id	sid	tid	token	lemma	pos
ejpam-3443	1	1	european	european	PROPN
ejpam-3443	1	2	journal	journal	PROPN
ejpam-3443	1	3	of	of	ADP
ejpam-3443	1	4	pure	pure	ADJ
ejpam-3443	1	5	and	and	CCONJ
ejpam-3443	1	6	applied	apply	VERB
ejpam-3443	1	7	mathematics	mathematic	NOUN
ejpam-3443	1	8	vol	vol	NOUN
ejpam-3443	1	9	.	.	PROPN
ejpam-3443	2	1	12	12	NUM
ejpam-3443	2	2	,	,	PUNCT
ejpam-3443	2	3	no	no	INTJ
ejpam-3443	2	4	.	.	NOUN
ejpam-3443	2	5	3	3	NUM
ejpam-3443	2	6	,	,	PUNCT
ejpam-3443	2	7	2019	2019	NUM
ejpam-3443	2	8	,	,	PUNCT
ejpam-3443	2	9	978	978	NUM
ejpam-3443	2	10	-	-	SYM
ejpam-3443	2	11	998	998	NUM
ejpam-3443	2	12	issn	issn	PROPN
ejpam-3443	2	13	1307	1307	NUM
ejpam-3443	2	14	-	-	SYM
ejpam-3443	2	15	5543	5543	NUM
ejpam-3443	2	16	–	–	PUNCT
ejpam-3443	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3443	2	18	published	publish	VERB
ejpam-3443	2	19	by	by	ADP
ejpam-3443	2	20	new	new	PROPN
ejpam-3443	2	21	york	york	PROPN
ejpam-3443	2	22	business	business	PROPN
ejpam-3443	2	23	global	global	ADJ
ejpam-3443	2	24	cost	cost	NOUN
ejpam-3443	2	25	effective	effective	ADJ
ejpam-3443	2	26	domination	domination	NOUN
ejpam-3443	2	27	in	in	ADP
ejpam-3443	2	28	the	the	DET
ejpam-3443	2	29	join	join	NOUN
ejpam-3443	2	30	,	,	PUNCT
ejpam-3443	2	31	corona	corona	NOUN
ejpam-3443	2	32	and	and	CCONJ
ejpam-3443	2	33	composition	composition	NOUN
ejpam-3443	2	34	of	of	ADP
ejpam-3443	2	35	graphs	graph	NOUN
ejpam-3443	2	36	ferdinand	ferdinand	PROPN
ejpam-3443	2	37	p.	p.	PROPN
ejpam-3443	2	38	jamil1	jamil1	PROPN
ejpam-3443	2	39	,	,	PUNCT
ejpam-3443	2	40	hearty	hearty	ADJ
ejpam-3443	2	41	m.	m.	NOUN
ejpam-3443	2	42	nuenaymaglanque2,∗	nuenaymaglanque2,∗	PROPN
ejpam-3443	2	43	1	1	NUM
ejpam-3443	2	44	department	department	NOUN
ejpam-3443	2	45	of	of	ADP
ejpam-3443	2	46	mathematics	mathematic	NOUN
ejpam-3443	2	47	and	and	CCONJ
ejpam-3443	2	48	statistics	statistic	NOUN
ejpam-3443	2	49	,	,	PUNCT
ejpam-3443	2	50	college	college	NOUN
ejpam-3443	2	51	of	of	ADP
ejpam-3443	2	52	science	science	NOUN
ejpam-3443	2	53	and	and	CCONJ
ejpam-3443	2	54	mathematics	mathematic	NOUN
ejpam-3443	2	55	center	center	NOUN
ejpam-3443	2	56	for	for	ADP
ejpam-3443	2	57	graph	graph	NOUN
ejpam-3443	2	58	theory	theory	NOUN
ejpam-3443	2	59	,	,	PUNCT
ejpam-3443	2	60	algebra	algebra	NOUN
ejpam-3443	2	61	and	and	CCONJ
ejpam-3443	2	62	analysis	analysis	NOUN
ejpam-3443	2	63	,	,	PUNCT
ejpam-3443	2	64	prism	prism	NOUN
ejpam-3443	2	65	,	,	PUNCT
ejpam-3443	2	66	msu	msu	PROPN
ejpam-3443	2	67	-	-	PUNCT
ejpam-3443	2	68	iligan	iligan	PROPN
ejpam-3443	2	69	institute	institute	PROPN
ejpam-3443	2	70	of	of	ADP
ejpam-3443	2	71	technology	technology	PROPN
ejpam-3443	2	72	,	,	PUNCT
ejpam-3443	2	73	9200	9200	NUM
ejpam-3443	2	74	iligan	iligan	ADJ
ejpam-3443	2	75	city	city	NOUN
ejpam-3443	2	76	,	,	PUNCT
ejpam-3443	2	77	philippines	philippines	PROPN
ejpam-3443	2	78	2	2	NUM
ejpam-3443	2	79	department	department	NOUN
ejpam-3443	2	80	of	of	ADP
ejpam-3443	2	81	applied	apply	VERB
ejpam-3443	2	82	mathematics	mathematic	NOUN
ejpam-3443	2	83	,	,	PUNCT
ejpam-3443	2	84	college	college	NOUN
ejpam-3443	2	85	of	of	ADP
ejpam-3443	2	86	science	science	NOUN
ejpam-3443	2	87	and	and	CCONJ
ejpam-3443	2	88	mathematics	mathematic	NOUN
ejpam-3443	2	89	,	,	PUNCT
ejpam-3443	2	90	university	university	NOUN
ejpam-3443	2	91	of	of	ADP
ejpam-3443	2	92	science	science	NOUN
ejpam-3443	2	93	and	and	CCONJ
ejpam-3443	2	94	technology	technology	NOUN
ejpam-3443	2	95	of	of	ADP
ejpam-3443	2	96	southern	southern	ADJ
ejpam-3443	2	97	philippines	philippine	NOUN
ejpam-3443	2	98	,	,	PUNCT
ejpam-3443	2	99	9000	9000	NUM
ejpam-3443	2	100	cagayan	cagayan	PROPN
ejpam-3443	2	101	de	de	PROPN
ejpam-3443	2	102	oro	oro	PROPN
ejpam-3443	2	103	city	city	NOUN
ejpam-3443	2	104	,	,	PUNCT
ejpam-3443	3	1	philippines	philippine	NOUN
ejpam-3443	3	2	abstract	abstract	ADJ
ejpam-3443	3	3	.	.	PUNCT
ejpam-3443	4	1	let	let	VERB
ejpam-3443	4	2	g	g	PRON
ejpam-3443	4	3	be	be	AUX
ejpam-3443	4	4	a	a	DET
ejpam-3443	4	5	connected	connected	ADJ
ejpam-3443	4	6	graph	graph	NOUN
ejpam-3443	4	7	.	.	PUNCT
ejpam-3443	5	1	a	a	DET
ejpam-3443	5	2	cost	cost	NOUN
ejpam-3443	5	3	effective	effective	ADJ
ejpam-3443	5	4	dominating	dominating	NOUN
ejpam-3443	5	5	set	set	VERB
ejpam-3443	5	6	in	in	ADP
ejpam-3443	5	7	a	a	DET
ejpam-3443	5	8	graph	graph	NOUN
ejpam-3443	5	9	g	g	NOUN
ejpam-3443	5	10	is	be	AUX
ejpam-3443	5	11	any	any	DET
ejpam-3443	5	12	set	set	NOUN
ejpam-3443	5	13	s	s	NOUN
ejpam-3443	5	14	of	of	ADP
ejpam-3443	5	15	vertices	vertex	NOUN
ejpam-3443	5	16	of	of	ADP
ejpam-3443	5	17	g	g	NOUN
ejpam-3443	5	18	satisfying	satisfy	VERB
ejpam-3443	5	19	the	the	DET
ejpam-3443	5	20	condition	condition	NOUN
ejpam-3443	5	21	that	that	SCONJ
ejpam-3443	5	22	each	each	DET
ejpam-3443	5	23	vertex	vertex	NOUN
ejpam-3443	5	24	in	in	ADP
ejpam-3443	5	25	s	s	PROPN
ejpam-3443	5	26	is	be	AUX
ejpam-3443	5	27	adjacent	adjacent	ADJ
ejpam-3443	5	28	to	to	ADP
ejpam-3443	5	29	at	at	ADV
ejpam-3443	5	30	least	least	ADJ
ejpam-3443	5	31	as	as	ADP
ejpam-3443	5	32	many	many	ADJ
ejpam-3443	5	33	vertices	vertex	NOUN
ejpam-3443	5	34	outside	outside	ADP
ejpam-3443	5	35	s	s	PRON
ejpam-3443	5	36	as	as	ADP
ejpam-3443	5	37	inside	inside	ADP
ejpam-3443	5	38	s	s	NOUN
ejpam-3443	5	39	and	and	CCONJ
ejpam-3443	5	40	every	every	DET
ejpam-3443	5	41	vertex	vertex	NOUN
ejpam-3443	5	42	outside	outside	ADP
ejpam-3443	5	43	s	s	PART
ejpam-3443	5	44	is	be	AUX
ejpam-3443	5	45	adjacent	adjacent	ADJ
ejpam-3443	5	46	to	to	ADP
ejpam-3443	5	47	at	at	ADV
ejpam-3443	5	48	least	least	ADV
ejpam-3443	5	49	one	one	NUM
ejpam-3443	5	50	vertex	vertex	NOUN
ejpam-3443	5	51	in	in	ADP
ejpam-3443	5	52	s.	s.	PROPN
ejpam-3443	5	53	the	the	DET
ejpam-3443	5	54	minimum	minimum	ADJ
ejpam-3443	5	55	cardinality	cardinality	NOUN
ejpam-3443	5	56	of	of	ADP
ejpam-3443	5	57	a	a	DET
ejpam-3443	5	58	cost	cost	NOUN
ejpam-3443	5	59	effective	effective	ADJ
ejpam-3443	5	60	dominating	dominating	NOUN
ejpam-3443	5	61	set	set	NOUN
ejpam-3443	5	62	is	be	AUX
ejpam-3443	5	63	the	the	DET
ejpam-3443	5	64	cost	cost	NOUN
ejpam-3443	5	65	effective	effective	ADJ
ejpam-3443	5	66	domination	domination	NOUN
ejpam-3443	5	67	number	number	NOUN
ejpam-3443	5	68	of	of	ADP
ejpam-3443	5	69	g.	g.	PROPN
ejpam-3443	5	70	the	the	DET
ejpam-3443	5	71	maximum	maximum	ADJ
ejpam-3443	5	72	cardinality	cardinality	NOUN
ejpam-3443	5	73	of	of	ADP
ejpam-3443	5	74	a	a	DET
ejpam-3443	5	75	cost	cost	NOUN
ejpam-3443	5	76	effective	effective	ADJ
ejpam-3443	5	77	dominating	dominating	NOUN
ejpam-3443	5	78	set	set	NOUN
ejpam-3443	5	79	is	be	AUX
ejpam-3443	5	80	the	the	DET
ejpam-3443	5	81	upper	upper	ADJ
ejpam-3443	5	82	cost	cost	NOUN
ejpam-3443	5	83	effective	effective	ADJ
ejpam-3443	5	84	domination	domination	NOUN
ejpam-3443	5	85	number	number	NOUN
ejpam-3443	5	86	of	of	ADP
ejpam-3443	5	87	g.	g.	PROPN
ejpam-3443	5	88	a	a	DET
ejpam-3443	5	89	cost	cost	NOUN
ejpam-3443	5	90	effective	effective	ADJ
ejpam-3443	5	91	dominating	dominating	NOUN
ejpam-3443	5	92	set	set	NOUN
ejpam-3443	5	93	is	be	AUX
ejpam-3443	5	94	said	say	VERB
ejpam-3443	5	95	to	to	PART
ejpam-3443	5	96	be	be	AUX
ejpam-3443	5	97	minimal	minimal	ADJ
ejpam-3443	5	98	if	if	SCONJ
ejpam-3443	5	99	it	it	PRON
ejpam-3443	5	100	does	do	AUX
ejpam-3443	5	101	not	not	PART
ejpam-3443	5	102	contain	contain	VERB
ejpam-3443	5	103	a	a	DET
ejpam-3443	5	104	proper	proper	ADJ
ejpam-3443	5	105	subset	subset	NOUN
ejpam-3443	5	106	which	which	PRON
ejpam-3443	5	107	is	be	AUX
ejpam-3443	5	108	itself	itself	PRON
ejpam-3443	5	109	a	a	DET
ejpam-3443	5	110	cost	cost	NOUN
ejpam-3443	5	111	effective	effective	ADJ
ejpam-3443	5	112	dominating	dominating	NOUN
ejpam-3443	5	113	in	in	ADP
ejpam-3443	5	114	g.	g.	PROPN
ejpam-3443	5	115	the	the	DET
ejpam-3443	5	116	maximum	maximum	ADJ
ejpam-3443	5	117	cardinality	cardinality	NOUN
ejpam-3443	5	118	of	of	ADP
ejpam-3443	5	119	a	a	DET
ejpam-3443	5	120	minimal	minimal	ADJ
ejpam-3443	5	121	cost	cost	NOUN
ejpam-3443	5	122	effective	effective	ADJ
ejpam-3443	5	123	dominating	dominating	NOUN
ejpam-3443	5	124	set	set	VERB
ejpam-3443	5	125	in	in	ADP
ejpam-3443	5	126	a	a	DET
ejpam-3443	5	127	graph	graph	NOUN
ejpam-3443	5	128	g	g	NOUN
ejpam-3443	5	129	is	be	AUX
ejpam-3443	5	130	the	the	DET
ejpam-3443	5	131	minimal	minimal	ADJ
ejpam-3443	5	132	cost	cost	NOUN
ejpam-3443	5	133	effective	effective	ADJ
ejpam-3443	5	134	domination	domination	NOUN
ejpam-3443	5	135	number	number	NOUN
ejpam-3443	5	136	of	of	ADP
ejpam-3443	5	137	g.	g.	PROPN
ejpam-3443	5	138	in	in	ADP
ejpam-3443	5	139	this	this	DET
ejpam-3443	5	140	paper	paper	NOUN
ejpam-3443	5	141	,	,	PUNCT
ejpam-3443	5	142	we	we	PRON
ejpam-3443	5	143	characterized	characterize	VERB
ejpam-3443	5	144	the	the	DET
ejpam-3443	5	145	cost	cost	NOUN
ejpam-3443	5	146	effective	effective	ADJ
ejpam-3443	5	147	dominating	dominating	NOUN
ejpam-3443	5	148	sets	set	NOUN
ejpam-3443	5	149	in	in	ADP
ejpam-3443	5	150	the	the	DET
ejpam-3443	5	151	join	join	NOUN
ejpam-3443	5	152	,	,	PUNCT
ejpam-3443	5	153	corona	corona	NOUN
ejpam-3443	5	154	and	and	CCONJ
ejpam-3443	5	155	composition	composition	NOUN
ejpam-3443	5	156	of	of	ADP
ejpam-3443	5	157	graphs	graph	NOUN
ejpam-3443	5	158	.	.	PUNCT
ejpam-3443	6	1	as	as	ADP
ejpam-3443	6	2	direct	direct	ADJ
ejpam-3443	6	3	consequences	consequence	NOUN
ejpam-3443	6	4	,	,	PUNCT
ejpam-3443	6	5	the	the	DET
ejpam-3443	6	6	bounds	bound	NOUN
ejpam-3443	6	7	or	or	CCONJ
ejpam-3443	6	8	the	the	DET
ejpam-3443	6	9	exact	exact	ADJ
ejpam-3443	6	10	cost	cost	NOUN
ejpam-3443	6	11	effective	effective	ADJ
ejpam-3443	6	12	domination	domination	NOUN
ejpam-3443	6	13	numbers	number	NOUN
ejpam-3443	6	14	,	,	PUNCT
ejpam-3443	6	15	minimal	minimal	ADJ
ejpam-3443	6	16	cost	cost	NOUN
ejpam-3443	6	17	effective	effective	ADJ
ejpam-3443	6	18	domination	domination	NOUN
ejpam-3443	6	19	numbers	number	NOUN
ejpam-3443	6	20	and	and	CCONJ
ejpam-3443	6	21	upper	upper	ADJ
ejpam-3443	6	22	cost	cost	NOUN
ejpam-3443	6	23	effective	effective	ADJ
ejpam-3443	6	24	domination	domination	NOUN
ejpam-3443	6	25	numbers	number	NOUN
ejpam-3443	6	26	of	of	ADP
ejpam-3443	6	27	these	these	DET
ejpam-3443	6	28	graphs	graph	NOUN
ejpam-3443	6	29	were	be	AUX
ejpam-3443	6	30	obtained	obtain	VERB
ejpam-3443	6	31	.	.	PUNCT
ejpam-3443	7	1	2010	2010	NUM
ejpam-3443	7	2	mathematics	mathematic	NOUN
ejpam-3443	7	3	subject	subject	NOUN
ejpam-3443	7	4	classifications	classification	NOUN
ejpam-3443	7	5	:	:	PUNCT
ejpam-3443	7	6	05c12	05c12	X
ejpam-3443	7	7	key	key	ADJ
ejpam-3443	7	8	words	word	NOUN
ejpam-3443	7	9	and	and	CCONJ
ejpam-3443	7	10	phrases	phrase	NOUN
ejpam-3443	7	11	:	:	PUNCT
ejpam-3443	7	12	cost	cost	VERB
ejpam-3443	7	13	effective	effective	ADJ
ejpam-3443	7	14	dominating	dominating	NOUN
ejpam-3443	7	15	set	set	NOUN
ejpam-3443	7	16	,	,	PUNCT
ejpam-3443	7	17	cost	cost	VERB
ejpam-3443	7	18	effective	effective	ADJ
ejpam-3443	7	19	domination	domination	NOUN
ejpam-3443	7	20	number	number	NOUN
ejpam-3443	7	21	,	,	PUNCT
ejpam-3443	7	22	join	join	NOUN
ejpam-3443	7	23	,	,	PUNCT
ejpam-3443	7	24	corona	corona	NOUN
ejpam-3443	7	25	,	,	PUNCT
ejpam-3443	7	26	composition	composition	NOUN
ejpam-3443	7	27	1	1	NUM
ejpam-3443	7	28	.	.	PUNCT
ejpam-3443	7	29	introduction	introduction	NOUN
ejpam-3443	7	30	throughout	throughout	ADP
ejpam-3443	7	31	this	this	DET
ejpam-3443	7	32	paper	paper	NOUN
ejpam-3443	7	33	,	,	PUNCT
ejpam-3443	7	34	we	we	PRON
ejpam-3443	7	35	consider	consider	VERB
ejpam-3443	7	36	simple	simple	ADJ
ejpam-3443	7	37	,	,	PUNCT
ejpam-3443	7	38	finite	finite	ADJ
ejpam-3443	7	39	and	and	CCONJ
ejpam-3443	7	40	undirected	undirected	ADJ
ejpam-3443	7	41	connected	connected	ADJ
ejpam-3443	7	42	graphs	graph	NOUN
ejpam-3443	7	43	g	g	NOUN
ejpam-3443	7	44	=	=	SYM
ejpam-3443	7	45	(	(	PUNCT
ejpam-3443	7	46	v	v	NOUN
ejpam-3443	7	47	(	(	PUNCT
ejpam-3443	7	48	g	g	NOUN
ejpam-3443	7	49	)	)	PUNCT
ejpam-3443	7	50	,	,	PUNCT
ejpam-3443	7	51	e(g	e(g	PROPN
ejpam-3443	7	52	)	)	PUNCT
ejpam-3443	7	53	)	)	PUNCT
ejpam-3443	7	54	.	.	PUNCT
ejpam-3443	8	1	all	all	DET
ejpam-3443	8	2	basic	basic	ADJ
ejpam-3443	8	3	graph	graph	NOUN
ejpam-3443	8	4	theoretic	theoretic	ADJ
ejpam-3443	8	5	concepts	concept	NOUN
ejpam-3443	8	6	used	use	VERB
ejpam-3443	8	7	here	here	ADV
ejpam-3443	8	8	are	be	AUX
ejpam-3443	8	9	adapted	adapt	VERB
ejpam-3443	8	10	from	from	ADP
ejpam-3443	8	11	[	[	X
ejpam-3443	8	12	1	1	NUM
ejpam-3443	8	13	]	]	PUNCT
ejpam-3443	8	14	.	.	PUNCT
ejpam-3443	9	1	the	the	DET
ejpam-3443	9	2	symbols	symbol	NOUN
ejpam-3443	9	3	v	v	ADP
ejpam-3443	9	4	(	(	PUNCT
ejpam-3443	9	5	g	g	NOUN
ejpam-3443	9	6	)	)	PUNCT
ejpam-3443	9	7	and	and	CCONJ
ejpam-3443	9	8	e(g	e(g	PROPN
ejpam-3443	9	9	)	)	PUNCT
ejpam-3443	9	10	are	be	AUX
ejpam-3443	9	11	the	the	DET
ejpam-3443	9	12	vertex	vertex	NOUN
ejpam-3443	9	13	set	set	NOUN
ejpam-3443	9	14	and	and	CCONJ
ejpam-3443	9	15	edge	edge	NOUN
ejpam-3443	9	16	set	set	NOUN
ejpam-3443	9	17	,	,	PUNCT
ejpam-3443	9	18	respectively	respectively	ADV
ejpam-3443	9	19	,	,	PUNCT
ejpam-3443	9	20	of	of	ADP
ejpam-3443	9	21	g.	g.	NOUN
ejpam-3443	9	22	for	for	ADP
ejpam-3443	9	23	s	s	PROPN
ejpam-3443	9	24	⊆	⊆	NUM
ejpam-3443	9	25	v	v	NOUN
ejpam-3443	9	26	(	(	PUNCT
ejpam-3443	9	27	g	g	NOUN
ejpam-3443	9	28	)	)	PUNCT
ejpam-3443	9	29	,	,	PUNCT
ejpam-3443	9	30	|s|	|s|	PROPN
ejpam-3443	9	31	is	be	AUX
ejpam-3443	9	32	the	the	DET
ejpam-3443	9	33	cardinality	cardinality	NOUN
ejpam-3443	9	34	of	of	ADP
ejpam-3443	9	35	s.	s.	PROPN
ejpam-3443	9	36	in	in	ADP
ejpam-3443	9	37	particular	particular	ADJ
ejpam-3443	9	38	,	,	PUNCT
ejpam-3443	9	39	|v	|v	PROPN
ejpam-3443	9	40	(	(	PUNCT
ejpam-3443	9	41	g)|	g)|	PROPN
ejpam-3443	9	42	is	be	AUX
ejpam-3443	9	43	called	call	VERB
ejpam-3443	9	44	the	the	DET
ejpam-3443	9	45	order	order	NOUN
ejpam-3443	9	46	of	of	ADP
ejpam-3443	9	47	g.	g.	PROPN
ejpam-3443	9	48	∗corresponding	∗corresponde	VERB
ejpam-3443	9	49	author	author	NOUN
ejpam-3443	9	50	.	.	PUNCT
ejpam-3443	10	1	doi	doi	NOUN
ejpam-3443	10	2	:	:	PUNCT
ejpam-3443	10	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3443	https://doi.org/10.29020/nybg.ejpam.v12i3.3443	NUM
ejpam-3443	10	4	email	email	NOUN
ejpam-3443	10	5	addresses	address	NOUN
ejpam-3443	10	6	:	:	PUNCT
ejpam-3443	10	7	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-3443	10	8	(	(	PUNCT
ejpam-3443	10	9	f.	f.	PROPN
ejpam-3443	10	10	jamil	jamil	PROPN
ejpam-3443	10	11	)	)	PUNCT
ejpam-3443	10	12	,	,	PUNCT
ejpam-3443	11	1	hearty15200@yahoo.com.ph	hearty15200@yahoo.com.ph	PROPN
ejpam-3443	11	2	(	(	PUNCT
ejpam-3443	11	3	h.	h.	PROPN
ejpam-3443	11	4	nuenay	nuenay	PROPN
ejpam-3443	11	5	-	-	PUNCT
ejpam-3443	11	6	maglanque	maglanque	ADJ
ejpam-3443	11	7	)	)	PUNCT
ejpam-3443	11	8	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3443	11	9	978	978	NUM
ejpam-3443	12	1	c	c	X
ejpam-3443	12	2	©	©	PROPN
ejpam-3443	12	3	2019	2019	NUM
ejpam-3443	12	4	ejpam	ejpam	NOUN
ejpam-3443	12	5	all	all	DET
ejpam-3443	12	6	rights	right	NOUN
ejpam-3443	12	7	reserved	reserve	VERB
ejpam-3443	12	8	.	.	PUNCT
ejpam-3443	13	1	f.jamil	f.jamil	PROPN
ejpam-3443	13	2	,	,	PUNCT
ejpam-3443	13	3	h.	h.	PROPN
ejpam-3443	13	4	nuenay	nuenay	PROPN
ejpam-3443	13	5	-	-	PUNCT
ejpam-3443	13	6	maglanque	maglanque	ADJ
ejpam-3443	13	7	/	/	SYM
ejpam-3443	13	8	eur	eur	NOUN
ejpam-3443	13	9	.	.	PUNCT
ejpam-3443	14	1	j.	j.	PROPN
ejpam-3443	14	2	pure	pure	PROPN
ejpam-3443	14	3	appl	appl	PROPN
ejpam-3443	14	4	.	.	PROPN
ejpam-3443	14	5	math	math	PROPN
ejpam-3443	14	6	,	,	PUNCT
ejpam-3443	14	7	12	12	NUM
ejpam-3443	14	8	(	(	PUNCT
ejpam-3443	14	9	3	3	NUM
ejpam-3443	14	10	)	)	PUNCT
ejpam-3443	14	11	(	(	PUNCT
ejpam-3443	14	12	2019	2019	NUM
ejpam-3443	14	13	)	)	PUNCT
ejpam-3443	14	14	,	,	PUNCT
ejpam-3443	14	15	978	978	NUM
ejpam-3443	14	16	-	-	SYM
ejpam-3443	14	17	998	998	NUM
ejpam-3443	14	18	979	979	NUM
ejpam-3443	14	19	given	give	VERB
ejpam-3443	14	20	graphs	graph	NOUN
ejpam-3443	14	21	g	g	NOUN
ejpam-3443	14	22	and	and	CCONJ
ejpam-3443	14	23	h	h	NOUN
ejpam-3443	14	24	with	with	ADP
ejpam-3443	14	25	disjoint	disjoint	ADJ
ejpam-3443	14	26	vertex	vertex	NOUN
ejpam-3443	14	27	sets	set	NOUN
ejpam-3443	14	28	,	,	PUNCT
ejpam-3443	14	29	the	the	DET
ejpam-3443	14	30	join	join	NOUN
ejpam-3443	14	31	of	of	ADP
ejpam-3443	14	32	g	g	PROPN
ejpam-3443	14	33	and	and	CCONJ
ejpam-3443	14	34	h	h	NOUN
ejpam-3443	14	35	is	be	AUX
ejpam-3443	14	36	the	the	DET
ejpam-3443	14	37	graph	graph	NOUN
ejpam-3443	14	38	g+h	g+h	PROPN
ejpam-3443	14	39	with	with	ADP
ejpam-3443	14	40	vertex	vertex	NOUN
ejpam-3443	14	41	set	set	VERB
ejpam-3443	14	42	v	v	NOUN
ejpam-3443	14	43	(	(	PUNCT
ejpam-3443	14	44	g	g	NOUN
ejpam-3443	14	45	)	)	PUNCT
ejpam-3443	14	46	∪	∪	NOUN
ejpam-3443	14	47	v	v	NOUN
ejpam-3443	14	48	(	(	PUNCT
ejpam-3443	14	49	h	h	NOUN
ejpam-3443	14	50	)	)	PUNCT
ejpam-3443	14	51	and	and	CCONJ
ejpam-3443	14	52	edge	edge	VERB
ejpam-3443	14	53	set	set	VERB
ejpam-3443	14	54	e(g	e(g	NOUN
ejpam-3443	14	55	)	)	PUNCT
ejpam-3443	14	56	∪	∪	ADP
ejpam-3443	14	57	e(h	e(h	PROPN
ejpam-3443	14	58	)	)	PUNCT
ejpam-3443	14	59	∪	∪	NOUN
ejpam-3443	14	60	{	{	PUNCT
ejpam-3443	14	61	uv	uv	NOUN
ejpam-3443	14	62	:	:	PUNCT
ejpam-3443	14	63	u	u	PROPN
ejpam-3443	14	64	∈	∈	PROPN
ejpam-3443	14	65	v	v	ADP
ejpam-3443	14	66	(	(	PUNCT
ejpam-3443	14	67	g	g	NOUN
ejpam-3443	14	68	)	)	PUNCT
ejpam-3443	14	69	,	,	PUNCT
ejpam-3443	14	70	v	v	X
ejpam-3443	14	71	∈	∈	PROPN
ejpam-3443	14	72	v	v	NOUN
ejpam-3443	14	73	(	(	PUNCT
ejpam-3443	14	74	h	h	NOUN
ejpam-3443	14	75	)	)	PUNCT
ejpam-3443	14	76	}	}	PUNCT
ejpam-3443	14	77	.	.	PUNCT
ejpam-3443	15	1	the	the	DET
ejpam-3443	15	2	corona	corona	NOUN
ejpam-3443	15	3	of	of	ADP
ejpam-3443	15	4	g	g	PROPN
ejpam-3443	15	5	and	and	CCONJ
ejpam-3443	15	6	h	h	NOUN
ejpam-3443	15	7	is	be	AUX
ejpam-3443	15	8	the	the	DET
ejpam-3443	15	9	graph	graph	NOUN
ejpam-3443	15	10	g	g	PROPN
ejpam-3443	15	11	◦	◦	NOUN
ejpam-3443	15	12	h	h	NOUN
ejpam-3443	15	13	obtained	obtain	VERB
ejpam-3443	15	14	by	by	ADP
ejpam-3443	15	15	taking	take	VERB
ejpam-3443	15	16	one	one	NUM
ejpam-3443	15	17	copy	copy	NOUN
ejpam-3443	15	18	of	of	ADP
ejpam-3443	15	19	g	g	PROPN
ejpam-3443	15	20	and	and	CCONJ
ejpam-3443	15	21	|v	|v	PROPN
ejpam-3443	15	22	(	(	PUNCT
ejpam-3443	15	23	g)|	g)|	NOUN
ejpam-3443	15	24	copies	copy	NOUN
ejpam-3443	15	25	of	of	ADP
ejpam-3443	15	26	h	h	NOUN
ejpam-3443	15	27	,	,	PUNCT
ejpam-3443	15	28	and	and	CCONJ
ejpam-3443	15	29	then	then	ADV
ejpam-3443	15	30	joining	join	VERB
ejpam-3443	15	31	the	the	DET
ejpam-3443	15	32	ith	ith	PROPN
ejpam-3443	15	33	vertex	vertex	NOUN
ejpam-3443	15	34	of	of	ADP
ejpam-3443	15	35	g	g	NOUN
ejpam-3443	15	36	to	to	ADP
ejpam-3443	15	37	every	every	DET
ejpam-3443	15	38	vertex	vertex	NOUN
ejpam-3443	15	39	in	in	ADP
ejpam-3443	15	40	the	the	DET
ejpam-3443	15	41	ith	ith	PROPN
ejpam-3443	15	42	copy	copy	NOUN
ejpam-3443	15	43	of	of	ADP
ejpam-3443	15	44	h.	h.	PROPN
ejpam-3443	15	45	the	the	DET
ejpam-3443	15	46	composition	composition	NOUN
ejpam-3443	15	47	(	(	PUNCT
ejpam-3443	15	48	or	or	CCONJ
ejpam-3443	15	49	lexicographic	lexicographic	ADJ
ejpam-3443	15	50	product	product	NOUN
ejpam-3443	15	51	)	)	PUNCT
ejpam-3443	16	1	g[h	g[h	ADP
ejpam-3443	16	2	]	]	PUNCT
ejpam-3443	16	3	of	of	ADP
ejpam-3443	16	4	g	g	PROPN
ejpam-3443	16	5	and	and	CCONJ
ejpam-3443	16	6	h	h	NOUN
ejpam-3443	16	7	is	be	AUX
ejpam-3443	16	8	the	the	DET
ejpam-3443	16	9	graph	graph	NOUN
ejpam-3443	16	10	with	with	ADP
ejpam-3443	16	11	v	v	NOUN
ejpam-3443	16	12	(	(	PUNCT
ejpam-3443	16	13	g[h	g[h	PROPN
ejpam-3443	16	14	]	]	PUNCT
ejpam-3443	16	15	)	)	PUNCT
ejpam-3443	16	16	=	=	SYM
ejpam-3443	16	17	v	v	X
ejpam-3443	16	18	(	(	PUNCT
ejpam-3443	16	19	g)×	g)×	NOUN
ejpam-3443	16	20	v	v	NOUN
ejpam-3443	16	21	(	(	PUNCT
ejpam-3443	16	22	h	h	NOUN
ejpam-3443	16	23	)	)	PUNCT
ejpam-3443	16	24	and	and	CCONJ
ejpam-3443	16	25	(	(	PUNCT
ejpam-3443	16	26	u	u	NOUN
ejpam-3443	16	27	,	,	PUNCT
ejpam-3443	16	28	v)(u′	v)(u′	NOUN
ejpam-3443	16	29	,	,	PUNCT
ejpam-3443	16	30	v′	v′	NOUN
ejpam-3443	16	31	)	)	PUNCT
ejpam-3443	16	32	∈	∈	NOUN
ejpam-3443	16	33	e(g[h	e(g[h	NOUN
ejpam-3443	16	34	]	]	PUNCT
ejpam-3443	16	35	)	)	PUNCT
ejpam-3443	16	36	if	if	SCONJ
ejpam-3443	16	37	and	and	CCONJ
ejpam-3443	16	38	only	only	ADV
ejpam-3443	16	39	if	if	SCONJ
ejpam-3443	16	40	either	either	CCONJ
ejpam-3443	16	41	uu′	uu′	PROPN
ejpam-3443	16	42	∈	∈	PROPN
ejpam-3443	16	43	e(g	e(g	PROPN
ejpam-3443	16	44	)	)	PUNCT
ejpam-3443	16	45	or	or	CCONJ
ejpam-3443	16	46	u	u	X
ejpam-3443	16	47	=	=	PUNCT
ejpam-3443	16	48	u′	u′	PROPN
ejpam-3443	16	49	and	and	CCONJ
ejpam-3443	16	50	vv′	vv′	NOUN
ejpam-3443	16	51	∈	∈	PROPN
ejpam-3443	16	52	e(h	e(h	PROPN
ejpam-3443	16	53	)	)	PUNCT
ejpam-3443	16	54	.	.	PUNCT
ejpam-3443	17	1	for	for	ADP
ejpam-3443	17	2	v	v	NUM
ejpam-3443	17	3	∈	∈	PROPN
ejpam-3443	17	4	v	v	NOUN
ejpam-3443	17	5	(	(	PUNCT
ejpam-3443	17	6	g	g	NOUN
ejpam-3443	17	7	)	)	PUNCT
ejpam-3443	17	8	,	,	PUNCT
ejpam-3443	17	9	the	the	DET
ejpam-3443	17	10	neighborhood	neighborhood	NOUN
ejpam-3443	17	11	of	of	ADP
ejpam-3443	17	12	v	v	NOUN
ejpam-3443	17	13	is	be	AUX
ejpam-3443	17	14	the	the	DET
ejpam-3443	17	15	set	set	NOUN
ejpam-3443	17	16	ng(v	ng(v	PUNCT
ejpam-3443	17	17	)	)	PUNCT
ejpam-3443	17	18	=	=	SYM
ejpam-3443	18	1	{	{	PUNCT
ejpam-3443	18	2	u	u	NOUN
ejpam-3443	18	3	∈	∈	PROPN
ejpam-3443	18	4	v	v	NOUN
ejpam-3443	18	5	(	(	PUNCT
ejpam-3443	18	6	g	g	NOUN
ejpam-3443	18	7	)	)	PUNCT
ejpam-3443	18	8	:	:	PUNCT
ejpam-3443	18	9	uv	uv	PROPN
ejpam-3443	18	10	∈	∈	PROPN
ejpam-3443	18	11	e(g	e(g	PROPN
ejpam-3443	18	12	)	)	PUNCT
ejpam-3443	18	13	}	}	PUNCT
ejpam-3443	18	14	.	.	PUNCT
ejpam-3443	19	1	the	the	DET
ejpam-3443	19	2	degree	degree	NOUN
ejpam-3443	19	3	of	of	ADP
ejpam-3443	19	4	a	a	DET
ejpam-3443	19	5	vertex	vertex	NOUN
ejpam-3443	19	6	v	v	ADP
ejpam-3443	19	7	∈	∈	NOUN
ejpam-3443	19	8	v	v	NOUN
ejpam-3443	19	9	(	(	PUNCT
ejpam-3443	19	10	g	g	NOUN
ejpam-3443	19	11	)	)	PUNCT
ejpam-3443	19	12	,	,	PUNCT
ejpam-3443	19	13	denoted	denote	VERB
ejpam-3443	19	14	by	by	ADP
ejpam-3443	19	15	degg(v	degg(v	PROPN
ejpam-3443	19	16	)	)	PUNCT
ejpam-3443	19	17	,	,	PUNCT
ejpam-3443	19	18	is	be	AUX
ejpam-3443	19	19	equal	equal	ADJ
ejpam-3443	19	20	to	to	ADP
ejpam-3443	19	21	the	the	DET
ejpam-3443	19	22	cardinality	cardinality	NOUN
ejpam-3443	19	23	of	of	ADP
ejpam-3443	19	24	ng(v	ng(v	PUNCT
ejpam-3443	19	25	)	)	PUNCT
ejpam-3443	19	26	and	and	CCONJ
ejpam-3443	19	27	the	the	DET
ejpam-3443	19	28	maximum	maximum	ADJ
ejpam-3443	19	29	degree	degree	NOUN
ejpam-3443	19	30	of	of	ADP
ejpam-3443	19	31	g	g	PROPN
ejpam-3443	19	32	is	be	AUX
ejpam-3443	19	33	∆(g	∆(g	NOUN
ejpam-3443	19	34	)	)	PUNCT
ejpam-3443	19	35	=	=	PUNCT
ejpam-3443	19	36	max{degg(v	max{degg(v	NOUN
ejpam-3443	19	37	)	)	PUNCT
ejpam-3443	19	38	:	:	PUNCT
ejpam-3443	19	39	v	v	X
ejpam-3443	19	40	∈	∈	PROPN
ejpam-3443	19	41	v	v	NOUN
ejpam-3443	19	42	(	(	PUNCT
ejpam-3443	19	43	g	g	NOUN
ejpam-3443	19	44	)	)	PUNCT
ejpam-3443	19	45	}	}	PUNCT
ejpam-3443	19	46	.	.	PUNCT
ejpam-3443	20	1	a	a	DET
ejpam-3443	20	2	vertex	vertex	NOUN
ejpam-3443	20	3	is	be	AUX
ejpam-3443	20	4	isolated	isolate	VERB
ejpam-3443	20	5	if	if	SCONJ
ejpam-3443	20	6	its	its	PRON
ejpam-3443	20	7	degree	degree	NOUN
ejpam-3443	20	8	is	be	AUX
ejpam-3443	20	9	zero	zero	NUM
ejpam-3443	20	10	,	,	PUNCT
ejpam-3443	20	11	and	and	CCONJ
ejpam-3443	20	12	a	a	DET
ejpam-3443	20	13	graph	graph	NOUN
ejpam-3443	20	14	is	be	AUX
ejpam-3443	20	15	isolate	isolate	NOUN
ejpam-3443	20	16	-	-	PUNCT
ejpam-3443	20	17	free	free	ADJ
ejpam-3443	20	18	if	if	SCONJ
ejpam-3443	20	19	it	it	PRON
ejpam-3443	20	20	has	have	VERB
ejpam-3443	20	21	no	no	DET
ejpam-3443	20	22	isolated	isolated	ADJ
ejpam-3443	20	23	vertices	vertex	NOUN
ejpam-3443	20	24	.	.	PUNCT
ejpam-3443	21	1	for	for	ADP
ejpam-3443	21	2	s	s	PROPN
ejpam-3443	21	3	⊆	⊆	NUM
ejpam-3443	21	4	v	v	NOUN
ejpam-3443	21	5	(	(	PUNCT
ejpam-3443	21	6	g	g	NOUN
ejpam-3443	21	7	)	)	PUNCT
ejpam-3443	21	8	,	,	PUNCT
ejpam-3443	21	9	ng(s	ng(s	NUM
ejpam-3443	21	10	)	)	PUNCT
ejpam-3443	21	11	=	=	SYM
ejpam-3443	21	12	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-3443	21	13	)	)	PUNCT
ejpam-3443	21	14	and	and	CCONJ
ejpam-3443	21	15	ng[s	ng[s	PROPN
ejpam-3443	21	16	]	]	PUNCT
ejpam-3443	21	17	=	=	SYM
ejpam-3443	21	18	s	s	X
ejpam-3443	21	19	∪	∪	NOUN
ejpam-3443	21	20	ng(s	ng(s	NUM
ejpam-3443	21	21	)	)	PUNCT
ejpam-3443	21	22	.	.	PUNCT
ejpam-3443	22	1	a	a	DET
ejpam-3443	22	2	dominating	dominating	NOUN
ejpam-3443	22	3	set	set	NOUN
ejpam-3443	22	4	of	of	ADP
ejpam-3443	22	5	g	g	PROPN
ejpam-3443	22	6	is	be	AUX
ejpam-3443	22	7	any	any	DET
ejpam-3443	22	8	s	s	NOUN
ejpam-3443	22	9	⊆	⊆	NUM
ejpam-3443	22	10	v	v	NOUN
ejpam-3443	22	11	(	(	PUNCT
ejpam-3443	22	12	g	g	NOUN
ejpam-3443	22	13	)	)	PUNCT
ejpam-3443	22	14	for	for	ADP
ejpam-3443	22	15	which	which	PRON
ejpam-3443	22	16	ng[s	ng[	NOUN
ejpam-3443	22	17	]	]	X
ejpam-3443	22	18	=	=	SYM
ejpam-3443	22	19	v	v	NOUN
ejpam-3443	22	20	(	(	PUNCT
ejpam-3443	22	21	g	g	NOUN
ejpam-3443	22	22	)	)	PUNCT
ejpam-3443	22	23	.	.	PUNCT
ejpam-3443	23	1	the	the	DET
ejpam-3443	23	2	domination	domination	NOUN
ejpam-3443	23	3	number	number	NOUN
ejpam-3443	23	4	of	of	ADP
ejpam-3443	23	5	g	g	NOUN
ejpam-3443	23	6	,	,	PUNCT
ejpam-3443	23	7	denoted	denote	VERB
ejpam-3443	23	8	by	by	ADP
ejpam-3443	23	9	,	,	PUNCT
ejpam-3443	23	10	γ(g	γ(g	PROPN
ejpam-3443	23	11	)	)	PUNCT
ejpam-3443	23	12	is	be	AUX
ejpam-3443	23	13	the	the	DET
ejpam-3443	23	14	smallest	small	ADJ
ejpam-3443	23	15	cardinality	cardinality	NOUN
ejpam-3443	23	16	of	of	ADP
ejpam-3443	23	17	a	a	DET
ejpam-3443	23	18	dominating	dominating	NOUN
ejpam-3443	23	19	set	set	NOUN
ejpam-3443	23	20	of	of	ADP
ejpam-3443	23	21	g.	g.	PROPN
ejpam-3443	23	22	a	a	DET
ejpam-3443	23	23	dominating	dominating	NOUN
ejpam-3443	23	24	set	set	NOUN
ejpam-3443	23	25	s	s	NOUN
ejpam-3443	23	26	of	of	ADP
ejpam-3443	23	27	g	g	PROPN
ejpam-3443	23	28	is	be	AUX
ejpam-3443	23	29	said	say	VERB
ejpam-3443	23	30	to	to	PART
ejpam-3443	23	31	be	be	AUX
ejpam-3443	23	32	a	a	DET
ejpam-3443	23	33	minimal	minimal	ADJ
ejpam-3443	23	34	dominating	dominating	NOUN
ejpam-3443	23	35	set	set	NOUN
ejpam-3443	23	36	if	if	SCONJ
ejpam-3443	23	37	it	it	PRON
ejpam-3443	23	38	has	have	VERB
ejpam-3443	23	39	no	no	DET
ejpam-3443	23	40	proper	proper	ADJ
ejpam-3443	23	41	subset	subset	NOUN
ejpam-3443	23	42	which	which	PRON
ejpam-3443	23	43	is	be	AUX
ejpam-3443	23	44	itself	itself	PRON
ejpam-3443	23	45	a	a	DET
ejpam-3443	23	46	dominating	dominating	NOUN
ejpam-3443	23	47	set	set	VERB
ejpam-3443	23	48	in	in	ADP
ejpam-3443	23	49	g.	g.	PROPN
ejpam-3443	23	50	the	the	DET
ejpam-3443	23	51	maximum	maximum	ADJ
ejpam-3443	23	52	cardinality	cardinality	NOUN
ejpam-3443	23	53	of	of	ADP
ejpam-3443	23	54	a	a	DET
ejpam-3443	23	55	minimal	minimal	ADJ
ejpam-3443	23	56	domination	domination	NOUN
ejpam-3443	23	57	set	set	VERB
ejpam-3443	23	58	in	in	ADP
ejpam-3443	23	59	g	g	PROPN
ejpam-3443	23	60	is	be	AUX
ejpam-3443	23	61	denoted	denote	VERB
ejpam-3443	23	62	by	by	ADP
ejpam-3443	23	63	γm(g	γm(g	NOUN
ejpam-3443	23	64	)	)	PUNCT
ejpam-3443	23	65	.	.	PUNCT
ejpam-3443	24	1	a	a	DET
ejpam-3443	24	2	dominating	dominating	NOUN
ejpam-3443	24	3	set	set	NOUN
ejpam-3443	24	4	s	s	NOUN
ejpam-3443	24	5	is	be	AUX
ejpam-3443	24	6	said	say	VERB
ejpam-3443	24	7	to	to	PART
ejpam-3443	24	8	be	be	AUX
ejpam-3443	24	9	an	an	DET
ejpam-3443	24	10	independent	independent	ADJ
ejpam-3443	24	11	dominating	dominating	NOUN
ejpam-3443	24	12	set	set	NOUN
ejpam-3443	24	13	of	of	ADP
ejpam-3443	24	14	g	g	PROPN
ejpam-3443	24	15	if	if	SCONJ
ejpam-3443	24	16	for	for	SCONJ
ejpam-3443	24	17	every	every	DET
ejpam-3443	24	18	two	two	NUM
ejpam-3443	24	19	vertices	vertex	NOUN
ejpam-3443	24	20	u	u	NOUN
ejpam-3443	24	21	,	,	PUNCT
ejpam-3443	24	22	v	v	ADP
ejpam-3443	24	23	∈	∈	PROPN
ejpam-3443	24	24	s	s	NOUN
ejpam-3443	24	25	,	,	PUNCT
ejpam-3443	24	26	uv	uv	PROPN
ejpam-3443	24	27	/∈	/∈	PUNCT
ejpam-3443	24	28	e(g	e(g	PROPN
ejpam-3443	24	29	)	)	PUNCT
ejpam-3443	24	30	.	.	PUNCT
ejpam-3443	25	1	the	the	DET
ejpam-3443	25	2	minimum	minimum	ADJ
ejpam-3443	25	3	cardinality	cardinality	NOUN
ejpam-3443	25	4	of	of	ADP
ejpam-3443	25	5	an	an	DET
ejpam-3443	25	6	independent	independent	ADJ
ejpam-3443	25	7	dominating	dominating	NOUN
ejpam-3443	25	8	set	set	NOUN
ejpam-3443	25	9	is	be	AUX
ejpam-3443	25	10	called	call	VERB
ejpam-3443	25	11	an	an	DET
ejpam-3443	25	12	independent	independent	ADJ
ejpam-3443	25	13	domination	domination	NOUN
ejpam-3443	25	14	number	number	NOUN
ejpam-3443	25	15	and	and	CCONJ
ejpam-3443	25	16	is	be	AUX
ejpam-3443	25	17	denoted	denote	VERB
ejpam-3443	25	18	by	by	ADP
ejpam-3443	25	19	i(g	i(g	NOUN
ejpam-3443	25	20	)	)	PUNCT
ejpam-3443	25	21	.	.	PUNCT
ejpam-3443	26	1	we	we	PRON
ejpam-3443	26	2	refer	refer	VERB
ejpam-3443	26	3	to	to	ADP
ejpam-3443	26	4	[	[	X
ejpam-3443	26	5	2–7	2–7	X
ejpam-3443	26	6	]	]	X
ejpam-3443	26	7	for	for	ADP
ejpam-3443	26	8	the	the	DET
ejpam-3443	26	9	fundamental	fundamental	ADJ
ejpam-3443	26	10	concepts	concept	NOUN
ejpam-3443	26	11	and	and	CCONJ
ejpam-3443	26	12	history	history	NOUN
ejpam-3443	26	13	of	of	ADP
ejpam-3443	26	14	the	the	DET
ejpam-3443	26	15	theory	theory	NOUN
ejpam-3443	26	16	of	of	ADP
ejpam-3443	26	17	domination	domination	NOUN
ejpam-3443	26	18	in	in	ADP
ejpam-3443	26	19	graphs	graph	NOUN
ejpam-3443	26	20	as	as	ADV
ejpam-3443	26	21	well	well	ADV
ejpam-3443	26	22	as	as	ADP
ejpam-3443	26	23	for	for	ADP
ejpam-3443	26	24	some	some	PRON
ejpam-3443	26	25	of	of	ADP
ejpam-3443	26	26	its	its	PRON
ejpam-3443	26	27	relevant	relevant	ADJ
ejpam-3443	26	28	applications	application	NOUN
ejpam-3443	26	29	.	.	PUNCT
ejpam-3443	27	1	investigation	investigation	NOUN
ejpam-3443	27	2	of	of	ADP
ejpam-3443	27	3	the	the	DET
ejpam-3443	27	4	concept	concept	NOUN
ejpam-3443	27	5	in	in	ADP
ejpam-3443	27	6	the	the	DET
ejpam-3443	27	7	join	join	NOUN
ejpam-3443	27	8	,	,	PUNCT
ejpam-3443	27	9	corona	corona	NOUN
ejpam-3443	27	10	or	or	CCONJ
ejpam-3443	27	11	composition	composition	NOUN
ejpam-3443	27	12	of	of	ADP
ejpam-3443	27	13	graphs	graph	NOUN
ejpam-3443	27	14	can	can	AUX
ejpam-3443	27	15	be	be	AUX
ejpam-3443	27	16	found	find	VERB
ejpam-3443	27	17	in	in	ADP
ejpam-3443	27	18	[	[	X
ejpam-3443	27	19	8	8	NUM
ejpam-3443	27	20	,	,	PUNCT
ejpam-3443	27	21	9	9	NUM
ejpam-3443	27	22	,	,	PUNCT
ejpam-3443	27	23	13	13	NUM
ejpam-3443	27	24	]	]	PUNCT
ejpam-3443	27	25	.	.	PUNCT
ejpam-3443	28	1	a	a	DET
ejpam-3443	28	2	subset	subset	NOUN
ejpam-3443	28	3	s	s	VERB
ejpam-3443	28	4	⊆	⊆	NUM
ejpam-3443	28	5	v	v	NOUN
ejpam-3443	28	6	(	(	PUNCT
ejpam-3443	28	7	g	g	NOUN
ejpam-3443	28	8	)	)	PUNCT
ejpam-3443	28	9	is	be	AUX
ejpam-3443	28	10	said	say	VERB
ejpam-3443	28	11	to	to	PART
ejpam-3443	28	12	be	be	AUX
ejpam-3443	28	13	a	a	DET
ejpam-3443	28	14	cost	cost	NOUN
ejpam-3443	28	15	effective	effective	ADJ
ejpam-3443	28	16	set	set	NOUN
ejpam-3443	28	17	of	of	ADP
ejpam-3443	28	18	g	g	PROPN
ejpam-3443	28	19	if	if	SCONJ
ejpam-3443	28	20	for	for	ADP
ejpam-3443	28	21	every	every	DET
ejpam-3443	28	22	v	v	NUM
ejpam-3443	28	23	∈	∈	PROPN
ejpam-3443	28	24	s	s	NOUN
ejpam-3443	28	25	,	,	PUNCT
ejpam-3443	28	26	|ng(v)∩s|	|ng(v)∩s|	PROPN
ejpam-3443	28	27	≤	≤	NUM
ejpam-3443	28	28	|ng(v	|ng(v	NOUN
ejpam-3443	28	29	)	)	PUNCT
ejpam-3443	28	30	\	\	NOUN
ejpam-3443	28	31	s|	s|	PROPN
ejpam-3443	28	32	.	.	PUNCT
ejpam-3443	29	1	a	a	DET
ejpam-3443	29	2	subset	subset	NOUN
ejpam-3443	29	3	s	s	VERB
ejpam-3443	29	4	⊆	⊆	NUM
ejpam-3443	29	5	v	v	NOUN
ejpam-3443	29	6	(	(	PUNCT
ejpam-3443	29	7	g	g	NOUN
ejpam-3443	29	8	)	)	PUNCT
ejpam-3443	29	9	is	be	AUX
ejpam-3443	29	10	said	say	VERB
ejpam-3443	29	11	to	to	PART
ejpam-3443	29	12	be	be	AUX
ejpam-3443	29	13	a	a	DET
ejpam-3443	29	14	very	very	ADV
ejpam-3443	29	15	cost	cost	NOUN
ejpam-3443	29	16	effective	effective	ADJ
ejpam-3443	29	17	set	set	NOUN
ejpam-3443	29	18	of	of	ADP
ejpam-3443	29	19	g	g	PROPN
ejpam-3443	29	20	if	if	SCONJ
ejpam-3443	29	21	for	for	ADP
ejpam-3443	29	22	every	every	DET
ejpam-3443	29	23	v	v	NUM
ejpam-3443	29	24	∈	∈	PROPN
ejpam-3443	29	25	s	s	NOUN
ejpam-3443	29	26	,	,	PUNCT
ejpam-3443	29	27	|ng(v	|ng(v	ADJ
ejpam-3443	29	28	)	)	PUNCT
ejpam-3443	29	29	∩	∩	NOUN
ejpam-3443	29	30	s|	s|	VERB
ejpam-3443	29	31	<	<	X
ejpam-3443	29	32	|ng(v	|ng(v	NOUN
ejpam-3443	29	33	)	)	PUNCT
ejpam-3443	29	34	\	\	NOUN
ejpam-3443	29	35	s|	s|	PROPN
ejpam-3443	29	36	.	.	PUNCT
ejpam-3443	30	1	a	a	DET
ejpam-3443	30	2	subset	subset	NOUN
ejpam-3443	30	3	s	s	VERB
ejpam-3443	30	4	⊆	⊆	NUM
ejpam-3443	30	5	v	v	NOUN
ejpam-3443	30	6	(	(	PUNCT
ejpam-3443	30	7	g	g	NOUN
ejpam-3443	30	8	)	)	PUNCT
ejpam-3443	30	9	is	be	AUX
ejpam-3443	30	10	said	say	VERB
ejpam-3443	30	11	to	to	PART
ejpam-3443	30	12	be	be	AUX
ejpam-3443	30	13	a	a	DET
ejpam-3443	30	14	(	(	PUNCT
ejpam-3443	30	15	very)cost	very)cost	X
ejpam-3443	30	16	effective	effective	ADJ
ejpam-3443	30	17	dominating	dominating	NOUN
ejpam-3443	30	18	set	set	NOUN
ejpam-3443	30	19	of	of	ADP
ejpam-3443	30	20	g	g	PROPN
ejpam-3443	30	21	if	if	SCONJ
ejpam-3443	30	22	s	s	VERB
ejpam-3443	30	23	is	be	AUX
ejpam-3443	30	24	both	both	PRON
ejpam-3443	30	25	a	a	DET
ejpam-3443	30	26	(	(	PUNCT
ejpam-3443	30	27	very	very	ADV
ejpam-3443	30	28	)	)	PUNCT
ejpam-3443	30	29	cost	cost	NOUN
ejpam-3443	30	30	effective	effective	ADJ
ejpam-3443	30	31	set	set	NOUN
ejpam-3443	30	32	and	and	CCONJ
ejpam-3443	30	33	a	a	DET
ejpam-3443	30	34	dominating	dominating	NOUN
ejpam-3443	30	35	set	set	NOUN
ejpam-3443	30	36	of	of	ADP
ejpam-3443	30	37	g.	g.	PROPN
ejpam-3443	30	38	the	the	DET
ejpam-3443	30	39	minimum	minimum	NOUN
ejpam-3443	30	40	(	(	PUNCT
ejpam-3443	30	41	resp	resp	NOUN
ejpam-3443	30	42	.	.	PUNCT
ejpam-3443	31	1	maximum	maximum	ADJ
ejpam-3443	31	2	)	)	PUNCT
ejpam-3443	31	3	cardinality	cardinality	NOUN
ejpam-3443	31	4	of	of	ADP
ejpam-3443	31	5	a	a	DET
ejpam-3443	31	6	cost	cost	NOUN
ejpam-3443	31	7	effective	effective	ADJ
ejpam-3443	31	8	dominating	dominating	NOUN
ejpam-3443	31	9	set	set	NOUN
ejpam-3443	31	10	of	of	ADP
ejpam-3443	31	11	a	a	DET
ejpam-3443	31	12	graph	graph	NOUN
ejpam-3443	31	13	g	g	NOUN
ejpam-3443	31	14	is	be	AUX
ejpam-3443	31	15	called	call	VERB
ejpam-3443	31	16	the	the	DET
ejpam-3443	31	17	cost	cost	NOUN
ejpam-3443	31	18	effective	effective	ADJ
ejpam-3443	31	19	domination	domination	NOUN
ejpam-3443	31	20	number	number	NOUN
ejpam-3443	31	21	(	(	PUNCT
ejpam-3443	31	22	resp	resp	NOUN
ejpam-3443	31	23	.	.	PUNCT
ejpam-3443	32	1	upper	upper	ADJ
ejpam-3443	32	2	cost	cost	NOUN
ejpam-3443	32	3	effective	effective	ADJ
ejpam-3443	32	4	domination	domination	NOUN
ejpam-3443	32	5	number	number	NOUN
ejpam-3443	32	6	)	)	PUNCT
ejpam-3443	32	7	of	of	ADP
ejpam-3443	32	8	g	g	NOUN
ejpam-3443	32	9	,	,	PUNCT
ejpam-3443	32	10	and	and	CCONJ
ejpam-3443	32	11	is	be	AUX
ejpam-3443	32	12	denoted	denote	VERB
ejpam-3443	32	13	by	by	ADP
ejpam-3443	32	14	γce(g	γce(g	PROPN
ejpam-3443	32	15	)	)	PUNCT
ejpam-3443	32	16	(	(	PUNCT
ejpam-3443	32	17	resp	resp	NOUN
ejpam-3443	32	18	.	.	PUNCT
ejpam-3443	33	1	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	33	2	)	)	PUNCT
ejpam-3443	33	3	)	)	PUNCT
ejpam-3443	33	4	.	.	PUNCT
ejpam-3443	34	1	the	the	DET
ejpam-3443	34	2	minimum	minimum	ADJ
ejpam-3443	34	3	cardinality	cardinality	NOUN
ejpam-3443	34	4	of	of	ADP
ejpam-3443	34	5	a	a	DET
ejpam-3443	34	6	very	very	ADV
ejpam-3443	34	7	cost	cost	NOUN
ejpam-3443	34	8	effective	effective	ADJ
ejpam-3443	34	9	dominating	dominating	NOUN
ejpam-3443	34	10	set	set	NOUN
ejpam-3443	34	11	of	of	ADP
ejpam-3443	34	12	a	a	DET
ejpam-3443	34	13	graph	graph	NOUN
ejpam-3443	34	14	g	g	NOUN
ejpam-3443	34	15	is	be	AUX
ejpam-3443	34	16	called	call	VERB
ejpam-3443	34	17	the	the	DET
ejpam-3443	34	18	very	very	ADV
ejpam-3443	34	19	cost	cost	NOUN
ejpam-3443	34	20	effective	effective	ADJ
ejpam-3443	34	21	domination	domination	NOUN
ejpam-3443	34	22	number	number	NOUN
ejpam-3443	34	23	of	of	ADP
ejpam-3443	34	24	g	g	NOUN
ejpam-3443	34	25	,	,	PUNCT
ejpam-3443	34	26	and	and	CCONJ
ejpam-3443	34	27	is	be	AUX
ejpam-3443	34	28	denoted	denote	VERB
ejpam-3443	34	29	by	by	ADP
ejpam-3443	34	30	γvce(g	γvce(g	NOUN
ejpam-3443	34	31	)	)	PUNCT
ejpam-3443	34	32	.	.	PUNCT
ejpam-3443	35	1	an	an	DET
ejpam-3443	35	2	excellent	excellent	ADJ
ejpam-3443	35	3	introduction	introduction	NOUN
ejpam-3443	35	4	and	and	CCONJ
ejpam-3443	35	5	exposition	exposition	NOUN
ejpam-3443	35	6	on	on	ADP
ejpam-3443	35	7	cost	cost	NOUN
ejpam-3443	35	8	effective	effective	ADJ
ejpam-3443	35	9	domination	domination	NOUN
ejpam-3443	35	10	in	in	ADP
ejpam-3443	35	11	graphs	graph	NOUN
ejpam-3443	35	12	can	can	AUX
ejpam-3443	35	13	be	be	AUX
ejpam-3443	35	14	found	find	VERB
ejpam-3443	35	15	in	in	ADP
ejpam-3443	35	16	[	[	X
ejpam-3443	35	17	11	11	NUM
ejpam-3443	35	18	,	,	PUNCT
ejpam-3443	35	19	12	12	NUM
ejpam-3443	35	20	]	]	PUNCT
ejpam-3443	35	21	.	.	PUNCT
ejpam-3443	36	1	a	a	DET
ejpam-3443	36	2	cost	cost	NOUN
ejpam-3443	36	3	effective	effective	ADJ
ejpam-3443	36	4	dominating	dominating	NOUN
ejpam-3443	36	5	set	set	NOUN
ejpam-3443	36	6	s	s	PROPN
ejpam-3443	36	7	⊆	⊆	NUM
ejpam-3443	36	8	v	v	NOUN
ejpam-3443	36	9	(	(	PUNCT
ejpam-3443	36	10	g	g	NOUN
ejpam-3443	36	11	)	)	PUNCT
ejpam-3443	36	12	is	be	AUX
ejpam-3443	36	13	a	a	DET
ejpam-3443	36	14	minimal	minimal	ADJ
ejpam-3443	36	15	cost	cost	NOUN
ejpam-3443	36	16	effective	effective	ADJ
ejpam-3443	36	17	set	set	NOUN
ejpam-3443	36	18	if	if	SCONJ
ejpam-3443	36	19	s	s	PRON
ejpam-3443	36	20	does	do	AUX
ejpam-3443	36	21	not	not	PART
ejpam-3443	36	22	contain	contain	VERB
ejpam-3443	36	23	a	a	DET
ejpam-3443	36	24	proper	proper	ADJ
ejpam-3443	36	25	subset	subset	NOUN
ejpam-3443	36	26	which	which	PRON
ejpam-3443	36	27	is	be	AUX
ejpam-3443	36	28	itself	itself	PRON
ejpam-3443	36	29	a	a	DET
ejpam-3443	36	30	cost	cost	NOUN
ejpam-3443	36	31	effective	effective	ADJ
ejpam-3443	36	32	dominating	dominating	NOUN
ejpam-3443	36	33	set	set	NOUN
ejpam-3443	36	34	.	.	PUNCT
ejpam-3443	37	1	we	we	PRON
ejpam-3443	37	2	use	use	VERB
ejpam-3443	37	3	the	the	DET
ejpam-3443	37	4	symbol	symbol	NOUN
ejpam-3443	37	5	γmce(g	γmce(g	PROPN
ejpam-3443	37	6	)	)	PUNCT
ejpam-3443	37	7	to	to	PART
ejpam-3443	37	8	denote	denote	VERB
ejpam-3443	37	9	the	the	DET
ejpam-3443	37	10	maximum	maximum	ADJ
ejpam-3443	37	11	cardinality	cardinality	NOUN
ejpam-3443	37	12	of	of	ADP
ejpam-3443	37	13	a	a	DET
ejpam-3443	37	14	minimal	minimal	ADJ
ejpam-3443	37	15	cost	cost	NOUN
ejpam-3443	37	16	effective	effective	ADJ
ejpam-3443	37	17	dominating	dominating	NOUN
ejpam-3443	37	18	set	set	NOUN
ejpam-3443	37	19	of	of	ADP
ejpam-3443	37	20	g.	g.	PROPN
ejpam-3443	37	21	it	it	PRON
ejpam-3443	37	22	is	be	AUX
ejpam-3443	37	23	worth	worth	ADJ
ejpam-3443	37	24	noting	note	VERB
ejpam-3443	37	25	that	that	SCONJ
ejpam-3443	37	26	,	,	PUNCT
ejpam-3443	37	27	in	in	ADP
ejpam-3443	37	28	particular	particular	ADJ
ejpam-3443	37	29	,	,	PUNCT
ejpam-3443	37	30	an	an	DET
ejpam-3443	37	31	independent	independent	ADJ
ejpam-3443	37	32	dominating	dominating	NOUN
ejpam-3443	37	33	set	set	NOUN
ejpam-3443	37	34	is	be	AUX
ejpam-3443	37	35	a	a	DET
ejpam-3443	37	36	minimal	minimal	ADJ
ejpam-3443	37	37	cost	cost	NOUN
ejpam-3443	37	38	effective	effective	ADJ
ejpam-3443	37	39	dominating	dominating	NOUN
ejpam-3443	37	40	set	set	NOUN
ejpam-3443	37	41	.	.	PUNCT
ejpam-3443	38	1	clearly	clearly	ADV
ejpam-3443	38	2	γ(g	γ(g	PROPN
ejpam-3443	38	3	)	)	PUNCT
ejpam-3443	38	4	≤	≤	NUM
ejpam-3443	38	5	γce(g	γce(g	PROPN
ejpam-3443	38	6	)	)	PUNCT
ejpam-3443	38	7	≤	≤	NOUN
ejpam-3443	39	1	γmce(g	γmce(g	PROPN
ejpam-3443	39	2	)	)	PUNCT
ejpam-3443	39	3	≤	≤	NUM
ejpam-3443	39	4	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	39	5	)	)	PUNCT
ejpam-3443	39	6	for	for	ADP
ejpam-3443	39	7	all	all	DET
ejpam-3443	39	8	graphs	graph	NOUN
ejpam-3443	39	9	g.	g.	NOUN
ejpam-3443	39	10	for	for	ADP
ejpam-3443	39	11	simplicity	simplicity	NOUN
ejpam-3443	39	12	,	,	PUNCT
ejpam-3443	39	13	we	we	PRON
ejpam-3443	39	14	use	use	VERB
ejpam-3443	39	15	the	the	DET
ejpam-3443	39	16	terms	term	NOUN
ejpam-3443	39	17	ced	ced	ADJ
ejpam-3443	39	18	-	-	PUNCT
ejpam-3443	39	19	set	set	VERB
ejpam-3443	39	20	,	,	PUNCT
ejpam-3443	39	21	γce	γce	NOUN
ejpam-3443	39	22	-	-	PUNCT
ejpam-3443	39	23	set	set	VERB
ejpam-3443	39	24	,	,	PUNCT
ejpam-3443	39	25	γ+ce	γ+ce	NOUN
ejpam-3443	39	26	-	-	PUNCT
ejpam-3443	39	27	set	set	VERB
ejpam-3443	39	28	and	and	CCONJ
ejpam-3443	39	29	γmce	γmce	NOUN
ejpam-3443	39	30	-	-	PUNCT
ejpam-3443	39	31	set	set	NOUN
ejpam-3443	39	32	to	to	PART
ejpam-3443	39	33	refer	refer	VERB
ejpam-3443	39	34	to	to	ADP
ejpam-3443	39	35	the	the	DET
ejpam-3443	39	36	cost	cost	NOUN
ejpam-3443	39	37	effective	effective	ADJ
ejpam-3443	39	38	dominating	dominating	NOUN
ejpam-3443	39	39	set	set	NOUN
ejpam-3443	39	40	,	,	PUNCT
ejpam-3443	39	41	the	the	DET
ejpam-3443	39	42	cost	cost	NOUN
ejpam-3443	39	43	effective	effective	ADJ
ejpam-3443	39	44	dominating	dominating	NOUN
ejpam-3443	39	45	sets	set	NOUN
ejpam-3443	39	46	with	with	ADP
ejpam-3443	39	47	cardinality	cardinality	PROPN
ejpam-3443	39	48	γce(g	γce(g	PROPN
ejpam-3443	39	49	)	)	PUNCT
ejpam-3443	39	50	,	,	PUNCT
ejpam-3443	39	51	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	39	52	)	)	PUNCT
ejpam-3443	39	53	and	and	CCONJ
ejpam-3443	39	54	γmce(g	γmce(g	PROPN
ejpam-3443	39	55	)	)	PUNCT
ejpam-3443	39	56	,	,	PUNCT
ejpam-3443	39	57	respectively	respectively	ADV
ejpam-3443	39	58	.	.	PUNCT
ejpam-3443	40	1	in	in	ADP
ejpam-3443	40	2	this	this	DET
ejpam-3443	40	3	paper	paper	NOUN
ejpam-3443	40	4	we	we	PRON
ejpam-3443	40	5	characterized	characterize	VERB
ejpam-3443	40	6	the	the	DET
ejpam-3443	40	7	cost	cost	NOUN
ejpam-3443	40	8	effective	effective	ADJ
ejpam-3443	40	9	dominating	dominating	NOUN
ejpam-3443	40	10	sets	set	NOUN
ejpam-3443	40	11	and	and	CCONJ
ejpam-3443	40	12	minimal	minimal	ADJ
ejpam-3443	40	13	cost	cost	NOUN
ejpam-3443	40	14	effective	effective	ADJ
ejpam-3443	40	15	dominating	dominating	NOUN
ejpam-3443	40	16	sets	set	NOUN
ejpam-3443	40	17	in	in	ADP
ejpam-3443	40	18	the	the	DET
ejpam-3443	40	19	join	join	NOUN
ejpam-3443	40	20	,	,	PUNCT
ejpam-3443	40	21	corona	corona	NOUN
ejpam-3443	40	22	and	and	CCONJ
ejpam-3443	40	23	composition	composition	NOUN
ejpam-3443	40	24	of	of	ADP
ejpam-3443	40	25	graphs	graph	NOUN
ejpam-3443	40	26	.	.	PUNCT
ejpam-3443	41	1	as	as	ADP
ejpam-3443	41	2	consequences	consequence	NOUN
ejpam-3443	41	3	,	,	PUNCT
ejpam-3443	41	4	we	we	PRON
ejpam-3443	41	5	determined	determine	VERB
ejpam-3443	41	6	the	the	DET
ejpam-3443	41	7	cost	cost	NOUN
ejpam-3443	41	8	effective	effective	ADJ
ejpam-3443	41	9	domination	domination	NOUN
ejpam-3443	41	10	number	number	NOUN
ejpam-3443	41	11	,	,	PUNCT
ejpam-3443	41	12	minimal	minimal	ADJ
ejpam-3443	41	13	cost	cost	NOUN
ejpam-3443	41	14	effective	effective	ADJ
ejpam-3443	41	15	domination	domination	NOUN
ejpam-3443	41	16	f.jamil	f.jamil	NOUN
ejpam-3443	41	17	,	,	PUNCT
ejpam-3443	41	18	h.	h.	PROPN
ejpam-3443	41	19	nuenay	nuenay	PROPN
ejpam-3443	41	20	-	-	PUNCT
ejpam-3443	41	21	maglanque	maglanque	ADJ
ejpam-3443	41	22	/	/	SYM
ejpam-3443	41	23	eur	eur	NOUN
ejpam-3443	41	24	.	.	PUNCT
ejpam-3443	42	1	j.	j.	PROPN
ejpam-3443	42	2	pure	pure	PROPN
ejpam-3443	42	3	appl	appl	PROPN
ejpam-3443	42	4	.	.	PROPN
ejpam-3443	42	5	math	math	PROPN
ejpam-3443	42	6	,	,	PUNCT
ejpam-3443	42	7	12	12	NUM
ejpam-3443	42	8	(	(	PUNCT
ejpam-3443	42	9	3	3	NUM
ejpam-3443	42	10	)	)	PUNCT
ejpam-3443	42	11	(	(	PUNCT
ejpam-3443	42	12	2019	2019	NUM
ejpam-3443	42	13	)	)	PUNCT
ejpam-3443	42	14	,	,	PUNCT
ejpam-3443	42	15	978	978	NUM
ejpam-3443	42	16	-	-	SYM
ejpam-3443	42	17	998	998	NUM
ejpam-3443	42	18	980	980	NUM
ejpam-3443	42	19	number	number	NOUN
ejpam-3443	42	20	and	and	CCONJ
ejpam-3443	42	21	upper	upper	ADJ
ejpam-3443	42	22	cost	cost	NOUN
ejpam-3443	42	23	effective	effective	ADJ
ejpam-3443	42	24	domination	domination	NOUN
ejpam-3443	42	25	number	number	NOUN
ejpam-3443	42	26	of	of	ADP
ejpam-3443	42	27	the	the	DET
ejpam-3443	42	28	aforementioned	aforementioned	ADJ
ejpam-3443	42	29	graphs	graph	NOUN
ejpam-3443	42	30	.	.	PUNCT
ejpam-3443	43	1	2	2	X
ejpam-3443	43	2	.	.	X
ejpam-3443	43	3	cost	cost	VERB
ejpam-3443	43	4	effective	effective	ADJ
ejpam-3443	43	5	domination	domination	NOUN
ejpam-3443	43	6	in	in	ADP
ejpam-3443	43	7	the	the	DET
ejpam-3443	43	8	join	join	NOUN
ejpam-3443	43	9	of	of	ADP
ejpam-3443	43	10	graphs	graph	NOUN
ejpam-3443	43	11	remark	remark	VERB
ejpam-3443	43	12	1	1	NUM
ejpam-3443	43	13	.	.	PUNCT
ejpam-3443	44	1	given	give	VERB
ejpam-3443	44	2	two	two	NUM
ejpam-3443	44	3	connected	connected	ADJ
ejpam-3443	44	4	graphs	graph	NOUN
ejpam-3443	44	5	g	g	NOUN
ejpam-3443	44	6	and	and	CCONJ
ejpam-3443	44	7	h	h	NOUN
ejpam-3443	44	8	,	,	PUNCT
ejpam-3443	44	9	a	a	DET
ejpam-3443	44	10	ced	ce	VERB
ejpam-3443	44	11	-	-	PUNCT
ejpam-3443	44	12	set	set	NOUN
ejpam-3443	44	13	s	s	NOUN
ejpam-3443	44	14	of	of	ADP
ejpam-3443	44	15	g+h	g+h	PROPN
ejpam-3443	44	16	,	,	PUNCT
ejpam-3443	44	17	where	where	SCONJ
ejpam-3443	44	18	s	s	VERB
ejpam-3443	44	19	⊆	⊆	NUM
ejpam-3443	44	20	v	v	NOUN
ejpam-3443	44	21	(	(	PUNCT
