	NUM
ejpam-3955	93	23	,	,	PUNCT
ejpam-3955	93	24	and	and	CCONJ
ejpam-3955	93	25	consequently	consequently	ADV
ejpam-3955	93	26	,	,	PUNCT
ejpam-3955	93	27	γ+ce(g	γ+ce(g	PROPN
ejpam-3955	93	28	)	)	PUNCT
ejpam-3955	93	29	≥	≥	NOUN
ejpam-3955	93	30	2	2	NUM
ejpam-3955	93	31	.	.	PUNCT
ejpam-3955	94	1	proof	proof	NOUN
ejpam-3955	94	2	.	.	PUNCT
ejpam-3955	95	1	let	let	VERB
ejpam-3955	95	2	s	s	PRON
ejpam-3955	95	3	be	be	AUX
ejpam-3955	95	4	a	a	DET
ejpam-3955	95	5	maximal	maximal	ADJ
ejpam-3955	95	6	independent	independent	ADJ
ejpam-3955	95	7	set	set	NOUN
ejpam-3955	95	8	of	of	ADP
ejpam-3955	95	9	g.	g.	PROPN
ejpam-3955	95	10	since	since	SCONJ
ejpam-3955	95	11	g	g	PROPN
ejpam-3955	95	12	6=	6=	PROPN
ejpam-3955	95	13	kn	kn	PROPN
ejpam-3955	95	14	,	,	PUNCT
ejpam-3955	95	15	|s|	|s|	PROPN
ejpam-3955	95	16	>	>	ADP
ejpam-3955	95	17	2	2	NUM
ejpam-3955	95	18	.	.	PUNCT
ejpam-3955	95	19	by	by	ADP
ejpam-3955	95	20	theorem	theorem	NOUN
ejpam-3955	95	21	3	3	NUM
ejpam-3955	95	22	,	,	PUNCT
ejpam-3955	95	23	s	s	VERB
ejpam-3955	95	24	is	be	AUX
ejpam-3955	95	25	a	a	DET
ejpam-3955	95	26	dominating	dominating	NOUN
ejpam-3955	95	27	set	set	VERB
ejpam-3955	95	28	in	in	ADP
ejpam-3955	95	29	g.	g.	PROPN
ejpam-3955	95	30	thus	thus	ADV
ejpam-3955	95	31	,	,	PUNCT
ejpam-3955	95	32	s	s	VERB
ejpam-3955	95	33	is	be	AUX
ejpam-3955	95	34	a	a	DET
ejpam-3955	95	35	minimal	minimal	ADJ
ejpam-3955	95	36	cost	cost	NOUN
ejpam-3955	95	37	effective	effective	ADJ
ejpam-3955	95	38	dominating	dominating	NOUN
ejpam-3955	95	39	set	set	VERB
ejpam-3955	95	40	in	in	ADP
ejpam-3955	95	41	g	g	NOUN
ejpam-3955	95	42	by	by	ADP
ejpam-3955	95	43	corollary	corollary	ADJ
ejpam-3955	95	44	2	2	NUM
ejpam-3955	95	45	.	.	PUNCT
ejpam-3955	96	1	consequently	consequently	ADV
ejpam-3955	96	2	,	,	PUNCT
ejpam-3955	96	3	γmce(g	γmce(g	PROPN
ejpam-3955	96	4	)	)	PUNCT
ejpam-3955	96	5	≥	≥	NOUN
ejpam-3955	96	6	2	2	NUM
ejpam-3955	96	7	.	.	PUNCT
ejpam-3955	96	8	theorem	theorem	NOUN
ejpam-3955	96	9	5	5	NUM
ejpam-3955	96	10	.	.	X
ejpam-3955	97	1	for	for	ADP
ejpam-3955	97	2	any	any	DET
ejpam-3955	97	3	complete	complete	ADJ
ejpam-3955	97	4	graph	graph	NOUN
ejpam-3955	97	5	kn	kn	NOUN
ejpam-3955	97	6	of	of	ADP
ejpam-3955	97	7	order	order	NOUN
ejpam-3955	97	8	n	n	PRON
ejpam-3955	97	9	≥	≥	NOUN
ejpam-3955	97	10	2	2	NUM
ejpam-3955	97	11	,	,	PUNCT
ejpam-3955	97	12	γ+ce(kn	γ+ce(kn	NUM
ejpam-3955	97	13	)	)	PUNCT
ejpam-3955	97	14	=	=	PUNCT
ejpam-3955	97	15	⌊	⌊	VERB
ejpam-3955	97	16	n+	n+	NUM
ejpam-3955	97	17	1	1	NUM
ejpam-3955	97	18	2	2	NUM
ejpam-3955	97	19	⌋	⌋	NOUN
ejpam-3955	97	20	.	.	PUNCT
ejpam-3955	98	1	proof	proof	NOUN
ejpam-3955	98	2	.	.	PUNCT
ejpam-3955	99	1	let	let	VERB
ejpam-3955	99	2	s	s	PRON
ejpam-3955	99	3	⊆	⊆	NUM
ejpam-3955	99	4	v	v	NOUN
ejpam-3955	99	5	(	(	PUNCT
ejpam-3955	99	6	kn	kn	PROPN
ejpam-3955	99	7	)	)	PUNCT
ejpam-3955	99	8	with	with	ADP
ejpam-3955	99	9	|s|	|s|	NOUN
ejpam-3955	99	10	=	=	SYM
ejpam-3955	99	11	⌊	⌊	VERB
ejpam-3955	99	12	n+1	n+1	NUM
ejpam-3955	99	13	2	2	NUM
ejpam-3955	99	14	⌋	⌋	NOUN
ejpam-3955	99	15	.	.	PUNCT
ejpam-3955	100	1	for	for	ADP
ejpam-3955	100	2	each	each	DET
ejpam-3955	100	3	u	u	PROPN
ejpam-3955	100	4	∈	∈	PROPN
ejpam-3955	100	5	s	s	PROPN
ejpam-3955	100	6	,	,	PUNCT
ejpam-3955	100	7	|nkn(u	|nkn(u	NOUN
ejpam-3955	100	8	)	)	PUNCT
ejpam-3955	100	9	∩	∩	NOUN
ejpam-3955	100	10	s|	s|	NOUN
ejpam-3955	100	11	=	=	SYM
ejpam-3955	100	12	|s|	|s|	PROPN
ejpam-3955	100	13	−	−	NOUN
ejpam-3955	100	14	1	1	NUM
ejpam-3955	100	15	=	=	SYM
ejpam-3955	100	16	⌊	⌊	VERB
ejpam-3955	100	17	n+	n+	NUM
ejpam-3955	100	18	1	1	NUM
ejpam-3955	100	19	2	2	NUM
ejpam-3955	100	20	⌋	⌋	NOUN
ejpam-3955	100	21	−	−	NOUN
ejpam-3955	100	22	1	1	NUM
ejpam-3955	100	23	and	and	CCONJ
ejpam-3955	100	24	|nkn(u	|nkn(u	NOUN
ejpam-3955	100	25	)	)	PUNCT
ejpam-3955	100	26	\	\	NOUN
ejpam-3955	100	27	s|	s|	NOUN
ejpam-3955	100	28	=	=	SYM
ejpam-3955	100	29	n−	n−	NOUN
ejpam-3955	100	30	|s|	|s|	NOUN
ejpam-3955	100	31	.	.	PUNCT
ejpam-3955	101	1	now	now	ADV
ejpam-3955	101	2	,	,	PUNCT
ejpam-3955	101	3	2	2	X
ejpam-3955	101	4	⌊	⌊	NOUN
ejpam-3955	101	5	n+1	n+1	SYM
ejpam-3955	101	6	2	2	NUM
ejpam-3955	101	7	⌋	⌋	NOUN
ejpam-3955	101	8	≤	≤	NUM
ejpam-3955	101	9	n+	n+	PUNCT
ejpam-3955	101	10	1	1	NUM
ejpam-3955	101	11	so	so	SCONJ
ejpam-3955	101	12	that	that	DET
ejpam-3955	101	13	|nkn(u	|nkn(u	NOUN
ejpam-3955	101	14	)	)	PUNCT
ejpam-3955	101	15	∩	∩	NOUN
ejpam-3955	101	16	s|	s|	VERB
ejpam-3955	101	17	=	=	PUNCT
ejpam-3955	102	1	⌊	⌊	VERB
ejpam-3955	102	2	n+	n+	NUM
ejpam-3955	102	3	1	1	NUM
ejpam-3955	102	4	2	2	NUM
ejpam-3955	102	5	⌋	⌋	NOUN
ejpam-3955	102	6	−	−	NOUN
ejpam-3955	102	7	1	1	NUM
ejpam-3955	102	8	≤	≤	NOUN
ejpam-3955	102	9	n−	n−	NOUN
ejpam-3955	102	10	⌊	⌊	VERB
ejpam-3955	102	11	n+	n+	ADP
ejpam-3955	102	12	1	1	NUM
ejpam-3955	102	13	2	2	NUM
ejpam-3955	102	14	⌋	⌋	NOUN
ejpam-3955	102	15	=	=	SYM
ejpam-3955	102	16	|nkn(u	|nkn(u	NOUN
ejpam-3955	102	17	)	)	PUNCT
ejpam-3955	102	18	\	\	PROPN
ejpam-3955	103	1	s|	s|	PROPN
ejpam-3955	103	2	.	.	PUNCT
ejpam-3955	104	1	thus	thus	ADV
ejpam-3955	104	2	,	,	PUNCT
ejpam-3955	104	3	s	s	VERB
ejpam-3955	104	4	is	be	AUX
ejpam-3955	104	5	a	a	DET
ejpam-3955	104	6	cost	cost	NOUN
ejpam-3955	104	7	effective	effective	ADJ
ejpam-3955	104	8	dominating	dominating	NOUN
ejpam-3955	104	9	set	set	VERB
ejpam-3955	104	10	in	in	ADP
ejpam-3955	104	11	kn	kn	PROPN
ejpam-3955	104	12	.	.	PUNCT
ejpam-3955	105	1	hence	hence	ADV
ejpam-3955	105	2	,	,	PUNCT
ejpam-3955	105	3	γ+ce(kn	γ+ce(kn	NUM
ejpam-3955	105	4	)	)	PUNCT
ejpam-3955	105	5	≥	≥	PRON
ejpam-3955	105	6	|s|	|s|	NOUN
ejpam-3955	105	7	=	=	SYM
ejpam-3955	105	8	⌊	⌊	PROPN
ejpam-3955	105	9	n+	n+	NUM
ejpam-3955	105	10	1	1	NUM
ejpam-3955	105	11	2	2	NUM
ejpam-3955	105	12	⌋	⌋	NOUN
ejpam-3955	105	13	.	.	PUNCT
ejpam-3955	106	1	let	let	VERB
ejpam-3955	106	2	s	s	PRON
ejpam-3955	106	3	be	be	AUX
ejpam-3955	106	4	a	a	DET
ejpam-3955	106	5	γ+ce	γ+ce	NOUN
ejpam-3955	106	6	-	-	PUNCT
ejpam-3955	106	7	set	set	NOUN
ejpam-3955	106	8	of	of	ADP
ejpam-3955	106	9	kn	kn	PROPN
ejpam-3955	106	10	.	.	PUNCT
ejpam-3955	107	1	for	for	ADP
ejpam-3955	107	2	each	each	DET
ejpam-3955	107	3	u	u	PROPN
ejpam-3955	107	4	∈	∈	PROPN
ejpam-3955	107	5	s	s	PROPN
ejpam-3955	107	6	,	,	PUNCT
ejpam-3955	107	7	|nkn(u	|nkn(u	NOUN
ejpam-3955	107	8	)	)	PUNCT
ejpam-3955	107	9	∩	∩	NOUN
ejpam-3955	107	10	s|	s|	NOUN
ejpam-3955	107	11	=	=	SYM
ejpam-3955	107	12	|s|	|s|	PROPN
ejpam-3955	107	13	−	−	NOUN
ejpam-3955	107	14	1	1	NUM
ejpam-3955	107	15	and	and	CCONJ
ejpam-3955	107	16	|nkn(u	|nkn(u	NOUN
ejpam-3955	107	17	)	)	PUNCT
ejpam-3955	107	18	\	\	NOUN
ejpam-3955	108	1	s|	s|	PROPN
ejpam-3955	108	2	=	=	SYM
ejpam-3955	108	3	|v	|v	PROPN
ejpam-3955	108	4	(	(	PUNCT
ejpam-3955	108	5	kn	kn	PROPN
ejpam-3955	108	6	)	)	PUNCT
ejpam-3955	108	7	\	\	PROPN
ejpam-3955	108	8	s|	s|	PROPN
ejpam-3955	108	9	=	=	SYM
ejpam-3955	108	10	|v	|v	PROPN
ejpam-3955	108	11	(	(	PUNCT
ejpam-3955	108	12	kn)|	kn)|	PROPN
ejpam-3955	108	13	−	−	PROPN
ejpam-3955	108	14	|s|	|s|	PROPN
ejpam-3955	108	15	=	=	SYM
ejpam-3955	108	16	n−	n−	PROPN
ejpam-3955	108	17	|s|	|s|	NOUN
ejpam-3955	108	18	.	.	PUNCT
ejpam-3955	109	1	h.	h.	PROPN
ejpam-3955	109	2	nuenay	nuenay	PROPN
ejpam-3955	109	3	-	-	PUNCT
ejpam-3955	109	4	maglanque	maglanque	ADJ
ejpam-3955	109	5	,	,	PUNCT
ejpam-3955	109	6	f.jamil	f.jamil	PROPN
ejpam-3955	109	7	/	/	SYM
ejpam-3955	109	8	eur	eur	PROPN
ejpam-3955	109	9	.	.	PUNCT
ejpam-3955	110	1	j.	j.	PROPN
ejpam-3955	110	2	pure	pure	PROPN
ejpam-3955	110	3	appl	appl	PROPN
ejpam-3955	110	4	.	.	PROPN
ejpam-3955	110	5	math	math	PROPN
ejpam-3955	110	6	,	,	PUNCT
ejpam-3955	110	7	14	14	NUM
ejpam-3955	110	8	(	(	PUNCT
ejpam-3955	110	9	2	2	NUM
ejpam-3955	110	10	)	)	PUNCT
ejpam-3955	110	11	(	(	PUNCT
ejpam-3955	110	12	2021	2021	NUM
ejpam-3955	110	13	)	)	PUNCT
ejpam-3955	110	14	,	,	PUNCT
ejpam-3955	110	15	537	537	NUM
ejpam-3955	110	16	-	-	SYM
ejpam-3955	110	17	550	550	NUM
ejpam-3955	110	18	541	541	NUM
ejpam-3955	110	19	since	since	SCONJ
ejpam-3955	110	20	s	s	NOUN
ejpam-3955	110	21	is	be	AUX
ejpam-3955	110	22	cost	cost	NOUN
ejpam-3955	110	23	effective	effective	ADJ
ejpam-3955	110	24	,	,	PUNCT
ejpam-3955	110	25	|s|	|s|	PROPN
ejpam-3955	110	26	−	−	PROPN
ejpam-3955	110	27	1	1	NUM
ejpam-3955	110	28	≤	≤	NOUN
ejpam-3955	110	29	n−	n−	NOUN
ejpam-3955	110	30	|s|	|s|	NOUN
ejpam-3955	110	31	,	,	PUNCT
ejpam-3955	110	32	or	or	CCONJ
ejpam-3955	110	33	equivalently	equivalently	ADV
ejpam-3955	110	34	,	,	PUNCT
ejpam-3955	110	35	2|s|	2|s|	NUM
ejpam-3955	110	36	≤	≤	NUM
ejpam-3955	110	37	n+	n+	PUNCT
ejpam-3955	110	38	1	1	X
ejpam-3955	110	39	.	.	PUNCT
ejpam-3955	111	1	thus	thus	ADV
ejpam-3955	111	2	,	,	PUNCT
ejpam-3955	111	3	|s|	|s|	VERB
ejpam-3955	111	4	≤	≤	ADV
ejpam-3955	111	5	1	1	NUM
ejpam-3955	111	6	2(n+	2(n+	NOUN
ejpam-3955	111	7	1	1	NUM
ejpam-3955	111	8	)	)	PUNCT
ejpam-3955	111	9	.	.	PUNCT
ejpam-3955	112	1	since	since	SCONJ
ejpam-3955	112	2	s	s	PROPN
ejpam-3955	112	3	is	be	AUX
ejpam-3955	112	4	a	a	DET
ejpam-3955	112	5	γ+ce	γ+ce	NOUN
ejpam-3955	112	6	-	-	PUNCT
ejpam-3955	112	7	set	set	NOUN
ejpam-3955	112	8	,	,	PUNCT
ejpam-3955	112	9	γ+ce(kn	γ+ce(kn	NUM
ejpam-3955	112	10	)	)	PUNCT
ejpam-3955	112	11	=	=	PUNCT
ejpam-3955	112	12	|s|	|s|	NOUN
ejpam-3955	112	13	=	=	SYM
ejpam-3955	112	14	⌊	⌊	PROPN
ejpam-3955	112	15	n+	n+	NUM
ejpam-3955	112	16	1	1	NUM
ejpam-3955	112	17	2	2	NUM
ejpam-3955	112	18	⌋	⌋	NOUN
ejpam-3955	112	19	.	.	PUNCT
ejpam-3955	113	1	corollary	corollary	ADJ
ejpam-3955	113	2	4	4	NUM
ejpam-3955	113	3	.	.	PUNCT
ejpam-3955	114	1	let	let	VERB
ejpam-3955	114	2	g	g	PRON
ejpam-3955	114	3	be	be	AUX
ejpam-3955	114	4	a	a	DET
ejpam-3955	114	5	nontrivial	nontrivial	ADJ
ejpam-3955	114	6	connected	connect	VERB
ejpam-3955	114	7	graph	graph	NOUN
ejpam-3955	114	8	of	of	ADP
ejpam-3955	114	9	order	order	NOUN
ejpam-3955	114	10	n	n	PRON
ejpam-3955	114	11	≥	≥	NOUN
ejpam-3955	114	12	2	2	NUM
ejpam-3955	114	13	.	.	PUNCT
ejpam-3955	115	1	then	then	ADV
ejpam-3955	115	2	(	(	PUNCT
ejpam-3955	115	3	i	i	NOUN
ejpam-3955	115	4	)	)	PUNCT
ejpam-3955	115	5	γce(g	γce(g	PROPN
ejpam-3955	115	6	)	)	PUNCT
ejpam-3955	115	7	=	=	SYM
ejpam-3955	115	8	1	1	NUM
ejpam-3955	115	9	if	if	SCONJ
ejpam-3955	115	10	and	and	CCONJ
ejpam-3955	115	11	only	only	ADV
ejpam-3955	115	12	if	if	SCONJ
ejpam-3955	115	13	g	g	NOUN
ejpam-3955	115	14	=	=	PROPN
ejpam-3955	115	15	k1	k1	PROPN
ejpam-3955	116	1	+	+	NOUN
ejpam-3955	116	2	h	h	NOUN
ejpam-3955	116	3	for	for	ADP
ejpam-3955	116	4	some	some	DET
ejpam-3955	116	5	subgraph	subgraph	NOUN
ejpam-3955	116	6	h	h	NOUN
ejpam-3955	116	7	of	of	ADP
ejpam-3955	116	8	g	g	PROPN
ejpam-3955	116	9	;	;	PUNCT
ejpam-3955	116	10	(	(	PUNCT
ejpam-3955	116	11	ii	ii	NOUN
ejpam-3955	116	12	)	)	PUNCT
ejpam-3955	116	13	γmce(g	γmce(g	NOUN
ejpam-3955	116	14	)	)	PUNCT
ejpam-3955	117	1	=	=	SYM
ejpam-3955	117	2	1	1	NUM
ejpam-3955	117	3	if	if	SCONJ
ejpam-3955	117	4	and	and	CCONJ
ejpam-3955	117	5	only	only	ADV
ejpam-3955	117	6	if	if	SCONJ
ejpam-3955	117	7	g	g	PROPN
ejpam-3955	117	8	=	=	PROPN
ejpam-3955	117	9	kn	kn	PROPN
ejpam-3955	117	10	;	;	PUNCT
ejpam-3955	117	11	(	(	PUNCT
ejpam-3955	117	12	iii	iii	X
ejpam-3955	117	13	)	)	PUNCT
ejpam-3955	117	14	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	117	15	)	)	PUNCT
ejpam-3955	117	16	=	=	PUNCT
ejpam-3955	117	17	1	1	NUM
ejpam-3955	117	18	if	if	SCONJ
ejpam-3955	117	19	and	and	CCONJ
ejpam-3955	117	20	only	only	ADV
ejpam-3955	117	21	if	if	SCONJ
ejpam-3955	117	22	g	g	PROPN
ejpam-3955	117	23	=	=	SYM
ejpam-3955	117	24	k2	k2	PROPN
ejpam-3955	117	25	.	.	PUNCT
ejpam-3955	118	1	proof	proof	NOUN
ejpam-3955	118	2	.	.	PUNCT
ejpam-3955	119	1	statement	statement	NOUN
ejpam-3955	119	2	(	(	PUNCT
ejpam-3955	119	3	i	i	NOUN
ejpam-3955	119	4	)	)	PUNCT
ejpam-3955	119	5	is	be	AUX
ejpam-3955	119	6	clear	clear	ADJ
ejpam-3955	119	7	,	,	PUNCT
ejpam-3955	119	8	while	while	SCONJ
ejpam-3955	119	9	statement	statement	NOUN
ejpam-3955	119	10	(	(	PUNCT
ejpam-3955	119	11	ii	ii	NOUN
ejpam-3955	119	12	)	)	PUNCT
ejpam-3955	119	13	follows	follow	VERB
ejpam-3955	119	14	immediately	immediately	ADV
ejpam-3955	119	15	from	from	ADP
ejpam-3955	119	16	theorem	theorem	ADJ
ejpam-3955	119	17	4	4	NUM
ejpam-3955	119	18	.	.	PUNCT
ejpam-3955	119	19	suppose	suppose	VERB
ejpam-3955	119	20	that	that	SCONJ
ejpam-3955	119	21	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	119	22	)	)	PUNCT
ejpam-3955	119	23	=	=	SYM
ejpam-3955	120	1	1	1	X
ejpam-3955	120	2	.	.	PUNCT
ejpam-3955	120	3	then	then	ADV
ejpam-3955	120	4	g	g	PROPN
ejpam-3955	120	5	is	be	AUX
ejpam-3955	120	6	complete	complete	ADJ
ejpam-3955	120	7	,	,	PUNCT
ejpam-3955	120	8	by	by	ADP
ejpam-3955	120	9	theorem	theorem	NOUN
ejpam-3955	120	10	4	4	NUM
ejpam-3955	120	11	.	.	PUNCT
ejpam-3955	120	12	now	now	ADV
ejpam-3955	120	13	,	,	PUNCT
ejpam-3955	120	14	γ+ce(kn	γ+ce(kn	PUNCT
ejpam-3955	120	15	)	)	PUNCT
ejpam-3955	120	16	=	=	PUNCT
ejpam-3955	120	17	⌊	⌊	VERB
ejpam-3955	120	18	n+1	n+1	NUM
ejpam-3955	120	19	2	2	NUM
ejpam-3955	120	20	⌋	⌋	NOUN
ejpam-3955	120	21	by	by	ADP
ejpam-3955	120	22	theorem	theorem	NOUN
ejpam-3955	120	23	5	5	NUM
ejpam-3955	120	24	.	.	PUNCT
ejpam-3955	120	25	thus	thus	ADV
ejpam-3955	120	26	,	,	PUNCT
ejpam-3955	120	27	γ+ce(kn	γ+ce(kn	PUNCT
ejpam-3955	120	28	)	)	PUNCT
ejpam-3955	120	29	=	=	SYM
ejpam-3955	120	30	1	1	NUM
ejpam-3955	120	31	if	if	SCONJ
ejpam-3955	120	32	and	and	CCONJ
ejpam-3955	120	33	only	only	ADV
ejpam-3955	120	34	if	if	SCONJ
ejpam-3955	120	35	n	n	PROPN
ejpam-3955	120	36	=	=	SYM
ejpam-3955	120	37	2	2	X
ejpam-3955	120	38	.	.	X
ejpam-3955	120	39	theorem	theorem	VERB
ejpam-3955	120	40	6	6	NUM
ejpam-3955	120	41	.	.	PUNCT
ejpam-3955	121	1	for	for	ADP
ejpam-3955	121	2	m	m	PROPN
ejpam-3955	121	3	,	,	PUNCT
ejpam-3955	121	4	n	n	PRON
ejpam-3955	121	5	≥	≥	NOUN
ejpam-3955	121	6	1	1	NUM
ejpam-3955	121	7	,	,	PUNCT
ejpam-3955	121	8	(	(	PUNCT
ejpam-3955	121	9	i	i	NOUN
ejpam-3955	121	10	)	)	PUNCT
ejpam-3955	121	11	γce(km	γce(km	PROPN
ejpam-3955	121	12	,	,	PUNCT
ejpam-3955	121	13	n	n	CCONJ
ejpam-3955	121	14	)	)	PUNCT
ejpam-3955	121	15	=	=	SYM
ejpam-3955	121	16	min	min	NOUN
ejpam-3955	121	17	{	{	PUNCT
ejpam-3955	121	18	m	m	PROPN
ejpam-3955	121	19	,	,	PUNCT
ejpam-3955	121	20	n	n	CCONJ
ejpam-3955	121	21	,	,	PUNCT
ejpam-3955	121	22	2	2	NUM
ejpam-3955	121	23	}	}	PUNCT
ejpam-3955	121	24	(	(	PUNCT
ejpam-3955	121	25	ii	ii	NOUN
ejpam-3955	121	26	)	)	PUNCT
ejpam-3955	121	27	γmce(km	γmce(km	PROPN
ejpam-3955	121	28	,	,	PUNCT
ejpam-3955	121	29	n	n	CCONJ
ejpam-3955	121	30	)	)	PUNCT
ejpam-3955	121	31	=	=	SYM
ejpam-3955	121	32	γ+ce(km	γ+ce(km	NUM
ejpam-3955	121	33	,	,	PUNCT
ejpam-3955	121	34	n	n	CCONJ
ejpam-3955	121	35	)	)	PUNCT
ejpam-3955	121	36	=	=	SYM
ejpam-3955	121	37	max	max	PROPN
ejpam-3955	121	38	{	{	PUNCT
ejpam-3955	121	39	m	m	PROPN
ejpam-3955	121	40	,	,	PUNCT
ejpam-3955	121	41	n	n	CCONJ
ejpam-3955	121	42	}	}	PUNCT
ejpam-3955	121	43	.	.	PUNCT
ejpam-3955	122	1	proof	proof	NOUN
ejpam-3955	122	2	.	.	PUNCT
ejpam-3955	123	1	the	the	DET
ejpam-3955	123	2	result	result	NOUN
ejpam-3955	123	3	is	be	AUX
ejpam-3955	123	4	obvious	obvious	ADJ
ejpam-3955	123	5	if	if	SCONJ
ejpam-3955	123	6	n	n	NOUN
ejpam-3955	123	7	=	=	SYM
ejpam-3955	123	8	1	1	NUM
ejpam-3955	123	9	or	or	CCONJ
ejpam-3955	123	10	m	m	VERB
ejpam-3955	123	11	=	=	ADJ
ejpam-3955	123	12	1	1	X
ejpam-3955	123	13	.	.	PUNCT
ejpam-3955	123	14	suppose	suppose	VERB
ejpam-3955	123	15	that	that	SCONJ
ejpam-3955	123	16	m	m	PROPN
ejpam-3955	123	17	,	,	PUNCT
ejpam-3955	123	18	n	n	PRON
ejpam-3955	123	19	≥	≥	NOUN
ejpam-3955	123	20	2	2	NUM
ejpam-3955	123	21	.	.	PUNCT
ejpam-3955	123	22	put	put	VERB
ejpam-3955	123	23	g	g	PROPN
ejpam-3955	123	24	=	=	SYM
ejpam-3955	123	25	km	km	PROPN
ejpam-3955	123	26	,	,	PUNCT
ejpam-3955	123	27	n.	n.	NOUN
ejpam-3955	123	28	we	we	PRON
ejpam-3955	123	29	claim	claim	VERB
ejpam-3955	123	30	that	that	SCONJ
ejpam-3955	123	31	s	s	VERB
ejpam-3955	123	32	⊆	⊆	NUM
ejpam-3955	123	33	v	v	NOUN
ejpam-3955	123	34	(	(	PUNCT
ejpam-3955	123	35	g	g	NOUN
ejpam-3955	123	36	)	)	PUNCT
ejpam-3955	123	37	is	be	AUX
ejpam-3955	123	38	a	a	DET
ejpam-3955	123	39	cost	cost	NOUN
ejpam-3955	123	40	effective	effective	ADJ
ejpam-3955	123	41	dominating	dominating	NOUN
ejpam-3955	123	42	set	set	VERB
ejpam-3955	123	43	in	in	ADP
ejpam-3955	123	44	g	g	PROPN
ejpam-3955	124	1	if	if	SCONJ
ejpam-3955	124	2	and	and	CCONJ
ejpam-3955	124	3	only	only	ADV
ejpam-3955	124	4	if	if	SCONJ
ejpam-3955	124	5	either	either	PRON
ejpam-3955	124	6	s	s	VERB
ejpam-3955	124	7	is	be	AUX
ejpam-3955	124	8	a	a	DET
ejpam-3955	124	9	partite	partite	ADJ
ejpam-3955	124	10	set	set	NOUN
ejpam-3955	124	11	of	of	ADP
ejpam-3955	124	12	km	km	PROPN
ejpam-3955	124	13	,	,	PUNCT
ejpam-3955	124	14	n	n	NOUN
ejpam-3955	124	15	or	or	CCONJ
ejpam-3955	124	16	s	s	NOUN
ejpam-3955	124	17	intersects	intersect	NOUN
ejpam-3955	124	18	each	each	DET
ejpam-3955	124	19	partite	partite	ADJ
ejpam-3955	124	20	set	set	NOUN
ejpam-3955	124	21	and	and	CCONJ
ejpam-3955	124	22	2	2	NUM
ejpam-3955	124	23	≤	≤	NOUN
ejpam-3955	124	24	|s|	|s|	NOUN
ejpam-3955	124	25	≤	≤	NUM
ejpam-3955	124	26	⌊	⌊	PROPN
ejpam-3955	124	27	n	n	ADV
ejpam-3955	124	28	2	2	NUM
ejpam-3955	124	29	⌋	⌋	NOUN
ejpam-3955	124	30	+	+	CCONJ
ejpam-3955	124	31	⌊	⌊	PROPN
ejpam-3955	124	32	m	m	PROPN
ejpam-3955	124	33	2	2	NUM
ejpam-3955	124	34	⌋	⌋	NOUN
ejpam-3955	124	35	.	.	PUNCT
ejpam-3955	125	1	since	since	SCONJ
ejpam-3955	125	2	partite	partite	ADJ
ejpam-3955	125	3	sets	set	NOUN
ejpam-3955	125	4	u	u	PROPN
ejpam-3955	125	5	,	,	PUNCT
ejpam-3955	125	6	v	v	NOUN
ejpam-3955	125	7	of	of	ADP
ejpam-3955	125	8	km	km	PROPN
ejpam-3955	125	9	,	,	PUNCT
ejpam-3955	125	10	n	n	PRON
ejpam-3955	125	11	are	be	AUX
ejpam-3955	125	12	independent	independent	ADJ
ejpam-3955	125	13	dominating	dominating	NOUN
ejpam-3955	125	14	sets	set	NOUN
ejpam-3955	125	15	of	of	ADP
ejpam-3955	125	16	g	g	NOUN
ejpam-3955	125	17	,	,	PUNCT
ejpam-3955	125	18	they	they	PRON
ejpam-3955	125	19	are	be	AUX
ejpam-3955	125	20	minimal	minimal	ADJ
ejpam-3955	125	21	cost	cost	NOUN
ejpam-3955	125	22	effective	effective	ADJ
ejpam-3955	125	23	dominating	dominating	NOUN
ejpam-3955	125	24	sets	set	NOUN
ejpam-3955	125	25	in	in	ADP
ejpam-3955	125	26	g	g	NOUN
ejpam-3955	125	27	by	by	ADP
ejpam-3955	125	28	proposition	proposition	NOUN
ejpam-3955	125	29	2	2	NUM
ejpam-3955	125	30	.	.	PUNCT
ejpam-3955	125	31	assume	assume	VERB
ejpam-3955	125	32	|u	|u	ADJ
ejpam-3955	125	33	|	|	NOUN
ejpam-3955	125	34	=	=	NOUN
ejpam-3955	125	35	m	m	NOUN
ejpam-3955	125	36	and	and	CCONJ
ejpam-3955	125	37	|v	|v	VERB
ejpam-3955	125	38	|	|	ADV
ejpam-3955	126	1	=	=	X
ejpam-3955	126	2	n.	n.	NOUN
ejpam-3955	126	3	let	let	VERB
ejpam-3955	126	4	s	s	PRON
ejpam-3955	126	5	be	be	AUX
ejpam-3955	126	6	a	a	DET
ejpam-3955	126	7	cost	cost	NOUN
ejpam-3955	126	8	effective	effective	ADJ
ejpam-3955	126	9	dominating	dominating	NOUN
ejpam-3955	126	10	set	set	VERB
ejpam-3955	126	11	in	in	ADP
ejpam-3955	126	12	g	g	NOUN
ejpam-3955	126	13	which	which	PRON
ejpam-3955	126	14	is	be	AUX
ejpam-3955	126	15	not	not	PART
ejpam-3955	126	16	a	a	DET
ejpam-3955	126	17	partite	partite	ADJ
ejpam-3955	126	18	set	set	NOUN
ejpam-3955	126	19	.	.	PUNCT
ejpam-3955	127	1	since	since	SCONJ
ejpam-3955	127	2	s	s	PROPN
ejpam-3955	127	3	is	be	AUX
ejpam-3955	127	4	a	a	DET
ejpam-3955	127	5	dominating	dominating	NOUN
ejpam-3955	127	6	set	set	NOUN
ejpam-3955	127	7	,	,	PUNCT
ejpam-3955	127	8	s	s	NOUN
ejpam-3955	127	9	intersects	intersect	NOUN
ejpam-3955	127	10	both	both	CCONJ
ejpam-3955	127	11	partite	partite	ADJ
ejpam-3955	127	12	sets	set	NOUN
ejpam-3955	127	13	.	.	PUNCT
ejpam-3955	128	1	let	let	VERB
ejpam-3955	128	2	v	v	X
ejpam-3955	128	3	∈	∈	VERB
ejpam-3955	128	4	s.	s.	PROPN
ejpam-3955	128	5	if	if	SCONJ
ejpam-3955	128	6	v	v	NUM
ejpam-3955	128	7	∈	∈	PROPN
ejpam-3955	128	8	u	u	NOUN
ejpam-3955	128	9	,	,	PUNCT
ejpam-3955	128	10	then	then	ADV
ejpam-3955	128	11	|s	|s	PROPN
ejpam-3955	128	12	∩	∩	NOUN
ejpam-3955	128	13	v	v	ADP
ejpam-3955	128	14	|	|	NOUN
ejpam-3955	128	15	=	=	SYM
ejpam-3955	128	16	|ng(v	|ng(v	NOUN
ejpam-3955	128	17	)	)	PUNCT
ejpam-3955	128	18	∩	∩	NOUN
ejpam-3955	128	19	s|	s|	VERB
ejpam-3955	128	20	≤	≤	NUM
ejpam-3955	128	21	|ng(v	|ng(v	NOUN
ejpam-3955	128	22	)	)	PUNCT
ejpam-3955	128	23	\	\	NOUN
ejpam-3955	128	24	s|	s|	PROPN
ejpam-3955	128	25	=	=	PUNCT
ejpam-3955	128	26	|v	|v	PROPN
ejpam-3955	128	27	\	\	PROPN
ejpam-3955	128	28	s|	s|	PROPN
ejpam-3955	128	29	.	.	PUNCT
ejpam-3955	129	1	consequently	consequently	ADV
ejpam-3955	129	2	,	,	PUNCT
ejpam-3955	129	3	|s	|s	PROPN
ejpam-3955	129	4	∩	∩	NOUN
ejpam-3955	129	5	v	v	ADP
ejpam-3955	129	6	|	|	ADV
ejpam-3955	129	7	≤	≤	PUNCT
ejpam-3955	129	8	⌊	⌊	VERB
ejpam-3955	129	9	n	n	ADV
ejpam-3955	129	10	2	2	NUM
ejpam-3955	129	11	⌋	⌋	NOUN
ejpam-3955	129	12	.	.	PUNCT
ejpam-3955	130	1	similarly	similarly	ADV
ejpam-3955	130	2	,	,	PUNCT
ejpam-3955	130	3	|s	|s	PROPN
ejpam-3955	130	4	∩	∩	NOUN
ejpam-3955	130	5	u	u	NOUN
ejpam-3955	130	6	|	|	ADV
ejpam-3955	130	7	≤	≤	X
ejpam-3955	130	8	⌊	⌊	PROPN
ejpam-3955	130	9	m	m	PROPN
ejpam-3955	130	10	2	2	NUM
ejpam-3955	130	11	⌋	⌋	NOUN
ejpam-3955	130	12	.	.	PUNCT
ejpam-3955	131	1	thus	thus	ADV
ejpam-3955	131	2	,	,	PUNCT
ejpam-3955	131	3	2	2	NUM
ejpam-3955	131	4	≤	≤	NOUN
ejpam-3955	131	5	|s|	|s|	NOUN
ejpam-3955	131	6	≤	≤	NUM
ejpam-3955	131	7	⌊	⌊	PROPN
ejpam-3955	131	8	n	n	ADV
ejpam-3955	131	9	2	2	NUM
ejpam-3955	131	10	⌋	⌋	NOUN
ejpam-3955	131	11	+	+	CCONJ
ejpam-3955	131	12	⌊	⌊	PROPN
ejpam-3955	131	13	m	m	PROPN
ejpam-3955	131	14	2	2	NUM
ejpam-3955	131	15	⌋	⌋	NOUN
ejpam-3955	131	16	.	.	PUNCT
ejpam-3955	132	1	the	the	DET
ejpam-3955	132	2	converse	converse	NOUN
ejpam-3955	132	3	is	be	AUX
ejpam-3955	132	4	obvious	obvious	ADJ
ejpam-3955	132	5	.	.	PUNCT
ejpam-3955	133	1	therefore	therefore	ADV
ejpam-3955	133	2	,	,	PUNCT
ejpam-3955	133	3	γce(g	γce(g	PROPN
ejpam-3955	133	4	)	)	PUNCT
ejpam-3955	133	5	=	=	PUNCT
ejpam-3955	133	6	min{m	min{m	PROPN
ejpam-3955	133	7	,	,	PUNCT
ejpam-3955	133	8	n	n	CCONJ
ejpam-3955	133	9	,	,	PUNCT
ejpam-3955	133	10	2	2	X
ejpam-3955	133	11	}	}	PUNCT
ejpam-3955	133	12	=	=	SYM
ejpam-3955	133	13	2	2	NUM
ejpam-3955	133	14	and	and	CCONJ
ejpam-3955	133	15	γmce(g	γmce(g	PROPN
ejpam-3955	133	16	)	)	PUNCT
ejpam-3955	134	1	=	=	SYM
ejpam-3955	134	2	max{m	max{m	NOUN
ejpam-3955	134	3	,	,	PUNCT
ejpam-3955	134	4	n	n	CCONJ
ejpam-3955	134	5	}	}	PUNCT
ejpam-3955	134	6	=	=	SYM
ejpam-3955	134	7	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	134	8	)	)	PUNCT
ejpam-3955	134	9	.	.	PUNCT
ejpam-3955	135	1	theorem	theorem	VERB
ejpam-3955	135	2	7	7	NUM
ejpam-3955	135	3	.	.	PUNCT
ejpam-3955	135	4	(	(	PUNCT
ejpam-3955	135	5	i	i	NOUN
ejpam-3955	135	6	)	)	PUNCT
ejpam-3955	135	7	for	for	ADP
ejpam-3955	135	8	n	n	X
ejpam-3955	135	9	≥	≥	NUM
ejpam-3955	135	10	2	2	NUM
ejpam-3955	135	11	,	,	PUNCT
ejpam-3955	135	12	γ+ce(pn	γ+ce(pn	NUM
ejpam-3955	135	13	)	)	PUNCT
ejpam-3955	135	14	=	=	SYM
ejpam-3955	136	1	⌊	⌊	VERB
ejpam-3955	136	2	2n	2n	NUM
ejpam-3955	136	3	3	3	NUM
ejpam-3955	136	4	⌋	⌋	NOUN
ejpam-3955	136	5	and	and	CCONJ
ejpam-3955	136	6	γmce(pn	γmce(pn	NOUN
ejpam-3955	136	7	)	)	PUNCT
ejpam-3955	136	8	=	=	PUNCT
ejpam-3955	136	9	⌈n	⌈n	NOUN
ejpam-3955	136	10	2	2	NUM
ejpam-3955	136	11	⌉	⌉	X
ejpam-3955	136	12	.	.	PUNCT
ejpam-3955	137	1	h.	h.	PROPN
ejpam-3955	137	2	nuenay	nuenay	PROPN
ejpam-3955	137	3	-	-	PUNCT
ejpam-3955	137	4	maglanque	maglanque	ADJ
ejpam-3955	137	5	,	,	PUNCT
ejpam-3955	137	6	f.jamil	f.jamil	PROPN
ejpam-3955	137	7	/	/	SYM
ejpam-3955	137	8	eur	eur	PROPN
ejpam-3955	137	9	.	.	PUNCT
ejpam-3955	138	1	j.	j.	PROPN
ejpam-3955	138	2	pure	pure	PROPN
ejpam-3955	138	3	appl	appl	PROPN
ejpam-3955	138	4	.	.	PROPN
ejpam-3955	138	5	math	math	PROPN
ejpam-3955	138	6	,	,	PUNCT
ejpam-3955	138	7	14	14	NUM
ejpam-3955	138	8	(	(	PUNCT
ejpam-3955	138	9	2	2	NUM
ejpam-3955	138	10	)	)	PUNCT
ejpam-3955	138	11	(	(	PUNCT
ejpam-3955	138	12	2021	2021	NUM
ejpam-3955	138	13	)	)	PUNCT
ejpam-3955	138	14	,	,	PUNCT
ejpam-3955	138	15	537	537	NUM
ejpam-3955	138	16	-	-	SYM
ejpam-3955	138	17	550	550	NUM
ejpam-3955	138	18	542	542	NUM
ejpam-3955	138	19	(	(	PUNCT
ejpam-3955	138	20	ii	ii	NOUN
ejpam-3955	138	21	)	)	PUNCT
ejpam-3955	138	22	for	for	ADP
ejpam-3955	138	23	n	n	X
ejpam-3955	138	24	≥	≥	NOUN
ejpam-3955	138	25	3	3	NUM
ejpam-3955	138	26	,	,	PUNCT
ejpam-3955	138	27	γ+ce(cn	γ+ce(cn	PUNCT
ejpam-3955	138	28	)	)	PUNCT
ejpam-3955	138	29	=	=	SYM
ejpam-3955	139	1	⌊	⌊	VERB
ejpam-3955	139	2	2n	2n	NUM
ejpam-3955	139	3	3	3	NUM
ejpam-3955	139	4	⌋	⌋	NOUN
ejpam-3955	139	5	and	and	CCONJ
ejpam-3955	139	6	γmce(cn	γmce(cn	NOUN
ejpam-3955	139	7	)	)	PUNCT
ejpam-3955	139	8	=	=	PUNCT
ejpam-3955	140	1	⌈	⌈	SYM
ejpam-3955	140	2	n−	n−	NOUN
ejpam-3955	140	3	1	1	NUM
ejpam-3955	140	4	2	2	NUM
ejpam-3955	140	5	⌉	⌉	ADP
ejpam-3955	140	6	proof	proof	NOUN
ejpam-3955	140	7	.	.	PUNCT
ejpam-3955	141	1	for	for	ADP
ejpam-3955	141	2	(	(	PUNCT
ejpam-3955	141	3	i	i	NOUN
ejpam-3955	141	4	)	)	PUNCT
ejpam-3955	141	5	,	,	PUNCT
ejpam-3955	141	6	let	let	VERB
ejpam-3955	141	7	pn	pn	VERB
ejpam-3955	141	8	=	=	PUNCT
ejpam-3955	142	1	[	[	X
ejpam-3955	142	2	v1	v1	NOUN
ejpam-3955	142	3	,	,	PUNCT
ejpam-3955	142	4	v2	v2	NOUN
ejpam-3955	142	5	,	,	PUNCT
ejpam-3955	142	6	.	.	PUNCT
ejpam-3955	142	7	.	.	PUNCT
ejpam-3955	142	8	.	.	PUNCT
ejpam-3955	143	1	,	,	PUNCT
ejpam-3955	143	2	vn	vn	AUX
ejpam-3955	143	3	]	]	X
ejpam-3955	143	4	be	be	AUX
ejpam-3955	143	5	a	a	DET
ejpam-3955	143	6	path	path	NOUN
ejpam-3955	143	7	of	of	ADP
ejpam-3955	143	8	order	order	NOUN
ejpam-3955	143	9	n	n	PRON
ejpam-3955	143	10	≥	≥	NOUN
ejpam-3955	143	11	2	2	NUM
ejpam-3955	143	12	.	.	PUNCT
ejpam-3955	144	1	the	the	DET
ejpam-3955	144	2	result	result	NOUN
ejpam-3955	144	3	is	be	AUX
ejpam-3955	144	4	clear	clear	ADJ
ejpam-3955	144	5	if	if	SCONJ
ejpam-3955	144	6	n	n	NOUN
ejpam-3955	144	7	=	=	SYM
ejpam-3955	144	8	2	2	X
ejpam-3955	144	9	.	.	PUNCT
ejpam-3955	144	10	suppose	suppose	VERB
ejpam-3955	144	11	that	that	SCONJ
ejpam-3955	144	12	n	n	PROPN
ejpam-3955	144	13	≥	≥	NOUN
ejpam-3955	144	14	3	3	NUM
ejpam-3955	144	15	,	,	PUNCT
ejpam-3955	144	16	and	and	CCONJ
ejpam-3955	144	17	let	let	VERB
ejpam-3955	144	18	n	n	PRON
ejpam-3955	144	19	=	=	SYM
ejpam-3955	144	20	3k	3k	X
ejpam-3955	144	21	+	+	CCONJ
ejpam-3955	144	22	j	j	NOUN
ejpam-3955	144	23	,	,	PUNCT
ejpam-3955	144	24	with	with	ADP
ejpam-3955	144	25	k	k	PROPN
ejpam-3955	144	26	≥	≥	NUM
ejpam-3955	144	27	1	1	NUM
ejpam-3955	144	28	and	and	CCONJ
ejpam-3955	144	29	0	0	NUM
ejpam-3955	144	30	≤	≤	NUM
ejpam-3955	144	31	j	j	PROPN
ejpam-3955	144	32	≤	≤	ADV
ejpam-3955	144	33	2	2	NUM
ejpam-3955	144	34	.	.	PUNCT
ejpam-3955	145	1	note	note	VERB
ejpam-3955	145	2	that	that	SCONJ
ejpam-3955	145	3	for	for	ADP
ejpam-3955	145	4	j	j	PROPN
ejpam-3955	145	5	=	=	SYM
ejpam-3955	145	6	0	0	PROPN
ejpam-3955	145	7	,	,	PUNCT
ejpam-3955	145	8	1	1	NUM
ejpam-3955	145	9	,	,	PUNCT
ejpam-3955	145	10	the	the	DET
ejpam-3955	145	11	set	set	NOUN
ejpam-3955	145	12	{	{	PUNCT
ejpam-3955	145	13	v1	v1	NOUN
ejpam-3955	145	14	,	,	PUNCT
ejpam-3955	145	15	v3	v3	PROPN
ejpam-3955	145	16	,	,	PUNCT
ejpam-3955	145	17	v4	v4	PROPN
ejpam-3955	145	18	,	,	PUNCT
ejpam-3955	145	19	.	.	PUNCT
ejpam-3955	145	20	.	.	PUNCT
ejpam-3955	146	1	.	.	PUNCT
ejpam-3955	147	1	,	,	PUNCT
ejpam-3955	147	2	v3k−3	v3k−3	PROPN
ejpam-3955	147	3	,	,	PUNCT
ejpam-3955	147	4	v3k−2	v3k−2	NOUN
ejpam-3955	147	5	,	,	PUNCT
ejpam-3955	147	6	v3k	v3k	PRON
ejpam-3955	147	7	}	}	PUNCT
ejpam-3955	147	8	is	be	AUX
ejpam-3955	147	9	a	a	DET
ejpam-3955	147	10	cost	cost	NOUN
ejpam-3955	147	11	effective	effective	ADJ
ejpam-3955	147	12	dominating	dominating	NOUN
ejpam-3955	147	13	set	set	VERB
ejpam-3955	147	14	in	in	ADP
ejpam-3955	147	15	pn	pn	PROPN
ejpam-3955	147	16	.	.	PROPN
ejpam-3955	148	1	on	on	ADP
ejpam-3955	148	2	the	the	DET
ejpam-3955	148	3	other	other	ADJ
ejpam-3955	148	4	hand	hand	NOUN
ejpam-3955	148	5	,	,	PUNCT
ejpam-3955	148	6	if	if	SCONJ
ejpam-3955	148	7	j	j	PROPN
ejpam-3955	148	8	=	=	SYM
ejpam-3955	148	9	2	2	NUM
ejpam-3955	148	10	,	,	PUNCT
ejpam-3955	148	11	then	then	ADV
ejpam-3955	148	12	set	set	VERB
ejpam-3955	148	13	{	{	PUNCT
ejpam-3955	148	14	v1	v1	PROPN
ejpam-3955	148	15	,	,	PUNCT
ejpam-3955	148	16	v3	v3	PROPN
ejpam-3955	148	17	,	,	PUNCT
ejpam-3955	148	18	v4	v4	PROPN
ejpam-3955	148	19	,	,	PUNCT
ejpam-3955	148	20	.	.	PUNCT
ejpam-3955	148	21	.	.	PUNCT
ejpam-3955	149	1	.	.	PUNCT
ejpam-3955	150	1	,	,	PUNCT
ejpam-3955	150	2	v3k−3	v3k−3	PROPN
ejpam-3955	150	3	,	,	PUNCT
ejpam-3955	150	4	v3k−2	v3k−2	NOUN
ejpam-3955	150	5	,	,	PUNCT
ejpam-3955	150	6	v3k	v3k	ADV
ejpam-3955	150	7	,	,	PUNCT
ejpam-3955	150	8	v3k+1	v3k+1	VERB
ejpam-3955	150	9	}	}	PUNCT
ejpam-3955	150	10	is	be	AUX
ejpam-3955	150	11	a	a	DET
ejpam-3955	150	12	cost	cost	NOUN
ejpam-3955	150	13	effective	effective	ADJ
ejpam-3955	150	14	dominating	dominating	NOUN
ejpam-3955	150	15	set	set	VERB
ejpam-3955	150	16	in	in	ADP
ejpam-3955	150	17	pn	pn	PROPN
ejpam-3955	150	18	.	.	PUNCT
ejpam-3955	151	1	in	in	ADP
ejpam-3955	151	2	any	any	DET
ejpam-3955	151	3	case	case	NOUN
ejpam-3955	151	4	,	,	PUNCT
ejpam-3955	151	5	γ+ce(pn	γ+ce(pn	NUM
