id	sid	tid	token	lemma	pos
ejpam-5189	1	1	european	european	PROPN
ejpam-5189	1	2	journal	journal	PROPN
ejpam-5189	1	3	of	of	ADP
ejpam-5189	1	4	pure	pure	ADJ
ejpam-5189	1	5	and	and	CCONJ
ejpam-5189	1	6	applied	apply	VERB
ejpam-5189	1	7	mathematics	mathematic	NOUN
ejpam-5189	1	8	vol	vol	NOUN
ejpam-5189	1	9	.	.	PROPN
ejpam-5189	2	1	17	17	NUM
ejpam-5189	2	2	,	,	PUNCT
ejpam-5189	2	3	no	no	INTJ
ejpam-5189	2	4	.	.	NOUN
ejpam-5189	2	5	3	3	NUM
ejpam-5189	2	6	,	,	PUNCT
ejpam-5189	2	7	2024	2024	NUM
ejpam-5189	2	8	,	,	PUNCT
ejpam-5189	2	9	1539	1539	NUM
ejpam-5189	2	10	-	-	SYM
ejpam-5189	2	11	1552	1552	NUM
ejpam-5189	2	12	issn	issn	PROPN
ejpam-5189	2	13	1307	1307	NUM
ejpam-5189	2	14	-	-	SYM
ejpam-5189	2	15	5543	5543	NUM
ejpam-5189	2	16	–	–	PUNCT
ejpam-5189	3	1	ejpam.com	ejpam.com	X
ejpam-5189	3	2	published	publish	VERB
ejpam-5189	3	3	by	by	ADP
ejpam-5189	3	4	new	new	PROPN
ejpam-5189	3	5	york	york	PROPN
ejpam-5189	3	6	business	business	PROPN
ejpam-5189	3	7	global	global	ADJ
ejpam-5189	3	8	convex	convex	NOUN
ejpam-5189	3	9	2	2	NUM
ejpam-5189	3	10	-	-	PUNCT
ejpam-5189	3	11	domination	domination	NOUN
ejpam-5189	3	12	in	in	ADP
ejpam-5189	3	13	graphs	graph	NOUN
ejpam-5189	3	14	sergio	sergio	PROPN
ejpam-5189	3	15	r.	r.	PROPN
ejpam-5189	3	16	canoy	canoy	PROPN
ejpam-5189	3	17	,	,	PUNCT
ejpam-5189	3	18	jr.1,2	jr.1,2	PROPN
ejpam-5189	3	19	,	,	PUNCT
ejpam-5189	3	20	ferdinand	ferdinand	PROPN
ejpam-5189	3	21	p.	p.	PROPN
ejpam-5189	3	22	jamil	jamil	PROPN
ejpam-5189	3	23	1,2	1,2	NUM
ejpam-5189	3	24	,	,	PUNCT
ejpam-5189	3	25	rona	rona	PROPN
ejpam-5189	3	26	jane	jane	PROPN
ejpam-5189	3	27	g.	g.	PROPN
ejpam-5189	3	28	fortosa	fortosa	PROPN
ejpam-5189	3	29	1,2,∗	1,2,∗	NUM
ejpam-5189	3	30	,	,	PUNCT
ejpam-5189	3	31	jead	jead	NOUN
ejpam-5189	3	32	m.	m.	NOUN
ejpam-5189	3	33	macalisang	macalisang	PROPN
ejpam-5189	3	34	1,2	1,2	NUM
ejpam-5189	3	35	1	1	NUM
ejpam-5189	3	36	department	department	NOUN
ejpam-5189	3	37	of	of	ADP
ejpam-5189	3	38	mathematics	mathematic	NOUN
ejpam-5189	3	39	and	and	CCONJ
ejpam-5189	3	40	statistics	statistic	NOUN
ejpam-5189	3	41	,	,	PUNCT
ejpam-5189	3	42	college	college	NOUN
ejpam-5189	3	43	of	of	ADP
ejpam-5189	3	44	science	science	NOUN
ejpam-5189	3	45	and	and	CCONJ
ejpam-5189	3	46	mathematics	mathematic	NOUN
ejpam-5189	3	47	,	,	PUNCT
ejpam-5189	3	48	msu	msu	PROPN
ejpam-5189	3	49	-	-	PUNCT
ejpam-5189	3	50	iligan	iligan	PROPN
ejpam-5189	3	51	institute	institute	PROPN
ejpam-5189	3	52	of	of	ADP
ejpam-5189	3	53	technology	technology	PROPN
ejpam-5189	3	54	,	,	PUNCT
ejpam-5189	3	55	9200	9200	NUM
ejpam-5189	3	56	iligan	iligan	ADJ
ejpam-5189	3	57	city	city	NOUN
ejpam-5189	3	58	,	,	PUNCT
ejpam-5189	3	59	philippines	philippine	NOUN
ejpam-5189	3	60	2	2	NUM
ejpam-5189	3	61	center	center	NOUN
ejpam-5189	3	62	of	of	ADP
ejpam-5189	3	63	mathematical	mathematical	ADJ
ejpam-5189	3	64	and	and	CCONJ
ejpam-5189	3	65	theoretical	theoretical	ADJ
ejpam-5189	3	66	physical	physical	ADJ
ejpam-5189	3	67	sciencesprism	sciencesprism	NOUN
ejpam-5189	3	68	,	,	PUNCT
ejpam-5189	3	69	msu	msu	PROPN
ejpam-5189	3	70	-	-	PUNCT
ejpam-5189	3	71	iligan	iligan	PROPN
ejpam-5189	3	72	institute	institute	PROPN
ejpam-5189	3	73	of	of	ADP
ejpam-5189	3	74	technology	technology	PROPN
ejpam-5189	3	75	,	,	PUNCT
ejpam-5189	3	76	9200	9200	NUM
ejpam-5189	3	77	iligan	iligan	ADJ
ejpam-5189	3	78	city	city	NOUN
ejpam-5189	3	79	,	,	PUNCT
ejpam-5189	3	80	philippines	philippine	NOUN
ejpam-5189	3	81	abstract	abstract	ADJ
ejpam-5189	3	82	.	.	PUNCT
ejpam-5189	4	1	let	let	VERB
ejpam-5189	4	2	g	g	PRON
ejpam-5189	4	3	be	be	AUX
ejpam-5189	4	4	a	a	DET
ejpam-5189	4	5	connected	connected	ADJ
ejpam-5189	4	6	graph	graph	NOUN
ejpam-5189	4	7	.	.	PUNCT
ejpam-5189	5	1	a	a	DET
ejpam-5189	5	2	set	set	NOUN
ejpam-5189	5	3	s	s	NOUN
ejpam-5189	5	4	⊆	⊆	NUM
ejpam-5189	5	5	v	v	NOUN
ejpam-5189	5	6	(	(	PUNCT
ejpam-5189	5	7	g	g	NOUN
ejpam-5189	5	8	)	)	PUNCT
ejpam-5189	5	9	is	be	AUX
ejpam-5189	5	10	convex	convex	ADJ
ejpam-5189	5	11	2	2	NUM
ejpam-5189	5	12	-	-	PUNCT
ejpam-5189	5	13	dominating	dominating	NOUN
ejpam-5189	5	14	if	if	SCONJ
ejpam-5189	5	15	s	s	NOUN
ejpam-5189	5	16	is	be	AUX
ejpam-5189	5	17	both	both	PRON
ejpam-5189	5	18	convex	convex	ADJ
ejpam-5189	5	19	and	and	CCONJ
ejpam-5189	5	20	2	2	NUM
ejpam-5189	5	21	-	-	PUNCT
ejpam-5189	5	22	dominating	dominating	NOUN
ejpam-5189	5	23	.	.	PUNCT
ejpam-5189	6	1	the	the	DET
ejpam-5189	6	2	minimum	minimum	ADJ
ejpam-5189	6	3	cardinality	cardinality	NOUN
ejpam-5189	6	4	among	among	ADP
ejpam-5189	6	5	all	all	DET
ejpam-5189	6	6	convex	convex	ADJ
ejpam-5189	6	7	2	2	NUM
ejpam-5189	6	8	-	-	PUNCT
ejpam-5189	6	9	dominating	dominating	NOUN
ejpam-5189	6	10	sets	set	NOUN
ejpam-5189	6	11	in	in	ADP
ejpam-5189	6	12	g	g	NOUN
ejpam-5189	6	13	,	,	PUNCT
ejpam-5189	6	14	denoted	denote	VERB
ejpam-5189	6	15	by	by	ADP
ejpam-5189	6	16	γ2con(g	γ2con(g	NOUN
ejpam-5189	6	17	)	)	PUNCT
ejpam-5189	6	18	,	,	PUNCT
ejpam-5189	6	19	is	be	AUX
ejpam-5189	6	20	called	call	VERB
ejpam-5189	6	21	the	the	DET
ejpam-5189	6	22	convex	convex	ADJ
ejpam-5189	6	23	2	2	NUM
ejpam-5189	6	24	-	-	PUNCT
ejpam-5189	6	25	domination	domination	NOUN
ejpam-5189	6	26	number	number	NOUN
ejpam-5189	6	27	of	of	ADP
ejpam-5189	6	28	g.	g.	PROPN
ejpam-5189	6	29	in	in	ADP
ejpam-5189	6	30	this	this	DET
ejpam-5189	6	31	paper	paper	NOUN
ejpam-5189	6	32	,	,	PUNCT
ejpam-5189	6	33	we	we	PRON
ejpam-5189	6	34	initiate	initiate	VERB
ejpam-5189	6	35	the	the	DET
ejpam-5189	6	36	study	study	NOUN
ejpam-5189	6	37	of	of	ADP
ejpam-5189	6	38	convex	convex	NOUN
ejpam-5189	6	39	2domination	2domination	NUM
ejpam-5189	6	40	in	in	ADP
ejpam-5189	6	41	graphs	graph	NOUN
ejpam-5189	6	42	.	.	PUNCT
ejpam-5189	7	1	we	we	PRON
ejpam-5189	7	2	show	show	VERB
ejpam-5189	7	3	that	that	SCONJ
ejpam-5189	7	4	any	any	DET
ejpam-5189	7	5	two	two	NUM
ejpam-5189	7	6	positive	positive	ADJ
ejpam-5189	7	7	integers	integer	NOUN
ejpam-5189	7	8	a	a	PRON
ejpam-5189	7	9	and	and	CCONJ
ejpam-5189	7	10	b	b	NOUN
ejpam-5189	7	11	with	with	ADP
ejpam-5189	7	12	6	6	NUM
ejpam-5189	7	13	≤	≤	NOUN
ejpam-5189	7	14	a	a	DET
ejpam-5189	7	15	≤	≤	NUM
ejpam-5189	7	16	b	b	NOUN
ejpam-5189	7	17	are	be	AUX
ejpam-5189	7	18	,	,	PUNCT
ejpam-5189	7	19	respectively	respectively	ADV
ejpam-5189	7	20	,	,	PUNCT
ejpam-5189	7	21	realizable	realizable	ADJ
ejpam-5189	7	22	as	as	ADP
ejpam-5189	7	23	the	the	DET
ejpam-5189	7	24	convex	convex	NOUN
ejpam-5189	7	25	domination	domination	NOUN
ejpam-5189	7	26	number	number	NOUN
ejpam-5189	7	27	and	and	CCONJ
ejpam-5189	7	28	convex	convex	ADJ
ejpam-5189	7	29	2	2	NUM
ejpam-5189	7	30	-	-	PUNCT
ejpam-5189	7	31	domination	domination	NOUN
ejpam-5189	7	32	number	number	NOUN
ejpam-5189	7	33	of	of	ADP
ejpam-5189	7	34	some	some	DET
ejpam-5189	7	35	connected	connected	ADJ
ejpam-5189	7	36	graph	graph	NOUN
ejpam-5189	7	37	.	.	PUNCT
ejpam-5189	8	1	furthermore	furthermore	ADV
ejpam-5189	8	2	,	,	PUNCT
ejpam-5189	8	3	we	we	PRON
ejpam-5189	8	4	characterize	characterize	VERB
ejpam-5189	8	5	the	the	DET
ejpam-5189	8	6	convex	convex	ADJ
ejpam-5189	8	7	2	2	NUM
ejpam-5189	8	8	-	-	PUNCT
ejpam-5189	8	9	dominating	dominating	NOUN
ejpam-5189	8	10	sets	set	NOUN
ejpam-5189	8	11	in	in	ADP
ejpam-5189	8	12	the	the	DET
ejpam-5189	8	13	join	join	NOUN
ejpam-5189	8	14	,	,	PUNCT
ejpam-5189	8	15	corona	corona	PROPN
ejpam-5189	8	16	,	,	PUNCT
ejpam-5189	8	17	lexicographic	lexicographic	ADJ
ejpam-5189	8	18	product	product	NOUN
ejpam-5189	8	19	,	,	PUNCT
ejpam-5189	8	20	and	and	CCONJ
ejpam-5189	8	21	cartesian	cartesian	ADJ
ejpam-5189	8	22	product	product	NOUN
ejpam-5189	8	23	of	of	ADP
ejpam-5189	8	24	two	two	NUM
ejpam-5189	8	25	graphs	graph	NOUN
ejpam-5189	8	26	and	and	CCONJ
ejpam-5189	8	27	determine	determine	VERB
ejpam-5189	8	28	the	the	DET
ejpam-5189	8	29	corresponding	correspond	VERB
ejpam-5189	8	30	convex	convex	ADJ
ejpam-5189	8	31	2	2	NUM
ejpam-5189	8	32	-	-	PUNCT
ejpam-5189	8	33	domination	domination	NOUN
ejpam-5189	8	34	number	number	NOUN
ejpam-5189	8	35	of	of	ADP
ejpam-5189	8	36	each	each	PRON
ejpam-5189	8	37	of	of	ADP
ejpam-5189	8	38	these	these	DET
ejpam-5189	8	39	graphs	graph	NOUN
ejpam-5189	8	40	.	.	PUNCT
ejpam-5189	9	1	2020	2020	NUM
ejpam-5189	9	2	mathematics	mathematic	NOUN
ejpam-5189	9	3	subject	subject	NOUN
ejpam-5189	9	4	classifications	classification	NOUN
ejpam-5189	9	5	:	:	PUNCT
ejpam-5189	9	6	05c69	05c69	X
ejpam-5189	9	7	key	key	ADJ
ejpam-5189	9	8	words	word	NOUN
ejpam-5189	9	9	and	and	CCONJ
ejpam-5189	9	10	phrases	phrase	NOUN
ejpam-5189	9	11	:	:	PUNCT
ejpam-5189	9	12	convex	convex	NOUN
ejpam-5189	9	13	,	,	PUNCT
ejpam-5189	9	14	2	2	NUM
ejpam-5189	9	15	-	-	PUNCT
ejpam-5189	9	16	dominating	dominating	NOUN
ejpam-5189	9	17	,	,	PUNCT
ejpam-5189	9	18	convex	convex	ADJ
ejpam-5189	9	19	2	2	NUM
ejpam-5189	9	20	-	-	PUNCT
ejpam-5189	9	21	domination	domination	NOUN
ejpam-5189	9	22	,	,	PUNCT
ejpam-5189	9	23	join	join	NOUN
ejpam-5189	9	24	,	,	PUNCT
ejpam-5189	9	25	corona	corona	PROPN
ejpam-5189	9	26	,	,	PUNCT
ejpam-5189	9	27	lexicographic	lexicographic	ADJ
ejpam-5189	9	28	product	product	NOUN
ejpam-5189	9	29	,	,	PUNCT
ejpam-5189	9	30	cartesian	cartesian	ADJ
ejpam-5189	9	31	product	product	NOUN
ejpam-5189	9	32	1	1	NUM
ejpam-5189	9	33	.	.	PUNCT
ejpam-5189	10	1	introduction	introduction	NOUN
ejpam-5189	10	2	domination	domination	NOUN
ejpam-5189	10	3	is	be	AUX
ejpam-5189	10	4	one	one	NUM
ejpam-5189	10	5	of	of	ADP
ejpam-5189	10	6	the	the	DET
ejpam-5189	10	7	well	well	ADV
ejpam-5189	10	8	-	-	PUNCT
ejpam-5189	10	9	studied	study	VERB
ejpam-5189	10	10	concepts	concept	NOUN
ejpam-5189	10	11	in	in	ADP
ejpam-5189	10	12	graph	graph	NOUN
ejpam-5189	10	13	theory	theory	NOUN
ejpam-5189	10	14	.	.	PUNCT
ejpam-5189	11	1	variations	variation	NOUN
ejpam-5189	11	2	of	of	ADP
ejpam-5189	11	3	domination	domination	NOUN
ejpam-5189	11	4	as	as	ADV
ejpam-5189	11	5	well	well	ADV
ejpam-5189	11	6	as	as	ADP
ejpam-5189	11	7	concepts	concept	NOUN
ejpam-5189	11	8	related	relate	VERB
ejpam-5189	11	9	to	to	ADP
ejpam-5189	11	10	it	it	PRON
ejpam-5189	11	11	have	have	AUX
ejpam-5189	11	12	been	be	AUX
ejpam-5189	11	13	introduced	introduce	VERB
ejpam-5189	11	14	and	and	CCONJ
ejpam-5189	11	15	explored	explore	VERB
ejpam-5189	11	16	in	in	ADP
ejpam-5189	11	17	various	various	ADJ
ejpam-5189	11	18	aspects	aspect	NOUN
ejpam-5189	11	19	and	and	CCONJ
ejpam-5189	11	20	in	in	ADP
ejpam-5189	11	21	several	several	ADJ
ejpam-5189	11	22	graphs	graph	NOUN
ejpam-5189	11	23	(	(	PUNCT
ejpam-5189	11	24	including	include	VERB
ejpam-5189	11	25	those	those	DET
ejpam-5189	11	26	graphs	graph	NOUN
ejpam-5189	11	27	resulting	result	VERB
ejpam-5189	11	28	from	from	ADP
ejpam-5189	11	29	binary	binary	ADJ
ejpam-5189	11	30	operations	operation	NOUN
ejpam-5189	11	31	)	)	PUNCT
ejpam-5189	11	32	.	.	PUNCT
ejpam-5189	12	1	two	two	NUM
ejpam-5189	12	2	of	of	ADP
ejpam-5189	12	3	its	its	PRON
ejpam-5189	12	4	variants	variant	NOUN
ejpam-5189	12	5	utilized	utilize	VERB
ejpam-5189	12	6	the	the	DET
ejpam-5189	12	7	concepts	concept	NOUN
ejpam-5189	12	8	of	of	ADP
ejpam-5189	12	9	geodetic	geodetic	ADJ
ejpam-5189	12	10	and	and	CCONJ
ejpam-5189	12	11	convex	convex	NOUN
ejpam-5189	12	12	sets	set	NOUN
ejpam-5189	12	13	.	.	PUNCT
ejpam-5189	13	1	for	for	ADP
ejpam-5189	13	2	studies	study	NOUN
ejpam-5189	13	3	that	that	PRON
ejpam-5189	13	4	involve	involve	VERB
ejpam-5189	13	5	these	these	DET
ejpam-5189	13	6	concepts	concept	NOUN
ejpam-5189	13	7	one	one	PRON
ejpam-5189	13	8	may	may	AUX
ejpam-5189	13	9	consider	consider	VERB
ejpam-5189	13	10	[	[	X
ejpam-5189	13	11	5	5	NUM
ejpam-5189	13	12	]	]	PUNCT
ejpam-5189	13	13	,	,	PUNCT
ejpam-5189	13	14	[	[	X
ejpam-5189	13	15	4	4	NUM
ejpam-5189	13	16	]	]	PUNCT
ejpam-5189	13	17	,	,	PUNCT
ejpam-5189	13	18	[	[	X
ejpam-5189	13	19	9	9	NUM
ejpam-5189	13	20	]	]	PUNCT
ejpam-5189	13	21	,	,	PUNCT
ejpam-5189	13	22	and	and	CCONJ
ejpam-5189	13	23	[	[	X
ejpam-5189	13	24	22	22	NUM
ejpam-5189	13	25	]	]	PUNCT
ejpam-5189	13	26	.	.	PUNCT
ejpam-5189	14	1	for	for	ADP
ejpam-5189	14	2	some	some	DET
ejpam-5189	14	3	variations	variation	NOUN
ejpam-5189	14	4	of	of	ADP
ejpam-5189	14	5	domination	domination	NOUN
ejpam-5189	14	6	,	,	PUNCT
ejpam-5189	14	7	one	one	PRON
ejpam-5189	14	8	may	may	AUX
ejpam-5189	14	9	refer	refer	VERB
ejpam-5189	14	10	to	to	ADP
ejpam-5189	14	11	[	[	X
ejpam-5189	14	12	3	3	NUM
ejpam-5189	14	13	]	]	PUNCT
ejpam-5189	14	14	,	,	PUNCT
ejpam-5189	14	15	[	[	X
ejpam-5189	14	16	10	10	NUM
ejpam-5189	14	17	]	]	PUNCT
ejpam-5189	14	18	,	,	PUNCT
ejpam-5189	14	19	[	[	X
ejpam-5189	14	20	13	13	NUM
ejpam-5189	14	21	]	]	PUNCT
ejpam-5189	14	22	,	,	PUNCT
ejpam-5189	14	23	[	[	X
ejpam-5189	14	24	20	20	NUM
ejpam-5189	14	25	]	]	PUNCT
ejpam-5189	14	26	,	,	PUNCT
ejpam-5189	14	27	[	[	X
ejpam-5189	14	28	23	23	NUM
ejpam-5189	14	29	]	]	PUNCT
ejpam-5189	14	30	and	and	CCONJ
ejpam-5189	14	31	[	[	X
ejpam-5189	14	32	25	25	NUM
ejpam-5189	14	33	]	]	PUNCT
ejpam-5189	14	34	.	.	PUNCT
ejpam-5189	15	1	recently	recently	ADV
ejpam-5189	15	2	,	,	PUNCT
ejpam-5189	15	3	motivated	motivate	VERB
ejpam-5189	15	4	by	by	ADP
ejpam-5189	15	5	some	some	DET
ejpam-5189	15	6	historical	historical	ADJ
ejpam-5189	15	7	and	and	CCONJ
ejpam-5189	15	8	theoretical	theoretical	ADJ
ejpam-5189	15	9	applications	application	NOUN
ejpam-5189	15	10	,	,	PUNCT
ejpam-5189	15	11	roman	roman	ADJ
ejpam-5189	15	12	and	and	CCONJ
ejpam-5189	15	13	italian	italian	ADJ
ejpam-5189	15	14	domination	domination	NOUN
ejpam-5189	15	15	concepts	concept	NOUN
ejpam-5189	15	16	have	have	AUX
ejpam-5189	15	17	also	also	ADV
ejpam-5189	15	18	been	be	AUX
ejpam-5189	15	19	studied	study	VERB
ejpam-5189	15	20	(	(	PUNCT
ejpam-5189	15	21	see	see	VERB
ejpam-5189	15	22	[	[	X
ejpam-5189	15	23	1	1	NUM
ejpam-5189	15	24	]	]	PUNCT
ejpam-5189	15	25	,	,	PUNCT
ejpam-5189	15	26	[	[	X
ejpam-5189	15	27	2	2	NUM
ejpam-5189	15	28	]	]	PUNCT
ejpam-5189	15	29	,	,	PUNCT
ejpam-5189	15	30	[	[	X
ejpam-5189	15	31	11	11	NUM
ejpam-5189	15	32	]	]	PUNCT
ejpam-5189	15	33	,	,	PUNCT
ejpam-5189	15	34	[	[	X
ejpam-5189	15	35	12	12	NUM
ejpam-5189	15	36	]	]	PUNCT
ejpam-5189	15	37	,	,	PUNCT
ejpam-5189	15	38	[	[	X
ejpam-5189	15	39	14	14	NUM
ejpam-5189	15	40	]	]	PUNCT
ejpam-5189	15	41	,	,	PUNCT
ejpam-5189	15	42	[	[	X
ejpam-5189	15	43	16	16	NUM
ejpam-5189	15	44	]	]	PUNCT
ejpam-5189	15	45	,	,	PUNCT
ejpam-5189	15	46	[	[	X
ejpam-5189	15	47	18	18	NUM
ejpam-5189	15	48	]	]	PUNCT
ejpam-5189	15	49	,	,	PUNCT
ejpam-5189	15	50	[	[	X
ejpam-5189	15	51	21	21	NUM
ejpam-5189	15	52	]	]	PUNCT
ejpam-5189	15	53	,	,	PUNCT
ejpam-5189	15	54	[	[	X
ejpam-5189	15	55	26	26	NUM
ejpam-5189	15	56	]	]	PUNCT
ejpam-5189	15	57	,	,	PUNCT
ejpam-5189	15	58	[	[	X
ejpam-5189	15	59	27	27	NUM
ejpam-5189	15	60	]	]	PUNCT
ejpam-5189	15	61	,	,	PUNCT
ejpam-5189	15	62	and	and	CCONJ
ejpam-5189	15	63	[	[	X
ejpam-5189	15	64	28	28	NUM
ejpam-5189	15	65	]	]	NUM
ejpam-5189	15	66	)	)	PUNCT
ejpam-5189	15	67	.	.	PUNCT
ejpam-5189	16	1	∗corresponding	∗corresponde	VERB
ejpam-5189	16	2	author	author	NOUN
ejpam-5189	16	3	.	.	PUNCT
ejpam-5189	17	1	doi	doi	NOUN
ejpam-5189	17	2	:	:	PUNCT
ejpam-5189	17	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5189	https://doi.org/10.29020/nybg.ejpam.v17i3.5189	PRON
ejpam-5189	17	4	email	email	NOUN
ejpam-5189	17	5	addresses	address	NOUN
ejpam-5189	17	6	:	:	PUNCT
ejpam-5189	17	7	sergio.cano@g.msuiit.edu.ph	sergio.cano@g.msuiit.edu.ph	PROPN
ejpam-5189	17	8	(	(	PUNCT
ejpam-5189	17	9	s.	s.	PROPN
ejpam-5189	17	10	canoy	canoy	PROPN
ejpam-5189	17	11	,	,	PUNCT
ejpam-5189	17	12	jr	jr	PROPN
ejpam-5189	17	13	.	.	PROPN
ejpam-5189	17	14	)	)	PUNCT
ejpam-5189	17	15	,	,	PUNCT
ejpam-5189	17	16	ferdinand.jamil@g.msuiit.edu.ph	ferdinand.jamil@g.msuiit.edu.ph	PROPN
ejpam-5189	17	17	(	(	PUNCT
ejpam-5189	17	18	f.	f.	PROPN
ejpam-5189	17	19	jamil	jamil	PROPN
ejpam-5189	17	20	)	)	PUNCT
ejpam-5189	17	21	,	,	PUNCT
ejpam-5189	17	22	ronajane.fortosa@g.msuiit.edu.ph	ronajane.fortosa@g.msuiit.edu.ph	PROPN
ejpam-5189	17	23	(	(	PUNCT
ejpam-5189	17	24	rj	rj	PROPN
ejpam-5189	17	25	.	.	PROPN
ejpam-5189	17	26	fortosa	fortosa	PROPN
ejpam-5189	17	27	)	)	PUNCT
ejpam-5189	17	28	,	,	PUNCT
ejpam-5189	17	29	jead.macalisang@g.msuiit.edu.ph	jead.macalisang@g.msuiit.edu.ph	PROPN
ejpam-5189	17	30	(	(	PUNCT
ejpam-5189	17	31	j.	j.	PROPN
ejpam-5189	17	32	macalisang	macalisang	PROPN
ejpam-5189	17	33	)	)	PUNCT
ejpam-5189	17	34	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5189	17	35	1539	1539	NUM
ejpam-5189	18	1	©	©	ADP
ejpam-5189	18	2	2024	2024	NUM
ejpam-5189	18	3	ejpam	ejpam	NOUN
ejpam-5189	18	4	all	all	DET
ejpam-5189	18	5	rights	right	NOUN
ejpam-5189	18	6	reserved	reserve	VERB
ejpam-5189	18	7	.	.	PUNCT
ejpam-5189	19	1	r.	r.	PROPN
ejpam-5189	19	2	j.	j.	PROPN
ejpam-5189	19	3	g.	g.	PROPN
ejpam-5189	19	4	fortosa	fortosa	PROPN
ejpam-5189	19	5	et	et	PROPN
ejpam-5189	19	6	al	al	PROPN
ejpam-5189	19	7	.	.	PUNCT
ejpam-5189	19	8	/	/	SYM
ejpam-5189	19	9	eur	eur	PROPN
ejpam-5189	19	10	.	.	PUNCT
ejpam-5189	20	1	j.	j.	PROPN
ejpam-5189	20	2	pure	pure	PROPN
ejpam-5189	20	3	appl	appl	PROPN
ejpam-5189	20	4	.	.	PROPN
ejpam-5189	20	5	math	math	PROPN
ejpam-5189	20	6	,	,	PUNCT
ejpam-5189	20	7	17	17	NUM
ejpam-5189	20	8	(	(	PUNCT
ejpam-5189	20	9	3	3	NUM
ejpam-5189	20	10	)	)	PUNCT
ejpam-5189	20	11	(	(	PUNCT
ejpam-5189	20	12	2024	2024	NUM
ejpam-5189	20	13	)	)	PUNCT
ejpam-5189	20	14	,	,	PUNCT
ejpam-5189	20	15	1539	1539	NUM
ejpam-5189	20	16	-	-	SYM
ejpam-5189	20	17	1552	1552	NUM
ejpam-5189	20	18	1540	1540	NUM
ejpam-5189	20	19	one	one	NUM
ejpam-5189	20	20	can	can	AUX
ejpam-5189	20	21	readily	readily	ADV
ejpam-5189	20	22	observe	observe	VERB
ejpam-5189	20	23	that	that	SCONJ
ejpam-5189	20	24	a	a	DET
ejpam-5189	20	25	variant	variant	NOUN
ejpam-5189	20	26	of	of	ADP
ejpam-5189	20	27	the	the	DET
ejpam-5189	20	28	domination	domination	NOUN
ejpam-5189	20	29	concept	concept	NOUN
ejpam-5189	20	30	is	be	AUX
ejpam-5189	20	31	usually	usually	ADV
ejpam-5189	20	32	obtained	obtain	VERB
ejpam-5189	20	33	by	by	ADP
ejpam-5189	20	34	combining	combine	VERB
ejpam-5189	20	35	a	a	DET
ejpam-5189	20	36	domination	domination	NOUN
ejpam-5189	20	37	concept	concept	NOUN
ejpam-5189	20	38	with	with	ADP
ejpam-5189	20	39	other	other	ADJ
ejpam-5189	20	40	graph	graph	NOUN
ejpam-5189	20	41	-	-	PUNCT
ejpam-5189	20	42	theoretic	theoretic	NOUN
ejpam-5189	20	43	concepts	concept	NOUN
ejpam-5189	20	44	.	.	PUNCT
ejpam-5189	21	1	for	for	ADP
ejpam-5189	21	2	example	example	NOUN
ejpam-5189	21	3	,	,	PUNCT
ejpam-5189	21	4	convex	convex	ADJ
ejpam-5189	21	5	domination	domination	NOUN
ejpam-5189	21	6	is	be	AUX
ejpam-5189	21	7	simply	simply	ADV
ejpam-5189	21	8	the	the	DET
ejpam-5189	21	9	combination	combination	NOUN
ejpam-5189	21	10	of	of	ADP
ejpam-5189	21	11	the	the	DET
ejpam-5189	21	12	standard	standard	ADJ
ejpam-5189	21	13	domination	domination	NOUN
ejpam-5189	21	14	and	and	CCONJ
ejpam-5189	21	15	the	the	DET
ejpam-5189	21	16	notion	notion	NOUN
ejpam-5189	21	17	of	of	ADP
ejpam-5189	21	18	convexity	convexity	NOUN
ejpam-5189	21	19	in	in	ADP
ejpam-5189	21	20	graphs	graph	NOUN
ejpam-5189	21	21	(	(	PUNCT
ejpam-5189	21	22	see	see	VERB
ejpam-5189	21	23	[	[	X
ejpam-5189	21	24	8	8	NUM
ejpam-5189	21	25	]	]	PUNCT
ejpam-5189	21	26	,	,	PUNCT
ejpam-5189	21	27	[	[	X
ejpam-5189	21	28	17	17	NUM
ejpam-5189	21	29	]	]	PUNCT
ejpam-5189	21	30	,	,	PUNCT
ejpam-5189	21	31	and	and	CCONJ
ejpam-5189	21	32	[	[	X
ejpam-5189	21	33	24	24	NUM
ejpam-5189	21	34	]	]	PUNCT
ejpam-5189	21	35	)	)	PUNCT
ejpam-5189	21	36	.	.	PUNCT
ejpam-5189	22	1	in	in	ADP
ejpam-5189	22	2	this	this	DET
ejpam-5189	22	3	paper	paper	NOUN
ejpam-5189	22	4	,	,	PUNCT
ejpam-5189	22	5	the	the	DET
ejpam-5189	22	6	concept	concept	NOUN
ejpam-5189	22	7	of	of	ADP
ejpam-5189	22	8	convex	convex	PROPN
ejpam-5189	22	9	2domination	2domination	NUM
ejpam-5189	22	10	will	will	AUX
ejpam-5189	22	11	be	be	AUX
ejpam-5189	22	12	introduced	introduce	VERB
ejpam-5189	22	13	and	and	CCONJ
ejpam-5189	22	14	investigated	investigate	VERB
ejpam-5189	22	15	.	.	PUNCT
ejpam-5189	23	1	this	this	DET
ejpam-5189	23	2	new	new	ADJ
ejpam-5189	23	3	concept	concept	NOUN
ejpam-5189	23	4	is	be	AUX
ejpam-5189	23	5	a	a	DET
ejpam-5189	23	6	combination	combination	NOUN
ejpam-5189	23	7	of	of	ADP
ejpam-5189	23	8	convexity	convexity	NOUN
ejpam-5189	23	9	and	and	CCONJ
ejpam-5189	23	10	2	2	NUM
ejpam-5189	23	11	-	-	PUNCT
ejpam-5189	23	12	domination	domination	NOUN
ejpam-5189	23	13	.	.	PUNCT
ejpam-5189	24	1	as	as	SCONJ
ejpam-5189	24	2	used	use	VERB
ejpam-5189	24	3	to	to	PART
ejpam-5189	24	4	model	model	VERB
ejpam-5189	24	5	a	a	DET
ejpam-5189	24	6	protection	protection	NOUN
ejpam-5189	24	7	strategy	strategy	NOUN
ejpam-5189	24	8	problem	problem	NOUN
ejpam-5189	24	9	in	in	ADP
ejpam-5189	24	10	a	a	DET
ejpam-5189	24	11	given	give	VERB
ejpam-5189	24	12	network	network	NOUN
ejpam-5189	24	13	,	,	PUNCT
ejpam-5189	24	14	every	every	DET
ejpam-5189	24	15	vertex	vertex	NOUN
ejpam-5189	24	16	(	(	PUNCT
ejpam-5189	24	17	location	location	NOUN
ejpam-5189	24	18	)	)	PUNCT
ejpam-5189	24	19	which	which	PRON
ejpam-5189	24	20	is	be	AUX
ejpam-5189	24	21	not	not	PART
ejpam-5189	24	22	in	in	ADP
ejpam-5189	24	23	a	a	DET
ejpam-5189	24	24	2	2	NUM
ejpam-5189	24	25	-	-	PUNCT
ejpam-5189	24	26	dominating	dominating	NOUN
ejpam-5189	24	27	set	set	NOUN
ejpam-5189	24	28	will	will	AUX
ejpam-5189	24	29	be	be	AUX
ejpam-5189	24	30	considered	consider	VERB
ejpam-5189	24	31	unsafe	unsafe	ADJ
ejpam-5189	24	32	(	(	PUNCT
ejpam-5189	24	33	as	as	SCONJ
ejpam-5189	24	34	it	it	PRON
ejpam-5189	24	35	contains	contain	VERB
ejpam-5189	24	36	no	no	DET
ejpam-5189	24	37	guard	guard	NOUN
ejpam-5189	24	38	)	)	PUNCT
ejpam-5189	24	39	.	.	PUNCT
ejpam-5189	25	1	hence	hence	ADV
ejpam-5189	25	2	,	,	PUNCT
ejpam-5189	25	3	the	the	DET
ejpam-5189	25	4	elements	element	NOUN
ejpam-5189	25	5	of	of	ADP
ejpam-5189	25	6	a	a	DET
ejpam-5189	25	7	2	2	NUM
ejpam-5189	25	8	-	-	PUNCT
ejpam-5189	25	9	dominating	dominating	NOUN
ejpam-5189	25	10	set	set	NOUN
ejpam-5189	25	11	are	be	AUX
ejpam-5189	25	12	the	the	DET
ejpam-5189	25	13	ones	one	NOUN
ejpam-5189	25	14	considered	consider	VERB
ejpam-5189	25	15	safe	safe	ADJ
ejpam-5189	25	16	locations	location	NOUN
ejpam-5189	25	17	in	in	ADP
ejpam-5189	25	18	the	the	DET
ejpam-5189	25	19	network	network	NOUN
ejpam-5189	25	20	and	and	CCONJ
ejpam-5189	25	21	each	each	DET
ejpam-5189	25	22	location	location	NOUN
ejpam-5189	25	23	contains	contain	VERB
ejpam-5189	25	24	a	a	DET
ejpam-5189	25	25	guard	guard	NOUN
ejpam-5189	25	26	.	.	PUNCT
ejpam-5189	26	1	to	to	PART
ejpam-5189	26	2	defend	defend	VERB
ejpam-5189	26	3	or	or	CCONJ
ejpam-5189	26	4	secure	secure	VERB
ejpam-5189	26	5	a	a	DET
ejpam-5189	26	6	given	give	VERB
ejpam-5189	26	7	network	network	NOUN
ejpam-5189	26	8	,	,	PUNCT
ejpam-5189	26	9	every	every	DET
ejpam-5189	26	10	unsafe	unsafe	ADJ
ejpam-5189	26	11	location	location	NOUN
ejpam-5189	26	12	must	must	AUX
ejpam-5189	26	13	be	be	AUX
ejpam-5189	26	14	adjacent	adjacent	ADJ
ejpam-5189	26	15	to	to	ADP
ejpam-5189	26	16	at	at	ADV
ejpam-5189	26	17	least	least	ADV
ejpam-5189	26	18	two	two	NUM
ejpam-5189	26	19	safe	safe	ADJ
ejpam-5189	26	20	locations	location	NOUN
ejpam-5189	26	21	.	.	PUNCT
ejpam-5189	27	1	this	this	PRON
ejpam-5189	27	2	ensures	ensure	VERB
ejpam-5189	27	3	that	that	SCONJ
ejpam-5189	27	4	when	when	SCONJ
ejpam-5189	27	5	an	an	DET
ejpam-5189	27	6	unsafe	unsafe	ADJ
ejpam-5189	27	7	location	location	NOUN
ejpam-5189	27	8	is	be	AUX
ejpam-5189	27	9	attacked	attack	VERB
ejpam-5189	27	10	,	,	PUNCT
ejpam-5189	27	11	a	a	DET
ejpam-5189	27	12	location	location	NOUN
ejpam-5189	27	13	is	be	AUX
ejpam-5189	27	14	within	within	ADP
ejpam-5189	27	15	the	the	DET
ejpam-5189	27	16	vicinity	vicinity	NOUN
ejpam-5189	27	17	of	of	ADP
ejpam-5189	27	18	the	the	DET
ejpam-5189	27	19	guards	guard	NOUN
ejpam-5189	27	20	from	from	ADP
ejpam-5189	27	21	these	these	DET
ejpam-5189	27	22	safe	safe	ADJ
ejpam-5189	27	23	locations	location	NOUN
ejpam-5189	27	24	.	.	PUNCT
ejpam-5189	28	1	the	the	DET
ejpam-5189	28	2	convexity	convexity	NOUN
ejpam-5189	28	3	property	property	NOUN
ejpam-5189	28	4	attached	attach	VERB
ejpam-5189	28	5	to	to	ADP
ejpam-5189	28	6	the	the	DET
ejpam-5189	28	7	concept	concept	NOUN
ejpam-5189	28	8	guarantees	guarantee	VERB
ejpam-5189	28	9	that	that	SCONJ
ejpam-5189	28	10	every	every	DET
ejpam-5189	28	11	location	location	NOUN
ejpam-5189	28	12	in	in	ADP
ejpam-5189	28	13	any	any	DET
ejpam-5189	28	14	shortest	short	ADJ
ejpam-5189	28	15	path	path	NOUN
ejpam-5189	28	16	connecting	connect	VERB
ejpam-5189	28	17	two	two	NUM
ejpam-5189	28	18	safe	safe	ADJ
ejpam-5189	28	19	locations	location	NOUN
ejpam-5189	28	20	is	be	AUX
ejpam-5189	28	21	also	also	ADV
ejpam-5189	28	22	safe	safe	ADJ
ejpam-5189	28	23	.	.	PUNCT
ejpam-5189	29	1	this	this	DET
ejpam-5189	29	2	newly	newly	ADV
ejpam-5189	29	3	defined	define	VERB
ejpam-5189	29	4	concept	concept	NOUN
ejpam-5189	29	5	is	be	AUX
ejpam-5189	29	6	useful	useful	ADJ
ejpam-5189	29	7	when	when	SCONJ
ejpam-5189	29	8	studying	study	VERB
ejpam-5189	29	9	a	a	DET
ejpam-5189	29	10	variation	variation	NOUN
ejpam-5189	29	11	of	of	ADP
ejpam-5189	29	12	italian	italian	ADJ
ejpam-5189	29	13	domination	domination	NOUN
ejpam-5189	29	14	,	,	PUNCT
ejpam-5189	29	15	in	in	ADP
ejpam-5189	29	16	particular	particular	ADJ
ejpam-5189	29	17	,	,	PUNCT
ejpam-5189	29	18	convex	convex	ADJ
ejpam-5189	29	19	italian	italian	ADJ
ejpam-5189	29	20	domination	domination	NOUN
ejpam-5189	29	21	[	[	X
ejpam-5189	29	22	19	19	NUM
ejpam-5189	29	23	]	]	PUNCT
ejpam-5189	29	24	.	.	PUNCT
ejpam-5189	30	1	2	2	X
ejpam-5189	30	2	.	.	X
ejpam-5189	30	3	terminologies	terminology	NOUN
ejpam-5189	30	4	and	and	CCONJ
ejpam-5189	30	5	notations	notation	NOUN
ejpam-5189	30	6	for	for	ADP
ejpam-5189	30	7	a	a	DET
ejpam-5189	30	8	connected	connected	ADJ
ejpam-5189	30	9	graph	graph	NOUN
ejpam-5189	30	10	g	g	PROPN
ejpam-5189	30	11	=	=	PUNCT
ejpam-5189	30	12	(	(	PUNCT
ejpam-5189	30	13	v	v	NOUN
ejpam-5189	30	14	(	(	PUNCT
ejpam-5189	30	15	g	g	NOUN
ejpam-5189	30	16	)	)	PUNCT
ejpam-5189	30	17	,	,	PUNCT
ejpam-5189	30	18	e(g	e(g	PROPN
ejpam-5189	30	19	)	)	PUNCT
ejpam-5189	30	20	and	and	CCONJ
ejpam-5189	30	21	vertices	vertice	VERB
ejpam-5189	30	22	u	u	NOUN
ejpam-5189	30	23	and	and	CCONJ
ejpam-5189	30	24	v	v	NOUN
ejpam-5189	30	25	of	of	ADP
ejpam-5189	30	26	g	g	NOUN
ejpam-5189	30	27	,	,	PUNCT
ejpam-5189	30	28	any	any	DET
ejpam-5189	30	29	shortest	short	ADJ
ejpam-5189	30	30	path	path	NOUN
ejpam-5189	30	31	joining	join	VERB
ejpam-5189	30	32	u	u	NOUN
ejpam-5189	30	33	and	and	CCONJ
ejpam-5189	30	34	v	v	NOUN
ejpam-5189	30	35	is	be	AUX
ejpam-5189	30	36	called	call	VERB
ejpam-5189	30	37	a	a	DET
ejpam-5189	30	38	u	u	NOUN
ejpam-5189	30	39	-	-	NOUN
ejpam-5189	30	40	v	v	ADJ
ejpam-5189	30	41	geodesic	geodesic	NOUN
ejpam-5189	30	42	.	.	PUNCT
ejpam-5189	31	1	the	the	DET
ejpam-5189	31	2	length	length	NOUN
ejpam-5189	31	3	of	of	ADP
ejpam-5189	31	4	a	a	DET
ejpam-5189	31	5	u	u	NOUN
ejpam-5189	31	6	-	-	NOUN
ejpam-5189	31	7	v	v	ADJ
ejpam-5189	31	8	geodesic	geodesic	NOUN
ejpam-5189	31	9	is	be	AUX
ejpam-5189	31	10	the	the	DET
ejpam-5189	31	11	distance	distance	NOUN
ejpam-5189	31	12	between	between	ADP
ejpam-5189	31	13	u	u	NOUN
ejpam-5189	31	14	and	and	CCONJ
ejpam-5189	31	15	v.	v.	ADP
ejpam-5189	31	16	this	this	DET
ejpam-5189	31	17	distance	distance	NOUN
ejpam-5189	31	18	is	be	AUX
ejpam-5189	31	19	denoted	denote	VERB
ejpam-5189	31	20	by	by	ADP
ejpam-5189	31	21	dg(u	dg(u	NOUN
ejpam-5189	31	22	,	,	PUNCT
ejpam-5189	31	23	v	v	NOUN
ejpam-5189	31	24	)	)	PUNCT
ejpam-5189	31	25	.	.	PUNCT
ejpam-5189	32	1	the	the	DET
ejpam-5189	32	2	set	set	NOUN
ejpam-5189	32	3	ig[u	ig[u	PROPN
ejpam-5189	32	4	,	,	PUNCT
ejpam-5189	32	5	v	v	NOUN
ejpam-5189	32	6	]	]	PUNCT
ejpam-5189	32	7	consists	consist	VERB
ejpam-5189	32	8	of	of	ADP
ejpam-5189	32	9	vertices	vertex	NOUN
ejpam-5189	32	10	u	u	NOUN
ejpam-5189	32	11	and	and	CCONJ
ejpam-5189	32	12	v	v	NOUN
ejpam-5189	32	13	and	and	CCONJ
ejpam-5189	32	14	those	those	PRON
ejpam-5189	32	15	lying	lie	VERB
ejpam-5189	32	16	on	on	ADP
ejpam-5189	32	17	any	any	DET
ejpam-5189	32	18	u	u	NOUN
ejpam-5189	32	19	-	-	NOUN
ejpam-5189	32	20	v	v	ADJ
ejpam-5189	32	21	geodesic	geodesic	NOUN
ejpam-5189	32	22	.	.	PUNCT
ejpam-5189	33	1	here	here	ADV
ejpam-5189	33	2	,	,	PUNCT
ejpam-5189	33	3	ig(u	ig(u	ADJ
ejpam-5189	33	4	,	,	PUNCT
ejpam-5189	33	5	v	v	NOUN
ejpam-5189	33	6	)	)	PUNCT
ejpam-5189	33	7	=	=	PUNCT
ejpam-5189	33	8	ig[u	ig[u	PROPN
ejpam-5189	33	9	,	,	PUNCT
ejpam-5189	33	10	v	v	NOUN
ejpam-5189	33	11	]	]	PUNCT
ejpam-5189	33	12	\	\	PUNCT
ejpam-5189	33	13	{	{	PUNCT
ejpam-5189	33	14	u	u	NOUN
ejpam-5189	33	15	,	,	PUNCT
ejpam-5189	33	16	v	v	NOUN
ejpam-5189	33	17	}	}	PUNCT
ejpam-5189	33	18	.	.	PUNCT
ejpam-5189	34	1	the	the	DET
ejpam-5189	34	2	set	set	NOUN
ejpam-5189	34	3	ng(u	ng(u	NOUN
ejpam-5189	34	4	)	)	PUNCT
ejpam-5189	34	5	is	be	AUX
ejpam-5189	34	6	called	call	VERB
ejpam-5189	34	7	the	the	DET
ejpam-5189	34	8	open	open	ADJ
ejpam-5189	34	9	neighborhood	neighborhood	NOUN
ejpam-5189	34	10	of	of	ADP
ejpam-5189	34	11	u	u	NOUN
ejpam-5189	34	12	,	,	PUNCT
ejpam-5189	34	13	i.e.	i.e.	X
ejpam-5189	34	14	,	,	PUNCT
ejpam-5189	34	15	ng(u	ng(u	NOUN
ejpam-5189	34	16	)	)	PUNCT
ejpam-5189	34	17	consists	consist	VERB
ejpam-5189	34	18	of	of	ADP
ejpam-5189	34	19	all	all	DET
ejpam-5189	34	20	v	v	ADP
ejpam-5189	34	21	∈	∈	NOUN
ejpam-5189	34	22	v	v	NOUN
ejpam-5189	34	23	(	(	PUNCT
ejpam-5189	34	24	g	g	NOUN
ejpam-5189	34	25	)	)	PUNCT
ejpam-5189	34	26	such	such	ADJ
ejpam-5189	34	27	that	that	SCONJ
ejpam-5189	34	28	uv	uv	PROPN
ejpam-5189	34	29	∈	∈	PROPN
ejpam-5189	34	30	e(g	e(g	PROPN
ejpam-5189	34	31	)	)	PUNCT
ejpam-5189	34	32	.	.	PUNCT
ejpam-5189	35	1	the	the	DET
ejpam-5189	35	2	closed	closed	ADJ
ejpam-5189	35	3	neighborhood	neighborhood	NOUN
ejpam-5189	35	4	of	of	ADP
ejpam-5189	35	5	u	u	NOUN
ejpam-5189	35	6	is	be	AUX
ejpam-5189	35	7	the	the	DET
ejpam-5189	35	8	set	set	NOUN
ejpam-5189	35	9	ng[u	ng[u	PROPN
ejpam-5189	35	10	]	]	X
ejpam-5189	35	11	=	=	SYM
ejpam-5189	35	12	ng(u	ng(u	PROPN
ejpam-5189	35	13	)	)	PUNCT
ejpam-5189	35	14	∪	∪	NOUN
ejpam-5189	35	15	{	{	PUNCT
ejpam-5189	35	16	u	u	NOUN
ejpam-5189	35	17	}	}	PUNCT
ejpam-5189	35	18	.	.	PUNCT
ejpam-5189	36	1	if	if	SCONJ
ejpam-5189	36	2	s	s	VERB
ejpam-5189	36	3	⊆	⊆	NUM
ejpam-5189	36	4	v	v	NOUN
ejpam-5189	36	5	(	(	PUNCT
ejpam-5189	36	6	g	g	NOUN
ejpam-5189	36	7	)	)	PUNCT
ejpam-5189	36	8	,	,	PUNCT
ejpam-5189	36	9	then	then	ADV
ejpam-5189	36	10	ng(s	ng(s	PUNCT
ejpam-5189	36	11	)	)	PUNCT
ejpam-5189	36	12	=	=	SYM
ejpam-5189	36	13	∪v∈sng(v	∪v∈sng(v	PROPN
ejpam-5189	36	14	)	)	PUNCT
ejpam-5189	36	15	and	and	CCONJ
ejpam-5189	36	16	ng[s	ng[s	PROPN
ejpam-5189	36	17	]	]	PUNCT
ejpam-5189	36	18	=	=	SYM
ejpam-5189	36	19	n(s	n(s	PROPN
ejpam-5189	36	20	)	)	PUNCT
ejpam-5189	36	21	∪	∪	ADP
ejpam-5189	36	22	s.	s.	PROPN
ejpam-5189	36	23	the	the	DET
ejpam-5189	36	24	degree	degree	NOUN
ejpam-5189	36	25	of	of	ADP
ejpam-5189	36	26	a	a	DET
ejpam-5189	36	27	vertex	vertex	NOUN
ejpam-5189	36	28	v	v	NOUN
ejpam-5189	36	29	,	,	PUNCT
ejpam-5189	36	30	denoted	denote	VERB
ejpam-5189	36	31	by	by	ADP
ejpam-5189	36	32	degg(v	degg(v	PROPN
ejpam-5189	36	33	)	)	PUNCT
ejpam-5189	36	34	,	,	PUNCT
ejpam-5189	36	35	is	be	AUX
ejpam-5189	36	36	given	give	VERB
ejpam-5189	36	37	by	by	ADP
ejpam-5189	36	38	degg(v	degg(v	PROPN
ejpam-5189	36	39	)	)	PUNCT
ejpam-5189	36	40	=	=	SYM
ejpam-5189	36	41	|n(v)|	|n(v)|	PROPN
ejpam-5189	36	42	.	.	PUNCT
ejpam-5189	36	43	a	a	DET
ejpam-5189	36	44	vertex	vertex	NOUN
ejpam-5189	36	45	of	of	ADP
ejpam-5189	36	46	degree	degree	NOUN
ejpam-5189	36	47	1	1	NUM
ejpam-5189	36	48	is	be	AUX
ejpam-5189	36	49	called	call	VERB
ejpam-5189	36	50	an	an	DET
ejpam-5189	36	51	end	end	NOUN
ejpam-5189	36	52	-	-	PUNCT
ejpam-5189	36	53	vertex	vertex	NOUN
ejpam-5189	36	54	or	or	CCONJ
ejpam-5189	36	55	a	a	DET
ejpam-5189	36	56	leaf	leaf	NOUN
ejpam-5189	36	57	.	.	PUNCT
ejpam-5189	37	1	if	if	SCONJ
ejpam-5189	37	2	v	v	NOUN
ejpam-5189	37	3	is	be	AUX
ejpam-5189	37	4	a	a	DET
ejpam-5189	37	5	leaf	leaf	NOUN
ejpam-5189	37	6	and	and	CCONJ
ejpam-5189	37	7	w	w	NOUN
ejpam-5189	37	8	∈	∈	PROPN
ejpam-5189	37	9	ng(v	ng(v	NOUN
ejpam-5189	37	10	)	)	PUNCT
ejpam-5189	37	11	,	,	PUNCT
ejpam-5189	37	12	then	then	ADV
ejpam-5189	37	13	w	w	PROPN
ejpam-5189	37	14	is	be	AUX
ejpam-5189	37	15	called	call	VERB
ejpam-5189	37	16	a	a	DET
ejpam-5189	37	17	support	support	NOUN
ejpam-5189	37	18	vertex	vertex	NOUN
ejpam-5189	37	19	.	.	PUNCT
ejpam-5189	38	1	a	a	DET
ejpam-5189	38	2	vertex	vertex	NOUN
ejpam-5189	38	3	v	v	NOUN
ejpam-5189	38	4	is	be	AUX
ejpam-5189	38	5	an	an	DET
ejpam-5189	38	6	extreme	extreme	ADJ
ejpam-5189	38	7	or	or	CCONJ
ejpam-5189	38	8	simplicial	simplicial	ADJ
ejpam-5189	38	9	vertex	vertex	NOUN
ejpam-5189	38	10	in	in	ADP
ejpam-5189	38	11	g	g	PROPN
ejpam-5189	38	12	if	if	SCONJ
ejpam-5189	38	13	ng(v	ng(v	NOUN
ejpam-5189	38	14	)	)	PUNCT
ejpam-5189	39	1	induces	induce	VERB
ejpam-5189	39	2	a	a	DET
ejpam-5189	39	3	complete	complete	ADJ
ejpam-5189	39	4	subgraph	subgraph	NOUN
ejpam-5189	39	5	of	of	ADP
ejpam-5189	39	6	g	g	NOUN
ejpam-5189	39	7	,	,	PUNCT
ejpam-5189	39	8	that	that	ADV
ejpam-5189	39	9	is	is	ADV
ejpam-5189	39	10	,	,	PUNCT
ejpam-5189	39	11	ext(g	ext(g	ADJ
ejpam-5189	39	12	)	)	PUNCT
ejpam-5189	40	1	=	=	PRON
ejpam-5189	40	2	{	{	PUNCT
ejpam-5189	40	3	v	v	NUM
ejpam-5189	40	4	∈	∈	NOUN
ejpam-5189	40	5	v	v	NOUN
ejpam-5189	40	6	(	(	PUNCT
ejpam-5189	40	7	g	g	NOUN
ejpam-5189	40	8	)	)	PUNCT
ejpam-5189	40	9	:	:	PUNCT
ejpam-5189	40	10	ng(v	ng(v	X
ejpam-5189	40	11	)	)	PUNCT
ejpam-5189	40	12	induces	induce	VERB
ejpam-5189	40	13	a	a	DET
ejpam-5189	40	14	complete	complete	ADJ
ejpam-5189	40	15	subgraph	subgraph	NOUN
ejpam-5189	40	16	of	of	ADP
ejpam-5189	40	17	g	g	NOUN
ejpam-5189	40	18	}	}	PUNCT
ejpam-5189	40	19	.	.	PUNCT
ejpam-5189	41	1	we	we	PRON
ejpam-5189	41	2	denote	denote	VERB
ejpam-5189	41	3	by	by	ADP
ejpam-5189	41	4	l(g	l(g	NOUN
ejpam-5189	41	5	)	)	PUNCT
ejpam-5189	41	6	,	,	PUNCT
ejpam-5189	41	7	s(g	s(g	PROPN
ejpam-5189	41	8	)	)	PUNCT
ejpam-5189	41	9	,	,	PUNCT
ejpam-5189	41	10	and	and	CCONJ
ejpam-5189	41	11	ext(g	ext(g	NOUN
ejpam-5189	41	12	)	)	PUNCT
ejpam-5189	41	13	the	the	DET
ejpam-5189	41	14	sets	set	NOUN
ejpam-5189	41	15	containing	contain	VERB
ejpam-5189	41	16	the	the	DET
ejpam-5189	41	17	leaves	leave	NOUN
ejpam-5189	41	18	,	,	PUNCT
ejpam-5189	41	19	the	the	DET
ejpam-5189	41	20	support	support	NOUN
ejpam-5189	41	21	,	,	PUNCT
ejpam-5189	41	22	and	and	CCONJ
ejpam-5189	41	23	the	the	DET
ejpam-5189	41	24	extreme	extreme	ADJ
ejpam-5189	41	25	vertices	vertex	NOUN
ejpam-5189	41	26	,	,	PUNCT
ejpam-5189	41	27	respectively	respectively	ADV
ejpam-5189	41	28	,	,	PUNCT
ejpam-5189	41	29	of	of	ADP
ejpam-5189	41	30	graph	graph	NOUN
ejpam-5189	41	31	g.	g.	PROPN
ejpam-5189	41	32	a	a	DET
ejpam-5189	41	33	set	set	NOUN
ejpam-5189	41	34	s	s	PROPN
ejpam-5189	41	35	⊆	⊆	NUM
ejpam-5189	41	36	v	v	NOUN
ejpam-5189	41	37	(	(	PUNCT
ejpam-5189	41	38	g	g	NOUN
ejpam-5189	41	39	)	)	PUNCT
ejpam-5189	41	40	is	be	AUX
ejpam-5189	41	41	non	non	ADJ
ejpam-5189	41	42	-	-	ADJ
ejpam-5189	41	43	connecting	connect	VERB
ejpam-5189	41	44	in	in	ADP
ejpam-5189	41	45	g	g	PROPN
ejpam-5189	41	46	if	if	SCONJ
ejpam-5189	41	47	for	for	ADP
ejpam-5189	41	48	every	every	DET
ejpam-5189	41	49	two	two	NUM
ejpam-5189	41	50	vertices	vertex	NOUN
ejpam-5189	41	51	x	x	X
ejpam-5189	41	52	,	,	PUNCT
ejpam-5189	41	53	y	y	PROPN
ejpam-5189	41	54	∈	∈	PROPN
ejpam-5189	41	55	v	v	ADP
ejpam-5189	41	56	(	(	PUNCT
ejpam-5189	41	57	g	g	NOUN
ejpam-5189	41	58	)	)	PUNCT
ejpam-5189	41	59	\	\	PROPN
ejpam-5189	42	1	s	s	PART
ejpam-5189	42	2	with	with	ADP
ejpam-5189	42	3	dg(x	dg(x	PROPN
ejpam-5189	42	4	,	,	PUNCT
ejpam-5189	42	5	y	y	NOUN
ejpam-5189	42	6	)	)	PUNCT
ejpam-5189	42	7	=	=	SYM
ejpam-5189	42	8	2	2	NUM
ejpam-5189	42	9	,	,	PUNCT
ejpam-5189	42	10	it	it	PRON