ejpam-3443	44	22	g	g	NOUN
ejpam-3443	44	23	)	)	PUNCT
ejpam-3443	44	24	,	,	PUNCT
ejpam-3443	44	25	need	need	AUX
ejpam-3443	44	26	not	not	PART
ejpam-3443	44	27	be	be	AUX
ejpam-3443	44	28	a	a	DET
ejpam-3443	44	29	ced	ced	ADV
ejpam-3443	44	30	-	-	PUNCT
ejpam-3443	44	31	set	set	NOUN
ejpam-3443	44	32	of	of	ADP
ejpam-3443	44	33	g	g	NOUN
ejpam-3443	44	34	as	as	SCONJ
ejpam-3443	44	35	shown	show	VERB
ejpam-3443	44	36	in	in	ADP
ejpam-3443	44	37	example	example	NOUN
ejpam-3443	44	38	1	1	NUM
ejpam-3443	44	39	.	.	PUNCT
ejpam-3443	44	40	example	example	NOUN
ejpam-3443	45	1	1	1	NUM
ejpam-3443	45	2	.	.	PUNCT
ejpam-3443	45	3	let	let	VERB
ejpam-3443	45	4	g	g	PROPN
ejpam-3443	45	5	=	=	PROPN
ejpam-3443	45	6	k5	k5	PROPN
ejpam-3443	45	7	◦	◦	NOUN
ejpam-3443	45	8	k3	k3	ADJ
ejpam-3443	45	9	.	.	PUNCT
ejpam-3443	46	1	consider	consider	VERB
ejpam-3443	46	2	the	the	DET
ejpam-3443	46	3	graph	graph	NOUN
ejpam-3443	46	4	g+k1	g+k1	NOUN
ejpam-3443	46	5	as	as	SCONJ
ejpam-3443	46	6	shown	show	VERB
ejpam-3443	46	7	in	in	ADP
ejpam-3443	46	8	figure	figure	NOUN
ejpam-3443	46	9	1	1	NUM
ejpam-3443	46	10	.	.	PUNCT
ejpam-3443	46	11	v1	v1	PROPN
ejpam-3443	46	12	v2	v2	PROPN
ejpam-3443	46	13	v3	v3	PROPN
ejpam-3443	46	14	v4	v4	PROPN
ejpam-3443	46	15	v5	v5	NOUN
ejpam-3443	46	16	u	u	NOUN
ejpam-3443	46	17	figure	figure	NOUN
ejpam-3443	46	18	1	1	NUM
ejpam-3443	46	19	:	:	PUNCT
ejpam-3443	46	20	the	the	DET
ejpam-3443	46	21	graph	graph	NOUN
ejpam-3443	46	22	g+k1	g+k1	NOUN
ejpam-3443	46	23	observe	observe	VERB
ejpam-3443	46	24	that	that	SCONJ
ejpam-3443	46	25	the	the	DET
ejpam-3443	46	26	set	set	NOUN
ejpam-3443	46	27	{	{	PUNCT
ejpam-3443	46	28	v1	v1	NOUN
ejpam-3443	46	29	,	,	PUNCT
ejpam-3443	46	30	v2	v2	PROPN
ejpam-3443	46	31	,	,	PUNCT
ejpam-3443	46	32	v3	v3	PROPN
ejpam-3443	46	33	,	,	PUNCT
ejpam-3443	46	34	v4	v4	PROPN
ejpam-3443	46	35	,	,	PUNCT
ejpam-3443	46	36	v5	v5	PROPN
ejpam-3443	46	37	}	}	PUNCT
ejpam-3443	46	38	⊆	⊆	NUM
ejpam-3443	46	39	v	v	NOUN
ejpam-3443	46	40	(	(	PUNCT
ejpam-3443	46	41	g	g	NOUN
ejpam-3443	46	42	)	)	PUNCT
ejpam-3443	46	43	is	be	AUX
ejpam-3443	46	44	a	a	DET
ejpam-3443	46	45	cost	cost	NOUN
ejpam-3443	46	46	effective	effective	ADJ
ejpam-3443	46	47	dominating	dominating	NOUN
ejpam-3443	46	48	set	set	NOUN
ejpam-3443	46	49	of	of	ADP
ejpam-3443	46	50	g+k1	g+k1	NOUN
ejpam-3443	46	51	but	but	CCONJ
ejpam-3443	46	52	not	not	PART
ejpam-3443	46	53	a	a	DET
ejpam-3443	46	54	cost	cost	NOUN
ejpam-3443	46	55	effective	effective	ADJ
ejpam-3443	46	56	dominating	dominating	NOUN
ejpam-3443	46	57	set	set	NOUN
ejpam-3443	46	58	of	of	ADP
ejpam-3443	46	59	g.	g.	PROPN
ejpam-3443	46	60	proposition	proposition	PROPN
ejpam-3443	47	1	1	1	NUM
ejpam-3443	47	2	.	.	PUNCT
ejpam-3443	48	1	let	let	VERB
ejpam-3443	48	2	g	g	PRON
ejpam-3443	48	3	be	be	AUX
ejpam-3443	48	4	a	a	DET
ejpam-3443	48	5	nontrivial	nontrivial	ADJ
ejpam-3443	48	6	connected	connect	VERB
ejpam-3443	48	7	graph	graph	NOUN
ejpam-3443	48	8	and	and	CCONJ
ejpam-3443	48	9	h	h	NOUN
ejpam-3443	48	10	be	be	AUX
ejpam-3443	48	11	any	any	DET
ejpam-3443	48	12	graph	graph	NOUN
ejpam-3443	48	13	.	.	PUNCT
ejpam-3443	49	1	if	if	SCONJ
ejpam-3443	49	2	s	s	VERB
ejpam-3443	49	3	⊆	⊆	NUM
ejpam-3443	49	4	v	v	NOUN
ejpam-3443	49	5	(	(	PUNCT
ejpam-3443	49	6	g	g	NOUN
ejpam-3443	49	7	)	)	PUNCT
ejpam-3443	49	8	is	be	AUX
ejpam-3443	49	9	a	a	DET
ejpam-3443	49	10	cost	cost	NOUN
ejpam-3443	49	11	effective	effective	ADJ
ejpam-3443	49	12	dominating	dominating	NOUN
ejpam-3443	49	13	set	set	NOUN
ejpam-3443	49	14	of	of	ADP
ejpam-3443	49	15	g	g	NOUN
ejpam-3443	49	16	,	,	PUNCT
ejpam-3443	49	17	then	then	ADV
ejpam-3443	49	18	s	s	VERB
ejpam-3443	49	19	is	be	AUX
ejpam-3443	49	20	a	a	DET
ejpam-3443	49	21	very	very	ADV
ejpam-3443	49	22	cost	cost	NOUN
ejpam-3443	49	23	effective	effective	ADJ
ejpam-3443	49	24	dominating	dominating	NOUN
ejpam-3443	49	25	set	set	NOUN
ejpam-3443	49	26	of	of	ADP
ejpam-3443	49	27	g+h	g+h	PROPN
ejpam-3443	49	28	.	.	PUNCT
ejpam-3443	50	1	proof	proof	NOUN
ejpam-3443	50	2	.	.	PUNCT
ejpam-3443	51	1	let	let	VERB
ejpam-3443	51	2	s	s	PRON
ejpam-3443	51	3	⊆	⊆	NUM
ejpam-3443	51	4	v	v	NOUN
ejpam-3443	51	5	(	(	PUNCT
ejpam-3443	51	6	g	g	NOUN
ejpam-3443	51	7	)	)	PUNCT
ejpam-3443	51	8	be	be	AUX
ejpam-3443	51	9	a	a	DET
ejpam-3443	51	10	cost	cost	NOUN
ejpam-3443	51	11	effective	effective	ADJ
ejpam-3443	51	12	dominating	dominating	NOUN
ejpam-3443	51	13	set	set	NOUN
ejpam-3443	51	14	of	of	ADP
ejpam-3443	51	15	g.	g.	PROPN
ejpam-3443	52	1	then	then	ADV
ejpam-3443	52	2	s	s	VERB
ejpam-3443	52	3	is	be	AUX
ejpam-3443	52	4	a	a	DET
ejpam-3443	52	5	dominating	dominating	NOUN
ejpam-3443	52	6	set	set	NOUN
ejpam-3443	52	7	of	of	ADP
ejpam-3443	52	8	g+h	g+h	PROPN
ejpam-3443	52	9	.	.	PUNCT
ejpam-3443	53	1	for	for	ADP
ejpam-3443	53	2	each	each	DET
ejpam-3443	53	3	v	v	NUM
ejpam-3443	53	4	∈	∈	PROPN
ejpam-3443	53	5	s	s	NOUN
ejpam-3443	53	6	,	,	PUNCT
ejpam-3443	53	7	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	53	8	)	)	PUNCT
ejpam-3443	53	9	∩	∩	NOUN
ejpam-3443	53	10	s|	s|	VERB
ejpam-3443	53	11	=	=	SYM
ejpam-3443	53	12	|ng(v	|ng(v	X
ejpam-3443	53	13	)	)	PUNCT
ejpam-3443	53	14	∩	∩	NOUN
ejpam-3443	53	15	s|	s|	VERB
ejpam-3443	53	16	≤	≤	NUM
ejpam-3443	53	17	|ng(v	|ng(v	NOUN
ejpam-3443	53	18	)	)	PUNCT
ejpam-3443	53	19	\	\	NOUN
ejpam-3443	53	20	s|	s|	VERB
ejpam-3443	53	21	<	<	X
ejpam-3443	53	22	|ng(v	|ng(v	NOUN
ejpam-3443	53	23	)	)	PUNCT
ejpam-3443	53	24	\	\	NOUN
ejpam-3443	54	1	s|+	s|+	NOUN
ejpam-3443	54	2	|v	|v	NOUN
ejpam-3443	54	3	(	(	PUNCT
ejpam-3443	54	4	h)|	h)|	NOUN
ejpam-3443	54	5	=	=	SYM
ejpam-3443	54	6	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	54	7	)	)	PUNCT
ejpam-3443	54	8	\	\	NOUN
ejpam-3443	54	9	s|	s|	PROPN
ejpam-3443	54	10	.	.	PUNCT
ejpam-3443	55	1	thus	thus	ADV
ejpam-3443	55	2	,	,	PUNCT
ejpam-3443	55	3	s	s	VERB
ejpam-3443	55	4	is	be	AUX
ejpam-3443	55	5	a	a	DET
ejpam-3443	55	6	very	very	ADV
ejpam-3443	55	7	cost	cost	NOUN
ejpam-3443	55	8	effective	effective	ADJ
ejpam-3443	55	9	dominating	dominating	NOUN
ejpam-3443	55	10	set	set	NOUN
ejpam-3443	55	11	of	of	ADP
ejpam-3443	55	12	g+h	g+h	PROPN
ejpam-3443	55	13	.	.	PUNCT
ejpam-3443	56	1	theorem	theorem	NOUN
ejpam-3443	56	2	1	1	NUM
ejpam-3443	56	3	.	.	PUNCT
ejpam-3443	57	1	let	let	VERB
ejpam-3443	57	2	g	g	NOUN
ejpam-3443	57	3	and	and	CCONJ
ejpam-3443	57	4	h	h	NOUN
ejpam-3443	57	5	be	be	AUX
ejpam-3443	57	6	nontrivial	nontrivial	ADJ
ejpam-3443	57	7	graphs	graph	NOUN
ejpam-3443	57	8	of	of	ADP
ejpam-3443	57	9	orders	order	NOUN
ejpam-3443	57	10	m	m	VERB
ejpam-3443	57	11	and	and	CCONJ
ejpam-3443	57	12	n	n	CCONJ
ejpam-3443	57	13	,	,	PUNCT
ejpam-3443	57	14	respectively	respectively	ADV
ejpam-3443	57	15	,	,	PUNCT
ejpam-3443	57	16	and	and	CCONJ
ejpam-3443	57	17	let	let	VERB
ejpam-3443	57	18	s	s	PRON
ejpam-3443	57	19	⊆	⊆	NUM
ejpam-3443	57	20	v	v	NOUN
ejpam-3443	57	21	(	(	PUNCT
ejpam-3443	57	22	g+h	g+h	PROPN
ejpam-3443	57	23	)	)	PUNCT
ejpam-3443	57	24	.	.	PUNCT
ejpam-3443	58	1	then	then	ADV
ejpam-3443	58	2	s	s	VERB
ejpam-3443	58	3	is	be	AUX
ejpam-3443	58	4	a	a	DET
ejpam-3443	58	5	cost	cost	NOUN
ejpam-3443	58	6	effective	effective	ADJ
ejpam-3443	58	7	dominating	dominating	NOUN
ejpam-3443	58	8	set	set	NOUN
ejpam-3443	58	9	of	of	ADP
ejpam-3443	58	10	g+h	g+h	PROPN
ejpam-3443	58	11	if	if	SCONJ
ejpam-3443	58	12	and	and	CCONJ
ejpam-3443	58	13	only	only	ADV
ejpam-3443	58	14	if	if	SCONJ
ejpam-3443	58	15	one	one	NUM
ejpam-3443	58	16	of	of	ADP
ejpam-3443	58	17	the	the	DET
ejpam-3443	58	18	following	follow	VERB
ejpam-3443	58	19	holds	hold	VERB
ejpam-3443	58	20	:	:	PUNCT
ejpam-3443	58	21	(	(	PUNCT
ejpam-3443	58	22	i	i	NOUN
ejpam-3443	58	23	)	)	PUNCT
ejpam-3443	58	24	s	s	VERB
ejpam-3443	58	25	⊆	⊆	NUM
ejpam-3443	58	26	v	v	NOUN
ejpam-3443	58	27	(	(	PUNCT
ejpam-3443	58	28	g	g	NOUN
ejpam-3443	58	29	)	)	PUNCT
ejpam-3443	58	30	is	be	AUX
ejpam-3443	58	31	a	a	DET
ejpam-3443	58	32	dominating	dominating	NOUN
ejpam-3443	58	33	set	set	NOUN
ejpam-3443	58	34	of	of	ADP
ejpam-3443	58	35	g	g	PROPN
ejpam-3443	58	36	and	and	CCONJ
ejpam-3443	58	37	|ng(v	|ng(v	NOUN
ejpam-3443	58	38	)	)	PUNCT
ejpam-3443	58	39	∩	∩	NOUN
ejpam-3443	58	40	s|	s|	VERB
ejpam-3443	58	41	≤	≤	NUM
ejpam-3443	58	42	n+	n+	NUM
ejpam-3443	58	43	|ng(v	|ng(v	NOUN
ejpam-3443	58	44	)	)	PUNCT
ejpam-3443	58	45	\	\	NOUN
ejpam-3443	58	46	s|	s|	NOUN
ejpam-3443	58	47	for	for	ADP
ejpam-3443	58	48	all	all	DET
ejpam-3443	58	49	v	v	ADP
ejpam-3443	58	50	∈	∈	NOUN
ejpam-3443	58	51	s	s	X
ejpam-3443	58	52	(	(	PUNCT
ejpam-3443	58	53	ii	ii	NOUN
ejpam-3443	58	54	)	)	PUNCT
ejpam-3443	58	55	s	s	PART
ejpam-3443	58	56	⊆	⊆	NUM
ejpam-3443	58	57	v	v	NOUN
ejpam-3443	58	58	(	(	PUNCT
ejpam-3443	58	59	h	h	NOUN
ejpam-3443	58	60	)	)	PUNCT
ejpam-3443	58	61	is	be	AUX
ejpam-3443	58	62	a	a	DET
ejpam-3443	58	63	dominating	dominating	NOUN
ejpam-3443	58	64	set	set	NOUN
ejpam-3443	58	65	of	of	ADP
ejpam-3443	58	66	h	h	NOUN
ejpam-3443	58	67	and	and	CCONJ
ejpam-3443	58	68	|nh(v)∩s|	|nh(v)∩s|	PROPN
ejpam-3443	58	69	≤	≤	NUM
ejpam-3443	58	70	m+	m+	NUM
ejpam-3443	58	71	|nh(v)\s|	|nh(v)\s|	NOUN
ejpam-3443	58	72	for	for	ADP
ejpam-3443	58	73	all	all	DET
ejpam-3443	58	74	v	v	ADP
ejpam-3443	58	75	∈	∈	NOUN
ejpam-3443	58	76	s	s	X
ejpam-3443	58	77	(	(	PUNCT
ejpam-3443	58	78	iii	iii	NOUN
ejpam-3443	58	79	)	)	PUNCT
ejpam-3443	58	80	s	s	PART
ejpam-3443	58	81	∩	∩	ADJ
ejpam-3443	58	82	v	v	X
ejpam-3443	58	83	(	(	PUNCT
ejpam-3443	58	84	g	g	NOUN
ejpam-3443	58	85	)	)	PUNCT
ejpam-3443	58	86	6=	6=	ADP
ejpam-3443	58	87	∅	∅	NOUN
ejpam-3443	58	88	and	and	CCONJ
ejpam-3443	58	89	s	s	X
ejpam-3443	58	90	∩	∩	ADJ
ejpam-3443	58	91	v	v	ADJ
ejpam-3443	58	92	(	(	PUNCT
ejpam-3443	58	93	h	h	NOUN
ejpam-3443	58	94	)	)	PUNCT
ejpam-3443	58	95	6=	6=	ADP
ejpam-3443	58	96	∅	∅	NOUN
ejpam-3443	58	97	satisfying	satisfy	VERB
ejpam-3443	58	98	(	(	PUNCT
ejpam-3443	58	99	a	a	NOUN
ejpam-3443	58	100	)	)	PUNCT
ejpam-3443	58	101	|ng(v	|ng(v	NOUN
ejpam-3443	58	102	)	)	PUNCT
ejpam-3443	58	103	∩	∩	NOUN
ejpam-3443	58	104	s|+	s|+	PROPN
ejpam-3443	58	105	2|s	2|s	NUM
ejpam-3443	58	106	∩	∩	NOUN
ejpam-3443	58	107	v	v	X
ejpam-3443	58	108	(	(	PUNCT
ejpam-3443	58	109	h)|	h)|	NOUN
ejpam-3443	58	110	≤	≤	NUM
ejpam-3443	58	111	n+	n+	NUM
ejpam-3443	58	112	|ng(v	|ng(v	NOUN
ejpam-3443	58	113	)	)	PUNCT
ejpam-3443	58	114	\	\	NOUN
ejpam-3443	58	115	s|	s|	NOUN
ejpam-3443	58	116	for	for	ADP
ejpam-3443	58	117	all	all	DET
ejpam-3443	58	118	v	v	ADP
ejpam-3443	58	119	∈	∈	NOUN
ejpam-3443	58	120	s	s	NOUN
ejpam-3443	58	121	∩	∩	ADJ
ejpam-3443	58	122	v	v	X
ejpam-3443	58	123	(	(	PUNCT
ejpam-3443	58	124	g	g	NOUN
ejpam-3443	58	125	)	)	PUNCT
ejpam-3443	58	126	(	(	PUNCT
ejpam-3443	58	127	b	b	X
ejpam-3443	58	128	)	)	PUNCT
ejpam-3443	58	129	|nh(v	|nh(v	NOUN
ejpam-3443	58	130	)	)	PUNCT
ejpam-3443	58	131	∩	∩	NOUN
ejpam-3443	58	132	s|+	s|+	PROPN
ejpam-3443	58	133	2|s	2|s	NUM
ejpam-3443	58	134	∩	∩	NOUN
ejpam-3443	58	135	v	v	X
ejpam-3443	58	136	(	(	PUNCT
ejpam-3443	58	137	g)|	g)|	NOUN
ejpam-3443	58	138	≤	≤	NUM
ejpam-3443	58	139	m+	m+	NUM
ejpam-3443	58	140	|nh(v	|nh(v	NUM
ejpam-3443	58	141	)	)	PUNCT
ejpam-3443	58	142	\	\	NOUN
ejpam-3443	58	143	s|	s|	NOUN
ejpam-3443	58	144	for	for	ADP
ejpam-3443	58	145	all	all	DET
ejpam-3443	58	146	v	v	ADP
ejpam-3443	58	147	∈	∈	NOUN
ejpam-3443	58	148	s	s	NOUN
ejpam-3443	58	149	∩	∩	ADJ
ejpam-3443	58	150	v	v	ADJ
ejpam-3443	58	151	(	(	PUNCT
ejpam-3443	58	152	h	h	NOUN
ejpam-3443	58	153	)	)	PUNCT
ejpam-3443	58	154	.	.	PUNCT
ejpam-3443	59	1	f.jamil	f.jamil	PROPN
ejpam-3443	59	2	,	,	PUNCT
ejpam-3443	59	3	h.	h.	PROPN
ejpam-3443	59	4	nuenay	nuenay	PROPN
ejpam-3443	59	5	-	-	PUNCT
ejpam-3443	59	6	maglanque	maglanque	ADJ
ejpam-3443	59	7	/	/	SYM
ejpam-3443	59	8	eur	eur	NOUN
ejpam-3443	59	9	.	.	PUNCT
ejpam-3443	60	1	j.	j.	PROPN
ejpam-3443	60	2	pure	pure	PROPN
ejpam-3443	60	3	appl	appl	PROPN
ejpam-3443	60	4	.	.	PROPN
ejpam-3443	60	5	math	math	PROPN
ejpam-3443	60	6	,	,	PUNCT
ejpam-3443	60	7	12	12	NUM
ejpam-3443	60	8	(	(	PUNCT
ejpam-3443	60	9	3	3	NUM
ejpam-3443	60	10	)	)	PUNCT
ejpam-3443	60	11	(	(	PUNCT
ejpam-3443	60	12	2019	2019	NUM
ejpam-3443	60	13	)	)	PUNCT
ejpam-3443	60	14	,	,	PUNCT
ejpam-3443	60	15	978	978	NUM
ejpam-3443	60	16	-	-	SYM
ejpam-3443	60	17	998	998	NUM
ejpam-3443	60	18	981	981	NUM
ejpam-3443	60	19	proof	proof	NOUN
ejpam-3443	60	20	.	.	PUNCT
ejpam-3443	61	1	let	let	VERB
ejpam-3443	61	2	s	s	PRON
ejpam-3443	61	3	⊆	⊆	NUM
ejpam-3443	61	4	v	v	NOUN
ejpam-3443	61	5	(	(	PUNCT
ejpam-3443	61	6	g+h	g+h	PROPN
ejpam-3443	61	7	)	)	PUNCT
ejpam-3443	61	8	.	.	PUNCT
ejpam-3443	62	1	suppose	suppose	VERB
ejpam-3443	62	2	that	that	SCONJ
ejpam-3443	62	3	s	s	VERB
ejpam-3443	62	4	is	be	AUX
ejpam-3443	62	5	a	a	DET
ejpam-3443	62	6	cost	cost	NOUN
ejpam-3443	62	7	effective	effective	ADJ
ejpam-3443	62	8	dominating	dominating	NOUN
ejpam-3443	62	9	set	set	NOUN
ejpam-3443	62	10	of	of	ADP
ejpam-3443	62	11	g+h	g+h	PROPN
ejpam-3443	62	12	.	.	PUNCT
ejpam-3443	63	1	if	if	SCONJ
ejpam-3443	63	2	s	s	VERB
ejpam-3443	63	3	⊆	⊆	NUM
ejpam-3443	63	4	v	v	NOUN
ejpam-3443	63	5	(	(	PUNCT
ejpam-3443	63	6	g	g	NOUN
ejpam-3443	63	7	)	)	PUNCT
ejpam-3443	63	8	,	,	PUNCT
ejpam-3443	63	9	then	then	ADV
ejpam-3443	63	10	s	s	VERB
ejpam-3443	63	11	is	be	AUX
ejpam-3443	63	12	a	a	DET
ejpam-3443	63	13	dominating	dominating	NOUN
ejpam-3443	63	14	set	set	NOUN
ejpam-3443	63	15	of	of	ADP
ejpam-3443	63	16	g	g	NOUN
ejpam-3443	63	17	,	,	PUNCT
ejpam-3443	63	18	and	and	CCONJ
ejpam-3443	63	19	for	for	ADP
ejpam-3443	63	20	each	each	DET
ejpam-3443	63	21	v	v	NUM
ejpam-3443	63	22	∈	∈	PROPN
ejpam-3443	63	23	s	s	NOUN
ejpam-3443	63	24	,	,	PUNCT
ejpam-3443	63	25	|ng(v	|ng(v	ADJ
ejpam-3443	63	26	)	)	PUNCT
ejpam-3443	63	27	∩	∩	NOUN
ejpam-3443	63	28	s|	s|	NOUN
ejpam-3443	63	29	=	=	SYM
ejpam-3443	63	30	|ng+h(v	|ng+h(v	X
ejpam-3443	63	31	)	)	PUNCT
ejpam-3443	63	32	∩	∩	NOUN
ejpam-3443	63	33	s|	s|	VERB
ejpam-3443	63	34	≤	≤	NUM
ejpam-3443	64	1	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	64	2	)	)	PUNCT
ejpam-3443	64	3	\	\	NOUN
ejpam-3443	64	4	s|	s|	PROPN
ejpam-3443	64	5	=	=	SYM
ejpam-3443	64	6	n+	n+	NUM
ejpam-3443	64	7	|ng(v	|ng(v	NOUN
ejpam-3443	64	8	)	)	PUNCT
ejpam-3443	64	9	\	\	NOUN
ejpam-3443	64	10	s|	s|	PROPN
ejpam-3443	64	11	.	.	PUNCT
ejpam-3443	65	1	similarly	similarly	ADV
ejpam-3443	65	2	,	,	PUNCT
ejpam-3443	65	3	if	if	SCONJ
ejpam-3443	65	4	s	s	VERB
ejpam-3443	65	5	⊆	⊆	NUM
ejpam-3443	65	6	v	v	NOUN
ejpam-3443	65	7	(	(	PUNCT
ejpam-3443	65	8	h	h	NOUN
ejpam-3443	65	9	)	)	PUNCT
ejpam-3443	65	10	,	,	PUNCT
ejpam-3443	65	11	then	then	ADV
ejpam-3443	65	12	s	s	VERB
ejpam-3443	65	13	is	be	AUX
ejpam-3443	65	14	dominating	dominate	VERB
ejpam-3443	65	15	of	of	ADP
ejpam-3443	65	16	h	h	NOUN
ejpam-3443	65	17	and	and	CCONJ
ejpam-3443	65	18	for	for	ADP
ejpam-3443	65	19	each	each	DET
ejpam-3443	65	20	v	v	NUM
ejpam-3443	65	21	∈	∈	PROPN
ejpam-3443	65	22	s	s	NOUN
ejpam-3443	65	23	,	,	PUNCT
ejpam-3443	65	24	|nh(v	|nh(v	NOUN
ejpam-3443	65	25	)	)	PUNCT
ejpam-3443	65	26	∩	∩	NOUN
ejpam-3443	65	27	s|	s|	VERB
ejpam-3443	65	28	≤	≤	NUM
ejpam-3443	66	1	m	m	VERB
ejpam-3443	66	2	+	+	NOUN
ejpam-3443	66	3	|nh(v	|nh(v	X
ejpam-3443	66	4	)	)	PUNCT
ejpam-3443	66	5	\	\	NOUN
ejpam-3443	66	6	s|	s|	PROPN
ejpam-3443	66	7	.	.	PUNCT
ejpam-3443	66	8	suppose	suppose	VERB
ejpam-3443	66	9	that	that	SCONJ
ejpam-3443	66	10	s1	s1	PROPN
ejpam-3443	66	11	=	=	SYM
ejpam-3443	66	12	s	s	PART
ejpam-3443	66	13	∩	∩	ADJ
ejpam-3443	66	14	v	v	X
ejpam-3443	66	15	(	(	PUNCT
ejpam-3443	66	16	g	g	NOUN
ejpam-3443	66	17	)	)	PUNCT
ejpam-3443	66	18	6=	6=	ADP
ejpam-3443	66	19	∅	∅	NOUN
ejpam-3443	66	20	and	and	CCONJ
ejpam-3443	66	21	s2	s2	VERB
ejpam-3443	66	22	=	=	SYM
ejpam-3443	66	23	s	s	PROPN
ejpam-3443	66	24	∩	∩	ADJ
ejpam-3443	66	25	v	v	X
ejpam-3443	66	26	(	(	PUNCT
ejpam-3443	66	27	h	h	NOUN
ejpam-3443	66	28	)	)	PUNCT
ejpam-3443	66	29	6=	6=	ADP
ejpam-3443	66	30	∅.	∅.	VERB
ejpam-3443	66	31	for	for	ADP
ejpam-3443	66	32	each	each	DET
ejpam-3443	66	33	v	v	NUM
ejpam-3443	66	34	∈	∈	PROPN
ejpam-3443	66	35	s1	s1	NOUN
ejpam-3443	66	36	,	,	PUNCT
ejpam-3443	66	37	|ng(v	|ng(v	NOUN
ejpam-3443	66	38	)	)	PUNCT
ejpam-3443	66	39	∩	∩	ADJ
ejpam-3443	66	40	s|+	s|+	NOUN
ejpam-3443	66	41	|s2|	|s2|	NOUN
ejpam-3443	66	42	=	=	SYM
ejpam-3443	66	43	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	66	44	)	)	PUNCT
ejpam-3443	66	45	∩	∩	NOUN
ejpam-3443	66	46	s|	s|	VERB
ejpam-3443	66	47	≤	≤	NUM
ejpam-3443	67	1	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	67	2	)	)	PUNCT
ejpam-3443	67	3	\	\	NOUN
ejpam-3443	67	4	s|	s|	NOUN
ejpam-3443	67	5	=	=	SYM
ejpam-3443	67	6	|ng(v	|ng(v	X
ejpam-3443	67	7	)	)	PUNCT
ejpam-3443	67	8	\	\	NOUN
ejpam-3443	68	1	s|+	s|+	PROPN
ejpam-3443	68	2	|v	|v	NOUN
ejpam-3443	68	3	(	(	PUNCT
ejpam-3443	68	4	h	h	NOUN
ejpam-3443	68	5	)	)	PUNCT
ejpam-3443	68	6	\	\	NOUN
ejpam-3443	68	7	s2|	s2|	PROPN
ejpam-3443	68	8	=	=	SYM
ejpam-3443	68	9	|ng(v	|ng(v	PROPN
ejpam-3443	68	10	)	)	PUNCT
ejpam-3443	68	11	\	\	NOUN
ejpam-3443	69	1	s|+	s|+	NOUN
ejpam-3443	69	2	n−	n−	NOUN
ejpam-3443	69	3	|s2|	|s2|	VERB
ejpam-3443	69	4	thus	thus	ADV
ejpam-3443	69	5	,	,	PUNCT
ejpam-3443	69	6	|ng(v	|ng(v	X
ejpam-3443	69	7	)	)	PUNCT
ejpam-3443	69	8	∩	∩	NOUN
ejpam-3443	69	9	s|+	s|+	NOUN
ejpam-3443	69	10	2|s2|	2|s2|	NUM
ejpam-3443	69	11	≤	≤	NUM
ejpam-3443	69	12	n+	n+	NUM
ejpam-3443	69	13	|ng(v	|ng(v	NOUN
ejpam-3443	69	14	)	)	PUNCT
ejpam-3443	69	15	\	\	NOUN
ejpam-3443	69	16	s|	s|	PROPN
ejpam-3443	69	17	.	.	PUNCT
ejpam-3443	70	1	similarly	similarly	ADV
ejpam-3443	70	2	,	,	PUNCT
ejpam-3443	70	3	for	for	ADP
ejpam-3443	70	4	each	each	DET
ejpam-3443	70	5	v	v	ADP
ejpam-3443	70	6	∈	∈	PROPN
ejpam-3443	70	7	s2	s2	PROPN
ejpam-3443	70	8	,	,	PUNCT
ejpam-3443	70	9	|nh(v	|nh(v	NOUN
ejpam-3443	70	10	)	)	PUNCT
ejpam-3443	70	11	∩	∩	NOUN
ejpam-3443	70	12	s|+	s|+	NOUN
ejpam-3443	70	13	2|s1|	2|s1|	X
ejpam-3443	70	14	≤	≤	NUM
ejpam-3443	70	15	m+	m+	NUM
ejpam-3443	70	16	|nh(v	|nh(v	NOUN
ejpam-3443	70	17	)	)	PUNCT
ejpam-3443	70	18	\	\	NOUN
ejpam-3443	70	19	s|	s|	PROPN
ejpam-3443	70	20	.	.	PUNCT
ejpam-3443	71	1	conversely	conversely	ADV
ejpam-3443	71	2	,	,	PUNCT
ejpam-3443	71	3	suppose	suppose	VERB
ejpam-3443	71	4	that	that	SCONJ
ejpam-3443	71	5	s	s	VERB
ejpam-3443	71	6	satisfies	satisfie	NOUN
ejpam-3443	71	7	property	property	NOUN
ejpam-3443	71	8	(	(	PUNCT
ejpam-3443	71	9	i	i	NOUN
ejpam-3443	71	10	)	)	PUNCT
ejpam-3443	71	11	.	.	PUNCT
ejpam-3443	72	1	then	then	ADV
ejpam-3443	72	2	s	s	VERB
ejpam-3443	72	3	is	be	AUX
ejpam-3443	72	4	a	a	DET
ejpam-3443	72	5	dominating	dominating	NOUN
ejpam-3443	72	6	set	set	NOUN
ejpam-3443	72	7	of	of	ADP
ejpam-3443	72	8	g	g	PROPN
ejpam-3443	72	9	+	+	CCONJ
ejpam-3443	72	10	h.	h.	PROPN
ejpam-3443	72	11	let	let	VERB
ejpam-3443	72	12	v	v	ADP
ejpam-3443	72	13	∈	∈	PROPN
ejpam-3443	72	14	s.	s.	PROPN
ejpam-3443	72	15	then	then	ADV
ejpam-3443	72	16	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	72	17	)	)	PUNCT
ejpam-3443	72	18	∩	∩	NOUN
ejpam-3443	72	19	s|	s|	VERB
ejpam-3443	72	20	=	=	SYM
ejpam-3443	72	21	|ng(v	|ng(v	X
ejpam-3443	72	22	)	)	PUNCT
ejpam-3443	72	23	∩	∩	NOUN
ejpam-3443	72	24	s|	s|	VERB
ejpam-3443	72	25	≤	≤	NUM
ejpam-3443	72	26	n+	n+	NUM
ejpam-3443	72	27	|ng(v	|ng(v	NOUN
ejpam-3443	72	28	)	)	PUNCT
ejpam-3443	72	29	\	\	NOUN
ejpam-3443	72	30	s|	s|	NOUN
ejpam-3443	72	31	=	=	SYM
ejpam-3443	72	32	|ng+h(v	|ng+h(v	X
ejpam-3443	72	33	)	)	PUNCT
ejpam-3443	72	34	\	\	NOUN
ejpam-3443	72	35	s|	s|	PROPN
ejpam-3443	72	36	.	.	PUNCT
ejpam-3443	73	1	thus	thus	ADV
ejpam-3443	73	2	,	,	PUNCT
ejpam-3443	73	3	s	s	VERB
ejpam-3443	73	4	is	be	AUX
ejpam-3443	73	5	a	a	DET
ejpam-3443	73	6	cost	cost	NOUN
ejpam-3443	73	7	effective	effective	ADJ
ejpam-3443	73	8	set	set	NOUN
ejpam-3443	73	9	of	of	ADP
ejpam-3443	73	10	g+h	g+h	PROPN
ejpam-3443	73	11	,	,	PUNCT
ejpam-3443	73	12	and	and	CCONJ
ejpam-3443	73	13	the	the	DET
ejpam-3443	73	14	conclusion	conclusion	NOUN
ejpam-3443	73	15	follows	follow	VERB
ejpam-3443	73	16	.	.	PUNCT
ejpam-3443	74	1	similarly	similarly	ADV
ejpam-3443	74	2	,	,	PUNCT
ejpam-3443	74	3	if	if	SCONJ
ejpam-3443	74	4	s	s	ADP
ejpam-3443	74	5	satisfies	satisfie	NOUN
ejpam-3443	74	6	(	(	PUNCT
ejpam-3443	74	7	ii	ii	NOUN
ejpam-3443	74	8	)	)	PUNCT
ejpam-3443	74	9	,	,	PUNCT
ejpam-3443	74	10	then	then	ADV
ejpam-3443	74	11	s	s	VERB
ejpam-3443	74	12	is	be	AUX
ejpam-3443	74	13	a	a	DET
ejpam-3443	74	14	cost	cost	NOUN
ejpam-3443	74	15	effective	effective	ADJ
ejpam-3443	74	16	dominating	dominating	NOUN
ejpam-3443	74	17	set	set	NOUN
ejpam-3443	74	18	of	of	ADP
ejpam-3443	74	19	g+h	g+h	PROPN
ejpam-3443	74	20	.	.	PUNCT
ejpam-3443	75	1	finally	finally	ADV
ejpam-3443	75	2	,	,	PUNCT
ejpam-3443	75	3	suppose	suppose	VERB
ejpam-3443	75	4	that	that	SCONJ
ejpam-3443	75	5	s	s	VERB
ejpam-3443	75	6	satisfies	satisfie	NOUN
ejpam-3443	75	7	(	(	PUNCT
ejpam-3443	75	8	iii	iii	NOUN
ejpam-3443	75	9	)	)	PUNCT
ejpam-3443	75	10	.	.	PUNCT
ejpam-3443	76	1	then	then	ADV
ejpam-3443	76	2	s	s	VERB
ejpam-3443	76	3	is	be	AUX
ejpam-3443	76	4	a	a	DET
ejpam-3443	76	5	dominating	dominating	NOUN
ejpam-3443	76	6	set	set	NOUN
ejpam-3443	76	7	of	of	ADP
ejpam-3443	76	8	g+h	g+h	PROPN
ejpam-3443	76	9	.	.	PUNCT
ejpam-3443	77	1	for	for	ADP
ejpam-3443	77	2	each	each	DET
ejpam-3443	77	3	v	v	NUM
ejpam-3443	77	4	∈	∈	PROPN
ejpam-3443	77	5	s	s	PART
ejpam-3443	77	6	∩	∩	ADJ
ejpam-3443	77	7	v	v	X
ejpam-3443	77	8	(	(	PUNCT
ejpam-3443	77	9	g	g	NOUN
ejpam-3443	77	10	)	)	PUNCT
ejpam-3443	77	11	,	,	PUNCT
ejpam-3443	77	12	we	we	PRON
ejpam-3443	77	13	have	have	VERB
ejpam-3443	77	14	from	from	ADP
ejpam-3443	77	15	property	property	NOUN
ejpam-3443	77	16	(	(	PUNCT
ejpam-3443	77	17	iii)(a	iii)(a	PROPN
ejpam-3443	77	18	)	)	PUNCT
ejpam-3443	77	19	,	,	PUNCT
ejpam-3443	77	20	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	77	21	)	)	PUNCT
ejpam-3443	77	22	∩	∩	NOUN
ejpam-3443	77	23	s|	s|	VERB
ejpam-3443	77	24	=	=	SYM
ejpam-3443	78	1	|ng(v	|ng(v	NOUN
ejpam-3443	78	2	)	)	PUNCT
ejpam-3443	78	3	∩	∩	NOUN
ejpam-3443	78	4	s|+	s|+	PROPN
ejpam-3443	78	5	|nh(v	|nh(v	NOUN
ejpam-3443	78	6	)	)	PUNCT
ejpam-3443	78	7	∩	∩	NOUN
ejpam-3443	78	8	s|	s|	VERB
ejpam-3443	78	9	=	=	SYM
ejpam-3443	78	10	|ng(v	|ng(v	NOUN
ejpam-3443	78	11	)	)	PUNCT
ejpam-3443	78	12	∩	∩	ADJ
ejpam-3443	78	13	s|+	s|+	PROPN
ejpam-3443	78	14	|s	|s	PROPN
ejpam-3443	78	15	∩	∩	NOUN
ejpam-3443	78	16	v	v	X
ejpam-3443	78	17	(	(	PUNCT
ejpam-3443	78	18	h)|	h)|	NOUN
ejpam-3443	78	19	≤	≤	NUM
ejpam-3443	78	20	n+	n+	NUM
ejpam-3443	78	21	|ng(v	|ng(v	NOUN
ejpam-3443	78	22	)	)	PUNCT
ejpam-3443	78	23	\	\	NOUN
ejpam-3443	78	24	s|	s|	VERB
ejpam-3443	78	25	−	−	PROPN
ejpam-3443	78	26	2|s	2|s	PROPN
ejpam-3443	78	27	∩	∩	NOUN
ejpam-3443	78	28	v	v	ADP
ejpam-3443	78	29	(	(	PUNCT
ejpam-3443	78	30	h)|+	h)|+	ADJ
ejpam-3443	78	31	|s	|s	PROPN
ejpam-3443	78	32	∩	∩	ADJ
ejpam-3443	78	33	v	v	X
ejpam-3443	78	34	(	(	PUNCT
ejpam-3443	78	35	h)|	h)|	NOUN
ejpam-3443	78	36	=	=	PUNCT
ejpam-3443	78	37	n+	n+	NUM
ejpam-3443	78	38	|ng(v	|ng(v	NOUN
ejpam-3443	78	39	)	)	PUNCT
ejpam-3443	78	40	\	\	NOUN
ejpam-3443	78	41	s|	s|	VERB
ejpam-3443	78	42	−	−	PROPN
ejpam-3443	78	43	|s	|s	PROPN
ejpam-3443	78	44	∩	∩	PROPN
ejpam-3443	78	45	v	v	NOUN
ejpam-3443	78	46	(	(	PUNCT
ejpam-3443	78	47	h)|	h)|	NOUN
ejpam-3443	78	48	=	=	SYM
ejpam-3443	78	49	|ng(v	|ng(v	PROPN
ejpam-3443	78	50	)	)	PUNCT
ejpam-3443	78	51	\	\	NOUN
ejpam-3443	79	1	s|+	s|+	PROPN
ejpam-3443	79	2	|v	|v	NOUN
ejpam-3443	79	3	(	(	PUNCT
ejpam-3443	79	4	h	h	NOUN
ejpam-3443	79	5	)	)	PUNCT
ejpam-3443	79	6	\	\	NOUN
ejpam-3443	79	7	s|	s|	NOUN
ejpam-3443	79	8	=	=	SYM
ejpam-3443	79	9	|ng+h(v	|ng+h(v	X
ejpam-3443	79	10	)	)	PUNCT
ejpam-3443	79	11	\	\	NOUN
ejpam-3443	79	12	s|	s|	PROPN
ejpam-3443	79	13	.	.	PUNCT
ejpam-3443	80	1	similarly	similarly	ADV
ejpam-3443	80	2	,	,	PUNCT
ejpam-3443	80	3	for	for	ADP
ejpam-3443	80	4	each	each	DET
ejpam-3443	80	5	v	v	X
ejpam-3443	80	6	∈	∈	PROPN
ejpam-3443	80	7	s∩v	s∩v	NOUN
ejpam-3443	80	8	(	(	PUNCT
ejpam-3443	80	9	h	h	NOUN
ejpam-3443	80	10	)	)	PUNCT
ejpam-3443	80	11	,	,	PUNCT
ejpam-3443	80	12	|nh(v)∩s|+	|nh(v)∩s|+	NOUN
ejpam-3443	80	13	2|s∩v	2|s∩v	NOUN
ejpam-3443	80	14	(	(	PUNCT
ejpam-3443	80	15	g)|	g)|	NOUN
ejpam-3443	80	16	≤	≤	NUM
ejpam-3443	80	17	m+	m+	NUM
ejpam-3443	80	18	|nh(v)\s|	|nh(v)\s|	NOUN
ejpam-3443	80	19	.	.	PROPN
ejpam-3443	80	20	therefore	therefore	ADV
ejpam-3443	80	21	,	,	PUNCT
ejpam-3443	80	22	s	s	VERB
ejpam-3443	80	23	is	be	AUX
ejpam-3443	80	24	a	a	DET
ejpam-3443	80	25	cost	cost	NOUN
ejpam-3443	80	26	effective	effective	ADJ
ejpam-3443	80	27	dominating	dominating	NOUN
ejpam-3443	80	28	set	set	NOUN
ejpam-3443	80	29	of	of	ADP
ejpam-3443	80	30	g+h	g+h	PROPN
ejpam-3443	80	31	.	.	PUNCT
ejpam-3443	81	1	in	in	ADP
ejpam-3443	81	2	view	view	NOUN
ejpam-3443	81	3	of	of	ADP
ejpam-3443	81	4	theorem	theorem	NOUN
ejpam-3443	81	5	1	1	NUM
ejpam-3443	81	6	,	,	PUNCT
ejpam-3443	81	7	all	all	DET
ejpam-3443	81	8	independent	independent	ADJ
ejpam-3443	81	9	dominating	dominating	NOUN
ejpam-3443	81	10	sets	set	NOUN
ejpam-3443	81	11	of	of	ADP
ejpam-3443	81	12	g	g	PROPN
ejpam-3443	81	13	and	and	CCONJ
ejpam-3443	81	14	all	all	DET
ejpam-3443	81	15	independent	independent	ADJ
ejpam-3443	81	16	dominating	dominating	NOUN
ejpam-3443	81	17	sets	set	NOUN
ejpam-3443	81	18	of	of	ADP
ejpam-3443	81	19	h	h	NOUN
ejpam-3443	81	20	are	be	AUX
ejpam-3443	81	21	cost	cost	VERB
ejpam-3443	81	22	effective	effective	ADJ
ejpam-3443	81	23	dominating	dominating	NOUN
ejpam-3443	81	24	sets	set	NOUN
ejpam-3443	81	25	of	of	ADP
ejpam-3443	81	26	g	g	PROPN
ejpam-3443	81	27	+	+	CCONJ
ejpam-3443	81	28	h.	h.	PROPN
ejpam-3443	82	1	moreover	moreover	ADV
ejpam-3443	82	2	,	,	PUNCT
ejpam-3443	82	3	if	if	SCONJ
ejpam-3443	82	4	m	m	PROPN
ejpam-3443	82	5	and	and	CCONJ
ejpam-3443	82	6	n	n	PRON
ejpam-3443	82	7	are	be	AUX
ejpam-3443	82	8	the	the	DET
ejpam-3443	82	9	orders	order	NOUN
ejpam-3443	82	10	of	of	ADP
ejpam-3443	82	11	g	g	PROPN
ejpam-3443	82	12	and	and	CCONJ
ejpam-3443	82	13	h	h	NOUN
ejpam-3443	82	14	,	,	PUNCT
ejpam-3443	82	15	respectively	respectively	ADV
ejpam-3443	82	16	,	,	PUNCT
ejpam-3443	82	17	and	and	CCONJ
ejpam-3443	82	18	if	if	SCONJ
ejpam-3443	82	19	m	m	VERB
ejpam-3443	82	20	≤	≤	NOUN
ejpam-3443	82	21	n	n	CCONJ
ejpam-3443	82	22	,	,	PUNCT
ejpam-3443	82	23	then	then	ADV
ejpam-3443	82	24	all	all	DET
ejpam-3443	82	25	dominating	dominating	NOUN
ejpam-3443	82	26	sets	set	NOUN
ejpam-3443	82	27	of	of	ADP
ejpam-3443	82	28	g	g	NOUN
ejpam-3443	82	29	are	be	AUX
ejpam-3443	82	30	cost	cost	VERB
ejpam-3443	82	31	effective	effective	ADJ
ejpam-3443	82	32	dominating	dominating	NOUN
ejpam-3443	82	33	sets	set	NOUN
ejpam-3443	82	34	of	of	ADP
ejpam-3443	82	35	g+h	g+h	NOUN
ejpam-3443	82	36	so	so	SCONJ
ejpam-3443	82	37	that	that	SCONJ
ejpam-3443	82	38	γce(g+h	γce(g+h	NOUN
ejpam-3443	82	39	)	)	PUNCT
ejpam-3443	82	40	≤	≤	PROPN
ejpam-3443	82	41	γ(g	γ(g	PROPN
ejpam-3443	82	42	)	)	PUNCT
ejpam-3443	82	43	.	.	PUNCT
ejpam-3443	83	1	f.jamil	f.jamil	PROPN
ejpam-3443	83	2	,	,	PUNCT
ejpam-3443	83	3	h.	h.	PROPN
ejpam-3443	83	4	nuenay	nuenay	PROPN
ejpam-3443	83	5	-	-	PUNCT
ejpam-3443	83	6	maglanque	maglanque	ADJ
ejpam-3443	83	7	/	/	SYM
ejpam-3443	83	8	eur	eur	NOUN
ejpam-3443	83	9	.	.	PUNCT
ejpam-3443	84	1	j.	j.	PROPN
ejpam-3443	84	2	pure	pure	PROPN
ejpam-3443	84	3	appl	appl	PROPN
ejpam-3443	84	4	.	.	PROPN
ejpam-3443	84	5	math	math	PROPN
ejpam-3443	84	6	,	,	PUNCT
ejpam-3443	84	7	12	12	NUM
ejpam-3443	84	8	(	(	PUNCT
ejpam-3443	84	9	3	3	NUM
ejpam-3443	84	10	)	)	PUNCT
ejpam-3443	84	11	(	(	PUNCT
ejpam-3443	84	12	2019	2019	NUM
ejpam-3443	84	13	)	)	PUNCT
ejpam-3443	84	14	,	,	PUNCT
ejpam-3443	84	15	978	978	NUM
ejpam-3443	84	16	-	-	SYM
ejpam-3443	84	17	998	998	NUM
ejpam-3443	84	18	982	982	NUM
ejpam-3443	84	19	corollary	corollary	ADJ
ejpam-3443	84	20	1	1	NUM
ejpam-3443	84	21	.	.	PUNCT
ejpam-3443	85	1	for	for	ADP
ejpam-3443	85	2	any	any	DET
ejpam-3443	85	3	graphs	graph	NOUN
ejpam-3443	85	4	g	g	NOUN
ejpam-3443	85	5	and	and	CCONJ
ejpam-3443	85	6	h	h	NOUN
ejpam-3443	85	7	,	,	PUNCT
ejpam-3443	85	8	γce(g+h	γce(g+h	ADJ
ejpam-3443	85	9	)	)	PUNCT
ejpam-3443	85	10	=	=	PUNCT
ejpam-3443	85	11			PROPN
ejpam-3443	85	12	1	1	NUM
ejpam-3443	85	13	,	,	PUNCT
ejpam-3443	85	14	if	if	SCONJ
ejpam-3443	85	15	γ(g	γ(g	PROPN
ejpam-3443	85	16	)	)	PUNCT
ejpam-3443	85	17	=	=	SYM
ejpam-3443	85	18	1	1	NUM
ejpam-3443	85	19	or	or	CCONJ
ejpam-3443	85	20	γ(h	γ(h	NOUN
ejpam-3443	85	21	)	)	PUNCT
ejpam-3443	85	22	=	=	SYM
ejpam-3443	85	23	1	1	NUM
ejpam-3443	85	24	2	2	NUM
ejpam-3443	85	25	,	,	PUNCT
ejpam-3443	85	26	otherwise	otherwise	ADV
ejpam-3443	85	27	.	.	PUNCT
ejpam-3443	86	1	proof	proof	NOUN
ejpam-3443	86	2	.	.	PUNCT
ejpam-3443	87	1	suppose	suppose	VERB
ejpam-3443	87	2	that	that	SCONJ
ejpam-3443	87	3	γ(g	γ(g	PROPN
ejpam-3443	87	4	)	)	PUNCT
ejpam-3443	87	5	=	=	SYM
ejpam-3443	87	6	1	1	NUM
ejpam-3443	87	7	,	,	PUNCT
ejpam-3443	87	8	and	and	CCONJ
ejpam-3443	87	9	let	let	VERB
ejpam-3443	87	10	s	s	PRON
ejpam-3443	87	11	=	=	NOUN
ejpam-3443	87	12	{	{	PUNCT
ejpam-3443	87	13	v	v	NOUN
ejpam-3443	87	14	}	}	PUNCT
ejpam-3443	87	15	be	be	AUX
ejpam-3443	87	16	a	a	DET
ejpam-3443	87	17	γ	γ	NOUN
ejpam-3443	87	18	-	-	PUNCT
ejpam-3443	87	19	set	set	NOUN
ejpam-3443	87	20	of	of	ADP
ejpam-3443	87	21	g.	g.	PROPN
ejpam-3443	87	22	then	then	ADV
ejpam-3443	87	23	,	,	PUNCT
ejpam-3443	87	24	|ng+h(v)∩s|	|ng+h(v)∩s|	NOUN
ejpam-3443	87	25	=	=	SYM
ejpam-3443	87	26	|ng(v	|ng(v	NOUN
ejpam-3443	87	27	)	)	PUNCT
ejpam-3443	87	28	∩	∩	NOUN
ejpam-3443	87	29	s|	s|	NOUN
ejpam-3443	87	30	=	=	SYM
ejpam-3443	87	31	0	0	PUNCT
ejpam-3443	87	32	<	<	X
ejpam-3443	87	33	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	87	34	)	)	PUNCT
ejpam-3443	87	35	\	\	NOUN
ejpam-3443	87	36	s|	s|	PROPN
ejpam-3443	87	37	.	.	PUNCT
ejpam-3443	88	1	thus	thus	ADV
ejpam-3443	88	2	,	,	PUNCT
ejpam-3443	88	3	s	s	VERB
ejpam-3443	88	4	is	be	AUX
ejpam-3443	88	5	a	a	DET
ejpam-3443	88	6	cost	cost	NOUN
ejpam-3443	88	7	effective	effective	ADJ
ejpam-3443	88	8	dominating	dominating	NOUN
ejpam-3443	88	9	set	set	NOUN
ejpam-3443	88	10	of	of	ADP
ejpam-3443	88	11	g	g	PROPN
ejpam-3443	88	12	+	+	CCONJ
ejpam-3443	88	13	h	h	NOUN
ejpam-3443	88	14	,	,	PUNCT
ejpam-3443	88	15	showing	show	VERB
ejpam-3443	88	16	that	that	SCONJ
ejpam-3443	88	17	γve(g	γve(g	PROPN
ejpam-3443	89	1	+	+	NUM
ejpam-3443	89	2	h	h	NOUN
ejpam-3443	89	3	)	)	PUNCT
ejpam-3443	89	4	=	=	SYM
ejpam-3443	89	5	1	1	X
ejpam-3443	89	6	.	.	X
ejpam-3443	89	7	similarly	similarly	ADV
ejpam-3443	89	8	,	,	PUNCT
ejpam-3443	89	9	if	if	SCONJ
ejpam-3443	89	10	γ(h	γ(h	NOUN
ejpam-3443	89	11	)	)	PUNCT
ejpam-3443	89	12	=	=	SYM
ejpam-3443	90	1	1	1	NUM
ejpam-3443	90	2	,	,	PUNCT
ejpam-3443	90	3	then	then	ADV
ejpam-3443	90	4	γce(g	γce(g	PROPN
ejpam-3443	91	1	+	+	CCONJ
ejpam-3443	91	2	h	h	NOUN
ejpam-3443	91	3	)	)	PUNCT
ejpam-3443	91	4	=	=	SYM
ejpam-3443	91	5	1	1	X
ejpam-3443	91	6	.	.	PUNCT
ejpam-3443	91	7	suppose	suppose	VERB
ejpam-3443	91	8	that	that	SCONJ
ejpam-3443	91	9	γ(g	γ(g	PROPN
ejpam-3443	91	10	)	)	PUNCT
ejpam-3443	91	11	≥	≥	NOUN
ejpam-3443	91	12	2	2	NUM
ejpam-3443	91	13	and	and	CCONJ
ejpam-3443	91	14	γ(h	γ(h	NOUN
ejpam-3443	91	15	)	)	PUNCT
ejpam-3443	91	16	≥	≥	NOUN
ejpam-3443	91	17	2	2	NUM
ejpam-3443	91	18	.	.	PUNCT
ejpam-3443	91	19	let	let	VERB
ejpam-3443	91	20	s	s	VERB
ejpam-3443	91	21	=	=	PUNCT
ejpam-3443	91	22	{	{	PUNCT
ejpam-3443	91	23	u	u	NOUN
ejpam-3443	91	24	,	,	PUNCT
ejpam-3443	91	25	v	v	NOUN
ejpam-3443	91	26	}	}	PUNCT
ejpam-3443	91	27	,	,	PUNCT
ejpam-3443	91	28	where	where	SCONJ
ejpam-3443	91	29	u	u	PROPN
ejpam-3443	91	30	∈	∈	PROPN
ejpam-3443	91	31	v	v	ADP
ejpam-3443	91	32	(	(	PUNCT
ejpam-3443	91	33	g	g	NOUN
ejpam-3443	91	34	)	)	PUNCT
ejpam-3443	91	35	and	and	CCONJ
ejpam-3443	91	36	v	v	ADP
ejpam-3443	91	37	∈	∈	PROPN
ejpam-3443	91	38	v	v	NOUN
ejpam-3443	91	39	(	(	PUNCT
ejpam-3443	91	40	h	h	NOUN
ejpam-3443	91	41	)	)	PUNCT
ejpam-3443	91	42	.	.	PUNCT
ejpam-3443	92	1	then	then	ADV
ejpam-3443	92	2	s	s	VERB
ejpam-3443	92	3	satisfies	satisfie	NOUN
ejpam-3443	92	4	theorem	theorem	VERB
ejpam-3443	92	5	1(iii	1(iii	NUM
ejpam-3443	92	6	)	)	PUNCT
ejpam-3443	92	7	so	so	SCONJ
ejpam-3443	92	8	that	that	PRON
ejpam-3443	92	9	s	s	VERB
ejpam-3443	92	10	is	be	AUX
ejpam-3443	92	11	a	a	DET
ejpam-3443	92	12	cost	cost	NOUN
ejpam-3443	92	13	effective	effective	ADJ
ejpam-3443	92	14	dominating	dominating	NOUN
ejpam-3443	92	15	set	set	NOUN
ejpam-3443	92	16	of	of	ADP
ejpam-3443	92	17	g+h	g+h	PROPN
ejpam-3443	92	18	.	.	PUNCT
ejpam-3443	93	1	in	in	ADP
ejpam-3443	93	2	this	this	DET
ejpam-3443	93	3	case	case	NOUN
ejpam-3443	93	4	,	,	PUNCT
ejpam-3443	93	5	γce(g+h	γce(g+h	ADJ
ejpam-3443	93	6	)	)	PUNCT
ejpam-3443	93	7	=	=	SYM
ejpam-3443	93	8	2	2	X
ejpam-3443	93	9	.	.	X
ejpam-3443	93	10	theorem	theorem	NOUN
ejpam-3443	93	11	2	2	NUM
ejpam-3443	93	12	.	.	PUNCT
ejpam-3443	94	1	let	let	VERB
ejpam-3443	94	2	g	g	NOUN
ejpam-3443	94	3	and	and	CCONJ
ejpam-3443	94	4	h	h	NOUN
ejpam-3443	94	5	be	be	AUX
ejpam-3443	94	6	nontrivial	nontrivial	ADJ
ejpam-3443	94	7	graphs	graph	NOUN
ejpam-3443	94	8	of	of	ADP
ejpam-3443	94	9	orders	order	NOUN
ejpam-3443	94	10	m	m	VERB
ejpam-3443	94	11	and	and	CCONJ
ejpam-3443	94	12	n	n	CCONJ
ejpam-3443	94	13	,	,	PUNCT
ejpam-3443	94	14	respectively	respectively	ADV
ejpam-3443	94	15	,	,	PUNCT
ejpam-3443	94	16	and	and	CCONJ
ejpam-3443	94	17	let	let	VERB
ejpam-3443	94	18	s	s	PRON
ejpam-3443	94	19	⊆	⊆	NUM
ejpam-3443	94	20	v	v	NOUN
ejpam-3443	94	21	(	(	PUNCT
ejpam-3443	94	22	g	g	PROPN
ejpam-3443	94	23	+	+	NOUN
ejpam-3443	94	24	h	h	NOUN
ejpam-3443	94	25	)	)	PUNCT
ejpam-3443	94	26	.	.	PUNCT
ejpam-3443	95	1	then	then	ADV
ejpam-3443	95	2	s	s	VERB
ejpam-3443	95	3	is	be	AUX
ejpam-3443	95	4	a	a	DET
ejpam-3443	95	5	minimal	minimal	ADJ
ejpam-3443	95	6	cost	cost	NOUN
ejpam-3443	95	7	effective	effective	ADJ
ejpam-3443	95	8	dominating	dominating	NOUN
ejpam-3443	95	9	set	set	NOUN
ejpam-3443	95	10	of	of	ADP
ejpam-3443	95	11	g	g	PROPN
ejpam-3443	95	12	+	+	CCONJ
ejpam-3443	95	13	h	h	NOUN
ejpam-3443	95	14	if	if	SCONJ
ejpam-3443	96	1	and	and	CCONJ
ejpam-3443	96	2	only	only	ADV
ejpam-3443	96	3	if	if	SCONJ
ejpam-3443	96	4	one	one	NUM
ejpam-3443	96	5	of	of	ADP
ejpam-3443	96	6	the	the	DET
ejpam-3443	96	7	following	follow	VERB
ejpam-3443	96	8	holds	hold	VERB
ejpam-3443	96	9	:	:	PUNCT
ejpam-3443	96	10	(	(	PUNCT
ejpam-3443	96	11	i	i	NOUN
ejpam-3443	96	12	)	)	PUNCT
ejpam-3443	96	13	s	s	VERB
ejpam-3443	96	14	⊆	⊆	NUM
ejpam-3443	96	15	v	v	NOUN
ejpam-3443	96	16	(	(	PUNCT
ejpam-3443	96	17	g	g	NOUN
ejpam-3443	96	18	)	)	PUNCT
ejpam-3443	96	19	is	be	AUX
ejpam-3443	96	20	a	a	DET
ejpam-3443	96	21	minimal	minimal	ADJ
ejpam-3443	96	22	dominating	dominating	NOUN
ejpam-3443	96	23	set	set	NOUN
ejpam-3443	96	24	of	of	ADP
ejpam-3443	96	25	g	g	PROPN
ejpam-3443	96	26	and	and	CCONJ
ejpam-3443	96	27	|ng(v	|ng(v	NOUN
ejpam-3443	96	28	)	)	PUNCT
ejpam-3443	96	29	∩	∩	NOUN
ejpam-3443	96	30	s|	s|	VERB
ejpam-3443	96	31	≤	≤	NUM
ejpam-3443	96	32	n+	n+	NUM
ejpam-3443	97	1	|ng(v	|ng(v	NOUN
ejpam-3443	97	2	)	)	PUNCT
ejpam-3443	97	3	\	\	NOUN
ejpam-3443	97	4	s|	s|	NOUN
ejpam-3443	97	5	for	for	ADP
ejpam-3443	97	6	all	all	DET
ejpam-3443	97	7	v	v	ADP
ejpam-3443	97	8	∈	∈	NOUN
ejpam-3443	97	9	s	s	X
ejpam-3443	97	10	(	(	PUNCT
ejpam-3443	97	11	ii	ii	NOUN
ejpam-3443	97	12	)	)	PUNCT
ejpam-3443	97	13	s	s	PART
ejpam-3443	97	14	⊆	⊆	NUM
ejpam-3443	97	15	v	v	NOUN
ejpam-3443	97	16	(	(	PUNCT
ejpam-3443	97	17	h	h	NOUN
ejpam-3443	97	18	)	)	PUNCT
ejpam-3443	97	19	is	be	AUX
ejpam-3443	97	20	a	a	DET
ejpam-3443	97	21	minimal	minimal	ADJ
ejpam-3443	97	22	dominating	dominating	NOUN
ejpam-3443	97	23	set	set	NOUN
ejpam-3443	97	24	of	of	ADP
ejpam-3443	97	25	h	h	NOUN
ejpam-3443	97	26	and	and	CCONJ
ejpam-3443	97	27	|nh(v)∩s|	|nh(v)∩s|	PROPN
ejpam-3443	97	28	≤	≤	NUM
ejpam-3443	97	29	m+	m+	NUM
ejpam-3443	97	30	|nh(v	|nh(v	NOUN
ejpam-3443	97	31	)	)	PUNCT
ejpam-3443	97	32	\s|	\s|	NOUN
ejpam-3443	97	33	for	for	ADP
ejpam-3443	97	34	all	all	DET
ejpam-3443	97	35	v	v	ADP
ejpam-3443	97	36	∈	∈	NOUN
ejpam-3443	97	37	s	s	X
ejpam-3443	97	38	(	(	PUNCT
ejpam-3443	97	39	iii	iii	NOUN
ejpam-3443	97	40	)	)	PUNCT
ejpam-3443	97	41	s	s	PART
ejpam-3443	97	42	=	=	PUNCT
ejpam-3443	97	43	{	{	PUNCT
ejpam-3443	97	44	u	u	NOUN
ejpam-3443	97	45	,	,	PUNCT
ejpam-3443	97	46	v	v	NOUN
ejpam-3443	97	47	}	}	PUNCT
ejpam-3443	97	48	,	,	PUNCT
ejpam-3443	97	49	where	where	SCONJ
ejpam-3443	97	50	u	u	PROPN
ejpam-3443	97	51	∈	∈	PROPN
ejpam-3443	97	52	v	v	ADP
ejpam-3443	97	53	(	(	PUNCT
ejpam-3443	97	54	g	g	NOUN
ejpam-3443	97	55	)	)	PUNCT
ejpam-3443	97	56	and	and	CCONJ
ejpam-3443	97	57	v	v	ADP
ejpam-3443	97	58	∈	∈	PROPN
ejpam-3443	97	59	v	v	NOUN
ejpam-3443	97	60	(	(	PUNCT
ejpam-3443	97	61	h	h	NOUN
ejpam-3443	97	62	)	)	PUNCT
ejpam-3443	97	63	do	do	AUX
ejpam-3443	97	64	not	not	PART
ejpam-3443	97	65	dominate	dominate	VERB
ejpam-3443	97	66	v	v	NOUN
ejpam-3443	97	67	(	(	PUNCT
ejpam-3443	97	68	g	g	NOUN
ejpam-3443	97	69	)	)	PUNCT
ejpam-3443	97	70	and	and	CCONJ
ejpam-3443	97	71	v	v	NOUN
ejpam-3443	97	72	(	(	PUNCT
ejpam-3443	97	73	h	h	NOUN
ejpam-3443	97	74	)	)	PUNCT
ejpam-3443	97	75	,	,	PUNCT
ejpam-3443	97	76	respectively	respectively	ADV
ejpam-3443	97	77	.	.	PUNCT
ejpam-3443	98	1	proof	proof	NOUN
ejpam-3443	98	2	.	.	PUNCT
ejpam-3443	99	1	suppose	suppose	VERB
ejpam-3443	99	2	that	that	SCONJ
ejpam-3443	99	3	s	s	VERB
ejpam-3443	99	4	is	be	AUX
ejpam-3443	99	5	a	a	DET
ejpam-3443	99	6	minimal	minimal	ADJ
ejpam-3443	99	7	cost	cost	NOUN
ejpam-3443	99	8	effective	effective	ADJ
ejpam-3443	99	9	dominating	dominating	NOUN
ejpam-3443	99	10	set	set	NOUN
ejpam-3443	99	11	of	of	ADP
ejpam-3443	99	12	g	g	PROPN
ejpam-3443	99	13	+	+	CCONJ
ejpam-3443	99	14	h.	h.	PROPN
ejpam-3443	99	15	suppose	suppose	VERB
ejpam-3443	99	16	that	that	SCONJ
ejpam-3443	99	17	s	s	VERB
ejpam-3443	99	18	⊆	⊆	NUM
ejpam-3443	99	19	v	v	NOUN
ejpam-3443	99	20	(	(	PUNCT
ejpam-3443	99	21	g	g	NOUN
ejpam-3443	99	22	)	)	PUNCT
ejpam-3443	99	23	.	.	PUNCT
ejpam-3443	100	1	by	by	ADP
ejpam-3443	100	2	theorem	theorem	NOUN
ejpam-3443	100	3	1	1	NUM
ejpam-3443	100	4	,	,	PUNCT
ejpam-3443	100	5	s	s	VERB
ejpam-3443	100	6	is	be	AUX
ejpam-3443	100	7	a	a	DET
ejpam-3443	100	8	dominating	dominating	NOUN
ejpam-3443	100	9	set	set	NOUN
ejpam-3443	100	10	of	of	ADP
ejpam-3443	100	11	g	g	NOUN
ejpam-3443	100	12	satisfying	satisfy	VERB
ejpam-3443	100	13	|ng(v	|ng(v	NOUN
ejpam-3443	100	14	)	)	PUNCT
ejpam-3443	100	15	∩	∩	NOUN
ejpam-3443	100	16	s|	s|	VERB
ejpam-3443	100	17	≤	≤	NUM
ejpam-3443	100	18	n+	n+	NUM
ejpam-3443	101	1	|ng(v	|ng(v	NOUN
ejpam-3443	101	2	)	)	PUNCT
ejpam-3443	101	3	\	\	NOUN
ejpam-3443	101	4	s|	s|	NOUN
ejpam-3443	101	5	(	(	PUNCT
ejpam-3443	101	6	1	1	X
ejpam-3443	101	7	)	)	PUNCT
ejpam-3443	101	8	for	for	ADP
ejpam-3443	101	9	all	all	PRON
ejpam-3443	101	10	v	v	NOUN
ejpam-3443	101	11	∈	∈	PROPN
ejpam-3443	101	12	s.	s.	PROPN
ejpam-3443	101	13	suppose	suppose	VERB
ejpam-3443	101	14	that	that	SCONJ
ejpam-3443	101	15	s	s	VERB
ejpam-3443	101	16	is	be	AUX
ejpam-3443	101	17	not	not	PART
ejpam-3443	101	18	a	a	DET
ejpam-3443	101	19	minimal	minimal	ADJ
ejpam-3443	101	20	dominating	dominating	NOUN
ejpam-3443	101	21	set	set	NOUN
ejpam-3443	101	22	of	of	ADP
ejpam-3443	101	23	g.	g.	PROPN
ejpam-3443	101	24	then	then	ADV
ejpam-3443	101	25	,	,	PUNCT
ejpam-3443	101	26	there	there	PRON
ejpam-3443	101	27	exists	exist	VERB
ejpam-3443	101	28	a	a	DET
ejpam-3443	101	29	dominating	dominating	NOUN
ejpam-3443	101	30	set	set	NOUN
ejpam-3443	101	31	s∗	s∗	VERB
ejpam-3443	101	32	⊆	⊆	NUM
ejpam-3443	101	33	s	s	NOUN
ejpam-3443	101	34	of	of	ADP
ejpam-3443	101	35	g	g	NOUN
ejpam-3443	101	36	with	with	ADP
ejpam-3443	101	37	|s∗|	|s∗|	NUM
ejpam-3443	101	38	≤	≤	NUM
ejpam-3443	101	39	|s|	|s|	PROPN
ejpam-3443	101	40	.	.	PUNCT
ejpam-3443	102	1	since	since	SCONJ
ejpam-3443	102	2	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	102	3	)	)	PUNCT
ejpam-3443	102	4	∩	∩	NOUN
ejpam-3443	102	5	s∗|	s∗|	PROPN
ejpam-3443	102	6	=	=	SYM
ejpam-3443	102	7	|ng(v	|ng(v	PROPN
ejpam-3443	102	8	)	)	PUNCT
ejpam-3443	102	9	∩	∩	NOUN
ejpam-3443	102	10	s∗|	s∗|	VERB
ejpam-3443	102	11	≤	≤	NUM
ejpam-3443	102	12	ng(v	ng(v	PUNCT
ejpam-3443	102	13	)	)	PUNCT
ejpam-3443	102	14	∩	∩	NOUN
ejpam-3443	102	15	s|	s|	NOUN
ejpam-3443	102	16	=	=	SYM
ejpam-3443	103	1	|ng+h(v	|ng+h(v	X
ejpam-3443	103	2	)	)	PUNCT
ejpam-3443	103	3	\	\	NOUN
ejpam-3443	103	4	s|	s|	VERB
ejpam-3443	103	5	≤	≤	NUM
ejpam-3443	103	6	|ng+h(v	|ng+h(v	NOUN
ejpam-3443	103	7	)	)	PUNCT
ejpam-3443	103	8	\	\	NOUN
ejpam-3443	103	9	s∗|	s∗|	PROPN
ejpam-3443	103	10	for	for	ADP
ejpam-3443	103	11	all	all	DET
ejpam-3443	103	12	v	v	NOUN
ejpam-3443	103	13	∈	∈	NOUN
ejpam-3443	103	14	s∗	s∗	NOUN
ejpam-3443	103	15	,	,	PUNCT
ejpam-3443	103	16	s∗	s∗	PROPN
ejpam-3443	103	17	is	be	AUX
ejpam-3443	103	18	a	a	DET
ejpam-3443	103	19	cost	cost	NOUN
ejpam-3443	103	20	effective	effective	ADJ
ejpam-3443	103	21	dominating	dominating	NOUN
ejpam-3443	103	22	set	set	NOUN
ejpam-3443	103	23	of	of	ADP
ejpam-3443	103	24	g	g	PROPN
ejpam-3443	103	25	,	,	PUNCT
ejpam-3443	103	26	contrary	contrary	ADV
ejpam-3443	103	27	to	to	ADP
ejpam-3443	103	28	the	the	DET
ejpam-3443	103	29	minimality	minimality	NOUN
ejpam-3443	103	30	of	of	ADP
ejpam-3443	103	31	s.	s.	PROPN
ejpam-3443	103	32	thus	thus	ADV
ejpam-3443	103	33	,	,	PUNCT
ejpam-3443	103	34	s	s	VERB
ejpam-3443	103	35	is	be	AUX
ejpam-3443	103	36	a	a	DET
ejpam-3443	103	37	minimal	minimal	ADJ
ejpam-3443	103	38	dominating	dominating	NOUN
ejpam-3443	103	39	set	set	NOUN
ejpam-3443	103	40	of	of	ADP
ejpam-3443	103	41	g.	g.	PROPN
ejpam-3443	103	42	similarly	similarly	ADV
ejpam-3443	103	43	,	,	PUNCT
ejpam-3443	103	44	if	if	SCONJ
ejpam-3443	103	45	s	s	VERB
ejpam-3443	103	46	⊆	⊆	NUM
ejpam-3443	103	47	v	v	NOUN
ejpam-3443	103	48	(	(	PUNCT
ejpam-3443	103	49	h	h	NOUN
ejpam-3443	103	50	)	)	PUNCT
ejpam-3443	103	51	,	,	PUNCT
ejpam-3443	103	52	then	then	ADV
ejpam-3443	103	53	property	property	NOUN
ejpam-3443	103	54	(	(	PUNCT
ejpam-3443	103	55	ii	ii	NOUN
ejpam-3443	103	56	)	)	PUNCT
ejpam-3443	103	57	holds	hold	VERB
ejpam-3443	103	58	.	.	PUNCT
ejpam-3443	104	1	suppose	suppose	VERB
ejpam-3443	104	2	that	that	SCONJ
ejpam-3443	104	3	s	s	VERB
ejpam-3443	104	4	∩	∩	ADJ
ejpam-3443	104	5	v	v	ADJ
ejpam-3443	104	6	(	(	PUNCT
ejpam-3443	104	7	g	g	NOUN
ejpam-3443	104	8	)	)	PUNCT
ejpam-3443	104	9	6=	6=	ADP
ejpam-3443	104	10	∅	∅	NOUN
ejpam-3443	104	11	and	and	CCONJ
ejpam-3443	104	12	s	s	X
ejpam-3443	104	13	∩	∩	ADJ
ejpam-3443	104	14	v	v	ADJ
ejpam-3443	104	15	(	(	PUNCT
ejpam-3443	104	16	h	h	NOUN
ejpam-3443	104	17	)	)	PUNCT
ejpam-3443	104	18	6=	6=	ADP
ejpam-3443	104	19	∅.	∅.	AUX
ejpam-3443	104	20	pick	pick	VERB
ejpam-3443	104	21	any	any	DET
ejpam-3443	104	22	u	u	NOUN
ejpam-3443	104	23	∈	∈	PROPN
ejpam-3443	104	24	s	s	PART
ejpam-3443	104	25	∩	∩	ADJ
ejpam-3443	104	26	v	v	X
ejpam-3443	104	27	(	(	PUNCT
ejpam-3443	104	28	g	g	NOUN
ejpam-3443	104	29	)	)	PUNCT
ejpam-3443	104	30	and	and	CCONJ
ejpam-3443	104	31	v	v	ADP
ejpam-3443	104	32	∈	∈	NOUN
ejpam-3443	104	33	s	s	PART
ejpam-3443	104	34	∩	∩	ADJ
ejpam-3443	104	35	v	v	ADJ
ejpam-3443	104	36	(	(	PUNCT
ejpam-3443	104	37	h	h	NOUN
ejpam-3443	104	38	)	)	PUNCT
ejpam-3443	104	39	.	.	PUNCT
ejpam-3443	105	1	then	then	ADV
ejpam-3443	105	2	{	{	PUNCT
ejpam-3443	105	3	u	u	NOUN
ejpam-3443	105	4	,	,	PUNCT
ejpam-3443	105	5	v	v	NOUN
ejpam-3443	105	6	}	}	PUNCT
ejpam-3443	105	7	satisfies	satisfie	NOUN
ejpam-3443	105	8	theorem	theorem	VERB
ejpam-3443	105	9	1(iii	1(iii	NUM
ejpam-3443	105	10	)	)	PUNCT
ejpam-3443	105	11	,	,	PUNCT
ejpam-3443	105	12	and	and	CCONJ
ejpam-3443	105	13	is	be	AUX
ejpam-3443	105	14	thus	thus	ADV
ejpam-3443	105	15	a	a	DET
ejpam-3443	105	16	cost	cost	NOUN
ejpam-3443	105	17	effective	effective	ADJ
ejpam-3443	105	18	dominating	dominating	NOUN
ejpam-3443	105	19	set	set	NOUN
ejpam-3443	105	20	of	of	ADP
ejpam-3443	105	21	g	g	PROPN
ejpam-3443	105	22	+	+	CCONJ
ejpam-3443	105	23	h.	h.	PROPN
ejpam-3443	105	24	therefore	therefore	ADV
ejpam-3443	105	25	,	,	PUNCT
ejpam-3443	105	26	in	in	ADP
ejpam-3443	105	27	this	this	DET
ejpam-3443	105	28	case	case	NOUN
ejpam-3443	105	29	,	,	PUNCT
ejpam-3443	105	30	if	if	SCONJ
ejpam-3443	105	31	s	s	VERB
ejpam-3443	105	32	is	be	AUX
ejpam-3443	105	33	a	a	DET
ejpam-3443	105	34	minimal	minimal	ADJ
ejpam-3443	105	35	cost	cost	NOUN
ejpam-3443	105	36	effective	effective	ADJ
ejpam-3443	105	37	set	set	NOUN
ejpam-3443	105	38	of	of	ADP
ejpam-3443	105	39	g+h	g+h	PROPN
ejpam-3443	105	40	,	,	PUNCT
ejpam-3443	105	41	then	then	ADV
ejpam-3443	105	42	s	s	AUX
ejpam-3443	105	43	=	=	SYM
ejpam-3443	105	44	{	{	PUNCT
ejpam-3443	105	45	u	u	NOUN
ejpam-3443	105	46	,	,	PUNCT
ejpam-3443	105	47	v	v	NOUN
ejpam-3443	105	48	}	}	PUNCT
ejpam-3443	105	49	for	for	ADP
ejpam-3443	105	50	some	some	DET
ejpam-3443	105	51	u	u	NOUN
ejpam-3443	105	52	∈	∈	PROPN
ejpam-3443	105	53	v	v	ADP
ejpam-3443	105	54	(	(	PUNCT
ejpam-3443	105	55	g	g	NOUN
ejpam-3443	105	56	)	)	PUNCT
ejpam-3443	105	57	and	and	CCONJ
ejpam-3443	105	58	v	v	ADP
ejpam-3443	105	59	∈	∈	PROPN
ejpam-3443	105	60	v	v	NOUN
ejpam-3443	105	61	(	(	PUNCT
ejpam-3443	105	62	h	h	NOUN
ejpam-3443	105	63	)	)	PUNCT
ejpam-3443	105	64	.	.	PUNCT
ejpam-3443	106	1	moreover	moreover	ADV
ejpam-3443	106	2	,	,	PUNCT