ejpam-3955	151	6	)	)	PUNCT
ejpam-3955	151	7	≥	≥	NOUN
ejpam-3955	151	8	⌊	⌊	VERB
ejpam-3955	151	9	2n	2n	NUM
ejpam-3955	151	10	3	3	NUM
ejpam-3955	151	11	⌋	⌋	NOUN
ejpam-3955	151	12	.	.	PUNCT
ejpam-3955	152	1	now	now	ADV
ejpam-3955	152	2	,	,	PUNCT
ejpam-3955	152	3	let	let	VERB
ejpam-3955	152	4	s	s	PRON
ejpam-3955	152	5	⊆	⊆	NUM
ejpam-3955	152	6	v	v	NOUN
ejpam-3955	152	7	(	(	PUNCT
ejpam-3955	152	8	pn	pn	NOUN
ejpam-3955	152	9	)	)	PUNCT
ejpam-3955	152	10	be	be	AUX
ejpam-3955	152	11	a	a	DET
ejpam-3955	152	12	γ+ce	γ+ce	NOUN
ejpam-3955	152	13	-	-	PUNCT
ejpam-3955	152	14	set	set	VERB
ejpam-3955	152	15	in	in	ADP
ejpam-3955	152	16	pn	pn	PROPN
ejpam-3955	152	17	.	.	PUNCT
ejpam-3955	152	18	being	be	AUX
ejpam-3955	152	19	a	a	DET
ejpam-3955	152	20	cost	cost	NOUN
ejpam-3955	152	21	effective	effective	ADJ
ejpam-3955	152	22	dominating	dominating	NOUN
ejpam-3955	152	23	set	set	NOUN
ejpam-3955	152	24	,	,	PUNCT
ejpam-3955	152	25	the	the	DET
ejpam-3955	152	26	vertices	vertex	NOUN
ejpam-3955	152	27	vi	vi	NOUN
ejpam-3955	152	28	,	,	PUNCT
ejpam-3955	152	29	vi+1	vi+1	NOUN
ejpam-3955	152	30	,	,	PUNCT
ejpam-3955	152	31	vi+2	vi+2	PROPN
ejpam-3955	152	32	can	can	AUX
ejpam-3955	152	33	not	not	PART
ejpam-3955	152	34	be	be	AUX
ejpam-3955	152	35	all	all	PRON
ejpam-3955	152	36	in	in	ADP
ejpam-3955	152	37	s	s	PRON
ejpam-3955	152	38	for	for	ADP
ejpam-3955	152	39	all	all	DET
ejpam-3955	152	40	i	i	PRON
ejpam-3955	152	41	=	=	NOUN
ejpam-3955	152	42	1	1	NUM
ejpam-3955	152	43	,	,	PUNCT
ejpam-3955	152	44	2	2	NUM
ejpam-3955	152	45	,	,	PUNCT
ejpam-3955	152	46	.	.	PUNCT
ejpam-3955	152	47	.	.	PUNCT
ejpam-3955	153	1	.	.	PUNCT
ejpam-3955	154	1	,	,	PUNCT
ejpam-3955	155	1	n	n	CCONJ
ejpam-3955	155	2	−	−	PROPN
ejpam-3955	155	3	2	2	NUM
ejpam-3955	155	4	.	.	PUNCT
ejpam-3955	156	1	in	in	ADP
ejpam-3955	156	2	particular	particular	ADJ
ejpam-3955	156	3	,	,	PUNCT
ejpam-3955	156	4	if	if	SCONJ
ejpam-3955	156	5	j	j	PROPN
ejpam-3955	156	6	=	=	SYM
ejpam-3955	156	7	0	0	PROPN
ejpam-3955	156	8	,	,	PUNCT
ejpam-3955	156	9	then	then	ADV
ejpam-3955	156	10	|s|	|s|	NOUN
ejpam-3955	156	11	≤	≤	ADJ
ejpam-3955	156	12	2k	2k	NUM
ejpam-3955	156	13	,	,	PUNCT
ejpam-3955	156	14	and	and	CCONJ
ejpam-3955	156	15	this	this	PRON
ejpam-3955	156	16	is	be	AUX
ejpam-3955	156	17	attained	attain	VERB
ejpam-3955	156	18	with	with	ADP
ejpam-3955	156	19	v3k	v3k	ADP
ejpam-3955	156	20	∈	∈	PROPN
ejpam-3955	156	21	s.	s.	PROPN
ejpam-3955	156	22	apparently	apparently	ADV
ejpam-3955	156	23	,	,	PUNCT
ejpam-3955	156	24	in	in	ADP
ejpam-3955	156	25	view	view	NOUN
ejpam-3955	156	26	of	of	ADP
ejpam-3955	156	27	this	this	PRON
ejpam-3955	156	28	,	,	PUNCT
ejpam-3955	156	29	|s|	|s|	VERB
ejpam-3955	156	30	≤	≤	NOUN
ejpam-3955	156	31	2k	2k	NOUN
ejpam-3955	156	32	for	for	ADP
ejpam-3955	156	33	j	j	PROPN
ejpam-3955	156	34	=	=	SYM
ejpam-3955	156	35	1	1	NUM
ejpam-3955	156	36	and	and	CCONJ
ejpam-3955	156	37	|s|	|s|	NOUN
ejpam-3955	156	38	≤	≤	NUM
ejpam-3955	156	39	2k	2k	NOUN
ejpam-3955	156	40	+	+	CCONJ
ejpam-3955	156	41	1	1	NUM
ejpam-3955	156	42	for	for	ADP
ejpam-3955	156	43	j	j	PROPN
ejpam-3955	156	44	=	=	SYM
ejpam-3955	156	45	2	2	X
ejpam-3955	156	46	.	.	PUNCT
ejpam-3955	156	47	indeed	indeed	ADV
ejpam-3955	156	48	,	,	PUNCT
ejpam-3955	156	49	γ+ce(pn	γ+ce(pn	NUM
ejpam-3955	156	50	)	)	PUNCT
ejpam-3955	157	1	=	=	SYM
ejpam-3955	157	2	⌊	⌊	VERB
ejpam-3955	157	3	2n	2n	NUM
ejpam-3955	157	4	3	3	NUM
ejpam-3955	157	5	⌋	⌋	NOUN
ejpam-3955	157	6	.	.	PUNCT
ejpam-3955	158	1	similarly	similarly	ADV
ejpam-3955	158	2	,	,	PUNCT
ejpam-3955	158	3	to	to	PART
ejpam-3955	158	4	prove	prove	VERB
ejpam-3955	158	5	the	the	DET
ejpam-3955	158	6	second	second	ADJ
ejpam-3955	158	7	part	part	NOUN
ejpam-3955	158	8	of	of	ADP
ejpam-3955	158	9	(	(	PUNCT
ejpam-3955	158	10	i	i	PROPN
ejpam-3955	158	11	)	)	PUNCT
ejpam-3955	158	12	,	,	PUNCT
ejpam-3955	158	13	we	we	PRON
ejpam-3955	158	14	write	write	VERB
ejpam-3955	158	15	n	n	PRON
ejpam-3955	158	16	=	=	SYM
ejpam-3955	158	17	2k	2k	PROPN
ejpam-3955	158	18	+	+	CCONJ
ejpam-3955	158	19	j	j	PROPN
ejpam-3955	158	20	,	,	PUNCT
ejpam-3955	158	21	with	with	ADP
ejpam-3955	158	22	0	0	NUM
ejpam-3955	158	23	≤	≤	NUM
ejpam-3955	158	24	j	j	PROPN
ejpam-3955	158	25	≤	≤	ADV
ejpam-3955	158	26	1	1	NUM
ejpam-3955	158	27	.	.	PUNCT
ejpam-3955	159	1	since	since	SCONJ
ejpam-3955	159	2	the	the	DET
ejpam-3955	159	3	sets	set	NOUN
ejpam-3955	159	4	{	{	PUNCT
ejpam-3955	159	5	v1	v1	NOUN
ejpam-3955	159	6	,	,	PUNCT
ejpam-3955	159	7	v3	v3	PROPN
ejpam-3955	159	8	,	,	PUNCT
ejpam-3955	159	9	v5	v5	PROPN
ejpam-3955	159	10	,	,	PUNCT
ejpam-3955	159	11	.	.	PUNCT
ejpam-3955	159	12	.	.	PUNCT
ejpam-3955	159	13	.	.	PUNCT
ejpam-3955	160	1	,	,	PUNCT
ejpam-3955	160	2	v2k−1	v2k−1	NOUN
ejpam-3955	160	3	}	}	PUNCT
ejpam-3955	160	4	and	and	CCONJ
ejpam-3955	160	5	{	{	PUNCT
ejpam-3955	160	6	v1	v1	PROPN
ejpam-3955	160	7	,	,	PUNCT
ejpam-3955	160	8	v3	v3	PROPN
ejpam-3955	160	9	,	,	PUNCT
ejpam-3955	160	10	v5	v5	PROPN
ejpam-3955	160	11	,	,	PUNCT
ejpam-3955	160	12	.	.	PUNCT
ejpam-3955	160	13	.	.	PUNCT
ejpam-3955	161	1	.	.	PUNCT
ejpam-3955	162	1	,	,	PUNCT
ejpam-3955	162	2	v2k−1	v2k−1	INTJ
ejpam-3955	162	3	,	,	PUNCT
ejpam-3955	162	4	v2k+1	v2k+1	AUX
ejpam-3955	162	5	}	}	PUNCT
ejpam-3955	162	6	are	be	AUX
ejpam-3955	162	7	minimal	minimal	ADJ
ejpam-3955	162	8	cost	cost	NOUN
ejpam-3955	162	9	effective	effective	ADJ
ejpam-3955	162	10	dominating	dominating	NOUN
ejpam-3955	162	11	sets	set	NOUN
ejpam-3955	162	12	in	in	ADP
ejpam-3955	162	13	pn	pn	PROPN
ejpam-3955	162	14	for	for	ADP
ejpam-3955	162	15	j	j	PROPN
ejpam-3955	162	16	=	=	SYM
ejpam-3955	162	17	0	0	PROPN
ejpam-3955	162	18	and	and	CCONJ
ejpam-3955	162	19	j	j	PROPN
ejpam-3955	162	20	=	=	SYM
ejpam-3955	162	21	1	1	NUM
ejpam-3955	162	22	,	,	PUNCT
ejpam-3955	162	23	respectively	respectively	ADV
ejpam-3955	162	24	,	,	PUNCT
ejpam-3955	162	25	we	we	PRON
ejpam-3955	162	26	have	have	VERB
ejpam-3955	162	27	γmce(pn	γmce(pn	ADJ
ejpam-3955	162	28	)	)	PUNCT
ejpam-3955	162	29	≥	≥	NOUN
ejpam-3955	162	30	⌈	⌈	NOUN
ejpam-3955	162	31	n	n	CCONJ
ejpam-3955	162	32	2	2	NUM
ejpam-3955	162	33	⌉	⌉	X
ejpam-3955	162	34	.	.	PUNCT
ejpam-3955	163	1	conversely	conversely	ADV
ejpam-3955	163	2	,	,	PUNCT
ejpam-3955	163	3	let	let	VERB
ejpam-3955	163	4	s	s	PRON
ejpam-3955	163	5	⊆	⊆	NUM
ejpam-3955	163	6	v	v	NOUN
ejpam-3955	163	7	(	(	PUNCT
ejpam-3955	163	8	pn	pn	NOUN
ejpam-3955	163	9	)	)	PUNCT
ejpam-3955	163	10	be	be	AUX
ejpam-3955	163	11	a	a	DET
ejpam-3955	163	12	minimal	minimal	ADJ
ejpam-3955	163	13	cost	cost	NOUN
ejpam-3955	163	14	effective	effective	ADJ
ejpam-3955	163	15	dominating	dominating	NOUN
ejpam-3955	163	16	set	set	VERB
ejpam-3955	163	17	in	in	ADP
ejpam-3955	163	18	pn	pn	PROPN
ejpam-3955	163	19	.	.	PUNCT
ejpam-3955	164	1	then	then	ADV
ejpam-3955	164	2	for	for	ADP
ejpam-3955	164	3	all	all	DET
ejpam-3955	164	4	i	i	PRON
ejpam-3955	164	5	=	=	NOUN
ejpam-3955	164	6	1	1	NUM
ejpam-3955	164	7	,	,	PUNCT
ejpam-3955	164	8	2	2	NUM
ejpam-3955	164	9	,	,	PUNCT
ejpam-3955	164	10	.	.	PUNCT
ejpam-3955	164	11	.	.	PUNCT
ejpam-3955	164	12	.	.	PUNCT
ejpam-3955	165	1	,	,	PUNCT
ejpam-3955	165	2	n−3	n−3	PROPN
ejpam-3955	165	3	,	,	PUNCT
ejpam-3955	165	4	|s∩{vi	|s∩{vi	PROPN
ejpam-3955	165	5	,	,	PUNCT
ejpam-3955	165	6	vi+1	vi+1	NOUN
ejpam-3955	165	7	,	,	PUNCT
ejpam-3955	165	8	vi+2	vi+2	NUM
ejpam-3955	165	9	,	,	PUNCT
ejpam-3955	165	10	vi+3}|	vi+3}|	NUM
ejpam-3955	165	11	≤	≤	NUM
ejpam-3955	165	12	2	2	NUM
ejpam-3955	165	13	.	.	PUNCT
ejpam-3955	166	1	thus	thus	ADV
ejpam-3955	166	2	,	,	PUNCT
ejpam-3955	166	3	|s|	|s|	VERB
ejpam-3955	166	4	≤	≤	X
ejpam-3955	166	5	⌈	⌈	NUM
ejpam-3955	166	6	2n	2n	NUM
ejpam-3955	166	7	4	4	NUM
ejpam-3955	166	8	⌉	⌉	NOUN
ejpam-3955	166	9	=	=	SYM
ejpam-3955	166	10	⌈	⌈	SYM
ejpam-3955	166	11	n	n	PRON
ejpam-3955	166	12	2	2	NUM
ejpam-3955	166	13	⌉	⌉	X
ejpam-3955	166	14	.	.	PUNCT
ejpam-3955	167	1	for	for	ADP
ejpam-3955	167	2	(	(	PUNCT
ejpam-3955	167	3	ii	ii	NOUN
ejpam-3955	167	4	)	)	PUNCT
ejpam-3955	167	5	,	,	PUNCT
ejpam-3955	167	6	let	let	VERB
ejpam-3955	167	7	cn	cn	PROPN
ejpam-3955	167	8	=	=	PUNCT
ejpam-3955	168	1	[	[	X
ejpam-3955	168	2	v1	v1	NOUN
ejpam-3955	168	3	,	,	PUNCT
ejpam-3955	168	4	v2	v2	NOUN
ejpam-3955	168	5	,	,	PUNCT
ejpam-3955	168	6	.	.	PUNCT
ejpam-3955	168	7	.	.	PUNCT
ejpam-3955	168	8	.	.	PUNCT
ejpam-3955	169	1	,	,	PUNCT
ejpam-3955	169	2	vn	vn	AUX
ejpam-3955	169	3	]	]	X
ejpam-3955	169	4	be	be	AUX
ejpam-3955	169	5	a	a	DET
ejpam-3955	169	6	cycle	cycle	NOUN
ejpam-3955	169	7	of	of	ADP
ejpam-3955	169	8	order	order	NOUN
ejpam-3955	169	9	n	n	PRON
ejpam-3955	169	10	≥	≥	NOUN
ejpam-3955	169	11	3	3	NUM
ejpam-3955	169	12	.	.	PUNCT
ejpam-3955	170	1	the	the	DET
ejpam-3955	170	2	result	result	NOUN
ejpam-3955	170	3	is	be	AUX
ejpam-3955	170	4	clear	clear	ADJ
ejpam-3955	170	5	if	if	SCONJ
ejpam-3955	170	6	n	n	PROPN
ejpam-3955	170	7	=	=	SYM
ejpam-3955	170	8	3	3	X
ejpam-3955	170	9	.	.	PUNCT
ejpam-3955	170	10	suppose	suppose	VERB
ejpam-3955	170	11	that	that	SCONJ
ejpam-3955	170	12	n	n	PROPN
ejpam-3955	170	13	≥	≥	NOUN
ejpam-3955	170	14	4	4	NUM
ejpam-3955	170	15	,	,	PUNCT
ejpam-3955	170	16	and	and	CCONJ
ejpam-3955	170	17	let	let	VERB
ejpam-3955	170	18	n	n	PROPN
ejpam-3955	170	19	=	=	SYM
ejpam-3955	170	20	3k+	3k+	PROPN
ejpam-3955	170	21	j	j	PROPN
ejpam-3955	170	22	,	,	PUNCT
ejpam-3955	170	23	with	with	ADP
ejpam-3955	170	24	k	k	PROPN
ejpam-3955	170	25	≥	≥	NUM
ejpam-3955	170	26	1	1	NUM
ejpam-3955	170	27	and	and	CCONJ
ejpam-3955	170	28	0	0	NUM
ejpam-3955	170	29	≤	≤	NUM
ejpam-3955	170	30	j	j	PROPN
ejpam-3955	170	31	≤	≤	ADV
ejpam-3955	170	32	2	2	NUM
ejpam-3955	170	33	.	.	PUNCT
ejpam-3955	171	1	note	note	VERB
ejpam-3955	171	2	that	that	SCONJ
ejpam-3955	171	3	for	for	ADP
ejpam-3955	171	4	j	j	PROPN
ejpam-3955	171	5	=	=	SYM
ejpam-3955	171	6	0	0	PROPN
ejpam-3955	171	7	,	,	PUNCT
ejpam-3955	171	8	1	1	NUM
ejpam-3955	171	9	,	,	PUNCT
ejpam-3955	171	10	the	the	DET
ejpam-3955	171	11	set	set	NOUN
ejpam-3955	171	12	{	{	PUNCT
ejpam-3955	171	13	v1	v1	NOUN
ejpam-3955	171	14	,	,	PUNCT
ejpam-3955	171	15	v3	v3	PROPN
ejpam-3955	171	16	,	,	PUNCT
ejpam-3955	171	17	v4	v4	PROPN
ejpam-3955	171	18	,	,	PUNCT
ejpam-3955	171	19	.	.	PUNCT
ejpam-3955	171	20	.	.	PUNCT
ejpam-3955	172	1	.	.	PUNCT
ejpam-3955	173	1	,	,	PUNCT
ejpam-3955	173	2	v3k−3	v3k−3	PROPN
ejpam-3955	173	3	,	,	PUNCT
ejpam-3955	173	4	v3k−2	v3k−2	NOUN
ejpam-3955	173	5	,	,	PUNCT
ejpam-3955	173	6	v3k	v3k	PRON
ejpam-3955	173	7	}	}	PUNCT
ejpam-3955	173	8	is	be	AUX
ejpam-3955	173	9	a	a	DET
ejpam-3955	173	10	cost	cost	NOUN
ejpam-3955	173	11	effective	effective	ADJ
ejpam-3955	173	12	dominating	dominating	NOUN
ejpam-3955	173	13	set	set	VERB
ejpam-3955	173	14	in	in	ADP
ejpam-3955	173	15	cn	cn	PROPN
ejpam-3955	173	16	.	.	PUNCT
ejpam-3955	174	1	on	on	ADP
ejpam-3955	174	2	the	the	DET
ejpam-3955	174	3	other	other	ADJ
ejpam-3955	174	4	hand	hand	NOUN
ejpam-3955	174	5	,	,	PUNCT
ejpam-3955	174	6	if	if	SCONJ
ejpam-3955	174	7	j	j	PROPN
ejpam-3955	174	8	=	=	SYM
ejpam-3955	174	9	2	2	NUM
ejpam-3955	174	10	,	,	PUNCT
ejpam-3955	174	11	then	then	ADV
ejpam-3955	174	12	set	set	VERB
ejpam-3955	174	13	{	{	PUNCT
ejpam-3955	174	14	v1	v1	PROPN
ejpam-3955	174	15	,	,	PUNCT
ejpam-3955	174	16	v3	v3	PROPN
ejpam-3955	174	17	,	,	PUNCT
ejpam-3955	174	18	v4	v4	PROPN
ejpam-3955	174	19	,	,	PUNCT
ejpam-3955	174	20	.	.	PUNCT
ejpam-3955	174	21	.	.	PUNCT
ejpam-3955	175	1	.	.	PUNCT
ejpam-3955	176	1	,	,	PUNCT
ejpam-3955	176	2	v3k−3	v3k−3	PROPN
ejpam-3955	176	3	,	,	PUNCT
ejpam-3955	176	4	v3k−2	v3k−2	NOUN
ejpam-3955	176	5	,	,	PUNCT
ejpam-3955	176	6	v3k	v3k	ADV
ejpam-3955	176	7	,	,	PUNCT
ejpam-3955	176	8	v3k+1	v3k+1	VERB
ejpam-3955	176	9	}	}	PUNCT
ejpam-3955	176	10	is	be	AUX
ejpam-3955	176	11	a	a	DET
ejpam-3955	176	12	cost	cost	NOUN
ejpam-3955	176	13	effective	effective	ADJ
ejpam-3955	176	14	dominating	dominating	NOUN
ejpam-3955	176	15	set	set	VERB
ejpam-3955	176	16	in	in	ADP
ejpam-3955	176	17	cn	cn	PROPN
ejpam-3955	176	18	.	.	PUNCT
ejpam-3955	177	1	in	in	ADP
ejpam-3955	177	2	any	any	DET
ejpam-3955	177	3	case	case	NOUN
ejpam-3955	177	4	,	,	PUNCT
ejpam-3955	177	5	γ+ce(cn	γ+ce(cn	NUM
ejpam-3955	177	6	)	)	PUNCT
ejpam-3955	177	7	≥	≥	NOUN
ejpam-3955	177	8	⌊	⌊	VERB
ejpam-3955	177	9	2n	2n	NUM
ejpam-3955	177	10	3	3	NUM
ejpam-3955	177	11	⌋	⌋	NOUN
ejpam-3955	177	12	.	.	PUNCT
ejpam-3955	178	1	now	now	ADV
ejpam-3955	178	2	,	,	PUNCT
ejpam-3955	178	3	let	let	VERB
ejpam-3955	178	4	s	s	PRON
ejpam-3955	178	5	⊆	⊆	NUM
ejpam-3955	178	6	v	v	NOUN
ejpam-3955	178	7	(	(	PUNCT
ejpam-3955	178	8	cn	cn	PROPN
ejpam-3955	178	9	)	)	PUNCT
ejpam-3955	178	10	be	be	AUX
ejpam-3955	178	11	a	a	DET
ejpam-3955	178	12	γ+ce	γ+ce	NOUN
ejpam-3955	178	13	-	-	PUNCT
ejpam-3955	178	14	set	set	NOUN
ejpam-3955	178	15	in	in	ADP
ejpam-3955	178	16	cn	cn	PROPN
ejpam-3955	178	17	.	.	PUNCT
ejpam-3955	179	1	this	this	PRON
ejpam-3955	179	2	means	mean	VERB
ejpam-3955	179	3	that	that	SCONJ
ejpam-3955	179	4	the	the	DET
ejpam-3955	179	5	vertices	vertex	NOUN
ejpam-3955	179	6	vi	vi	NOUN
ejpam-3955	179	7	,	,	PUNCT
ejpam-3955	179	8	vi+1	vi+1	NOUN
ejpam-3955	179	9	,	,	PUNCT
ejpam-3955	179	10	vi+2	vi+2	PROPN
ejpam-3955	179	11	can	can	AUX
ejpam-3955	179	12	not	not	PART
ejpam-3955	179	13	be	be	AUX
ejpam-3955	179	14	all	all	PRON
ejpam-3955	179	15	in	in	ADP
ejpam-3955	179	16	s	s	PRON
ejpam-3955	179	17	for	for	ADP
ejpam-3955	179	18	all	all	DET
ejpam-3955	179	19	i	i	PRON
ejpam-3955	179	20	=	=	NOUN
ejpam-3955	179	21	1	1	NUM
ejpam-3955	179	22	,	,	PUNCT
ejpam-3955	179	23	2	2	NUM
ejpam-3955	179	24	,	,	PUNCT
ejpam-3955	179	25	.	.	PUNCT
ejpam-3955	179	26	.	.	PUNCT
ejpam-3955	180	1	.	.	PUNCT
ejpam-3955	181	1	,	,	PUNCT
ejpam-3955	181	2	n−	n−	NOUN
ejpam-3955	181	3	2	2	NUM
ejpam-3955	181	4	.	.	PUNCT
ejpam-3955	182	1	in	in	ADP
ejpam-3955	182	2	particular	particular	ADJ
ejpam-3955	182	3	,	,	PUNCT
ejpam-3955	182	4	if	if	SCONJ
ejpam-3955	182	5	j	j	PROPN
ejpam-3955	182	6	=	=	SYM
ejpam-3955	182	7	0	0	PROPN
ejpam-3955	182	8	,	,	PUNCT
ejpam-3955	182	9	then	then	ADV
ejpam-3955	182	10	|s|	|s|	NOUN
ejpam-3955	182	11	≤	≤	ADJ
ejpam-3955	182	12	2k	2k	NUM
ejpam-3955	182	13	,	,	PUNCT
ejpam-3955	182	14	and	and	CCONJ
ejpam-3955	182	15	this	this	PRON
ejpam-3955	182	16	is	be	AUX
ejpam-3955	182	17	attained	attain	VERB
ejpam-3955	182	18	with	with	ADP
ejpam-3955	182	19	v3k	v3k	ADP
ejpam-3955	182	20	∈	∈	PROPN
ejpam-3955	182	21	s.	s.	PROPN
ejpam-3955	182	22	apparently	apparently	ADV
ejpam-3955	182	23	,	,	PUNCT
ejpam-3955	182	24	in	in	ADP
ejpam-3955	182	25	view	view	NOUN
ejpam-3955	182	26	of	of	ADP
ejpam-3955	182	27	this	this	PRON
ejpam-3955	182	28	,	,	PUNCT
ejpam-3955	182	29	|s|	|s|	VERB
ejpam-3955	182	30	≤	≤	NOUN
ejpam-3955	182	31	2k	2k	NOUN
ejpam-3955	182	32	for	for	ADP
ejpam-3955	182	33	j	j	PROPN
ejpam-3955	182	34	=	=	SYM
ejpam-3955	182	35	1	1	NUM
ejpam-3955	182	36	and	and	CCONJ
ejpam-3955	182	37	|s|	|s|	NOUN
ejpam-3955	182	38	≤	≤	NUM
ejpam-3955	182	39	2k	2k	NOUN
ejpam-3955	182	40	+	+	CCONJ
ejpam-3955	182	41	1	1	NUM
ejpam-3955	182	42	for	for	ADP
ejpam-3955	182	43	j	j	PROPN
ejpam-3955	182	44	=	=	SYM
ejpam-3955	182	45	2	2	X
ejpam-3955	182	46	.	.	PUNCT
ejpam-3955	182	47	indeed	indeed	ADV
ejpam-3955	182	48	,	,	PUNCT
ejpam-3955	182	49	γ+ce(cn	γ+ce(cn	PUNCT
ejpam-3955	182	50	)	)	PUNCT
ejpam-3955	183	1	=	=	SYM
ejpam-3955	183	2	⌊	⌊	VERB
ejpam-3955	183	3	2n	2n	NUM
ejpam-3955	183	4	3	3	NUM
ejpam-3955	183	5	⌋	⌋	NOUN
ejpam-3955	183	6	.	.	PUNCT
ejpam-3955	184	1	to	to	PART
ejpam-3955	184	2	prove	prove	VERB
ejpam-3955	184	3	the	the	DET
ejpam-3955	184	4	second	second	ADJ
ejpam-3955	184	5	part	part	NOUN
ejpam-3955	184	6	of	of	ADP
ejpam-3955	184	7	(	(	PUNCT
ejpam-3955	184	8	ii	ii	NOUN
ejpam-3955	184	9	)	)	PUNCT
ejpam-3955	184	10	,	,	PUNCT
ejpam-3955	184	11	we	we	PRON
ejpam-3955	184	12	write	write	VERB
ejpam-3955	184	13	n	n	PRON
ejpam-3955	184	14	=	=	SYM
ejpam-3955	184	15	2k	2k	PROPN
ejpam-3955	184	16	+	+	CCONJ
ejpam-3955	184	17	j	j	PROPN
ejpam-3955	184	18	,	,	PUNCT
ejpam-3955	184	19	with	with	ADP
ejpam-3955	184	20	0	0	NUM
ejpam-3955	184	21	≤	≤	NUM
ejpam-3955	184	22	j	j	PROPN
ejpam-3955	184	23	≤	≤	ADV
ejpam-3955	184	24	1	1	NUM
ejpam-3955	184	25	.	.	PUNCT
ejpam-3955	185	1	since	since	SCONJ
ejpam-3955	185	2	the	the	DET
ejpam-3955	185	3	sets	set	NOUN
ejpam-3955	185	4	{	{	PUNCT
ejpam-3955	185	5	v1	v1	NOUN
ejpam-3955	185	6	,	,	PUNCT
ejpam-3955	185	7	v3	v3	PROPN
ejpam-3955	185	8	,	,	PUNCT
ejpam-3955	185	9	v5	v5	PROPN
ejpam-3955	185	10	,	,	PUNCT
ejpam-3955	185	11	.	.	PUNCT
ejpam-3955	185	12	.	.	PUNCT
ejpam-3955	185	13	.	.	PUNCT
ejpam-3955	186	1	,	,	PUNCT
ejpam-3955	186	2	v2k−1	v2k−1	NOUN
ejpam-3955	186	3	}	}	PUNCT
ejpam-3955	186	4	and	and	CCONJ
ejpam-3955	186	5	{	{	PUNCT
ejpam-3955	186	6	v1	v1	PROPN
ejpam-3955	186	7	,	,	PUNCT
ejpam-3955	186	8	v3	v3	PROPN
ejpam-3955	186	9	,	,	PUNCT
ejpam-3955	186	10	v5	v5	PROPN
ejpam-3955	186	11	,	,	PUNCT
ejpam-3955	186	12	.	.	PUNCT
ejpam-3955	186	13	.	.	PUNCT
ejpam-3955	187	1	.	.	PUNCT
ejpam-3955	188	1	,	,	PUNCT
ejpam-3955	188	2	v2k−2	v2k−2	PROPN
ejpam-3955	188	3	,	,	PUNCT
ejpam-3955	188	4	v2k	v2k	AUX
ejpam-3955	188	5	}	}	PUNCT
ejpam-3955	188	6	are	be	AUX
ejpam-3955	188	7	minimal	minimal	ADJ
ejpam-3955	188	8	cost	cost	NOUN
ejpam-3955	188	9	effective	effective	ADJ
ejpam-3955	188	10	dominating	dominating	NOUN
ejpam-3955	188	11	sets	set	NOUN
ejpam-3955	188	12	in	in	ADP
ejpam-3955	188	13	cn	cn	PROPN
ejpam-3955	188	14	for	for	ADP
ejpam-3955	188	15	j	j	PROPN
ejpam-3955	188	16	=	=	SYM
ejpam-3955	188	17	0	0	PROPN
ejpam-3955	188	18	and	and	CCONJ
ejpam-3955	188	19	j	j	PROPN
ejpam-3955	188	20	=	=	SYM
ejpam-3955	188	21	1	1	NUM
ejpam-3955	188	22	,	,	PUNCT
ejpam-3955	188	23	respectively	respectively	ADV
ejpam-3955	188	24	,	,	PUNCT
ejpam-3955	188	25	we	we	PRON
ejpam-3955	188	26	have	have	VERB
ejpam-3955	188	27	γmce(cn	γmce(cn	PROPN
ejpam-3955	188	28	)	)	PUNCT
ejpam-3955	188	29	≥	≥	NOUN
ejpam-3955	189	1	⌈	⌈	X
ejpam-3955	189	2	n−1	n−1	PROPN
ejpam-3955	189	3	2	2	NUM
ejpam-3955	189	4	⌉	⌉	X
ejpam-3955	189	5	.	.	PUNCT
ejpam-3955	190	1	conversely	conversely	ADV
ejpam-3955	190	2	,	,	PUNCT
ejpam-3955	190	3	let	let	VERB
ejpam-3955	190	4	s	s	PRON
ejpam-3955	190	5	⊆	⊆	NUM
ejpam-3955	190	6	v	v	NOUN
ejpam-3955	190	7	(	(	PUNCT
ejpam-3955	190	8	cn	cn	PROPN
ejpam-3955	190	9	)	)	PUNCT
ejpam-3955	190	10	be	be	AUX
ejpam-3955	190	11	a	a	DET
ejpam-3955	190	12	minimal	minimal	ADJ
ejpam-3955	190	13	cost	cost	NOUN
ejpam-3955	190	14	effective	effective	ADJ
ejpam-3955	190	15	dominating	dominating	NOUN
ejpam-3955	190	16	set	set	VERB
ejpam-3955	190	17	in	in	ADP
ejpam-3955	190	18	cn	cn	PROPN
ejpam-3955	190	19	.	.	PUNCT
ejpam-3955	190	20	note	note	VERB
ejpam-3955	190	21	that	that	SCONJ
ejpam-3955	190	22	for	for	ADP
ejpam-3955	190	23	any	any	DET
ejpam-3955	190	24	n	n	PRON
ejpam-3955	190	25	≥	≥	NOUN
ejpam-3955	190	26	3	3	NUM
ejpam-3955	190	27	,	,	PUNCT
ejpam-3955	190	28	vn	vn	PROPN
ejpam-3955	190	29	/∈	/∈	PUNCT
ejpam-3955	190	30	s.	s.	PROPN
ejpam-3955	190	31	also	also	ADV
ejpam-3955	190	32	,	,	PUNCT
ejpam-3955	190	33	for	for	ADP
ejpam-3955	190	34	all	all	DET
ejpam-3955	190	35	i	i	PRON
ejpam-3955	190	36	=	=	NOUN
ejpam-3955	190	37	1	1	NUM
ejpam-3955	190	38	,	,	PUNCT
ejpam-3955	190	39	2	2	NUM
ejpam-3955	190	40	,	,	PUNCT
ejpam-3955	190	41	.	.	PUNCT
ejpam-3955	190	42	.	.	PUNCT
ejpam-3955	190	43	.	.	PUNCT
ejpam-3955	191	1	,	,	PUNCT
ejpam-3955	191	2	n−	n−	NOUN
ejpam-3955	191	3	3	3	NUM
ejpam-3955	191	4	,	,	PUNCT
ejpam-3955	191	5	|s	|s	PROPN
ejpam-3955	191	6	∩	∩	NOUN
ejpam-3955	191	7	{	{	PUNCT
ejpam-3955	191	8	vi	vi	PROPN
ejpam-3955	191	9	,	,	PUNCT
ejpam-3955	191	10	vi+1	vi+1	ADJ
ejpam-3955	191	11	,	,	PUNCT
ejpam-3955	191	12	vi+2	vi+2	NUM
ejpam-3955	191	13	,	,	PUNCT
ejpam-3955	191	14	vi+3}|	vi+3}|	NUM
ejpam-3955	191	15	≤	≤	NUM
ejpam-3955	191	16	2	2	NUM
ejpam-3955	191	17	.	.	PUNCT
ejpam-3955	191	18	thus	thus	ADV
ejpam-3955	191	19	,	,	PUNCT
ejpam-3955	191	20	|s|	|s|	VERB
ejpam-3955	191	21	≤	≤	X
ejpam-3955	191	22	⌈	⌈	NOUN
ejpam-3955	191	23	n−1	n−1	PROPN
ejpam-3955	191	24	2	2	NUM
ejpam-3955	191	25	⌉	⌉	X
ejpam-3955	191	26	.	.	PUNCT
ejpam-3955	192	1	therefore	therefore	ADV
ejpam-3955	192	2	,	,	PUNCT
ejpam-3955	192	3	γmce(cn	γmce(cn	NOUN
ejpam-3955	192	4	)	)	PUNCT
ejpam-3955	192	5	=	=	PUNCT
ejpam-3955	193	1	⌈	⌈	PROPN
ejpam-3955	193	2	n−1	n−1	PROPN
ejpam-3955	193	3	2	2	NUM
ejpam-3955	193	4	⌉	⌉	X
ejpam-3955	193	5	.	.	PUNCT
ejpam-3955	194	1	proposition	proposition	NOUN
ejpam-3955	194	2	2	2	NUM
ejpam-3955	194	3	.	.	X
ejpam-3955	195	1	for	for	ADP
ejpam-3955	195	2	any	any	DET
ejpam-3955	195	3	double	double	ADJ
ejpam-3955	195	4	star	star	NOUN
ejpam-3955	195	5	graph	graph	NOUN
ejpam-3955	195	6	sr	sr	PROPN
ejpam-3955	195	7	,	,	PUNCT
ejpam-3955	195	8	s	s	VERB
ejpam-3955	195	9	where	where	SCONJ
ejpam-3955	195	10	r	r	NOUN
ejpam-3955	195	11	,	,	PUNCT
ejpam-3955	195	12	s	s	PART
ejpam-3955	195	13	≥	≥	NOUN
ejpam-3955	195	14	1	1	NUM
ejpam-3955	195	15	,	,	PUNCT
ejpam-3955	195	16	(	(	PUNCT
ejpam-3955	195	17	i	i	NOUN
ejpam-3955	195	18	)	)	PUNCT
ejpam-3955	195	19	γce(sr	γce(sr	NOUN
ejpam-3955	195	20	,	,	PUNCT
ejpam-3955	195	21	s	s	PART
ejpam-3955	195	22	)	)	PUNCT
ejpam-3955	195	23	=	=	SYM
ejpam-3955	195	24	2	2	NUM
ejpam-3955	195	25	(	(	PUNCT
ejpam-3955	195	26	ii	ii	NOUN
ejpam-3955	195	27	)	)	PUNCT
ejpam-3955	195	28	γ+ce(sr	γ+ce(sr	PUNCT
ejpam-3955	195	29	,	,	PUNCT
ejpam-3955	195	30	s	s	X
ejpam-3955	195	31	)	)	PUNCT
ejpam-3955	195	32	=	=	SYM
ejpam-3955	196	1	r	r	NOUN
ejpam-3955	196	2	+	+	NUM
ejpam-3955	196	3	s	s	NOUN
ejpam-3955	196	4	=	=	SYM
ejpam-3955	196	5	γmce(sr	γmce(sr	NOUN
ejpam-3955	196	6	,	,	PUNCT
ejpam-3955	196	7	s	s	NOUN
ejpam-3955	196	8	)	)	PUNCT
ejpam-3955	196	9	.	.	PUNCT
ejpam-3955	197	1	proof	proof	NOUN
ejpam-3955	197	2	.	.	PUNCT
ejpam-3955	198	1	let	let	VERB
ejpam-3955	198	2	u	u	PRON
ejpam-3955	198	3	and	and	CCONJ
ejpam-3955	198	4	v	v	NOUN
ejpam-3955	198	5	be	be	AUX
ejpam-3955	198	6	the	the	DET
ejpam-3955	198	7	two	two	NUM
ejpam-3955	198	8	central	central	ADJ
ejpam-3955	198	9	vertices	vertex	NOUN
ejpam-3955	198	10	of	of	ADP
ejpam-3955	198	11	g	g	PROPN
ejpam-3955	198	12	=	=	SYM
ejpam-3955	198	13	sr	sr	PROPN
ejpam-3955	198	14	,	,	PUNCT
ejpam-3955	198	15	s	s	PART
ejpam-3955	198	16	,	,	PUNCT
ejpam-3955	198	17	and	and	CCONJ
ejpam-3955	198	18	let	let	VERB
ejpam-3955	198	19	u	u	PRON
ejpam-3955	198	20	and	and	CCONJ
ejpam-3955	198	21	v	v	NOUN
ejpam-3955	198	22	be	be	AUX
ejpam-3955	198	23	the	the	DET
ejpam-3955	198	24	sets	set	NOUN
ejpam-3955	198	25	of	of	ADP
ejpam-3955	198	26	all	all	DET
ejpam-3955	198	27	leaves	leave	NOUN
ejpam-3955	198	28	adjacent	adjacent	ADJ
ejpam-3955	198	29	to	to	ADP
ejpam-3955	198	30	u	u	NOUN
ejpam-3955	198	31	and	and	CCONJ
ejpam-3955	198	32	v	v	NOUN
ejpam-3955	198	33	,	,	PUNCT
ejpam-3955	198	34	respectively	respectively	ADV
ejpam-3955	198	35	,	,	PUNCT
ejpam-3955	198	36	with	with	ADP
ejpam-3955	198	37	|u	|u	ADJ
ejpam-3955	198	38	|	|	NOUN
ejpam-3955	198	39	=	=	SYM
ejpam-3955	198	40	r	r	NOUN
ejpam-3955	198	41	and	and	CCONJ
ejpam-3955	198	42	|v	|v	ADJ
ejpam-3955	198	43	|	|	ADV
ejpam-3955	198	44	=	=	PUNCT
ejpam-3955	198	45	s.	s.	PROPN
ejpam-3955	198	46	let	let	VERB
ejpam-3955	198	47	s	s	PRON
ejpam-3955	198	48	be	be	AUX
ejpam-3955	198	49	a	a	DET
ejpam-3955	198	50	cost	cost	NOUN
ejpam-3955	198	51	effective	effective	ADJ
ejpam-3955	198	52	dominating	dominating	NOUN
ejpam-3955	198	53	set	set	VERB
ejpam-3955	198	54	in	in	ADP
ejpam-3955	198	55	g.	g.	PROPN
ejpam-3955	198	56	note	note	VERB
ejpam-3955	198	57	that	that	SCONJ
ejpam-3955	198	58	if	if	SCONJ
ejpam-3955	198	59	u	u	PROPN
ejpam-3955	198	60	∈	∈	PROPN
ejpam-3955	198	61	s	s	PROPN
ejpam-3955	198	62	,	,	PUNCT
ejpam-3955	198	63	then	then	ADV
ejpam-3955	198	64	u	u	PROPN
ejpam-3955	198	65	∩	∩	NOUN
ejpam-3955	198	66	s	s	PART
ejpam-3955	198	67	=	=	NOUN
ejpam-3955	198	68	∅	∅	NOUN
ejpam-3955	198	69	and	and	CCONJ
ejpam-3955	198	70	if	if	SCONJ
ejpam-3955	198	71	u	u	PROPN
ejpam-3955	198	72	/∈	/∈	PUNCT
ejpam-3955	198	73	s	s	PART
ejpam-3955	198	74	,	,	PUNCT
ejpam-3955	198	75	then	then	ADV
ejpam-3955	198	76	u	u	PROPN
ejpam-3955	198	77	⊆	⊆	NUM
ejpam-3955	198	78	s.	s.	PROPN
ejpam-3955	198	79	similar	similar	ADJ
ejpam-3955	198	80	statements	statement	NOUN
ejpam-3955	198	81	apply	apply	VERB
ejpam-3955	198	82	if	if	SCONJ
ejpam-3955	198	83	v	v	ADP
ejpam-3955	198	84	∈	∈	PROPN
ejpam-3955	198	85	s	s	X
ejpam-3955	198	86	and	and	CCONJ
ejpam-3955	198	87	v	v	NOUN
ejpam-3955	198	88	∩	∩	X
ejpam-3955	198	89	s	s	PART
ejpam-3955	198	90	=	=	PUNCT
ejpam-3955	198	91	∅.	∅.	NOUN
ejpam-3955	198	92	thus	thus	ADV
ejpam-3955	198	93	,	,	PUNCT
ejpam-3955	198	94	s	s	X
ejpam-3955	198	95	is	be	AUX
ejpam-3955	198	96	one	one	NUM
ejpam-3955	198	97	of	of	ADP
ejpam-3955	198	98	the	the	DET
ejpam-3955	198	99	following	following	NOUN
ejpam-3955	198	100	:	:	PUNCT
ejpam-3955	198	101	(	(	PUNCT
ejpam-3955	198	102	i	i	NOUN
ejpam-3955	198	103	)	)	PUNCT
ejpam-3955	199	1	s	s	AUX
ejpam-3955	199	2	=	=	PUNCT
ejpam-3955	199	3	{	{	PUNCT
ejpam-3955	199	4	u	u	NOUN
ejpam-3955	199	5	,	,	PUNCT
ejpam-3955	199	6	v	v	NOUN
ejpam-3955	199	7	}	}	PUNCT
ejpam-3955	199	8	,	,	PUNCT
ejpam-3955	199	9	(	(	PUNCT
ejpam-3955	199	10	ii	ii	NOUN
ejpam-3955	199	11	)	)	PUNCT
ejpam-3955	199	12	s	s	PART
ejpam-3955	199	13	=	=	PUNCT
ejpam-3955	199	14	{	{	PUNCT
ejpam-3955	199	15	u	u	NOUN
ejpam-3955	199	16	}	}	PUNCT
ejpam-3955	199	17	∪	∪	VERB
ejpam-3955	199	18	v	v	NOUN
ejpam-3955	199	19	,	,	PUNCT
ejpam-3955	199	20	(	(	PUNCT
ejpam-3955	199	21	iii	iii	NOUN
ejpam-3955	199	22	)	)	PUNCT
ejpam-3955	199	23	s	s	PART
ejpam-3955	199	24	=	=	PUNCT
ejpam-3955	199	25	{	{	PUNCT
ejpam-3955	199	26	v	v	NOUN
ejpam-3955	199	27	}	}	PUNCT
ejpam-3955	199	28	∪	∪	NOUN
ejpam-3955	199	29	u	u	PROPN
ejpam-3955	199	30	,	,	PUNCT
ejpam-3955	199	31	(	(	PUNCT
ejpam-3955	199	32	iv	iv	X
ejpam-3955	199	33	)	)	PUNCT
ejpam-3955	199	34	s	s	PART
ejpam-3955	199	35	=	=	SYM
ejpam-3955	199	36	u	u	NOUN
ejpam-3955	199	37	∪	∪	NOUN
ejpam-3955	199	38	v.	v.	ADP
ejpam-3955	199	39	h.	h.	PROPN
ejpam-3955	199	40	nuenay	nuenay	PROPN
ejpam-3955	199	41	-	-	PUNCT
ejpam-3955	199	42	maglanque	maglanque	ADJ
ejpam-3955	199	43	,	,	PUNCT
ejpam-3955	199	44	f.jamil	f.jamil	PROPN
ejpam-3955	199	45	/	/	SYM
ejpam-3955	199	46	eur	eur	PROPN
ejpam-3955	199	47	.	.	PUNCT
ejpam-3955	200	1	j.	j.	PROPN
ejpam-3955	200	2	pure	pure	PROPN
ejpam-3955	200	3	appl	appl	PROPN
ejpam-3955	200	4	.	.	PROPN
ejpam-3955	200	5	math	math	PROPN
ejpam-3955	200	6	,	,	PUNCT
ejpam-3955	200	7	14	14	NUM
ejpam-3955	200	8	(	(	PUNCT
ejpam-3955	200	9	2	2	NUM
ejpam-3955	200	10	)	)	PUNCT
ejpam-3955	200	11	(	(	PUNCT
ejpam-3955	200	12	2021	2021	NUM
ejpam-3955	200	13	)	)	PUNCT
ejpam-3955	200	14	,	,	PUNCT
ejpam-3955	200	15	537	537	NUM
ejpam-3955	200	16	-	-	SYM
ejpam-3955	200	17	550	550	NUM
ejpam-3955	200	18	543	543	NUM
ejpam-3955	200	19	therefore	therefore	ADV
ejpam-3955	200	20	,	,	PUNCT
ejpam-3955	200	21	γce(g	γce(g	PROPN
ejpam-3955	200	22	)	)	PUNCT
ejpam-3955	200	23	=	=	SYM
ejpam-3955	200	24	2	2	NUM
ejpam-3955	200	25	and	and	CCONJ
ejpam-3955	200	26	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	200	27	)	)	PUNCT
ejpam-3955	201	1	=	=	PUNCT
ejpam-3955	201	2	|u	|u	ADJ
ejpam-3955	201	3	|+	|+	X
ejpam-3955	201	4	|v	|v	NOUN
ejpam-3955	201	5	|	|	ADV
ejpam-3955	202	1	=	=	SYM
ejpam-3955	202	2	r	r	NOUN
ejpam-3955	202	3	+	+	PROPN
ejpam-3955	202	4	s.	s.	PROPN
ejpam-3955	202	5	note	note	VERB
ejpam-3955	202	6	further	far	ADV
ejpam-3955	202	7	that	that	SCONJ
ejpam-3955	202	8	if	if	SCONJ
ejpam-3955	202	9	u	u	NOUN
ejpam-3955	202	10	,	,	PUNCT
ejpam-3955	202	11	v	v	NOUN
ejpam-3955	202	12	/∈	/∈	SYM
ejpam-3955	202	13	s	s	X
ejpam-3955	202	14	,	,	PUNCT
ejpam-3955	202	15	then	then	ADV
ejpam-3955	202	16	s	s	VERB
ejpam-3955	202	17	\	\	X
ejpam-3955	202	18	{	{	PUNCT
ejpam-3955	202	19	x	x	NOUN
ejpam-3955	202	20	}	}	PUNCT
ejpam-3955	202	21	is	be	AUX
ejpam-3955	202	22	not	not	PART
ejpam-3955	202	23	a	a	DET
ejpam-3955	202	24	dominating	dominating	NOUN
ejpam-3955	202	25	set	set	NOUN
ejpam-3955	202	26	in	in	ADP
ejpam-3955	202	27	g	g	NOUN
ejpam-3955	202	28	,	,	PUNCT
ejpam-3955	202	29	hence	hence	ADV
ejpam-3955	202	30	not	not	PART
ejpam-3955	202	31	a	a	DET
ejpam-3955	202	32	cost	cost	NOUN
ejpam-3955	202	33	effective	effective	ADJ
ejpam-3955	202	34	dominating	dominating	NOUN
ejpam-3955	202	35	set	set	VERB
ejpam-3955	202	36	in	in	ADP
ejpam-3955	202	37	g	g	NOUN
ejpam-3955	202	38	for	for	ADP
ejpam-3955	202	39	any	any	DET
ejpam-3955	202	40	x	x	SYM
ejpam-3955	202	41	∈	∈	PROPN
ejpam-3955	202	42	u	u	NOUN
ejpam-3955	202	43	∪	∪	NOUN
ejpam-3955	202	44	v.	v.	ADP
ejpam-3955	202	45	this	this	PRON
ejpam-3955	202	46	means	mean	VERB
ejpam-3955	202	47	that	that	SCONJ
ejpam-3955	202	48	u	u	PROPN
ejpam-3955	202	49	∪	∪	NOUN
ejpam-3955	202	50	v	v	NOUN
ejpam-3955	202	51	is	be	AUX
ejpam-3955	202	52	a	a	DET
ejpam-3955	202	53	minimal	minimal	ADJ
ejpam-3955	202	54	cost	cost	NOUN
ejpam-3955	202	55	effective	effective	ADJ
ejpam-3955	202	56	dominating	dominating	NOUN
ejpam-3955	202	57	set	set	VERB
ejpam-3955	202	58	in	in	ADP
ejpam-3955	202	59	g.	g.	PROPN