ejpam-5189	42	11	holds	hold	VERB
ejpam-5189	42	12	that	that	SCONJ
ejpam-5189	42	13	ng(x	ng(x	NUM
ejpam-5189	42	14	)	)	PUNCT
ejpam-5189	42	15	∩ng(y	∩ng(y	PROPN
ejpam-5189	42	16	)	)	PUNCT
ejpam-5189	42	17	∩	∩	NOUN
ejpam-5189	42	18	s	s	PART
ejpam-5189	42	19	=	=	PUNCT
ejpam-5189	42	20	∅.	∅.	VERB
ejpam-5189	42	21	a	a	DET
ejpam-5189	42	22	set	set	NOUN
ejpam-5189	42	23	s	s	NOUN
ejpam-5189	42	24	⊆	⊆	NUM
ejpam-5189	42	25	v	v	NOUN
ejpam-5189	42	26	(	(	PUNCT
ejpam-5189	42	27	g	g	NOUN
ejpam-5189	42	28	)	)	PUNCT
ejpam-5189	42	29	is	be	AUX
ejpam-5189	42	30	independent	independent	ADJ
ejpam-5189	42	31	if	if	SCONJ
ejpam-5189	42	32	dg(x	dg(x	NUM
ejpam-5189	42	33	,	,	PUNCT
ejpam-5189	42	34	y	y	NOUN
ejpam-5189	42	35	)	)	PUNCT
ejpam-5189	42	36	̸=	̸=	NOUN
ejpam-5189	42	37	1	1	NUM
ejpam-5189	42	38	for	for	ADP
ejpam-5189	42	39	every	every	DET
ejpam-5189	42	40	pair	pair	NOUN
ejpam-5189	42	41	of	of	ADP
ejpam-5189	42	42	distinct	distinct	ADJ
ejpam-5189	42	43	vertices	vertex	NOUN
ejpam-5189	42	44	x	x	X
ejpam-5189	42	45	,	,	PUNCT
ejpam-5189	42	46	y	y	PROPN
ejpam-5189	42	47	∈	∈	PROPN
ejpam-5189	42	48	s.	s.	PROPN
ejpam-5189	42	49	the	the	DET
ejpam-5189	42	50	set	set	PROPN
ejpam-5189	42	51	ind(g	ind(g	PROPN
ejpam-5189	42	52	)	)	PUNCT
ejpam-5189	42	53	denotes	denote	VERB
ejpam-5189	42	54	the	the	DET
ejpam-5189	42	55	set	set	NOUN
ejpam-5189	42	56	of	of	ADP
ejpam-5189	42	57	all	all	DET
ejpam-5189	42	58	vertices	vertex	NOUN
ejpam-5189	42	59	v	v	NOUN
ejpam-5189	42	60	of	of	ADP
ejpam-5189	42	61	g	g	NOUN
ejpam-5189	42	62	such	such	ADJ
ejpam-5189	42	63	that	that	SCONJ
ejpam-5189	42	64	ng(v	ng(v	PUNCT
ejpam-5189	42	65	)	)	PUNCT
ejpam-5189	42	66	is	be	AUX
ejpam-5189	42	67	an	an	DET
ejpam-5189	42	68	independent	independent	ADJ
ejpam-5189	42	69	subset	subset	NOUN
ejpam-5189	42	70	of	of	ADP
ejpam-5189	42	71	v	v	NOUN
ejpam-5189	42	72	(	(	PUNCT
ejpam-5189	42	73	g	g	NOUN
ejpam-5189	42	74	)	)	PUNCT
ejpam-5189	42	75	.	.	PUNCT
ejpam-5189	43	1	clearly	clearly	ADV
ejpam-5189	43	2	,	,	PUNCT
ejpam-5189	43	3	l(g	l(g	NOUN
ejpam-5189	43	4	)	)	PUNCT
ejpam-5189	43	5	⊆	⊆	NUM
ejpam-5189	43	6	ind(g	ind(g	NUM
ejpam-5189	43	7	)	)	PUNCT
ejpam-5189	43	8	.	.	PUNCT
ejpam-5189	44	1	a	a	DET
ejpam-5189	44	2	set	set	NOUN
ejpam-5189	44	3	s	s	NOUN
ejpam-5189	44	4	⊆	⊆	NUM
ejpam-5189	44	5	v	v	NOUN
ejpam-5189	44	6	(	(	PUNCT
ejpam-5189	44	7	g	g	NOUN
ejpam-5189	44	8	)	)	PUNCT
ejpam-5189	44	9	is	be	AUX
ejpam-5189	44	10	said	say	VERB
ejpam-5189	44	11	to	to	PART
ejpam-5189	44	12	be	be	AUX
ejpam-5189	44	13	dominating	dominate	VERB
ejpam-5189	44	14	(	(	PUNCT
ejpam-5189	44	15	resp	resp	NOUN
ejpam-5189	44	16	.	.	PUNCT
ejpam-5189	45	1	2	2	NUM
ejpam-5189	45	2	-	-	PUNCT
ejpam-5189	45	3	dominating	dominating	NOUN
ejpam-5189	45	4	)	)	PUNCT
ejpam-5189	45	5	in	in	ADP
ejpam-5189	45	6	g	g	PROPN
ejpam-5189	45	7	if	if	SCONJ
ejpam-5189	45	8	n	n	PROPN
ejpam-5189	45	9	[	[	X
ejpam-5189	45	10	s	s	X
ejpam-5189	45	11	]	]	X
ejpam-5189	45	12	=	=	SYM
ejpam-5189	45	13	v	v	X
ejpam-5189	45	14	(	(	PUNCT
ejpam-5189	45	15	g	g	NOUN
ejpam-5189	45	16	)	)	PUNCT
ejpam-5189	45	17	(	(	PUNCT
ejpam-5189	45	18	resp	resp	NOUN
ejpam-5189	45	19	.	.	PUNCT
ejpam-5189	46	1	|ng(v	|ng(v	PART
ejpam-5189	46	2	)	)	PUNCT
ejpam-5189	46	3	∩	∩	NOUN
ejpam-5189	46	4	s|	s|	VERB
ejpam-5189	46	5	≥	≥	NUM
ejpam-5189	46	6	2	2	NUM
ejpam-5189	46	7	for	for	ADP
ejpam-5189	46	8	every	every	PRON
ejpam-5189	46	9	v	v	NUM
ejpam-5189	46	10	∈	∈	NOUN
ejpam-5189	46	11	v	v	NOUN
ejpam-5189	46	12	(	(	PUNCT
ejpam-5189	46	13	g	g	NOUN
ejpam-5189	46	14	)	)	PUNCT
ejpam-5189	46	15	\	\	PROPN
ejpam-5189	47	1	s	s	X
ejpam-5189	47	2	)	)	PUNCT
ejpam-5189	47	3	.	.	PUNCT
ejpam-5189	48	1	the	the	DET
ejpam-5189	48	2	smallest	small	ADJ
ejpam-5189	48	3	cardinality	cardinality	NOUN
ejpam-5189	48	4	of	of	ADP
ejpam-5189	48	5	a	a	DET
ejpam-5189	48	6	dominating	dominating	NOUN
ejpam-5189	48	7	(	(	PUNCT
ejpam-5189	48	8	resp	resp	NOUN
ejpam-5189	48	9	.	.	PUNCT
ejpam-5189	49	1	2	2	NUM
ejpam-5189	49	2	-	-	PUNCT
ejpam-5189	49	3	dominating	dominating	NOUN
ejpam-5189	49	4	)	)	PUNCT
ejpam-5189	49	5	set	set	NOUN
ejpam-5189	49	6	s	s	PART
ejpam-5189	49	7	is	be	AUX
ejpam-5189	49	8	called	call	VERB
ejpam-5189	49	9	the	the	DET
ejpam-5189	49	10	domination	domination	NOUN
ejpam-5189	49	11	number	number	NOUN
ejpam-5189	49	12	(	(	PUNCT
ejpam-5189	49	13	resp	resp	NOUN
ejpam-5189	49	14	.	.	PUNCT
ejpam-5189	50	1	2	2	NUM
ejpam-5189	50	2	-	-	PUNCT
ejpam-5189	50	3	domination	domination	NOUN
ejpam-5189	50	4	number	number	NOUN
ejpam-5189	50	5	)	)	PUNCT
ejpam-5189	50	6	of	of	ADP
ejpam-5189	50	7	g	g	PROPN
ejpam-5189	50	8	and	and	CCONJ
ejpam-5189	50	9	is	be	AUX
ejpam-5189	50	10	denoted	denote	VERB
ejpam-5189	50	11	by	by	ADP
ejpam-5189	50	12	γ(g	γ(g	PROPN
ejpam-5189	50	13	)	)	PUNCT
ejpam-5189	50	14	(	(	PUNCT
ejpam-5189	50	15	resp	resp	NOUN
ejpam-5189	50	16	.	.	PUNCT
ejpam-5189	51	1	γ2(g	γ2(g	VERB
ejpam-5189	51	2	)	)	PUNCT
ejpam-5189	51	3	)	)	PUNCT
ejpam-5189	51	4	.	.	PUNCT
ejpam-5189	52	1	any	any	DET
ejpam-5189	52	2	dominating	dominating	NOUN
ejpam-5189	52	3	(	(	PUNCT
ejpam-5189	52	4	resp	resp	NOUN
ejpam-5189	52	5	.	.	PUNCT
ejpam-5189	53	1	2	2	NUM
ejpam-5189	53	2	-	-	PUNCT
ejpam-5189	53	3	dominating	dominating	NOUN
ejpam-5189	53	4	)	)	PUNCT
ejpam-5189	53	5	set	set	VERB
ejpam-5189	53	6	with	with	ADP
ejpam-5189	53	7	cardinality	cardinality	PROPN
ejpam-5189	53	8	γ(g	γ(g	PROPN
ejpam-5189	53	9	)	)	PUNCT
ejpam-5189	53	10	(	(	PUNCT
ejpam-5189	53	11	resp	resp	NOUN
ejpam-5189	53	12	.	.	PUNCT
ejpam-5189	54	1	γ2(g	γ2(g	VERB
ejpam-5189	54	2	)	)	PUNCT
ejpam-5189	54	3	)	)	PUNCT
ejpam-5189	54	4	is	be	AUX
ejpam-5189	54	5	called	call	VERB
ejpam-5189	54	6	a	a	DET
ejpam-5189	54	7	γ	γ	NOUN
ejpam-5189	54	8	-	-	PUNCT
ejpam-5189	54	9	set	set	ADJ
ejpam-5189	54	10	(	(	PUNCT
ejpam-5189	54	11	resp	resp	NOUN
ejpam-5189	54	12	.	.	PUNCT
ejpam-5189	55	1	γ2	γ2	NOUN
ejpam-5189	55	2	-	-	PUNCT
ejpam-5189	55	3	set	set	NOUN
ejpam-5189	55	4	)	)	PUNCT
ejpam-5189	55	5	in	in	ADP
ejpam-5189	55	6	g.	g.	PROPN
ejpam-5189	55	7	if	if	SCONJ
ejpam-5189	55	8	{	{	PUNCT
ejpam-5189	55	9	v	v	NOUN
ejpam-5189	55	10	}	}	PUNCT
ejpam-5189	55	11	is	be	AUX
ejpam-5189	55	12	a	a	DET
ejpam-5189	55	13	dominating	dominating	NOUN
ejpam-5189	55	14	set	set	NOUN
ejpam-5189	55	15	in	in	ADP
ejpam-5189	55	16	g	g	PROPN
ejpam-5189	55	17	,	,	PUNCT
ejpam-5189	55	18	then	then	ADV
ejpam-5189	55	19	we	we	PRON
ejpam-5189	55	20	call	call	VERB
ejpam-5189	55	21	v	v	ADP
ejpam-5189	55	22	a	a	DET
ejpam-5189	55	23	dominating	dominating	NOUN
ejpam-5189	55	24	vertex	vertex	NOUN
ejpam-5189	55	25	in	in	ADP
ejpam-5189	55	26	g.	g.	PROPN
ejpam-5189	55	27	a	a	DET
ejpam-5189	55	28	set	set	NOUN
ejpam-5189	55	29	s	s	PROPN
ejpam-5189	55	30	⊆	⊆	NUM
ejpam-5189	55	31	v	v	NOUN
ejpam-5189	55	32	(	(	PUNCT
ejpam-5189	55	33	g	g	NOUN
ejpam-5189	55	34	)	)	PUNCT
ejpam-5189	55	35	is	be	AUX
ejpam-5189	55	36	a	a	DET
ejpam-5189	55	37	clique	clique	NOUN
ejpam-5189	55	38	if	if	SCONJ
ejpam-5189	55	39	the	the	DET
ejpam-5189	55	40	graph	graph	NOUN
ejpam-5189	55	41	⟨s⟩	⟨s⟩	VERB
ejpam-5189	55	42	induced	induce	VERB
ejpam-5189	55	43	by	by	ADP
ejpam-5189	55	44	s	s	PROPN
ejpam-5189	55	45	is	be	AUX
ejpam-5189	55	46	a	a	DET
ejpam-5189	55	47	complete	complete	ADJ
ejpam-5189	55	48	graph	graph	NOUN
ejpam-5189	55	49	.	.	PUNCT
ejpam-5189	56	1	a	a	DET
ejpam-5189	56	2	r.	r.	PROPN
ejpam-5189	56	3	j.	j.	PROPN
ejpam-5189	56	4	g.	g.	PROPN
ejpam-5189	56	5	fortosa	fortosa	PROPN
ejpam-5189	56	6	et	et	PROPN
ejpam-5189	56	7	al	al	PROPN
ejpam-5189	56	8	.	.	PUNCT
ejpam-5189	56	9	/	/	SYM
ejpam-5189	56	10	eur	eur	PROPN
ejpam-5189	56	11	.	.	PUNCT
ejpam-5189	57	1	j.	j.	PROPN
ejpam-5189	57	2	pure	pure	PROPN
ejpam-5189	57	3	appl	appl	PROPN
ejpam-5189	57	4	.	.	PROPN
ejpam-5189	57	5	math	math	PROPN
ejpam-5189	57	6	,	,	PUNCT
ejpam-5189	57	7	17	17	NUM
ejpam-5189	57	8	(	(	PUNCT
ejpam-5189	57	9	3	3	NUM
ejpam-5189	57	10	)	)	PUNCT
ejpam-5189	57	11	(	(	PUNCT
ejpam-5189	57	12	2024	2024	NUM
ejpam-5189	57	13	)	)	PUNCT
ejpam-5189	57	14	,	,	PUNCT
ejpam-5189	57	15	1539	1539	NUM
ejpam-5189	57	16	-	-	SYM
ejpam-5189	57	17	1552	1552	NUM
ejpam-5189	57	18	1541	1541	NUM
ejpam-5189	57	19	set	set	NOUN
ejpam-5189	57	20	s	s	PROPN
ejpam-5189	57	21	⊆	⊆	NUM
ejpam-5189	57	22	v	v	NOUN
ejpam-5189	57	23	(	(	PUNCT
ejpam-5189	57	24	g	g	NOUN
ejpam-5189	57	25	)	)	PUNCT
ejpam-5189	57	26	is	be	AUX
ejpam-5189	57	27	clique	clique	ADJ
ejpam-5189	57	28	dominating	dominating	NOUN
ejpam-5189	57	29	(	(	PUNCT
ejpam-5189	57	30	resp	resp	PROPN
ejpam-5189	57	31	.	.	PUNCT
ejpam-5189	58	1	clique	clique	NOUN
ejpam-5189	58	2	2	2	NUM
ejpam-5189	58	3	-	-	PUNCT
ejpam-5189	58	4	dominating	dominating	NOUN
ejpam-5189	58	5	)	)	PUNCT
ejpam-5189	58	6	if	if	SCONJ
ejpam-5189	58	7	s	s	VERB
ejpam-5189	58	8	is	be	AUX
ejpam-5189	58	9	both	both	PRON
ejpam-5189	58	10	a	a	DET
ejpam-5189	58	11	clique	clique	NOUN
ejpam-5189	58	12	and	and	CCONJ
ejpam-5189	58	13	dominating	dominating	NOUN
ejpam-5189	58	14	(	(	PUNCT
ejpam-5189	58	15	resp	resp	NOUN
ejpam-5189	58	16	.	.	PUNCT
ejpam-5189	59	1	a	a	DET
ejpam-5189	59	2	clique	clique	NOUN
ejpam-5189	59	3	and	and	CCONJ
ejpam-5189	59	4	2	2	NUM
ejpam-5189	59	5	-	-	PUNCT
ejpam-5189	59	6	dominating	dominating	NOUN
ejpam-5189	59	7	)	)	PUNCT
ejpam-5189	59	8	.	.	PUNCT
ejpam-5189	60	1	the	the	DET
ejpam-5189	60	2	smallest	small	ADJ
ejpam-5189	60	3	cardinality	cardinality	NOUN
ejpam-5189	60	4	of	of	ADP
ejpam-5189	60	5	a	a	DET
ejpam-5189	60	6	clique	clique	NOUN
ejpam-5189	60	7	dominating	dominating	NOUN
ejpam-5189	60	8	(	(	PUNCT
ejpam-5189	60	9	resp	resp	PROPN
ejpam-5189	60	10	.	.	PUNCT
ejpam-5189	61	1	clique	clique	NOUN
ejpam-5189	61	2	2	2	NUM
ejpam-5189	61	3	-	-	PUNCT
ejpam-5189	61	4	dominating	dominating	NOUN
ejpam-5189	61	5	)	)	PUNCT
ejpam-5189	61	6	set	set	VERB
ejpam-5189	61	7	in	in	ADP
ejpam-5189	61	8	g	g	NOUN
ejpam-5189	61	9	,	,	PUNCT
ejpam-5189	61	10	denoted	denote	VERB
ejpam-5189	61	11	by	by	ADP
ejpam-5189	61	12	γcl(g	γcl(g	NOUN
ejpam-5189	61	13	)	)	PUNCT
ejpam-5189	61	14	(	(	PUNCT
ejpam-5189	61	15	resp	resp	NOUN
ejpam-5189	61	16	.	.	PUNCT
ejpam-5189	62	1	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	62	2	)	)	PUNCT
ejpam-5189	62	3	)	)	PUNCT
ejpam-5189	62	4	,	,	PUNCT
ejpam-5189	62	5	is	be	AUX
ejpam-5189	62	6	called	call	VERB
ejpam-5189	62	7	the	the	DET
ejpam-5189	62	8	clique	clique	ADJ
ejpam-5189	62	9	domination	domination	NOUN
ejpam-5189	62	10	number	number	NOUN
ejpam-5189	62	11	(	(	PUNCT
ejpam-5189	62	12	resp	resp	NOUN
ejpam-5189	62	13	.	.	PUNCT
ejpam-5189	63	1	clique	clique	ADJ
ejpam-5189	63	2	2	2	NUM
ejpam-5189	63	3	-	-	PUNCT
ejpam-5189	63	4	domination	domination	NOUN
ejpam-5189	63	5	number	number	NOUN
ejpam-5189	63	6	)	)	PUNCT
ejpam-5189	63	7	of	of	ADP
ejpam-5189	63	8	g.	g.	PROPN
ejpam-5189	63	9	any	any	DET
ejpam-5189	63	10	clique	clique	NOUN
ejpam-5189	63	11	dominating	dominating	NOUN
ejpam-5189	63	12	(	(	PUNCT
ejpam-5189	63	13	resp	resp	PROPN
ejpam-5189	63	14	.	.	PUNCT
ejpam-5189	64	1	clique	clique	NOUN
ejpam-5189	64	2	2	2	NUM
ejpam-5189	64	3	-	-	PUNCT
ejpam-5189	64	4	dominating	dominating	NOUN
ejpam-5189	64	5	)	)	PUNCT
ejpam-5189	64	6	set	set	VERB
ejpam-5189	64	7	in	in	ADP
ejpam-5189	64	8	g	g	NOUN
ejpam-5189	64	9	with	with	ADP
ejpam-5189	64	10	cardinality	cardinality	PROPN
ejpam-5189	64	11	γcl(g	γcl(g	PROPN
ejpam-5189	64	12	)	)	PUNCT
ejpam-5189	64	13	(	(	PUNCT
ejpam-5189	64	14	resp	resp	NOUN
ejpam-5189	64	15	.	.	PUNCT
ejpam-5189	65	1	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	65	2	)	)	PUNCT
ejpam-5189	65	3	)	)	PUNCT
ejpam-5189	65	4	is	be	AUX
ejpam-5189	65	5	called	call	VERB
ejpam-5189	65	6	a	a	DET
ejpam-5189	65	7	γcl	γcl	PROPN
ejpam-5189	65	8	-	-	PUNCT
ejpam-5189	65	9	set	set	VERB
ejpam-5189	65	10	(	(	PUNCT
ejpam-5189	65	11	resp	resp	NOUN
ejpam-5189	65	12	.	.	PUNCT
ejpam-5189	66	1	γ2cl	γ2cl	PROPN
ejpam-5189	66	2	-	-	PUNCT
ejpam-5189	66	3	set	set	NOUN
ejpam-5189	66	4	)	)	PUNCT
ejpam-5189	66	5	in	in	ADP
ejpam-5189	66	6	g.	g.	PROPN
ejpam-5189	66	7	we	we	PRON
ejpam-5189	66	8	note	note	VERB
ejpam-5189	66	9	that	that	SCONJ
ejpam-5189	66	10	not	not	PART
ejpam-5189	66	11	every	every	DET
ejpam-5189	66	12	connected	connected	ADJ
ejpam-5189	66	13	graph	graph	NOUN
ejpam-5189	66	14	admits	admit	VERB
ejpam-5189	66	15	a	a	DET
ejpam-5189	66	16	clique	clique	NOUN
ejpam-5189	66	17	dominating	dominating	NOUN
ejpam-5189	66	18	set	set	NOUN
ejpam-5189	66	19	(	(	PUNCT
ejpam-5189	66	20	for	for	ADP
ejpam-5189	66	21	example	example	NOUN
ejpam-5189	66	22	,	,	PUNCT
ejpam-5189	66	23	pn	pn	PROPN
ejpam-5189	66	24	and	and	CCONJ
ejpam-5189	66	25	cn	cn	PROPN
ejpam-5189	66	26	,	,	PUNCT
ejpam-5189	66	27	where	where	SCONJ
ejpam-5189	66	28	n	n	PRON
ejpam-5189	66	29	≥	≥	NOUN
ejpam-5189	66	30	5	5	NUM
ejpam-5189	66	31	,	,	PUNCT
ejpam-5189	66	32	do	do	AUX
ejpam-5189	66	33	not	not	PART
ejpam-5189	66	34	admit	admit	VERB
ejpam-5189	66	35	a	a	DET
ejpam-5189	66	36	clique	clique	NOUN
ejpam-5189	66	37	dominating	dominating	NOUN
ejpam-5189	66	38	set	set	NOUN
ejpam-5189	66	39	)	)	PUNCT
ejpam-5189	66	40	.	.	PUNCT
ejpam-5189	67	1	a	a	DET
ejpam-5189	67	2	set	set	NOUN
ejpam-5189	67	3	s	s	NOUN
ejpam-5189	67	4	⊆	⊆	NUM
ejpam-5189	67	5	v	v	NOUN
ejpam-5189	67	6	(	(	PUNCT
ejpam-5189	67	7	g	g	NOUN
ejpam-5189	67	8	)	)	PUNCT
ejpam-5189	67	9	is	be	AUX
ejpam-5189	67	10	convex	convex	ADJ
ejpam-5189	67	11	if	if	SCONJ
ejpam-5189	67	12	for	for	ADP
ejpam-5189	67	13	every	every	DET
ejpam-5189	67	14	two	two	NUM
ejpam-5189	67	15	vertices	vertex	NOUN
ejpam-5189	67	16	x	x	X
ejpam-5189	67	17	,	,	PUNCT
ejpam-5189	67	18	y	y	PROPN
ejpam-5189	67	19	∈	∈	PROPN
ejpam-5189	67	20	s	s	X
ejpam-5189	67	21	,	,	PUNCT
ejpam-5189	67	22	it	it	PRON
ejpam-5189	67	23	holds	hold	VERB
ejpam-5189	67	24	that	that	PRON
ejpam-5189	67	25	ig(x	ig(x	ADJ
ejpam-5189	67	26	,	,	PUNCT
ejpam-5189	67	27	y	y	PROPN
ejpam-5189	67	28	)	)	PUNCT
ejpam-5189	67	29	⊆	⊆	NUM
ejpam-5189	67	30	s.	s.	PROPN
ejpam-5189	67	31	a	a	DET
ejpam-5189	67	32	set	set	NOUN
ejpam-5189	67	33	s	s	PROPN
ejpam-5189	67	34	⊆	⊆	NUM
ejpam-5189	67	35	v	v	NOUN
ejpam-5189	67	36	(	(	PUNCT
ejpam-5189	67	37	g	g	NOUN
ejpam-5189	67	38	)	)	PUNCT
ejpam-5189	67	39	is	be	AUX
ejpam-5189	67	40	convex	convex	ADJ
ejpam-5189	67	41	dominating	dominating	NOUN
ejpam-5189	67	42	(	(	PUNCT
ejpam-5189	67	43	resp	resp	NOUN
ejpam-5189	67	44	.	.	PUNCT
ejpam-5189	68	1	convex	convex	PROPN
ejpam-5189	68	2	2	2	NUM
ejpam-5189	68	3	-	-	PUNCT
ejpam-5189	68	4	dominating	dominating	NOUN
ejpam-5189	68	5	)	)	PUNCT
ejpam-5189	68	6	if	if	SCONJ
ejpam-5189	68	7	s	s	NOUN
ejpam-5189	68	8	is	be	AUX
ejpam-5189	68	9	both	both	PRON
ejpam-5189	68	10	convex	convex	ADJ
ejpam-5189	68	11	and	and	CCONJ
ejpam-5189	68	12	dominating	dominating	NOUN
ejpam-5189	68	13	(	(	PUNCT
ejpam-5189	68	14	resp	resp	NOUN
ejpam-5189	68	15	.	.	PUNCT
ejpam-5189	69	1	2	2	NUM
ejpam-5189	69	2	-	-	PUNCT
ejpam-5189	69	3	dominating	dominating	NOUN
ejpam-5189	69	4	)	)	PUNCT
ejpam-5189	69	5	.	.	PUNCT
ejpam-5189	70	1	the	the	DET
ejpam-5189	70	2	minimum	minimum	ADJ
ejpam-5189	70	3	cardinality	cardinality	NOUN
ejpam-5189	70	4	among	among	ADP
ejpam-5189	70	5	all	all	DET
ejpam-5189	70	6	convex	convex	NOUN
ejpam-5189	70	7	dominating	dominating	NOUN
ejpam-5189	70	8	(	(	PUNCT
ejpam-5189	70	9	convex	convex	ADJ
ejpam-5189	70	10	2	2	NUM
ejpam-5189	70	11	-	-	PUNCT
ejpam-5189	70	12	dominating	dominating	NOUN
ejpam-5189	70	13	)	)	PUNCT
ejpam-5189	70	14	sets	set	NOUN
ejpam-5189	70	15	in	in	ADP
ejpam-5189	70	16	g	g	NOUN
ejpam-5189	70	17	,	,	PUNCT
ejpam-5189	70	18	denoted	denote	VERB
ejpam-5189	70	19	by	by	ADP
ejpam-5189	70	20	γcon(g	γcon(g	PROPN
ejpam-5189	70	21	)	)	PUNCT
ejpam-5189	70	22	(	(	PUNCT
ejpam-5189	70	23	resp	resp	NOUN
ejpam-5189	70	24	.	.	PUNCT
ejpam-5189	71	1	γ2con(g	γ2con(g	NUM
ejpam-5189	71	2	)	)	PUNCT
ejpam-5189	71	3	,	,	PUNCT
ejpam-5189	71	4	is	be	AUX
ejpam-5189	71	5	called	call	VERB
ejpam-5189	71	6	the	the	DET
ejpam-5189	71	7	convex	convex	ADJ
ejpam-5189	71	8	domination	domination	NOUN
ejpam-5189	71	9	number	number	NOUN
ejpam-5189	71	10	(	(	PUNCT
ejpam-5189	71	11	resp	resp	NOUN
ejpam-5189	71	12	.	.	PUNCT
ejpam-5189	72	1	convex	convex	PROPN
ejpam-5189	72	2	2	2	NUM
ejpam-5189	72	3	-	-	PUNCT
ejpam-5189	72	4	domination	domination	NOUN
ejpam-5189	72	5	number	number	NOUN
ejpam-5189	72	6	)	)	PUNCT
ejpam-5189	72	7	of	of	ADP
ejpam-5189	72	8	g.	g.	PROPN
ejpam-5189	72	9	any	any	DET
ejpam-5189	72	10	convex	convex	NOUN
ejpam-5189	72	11	dominating	dominating	NOUN
ejpam-5189	72	12	(	(	PUNCT
ejpam-5189	72	13	resp	resp	NOUN
ejpam-5189	72	14	.	.	PUNCT
ejpam-5189	73	1	convex	convex	PROPN
ejpam-5189	73	2	2	2	NUM
ejpam-5189	73	3	-	-	PUNCT
ejpam-5189	73	4	dominating	dominating	NOUN
ejpam-5189	73	5	)	)	PUNCT
ejpam-5189	73	6	set	set	VERB
ejpam-5189	73	7	in	in	ADP
ejpam-5189	73	8	g	g	PROPN
ejpam-5189	73	9	with	with	ADP
ejpam-5189	73	10	cardinality	cardinality	PROPN
ejpam-5189	73	11	γcon(g	γcon(g	PROPN
ejpam-5189	73	12	)	)	PUNCT
ejpam-5189	73	13	(	(	PUNCT
ejpam-5189	73	14	resp	resp	NOUN
ejpam-5189	73	15	.	.	PUNCT
ejpam-5189	74	1	γ2con(g	γ2con(g	NUM
ejpam-5189	74	2	)	)	PUNCT
ejpam-5189	74	3	)	)	PUNCT
ejpam-5189	74	4	is	be	AUX
ejpam-5189	74	5	called	call	VERB
ejpam-5189	74	6	a	a	DET
ejpam-5189	74	7	γcon	γcon	NOUN
ejpam-5189	74	8	-	-	PUNCT
ejpam-5189	74	9	set	set	VERB
ejpam-5189	74	10	(	(	PUNCT
ejpam-5189	74	11	resp	resp	NOUN
ejpam-5189	74	12	.	.	PUNCT
ejpam-5189	75	1	γ2con	γ2con	NOUN
ejpam-5189	75	2	-	-	PUNCT
ejpam-5189	75	3	set	set	NOUN
ejpam-5189	75	4	)	)	PUNCT
ejpam-5189	75	5	in	in	ADP
ejpam-5189	75	6	g.	g.	PROPN
ejpam-5189	75	7	3	3	NUM
ejpam-5189	75	8	.	.	PUNCT
ejpam-5189	75	9	results	result	NOUN
ejpam-5189	75	10	proposition	proposition	NOUN
ejpam-5189	75	11	1	1	X
ejpam-5189	75	12	.	.	PUNCT
ejpam-5189	76	1	let	let	VERB
ejpam-5189	76	2	g	g	NOUN
ejpam-5189	76	3	be	be	AUX
ejpam-5189	76	4	any	any	DET
ejpam-5189	76	5	connected	connected	ADJ
ejpam-5189	76	6	graph	graph	NOUN
ejpam-5189	76	7	on	on	ADP
ejpam-5189	76	8	n	n	DET
ejpam-5189	76	9	vertices	vertex	NOUN
ejpam-5189	76	10	.	.	PUNCT
ejpam-5189	77	1	then	then	ADV
ejpam-5189	77	2	max{γcon(g	max{γcon(g	NUM
ejpam-5189	77	3	)	)	PUNCT
ejpam-5189	77	4	,	,	PUNCT
ejpam-5189	77	5	γ2(g	γ2(g	VERB
ejpam-5189	77	6	)	)	PUNCT
ejpam-5189	77	7	}	}	PUNCT
ejpam-5189	77	8	≤	≤	NOUN
ejpam-5189	77	9	γ2con(g	γ2con(g	NUM
ejpam-5189	77	10	)	)	PUNCT
ejpam-5189	77	11	≤	≤	NOUN
ejpam-5189	77	12	n.	n.	NOUN
ejpam-5189	77	13	moreover	moreover	ADV
ejpam-5189	77	14	,	,	PUNCT
ejpam-5189	77	15	(	(	PUNCT
ejpam-5189	77	16	i	i	NOUN
ejpam-5189	77	17	)	)	PUNCT
ejpam-5189	77	18	γ2con(g	γ2con(g	X
ejpam-5189	77	19	)	)	PUNCT
ejpam-5189	77	20	=	=	SYM
ejpam-5189	77	21	1	1	NUM
ejpam-5189	77	22	if	if	SCONJ
ejpam-5189	77	23	and	and	CCONJ
ejpam-5189	77	24	only	only	ADV
ejpam-5189	77	25	if	if	SCONJ
ejpam-5189	77	26	g	g	PROPN
ejpam-5189	77	27	=	=	PROPN
ejpam-5189	77	28	k1	k1	PROPN
ejpam-5189	77	29	.	.	PUNCT
ejpam-5189	77	30	(	(	PUNCT
ejpam-5189	77	31	ii	ii	NOUN
ejpam-5189	77	32	)	)	PUNCT
ejpam-5189	77	33	γ2con(g	γ2con(g	NOUN
ejpam-5189	77	34	)	)	PUNCT
ejpam-5189	77	35	=	=	SYM
ejpam-5189	77	36	2	2	NUM
ejpam-5189	77	37	if	if	SCONJ
ejpam-5189	77	38	and	and	CCONJ
ejpam-5189	77	39	only	only	ADV
ejpam-5189	77	40	if	if	SCONJ
ejpam-5189	77	41	g	g	PROPN
ejpam-5189	77	42	=	=	SYM
ejpam-5189	77	43	k2	k2	PROPN
ejpam-5189	77	44	or	or	CCONJ
ejpam-5189	77	45	g	g	NOUN
ejpam-5189	77	46	=	=	PUNCT
ejpam-5189	77	47	k2+h	k2+h	VERB
ejpam-5189	77	48	for	for	ADP
ejpam-5189	77	49	some	some	DET
ejpam-5189	77	50	graph	graph	NOUN
ejpam-5189	77	51	h	h	NOUN
ejpam-5189	77	52	of	of	ADP
ejpam-5189	77	53	order	order	NOUN
ejpam-5189	77	54	n−2	n−2	PROPN
ejpam-5189	77	55	.	.	PUNCT
ejpam-5189	78	1	proof	proof	NOUN
ejpam-5189	78	2	.	.	PUNCT
ejpam-5189	79	1	the	the	DET
ejpam-5189	79	2	definition	definition	NOUN
ejpam-5189	79	3	of	of	ADP
ejpam-5189	79	4	the	the	DET
ejpam-5189	79	5	convex	convex	ADJ
ejpam-5189	79	6	2	2	NUM
ejpam-5189	79	7	-	-	PUNCT
ejpam-5189	79	8	dominating	dominate	VERB
ejpam-5189	79	9	set	set	NOUN
ejpam-5189	79	10	implies	imply	VERB
ejpam-5189	79	11	that	that	SCONJ
ejpam-5189	79	12	max{γcon(g	max{γcon(g	PROPN
ejpam-5189	79	13	)	)	PUNCT
ejpam-5189	79	14	,	,	PUNCT
ejpam-5189	79	15	γ2(g	γ2(g	VERB
ejpam-5189	79	16	)	)	PUNCT
ejpam-5189	79	17	}	}	PUNCT
ejpam-5189	79	18	≤	≤	NOUN
ejpam-5189	79	19	γ2con(g	γ2con(g	NUM
ejpam-5189	79	20	)	)	PUNCT
ejpam-5189	79	21	.	.	PUNCT
ejpam-5189	80	1	since	since	SCONJ
ejpam-5189	80	2	v	v	NOUN
ejpam-5189	80	3	(	(	PUNCT
ejpam-5189	80	4	g	g	NOUN
ejpam-5189	80	5	)	)	PUNCT
ejpam-5189	80	6	is	be	AUX
ejpam-5189	80	7	convex	convex	ADJ
ejpam-5189	80	8	2	2	NUM
ejpam-5189	80	9	-	-	PUNCT
ejpam-5189	80	10	dominating	dominating	NOUN
ejpam-5189	80	11	,	,	PUNCT
ejpam-5189	80	12	the	the	DET
ejpam-5189	80	13	given	give	VERB
ejpam-5189	80	14	upper	upper	ADJ
ejpam-5189	80	15	bound	bind	VERB
ejpam-5189	80	16	follows	follow	VERB
ejpam-5189	80	17	.	.	PUNCT
ejpam-5189	81	1	(	(	PUNCT
ejpam-5189	81	2	i	i	NOUN
ejpam-5189	81	3	)	)	PUNCT
ejpam-5189	81	4	clearly	clearly	ADV
ejpam-5189	81	5	,	,	PUNCT
ejpam-5189	81	6	γ2con(k1	γ2con(k1	PROPN
ejpam-5189	81	7	)	)	PUNCT
ejpam-5189	81	8	=	=	SYM
ejpam-5189	82	1	1	1	X
ejpam-5189	82	2	.	.	PUNCT
ejpam-5189	82	3	suppose	suppose	VERB
ejpam-5189	82	4	γ2con(g	γ2con(g	X
ejpam-5189	82	5	)	)	PUNCT
ejpam-5189	82	6	=	=	SYM
ejpam-5189	82	7	1	1	X
ejpam-5189	82	8	,	,	PUNCT
ejpam-5189	82	9	say	say	VERB
ejpam-5189	82	10	s	s	X
ejpam-5189	82	11	=	=	VERB
ejpam-5189	82	12	{	{	PUNCT
ejpam-5189	82	13	v	v	NOUN
ejpam-5189	82	14	}	}	PUNCT
ejpam-5189	82	15	is	be	AUX
ejpam-5189	82	16	a	a	DET
ejpam-5189	82	17	γ2con	γ2con	NOUN
ejpam-5189	82	18	-	-	PUNCT
ejpam-5189	82	19	set	set	NOUN
ejpam-5189	82	20	of	of	ADP
ejpam-5189	82	21	g.	g.	PROPN
ejpam-5189	82	22	if	if	SCONJ
ejpam-5189	82	23	g	g	PROPN
ejpam-5189	82	24	̸=	̸=	PROPN
ejpam-5189	82	25	k1	k1	NOUN
ejpam-5189	82	26	,	,	PUNCT
ejpam-5189	82	27	then	then	ADV
ejpam-5189	82	28	there	there	PRON
ejpam-5189	82	29	exists	exist	VERB
ejpam-5189	82	30	w	w	PROPN
ejpam-5189	82	31	∈	∈	PROPN
ejpam-5189	82	32	v	v	NOUN
ejpam-5189	82	33	(	(	PUNCT
ejpam-5189	82	34	g)\s	g)\s	NOUN
ejpam-5189	82	35	.	.	PUNCT
ejpam-5189	83	1	since	since	SCONJ
ejpam-5189	83	2	|s|	|s|	NOUN
ejpam-5189	83	3	=	=	SYM
ejpam-5189	83	4	1	1	NUM
ejpam-5189	83	5	,	,	PUNCT
ejpam-5189	83	6	|ng(w	|ng(w	NOUN
ejpam-5189	83	7	)	)	PUNCT
ejpam-5189	83	8	∩	∩	NOUN
ejpam-5189	83	9	s|	s|	VERB
ejpam-5189	83	10	≤	≤	NUM
ejpam-5189	83	11	1	1	NUM
ejpam-5189	83	12	,	,	PUNCT
ejpam-5189	83	13	a	a	DET
ejpam-5189	83	14	contradiction	contradiction	NOUN
ejpam-5189	83	15	.	.	PUNCT
ejpam-5189	84	1	thus	thus	ADV
ejpam-5189	84	2	,	,	PUNCT
ejpam-5189	84	3	g	g	PROPN
ejpam-5189	84	4	=	=	SYM
ejpam-5189	84	5	k1	k1	PROPN
ejpam-5189	84	6	.	.	PUNCT
ejpam-5189	85	1	(	(	PUNCT
ejpam-5189	85	2	ii	ii	NOUN
ejpam-5189	85	3	)	)	PUNCT
ejpam-5189	85	4	suppose	suppose	VERB
ejpam-5189	85	5	γ2con(g	γ2con(g	X
ejpam-5189	85	6	)	)	PUNCT
ejpam-5189	85	7	=	=	SYM
ejpam-5189	85	8	2	2	NUM
ejpam-5189	85	9	and	and	CCONJ
ejpam-5189	85	10	suppose	suppose	VERB
ejpam-5189	85	11	g	g	PROPN
ejpam-5189	85	12	̸=	̸=	PROPN
ejpam-5189	85	13	k2	k2	PROPN
ejpam-5189	85	14	.	.	PUNCT
ejpam-5189	86	1	let	let	VERB
ejpam-5189	86	2	s	s	PRON
ejpam-5189	86	3	=	=	PUNCT
ejpam-5189	86	4	{	{	PUNCT
ejpam-5189	86	5	x	x	PROPN
ejpam-5189	86	6	,	,	PUNCT
ejpam-5189	86	7	y	y	PROPN
ejpam-5189	86	8	}	}	PUNCT
ejpam-5189	86	9	be	be	AUX
ejpam-5189	86	10	a	a	DET
ejpam-5189	86	11	γ2con	γ2con	NOUN
ejpam-5189	86	12	-	-	PUNCT
ejpam-5189	86	13	set	set	NOUN
ejpam-5189	86	14	in	in	ADP
ejpam-5189	86	15	g.	g.	PROPN
ejpam-5189	86	16	since	since	SCONJ
ejpam-5189	86	17	s	s	PROPN
ejpam-5189	86	18	is	be	AUX
ejpam-5189	86	19	convex	convex	PROPN
ejpam-5189	86	20	,	,	PUNCT
ejpam-5189	86	21	xy	xy	PROPN
ejpam-5189	86	22	∈	∈	PROPN
ejpam-5189	86	23	e(g	e(g	PROPN
ejpam-5189	86	24	)	)	PUNCT
ejpam-5189	86	25	.	.	PUNCT
ejpam-5189	87	1	let	let	VERB
ejpam-5189	87	2	h	h	NOUN
ejpam-5189	87	3	=	=	PUNCT
ejpam-5189	87	4	⟨v	⟨v	PROPN
ejpam-5189	87	5	(	(	PUNCT
ejpam-5189	87	6	g)\s⟩.	g)\s⟩.	NUM
ejpam-5189	87	7	since	since	SCONJ
ejpam-5189	87	8	s	s	PRON
ejpam-5189	87	9	is	be	AUX
ejpam-5189	87	10	a	a	DET
ejpam-5189	87	11	2	2	NUM
ejpam-5189	87	12	-	-	PUNCT
ejpam-5189	87	13	dominating	dominating	NOUN
ejpam-5189	87	14	set	set	NOUN
ejpam-5189	87	15	,	,	PUNCT
ejpam-5189	87	16	z	z	PROPN
ejpam-5189	87	17	∈	∈	PROPN
ejpam-5189	87	18	ng(x	ng(x	NUM
ejpam-5189	87	19	)	)	PUNCT
ejpam-5189	87	20	∩ng(y	∩ng(y	PROPN
ejpam-5189	87	21	)	)	PUNCT
ejpam-5189	87	22	for	for	ADP
ejpam-5189	87	23	all	all	DET
ejpam-5189	87	24	z	z	NOUN
ejpam-5189	87	25	∈	∈	PROPN
ejpam-5189	87	26	v	v	ADP
ejpam-5189	87	27	(	(	PUNCT
ejpam-5189	87	28	h	h	NOUN
ejpam-5189	87	29	)	)	PUNCT
ejpam-5189	87	30	.	.	PUNCT
ejpam-5189	88	1	hence	hence	ADV
ejpam-5189	88	2	,	,	PUNCT
ejpam-5189	88	3	g	g	PROPN
ejpam-5189	88	4	=	=	PUNCT
ejpam-5189	88	5	⟨s⟩+h	⟨s⟩+h	PUNCT
ejpam-5189	88	6	∼=	∼=	PROPN
ejpam-5189	88	7	k2	k2	NOUN
ejpam-5189	88	8	+	+	PROPN
ejpam-5189	88	9	h.	h.	NOUN
ejpam-5189	88	10	for	for	ADP
ejpam-5189	88	11	the	the	DET
ejpam-5189	88	12	converse	converse	NOUN
ejpam-5189	88	13	,	,	PUNCT
ejpam-5189	88	14	suppose	suppose	VERB
ejpam-5189	88	15	that	that	SCONJ
ejpam-5189	88	16	g	g	PROPN
ejpam-5189	88	17	=	=	SYM
ejpam-5189	88	18	k2	k2	PROPN
ejpam-5189	88	19	.	.	PUNCT
ejpam-5189	89	1	then	then	ADV
ejpam-5189	89	2	γ2con(g	γ2con(g	NUM
ejpam-5189	89	3	)	)	PUNCT
ejpam-5189	89	4	=	=	SYM
ejpam-5189	90	1	2	2	X
ejpam-5189	90	2	.	.	PUNCT
ejpam-5189	91	1	next	next	ADV
ejpam-5189	91	2	,	,	PUNCT
ejpam-5189	91	3	suppose	suppose	VERB
ejpam-5189	91	4	that	that	SCONJ
ejpam-5189	91	5	g	g	PROPN
ejpam-5189	91	6	=	=	PROPN
ejpam-5189	91	7	k2	k2	PROPN
ejpam-5189	91	8	+	+	PROPN
ejpam-5189	91	9	h	h	NOUN
ejpam-5189	91	10	for	for	ADP
ejpam-5189	91	11	some	some	DET
ejpam-5189	91	12	graph	graph	NOUN
ejpam-5189	91	13	h.	h.	PROPN
ejpam-5189	92	1	then	then	ADV
ejpam-5189	92	2	d	d	PROPN
ejpam-5189	92	3	=	=	SYM
ejpam-5189	92	4	v	v	PROPN
ejpam-5189	92	5	(	(	PUNCT
ejpam-5189	92	6	k2	k2	NOUN
ejpam-5189	92	7	)	)	PUNCT
ejpam-5189	92	8	is	be	AUX
ejpam-5189	92	9	a	a	DET
ejpam-5189	92	10	convex	convex	ADJ
ejpam-5189	92	11	2	2	NUM
ejpam-5189	92	12	-	-	PUNCT
ejpam-5189	92	13	dominating	dominating	NOUN
ejpam-5189	92	14	set	set	NOUN
ejpam-5189	92	15	in	in	ADP
ejpam-5189	92	16	g.	g.	PROPN
ejpam-5189	92	17	hence	hence	ADV
ejpam-5189	92	18	,	,	PUNCT
ejpam-5189	92	19	γ2con(g	γ2con(g	X
ejpam-5189	92	20	)	)	PUNCT
ejpam-5189	92	21	=	=	SYM
ejpam-5189	92	22	|d|	|d|	NOUN
ejpam-5189	92	23	=	=	SYM
ejpam-5189	92	24	2	2	X
ejpam-5189	92	25	.	.	X
ejpam-5189	92	26	proposition	proposition	NOUN
ejpam-5189	92	27	2	2	NUM
ejpam-5189	92	28	.	.	PUNCT
ejpam-5189	93	1	let	let	VERB
ejpam-5189	93	2	g	g	PRON
ejpam-5189	93	3	be	be	AUX
ejpam-5189	93	4	a	a	DET
ejpam-5189	93	5	connected	connected	ADJ
ejpam-5189	93	6	graph	graph	NOUN
ejpam-5189	93	7	and	and	CCONJ
ejpam-5189	93	8	let	let	VERB
ejpam-5189	93	9	s	s	PRON
ejpam-5189	93	10	be	be	AUX
ejpam-5189	93	11	a	a	DET
ejpam-5189	93	12	convex	convex	ADJ
ejpam-5189	93	13	2	2	NUM
ejpam-5189	93	14	-	-	PUNCT
ejpam-5189	93	15	dominating	dominating	NOUN
ejpam-5189	93	16	set	set	NOUN
ejpam-5189	93	17	in	in	ADP
ejpam-5189	93	18	g.	g.	PROPN
ejpam-5189	93	19	then	then	ADV
ejpam-5189	93	20	each	each	PRON
ejpam-5189	93	21	of	of	ADP
ejpam-5189	93	22	the	the	DET
ejpam-5189	93	23	following	follow	VERB
ejpam-5189	93	24	holds	hold	NOUN
ejpam-5189	93	25	:	:	PUNCT
ejpam-5189	93	26	r.	r.	PROPN
ejpam-5189	93	27	j.	j.	PROPN
ejpam-5189	93	28	g.	g.	PROPN
ejpam-5189	93	29	fortosa	fortosa	PROPN
ejpam-5189	94	1	et	et	PROPN
ejpam-5189	94	2	al	al	PROPN
ejpam-5189	94	3	.	.	PUNCT
ejpam-5189	94	4	/	/	SYM
ejpam-5189	94	5	eur	eur	PROPN
ejpam-5189	94	6	.	.	PUNCT
ejpam-5189	95	1	j.	j.	PROPN
ejpam-5189	95	2	pure	pure	PROPN
ejpam-5189	95	3	appl	appl	PROPN
ejpam-5189	95	4	.	.	PROPN
ejpam-5189	95	5	math	math	PROPN
ejpam-5189	95	6	,	,	PUNCT
ejpam-5189	95	7	17	17	NUM
ejpam-5189	95	8	(	(	PUNCT
ejpam-5189	95	9	3	3	NUM
ejpam-5189	95	10	)	)	PUNCT
ejpam-5189	95	11	(	(	PUNCT
ejpam-5189	95	12	2024	2024	NUM
ejpam-5189	95	13	)	)	PUNCT
ejpam-5189	95	14	,	,	PUNCT
ejpam-5189	95	15	1539	1539	NUM
ejpam-5189	95	16	-	-	SYM
ejpam-5189	95	17	1552	1552	NUM
ejpam-5189	95	18	1542	1542	NUM
ejpam-5189	95	19	(	(	PUNCT
ejpam-5189	95	20	i	i	NOUN
ejpam-5189	95	21	)	)	PUNCT
ejpam-5189	95	22	s(g	s(g	PROPN
ejpam-5189	95	23	)	)	PUNCT
ejpam-5189	95	24	∪	∪	ADP
ejpam-5189	95	25	ind(g	ind(g	PROPN
ejpam-5189	95	26	)	)	PUNCT
ejpam-5189	96	1	⊆	⊆	NUM
ejpam-5189	96	2	s.	s.	PROPN
ejpam-5189	96	3	(	(	PUNCT
ejpam-5189	96	4	ii	ii	PROPN
ejpam-5189	96	5	)	)	PUNCT
ejpam-5189	96	6	if	if	SCONJ
ejpam-5189	96	7	v	v	NUM
ejpam-5189	96	8	∈	∈	PROPN
ejpam-5189	96	9	v	v	NOUN
ejpam-5189	96	10	(	(	PUNCT
ejpam-5189	96	11	g	g	NOUN
ejpam-5189	96	12	)	)	PUNCT
ejpam-5189	96	13	\	\	PROPN
ejpam-5189	97	1	s	s	X
ejpam-5189	97	2	,	,	PUNCT
ejpam-5189	97	3	then	then	ADV
ejpam-5189	97	4	⟨ng(v	⟨ng(v	NUM
ejpam-5189	97	5	)	)	PUNCT
ejpam-5189	97	6	∩	∩	NOUN
ejpam-5189	97	7	s⟩	s⟩	NOUN
ejpam-5189	97	8	is	be	AUX
ejpam-5189	97	9	a	a	DET
ejpam-5189	97	10	non	non	ADJ
ejpam-5189	97	11	-	-	ADJ
ejpam-5189	97	12	trivial	trivial	ADJ
ejpam-5189	97	13	complete	complete	ADJ
ejpam-5189	97	14	graph	graph	NOUN
ejpam-5189	97	15	.	.	PUNCT
ejpam-5189	98	1	proof	proof	NOUN
ejpam-5189	98	2	.	.	PUNCT
ejpam-5189	99	1	(	(	PUNCT
ejpam-5189	99	2	i	i	NOUN
ejpam-5189	99	3	)	)	PUNCT
ejpam-5189	99	4	let	let	VERB
ejpam-5189	99	5	p	p	PROPN
ejpam-5189	99	6	∈	∈	PROPN
ejpam-5189	99	7	ind(g	ind(g	PROPN
ejpam-5189	99	8	)	)	PUNCT
ejpam-5189	99	9	.	.	PUNCT
ejpam-5189	100	1	if	if	SCONJ
ejpam-5189	100	2	p	p	PROPN
ejpam-5189	100	3	∈	∈	PROPN
ejpam-5189	100	4	v	v	ADP
ejpam-5189	100	5	(	(	PUNCT
ejpam-5189	100	6	g	g	NOUN
ejpam-5189	100	7	)	)	PUNCT
ejpam-5189	100	8	\	\	PROPN
ejpam-5189	100	9	s	s	X
ejpam-5189	100	10	,	,	PUNCT
ejpam-5189	100	11	then	then	ADV
ejpam-5189	100	12	there	there	PRON
ejpam-5189	100	13	exist	exist	VERB
ejpam-5189	100	14	s	s	PROPN
ejpam-5189	100	15	,	,	PUNCT
ejpam-5189	100	16	t	t	PROPN
ejpam-5189	100	17	∈	∈	PROPN
ejpam-5189	100	18	s	s	PART
ejpam-5189	100	19	∩	∩	NOUN
ejpam-5189	100	20	ng(p	ng(p	X
ejpam-5189	100	21	)	)	PUNCT
ejpam-5189	100	22	because	because	SCONJ
ejpam-5189	100	23	s	s	VERB
ejpam-5189	100	24	is	be	AUX
ejpam-5189	100	25	a	a	DET
ejpam-5189	100	26	2	2	NUM
ejpam-5189	100	27	-	-	PUNCT
ejpam-5189	100	28	dominating	dominating	NOUN
ejpam-5189	100	29	set	set	NOUN
ejpam-5189	100	30	.	.	PUNCT
ejpam-5189	101	1	this	this	PRON
ejpam-5189	101	2	is	be	AUX
ejpam-5189	101	3	not	not	PART
ejpam-5189	101	4	possible	possible	ADJ
ejpam-5189	101	5	since	since	SCONJ
ejpam-5189	101	6	st	st	PROPN
ejpam-5189	101	7	/∈	/∈	PROPN
ejpam-5189	101	8	e(g	e(g	PROPN
ejpam-5189	101	9	)	)	PUNCT
ejpam-5189	101	10	and	and	CCONJ
ejpam-5189	101	11	s	s	VERB
ejpam-5189	101	12	is	be	AUX
ejpam-5189	101	13	convex	convex	PROPN
ejpam-5189	101	14	.	.	PUNCT
ejpam-5189	102	1	therefore	therefore	ADV
ejpam-5189	102	2	,	,	PUNCT
ejpam-5189	102	3	p	p	PROPN
ejpam-5189	102	4	∈	∈	PROPN
ejpam-5189	102	5	s	s	PART
ejpam-5189	102	6	,	,	PUNCT
ejpam-5189	102	7	showing	show	VERB
ejpam-5189	102	8	that	that	PRON
ejpam-5189	102	9	ind(g	ind(g	NOUN
ejpam-5189	102	10	)	)	PUNCT
ejpam-5189	102	11	⊆	⊆	NUM
ejpam-5189	102	12	s.	s.	PROPN
ejpam-5189	102	13	next	next	ADV
ejpam-5189	102	14	,	,	PUNCT
ejpam-5189	102	15	let	let	VERB
ejpam-5189	102	16	w	w	PROPN
ejpam-5189	102	17	∈	∈	PROPN
ejpam-5189	102	18	s(g	s(g	PROPN
ejpam-5189	102	19	)	)	PUNCT
ejpam-5189	102	20	and	and	CCONJ
ejpam-5189	102	21	let	let	VERB
ejpam-5189	102	22	z	z	NOUN
ejpam-5189	102	23	∈	∈	PROPN
ejpam-5189	102	24	l(g	l(g	X
ejpam-5189	102	25	)	)	PUNCT
ejpam-5189	102	26	∩	∩	NOUN
ejpam-5189	102	27	ng(w	ng(w	NOUN
ejpam-5189	102	28	)	)	PUNCT
ejpam-5189	102	29	.	.	PUNCT
ejpam-5189	103	1	since	since	SCONJ
ejpam-5189	103	2	z	z	PROPN
ejpam-5189	103	3	∈	∈	PROPN
ejpam-5189	103	4	s	s	PART
ejpam-5189	103	5	and	and	CCONJ
ejpam-5189	103	6	s	s	NOUN
ejpam-5189	103	7	is	be	AUX
ejpam-5189	103	8	convex	convex	ADJ
ejpam-5189	103	9	,	,	PUNCT
ejpam-5189	103	10	there	there	PRON
ejpam-5189	103	11	exists	exist	VERB
ejpam-5189	103	12	no	no	DET
ejpam-5189	103	13	u	u	NOUN
ejpam-5189	103	14	∈	∈	PROPN
ejpam-5189	103	15	s	s	PART
ejpam-5189	103	16	\	\	X
ejpam-5189	103	17	{	{	PUNCT
ejpam-5189	103	18	z	z	NOUN
ejpam-5189	103	19	}	}	PUNCT
ejpam-5189	103	20	such	such	ADJ
ejpam-5189	103	21	that	that	SCONJ
ejpam-5189	103	22	uw	uw	PROPN
ejpam-5189	103	23	∈	∈	PROPN
ejpam-5189	103	24	e(g	e(g	PROPN
ejpam-5189	103	25	)	)	PUNCT
ejpam-5189	103	26	.	.	PUNCT
ejpam-5189	104	1	this	this	DET
ejpam-5189	104	2	forces	force	NOUN
ejpam-5189	104	3	w	w	PROPN
ejpam-5189	104	4	∈	∈	PROPN
ejpam-5189	104	5	s.	s.	PROPN
ejpam-5189	104	6	since	since	SCONJ
ejpam-5189	104	7	w	w	PROPN
ejpam-5189	104	8	was	be	AUX
ejpam-5189	104	9	arbitrarily	arbitrarily	ADV
ejpam-5189	104	10	chosen	choose	VERB
ejpam-5189	104	11	,	,	PUNCT
ejpam-5189	104	12	s(g	s(g	PROPN
ejpam-5189	104	13	)	)	PUNCT
ejpam-5189	104	14	⊆	⊆	NUM
ejpam-5189	104	15	s.	s.	PROPN
ejpam-5189	104	16	(	(	PUNCT
ejpam-5189	104	17	ii	ii	NOUN
ejpam-5189	104	18	)	)	PUNCT
ejpam-5189	104	19	let	let	VERB
ejpam-5189	104	20	v	v	NUM
ejpam-5189	104	21	∈	∈	PROPN
ejpam-5189	104	22	v	v	NOUN
ejpam-5189	104	23	(	(	PUNCT
ejpam-5189	104	24	g)\s	g)\s	NOUN
ejpam-5189	104	25	.	.	PUNCT
ejpam-5189	105	1	since	since	SCONJ
ejpam-5189	105	2	s	s	PROPN
ejpam-5189	105	3	is	be	AUX
ejpam-5189	105	4	2	2	NUM
ejpam-5189	105	5	-	-	PUNCT
ejpam-5189	105	6	dominating	dominating	NOUN
ejpam-5189	105	7	,	,	PUNCT
ejpam-5189	105	8	|ng(v	|ng(v	ADJ
ejpam-5189	105	9	)	)	PUNCT
ejpam-5189	105	10	∩	∩	NOUN
ejpam-5189	105	11	s|	s|	VERB
ejpam-5189	105	12	≥	≥	NOUN
ejpam-5189	105	13	2	2	X
ejpam-5189	105	14	.	.	PUNCT
ejpam-5189	106	1	let	let	VERB
ejpam-5189	106	2	x	x	PRON
ejpam-5189	106	3	,	,	PUNCT
ejpam-5189	106	4	y	y	PROPN
ejpam-5189	106	5	∈	∈	PROPN
ejpam-5189	106	6	ng(v	ng(v	PUNCT
ejpam-5189	106	7	)	)	PUNCT
ejpam-5189	106	8	∩	∩	NOUN
ejpam-5189	106	9	s	s	PART
ejpam-5189	106	10	with	with	ADP
ejpam-5189	106	11	x	x	PART
ejpam-5189	106	12	̸=	̸=	PROPN
ejpam-5189	106	13	y.	y.	NOUN
ejpam-5189	106	14	since	since	SCONJ
ejpam-5189	106	15	v	v	NUM
ejpam-5189	106	16	∈	∈	PROPN
ejpam-5189	106	17	v	v	NOUN
ejpam-5189	106	18	(	(	PUNCT
ejpam-5189	106	19	g)\s	g)\s	NOUN
ejpam-5189	106	20	and	and	CCONJ
ejpam-5189	106	21	s	s	NOUN
ejpam-5189	106	22	is	be	AUX
ejpam-5189	106	23	convex	convex	PROPN
ejpam-5189	106	24	,	,	PUNCT
ejpam-5189	106	25	xy	xy	PROPN
ejpam-5189	106	26	∈	∈	PROPN
ejpam-5189	106	27	e(g	e(g	PROPN
ejpam-5189	106	28	)	)	PUNCT
ejpam-5189	106	29	.	.	PUNCT
ejpam-5189	107	1	thus	thus	ADV
ejpam-5189	107	2	,	,	PUNCT
ejpam-5189	107	3	⟨ng(v	⟨ng(v	NUM
ejpam-5189	107	4	)	)	PUNCT
ejpam-5189	107	5	∩	∩	NOUN
ejpam-5189	107	6	s⟩	s⟩	NOUN
ejpam-5189	107	7	is	be	AUX
ejpam-5189	107	8	a	a	DET
ejpam-5189	107	9	(	(	PUNCT
ejpam-5189	107	10	non	non	ADJ
ejpam-5189	107	11	-	-	ADJ
ejpam-5189	107	12	trivial	trivial	ADJ
ejpam-5189	107	13	)	)	PUNCT
ejpam-5189	107	14	complete	complete	ADJ
ejpam-5189	107	15	subgraph	subgraph	NOUN
ejpam-5189	107	16	of	of	ADP
ejpam-5189	107	17	g.	g.	PROPN
ejpam-5189	107	18	corollary	corollary	PROPN
ejpam-5189	107	19	1	1	PROPN
ejpam-5189	107	20	.	.	PUNCT
ejpam-5189	108	1	let	let	VERB
ejpam-5189	108	2	g	g	PRON
ejpam-5189	108	3	be	be	AUX
ejpam-5189	108	4	a	a	DET
ejpam-5189	108	5	connected	connected	ADJ
ejpam-5189	108	6	non	non	ADJ
ejpam-5189	108	7	-	-	ADJ
ejpam-5189	108	8	trivial	trivial	ADJ
ejpam-5189	108	9	graph	graph	NOUN
ejpam-5189	108	10	.	.	PUNCT
ejpam-5189	109	1	if	if	SCONJ
ejpam-5189	109	2	γ2con(g	γ2con(g	NUM
ejpam-5189	110	1	)	)	PUNCT
ejpam-5189	110	2	=	=	SYM
ejpam-5189	110	3	2	2	NUM
ejpam-5189	110	4	,	,	PUNCT
ejpam-5189	110	5	then	then	ADV
ejpam-5189	110	6	γ(g	γ(g	PROPN