ejpam-3443	106	3	u	u	NOUN
ejpam-3443	106	4	and	and	CCONJ
ejpam-3443	106	5	v	v	AUX
ejpam-3443	106	6	do	do	AUX
ejpam-3443	106	7	not	not	PART
ejpam-3443	106	8	dominate	dominate	VERB
ejpam-3443	106	9	v	v	NOUN
ejpam-3443	106	10	(	(	PUNCT
ejpam-3443	106	11	g	g	NOUN
ejpam-3443	106	12	)	)	PUNCT
ejpam-3443	106	13	and	and	CCONJ
ejpam-3443	106	14	v	v	NOUN
ejpam-3443	106	15	(	(	PUNCT
ejpam-3443	106	16	h	h	NOUN
ejpam-3443	106	17	)	)	PUNCT
ejpam-3443	106	18	,	,	PUNCT
ejpam-3443	106	19	respectively	respectively	ADV
ejpam-3443	106	20	.	.	PUNCT
ejpam-3443	107	1	conversely	conversely	ADV
ejpam-3443	107	2	,	,	PUNCT
ejpam-3443	107	3	following	follow	VERB
ejpam-3443	107	4	similar	similar	ADJ
ejpam-3443	107	5	arguments	argument	NOUN
ejpam-3443	107	6	,	,	PUNCT
ejpam-3443	107	7	if	if	SCONJ
ejpam-3443	107	8	property	property	NOUN
ejpam-3443	107	9	(	(	PUNCT
ejpam-3443	107	10	i	i	NOUN
ejpam-3443	107	11	)	)	PUNCT
ejpam-3443	107	12	or	or	CCONJ
ejpam-3443	107	13	property	property	NOUN
ejpam-3443	107	14	(	(	PUNCT
ejpam-3443	107	15	ii	ii	NOUN
ejpam-3443	107	16	)	)	PUNCT
ejpam-3443	107	17	holds	hold	VERB
ejpam-3443	107	18	,	,	PUNCT
ejpam-3443	107	19	then	then	ADV
ejpam-3443	107	20	s	s	VERB
ejpam-3443	107	21	is	be	AUX
ejpam-3443	107	22	a	a	DET
ejpam-3443	107	23	minimal	minimal	ADJ
ejpam-3443	107	24	cost	cost	NOUN
ejpam-3443	107	25	effective	effective	ADJ
ejpam-3443	107	26	dominating	dominating	NOUN
ejpam-3443	107	27	set	set	NOUN
ejpam-3443	107	28	of	of	ADP
ejpam-3443	107	29	g	g	PROPN
ejpam-3443	107	30	+	+	CCONJ
ejpam-3443	107	31	h.	h.	PROPN
ejpam-3443	107	32	suppose	suppose	VERB
ejpam-3443	107	33	that	that	SCONJ
ejpam-3443	107	34	s	s	VERB
ejpam-3443	107	35	=	=	PUNCT
ejpam-3443	107	36	{	{	PUNCT
ejpam-3443	107	37	u	u	NOUN
ejpam-3443	107	38	,	,	PUNCT
ejpam-3443	107	39	v	v	NOUN
ejpam-3443	107	40	}	}	PUNCT
ejpam-3443	107	41	,	,	PUNCT
ejpam-3443	107	42	where	where	SCONJ
ejpam-3443	107	43	u	u	PROPN
ejpam-3443	107	44	∈	∈	PROPN
ejpam-3443	107	45	v	v	ADP
ejpam-3443	107	46	(	(	PUNCT
ejpam-3443	107	47	g	g	NOUN
ejpam-3443	107	48	)	)	PUNCT
ejpam-3443	107	49	and	and	CCONJ
ejpam-3443	107	50	v	v	ADP
ejpam-3443	107	51	∈	∈	PROPN
ejpam-3443	107	52	v	v	NOUN
ejpam-3443	107	53	(	(	PUNCT
ejpam-3443	107	54	h	h	NOUN
ejpam-3443	107	55	)	)	PUNCT
ejpam-3443	107	56	and	and	CCONJ
ejpam-3443	107	57	u	u	PROPN
ejpam-3443	107	58	and	and	CCONJ
ejpam-3443	107	59	v	v	AUX
ejpam-3443	107	60	do	do	AUX
ejpam-3443	107	61	not	not	PART
ejpam-3443	107	62	dominate	dominate	VERB
ejpam-3443	107	63	v	v	NOUN
ejpam-3443	107	64	(	(	PUNCT
ejpam-3443	107	65	g	g	NOUN
ejpam-3443	107	66	)	)	PUNCT
ejpam-3443	107	67	and	and	CCONJ
ejpam-3443	107	68	v	v	NOUN
ejpam-3443	107	69	(	(	PUNCT
ejpam-3443	107	70	h	h	NOUN
ejpam-3443	107	71	)	)	PUNCT
ejpam-3443	107	72	,	,	PUNCT
ejpam-3443	107	73	respectively	respectively	ADV
ejpam-3443	107	74	.	.	PUNCT
ejpam-3443	108	1	by	by	ADP
ejpam-3443	108	2	theorem	theorem	NOUN
ejpam-3443	108	3	1	1	NUM
ejpam-3443	108	4	,	,	PUNCT
ejpam-3443	108	5	s	s	VERB
ejpam-3443	108	6	is	be	AUX
ejpam-3443	108	7	a	a	DET
ejpam-3443	108	8	cost	cost	NOUN
ejpam-3443	108	9	effective	effective	ADJ
ejpam-3443	108	10	dominating	dominating	NOUN
ejpam-3443	108	11	set	set	NOUN
ejpam-3443	108	12	of	of	ADP
ejpam-3443	108	13	g	g	PROPN
ejpam-3443	108	14	+	+	CCONJ
ejpam-3443	108	15	h.	h.	PROPN
ejpam-3443	108	16	since	since	SCONJ
ejpam-3443	108	17	u	u	PROPN
ejpam-3443	108	18	and	and	CCONJ
ejpam-3443	108	19	v	v	NOUN
ejpam-3443	108	20	each	each	PRON
ejpam-3443	108	21	does	do	AUX
ejpam-3443	108	22	not	not	PART
ejpam-3443	108	23	dominate	dominate	VERB
ejpam-3443	108	24	v	v	NOUN
ejpam-3443	108	25	(	(	PUNCT
ejpam-3443	108	26	g+h	g+h	PROPN
ejpam-3443	108	27	)	)	PUNCT
ejpam-3443	108	28	,	,	PUNCT
ejpam-3443	108	29	s	s	VERB
ejpam-3443	108	30	is	be	AUX
ejpam-3443	108	31	a	a	DET
ejpam-3443	108	32	minimal	minimal	ADJ
ejpam-3443	108	33	cost	cost	NOUN
ejpam-3443	108	34	effective	effective	ADJ
ejpam-3443	108	35	dominating	dominating	NOUN
ejpam-3443	108	36	set	set	NOUN
ejpam-3443	108	37	of	of	ADP
ejpam-3443	108	38	g+h	g+h	PROPN
ejpam-3443	108	39	.	.	PUNCT
ejpam-3443	109	1	f.jamil	f.jamil	PROPN
ejpam-3443	109	2	,	,	PUNCT
ejpam-3443	109	3	h.	h.	PROPN
ejpam-3443	109	4	nuenay	nuenay	PROPN
ejpam-3443	109	5	-	-	PUNCT
ejpam-3443	109	6	maglanque	maglanque	ADJ
ejpam-3443	109	7	/	/	SYM
ejpam-3443	109	8	eur	eur	NOUN
ejpam-3443	109	9	.	.	PUNCT
ejpam-3443	110	1	j.	j.	PROPN
ejpam-3443	110	2	pure	pure	PROPN
ejpam-3443	110	3	appl	appl	PROPN
ejpam-3443	110	4	.	.	PROPN
ejpam-3443	110	5	math	math	PROPN
ejpam-3443	110	6	,	,	PUNCT
ejpam-3443	110	7	12	12	NUM
ejpam-3443	110	8	(	(	PUNCT
ejpam-3443	110	9	3	3	NUM
ejpam-3443	110	10	)	)	PUNCT
ejpam-3443	110	11	(	(	PUNCT
ejpam-3443	110	12	2019	2019	NUM
ejpam-3443	110	13	)	)	PUNCT
ejpam-3443	110	14	,	,	PUNCT
ejpam-3443	110	15	978	978	NUM
ejpam-3443	110	16	-	-	SYM
ejpam-3443	110	17	998	998	NUM
ejpam-3443	110	18	983	983	NUM
ejpam-3443	110	19	corollary	corollary	ADJ
ejpam-3443	110	20	2	2	NUM
ejpam-3443	110	21	.	.	PUNCT
ejpam-3443	111	1	let	let	VERB
ejpam-3443	111	2	g	g	NOUN
ejpam-3443	111	3	and	and	CCONJ
ejpam-3443	111	4	h	h	PROPN
ejpam-3443	111	5	be	be	AUX
ejpam-3443	111	6	isolate	isolate	NOUN
ejpam-3443	111	7	-	-	PUNCT
ejpam-3443	111	8	free	free	ADJ
ejpam-3443	111	9	graphs	graph	NOUN
ejpam-3443	111	10	with	with	ADP
ejpam-3443	111	11	g	g	PROPN
ejpam-3443	111	12	noncomplete	noncomplete	NOUN
ejpam-3443	111	13	.	.	PUNCT
ejpam-3443	112	1	then	then	ADV
ejpam-3443	112	2	,	,	PUNCT
ejpam-3443	112	3	max{γmce(g	max{γmce(g	PROPN
ejpam-3443	112	4	)	)	PUNCT
ejpam-3443	112	5	,	,	PUNCT
ejpam-3443	112	6	γmce(h	γmce(h	NOUN
ejpam-3443	112	7	)	)	PUNCT
ejpam-3443	112	8	}	}	PUNCT
ejpam-3443	112	9	≤	≤	NUM
ejpam-3443	112	10	γmce(g+h	γmce(g+h	NOUN
ejpam-3443	112	11	)	)	PUNCT
ejpam-3443	112	12	≤	≤	NUM
ejpam-3443	112	13	max{γm(g	max{γm(g	PROPN
ejpam-3443	112	14	)	)	PUNCT
ejpam-3443	112	15	,	,	PUNCT
ejpam-3443	112	16	γm(h	γm(h	NUM
ejpam-3443	112	17	)	)	PUNCT
ejpam-3443	112	18	}	}	PUNCT
ejpam-3443	112	19	.	.	PUNCT
ejpam-3443	113	1	proof	proof	NOUN
ejpam-3443	113	2	.	.	PUNCT
ejpam-3443	114	1	let	let	VERB
ejpam-3443	114	2	s	s	PRON
ejpam-3443	114	3	⊆	⊆	NUM
ejpam-3443	114	4	v	v	NOUN
ejpam-3443	114	5	(	(	PUNCT
ejpam-3443	114	6	g	g	PROPN
ejpam-3443	114	7	+	+	NOUN
ejpam-3443	114	8	h	h	NOUN
ejpam-3443	114	9	)	)	PUNCT
ejpam-3443	114	10	be	be	VERB
ejpam-3443	114	11	a	a	DET
ejpam-3443	114	12	γmce	γmce	NOUN
ejpam-3443	114	13	-	-	PUNCT
ejpam-3443	114	14	set	set	NOUN
ejpam-3443	114	15	of	of	ADP
ejpam-3443	114	16	g	g	PROPN
ejpam-3443	114	17	+	+	CCONJ
ejpam-3443	114	18	h.	h.	NOUN
ejpam-3443	114	19	in	in	ADP
ejpam-3443	114	20	view	view	NOUN
ejpam-3443	114	21	of	of	ADP
ejpam-3443	114	22	theorem	theorem	NOUN
ejpam-3443	114	23	2	2	NUM
ejpam-3443	114	24	,	,	PUNCT
ejpam-3443	114	25	since	since	SCONJ
ejpam-3443	114	26	g	g	PROPN
ejpam-3443	114	27	is	be	AUX
ejpam-3443	114	28	noncomplete	noncomplete	ADJ
ejpam-3443	114	29	,	,	PUNCT
ejpam-3443	114	30	γmce(g+h	γmce(g+h	NOUN
ejpam-3443	114	31	)	)	PUNCT
ejpam-3443	114	32	≥	≥	NOUN
ejpam-3443	114	33	2	2	NUM
ejpam-3443	114	34	.	.	PUNCT
ejpam-3443	115	1	by	by	ADP
ejpam-3443	115	2	the	the	DET
ejpam-3443	115	3	same	same	ADJ
ejpam-3443	115	4	theorem	theorem	NOUN
ejpam-3443	115	5	,	,	PUNCT
ejpam-3443	115	6	if	if	SCONJ
ejpam-3443	115	7	s	s	VERB
ejpam-3443	115	8	⊆	⊆	NUM
ejpam-3443	115	9	v	v	NOUN
ejpam-3443	115	10	(	(	PUNCT
ejpam-3443	115	11	g	g	NOUN
ejpam-3443	115	12	)	)	PUNCT
ejpam-3443	115	13	,	,	PUNCT
ejpam-3443	115	14	then	then	ADV
ejpam-3443	115	15	s	s	VERB
ejpam-3443	115	16	is	be	AUX
ejpam-3443	115	17	a	a	DET
ejpam-3443	115	18	minimal	minimal	ADJ
ejpam-3443	115	19	dominating	dominating	NOUN
ejpam-3443	115	20	set	set	NOUN
ejpam-3443	115	21	of	of	ADP
ejpam-3443	115	22	g	g	NOUN
ejpam-3443	115	23	so	so	SCONJ
ejpam-3443	115	24	that	that	SCONJ
ejpam-3443	115	25	|s|	|s|	VERB
ejpam-3443	115	26	≤	≤	NOUN
ejpam-3443	115	27	γm(g	γm(g	NUM
ejpam-3443	115	28	)	)	PUNCT
ejpam-3443	115	29	.	.	PUNCT
ejpam-3443	116	1	similarly	similarly	ADV
ejpam-3443	116	2	,	,	PUNCT
ejpam-3443	116	3	if	if	SCONJ
ejpam-3443	116	4	s	s	VERB
ejpam-3443	116	5	⊆	⊆	NUM
ejpam-3443	116	6	v	v	NOUN
ejpam-3443	116	7	(	(	PUNCT
ejpam-3443	116	8	h	h	NOUN
ejpam-3443	116	9	)	)	PUNCT
ejpam-3443	116	10	,	,	PUNCT
ejpam-3443	116	11	then	then	ADV
ejpam-3443	116	12	|s|	|s|	NOUN
ejpam-3443	116	13	≤	≤	NUM
ejpam-3443	116	14	γm(h	γm(h	NUM
ejpam-3443	116	15	)	)	PUNCT
ejpam-3443	116	16	.	.	PUNCT
ejpam-3443	117	1	hence	hence	ADV
ejpam-3443	117	2	,	,	PUNCT
ejpam-3443	117	3	γmce(g+h	γmce(g+h	NOUN
ejpam-3443	117	4	)	)	PUNCT
ejpam-3443	117	5	≤	≤	NUM
ejpam-3443	117	6	max{γm(g	max{γm(g	PROPN
ejpam-3443	117	7	)	)	PUNCT
ejpam-3443	117	8	,	,	PUNCT
ejpam-3443	117	9	γm(h	γm(h	NUM
ejpam-3443	117	10	)	)	PUNCT
ejpam-3443	117	11	}	}	PUNCT
ejpam-3443	117	12	.	.	PUNCT
ejpam-3443	118	1	on	on	ADP
ejpam-3443	118	2	the	the	DET
ejpam-3443	118	3	other	other	ADJ
ejpam-3443	118	4	hand	hand	NOUN
ejpam-3443	118	5	,	,	PUNCT
ejpam-3443	118	6	by	by	ADP
ejpam-3443	118	7	proposition	proposition	NOUN
ejpam-3443	118	8	1	1	NUM
ejpam-3443	118	9	and	and	CCONJ
ejpam-3443	118	10	theorem	theorem	VERB
ejpam-3443	118	11	1	1	NUM
ejpam-3443	118	12	,	,	PUNCT
ejpam-3443	118	13	every	every	DET
ejpam-3443	118	14	minimal	minimal	ADJ
ejpam-3443	118	15	cost	cost	NOUN
ejpam-3443	118	16	effective	effective	ADJ
ejpam-3443	118	17	dominating	dominating	NOUN
ejpam-3443	118	18	set	set	NOUN
ejpam-3443	118	19	of	of	ADP
ejpam-3443	118	20	g	g	PROPN
ejpam-3443	118	21	is	be	AUX
ejpam-3443	118	22	a	a	DET
ejpam-3443	118	23	minimal	minimal	ADJ
ejpam-3443	118	24	cost	cost	NOUN
ejpam-3443	118	25	effective	effective	ADJ
ejpam-3443	118	26	dominating	dominating	NOUN
ejpam-3443	118	27	set	set	NOUN
ejpam-3443	118	28	of	of	ADP
ejpam-3443	118	29	g+h	g+h	PROPN
ejpam-3443	118	30	.	.	PUNCT
ejpam-3443	119	1	thus	thus	ADV
ejpam-3443	119	2	,	,	PUNCT
ejpam-3443	119	3	γmce(g	γmce(g	PROPN
ejpam-3443	119	4	)	)	PUNCT
ejpam-3443	119	5	≤	≤	NOUN
ejpam-3443	120	1	γmce(g	γmce(g	NOUN
ejpam-3443	120	2	+	+	CCONJ
ejpam-3443	120	3	h	h	NOUN
ejpam-3443	120	4	)	)	PUNCT
ejpam-3443	120	5	.	.	PUNCT
ejpam-3443	121	1	similarly	similarly	ADV
ejpam-3443	121	2	,	,	PUNCT
ejpam-3443	121	3	γmce(h	γmce(h	NOUN
ejpam-3443	121	4	)	)	PUNCT
ejpam-3443	121	5	≤	≤	NOUN
ejpam-3443	122	1	γmce(g	γmce(g	NOUN
ejpam-3443	122	2	+	+	CCONJ
ejpam-3443	122	3	h	h	NOUN
ejpam-3443	122	4	)	)	PUNCT
ejpam-3443	122	5	.	.	PUNCT
ejpam-3443	123	1	thus	thus	ADV
ejpam-3443	123	2	,	,	PUNCT
ejpam-3443	123	3	max{γmce(g	max{γmce(g	PROPN
ejpam-3443	123	4	)	)	PUNCT
ejpam-3443	123	5	,	,	PUNCT
ejpam-3443	123	6	γmce(h	γmce(h	NOUN
ejpam-3443	123	7	)	)	PUNCT
ejpam-3443	123	8	}	}	PUNCT
ejpam-3443	123	9	≤	≤	NUM
ejpam-3443	123	10	γmce(g+h	γmce(g+h	NOUN
ejpam-3443	123	11	)	)	PUNCT
ejpam-3443	123	12	.	.	PUNCT
ejpam-3443	124	1	therefore	therefore	ADV
ejpam-3443	124	2	,	,	PUNCT
ejpam-3443	124	3	max{γmce(g	max{γmce(g	PROPN
ejpam-3443	124	4	)	)	PUNCT
ejpam-3443	124	5	,	,	PUNCT
ejpam-3443	124	6	γmce(h	γmce(h	NOUN
ejpam-3443	124	7	)	)	PUNCT
ejpam-3443	124	8	}	}	PUNCT
ejpam-3443	124	9	≤	≤	NUM
ejpam-3443	124	10	γmce(g+h	γmce(g+h	NOUN
ejpam-3443	124	11	)	)	PUNCT
ejpam-3443	124	12	≤	≤	NUM
ejpam-3443	124	13	max{γm(g	max{γm(g	PROPN
ejpam-3443	124	14	)	)	PUNCT
ejpam-3443	124	15	,	,	PUNCT
ejpam-3443	124	16	γm(h	γm(h	NUM
ejpam-3443	124	17	)	)	PUNCT
ejpam-3443	124	18	}	}	PUNCT
ejpam-3443	124	19	.	.	PUNCT
ejpam-3443	125	1	corollary	corollary	ADJ
ejpam-3443	125	2	3	3	X
ejpam-3443	125	3	.	.	PUNCT
ejpam-3443	126	1	let	let	VERB
ejpam-3443	126	2	g	g	NOUN
ejpam-3443	126	3	be	be	AUX
ejpam-3443	126	4	any	any	DET
ejpam-3443	126	5	isolate	isolate	NOUN
ejpam-3443	126	6	-	-	PUNCT
ejpam-3443	126	7	free	free	ADJ
ejpam-3443	126	8	graph	graph	NOUN
ejpam-3443	126	9	and	and	CCONJ
ejpam-3443	126	10	m	m	PRON
ejpam-3443	126	11	≥	≥	NOUN
ejpam-3443	126	12	1	1	NUM
ejpam-3443	126	13	.	.	PUNCT
ejpam-3443	127	1	then	then	ADV
ejpam-3443	127	2	γmce(g	γmce(g	PROPN
ejpam-3443	127	3	)	)	PUNCT
ejpam-3443	127	4	≤	≤	NUM
ejpam-3443	127	5	γmce(g+km	γmce(g+km	PROPN
ejpam-3443	127	6	)	)	PUNCT
ejpam-3443	127	7	≤	≤	NOUN
ejpam-3443	127	8	γm(g	γm(g	NUM
ejpam-3443	127	9	)	)	PUNCT
ejpam-3443	127	10	.	.	PUNCT
ejpam-3443	128	1	in	in	ADP
ejpam-3443	128	2	particular	particular	ADJ
ejpam-3443	128	3	,	,	PUNCT
ejpam-3443	128	4	if	if	SCONJ
ejpam-3443	128	5	g	g	PROPN
ejpam-3443	128	6	is	be	AUX
ejpam-3443	128	7	any	any	PRON
ejpam-3443	128	8	of	of	ADP
ejpam-3443	128	9	the	the	DET
ejpam-3443	128	10	following	following	NOUN
ejpam-3443	128	11	:	:	PUNCT
ejpam-3443	128	12	kn	kn	PROPN
ejpam-3443	128	13	,	,	PUNCT
ejpam-3443	128	14	kr	kr	PROPN
ejpam-3443	128	15	,	,	PUNCT
ejpam-3443	128	16	s	s	PROPN
ejpam-3443	128	17	,	,	PUNCT
ejpam-3443	128	18	pn	pn	NOUN
ejpam-3443	128	19	,	,	PUNCT
ejpam-3443	128	20	cn	cn	PROPN
ejpam-3443	128	21	,	,	PUNCT
ejpam-3443	128	22	then	then	ADV
ejpam-3443	128	23	γmce(g+km	γmce(g+km	PROPN
ejpam-3443	128	24	)	)	PUNCT
ejpam-3443	129	1	=	=	SYM
ejpam-3443	129	2	γmce(g	γmce(g	PROPN
ejpam-3443	129	3	)	)	PUNCT
ejpam-3443	129	4	.	.	PUNCT
ejpam-3443	130	1	in	in	ADP
ejpam-3443	130	2	view	view	NOUN
ejpam-3443	130	3	of	of	ADP
ejpam-3443	130	4	corollary	corollary	ADJ
ejpam-3443	130	5	3	3	NUM
ejpam-3443	130	6	and	and	CCONJ
ejpam-3443	130	7	results	result	NOUN
ejpam-3443	130	8	on	on	ADP
ejpam-3443	130	9	the	the	DET
ejpam-3443	130	10	minimal	minimal	ADJ
ejpam-3443	130	11	dominating	dominating	NOUN
ejpam-3443	130	12	sets	set	NOUN
ejpam-3443	130	13	by	by	ADP
ejpam-3443	130	14	[	[	X
ejpam-3443	130	15	10	10	NUM
ejpam-3443	130	16	]	]	PUNCT
ejpam-3443	130	17	,	,	PUNCT
ejpam-3443	130	18	the	the	DET
ejpam-3443	130	19	lower	low	ADJ
ejpam-3443	130	20	and	and	CCONJ
ejpam-3443	130	21	upper	upper	ADJ
ejpam-3443	130	22	bounds	bound	NOUN
ejpam-3443	130	23	in	in	ADP
ejpam-3443	130	24	corollary	corollary	ADJ
ejpam-3443	130	25	2	2	NUM
ejpam-3443	130	26	are	be	AUX
ejpam-3443	130	27	sharp	sharp	ADJ
ejpam-3443	130	28	.	.	PUNCT
ejpam-3443	131	1	the	the	DET
ejpam-3443	131	2	following	follow	VERB
ejpam-3443	131	3	is	be	AUX
ejpam-3443	131	4	directly	directly	ADV
ejpam-3443	131	5	from	from	ADP
ejpam-3443	131	6	proposition	proposition	NOUN
ejpam-3443	131	7	1	1	NUM
ejpam-3443	131	8	.	.	PUNCT
ejpam-3443	131	9	proposition	proposition	NOUN
ejpam-3443	131	10	2	2	NUM
ejpam-3443	131	11	.	.	X
ejpam-3443	132	1	for	for	ADP
ejpam-3443	132	2	any	any	DET
ejpam-3443	132	3	connected	connected	ADJ
ejpam-3443	132	4	graph	graph	NOUN
ejpam-3443	132	5	g	g	PROPN
ejpam-3443	132	6	,	,	PUNCT
ejpam-3443	132	7	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	132	8	)	)	PUNCT
ejpam-3443	132	9	≤	≤	NUM
ejpam-3443	132	10	γ+ce(g+k1	γ+ce(g+k1	ADJ
ejpam-3443	132	11	)	)	PUNCT
ejpam-3443	132	12	,	,	PUNCT
ejpam-3443	132	13	and	and	CCONJ
ejpam-3443	132	14	this	this	DET
ejpam-3443	132	15	bound	bind	VERB
ejpam-3443	132	16	is	be	AUX
ejpam-3443	132	17	sharp	sharp	ADJ
ejpam-3443	132	18	.	.	PUNCT
ejpam-3443	133	1	consider	consider	VERB
ejpam-3443	133	2	the	the	DET
ejpam-3443	133	3	graph	graph	NOUN
ejpam-3443	133	4	g	g	PROPN
ejpam-3443	133	5	=	=	PROPN
ejpam-3443	133	6	kn	kn	PROPN
ejpam-3443	133	7	for	for	ADP
ejpam-3443	133	8	n	n	NOUN
ejpam-3443	133	9	=	=	SYM
ejpam-3443	133	10	2k	2k	PROPN
ejpam-3443	134	1	+	+	CCONJ
ejpam-3443	134	2	1	1	NUM
ejpam-3443	134	3	,	,	PUNCT
ejpam-3443	134	4	k	k	X
ejpam-3443	134	5	≥	≥	PROPN
ejpam-3443	134	6	0	0	NUM
ejpam-3443	134	7	.	.	PUNCT
ejpam-3443	134	8	note	note	VERB
ejpam-3443	134	9	that	that	PRON
ejpam-3443	134	10	γ+ce(kn	γ+ce(kn	PUNCT
ejpam-3443	134	11	)	)	PUNCT
ejpam-3443	134	12	=	=	PUNCT
ejpam-3443	135	1	⌊	⌊	VERB
ejpam-3443	135	2	n+	n+	NUM
ejpam-3443	135	3	1	1	NUM
ejpam-3443	135	4	2	2	NUM
ejpam-3443	135	5	⌋	⌋	NOUN
ejpam-3443	135	6	=	=	PUNCT
ejpam-3443	135	7	⌊	⌊	VERB
ejpam-3443	135	8	2k	2k	NOUN
ejpam-3443	135	9	+	+	CCONJ
ejpam-3443	136	1	1	1	NUM
ejpam-3443	136	2	+	+	SYM
ejpam-3443	136	3	1	1	NUM
ejpam-3443	136	4	2	2	NUM
ejpam-3443	136	5	⌋	⌋	NOUN
ejpam-3443	136	6	=	=	PUNCT
ejpam-3443	137	1	k	k	PROPN
ejpam-3443	138	1	+	+	NOUN
ejpam-3443	138	2	1	1	X
ejpam-3443	138	3	.	.	PUNCT
ejpam-3443	138	4	now	now	ADV
ejpam-3443	138	5	,	,	PUNCT
ejpam-3443	138	6	g+k1	g+k1	PROPN
ejpam-3443	138	7	=	=	SYM
ejpam-3443	138	8	kn+1	kn+1	PROPN
ejpam-3443	138	9	where	where	SCONJ
ejpam-3443	138	10	n+	n+	ADP
ejpam-3443	138	11	1	1	NUM
ejpam-3443	138	12	is	be	AUX
ejpam-3443	138	13	even	even	ADV
ejpam-3443	138	14	.	.	PUNCT
ejpam-3443	139	1	now	now	ADV
ejpam-3443	139	2	,	,	PUNCT
ejpam-3443	139	3	γ+ce(g+k1	γ+ce(g+k1	ADJ
ejpam-3443	139	4	)	)	PUNCT
ejpam-3443	140	1	=	=	SYM
ejpam-3443	140	2	γ+ce(kn+1	γ+ce(kn+1	X
ejpam-3443	140	3	)	)	PUNCT
ejpam-3443	140	4	=	=	SYM
ejpam-3443	141	1	⌊	⌊	PROPN
ejpam-3443	141	2	(	(	PUNCT
ejpam-3443	141	3	2k	2k	NUM
ejpam-3443	141	4	+	+	CCONJ
ejpam-3443	141	5	1	1	NUM
ejpam-3443	141	6	+	+	NUM
ejpam-3443	141	7	1	1	NUM
ejpam-3443	141	8	)	)	PUNCT
ejpam-3443	141	9	+	+	CCONJ
ejpam-3443	141	10	1	1	NUM
ejpam-3443	141	11	2	2	NUM
ejpam-3443	141	12	⌋	⌋	NOUN
ejpam-3443	141	13	=	=	PUNCT
ejpam-3443	142	1	⌊	⌊	VERB
ejpam-3443	142	2	2k	2k	NOUN
ejpam-3443	142	3	+	+	CCONJ
ejpam-3443	142	4	3	3	NUM
ejpam-3443	142	5	2	2	NUM
ejpam-3443	142	6	⌋	⌋	NOUN
ejpam-3443	143	1	=	=	PUNCT
ejpam-3443	143	2	k	k	PROPN
ejpam-3443	144	1	+	+	CCONJ
ejpam-3443	144	2	1	1	NUM
ejpam-3443	144	3	=	=	SYM
ejpam-3443	144	4	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	144	5	)	)	PUNCT
ejpam-3443	144	6	.	.	PUNCT
ejpam-3443	145	1	thus	thus	ADV
ejpam-3443	145	2	,	,	PUNCT
ejpam-3443	145	3	the	the	DET
ejpam-3443	145	4	bound	bind	VERB
ejpam-3443	145	5	in	in	ADP
ejpam-3443	145	6	proposition	proposition	NOUN
ejpam-3443	145	7	2	2	NUM
ejpam-3443	145	8	is	be	AUX
ejpam-3443	145	9	sharp	sharp	ADJ
ejpam-3443	145	10	.	.	PUNCT
ejpam-3443	146	1	however	however	ADV
ejpam-3443	146	2	,	,	PUNCT
ejpam-3443	146	3	strict	strict	ADJ
ejpam-3443	146	4	inequality	inequality	NOUN
ejpam-3443	146	5	in	in	ADP
ejpam-3443	146	6	proposition	proposition	NOUN
ejpam-3443	146	7	2	2	NUM
ejpam-3443	146	8	may	may	AUX
ejpam-3443	146	9	be	be	AUX
ejpam-3443	146	10	attained	attain	VERB
ejpam-3443	146	11	as	as	SCONJ
ejpam-3443	146	12	illustrated	illustrate	VERB
ejpam-3443	146	13	by	by	ADP
ejpam-3443	146	14	the	the	DET
ejpam-3443	146	15	following	follow	VERB
ejpam-3443	146	16	example	example	NOUN
ejpam-3443	146	17	.	.	PUNCT
ejpam-3443	147	1	f.jamil	f.jamil	PROPN
ejpam-3443	147	2	,	,	PUNCT
ejpam-3443	147	3	h.	h.	PROPN
ejpam-3443	147	4	nuenay	nuenay	PROPN
ejpam-3443	147	5	-	-	PUNCT
ejpam-3443	147	6	maglanque	maglanque	ADJ
ejpam-3443	147	7	/	/	SYM
ejpam-3443	147	8	eur	eur	NOUN
ejpam-3443	147	9	.	.	PUNCT
ejpam-3443	148	1	j.	j.	PROPN
ejpam-3443	148	2	pure	pure	PROPN
ejpam-3443	148	3	appl	appl	PROPN
ejpam-3443	148	4	.	.	PROPN
ejpam-3443	148	5	math	math	PROPN
ejpam-3443	148	6	,	,	PUNCT
ejpam-3443	148	7	12	12	NUM
ejpam-3443	148	8	(	(	PUNCT
ejpam-3443	148	9	3	3	NUM
ejpam-3443	148	10	)	)	PUNCT
ejpam-3443	148	11	(	(	PUNCT
ejpam-3443	148	12	2019	2019	NUM
ejpam-3443	148	13	)	)	PUNCT
ejpam-3443	148	14	,	,	PUNCT
ejpam-3443	148	15	978	978	NUM
ejpam-3443	148	16	-	-	SYM
ejpam-3443	148	17	998	998	NUM
ejpam-3443	148	18	984	984	NUM
ejpam-3443	148	19	v2	v2	PROPN
ejpam-3443	148	20	v4	v4	PROPN
ejpam-3443	148	21	v3	v3	PROPN
ejpam-3443	148	22	v1	v1	PROPN
ejpam-3443	148	23	v5	v5	PROPN
ejpam-3443	148	24	v6	v6	NOUN
ejpam-3443	148	25	u	u	NOUN
ejpam-3443	148	26	figure	figure	NOUN
ejpam-3443	148	27	2	2	NUM
ejpam-3443	148	28	:	:	PUNCT
ejpam-3443	148	29	g+k1	g+k1	NOUN
ejpam-3443	148	30	example	example	NOUN
ejpam-3443	148	31	2	2	X
ejpam-3443	148	32	.	.	PUNCT
ejpam-3443	149	1	let	let	VERB
ejpam-3443	149	2	g	g	PROPN
ejpam-3443	149	3	=	=	PUNCT
ejpam-3443	149	4	c3	c3	PROPN
ejpam-3443	149	5	◦	◦	NOUN
ejpam-3443	149	6	k1	k1	PROPN
ejpam-3443	149	7	and	and	CCONJ
ejpam-3443	149	8	v	v	NOUN
ejpam-3443	149	9	(	(	PUNCT
ejpam-3443	149	10	g	g	NOUN
ejpam-3443	149	11	)	)	PUNCT
ejpam-3443	149	12	=	=	SYM
ejpam-3443	149	13	{	{	PUNCT
ejpam-3443	149	14	v1	v1	PROPN
ejpam-3443	149	15	,	,	PUNCT
ejpam-3443	149	16	v2	v2	PROPN
ejpam-3443	149	17	,	,	PUNCT
ejpam-3443	149	18	.	.	PUNCT
ejpam-3443	149	19	.	.	PUNCT
ejpam-3443	150	1	.	.	PUNCT
ejpam-3443	151	1	,	,	PUNCT
ejpam-3443	151	2	v6	v6	PROPN
ejpam-3443	151	3	}	}	PUNCT
ejpam-3443	151	4	.	.	PUNCT
ejpam-3443	152	1	consider	consider	VERB
ejpam-3443	152	2	the	the	DET
ejpam-3443	152	3	join	join	NOUN
ejpam-3443	152	4	g+k1	g+k1	NOUN
ejpam-3443	152	5	as	as	SCONJ
ejpam-3443	152	6	shown	show	VERB
ejpam-3443	152	7	in	in	ADP
ejpam-3443	152	8	figure	figure	NOUN
ejpam-3443	152	9	2	2	NUM
ejpam-3443	152	10	.	.	X
ejpam-3443	152	11	observe	observe	VERB
ejpam-3443	152	12	that	that	SCONJ
ejpam-3443	152	13	the	the	DET
ejpam-3443	152	14	set	set	NOUN
ejpam-3443	152	15	{	{	PUNCT
ejpam-3443	152	16	v2	v2	PROPN
ejpam-3443	152	17	,	,	PUNCT
ejpam-3443	152	18	v5	v5	PROPN
ejpam-3443	152	19	,	,	PUNCT
ejpam-3443	152	20	v6	v6	NOUN
ejpam-3443	152	21	}	}	PUNCT
ejpam-3443	152	22	is	be	AUX
ejpam-3443	152	23	a	a	DET
ejpam-3443	152	24	γ+ce	γ+ce	NOUN
ejpam-3443	152	25	-	-	PUNCT
ejpam-3443	152	26	set	set	NOUN
ejpam-3443	152	27	of	of	ADP
ejpam-3443	152	28	g.	g.	PROPN
ejpam-3443	152	29	on	on	ADP
ejpam-3443	152	30	the	the	DET
ejpam-3443	152	31	other	other	ADJ
ejpam-3443	152	32	hand	hand	NOUN
ejpam-3443	152	33	,	,	PUNCT
ejpam-3443	152	34	the	the	DET
ejpam-3443	152	35	set	set	NOUN
ejpam-3443	152	36	{	{	PUNCT
ejpam-3443	152	37	v2	v2	PROPN
ejpam-3443	152	38	,	,	PUNCT
ejpam-3443	152	39	v5	v5	PROPN
ejpam-3443	152	40	,	,	PUNCT
ejpam-3443	152	41	v6	v6	NOUN
ejpam-3443	152	42	,	,	PUNCT
ejpam-3443	152	43	u	u	NOUN
ejpam-3443	152	44	}	}	PUNCT
ejpam-3443	152	45	is	be	AUX
ejpam-3443	152	46	a	a	DET
ejpam-3443	152	47	γ+ce	γ+ce	NOUN
ejpam-3443	152	48	-	-	PUNCT
ejpam-3443	152	49	set	set	VERB
ejpam-3443	152	50	in	in	ADP
ejpam-3443	152	51	g+k1	g+k1	NOUN
ejpam-3443	152	52	.	.	PUNCT
ejpam-3443	153	1	thus	thus	ADV
ejpam-3443	153	2	,	,	PUNCT
ejpam-3443	153	3	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	153	4	)	)	PUNCT
ejpam-3443	153	5	=	=	SYM
ejpam-3443	153	6	3	3	NUM
ejpam-3443	153	7	<	<	SYM
ejpam-3443	153	8	4	4	NUM
ejpam-3443	153	9	=	=	NOUN
ejpam-3443	153	10	γ+ce(g+k1	γ+ce(g+k1	ADJ
ejpam-3443	153	11	)	)	PUNCT
ejpam-3443	153	12	.	.	PUNCT
ejpam-3443	153	13	.	.	PUNCT
ejpam-3443	154	1	remark	remark	NOUN
ejpam-3443	154	2	2	2	NUM
ejpam-3443	154	3	.	.	PUNCT
ejpam-3443	155	1	[	[	X
ejpam-3443	155	2	11	11	NUM
ejpam-3443	155	3	]	]	PUNCT
ejpam-3443	155	4	for	for	ADP
ejpam-3443	155	5	any	any	DET
ejpam-3443	155	6	connected	connected	ADJ
ejpam-3443	155	7	graph	graph	NOUN
ejpam-3443	155	8	g	g	NOUN
ejpam-3443	155	9	of	of	ADP
ejpam-3443	155	10	order	order	NOUN
ejpam-3443	155	11	n	n	PRON
ejpam-3443	155	12	≥	≥	NOUN
ejpam-3443	155	13	2	2	NUM
ejpam-3443	155	14	,	,	PUNCT
ejpam-3443	155	15	γce(g	γce(g	NOUN
ejpam-3443	155	16	)	)	PUNCT
ejpam-3443	155	17	≤	≤	PUNCT
ejpam-3443	155	18	⌊	⌊	VERB
ejpam-3443	155	19	n	n	ADV
ejpam-3443	155	20	2	2	NUM
ejpam-3443	155	21	⌋	⌋	NOUN
ejpam-3443	155	22	.	.	PUNCT
ejpam-3443	156	1	theorem	theorem	VERB
ejpam-3443	156	2	3	3	X
ejpam-3443	156	3	.	.	PUNCT
ejpam-3443	157	1	let	let	VERB
ejpam-3443	157	2	g	g	NOUN
ejpam-3443	158	1	and	and	CCONJ
ejpam-3443	158	2	h	h	NOUN
ejpam-3443	158	3	be	be	VERB
ejpam-3443	158	4	any	any	DET
ejpam-3443	158	5	connected	connected	ADJ
ejpam-3443	158	6	nontrivial	nontrivial	ADJ
ejpam-3443	158	7	graphs	graph	NOUN
ejpam-3443	158	8	.	.	PUNCT
ejpam-3443	159	1	then	then	ADV
ejpam-3443	159	2	,	,	PUNCT
ejpam-3443	159	3	max	max	PROPN
ejpam-3443	159	4	{	{	PUNCT
ejpam-3443	159	5	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	159	6	)	)	PUNCT
ejpam-3443	159	7	,	,	PUNCT
ejpam-3443	159	8	γ+ce(h	γ+ce(h	PROPN
ejpam-3443	159	9	)	)	PUNCT
ejpam-3443	159	10	,	,	PUNCT
ejpam-3443	159	11	α+	α+	X
ejpam-3443	159	12	β	β	X
ejpam-3443	159	13	}	}	PUNCT
ejpam-3443	159	14	≤	≤	PROPN
ejpam-3443	159	15	γ+ce(g+h	γ+ce(g+h	PROPN
ejpam-3443	159	16	)	)	PUNCT
ejpam-3443	159	17	,	,	PUNCT
ejpam-3443	159	18	where	where	SCONJ
ejpam-3443	159	19	α	α	PROPN
ejpam-3443	159	20	=	=	SYM
ejpam-3443	159	21	max	max	PROPN
ejpam-3443	159	22	{	{	PUNCT
ejpam-3443	159	23	|s|	|s|	NOUN
ejpam-3443	159	24	:	:	PUNCT
ejpam-3443	159	25	s	s	PROPN
ejpam-3443	159	26	⊆	⊆	NUM
ejpam-3443	159	27	v	v	NOUN
ejpam-3443	159	28	(	(	PUNCT
ejpam-3443	159	29	g	g	NOUN
ejpam-3443	159	30	)	)	PUNCT
ejpam-3443	159	31	is	be	AUX
ejpam-3443	159	32	a	a	DET
ejpam-3443	159	33	ced	ced	ADV
ejpam-3443	159	34	-	-	PUNCT
ejpam-3443	159	35	set	set	NOUN
ejpam-3443	159	36	of	of	ADP
ejpam-3443	159	37	g	g	NOUN
ejpam-3443	159	38	with	with	ADP
ejpam-3443	159	39	|s|	|s|	NOUN
ejpam-3443	159	40	≤	≤	NOUN
ejpam-3443	159	41	⌊m	⌊m	ADP
ejpam-3443	159	42	2	2	NUM
ejpam-3443	159	43	⌋	⌋	NOUN
ejpam-3443	159	44	}	}	PUNCT
ejpam-3443	159	45	,	,	PUNCT
ejpam-3443	159	46	and	and	CCONJ
ejpam-3443	159	47	β	β	X
ejpam-3443	159	48	=	=	SYM
ejpam-3443	159	49	max	max	PROPN
ejpam-3443	159	50	{	{	PUNCT
ejpam-3443	159	51	|s|	|s|	NOUN
ejpam-3443	159	52	:	:	PUNCT
ejpam-3443	159	53	s	s	PROPN
ejpam-3443	159	54	⊆	⊆	NUM
ejpam-3443	159	55	v	v	NOUN
ejpam-3443	159	56	(	(	PUNCT
ejpam-3443	159	57	h	h	NOUN
ejpam-3443	159	58	)	)	PUNCT
ejpam-3443	159	59	is	be	AUX
ejpam-3443	159	60	a	a	DET
ejpam-3443	159	61	ced	ced	ADV
ejpam-3443	159	62	-	-	PUNCT
ejpam-3443	159	63	set	set	NOUN
ejpam-3443	159	64	of	of	ADP
ejpam-3443	159	65	h	h	NOUN
ejpam-3443	159	66	with	with	ADP
ejpam-3443	159	67	|s|	|s|	NOUN
ejpam-3443	159	68	≤	≤	NUM
ejpam-3443	159	69	⌊n	⌊n	ADJ
ejpam-3443	159	70	2	2	NUM
ejpam-3443	159	71	⌋	⌋	NOUN
ejpam-3443	159	72	}	}	PUNCT
ejpam-3443	159	73	.	.	PUNCT
ejpam-3443	160	1	proof	proof	NOUN
ejpam-3443	160	2	.	.	PUNCT
ejpam-3443	161	1	first	first	ADV
ejpam-3443	161	2	,	,	PUNCT
ejpam-3443	161	3	note	note	VERB
ejpam-3443	161	4	that	that	SCONJ
ejpam-3443	161	5	the	the	DET
ejpam-3443	161	6	existence	existence	NOUN
ejpam-3443	161	7	of	of	ADP
ejpam-3443	161	8	α	α	PROPN
ejpam-3443	161	9	and	and	CCONJ
ejpam-3443	161	10	β	β	X
ejpam-3443	161	11	is	be	AUX
ejpam-3443	161	12	guaranteed	guarantee	VERB
ejpam-3443	161	13	by	by	ADP
ejpam-3443	161	14	remark	remark	NOUN
ejpam-3443	161	15	2	2	NUM
ejpam-3443	161	16	.	.	PUNCT
ejpam-3443	161	17	by	by	ADP
ejpam-3443	161	18	proposition	proposition	NOUN
ejpam-3443	161	19	1	1	NUM
ejpam-3443	161	20	and	and	CCONJ
ejpam-3443	161	21	theorem	theorem	VERB
ejpam-3443	161	22	1	1	NUM
ejpam-3443	161	23	,	,	PUNCT
ejpam-3443	161	24	every	every	DET
ejpam-3443	161	25	γ+ce	γ+ce	NOUN
ejpam-3443	161	26	-	-	PUNCT
ejpam-3443	161	27	set	set	NOUN
ejpam-3443	161	28	of	of	ADP
ejpam-3443	161	29	g	g	PROPN
ejpam-3443	161	30	is	be	AUX
ejpam-3443	161	31	a	a	DET
ejpam-3443	161	32	cost	cost	NOUN
ejpam-3443	161	33	effective	effective	ADJ
ejpam-3443	161	34	dominating	dominating	NOUN
ejpam-3443	161	35	set	set	NOUN
ejpam-3443	161	36	of	of	ADP
ejpam-3443	161	37	g+h	g+h	PROPN
ejpam-3443	161	38	.	.	PUNCT
ejpam-3443	162	1	hence	hence	ADV
ejpam-3443	162	2	,	,	PUNCT
ejpam-3443	162	3	γ+ce(g+h	γ+ce(g+h	PROPN
ejpam-3443	162	4	)	)	PUNCT
ejpam-3443	162	5	≥	≥	NOUN
ejpam-3443	162	6	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	162	7	)	)	PUNCT
ejpam-3443	162	8	.	.	PUNCT
ejpam-3443	163	1	similarly	similarly	ADV
ejpam-3443	163	2	,	,	PUNCT
ejpam-3443	163	3	γ+ce(g+h	γ+ce(g+h	PROPN
ejpam-3443	163	4	)	)	PUNCT
ejpam-3443	163	5	≥	≥	PROPN
ejpam-3443	163	6	γ+ce(h	γ+ce(h	PROPN
ejpam-3443	163	7	)	)	PUNCT
ejpam-3443	163	8	.	.	PUNCT
ejpam-3443	164	1	now	now	ADV
ejpam-3443	164	2	,	,	PUNCT
ejpam-3443	164	3	let	let	VERB
ejpam-3443	164	4	s1	s1	PROPN
ejpam-3443	164	5	⊆	⊆	NUM
ejpam-3443	164	6	v	v	NOUN
ejpam-3443	164	7	(	(	PUNCT
ejpam-3443	164	8	g	g	NOUN
ejpam-3443	164	9	)	)	PUNCT
ejpam-3443	164	10	be	be	AUX
ejpam-3443	164	11	a	a	DET
ejpam-3443	164	12	cost	cost	NOUN
ejpam-3443	164	13	effective	effective	ADJ
ejpam-3443	164	14	dominating	dominating	NOUN
ejpam-3443	164	15	set	set	NOUN
ejpam-3443	164	16	of	of	ADP
ejpam-3443	164	17	g	g	NOUN
ejpam-3443	164	18	with	with	ADP
ejpam-3443	164	19	|s1|	|s1|	NOUN
ejpam-3443	164	20	≤	≤	VERB
ejpam-3443	164	21	⌊	⌊	PROPN
ejpam-3443	164	22	m	m	PROPN
ejpam-3443	164	23	2	2	NUM
ejpam-3443	164	24	⌋	⌋	NOUN
ejpam-3443	164	25	,	,	PUNCT
ejpam-3443	164	26	and	and	CCONJ
ejpam-3443	164	27	s2	s2	VERB
ejpam-3443	164	28	⊆	⊆	NUM
ejpam-3443	164	29	v	v	NOUN
ejpam-3443	164	30	(	(	PUNCT
ejpam-3443	164	31	h	h	NOUN
ejpam-3443	164	32	)	)	PUNCT
ejpam-3443	164	33	a	a	DET
ejpam-3443	164	34	cost	cost	NOUN
ejpam-3443	164	35	effective	effective	ADJ
ejpam-3443	164	36	dominating	dominating	NOUN
ejpam-3443	164	37	set	set	NOUN
ejpam-3443	164	38	of	of	ADP
ejpam-3443	164	39	h	h	NOUN
ejpam-3443	164	40	with	with	ADP
ejpam-3443	164	41	|s2|	|s2|	NOUN
ejpam-3443	164	42	≤	≤	NUM
ejpam-3443	164	43	⌊	⌊	VERB
ejpam-3443	164	44	n	n	ADV
ejpam-3443	164	45	2	2	NUM
ejpam-3443	164	46	⌋	⌋	NOUN
ejpam-3443	164	47	,	,	PUNCT
ejpam-3443	164	48	and	and	CCONJ
ejpam-3443	164	49	put	put	VERB
ejpam-3443	164	50	s	s	NOUN
ejpam-3443	164	51	=	=	PUNCT
ejpam-3443	164	52	s1∪s2	s1∪s2	NOUN
ejpam-3443	164	53	.	.	PUNCT
ejpam-3443	165	1	for	for	ADP
ejpam-3443	165	2	each	each	DET
ejpam-3443	165	3	v	v	NUM
ejpam-3443	165	4	∈	∈	PROPN
ejpam-3443	165	5	s1	s1	NOUN
ejpam-3443	165	6	,	,	PUNCT
ejpam-3443	165	7	|ng(v	|ng(v	NOUN
ejpam-3443	165	8	)	)	PUNCT
ejpam-3443	165	9	∩	∩	NOUN
ejpam-3443	165	10	s|+	s|+	NOUN
ejpam-3443	165	11	2|s2|	2|s2|	NUM
ejpam-3443	165	12	≤	≤	NUM
ejpam-3443	165	13	|ng(v	|ng(v	NOUN
ejpam-3443	165	14	)	)	PUNCT
ejpam-3443	165	15	\	\	NOUN
ejpam-3443	166	1	s|+	s|+	NOUN
ejpam-3443	166	2	2	2	NUM
ejpam-3443	166	3	⌊n	⌊n	NOUN
ejpam-3443	166	4	2	2	NUM
ejpam-3443	166	5	⌋	⌋	NOUN
ejpam-3443	166	6	≤	≤	NUM
ejpam-3443	166	7	|ng(v	|ng(v	NOUN
ejpam-3443	166	8	)	)	PUNCT
ejpam-3443	166	9	\	\	PUNCT
ejpam-3443	167	1	s|+	s|+	NOUN
ejpam-3443	167	2	n.	n.	NOUN
ejpam-3443	167	3	similarly	similarly	ADV
ejpam-3443	167	4	,	,	PUNCT
ejpam-3443	167	5	for	for	ADP
ejpam-3443	167	6	each	each	DET
ejpam-3443	167	7	v	v	ADP
ejpam-3443	167	8	∈	∈	PROPN
ejpam-3443	167	9	s2	s2	PROPN
ejpam-3443	167	10	,	,	PUNCT
ejpam-3443	167	11	|ng(v	|ng(v	ADJ
ejpam-3443	167	12	)	)	PUNCT
ejpam-3443	167	13	∩	∩	NOUN
ejpam-3443	167	14	s|+	s|+	NOUN
ejpam-3443	167	15	2|s1|	2|s1|	X
ejpam-3443	167	16	≤	≤	NUM
ejpam-3443	167	17	|ng(v	|ng(v	NOUN
ejpam-3443	167	18	)	)	PUNCT
ejpam-3443	167	19	\	\	NOUN
ejpam-3443	167	20	s|+m	s|+m	PROPN
ejpam-3443	167	21	.	.	PUNCT
ejpam-3443	168	1	by	by	ADP
ejpam-3443	168	2	theorem	theorem	NOUN
ejpam-3443	168	3	1	1	NUM
ejpam-3443	168	4	,	,	PUNCT
ejpam-3443	168	5	s	s	VERB
ejpam-3443	168	6	is	be	AUX
ejpam-3443	168	7	a	a	DET
ejpam-3443	168	8	cost	cost	NOUN
ejpam-3443	168	9	effective	effective	ADJ
ejpam-3443	168	10	dominating	dominating	NOUN
ejpam-3443	168	11	set	set	NOUN
ejpam-3443	168	12	of	of	ADP
ejpam-3443	168	13	g	g	PROPN
ejpam-3443	168	14	+	+	PROPN
ejpam-3443	168	15	h.	h.	PROPN
ejpam-3443	168	16	thus	thus	ADV
ejpam-3443	168	17	,	,	PUNCT
ejpam-3443	168	18	|s|	|s|	VERB
ejpam-3443	168	19	≤	≤	NOUN
ejpam-3443	168	20	γ+ce(g	γ+ce(g	PROPN
ejpam-3443	169	1	+	+	PROPN
ejpam-3443	170	1	h	h	NOUN
ejpam-3443	170	2	)	)	PUNCT
ejpam-3443	170	3	.	.	PUNCT
ejpam-3443	171	1	since	since	SCONJ
ejpam-3443	171	2	s1	s1	PROPN
ejpam-3443	171	3	and	and	CCONJ
ejpam-3443	171	4	s2	s2	NOUN
ejpam-3443	171	5	are	be	AUX
ejpam-3443	171	6	arbitrary	arbitrary	ADJ
ejpam-3443	171	7	,	,	PUNCT
ejpam-3443	171	8	α	α	PROPN
ejpam-3443	171	9	+	+	X
ejpam-3443	171	10	β	β	X
ejpam-3443	171	11	≤	≤	NUM
ejpam-3443	171	12	γ+ce(g	γ+ce(g	PROPN
ejpam-3443	172	1	+	+	CCONJ
ejpam-3443	173	1	h	h	NOUN
ejpam-3443	173	2	)	)	PUNCT
ejpam-3443	173	3	.	.	PUNCT
ejpam-3443	174	1	the	the	DET
ejpam-3443	174	2	inequality	inequality	NOUN
ejpam-3443	174	3	follows	follow	VERB
ejpam-3443	174	4	immediately	immediately	ADV
ejpam-3443	174	5	.	.	PUNCT
ejpam-3443	175	1	f.jamil	f.jamil	PROPN
ejpam-3443	175	2	,	,	PUNCT
ejpam-3443	175	3	h.	h.	PROPN
ejpam-3443	175	4	nuenay	nuenay	PROPN
ejpam-3443	175	5	-	-	PUNCT
ejpam-3443	175	6	maglanque	maglanque	ADJ
ejpam-3443	175	7	/	/	SYM
ejpam-3443	175	8	eur	eur	NOUN
ejpam-3443	175	9	.	.	PUNCT
ejpam-3443	176	1	j.	j.	PROPN
ejpam-3443	176	2	pure	pure	PROPN
ejpam-3443	176	3	appl	appl	PROPN
ejpam-3443	176	4	.	.	PROPN
ejpam-3443	176	5	math	math	PROPN
ejpam-3443	176	6	,	,	PUNCT
ejpam-3443	176	7	12	12	NUM
ejpam-3443	176	8	(	(	PUNCT
ejpam-3443	176	9	3	3	NUM
ejpam-3443	176	10	)	)	PUNCT
ejpam-3443	176	11	(	(	PUNCT
ejpam-3443	176	12	2019	2019	NUM
ejpam-3443	176	13	)	)	PUNCT
ejpam-3443	176	14	,	,	PUNCT
ejpam-3443	176	15	978	978	NUM
ejpam-3443	176	16	-	-	SYM
ejpam-3443	176	17	998	998	NUM
ejpam-3443	176	18	985	985	NUM
ejpam-3443	176	19	theorem	theorem	NOUN
ejpam-3443	176	20	4	4	NUM
ejpam-3443	176	21	.	.	PUNCT
ejpam-3443	177	1	let	let	VERB
ejpam-3443	177	2	g	g	PRON
ejpam-3443	177	3	be	be	AUX
ejpam-3443	177	4	a	a	DET
ejpam-3443	177	5	connected	connected	ADJ
ejpam-3443	177	6	graph	graph	NOUN
ejpam-3443	177	7	of	of	ADP
ejpam-3443	177	8	order	order	NOUN
ejpam-3443	177	9	m.	m.	NOUN
ejpam-3443	177	10	then	then	ADV
ejpam-3443	177	11	for	for	ADP
ejpam-3443	177	12	n	n	PROPN
ejpam-3443	177	13	≥	≥	NOUN
ejpam-3443	177	14	m	m	PROPN
ejpam-3443	177	15	,	,	PUNCT
ejpam-3443	177	16	γ+ce(g+kn	γ+ce(g+kn	NOUN
ejpam-3443	177	17	)	)	PUNCT
ejpam-3443	177	18	≤	≤	NUM
ejpam-3443	178	1	m+	m+	NUM
ejpam-3443	178	2	n+	n+	NOUN
ejpam-3443	178	3	1	1	NUM
ejpam-3443	178	4	2	2	NUM
ejpam-3443	178	5	.	.	PUNCT
ejpam-3443	179	1	proof	proof	NOUN
ejpam-3443	179	2	.	.	PUNCT
ejpam-3443	180	1	let	let	VERB
ejpam-3443	180	2	s	s	PRON
ejpam-3443	180	3	⊆	⊆	NUM
ejpam-3443	180	4	v	v	NOUN
ejpam-3443	180	5	(	(	PUNCT
ejpam-3443	180	6	g	g	PROPN
ejpam-3443	180	7	+	+	PROPN
ejpam-3443	180	8	kn	kn	PROPN
ejpam-3443	180	9	)	)	PUNCT
ejpam-3443	180	10	be	be	VERB
ejpam-3443	180	11	a	a	DET
ejpam-3443	180	12	γ+ce	γ+ce	NOUN
ejpam-3443	180	13	-	-	PUNCT
ejpam-3443	180	14	set	set	NOUN
ejpam-3443	180	15	of	of	ADP
ejpam-3443	180	16	g	g	PROPN
ejpam-3443	180	17	+	+	CCONJ
ejpam-3443	180	18	kn	kn	PROPN
ejpam-3443	180	19	.	.	PUNCT
ejpam-3443	181	1	since	since	SCONJ
ejpam-3443	181	2	s	s	PROPN
ejpam-3443	181	3	is	be	AUX
ejpam-3443	181	4	a	a	DET
ejpam-3443	181	5	γ+ce	γ+ce	NOUN
ejpam-3443	181	6	-	-	PUNCT
ejpam-3443	181	7	set	set	VERB
ejpam-3443	181	8	and	and	CCONJ
ejpam-3443	181	9	v	v	NOUN
ejpam-3443	181	10	(	(	PUNCT
ejpam-3443	181	11	g	g	NOUN
ejpam-3443	181	12	)	)	PUNCT
ejpam-3443	181	13	satisfies	satisfie	NOUN
ejpam-3443	181	14	theorem	theorem	VERB
ejpam-3443	181	15	1(i	1(i	NUM
ejpam-3443	181	16	)	)	PUNCT
ejpam-3443	181	17	,	,	PUNCT
ejpam-3443	181	18	if	if	SCONJ
ejpam-3443	181	19	s	s	VERB
ejpam-3443	181	20	⊆	⊆	NUM
ejpam-3443	181	21	v	v	NOUN
ejpam-3443	181	22	(	(	PUNCT
ejpam-3443	181	23	g	g	NOUN
ejpam-3443	181	24	)	)	PUNCT
ejpam-3443	181	25	,	,	PUNCT
ejpam-3443	181	26	then	then	ADV
ejpam-3443	181	27	s	s	VERB
ejpam-3443	181	28	=	=	SYM
ejpam-3443	181	29	v	v	PROPN
ejpam-3443	181	30	(	(	PUNCT
ejpam-3443	181	31	g	g	NOUN
ejpam-3443	181	32	)	)	PUNCT
ejpam-3443	181	33	.	.	PUNCT
ejpam-3443	182	1	suppose	suppose	VERB
ejpam-3443	182	2	that	that	SCONJ
ejpam-3443	182	3	s	s	VERB
ejpam-3443	182	4	⊆	⊆	NUM
ejpam-3443	182	5	v	v	NOUN
ejpam-3443	182	6	(	(	PUNCT
ejpam-3443	182	7	kn	kn	PROPN
ejpam-3443	182	8	)	)	PUNCT
ejpam-3443	182	9	.	.	PUNCT
ejpam-3443	183	1	then	then	ADV
ejpam-3443	183	2	s	s	VERB
ejpam-3443	183	3	is	be	AUX
ejpam-3443	183	4	dominating	dominate	VERB
ejpam-3443	183	5	set	set	NOUN
ejpam-3443	183	6	of	of	ADP
ejpam-3443	183	7	kn	kn	PROPN
ejpam-3443	183	8	and	and	CCONJ
ejpam-3443	183	9	for	for	ADP
ejpam-3443	183	10	a	a	DET
ejpam-3443	183	11	given	give	VERB
ejpam-3443	183	12	v	v	NUM
ejpam-3443	183	13	∈	∈	PROPN
ejpam-3443	183	14	s	s	NOUN
ejpam-3443	183	15	,	,	PUNCT
ejpam-3443	183	16	|s|	|s|	NOUN
ejpam-3443	183	17	−	−	PROPN
ejpam-3443	183	18	1	1	NUM
ejpam-3443	183	19	=	=	SYM
ejpam-3443	183	20	|nkn(v	|nkn(v	PROPN
ejpam-3443	183	21	)	)	PUNCT
ejpam-3443	183	22	∩	∩	NOUN
ejpam-3443	183	23	s|	s|	VERB
ejpam-3443	183	24	≤	≤	NUM
ejpam-3443	183	25	m	m	VERB
ejpam-3443	183	26	+	+	X
ejpam-3443	183	27	|nkn(v	|nkn(v	ADJ
ejpam-3443	183	28	)	)	PUNCT
ejpam-3443	183	29	\	\	NOUN
ejpam-3443	184	1	s|	s|	NOUN
ejpam-3443	184	2	=	=	PUNCT
ejpam-3443	185	1	m	m	VERB
ejpam-3443	185	2	+	+	NUM
ejpam-3443	185	3	n	n	CCONJ
ejpam-3443	185	4	−	−	PROPN
ejpam-3443	185	5	|s|	|s|	PROPN
ejpam-3443	185	6	so	so	SCONJ
ejpam-3443	185	7	that	that	SCONJ
ejpam-3443	185	8	|s|	|s|	NOUN
ejpam-3443	185	9	≤	≤	PROPN
ejpam-3443	185	10	m+n+1	m+n+1	NOUN
ejpam-3443	185	11	2	2	NUM
ejpam-3443	185	12	.	.	PUNCT
ejpam-3443	186	1	now	now	ADV
ejpam-3443	186	2	suppose	suppose	VERB
ejpam-3443	186	3	that	that	SCONJ
ejpam-3443	186	4	s1	s1	PROPN
ejpam-3443	186	5	=	=	SYM
ejpam-3443	186	6	s	s	PART
ejpam-3443	186	7	∩	∩	ADJ
ejpam-3443	186	8	v	v	X
ejpam-3443	186	9	(	(	PUNCT
ejpam-3443	186	10	g	g	NOUN
ejpam-3443	186	11	)	)	PUNCT
ejpam-3443	186	12	6=	6=	ADP
ejpam-3443	186	13	∅	∅	NOUN
ejpam-3443	186	14	and	and	CCONJ
ejpam-3443	186	15	s2	s2	VERB
ejpam-3443	186	16	=	=	SYM
ejpam-3443	186	17	s	s	PROPN
ejpam-3443	186	18	∩	∩	ADJ
ejpam-3443	186	19	v	v	X
ejpam-3443	186	20	(	(	PUNCT
ejpam-3443	186	21	kn	kn	PROPN
ejpam-3443	186	22	)	)	PUNCT
ejpam-3443	186	23	6=	6=	ADP
ejpam-3443	186	24	∅.	∅.	VERB
ejpam-3443	186	25	by	by	ADP
ejpam-3443	186	26	theorem	theorem	NOUN
ejpam-3443	186	27	1	1	NUM
ejpam-3443	186	28	,	,	PUNCT
ejpam-3443	186	29	in	in	ADP
ejpam-3443	186	30	particular	particular	ADJ
ejpam-3443	186	31	,	,	PUNCT
ejpam-3443	186	32	for	for	ADP
ejpam-3443	186	33	each	each	DET
ejpam-3443	186	34	u	u	PROPN
ejpam-3443	186	35	∈	∈	PROPN
ejpam-3443	186	36	s2	s2	PROPN
ejpam-3443	186	37	,	,	PUNCT
ejpam-3443	186	38	2|s1|	2|s1|	NUM
ejpam-3443	186	39	≤	≤	NUM
ejpam-3443	186	40	m+	m+	NUM
ejpam-3443	186	41	|nkn(u	|nkn(u	NOUN
ejpam-3443	186	42	)	)	PUNCT
ejpam-3443	186	43	\	\	PROPN
ejpam-3443	186	44	s|	s|	VERB
ejpam-3443	186	45	−	−	PROPN
ejpam-3443	186	46	|nkn(u	|nkn(u	NOUN
ejpam-3443	186	47	)	)	PUNCT
ejpam-3443	186	48	∩	∩	NOUN
ejpam-3443	186	49	s|	s|	NOUN
ejpam-3443	186	50	=	=	SYM
ejpam-3443	187	1	m+	m+	NUM
ejpam-3443	187	2	n−	n−	NOUN
ejpam-3443	187	3	2|s2|+	2|s2|+	NOUN
ejpam-3443	187	4	1	1	NUM
ejpam-3443	187	5	,	,	PUNCT
ejpam-3443	187	6	or	or	CCONJ
ejpam-3443	187	7	equivalently	equivalently	ADV
ejpam-3443	187	8	,	,	PUNCT
ejpam-3443	187	9	|s|	|s|	PROPN
ejpam-3443	187	10	≤	≤	NUM
ejpam-3443	187	11	m+	m+	NUM
ejpam-3443	187	12	n+	n+	NOUN
ejpam-3443	187	13	1	1	NUM
ejpam-3443	187	14	2	2	NUM
ejpam-3443	187	15	.	.	PUNCT
ejpam-3443	188	1	3	3	X
ejpam-3443	188	2	.	.	X
ejpam-3443	188	3	cost	cost	VERB
ejpam-3443	188	4	effective	effective	ADJ
ejpam-3443	188	5	domination	domination	NOUN
ejpam-3443	188	6	in	in	ADP
ejpam-3443	188	7	the	the	DET
ejpam-3443	188	8	corona	corona	NOUN
ejpam-3443	188	9	of	of	ADP
ejpam-3443	188	10	graphs	graph	NOUN
ejpam-3443	188	11	theorem	theorem	VERB
ejpam-3443	188	12	5	5	NUM
ejpam-3443	188	13	.	.	PUNCT
ejpam-3443	189	1	[	[	X
ejpam-3443	189	2	8	8	NUM
ejpam-3443	189	3	]	]	PUNCT
ejpam-3443	189	4	let	let	VERB
ejpam-3443	189	5	g	g	PRON
ejpam-3443	189	6	be	be	AUX
ejpam-3443	189	7	a	a	DET
ejpam-3443	189	8	connected	connected	ADJ
ejpam-3443	189	9	graph	graph	NOUN
ejpam-3443	189	10	of	of	ADP
ejpam-3443	189	11	order	order	NOUN
ejpam-3443	189	12	n	n	NOUN
ejpam-3443	189	13	and	and	CCONJ
ejpam-3443	189	14	let	let	VERB
ejpam-3443	189	15	h	h	NOUN
ejpam-3443	189	16	be	be	AUX
ejpam-3443	189	17	any	any	DET
ejpam-3443	189	18	graph	graph	NOUN
ejpam-3443	189	19	of	of	ADP
ejpam-3443	189	20	order	order	NOUN
ejpam-3443	189	21	m.	m.	NOUN
ejpam-3443	189	22	then	then	ADV
ejpam-3443	189	23	s	s	VERB
ejpam-3443	189	24	⊆	⊆	NUM
ejpam-3443	189	25	v	v	NOUN
ejpam-3443	189	26	(	(	PUNCT
ejpam-3443	189	27	g	g	PROPN
ejpam-3443	189	28	◦	◦	NOUN
ejpam-3443	189	29	h	h	NOUN
ejpam-3443	189	30	)	)	PUNCT
ejpam-3443	189	31	is	be	AUX
ejpam-3443	189	32	a	a	DET
ejpam-3443	189	33	dominating	dominating	NOUN
ejpam-3443	189	34	set	set	NOUN
ejpam-3443	189	35	of	of	ADP
ejpam-3443	189	36	g	g	PROPN
ejpam-3443	189	37	◦	◦	NOUN
ejpam-3443	189	38	h	h	NOUN
ejpam-3443	189	39	if	if	SCONJ
ejpam-3443	190	1	and	and	CCONJ
ejpam-3443	190	2	only	only	ADV
ejpam-3443	190	3	if	if	SCONJ
ejpam-3443	190	4	s	s	ADP
ejpam-3443	190	5	∩	∩	ADJ
ejpam-3443	190	6	v	v	X
ejpam-3443	190	7	(	(	PUNCT
ejpam-3443	190	8	hv	hv	PROPN
ejpam-3443	190	9	+	+	PROPN
ejpam-3443	190	10	v	v	NOUN
ejpam-3443	190	11	)	)	PUNCT
ejpam-3443	190	12	is	be	AUX
ejpam-3443	190	13	a	a	DET
ejpam-3443	190	14	dominating	dominating	NOUN
ejpam-3443	190	15	set	set	NOUN
ejpam-3443	190	16	of	of	ADP
ejpam-3443	190	17	hv	hv	PROPN
ejpam-3443	190	18	+	+	X
ejpam-3443	190	19	v	v	NOUN
ejpam-3443	190	20	for	for	ADP
ejpam-3443	190	21	each	each	DET
ejpam-3443	190	22	v	v	NUM
ejpam-3443	190	23	∈	∈	PROPN
ejpam-3443	190	24	v	v	NOUN
ejpam-3443	190	25	(	(	PUNCT
ejpam-3443	190	26	g	g	NOUN
ejpam-3443	190	27	)	)	PUNCT
ejpam-3443	190	28	.	.	PUNCT
ejpam-3443	191	1	corollary	corollary	ADJ
ejpam-3443	191	2	4	4	NUM
ejpam-3443	191	3	.	.	PUNCT
ejpam-3443	192	1	let	let	VERB
ejpam-3443	192	2	g	g	PRON
ejpam-3443	192	3	be	be	AUX
ejpam-3443	192	4	a	a	DET
ejpam-3443	192	5	connected	connected	ADJ
ejpam-3443	192	6	graph	graph	NOUN
ejpam-3443	192	7	and	and	CCONJ
ejpam-3443	192	8	h	h	NOUN
ejpam-3443	192	9	be	be	AUX
ejpam-3443	192	10	any	any	DET
ejpam-3443	192	11	graph	graph	NOUN
ejpam-3443	192	12	,	,	PUNCT
ejpam-3443	192	13	and	and	CCONJ
ejpam-3443	192	14	s	s	VERB
ejpam-3443	192	15	⊆	⊆	NUM
ejpam-3443	192	16	v	v	NOUN
ejpam-3443	192	17	(	(	PUNCT
ejpam-3443	192	18	g	g	PROPN
ejpam-3443	192	19	◦	◦	NOUN
ejpam-3443	192	20	h	h	NOUN
ejpam-3443	192	21	)	)	PUNCT
ejpam-3443	192	22	.	.	PUNCT
ejpam-3443	193	1	if	if	SCONJ
ejpam-3443	193	2	s	s	NOUN
ejpam-3443	193	3	is	be	AUX
ejpam-3443	193	4	a	a	DET
ejpam-3443	193	5	cost	cost	NOUN
ejpam-3443	193	6	effective	effective	ADJ
ejpam-3443	193	7	dominating	dominating	NOUN
ejpam-3443	193	8	set	set	NOUN
ejpam-3443	193	9	of	of	ADP
ejpam-3443	193	10	g	g	PROPN
ejpam-3443	193	11	◦	◦	NOUN
ejpam-3443	193	12	h	h	NOUN
ejpam-3443	193	13	,	,	PUNCT
ejpam-3443	193	14	then	then	ADV
ejpam-3443	193	15	s	s	VERB
ejpam-3443	193	16	∩	∩	ADJ
ejpam-3443	193	17	v	v	X
ejpam-3443	193	18	(	(	PUNCT
ejpam-3443	193	19	hv	hv	PROPN
ejpam-3443	193	20	+	+	PROPN
ejpam-3443	193	21	v	v	NOUN
ejpam-3443	193	22	)	)	PUNCT
ejpam-3443	193	23	is	be	AUX
ejpam-3443	193	24	a	a	DET
ejpam-3443	193	25	dominating	dominating	NOUN
ejpam-3443	193	26	set	set	NOUN
ejpam-3443	193	27	of	of	ADP
ejpam-3443	193	28	hv	hv	PROPN
ejpam-3443	193	29	+	+	X
ejpam-3443	193	30	v	v	NOUN
ejpam-3443	193	31	for	for	ADP
ejpam-3443	193	32	each	each	DET
ejpam-3443	193	33	v	v	NUM
ejpam-3443	193	34	∈	∈	PROPN
ejpam-3443	193	35	v	v	NOUN
ejpam-3443	193	36	(	(	PUNCT
ejpam-3443	193	37	g	g	NOUN
ejpam-3443	193	38	)	)	PUNCT
ejpam-3443	193	39	.	.	PUNCT
ejpam-3443	194	1	corollary	corollary	ADJ
ejpam-3443	194	2	4	4	NUM
ejpam-3443	194	3	guarantees	guarantee	VERB
ejpam-3443	194	4	that	that	SCONJ
ejpam-3443	194	5	if	if	SCONJ
ejpam-3443	194	6	s	s	NOUN
ejpam-3443	194	7	is	be	AUX
ejpam-3443	194	8	a	a	DET
ejpam-3443	194	9	cost	cost	NOUN
ejpam-3443	194	10	effective	effective	ADJ
ejpam-3443	194	11	dominating	dominating	NOUN
ejpam-3443	194	12	set	set	NOUN
ejpam-3443	194	13	of	of	ADP
ejpam-3443	194	14	g	g	PROPN
ejpam-3443	194	15	◦	◦	NOUN
ejpam-3443	194	16	h	h	NOUN
ejpam-3443	194	17	,	,	PUNCT
ejpam-3443	194	18	then	then	ADV
ejpam-3443	194	19	s	s	VERB
ejpam-3443	194	20	∩	∩	ADJ
ejpam-3443	194	21	v	v	X
ejpam-3443	194	22	(	(	PUNCT
ejpam-3443	194	23	hv	hv	PROPN
ejpam-3443	194	24	+	+	PROPN
ejpam-3443	194	25	v	v	NOUN
ejpam-3443	194	26	)	)	PUNCT
ejpam-3443	194	27	6=	6=	ADP
ejpam-3443	194	28	∅	∅	NOUN
ejpam-3443	194	29	for	for	ADP
ejpam-3443	194	30	each	each	DET
ejpam-3443	194	31	v	v	NUM
ejpam-3443	194	32	∈	∈	PROPN
ejpam-3443	194	33	v	v	NOUN
ejpam-3443	194	34	(	(	PUNCT
ejpam-3443	194	35	g	g	NOUN
ejpam-3443	194	36	)	)	PUNCT
ejpam-3443	194	37	.	.	PUNCT
ejpam-3443	195	1	proposition	proposition	NOUN
ejpam-3443	195	2	3	3	X
ejpam-3443	195	3	.	.	PUNCT
ejpam-3443	196	1	let	let	VERB
ejpam-3443	196	2	g	g	PRON
ejpam-3443	196	3	be	be	AUX
ejpam-3443	196	4	a	a	DET
ejpam-3443	196	5	connected	connected	ADJ
ejpam-3443	196	6	graph	graph	NOUN
ejpam-3443	196	7	and	and	CCONJ
ejpam-3443	196	8	h	h	NOUN
ejpam-3443	196	9	be	be	AUX
ejpam-3443	196	10	any	any	DET
ejpam-3443	196	11	isolate	isolate	NOUN
ejpam-3443	196	12	-	-	PUNCT
ejpam-3443	196	13	free	free	ADJ
ejpam-3443	196	14	graph	graph	NOUN
ejpam-3443	196	15	.	.	PUNCT
ejpam-3443	197	1	if	if	SCONJ
ejpam-3443	197	2	for	for	ADP
ejpam-3443	197	3	each	each	DET
ejpam-3443	197	4	v	v	NUM
ejpam-3443	197	5	∈	∈	PROPN
ejpam-3443	197	6	v	v	NOUN
ejpam-3443	197	7	(	(	PUNCT
ejpam-3443	197	8	g	g	NOUN
ejpam-3443	197	9	)	)	PUNCT
ejpam-3443	197	10	,	,	PUNCT
ejpam-3443	197	11	sv	sv	PROPN
ejpam-3443	197	12	⊆	⊆	NUM
ejpam-3443	197	13	v	v	X
ejpam-3443	197	14	(	(	PUNCT
ejpam-3443	197	15	hv	hv	X
ejpam-3443	197	16	)	)	PUNCT
ejpam-3443	197	17	is	be	AUX
ejpam-3443	197	18	a	a	DET
ejpam-3443	197	19	cost	cost	NOUN
ejpam-3443	197	20	effective	effective	ADJ