ejpam-3955	202	60	therefore	therefore	ADV
ejpam-3955	202	61	,	,	PUNCT
ejpam-3955	202	62	γmce(g	γmce(g	PROPN
ejpam-3955	202	63	)	)	PUNCT
ejpam-3955	202	64	=	=	PUNCT
ejpam-3955	203	1	|u	|u	ADJ
ejpam-3955	203	2	|+	|+	X
ejpam-3955	203	3	|v	|v	NOUN
ejpam-3955	203	4	|	|	ADV
ejpam-3955	204	1	=	=	SYM
ejpam-3955	204	2	r	r	NOUN
ejpam-3955	204	3	+	+	PROPN
ejpam-3955	204	4	s.	s.	PROPN
ejpam-3955	204	5	corollary	corollary	NOUN
ejpam-3955	204	6	5	5	NUM
ejpam-3955	204	7	.	.	PUNCT
ejpam-3955	205	1	if	if	SCONJ
ejpam-3955	205	2	g	g	PROPN
ejpam-3955	205	3	is	be	AUX
ejpam-3955	205	4	any	any	PRON
ejpam-3955	205	5	of	of	ADP
ejpam-3955	205	6	the	the	DET
ejpam-3955	205	7	following	follow	VERB
ejpam-3955	205	8	graphs	graph	NOUN
ejpam-3955	205	9	:	:	PUNCT
ejpam-3955	205	10	pn	pn	PROPN
ejpam-3955	205	11	(	(	PUNCT
ejpam-3955	205	12	n	n	CCONJ
ejpam-3955	205	13	≥	≥	NOUN
ejpam-3955	205	14	2	2	NUM
ejpam-3955	205	15	)	)	PUNCT
ejpam-3955	205	16	,	,	PUNCT
ejpam-3955	205	17	cn	cn	PROPN
ejpam-3955	205	18	(	(	PUNCT
ejpam-3955	205	19	n	n	CCONJ
ejpam-3955	205	20	≥	≥	NOUN
ejpam-3955	205	21	3	3	NUM
ejpam-3955	205	22	)	)	PUNCT
ejpam-3955	205	23	,	,	PUNCT
ejpam-3955	205	24	km	km	PROPN
ejpam-3955	205	25	,	,	PUNCT
ejpam-3955	205	26	n	n	CCONJ
ejpam-3955	205	27	(	(	PUNCT
ejpam-3955	205	28	m	m	PROPN
ejpam-3955	205	29	,	,	PUNCT
ejpam-3955	205	30	n	n	PRON
ejpam-3955	205	31	≥	≥	NOUN
ejpam-3955	205	32	2	2	NUM
ejpam-3955	205	33	)	)	PUNCT
ejpam-3955	205	34	,	,	PUNCT
ejpam-3955	205	35	kn	kn	PROPN
ejpam-3955	205	36	(	(	PUNCT
ejpam-3955	205	37	n	n	CCONJ
ejpam-3955	205	38	≥	≥	NUM
ejpam-3955	205	39	1	1	NUM
ejpam-3955	205	40	)	)	PUNCT
ejpam-3955	205	41	and	and	CCONJ
ejpam-3955	205	42	sr	sr	PROPN
ejpam-3955	205	43	,	,	PUNCT
ejpam-3955	205	44	s	s	PROPN
ejpam-3955	205	45	,	,	PUNCT
ejpam-3955	205	46	then	then	ADV
ejpam-3955	205	47	γmce(g	γmce(g	PROPN
ejpam-3955	205	48	)	)	PUNCT
ejpam-3955	205	49	=	=	SYM
ejpam-3955	205	50	γm(g	γm(g	PROPN
ejpam-3955	205	51	)	)	PUNCT
ejpam-3955	205	52	.	.	PUNCT
ejpam-3955	206	1	theorem	theorem	ADJ
ejpam-3955	206	2	8	8	NUM
ejpam-3955	206	3	.	.	PUNCT
ejpam-3955	207	1	let	let	VERB
ejpam-3955	207	2	g	g	PRON
ejpam-3955	207	3	be	be	AUX
ejpam-3955	207	4	a	a	DET
ejpam-3955	207	5	connected	connected	ADJ
ejpam-3955	207	6	graph	graph	NOUN
ejpam-3955	207	7	of	of	ADP
ejpam-3955	207	8	order	order	NOUN
ejpam-3955	207	9	n	n	PRON
ejpam-3955	207	10	≥	≥	NOUN
ejpam-3955	207	11	2	2	NUM
ejpam-3955	207	12	.	.	PUNCT
ejpam-3955	208	1	then	then	ADV
ejpam-3955	208	2	,	,	PUNCT
ejpam-3955	208	3	(	(	PUNCT
ejpam-3955	208	4	i.	i.	NOUN
ejpam-3955	208	5	)	)	PUNCT
ejpam-3955	208	6	γmce(g	γmce(g	NOUN
ejpam-3955	208	7	)	)	PUNCT
ejpam-3955	209	1	=	=	PUNCT
ejpam-3955	209	2	n−	n−	NOUN
ejpam-3955	209	3	1	1	NUM
ejpam-3955	209	4	if	if	SCONJ
ejpam-3955	209	5	and	and	CCONJ
ejpam-3955	209	6	only	only	ADV
ejpam-3955	209	7	if	if	SCONJ
ejpam-3955	209	8	g	g	NOUN
ejpam-3955	209	9	=	=	SYM
ejpam-3955	209	10	k1,n−1	k1,n−1	PROPN
ejpam-3955	209	11	(	(	PUNCT
ejpam-3955	209	12	ii	ii	PROPN
ejpam-3955	209	13	.	.	PUNCT
ejpam-3955	209	14	)	)	PUNCT
ejpam-3955	209	15	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	209	16	)	)	PUNCT
ejpam-3955	210	1	=	=	PUNCT
ejpam-3955	210	2	n−	n−	NOUN
ejpam-3955	210	3	1	1	NUM
ejpam-3955	210	4	if	if	SCONJ
ejpam-3955	210	5	and	and	CCONJ
ejpam-3955	210	6	only	only	ADV
ejpam-3955	210	7	if	if	SCONJ
ejpam-3955	210	8	g	g	PROPN
ejpam-3955	210	9	=	=	SYM
ejpam-3955	210	10	k1	k1	PROPN
ejpam-3955	210	11	+	+	CCONJ
ejpam-3955	210	12	t⋃	t⋃	PROPN
ejpam-3955	210	13	j=1	j=1	PROPN
ejpam-3955	210	14	krj	krj	PROPN
ejpam-3955	210	15	,	,	PUNCT
ejpam-3955	210	16	where	where	SCONJ
ejpam-3955	210	17	1	1	NUM
ejpam-3955	210	18	≤	≤	NUM
ejpam-3955	210	19	rj	rj	PROPN
ejpam-3955	210	20	≤	≤	PROPN
ejpam-3955	210	21	2	2	NUM
ejpam-3955	210	22	and	and	CCONJ
ejpam-3955	210	23	∑	∑	PROPN
ejpam-3955	210	24	rj	rj	PROPN
ejpam-3955	210	25	=	=	PUNCT
ejpam-3955	210	26	n−	n−	PROPN
ejpam-3955	210	27	1	1	NUM
ejpam-3955	210	28	.	.	PUNCT
ejpam-3955	211	1	proof	proof	NOUN
ejpam-3955	211	2	.	.	PUNCT
ejpam-3955	212	1	let	let	VERB
ejpam-3955	212	2	s	s	PRON
ejpam-3955	212	3	⊆	⊆	NUM
ejpam-3955	212	4	v	v	NOUN
ejpam-3955	212	5	(	(	PUNCT
ejpam-3955	212	6	g	g	NOUN
ejpam-3955	212	7	)	)	PUNCT
ejpam-3955	212	8	be	be	AUX
ejpam-3955	212	9	a	a	DET
ejpam-3955	212	10	cost	cost	NOUN
ejpam-3955	212	11	effective	effective	ADJ
ejpam-3955	212	12	set	set	VERB
ejpam-3955	212	13	with	with	ADP
ejpam-3955	212	14	|s|	|s|	NOUN
ejpam-3955	212	15	=	=	PUNCT
ejpam-3955	212	16	n	n	CCONJ
ejpam-3955	212	17	−	−	PROPN
ejpam-3955	212	18	1	1	NUM
ejpam-3955	212	19	,	,	PUNCT
ejpam-3955	212	20	and	and	CCONJ
ejpam-3955	212	21	let	let	VERB
ejpam-3955	212	22	v	v	NUM
ejpam-3955	212	23	∈	∈	PROPN
ejpam-3955	212	24	v	v	NOUN
ejpam-3955	212	25	(	(	PUNCT
ejpam-3955	212	26	g	g	NOUN
ejpam-3955	212	27	)	)	PUNCT
ejpam-3955	212	28	\	\	PUNCT
ejpam-3955	213	1	s.	s.	PROPN
ejpam-3955	213	2	since	since	SCONJ
ejpam-3955	213	3	g	g	PROPN
ejpam-3955	213	4	is	be	AUX
ejpam-3955	213	5	connected	connect	VERB
ejpam-3955	213	6	and	and	CCONJ
ejpam-3955	213	7	s	s	NOUN
ejpam-3955	213	8	is	be	AUX
ejpam-3955	213	9	cost	cost	NOUN
ejpam-3955	213	10	effective	effective	ADJ
ejpam-3955	213	11	,	,	PUNCT
ejpam-3955	213	12	it	it	PRON
ejpam-3955	213	13	follows	follow	VERB
ejpam-3955	213	14	that	that	SCONJ
ejpam-3955	213	15	uv	uv	PROPN
ejpam-3955	213	16	∈	∈	PROPN
ejpam-3955	213	17	e(g	e(g	PROPN
ejpam-3955	213	18	)	)	PUNCT
ejpam-3955	213	19	and	and	CCONJ
ejpam-3955	213	20	|ng(u	|ng(u	X
ejpam-3955	213	21	)	)	PUNCT
ejpam-3955	213	22	∩	∩	NOUN
ejpam-3955	213	23	s|	s|	VERB
ejpam-3955	213	24	≤	≤	NUM
ejpam-3955	213	25	1	1	NUM
ejpam-3955	213	26	for	for	ADP
ejpam-3955	213	27	all	all	DET
ejpam-3955	213	28	u	u	PROPN
ejpam-3955	213	29	∈	∈	PROPN
ejpam-3955	213	30	s.	s.	PROPN
ejpam-3955	213	31	if	if	SCONJ
ejpam-3955	213	32	there	there	PRON
ejpam-3955	213	33	exists	exist	VERB
ejpam-3955	213	34	w	w	PROPN
ejpam-3955	213	35	∈	∈	PROPN
ejpam-3955	213	36	s	s	VERB
ejpam-3955	213	37	such	such	ADJ
ejpam-3955	213	38	that	that	SCONJ
ejpam-3955	213	39	|ng(w	|ng(w	X
ejpam-3955	213	40	)	)	PUNCT
ejpam-3955	213	41	∩	∩	NOUN
ejpam-3955	213	42	s|	s|	NOUN
ejpam-3955	213	43	=	=	SYM
ejpam-3955	213	44	1	1	NUM
ejpam-3955	213	45	then	then	ADV
ejpam-3955	213	46	s′	s′	PUNCT
ejpam-3955	213	47	=	=	SYM
ejpam-3955	213	48	s	s	PART
ejpam-3955	213	49	\	\	X
ejpam-3955	213	50	{	{	PUNCT
ejpam-3955	213	51	w	w	NOUN
ejpam-3955	213	52	}	}	PUNCT
ejpam-3955	213	53	is	be	AUX
ejpam-3955	213	54	a	a	DET
ejpam-3955	213	55	cost	cost	NOUN
ejpam-3955	213	56	effective	effective	ADJ
ejpam-3955	213	57	set	set	VERB
ejpam-3955	213	58	dominating	dominating	NOUN
ejpam-3955	213	59	set	set	VERB
ejpam-3955	213	60	in	in	ADP
ejpam-3955	213	61	g.	g.	PROPN
ejpam-3955	213	62	if	if	SCONJ
ejpam-3955	213	63	s	s	VERB
ejpam-3955	213	64	is	be	AUX
ejpam-3955	213	65	a	a	DET
ejpam-3955	213	66	minimal	minimal	ADJ
ejpam-3955	213	67	cost	cost	NOUN
ejpam-3955	213	68	effective	effective	ADJ
ejpam-3955	213	69	set	set	NOUN
ejpam-3955	213	70	,	,	PUNCT
ejpam-3955	213	71	then	then	ADV
ejpam-3955	213	72	〈	〈	PROPN
ejpam-3955	213	73	s	s	PROPN
ejpam-3955	213	74	〉	〉	PROPN
ejpam-3955	213	75	=	=	SYM
ejpam-3955	213	76	kn−1	kn−1	PROPN
ejpam-3955	213	77	.	.	PUNCT
ejpam-3955	214	1	thus	thus	ADV
ejpam-3955	214	2	,	,	PUNCT
ejpam-3955	214	3	g	g	PROPN
ejpam-3955	214	4	=	=	PUNCT
ejpam-3955	214	5	k1,n−1	k1,n−1	PROPN
ejpam-3955	214	6	.	.	PUNCT
ejpam-3955	215	1	otherwise	otherwise	ADV
ejpam-3955	215	2	,	,	PUNCT
ejpam-3955	215	3	g	g	PROPN
ejpam-3955	215	4	=	=	PROPN
ejpam-3955	215	5	k1	k1	PROPN
ejpam-3955	215	6	+	+	CCONJ
ejpam-3955	215	7	t⋃	t⋃	PROPN
ejpam-3955	215	8	j=1	j=1	PROPN
ejpam-3955	215	9	krj	krj	PROPN
ejpam-3955	215	10	,	,	PUNCT
ejpam-3955	215	11	where	where	SCONJ
ejpam-3955	215	12	1	1	NUM
ejpam-3955	215	13	≤	≤	NUM
ejpam-3955	215	14	rj	rj	PROPN
ejpam-3955	215	15	≤	≤	PROPN
ejpam-3955	215	16	2	2	NUM
ejpam-3955	215	17	and	and	CCONJ
ejpam-3955	215	18	∑	∑	PROPN
ejpam-3955	215	19	rj	rj	PROPN
ejpam-3955	215	20	=	=	PUNCT
ejpam-3955	215	21	n−	n−	PROPN
ejpam-3955	215	22	1	1	NUM
ejpam-3955	215	23	.	.	PUNCT
ejpam-3955	216	1	the	the	DET
ejpam-3955	216	2	converse	converse	NOUN
ejpam-3955	216	3	is	be	AUX
ejpam-3955	216	4	clear	clear	ADJ
ejpam-3955	216	5	.	.	PUNCT
ejpam-3955	217	1	theorem	theorem	ADJ
ejpam-3955	217	2	9	9	NUM
ejpam-3955	217	3	.	.	X
ejpam-3955	218	1	for	for	ADP
ejpam-3955	218	2	a	a	DET
ejpam-3955	218	3	connected	connected	ADJ
ejpam-3955	218	4	graph	graph	NOUN
ejpam-3955	218	5	g	g	NOUN
ejpam-3955	218	6	of	of	ADP
ejpam-3955	218	7	order	order	NOUN
ejpam-3955	218	8	n	n	PRON
ejpam-3955	218	9	≥	≥	NUM
ejpam-3955	218	10	5	5	NUM
ejpam-3955	218	11	,	,	PUNCT
ejpam-3955	218	12	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	218	13	)	)	PUNCT
ejpam-3955	218	14	≥	≥	NOUN
ejpam-3955	218	15	3	3	NUM
ejpam-3955	218	16	.	.	PUNCT
ejpam-3955	218	17	proof	proof	NOUN
ejpam-3955	218	18	.	.	PUNCT
ejpam-3955	219	1	suppose	suppose	VERB
ejpam-3955	219	2	that	that	SCONJ
ejpam-3955	219	3	g	g	PROPN
ejpam-3955	219	4	is	be	AUX
ejpam-3955	219	5	a	a	DET
ejpam-3955	219	6	complete	complete	ADJ
ejpam-3955	219	7	graph	graph	NOUN
ejpam-3955	219	8	of	of	ADP
ejpam-3955	219	9	order	order	NOUN
ejpam-3955	219	10	n	n	PRON
ejpam-3955	219	11	≥	≥	NOUN
ejpam-3955	219	12	5	5	NUM
ejpam-3955	219	13	.	.	PUNCT
ejpam-3955	220	1	if	if	SCONJ
ejpam-3955	220	2	s	s	VERB
ejpam-3955	220	3	⊆	⊆	NUM
ejpam-3955	220	4	v	v	NOUN
ejpam-3955	220	5	(	(	PUNCT
ejpam-3955	220	6	g	g	NOUN
ejpam-3955	220	7	)	)	PUNCT
ejpam-3955	220	8	is	be	AUX
ejpam-3955	220	9	a	a	DET
ejpam-3955	220	10	γ+ce	γ+ce	NOUN
ejpam-3955	220	11	-	-	PUNCT
ejpam-3955	220	12	set	set	NOUN
ejpam-3955	220	13	in	in	ADP
ejpam-3955	220	14	g	g	NOUN
ejpam-3955	220	15	,	,	PUNCT
ejpam-3955	220	16	then	then	ADV
ejpam-3955	220	17	by	by	ADP
ejpam-3955	220	18	theorem	theorem	NOUN
ejpam-3955	220	19	5	5	NUM
ejpam-3955	220	20	,	,	PUNCT
ejpam-3955	220	21	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	220	22	)	)	PUNCT
ejpam-3955	220	23	=	=	PUNCT
ejpam-3955	220	24	|s|	|s|	NOUN
ejpam-3955	220	25	=	=	SYM
ejpam-3955	220	26	⌊	⌊	PROPN
ejpam-3955	220	27	1	1	NUM
ejpam-3955	220	28	2(n+	2(n+	NOUN
ejpam-3955	220	29	1	1	NUM
ejpam-3955	220	30	)	)	PUNCT
ejpam-3955	220	31	⌋	⌋	NOUN
ejpam-3955	220	32	≥	≥	NUM
ejpam-3955	220	33	⌊	⌊	VERB
ejpam-3955	220	34	1	1	NUM
ejpam-3955	220	35	2(5	2(5	NOUN
ejpam-3955	220	36	+	+	CCONJ
ejpam-3955	220	37	1	1	NUM
ejpam-3955	220	38	)	)	PUNCT
ejpam-3955	220	39	⌋	⌋	NOUN
ejpam-3955	221	1	=	=	PUNCT
ejpam-3955	221	2	3	3	X
ejpam-3955	221	3	.	.	PUNCT
ejpam-3955	221	4	suppose	suppose	VERB
ejpam-3955	221	5	that	that	SCONJ
ejpam-3955	221	6	g	g	PROPN
ejpam-3955	221	7	is	be	AUX
ejpam-3955	221	8	not	not	PART
ejpam-3955	221	9	complete	complete	ADJ
ejpam-3955	221	10	.	.	PUNCT
ejpam-3955	222	1	then	then	ADV
ejpam-3955	222	2	there	there	PRON
ejpam-3955	222	3	exist	exist	VERB
ejpam-3955	222	4	u	u	NOUN
ejpam-3955	222	5	,	,	PUNCT
ejpam-3955	222	6	v	v	NOUN
ejpam-3955	222	7	∈	∈	PROPN
ejpam-3955	222	8	v	v	NOUN
ejpam-3955	222	9	(	(	PUNCT
ejpam-3955	222	10	g	g	NOUN
ejpam-3955	222	11	)	)	PUNCT
ejpam-3955	223	1	such	such	ADJ
ejpam-3955	223	2	that	that	PRON
ejpam-3955	223	3	uv	uv	NOUN
ejpam-3955	223	4	/∈	/∈	PUNCT
ejpam-3955	223	5	e(g	e(g	PROPN
ejpam-3955	223	6	)	)	PUNCT
ejpam-3955	223	7	.	.	PUNCT
ejpam-3955	224	1	then	then	ADV
ejpam-3955	224	2	{	{	PUNCT
ejpam-3955	224	3	u	u	NOUN
ejpam-3955	224	4	,	,	PUNCT
ejpam-3955	224	5	v	v	NOUN
ejpam-3955	224	6	}	}	PUNCT
ejpam-3955	224	7	is	be	AUX
ejpam-3955	224	8	a	a	DET
ejpam-3955	224	9	cost	cost	NOUN
ejpam-3955	224	10	effective	effective	ADJ
ejpam-3955	224	11	set	set	NOUN
ejpam-3955	224	12	in	in	ADP
ejpam-3955	224	13	g.	g.	PROPN
ejpam-3955	224	14	suppose	suppose	VERB
ejpam-3955	224	15	that	that	SCONJ
ejpam-3955	224	16	ng[{u	ng[{u	PROPN
ejpam-3955	224	17	,	,	PUNCT
ejpam-3955	224	18	v	v	NOUN
ejpam-3955	224	19	}	}	PUNCT
ejpam-3955	224	20	]	]	PUNCT
ejpam-3955	224	21	6=	6=	NUM
ejpam-3955	224	22	v	v	ADP
ejpam-3955	224	23	(	(	PUNCT
ejpam-3955	224	24	g	g	NOUN
ejpam-3955	224	25	)	)	PUNCT
ejpam-3955	224	26	.	.	PUNCT
ejpam-3955	225	1	let	let	VERB
ejpam-3955	225	2	v1	v1	VERB
ejpam-3955	225	3	∈	∈	PROPN
ejpam-3955	225	4	v	v	NOUN
ejpam-3955	225	5	(	(	PUNCT
ejpam-3955	225	6	g	g	NOUN
ejpam-3955	225	7	)	)	PUNCT
ejpam-3955	225	8	\	\	PROPN
ejpam-3955	225	9	ng[{u	ng[{u	PROPN
ejpam-3955	225	10	,	,	PUNCT
ejpam-3955	225	11	v	v	NOUN
ejpam-3955	225	12	}	}	PUNCT
ejpam-3955	225	13	]	]	PUNCT
ejpam-3955	225	14	and	and	CCONJ
ejpam-3955	225	15	put	put	VERB
ejpam-3955	225	16	s1	s1	NOUN
ejpam-3955	225	17	=	=	PUNCT
ejpam-3955	225	18	{	{	PUNCT
ejpam-3955	225	19	u	u	NOUN
ejpam-3955	225	20	,	,	PUNCT
ejpam-3955	225	21	v	v	NOUN
ejpam-3955	225	22	,	,	PUNCT
ejpam-3955	225	23	v1	v1	NOUN
ejpam-3955	225	24	}	}	PUNCT
ejpam-3955	225	25	.	.	PUNCT
ejpam-3955	226	1	if	if	SCONJ
ejpam-3955	226	2	ng[s1	ng[s1	PROPN
ejpam-3955	226	3	]	]	X
ejpam-3955	226	4	=	=	SYM
ejpam-3955	226	5	v	v	X
ejpam-3955	226	6	(	(	PUNCT
ejpam-3955	226	7	g	g	NOUN
ejpam-3955	226	8	)	)	PUNCT
ejpam-3955	226	9	,	,	PUNCT
ejpam-3955	226	10	then	then	ADV
ejpam-3955	226	11	s1	s1	NOUN
ejpam-3955	226	12	is	be	AUX
ejpam-3955	226	13	a	a	DET
ejpam-3955	226	14	cost	cost	NOUN
ejpam-3955	226	15	effective	effective	ADJ
ejpam-3955	226	16	dominating	dominating	NOUN
ejpam-3955	226	17	set	set	VERB
ejpam-3955	226	18	in	in	ADP
ejpam-3955	226	19	g.	g.	PROPN
ejpam-3955	226	20	suppose	suppose	VERB
ejpam-3955	226	21	that	that	SCONJ
ejpam-3955	226	22	ng[s1	ng[s1	PROPN
ejpam-3955	226	23	]	]	X
ejpam-3955	226	24	6=	6=	ADP
ejpam-3955	226	25	v	v	ADP
ejpam-3955	226	26	(	(	PUNCT
ejpam-3955	226	27	g	g	NOUN
ejpam-3955	226	28	)	)	PUNCT
ejpam-3955	226	29	.	.	PUNCT
ejpam-3955	227	1	let	let	VERB
ejpam-3955	227	2	v2	v2	PROPN
ejpam-3955	227	3	∈	∈	PROPN
ejpam-3955	227	4	v	v	NOUN
ejpam-3955	227	5	(	(	PUNCT
ejpam-3955	227	6	g	g	NOUN
ejpam-3955	227	7	)	)	PUNCT
ejpam-3955	227	8	\ng[s1	\ng[s1	PROPN
ejpam-3955	227	9	]	]	PUNCT
ejpam-3955	227	10	and	and	CCONJ
ejpam-3955	227	11	put	put	VERB
ejpam-3955	227	12	s2	s2	NOUN
ejpam-3955	227	13	=	=	SYM
ejpam-3955	227	14	{	{	PUNCT
ejpam-3955	227	15	u	u	NOUN
ejpam-3955	227	16	,	,	PUNCT
ejpam-3955	227	17	v	v	NOUN
ejpam-3955	227	18	,	,	PUNCT
ejpam-3955	227	19	v1	v1	NOUN
ejpam-3955	227	20	,	,	PUNCT
ejpam-3955	227	21	v2	v2	PROPN
ejpam-3955	227	22	}	}	PUNCT
ejpam-3955	227	23	.	.	PUNCT
ejpam-3955	228	1	if	if	SCONJ
ejpam-3955	228	2	ng[s2	ng[s2	PROPN
ejpam-3955	228	3	]	]	X
ejpam-3955	228	4	=	=	SYM
ejpam-3955	228	5	v	v	NOUN
ejpam-3955	228	6	(	(	PUNCT
ejpam-3955	228	7	g	g	NOUN
ejpam-3955	228	8	)	)	PUNCT
ejpam-3955	228	9	,	,	PUNCT
ejpam-3955	228	10	then	then	ADV
ejpam-3955	228	11	s2	s2	PROPN
ejpam-3955	228	12	is	be	AUX
ejpam-3955	228	13	a	a	DET
ejpam-3955	228	14	cost	cost	NOUN
ejpam-3955	228	15	effective	effective	ADJ
ejpam-3955	228	16	dominating	dominating	NOUN
ejpam-3955	228	17	set	set	VERB
ejpam-3955	228	18	in	in	ADP
ejpam-3955	228	19	g.	g.	PROPN
ejpam-3955	228	20	continuing	continue	VERB
ejpam-3955	228	21	in	in	ADP
ejpam-3955	228	22	this	this	DET
ejpam-3955	228	23	manner	manner	NOUN
ejpam-3955	228	24	,	,	PUNCT
ejpam-3955	228	25	there	there	PRON
ejpam-3955	228	26	exists	exist	VERB
ejpam-3955	228	27	a	a	DET
ejpam-3955	228	28	positive	positive	ADJ
ejpam-3955	228	29	integer	integer	NOUN
ejpam-3955	228	30	k	k	PROPN
ejpam-3955	228	31	≥	≥	NUM
ejpam-3955	228	32	1	1	NUM
ejpam-3955	228	33	such	such	ADJ
ejpam-3955	228	34	that	that	PRON
ejpam-3955	228	35	vk	vk	NOUN
ejpam-3955	228	36	/∈	/∈	PUNCT
ejpam-3955	229	1	ng[sk−1	ng[sk−1	PROPN
ejpam-3955	229	2	]	]	PUNCT
ejpam-3955	229	3	and	and	CCONJ
ejpam-3955	229	4	ng[sk	ng[sk	NOUN
ejpam-3955	229	5	]	]	X
ejpam-3955	229	6	=	=	SYM
ejpam-3955	229	7	v	v	X
ejpam-3955	229	8	(	(	PUNCT
ejpam-3955	229	9	g	g	NOUN
ejpam-3955	229	10	)	)	PUNCT
ejpam-3955	229	11	wth	wth	NOUN
ejpam-3955	229	12	s0	s0	NOUN
ejpam-3955	229	13	=	=	PUNCT
ejpam-3955	229	14	{	{	PUNCT
ejpam-3955	229	15	u	u	NOUN
ejpam-3955	229	16	,	,	PUNCT
ejpam-3955	229	17	v	v	NOUN
ejpam-3955	229	18	}	}	PUNCT
ejpam-3955	229	19	.	.	PUNCT
ejpam-3955	230	1	thus	thus	ADV
ejpam-3955	230	2	,	,	PUNCT
ejpam-3955	230	3	sk	sk	X
ejpam-3955	230	4	is	be	AUX
ejpam-3955	230	5	a	a	DET
ejpam-3955	230	6	cost	cost	NOUN
ejpam-3955	230	7	effective	effective	ADJ
ejpam-3955	230	8	dominating	dominating	NOUN
ejpam-3955	230	9	set	set	VERB
ejpam-3955	230	10	in	in	ADP
ejpam-3955	230	11	g.	g.	PROPN
ejpam-3955	230	12	consequently	consequently	ADV
ejpam-3955	230	13	,	,	PUNCT
ejpam-3955	230	14	γ+ce(g	γ+ce(g	PROPN
ejpam-3955	230	15	)	)	PUNCT
ejpam-3955	230	16	≥	≥	NOUN
ejpam-3955	230	17	3	3	X
ejpam-3955	230	18	.	.	PUNCT
ejpam-3955	230	19	suppose	suppose	VERB
ejpam-3955	230	20	that	that	SCONJ
ejpam-3955	230	21	ng[{u	ng[{u	PROPN
ejpam-3955	230	22	,	,	PUNCT
ejpam-3955	230	23	v	v	NOUN
ejpam-3955	230	24	}	}	PUNCT
ejpam-3955	230	25	]	]	PUNCT
ejpam-3955	230	26	=	=	SYM
ejpam-3955	230	27	v	v	X
ejpam-3955	230	28	(	(	PUNCT
ejpam-3955	230	29	g	g	NOUN
ejpam-3955	230	30	)	)	PUNCT
ejpam-3955	230	31	.	.	PUNCT
ejpam-3955	231	1	note	note	VERB
ejpam-3955	231	2	that	that	SCONJ
ejpam-3955	231	3	,	,	PUNCT
ejpam-3955	231	4	since	since	SCONJ
ejpam-3955	231	5	|v	|v	PROPN
ejpam-3955	231	6	(	(	PUNCT
ejpam-3955	231	7	g)|	g)|	X
ejpam-3955	231	8	≥	≥	NOUN
ejpam-3955	231	9	5	5	NUM
ejpam-3955	231	10	,	,	PUNCT
ejpam-3955	231	11	g	g	PROPN
ejpam-3955	231	12	has	have	VERB
ejpam-3955	231	13	at	at	ADV
ejpam-3955	231	14	least	least	ADV
ejpam-3955	231	15	three	three	NUM
ejpam-3955	231	16	more	more	ADJ
ejpam-3955	231	17	vertices	vertex	NOUN
ejpam-3955	231	18	v1	v1	NOUN
ejpam-3955	231	19	,	,	PUNCT
ejpam-3955	231	20	v2	v2	PROPN
ejpam-3955	231	21	and	and	CCONJ
ejpam-3955	231	22	v3	v3	PROPN
ejpam-3955	231	23	other	other	ADJ
ejpam-3955	231	24	than	than	ADP
ejpam-3955	231	25	u	u	NOUN
ejpam-3955	231	26	and	and	CCONJ
ejpam-3955	231	27	v.	v.	ADP
ejpam-3955	231	28	further	far	ADV
ejpam-3955	231	29	,	,	PUNCT
ejpam-3955	231	30	since	since	SCONJ
ejpam-3955	231	31	{	{	PUNCT
ejpam-3955	231	32	u	u	NOUN
ejpam-3955	231	33	,	,	PUNCT
ejpam-3955	231	34	v	v	NOUN
ejpam-3955	231	35	}	}	PUNCT
ejpam-3955	231	36	is	be	AUX
ejpam-3955	231	37	a	a	DET
ejpam-3955	231	38	dominating	dominating	NOUN
ejpam-3955	231	39	set	set	NOUN
ejpam-3955	231	40	in	in	ADP
ejpam-3955	231	41	g	g	NOUN
ejpam-3955	231	42	,	,	PUNCT
ejpam-3955	231	43	at	at	ADV
ejpam-3955	231	44	least	least	ADV
ejpam-3955	231	45	two	two	NUM
ejpam-3955	231	46	vertices	vertex	NOUN
ejpam-3955	231	47	in	in	ADP
ejpam-3955	231	48	v	v	ADP
ejpam-3955	231	49	(	(	PUNCT
ejpam-3955	231	50	g	g	NOUN
ejpam-3955	231	51	)	)	PUNCT
ejpam-3955	231	52	\	\	NOUN
ejpam-3955	231	53	{	{	PUNCT
ejpam-3955	231	54	u	u	NOUN
ejpam-3955	231	55	,	,	PUNCT
ejpam-3955	231	56	v	v	NOUN
ejpam-3955	231	57	}	}	PUNCT
ejpam-3955	231	58	are	be	AUX
ejpam-3955	231	59	adjacent	adjacent	ADJ
ejpam-3955	231	60	to	to	ADP
ejpam-3955	231	61	either	either	CCONJ
ejpam-3955	231	62	u	u	PROPN
ejpam-3955	231	63	or	or	CCONJ
ejpam-3955	231	64	v	v	NOUN
ejpam-3955	231	65	or	or	CCONJ
ejpam-3955	231	66	both	both	PRON
ejpam-3955	231	67	.	.	PUNCT
ejpam-3955	232	1	consider	consider	VERB
ejpam-3955	232	2	the	the	DET
ejpam-3955	232	3	following	follow	VERB
ejpam-3955	232	4	cases	case	NOUN
ejpam-3955	232	5	.	.	PUNCT
ejpam-3955	233	1	case	case	NOUN
ejpam-3955	233	2	1	1	NUM
ejpam-3955	233	3	:	:	PUNCT
ejpam-3955	233	4	suppose	suppose	VERB
ejpam-3955	233	5	that	that	SCONJ
ejpam-3955	233	6	v1v2	v1v2	PROPN
ejpam-3955	233	7	/∈	/∈	PUNCT
ejpam-3955	233	8	e(g	e(g	PROPN
ejpam-3955	233	9	)	)	PUNCT
ejpam-3955	233	10	.	.	PUNCT
ejpam-3955	234	1	subcase	subcase	PROPN
ejpam-3955	234	2	1	1	NUM
ejpam-3955	235	1	:	:	PUNCT
ejpam-3955	235	2	consider	consider	VERB
ejpam-3955	235	3	having	have	VERB
ejpam-3955	235	4	v1	v1	NOUN
ejpam-3955	235	5	,	,	PUNCT
ejpam-3955	235	6	v2	v2	PROPN
ejpam-3955	235	7	being	be	AUX
ejpam-3955	235	8	adjacent	adjacent	ADJ
ejpam-3955	235	9	only	only	ADV
ejpam-3955	235	10	to	to	ADP
ejpam-3955	235	11	either	either	CCONJ
ejpam-3955	235	12	u	u	PROPN
ejpam-3955	235	13	or	or	CCONJ
ejpam-3955	235	14	v.	v.	ADP
ejpam-3955	235	15	assume	assume	VERB
ejpam-3955	235	16	that	that	SCONJ
ejpam-3955	235	17	v1	v1	NOUN
ejpam-3955	235	18	and	and	CCONJ
ejpam-3955	235	19	v2	v2	NOUN
ejpam-3955	235	20	are	be	AUX
ejpam-3955	235	21	adjacent	adjacent	ADJ
ejpam-3955	235	22	to	to	PART
ejpam-3955	235	23	u.	u.	VERB
ejpam-3955	235	24	since	since	SCONJ
ejpam-3955	235	25	s∗	s∗	PROPN
ejpam-3955	235	26	=	=	SYM
ejpam-3955	235	27	{	{	PUNCT
ejpam-3955	235	28	v1	v1	PROPN
ejpam-3955	235	29	,	,	PUNCT
ejpam-3955	235	30	v2	v2	PROPN
ejpam-3955	235	31	,	,	PUNCT
ejpam-3955	235	32	v	v	NOUN
ejpam-3955	235	33	}	}	PUNCT
ejpam-3955	235	34	is	be	AUX
ejpam-3955	235	35	a	a	DET
ejpam-3955	235	36	cost	cost	NOUN
ejpam-3955	235	37	effective	effective	ADJ
ejpam-3955	235	38	set	set	NOUN
ejpam-3955	235	39	in	in	ADP
ejpam-3955	235	40	g	g	NOUN
ejpam-3955	235	41	,	,	PUNCT
ejpam-3955	235	42	one	one	PRON
ejpam-3955	235	43	can	can	AUX
ejpam-3955	235	44	construct	construct	VERB
ejpam-3955	235	45	a	a	DET
ejpam-3955	235	46	cost	cost	NOUN
ejpam-3955	235	47	effective	effective	ADJ
ejpam-3955	235	48	dominating	dominating	NOUN
ejpam-3955	235	49	set	set	NOUN
ejpam-3955	235	50	s	s	AUX
ejpam-3955	235	51	beginning	begin	VERB
ejpam-3955	235	52	with	with	ADP
ejpam-3955	235	53	s∗	s∗	PROPN
ejpam-3955	235	54	as	as	SCONJ
ejpam-3955	235	55	done	do	VERB
ejpam-3955	235	56	above	above	ADV
ejpam-3955	235	57	.	.	PUNCT
ejpam-3955	236	1	consequently	consequently	ADV
ejpam-3955	236	2	,	,	PUNCT
ejpam-3955	236	3	|s|	|s|	X
ejpam-3955	236	4	≥	≥	NOUN
ejpam-3955	236	5	3	3	NUM
ejpam-3955	236	6	.	.	PUNCT
ejpam-3955	237	1	h.	h.	PROPN
ejpam-3955	237	2	nuenay	nuenay	PROPN
ejpam-3955	237	3	-	-	PUNCT
ejpam-3955	237	4	maglanque	maglanque	ADJ
ejpam-3955	237	5	,	,	PUNCT
ejpam-3955	237	6	f.jamil	f.jamil	PROPN
ejpam-3955	237	7	/	/	SYM
ejpam-3955	237	8	eur	eur	PROPN
ejpam-3955	237	9	.	.	PUNCT
ejpam-3955	238	1	j.	j.	PROPN
ejpam-3955	238	2	pure	pure	PROPN
ejpam-3955	238	3	appl	appl	PROPN
ejpam-3955	238	4	.	.	PROPN
ejpam-3955	238	5	math	math	PROPN
ejpam-3955	238	6	,	,	PUNCT
ejpam-3955	238	7	14	14	NUM
ejpam-3955	238	8	(	(	PUNCT
ejpam-3955	238	9	2	2	NUM
ejpam-3955	238	10	)	)	PUNCT
ejpam-3955	238	11	(	(	PUNCT
ejpam-3955	238	12	2021	2021	NUM
ejpam-3955	238	13	)	)	PUNCT
ejpam-3955	238	14	,	,	PUNCT
ejpam-3955	238	15	537	537	NUM
ejpam-3955	238	16	-	-	SYM
ejpam-3955	238	17	550	550	NUM
ejpam-3955	238	18	544	544	NUM
ejpam-3955	238	19	subcase	subcase	NOUN
ejpam-3955	238	20	2	2	NUM
ejpam-3955	238	21	:	:	PUNCT
ejpam-3955	238	22	consider	consider	VERB
ejpam-3955	238	23	v1	v1	NOUN
ejpam-3955	238	24	being	be	AUX
ejpam-3955	238	25	adjacent	adjacent	ADJ
ejpam-3955	238	26	to	to	ADP
ejpam-3955	238	27	both	both	PRON
ejpam-3955	238	28	u	u	NOUN
ejpam-3955	238	29	and	and	CCONJ
ejpam-3955	238	30	v	v	NOUN
ejpam-3955	238	31	and	and	CCONJ
ejpam-3955	238	32	v2	v2	NOUN
ejpam-3955	238	33	being	be	AUX
ejpam-3955	238	34	adjacent	adjacent	ADJ
ejpam-3955	238	35	only	only	ADV
ejpam-3955	238	36	to	to	ADP
ejpam-3955	238	37	either	either	CCONJ
ejpam-3955	238	38	u	u	PROPN
ejpam-3955	238	39	or	or	CCONJ
ejpam-3955	238	40	v.	v.	ADP
ejpam-3955	238	41	note	note	VERB
ejpam-3955	238	42	that	that	SCONJ
ejpam-3955	238	43	since	since	SCONJ
ejpam-3955	238	44	{	{	PUNCT
ejpam-3955	238	45	u	u	NOUN
ejpam-3955	238	46	,	,	PUNCT
ejpam-3955	238	47	v	v	NOUN
ejpam-3955	238	48	}	}	PUNCT
ejpam-3955	238	49	is	be	AUX
ejpam-3955	238	50	a	a	DET
ejpam-3955	238	51	dominating	dominating	NOUN
ejpam-3955	238	52	set	set	NOUN
ejpam-3955	238	53	in	in	ADP
ejpam-3955	238	54	g	g	PROPN
ejpam-3955	238	55	,	,	PUNCT
ejpam-3955	238	56	v3	v3	PROPN
ejpam-3955	238	57	∈	∈	PROPN
ejpam-3955	238	58	ng({u	ng({u	SYM
ejpam-3955	238	59	,	,	PUNCT
ejpam-3955	238	60	v	v	NOUN
ejpam-3955	238	61	}	}	PUNCT
ejpam-3955	238	62	)	)	PUNCT
ejpam-3955	238	63	.	.	PUNCT
ejpam-3955	239	1	if	if	SCONJ
ejpam-3955	239	2	v3	v3	PROPN
ejpam-3955	239	3	/∈	/∈	PUNCT
ejpam-3955	239	4	ng(v1	ng(v1	NOUN
ejpam-3955	239	5	)	)	PUNCT
ejpam-3955	239	6	∩ng(v2	∩ng(v2	NOUN
ejpam-3955	239	7	)	)	PUNCT
ejpam-3955	239	8	,	,	PUNCT
ejpam-3955	239	9	then	then	ADV
ejpam-3955	239	10	the	the	DET
ejpam-3955	239	11	set	set	NOUN
ejpam-3955	239	12	s∗	s∗	PROPN
ejpam-3955	239	13	=	=	SYM
ejpam-3955	239	14	{	{	PUNCT
ejpam-3955	239	15	v1	v1	PROPN
ejpam-3955	239	16	,	,	PUNCT
ejpam-3955	239	17	v2	v2	PROPN
ejpam-3955	239	18	,	,	PUNCT
ejpam-3955	239	19	v3	v3	PROPN
ejpam-3955	239	20	}	}	PUNCT
ejpam-3955	239	21	is	be	AUX
ejpam-3955	239	22	a	a	DET
ejpam-3955	239	23	cost	cost	NOUN
ejpam-3955	239	24	effective	effective	ADJ
ejpam-3955	239	25	set	set	NOUN
ejpam-3955	239	26	in	in	ADP
ejpam-3955	239	27	g	g	NOUN
ejpam-3955	239	28	,	,	PUNCT
ejpam-3955	239	29	and	and	CCONJ
ejpam-3955	239	30	one	one	PRON
ejpam-3955	239	31	can	can	AUX
ejpam-3955	239	32	construct	construct	VERB
ejpam-3955	239	33	a	a	DET
ejpam-3955	239	34	cost	cost	NOUN
ejpam-3955	239	35	effective	effective	ADJ
ejpam-3955	239	36	dominating	dominating	NOUN
ejpam-3955	239	37	set	set	NOUN
ejpam-3955	239	38	s	s	AUX
ejpam-3955	239	39	beginning	begin	VERB
ejpam-3955	239	40	with	with	ADP
ejpam-3955	239	41	s∗.	s∗.	ADJ
ejpam-3955	239	42	on	on	ADP
ejpam-3955	239	43	the	the	DET
ejpam-3955	239	44	other	other	ADJ
ejpam-3955	239	45	hand	hand	NOUN
ejpam-3955	239	46	,	,	PUNCT
ejpam-3955	239	47	if	if	SCONJ
ejpam-3955	239	48	v3	v3	PROPN
ejpam-3955	239	49	∈	∈	PROPN
ejpam-3955	239	50	ng(v1	ng(v1	NOUN
ejpam-3955	239	51	)	)	PUNCT
ejpam-3955	239	52	∩ng(v2	∩ng(v2	NOUN
ejpam-3955	239	53	)	)	PUNCT
ejpam-3955	239	54	,	,	PUNCT
ejpam-3955	239	55	then	then	ADV
ejpam-3955	239	56	the	the	DET
ejpam-3955	239	57	set	set	NOUN
ejpam-3955	239	58	s	s	PART
ejpam-3955	239	59	=	=	SYM
ejpam-3955	239	60	{	{	PUNCT
ejpam-3955	239	61	u	u	NOUN
ejpam-3955	239	62	,	,	PUNCT
ejpam-3955	239	63	v	v	NOUN
ejpam-3955	239	64	,	,	PUNCT
ejpam-3955	239	65	v3	v3	PROPN
ejpam-3955	239	66	}	}	PUNCT
ejpam-3955	239	67	is	be	AUX
ejpam-3955	239	68	a	a	DET
ejpam-3955	239	69	cost	cost	NOUN
ejpam-3955	239	70	effective	effective	ADJ
ejpam-3955	239	71	dominating	dominating	NOUN
ejpam-3955	239	72	set	set	VERB
ejpam-3955	239	73	in	in	ADP
ejpam-3955	239	74	g.	g.	PROPN
ejpam-3955	239	75	thus	thus	ADV
ejpam-3955	239	76	,	,	PUNCT
ejpam-3955	239	77	|s|	|s|	X
ejpam-3955	239	78	≥	≥	NOUN
ejpam-3955	239	79	3	3	NUM
ejpam-3955	239	80	.	.	PUNCT
ejpam-3955	239	81	subcase	subcase	PROPN
ejpam-3955	239	82	3	3	NUM
ejpam-3955	239	83	:	:	PUNCT
ejpam-3955	239	84	suppose	suppose	VERB
ejpam-3955	239	85	that	that	SCONJ
ejpam-3955	239	86	v1	v1	NOUN
ejpam-3955	239	87	,	,	PUNCT
ejpam-3955	239	88	v2	v2	PROPN
ejpam-3955	239	89	are	be	AUX
ejpam-3955	239	90	both	both	ADV
ejpam-3955	239	91	adjacent	adjacent	ADJ
ejpam-3955	239	92	to	to	ADP
ejpam-3955	239	93	u	u	NOUN
ejpam-3955	239	94	and	and	CCONJ
ejpam-3955	239	95	v.	v.	INTJ
ejpam-3955	239	96	if	if	SCONJ
ejpam-3955	239	97	v3	v3	PROPN
ejpam-3955	239	98	∈	∈	PROPN
ejpam-3955	239	99	ng(v1)∩ng(v2	ng(v1)∩ng(v2	NUM
ejpam-3955	239	100	)	)	PUNCT
ejpam-3955	239	101	,	,	PUNCT
ejpam-3955	239	102	then	then	ADV
ejpam-3955	239	103	the	the	DET
ejpam-3955	239	104	set	set	NOUN
ejpam-3955	239	105	s∗	s∗	PROPN
ejpam-3955	239	106	=	=	SYM
ejpam-3955	239	107	{	{	PUNCT
ejpam-3955	239	108	u	u	NOUN
ejpam-3955	239	109	,	,	PUNCT
ejpam-3955	239	110	v	v	NOUN
ejpam-3955	239	111	,	,	PUNCT
ejpam-3955	239	112	v3	v3	PROPN
ejpam-3955	239	113	}	}	PUNCT
ejpam-3955	239	114	is	be	AUX
ejpam-3955	239	115	a	a	DET
ejpam-3955	239	116	cost	cost	NOUN
ejpam-3955	239	117	effective	effective	ADJ
ejpam-3955	239	118	dominating	dominating	NOUN
ejpam-3955	239	119	set	set	VERB
ejpam-3955	239	120	in	in	ADP
ejpam-3955	239	121	g.	g.	PROPN
ejpam-3955	239	122	if	if	SCONJ
ejpam-3955	239	123	v3	v3	PROPN
ejpam-3955	239	124	/∈	/∈	PUNCT
ejpam-3955	239	125	ng(v1)∩ng(v2	ng(v1)∩ng(v2	NUM
ejpam-3955	239	126	)	)	PUNCT
ejpam-3955	239	127	,	,	PUNCT
ejpam-3955	239	128	then	then	ADV
ejpam-3955	239	129	one	one	PRON
ejpam-3955	239	130	can	can	AUX
ejpam-3955	239	131	start	start	VERB
ejpam-3955	239	132	with	with	ADP
ejpam-3955	239	133	the	the	DET
ejpam-3955	239	134	cost	cost	NOUN
ejpam-3955	239	135	effective	effective	ADJ
ejpam-3955	239	136	set	set	NOUN
ejpam-3955	239	137	s∗	s∗	PROPN
ejpam-3955	239	138	=	=	SYM
ejpam-3955	239	139	{	{	PUNCT
ejpam-3955	239	140	v1	v1	PROPN
ejpam-3955	239	141	,	,	PUNCT
ejpam-3955	239	142	v,2	v,2	X
ejpam-3955	239	143	,	,	PUNCT
ejpam-3955	239	144	v3	v3	PROPN
ejpam-3955	239	145	}	}	PUNCT
ejpam-3955	239	146	to	to	PART
ejpam-3955	239	147	construct	construct	VERB
ejpam-3955	239	148	a	a	DET
ejpam-3955	239	149	cost	cost	NOUN
ejpam-3955	239	150	effective	effective	ADJ
ejpam-3955	239	151	dominating	dominating	NOUN
ejpam-3955	239	152	set	set	NOUN
ejpam-3955	239	153	s	s	PROPN
ejpam-3955	239	154	in	in	ADP
ejpam-3955	239	155	g.	g.	NOUN
ejpam-3955	239	156	case	case	NOUN
ejpam-3955	239	157	2	2	NUM
ejpam-3955	239	158	:	:	PUNCT
ejpam-3955	239	159	suppose	suppose	VERB