ejpam-5189	110	7	)	)	PUNCT
ejpam-5189	110	8	=	=	SYM
ejpam-5189	110	9	1	1	X
ejpam-5189	110	10	.	.	X
ejpam-5189	110	11	observe	observe	VERB
ejpam-5189	110	12	that	that	SCONJ
ejpam-5189	110	13	since	since	SCONJ
ejpam-5189	110	14	γ(p3	γ(p3	ADV
ejpam-5189	110	15	)	)	PUNCT
ejpam-5189	110	16	=	=	SYM
ejpam-5189	110	17	1	1	NUM
ejpam-5189	110	18	and	and	CCONJ
ejpam-5189	110	19	γ2con(p3	γ2con(p3	PROPN
ejpam-5189	110	20	)	)	PUNCT
ejpam-5189	110	21	=	=	SYM
ejpam-5189	110	22	3	3	NUM
ejpam-5189	110	23	,	,	PUNCT
ejpam-5189	110	24	the	the	DET
ejpam-5189	110	25	converse	converse	NOUN
ejpam-5189	110	26	of	of	ADP
ejpam-5189	110	27	corollary	corollary	ADJ
ejpam-5189	110	28	1	1	NUM
ejpam-5189	110	29	is	be	AUX
ejpam-5189	110	30	not	not	PART
ejpam-5189	110	31	true	true	ADJ
ejpam-5189	110	32	.	.	PUNCT
ejpam-5189	111	1	proposition	proposition	NOUN
ejpam-5189	111	2	3	3	X
ejpam-5189	111	3	.	.	PUNCT
ejpam-5189	112	1	let	let	VERB
ejpam-5189	112	2	g	g	PRON
ejpam-5189	112	3	be	be	AUX
ejpam-5189	112	4	a	a	DET
ejpam-5189	112	5	connected	connected	ADJ
ejpam-5189	112	6	graph	graph	NOUN
ejpam-5189	112	7	of	of	ADP
ejpam-5189	112	8	order	order	NOUN
ejpam-5189	112	9	n	n	PRON
ejpam-5189	112	10	≥	≥	NOUN
ejpam-5189	112	11	2	2	NUM
ejpam-5189	112	12	.	.	PUNCT
ejpam-5189	113	1	if	if	SCONJ
ejpam-5189	113	2	γ2con(g	γ2con(g	NUM
ejpam-5189	113	3	)	)	PUNCT
ejpam-5189	113	4	=	=	SYM
ejpam-5189	114	1	n	n	CCONJ
ejpam-5189	114	2	,	,	PUNCT
ejpam-5189	114	3	then	then	ADV
ejpam-5189	114	4	ext(g	ext(g	PROPN
ejpam-5189	114	5	)	)	PUNCT
ejpam-5189	114	6	\	\	PUNCT
ejpam-5189	115	1	l(g	l(g	NOUN
ejpam-5189	115	2	)	)	PUNCT
ejpam-5189	115	3	=	=	PUNCT
ejpam-5189	115	4	∅.	∅.	PRON
ejpam-5189	115	5	moreover	moreover	ADV
ejpam-5189	115	6	,	,	PUNCT
ejpam-5189	115	7	if	if	SCONJ
ejpam-5189	115	8	v	v	X
ejpam-5189	115	9	(	(	PUNCT
ejpam-5189	115	10	g	g	NOUN
ejpam-5189	115	11	)	)	PUNCT
ejpam-5189	115	12	=	=	SYM
ejpam-5189	115	13	s(g	s(g	PROPN
ejpam-5189	115	14	)	)	PUNCT
ejpam-5189	115	15	∪	∪	ADP
ejpam-5189	115	16	ind(g	ind(g	PROPN
ejpam-5189	115	17	)	)	PUNCT
ejpam-5189	115	18	,	,	PUNCT
ejpam-5189	115	19	then	then	ADV
ejpam-5189	115	20	γ2con(g	γ2con(g	NUM
ejpam-5189	115	21	)	)	PUNCT
ejpam-5189	115	22	=	=	SYM
ejpam-5189	115	23	n.	n.	NOUN
ejpam-5189	115	24	proof	proof	NOUN
ejpam-5189	115	25	.	.	PUNCT
ejpam-5189	115	26	suppose	suppose	VERB
ejpam-5189	115	27	that	that	SCONJ
ejpam-5189	115	28	γ2con(g	γ2con(g	VERB
ejpam-5189	115	29	)	)	PUNCT
ejpam-5189	115	30	=	=	VERB
ejpam-5189	115	31	n.	n.	NOUN
ejpam-5189	115	32	suppose	suppose	VERB
ejpam-5189	115	33	there	there	PRON
ejpam-5189	115	34	exists	exist	VERB
ejpam-5189	115	35	v	v	ADP
ejpam-5189	115	36	∈	∈	PROPN
ejpam-5189	115	37	ext(g	ext(g	PROPN
ejpam-5189	115	38	)	)	PUNCT
ejpam-5189	115	39	\	\	PUNCT
ejpam-5189	115	40	l(g	l(g	NOUN
ejpam-5189	115	41	)	)	PUNCT
ejpam-5189	115	42	.	.	PUNCT
ejpam-5189	116	1	then	then	ADV
ejpam-5189	116	2	|ng(v)|	|ng(v)|	NOUN
ejpam-5189	116	3	≥	≥	X
ejpam-5189	116	4	2	2	NUM
ejpam-5189	116	5	.	.	PUNCT
ejpam-5189	116	6	let	let	VERB
ejpam-5189	116	7	s	s	NOUN
ejpam-5189	116	8	=	=	X
ejpam-5189	116	9	v	v	PROPN
ejpam-5189	116	10	(	(	PUNCT
ejpam-5189	116	11	g)\{v	g)\{v	PROPN
ejpam-5189	116	12	}	}	PUNCT
ejpam-5189	116	13	.	.	PUNCT
ejpam-5189	117	1	then	then	ADV
ejpam-5189	117	2	s	s	VERB
ejpam-5189	117	3	is	be	AUX
ejpam-5189	117	4	a	a	DET
ejpam-5189	117	5	convex	convex	ADJ
ejpam-5189	117	6	2	2	NUM
ejpam-5189	117	7	-	-	PUNCT
ejpam-5189	117	8	dominating	dominating	NOUN
ejpam-5189	117	9	set	set	NOUN
ejpam-5189	117	10	in	in	ADP
ejpam-5189	117	11	g.	g.	PROPN
ejpam-5189	117	12	hence	hence	ADV
ejpam-5189	117	13	,	,	PUNCT
ejpam-5189	117	14	γ2con(g	γ2con(g	NUM
ejpam-5189	117	15	)	)	PUNCT
ejpam-5189	117	16	≤	≤	NUM
ejpam-5189	117	17	|s|	|s|	PROPN
ejpam-5189	117	18	=	=	SYM
ejpam-5189	117	19	n−	n−	NOUN
ejpam-5189	117	20	1	1	NUM
ejpam-5189	117	21	,	,	PUNCT
ejpam-5189	117	22	a	a	DET
ejpam-5189	117	23	contradiction	contradiction	NOUN
ejpam-5189	117	24	.	.	PUNCT
ejpam-5189	118	1	thus	thus	ADV
ejpam-5189	118	2	,	,	PUNCT
ejpam-5189	118	3	ext(g	ext(g	ADJ
ejpam-5189	118	4	)	)	PUNCT
ejpam-5189	118	5	\	\	PUNCT
ejpam-5189	118	6	l(g	l(g	NOUN
ejpam-5189	118	7	)	)	PUNCT
ejpam-5189	118	8	=	=	PUNCT
ejpam-5189	118	9	∅.	∅.	PRON
ejpam-5189	118	10	the	the	DET
ejpam-5189	118	11	remaining	remain	VERB
ejpam-5189	118	12	part	part	NOUN
ejpam-5189	118	13	follows	follow	VERB
ejpam-5189	118	14	from	from	ADP
ejpam-5189	118	15	proposition	proposition	NOUN
ejpam-5189	118	16	2	2	NUM
ejpam-5189	118	17	.	.	PUNCT
ejpam-5189	118	18	corollary	corollary	ADJ
ejpam-5189	118	19	2	2	NUM
ejpam-5189	118	20	.	.	PUNCT
ejpam-5189	119	1	let	let	VERB
ejpam-5189	119	2	g	g	PRON
ejpam-5189	119	3	be	be	AUX
ejpam-5189	119	4	a	a	DET
ejpam-5189	119	5	connected	connected	ADJ
ejpam-5189	119	6	graph	graph	NOUN
ejpam-5189	119	7	of	of	ADP
ejpam-5189	119	8	order	order	NOUN
ejpam-5189	119	9	n.	n.	NOUN
ejpam-5189	119	10	then	then	ADV
ejpam-5189	119	11	each	each	PRON
ejpam-5189	119	12	of	of	ADP
ejpam-5189	119	13	the	the	DET
ejpam-5189	119	14	following	follow	VERB
ejpam-5189	119	15	holds	hold	NOUN
ejpam-5189	119	16	.	.	PUNCT
ejpam-5189	120	1	(	(	PUNCT
ejpam-5189	120	2	i	i	NOUN
ejpam-5189	120	3	)	)	PUNCT
ejpam-5189	120	4	γ2con(kn	γ2con(kn	NUM
ejpam-5189	120	5	)	)	PUNCT
ejpam-5189	121	1	=	=	PRON
ejpam-5189	121	2	{	{	PUNCT
ejpam-5189	121	3	1	1	NUM
ejpam-5189	121	4	,	,	PUNCT
ejpam-5189	121	5	n	n	NOUN
ejpam-5189	121	6	=	=	SYM
ejpam-5189	121	7	1	1	NUM
ejpam-5189	121	8	2	2	NUM
ejpam-5189	121	9	,	,	PUNCT
ejpam-5189	121	10	n	n	PRON
ejpam-5189	121	11	≥	≥	NOUN
ejpam-5189	121	12	2	2	NUM
ejpam-5189	121	13	.	.	PUNCT
ejpam-5189	121	14	(	(	PUNCT
ejpam-5189	121	15	ii	ii	NOUN
ejpam-5189	121	16	)	)	PUNCT
ejpam-5189	121	17	γ2con(pn	γ2con(pn	NUM
ejpam-5189	121	18	)	)	PUNCT
ejpam-5189	121	19	=	=	SYM
ejpam-5189	121	20	n	n	CCONJ
ejpam-5189	121	21	,	,	PUNCT
ejpam-5189	121	22	for	for	ADP
ejpam-5189	121	23	all	all	DET
ejpam-5189	121	24	n	n	PRON
ejpam-5189	121	25	≥	≥	NOUN
ejpam-5189	121	26	1	1	NUM
ejpam-5189	121	27	.	.	PUNCT
ejpam-5189	122	1	(	(	PUNCT
ejpam-5189	122	2	iii	iii	NOUN
ejpam-5189	122	3	)	)	PUNCT
ejpam-5189	122	4	γ2con(cn	γ2con(cn	NOUN
ejpam-5189	122	5	)	)	PUNCT
ejpam-5189	123	1	=	=	PRON
ejpam-5189	123	2	{	{	PUNCT
ejpam-5189	123	3	2	2	NUM
ejpam-5189	123	4	,	,	PUNCT
ejpam-5189	123	5	n	n	NOUN
ejpam-5189	123	6	=	=	SYM
ejpam-5189	123	7	3	3	NUM
ejpam-5189	123	8	n	n	CCONJ
ejpam-5189	123	9	,	,	PUNCT
ejpam-5189	123	10	n	n	PRON
ejpam-5189	123	11	≥	≥	NOUN
ejpam-5189	123	12	4	4	NUM
ejpam-5189	123	13	.	.	PUNCT
ejpam-5189	123	14	(	(	PUNCT
ejpam-5189	123	15	iv	iv	X
ejpam-5189	123	16	)	)	PUNCT
ejpam-5189	123	17	γ2con(k1,n	γ2con(k1,n	NOUN
ejpam-5189	123	18	)	)	PUNCT
ejpam-5189	123	19	=	=	SYM
ejpam-5189	123	20	n+	n+	PUNCT
ejpam-5189	123	21	1	1	NUM
ejpam-5189	123	22	,	,	PUNCT
ejpam-5189	123	23	for	for	ADP
ejpam-5189	123	24	all	all	DET
ejpam-5189	123	25	n	n	PRON
ejpam-5189	123	26	≥	≥	NUM
ejpam-5189	123	27	1	1	NUM
ejpam-5189	123	28	.	.	PUNCT
ejpam-5189	124	1	proposition	proposition	NOUN
ejpam-5189	124	2	4	4	NUM
ejpam-5189	124	3	.	.	PUNCT
ejpam-5189	125	1	let	let	VERB
ejpam-5189	125	2	g	g	PROPN
ejpam-5189	125	3	=	=	SYM
ejpam-5189	125	4	kn1,n2,	kn1,n2,	PROPN
ejpam-5189	125	5	...	...	PUNCT
ejpam-5189	125	6	,nk	,nk	PUNCT
ejpam-5189	125	7	be	be	AUX
ejpam-5189	125	8	the	the	DET
ejpam-5189	125	9	complete	complete	ADJ
ejpam-5189	125	10	k	k	ADJ
ejpam-5189	125	11	-	-	ADJ
ejpam-5189	125	12	partite	partite	ADJ
ejpam-5189	125	13	graph	graph	NOUN
ejpam-5189	125	14	with	with	ADP
ejpam-5189	125	15	2	2	NUM
ejpam-5189	125	16	≤	≤	NUM
ejpam-5189	125	17	n1	n1	PROPN
ejpam-5189	125	18	≤	≤	NOUN
ejpam-5189	125	19	n2	n2	NOUN
ejpam-5189	125	20	≤	≤	NOUN
ejpam-5189	125	21	·	·	PUNCT
ejpam-5189	125	22	·	·	PUNCT
ejpam-5189	125	23	·	·	PUNCT
ejpam-5189	126	1	≤	≤	NUM
ejpam-5189	126	2	nk	nk	PROPN
ejpam-5189	126	3	,	,	PUNCT
ejpam-5189	126	4	where	where	SCONJ
ejpam-5189	126	5	k	k	PROPN
ejpam-5189	126	6	≥	≥	NUM
ejpam-5189	126	7	2	2	NUM
ejpam-5189	126	8	.	.	PUNCT
ejpam-5189	126	9	then	then	ADV
ejpam-5189	126	10	γ2con(g	γ2con(g	NUM
ejpam-5189	126	11	)	)	PUNCT
ejpam-5189	126	12	=	=	PRON
ejpam-5189	126	13	{	{	PUNCT
ejpam-5189	126	14	n1	n1	PROPN
ejpam-5189	126	15	+	+	CCONJ
ejpam-5189	126	16	n2	n2	ADJ
ejpam-5189	126	17	if	if	SCONJ
ejpam-5189	126	18	k	k	PROPN
ejpam-5189	126	19	=	=	SYM
ejpam-5189	126	20	2	2	NUM
ejpam-5189	126	21	3	3	NUM
ejpam-5189	126	22	if	if	SCONJ
ejpam-5189	126	23	k	k	PROPN
ejpam-5189	126	24	≥	≥	NUM
ejpam-5189	126	25	3	3	NUM
ejpam-5189	126	26	.	.	PUNCT
ejpam-5189	126	27	r.	r.	PROPN
ejpam-5189	126	28	j.	j.	PROPN
ejpam-5189	126	29	g.	g.	PROPN
ejpam-5189	126	30	fortosa	fortosa	PROPN
ejpam-5189	126	31	et	et	PROPN
ejpam-5189	126	32	al	al	PROPN
ejpam-5189	126	33	.	.	PUNCT
ejpam-5189	126	34	/	/	SYM
ejpam-5189	126	35	eur	eur	PROPN
ejpam-5189	126	36	.	.	PUNCT
ejpam-5189	127	1	j.	j.	PROPN
ejpam-5189	127	2	pure	pure	PROPN
ejpam-5189	127	3	appl	appl	PROPN
ejpam-5189	127	4	.	.	PROPN
ejpam-5189	127	5	math	math	PROPN
ejpam-5189	127	6	,	,	PUNCT
ejpam-5189	127	7	17	17	NUM
ejpam-5189	127	8	(	(	PUNCT
ejpam-5189	127	9	3	3	NUM
ejpam-5189	127	10	)	)	PUNCT
ejpam-5189	127	11	(	(	PUNCT
ejpam-5189	127	12	2024	2024	NUM
ejpam-5189	127	13	)	)	PUNCT
ejpam-5189	127	14	,	,	PUNCT
ejpam-5189	127	15	1539	1539	NUM
ejpam-5189	127	16	-	-	SYM
ejpam-5189	127	17	1552	1552	NUM
ejpam-5189	127	18	1543	1543	NUM
ejpam-5189	127	19	proof	proof	NOUN
ejpam-5189	127	20	.	.	PUNCT
ejpam-5189	128	1	let	let	VERB
ejpam-5189	128	2	sn1	sn1	PROPN
ejpam-5189	128	3	,	,	PUNCT
ejpam-5189	128	4	sn2	sn2	PROPN
ejpam-5189	128	5	,	,	PUNCT
ejpam-5189	128	6	.	.	PUNCT
ejpam-5189	128	7	.	.	PUNCT
ejpam-5189	129	1	.	.	PUNCT
ejpam-5189	130	1	,	,	PUNCT
ejpam-5189	130	2	snk	snk	PROPN
ejpam-5189	130	3	be	be	AUX
ejpam-5189	130	4	the	the	DET
ejpam-5189	130	5	partite	partite	ADJ
ejpam-5189	130	6	sets	set	NOUN
ejpam-5189	130	7	in	in	ADP
ejpam-5189	130	8	g.	g.	PROPN
ejpam-5189	130	9	suppose	suppose	VERB
ejpam-5189	130	10	first	first	ADV
ejpam-5189	130	11	that	that	SCONJ
ejpam-5189	130	12	k	k	PROPN
ejpam-5189	130	13	=	=	SYM
ejpam-5189	130	14	2	2	X
ejpam-5189	130	15	.	.	PUNCT
ejpam-5189	130	16	suppose	suppose	VERB
ejpam-5189	130	17	further	far	ADV
ejpam-5189	130	18	that	that	SCONJ
ejpam-5189	130	19	d	d	PROPN
ejpam-5189	130	20	̸=	̸=	PROPN
ejpam-5189	130	21	v	v	ADP
ejpam-5189	130	22	(	(	PUNCT
ejpam-5189	130	23	g	g	NOUN
ejpam-5189	130	24	)	)	PUNCT
ejpam-5189	130	25	,	,	PUNCT
ejpam-5189	130	26	say	say	VERB
ejpam-5189	130	27	v	v	NUM
ejpam-5189	130	28	∈	∈	PROPN
ejpam-5189	130	29	v	v	NOUN
ejpam-5189	130	30	(	(	PUNCT
ejpam-5189	130	31	g	g	NOUN
ejpam-5189	130	32	)	)	PUNCT
ejpam-5189	130	33	\	\	PROPN
ejpam-5189	130	34	d.	d.	NOUN
ejpam-5189	130	35	we	we	PRON
ejpam-5189	130	36	may	may	AUX
ejpam-5189	130	37	assume	assume	VERB
ejpam-5189	130	38	that	that	SCONJ
ejpam-5189	130	39	v	v	NUM
ejpam-5189	130	40	∈	∈	PROPN
ejpam-5189	130	41	sn1	sn1	PROPN
ejpam-5189	130	42	.	.	PUNCT
ejpam-5189	131	1	since	since	SCONJ
ejpam-5189	131	2	d	d	PROPN
ejpam-5189	131	3	is	be	AUX
ejpam-5189	131	4	2	2	NUM
ejpam-5189	131	5	-	-	PUNCT
ejpam-5189	131	6	dominating	dominating	NOUN
ejpam-5189	131	7	,	,	PUNCT
ejpam-5189	131	8	there	there	PRON
ejpam-5189	131	9	exist	exist	VERB
ejpam-5189	131	10	a	a	DET
ejpam-5189	131	11	,	,	PUNCT
ejpam-5189	131	12	b	b	PROPN
ejpam-5189	131	13	∈	∈	PROPN
ejpam-5189	131	14	sn2	sn2	PROPN
ejpam-5189	131	15	∩ng(v	∩ng(v	PROPN
ejpam-5189	131	16	)	)	PUNCT
ejpam-5189	131	17	.	.	PUNCT
ejpam-5189	132	1	this	this	PRON
ejpam-5189	132	2	,	,	PUNCT
ejpam-5189	132	3	however	however	ADV
ejpam-5189	132	4	,	,	PUNCT
ejpam-5189	132	5	implies	imply	VERB
ejpam-5189	132	6	that	that	SCONJ
ejpam-5189	132	7	d	d	NOUN
ejpam-5189	132	8	is	be	AUX
ejpam-5189	132	9	not	not	PART
ejpam-5189	132	10	convex	convex	ADJ
ejpam-5189	132	11	,	,	PUNCT
ejpam-5189	132	12	a	a	DET
ejpam-5189	132	13	contradiction	contradiction	NOUN
ejpam-5189	132	14	.	.	PUNCT
ejpam-5189	133	1	thus	thus	ADV
ejpam-5189	133	2	,	,	PUNCT
ejpam-5189	133	3	d	d	PROPN
ejpam-5189	133	4	=	=	SYM
ejpam-5189	133	5	v	v	X
ejpam-5189	133	6	(	(	PUNCT
ejpam-5189	133	7	g	g	NOUN
ejpam-5189	133	8	)	)	PUNCT
ejpam-5189	133	9	,	,	PUNCT
ejpam-5189	133	10	showing	show	VERB
ejpam-5189	133	11	that	that	SCONJ
ejpam-5189	133	12	γ2con(g	γ2con(g	VERB
ejpam-5189	133	13	)	)	PUNCT
ejpam-5189	133	14	=	=	SYM
ejpam-5189	133	15	n1	n1	PROPN
ejpam-5189	133	16	+	+	CCONJ
ejpam-5189	133	17	n2	n2	ADJ
ejpam-5189	133	18	.	.	PUNCT
ejpam-5189	134	1	next	next	ADV
ejpam-5189	134	2	,	,	PUNCT
ejpam-5189	134	3	suppose	suppose	VERB
ejpam-5189	134	4	that	that	SCONJ
ejpam-5189	134	5	k	k	PROPN
ejpam-5189	134	6	≥	≥	NUM
ejpam-5189	134	7	3	3	NUM
ejpam-5189	134	8	.	.	PUNCT
ejpam-5189	135	1	since	since	SCONJ
ejpam-5189	135	2	g	g	PROPN
ejpam-5189	135	3	is	be	AUX
ejpam-5189	135	4	non	non	ADJ
ejpam-5189	135	5	-	-	ADJ
ejpam-5189	135	6	trivial	trivial	ADJ
ejpam-5189	135	7	and	and	CCONJ
ejpam-5189	135	8	g	g	PROPN
ejpam-5189	135	9	̸=	̸=	PROPN
ejpam-5189	135	10	k2	k2	PROPN
ejpam-5189	135	11	+	+	PROPN
ejpam-5189	135	12	h	h	NOUN
ejpam-5189	135	13	for	for	ADP
ejpam-5189	135	14	any	any	DET
ejpam-5189	135	15	graph	graph	NOUN
ejpam-5189	135	16	h	h	NOUN
ejpam-5189	135	17	,	,	PUNCT
ejpam-5189	135	18	γ2con(g	γ2con(g	NUM
ejpam-5189	135	19	)	)	PUNCT
ejpam-5189	135	20	≥	≥	NOUN
ejpam-5189	135	21	3	3	NUM
ejpam-5189	135	22	by	by	ADP
ejpam-5189	135	23	proposition	proposition	NOUN
ejpam-5189	135	24	1	1	NUM
ejpam-5189	135	25	.	.	PUNCT
ejpam-5189	135	26	pick	pick	VERB
ejpam-5189	135	27	any	any	DET
ejpam-5189	135	28	vi	vi	PROPN
ejpam-5189	135	29	∈	∈	PROPN
ejpam-5189	135	30	sni	sni	NOUN
ejpam-5189	135	31	for	for	ADP
ejpam-5189	135	32	i	i	PROPN
ejpam-5189	135	33	=	=	NOUN
ejpam-5189	135	34	1	1	NUM
ejpam-5189	135	35	,	,	PUNCT
ejpam-5189	135	36	2	2	NUM
ejpam-5189	135	37	,	,	PUNCT
ejpam-5189	135	38	3	3	NUM
ejpam-5189	135	39	and	and	CCONJ
ejpam-5189	135	40	let	let	VERB
ejpam-5189	135	41	s	s	AUX
ejpam-5189	135	42	=	=	NOUN
ejpam-5189	135	43	{	{	PUNCT
ejpam-5189	135	44	v1	v1	PROPN
ejpam-5189	135	45	,	,	PUNCT
ejpam-5189	135	46	v2	v2	PROPN
ejpam-5189	135	47	,	,	PUNCT
ejpam-5189	135	48	v3	v3	PROPN
ejpam-5189	135	49	}	}	PUNCT
ejpam-5189	135	50	.	.	PUNCT
ejpam-5189	136	1	then	then	ADV
ejpam-5189	136	2	⟨s⟩	⟨s⟩	PROPN
ejpam-5189	136	3	is	be	AUX
ejpam-5189	136	4	complete	complete	ADJ
ejpam-5189	136	5	.	.	PUNCT
ejpam-5189	137	1	hence	hence	ADV
ejpam-5189	137	2	,	,	PUNCT
ejpam-5189	137	3	s	s	VERB
ejpam-5189	137	4	is	be	AUX
ejpam-5189	137	5	a	a	DET
ejpam-5189	137	6	convex	convex	NOUN
ejpam-5189	137	7	set	set	VERB
ejpam-5189	137	8	in	in	ADP
ejpam-5189	137	9	g.	g.	PROPN
ejpam-5189	137	10	clearly	clearly	ADV
ejpam-5189	137	11	,	,	PUNCT
ejpam-5189	137	12	s	s	VERB
ejpam-5189	137	13	is	be	AUX
ejpam-5189	137	14	also	also	ADV
ejpam-5189	137	15	a	a	DET
ejpam-5189	137	16	2	2	NUM
ejpam-5189	137	17	-	-	PUNCT
ejpam-5189	137	18	dominating	dominating	NOUN
ejpam-5189	137	19	set	set	NOUN
ejpam-5189	137	20	.	.	PUNCT
ejpam-5189	138	1	therefore	therefore	ADV
ejpam-5189	138	2	,	,	PUNCT
ejpam-5189	138	3	γ2con(g	γ2con(g	X
ejpam-5189	138	4	)	)	PUNCT
ejpam-5189	138	5	=	=	SYM
ejpam-5189	138	6	|s|	|s|	NOUN
ejpam-5189	138	7	=	=	SYM
ejpam-5189	138	8	3	3	X
ejpam-5189	138	9	.	.	PUNCT
ejpam-5189	138	10	theorem	theorem	NOUN
ejpam-5189	138	11	1	1	NUM
ejpam-5189	138	12	.	.	PUNCT
ejpam-5189	139	1	[	[	X
ejpam-5189	139	2	15	15	NUM
ejpam-5189	139	3	]	]	X
ejpam-5189	139	4	for	for	ADP
ejpam-5189	139	5	a	a	DET
ejpam-5189	139	6	cycle	cycle	NOUN
ejpam-5189	139	7	cn	cn	NOUN
ejpam-5189	139	8	on	on	ADP
ejpam-5189	139	9	n	n	NUM
ejpam-5189	139	10	≥	≥	NUM
ejpam-5189	139	11	6	6	NUM
ejpam-5189	139	12	vertices	vertex	NOUN
ejpam-5189	139	13	,	,	PUNCT
ejpam-5189	139	14	γcon(cn	γcon(cn	NOUN
ejpam-5189	139	15	)	)	PUNCT
ejpam-5189	139	16	=	=	SYM
ejpam-5189	139	17	n.	n.	NOUN
ejpam-5189	139	18	theorem	theorem	NOUN
ejpam-5189	139	19	2	2	X
ejpam-5189	139	20	.	.	PUNCT
ejpam-5189	139	21	let	let	VERB
ejpam-5189	139	22	a	a	PRON
ejpam-5189	139	23	and	and	CCONJ
ejpam-5189	139	24	b	b	NOUN
ejpam-5189	139	25	be	be	AUX
ejpam-5189	139	26	positive	positive	ADJ
ejpam-5189	139	27	integers	integer	NOUN
ejpam-5189	139	28	such	such	ADJ
ejpam-5189	139	29	that	that	SCONJ
ejpam-5189	139	30	6	6	NUM
ejpam-5189	139	31	≤	≤	NUM
ejpam-5189	139	32	a	a	DET
ejpam-5189	139	33	≤	≤	PROPN
ejpam-5189	139	34	b.	b.	NOUN
ejpam-5189	140	1	then	then	ADV
ejpam-5189	140	2	there	there	PRON
ejpam-5189	140	3	exists	exist	VERB
ejpam-5189	140	4	a	a	DET
ejpam-5189	140	5	connected	connected	ADJ
ejpam-5189	140	6	graph	graph	NOUN
ejpam-5189	140	7	g	g	ADP
ejpam-5189	140	8	such	such	ADJ
ejpam-5189	140	9	that	that	DET
ejpam-5189	140	10	γcon(g	γcon(g	NOUN
ejpam-5189	140	11	)	)	PUNCT
ejpam-5189	140	12	=	=	SYM
ejpam-5189	140	13	a	a	PRON
ejpam-5189	140	14	and	and	CCONJ
ejpam-5189	140	15	γ2con(g	γ2con(g	NUM
ejpam-5189	140	16	)	)	PUNCT
ejpam-5189	140	17	=	=	SYM
ejpam-5189	140	18	b.	b.	PROPN
ejpam-5189	140	19	proof	proof	NOUN
ejpam-5189	140	20	.	.	PUNCT
ejpam-5189	141	1	consider	consider	VERB
ejpam-5189	141	2	the	the	DET
ejpam-5189	141	3	following	follow	VERB
ejpam-5189	141	4	cases	case	NOUN
ejpam-5189	141	5	:	:	PUNCT
ejpam-5189	141	6	case	case	NOUN
ejpam-5189	141	7	1	1	NUM
ejpam-5189	141	8	:	:	PUNCT
ejpam-5189	141	9	a	a	DET
ejpam-5189	141	10	=	=	X
ejpam-5189	141	11	b.	b.	PROPN
ejpam-5189	141	12	let	let	VERB
ejpam-5189	141	13	g	g	NOUN
ejpam-5189	141	14	=	=	VERB
ejpam-5189	141	15	ca	can	AUX
ejpam-5189	141	16	.	.	PUNCT
ejpam-5189	142	1	then	then	ADV
ejpam-5189	142	2	γcon(g	γcon(g	PROPN
ejpam-5189	142	3	)	)	PUNCT
ejpam-5189	142	4	=	=	SYM
ejpam-5189	143	1	a	a	DET
ejpam-5189	143	2	=	=	SYM
ejpam-5189	143	3	γ2con(g	γ2con(g	NUM
ejpam-5189	143	4	)	)	PUNCT
ejpam-5189	143	5	,	,	PUNCT
ejpam-5189	143	6	by	by	ADP
ejpam-5189	143	7	theorem	theorem	NOUN
ejpam-5189	143	8	1	1	NUM
ejpam-5189	143	9	and	and	CCONJ
ejpam-5189	143	10	corollary	corollary	ADJ
ejpam-5189	143	11	2(iii	2(iii	NUM
ejpam-5189	143	12	)	)	PUNCT
ejpam-5189	143	13	.	.	PUNCT
ejpam-5189	144	1	case	case	NOUN
ejpam-5189	144	2	2	2	NUM
ejpam-5189	144	3	:	:	PUNCT
ejpam-5189	144	4	a	a	DET
ejpam-5189	144	5	<	<	X
ejpam-5189	144	6	b.	b.	NOUN
ejpam-5189	144	7	let	let	VERB
ejpam-5189	144	8	m	m	VERB
ejpam-5189	144	9	=	=	SYM
ejpam-5189	144	10	b	b	X
ejpam-5189	144	11	−	−	NOUN
ejpam-5189	144	12	a.	a.	NOUN
ejpam-5189	144	13	consider	consider	VERB
ejpam-5189	144	14	the	the	DET
ejpam-5189	144	15	graph	graph	NOUN
ejpam-5189	144	16	g	g	NOUN
ejpam-5189	144	17	in	in	ADP
ejpam-5189	144	18	figure	figure	NOUN
ejpam-5189	144	19	1	1	NUM
ejpam-5189	144	20	.	.	PUNCT
ejpam-5189	145	1	let	let	VERB
ejpam-5189	145	2	s	s	PRON
ejpam-5189	145	3	be	be	AUX
ejpam-5189	145	4	a	a	DET
ejpam-5189	145	5	γcon	γcon	NOUN
ejpam-5189	145	6	-	-	PUNCT
ejpam-5189	145	7	set	set	NOUN
ejpam-5189	145	8	in	in	ADP
ejpam-5189	145	9	g.	g.	PROPN
ejpam-5189	145	10	since	since	SCONJ
ejpam-5189	145	11	s	s	PROPN
ejpam-5189	145	12	is	be	AUX
ejpam-5189	145	13	a	a	DET
ejpam-5189	145	14	convex	convex	ADJ
ejpam-5189	145	15	dominating	dominating	NOUN
ejpam-5189	145	16	set	set	NOUN
ejpam-5189	145	17	,	,	PUNCT
ejpam-5189	145	18	va	va	PROPN
ejpam-5189	145	19	∈	∈	PROPN
ejpam-5189	145	20	s.	s.	PROPN
ejpam-5189	145	21	by	by	ADP
ejpam-5189	145	22	observation	observation	NOUN
ejpam-5189	145	23	1	1	NUM
ejpam-5189	145	24	,	,	PUNCT
ejpam-5189	145	25	{	{	PUNCT
ejpam-5189	145	26	v1	v1	NOUN
ejpam-5189	145	27	,	,	PUNCT
ejpam-5189	145	28	v2	v2	NOUN
ejpam-5189	145	29	,	,	PUNCT
ejpam-5189	145	30	.	.	PUNCT
ejpam-5189	145	31	.	.	PUNCT
ejpam-5189	146	1	.	.	PUNCT
ejpam-5189	147	1	,	,	PUNCT
ejpam-5189	147	2	va−1	va−1	VERB
ejpam-5189	147	3	}	}	PUNCT
ejpam-5189	147	4	⊆	⊆	NUM
ejpam-5189	147	5	s.	s.	PROPN
ejpam-5189	147	6	since	since	SCONJ
ejpam-5189	147	7	s	s	PROPN
ejpam-5189	147	8	is	be	AUX
ejpam-5189	147	9	a	a	DET
ejpam-5189	147	10	γcon	γcon	NOUN
ejpam-5189	147	11	-	-	PUNCT
ejpam-5189	147	12	set	set	NOUN
ejpam-5189	147	13	in	in	ADP
ejpam-5189	147	14	g	g	NOUN
ejpam-5189	147	15	,	,	PUNCT
ejpam-5189	147	16	s	s	PART
ejpam-5189	147	17	=	=	NOUN
ejpam-5189	147	18	{	{	PUNCT
ejpam-5189	147	19	v1	v1	PROPN
ejpam-5189	147	20	,	,	PUNCT
ejpam-5189	147	21	v2	v2	PROPN
ejpam-5189	147	22	,	,	PUNCT
ejpam-5189	147	23	.	.	PUNCT
ejpam-5189	147	24	.	.	PUNCT
ejpam-5189	148	1	.	.	PUNCT
ejpam-5189	149	1	,	,	PUNCT
ejpam-5189	149	2	va	va	NOUN
ejpam-5189	149	3	}	}	PUNCT
ejpam-5189	149	4	.	.	PUNCT
ejpam-5189	150	1	hence	hence	ADV
ejpam-5189	150	2	,	,	PUNCT
ejpam-5189	150	3	γcon(g	γcon(g	PROPN
ejpam-5189	150	4	)	)	PUNCT
ejpam-5189	150	5	=	=	SYM
ejpam-5189	150	6	|s|	|s|	NOUN
ejpam-5189	150	7	=	=	NOUN
ejpam-5189	150	8	a.	a.	NOUN
ejpam-5189	150	9	next	next	ADV
ejpam-5189	150	10	,	,	PUNCT
ejpam-5189	150	11	let	let	VERB
ejpam-5189	150	12	d	d	PRON
ejpam-5189	150	13	be	be	AUX
ejpam-5189	150	14	a	a	DET
ejpam-5189	150	15	γ2con	γ2con	NOUN
ejpam-5189	150	16	-	-	PUNCT
ejpam-5189	150	17	set	set	NOUN
ejpam-5189	150	18	in	in	ADP
ejpam-5189	150	19	g.	g.	PROPN
ejpam-5189	150	20	since	since	SCONJ
ejpam-5189	150	21	ind(g	ind(g	PROPN
ejpam-5189	150	22	)	)	PUNCT
ejpam-5189	151	1	=	=	SYM
ejpam-5189	151	2	v	v	X
ejpam-5189	151	3	(	(	PUNCT
ejpam-5189	151	4	g	g	NOUN
ejpam-5189	151	5	)	)	PUNCT
ejpam-5189	151	6	,	,	PUNCT
ejpam-5189	151	7	γ2con(g	γ2con(g	X
ejpam-5189	151	8	)	)	PUNCT
ejpam-5189	151	9	=	=	SYM
ejpam-5189	152	1	|d|	|d|	PROPN
ejpam-5189	152	2	=	=	SYM
ejpam-5189	152	3	|v	|v	PROPN
ejpam-5189	152	4	(	(	PUNCT
ejpam-5189	152	5	g)|	g)|	NOUN
ejpam-5189	152	6	=	=	PUNCT
ejpam-5189	152	7	a+m	a+m	NUM
ejpam-5189	152	8	=	=	SYM
ejpam-5189	152	9	b	b	X
ejpam-5189	152	10	by	by	ADP
ejpam-5189	152	11	proposition	proposition	NOUN
ejpam-5189	152	12	3	3	NUM
ejpam-5189	152	13	.	.	PUNCT
ejpam-5189	152	14	v1	v1	VERB
ejpam-5189	152	15	v2	v2	X
ejpam-5189	152	16	·	·	PUNCT
ejpam-5189	152	17	·	·	PUNCT
ejpam-5189	152	18	·	·	PUNCT
ejpam-5189	153	1	v3	v3	PROPN
ejpam-5189	153	2	va−2	va−2	PROPN
ejpam-5189	153	3	va−1	va−1	PROPN
ejpam-5189	153	4	va	va	PROPN
ejpam-5189	154	1	x1	x1	PROPN
ejpam-5189	154	2	x2	x2	PROPN
ejpam-5189	154	3	·	·	PUNCT
ejpam-5189	154	4	·	·	PUNCT
ejpam-5189	154	5	·	·	PUNCT
ejpam-5189	155	1	xm−1	xm−1	PROPN
ejpam-5189	155	2	xm	xm	PROPN
ejpam-5189	155	3	figure	figure	VERB
ejpam-5189	155	4	1	1	NUM
ejpam-5189	155	5	:	:	PUNCT
ejpam-5189	155	6	a	a	DET
ejpam-5189	155	7	graph	graph	NOUN
ejpam-5189	155	8	g	g	NOUN
ejpam-5189	155	9	with	with	ADP
ejpam-5189	155	10	γcon(g	γcon(g	NOUN
ejpam-5189	155	11	)	)	PUNCT
ejpam-5189	155	12	=	=	SYM
ejpam-5189	155	13	a	a	PRON
ejpam-5189	155	14	and	and	CCONJ
ejpam-5189	155	15	γ2con(g	γ2con(g	NUM
ejpam-5189	155	16	)	)	PUNCT
ejpam-5189	156	1	=	=	SYM
ejpam-5189	156	2	b	b	PROPN
ejpam-5189	156	3	this	this	PRON
ejpam-5189	156	4	proves	prove	VERB
ejpam-5189	156	5	the	the	DET
ejpam-5189	156	6	assertion	assertion	NOUN
ejpam-5189	156	7	.	.	PUNCT
ejpam-5189	157	1	the	the	DET
ejpam-5189	157	2	join	join	NOUN
ejpam-5189	157	3	of	of	ADP
ejpam-5189	157	4	two	two	NUM
ejpam-5189	157	5	graphs	graph	NOUN
ejpam-5189	157	6	g	g	NOUN
ejpam-5189	157	7	and	and	CCONJ
ejpam-5189	157	8	h	h	NOUN
ejpam-5189	157	9	,	,	PUNCT
ejpam-5189	157	10	denoted	denote	VERB
ejpam-5189	157	11	by	by	ADP
ejpam-5189	157	12	g	g	PROPN
ejpam-5189	157	13	+	+	PROPN
ejpam-5189	157	14	h	h	NOUN
ejpam-5189	157	15	,	,	PUNCT
ejpam-5189	157	16	is	be	AUX
ejpam-5189	157	17	the	the	DET
ejpam-5189	157	18	graph	graph	NOUN
ejpam-5189	157	19	with	with	ADP
ejpam-5189	157	20	v	v	NOUN
ejpam-5189	157	21	(	(	PUNCT
ejpam-5189	157	22	g+h	g+h	NOUN
ejpam-5189	157	23	)	)	PUNCT
ejpam-5189	157	24	=	=	SYM
ejpam-5189	157	25	v	v	X
ejpam-5189	157	26	(	(	PUNCT
ejpam-5189	157	27	g)∪v	g)∪v	NOUN
ejpam-5189	157	28	(	(	PUNCT
ejpam-5189	157	29	h	h	NOUN
ejpam-5189	157	30	)	)	PUNCT
ejpam-5189	157	31	and	and	CCONJ
ejpam-5189	157	32	e(g+h	e(g+h	NUM
ejpam-5189	157	33	)	)	PUNCT
ejpam-5189	158	1	=	=	PUNCT
ejpam-5189	158	2	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	X
ejpam-5189	158	3	:	:	PUNCT
ejpam-5189	158	4	u	u	PROPN
ejpam-5189	158	5	∈	∈	PROPN
ejpam-5189	158	6	v	v	ADP
ejpam-5189	158	7	(	(	PUNCT
ejpam-5189	158	8	g	g	NOUN
ejpam-5189	158	9	)	)	PUNCT
ejpam-5189	158	10	and	and	CCONJ
ejpam-5189	158	11	v	v	ADP
ejpam-5189	158	12	∈	∈	NOUN
ejpam-5189	158	13	v	v	NOUN
ejpam-5189	158	14	(	(	PUNCT
ejpam-5189	158	15	g	g	NOUN
ejpam-5189	158	16	)	)	PUNCT
ejpam-5189	158	17	}	}	PUNCT
ejpam-5189	158	18	,	,	PUNCT
ejpam-5189	158	19	where	where	SCONJ
ejpam-5189	158	20	“	"	PUNCT
ejpam-5189	158	21	∪	∪	NOUN
ejpam-5189	158	22	”	"	PUNCT
ejpam-5189	158	23	refers	refer	VERB
ejpam-5189	158	24	to	to	ADP
ejpam-5189	158	25	a	a	DET
ejpam-5189	158	26	disjoint	disjoint	NOUN
ejpam-5189	158	27	union	union	NOUN
ejpam-5189	158	28	of	of	ADP
ejpam-5189	158	29	sets	set	NOUN
ejpam-5189	158	30	.	.	PUNCT
ejpam-5189	159	1	theorem	theorem	NOUN
ejpam-5189	159	2	3	3	X
ejpam-5189	159	3	.	.	PUNCT
ejpam-5189	160	1	let	let	VERB
ejpam-5189	160	2	g	g	NOUN
ejpam-5189	160	3	and	and	CCONJ
ejpam-5189	160	4	h	h	NOUN
ejpam-5189	160	5	be	be	AUX
ejpam-5189	160	6	non	non	ADJ
ejpam-5189	160	7	-	-	ADJ
ejpam-5189	160	8	complete	complete	ADJ
ejpam-5189	160	9	graphs	graph	NOUN
ejpam-5189	160	10	.	.	PUNCT
ejpam-5189	161	1	then	then	ADV
ejpam-5189	161	2	s	s	VERB
ejpam-5189	161	3	⊆	⊆	NUM
ejpam-5189	161	4	v	v	NOUN
ejpam-5189	161	5	(	(	PUNCT
ejpam-5189	161	6	g	g	PROPN
ejpam-5189	161	7	+	+	NOUN
ejpam-5189	161	8	h	h	NOUN
ejpam-5189	161	9	)	)	PUNCT
ejpam-5189	161	10	is	be	AUX
ejpam-5189	161	11	a	a	DET
ejpam-5189	161	12	convex	convex	ADJ
ejpam-5189	161	13	2	2	NUM
ejpam-5189	161	14	-	-	PUNCT
ejpam-5189	161	15	dominating	dominating	NOUN
ejpam-5189	161	16	set	set	NOUN
ejpam-5189	161	17	in	in	ADP
ejpam-5189	161	18	g+h	g+h	PROPN
ejpam-5189	161	19	if	if	SCONJ
ejpam-5189	161	20	and	and	CCONJ
ejpam-5189	161	21	only	only	ADV
ejpam-5189	161	22	if	if	SCONJ
ejpam-5189	161	23	one	one	NUM
ejpam-5189	161	24	of	of	ADP
ejpam-5189	161	25	the	the	DET
ejpam-5189	161	26	following	follow	VERB
ejpam-5189	161	27	holds	hold	NOUN
ejpam-5189	161	28	:	:	PUNCT
ejpam-5189	161	29	r.	r.	PROPN
ejpam-5189	161	30	j.	j.	PROPN
ejpam-5189	161	31	g.	g.	PROPN
ejpam-5189	161	32	fortosa	fortosa	PROPN
ejpam-5189	161	33	et	et	PROPN
ejpam-5189	161	34	al	al	PROPN
ejpam-5189	161	35	.	.	PUNCT
ejpam-5189	161	36	/	/	SYM
ejpam-5189	161	37	eur	eur	PROPN
ejpam-5189	161	38	.	.	PUNCT
ejpam-5189	162	1	j.	j.	PROPN
ejpam-5189	162	2	pure	pure	PROPN
ejpam-5189	162	3	appl	appl	PROPN
ejpam-5189	162	4	.	.	PROPN
ejpam-5189	162	5	math	math	PROPN
ejpam-5189	162	6	,	,	PUNCT
ejpam-5189	162	7	17	17	NUM
ejpam-5189	162	8	(	(	PUNCT
ejpam-5189	162	9	3	3	NUM
ejpam-5189	162	10	)	)	PUNCT
ejpam-5189	162	11	(	(	PUNCT
ejpam-5189	162	12	2024	2024	NUM
ejpam-5189	162	13	)	)	PUNCT
ejpam-5189	162	14	,	,	PUNCT
ejpam-5189	162	15	1539	1539	NUM
ejpam-5189	162	16	-	-	SYM
ejpam-5189	162	17	1552	1552	NUM
ejpam-5189	162	18	1544	1544	NUM
ejpam-5189	162	19	(	(	PUNCT
ejpam-5189	162	20	i	i	NOUN
ejpam-5189	162	21	)	)	PUNCT
ejpam-5189	162	22	s	s	PART
ejpam-5189	162	23	=	=	SYM
ejpam-5189	162	24	v	v	PROPN
ejpam-5189	162	25	(	(	PUNCT
ejpam-5189	162	26	g+h	g+h	PROPN
ejpam-5189	162	27	)	)	PUNCT
ejpam-5189	162	28	.	.	PUNCT
ejpam-5189	163	1	(	(	PUNCT
ejpam-5189	163	2	ii	ii	X
ejpam-5189	163	3	)	)	PUNCT
ejpam-5189	163	4	s	s	VERB
ejpam-5189	163	5	is	be	AUX
ejpam-5189	163	6	a	a	DET
ejpam-5189	163	7	clique	clique	ADJ
ejpam-5189	163	8	2	2	NUM
ejpam-5189	163	9	-	-	PUNCT
ejpam-5189	163	10	dominating	dominating	NOUN
ejpam-5189	163	11	set	set	NOUN
ejpam-5189	163	12	in	in	ADP
ejpam-5189	163	13	g.	g.	PROPN
ejpam-5189	163	14	(	(	PUNCT
ejpam-5189	163	15	iii	iii	X
ejpam-5189	163	16	)	)	PUNCT
ejpam-5189	163	17	s	s	VERB
ejpam-5189	163	18	is	be	AUX
ejpam-5189	163	19	a	a	DET
ejpam-5189	163	20	clique	clique	ADJ
ejpam-5189	163	21	2	2	NUM
ejpam-5189	163	22	-	-	PUNCT
ejpam-5189	163	23	dominating	dominating	NOUN
ejpam-5189	163	24	set	set	NOUN
ejpam-5189	163	25	in	in	ADP
ejpam-5189	163	26	h.	h.	PROPN
ejpam-5189	163	27	(	(	PUNCT
ejpam-5189	163	28	iv	iv	X
ejpam-5189	163	29	)	)	PUNCT
ejpam-5189	163	30	s	s	PART
ejpam-5189	163	31	=	=	PUNCT
ejpam-5189	163	32	sg	sg	X
ejpam-5189	163	33	∪	∪	NOUN
ejpam-5189	163	34	sh	sh	VERB
ejpam-5189	163	35	where	where	SCONJ
ejpam-5189	163	36	∅	∅	NOUN
ejpam-5189	163	37	̸=	̸=	PROPN
ejpam-5189	163	38	sg	sg	ADP
ejpam-5189	163	39	⊆	⊆	NUM
ejpam-5189	163	40	v	v	NOUN
ejpam-5189	163	41	(	(	PUNCT
ejpam-5189	163	42	g	g	NOUN
ejpam-5189	163	43	)	)	PUNCT
ejpam-5189	163	44	and	and	CCONJ
ejpam-5189	163	45	∅	∅	NOUN
ejpam-5189	163	46	̸=	̸=	PROPN
ejpam-5189	163	47	sh	sh	NUM
ejpam-5189	163	48	⊆	⊆	NUM
ejpam-5189	163	49	v	v	NOUN
ejpam-5189	163	50	(	(	PUNCT
ejpam-5189	163	51	h	h	NOUN
ejpam-5189	163	52	)	)	PUNCT
ejpam-5189	163	53	satisfy	satisfy	NOUN
ejpam-5189	163	54	any	any	PRON
ejpam-5189	163	55	of	of	ADP
ejpam-5189	163	56	the	the	DET
ejpam-5189	163	57	following	following	NOUN
ejpam-5189	163	58	:	:	PUNCT
ejpam-5189	163	59	(	(	PUNCT
ejpam-5189	163	60	a	a	X
ejpam-5189	163	61	)	)	PUNCT
ejpam-5189	163	62	sg	sg	NOUN
ejpam-5189	163	63	and	and	CCONJ
ejpam-5189	163	64	sh	sh	PROPN
ejpam-5189	163	65	are	be	AUX
ejpam-5189	163	66	cliques	clique	NOUN
ejpam-5189	163	67	in	in	ADP
ejpam-5189	163	68	g	g	PROPN
ejpam-5189	163	69	and	and	CCONJ
ejpam-5189	163	70	h	h	NOUN
ejpam-5189	163	71	,	,	PUNCT
ejpam-5189	163	72	respectively	respectively	ADV
ejpam-5189	163	73	,	,	PUNCT
ejpam-5189	163	74	where	where	SCONJ
ejpam-5189	163	75	|sg|	|sg|	NOUN
ejpam-5189	163	76	≥	≥	NOUN
ejpam-5189	163	77	2	2	NUM
ejpam-5189	163	78	and	and	CCONJ
ejpam-5189	163	79	|sh	|sh	ADP
ejpam-5189	163	80	|	|	ADV
ejpam-5189	163	81	≥	≥	NOUN
ejpam-5189	163	82	2	2	NUM
ejpam-5189	163	83	.	.	PUNCT
ejpam-5189	164	1	(	(	PUNCT
ejpam-5189	164	2	b	b	X
ejpam-5189	164	3	)	)	PUNCT
ejpam-5189	164	4	sg	sg	NOUN
ejpam-5189	164	5	and	and	CCONJ
ejpam-5189	164	6	sh	sh	PROPN
ejpam-5189	164	7	are	be	AUX
ejpam-5189	164	8	dominating	dominate	VERB
ejpam-5189	164	9	sets	set	NOUN
ejpam-5189	164	10	in	in	ADP
ejpam-5189	164	11	g	g	PROPN
ejpam-5189	164	12	and	and	CCONJ
ejpam-5189	164	13	h	h	NOUN
ejpam-5189	164	14	,	,	PUNCT
ejpam-5189	164	15	respectively	respectively	ADV
ejpam-5189	164	16	,	,	PUNCT
ejpam-5189	164	17	with	with	ADP
ejpam-5189	164	18	|sg|	|sg|	NOUN
ejpam-5189	164	19	=	=	SYM
ejpam-5189	164	20	|sh	|sh	ADP
ejpam-5189	164	21	|	|	ADV
ejpam-5189	164	22	=	=	SYM
ejpam-5189	164	23	1	1	X
ejpam-5189	164	24	.	.	PUNCT
ejpam-5189	165	1	(	(	PUNCT
ejpam-5189	165	2	c	c	X
ejpam-5189	165	3	)	)	PUNCT
ejpam-5189	165	4	|sg|	|sg|	NOUN
ejpam-5189	165	5	=	=	SYM
ejpam-5189	165	6	1	1	NUM
ejpam-5189	165	7	and	and	CCONJ
ejpam-5189	165	8	sh	sh	PROPN
ejpam-5189	165	9	is	be	AUX
ejpam-5189	165	10	a	a	DET
ejpam-5189	165	11	clique	clique	NOUN
ejpam-5189	165	12	dominating	dominating	NOUN
ejpam-5189	165	13	set	set	VERB
ejpam-5189	165	14	in	in	ADP
ejpam-5189	165	15	h	h	NOUN
ejpam-5189	165	16	with	with	ADP
ejpam-5189	165	17	|sh	|sh	NUM
ejpam-5189	165	18	|	|	ADV
ejpam-5189	165	19	≥	≥	NOUN
ejpam-5189	165	20	2	2	NUM
ejpam-5189	165	21	.	.	PUNCT
ejpam-5189	166	1	(	(	PUNCT
ejpam-5189	166	2	d	d	X
ejpam-5189	166	3	)	)	PUNCT
ejpam-5189	166	4	|sh	|sh	ADP
ejpam-5189	166	5	|	|	ADV
ejpam-5189	166	6	=	=	SYM
ejpam-5189	166	7	1	1	NUM
ejpam-5189	166	8	and	and	CCONJ
ejpam-5189	166	9	sg	sg	PROPN
ejpam-5189	166	10	is	be	AUX
ejpam-5189	166	11	a	a	DET
ejpam-5189	166	12	clique	clique	NOUN
ejpam-5189	166	13	dominating	dominating	NOUN
ejpam-5189	166	14	set	set	VERB
ejpam-5189	166	15	in	in	ADP
ejpam-5189	166	16	g	g	NOUN
ejpam-5189	166	17	with	with	ADP
ejpam-5189	166	18	|sg|	|sg|	PROPN
ejpam-5189	166	19	≥	≥	NOUN
ejpam-5189	166	20	2	2	NUM
ejpam-5189	166	21	.	.	PUNCT
ejpam-5189	167	1	proof	proof	NOUN
ejpam-5189	167	2	.	.	PUNCT
ejpam-5189	168	1	suppose	suppose	VERB
ejpam-5189	168	2	s	s	PRON
ejpam-5189	168	3	is	be	AUX
ejpam-5189	168	4	a	a	DET
ejpam-5189	168	5	convex	convex	ADJ
ejpam-5189	168	6	2	2	NUM
ejpam-5189	168	7	-	-	PUNCT
ejpam-5189	168	8	dominating	dominating	NOUN
ejpam-5189	168	9	set	set	NOUN
ejpam-5189	168	10	in	in	ADP
ejpam-5189	168	11	g+h	g+h	PROPN
ejpam-5189	168	12	where	where	SCONJ
ejpam-5189	168	13	s	s	AUX
ejpam-5189	168	14	̸=	̸=	PROPN
ejpam-5189	168	15	v	v	NOUN
ejpam-5189	168	16	(	(	PUNCT
ejpam-5189	168	17	g+h	g+h	PROPN
ejpam-5189	168	18	)	)	PUNCT
ejpam-5189	168	19	.	.	PUNCT
ejpam-5189	169	1	suppose	suppose	VERB
ejpam-5189	169	2	first	first	ADV
ejpam-5189	169	3	that	that	PRON
ejpam-5189	169	4	s	s	VERB
ejpam-5189	169	5	⊆	⊆	NUM
ejpam-5189	169	6	v	v	NOUN
ejpam-5189	169	7	(	(	PUNCT
ejpam-5189	169	8	g	g	NOUN
ejpam-5189	169	9	)	)	PUNCT
ejpam-5189	169	10	.	.	PUNCT
ejpam-5189	170	1	since	since	SCONJ
ejpam-5189	170	2	s	s	PROPN
ejpam-5189	170	3	is	be	AUX
ejpam-5189	170	4	a	a	DET
ejpam-5189	170	5	convex	convex	ADJ
ejpam-5189	170	6	2	2	NUM
ejpam-5189	170	7	-	-	PUNCT
ejpam-5189	170	8	dominating	dominating	NOUN
ejpam-5189	170	9	set	set	NOUN
ejpam-5189	170	10	in	in	ADP
ejpam-5189	170	11	g+h	g+h	PROPN
ejpam-5189	170	12	,	,	PUNCT
ejpam-5189	170	13	s	s	VERB
ejpam-5189	170	14	must	must	AUX
ejpam-5189	170	15	be	be	AUX
ejpam-5189	170	16	a	a	DET
ejpam-5189	170	17	clique	clique	ADJ
ejpam-5189	170	18	2	2	NUM
ejpam-5189	170	19	-	-	PUNCT
ejpam-5189	170	20	dominating	dominating	NOUN
ejpam-5189	170	21	set	set	NOUN
ejpam-5189	170	22	in	in	ADP
ejpam-5189	170	23	g.	g.	PROPN
ejpam-5189	170	24	similarly	similarly	ADV
ejpam-5189	170	25	,	,	PUNCT
ejpam-5189	170	26	if	if	SCONJ
ejpam-5189	170	27	s	s	VERB
ejpam-5189	170	28	⊆	⊆	NUM
ejpam-5189	170	29	v	v	NOUN
ejpam-5189	170	30	(	(	PUNCT
ejpam-5189	170	31	h	h	NOUN
ejpam-5189	170	32	)	)	PUNCT
ejpam-5189	170	33	,	,	PUNCT
ejpam-5189	170	34	s	s	VERB
ejpam-5189	170	35	is	be	AUX
ejpam-5189	170	36	a	a	DET
ejpam-5189	170	37	clique	clique	ADJ
ejpam-5189	170	38	2	2	NUM
ejpam-5189	170	39	-	-	PUNCT
ejpam-5189	170	40	dominating	dominating	NOUN
ejpam-5189	170	41	set	set	NOUN
ejpam-5189	170	42	in	in	ADP
ejpam-5189	170	43	h.	h.	PROPN
ejpam-5189	170	44	hence	hence	ADV
ejpam-5189	170	45	,	,	PUNCT
ejpam-5189	170	46	(	(	PUNCT
ejpam-5189	170	47	ii	ii	NOUN
ejpam-5189	170	48	)	)	PUNCT
ejpam-5189	170	49	or	or	CCONJ
ejpam-5189	170	50	(	(	PUNCT
ejpam-5189	170	51	iii	iii	NOUN
ejpam-5189	170	52	)	)	PUNCT
ejpam-5189	170	53	holds	hold	VERB
ejpam-5189	170	54	.	.	PUNCT
ejpam-5189	171	1	next	next	ADV
ejpam-5189	171	2	,	,	PUNCT
ejpam-5189	171	3	suppose	suppose	VERB
ejpam-5189	171	4	that	that	SCONJ
ejpam-5189	171	5	sg	sg	VERB
ejpam-5189	171	6	=	=	SYM
ejpam-5189	171	7	s	s	PROPN
ejpam-5189	171	8	∩	∩	ADJ
ejpam-5189	171	9	v	v	X
ejpam-5189	171	10	(	(	PUNCT
ejpam-5189	171	11	g	g	NOUN
ejpam-5189	171	12	)	)	PUNCT
ejpam-5189	171	13	̸=	̸=	PROPN
ejpam-5189	171	14	∅	∅	NOUN
ejpam-5189	171	15	and	and	CCONJ
ejpam-5189	171	16	sh	sh	INTJ
ejpam-5189	171	17	=	=	SYM
ejpam-5189	171	18	s	s	PROPN
ejpam-5189	171	19	∩	∩	ADJ
ejpam-5189	171	20	v	v	ADJ
ejpam-5189	171	21	(	(	PUNCT
ejpam-5189	171	22	h	h	NOUN
ejpam-5189	171	23	)	)	PUNCT
ejpam-5189	171	24	̸=	̸=	PROPN
ejpam-5189	171	25	∅.	∅.	ADV
ejpam-5189	171	26	since	since	SCONJ
ejpam-5189	171	27	s	s	PRON
ejpam-5189	171	28	is	be	AUX
ejpam-5189	171	29	convex	convex	ADJ
ejpam-5189	171	30	and	and	CCONJ
ejpam-5189	171	31	g	g	PROPN
ejpam-5189	171	32	and	and	CCONJ
ejpam-5189	171	33	h	h	NOUN
ejpam-5189	171	34	are	be	AUX
ejpam-5189	171	35	non	non	ADJ
ejpam-5189	171	36	-	-	ADJ
ejpam-5189	171	37	complete	complete	ADJ
ejpam-5189	171	38	,	,	PUNCT
ejpam-5189	171	39	sg	sg	PROPN
ejpam-5189	171	40	and	and	CCONJ
ejpam-5189	171	41	sh	sh	PROPN
ejpam-5189	171	42	are	be	AUX
ejpam-5189	171	43	cliques	clique	NOUN
ejpam-5189	171	44	in	in	ADP
ejpam-5189	171	45	g	g	PROPN
ejpam-5189	171	46	and	and	CCONJ
ejpam-5189	171	47	h	h	NOUN
ejpam-5189	171	48	,	,	PUNCT
ejpam-5189	171	49	respectively	respectively	ADV
ejpam-5189	171	50	.	.	PUNCT
ejpam-5189	172	1	if	if	SCONJ
ejpam-5189	172	2	|sg|	|sg|	NOUN