ejpam-3443	197	21	dominating	dominating	NOUN
ejpam-3443	197	22	set	set	NOUN
ejpam-3443	197	23	of	of	ADP
ejpam-3443	197	24	hv	hv	PROPN
ejpam-3443	197	25	,	,	PUNCT
ejpam-3443	197	26	then	then	ADV
ejpam-3443	197	27	∪v∈v	∪v∈v	VERB
ejpam-3443	197	28	(	(	PUNCT
ejpam-3443	197	29	g)sv	g)sv	PROPN
ejpam-3443	197	30	is	be	AUX
ejpam-3443	197	31	a	a	DET
ejpam-3443	197	32	cost	cost	NOUN
ejpam-3443	197	33	effective	effective	ADJ
ejpam-3443	197	34	dominating	dominating	NOUN
ejpam-3443	197	35	set	set	NOUN
ejpam-3443	197	36	of	of	ADP
ejpam-3443	197	37	g	g	PROPN
ejpam-3443	197	38	◦	◦	NOUN
ejpam-3443	197	39	h.	h.	NOUN
ejpam-3443	197	40	proof	proof	NOUN
ejpam-3443	197	41	.	.	PUNCT
ejpam-3443	198	1	for	for	ADP
ejpam-3443	198	2	each	each	DET
ejpam-3443	198	3	v	v	NUM
ejpam-3443	198	4	∈	∈	PROPN
ejpam-3443	198	5	v	v	NOUN
ejpam-3443	198	6	(	(	PUNCT
ejpam-3443	198	7	g	g	NOUN
ejpam-3443	198	8	)	)	PUNCT
ejpam-3443	198	9	,	,	PUNCT
ejpam-3443	198	10	let	let	VERB
ejpam-3443	198	11	sv	sv	PROPN
ejpam-3443	198	12	⊆	⊆	NUM
ejpam-3443	198	13	v	v	X
ejpam-3443	198	14	(	(	PUNCT
ejpam-3443	198	15	hv	hv	NOUN
ejpam-3443	198	16	)	)	PUNCT
ejpam-3443	198	17	be	be	VERB
ejpam-3443	198	18	a	a	DET
ejpam-3443	198	19	cost	cost	NOUN
ejpam-3443	198	20	effective	effective	ADJ
ejpam-3443	198	21	dominating	dominating	NOUN
ejpam-3443	198	22	set	set	NOUN
ejpam-3443	198	23	of	of	ADP
ejpam-3443	198	24	hv	hv	PROPN
ejpam-3443	198	25	.	.	PUNCT
ejpam-3443	199	1	then	then	ADV
ejpam-3443	199	2	sv	sv	PROPN
ejpam-3443	199	3	is	be	AUX
ejpam-3443	199	4	a	a	DET
ejpam-3443	199	5	very	very	ADV
ejpam-3443	199	6	cost	cost	NOUN
ejpam-3443	199	7	effective	effective	ADJ
ejpam-3443	199	8	dominating	dominating	NOUN
ejpam-3443	199	9	set	set	NOUN
ejpam-3443	199	10	of	of	ADP
ejpam-3443	199	11	hv	hv	PROPN
ejpam-3443	199	12	+	+	PROPN
ejpam-3443	199	13	v	v	NOUN
ejpam-3443	199	14	,	,	PUNCT
ejpam-3443	199	15	by	by	ADP
ejpam-3443	199	16	proposition	proposition	NOUN
ejpam-3443	199	17	1	1	NUM
ejpam-3443	199	18	.	.	PUNCT
ejpam-3443	200	1	let	let	VERB
ejpam-3443	200	2	s	s	NOUN
ejpam-3443	200	3	=	=	VERB
ejpam-3443	200	4	∪v∈v	∪v∈v	X
ejpam-3443	200	5	(	(	PUNCT
ejpam-3443	200	6	g)sv	g)sv	PROPN
ejpam-3443	200	7	.	.	PUNCT
ejpam-3443	201	1	then	then	ADV
ejpam-3443	201	2	s	s	VERB
ejpam-3443	201	3	is	be	AUX
ejpam-3443	201	4	a	a	DET
ejpam-3443	201	5	dominating	dominating	NOUN
ejpam-3443	201	6	set	set	NOUN
ejpam-3443	201	7	of	of	ADP
ejpam-3443	201	8	g	g	PROPN
ejpam-3443	201	9	◦	◦	PROPN
ejpam-3443	201	10	h.	h.	PROPN
ejpam-3443	201	11	let	let	VERB
ejpam-3443	201	12	u	u	PRON
ejpam-3443	201	13	∈	∈	PROPN
ejpam-3443	201	14	sv	sv	PROPN
ejpam-3443	201	15	.	.	PUNCT
ejpam-3443	202	1	then	then	ADV
ejpam-3443	202	2	,	,	PUNCT
ejpam-3443	202	3	|ng	|ng	VERB
ejpam-3443	202	4	◦	◦	NOUN
ejpam-3443	202	5	h(u	h(u	NOUN
ejpam-3443	202	6	)	)	PUNCT
ejpam-3443	202	7	∩	∩	NOUN
ejpam-3443	202	8	s|	s|	NOUN
ejpam-3443	202	9	=	=	SYM
ejpam-3443	202	10	|nhv+v(u	|nhv+v(u	NUM
ejpam-3443	202	11	)	)	PUNCT
ejpam-3443	202	12	∩	∩	NOUN
ejpam-3443	202	13	sv|	sv|	ADJ
ejpam-3443	202	14	≤	≤	NOUN
ejpam-3443	202	15	|nhv+v(u	|nhv+v(u	NUM
ejpam-3443	202	16	)	)	PUNCT
ejpam-3443	202	17	\	\	PUNCT
ejpam-3443	203	1	sv|	sv|	NOUN
ejpam-3443	203	2	=	=	SYM
ejpam-3443	203	3	|ng	|ng	VERB
ejpam-3443	203	4	◦	◦	NOUN
ejpam-3443	203	5	h(u	h(u	NOUN
ejpam-3443	203	6	)	)	PUNCT
ejpam-3443	203	7	\	\	PROPN
ejpam-3443	203	8	s|	s|	PROPN
ejpam-3443	203	9	,	,	PUNCT
ejpam-3443	203	10	showing	show	VERB
ejpam-3443	203	11	that	that	SCONJ
ejpam-3443	203	12	s	s	VERB
ejpam-3443	203	13	is	be	AUX
ejpam-3443	203	14	a	a	DET
ejpam-3443	203	15	cost	cost	NOUN
ejpam-3443	203	16	effective	effective	ADJ
ejpam-3443	203	17	dominating	dominating	NOUN
ejpam-3443	203	18	set	set	NOUN
ejpam-3443	203	19	of	of	ADP
ejpam-3443	203	20	g	g	PROPN
ejpam-3443	203	21	◦	◦	PROPN
ejpam-3443	203	22	h.	h.	PROPN
ejpam-3443	203	23	f.jamil	f.jamil	PROPN
ejpam-3443	203	24	,	,	PUNCT
ejpam-3443	203	25	h.	h.	PROPN
ejpam-3443	203	26	nuenay	nuenay	PROPN
ejpam-3443	203	27	-	-	PUNCT
ejpam-3443	203	28	maglanque	maglanque	ADJ
ejpam-3443	203	29	/	/	SYM
ejpam-3443	203	30	eur	eur	NOUN
ejpam-3443	203	31	.	.	PUNCT
ejpam-3443	204	1	j.	j.	PROPN
ejpam-3443	204	2	pure	pure	PROPN
ejpam-3443	204	3	appl	appl	PROPN
ejpam-3443	204	4	.	.	PROPN
ejpam-3443	204	5	math	math	PROPN
ejpam-3443	204	6	,	,	PUNCT
ejpam-3443	204	7	12	12	NUM
ejpam-3443	204	8	(	(	PUNCT
ejpam-3443	204	9	3	3	NUM
ejpam-3443	204	10	)	)	PUNCT
ejpam-3443	204	11	(	(	PUNCT
ejpam-3443	204	12	2019	2019	NUM
ejpam-3443	204	13	)	)	PUNCT
ejpam-3443	204	14	,	,	PUNCT
ejpam-3443	204	15	978	978	NUM
ejpam-3443	204	16	-	-	SYM
ejpam-3443	204	17	998	998	NUM
ejpam-3443	204	18	986	986	NUM
ejpam-3443	204	19	proposition	proposition	NOUN
ejpam-3443	204	20	4	4	NUM
ejpam-3443	204	21	.	.	PUNCT
ejpam-3443	205	1	let	let	VERB
ejpam-3443	205	2	g	g	PRON
ejpam-3443	205	3	be	be	AUX
ejpam-3443	205	4	a	a	DET
ejpam-3443	205	5	connected	connected	ADJ
ejpam-3443	205	6	graph	graph	NOUN
ejpam-3443	205	7	and	and	CCONJ
ejpam-3443	205	8	h	h	NOUN
ejpam-3443	205	9	be	be	AUX
ejpam-3443	205	10	any	any	DET
ejpam-3443	205	11	graph	graph	NOUN
ejpam-3443	205	12	of	of	ADP
ejpam-3443	205	13	order	order	NOUN
ejpam-3443	205	14	n	n	PRON
ejpam-3443	205	15	≥	≥	NOUN
ejpam-3443	205	16	2	2	NUM
ejpam-3443	205	17	.	.	PUNCT
ejpam-3443	206	1	for	for	ADP
ejpam-3443	206	2	each	each	DET
ejpam-3443	206	3	v	v	NUM
ejpam-3443	206	4	∈	∈	PROPN
ejpam-3443	206	5	v	v	NOUN
ejpam-3443	206	6	(	(	PUNCT
ejpam-3443	206	7	g	g	NOUN
ejpam-3443	206	8	)	)	PUNCT
ejpam-3443	206	9	with	with	ADP
ejpam-3443	206	10	degg(v	degg(v	PROPN
ejpam-3443	206	11	)	)	PUNCT
ejpam-3443	206	12	≤	≤	NOUN
ejpam-3443	206	13	n	n	CCONJ
ejpam-3443	206	14	,	,	PUNCT
ejpam-3443	206	15	let	let	VERB
ejpam-3443	206	16	sv	sv	INTJ
ejpam-3443	206	17	=	=	PUNCT
ejpam-3443	206	18	{	{	PUNCT
ejpam-3443	206	19	v	v	NOUN
ejpam-3443	206	20	}	}	PUNCT
ejpam-3443	206	21	,	,	PUNCT
ejpam-3443	206	22	and	and	CCONJ
ejpam-3443	206	23	for	for	ADP
ejpam-3443	206	24	each	each	DET
ejpam-3443	206	25	v	v	NUM
ejpam-3443	206	26	∈	∈	PROPN
ejpam-3443	206	27	v	v	NOUN
ejpam-3443	206	28	(	(	PUNCT
ejpam-3443	206	29	g	g	NOUN
ejpam-3443	206	30	)	)	PUNCT
ejpam-3443	206	31	with	with	ADP
ejpam-3443	206	32	degg(v	degg(v	PROPN
ejpam-3443	206	33	)	)	PUNCT
ejpam-3443	206	34	>	>	X
ejpam-3443	206	35	n	n	CCONJ
ejpam-3443	206	36	,	,	PUNCT
ejpam-3443	206	37	let	let	VERB
ejpam-3443	206	38	sv	sv	PROPN
ejpam-3443	206	39	⊆	⊆	NUM
ejpam-3443	206	40	v	v	X
ejpam-3443	206	41	(	(	PUNCT
ejpam-3443	206	42	hv	hv	NOUN
ejpam-3443	206	43	)	)	PUNCT
ejpam-3443	206	44	be	be	VERB
ejpam-3443	206	45	a	a	DET
ejpam-3443	206	46	cost	cost	NOUN
ejpam-3443	206	47	effective	effective	ADJ
ejpam-3443	206	48	dominating	dominating	NOUN
ejpam-3443	206	49	set	set	NOUN
ejpam-3443	206	50	of	of	ADP
ejpam-3443	206	51	hv	hv	PROPN
ejpam-3443	206	52	.	.	PUNCT
ejpam-3443	207	1	then	then	ADV
ejpam-3443	207	2	∪v∈v	∪v∈v	X
ejpam-3443	207	3	(	(	PUNCT
ejpam-3443	207	4	g)sv	g)sv	PROPN
ejpam-3443	207	5	is	be	AUX
ejpam-3443	207	6	a	a	DET
ejpam-3443	207	7	cost	cost	NOUN
ejpam-3443	207	8	effective	effective	ADJ
ejpam-3443	207	9	dominating	dominating	NOUN
ejpam-3443	207	10	set	set	NOUN
ejpam-3443	207	11	of	of	ADP
ejpam-3443	207	12	g	g	PROPN
ejpam-3443	207	13	◦	◦	NOUN
ejpam-3443	207	14	h.	h.	PROPN
ejpam-3443	207	15	consequently	consequently	ADV
ejpam-3443	207	16	,	,	PUNCT
ejpam-3443	207	17	γce(g	γce(g	PROPN
ejpam-3443	207	18	◦	◦	NOUN
ejpam-3443	207	19	h	h	NOUN
ejpam-3443	207	20	)	)	PUNCT
ejpam-3443	207	21	≤	≤	NOUN
ejpam-3443	207	22	|v	|v	X
ejpam-3443	207	23	(	(	PUNCT
ejpam-3443	207	24	g)|+	g)|+	NOUN
ejpam-3443	207	25	(	(	PUNCT
ejpam-3443	207	26	γce(h)−	γce(h)−	PROPN
ejpam-3443	207	27	1)|l|	1)|l|	NOUN
ejpam-3443	207	28	,	,	PUNCT
ejpam-3443	207	29	where	where	SCONJ
ejpam-3443	207	30	l	l	NOUN
ejpam-3443	207	31	=	=	PUNCT
ejpam-3443	207	32	{	{	PUNCT
ejpam-3443	207	33	v	v	NUM
ejpam-3443	207	34	∈	∈	NOUN
ejpam-3443	207	35	v	v	NOUN
ejpam-3443	207	36	(	(	PUNCT
ejpam-3443	207	37	g	g	NOUN
ejpam-3443	207	38	)	)	PUNCT
ejpam-3443	207	39	:	:	PUNCT
ejpam-3443	207	40	degg(v	degg(v	PROPN
ejpam-3443	207	41	)	)	PUNCT
ejpam-3443	207	42	>	>	X
ejpam-3443	207	43	n	n	CCONJ
ejpam-3443	207	44	}	}	PUNCT
ejpam-3443	207	45	.	.	PUNCT
ejpam-3443	208	1	proof	proof	NOUN
ejpam-3443	208	2	.	.	PUNCT
ejpam-3443	209	1	let	let	VERB
ejpam-3443	209	2	s	s	NOUN
ejpam-3443	209	3	=	=	VERB
ejpam-3443	209	4	∪v∈v	∪v∈v	X
ejpam-3443	209	5	(	(	PUNCT
ejpam-3443	209	6	g)sv	g)sv	PROPN
ejpam-3443	209	7	.	.	PUNCT
ejpam-3443	210	1	then	then	ADV
ejpam-3443	210	2	s	s	VERB
ejpam-3443	210	3	is	be	AUX
ejpam-3443	210	4	a	a	DET
ejpam-3443	210	5	dominating	dominating	NOUN
ejpam-3443	210	6	set	set	NOUN
ejpam-3443	210	7	of	of	ADP
ejpam-3443	210	8	g	g	PROPN
ejpam-3443	210	9	◦	◦	PROPN
ejpam-3443	210	10	h.	h.	PROPN
ejpam-3443	210	11	let	let	VERB
ejpam-3443	210	12	v	v	NUM
ejpam-3443	210	13	∈	∈	PROPN
ejpam-3443	210	14	v	v	NOUN
ejpam-3443	210	15	(	(	PUNCT
ejpam-3443	210	16	g	g	NOUN
ejpam-3443	210	17	)	)	PUNCT
ejpam-3443	210	18	with	with	ADP
ejpam-3443	210	19	degg(v	degg(v	PROPN
ejpam-3443	210	20	)	)	PUNCT
ejpam-3443	210	21	≤	≤	NOUN
ejpam-3443	210	22	n.	n.	NOUN
ejpam-3443	210	23	then	then	ADV
ejpam-3443	210	24	|ng	|ng	VERB
ejpam-3443	210	25	◦	◦	NOUN
ejpam-3443	210	26	h(v	h(v	ADJ
ejpam-3443	210	27	)	)	PUNCT
ejpam-3443	210	28	∩	∩	NOUN
ejpam-3443	210	29	s|	s|	VERB
ejpam-3443	210	30	≤	≤	NUM
ejpam-3443	210	31	degg(v	degg(v	PROPN
ejpam-3443	210	32	)	)	PUNCT
ejpam-3443	210	33	≤	≤	NOUN
ejpam-3443	210	34	n	n	PRON
ejpam-3443	210	35	≤	≤	NOUN
ejpam-3443	210	36	|ng	|ng	VERB
ejpam-3443	210	37	◦	◦	NOUN
ejpam-3443	210	38	h(v	h(v	NOUN
ejpam-3443	210	39	)	)	PUNCT
ejpam-3443	210	40	\	\	PROPN
ejpam-3443	210	41	s|	s|	PROPN
ejpam-3443	210	42	.	.	PUNCT
ejpam-3443	211	1	suppose	suppose	VERB
ejpam-3443	211	2	that	that	SCONJ
ejpam-3443	211	3	degg(v	degg(v	PROPN
ejpam-3443	211	4	)	)	PUNCT
ejpam-3443	211	5	>	>	PUNCT
ejpam-3443	212	1	n.	n.	PROPN
ejpam-3443	212	2	then	then	ADV
ejpam-3443	212	3	sv	sv	PROPN
ejpam-3443	212	4	is	be	AUX
ejpam-3443	212	5	a	a	DET
ejpam-3443	212	6	cost	cost	NOUN
ejpam-3443	212	7	effective	effective	ADJ
ejpam-3443	212	8	dominating	dominating	NOUN
ejpam-3443	212	9	set	set	NOUN
ejpam-3443	212	10	of	of	ADP
ejpam-3443	212	11	hv	hv	PROPN
ejpam-3443	212	12	.	.	PUNCT
ejpam-3443	213	1	by	by	ADP
ejpam-3443	213	2	proposition	proposition	NOUN
ejpam-3443	213	3	1	1	NUM
ejpam-3443	213	4	,	,	PUNCT
ejpam-3443	213	5	sv	sv	PROPN
ejpam-3443	213	6	is	be	AUX
ejpam-3443	213	7	a	a	DET
ejpam-3443	213	8	very	very	ADV
ejpam-3443	213	9	cost	cost	NOUN
ejpam-3443	213	10	effective	effective	ADJ
ejpam-3443	213	11	dominating	dominating	NOUN
ejpam-3443	213	12	set	set	NOUN
ejpam-3443	213	13	of	of	ADP
ejpam-3443	213	14	hv	hv	PROPN
ejpam-3443	213	15	+	+	X
ejpam-3443	213	16	v.	v.	CCONJ
ejpam-3443	213	17	thus	thus	ADV
ejpam-3443	213	18	,	,	PUNCT
ejpam-3443	213	19	for	for	SCONJ
ejpam-3443	213	20	each	each	DET
ejpam-3443	213	21	u	u	PROPN
ejpam-3443	213	22	∈	∈	PROPN
ejpam-3443	213	23	sv	sv	PROPN
ejpam-3443	213	24	,	,	PUNCT
ejpam-3443	213	25	|ng	|ng	VERB
ejpam-3443	213	26	◦	◦	NOUN
ejpam-3443	213	27	h(u	h(u	NOUN
ejpam-3443	213	28	)	)	PUNCT
ejpam-3443	214	1	∩	∩	NOUN
ejpam-3443	214	2	s|	s|	NOUN
ejpam-3443	214	3	=	=	SYM
ejpam-3443	214	4	|nhv+v(u	|nhv+v(u	NUM
ejpam-3443	214	5	)	)	PUNCT
ejpam-3443	214	6	∩	∩	NOUN
ejpam-3443	214	7	sv|	sv|	ADJ
ejpam-3443	214	8	<	<	X
ejpam-3443	214	9	|nhv+v(u	|nhv+v(u	NUM
ejpam-3443	214	10	)	)	PUNCT
ejpam-3443	214	11	\	\	PUNCT
ejpam-3443	215	1	sv|	sv|	NOUN
ejpam-3443	215	2	=	=	SYM
ejpam-3443	215	3	|ng	|ng	VERB
ejpam-3443	215	4	◦	◦	NOUN
ejpam-3443	215	5	h(u	h(u	NOUN
ejpam-3443	215	6	)	)	PUNCT
ejpam-3443	215	7	\	\	PROPN
ejpam-3443	215	8	s|	s|	PROPN
ejpam-3443	215	9	.	.	PUNCT
ejpam-3443	216	1	therefore	therefore	ADV
ejpam-3443	216	2	,	,	PUNCT
ejpam-3443	216	3	s	s	VERB
ejpam-3443	216	4	is	be	AUX
ejpam-3443	216	5	a	a	DET
ejpam-3443	216	6	cost	cost	NOUN
ejpam-3443	216	7	effective	effective	ADJ
ejpam-3443	216	8	dominating	dominating	NOUN
ejpam-3443	216	9	set	set	NOUN
ejpam-3443	216	10	of	of	ADP
ejpam-3443	216	11	g	g	PROPN
ejpam-3443	216	12	◦	◦	NOUN
ejpam-3443	216	13	h.	h.	NOUN
ejpam-3443	216	14	corollary	corollary	ADJ
ejpam-3443	216	15	5	5	PROPN
ejpam-3443	216	16	.	.	PUNCT
ejpam-3443	217	1	for	for	ADP
ejpam-3443	217	2	any	any	DET
ejpam-3443	217	3	nontrivial	nontrivial	ADJ
ejpam-3443	217	4	connected	connect	VERB
ejpam-3443	217	5	graph	graph	NOUN
ejpam-3443	217	6	g	g	NOUN
ejpam-3443	217	7	of	of	ADP
ejpam-3443	217	8	order	order	NOUN
ejpam-3443	217	9	m	m	VERB
ejpam-3443	217	10	and	and	CCONJ
ejpam-3443	217	11	any	any	DET
ejpam-3443	217	12	graph	graph	NOUN
ejpam-3443	217	13	h	h	NOUN
ejpam-3443	217	14	,	,	PUNCT
ejpam-3443	217	15	if	if	SCONJ
ejpam-3443	217	16	∆(g	∆(g	NOUN
ejpam-3443	217	17	)	)	PUNCT
ejpam-3443	217	18	≤	≤	NOUN
ejpam-3443	217	19	|v	|v	PROPN
ejpam-3443	217	20	(	(	PUNCT
ejpam-3443	217	21	h)|	h)|	PROPN
ejpam-3443	217	22	,	,	PUNCT
ejpam-3443	217	23	then	then	ADV
ejpam-3443	217	24	γce(g	γce(g	PROPN
ejpam-3443	217	25	◦	◦	NOUN
ejpam-3443	217	26	h	h	NOUN
ejpam-3443	217	27	)	)	PUNCT
ejpam-3443	217	28	=	=	PUNCT
ejpam-3443	217	29	m.	m.	NOUN
ejpam-3443	217	30	definition	definition	NOUN
ejpam-3443	217	31	1	1	NUM
ejpam-3443	217	32	.	.	PUNCT
ejpam-3443	218	1	let	let	VERB
ejpam-3443	218	2	g	g	NOUN
ejpam-3443	218	3	be	be	AUX
ejpam-3443	218	4	any	any	DET
ejpam-3443	218	5	graph	graph	NOUN
ejpam-3443	218	6	.	.	PUNCT
ejpam-3443	219	1	a	a	DET
ejpam-3443	219	2	subset	subset	NOUN
ejpam-3443	219	3	s	s	VERB
ejpam-3443	219	4	⊆	⊆	NUM
ejpam-3443	219	5	v	v	NOUN
ejpam-3443	219	6	(	(	PUNCT
ejpam-3443	219	7	g	g	NOUN
ejpam-3443	219	8	)	)	PUNCT
ejpam-3443	219	9	is	be	AUX
ejpam-3443	219	10	called	call	VERB
ejpam-3443	219	11	a	a	DET
ejpam-3443	219	12	kn	kn	NOUN
ejpam-3443	219	13	-	-	PUNCT
ejpam-3443	219	14	cost	cost	NOUN
ejpam-3443	219	15	effective	effective	ADJ
ejpam-3443	219	16	set	set	NOUN
ejpam-3443	219	17	of	of	ADP
ejpam-3443	219	18	g	g	PROPN
ejpam-3443	219	19	if	if	SCONJ
ejpam-3443	219	20	s	s	VERB
ejpam-3443	219	21	is	be	AUX
ejpam-3443	219	22	a	a	DET
ejpam-3443	219	23	cost	cost	NOUN
ejpam-3443	219	24	effective	effective	ADJ
ejpam-3443	219	25	set	set	NOUN
ejpam-3443	219	26	of	of	ADP
ejpam-3443	219	27	kn	kn	PROPN
ejpam-3443	220	1	+	+	PROPN
ejpam-3443	220	2	g.	g.	PROPN
ejpam-3443	220	3	a	a	DET
ejpam-3443	220	4	kn	kn	NOUN
ejpam-3443	220	5	-	-	PUNCT
ejpam-3443	220	6	cost	cost	NOUN
ejpam-3443	220	7	effective	effective	ADJ
ejpam-3443	220	8	set	set	NOUN
ejpam-3443	220	9	which	which	PRON
ejpam-3443	220	10	is	be	AUX
ejpam-3443	220	11	dominating	dominate	VERB
ejpam-3443	220	12	in	in	ADP
ejpam-3443	220	13	g	g	PROPN
ejpam-3443	220	14	is	be	AUX
ejpam-3443	220	15	called	call	VERB
ejpam-3443	220	16	a	a	DET
ejpam-3443	220	17	kn	kn	NOUN
ejpam-3443	220	18	-	-	PUNCT
ejpam-3443	220	19	cost	cost	NOUN
ejpam-3443	220	20	effective	effective	ADJ
ejpam-3443	220	21	dominating	dominating	NOUN
ejpam-3443	220	22	set	set	NOUN
ejpam-3443	220	23	of	of	ADP
ejpam-3443	220	24	g.	g.	PROPN
ejpam-3443	220	25	a	a	DET
ejpam-3443	220	26	kn	kn	NOUN
ejpam-3443	220	27	-	-	PUNCT
ejpam-3443	220	28	cost	cost	NOUN
ejpam-3443	220	29	effective	effective	ADJ
ejpam-3443	220	30	dominating	dominating	NOUN
ejpam-3443	220	31	set	set	NOUN
ejpam-3443	220	32	is	be	AUX
ejpam-3443	220	33	called	call	VERB
ejpam-3443	220	34	minimal	minimal	ADJ
ejpam-3443	220	35	kn	kn	NOUN
ejpam-3443	220	36	-	-	PUNCT
ejpam-3443	220	37	cost	cost	NOUN
ejpam-3443	220	38	effective	effective	ADJ
ejpam-3443	220	39	dominating	dominating	NOUN
ejpam-3443	220	40	set	set	NOUN
ejpam-3443	220	41	if	if	SCONJ
ejpam-3443	220	42	it	it	PRON
ejpam-3443	220	43	does	do	AUX
ejpam-3443	220	44	not	not	PART
ejpam-3443	220	45	contain	contain	VERB
ejpam-3443	220	46	a	a	DET
ejpam-3443	220	47	proper	proper	ADJ
ejpam-3443	220	48	subset	subset	NOUN
ejpam-3443	220	49	that	that	PRON
ejpam-3443	220	50	is	be	AUX
ejpam-3443	220	51	itself	itself	PRON
ejpam-3443	220	52	kn	kn	ADJ
ejpam-3443	220	53	-	-	PUNCT
ejpam-3443	220	54	cost	cost	NOUN
ejpam-3443	220	55	effective	effective	ADJ
ejpam-3443	220	56	dominating	dominating	NOUN
ejpam-3443	220	57	set	set	NOUN
ejpam-3443	220	58	.	.	PUNCT
ejpam-3443	221	1	the	the	DET
ejpam-3443	221	2	symbols	symbol	NOUN
ejpam-3443	221	3	γknce(g	γknce(g	PROPN
ejpam-3443	221	4	)	)	PUNCT
ejpam-3443	221	5	,	,	PUNCT
ejpam-3443	221	6	γknmce(g	γknmce(g	PROPN
ejpam-3443	221	7	)	)	PUNCT
ejpam-3443	221	8	and	and	CCONJ
ejpam-3443	221	9	γ+knce	γ+knce	PROPN
ejpam-3443	221	10	(	(	PUNCT
ejpam-3443	221	11	g	g	NOUN
ejpam-3443	221	12	)	)	PUNCT
ejpam-3443	221	13	denote	denote	VERB
ejpam-3443	221	14	the	the	DET
ejpam-3443	221	15	minimum	minimum	ADJ
ejpam-3443	221	16	cardinality	cardinality	NOUN
ejpam-3443	221	17	of	of	ADP
ejpam-3443	221	18	a	a	DET
ejpam-3443	221	19	kn	kn	NOUN
ejpam-3443	221	20	-	-	PUNCT
ejpam-3443	221	21	cost	cost	NOUN
ejpam-3443	221	22	effective	effective	ADJ
ejpam-3443	221	23	dominating	dominating	NOUN
ejpam-3443	221	24	set	set	NOUN
ejpam-3443	221	25	,	,	PUNCT
ejpam-3443	222	1	the	the	DET
ejpam-3443	222	2	maximum	maximum	ADJ
ejpam-3443	222	3	cardinality	cardinality	NOUN
ejpam-3443	222	4	of	of	ADP
ejpam-3443	222	5	a	a	DET
ejpam-3443	222	6	minimal	minimal	ADJ
ejpam-3443	222	7	kn	kn	NOUN
ejpam-3443	222	8	-	-	PUNCT
ejpam-3443	222	9	cost	cost	NOUN
ejpam-3443	222	10	effective	effective	ADJ
ejpam-3443	222	11	dominating	dominating	NOUN
ejpam-3443	222	12	set	set	NOUN
ejpam-3443	222	13	and	and	CCONJ
ejpam-3443	222	14	maximum	maximum	ADJ
ejpam-3443	222	15	cardinality	cardinality	NOUN
ejpam-3443	222	16	of	of	ADP
ejpam-3443	222	17	a	a	DET
ejpam-3443	222	18	kn	kn	NOUN
ejpam-3443	222	19	-	-	PUNCT
ejpam-3443	222	20	cost	cost	NOUN
ejpam-3443	222	21	effective	effective	ADJ
ejpam-3443	222	22	dominating	dominating	NOUN
ejpam-3443	222	23	set	set	NOUN
ejpam-3443	222	24	,	,	PUNCT
ejpam-3443	222	25	respectively	respectively	ADV
ejpam-3443	222	26	,	,	PUNCT
ejpam-3443	222	27	in	in	ADP
ejpam-3443	222	28	g.	g.	PROPN
ejpam-3443	222	29	remark	remark	PROPN
ejpam-3443	222	30	3	3	NUM
ejpam-3443	222	31	.	.	PUNCT
ejpam-3443	223	1	every	every	DET
ejpam-3443	223	2	cost	cost	NOUN
ejpam-3443	223	3	effective	effective	ADJ
ejpam-3443	223	4	(	(	PUNCT
ejpam-3443	223	5	dominating	dominating	NOUN
ejpam-3443	223	6	)	)	PUNCT
ejpam-3443	223	7	set	set	NOUN
ejpam-3443	223	8	of	of	ADP
ejpam-3443	223	9	g	g	PROPN
ejpam-3443	223	10	is	be	AUX
ejpam-3443	223	11	a	a	DET
ejpam-3443	223	12	kn	kn	NOUN
ejpam-3443	223	13	-	-	PUNCT
ejpam-3443	223	14	cost	cost	NOUN
ejpam-3443	223	15	effective	effective	ADJ
ejpam-3443	223	16	(	(	PUNCT
ejpam-3443	223	17	dominating	dominating	NOUN
ejpam-3443	223	18	)	)	PUNCT
ejpam-3443	223	19	set	set	NOUN
ejpam-3443	223	20	of	of	ADP
ejpam-3443	223	21	g.	g.	PROPN
ejpam-3443	223	22	consequently	consequently	ADV
ejpam-3443	223	23	,	,	PUNCT
ejpam-3443	223	24	γknce(g	γknce(g	PROPN
ejpam-3443	223	25	)	)	PUNCT
ejpam-3443	223	26	≤	≤	NUM
ejpam-3443	223	27	γce(g	γce(g	PROPN
ejpam-3443	223	28	)	)	PUNCT
ejpam-3443	223	29	and	and	CCONJ
ejpam-3443	223	30	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	223	31	)	)	PUNCT
ejpam-3443	223	32	≤	≤	PUNCT
ejpam-3443	224	1	γ+knce	γ+knce	NOUN
ejpam-3443	224	2	(	(	PUNCT
ejpam-3443	224	3	g	g	NOUN
ejpam-3443	224	4	)	)	PUNCT
ejpam-3443	224	5	.	.	PUNCT
ejpam-3443	225	1	remark	remark	PROPN
ejpam-3443	225	2	4	4	NUM
ejpam-3443	225	3	.	.	PUNCT
ejpam-3443	226	1	if	if	SCONJ
ejpam-3443	226	2	c1	c1	PROPN
ejpam-3443	226	3	,	,	PUNCT
ejpam-3443	226	4	c2	c2	PROPN
ejpam-3443	226	5	,	,	PUNCT
ejpam-3443	226	6	.	.	PUNCT
ejpam-3443	226	7	.	.	PUNCT
ejpam-3443	227	1	.	.	PUNCT
ejpam-3443	228	1	,	,	PUNCT
ejpam-3443	228	2	cn	cn	PROPN
ejpam-3443	228	3	are	be	AUX
ejpam-3443	228	4	the	the	DET
ejpam-3443	228	5	components	component	NOUN
ejpam-3443	228	6	of	of	ADP
ejpam-3443	228	7	a	a	DET
ejpam-3443	228	8	graph	graph	NOUN
ejpam-3443	228	9	g	g	NOUN
ejpam-3443	228	10	and	and	CCONJ
ejpam-3443	228	11	s	s	VERB
ejpam-3443	228	12	⊆	⊆	NUM
ejpam-3443	228	13	v	v	NOUN
ejpam-3443	228	14	(	(	PUNCT
ejpam-3443	228	15	g	g	NOUN
ejpam-3443	228	16	)	)	PUNCT
ejpam-3443	228	17	,	,	PUNCT
ejpam-3443	228	18	then	then	ADV
ejpam-3443	228	19	s	s	VERB
ejpam-3443	228	20	is	be	AUX
ejpam-3443	228	21	a	a	DET
ejpam-3443	228	22	kn	kn	NOUN
ejpam-3443	228	23	-	-	PUNCT
ejpam-3443	228	24	cost	cost	NOUN
ejpam-3443	228	25	effective	effective	ADJ
ejpam-3443	228	26	dominating	dominating	NOUN
ejpam-3443	228	27	set	set	NOUN
ejpam-3443	228	28	of	of	ADP
ejpam-3443	228	29	g	g	PROPN
ejpam-3443	228	30	if	if	SCONJ
ejpam-3443	229	1	and	and	CCONJ
ejpam-3443	229	2	only	only	ADV
ejpam-3443	229	3	if	if	SCONJ
ejpam-3443	229	4	s	s	ADP
ejpam-3443	229	5	∩	∩	ADJ
ejpam-3443	229	6	v	v	ADJ
ejpam-3443	229	7	(	(	PUNCT
ejpam-3443	229	8	ck	ck	NOUN
ejpam-3443	229	9	)	)	PUNCT
ejpam-3443	229	10	is	be	AUX
ejpam-3443	229	11	a	a	DET
ejpam-3443	229	12	kn	kn	NOUN
ejpam-3443	229	13	-	-	PUNCT
ejpam-3443	229	14	cost	cost	NOUN
ejpam-3443	229	15	effective	effective	ADJ
ejpam-3443	229	16	dominating	dominating	NOUN
ejpam-3443	229	17	set	set	NOUN
ejpam-3443	229	18	of	of	ADP
ejpam-3443	229	19	ck	ck	PROPN
ejpam-3443	229	20	for	for	ADP
ejpam-3443	229	21	all	all	PRON
ejpam-3443	229	22	k	k	NOUN
ejpam-3443	229	23	=	=	SYM
ejpam-3443	229	24	1	1	NUM
ejpam-3443	229	25	,	,	PUNCT
ejpam-3443	229	26	2	2	NUM
ejpam-3443	229	27	,	,	PUNCT
ejpam-3443	229	28	.	.	PUNCT
ejpam-3443	229	29	.	.	PUNCT
ejpam-3443	230	1	.	.	PUNCT
ejpam-3443	231	1	,	,	PUNCT
ejpam-3443	231	2	n.	n.	PROPN
ejpam-3443	231	3	lemma	lemma	PROPN
ejpam-3443	231	4	1	1	X
ejpam-3443	231	5	.	.	PUNCT
ejpam-3443	232	1	let	let	VERB
ejpam-3443	232	2	g	g	PRON
ejpam-3443	232	3	be	be	AUX
ejpam-3443	232	4	a	a	DET
ejpam-3443	232	5	connected	connected	ADJ
ejpam-3443	232	6	graph	graph	NOUN
ejpam-3443	232	7	and	and	CCONJ
ejpam-3443	232	8	h	h	NOUN
ejpam-3443	232	9	any	any	DET
ejpam-3443	232	10	graph	graph	NOUN
ejpam-3443	232	11	,	,	PUNCT
ejpam-3443	232	12	and	and	CCONJ
ejpam-3443	232	13	let	let	VERB
ejpam-3443	232	14	s	s	PRON
ejpam-3443	232	15	⊆	⊆	NUM
ejpam-3443	232	16	v	v	NOUN
ejpam-3443	232	17	(	(	PUNCT
ejpam-3443	232	18	g	g	PROPN
ejpam-3443	232	19	◦	◦	NOUN
ejpam-3443	232	20	h	h	NOUN
ejpam-3443	232	21	)	)	PUNCT
ejpam-3443	232	22	and	and	CCONJ
ejpam-3443	232	23	v	v	ADP
ejpam-3443	232	24	∈	∈	NOUN
ejpam-3443	232	25	v	v	NOUN
ejpam-3443	232	26	(	(	PUNCT
ejpam-3443	232	27	g)\s	g)\s	NOUN
ejpam-3443	232	28	.	.	PUNCT
ejpam-3443	233	1	if	if	SCONJ
ejpam-3443	233	2	s	s	NOUN
ejpam-3443	233	3	is	be	AUX
ejpam-3443	233	4	a	a	DET
ejpam-3443	233	5	cost	cost	NOUN
ejpam-3443	233	6	effective	effective	ADJ
ejpam-3443	233	7	dominating	dominating	NOUN
ejpam-3443	233	8	set	set	NOUN
ejpam-3443	233	9	of	of	ADP
ejpam-3443	233	10	g	g	PROPN
ejpam-3443	233	11	◦	◦	NOUN
ejpam-3443	233	12	h	h	NOUN
ejpam-3443	233	13	,	,	PUNCT
ejpam-3443	233	14	then	then	ADV
ejpam-3443	233	15	s∩v	s∩v	PROPN
ejpam-3443	233	16	(	(	PUNCT
ejpam-3443	233	17	hv	hv	PROPN
ejpam-3443	233	18	)	)	PUNCT
ejpam-3443	233	19	is	be	AUX
ejpam-3443	233	20	a	a	DET
ejpam-3443	233	21	k1	k1	NOUN
ejpam-3443	233	22	-	-	PUNCT
ejpam-3443	233	23	cost	cost	NOUN
ejpam-3443	233	24	effective	effective	ADJ
ejpam-3443	233	25	dominating	dominating	NOUN
ejpam-3443	233	26	set	set	NOUN
ejpam-3443	233	27	of	of	ADP
ejpam-3443	233	28	hv	hv	PROPN
ejpam-3443	233	29	.	.	PUNCT
ejpam-3443	234	1	f.jamil	f.jamil	PROPN
ejpam-3443	234	2	,	,	PUNCT
ejpam-3443	234	3	h.	h.	PROPN
ejpam-3443	234	4	nuenay	nuenay	PROPN
ejpam-3443	234	5	-	-	PUNCT
ejpam-3443	234	6	maglanque	maglanque	ADJ
ejpam-3443	234	7	/	/	SYM
ejpam-3443	234	8	eur	eur	NOUN
ejpam-3443	234	9	.	.	PUNCT
ejpam-3443	235	1	j.	j.	PROPN
ejpam-3443	235	2	pure	pure	PROPN
ejpam-3443	235	3	appl	appl	PROPN
ejpam-3443	235	4	.	.	PROPN
ejpam-3443	235	5	math	math	PROPN
ejpam-3443	235	6	,	,	PUNCT
ejpam-3443	235	7	12	12	NUM
ejpam-3443	235	8	(	(	PUNCT
ejpam-3443	235	9	3	3	NUM
ejpam-3443	235	10	)	)	PUNCT
ejpam-3443	235	11	(	(	PUNCT
ejpam-3443	235	12	2019	2019	NUM
ejpam-3443	235	13	)	)	PUNCT
ejpam-3443	235	14	,	,	PUNCT
ejpam-3443	235	15	978	978	NUM
ejpam-3443	235	16	-	-	SYM
ejpam-3443	235	17	998	998	NUM
ejpam-3443	235	18	987	987	NUM
ejpam-3443	235	19	proof	proof	NOUN
ejpam-3443	235	20	.	.	PUNCT
ejpam-3443	235	21	suppose	suppose	VERB
ejpam-3443	235	22	that	that	SCONJ
ejpam-3443	235	23	s	s	VERB
ejpam-3443	235	24	is	be	AUX
ejpam-3443	235	25	a	a	DET
ejpam-3443	235	26	cost	cost	NOUN
ejpam-3443	235	27	effective	effective	ADJ
ejpam-3443	235	28	dominating	dominating	NOUN
ejpam-3443	235	29	set	set	NOUN
ejpam-3443	235	30	of	of	ADP
ejpam-3443	235	31	g	g	NOUN
ejpam-3443	235	32	◦	◦	NOUN
ejpam-3443	235	33	h	h	NOUN
ejpam-3443	235	34	and	and	CCONJ
ejpam-3443	235	35	v	v	ADP
ejpam-3443	235	36	∈	∈	NOUN
ejpam-3443	235	37	v	v	NOUN
ejpam-3443	235	38	(	(	PUNCT
ejpam-3443	235	39	g)\s	g)\s	NOUN
ejpam-3443	235	40	.	.	PUNCT
ejpam-3443	236	1	let	let	VERB
ejpam-3443	236	2	sv	sv	INTJ
ejpam-3443	236	3	=	=	SYM
ejpam-3443	236	4	s∩v	s∩v	PROPN
ejpam-3443	236	5	(	(	PUNCT
ejpam-3443	236	6	hv	hv	PROPN
ejpam-3443	236	7	)	)	PUNCT
ejpam-3443	236	8	and	and	CCONJ
ejpam-3443	236	9	let	let	VERB
ejpam-3443	236	10	u	u	PRON
ejpam-3443	236	11	∈	∈	PROPN
ejpam-3443	236	12	sv	sv	PROPN
ejpam-3443	236	13	.	.	PUNCT
ejpam-3443	237	1	then	then	ADV
ejpam-3443	237	2	,	,	PUNCT
ejpam-3443	237	3	|nhv+v(u)∩sv|	|nhv+v(u)∩sv|	PROPN
ejpam-3443	237	4	=	=	NOUN
ejpam-3443	237	5	|ng	|ng	PRON
ejpam-3443	237	6	◦	◦	VERB
ejpam-3443	237	7	h(u)∩s|	h(u)∩s|	NOUN
ejpam-3443	237	8	≤	≤	NOUN
ejpam-3443	237	9	|ng	|ng	NOUN
ejpam-3443	237	10	◦	◦	NOUN
ejpam-3443	237	11	h(u)\s|	h(u)\s|	NOUN
ejpam-3443	237	12	=	=	SYM
ejpam-3443	237	13	|nhv+v(u	|nhv+v(u	NUM
ejpam-3443	237	14	)	)	PUNCT
ejpam-3443	237	15	\	\	PROPN
ejpam-3443	237	16	sv|	sv|	PROPN
ejpam-3443	237	17	.	.	PUNCT
ejpam-3443	237	18	theorem	theorem	VERB
ejpam-3443	237	19	6	6	NUM
ejpam-3443	237	20	.	.	PUNCT
ejpam-3443	238	1	let	let	VERB
ejpam-3443	238	2	g	g	PRON
ejpam-3443	238	3	be	be	AUX
ejpam-3443	238	4	a	a	DET
ejpam-3443	238	5	connected	connected	ADJ
ejpam-3443	238	6	graph	graph	NOUN
ejpam-3443	238	7	and	and	CCONJ
ejpam-3443	238	8	h	h	NOUN
ejpam-3443	238	9	an	an	DET
ejpam-3443	238	10	isolate	isolate	NOUN
ejpam-3443	238	11	-	-	PUNCT
ejpam-3443	238	12	free	free	ADJ
ejpam-3443	238	13	graph	graph	NOUN
ejpam-3443	238	14	of	of	ADP
ejpam-3443	238	15	order	order	NOUN
ejpam-3443	238	16	n	n	CCONJ
ejpam-3443	238	17	,	,	PUNCT
ejpam-3443	238	18	and	and	CCONJ
ejpam-3443	238	19	let	let	VERB
ejpam-3443	238	20	s	s	PRON
ejpam-3443	238	21	⊆	⊆	NUM
ejpam-3443	238	22	v	v	NOUN
ejpam-3443	238	23	(	(	PUNCT
ejpam-3443	238	24	g	g	PROPN
ejpam-3443	238	25	◦	◦	NOUN
ejpam-3443	238	26	h	h	NOUN
ejpam-3443	238	27	)	)	PUNCT
ejpam-3443	238	28	.	.	PUNCT
ejpam-3443	239	1	then	then	ADV
ejpam-3443	239	2	s	s	VERB
ejpam-3443	239	3	is	be	AUX
ejpam-3443	239	4	a	a	DET
ejpam-3443	239	5	cost	cost	NOUN
ejpam-3443	239	6	effective	effective	ADJ
ejpam-3443	239	7	dominating	dominating	NOUN
ejpam-3443	239	8	set	set	NOUN
ejpam-3443	239	9	of	of	ADP
ejpam-3443	239	10	g	g	PROPN
ejpam-3443	239	11	◦	◦	NOUN
ejpam-3443	239	12	h	h	NOUN
ejpam-3443	239	13	if	if	SCONJ
ejpam-3443	240	1	and	and	CCONJ
ejpam-3443	240	2	only	only	ADV
ejpam-3443	240	3	if	if	SCONJ
ejpam-3443	240	4	the	the	DET
ejpam-3443	240	5	following	follow	VERB
ejpam-3443	240	6	hold	hold	NOUN
ejpam-3443	240	7	:	:	PUNCT
ejpam-3443	240	8	(	(	PUNCT
ejpam-3443	240	9	i	i	NOUN
ejpam-3443	240	10	)	)	PUNCT
ejpam-3443	240	11	for	for	ADP
ejpam-3443	240	12	each	each	DET
ejpam-3443	240	13	v	v	NUM
ejpam-3443	240	14	∈	∈	PROPN
ejpam-3443	240	15	s	s	PART
ejpam-3443	240	16	∩	∩	ADJ
ejpam-3443	240	17	v	v	X
ejpam-3443	240	18	(	(	PUNCT
ejpam-3443	240	19	g	g	NOUN
ejpam-3443	240	20	)	)	PUNCT
ejpam-3443	240	21	,	,	PUNCT
ejpam-3443	240	22	s	s	VERB
ejpam-3443	240	23	∩	∩	ADJ
ejpam-3443	240	24	v	v	X
ejpam-3443	240	25	(	(	PUNCT
ejpam-3443	240	26	hv	hv	X
ejpam-3443	240	27	)	)	PUNCT
ejpam-3443	240	28	is	be	AUX
ejpam-3443	240	29	a	a	DET
ejpam-3443	240	30	cost	cost	NOUN
ejpam-3443	240	31	effective	effective	ADJ
ejpam-3443	240	32	set	set	NOUN
ejpam-3443	240	33	of	of	ADP
ejpam-3443	240	34	hv	hv	PROPN
ejpam-3443	240	35	satisfying	satisfy	VERB
ejpam-3443	240	36	|s	|s	PROPN
ejpam-3443	240	37	∩	∩	ADJ
ejpam-3443	240	38	v	v	NOUN
ejpam-3443	240	39	(	(	PUNCT
ejpam-3443	240	40	hv)|	hv)|	X
ejpam-3443	240	41	≤	≤	NUM
ejpam-3443	240	42	1	1	NUM
ejpam-3443	240	43	2	2	NUM
ejpam-3443	240	44	(	(	PUNCT
ejpam-3443	240	45	n+	n+	NUM
ejpam-3443	240	46	|ng(v	|ng(v	ADJ
ejpam-3443	240	47	)	)	PUNCT
ejpam-3443	240	48	\	\	NOUN
ejpam-3443	240	49	s|	s|	VERB
ejpam-3443	240	50	−	−	NOUN
ejpam-3443	240	51	|ng(v	|ng(v	NOUN
ejpam-3443	240	52	)	)	PUNCT
ejpam-3443	240	53	∩	∩	NOUN
ejpam-3443	240	54	s|	s|	PROPN
ejpam-3443	240	55	)	)	PUNCT
ejpam-3443	240	56	.	.	PUNCT
ejpam-3443	241	1	(	(	PUNCT
ejpam-3443	241	2	ii	ii	NOUN
ejpam-3443	241	3	)	)	PUNCT
ejpam-3443	241	4	for	for	ADP
ejpam-3443	241	5	each	each	PRON
ejpam-3443	241	6	v	v	NUM
ejpam-3443	241	7	∈	∈	PROPN
ejpam-3443	241	8	v	v	NOUN
ejpam-3443	241	9	(	(	PUNCT
ejpam-3443	241	10	g	g	NOUN
ejpam-3443	241	11	)	)	PUNCT
ejpam-3443	241	12	\	\	PROPN
ejpam-3443	242	1	s	s	PROPN
ejpam-3443	242	2	,	,	PUNCT
ejpam-3443	242	3	s	s	PART
ejpam-3443	242	4	∩	∩	ADJ
ejpam-3443	242	5	v	v	X
ejpam-3443	242	6	(	(	PUNCT
ejpam-3443	242	7	hv	hv	X
ejpam-3443	242	8	)	)	PUNCT
ejpam-3443	242	9	is	be	AUX
ejpam-3443	242	10	a	a	DET
ejpam-3443	242	11	k1	k1	NOUN
ejpam-3443	242	12	-	-	PUNCT
ejpam-3443	242	13	cost	cost	NOUN
ejpam-3443	242	14	effective	effective	ADJ
ejpam-3443	242	15	dominating	dominating	NOUN
ejpam-3443	242	16	set	set	NOUN
ejpam-3443	242	17	of	of	ADP
ejpam-3443	242	18	hv	hv	PROPN
ejpam-3443	242	19	proof	proof	NOUN
ejpam-3443	242	20	.	.	PUNCT
ejpam-3443	243	1	suppose	suppose	VERB
ejpam-3443	243	2	that	that	SCONJ
ejpam-3443	243	3	s	s	VERB
ejpam-3443	243	4	is	be	AUX
ejpam-3443	243	5	a	a	DET
ejpam-3443	243	6	cost	cost	NOUN
ejpam-3443	243	7	effective	effective	ADJ
ejpam-3443	243	8	dominating	dominating	NOUN
ejpam-3443	243	9	set	set	NOUN
ejpam-3443	243	10	of	of	ADP
ejpam-3443	243	11	g	g	PROPN
ejpam-3443	243	12	◦	◦	PROPN
ejpam-3443	243	13	h.	h.	NOUN
ejpam-3443	243	14	by	by	ADP
ejpam-3443	243	15	corollary	corollary	ADJ
ejpam-3443	243	16	4	4	NUM
ejpam-3443	243	17	,	,	PUNCT
ejpam-3443	243	18	s	s	VERB
ejpam-3443	243	19	∩	∩	ADJ
ejpam-3443	243	20	v	v	X
ejpam-3443	243	21	(	(	PUNCT
ejpam-3443	243	22	hv	hv	PROPN
ejpam-3443	243	23	+	+	PROPN
ejpam-3443	243	24	v	v	NOUN
ejpam-3443	243	25	)	)	PUNCT
ejpam-3443	243	26	is	be	AUX
ejpam-3443	243	27	a	a	DET
ejpam-3443	243	28	dominating	dominating	NOUN
ejpam-3443	243	29	set	set	NOUN
ejpam-3443	243	30	of	of	ADP
ejpam-3443	243	31	hv	hv	PROPN
ejpam-3443	243	32	+	+	X
ejpam-3443	243	33	v	v	NOUN
ejpam-3443	243	34	for	for	ADP
ejpam-3443	243	35	each	each	DET
ejpam-3443	243	36	v	v	NUM
ejpam-3443	243	37	∈	∈	PROPN
ejpam-3443	243	38	v	v	NOUN
ejpam-3443	243	39	(	(	PUNCT
ejpam-3443	243	40	g	g	NOUN
ejpam-3443	243	41	)	)	PUNCT
ejpam-3443	243	42	.	.	PUNCT
ejpam-3443	244	1	let	let	VERB
ejpam-3443	244	2	v	v	NUM
ejpam-3443	244	3	∈	∈	NOUN
ejpam-3443	244	4	s	s	PART
ejpam-3443	244	5	∩	∩	ADJ
ejpam-3443	244	6	v	v	X
ejpam-3443	244	7	(	(	PUNCT
ejpam-3443	244	8	g	g	NOUN
ejpam-3443	244	9	)	)	PUNCT
ejpam-3443	244	10	,	,	PUNCT
ejpam-3443	244	11	and	and	CCONJ
ejpam-3443	244	12	put	put	VERB
ejpam-3443	244	13	sv	sv	NOUN
ejpam-3443	244	14	=	=	SYM
ejpam-3443	244	15	s	s	PROPN
ejpam-3443	244	16	∩	∩	ADJ
ejpam-3443	244	17	v	v	X
ejpam-3443	244	18	(	(	PUNCT
ejpam-3443	244	19	hv	hv	PROPN
ejpam-3443	244	20	)	)	PUNCT
ejpam-3443	244	21	.	.	PUNCT
ejpam-3443	245	1	we	we	PRON
ejpam-3443	245	2	claim	claim	VERB
ejpam-3443	245	3	that	that	SCONJ
ejpam-3443	245	4	sv	sv	PROPN
ejpam-3443	245	5	is	be	AUX
ejpam-3443	245	6	a	a	DET
ejpam-3443	245	7	cost	cost	NOUN
ejpam-3443	245	8	effective	effective	ADJ
ejpam-3443	245	9	set	set	NOUN
ejpam-3443	245	10	of	of	ADP
ejpam-3443	245	11	hv	hv	PROPN
ejpam-3443	245	12	.	.	PUNCT
ejpam-3443	246	1	let	let	VERB
ejpam-3443	246	2	u	u	PRON
ejpam-3443	246	3	∈	∈	PROPN
ejpam-3443	246	4	sv	sv	PROPN
ejpam-3443	246	5	.	.	PUNCT
ejpam-3443	247	1	then	then	ADV
ejpam-3443	247	2	1	1	NUM
ejpam-3443	247	3	+	+	NUM
ejpam-3443	247	4	|nhv(u	|nhv(u	NOUN
ejpam-3443	247	5	)	)	PUNCT
ejpam-3443	247	6	∩	∩	NOUN
ejpam-3443	247	7	sv|	sv|	ADJ
ejpam-3443	247	8	=	=	SYM
ejpam-3443	247	9	|nhv+v(u	|nhv+v(u	NUM
ejpam-3443	247	10	)	)	PUNCT
ejpam-3443	247	11	∩	∩	NOUN
ejpam-3443	247	12	s|	s|	NOUN
ejpam-3443	247	13	=	=	SYM
ejpam-3443	247	14	|ng	|ng	VERB
ejpam-3443	247	15	◦	◦	NOUN
ejpam-3443	247	16	h(u	h(u	NOUN
ejpam-3443	247	17	)	)	PUNCT
ejpam-3443	247	18	∩	∩	NOUN
ejpam-3443	247	19	s|	s|	VERB
ejpam-3443	247	20	≤	≤	NUM
ejpam-3443	247	21	|ng	|ng	NOUN
ejpam-3443	247	22	◦	◦	NOUN
ejpam-3443	247	23	h(u	h(u	NOUN
ejpam-3443	247	24	)	)	PUNCT
ejpam-3443	248	1	\	\	PROPN
ejpam-3443	248	2	s|	s|	NOUN
ejpam-3443	248	3	=	=	SYM
ejpam-3443	248	4	|nhv(u	|nhv(u	NOUN
ejpam-3443	248	5	)	)	PUNCT
ejpam-3443	248	6	\	\	NOUN
ejpam-3443	249	1	sv|	sv|	PROPN
ejpam-3443	249	2	.	.	PUNCT
ejpam-3443	250	1	necessarily	necessarily	ADV
ejpam-3443	250	2	,	,	PUNCT
ejpam-3443	250	3	|nhv(u	|nhv(u	NOUN
ejpam-3443	250	4	)	)	PUNCT
ejpam-3443	250	5	∩	∩	NOUN
ejpam-3443	250	6	sv|	sv|	ADJ
ejpam-3443	250	7	<	<	X
ejpam-3443	250	8	|nhv(u	|nhv(u	NOUN
ejpam-3443	250	9	)	)	PUNCT
ejpam-3443	250	10	\	\	NOUN
ejpam-3443	250	11	sv|	sv|	PROPN
ejpam-3443	250	12	.	.	PUNCT
ejpam-3443	251	1	since	since	SCONJ
ejpam-3443	251	2	u	u	NOUN
ejpam-3443	251	3	is	be	AUX
ejpam-3443	251	4	arbitrary	arbitrary	ADJ
ejpam-3443	251	5	,	,	PUNCT
ejpam-3443	251	6	sv	sv	PROPN
ejpam-3443	251	7	is	be	AUX
ejpam-3443	251	8	a	a	DET
ejpam-3443	251	9	cost	cost	NOUN
ejpam-3443	251	10	effective	effective	ADJ
ejpam-3443	251	11	set	set	NOUN
ejpam-3443	251	12	of	of	ADP
ejpam-3443	251	13	hv	hv	PROPN
ejpam-3443	251	14	.	.	PUNCT
ejpam-3443	252	1	further	far	ADV
ejpam-3443	252	2	,	,	PUNCT
ejpam-3443	252	3	since	since	SCONJ
ejpam-3443	252	4	v	v	NUM
ejpam-3443	252	5	∈	∈	NOUN
ejpam-3443	252	6	s	s	NOUN
ejpam-3443	252	7	,	,	PUNCT
ejpam-3443	252	8	|ng(v	|ng(v	ADJ
ejpam-3443	252	9	)	)	PUNCT
ejpam-3443	252	10	∩	∩	NOUN
ejpam-3443	252	11	s|+	s|+	PROPN
ejpam-3443	252	12	|sv|	|sv|	NOUN
ejpam-3443	252	13	=	=	PUNCT
ejpam-3443	252	14	|ng	|ng	VERB
ejpam-3443	252	15	◦	◦	NOUN
ejpam-3443	252	16	h(v	h(v	ADJ
ejpam-3443	252	17	)	)	PUNCT
ejpam-3443	252	18	∩	∩	NOUN
ejpam-3443	252	19	s|	s|	VERB
ejpam-3443	252	20	≤	≤	NUM
ejpam-3443	252	21	|ng	|ng	VERB
ejpam-3443	252	22	◦	◦	NOUN
ejpam-3443	252	23	h(v	h(v	NOUN
ejpam-3443	252	24	)	)	PUNCT
ejpam-3443	252	25	\	\	NOUN
ejpam-3443	253	1	s|	s|	NOUN
ejpam-3443	253	2	=	=	SYM
ejpam-3443	253	3	|ng(v	|ng(v	X
ejpam-3443	253	4	)	)	PUNCT
ejpam-3443	253	5	\	\	NOUN
ejpam-3443	254	1	s|+	s|+	PROPN
ejpam-3443	254	2	n−	n−	NOUN
ejpam-3443	254	3	|sv|	|sv|	VERB
ejpam-3443	254	4	,	,	PUNCT
ejpam-3443	254	5	or	or	CCONJ
ejpam-3443	254	6	equivalently	equivalently	ADV
ejpam-3443	254	7	,	,	PUNCT
ejpam-3443	254	8	|sv|	|sv|	PROPN
ejpam-3443	254	9	≤	≤	NUM
ejpam-3443	254	10	1	1	NUM
ejpam-3443	254	11	2	2	NUM
ejpam-3443	254	12	(	(	PUNCT
ejpam-3443	254	13	n+	n+	NUM
ejpam-3443	254	14	|ng(v	|ng(v	ADJ
ejpam-3443	254	15	)	)	PUNCT
ejpam-3443	254	16	\	\	NOUN
ejpam-3443	254	17	s|	s|	VERB
ejpam-3443	254	18	−	−	NOUN
ejpam-3443	254	19	|ng(v	|ng(v	NOUN
ejpam-3443	254	20	)	)	PUNCT
ejpam-3443	254	21	∩	∩	NOUN
ejpam-3443	254	22	s|	s|	NOUN
ejpam-3443	254	23	)	)	PUNCT
ejpam-3443	254	24	.	.	PUNCT
ejpam-3443	255	1	this	this	PRON
ejpam-3443	255	2	establishes	establish	VERB
ejpam-3443	255	3	property	property	NOUN
ejpam-3443	255	4	(	(	PUNCT
ejpam-3443	255	5	i	i	NOUN
ejpam-3443	255	6	)	)	PUNCT
ejpam-3443	255	7	.	.	PUNCT
ejpam-3443	256	1	property	property	NOUN
ejpam-3443	256	2	(	(	PUNCT
ejpam-3443	256	3	ii	ii	NOUN
ejpam-3443	256	4	)	)	PUNCT
ejpam-3443	256	5	follows	follow	VERB
ejpam-3443	256	6	immediately	immediately	ADV
ejpam-3443	256	7	from	from	ADP
ejpam-3443	256	8	lemma	lemma	PROPN
ejpam-3443	256	9	1	1	NUM
ejpam-3443	256	10	.	.	PUNCT
ejpam-3443	256	11	conversely	conversely	ADV
ejpam-3443	256	12	,	,	PUNCT
ejpam-3443	256	13	suppose	suppose	VERB
ejpam-3443	256	14	that	that	SCONJ
ejpam-3443	256	15	s	s	AUX
ejpam-3443	256	16	satisfies	satisfie	NOUN
ejpam-3443	256	17	all	all	DET
ejpam-3443	256	18	the	the	DET
ejpam-3443	256	19	above	above	ADJ
ejpam-3443	256	20	prescribed	prescribed	ADJ
ejpam-3443	256	21	properties	property	NOUN
ejpam-3443	256	22	.	.	PUNCT
ejpam-3443	257	1	in	in	ADP
ejpam-3443	257	2	any	any	DET
ejpam-3443	257	3	case	case	NOUN
ejpam-3443	257	4	,	,	PUNCT
ejpam-3443	257	5	for	for	ADP
ejpam-3443	257	6	v	v	ADP
ejpam-3443	257	7	∈	∈	PROPN
ejpam-3443	257	8	v	v	NOUN
ejpam-3443	257	9	(	(	PUNCT
ejpam-3443	257	10	g	g	NOUN
ejpam-3443	257	11	)	)	PUNCT
ejpam-3443	257	12	,	,	PUNCT
ejpam-3443	257	13	s	s	VERB
ejpam-3443	257	14	∩	∩	ADJ
ejpam-3443	257	15	v	v	X
ejpam-3443	257	16	(	(	PUNCT
ejpam-3443	257	17	hv	hv	PROPN
ejpam-3443	257	18	+	+	PROPN
ejpam-3443	257	19	v	v	NOUN
ejpam-3443	257	20	)	)	PUNCT
ejpam-3443	257	21	is	be	AUX
ejpam-3443	257	22	a	a	DET
ejpam-3443	257	23	dominating	dominating	NOUN
ejpam-3443	257	24	set	set	NOUN
ejpam-3443	257	25	of	of	ADP
ejpam-3443	257	26	hv	hv	PROPN
ejpam-3443	257	27	+	+	X
ejpam-3443	257	28	v.	v.	CCONJ
ejpam-3443	257	29	thus	thus	ADV
ejpam-3443	257	30	,	,	PUNCT
ejpam-3443	257	31	s	s	VERB
ejpam-3443	257	32	is	be	AUX
ejpam-3443	257	33	a	a	DET
ejpam-3443	257	34	dominating	dominating	NOUN
ejpam-3443	257	35	set	set	NOUN
ejpam-3443	257	36	of	of	ADP
ejpam-3443	257	37	g	g	PROPN
ejpam-3443	257	38	◦	◦	NOUN
ejpam-3443	257	39	h	h	NOUN
ejpam-3443	257	40	by	by	ADP
ejpam-3443	257	41	theorem	theorem	NOUN
ejpam-3443	257	42	5	5	NUM
ejpam-3443	257	43	.	.	PUNCT
ejpam-3443	258	1	let	let	VERB
ejpam-3443	258	2	u	u	PRON
ejpam-3443	258	3	∈	∈	PROPN
ejpam-3443	258	4	s.	s.	PROPN
ejpam-3443	258	5	in	in	ADP
ejpam-3443	258	6	view	view	NOUN
ejpam-3443	258	7	of	of	ADP
ejpam-3443	258	8	corollary	corollary	ADJ
ejpam-3443	258	9	4	4	NUM
ejpam-3443	258	10	,	,	PUNCT
ejpam-3443	258	11	u	u	PROPN
ejpam-3443	258	12	∈	∈	PROPN
ejpam-3443	258	13	s	s	PART
ejpam-3443	258	14	∩	∩	ADJ
ejpam-3443	258	15	v	v	X
ejpam-3443	258	16	(	(	PUNCT
ejpam-3443	258	17	hv	hv	PROPN
ejpam-3443	258	18	+	+	PROPN
ejpam-3443	258	19	v	v	NOUN
ejpam-3443	258	20	)	)	PUNCT
ejpam-3443	258	21	for	for	ADP
ejpam-3443	258	22	some	some	DET
ejpam-3443	258	23	v	v	ADP
ejpam-3443	258	24	∈	∈	PROPN
ejpam-3443	258	25	v	v	NOUN
ejpam-3443	258	26	(	(	PUNCT
ejpam-3443	258	27	g	g	NOUN
ejpam-3443	258	28	)	)	PUNCT
ejpam-3443	258	29	.	.	PUNCT
ejpam-3443	259	1	suppose	suppose	VERB
ejpam-3443	259	2	that	that	SCONJ
ejpam-3443	259	3	v	v	X
ejpam-3443	259	4	∈	∈	PRON
ejpam-3443	259	5	s.	s.	PROPN
ejpam-3443	259	6	by	by	ADP
ejpam-3443	259	7	property	property	NOUN
ejpam-3443	259	8	(	(	PUNCT
ejpam-3443	259	9	i	i	NOUN
ejpam-3443	259	10	)	)	PUNCT
ejpam-3443	259	11	,	,	PUNCT
ejpam-3443	259	12	sv	sv	PROPN
ejpam-3443	260	1	=	=	SYM
ejpam-3443	260	2	s	s	PROPN
ejpam-3443	260	3	∩	∩	ADJ
ejpam-3443	260	4	v	v	X
ejpam-3443	260	5	(	(	PUNCT
ejpam-3443	260	6	hv	hv	X
ejpam-3443	260	7	)	)	PUNCT
ejpam-3443	260	8	is	be	AUX
ejpam-3443	260	9	a	a	DET
ejpam-3443	260	10	cost	cost	NOUN
ejpam-3443	260	11	effective	effective	ADJ
ejpam-3443	260	12	set	set	NOUN
ejpam-3443	260	13	of	of	ADP
ejpam-3443	260	14	hv	hv	PROPN
ejpam-3443	260	15	satisfying	satisfy	VERB
ejpam-3443	260	16	|sv|	|sv|	PROPN
ejpam-3443	260	17	≤	≤	ADJ
ejpam-3443	260	18	1	1	NUM
ejpam-3443	260	19	2	2	NUM
ejpam-3443	260	20	(	(	PUNCT
ejpam-3443	260	21	n+	n+	NUM
ejpam-3443	261	1	|ng(v	|ng(v	ADJ
ejpam-3443	261	2	)	)	PUNCT
ejpam-3443	261	3	\	\	NOUN
ejpam-3443	261	4	s|	s|	VERB
ejpam-3443	261	5	−	−	NOUN
ejpam-3443	261	6	|ng(v	|ng(v	NOUN
ejpam-3443	261	7	)	)	PUNCT
ejpam-3443	261	8	∩	∩	NOUN
ejpam-3443	261	9	s|	s|	NOUN
ejpam-3443	261	10	)	)	PUNCT
ejpam-3443	261	11	.	.	PUNCT
ejpam-3443	262	1	if	if	SCONJ
ejpam-3443	262	2	u	u	PROPN
ejpam-3443	262	3	=	=	PROPN
ejpam-3443	262	4	v	v	NOUN
ejpam-3443	262	5	,	,	PUNCT
ejpam-3443	262	6	then	then	ADV
ejpam-3443	262	7	|ng	|ng	VERB
ejpam-3443	262	8	◦	◦	NOUN
ejpam-3443	262	9	h(u	h(u	NOUN
ejpam-3443	262	10	)	)	PUNCT
ejpam-3443	262	11	∩	∩	NOUN
ejpam-3443	262	12	s|	s|	VERB
ejpam-3443	262	13	=	=	SYM
ejpam-3443	262	14	|ng(u	|ng(u	X
ejpam-3443	262	15	)	)	PUNCT
ejpam-3443	262	16	∩	∩	NOUN
ejpam-3443	262	17	s|+	s|+	PROPN
ejpam-3443	262	18	|sv|	|sv|	PROPN
ejpam-3443	262	19	≤	≤	ADJ
ejpam-3443	262	20	|ng(u	|ng(u	NUM
ejpam-3443	262	21	)	)	PUNCT
ejpam-3443	262	22	∩	∩	NOUN
ejpam-3443	262	23	s|+	s|+	NOUN
ejpam-3443	262	24	n+	n+	NUM
ejpam-3443	262	25	|ng(v	|ng(v	NOUN
ejpam-3443	262	26	)	)	PUNCT
ejpam-3443	262	27	\	\	NOUN
ejpam-3443	262	28	s|	s|	VERB
ejpam-3443	262	29	−	−	PROPN
ejpam-3443	262	30	|ng(u	|ng(u	NUM
ejpam-3443	262	31	)	)	PUNCT
ejpam-3443	262	32	∩	∩	NOUN
ejpam-3443	262	33	s|	s|	VERB
ejpam-3443	262	34	−	−	PROPN
ejpam-3443	262	35	|sv|	|sv|	NOUN
ejpam-3443	262	36	=	=	SYM
ejpam-3443	262	37	|ng(v	|ng(v	PROPN
ejpam-3443	262	38	)	)	PUNCT
ejpam-3443	262	39	\	\	NOUN
ejpam-3443	263	1	s|+	s|+	PROPN
ejpam-3443	263	2	|v	|v	PROPN
ejpam-3443	263	3	(	(	PUNCT
ejpam-3443	263	4	hv	hv	NOUN
ejpam-3443	263	5	)	)	PUNCT
ejpam-3443	263	6	\	\	PUNCT
ejpam-3443	264	1	sv|	sv|	PROPN
ejpam-3443	264	2	f.jamil	f.jamil	PROPN
ejpam-3443	264	3	,	,	PUNCT
ejpam-3443	264	4	h.	h.	PROPN
ejpam-3443	264	5	nuenay	nuenay	PROPN
ejpam-3443	264	6	-	-	PUNCT
ejpam-3443	264	7	maglanque	maglanque	ADJ
ejpam-3443	264	8	/	/	SYM
ejpam-3443	264	9	eur	eur	NOUN
ejpam-3443	264	10	.	.	PUNCT
ejpam-3443	265	1	j.	j.	PROPN
ejpam-3443	265	2	pure	pure	PROPN
ejpam-3443	265	3	appl	appl	PROPN
ejpam-3443	265	4	.	.	PROPN
ejpam-3443	265	5	math	math	PROPN
ejpam-3443	265	6	,	,	PUNCT
ejpam-3443	265	7	12	12	NUM
ejpam-3443	265	8	(	(	PUNCT
ejpam-3443	265	9	3	3	NUM
ejpam-3443	265	10	)	)	PUNCT
ejpam-3443	265	11	(	(	PUNCT
ejpam-3443	265	12	2019	2019	NUM
ejpam-3443	265	13	)	)	PUNCT
ejpam-3443	265	14	,	,	PUNCT
ejpam-3443	265	15	978	978	NUM
ejpam-3443	265	16	-	-	SYM
ejpam-3443	265	17	998	998	NUM
ejpam-3443	265	18	988	988	NUM
ejpam-3443	265	19	=	=	SYM
ejpam-3443	265	20	|ng	|ng	NOUN
ejpam-3443	265	21	◦	◦	NOUN
ejpam-3443	265	22	h(u	h(u	NOUN
ejpam-3443	265	23	)	)	PUNCT
ejpam-3443	265	24	\	\	PROPN
ejpam-3443	266	1	s|	s|	PROPN
ejpam-3443	266	2	.	.	PUNCT
ejpam-3443	267	1	if	if	SCONJ
ejpam-3443	267	2	u	u	PROPN
ejpam-3443	267	3	∈	∈	PROPN
ejpam-3443	267	4	sv	sv	PROPN
ejpam-3443	267	5	,	,	PUNCT
ejpam-3443	267	6	then	then	ADV
ejpam-3443	267	7	|ng	|ng	VERB
ejpam-3443	267	8	◦	◦	NOUN
ejpam-3443	267	9	h(u	h(u	NOUN
ejpam-3443	267	10	)	)	PUNCT
ejpam-3443	267	11	∩	∩	NOUN
ejpam-3443	267	12	s|	s|	NOUN
ejpam-3443	267	13	=	=	SYM
ejpam-3443	267	14	|nhv(u	|nhv(u	NOUN
ejpam-3443	267	15	)	)	PUNCT
ejpam-3443	267	16	∩	∩	NOUN
ejpam-3443	267	17	sv|	sv|	ADJ
ejpam-3443	267	18	≤	≤	NUM
ejpam-3443	267	19	|nhv(u	|nhv(u	NOUN
ejpam-3443	267	20	)	)	PUNCT
ejpam-3443	267	21	\	\	PUNCT
ejpam-3443	268	1	sv|	sv|	NOUN
ejpam-3443	268	2	=	=	SYM
ejpam-3443	268	3	|ng	|ng	VERB
ejpam-3443	268	4	◦	◦	NOUN
ejpam-3443	268	5	h(u	h(u	NOUN
ejpam-3443	268	6	)	)	PUNCT
ejpam-3443	268	7	\	\	PROPN
ejpam-3443	268	8	s|	s|	PROPN
ejpam-3443	268	9	.	.	PUNCT
ejpam-3443	269	1	now	now	ADV
ejpam-3443	269	2	,	,	PUNCT
ejpam-3443	269	3	suppose	suppose	VERB
ejpam-3443	269	4	that	that	SCONJ
ejpam-3443	269	5	v	v	NOUN
ejpam-3443	269	6	/∈	/∈	PUNCT
ejpam-3443	269	7	s.	s.	PROPN
ejpam-3443	269	8	then	then	ADV
ejpam-3443	269	9	,	,	PUNCT
ejpam-3443	269	10	by	by	ADP
ejpam-3443	269	11	property	property	NOUN
ejpam-3443	269	12	(	(	PUNCT
ejpam-3443	269	13	ii	ii	NOUN
ejpam-3443	269	14	)	)	PUNCT
ejpam-3443	269	15	,	,	PUNCT
ejpam-3443	269	16	sv	sv	PROPN
ejpam-3443	269	17	=	=	SYM
ejpam-3443	269	18	s	s	PROPN
ejpam-3443	269	19	∩	∩	ADJ
ejpam-3443	269	20	v	v	X
ejpam-3443	269	21	(	(	PUNCT
ejpam-3443	269	22	hv	hv	X
ejpam-3443	269	23	)	)	PUNCT
ejpam-3443	269	24	is	be	AUX
ejpam-3443	269	25	a	a	DET
ejpam-3443	269	26	k1	k1	NOUN
ejpam-3443	269	27	-	-	PUNCT
ejpam-3443	269	28	cost	cost	NOUN
ejpam-3443	269	29	effective	effective	ADJ
ejpam-3443	269	30	dominating	dominating	NOUN
ejpam-3443	269	31	set	set	NOUN
ejpam-3443	269	32	of	of	ADP
ejpam-3443	269	33	hv	hv	PROPN
ejpam-3443	269	34	.	.	PUNCT
ejpam-3443	270	1	since	since	SCONJ
ejpam-3443	270	2	ng	ng	PROPN
ejpam-3443	270	3	◦	◦	PROPN
ejpam-3443	270	4	h(u)∩s	h(u)∩s	NOUN
ejpam-3443	270	5	=	=	PUNCT
ejpam-3443	270	6	nhv+v(u)∩sv	nhv+v(u)∩sv	NOUN
ejpam-3443	270	7	and	and	CCONJ
ejpam-3443	270	8	ng	ng	PROPN
ejpam-3443	270	9	◦	◦	NOUN
ejpam-3443	270	10	h(u)\s	h(u)\s	NOUN
ejpam-3443	270	11	=	=	SYM
ejpam-3443	270	12	nhv+v(u)\	nhv+v(u)\	ADV
ejpam-3443	270	13	sv	sv	INTJ
ejpam-3443	270	14	,	,	PUNCT
ejpam-3443	270	15	the	the	DET
ejpam-3443	270	16	desired	desire	VERB
ejpam-3443	270	17	inequality	inequality	NOUN
ejpam-3443	270	18	follows	follow	VERB
ejpam-3443	270	19	.	.	PUNCT
ejpam-3443	271	1	therefore	therefore	ADV
ejpam-3443	271	2	,	,	PUNCT
ejpam-3443	271	3	s	s	VERB
ejpam-3443	271	4	is	be	AUX
ejpam-3443	271	5	a	a	DET
ejpam-3443	271	6	cost	cost	NOUN