ejpam-3955	239	160	that	that	SCONJ
ejpam-3955	239	161	v1v2	v1v2	PROPN
ejpam-3955	239	162	∈	∈	PROPN
ejpam-3955	239	163	e(g	e(g	PROPN
ejpam-3955	239	164	)	)	PUNCT
ejpam-3955	239	165	.	.	PUNCT
ejpam-3955	240	1	subcase	subcase	PROPN
ejpam-3955	240	2	1	1	NUM
ejpam-3955	240	3	:	:	PUNCT
ejpam-3955	240	4	suppose	suppose	VERB
ejpam-3955	240	5	that	that	SCONJ
ejpam-3955	240	6	v1	v1	NOUN
ejpam-3955	240	7	,	,	PUNCT
ejpam-3955	240	8	v2	v2	PROPN
ejpam-3955	240	9	are	be	AUX
ejpam-3955	240	10	adjacent	adjacent	ADJ
ejpam-3955	240	11	only	only	ADV
ejpam-3955	240	12	to	to	ADP
ejpam-3955	240	13	either	either	CCONJ
ejpam-3955	240	14	u	u	PROPN
ejpam-3955	240	15	or	or	CCONJ
ejpam-3955	240	16	v.	v.	ADP
ejpam-3955	240	17	assume	assume	VERB
ejpam-3955	240	18	that	that	SCONJ
ejpam-3955	240	19	v1	v1	NOUN
ejpam-3955	240	20	,	,	PUNCT
ejpam-3955	240	21	v2	v2	PROPN
ejpam-3955	240	22	are	be	AUX
ejpam-3955	240	23	adjacent	adjacent	ADJ
ejpam-3955	240	24	to	to	PART
ejpam-3955	240	25	u.	u.	VERB
ejpam-3955	240	26	since	since	SCONJ
ejpam-3955	240	27	the	the	DET
ejpam-3955	240	28	set	set	NOUN
ejpam-3955	240	29	s∗	s∗	PROPN
ejpam-3955	240	30	=	=	SYM
ejpam-3955	240	31	{	{	PUNCT
ejpam-3955	240	32	v1	v1	PROPN
ejpam-3955	240	33	,	,	PUNCT
ejpam-3955	240	34	v2	v2	PROPN
ejpam-3955	240	35	,	,	PUNCT
ejpam-3955	240	36	v	v	NOUN
ejpam-3955	240	37	}	}	PUNCT
ejpam-3955	240	38	is	be	AUX
ejpam-3955	240	39	a	a	DET
ejpam-3955	240	40	cost	cost	NOUN
ejpam-3955	240	41	effective	effective	ADJ
ejpam-3955	240	42	set	set	NOUN
ejpam-3955	240	43	in	in	ADP
ejpam-3955	240	44	g	g	NOUN
ejpam-3955	240	45	,	,	PUNCT
ejpam-3955	240	46	one	one	PRON
ejpam-3955	240	47	can	can	AUX
ejpam-3955	240	48	construct	construct	VERB
ejpam-3955	240	49	a	a	DET
ejpam-3955	240	50	cost	cost	NOUN
ejpam-3955	240	51	effective	effective	ADJ
ejpam-3955	240	52	dominating	dominating	NOUN
ejpam-3955	240	53	set	set	NOUN
ejpam-3955	240	54	s	s	PRON
ejpam-3955	240	55	in	in	ADP
ejpam-3955	240	56	g	g	NOUN
ejpam-3955	240	57	starting	start	VERB
ejpam-3955	240	58	with	with	ADP
ejpam-3955	240	59	s∗.	s∗.	PROPN
ejpam-3955	240	60	clearly	clearly	ADV
ejpam-3955	240	61	,	,	PUNCT
ejpam-3955	240	62	|s|	|s|	X
ejpam-3955	240	63	≥	≥	NOUN
ejpam-3955	240	64	3	3	NUM
ejpam-3955	240	65	.	.	PUNCT
ejpam-3955	240	66	subcase	subcase	PROPN
ejpam-3955	240	67	2	2	NUM
ejpam-3955	240	68	:	:	PUNCT
ejpam-3955	240	69	suppose	suppose	VERB
ejpam-3955	240	70	that	that	SCONJ
ejpam-3955	240	71	v1	v1	NOUN
ejpam-3955	240	72	is	be	AUX
ejpam-3955	240	73	adjacent	adjacent	ADJ
ejpam-3955	240	74	to	to	ADP
ejpam-3955	240	75	both	both	PRON
ejpam-3955	240	76	u	u	NOUN
ejpam-3955	240	77	and	and	CCONJ
ejpam-3955	240	78	v	v	NOUN
ejpam-3955	240	79	and	and	CCONJ
ejpam-3955	240	80	v2	v2	NOUN
ejpam-3955	240	81	is	be	AUX
ejpam-3955	240	82	adjacent	adjacent	ADJ
ejpam-3955	240	83	only	only	ADV
ejpam-3955	240	84	to	to	ADP
ejpam-3955	240	85	either	either	CCONJ
ejpam-3955	240	86	u	u	PROPN
ejpam-3955	240	87	or	or	CCONJ
ejpam-3955	240	88	v.	v.	ADP
ejpam-3955	240	89	assume	assume	VERB
ejpam-3955	240	90	that	that	SCONJ
ejpam-3955	240	91	v2	v2	PROPN
ejpam-3955	240	92	∈	∈	PROPN
ejpam-3955	240	93	ng(u	ng(u	NOUN
ejpam-3955	240	94	)	)	PUNCT
ejpam-3955	240	95	.	.	PUNCT
ejpam-3955	241	1	then	then	ADV
ejpam-3955	241	2	the	the	DET
ejpam-3955	241	3	set	set	NOUN
ejpam-3955	241	4	s	s	PART
ejpam-3955	241	5	=	=	SYM
ejpam-3955	241	6	{	{	PUNCT
ejpam-3955	241	7	u	u	NOUN
ejpam-3955	241	8	,	,	PUNCT
ejpam-3955	241	9	v	v	NOUN
ejpam-3955	241	10	,	,	PUNCT
ejpam-3955	241	11	v2	v2	PROPN
ejpam-3955	241	12	}	}	PUNCT
ejpam-3955	241	13	is	be	AUX
ejpam-3955	241	14	a	a	DET
ejpam-3955	241	15	cost	cost	NOUN
ejpam-3955	241	16	effective	effective	ADJ
ejpam-3955	241	17	dominating	dominating	NOUN
ejpam-3955	241	18	set	set	VERB
ejpam-3955	241	19	in	in	ADP
ejpam-3955	241	20	g.	g.	PROPN
ejpam-3955	241	21	subcase	subcase	PROPN
ejpam-3955	241	22	3	3	NUM
ejpam-3955	241	23	:	:	PUNCT
ejpam-3955	241	24	suppose	suppose	VERB
ejpam-3955	241	25	that	that	SCONJ
ejpam-3955	241	26	v1	v1	NOUN
ejpam-3955	241	27	,	,	PUNCT
ejpam-3955	241	28	v2	v2	PROPN
ejpam-3955	241	29	are	be	AUX
ejpam-3955	241	30	both	both	ADV
ejpam-3955	241	31	adjacent	adjacent	ADJ
ejpam-3955	241	32	to	to	ADP
ejpam-3955	241	33	u	u	NOUN
ejpam-3955	241	34	and	and	CCONJ
ejpam-3955	241	35	v.	v.	INTJ
ejpam-3955	241	36	if	if	SCONJ
ejpam-3955	241	37	v3	v3	PROPN
ejpam-3955	241	38	∈	∈	PROPN
ejpam-3955	241	39	ng(v1)∩ng(v2	ng(v1)∩ng(v2	NUM
ejpam-3955	241	40	)	)	PUNCT
ejpam-3955	241	41	,	,	PUNCT
ejpam-3955	241	42	then	then	ADV
ejpam-3955	241	43	the	the	DET
ejpam-3955	241	44	set	set	NOUN
ejpam-3955	241	45	s	s	PART
ejpam-3955	241	46	=	=	SYM
ejpam-3955	241	47	{	{	PUNCT
ejpam-3955	241	48	u	u	NOUN
ejpam-3955	241	49	,	,	PUNCT
ejpam-3955	241	50	v	v	NOUN
ejpam-3955	241	51	,	,	PUNCT
ejpam-3955	241	52	v2	v2	PROPN
ejpam-3955	241	53	}	}	PUNCT
ejpam-3955	241	54	is	be	AUX
ejpam-3955	241	55	a	a	DET
ejpam-3955	241	56	cost	cost	NOUN
ejpam-3955	241	57	effective	effective	ADJ
ejpam-3955	241	58	dominating	dominating	NOUN
ejpam-3955	241	59	set	set	VERB
ejpam-3955	241	60	in	in	ADP
ejpam-3955	241	61	g.	g.	PROPN
ejpam-3955	241	62	if	if	SCONJ
ejpam-3955	241	63	v3	v3	PROPN
ejpam-3955	241	64	/∈	/∈	PUNCT
ejpam-3955	241	65	ng(v1)∩ng(v2	ng(v1)∩ng(v2	NUM
ejpam-3955	241	66	)	)	PUNCT
ejpam-3955	241	67	,	,	PUNCT
ejpam-3955	241	68	then	then	ADV
ejpam-3955	241	69	the	the	DET
ejpam-3955	241	70	set	set	NOUN
ejpam-3955	241	71	s∗	s∗	PROPN
ejpam-3955	241	72	=	=	SYM
ejpam-3955	241	73	{	{	PUNCT
ejpam-3955	241	74	v1	v1	PROPN
ejpam-3955	241	75	,	,	PUNCT
ejpam-3955	241	76	v2	v2	PROPN
ejpam-3955	241	77	,	,	PUNCT
ejpam-3955	241	78	v3	v3	PROPN
ejpam-3955	241	79	}	}	PUNCT
ejpam-3955	241	80	is	be	AUX
ejpam-3955	241	81	a	a	DET
ejpam-3955	241	82	cost	cost	NOUN
ejpam-3955	241	83	effective	effective	ADJ
ejpam-3955	241	84	set	set	NOUN
ejpam-3955	241	85	in	in	ADP
ejpam-3955	241	86	g	g	NOUN
ejpam-3955	241	87	,	,	PUNCT
ejpam-3955	241	88	and	and	CCONJ
ejpam-3955	241	89	one	one	PRON
ejpam-3955	241	90	can	can	AUX
ejpam-3955	241	91	construct	construct	VERB
ejpam-3955	241	92	a	a	DET
ejpam-3955	241	93	cost	cost	NOUN
ejpam-3955	241	94	effective	effective	ADJ
ejpam-3955	241	95	dominating	dominating	NOUN
ejpam-3955	241	96	set	set	NOUN
ejpam-3955	241	97	s	s	PRON
ejpam-3955	241	98	in	in	ADP
ejpam-3955	241	99	g	g	NOUN
ejpam-3955	241	100	starting	start	VERB
ejpam-3955	241	101	with	with	ADP
ejpam-3955	241	102	s∗.	s∗.	ADJ
ejpam-3955	241	103	in	in	ADP
ejpam-3955	241	104	both	both	DET
ejpam-3955	241	105	cases	case	NOUN
ejpam-3955	241	106	,	,	PUNCT
ejpam-3955	241	107	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	241	108	)	)	PUNCT
ejpam-3955	241	109	≥	≥	NOUN
ejpam-3955	241	110	3	3	NUM
ejpam-3955	241	111	.	.	PUNCT
ejpam-3955	241	112	corollary	corollary	ADJ
ejpam-3955	241	113	6	6	NUM
ejpam-3955	241	114	.	.	PUNCT
ejpam-3955	242	1	if	if	SCONJ
ejpam-3955	242	2	g	g	PROPN
ejpam-3955	242	3	is	be	AUX
ejpam-3955	242	4	a	a	DET
ejpam-3955	242	5	connected	connected	ADJ
ejpam-3955	242	6	graph	graph	NOUN
ejpam-3955	242	7	of	of	ADP
ejpam-3955	242	8	order	order	NOUN
ejpam-3955	242	9	n	n	PRON
ejpam-3955	242	10	≥	≥	NOUN
ejpam-3955	242	11	3	3	NUM
ejpam-3955	242	12	,	,	PUNCT
ejpam-3955	242	13	then	then	ADV
ejpam-3955	242	14	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	242	15	)	)	PUNCT
ejpam-3955	242	16	=	=	SYM
ejpam-3955	242	17	2	2	NUM
ejpam-3955	242	18	if	if	SCONJ
ejpam-3955	242	19	and	and	CCONJ
ejpam-3955	242	20	only	only	ADV
ejpam-3955	242	21	if	if	SCONJ
ejpam-3955	242	22	g	g	PROPN
ejpam-3955	242	23	is	be	AUX
ejpam-3955	242	24	one	one	NUM
ejpam-3955	242	25	of	of	ADP
ejpam-3955	242	26	the	the	DET
ejpam-3955	242	27	following	follow	VERB
ejpam-3955	242	28	graphs	graph	NOUN
ejpam-3955	242	29	:	:	PUNCT
ejpam-3955	242	30	p3	p3	NOUN
ejpam-3955	242	31	,	,	PUNCT
ejpam-3955	242	32	p4	p4	ADJ
ejpam-3955	242	33	,	,	PUNCT
ejpam-3955	242	34	c3	c3	PROPN
ejpam-3955	242	35	,	,	PUNCT
ejpam-3955	242	36	c4	c4	NOUN
ejpam-3955	242	37	,	,	PUNCT
ejpam-3955	242	38	k4	k4	NOUN
ejpam-3955	242	39	or	or	CCONJ
ejpam-3955	242	40	k2	k2	NOUN
ejpam-3955	242	41	+	+	NOUN
ejpam-3955	242	42	k2	k2	ADJ
ejpam-3955	242	43	.	.	PUNCT
ejpam-3955	243	1	proof	proof	NOUN
ejpam-3955	243	2	.	.	PUNCT
ejpam-3955	244	1	suppose	suppose	VERB
ejpam-3955	244	2	that	that	SCONJ
ejpam-3955	244	3	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	244	4	)	)	PUNCT
ejpam-3955	244	5	=	=	SYM
ejpam-3955	244	6	2	2	NUM
ejpam-3955	244	7	and	and	CCONJ
ejpam-3955	244	8	let	let	VERB
ejpam-3955	244	9	s	s	PRON
ejpam-3955	244	10	=	=	PUNCT
ejpam-3955	244	11	{	{	PUNCT
ejpam-3955	244	12	u	u	NOUN
ejpam-3955	244	13	,	,	PUNCT
ejpam-3955	244	14	v	v	NOUN
ejpam-3955	244	15	}	}	PUNCT
ejpam-3955	244	16	be	be	AUX
ejpam-3955	244	17	a	a	DET
ejpam-3955	244	18	γ+ce	γ+ce	NOUN
ejpam-3955	244	19	-	-	PUNCT
ejpam-3955	244	20	set	set	VERB
ejpam-3955	244	21	in	in	ADP
ejpam-3955	244	22	g.	g.	PROPN
ejpam-3955	244	23	let	let	VERB
ejpam-3955	244	24	d	d	PROPN
ejpam-3955	244	25	=	=	SYM
ejpam-3955	244	26	v	v	PROPN
ejpam-3955	244	27	(	(	PUNCT
ejpam-3955	244	28	g)\s	g)\s	NOUN
ejpam-3955	244	29	.	.	PUNCT
ejpam-3955	245	1	if	if	SCONJ
ejpam-3955	245	2	|d|	|d|	PROPN
ejpam-3955	245	3	=	=	SYM
ejpam-3955	245	4	1	1	NUM
ejpam-3955	245	5	,	,	PUNCT
ejpam-3955	245	6	then	then	ADV
ejpam-3955	245	7	either	either	CCONJ
ejpam-3955	245	8	g	g	PROPN
ejpam-3955	245	9	=	=	PROPN
ejpam-3955	245	10	c3	c3	PROPN
ejpam-3955	245	11	or	or	CCONJ
ejpam-3955	245	12	g	g	PROPN
ejpam-3955	245	13	=	=	PROPN
ejpam-3955	245	14	p3	p3	PROPN
ejpam-3955	245	15	.	.	PUNCT
ejpam-3955	246	1	if	if	SCONJ
ejpam-3955	246	2	|d|	|d|	PROPN
ejpam-3955	246	3	=	=	SYM
ejpam-3955	246	4	2	2	NUM
ejpam-3955	246	5	,	,	PUNCT
ejpam-3955	246	6	then	then	ADV
ejpam-3955	246	7	g	g	PROPN
ejpam-3955	246	8	is	be	AUX
ejpam-3955	246	9	any	any	PRON
ejpam-3955	246	10	of	of	ADP
ejpam-3955	246	11	the	the	DET
ejpam-3955	246	12	following	following	NOUN
ejpam-3955	246	13	:	:	PUNCT
ejpam-3955	246	14	p4	p4	ADJ
ejpam-3955	246	15	,	,	PUNCT
ejpam-3955	246	16	c4	c4	NOUN
ejpam-3955	246	17	,	,	PUNCT
ejpam-3955	246	18	k2	k2	PROPN
ejpam-3955	246	19	+	+	PROPN
ejpam-3955	246	20	k2	k2	ADJ
ejpam-3955	246	21	,	,	PUNCT
ejpam-3955	246	22	or	or	CCONJ
ejpam-3955	246	23	k4	k4	PROPN
ejpam-3955	246	24	.	.	PUNCT
ejpam-3955	246	25	suppose	suppose	VERB
ejpam-3955	247	1	that	that	SCONJ
ejpam-3955	247	2	|d|	|d|	PROPN
ejpam-3955	247	3	≥	≥	NUM
ejpam-3955	247	4	3	3	NUM
ejpam-3955	247	5	.	.	PUNCT
ejpam-3955	247	6	then	then	ADV
ejpam-3955	247	7	|v	|v	PROPN
ejpam-3955	247	8	(	(	PUNCT
ejpam-3955	247	9	g)|	g)|	X
ejpam-3955	247	10	≥	≥	NOUN
ejpam-3955	247	11	5	5	NUM
ejpam-3955	247	12	.	.	PUNCT
ejpam-3955	247	13	by	by	ADP
ejpam-3955	247	14	theorem	theorem	NOUN
ejpam-3955	247	15	9	9	NUM
ejpam-3955	247	16	,	,	PUNCT
ejpam-3955	247	17	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	247	18	)	)	PUNCT
ejpam-3955	247	19	>	>	X
ejpam-3955	248	1	2	2	NUM
ejpam-3955	248	2	,	,	PUNCT
ejpam-3955	248	3	and	and	CCONJ
ejpam-3955	248	4	the	the	DET
ejpam-3955	248	5	desired	desire	VERB
ejpam-3955	248	6	conclusion	conclusion	NOUN
ejpam-3955	248	7	follows	follow	VERB
ejpam-3955	248	8	.	.	PUNCT
ejpam-3955	249	1	for	for	ADP
ejpam-3955	249	2	the	the	DET
ejpam-3955	249	3	converse	converse	NOUN
ejpam-3955	249	4	,	,	PUNCT
ejpam-3955	249	5	it	it	PRON
ejpam-3955	249	6	is	be	AUX
ejpam-3955	249	7	easy	easy	ADJ
ejpam-3955	249	8	to	to	PART
ejpam-3955	249	9	verify	verify	VERB
ejpam-3955	249	10	that	that	SCONJ
ejpam-3955	249	11	if	if	SCONJ
ejpam-3955	249	12	g	g	PROPN
ejpam-3955	249	13	is	be	AUX
ejpam-3955	249	14	one	one	NUM
ejpam-3955	249	15	of	of	ADP
ejpam-3955	249	16	the	the	DET
ejpam-3955	249	17	following	follow	VERB
ejpam-3955	249	18	graphs	graph	NOUN
ejpam-3955	249	19	:	:	PUNCT
ejpam-3955	249	20	p3	p3	NOUN
ejpam-3955	249	21	,	,	PUNCT
ejpam-3955	249	22	p4	p4	ADJ
ejpam-3955	249	23	,	,	PUNCT
ejpam-3955	249	24	c3	c3	PROPN
ejpam-3955	249	25	,	,	PUNCT
ejpam-3955	249	26	c4	c4	NOUN
ejpam-3955	249	27	,	,	PUNCT
ejpam-3955	249	28	k2	k2	PROPN
ejpam-3955	249	29	+	+	PROPN
ejpam-3955	249	30	k2	k2	ADJ
ejpam-3955	249	31	,	,	PUNCT
ejpam-3955	249	32	or	or	CCONJ
ejpam-3955	249	33	k4	k4	NOUN
ejpam-3955	249	34	,	,	PUNCT
ejpam-3955	249	35	then	then	ADV
ejpam-3955	249	36	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	249	37	)	)	PUNCT
ejpam-3955	250	1	=	=	SYM
ejpam-3955	250	2	2	2	X
ejpam-3955	250	3	.	.	X
ejpam-3955	250	4	theorem	theorem	NOUN
ejpam-3955	250	5	10	10	NUM
ejpam-3955	250	6	.	.	PUNCT
ejpam-3955	251	1	let	let	VERB
ejpam-3955	251	2	g	g	PRON
ejpam-3955	251	3	be	be	AUX
ejpam-3955	251	4	a	a	DET
ejpam-3955	251	5	connected	connected	ADJ
ejpam-3955	251	6	noncomplete	noncomplete	ADJ
ejpam-3955	251	7	graph	graph	NOUN
ejpam-3955	251	8	.	.	PUNCT
ejpam-3955	252	1	(	(	PUNCT
ejpam-3955	252	2	i	i	NOUN
ejpam-3955	252	3	)	)	PUNCT
ejpam-3955	252	4	if	if	SCONJ
ejpam-3955	252	5	γm(g	γm(g	NUM
ejpam-3955	252	6	)	)	PUNCT
ejpam-3955	252	7	=	=	SYM
ejpam-3955	252	8	2	2	NUM
ejpam-3955	252	9	,	,	PUNCT
ejpam-3955	252	10	then	then	ADV
ejpam-3955	252	11	γmce(g	γmce(g	PROPN
ejpam-3955	252	12	)	)	PUNCT
ejpam-3955	252	13	=	=	SYM
ejpam-3955	252	14	2	2	X
ejpam-3955	252	15	.	.	PUNCT
ejpam-3955	252	16	(	(	PUNCT
ejpam-3955	252	17	ii	ii	NOUN
ejpam-3955	252	18	)	)	PUNCT
ejpam-3955	252	19	if	if	SCONJ
ejpam-3955	252	20	γmce(g	γmce(g	NOUN
ejpam-3955	252	21	)	)	PUNCT
ejpam-3955	253	1	=	=	SYM
ejpam-3955	253	2	2	2	NUM
ejpam-3955	253	3	,	,	PUNCT
ejpam-3955	253	4	then	then	ADV
ejpam-3955	253	5	for	for	ADP
ejpam-3955	253	6	each	each	DET
ejpam-3955	253	7	pair	pair	NOUN
ejpam-3955	253	8	of	of	ADP
ejpam-3955	253	9	nonadjacent	nonadjacent	NOUN
ejpam-3955	253	10	vertices	vertex	NOUN
ejpam-3955	253	11	u	u	NOUN
ejpam-3955	253	12	and	and	CCONJ
ejpam-3955	253	13	v	v	NOUN
ejpam-3955	253	14	of	of	ADP
ejpam-3955	253	15	g	g	NOUN
ejpam-3955	253	16	,	,	PUNCT
ejpam-3955	253	17	{	{	PUNCT
ejpam-3955	253	18	u	u	NOUN
ejpam-3955	253	19	,	,	PUNCT
ejpam-3955	253	20	v	v	NOUN
ejpam-3955	253	21	}	}	PUNCT
ejpam-3955	253	22	is	be	AUX
ejpam-3955	253	23	a	a	DET
ejpam-3955	253	24	dominating	dominating	NOUN
ejpam-3955	253	25	set	set	VERB
ejpam-3955	253	26	in	in	ADP
ejpam-3955	253	27	g	g	NOUN
ejpam-3955	253	28	proof	proof	NOUN
ejpam-3955	253	29	.	.	PUNCT
ejpam-3955	254	1	for	for	ADP
ejpam-3955	254	2	(	(	PUNCT
ejpam-3955	254	3	i	i	NOUN
ejpam-3955	254	4	)	)	PUNCT
ejpam-3955	254	5	,	,	PUNCT
ejpam-3955	254	6	observe	observe	VERB
ejpam-3955	254	7	that	that	SCONJ
ejpam-3955	254	8	by	by	ADP
ejpam-3955	254	9	theorem	theorem	ADJ
ejpam-3955	254	10	4	4	NUM
ejpam-3955	254	11	and	and	CCONJ
ejpam-3955	254	12	corollary	corollary	ADJ
ejpam-3955	254	13	2	2	NUM
ejpam-3955	254	14	,	,	PUNCT
ejpam-3955	254	15	2	2	NUM
ejpam-3955	254	16	≤	≤	NUM
ejpam-3955	254	17	γmce(g	γmce(g	PROPN
ejpam-3955	254	18	)	)	PUNCT
ejpam-3955	254	19	≤	≤	NUM
ejpam-3955	254	20	2	2	NUM
ejpam-3955	254	21	.	.	PUNCT
ejpam-3955	255	1	thus	thus	ADV
ejpam-3955	255	2	,	,	PUNCT
ejpam-3955	255	3	γmce(g	γmce(g	PROPN
ejpam-3955	255	4	)	)	PUNCT
ejpam-3955	255	5	=	=	SYM
ejpam-3955	256	1	2	2	X
ejpam-3955	256	2	.	.	PUNCT
ejpam-3955	256	3	to	to	PART
ejpam-3955	256	4	prove	prove	VERB
ejpam-3955	256	5	(	(	PUNCT
ejpam-3955	256	6	ii	ii	NOUN
ejpam-3955	256	7	)	)	PUNCT
ejpam-3955	256	8	,	,	PUNCT
ejpam-3955	256	9	suppose	suppose	VERB
ejpam-3955	256	10	that	that	SCONJ
ejpam-3955	256	11	γmce(g	γmce(g	NOUN
ejpam-3955	256	12	)	)	PUNCT
ejpam-3955	256	13	=	=	SYM
ejpam-3955	256	14	2	2	NUM
ejpam-3955	256	15	and	and	CCONJ
ejpam-3955	256	16	let	let	VERB
ejpam-3955	256	17	u	u	NOUN
ejpam-3955	256	18	,	,	PUNCT
ejpam-3955	256	19	v	v	PROPN
ejpam-3955	256	20	∈	∈	PROPN
ejpam-3955	256	21	v	v	NOUN
ejpam-3955	256	22	(	(	PUNCT
ejpam-3955	256	23	g	g	NOUN
ejpam-3955	256	24	)	)	PUNCT
ejpam-3955	256	25	with	with	ADP
ejpam-3955	256	26	uv	uv	PROPN
ejpam-3955	256	27	/∈	/∈	PUNCT
ejpam-3955	256	28	e(g	e(g	PROPN
ejpam-3955	256	29	)	)	PUNCT
ejpam-3955	256	30	.	.	PUNCT
ejpam-3955	257	1	then	then	ADV
ejpam-3955	257	2	{	{	PUNCT
ejpam-3955	257	3	u	u	NOUN
ejpam-3955	257	4	,	,	PUNCT
ejpam-3955	257	5	v	v	NOUN
ejpam-3955	257	6	}	}	PUNCT
ejpam-3955	257	7	is	be	AUX
ejpam-3955	257	8	a	a	DET
ejpam-3955	257	9	cost	cost	NOUN
ejpam-3955	257	10	effective	effective	ADJ
ejpam-3955	257	11	set	set	NOUN
ejpam-3955	257	12	in	in	ADP
ejpam-3955	257	13	g	g	NOUN
ejpam-3955	257	14	,	,	PUNCT
ejpam-3955	257	15	and	and	CCONJ
ejpam-3955	257	16	as	as	SCONJ
ejpam-3955	257	17	previously	previously	ADV
ejpam-3955	257	18	done	do	VERB
ejpam-3955	257	19	,	,	PUNCT
ejpam-3955	257	20	one	one	PRON
ejpam-3955	257	21	can	can	AUX
ejpam-3955	257	22	h.	h.	PROPN
ejpam-3955	257	23	nuenay	nuenay	PROPN
ejpam-3955	257	24	-	-	PUNCT
ejpam-3955	257	25	maglanque	maglanque	ADJ
ejpam-3955	257	26	,	,	PUNCT
ejpam-3955	257	27	f.jamil	f.jamil	PROPN
ejpam-3955	257	28	/	/	SYM
ejpam-3955	257	29	eur	eur	PROPN
ejpam-3955	257	30	.	.	PUNCT
ejpam-3955	258	1	j.	j.	PROPN
ejpam-3955	258	2	pure	pure	PROPN
ejpam-3955	258	3	appl	appl	PROPN
ejpam-3955	258	4	.	.	PROPN
ejpam-3955	258	5	math	math	PROPN
ejpam-3955	258	6	,	,	PUNCT
ejpam-3955	258	7	14	14	NUM
ejpam-3955	258	8	(	(	PUNCT
ejpam-3955	258	9	2	2	NUM
ejpam-3955	258	10	)	)	PUNCT
ejpam-3955	258	11	(	(	PUNCT
ejpam-3955	258	12	2021	2021	NUM
ejpam-3955	258	13	)	)	PUNCT
ejpam-3955	258	14	,	,	PUNCT
ejpam-3955	258	15	537	537	NUM
ejpam-3955	258	16	-	-	SYM
ejpam-3955	258	17	550	550	NUM
ejpam-3955	258	18	545	545	NUM
ejpam-3955	258	19	construct	construct	VERB
ejpam-3955	258	20	a	a	DET
ejpam-3955	258	21	minimal	minimal	ADJ
ejpam-3955	258	22	cost	cost	NOUN
ejpam-3955	258	23	effective	effective	ADJ
ejpam-3955	258	24	dominating	dominating	NOUN
ejpam-3955	258	25	set	set	NOUN
ejpam-3955	258	26	s	s	PRON
ejpam-3955	258	27	in	in	ADP
ejpam-3955	258	28	g	g	NOUN
ejpam-3955	258	29	beginning	begin	VERB
ejpam-3955	258	30	with	with	ADP
ejpam-3955	258	31	the	the	DET
ejpam-3955	258	32	vertices	vertex	NOUN
ejpam-3955	258	33	u	u	NOUN
ejpam-3955	258	34	and	and	CCONJ
ejpam-3955	258	35	v.	v.	NOUN
ejpam-3955	258	36	since	since	SCONJ
ejpam-3955	258	37	γmce(g	γmce(g	PROPN
ejpam-3955	258	38	)	)	PUNCT
ejpam-3955	258	39	=	=	SYM
ejpam-3955	258	40	2	2	NUM
ejpam-3955	258	41	,	,	PUNCT
ejpam-3955	258	42	|s|	|s|	NOUN
ejpam-3955	258	43	=	=	SYM
ejpam-3955	258	44	2	2	NUM
ejpam-3955	258	45	and	and	CCONJ
ejpam-3955	258	46	s	s	NOUN
ejpam-3955	258	47	=	=	PUNCT
ejpam-3955	258	48	{	{	PUNCT
ejpam-3955	258	49	u	u	NOUN
ejpam-3955	258	50	,	,	PUNCT
ejpam-3955	258	51	v	v	NOUN
ejpam-3955	258	52	}	}	PUNCT
ejpam-3955	258	53	.	.	PUNCT
ejpam-3955	259	1	thus	thus	ADV
ejpam-3955	259	2	,	,	PUNCT
ejpam-3955	259	3	s	s	VERB
ejpam-3955	259	4	=	=	PUNCT
ejpam-3955	259	5	{	{	PUNCT
ejpam-3955	259	6	u	u	NOUN
ejpam-3955	259	7	,	,	PUNCT
ejpam-3955	259	8	v	v	NOUN
ejpam-3955	259	9	}	}	PUNCT
ejpam-3955	259	10	is	be	AUX
ejpam-3955	259	11	a	a	DET
ejpam-3955	259	12	dominating	dominating	NOUN
ejpam-3955	259	13	set	set	VERB
ejpam-3955	259	14	in	in	ADP
ejpam-3955	259	15	g.	g.	PROPN
ejpam-3955	259	16	remark	remark	PROPN
ejpam-3955	259	17	4	4	NUM
ejpam-3955	259	18	.	.	PUNCT
ejpam-3955	260	1	the	the	DET
ejpam-3955	260	2	converse	converse	NOUN
ejpam-3955	260	3	of	of	ADP
ejpam-3955	260	4	each	each	PRON
ejpam-3955	260	5	of	of	ADP
ejpam-3955	260	6	the	the	DET
ejpam-3955	260	7	statements	statement	NOUN
ejpam-3955	260	8	in	in	ADP
ejpam-3955	260	9	theorem	theorem	NOUN
ejpam-3955	260	10	10	10	NUM
ejpam-3955	260	11	need	need	AUX
ejpam-3955	260	12	not	not	PART
ejpam-3955	260	13	be	be	AUX
ejpam-3955	260	14	true	true	ADJ
ejpam-3955	260	15	.	.	PUNCT
ejpam-3955	261	1	example	example	NOUN
ejpam-3955	262	1	1	1	NUM
ejpam-3955	262	2	.	.	PUNCT
ejpam-3955	262	3	let	let	VERB
ejpam-3955	262	4	g	g	PRON
ejpam-3955	262	5	be	be	AUX
ejpam-3955	262	6	a	a	DET
ejpam-3955	262	7	noncomplete	noncomplete	ADJ
ejpam-3955	262	8	connected	connect	VERB
ejpam-3955	262	9	graph	graph	NOUN
ejpam-3955	262	10	of	of	ADP
ejpam-3955	262	11	order	order	NOUN
ejpam-3955	262	12	n	n	PRON
ejpam-3955	262	13	≥	≥	NOUN
ejpam-3955	262	14	3	3	NUM
ejpam-3955	262	15	.	.	PUNCT
ejpam-3955	263	1	then	then	ADV
ejpam-3955	263	2	γmce(g	γmce(g	ADV
ejpam-3955	263	3	)	)	PUNCT
ejpam-3955	263	4	=	=	SYM
ejpam-3955	263	5	2	2	NUM
ejpam-3955	263	6	if	if	SCONJ
ejpam-3955	263	7	g	g	PROPN
ejpam-3955	263	8	is	be	AUX
ejpam-3955	263	9	any	any	PRON
ejpam-3955	263	10	of	of	ADP
ejpam-3955	263	11	the	the	DET
ejpam-3955	263	12	following	following	NOUN
ejpam-3955	263	13	:	:	PUNCT
ejpam-3955	263	14	(	(	PUNCT
ejpam-3955	263	15	i	i	NOUN
ejpam-3955	263	16	)	)	PUNCT
ejpam-3955	263	17	g	g	PROPN
ejpam-3955	263	18	=	=	SYM
ejpam-3955	263	19	k2	k2	PROPN
ejpam-3955	263	20	+	+	PROPN
ejpam-3955	263	21	kn	kn	PROPN
ejpam-3955	263	22	,	,	PUNCT
ejpam-3955	263	23	n	n	PRON
ejpam-3955	263	24	≥	≥	NOUN
ejpam-3955	263	25	1	1	NUM
ejpam-3955	263	26	;	;	PUNCT
ejpam-3955	263	27	(	(	PUNCT
ejpam-3955	263	28	ii	ii	NOUN
ejpam-3955	263	29	)	)	PUNCT
ejpam-3955	263	30	g	g	NOUN
ejpam-3955	263	31	is	be	AUX
ejpam-3955	263	32	obtained	obtain	VERB
ejpam-3955	263	33	from	from	ADP
ejpam-3955	263	34	kn	kn	PROPN
ejpam-3955	263	35	by	by	ADP
ejpam-3955	263	36	adding	add	VERB
ejpam-3955	263	37	a	a	DET
ejpam-3955	263	38	pendant	pendant	ADJ
ejpam-3955	263	39	edge	edge	NOUN
ejpam-3955	263	40	where	where	SCONJ
ejpam-3955	263	41	n	n	PRON
ejpam-3955	263	42	≥	≥	NOUN
ejpam-3955	263	43	2	2	NUM
ejpam-3955	263	44	;	;	PUNCT
ejpam-3955	263	45	or	or	CCONJ
ejpam-3955	263	46	(	(	PUNCT
ejpam-3955	263	47	iii	iii	X
ejpam-3955	263	48	)	)	PUNCT
ejpam-3955	263	49	g	g	NOUN
ejpam-3955	263	50	is	be	AUX
ejpam-3955	263	51	the	the	DET
ejpam-3955	263	52	k2	k2	NOUN
ejpam-3955	263	53	-	-	PUNCT
ejpam-3955	263	54	gluing	gluing	NOUN
ejpam-3955	263	55	of	of	ADP
ejpam-3955	263	56	k3	k3	NOUN
ejpam-3955	263	57	and	and	CCONJ
ejpam-3955	263	58	kn	kn	PROPN
ejpam-3955	263	59	,	,	PUNCT
ejpam-3955	263	60	n	n	PRON
ejpam-3955	263	61	≥	≥	NOUN
ejpam-3955	263	62	3	3	NUM
ejpam-3955	263	63	.	.	NOUN
ejpam-3955	263	64	2.1	2.1	NUM
ejpam-3955	263	65	.	.	PUNCT
ejpam-3955	264	1	nordhauss	nordhauss	ADJ
ejpam-3955	264	2	-	-	PUNCT
ejpam-3955	264	3	gaddum	gaddum	NOUN
ejpam-3955	264	4	type	type	NOUN
ejpam-3955	264	5	results	result	NOUN
ejpam-3955	264	6	remark	remark	VERB
ejpam-3955	264	7	5	5	NUM
ejpam-3955	264	8	.	.	PUNCT
ejpam-3955	265	1	following	follow	VERB
ejpam-3955	265	2	a	a	DET
ejpam-3955	265	3	similar	similar	ADJ
ejpam-3955	265	4	proof	proof	NOUN
ejpam-3955	265	5	,	,	PUNCT
ejpam-3955	265	6	the	the	DET
ejpam-3955	265	7	statement	statement	NOUN
ejpam-3955	265	8	in	in	ADP
ejpam-3955	265	9	corollary	corollary	ADJ
ejpam-3955	265	10	1	1	NUM
ejpam-3955	265	11	remains	remain	VERB
ejpam-3955	265	12	true	true	ADJ
ejpam-3955	265	13	if	if	SCONJ
ejpam-3955	265	14	γce(g	γce(g	PROPN
ejpam-3955	265	15	)	)	PUNCT
ejpam-3955	265	16	is	be	AUX
ejpam-3955	265	17	changed	change	VERB
ejpam-3955	265	18	to	to	ADP
ejpam-3955	265	19	γce(g)+	γce(g)+	PROPN
ejpam-3955	265	20	or	or	CCONJ
ejpam-3955	265	21	γmce(g	γmce(g	PROPN
ejpam-3955	265	22	)	)	PUNCT
ejpam-3955	265	23	.	.	PUNCT
ejpam-3955	266	1	let	let	VERB
ejpam-3955	266	2	ξ	ξ	X
ejpam-3955	266	3	be	be	AUX
ejpam-3955	266	4	an	an	DET
ejpam-3955	266	5	infinite	infinite	ADJ
ejpam-3955	266	6	collection	collection	NOUN
ejpam-3955	266	7	of	of	ADP
ejpam-3955	266	8	all	all	DET
ejpam-3955	266	9	connected	connected	ADJ
ejpam-3955	266	10	graph	graph	NOUN
ejpam-3955	266	11	g	g	ADP
ejpam-3955	266	12	such	such	ADJ
ejpam-3955	266	13	that	that	SCONJ
ejpam-3955	266	14	g	g	PROPN
ejpam-3955	266	15	is	be	AUX
ejpam-3955	266	16	also	also	ADV
ejpam-3955	266	17	connected	connect	VERB
ejpam-3955	266	18	.	.	PUNCT
ejpam-3955	267	1	theorem	theorem	VERB
ejpam-3955	267	2	11	11	NUM
ejpam-3955	267	3	.	.	PUNCT
ejpam-3955	268	1	for	for	ADP
ejpam-3955	268	2	all	all	PRON
ejpam-3955	268	3	g	g	PROPN
ejpam-3955	268	4	∈	∈	PROPN
ejpam-3955	268	5	ξ	ξ	NOUN
ejpam-3955	268	6	of	of	ADP
ejpam-3955	268	7	order	order	NOUN
ejpam-3955	268	8	n	n	DET
ejpam-3955	268	9	≥	≥	NOUN
ejpam-3955	268	10	4	4	NUM
ejpam-3955	268	11	,	,	PUNCT
ejpam-3955	268	12	(	(	PUNCT
ejpam-3955	268	13	i	i	NOUN
ejpam-3955	268	14	)	)	PUNCT
ejpam-3955	268	15	4	4	NUM
ejpam-3955	268	16	≤	≤	NUM
ejpam-3955	268	17	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	268	18	)	)	PUNCT
ejpam-3955	268	19	+	+	CCONJ
ejpam-3955	268	20	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	268	21	)	)	PUNCT
ejpam-3955	268	22	≤	≤	NOUN
ejpam-3955	269	1	2n−	2n−	NUM
ejpam-3955	269	2	4	4	NUM
ejpam-3955	269	3	;	;	PUNCT
ejpam-3955	269	4	and	and	CCONJ
ejpam-3955	269	5	(	(	PUNCT
ejpam-3955	269	6	ii	ii	NOUN
ejpam-3955	269	7	)	)	PUNCT
ejpam-3955	269	8	4	4	NUM
ejpam-3955	269	9	≤	≤	NUM
ejpam-3955	269	10	γ+ce(g)γ+ce(g	γ+ce(g)γ+ce(g	PROPN
ejpam-3955	269	11	)	)	PUNCT
ejpam-3955	269	12	≤	≤	NUM
ejpam-3955	269	13	n2	n2	NOUN
ejpam-3955	269	14	−	−	PROPN
ejpam-3955	269	15	4n+	4n+	NUM
ejpam-3955	269	16	4	4	X
ejpam-3955	269	17	.	.	PUNCT
ejpam-3955	270	1	in	in	ADP
ejpam-3955	270	2	particular	particular	ADJ
ejpam-3955	270	3	,	,	PUNCT
ejpam-3955	270	4	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	270	5	)	)	PUNCT
ejpam-3955	270	6	+	+	CCONJ
ejpam-3955	270	7	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	270	8	)	)	PUNCT
ejpam-3955	270	9	=	=	PUNCT
ejpam-3955	270	10	4	4	NUM
ejpam-3955	270	11	if	if	SCONJ
ejpam-3955	270	12	and	and	CCONJ
ejpam-3955	270	13	only	only	ADV
ejpam-3955	270	14	if	if	SCONJ
ejpam-3955	270	15	n	n	NOUN
ejpam-3955	270	16	=	=	SYM
ejpam-3955	270	17	4	4	NUM
ejpam-3955	270	18	,	,	PUNCT
ejpam-3955	270	19	and	and	CCONJ
ejpam-3955	270	20	γ+ce(g)γ+ce(g	γ+ce(g)γ+ce(g	NOUN
ejpam-3955	270	21	)	)	PUNCT
ejpam-3955	271	1	=	=	SYM
ejpam-3955	271	2	4	4	NUM
ejpam-3955	271	3	if	if	SCONJ
ejpam-3955	271	4	and	and	CCONJ
ejpam-3955	271	5	only	only	ADV
ejpam-3955	271	6	if	if	SCONJ
ejpam-3955	271	7	n	n	NOUN
ejpam-3955	271	8	=	=	SYM
ejpam-3955	271	9	4	4	X
ejpam-3955	271	10	.	.	PUNCT
ejpam-3955	272	1	proof	proof	NOUN
ejpam-3955	272	2	.	.	PUNCT
ejpam-3955	273	1	let	let	VERB
ejpam-3955	273	2	g	g	PROPN
ejpam-3955	273	3	∈	∈	PROPN
ejpam-3955	273	4	ξ	ξ	X
ejpam-3955	273	5	be	be	NOUN
ejpam-3955	273	6	of	of	ADP
ejpam-3955	273	7	order	order	NOUN
ejpam-3955	273	8	n	n	PRON
ejpam-3955	273	9	≥	≥	NOUN
ejpam-3955	273	10	4	4	NUM
ejpam-3955	273	11	.	.	PUNCT
ejpam-3955	273	12	by	by	ADP
ejpam-3955	273	13	theorem	theorem	NOUN
ejpam-3955	273	14	8	8	NUM
ejpam-3955	273	15	and	and	CCONJ
ejpam-3955	273	16	remark	remark	NOUN
ejpam-3955	273	17	5	5	NUM
ejpam-3955	273	18	,	,	PUNCT
ejpam-3955	273	19	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	273	20	)	)	PUNCT
ejpam-3955	273	21	6=	6=	ADP
ejpam-3955	274	1	n	n	PROPN
ejpam-3955	274	2	and	and	CCONJ
ejpam-3955	274	3	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	274	4	)	)	PUNCT
ejpam-3955	275	1	6=	6=	VERB
ejpam-3955	275	2	n−	n−	NOUN
ejpam-3955	275	3	1	1	NUM
ejpam-3955	275	4	.	.	PUNCT
ejpam-3955	276	1	thus	thus	ADV
ejpam-3955	276	2	,	,	PUNCT
ejpam-3955	276	3	theorem	theorem	VERB
ejpam-3955	276	4	4	4	NUM
ejpam-3955	276	5	yield	yield	VERB
ejpam-3955	276	6	4	4	NUM
ejpam-3955	276	7	≤	≤	NUM
ejpam-3955	276	8	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	276	9	)	)	PUNCT
ejpam-3955	277	1	+	+	CCONJ
ejpam-3955	277	2	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	277	3	)	)	PUNCT
ejpam-3955	277	4	≤	≤	NOUN
ejpam-3955	277	5	(	(	PUNCT
ejpam-3955	277	6	n−	n−	NOUN
ejpam-3955	277	7	2	2	NUM
ejpam-3955	277	8	)	)	PUNCT
ejpam-3955	278	1	+	+	CCONJ
ejpam-3955	278	2	(	(	PUNCT
ejpam-3955	278	3	n−	n−	NOUN
ejpam-3955	278	4	2	2	NUM
ejpam-3955	278	5	)	)	PUNCT
ejpam-3955	278	6	=	=	PUNCT
ejpam-3955	279	1	2n−	2n−	NUM
ejpam-3955	279	2	4	4	NUM
ejpam-3955	279	3	and	and	CCONJ
ejpam-3955	279	4	4	4	NUM
ejpam-3955	279	5	=	=	SYM
ejpam-3955	279	6	(	(	PUNCT
ejpam-3955	279	7	2)(2	2)(2	NUM
ejpam-3955	279	8	)	)	PUNCT
ejpam-3955	279	9	≤	≤	NUM
ejpam-3955	279	10	γ+ce(g)γ+ce(g	γ+ce(g)γ+ce(g	NOUN
ejpam-3955	279	11	)	)	PUNCT
ejpam-3955	279	12	≤	≤	NOUN
ejpam-3955	280	1	(	(	PUNCT
ejpam-3955	280	2	n−	n−	NOUN
ejpam-3955	280	3	2)(n−	2)(n−	NUM
ejpam-3955	280	4	2	2	NUM
ejpam-3955	280	5	)	)	PUNCT
ejpam-3955	280	6	=	=	SYM
ejpam-3955	280	7	n2	n2	NOUN
ejpam-3955	280	8	−	−	PROPN
ejpam-3955	280	9	4n+	4n+	NUM
ejpam-3955	280	10	4	4	X
ejpam-3955	280	11	.	.	PUNCT
ejpam-3955	280	12	suppose	suppose	VERB
ejpam-3955	280	13	that	that	SCONJ
ejpam-3955	280	14	γ+ce(g	γ+ce(g	PROPN
ejpam-3955	280	15	)	)	PUNCT
ejpam-3955	281	1	+	+	CCONJ
ejpam-3955	281	2	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	281	3	)	)	PUNCT
ejpam-3955	281	4	=	=	PUNCT
ejpam-3955	282	1	4	4	X
ejpam-3955	282	2	.	.	PUNCT
ejpam-3955	282	3	then	then	ADV
ejpam-3955	282	4	,	,	PUNCT
ejpam-3955	282	5	necessarily	necessarily	ADV
ejpam-3955	282	6	,	,	PUNCT
ejpam-3955	282	7	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	282	8	)	)	PUNCT
ejpam-3955	282	9	=	=	SYM
ejpam-3955	282	10	2	2	NUM
ejpam-3955	282	11	and	and	CCONJ
ejpam-3955	282	12	γce(g	γce(g	NOUN
ejpam-3955	282	13	)	)	PUNCT
ejpam-3955	282	14	=	=	SYM
ejpam-3955	283	1	2	2	X