ejpam-5189	172	3	≥	≥	NOUN
ejpam-5189	172	4	2	2	NUM
ejpam-5189	172	5	and	and	CCONJ
ejpam-5189	172	6	|sh	|sh	ADP
ejpam-5189	172	7	|	|	ADV
ejpam-5189	172	8	≥	≥	NOUN
ejpam-5189	172	9	2	2	NUM
ejpam-5189	172	10	,	,	PUNCT
ejpam-5189	172	11	then	then	ADV
ejpam-5189	172	12	(	(	PUNCT
ejpam-5189	172	13	a	a	X
ejpam-5189	172	14	)	)	PUNCT
ejpam-5189	172	15	holds	hold	NOUN
ejpam-5189	172	16	.	.	PUNCT
ejpam-5189	173	1	suppose	suppose	VERB
ejpam-5189	173	2	|sg|	|sg|	NOUN
ejpam-5189	173	3	=	=	SYM
ejpam-5189	173	4	1	1	NUM
ejpam-5189	173	5	and	and	CCONJ
ejpam-5189	173	6	|sh	|sh	PROPN
ejpam-5189	173	7	|	|	ADV
ejpam-5189	173	8	=	=	SYM
ejpam-5189	173	9	1	1	X
ejpam-5189	173	10	.	.	PUNCT
ejpam-5189	174	1	since	since	SCONJ
ejpam-5189	174	2	s	s	PROPN
ejpam-5189	174	3	is	be	AUX
ejpam-5189	174	4	2	2	NUM
ejpam-5189	174	5	-	-	PUNCT
ejpam-5189	174	6	dominating	dominating	NOUN
ejpam-5189	174	7	in	in	ADP
ejpam-5189	174	8	g	g	PROPN
ejpam-5189	175	1	+	+	CCONJ
ejpam-5189	175	2	h	h	NOUN
ejpam-5189	175	3	,	,	PUNCT
ejpam-5189	175	4	it	it	PRON
ejpam-5189	175	5	follows	follow	VERB
ejpam-5189	175	6	that	that	SCONJ
ejpam-5189	175	7	sg	sg	PROPN
ejpam-5189	175	8	and	and	CCONJ
ejpam-5189	175	9	sh	sh	PROPN
ejpam-5189	175	10	are	be	AUX
ejpam-5189	175	11	dominating	dominate	VERB
ejpam-5189	175	12	sets	set	NOUN
ejpam-5189	175	13	in	in	ADP
ejpam-5189	175	14	g	g	PROPN
ejpam-5189	175	15	and	and	CCONJ
ejpam-5189	175	16	h	h	NOUN
ejpam-5189	175	17	,	,	PUNCT
ejpam-5189	175	18	respectively	respectively	ADV
ejpam-5189	175	19	,	,	PUNCT
ejpam-5189	175	20	showing	show	VERB
ejpam-5189	175	21	that	that	SCONJ
ejpam-5189	175	22	(	(	PUNCT
ejpam-5189	175	23	b	b	X
ejpam-5189	175	24	)	)	PUNCT
ejpam-5189	175	25	holds	hold	VERB
ejpam-5189	175	26	.	.	PUNCT
ejpam-5189	176	1	suppose	suppose	VERB
ejpam-5189	176	2	|sg|	|sg|	NOUN
ejpam-5189	176	3	=	=	SYM
ejpam-5189	176	4	1	1	NUM
ejpam-5189	176	5	and	and	CCONJ
ejpam-5189	176	6	|sh	|sh	ADP
ejpam-5189	176	7	|	|	ADV
ejpam-5189	176	8	≥	≥	NOUN
ejpam-5189	176	9	2	2	NUM
ejpam-5189	176	10	.	.	PUNCT
ejpam-5189	177	1	since	since	SCONJ
ejpam-5189	177	2	sh	sh	PROPN
ejpam-5189	177	3	̸=	̸=	PROPN
ejpam-5189	177	4	v	v	PROPN
ejpam-5189	177	5	(	(	PUNCT
ejpam-5189	177	6	h	h	NOUN
ejpam-5189	177	7	)	)	PUNCT
ejpam-5189	177	8	(	(	PUNCT
ejpam-5189	177	9	otherwise	otherwise	ADV
ejpam-5189	177	10	s	s	VERB
ejpam-5189	177	11	=	=	SYM
ejpam-5189	177	12	v	v	PROPN
ejpam-5189	177	13	(	(	PUNCT
ejpam-5189	177	14	g+h	g+h	NOUN
ejpam-5189	177	15	)	)	PUNCT
ejpam-5189	177	16	)	)	PUNCT
ejpam-5189	177	17	and	and	CCONJ
ejpam-5189	177	18	s	s	VERB
ejpam-5189	177	19	is	be	AUX
ejpam-5189	177	20	convex	convex	ADJ
ejpam-5189	177	21	2	2	NUM
ejpam-5189	177	22	-	-	PUNCT
ejpam-5189	177	23	dominating	dominating	NOUN
ejpam-5189	177	24	in	in	ADP
ejpam-5189	177	25	g+h	g+h	PROPN
ejpam-5189	177	26	,	,	PUNCT
ejpam-5189	177	27	sh	sh	PROPN
ejpam-5189	177	28	is	be	AUX
ejpam-5189	177	29	a	a	DET
ejpam-5189	177	30	clique	clique	NOUN
ejpam-5189	177	31	dominating	dominating	NOUN
ejpam-5189	177	32	set	set	VERB
ejpam-5189	177	33	in	in	ADP
ejpam-5189	177	34	h.	h.	PROPN
ejpam-5189	177	35	hence	hence	ADV
ejpam-5189	177	36	,	,	PUNCT
ejpam-5189	177	37	(	(	PUNCT
ejpam-5189	177	38	c	c	X
ejpam-5189	177	39	)	)	PUNCT
ejpam-5189	177	40	holds	hold	NOUN
ejpam-5189	177	41	.	.	PUNCT
ejpam-5189	178	1	similarly	similarly	ADV
ejpam-5189	178	2	,	,	PUNCT
ejpam-5189	178	3	(	(	PUNCT
ejpam-5189	178	4	d	d	X
ejpam-5189	178	5	)	)	PUNCT
ejpam-5189	178	6	holds	hold	VERB
ejpam-5189	178	7	if	if	SCONJ
ejpam-5189	178	8	|sg|	|sg|	NOUN
ejpam-5189	178	9	≥	≥	NOUN
ejpam-5189	178	10	2	2	NUM
ejpam-5189	178	11	and	and	CCONJ
ejpam-5189	178	12	|sh	|sh	ADP
ejpam-5189	178	13	|	|	ADV
ejpam-5189	178	14	=	=	SYM
ejpam-5189	178	15	1	1	X
ejpam-5189	178	16	.	.	PUNCT
ejpam-5189	179	1	the	the	DET
ejpam-5189	179	2	converse	converse	NOUN
ejpam-5189	179	3	is	be	AUX
ejpam-5189	179	4	clear	clear	ADJ
ejpam-5189	179	5	.	.	PUNCT
ejpam-5189	180	1	corollary	corollary	ADJ
ejpam-5189	180	2	3	3	X
ejpam-5189	180	3	.	.	PUNCT
ejpam-5189	181	1	let	let	VERB
ejpam-5189	181	2	g	g	NOUN
ejpam-5189	181	3	and	and	CCONJ
ejpam-5189	181	4	h	h	NOUN
ejpam-5189	181	5	be	be	AUX
ejpam-5189	181	6	non	non	ADJ
ejpam-5189	181	7	-	-	ADJ
ejpam-5189	181	8	complete	complete	ADJ
ejpam-5189	181	9	graphs	graph	NOUN
ejpam-5189	181	10	such	such	ADJ
ejpam-5189	181	11	that	that	PRON
ejpam-5189	181	12	γ(g	γ(g	PROPN
ejpam-5189	181	13	)	)	PUNCT
ejpam-5189	182	1	=	=	SYM
ejpam-5189	182	2	γ(h	γ(h	NOUN
ejpam-5189	182	3	)	)	PUNCT
ejpam-5189	182	4	=	=	SYM
ejpam-5189	183	1	1	1	X
ejpam-5189	183	2	.	.	X
ejpam-5189	183	3	then	then	ADV
ejpam-5189	183	4	γ2con(g+h	γ2con(g+h	PROPN
ejpam-5189	183	5	)	)	PUNCT
ejpam-5189	183	6	=	=	SYM
ejpam-5189	184	1	2	2	X
ejpam-5189	184	2	.	.	X
ejpam-5189	184	3	lemma	lemma	PROPN
ejpam-5189	184	4	1	1	X
ejpam-5189	184	5	.	.	PUNCT
ejpam-5189	185	1	let	let	VERB
ejpam-5189	185	2	g	g	PRON
ejpam-5189	185	3	be	be	AUX
ejpam-5189	185	4	a	a	DET
ejpam-5189	185	5	non	non	ADJ
ejpam-5189	185	6	-	-	ADJ
ejpam-5189	185	7	trivial	trivial	ADJ
ejpam-5189	185	8	connected	connected	ADJ
ejpam-5189	185	9	graph	graph	NOUN
ejpam-5189	185	10	.	.	PUNCT
ejpam-5189	186	1	if	if	SCONJ
ejpam-5189	186	2	g	g	PROPN
ejpam-5189	186	3	admits	admit	VERB
ejpam-5189	186	4	a	a	DET
ejpam-5189	186	5	clique	clique	ADJ
ejpam-5189	186	6	2	2	NUM
ejpam-5189	186	7	-	-	PUNCT
ejpam-5189	186	8	dominating	dominating	NOUN
ejpam-5189	186	9	set	set	NOUN
ejpam-5189	186	10	,	,	PUNCT
ejpam-5189	186	11	then	then	ADV
ejpam-5189	186	12	1	1	NUM
ejpam-5189	186	13	+	+	SYM
ejpam-5189	186	14	γcl(g	γcl(g	X
ejpam-5189	186	15	)	)	PUNCT
ejpam-5189	186	16	≤	≤	NUM
ejpam-5189	186	17	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	186	18	)	)	PUNCT
ejpam-5189	186	19	.	.	PUNCT
ejpam-5189	187	1	proof	proof	NOUN
ejpam-5189	187	2	.	.	PUNCT
ejpam-5189	188	1	letd	letd	PROPN
ejpam-5189	188	2	be	be	AUX
ejpam-5189	188	3	a	a	DET
ejpam-5189	188	4	γ2cl	γ2cl	NOUN
ejpam-5189	188	5	-	-	PUNCT
ejpam-5189	188	6	set	set	VERB
ejpam-5189	188	7	ing	ing	NOUN
ejpam-5189	188	8	.	.	PUNCT
ejpam-5189	189	1	then	then	ADV
ejpam-5189	189	2	,	,	PUNCT
ejpam-5189	189	3	clearly	clearly	ADV
ejpam-5189	189	4	,	,	PUNCT
ejpam-5189	189	5	|d|	|d|	PROPN
ejpam-5189	189	6	≥	≥	NUM
ejpam-5189	189	7	2	2	NUM
ejpam-5189	189	8	.	.	PUNCT
ejpam-5189	190	1	let	let	VERB
ejpam-5189	190	2	v	v	NUM
ejpam-5189	190	3	∈	∈	PROPN
ejpam-5189	190	4	d	d	NOUN
ejpam-5189	190	5	and	and	CCONJ
ejpam-5189	190	6	setd∗	setd∗	NOUN
ejpam-5189	190	7	=	=	PUNCT
ejpam-5189	190	8	d\{v	d\{v	NOUN
ejpam-5189	190	9	}	}	PUNCT
ejpam-5189	190	10	.	.	PUNCT
ejpam-5189	191	1	if	if	SCONJ
ejpam-5189	191	2	|d|	|d|	PROPN
ejpam-5189	191	3	=	=	SYM
ejpam-5189	191	4	2	2	NUM
ejpam-5189	191	5	,	,	PUNCT
ejpam-5189	191	6	then	then	ADV
ejpam-5189	191	7	|d∗|	|d∗|	PUNCT
ejpam-5189	191	8	=	=	SYM
ejpam-5189	191	9	1	1	NUM
ejpam-5189	191	10	and	and	CCONJ
ejpam-5189	191	11	d∗	d∗	PROPN
ejpam-5189	191	12	is	be	AUX
ejpam-5189	191	13	a	a	DET
ejpam-5189	191	14	dominating	dominating	NOUN
ejpam-5189	191	15	set	set	VERB
ejpam-5189	191	16	in	in	ADP
ejpam-5189	191	17	g.	g.	PROPN
ejpam-5189	191	18	suppose	suppose	VERB
ejpam-5189	191	19	|d|	|d|	PROPN
ejpam-5189	191	20	≥	≥	NUM
ejpam-5189	191	21	3	3	NUM
ejpam-5189	191	22	let	let	VERB
ejpam-5189	191	23	z	z	NOUN
ejpam-5189	191	24	∈	∈	PROPN
ejpam-5189	191	25	v	v	ADP
ejpam-5189	191	26	(	(	PUNCT
ejpam-5189	191	27	g	g	NOUN
ejpam-5189	191	28	)	)	PUNCT
ejpam-5189	191	29	\	\	PUNCT
ejpam-5189	192	1	d∗.	d∗.	PROPN
ejpam-5189	192	2	if	if	SCONJ
ejpam-5189	192	3	z	z	PROPN
ejpam-5189	192	4	∈	∈	PROPN
ejpam-5189	192	5	d	d	NOUN
ejpam-5189	192	6	,	,	PUNCT
ejpam-5189	192	7	then	then	ADV
ejpam-5189	192	8	zw	zw	PROPN
ejpam-5189	192	9	∈	∈	PROPN
ejpam-5189	192	10	e(g	e(g	PROPN
ejpam-5189	192	11	)	)	PUNCT
ejpam-5189	192	12	for	for	ADP
ejpam-5189	192	13	every	every	DET
ejpam-5189	192	14	w	w	PROPN
ejpam-5189	192	15	∈	∈	PROPN
ejpam-5189	192	16	d∗.	d∗.	PROPN
ejpam-5189	192	17	suppose	suppose	VERB
ejpam-5189	192	18	z	z	PROPN
ejpam-5189	192	19	∈	∈	PROPN
ejpam-5189	192	20	v	v	ADP
ejpam-5189	192	21	(	(	PUNCT
ejpam-5189	192	22	g	g	NOUN
ejpam-5189	192	23	)	)	PUNCT
ejpam-5189	192	24	\	\	PROPN
ejpam-5189	192	25	d.	d.	PROPN
ejpam-5189	192	26	since	since	SCONJ
ejpam-5189	192	27	d	d	PROPN
ejpam-5189	192	28	is	be	AUX
ejpam-5189	192	29	2	2	NUM
ejpam-5189	192	30	-	-	PUNCT
ejpam-5189	192	31	dominating	dominating	NOUN
ejpam-5189	192	32	,	,	PUNCT
ejpam-5189	192	33	|ng(z)∩d|	|ng(z)∩d|	X
ejpam-5189	192	34	≥	≥	NOUN
ejpam-5189	192	35	2	2	X
ejpam-5189	192	36	.	.	PUNCT
ejpam-5189	193	1	it	it	PRON
ejpam-5189	193	2	follows	follow	VERB
ejpam-5189	193	3	that	that	SCONJ
ejpam-5189	193	4	|ng(z)∩d∗|	|ng(z)∩d∗|	ADJ
ejpam-5189	193	5	≥	≥	NOUN
ejpam-5189	193	6	1	1	NUM
ejpam-5189	193	7	,	,	PUNCT
ejpam-5189	193	8	showing	show	VERB
ejpam-5189	193	9	that	that	DET
ejpam-5189	193	10	d∗	d∗	NOUN
ejpam-5189	193	11	is	be	AUX
ejpam-5189	193	12	a	a	DET
ejpam-5189	193	13	clique	clique	NOUN
ejpam-5189	193	14	dominating	dominating	NOUN
ejpam-5189	193	15	set	set	VERB
ejpam-5189	193	16	in	in	ADP
ejpam-5189	193	17	g.	g.	PROPN
ejpam-5189	193	18	thus	thus	ADV
ejpam-5189	193	19	,	,	PUNCT
ejpam-5189	193	20	γcl(g	γcl(g	PROPN
ejpam-5189	193	21	)	)	PUNCT
ejpam-5189	193	22	≤	≤	NOUN
ejpam-5189	193	23	|d∗|	|d∗|	PART
ejpam-5189	193	24	=	=	SYM
ejpam-5189	193	25	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	193	26	)	)	PUNCT
ejpam-5189	193	27	−	−	PROPN
ejpam-5189	194	1	1	1	X
ejpam-5189	194	2	.	.	PUNCT
ejpam-5189	195	1	this	this	PRON
ejpam-5189	195	2	proves	prove	VERB
ejpam-5189	195	3	the	the	DET
ejpam-5189	195	4	assertion	assertion	NOUN
ejpam-5189	195	5	.	.	PUNCT
ejpam-5189	196	1	the	the	DET
ejpam-5189	196	2	next	next	ADJ
ejpam-5189	196	3	result	result	NOUN
ejpam-5189	196	4	follows	follow	VERB
ejpam-5189	196	5	from	from	ADP
ejpam-5189	196	6	theorem	theorem	ADJ
ejpam-5189	196	7	3	3	NUM
ejpam-5189	196	8	and	and	CCONJ
ejpam-5189	196	9	lemma	lemma	PROPN
ejpam-5189	196	10	1	1	NUM
ejpam-5189	196	11	.	.	PUNCT
ejpam-5189	196	12	corollary	corollary	ADJ
ejpam-5189	196	13	4	4	NUM
ejpam-5189	196	14	.	.	PUNCT
ejpam-5189	197	1	let	let	VERB
ejpam-5189	197	2	g	g	NOUN
ejpam-5189	197	3	and	and	CCONJ
ejpam-5189	197	4	h	h	NOUN
ejpam-5189	197	5	be	be	AUX
ejpam-5189	197	6	non	non	ADJ
ejpam-5189	197	7	-	-	ADJ
ejpam-5189	197	8	complete	complete	ADJ
ejpam-5189	197	9	graphs	graph	NOUN
ejpam-5189	197	10	such	such	ADJ
ejpam-5189	197	11	that	that	PRON
ejpam-5189	197	12	γ(g	γ(g	PROPN
ejpam-5189	197	13	)	)	PUNCT
ejpam-5189	197	14	̸=	̸=	PROPN
ejpam-5189	197	15	1	1	NUM
ejpam-5189	197	16	and	and	CCONJ
ejpam-5189	197	17	γ(h	γ(h	NOUN
ejpam-5189	197	18	)	)	PUNCT
ejpam-5189	197	19	̸=	̸=	PROPN
ejpam-5189	197	20	1	1	NUM
ejpam-5189	197	21	.	.	PUNCT
ejpam-5189	198	1	(	(	PUNCT
ejpam-5189	198	2	i	i	NOUN
ejpam-5189	198	3	)	)	PUNCT
ejpam-5189	198	4	if	if	SCONJ
ejpam-5189	198	5	g	g	PROPN
ejpam-5189	198	6	and	and	CCONJ
ejpam-5189	198	7	h	h	PRON
ejpam-5189	198	8	both	both	PRON
ejpam-5189	198	9	admit	admit	VERB
ejpam-5189	198	10	a	a	DET
ejpam-5189	198	11	clique	clique	NOUN
ejpam-5189	198	12	2	2	NUM
ejpam-5189	198	13	-	-	PUNCT
ejpam-5189	198	14	dominating	dominating	NOUN
ejpam-5189	198	15	set	set	NOUN
ejpam-5189	198	16	(	(	PUNCT
ejpam-5189	198	17	a	a	DET
ejpam-5189	198	18	clique	clique	NOUN
ejpam-5189	198	19	dominating	dominating	NOUN
ejpam-5189	198	20	set	set	NOUN
ejpam-5189	198	21	)	)	PUNCT
ejpam-5189	198	22	,	,	PUNCT
ejpam-5189	198	23	then	then	ADV
ejpam-5189	198	24	γ2con(g+h	γ2con(g+h	PROPN
ejpam-5189	198	25	)	)	PUNCT
ejpam-5189	198	26	=	=	SYM
ejpam-5189	198	27	min{1	min{1	NOUN
ejpam-5189	198	28	+	+	CCONJ
ejpam-5189	198	29	γcl(g	γcl(g	PROPN
ejpam-5189	198	30	)	)	PUNCT
ejpam-5189	198	31	,	,	PUNCT
ejpam-5189	198	32	1	1	NUM
ejpam-5189	198	33	+	+	CCONJ
ejpam-5189	198	34	γcl(h	γcl(h	PROPN
ejpam-5189	198	35	)	)	PUNCT
ejpam-5189	198	36	,	,	PUNCT
ejpam-5189	198	37	4	4	NUM
ejpam-5189	198	38	}	}	PUNCT
ejpam-5189	198	39	.	.	PUNCT
ejpam-5189	199	1	r.	r.	PROPN
ejpam-5189	199	2	j.	j.	PROPN
ejpam-5189	199	3	g.	g.	PROPN
ejpam-5189	199	4	fortosa	fortosa	PROPN
ejpam-5189	199	5	et	et	PROPN
ejpam-5189	199	6	al	al	PROPN
ejpam-5189	199	7	.	.	PUNCT
ejpam-5189	199	8	/	/	SYM
ejpam-5189	199	9	eur	eur	PROPN
ejpam-5189	199	10	.	.	PUNCT
ejpam-5189	200	1	j.	j.	PROPN
ejpam-5189	200	2	pure	pure	PROPN
ejpam-5189	200	3	appl	appl	PROPN
ejpam-5189	200	4	.	.	PROPN
ejpam-5189	200	5	math	math	PROPN
ejpam-5189	200	6	,	,	PUNCT
ejpam-5189	200	7	17	17	NUM
ejpam-5189	200	8	(	(	PUNCT
ejpam-5189	200	9	3	3	NUM
ejpam-5189	200	10	)	)	PUNCT
ejpam-5189	200	11	(	(	PUNCT
ejpam-5189	200	12	2024	2024	NUM
ejpam-5189	200	13	)	)	PUNCT
ejpam-5189	200	14	,	,	PUNCT
ejpam-5189	200	15	1539	1539	NUM
ejpam-5189	200	16	-	-	SYM
ejpam-5189	200	17	1552	1552	NUM
ejpam-5189	200	18	1545	1545	NUM
ejpam-5189	200	19	(	(	PUNCT
ejpam-5189	200	20	ii	ii	NOUN
ejpam-5189	200	21	)	)	PUNCT
ejpam-5189	200	22	if	if	SCONJ
ejpam-5189	200	23	g	g	PROPN
ejpam-5189	200	24	admits	admit	VERB
ejpam-5189	200	25	a	a	DET
ejpam-5189	200	26	clique	clique	NOUN
ejpam-5189	200	27	dominating	dominating	NOUN
ejpam-5189	200	28	set	set	NOUN
ejpam-5189	200	29	but	but	CCONJ
ejpam-5189	200	30	h	h	NOUN
ejpam-5189	200	31	does	do	VERB
ejpam-5189	200	32	not	not	PART
ejpam-5189	200	33	,	,	PUNCT
ejpam-5189	200	34	then	then	ADV
ejpam-5189	200	35	γ2con(g+h	γ2con(g+h	PROPN
ejpam-5189	200	36	)	)	PUNCT
ejpam-5189	201	1	=	=	SYM
ejpam-5189	201	2	min{1	min{1	NOUN
ejpam-5189	201	3	+	+	CCONJ
ejpam-5189	201	4	γcl(g	γcl(g	PROPN
ejpam-5189	201	5	)	)	PUNCT
ejpam-5189	201	6	,	,	PUNCT
ejpam-5189	201	7	4	4	NUM
ejpam-5189	201	8	}	}	PUNCT
ejpam-5189	201	9	.	.	PUNCT
ejpam-5189	202	1	(	(	PUNCT
ejpam-5189	202	2	iii	iii	X
ejpam-5189	202	3	)	)	PUNCT
ejpam-5189	202	4	if	if	SCONJ
ejpam-5189	202	5	g	g	PROPN
ejpam-5189	202	6	and	and	CCONJ
ejpam-5189	202	7	h	h	NOUN
ejpam-5189	202	8	are	be	AUX
ejpam-5189	202	9	disconnected	disconnected	ADJ
ejpam-5189	202	10	graphs	graph	NOUN
ejpam-5189	202	11	,	,	PUNCT
ejpam-5189	202	12	then	then	ADV
ejpam-5189	202	13	γ2con(g+h	γ2con(g+h	PROPN
ejpam-5189	202	14	)	)	PUNCT
ejpam-5189	202	15	=	=	PRON
ejpam-5189	202	16	{	{	PUNCT
ejpam-5189	202	17	4	4	NUM
ejpam-5189	202	18	if	if	SCONJ
ejpam-5189	202	19	e(g	e(g	NOUN
ejpam-5189	202	20	)	)	PUNCT
ejpam-5189	202	21	̸=	̸=	PROPN
ejpam-5189	202	22	∅	∅	NOUN
ejpam-5189	202	23	and	and	CCONJ
ejpam-5189	202	24	e(h	e(h	PROPN
ejpam-5189	202	25	)	)	PUNCT
ejpam-5189	202	26	̸=	̸=	PROPN
ejpam-5189	202	27	∅	∅	NOUN
ejpam-5189	202	28	|v	|v	NOUN
ejpam-5189	202	29	(	(	PUNCT
ejpam-5189	202	30	g+h)|	g+h)|	PROPN
ejpam-5189	202	31	if	if	SCONJ
ejpam-5189	202	32	e(g	e(g	NOUN
ejpam-5189	202	33	)	)	PUNCT
ejpam-5189	203	1	=	=	NOUN
ejpam-5189	203	2	∅	∅	NOUN
ejpam-5189	203	3	or	or	CCONJ
ejpam-5189	203	4	e(h	e(h	PROPN
ejpam-5189	203	5	)	)	PUNCT
ejpam-5189	203	6	=	=	PUNCT
ejpam-5189	203	7	∅.	∅.	NOUN
ejpam-5189	203	8	theorem	theorem	VERB
ejpam-5189	203	9	4	4	NUM
ejpam-5189	203	10	.	.	PUNCT
ejpam-5189	204	1	let	let	VERB
ejpam-5189	204	2	g	g	PRON
ejpam-5189	204	3	be	be	AUX
ejpam-5189	204	4	a	a	DET
ejpam-5189	204	5	non	non	ADJ
ejpam-5189	204	6	-	-	ADJ
ejpam-5189	204	7	complete	complete	ADJ
ejpam-5189	204	8	graph	graph	NOUN
ejpam-5189	204	9	and	and	CCONJ
ejpam-5189	204	10	let	let	VERB
ejpam-5189	204	11	n	n	PRON
ejpam-5189	204	12	be	be	AUX
ejpam-5189	204	13	a	a	DET
ejpam-5189	204	14	positive	positive	ADJ
ejpam-5189	204	15	integer	integer	NOUN
ejpam-5189	204	16	.	.	PUNCT
ejpam-5189	205	1	a	a	DET
ejpam-5189	205	2	subset	subset	NOUN
ejpam-5189	205	3	s	s	VERB
ejpam-5189	205	4	⊆	⊆	NUM
ejpam-5189	205	5	v	v	NOUN
ejpam-5189	205	6	(	(	PUNCT
ejpam-5189	205	7	kn	kn	NOUN
ejpam-5189	205	8	+	+	CCONJ
ejpam-5189	205	9	g	g	NOUN
ejpam-5189	205	10	)	)	PUNCT
ejpam-5189	205	11	is	be	AUX
ejpam-5189	205	12	convex	convex	ADJ
ejpam-5189	205	13	2	2	NUM
ejpam-5189	205	14	-	-	PUNCT
ejpam-5189	205	15	dominating	dominating	NOUN
ejpam-5189	205	16	in	in	ADP
ejpam-5189	205	17	kn	kn	PROPN
ejpam-5189	205	18	+	+	CCONJ
ejpam-5189	205	19	g	g	PROPN
ejpam-5189	205	20	if	if	SCONJ
ejpam-5189	206	1	and	and	CCONJ
ejpam-5189	206	2	only	only	ADV
ejpam-5189	206	3	if	if	SCONJ
ejpam-5189	206	4	one	one	NUM
ejpam-5189	206	5	of	of	ADP
ejpam-5189	206	6	the	the	DET
ejpam-5189	206	7	following	follow	VERB
ejpam-5189	206	8	holds	hold	VERB
ejpam-5189	206	9	:	:	PUNCT
ejpam-5189	206	10	(	(	PUNCT
ejpam-5189	206	11	i	i	NOUN
ejpam-5189	206	12	)	)	PUNCT
ejpam-5189	206	13	s	s	VERB
ejpam-5189	206	14	⊆	⊆	NUM
ejpam-5189	206	15	v	v	NOUN
ejpam-5189	206	16	(	(	PUNCT
ejpam-5189	206	17	kn	kn	PROPN
ejpam-5189	206	18	)	)	PUNCT
ejpam-5189	206	19	and	and	CCONJ
ejpam-5189	206	20	|s|	|s|	PROPN
ejpam-5189	206	21	≥	≥	PROPN
ejpam-5189	206	22	2	2	NUM
ejpam-5189	206	23	.	.	PUNCT
ejpam-5189	206	24	(	(	PUNCT
ejpam-5189	206	25	ii	ii	NOUN
ejpam-5189	206	26	)	)	PUNCT
ejpam-5189	206	27	s	s	VERB
ejpam-5189	206	28	is	be	AUX
ejpam-5189	206	29	a	a	DET
ejpam-5189	206	30	clique	clique	ADJ
ejpam-5189	206	31	2	2	NUM
ejpam-5189	206	32	-	-	PUNCT
ejpam-5189	206	33	dominating	dominating	NOUN
ejpam-5189	206	34	set	set	NOUN
ejpam-5189	206	35	in	in	ADP
ejpam-5189	206	36	g.	g.	PROPN
ejpam-5189	206	37	(	(	PUNCT
ejpam-5189	206	38	iii	iii	PROPN
ejpam-5189	206	39	)	)	PUNCT
ejpam-5189	206	40	s	s	PART
ejpam-5189	206	41	=	=	PUNCT
ejpam-5189	206	42	sg	sg	PROPN
ejpam-5189	206	43	∪	∪	PROPN
ejpam-5189	206	44	sn	sn	PROPN
ejpam-5189	206	45	where	where	SCONJ
ejpam-5189	206	46	∅	∅	NOUN
ejpam-5189	206	47	̸=	̸=	PROPN
ejpam-5189	206	48	sg	sg	ADP
ejpam-5189	206	49	⊆	⊆	NUM
ejpam-5189	206	50	v	v	NOUN
ejpam-5189	206	51	(	(	PUNCT
ejpam-5189	206	52	g	g	NOUN
ejpam-5189	206	53	)	)	PUNCT
ejpam-5189	206	54	and	and	CCONJ
ejpam-5189	206	55	∅	∅	NOUN
ejpam-5189	206	56	̸=	̸=	PROPN
ejpam-5189	206	57	sn	sn	PROPN
ejpam-5189	206	58	⊆	⊆	NUM
ejpam-5189	206	59	v	v	NOUN
ejpam-5189	206	60	(	(	PUNCT
ejpam-5189	206	61	kn	kn	NOUN
ejpam-5189	206	62	)	)	PUNCT
ejpam-5189	206	63	satisfies	satisfy	VERB
ejpam-5189	206	64	any	any	PRON
ejpam-5189	206	65	of	of	ADP
ejpam-5189	206	66	the	the	DET
ejpam-5189	206	67	following	following	NOUN
ejpam-5189	206	68	:	:	PUNCT
ejpam-5189	206	69	(	(	PUNCT
ejpam-5189	206	70	a	a	X
ejpam-5189	206	71	)	)	PUNCT
ejpam-5189	206	72	sn	sn	PROPN
ejpam-5189	206	73	=	=	SYM
ejpam-5189	206	74	v	v	PROPN
ejpam-5189	206	75	(	(	PUNCT
ejpam-5189	206	76	kn	kn	PROPN
ejpam-5189	206	77	)	)	PUNCT
ejpam-5189	206	78	and	and	CCONJ
ejpam-5189	206	79	v	v	NOUN
ejpam-5189	206	80	(	(	PUNCT
ejpam-5189	206	81	g	g	NOUN
ejpam-5189	206	82	)	)	PUNCT
ejpam-5189	206	83	\	\	PROPN
ejpam-5189	207	1	sg	sg	PROPN
ejpam-5189	207	2	is	be	AUX
ejpam-5189	207	3	a	a	DET
ejpam-5189	207	4	non	non	ADJ
ejpam-5189	207	5	-	-	ADJ
ejpam-5189	207	6	connecting	connecting	ADJ
ejpam-5189	207	7	set	set	NOUN
ejpam-5189	207	8	in	in	ADP
ejpam-5189	207	9	g	g	PROPN
ejpam-5189	207	10	,	,	PUNCT
ejpam-5189	207	11	where	where	SCONJ
ejpam-5189	207	12	,	,	PUNCT
ejpam-5189	207	13	in	in	ADP
ejpam-5189	207	14	addition	addition	NOUN
ejpam-5189	207	15	,	,	PUNCT
ejpam-5189	207	16	sg	sg	PROPN
ejpam-5189	207	17	is	be	AUX
ejpam-5189	207	18	dominating	dominate	VERB
ejpam-5189	207	19	if	if	SCONJ
ejpam-5189	207	20	n	n	NOUN
ejpam-5189	207	21	=	=	SYM
ejpam-5189	207	22	1	1	X
ejpam-5189	207	23	.	.	PUNCT
ejpam-5189	208	1	(	(	PUNCT
ejpam-5189	208	2	b	b	X
ejpam-5189	208	3	)	)	PUNCT
ejpam-5189	208	4	sn	sn	PROPN
ejpam-5189	208	5	̸=	̸=	PROPN
ejpam-5189	208	6	v	v	NOUN
ejpam-5189	208	7	(	(	PUNCT
ejpam-5189	208	8	kn	kn	PROPN
ejpam-5189	208	9	)	)	PUNCT
ejpam-5189	208	10	with	with	ADP
ejpam-5189	208	11	|sn|	|sn|	PROPN
ejpam-5189	208	12	=	=	SYM
ejpam-5189	208	13	1	1	NUM
ejpam-5189	208	14	and	and	CCONJ
ejpam-5189	208	15	sg	sg	PROPN
ejpam-5189	208	16	is	be	AUX
ejpam-5189	208	17	a	a	DET
ejpam-5189	208	18	clique	clique	NOUN
ejpam-5189	208	19	dominating	dominating	NOUN
ejpam-5189	208	20	set	set	VERB
ejpam-5189	208	21	in	in	ADP
ejpam-5189	208	22	g.	g.	PROPN
ejpam-5189	208	23	(	(	PUNCT
ejpam-5189	208	24	c	c	X
ejpam-5189	208	25	)	)	PUNCT
ejpam-5189	208	26	sn	sn	PROPN
ejpam-5189	208	27	̸=	̸=	PROPN
ejpam-5189	208	28	v	v	NOUN
ejpam-5189	208	29	(	(	PUNCT
ejpam-5189	208	30	kn	kn	PROPN
ejpam-5189	208	31	)	)	PUNCT
ejpam-5189	208	32	with	with	ADP
ejpam-5189	208	33	|sn|	|sn|	PROPN
ejpam-5189	208	34	≥	≥	NUM
ejpam-5189	208	35	2	2	NUM
ejpam-5189	208	36	and	and	CCONJ
ejpam-5189	208	37	sg	sg	PROPN
ejpam-5189	208	38	is	be	AUX
ejpam-5189	208	39	a	a	DET
ejpam-5189	208	40	clique	clique	NOUN
ejpam-5189	208	41	in	in	ADP
ejpam-5189	208	42	g.	g.	PROPN
ejpam-5189	208	43	proof	proof	PROPN
ejpam-5189	208	44	.	.	PUNCT
ejpam-5189	209	1	suppose	suppose	VERB
ejpam-5189	209	2	s	s	PRON
ejpam-5189	209	3	is	be	AUX
ejpam-5189	209	4	a	a	DET
ejpam-5189	209	5	convex	convex	ADJ
ejpam-5189	209	6	2	2	NUM
ejpam-5189	209	7	-	-	PUNCT
ejpam-5189	209	8	dominating	dominating	NOUN
ejpam-5189	209	9	set	set	NOUN
ejpam-5189	209	10	in	in	ADP
ejpam-5189	209	11	kn	kn	PROPN
ejpam-5189	210	1	+	+	CCONJ
ejpam-5189	210	2	g.	g.	PROPN
ejpam-5189	211	1	if	if	SCONJ
ejpam-5189	211	2	s	s	VERB
ejpam-5189	211	3	⊆	⊆	NUM
ejpam-5189	211	4	v	v	NOUN
ejpam-5189	211	5	(	(	PUNCT
ejpam-5189	211	6	kn	kn	PROPN
ejpam-5189	211	7	)	)	PUNCT
ejpam-5189	211	8	,	,	PUNCT
ejpam-5189	211	9	then	then	ADV
ejpam-5189	211	10	|s|	|s|	NOUN
ejpam-5189	211	11	≥	≥	NOUN
ejpam-5189	211	12	2	2	NUM
ejpam-5189	211	13	,	,	PUNCT
ejpam-5189	211	14	showing	show	VERB
ejpam-5189	211	15	that	that	SCONJ
ejpam-5189	211	16	(	(	PUNCT
ejpam-5189	211	17	i	i	NOUN
ejpam-5189	211	18	)	)	PUNCT
ejpam-5189	211	19	holds	hold	VERB
ejpam-5189	211	20	.	.	PUNCT
ejpam-5189	212	1	suppose	suppose	VERB
ejpam-5189	212	2	that	that	SCONJ
ejpam-5189	212	3	s	s	VERB
ejpam-5189	212	4	⊆	⊆	NUM
ejpam-5189	212	5	v	v	NOUN
ejpam-5189	212	6	(	(	PUNCT
ejpam-5189	212	7	g	g	NOUN
ejpam-5189	212	8	)	)	PUNCT
ejpam-5189	212	9	.	.	PUNCT
ejpam-5189	213	1	since	since	SCONJ
ejpam-5189	213	2	g	g	PROPN
ejpam-5189	213	3	is	be	AUX
ejpam-5189	213	4	non	non	ADJ
ejpam-5189	213	5	-	-	ADJ
ejpam-5189	213	6	complete	complete	ADJ
ejpam-5189	213	7	and	and	CCONJ
ejpam-5189	213	8	s	s	NOUN
ejpam-5189	213	9	is	be	AUX
ejpam-5189	213	10	convex	convex	ADJ
ejpam-5189	213	11	and	and	CCONJ
ejpam-5189	213	12	2	2	NUM
ejpam-5189	213	13	-	-	PUNCT
ejpam-5189	213	14	dominating	dominating	NOUN
ejpam-5189	213	15	in	in	ADP
ejpam-5189	213	16	g	g	PROPN
ejpam-5189	214	1	+	+	CCONJ
ejpam-5189	214	2	h	h	NOUN
ejpam-5189	214	3	,	,	PUNCT
ejpam-5189	214	4	s	s	PART
ejpam-5189	214	5	is	be	AUX
ejpam-5189	214	6	a	a	DET
ejpam-5189	214	7	clique	clique	NOUN
ejpam-5189	214	8	dominating	dominating	NOUN
ejpam-5189	214	9	set	set	VERB
ejpam-5189	214	10	in	in	ADP
ejpam-5189	214	11	g.	g.	PROPN
ejpam-5189	214	12	hence	hence	ADV
ejpam-5189	214	13	,	,	PUNCT
ejpam-5189	214	14	(	(	PUNCT
ejpam-5189	214	15	ii	ii	NOUN
ejpam-5189	214	16	)	)	PUNCT
ejpam-5189	214	17	holds	hold	VERB
ejpam-5189	214	18	.	.	PUNCT
ejpam-5189	215	1	next	next	ADV
ejpam-5189	215	2	,	,	PUNCT
ejpam-5189	215	3	suppose	suppose	VERB
ejpam-5189	215	4	sg	sg	ADP
ejpam-5189	215	5	=	=	PROPN
ejpam-5189	215	6	v	v	PROPN
ejpam-5189	215	7	(	(	PUNCT
ejpam-5189	215	8	g	g	NOUN
ejpam-5189	215	9	)	)	PUNCT
ejpam-5189	215	10	∩	∩	PROPN
ejpam-5189	215	11	s	s	PART
ejpam-5189	215	12	̸=	̸=	PROPN
ejpam-5189	215	13	∅	∅	NOUN
ejpam-5189	215	14	and	and	CCONJ
ejpam-5189	215	15	sn	sn	NOUN
ejpam-5189	215	16	=	=	SYM
ejpam-5189	215	17	v	v	PROPN
ejpam-5189	215	18	(	(	PUNCT
ejpam-5189	215	19	kn	kn	NOUN
ejpam-5189	215	20	)	)	PUNCT
ejpam-5189	215	21	∩	∩	PROPN
ejpam-5189	215	22	s	s	PART
ejpam-5189	215	23	̸=	̸=	PROPN
ejpam-5189	215	24	∅.	∅.	ADV
ejpam-5189	215	25	suppose	suppose	VERB
ejpam-5189	215	26	first	first	ADV
ejpam-5189	215	27	that	that	SCONJ
ejpam-5189	215	28	sn	sn	PROPN
ejpam-5189	215	29	=	=	SYM
ejpam-5189	215	30	v	v	PROPN
ejpam-5189	215	31	(	(	PUNCT
ejpam-5189	215	32	kn	kn	PROPN
ejpam-5189	215	33	)	)	PUNCT
ejpam-5189	215	34	.	.	PUNCT
ejpam-5189	216	1	let	let	VERB
ejpam-5189	216	2	p	p	PRON
ejpam-5189	216	3	,	,	PUNCT
ejpam-5189	216	4	q	q	PROPN
ejpam-5189	216	5	∈	∈	NOUN
ejpam-5189	216	6	sg	sg	ADP
ejpam-5189	216	7	such	such	ADJ
ejpam-5189	216	8	that	that	DET
ejpam-5189	216	9	dg(p	dg(p	NOUN
ejpam-5189	216	10	,	,	PUNCT
ejpam-5189	216	11	q	q	X
ejpam-5189	216	12	)	)	PUNCT
ejpam-5189	216	13	=	=	SYM
ejpam-5189	216	14	2	2	X
ejpam-5189	216	15	.	.	PUNCT
ejpam-5189	217	1	since	since	SCONJ
ejpam-5189	217	2	s	s	NOUN
ejpam-5189	217	3	is	be	AUX
ejpam-5189	217	4	convex	convex	ADJ
ejpam-5189	217	5	in	in	ADP
ejpam-5189	217	6	kn	kn	PROPN
ejpam-5189	217	7	+	+	CCONJ
ejpam-5189	217	8	g	g	PROPN
ejpam-5189	217	9	,	,	PUNCT
ejpam-5189	217	10	ig(p	ig(p	ADJ
ejpam-5189	217	11	,	,	PUNCT
ejpam-5189	217	12	q	q	X
ejpam-5189	217	13	)	)	PUNCT
ejpam-5189	217	14	=	=	SYM
ejpam-5189	217	15	ikn+g(p	ikn+g(p	NOUN
ejpam-5189	217	16	,	,	PUNCT
ejpam-5189	217	17	q	q	ADJ
ejpam-5189	217	18	)	)	PUNCT
ejpam-5189	217	19	\	\	PROPN
ejpam-5189	217	20	v	v	X
ejpam-5189	217	21	(	(	PUNCT
ejpam-5189	217	22	kn	kn	PROPN
ejpam-5189	217	23	)	)	PUNCT
ejpam-5189	217	24	⊆	⊆	NUM
ejpam-5189	217	25	ikn+g(p	ikn+g(p	NOUN
ejpam-5189	217	26	,	,	PUNCT
ejpam-5189	217	27	q	q	NOUN
ejpam-5189	217	28	)	)	PUNCT
ejpam-5189	217	29	⊆	⊆	NUM
ejpam-5189	217	30	s.	s.	PROPN
ejpam-5189	217	31	it	it	PRON
ejpam-5189	217	32	follows	follow	VERB
ejpam-5189	217	33	that	that	SCONJ
ejpam-5189	217	34	ig(p	ig(p	ADJ
ejpam-5189	217	35	,	,	PUNCT
ejpam-5189	217	36	q	q	X
ejpam-5189	217	37	)	)	PUNCT
ejpam-5189	217	38	⊆	⊆	NUM
ejpam-5189	217	39	sg	sg	NOUN
ejpam-5189	217	40	.	.	PUNCT
ejpam-5189	218	1	hence	hence	ADV
ejpam-5189	218	2	,	,	PUNCT
ejpam-5189	218	3	ng(p	ng(p	X
ejpam-5189	218	4	)	)	PUNCT
ejpam-5189	218	5	∩	∩	NOUN
ejpam-5189	218	6	ng(q	ng(q	NOUN
ejpam-5189	218	7	)	)	PUNCT
ejpam-5189	218	8	∩	∩	NOUN
ejpam-5189	218	9	(	(	PUNCT
ejpam-5189	218	10	v	v	NOUN
ejpam-5189	218	11	(	(	PUNCT
ejpam-5189	218	12	g	g	NOUN
ejpam-5189	218	13	)	)	PUNCT
ejpam-5189	218	14	\	\	PROPN
ejpam-5189	218	15	sg	sg	PROPN
ejpam-5189	218	16	)	)	PUNCT
ejpam-5189	218	17	=	=	PUNCT
ejpam-5189	218	18	∅.	∅.	ADP
ejpam-5189	218	19	this	this	PRON
ejpam-5189	218	20	shows	show	VERB
ejpam-5189	218	21	that	that	SCONJ
ejpam-5189	218	22	v	v	X
ejpam-5189	218	23	(	(	PUNCT
ejpam-5189	218	24	g	g	NOUN
ejpam-5189	218	25	)	)	PUNCT
ejpam-5189	218	26	\	\	PROPN
ejpam-5189	218	27	sg	sg	PROPN
ejpam-5189	218	28	is	be	AUX
ejpam-5189	218	29	a	a	DET
ejpam-5189	218	30	non	non	ADJ
ejpam-5189	218	31	-	-	ADJ
ejpam-5189	218	32	connecting	connecting	ADJ
ejpam-5189	218	33	set	set	NOUN
ejpam-5189	218	34	in	in	ADP
ejpam-5189	218	35	g.	g.	PROPN
ejpam-5189	218	36	if	if	SCONJ
ejpam-5189	218	37	n	n	PROPN
ejpam-5189	218	38	=	=	SYM
ejpam-5189	218	39	1	1	NUM
ejpam-5189	218	40	,	,	PUNCT
ejpam-5189	218	41	then	then	ADV
ejpam-5189	218	42	sg	sg	PROPN
ejpam-5189	218	43	is	be	AUX
ejpam-5189	218	44	a	a	DET
ejpam-5189	218	45	dominating	dominating	NOUN
ejpam-5189	218	46	set	set	NOUN
ejpam-5189	218	47	because	because	SCONJ
ejpam-5189	218	48	s	s	VERB
ejpam-5189	218	49	is	be	AUX
ejpam-5189	218	50	a	a	DET
ejpam-5189	218	51	2	2	NUM
ejpam-5189	218	52	-	-	PUNCT
ejpam-5189	218	53	dominating	dominating	NOUN
ejpam-5189	218	54	set	set	NOUN
ejpam-5189	218	55	in	in	ADP
ejpam-5189	218	56	kn	kn	PROPN
ejpam-5189	218	57	+	+	CCONJ
ejpam-5189	218	58	g.	g.	PROPN
ejpam-5189	218	59	thus	thus	ADV
ejpam-5189	218	60	,	,	PUNCT
ejpam-5189	218	61	(	(	PUNCT
ejpam-5189	218	62	a	a	PRON
ejpam-5189	218	63	)	)	PUNCT
ejpam-5189	218	64	holds	hold	NOUN
ejpam-5189	218	65	.	.	PUNCT
ejpam-5189	219	1	now	now	ADV
ejpam-5189	219	2	suppose	suppose	VERB
ejpam-5189	219	3	that	that	SCONJ
ejpam-5189	219	4	sn	sn	PROPN
ejpam-5189	219	5	̸=	̸=	PROPN
ejpam-5189	219	6	v	v	NOUN
ejpam-5189	219	7	(	(	PUNCT
ejpam-5189	219	8	kn	kn	PROPN
ejpam-5189	219	9	)	)	PUNCT
ejpam-5189	219	10	.	.	PUNCT
ejpam-5189	220	1	since	since	SCONJ
ejpam-5189	220	2	s	s	PROPN
ejpam-5189	220	3	is	be	AUX
ejpam-5189	220	4	convex	convex	PROPN
ejpam-5189	220	5	,	,	PUNCT
ejpam-5189	220	6	sg	sg	PROPN
ejpam-5189	220	7	is	be	AUX
ejpam-5189	220	8	a	a	DET
ejpam-5189	220	9	clique	clique	NOUN
ejpam-5189	220	10	in	in	ADP
ejpam-5189	220	11	g.	g.	PROPN
ejpam-5189	220	12	moreover	moreover	ADV
ejpam-5189	220	13	,	,	PUNCT
ejpam-5189	220	14	since	since	SCONJ
ejpam-5189	220	15	s	s	NOUN
ejpam-5189	220	16	is	be	AUX
ejpam-5189	220	17	2	2	NUM
ejpam-5189	220	18	-	-	PUNCT
ejpam-5189	220	19	dominating	dominating	NOUN
ejpam-5189	220	20	in	in	ADP
ejpam-5189	220	21	kn	kn	PROPN
ejpam-5189	220	22	+	+	CCONJ
ejpam-5189	220	23	g	g	PROPN
ejpam-5189	220	24	,	,	PUNCT
ejpam-5189	220	25	sg	sg	PROPN
ejpam-5189	220	26	is	be	AUX
ejpam-5189	220	27	a	a	DET
ejpam-5189	220	28	dominating	dominating	NOUN
ejpam-5189	220	29	set	set	VERB
ejpam-5189	220	30	in	in	ADP
ejpam-5189	220	31	g	g	PROPN
ejpam-5189	220	32	if	if	SCONJ
ejpam-5189	220	33	|sn|	|sn|	NOUN
ejpam-5189	220	34	=	=	SYM
ejpam-5189	220	35	1	1	X
ejpam-5189	220	36	.	.	PUNCT
ejpam-5189	221	1	this	this	PRON
ejpam-5189	221	2	shows	show	VERB
ejpam-5189	221	3	that	that	SCONJ
ejpam-5189	221	4	(	(	PUNCT
ejpam-5189	221	5	b	b	NOUN
ejpam-5189	221	6	)	)	PUNCT
ejpam-5189	221	7	or	or	CCONJ
ejpam-5189	221	8	(	(	PUNCT
ejpam-5189	221	9	c	c	NOUN
ejpam-5189	221	10	)	)	PUNCT
ejpam-5189	221	11	holds	hold	NOUN
ejpam-5189	221	12	.	.	PUNCT
ejpam-5189	222	1	the	the	DET
ejpam-5189	222	2	converse	converse	NOUN
ejpam-5189	222	3	is	be	AUX
ejpam-5189	222	4	easy	easy	ADJ
ejpam-5189	222	5	.	.	PUNCT
ejpam-5189	223	1	the	the	DET
ejpam-5189	223	2	next	next	ADJ
ejpam-5189	223	3	result	result	NOUN
ejpam-5189	223	4	is	be	AUX
ejpam-5189	223	5	immediate	immediate	ADJ
ejpam-5189	223	6	from	from	ADP
ejpam-5189	223	7	theorem	theorem	ADJ
ejpam-5189	223	8	4	4	NUM
ejpam-5189	223	9	.	.	PUNCT
ejpam-5189	223	10	corollary	corollary	ADJ
ejpam-5189	223	11	5	5	NUM
ejpam-5189	223	12	.	.	PUNCT
ejpam-5189	224	1	let	let	VERB
ejpam-5189	224	2	g	g	PRON
ejpam-5189	224	3	be	be	AUX
ejpam-5189	224	4	a	a	DET
ejpam-5189	224	5	non	non	ADJ
ejpam-5189	224	6	-	-	ADJ
ejpam-5189	224	7	complete	complete	ADJ
ejpam-5189	224	8	graph	graph	NOUN
ejpam-5189	224	9	and	and	CCONJ
ejpam-5189	224	10	let	let	VERB
ejpam-5189	224	11	n	n	PRON
ejpam-5189	224	12	be	be	AUX
ejpam-5189	224	13	a	a	DET
ejpam-5189	224	14	positive	positive	ADJ
ejpam-5189	224	15	integer	integer	NOUN
ejpam-5189	224	16	.	.	PUNCT
ejpam-5189	225	1	then	then	ADV
ejpam-5189	225	2	γ2con(kn	γ2con(kn	PUNCT
ejpam-5189	226	1	+	+	NOUN
ejpam-5189	226	2	g	g	NOUN
ejpam-5189	226	3	)	)	PUNCT
ejpam-5189	226	4	=	=	PRON
ejpam-5189	226	5	{	{	PUNCT
ejpam-5189	227	1	1	1	NUM
ejpam-5189	227	2	+	+	NUM
ejpam-5189	227	3	ψg	ψg	NOUN
ejpam-5189	227	4	if	if	SCONJ
ejpam-5189	227	5	n	n	NOUN
ejpam-5189	227	6	=	=	SYM
ejpam-5189	227	7	1	1	NUM
ejpam-5189	227	8	2	2	NUM
ejpam-5189	227	9	if	if	SCONJ
ejpam-5189	227	10	n	n	PRON
ejpam-5189	227	11	≥	≥	NOUN
ejpam-5189	227	12	2	2	NUM
ejpam-5189	227	13	where	where	SCONJ
ejpam-5189	227	14	ψg	ψg	NOUN
ejpam-5189	227	15	=	=	NOUN
ejpam-5189	227	16	min{|s|	min{|s|	NOUN
ejpam-5189	227	17	:	:	PUNCT
ejpam-5189	227	18	s	s	VERB
ejpam-5189	227	19	is	be	AUX
ejpam-5189	227	20	a	a	DET
ejpam-5189	227	21	dominating	dominating	NOUN
ejpam-5189	227	22	set	set	NOUN
ejpam-5189	227	23	and	and	CCONJ
ejpam-5189	227	24	v	v	NOUN
ejpam-5189	227	25	(	(	PUNCT
ejpam-5189	227	26	g	g	NOUN
ejpam-5189	227	27	)	)	PUNCT
ejpam-5189	227	28	\s	\s	NOUN
ejpam-5189	227	29	is	be	AUX
ejpam-5189	227	30	a	a	DET
ejpam-5189	227	31	non	non	ADJ
ejpam-5189	227	32	-	-	ADJ
ejpam-5189	227	33	connecting	connecting	ADJ
ejpam-5189	227	34	set	set	NOUN
ejpam-5189	227	35	in	in	ADP
ejpam-5189	227	36	g	g	NOUN
ejpam-5189	227	37	}	}	PUNCT
ejpam-5189	227	38	.	.	PUNCT
ejpam-5189	228	1	r.	r.	PROPN
ejpam-5189	228	2	j.	j.	PROPN
ejpam-5189	228	3	g.	g.	PROPN
ejpam-5189	228	4	fortosa	fortosa	PROPN
ejpam-5189	228	5	et	et	PROPN
ejpam-5189	228	6	al	al	PROPN
ejpam-5189	228	7	.	.	PUNCT
ejpam-5189	228	8	/	/	SYM
ejpam-5189	228	9	eur	eur	PROPN
ejpam-5189	228	10	.	.	PUNCT
ejpam-5189	229	1	j.	j.	PROPN
ejpam-5189	229	2	pure	pure	PROPN
ejpam-5189	229	3	appl	appl	PROPN
ejpam-5189	229	4	.	.	PROPN
ejpam-5189	229	5	math	math	PROPN
ejpam-5189	229	6	,	,	PUNCT
ejpam-5189	229	7	17	17	NUM
ejpam-5189	229	8	(	(	PUNCT
ejpam-5189	229	9	3	3	NUM
ejpam-5189	229	10	)	)	PUNCT
ejpam-5189	229	11	(	(	PUNCT
ejpam-5189	229	12	2024	2024	NUM
ejpam-5189	229	13	)	)	PUNCT
ejpam-5189	229	14	,	,	PUNCT
ejpam-5189	229	15	1539	1539	NUM
ejpam-5189	229	16	-	-	SYM
ejpam-5189	229	17	1552	1552	NUM
ejpam-5189	229	18	1546	1546	NUM
ejpam-5189	229	19	let	let	VERB
ejpam-5189	229	20	g	g	PROPN
ejpam-5189	229	21	and	and	CCONJ
ejpam-5189	229	22	h	h	NOUN
ejpam-5189	229	23	be	be	AUX
ejpam-5189	229	24	connected	connect	VERB
ejpam-5189	229	25	graphs	graph	NOUN
ejpam-5189	229	26	.	.	PUNCT
ejpam-5189	230	1	the	the	DET
ejpam-5189	230	2	corona	corona	NOUN
ejpam-5189	230	3	of	of	ADP
ejpam-5189	230	4	g	g	PROPN
ejpam-5189	230	5	and	and	CCONJ
ejpam-5189	230	6	h	h	NOUN
ejpam-5189	230	7	is	be	AUX
ejpam-5189	230	8	the	the	DET
ejpam-5189	230	9	graph	graph	NOUN
ejpam-5189	230	10	g	g	PROPN
ejpam-5189	230	11	◦	◦	NOUN
ejpam-5189	230	12	h	h	NOUN
ejpam-5189	230	13	obtained	obtain	VERB
ejpam-5189	230	14	by	by	ADP
ejpam-5189	230	15	taking	take	VERB
ejpam-5189	230	16	one	one	NUM
ejpam-5189	230	17	copy	copy	NOUN
ejpam-5189	230	18	of	of	ADP
ejpam-5189	230	19	g	g	PROPN
ejpam-5189	230	20	and	and	CCONJ
ejpam-5189	230	21	|v	|v	PROPN
ejpam-5189	230	22	(	(	PUNCT
ejpam-5189	230	23	g)|	g)|	NOUN
ejpam-5189	230	24	copies	copy	NOUN
ejpam-5189	230	25	of	of	ADP
ejpam-5189	230	26	h	h	NOUN
ejpam-5189	230	27	,	,	PUNCT
ejpam-5189	230	28	and	and	CCONJ
ejpam-5189	230	29	then	then	ADV
ejpam-5189	230	30	joining	join	VERB
ejpam-5189	230	31	the	the	DET
ejpam-5189	230	32	ith	ith	PROPN
ejpam-5189	230	33	vertex	vertex	NOUN
ejpam-5189	230	34	of	of	ADP
ejpam-5189	230	35	g	g	NOUN
ejpam-5189	230	36	to	to	ADP
ejpam-5189	230	37	every	every	DET
ejpam-5189	230	38	vertex	vertex	NOUN
ejpam-5189	230	39	of	of	ADP
ejpam-5189	230	40	the	the	DET
ejpam-5189	230	41	ith	ith	PROPN
ejpam-5189	230	42	copy	copy	NOUN
ejpam-5189	230	43	of	of	ADP
ejpam-5189	230	44	h.	h.	PROPN
ejpam-5189	230	45	for	for	ADP
ejpam-5189	230	46	convenience	convenience	NOUN
ejpam-5189	230	47	,	,	PUNCT
ejpam-5189	230	48	we	we	PRON
ejpam-5189	230	49	write	write	VERB
ejpam-5189	230	50	hv	hv	PROPN
ejpam-5189	230	51	to	to	PART
ejpam-5189	230	52	denote	denote	VERB
ejpam-5189	230	53	the	the	DET
ejpam-5189	230	54	copy	copy	NOUN
ejpam-5189	230	55	of	of	ADP
ejpam-5189	230	56	h	h	NOUN
ejpam-5189	230	57	joined	join	VERB
ejpam-5189	230	58	to	to	ADP
ejpam-5189	230	59	v	v	VERB
ejpam-5189	230	60	and	and	CCONJ
ejpam-5189	230	61	write	write	VERB
ejpam-5189	230	62	hv	hv	PROPN
ejpam-5189	231	1	+	+	PROPN
ejpam-5189	231	2	v	v	NOUN
ejpam-5189	231	3	=	=	SYM
ejpam-5189	231	4	hv	hv	PROPN
ejpam-5189	231	5	+	+	PROPN
ejpam-5189	231	6	⟨v⟩.	⟨v⟩.	PROPN
ejpam-5189	231	7	remark	remark	NOUN
ejpam-5189	231	8	1	1	NUM
ejpam-5189	231	9	.	.	PUNCT
ejpam-5189	232	1	let	let	VERB
ejpam-5189	232	2	g	g	PRON
ejpam-5189	232	3	be	be	AUX
ejpam-5189	232	4	a	a	DET
ejpam-5189	232	5	non	non	ADJ
ejpam-5189	232	6	-	-	ADJ
ejpam-5189	232	7	trivial	trivial	ADJ
ejpam-5189	232	8	connected	connected	ADJ
ejpam-5189	232	9	graph	graph	NOUN
ejpam-5189	232	10	.	.	PUNCT
ejpam-5189	233	1	if	if	SCONJ
ejpam-5189	233	2	s	s	PROPN
ejpam-5189	233	3	is	be	AUX
ejpam-5189	233	4	a	a	DET
ejpam-5189	233	5	clique	clique	NOUN
ejpam-5189	233	6	in	in	ADP
ejpam-5189	233	7	g	g	PROPN
ejpam-5189	233	8	,	,	PUNCT
ejpam-5189	233	9	then	then	ADV
ejpam-5189	233	10	v	v	X
ejpam-5189	233	11	(	(	PUNCT
ejpam-5189	233	12	g	g	NOUN
ejpam-5189	233	13	)	)	PUNCT
ejpam-5189	233	14	\	\	PROPN
ejpam-5189	234	1	s	s	PART
ejpam-5189	234	2	is	be	AUX
ejpam-5189	234	3	a	a	DET
ejpam-5189	234	4	non	non	ADJ
ejpam-5189	234	5	-	-	ADJ
ejpam-5189	234	6	connecting	connecting	ADJ