ejpam-3443	271	7	effective	effective	ADJ
ejpam-3443	271	8	set	set	NOUN
ejpam-3443	271	9	of	of	ADP
ejpam-3443	271	10	g	g	PROPN
ejpam-3443	271	11	◦	◦	PROPN
ejpam-3443	271	12	h.	h.	PROPN
ejpam-3443	271	13	remark	remark	NOUN
ejpam-3443	271	14	5	5	NUM
ejpam-3443	271	15	.	.	PUNCT
ejpam-3443	272	1	the	the	DET
ejpam-3443	272	2	conclusion	conclusion	NOUN
ejpam-3443	272	3	in	in	ADP
ejpam-3443	272	4	theorem	theorem	NOUN
ejpam-3443	272	5	6	6	NUM
ejpam-3443	272	6	still	still	ADV
ejpam-3443	272	7	holds	hold	VERB
ejpam-3443	272	8	even	even	ADV
ejpam-3443	272	9	if	if	SCONJ
ejpam-3443	272	10	the	the	DET
ejpam-3443	272	11	graph	graph	NOUN
ejpam-3443	272	12	h	h	NOUN
ejpam-3443	272	13	contains	contain	VERB
ejpam-3443	272	14	an	an	DET
ejpam-3443	272	15	isolated	isolated	ADJ
ejpam-3443	272	16	vertex	vertex	NOUN
ejpam-3443	272	17	.	.	PUNCT
ejpam-3443	273	1	suppose	suppose	VERB
ejpam-3443	273	2	that	that	SCONJ
ejpam-3443	273	3	u	u	PROPN
ejpam-3443	273	4	is	be	AUX
ejpam-3443	273	5	an	an	DET
ejpam-3443	273	6	isolated	isolated	ADJ
ejpam-3443	273	7	vertex	vertex	NOUN
ejpam-3443	273	8	of	of	ADP
ejpam-3443	273	9	h.	h.	PROPN
ejpam-3443	273	10	for	for	ADP
ejpam-3443	273	11	v	v	NOUN
ejpam-3443	273	12	∈	∈	PROPN
ejpam-3443	273	13	s∩v	s∩v	NOUN
ejpam-3443	273	14	(	(	PUNCT
ejpam-3443	273	15	g	g	NOUN
ejpam-3443	273	16	)	)	PUNCT
ejpam-3443	273	17	,	,	PUNCT
ejpam-3443	273	18	u	u	NOUN
ejpam-3443	273	19	/∈	/∈	INTJ
ejpam-3443	273	20	s∩v	s∩v	PROPN
ejpam-3443	273	21	(	(	PUNCT
ejpam-3443	273	22	hv	hv	PROPN
ejpam-3443	273	23	)	)	PUNCT
ejpam-3443	273	24	.	.	PUNCT
ejpam-3443	274	1	in	in	ADP
ejpam-3443	274	2	fact	fact	NOUN
ejpam-3443	274	3	,	,	PUNCT
ejpam-3443	274	4	if	if	SCONJ
ejpam-3443	274	5	h	h	NOUN
ejpam-3443	274	6	is	be	AUX
ejpam-3443	274	7	an	an	DET
ejpam-3443	274	8	empty	empty	ADJ
ejpam-3443	274	9	graph	graph	NOUN
ejpam-3443	274	10	,	,	PUNCT
ejpam-3443	274	11	then	then	ADV
ejpam-3443	274	12	s	s	VERB
ejpam-3443	274	13	∩v	∩v	NOUN
ejpam-3443	274	14	(	(	PUNCT
ejpam-3443	274	15	hv	hv	NOUN
ejpam-3443	274	16	)	)	PUNCT
ejpam-3443	274	17	=	=	NOUN
ejpam-3443	274	18	∅	∅	NOUN
ejpam-3443	274	19	which	which	PRON
ejpam-3443	274	20	is	be	AUX
ejpam-3443	274	21	a	a	DET
ejpam-3443	274	22	cost	cost	NOUN
ejpam-3443	274	23	effective	effective	ADJ
ejpam-3443	274	24	set	set	NOUN
ejpam-3443	274	25	,	,	PUNCT
ejpam-3443	274	26	and	and	CCONJ
ejpam-3443	274	27	the	the	DET
ejpam-3443	274	28	claim	claim	NOUN
ejpam-3443	274	29	in	in	ADP
ejpam-3443	274	30	the	the	DET
ejpam-3443	274	31	necessity	necessity	NOUN
ejpam-3443	274	32	part	part	NOUN
ejpam-3443	274	33	holds	hold	VERB
ejpam-3443	274	34	.	.	PUNCT
ejpam-3443	275	1	lemma	lemma	PROPN
ejpam-3443	275	2	2	2	X
ejpam-3443	275	3	.	.	PUNCT
ejpam-3443	276	1	let	let	VERB
ejpam-3443	276	2	g	g	PRON
ejpam-3443	276	3	be	be	AUX
ejpam-3443	276	4	an	an	DET
ejpam-3443	276	5	isolate	isolate	NOUN
ejpam-3443	276	6	-	-	PUNCT
ejpam-3443	276	7	free	free	ADJ
ejpam-3443	276	8	graph	graph	NOUN
ejpam-3443	276	9	.	.	PUNCT
ejpam-3443	277	1	every	every	DET
ejpam-3443	277	2	cost	cost	NOUN
ejpam-3443	277	3	effective	effective	ADJ
ejpam-3443	277	4	set	set	NOUN
ejpam-3443	277	5	of	of	ADP
ejpam-3443	277	6	maximum	maximum	ADJ
ejpam-3443	277	7	cardinality	cardinality	NOUN
ejpam-3443	277	8	is	be	AUX
ejpam-3443	277	9	a	a	DET
ejpam-3443	277	10	dominating	dominating	NOUN
ejpam-3443	277	11	set	set	NOUN
ejpam-3443	277	12	of	of	ADP
ejpam-3443	277	13	g.	g.	PROPN
ejpam-3443	277	14	proof	proof	PROPN
ejpam-3443	277	15	.	.	PUNCT
ejpam-3443	278	1	let	let	VERB
ejpam-3443	278	2	s	s	PRON
ejpam-3443	278	3	⊆	⊆	NUM
ejpam-3443	278	4	v	v	NOUN
ejpam-3443	278	5	(	(	PUNCT
ejpam-3443	278	6	g	g	NOUN
ejpam-3443	278	7	)	)	PUNCT
ejpam-3443	278	8	be	be	AUX
ejpam-3443	278	9	a	a	DET
ejpam-3443	278	10	cost	cost	NOUN
ejpam-3443	278	11	effective	effective	ADJ
ejpam-3443	278	12	set	set	NOUN
ejpam-3443	278	13	of	of	ADP
ejpam-3443	278	14	g	g	NOUN
ejpam-3443	278	15	of	of	ADP
ejpam-3443	278	16	maximum	maximum	ADJ
ejpam-3443	278	17	cardinality	cardinality	NOUN
ejpam-3443	278	18	.	.	PUNCT
ejpam-3443	279	1	suppose	suppose	VERB
ejpam-3443	279	2	that	that	SCONJ
ejpam-3443	279	3	s	s	VERB
ejpam-3443	279	4	is	be	AUX
ejpam-3443	279	5	not	not	PART
ejpam-3443	279	6	a	a	DET
ejpam-3443	279	7	dominating	dominating	NOUN
ejpam-3443	279	8	set	set	NOUN
ejpam-3443	279	9	of	of	ADP
ejpam-3443	279	10	g	g	NOUN
ejpam-3443	279	11	,	,	PUNCT
ejpam-3443	279	12	and	and	CCONJ
ejpam-3443	279	13	let	let	VERB
ejpam-3443	279	14	v	v	NUM
ejpam-3443	279	15	∈	∈	PROPN
ejpam-3443	279	16	v	v	NOUN
ejpam-3443	279	17	(	(	PUNCT
ejpam-3443	279	18	g	g	NOUN
ejpam-3443	279	19	)	)	PUNCT
ejpam-3443	279	20	\ng[s	\ng[s	PROPN
ejpam-3443	279	21	]	]	PUNCT
ejpam-3443	279	22	.	.	PUNCT
ejpam-3443	280	1	define	define	VERB
ejpam-3443	280	2	s∗	s∗	PROPN
ejpam-3443	280	3	=	=	SYM
ejpam-3443	280	4	s	s	NOUN
ejpam-3443	280	5	∪	∪	X
ejpam-3443	280	6	{	{	PUNCT
ejpam-3443	280	7	v	v	NOUN
ejpam-3443	280	8	}	}	PUNCT
ejpam-3443	280	9	.	.	PUNCT
ejpam-3443	281	1	for	for	ADP
ejpam-3443	281	2	each	each	DET
ejpam-3443	281	3	u	u	PROPN
ejpam-3443	281	4	∈	∈	PROPN
ejpam-3443	281	5	s	s	PROPN
ejpam-3443	281	6	,	,	PUNCT
ejpam-3443	281	7	ng(u)∩s∗	ng(u)∩s∗	PROPN
ejpam-3443	281	8	=	=	PROPN
ejpam-3443	281	9	ng(u)∩s	ng(u)∩s	PROPN
ejpam-3443	281	10	and	and	CCONJ
ejpam-3443	281	11	ng(u	ng(u	NOUN
ejpam-3443	281	12	)	)	PUNCT
ejpam-3443	281	13	\s∗	\s∗	NOUN
ejpam-3443	281	14	=	=	SYM
ejpam-3443	281	15	ng(u	ng(u	NOUN
ejpam-3443	281	16	)	)	PUNCT
ejpam-3443	281	17	\s	\	NOUN
ejpam-3443	281	18	so	so	SCONJ
ejpam-3443	281	19	that	that	SCONJ
ejpam-3443	281	20	|ng(u)∩s∗|	|ng(u)∩s∗|	NOUN
ejpam-3443	281	21	≤	≤	ADJ
ejpam-3443	281	22	|ng(u	|ng(u	NUM
ejpam-3443	281	23	)	)	PUNCT
ejpam-3443	281	24	\	\	PROPN
ejpam-3443	281	25	s∗|	s∗|	PROPN
ejpam-3443	281	26	.	.	PUNCT
ejpam-3443	282	1	we	we	PRON
ejpam-3443	282	2	also	also	ADV
ejpam-3443	282	3	have	have	VERB
ejpam-3443	282	4	|ng(v	|ng(v	VERB
ejpam-3443	282	5	)	)	PUNCT
ejpam-3443	282	6	∩	∩	NOUN
ejpam-3443	282	7	s∗|	s∗|	VERB
ejpam-3443	282	8	=	=	SYM
ejpam-3443	282	9	0	0	NUM
ejpam-3443	282	10	≤	≤	NUM
ejpam-3443	282	11	|ng(v	|ng(v	NOUN
ejpam-3443	282	12	)	)	PUNCT
ejpam-3443	282	13	\	\	NOUN
ejpam-3443	282	14	s∗|	s∗|	PROPN
ejpam-3443	282	15	.	.	PUNCT
ejpam-3443	283	1	thus	thus	ADV
ejpam-3443	283	2	,	,	PUNCT
ejpam-3443	283	3	s∗	s∗	PROPN
ejpam-3443	283	4	is	be	AUX
ejpam-3443	283	5	a	a	DET
ejpam-3443	283	6	cost	cost	NOUN
ejpam-3443	283	7	effective	effective	ADJ
ejpam-3443	283	8	set	set	NOUN
ejpam-3443	283	9	of	of	ADP
ejpam-3443	283	10	g	g	NOUN
ejpam-3443	283	11	,	,	PUNCT
ejpam-3443	283	12	contradicting	contradict	VERB
ejpam-3443	283	13	the	the	DET
ejpam-3443	283	14	assumption	assumption	NOUN
ejpam-3443	283	15	on	on	ADP
ejpam-3443	283	16	s	s	AUX
ejpam-3443	283	17	being	be	AUX
ejpam-3443	283	18	a	a	DET
ejpam-3443	283	19	cost	cost	NOUN
ejpam-3443	283	20	effective	effective	ADJ
ejpam-3443	283	21	set	set	NOUN
ejpam-3443	283	22	of	of	ADP
ejpam-3443	283	23	maximum	maximum	ADJ
ejpam-3443	283	24	cardinality	cardinality	NOUN
ejpam-3443	283	25	.	.	PUNCT
ejpam-3443	284	1	therefore	therefore	ADV
ejpam-3443	284	2	,	,	PUNCT
ejpam-3443	284	3	s	s	VERB
ejpam-3443	284	4	is	be	AUX
ejpam-3443	284	5	a	a	DET
ejpam-3443	284	6	dominating	dominating	NOUN
ejpam-3443	284	7	set	set	NOUN
ejpam-3443	284	8	of	of	ADP
ejpam-3443	284	9	g.	g.	PROPN
ejpam-3443	284	10	corollary	corollary	PROPN
ejpam-3443	284	11	6	6	NUM
ejpam-3443	284	12	.	.	PUNCT
ejpam-3443	285	1	let	let	VERB
ejpam-3443	285	2	g	g	NOUN
ejpam-3443	285	3	and	and	CCONJ
ejpam-3443	285	4	h	h	NOUN
ejpam-3443	285	5	be	be	AUX
ejpam-3443	285	6	nontrivial	nontrivial	ADJ
ejpam-3443	285	7	connected	connect	VERB
ejpam-3443	285	8	graphs	graph	NOUN
ejpam-3443	285	9	of	of	ADP
ejpam-3443	285	10	orders	order	NOUN
ejpam-3443	285	11	m	m	VERB
ejpam-3443	285	12	and	and	CCONJ
ejpam-3443	285	13	n	n	CCONJ
ejpam-3443	285	14	,	,	PUNCT
ejpam-3443	285	15	respectively	respectively	ADV
ejpam-3443	285	16	.	.	PUNCT
ejpam-3443	286	1	then	then	ADV
ejpam-3443	286	2	(	(	PUNCT
ejpam-3443	286	3	i	i	NOUN
ejpam-3443	286	4	)	)	PUNCT
ejpam-3443	286	5	γce(g	γce(g	PROPN
ejpam-3443	287	1	◦	◦	NOUN
ejpam-3443	287	2	h	h	NOUN
ejpam-3443	287	3	)	)	PUNCT
ejpam-3443	287	4	=	=	SYM
ejpam-3443	287	5	mγk1ce(h)−	mγk1ce(h)−	NOUN
ejpam-3443	287	6	(	(	PUNCT
ejpam-3443	287	7	γk1ce(h)−	γk1ce(h)−	NOUN
ejpam-3443	287	8	1	1	NUM
ejpam-3443	287	9	)	)	PUNCT
ejpam-3443	288	1	γ+knce	γ+knce	NOUN
ejpam-3443	288	2	(	(	PUNCT
ejpam-3443	288	3	g	g	NOUN
ejpam-3443	288	4	)	)	PUNCT
ejpam-3443	288	5	whenever	whenever	SCONJ
ejpam-3443	288	6	∆(g	∆(g	NOUN
ejpam-3443	288	7	)	)	PUNCT
ejpam-3443	288	8	>	>	X
ejpam-3443	289	1	n	n	CCONJ
ejpam-3443	289	2	;	;	PUNCT
ejpam-3443	289	3	(	(	PUNCT
ejpam-3443	289	4	ii	ii	NOUN
ejpam-3443	289	5	)	)	PUNCT
ejpam-3443	289	6	γmce(g	γmce(g	PROPN
ejpam-3443	289	7	◦	◦	NOUN
ejpam-3443	289	8	h	h	NOUN
ejpam-3443	289	9	)	)	PUNCT
ejpam-3443	289	10	=	=	SYM
ejpam-3443	289	11	mγk1mce(h	mγk1mce(h	PROPN
ejpam-3443	289	12	)	)	PUNCT
ejpam-3443	289	13	;	;	PUNCT
ejpam-3443	289	14	and	and	CCONJ
ejpam-3443	289	15	(	(	PUNCT
ejpam-3443	289	16	iii	iii	NOUN
ejpam-3443	289	17	)	)	PUNCT
ejpam-3443	289	18	mγ+k1ce	mγ+k1ce	PROPN
ejpam-3443	289	19	(	(	PUNCT
ejpam-3443	289	20	h	h	NOUN
ejpam-3443	289	21	)	)	PUNCT
ejpam-3443	289	22	≤	≤	NOUN
ejpam-3443	289	23	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	289	24	◦	◦	NOUN
ejpam-3443	289	25	h	h	NOUN
ejpam-3443	289	26	)	)	PUNCT
ejpam-3443	289	27	≤	≤	NOUN
ejpam-3443	289	28	|l|	|l|	VERB
ejpam-3443	289	29	+	+	X
ejpam-3443	289	30	mγ+k1ce	mγ+k1ce	PROPN
ejpam-3443	289	31	(	(	PUNCT
ejpam-3443	289	32	h	h	NOUN
ejpam-3443	289	33	)	)	PUNCT
ejpam-3443	289	34	,	,	PUNCT
ejpam-3443	289	35	where	where	SCONJ
ejpam-3443	289	36	l	l	NOUN
ejpam-3443	289	37	=	=	PUNCT
ejpam-3443	289	38	{	{	PUNCT
ejpam-3443	289	39	v	v	NUM
ejpam-3443	289	40	∈	∈	NOUN
ejpam-3443	289	41	v	v	NOUN
ejpam-3443	289	42	(	(	PUNCT
ejpam-3443	289	43	g	g	NOUN
ejpam-3443	289	44	)	)	PUNCT
ejpam-3443	289	45	:	:	PUNCT
ejpam-3443	289	46	degg(v	degg(v	PROPN
ejpam-3443	289	47	)	)	PUNCT
ejpam-3443	289	48	≥	≥	NOUN
ejpam-3443	289	49	2γ+k1ce	2γ+k1ce	NUM
ejpam-3443	289	50	(	(	PUNCT
ejpam-3443	289	51	h)−	h)−	PROPN
ejpam-3443	289	52	n	n	CCONJ
ejpam-3443	289	53	}	}	PUNCT
ejpam-3443	289	54	.	.	PUNCT
ejpam-3443	290	1	proof	proof	NOUN
ejpam-3443	290	2	.	.	PUNCT
ejpam-3443	291	1	let	let	VERB
ejpam-3443	291	2	d	d	NOUN
ejpam-3443	291	3	⊆	⊆	NUM
ejpam-3443	291	4	v	v	ADP
ejpam-3443	291	5	(	(	PUNCT
ejpam-3443	291	6	g	g	NOUN
ejpam-3443	291	7	)	)	PUNCT
ejpam-3443	291	8	be	be	VERB
ejpam-3443	291	9	a	a	DET
ejpam-3443	291	10	γ+knce	γ+knce	NOUN
ejpam-3443	291	11	set	set	NOUN
ejpam-3443	291	12	of	of	ADP
ejpam-3443	291	13	g.	g.	PROPN
ejpam-3443	291	14	note	note	VERB
ejpam-3443	291	15	that	that	SCONJ
ejpam-3443	291	16	if	if	SCONJ
ejpam-3443	291	17	∆(g	∆(g	PROPN
ejpam-3443	291	18	)	)	PUNCT
ejpam-3443	291	19	>	>	X
ejpam-3443	292	1	n	n	CCONJ
ejpam-3443	292	2	,	,	PUNCT
ejpam-3443	292	3	then	then	ADV
ejpam-3443	292	4	d	d	PROPN
ejpam-3443	292	5	6=	6=	PROPN
ejpam-3443	292	6	v	v	PROPN
ejpam-3443	292	7	(	(	PUNCT
ejpam-3443	292	8	g).for	g).for	NOUN
ejpam-3443	292	9	each	each	PRON
ejpam-3443	292	10	v	v	ADP
ejpam-3443	292	11	∈	∈	PROPN
ejpam-3443	292	12	v	v	NOUN
ejpam-3443	292	13	(	(	PUNCT
ejpam-3443	292	14	g	g	NOUN
ejpam-3443	292	15	)	)	PUNCT
ejpam-3443	292	16	\d	\d	NOUN
ejpam-3443	292	17	,	,	PUNCT
ejpam-3443	292	18	let	let	VERB
ejpam-3443	292	19	sv	sv	PROPN
ejpam-3443	292	20	⊆	⊆	NUM
ejpam-3443	292	21	v	v	X
ejpam-3443	292	22	(	(	PUNCT
ejpam-3443	292	23	hv	hv	NOUN
ejpam-3443	292	24	)	)	PUNCT
ejpam-3443	292	25	be	be	AUX
ejpam-3443	292	26	a	a	DET
ejpam-3443	292	27	γk1ce	γk1ce	NUM
ejpam-3443	292	28	-	-	PUNCT
ejpam-3443	292	29	set	set	NOUN
ejpam-3443	292	30	of	of	ADP
ejpam-3443	292	31	hv	hv	PROPN
ejpam-3443	292	32	.	.	PUNCT
ejpam-3443	293	1	put	put	VERB
ejpam-3443	293	2	s	s	PART
ejpam-3443	294	1	=	=	X
ejpam-3443	294	2	d	d	X
ejpam-3443	294	3	∪	∪	X
ejpam-3443	294	4	(	(	PUNCT
ejpam-3443	294	5	⋃	⋃	NOUN
ejpam-3443	294	6	v∈v	v∈v	NOUN
ejpam-3443	294	7	(	(	PUNCT
ejpam-3443	294	8	g)\d	g)\d	NOUN
ejpam-3443	294	9	sv	sv	PROPN
ejpam-3443	294	10	)	)	PUNCT
ejpam-3443	294	11	.	.	PUNCT
ejpam-3443	295	1	for	for	ADP
ejpam-3443	295	2	each	each	DET
ejpam-3443	295	3	v	v	NUM
ejpam-3443	295	4	∈	∈	PROPN
ejpam-3443	295	5	s	s	PART
ejpam-3443	295	6	∩	∩	ADJ
ejpam-3443	295	7	v	v	X
ejpam-3443	295	8	(	(	PUNCT
ejpam-3443	295	9	g	g	NOUN
ejpam-3443	295	10	)	)	PUNCT
ejpam-3443	295	11	=	=	SYM
ejpam-3443	296	1	d	d	PROPN
ejpam-3443	296	2	,	,	PUNCT
ejpam-3443	296	3	s	s	X
ejpam-3443	296	4	∩	∩	ADJ
ejpam-3443	296	5	v	v	X
ejpam-3443	296	6	(	(	PUNCT
ejpam-3443	296	7	hv	hv	NOUN
ejpam-3443	296	8	)	)	PUNCT
ejpam-3443	296	9	=	=	NOUN
ejpam-3443	296	10	∅	∅	NOUN
ejpam-3443	296	11	so	so	SCONJ
ejpam-3443	296	12	that	that	SCONJ
ejpam-3443	296	13	|s	|s	PROPN
ejpam-3443	296	14	∩	∩	PROPN
ejpam-3443	296	15	v	v	X
ejpam-3443	296	16	(	(	PUNCT
ejpam-3443	296	17	hv)|	hv)|	NOUN
ejpam-3443	296	18	=	=	SYM
ejpam-3443	296	19	0	0	NUM
ejpam-3443	296	20	≤	≤	NOUN
ejpam-3443	296	21	|v	|v	X
ejpam-3443	296	22	(	(	PUNCT
ejpam-3443	296	23	h)|+	h)|+	ADJ
ejpam-3443	296	24	|ng(v	|ng(v	NOUN
ejpam-3443	296	25	)	)	PUNCT
ejpam-3443	296	26	\	\	NOUN
ejpam-3443	296	27	s|	s|	VERB
ejpam-3443	296	28	−	−	NOUN
ejpam-3443	296	29	|ng(v	|ng(v	NOUN
ejpam-3443	296	30	)	)	PUNCT
ejpam-3443	296	31	∩	∩	NOUN
ejpam-3443	296	32	s|	s|	NOUN
ejpam-3443	296	33	.	.	PUNCT
ejpam-3443	297	1	f.jamil	f.jamil	PROPN
ejpam-3443	297	2	,	,	PUNCT
ejpam-3443	297	3	h.	h.	PROPN
ejpam-3443	297	4	nuenay	nuenay	PROPN
ejpam-3443	297	5	-	-	PUNCT
ejpam-3443	297	6	maglanque	maglanque	ADJ
ejpam-3443	297	7	/	/	SYM
ejpam-3443	297	8	eur	eur	NOUN
ejpam-3443	297	9	.	.	PUNCT
ejpam-3443	298	1	j.	j.	PROPN
ejpam-3443	298	2	pure	pure	PROPN
ejpam-3443	298	3	appl	appl	PROPN
ejpam-3443	298	4	.	.	PROPN
ejpam-3443	298	5	math	math	PROPN
ejpam-3443	298	6	,	,	PUNCT
ejpam-3443	298	7	12	12	NUM
ejpam-3443	298	8	(	(	PUNCT
ejpam-3443	298	9	3	3	NUM
ejpam-3443	298	10	)	)	PUNCT
ejpam-3443	298	11	(	(	PUNCT
ejpam-3443	298	12	2019	2019	NUM
ejpam-3443	298	13	)	)	PUNCT
ejpam-3443	298	14	,	,	PUNCT
ejpam-3443	298	15	978	978	NUM
ejpam-3443	298	16	-	-	SYM
ejpam-3443	298	17	998	998	NUM
ejpam-3443	298	18	989	989	NUM
ejpam-3443	298	19	for	for	ADP
ejpam-3443	298	20	each	each	DET
ejpam-3443	298	21	v	v	NUM
ejpam-3443	298	22	∈	∈	PROPN
ejpam-3443	298	23	v	v	NOUN
ejpam-3443	298	24	(	(	PUNCT
ejpam-3443	298	25	g	g	NOUN
ejpam-3443	298	26	)	)	PUNCT
ejpam-3443	298	27	\	\	PART
ejpam-3443	299	1	s	s	PART
ejpam-3443	299	2	=	=	SYM
ejpam-3443	299	3	v	v	X
ejpam-3443	299	4	(	(	PUNCT
ejpam-3443	299	5	g	g	NOUN
ejpam-3443	299	6	)	)	PUNCT
ejpam-3443	299	7	\d	\d	NOUN
ejpam-3443	299	8	,	,	PUNCT
ejpam-3443	299	9	sv	sv	PUNCT
ejpam-3443	300	1	=	=	SYM
ejpam-3443	300	2	s	s	PROPN
ejpam-3443	300	3	∩	∩	ADJ
ejpam-3443	300	4	v	v	X
ejpam-3443	300	5	(	(	PUNCT
ejpam-3443	300	6	hv	hv	X
ejpam-3443	300	7	)	)	PUNCT
ejpam-3443	300	8	is	be	AUX
ejpam-3443	300	9	a	a	DET
ejpam-3443	300	10	k1	k1	NOUN
ejpam-3443	300	11	-	-	PUNCT
ejpam-3443	300	12	cost	cost	NOUN
ejpam-3443	300	13	effective	effective	ADJ
ejpam-3443	300	14	dominating	dominating	NOUN
ejpam-3443	300	15	set	set	NOUN
ejpam-3443	300	16	of	of	ADP
ejpam-3443	300	17	hv	hv	PROPN
ejpam-3443	300	18	.	.	PUNCT
ejpam-3443	301	1	by	by	ADP
ejpam-3443	301	2	theorem	theorem	NOUN
ejpam-3443	301	3	6	6	NUM
ejpam-3443	301	4	,	,	PUNCT
ejpam-3443	301	5	s	s	VERB
ejpam-3443	301	6	is	be	AUX
ejpam-3443	301	7	a	a	DET
ejpam-3443	301	8	cost	cost	NOUN
ejpam-3443	301	9	effective	effective	ADJ
ejpam-3443	301	10	dominating	dominating	NOUN
ejpam-3443	301	11	set	set	NOUN
ejpam-3443	301	12	of	of	ADP
ejpam-3443	301	13	g	g	PROPN
ejpam-3443	301	14	◦	◦	NOUN
ejpam-3443	301	15	h	h	NOUN
ejpam-3443	301	16	,	,	PUNCT
ejpam-3443	301	17	and	and	CCONJ
ejpam-3443	301	18	γce(g	γce(g	PROPN
ejpam-3443	302	1	◦	◦	NOUN
ejpam-3443	302	2	h	h	NOUN
ejpam-3443	302	3	)	)	PUNCT
ejpam-3443	302	4	≤	≤	NUM
ejpam-3443	302	5	|s|	|s|	NOUN
ejpam-3443	302	6	=	=	SYM
ejpam-3443	302	7	|d|+	|d|+	NOUN
ejpam-3443	302	8	∑	∑	PUNCT
ejpam-3443	302	9	v∈v	v∈v	NOUN
ejpam-3443	302	10	(	(	PUNCT
ejpam-3443	302	11	g)\d	g)\d	NOUN
ejpam-3443	302	12	|sv|	|sv|	PROPN
ejpam-3443	302	13	=	=	SYM
ejpam-3443	302	14	γ+knce	γ+knce	PROPN
ejpam-3443	302	15	(	(	PUNCT
ejpam-3443	302	16	g	g	NOUN
ejpam-3443	302	17	)	)	PUNCT
ejpam-3443	302	18	+	+	CCONJ
ejpam-3443	302	19	(	(	PUNCT
ejpam-3443	302	20	|v	|v	X
ejpam-3443	302	21	(	(	PUNCT
ejpam-3443	302	22	g)|	g)|	NOUN
ejpam-3443	302	23	−	−	PROPN
ejpam-3443	302	24	γ+knce	γ+knce	PROPN
ejpam-3443	302	25	(	(	PUNCT
ejpam-3443	302	26	g	g	NOUN
ejpam-3443	302	27	)	)	PUNCT
ejpam-3443	302	28	)	)	PUNCT
ejpam-3443	303	1	γk1ce(h	γk1ce(h	PROPN
ejpam-3443	303	2	)	)	PUNCT
ejpam-3443	304	1	=	=	SYM
ejpam-3443	304	2	|v	|v	PROPN
ejpam-3443	304	3	(	(	PUNCT
ejpam-3443	304	4	g)|γk1ce(h)−	g)|γk1ce(h)−	X
ejpam-3443	304	5	(	(	PUNCT
ejpam-3443	304	6	γk1ce(h)−	γk1ce(h)−	NOUN
ejpam-3443	304	7	1	1	NUM
ejpam-3443	304	8	)	)	PUNCT
ejpam-3443	304	9	γ+knce	γ+knce	NOUN
ejpam-3443	305	1	(	(	PUNCT
ejpam-3443	305	2	g	g	NOUN
ejpam-3443	305	3	)	)	PUNCT
ejpam-3443	305	4	.	.	PUNCT
ejpam-3443	306	1	conversely	conversely	ADV
ejpam-3443	306	2	,	,	PUNCT
ejpam-3443	306	3	let	let	VERB
ejpam-3443	306	4	s	s	PRON
ejpam-3443	306	5	⊆	⊆	NUM
ejpam-3443	306	6	v	v	NOUN
ejpam-3443	306	7	(	(	PUNCT
ejpam-3443	306	8	g	g	PROPN
ejpam-3443	306	9	◦	◦	NOUN
ejpam-3443	306	10	h	h	NOUN
ejpam-3443	306	11	)	)	PUNCT
ejpam-3443	306	12	be	be	VERB
ejpam-3443	306	13	a	a	DET
ejpam-3443	306	14	γce	γce	NOUN
ejpam-3443	306	15	-	-	PUNCT
ejpam-3443	306	16	set	set	NOUN
ejpam-3443	306	17	of	of	ADP
ejpam-3443	306	18	g	g	PROPN
ejpam-3443	306	19	◦	◦	NOUN
ejpam-3443	306	20	h.	h.	NOUN
ejpam-3443	306	21	in	in	ADP
ejpam-3443	306	22	view	view	NOUN
ejpam-3443	306	23	of	of	ADP
ejpam-3443	306	24	theorem	theorem	NOUN
ejpam-3443	306	25	6	6	NUM
ejpam-3443	306	26	we	we	PRON
ejpam-3443	306	27	can	can	AUX
ejpam-3443	306	28	write	write	VERB
ejpam-3443	306	29	|s|	|s|	NOUN
ejpam-3443	306	30	=	=	SYM
ejpam-3443	306	31	∑	∑	PUNCT
ejpam-3443	306	32	v∈s∩v	v∈s∩v	NOUN
ejpam-3443	306	33	(	(	PUNCT
ejpam-3443	306	34	g	g	NOUN
ejpam-3443	306	35	)	)	PUNCT
ejpam-3443	306	36	(	(	PUNCT
ejpam-3443	306	37	1	1	NUM
ejpam-3443	306	38	+	+	NUM
ejpam-3443	306	39	|s	|s	PROPN
ejpam-3443	306	40	∩	∩	ADJ
ejpam-3443	306	41	v	v	NOUN
ejpam-3443	306	42	(	(	PUNCT
ejpam-3443	306	43	hv)|	hv)|	NOUN
ejpam-3443	306	44	)	)	PUNCT
ejpam-3443	306	45	+	+	CCONJ
ejpam-3443	306	46	∑	∑	PUNCT
ejpam-3443	306	47	v∈v	v∈v	NOUN
ejpam-3443	306	48	(	(	PUNCT
ejpam-3443	306	49	g)\s	g)\s	NOUN
ejpam-3443	306	50	γk1ce(h	γk1ce(h	PROPN
ejpam-3443	306	51	)	)	PUNCT
ejpam-3443	306	52	.	.	PUNCT
ejpam-3443	307	1	now	now	ADV
ejpam-3443	307	2	s	s	VERB
ejpam-3443	307	3	can	can	AUX
ejpam-3443	307	4	be	be	AUX
ejpam-3443	307	5	made	make	VERB
ejpam-3443	307	6	as	as	ADV
ejpam-3443	307	7	small	small	ADJ
ejpam-3443	307	8	as	as	SCONJ
ejpam-3443	307	9	desired	desire	VERB
ejpam-3443	307	10	if	if	SCONJ
ejpam-3443	307	11	s	s	ADP
ejpam-3443	307	12	∩	∩	ADJ
ejpam-3443	307	13	v	v	X
ejpam-3443	307	14	(	(	PUNCT
ejpam-3443	307	15	hv	hv	X
ejpam-3443	307	16	)	)	PUNCT
ejpam-3443	307	17	can	can	AUX
ejpam-3443	307	18	be	be	AUX
ejpam-3443	307	19	made	make	VERB
ejpam-3443	307	20	∅	∅	NOUN
ejpam-3443	307	21	for	for	ADP
ejpam-3443	307	22	all	all	PRON
ejpam-3443	307	23	v	v	ADP
ejpam-3443	307	24	∈	∈	NOUN
ejpam-3443	307	25	s	s	NOUN
ejpam-3443	307	26	∩	∩	ADJ
ejpam-3443	307	27	v	v	X
ejpam-3443	307	28	(	(	PUNCT
ejpam-3443	307	29	g	g	NOUN
ejpam-3443	307	30	)	)	PUNCT
ejpam-3443	307	31	.	.	PUNCT
ejpam-3443	308	1	this	this	PRON
ejpam-3443	308	2	is	be	AUX
ejpam-3443	308	3	attained	attain	VERB
ejpam-3443	308	4	when	when	SCONJ
ejpam-3443	308	5	s∩v	s∩v	PROPN
ejpam-3443	308	6	(	(	PUNCT
ejpam-3443	308	7	g	g	NOUN
ejpam-3443	308	8	)	)	PUNCT
ejpam-3443	308	9	is	be	AUX
ejpam-3443	308	10	a	a	DET
ejpam-3443	308	11	kn	kn	NOUN
ejpam-3443	308	12	-	-	PUNCT
ejpam-3443	308	13	cost	cost	NOUN
ejpam-3443	308	14	effective	effective	ADJ
ejpam-3443	308	15	set	set	NOUN
ejpam-3443	308	16	of	of	ADP
ejpam-3443	308	17	g	g	NOUN
ejpam-3443	308	18	so	so	SCONJ
ejpam-3443	309	1	that	that	SCONJ
ejpam-3443	309	2	|s∩v	|s∩v	PROPN
ejpam-3443	309	3	(	(	PUNCT
ejpam-3443	309	4	g)|	g)|	NOUN
ejpam-3443	309	5	≤	≤	NUM
ejpam-3443	309	6	γ+knce	γ+knce	NOUN
ejpam-3443	309	7	(	(	PUNCT
ejpam-3443	309	8	g	g	NOUN
ejpam-3443	309	9	)	)	PUNCT
ejpam-3443	309	10	and	and	CCONJ
ejpam-3443	309	11	|v	|v	PROPN
ejpam-3443	309	12	(	(	PUNCT
ejpam-3443	309	13	g	g	NOUN
ejpam-3443	309	14	)	)	PUNCT
ejpam-3443	309	15	\	\	PROPN
ejpam-3443	309	16	s|	s|	VERB
ejpam-3443	309	17	≥	≥	NUM
ejpam-3443	309	18	|v	|v	X
ejpam-3443	309	19	(	(	PUNCT
ejpam-3443	309	20	g)|	g)|	NOUN
ejpam-3443	309	21	−	−	PROPN
ejpam-3443	309	22	γ+knce	γ+knce	PROPN
ejpam-3443	309	23	(	(	PUNCT
ejpam-3443	309	24	g	g	NOUN
ejpam-3443	309	25	)	)	PUNCT
ejpam-3443	309	26	by	by	ADP
ejpam-3443	309	27	lemma	lemma	PROPN
ejpam-3443	309	28	2	2	NUM
ejpam-3443	309	29	.	.	PUNCT
ejpam-3443	309	30	therefore	therefore	ADV
ejpam-3443	309	31	,	,	PUNCT
ejpam-3443	309	32	γce(g	γce(g	PROPN
ejpam-3443	309	33	◦	◦	NOUN
ejpam-3443	309	34	h	h	NOUN
ejpam-3443	309	35	)	)	PUNCT
ejpam-3443	309	36	=	=	SYM
ejpam-3443	309	37	|s|	|s|	PROPN
ejpam-3443	309	38	=	=	SYM
ejpam-3443	309	39	|s	|s	PROPN
ejpam-3443	309	40	∩	∩	ADJ
ejpam-3443	309	41	v	v	X
ejpam-3443	309	42	(	(	PUNCT
ejpam-3443	309	43	g)|+	g)|+	PROPN
ejpam-3443	309	44	∑	∑	PUNCT
ejpam-3443	309	45	v∈v	v∈v	NOUN
ejpam-3443	309	46	(	(	PUNCT
ejpam-3443	309	47	g)\s	g)\s	NOUN
ejpam-3443	309	48	γk1ce(h	γk1ce(h	PROPN
ejpam-3443	309	49	)	)	PUNCT
ejpam-3443	309	50	≥	≥	NOUN
ejpam-3443	310	1	γ+knce	γ+knce	NOUN
ejpam-3443	310	2	(	(	PUNCT
ejpam-3443	310	3	g	g	NOUN
ejpam-3443	310	4	)	)	PUNCT
ejpam-3443	310	5	+	+	CCONJ
ejpam-3443	310	6	(	(	PUNCT
ejpam-3443	310	7	|v	|v	X
ejpam-3443	310	8	(	(	PUNCT
ejpam-3443	310	9	g)|	g)|	PROPN
ejpam-3443	310	10	−	−	PROPN
ejpam-3443	310	11	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	310	12	)	)	PUNCT
ejpam-3443	310	13	)	)	PUNCT
ejpam-3443	311	1	γk1ce(h	γk1ce(h	PROPN
ejpam-3443	311	2	)	)	PUNCT
ejpam-3443	312	1	this	this	PRON
ejpam-3443	312	2	proves	prove	VERB
ejpam-3443	312	3	statement	statement	NOUN
ejpam-3443	312	4	(	(	PUNCT
ejpam-3443	312	5	i	i	NOUN
ejpam-3443	312	6	)	)	PUNCT
ejpam-3443	312	7	.	.	PUNCT
ejpam-3443	313	1	to	to	PART
ejpam-3443	313	2	prove	prove	VERB
ejpam-3443	313	3	statement	statement	NOUN
ejpam-3443	313	4	(	(	PUNCT
ejpam-3443	313	5	ii	ii	NOUN
ejpam-3443	313	6	)	)	PUNCT
ejpam-3443	313	7	,	,	PUNCT
ejpam-3443	313	8	let	let	VERB
ejpam-3443	313	9	s	s	PRON
ejpam-3443	313	10	=	=	PUNCT
ejpam-3443	313	11	⋃	⋃	NOUN
ejpam-3443	313	12	v∈v	v∈v	NOUN
ejpam-3443	313	13	(	(	PUNCT
ejpam-3443	313	14	g	g	NOUN
ejpam-3443	313	15	)	)	PUNCT
ejpam-3443	313	16	sv	sv	NOUN
ejpam-3443	313	17	,	,	PUNCT
ejpam-3443	313	18	where	where	SCONJ
ejpam-3443	313	19	sv	sv	PROPN
ejpam-3443	313	20	⊆	⊆	NUM
ejpam-3443	313	21	v	v	PROPN
ejpam-3443	313	22	(	(	PUNCT
ejpam-3443	313	23	hv	hv	X
ejpam-3443	313	24	)	)	PUNCT
ejpam-3443	313	25	is	be	AUX
ejpam-3443	313	26	a	a	DET
ejpam-3443	313	27	γk1mce	γk1mce	NOUN
ejpam-3443	313	28	-	-	PUNCT
ejpam-3443	313	29	set	set	NOUN
ejpam-3443	313	30	of	of	ADP
ejpam-3443	313	31	hv	hv	PROPN
ejpam-3443	313	32	for	for	ADP
ejpam-3443	313	33	each	each	DET
ejpam-3443	313	34	v	v	NUM
ejpam-3443	313	35	∈	∈	PROPN
ejpam-3443	313	36	v	v	NOUN
ejpam-3443	313	37	(	(	PUNCT
ejpam-3443	313	38	g	g	NOUN
ejpam-3443	313	39	)	)	PUNCT
ejpam-3443	313	40	.	.	PUNCT
ejpam-3443	314	1	by	by	ADP
ejpam-3443	314	2	theorem	theorem	NOUN
ejpam-3443	314	3	6	6	NUM
ejpam-3443	314	4	,	,	PUNCT
ejpam-3443	314	5	s	s	VERB
ejpam-3443	314	6	is	be	AUX
ejpam-3443	314	7	a	a	DET
ejpam-3443	314	8	cost	cost	NOUN
ejpam-3443	314	9	effective	effective	ADJ
ejpam-3443	314	10	dominating	dominating	NOUN
ejpam-3443	314	11	set	set	NOUN
ejpam-3443	314	12	of	of	ADP
ejpam-3443	314	13	g	g	PROPN
ejpam-3443	314	14	◦	◦	PROPN
ejpam-3443	314	15	h.	h.	PROPN
ejpam-3443	314	16	since	since	SCONJ
ejpam-3443	314	17	sv	sv	PROPN
ejpam-3443	314	18	is	be	AUX
ejpam-3443	314	19	a	a	DET
ejpam-3443	314	20	minimal	minimal	ADJ
ejpam-3443	314	21	cost	cost	NOUN
ejpam-3443	314	22	effective	effective	ADJ
ejpam-3443	314	23	dominating	dominating	NOUN
ejpam-3443	314	24	set	set	NOUN
ejpam-3443	314	25	of	of	ADP
ejpam-3443	314	26	hv	hv	PROPN
ejpam-3443	314	27	+	+	X
ejpam-3443	314	28	v	v	NOUN
ejpam-3443	314	29	for	for	ADP
ejpam-3443	314	30	each	each	DET
ejpam-3443	314	31	v	v	NUM
ejpam-3443	314	32	∈	∈	PROPN
ejpam-3443	314	33	v	v	NOUN
ejpam-3443	314	34	(	(	PUNCT
ejpam-3443	314	35	g	g	NOUN
ejpam-3443	314	36	)	)	PUNCT
ejpam-3443	314	37	,	,	PUNCT
ejpam-3443	314	38	s	s	VERB
ejpam-3443	314	39	is	be	AUX
ejpam-3443	314	40	a	a	DET
ejpam-3443	314	41	minimal	minimal	ADJ
ejpam-3443	314	42	cost	cost	NOUN
ejpam-3443	314	43	effective	effective	ADJ
ejpam-3443	314	44	dominating	dominating	NOUN
ejpam-3443	314	45	set	set	NOUN
ejpam-3443	314	46	of	of	ADP
ejpam-3443	314	47	g	g	PROPN
ejpam-3443	314	48	◦	◦	NOUN
ejpam-3443	314	49	h.	h.	PROPN
ejpam-3443	314	50	thus	thus	ADV
ejpam-3443	314	51	,	,	PUNCT
ejpam-3443	314	52	γmce(g	γmce(g	PROPN
ejpam-3443	314	53	◦	◦	NOUN
ejpam-3443	314	54	h	h	NOUN
ejpam-3443	314	55	)	)	PUNCT
ejpam-3443	314	56	≥	≥	NOUN
ejpam-3443	314	57	|s|	|s|	NOUN
ejpam-3443	314	58	=	=	SYM
ejpam-3443	314	59	|v	|v	PROPN
ejpam-3443	314	60	(	(	PUNCT
ejpam-3443	314	61	g)|γk1mce(h	g)|γk1mce(h	NOUN
ejpam-3443	314	62	)	)	PUNCT
ejpam-3443	314	63	.	.	PUNCT
ejpam-3443	315	1	conversely	conversely	ADV
ejpam-3443	315	2	,	,	PUNCT
ejpam-3443	315	3	let	let	VERB
ejpam-3443	315	4	s	s	PRON
ejpam-3443	315	5	⊆	⊆	NUM
ejpam-3443	315	6	v	v	NOUN
ejpam-3443	315	7	(	(	PUNCT
ejpam-3443	315	8	g	g	PROPN
ejpam-3443	315	9	◦	◦	NOUN
ejpam-3443	315	10	h	h	NOUN
ejpam-3443	315	11	)	)	PUNCT
ejpam-3443	315	12	be	be	VERB
ejpam-3443	315	13	a	a	DET
ejpam-3443	315	14	γmce	γmce	NOUN
ejpam-3443	315	15	-	-	PUNCT
ejpam-3443	315	16	set	set	NOUN
ejpam-3443	315	17	of	of	ADP
ejpam-3443	315	18	g	g	PROPN
ejpam-3443	315	19	◦	◦	PROPN
ejpam-3443	315	20	h.	h.	PROPN
ejpam-3443	315	21	let	let	VERB
ejpam-3443	315	22	v	v	NUM
ejpam-3443	315	23	∈	∈	PROPN
ejpam-3443	315	24	v	v	NOUN
ejpam-3443	315	25	(	(	PUNCT
ejpam-3443	315	26	g	g	NOUN
ejpam-3443	315	27	)	)	PUNCT
ejpam-3443	315	28	\	\	PUNCT
ejpam-3443	316	1	s.	s.	PROPN
ejpam-3443	316	2	by	by	ADP
ejpam-3443	316	3	theorem	theorem	PROPN
ejpam-3443	316	4	6(ii	6(ii	PROPN
ejpam-3443	316	5	)	)	PUNCT
ejpam-3443	316	6	and	and	CCONJ
ejpam-3443	316	7	the	the	DET
ejpam-3443	316	8	minimality	minimality	NOUN
ejpam-3443	316	9	of	of	ADP
ejpam-3443	316	10	s	s	PROPN
ejpam-3443	316	11	,	,	PUNCT
ejpam-3443	316	12	s	s	PART
ejpam-3443	316	13	∩	∩	ADJ
ejpam-3443	316	14	v	v	X
ejpam-3443	316	15	(	(	PUNCT
ejpam-3443	316	16	hv	hv	X
ejpam-3443	316	17	)	)	PUNCT
ejpam-3443	316	18	is	be	AUX
ejpam-3443	316	19	a	a	DET
ejpam-3443	316	20	minimal	minimal	ADJ
ejpam-3443	316	21	k1	k1	NOUN
ejpam-3443	316	22	-	-	PUNCT
ejpam-3443	316	23	cost	cost	NOUN
ejpam-3443	316	24	effective	effective	ADJ
ejpam-3443	316	25	dominating	dominating	NOUN
ejpam-3443	316	26	set	set	NOUN
ejpam-3443	316	27	of	of	ADP
ejpam-3443	316	28	hv	hv	PROPN
ejpam-3443	316	29	.	.	PUNCT
ejpam-3443	317	1	let	let	VERB
ejpam-3443	317	2	v	v	NUM
ejpam-3443	317	3	∈	∈	NOUN
ejpam-3443	317	4	s	s	PART
ejpam-3443	317	5	∩	∩	ADJ
ejpam-3443	317	6	v	v	X
ejpam-3443	317	7	(	(	PUNCT
ejpam-3443	317	8	g	g	NOUN
ejpam-3443	317	9	)	)	PUNCT
ejpam-3443	317	10	.	.	PUNCT
ejpam-3443	318	1	by	by	ADP
ejpam-3443	318	2	theorem	theorem	NOUN
ejpam-3443	318	3	6(i	6(i	NUM
ejpam-3443	318	4	)	)	PUNCT
ejpam-3443	318	5	,	,	PUNCT
ejpam-3443	318	6	sv	sv	PROPN
ejpam-3443	318	7	=	=	SYM
ejpam-3443	318	8	s	s	PROPN
ejpam-3443	318	9	∩	∩	ADJ
ejpam-3443	318	10	v	v	X
ejpam-3443	318	11	(	(	PUNCT
ejpam-3443	318	12	hv	hv	X
ejpam-3443	318	13	)	)	PUNCT
ejpam-3443	318	14	is	be	AUX
ejpam-3443	318	15	a	a	DET
ejpam-3443	318	16	cost	cost	NOUN
ejpam-3443	318	17	effective	effective	ADJ
ejpam-3443	318	18	set	set	NOUN
ejpam-3443	318	19	of	of	ADP
ejpam-3443	318	20	hv	hv	PROPN
ejpam-3443	318	21	satisfying	satisfy	VERB
ejpam-3443	318	22	|sv|	|sv|	PROPN
ejpam-3443	318	23	≤	≤	ADJ
ejpam-3443	318	24	1	1	NUM
ejpam-3443	318	25	2	2	NUM
ejpam-3443	318	26	(	(	PUNCT
ejpam-3443	318	27	n+	n+	NUM
ejpam-3443	319	1	|ng(v	|ng(v	ADJ
ejpam-3443	319	2	)	)	PUNCT
ejpam-3443	319	3	\	\	NOUN
ejpam-3443	319	4	s|	s|	VERB
ejpam-3443	319	5	−	−	NOUN
ejpam-3443	319	6	|ng(v	|ng(v	NOUN
ejpam-3443	319	7	)	)	PUNCT
ejpam-3443	319	8	∩	∩	NOUN
ejpam-3443	319	9	s|	s|	PROPN
ejpam-3443	319	10	)	)	PUNCT
ejpam-3443	319	11	<	<	X
ejpam-3443	319	12	n	n	PRON
ejpam-3443	319	13	2	2	NUM
ejpam-3443	319	14	.	.	PUNCT
ejpam-3443	320	1	thus	thus	ADV
ejpam-3443	320	2	,	,	PUNCT
ejpam-3443	320	3	|ng(v	|ng(v	NOUN
ejpam-3443	320	4	)	)	PUNCT
ejpam-3443	320	5	∩	∩	NOUN
ejpam-3443	320	6	s|	s|	VERB
ejpam-3443	320	7	≤	≤	NUM
ejpam-3443	320	8	|ng(v	|ng(v	NOUN
ejpam-3443	320	9	)	)	PUNCT
ejpam-3443	320	10	∩	∩	NOUN
ejpam-3443	320	11	s|+	s|+	PROPN
ejpam-3443	320	12	2|sv|	2|sv|	PROPN
ejpam-3443	320	13	=	=	SYM
ejpam-3443	320	14	|ng	|ng	VERB
ejpam-3443	320	15	◦	◦	NOUN
ejpam-3443	320	16	h(v	h(v	NOUN
ejpam-3443	320	17	)	)	PUNCT
ejpam-3443	320	18	∩	∩	NOUN
ejpam-3443	320	19	s|+	s|+	NOUN
ejpam-3443	320	20	|sv|	|sv|	PROPN
ejpam-3443	320	21	≤	≤	NOUN
ejpam-3443	320	22	|ng	|ng	AUX
ejpam-3443	320	23	◦	◦	NOUN
ejpam-3443	320	24	h(v	h(v	NOUN
ejpam-3443	320	25	)	)	PUNCT
ejpam-3443	320	26	\	\	PUNCT
ejpam-3443	321	1	s|+	s|+	NOUN
ejpam-3443	321	2	|sv|	|sv|	NOUN
ejpam-3443	321	3	=	=	SYM
ejpam-3443	321	4	|ng(v	|ng(v	PROPN
ejpam-3443	321	5	)	)	PUNCT
ejpam-3443	321	6	\	\	NOUN
ejpam-3443	322	1	s|+	s|+	PROPN
ejpam-3443	322	2	n.	n.	NOUN
ejpam-3443	322	3	let	let	VERB
ejpam-3443	322	4	s∗	s∗	PROPN
ejpam-3443	322	5	=	=	SYM
ejpam-3443	322	6	s	s	PART
ejpam-3443	322	7	\	\	PROPN
ejpam-3443	322	8	sv	sv	PROPN
ejpam-3443	322	9	.	.	PUNCT
ejpam-3443	323	1	since	since	SCONJ
ejpam-3443	323	2	v	v	NOUN
ejpam-3443	323	3	dominates	dominate	VERB
ejpam-3443	323	4	v	v	NOUN
ejpam-3443	323	5	(	(	PUNCT
ejpam-3443	323	6	hv	hv	PROPN
ejpam-3443	323	7	+	+	PROPN
ejpam-3443	323	8	v	v	NOUN
ejpam-3443	323	9	)	)	PUNCT
ejpam-3443	323	10	,	,	PUNCT
ejpam-3443	323	11	s∗	s∗	PROPN
ejpam-3443	323	12	is	be	AUX
ejpam-3443	323	13	a	a	DET
ejpam-3443	323	14	dominating	dominating	NOUN
ejpam-3443	323	15	set	set	NOUN
ejpam-3443	323	16	of	of	ADP
ejpam-3443	323	17	g	g	PROPN
ejpam-3443	323	18	◦	◦	PROPN
ejpam-3443	323	19	h.	h.	PROPN
ejpam-3443	323	20	note	note	VERB
ejpam-3443	323	21	that	that	SCONJ
ejpam-3443	323	22	each	each	DET
ejpam-3443	323	23	u	u	PROPN
ejpam-3443	323	24	∈	∈	PROPN
ejpam-3443	323	25	s∗	s∗	PROPN
ejpam-3443	323	26	\	\	PROPN
ejpam-3443	323	27	{	{	PUNCT
ejpam-3443	323	28	v	v	NOUN
ejpam-3443	323	29	}	}	PUNCT
ejpam-3443	323	30	is	be	AUX
ejpam-3443	323	31	cost	cost	VERB
ejpam-3443	323	32	effective	effective	ADJ
ejpam-3443	323	33	relative	relative	NOUN
ejpam-3443	323	34	to	to	PART
ejpam-3443	323	35	s∗	s∗	VERB
ejpam-3443	323	36	as	as	SCONJ
ejpam-3443	323	37	it	it	PRON
ejpam-3443	323	38	is	be	AUX
ejpam-3443	323	39	relative	relative	ADJ
ejpam-3443	323	40	to	to	ADP
ejpam-3443	323	41	s	s	PRON
ejpam-3443	323	42	in	in	ADP
ejpam-3443	323	43	g	g	PROPN
ejpam-3443	323	44	◦	◦	NOUN
ejpam-3443	323	45	h.	h.	NOUN
ejpam-3443	323	46	now	now	ADV
ejpam-3443	323	47	,	,	PUNCT
ejpam-3443	323	48	|ng	|ng	VERB
ejpam-3443	323	49	◦	◦	NOUN
ejpam-3443	323	50	h(v	h(v	ADJ
ejpam-3443	323	51	)	)	PUNCT
ejpam-3443	323	52	∩	∩	NOUN
ejpam-3443	323	53	s∗|	s∗|	PROPN
ejpam-3443	323	54	=	=	SYM
ejpam-3443	323	55	ng(v	ng(v	X
ejpam-3443	323	56	)	)	PUNCT
ejpam-3443	323	57	∩	∩	NOUN
ejpam-3443	323	58	s|	s|	VERB
ejpam-3443	323	59	f.jamil	f.jamil	NOUN
ejpam-3443	323	60	,	,	PUNCT
ejpam-3443	323	61	h.	h.	PROPN
ejpam-3443	323	62	nuenay	nuenay	PROPN
ejpam-3443	323	63	-	-	PUNCT
ejpam-3443	323	64	maglanque	maglanque	ADJ
ejpam-3443	323	65	/	/	SYM
ejpam-3443	323	66	eur	eur	NOUN
ejpam-3443	323	67	.	.	PUNCT
ejpam-3443	324	1	j.	j.	PROPN
ejpam-3443	324	2	pure	pure	PROPN
ejpam-3443	324	3	appl	appl	PROPN
ejpam-3443	324	4	.	.	PROPN
ejpam-3443	324	5	math	math	PROPN
ejpam-3443	324	6	,	,	PUNCT
ejpam-3443	324	7	12	12	NUM
ejpam-3443	324	8	(	(	PUNCT
ejpam-3443	324	9	3	3	NUM
ejpam-3443	324	10	)	)	PUNCT
ejpam-3443	324	11	(	(	PUNCT
ejpam-3443	324	12	2019	2019	NUM
ejpam-3443	324	13	)	)	PUNCT
ejpam-3443	324	14	,	,	PUNCT
ejpam-3443	324	15	978	978	NUM
ejpam-3443	324	16	-	-	SYM
ejpam-3443	324	17	998	998	NUM
ejpam-3443	324	18	990	990	NUM
ejpam-3443	324	19	≤	≤	NUM
ejpam-3443	324	20	|ng(v	|ng(v	NOUN
ejpam-3443	324	21	)	)	PUNCT
ejpam-3443	324	22	\	\	NOUN
ejpam-3443	325	1	s|+	s|+	NOUN
ejpam-3443	325	2	n	n	NOUN
ejpam-3443	325	3	=	=	SYM
ejpam-3443	325	4	|ng	|ng	X
ejpam-3443	325	5	◦	◦	NOUN
ejpam-3443	325	6	h(v	h(v	NOUN
ejpam-3443	325	7	)	)	PUNCT
ejpam-3443	325	8	\	\	PROPN
ejpam-3443	325	9	s∗|	s∗|	PROPN
ejpam-3443	325	10	.	.	PUNCT
ejpam-3443	326	1	since	since	SCONJ
ejpam-3443	326	2	s	s	NOUN
ejpam-3443	326	3	is	be	AUX
ejpam-3443	326	4	minimal	minimal	ADJ
ejpam-3443	326	5	,	,	PUNCT
ejpam-3443	326	6	s	s	PART
ejpam-3443	326	7	=	=	PUNCT
ejpam-3443	326	8	s∗	s∗	PROPN
ejpam-3443	326	9	,	,	PUNCT
ejpam-3443	326	10	and	and	CCONJ
ejpam-3443	326	11	sv	sv	X
ejpam-3443	326	12	=	=	NOUN
ejpam-3443	326	13	∅.	∅.	NOUN
ejpam-3443	326	14	since	since	SCONJ
ejpam-3443	326	15	v	v	NOUN
ejpam-3443	326	16	is	be	AUX
ejpam-3443	326	17	arbitrary	arbitrary	ADJ
ejpam-3443	326	18	,	,	PUNCT
ejpam-3443	326	19	γmce(g	γmce(g	PROPN
ejpam-3443	326	20	◦	◦	NOUN
ejpam-3443	326	21	h	h	NOUN
ejpam-3443	326	22	)	)	PUNCT
ejpam-3443	326	23	=	=	PUNCT
ejpam-3443	326	24	|s|	|s|	PROPN
ejpam-3443	326	25	=	=	PUNCT
ejpam-3443	326	26	∑	∑	PUNCT
ejpam-3443	326	27	v∈s∩v	v∈s∩v	NOUN
ejpam-3443	326	28	(	(	PUNCT
ejpam-3443	326	29	g	g	NOUN
ejpam-3443	326	30	)	)	PUNCT
ejpam-3443	326	31	|s	|s	PROPN
ejpam-3443	326	32	∩	∩	PROPN
ejpam-3443	326	33	v	v	X
ejpam-3443	326	34	(	(	PUNCT
ejpam-3443	326	35	hv	hv	NOUN
ejpam-3443	326	36	+	+	NOUN
ejpam-3443	326	37	v)|+	v)|+	NOUN
ejpam-3443	326	38	∑	∑	PUNCT
ejpam-3443	326	39	v∈v	v∈v	NOUN
ejpam-3443	326	40	(	(	PUNCT
ejpam-3443	326	41	g)\s	g)\s	NOUN
ejpam-3443	326	42	|s	|s	PROPN
ejpam-3443	326	43	∩	∩	PROPN
ejpam-3443	326	44	v	v	NOUN
ejpam-3443	326	45	(	(	PUNCT
ejpam-3443	326	46	hv)|	hv)|	X
ejpam-3443	326	47	≤	≤	ADJ
ejpam-3443	326	48	∑	∑	PUNCT
ejpam-3443	326	49	v∈v	v∈v	NOUN
ejpam-3443	326	50	(	(	PUNCT
ejpam-3443	326	51	g	g	NOUN
ejpam-3443	326	52	)	)	PUNCT
ejpam-3443	326	53	γk1mce(h	γk1mce(h	PROPN
ejpam-3443	326	54	)	)	PUNCT
ejpam-3443	326	55	.	.	PUNCT
ejpam-3443	327	1	finally	finally	ADV
ejpam-3443	327	2	,	,	PUNCT
ejpam-3443	327	3	we	we	PRON
ejpam-3443	327	4	prove	prove	VERB
ejpam-3443	327	5	statement	statement	NOUN
ejpam-3443	327	6	(	(	PUNCT
ejpam-3443	327	7	iii	iii	NOUN
ejpam-3443	327	8	)	)	PUNCT
ejpam-3443	327	9	.	.	PUNCT
ejpam-3443	328	1	for	for	ADP
ejpam-3443	328	2	each	each	DET
ejpam-3443	328	3	v	v	NUM
ejpam-3443	328	4	∈	∈	PROPN
ejpam-3443	328	5	v	v	NOUN
ejpam-3443	328	6	(	(	PUNCT
ejpam-3443	328	7	g	g	NOUN
ejpam-3443	328	8	)	)	PUNCT
ejpam-3443	328	9	,	,	PUNCT
ejpam-3443	328	10	let	let	VERB
ejpam-3443	328	11	sv	sv	PROPN
ejpam-3443	328	12	⊆	⊆	NUM
ejpam-3443	328	13	v	v	X
ejpam-3443	328	14	(	(	PUNCT
ejpam-3443	328	15	hv	hv	NOUN
ejpam-3443	328	16	)	)	PUNCT
ejpam-3443	328	17	be	be	VERB
ejpam-3443	328	18	a	a	DET
ejpam-3443	328	19	γ+k1ce	γ+k1ce	NOUN
ejpam-3443	328	20	-set	-set	PUNCT
ejpam-3443	328	21	of	of	ADP
ejpam-3443	328	22	hv	hv	PROPN
ejpam-3443	328	23	.	.	PUNCT
ejpam-3443	329	1	by	by	ADP
ejpam-3443	329	2	proposition	proposition	NOUN
ejpam-3443	329	3	3	3	NUM
ejpam-3443	329	4	,	,	PUNCT
ejpam-3443	329	5	s	s	PART
ejpam-3443	329	6	=	=	SYM
ejpam-3443	329	7	∪v∈v	∪v∈v	X
ejpam-3443	329	8	(	(	PUNCT
ejpam-3443	329	9	g)sv	g)sv	PROPN
ejpam-3443	329	10	is	be	AUX
ejpam-3443	329	11	a	a	DET
ejpam-3443	329	12	cost	cost	NOUN
ejpam-3443	329	13	effective	effective	ADJ
ejpam-3443	329	14	dominating	dominating	NOUN
ejpam-3443	329	15	set	set	NOUN
ejpam-3443	329	16	of	of	ADP
ejpam-3443	329	17	g	g	PROPN
ejpam-3443	329	18	◦	◦	NOUN
ejpam-3443	329	19	h.	h.	NOUN
ejpam-3443	329	20	thus	thus	ADV
ejpam-3443	329	21	γ+ce(g	γ+ce(g	PROPN
ejpam-3443	329	22	◦	◦	NOUN
ejpam-3443	329	23	h	h	NOUN
ejpam-3443	329	24	)	)	PUNCT
ejpam-3443	329	25	≥	≥	NOUN
ejpam-3443	329	26	mγ+k1ce	mγ+k1ce	X
ejpam-3443	329	27	(	(	PUNCT
ejpam-3443	329	28	h	h	NOUN
ejpam-3443	329	29	)	)	PUNCT
ejpam-3443	329	30	.	.	PUNCT
ejpam-3443	330	1	now	now	ADV
ejpam-3443	330	2	,	,	PUNCT
ejpam-3443	330	3	suppose	suppose	VERB
ejpam-3443	330	4	that	that	SCONJ
ejpam-3443	330	5	γ+ce(g	γ+ce(g	PROPN
ejpam-3443	330	6	◦	◦	NOUN
ejpam-3443	330	7	h	h	NOUN
ejpam-3443	330	8	)	)	PUNCT
ejpam-3443	330	9	>	>	X
ejpam-3443	330	10	mγ+k1ce	mγ+k1ce	PROPN
ejpam-3443	330	11	(	(	PUNCT
ejpam-3443	330	12	h	h	NOUN
ejpam-3443	330	13	)	)	PUNCT
ejpam-3443	330	14	,	,	PUNCT
ejpam-3443	330	15	and	and	CCONJ
ejpam-3443	330	16	let	let	VERB
ejpam-3443	330	17	s	s	PRON
ejpam-3443	330	18	⊆	⊆	NUM
ejpam-3443	330	19	v	v	NOUN
ejpam-3443	330	20	(	(	PUNCT
ejpam-3443	330	21	g	g	PROPN
ejpam-3443	330	22	◦	◦	NOUN
ejpam-3443	330	23	h	h	NOUN
ejpam-3443	330	24	)	)	PUNCT
ejpam-3443	330	25	be	be	VERB
ejpam-3443	330	26	a	a	DET
ejpam-3443	330	27	γ+ce	γ+ce	NOUN
ejpam-3443	330	28	-	-	PUNCT
ejpam-3443	330	29	set	set	NOUN
ejpam-3443	330	30	of	of	ADP
ejpam-3443	330	31	g	g	PROPN
ejpam-3443	330	32	◦	◦	NOUN
ejpam-3443	330	33	h.	h.	NOUN
ejpam-3443	330	34	then	then	ADV
ejpam-3443	330	35	there	there	PRON
ejpam-3443	330	36	exists	exist	VERB
ejpam-3443	330	37	v	v	ADP
ejpam-3443	330	38	∈	∈	PROPN
ejpam-3443	330	39	s	s	PART
ejpam-3443	330	40	∩	∩	ADJ
ejpam-3443	330	41	v	v	X
ejpam-3443	330	42	(	(	PUNCT
ejpam-3443	330	43	g	g	NOUN
ejpam-3443	330	44	)	)	PUNCT
ejpam-3443	330	45	such	such	ADJ
ejpam-3443	330	46	that	that	SCONJ
ejpam-3443	330	47	|s	|s	PROPN
ejpam-3443	330	48	∩	∩	PROPN
ejpam-3443	330	49	v	v	X
ejpam-3443	330	50	(	(	PUNCT
ejpam-3443	330	51	hv	hv	PROPN
ejpam-3443	330	52	+	+	CCONJ
ejpam-3443	330	53	v)|	v)|	NOUN
ejpam-3443	330	54	=	=	SYM
ejpam-3443	330	55	1	1	NUM
ejpam-3443	330	56	+	+	CCONJ
ejpam-3443	330	57	γ+k1ce	γ+k1ce	PROPN
ejpam-3443	330	58	(	(	PUNCT
ejpam-3443	330	59	h	h	NOUN
ejpam-3443	330	60	)	)	PUNCT
ejpam-3443	330	61	.	.	PUNCT
ejpam-3443	331	1	thus	thus	ADV
ejpam-3443	331	2	,	,	PUNCT
ejpam-3443	331	3	sv	sv	INTJ
ejpam-3443	331	4	=	=	SYM
ejpam-3443	331	5	s	s	PROPN
ejpam-3443	331	6	∩	∩	ADJ
ejpam-3443	331	7	v	v	X
ejpam-3443	331	8	(	(	PUNCT
ejpam-3443	331	9	hv	hv	X
ejpam-3443	331	10	)	)	PUNCT
ejpam-3443	331	11	is	be	AUX
ejpam-3443	331	12	a	a	DET
ejpam-3443	331	13	very	very	ADV
ejpam-3443	331	14	cost	cost	NOUN
ejpam-3443	331	15	effective	effective	ADJ
ejpam-3443	331	16	set	set	NOUN
ejpam-3443	331	17	of	of	ADP
ejpam-3443	331	18	hv	hv	PROPN
ejpam-3443	331	19	of	of	ADP
ejpam-3443	331	20	cardinality	cardinality	PROPN
ejpam-3443	331	21	γ+k1ce	γ+k1ce	PROPN
ejpam-3443	331	22	(	(	PUNCT
ejpam-3443	331	23	h	h	NOUN
ejpam-3443	331	24	)	)	PUNCT
ejpam-3443	331	25	and	and	CCONJ
ejpam-3443	331	26	satisfying	satisfy	VERB
ejpam-3443	331	27	γ+k1ce	γ+k1ce	PROPN
ejpam-3443	331	28	(	(	PUNCT
ejpam-3443	331	29	h	h	NOUN
ejpam-3443	331	30	)	)	PUNCT
ejpam-3443	331	31	≤	≤	NUM
ejpam-3443	331	32	1	1	NUM
ejpam-3443	331	33	2	2	NUM
ejpam-3443	331	34	(	(	PUNCT
ejpam-3443	331	35	n+	n+	NUM
ejpam-3443	331	36	|ng(v	|ng(v	ADJ
ejpam-3443	331	37	)	)	PUNCT
ejpam-3443	331	38	\	\	NOUN
ejpam-3443	331	39	s|	s|	VERB
ejpam-3443	331	40	−	−	NOUN
ejpam-3443	331	41	|ng(v	|ng(v	NOUN
ejpam-3443	331	42	)	)	PUNCT
ejpam-3443	331	43	∩	∩	NOUN
ejpam-3443	331	44	s|	s|	PROPN
ejpam-3443	331	45	)	)	PUNCT
ejpam-3443	331	46	≤	≤	NOUN
ejpam-3443	331	47	1	1	NUM
ejpam-3443	331	48	2	2	NUM
ejpam-3443	331	49	(	(	PUNCT
ejpam-3443	331	50	n+	n+	NUM
ejpam-3443	331	51	degg(v	degg(v	PROPN
ejpam-3443	331	52	)	)	PUNCT
ejpam-3443	331	53	)	)	PUNCT
ejpam-3443	331	54	.	.	PUNCT
ejpam-3443	332	1	in	in	ADP
ejpam-3443	332	2	other	other	ADJ
ejpam-3443	332	3	words	word	NOUN
ejpam-3443	332	4	,	,	PUNCT
ejpam-3443	332	5	degg(v	degg(v	PROPN
ejpam-3443	332	6	)	)	PUNCT
ejpam-3443	332	7	≥	≥	NOUN
ejpam-3443	332	8	2γk1ce	2γk1ce	NUM
ejpam-3443	332	9	+	+	CCONJ
ejpam-3443	332	10	(	(	PUNCT
ejpam-3443	332	11	h)−	h)−	PROPN
ejpam-3443	332	12	n.	n.	PROPN
ejpam-3443	332	13	thus	thus	ADV
ejpam-3443	332	14	,	,	PUNCT
ejpam-3443	332	15	v	v	PROPN
ejpam-3443	332	16	∈	∈	PROPN
ejpam-3443	332	17	l.	l.	NOUN
ejpam-3443	332	18	therefore	therefore	ADV
ejpam-3443	332	19	,	,	PUNCT
ejpam-3443	332	20	γ+ce(g	γ+ce(g	PROPN
ejpam-3443	332	21	◦	◦	NOUN
ejpam-3443	332	22	h	h	NOUN
ejpam-3443	332	23	)	)	PUNCT
ejpam-3443	332	24	≤	≤	NOUN
ejpam-3443	332	25	|l|	|l|	VERB
ejpam-3443	332	26	(	(	PUNCT
ejpam-3443	332	27	1	1	NUM
ejpam-3443	332	28	+	+	CCONJ
ejpam-3443	332	29	γ+k1ce	γ+k1ce	ADJ
ejpam-3443	332	30	(	(	PUNCT
ejpam-3443	332	31	h	h	NOUN
ejpam-3443	332	32	)	)	PUNCT
ejpam-3443	332	33	)	)	PUNCT
ejpam-3443	333	1	+	+	CCONJ
ejpam-3443	333	2	(	(	PUNCT
ejpam-3443	333	3	m−	m−	PROPN
ejpam-3443	333	4	|l|	|l|	PROPN
ejpam-3443	333	5	)	)	PUNCT
ejpam-3443	333	6	γ+k1ce	γ+k1ce	NOUN
ejpam-3443	333	7	(	(	PUNCT
ejpam-3443	333	8	h	h	NOUN
ejpam-3443	333	9	)	)	PUNCT
ejpam-3443	333	10	=	=	X
ejpam-3443	333	11	|l|+mγ+k1ce	|l|+mγ+k1ce	X
ejpam-3443	333	12	(	(	PUNCT
ejpam-3443	333	13	h	h	NOUN
ejpam-3443	333	14	)	)	PUNCT
ejpam-3443	333	15	.	.	PUNCT
ejpam-3443	334	1	remark	remark	PROPN
ejpam-3443	334	2	6	6	NUM
ejpam-3443	334	3	.	.	PUNCT
ejpam-3443	335	1	the	the	DET
ejpam-3443	335	2	bounds	bound	NOUN
ejpam-3443	335	3	in	in	ADP
ejpam-3443	335	4	corollary	corollary	ADJ
ejpam-3443	335	5	4.2.10	4.2.10	NUM
ejpam-3443	335	6	are	be	AUX
ejpam-3443	335	7	sharp	sharp	ADJ
ejpam-3443	335	8	.	.	PUNCT
ejpam-3443	336	1	note	note	NOUN
ejpam-3443	336	2	,	,	PUNCT
ejpam-3443	336	3	for	for	ADP
ejpam-3443	336	4	example	example	NOUN
ejpam-3443	337	1	that	that	SCONJ
ejpam-3443	337	2	γ+ce(p3	γ+ce(p3	PROPN
ejpam-3443	337	3	◦	◦	NOUN
ejpam-3443	337	4	k4	k4	NOUN
ejpam-3443	337	5	)	)	PUNCT
ejpam-3443	337	6	=	=	SYM
ejpam-3443	337	7	9	9	NUM
ejpam-3443	337	8	=	=	SYM
ejpam-3443	337	9	3γ+k1ce	3γ+k1ce	NUM
ejpam-3443	337	10	(	(	PUNCT
ejpam-3443	337	11	k4	k4	PROPN
ejpam-3443	337	12	)	)	PUNCT
ejpam-3443	337	13	.	.	PUNCT
ejpam-3443	338	1	verify	verify	VERB
ejpam-3443	338	2	also	also	ADV
ejpam-3443	338	3	that	that	SCONJ
ejpam-3443	338	4	γ+ce(p3	γ+ce(p3	PUNCT
ejpam-3443	338	5	◦	◦	NOUN
ejpam-3443	338	6	k1,3	k1,3	NOUN
ejpam-3443	338	7	)	)	PUNCT
ejpam-3443	338	8	=	=	SYM
ejpam-3443	339	1	10	10	NUM
ejpam-3443	339	2	=	=	SYM
ejpam-3443	339	3	1	1	NUM
ejpam-3443	339	4	+	+	X
ejpam-3443	339	5	3γ+k1ce	3γ+k1ce	NUM
ejpam-3443	339	6	(	(	PUNCT
ejpam-3443	339	7	k1,3	k1,3	PROPN
ejpam-3443	339	8	)	)	PUNCT
ejpam-3443	339	9	.	.	PUNCT
ejpam-3443	340	1	corollary	corollary	ADJ
ejpam-3443	340	2	7	7	NUM
ejpam-3443	340	3	.	.	PUNCT
ejpam-3443	341	1	let	let	VERB
ejpam-3443	341	2	g	g	PRON
ejpam-3443	341	3	be	be	AUX
ejpam-3443	341	4	a	a	DET
ejpam-3443	341	5	connected	connected	ADJ
ejpam-3443	341	6	graph	graph	NOUN
ejpam-3443	341	7	and	and	CCONJ
ejpam-3443	341	8	m	m	PRON
ejpam-3443	341	9	≥	≥	NOUN
ejpam-3443	341	10	2	2	NUM
ejpam-3443	341	11	.	.	PUNCT
ejpam-3443	342	1	then	then	ADV
ejpam-3443	342	2	(	(	PUNCT
ejpam-3443	342	3	i	i	NOUN
ejpam-3443	342	4	)	)	PUNCT
ejpam-3443	342	5	γce(g	γce(g	PROPN
ejpam-3443	342	6	◦	◦	NOUN
ejpam-3443	342	7	km	km	NOUN
ejpam-3443	342	8	)	)	PUNCT
ejpam-3443	342	9	=	=	SYM
ejpam-3443	342	10	|v	|v	PROPN
ejpam-3443	342	11	(	(	PUNCT
ejpam-3443	342	12	g)|	g)|	NOUN
ejpam-3443	342	13	;	;	PUNCT
ejpam-3443	342	14	(	(	PUNCT
ejpam-3443	342	15	ii	ii	NOUN
ejpam-3443	342	16	)	)	PUNCT
ejpam-3443	342	17	γmce(g	γmce(g	PROPN
ejpam-3443	342	18	◦	◦	NOUN
ejpam-3443	342	19	km	km	NOUN
ejpam-3443	342	20	)	)	PUNCT
ejpam-3443	342	21	=	=	SYM
ejpam-3443	342	22	|v	|v	PROPN
ejpam-3443	342	23	(	(	PUNCT
ejpam-3443	342	24	g)|	g)|	NOUN
ejpam-3443	342	25	;	;	PUNCT
ejpam-3443	342	26	and	and	CCONJ
ejpam-3443	342	27	(	(	PUNCT
ejpam-3443	342	28	iii	iii	NOUN
ejpam-3443	342	29	)	)	PUNCT
ejpam-3443	342	30	γ+ce(g	γ+ce(g	PROPN
ejpam-3443	342	31	◦	◦	NOUN
ejpam-3443	342	32	km	km	NOUN
ejpam-3443	342	33	)	)	PUNCT
ejpam-3443	342	34	=	=	SYM
ejpam-3443	342	35	|v	|v	PROPN
ejpam-3443	342	36	(	(	PUNCT
ejpam-3443	342	37	g)|	g)|	NOUN
ejpam-3443	342	38	⌊	⌊	PROPN
ejpam-3443	342	39	m+2	m+2	ADP
ejpam-3443	342	40	2	2	NUM
ejpam-3443	342	41	⌋	⌋	NOUN
ejpam-3443	342	42	.	.	PUNCT
ejpam-3443	343	1	proof	proof	NOUN
ejpam-3443	343	2	.	.	PUNCT
ejpam-3443	344	1	statement	statement	NOUN
ejpam-3443	344	2	(	(	PUNCT
ejpam-3443	344	3	i	i	NOUN
ejpam-3443	344	4	)	)	PUNCT
ejpam-3443	344	5	follows	follow	VERB
ejpam-3443	344	6	from	from	ADP
ejpam-3443	344	7	corollary	corollary	ADJ
ejpam-3443	344	8	5	5	NUM
ejpam-3443	344	9	and	and	CCONJ
ejpam-3443	344	10	corollary	corollary	ADJ
ejpam-3443	344	11	6	6	NUM
ejpam-3443	344	12	.	.	PUNCT
ejpam-3443	345	1	corollary	corollary	ADJ
ejpam-3443	345	2	6	6	NUM
ejpam-3443	345	3	also	also	ADV
ejpam-3443	345	4	yields	yield	VERB