ejpam-3955	283	2	.	.	PUNCT
ejpam-3955	283	3	by	by	ADP
ejpam-3955	283	4	theorem	theorem	NOUN
ejpam-3955	283	5	9	9	NUM
ejpam-3955	283	6	,	,	PUNCT
ejpam-3955	283	7	n	n	NOUN
ejpam-3955	283	8	=	=	SYM
ejpam-3955	283	9	4	4	X
ejpam-3955	283	10	.	.	PUNCT
ejpam-3955	284	1	conversely	conversely	ADV
ejpam-3955	284	2	,	,	PUNCT
ejpam-3955	284	3	if	if	SCONJ
ejpam-3955	284	4	n	n	NOUN
ejpam-3955	284	5	=	=	SYM
ejpam-3955	284	6	4	4	NUM
ejpam-3955	284	7	,	,	PUNCT
ejpam-3955	284	8	then	then	ADV
ejpam-3955	284	9	γ+ce(g)+γ+ce(g	γ+ce(g)+γ+ce(g	NUM
ejpam-3955	284	10	)	)	PUNCT
ejpam-3955	285	1	=	=	SYM
ejpam-3955	285	2	4	4	NUM
ejpam-3955	285	3	similarly	similarly	ADV
ejpam-3955	285	4	,	,	PUNCT
ejpam-3955	285	5	γ+ce(g)γ+ce(g	γ+ce(g)γ+ce(g	PROPN
ejpam-3955	285	6	)	)	PUNCT
ejpam-3955	285	7	=	=	SYM
ejpam-3955	285	8	4	4	NUM
ejpam-3955	286	1	if	if	SCONJ
ejpam-3955	286	2	and	and	CCONJ
ejpam-3955	286	3	only	only	ADV
ejpam-3955	286	4	if	if	SCONJ
ejpam-3955	286	5	n	n	NOUN
ejpam-3955	286	6	=	=	SYM
ejpam-3955	286	7	4	4	X
ejpam-3955	286	8	.	.	PUNCT
ejpam-3955	286	9	corollary	corollary	ADJ
ejpam-3955	286	10	7	7	NUM
ejpam-3955	286	11	.	.	PUNCT
ejpam-3955	287	1	if	if	SCONJ
ejpam-3955	287	2	g	g	PROPN
ejpam-3955	287	3	∈	∈	PROPN
ejpam-3955	287	4	ξ	ξ	PROPN
ejpam-3955	287	5	of	of	ADP
ejpam-3955	287	6	order	order	NOUN
ejpam-3955	287	7	n	n	PRON
ejpam-3955	287	8	≥	≥	NOUN
ejpam-3955	287	9	4	4	NUM
ejpam-3955	287	10	,	,	PUNCT
ejpam-3955	287	11	then	then	ADV
ejpam-3955	287	12	(	(	PUNCT
ejpam-3955	287	13	i	i	NOUN
ejpam-3955	287	14	)	)	PUNCT
ejpam-3955	287	15	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	287	16	)	)	PUNCT
ejpam-3955	287	17	+	+	CCONJ
ejpam-3955	287	18	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	287	19	)	)	PUNCT
ejpam-3955	287	20	=	=	PUNCT
ejpam-3955	287	21	4	4	NUM
ejpam-3955	287	22	if	if	SCONJ
ejpam-3955	287	23	and	and	CCONJ
ejpam-3955	287	24	only	only	ADV
ejpam-3955	287	25	if	if	SCONJ
ejpam-3955	287	26	g	g	NOUN
ejpam-3955	287	27	=	=	SYM
ejpam-3955	287	28	p4	p4	PROPN
ejpam-3955	287	29	,	,	PUNCT
ejpam-3955	287	30	h.	h.	PROPN
ejpam-3955	287	31	nuenay	nuenay	PROPN
ejpam-3955	287	32	-	-	PUNCT
ejpam-3955	287	33	maglanque	maglanque	ADJ
ejpam-3955	287	34	,	,	PUNCT
ejpam-3955	287	35	f.jamil	f.jamil	PROPN
ejpam-3955	287	36	/	/	SYM
ejpam-3955	287	37	eur	eur	PROPN
ejpam-3955	287	38	.	.	PUNCT
ejpam-3955	288	1	j.	j.	PROPN
ejpam-3955	288	2	pure	pure	PROPN
ejpam-3955	288	3	appl	appl	PROPN
ejpam-3955	288	4	.	.	PROPN
ejpam-3955	288	5	math	math	PROPN
ejpam-3955	288	6	,	,	PUNCT
ejpam-3955	288	7	14	14	NUM
ejpam-3955	288	8	(	(	PUNCT
ejpam-3955	288	9	2	2	NUM
ejpam-3955	288	10	)	)	PUNCT
ejpam-3955	288	11	(	(	PUNCT
ejpam-3955	288	12	2021	2021	NUM
ejpam-3955	288	13	)	)	PUNCT
ejpam-3955	288	14	,	,	PUNCT
ejpam-3955	288	15	537	537	NUM
ejpam-3955	288	16	-	-	SYM
ejpam-3955	288	17	550	550	NUM
ejpam-3955	288	18	546	546	NUM
ejpam-3955	288	19	(	(	PUNCT
ejpam-3955	288	20	ii	ii	NOUN
ejpam-3955	288	21	)	)	PUNCT
ejpam-3955	288	22	γ+ce(g)γ+ce(g	γ+ce(g)γ+ce(g	NOUN
ejpam-3955	288	23	)	)	PUNCT
ejpam-3955	289	1	=	=	SYM
ejpam-3955	289	2	4	4	NUM
ejpam-3955	289	3	if	if	SCONJ
ejpam-3955	289	4	and	and	CCONJ
ejpam-3955	289	5	only	only	ADV
ejpam-3955	289	6	if	if	SCONJ
ejpam-3955	289	7	g	g	NOUN
ejpam-3955	289	8	=	=	SYM
ejpam-3955	289	9	p4	p4	ADJ
ejpam-3955	289	10	.	.	PUNCT
ejpam-3955	290	1	proof	proof	NOUN
ejpam-3955	290	2	.	.	PUNCT
ejpam-3955	291	1	the	the	DET
ejpam-3955	291	2	result	result	NOUN
ejpam-3955	291	3	follows	follow	VERB
ejpam-3955	291	4	from	from	ADP
ejpam-3955	291	5	theorem	theorem	ADJ
ejpam-3955	291	6	11	11	NUM
ejpam-3955	291	7	and	and	CCONJ
ejpam-3955	291	8	corollary	corollary	ADJ
ejpam-3955	291	9	6	6	NUM
ejpam-3955	291	10	.	.	PUNCT
ejpam-3955	292	1	theorem	theorem	VERB
ejpam-3955	292	2	11	11	NUM
ejpam-3955	292	3	and	and	CCONJ
ejpam-3955	292	4	theorem	theorem	VERB
ejpam-3955	292	5	9	9	NUM
ejpam-3955	292	6	imply	imply	VERB
ejpam-3955	292	7	that	that	SCONJ
ejpam-3955	292	8	if	if	SCONJ
ejpam-3955	292	9	g	g	PROPN
ejpam-3955	292	10	∈	∈	PROPN
ejpam-3955	292	11	ξ	ξ	X
ejpam-3955	292	12	is	be	AUX
ejpam-3955	292	13	of	of	ADP
ejpam-3955	292	14	order	order	NOUN
ejpam-3955	292	15	n	n	PRON
ejpam-3955	292	16	≥	≥	NUM
ejpam-3955	292	17	5	5	NUM
ejpam-3955	292	18	,	,	PUNCT
ejpam-3955	292	19	then	then	ADV
ejpam-3955	292	20	6	6	NUM
ejpam-3955	292	21	≤	≤	NUM
ejpam-3955	292	22	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	292	23	)	)	PUNCT
ejpam-3955	292	24	+	+	CCONJ
ejpam-3955	292	25	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	292	26	)	)	PUNCT
ejpam-3955	292	27	≤	≤	NOUN
ejpam-3955	293	1	2n−	2n−	NUM
ejpam-3955	293	2	4	4	NUM
ejpam-3955	293	3	(	(	PUNCT
ejpam-3955	293	4	1	1	NUM
ejpam-3955	293	5	)	)	PUNCT
ejpam-3955	293	6	and	and	CCONJ
ejpam-3955	293	7	9	9	NUM
ejpam-3955	293	8	≤	≤	NUM
ejpam-3955	293	9	γ+ce(g)γ+ce(g	γ+ce(g)γ+ce(g	PROPN
ejpam-3955	293	10	)	)	PUNCT
ejpam-3955	293	11	≤	≤	NUM
ejpam-3955	293	12	n2	n2	NOUN
ejpam-3955	293	13	−	−	PROPN
ejpam-3955	293	14	4n+	4n+	NUM
ejpam-3955	293	15	4	4	NUM
ejpam-3955	293	16	.	.	PUNCT
ejpam-3955	293	17	(	(	PUNCT
ejpam-3955	293	18	2	2	X
ejpam-3955	293	19	)	)	PUNCT
ejpam-3955	293	20	since	since	SCONJ
ejpam-3955	293	21	γ+ce(c5	γ+ce(c5	NUM
ejpam-3955	293	22	)	)	PUNCT
ejpam-3955	293	23	=	=	SYM
ejpam-3955	293	24	γ+ce(c5	γ+ce(c5	PROPN
ejpam-3955	293	25	)	)	PUNCT
ejpam-3955	294	1	=	=	SYM
ejpam-3955	294	2	3	3	X
ejpam-3955	294	3	,	,	PUNCT
ejpam-3955	294	4	bounds	bound	VERB
ejpam-3955	294	5	in	in	ADP
ejpam-3955	294	6	equations	equation	NOUN
ejpam-3955	294	7	1	1	NUM
ejpam-3955	294	8	and	and	CCONJ
ejpam-3955	294	9	2	2	NUM
ejpam-3955	294	10	are	be	AUX
ejpam-3955	294	11	sharp	sharp	ADJ
ejpam-3955	294	12	.	.	PUNCT
ejpam-3955	295	1	following	follow	VERB
ejpam-3955	295	2	the	the	DET
ejpam-3955	295	3	proof	proof	NOUN
ejpam-3955	295	4	of	of	ADP
ejpam-3955	295	5	theorem	theorem	NOUN
ejpam-3955	295	6	11	11	NUM
ejpam-3955	295	7	,	,	PUNCT
ejpam-3955	295	8	the	the	DET
ejpam-3955	295	9	following	follow	VERB
ejpam-3955	295	10	is	be	AUX
ejpam-3955	295	11	true	true	ADJ
ejpam-3955	295	12	.	.	PUNCT
ejpam-3955	296	1	theorem	theorem	ADJ
ejpam-3955	296	2	12	12	NUM
ejpam-3955	296	3	.	.	PUNCT
ejpam-3955	297	1	for	for	ADP
ejpam-3955	297	2	all	all	PRON
ejpam-3955	297	3	g	g	PROPN
ejpam-3955	297	4	∈	∈	PROPN
ejpam-3955	297	5	ξ	ξ	NOUN
ejpam-3955	297	6	of	of	ADP
ejpam-3955	297	7	order	order	NOUN
ejpam-3955	297	8	n	n	DET
ejpam-3955	297	9	≥	≥	NOUN
ejpam-3955	297	10	4	4	NUM
ejpam-3955	297	11	,	,	PUNCT
ejpam-3955	297	12	(	(	PUNCT
ejpam-3955	297	13	i	i	NOUN
ejpam-3955	297	14	)	)	PUNCT
ejpam-3955	297	15	4	4	NUM
ejpam-3955	297	16	≤	≤	PUNCT
ejpam-3955	297	17	γmce(g	γmce(g	PROPN
ejpam-3955	297	18	)	)	PUNCT
ejpam-3955	297	19	+	+	CCONJ
ejpam-3955	297	20	γmce(g	γmce(g	NOUN
ejpam-3955	297	21	)	)	PUNCT
ejpam-3955	297	22	≤	≤	NOUN
ejpam-3955	298	1	2n−	2n−	NUM
ejpam-3955	298	2	4	4	NUM
ejpam-3955	298	3	;	;	PUNCT
ejpam-3955	298	4	and	and	CCONJ
ejpam-3955	298	5	(	(	PUNCT
ejpam-3955	298	6	ii	ii	NOUN
ejpam-3955	298	7	)	)	PUNCT
ejpam-3955	298	8	4	4	NUM
ejpam-3955	298	9	≤	≤	NUM
ejpam-3955	298	10	γmce(g)γmce(g	γmce(g)γmce(g	NOUN
ejpam-3955	298	11	)	)	PUNCT
ejpam-3955	298	12	≤	≤	NUM
ejpam-3955	298	13	n2	n2	NOUN
ejpam-3955	298	14	−	−	PROPN
ejpam-3955	298	15	4n+	4n+	NUM
ejpam-3955	298	16	4	4	X
ejpam-3955	298	17	.	.	X
ejpam-3955	299	1	proof	proof	NOUN
ejpam-3955	299	2	.	.	PUNCT
ejpam-3955	300	1	let	let	VERB
ejpam-3955	300	2	g	g	PROPN
ejpam-3955	300	3	∈	∈	PROPN
ejpam-3955	300	4	ξ	ξ	X
ejpam-3955	300	5	be	be	NOUN
ejpam-3955	300	6	of	of	ADP
ejpam-3955	300	7	order	order	NOUN
ejpam-3955	300	8	n	n	PRON
ejpam-3955	300	9	≥	≥	NOUN
ejpam-3955	300	10	4	4	NUM
ejpam-3955	300	11	.	.	PUNCT
ejpam-3955	300	12	note	note	VERB
ejpam-3955	300	13	that	that	SCONJ
ejpam-3955	300	14	whenever	whenever	SCONJ
ejpam-3955	300	15	g	g	PROPN
ejpam-3955	300	16	is	be	AUX
ejpam-3955	300	17	kn	kn	PROPN
ejpam-3955	300	18	or	or	CCONJ
ejpam-3955	300	19	k1,n−1	k1,n−1	ADJ
ejpam-3955	300	20	,	,	PUNCT
ejpam-3955	300	21	g	g	PROPN
ejpam-3955	300	22	is	be	AUX
ejpam-3955	300	23	disconnected	disconnect	VERB
ejpam-3955	300	24	.	.	PUNCT
ejpam-3955	301	1	thus	thus	ADV
ejpam-3955	301	2	,	,	PUNCT
ejpam-3955	301	3	theorem	theorem	VERB
ejpam-3955	301	4	8	8	NUM
ejpam-3955	301	5	and	and	CCONJ
ejpam-3955	301	6	corollary	corollary	ADJ
ejpam-3955	301	7	4	4	NUM
ejpam-3955	301	8	imply	imply	NOUN
ejpam-3955	301	9	that	that	DET
ejpam-3955	301	10	γmce(g	γmce(g	NOUN
ejpam-3955	301	11	)	)	PUNCT
ejpam-3955	302	1	+	+	CCONJ
ejpam-3955	302	2	γmce(g	γmce(g	ADV
ejpam-3955	302	3	)	)	PUNCT
ejpam-3955	302	4	≤	≤	NOUN
ejpam-3955	302	5	(	(	PUNCT
ejpam-3955	302	6	n−	n−	NOUN
ejpam-3955	302	7	2	2	NUM
ejpam-3955	302	8	)	)	PUNCT
ejpam-3955	302	9	+	+	CCONJ
ejpam-3955	302	10	(	(	PUNCT
ejpam-3955	302	11	n−	n−	NOUN
ejpam-3955	302	12	2	2	NUM
ejpam-3955	302	13	)	)	PUNCT
ejpam-3955	302	14	=	=	PUNCT
ejpam-3955	303	1	2n−	2n−	NUM
ejpam-3955	303	2	4	4	NUM
ejpam-3955	303	3	and	and	CCONJ
ejpam-3955	303	4	γmce(g)γmce(g	γmce(g)γmce(g	NOUN
ejpam-3955	303	5	)	)	PUNCT
ejpam-3955	303	6	≤	≤	NUM
ejpam-3955	303	7	(	(	PUNCT
ejpam-3955	303	8	n−	n−	NOUN
ejpam-3955	303	9	2)(n−	2)(n−	NUM
ejpam-3955	303	10	2	2	NUM
ejpam-3955	303	11	)	)	PUNCT
ejpam-3955	303	12	=	=	SYM
ejpam-3955	303	13	n2	n2	NOUN
ejpam-3955	303	14	−	−	PROPN
ejpam-3955	303	15	4n+	4n+	NUM
ejpam-3955	303	16	4	4	NUM
ejpam-3955	303	17	.	.	PUNCT
ejpam-3955	304	1	the	the	DET
ejpam-3955	304	2	left	left	ADJ
ejpam-3955	304	3	inequalities	inequality	NOUN
ejpam-3955	304	4	follow	follow	VERB
ejpam-3955	304	5	from	from	ADP
ejpam-3955	304	6	theorem	theorem	ADJ
ejpam-3955	304	7	4	4	NUM
ejpam-3955	304	8	.	.	NOUN
ejpam-3955	304	9	remark	remark	NOUN
ejpam-3955	304	10	6	6	NUM
ejpam-3955	304	11	.	.	PUNCT
ejpam-3955	305	1	the	the	DET
ejpam-3955	305	2	bounds	bound	NOUN
ejpam-3955	305	3	given	give	VERB
ejpam-3955	305	4	in	in	ADP
ejpam-3955	305	5	theorem	theorem	ADJ
ejpam-3955	305	6	12	12	NUM
ejpam-3955	305	7	are	be	AUX
ejpam-3955	305	8	sharp	sharp	ADJ
ejpam-3955	305	9	.	.	PUNCT
ejpam-3955	306	1	to	to	PART
ejpam-3955	306	2	see	see	VERB
ejpam-3955	306	3	this	this	PRON
ejpam-3955	306	4	,	,	PUNCT
ejpam-3955	306	5	consider	consider	VERB
ejpam-3955	306	6	the	the	DET
ejpam-3955	306	7	graph	graph	NOUN
ejpam-3955	306	8	g	g	NOUN
ejpam-3955	306	9	=	=	NOUN
ejpam-3955	306	10	p4	p4	ADJ
ejpam-3955	306	11	.	.	PUNCT
ejpam-3955	307	1	observe	observe	VERB
ejpam-3955	307	2	that	that	SCONJ
ejpam-3955	307	3	γmce(p4	γmce(p4	NOUN
ejpam-3955	307	4	)	)	PUNCT
ejpam-3955	307	5	=	=	SYM
ejpam-3955	307	6	2	2	NUM
ejpam-3955	307	7	=	=	SYM
ejpam-3955	307	8	γmce(p4	γmce(p4	NOUN
ejpam-3955	307	9	)	)	PUNCT
ejpam-3955	307	10	.	.	PUNCT
ejpam-3955	308	1	2.2	2.2	NUM
ejpam-3955	308	2	.	.	PUNCT
ejpam-3955	308	3	realization	realization	NOUN
ejpam-3955	308	4	problem	problem	NOUN
ejpam-3955	308	5	theorem	theorem	VERB
ejpam-3955	308	6	13	13	NUM
ejpam-3955	308	7	.	.	PUNCT
ejpam-3955	309	1	for	for	ADP
ejpam-3955	309	2	every	every	DET
ejpam-3955	309	3	positive	positive	ADJ
ejpam-3955	309	4	integers	integer	NOUN
ejpam-3955	309	5	a	a	DET
ejpam-3955	309	6	,	,	PUNCT
ejpam-3955	309	7	b	b	NOUN
ejpam-3955	309	8	,	,	PUNCT
ejpam-3955	309	9	c	c	NOUN
ejpam-3955	309	10	with	with	ADP
ejpam-3955	309	11	1	1	NUM
ejpam-3955	309	12	≤	≤	NOUN
ejpam-3955	309	13	a	a	DET
ejpam-3955	309	14	≤	≤	NUM
ejpam-3955	309	15	b	b	NOUN
ejpam-3955	309	16	≤	≤	NUM
ejpam-3955	309	17	c	c	NOUN
ejpam-3955	309	18	there	there	PRON
ejpam-3955	309	19	exists	exist	VERB
ejpam-3955	309	20	a	a	DET
ejpam-3955	309	21	connected	connected	ADJ
ejpam-3955	309	22	graph	graph	NOUN
ejpam-3955	309	23	g	g	ADP
ejpam-3955	309	24	such	such	ADJ
ejpam-3955	309	25	that	that	DET
ejpam-3955	309	26	γce(g	γce(g	NOUN
ejpam-3955	309	27	)	)	PUNCT
ejpam-3955	310	1	=	=	SYM
ejpam-3955	310	2	a	a	PRON
ejpam-3955	310	3	,	,	PUNCT
ejpam-3955	310	4	γmce(g	γmce(g	PROPN
ejpam-3955	310	5	)	)	PUNCT
ejpam-3955	310	6	=	=	SYM
ejpam-3955	310	7	b	b	PROPN
ejpam-3955	310	8	and	and	CCONJ
ejpam-3955	310	9	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	310	10	)	)	PUNCT
ejpam-3955	311	1	=	=	SYM
ejpam-3955	311	2	c.	c.	NOUN
ejpam-3955	311	3	proof	proof	NOUN
ejpam-3955	311	4	.	.	PUNCT
ejpam-3955	312	1	suppose	suppose	VERB
ejpam-3955	312	2	that	that	SCONJ
ejpam-3955	312	3	a	a	DET
ejpam-3955	312	4	=	=	SYM
ejpam-3955	312	5	b	b	PROPN
ejpam-3955	312	6	=	=	PROPN
ejpam-3955	312	7	c.	c.	PROPN
ejpam-3955	312	8	write	write	VERB
ejpam-3955	312	9	v	v	PROPN
ejpam-3955	312	10	(	(	PUNCT
ejpam-3955	312	11	k1,a−1	k1,a−1	PROPN
ejpam-3955	312	12	)	)	PUNCT
ejpam-3955	313	1	=	=	PRON
ejpam-3955	313	2	{	{	PUNCT
ejpam-3955	313	3	x	x	NOUN
ejpam-3955	313	4	,	,	PUNCT
ejpam-3955	313	5	u1	u1	NOUN
ejpam-3955	313	6	,	,	PUNCT
ejpam-3955	313	7	u2	u2	NOUN
ejpam-3955	313	8	,	,	PUNCT
ejpam-3955	313	9	.	.	PUNCT
ejpam-3955	313	10	.	.	PUNCT
ejpam-3955	313	11	.	.	PUNCT
ejpam-3955	314	1	,	,	PUNCT
ejpam-3955	314	2	ua−1	ua−1	NOUN
ejpam-3955	314	3	}	}	PUNCT
ejpam-3955	314	4	as	as	ADP
ejpam-3955	314	5	in	in	ADP
ejpam-3955	314	6	figure	figure	NOUN
ejpam-3955	314	7	1	1	NUM
ejpam-3955	314	8	.	.	PUNCT
ejpam-3955	314	9	obtain	obtain	VERB
ejpam-3955	314	10	g	g	NOUN
ejpam-3955	314	11	from	from	ADP
ejpam-3955	314	12	k1,a−1	k1,a−1	NOUN
ejpam-3955	314	13	by	by	ADP
ejpam-3955	314	14	adding	add	VERB
ejpam-3955	314	15	pendant	pendant	ADJ
ejpam-3955	314	16	edges	edge	NOUN
ejpam-3955	314	17	vjuj	vjuj	ADV
ejpam-3955	314	18	,	,	PUNCT
ejpam-3955	314	19	j	j	PROPN
ejpam-3955	314	20	=	=	SYM
ejpam-3955	314	21	1	1	NUM
ejpam-3955	314	22	,	,	PUNCT
ejpam-3955	314	23	2	2	NUM
ejpam-3955	314	24	,	,	PUNCT
ejpam-3955	314	25	.	.	PUNCT
ejpam-3955	314	26	.	.	PUNCT
ejpam-3955	315	1	.	.	PUNCT
ejpam-3955	316	1	,	,	PUNCT
ejpam-3955	316	2	a−	a−	PROPN
ejpam-3955	316	3	1	1	NUM
ejpam-3955	316	4	and	and	CCONJ
ejpam-3955	316	5	then	then	ADV
ejpam-3955	316	6	adding	add	VERB
ejpam-3955	316	7	new	new	ADJ
ejpam-3955	316	8	edges	edge	NOUN
ejpam-3955	316	9	va−1wa−1	va−1wa−1	NOUN
ejpam-3955	316	10	and	and	CCONJ
ejpam-3955	316	11	wa−1x	wa−1x	PROPN
ejpam-3955	316	12	as	as	SCONJ
ejpam-3955	316	13	shown	show	VERB
ejpam-3955	316	14	in	in	ADP
ejpam-3955	316	15	figure	figure	NOUN
ejpam-3955	316	16	1	1	NUM
ejpam-3955	316	17	.	.	PUNCT
ejpam-3955	316	18	write	write	VERB
ejpam-3955	316	19	d	d	PROPN
ejpam-3955	316	20	=	=	SYM
ejpam-3955	316	21	{	{	PUNCT
ejpam-3955	316	22	ua−1	ua−1	PROPN
ejpam-3955	316	23	,	,	PUNCT
ejpam-3955	316	24	va−1	va−1	PROPN
ejpam-3955	316	25	,	,	PUNCT
ejpam-3955	316	26	wa−1	wa−1	NOUN
ejpam-3955	316	27	,	,	PUNCT
ejpam-3955	316	28	x	x	NOUN
ejpam-3955	316	29	}	}	PUNCT
ejpam-3955	316	30	.	.	PUNCT
ejpam-3955	317	1	observe	observe	VERB
ejpam-3955	317	2	that	that	SCONJ
ejpam-3955	317	3	for	for	ADP
ejpam-3955	317	4	any	any	DET
ejpam-3955	317	5	s	s	NOUN
ejpam-3955	317	6	,	,	PUNCT
ejpam-3955	317	7	t	t	PROPN
ejpam-3955	317	8	∈	∈	PROPN
ejpam-3955	317	9	d	d	X
ejpam-3955	317	10	,	,	PUNCT
ejpam-3955	317	11	the	the	DET
ejpam-3955	317	12	sets	set	NOUN
ejpam-3955	317	13	{	{	PUNCT
ejpam-3955	317	14	v1	v1	NOUN
ejpam-3955	317	15	,	,	PUNCT
ejpam-3955	317	16	v2	v2	PROPN
ejpam-3955	317	17	,	,	PUNCT
ejpam-3955	317	18	v3	v3	PROPN
ejpam-3955	317	19	.	.	PUNCT
ejpam-3955	317	20	.	.	PUNCT
ejpam-3955	318	1	.	.	PUNCT
ejpam-3955	319	1	,	,	PUNCT
ejpam-3955	319	2	va−2	va−2	PROPN
ejpam-3955	319	3	,	,	PUNCT
ejpam-3955	319	4	s	s	PROPN
ejpam-3955	319	5	,	,	PUNCT
ejpam-3955	319	6	t	t	PROPN
ejpam-3955	319	7	}	}	PUNCT
ejpam-3955	319	8	,	,	PUNCT
ejpam-3955	319	9	{	{	PUNCT
ejpam-3955	319	10	u1	u1	NOUN
ejpam-3955	319	11	,	,	PUNCT
ejpam-3955	319	12	u2	u2	NOUN
ejpam-3955	319	13	,	,	PUNCT
ejpam-3955	319	14	.	.	PUNCT
ejpam-3955	319	15	.	.	PUNCT
ejpam-3955	320	1	.	.	PUNCT
ejpam-3955	321	1	,	,	PUNCT
ejpam-3955	321	2	ua−2	ua−2	NOUN
ejpam-3955	321	3	,	,	PUNCT
ejpam-3955	321	4	p	p	X
ejpam-3955	321	5	,	,	PUNCT
ejpam-3955	321	6	r	r	NOUN
ejpam-3955	321	7	}	}	PUNCT
ejpam-3955	321	8	where	where	SCONJ
ejpam-3955	321	9	p	p	X
ejpam-3955	321	10	,	,	PUNCT
ejpam-3955	321	11	r	r	NOUN
ejpam-3955	321	12	∈	∈	PROPN
ejpam-3955	321	13	d	d	SYM
ejpam-3955	321	14	\	\	X
ejpam-3955	321	15	{	{	PUNCT
ejpam-3955	321	16	x	x	NOUN
ejpam-3955	321	17	}	}	PUNCT
ejpam-3955	321	18	and	and	CCONJ
ejpam-3955	321	19	sets	set	NOUN
ejpam-3955	321	20	of	of	ADP
ejpam-3955	321	21	the	the	DET
ejpam-3955	321	22	form	form	NOUN
ejpam-3955	321	23	{	{	PUNCT
ejpam-3955	321	24	uj	uj	PROPN
ejpam-3955	321	25	,	,	PUNCT
ejpam-3955	321	26	vk	vk	INTJ
ejpam-3955	321	27	:	:	PUNCT
ejpam-3955	321	28	j	j	PROPN
ejpam-3955	321	29	6=	6=	PROPN
ejpam-3955	322	1	k	k	PROPN
ejpam-3955	322	2	,	,	PUNCT
ejpam-3955	322	3	j	j	PROPN
ejpam-3955	322	4	,	,	PUNCT
ejpam-3955	322	5	k	k	PROPN
ejpam-3955	322	6	=	=	SYM
ejpam-3955	322	7	1	1	NUM
ejpam-3955	322	8	,	,	PUNCT
ejpam-3955	322	9	2	2	NUM
ejpam-3955	322	10	,	,	PUNCT
ejpam-3955	322	11	.	.	PUNCT
ejpam-3955	322	12	.	.	PUNCT
ejpam-3955	323	1	.	.	PUNCT
ejpam-3955	324	1	,	,	PUNCT
ejpam-3955	324	2	a	a	DET
ejpam-3955	324	3	−	−	NOUN
ejpam-3955	324	4	2	2	NUM
ejpam-3955	324	5	}	}	PUNCT
ejpam-3955	324	6	∪	∪	ADJ
ejpam-3955	324	7	{	{	PUNCT
ejpam-3955	324	8	s	s	PROPN
ejpam-3955	324	9	,	,	PUNCT
ejpam-3955	324	10	t	t	PROPN
ejpam-3955	324	11	}	}	PUNCT
ejpam-3955	324	12	are	be	AUX
ejpam-3955	324	13	the	the	DET
ejpam-3955	324	14	only	only	ADJ
ejpam-3955	324	15	cost	cost	NOUN
ejpam-3955	324	16	effective	effective	ADJ
ejpam-3955	324	17	dominating	dominating	NOUN
ejpam-3955	324	18	sets	set	NOUN
ejpam-3955	324	19	in	in	ADP
ejpam-3955	324	20	g.	g.	PROPN
ejpam-3955	324	21	therefore	therefore	ADV
ejpam-3955	324	22	,	,	PUNCT
ejpam-3955	324	23	γce(g	γce(g	PROPN
ejpam-3955	324	24	)	)	PUNCT
ejpam-3955	324	25	=	=	SYM
ejpam-3955	325	1	a	a	PRON
ejpam-3955	325	2	,	,	PUNCT
ejpam-3955	325	3	γmce(g	γmce(g	PROPN
ejpam-3955	325	4	)	)	PUNCT
ejpam-3955	325	5	=	=	SYM
ejpam-3955	325	6	b	b	PROPN
ejpam-3955	325	7	and	and	CCONJ
ejpam-3955	325	8	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	325	9	)	)	PUNCT
ejpam-3955	326	1	=	=	SYM
ejpam-3955	326	2	c.	c.	PROPN
ejpam-3955	326	3	h.	h.	PROPN
ejpam-3955	326	4	nuenay	nuenay	PROPN
ejpam-3955	326	5	-	-	PUNCT
ejpam-3955	326	6	maglanque	maglanque	ADJ
ejpam-3955	326	7	,	,	PUNCT
ejpam-3955	326	8	f.jamil	f.jamil	PROPN
ejpam-3955	326	9	/	/	SYM
ejpam-3955	326	10	eur	eur	PROPN
ejpam-3955	326	11	.	.	PUNCT
ejpam-3955	327	1	j.	j.	PROPN
ejpam-3955	327	2	pure	pure	PROPN
ejpam-3955	327	3	appl	appl	PROPN
ejpam-3955	327	4	.	.	PROPN
ejpam-3955	327	5	math	math	PROPN
ejpam-3955	327	6	,	,	PUNCT
ejpam-3955	327	7	14	14	NUM
ejpam-3955	327	8	(	(	PUNCT
ejpam-3955	327	9	2	2	NUM
ejpam-3955	327	10	)	)	PUNCT
ejpam-3955	327	11	(	(	PUNCT
ejpam-3955	327	12	2021	2021	NUM
ejpam-3955	327	13	)	)	PUNCT
ejpam-3955	327	14	,	,	PUNCT
ejpam-3955	327	15	537	537	NUM
ejpam-3955	327	16	-	-	SYM
ejpam-3955	327	17	550	550	NUM
ejpam-3955	327	18	547	547	NUM
ejpam-3955	327	19	....................................	....................................	PUNCT
ejpam-3955	327	20	....................................	....................................	PUNCT
ejpam-3955	328	1	....................................	....................................	PUNCT
ejpam-3955	328	2	....................................	....................................	PUNCT
ejpam-3955	329	1	........................................................................	........................................................................	PUNCT
ejpam-3955	329	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	329	3	.......	.......	PUNCT
ejpam-3955	329	4	..	..	PUNCT
ejpam-3955	329	5	........	........	PUNCT
ejpam-3955	329	6	........	........	PUNCT
ejpam-3955	329	7	........	........	PUNCT
ejpam-3955	329	8	........	........	PUNCT
ejpam-3955	329	9	........	........	PUNCT
ejpam-3955	329	10	........	........	PUNCT
ejpam-3955	330	1	........	........	PUNCT
ejpam-3955	330	2	..	..	PUNCT
ejpam-3955	331	1	..........	..........	PUNCT
ejpam-3955	331	2	.........	.........	PUNCT
ejpam-3955	332	1	.........	.........	PUNCT
ejpam-3955	332	2	.........	.........	PUNCT
ejpam-3955	333	1	.........	.........	PUNCT
ejpam-3955	333	2	.........	.........	PUNCT
ejpam-3955	334	1	.........	.........	PUNCT
ejpam-3955	334	2	.........	.........	PUNCT
ejpam-3955	334	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	334	4	.	.	PUNCT
ejpam-3955	334	5	.	.	PUNCT
ejpam-3955	334	6	.	.	PUNCT
ejpam-3955	335	1	u1	u1	PROPN
ejpam-3955	335	2	u2	u2	PROPN
ejpam-3955	335	3	u3u4	u3u4	PROPN
ejpam-3955	335	4	ua−1	ua−1	PROPN
ejpam-3955	335	5	x	x	SYM
ejpam-3955	335	6	k1,a−1	k1,a−1	PROPN
ejpam-3955	335	7	....................................	....................................	PUNCT
ejpam-3955	336	1	....................................	....................................	PUNCT
ejpam-3955	336	2	....................................	....................................	PUNCT
ejpam-3955	337	1	....................................	....................................	PUNCT
ejpam-3955	337	2	........................................................................	........................................................................	PUNCT
ejpam-3955	338	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	338	2	.......	.......	PUNCT
ejpam-3955	338	3	..	..	PUNCT
ejpam-3955	338	4	........	........	PUNCT
ejpam-3955	338	5	........	........	PUNCT
ejpam-3955	338	6	........	........	PUNCT
ejpam-3955	338	7	........	........	PUNCT
ejpam-3955	338	8	........	........	PUNCT
ejpam-3955	338	9	........	........	PUNCT
ejpam-3955	338	10	........	........	PUNCT
ejpam-3955	338	11	..	..	PUNCT
ejpam-3955	339	1	..........	..........	PUNCT
ejpam-3955	339	2	.........	.........	PUNCT
ejpam-3955	340	1	.........	.........	PUNCT
ejpam-3955	340	2	.........	.........	PUNCT
ejpam-3955	341	1	.........	.........	PUNCT
ejpam-3955	341	2	.........	.........	PUNCT
ejpam-3955	342	1	.........	.........	PUNCT
ejpam-3955	342	2	.........	.........	PUNCT
ejpam-3955	342	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	342	4	.	.	PUNCT
ejpam-3955	342	5	.	.	PUNCT
ejpam-3955	342	6	.	.	PUNCT
ejpam-3955	343	1	....................................	....................................	PUNCT
ejpam-3955	343	2	........................................................................	........................................................................	PUNCT
ejpam-3955	344	1	....................................	....................................	PUNCT
ejpam-3955	344	2	....................................	....................................	PUNCT
ejpam-3955	344	3	............................................................................	............................................................................	PUNCT
ejpam-3955	344	4	........................................	........................................	PUNCT
ejpam-3955	344	5	........................................	........................................	PUNCT
ejpam-3955	345	1	.........	.........	PUNCT
ejpam-3955	345	2	........	........	PUNCT
ejpam-3955	345	3	........	........	PUNCT
ejpam-3955	345	4	........	........	PUNCT
ejpam-3955	345	5	.......	.......	PUNCT
ejpam-3955	346	1	.............................................	.............................................	PUNCT
ejpam-3955	346	2	.........	.........	PUNCT
ejpam-3955	347	1	.........	.........	PUNCT
ejpam-3955	347	2	.....	.....	PUNCT
ejpam-3955	347	3	.....................	.....................	PUNCT
ejpam-3955	347	4	........................	........................	PUNCT
ejpam-3955	347	5	...............................	...............................	PUNCT
ejpam-3955	347	6	.......................................................................................................	.......................................................................................................	PUNCT
ejpam-3955	348	1	u1	u1	NOUN
ejpam-3955	348	2	x	x	SYM
ejpam-3955	348	3	v1	v1	PROPN
ejpam-3955	348	4	u2	u2	PROPN
ejpam-3955	348	5	v2	v2	PROPN
ejpam-3955	348	6	u3	u3	NOUN
ejpam-3955	348	7	v3	v3	PROPN
ejpam-3955	348	8	u4	u4	PROPN
ejpam-3955	348	9	v4	v4	PROPN
ejpam-3955	348	10	ua−1va−1	ua−1va−1	NOUN
ejpam-3955	348	11	wa−1	wa−1	NOUN
ejpam-3955	348	12	figure	figure	NOUN
ejpam-3955	348	13	1	1	NUM
ejpam-3955	348	14	:	:	PUNCT
ejpam-3955	348	15	g	g	PROPN
ejpam-3955	348	16	obtained	obtain	VERB
ejpam-3955	348	17	from	from	ADP
ejpam-3955	348	18	k1,a−1	k1,a−1	PROPN
ejpam-3955	348	19	....................................	....................................	PUNCT
ejpam-3955	348	20	....................................	....................................	PUNCT
ejpam-3955	348	21	....................................	....................................	PUNCT
ejpam-3955	349	1	....................................	....................................	PUNCT
ejpam-3955	349	2	........................................................................	........................................................................	PUNCT
ejpam-3955	350	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	350	2	.......	.......	PUNCT
ejpam-3955	350	3	..	..	PUNCT
ejpam-3955	350	4	........	........	PUNCT
ejpam-3955	350	5	........	........	PUNCT
ejpam-3955	350	6	........	........	PUNCT
ejpam-3955	350	7	........	........	PUNCT
ejpam-3955	350	8	........	........	PUNCT
ejpam-3955	350	9	........	........	PUNCT
ejpam-3955	350	10	........	........	PUNCT
ejpam-3955	350	11	..	..	PUNCT
ejpam-3955	351	1	..........	..........	PUNCT
ejpam-3955	351	2	.........	.........	PUNCT
ejpam-3955	352	1	.........	.........	PUNCT
ejpam-3955	352	2	.........	.........	PUNCT
ejpam-3955	353	1	.........	.........	PUNCT
ejpam-3955	353	2	.........	.........	PUNCT
ejpam-3955	354	1	.........	.........	PUNCT
ejpam-3955	354	2	.........	.........	PUNCT
ejpam-3955	354	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	354	4	.	.	PUNCT
ejpam-3955	354	5	.	.	PUNCT
ejpam-3955	354	6	.	.	PUNCT
ejpam-3955	355	1	....................................	....................................	PUNCT
ejpam-3955	355	2	........................................................................	........................................................................	PUNCT
ejpam-3955	356	1	....................................	....................................	PUNCT
ejpam-3955	356	2	....................................	....................................	PUNCT
ejpam-3955	356	3	........................................	........................................	PUNCT
ejpam-3955	356	4	........................................	........................................	PUNCT
ejpam-3955	357	1	.........	.........	PUNCT
ejpam-3955	357	2	........	........	PUNCT
ejpam-3955	357	3	........	........	PUNCT
ejpam-3955	357	4	........	........	PUNCT
ejpam-3955	357	5	.......	.......	PUNCT
ejpam-3955	358	1	.............................................	.............................................	PUNCT
ejpam-3955	358	2	.........	.........	PUNCT
ejpam-3955	359	1	.........	.........	PUNCT
ejpam-3955	360	1	.....	.....	PUNCT
ejpam-3955	360	2	u1	u1	NOUN
ejpam-3955	360	3	x	x	SYM
ejpam-3955	360	4	v1	v1	NOUN
ejpam-3955	360	5	u2	u2	PROPN
ejpam-3955	360	6	v2	v2	PROPN
ejpam-3955	360	7	u3	u3	NOUN
ejpam-3955	360	8	v3	v3	PROPN
ejpam-3955	360	9	u4	u4	PROPN
ejpam-3955	360	10	v4	v4	PROPN
ejpam-3955	360	11	uava	uava	NOUN
ejpam-3955	360	12	............	............	PUNCT
ejpam-3955	360	13	..............	..............	PUNCT
ejpam-3955	360	14	......................	......................	PUNCT
ejpam-3955	361	1	....................................................................................	....................................................................................	PUNCT
ejpam-3955	361	2	g1	g1	PROPN
ejpam-3955	361	3	:	:	PUNCT
ejpam-3955	361	4	figure	figure	VERB
ejpam-3955	361	5	2	2	NUM
ejpam-3955	361	6	:	:	PUNCT
ejpam-3955	361	7	g1	g1	NOUN
ejpam-3955	361	8	obtained	obtain	VERB
ejpam-3955	361	9	from	from	ADP
ejpam-3955	361	10	k1,a	k1,a	PROPN
ejpam-3955	361	11	suppose	suppose	VERB
ejpam-3955	361	12	that	that	SCONJ
ejpam-3955	361	13	a	a	DET
ejpam-3955	361	14	=	=	SYM
ejpam-3955	361	15	b	b	PROPN
ejpam-3955	361	16	and	and	CCONJ
ejpam-3955	361	17	c	c	NOUN
ejpam-3955	361	18	=	=	SYM
ejpam-3955	361	19	b	b	PROPN
ejpam-3955	362	1	+	+	CCONJ
ejpam-3955	362	2	1	1	X
ejpam-3955	362	3	.	.	PUNCT
ejpam-3955	362	4	obtain	obtain	VERB
ejpam-3955	362	5	the	the	DET
ejpam-3955	362	6	graph	graph	NOUN
ejpam-3955	362	7	g	g	NOUN
ejpam-3955	362	8	=	=	PUNCT
ejpam-3955	362	9	g1	g1	PROPN
ejpam-3955	362	10	from	from	ADP
ejpam-3955	362	11	k1,a	k1,a	PROPN
ejpam-3955	362	12	by	by	ADP
ejpam-3955	362	13	adding	add	VERB
ejpam-3955	362	14	pendant	pendant	ADJ
ejpam-3955	362	15	edges	edge	NOUN
ejpam-3955	362	16	ujvj	ujvj	NOUN
ejpam-3955	362	17	,	,	PUNCT
ejpam-3955	362	18	j	j	PROPN
ejpam-3955	362	19	=	=	SYM
ejpam-3955	362	20	1	1	NUM
ejpam-3955	362	21	,	,	PUNCT
ejpam-3955	362	22	2	2	NUM
ejpam-3955	362	23	,	,	PUNCT
ejpam-3955	362	24	.	.	PUNCT