ejpam-5189	234	7	set	set	NOUN
ejpam-5189	234	8	.	.	PUNCT
ejpam-5189	235	1	theorem	theorem	VERB
ejpam-5189	235	2	5	5	NUM
ejpam-5189	235	3	.	.	PUNCT
ejpam-5189	236	1	let	let	VERB
ejpam-5189	236	2	g	g	PRON
ejpam-5189	236	3	be	be	AUX
ejpam-5189	236	4	a	a	DET
ejpam-5189	236	5	non	non	ADJ
ejpam-5189	236	6	-	-	ADJ
ejpam-5189	236	7	trivial	trivial	ADJ
ejpam-5189	236	8	connected	connected	ADJ
ejpam-5189	236	9	graph	graph	NOUN
ejpam-5189	236	10	and	and	CCONJ
ejpam-5189	236	11	let	let	VERB
ejpam-5189	236	12	h	h	NOUN
ejpam-5189	236	13	be	be	AUX
ejpam-5189	236	14	any	any	DET
ejpam-5189	236	15	graph	graph	NOUN
ejpam-5189	236	16	.	.	PUNCT
ejpam-5189	237	1	then	then	ADV
ejpam-5189	237	2	s	s	VERB
ejpam-5189	237	3	is	be	AUX
ejpam-5189	237	4	a	a	DET
ejpam-5189	237	5	convex	convex	ADJ
ejpam-5189	237	6	2	2	NUM
ejpam-5189	237	7	-	-	PUNCT
ejpam-5189	237	8	dominating	dominating	NOUN
ejpam-5189	237	9	set	set	NOUN
ejpam-5189	237	10	in	in	ADP
ejpam-5189	237	11	g	g	PROPN
ejpam-5189	237	12	◦	◦	NOUN
ejpam-5189	237	13	h	h	NOUN
ejpam-5189	237	14	if	if	SCONJ
ejpam-5189	238	1	and	and	CCONJ
ejpam-5189	238	2	only	only	ADV
ejpam-5189	238	3	if	if	SCONJ
ejpam-5189	238	4	s	s	VERB
ejpam-5189	238	5	=	=	SYM
ejpam-5189	238	6	v	v	X
ejpam-5189	238	7	(	(	PUNCT
ejpam-5189	238	8	g	g	NOUN
ejpam-5189	238	9	)	)	PUNCT
ejpam-5189	238	10	∪	∪	NOUN
ejpam-5189	238	11	(	(	PUNCT
ejpam-5189	238	12	⋃	⋃	ADJ
ejpam-5189	238	13	v∈v	v∈v	NOUN
ejpam-5189	238	14	(	(	PUNCT
ejpam-5189	238	15	g	g	NOUN
ejpam-5189	238	16	)	)	PUNCT
ejpam-5189	238	17	sv	sv	NOUN
ejpam-5189	238	18	)	)	PUNCT
ejpam-5189	238	19	where	where	SCONJ
ejpam-5189	238	20	sv	sv	PROPN
ejpam-5189	238	21	is	be	AUX
ejpam-5189	238	22	dominating	dominate	VERB
ejpam-5189	238	23	and	and	CCONJ
ejpam-5189	238	24	v	v	NOUN
ejpam-5189	238	25	(	(	PUNCT
ejpam-5189	238	26	hv	hv	NOUN
ejpam-5189	238	27	)	)	PUNCT
ejpam-5189	238	28	\	\	PROPN
ejpam-5189	239	1	sv	sv	PROPN
ejpam-5189	239	2	is	be	AUX
ejpam-5189	239	3	a	a	DET
ejpam-5189	239	4	non	non	ADJ
ejpam-5189	239	5	-	-	ADJ
ejpam-5189	239	6	connecting	connecting	ADJ
ejpam-5189	239	7	set	set	NOUN
ejpam-5189	239	8	in	in	ADP
ejpam-5189	239	9	hv	hv	PROPN
ejpam-5189	239	10	for	for	ADP
ejpam-5189	239	11	each	each	DET
ejpam-5189	239	12	v	v	NUM
ejpam-5189	239	13	∈	∈	PROPN
ejpam-5189	239	14	v	v	NOUN
ejpam-5189	239	15	(	(	PUNCT
ejpam-5189	239	16	g	g	NOUN
ejpam-5189	239	17	)	)	PUNCT
ejpam-5189	239	18	.	.	PUNCT
ejpam-5189	240	1	proof	proof	NOUN
ejpam-5189	240	2	.	.	PUNCT
ejpam-5189	241	1	let	let	VERB
ejpam-5189	241	2	s	s	PRON
ejpam-5189	241	3	be	be	AUX
ejpam-5189	241	4	a	a	DET
ejpam-5189	241	5	convex	convex	ADJ
ejpam-5189	241	6	2	2	NUM
ejpam-5189	241	7	-	-	PUNCT
ejpam-5189	241	8	dominating	dominating	NOUN
ejpam-5189	241	9	set	set	NOUN
ejpam-5189	241	10	in	in	ADP
ejpam-5189	241	11	g	g	PROPN
ejpam-5189	241	12	◦	◦	PROPN
ejpam-5189	241	13	h.	h.	PROPN
ejpam-5189	241	14	let	let	VERB
ejpam-5189	241	15	a	a	DET
ejpam-5189	241	16	=	=	X
ejpam-5189	241	17	s	s	NOUN
ejpam-5189	241	18	∩	∩	ADJ
ejpam-5189	241	19	v	v	X
ejpam-5189	241	20	(	(	PUNCT
ejpam-5189	241	21	g	g	NOUN
ejpam-5189	241	22	)	)	PUNCT
ejpam-5189	241	23	and	and	CCONJ
ejpam-5189	241	24	let	let	VERB
ejpam-5189	241	25	sv	sv	VERB
ejpam-5189	241	26	=	=	SYM
ejpam-5189	241	27	s	s	PROPN
ejpam-5189	241	28	∩	∩	ADJ
ejpam-5189	241	29	v	v	X
ejpam-5189	241	30	(	(	PUNCT
ejpam-5189	241	31	hv	hv	PROPN
ejpam-5189	241	32	)	)	PUNCT
ejpam-5189	241	33	for	for	ADP
ejpam-5189	241	34	each	each	DET
ejpam-5189	241	35	v	v	NUM
ejpam-5189	241	36	∈	∈	PROPN
ejpam-5189	241	37	v	v	NOUN
ejpam-5189	241	38	(	(	PUNCT
ejpam-5189	241	39	g	g	NOUN
ejpam-5189	241	40	)	)	PUNCT
ejpam-5189	241	41	.	.	PUNCT
ejpam-5189	242	1	then	then	ADV
ejpam-5189	242	2	s	s	VERB
ejpam-5189	242	3	=	=	PUNCT
ejpam-5189	242	4	a	a	DET
ejpam-5189	242	5	∪	∪	X
ejpam-5189	242	6	(	(	PUNCT
ejpam-5189	242	7	⋃	⋃	NOUN
ejpam-5189	242	8	v∈v	v∈v	NOUN
ejpam-5189	242	9	(	(	PUNCT
ejpam-5189	242	10	g	g	NOUN
ejpam-5189	242	11	)	)	PUNCT
ejpam-5189	242	12	sv	sv	NOUN
ejpam-5189	242	13	)	)	PUNCT
ejpam-5189	242	14	.	.	PUNCT
ejpam-5189	243	1	suppose	suppose	VERB
ejpam-5189	243	2	a	a	DET
ejpam-5189	243	3	̸=	̸=	PROPN
ejpam-5189	243	4	v	v	NOUN
ejpam-5189	243	5	(	(	PUNCT
ejpam-5189	243	6	g	g	NOUN
ejpam-5189	243	7	)	)	PUNCT
ejpam-5189	243	8	.	.	PUNCT
ejpam-5189	244	1	then	then	ADV
ejpam-5189	244	2	there	there	PRON
ejpam-5189	244	3	exists	exist	VERB
ejpam-5189	244	4	u	u	PROPN
ejpam-5189	244	5	∈	∈	PROPN
ejpam-5189	244	6	v	v	ADP
ejpam-5189	244	7	(	(	PUNCT
ejpam-5189	244	8	g	g	NOUN
ejpam-5189	244	9	)	)	PUNCT
ejpam-5189	244	10	\	\	NOUN
ejpam-5189	244	11	a.	a.	NOUN
ejpam-5189	244	12	since	since	SCONJ
ejpam-5189	244	13	s	s	PROPN
ejpam-5189	244	14	is	be	AUX
ejpam-5189	244	15	a	a	DET
ejpam-5189	244	16	dominating	dominating	NOUN
ejpam-5189	244	17	set	set	NOUN
ejpam-5189	244	18	,	,	PUNCT
ejpam-5189	244	19	su	su	PROPN
ejpam-5189	244	20	̸=	̸=	PROPN
ejpam-5189	244	21	∅.	∅.	ADV
ejpam-5189	244	22	since	since	SCONJ
ejpam-5189	244	23	g	g	PROPN
ejpam-5189	244	24	is	be	AUX
ejpam-5189	244	25	a	a	DET
ejpam-5189	244	26	non	non	ADJ
ejpam-5189	244	27	-	-	ADJ
ejpam-5189	244	28	trivial	trivial	ADJ
ejpam-5189	244	29	connected	connected	ADJ
ejpam-5189	244	30	graph	graph	NOUN
ejpam-5189	244	31	,	,	PUNCT
ejpam-5189	244	32	⟨s⟩	⟨s⟩	PROPN
ejpam-5189	244	33	is	be	AUX
ejpam-5189	244	34	disconnected	disconnect	VERB
ejpam-5189	244	35	,	,	PUNCT
ejpam-5189	244	36	a	a	DET
ejpam-5189	244	37	contradiction	contradiction	NOUN
ejpam-5189	244	38	to	to	ADP
ejpam-5189	244	39	the	the	DET
ejpam-5189	244	40	assumption	assumption	NOUN
ejpam-5189	244	41	that	that	SCONJ
ejpam-5189	244	42	s	s	VERB
ejpam-5189	244	43	is	be	AUX
ejpam-5189	244	44	convex	convex	NOUN
ejpam-5189	244	45	.	.	PUNCT
ejpam-5189	245	1	hence	hence	ADV
ejpam-5189	245	2	,	,	PUNCT
ejpam-5189	245	3	a	a	DET
ejpam-5189	245	4	=	=	SYM
ejpam-5189	245	5	v	v	NOUN
ejpam-5189	245	6	(	(	PUNCT
ejpam-5189	245	7	g	g	NOUN
ejpam-5189	245	8	)	)	PUNCT
ejpam-5189	245	9	and	and	CCONJ
ejpam-5189	245	10	s	s	VERB
ejpam-5189	245	11	=	=	SYM
ejpam-5189	245	12	v	v	NOUN
ejpam-5189	245	13	(	(	PUNCT
ejpam-5189	245	14	g)∪	g)∪	VERB
ejpam-5189	245	15	(	(	PUNCT
ejpam-5189	245	16	⋃	⋃	ADJ
ejpam-5189	245	17	v∈v	v∈v	NOUN
ejpam-5189	245	18	(	(	PUNCT
ejpam-5189	245	19	g	g	NOUN
ejpam-5189	245	20	)	)	PUNCT
ejpam-5189	245	21	sv	sv	NOUN
ejpam-5189	245	22	)	)	PUNCT
ejpam-5189	245	23	.	.	PUNCT
ejpam-5189	246	1	next	next	ADV
ejpam-5189	246	2	,	,	PUNCT
ejpam-5189	246	3	let	let	VERB
ejpam-5189	246	4	v	v	NUM
ejpam-5189	246	5	∈	∈	PROPN
ejpam-5189	246	6	v	v	NOUN
ejpam-5189	246	7	(	(	PUNCT
ejpam-5189	246	8	g	g	NOUN
ejpam-5189	246	9	)	)	PUNCT
ejpam-5189	246	10	.	.	PUNCT
ejpam-5189	247	1	since	since	SCONJ
ejpam-5189	247	2	v	v	NUM
ejpam-5189	247	3	∈	∈	PROPN
ejpam-5189	247	4	s	s	PART
ejpam-5189	247	5	and	and	CCONJ
ejpam-5189	247	6	s	s	X
ejpam-5189	247	7	∩	∩	X
ejpam-5189	247	8	[	[	X
ejpam-5189	247	9	v	v	X
ejpam-5189	247	10	(	(	PUNCT
ejpam-5189	247	11	hv	hv	NOUN
ejpam-5189	247	12	)	)	PUNCT
ejpam-5189	247	13	∪	∪	NOUN
ejpam-5189	247	14	{	{	PUNCT
ejpam-5189	247	15	v	v	NOUN
ejpam-5189	247	16	}	}	PUNCT
ejpam-5189	247	17	]	]	PUNCT
ejpam-5189	247	18	is	be	AUX
ejpam-5189	247	19	a	a	DET
ejpam-5189	247	20	convex	convex	ADJ
ejpam-5189	247	21	2	2	NUM
ejpam-5189	247	22	-	-	PUNCT
ejpam-5189	247	23	dominating	dominating	NOUN
ejpam-5189	247	24	set	set	NOUN
ejpam-5189	247	25	in	in	ADP
ejpam-5189	247	26	v	v	PRON
ejpam-5189	247	27	+	+	PROPN
ejpam-5189	247	28	hv	hv	PROPN
ejpam-5189	247	29	,	,	PUNCT
ejpam-5189	247	30	sv	sv	PROPN
ejpam-5189	247	31	is	be	AUX
ejpam-5189	247	32	a	a	DET
ejpam-5189	247	33	dominating	dominating	NOUN
ejpam-5189	247	34	set	set	NOUN
ejpam-5189	247	35	,	,	PUNCT
ejpam-5189	247	36	and	and	CCONJ
ejpam-5189	247	37	v	v	NOUN
ejpam-5189	247	38	(	(	PUNCT
ejpam-5189	247	39	hv	hv	NOUN
ejpam-5189	247	40	)	)	PUNCT
ejpam-5189	247	41	\	\	PROPN
ejpam-5189	248	1	sv	sv	PROPN
ejpam-5189	248	2	is	be	AUX
ejpam-5189	248	3	a	a	DET
ejpam-5189	248	4	non	non	ADJ
ejpam-5189	248	5	-	-	ADJ
ejpam-5189	248	6	connecting	connecting	ADJ
ejpam-5189	248	7	set	set	NOUN
ejpam-5189	248	8	in	in	ADP
ejpam-5189	248	9	hv	hv	PROPN
ejpam-5189	248	10	by	by	ADP
ejpam-5189	248	11	theorem	theorem	NOUN
ejpam-5189	248	12	4(iii)(a	4(iii)(a	PROPN
ejpam-5189	248	13	)	)	PUNCT
ejpam-5189	248	14	.	.	PUNCT
ejpam-5189	249	1	conversely	conversely	ADV
ejpam-5189	249	2	,	,	PUNCT
ejpam-5189	249	3	suppose	suppose	VERB
ejpam-5189	249	4	that	that	SCONJ
ejpam-5189	249	5	s	s	VERB
ejpam-5189	249	6	has	have	VERB
ejpam-5189	249	7	the	the	DET
ejpam-5189	249	8	given	give	VERB
ejpam-5189	249	9	form	form	NOUN
ejpam-5189	249	10	and	and	CCONJ
ejpam-5189	249	11	satisfies	satisfy	VERB
ejpam-5189	249	12	the	the	DET
ejpam-5189	249	13	given	give	VERB
ejpam-5189	249	14	property	property	NOUN
ejpam-5189	249	15	.	.	PUNCT
ejpam-5189	250	1	then	then	ADV
ejpam-5189	250	2	s	s	VERB
ejpam-5189	250	3	is	be	AUX
ejpam-5189	250	4	a	a	DET
ejpam-5189	250	5	2	2	NUM
ejpam-5189	250	6	-	-	PUNCT
ejpam-5189	250	7	dominating	dominating	NOUN
ejpam-5189	250	8	set	set	NOUN
ejpam-5189	250	9	in	in	ADP
ejpam-5189	250	10	v+hv	v+hv	PROPN
ejpam-5189	250	11	.	.	PUNCT
ejpam-5189	251	1	by	by	ADP
ejpam-5189	251	2	theorem	theorem	NOUN
ejpam-5189	251	3	4(iii)(a	4(iii)(a	PROPN
ejpam-5189	251	4	)	)	PUNCT
ejpam-5189	251	5	,	,	PUNCT
ejpam-5189	251	6	sv∪{v	sv∪{v	NOUN
ejpam-5189	251	7	}	}	PUNCT
ejpam-5189	251	8	is	be	AUX
ejpam-5189	251	9	a	a	DET
ejpam-5189	251	10	convex	convex	ADJ
ejpam-5189	251	11	2	2	NUM
ejpam-5189	251	12	-	-	PUNCT
ejpam-5189	251	13	dominating	dominating	NOUN
ejpam-5189	251	14	set	set	NOUN
ejpam-5189	251	15	in	in	ADP
ejpam-5189	251	16	v+hv	v+hv	NOUN
ejpam-5189	251	17	for	for	ADP
ejpam-5189	251	18	each	each	DET
ejpam-5189	251	19	v	v	NUM
ejpam-5189	251	20	∈	∈	PROPN
ejpam-5189	251	21	v	v	NOUN
ejpam-5189	251	22	(	(	PUNCT
ejpam-5189	251	23	g	g	NOUN
ejpam-5189	251	24	)	)	PUNCT
ejpam-5189	251	25	.	.	PUNCT
ejpam-5189	252	1	since	since	SCONJ
ejpam-5189	252	2	g	g	PROPN
ejpam-5189	252	3	is	be	AUX
ejpam-5189	252	4	connected	connect	VERB
ejpam-5189	252	5	,	,	PUNCT
ejpam-5189	252	6	it	it	PRON
ejpam-5189	252	7	follows	follow	VERB
ejpam-5189	252	8	that	that	SCONJ
ejpam-5189	252	9	⋃	⋃	PROPN
ejpam-5189	252	10	v∈v	v∈v	NOUN
ejpam-5189	252	11	(	(	PUNCT
ejpam-5189	252	12	g	g	NOUN
ejpam-5189	252	13	)	)	PUNCT
ejpam-5189	252	14	(	(	PUNCT
ejpam-5189	252	15	sv	sv	INTJ
ejpam-5189	252	16	∪	∪	PROPN
ejpam-5189	252	17	{	{	PUNCT
ejpam-5189	252	18	v	v	NOUN
ejpam-5189	252	19	}	}	PUNCT
ejpam-5189	252	20	)	)	PUNCT
ejpam-5189	253	1	=	=	PUNCT
ejpam-5189	253	2	s	s	VERB
ejpam-5189	253	3	is	be	AUX
ejpam-5189	253	4	a	a	DET
ejpam-5189	253	5	convex	convex	NOUN
ejpam-5189	253	6	set	set	VERB
ejpam-5189	253	7	in	in	ADP
ejpam-5189	253	8	g	g	PROPN
ejpam-5189	253	9	◦	◦	NOUN
ejpam-5189	253	10	h.	h.	NOUN
ejpam-5189	253	11	hence	hence	ADV
ejpam-5189	253	12	,	,	PUNCT
ejpam-5189	253	13	s	s	VERB
ejpam-5189	253	14	is	be	AUX
ejpam-5189	253	15	a	a	DET
ejpam-5189	253	16	convex	convex	ADJ
ejpam-5189	253	17	2	2	NUM
ejpam-5189	253	18	-	-	PUNCT
ejpam-5189	253	19	dominating	dominating	NOUN
ejpam-5189	253	20	set	set	NOUN
ejpam-5189	253	21	in	in	ADP
ejpam-5189	253	22	g	g	PROPN
ejpam-5189	253	23	◦	◦	NOUN
ejpam-5189	253	24	h.	h.	NOUN
ejpam-5189	253	25	corollary	corollary	ADJ
ejpam-5189	253	26	6	6	NUM
ejpam-5189	253	27	.	.	PUNCT
ejpam-5189	254	1	let	let	VERB
ejpam-5189	254	2	g	g	PRON
ejpam-5189	254	3	be	be	AUX
ejpam-5189	254	4	a	a	DET
ejpam-5189	254	5	nontrivial	nontrivial	ADJ
ejpam-5189	254	6	connected	connect	VERB
ejpam-5189	254	7	graph	graph	NOUN
ejpam-5189	254	8	of	of	ADP
ejpam-5189	254	9	order	order	NOUN
ejpam-5189	254	10	m	m	VERB
ejpam-5189	254	11	and	and	CCONJ
ejpam-5189	254	12	let	let	VERB
ejpam-5189	254	13	h	h	NOUN
ejpam-5189	254	14	be	be	AUX
ejpam-5189	254	15	any	any	DET
ejpam-5189	254	16	graph	graph	NOUN
ejpam-5189	254	17	.	.	PUNCT
ejpam-5189	255	1	then	then	ADV
ejpam-5189	255	2	γ2con(g	γ2con(g	X
ejpam-5189	255	3	◦	◦	NOUN
ejpam-5189	255	4	h	h	NOUN
ejpam-5189	255	5	)	)	PUNCT
ejpam-5189	256	1	=	=	PUNCT
ejpam-5189	256	2	m(1	m(1	NOUN
ejpam-5189	256	3	+	+	CCONJ
ejpam-5189	256	4	ψh	ψh	NOUN
ejpam-5189	256	5	)	)	PUNCT
ejpam-5189	256	6	,	,	PUNCT
ejpam-5189	256	7	where	where	SCONJ
ejpam-5189	256	8	ψh	ψh	ADP
ejpam-5189	256	9	=	=	NOUN
ejpam-5189	256	10	min{|s|	min{|s|	NOUN
ejpam-5189	256	11	:	:	PUNCT
ejpam-5189	256	12	s	s	VERB
ejpam-5189	256	13	is	be	AUX
ejpam-5189	256	14	a	a	DET
ejpam-5189	256	15	dominating	dominating	NOUN
ejpam-5189	256	16	set	set	NOUN
ejpam-5189	256	17	and	and	CCONJ
ejpam-5189	256	18	v	v	NOUN
ejpam-5189	256	19	(	(	PUNCT
ejpam-5189	256	20	h)\s	h)\s	NOUN
ejpam-5189	256	21	is	be	AUX
ejpam-5189	256	22	a	a	DET
ejpam-5189	256	23	non	non	ADJ
ejpam-5189	256	24	-	-	ADJ
ejpam-5189	256	25	connecting	connecting	ADJ
ejpam-5189	256	26	set	set	NOUN
ejpam-5189	256	27	in	in	ADP
ejpam-5189	256	28	h	h	NOUN
ejpam-5189	256	29	}	}	PUNCT
ejpam-5189	256	30	.	.	PUNCT
ejpam-5189	257	1	proof	proof	NOUN
ejpam-5189	257	2	.	.	PUNCT
ejpam-5189	258	1	let	let	VERB
ejpam-5189	258	2	s	s	PRON
ejpam-5189	258	3	=	=	X
ejpam-5189	258	4	v	v	ADJ
ejpam-5189	258	5	(	(	PUNCT
ejpam-5189	258	6	g	g	NOUN
ejpam-5189	258	7	)	)	PUNCT
ejpam-5189	258	8	∪	∪	NOUN
ejpam-5189	258	9	(	(	PUNCT
ejpam-5189	258	10	⋃	⋃	ADJ
ejpam-5189	258	11	v∈v	v∈v	NOUN
ejpam-5189	258	12	(	(	PUNCT
ejpam-5189	258	13	g	g	NOUN
ejpam-5189	258	14	)	)	PUNCT
ejpam-5189	258	15	sv	sv	NOUN
ejpam-5189	258	16	)	)	PUNCT
ejpam-5189	258	17	be	be	AUX
ejpam-5189	258	18	a	a	DET
ejpam-5189	258	19	γ2con	γ2con	NOUN
ejpam-5189	258	20	-	-	PUNCT
ejpam-5189	258	21	set	set	NOUN
ejpam-5189	258	22	in	in	ADP
ejpam-5189	258	23	g	g	PROPN
ejpam-5189	258	24	◦	◦	NOUN
ejpam-5189	258	25	h.	h.	NOUN
ejpam-5189	258	26	by	by	ADP
ejpam-5189	258	27	theorem	theorem	NOUN
ejpam-5189	258	28	5	5	NUM
ejpam-5189	258	29	,	,	PUNCT
ejpam-5189	258	30	sv	sv	X
ejpam-5189	258	31	is	be	AUX
ejpam-5189	258	32	a	a	DET
ejpam-5189	258	33	dominating	dominating	NOUN
ejpam-5189	258	34	set	set	NOUN
ejpam-5189	258	35	,	,	PUNCT
ejpam-5189	258	36	and	and	CCONJ
ejpam-5189	258	37	v	v	NOUN
ejpam-5189	258	38	(	(	PUNCT
ejpam-5189	258	39	hv	hv	NOUN
ejpam-5189	258	40	)	)	PUNCT
ejpam-5189	258	41	\	\	PROPN
ejpam-5189	259	1	sv	sv	PROPN
ejpam-5189	259	2	is	be	AUX
ejpam-5189	259	3	a	a	DET
ejpam-5189	259	4	non	non	ADJ
ejpam-5189	259	5	-	-	ADJ
ejpam-5189	259	6	connecting	connecting	ADJ
ejpam-5189	259	7	set	set	NOUN
ejpam-5189	259	8	in	in	ADP
ejpam-5189	259	9	hv	hv	PROPN
ejpam-5189	259	10	.	.	PUNCT
ejpam-5189	260	1	thus	thus	ADV
ejpam-5189	260	2	γ2con(g	γ2con(g	PRON
ejpam-5189	260	3	◦	◦	NOUN
ejpam-5189	260	4	h	h	NOUN
ejpam-5189	260	5	)	)	PUNCT
ejpam-5189	260	6	=	=	SYM
ejpam-5189	260	7	|s|	|s|	PROPN
ejpam-5189	260	8	=	=	PUNCT
ejpam-5189	260	9	|v	|v	PROPN
ejpam-5189	260	10	(	(	PUNCT
ejpam-5189	260	11	g)|+	g)|+	PROPN
ejpam-5189	260	12	∑	∑	PUNCT
ejpam-5189	260	13	v∈v	v∈v	PROPN
ejpam-5189	260	14	(	(	PUNCT
ejpam-5189	260	15	g	g	NOUN
ejpam-5189	260	16	)	)	PUNCT
ejpam-5189	260	17	|sv|	|sv|	PROPN
ejpam-5189	260	18	≥	≥	NOUN
ejpam-5189	260	19	m(1	m(1	NOUN
ejpam-5189	260	20	+	+	CCONJ
ejpam-5189	260	21	ψh	ψh	NOUN
ejpam-5189	260	22	)	)	PUNCT
ejpam-5189	260	23	.	.	PUNCT
ejpam-5189	261	1	next	next	ADV
ejpam-5189	261	2	,	,	PUNCT
ejpam-5189	261	3	let	let	VERB
ejpam-5189	261	4	dv	dv	PROPN
ejpam-5189	261	5	be	be	AUX
ejpam-5189	261	6	a	a	DET
ejpam-5189	261	7	dominating	dominating	NOUN
ejpam-5189	261	8	set	set	NOUN
ejpam-5189	261	9	in	in	ADP
ejpam-5189	261	10	hv	hv	PROPN
ejpam-5189	261	11	such	such	ADJ
ejpam-5189	261	12	that	that	PRON
ejpam-5189	261	13	v	v	NOUN
ejpam-5189	261	14	(	(	PUNCT
ejpam-5189	261	15	hv	hv	PROPN
ejpam-5189	261	16	)	)	PUNCT
ejpam-5189	261	17	\dv	\dv	PROPN
ejpam-5189	261	18	is	be	AUX
ejpam-5189	261	19	non	non	ADJ
ejpam-5189	261	20	-	-	ADJ
ejpam-5189	261	21	connecting	connecting	ADJ
ejpam-5189	261	22	and	and	CCONJ
ejpam-5189	261	23	|dv|	|dv|	NOUN
ejpam-5189	261	24	=	=	SYM
ejpam-5189	261	25	ψh	ψh	NOUN
ejpam-5189	261	26	for	for	ADP
ejpam-5189	261	27	each	each	DET
ejpam-5189	261	28	v	v	NUM
ejpam-5189	261	29	∈	∈	PROPN
ejpam-5189	261	30	v	v	NOUN
ejpam-5189	261	31	(	(	PUNCT
ejpam-5189	261	32	g	g	NOUN
ejpam-5189	261	33	)	)	PUNCT
ejpam-5189	261	34	.	.	PUNCT
ejpam-5189	262	1	then	then	ADV
ejpam-5189	262	2	s∗	s∗	PROPN
ejpam-5189	262	3	=	=	SYM
ejpam-5189	262	4	v	v	NOUN
ejpam-5189	262	5	(	(	PUNCT
ejpam-5189	262	6	g)∪	g)∪	VERB
ejpam-5189	262	7	(	(	PUNCT
ejpam-5189	262	8	⋃	⋃	NOUN
ejpam-5189	262	9	v∈v	v∈v	NOUN
ejpam-5189	262	10	(	(	PUNCT
ejpam-5189	262	11	g)dv	g)dv	PROPN
ejpam-5189	262	12	)	)	PUNCT
ejpam-5189	262	13	is	be	AUX
ejpam-5189	262	14	a	a	DET
ejpam-5189	262	15	convex	convex	ADJ
ejpam-5189	262	16	2	2	NUM
ejpam-5189	262	17	-	-	PUNCT
ejpam-5189	262	18	dominating	dominating	NOUN
ejpam-5189	262	19	set	set	NOUN
ejpam-5189	262	20	in	in	ADP
ejpam-5189	262	21	g	g	PROPN
ejpam-5189	262	22	◦	◦	NOUN
ejpam-5189	262	23	h	h	NOUN
ejpam-5189	262	24	by	by	ADP
ejpam-5189	262	25	theorem	theorem	NOUN
ejpam-5189	262	26	5	5	NUM
ejpam-5189	262	27	.	.	PUNCT
ejpam-5189	263	1	hence	hence	ADV
ejpam-5189	263	2	,	,	PUNCT
ejpam-5189	263	3	γ2con(g	γ2con(g	ADV
ejpam-5189	263	4	◦	◦	NOUN
ejpam-5189	263	5	h	h	NOUN
ejpam-5189	263	6	)	)	PUNCT
ejpam-5189	263	7	≤	≤	NOUN
ejpam-5189	263	8	|s∗|	|s∗|	NUM
ejpam-5189	264	1	r.	r.	PROPN
ejpam-5189	264	2	j.	j.	PROPN
ejpam-5189	264	3	g.	g.	PROPN
ejpam-5189	264	4	fortosa	fortosa	PROPN
ejpam-5189	264	5	et	et	PROPN
ejpam-5189	264	6	al	al	PROPN
ejpam-5189	264	7	.	.	PUNCT
ejpam-5189	264	8	/	/	SYM
ejpam-5189	264	9	eur	eur	PROPN
ejpam-5189	264	10	.	.	PUNCT
ejpam-5189	265	1	j.	j.	PROPN
ejpam-5189	265	2	pure	pure	PROPN
ejpam-5189	265	3	appl	appl	PROPN
ejpam-5189	265	4	.	.	PROPN
ejpam-5189	265	5	math	math	PROPN
ejpam-5189	265	6	,	,	PUNCT
ejpam-5189	265	7	17	17	NUM
ejpam-5189	265	8	(	(	PUNCT
ejpam-5189	265	9	3	3	NUM
ejpam-5189	265	10	)	)	PUNCT
ejpam-5189	265	11	(	(	PUNCT
ejpam-5189	265	12	2024	2024	NUM
ejpam-5189	265	13	)	)	PUNCT
ejpam-5189	265	14	,	,	PUNCT
ejpam-5189	265	15	1539	1539	NUM
ejpam-5189	265	16	-	-	SYM
ejpam-5189	265	17	1552	1552	NUM
ejpam-5189	265	18	1547	1547	NUM
ejpam-5189	265	19	=	=	SYM
ejpam-5189	265	20	|v	|v	PROPN
ejpam-5189	265	21	(	(	PUNCT
ejpam-5189	265	22	g)|+	g)|+	PROPN
ejpam-5189	265	23	∑	∑	PUNCT
ejpam-5189	265	24	v∈v	v∈v	PROPN
ejpam-5189	265	25	(	(	PUNCT
ejpam-5189	265	26	g	g	NOUN
ejpam-5189	265	27	)	)	PUNCT
ejpam-5189	265	28	|dv|	|dv|	NOUN
ejpam-5189	265	29	=	=	SYM
ejpam-5189	265	30	m(1	m(1	NOUN
ejpam-5189	265	31	+	+	CCONJ
ejpam-5189	265	32	ψh	ψh	NOUN
ejpam-5189	265	33	)	)	PUNCT
ejpam-5189	265	34	.	.	PUNCT
ejpam-5189	266	1	this	this	PRON
ejpam-5189	266	2	proves	prove	VERB
ejpam-5189	266	3	the	the	DET
ejpam-5189	266	4	desired	desire	VERB
ejpam-5189	266	5	equality	equality	NOUN
ejpam-5189	266	6	.	.	PUNCT
ejpam-5189	267	1	the	the	DET
ejpam-5189	267	2	cartesian	cartesian	ADJ
ejpam-5189	267	3	product	product	NOUN
ejpam-5189	267	4	g	g	ADP
ejpam-5189	267	5	×	×	NOUN
ejpam-5189	267	6	h	h	NOUN
ejpam-5189	267	7	of	of	ADP
ejpam-5189	267	8	two	two	NUM
ejpam-5189	267	9	graphs	graph	NOUN
ejpam-5189	267	10	g	g	NOUN
ejpam-5189	267	11	and	and	CCONJ
ejpam-5189	267	12	h	h	NOUN
ejpam-5189	267	13	is	be	AUX
ejpam-5189	267	14	the	the	DET
ejpam-5189	267	15	graph	graph	NOUN
ejpam-5189	267	16	with	with	ADP
ejpam-5189	267	17	v	v	NOUN
ejpam-5189	267	18	(	(	PUNCT
ejpam-5189	267	19	g×h	g×h	NOUN
ejpam-5189	267	20	)	)	PUNCT
ejpam-5189	267	21	=	=	SYM
ejpam-5189	267	22	v	v	NOUN
ejpam-5189	267	23	(	(	PUNCT
ejpam-5189	267	24	g)×	g)×	NOUN
ejpam-5189	267	25	v	v	NOUN
ejpam-5189	267	26	(	(	PUNCT
ejpam-5189	267	27	h	h	NOUN
ejpam-5189	267	28	)	)	PUNCT
ejpam-5189	267	29	and	and	CCONJ
ejpam-5189	267	30	(	(	PUNCT
ejpam-5189	267	31	u	u	NOUN
ejpam-5189	267	32	,	,	PUNCT
ejpam-5189	267	33	u′)(v	u′)(v	NOUN
ejpam-5189	267	34	,	,	PUNCT
ejpam-5189	267	35	v′	v′	NOUN
ejpam-5189	267	36	)	)	PUNCT
ejpam-5189	267	37	∈	∈	PROPN
ejpam-5189	267	38	e(g×h	e(g×h	NOUN
ejpam-5189	267	39	)	)	PUNCT
ejpam-5189	267	40	if	if	SCONJ
ejpam-5189	267	41	and	and	CCONJ
ejpam-5189	267	42	only	only	ADV
ejpam-5189	267	43	if	if	SCONJ
ejpam-5189	267	44	either	either	DET
ejpam-5189	267	45	uv	uv	PROPN
ejpam-5189	267	46	∈	∈	PROPN
ejpam-5189	267	47	e(g	e(g	PROPN
ejpam-5189	267	48	)	)	PUNCT
ejpam-5189	267	49	and	and	CCONJ
ejpam-5189	267	50	u′	u′	PROPN
ejpam-5189	267	51	=	=	SYM
ejpam-5189	267	52	v′	v′	NOUN
ejpam-5189	267	53	or	or	CCONJ
ejpam-5189	267	54	u	u	NOUN
ejpam-5189	267	55	=	=	PROPN
ejpam-5189	267	56	v	v	PROPN
ejpam-5189	267	57	and	and	CCONJ
ejpam-5189	267	58	u′v′	u′v′	PROPN
ejpam-5189	267	59	∈	∈	PROPN
ejpam-5189	267	60	e(h	e(h	PROPN
ejpam-5189	267	61	)	)	PUNCT
ejpam-5189	267	62	.	.	PUNCT
ejpam-5189	268	1	the	the	DET
ejpam-5189	268	2	next	next	ADJ
ejpam-5189	268	3	result	result	NOUN
ejpam-5189	268	4	obtained	obtain	VERB
ejpam-5189	268	5	by	by	ADP
ejpam-5189	268	6	canoy	canoy	NOUN
ejpam-5189	268	7	and	and	CCONJ
ejpam-5189	268	8	garces	garce	NOUN
ejpam-5189	268	9	characterizes	characterize	VERB
ejpam-5189	268	10	convex	convex	NOUN
ejpam-5189	268	11	sets	set	NOUN
ejpam-5189	268	12	in	in	ADP
ejpam-5189	268	13	the	the	DET
ejpam-5189	268	14	cartesian	cartesian	ADJ
ejpam-5189	268	15	product	product	NOUN
ejpam-5189	268	16	of	of	ADP
ejpam-5189	268	17	graphs	graph	NOUN
ejpam-5189	268	18	.	.	PUNCT
ejpam-5189	269	1	theorem	theorem	VERB
ejpam-5189	269	2	6	6	NUM
ejpam-5189	269	3	.	.	PUNCT
ejpam-5189	270	1	[	[	X
ejpam-5189	270	2	7	7	X
ejpam-5189	270	3	]	]	X
ejpam-5189	270	4	let	let	VERB
ejpam-5189	270	5	g	g	NOUN
ejpam-5189	270	6	and	and	CCONJ
ejpam-5189	270	7	h	h	NOUN
ejpam-5189	270	8	be	be	AUX
ejpam-5189	270	9	connected	connect	VERB
ejpam-5189	270	10	graphs	graph	NOUN
ejpam-5189	270	11	.	.	PUNCT
ejpam-5189	271	1	a	a	DET
ejpam-5189	271	2	subset	subset	NOUN
ejpam-5189	271	3	s	s	X
ejpam-5189	271	4	of	of	ADP
ejpam-5189	271	5	v	v	NOUN
ejpam-5189	271	6	(	(	PUNCT
ejpam-5189	271	7	g	g	NOUN
ejpam-5189	271	8	□	□	NOUN
ejpam-5189	271	9	h	h	NOUN
ejpam-5189	271	10	)	)	PUNCT
ejpam-5189	271	11	is	be	AUX
ejpam-5189	271	12	convex	convex	ADJ
ejpam-5189	271	13	if	if	SCONJ
ejpam-5189	271	14	and	and	CCONJ
ejpam-5189	271	15	only	only	ADV
ejpam-5189	271	16	if	if	SCONJ
ejpam-5189	271	17	s	s	NOUN
ejpam-5189	271	18	=	=	VERB
ejpam-5189	271	19	s1	s1	PROPN
ejpam-5189	271	20	×	×	PROPN
ejpam-5189	271	21	s2	s2	PROPN
ejpam-5189	271	22	,	,	PUNCT
ejpam-5189	271	23	where	where	SCONJ
ejpam-5189	271	24	s1	s1	NOUN
ejpam-5189	271	25	and	and	CCONJ
ejpam-5189	271	26	s2	s2	PROPN
ejpam-5189	271	27	are	be	AUX
ejpam-5189	271	28	convex	convex	NOUN
ejpam-5189	271	29	sets	set	NOUN
ejpam-5189	271	30	in	in	ADP
ejpam-5189	271	31	g	g	PROPN
ejpam-5189	271	32	and	and	CCONJ
ejpam-5189	271	33	h	h	NOUN
ejpam-5189	271	34	,	,	PUNCT
ejpam-5189	271	35	respectively	respectively	ADV
ejpam-5189	271	36	.	.	PUNCT
ejpam-5189	272	1	lemma	lemma	PROPN
ejpam-5189	272	2	2	2	X
ejpam-5189	272	3	.	.	PUNCT
ejpam-5189	273	1	let	let	VERB
ejpam-5189	273	2	g	g	NOUN
ejpam-5189	273	3	and	and	CCONJ
ejpam-5189	273	4	h	h	NOUN
ejpam-5189	273	5	be	be	AUX
ejpam-5189	273	6	connected	connect	VERB
ejpam-5189	273	7	graphs	graph	NOUN
ejpam-5189	273	8	.	.	PUNCT
ejpam-5189	274	1	if	if	SCONJ
ejpam-5189	274	2	a	a	DET
ejpam-5189	274	3	subset	subset	NOUN
ejpam-5189	274	4	s	s	X
ejpam-5189	274	5	=	=	X
ejpam-5189	274	6	s1	s1	PROPN
ejpam-5189	274	7	×	×	PROPN
ejpam-5189	274	8	s2	s2	NOUN
ejpam-5189	274	9	of	of	ADP
ejpam-5189	274	10	v	v	NOUN
ejpam-5189	274	11	(	(	PUNCT
ejpam-5189	274	12	g	g	NOUN
ejpam-5189	274	13	□	□	NOUN
ejpam-5189	274	14	h	h	NOUN
ejpam-5189	274	15	)	)	PUNCT
ejpam-5189	274	16	is	be	AUX
ejpam-5189	274	17	a	a	DET
ejpam-5189	274	18	2	2	NUM
ejpam-5189	274	19	-	-	PUNCT
ejpam-5189	274	20	dominating	dominating	NOUN
ejpam-5189	274	21	set	set	NOUN
ejpam-5189	274	22	in	in	ADP
ejpam-5189	274	23	g	g	PROPN
ejpam-5189	274	24	□	□	PROPN
ejpam-5189	274	25	h	h	NOUN
ejpam-5189	274	26	,	,	PUNCT
ejpam-5189	274	27	then	then	ADV
ejpam-5189	274	28	s1	s1	PROPN
ejpam-5189	274	29	and	and	CCONJ
ejpam-5189	274	30	s2	s2	PROPN
ejpam-5189	274	31	are	be	AUX
ejpam-5189	274	32	2	2	NUM
ejpam-5189	274	33	-	-	PUNCT
ejpam-5189	274	34	dominating	dominating	NOUN
ejpam-5189	274	35	sets	set	NOUN
ejpam-5189	274	36	in	in	ADP
ejpam-5189	274	37	g	g	PROPN
ejpam-5189	274	38	and	and	CCONJ
ejpam-5189	274	39	h	h	NOUN
ejpam-5189	274	40	,	,	PUNCT
ejpam-5189	274	41	respectively	respectively	ADV
ejpam-5189	274	42	.	.	PUNCT
ejpam-5189	275	1	proof	proof	NOUN
ejpam-5189	275	2	.	.	PUNCT
ejpam-5189	276	1	suppose	suppose	VERB
ejpam-5189	276	2	that	that	SCONJ
ejpam-5189	276	3	s	s	VERB
ejpam-5189	276	4	is	be	AUX
ejpam-5189	276	5	a	a	DET
ejpam-5189	276	6	2	2	NUM
ejpam-5189	276	7	-	-	PUNCT
ejpam-5189	276	8	dominating	dominating	NOUN
ejpam-5189	276	9	set	set	NOUN
ejpam-5189	276	10	in	in	ADP
ejpam-5189	276	11	g	g	NOUN
ejpam-5189	276	12	□	□	PROPN
ejpam-5189	276	13	h	h	NOUN
ejpam-5189	276	14	and	and	CCONJ
ejpam-5189	276	15	let	let	VERB
ejpam-5189	276	16	v	v	NUM
ejpam-5189	276	17	∈	∈	PROPN
ejpam-5189	276	18	v	v	NOUN
ejpam-5189	276	19	(	(	PUNCT
ejpam-5189	276	20	g	g	NOUN
ejpam-5189	276	21	)	)	PUNCT
ejpam-5189	276	22	\	\	NOUN
ejpam-5189	276	23	s1	s1	PROPN
ejpam-5189	276	24	.	.	PUNCT
ejpam-5189	276	25	pick	pick	VERB
ejpam-5189	276	26	any	any	DET
ejpam-5189	276	27	p	p	PROPN
ejpam-5189	276	28	∈	∈	PROPN
ejpam-5189	276	29	v	v	ADP
ejpam-5189	276	30	(	(	PUNCT
ejpam-5189	276	31	h	h	NOUN
ejpam-5189	276	32	)	)	PUNCT
ejpam-5189	276	33	.	.	PUNCT
ejpam-5189	277	1	since	since	SCONJ
ejpam-5189	277	2	s	s	PROPN
ejpam-5189	277	3	is	be	AUX
ejpam-5189	277	4	2	2	NUM
ejpam-5189	277	5	-	-	PUNCT
ejpam-5189	277	6	dominating	dominating	NOUN
ejpam-5189	277	7	in	in	ADP
ejpam-5189	277	8	g	g	NOUN
ejpam-5189	277	9	□	□	PROPN
ejpam-5189	277	10	h	h	NOUN
ejpam-5189	277	11	and	and	CCONJ
ejpam-5189	277	12	(	(	PUNCT
ejpam-5189	277	13	v	v	NOUN
ejpam-5189	277	14	,	,	PUNCT
ejpam-5189	277	15	p	p	NOUN
ejpam-5189	277	16	)	)	PUNCT
ejpam-5189	277	17	/∈	/∈	PUNCT
ejpam-5189	278	1	s	s	X
ejpam-5189	278	2	,	,	PUNCT
ejpam-5189	278	3	there	there	PRON
ejpam-5189	278	4	exist	exist	VERB
ejpam-5189	278	5	(	(	PUNCT
ejpam-5189	278	6	u	u	NOUN
ejpam-5189	278	7	,	,	PUNCT
ejpam-5189	278	8	q	q	NOUN
ejpam-5189	278	9	)	)	PUNCT
ejpam-5189	278	10	,	,	PUNCT
ejpam-5189	278	11	(	(	PUNCT
ejpam-5189	278	12	w	w	PROPN
ejpam-5189	278	13	,	,	PUNCT
ejpam-5189	278	14	t	t	PROPN
ejpam-5189	278	15	)	)	PUNCT
ejpam-5189	278	16	∈	∈	PROPN
ejpam-5189	278	17	s∩ng	s∩ng	NOUN
ejpam-5189	278	18	□	□	NOUN
ejpam-5189	278	19	h((v	h((v	NOUN
ejpam-5189	278	20	,	,	PUNCT
ejpam-5189	278	21	p	p	NOUN
ejpam-5189	278	22	)	)	PUNCT
ejpam-5189	278	23	)	)	PUNCT
ejpam-5189	278	24	.	.	PUNCT
ejpam-5189	279	1	this	this	PRON
ejpam-5189	279	2	implies	imply	VERB
ejpam-5189	279	3	that	that	SCONJ
ejpam-5189	279	4	p	p	X
ejpam-5189	279	5	=	=	X
ejpam-5189	279	6	q	q	X
ejpam-5189	279	7	=	=	SYM
ejpam-5189	279	8	t	t	PROPN
ejpam-5189	279	9	,	,	PUNCT
ejpam-5189	279	10	u	u	NOUN
ejpam-5189	279	11	̸=	̸=	PROPN
ejpam-5189	279	12	w	w	PROPN
ejpam-5189	279	13	,	,	PUNCT
ejpam-5189	279	14	and	and	CCONJ
ejpam-5189	279	15	u	u	NOUN
ejpam-5189	279	16	,	,	PUNCT
ejpam-5189	279	17	w	w	PROPN
ejpam-5189	279	18	∈	∈	PROPN
ejpam-5189	279	19	s1∩ng(v	s1∩ng(v	PROPN
ejpam-5189	279	20	)	)	PUNCT
ejpam-5189	279	21	.	.	PUNCT
ejpam-5189	280	1	thus	thus	ADV
ejpam-5189	280	2	,	,	PUNCT
ejpam-5189	280	3	s1	s1	PROPN
ejpam-5189	280	4	is	be	AUX
ejpam-5189	280	5	a	a	DET
ejpam-5189	280	6	2	2	NUM
ejpam-5189	280	7	-	-	PUNCT
ejpam-5189	280	8	dominating	dominating	NOUN
ejpam-5189	280	9	set	set	NOUN
ejpam-5189	280	10	in	in	ADP
ejpam-5189	280	11	g.	g.	PROPN
ejpam-5189	280	12	a	a	DET
ejpam-5189	280	13	similar	similar	ADJ
ejpam-5189	280	14	argument	argument	NOUN
ejpam-5189	280	15	can	can	AUX
ejpam-5189	280	16	be	be	AUX
ejpam-5189	280	17	used	use	VERB
ejpam-5189	280	18	to	to	PART
ejpam-5189	280	19	show	show	VERB
ejpam-5189	280	20	that	that	SCONJ
ejpam-5189	280	21	s2	s2	NOUN
ejpam-5189	280	22	is	be	AUX
ejpam-5189	280	23	a	a	DET
ejpam-5189	280	24	2	2	NUM
ejpam-5189	280	25	-	-	PUNCT
ejpam-5189	280	26	dominating	dominating	NOUN
ejpam-5189	280	27	set	set	NOUN
ejpam-5189	280	28	in	in	ADP
ejpam-5189	280	29	h.	h.	PROPN
ejpam-5189	280	30	theorem	theorem	PROPN
ejpam-5189	280	31	7	7	X
ejpam-5189	280	32	.	.	PUNCT
ejpam-5189	281	1	let	let	VERB
ejpam-5189	281	2	g	g	NOUN
ejpam-5189	282	1	and	and	CCONJ
ejpam-5189	282	2	h	h	NOUN
ejpam-5189	282	3	be	be	AUX
ejpam-5189	282	4	connected	connect	VERB
ejpam-5189	282	5	graphs	graph	NOUN
ejpam-5189	282	6	.	.	PUNCT
ejpam-5189	283	1	a	a	DET
ejpam-5189	283	2	subset	subset	NOUN
ejpam-5189	283	3	s	s	X
ejpam-5189	283	4	of	of	ADP
ejpam-5189	283	5	v	v	NOUN
ejpam-5189	283	6	(	(	PUNCT
ejpam-5189	283	7	g	g	NOUN
ejpam-5189	283	8	□	□	NOUN
ejpam-5189	283	9	h	h	NOUN
ejpam-5189	283	10	)	)	PUNCT
ejpam-5189	283	11	is	be	AUX
ejpam-5189	283	12	a	a	DET
ejpam-5189	283	13	convex	convex	ADJ
ejpam-5189	283	14	2	2	NUM
ejpam-5189	283	15	-	-	PUNCT
ejpam-5189	283	16	dominating	dominating	NOUN
ejpam-5189	283	17	set	set	NOUN
ejpam-5189	283	18	in	in	ADP
ejpam-5189	283	19	g	g	PROPN
ejpam-5189	283	20	□	□	PROPN
ejpam-5189	283	21	h	h	NOUN
ejpam-5189	283	22	if	if	SCONJ
ejpam-5189	284	1	and	and	CCONJ
ejpam-5189	284	2	only	only	ADV
ejpam-5189	284	3	if	if	SCONJ
ejpam-5189	284	4	s	s	NOUN
ejpam-5189	284	5	=	=	VERB
ejpam-5189	284	6	s1	s1	PROPN
ejpam-5189	284	7	×	×	NOUN
ejpam-5189	284	8	s2	s2	NOUN
ejpam-5189	284	9	and	and	CCONJ
ejpam-5189	284	10	(	(	PUNCT
ejpam-5189	284	11	i	i	NOUN
ejpam-5189	284	12	)	)	PUNCT
ejpam-5189	284	13	s1	s1	PROPN
ejpam-5189	284	14	is	be	AUX
ejpam-5189	284	15	a	a	DET
ejpam-5189	284	16	convex	convex	ADJ
ejpam-5189	284	17	2	2	NUM
ejpam-5189	284	18	-	-	PUNCT
ejpam-5189	284	19	dominating	dominating	NOUN
ejpam-5189	284	20	set	set	NOUN
ejpam-5189	284	21	in	in	ADP
ejpam-5189	284	22	g	g	PROPN
ejpam-5189	284	23	and	and	CCONJ
ejpam-5189	284	24	s2	s2	PROPN
ejpam-5189	284	25	=	=	SYM
ejpam-5189	284	26	v	v	PROPN
ejpam-5189	284	27	(	(	PUNCT
ejpam-5189	284	28	h	h	NOUN
ejpam-5189	284	29	)	)	PUNCT
ejpam-5189	284	30	,	,	PUNCT
ejpam-5189	284	31	or	or	CCONJ
ejpam-5189	284	32	(	(	PUNCT
ejpam-5189	284	33	ii	ii	NOUN
ejpam-5189	284	34	)	)	PUNCT
ejpam-5189	284	35	s2	s2	NOUN
ejpam-5189	284	36	is	be	AUX
ejpam-5189	284	37	a	a	DET
ejpam-5189	284	38	convex	convex	ADJ
ejpam-5189	284	39	2	2	NUM
ejpam-5189	284	40	-	-	PUNCT
ejpam-5189	284	41	dominating	dominating	NOUN
ejpam-5189	284	42	set	set	NOUN
ejpam-5189	284	43	in	in	ADP
ejpam-5189	284	44	h	h	NOUN
ejpam-5189	284	45	and	and	CCONJ
ejpam-5189	284	46	s1	s1	PROPN
ejpam-5189	284	47	=	=	SYM
ejpam-5189	284	48	v	v	PROPN
ejpam-5189	284	49	(	(	PUNCT
ejpam-5189	284	50	g	g	NOUN
ejpam-5189	284	51	)	)	PUNCT
ejpam-5189	284	52	.	.	PUNCT
ejpam-5189	285	1	proof	proof	NOUN
ejpam-5189	285	2	.	.	PUNCT
ejpam-5189	286	1	let	let	VERB
ejpam-5189	286	2	s	s	PRON
ejpam-5189	286	3	be	be	AUX
ejpam-5189	286	4	a	a	DET
ejpam-5189	286	5	convex	convex	ADJ
ejpam-5189	286	6	2	2	NUM
ejpam-5189	286	7	-	-	PUNCT
ejpam-5189	286	8	dominating	dominating	NOUN
ejpam-5189	286	9	set	set	NOUN
ejpam-5189	286	10	in	in	ADP
ejpam-5189	286	11	g	g	PROPN
ejpam-5189	286	12	□	□	PROPN
ejpam-5189	286	13	h.	h.	NOUN
ejpam-5189	286	14	by	by	ADP
ejpam-5189	286	15	theorem	theorem	ADJ
ejpam-5189	286	16	6	6	NUM
ejpam-5189	286	17	,	,	PUNCT
ejpam-5189	286	18	s	s	PART
ejpam-5189	286	19	=	=	SYM
ejpam-5189	286	20	s1	s1	PROPN
ejpam-5189	286	21	×	×	PROPN
ejpam-5189	286	22	s2	s2	PROPN
ejpam-5189	286	23	,	,	PUNCT
ejpam-5189	286	24	where	where	SCONJ
ejpam-5189	286	25	s1	s1	NOUN
ejpam-5189	286	26	and	and	CCONJ
ejpam-5189	286	27	s2	s2	PROPN
ejpam-5189	286	28	are	be	AUX
ejpam-5189	286	29	convex	convex	NOUN
ejpam-5189	286	30	sets	set	NOUN
ejpam-5189	286	31	in	in	ADP
ejpam-5189	286	32	g	g	PROPN
ejpam-5189	286	33	and	and	CCONJ
ejpam-5189	286	34	h	h	NOUN
ejpam-5189	286	35	,	,	PUNCT
ejpam-5189	286	36	respectively	respectively	ADV
ejpam-5189	286	37	.	.	PUNCT
ejpam-5189	287	1	by	by	ADP
ejpam-5189	287	2	lemma	lemma	PROPN
ejpam-5189	287	3	2	2	NUM
ejpam-5189	287	4	,	,	PUNCT
ejpam-5189	287	5	s1	s1	NOUN
ejpam-5189	287	6	and	and	CCONJ
ejpam-5189	287	7	s2	s2	PROPN
ejpam-5189	287	8	are	be	AUX
ejpam-5189	287	9	2	2	NUM
ejpam-5189	287	10	-	-	PUNCT
ejpam-5189	287	11	dominating	dominating	NOUN
ejpam-5189	287	12	sets	set	NOUN
ejpam-5189	287	13	in	in	ADP
ejpam-5189	287	14	g	g	PROPN
ejpam-5189	287	15	and	and	CCONJ
ejpam-5189	287	16	h	h	NOUN
ejpam-5189	287	17	,	,	PUNCT
ejpam-5189	287	18	respectively	respectively	ADV
ejpam-5189	287	19	.	.	PUNCT
ejpam-5189	288	1	suppose	suppose	VERB
ejpam-5189	288	2	s1	s1	PROPN
ejpam-5189	288	3	̸=	̸=	PROPN
ejpam-5189	288	4	v	v	NOUN
ejpam-5189	288	5	(	(	PUNCT
ejpam-5189	288	6	g	g	NOUN
ejpam-5189	288	7	)	)	PUNCT
ejpam-5189	288	8	and	and	CCONJ
ejpam-5189	288	9	s2	s2	VERB
ejpam-5189	288	10	̸=	̸=	PROPN
ejpam-5189	288	11	v	v	NOUN
ejpam-5189	288	12	(	(	PUNCT
ejpam-5189	288	13	h	h	NOUN
ejpam-5189	288	14	)	)	PUNCT
ejpam-5189	288	15	.	.	PUNCT
ejpam-5189	289	1	pick	pick	VERB
ejpam-5189	289	2	any	any	DET
ejpam-5189	289	3	x	x	SYM
ejpam-5189	289	4	∈	∈	PROPN
ejpam-5189	289	5	v	v	ADP
ejpam-5189	289	6	(	(	PUNCT
ejpam-5189	289	7	g	g	NOUN
ejpam-5189	289	8	)	)	PUNCT
ejpam-5189	289	9	\	\	NOUN
ejpam-5189	289	10	s1	s1	NOUN
ejpam-5189	289	11	and	and	CCONJ
ejpam-5189	289	12	a	a	DET
ejpam-5189	289	13	∈	∈	PROPN
ejpam-5189	289	14	v	v	ADP
ejpam-5189	289	15	(	(	PUNCT
ejpam-5189	289	16	h	h	NOUN
ejpam-5189	289	17	)	)	PUNCT
ejpam-5189	289	18	\	\	NOUN
ejpam-5189	289	19	s2	s2	PROPN
ejpam-5189	289	20	.	.	PUNCT
ejpam-5189	290	1	then	then	ADV
ejpam-5189	290	2	(	(	PUNCT
ejpam-5189	290	3	x	x	X
ejpam-5189	290	4	,	,	PUNCT
ejpam-5189	290	5	d	d	NOUN
ejpam-5189	290	6	)	)	PUNCT
ejpam-5189	290	7	,	,	PUNCT
ejpam-5189	290	8	(	(	PUNCT
ejpam-5189	290	9	z	z	X
ejpam-5189	290	10	,	,	PUNCT
ejpam-5189	290	11	a	a	PRON
ejpam-5189	290	12	)	)	PUNCT
ejpam-5189	290	13	/∈	/∈	PUNCT
ejpam-5189	290	14	s	s	NOUN
ejpam-5189	290	15	for	for	ADP
ejpam-5189	290	16	all	all	PRON
ejpam-5189	290	17	d	d	PROPN
ejpam-5189	290	18	∈	∈	PROPN
ejpam-5189	290	19	v	v	ADP
ejpam-5189	290	20	(	(	PUNCT
ejpam-5189	290	21	h	h	NOUN
ejpam-5189	290	22	)	)	PUNCT
ejpam-5189	290	23	and	and	CCONJ
ejpam-5189	290	24	z	z	NOUN
ejpam-5189	290	25	∈	∈	PROPN
ejpam-5189	290	26	v	v	ADP
ejpam-5189	290	27	(	(	PUNCT
ejpam-5189	290	28	g	g	NOUN
ejpam-5189	290	29	)	)	PUNCT
ejpam-5189	290	30	.	.	PUNCT
ejpam-5189	291	1	it	it	PRON
ejpam-5189	291	2	follows	follow	VERB
ejpam-5189	291	3	that	that	SCONJ
ejpam-5189	291	4	ng	ng	PROPN
ejpam-5189	291	5	□	□	PROPN
ejpam-5189	291	6	h((x	h((x	NOUN
ejpam-5189	291	7	,	,	PUNCT
ejpam-5189	291	8	a	a	PRON
ejpam-5189	291	9	)	)	PUNCT
ejpam-5189	291	10	)	)	PUNCT
ejpam-5189	291	11	∩	∩	NOUN
ejpam-5189	291	12	(	(	PUNCT
ejpam-5189	291	13	s1	s1	PROPN
ejpam-5189	291	14	×	×	PROPN
ejpam-5189	291	15	s2	s2	PROPN
ejpam-5189	291	16	)	)	PUNCT
ejpam-5189	291	17	=	=	PUNCT
ejpam-5189	291	18	∅	∅	NOUN
ejpam-5189	291	19	,	,	PUNCT
ejpam-5189	291	20	implying	imply	VERB
ejpam-5189	291	21	that	that	SCONJ
ejpam-5189	291	22	s1	s1	PROPN
ejpam-5189	291	23	×	×	NOUN
ejpam-5189	291	24	s2	s2	NOUN
ejpam-5189	291	25	is	be	AUX
ejpam-5189	291	26	a	a	DET
ejpam-5189	291	27	not	not	PART
ejpam-5189	291	28	a	a	DET
ejpam-5189	291	29	2	2	NUM
ejpam-5189	291	30	-	-	PUNCT
ejpam-5189	291	31	dominating	dominating	NOUN
ejpam-5189	291	32	set	set	NOUN
ejpam-5189	291	33	in	in	ADP
ejpam-5189	291	34	g	g	PROPN
ejpam-5189	291	35	□	□	PROPN
ejpam-5189	291	36	h	h	NOUN
ejpam-5189	291	37	,	,	PUNCT
ejpam-5189	291	38	contrary	contrary	ADJ
ejpam-5189	291	39	to	to	ADP
ejpam-5189	291	40	our	our	PRON
ejpam-5189	291	41	assumption	assumption	NOUN
ejpam-5189	291	42	of	of	ADP
ejpam-5189	291	43	the	the	DET
ejpam-5189	291	44	set	set	NOUN
ejpam-5189	291	45	.	.	PUNCT
ejpam-5189	292	1	hence	hence	ADV
ejpam-5189	292	2	,	,	PUNCT