ejpam-3443	345	5	statement	statement	NOUN
ejpam-3443	345	6	(	(	PUNCT
ejpam-3443	345	7	ii	ii	NOUN
ejpam-3443	345	8	)	)	PUNCT
ejpam-3443	345	9	and	and	CCONJ
ejpam-3443	345	10	statement	statement	NOUN
ejpam-3443	345	11	(	(	PUNCT
ejpam-3443	345	12	iii	iii	NOUN
ejpam-3443	345	13	)	)	PUNCT
ejpam-3443	345	14	and	and	CCONJ
ejpam-3443	345	15	the	the	DET
ejpam-3443	345	16	fact	fact	NOUN
ejpam-3443	345	17	that	that	SCONJ
ejpam-3443	345	18	γk1ce(km	γk1ce(km	PROPN
ejpam-3443	345	19	)	)	PUNCT
ejpam-3443	345	20	=	=	SYM
ejpam-3443	345	21	1	1	NUM
ejpam-3443	345	22	,	,	PUNCT
ejpam-3443	345	23	γk1mce(km	γk1mce(km	PROPN
ejpam-3443	345	24	)	)	PUNCT
ejpam-3443	345	25	=	=	SYM
ejpam-3443	345	26	1	1	NUM
ejpam-3443	345	27	and	and	CCONJ
ejpam-3443	345	28	γ+k1ce	γ+k1ce	PROPN
ejpam-3443	345	29	(	(	PUNCT
ejpam-3443	345	30	km	km	NOUN
ejpam-3443	345	31	)	)	PUNCT
ejpam-3443	345	32	=	=	PUNCT
ejpam-3443	346	1	⌊	⌊	VERB
ejpam-3443	346	2	m+2	m+2	SYM
ejpam-3443	346	3	2	2	NUM
ejpam-3443	346	4	⌋	⌋	NOUN
ejpam-3443	346	5	.	.	PUNCT
ejpam-3443	347	1	f.jamil	f.jamil	PROPN
ejpam-3443	347	2	,	,	PUNCT
ejpam-3443	347	3	h.	h.	PROPN
ejpam-3443	347	4	nuenay	nuenay	PROPN
ejpam-3443	347	5	-	-	PUNCT
ejpam-3443	347	6	maglanque	maglanque	ADJ
ejpam-3443	347	7	/	/	SYM
ejpam-3443	347	8	eur	eur	NOUN
ejpam-3443	347	9	.	.	PUNCT
ejpam-3443	348	1	j.	j.	PROPN
ejpam-3443	348	2	pure	pure	PROPN
ejpam-3443	348	3	appl	appl	PROPN
ejpam-3443	348	4	.	.	PROPN
ejpam-3443	348	5	math	math	PROPN
ejpam-3443	348	6	,	,	PUNCT
ejpam-3443	348	7	12	12	NUM
ejpam-3443	348	8	(	(	PUNCT
ejpam-3443	348	9	3	3	NUM
ejpam-3443	348	10	)	)	PUNCT
ejpam-3443	348	11	(	(	PUNCT
ejpam-3443	348	12	2019	2019	NUM
ejpam-3443	348	13	)	)	PUNCT
ejpam-3443	348	14	,	,	PUNCT
ejpam-3443	348	15	978	978	NUM
ejpam-3443	348	16	-	-	SYM
ejpam-3443	348	17	998	998	NUM
ejpam-3443	348	18	991	991	NUM
ejpam-3443	348	19	example	example	NOUN
ejpam-3443	349	1	3	3	NUM
ejpam-3443	349	2	.	.	PUNCT
ejpam-3443	350	1	if	if	SCONJ
ejpam-3443	350	2	g	g	PROPN
ejpam-3443	350	3	is	be	AUX
ejpam-3443	350	4	either	either	CCONJ
ejpam-3443	350	5	the	the	DET
ejpam-3443	350	6	path	path	NOUN
ejpam-3443	350	7	pn	pn	PROPN
ejpam-3443	350	8	or	or	CCONJ
ejpam-3443	350	9	the	the	DET
ejpam-3443	350	10	cycle	cycle	NOUN
ejpam-3443	350	11	cn	cn	NOUN
ejpam-3443	350	12	of	of	ADP
ejpam-3443	350	13	order	order	NOUN
ejpam-3443	350	14	n	n	NOUN
ejpam-3443	350	15	and	and	CCONJ
ejpam-3443	350	16	m	m	PRON
ejpam-3443	350	17	≥	≥	NOUN
ejpam-3443	350	18	2	2	NUM
ejpam-3443	350	19	,	,	PUNCT
ejpam-3443	350	20	then	then	ADV
ejpam-3443	350	21	(	(	PUNCT
ejpam-3443	350	22	i	i	NOUN
ejpam-3443	350	23	)	)	PUNCT
ejpam-3443	350	24	γce(g	γce(g	PROPN
ejpam-3443	351	1	◦	◦	NOUN
ejpam-3443	351	2	km	km	NOUN
ejpam-3443	351	3	)	)	PUNCT
ejpam-3443	351	4	=	=	SYM
ejpam-3443	352	1	n	n	CCONJ
ejpam-3443	352	2	;	;	PUNCT
ejpam-3443	352	3	(	(	PUNCT
ejpam-3443	352	4	ii	ii	NOUN
ejpam-3443	352	5	)	)	PUNCT
ejpam-3443	352	6	γmce(g	γmce(g	PROPN
ejpam-3443	352	7	◦	◦	NOUN
ejpam-3443	352	8	km	km	NOUN
ejpam-3443	352	9	)	)	PUNCT
ejpam-3443	352	10	=	=	SYM
ejpam-3443	352	11	n	n	CCONJ
ejpam-3443	352	12	;	;	PUNCT
ejpam-3443	352	13	and	and	CCONJ
ejpam-3443	352	14	(	(	PUNCT
ejpam-3443	352	15	iii	iii	NOUN
ejpam-3443	352	16	)	)	PUNCT
ejpam-3443	352	17	γ+ce(g	γ+ce(g	PROPN
ejpam-3443	352	18	◦	◦	NOUN
ejpam-3443	352	19	km	km	NOUN
ejpam-3443	352	20	)	)	PUNCT
ejpam-3443	352	21	=	=	PUNCT
ejpam-3443	353	1	n	n	CCONJ
ejpam-3443	353	2	⌊	⌊	VERB
ejpam-3443	353	3	m+2	m+2	ADP
ejpam-3443	353	4	2	2	NUM
ejpam-3443	353	5	⌋	⌋	NOUN
ejpam-3443	353	6	.	.	PUNCT
ejpam-3443	354	1	example	example	NOUN
ejpam-3443	355	1	4	4	NUM
ejpam-3443	355	2	.	.	X
ejpam-3443	355	3	for	for	ADP
ejpam-3443	355	4	the	the	DET
ejpam-3443	355	5	complete	complete	ADJ
ejpam-3443	355	6	graph	graph	NOUN
ejpam-3443	355	7	kn	kn	PROPN
ejpam-3443	355	8	of	of	ADP
ejpam-3443	355	9	order	order	NOUN
ejpam-3443	355	10	n	n	PRON
ejpam-3443	355	11	≥	≥	NOUN
ejpam-3443	355	12	2	2	NUM
ejpam-3443	355	13	and	and	CCONJ
ejpam-3443	355	14	m	m	PROPN
ejpam-3443	355	15	≥	≥	NOUN
ejpam-3443	355	16	2	2	NUM
ejpam-3443	355	17	,	,	PUNCT
ejpam-3443	355	18	(	(	PUNCT
ejpam-3443	355	19	i	i	NOUN
ejpam-3443	355	20	)	)	PUNCT
ejpam-3443	355	21	γce(kn	γce(kn	NOUN
ejpam-3443	355	22	◦	◦	NOUN
ejpam-3443	355	23	km	km	NOUN
ejpam-3443	355	24	)	)	PUNCT
ejpam-3443	355	25	=	=	SYM
ejpam-3443	355	26	n	n	CCONJ
ejpam-3443	355	27	;	;	PUNCT
ejpam-3443	355	28	(	(	PUNCT
ejpam-3443	355	29	ii	ii	NOUN
ejpam-3443	355	30	)	)	PUNCT
ejpam-3443	355	31	γmce(kn	γmce(kn	NOUN
ejpam-3443	355	32	◦	◦	NOUN
ejpam-3443	355	33	km	km	NOUN
ejpam-3443	355	34	)	)	PUNCT
ejpam-3443	355	35	=	=	SYM
ejpam-3443	355	36	n	n	CCONJ
ejpam-3443	355	37	;	;	PUNCT
ejpam-3443	355	38	and	and	CCONJ
ejpam-3443	355	39	(	(	PUNCT
ejpam-3443	355	40	iii	iii	NOUN
ejpam-3443	355	41	)	)	PUNCT
ejpam-3443	355	42	γ+ce(kn	γ+ce(kn	NUM
ejpam-3443	355	43	◦	◦	NOUN
ejpam-3443	355	44	km	km	NOUN
ejpam-3443	355	45	)	)	PUNCT
ejpam-3443	355	46	=	=	PUNCT
ejpam-3443	356	1	n	n	CCONJ
ejpam-3443	356	2	⌊	⌊	VERB
ejpam-3443	356	3	m+2	m+2	ADP
ejpam-3443	356	4	2	2	NUM
ejpam-3443	356	5	⌋	⌋	NOUN
ejpam-3443	356	6	.	.	PUNCT
ejpam-3443	357	1	proposition	proposition	NOUN
ejpam-3443	357	2	5	5	NUM
ejpam-3443	357	3	.	.	PUNCT
ejpam-3443	358	1	let	let	VERB
ejpam-3443	358	2	g	g	PRON
ejpam-3443	358	3	be	be	AUX
ejpam-3443	358	4	a	a	DET
ejpam-3443	358	5	connected	connected	ADJ
ejpam-3443	358	6	graph	graph	NOUN
ejpam-3443	358	7	and	and	CCONJ
ejpam-3443	358	8	h	h	NOUN
ejpam-3443	358	9	the	the	DET
ejpam-3443	358	10	union	union	NOUN
ejpam-3443	358	11	of	of	ADP
ejpam-3443	358	12	k	k	PROPN
ejpam-3443	358	13	isolated	isolated	ADJ
ejpam-3443	358	14	vertices	vertex	NOUN
ejpam-3443	358	15	and	and	CCONJ
ejpam-3443	358	16	k	k	PROPN
ejpam-3443	358	17	isolate	isolate	NOUN
ejpam-3443	358	18	-	-	PUNCT
ejpam-3443	358	19	free	free	ADJ
ejpam-3443	358	20	subgraph	subgraph	NOUN
ejpam-3443	358	21	.	.	PUNCT
ejpam-3443	359	1	then	then	ADV
ejpam-3443	359	2	(	(	PUNCT
ejpam-3443	359	3	i	i	NOUN
ejpam-3443	359	4	)	)	PUNCT
ejpam-3443	359	5	γce(g	γce(g	PROPN
ejpam-3443	360	1	◦	◦	NOUN
ejpam-3443	360	2	h	h	NOUN
ejpam-3443	360	3	)	)	PUNCT
ejpam-3443	360	4	=	=	SYM
ejpam-3443	360	5	|v	|v	PROPN
ejpam-3443	360	6	(	(	PUNCT
ejpam-3443	360	7	g)|	g)|	NOUN
ejpam-3443	360	8	(	(	PUNCT
ejpam-3443	360	9	k	k	PROPN
ejpam-3443	360	10	+	+	CCONJ
ejpam-3443	360	11	γk1ce(k))−	γk1ce(k))−	NOUN
ejpam-3443	360	12	γ+knce	γ+knce	NOUN
ejpam-3443	360	13	(	(	PUNCT
ejpam-3443	360	14	g	g	NOUN
ejpam-3443	360	15	)	)	PUNCT
ejpam-3443	360	16	(	(	PUNCT
ejpam-3443	360	17	γk1ce(k	γk1ce(k	PROPN
ejpam-3443	360	18	)	)	PUNCT
ejpam-3443	361	1	+	+	CCONJ
ejpam-3443	362	1	k	k	X
ejpam-3443	363	1	−	−	NOUN
ejpam-3443	364	1	1	1	NUM
ejpam-3443	364	2	)	)	PUNCT
ejpam-3443	364	3	;	;	PUNCT
ejpam-3443	364	4	(	(	PUNCT
ejpam-3443	364	5	ii	ii	NOUN
ejpam-3443	364	6	)	)	PUNCT
ejpam-3443	364	7	γmce(g	γmce(g	PROPN
ejpam-3443	364	8	◦	◦	NOUN
ejpam-3443	364	9	h	h	NOUN
ejpam-3443	364	10	)	)	PUNCT
ejpam-3443	365	1	=	=	SYM
ejpam-3443	365	2	|v	|v	PROPN
ejpam-3443	365	3	(	(	PUNCT
ejpam-3443	365	4	g)|	g)|	NOUN
ejpam-3443	365	5	(	(	PUNCT
ejpam-3443	365	6	k	k	PROPN
ejpam-3443	365	7	+	+	PROPN
ejpam-3443	365	8	γk1mce(k	γk1mce(k	PROPN
ejpam-3443	365	9	)	)	PUNCT
ejpam-3443	365	10	)	)	PUNCT
ejpam-3443	365	11	;	;	PUNCT
ejpam-3443	365	12	and	and	CCONJ
ejpam-3443	365	13	(	(	PUNCT
ejpam-3443	365	14	iii	iii	NOUN
ejpam-3443	365	15	)	)	PUNCT
ejpam-3443	365	16	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	366	1	◦	◦	NOUN
ejpam-3443	366	2	h	h	NOUN
ejpam-3443	366	3	)	)	PUNCT
ejpam-3443	366	4	=	=	SYM
ejpam-3443	366	5	|v	|v	PROPN
ejpam-3443	366	6	(	(	PUNCT
ejpam-3443	366	7	g)|	g)|	PROPN
ejpam-3443	366	8	(	(	PUNCT
ejpam-3443	366	9	k	k	PROPN
ejpam-3443	366	10	+	+	X
ejpam-3443	366	11	γ+k1ce	γ+k1ce	PROPN
ejpam-3443	366	12	(	(	PUNCT
ejpam-3443	366	13	k	k	NOUN
ejpam-3443	366	14	)	)	PUNCT
ejpam-3443	366	15	)	)	PUNCT
ejpam-3443	366	16	.	.	PUNCT
ejpam-3443	367	1	proof	proof	NOUN
ejpam-3443	367	2	.	.	PUNCT
ejpam-3443	368	1	let	let	VERB
ejpam-3443	368	2	d	d	NOUN
ejpam-3443	368	3	⊆	⊆	NUM
ejpam-3443	368	4	v	v	ADP
ejpam-3443	368	5	(	(	PUNCT
ejpam-3443	368	6	g	g	NOUN
ejpam-3443	368	7	)	)	PUNCT
ejpam-3443	368	8	be	be	AUX
ejpam-3443	368	9	a	a	DET
ejpam-3443	368	10	kn	kn	NOUN
ejpam-3443	368	11	-	-	PUNCT
ejpam-3443	368	12	cost	cost	NOUN
ejpam-3443	368	13	effective	effective	ADJ
ejpam-3443	368	14	set	set	NOUN
ejpam-3443	368	15	of	of	ADP
ejpam-3443	368	16	g	g	NOUN
ejpam-3443	368	17	of	of	ADP
ejpam-3443	368	18	maximum	maximum	ADJ
ejpam-3443	368	19	cardinality	cardinality	NOUN
ejpam-3443	368	20	.	.	PUNCT
ejpam-3443	369	1	for	for	ADP
ejpam-3443	369	2	each	each	DET
ejpam-3443	369	3	v	v	NOUN
ejpam-3443	369	4	∈	∈	PROPN
ejpam-3443	369	5	d	d	NOUN
ejpam-3443	369	6	,	,	PUNCT
ejpam-3443	369	7	define	define	VERB
ejpam-3443	369	8	sv	sv	INTJ
ejpam-3443	370	1	=	=	SYM
ejpam-3443	370	2	{	{	PUNCT
ejpam-3443	370	3	v	v	NOUN
ejpam-3443	370	4	}	}	PUNCT
ejpam-3443	370	5	,	,	PUNCT
ejpam-3443	370	6	and	and	CCONJ
ejpam-3443	370	7	for	for	ADP
ejpam-3443	370	8	each	each	PRON
ejpam-3443	370	9	v	v	NUM
ejpam-3443	370	10	∈	∈	PROPN
ejpam-3443	370	11	v	v	NOUN
ejpam-3443	370	12	(	(	PUNCT
ejpam-3443	370	13	g	g	NOUN
ejpam-3443	370	14	)	)	PUNCT
ejpam-3443	370	15	\	\	PUNCT
ejpam-3443	371	1	d	d	X
ejpam-3443	371	2	,	,	PUNCT
ejpam-3443	371	3	let	let	VERB
ejpam-3443	371	4	sv	sv	INTJ
ejpam-3443	371	5	=	=	PUNCT
ejpam-3443	371	6	(	(	PUNCT
ejpam-3443	371	7	lv	lv	PROPN
ejpam-3443	371	8	∪	∪	X
ejpam-3443	371	9	pv	pv	NOUN
ejpam-3443	371	10	)	)	PUNCT
ejpam-3443	371	11	⊆	⊆	NUM
ejpam-3443	371	12	v	v	X
ejpam-3443	371	13	(	(	PUNCT
ejpam-3443	371	14	hv	hv	PROPN
ejpam-3443	371	15	)	)	PUNCT
ejpam-3443	371	16	where	where	SCONJ
ejpam-3443	371	17	lv	lv	PROPN
ejpam-3443	371	18	=	=	SYM
ejpam-3443	371	19	∪ki=1{ui	∪ki=1{ui	PROPN
ejpam-3443	371	20	}	}	PUNCT
ejpam-3443	371	21	be	be	AUX
ejpam-3443	371	22	the	the	DET
ejpam-3443	371	23	union	union	NOUN
ejpam-3443	371	24	of	of	ADP
ejpam-3443	371	25	k	k	PROPN
ejpam-3443	371	26	isolated	isolate	VERB
ejpam-3443	371	27	vertices	vertex	NOUN
ejpam-3443	371	28	and	and	CCONJ
ejpam-3443	371	29	pv	pv	VERB
ejpam-3443	371	30	⊆	⊆	NUM
ejpam-3443	371	31	v	v	NOUN
ejpam-3443	371	32	(	(	PUNCT
ejpam-3443	371	33	kv	kv	PROPN
ejpam-3443	371	34	)	)	PUNCT
ejpam-3443	371	35	be	be	AUX
ejpam-3443	371	36	a	a	DET
ejpam-3443	371	37	γk1ce	γk1ce	NUM
ejpam-3443	371	38	-	-	PUNCT
ejpam-3443	371	39	set	set	NOUN
ejpam-3443	371	40	of	of	ADP
ejpam-3443	371	41	kv	kv	PROPN
ejpam-3443	371	42	.	.	PUNCT
ejpam-3443	372	1	put	put	VERB
ejpam-3443	372	2	s	s	PART
ejpam-3443	372	3	=	=	X
ejpam-3443	372	4	∪v∈v	∪v∈v	X
ejpam-3443	372	5	(	(	PUNCT
ejpam-3443	372	6	g)sv	g)sv	PROPN
ejpam-3443	372	7	.	.	PROPN
ejpam-3443	372	8	for	for	ADP
ejpam-3443	372	9	each	each	DET
ejpam-3443	372	10	v	v	NUM
ejpam-3443	372	11	∈	∈	PROPN
ejpam-3443	372	12	s	s	PART
ejpam-3443	372	13	∩	∩	ADJ
ejpam-3443	372	14	v	v	X
ejpam-3443	372	15	(	(	PUNCT
ejpam-3443	372	16	g	g	NOUN
ejpam-3443	372	17	)	)	PUNCT
ejpam-3443	372	18	=	=	SYM
ejpam-3443	373	1	d	d	PROPN
ejpam-3443	373	2	,	,	PUNCT
ejpam-3443	373	3	s	s	X
ejpam-3443	373	4	∩	∩	ADJ
ejpam-3443	373	5	v	v	NOUN
ejpam-3443	373	6	(	(	PUNCT
ejpam-3443	373	7	hv)|	hv)|	NOUN
ejpam-3443	373	8	=	=	NOUN
ejpam-3443	373	9	∅	∅	NOUN
ejpam-3443	373	10	so	so	SCONJ
ejpam-3443	373	11	that	that	SCONJ
ejpam-3443	373	12	|s	|s	PROPN
ejpam-3443	373	13	∩	∩	PROPN
ejpam-3443	373	14	v	v	X
ejpam-3443	373	15	(	(	PUNCT
ejpam-3443	373	16	hv)|	hv)|	NOUN
ejpam-3443	373	17	=	=	SYM
ejpam-3443	373	18	0	0	NUM
ejpam-3443	373	19	≤	≤	NOUN
ejpam-3443	373	20	|v	|v	X
ejpam-3443	373	21	(	(	PUNCT
ejpam-3443	373	22	h)|+	h)|+	ADJ
ejpam-3443	373	23	|ng(v	|ng(v	NOUN
ejpam-3443	373	24	)	)	PUNCT
ejpam-3443	373	25	\	\	NOUN
ejpam-3443	373	26	s|	s|	VERB
ejpam-3443	373	27	−	−	NOUN
ejpam-3443	373	28	|ng(v	|ng(v	NOUN
ejpam-3443	373	29	)	)	PUNCT
ejpam-3443	373	30	∩	∩	NOUN
ejpam-3443	373	31	s|	s|	VERB
ejpam-3443	373	32	.	.	PUNCT
ejpam-3443	374	1	for	for	ADP
ejpam-3443	374	2	each	each	PRON
ejpam-3443	374	3	v	v	NUM
ejpam-3443	374	4	∈	∈	PROPN
ejpam-3443	374	5	v	v	NOUN
ejpam-3443	374	6	(	(	PUNCT
ejpam-3443	374	7	g	g	NOUN
ejpam-3443	374	8	)	)	PUNCT
ejpam-3443	374	9	\	\	PART
ejpam-3443	375	1	s	s	PART
ejpam-3443	375	2	=	=	SYM
ejpam-3443	375	3	v	v	X
ejpam-3443	375	4	(	(	PUNCT
ejpam-3443	375	5	g	g	NOUN
ejpam-3443	375	6	)	)	PUNCT
ejpam-3443	375	7	\d	\d	NOUN
ejpam-3443	375	8	,	,	PUNCT
ejpam-3443	375	9	s	s	PART
ejpam-3443	375	10	∩	∩	ADJ
ejpam-3443	375	11	v	v	X
ejpam-3443	375	12	(	(	PUNCT
ejpam-3443	375	13	hv	hv	NOUN
ejpam-3443	375	14	)	)	PUNCT
ejpam-3443	375	15	=	=	PRON
ejpam-3443	376	1	sv	sv	PROPN
ejpam-3443	376	2	is	be	AUX
ejpam-3443	376	3	a	a	DET
ejpam-3443	376	4	k1	k1	NOUN
ejpam-3443	376	5	-	-	PUNCT
ejpam-3443	376	6	cost	cost	NOUN
ejpam-3443	376	7	effective	effective	ADJ
ejpam-3443	376	8	dominating	dominating	NOUN
ejpam-3443	376	9	set	set	NOUN
ejpam-3443	376	10	of	of	ADP
ejpam-3443	376	11	hv	hv	PROPN
ejpam-3443	376	12	.	.	PUNCT
ejpam-3443	377	1	by	by	ADP
ejpam-3443	377	2	remark	remark	NOUN
ejpam-3443	377	3	6	6	NUM
ejpam-3443	377	4	,	,	PUNCT
ejpam-3443	377	5	s	s	VERB
ejpam-3443	377	6	is	be	AUX
ejpam-3443	377	7	a	a	DET
ejpam-3443	377	8	cost	cost	NOUN
ejpam-3443	377	9	effective	effective	ADJ
ejpam-3443	377	10	dominating	dominating	NOUN
ejpam-3443	377	11	set	set	NOUN
ejpam-3443	377	12	of	of	ADP
ejpam-3443	377	13	g	g	PROPN
ejpam-3443	377	14	◦	◦	NOUN
ejpam-3443	377	15	h	h	NOUN
ejpam-3443	377	16	,	,	PUNCT
ejpam-3443	377	17	and	and	CCONJ
ejpam-3443	377	18	γce(g	γce(g	PROPN
ejpam-3443	378	1	◦	◦	NOUN
ejpam-3443	378	2	h	h	NOUN
ejpam-3443	378	3	)	)	PUNCT
ejpam-3443	378	4	≤	≤	NUM
ejpam-3443	378	5	|s|	|s|	NOUN
ejpam-3443	378	6	=	=	SYM
ejpam-3443	378	7	|d|+	|d|+	NOUN
ejpam-3443	378	8	∑	∑	PUNCT
ejpam-3443	378	9	v∈v	v∈v	NOUN
ejpam-3443	378	10	(	(	PUNCT
ejpam-3443	378	11	g)\d	g)\d	NOUN
ejpam-3443	378	12	|sv|	|sv|	PROPN
ejpam-3443	378	13	=	=	SYM
ejpam-3443	378	14	γ+knce	γ+knce	PROPN
ejpam-3443	378	15	(	(	PUNCT
ejpam-3443	378	16	g	g	NOUN
ejpam-3443	378	17	)	)	PUNCT
ejpam-3443	378	18	+	+	CCONJ
ejpam-3443	378	19	(	(	PUNCT
ejpam-3443	378	20	|v	|v	X
ejpam-3443	378	21	(	(	PUNCT
ejpam-3443	378	22	g)|	g)|	NOUN
ejpam-3443	378	23	−	−	PROPN
ejpam-3443	378	24	γ+knce	γ+knce	PROPN
ejpam-3443	378	25	(	(	PUNCT
ejpam-3443	378	26	g	g	NOUN
ejpam-3443	378	27	)	)	PUNCT
ejpam-3443	378	28	)	)	PUNCT
ejpam-3443	378	29	(	(	PUNCT
ejpam-3443	378	30	k	k	X
ejpam-3443	378	31	+	+	NUM
ejpam-3443	378	32	γk1ce(k	γk1ce(k	NOUN
ejpam-3443	378	33	)	)	PUNCT
ejpam-3443	378	34	)	)	PUNCT
ejpam-3443	379	1	=	=	SYM
ejpam-3443	379	2	|v	|v	PROPN
ejpam-3443	379	3	(	(	PUNCT
ejpam-3443	379	4	g)|	g)|	NOUN
ejpam-3443	379	5	(	(	PUNCT
ejpam-3443	379	6	k	k	PROPN
ejpam-3443	379	7	+	+	CCONJ
ejpam-3443	379	8	γk1ce(k))−	γk1ce(k))−	PROPN
ejpam-3443	379	9	(	(	PUNCT
ejpam-3443	379	10	γk1ce(k	γk1ce(k	PROPN
ejpam-3443	379	11	)	)	PUNCT
ejpam-3443	379	12	+	+	CCONJ
ejpam-3443	380	1	k	k	PROPN
ejpam-3443	381	1	−	−	NOUN
ejpam-3443	382	1	1	1	NUM
ejpam-3443	382	2	)	)	PUNCT
ejpam-3443	382	3	γ+knce	γ+knce	NOUN
ejpam-3443	382	4	(	(	PUNCT
ejpam-3443	382	5	g	g	NOUN
ejpam-3443	382	6	)	)	PUNCT
ejpam-3443	382	7	.	.	PUNCT
ejpam-3443	383	1	conversely	conversely	ADV
ejpam-3443	383	2	,	,	PUNCT
ejpam-3443	383	3	let	let	VERB
ejpam-3443	383	4	s	s	PRON
ejpam-3443	383	5	⊆	⊆	NUM
ejpam-3443	383	6	v	v	NOUN
ejpam-3443	383	7	(	(	PUNCT
ejpam-3443	383	8	g	g	PROPN
ejpam-3443	383	9	◦	◦	NOUN
ejpam-3443	383	10	h	h	NOUN
ejpam-3443	383	11	)	)	PUNCT
ejpam-3443	383	12	be	be	VERB
ejpam-3443	383	13	a	a	DET
ejpam-3443	383	14	γce	γce	NOUN
ejpam-3443	383	15	-	-	PUNCT
ejpam-3443	383	16	set	set	NOUN
ejpam-3443	383	17	of	of	ADP
ejpam-3443	383	18	g	g	PROPN
ejpam-3443	383	19	◦	◦	NOUN
ejpam-3443	383	20	h.	h.	NOUN
ejpam-3443	383	21	in	in	ADP
ejpam-3443	383	22	view	view	NOUN
ejpam-3443	383	23	of	of	ADP
ejpam-3443	383	24	theorem	theorem	NOUN
ejpam-3443	383	25	6	6	NUM
ejpam-3443	383	26	we	we	PRON
ejpam-3443	383	27	can	can	AUX
ejpam-3443	383	28	write	write	VERB
ejpam-3443	383	29	|s|	|s|	NOUN
ejpam-3443	383	30	=	=	SYM
ejpam-3443	383	31	∑	∑	PUNCT
ejpam-3443	383	32	v∈s∩v	v∈s∩v	NOUN
ejpam-3443	383	33	(	(	PUNCT
ejpam-3443	383	34	g	g	NOUN
ejpam-3443	383	35	)	)	PUNCT
ejpam-3443	383	36	(	(	PUNCT
ejpam-3443	383	37	1	1	NUM
ejpam-3443	383	38	+	+	NUM
ejpam-3443	383	39	|s	|s	PROPN
ejpam-3443	383	40	∩	∩	ADJ
ejpam-3443	383	41	v	v	NOUN
ejpam-3443	383	42	(	(	PUNCT
ejpam-3443	383	43	hv)|	hv)|	NOUN
ejpam-3443	383	44	)	)	PUNCT
ejpam-3443	383	45	+	+	CCONJ
ejpam-3443	383	46	∑	∑	PUNCT
ejpam-3443	383	47	v∈v	v∈v	NOUN
ejpam-3443	383	48	(	(	PUNCT
ejpam-3443	383	49	g)\s	g)\s	NOUN
ejpam-3443	383	50	γk1ce(k	γk1ce(k	NOUN
ejpam-3443	383	51	)	)	PUNCT
ejpam-3443	384	1	+	+	CCONJ
ejpam-3443	384	2	k.	k.	PROPN
ejpam-3443	385	1	now	now	ADV
ejpam-3443	385	2	s	s	VERB
ejpam-3443	385	3	can	can	AUX
ejpam-3443	385	4	be	be	AUX
ejpam-3443	385	5	made	make	VERB
ejpam-3443	385	6	as	as	ADV
ejpam-3443	385	7	small	small	ADJ
ejpam-3443	385	8	as	as	SCONJ
ejpam-3443	385	9	desired	desire	VERB
ejpam-3443	385	10	if	if	SCONJ
ejpam-3443	385	11	s	s	ADP
ejpam-3443	385	12	∩	∩	ADJ
ejpam-3443	385	13	v	v	X
ejpam-3443	385	14	(	(	PUNCT
ejpam-3443	385	15	hv	hv	X
ejpam-3443	385	16	)	)	PUNCT
ejpam-3443	385	17	can	can	AUX
ejpam-3443	385	18	be	be	AUX
ejpam-3443	385	19	made	make	VERB
ejpam-3443	385	20	∅	∅	NOUN
ejpam-3443	385	21	for	for	ADP
ejpam-3443	385	22	all	all	PRON
ejpam-3443	385	23	v	v	ADP
ejpam-3443	385	24	∈	∈	NOUN
ejpam-3443	385	25	s	s	NOUN
ejpam-3443	385	26	∩	∩	ADJ
ejpam-3443	385	27	v	v	X
ejpam-3443	385	28	(	(	PUNCT
ejpam-3443	385	29	g	g	NOUN
ejpam-3443	385	30	)	)	PUNCT
ejpam-3443	385	31	.	.	PUNCT
ejpam-3443	386	1	this	this	PRON
ejpam-3443	386	2	is	be	AUX
ejpam-3443	386	3	attained	attain	VERB
ejpam-3443	386	4	when	when	SCONJ
ejpam-3443	386	5	s∩v	s∩v	PROPN
ejpam-3443	386	6	(	(	PUNCT
ejpam-3443	386	7	g	g	NOUN
ejpam-3443	386	8	)	)	PUNCT
ejpam-3443	386	9	is	be	AUX
ejpam-3443	386	10	a	a	DET
ejpam-3443	386	11	kn	kn	NOUN
ejpam-3443	386	12	-	-	PUNCT
ejpam-3443	386	13	cost	cost	NOUN
ejpam-3443	386	14	effective	effective	ADJ
ejpam-3443	386	15	set	set	NOUN
ejpam-3443	386	16	of	of	ADP
ejpam-3443	386	17	g	g	NOUN
ejpam-3443	386	18	so	so	SCONJ
ejpam-3443	387	1	that	that	SCONJ
ejpam-3443	387	2	|s∩v	|s∩v	PROPN
ejpam-3443	387	3	(	(	PUNCT
ejpam-3443	387	4	g)|	g)|	NOUN
ejpam-3443	387	5	≤	≤	NUM
ejpam-3443	387	6	γ+knce	γ+knce	NOUN
ejpam-3443	387	7	(	(	PUNCT
ejpam-3443	387	8	g	g	NOUN
ejpam-3443	387	9	)	)	PUNCT
ejpam-3443	387	10	and	and	CCONJ
ejpam-3443	387	11	|v	|v	PROPN
ejpam-3443	387	12	(	(	PUNCT
ejpam-3443	387	13	g	g	NOUN
ejpam-3443	387	14	)	)	PUNCT
ejpam-3443	387	15	\	\	PROPN
ejpam-3443	387	16	s|	s|	VERB
ejpam-3443	387	17	≥	≥	NUM
ejpam-3443	387	18	|v	|v	X
ejpam-3443	387	19	(	(	PUNCT
ejpam-3443	387	20	g)|	g)|	NOUN
ejpam-3443	387	21	−	−	PROPN
ejpam-3443	388	1	γ+knce	γ+knce	PROPN
ejpam-3443	388	2	(	(	PUNCT
ejpam-3443	388	3	g	g	NOUN
ejpam-3443	388	4	)	)	PUNCT
ejpam-3443	388	5	.	.	PUNCT
ejpam-3443	389	1	therefore	therefore	ADV
ejpam-3443	389	2	,	,	PUNCT
ejpam-3443	389	3	γce(g	γce(g	PROPN
ejpam-3443	389	4	◦	◦	NOUN
ejpam-3443	389	5	h	h	NOUN
ejpam-3443	389	6	)	)	PUNCT
ejpam-3443	389	7	=	=	SYM
ejpam-3443	389	8	|s|	|s|	PROPN
ejpam-3443	389	9	=	=	SYM
ejpam-3443	389	10	|s	|s	PROPN
ejpam-3443	389	11	∩	∩	ADJ
ejpam-3443	389	12	v	v	X
ejpam-3443	389	13	(	(	PUNCT
ejpam-3443	389	14	g)|+	g)|+	PROPN
ejpam-3443	389	15	∑	∑	PUNCT
ejpam-3443	389	16	v∈v	v∈v	NOUN
ejpam-3443	389	17	(	(	PUNCT
ejpam-3443	389	18	g)\s	g)\s	NOUN
ejpam-3443	389	19	(	(	PUNCT
ejpam-3443	389	20	γk1ce(k	γk1ce(k	PROPN
ejpam-3443	389	21	)	)	PUNCT
ejpam-3443	389	22	+	+	SYM
ejpam-3443	389	23	k	k	X
ejpam-3443	389	24	)	)	PUNCT
ejpam-3443	389	25	f.jamil	f.jamil	NOUN
ejpam-3443	389	26	,	,	PUNCT
ejpam-3443	389	27	h.	h.	PROPN
ejpam-3443	389	28	nuenay	nuenay	PROPN
ejpam-3443	389	29	-	-	PUNCT
ejpam-3443	389	30	maglanque	maglanque	ADJ
ejpam-3443	389	31	/	/	SYM
ejpam-3443	389	32	eur	eur	NOUN
ejpam-3443	389	33	.	.	PUNCT
ejpam-3443	390	1	j.	j.	PROPN
ejpam-3443	390	2	pure	pure	PROPN
ejpam-3443	390	3	appl	appl	PROPN
ejpam-3443	390	4	.	.	PROPN
ejpam-3443	390	5	math	math	PROPN
ejpam-3443	390	6	,	,	PUNCT
ejpam-3443	390	7	12	12	NUM
ejpam-3443	390	8	(	(	PUNCT
ejpam-3443	390	9	3	3	NUM
ejpam-3443	390	10	)	)	PUNCT
ejpam-3443	390	11	(	(	PUNCT
ejpam-3443	390	12	2019	2019	NUM
ejpam-3443	390	13	)	)	PUNCT
ejpam-3443	390	14	,	,	PUNCT
ejpam-3443	390	15	978	978	NUM
ejpam-3443	390	16	-	-	SYM
ejpam-3443	390	17	998	998	NUM
ejpam-3443	390	18	992	992	NUM
ejpam-3443	390	19	≥	≥	NOUN
ejpam-3443	390	20	γ+knce	γ+knce	NOUN
ejpam-3443	390	21	(	(	PUNCT
ejpam-3443	390	22	g	g	NOUN
ejpam-3443	390	23	)	)	PUNCT
ejpam-3443	391	1	+	+	CCONJ
ejpam-3443	391	2	(	(	PUNCT
ejpam-3443	391	3	|v	|v	X
ejpam-3443	391	4	(	(	PUNCT
ejpam-3443	391	5	g)|	g)|	NOUN
ejpam-3443	391	6	−	−	PROPN
ejpam-3443	391	7	γ+knce	γ+knce	PROPN
ejpam-3443	391	8	(	(	PUNCT
ejpam-3443	391	9	g	g	NOUN
ejpam-3443	391	10	)	)	PUNCT
ejpam-3443	391	11	)	)	PUNCT
ejpam-3443	392	1	(	(	PUNCT
ejpam-3443	392	2	k	k	X
ejpam-3443	392	3	+	+	NUM
ejpam-3443	392	4	γk1ce(k	γk1ce(k	NOUN
ejpam-3443	392	5	)	)	PUNCT
ejpam-3443	392	6	)	)	PUNCT
ejpam-3443	393	1	=	=	SYM
ejpam-3443	393	2	|v	|v	PROPN
ejpam-3443	393	3	(	(	PUNCT
ejpam-3443	393	4	g)|	g)|	NOUN
ejpam-3443	393	5	(	(	PUNCT
ejpam-3443	393	6	k	k	PROPN
ejpam-3443	393	7	+	+	CCONJ
ejpam-3443	393	8	γk1ce(k))−	γk1ce(k))−	NOUN
ejpam-3443	393	9	γ+knce	γ+knce	NOUN
ejpam-3443	393	10	(	(	PUNCT
ejpam-3443	393	11	g	g	NOUN
ejpam-3443	393	12	)	)	PUNCT
ejpam-3443	393	13	(	(	PUNCT
ejpam-3443	393	14	γk1ce(k	γk1ce(k	PROPN
ejpam-3443	393	15	)	)	PUNCT
ejpam-3443	393	16	+	+	CCONJ
ejpam-3443	394	1	k	k	PROPN
ejpam-3443	394	2	−	−	NOUN
ejpam-3443	394	3	1	1	X
ejpam-3443	394	4	)	)	PUNCT
ejpam-3443	394	5	this	this	PRON
ejpam-3443	394	6	proves	prove	VERB
ejpam-3443	394	7	statement	statement	NOUN
ejpam-3443	394	8	(	(	PUNCT
ejpam-3443	394	9	i	i	NOUN
ejpam-3443	394	10	)	)	PUNCT
ejpam-3443	394	11	.	.	PUNCT
ejpam-3443	395	1	to	to	PART
ejpam-3443	395	2	prove	prove	VERB
ejpam-3443	395	3	statement	statement	NOUN
ejpam-3443	395	4	(	(	PUNCT
ejpam-3443	395	5	ii	ii	NOUN
ejpam-3443	395	6	)	)	PUNCT
ejpam-3443	395	7	,	,	PUNCT
ejpam-3443	395	8	let	let	VERB
ejpam-3443	395	9	h	h	PRON
ejpam-3443	395	10	be	be	AUX
ejpam-3443	395	11	of	of	ADP
ejpam-3443	395	12	order	order	NOUN
ejpam-3443	395	13	n	n	NOUN
ejpam-3443	395	14	and	and	CCONJ
ejpam-3443	395	15	s	s	VERB
ejpam-3443	395	16	=	=	SYM
ejpam-3443	396	1	∪v∈v	∪v∈v	X
ejpam-3443	396	2	(	(	PUNCT
ejpam-3443	396	3	g)sv	g)sv	PROPN
ejpam-3443	396	4	,	,	PUNCT
ejpam-3443	396	5	where	where	SCONJ
ejpam-3443	396	6	sv	sv	PROPN
ejpam-3443	396	7	=	=	SYM
ejpam-3443	396	8	lv∪pv	lv∪pv	PROPN
ejpam-3443	396	9	⊆	⊆	NUM
ejpam-3443	396	10	v	v	ADP
ejpam-3443	396	11	(	(	PUNCT
ejpam-3443	396	12	hv	hv	X
ejpam-3443	396	13	)	)	PUNCT
ejpam-3443	396	14	is	be	AUX
ejpam-3443	396	15	a	a	DET
ejpam-3443	396	16	γk1mce	γk1mce	NOUN
ejpam-3443	396	17	-	-	PUNCT
ejpam-3443	396	18	set	set	NOUN
ejpam-3443	396	19	of	of	ADP
ejpam-3443	396	20	hv	hv	PROPN
ejpam-3443	396	21	for	for	ADP
ejpam-3443	396	22	each	each	DET
ejpam-3443	396	23	v	v	NUM
ejpam-3443	396	24	∈	∈	PROPN
ejpam-3443	396	25	v	v	NOUN
ejpam-3443	396	26	(	(	PUNCT
ejpam-3443	396	27	g	g	NOUN
ejpam-3443	396	28	)	)	PUNCT
ejpam-3443	396	29	,	,	PUNCT
ejpam-3443	396	30	with	with	ADP
ejpam-3443	396	31	lv	lv	PROPN
ejpam-3443	396	32	=	=	SYM
ejpam-3443	396	33	∪ki=1{ui	∪ki=1{ui	PROPN
ejpam-3443	396	34	}	}	PUNCT
ejpam-3443	396	35	a	a	DET
ejpam-3443	396	36	union	union	NOUN
ejpam-3443	396	37	of	of	ADP
ejpam-3443	396	38	k	k	PROPN
ejpam-3443	396	39	isolated	isolate	VERB
ejpam-3443	396	40	vertices	vertex	NOUN
ejpam-3443	396	41	and	and	CCONJ
ejpam-3443	396	42	pv	pv	VERB
ejpam-3443	396	43	⊆	⊆	NUM
ejpam-3443	396	44	v	v	NOUN
ejpam-3443	396	45	(	(	PUNCT
ejpam-3443	396	46	kv	kv	PROPN
ejpam-3443	396	47	)	)	PUNCT
ejpam-3443	396	48	be	be	AUX
ejpam-3443	396	49	a	a	DET
ejpam-3443	396	50	γk1mce	γk1mce	NOUN
ejpam-3443	396	51	-	-	PUNCT
ejpam-3443	396	52	set	set	NOUN
ejpam-3443	396	53	of	of	ADP
ejpam-3443	396	54	kv	kv	PROPN
ejpam-3443	396	55	.	.	PUNCT
ejpam-3443	397	1	by	by	ADP
ejpam-3443	397	2	theorem	theorem	NOUN
ejpam-3443	397	3	6	6	NUM
ejpam-3443	397	4	,	,	PUNCT
ejpam-3443	397	5	s	s	VERB
ejpam-3443	397	6	is	be	AUX
ejpam-3443	397	7	a	a	DET
ejpam-3443	397	8	cost	cost	NOUN
ejpam-3443	397	9	effective	effective	ADJ
ejpam-3443	397	10	dominating	dominating	NOUN
ejpam-3443	397	11	set	set	NOUN
ejpam-3443	397	12	of	of	ADP
ejpam-3443	397	13	g	g	PROPN
ejpam-3443	397	14	◦	◦	NOUN
ejpam-3443	397	15	h.	h.	PROPN
ejpam-3443	397	16	since	since	SCONJ
ejpam-3443	397	17	sv	sv	PROPN
ejpam-3443	397	18	is	be	AUX
ejpam-3443	397	19	a	a	DET
ejpam-3443	397	20	minimal	minimal	ADJ
ejpam-3443	397	21	cost	cost	NOUN
ejpam-3443	397	22	effective	effective	ADJ
ejpam-3443	397	23	dominating	dominating	NOUN
ejpam-3443	397	24	set	set	NOUN
ejpam-3443	397	25	of	of	ADP
ejpam-3443	397	26	hv	hv	PROPN
ejpam-3443	397	27	+	+	X
ejpam-3443	397	28	v	v	NOUN
ejpam-3443	397	29	for	for	ADP
ejpam-3443	397	30	each	each	DET
ejpam-3443	397	31	v	v	NUM
ejpam-3443	397	32	∈	∈	PROPN
ejpam-3443	397	33	v	v	NOUN
ejpam-3443	397	34	(	(	PUNCT
ejpam-3443	397	35	g	g	NOUN
ejpam-3443	397	36	)	)	PUNCT
ejpam-3443	397	37	,	,	PUNCT
ejpam-3443	397	38	s	s	VERB
ejpam-3443	397	39	is	be	AUX
ejpam-3443	397	40	a	a	DET
ejpam-3443	397	41	minimal	minimal	ADJ
ejpam-3443	397	42	cost	cost	NOUN
ejpam-3443	397	43	effective	effective	ADJ
ejpam-3443	397	44	dominating	dominating	NOUN
ejpam-3443	397	45	set	set	NOUN
ejpam-3443	397	46	of	of	ADP
ejpam-3443	397	47	g	g	PROPN
ejpam-3443	397	48	◦	◦	NOUN
ejpam-3443	397	49	h.	h.	PROPN
ejpam-3443	397	50	thus	thus	ADV
ejpam-3443	397	51	,	,	PUNCT
ejpam-3443	397	52	γmce(g	γmce(g	PROPN
ejpam-3443	397	53	◦	◦	NOUN
ejpam-3443	397	54	h	h	NOUN
ejpam-3443	397	55	)	)	PUNCT
ejpam-3443	397	56	≥	≥	NOUN
ejpam-3443	397	57	|s|	|s|	NOUN
ejpam-3443	397	58	=	=	SYM
ejpam-3443	397	59	|v	|v	X
ejpam-3443	397	60	(	(	PUNCT
ejpam-3443	397	61	g)|	g)|	NOUN
ejpam-3443	397	62	(	(	PUNCT
ejpam-3443	397	63	k	k	PROPN
ejpam-3443	397	64	+	+	PROPN
ejpam-3443	397	65	γk1mce(k	γk1mce(k	PROPN
ejpam-3443	397	66	)	)	PUNCT
ejpam-3443	397	67	)	)	PUNCT
ejpam-3443	397	68	.	.	PUNCT
ejpam-3443	398	1	conversely	conversely	ADV
ejpam-3443	398	2	,	,	PUNCT
ejpam-3443	398	3	let	let	VERB
ejpam-3443	398	4	s	s	PRON
ejpam-3443	398	5	⊆	⊆	NUM
ejpam-3443	398	6	v	v	NOUN
ejpam-3443	398	7	(	(	PUNCT
ejpam-3443	398	8	g	g	PROPN
ejpam-3443	398	9	◦	◦	NOUN
ejpam-3443	398	10	h	h	NOUN
ejpam-3443	398	11	)	)	PUNCT
ejpam-3443	398	12	be	be	VERB
ejpam-3443	398	13	a	a	DET
ejpam-3443	398	14	γmce	γmce	NOUN
ejpam-3443	398	15	-	-	PUNCT
ejpam-3443	398	16	set	set	NOUN
ejpam-3443	398	17	of	of	ADP
ejpam-3443	398	18	g	g	PROPN
ejpam-3443	398	19	◦	◦	PROPN
ejpam-3443	398	20	h.	h.	PROPN
ejpam-3443	398	21	let	let	VERB
ejpam-3443	398	22	v	v	NUM
ejpam-3443	398	23	∈	∈	PROPN
ejpam-3443	398	24	v	v	NOUN
ejpam-3443	398	25	(	(	PUNCT
ejpam-3443	398	26	g	g	NOUN
ejpam-3443	398	27	)	)	PUNCT
ejpam-3443	398	28	\	\	PUNCT
ejpam-3443	399	1	s.	s.	PROPN
ejpam-3443	399	2	by	by	ADP
ejpam-3443	399	3	theorem	theorem	PROPN
ejpam-3443	399	4	6(ii	6(ii	PROPN
ejpam-3443	399	5	)	)	PUNCT
ejpam-3443	399	6	and	and	CCONJ
ejpam-3443	399	7	the	the	DET
ejpam-3443	399	8	minimality	minimality	NOUN
ejpam-3443	399	9	of	of	ADP
ejpam-3443	399	10	s	s	PROPN
ejpam-3443	399	11	,	,	PUNCT
ejpam-3443	399	12	s	s	PART
ejpam-3443	399	13	∩	∩	ADJ
ejpam-3443	399	14	v	v	X
ejpam-3443	399	15	(	(	PUNCT
ejpam-3443	399	16	hv	hv	X
ejpam-3443	399	17	)	)	PUNCT
ejpam-3443	399	18	is	be	AUX
ejpam-3443	399	19	a	a	DET
ejpam-3443	399	20	minimal	minimal	ADJ
ejpam-3443	399	21	k1	k1	NOUN
ejpam-3443	399	22	-	-	PUNCT
ejpam-3443	399	23	cost	cost	NOUN
ejpam-3443	399	24	effective	effective	ADJ
ejpam-3443	399	25	dominating	dominating	NOUN
ejpam-3443	399	26	set	set	NOUN
ejpam-3443	399	27	of	of	ADP
ejpam-3443	399	28	hv	hv	PROPN
ejpam-3443	399	29	.	.	PUNCT
ejpam-3443	400	1	let	let	VERB
ejpam-3443	400	2	v	v	NUM
ejpam-3443	400	3	∈	∈	NOUN
ejpam-3443	400	4	s	s	PART
ejpam-3443	400	5	∩	∩	ADJ
ejpam-3443	400	6	v	v	X
ejpam-3443	400	7	(	(	PUNCT
ejpam-3443	400	8	g	g	NOUN
ejpam-3443	400	9	)	)	PUNCT
ejpam-3443	400	10	.	.	PUNCT
ejpam-3443	401	1	if	if	SCONJ
ejpam-3443	401	2	v	v	NOUN
ejpam-3443	401	3	is	be	AUX
ejpam-3443	401	4	cost	cost	VERB
ejpam-3443	401	5	effective	effective	ADJ
ejpam-3443	401	6	relative	relative	NOUN
ejpam-3443	401	7	to	to	ADP
ejpam-3443	401	8	s	s	PROPN
ejpam-3443	401	9	∩	∩	ADJ
ejpam-3443	401	10	v	v	ADJ
ejpam-3443	401	11	(	(	PUNCT
ejpam-3443	401	12	g	g	NOUN
ejpam-3443	401	13	)	)	PUNCT
ejpam-3443	401	14	,	,	PUNCT
ejpam-3443	401	15	then	then	ADV
ejpam-3443	401	16	the	the	DET
ejpam-3443	401	17	minimality	minimality	NOUN
ejpam-3443	401	18	of	of	ADP
ejpam-3443	401	19	s	s	PRON
ejpam-3443	401	20	implies	imply	VERB
ejpam-3443	401	21	that	that	SCONJ
ejpam-3443	401	22	s	s	VERB
ejpam-3443	401	23	∩	∩	ADJ
ejpam-3443	401	24	v	v	X
ejpam-3443	401	25	(	(	PUNCT
ejpam-3443	401	26	hv	hv	PROPN
ejpam-3443	401	27	+	+	PROPN
ejpam-3443	401	28	v	v	NOUN
ejpam-3443	401	29	)	)	PUNCT
ejpam-3443	401	30	=	=	PRON
ejpam-3443	401	31	{	{	PUNCT
ejpam-3443	401	32	v	v	NOUN
ejpam-3443	401	33	}	}	PUNCT
ejpam-3443	401	34	.	.	PUNCT
ejpam-3443	402	1	suppose	suppose	VERB
ejpam-3443	402	2	that	that	SCONJ
ejpam-3443	402	3	v	v	NOUN
ejpam-3443	402	4	is	be	AUX
ejpam-3443	402	5	not	not	PART
ejpam-3443	402	6	cost	cost	VERB
ejpam-3443	402	7	effective	effective	ADJ
ejpam-3443	402	8	relative	relative	NOUN
ejpam-3443	402	9	to	to	ADP
ejpam-3443	402	10	s	s	PROPN
ejpam-3443	402	11	∩	∩	ADJ
ejpam-3443	402	12	v	v	ADJ
ejpam-3443	402	13	(	(	PUNCT
ejpam-3443	402	14	g	g	NOUN
ejpam-3443	402	15	)	)	PUNCT
ejpam-3443	402	16	.	.	PUNCT
ejpam-3443	403	1	by	by	ADP
ejpam-3443	403	2	theorem	theorem	NOUN
ejpam-3443	403	3	6(i	6(i	NUM
ejpam-3443	403	4	)	)	PUNCT
ejpam-3443	403	5	,	,	PUNCT
ejpam-3443	403	6	sv	sv	PROPN
ejpam-3443	403	7	=	=	SYM
ejpam-3443	403	8	s	s	PROPN
ejpam-3443	403	9	∩	∩	ADJ
ejpam-3443	403	10	v	v	X
ejpam-3443	403	11	(	(	PUNCT
ejpam-3443	403	12	hv	hv	X
ejpam-3443	403	13	)	)	PUNCT
ejpam-3443	403	14	is	be	AUX
ejpam-3443	403	15	a	a	DET
ejpam-3443	403	16	cost	cost	NOUN
ejpam-3443	403	17	effective	effective	ADJ
ejpam-3443	403	18	set	set	NOUN
ejpam-3443	403	19	of	of	ADP
ejpam-3443	403	20	hv	hv	PROPN
ejpam-3443	403	21	satisfying	satisfy	VERB
ejpam-3443	403	22	|sv|	|sv|	PROPN
ejpam-3443	403	23	≤	≤	ADJ
ejpam-3443	403	24	1	1	NUM
ejpam-3443	403	25	2	2	NUM
ejpam-3443	403	26	(	(	PUNCT
ejpam-3443	403	27	n+	n+	NUM
ejpam-3443	404	1	|ng(v	|ng(v	ADJ
ejpam-3443	404	2	)	)	PUNCT
ejpam-3443	404	3	\	\	NOUN
ejpam-3443	404	4	s|	s|	VERB
ejpam-3443	404	5	−	−	NOUN
ejpam-3443	404	6	|ng(v	|ng(v	NOUN
ejpam-3443	404	7	)	)	PUNCT
ejpam-3443	404	8	∩	∩	NOUN
ejpam-3443	404	9	s|	s|	PROPN
ejpam-3443	404	10	)	)	PUNCT
ejpam-3443	404	11	<	<	X
ejpam-3443	404	12	n	n	PRON
ejpam-3443	404	13	2	2	NUM
ejpam-3443	404	14	.	.	PUNCT
ejpam-3443	405	1	thus	thus	ADV
ejpam-3443	405	2	,	,	PUNCT
ejpam-3443	405	3	|ng(v	|ng(v	NOUN
ejpam-3443	405	4	)	)	PUNCT
ejpam-3443	405	5	∩	∩	NOUN
ejpam-3443	405	6	s|	s|	VERB
ejpam-3443	405	7	≤	≤	NUM
ejpam-3443	405	8	|ng(v	|ng(v	NOUN
ejpam-3443	405	9	)	)	PUNCT
ejpam-3443	405	10	∩	∩	NOUN
ejpam-3443	405	11	s|+	s|+	PROPN
ejpam-3443	405	12	2|sv|	2|sv|	PROPN
ejpam-3443	405	13	=	=	SYM
ejpam-3443	405	14	|ng	|ng	VERB
ejpam-3443	405	15	◦	◦	NOUN
ejpam-3443	405	16	h(v	h(v	NOUN
ejpam-3443	405	17	)	)	PUNCT
ejpam-3443	405	18	∩	∩	NOUN
ejpam-3443	405	19	s|+	s|+	NOUN
ejpam-3443	405	20	|sv|	|sv|	PROPN
ejpam-3443	405	21	≤	≤	NOUN
ejpam-3443	405	22	|ng	|ng	AUX
ejpam-3443	405	23	◦	◦	NOUN
ejpam-3443	405	24	h(v	h(v	NOUN
ejpam-3443	405	25	)	)	PUNCT
ejpam-3443	405	26	\	\	PUNCT
ejpam-3443	406	1	s|+	s|+	NOUN
ejpam-3443	406	2	|sv|	|sv|	NOUN
ejpam-3443	406	3	=	=	SYM
ejpam-3443	406	4	|ng(v	|ng(v	PROPN
ejpam-3443	406	5	)	)	PUNCT
ejpam-3443	406	6	\	\	NOUN
ejpam-3443	407	1	s|+	s|+	PROPN
ejpam-3443	407	2	n.	n.	NOUN
ejpam-3443	407	3	let	let	VERB
ejpam-3443	407	4	s∗	s∗	PROPN
ejpam-3443	407	5	=	=	SYM
ejpam-3443	407	6	s	s	PART
ejpam-3443	407	7	\	\	PROPN
ejpam-3443	407	8	sv	sv	PROPN
ejpam-3443	407	9	.	.	PUNCT
ejpam-3443	408	1	since	since	SCONJ
ejpam-3443	408	2	v	v	NOUN
ejpam-3443	408	3	dominates	dominate	VERB
ejpam-3443	408	4	v	v	NOUN
ejpam-3443	408	5	(	(	PUNCT
ejpam-3443	408	6	hv	hv	PROPN
ejpam-3443	408	7	+	+	PROPN
ejpam-3443	408	8	v	v	NOUN
ejpam-3443	408	9	)	)	PUNCT
ejpam-3443	408	10	,	,	PUNCT
ejpam-3443	408	11	s∗	s∗	PROPN
ejpam-3443	408	12	is	be	AUX
ejpam-3443	408	13	a	a	DET
ejpam-3443	408	14	dominating	dominating	NOUN
ejpam-3443	408	15	set	set	NOUN
ejpam-3443	408	16	of	of	ADP
ejpam-3443	408	17	g	g	PROPN
ejpam-3443	408	18	◦	◦	NOUN
ejpam-3443	408	19	h.	h.	PROPN
ejpam-3443	408	20	clearly	clearly	ADV
ejpam-3443	408	21	,	,	PUNCT
ejpam-3443	408	22	each	each	DET
ejpam-3443	408	23	u	u	PROPN
ejpam-3443	408	24	∈	∈	PROPN
ejpam-3443	408	25	s∗	s∗	PROPN
ejpam-3443	408	26	\	\	PROPN
ejpam-3443	408	27	{	{	PUNCT
ejpam-3443	408	28	v	v	NOUN
ejpam-3443	408	29	}	}	PUNCT
ejpam-3443	408	30	is	be	AUX
ejpam-3443	408	31	cost	cost	VERB
ejpam-3443	408	32	effective	effective	ADJ
ejpam-3443	408	33	relative	relative	NOUN
ejpam-3443	408	34	to	to	PART
ejpam-3443	408	35	s∗	s∗	VERB
ejpam-3443	408	36	as	as	SCONJ
ejpam-3443	408	37	it	it	PRON
ejpam-3443	408	38	is	be	AUX
ejpam-3443	408	39	relative	relative	ADJ
ejpam-3443	408	40	to	to	ADP
ejpam-3443	408	41	s	s	PRON
ejpam-3443	408	42	in	in	ADP
ejpam-3443	408	43	g	g	PROPN
ejpam-3443	408	44	◦	◦	NOUN
ejpam-3443	408	45	h.	h.	NOUN
ejpam-3443	408	46	now	now	ADV
ejpam-3443	408	47	,	,	PUNCT
ejpam-3443	408	48	|ng	|ng	VERB
ejpam-3443	408	49	◦	◦	NOUN
ejpam-3443	408	50	h(v	h(v	ADJ
ejpam-3443	408	51	)	)	PUNCT
ejpam-3443	408	52	∩	∩	NOUN
ejpam-3443	408	53	s∗|	s∗|	PROPN
ejpam-3443	408	54	=	=	SYM
ejpam-3443	408	55	ng(v	ng(v	X
ejpam-3443	408	56	)	)	PUNCT
ejpam-3443	408	57	∩	∩	NOUN
ejpam-3443	408	58	s|	s|	VERB
ejpam-3443	408	59	≤	≤	NUM
ejpam-3443	408	60	|ng(v	|ng(v	NOUN
ejpam-3443	408	61	)	)	PUNCT
ejpam-3443	408	62	\	\	NOUN
ejpam-3443	409	1	s|+	s|+	NOUN
ejpam-3443	409	2	n	n	NOUN
ejpam-3443	409	3	=	=	SYM
ejpam-3443	409	4	|ng	|ng	X
ejpam-3443	409	5	◦	◦	NOUN
ejpam-3443	409	6	h(v	h(v	NOUN
ejpam-3443	409	7	)	)	PUNCT
ejpam-3443	409	8	\	\	PROPN
ejpam-3443	409	9	s∗|	s∗|	PROPN
ejpam-3443	409	10	.	.	PUNCT
ejpam-3443	410	1	since	since	SCONJ
ejpam-3443	410	2	s	s	NOUN
ejpam-3443	410	3	is	be	AUX
ejpam-3443	410	4	minimal	minimal	ADJ
ejpam-3443	410	5	,	,	PUNCT
ejpam-3443	410	6	s	s	PART
ejpam-3443	410	7	=	=	PUNCT
ejpam-3443	410	8	s∗	s∗	PROPN
ejpam-3443	410	9	,	,	PUNCT
ejpam-3443	410	10	and	and	CCONJ
ejpam-3443	410	11	sv	sv	X
ejpam-3443	410	12	=	=	NOUN
ejpam-3443	410	13	∅.	∅.	VERB
ejpam-3443	410	14	thus	thus	ADV
ejpam-3443	410	15	,	,	PUNCT
ejpam-3443	410	16	γmce(g	γmce(g	PROPN
ejpam-3443	410	17	◦	◦	NOUN
ejpam-3443	410	18	h	h	NOUN
ejpam-3443	410	19	)	)	PUNCT
ejpam-3443	410	20	=	=	PUNCT
ejpam-3443	410	21	|s|	|s|	PROPN
ejpam-3443	410	22	=	=	PUNCT
ejpam-3443	410	23	∑	∑	PUNCT
ejpam-3443	410	24	v∈s∩v	v∈s∩v	NOUN
ejpam-3443	410	25	(	(	PUNCT
ejpam-3443	410	26	g	g	NOUN
ejpam-3443	410	27	)	)	PUNCT
ejpam-3443	410	28	|s	|s	PROPN
ejpam-3443	410	29	∩	∩	PROPN
ejpam-3443	410	30	v	v	X
ejpam-3443	410	31	(	(	PUNCT
ejpam-3443	410	32	hv	hv	NOUN
ejpam-3443	410	33	+	+	NOUN
ejpam-3443	410	34	v)|+	v)|+	NOUN
ejpam-3443	410	35	∑	∑	PUNCT
ejpam-3443	410	36	v∈v	v∈v	NOUN
ejpam-3443	410	37	(	(	PUNCT
ejpam-3443	410	38	g)\s	g)\s	NOUN
ejpam-3443	410	39	|s	|s	PROPN
ejpam-3443	410	40	∩	∩	PROPN
ejpam-3443	410	41	v	v	NOUN
ejpam-3443	410	42	(	(	PUNCT
ejpam-3443	410	43	hv)|	hv)|	X
ejpam-3443	410	44	≤	≤	ADJ
ejpam-3443	410	45	∑	∑	PUNCT
ejpam-3443	410	46	v∈v	v∈v	NOUN
ejpam-3443	410	47	(	(	PUNCT
ejpam-3443	410	48	g	g	NOUN
ejpam-3443	410	49	)	)	PUNCT
ejpam-3443	410	50	(	(	PUNCT
ejpam-3443	410	51	k	k	PROPN
ejpam-3443	410	52	+	+	PROPN
ejpam-3443	410	53	γk1mce(k	γk1mce(k	PROPN
ejpam-3443	410	54	)	)	PUNCT
ejpam-3443	410	55	)	)	PUNCT
ejpam-3443	411	1	=	=	SYM
ejpam-3443	411	2	|v	|v	PROPN
ejpam-3443	411	3	(	(	PUNCT
ejpam-3443	411	4	g)|	g)|	NOUN
ejpam-3443	411	5	(	(	PUNCT
ejpam-3443	411	6	k	k	PROPN
ejpam-3443	411	7	+	+	PROPN
ejpam-3443	411	8	γk1mce(k	γk1mce(k	PROPN
ejpam-3443	411	9	)	)	PUNCT
ejpam-3443	411	10	)	)	PUNCT
ejpam-3443	411	11	.	.	PUNCT
ejpam-3443	412	1	finally	finally	ADV
ejpam-3443	412	2	,	,	PUNCT
ejpam-3443	412	3	we	we	PRON
ejpam-3443	412	4	prove	prove	VERB
ejpam-3443	412	5	statement	statement	NOUN
ejpam-3443	412	6	(	(	PUNCT
ejpam-3443	412	7	iii	iii	NOUN
ejpam-3443	412	8	)	)	PUNCT
ejpam-3443	412	9	.	.	PUNCT
ejpam-3443	413	1	for	for	ADP
ejpam-3443	413	2	each	each	DET
ejpam-3443	413	3	v	v	NUM
ejpam-3443	413	4	∈	∈	PROPN
ejpam-3443	413	5	v	v	NOUN
ejpam-3443	413	6	(	(	PUNCT
ejpam-3443	413	7	g	g	NOUN
ejpam-3443	413	8	)	)	PUNCT
ejpam-3443	413	9	,	,	PUNCT
ejpam-3443	413	10	let	let	VERB
ejpam-3443	413	11	sv	sv	PROPN
ejpam-3443	413	12	⊆	⊆	NUM
ejpam-3443	413	13	v	v	X
ejpam-3443	413	14	(	(	PUNCT
ejpam-3443	413	15	hv	hv	NOUN
ejpam-3443	413	16	)	)	PUNCT
ejpam-3443	413	17	be	be	VERB
ejpam-3443	413	18	a	a	DET
ejpam-3443	413	19	γ+k1ce	γ+k1ce	NOUN
ejpam-3443	413	20	-set	-set	PUNCT
ejpam-3443	413	21	of	of	ADP
ejpam-3443	413	22	hv	hv	PROPN
ejpam-3443	413	23	,	,	PUNCT
ejpam-3443	413	24	with	with	ADP
ejpam-3443	413	25	sv	sv	PROPN
ejpam-3443	414	1	=	=	PUNCT
ejpam-3443	414	2	lv	lv	PROPN
ejpam-3443	414	3	∪	∪	ADV
ejpam-3443	414	4	pv	pv	VERB
ejpam-3443	414	5	⊆	⊆	NUM
ejpam-3443	414	6	v	v	NOUN
ejpam-3443	414	7	(	(	PUNCT
ejpam-3443	414	8	hv	hv	PROPN
ejpam-3443	414	9	)	)	PUNCT
ejpam-3443	414	10	where	where	SCONJ
ejpam-3443	414	11	lv	lv	PROPN
ejpam-3443	414	12	=	=	SYM
ejpam-3443	414	13	∪ki=1{ui	∪ki=1{ui	PROPN
ejpam-3443	414	14	}	}	PUNCT
ejpam-3443	414	15	is	be	AUX
ejpam-3443	414	16	a	a	DET
ejpam-3443	414	17	union	union	NOUN
ejpam-3443	414	18	of	of	ADP
ejpam-3443	414	19	k	k	PROPN
ejpam-3443	414	20	isolated	isolate	VERB
ejpam-3443	414	21	vertices	vertex	NOUN
ejpam-3443	414	22	f.jamil	f.jamil	PROPN
ejpam-3443	414	23	,	,	PUNCT
ejpam-3443	414	24	h.	h.	PROPN
ejpam-3443	414	25	nuenay	nuenay	PROPN
ejpam-3443	414	26	-	-	PUNCT
ejpam-3443	414	27	maglanque	maglanque	ADJ
ejpam-3443	414	28	/	/	SYM
ejpam-3443	414	29	eur	eur	NOUN
ejpam-3443	414	30	.	.	PUNCT
ejpam-3443	415	1	j.	j.	PROPN
ejpam-3443	415	2	pure	pure	PROPN
ejpam-3443	415	3	appl	appl	PROPN
ejpam-3443	415	4	.	.	PROPN
ejpam-3443	415	5	math	math	PROPN
ejpam-3443	415	6	,	,	PUNCT
ejpam-3443	415	7	12	12	NUM
ejpam-3443	415	8	(	(	PUNCT
ejpam-3443	415	9	3	3	NUM
ejpam-3443	415	10	)	)	PUNCT
ejpam-3443	415	11	(	(	PUNCT
ejpam-3443	415	12	2019	2019	NUM
ejpam-3443	415	13	)	)	PUNCT
ejpam-3443	415	14	,	,	PUNCT
ejpam-3443	415	15	978	978	NUM
ejpam-3443	415	16	-	-	SYM
ejpam-3443	415	17	998	998	NUM
ejpam-3443	415	18	993	993	NUM
ejpam-3443	415	19	and	and	CCONJ
ejpam-3443	415	20	pv	pv	VERB
ejpam-3443	415	21	⊆	⊆	NUM
ejpam-3443	415	22	v	v	NOUN
ejpam-3443	415	23	(	(	PUNCT
ejpam-3443	415	24	kv	kv	PROPN
ejpam-3443	415	25	)	)	PUNCT
ejpam-3443	415	26	is	be	AUX
ejpam-3443	415	27	a	a	DET
ejpam-3443	415	28	γ+k1ce	γ+k1ce	NOUN
ejpam-3443	415	29	-set	-set	PUNCT
ejpam-3443	415	30	of	of	ADP
ejpam-3443	415	31	kv	kv	PROPN
ejpam-3443	415	32	.	.	PUNCT
ejpam-3443	416	1	then	then	ADV
ejpam-3443	416	2	s	s	VERB
ejpam-3443	416	3	=	=	SYM
ejpam-3443	416	4	∪v∈v	∪v∈v	NOUN
ejpam-3443	416	5	(	(	PUNCT
ejpam-3443	416	6	g)sv	g)sv	PROPN
ejpam-3443	416	7	satisfies	satisfy	VERB
ejpam-3443	416	8	the	the	DET
ejpam-3443	416	9	properties	property	NOUN
ejpam-3443	416	10	of	of	ADP
ejpam-3443	416	11	theorem	theorem	ADJ
ejpam-3443	416	12	6	6	NUM
ejpam-3443	416	13	,	,	PUNCT
ejpam-3443	416	14	and	and	CCONJ
ejpam-3443	416	15	thus	thus	ADV
ejpam-3443	416	16	is	be	AUX
ejpam-3443	416	17	a	a	DET
ejpam-3443	416	18	cost	cost	NOUN
ejpam-3443	416	19	effective	effective	ADJ
ejpam-3443	416	20	dominating	dominating	NOUN
ejpam-3443	416	21	set	set	NOUN
ejpam-3443	416	22	of	of	ADP
ejpam-3443	416	23	g	g	PROPN
ejpam-3443	416	24	◦	◦	NOUN
ejpam-3443	416	25	h.	h.	NOUN
ejpam-3443	416	26	it	it	PRON
ejpam-3443	416	27	follows	follow	VERB
ejpam-3443	416	28	that	that	SCONJ
ejpam-3443	416	29	γ+ce(g	γ+ce(g	PROPN
ejpam-3443	416	30	◦	◦	NOUN
ejpam-3443	416	31	h	h	NOUN
ejpam-3443	416	32	)	)	PUNCT
ejpam-3443	416	33	≥	≥	NOUN
ejpam-3443	416	34	|s|	|s|	NOUN
ejpam-3443	416	35	=	=	SYM
ejpam-3443	416	36	∑	∑	PUNCT
ejpam-3443	416	37	v∈v	v∈v	NOUN
ejpam-3443	416	38	(	(	PUNCT
ejpam-3443	416	39	g	g	NOUN
ejpam-3443	416	40	)	)	PUNCT
ejpam-3443	416	41	sv	sv	NOUN
ejpam-3443	417	1	=	=	SYM
ejpam-3443	417	2	|v	|v	PROPN
ejpam-3443	417	3	(	(	PUNCT
ejpam-3443	417	4	g)|	g)|	PROPN
ejpam-3443	417	5	(	(	PUNCT
ejpam-3443	417	6	k	k	PROPN
ejpam-3443	417	7	+	+	X
ejpam-3443	417	8	γ+k1ce	γ+k1ce	PROPN
ejpam-3443	417	9	(	(	PUNCT
ejpam-3443	417	10	k	k	NOUN
ejpam-3443	417	11	)	)	PUNCT
ejpam-3443	417	12	)	)	PUNCT
ejpam-3443	417	13	.	.	PUNCT
ejpam-3443	418	1	conversely	conversely	ADV
ejpam-3443	418	2	,	,	PUNCT
ejpam-3443	418	3	suppose	suppose	VERB
ejpam-3443	418	4	that	that	SCONJ
ejpam-3443	418	5	s	s	VERB
ejpam-3443	418	6	⊆	⊆	NUM
ejpam-3443	418	7	v	v	NOUN
ejpam-3443	418	8	(	(	PUNCT
ejpam-3443	418	9	g	g	PROPN
ejpam-3443	418	10	◦	◦	NOUN
ejpam-3443	418	11	h	h	NOUN
ejpam-3443	418	12	)	)	PUNCT
ejpam-3443	418	13	is	be	AUX
ejpam-3443	418	14	a	a	DET
ejpam-3443	418	15	γ+ce	γ+ce	NOUN
ejpam-3443	418	16	-	-	PUNCT
ejpam-3443	418	17	set	set	NOUN
ejpam-3443	418	18	of	of	ADP
ejpam-3443	418	19	g	g	PROPN
ejpam-3443	418	20	◦	◦	NOUN
ejpam-3443	418	21	h.	h.	NOUN
ejpam-3443	418	22	then	then	ADV
ejpam-3443	418	23	,	,	PUNCT
ejpam-3443	418	24	γ+ce(g	γ+ce(g	PROPN
ejpam-3443	418	25	◦	◦	NOUN
ejpam-3443	418	26	h	h	NOUN
ejpam-3443	418	27	)	)	PUNCT
ejpam-3443	418	28	=	=	PUNCT
ejpam-3443	418	29	|s|	|s|	PROPN
ejpam-3443	418	30	=	=	PUNCT
ejpam-3443	418	31	∑	∑	PUNCT
ejpam-3443	418	32	v∈s∩v	v∈s∩v	NOUN
ejpam-3443	418	33	(	(	PUNCT
ejpam-3443	418	34	g	g	NOUN
ejpam-3443	418	35	)	)	PUNCT
ejpam-3443	418	36	s	s	PART
ejpam-3443	418	37	∩	∩	ADJ
ejpam-3443	418	38	v	v	X
ejpam-3443	418	39	(	(	PUNCT
ejpam-3443	418	40	hv	hv	PROPN
ejpam-3443	418	41	+	+	PROPN
ejpam-3443	418	42	v	v	NOUN
ejpam-3443	418	43	)	)	PUNCT
ejpam-3443	419	1	+	+	CCONJ
ejpam-3443	419	2	∑	∑	PUNCT
ejpam-3443	419	3	v∈v	v∈v	NOUN
ejpam-3443	419	4	(	(	PUNCT
ejpam-3443	419	5	g)\s	g)\s	NOUN
ejpam-3443	419	6	s	s	PART
ejpam-3443	419	7	∩	∩	ADJ
ejpam-3443	419	8	v	v	X
ejpam-3443	419	9	(	(	PUNCT
ejpam-3443	419	10	hv	hv	NOUN
ejpam-3443	419	11	)	)	PUNCT
ejpam-3443	419	12	≤	≤	NOUN
ejpam-3443	419	13	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	419	14	)	)	PUNCT
ejpam-3443	419	15	(	(	PUNCT
ejpam-3443	419	16	γ+k1ce	γ+k1ce	X
ejpam-3443	419	17	(	(	PUNCT
ejpam-3443	419	18	k	k	NOUN
ejpam-3443	419	19	)	)	PUNCT
ejpam-3443	419	20	+	+	SYM
ejpam-3443	419	21	k	k	X
ejpam-3443	419	22	)	)	PUNCT
ejpam-3443	420	1	+	+	CCONJ
ejpam-3443	420	2	(	(	PUNCT
ejpam-3443	420	3	|v	|v	X
ejpam-3443	420	4	(	(	PUNCT
ejpam-3443	420	5	g)|	g)|	PROPN
ejpam-3443	420	6	−	−	PROPN
ejpam-3443	420	7	γ+ce(g	γ+ce(g	NOUN
ejpam-3443	420	8	)	)	PUNCT
ejpam-3443	420	9	)	)	PUNCT
ejpam-3443	421	1	(	(	PUNCT
ejpam-3443	421	2	γ+k1ce	γ+k1ce	X
ejpam-3443	421	3	(	(	PUNCT
ejpam-3443	421	4	k	k	NOUN
ejpam-3443	421	5	)	)	PUNCT
ejpam-3443	421	6	+	+	CCONJ
ejpam-3443	421	7	k	k	X
ejpam-3443	421	8	)	)	PUNCT
ejpam-3443	421	9	≤	≤	PUNCT
ejpam-3443	422	1	γ+knce	γ+knce	NOUN
ejpam-3443	422	2	(	(	PUNCT
ejpam-3443	422	3	g	g	NOUN
ejpam-3443	422	4	)	)	PUNCT
ejpam-3443	422	5	(	(	PUNCT
ejpam-3443	422	6	γ+k1ce	γ+k1ce	X
ejpam-3443	422	7	(	(	PUNCT
ejpam-3443	422	8	k	k	NOUN
ejpam-3443	422	9	)	)	PUNCT
ejpam-3443	422	10	+	+	SYM
ejpam-3443	422	11	k	k	X
ejpam-3443	422	12	)	)	PUNCT
ejpam-3443	423	1	+	+	CCONJ
ejpam-3443	423	2	(	(	PUNCT
ejpam-3443	423	3	|v	|v	X
ejpam-3443	423	4	(	(	PUNCT
ejpam-3443	423	5	g)|	g)|	NOUN
ejpam-3443	423	6	−	−	PROPN
ejpam-3443	423	7	γ+knce	γ+knce	PROPN
ejpam-3443	423	8	(	(	PUNCT
ejpam-3443	423	9	g	g	NOUN
ejpam-3443	423	10	)	)	PUNCT
ejpam-3443	423	11	)	)	PUNCT
ejpam-3443	423	12	(	(	PUNCT
ejpam-3443	423	13	γ+k1ce	γ+k1ce	X
ejpam-3443	423	14	(	(	PUNCT
ejpam-3443	423	15	k	k	NOUN
ejpam-3443	423	16	)	)	PUNCT
ejpam-3443	423	17	+	+	SYM
ejpam-3443	423	18	k	k	X
ejpam-3443	423	19	)	)	PUNCT
ejpam-3443	424	1	=	=	SYM
ejpam-3443	424	2	|v	|v	PROPN
ejpam-3443	424	3	(	(	PUNCT
ejpam-3443	424	4	g)|	g)|	PROPN
ejpam-3443	424	5	(	(	PUNCT
ejpam-3443	424	6	k	k	PROPN
ejpam-3443	424	7	+	+	X
ejpam-3443	424	8	γ+k1ce	γ+k1ce	PROPN
ejpam-3443	424	9	(	(	PUNCT
ejpam-3443	424	10	k	k	NOUN
ejpam-3443	424	11	)	)	PUNCT
ejpam-3443	424	12	)	)	PUNCT
ejpam-3443	424	13	.	.	PUNCT
ejpam-3443	425	1	4	4	X
ejpam-3443	425	2	.	.	X
ejpam-3443	425	3	composition	composition	NOUN
ejpam-3443	425	4	of	of	ADP
ejpam-3443	425	5	graphs	graph	NOUN
ejpam-3443	425	6	theorem	theorem	VERB
ejpam-3443	425	7	7	7	NUM
ejpam-3443	425	8	.	.	PUNCT
ejpam-3443	426	1	[	[	X
ejpam-3443	426	2	9	9	NUM
ejpam-3443	426	3	]	]	PUNCT
ejpam-3443	426	4	let	let	VERB
ejpam-3443	426	5	g	g	NOUN
ejpam-3443	426	6	and	and	CCONJ
ejpam-3443	426	7	h	h	NOUN