ejpam-3955	362	25	.	.	PUNCT
ejpam-3955	363	1	.	.	PUNCT
ejpam-3955	364	1	,	,	PUNCT
ejpam-3955	364	2	a	a	DET
ejpam-3955	364	3	and	and	CCONJ
ejpam-3955	364	4	an	an	DET
ejpam-3955	364	5	edge	edge	NOUN
ejpam-3955	364	6	xva	xva	NOUN
ejpam-3955	364	7	as	as	SCONJ
ejpam-3955	364	8	shown	show	VERB
ejpam-3955	364	9	in	in	ADP
ejpam-3955	364	10	figure	figure	NOUN
ejpam-3955	364	11	2	2	NUM
ejpam-3955	364	12	.	.	X
ejpam-3955	364	13	observe	observe	VERB
ejpam-3955	364	14	that	that	SCONJ
ejpam-3955	364	15	the	the	DET
ejpam-3955	364	16	sets	set	NOUN
ejpam-3955	364	17	{	{	PUNCT
ejpam-3955	364	18	u1	u1	NOUN
ejpam-3955	364	19	,	,	PUNCT
ejpam-3955	364	20	u2	u2	NOUN
ejpam-3955	364	21	,	,	PUNCT
ejpam-3955	364	22	.	.	PUNCT
ejpam-3955	364	23	.	.	PUNCT
ejpam-3955	365	1	.	.	PUNCT
ejpam-3955	366	1	,	,	PUNCT
ejpam-3955	366	2	ua	ua	PROPN
ejpam-3955	366	3	}	}	PUNCT
ejpam-3955	366	4	,	,	PUNCT
ejpam-3955	366	5	{	{	PUNCT
ejpam-3955	366	6	v1	v1	NOUN
ejpam-3955	366	7	,	,	PUNCT
ejpam-3955	366	8	v2	v2	NOUN
ejpam-3955	366	9	,	,	PUNCT
ejpam-3955	366	10	.	.	PUNCT
ejpam-3955	366	11	.	.	PUNCT
ejpam-3955	367	1	.	.	PUNCT
ejpam-3955	368	1	,	,	PUNCT
ejpam-3955	368	2	va	va	PROPN
ejpam-3955	368	3	}	}	PUNCT
ejpam-3955	368	4	,	,	PUNCT
ejpam-3955	368	5	{	{	PUNCT
ejpam-3955	368	6	x	x	NOUN
ejpam-3955	368	7	,	,	PUNCT
ejpam-3955	368	8	v1	v1	NOUN
ejpam-3955	368	9	,	,	PUNCT
ejpam-3955	368	10	v2	v2	NOUN
ejpam-3955	368	11	,	,	PUNCT
ejpam-3955	368	12	.	.	PUNCT
ejpam-3955	368	13	.	.	PUNCT
ejpam-3955	369	1	.	.	PUNCT
ejpam-3955	370	1	,	,	PUNCT
ejpam-3955	370	2	va−1	va−1	VERB
ejpam-3955	370	3	}	}	PUNCT
ejpam-3955	370	4	and	and	CCONJ
ejpam-3955	370	5	sets	set	VERB
ejpam-3955	370	6	{	{	PUNCT
ejpam-3955	370	7	vj	vj	INTJ
ejpam-3955	370	8	,	,	PUNCT
ejpam-3955	370	9	uk	uk	PROPN
ejpam-3955	370	10	:	:	PUNCT
ejpam-3955	370	11	j	j	PROPN
ejpam-3955	370	12	6=	6=	PROPN
ejpam-3955	371	1	k	k	PROPN
ejpam-3955	371	2	,	,	PUNCT
ejpam-3955	371	3	j	j	PROPN
ejpam-3955	371	4	,	,	PUNCT
ejpam-3955	371	5	k	k	PROPN
ejpam-3955	371	6	=	=	SYM
ejpam-3955	371	7	1	1	NUM
ejpam-3955	371	8	,	,	PUNCT
ejpam-3955	371	9	2	2	NUM
ejpam-3955	371	10	,	,	PUNCT
ejpam-3955	371	11	.	.	PUNCT
ejpam-3955	371	12	.	.	PUNCT
ejpam-3955	372	1	.	.	PUNCT
ejpam-3955	373	1	,	,	PUNCT
ejpam-3955	373	2	a	a	PRON
ejpam-3955	373	3	}	}	PUNCT
ejpam-3955	373	4	are	be	AUX
ejpam-3955	373	5	the	the	DET
ejpam-3955	373	6	only	only	ADJ
ejpam-3955	373	7	minimal	minimal	ADJ
ejpam-3955	373	8	cost	cost	NOUN
ejpam-3955	373	9	effective	effective	ADJ
ejpam-3955	373	10	dominating	dominating	NOUN
ejpam-3955	373	11	sets	set	NOUN
ejpam-3955	373	12	in	in	ADP
ejpam-3955	373	13	g.	g.	PROPN
ejpam-3955	373	14	thus	thus	ADV
ejpam-3955	373	15	,	,	PUNCT
ejpam-3955	373	16	γmce(g	γmce(g	PROPN
ejpam-3955	373	17	)	)	PUNCT
ejpam-3955	373	18	=	=	PUNCT
ejpam-3955	374	1	a	a	DET
ejpam-3955	374	2	=	=	X
ejpam-3955	374	3	b.	b.	PROPN
ejpam-3955	374	4	also	also	ADV
ejpam-3955	374	5	,	,	PUNCT
ejpam-3955	374	6	note	note	VERB
ejpam-3955	374	7	that	that	SCONJ
ejpam-3955	374	8	the	the	DET
ejpam-3955	374	9	set	set	NOUN
ejpam-3955	374	10	{	{	PUNCT
ejpam-3955	374	11	x	x	NOUN
ejpam-3955	374	12	,	,	PUNCT
ejpam-3955	374	13	v1	v1	NOUN
ejpam-3955	374	14	,	,	PUNCT
ejpam-3955	374	15	v2	v2	NOUN
ejpam-3955	374	16	,	,	PUNCT
ejpam-3955	374	17	.	.	PUNCT
ejpam-3955	374	18	.	.	PUNCT
ejpam-3955	375	1	.	.	PUNCT
ejpam-3955	376	1	,	,	PUNCT
ejpam-3955	376	2	va	va	PROPN
ejpam-3955	376	3	}	}	PUNCT
ejpam-3955	376	4	is	be	AUX
ejpam-3955	376	5	a	a	DET
ejpam-3955	376	6	γ+ce	γ+ce	NOUN
ejpam-3955	376	7	-	-	PUNCT
ejpam-3955	376	8	set	set	VERB
ejpam-3955	376	9	in	in	ADP
ejpam-3955	376	10	g.	g.	PROPN
ejpam-3955	376	11	therefore	therefore	ADV
ejpam-3955	376	12	γ+ce(g	γ+ce(g	PROPN
ejpam-3955	376	13	)	)	PUNCT
ejpam-3955	377	1	=	=	SYM
ejpam-3955	377	2	a+	a+	PUNCT
ejpam-3955	377	3	1	1	NUM
ejpam-3955	377	4	=	=	SYM
ejpam-3955	377	5	b+	b+	X
ejpam-3955	377	6	1	1	NUM
ejpam-3955	377	7	=	=	SYM
ejpam-3955	377	8	c.	c.	NOUN
ejpam-3955	377	9	suppose	suppose	VERB
ejpam-3955	377	10	that	that	SCONJ
ejpam-3955	377	11	a	a	DET
ejpam-3955	377	12	=	=	SYM
ejpam-3955	377	13	b	b	PROPN
ejpam-3955	377	14	and	and	CCONJ
ejpam-3955	377	15	c	c	NOUN
ejpam-3955	377	16	=	=	PUNCT
ejpam-3955	377	17	b+	b+	PROPN
ejpam-3955	377	18	k	k	X
ejpam-3955	377	19	for	for	ADP
ejpam-3955	377	20	k	k	PROPN
ejpam-3955	377	21	≥	≥	PROPN
ejpam-3955	377	22	2	2	NUM
ejpam-3955	377	23	.	.	PUNCT
ejpam-3955	378	1	let	let	VERB
ejpam-3955	378	2	v	v	NOUN
ejpam-3955	378	3	(	(	PUNCT
ejpam-3955	378	4	k2k	k2k	PROPN
ejpam-3955	378	5	)	)	PUNCT
ejpam-3955	378	6	=	=	SYM
ejpam-3955	378	7	{	{	PUNCT
ejpam-3955	378	8	w1	w1	NOUN
ejpam-3955	378	9	,	,	PUNCT
ejpam-3955	378	10	w2	w2	NOUN
ejpam-3955	378	11	,	,	PUNCT
ejpam-3955	378	12	.	.	PUNCT
ejpam-3955	378	13	.	.	PUNCT
ejpam-3955	379	1	.	.	PUNCT
ejpam-3955	380	1	,	,	PUNCT
ejpam-3955	380	2	w2k	w2k	PROPN
ejpam-3955	380	3	}	}	PUNCT
ejpam-3955	380	4	.	.	PUNCT
ejpam-3955	381	1	obtain	obtain	VERB
ejpam-3955	381	2	g	g	PROPN
ejpam-3955	381	3	=	=	PROPN
ejpam-3955	381	4	g2	g2	PROPN
ejpam-3955	381	5	from	from	ADP
ejpam-3955	381	6	g1	g1	NOUN
ejpam-3955	381	7	by	by	ADP
ejpam-3955	381	8	joining	join	VERB
ejpam-3955	381	9	complete	complete	ADJ
ejpam-3955	381	10	graph	graph	NOUN
ejpam-3955	381	11	k2k	k2k	VERB
ejpam-3955	381	12	to	to	ADP
ejpam-3955	381	13	exactly	exactly	ADV
ejpam-3955	381	14	one	one	NUM
ejpam-3955	381	15	of	of	ADP
ejpam-3955	381	16	the	the	DET
ejpam-3955	381	17	end	end	NOUN
ejpam-3955	381	18	vertices	vertex	NOUN
ejpam-3955	381	19	of	of	ADP
ejpam-3955	381	20	g1	g1	NOUN
ejpam-3955	381	21	,	,	PUNCT
ejpam-3955	381	22	say	say	VERB
ejpam-3955	381	23	v1	v1	NOUN
ejpam-3955	381	24	,	,	PUNCT
ejpam-3955	381	25	as	as	SCONJ
ejpam-3955	381	26	shown	show	VERB
ejpam-3955	381	27	in	in	ADP
ejpam-3955	381	28	figure	figure	NOUN
ejpam-3955	381	29	3	3	NUM
ejpam-3955	381	30	.	.	PUNCT
ejpam-3955	381	31	....................................	....................................	PUNCT
ejpam-3955	381	32	....................................	....................................	PUNCT
ejpam-3955	382	1	....................................	....................................	PUNCT
ejpam-3955	382	2	....................................	....................................	PUNCT
ejpam-3955	383	1	........................................................................	........................................................................	PUNCT
ejpam-3955	383	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	383	3	.......	.......	PUNCT
ejpam-3955	383	4	..	..	PUNCT
ejpam-3955	383	5	........	........	PUNCT
ejpam-3955	383	6	........	........	PUNCT
ejpam-3955	383	7	........	........	PUNCT
ejpam-3955	383	8	........	........	PUNCT
ejpam-3955	383	9	........	........	PUNCT
ejpam-3955	383	10	........	........	PUNCT
ejpam-3955	384	1	........	........	PUNCT
ejpam-3955	384	2	..	..	PUNCT
ejpam-3955	385	1	..........	..........	PUNCT
ejpam-3955	385	2	.........	.........	PUNCT
ejpam-3955	386	1	.........	.........	PUNCT
ejpam-3955	386	2	.........	.........	PUNCT
ejpam-3955	387	1	.........	.........	PUNCT
ejpam-3955	387	2	.........	.........	PUNCT
ejpam-3955	388	1	.........	.........	PUNCT
ejpam-3955	388	2	.........	.........	PUNCT
ejpam-3955	388	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	388	4	.	.	PUNCT
ejpam-3955	388	5	.	.	PUNCT
ejpam-3955	388	6	.	.	PUNCT
ejpam-3955	389	1	....................................	....................................	PUNCT
ejpam-3955	389	2	........................................................................	........................................................................	PUNCT
ejpam-3955	390	1	....................................	....................................	PUNCT
ejpam-3955	390	2	....................................	....................................	PUNCT
ejpam-3955	390	3	........................................	........................................	PUNCT
ejpam-3955	390	4	........................................	........................................	PUNCT
ejpam-3955	391	1	.........	.........	PUNCT
ejpam-3955	391	2	........	........	PUNCT
ejpam-3955	391	3	........	........	PUNCT
ejpam-3955	391	4	........	........	PUNCT
ejpam-3955	391	5	.......	.......	PUNCT
ejpam-3955	392	1	.............................................	.............................................	PUNCT
ejpam-3955	392	2	.........	.........	PUNCT
ejpam-3955	393	1	.........	.........	PUNCT
ejpam-3955	394	1	.....	.....	PUNCT
ejpam-3955	394	2	u1	u1	NOUN
ejpam-3955	394	3	x	x	SYM
ejpam-3955	394	4	v1	v1	NOUN
ejpam-3955	394	5	u2	u2	PROPN
ejpam-3955	394	6	v2	v2	PROPN
ejpam-3955	394	7	u3	u3	NOUN
ejpam-3955	394	8	v3	v3	PROPN
ejpam-3955	394	9	u4	u4	PROPN
ejpam-3955	394	10	v4	v4	PROPN
ejpam-3955	394	11	uava	uava	NOUN
ejpam-3955	394	12	............	............	PUNCT
ejpam-3955	394	13	..............	..............	PUNCT
ejpam-3955	394	14	......................	......................	PUNCT
ejpam-3955	395	1	....................................................................................	....................................................................................	PUNCT
ejpam-3955	396	1	g1	g1	PROPN
ejpam-3955	396	2	....................................	....................................	PUNCT
ejpam-3955	396	3	....................................	....................................	PUNCT
ejpam-3955	396	4	....................................	....................................	PUNCT
ejpam-3955	397	1	....................................	....................................	PUNCT
ejpam-3955	397	2	........................................................................	........................................................................	PUNCT
ejpam-3955	398	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	398	2	.......	.......	PUNCT
ejpam-3955	398	3	..	..	PUNCT
ejpam-3955	398	4	........	........	PUNCT
ejpam-3955	398	5	........	........	PUNCT
ejpam-3955	398	6	........	........	PUNCT
ejpam-3955	398	7	........	........	PUNCT
ejpam-3955	398	8	........	........	PUNCT
ejpam-3955	398	9	........	........	PUNCT
ejpam-3955	398	10	........	........	PUNCT
ejpam-3955	398	11	..	..	PUNCT
ejpam-3955	399	1	..........	..........	PUNCT
ejpam-3955	399	2	.........	.........	PUNCT
ejpam-3955	400	1	.........	.........	PUNCT
ejpam-3955	400	2	.........	.........	PUNCT
ejpam-3955	401	1	.........	.........	PUNCT
ejpam-3955	401	2	.........	.........	PUNCT
ejpam-3955	402	1	.........	.........	PUNCT
ejpam-3955	402	2	.........	.........	PUNCT
ejpam-3955	402	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	402	4	.	.	PUNCT
ejpam-3955	402	5	.	.	PUNCT
ejpam-3955	402	6	.	.	PUNCT
ejpam-3955	403	1	....................................	....................................	PUNCT
ejpam-3955	403	2	........................................................................	........................................................................	PUNCT
ejpam-3955	404	1	....................................	....................................	PUNCT
ejpam-3955	404	2	....................................	....................................	PUNCT
ejpam-3955	404	3	........................................	........................................	PUNCT
ejpam-3955	404	4	........................................	........................................	PUNCT
ejpam-3955	405	1	.........	.........	PUNCT
ejpam-3955	405	2	........	........	PUNCT
ejpam-3955	405	3	........	........	PUNCT
ejpam-3955	405	4	........	........	PUNCT
ejpam-3955	405	5	.......	.......	PUNCT
ejpam-3955	406	1	.............................................	.............................................	PUNCT
ejpam-3955	406	2	.........	.........	PUNCT
ejpam-3955	407	1	.........	.........	PUNCT
ejpam-3955	408	1	.....	.....	PUNCT
ejpam-3955	408	2	u1	u1	NOUN
ejpam-3955	408	3	x	x	SYM
ejpam-3955	408	4	v1	v1	NOUN
ejpam-3955	408	5	u2	u2	PROPN
ejpam-3955	408	6	v2	v2	PROPN
ejpam-3955	408	7	u3	u3	NOUN
ejpam-3955	408	8	v3	v3	PROPN
ejpam-3955	408	9	u4	u4	PROPN
ejpam-3955	408	10	v4	v4	PROPN
ejpam-3955	408	11	uava	uava	NOUN
ejpam-3955	408	12	............	............	PUNCT
ejpam-3955	408	13	..............	..............	PUNCT
ejpam-3955	408	14	......................	......................	PUNCT
ejpam-3955	408	15	....................................................................................	....................................................................................	PUNCT
ejpam-3955	409	1	g2	g2	PROPN
ejpam-3955	409	2	....................................	....................................	PUNCT
ejpam-3955	409	3	....................................	....................................	PUNCT
ejpam-3955	410	1	....................................	....................................	PUNCT
ejpam-3955	410	2	....................................	....................................	PUNCT
ejpam-3955	411	1	....................................	....................................	PUNCT
ejpam-3955	411	2	................................................................................................	................................................................................................	PUNCT
ejpam-3955	411	3	............................................................................	............................................................................	PUNCT
ejpam-3955	412	1	................	................	PUNCT
ejpam-3955	412	2	...............	...............	PUNCT
ejpam-3955	412	3	...............	...............	PUNCT
ejpam-3955	412	4	...............	...............	PUNCT
ejpam-3955	412	5	...............	...............	PUNCT
ejpam-3955	412	6	........	........	PUNCT
ejpam-3955	412	7	............	............	PUNCT
ejpam-3955	412	8	...........	...........	PUNCT
ejpam-3955	412	9	...........	...........	PUNCT
ejpam-3955	412	10	...........	...........	PUNCT
ejpam-3955	412	11	...........	...........	PUNCT
ejpam-3955	412	12	...........	...........	PUNCT
ejpam-3955	412	13	...........	...........	PUNCT
ejpam-3955	412	14	...........	...........	PUNCT
ejpam-3955	412	15	...........	...........	PUNCT
ejpam-3955	412	16	...........	...........	PUNCT
ejpam-3955	412	17	...........	...........	PUNCT
ejpam-3955	412	18	..........	..........	PUNCT
ejpam-3955	413	1	..........	..........	PUNCT
ejpam-3955	413	2	..........	..........	PUNCT
ejpam-3955	414	1	..........	..........	PUNCT
ejpam-3955	414	2	..........	..........	PUNCT
ejpam-3955	415	1	..........	..........	PUNCT
ejpam-3955	415	2	..........	..........	PUNCT
ejpam-3955	416	1	..........	..........	PUNCT
ejpam-3955	416	2	..........	..........	PUNCT
ejpam-3955	417	1	..........	..........	PUNCT
ejpam-3955	417	2	..........	..........	PUNCT
ejpam-3955	418	1	..........	..........	PUNCT
ejpam-3955	418	2	..........	..........	PUNCT
ejpam-3955	419	1	..	..	PUNCT
ejpam-3955	419	2	.........	.........	PUNCT
ejpam-3955	420	1	........	........	PUNCT
ejpam-3955	420	2	........	........	PUNCT
ejpam-3955	421	1	.....	.....	PUNCT
ejpam-3955	421	2	.........	.........	PUNCT
ejpam-3955	422	1	......	......	PUNCT
ejpam-3955	422	2	.........	.........	PUNCT
ejpam-3955	422	3	.	.	PUNCT
ejpam-3955	422	4	.........	.........	PUNCT
ejpam-3955	423	1	........	........	PUNCT
ejpam-3955	423	2	........	........	PUNCT
ejpam-3955	424	1	.....	.....	PUNCT
ejpam-3955	424	2	.........	.........	PUNCT
ejpam-3955	424	3	........	........	PUNCT
ejpam-3955	424	4	........	........	PUNCT
ejpam-3955	425	1	.....	.....	PUNCT
ejpam-3955	425	2	.........................................................................	.........................................................................	PUNCT
ejpam-3955	425	3	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-3955	426	1	........................................................................................................................................................................	........................................................................................................................................................................	PROPN
ejpam-3955	426	2	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-3955	427	1	....................................................................................................................................................................	....................................................................................................................................................................	PUNCT
ejpam-3955	427	2	.....................................................................................................................................................................................................................	.....................................................................................................................................................................................................................	PUNCT
ejpam-3955	428	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-3955	428	2	...	...	PUNCT
ejpam-3955	429	1	w1	w1	NOUN
ejpam-3955	429	2	w2	w2	NOUN
ejpam-3955	429	3	w2k−2	w2k−2	PROPN
ejpam-3955	429	4	w2k−1	w2k−1	PROPN
ejpam-3955	429	5	w2k	w2k	PROPN
ejpam-3955	429	6	figure	figure	NOUN
ejpam-3955	429	7	3	3	NUM
ejpam-3955	429	8	:	:	PUNCT
ejpam-3955	429	9	g2	g2	PROPN
ejpam-3955	429	10	obtained	obtain	VERB
ejpam-3955	429	11	from	from	ADP
ejpam-3955	429	12	k1	k1	PROPN
ejpam-3955	429	13	observe	observe	VERB
ejpam-3955	429	14	that	that	SCONJ
ejpam-3955	429	15	for	for	ADP
ejpam-3955	429	16	each	each	DET
ejpam-3955	429	17	r	r	NOUN
ejpam-3955	429	18	∈	∈	PROPN
ejpam-3955	429	19	{	{	PUNCT
ejpam-3955	429	20	ua	ua	PROPN
ejpam-3955	429	21	,	,	PUNCT
ejpam-3955	429	22	va	va	PROPN
ejpam-3955	429	23	}	}	PUNCT
ejpam-3955	429	24	,	,	PUNCT
ejpam-3955	429	25	the	the	DET
ejpam-3955	429	26	set	set	NOUN
ejpam-3955	429	27	{	{	PUNCT
ejpam-3955	429	28	r	r	NOUN
ejpam-3955	429	29	,	,	PUNCT
ejpam-3955	429	30	u2	u2	NOUN
ejpam-3955	429	31	,	,	PUNCT
ejpam-3955	429	32	u3	u3	NOUN
ejpam-3955	429	33	,	,	PUNCT
ejpam-3955	429	34	.	.	PUNCT
ejpam-3955	429	35	.	.	PUNCT
ejpam-3955	429	36	.	.	PUNCT
ejpam-3955	430	1	,	,	PUNCT
ejpam-3955	430	2	ua−1	ua−1	PROPN
ejpam-3955	430	3	,	,	PUNCT
ejpam-3955	430	4	v1	v1	PROPN
ejpam-3955	430	5	}	}	PUNCT
ejpam-3955	430	6	is	be	AUX
ejpam-3955	430	7	a	a	DET
ejpam-3955	430	8	γce	γce	NOUN
ejpam-3955	430	9	-	-	PUNCT
ejpam-3955	430	10	set	set	VERB
ejpam-3955	430	11	in	in	ADP
ejpam-3955	430	12	h.	h.	PROPN
ejpam-3955	430	13	nuenay	nuenay	PROPN
ejpam-3955	430	14	-	-	PUNCT
ejpam-3955	430	15	maglanque	maglanque	ADJ
ejpam-3955	430	16	,	,	PUNCT
ejpam-3955	430	17	f.jamil	f.jamil	PROPN
ejpam-3955	430	18	/	/	SYM
ejpam-3955	430	19	eur	eur	PROPN
ejpam-3955	430	20	.	.	PUNCT
ejpam-3955	431	1	j.	j.	PROPN
ejpam-3955	431	2	pure	pure	PROPN
ejpam-3955	431	3	appl	appl	PROPN
ejpam-3955	431	4	.	.	PROPN
ejpam-3955	431	5	math	math	PROPN
ejpam-3955	431	6	,	,	PUNCT
ejpam-3955	431	7	14	14	NUM
ejpam-3955	431	8	(	(	PUNCT
ejpam-3955	431	9	2	2	NUM
ejpam-3955	431	10	)	)	PUNCT
ejpam-3955	431	11	(	(	PUNCT
ejpam-3955	431	12	2021	2021	NUM
ejpam-3955	431	13	)	)	PUNCT
ejpam-3955	431	14	,	,	PUNCT
ejpam-3955	431	15	537	537	NUM
ejpam-3955	431	16	-	-	SYM
ejpam-3955	431	17	550	550	NUM
ejpam-3955	431	18	548	548	NUM
ejpam-3955	431	19	g.	g.	NOUN
ejpam-3955	431	20	thus	thus	ADV
ejpam-3955	431	21	,	,	PUNCT
ejpam-3955	431	22	γce(g	γce(g	PROPN
ejpam-3955	431	23	)	)	PUNCT
ejpam-3955	431	24	=	=	SYM
ejpam-3955	432	1	1	1	NUM
ejpam-3955	432	2	+	+	CCONJ
ejpam-3955	432	3	a	a	DET
ejpam-3955	432	4	−	−	PROPN
ejpam-3955	432	5	1	1	NUM
ejpam-3955	432	6	=	=	NOUN
ejpam-3955	432	7	a.	a.	NOUN
ejpam-3955	432	8	also	also	ADV
ejpam-3955	432	9	,	,	PUNCT
ejpam-3955	432	10	γmce(g	γmce(g	PROPN
ejpam-3955	432	11	)	)	PUNCT
ejpam-3955	433	1	=	=	SYM
ejpam-3955	433	2	b	b	NOUN
ejpam-3955	433	3	which	which	PRON
ejpam-3955	433	4	is	be	AUX
ejpam-3955	433	5	determined	determine	VERB
ejpam-3955	433	6	by	by	ADP
ejpam-3955	433	7	the	the	DET
ejpam-3955	433	8	set	set	NOUN
ejpam-3955	433	9	{	{	PUNCT
ejpam-3955	433	10	x	x	NOUN
ejpam-3955	433	11	,	,	PUNCT
ejpam-3955	433	12	v2	v2	PROPN
ejpam-3955	433	13	,	,	PUNCT
ejpam-3955	433	14	v3	v3	PROPN
ejpam-3955	433	15	,	,	PUNCT
ejpam-3955	433	16	.	.	PUNCT
ejpam-3955	433	17	.	.	PUNCT
ejpam-3955	434	1	.	.	PUNCT
ejpam-3955	435	1	,	,	PUNCT
ejpam-3955	435	2	va−1	va−1	NOUN
ejpam-3955	435	3	,	,	PUNCT
ejpam-3955	435	4	z	z	NOUN
ejpam-3955	435	5	}	}	PUNCT
ejpam-3955	435	6	where	where	SCONJ
ejpam-3955	435	7	z	z	PROPN
ejpam-3955	435	8	∈	∈	PROPN
ejpam-3955	435	9	v	v	ADP
ejpam-3955	435	10	(	(	PUNCT
ejpam-3955	435	11	k2k+v1	k2k+v1	PROPN
ejpam-3955	435	12	)	)	PUNCT
ejpam-3955	435	13	.	.	PUNCT
ejpam-3955	436	1	moreover	moreover	ADV
ejpam-3955	436	2	,	,	PUNCT
ejpam-3955	436	3	note	note	VERB
ejpam-3955	436	4	that	that	SCONJ
ejpam-3955	436	5	the	the	DET
ejpam-3955	436	6	set	set	NOUN
ejpam-3955	436	7	{	{	PUNCT
ejpam-3955	436	8	x	x	NOUN
ejpam-3955	436	9	,	,	PUNCT
ejpam-3955	436	10	v2	v2	PROPN
ejpam-3955	436	11	,	,	PUNCT
ejpam-3955	436	12	v3	v3	PROPN
ejpam-3955	436	13	,	,	PUNCT
ejpam-3955	436	14	.	.	PUNCT
ejpam-3955	436	15	.	.	PUNCT
ejpam-3955	436	16	.	.	PUNCT
ejpam-3955	436	17	,	,	PUNCT
ejpam-3955	436	18	va	va	PROPN
ejpam-3955	436	19	,	,	PUNCT
ejpam-3955	436	20	w1	w1	NOUN
ejpam-3955	436	21	,	,	PUNCT
ejpam-3955	436	22	w2	w2	NOUN
ejpam-3955	436	23	,	,	PUNCT
ejpam-3955	436	24	.	.	PUNCT
ejpam-3955	436	25	.	.	PUNCT
ejpam-3955	436	26	.	.	PUNCT
ejpam-3955	436	27	,	,	PUNCT
ejpam-3955	436	28	wk−1	wk−1	PROPN
ejpam-3955	436	29	,	,	PUNCT
ejpam-3955	436	30	wk	wk	ADP
ejpam-3955	436	31	}	}	PUNCT
ejpam-3955	436	32	is	be	AUX
ejpam-3955	436	33	a	a	DET
ejpam-3955	436	34	γ+ce	γ+ce	NOUN
ejpam-3955	436	35	-	-	PUNCT
ejpam-3955	436	36	set	set	VERB
ejpam-3955	436	37	in	in	ADP
ejpam-3955	436	38	g.	g.	PROPN
ejpam-3955	436	39	therefore	therefore	ADV
ejpam-3955	436	40	,	,	PUNCT
ejpam-3955	436	41	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	436	42	)	)	PUNCT
ejpam-3955	436	43	=	=	SYM
ejpam-3955	437	1	1+a−1+k	1+a−1+k	NUM
ejpam-3955	437	2	=	=	SYM
ejpam-3955	437	3	a+k	a+k	NOUN
ejpam-3955	437	4	=	=	SYM
ejpam-3955	437	5	b+k	b+k	NUM
ejpam-3955	437	6	=	=	SYM
ejpam-3955	437	7	c.	c.	NOUN
ejpam-3955	437	8	suppose	suppose	VERB
ejpam-3955	437	9	that	that	SCONJ
ejpam-3955	437	10	b	b	X
ejpam-3955	437	11	=	=	PUNCT
ejpam-3955	437	12	a	a	DET
ejpam-3955	437	13	+	+	NUM
ejpam-3955	437	14	1	1	NUM
ejpam-3955	437	15	and	and	CCONJ
ejpam-3955	437	16	c	c	NOUN
ejpam-3955	437	17	=	=	SYM
ejpam-3955	437	18	b.	b.	PROPN
ejpam-3955	437	19	obtain	obtain	VERB
ejpam-3955	437	20	g	g	PROPN
ejpam-3955	437	21	=	=	SYM
ejpam-3955	437	22	g3	g3	PROPN
ejpam-3955	437	23	is	be	AUX
ejpam-3955	437	24	from	from	ADP
ejpam-3955	437	25	k1,a	k1,a	PROPN
ejpam-3955	437	26	by	by	ADP
ejpam-3955	437	27	adding	add	VERB
ejpam-3955	437	28	pendant	pendant	ADJ
ejpam-3955	437	29	edges	edge	NOUN
ejpam-3955	437	30	ujvj	ujvj	NOUN
ejpam-3955	437	31	,	,	PUNCT
ejpam-3955	437	32	j	j	PROPN
ejpam-3955	437	33	=	=	SYM
ejpam-3955	437	34	1	1	NUM
ejpam-3955	437	35	,	,	PUNCT
ejpam-3955	437	36	2	2	NUM
ejpam-3955	437	37	,	,	PUNCT
ejpam-3955	437	38	.	.	PUNCT
ejpam-3955	437	39	.	.	PUNCT
ejpam-3955	438	1	.	.	PUNCT
ejpam-3955	439	1	,	,	PUNCT
ejpam-3955	439	2	a	a	PRON
ejpam-3955	439	3	as	as	ADV
ejpam-3955	439	4	shown	show	VERB
ejpam-3955	439	5	in	in	ADP
ejpam-3955	439	6	figure	figure	NOUN
ejpam-3955	439	7	4	4	NUM
ejpam-3955	439	8	.	.	PUNCT
ejpam-3955	440	1	then	then	ADV
ejpam-3955	440	2	γce(g	γce(g	NUM
ejpam-3955	440	3	)	)	PUNCT
ejpam-3955	440	4	=	=	PUNCT
ejpam-3955	441	1	a	a	PRON
ejpam-3955	441	2	which	which	PRON
ejpam-3955	441	3	is	be	AUX
ejpam-3955	441	4	determined	determine	VERB
ejpam-3955	441	5	by	by	ADP
ejpam-3955	441	6	....................................	....................................	PUNCT
ejpam-3955	441	7	....................................	....................................	PUNCT
ejpam-3955	441	8	....................................	....................................	PUNCT
ejpam-3955	442	1	....................................	....................................	PUNCT
ejpam-3955	442	2	........................................................................	........................................................................	PUNCT
ejpam-3955	443	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	443	2	.......	.......	PUNCT
ejpam-3955	443	3	..	..	PUNCT
ejpam-3955	443	4	........	........	PUNCT
ejpam-3955	443	5	........	........	PUNCT
ejpam-3955	443	6	........	........	PUNCT
ejpam-3955	443	7	........	........	PUNCT
ejpam-3955	443	8	........	........	PUNCT
ejpam-3955	443	9	........	........	PUNCT
ejpam-3955	443	10	........	........	PUNCT
ejpam-3955	443	11	..	..	PUNCT
ejpam-3955	444	1	..........	..........	PUNCT
ejpam-3955	444	2	.........	.........	PUNCT
ejpam-3955	445	1	.........	.........	PUNCT
ejpam-3955	445	2	.........	.........	PUNCT
ejpam-3955	446	1	.........	.........	PUNCT
ejpam-3955	446	2	.........	.........	PUNCT
ejpam-3955	447	1	.........	.........	PUNCT
ejpam-3955	447	2	.........	.........	PUNCT
ejpam-3955	447	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	447	4	.	.	PUNCT
ejpam-3955	447	5	.	.	PUNCT
ejpam-3955	447	6	.	.	PUNCT
ejpam-3955	448	1	u1	u1	PROPN
ejpam-3955	448	2	u2	u2	PROPN
ejpam-3955	448	3	u3u4	u3u4	PROPN
ejpam-3955	448	4	ua	ua	PROPN
ejpam-3955	448	5	x	x	X
ejpam-3955	448	6	k1,a	k1,a	PROPN
ejpam-3955	448	7	....................................	....................................	PUNCT
ejpam-3955	448	8	....................................	....................................	PUNCT
ejpam-3955	449	1	....................................	....................................	PUNCT
ejpam-3955	449	2	....................................	....................................	PUNCT
ejpam-3955	450	1	........................................................................	........................................................................	PUNCT
ejpam-3955	450	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	450	3	.......	.......	PUNCT
ejpam-3955	450	4	..	..	PUNCT
ejpam-3955	450	5	........	........	PUNCT
ejpam-3955	450	6	........	........	PUNCT
ejpam-3955	450	7	........	........	PUNCT
ejpam-3955	450	8	........	........	PUNCT
ejpam-3955	450	9	........	........	PUNCT
ejpam-3955	450	10	........	........	PUNCT
ejpam-3955	451	1	........	........	PUNCT
ejpam-3955	451	2	..	..	PUNCT
ejpam-3955	452	1	..........	..........	PUNCT
ejpam-3955	452	2	.........	.........	PUNCT
ejpam-3955	453	1	.........	.........	PUNCT
ejpam-3955	453	2	.........	.........	PUNCT
ejpam-3955	454	1	.........	.........	PUNCT
ejpam-3955	454	2	.........	.........	PUNCT
ejpam-3955	455	1	.........	.........	PUNCT
ejpam-3955	455	2	.........	.........	PUNCT
ejpam-3955	455	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	455	4	.	.	PUNCT
ejpam-3955	455	5	.	.	PUNCT
ejpam-3955	455	6	.	.	PUNCT
ejpam-3955	456	1	....................................	....................................	PUNCT
ejpam-3955	456	2	........................................................................	........................................................................	PUNCT
ejpam-3955	457	1	....................................	....................................	PUNCT
ejpam-3955	457	2	....................................	....................................	PUNCT
ejpam-3955	457	3	........................................	........................................	PUNCT
ejpam-3955	457	4	........................................	........................................	PUNCT
ejpam-3955	458	1	.........	.........	PUNCT
ejpam-3955	458	2	........	........	PUNCT
ejpam-3955	458	3	........	........	PUNCT
ejpam-3955	458	4	........	........	PUNCT
ejpam-3955	458	5	.......	.......	PUNCT
ejpam-3955	459	1	.............................................	.............................................	PUNCT
ejpam-3955	459	2	.........	.........	PUNCT
ejpam-3955	460	1	.........	.........	PUNCT
ejpam-3955	460	2	.....	.....	PUNCT
ejpam-3955	460	3	u1	u1	NOUN
ejpam-3955	460	4	x	x	SYM
ejpam-3955	460	5	v1	v1	NOUN
ejpam-3955	460	6	u2	u2	PROPN
ejpam-3955	460	7	v2	v2	PROPN
ejpam-3955	460	8	u3	u3	NOUN
ejpam-3955	460	9	v3	v3	PROPN
ejpam-3955	460	10	u4	u4	PROPN
ejpam-3955	460	11	v4	v4	PROPN
ejpam-3955	460	12	uava	uava	PROPN
ejpam-3955	460	13	g3	g3	PROPN
ejpam-3955	460	14	figure	figure	NOUN
ejpam-3955	460	15	4	4	NUM
ejpam-3955	460	16	:	:	PUNCT
ejpam-3955	460	17	g3	g3	NOUN
ejpam-3955	460	18	obtained	obtain	VERB
ejpam-3955	460	19	from	from	ADP
ejpam-3955	460	20	k1,a	k1,a	PROPN
ejpam-3955	460	21	the	the	DET
ejpam-3955	460	22	set	set	NOUN
ejpam-3955	460	23	{	{	PUNCT
ejpam-3955	460	24	u1	u1	NOUN
ejpam-3955	460	25	,	,	PUNCT