ejpam-5189	292	3	s1	s1	PROPN
ejpam-5189	292	4	=	=	SYM
ejpam-5189	292	5	v	v	PROPN
ejpam-5189	292	6	(	(	PUNCT
ejpam-5189	292	7	g	g	NOUN
ejpam-5189	292	8	)	)	PUNCT
ejpam-5189	292	9	or	or	CCONJ
ejpam-5189	292	10	s2	s2	VERB
ejpam-5189	292	11	=	=	SYM
ejpam-5189	292	12	v	v	PROPN
ejpam-5189	292	13	(	(	PUNCT
ejpam-5189	292	14	h	h	NOUN
ejpam-5189	292	15	)	)	PUNCT
ejpam-5189	292	16	.	.	PUNCT
ejpam-5189	293	1	this	this	PRON
ejpam-5189	293	2	shows	show	VERB
ejpam-5189	293	3	that	that	SCONJ
ejpam-5189	293	4	(	(	PUNCT
ejpam-5189	293	5	i	i	NOUN
ejpam-5189	293	6	)	)	PUNCT
ejpam-5189	293	7	or	or	CCONJ
ejpam-5189	293	8	(	(	PUNCT
ejpam-5189	293	9	ii	ii	NOUN
ejpam-5189	293	10	)	)	PUNCT
ejpam-5189	293	11	holds	hold	VERB
ejpam-5189	293	12	.	.	PUNCT
ejpam-5189	294	1	for	for	ADP
ejpam-5189	294	2	the	the	DET
ejpam-5189	294	3	converse	converse	NOUN
ejpam-5189	294	4	,	,	PUNCT
ejpam-5189	294	5	suppose	suppose	VERB
ejpam-5189	294	6	that	that	SCONJ
ejpam-5189	294	7	(	(	PUNCT
ejpam-5189	294	8	i	i	NOUN
ejpam-5189	294	9	)	)	PUNCT
ejpam-5189	294	10	holds	hold	VERB
ejpam-5189	294	11	.	.	PUNCT
ejpam-5189	295	1	by	by	ADP
ejpam-5189	295	2	theorem	theorem	NOUN
ejpam-5189	295	3	6	6	NUM
ejpam-5189	295	4	,	,	PUNCT
ejpam-5189	295	5	s	s	PART
ejpam-5189	295	6	=	=	SYM
ejpam-5189	295	7	s1	s1	PROPN
ejpam-5189	295	8	×	×	PROPN
ejpam-5189	295	9	s2	s2	NOUN
ejpam-5189	295	10	is	be	AUX
ejpam-5189	295	11	a	a	DET
ejpam-5189	295	12	convex	convex	NOUN
ejpam-5189	295	13	set	set	VERB
ejpam-5189	295	14	in	in	ADP
ejpam-5189	295	15	g	g	PROPN
ejpam-5189	295	16	□	□	PROPN
ejpam-5189	295	17	h.	h.	PROPN
ejpam-5189	295	18	let	let	PROPN
ejpam-5189	295	19	(	(	PUNCT
ejpam-5189	295	20	v	v	NOUN
ejpam-5189	295	21	,	,	PUNCT
ejpam-5189	295	22	p	p	NOUN
ejpam-5189	295	23	)	)	PUNCT
ejpam-5189	295	24	∈	∈	PROPN
ejpam-5189	295	25	v	v	NOUN
ejpam-5189	295	26	(	(	PUNCT
ejpam-5189	295	27	g	g	NOUN
ejpam-5189	295	28	□	□	NOUN
ejpam-5189	295	29	h	h	NOUN
ejpam-5189	295	30	)	)	PUNCT
ejpam-5189	295	31	\	\	PUNCT
ejpam-5189	296	1	s.	s.	PROPN
ejpam-5189	296	2	then	then	ADV
ejpam-5189	296	3	v	v	NOUN
ejpam-5189	296	4	/∈	/∈	PUNCT
ejpam-5189	296	5	s1	s1	NOUN
ejpam-5189	296	6	.	.	PUNCT
ejpam-5189	297	1	since	since	SCONJ
ejpam-5189	297	2	s1	s1	PROPN
ejpam-5189	297	3	is	be	AUX
ejpam-5189	297	4	2	2	NUM
ejpam-5189	297	5	-	-	PUNCT
ejpam-5189	297	6	dominating	dominating	NOUN
ejpam-5189	297	7	,	,	PUNCT
ejpam-5189	297	8	there	there	PRON
ejpam-5189	297	9	exist	exist	VERB
ejpam-5189	297	10	u	u	NOUN
ejpam-5189	297	11	,	,	PUNCT
ejpam-5189	297	12	w	w	PROPN
ejpam-5189	297	13	∈	∈	PROPN
ejpam-5189	297	14	s1	s1	NOUN
ejpam-5189	297	15	such	such	ADJ
ejpam-5189	297	16	that	that	SCONJ
ejpam-5189	297	17	u	u	NOUN
ejpam-5189	297	18	,	,	PUNCT
ejpam-5189	297	19	w	w	PROPN
ejpam-5189	297	20	∈	∈	PROPN
ejpam-5189	297	21	ng(v	ng(v	NOUN
ejpam-5189	297	22	)	)	PUNCT
ejpam-5189	297	23	.	.	PUNCT
ejpam-5189	298	1	consequently	consequently	ADV
ejpam-5189	298	2	,	,	PUNCT
ejpam-5189	298	3	(	(	PUNCT
ejpam-5189	298	4	u	u	NOUN
ejpam-5189	298	5	,	,	PUNCT
ejpam-5189	298	6	p	p	NOUN
ejpam-5189	298	7	)	)	PUNCT
ejpam-5189	298	8	,	,	PUNCT
ejpam-5189	298	9	(	(	PUNCT
ejpam-5189	298	10	w	w	X
ejpam-5189	298	11	,	,	PUNCT
ejpam-5189	298	12	p	p	NOUN
ejpam-5189	298	13	)	)	PUNCT
ejpam-5189	298	14	∈	∈	PROPN
ejpam-5189	298	15	ng	ng	PROPN
ejpam-5189	298	16	□	□	PROPN
ejpam-5189	298	17	h((v	h((v	NOUN
ejpam-5189	298	18	,	,	PUNCT
ejpam-5189	298	19	p))∩s	p))∩s	NOUN
ejpam-5189	298	20	.	.	PUNCT
ejpam-5189	299	1	hence	hence	ADV
ejpam-5189	299	2	,	,	PUNCT
ejpam-5189	299	3	s	s	VERB
ejpam-5189	299	4	is	be	AUX
ejpam-5189	299	5	a	a	DET
ejpam-5189	299	6	convex	convex	ADJ
ejpam-5189	299	7	2	2	NUM
ejpam-5189	299	8	-	-	PUNCT
ejpam-5189	299	9	dominating	dominating	NOUN
ejpam-5189	299	10	set	set	NOUN
ejpam-5189	299	11	in	in	ADP
ejpam-5189	299	12	g	g	PROPN
ejpam-5189	299	13	□	□	PROPN
ejpam-5189	299	14	h.	h.	NOUN
ejpam-5189	299	15	the	the	DET
ejpam-5189	299	16	same	same	ADJ
ejpam-5189	299	17	conclusion	conclusion	NOUN
ejpam-5189	299	18	is	be	AUX
ejpam-5189	299	19	obtained	obtain	VERB
ejpam-5189	299	20	if	if	SCONJ
ejpam-5189	299	21	(	(	PUNCT
ejpam-5189	299	22	ii	ii	NOUN
ejpam-5189	299	23	)	)	PUNCT
ejpam-5189	299	24	holds	hold	VERB
ejpam-5189	299	25	.	.	PUNCT
ejpam-5189	300	1	corollary	corollary	ADJ
ejpam-5189	300	2	7	7	NUM
ejpam-5189	300	3	.	.	PUNCT
ejpam-5189	301	1	let	let	VERB
ejpam-5189	301	2	g	g	NOUN
ejpam-5189	301	3	and	and	CCONJ
ejpam-5189	301	4	h	h	NOUN
ejpam-5189	301	5	be	be	AUX
ejpam-5189	301	6	connected	connect	VERB
ejpam-5189	301	7	graphs	graph	NOUN
ejpam-5189	301	8	of	of	ADP
ejpam-5189	301	9	orders	order	NOUN
ejpam-5189	301	10	m	m	VERB
ejpam-5189	301	11	and	and	CCONJ
ejpam-5189	301	12	n	n	CCONJ
ejpam-5189	301	13	,	,	PUNCT
ejpam-5189	301	14	respectively	respectively	ADV
ejpam-5189	301	15	.	.	PUNCT
ejpam-5189	302	1	then	then	ADV
ejpam-5189	302	2	γ2con(g	γ2con(g	NUM
ejpam-5189	302	3	□	□	NOUN
ejpam-5189	302	4	h	h	NOUN
ejpam-5189	302	5	)	)	PUNCT
ejpam-5189	302	6	=	=	SYM
ejpam-5189	302	7	min{mγ2con(h	min{mγ2con(h	PROPN
ejpam-5189	302	8	)	)	PUNCT
ejpam-5189	302	9	,	,	PUNCT
ejpam-5189	302	10	nγ2con(g	nγ2con(g	PROPN
ejpam-5189	302	11	)	)	PUNCT
ejpam-5189	302	12	}	}	PUNCT
ejpam-5189	302	13	.	.	PUNCT
ejpam-5189	303	1	r.	r.	PROPN
ejpam-5189	303	2	j.	j.	PROPN
ejpam-5189	303	3	g.	g.	PROPN
ejpam-5189	303	4	fortosa	fortosa	PROPN
ejpam-5189	303	5	et	et	PROPN
ejpam-5189	303	6	al	al	PROPN
ejpam-5189	303	7	.	.	PUNCT
ejpam-5189	303	8	/	/	SYM
ejpam-5189	303	9	eur	eur	PROPN
ejpam-5189	303	10	.	.	PUNCT
ejpam-5189	304	1	j.	j.	PROPN
ejpam-5189	304	2	pure	pure	PROPN
ejpam-5189	304	3	appl	appl	PROPN
ejpam-5189	304	4	.	.	PROPN
ejpam-5189	304	5	math	math	PROPN
ejpam-5189	304	6	,	,	PUNCT
ejpam-5189	304	7	17	17	NUM
ejpam-5189	304	8	(	(	PUNCT
ejpam-5189	304	9	3	3	NUM
ejpam-5189	304	10	)	)	PUNCT
ejpam-5189	304	11	(	(	PUNCT
ejpam-5189	304	12	2024	2024	NUM
ejpam-5189	304	13	)	)	PUNCT
ejpam-5189	304	14	,	,	PUNCT
ejpam-5189	304	15	1539	1539	NUM
ejpam-5189	304	16	-	-	SYM
ejpam-5189	304	17	1552	1552	NUM
ejpam-5189	304	18	1548	1548	NUM
ejpam-5189	304	19	proof	proof	NOUN
ejpam-5189	304	20	.	.	PUNCT
ejpam-5189	305	1	let	let	VERB
ejpam-5189	305	2	s	s	PRON
ejpam-5189	305	3	be	be	AUX
ejpam-5189	305	4	a	a	DET
ejpam-5189	305	5	γ2con	γ2con	NOUN
ejpam-5189	305	6	-	-	PUNCT
ejpam-5189	305	7	set	set	NOUN
ejpam-5189	305	8	in	in	ADP
ejpam-5189	305	9	g	g	PROPN
ejpam-5189	305	10	□	□	PROPN
ejpam-5189	305	11	h.	h.	NOUN
ejpam-5189	305	12	by	by	ADP
ejpam-5189	305	13	theorem	theorem	ADJ
ejpam-5189	305	14	7	7	NUM
ejpam-5189	305	15	,	,	PUNCT
ejpam-5189	305	16	s	s	PART
ejpam-5189	305	17	=	=	PUNCT
ejpam-5189	305	18	s1×v	s1×v	PROPN
ejpam-5189	305	19	(	(	PUNCT
ejpam-5189	305	20	h	h	NOUN
ejpam-5189	305	21	)	)	PUNCT
ejpam-5189	305	22	or	or	CCONJ
ejpam-5189	305	23	s	s	X
ejpam-5189	305	24	=	=	SYM
ejpam-5189	305	25	v	v	NOUN
ejpam-5189	305	26	(	(	PUNCT
ejpam-5189	305	27	g)×s2	g)×s2	ADJ
ejpam-5189	305	28	,	,	PUNCT
ejpam-5189	305	29	where	where	SCONJ
ejpam-5189	305	30	s1	s1	PROPN
ejpam-5189	305	31	is	be	AUX
ejpam-5189	305	32	a	a	DET
ejpam-5189	305	33	convex	convex	ADJ
ejpam-5189	305	34	2	2	NUM
ejpam-5189	305	35	-	-	PUNCT
ejpam-5189	305	36	dominating	dominating	NOUN
ejpam-5189	305	37	set	set	NOUN
ejpam-5189	305	38	in	in	ADP
ejpam-5189	305	39	g	g	PROPN
ejpam-5189	305	40	and	and	CCONJ
ejpam-5189	305	41	s2	s2	PROPN
ejpam-5189	305	42	is	be	AUX
ejpam-5189	305	43	a	a	DET
ejpam-5189	305	44	convex	convex	ADJ
ejpam-5189	305	45	2	2	NUM
ejpam-5189	305	46	-	-	PUNCT
ejpam-5189	305	47	dominating	dominating	NOUN
ejpam-5189	305	48	set	set	NOUN
ejpam-5189	305	49	in	in	ADP
ejpam-5189	305	50	h.	h.	PROPN
ejpam-5189	305	51	thus	thus	ADV
ejpam-5189	305	52	,	,	PUNCT
ejpam-5189	305	53	γ2con(g	γ2con(g	ADV
ejpam-5189	305	54	□	□	SYM
ejpam-5189	305	55	h	h	NOUN
ejpam-5189	305	56	)	)	PUNCT
ejpam-5189	305	57	=	=	SYM
ejpam-5189	305	58	|s|	|s|	NOUN
ejpam-5189	305	59	≥	≥	NOUN
ejpam-5189	305	60	min{nγ2con(g),mγ2con(h	min{nγ2con(g),mγ2con(h	NOUN
ejpam-5189	305	61	)	)	PUNCT
ejpam-5189	305	62	}	}	PUNCT
ejpam-5189	305	63	.	.	PUNCT
ejpam-5189	306	1	next	next	ADV
ejpam-5189	306	2	,	,	PUNCT
ejpam-5189	306	3	suppose	suppose	VERB
ejpam-5189	306	4	that	that	SCONJ
ejpam-5189	306	5	s′	s′	ADJ
ejpam-5189	306	6	1	1	NUM
ejpam-5189	306	7	and	and	CCONJ
ejpam-5189	306	8	s	s	PRON
ejpam-5189	306	9	′	′	ADJ
ejpam-5189	306	10	2	2	NUM
ejpam-5189	306	11	are	be	AUX
ejpam-5189	306	12	γ2con	γ2con	NOUN
ejpam-5189	306	13	-	-	PUNCT
ejpam-5189	306	14	sets	set	VERB
ejpam-5189	306	15	ing	ing	ADJ
ejpam-5189	306	16	andh	andh	NOUN
ejpam-5189	306	17	,	,	PUNCT
ejpam-5189	306	18	respectively	respectively	ADV
ejpam-5189	306	19	.	.	PUNCT
ejpam-5189	307	1	then	then	ADV
ejpam-5189	307	2	by	by	ADP
ejpam-5189	307	3	theorem	theorem	NOUN
ejpam-5189	307	4	7	7	NUM
ejpam-5189	307	5	,	,	PUNCT
ejpam-5189	307	6	s′	s′	ADJ
ejpam-5189	307	7	=	=	PUNCT
ejpam-5189	307	8	s′	s′	NUM
ejpam-5189	307	9	1	1	NUM
ejpam-5189	307	10	×	×	NOUN
ejpam-5189	307	11	v	v	NOUN
ejpam-5189	307	12	(	(	PUNCT
ejpam-5189	307	13	h	h	NOUN
ejpam-5189	307	14	)	)	PUNCT
ejpam-5189	307	15	and	and	CCONJ
ejpam-5189	307	16	s∗	s∗	PROPN
ejpam-5189	307	17	=	=	SYM
ejpam-5189	307	18	v	v	PROPN
ejpam-5189	307	19	(	(	PUNCT
ejpam-5189	307	20	g)×	g)×	NOUN
ejpam-5189	307	21	s′	s′	ADJ
ejpam-5189	307	22	2	2	NUM
ejpam-5189	307	23	are	be	AUX
ejpam-5189	307	24	convex	convex	ADJ
ejpam-5189	307	25	2	2	NUM
ejpam-5189	307	26	-	-	PUNCT
ejpam-5189	307	27	dominating	dominating	NOUN
ejpam-5189	307	28	sets	set	NOUN
ejpam-5189	307	29	in	in	ADP
ejpam-5189	307	30	g	g	PROPN
ejpam-5189	307	31	□	□	PROPN
ejpam-5189	307	32	h.	h.	NOUN
ejpam-5189	307	33	it	it	PRON
ejpam-5189	307	34	follows	follow	VERB
ejpam-5189	307	35	that	that	SCONJ
ejpam-5189	307	36	γ2con(g	γ2con(g	ADV
ejpam-5189	307	37	□	□	SYM
ejpam-5189	307	38	h	h	NOUN
ejpam-5189	307	39	)	)	PUNCT
ejpam-5189	307	40	≤	≤	NOUN
ejpam-5189	307	41	min{|s′|	min{|s′|	NOUN
ejpam-5189	307	42	,	,	PUNCT
ejpam-5189	307	43	|s∗|	|s∗|	NUM
ejpam-5189	307	44	}	}	PUNCT
ejpam-5189	307	45	=	=	SYM
ejpam-5189	307	46	min{nγ2con(g),mγ2con(h	min{nγ2con(g),mγ2con(h	NOUN
ejpam-5189	307	47	)	)	PUNCT
ejpam-5189	307	48	}	}	PUNCT
ejpam-5189	307	49	.	.	PUNCT
ejpam-5189	308	1	this	this	PRON
ejpam-5189	308	2	proves	prove	VERB
ejpam-5189	308	3	the	the	DET
ejpam-5189	308	4	desired	desire	VERB
ejpam-5189	308	5	equality	equality	NOUN
ejpam-5189	308	6	.	.	PUNCT
ejpam-5189	309	1	the	the	DET
ejpam-5189	309	2	lexicographic	lexicographic	ADJ
ejpam-5189	309	3	product	product	NOUN
ejpam-5189	309	4	of	of	ADP
ejpam-5189	309	5	two	two	NUM
ejpam-5189	309	6	graphs	graph	NOUN
ejpam-5189	309	7	g	g	NOUN
ejpam-5189	309	8	and	and	CCONJ
ejpam-5189	309	9	h	h	NOUN
ejpam-5189	309	10	is	be	AUX
ejpam-5189	309	11	the	the	DET
ejpam-5189	309	12	graph	graph	NOUN
ejpam-5189	309	13	g[h	g[h	PROPN
ejpam-5189	309	14	]	]	PUNCT
ejpam-5189	309	15	with	with	ADP
ejpam-5189	309	16	v	v	NOUN
ejpam-5189	309	17	(	(	PUNCT
ejpam-5189	309	18	g[h	g[h	PROPN
ejpam-5189	309	19	]	]	PUNCT
ejpam-5189	309	20	)	)	PUNCT
ejpam-5189	309	21	=	=	SYM
ejpam-5189	309	22	v	v	X
ejpam-5189	309	23	(	(	PUNCT
ejpam-5189	309	24	g)×v	g)×v	PROPN
ejpam-5189	309	25	(	(	PUNCT
ejpam-5189	309	26	h	h	NOUN
ejpam-5189	309	27	)	)	PUNCT
ejpam-5189	309	28	and	and	CCONJ
ejpam-5189	309	29	(	(	PUNCT
ejpam-5189	309	30	u1	u1	NOUN
ejpam-5189	309	31	,	,	PUNCT
ejpam-5189	309	32	u2)(v1	u2)(v1	NOUN
ejpam-5189	309	33	,	,	PUNCT
ejpam-5189	309	34	v2	v2	NOUN
ejpam-5189	309	35	)	)	PUNCT
ejpam-5189	309	36	∈	∈	NOUN
ejpam-5189	309	37	e(g[h	e(g[h	NOUN
ejpam-5189	309	38	]	]	PUNCT
ejpam-5189	309	39	)	)	PUNCT
ejpam-5189	310	1	if	if	SCONJ
ejpam-5189	310	2	and	and	CCONJ
ejpam-5189	310	3	only	only	ADV
ejpam-5189	310	4	if	if	SCONJ
ejpam-5189	310	5	either	either	CCONJ
ejpam-5189	310	6	u1v1	u1v1	PROPN
ejpam-5189	310	7	∈	∈	PROPN
ejpam-5189	310	8	e(g	e(g	PROPN
ejpam-5189	310	9	)	)	PUNCT
ejpam-5189	310	10	or	or	CCONJ
ejpam-5189	310	11	u1	u1	NOUN
ejpam-5189	310	12	=	=	SYM
ejpam-5189	310	13	v1	v1	NOUN
ejpam-5189	310	14	and	and	CCONJ
ejpam-5189	310	15	u2v2	u2v2	ADJ
ejpam-5189	310	16	∈	∈	PROPN
ejpam-5189	310	17	e(h	e(h	PROPN
ejpam-5189	310	18	)	)	PUNCT
ejpam-5189	310	19	.	.	PUNCT
ejpam-5189	310	20	theorem	theorem	VERB
ejpam-5189	310	21	8	8	NUM
ejpam-5189	310	22	.	.	PUNCT
ejpam-5189	311	1	[	[	X
ejpam-5189	311	2	7	7	X
ejpam-5189	311	3	]	]	X
ejpam-5189	311	4	let	let	VERB
ejpam-5189	311	5	g	g	NOUN
ejpam-5189	311	6	and	and	CCONJ
ejpam-5189	311	7	h	h	NOUN
ejpam-5189	311	8	be	be	AUX
ejpam-5189	311	9	connected	connect	VERB
ejpam-5189	311	10	non	non	ADJ
ejpam-5189	311	11	-	-	ADJ
ejpam-5189	311	12	complete	complete	ADJ
ejpam-5189	311	13	graphs	graph	NOUN
ejpam-5189	311	14	and	and	CCONJ
ejpam-5189	311	15	let	let	VERB
ejpam-5189	311	16	c	c	PRON
ejpam-5189	311	17	be	be	AUX
ejpam-5189	311	18	a	a	DET
ejpam-5189	311	19	proper	proper	ADJ
ejpam-5189	311	20	subset	subset	NOUN
ejpam-5189	311	21	of	of	ADP
ejpam-5189	311	22	v	v	NOUN
ejpam-5189	311	23	(	(	PUNCT
ejpam-5189	311	24	g[h	g[h	PROPN
ejpam-5189	311	25	]	]	PUNCT
ejpam-5189	311	26	)	)	PUNCT
ejpam-5189	311	27	.	.	PUNCT
ejpam-5189	312	1	then	then	ADV
ejpam-5189	312	2	c	c	PROPN
ejpam-5189	312	3	is	be	AUX
ejpam-5189	312	4	convex	convex	ADJ
ejpam-5189	312	5	in	in	ADP
ejpam-5189	312	6	g[h	g[h	PROPN
ejpam-5189	312	7	]	]	PUNCT
ejpam-5189	312	8	if	if	SCONJ
ejpam-5189	312	9	and	and	CCONJ
ejpam-5189	312	10	only	only	ADV
ejpam-5189	312	11	if	if	SCONJ
ejpam-5189	312	12	c	c	PROPN
ejpam-5189	312	13	is	be	AUX
ejpam-5189	312	14	a	a	DET
ejpam-5189	312	15	clique	clique	NOUN
ejpam-5189	312	16	.	.	PUNCT
ejpam-5189	313	1	theorem	theorem	NOUN
ejpam-5189	313	2	9	9	NUM
ejpam-5189	313	3	.	.	PUNCT
ejpam-5189	314	1	let	let	VERB
ejpam-5189	314	2	g	g	NOUN
ejpam-5189	314	3	and	and	CCONJ
ejpam-5189	314	4	h	h	NOUN
ejpam-5189	314	5	be	be	AUX
ejpam-5189	314	6	connected	connect	VERB
ejpam-5189	314	7	non	non	ADJ
ejpam-5189	314	8	-	-	ADJ
ejpam-5189	314	9	complete	complete	ADJ
ejpam-5189	314	10	graphs	graph	NOUN
ejpam-5189	314	11	.	.	PUNCT
ejpam-5189	315	1	a	a	DET
ejpam-5189	315	2	set	set	NOUN
ejpam-5189	315	3	c	c	NOUN
ejpam-5189	315	4	=	=	SYM
ejpam-5189	315	5	∪x∈s({x}×tx	∪x∈s({x}×tx	PROPN
ejpam-5189	315	6	)	)	PUNCT
ejpam-5189	315	7	⊆	⊆	NUM
ejpam-5189	315	8	v	v	NOUN
ejpam-5189	315	9	(	(	PUNCT
ejpam-5189	315	10	g[h	g[h	PROPN
ejpam-5189	315	11	]	]	PUNCT
ejpam-5189	315	12	)	)	PUNCT
ejpam-5189	315	13	is	be	AUX
ejpam-5189	315	14	convex	convex	ADJ
ejpam-5189	315	15	2	2	NUM
ejpam-5189	315	16	-	-	PUNCT
ejpam-5189	315	17	dominating	dominating	NOUN
ejpam-5189	315	18	if	if	SCONJ
ejpam-5189	315	19	and	and	CCONJ
ejpam-5189	315	20	only	only	ADV
ejpam-5189	315	21	if	if	SCONJ
ejpam-5189	315	22	c	c	PROPN
ejpam-5189	315	23	=	=	SYM
ejpam-5189	315	24	v	v	PROPN
ejpam-5189	315	25	(	(	PUNCT
ejpam-5189	315	26	g[h	g[h	PROPN
ejpam-5189	315	27	]	]	PUNCT
ejpam-5189	315	28	)	)	PUNCT
ejpam-5189	315	29	or	or	CCONJ
ejpam-5189	315	30	s	s	VERB
ejpam-5189	315	31	and	and	CCONJ
ejpam-5189	315	32	each	each	DET
ejpam-5189	315	33	tx	tx	PROPN
ejpam-5189	315	34	are	be	AUX
ejpam-5189	315	35	cliques	clique	NOUN
ejpam-5189	315	36	in	in	ADP
ejpam-5189	315	37	g	g	PROPN
ejpam-5189	315	38	and	and	CCONJ
ejpam-5189	315	39	h	h	NOUN
ejpam-5189	315	40	,	,	PUNCT
ejpam-5189	315	41	respectively	respectively	ADV
ejpam-5189	315	42	,	,	PUNCT
ejpam-5189	315	43	and	and	CCONJ
ejpam-5189	315	44	satisfy	satisfy	VERB
ejpam-5189	315	45	one	one	NUM
ejpam-5189	315	46	of	of	ADP
ejpam-5189	315	47	the	the	DET
ejpam-5189	315	48	following	following	ADJ
ejpam-5189	315	49	conditions	condition	NOUN
ejpam-5189	315	50	:	:	PUNCT
ejpam-5189	315	51	(	(	PUNCT
ejpam-5189	315	52	i	i	NOUN
ejpam-5189	315	53	)	)	PUNCT
ejpam-5189	315	54	s	s	AUX
ejpam-5189	315	55	is	be	AUX
ejpam-5189	315	56	a	a	DET
ejpam-5189	315	57	2	2	NUM
ejpam-5189	315	58	-	-	PUNCT
ejpam-5189	315	59	dominating	dominating	NOUN
ejpam-5189	315	60	set	set	NOUN
ejpam-5189	315	61	in	in	ADP
ejpam-5189	315	62	g	g	PROPN
ejpam-5189	315	63	and	and	CCONJ
ejpam-5189	315	64	(	(	PUNCT
ejpam-5189	315	65	a	a	X
ejpam-5189	315	66	)	)	PUNCT
ejpam-5189	315	67	|s|	|s|	PROPN
ejpam-5189	315	68	≥	≥	NOUN
ejpam-5189	315	69	3	3	NUM
ejpam-5189	315	70	or	or	CCONJ
ejpam-5189	315	71	(	(	PUNCT
ejpam-5189	315	72	b	b	NOUN
ejpam-5189	315	73	)	)	PUNCT
ejpam-5189	315	74	for	for	ADP
ejpam-5189	315	75	each	each	DET
ejpam-5189	315	76	x	x	SYM
ejpam-5189	315	77	∈	∈	PROPN
ejpam-5189	315	78	s	s	PART
ejpam-5189	315	79	,	,	PUNCT
ejpam-5189	315	80	tx	tx	PROPN
ejpam-5189	315	81	is	be	AUX
ejpam-5189	315	82	dominating	dominate	VERB
ejpam-5189	315	83	in	in	ADP
ejpam-5189	315	84	h	h	NOUN
ejpam-5189	315	85	or	or	CCONJ
ejpam-5189	315	86	|ty|	|ty|	PROPN
ejpam-5189	315	87	≥	≥	NOUN
ejpam-5189	315	88	2	2	NUM
ejpam-5189	315	89	when	when	SCONJ
ejpam-5189	315	90	s	s	VERB
ejpam-5189	315	91	=	=	SYM
ejpam-5189	315	92	{	{	PUNCT
ejpam-5189	315	93	x	x	PROPN
ejpam-5189	315	94	,	,	PUNCT
ejpam-5189	315	95	y	y	PROPN
ejpam-5189	315	96	}	}	PUNCT
ejpam-5189	315	97	.	.	PUNCT
ejpam-5189	316	1	(	(	PUNCT
ejpam-5189	316	2	ii	ii	NOUN
ejpam-5189	316	3	)	)	PUNCT
ejpam-5189	316	4	s	s	VERB
ejpam-5189	316	5	is	be	AUX
ejpam-5189	316	6	a	a	DET
ejpam-5189	316	7	dominating	dominating	NOUN
ejpam-5189	316	8	set	set	VERB
ejpam-5189	316	9	in	in	ADP
ejpam-5189	316	10	g	g	PROPN
ejpam-5189	316	11	such	such	ADJ
ejpam-5189	316	12	that	that	PRON
ejpam-5189	316	13	(	(	PUNCT
ejpam-5189	316	14	c	c	X
ejpam-5189	316	15	)	)	PUNCT
ejpam-5189	316	16	tx	tx	PROPN
ejpam-5189	316	17	is	be	AUX
ejpam-5189	316	18	2	2	NUM
ejpam-5189	316	19	-	-	PUNCT
ejpam-5189	316	20	dominating	dominating	NOUN
ejpam-5189	316	21	in	in	ADP
ejpam-5189	316	22	h	h	NOUN
ejpam-5189	317	1	whenever	whenever	SCONJ
ejpam-5189	317	2	s	s	VERB
ejpam-5189	317	3	=	=	PRON
ejpam-5189	317	4	{	{	PUNCT
ejpam-5189	317	5	x	x	NOUN
ejpam-5189	317	6	}	}	PUNCT
ejpam-5189	317	7	and	and	CCONJ
ejpam-5189	317	8	(	(	PUNCT
ejpam-5189	317	9	d	d	NOUN
ejpam-5189	317	10	)	)	PUNCT
ejpam-5189	317	11	for	for	ADP
ejpam-5189	317	12	each	each	PRON
ejpam-5189	317	13	v	v	NUM
ejpam-5189	317	14	∈	∈	PROPN
ejpam-5189	317	15	v	v	NOUN
ejpam-5189	317	16	(	(	PUNCT
ejpam-5189	317	17	g	g	NOUN
ejpam-5189	317	18	)	)	PUNCT
ejpam-5189	317	19	\	\	PROPN
ejpam-5189	318	1	s	s	PART
ejpam-5189	318	2	with	with	ADP
ejpam-5189	318	3	|ng(v	|ng(v	NOUN
ejpam-5189	318	4	)	)	PUNCT
ejpam-5189	318	5	∩	∩	NOUN
ejpam-5189	318	6	s|	s|	NOUN
ejpam-5189	318	7	=	=	SYM
ejpam-5189	318	8	1	1	NUM
ejpam-5189	318	9	,	,	PUNCT
ejpam-5189	318	10	it	it	PRON
ejpam-5189	318	11	holds	hold	VERB
ejpam-5189	318	12	that	that	SCONJ
ejpam-5189	318	13	|tz|	|tz|	NOUN
ejpam-5189	318	14	≥	≥	NOUN
ejpam-5189	318	15	2	2	NUM
ejpam-5189	318	16	for	for	ADP
ejpam-5189	318	17	z	z	PROPN
ejpam-5189	318	18	∈	∈	PROPN
ejpam-5189	318	19	ng(v	ng(v	NOUN
ejpam-5189	318	20	)	)	PUNCT
ejpam-5189	318	21	∩	∩	PROPN
ejpam-5189	318	22	s.	s.	PROPN
ejpam-5189	318	23	proof	proof	PROPN
ejpam-5189	318	24	.	.	PUNCT
ejpam-5189	319	1	suppose	suppose	VERB
ejpam-5189	319	2	c	c	NOUN
ejpam-5189	319	3	is	be	AUX
ejpam-5189	319	4	convex	convex	ADJ
ejpam-5189	319	5	2	2	NUM
ejpam-5189	319	6	-	-	PUNCT
ejpam-5189	319	7	dominating	dominating	NOUN
ejpam-5189	319	8	and	and	CCONJ
ejpam-5189	319	9	c	c	PROPN
ejpam-5189	319	10	̸=	̸=	PROPN
ejpam-5189	319	11	v	v	NOUN
ejpam-5189	319	12	(	(	PUNCT
ejpam-5189	319	13	g[h	g[h	PROPN
ejpam-5189	319	14	]	]	PUNCT
ejpam-5189	319	15	)	)	PUNCT
ejpam-5189	319	16	.	.	PUNCT
ejpam-5189	320	1	by	by	ADP
ejpam-5189	320	2	theorem	theorem	NOUN
ejpam-5189	320	3	8	8	NUM
ejpam-5189	320	4	,	,	PUNCT
ejpam-5189	320	5	s	s	PART
ejpam-5189	320	6	and	and	CCONJ
ejpam-5189	320	7	tx	tx	PROPN
ejpam-5189	320	8	are	be	AUX
ejpam-5189	320	9	cliques	clique	NOUN
ejpam-5189	320	10	in	in	ADP
ejpam-5189	320	11	g	g	PROPN
ejpam-5189	320	12	and	and	CCONJ
ejpam-5189	320	13	h	h	NOUN
ejpam-5189	320	14	,	,	PUNCT
ejpam-5189	320	15	respectively	respectively	ADV
ejpam-5189	320	16	,	,	PUNCT
ejpam-5189	320	17	for	for	SCONJ
ejpam-5189	320	18	each	each	DET
ejpam-5189	320	19	x	x	SYM
ejpam-5189	320	20	∈	∈	PROPN
ejpam-5189	320	21	s.	s.	PROPN
ejpam-5189	320	22	suppose	suppose	VERB
ejpam-5189	320	23	s	s	NOUN
ejpam-5189	320	24	is	be	AUX
ejpam-5189	320	25	2	2	NUM
ejpam-5189	320	26	-	-	PUNCT
ejpam-5189	320	27	dominating	dominating	NOUN
ejpam-5189	320	28	in	in	ADP
ejpam-5189	320	29	g	g	NOUN
ejpam-5189	320	30	and	and	CCONJ
ejpam-5189	320	31	let	let	VERB
ejpam-5189	320	32	x	x	PROPN
ejpam-5189	320	33	∈	∈	PROPN
ejpam-5189	320	34	s.	s.	PROPN
ejpam-5189	320	35	if	if	SCONJ
ejpam-5189	320	36	|s|	|s|	NOUN
ejpam-5189	320	37	≥	≥	PROPN
ejpam-5189	320	38	3	3	NUM
ejpam-5189	320	39	,	,	PUNCT
ejpam-5189	320	40	then	then	ADV
ejpam-5189	320	41	(	(	PUNCT
ejpam-5189	320	42	i)(a	i)(a	NOUN
ejpam-5189	320	43	)	)	PUNCT
ejpam-5189	320	44	holds	hold	VERB
ejpam-5189	320	45	.	.	PUNCT
ejpam-5189	321	1	suppose	suppose	VERB
ejpam-5189	321	2	|s|	|s|	PROPN
ejpam-5189	321	3	=	=	SYM
ejpam-5189	321	4	2	2	NUM
ejpam-5189	321	5	,	,	PUNCT
ejpam-5189	321	6	say	say	VERB
ejpam-5189	321	7	s	s	X
ejpam-5189	321	8	=	=	PUNCT
ejpam-5189	321	9	{	{	PUNCT
ejpam-5189	321	10	x	x	PROPN
ejpam-5189	321	11	,	,	PUNCT
ejpam-5189	321	12	y	y	NOUN
ejpam-5189	321	13	}	}	PUNCT
ejpam-5189	321	14	and	and	CCONJ
ejpam-5189	321	15	suppose	suppose	VERB
ejpam-5189	321	16	that	that	SCONJ
ejpam-5189	321	17	|ty|	|ty|	PROPN
ejpam-5189	321	18	=	=	SYM
ejpam-5189	321	19	1	1	X
ejpam-5189	321	20	.	.	PUNCT
ejpam-5189	322	1	let	let	VERB
ejpam-5189	322	2	p	p	PRON
ejpam-5189	322	3	∈	∈	PROPN
ejpam-5189	322	4	v	v	ADP
ejpam-5189	322	5	(	(	PUNCT
ejpam-5189	322	6	h	h	NOUN
ejpam-5189	322	7	)	)	PUNCT
ejpam-5189	322	8	\	\	PROPN
ejpam-5189	322	9	tx	tx	PROPN
ejpam-5189	322	10	and	and	CCONJ
ejpam-5189	322	11	q	q	ADJ
ejpam-5189	322	12	∈	∈	PROPN
ejpam-5189	323	1	ty	ty	INTJ
ejpam-5189	323	2	.	.	PUNCT
ejpam-5189	324	1	then	then	ADV
ejpam-5189	324	2	(	(	PUNCT
ejpam-5189	324	3	y	y	NOUN
ejpam-5189	324	4	,	,	PUNCT
ejpam-5189	324	5	q	q	X
ejpam-5189	324	6	)	)	PUNCT
ejpam-5189	324	7	∈	∈	PROPN
ejpam-5189	324	8	c	c	NOUN
ejpam-5189	324	9	∩	∩	X
ejpam-5189	324	10	ng[h]((x	ng[h]((x	X
ejpam-5189	324	11	,	,	PUNCT
ejpam-5189	324	12	p	p	NOUN
ejpam-5189	324	13	)	)	PUNCT
ejpam-5189	324	14	)	)	PUNCT
ejpam-5189	324	15	.	.	PUNCT
ejpam-5189	325	1	since	since	SCONJ
ejpam-5189	325	2	c	c	PROPN
ejpam-5189	325	3	is	be	AUX
ejpam-5189	325	4	2	2	NUM
ejpam-5189	325	5	-	-	PUNCT
ejpam-5189	325	6	dominating	dominating	NOUN
ejpam-5189	325	7	in	in	ADP
ejpam-5189	325	8	g[h	g[h	PROPN
ejpam-5189	325	9	]	]	PUNCT
ejpam-5189	325	10	,	,	PUNCT
ejpam-5189	325	11	there	there	PRON
ejpam-5189	325	12	exists	exist	VERB
ejpam-5189	325	13	(	(	PUNCT
ejpam-5189	325	14	z	z	NOUN
ejpam-5189	325	15	,	,	PUNCT
ejpam-5189	325	16	t	t	PROPN
ejpam-5189	325	17	)	)	PUNCT
ejpam-5189	325	18	∈	∈	PROPN
ejpam-5189	325	19	(	(	PUNCT
ejpam-5189	325	20	c	c	NOUN
ejpam-5189	325	21	\	\	X
ejpam-5189	325	22	{	{	PUNCT
ejpam-5189	325	23	(	(	PUNCT
ejpam-5189	325	24	y	y	PROPN
ejpam-5189	325	25	,	,	PUNCT
ejpam-5189	325	26	q	q	NOUN
ejpam-5189	325	27	)	)	PUNCT
ejpam-5189	325	28	}	}	PUNCT
ejpam-5189	325	29	)	)	PUNCT
ejpam-5189	325	30	∩ng[h]((x	∩ng[h]((x	NOUN
ejpam-5189	325	31	,	,	PUNCT
ejpam-5189	325	32	p	p	NOUN
ejpam-5189	325	33	)	)	PUNCT
ejpam-5189	325	34	)	)	PUNCT
ejpam-5189	325	35	.	.	PUNCT
ejpam-5189	326	1	since	since	SCONJ
ejpam-5189	326	2	ty	ty	NUM
ejpam-5189	326	3	=	=	PUNCT
ejpam-5189	326	4	{	{	PUNCT
ejpam-5189	326	5	q	q	X
ejpam-5189	326	6	}	}	PUNCT
ejpam-5189	326	7	,	,	PUNCT
ejpam-5189	326	8	z	z	NOUN
ejpam-5189	326	9	=	=	PUNCT
ejpam-5189	326	10	x	x	X
ejpam-5189	326	11	and	and	CCONJ
ejpam-5189	326	12	t	t	PROPN
ejpam-5189	326	13	∈	∈	PROPN
ejpam-5189	326	14	tx	tx	PROPN
ejpam-5189	326	15	∩	∩	NOUN
ejpam-5189	326	16	nh(p	nh(p	NUM
ejpam-5189	326	17	)	)	PUNCT
ejpam-5189	326	18	.	.	PUNCT
ejpam-5189	327	1	therefore	therefore	ADV
ejpam-5189	327	2	,	,	PUNCT
ejpam-5189	327	3	tx	tx	PROPN
ejpam-5189	327	4	is	be	AUX
ejpam-5189	327	5	a	a	DET
ejpam-5189	327	6	(	(	PUNCT
ejpam-5189	327	7	clique	clique	NOUN
ejpam-5189	327	8	)	)	PUNCT
ejpam-5189	327	9	dominating	dominating	NOUN
ejpam-5189	327	10	set	set	VERB
ejpam-5189	327	11	in	in	ADP
ejpam-5189	327	12	h	h	NOUN
ejpam-5189	327	13	,	,	PUNCT
ejpam-5189	327	14	showing	show	VERB
ejpam-5189	327	15	that	that	SCONJ
ejpam-5189	327	16	(	(	PUNCT
ejpam-5189	327	17	i)(b	i)(b	NUM
ejpam-5189	327	18	)	)	PUNCT
ejpam-5189	327	19	holds	hold	VERB
ejpam-5189	327	20	.	.	PUNCT
ejpam-5189	328	1	next	next	ADV
ejpam-5189	328	2	,	,	PUNCT
ejpam-5189	328	3	suppose	suppose	VERB
ejpam-5189	328	4	that	that	SCONJ
ejpam-5189	328	5	s	s	VERB
ejpam-5189	328	6	is	be	AUX
ejpam-5189	328	7	not	not	PART
ejpam-5189	328	8	2	2	NUM
ejpam-5189	328	9	-	-	PUNCT
ejpam-5189	328	10	dominating	dominating	NOUN
ejpam-5189	328	11	.	.	PUNCT
ejpam-5189	329	1	since	since	SCONJ
ejpam-5189	329	2	c	c	PROPN
ejpam-5189	329	3	is	be	AUX
ejpam-5189	329	4	dominating	dominate	VERB
ejpam-5189	329	5	,	,	PUNCT
ejpam-5189	329	6	it	it	PRON
ejpam-5189	329	7	follows	follow	VERB
ejpam-5189	329	8	that	that	SCONJ
ejpam-5189	329	9	s	s	VERB
ejpam-5189	329	10	is	be	AUX
ejpam-5189	329	11	a	a	DET
ejpam-5189	329	12	(	(	PUNCT
ejpam-5189	329	13	clique	clique	NOUN
ejpam-5189	329	14	)	)	PUNCT
ejpam-5189	329	15	dominating	dominating	NOUN
ejpam-5189	329	16	set	set	VERB
ejpam-5189	329	17	in	in	ADP
ejpam-5189	329	18	g.	g.	PROPN
ejpam-5189	329	19	suppose	suppose	VERB
ejpam-5189	329	20	first	first	ADV
ejpam-5189	329	21	that	that	SCONJ
ejpam-5189	329	22	|s|	|s|	PROPN
ejpam-5189	329	23	=	=	SYM
ejpam-5189	329	24	1	1	NUM
ejpam-5189	329	25	,	,	PUNCT
ejpam-5189	329	26	say	say	VERB
ejpam-5189	329	27	s	s	X
ejpam-5189	329	28	=	=	PUNCT
ejpam-5189	329	29	{	{	PUNCT
ejpam-5189	329	30	x	x	NOUN
ejpam-5189	329	31	}	}	PUNCT
ejpam-5189	329	32	.	.	PUNCT
ejpam-5189	330	1	let	let	VERB
ejpam-5189	330	2	d	d	X
ejpam-5189	330	3	∈	∈	PROPN
ejpam-5189	330	4	v	v	ADP
ejpam-5189	330	5	(	(	PUNCT
ejpam-5189	330	6	h	h	NOUN
ejpam-5189	330	7	)	)	PUNCT
ejpam-5189	330	8	\	\	PROPN
ejpam-5189	331	1	tx	tx	PROPN
ejpam-5189	331	2	.	.	PUNCT
ejpam-5189	332	1	since	since	SCONJ
ejpam-5189	332	2	c	c	PROPN
ejpam-5189	332	3	is	be	AUX
ejpam-5189	332	4	2	2	NUM
ejpam-5189	332	5	-	-	PUNCT
ejpam-5189	332	6	dominating	dominate	VERB
ejpam-5189	332	7	and	and	CCONJ
ejpam-5189	332	8	(	(	PUNCT
ejpam-5189	332	9	x	x	X
ejpam-5189	332	10	,	,	PUNCT
ejpam-5189	332	11	d	d	NOUN
ejpam-5189	332	12	)	)	PUNCT
ejpam-5189	332	13	/∈	/∈	PUNCT
ejpam-5189	333	1	c	c	X
ejpam-5189	333	2	,	,	PUNCT
ejpam-5189	333	3	there	there	PRON
ejpam-5189	333	4	exist	exist	VERB
ejpam-5189	333	5	(	(	PUNCT
ejpam-5189	333	6	v	v	NOUN
ejpam-5189	333	7	,	,	PUNCT
ejpam-5189	333	8	l	l	NOUN
ejpam-5189	333	9	)	)	PUNCT
ejpam-5189	333	10	,	,	PUNCT
ejpam-5189	333	11	(	(	PUNCT
ejpam-5189	333	12	w	w	PROPN
ejpam-5189	333	13	,	,	PUNCT
ejpam-5189	333	14	s	s	NOUN
ejpam-5189	333	15	)	)	PUNCT
ejpam-5189	333	16	∈	∈	PROPN
ejpam-5189	333	17	c∩ng[h]((x	c∩ng[h]((x	NOUN
ejpam-5189	333	18	,	,	PUNCT
ejpam-5189	333	19	d	d	NOUN
ejpam-5189	333	20	)	)	PUNCT
ejpam-5189	333	21	)	)	PUNCT
ejpam-5189	333	22	.	.	PUNCT
ejpam-5189	334	1	this	this	PRON
ejpam-5189	334	2	implies	imply	VERB
ejpam-5189	334	3	that	that	SCONJ
ejpam-5189	334	4	v	v	AUX
ejpam-5189	334	5	=	=	SYM
ejpam-5189	334	6	w	w	NOUN
ejpam-5189	334	7	=	=	PUNCT
ejpam-5189	334	8	x	x	X
ejpam-5189	334	9	and	and	CCONJ
ejpam-5189	334	10	l	l	NOUN
ejpam-5189	334	11	,	,	PUNCT
ejpam-5189	334	12	s	s	PROPN
ejpam-5189	334	13	∈	∈	PROPN
ejpam-5189	334	14	tx∩nh(d	tx∩nh(d	PROPN
ejpam-5189	334	15	)	)	PUNCT
ejpam-5189	334	16	.	.	PUNCT
ejpam-5189	335	1	thus	thus	ADV
ejpam-5189	335	2	,	,	PUNCT
ejpam-5189	335	3	tx	tx	PROPN
ejpam-5189	335	4	is	be	AUX
ejpam-5189	335	5	a	a	DET
ejpam-5189	335	6	(	(	PUNCT
ejpam-5189	335	7	clique	clique	NOUN
ejpam-5189	335	8	)	)	PUNCT
ejpam-5189	335	9	2	2	NUM
ejpam-5189	335	10	-	-	PUNCT
ejpam-5189	335	11	dominating	dominating	NOUN
ejpam-5189	335	12	set	set	NOUN
ejpam-5189	335	13	in	in	ADP
ejpam-5189	335	14	h.	h.	PROPN
ejpam-5189	335	15	finally	finally	ADV
ejpam-5189	335	16	,	,	PUNCT
ejpam-5189	335	17	let	let	VERB
ejpam-5189	335	18	v	v	NUM
ejpam-5189	335	19	∈	∈	PROPN
ejpam-5189	335	20	v	v	NOUN
ejpam-5189	335	21	(	(	PUNCT
ejpam-5189	335	22	g	g	NOUN
ejpam-5189	335	23	)	)	PUNCT
ejpam-5189	335	24	\	\	PROPN
ejpam-5189	336	1	s	s	PART
ejpam-5189	336	2	with	with	ADP
ejpam-5189	336	3	|ng(v	|ng(v	NOUN
ejpam-5189	336	4	)	)	PUNCT
ejpam-5189	336	5	∩	∩	NOUN
ejpam-5189	336	6	s|	s|	NOUN
ejpam-5189	336	7	=	=	SYM
ejpam-5189	336	8	1	1	NUM
ejpam-5189	336	9	,	,	PUNCT
ejpam-5189	336	10	say	say	VERB
ejpam-5189	336	11	ng(v	ng(v	NOUN
ejpam-5189	336	12	)	)	PUNCT
ejpam-5189	337	1	∩	∩	NOUN
ejpam-5189	337	2	s	s	PART
ejpam-5189	337	3	=	=	X
ejpam-5189	337	4	{	{	PUNCT
ejpam-5189	337	5	z	z	NOUN
ejpam-5189	337	6	}	}	PUNCT
ejpam-5189	337	7	.	.	PUNCT
ejpam-5189	338	1	since	since	SCONJ
ejpam-5189	338	2	c	c	PROPN
ejpam-5189	338	3	is	be	AUX
ejpam-5189	338	4	2	2	NUM
ejpam-5189	338	5	-	-	PUNCT
ejpam-5189	338	6	dominating	dominating	NOUN
ejpam-5189	338	7	,	,	PUNCT
ejpam-5189	338	8	|tz|	|tz|	NOUN
ejpam-5189	338	9	≥	≥	NOUN
ejpam-5189	338	10	2	2	NUM
ejpam-5189	338	11	,	,	PUNCT
ejpam-5189	338	12	showing	show	VERB
ejpam-5189	338	13	that	that	SCONJ
ejpam-5189	338	14	(	(	PUNCT
ejpam-5189	338	15	ii	ii	NOUN
ejpam-5189	338	16	)	)	PUNCT
ejpam-5189	338	17	holds	hold	VERB
ejpam-5189	338	18	.	.	PUNCT
ejpam-5189	339	1	the	the	DET
ejpam-5189	339	2	converse	converse	NOUN
ejpam-5189	339	3	is	be	AUX
ejpam-5189	339	4	easy	easy	ADJ
ejpam-5189	339	5	.	.	PUNCT
ejpam-5189	340	1	r.	r.	PROPN
ejpam-5189	340	2	j.	j.	PROPN
ejpam-5189	340	3	g.	g.	PROPN
ejpam-5189	340	4	fortosa	fortosa	PROPN
ejpam-5189	340	5	et	et	PROPN
ejpam-5189	340	6	al	al	PROPN
ejpam-5189	340	7	.	.	PUNCT
ejpam-5189	340	8	/	/	SYM
ejpam-5189	340	9	eur	eur	PROPN
ejpam-5189	340	10	.	.	PUNCT
ejpam-5189	341	1	j.	j.	PROPN
ejpam-5189	341	2	pure	pure	PROPN
ejpam-5189	341	3	appl	appl	PROPN
ejpam-5189	341	4	.	.	PROPN
ejpam-5189	341	5	math	math	PROPN
ejpam-5189	341	6	,	,	PUNCT
ejpam-5189	341	7	17	17	NUM
ejpam-5189	341	8	(	(	PUNCT
ejpam-5189	341	9	3	3	NUM
ejpam-5189	341	10	)	)	PUNCT
ejpam-5189	341	11	(	(	PUNCT
ejpam-5189	341	12	2024	2024	NUM
ejpam-5189	341	13	)	)	PUNCT
ejpam-5189	341	14	,	,	PUNCT
ejpam-5189	341	15	1539	1539	NUM
ejpam-5189	341	16	-	-	SYM
ejpam-5189	341	17	1552	1552	NUM
ejpam-5189	341	18	1549	1549	NUM
ejpam-5189	341	19	corollary	corollary	ADJ
ejpam-5189	341	20	8	8	NUM
ejpam-5189	341	21	.	.	PUNCT
ejpam-5189	342	1	let	let	VERB
ejpam-5189	342	2	g	g	NOUN
ejpam-5189	342	3	and	and	CCONJ
ejpam-5189	342	4	h	h	NOUN
ejpam-5189	342	5	be	be	AUX
ejpam-5189	342	6	connected	connect	VERB
ejpam-5189	342	7	two	two	NUM
ejpam-5189	342	8	non	non	ADJ
ejpam-5189	342	9	-	-	ADJ
ejpam-5189	342	10	complete	complete	ADJ
ejpam-5189	342	11	graphs	graph	NOUN
ejpam-5189	342	12	of	of	ADP
ejpam-5189	342	13	orders	order	NOUN
ejpam-5189	342	14	m	m	VERB
ejpam-5189	342	15	and	and	CCONJ
ejpam-5189	342	16	n	n	CCONJ
ejpam-5189	342	17	,	,	PUNCT
ejpam-5189	342	18	respectively	respectively	ADV
ejpam-5189	342	19	.	.	PUNCT
ejpam-5189	343	1	if	if	SCONJ
ejpam-5189	343	2	g	g	PROPN
ejpam-5189	343	3	and	and	CCONJ
ejpam-5189	343	4	h	h	NOUN
ejpam-5189	343	5	do	do	AUX
ejpam-5189	343	6	not	not	PART
ejpam-5189	343	7	admit	admit	VERB
ejpam-5189	343	8	a	a	DET
ejpam-5189	343	9	clique	clique	NOUN
ejpam-5189	343	10	dominating	dominating	NOUN
ejpam-5189	343	11	set	set	NOUN
ejpam-5189	343	12	,	,	PUNCT
ejpam-5189	343	13	then	then	ADV
ejpam-5189	343	14	γ2con(g[h	γ2con(g[h	ADJ
ejpam-5189	343	15	]	]	PUNCT
ejpam-5189	343	16	)	)	PUNCT
ejpam-5189	343	17	=	=	SYM
ejpam-5189	343	18	mn	mn	PROPN
ejpam-5189	343	19	.	.	PUNCT
ejpam-5189	343	20	corollary	corollary	ADJ
ejpam-5189	343	21	9	9	NUM
ejpam-5189	343	22	.	.	PUNCT
ejpam-5189	344	1	let	let	VERB
ejpam-5189	344	2	g	g	NOUN
ejpam-5189	344	3	and	and	CCONJ
ejpam-5189	344	4	h	h	NOUN
ejpam-5189	344	5	be	be	AUX
ejpam-5189	344	6	connected	connect	VERB
ejpam-5189	344	7	non	non	ADJ
ejpam-5189	344	8	-	-	ADJ
ejpam-5189	344	9	complete	complete	ADJ
ejpam-5189	344	10	graphs	graph	NOUN
ejpam-5189	344	11	.	.	PUNCT
ejpam-5189	345	1	then	then	ADV
ejpam-5189	345	2	γ2con(g[h	γ2con(g[h	NOUN
ejpam-5189	345	3	]	]	PUNCT
ejpam-5189	345	4	)	)	PUNCT
ejpam-5189	345	5	=	=	SYM
ejpam-5189	345	6	2	2	NUM
ejpam-5189	345	7	if	if	SCONJ
ejpam-5189	345	8	and	and	CCONJ
ejpam-5189	345	9	only	only	ADV
ejpam-5189	345	10	if	if	SCONJ
ejpam-5189	345	11	γcl(g	γcl(g	NUM
ejpam-5189	345	12	)	)	PUNCT
ejpam-5189	345	13	=	=	SYM
ejpam-5189	345	14	1	1	NUM
ejpam-5189	345	15	and	and	CCONJ
ejpam-5189	345	16	γ2cl(h	γ2cl(h	PROPN
ejpam-5189	345	17	)	)	PUNCT
ejpam-5189	345	18	=	=	SYM
ejpam-5189	345	19	2	2	NUM
ejpam-5189	345	20	or	or	CCONJ
ejpam-5189	345	21	γcl(h	γcl(h	PROPN
ejpam-5189	345	22	)	)	PUNCT
ejpam-5189	345	23	=	=	SYM
ejpam-5189	345	24	1	1	NUM
ejpam-5189	345	25	and	and	CCONJ
ejpam-5189	345	26	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	345	27	)	)	PUNCT
ejpam-5189	345	28	=	=	SYM
ejpam-5189	346	1	2	2	X
ejpam-5189	346	2	.	.	PUNCT
ejpam-5189	346	3	proof	proof	NOUN
ejpam-5189	346	4	.	.	PUNCT
ejpam-5189	347	1	suppose	suppose	VERB
ejpam-5189	347	2	γ2con(g[h	γ2con(g[h	NOUN
ejpam-5189	347	3	]	]	X
ejpam-5189	347	4	)	)	PUNCT
ejpam-5189	347	5	=	=	SYM
ejpam-5189	347	6	2	2	NUM
ejpam-5189	347	7	and	and	CCONJ
ejpam-5189	347	8	let	let	VERB
ejpam-5189	347	9	c	c	NOUN
ejpam-5189	347	10	=	=	PRON
ejpam-5189	347	11	{	{	PUNCT
ejpam-5189	347	12	(	(	PUNCT
ejpam-5189	347	13	x	x	NOUN
ejpam-5189	347	14	,	,	PUNCT
ejpam-5189	347	15	a	a	PRON
ejpam-5189	347	16	)	)	PUNCT
ejpam-5189	347	17	,	,	PUNCT
ejpam-5189	347	18	(	(	PUNCT
ejpam-5189	347	19	y	y	PROPN
ejpam-5189	347	20	,	,	PUNCT
ejpam-5189	347	21	b	b	NOUN
ejpam-5189	347	22	)	)	PUNCT
ejpam-5189	347	23	}	}	PUNCT
ejpam-5189	347	24	be	be	AUX
ejpam-5189	347	25	a	a	DET
ejpam-5189	347	26	γ2con	γ2con	NOUN
ejpam-5189	347	27	-	-	PUNCT
ejpam-5189	347	28	set	set	NOUN
ejpam-5189	347	29	in	in	ADP
ejpam-5189	347	30	g[h	g[h	NOUN
ejpam-5189	347	31	]	]	PUNCT
ejpam-5189	347	32	.	.	PUNCT
ejpam-5189	348	1	then	then	ADV
ejpam-5189	348	2	(	(	PUNCT
ejpam-5189	348	3	x	x	X
ejpam-5189	348	4	,	,	PUNCT
ejpam-5189	348	5	a	a	PRON
ejpam-5189	348	6	)	)	PUNCT
ejpam-5189	348	7	,	,	PUNCT
ejpam-5189	348	8	(	(	PUNCT
ejpam-5189	348	9	y	y	PROPN
ejpam-5189	348	10	,	,	PUNCT
ejpam-5189	348	11	b	b	NOUN
ejpam-5189	348	12	)	)	PUNCT
ejpam-5189	348	13	∈	∈	NOUN
ejpam-5189	348	14	e(g[h	e(g[h	NOUN
ejpam-5189	348	15	]	]	PUNCT
ejpam-5189	348	16	)	)	PUNCT
ejpam-5189	348	17	because	because	SCONJ
ejpam-5189	348	18	c	c	PROPN
ejpam-5189	348	19	is	be	AUX
ejpam-5189	348	20	convex	convex	ADJ
ejpam-5189	348	21	.	.	PUNCT
ejpam-5189	349	1	if	if	SCONJ
ejpam-5189	349	2	x	x	X
ejpam-5189	349	3	=	=	SYM
ejpam-5189	349	4	y	y	PROPN
ejpam-5189	349	5	,	,	PUNCT
ejpam-5189	349	6	then	then	ADV
ejpam-5189	349	7	ab	ab	PROPN
ejpam-5189	349	8	∈	∈	PROPN
ejpam-5189	349	9	e(h	e(h	PROPN
ejpam-5189	349	10	)	)	PUNCT
ejpam-5189	349	11	.	.	PUNCT
ejpam-5189	350	1	hence	hence	ADV
ejpam-5189	350	2	,	,	PUNCT
ejpam-5189	350	3	γcl(g	γcl(g	PROPN
ejpam-5189	350	4	)	)	PUNCT
ejpam-5189	350	5	=	=	SYM
ejpam-5189	350	6	1	1	NUM
ejpam-5189	350	7	(	(	PUNCT
ejpam-5189	350	8	x	x	X
ejpam-5189	350	9	is	be	AUX
ejpam-5189	350	10	a	a	DET
ejpam-5189	350	11	dominating	dominating	NOUN
ejpam-5189	350	12	vertex	vertex	NOUN
ejpam-5189	350	13	of	of	ADP
ejpam-5189	350	14	g	g	NOUN
ejpam-5189	350	15	)	)	PUNCT
ejpam-5189	350	16	and	and	CCONJ
ejpam-5189	350	17	so	so	ADV
ejpam-5189	350	18	γ2cl(h	γ2cl(h	PROPN
ejpam-5189	350	19	)	)	PUNCT
ejpam-5189	350	20	=	=	SYM
ejpam-5189	350	21	2	2	NUM
ejpam-5189	350	22	by	by	ADP
ejpam-5189	350	23	theorem	theorem	NOUN
ejpam-5189	350	24	9(ii)(c	9(ii)(c	NUM
ejpam-5189	350	25	)	)	PUNCT
ejpam-5189	350	26	.	.	PUNCT
ejpam-5189	351	1	suppose	suppose	VERB
ejpam-5189	351	2	x	x	PUNCT