ejpam-3443	426	8	be	be	AUX
ejpam-3443	426	9	connected	connect	VERB
ejpam-3443	426	10	graphs	graph	NOUN
ejpam-3443	426	11	.	.	PUNCT
ejpam-3443	427	1	then	then	ADV
ejpam-3443	427	2	c	c	X
ejpam-3443	427	3	=	=	PUNCT
ejpam-3443	427	4	⋃	⋃	PROPN
ejpam-3443	427	5	x∈s	x∈s	NOUN
ejpam-3443	427	6	(	(	PUNCT
ejpam-3443	427	7	{	{	PUNCT
ejpam-3443	427	8	x}×tx	x}×tx	NUM
ejpam-3443	427	9	)	)	PUNCT
ejpam-3443	427	10	⊆	⊆	NUM
ejpam-3443	427	11	v	v	NOUN
ejpam-3443	427	12	(	(	PUNCT
ejpam-3443	427	13	g[h	g[h	PROPN
ejpam-3443	427	14	]	]	PUNCT
ejpam-3443	427	15	)	)	PUNCT
ejpam-3443	427	16	,	,	PUNCT
ejpam-3443	427	17	where	where	SCONJ
ejpam-3443	427	18	s	s	VERB
ejpam-3443	427	19	⊆	⊆	NUM
ejpam-3443	427	20	v	v	NOUN
ejpam-3443	427	21	(	(	PUNCT
ejpam-3443	427	22	g	g	NOUN
ejpam-3443	427	23	)	)	PUNCT
ejpam-3443	427	24	and	and	CCONJ
ejpam-3443	427	25	tx	tx	VERB
ejpam-3443	427	26	⊆	⊆	NUM
ejpam-3443	427	27	v	v	NOUN
ejpam-3443	427	28	(	(	PUNCT
ejpam-3443	427	29	h	h	NOUN
ejpam-3443	427	30	)	)	PUNCT
ejpam-3443	427	31	for	for	ADP
ejpam-3443	427	32	every	every	DET
ejpam-3443	427	33	x	x	SYM
ejpam-3443	427	34	∈	∈	PROPN
ejpam-3443	427	35	s	s	NOUN
ejpam-3443	427	36	,	,	PUNCT
ejpam-3443	427	37	is	be	AUX
ejpam-3443	427	38	a	a	DET
ejpam-3443	427	39	dominating	dominating	NOUN
ejpam-3443	427	40	set	set	NOUN
ejpam-3443	427	41	of	of	ADP
ejpam-3443	427	42	g[h	g[h	NOUN
ejpam-3443	427	43	]	]	PUNCT
ejpam-3443	427	44	if	if	SCONJ
ejpam-3443	427	45	and	and	CCONJ
ejpam-3443	427	46	only	only	ADV
ejpam-3443	427	47	if	if	SCONJ
ejpam-3443	427	48	either	either	CCONJ
ejpam-3443	427	49	(	(	PUNCT
ejpam-3443	427	50	i	i	NOUN
ejpam-3443	427	51	)	)	PUNCT
ejpam-3443	427	52	s	s	VERB
ejpam-3443	427	53	is	be	AUX
ejpam-3443	427	54	a	a	DET
ejpam-3443	427	55	total	total	ADJ
ejpam-3443	427	56	dominating	dominating	NOUN
ejpam-3443	427	57	set	set	NOUN
ejpam-3443	427	58	of	of	ADP
ejpam-3443	427	59	g	g	NOUN
ejpam-3443	427	60	,	,	PUNCT
ejpam-3443	427	61	or	or	CCONJ
ejpam-3443	427	62	(	(	PUNCT
ejpam-3443	427	63	ii	ii	NOUN
ejpam-3443	427	64	)	)	PUNCT
ejpam-3443	428	1	s	s	VERB
ejpam-3443	428	2	is	be	AUX
ejpam-3443	428	3	a	a	DET
ejpam-3443	428	4	dominating	dominating	NOUN
ejpam-3443	428	5	set	set	NOUN
ejpam-3443	428	6	of	of	ADP
ejpam-3443	428	7	g	g	PROPN
ejpam-3443	428	8	and	and	CCONJ
ejpam-3443	428	9	tx	tx	PROPN
ejpam-3443	428	10	is	be	AUX
ejpam-3443	428	11	a	a	DET
ejpam-3443	428	12	dominating	dominating	NOUN
ejpam-3443	428	13	set	set	NOUN
ejpam-3443	428	14	of	of	ADP
ejpam-3443	428	15	h	h	NOUN
ejpam-3443	428	16	for	for	ADP
ejpam-3443	428	17	every	every	DET
ejpam-3443	428	18	x	x	SYM
ejpam-3443	428	19	∈	∈	PROPN
ejpam-3443	428	20	s	s	PART
ejpam-3443	428	21	\ng(s	\ng(s	NOUN
ejpam-3443	428	22	)	)	PUNCT
ejpam-3443	428	23	.	.	PUNCT
ejpam-3443	429	1	theorem	theorem	VERB
ejpam-3443	429	2	8	8	NUM
ejpam-3443	429	3	.	.	PUNCT
ejpam-3443	430	1	[	[	X
ejpam-3443	430	2	9	9	NUM
ejpam-3443	430	3	]	]	PUNCT
ejpam-3443	430	4	let	let	VERB
ejpam-3443	430	5	g	g	NOUN
ejpam-3443	430	6	and	and	CCONJ
ejpam-3443	430	7	h	h	NOUN
ejpam-3443	430	8	be	be	AUX
ejpam-3443	430	9	nontrivial	nontrivial	ADJ
ejpam-3443	430	10	connected	connect	VERB
ejpam-3443	430	11	graphs	graph	NOUN
ejpam-3443	430	12	with	with	ADP
ejpam-3443	430	13	γ(h	γ(h	NOUN
ejpam-3443	430	14	)	)	PUNCT
ejpam-3443	430	15	=	=	SYM
ejpam-3443	431	1	1	1	X
ejpam-3443	431	2	.	.	PUNCT
ejpam-3443	431	3	then	then	ADV
ejpam-3443	431	4	γ(g[h	γ(g[h	NOUN
ejpam-3443	431	5	]	]	PUNCT
ejpam-3443	431	6	)	)	PUNCT
ejpam-3443	431	7	=	=	SYM
ejpam-3443	431	8	1	1	X
ejpam-3443	431	9	.	.	NOUN
ejpam-3443	431	10	remark	remark	NOUN
ejpam-3443	431	11	7	7	NUM
ejpam-3443	431	12	.	.	PUNCT
ejpam-3443	432	1	let	let	VERB
ejpam-3443	432	2	g	g	NOUN
ejpam-3443	432	3	and	and	CCONJ
ejpam-3443	432	4	h	h	NOUN
ejpam-3443	432	5	be	be	AUX
ejpam-3443	432	6	connected	connect	VERB
ejpam-3443	432	7	graphs	graph	NOUN
ejpam-3443	432	8	.	.	PUNCT
ejpam-3443	433	1	for	for	ADP
ejpam-3443	433	2	c	c	NOUN
ejpam-3443	433	3	=	=	SYM
ejpam-3443	433	4	∪u∈s	∪u∈s	X
ejpam-3443	433	5	(	(	PUNCT
ejpam-3443	433	6	{	{	PUNCT
ejpam-3443	433	7	x	x	NOUN
ejpam-3443	433	8	}	}	PUNCT
ejpam-3443	433	9	×	×	PROPN
ejpam-3443	433	10	tx	tx	PROPN
ejpam-3443	433	11	)	)	PUNCT
ejpam-3443	433	12	⊆	⊆	NUM
ejpam-3443	433	13	v	v	NOUN
ejpam-3443	433	14	(	(	PUNCT
ejpam-3443	433	15	g[h	g[h	PROPN
ejpam-3443	433	16	]	]	PUNCT
ejpam-3443	433	17	)	)	PUNCT
ejpam-3443	433	18	and	and	CCONJ
ejpam-3443	433	19	(	(	PUNCT
ejpam-3443	433	20	u	u	NOUN
ejpam-3443	433	21	,	,	PUNCT
ejpam-3443	433	22	v	v	NOUN
ejpam-3443	433	23	)	)	PUNCT
ejpam-3443	433	24	∈	∈	PROPN
ejpam-3443	433	25	c	c	X
ejpam-3443	433	26	,	,	PUNCT
ejpam-3443	433	27	|ng[h]((u	|ng[h]((u	PROPN
ejpam-3443	433	28	,	,	PUNCT
ejpam-3443	433	29	v	v	NOUN
ejpam-3443	433	30	)	)	PUNCT
ejpam-3443	433	31	)	)	PUNCT
ejpam-3443	433	32	∩	∩	NOUN
ejpam-3443	433	33	c|	c|	PROPN
ejpam-3443	433	34	=	=	SYM
ejpam-3443	433	35	∑	∑	NOUN
ejpam-3443	433	36	x∈s∩ng(u	x∈s∩ng(u	PROPN
ejpam-3443	433	37	)	)	PUNCT
ejpam-3443	433	38	|tx|+	|tx|+	PROPN
ejpam-3443	433	39	|nh(v	|nh(v	NOUN
ejpam-3443	433	40	)	)	PUNCT
ejpam-3443	433	41	∩	∩	NOUN
ejpam-3443	433	42	tu|	tu|	ADP
ejpam-3443	433	43	(	(	PUNCT
ejpam-3443	433	44	2	2	NUM
ejpam-3443	433	45	)	)	PUNCT
ejpam-3443	433	46	and	and	CCONJ
ejpam-3443	433	47	|ng[h]((u	|ng[h]((u	NUM
ejpam-3443	433	48	,	,	PUNCT
ejpam-3443	433	49	v	v	NOUN
ejpam-3443	433	50	)	)	PUNCT
ejpam-3443	433	51	)	)	PUNCT
ejpam-3443	433	52	\	\	PROPN
ejpam-3443	434	1	c|	c|	PROPN
ejpam-3443	434	2	=	=	SYM
ejpam-3443	434	3	|ng(u	|ng(u	PROPN
ejpam-3443	434	4	)	)	PUNCT
ejpam-3443	434	5	\	\	X
ejpam-3443	435	1	s||v	s||v	PROPN
ejpam-3443	435	2	(	(	PUNCT
ejpam-3443	435	3	h)|+	h)|+	PROPN
ejpam-3443	435	4	|nh(v	|nh(v	NOUN
ejpam-3443	435	5	)	)	PUNCT
ejpam-3443	435	6	\	\	NOUN
ejpam-3443	435	7	tu|+	tu|+	PROPN
ejpam-3443	435	8	∑	∑	PUNCT
ejpam-3443	435	9	x∈ng(u)∩s	x∈ng(u)∩s	PROPN
ejpam-3443	435	10	|v	|v	PROPN
ejpam-3443	435	11	(	(	PUNCT
ejpam-3443	435	12	h	h	NOUN
ejpam-3443	435	13	)	)	PUNCT
ejpam-3443	435	14	\	\	NOUN
ejpam-3443	435	15	tx|	tx|	PROPN
ejpam-3443	435	16	(	(	PUNCT
ejpam-3443	435	17	3	3	X
ejpam-3443	435	18	)	)	PUNCT
ejpam-3443	435	19	it	it	PRON
ejpam-3443	435	20	is	be	AUX
ejpam-3443	435	21	worth	worth	ADJ
ejpam-3443	435	22	noting	note	VERB
ejpam-3443	435	23	that	that	SCONJ
ejpam-3443	435	24	a	a	DET
ejpam-3443	435	25	graph	graph	NOUN
ejpam-3443	435	26	may	may	AUX
ejpam-3443	435	27	not	not	PART
ejpam-3443	435	28	have	have	VERB
ejpam-3443	435	29	a	a	DET
ejpam-3443	435	30	total	total	ADJ
ejpam-3443	435	31	dominating	dominating	NOUN
ejpam-3443	435	32	set	set	NOUN
ejpam-3443	435	33	that	that	PRON
ejpam-3443	435	34	is	be	AUX
ejpam-3443	435	35	cost	cost	NOUN
ejpam-3443	435	36	effective	effective	ADJ
ejpam-3443	435	37	.	.	PUNCT
ejpam-3443	436	1	a	a	DET
ejpam-3443	436	2	good	good	ADJ
ejpam-3443	436	3	example	example	NOUN
ejpam-3443	436	4	is	be	AUX
ejpam-3443	436	5	the	the	DET
ejpam-3443	436	6	path	path	NOUN
ejpam-3443	436	7	p3	p3	PROPN
ejpam-3443	436	8	.	.	PUNCT
ejpam-3443	437	1	f.jamil	f.jamil	PROPN
ejpam-3443	437	2	,	,	PUNCT
ejpam-3443	437	3	h.	h.	PROPN
ejpam-3443	437	4	nuenay	nuenay	PROPN
ejpam-3443	437	5	-	-	PUNCT
ejpam-3443	437	6	maglanque	maglanque	ADJ
ejpam-3443	437	7	/	/	SYM
ejpam-3443	437	8	eur	eur	NOUN
ejpam-3443	437	9	.	.	PUNCT
ejpam-3443	438	1	j.	j.	PROPN
ejpam-3443	438	2	pure	pure	PROPN
ejpam-3443	438	3	appl	appl	PROPN
ejpam-3443	438	4	.	.	PROPN
ejpam-3443	438	5	math	math	PROPN
ejpam-3443	438	6	,	,	PUNCT
ejpam-3443	438	7	12	12	NUM
ejpam-3443	438	8	(	(	PUNCT
ejpam-3443	438	9	3	3	NUM
ejpam-3443	438	10	)	)	PUNCT
ejpam-3443	438	11	(	(	PUNCT
ejpam-3443	438	12	2019	2019	NUM
ejpam-3443	438	13	)	)	PUNCT
ejpam-3443	438	14	,	,	PUNCT
ejpam-3443	438	15	978	978	NUM
ejpam-3443	438	16	-	-	SYM
ejpam-3443	438	17	998	998	NUM
ejpam-3443	438	18	994	994	NUM
ejpam-3443	438	19	theorem	theorem	NOUN
ejpam-3443	438	20	9	9	NUM
ejpam-3443	438	21	.	.	PUNCT
ejpam-3443	439	1	let	let	VERB
ejpam-3443	439	2	g	g	NOUN
ejpam-3443	439	3	and	and	CCONJ
ejpam-3443	439	4	h	h	NOUN
ejpam-3443	439	5	be	be	AUX
ejpam-3443	439	6	nontrivial	nontrivial	ADJ
ejpam-3443	439	7	connected	connected	ADJ
ejpam-3443	439	8	graphs	graph	NOUN
ejpam-3443	439	9	,	,	PUNCT
ejpam-3443	439	10	and	and	CCONJ
ejpam-3443	439	11	c	c	X
ejpam-3443	439	12	=	=	SYM
ejpam-3443	439	13	∪x∈s({x	∪x∈s({x	ADJ
ejpam-3443	439	14	}	}	PUNCT
ejpam-3443	439	15	×	×	NOUN
ejpam-3443	439	16	tx	tx	PROPN
ejpam-3443	439	17	)	)	PUNCT
ejpam-3443	439	18	⊆	⊆	NUM
ejpam-3443	439	19	v	v	NOUN
ejpam-3443	439	20	(	(	PUNCT
ejpam-3443	439	21	g[h	g[h	PROPN
ejpam-3443	439	22	]	]	PUNCT
ejpam-3443	439	23	)	)	PUNCT
ejpam-3443	439	24	,	,	PUNCT
ejpam-3443	439	25	where	where	SCONJ
ejpam-3443	439	26	s	s	VERB
ejpam-3443	439	27	⊆	⊆	NUM
ejpam-3443	439	28	v	v	NOUN
ejpam-3443	439	29	(	(	PUNCT
ejpam-3443	439	30	g	g	NOUN
ejpam-3443	439	31	)	)	PUNCT
ejpam-3443	439	32	and	and	CCONJ
ejpam-3443	439	33	tx	tx	VERB
ejpam-3443	439	34	⊆	⊆	NUM
ejpam-3443	439	35	v	v	NOUN
ejpam-3443	439	36	(	(	PUNCT
ejpam-3443	439	37	h	h	NOUN
ejpam-3443	439	38	)	)	PUNCT
ejpam-3443	439	39	for	for	ADP
ejpam-3443	439	40	each	each	DET
ejpam-3443	439	41	x	x	PROPN
ejpam-3443	439	42	∈	∈	PROPN
ejpam-3443	439	43	s.	s.	PROPN
ejpam-3443	439	44	if	if	SCONJ
ejpam-3443	439	45	s	s	PROPN
ejpam-3443	439	46	is	be	AUX
ejpam-3443	439	47	an	an	DET
ejpam-3443	439	48	independent	independent	ADJ
ejpam-3443	439	49	dominating	dominating	NOUN
ejpam-3443	439	50	set	set	NOUN
ejpam-3443	439	51	of	of	ADP
ejpam-3443	439	52	g	g	PROPN
ejpam-3443	439	53	and	and	CCONJ
ejpam-3443	439	54	tx	tx	PROPN
ejpam-3443	439	55	is	be	AUX
ejpam-3443	439	56	a	a	DET
ejpam-3443	439	57	dominating	dominating	NOUN
ejpam-3443	439	58	set	set	NOUN
ejpam-3443	439	59	of	of	ADP
ejpam-3443	439	60	h	h	NOUN
ejpam-3443	439	61	for	for	ADP
ejpam-3443	439	62	each	each	DET
ejpam-3443	439	63	x	x	SYM
ejpam-3443	439	64	∈	∈	PROPN
ejpam-3443	439	65	s	s	NOUN
ejpam-3443	439	66	,	,	PUNCT
ejpam-3443	439	67	then	then	ADV
ejpam-3443	439	68	c	c	PROPN
ejpam-3443	439	69	is	be	AUX
ejpam-3443	439	70	a	a	DET
ejpam-3443	439	71	cost	cost	NOUN
ejpam-3443	439	72	effective	effective	ADJ
ejpam-3443	439	73	dominating	dominating	NOUN
ejpam-3443	439	74	set	set	NOUN
ejpam-3443	439	75	of	of	ADP
ejpam-3443	439	76	g[h	g[h	PROPN
ejpam-3443	439	77	]	]	PUNCT
ejpam-3443	439	78	.	.	PUNCT
ejpam-3443	440	1	proof	proof	NOUN
ejpam-3443	440	2	.	.	PUNCT
ejpam-3443	441	1	suppose	suppose	VERB
ejpam-3443	441	2	that	that	SCONJ
ejpam-3443	441	3	s	s	VERB
ejpam-3443	441	4	is	be	AUX
ejpam-3443	441	5	an	an	DET
ejpam-3443	441	6	independent	independent	ADJ
ejpam-3443	441	7	dominating	dominating	NOUN
ejpam-3443	441	8	set	set	NOUN
ejpam-3443	441	9	of	of	ADP
ejpam-3443	441	10	g	g	PROPN
ejpam-3443	441	11	and	and	CCONJ
ejpam-3443	441	12	tx	tx	PROPN
ejpam-3443	441	13	is	be	AUX
ejpam-3443	441	14	a	a	DET
ejpam-3443	441	15	dominating	dominating	NOUN
ejpam-3443	441	16	set	set	NOUN
ejpam-3443	441	17	of	of	ADP
ejpam-3443	441	18	h	h	NOUN
ejpam-3443	441	19	for	for	ADP
ejpam-3443	441	20	each	each	DET
ejpam-3443	441	21	x	x	SYM
ejpam-3443	441	22	∈	∈	PROPN
ejpam-3443	441	23	s.	s.	PROPN
ejpam-3443	441	24	by	by	ADP
ejpam-3443	441	25	theorem	theorem	NOUN
ejpam-3443	441	26	7	7	NUM
ejpam-3443	441	27	,	,	PUNCT
ejpam-3443	441	28	c	c	PROPN
ejpam-3443	441	29	is	be	AUX
ejpam-3443	441	30	a	a	DET
ejpam-3443	441	31	dominating	dominating	NOUN
ejpam-3443	441	32	set	set	NOUN
ejpam-3443	441	33	of	of	ADP
ejpam-3443	441	34	g[h	g[h	PROPN
ejpam-3443	441	35	]	]	PUNCT
ejpam-3443	441	36	.	.	PUNCT
ejpam-3443	442	1	let	let	VERB
ejpam-3443	442	2	u	u	PRON
ejpam-3443	442	3	∈	∈	PROPN
ejpam-3443	442	4	s	s	X
ejpam-3443	442	5	and	and	CCONJ
ejpam-3443	442	6	v	v	ADP
ejpam-3443	442	7	∈	∈	PROPN
ejpam-3443	442	8	tu	tu	PROPN
ejpam-3443	442	9	.	.	PUNCT
ejpam-3443	443	1	since	since	SCONJ
ejpam-3443	443	2	g	g	PROPN
ejpam-3443	443	3	is	be	AUX
ejpam-3443	443	4	nontrivial	nontrivial	ADJ
ejpam-3443	443	5	and	and	CCONJ
ejpam-3443	443	6	s	s	NOUN
ejpam-3443	443	7	is	be	AUX
ejpam-3443	443	8	independent	independent	ADJ
ejpam-3443	443	9	,	,	PUNCT
ejpam-3443	443	10	ng(u	ng(u	NOUN
ejpam-3443	444	1	)	)	PUNCT
ejpam-3443	444	2	\	\	PROPN
ejpam-3443	444	3	s	s	PART
ejpam-3443	444	4	6=	6=	ADP
ejpam-3443	444	5	∅.	∅.	VERB
ejpam-3443	444	6	using	use	VERB
ejpam-3443	444	7	equations	equation	NOUN
ejpam-3443	444	8	2	2	NUM
ejpam-3443	444	9	and	and	CCONJ
ejpam-3443	444	10	3	3	NUM
ejpam-3443	444	11	,	,	PUNCT
ejpam-3443	444	12	|ng[h](u	|ng[h](u	ADV
ejpam-3443	444	13	,	,	PUNCT
ejpam-3443	444	14	v	v	NOUN
ejpam-3443	444	15	)	)	PUNCT
ejpam-3443	444	16	∩	∩	NOUN
ejpam-3443	444	17	c|	c|	PROPN
ejpam-3443	444	18	=	=	SYM
ejpam-3443	444	19	|nh(v	|nh(v	NOUN
ejpam-3443	444	20	)	)	PUNCT
ejpam-3443	444	21	∩	∩	NOUN
ejpam-3443	444	22	tu|	tu|	ADP
ejpam-3443	444	23	<	<	X
ejpam-3443	444	24	|nh(v	|nh(v	NOUN
ejpam-3443	444	25	)	)	PUNCT
ejpam-3443	444	26	\	\	NOUN
ejpam-3443	444	27	tu|+	tu|+	PROPN
ejpam-3443	444	28	|ng(u	|ng(u	PROPN
ejpam-3443	444	29	)	)	PUNCT
ejpam-3443	444	30	\	\	X
ejpam-3443	445	1	s||v	s||v	PROPN
ejpam-3443	445	2	(	(	PUNCT
ejpam-3443	445	3	h)|	h)|	PROPN
ejpam-3443	445	4	=	=	PUNCT
ejpam-3443	445	5	|ng[h]((u	|ng[h]((u	PROPN
ejpam-3443	445	6	,	,	PUNCT
ejpam-3443	445	7	v	v	NOUN
ejpam-3443	445	8	)	)	PUNCT
ejpam-3443	445	9	)	)	PUNCT
ejpam-3443	445	10	\	\	PROPN
ejpam-3443	446	1	c|	c|	PROPN
ejpam-3443	446	2	.	.	PUNCT
ejpam-3443	447	1	since	since	SCONJ
ejpam-3443	447	2	u	u	PROPN
ejpam-3443	447	3	and	and	CCONJ
ejpam-3443	447	4	v	v	NOUN
ejpam-3443	447	5	are	be	AUX
ejpam-3443	447	6	arbitrary	arbitrary	ADJ
ejpam-3443	447	7	,	,	PUNCT
ejpam-3443	447	8	c	c	PROPN
ejpam-3443	447	9	is	be	AUX
ejpam-3443	447	10	a	a	DET
ejpam-3443	447	11	cost	cost	NOUN
ejpam-3443	447	12	effective	effective	ADJ
ejpam-3443	447	13	dominating	dominating	NOUN
ejpam-3443	447	14	set	set	NOUN
ejpam-3443	447	15	of	of	ADP
ejpam-3443	447	16	g[h	g[h	PROPN
ejpam-3443	447	17	]	]	PUNCT
ejpam-3443	447	18	.	.	PUNCT
ejpam-3443	448	1	corollary	corollary	ADJ
ejpam-3443	448	2	8	8	NUM
ejpam-3443	448	3	.	.	PUNCT
ejpam-3443	449	1	for	for	ADP
ejpam-3443	449	2	any	any	DET
ejpam-3443	449	3	nontrivial	nontrivial	ADJ
ejpam-3443	449	4	connected	connect	VERB
ejpam-3443	449	5	graphs	graph	NOUN
ejpam-3443	449	6	g	g	NOUN
ejpam-3443	449	7	and	and	CCONJ
ejpam-3443	449	8	h	h	NOUN
ejpam-3443	449	9	,	,	PUNCT
ejpam-3443	449	10	γce(g[h	γce(g[h	NUM
ejpam-3443	449	11	]	]	PUNCT
ejpam-3443	449	12	)	)	PUNCT
ejpam-3443	449	13	≤	≤	NUM
ejpam-3443	449	14	γi(g)γ(h	γi(g)γ(h	NOUN
ejpam-3443	449	15	)	)	PUNCT
ejpam-3443	449	16	.	.	PUNCT
ejpam-3443	450	1	corollary	corollary	ADJ
ejpam-3443	450	2	9	9	NUM
ejpam-3443	450	3	.	.	PUNCT
ejpam-3443	451	1	for	for	ADP
ejpam-3443	451	2	any	any	DET
ejpam-3443	451	3	nontrivial	nontrivial	ADJ
ejpam-3443	451	4	connected	connect	VERB
ejpam-3443	451	5	graphs	graph	NOUN
ejpam-3443	451	6	g	g	NOUN
ejpam-3443	451	7	and	and	CCONJ
ejpam-3443	451	8	h	h	NOUN
ejpam-3443	451	9	with	with	ADP
ejpam-3443	451	10	g	g	PROPN
ejpam-3443	451	11	claw	claw	NOUN
ejpam-3443	451	12	-	-	PUNCT
ejpam-3443	451	13	free	free	ADJ
ejpam-3443	451	14	,	,	PUNCT
ejpam-3443	451	15	γce(g[h	γce(g[h	NUM
ejpam-3443	451	16	]	]	PUNCT
ejpam-3443	451	17	)	)	PUNCT
ejpam-3443	451	18	=	=	SYM
ejpam-3443	451	19	γ(g)γ(h	γ(g)γ(h	NOUN
ejpam-3443	451	20	)	)	PUNCT
ejpam-3443	451	21	.	.	PUNCT
ejpam-3443	452	1	theorem	theorem	ADJ
ejpam-3443	452	2	10	10	NUM
ejpam-3443	452	3	.	.	PUNCT
ejpam-3443	453	1	let	let	VERB
ejpam-3443	453	2	g	g	NOUN
ejpam-3443	453	3	and	and	CCONJ
ejpam-3443	453	4	h	h	NOUN
ejpam-3443	453	5	be	be	AUX
ejpam-3443	453	6	nontrivial	nontrivial	ADJ
ejpam-3443	453	7	connected	connected	ADJ
ejpam-3443	453	8	graphs	graph	NOUN
ejpam-3443	453	9	,	,	PUNCT
ejpam-3443	453	10	and	and	CCONJ
ejpam-3443	453	11	let	let	VERB
ejpam-3443	453	12	c	c	NOUN
ejpam-3443	453	13	=	=	SYM
ejpam-3443	453	14	∪x∈s({x}×tx	∪x∈s({x}×tx	PROPN
ejpam-3443	453	15	)	)	PUNCT
ejpam-3443	453	16	⊆	⊆	NUM
ejpam-3443	453	17	v	v	NOUN
ejpam-3443	453	18	(	(	PUNCT
ejpam-3443	453	19	g[h	g[h	PROPN
ejpam-3443	453	20	]	]	PUNCT
ejpam-3443	453	21	)	)	PUNCT
ejpam-3443	453	22	.	.	PUNCT
ejpam-3443	454	1	if	if	SCONJ
ejpam-3443	454	2	c	c	PROPN
ejpam-3443	454	3	has	have	VERB
ejpam-3443	454	4	the	the	DET
ejpam-3443	454	5	following	follow	VERB
ejpam-3443	454	6	properties	property	NOUN
ejpam-3443	454	7	:	:	PUNCT
ejpam-3443	454	8	(	(	PUNCT
ejpam-3443	454	9	i	i	NOUN
ejpam-3443	454	10	)	)	PUNCT
ejpam-3443	454	11	s	s	VERB
ejpam-3443	454	12	is	be	AUX
ejpam-3443	454	13	a	a	DET
ejpam-3443	454	14	cost	cost	NOUN
ejpam-3443	454	15	effective	effective	ADJ
ejpam-3443	454	16	dominating	dominating	NOUN
ejpam-3443	454	17	set	set	NOUN
ejpam-3443	454	18	of	of	ADP
ejpam-3443	454	19	g	g	NOUN
ejpam-3443	454	20	;	;	PUNCT
ejpam-3443	454	21	(	(	PUNCT
ejpam-3443	454	22	ii	ii	NOUN
ejpam-3443	454	23	)	)	PUNCT
ejpam-3443	454	24	for	for	ADP
ejpam-3443	454	25	each	each	DET
ejpam-3443	454	26	x	x	SYM
ejpam-3443	454	27	∈	∈	PROPN
ejpam-3443	454	28	s	s	PART
ejpam-3443	454	29	\ng(s	\ng(s	NOUN
ejpam-3443	454	30	)	)	PUNCT
ejpam-3443	454	31	,	,	PUNCT
ejpam-3443	454	32	tx	tx	PROPN
ejpam-3443	454	33	is	be	AUX
ejpam-3443	454	34	a	a	DET
ejpam-3443	454	35	dominating	dominating	NOUN
ejpam-3443	454	36	set	set	NOUN
ejpam-3443	454	37	of	of	ADP
ejpam-3443	454	38	h	h	NOUN
ejpam-3443	454	39	;	;	PUNCT
ejpam-3443	454	40	and	and	CCONJ
ejpam-3443	454	41	(	(	PUNCT
ejpam-3443	454	42	iii	iii	NOUN
ejpam-3443	454	43	)	)	PUNCT
ejpam-3443	454	44	for	for	ADP
ejpam-3443	454	45	each	each	DET
ejpam-3443	454	46	x	x	SYM
ejpam-3443	454	47	∈	∈	PROPN
ejpam-3443	454	48	s	s	NOUN
ejpam-3443	454	49	∩ng(s	∩ng(s	NOUN
ejpam-3443	454	50	)	)	PUNCT
ejpam-3443	454	51	,	,	PUNCT
ejpam-3443	454	52	tx	tx	PROPN
ejpam-3443	454	53	is	be	AUX
ejpam-3443	454	54	a	a	DET
ejpam-3443	454	55	cost	cost	NOUN
ejpam-3443	454	56	effective	effective	ADJ
ejpam-3443	454	57	set	set	NOUN
ejpam-3443	454	58	of	of	ADP
ejpam-3443	454	59	h	h	NOUN
ejpam-3443	454	60	,	,	PUNCT
ejpam-3443	454	61	then	then	ADV
ejpam-3443	454	62	c	c	PROPN
ejpam-3443	454	63	is	be	AUX
ejpam-3443	454	64	a	a	DET
ejpam-3443	454	65	cost	cost	NOUN
ejpam-3443	454	66	effective	effective	ADJ
ejpam-3443	454	67	dominating	dominating	NOUN
ejpam-3443	454	68	set	set	NOUN
ejpam-3443	454	69	of	of	ADP
ejpam-3443	454	70	g[h	g[h	PROPN
ejpam-3443	454	71	]	]	PUNCT
ejpam-3443	454	72	.	.	PUNCT
ejpam-3443	455	1	proof	proof	NOUN
ejpam-3443	455	2	.	.	PUNCT
ejpam-3443	456	1	by	by	ADP
ejpam-3443	456	2	theorem	theorem	ADJ
ejpam-3443	456	3	7	7	NUM
ejpam-3443	456	4	,	,	PUNCT
ejpam-3443	456	5	properties	property	NOUN
ejpam-3443	456	6	(	(	PUNCT
ejpam-3443	456	7	i	i	NOUN
ejpam-3443	456	8	)	)	PUNCT
ejpam-3443	456	9	and	and	CCONJ
ejpam-3443	456	10	(	(	PUNCT
ejpam-3443	456	11	ii	ii	NOUN
ejpam-3443	456	12	)	)	PUNCT
ejpam-3443	456	13	imply	imply	VERB
ejpam-3443	456	14	that	that	SCONJ
ejpam-3443	456	15	c	c	PROPN
ejpam-3443	456	16	is	be	AUX
ejpam-3443	456	17	a	a	DET
ejpam-3443	456	18	dominating	dominating	NOUN
ejpam-3443	456	19	set	set	NOUN
ejpam-3443	456	20	of	of	ADP
ejpam-3443	456	21	g[h	g[h	PROPN
ejpam-3443	456	22	]	]	PUNCT
ejpam-3443	456	23	.	.	PUNCT
ejpam-3443	457	1	let	let	AUX
ejpam-3443	457	2	(	(	PUNCT
ejpam-3443	457	3	x	x	NOUN
ejpam-3443	457	4	,	,	PUNCT
ejpam-3443	457	5	y	y	NOUN
ejpam-3443	457	6	)	)	PUNCT
ejpam-3443	457	7	∈	∈	PROPN
ejpam-3443	457	8	c.	c.	NOUN
ejpam-3443	457	9	suppose	suppose	VERB
ejpam-3443	457	10	that	that	SCONJ
ejpam-3443	457	11	x	x	PUNCT
ejpam-3443	457	12	∈	∈	NOUN
ejpam-3443	457	13	s	s	PART
ejpam-3443	457	14	\ng(s	\ng(s	NOUN
ejpam-3443	457	15	)	)	PUNCT
ejpam-3443	457	16	.	.	PUNCT
ejpam-3443	458	1	then	then	ADV
ejpam-3443	458	2	ng(x	ng(x	NUM
ejpam-3443	458	3	)	)	PUNCT
ejpam-3443	458	4	\	\	PROPN
ejpam-3443	458	5	s	s	PART
ejpam-3443	458	6	6=	6=	NUM
ejpam-3443	458	7	∅.	∅.	VERB
ejpam-3443	458	8	following	follow	VERB
ejpam-3443	458	9	equations	equation	NOUN
ejpam-3443	458	10	2	2	NUM
ejpam-3443	458	11	and	and	CCONJ
ejpam-3443	458	12	3	3	NUM
ejpam-3443	458	13	,	,	PUNCT
ejpam-3443	458	14	|ng[h]((x	|ng[h]((x	NUM
ejpam-3443	458	15	,	,	PUNCT
ejpam-3443	458	16	y	y	NOUN
ejpam-3443	458	17	)	)	PUNCT
ejpam-3443	458	18	)	)	PUNCT
ejpam-3443	458	19	∩	∩	NOUN
ejpam-3443	458	20	c|	c|	PROPN
ejpam-3443	458	21	=	=	SYM
ejpam-3443	458	22	|nh(y	|nh(y	PROPN
ejpam-3443	458	23	)	)	PUNCT
ejpam-3443	458	24	∩	∩	NOUN
ejpam-3443	458	25	tx|	tx|	VERB
ejpam-3443	458	26	<	<	X
ejpam-3443	458	27	|ng(x	|ng(x	NOUN
ejpam-3443	458	28	)	)	PUNCT
ejpam-3443	458	29	\	\	X
ejpam-3443	459	1	s||v	s||v	PROPN
ejpam-3443	459	2	(	(	PUNCT
ejpam-3443	459	3	h)|+	h)|+	PROPN
ejpam-3443	459	4	|nh(y	|nh(y	SYM
ejpam-3443	459	5	)	)	PUNCT
ejpam-3443	459	6	\	\	NOUN
ejpam-3443	459	7	tx|	tx|	NOUN
ejpam-3443	459	8	=	=	PUNCT
ejpam-3443	459	9	|ng[h]((x	|ng[h]((x	NUM
ejpam-3443	459	10	,	,	PUNCT
ejpam-3443	459	11	y	y	NOUN
ejpam-3443	459	12	)	)	PUNCT
ejpam-3443	459	13	)	)	PUNCT
ejpam-3443	459	14	\	\	PROPN
ejpam-3443	459	15	c|	c|	PROPN
ejpam-3443	459	16	.	.	PUNCT
ejpam-3443	459	17	suppose	suppose	VERB
ejpam-3443	459	18	that	that	SCONJ
ejpam-3443	459	19	x	x	PUNCT
ejpam-3443	459	20	∈	∈	NOUN
ejpam-3443	459	21	s	s	NOUN
ejpam-3443	459	22	∩ng(s	∩ng(s	NOUN
ejpam-3443	459	23	)	)	PUNCT
ejpam-3443	459	24	.	.	PUNCT
ejpam-3443	460	1	properties	property	NOUN
ejpam-3443	460	2	(	(	PUNCT
ejpam-3443	460	3	i	i	NOUN
ejpam-3443	460	4	)	)	PUNCT
ejpam-3443	460	5	and	and	CCONJ
ejpam-3443	460	6	(	(	PUNCT
ejpam-3443	460	7	iii	iii	NOUN
ejpam-3443	460	8	)	)	PUNCT
ejpam-3443	460	9	and	and	CCONJ
ejpam-3443	460	10	equations	equation	NOUN
ejpam-3443	460	11	2	2	NUM
ejpam-3443	460	12	and	and	CCONJ
ejpam-3443	460	13	3	3	NUM
ejpam-3443	460	14	yield	yield	NOUN
ejpam-3443	460	15	|ng[h]((x	|ng[h]((x	PROPN
ejpam-3443	460	16	,	,	PUNCT
ejpam-3443	460	17	y	y	NOUN
ejpam-3443	460	18	)	)	PUNCT
ejpam-3443	460	19	)	)	PUNCT
ejpam-3443	461	1	∩	∩	NOUN
ejpam-3443	461	2	c|	c|	PROPN
ejpam-3443	461	3	=	=	SYM
ejpam-3443	461	4	∑	∑	NOUN
ejpam-3443	461	5	x∈s∩ng(u	x∈s∩ng(u	PROPN
ejpam-3443	461	6	)	)	PUNCT
ejpam-3443	461	7	|tx|+	|tx|+	X
ejpam-3443	461	8	|nh(y	|nh(y	NUM
ejpam-3443	461	9	)	)	PUNCT
ejpam-3443	461	10	∩	∩	NOUN
ejpam-3443	461	11	tx|	tx|	VERB
ejpam-3443	461	12	≤	≤	NUM
ejpam-3443	461	13	|s	|s	PROPN
ejpam-3443	461	14	∩ng(x)||v	∩ng(x)||v	PUNCT
ejpam-3443	462	1	(	(	PUNCT
ejpam-3443	462	2	h)|+	h)|+	PROPN
ejpam-3443	462	3	|nh(y	|nh(y	SYM
ejpam-3443	462	4	)	)	PUNCT
ejpam-3443	462	5	∩	∩	NOUN
ejpam-3443	462	6	tx|	tx|	VERB
ejpam-3443	462	7	f.jamil	f.jamil	NOUN
ejpam-3443	462	8	,	,	PUNCT
ejpam-3443	462	9	h.	h.	PROPN
ejpam-3443	462	10	nuenay	nuenay	PROPN
ejpam-3443	462	11	-	-	PUNCT
ejpam-3443	462	12	maglanque	maglanque	ADJ
ejpam-3443	462	13	/	/	SYM
ejpam-3443	462	14	eur	eur	NOUN
ejpam-3443	462	15	.	.	PUNCT
ejpam-3443	463	1	j.	j.	PROPN
ejpam-3443	463	2	pure	pure	PROPN
ejpam-3443	463	3	appl	appl	PROPN
ejpam-3443	463	4	.	.	PROPN
ejpam-3443	463	5	math	math	PROPN
ejpam-3443	463	6	,	,	PUNCT
ejpam-3443	463	7	12	12	NUM
ejpam-3443	463	8	(	(	PUNCT
ejpam-3443	463	9	3	3	NUM
ejpam-3443	463	10	)	)	PUNCT
ejpam-3443	463	11	(	(	PUNCT
ejpam-3443	463	12	2019	2019	NUM
ejpam-3443	463	13	)	)	PUNCT
ejpam-3443	463	14	,	,	PUNCT
ejpam-3443	463	15	978	978	NUM
ejpam-3443	463	16	-	-	SYM
ejpam-3443	463	17	998	998	NUM
ejpam-3443	463	18	995	995	NUM
ejpam-3443	463	19	≤	≤	NUM
ejpam-3443	463	20	|ng(x	|ng(x	NUM
ejpam-3443	463	21	)	)	PUNCT
ejpam-3443	463	22	\	\	X
ejpam-3443	464	1	s||v	s||v	PROPN
ejpam-3443	464	2	(	(	PUNCT
ejpam-3443	464	3	h)|+	h)|+	PROPN
ejpam-3443	464	4	|nh(y	|nh(y	SYM
ejpam-3443	464	5	)	)	PUNCT
ejpam-3443	464	6	\	\	PUNCT
ejpam-3443	465	1	tx|+	tx|+	PROPN
ejpam-3443	465	2	∑	∑	PUNCT
ejpam-3443	465	3	z∈ng(x)∩s	z∈ng(x)∩s	PROPN
ejpam-3443	465	4	|v	|v	PROPN
ejpam-3443	465	5	(	(	PUNCT
ejpam-3443	465	6	h	h	NOUN
ejpam-3443	465	7	)	)	PUNCT
ejpam-3443	465	8	\	\	NOUN
ejpam-3443	466	1	tz|	tz|	NOUN
ejpam-3443	466	2	=	=	PUNCT
ejpam-3443	466	3	|ng[h]((x	|ng[h]((x	NUM
ejpam-3443	466	4	,	,	PUNCT
ejpam-3443	466	5	y	y	NOUN
ejpam-3443	466	6	)	)	PUNCT
ejpam-3443	466	7	)	)	PUNCT
ejpam-3443	466	8	\	\	PROPN
ejpam-3443	467	1	c|	c|	PROPN
ejpam-3443	467	2	.	.	PUNCT
ejpam-3443	468	1	accordingly	accordingly	ADV
ejpam-3443	468	2	,	,	PUNCT
ejpam-3443	468	3	c	c	PROPN
ejpam-3443	468	4	is	be	AUX
ejpam-3443	468	5	a	a	DET
ejpam-3443	468	6	cost	cost	NOUN
ejpam-3443	468	7	effective	effective	ADJ
ejpam-3443	468	8	dominating	dominating	NOUN
ejpam-3443	468	9	set	set	NOUN
ejpam-3443	468	10	of	of	ADP
ejpam-3443	468	11	g[h	g[h	PROPN
ejpam-3443	468	12	]	]	PUNCT
ejpam-3443	468	13	.	.	PUNCT
ejpam-3443	469	1	removing	remove	VERB
ejpam-3443	469	2	the	the	DET
ejpam-3443	469	3	condition	condition	NOUN
ejpam-3443	469	4	that	that	PRON
ejpam-3443	469	5	s	s	VERB
ejpam-3443	469	6	is	be	AUX
ejpam-3443	469	7	a	a	DET
ejpam-3443	469	8	cost	cost	NOUN
ejpam-3443	469	9	effective	effective	ADJ
ejpam-3443	469	10	set	set	NOUN
ejpam-3443	469	11	of	of	ADP
ejpam-3443	469	12	g	g	PROPN
ejpam-3443	469	13	in	in	ADP
ejpam-3443	469	14	theorem	theorem	NOUN
ejpam-3443	469	15	10(i	10(i	NUM
ejpam-3443	469	16	)	)	PUNCT
ejpam-3443	469	17	may	may	AUX
ejpam-3443	469	18	not	not	PART
ejpam-3443	469	19	yield	yield	VERB
ejpam-3443	469	20	a	a	DET
ejpam-3443	469	21	cost	cost	NOUN
ejpam-3443	469	22	effective	effective	ADJ
ejpam-3443	469	23	dominating	dominating	NOUN
ejpam-3443	469	24	set	set	VERB
ejpam-3443	469	25	c	c	PROPN
ejpam-3443	469	26	of	of	ADP
ejpam-3443	469	27	g[h	g[h	PROPN
ejpam-3443	469	28	]	]	PUNCT
ejpam-3443	469	29	.	.	PUNCT
ejpam-3443	470	1	consider	consider	VERB
ejpam-3443	470	2	,	,	PUNCT
ejpam-3443	470	3	for	for	ADP
ejpam-3443	470	4	example	example	NOUN
ejpam-3443	470	5	,	,	PUNCT
ejpam-3443	470	6	the	the	DET
ejpam-3443	470	7	set	set	NOUN
ejpam-3443	470	8	c	c	NOUN
ejpam-3443	470	9	=	=	SYM
ejpam-3443	470	10	v	v	PROPN
ejpam-3443	470	11	(	(	PUNCT
ejpam-3443	470	12	k3	k3	PROPN
ejpam-3443	470	13	)	)	PUNCT
ejpam-3443	470	14	×	×	PROPN
ejpam-3443	470	15	u	u	NOUN
ejpam-3443	470	16	in	in	ADP
ejpam-3443	470	17	the	the	DET
ejpam-3443	470	18	composition	composition	NOUN
ejpam-3443	470	19	g	g	NOUN
ejpam-3443	470	20	=	=	PUNCT
ejpam-3443	470	21	k3[k1,4	k3[k1,4	X
ejpam-3443	470	22	]	]	PUNCT
ejpam-3443	470	23	,	,	PUNCT
ejpam-3443	470	24	where	where	SCONJ
ejpam-3443	470	25	u	u	NOUN
ejpam-3443	470	26	is	be	AUX
ejpam-3443	470	27	the	the	DET
ejpam-3443	470	28	partite	partite	ADJ
ejpam-3443	470	29	set	set	NOUN
ejpam-3443	470	30	of	of	ADP
ejpam-3443	470	31	k1,4	k1,4	PROPN
ejpam-3443	470	32	with	with	ADP
ejpam-3443	470	33	|u	|u	ADJ
ejpam-3443	470	34	|	|	NOUN
ejpam-3443	470	35	=	=	NOUN
ejpam-3443	470	36	4	4	NUM
ejpam-3443	470	37	.	.	X
ejpam-3443	471	1	for	for	ADP
ejpam-3443	471	2	each	each	DET
ejpam-3443	471	3	x	x	SYM
ejpam-3443	471	4	∈	∈	PROPN
ejpam-3443	471	5	v	v	NOUN
ejpam-3443	471	6	(	(	PUNCT
ejpam-3443	471	7	k3	k3	PROPN
ejpam-3443	471	8	)	)	PUNCT
ejpam-3443	471	9	and	and	CCONJ
ejpam-3443	471	10	u	u	PROPN
ejpam-3443	471	11	∈	∈	PROPN
ejpam-3443	471	12	u	u	NOUN
ejpam-3443	471	13	,	,	PUNCT
ejpam-3443	471	14	|ng((x	|ng((x	PROPN
ejpam-3443	471	15	,	,	PUNCT
ejpam-3443	471	16	u	u	NOUN
ejpam-3443	471	17	)	)	PUNCT
ejpam-3443	471	18	)	)	PUNCT
ejpam-3443	471	19	∩	∩	NOUN
ejpam-3443	471	20	c|	c|	PROPN
ejpam-3443	471	21	=	=	SYM
ejpam-3443	471	22	8	8	NUM
ejpam-3443	471	23	,	,	PUNCT
ejpam-3443	471	24	and	and	CCONJ
ejpam-3443	471	25	|ng((x	|ng((x	NOUN
ejpam-3443	471	26	,	,	PUNCT
ejpam-3443	471	27	u	u	NOUN
ejpam-3443	471	28	)	)	PUNCT
ejpam-3443	471	29	)	)	PUNCT
ejpam-3443	471	30	\	\	PROPN
ejpam-3443	472	1	c|	c|	PROPN
ejpam-3443	472	2	=	=	SYM
ejpam-3443	472	3	3	3	X
ejpam-3443	472	4	.	.	PUNCT
ejpam-3443	473	1	thus	thus	ADV
ejpam-3443	473	2	,	,	PUNCT
ejpam-3443	473	3	c	c	PROPN
ejpam-3443	473	4	is	be	AUX
ejpam-3443	473	5	not	not	PART
ejpam-3443	473	6	a	a	DET
ejpam-3443	473	7	cost	cost	NOUN
ejpam-3443	473	8	effective	effective	ADJ
ejpam-3443	473	9	set	set	NOUN
ejpam-3443	473	10	,	,	PUNCT
ejpam-3443	473	11	hence	hence	ADV
ejpam-3443	473	12	not	not	PART
ejpam-3443	473	13	a	a	DET
ejpam-3443	473	14	cost	cost	NOUN
ejpam-3443	473	15	effective	effective	ADJ
ejpam-3443	473	16	dominating	dominating	NOUN
ejpam-3443	473	17	set	set	NOUN
ejpam-3443	473	18	,	,	PUNCT
ejpam-3443	473	19	of	of	ADP
ejpam-3443	473	20	g.	g.	PROPN
ejpam-3443	473	21	next	next	ADV
ejpam-3443	473	22	,	,	PUNCT
ejpam-3443	473	23	let	let	VERB
ejpam-3443	473	24	s	s	PRON
ejpam-3443	473	25	◦	◦	VERB
ejpam-3443	473	26	=	=	SYM
ejpam-3443	473	27	s	s	PART
ejpam-3443	473	28	∩ng(s	∩ng(s	NOUN
ejpam-3443	473	29	)	)	PUNCT
ejpam-3443	473	30	.	.	PUNCT
ejpam-3443	474	1	theorem	theorem	VERB
ejpam-3443	474	2	11	11	NUM
ejpam-3443	474	3	.	.	PUNCT
ejpam-3443	475	1	for	for	ADP
ejpam-3443	475	2	all	all	DET
ejpam-3443	475	3	nontrivial	nontrivial	ADJ
ejpam-3443	475	4	connected	connect	VERB
ejpam-3443	475	5	graphs	graph	NOUN
ejpam-3443	475	6	g	g	NOUN
ejpam-3443	475	7	and	and	CCONJ
ejpam-3443	475	8	p	p	X
ejpam-3443	475	9	≥	≥	NUM
ejpam-3443	475	10	2	2	NUM
ejpam-3443	475	11	,	,	PUNCT
ejpam-3443	475	12	(	(	PUNCT
ejpam-3443	475	13	i	i	NOUN
ejpam-3443	475	14	)	)	PUNCT
ejpam-3443	475	15	γce(g[kp	γce(g[kp	NOUN
ejpam-3443	475	16	]	]	PUNCT
ejpam-3443	475	17	)	)	PUNCT
ejpam-3443	475	18	=	=	SYM
ejpam-3443	475	19	γ(g	γ(g	PROPN
ejpam-3443	475	20	)	)	PUNCT
ejpam-3443	475	21	;	;	PUNCT
ejpam-3443	475	22	(	(	PUNCT
ejpam-3443	475	23	ii	ii	NOUN
ejpam-3443	475	24	)	)	PUNCT
ejpam-3443	475	25	γmce(g[kp	γmce(g[kp	PROPN
ejpam-3443	475	26	]	]	PUNCT
ejpam-3443	475	27	)	)	PUNCT
ejpam-3443	475	28	=	=	SYM
ejpam-3443	475	29	γmce(g	γmce(g	PROPN
ejpam-3443	475	30	)	)	PUNCT
ejpam-3443	475	31	;	;	PUNCT
ejpam-3443	475	32	and	and	CCONJ
ejpam-3443	475	33	(	(	PUNCT
ejpam-3443	475	34	iii	iii	X
ejpam-3443	475	35	)	)	PUNCT
ejpam-3443	475	36	γ+ce(g[kp	γ+ce(g[kp	NOUN
ejpam-3443	475	37	]	]	PUNCT
ejpam-3443	475	38	)	)	PUNCT
ejpam-3443	475	39	≥	≥	PROPN
ejpam-3443	475	40	max{p|s|	max{p|s|	INTJ
ejpam-3443	476	1	−	−	PROPN
ejpam-3443	477	1	(	(	PUNCT
ejpam-3443	477	2	p−	p−	INTJ
ejpam-3443	477	3	⌊	⌊	NOUN
ejpam-3443	477	4	p+1	p+1	NOUN
ejpam-3443	477	5	2	2	NUM
ejpam-3443	477	6	⌋	⌋	NOUN
ejpam-3443	477	7	)	)	PUNCT
ejpam-3443	477	8	|s	|s	PROPN
ejpam-3443	477	9	◦	◦	NOUN
ejpam-3443	477	10	|	|	NOUN
ejpam-3443	477	11	:	:	PUNCT
ejpam-3443	477	12	s	s	VERB
ejpam-3443	477	13	is	be	AUX
ejpam-3443	477	14	a	a	DET
ejpam-3443	477	15	γ+ce	γ+ce	NOUN
ejpam-3443	477	16	−	−	NOUN
ejpam-3443	477	17	set	set	NOUN
ejpam-3443	477	18	of	of	ADP
ejpam-3443	477	19	g	g	NOUN
ejpam-3443	477	20	}	}	PUNCT
ejpam-3443	477	21	.	.	PUNCT
ejpam-3443	478	1	proof	proof	NOUN
ejpam-3443	478	2	.	.	PUNCT
ejpam-3443	479	1	let	let	VERB
ejpam-3443	479	2	s	s	PRON
ejpam-3443	479	3	⊆	⊆	NUM
ejpam-3443	479	4	v	v	NOUN
ejpam-3443	479	5	(	(	PUNCT
ejpam-3443	479	6	g	g	NOUN
ejpam-3443	479	7	)	)	PUNCT
ejpam-3443	479	8	be	be	AUX
ejpam-3443	479	9	a	a	DET
ejpam-3443	479	10	γ	γ	NOUN
ejpam-3443	479	11	-	-	PUNCT
ejpam-3443	479	12	set	set	NOUN
ejpam-3443	479	13	of	of	ADP
ejpam-3443	479	14	g	g	NOUN
ejpam-3443	479	15	,	,	PUNCT
ejpam-3443	479	16	and	and	CCONJ
ejpam-3443	479	17	let	let	VERB
ejpam-3443	479	18	v	v	NUM
ejpam-3443	479	19	∈	∈	PROPN
ejpam-3443	479	20	v	v	NOUN
ejpam-3443	479	21	(	(	PUNCT
ejpam-3443	479	22	kp	kp	PROPN
ejpam-3443	479	23	)	)	PUNCT
ejpam-3443	479	24	.	.	PUNCT
ejpam-3443	480	1	define	define	VERB
ejpam-3443	480	2	c	c	NOUN
ejpam-3443	480	3	=	=	SYM
ejpam-3443	480	4	s	s	PROPN
ejpam-3443	480	5	×	×	NOUN
ejpam-3443	480	6	{	{	PUNCT
ejpam-3443	480	7	v	v	NOUN
ejpam-3443	480	8	}	}	PUNCT
ejpam-3443	480	9	.	.	PUNCT
ejpam-3443	481	1	by	by	ADP
ejpam-3443	481	2	theorem	theorem	NOUN
ejpam-3443	481	3	7	7	NUM
ejpam-3443	481	4	,	,	PUNCT
ejpam-3443	481	5	c	c	PROPN
ejpam-3443	481	6	is	be	AUX
ejpam-3443	481	7	a	a	DET
ejpam-3443	481	8	dominating	dominating	NOUN
ejpam-3443	481	9	set	set	NOUN
ejpam-3443	481	10	of	of	ADP
ejpam-3443	481	11	g[km	g[km	PROPN
ejpam-3443	481	12	]	]	PUNCT
ejpam-3443	481	13	.	.	PUNCT
ejpam-3443	482	1	for	for	ADP
ejpam-3443	482	2	each	each	DET
ejpam-3443	482	3	u	u	PROPN
ejpam-3443	482	4	∈	∈	PROPN
ejpam-3443	482	5	s	s	PROPN
ejpam-3443	482	6	,	,	PUNCT
ejpam-3443	482	7	|ng[kp]((u	|ng[kp]((u	NOUN
ejpam-3443	482	8	,	,	PUNCT
ejpam-3443	482	9	v	v	NOUN
ejpam-3443	482	10	)	)	PUNCT
ejpam-3443	482	11	)	)	PUNCT
ejpam-3443	482	12	∩	∩	PROPN
ejpam-3443	482	13	c|	c|	PROPN
ejpam-3443	482	14	=	=	SYM
ejpam-3443	482	15	|ng(u	|ng(u	ADJ
ejpam-3443	482	16	)	)	PUNCT
ejpam-3443	482	17	∩	∩	NOUN
ejpam-3443	482	18	s|	s|	VERB
ejpam-3443	482	19	≤	≤	NUM
ejpam-3443	482	20	p|ng(u	p|ng(u	NOUN
ejpam-3443	482	21	)	)	PUNCT
ejpam-3443	482	22	\	\	NOUN
ejpam-3443	483	1	s|+	s|+	NOUN
ejpam-3443	483	2	(	(	PUNCT
ejpam-3443	483	3	p−	p−	NOUN
ejpam-3443	483	4	1	1	NUM
ejpam-3443	483	5	)	)	PUNCT
ejpam-3443	483	6	+	+	CCONJ
ejpam-3443	483	7	(	(	PUNCT
ejpam-3443	483	8	p−	p−	NOUN
ejpam-3443	483	9	1)|ng(u	1)|ng(u	NUM
ejpam-3443	483	10	)	)	PUNCT
ejpam-3443	483	11	∩	∩	NOUN
ejpam-3443	483	12	s|	s|	NOUN
ejpam-3443	483	13	=	=	SYM
ejpam-3443	483	14	|ng[kp]((u	|ng[kp]((u	NOUN
ejpam-3443	483	15	,	,	PUNCT
ejpam-3443	483	16	v	v	NOUN
ejpam-3443	483	17	)	)	PUNCT
ejpam-3443	483	18	)	)	PUNCT
ejpam-3443	483	19	\	\	PROPN
ejpam-3443	484	1	c|	c|	PROPN
ejpam-3443	484	2	.	.	PUNCT
ejpam-3443	485	1	thus	thus	ADV
ejpam-3443	485	2	,	,	PUNCT
ejpam-3443	485	3	c	c	PROPN
ejpam-3443	485	4	is	be	AUX
ejpam-3443	485	5	a	a	DET
ejpam-3443	485	6	cost	cost	NOUN
ejpam-3443	485	7	effective	effective	ADJ
ejpam-3443	485	8	dominating	dominating	NOUN
ejpam-3443	485	9	set	set	NOUN
ejpam-3443	485	10	of	of	ADP
ejpam-3443	485	11	g[kp	g[kp	NOUN
ejpam-3443	485	12	]	]	PUNCT
ejpam-3443	485	13	so	so	SCONJ
ejpam-3443	485	14	that	that	SCONJ
ejpam-3443	485	15	γce(g[kp	γce(g[kp	NOUN
ejpam-3443	485	16	]	]	PUNCT
ejpam-3443	485	17	)	)	PUNCT
ejpam-3443	485	18	≤	≤	NUM
ejpam-3443	485	19	|s|	|s|	PROPN
ejpam-3443	485	20	=	=	SYM
ejpam-3443	485	21	γ(g	γ(g	PROPN
ejpam-3443	485	22	)	)	PUNCT
ejpam-3443	485	23	.	.	PUNCT
ejpam-3443	486	1	by	by	ADP
ejpam-3443	486	2	theorem	theorem	NOUN
ejpam-3443	486	3	8	8	NUM
ejpam-3443	486	4	,	,	PUNCT
ejpam-3443	486	5	γce(g[kp	γce(g[kp	NOUN
ejpam-3443	486	6	]	]	PUNCT
ejpam-3443	486	7	)	)	PUNCT
ejpam-3443	486	8	=	=	PUNCT
ejpam-3443	486	9	γ(g	γ(g	PROPN
ejpam-3443	486	10	)	)	PUNCT
ejpam-3443	486	11	.	.	PUNCT
ejpam-3443	487	1	suppose	suppose	VERB
ejpam-3443	487	2	that	that	SCONJ
ejpam-3443	487	3	s	s	VERB
ejpam-3443	487	4	is	be	AUX
ejpam-3443	487	5	a	a	DET
ejpam-3443	487	6	γmce	γmce	NOUN
ejpam-3443	487	7	-	-	PUNCT
ejpam-3443	487	8	set	set	NOUN
ejpam-3443	487	9	of	of	ADP
ejpam-3443	487	10	g.	g.	PROPN
ejpam-3443	487	11	by	by	ADP
ejpam-3443	487	12	theorem	theorem	NOUN
ejpam-3443	487	13	10	10	NUM
ejpam-3443	487	14	,	,	PUNCT
ejpam-3443	487	15	c	c	X
ejpam-3443	487	16	=	=	SYM
ejpam-3443	487	17	s	s	PROPN
ejpam-3443	487	18	×	×	NOUN
ejpam-3443	487	19	{	{	PUNCT
ejpam-3443	487	20	v	v	NOUN
ejpam-3443	487	21	}	}	PUNCT
ejpam-3443	487	22	is	be	AUX
ejpam-3443	487	23	a	a	DET
ejpam-3443	487	24	cost	cost	NOUN
ejpam-3443	487	25	effective	effective	ADJ
ejpam-3443	487	26	dominating	dominating	NOUN
ejpam-3443	487	27	set	set	NOUN
ejpam-3443	487	28	of	of	ADP
ejpam-3443	487	29	g[kp	g[kp	PROPN
ejpam-3443	487	30	]	]	PUNCT
ejpam-3443	487	31	.	.	PUNCT
ejpam-3443	488	1	let	let	VERB
ejpam-3443	488	2	(	(	PUNCT
ejpam-3443	488	3	u	u	NOUN
ejpam-3443	488	4	,	,	PUNCT
ejpam-3443	488	5	v	v	NOUN
ejpam-3443	488	6	)	)	PUNCT
ejpam-3443	488	7	∈	∈	PROPN
ejpam-3443	488	8	c	c	NOUN
ejpam-3443	488	9	,	,	PUNCT
ejpam-3443	488	10	and	and	CCONJ
ejpam-3443	488	11	put	put	VERB
ejpam-3443	488	12	c∗	c∗	NOUN
ejpam-3443	488	13	=	=	PUNCT
ejpam-3443	488	14	c	c	NOUN
ejpam-3443	488	15	\	\	X
ejpam-3443	488	16	{	{	PUNCT
ejpam-3443	488	17	(	(	PUNCT
ejpam-3443	488	18	u	u	NOUN
ejpam-3443	488	19	,	,	PUNCT
ejpam-3443	488	20	v	v	NOUN
ejpam-3443	488	21	)	)	PUNCT
ejpam-3443	488	22	}	}	PUNCT
ejpam-3443	488	23	.	.	PUNCT
ejpam-3443	489	1	then	then	ADV
ejpam-3443	489	2	c∗	c∗	PROPN
ejpam-3443	489	3	=	=	SYM
ejpam-3443	489	4	s∗×{v	s∗×{v	PROPN
ejpam-3443	489	5	}	}	PUNCT
ejpam-3443	489	6	,	,	PUNCT
ejpam-3443	489	7	where	where	SCONJ
ejpam-3443	489	8	s∗	s∗	PROPN
ejpam-3443	489	9	=	=	SYM
ejpam-3443	489	10	s	s	PART
ejpam-3443	489	11	\	\	X
ejpam-3443	489	12	{	{	PUNCT
ejpam-3443	489	13	u	u	NOUN
ejpam-3443	489	14	}	}	PUNCT
ejpam-3443	489	15	.	.	PUNCT
ejpam-3443	490	1	let	let	AUX
ejpam-3443	490	2	w	w	NOUN
ejpam-3443	490	3	∈	∈	PROPN
ejpam-3443	490	4	s∗.	s∗.	ADJ
ejpam-3443	490	5	if	if	SCONJ
ejpam-3443	490	6	u	u	PROPN
ejpam-3443	490	7	/∈	/∈	PUNCT
ejpam-3443	490	8	ng(w	ng(w	NOUN
ejpam-3443	490	9	)	)	PUNCT
ejpam-3443	490	10	,	,	PUNCT
ejpam-3443	490	11	then	then	ADV
ejpam-3443	490	12	|ng(w	|ng(w	X
ejpam-3443	490	13	)	)	PUNCT
ejpam-3443	490	14	∩	∩	NOUN
ejpam-3443	490	15	s∗|	s∗|	PROPN
ejpam-3443	490	16	=	=	SYM
ejpam-3443	490	17	|ng(w	|ng(w	NOUN
ejpam-3443	490	18	)	)	PUNCT
ejpam-3443	490	19	∩	∩	NOUN
ejpam-3443	490	20	s|	s|	VERB
ejpam-3443	490	21	≤	≤	NUM
ejpam-3443	490	22	|ng(w	|ng(w	X
ejpam-3443	490	23	)	)	PUNCT
ejpam-3443	490	24	\	\	NOUN
ejpam-3443	490	25	s|	s|	NOUN
ejpam-3443	490	26	=	=	SYM
ejpam-3443	490	27	|ng(w	|ng(w	X
ejpam-3443	490	28	)	)	PUNCT
ejpam-3443	490	29	\	\	NOUN
ejpam-3443	490	30	s∗|	s∗|	PROPN
ejpam-3443	490	31	.	.	PUNCT
ejpam-3443	491	1	if	if	SCONJ
ejpam-3443	491	2	u	u	PROPN
ejpam-3443	491	3	∈	∈	PROPN
ejpam-3443	491	4	ng(w	ng(w	NOUN
ejpam-3443	491	5	)	)	PUNCT
ejpam-3443	491	6	,	,	PUNCT
ejpam-3443	491	7	then	then	ADV
ejpam-3443	491	8	|ng(w	|ng(w	X
ejpam-3443	491	9	)	)	PUNCT
ejpam-3443	491	10	∩	∩	NOUN
ejpam-3443	491	11	s∗|	s∗|	PROPN
ejpam-3443	491	12	=	=	SYM
ejpam-3443	491	13	|ng(w	|ng(w	NOUN
ejpam-3443	491	14	)	)	PUNCT
ejpam-3443	491	15	∩	∩	NOUN
ejpam-3443	491	16	s|	s|	VERB
ejpam-3443	491	17	−	−	PROPN
ejpam-3443	491	18	1	1	NUM
ejpam-3443	491	19	<	<	X
ejpam-3443	491	20	|ng(w	|ng(w	NOUN
ejpam-3443	491	21	)	)	PUNCT
ejpam-3443	491	22	\	\	NOUN
ejpam-3443	492	1	s|+	s|+	NOUN
ejpam-3443	492	2	1	1	NUM
ejpam-3443	492	3	=	=	SYM
ejpam-3443	492	4	|ng(w	|ng(w	NOUN
ejpam-3443	492	5	)	)	PUNCT
ejpam-3443	492	6	\	\	NOUN
ejpam-3443	492	7	s∗|	s∗|	PROPN
ejpam-3443	492	8	.	.	PUNCT
ejpam-3443	492	9	f.jamil	f.jamil	PROPN
ejpam-3443	492	10	,	,	PUNCT
ejpam-3443	492	11	h.	h.	PROPN
ejpam-3443	492	12	nuenay	nuenay	PROPN
ejpam-3443	492	13	-	-	PUNCT
ejpam-3443	492	14	maglanque	maglanque	ADJ
ejpam-3443	492	15	/	/	SYM
ejpam-3443	492	16	eur	eur	NOUN
ejpam-3443	492	17	.	.	PUNCT
ejpam-3443	493	1	j.	j.	PROPN
ejpam-3443	493	2	pure	pure	PROPN
ejpam-3443	493	3	appl	appl	PROPN
ejpam-3443	493	4	.	.	PROPN
ejpam-3443	493	5	math	math	PROPN
ejpam-3443	493	6	,	,	PUNCT
ejpam-3443	493	7	12	12	NUM
ejpam-3443	493	8	(	(	PUNCT
ejpam-3443	493	9	3	3	NUM
ejpam-3443	493	10	)	)	PUNCT
ejpam-3443	493	11	(	(	PUNCT
ejpam-3443	493	12	2019	2019	NUM
ejpam-3443	493	13	)	)	PUNCT
ejpam-3443	493	14	,	,	PUNCT
ejpam-3443	493	15	978	978	NUM
ejpam-3443	493	16	-	-	SYM
ejpam-3443	493	17	998	998	NUM
ejpam-3443	493	18	996	996	NUM
ejpam-3443	493	19	that	that	PRON
ejpam-3443	493	20	is	be	AUX
ejpam-3443	493	21	,	,	PUNCT
ejpam-3443	493	22	s∗	s∗	PROPN
ejpam-3443	493	23	is	be	AUX
ejpam-3443	493	24	a	a	DET
ejpam-3443	493	25	cost	cost	NOUN
ejpam-3443	493	26	effective	effective	ADJ
ejpam-3443	493	27	set	set	NOUN
ejpam-3443	493	28	of	of	ADP
ejpam-3443	493	29	g.	g.	PROPN
ejpam-3443	493	30	since	since	SCONJ
ejpam-3443	493	31	s	s	PROPN
ejpam-3443	493	32	is	be	AUX
ejpam-3443	493	33	a	a	DET
ejpam-3443	493	34	minimal	minimal	ADJ
ejpam-3443	493	35	cost	cost	NOUN
ejpam-3443	493	36	effective	effective	ADJ
ejpam-3443	493	37	dominating	dominating	NOUN
ejpam-3443	493	38	set	set	NOUN
ejpam-3443	493	39	of	of	ADP
ejpam-3443	493	40	g	g	NOUN
ejpam-3443	493	41	,	,	PUNCT
ejpam-3443	493	42	s∗	s∗	PROPN
ejpam-3443	493	43	is	be	AUX
ejpam-3443	493	44	not	not	PART
ejpam-3443	493	45	a	a	DET
ejpam-3443	493	46	dominating	dominating	NOUN
ejpam-3443	493	47	set	set	NOUN
ejpam-3443	493	48	of	of	ADP
ejpam-3443	493	49	g.	g.	PROPN
ejpam-3443	493	50	by	by	ADP
ejpam-3443	493	51	theorem	theorem	VERB
ejpam-3443	493	52	7	7	NUM
ejpam-3443	493	53	,	,	PUNCT
ejpam-3443	493	54	c∗	c∗	NOUN
ejpam-3443	493	55	is	be	AUX
ejpam-3443	493	56	not	not	PART
ejpam-3443	493	57	a	a	DET
ejpam-3443	493	58	dominating	dominating	NOUN
ejpam-3443	493	59	set	set	NOUN
ejpam-3443	493	60	,	,	PUNCT
ejpam-3443	493	61	hence	hence	ADV
ejpam-3443	493	62	not	not	PART
ejpam-3443	493	63	a	a	DET
ejpam-3443	493	64	cost	cost	NOUN
ejpam-3443	493	65	effective	effective	ADJ
ejpam-3443	493	66	dominating	dominating	NOUN
ejpam-3443	493	67	set	set	NOUN
ejpam-3443	493	68	,	,	PUNCT
ejpam-3443	493	69	of	of	ADP
ejpam-3443	493	70	g[kp	g[kp	NOUN
ejpam-3443	493	71	]	]	PUNCT
ejpam-3443	493	72	.	.	PUNCT
ejpam-3443	494	1	this	this	PRON
ejpam-3443	494	2	shows	show	VERB
ejpam-3443	494	3	that	that	SCONJ
ejpam-3443	494	4	c	c	PROPN
ejpam-3443	494	5	is	be	AUX
ejpam-3443	494	6	a	a	DET
ejpam-3443	494	7	minimal	minimal	ADJ
ejpam-3443	494	8	cost	cost	NOUN
ejpam-3443	494	9	effective	effective	ADJ
ejpam-3443	494	10	dominating	dominating	NOUN
ejpam-3443	494	11	set	set	NOUN
ejpam-3443	494	12	of	of	ADP
ejpam-3443	494	13	g	g	PROPN
ejpam-3443	494	14	◦	◦	NOUN
ejpam-3443	494	15	h.	h.	PROPN
ejpam-3443	494	16	thus	thus	ADV
ejpam-3443	494	17	,	,	PUNCT
ejpam-3443	494	18	γmce(g[kp	γmce(g[kp	NUM
ejpam-3443	494	19	]	]	PUNCT
ejpam-3443	494	20	)	)	PUNCT
ejpam-3443	494	21	≥	≥	PROPN
ejpam-3443	494	22	|c|	|c|	PROPN
ejpam-3443	494	23	=	=	SYM
ejpam-3443	494	24	|s|	|s|	PROPN
ejpam-3443	494	25	=	=	PUNCT
ejpam-3443	494	26	γmce(g	γmce(g	PROPN
ejpam-3443	494	27	)	)	PUNCT
ejpam-3443	494	28	.	.	PUNCT
ejpam-3443	495	1	conversely	conversely	ADV
ejpam-3443	495	2	,	,	PUNCT
ejpam-3443	495	3	suppose	suppose	VERB
ejpam-3443	495	4	that	that	SCONJ
ejpam-3443	495	5	c	c	AUX
ejpam-3443	495	6	=	=	SYM
ejpam-3443	495	7	∪u∈s	∪u∈s	X
ejpam-3443	495	8	(	(	PUNCT
ejpam-3443	495	9	{	{	PUNCT
ejpam-3443	495	10	u	u	NOUN
ejpam-3443	495	11	}	}	PUNCT
ejpam-3443	495	12	×	×	PROPN
ejpam-3443	495	13	tu	tu	PROPN
ejpam-3443	495	14	)	)	PUNCT
ejpam-3443	495	15	⊆	⊆	NUM
ejpam-3443	495	16	v	v	NOUN
ejpam-3443	495	17	(	(	PUNCT
ejpam-3443	495	18	g[kp	g[kp	NOUN
ejpam-3443	495	19	]	]	PUNCT
ejpam-3443	495	20	)	)	PUNCT
ejpam-3443	495	21	is	be	AUX
ejpam-3443	495	22	a	a	DET
ejpam-3443	495	23	minimal	minimal	ADJ
ejpam-3443	495	24	cost	cost	NOUN
ejpam-3443	495	25	effective	effective	ADJ
ejpam-3443	495	26	dominating	dominating	NOUN
ejpam-3443	495	27	set	set	NOUN
ejpam-3443	495	28	of	of	ADP
ejpam-3443	495	29	g[kp	g[kp	PROPN
ejpam-3443	495	30	]	]	PUNCT
ejpam-3443	495	31	.	.	PUNCT
ejpam-3443	496	1	we	we	PRON
ejpam-3443	496	2	claim	claim	VERB
ejpam-3443	496	3	that	that	SCONJ
ejpam-3443	496	4	|tu|	|tu|	NOUN
ejpam-3443	496	5	=	=	SYM
ejpam-3443	496	6	1	1	NUM
ejpam-3443	496	7	for	for	ADP
ejpam-3443	496	8	each	each	DET
ejpam-3443	496	9	u	u	PROPN
ejpam-3443	496	10	∈	∈	PROPN
ejpam-3443	496	11	s.	s.	PROPN
ejpam-3443	496	12	suppose	suppose	VERB
ejpam-3443	496	13	that	that	SCONJ
ejpam-3443	496	14	|tu|	|tu|	PROPN
ejpam-3443	496	15	≥	≥	NOUN
ejpam-3443	496	16	2	2	NUM
ejpam-3443	496	17	for	for	ADP
ejpam-3443	496	18	some	some	DET
ejpam-3443	496	19	u	u	NOUN
ejpam-3443	496	20	∈	∈	PROPN
ejpam-3443	496	21	s.	s.	PROPN
ejpam-3443	496	22	let	let	VERB
ejpam-3443	496	23	c∗	c∗	PROPN
ejpam-3443	496	24	=	=	PUNCT
ejpam-3443	496	25	c	c	NOUN
ejpam-3443	496	26	\	\	X
ejpam-3443	496	27	{	{	PUNCT
ejpam-3443	496	28	(	(	PUNCT
ejpam-3443	496	29	u	u	NOUN
ejpam-3443	496	30	,	,	PUNCT
ejpam-3443	496	31	x	x	NOUN
ejpam-3443	496	32	)	)	PUNCT
ejpam-3443	496	33	}	}	PUNCT
ejpam-3443	496	34	,	,	PUNCT
ejpam-3443	496	35	where	where	SCONJ
ejpam-3443	496	36	x	x	PUNCT
ejpam-3443	496	37	∈	∈	PROPN
ejpam-3443	496	38	tu	tu	PROPN
ejpam-3443	496	39	,	,	PUNCT
ejpam-3443	496	40	and	and	CCONJ
ejpam-3443	496	41	let	let	VERB
ejpam-3443	496	42	v	v	X
ejpam-3443	496	43	∈	∈	PROPN
ejpam-3443	496	44	tu	tu	X
ejpam-3443	496	45	\	\	PROPN
ejpam-3443	496	46	{	{	PUNCT
ejpam-3443	496	47	x	x	NOUN
ejpam-3443	496	48	}	}	PUNCT
ejpam-3443	496	49	.	.	PUNCT
ejpam-3443	497	1	since	since	SCONJ
ejpam-3443	497	2	the	the	DET
ejpam-3443	497	3	g	g	NOUN
ejpam-3443	497	4	-	-	PUNCT
ejpam-3443	497	5	projection	projection	NOUN
ejpam-3443	497	6	c∗g	c∗g	PUNCT
ejpam-3443	497	7	=	=	SYM
ejpam-3443	497	8	s	s	PROPN
ejpam-3443	497	9	and	and	CCONJ
ejpam-3443	497	10	every	every	DET
ejpam-3443	497	11	subset	subset	NOUN
ejpam-3443	497	12	of	of	ADP
ejpam-3443	497	13	v	v	PROPN
ejpam-3443	497	14	(	(	PUNCT
ejpam-3443	497	15	kp	kp	PROPN
ejpam-3443	497	16	)	)	PUNCT
ejpam-3443	497	17	is	be	AUX
ejpam-3443	497	18	dominating	dominate	VERB
ejpam-3443	497	19	of	of	ADP
ejpam-3443	497	20	kp	kp	PROPN
ejpam-3443	497	21	,	,	PUNCT
ejpam-3443	497	22	c	c	PROPN
ejpam-3443	497	23	∗	∗	NOUN
ejpam-3443	497	24	is	be	AUX
ejpam-3443	497	25	dominating	dominate	VERB
ejpam-3443	497	26	of	of	ADP
ejpam-3443	497	27	g[kp	g[kp	PROPN
ejpam-3443	497	28	]	]	PUNCT
ejpam-3443	497	29	by	by	ADP
ejpam-3443	497	30	theorem	theorem	NOUN
ejpam-3443	497	31	7	7	NUM
ejpam-3443	497	32	.	.	PUNCT
ejpam-3443	498	1	in	in	ADP
ejpam-3443	498	2	view	view	NOUN
ejpam-3443	498	3	of	of	ADP
ejpam-3443	498	4	equations	equation	NOUN