ejpam-3955	460	26	u2	u2	NOUN
ejpam-3955	460	27	,	,	PUNCT
ejpam-3955	460	28	.	.	PUNCT
ejpam-3955	460	29	.	.	PUNCT
ejpam-3955	461	1	.	.	PUNCT
ejpam-3955	462	1	,	,	PUNCT
ejpam-3955	462	2	ua	ua	PROPN
ejpam-3955	462	3	}	}	PUNCT
ejpam-3955	462	4	.	.	PUNCT
ejpam-3955	463	1	also	also	ADV
ejpam-3955	463	2	,	,	PUNCT
ejpam-3955	463	3	γmce(g	γmce(g	PROPN
ejpam-3955	463	4	)	)	PUNCT
ejpam-3955	463	5	=	=	SYM
ejpam-3955	463	6	a+	a+	PUNCT
ejpam-3955	463	7	1	1	NUM
ejpam-3955	463	8	=	=	SYM
ejpam-3955	463	9	b	b	PROPN
ejpam-3955	463	10	and	and	CCONJ
ejpam-3955	463	11	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	463	12	)	)	PUNCT
ejpam-3955	464	1	=	=	PUNCT
ejpam-3955	465	1	c	c	NOUN
ejpam-3955	465	2	which	which	PRON
ejpam-3955	465	3	are	be	AUX
ejpam-3955	465	4	determined	determine	VERB
ejpam-3955	465	5	by	by	ADP
ejpam-3955	465	6	the	the	DET
ejpam-3955	465	7	set	set	NOUN
ejpam-3955	465	8	{	{	PUNCT
ejpam-3955	465	9	v1	v1	NOUN
ejpam-3955	465	10	,	,	PUNCT
ejpam-3955	465	11	v2	v2	PROPN
ejpam-3955	465	12	,	,	PUNCT
ejpam-3955	465	13	.	.	PUNCT
ejpam-3955	465	14	.	.	PUNCT
ejpam-3955	466	1	.	.	PUNCT
ejpam-3955	467	1	,	,	PUNCT
ejpam-3955	467	2	va	va	NOUN
ejpam-3955	467	3	,	,	PUNCT
ejpam-3955	467	4	x	x	NOUN
ejpam-3955	467	5	}	}	PUNCT
ejpam-3955	467	6	.	.	PUNCT
ejpam-3955	467	7	suppose	suppose	VERB
ejpam-3955	467	8	that	that	SCONJ
ejpam-3955	467	9	c	c	PROPN
ejpam-3955	467	10	=	=	SYM
ejpam-3955	467	11	b	b	PROPN
ejpam-3955	467	12	+	+	CCONJ
ejpam-3955	467	13	k	k	PROPN
ejpam-3955	467	14	,	,	PUNCT
ejpam-3955	467	15	k	k	PROPN
ejpam-3955	467	16	≥	≥	NUM
ejpam-3955	467	17	2	2	NUM
ejpam-3955	467	18	.	.	PUNCT
ejpam-3955	467	19	obtain	obtain	VERB
ejpam-3955	467	20	g	g	NOUN
ejpam-3955	467	21	by	by	ADP
ejpam-3955	467	22	joining	join	VERB
ejpam-3955	467	23	the	the	DET
ejpam-3955	467	24	complete	complete	ADJ
ejpam-3955	467	25	graph	graph	NOUN
ejpam-3955	467	26	k2k	k2k	VERB
ejpam-3955	467	27	to	to	ADP
ejpam-3955	467	28	exactly	exactly	ADV
ejpam-3955	467	29	one	one	NUM
ejpam-3955	467	30	of	of	ADP
ejpam-3955	467	31	end	end	NOUN
ejpam-3955	467	32	vertices	vertex	NOUN
ejpam-3955	467	33	of	of	ADP
ejpam-3955	467	34	g3	g3	NOUN
ejpam-3955	467	35	say	say	VERB
ejpam-3955	467	36	in	in	ADP
ejpam-3955	467	37	v1	v1	NOUN
ejpam-3955	467	38	,	,	PUNCT
ejpam-3955	467	39	as	as	SCONJ
ejpam-3955	467	40	shown	show	VERB
ejpam-3955	467	41	in	in	ADP
ejpam-3955	467	42	figure	figure	NOUN
ejpam-3955	467	43	5	5	NUM
ejpam-3955	467	44	.	.	PUNCT
ejpam-3955	467	45	....................................	....................................	PUNCT
ejpam-3955	467	46	....................................	....................................	PUNCT
ejpam-3955	468	1	....................................	....................................	PUNCT
ejpam-3955	468	2	....................................	....................................	PUNCT
ejpam-3955	469	1	........................................................................	........................................................................	PUNCT
ejpam-3955	469	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	469	3	.......	.......	PUNCT
ejpam-3955	469	4	..	..	PUNCT
ejpam-3955	469	5	........	........	PUNCT
ejpam-3955	469	6	........	........	PUNCT
ejpam-3955	469	7	........	........	PUNCT
ejpam-3955	469	8	........	........	PUNCT
ejpam-3955	469	9	........	........	PUNCT
ejpam-3955	469	10	........	........	PUNCT
ejpam-3955	470	1	........	........	PUNCT
ejpam-3955	470	2	..	..	PUNCT
ejpam-3955	471	1	..........	..........	PUNCT
ejpam-3955	471	2	.........	.........	PUNCT
ejpam-3955	472	1	.........	.........	PUNCT
ejpam-3955	472	2	.........	.........	PUNCT
ejpam-3955	473	1	.........	.........	PUNCT
ejpam-3955	473	2	.........	.........	PUNCT
ejpam-3955	474	1	.........	.........	PUNCT
ejpam-3955	474	2	.........	.........	PUNCT
ejpam-3955	474	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	474	4	.	.	PUNCT
ejpam-3955	474	5	.	.	PUNCT
ejpam-3955	474	6	.	.	PUNCT
ejpam-3955	475	1	....................................	....................................	PUNCT
ejpam-3955	475	2	........................................................................	........................................................................	PUNCT
ejpam-3955	476	1	....................................	....................................	PUNCT
ejpam-3955	476	2	....................................	....................................	PUNCT
ejpam-3955	476	3	........................................	........................................	PUNCT
ejpam-3955	476	4	........................................	........................................	PUNCT
ejpam-3955	477	1	.........	.........	PUNCT
ejpam-3955	477	2	........	........	PUNCT
ejpam-3955	477	3	........	........	PUNCT
ejpam-3955	477	4	........	........	PUNCT
ejpam-3955	477	5	.......	.......	PUNCT
ejpam-3955	478	1	.............................................	.............................................	PUNCT
ejpam-3955	478	2	.........	.........	PUNCT
ejpam-3955	479	1	.........	.........	PUNCT
ejpam-3955	479	2	.....	.....	PUNCT
ejpam-3955	479	3	u1	u1	NOUN
ejpam-3955	479	4	x	x	SYM
ejpam-3955	479	5	v1	v1	NOUN
ejpam-3955	479	6	u2	u2	PROPN
ejpam-3955	479	7	v2	v2	PROPN
ejpam-3955	479	8	u3	u3	NOUN
ejpam-3955	479	9	v3	v3	PROPN
ejpam-3955	479	10	u4	u4	PROPN
ejpam-3955	479	11	v4	v4	PROPN
ejpam-3955	479	12	uava	uava	PROPN
ejpam-3955	479	13	g3	g3	PROPN
ejpam-3955	479	14	....................................	....................................	PUNCT
ejpam-3955	479	15	....................................	....................................	PUNCT
ejpam-3955	480	1	....................................	....................................	PUNCT
ejpam-3955	480	2	....................................	....................................	PUNCT
ejpam-3955	481	1	........................................................................	........................................................................	PUNCT
ejpam-3955	481	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	481	3	.......	.......	PUNCT
ejpam-3955	481	4	..	..	PUNCT
ejpam-3955	481	5	........	........	PUNCT
ejpam-3955	481	6	........	........	PUNCT
ejpam-3955	481	7	........	........	PUNCT
ejpam-3955	481	8	........	........	PUNCT
ejpam-3955	481	9	........	........	PUNCT
ejpam-3955	481	10	........	........	PUNCT
ejpam-3955	482	1	........	........	PUNCT
ejpam-3955	482	2	..	..	PUNCT
ejpam-3955	483	1	..........	..........	PUNCT
ejpam-3955	483	2	.........	.........	PUNCT
ejpam-3955	484	1	.........	.........	PUNCT
ejpam-3955	484	2	.........	.........	PUNCT
ejpam-3955	485	1	.........	.........	PUNCT
ejpam-3955	485	2	.........	.........	PUNCT
ejpam-3955	486	1	.........	.........	PUNCT
ejpam-3955	486	2	.........	.........	PUNCT
ejpam-3955	486	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	486	4	.	.	PUNCT
ejpam-3955	486	5	.	.	PUNCT
ejpam-3955	486	6	.	.	PUNCT
ejpam-3955	487	1	....................................	....................................	PUNCT
ejpam-3955	487	2	........................................................................	........................................................................	PUNCT
ejpam-3955	488	1	....................................	....................................	PUNCT
ejpam-3955	488	2	....................................	....................................	PUNCT
ejpam-3955	488	3	........................................	........................................	PUNCT
ejpam-3955	488	4	........................................	........................................	PUNCT
ejpam-3955	489	1	.........	.........	PUNCT
ejpam-3955	489	2	........	........	PUNCT
ejpam-3955	489	3	........	........	PUNCT
ejpam-3955	489	4	........	........	PUNCT
ejpam-3955	489	5	.......	.......	PUNCT
ejpam-3955	490	1	.............................................	.............................................	PUNCT
ejpam-3955	490	2	.........	.........	PUNCT
ejpam-3955	491	1	.........	.........	PUNCT
ejpam-3955	491	2	.....	.....	PUNCT
ejpam-3955	491	3	u1	u1	NOUN
ejpam-3955	491	4	x	x	SYM
ejpam-3955	491	5	v1	v1	NOUN
ejpam-3955	491	6	u2	u2	PROPN
ejpam-3955	491	7	v2	v2	PROPN
ejpam-3955	491	8	u3	u3	NOUN
ejpam-3955	491	9	v3	v3	PROPN
ejpam-3955	491	10	u4	u4	PROPN
ejpam-3955	491	11	v4	v4	PROPN
ejpam-3955	491	12	uava	uava	NOUN
ejpam-3955	491	13	g4	g4	NOUN
ejpam-3955	491	14	....................................	....................................	PUNCT
ejpam-3955	491	15	....................................	....................................	PUNCT
ejpam-3955	491	16	....................................	....................................	PUNCT
ejpam-3955	491	17	....................................	....................................	PUNCT
ejpam-3955	491	18	....................................	....................................	PUNCT
ejpam-3955	491	19	................................................................................................	................................................................................................	PUNCT
ejpam-3955	491	20	............................................................................	............................................................................	PUNCT
ejpam-3955	491	21	................	................	PUNCT
ejpam-3955	491	22	...............	...............	PUNCT
ejpam-3955	491	23	...............	...............	PUNCT
ejpam-3955	491	24	...............	...............	PUNCT
ejpam-3955	491	25	...............	...............	PUNCT
ejpam-3955	491	26	........	........	PUNCT
ejpam-3955	491	27	............	............	PUNCT
ejpam-3955	491	28	...........	...........	PUNCT
ejpam-3955	491	29	...........	...........	PUNCT
ejpam-3955	491	30	...........	...........	PUNCT
ejpam-3955	491	31	...........	...........	PUNCT
ejpam-3955	491	32	...........	...........	PUNCT
ejpam-3955	491	33	...........	...........	PUNCT
ejpam-3955	491	34	...........	...........	PUNCT
ejpam-3955	491	35	...........	...........	PUNCT
ejpam-3955	491	36	...........	...........	PUNCT
ejpam-3955	491	37	...........	...........	PUNCT
ejpam-3955	491	38	..........	..........	PUNCT
ejpam-3955	492	1	..........	..........	PUNCT
ejpam-3955	492	2	..........	..........	PUNCT
ejpam-3955	493	1	..........	..........	PUNCT
ejpam-3955	493	2	..........	..........	PUNCT
ejpam-3955	494	1	..........	..........	PUNCT
ejpam-3955	494	2	..........	..........	PUNCT
ejpam-3955	495	1	..........	..........	PUNCT
ejpam-3955	495	2	..........	..........	PUNCT
ejpam-3955	496	1	..........	..........	PUNCT
ejpam-3955	496	2	..........	..........	PUNCT
ejpam-3955	497	1	..........	..........	PUNCT
ejpam-3955	497	2	..........	..........	PUNCT
ejpam-3955	498	1	..	..	PUNCT
ejpam-3955	498	2	.........	.........	PUNCT
ejpam-3955	499	1	........	........	PUNCT
ejpam-3955	499	2	........	........	PUNCT
ejpam-3955	500	1	.....	.....	PUNCT
ejpam-3955	500	2	.........	.........	PUNCT
ejpam-3955	501	1	......	......	PUNCT
ejpam-3955	501	2	.........	.........	PUNCT
ejpam-3955	501	3	.	.	PUNCT
ejpam-3955	501	4	.........	.........	PUNCT
ejpam-3955	502	1	........	........	PUNCT
ejpam-3955	502	2	........	........	PUNCT
ejpam-3955	503	1	.....	.....	PUNCT
ejpam-3955	503	2	.........	.........	PUNCT
ejpam-3955	503	3	........	........	PUNCT
ejpam-3955	503	4	........	........	PUNCT
ejpam-3955	504	1	.....	.....	PUNCT
ejpam-3955	504	2	.........................................................................	.........................................................................	PUNCT
ejpam-3955	504	3	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-3955	505	1	........................................................................................................................................................................	........................................................................................................................................................................	PROPN
ejpam-3955	505	2	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-3955	506	1	....................................................................................................................................................................	....................................................................................................................................................................	PUNCT
ejpam-3955	506	2	.....................................................................................................................................................................................................................	.....................................................................................................................................................................................................................	PUNCT
ejpam-3955	507	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-3955	507	2	...	...	PUNCT
ejpam-3955	508	1	w1	w1	NOUN
ejpam-3955	508	2	w2	w2	NOUN
ejpam-3955	508	3	w2k−2	w2k−2	PROPN
ejpam-3955	508	4	w2k−1	w2k−1	PROPN
ejpam-3955	508	5	w2k	w2k	PROPN
ejpam-3955	508	6	figure	figure	NOUN
ejpam-3955	508	7	5	5	NUM
ejpam-3955	508	8	:	:	PUNCT
ejpam-3955	508	9	g4	g4	NOUN
ejpam-3955	508	10	obtained	obtain	VERB
ejpam-3955	508	11	from	from	ADP
ejpam-3955	508	12	g3	g3	PROPN
ejpam-3955	508	13	now	now	ADV
ejpam-3955	508	14	,	,	PUNCT
ejpam-3955	508	15	γce(g	γce(g	PROPN
ejpam-3955	508	16	)	)	PUNCT
ejpam-3955	508	17	=	=	PUNCT
ejpam-3955	509	1	a	a	PRON
ejpam-3955	509	2	which	which	PRON
ejpam-3955	509	3	is	be	AUX
ejpam-3955	509	4	determined	determine	VERB
ejpam-3955	509	5	by	by	ADP
ejpam-3955	509	6	the	the	DET
ejpam-3955	509	7	set	set	NOUN
ejpam-3955	509	8	{	{	PUNCT
ejpam-3955	509	9	u2	u2	NOUN
ejpam-3955	509	10	,	,	PUNCT
ejpam-3955	509	11	u3	u3	NOUN
ejpam-3955	509	12	,	,	PUNCT
ejpam-3955	509	13	.	.	PUNCT
ejpam-3955	509	14	.	.	PUNCT
ejpam-3955	510	1	.	.	PUNCT
ejpam-3955	511	1	,	,	PUNCT
ejpam-3955	511	2	ua	ua	PROPN
ejpam-3955	511	3	,	,	PUNCT
ejpam-3955	511	4	v1	v1	PROPN
ejpam-3955	511	5	}	}	PUNCT
ejpam-3955	511	6	.	.	PUNCT
ejpam-3955	512	1	note	note	VERB
ejpam-3955	512	2	that	that	SCONJ
ejpam-3955	512	3	γmce(k2k	γmce(k2k	VERB
ejpam-3955	512	4	)	)	PUNCT
ejpam-3955	512	5	=	=	SYM
ejpam-3955	512	6	1	1	X
ejpam-3955	512	7	.	.	PUNCT
ejpam-3955	513	1	thus	thus	ADV
ejpam-3955	513	2	,	,	PUNCT
ejpam-3955	513	3	γmce(g	γmce(g	PROPN
ejpam-3955	513	4	)	)	PUNCT
ejpam-3955	513	5	=	=	PUNCT
ejpam-3955	514	1	a	a	DET
ejpam-3955	514	2	+	+	NUM
ejpam-3955	514	3	1	1	NUM
ejpam-3955	514	4	=	=	SYM
ejpam-3955	514	5	b	b	NOUN
ejpam-3955	514	6	which	which	PRON
ejpam-3955	514	7	is	be	AUX
ejpam-3955	514	8	determined	determine	VERB
ejpam-3955	514	9	by	by	ADP
ejpam-3955	514	10	the	the	DET
ejpam-3955	514	11	set	set	NOUN
ejpam-3955	514	12	{	{	PUNCT
ejpam-3955	514	13	x	x	NOUN
ejpam-3955	514	14	,	,	PUNCT
ejpam-3955	514	15	v2	v2	PROPN
ejpam-3955	514	16	,	,	PUNCT
ejpam-3955	514	17	v3	v3	PROPN
ejpam-3955	514	18	,	,	PUNCT
ejpam-3955	514	19	.	.	PUNCT
ejpam-3955	514	20	.	.	PUNCT
ejpam-3955	515	1	.	.	PUNCT
ejpam-3955	516	1	,	,	PUNCT
ejpam-3955	516	2	va	va	NOUN
ejpam-3955	516	3	,	,	PUNCT
ejpam-3955	516	4	z	z	NOUN
ejpam-3955	516	5	}	}	PUNCT
ejpam-3955	516	6	z	z	NOUN
ejpam-3955	516	7	∈	∈	PROPN
ejpam-3955	516	8	v	v	ADP
ejpam-3955	516	9	(	(	PUNCT
ejpam-3955	516	10	k2k+v1	k2k+v1	PROPN
ejpam-3955	516	11	)	)	PUNCT
ejpam-3955	516	12	.	.	PUNCT
ejpam-3955	517	1	also	also	ADV
ejpam-3955	517	2	,	,	PUNCT
ejpam-3955	517	3	observe	observe	VERB
ejpam-3955	517	4	that	that	SCONJ
ejpam-3955	517	5	the	the	DET
ejpam-3955	517	6	set	set	NOUN
ejpam-3955	517	7	{	{	PUNCT
ejpam-3955	517	8	w1	w1	NOUN
ejpam-3955	517	9	,	,	PUNCT
ejpam-3955	517	10	w2	w2	NOUN
ejpam-3955	517	11	,	,	PUNCT
ejpam-3955	517	12	.	.	PUNCT
ejpam-3955	517	13	.	.	PUNCT
ejpam-3955	517	14	.	.	PUNCT
ejpam-3955	518	1	,	,	PUNCT
ejpam-3955	518	2	wk	wk	X
ejpam-3955	518	3	}	}	PUNCT
ejpam-3955	518	4	is	be	AUX
ejpam-3955	518	5	a	a	DET
ejpam-3955	518	6	γ+ce	γ+ce	NOUN
ejpam-3955	518	7	-	-	PUNCT
ejpam-3955	518	8	set	set	NOUN
ejpam-3955	518	9	in	in	ADP
ejpam-3955	518	10	k2k	k2k	PROPN
ejpam-3955	518	11	.	.	PUNCT
ejpam-3955	519	1	thus	thus	ADV
ejpam-3955	519	2	,	,	PUNCT
ejpam-3955	519	3	{	{	PUNCT
ejpam-3955	519	4	x	x	NOUN
ejpam-3955	519	5	,	,	PUNCT
ejpam-3955	519	6	v1	v1	NOUN
ejpam-3955	519	7	,	,	PUNCT
ejpam-3955	519	8	v2	v2	NOUN
ejpam-3955	519	9	,	,	PUNCT
ejpam-3955	519	10	.	.	PUNCT
ejpam-3955	519	11	.	.	PUNCT
ejpam-3955	520	1	.	.	PUNCT
ejpam-3955	521	1	,	,	PUNCT
ejpam-3955	521	2	va	va	PROPN
ejpam-3955	521	3	,	,	PUNCT
ejpam-3955	521	4	w1	w1	NOUN
ejpam-3955	521	5	,	,	PUNCT
ejpam-3955	521	6	.	.	PUNCT
ejpam-3955	521	7	.	.	PUNCT
ejpam-3955	522	1	.	.	PUNCT
ejpam-3955	523	1	,	,	PUNCT
ejpam-3955	523	2	wk	wk	X
ejpam-3955	523	3	}	}	PUNCT
ejpam-3955	523	4	is	be	AUX
ejpam-3955	523	5	a	a	DET
ejpam-3955	523	6	γ+ce	γ+ce	NOUN
ejpam-3955	523	7	-	-	PUNCT
ejpam-3955	523	8	set	set	VERB
ejpam-3955	523	9	in	in	ADP
ejpam-3955	523	10	g.	g.	PROPN
ejpam-3955	523	11	therefore	therefore	ADV
ejpam-3955	523	12	,	,	PUNCT
ejpam-3955	523	13	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	523	14	)	)	PUNCT
ejpam-3955	523	15	=	=	SYM
ejpam-3955	524	1	1	1	NUM
ejpam-3955	524	2	+	+	NUM
ejpam-3955	524	3	a+	a+	X
ejpam-3955	524	4	k	k	X
ejpam-3955	524	5	=	=	X
ejpam-3955	524	6	b+	b+	X
ejpam-3955	524	7	k	k	X
ejpam-3955	524	8	=	=	SYM
ejpam-3955	524	9	c.	c.	PROPN
ejpam-3955	524	10	suppose	suppose	VERB
ejpam-3955	524	11	that	that	SCONJ
ejpam-3955	524	12	b	b	X
ejpam-3955	524	13	=	=	PUNCT
ejpam-3955	524	14	a+k	a+k	PROPN
ejpam-3955	524	15	and	and	CCONJ
ejpam-3955	524	16	c	c	PROPN
ejpam-3955	524	17	=	=	PROPN
ejpam-3955	524	18	b.	b.	PROPN
ejpam-3955	524	19	obtain	obtain	VERB
ejpam-3955	524	20	g	g	NOUN
ejpam-3955	524	21	=	=	PUNCT
ejpam-3955	524	22	g5	g5	NOUN
ejpam-3955	524	23	from	from	ADP
ejpam-3955	524	24	g3	g3	PROPN
ejpam-3955	524	25	by	by	ADP
ejpam-3955	524	26	adding	add	VERB
ejpam-3955	524	27	k	k	PROPN
ejpam-3955	524	28	pendant	pendant	ADJ
ejpam-3955	524	29	edges	edge	NOUN
ejpam-3955	524	30	vahj	vahj	VERB
ejpam-3955	524	31	,	,	PUNCT
ejpam-3955	524	32	j	j	PROPN
ejpam-3955	524	33	=	=	SYM
ejpam-3955	524	34	1	1	NUM
ejpam-3955	524	35	,	,	PUNCT
ejpam-3955	524	36	2	2	NUM
ejpam-3955	524	37	,	,	PUNCT
ejpam-3955	524	38	.	.	PUNCT
ejpam-3955	524	39	.	.	PUNCT
ejpam-3955	525	1	.	.	PUNCT
ejpam-3955	526	1	,	,	PUNCT
ejpam-3955	526	2	k	k	PROPN
ejpam-3955	526	3	as	as	SCONJ
ejpam-3955	526	4	shown	show	VERB
ejpam-3955	526	5	in	in	ADP
ejpam-3955	526	6	figure	figure	NOUN
ejpam-3955	526	7	6	6	NUM
ejpam-3955	526	8	.	.	PUNCT
ejpam-3955	527	1	then	then	ADV
ejpam-3955	527	2	γce(g	γce(g	NUM
ejpam-3955	527	3	)	)	PUNCT
ejpam-3955	527	4	=	=	PUNCT
ejpam-3955	528	1	a	a	PRON
ejpam-3955	528	2	which	which	PRON
ejpam-3955	528	3	is	be	AUX
ejpam-3955	528	4	determined	determine	VERB
ejpam-3955	528	5	by	by	ADP
ejpam-3955	528	6	the	the	DET
ejpam-3955	528	7	references	reference	NOUN
ejpam-3955	528	8	549	549	NUM
ejpam-3955	528	9	....................................	....................................	PUNCT
ejpam-3955	528	10	....................................	....................................	PUNCT
ejpam-3955	528	11	....................................	....................................	PUNCT
ejpam-3955	529	1	....................................	....................................	PUNCT
ejpam-3955	529	2	........................................................................	........................................................................	PUNCT
ejpam-3955	530	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	530	2	.......	.......	PUNCT
ejpam-3955	530	3	..	..	PUNCT
ejpam-3955	530	4	........	........	PUNCT
ejpam-3955	530	5	........	........	PUNCT
ejpam-3955	530	6	........	........	PUNCT
ejpam-3955	530	7	........	........	PUNCT
ejpam-3955	530	8	........	........	PUNCT
ejpam-3955	530	9	........	........	PUNCT
ejpam-3955	530	10	........	........	PUNCT
ejpam-3955	530	11	..	..	PUNCT
ejpam-3955	531	1	..........	..........	PUNCT
ejpam-3955	531	2	.........	.........	PUNCT
ejpam-3955	532	1	.........	.........	PUNCT
ejpam-3955	532	2	.........	.........	PUNCT
ejpam-3955	533	1	.........	.........	PUNCT
ejpam-3955	533	2	.........	.........	PUNCT
ejpam-3955	534	1	.........	.........	PUNCT
ejpam-3955	534	2	.........	.........	PUNCT
ejpam-3955	534	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	534	4	.	.	PUNCT
ejpam-3955	534	5	.	.	PUNCT
ejpam-3955	534	6	.	.	PUNCT
ejpam-3955	535	1	....................................	....................................	PUNCT
ejpam-3955	535	2	........................................................................	........................................................................	PUNCT
ejpam-3955	536	1	....................................	....................................	PUNCT
ejpam-3955	536	2	....................................	....................................	PUNCT
ejpam-3955	536	3	........................................	........................................	PUNCT
ejpam-3955	536	4	........................................	........................................	PUNCT
ejpam-3955	537	1	.........	.........	PUNCT
ejpam-3955	537	2	........	........	PUNCT
ejpam-3955	537	3	........	........	PUNCT
ejpam-3955	537	4	........	........	PUNCT
ejpam-3955	537	5	.......	.......	PUNCT
ejpam-3955	538	1	.............................................	.............................................	PUNCT
ejpam-3955	538	2	.........	.........	PUNCT
ejpam-3955	539	1	.........	.........	PUNCT
ejpam-3955	539	2	.....	.....	PUNCT
ejpam-3955	539	3	u1	u1	NOUN
ejpam-3955	539	4	x	x	SYM
ejpam-3955	539	5	v1	v1	NOUN
ejpam-3955	539	6	u2	u2	PROPN
ejpam-3955	539	7	v2	v2	PROPN
ejpam-3955	539	8	u3	u3	NOUN
ejpam-3955	539	9	v3	v3	PROPN
ejpam-3955	539	10	u4	u4	PROPN
ejpam-3955	539	11	v4	v4	PROPN
ejpam-3955	539	12	ua	ua	PROPN
ejpam-3955	539	13	va	va	PROPN
ejpam-3955	539	14	g5	g5	PROPN
ejpam-3955	539	15	....................................	....................................	PUNCT
ejpam-3955	539	16	....................................	....................................	PUNCT
ejpam-3955	540	1	....................................	....................................	PUNCT
ejpam-3955	540	2	....................................	....................................	PUNCT
ejpam-3955	541	1	....................................	....................................	PUNCT
ejpam-3955	541	2	............................................................................................................................................................	............................................................................................................................................................	PUNCT
ejpam-3955	542	1	................................................	................................................	PUNCT
ejpam-3955	542	2	..........	..........	PUNCT
ejpam-3955	543	1	.........	.........	PUNCT
ejpam-3955	543	2	.........	.........	PUNCT
ejpam-3955	544	1	.........	.........	PUNCT
ejpam-3955	544	2	.........	.........	PUNCT
ejpam-3955	545	1	.........	.........	PUNCT
ejpam-3955	545	2	.........	.........	PUNCT
ejpam-3955	546	1	.........	.........	PUNCT
ejpam-3955	546	2	.........	.........	PUNCT
ejpam-3955	547	1	.........	.........	PUNCT
ejpam-3955	547	2	..	..	PUNCT
ejpam-3955	547	3	............	............	PUNCT
ejpam-3955	547	4	...........	...........	PUNCT
ejpam-3955	547	5	...........	...........	PUNCT
ejpam-3955	547	6	...........	...........	PUNCT
ejpam-3955	547	7	...........	...........	PUNCT
ejpam-3955	547	8	...........	...........	PUNCT
ejpam-3955	547	9	.	.	PUNCT
ejpam-3955	548	1	.................	.................	PUNCT
ejpam-3955	548	2	................	................	PUNCT
ejpam-3955	548	3	...............	...............	PUNCT
ejpam-3955	548	4	........................................	........................................	PUNCT
ejpam-3955	548	5	...	...	PUNCT
ejpam-3955	549	1	h1	h1	VERB
ejpam-3955	549	2	h2	h2	PROPN
ejpam-3955	549	3	h3	h3	PROPN
ejpam-3955	549	4	h4	h4	PROPN
ejpam-3955	549	5	h5	h5	PROPN
ejpam-3955	549	6	hk	hk	PROPN
ejpam-3955	549	7	figure	figure	NOUN
ejpam-3955	549	8	6	6	NUM
ejpam-3955	549	9	:	:	PUNCT
ejpam-3955	549	10	g5	g5	NOUN
ejpam-3955	549	11	obtained	obtain	VERB
ejpam-3955	549	12	from	from	ADP
ejpam-3955	549	13	g3	g3	PROPN
ejpam-3955	549	14	set	set	NOUN
ejpam-3955	549	15	{	{	PUNCT
ejpam-3955	549	16	u1	u1	NOUN
ejpam-3955	549	17	,	,	PUNCT
ejpam-3955	549	18	u2	u2	NOUN
ejpam-3955	549	19	,	,	PUNCT
ejpam-3955	549	20	.	.	PUNCT
ejpam-3955	549	21	.	.	PUNCT
ejpam-3955	550	1	.	.	PUNCT
ejpam-3955	551	1	,	,	PUNCT
ejpam-3955	551	2	ua−1	ua−1	PROPN
ejpam-3955	551	3	,	,	PUNCT
ejpam-3955	551	4	ua	ua	PROPN
ejpam-3955	551	5	}	}	PUNCT
ejpam-3955	551	6	.	.	PUNCT
ejpam-3955	552	1	also	also	ADV
ejpam-3955	552	2	,	,	PUNCT
ejpam-3955	552	3	observe	observe	VERB
ejpam-3955	552	4	that	that	SCONJ
ejpam-3955	552	5	the	the	DET
ejpam-3955	552	6	set	set	NOUN
ejpam-3955	552	7	{	{	PUNCT
ejpam-3955	552	8	v1	v1	NOUN
ejpam-3955	552	9	,	,	PUNCT
ejpam-3955	552	10	v2	v2	PROPN
ejpam-3955	552	11	,	,	PUNCT
ejpam-3955	552	12	.	.	PUNCT
ejpam-3955	552	13	.	.	PUNCT
ejpam-3955	553	1	.	.	PUNCT
ejpam-3955	554	1	,	,	PUNCT
ejpam-3955	554	2	va−1	va−1	NOUN
ejpam-3955	554	3	,	,	PUNCT
ejpam-3955	554	4	x	x	NOUN
ejpam-3955	554	5	,	,	PUNCT
ejpam-3955	554	6	h1	h1	PROPN
ejpam-3955	554	7	,	,	PUNCT
ejpam-3955	554	8	h2	h2	PROPN
ejpam-3955	554	9	,	,	PUNCT
ejpam-3955	554	10	.	.	PUNCT
ejpam-3955	554	11	.	.	PUNCT
ejpam-3955	555	1	.	.	PUNCT
ejpam-3955	556	1	,	,	PUNCT
ejpam-3955	556	2	hk	hk	PROPN
ejpam-3955	556	3	}	}	PUNCT
ejpam-3955	556	4	is	be	AUX
ejpam-3955	556	5	a	a	DET
ejpam-3955	556	6	γmce	γmce	NOUN
ejpam-3955	556	7	-	-	PUNCT
ejpam-3955	556	8	set	set	NOUN
ejpam-3955	556	9	in	in	ADP
ejpam-3955	556	10	g	g	PROPN
ejpam-3955	556	11	and	and	CCONJ
ejpam-3955	556	12	is	be	AUX
ejpam-3955	556	13	the	the	DET
ejpam-3955	556	14	only	only	ADJ
ejpam-3955	556	15	cost	cost	NOUN
ejpam-3955	556	16	effective	effective	ADJ
ejpam-3955	556	17	dominating	dominating	NOUN
ejpam-3955	556	18	set	set	VERB
ejpam-3955	556	19	in	in	ADP
ejpam-3955	556	20	g	g	NOUN
ejpam-3955	556	21	which	which	PRON
ejpam-3955	556	22	is	be	AUX
ejpam-3955	556	23	of	of	ADP
ejpam-3955	556	24	maximum	maximum	ADJ
ejpam-3955	556	25	order	order	NOUN
ejpam-3955	556	26	.	.	PUNCT
ejpam-3955	557	1	thus	thus	ADV
ejpam-3955	557	2	,	,	PUNCT
ejpam-3955	557	3	γmce(g	γmce(g	PROPN
ejpam-3955	557	4	)	)	PUNCT
ejpam-3955	557	5	=	=	PUNCT
ejpam-3955	558	1	a	a	DET
ejpam-3955	558	2	−	−	PROPN
ejpam-3955	558	3	1	1	NUM
ejpam-3955	558	4	+	+	SYM
ejpam-3955	558	5	1	1	NUM
ejpam-3955	558	6	+	+	CCONJ
ejpam-3955	558	7	k	k	NOUN
ejpam-3955	558	8	=	=	PUNCT
ejpam-3955	558	9	a	a	PROPN
ejpam-3955	558	10	+	+	X
ejpam-3955	558	11	k	k	NOUN
ejpam-3955	558	12	=	=	SYM
ejpam-3955	558	13	b	b	PROPN
ejpam-3955	558	14	=	=	SYM
ejpam-3955	558	15	c	c	PROPN
ejpam-3955	558	16	=	=	PUNCT
ejpam-3955	558	17	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	558	18	)	)	PUNCT
ejpam-3955	558	19	.	.	PUNCT
ejpam-3955	559	1	now	now	ADV
ejpam-3955	559	2	,	,	PUNCT
ejpam-3955	559	3	suppose	suppose	VERB
ejpam-3955	559	4	that	that	SCONJ
ejpam-3955	559	5	c	c	PROPN
ejpam-3955	559	6	=	=	SYM
ejpam-3955	559	7	b+	b+	PROPN
ejpam-3955	559	8	t	t	PROPN
ejpam-3955	559	9	,	,	PUNCT
ejpam-3955	559	10	t	t	PROPN
ejpam-3955	559	11	≥	≥	NUM
ejpam-3955	559	12	1	1	NUM
ejpam-3955	559	13	.	.	PUNCT
ejpam-3955	560	1	obtain	obtain	VERB
ejpam-3955	560	2	g	g	NOUN
ejpam-3955	560	3	=	=	SYM
ejpam-3955	560	4	g6	g6	ADJ
ejpam-3955	560	5	from	from	ADP
ejpam-3955	560	6	g5	g5	NOUN
ejpam-3955	560	7	by	by	ADP
ejpam-3955	560	8	joining	join	VERB
ejpam-3955	560	9	complete	complete	ADJ
ejpam-3955	560	10	graph	graph	NOUN
ejpam-3955	560	11	k2	k2	PROPN
ejpam-3955	560	12	t	t	PROPN
ejpam-3955	560	13	to	to	ADP
ejpam-3955	560	14	exactly	exactly	ADV
ejpam-3955	560	15	one	one	NUM
ejpam-3955	560	16	of	of	ADP
ejpam-3955	560	17	the	the	DET
ejpam-3955	560	18	end	end	NOUN
ejpam-3955	560	19	vertices	vertex	NOUN
ejpam-3955	560	20	of	of	ADP
ejpam-3955	560	21	g4	g4	NOUN
ejpam-3955	560	22	,	,	PUNCT
ejpam-3955	560	23	say	say	VERB
ejpam-3955	560	24	v1	v1	NOUN
ejpam-3955	560	25	,	,	PUNCT
ejpam-3955	560	26	as	as	SCONJ
ejpam-3955	560	27	shown	show	VERB
ejpam-3955	560	28	in	in	ADP
ejpam-3955	560	29	figure	figure	NOUN
ejpam-3955	560	30	7	7	NUM
ejpam-3955	560	31	.	.	PUNCT
ejpam-3955	560	32	....................................	....................................	PUNCT
ejpam-3955	561	1	....................................	....................................	PUNCT
ejpam-3955	561	2	....................................	....................................	PUNCT