ejpam-5189	351	3	̸=	̸=	PROPN
ejpam-5189	351	4	y.	y.	PROPN
ejpam-5189	351	5	then	then	ADV
ejpam-5189	351	6	{	{	PUNCT
ejpam-5189	351	7	x	x	X
ejpam-5189	351	8	,	,	PUNCT
ejpam-5189	351	9	y	y	PRON
ejpam-5189	351	10	}	}	PUNCT
ejpam-5189	351	11	is	be	AUX
ejpam-5189	351	12	a	a	DET
ejpam-5189	351	13	2	2	NUM
ejpam-5189	351	14	-	-	PUNCT
ejpam-5189	351	15	dominating	dominating	NOUN
ejpam-5189	351	16	set	set	NOUN
ejpam-5189	351	17	in	in	ADP
ejpam-5189	351	18	g	g	PROPN
ejpam-5189	351	19	,	,	PUNCT
ejpam-5189	351	20	i.e.	i.e.	X
ejpam-5189	351	21	,	,	PUNCT
ejpam-5189	351	22	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	351	23	)	)	PUNCT
ejpam-5189	351	24	=	=	SYM
ejpam-5189	352	1	2	2	X
ejpam-5189	352	2	.	.	PUNCT
ejpam-5189	352	3	since	since	SCONJ
ejpam-5189	352	4	|tx|	|tx|	NOUN
ejpam-5189	352	5	=	=	PUNCT
ejpam-5189	352	6	|ty|	|ty|	ADJ
ejpam-5189	352	7	=	=	SYM
ejpam-5189	352	8	1	1	NUM
ejpam-5189	352	9	,	,	PUNCT
ejpam-5189	352	10	tx	tx	PROPN
ejpam-5189	352	11	and	and	CCONJ
ejpam-5189	352	12	ty	ty	PRON
ejpam-5189	352	13	are	be	AUX
ejpam-5189	352	14	clique	clique	ADJ
ejpam-5189	352	15	dominating	dominating	NOUN
ejpam-5189	352	16	sets	set	NOUN
ejpam-5189	352	17	in	in	ADP
ejpam-5189	352	18	h	h	NOUN
ejpam-5189	352	19	by	by	ADP
ejpam-5189	352	20	theorem	theorem	NOUN
ejpam-5189	352	21	9(i)(b	9(i)(b	NUM
ejpam-5189	352	22	)	)	PUNCT
ejpam-5189	352	23	.	.	PUNCT
ejpam-5189	353	1	thus	thus	ADV
ejpam-5189	353	2	,	,	PUNCT
ejpam-5189	353	3	γcl(h	γcl(h	PROPN
ejpam-5189	353	4	)	)	PUNCT
ejpam-5189	353	5	=	=	SYM
ejpam-5189	353	6	1	1	X
ejpam-5189	353	7	.	.	PUNCT
ejpam-5189	354	1	the	the	DET
ejpam-5189	354	2	converse	converse	NOUN
ejpam-5189	354	3	follows	follow	VERB
ejpam-5189	354	4	from	from	ADP
ejpam-5189	354	5	theorem	theorem	ADJ
ejpam-5189	354	6	9	9	NUM
ejpam-5189	354	7	.	.	PUNCT
ejpam-5189	354	8	corollary	corollary	ADJ
ejpam-5189	354	9	10	10	NUM
ejpam-5189	354	10	.	.	PUNCT
ejpam-5189	355	1	let	let	VERB
ejpam-5189	355	2	g	g	NOUN
ejpam-5189	355	3	and	and	CCONJ
ejpam-5189	355	4	h	h	NOUN
ejpam-5189	355	5	be	be	AUX
ejpam-5189	355	6	connected	connect	VERB
ejpam-5189	355	7	non	non	ADJ
ejpam-5189	355	8	-	-	ADJ
ejpam-5189	355	9	complete	complete	ADJ
ejpam-5189	355	10	graphs	graph	NOUN
ejpam-5189	355	11	.	.	PUNCT
ejpam-5189	356	1	then	then	ADV
ejpam-5189	356	2	γ2con(g[h	γ2con(g[h	NOUN
ejpam-5189	356	3	]	]	PUNCT
ejpam-5189	356	4	)	)	PUNCT
ejpam-5189	356	5	=	=	SYM
ejpam-5189	356	6	3	3	NUM
ejpam-5189	356	7	if	if	SCONJ
ejpam-5189	356	8	and	and	CCONJ
ejpam-5189	356	9	only	only	ADV
ejpam-5189	356	10	if	if	SCONJ
ejpam-5189	356	11	one	one	NUM
ejpam-5189	356	12	of	of	ADP
ejpam-5189	356	13	the	the	DET
ejpam-5189	356	14	following	follow	VERB
ejpam-5189	356	15	holds	hold	VERB
ejpam-5189	356	16	:	:	PUNCT
ejpam-5189	356	17	(	(	PUNCT
ejpam-5189	356	18	i	i	NOUN
ejpam-5189	356	19	)	)	PUNCT
ejpam-5189	356	20	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	356	21	)	)	PUNCT
ejpam-5189	356	22	=	=	SYM
ejpam-5189	357	1	3	3	X
ejpam-5189	357	2	.	.	PUNCT
ejpam-5189	357	3	(	(	PUNCT
ejpam-5189	357	4	ii	ii	NOUN
ejpam-5189	357	5	)	)	PUNCT
ejpam-5189	357	6	γcl(g	γcl(g	PROPN
ejpam-5189	357	7	)	)	PUNCT
ejpam-5189	357	8	=	=	SYM
ejpam-5189	357	9	1	1	NUM
ejpam-5189	357	10	and	and	CCONJ
ejpam-5189	357	11	γ2cl(h	γ2cl(h	PROPN
ejpam-5189	357	12	)	)	PUNCT
ejpam-5189	357	13	=	=	SYM
ejpam-5189	357	14	3	3	X
ejpam-5189	357	15	.	.	PUNCT
ejpam-5189	357	16	(	(	PUNCT
ejpam-5189	357	17	iii	iii	X
ejpam-5189	357	18	)	)	PUNCT
ejpam-5189	357	19	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	357	20	)	)	PUNCT
ejpam-5189	357	21	=	=	SYM
ejpam-5189	357	22	2	2	NUM
ejpam-5189	357	23	and	and	CCONJ
ejpam-5189	357	24	γcl(h	γcl(h	PROPN
ejpam-5189	357	25	)	)	PUNCT
ejpam-5189	357	26	=	=	SYM
ejpam-5189	357	27	2	2	X
ejpam-5189	357	28	.	.	PUNCT
ejpam-5189	357	29	(	(	PUNCT
ejpam-5189	357	30	iv	iv	X
ejpam-5189	357	31	)	)	PUNCT
ejpam-5189	357	32	γcl(g	γcl(g	PROPN
ejpam-5189	357	33	)	)	PUNCT
ejpam-5189	357	34	=	=	SYM
ejpam-5189	358	1	γcl(h	γcl(h	PROPN
ejpam-5189	358	2	)	)	PUNCT
ejpam-5189	358	3	=	=	SYM
ejpam-5189	358	4	1	1	NUM
ejpam-5189	358	5	,	,	PUNCT
ejpam-5189	358	6	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	358	7	)	)	PUNCT
ejpam-5189	358	8	̸=	̸=	PROPN
ejpam-5189	358	9	2	2	NUM
ejpam-5189	358	10	,	,	PUNCT
ejpam-5189	358	11	and	and	CCONJ
ejpam-5189	358	12	γ2cl(h	γ2cl(h	PROPN
ejpam-5189	358	13	)	)	PUNCT
ejpam-5189	358	14	̸=	̸=	PROPN
ejpam-5189	358	15	2	2	NUM
ejpam-5189	358	16	.	.	PUNCT
ejpam-5189	359	1	(	(	PUNCT
ejpam-5189	359	2	v	v	NOUN
ejpam-5189	359	3	)	)	PUNCT
ejpam-5189	359	4	γcl(h	γcl(h	PROPN
ejpam-5189	359	5	)	)	PUNCT
ejpam-5189	359	6	=	=	SYM
ejpam-5189	359	7	2	2	NUM
ejpam-5189	359	8	,	,	PUNCT
ejpam-5189	359	9	γcl(g	γcl(g	NUM
ejpam-5189	359	10	)	)	PUNCT
ejpam-5189	359	11	=	=	SYM
ejpam-5189	359	12	1	1	NUM
ejpam-5189	359	13	,	,	PUNCT
ejpam-5189	359	14	and	and	CCONJ
ejpam-5189	359	15	γ2cl(h	γ2cl(h	PROPN
ejpam-5189	359	16	)	)	PUNCT
ejpam-5189	359	17	̸=	̸=	PROPN
ejpam-5189	359	18	2	2	NUM
ejpam-5189	359	19	.	.	PUNCT
ejpam-5189	360	1	proof	proof	NOUN
ejpam-5189	360	2	.	.	PUNCT
ejpam-5189	361	1	suppose	suppose	VERB
ejpam-5189	361	2	γ2con(g[h	γ2con(g[h	NOUN
ejpam-5189	361	3	]	]	X
ejpam-5189	361	4	)	)	PUNCT
ejpam-5189	361	5	=	=	SYM
ejpam-5189	361	6	3	3	NUM
ejpam-5189	361	7	and	and	CCONJ
ejpam-5189	361	8	let	let	VERB
ejpam-5189	361	9	c	c	NOUN
ejpam-5189	361	10	=	=	PRON
ejpam-5189	361	11	{	{	PUNCT
ejpam-5189	361	12	(	(	PUNCT
ejpam-5189	361	13	w	w	PROPN
ejpam-5189	361	14	,	,	PUNCT
ejpam-5189	361	15	p	p	NOUN
ejpam-5189	361	16	)	)	PUNCT
ejpam-5189	361	17	,	,	PUNCT
ejpam-5189	361	18	(	(	PUNCT
ejpam-5189	361	19	u	u	NOUN
ejpam-5189	361	20	,	,	PUNCT
ejpam-5189	361	21	q	q	NOUN
ejpam-5189	361	22	)	)	PUNCT
ejpam-5189	361	23	,	,	PUNCT
ejpam-5189	361	24	(	(	PUNCT
ejpam-5189	361	25	v	v	NOUN
ejpam-5189	361	26	,	,	PUNCT
ejpam-5189	361	27	r	r	NOUN
ejpam-5189	361	28	)	)	PUNCT
ejpam-5189	361	29	}	}	PUNCT
ejpam-5189	361	30	be	be	AUX
ejpam-5189	361	31	a	a	DET
ejpam-5189	361	32	γ2con	γ2con	NOUN
ejpam-5189	361	33	-	-	PUNCT
ejpam-5189	361	34	set	set	NOUN
ejpam-5189	361	35	in	in	ADP
ejpam-5189	361	36	g[h	g[h	NOUN
ejpam-5189	361	37	]	]	PUNCT
ejpam-5189	361	38	.	.	PUNCT
ejpam-5189	362	1	then	then	ADV
ejpam-5189	362	2	c	c	PROPN
ejpam-5189	362	3	is	be	AUX
ejpam-5189	362	4	a	a	DET
ejpam-5189	362	5	clique	clique	NOUN
ejpam-5189	362	6	by	by	ADP
ejpam-5189	362	7	theorem	theorem	NOUN
ejpam-5189	362	8	8	8	NUM
ejpam-5189	362	9	.	.	PUNCT
ejpam-5189	363	1	if	if	SCONJ
ejpam-5189	363	2	u	u	PROPN
ejpam-5189	363	3	,	,	PUNCT
ejpam-5189	363	4	v	v	NOUN
ejpam-5189	363	5	,	,	PUNCT
ejpam-5189	363	6	and	and	CCONJ
ejpam-5189	363	7	w	w	NOUN
ejpam-5189	363	8	are	be	AUX
ejpam-5189	363	9	distinct	distinct	ADJ
ejpam-5189	363	10	vertices	vertex	NOUN
ejpam-5189	363	11	of	of	ADP
ejpam-5189	363	12	g	g	NOUN
ejpam-5189	363	13	,	,	PUNCT
ejpam-5189	363	14	then	then	ADV
ejpam-5189	363	15	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	363	16	)	)	PUNCT
ejpam-5189	363	17	=	=	SYM
ejpam-5189	363	18	3	3	NUM
ejpam-5189	363	19	,	,	PUNCT
ejpam-5189	363	20	showing	show	VERB
ejpam-5189	363	21	that	that	SCONJ
ejpam-5189	363	22	(	(	PUNCT
ejpam-5189	363	23	i	i	NOUN
ejpam-5189	363	24	)	)	PUNCT
ejpam-5189	363	25	holds	hold	VERB
ejpam-5189	363	26	.	.	PUNCT
ejpam-5189	364	1	if	if	SCONJ
ejpam-5189	364	2	w	w	PROPN
ejpam-5189	364	3	=	=	SYM
ejpam-5189	364	4	u	u	NOUN
ejpam-5189	364	5	=	=	PROPN
ejpam-5189	364	6	v	v	NOUN
ejpam-5189	364	7	,	,	PUNCT
ejpam-5189	364	8	then	then	ADV
ejpam-5189	364	9	{	{	PUNCT
ejpam-5189	364	10	p	p	X
ejpam-5189	364	11	,	,	PUNCT
ejpam-5189	364	12	q	q	ADJ
ejpam-5189	364	13	,	,	PUNCT
ejpam-5189	364	14	r	r	NOUN
ejpam-5189	364	15	}	}	PUNCT
ejpam-5189	364	16	is	be	AUX
ejpam-5189	364	17	a	a	DET
ejpam-5189	364	18	clique	clique	NOUN
ejpam-5189	364	19	in	in	ADP
ejpam-5189	364	20	h.	h.	PROPN
ejpam-5189	364	21	hence	hence	ADV
ejpam-5189	364	22	,	,	PUNCT
ejpam-5189	364	23	γcl(g	γcl(g	PROPN
ejpam-5189	364	24	)	)	PUNCT
ejpam-5189	364	25	=	=	SYM
ejpam-5189	364	26	1	1	NUM
ejpam-5189	364	27	(	(	PUNCT
ejpam-5189	364	28	w	w	NOUN
ejpam-5189	364	29	is	be	AUX
ejpam-5189	364	30	a	a	DET
ejpam-5189	364	31	dominating	dominating	NOUN
ejpam-5189	364	32	vertex	vertex	NOUN
ejpam-5189	364	33	of	of	ADP
ejpam-5189	364	34	g	g	NOUN
ejpam-5189	364	35	)	)	PUNCT
ejpam-5189	364	36	and	and	CCONJ
ejpam-5189	364	37	γ2cl(h	γ2cl(h	PROPN
ejpam-5189	364	38	)	)	PUNCT
ejpam-5189	364	39	=	=	SYM
ejpam-5189	364	40	3	3	NUM
ejpam-5189	364	41	by	by	ADP
ejpam-5189	364	42	theorem	theorem	ADJ
ejpam-5189	364	43	9(ii	9(ii	PROPN
ejpam-5189	364	44	)	)	PUNCT
ejpam-5189	364	45	.	.	PUNCT
ejpam-5189	365	1	this	this	PRON
ejpam-5189	365	2	shows	show	VERB
ejpam-5189	365	3	that	that	SCONJ
ejpam-5189	365	4	(	(	PUNCT
ejpam-5189	365	5	ii	ii	NOUN
ejpam-5189	365	6	)	)	PUNCT
ejpam-5189	365	7	holds	hold	VERB
ejpam-5189	365	8	.	.	PUNCT
ejpam-5189	366	1	suppose	suppose	VERB
ejpam-5189	366	2	now	now	ADV
ejpam-5189	366	3	that	that	SCONJ
ejpam-5189	366	4	w	w	PROPN
ejpam-5189	366	5	=	=	SYM
ejpam-5189	366	6	u	u	NOUN
ejpam-5189	366	7	and	and	CCONJ
ejpam-5189	366	8	v	v	ADP
ejpam-5189	366	9	̸=	̸=	PROPN
ejpam-5189	366	10	w.	w.	NOUN
ejpam-5189	366	11	then	then	ADV
ejpam-5189	366	12	q	q	PROPN
ejpam-5189	366	13	=	=	PUNCT
ejpam-5189	366	14	{	{	PUNCT
ejpam-5189	366	15	v	v	NOUN
ejpam-5189	366	16	,	,	PUNCT
ejpam-5189	366	17	w	w	NOUN
ejpam-5189	366	18	}	}	PUNCT
ejpam-5189	366	19	is	be	AUX
ejpam-5189	366	20	a	a	DET
ejpam-5189	366	21	clique	clique	NOUN
ejpam-5189	366	22	dominating	dominating	NOUN
ejpam-5189	366	23	set	set	VERB
ejpam-5189	366	24	in	in	ADP
ejpam-5189	366	25	g.	g.	PROPN
ejpam-5189	366	26	if	if	SCONJ
ejpam-5189	366	27	q	q	NOUN
ejpam-5189	366	28	is	be	AUX
ejpam-5189	366	29	2	2	NUM
ejpam-5189	366	30	-	-	PUNCT
ejpam-5189	366	31	dominating	dominating	NOUN
ejpam-5189	366	32	,	,	PUNCT
ejpam-5189	366	33	then	then	ADV
ejpam-5189	366	34	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	366	35	)	)	PUNCT
ejpam-5189	367	1	=	=	SYM
ejpam-5189	367	2	2	2	X
ejpam-5189	367	3	.	.	PUNCT
ejpam-5189	367	4	since	since	SCONJ
ejpam-5189	367	5	γ2con(g[h	γ2con(g[h	NOUN
ejpam-5189	367	6	]	]	PUNCT
ejpam-5189	367	7	)	)	PUNCT
ejpam-5189	367	8	̸=	̸=	PROPN
ejpam-5189	367	9	2	2	NUM
ejpam-5189	367	10	,	,	PUNCT
ejpam-5189	367	11	γcl(h	γcl(h	PROPN
ejpam-5189	367	12	)	)	PUNCT
ejpam-5189	367	13	̸=	̸=	PROPN
ejpam-5189	367	14	1	1	NUM
ejpam-5189	367	15	.	.	PUNCT
ejpam-5189	368	1	it	it	PRON
ejpam-5189	368	2	follows	follow	VERB
ejpam-5189	368	3	that	that	SCONJ
ejpam-5189	368	4	{	{	PUNCT
ejpam-5189	368	5	p	p	X
ejpam-5189	368	6	,	,	PUNCT
ejpam-5189	368	7	q	q	X
ejpam-5189	368	8	}	}	PUNCT
ejpam-5189	368	9	is	be	AUX
ejpam-5189	368	10	a	a	DET
ejpam-5189	368	11	γcl	γcl	NOUN
ejpam-5189	368	12	-	-	PUNCT
ejpam-5189	368	13	set	set	VERB
ejpam-5189	368	14	in	in	ADP
ejpam-5189	368	15	h	h	NOUN
ejpam-5189	368	16	,	,	PUNCT
ejpam-5189	368	17	i.e.	i.e.	X
ejpam-5189	368	18	,	,	PUNCT
ejpam-5189	368	19	γcl(h	γcl(h	PROPN
ejpam-5189	368	20	)	)	PUNCT
ejpam-5189	368	21	=	=	SYM
ejpam-5189	368	22	2	2	X
ejpam-5189	368	23	.	.	X
ejpam-5189	369	1	hence	hence	ADV
ejpam-5189	369	2	,	,	PUNCT
ejpam-5189	369	3	(	(	PUNCT
ejpam-5189	369	4	iii	iii	NOUN
ejpam-5189	369	5	)	)	PUNCT
ejpam-5189	369	6	holds	hold	VERB
ejpam-5189	369	7	.	.	PUNCT
ejpam-5189	370	1	suppose	suppose	VERB
ejpam-5189	370	2	q	q	NOUN
ejpam-5189	370	3	is	be	AUX
ejpam-5189	370	4	not	not	PART
ejpam-5189	370	5	2	2	NUM
ejpam-5189	370	6	-	-	PUNCT
ejpam-5189	370	7	dominating	dominating	NOUN
ejpam-5189	370	8	.	.	PUNCT
ejpam-5189	371	1	let	let	VERB
ejpam-5189	371	2	z	z	NOUN
ejpam-5189	371	3	∈	∈	PROPN
ejpam-5189	371	4	v	v	ADP
ejpam-5189	371	5	(	(	PUNCT
ejpam-5189	371	6	g	g	NOUN
ejpam-5189	371	7	)	)	PUNCT
ejpam-5189	371	8	\	\	PUNCT
ejpam-5189	372	1	q	q	NOUN
ejpam-5189	372	2	such	such	ADJ
ejpam-5189	372	3	that	that	SCONJ
ejpam-5189	372	4	z	z	NOUN
ejpam-5189	372	5	/∈	/∈	PUNCT
ejpam-5189	372	6	ng(w	ng(w	NOUN
ejpam-5189	372	7	)	)	PUNCT
ejpam-5189	372	8	∩	∩	NOUN
ejpam-5189	372	9	ng(v	ng(v	NUM
ejpam-5189	372	10	)	)	PUNCT
ejpam-5189	372	11	.	.	PUNCT
ejpam-5189	373	1	since	since	SCONJ
ejpam-5189	373	2	c	c	PROPN
ejpam-5189	373	3	is	be	AUX
ejpam-5189	373	4	2	2	NUM
ejpam-5189	373	5	-	-	PUNCT
ejpam-5189	373	6	dominating	dominating	NOUN
ejpam-5189	373	7	,	,	PUNCT
ejpam-5189	373	8	this	this	PRON
ejpam-5189	373	9	implies	imply	VERB
ejpam-5189	373	10	that	that	SCONJ
ejpam-5189	373	11	z	z	PROPN
ejpam-5189	373	12	∈	∈	PROPN
ejpam-5189	373	13	ng(w	ng(w	NOUN
ejpam-5189	373	14	)	)	PUNCT
ejpam-5189	373	15	.	.	PUNCT
ejpam-5189	374	1	it	it	PRON
ejpam-5189	374	2	follows	follow	VERB
ejpam-5189	374	3	that	that	SCONJ
ejpam-5189	374	4	w	w	NOUN
ejpam-5189	374	5	is	be	AUX
ejpam-5189	374	6	a	a	DET
ejpam-5189	374	7	dominating	dominating	NOUN
ejpam-5189	374	8	vertex	vertex	NOUN
ejpam-5189	374	9	of	of	ADP
ejpam-5189	374	10	g.	g.	PROPN
ejpam-5189	374	11	thus	thus	ADV
ejpam-5189	374	12	,	,	PUNCT
ejpam-5189	374	13	γcl(g	γcl(g	X
ejpam-5189	374	14	)	)	PUNCT
ejpam-5189	374	15	=	=	SYM
ejpam-5189	375	1	1	1	X
ejpam-5189	375	2	.	.	PUNCT
ejpam-5189	375	3	by	by	ADP
ejpam-5189	375	4	corollary	corollary	ADJ
ejpam-5189	375	5	9	9	NUM
ejpam-5189	375	6	,	,	PUNCT
ejpam-5189	375	7	γ2cl(h	γ2cl(h	PROPN
ejpam-5189	375	8	)	)	PUNCT
ejpam-5189	375	9	̸=	̸=	PROPN
ejpam-5189	375	10	2	2	NUM
ejpam-5189	375	11	.	.	PUNCT
ejpam-5189	375	12	suppose	suppose	VERB
ejpam-5189	375	13	γcl(h	γcl(h	ADP
ejpam-5189	375	14	)	)	PUNCT
ejpam-5189	375	15	=	=	SYM
ejpam-5189	375	16	1	1	NUM
ejpam-5189	375	17	(	(	PUNCT
ejpam-5189	375	18	p	p	NOUN
ejpam-5189	375	19	or	or	CCONJ
ejpam-5189	375	20	q	q	NOUN
ejpam-5189	375	21	is	be	AUX
ejpam-5189	375	22	a	a	DET
ejpam-5189	375	23	dominating	dominating	NOUN
ejpam-5189	375	24	vertex	vertex	NOUN
ejpam-5189	375	25	of	of	ADP
ejpam-5189	375	26	h	h	NOUN
ejpam-5189	375	27	)	)	PUNCT
ejpam-5189	375	28	.	.	PUNCT
ejpam-5189	376	1	since	since	SCONJ
ejpam-5189	376	2	γ2con(g[h	γ2con(g[h	VERB
ejpam-5189	376	3	]	]	PUNCT
ejpam-5189	376	4	)	)	PUNCT
ejpam-5189	376	5	̸=	̸=	PROPN
ejpam-5189	376	6	2	2	NUM
ejpam-5189	376	7	,	,	PUNCT
ejpam-5189	376	8	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	376	9	)	)	PUNCT
ejpam-5189	376	10	̸=	̸=	PROPN
ejpam-5189	376	11	2	2	NUM
ejpam-5189	376	12	.	.	PUNCT
ejpam-5189	376	13	therefore	therefore	ADV
ejpam-5189	376	14	,	,	PUNCT
ejpam-5189	376	15	(	(	PUNCT
ejpam-5189	376	16	iv	iv	X
ejpam-5189	376	17	)	)	PUNCT
ejpam-5189	376	18	holds	hold	NOUN
ejpam-5189	376	19	.	.	PUNCT
ejpam-5189	377	1	if	if	SCONJ
ejpam-5189	377	2	γcl(h	γcl(h	PROPN
ejpam-5189	377	3	)	)	PUNCT
ejpam-5189	377	4	̸=	̸=	PROPN
ejpam-5189	377	5	1	1	NUM
ejpam-5189	377	6	,	,	PUNCT
ejpam-5189	377	7	then	then	ADV
ejpam-5189	377	8	γcl(h	γcl(h	PROPN
ejpam-5189	377	9	)	)	PUNCT
ejpam-5189	377	10	=	=	SYM
ejpam-5189	377	11	2	2	NUM
ejpam-5189	377	12	,	,	PUNCT
ejpam-5189	377	13	showing	show	VERB
ejpam-5189	377	14	that	that	SCONJ
ejpam-5189	377	15	(	(	PUNCT
ejpam-5189	377	16	v	v	NOUN
ejpam-5189	377	17	)	)	PUNCT
ejpam-5189	377	18	holds	hold	NOUN
ejpam-5189	377	19	.	.	PUNCT
ejpam-5189	378	1	for	for	ADP
ejpam-5189	378	2	the	the	DET
ejpam-5189	378	3	converse	converse	NOUN
ejpam-5189	378	4	,	,	PUNCT
ejpam-5189	378	5	suppose	suppose	VERB
ejpam-5189	378	6	first	first	ADV
ejpam-5189	378	7	that	that	SCONJ
ejpam-5189	378	8	(	(	PUNCT
ejpam-5189	378	9	i	i	NOUN
ejpam-5189	378	10	)	)	PUNCT
ejpam-5189	378	11	holds	hold	VERB
ejpam-5189	378	12	.	.	PUNCT
ejpam-5189	379	1	let	let	VERB
ejpam-5189	379	2	s	s	VERB
ejpam-5189	379	3	=	=	PUNCT
ejpam-5189	379	4	{	{	PUNCT
ejpam-5189	379	5	x	x	PROPN
ejpam-5189	379	6	,	,	PUNCT
ejpam-5189	379	7	y	y	PROPN
ejpam-5189	379	8	,	,	PUNCT
ejpam-5189	379	9	z	z	NOUN
ejpam-5189	379	10	}	}	PUNCT
ejpam-5189	379	11	be	be	AUX
ejpam-5189	379	12	a	a	DET
ejpam-5189	379	13	γ2cl	γ2cl	NOUN
ejpam-5189	379	14	-	-	PUNCT
ejpam-5189	379	15	set	set	VERB
ejpam-5189	379	16	in	in	ADP
ejpam-5189	379	17	g	g	PROPN
ejpam-5189	379	18	and	and	CCONJ
ejpam-5189	379	19	pick	pick	VERB
ejpam-5189	379	20	any	any	DET
ejpam-5189	379	21	p	p	PROPN
ejpam-5189	379	22	∈	∈	PROPN
ejpam-5189	379	23	v	v	ADP
ejpam-5189	379	24	(	(	PUNCT
ejpam-5189	379	25	h	h	NOUN
ejpam-5189	379	26	)	)	PUNCT
ejpam-5189	379	27	.	.	PUNCT
ejpam-5189	380	1	then	then	ADV
ejpam-5189	380	2	c1	c1	PROPN
ejpam-5189	380	3	=	=	SYM
ejpam-5189	380	4	{	{	PUNCT
ejpam-5189	380	5	(	(	PUNCT
ejpam-5189	380	6	x	x	NOUN
ejpam-5189	380	7	,	,	PUNCT
ejpam-5189	380	8	a	a	PRON
ejpam-5189	380	9	)	)	PUNCT
ejpam-5189	380	10	,	,	PUNCT
ejpam-5189	380	11	(	(	PUNCT
ejpam-5189	380	12	y	y	NOUN
ejpam-5189	380	13	,	,	PUNCT
ejpam-5189	380	14	a	a	PRON
ejpam-5189	380	15	)	)	PUNCT
ejpam-5189	380	16	,	,	PUNCT
ejpam-5189	380	17	(	(	PUNCT
ejpam-5189	380	18	z	z	X
ejpam-5189	380	19	,	,	PUNCT
ejpam-5189	380	20	a	a	PRON
ejpam-5189	380	21	)	)	PUNCT
ejpam-5189	380	22	}	}	PUNCT
ejpam-5189	380	23	is	be	AUX
ejpam-5189	380	24	a	a	DET
ejpam-5189	380	25	γ2con	γ2con	NOUN
ejpam-5189	380	26	-	-	PUNCT
ejpam-5189	380	27	set	set	NOUN
ejpam-5189	380	28	of	of	ADP
ejpam-5189	380	29	g[h	g[h	NOUN
ejpam-5189	380	30	]	]	PUNCT
ejpam-5189	380	31	by	by	ADP
ejpam-5189	380	32	theorem	theorem	ADJ
ejpam-5189	380	33	9	9	NUM
ejpam-5189	380	34	and	and	CCONJ
ejpam-5189	380	35	corollary	corollary	ADJ
ejpam-5189	380	36	9	9	NUM
ejpam-5189	380	37	.	.	PUNCT
ejpam-5189	381	1	suppose	suppose	VERB
ejpam-5189	381	2	(	(	PUNCT
ejpam-5189	381	3	ii	ii	NOUN
ejpam-5189	381	4	)	)	PUNCT
ejpam-5189	381	5	holds	hold	VERB
ejpam-5189	381	6	,	,	PUNCT
ejpam-5189	381	7	say	say	VERB
ejpam-5189	381	8	d	d	X
ejpam-5189	381	9	=	=	PUNCT
ejpam-5189	381	10	{	{	PUNCT
ejpam-5189	381	11	p	p	X
ejpam-5189	381	12	,	,	PUNCT
ejpam-5189	381	13	q	q	ADJ
ejpam-5189	381	14	,	,	PUNCT
ejpam-5189	381	15	t	t	PROPN
ejpam-5189	381	16	}	}	PUNCT
ejpam-5189	381	17	is	be	AUX
ejpam-5189	381	18	a	a	DET
ejpam-5189	381	19	γ2cl	γ2cl	NOUN
ejpam-5189	381	20	-	-	PUNCT
ejpam-5189	381	21	set	set	NOUN
ejpam-5189	381	22	in	in	ADP
ejpam-5189	381	23	h.	h.	PROPN
ejpam-5189	381	24	let	let	VERB
ejpam-5189	381	25	v	v	PART
ejpam-5189	381	26	be	be	AUX
ejpam-5189	381	27	a	a	DET
ejpam-5189	381	28	dominating	dominating	NOUN
ejpam-5189	381	29	vertex	vertex	NOUN
ejpam-5189	381	30	in	in	ADP
ejpam-5189	381	31	g.	g.	PROPN
ejpam-5189	382	1	then	then	ADV
ejpam-5189	382	2	c2	c2	PROPN
ejpam-5189	382	3	=	=	SYM
ejpam-5189	382	4	{	{	PUNCT
ejpam-5189	382	5	(	(	PUNCT
ejpam-5189	382	6	v	v	NOUN
ejpam-5189	382	7	,	,	PUNCT
ejpam-5189	382	8	p	p	NOUN
ejpam-5189	382	9	)	)	PUNCT
ejpam-5189	382	10	,	,	PUNCT
ejpam-5189	382	11	(	(	PUNCT
ejpam-5189	382	12	v	v	NOUN
ejpam-5189	382	13	,	,	PUNCT
ejpam-5189	382	14	q	q	NOUN
ejpam-5189	382	15	)	)	PUNCT
ejpam-5189	382	16	,	,	PUNCT
ejpam-5189	382	17	(	(	PUNCT
ejpam-5189	382	18	v	v	NOUN
ejpam-5189	382	19	,	,	PUNCT
ejpam-5189	382	20	t	t	PROPN
ejpam-5189	382	21	)	)	PUNCT
ejpam-5189	382	22	}	}	PUNCT
ejpam-5189	382	23	is	be	AUX
ejpam-5189	382	24	a	a	DET
ejpam-5189	382	25	γ2con	γ2con	NOUN
ejpam-5189	382	26	-	-	PUNCT
ejpam-5189	382	27	set	set	NOUN
ejpam-5189	382	28	of	of	ADP
ejpam-5189	382	29	g[h	g[h	NOUN
ejpam-5189	382	30	]	]	PUNCT
ejpam-5189	382	31	by	by	ADP
ejpam-5189	382	32	theorem	theorem	ADJ
ejpam-5189	382	33	9	9	NUM
ejpam-5189	382	34	and	and	CCONJ
ejpam-5189	382	35	corollary	corollary	ADJ
ejpam-5189	382	36	9	9	NUM
ejpam-5189	382	37	.	.	PUNCT
ejpam-5189	383	1	next	next	ADV
ejpam-5189	383	2	,	,	PUNCT
ejpam-5189	383	3	suppose	suppose	VERB
ejpam-5189	383	4	(	(	PUNCT
ejpam-5189	383	5	iii	iii	NOUN
ejpam-5189	383	6	)	)	PUNCT
ejpam-5189	383	7	holds	hold	VERB
ejpam-5189	383	8	.	.	PUNCT
ejpam-5189	384	1	let	let	VERB
ejpam-5189	384	2	{	{	PUNCT
ejpam-5189	384	3	x	x	NOUN
ejpam-5189	384	4	,	,	PUNCT
ejpam-5189	384	5	y	y	PROPN
ejpam-5189	384	6	}	}	PUNCT
ejpam-5189	384	7	be	be	AUX
ejpam-5189	384	8	a	a	DET
ejpam-5189	384	9	γ2cl	γ2cl	NOUN
ejpam-5189	384	10	-	-	PUNCT
ejpam-5189	384	11	set	set	VERB
ejpam-5189	384	12	in	in	ADP
ejpam-5189	384	13	g	g	NOUN
ejpam-5189	384	14	and	and	CCONJ
ejpam-5189	384	15	let	let	VERB
ejpam-5189	384	16	{	{	PUNCT
ejpam-5189	384	17	k	k	NOUN
ejpam-5189	384	18	,	,	PUNCT
ejpam-5189	384	19	l	l	NOUN
ejpam-5189	384	20	}	}	PUNCT
ejpam-5189	384	21	be	be	AUX
ejpam-5189	384	22	γcl	γcl	NOUN
ejpam-5189	384	23	-	-	PUNCT
ejpam-5189	384	24	set	set	VERB
ejpam-5189	384	25	in	in	ADP
ejpam-5189	384	26	h.	h.	PROPN
ejpam-5189	384	27	then	then	ADV
ejpam-5189	384	28	c3	c3	PROPN
ejpam-5189	384	29	=	=	PUNCT
ejpam-5189	384	30	{	{	PUNCT
ejpam-5189	384	31	(	(	PUNCT
ejpam-5189	384	32	x	x	NOUN
ejpam-5189	384	33	,	,	PUNCT
ejpam-5189	384	34	k	k	NOUN
ejpam-5189	384	35	)	)	PUNCT
ejpam-5189	384	36	,	,	PUNCT
ejpam-5189	384	37	(	(	PUNCT
ejpam-5189	384	38	x	x	X
ejpam-5189	384	39	,	,	PUNCT
ejpam-5189	384	40	l	l	NOUN
ejpam-5189	384	41	)	)	PUNCT
ejpam-5189	384	42	,	,	PUNCT
ejpam-5189	384	43	(	(	PUNCT
ejpam-5189	384	44	y	y	NOUN
ejpam-5189	384	45	,	,	PUNCT
ejpam-5189	384	46	k	k	NOUN
ejpam-5189	384	47	)	)	PUNCT
ejpam-5189	384	48	}	}	PUNCT
ejpam-5189	384	49	is	be	AUX
ejpam-5189	384	50	a	a	DET
ejpam-5189	384	51	γ2con	γ2con	NOUN
ejpam-5189	384	52	-	-	PUNCT
ejpam-5189	384	53	set	set	NOUN
ejpam-5189	384	54	of	of	ADP
ejpam-5189	384	55	g[h	g[h	NOUN
ejpam-5189	384	56	]	]	PUNCT
ejpam-5189	384	57	by	by	ADP
ejpam-5189	384	58	theorem	theorem	ADJ
ejpam-5189	384	59	9	9	NUM
ejpam-5189	384	60	and	and	CCONJ
ejpam-5189	384	61	corollary	corollary	ADJ
ejpam-5189	384	62	9	9	NUM
ejpam-5189	384	63	.	.	PUNCT
ejpam-5189	384	64	suppose	suppose	VERB
ejpam-5189	384	65	now	now	ADV
ejpam-5189	384	66	that	that	SCONJ
ejpam-5189	384	67	(	(	PUNCT
ejpam-5189	384	68	iv	iv	X
ejpam-5189	384	69	)	)	PUNCT
ejpam-5189	384	70	holds	hold	NOUN
ejpam-5189	384	71	.	.	PUNCT
ejpam-5189	385	1	let	let	VERB
ejpam-5189	385	2	w	w	NOUN
ejpam-5189	386	1	and	and	CCONJ
ejpam-5189	386	2	p	p	NOUN
ejpam-5189	386	3	be	be	AUX
ejpam-5189	386	4	dominating	dominate	VERB
ejpam-5189	386	5	vertices	vertex	NOUN
ejpam-5189	386	6	of	of	ADP
ejpam-5189	386	7	g	g	PROPN
ejpam-5189	386	8	and	and	CCONJ
ejpam-5189	387	1	r.	r.	PROPN
ejpam-5189	387	2	j.	j.	PROPN
ejpam-5189	387	3	g.	g.	PROPN
ejpam-5189	387	4	fortosa	fortosa	PROPN
ejpam-5189	387	5	et	et	PROPN
ejpam-5189	387	6	al	al	PROPN
ejpam-5189	387	7	.	.	PUNCT
ejpam-5189	387	8	/	/	SYM
ejpam-5189	387	9	eur	eur	PROPN
ejpam-5189	387	10	.	.	PUNCT
ejpam-5189	388	1	j.	j.	PROPN
ejpam-5189	388	2	pure	pure	PROPN
ejpam-5189	388	3	appl	appl	PROPN
ejpam-5189	388	4	.	.	PROPN
ejpam-5189	388	5	math	math	PROPN
ejpam-5189	388	6	,	,	PUNCT
ejpam-5189	388	7	17	17	NUM
ejpam-5189	388	8	(	(	PUNCT
ejpam-5189	388	9	3	3	NUM
ejpam-5189	388	10	)	)	PUNCT
ejpam-5189	388	11	(	(	PUNCT
ejpam-5189	388	12	2024	2024	NUM
ejpam-5189	388	13	)	)	PUNCT
ejpam-5189	388	14	,	,	PUNCT
ejpam-5189	388	15	1539	1539	NUM
ejpam-5189	388	16	-	-	SYM
ejpam-5189	388	17	1552	1552	NUM
ejpam-5189	388	18	1550	1550	NUM
ejpam-5189	388	19	h	h	NOUN
ejpam-5189	388	20	,	,	PUNCT
ejpam-5189	388	21	respectively	respectively	ADV
ejpam-5189	388	22	.	.	PUNCT
ejpam-5189	389	1	let	let	VERB
ejpam-5189	389	2	u	u	PRON
ejpam-5189	389	3	∈	∈	PROPN
ejpam-5189	389	4	ng(w	ng(w	NOUN
ejpam-5189	389	5	)	)	PUNCT
ejpam-5189	389	6	and	and	CCONJ
ejpam-5189	389	7	s	s	PROPN
ejpam-5189	389	8	∈	∈	NOUN
ejpam-5189	389	9	nh(p	nh(p	NUM
ejpam-5189	389	10	)	)	PUNCT
ejpam-5189	389	11	.	.	PUNCT
ejpam-5189	390	1	let	let	VERB
ejpam-5189	390	2	c4	c4	NOUN
ejpam-5189	390	3	=	=	SYM
ejpam-5189	390	4	{	{	PUNCT
ejpam-5189	390	5	(	(	PUNCT
ejpam-5189	390	6	w	w	PROPN
ejpam-5189	390	7	,	,	PUNCT
ejpam-5189	390	8	p	p	NOUN
ejpam-5189	390	9	)	)	PUNCT
ejpam-5189	390	10	,	,	PUNCT
ejpam-5189	390	11	(	(	PUNCT
ejpam-5189	390	12	w	w	PROPN
ejpam-5189	390	13	,	,	PUNCT
ejpam-5189	390	14	s	s	PART
ejpam-5189	390	15	)	)	PUNCT
ejpam-5189	390	16	,	,	PUNCT
ejpam-5189	390	17	(	(	PUNCT
ejpam-5189	390	18	u	u	NOUN
ejpam-5189	390	19	,	,	PUNCT
ejpam-5189	390	20	p	p	NOUN
ejpam-5189	390	21	)	)	PUNCT
ejpam-5189	390	22	}	}	PUNCT
ejpam-5189	390	23	.	.	PUNCT
ejpam-5189	391	1	by	by	ADP
ejpam-5189	391	2	theorem	theorem	NOUN
ejpam-5189	391	3	9	9	NUM
ejpam-5189	391	4	and	and	CCONJ
ejpam-5189	391	5	corollary	corollary	ADJ
ejpam-5189	391	6	9	9	NUM
ejpam-5189	391	7	,	,	PUNCT
ejpam-5189	391	8	c3	c3	PROPN
ejpam-5189	391	9	is	be	AUX
ejpam-5189	391	10	a	a	DET
ejpam-5189	391	11	γ2con	γ2con	NOUN
ejpam-5189	391	12	-	-	PUNCT
ejpam-5189	391	13	set	set	NOUN
ejpam-5189	391	14	of	of	ADP
ejpam-5189	391	15	g[h	g[h	NOUN
ejpam-5189	391	16	]	]	PUNCT
ejpam-5189	391	17	.	.	PUNCT
ejpam-5189	392	1	lastly	lastly	ADV
ejpam-5189	392	2	,	,	PUNCT
ejpam-5189	392	3	suppose	suppose	VERB
ejpam-5189	392	4	that	that	SCONJ
ejpam-5189	392	5	(	(	PUNCT
ejpam-5189	392	6	v	v	NOUN
ejpam-5189	392	7	)	)	PUNCT
ejpam-5189	392	8	holds	hold	VERB
ejpam-5189	392	9	.	.	PUNCT
ejpam-5189	393	1	let	let	VERB
ejpam-5189	393	2	w	w	PRON
ejpam-5189	393	3	be	be	AUX
ejpam-5189	393	4	a	a	DET
ejpam-5189	393	5	dominating	dominating	NOUN
ejpam-5189	393	6	vertex	vertex	NOUN
ejpam-5189	393	7	of	of	ADP
ejpam-5189	393	8	g	g	PROPN
ejpam-5189	393	9	,	,	PUNCT
ejpam-5189	393	10	v	v	NOUN
ejpam-5189	393	11	∈	∈	NOUN
ejpam-5189	393	12	ng(w	ng(w	NOUN
ejpam-5189	393	13	)	)	PUNCT
ejpam-5189	393	14	,	,	PUNCT
ejpam-5189	393	15	and	and	CCONJ
ejpam-5189	393	16	let	let	VERB
ejpam-5189	393	17	r	r	NOUN
ejpam-5189	393	18	=	=	PUNCT
ejpam-5189	393	19	{	{	PUNCT
ejpam-5189	393	20	a	a	PRON
ejpam-5189	393	21	,	,	PUNCT
ejpam-5189	393	22	b	b	AUX
ejpam-5189	393	23	}	}	PUNCT
ejpam-5189	393	24	be	be	AUX
ejpam-5189	393	25	a	a	DET
ejpam-5189	393	26	γcl	γcl	NOUN
ejpam-5189	393	27	-	-	PUNCT
ejpam-5189	393	28	set	set	VERB
ejpam-5189	393	29	in	in	ADP
ejpam-5189	393	30	h.	h.	PROPN
ejpam-5189	393	31	then	then	ADV
ejpam-5189	393	32	c5	c5	PROPN
ejpam-5189	393	33	=	=	PUNCT
ejpam-5189	393	34	{	{	PUNCT
ejpam-5189	393	35	(	(	PUNCT
ejpam-5189	393	36	w	w	PROPN
ejpam-5189	393	37	,	,	PUNCT
ejpam-5189	393	38	a	a	NOUN
ejpam-5189	393	39	)	)	PUNCT
ejpam-5189	393	40	,	,	PUNCT
ejpam-5189	393	41	(	(	PUNCT
ejpam-5189	393	42	w	w	PROPN
ejpam-5189	393	43	,	,	PUNCT
ejpam-5189	393	44	b	b	NOUN
ejpam-5189	393	45	)	)	PUNCT
ejpam-5189	393	46	,	,	PUNCT
ejpam-5189	393	47	(	(	PUNCT
ejpam-5189	393	48	v	v	NOUN
ejpam-5189	393	49	,	,	PUNCT
ejpam-5189	393	50	a	a	PRON
ejpam-5189	393	51	)	)	PUNCT
ejpam-5189	393	52	}	}	PUNCT
ejpam-5189	393	53	is	be	AUX
ejpam-5189	393	54	a	a	DET
ejpam-5189	393	55	γ2con	γ2con	NOUN
ejpam-5189	393	56	-	-	PUNCT
ejpam-5189	393	57	set	set	NOUN
ejpam-5189	393	58	of	of	ADP
ejpam-5189	393	59	g[h	g[h	NOUN
ejpam-5189	393	60	]	]	PUNCT
ejpam-5189	393	61	by	by	ADP
ejpam-5189	393	62	theorem	theorem	ADJ
ejpam-5189	393	63	9	9	NUM
ejpam-5189	393	64	and	and	CCONJ
ejpam-5189	393	65	corollary	corollary	ADJ
ejpam-5189	393	66	9	9	NUM
ejpam-5189	393	67	.	.	PUNCT
ejpam-5189	393	68	accordingly	accordingly	ADV
ejpam-5189	393	69	,	,	PUNCT
ejpam-5189	393	70	γ2con(g[h	γ2con(g[h	ADJ
ejpam-5189	393	71	]	]	PUNCT
ejpam-5189	393	72	)	)	PUNCT
ejpam-5189	394	1	=	=	SYM
ejpam-5189	394	2	3	3	X
ejpam-5189	394	3	.	.	PUNCT
ejpam-5189	394	4	corollary	corollary	ADJ
ejpam-5189	394	5	11	11	NUM
ejpam-5189	394	6	.	.	PUNCT
ejpam-5189	395	1	let	let	VERB
ejpam-5189	395	2	g	g	NOUN
ejpam-5189	395	3	and	and	CCONJ
ejpam-5189	395	4	h	h	NOUN
ejpam-5189	395	5	be	be	AUX
ejpam-5189	395	6	connected	connect	VERB
ejpam-5189	395	7	non	non	ADJ
ejpam-5189	395	8	-	-	ADJ
ejpam-5189	395	9	complete	complete	ADJ
ejpam-5189	395	10	graphs	graph	NOUN
ejpam-5189	396	1	such	such	ADJ
ejpam-5189	396	2	that	that	SCONJ
ejpam-5189	396	3	γcl(g	γcl(g	NUM
ejpam-5189	396	4	)	)	PUNCT
ejpam-5189	396	5	≥	≥	NOUN
ejpam-5189	396	6	2	2	NUM
ejpam-5189	396	7	.	.	PUNCT
ejpam-5189	396	8	suppose	suppose	VERB
ejpam-5189	396	9	h	h	NOUN
ejpam-5189	396	10	does	do	AUX
ejpam-5189	396	11	not	not	PART
ejpam-5189	396	12	admit	admit	VERB
ejpam-5189	396	13	a	a	DET
ejpam-5189	396	14	clique	clique	NOUN
ejpam-5189	396	15	dominating	dominating	NOUN
ejpam-5189	396	16	set	set	NOUN
ejpam-5189	396	17	.	.	PUNCT
ejpam-5189	397	1	(	(	PUNCT
ejpam-5189	397	2	i	i	NOUN
ejpam-5189	397	3	)	)	PUNCT
ejpam-5189	397	4	if	if	SCONJ
ejpam-5189	397	5	g	g	PROPN
ejpam-5189	397	6	admits	admit	VERB
ejpam-5189	397	7	a	a	DET
ejpam-5189	397	8	clique	clique	ADJ
ejpam-5189	397	9	2	2	NUM
ejpam-5189	397	10	-	-	PUNCT
ejpam-5189	397	11	dominating	dominating	NOUN
ejpam-5189	397	12	set	set	NOUN
ejpam-5189	397	13	,	,	PUNCT
ejpam-5189	397	14	then	then	ADV
ejpam-5189	397	15	γ2con(g[h	γ2con(g[h	ADJ
ejpam-5189	397	16	]	]	X
ejpam-5189	397	17	)	)	PUNCT
ejpam-5189	397	18	≤	≤	NUM
ejpam-5189	397	19	min{2γcl(g	min{2γcl(g	PROPN
ejpam-5189	397	20	)	)	PUNCT
ejpam-5189	397	21	,	,	PUNCT
ejpam-5189	397	22	γ2cl(g	γ2cl(g	PROPN
ejpam-5189	397	23	)	)	PUNCT
ejpam-5189	397	24	}	}	PUNCT
ejpam-5189	397	25	.	.	PUNCT
ejpam-5189	398	1	(	(	PUNCT
ejpam-5189	398	2	ii	ii	NOUN
ejpam-5189	398	3	)	)	PUNCT
ejpam-5189	398	4	if	if	SCONJ
ejpam-5189	398	5	g	g	PROPN
ejpam-5189	398	6	does	do	AUX
ejpam-5189	398	7	not	not	PART
ejpam-5189	398	8	admit	admit	VERB
ejpam-5189	398	9	a	a	DET
ejpam-5189	398	10	clique	clique	ADJ
ejpam-5189	398	11	2	2	NUM
ejpam-5189	398	12	-	-	PUNCT
ejpam-5189	398	13	dominating	dominating	NOUN
ejpam-5189	398	14	set	set	NOUN
ejpam-5189	398	15	,	,	PUNCT
ejpam-5189	398	16	then	then	ADV
ejpam-5189	398	17	γ2con(g[h	γ2con(g[h	ADJ
ejpam-5189	398	18	]	]	PUNCT
ejpam-5189	398	19	)	)	PUNCT
ejpam-5189	398	20	≤	≤	NUM
ejpam-5189	398	21	2γcl(g	2γcl(g	NUM
ejpam-5189	398	22	)	)	PUNCT
ejpam-5189	398	23	.	.	PUNCT
ejpam-5189	399	1	the	the	DET
ejpam-5189	399	2	bound	bind	VERB
ejpam-5189	399	3	given	give	VERB
ejpam-5189	399	4	in	in	ADP
ejpam-5189	399	5	corollary	corollary	ADJ
ejpam-5189	399	6	11	11	NUM
ejpam-5189	399	7	is	be	AUX
ejpam-5189	399	8	sharp	sharp	ADJ
ejpam-5189	399	9	.	.	PUNCT
ejpam-5189	400	1	indeed	indeed	ADV
ejpam-5189	400	2	,	,	PUNCT
ejpam-5189	400	3	γ2con(p4[pn	γ2con(p4[pn	PROPN
ejpam-5189	400	4	]	]	PUNCT
ejpam-5189	400	5	)	)	PUNCT
ejpam-5189	400	6	=	=	SYM
ejpam-5189	401	1	4	4	NUM
ejpam-5189	401	2	=	=	SYM
ejpam-5189	401	3	2γcl(p4	2γcl(p4	NOUN
ejpam-5189	401	4	)	)	PUNCT
ejpam-5189	401	5	and	and	CCONJ
ejpam-5189	401	6	γ2con(c4[cn	γ2con(c4[cn	NOUN
ejpam-5189	401	7	]	]	X
ejpam-5189	401	8	)	)	PUNCT
ejpam-5189	401	9	=	=	SYM
ejpam-5189	401	10	4	4	NUM
ejpam-5189	401	11	=	=	SYM
ejpam-5189	401	12	2γcl(c4	2γcl(c4	NUM
ejpam-5189	401	13	)	)	PUNCT
ejpam-5189	401	14	for	for	ADP
ejpam-5189	401	15	all	all	DET
ejpam-5189	401	16	n	n	PRON
ejpam-5189	401	17	≥	≥	NUM
ejpam-5189	401	18	5	5	NUM
ejpam-5189	401	19	.	.	PUNCT
ejpam-5189	402	1	the	the	DET
ejpam-5189	402	2	next	next	ADJ
ejpam-5189	402	3	result	result	NOUN
ejpam-5189	402	4	is	be	AUX
ejpam-5189	402	5	a	a	DET
ejpam-5189	402	6	rectification	rectification	NOUN
ejpam-5189	402	7	of	of	ADP
ejpam-5189	402	8	the	the	DET
ejpam-5189	402	9	one	one	NOUN
ejpam-5189	402	10	obtained	obtain	VERB
ejpam-5189	402	11	by	by	ADP
ejpam-5189	402	12	canoy	canoy	NOUN
ejpam-5189	402	13	and	and	CCONJ
ejpam-5189	402	14	garces	garce	NOUN
ejpam-5189	402	15	in	in	ADP
ejpam-5189	402	16	[	[	X
ejpam-5189	402	17	7	7	NUM
ejpam-5189	402	18	]	]	PUNCT
ejpam-5189	402	19	.	.	PUNCT
ejpam-5189	403	1	theorem	theorem	ADJ
ejpam-5189	403	2	10	10	NUM
ejpam-5189	403	3	.	.	PUNCT
ejpam-5189	404	1	[	[	X
ejpam-5189	404	2	6	6	NUM
ejpam-5189	404	3	]	]	PUNCT
ejpam-5189	404	4	let	let	VERB
ejpam-5189	404	5	g	g	PRON
ejpam-5189	404	6	be	be	AUX
ejpam-5189	404	7	a	a	DET
ejpam-5189	404	8	connected	connected	ADJ
ejpam-5189	404	9	graph	graph	NOUN
ejpam-5189	404	10	and	and	CCONJ
ejpam-5189	404	11	m	m	VERB
ejpam-5189	404	12	a	a	DET
ejpam-5189	404	13	positive	positive	ADJ
ejpam-5189	404	14	integer	integer	NOUN
ejpam-5189	404	15	.	.	PUNCT
ejpam-5189	405	1	a	a	DET
ejpam-5189	405	2	set	set	NOUN
ejpam-5189	405	3	c	c	X
ejpam-5189	405	4	=	=	SYM
ejpam-5189	405	5	∪v∈s({x}×tx	∪v∈s({x}×tx	X
ejpam-5189	405	6	)	)	PUNCT
ejpam-5189	405	7	⊆	⊆	NUM
ejpam-5189	405	8	v	v	X
ejpam-5189	405	9	(	(	PUNCT
ejpam-5189	405	10	g[km	g[km	PROPN
ejpam-5189	405	11	]	]	X
ejpam-5189	405	12	)	)	PUNCT
ejpam-5189	405	13	,	,	PUNCT
ejpam-5189	405	14	where	where	SCONJ
ejpam-5189	405	15	s	s	VERB
ejpam-5189	405	16	⊆	⊆	NUM
ejpam-5189	405	17	v	v	NOUN
ejpam-5189	405	18	(	(	PUNCT
ejpam-5189	405	19	g	g	NOUN
ejpam-5189	405	20	)	)	PUNCT
ejpam-5189	405	21	and	and	CCONJ
ejpam-5189	405	22	tx	tx	VERB
ejpam-5189	405	23	⊆	⊆	NUM
ejpam-5189	405	24	v	v	NOUN
ejpam-5189	405	25	(	(	PUNCT
ejpam-5189	405	26	km	km	PROPN
ejpam-5189	405	27	)	)	PUNCT
ejpam-5189	405	28	for	for	ADP
ejpam-5189	405	29	all	all	PRON
ejpam-5189	405	30	x	x	SYM
ejpam-5189	405	31	∈	∈	PROPN
ejpam-5189	405	32	s	s	NOUN
ejpam-5189	405	33	,	,	PUNCT
ejpam-5189	405	34	is	be	AUX
ejpam-5189	405	35	convex	convex	ADJ
ejpam-5189	405	36	in	in	ADP
ejpam-5189	405	37	g[km	g[km	PROPN
ejpam-5189	405	38	]	]	X
ejpam-5189	405	39	if	if	SCONJ
ejpam-5189	405	40	and	and	CCONJ
ejpam-5189	405	41	only	only	ADV
ejpam-5189	405	42	if	if	SCONJ
ejpam-5189	405	43	s	s	NOUN
ejpam-5189	405	44	is	be	AUX
ejpam-5189	405	45	convex	convex	ADJ
ejpam-5189	405	46	in	in	ADP
ejpam-5189	405	47	g	g	PROPN
ejpam-5189	405	48	and	and	CCONJ
ejpam-5189	405	49	tx	tx	PROPN
ejpam-5189	405	50	=	=	SYM
ejpam-5189	405	51	v	v	PROPN
ejpam-5189	405	52	(	(	PUNCT
ejpam-5189	405	53	km	km	PROPN
ejpam-5189	405	54	)	)	PUNCT
ejpam-5189	405	55	for	for	ADP
ejpam-5189	405	56	each	each	DET
ejpam-5189	405	57	x	x	SYM
ejpam-5189	405	58	∈	∈	PROPN
ejpam-5189	405	59	s0	s0	NOUN
ejpam-5189	405	60	=	=	PUNCT
ejpam-5189	405	61	i(s)∩s	i(s)∩s	PROPN
ejpam-5189	405	62	.	.	PUNCT
ejpam-5189	406	1	theorem	theorem	VERB
ejpam-5189	406	2	11	11	NUM
ejpam-5189	406	3	.	.	PUNCT
ejpam-5189	407	1	let	let	VERB
ejpam-5189	407	2	g	g	PRON
ejpam-5189	407	3	be	be	AUX
ejpam-5189	407	4	a	a	DET
ejpam-5189	407	5	non	non	ADJ
ejpam-5189	407	6	-	-	ADJ
ejpam-5189	407	7	trivial	trivial	ADJ
ejpam-5189	407	8	connected	connected	ADJ
ejpam-5189	407	9	graph	graph	NOUN
ejpam-5189	407	10	and	and	CCONJ
ejpam-5189	407	11	m	m	VERB
ejpam-5189	407	12	a	a	DET
ejpam-5189	407	13	positive	positive	ADJ
ejpam-5189	407	14	integer	integer	NOUN
ejpam-5189	407	15	.	.	PUNCT
ejpam-5189	408	1	a	a	DET
ejpam-5189	408	2	set	set	NOUN
ejpam-5189	408	3	c	c	X
ejpam-5189	408	4	=	=	SYM
ejpam-5189	408	5	∪v∈s({x}×tx	∪v∈s({x}×tx	X
ejpam-5189	408	6	)	)	PUNCT
ejpam-5189	408	7	⊆	⊆	NUM
ejpam-5189	408	8	v	v	NOUN
ejpam-5189	408	9	(	(	PUNCT
ejpam-5189	408	10	g[h	g[h	PROPN
ejpam-5189	408	11	]	]	PUNCT
ejpam-5189	408	12	)	)	PUNCT
ejpam-5189	408	13	,	,	PUNCT
ejpam-5189	408	14	where	where	SCONJ
ejpam-5189	408	15	s	s	VERB
ejpam-5189	408	16	⊆	⊆	NUM
ejpam-5189	408	17	v	v	NOUN
ejpam-5189	408	18	(	(	PUNCT
ejpam-5189	408	19	g	g	NOUN
ejpam-5189	408	20	)	)	PUNCT
ejpam-5189	408	21	and	and	CCONJ
ejpam-5189	408	22	tx	tx	VERB
ejpam-5189	408	23	⊆	⊆	NUM
ejpam-5189	408	24	v	v	NOUN
ejpam-5189	408	25	(	(	PUNCT
ejpam-5189	408	26	km	km	PROPN
ejpam-5189	408	27	)	)	PUNCT
ejpam-5189	408	28	for	for	ADP
ejpam-5189	408	29	all	all	PRON
ejpam-5189	408	30	x	x	SYM
ejpam-5189	408	31	∈	∈	PROPN
ejpam-5189	408	32	s	s	NOUN
ejpam-5189	408	33	,	,	PUNCT
ejpam-5189	408	34	is	be	AUX
ejpam-5189	408	35	convex	convex	ADJ
ejpam-5189	408	36	2	2	NUM
ejpam-5189	408	37	-	-	PUNCT
ejpam-5189	408	38	dominating	dominating	NOUN
ejpam-5189	408	39	in	in	ADP
ejpam-5189	408	40	g[km	g[km	PROPN
ejpam-5189	408	41	]	]	X
ejpam-5189	408	42	if	if	SCONJ
ejpam-5189	408	43	and	and	CCONJ
ejpam-5189	408	44	only	only	ADV
ejpam-5189	408	45	if	if	SCONJ
ejpam-5189	408	46	s	s	NOUN
ejpam-5189	408	47	is	be	AUX
ejpam-5189	408	48	convex	convex	ADJ
ejpam-5189	408	49	2	2	NUM
ejpam-5189	408	50	-	-	PUNCT
ejpam-5189	408	51	dominating	dominating	NOUN
ejpam-5189	408	52	in	in	ADP
ejpam-5189	408	53	g	g	PROPN
ejpam-5189	408	54	and	and	CCONJ
ejpam-5189	408	55	tx	tx	PROPN
ejpam-5189	408	56	=	=	SYM
ejpam-5189	408	57	v	v	PROPN
ejpam-5189	408	58	(	(	PUNCT
ejpam-5189	408	59	km	km	PROPN