ejpam-3443	498	5	(	(	PUNCT
ejpam-3443	498	6	1	1	NUM
ejpam-3443	498	7	)	)	PUNCT
ejpam-3443	498	8	and	and	CCONJ
ejpam-3443	498	9	(	(	PUNCT
ejpam-3443	498	10	2	2	NUM
ejpam-3443	498	11	)	)	PUNCT
ejpam-3443	498	12	,	,	PUNCT
ejpam-3443	498	13	|ng[kp]((u	|ng[kp]((u	NOUN
ejpam-3443	498	14	,	,	PUNCT
ejpam-3443	498	15	v	v	NOUN
ejpam-3443	498	16	)	)	PUNCT
ejpam-3443	498	17	)	)	PUNCT
ejpam-3443	498	18	∩	∩	NOUN
ejpam-3443	498	19	c∗|	c∗|	PROPN
ejpam-3443	498	20	≤	≤	NUM
ejpam-3443	498	21	|ng[kp]((u	|ng[kp]((u	NOUN
ejpam-3443	498	22	,	,	PUNCT
ejpam-3443	498	23	v	v	NOUN
ejpam-3443	498	24	)	)	PUNCT
ejpam-3443	498	25	)	)	PUNCT
ejpam-3443	498	26	∩	∩	PROPN
ejpam-3443	498	27	c|	c|	PROPN
ejpam-3443	498	28	,	,	PUNCT
ejpam-3443	498	29	and	and	CCONJ
ejpam-3443	498	30	|ng[kp]((u	|ng[kp]((u	NOUN
ejpam-3443	498	31	,	,	PUNCT
ejpam-3443	498	32	v	v	NOUN
ejpam-3443	498	33	)	)	PUNCT
ejpam-3443	498	34	)	)	PUNCT
ejpam-3443	498	35	\	\	PROPN
ejpam-3443	498	36	c∗|	c∗|	PROPN
ejpam-3443	498	37	≥	≥	NOUN
ejpam-3443	498	38	|ng[kp]((u	|ng[kp]((u	NOUN
ejpam-3443	498	39	,	,	PUNCT
ejpam-3443	498	40	v	v	NOUN
ejpam-3443	498	41	)	)	PUNCT
ejpam-3443	498	42	)	)	PUNCT
ejpam-3443	498	43	\	\	PROPN
ejpam-3443	499	1	c|	c|	PROPN
ejpam-3443	499	2	.	.	PUNCT
ejpam-3443	500	1	thus	thus	ADV
ejpam-3443	500	2	,	,	PUNCT
ejpam-3443	500	3	c∗	c∗	PROPN
ejpam-3443	500	4	is	be	AUX
ejpam-3443	500	5	a	a	DET
ejpam-3443	500	6	cost	cost	NOUN
ejpam-3443	500	7	effective	effective	ADJ
ejpam-3443	500	8	set	set	NOUN
ejpam-3443	500	9	of	of	ADP
ejpam-3443	500	10	g[kp	g[kp	PROPN
ejpam-3443	500	11	]	]	PUNCT
ejpam-3443	500	12	.	.	PUNCT
ejpam-3443	501	1	consequently	consequently	ADV
ejpam-3443	501	2	,	,	PUNCT
ejpam-3443	501	3	c∗	c∗	PROPN
ejpam-3443	501	4	is	be	AUX
ejpam-3443	501	5	a	a	DET
ejpam-3443	501	6	cost	cost	NOUN
ejpam-3443	501	7	effective	effective	ADJ
ejpam-3443	501	8	dominating	dominating	NOUN
ejpam-3443	501	9	set	set	NOUN
ejpam-3443	501	10	of	of	ADP
ejpam-3443	501	11	g[kp	g[kp	PROPN
ejpam-3443	501	12	]	]	PROPN
ejpam-3443	501	13	,	,	PUNCT
ejpam-3443	501	14	a	a	DET
ejpam-3443	501	15	contradiction	contradiction	NOUN
ejpam-3443	501	16	.	.	PUNCT
ejpam-3443	502	1	thus	thus	ADV
ejpam-3443	502	2	|tu|	|tu|	ADJ
ejpam-3443	502	3	=	=	SYM
ejpam-3443	502	4	1	1	NUM
ejpam-3443	502	5	for	for	ADP
ejpam-3443	502	6	all	all	PRON
ejpam-3443	502	7	u	u	PROPN
ejpam-3443	502	8	∈	∈	PROPN
ejpam-3443	502	9	s.	s.	PROPN
ejpam-3443	502	10	in	in	ADP
ejpam-3443	502	11	view	view	NOUN
ejpam-3443	502	12	of	of	ADP
ejpam-3443	502	13	the	the	DET
ejpam-3443	502	14	proof	proof	NOUN
ejpam-3443	502	15	of	of	ADP
ejpam-3443	502	16	the	the	DET
ejpam-3443	502	17	necessity	necessity	NOUN
ejpam-3443	502	18	part	part	NOUN
ejpam-3443	502	19	of	of	ADP
ejpam-3443	502	20	the	the	DET
ejpam-3443	502	21	statement	statement	NOUN
ejpam-3443	502	22	,	,	PUNCT
ejpam-3443	502	23	we	we	PRON
ejpam-3443	502	24	may	may	AUX
ejpam-3443	502	25	assume	assume	VERB
ejpam-3443	502	26	that	that	SCONJ
ejpam-3443	502	27	for	for	ADP
ejpam-3443	502	28	some	some	DET
ejpam-3443	502	29	v	v	ADP
ejpam-3443	502	30	∈	∈	PROPN
ejpam-3443	502	31	v	v	NOUN
ejpam-3443	502	32	(	(	PUNCT
ejpam-3443	502	33	kp	kp	PROPN
ejpam-3443	502	34	)	)	PUNCT
ejpam-3443	502	35	,	,	PUNCT
ejpam-3443	502	36	tu	tu	PROPN
ejpam-3443	502	37	=	=	PUNCT
ejpam-3443	502	38	{	{	PUNCT
ejpam-3443	502	39	v	v	NOUN
ejpam-3443	502	40	}	}	PUNCT
ejpam-3443	502	41	for	for	ADP
ejpam-3443	502	42	all	all	DET
ejpam-3443	502	43	u	u	PROPN
ejpam-3443	502	44	∈	∈	PROPN
ejpam-3443	502	45	s.	s.	PROPN
ejpam-3443	502	46	clearly	clearly	ADV
ejpam-3443	502	47	,	,	PUNCT
ejpam-3443	502	48	the	the	DET
ejpam-3443	502	49	minimality	minimality	NOUN
ejpam-3443	502	50	of	of	ADP
ejpam-3443	502	51	c	c	PROPN
ejpam-3443	502	52	implies	imply	VERB
ejpam-3443	502	53	that	that	SCONJ
ejpam-3443	502	54	s	s	VERB
ejpam-3443	502	55	is	be	AUX
ejpam-3443	502	56	a	a	DET
ejpam-3443	502	57	minimal	minimal	ADJ
ejpam-3443	502	58	cost	cost	NOUN
ejpam-3443	502	59	effective	effective	ADJ
ejpam-3443	502	60	dominating	dominating	NOUN
ejpam-3443	502	61	set	set	NOUN
ejpam-3443	502	62	of	of	ADP
ejpam-3443	502	63	g.	g.	PROPN
ejpam-3443	502	64	thus	thus	ADV
ejpam-3443	502	65	,	,	PUNCT
ejpam-3443	502	66	γmce(g	γmce(g	PROPN
ejpam-3443	502	67	)	)	PUNCT
ejpam-3443	502	68	≥	≥	NOUN
ejpam-3443	502	69	|s|	|s|	NOUN
ejpam-3443	502	70	=	=	SYM
ejpam-3443	502	71	|c|	|c|	PROPN
ejpam-3443	502	72	.	.	PUNCT
ejpam-3443	503	1	since	since	SCONJ
ejpam-3443	503	2	c	c	PROPN
ejpam-3443	503	3	is	be	AUX
ejpam-3443	503	4	arbitrary	arbitrary	ADJ
ejpam-3443	503	5	,	,	PUNCT
ejpam-3443	503	6	γmce(g	γmce(g	PROPN
ejpam-3443	503	7	)	)	PUNCT
ejpam-3443	503	8	≥	≥	NOUN
ejpam-3443	503	9	γmce(g[kp	γmce(g[kp	NUM
ejpam-3443	503	10	]	]	PUNCT
ejpam-3443	503	11	)	)	PUNCT
ejpam-3443	503	12	.	.	PUNCT
ejpam-3443	504	1	now	now	ADV
ejpam-3443	504	2	,	,	PUNCT
ejpam-3443	504	3	let	let	VERB
ejpam-3443	504	4	s	s	PRON
ejpam-3443	504	5	⊆	⊆	NUM
ejpam-3443	504	6	v	v	NOUN
ejpam-3443	504	7	(	(	PUNCT
ejpam-3443	504	8	g	g	NOUN
ejpam-3443	504	9	)	)	PUNCT
ejpam-3443	504	10	be	be	AUX
ejpam-3443	504	11	a	a	DET
ejpam-3443	504	12	γ+ce	γ+ce	NOUN
ejpam-3443	504	13	-	-	PUNCT
ejpam-3443	504	14	set	set	NOUN
ejpam-3443	504	15	of	of	ADP
ejpam-3443	504	16	g.	g.	PROPN
ejpam-3443	504	17	for	for	ADP
ejpam-3443	504	18	each	each	DET
ejpam-3443	504	19	u	u	PROPN
ejpam-3443	504	20	∈	∈	PROPN
ejpam-3443	504	21	s	s	PART
ejpam-3443	504	22	∩	∩	NOUN
ejpam-3443	504	23	ng(s	ng(s	NUM
ejpam-3443	504	24	)	)	PUNCT
ejpam-3443	504	25	,	,	PUNCT
ejpam-3443	504	26	let	let	VERB
ejpam-3443	504	27	tu	tu	PROPN
ejpam-3443	504	28	⊆	⊆	NUM
ejpam-3443	504	29	v	v	X
ejpam-3443	504	30	(	(	PUNCT
ejpam-3443	504	31	kp	kp	INTJ
ejpam-3443	504	32	)	)	PUNCT
ejpam-3443	504	33	be	be	AUX
ejpam-3443	504	34	a	a	DET
ejpam-3443	504	35	γ+ce	γ+ce	NOUN
ejpam-3443	504	36	-	-	PUNCT
ejpam-3443	504	37	set	set	NOUN
ejpam-3443	504	38	of	of	ADP
ejpam-3443	504	39	kp	kp	NOUN
ejpam-3443	504	40	,	,	PUNCT
ejpam-3443	504	41	and	and	CCONJ
ejpam-3443	504	42	for	for	ADP
ejpam-3443	504	43	each	each	DET
ejpam-3443	504	44	u	u	NOUN
ejpam-3443	504	45	∈	∈	PROPN
ejpam-3443	504	46	s	s	PART
ejpam-3443	504	47	\	\	NOUN
ejpam-3443	504	48	ng(s	ng(s	NUM
ejpam-3443	504	49	)	)	PUNCT
ejpam-3443	504	50	,	,	PUNCT
ejpam-3443	504	51	let	let	VERB
ejpam-3443	504	52	tu	tu	PROPN
ejpam-3443	504	53	=	=	SYM
ejpam-3443	504	54	v	v	PROPN
ejpam-3443	504	55	(	(	PUNCT
ejpam-3443	504	56	kp	kp	PROPN
ejpam-3443	504	57	)	)	PUNCT
ejpam-3443	504	58	.	.	PUNCT
ejpam-3443	505	1	by	by	ADP
ejpam-3443	505	2	theorem	theorem	NOUN
ejpam-3443	505	3	10	10	NUM
ejpam-3443	505	4	,	,	PUNCT
ejpam-3443	505	5	c	c	NOUN
ejpam-3443	505	6	=	=	SYM
ejpam-3443	505	7	∪u∈s	∪u∈s	X
ejpam-3443	505	8	(	(	PUNCT
ejpam-3443	505	9	{	{	PUNCT
ejpam-3443	505	10	u	u	NOUN
ejpam-3443	505	11	}	}	PUNCT
ejpam-3443	505	12	×	×	PROPN
ejpam-3443	505	13	tu	tu	PROPN
ejpam-3443	505	14	)	)	PUNCT
ejpam-3443	505	15	is	be	AUX
ejpam-3443	505	16	a	a	DET
ejpam-3443	505	17	cost	cost	NOUN
ejpam-3443	505	18	effective	effective	ADJ
ejpam-3443	505	19	dominating	dominating	NOUN
ejpam-3443	505	20	set	set	NOUN
ejpam-3443	505	21	of	of	ADP
ejpam-3443	505	22	g[h	g[h	NOUN
ejpam-3443	505	23	]	]	PUNCT
ejpam-3443	505	24	.	.	PUNCT
ejpam-3443	506	1	thus	thus	ADV
ejpam-3443	506	2	,	,	PUNCT
ejpam-3443	506	3	γ+ce(g[km	γ+ce(g[km	NOUN
ejpam-3443	506	4	]	]	PUNCT
ejpam-3443	506	5	)	)	PUNCT
ejpam-3443	506	6	≥	≥	PROPN
ejpam-3443	507	1	|c|	|c|	PROPN
ejpam-3443	507	2	=	=	SYM
ejpam-3443	507	3	|s	|s	PROPN
ejpam-3443	507	4	◦	◦	NOUN
ejpam-3443	507	5	|γ+ce(kp	|γ+ce(kp	NOUN
ejpam-3443	507	6	)	)	PUNCT
ejpam-3443	508	1	+	+	CCONJ
ejpam-3443	509	1	(	(	PUNCT
ejpam-3443	509	2	|s|	|s|	NOUN
ejpam-3443	509	3	−	−	PROPN
ejpam-3443	509	4	|s	|s	PROPN
ejpam-3443	509	5	◦	◦	NOUN
ejpam-3443	509	6	|	|	NOUN
ejpam-3443	509	7	)	)	PUNCT
ejpam-3443	509	8	|v	|v	PROPN
ejpam-3443	509	9	(	(	PUNCT
ejpam-3443	509	10	kp)|	kp)|	PROPN
ejpam-3443	509	11	.	.	PROPN
ejpam-3443	510	1	following	follow	VERB
ejpam-3443	510	2	a	a	DET
ejpam-3443	510	3	similar	similar	ADJ
ejpam-3443	510	4	proof	proof	NOUN
ejpam-3443	510	5	shows	show	VERB
ejpam-3443	510	6	that	that	SCONJ
ejpam-3443	510	7	if	if	SCONJ
ejpam-3443	510	8	g	g	PROPN
ejpam-3443	510	9	and	and	CCONJ
ejpam-3443	510	10	h	h	NOUN
ejpam-3443	510	11	are	be	AUX
ejpam-3443	510	12	nontrivial	nontrivial	ADJ
ejpam-3443	510	13	connected	connect	VERB
ejpam-3443	510	14	graphs	graph	NOUN
ejpam-3443	510	15	with	with	ADP
ejpam-3443	510	16	γ(h	γ(h	NOUN
ejpam-3443	510	17	)	)	PUNCT
ejpam-3443	510	18	=	=	SYM
ejpam-3443	510	19	1	1	NUM
ejpam-3443	510	20	,	,	PUNCT
ejpam-3443	510	21	γmce(g[h	γmce(g[h	NOUN
ejpam-3443	510	22	]	]	PUNCT
ejpam-3443	510	23	)	)	PUNCT
ejpam-3443	510	24	=	=	PUNCT
ejpam-3443	511	1	γce(g[h	γce(g[h	NUM
ejpam-3443	511	2	]	]	PUNCT
ejpam-3443	511	3	)	)	PUNCT
ejpam-3443	511	4	=	=	SYM
ejpam-3443	511	5	γ(g	γ(g	PROPN
ejpam-3443	511	6	)	)	PUNCT
ejpam-3443	511	7	.	.	PUNCT
ejpam-3443	512	1	theorem	theorem	NOUN
ejpam-3443	512	2	12	12	NUM
ejpam-3443	512	3	.	.	PUNCT
ejpam-3443	513	1	let	let	VERB
ejpam-3443	513	2	g	g	PRON
ejpam-3443	513	3	be	be	AUX
ejpam-3443	513	4	a	a	DET
ejpam-3443	513	5	noncomplete	noncomplete	ADJ
ejpam-3443	513	6	connected	connect	VERB
ejpam-3443	513	7	graph	graph	NOUN
ejpam-3443	513	8	and	and	CCONJ
ejpam-3443	513	9	p	p	PRON
ejpam-3443	513	10	≥	≥	NUM
ejpam-3443	513	11	3	3	NUM
ejpam-3443	513	12	.	.	PUNCT
ejpam-3443	514	1	then	then	ADV
ejpam-3443	514	2	(	(	PUNCT
ejpam-3443	514	3	i	i	NOUN
ejpam-3443	514	4	)	)	PUNCT
ejpam-3443	514	5	γce(kp[g	γce(kp[g	PROPN
ejpam-3443	514	6	]	]	X
ejpam-3443	514	7	)	)	PUNCT
ejpam-3443	514	8	=	=	PUNCT
ejpam-3443	514	9			PUNCT
ejpam-3443	514	10	1	1	NUM
ejpam-3443	514	11	,	,	PUNCT
ejpam-3443	514	12	if	if	SCONJ
ejpam-3443	514	13	γ(g	γ(g	PROPN
ejpam-3443	514	14	)	)	PUNCT
ejpam-3443	514	15	=	=	SYM
ejpam-3443	514	16	1	1	NUM
ejpam-3443	514	17	2	2	NUM
ejpam-3443	514	18	,	,	PUNCT
ejpam-3443	514	19	otherwise	otherwise	ADV
ejpam-3443	514	20	.	.	PUNCT
ejpam-3443	515	1	(	(	PUNCT
ejpam-3443	515	2	ii	ii	X
ejpam-3443	515	3	)	)	PUNCT
ejpam-3443	515	4	γmce(kp[g	γmce(kp[g	PROPN
ejpam-3443	515	5	]	]	X
ejpam-3443	515	6	)	)	PUNCT
ejpam-3443	515	7	=	=	SYM
ejpam-3443	515	8	γm(g	γm(g	NOUN
ejpam-3443	515	9	)	)	PUNCT
ejpam-3443	515	10	;	;	PUNCT
ejpam-3443	515	11	and	and	CCONJ
ejpam-3443	515	12	(	(	PUNCT
ejpam-3443	515	13	iii	iii	X
ejpam-3443	515	14	)	)	PUNCT
ejpam-3443	515	15	γ+ce(kp[g	γ+ce(kp[g	NOUN
ejpam-3443	515	16	]	]	X
ejpam-3443	515	17	)	)	PUNCT
ejpam-3443	515	18	=	=	PUNCT
ejpam-3443	516	1	⌊	⌊	VERB
ejpam-3443	516	2	p+1	p+1	NOUN
ejpam-3443	516	3	2	2	NUM
ejpam-3443	516	4	⌋	⌋	NOUN
ejpam-3443	516	5	|v	|v	NOUN
ejpam-3443	516	6	(	(	PUNCT
ejpam-3443	516	7	g)|	g)|	NOUN
ejpam-3443	516	8	.	.	PUNCT
ejpam-3443	517	1	proof	proof	NOUN
ejpam-3443	517	2	.	.	PUNCT
ejpam-3443	518	1	let	let	VERB
ejpam-3443	518	2	x	x	PRON
ejpam-3443	518	3	,	,	PUNCT
ejpam-3443	518	4	y	y	PROPN
ejpam-3443	518	5	∈	∈	PROPN
ejpam-3443	518	6	v	v	PROPN
ejpam-3443	518	7	(	(	PUNCT
ejpam-3443	518	8	kp	kp	INTJ
ejpam-3443	518	9	)	)	PUNCT
ejpam-3443	518	10	be	be	AUX
ejpam-3443	518	11	distinct	distinct	ADJ
ejpam-3443	518	12	and	and	CCONJ
ejpam-3443	518	13	u	u	NOUN
ejpam-3443	518	14	∈	∈	PROPN
ejpam-3443	518	15	v	v	NOUN
ejpam-3443	518	16	(	(	PUNCT
ejpam-3443	518	17	g	g	NOUN
ejpam-3443	518	18	)	)	PUNCT
ejpam-3443	518	19	.	.	PUNCT
ejpam-3443	519	1	by	by	ADP
ejpam-3443	519	2	theorem	theorem	NOUN
ejpam-3443	519	3	10	10	NUM
ejpam-3443	519	4	,	,	PUNCT
ejpam-3443	519	5	c	c	NOUN
ejpam-3443	519	6	=	=	SYM
ejpam-3443	519	7	{	{	PUNCT
ejpam-3443	519	8	x	x	PROPN
ejpam-3443	519	9	,	,	PUNCT
ejpam-3443	519	10	y	y	PROPN
ejpam-3443	519	11	}	}	PUNCT
ejpam-3443	519	12	×	×	NOUN
ejpam-3443	519	13	{	{	PUNCT
ejpam-3443	519	14	v	v	NOUN
ejpam-3443	519	15	}	}	PUNCT
ejpam-3443	519	16	is	be	AUX
ejpam-3443	519	17	a	a	DET
ejpam-3443	519	18	cost	cost	NOUN
ejpam-3443	519	19	effective	effective	ADJ
ejpam-3443	519	20	dominating	dominating	NOUN
ejpam-3443	519	21	set	set	NOUN
ejpam-3443	519	22	of	of	ADP
ejpam-3443	519	23	kp[g	kp[g	NOUN
ejpam-3443	519	24	]	]	PUNCT
ejpam-3443	519	25	.	.	PUNCT
ejpam-3443	520	1	thus	thus	ADV
ejpam-3443	520	2	,	,	PUNCT
ejpam-3443	520	3	γce(kp[g	γce(kp[g	PROPN
ejpam-3443	520	4	]	]	X
ejpam-3443	520	5	)	)	PUNCT
ejpam-3443	520	6	≤	≤	NOUN
ejpam-3443	520	7	|c|	|c|	PROPN
ejpam-3443	520	8	=	=	SYM
ejpam-3443	520	9	2	2	X
ejpam-3443	520	10	.	.	PUNCT
ejpam-3443	520	11	f.jamil	f.jamil	PROPN
ejpam-3443	520	12	,	,	PUNCT
ejpam-3443	520	13	h.	h.	PROPN
ejpam-3443	520	14	nuenay	nuenay	PROPN
ejpam-3443	520	15	-	-	PUNCT
ejpam-3443	520	16	maglanque	maglanque	ADJ
ejpam-3443	520	17	/	/	SYM
ejpam-3443	520	18	eur	eur	NOUN
ejpam-3443	520	19	.	.	PUNCT
ejpam-3443	521	1	j.	j.	PROPN
ejpam-3443	521	2	pure	pure	PROPN
ejpam-3443	521	3	appl	appl	PROPN
ejpam-3443	521	4	.	.	PROPN
ejpam-3443	521	5	math	math	PROPN
ejpam-3443	521	6	,	,	PUNCT
ejpam-3443	521	7	12	12	NUM
ejpam-3443	521	8	(	(	PUNCT
ejpam-3443	521	9	3	3	NUM
ejpam-3443	521	10	)	)	PUNCT
ejpam-3443	521	11	(	(	PUNCT
ejpam-3443	521	12	2019	2019	NUM
ejpam-3443	521	13	)	)	PUNCT
ejpam-3443	521	14	,	,	PUNCT
ejpam-3443	521	15	978	978	NUM
ejpam-3443	521	16	-	-	SYM
ejpam-3443	521	17	998	998	NUM
ejpam-3443	521	18	997	997	NUM
ejpam-3443	521	19	also	also	ADV
ejpam-3443	521	20	,	,	PUNCT
ejpam-3443	521	21	by	by	ADP
ejpam-3443	521	22	theorem	theorem	NOUN
ejpam-3443	521	23	10	10	NUM
ejpam-3443	521	24	,	,	PUNCT
ejpam-3443	521	25	for	for	ADP
ejpam-3443	521	26	any	any	DET
ejpam-3443	521	27	x	x	SYM
ejpam-3443	521	28	∈	∈	PROPN
ejpam-3443	521	29	v	v	NOUN
ejpam-3443	521	30	(	(	PUNCT
ejpam-3443	521	31	kp	kp	PROPN
ejpam-3443	521	32	)	)	PUNCT
ejpam-3443	521	33	and	and	CCONJ
ejpam-3443	521	34	any	any	DET
ejpam-3443	521	35	dominating	dominating	NOUN
ejpam-3443	521	36	set	set	NOUN
ejpam-3443	521	37	s	s	PROPN
ejpam-3443	521	38	⊆	⊆	NUM
ejpam-3443	521	39	v	v	NOUN
ejpam-3443	521	40	(	(	PUNCT
ejpam-3443	521	41	g	g	NOUN
ejpam-3443	521	42	)	)	PUNCT
ejpam-3443	521	43	of	of	ADP
ejpam-3443	521	44	g	g	NOUN
ejpam-3443	521	45	,	,	PUNCT
ejpam-3443	521	46	c	c	NOUN
ejpam-3443	521	47	=	=	SYM
ejpam-3443	521	48	{	{	PUNCT
ejpam-3443	521	49	x}×s	x}×s	PROPN
ejpam-3443	521	50	is	be	AUX
ejpam-3443	521	51	a	a	DET
ejpam-3443	521	52	cost	cost	NOUN
ejpam-3443	521	53	effective	effective	ADJ
ejpam-3443	521	54	dominating	dominating	NOUN
ejpam-3443	521	55	set	set	NOUN
ejpam-3443	521	56	of	of	ADP
ejpam-3443	521	57	kp[g	kp[g	NOUN
ejpam-3443	521	58	]	]	PUNCT
ejpam-3443	521	59	.	.	PUNCT
ejpam-3443	522	1	thus	thus	ADV
ejpam-3443	522	2	,	,	PUNCT
ejpam-3443	522	3	γce(kp[g	γce(kp[g	NOUN
ejpam-3443	522	4	]	]	X
ejpam-3443	522	5	)	)	PUNCT
ejpam-3443	522	6	=	=	SYM
ejpam-3443	523	1	min{γ(g	min{γ(g	PROPN
ejpam-3443	523	2	)	)	PUNCT
ejpam-3443	523	3	,	,	PUNCT
ejpam-3443	523	4	2	2	NUM
ejpam-3443	523	5	}	}	PUNCT
ejpam-3443	523	6	,	,	PUNCT
ejpam-3443	523	7	and	and	CCONJ
ejpam-3443	523	8	the	the	DET
ejpam-3443	523	9	conclusion	conclusion	NOUN
ejpam-3443	523	10	follows	follow	VERB
ejpam-3443	523	11	.	.	PUNCT
ejpam-3443	524	1	to	to	PART
ejpam-3443	524	2	prove	prove	VERB
ejpam-3443	524	3	statement	statement	NOUN
ejpam-3443	524	4	(	(	PUNCT
ejpam-3443	524	5	ii	ii	NOUN
ejpam-3443	524	6	)	)	PUNCT
ejpam-3443	524	7	,	,	PUNCT
ejpam-3443	524	8	note	note	VERB
ejpam-3443	524	9	first	first	ADV
ejpam-3443	524	10	that	that	SCONJ
ejpam-3443	524	11	since	since	SCONJ
ejpam-3443	524	12	g	g	PROPN
ejpam-3443	524	13	is	be	AUX
ejpam-3443	524	14	not	not	PART
ejpam-3443	524	15	complete	complete	ADJ
ejpam-3443	524	16	,	,	PUNCT
ejpam-3443	524	17	γm(g	γm(g	NUM
ejpam-3443	524	18	)	)	PUNCT
ejpam-3443	524	19	≥	≥	NOUN
ejpam-3443	525	1	2	2	X
ejpam-3443	525	2	.	.	PUNCT
ejpam-3443	525	3	let	let	VERB
ejpam-3443	525	4	s	s	PRON
ejpam-3443	525	5	⊆	⊆	NUM
ejpam-3443	525	6	v	v	NOUN
ejpam-3443	525	7	(	(	PUNCT
ejpam-3443	525	8	g	g	NOUN
ejpam-3443	525	9	)	)	PUNCT
ejpam-3443	525	10	be	be	AUX
ejpam-3443	525	11	a	a	DET
ejpam-3443	525	12	minimal	minimal	ADJ
ejpam-3443	525	13	dominating	dominating	NOUN
ejpam-3443	525	14	set	set	NOUN
ejpam-3443	525	15	of	of	ADP
ejpam-3443	525	16	g	g	PROPN
ejpam-3443	525	17	and	and	CCONJ
ejpam-3443	525	18	x	x	SYM
ejpam-3443	525	19	∈	∈	PROPN
ejpam-3443	525	20	v	v	X
ejpam-3443	525	21	(	(	PUNCT
ejpam-3443	525	22	kp	kp	PROPN
ejpam-3443	525	23	)	)	PUNCT
ejpam-3443	525	24	.	.	PUNCT
ejpam-3443	526	1	in	in	ADP
ejpam-3443	526	2	view	view	NOUN
ejpam-3443	526	3	of	of	ADP
ejpam-3443	526	4	theorem	theorem	NOUN
ejpam-3443	526	5	7	7	NUM
ejpam-3443	526	6	,	,	PUNCT
ejpam-3443	526	7	c	c	NOUN
ejpam-3443	526	8	=	=	SYM
ejpam-3443	526	9	{	{	PUNCT
ejpam-3443	526	10	x	x	NOUN
ejpam-3443	526	11	}	}	PUNCT
ejpam-3443	526	12	×	×	NOUN
ejpam-3443	526	13	s	s	NOUN
ejpam-3443	526	14	is	be	AUX
ejpam-3443	526	15	a	a	DET
ejpam-3443	526	16	minimal	minimal	ADJ
ejpam-3443	526	17	cost	cost	NOUN
ejpam-3443	526	18	effective	effective	ADJ
ejpam-3443	526	19	dominating	dominating	NOUN
ejpam-3443	526	20	set	set	NOUN
ejpam-3443	526	21	of	of	ADP
ejpam-3443	526	22	kp[g	kp[g	NOUN
ejpam-3443	526	23	]	]	PUNCT
ejpam-3443	526	24	.	.	PUNCT
ejpam-3443	527	1	consequently	consequently	ADV
ejpam-3443	527	2	,	,	PUNCT
ejpam-3443	527	3	γmce(kp[g	γmce(kp[g	PROPN
ejpam-3443	527	4	]	]	X
ejpam-3443	527	5	)	)	PUNCT
ejpam-3443	527	6	≥	≥	PROPN
ejpam-3443	527	7	|c|	|c|	PROPN
ejpam-3443	527	8	=	=	SYM
ejpam-3443	527	9	|s|	|s|	PROPN
ejpam-3443	527	10	.	.	PUNCT
ejpam-3443	528	1	since	since	SCONJ
ejpam-3443	528	2	s	s	NOUN
ejpam-3443	528	3	is	be	AUX
ejpam-3443	528	4	arbitrary	arbitrary	ADJ
ejpam-3443	528	5	,	,	PUNCT
ejpam-3443	528	6	γmce(kp[g	γmce(kp[g	PROPN
ejpam-3443	528	7	]	]	X
ejpam-3443	528	8	)	)	PUNCT
ejpam-3443	528	9	≥	≥	NOUN
ejpam-3443	528	10	γm(g	γm(g	NUM
ejpam-3443	528	11	)	)	PUNCT
ejpam-3443	528	12	.	.	PUNCT
ejpam-3443	529	1	conversely	conversely	ADV
ejpam-3443	529	2	,	,	PUNCT
ejpam-3443	529	3	let	let	VERB
ejpam-3443	529	4	c	c	NOUN
ejpam-3443	529	5	=	=	SYM
ejpam-3443	529	6	∪u∈s	∪u∈s	X
ejpam-3443	529	7	(	(	PUNCT
ejpam-3443	529	8	{	{	PUNCT
ejpam-3443	529	9	u	u	NOUN
ejpam-3443	529	10	}	}	PUNCT
ejpam-3443	529	11	×	×	PROPN
ejpam-3443	529	12	tu	tu	PROPN
ejpam-3443	529	13	)	)	PUNCT
ejpam-3443	529	14	⊆	⊆	NUM
ejpam-3443	529	15	v	v	NOUN
ejpam-3443	529	16	(	(	PUNCT
ejpam-3443	529	17	kp[g	kp[g	NOUN
ejpam-3443	529	18	]	]	PUNCT
ejpam-3443	529	19	)	)	PUNCT
ejpam-3443	529	20	be	be	AUX
ejpam-3443	529	21	a	a	DET
ejpam-3443	529	22	γmce	γmce	NOUN
ejpam-3443	529	23	-	-	PUNCT
ejpam-3443	529	24	set	set	NOUN
ejpam-3443	529	25	of	of	ADP
ejpam-3443	529	26	kp[g	kp[g	NOUN
ejpam-3443	529	27	]	]	PUNCT
ejpam-3443	529	28	.	.	PUNCT
ejpam-3443	530	1	since	since	SCONJ
ejpam-3443	530	2	c	c	PROPN
ejpam-3443	530	3	is	be	AUX
ejpam-3443	530	4	a	a	DET
ejpam-3443	530	5	dominating	dominating	NOUN
ejpam-3443	530	6	set	set	NOUN
ejpam-3443	530	7	of	of	ADP
ejpam-3443	530	8	kp[g	kp[g	PROPN
ejpam-3443	530	9	]	]	PUNCT
ejpam-3443	530	10	,	,	PUNCT
ejpam-3443	530	11	either	either	CCONJ
ejpam-3443	530	12	s	s	PART
ejpam-3443	530	13	ia	ia	PROPN
ejpam-3443	530	14	total	total	ADJ
ejpam-3443	530	15	dominating	dominating	NOUN
ejpam-3443	530	16	set	set	NOUN
ejpam-3443	530	17	of	of	ADP
ejpam-3443	530	18	kp	kp	PROPN
ejpam-3443	530	19	or	or	CCONJ
ejpam-3443	530	20	s	s	PROPN
ejpam-3443	530	21	is	be	AUX
ejpam-3443	530	22	a	a	DET
ejpam-3443	530	23	dominating	dominating	NOUN
ejpam-3443	530	24	set	set	NOUN
ejpam-3443	530	25	of	of	ADP
ejpam-3443	530	26	kp	kp	NOUN
ejpam-3443	530	27	,	,	PUNCT
ejpam-3443	530	28	in	in	ADP
ejpam-3443	530	29	which	which	DET
ejpam-3443	530	30	case	case	NOUN
ejpam-3443	530	31	tu	tu	PROPN
ejpam-3443	530	32	is	be	AUX
ejpam-3443	530	33	a	a	DET
ejpam-3443	530	34	dominating	dominating	NOUN
ejpam-3443	530	35	set	set	NOUN
ejpam-3443	530	36	for	for	ADP
ejpam-3443	530	37	each	each	DET
ejpam-3443	530	38	u	u	NOUN
ejpam-3443	530	39	∈	∈	PROPN
ejpam-3443	530	40	s	s	PART
ejpam-3443	530	41	\	\	NOUN
ejpam-3443	530	42	nkp(s	nkp(s	PROPN
ejpam-3443	530	43	)	)	PUNCT
ejpam-3443	530	44	.	.	PUNCT
ejpam-3443	531	1	since	since	SCONJ
ejpam-3443	531	2	c	c	PROPN
ejpam-3443	531	3	is	be	AUX
ejpam-3443	531	4	minimal	minimal	ADJ
ejpam-3443	531	5	,	,	PUNCT
ejpam-3443	531	6	if	if	SCONJ
ejpam-3443	531	7	s	s	VERB
ejpam-3443	531	8	is	be	AUX
ejpam-3443	531	9	a	a	DET
ejpam-3443	531	10	total	total	ADJ
ejpam-3443	531	11	dominating	dominating	NOUN
ejpam-3443	531	12	set	set	NOUN
ejpam-3443	531	13	in	in	ADP
ejpam-3443	531	14	kp	kp	PROPN
ejpam-3443	531	15	,	,	PUNCT
ejpam-3443	531	16	then	then	ADV
ejpam-3443	531	17	c	c	X
ejpam-3443	531	18	=	=	PRON
ejpam-3443	531	19	{	{	PUNCT
ejpam-3443	531	20	(	(	PUNCT
ejpam-3443	531	21	x	x	NOUN
ejpam-3443	531	22	,	,	PUNCT
ejpam-3443	531	23	y	y	PROPN
ejpam-3443	531	24	)	)	PUNCT
ejpam-3443	531	25	,	,	PUNCT
ejpam-3443	531	26	(	(	PUNCT
ejpam-3443	531	27	u	u	NOUN
ejpam-3443	531	28	,	,	PUNCT
ejpam-3443	531	29	v	v	NOUN
ejpam-3443	531	30	)	)	PUNCT
ejpam-3443	531	31	}	}	PUNCT
ejpam-3443	531	32	for	for	ADP
ejpam-3443	531	33	some	some	DET
ejpam-3443	531	34	x	x	NOUN
ejpam-3443	531	35	,	,	PUNCT
ejpam-3443	531	36	u	u	PROPN
ejpam-3443	531	37	∈	∈	PROPN
ejpam-3443	531	38	v	v	NOUN
ejpam-3443	531	39	(	(	PUNCT
ejpam-3443	531	40	kp	kp	PROPN
ejpam-3443	531	41	)	)	PUNCT
ejpam-3443	531	42	.	.	PUNCT
ejpam-3443	532	1	on	on	ADP
ejpam-3443	532	2	the	the	DET
ejpam-3443	532	3	other	other	ADJ
ejpam-3443	532	4	hand	hand	NOUN
ejpam-3443	532	5	,	,	PUNCT
ejpam-3443	532	6	if	if	SCONJ
ejpam-3443	532	7	s	s	VERB
ejpam-3443	532	8	is	be	AUX
ejpam-3443	532	9	not	not	PART
ejpam-3443	532	10	a	a	DET
ejpam-3443	532	11	total	total	ADJ
ejpam-3443	532	12	dominating	dominating	NOUN
ejpam-3443	532	13	set	set	NOUN
ejpam-3443	532	14	,	,	PUNCT
ejpam-3443	532	15	then	then	ADV
ejpam-3443	532	16	c	c	X
ejpam-3443	532	17	=	=	SYM
ejpam-3443	532	18	{	{	PUNCT
ejpam-3443	532	19	x}×s	x}×s	PROPN
ejpam-3443	532	20	for	for	ADP
ejpam-3443	532	21	some	some	DET
ejpam-3443	532	22	x	x	SYM
ejpam-3443	532	23	∈	∈	PROPN
ejpam-3443	532	24	v	v	NOUN
ejpam-3443	532	25	(	(	PUNCT
ejpam-3443	532	26	kp	kp	PROPN
ejpam-3443	532	27	)	)	PUNCT
ejpam-3443	532	28	and	and	CCONJ
ejpam-3443	532	29	s	s	VERB
ejpam-3443	532	30	is	be	AUX
ejpam-3443	532	31	a	a	DET
ejpam-3443	532	32	minimal	minimal	ADJ
ejpam-3443	532	33	dominating	dominating	NOUN
ejpam-3443	532	34	set	set	NOUN
ejpam-3443	532	35	of	of	ADP
ejpam-3443	532	36	g.	g.	PROPN
ejpam-3443	532	37	thus	thus	ADV
ejpam-3443	532	38	,	,	PUNCT
ejpam-3443	532	39	γmce(kp[g	γmce(kp[g	PROPN
ejpam-3443	532	40	]	]	X
ejpam-3443	532	41	)	)	PUNCT
ejpam-3443	532	42	≤	≤	NOUN
ejpam-3443	532	43	max{2	max{2	PROPN
ejpam-3443	532	44	,	,	PUNCT
ejpam-3443	532	45	γm(g	γm(g	NOUN
ejpam-3443	532	46	)	)	PUNCT
ejpam-3443	532	47	}	}	PUNCT
ejpam-3443	532	48	=	=	SYM
ejpam-3443	532	49	γm(g	γm(g	NOUN
ejpam-3443	532	50	)	)	PUNCT
ejpam-3443	532	51	.	.	PUNCT
ejpam-3443	533	1	this	this	PRON
ejpam-3443	533	2	proves	prove	VERB
ejpam-3443	533	3	statement	statement	NOUN
ejpam-3443	533	4	(	(	PUNCT
ejpam-3443	533	5	ii	ii	NOUN
ejpam-3443	533	6	)	)	PUNCT
ejpam-3443	533	7	.	.	PUNCT
ejpam-3443	534	1	to	to	PART
ejpam-3443	534	2	prove	prove	VERB
ejpam-3443	534	3	statement	statement	NOUN
ejpam-3443	534	4	(	(	PUNCT
ejpam-3443	534	5	iii	iii	NOUN
ejpam-3443	534	6	)	)	PUNCT
ejpam-3443	534	7	,	,	PUNCT
ejpam-3443	534	8	let	let	VERB
ejpam-3443	534	9	c	c	NOUN
ejpam-3443	534	10	=	=	SYM
ejpam-3443	534	11	∪u∈s	∪u∈s	X
ejpam-3443	534	12	(	(	PUNCT
ejpam-3443	534	13	{	{	PUNCT
ejpam-3443	534	14	u	u	NOUN
ejpam-3443	534	15	}	}	PUNCT
ejpam-3443	534	16	×	×	NOUN
ejpam-3443	534	17	v	v	NOUN
ejpam-3443	534	18	(	(	PUNCT
ejpam-3443	534	19	g	g	NOUN
ejpam-3443	534	20	)	)	PUNCT
ejpam-3443	534	21	)	)	PUNCT
ejpam-3443	534	22	,	,	PUNCT
ejpam-3443	534	23	where	where	SCONJ
ejpam-3443	534	24	s	s	VERB
ejpam-3443	534	25	⊆	⊆	NUM
ejpam-3443	534	26	v	v	NOUN
ejpam-3443	534	27	(	(	PUNCT
ejpam-3443	534	28	kp	kp	PROPN
ejpam-3443	534	29	)	)	PUNCT
ejpam-3443	534	30	ia	ia	PROPN
ejpam-3443	534	31	a	a	DET
ejpam-3443	534	32	γ+ce	γ+ce	NOUN
ejpam-3443	534	33	-	-	PUNCT
ejpam-3443	534	34	set	set	NOUN
ejpam-3443	534	35	in	in	ADP
ejpam-3443	534	36	kp	kp	NOUN
ejpam-3443	534	37	.	.	PUNCT
ejpam-3443	535	1	by	by	ADP
ejpam-3443	535	2	theorem	theorem	NOUN
ejpam-3443	535	3	10	10	NUM
ejpam-3443	535	4	,	,	PUNCT
ejpam-3443	535	5	c	c	PROPN
ejpam-3443	535	6	is	be	AUX
ejpam-3443	535	7	a	a	DET
ejpam-3443	535	8	cost	cost	NOUN
ejpam-3443	535	9	effective	effective	ADJ
ejpam-3443	535	10	dominating	dominating	NOUN
ejpam-3443	535	11	set	set	NOUN
ejpam-3443	535	12	of	of	ADP
ejpam-3443	535	13	kp[g	kp[g	NOUN
ejpam-3443	535	14	]	]	PUNCT
ejpam-3443	535	15	.	.	PUNCT
ejpam-3443	536	1	consequently	consequently	ADV
ejpam-3443	536	2	,	,	PUNCT
ejpam-3443	536	3	γ+ce(kp[g	γ+ce(kp[g	NOUN
ejpam-3443	536	4	]	]	X
ejpam-3443	536	5	)	)	PUNCT
ejpam-3443	536	6	≥	≥	PROPN
ejpam-3443	536	7	|s|	|s|	PROPN
ejpam-3443	536	8	×	×	PROPN
ejpam-3443	536	9	|v	|v	PROPN
ejpam-3443	536	10	(	(	PUNCT
ejpam-3443	536	11	g)|	g)|	NOUN
ejpam-3443	536	12	.	.	PUNCT
ejpam-3443	537	1	conversely	conversely	ADV
ejpam-3443	537	2	,	,	PUNCT
ejpam-3443	537	3	let	let	VERB
ejpam-3443	537	4	c	c	NOUN
ejpam-3443	537	5	=	=	SYM
ejpam-3443	537	6	∪u∈s	∪u∈s	X
ejpam-3443	537	7	(	(	PUNCT
ejpam-3443	537	8	{	{	PUNCT
ejpam-3443	537	9	u	u	NOUN
ejpam-3443	537	10	}	}	PUNCT
ejpam-3443	537	11	×	×	PROPN
ejpam-3443	537	12	tu	tu	PROPN
ejpam-3443	537	13	)	)	PUNCT
ejpam-3443	537	14	be	be	AUX
ejpam-3443	537	15	a	a	DET
ejpam-3443	537	16	γ+ce	γ+ce	NOUN
ejpam-3443	537	17	-	-	PUNCT
ejpam-3443	537	18	set	set	NOUN
ejpam-3443	537	19	of	of	ADP
ejpam-3443	537	20	kp[g	kp[g	NOUN
ejpam-3443	537	21	]	]	PUNCT
ejpam-3443	537	22	.	.	PUNCT
ejpam-3443	538	1	in	in	ADP
ejpam-3443	538	2	view	view	NOUN
ejpam-3443	538	3	of	of	ADP
ejpam-3443	538	4	theorem	theorem	NOUN
ejpam-3443	538	5	10	10	NUM
ejpam-3443	538	6	,	,	PUNCT
ejpam-3443	538	7	since	since	SCONJ
ejpam-3443	538	8	we	we	PRON
ejpam-3443	538	9	want	want	VERB
ejpam-3443	538	10	the	the	DET
ejpam-3443	538	11	largest	large	ADJ
ejpam-3443	538	12	possible	possible	ADJ
ejpam-3443	538	13	cardinality	cardinality	NOUN
ejpam-3443	538	14	of	of	ADP
ejpam-3443	538	15	c	c	PROPN
ejpam-3443	538	16	,	,	PUNCT
ejpam-3443	538	17	we	we	PRON
ejpam-3443	538	18	assume	assume	VERB
ejpam-3443	538	19	that	that	SCONJ
ejpam-3443	538	20	tu	tu	PROPN
ejpam-3443	538	21	=	=	SYM
ejpam-3443	538	22	v	v	PROPN
ejpam-3443	538	23	(	(	PUNCT
ejpam-3443	538	24	g	g	NOUN
ejpam-3443	538	25	)	)	PUNCT
ejpam-3443	538	26	,	,	PUNCT
ejpam-3443	538	27	which	which	PRON
ejpam-3443	538	28	is	be	AUX
ejpam-3443	538	29	a	a	DET
ejpam-3443	538	30	dominating	dominating	NOUN
ejpam-3443	538	31	set	set	NOUN
ejpam-3443	538	32	of	of	ADP
ejpam-3443	538	33	g.	g.	PROPN
ejpam-3443	538	34	let	let	VERB
ejpam-3443	538	35	u	u	PRON
ejpam-3443	538	36	∈	∈	PROPN
ejpam-3443	538	37	s.	s.	PROPN
ejpam-3443	538	38	equation	equation	NOUN
ejpam-3443	538	39	2	2	NUM
ejpam-3443	538	40	and	and	CCONJ
ejpam-3443	538	41	equation	equation	NOUN
ejpam-3443	538	42	3	3	NUM
ejpam-3443	538	43	,	,	PUNCT
ejpam-3443	538	44	respectively	respectively	ADV
ejpam-3443	538	45	,	,	PUNCT
ejpam-3443	538	46	yield	yield	NOUN
ejpam-3443	538	47	|nkp[g]((u	|nkp[g]((u	NOUN
ejpam-3443	538	48	,	,	PUNCT
ejpam-3443	538	49	v	v	NOUN
ejpam-3443	538	50	)	)	PUNCT
ejpam-3443	538	51	)	)	PUNCT
ejpam-3443	538	52	∩	∩	PROPN
ejpam-3443	538	53	c|	c|	PROPN
ejpam-3443	538	54	=	=	SYM
ejpam-3443	538	55	|nkp(u	|nkp(u	NOUN
ejpam-3443	538	56	)	)	PUNCT
ejpam-3443	538	57	∩	∩	NOUN
ejpam-3443	538	58	s||v	s||v	PROPN
ejpam-3443	538	59	(	(	PUNCT
ejpam-3443	538	60	g)|+	g)|+	NOUN
ejpam-3443	538	61	|ng(v	|ng(v	NOUN
ejpam-3443	538	62	)	)	PUNCT
ejpam-3443	538	63	∩	∩	ADJ
ejpam-3443	538	64	v	v	X
ejpam-3443	538	65	(	(	PUNCT
ejpam-3443	538	66	g)|	g)|	NOUN
ejpam-3443	538	67	=	=	SYM
ejpam-3443	538	68	(	(	PUNCT
ejpam-3443	538	69	|s|	|s|	NOUN
ejpam-3443	538	70	−	−	PROPN
ejpam-3443	538	71	1	1	NUM
ejpam-3443	538	72	)	)	PUNCT
ejpam-3443	538	73	|v	|v	PROPN
ejpam-3443	538	74	(	(	PUNCT
ejpam-3443	538	75	g)|+	g)|+	NOUN
ejpam-3443	538	76	|ng(v)|	|ng(v)|	NOUN
ejpam-3443	538	77	.	.	PUNCT
ejpam-3443	539	1	and	and	CCONJ
ejpam-3443	539	2	|nkp[g]((u	|nkp[g]((u	NOUN
ejpam-3443	539	3	,	,	PUNCT
ejpam-3443	539	4	v	v	NOUN
ejpam-3443	539	5	)	)	PUNCT
ejpam-3443	539	6	)	)	PUNCT
ejpam-3443	540	1	\	\	PROPN
ejpam-3443	540	2	c|	c|	PROPN
ejpam-3443	540	3	=	=	SYM
ejpam-3443	540	4	|nkp(u	|nkp(u	NOUN
ejpam-3443	540	5	)	)	PUNCT
ejpam-3443	540	6	\	\	PUNCT
ejpam-3443	541	1	s||v	s||v	PROPN
ejpam-3443	541	2	(	(	PUNCT
ejpam-3443	541	3	g)|	g)|	NOUN
ejpam-3443	541	4	=	=	PUNCT
ejpam-3443	541	5	(	(	PUNCT
ejpam-3443	541	6	p−	p−	NOUN
ejpam-3443	541	7	|s|	|s|	NOUN
ejpam-3443	541	8	)	)	PUNCT
ejpam-3443	541	9	|v	|v	PROPN
ejpam-3443	541	10	(	(	PUNCT
ejpam-3443	541	11	g)|	g)|	NOUN
ejpam-3443	541	12	.	.	PUNCT
ejpam-3443	542	1	for	for	ADP
ejpam-3443	542	2	each	each	DET
ejpam-3443	542	3	v	v	NUM
ejpam-3443	542	4	∈	∈	PROPN
ejpam-3443	542	5	v	v	NOUN
ejpam-3443	542	6	(	(	PUNCT
ejpam-3443	542	7	g	g	NOUN
ejpam-3443	542	8	)	)	PUNCT
ejpam-3443	542	9	.	.	PUNCT
ejpam-3443	543	1	since	since	SCONJ
ejpam-3443	543	2	c	c	PROPN
ejpam-3443	543	3	is	be	AUX
ejpam-3443	543	4	a	a	DET
ejpam-3443	543	5	cost	cost	NOUN
ejpam-3443	543	6	effective	effective	ADJ
ejpam-3443	543	7	set	set	NOUN
ejpam-3443	543	8	of	of	ADP
ejpam-3443	543	9	kp[g	kp[g	NOUN
ejpam-3443	543	10	]	]	PUNCT
ejpam-3443	543	11	,	,	PUNCT
ejpam-3443	543	12	(	(	PUNCT
ejpam-3443	543	13	|s|	|s|	NOUN
ejpam-3443	543	14	−	−	NOUN
ejpam-3443	543	15	1	1	NUM
ejpam-3443	543	16	)	)	PUNCT
ejpam-3443	543	17	|v	|v	PROPN
ejpam-3443	543	18	(	(	PUNCT
ejpam-3443	543	19	g)|+	g)|+	NOUN
ejpam-3443	543	20	|ng(v)|	|ng(v)|	NOUN
ejpam-3443	543	21	≤	≤	NOUN
ejpam-3443	543	22	(	(	PUNCT
ejpam-3443	543	23	p−	p−	NOUN
ejpam-3443	543	24	|s|	|s|	NOUN
ejpam-3443	543	25	)	)	PUNCT
ejpam-3443	543	26	|v	|v	PROPN
ejpam-3443	543	27	(	(	PUNCT
ejpam-3443	543	28	g)|	g)|	NOUN
ejpam-3443	543	29	,	,	PUNCT
ejpam-3443	543	30	or	or	CCONJ
ejpam-3443	543	31	equivalently	equivalently	ADV
ejpam-3443	543	32	,	,	PUNCT
ejpam-3443	543	33	2|s||v	2|s||v	PROPN
ejpam-3443	543	34	(	(	PUNCT
ejpam-3443	543	35	g)|	g)|	NOUN
ejpam-3443	543	36	≤	≤	NOUN
ejpam-3443	543	37	(	(	PUNCT
ejpam-3443	543	38	p+	p+	PROPN
ejpam-3443	543	39	1)|v	1)|v	NUM
ejpam-3443	543	40	(	(	PUNCT
ejpam-3443	543	41	g)|	g)|	NOUN
ejpam-3443	543	42	−	−	NOUN
ejpam-3443	543	43	|ng(v)|	|ng(v)|	NOUN
ejpam-3443	543	44	for	for	ADP
ejpam-3443	543	45	each	each	DET
ejpam-3443	543	46	v	v	NUM
ejpam-3443	543	47	∈	∈	PROPN
ejpam-3443	543	48	v	v	NOUN
ejpam-3443	543	49	(	(	PUNCT
ejpam-3443	543	50	g	g	NOUN
ejpam-3443	543	51	)	)	PUNCT
ejpam-3443	543	52	.	.	PUNCT
ejpam-3443	544	1	thus	thus	ADV
ejpam-3443	544	2	,	,	PUNCT
ejpam-3443	544	3	|s|	|s|	VERB
ejpam-3443	544	4	<	<	X
ejpam-3443	544	5	1	1	NUM
ejpam-3443	544	6	2	2	NUM
ejpam-3443	544	7	(	(	PUNCT
ejpam-3443	544	8	p+	p+	NOUN
ejpam-3443	544	9	1	1	NUM
ejpam-3443	544	10	)	)	PUNCT
ejpam-3443	544	11	.	.	PUNCT
ejpam-3443	545	1	therefore	therefore	ADV
ejpam-3443	545	2	,	,	PUNCT
ejpam-3443	545	3	γ+ce(kp[g	γ+ce(kp[g	NOUN
ejpam-3443	545	4	]	]	X
ejpam-3443	545	5	)	)	PUNCT
ejpam-3443	545	6	=	=	SYM
ejpam-3443	545	7	|c|	|c|	PROPN
ejpam-3443	545	8	=	=	SYM
ejpam-3443	545	9	|s||v	|s||v	NOUN
ejpam-3443	545	10	(	(	PUNCT
ejpam-3443	545	11	g)|	g)|	NOUN
ejpam-3443	545	12	≤	≤	NOUN
ejpam-3443	546	1	⌊	⌊	PROPN
ejpam-3443	546	2	p+	p+	NOUN
ejpam-3443	546	3	1	1	NUM
ejpam-3443	546	4	2	2	NUM
ejpam-3443	546	5	⌋	⌋	NOUN
ejpam-3443	546	6	|v	|v	X
ejpam-3443	546	7	(	(	PUNCT
ejpam-3443	546	8	g)|	g)|	NOUN
ejpam-3443	546	9	,	,	PUNCT
ejpam-3443	546	10	and	and	CCONJ
ejpam-3443	546	11	the	the	DET
ejpam-3443	546	12	desired	desire	VERB
ejpam-3443	546	13	conclusion	conclusion	NOUN
ejpam-3443	546	14	follows	follow	VERB
ejpam-3443	546	15	.	.	PUNCT
ejpam-3443	547	1	references	reference	NOUN
ejpam-3443	547	2	998	998	NUM
ejpam-3443	547	3	references	reference	NOUN
ejpam-3443	547	4	[	[	X
ejpam-3443	547	5	1	1	NUM
ejpam-3443	547	6	]	]	PUNCT
ejpam-3443	547	7	buckley	buckley	NOUN
ejpam-3443	547	8	,	,	PUNCT
ejpam-3443	547	9	fred	fred	PROPN
ejpam-3443	547	10	and	and	CCONJ
ejpam-3443	547	11	frank	frank	PROPN
ejpam-3443	547	12	harary	harary	PROPN
ejpam-3443	547	13	,	,	PUNCT
ejpam-3443	547	14	distance	distance	NOUN
ejpam-3443	547	15	in	in	ADP
ejpam-3443	547	16	graphs	graph	NOUN
ejpam-3443	547	17	,	,	PUNCT
ejpam-3443	547	18	redwood	redwood	NOUN
ejpam-3443	547	19	city	city	NOUN
ejpam-3443	547	20	,	,	PUNCT
ejpam-3443	547	21	ca	ca	NOUN
ejpam-3443	547	22	:	:	PUNCT
ejpam-3443	547	23	addisonwesley	addisonwesley	ADJ
ejpam-3443	547	24	,	,	PUNCT
ejpam-3443	547	25	1990	1990	NUM
ejpam-3443	547	26	.	.	PUNCT
ejpam-3443	548	1	[	[	X
ejpam-3443	548	2	2	2	NUM
ejpam-3443	548	3	]	]	PUNCT
ejpam-3443	548	4	c.	c.	PROPN
ejpam-3443	548	5	berge	berge	PROPN
ejpam-3443	548	6	,	,	PUNCT
ejpam-3443	548	7	theory	theory	NOUN
ejpam-3443	548	8	of	of	ADP
ejpam-3443	548	9	graphs	graph	NOUN
ejpam-3443	548	10	and	and	CCONJ
ejpam-3443	548	11	its	its	PRON
ejpam-3443	548	12	applications	application	NOUN
ejpam-3443	548	13	,	,	PUNCT
ejpam-3443	548	14	methuen	methuen	PROPN
ejpam-3443	548	15	,	,	PUNCT
ejpam-3443	548	16	london	london	PROPN
ejpam-3443	548	17	,	,	PUNCT
ejpam-3443	548	18	1962	1962	NUM
ejpam-3443	549	1	[	[	X
ejpam-3443	549	2	3	3	X
ejpam-3443	549	3	]	]	X
ejpam-3443	549	4	j.a	j.a	PROPN
ejpam-3443	549	5	.	.	PROPN
ejpam-3443	549	6	bondy	bondy	PROPN
ejpam-3443	549	7	and	and	CCONJ
ejpam-3443	549	8	geng	geng	PROPN
ejpam-3443	549	9	-	-	PUNCT
ejpam-3443	549	10	hau	hau	PROPN
ejpam-3443	549	11	fan	fan	PROPN
ejpam-3443	549	12	,	,	PUNCT
ejpam-3443	549	13	a	a	DET
ejpam-3443	549	14	sufficient	sufficient	ADJ
ejpam-3443	549	15	condition	condition	NOUN
ejpam-3443	549	16	for	for	ADP
ejpam-3443	549	17	dominating	dominating	NOUN
ejpam-3443	549	18	cycles	cycle	NOUN
ejpam-3443	549	19	,	,	PUNCT
ejpam-3443	549	20	discrete	discrete	ADJ
ejpam-3443	549	21	math	math	NOUN
ejpam-3443	549	22	,	,	PUNCT
ejpam-3443	549	23	vol	vol	NOUN
ejpam-3443	549	24	.	.	PUNCT
ejpam-3443	550	1	67(2	67(2	NUM
ejpam-3443	550	2	):	):	PUNCT
ejpam-3443	550	3	205	205	NUM
ejpam-3443	550	4	-	-	SYM
ejpam-3443	550	5	208	208	NUM
ejpam-3443	550	6	,	,	PUNCT
ejpam-3443	550	7	1987	1987	NUM
ejpam-3443	550	8	[	[	X
ejpam-3443	550	9	4	4	NUM
ejpam-3443	550	10	]	]	X
ejpam-3443	550	11	e.j	e.j	PROPN
ejpam-3443	550	12	.	.	PROPN
ejpam-3443	550	13	cockayne	cockayne	PROPN
ejpam-3443	550	14	and	and	CCONJ
ejpam-3443	550	15	s.t	s.t	PROPN
ejpam-3443	550	16	.	.	PROPN
ejpam-3443	550	17	hedetniemi	hedetniemi	PROPN
ejpam-3443	550	18	,	,	PUNCT
ejpam-3443	550	19	towards	towards	ADP
ejpam-3443	550	20	a	a	DET
ejpam-3443	550	21	theory	theory	NOUN
ejpam-3443	550	22	of	of	ADP
ejpam-3443	550	23	domination	domination	NOUN
ejpam-3443	550	24	in	in	ADP
ejpam-3443	550	25	graphs	graph	NOUN
ejpam-3443	550	26	.	.	PUNCT
ejpam-3443	551	1	networks	network	NOUN
ejpam-3443	551	2	,	,	PUNCT
ejpam-3443	551	3	7(3	7(3	NUM
ejpam-3443	551	4	):	):	PUNCT
ejpam-3443	551	5	247	247	NUM
ejpam-3443	551	6	-	-	SYM
ejpam-3443	551	7	261	261	NUM
ejpam-3443	551	8	,	,	PUNCT
ejpam-3443	551	9	1997	1997	NUM
ejpam-3443	551	10	.	.	PUNCT
ejpam-3443	552	1	[	[	X
ejpam-3443	552	2	5	5	X
ejpam-3443	552	3	]	]	X
ejpam-3443	552	4	t.w	t.w	PROPN
ejpam-3443	552	5	.	.	PROPN
ejpam-3443	552	6	haynes	haynes	PROPN
ejpam-3443	552	7	,	,	PUNCT
ejpam-3443	552	8	s.t	s.t	PROPN
ejpam-3443	552	9	.	.	PROPN
ejpam-3443	552	10	hedetniemi	hedetniemi	PROPN
ejpam-3443	552	11	,	,	PUNCT
ejpam-3443	552	12	and	and	CCONJ
ejpam-3443	552	13	p.j	p.j	PROPN
ejpam-3443	552	14	.	.	PROPN
ejpam-3443	552	15	slater	slater	PROPN
ejpam-3443	552	16	,	,	PUNCT
ejpam-3443	552	17	fundamentals	fundamental	NOUN
ejpam-3443	552	18	of	of	ADP
ejpam-3443	552	19	domination	domination	NOUN
ejpam-3443	552	20	in	in	ADP
ejpam-3443	552	21	graphs	graph	NOUN
ejpam-3443	552	22	.	.	PUNCT
ejpam-3443	553	1	marcel	marcel	PROPN
ejpam-3443	553	2	dekker	dekker	PROPN
ejpam-3443	553	3	,	,	PUNCT
ejpam-3443	553	4	inc	inc	PROPN
ejpam-3443	553	5	.	.	PROPN
ejpam-3443	553	6	new	new	PROPN
ejpam-3443	553	7	york	york	PROPN
ejpam-3443	553	8	(	(	PUNCT
ejpam-3443	553	9	1998	1998	NUM
ejpam-3443	553	10	)	)	PUNCT
ejpam-3443	553	11	.	.	PUNCT
ejpam-3443	554	1	[	[	X
ejpam-3443	554	2	6	6	NUM
ejpam-3443	554	3	]	]	PUNCT
ejpam-3443	554	4	t.	t.	PROPN
ejpam-3443	554	5	haynes	haynes	PROPN
ejpam-3443	554	6	,	,	PUNCT
ejpam-3443	554	7	s.	s.	PROPN
ejpam-3443	554	8	hedetniemi	hedetniemi	ADV
ejpam-3443	554	9	and	and	CCONJ
ejpam-3443	554	10	m.	m.	PROPN
ejpam-3443	554	11	henning	henning	PROPN
ejpam-3443	554	12	,	,	PUNCT
ejpam-3443	554	13	domination	domination	NOUN
ejpam-3443	554	14	in	in	ADP
ejpam-3443	554	15	graphs	graph	NOUN
ejpam-3443	554	16	applied	apply	VERB
ejpam-3443	554	17	to	to	ADP
ejpam-3443	554	18	electrical	electrical	ADJ
ejpam-3443	554	19	power	power	NOUN
ejpam-3443	554	20	networks	network	NOUN
ejpam-3443	554	21	,	,	PUNCT
ejpam-3443	554	22	j.	j.	PROPN
ejpam-3443	554	23	discrete	discrete	PROPN
ejpam-3443	554	24	math	math	NOUN
ejpam-3443	554	25	,	,	PUNCT
ejpam-3443	554	26	vol	vol	NOUN
ejpam-3443	554	27	.	.	PUNCT
ejpam-3443	554	28	15(4	15(4	NUM
ejpam-3443	554	29	)	)	PUNCT
ejpam-3443	554	30	,	,	PUNCT
ejpam-3443	554	31	2000	2000	NUM
ejpam-3443	554	32	.	.	PUNCT
ejpam-3443	555	1	[	[	X
ejpam-3443	555	2	7	7	X
ejpam-3443	555	3	]	]	X
ejpam-3443	555	4	o.	o.	ADJ
ejpam-3443	555	5	ore	ore	PROPN
ejpam-3443	555	6	,	,	PUNCT
ejpam-3443	555	7	theory	theory	NOUN
ejpam-3443	555	8	of	of	ADP
ejpam-3443	555	9	graphs	graph	NOUN
ejpam-3443	555	10	,	,	PUNCT
ejpam-3443	555	11	amer	amer	PROPN
ejpam-3443	555	12	.	.	PROPN
ejpam-3443	555	13	math	math	PROPN
ejpam-3443	555	14	.	.	PUNCT
ejpam-3443	556	1	soc	soc	PROPN
ejpam-3443	556	2	.	.	PUNCT
ejpam-3443	557	1	transl	transl	PROPN
ejpam-3443	557	2	.	.	PUNCT
ejpam-3443	558	1	,	,	PUNCT
ejpam-3443	558	2	38	38	NUM
ejpam-3443	558	3	(	(	PUNCT
ejpam-3443	558	4	amer	amer	PROPN
ejpam-3443	558	5	.	.	PROPN
ejpam-3443	558	6	math	math	PROPN
ejpam-3443	558	7	.	.	PUNCT
ejpam-3443	559	1	soc	soc	PROPN
ejpam-3443	559	2	.	.	PUNCT
ejpam-3443	559	3	,	,	PUNCT
ejpam-3443	559	4	prividence	prividence	NOUN
ejpam-3443	559	5	,	,	PUNCT
ejpam-3443	559	6	ri	ri	NOUN
ejpam-3443	559	7	,	,	PUNCT
ejpam-3443	559	8	1962	1962	NUM
ejpam-3443	559	9	)	)	PUNCT
ejpam-3443	559	10	,	,	PUNCT
ejpam-3443	559	11	206	206	NUM
ejpam-3443	559	12	-	-	SYM
ejpam-3443	559	13	212	212	NUM
ejpam-3443	559	14	.	.	PUNCT
ejpam-3443	560	1	[	[	X
ejpam-3443	560	2	8	8	X
ejpam-3443	560	3	]	]	X
ejpam-3443	560	4	s.	s.	PROPN
ejpam-3443	560	5	canoy	canoy	PROPN
ejpam-3443	560	6	jr	jr	PROPN
ejpam-3443	560	7	,	,	PUNCT
ejpam-3443	560	8	and	and	CCONJ
ejpam-3443	560	9	c.	c.	PROPN
ejpam-3443	560	10	go	go	VERB
ejpam-3443	560	11	,	,	PUNCT
ejpam-3443	560	12	domination	domination	NOUN
ejpam-3443	560	13	in	in	ADP
ejpam-3443	560	14	the	the	DET
ejpam-3443	560	15	join	join	NOUN
ejpam-3443	560	16	and	and	CCONJ
ejpam-3443	560	17	corona	corona	NOUN
ejpam-3443	560	18	of	of	ADP
ejpam-3443	560	19	graphs	graph	NOUN
ejpam-3443	560	20	,	,	PUNCT
ejpam-3443	560	21	international	international	PROPN
ejpam-3443	560	22	mathematical	mathematical	ADJ
ejpam-3443	560	23	forum	forum	PROPN
ejpam-3443	560	24	,	,	PUNCT
ejpam-3443	560	25	vol	vol	NOUN
ejpam-3443	560	26	.	.	PUNCT
ejpam-3443	561	1	6(16	6(16	NUM
ejpam-3443	561	2	):	):	PUNCT
ejpam-3443	561	3	763	763	NUM
ejpam-3443	561	4	771	771	NUM
ejpam-3443	561	5	,	,	PUNCT
ejpam-3443	561	6	2011	2011	NUM
ejpam-3443	561	7	.	.	PUNCT
ejpam-3443	562	1	[	[	X
ejpam-3443	562	2	9	9	NUM
ejpam-3443	562	3	]	]	PUNCT
ejpam-3443	562	4	s.	s.	PROPN
ejpam-3443	562	5	canoy	canoy	PROPN
ejpam-3443	562	6	jr	jr	PROPN
ejpam-3443	562	7	,	,	PUNCT
ejpam-3443	562	8	and	and	CCONJ
ejpam-3443	562	9	c.	c.	PROPN
ejpam-3443	562	10	go	go	VERB
ejpam-3443	562	11	,	,	PUNCT
ejpam-3443	562	12	domination	domination	NOUN
ejpam-3443	562	13	in	in	ADP
ejpam-3443	562	14	the	the	DET
ejpam-3443	562	15	composition	composition	NOUN
ejpam-3443	562	16	of	of	ADP
ejpam-3443	562	17	graphs	graph	NOUN
ejpam-3443	562	18	,	,	PUNCT
ejpam-3443	562	19	akce	akce	ADJ
ejpam-3443	562	20	journal	journal	NOUN
ejpam-3443	562	21	of	of	ADP
ejpam-3443	562	22	graph	graph	NOUN
ejpam-3443	562	23	theory	theory	NOUN
ejpam-3443	562	24	,	,	PUNCT
ejpam-3443	562	25	to	to	PART
ejpam-3443	562	26	appear	appear	VERB
ejpam-3443	562	27	.	.	PUNCT
ejpam-3443	563	1	[	[	X
ejpam-3443	563	2	10	10	NUM
ejpam-3443	563	3	]	]	X
ejpam-3443	563	4	f.v	f.v	PROPN
ejpam-3443	563	5	.	.	PROPN
ejpam-3443	563	6	fomin	fomin	PROPN
ejpam-3443	563	7	,	,	PUNCT
ejpam-3443	563	8	f.	f.	PROPN
ejpam-3443	563	9	gradoni	gradoni	PROPN
ejpam-3443	563	10	,	,	PUNCT
ejpam-3443	563	11	a.	a.	NOUN
ejpam-3443	563	12	pyatkin	pyatkin	PROPN
ejpam-3443	563	13	and	and	CCONJ
ejpam-3443	563	14	a.	a.	NOUN
ejpam-3443	563	15	stepanov	stepanov	PROPN
ejpam-3443	563	16	,	,	PUNCT
ejpam-3443	563	17	on	on	ADP
ejpam-3443	563	18	maximum	maximum	ADJ
ejpam-3443	563	19	number	number	NOUN
ejpam-3443	563	20	of	of	ADP
ejpam-3443	563	21	minimal	minimal	ADJ
ejpam-3443	563	22	dominating	dominating	NOUN
ejpam-3443	563	23	sets	set	NOUN
ejpam-3443	563	24	in	in	ADP
ejpam-3443	563	25	graphs	graph	NOUN
ejpam-3443	563	26	,	,	PUNCT
ejpam-3443	563	27	discrete	discrete	ADJ
ejpam-3443	563	28	mathematics	mathematic	NOUN
ejpam-3443	563	29	,	,	PUNCT
ejpam-3443	563	30	22:157	22:157	NUM
ejpam-3443	563	31	-	-	SYM
ejpam-3443	563	32	162	162	NUM
ejpam-3443	563	33	,	,	PUNCT
ejpam-3443	563	34	2005	2005	NUM
ejpam-3443	563	35	.	.	PUNCT
ejpam-3443	564	1	[	[	X
ejpam-3443	564	2	11	11	NUM
ejpam-3443	564	3	]	]	X
ejpam-3443	564	4	t.w	t.w	PROPN
ejpam-3443	564	5	.	.	PROPN
ejpam-3443	564	6	haynes	haynes	PROPN
ejpam-3443	564	7	,	,	PUNCT
ejpam-3443	564	8	s.m	s.m	PROPN
ejpam-3443	564	9	.	.	PROPN
ejpam-3443	564	10	hedetniemi	hedetniemi	PROPN
ejpam-3443	564	11	,	,	PUNCT
ejpam-3443	564	12	s.t	s.t	PROPN
ejpam-3443	564	13	.	.	PROPN
ejpam-3443	564	14	hedetniemi	hedetniemi	PROPN
ejpam-3443	564	15	,	,	PUNCT
ejpam-3443	564	16	t.l	t.l	PROPN
ejpam-3443	564	17	.	.	PROPN
ejpam-3443	564	18	mccoy	mccoy	PROPN
ejpam-3443	564	19	,	,	PUNCT
ejpam-3443	564	20	i.	i.	PROPN
ejpam-3443	564	21	vasylieva	vasylieva	PROPN
ejpam-3443	564	22	,	,	PUNCT
ejpam-3443	564	23	cost	cost	VERB
ejpam-3443	564	24	effective	effective	ADJ
ejpam-3443	564	25	domination	domination	NOUN
ejpam-3443	564	26	in	in	ADP
ejpam-3443	564	27	graphs	graph	NOUN
ejpam-3443	564	28	,	,	PUNCT
ejpam-3443	564	29	cong	cong	PROPN
ejpam-3443	564	30	.	.	PUNCT
ejpam-3443	565	1	numer	numer	PROPN
ejpam-3443	565	2	.	.	PROPN
ejpam-3443	565	3	,	,	PUNCT
ejpam-3443	565	4	vol	vol	VERB
ejpam-3443	565	5	211	211	NUM
ejpam-3443	565	6	(	(	PUNCT
ejpam-3443	565	7	2012	2012	NUM
ejpam-3443	565	8	)	)	PUNCT
ejpam-3443	565	9	,	,	PUNCT
ejpam-3443	565	10	197	197	NUM
ejpam-3443	565	11	209	209	NUM
ejpam-3443	565	12	.	.	PUNCT
ejpam-3443	566	1	[	[	X
ejpam-3443	566	2	12	12	NUM
ejpam-3443	566	3	]	]	X
ejpam-3443	566	4	t.w	t.w	PROPN
ejpam-3443	566	5	.	.	PROPN
ejpam-3443	566	6	haynes	haynes	PROPN
ejpam-3443	566	7	,	,	PUNCT
ejpam-3443	566	8	s.t	s.t	PROPN
ejpam-3443	566	9	.	.	PROPN
ejpam-3443	566	10	hedetniemi	hedetniemi	PROPN
ejpam-3443	566	11	,	,	PUNCT
ejpam-3443	566	12	t.l	t.l	PROPN
ejpam-3443	566	13	.	.	PROPN
ejpam-3443	566	14	mccoy	mccoy	PROPN
ejpam-3443	566	15	and	and	CCONJ
ejpam-3443	566	16	t.k	t.k	PROPN
ejpam-3443	566	17	.	.	PROPN
ejpam-3443	566	18	rodriguez	rodriguez	PROPN
ejpam-3443	566	19	,	,	PUNCT
ejpam-3443	566	20	bounds	bound	VERB
ejpam-3443	566	21	on	on	ADP
ejpam-3443	566	22	cost	cost	NOUN
ejpam-3443	566	23	effective	effective	ADJ
ejpam-3443	566	24	domination	domination	NOUN
ejpam-3443	566	25	numbers	number	NOUN
ejpam-3443	566	26	,	,	PUNCT
ejpam-3443	566	27	quaestiones	quaestione	NOUN
ejpam-3443	566	28	mathematicae	mathematicae	PROPN
ejpam-3443	566	29	,	,	PUNCT
ejpam-3443	566	30	vol	vol	NOUN
ejpam-3443	566	31	.	.	PUNCT
ejpam-3443	567	1	39(6	39(6	NUM
ejpam-3443	567	2	):	):	PUNCT
ejpam-3443	567	3	773	773	NUM
ejpam-3443	567	4	-	-	SYM
ejpam-3443	567	5	783	783	NUM
ejpam-3443	567	6	,	,	PUNCT
ejpam-3443	567	7	2016	2016	NUM
ejpam-3443	567	8	.	.	PUNCT
ejpam-3443	568	1	[	[	X
ejpam-3443	568	2	13	13	NUM
ejpam-3443	568	3	]	]	PUNCT
ejpam-3443	568	4	h.	h.	PROPN
ejpam-3443	568	5	nuenay	nuenay	PROPN
ejpam-3443	568	6	and	and	CCONJ
ejpam-3443	568	7	f.	f.	PROPN
ejpam-3443	568	8	jamil	jamil	PROPN
ejpam-3443	568	9	on	on	ADP
ejpam-3443	568	10	the	the	DET
ejpam-3443	568	11	minimal	minimal	ADJ
ejpam-3443	568	12	geodetic	geodetic	ADJ
ejpam-3443	568	13	domination	domination	NOUN
ejpam-3443	568	14	in	in	ADP
ejpam-3443	568	15	graphs	graph	NOUN
ejpam-3443	568	16	,	,	PUNCT
ejpam-3443	568	17	discussiones	discussione	NOUN
ejpam-3443	568	18	mathematicae	mathematicae	VERB
ejpam-3443	568	19	,	,	PUNCT
ejpam-3443	568	20	graph	graph	NOUN
ejpam-3443	568	21	theory	theory	NOUN
ejpam-3443	568	22	.	.	PUNCT
ejpam-3443	569	1	vol.45	vol.45	ADJ
ejpam-3443	569	2	,	,	PUNCT
ejpam-3443	569	3	403	403	NUM
ejpam-3443	569	4	-	-	SYM
ejpam-3443	569	5	418	418	NUM
ejpam-3443	569	6	,	,	PUNCT
ejpam-3443	569	7	2015	2015	NUM
ejpam-3443	569	8	.	.	PUNCT