ejpam-3955	562	1	....................................	....................................	PUNCT
ejpam-3955	562	2	........................................................................	........................................................................	PUNCT
ejpam-3955	563	1	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	563	2	.......	.......	PUNCT
ejpam-3955	563	3	..	..	PUNCT
ejpam-3955	563	4	........	........	PUNCT
ejpam-3955	563	5	........	........	PUNCT
ejpam-3955	563	6	........	........	PUNCT
ejpam-3955	563	7	........	........	PUNCT
ejpam-3955	563	8	........	........	PUNCT
ejpam-3955	563	9	........	........	PUNCT
ejpam-3955	563	10	........	........	PUNCT
ejpam-3955	563	11	..	..	PUNCT
ejpam-3955	564	1	..........	..........	PUNCT
ejpam-3955	564	2	.........	.........	PUNCT
ejpam-3955	565	1	.........	.........	PUNCT
ejpam-3955	565	2	.........	.........	PUNCT
ejpam-3955	566	1	.........	.........	PUNCT
ejpam-3955	566	2	.........	.........	PUNCT
ejpam-3955	567	1	.........	.........	PUNCT
ejpam-3955	567	2	.........	.........	PUNCT
ejpam-3955	567	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	567	4	.	.	PUNCT
ejpam-3955	567	5	.	.	PUNCT
ejpam-3955	567	6	.	.	PUNCT
ejpam-3955	568	1	....................................	....................................	PUNCT
ejpam-3955	568	2	........................................................................	........................................................................	PUNCT
ejpam-3955	569	1	....................................	....................................	PUNCT
ejpam-3955	569	2	....................................	....................................	PUNCT
ejpam-3955	569	3	........................................	........................................	PUNCT
ejpam-3955	569	4	........................................	........................................	PUNCT
ejpam-3955	570	1	.........	.........	PUNCT
ejpam-3955	570	2	........	........	PUNCT
ejpam-3955	570	3	........	........	PUNCT
ejpam-3955	570	4	........	........	PUNCT
ejpam-3955	570	5	.......	.......	PUNCT
ejpam-3955	571	1	.............................................	.............................................	PUNCT
ejpam-3955	571	2	.........	.........	PUNCT
ejpam-3955	572	1	.........	.........	PUNCT
ejpam-3955	572	2	.....	.....	PUNCT
ejpam-3955	572	3	u1	u1	NOUN
ejpam-3955	572	4	x	x	SYM
ejpam-3955	572	5	v1	v1	NOUN
ejpam-3955	572	6	u2	u2	PROPN
ejpam-3955	572	7	v2	v2	PROPN
ejpam-3955	572	8	u3	u3	NOUN
ejpam-3955	572	9	v3	v3	PROPN
ejpam-3955	572	10	u4	u4	PROPN
ejpam-3955	572	11	v4	v4	PROPN
ejpam-3955	572	12	ua	ua	PROPN
ejpam-3955	572	13	va	va	PROPN
ejpam-3955	572	14	g5	g5	PROPN
ejpam-3955	572	15	....................................	....................................	PUNCT
ejpam-3955	572	16	....................................	....................................	PUNCT
ejpam-3955	573	1	....................................	....................................	PUNCT
ejpam-3955	573	2	....................................	....................................	PUNCT
ejpam-3955	574	1	....................................	....................................	PUNCT
ejpam-3955	574	2	............................................................................................................................................................	............................................................................................................................................................	PUNCT
ejpam-3955	575	1	................................................	................................................	PUNCT
ejpam-3955	575	2	..........	..........	PUNCT
ejpam-3955	576	1	.........	.........	PUNCT
ejpam-3955	576	2	.........	.........	PUNCT
ejpam-3955	577	1	.........	.........	PUNCT
ejpam-3955	577	2	.........	.........	PUNCT
ejpam-3955	578	1	.........	.........	PUNCT
ejpam-3955	578	2	.........	.........	PUNCT
ejpam-3955	579	1	.........	.........	PUNCT
ejpam-3955	579	2	.........	.........	PUNCT
ejpam-3955	580	1	.........	.........	PUNCT
ejpam-3955	580	2	..	..	PUNCT
ejpam-3955	580	3	............	............	PUNCT
ejpam-3955	580	4	...........	...........	PUNCT
ejpam-3955	580	5	...........	...........	PUNCT
ejpam-3955	580	6	...........	...........	PUNCT
ejpam-3955	580	7	...........	...........	PUNCT
ejpam-3955	580	8	...........	...........	PUNCT
ejpam-3955	580	9	.	.	PUNCT
ejpam-3955	581	1	.................	.................	PUNCT
ejpam-3955	581	2	................	................	PUNCT
ejpam-3955	581	3	...............	...............	PUNCT
ejpam-3955	581	4	........................................	........................................	PUNCT
ejpam-3955	581	5	...	...	PUNCT
ejpam-3955	582	1	h1	h1	VERB
ejpam-3955	582	2	h2	h2	PROPN
ejpam-3955	582	3	h3	h3	NOUN
ejpam-3955	582	4	h4	h4	PROPN
ejpam-3955	582	5	h5	h5	PROPN
ejpam-3955	582	6	hk	hk	PROPN
ejpam-3955	582	7	....................................	....................................	PUNCT
ejpam-3955	582	8	....................................	....................................	PUNCT
ejpam-3955	583	1	....................................	....................................	PUNCT
ejpam-3955	583	2	....................................	....................................	PUNCT
ejpam-3955	584	1	........................................................................	........................................................................	PUNCT
ejpam-3955	584	2	.......................................................................................................................................	.......................................................................................................................................	PUNCT
ejpam-3955	584	3	.......	.......	PUNCT
ejpam-3955	584	4	..	..	PUNCT
ejpam-3955	584	5	........	........	PUNCT
ejpam-3955	584	6	........	........	PUNCT
ejpam-3955	584	7	........	........	PUNCT
ejpam-3955	584	8	........	........	PUNCT
ejpam-3955	584	9	........	........	PUNCT
ejpam-3955	584	10	........	........	PUNCT
ejpam-3955	585	1	........	........	PUNCT
ejpam-3955	585	2	..	..	PUNCT
ejpam-3955	586	1	..........	..........	PUNCT
ejpam-3955	586	2	.........	.........	PUNCT
ejpam-3955	587	1	.........	.........	PUNCT
ejpam-3955	587	2	.........	.........	PUNCT
ejpam-3955	588	1	.........	.........	PUNCT
ejpam-3955	588	2	.........	.........	PUNCT
ejpam-3955	589	1	.........	.........	PUNCT
ejpam-3955	589	2	.........	.........	PUNCT
ejpam-3955	589	3	...................................................................................	...................................................................................	PUNCT
ejpam-3955	589	4	.	.	PUNCT
ejpam-3955	589	5	.	.	PUNCT
ejpam-3955	589	6	.	.	PUNCT
ejpam-3955	590	1	....................................	....................................	PUNCT
ejpam-3955	590	2	........................................................................	........................................................................	PUNCT
ejpam-3955	591	1	....................................	....................................	PUNCT
ejpam-3955	591	2	....................................	....................................	PUNCT
ejpam-3955	591	3	........................................	........................................	PUNCT
ejpam-3955	591	4	........................................	........................................	PUNCT
ejpam-3955	592	1	.........	.........	PUNCT
ejpam-3955	592	2	........	........	PUNCT
ejpam-3955	592	3	........	........	PUNCT
ejpam-3955	592	4	........	........	PUNCT
ejpam-3955	592	5	.......	.......	PUNCT
ejpam-3955	593	1	.............................................	.............................................	PUNCT
ejpam-3955	593	2	.........	.........	PUNCT
ejpam-3955	594	1	.........	.........	PUNCT
ejpam-3955	594	2	.....	.....	PUNCT
ejpam-3955	594	3	u1	u1	NOUN
ejpam-3955	594	4	x	x	SYM
ejpam-3955	594	5	v1	v1	NOUN
ejpam-3955	594	6	u2	u2	PROPN
ejpam-3955	594	7	v2	v2	PROPN
ejpam-3955	594	8	u3	u3	NOUN
ejpam-3955	594	9	v3	v3	PROPN
ejpam-3955	594	10	u4	u4	PROPN
ejpam-3955	594	11	v4	v4	PROPN
ejpam-3955	594	12	ua	ua	PROPN
ejpam-3955	594	13	va	va	PROPN
ejpam-3955	595	1	g6	g6	PROPN
ejpam-3955	595	2	....................................	....................................	PUNCT
ejpam-3955	595	3	....................................	....................................	PUNCT
ejpam-3955	596	1	....................................	....................................	PUNCT
ejpam-3955	596	2	....................................	....................................	PUNCT
ejpam-3955	597	1	....................................	....................................	PUNCT
ejpam-3955	597	2	............................................................................................................................................................	............................................................................................................................................................	PUNCT
ejpam-3955	598	1	................................................	................................................	PUNCT
ejpam-3955	598	2	..........	..........	PUNCT
ejpam-3955	599	1	.........	.........	PUNCT
ejpam-3955	599	2	.........	.........	PUNCT
ejpam-3955	600	1	.........	.........	PUNCT
ejpam-3955	600	2	.........	.........	PUNCT
ejpam-3955	601	1	.........	.........	PUNCT
ejpam-3955	601	2	.........	.........	PUNCT
ejpam-3955	602	1	.........	.........	PUNCT
ejpam-3955	602	2	.........	.........	PUNCT
ejpam-3955	603	1	.........	.........	PUNCT
ejpam-3955	603	2	..	..	PUNCT
ejpam-3955	603	3	............	............	PUNCT
ejpam-3955	603	4	...........	...........	PUNCT
ejpam-3955	603	5	...........	...........	PUNCT
ejpam-3955	603	6	...........	...........	PUNCT
ejpam-3955	603	7	...........	...........	PUNCT
ejpam-3955	603	8	...........	...........	PUNCT
ejpam-3955	603	9	.	.	PUNCT
ejpam-3955	604	1	.................	.................	PUNCT
ejpam-3955	604	2	................	................	PUNCT
ejpam-3955	604	3	...............	...............	PUNCT
ejpam-3955	604	4	........................................	........................................	PUNCT
ejpam-3955	604	5	...	...	PUNCT
ejpam-3955	605	1	h1	h1	VERB
ejpam-3955	605	2	h2	h2	PROPN
ejpam-3955	605	3	h3	h3	NOUN
ejpam-3955	605	4	h4	h4	PROPN
ejpam-3955	605	5	h5	h5	PROPN
ejpam-3955	605	6	hk	hk	PROPN
ejpam-3955	605	7	....................................	....................................	PUNCT
ejpam-3955	605	8	....................................	....................................	PUNCT
ejpam-3955	606	1	....................................	....................................	PUNCT
ejpam-3955	606	2	....................................	....................................	PUNCT
ejpam-3955	607	1	....................................	....................................	PUNCT
ejpam-3955	607	2	................................................................................................	................................................................................................	PUNCT
ejpam-3955	607	3	............................................................................	............................................................................	PUNCT
ejpam-3955	608	1	................	................	PUNCT
ejpam-3955	608	2	...............	...............	PUNCT
ejpam-3955	608	3	...............	...............	PUNCT
ejpam-3955	608	4	...............	...............	PUNCT
ejpam-3955	608	5	...............	...............	PUNCT
ejpam-3955	608	6	........	........	PUNCT
ejpam-3955	608	7	............	............	PUNCT
ejpam-3955	608	8	...........	...........	PUNCT
ejpam-3955	608	9	...........	...........	PUNCT
ejpam-3955	608	10	...........	...........	PUNCT
ejpam-3955	608	11	...........	...........	PUNCT
ejpam-3955	608	12	...........	...........	PUNCT
ejpam-3955	608	13	...........	...........	PUNCT
ejpam-3955	608	14	...........	...........	PUNCT
ejpam-3955	608	15	...........	...........	PUNCT
ejpam-3955	608	16	...........	...........	PUNCT
ejpam-3955	608	17	...........	...........	PUNCT
ejpam-3955	608	18	..........	..........	PUNCT
ejpam-3955	609	1	..........	..........	PUNCT
ejpam-3955	609	2	..........	..........	PUNCT
ejpam-3955	610	1	..........	..........	PUNCT
ejpam-3955	610	2	..........	..........	PUNCT
ejpam-3955	611	1	..........	..........	PUNCT
ejpam-3955	611	2	..........	..........	PUNCT
ejpam-3955	612	1	..........	..........	PUNCT
ejpam-3955	612	2	..........	..........	PUNCT
ejpam-3955	613	1	..........	..........	PUNCT
ejpam-3955	613	2	..........	..........	PUNCT
ejpam-3955	614	1	..........	..........	PUNCT
ejpam-3955	614	2	..........	..........	PUNCT
ejpam-3955	615	1	..	..	PUNCT
ejpam-3955	615	2	.........	.........	PUNCT
ejpam-3955	616	1	........	........	PUNCT
ejpam-3955	616	2	........	........	PUNCT
ejpam-3955	617	1	.....	.....	PUNCT
ejpam-3955	617	2	.........	.........	PUNCT
ejpam-3955	618	1	......	......	PUNCT
ejpam-3955	618	2	.........	.........	PUNCT
ejpam-3955	618	3	.	.	PUNCT
ejpam-3955	618	4	.........	.........	PUNCT
ejpam-3955	619	1	........	........	PUNCT
ejpam-3955	619	2	........	........	PUNCT
ejpam-3955	620	1	.....	.....	PUNCT
ejpam-3955	620	2	.........	.........	PUNCT
ejpam-3955	620	3	........	........	PUNCT
ejpam-3955	620	4	........	........	PUNCT
ejpam-3955	621	1	.....	.....	PUNCT
ejpam-3955	621	2	.........................................................................	.........................................................................	PUNCT
ejpam-3955	621	3	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-3955	622	1	........................................................................................................................................................................	........................................................................................................................................................................	PROPN
ejpam-3955	622	2	......................................................................................................................	......................................................................................................................	PUNCT
ejpam-3955	623	1	....................................................................................................................................................................	....................................................................................................................................................................	PUNCT
ejpam-3955	623	2	.....................................................................................................................................................................................................................	.....................................................................................................................................................................................................................	PUNCT
ejpam-3955	624	1	..................................................................................................	..................................................................................................	PUNCT
ejpam-3955	624	2	...	...	PUNCT
ejpam-3955	625	1	w1	w1	NOUN
ejpam-3955	625	2	w2	w2	PROPN
ejpam-3955	625	3	w2t−2	w2t−2	PROPN
ejpam-3955	625	4	w2t−1	w2t−1	PROPN
ejpam-3955	625	5	w2	w2	PROPN
ejpam-3955	625	6	t	t	PROPN
ejpam-3955	625	7	figure	figure	NOUN
ejpam-3955	625	8	7	7	NUM
ejpam-3955	625	9	:	:	PUNCT
ejpam-3955	625	10	g6	g6	NOUN
ejpam-3955	625	11	obtained	obtain	VERB
ejpam-3955	625	12	from	from	ADP
ejpam-3955	625	13	g5	g5	NOUN
ejpam-3955	625	14	then	then	ADV
ejpam-3955	625	15	the	the	DET
ejpam-3955	625	16	set	set	NOUN
ejpam-3955	625	17	{	{	PUNCT
ejpam-3955	625	18	u2	u2	NOUN
ejpam-3955	625	19	,	,	PUNCT
ejpam-3955	625	20	u3	u3	NOUN
ejpam-3955	625	21	,	,	PUNCT
ejpam-3955	625	22	.	.	PUNCT
ejpam-3955	625	23	.	.	PUNCT
ejpam-3955	626	1	.	.	PUNCT
ejpam-3955	627	1	,	,	PUNCT
ejpam-3955	627	2	ua−1	ua−1	PROPN
ejpam-3955	627	3	,	,	PUNCT
ejpam-3955	627	4	v1	v1	PROPN
ejpam-3955	627	5	,	,	PUNCT
ejpam-3955	627	6	va	va	NOUN
ejpam-3955	627	7	}	}	PUNCT
ejpam-3955	627	8	is	be	AUX
ejpam-3955	627	9	a	a	DET
ejpam-3955	627	10	γce	γce	NOUN
ejpam-3955	627	11	-	-	PUNCT
ejpam-3955	627	12	set	set	VERB
ejpam-3955	627	13	in	in	ADP
ejpam-3955	627	14	g.	g.	PROPN
ejpam-3955	627	15	thus	thus	ADV
ejpam-3955	627	16	,	,	PUNCT
ejpam-3955	627	17	γce(g	γce(g	PROPN
ejpam-3955	627	18	)	)	PUNCT
ejpam-3955	627	19	=	=	PUNCT
ejpam-3955	628	1	a	a	DET
ejpam-3955	628	2	−	−	PROPN
ejpam-3955	628	3	2	2	NUM
ejpam-3955	628	4	+	+	CCONJ
ejpam-3955	628	5	2	2	NUM
ejpam-3955	628	6	=	=	SYM
ejpam-3955	628	7	a.	a.	NOUN
ejpam-3955	628	8	also	also	ADV
ejpam-3955	628	9	,	,	PUNCT
ejpam-3955	628	10	since	since	SCONJ
ejpam-3955	628	11	γmce(k2	γmce(k2	NOUN
ejpam-3955	628	12	t	t	NOUN
ejpam-3955	628	13	+	+	CCONJ
ejpam-3955	628	14	v1	v1	NOUN
ejpam-3955	628	15	)	)	PUNCT
ejpam-3955	628	16	=	=	SYM
ejpam-3955	628	17	1	1	NUM
ejpam-3955	628	18	,	,	PUNCT
ejpam-3955	628	19	γmce(g	γmce(g	PROPN
ejpam-3955	628	20	)	)	PUNCT
ejpam-3955	628	21	=	=	PUNCT
ejpam-3955	629	1	a	a	DET
ejpam-3955	629	2	+	+	X
ejpam-3955	629	3	k	k	NOUN
ejpam-3955	629	4	=	=	SYM
ejpam-3955	629	5	b	b	PROPN
ejpam-3955	629	6	which	which	PRON
ejpam-3955	629	7	is	be	AUX
ejpam-3955	629	8	determined	determine	VERB
ejpam-3955	629	9	by	by	ADP
ejpam-3955	629	10	the	the	DET
ejpam-3955	629	11	set	set	NOUN
ejpam-3955	629	12	{	{	PUNCT
ejpam-3955	629	13	v1	v1	NOUN
ejpam-3955	629	14	,	,	PUNCT
ejpam-3955	629	15	v2	v2	PROPN
ejpam-3955	629	16	,	,	PUNCT
ejpam-3955	629	17	.	.	PUNCT
ejpam-3955	629	18	.	.	PUNCT
ejpam-3955	630	1	.	.	PUNCT
ejpam-3955	631	1	,	,	PUNCT
ejpam-3955	631	2	va−1	va−1	NOUN
ejpam-3955	631	3	,	,	PUNCT
ejpam-3955	631	4	x	x	NOUN
ejpam-3955	631	5	,	,	PUNCT
ejpam-3955	631	6	h1	h1	PROPN
ejpam-3955	631	7	,	,	PUNCT
ejpam-3955	631	8	.	.	PUNCT
ejpam-3955	631	9	.	.	PUNCT
ejpam-3955	632	1	.	.	PUNCT
ejpam-3955	633	1	,	,	PUNCT
ejpam-3955	633	2	hk	hk	PROPN
ejpam-3955	633	3	}	}	PUNCT
ejpam-3955	633	4	.	.	PUNCT
ejpam-3955	634	1	also	also	ADV
ejpam-3955	634	2	,	,	PUNCT
ejpam-3955	634	3	observe	observe	VERB
ejpam-3955	634	4	that	that	SCONJ
ejpam-3955	634	5	since	since	SCONJ
ejpam-3955	634	6	the	the	DET
ejpam-3955	634	7	set	set	NOUN
ejpam-3955	634	8	{	{	PUNCT
ejpam-3955	634	9	v1	v1	NOUN
ejpam-3955	634	10	,	,	PUNCT
ejpam-3955	634	11	v2	v2	PROPN
ejpam-3955	634	12	,	,	PUNCT
ejpam-3955	634	13	.	.	PUNCT
ejpam-3955	634	14	.	.	PUNCT
ejpam-3955	635	1	.	.	PUNCT
ejpam-3955	636	1	,	,	PUNCT
ejpam-3955	636	2	va−1	va−1	NOUN
ejpam-3955	636	3	,	,	PUNCT
ejpam-3955	636	4	x	x	NOUN
ejpam-3955	636	5	,	,	PUNCT
ejpam-3955	636	6	h1	h1	PROPN
ejpam-3955	636	7	,	,	PUNCT
ejpam-3955	636	8	.	.	PUNCT
ejpam-3955	636	9	.	.	PUNCT
ejpam-3955	637	1	.	.	PUNCT
ejpam-3955	638	1	,	,	PUNCT
ejpam-3955	638	2	hk	hk	PROPN
ejpam-3955	638	3	,	,	PUNCT
ejpam-3955	638	4	w1	w1	NOUN
ejpam-3955	638	5	,	,	PUNCT
ejpam-3955	638	6	.	.	PUNCT
ejpam-3955	638	7	.	.	PUNCT
ejpam-3955	639	1	.	.	PUNCT
ejpam-3955	640	1	,	,	PUNCT
ejpam-3955	640	2	wt	wt	PROPN
ejpam-3955	640	3	}	}	PUNCT
ejpam-3955	640	4	is	be	AUX
ejpam-3955	640	5	a	a	DET
ejpam-3955	640	6	γ+ce	γ+ce	NOUN
ejpam-3955	640	7	-	-	PUNCT
ejpam-3955	640	8	set	set	NOUN
ejpam-3955	640	9	in	in	ADP
ejpam-3955	640	10	g	g	PROPN
ejpam-3955	640	11	,	,	PUNCT
ejpam-3955	640	12	γ+ce(g	γ+ce(g	NOUN
ejpam-3955	640	13	)	)	PUNCT
ejpam-3955	641	1	=	=	PUNCT
ejpam-3955	641	2	a−1	a−1	PROPN
ejpam-3955	641	3	+	+	PROPN
ejpam-3955	641	4	1+k+t	1+k+t	PROPN
ejpam-3955	641	5	=	=	SYM
ejpam-3955	641	6	a+k+t	a+k+t	NOUN
ejpam-3955	641	7	=	=	SYM
ejpam-3955	641	8	b+k	b+k	NUM
ejpam-3955	641	9	=	=	SYM
ejpam-3955	641	10	c.	c.	NOUN
ejpam-3955	641	11	references	reference	NOUN
ejpam-3955	641	12	[	[	X
ejpam-3955	641	13	1	1	NUM
ejpam-3955	641	14	]	]	PUNCT
ejpam-3955	641	15	r.	r.	PROPN
ejpam-3955	641	16	aharoni	aharoni	PROPN
ejpam-3955	641	17	,	,	PUNCT
ejpam-3955	641	18	e.c	e.c	PROPN
ejpam-3955	641	19	.	.	PROPN
ejpam-3955	641	20	milner	milner	PROPN
ejpam-3955	641	21	,	,	PUNCT
ejpam-3955	641	22	k.	k.	PROPN
ejpam-3955	641	23	prikry	prikry	PROPN
ejpam-3955	641	24	,	,	PUNCT
ejpam-3955	641	25	unfriendly	unfriendly	ADJ
ejpam-3955	641	26	partitions	partition	NOUN
ejpam-3955	641	27	of	of	ADP
ejpam-3955	641	28	a	a	DET
ejpam-3955	641	29	graph	graph	NOUN
ejpam-3955	641	30	,	,	PUNCT
ejpam-3955	641	31	j.	j.	PROPN
ejpam-3955	641	32	combin	combin	PROPN
ejpam-3955	641	33	.	.	PUNCT
ejpam-3955	642	1	theory	theory	NOUN
ejpam-3955	642	2	,	,	PUNCT
ejpam-3955	642	3	ser	ser	PROPN
ejpam-3955	642	4	.	.	PUNCT
ejpam-3955	643	1	b	b	ADP
ejpam-3955	643	2	50	50	NUM
ejpam-3955	643	3	(	(	PUNCT
ejpam-3955	643	4	1	1	NUM
ejpam-3955	643	5	)	)	PUNCT
ejpam-3955	643	6	(	(	PUNCT
ejpam-3955	643	7	1990	1990	NUM
ejpam-3955	643	8	)	)	PUNCT
ejpam-3955	643	9	1−10	1−10	NUM
ejpam-3955	643	10	.	.	PUNCT
ejpam-3955	644	1	[	[	X
ejpam-3955	644	2	2	2	X
ejpam-3955	644	3	]	]	X
ejpam-3955	644	4	t.w	t.w	PROPN
ejpam-3955	644	5	.	.	PROPN
ejpam-3955	644	6	haynes	haynes	PROPN
ejpam-3955	644	7	,	,	PUNCT
ejpam-3955	644	8	s.m	s.m	PROPN
ejpam-3955	644	9	.	.	PROPN
ejpam-3955	644	10	hedetniemi	hedetniemi	PROPN
ejpam-3955	644	11	,	,	PUNCT
ejpam-3955	644	12	s.t	s.t	PROPN
ejpam-3955	644	13	.	.	PROPN
ejpam-3955	644	14	hedetniemi	hedetniemi	PROPN
ejpam-3955	644	15	,	,	PUNCT
ejpam-3955	644	16	t.l	t.l	PROPN
ejpam-3955	644	17	.	.	PROPN
ejpam-3955	644	18	mccoy	mccoy	PROPN
ejpam-3955	644	19	,	,	PUNCT
ejpam-3955	644	20	i.	i.	PROPN
ejpam-3955	644	21	vasylieva	vasylieva	PROPN
ejpam-3955	644	22	,	,	PUNCT
ejpam-3955	644	23	cost	cost	VERB
ejpam-3955	644	24	effective	effective	ADJ
ejpam-3955	644	25	domination	domination	NOUN
ejpam-3955	644	26	in	in	ADP
ejpam-3955	644	27	graphs	graph	NOUN
ejpam-3955	644	28	,	,	PUNCT
ejpam-3955	644	29	cong	cong	PROPN
ejpam-3955	644	30	.	.	PUNCT
ejpam-3955	645	1	numer	numer	PROPN
ejpam-3955	645	2	.	.	PUNCT
ejpam-3955	646	1	211	211	NUM
ejpam-3955	646	2	(	(	PUNCT
ejpam-3955	646	3	2012	2012	NUM
ejpam-3955	646	4	)	)	PUNCT
ejpam-3955	646	5	197−209	197−209	X
ejpam-3955	646	6	.	.	PUNCT
ejpam-3955	646	7	references	reference	NOUN
ejpam-3955	646	8	550	550	NUM
ejpam-3955	646	9	[	[	X
ejpam-3955	646	10	3	3	NUM
ejpam-3955	646	11	]	]	X
ejpam-3955	646	12	bostjan	bostjan	NOUN
ejpam-3955	646	13	bresar	bresar	VERB
ejpam-3955	646	14	vizing	vizing	ADJ
ejpam-3955	646	15	-	-	PUNCT
ejpam-3955	646	16	like	like	ADJ
ejpam-3955	646	17	conjecture	conjecture	NOUN
ejpam-3955	646	18	for	for	ADP
ejpam-3955	646	19	the	the	DET
ejpam-3955	646	20	upper	upper	ADJ
ejpam-3955	646	21	domination	domination	NOUN
ejpam-3955	646	22	of	of	ADP
ejpam-3955	646	23	cartesian	cartesian	ADJ
ejpam-3955	646	24	products	product	NOUN
ejpam-3955	646	25	of	of	ADP
ejpam-3955	646	26	graphs	graph	NOUN
ejpam-3955	646	27	-the	-the	DET
ejpam-3955	646	28	proof	proof	NOUN
ejpam-3955	646	29	the	the	DET
ejpam-3955	646	30	electronic	electronic	ADJ
ejpam-3955	646	31	journal	journal	NOUN
ejpam-3955	646	32	of	of	ADP
ejpam-3955	646	33	combinatorics	combinatoric	NOUN
ejpam-3955	646	34	12	12	NUM
ejpam-3955	646	35	(	(	PUNCT
ejpam-3955	646	36	2005	2005	NUM
ejpam-3955	646	37	)	)	PUNCT
ejpam-3955	647	1	[	[	X
ejpam-3955	647	2	4	4	NUM
ejpam-3955	647	3	]	]	X
ejpam-3955	647	4	f.	f.	PROPN
ejpam-3955	647	5	buckley	buckley	PROPN
ejpam-3955	647	6	,	,	PUNCT
ejpam-3955	647	7	f.	f.	PROPN
ejpam-3955	647	8	harary	harary	PROPN
ejpam-3955	647	9	.	.	PUNCT
ejpam-3955	648	1	distance	distance	NOUN
ejpam-3955	648	2	in	in	ADP
ejpam-3955	648	3	graphs	graph	NOUN
ejpam-3955	648	4	.	.	PUNCT
ejpam-3955	649	1	redwood	redwood	NOUN
ejpam-3955	649	2	city	city	NOUN
ejpam-3955	649	3	.	.	PUNCT
ejpam-3955	650	1	ca	can	AUX
ejpam-3955	650	2	:	:	PUNCT
ejpam-3955	650	3	addison	addison	PROPN
ejpam-3955	650	4	-	-	PUNCT
ejpam-3955	650	5	wesley	wesley	PROPN
ejpam-3955	650	6	.	.	PUNCT
ejpam-3955	651	1	[	[	X
ejpam-3955	651	2	5	5	NUM
ejpam-3955	651	3	]	]	X
ejpam-3955	651	4	f.v	f.v	PROPN
ejpam-3955	651	5	.	.	PROPN
ejpam-3955	651	6	fomin	fomin	PROPN
ejpam-3955	651	7	,	,	PUNCT
ejpam-3955	651	8	f.	f.	PROPN
ejpam-3955	651	9	gradoni	gradoni	PROPN
ejpam-3955	651	10	,	,	PUNCT
ejpam-3955	651	11	a.	a.	NOUN
ejpam-3955	651	12	pyatkin	pyatkin	PROPN
ejpam-3955	651	13	and	and	CCONJ
ejpam-3955	651	14	a.	a.	NOUN
ejpam-3955	651	15	stepanov	stepanov	PROPN
ejpam-3955	651	16	,	,	PUNCT
ejpam-3955	651	17	on	on	ADP
ejpam-3955	651	18	maximum	maximum	ADJ
ejpam-3955	651	19	number	number	NOUN
ejpam-3955	651	20	of	of	ADP
ejpam-3955	651	21	minimal	minimal	ADJ
ejpam-3955	651	22	dominating	dominating	NOUN
ejpam-3955	651	23	sets	set	NOUN
ejpam-3955	651	24	in	in	ADP
ejpam-3955	651	25	graphs	graph	NOUN
ejpam-3955	651	26	,	,	PUNCT
ejpam-3955	651	27	discrete	discrete	ADJ
ejpam-3955	651	28	mathematics	mathematic	NOUN
ejpam-3955	651	29	,	,	PUNCT
ejpam-3955	651	30	22:157	22:157	NUM
ejpam-3955	651	31	-	-	SYM
ejpam-3955	651	32	162	162	NUM
ejpam-3955	651	33	,	,	PUNCT
ejpam-3955	651	34	2005	2005	NUM
ejpam-3955	651	35	.	.	PUNCT
ejpam-3955	652	1	[	[	X
ejpam-3955	652	2	6	6	NUM
ejpam-3955	652	3	]	]	SYM
ejpam-3955	652	4	s.m	s.m	PROPN
ejpam-3955	652	5	.	.	PROPN
ejpam-3955	652	6	hedetniemi	hedetniemi	PROPN
ejpam-3955	652	7	,	,	PUNCT
ejpam-3955	652	8	s.t	s.t	PROPN
ejpam-3955	652	9	.	.	PROPN
ejpam-3955	652	10	hedetniemi	hedetniemi	PROPN
ejpam-3955	652	11	,	,	PUNCT
ejpam-3955	652	12	a.a	a.a	PROPN
ejpam-3955	652	13	.	.	PROPN
ejpam-3955	652	14	mcrae	mcrae	PROPN
ejpam-3955	652	15	,	,	PUNCT
ejpam-3955	652	16	very	very	ADV
ejpam-3955	652	17	cost	cost	VERB
ejpam-3955	652	18	effective	effective	ADJ
ejpam-3955	652	19	bipartitions	bipartition	NOUN
ejpam-3955	652	20	in	in	ADP
ejpam-3955	652	21	graphs	graph	NOUN
ejpam-3955	652	22	.	.	PUNCT
ejpam-3955	653	1	akce	akce	PROPN
ejpam-3955	653	2	international	international	PROPN
ejpam-3955	653	3	journal	journal	NOUN
ejpam-3955	653	4	of	of	ADP
ejpam-3955	653	5	graphs	graph	NOUN
ejpam-3955	653	6	and	and	CCONJ
ejpam-3955	653	7	combinatorics	combinatoric	NOUN
ejpam-3955	653	8	.	.	PUNCT
ejpam-3955	654	1	12(2015)155	12(2015)155	PROPN
ejpam-3955	654	2	-	-	PUNCT
ejpam-3955	654	3	160	160	NUM
ejpam-3955	654	4	.	.	PUNCT
ejpam-3955	655	1	[	[	X
ejpam-3955	655	2	7	7	X
ejpam-3955	655	3	]	]	X
ejpam-3955	655	4	f.	f.	PROPN
ejpam-3955	655	5	jamil	jamil	PROPN
ejpam-3955	655	6	and	and	CCONJ
ejpam-3955	655	7	h.	h.	PROPN
ejpam-3955	655	8	maglanque	maglanque	PROPN
ejpam-3955	655	9	on	on	ADP
ejpam-3955	655	10	cost	cost	NOUN
ejpam-3955	655	11	effective	effective	ADJ
ejpam-3955	655	12	domination	domination	NOUN
ejpam-3955	655	13	in	in	ADP
ejpam-3955	655	14	join	join	NOUN
ejpam-3955	655	15	,	,	PUNCT
ejpam-3955	655	16	corona	corona	NOUN
ejpam-3955	655	17	and	and	CCONJ
ejpam-3955	655	18	composition	composition	NOUN
ejpam-3955	655	19	of	of	ADP
ejpam-3955	655	20	graphs	graph	NOUN
ejpam-3955	655	21	,	,	PUNCT
ejpam-3955	655	22	european	european	ADJ
ejpam-3955	655	23	journal	journal	NOUN
ejpam-3955	655	24	of	of	ADP
ejpam-3955	655	25	pure	pure	ADJ
ejpam-3955	655	26	and	and	CCONJ
ejpam-3955	655	27	applied	applied	ADJ
ejpam-3955	655	28	mathematics	mathematic	NOUN
ejpam-3955	655	29	,	,	PUNCT
ejpam-3955	655	30	graph	graph	NOUN
ejpam-3955	655	31	theory	theory	NOUN
ejpam-3955	655	32	.	.	PUNCT
ejpam-3955	656	1	vol.12	vol.12	NOUN
ejpam-3955	656	2	,	,	PUNCT
ejpam-3955	656	3	no.3	no.3	NOUN
ejpam-3955	656	4	,	,	PUNCT
ejpam-3955	656	5	pp	pp	ADJ
ejpam-3955	656	6	.	.	PUNCT
ejpam-3955	657	1	978	978	NUM
ejpam-3955	657	2	-	-	SYM
ejpam-3955	657	3	998	998	NUM
ejpam-3955	657	4	,	,	PUNCT
ejpam-3955	657	5	2019	2019	NUM
ejpam-3955	657	6	.	.	PUNCT
ejpam-3955	658	1	[	[	X
ejpam-3955	658	2	8	8	X
ejpam-3955	658	3	]	]	X
ejpam-3955	658	4	h.	h.	PROPN
ejpam-3955	658	5	nuenay	nuenay	PROPN
ejpam-3955	658	6	and	and	CCONJ
ejpam-3955	658	7	f.	f.	PROPN
ejpam-3955	658	8	jamil	jamil	PROPN
ejpam-3955	658	9	on	on	ADP
ejpam-3955	658	10	the	the	DET
ejpam-3955	658	11	minimal	minimal	ADJ
ejpam-3955	658	12	geodetic	geodetic	ADJ
ejpam-3955	658	13	domination	domination	NOUN
ejpam-3955	658	14	in	in	ADP
ejpam-3955	658	15	graphs	graph	NOUN
ejpam-3955	658	16	,	,	PUNCT
ejpam-3955	658	17	discussiones	discussione	NOUN
ejpam-3955	658	18	mathematicae	mathematicae	VERB
ejpam-3955	658	19	,	,	PUNCT
ejpam-3955	658	20	graph	graph	NOUN
ejpam-3955	658	21	theory	theory	NOUN
ejpam-3955	658	22	.	.	PUNCT
ejpam-3955	659	1	vol.45	vol.45	ADJ
ejpam-3955	659	2	,	,	PUNCT
ejpam-3955	659	3	pp	pp	ADJ
ejpam-3955	659	4	.	.	PUNCT
ejpam-3955	660	1	403	403	NUM
ejpam-3955	660	2	-	-	SYM
ejpam-3955	660	3	418	418	NUM
ejpam-3955	660	4	,	,	PUNCT
ejpam-3955	660	5	2015	2015	NUM
ejpam-3955	660	6	.	.	PUNCT