ejpam-5189	408	60	)	)	PUNCT
ejpam-5189	408	61	for	for	ADP
ejpam-5189	408	62	each	each	DET
ejpam-5189	408	63	x	x	SYM
ejpam-5189	408	64	∈	∈	PROPN
ejpam-5189	408	65	s0	s0	NOUN
ejpam-5189	408	66	=	=	PUNCT
ejpam-5189	408	67	i(s	i(s	NOUN
ejpam-5189	408	68	)	)	PUNCT
ejpam-5189	408	69	∩	∩	NOUN
ejpam-5189	408	70	s.	s.	PROPN
ejpam-5189	408	71	proof	proof	PROPN
ejpam-5189	408	72	.	.	PUNCT
ejpam-5189	409	1	suppose	suppose	VERB
ejpam-5189	409	2	c	c	NOUN
ejpam-5189	409	3	is	be	AUX
ejpam-5189	409	4	convex	convex	ADJ
ejpam-5189	409	5	2	2	NUM
ejpam-5189	409	6	-	-	PUNCT
ejpam-5189	409	7	dominating	dominating	NOUN
ejpam-5189	409	8	in	in	ADP
ejpam-5189	409	9	g[km	g[km	PROPN
ejpam-5189	409	10	]	]	PUNCT
ejpam-5189	409	11	.	.	PUNCT
ejpam-5189	410	1	by	by	ADP
ejpam-5189	410	2	theorem	theorem	NOUN
ejpam-5189	410	3	10	10	NUM
ejpam-5189	410	4	,	,	PUNCT
ejpam-5189	410	5	s	s	VERB
ejpam-5189	410	6	is	be	AUX
ejpam-5189	410	7	convex	convex	ADJ
ejpam-5189	410	8	in	in	ADP
ejpam-5189	410	9	g	g	PROPN
ejpam-5189	410	10	and	and	CCONJ
ejpam-5189	410	11	tx	tx	PROPN
ejpam-5189	410	12	=	=	SYM
ejpam-5189	410	13	v	v	PROPN
ejpam-5189	410	14	(	(	PUNCT
ejpam-5189	410	15	km	km	PROPN
ejpam-5189	410	16	)	)	PUNCT
ejpam-5189	410	17	for	for	ADP
ejpam-5189	410	18	each	each	DET
ejpam-5189	410	19	x	x	SYM
ejpam-5189	410	20	∈	∈	PROPN
ejpam-5189	410	21	s0	s0	NOUN
ejpam-5189	410	22	=	=	PUNCT
ejpam-5189	410	23	i(s	i(s	NOUN
ejpam-5189	410	24	)	)	PUNCT
ejpam-5189	410	25	∩	∩	NOUN
ejpam-5189	410	26	s.	s.	PROPN
ejpam-5189	410	27	let	let	VERB
ejpam-5189	410	28	v	v	ADP
ejpam-5189	410	29	∈	∈	PROPN
ejpam-5189	410	30	v	v	NOUN
ejpam-5189	410	31	(	(	PUNCT
ejpam-5189	410	32	g	g	NOUN
ejpam-5189	410	33	)	)	PUNCT
ejpam-5189	410	34	\	\	PROPN
ejpam-5189	410	35	s	s	PART
ejpam-5189	410	36	and	and	CCONJ
ejpam-5189	410	37	choose	choose	VERB
ejpam-5189	410	38	any	any	DET
ejpam-5189	410	39	p	p	PROPN
ejpam-5189	410	40	∈	∈	PROPN
ejpam-5189	410	41	v	v	NOUN
ejpam-5189	410	42	(	(	PUNCT
ejpam-5189	410	43	km	km	PROPN
ejpam-5189	410	44	)	)	PUNCT
ejpam-5189	410	45	.	.	PUNCT
ejpam-5189	411	1	since	since	SCONJ
ejpam-5189	411	2	(	(	PUNCT
ejpam-5189	411	3	v	v	NOUN
ejpam-5189	411	4	,	,	PUNCT
ejpam-5189	411	5	p	p	NOUN
ejpam-5189	411	6	)	)	PUNCT
ejpam-5189	411	7	/∈	/∈	PUNCT
ejpam-5189	412	1	c	c	NOUN
ejpam-5189	413	1	and	and	CCONJ
ejpam-5189	413	2	c	c	PROPN
ejpam-5189	413	3	is	be	AUX
ejpam-5189	413	4	2	2	NUM
ejpam-5189	413	5	-	-	PUNCT
ejpam-5189	413	6	dominating	dominating	NOUN
ejpam-5189	413	7	in	in	ADP
ejpam-5189	413	8	g[km	g[km	PROPN
ejpam-5189	413	9	]	]	PUNCT
ejpam-5189	413	10	,	,	PUNCT
ejpam-5189	413	11	there	there	PRON
ejpam-5189	413	12	exist	exist	VERB
ejpam-5189	413	13	two	two	NUM
ejpam-5189	413	14	vertices	vertex	NOUN
ejpam-5189	413	15	(	(	PUNCT
ejpam-5189	413	16	w	w	PROPN
ejpam-5189	413	17	,	,	PUNCT
ejpam-5189	413	18	t	t	PROPN
ejpam-5189	413	19	)	)	PUNCT
ejpam-5189	413	20	,	,	PUNCT
ejpam-5189	413	21	(	(	PUNCT
ejpam-5189	413	22	z	z	X
ejpam-5189	413	23	,	,	PUNCT
ejpam-5189	413	24	s	s	NOUN
ejpam-5189	413	25	)	)	PUNCT
ejpam-5189	413	26	∈	∈	PROPN
ejpam-5189	413	27	c	c	NOUN
ejpam-5189	413	28	∩	∩	ADJ
ejpam-5189	413	29	ng[km]((v	ng[km]((v	NOUN
ejpam-5189	413	30	,	,	PUNCT
ejpam-5189	413	31	p	p	NOUN
ejpam-5189	413	32	)	)	PUNCT
ejpam-5189	413	33	)	)	PUNCT
ejpam-5189	413	34	.	.	PUNCT
ejpam-5189	414	1	this	this	PRON
ejpam-5189	414	2	implies	imply	VERB
ejpam-5189	414	3	that	that	SCONJ
ejpam-5189	414	4	w	w	X
ejpam-5189	414	5	,	,	PUNCT
ejpam-5189	414	6	z	z	PROPN
ejpam-5189	414	7	∈	∈	PROPN
ejpam-5189	414	8	s	s	PART
ejpam-5189	414	9	∩	∩	NOUN
ejpam-5189	414	10	ng(v	ng(v	NUM
ejpam-5189	414	11	)	)	PUNCT
ejpam-5189	414	12	.	.	PUNCT
ejpam-5189	415	1	therefore	therefore	ADV
ejpam-5189	415	2	,	,	PUNCT
ejpam-5189	415	3	s	s	VERB
ejpam-5189	415	4	is	be	AUX
ejpam-5189	415	5	a	a	DET
ejpam-5189	415	6	2	2	NUM
ejpam-5189	415	7	-	-	PUNCT
ejpam-5189	415	8	dominating	dominating	NOUN
ejpam-5189	415	9	set	set	NOUN
ejpam-5189	415	10	in	in	ADP
ejpam-5189	415	11	g.	g.	PROPN
ejpam-5189	415	12	conversely	conversely	ADV
ejpam-5189	415	13	,	,	PUNCT
ejpam-5189	415	14	suppose	suppose	VERB
ejpam-5189	415	15	that	that	SCONJ
ejpam-5189	415	16	s	s	VERB
ejpam-5189	415	17	is	be	AUX
ejpam-5189	415	18	convex	convex	ADJ
ejpam-5189	415	19	in	in	ADP
ejpam-5189	415	20	g	g	PROPN
ejpam-5189	415	21	and	and	CCONJ
ejpam-5189	415	22	tx	tx	PROPN
ejpam-5189	415	23	=	=	SYM
ejpam-5189	415	24	v	v	PROPN
ejpam-5189	415	25	(	(	PUNCT
ejpam-5189	415	26	km	km	PROPN
ejpam-5189	415	27	)	)	PUNCT
ejpam-5189	415	28	for	for	ADP
ejpam-5189	415	29	each	each	DET
ejpam-5189	415	30	x	x	SYM
ejpam-5189	415	31	∈	∈	PROPN
ejpam-5189	415	32	s0	s0	NOUN
ejpam-5189	415	33	=	=	PUNCT
ejpam-5189	415	34	i(s)∩s	i(s)∩s	PROPN
ejpam-5189	415	35	.	.	PUNCT
ejpam-5189	416	1	then	then	ADV
ejpam-5189	416	2	c	c	PROPN
ejpam-5189	416	3	is	be	AUX
ejpam-5189	416	4	convex	convex	ADJ
ejpam-5189	416	5	in	in	ADP
ejpam-5189	416	6	g[km	g[km	PROPN
ejpam-5189	416	7	]	]	PUNCT
ejpam-5189	416	8	by	by	ADP
ejpam-5189	416	9	theorem	theorem	NOUN
ejpam-5189	416	10	10	10	NUM
ejpam-5189	416	11	.	.	PUNCT
ejpam-5189	417	1	let	let	AUX
ejpam-5189	417	2	(	(	PUNCT
ejpam-5189	417	3	y	y	NOUN
ejpam-5189	417	4	,	,	PUNCT
ejpam-5189	417	5	d	d	NOUN
ejpam-5189	417	6	)	)	PUNCT
ejpam-5189	417	7	∈	∈	NOUN
ejpam-5189	417	8	v	v	NOUN
ejpam-5189	417	9	(	(	PUNCT
ejpam-5189	417	10	g[km])\c	g[km])\c	NOUN
ejpam-5189	417	11	.	.	PROPN
ejpam-5189	417	12	suppose	suppose	VERB
ejpam-5189	417	13	y	y	PROPN
ejpam-5189	417	14	∈	∈	PROPN
ejpam-5189	417	15	s.	s.	PROPN
ejpam-5189	417	16	since	since	SCONJ
ejpam-5189	417	17	s	s	PROPN
ejpam-5189	417	18	is	be	AUX
ejpam-5189	417	19	convex	convex	ADJ
ejpam-5189	417	20	2	2	NUM
ejpam-5189	417	21	-	-	PUNCT
ejpam-5189	417	22	dominating	dominating	NOUN
ejpam-5189	417	23	,	,	PUNCT
ejpam-5189	417	24	it	it	PRON
ejpam-5189	417	25	follows	follow	VERB
ejpam-5189	417	26	that	that	SCONJ
ejpam-5189	417	27	|s|	|s|	VERB
ejpam-5189	417	28	≥	≥	NUM
ejpam-5189	417	29	2	2	NUM
ejpam-5189	417	30	and	and	CCONJ
ejpam-5189	417	31	⟨s⟩	⟨s⟩	PROPN
ejpam-5189	417	32	is	be	AUX
ejpam-5189	417	33	connected	connect	VERB
ejpam-5189	417	34	.	.	PUNCT
ejpam-5189	418	1	let	let	VERB
ejpam-5189	418	2	u	u	PRON
ejpam-5189	418	3	∈	∈	PROPN
ejpam-5189	418	4	s	s	PART
ejpam-5189	418	5	∩	∩	NOUN
ejpam-5189	418	6	ng(y	ng(y	NOUN
ejpam-5189	418	7	)	)	PUNCT
ejpam-5189	418	8	.	.	PUNCT
ejpam-5189	419	1	pick	pick	VERB
ejpam-5189	419	2	any	any	DET
ejpam-5189	419	3	a	a	DET
ejpam-5189	419	4	∈	∈	ADJ
ejpam-5189	419	5	ty	ty	INTJ
ejpam-5189	419	6	and	and	CCONJ
ejpam-5189	420	1	b	b	PROPN
ejpam-5189	420	2	∈	∈	PROPN
ejpam-5189	420	3	tu	tu	PROPN
ejpam-5189	420	4	.	.	PUNCT
ejpam-5189	421	1	then	then	ADV
ejpam-5189	421	2	(	(	PUNCT
ejpam-5189	421	3	y	y	NOUN
ejpam-5189	421	4	,	,	PUNCT
ejpam-5189	421	5	a	a	PRON
ejpam-5189	421	6	)	)	PUNCT
ejpam-5189	421	7	,	,	PUNCT
ejpam-5189	421	8	(	(	PUNCT
ejpam-5189	421	9	u	u	NOUN
ejpam-5189	421	10	,	,	PUNCT
ejpam-5189	421	11	b	b	NOUN
ejpam-5189	421	12	)	)	PUNCT
ejpam-5189	421	13	∈	∈	PROPN
ejpam-5189	421	14	c	c	NOUN
ejpam-5189	421	15	∩	∩	X
ejpam-5189	421	16	ng[km]((y	ng[km]((y	NOUN
ejpam-5189	421	17	,	,	PUNCT
ejpam-5189	421	18	d	d	NOUN
ejpam-5189	421	19	)	)	PUNCT
ejpam-5189	421	20	)	)	PUNCT
ejpam-5189	421	21	.	.	PUNCT
ejpam-5189	422	1	next	next	ADV
ejpam-5189	422	2	,	,	PUNCT
ejpam-5189	422	3	suppose	suppose	VERB
ejpam-5189	422	4	that	that	SCONJ
ejpam-5189	422	5	y	y	PROPN
ejpam-5189	422	6	/∈	/∈	PUNCT
ejpam-5189	422	7	s.	s.	PROPN
ejpam-5189	422	8	since	since	SCONJ
ejpam-5189	422	9	s	s	PROPN
ejpam-5189	422	10	is	be	AUX
ejpam-5189	422	11	2	2	NUM
ejpam-5189	422	12	-	-	PUNCT
ejpam-5189	422	13	dominating	dominating	NOUN
ejpam-5189	422	14	in	in	ADP
ejpam-5189	422	15	g	g	NOUN
ejpam-5189	422	16	,	,	PUNCT
ejpam-5189	422	17	there	there	PRON
ejpam-5189	422	18	exist	exist	VERB
ejpam-5189	422	19	distinct	distinct	ADJ
ejpam-5189	422	20	vertices	vertex	NOUN
ejpam-5189	422	21	v	v	ADP
ejpam-5189	422	22	,	,	PUNCT
ejpam-5189	422	23	w	w	PROPN
ejpam-5189	422	24	∈	∈	PROPN
ejpam-5189	422	25	s	s	PART
ejpam-5189	422	26	∩ng(y	∩ng(y	PROPN
ejpam-5189	422	27	)	)	PUNCT
ejpam-5189	422	28	.	.	PUNCT
ejpam-5189	423	1	choose	choose	VERB
ejpam-5189	423	2	any	any	DET
ejpam-5189	423	3	p	p	PROPN
ejpam-5189	423	4	∈	∈	PROPN
ejpam-5189	423	5	tv	tv	NOUN
ejpam-5189	423	6	and	and	CCONJ
ejpam-5189	423	7	q	q	NOUN
ejpam-5189	423	8	∈	∈	PROPN
ejpam-5189	423	9	tw	tw	NOUN
ejpam-5189	423	10	.	.	PUNCT
ejpam-5189	424	1	then	then	ADV
ejpam-5189	424	2	(	(	PUNCT
ejpam-5189	424	3	v	v	NOUN
ejpam-5189	424	4	,	,	PUNCT
ejpam-5189	424	5	p	p	NOUN
ejpam-5189	424	6	)	)	PUNCT
ejpam-5189	424	7	,	,	PUNCT
ejpam-5189	424	8	(	(	PUNCT
ejpam-5189	424	9	w	w	NOUN
ejpam-5189	424	10	,	,	PUNCT
ejpam-5189	424	11	q	q	NOUN
ejpam-5189	424	12	)	)	PUNCT
ejpam-5189	424	13	∈	∈	PROPN
ejpam-5189	424	14	c	c	NOUN
ejpam-5189	424	15	∩ng[km]((y	∩ng[km]((y	NOUN
ejpam-5189	424	16	,	,	PUNCT
ejpam-5189	424	17	d	d	NOUN
ejpam-5189	424	18	)	)	PUNCT
ejpam-5189	424	19	)	)	PUNCT
ejpam-5189	424	20	.	.	PUNCT
ejpam-5189	425	1	thus	thus	ADV
ejpam-5189	425	2	,	,	PUNCT
ejpam-5189	425	3	c	c	PROPN
ejpam-5189	425	4	is	be	AUX
ejpam-5189	425	5	a	a	DET
ejpam-5189	425	6	2	2	NUM
ejpam-5189	425	7	-	-	PUNCT
ejpam-5189	425	8	dominating	dominating	NOUN
ejpam-5189	425	9	set	set	NOUN
ejpam-5189	425	10	in	in	ADP
ejpam-5189	425	11	g[km	g[km	PROPN
ejpam-5189	425	12	]	]	PUNCT
ejpam-5189	425	13	.	.	PUNCT
ejpam-5189	426	1	corollary	corollary	ADJ
ejpam-5189	426	2	12	12	NUM
ejpam-5189	426	3	.	.	PUNCT
ejpam-5189	427	1	let	let	VERB
ejpam-5189	427	2	g	g	PRON
ejpam-5189	427	3	be	be	AUX
ejpam-5189	427	4	a	a	DET
ejpam-5189	427	5	non	non	ADJ
ejpam-5189	427	6	-	-	ADJ
ejpam-5189	427	7	trivial	trivial	ADJ
ejpam-5189	427	8	connected	connected	ADJ
ejpam-5189	427	9	graph	graph	NOUN
ejpam-5189	427	10	and	and	CCONJ
ejpam-5189	427	11	let	let	VERB
ejpam-5189	427	12	m	m	PRON
ejpam-5189	427	13	≥	≥	NOUN
ejpam-5189	427	14	2	2	NUM
ejpam-5189	427	15	.	.	PUNCT
ejpam-5189	427	16	then	then	ADV
ejpam-5189	427	17	γ2con(g[km	γ2con(g[km	PROPN
ejpam-5189	427	18	]	]	PUNCT
ejpam-5189	427	19	)	)	PUNCT
ejpam-5189	427	20	=	=	SYM
ejpam-5189	427	21	min{|s|+	min{|s|+	PROPN
ejpam-5189	427	22	(	(	PUNCT
ejpam-5189	427	23	m−	m−	PROPN
ejpam-5189	427	24	1)|s0|	1)|s0|	NUM
ejpam-5189	427	25	:	:	PUNCT
ejpam-5189	427	26	s	s	X
ejpam-5189	427	27	is	be	AUX
ejpam-5189	427	28	a	a	DET
ejpam-5189	427	29	convex	convex	ADJ
ejpam-5189	427	30	2	2	NUM
ejpam-5189	427	31	-	-	PUNCT
ejpam-5189	427	32	dominating	dominating	NOUN
ejpam-5189	427	33	set	set	NOUN
ejpam-5189	427	34	in	in	ADP
ejpam-5189	427	35	g	g	NOUN
ejpam-5189	427	36	}	}	PUNCT
ejpam-5189	427	37	.	.	PUNCT
ejpam-5189	428	1	references	reference	NOUN
ejpam-5189	428	2	1551	1551	NUM
ejpam-5189	428	3	conclusion	conclusion	NOUN
ejpam-5189	428	4	convex	convex	VERB
ejpam-5189	428	5	2	2	NUM
ejpam-5189	428	6	-	-	PUNCT
ejpam-5189	428	7	domination	domination	NOUN
ejpam-5189	428	8	has	have	AUX
ejpam-5189	428	9	been	be	AUX
ejpam-5189	428	10	introduced	introduce	VERB
ejpam-5189	428	11	and	and	CCONJ
ejpam-5189	428	12	initially	initially	ADV
ejpam-5189	428	13	studied	study	VERB
ejpam-5189	428	14	in	in	ADP
ejpam-5189	428	15	this	this	DET
ejpam-5189	428	16	paper	paper	NOUN
ejpam-5189	428	17	.	.	PUNCT
ejpam-5189	429	1	it	it	PRON
ejpam-5189	429	2	was	be	AUX
ejpam-5189	429	3	shown	show	VERB
ejpam-5189	429	4	that	that	SCONJ
ejpam-5189	429	5	every	every	DET
ejpam-5189	429	6	support	support	NOUN
ejpam-5189	429	7	vertex	vertex	NOUN
ejpam-5189	429	8	and	and	CCONJ
ejpam-5189	429	9	every	every	DET
ejpam-5189	429	10	vertex	vertex	NOUN
ejpam-5189	429	11	with	with	ADP
ejpam-5189	429	12	an	an	DET
ejpam-5189	429	13	independent	independent	ADJ
ejpam-5189	429	14	open	open	ADJ
ejpam-5189	429	15	neighborhood	neighborhood	NOUN
ejpam-5189	429	16	belong	belong	VERB
ejpam-5189	429	17	to	to	ADP
ejpam-5189	429	18	every	every	DET
ejpam-5189	429	19	convex	convex	ADJ
ejpam-5189	429	20	2	2	NUM
ejpam-5189	429	21	-	-	PUNCT
ejpam-5189	429	22	dominating	dominating	NOUN
ejpam-5189	429	23	set	set	NOUN
ejpam-5189	429	24	in	in	ADP
ejpam-5189	429	25	a	a	DET
ejpam-5189	429	26	connected	connected	ADJ
ejpam-5189	429	27	graph	graph	NOUN
ejpam-5189	429	28	.	.	PUNCT
ejpam-5189	430	1	the	the	DET
ejpam-5189	430	2	convex	convex	ADJ
ejpam-5189	430	3	2	2	NUM
ejpam-5189	430	4	-	-	PUNCT
ejpam-5189	430	5	domination	domination	NOUN
ejpam-5189	430	6	number	number	NOUN
ejpam-5189	430	7	of	of	ADP
ejpam-5189	430	8	a	a	DET
ejpam-5189	430	9	connected	connected	ADJ
ejpam-5189	430	10	graph	graph	NOUN
ejpam-5189	430	11	is	be	AUX
ejpam-5189	430	12	at	at	ADP
ejpam-5189	430	13	least	least	ADJ
ejpam-5189	430	14	equal	equal	ADJ
ejpam-5189	430	15	to	to	ADP
ejpam-5189	430	16	its	its	PRON
ejpam-5189	430	17	convex	convex	ADJ
ejpam-5189	430	18	domination	domination	NOUN
ejpam-5189	430	19	number	number	NOUN
ejpam-5189	430	20	.	.	PUNCT
ejpam-5189	431	1	moreover	moreover	ADV
ejpam-5189	431	2	,	,	PUNCT
ejpam-5189	431	3	the	the	DET
ejpam-5189	431	4	difference	difference	NOUN
ejpam-5189	431	5	of	of	ADP
ejpam-5189	431	6	these	these	DET
ejpam-5189	431	7	two	two	NUM
ejpam-5189	431	8	parameters	parameter	NOUN
ejpam-5189	431	9	can	can	AUX
ejpam-5189	431	10	be	be	AUX
ejpam-5189	431	11	made	make	VERB
ejpam-5189	431	12	arbitrarily	arbitrarily	ADV
ejpam-5189	431	13	large	large	ADJ
ejpam-5189	431	14	.	.	PUNCT
ejpam-5189	432	1	convex	convex	PROPN
ejpam-5189	432	2	2	2	NUM
ejpam-5189	432	3	-	-	PUNCT
ejpam-5189	432	4	domination	domination	NOUN
ejpam-5189	432	5	has	have	AUX
ejpam-5189	432	6	been	be	AUX
ejpam-5189	432	7	investigated	investigate	VERB
ejpam-5189	432	8	for	for	ADP
ejpam-5189	432	9	the	the	DET
ejpam-5189	432	10	join	join	NOUN
ejpam-5189	432	11	and	and	CCONJ
ejpam-5189	432	12	corona	corona	NOUN
ejpam-5189	432	13	of	of	ADP
ejpam-5189	432	14	two	two	NUM
ejpam-5189	432	15	graphs	graph	NOUN
ejpam-5189	432	16	as	as	ADV
ejpam-5189	432	17	well	well	ADV
ejpam-5189	432	18	as	as	ADP
ejpam-5189	432	19	for	for	ADP
ejpam-5189	432	20	the	the	DET
ejpam-5189	432	21	lexicographic	lexicographic	ADJ
ejpam-5189	432	22	and	and	CCONJ
ejpam-5189	432	23	cartesian	cartesian	ADJ
ejpam-5189	432	24	products	product	NOUN
ejpam-5189	432	25	of	of	ADP
ejpam-5189	432	26	graphs	graph	NOUN
ejpam-5189	432	27	.	.	PUNCT
ejpam-5189	433	1	for	for	ADP
ejpam-5189	433	2	some	some	DET
ejpam-5189	433	3	graphs	graph	NOUN
ejpam-5189	433	4	(	(	PUNCT
ejpam-5189	433	5	especially	especially	ADV
ejpam-5189	433	6	for	for	ADP
ejpam-5189	433	7	some	some	DET
ejpam-5189	433	8	join	join	NOUN
ejpam-5189	433	9	and	and	CCONJ
ejpam-5189	433	10	lexicographic	lexicographic	ADJ
ejpam-5189	433	11	product	product	NOUN
ejpam-5189	433	12	of	of	ADP
ejpam-5189	433	13	graphs	graph	NOUN
ejpam-5189	433	14	)	)	PUNCT
ejpam-5189	433	15	,	,	PUNCT
ejpam-5189	433	16	convex	convex	ADJ
ejpam-5189	433	17	2	2	NUM
ejpam-5189	433	18	-	-	PUNCT
ejpam-5189	433	19	domination	domination	NOUN
ejpam-5189	433	20	is	be	AUX
ejpam-5189	433	21	related	relate	VERB
ejpam-5189	433	22	to	to	ADP
ejpam-5189	433	23	clique	clique	ADJ
ejpam-5189	433	24	domination	domination	NOUN
ejpam-5189	433	25	.	.	PUNCT
ejpam-5189	434	1	the	the	DET
ejpam-5189	434	2	newly	newly	ADV
ejpam-5189	434	3	defined	define	VERB
ejpam-5189	434	4	concept	concept	NOUN
ejpam-5189	434	5	can	can	AUX
ejpam-5189	434	6	be	be	AUX
ejpam-5189	434	7	studied	study	VERB
ejpam-5189	434	8	for	for	ADP
ejpam-5189	434	9	other	other	ADJ
ejpam-5189	434	10	graphs	graph	NOUN
ejpam-5189	434	11	.	.	PUNCT
ejpam-5189	435	1	it	it	PRON
ejpam-5189	435	2	is	be	AUX
ejpam-5189	435	3	also	also	ADV
ejpam-5189	435	4	interesting	interesting	ADJ
ejpam-5189	435	5	to	to	PART
ejpam-5189	435	6	determine	determine	VERB
ejpam-5189	435	7	the	the	DET
ejpam-5189	435	8	complexity	complexity	NOUN
ejpam-5189	435	9	of	of	ADP
ejpam-5189	435	10	the	the	DET
ejpam-5189	435	11	convex	convex	ADJ
ejpam-5189	435	12	2	2	NUM
ejpam-5189	435	13	-	-	PUNCT
ejpam-5189	435	14	domination	domination	NOUN
ejpam-5189	435	15	problem	problem	NOUN
ejpam-5189	435	16	.	.	PUNCT
ejpam-5189	436	1	references	reference	NOUN
ejpam-5189	436	2	[	[	X
ejpam-5189	436	3	1	1	NUM
ejpam-5189	436	4	]	]	PUNCT
ejpam-5189	436	5	s.	s.	PROPN
ejpam-5189	436	6	banerjee	banerjee	PROPN
ejpam-5189	436	7	,	,	PUNCT
ejpam-5189	436	8	j.m	j.m	PROPN
ejpam-5189	436	9	.	.	PROPN
ejpam-5189	436	10	keil	keil	PROPN
ejpam-5189	436	11	,	,	PUNCT
ejpam-5189	436	12	and	and	CCONJ
ejpam-5189	436	13	d.	d.	PROPN
ejpam-5189	436	14	pradhan	pradhan	PROPN
ejpam-5189	436	15	.	.	PUNCT
ejpam-5189	437	1	perfect	perfect	ADJ
ejpam-5189	437	2	roman	roman	ADJ
ejpam-5189	437	3	domination	domination	NOUN
ejpam-5189	437	4	in	in	ADP
ejpam-5189	437	5	graphs	graph	NOUN
ejpam-5189	437	6	.	.	PUNCT
ejpam-5189	438	1	theoretical	theoretical	ADJ
ejpam-5189	438	2	computer	computer	NOUN
ejpam-5189	438	3	science	science	NOUN
ejpam-5189	438	4	,	,	PUNCT
ejpam-5189	438	5	796:1–21	796:1–21	NUM
ejpam-5189	438	6	,	,	PUNCT
ejpam-5189	438	7	2019	2019	NUM
ejpam-5189	438	8	.	.	PUNCT
ejpam-5189	439	1	[	[	X
ejpam-5189	439	2	2	2	NUM
ejpam-5189	439	3	]	]	X
ejpam-5189	439	4	r.a	r.a	PROPN
ejpam-5189	439	5	.	.	PROPN
ejpam-5189	439	6	beeler	beeler	PROPN
ejpam-5189	439	7	,	,	PUNCT
ejpam-5189	439	8	t.w	t.w	PROPN
ejpam-5189	439	9	.	.	PROPN
ejpam-5189	439	10	haynes	haynes	PROPN
ejpam-5189	439	11	,	,	PUNCT
ejpam-5189	439	12	and	and	CCONJ
ejpam-5189	439	13	s.t	s.t	PROPN
ejpam-5189	439	14	.	.	PROPN
ejpam-5189	439	15	hedetnieme	hedetnieme	PROPN
ejpam-5189	439	16	.	.	PUNCT
ejpam-5189	440	1	double	double	ADJ
ejpam-5189	440	2	roman	roman	ADJ
ejpam-5189	440	3	domination	domination	NOUN
ejpam-5189	440	4	.	.	PUNCT
ejpam-5189	441	1	discrete	discrete	ADJ
ejpam-5189	441	2	applied	apply	VERB
ejpam-5189	441	3	mathematics	mathematic	NOUN
ejpam-5189	441	4	,	,	PUNCT
ejpam-5189	441	5	211:23–29	211:23–29	NUM
ejpam-5189	441	6	,	,	PUNCT
ejpam-5189	441	7	2016	2016	NUM
ejpam-5189	441	8	.	.	PUNCT
ejpam-5189	442	1	[	[	X
ejpam-5189	442	2	3	3	X
ejpam-5189	442	3	]	]	X
ejpam-5189	442	4	b.	b.	NOUN
ejpam-5189	442	5	brešar	brešar	PROPN
ejpam-5189	442	6	and	and	CCONJ
ejpam-5189	442	7	s.	s.	PROPN
ejpam-5189	442	8	brezovnik	brezovnik	PROPN
ejpam-5189	442	9	.	.	PUNCT
ejpam-5189	443	1	grundy	grundy	PROPN
ejpam-5189	443	2	domination	domination	NOUN
ejpam-5189	443	3	and	and	CCONJ
ejpam-5189	443	4	zero	zero	NUM
ejpam-5189	443	5	forcing	force	VERB
ejpam-5189	443	6	in	in	ADP
ejpam-5189	443	7	regular	regular	ADJ
ejpam-5189	443	8	graphs	graph	NOUN
ejpam-5189	443	9	.	.	PUNCT
ejpam-5189	444	1	bulletin	bulletin	NOUN
ejpam-5189	444	2	of	of	ADP
ejpam-5189	444	3	the	the	DET
ejpam-5189	444	4	malaysian	malaysian	PROPN
ejpam-5189	444	5	mathematical	mathematical	PROPN
ejpam-5189	444	6	sciences	sciences	PROPN
ejpam-5189	444	7	society	society	NOUN
ejpam-5189	444	8	,	,	PUNCT
ejpam-5189	444	9	44(6):3637–3661	44(6):3637–3661	NUM
ejpam-5189	444	10	,	,	PUNCT
ejpam-5189	444	11	2021	2021	NUM
ejpam-5189	444	12	.	.	PUNCT
ejpam-5189	445	1	[	[	X
ejpam-5189	445	2	4	4	X
ejpam-5189	445	3	]	]	PUNCT
ejpam-5189	445	4	g.	g.	NOUN
ejpam-5189	445	5	cagaanan	cagaanan	PROPN
ejpam-5189	445	6	and	and	CCONJ
ejpam-5189	445	7	s.	s.	PROPN
ejpam-5189	445	8	canoy	canoy	PROPN
ejpam-5189	445	9	jr	jr	PROPN
ejpam-5189	445	10	.	.	PROPN
ejpam-5189	445	11	on	on	ADP
ejpam-5189	445	12	the	the	DET
ejpam-5189	445	13	geodetic	geodetic	ADJ
ejpam-5189	445	14	covers	cover	NOUN
ejpam-5189	445	15	and	and	CCONJ
ejpam-5189	445	16	geodetic	geodetic	ADJ
ejpam-5189	445	17	bases	basis	NOUN
ejpam-5189	445	18	of	of	ADP
ejpam-5189	445	19	the	the	DET
ejpam-5189	445	20	composition	composition	NOUN
ejpam-5189	446	1	g	g	PROPN
ejpam-5189	446	2	[	[	X
ejpam-5189	446	3	km	km	X
ejpam-5189	446	4	]	]	PUNCT
ejpam-5189	446	5	.	.	PUNCT
ejpam-5189	447	1	ars	ars	PROPN
ejpam-5189	447	2	combinatoria	combinatoria	PROPN
ejpam-5189	447	3	,	,	PUNCT
ejpam-5189	447	4	79:33–45	79:33–45	NUM
ejpam-5189	447	5	,	,	PUNCT
ejpam-5189	447	6	2006	2006	NUM
ejpam-5189	447	7	.	.	PUNCT
ejpam-5189	448	1	[	[	X
ejpam-5189	448	2	5	5	X
ejpam-5189	448	3	]	]	PUNCT
ejpam-5189	448	4	g.	g.	NOUN
ejpam-5189	448	5	cagaanan	cagaanan	PROPN
ejpam-5189	448	6	and	and	CCONJ
ejpam-5189	448	7	s.	s.	PROPN
ejpam-5189	448	8	canoy	canoy	PROPN
ejpam-5189	448	9	jr	jr	PROPN
ejpam-5189	448	10	.	.	PROPN
ejpam-5189	448	11	bounds	bound	VERB
ejpam-5189	448	12	for	for	ADP
ejpam-5189	448	13	the	the	DET
ejpam-5189	448	14	geodetic	geodetic	ADJ
ejpam-5189	448	15	number	number	NOUN
ejpam-5189	448	16	of	of	ADP
ejpam-5189	448	17	the	the	DET
ejpam-5189	448	18	cartesian	cartesian	ADJ
ejpam-5189	448	19	product	product	NOUN
ejpam-5189	448	20	of	of	ADP
ejpam-5189	448	21	graphs	graph	NOUN
ejpam-5189	448	22	.	.	PUNCT
ejpam-5189	449	1	utilitas	utilitas	PROPN
ejpam-5189	449	2	mathematica	mathematica	PROPN
ejpam-5189	449	3	,	,	PUNCT
ejpam-5189	449	4	79:91–98	79:91–98	NUM
ejpam-5189	449	5	,	,	PUNCT
ejpam-5189	449	6	2009	2009	NUM
ejpam-5189	449	7	.	.	PUNCT
ejpam-5189	450	1	[	[	X
ejpam-5189	450	2	6	6	NUM
ejpam-5189	450	3	]	]	X
ejpam-5189	450	4	s.r	s.r	PROPN
ejpam-5189	450	5	.	.	PROPN
ejpam-5189	450	6	canoy	canoy	PROPN
ejpam-5189	450	7	.	.	PUNCT
ejpam-5189	451	1	a	a	DET
ejpam-5189	451	2	short	short	ADJ
ejpam-5189	451	3	note	note	NOUN
ejpam-5189	451	4	on	on	ADP
ejpam-5189	451	5	convexity	convexity	NOUN
ejpam-5189	451	6	and	and	CCONJ
ejpam-5189	451	7	convex	convex	NOUN
ejpam-5189	451	8	domination	domination	NOUN
ejpam-5189	451	9	in	in	ADP
ejpam-5189	451	10	g[km	g[km	PROPN
ejpam-5189	451	11	]	]	PUNCT
ejpam-5189	451	12	.	.	PUNCT
ejpam-5189	452	1	applied	apply	VERB
ejpam-5189	452	2	mathematical	mathematical	ADJ
ejpam-5189	452	3	sciences	science	NOUN
ejpam-5189	452	4	,	,	PUNCT
ejpam-5189	452	5	8(115):5737–5741	8(115):5737–5741	NUM
ejpam-5189	452	6	,	,	PUNCT
ejpam-5189	452	7	2014	2014	NUM
ejpam-5189	452	8	.	.	PUNCT
ejpam-5189	453	1	[	[	X
ejpam-5189	453	2	7	7	X
ejpam-5189	453	3	]	]	X
ejpam-5189	453	4	s.r	s.r	PROPN
ejpam-5189	453	5	.	.	PROPN
ejpam-5189	453	6	canoy	canoy	PROPN
ejpam-5189	453	7	and	and	CCONJ
ejpam-5189	453	8	i.j.l	i.j.l	NOUN
ejpam-5189	453	9	.	.	PROPN
ejpam-5189	453	10	garces	garces	PROPN
ejpam-5189	453	11	.	.	PUNCT
ejpam-5189	454	1	convex	convex	PROPN
ejpam-5189	454	2	sets	set	NOUN
ejpam-5189	454	3	under	under	ADP
ejpam-5189	454	4	some	some	DET
ejpam-5189	454	5	graph	graph	NOUN
ejpam-5189	454	6	operations	operation	NOUN
ejpam-5189	454	7	.	.	PUNCT
ejpam-5189	455	1	graphs	graph	NOUN
ejpam-5189	455	2	and	and	CCONJ
ejpam-5189	455	3	combinatorics	combinatoric	NOUN
ejpam-5189	455	4	,	,	PUNCT
ejpam-5189	455	5	18(4):787–793	18(4):787–793	NUM
ejpam-5189	455	6	,	,	PUNCT
ejpam-5189	455	7	2002	2002	NUM
ejpam-5189	455	8	.	.	PUNCT
ejpam-5189	456	1	[	[	X
ejpam-5189	456	2	8	8	NUM
ejpam-5189	456	3	]	]	X
ejpam-5189	456	4	g.	g.	PROPN
ejpam-5189	456	5	chartrand	chartrand	PROPN
ejpam-5189	456	6	,	,	PUNCT
ejpam-5189	456	7	j.f	j.f	PROPN
ejpam-5189	456	8	.	.	PROPN
ejpam-5189	456	9	fink	fink	PROPN
ejpam-5189	456	10	,	,	PUNCT
ejpam-5189	456	11	and	and	CCONJ
ejpam-5189	456	12	p.	p.	PROPN
ejpam-5189	456	13	zhang	zhang	PROPN
ejpam-5189	456	14	.	.	PUNCT
ejpam-5189	457	1	convexity	convexity	NOUN
ejpam-5189	457	2	in	in	ADP
ejpam-5189	457	3	oriented	orient	VERB
ejpam-5189	457	4	graphs	graph	NOUN
ejpam-5189	457	5	.	.	PUNCT
ejpam-5189	458	1	discrete	discrete	ADJ
ejpam-5189	458	2	applied	applied	ADJ
ejpam-5189	458	3	mathematics	mathematic	NOUN
ejpam-5189	458	4	,	,	PUNCT
ejpam-5189	458	5	116(1	116(1	NUM
ejpam-5189	458	6	-	-	SYM
ejpam-5189	458	7	2):115–126	2):115–126	NOUN
ejpam-5189	458	8	,	,	PUNCT
ejpam-5189	458	9	2002	2002	NUM
ejpam-5189	458	10	.	.	PUNCT
ejpam-5189	459	1	[	[	X
ejpam-5189	459	2	9	9	NUM
ejpam-5189	459	3	]	]	X
ejpam-5189	459	4	g.	g.	NOUN
ejpam-5189	459	5	chartrand	chartrand	PROPN
ejpam-5189	459	6	and	and	CCONJ
ejpam-5189	459	7	p.	p.	PROPN
ejpam-5189	459	8	zhang	zhang	PROPN
ejpam-5189	459	9	.	.	PUNCT
ejpam-5189	460	1	convexity	convexity	NOUN
ejpam-5189	460	2	in	in	ADP
ejpam-5189	460	3	graphs	graph	NOUN
ejpam-5189	460	4	.	.	PUNCT
ejpam-5189	461	1	congr	congr	NOUN
ejpam-5189	461	2	.	.	PUNCT
ejpam-5189	462	1	numerantium	numerantium	ADJ
ejpam-5189	462	2	,	,	PUNCT
ejpam-5189	462	3	136:19–32	136:19–32	NUM
ejpam-5189	462	4	,	,	PUNCT
ejpam-5189	462	5	1999	1999	NUM
ejpam-5189	462	6	.	.	PUNCT
ejpam-5189	463	1	[	[	X
ejpam-5189	463	2	10	10	NUM
ejpam-5189	463	3	]	]	X
ejpam-5189	463	4	m.	m.	NOUN
ejpam-5189	463	5	chellali	chellali	PROPN
ejpam-5189	463	6	.	.	PUNCT
ejpam-5189	464	1	bounds	bound	VERB
ejpam-5189	464	2	on	on	ADP
ejpam-5189	464	3	the	the	DET
ejpam-5189	464	4	2	2	NUM
ejpam-5189	464	5	-	-	PUNCT
ejpam-5189	464	6	domination	domination	NOUN
ejpam-5189	464	7	number	number	NOUN
ejpam-5189	464	8	in	in	ADP
ejpam-5189	464	9	cactus	cactus	NOUN
ejpam-5189	464	10	graphs	graph	NOUN
ejpam-5189	464	11	.	.	PUNCT
ejpam-5189	465	1	opuscula	opuscula	PROPN
ejpam-5189	465	2	mathematica	mathematica	PROPN
ejpam-5189	465	3	,	,	PUNCT
ejpam-5189	465	4	26(1):5–12	26(1):5–12	NUM
ejpam-5189	465	5	,	,	PUNCT
ejpam-5189	465	6	2006	2006	NUM
ejpam-5189	465	7	.	.	PUNCT
ejpam-5189	466	1	[	[	X
ejpam-5189	466	2	11	11	NUM
ejpam-5189	466	3	]	]	PUNCT
ejpam-5189	466	4	m.	m.	NOUN
ejpam-5189	466	5	chellali	chellali	PROPN
ejpam-5189	466	6	,	,	PUNCT
ejpam-5189	466	7	t.w	t.w	PROPN
ejpam-5189	466	8	.	.	PROPN
ejpam-5189	466	9	haynes	haynes	PROPN
ejpam-5189	466	10	,	,	PUNCT
ejpam-5189	466	11	and	and	CCONJ
ejpam-5189	466	12	s.t	s.t	PROPN
ejpam-5189	466	13	.	.	PROPN
ejpam-5189	466	14	hedetnieme	hedetnieme	PROPN
ejpam-5189	466	15	.	.	PUNCT
ejpam-5189	467	1	roman	roman	ADJ
ejpam-5189	467	2	{	{	PUNCT
ejpam-5189	467	3	2}domination	2}domination	NOUN
ejpam-5189	467	4	.	.	PUNCT
ejpam-5189	468	1	discrete	discrete	ADJ
ejpam-5189	468	2	applied	apply	VERB
ejpam-5189	468	3	math	math	NOUN
ejpam-5189	468	4	,	,	PUNCT
ejpam-5189	468	5	204:22–28	204:22–28	NUM
ejpam-5189	468	6	,	,	PUNCT
ejpam-5189	468	7	2016	2016	NUM
ejpam-5189	468	8	.	.	PUNCT
ejpam-5189	469	1	references	reference	NOUN
ejpam-5189	469	2	1552	1552	NUM
ejpam-5189	469	3	[	[	X
ejpam-5189	469	4	12	12	NUM
ejpam-5189	469	5	]	]	PUNCT
ejpam-5189	469	6	m.	m.	NOUN
ejpam-5189	469	7	chellali	chellali	PROPN
ejpam-5189	469	8	,	,	PUNCT
ejpam-5189	469	9	t.w	t.w	PROPN
ejpam-5189	469	10	.	.	PROPN
ejpam-5189	469	11	haynes	haynes	PROPN
ejpam-5189	469	12	,	,	PUNCT
ejpam-5189	469	13	s.t	s.t	PROPN
ejpam-5189	469	14	.	.	PROPN
ejpam-5189	469	15	hedetniemi	hedetniemi	PROPN
ejpam-5189	469	16	,	,	PUNCT
ejpam-5189	469	17	and	and	CCONJ
ejpam-5189	469	18	a.a	a.a	PROPN
ejpam-5189	469	19	.	.	PROPN
ejpam-5189	469	20	mcrae	mcrae	PROPN
ejpam-5189	469	21	.	.	PUNCT
ejpam-5189	470	1	roman	roman	ADJ
ejpam-5189	470	2	2	2	NUM
ejpam-5189	470	3	-	-	PUNCT
ejpam-5189	470	4	domination	domination	NOUN
ejpam-5189	470	5	.	.	PUNCT
ejpam-5189	471	1	discrete	discrete	ADJ
ejpam-5189	471	2	applied	apply	VERB
ejpam-5189	471	3	mathematics	mathematic	NOUN
ejpam-5189	471	4	,	,	PUNCT
ejpam-5189	471	5	204:22–28	204:22–28	NUM
ejpam-5189	471	6	,	,	PUNCT
ejpam-5189	471	7	2016	2016	NUM
ejpam-5189	471	8	.	.	PUNCT
ejpam-5189	472	1	[	[	X
ejpam-5189	472	2	13	13	NUM
ejpam-5189	472	3	]	]	SYM
ejpam-5189	472	4	e.j	e.j	PROPN
ejpam-5189	472	5	.	.	PROPN
ejpam-5189	472	6	cockayne	cockayne	PROPN
ejpam-5189	472	7	,	,	PUNCT
ejpam-5189	472	8	r.m	r.m	PROPN
ejpam-5189	472	9	.	.	PROPN
ejpam-5189	472	10	dawes	dawes	PROPN
ejpam-5189	472	11	,	,	PUNCT
ejpam-5189	472	12	and	and	CCONJ
ejpam-5189	472	13	s.t	s.t	PROPN
ejpam-5189	472	14	.	.	PROPN
ejpam-5189	472	15	hedetniemi	hedetniemi	PROPN
ejpam-5189	472	16	.	.	PUNCT
ejpam-5189	473	1	total	total	ADJ
ejpam-5189	473	2	domination	domination	NOUN
ejpam-5189	473	3	in	in	ADP
ejpam-5189	473	4	graphs	graph	NOUN
ejpam-5189	473	5	.	.	PUNCT
ejpam-5189	474	1	networks	network	NOUN
ejpam-5189	474	2	,	,	PUNCT
ejpam-5189	474	3	10(3):211–219	10(3):211–219	NUM
ejpam-5189	474	4	,	,	PUNCT
ejpam-5189	474	5	1980	1980	NUM
ejpam-5189	474	6	.	.	PUNCT
ejpam-5189	475	1	[	[	X
ejpam-5189	475	2	14	14	NUM
ejpam-5189	475	3	]	]	X
ejpam-5189	475	4	e.j	e.j	PROPN
ejpam-5189	475	5	.	.	PROPN
ejpam-5189	475	6	cockayne	cockayne	PROPN
ejpam-5189	475	7	,	,	PUNCT
ejpam-5189	475	8	p.a	p.a	PROPN
ejpam-5189	475	9	.	.	PROPN
ejpam-5189	475	10	deryer	deryer	PROPN
ejpam-5189	475	11	,	,	PUNCT
ejpam-5189	475	12	s.m	s.m	PROPN
ejpam-5189	475	13	.	.	PROPN
ejpam-5189	475	14	hedetnieme	hedetnieme	PROPN
ejpam-5189	475	15	,	,	PUNCT
ejpam-5189	475	16	and	and	CCONJ
ejpam-5189	475	17	s.t	s.t	PROPN
ejpam-5189	475	18	.	.	PROPN
ejpam-5189	475	19	hedetnieme	hedetnieme	PROPN
ejpam-5189	475	20	.	.	PUNCT
ejpam-5189	476	1	roman	roman	ADJ
ejpam-5189	476	2	domination	domination	NOUN
ejpam-5189	476	3	in	in	ADP
ejpam-5189	476	4	graphs	graph	NOUN
ejpam-5189	476	5	.	.	PUNCT
ejpam-5189	477	1	discrete	discrete	ADJ
ejpam-5189	477	2	mathematics	mathematic	NOUN
ejpam-5189	477	3	,	,	PUNCT
ejpam-5189	477	4	278(13):11–22	278(13):11–22	NUM
ejpam-5189	477	5	,	,	PUNCT
ejpam-5189	477	6	2004	2004	NUM
ejpam-5189	477	7	.	.	PUNCT
ejpam-5189	478	1	[	[	X
ejpam-5189	478	2	15	15	NUM
ejpam-5189	478	3	]	]	X
ejpam-5189	478	4	j.	j.	PROPN
ejpam-5189	478	5	cyman	cyman	PROPN
ejpam-5189	478	6	,	,	PUNCT
ejpam-5189	478	7	m.	m.	NOUN
ejpam-5189	478	8	lemańska	lemańska	NOUN
ejpam-5189	478	9	,	,	PUNCT
ejpam-5189	478	10	and	and	CCONJ
ejpam-5189	478	11	j.	j.	PROPN
ejpam-5189	478	12	raczek	raczek	PROPN
ejpam-5189	478	13	.	.	PUNCT
ejpam-5189	479	1	graphs	graph	NOUN
ejpam-5189	479	2	with	with	ADP
ejpam-5189	479	3	convex	convex	ADJ
ejpam-5189	479	4	domination	domination	NOUN
ejpam-5189	479	5	number	number	NOUN
ejpam-5189	479	6	close	close	ADJ
ejpam-5189	479	7	to	to	ADP
ejpam-5189	479	8	their	their	PRON
ejpam-5189	479	9	order	order	NOUN
ejpam-5189	479	10	.	.	PUNCT
ejpam-5189	480	1	discussiones	discussione	NOUN
ejpam-5189	480	2	mathematicae	mathematicae	PROPN
ejpam-5189	480	3	graph	graph	NOUN
ejpam-5189	480	4	theory	theory	NOUN
ejpam-5189	480	5	,	,	PUNCT
ejpam-5189	480	6	26(2):307–316	26(2):307–316	NUM
ejpam-5189	480	7	,	,	PUNCT
ejpam-5189	480	8	2006	2006	NUM
ejpam-5189	480	9	.	.	PUNCT
ejpam-5189	481	1	[	[	X
ejpam-5189	481	2	16	16	NUM
ejpam-5189	481	3	]	]	X
ejpam-5189	481	4	m.	m.	NOUN
ejpam-5189	481	5	dettlaff	dettlaff	VERB
ejpam-5189	481	6	and	and	CCONJ
ejpam-5189	481	7	m.	m.	NOUN
ejpam-5189	482	1	lemańskaand	lemańskaand	PROPN
ejpam-5189	482	2	j.a	j.a	PROPN
ejpam-5189	482	3	.	.	PROPN
ejpam-5189	482	4	rodŕıguez	rodŕıguez	PROPN
ejpam-5189	482	5	-	-	NOUN
ejpam-5189	482	6	velázquez	velázquez	NOUN
ejpam-5189	482	7	.	.	PUNCT
ejpam-5189	483	1	secure	secure	ADJ
ejpam-5189	483	2	italian	italian	ADJ
ejpam-5189	483	3	domination	domination	NOUN
ejpam-5189	483	4	in	in	ADP
ejpam-5189	483	5	graphs	graph	NOUN
ejpam-5189	483	6	.	.	PUNCT
ejpam-5189	484	1	journal	journal	NOUN
ejpam-5189	484	2	of	of	ADP
ejpam-5189	484	3	combinatorial	combinatorial	ADJ
ejpam-5189	484	4	optimization	optimization	NOUN
ejpam-5189	484	5	,	,	PUNCT
ejpam-5189	484	6	41:56–72	41:56–72	NUM
ejpam-5189	484	7	,	,	PUNCT
ejpam-5189	484	8	2021	2021	NUM
ejpam-5189	484	9	.	.	PUNCT
ejpam-5189	485	1	[	[	X
ejpam-5189	485	2	17	17	NUM
ejpam-5189	485	3	]	]	PUNCT
ejpam-5189	485	4	m.	m.	NOUN
ejpam-5189	485	5	farber	farber	PROPN
ejpam-5189	485	6	and	and	CCONJ
ejpam-5189	485	7	r.e	r.e	PROPN
ejpam-5189	485	8	.	.	PROPN
ejpam-5189	485	9	jamison	jamison	PROPN
ejpam-5189	485	10	.	.	PUNCT
ejpam-5189	486	1	convexity	convexity	NOUN
ejpam-5189	486	2	in	in	ADP
ejpam-5189	486	3	graphs	graph	NOUN
ejpam-5189	486	4	and	and	CCONJ
ejpam-5189	486	5	hypergraphs	hypergraph	NOUN
ejpam-5189	486	6	.	.	PUNCT
ejpam-5189	487	1	siam	siam	PROPN
ejpam-5189	487	2	journal	journal	PROPN
ejpam-5189	487	3	on	on	ADP
ejpam-5189	487	4	algebraic	algebraic	ADJ
ejpam-5189	487	5	discrete	discrete	ADJ
ejpam-5189	487	6	methods	method	NOUN
ejpam-5189	487	7	,	,	PUNCT
ejpam-5189	487	8	7(3):433–444	7(3):433–444	NUM
ejpam-5189	487	9	,	,	PUNCT
ejpam-5189	487	10	1986	1986	NUM
ejpam-5189	487	11	.	.	PUNCT
ejpam-5189	488	1	[	[	X
ejpam-5189	488	2	18	18	NUM
ejpam-5189	488	3	]	]	X
ejpam-5189	488	4	r.j	r.j	PROPN
ejpam-5189	488	5	.	.	PROPN
ejpam-5189	488	6	fortosa	fortosa	PROPN
ejpam-5189	488	7	and	and	CCONJ
ejpam-5189	488	8	s.r	s.r	PROPN
ejpam-5189	488	9	.	.	PROPN
ejpam-5189	488	10	canoy	canoy	PROPN
ejpam-5189	488	11	.	.	PUNCT
ejpam-5189	489	1	convex	convex	VERB
ejpam-5189	489	2	roman	roman	ADJ
ejpam-5189	489	3	dominating	dominating	NOUN
ejpam-5189	489	4	function	function	NOUN
ejpam-5189	489	5	in	in	ADP
ejpam-5189	489	6	graphs	graph	NOUN
ejpam-5189	489	7	.	.	PUNCT
ejpam-5189	490	1	european	european	ADJ
ejpam-5189	490	2	journal	journal	PROPN
ejpam-5189	490	3	of	of	ADP
ejpam-5189	490	4	pure	pure	ADJ
ejpam-5189	490	5	and	and	CCONJ
ejpam-5189	490	6	applied	applied	ADJ
ejpam-5189	490	7	mathematics	mathematic	NOUN
ejpam-5189	490	8	,	,	PUNCT
ejpam-5189	490	9	16(3):1705–1716	16(3):1705–1716	NUM
ejpam-5189	490	10	,	,	PUNCT
ejpam-5189	490	11	2023	2023	NUM
ejpam-5189	490	12	.	.	PUNCT
ejpam-5189	491	1	[	[	X
ejpam-5189	491	2	19	19	NUM
ejpam-5189	491	3	]	]	X
ejpam-5189	491	4	r.j	r.j	PROPN
ejpam-5189	491	5	.	.	PROPN
ejpam-5189	491	6	fortosa	fortosa	PROPN
ejpam-5189	491	7	,	,	PUNCT
ejpam-5189	491	8	s.r	s.r	PROPN
ejpam-5189	491	9	.	.	PROPN
ejpam-5189	491	10	canoy	canoy	PROPN
ejpam-5189	491	11	,	,	PUNCT
ejpam-5189	491	12	and	and	CCONJ
ejpam-5189	491	13	f.p	f.p	PROPN
ejpam-5189	491	14	.	.	PROPN
ejpam-5189	491	15	jamil	jamil	PROPN
ejpam-5189	491	16	.	.	PUNCT
ejpam-5189	492	1	convex	convex	PROPN
ejpam-5189	492	2	italian	italian	PROPN
ejpam-5189	492	3	in	in	ADP
ejpam-5189	492	4	graphs	graph	NOUN
ejpam-5189	492	5	.	.	PUNCT
ejpam-5189	493	1	kyungpook	kyungpook	PROPN
ejpam-5189	493	2	mathematical	mathematical	PROPN
ejpam-5189	493	3	journal	journal	PROPN
ejpam-5189	493	4	,	,	PUNCT
ejpam-5189	493	5	submitted	submit	VERB
ejpam-5189	493	6	.	.	PUNCT
ejpam-5189	494	1	[	[	X
ejpam-5189	494	2	20	20	NUM
ejpam-5189	494	3	]	]	X
ejpam-5189	494	4	w.	w.	PROPN
ejpam-5189	494	5	goddard	goddard	PROPN
ejpam-5189	494	6	and	and	CCONJ
ejpam-5189	494	7	m.a	m.a	PROPN
ejpam-5189	494	8	.	.	PROPN
ejpam-5189	494	9	henning	henning	PROPN
ejpam-5189	494	10	.	.	PUNCT
ejpam-5189	495	1	domination	domination	NOUN
ejpam-5189	495	2	in	in	ADP
ejpam-5189	495	3	planar	planar	ADJ
ejpam-5189	495	4	graphs	graph	NOUN
ejpam-5189	495	5	with	with	ADP
ejpam-5189	495	6	small	small	ADJ
ejpam-5189	495	7	diameter	diameter	NOUN
ejpam-5189	495	8	.	.	PUNCT
ejpam-5189	496	1	journal	journal	PROPN
ejpam-5189	496	2	of	of	ADP
ejpam-5189	496	3	graph	graph	NOUN
ejpam-5189	496	4	theory	theory	NOUN
ejpam-5189	496	5	,	,	PUNCT
ejpam-5189	496	6	40(1):1–25	40(1):1–25	NUM
ejpam-5189	496	7	,	,	PUNCT
ejpam-5189	496	8	2002	2002	NUM
ejpam-5189	496	9	.	.	PUNCT
ejpam-5189	497	1	[	[	X
ejpam-5189	497	2	21	21	NUM
ejpam-5189	497	3	]	]	X
ejpam-5189	497	4	g.	g.	PROPN
ejpam-5189	497	5	hao	hao	PROPN
ejpam-5189	497	6	,	,	PUNCT
ejpam-5189	497	7	p.	p.	PROPN
ejpam-5189	497	8	jalilolghadr	jalilolghadr	PROPN
ejpam-5189	497	9	,	,	PUNCT
ejpam-5189	497	10	and	and	CCONJ
ejpam-5189	497	11	d.a	d.a	PROPN
ejpam-5189	497	12	.	.	PROPN
ejpam-5189	497	13	mojdeh	mojdeh	PROPN
ejpam-5189	497	14	.	.	PUNCT
ejpam-5189	498	1	perfect	perfect	ADJ
ejpam-5189	498	2	double	double	ADJ
ejpam-5189	498	3	italian	italian	ADJ
ejpam-5189	498	4	domination	domination	NOUN
ejpam-5189	498	5	of	of	ADP
ejpam-5189	498	6	a	a	DET
ejpam-5189	498	7	graph	graph	NOUN
ejpam-5189	498	8	.	.	PUNCT
ejpam-5189	499	1	akce	akce	PROPN
ejpam-5189	499	2	international	international	PROPN
ejpam-5189	499	3	journal	journal	NOUN
ejpam-5189	499	4	of	of	ADP
ejpam-5189	499	5	graphs	graph	NOUN
ejpam-5189	499	6	and	and	CCONJ
ejpam-5189	499	7	combinatorics	combinatoric	NOUN
ejpam-5189	499	8	,	,	PUNCT
ejpam-5189	499	9	20(3):247–257	20(3):247–257	NOUN
ejpam-5189	499	10	,	,	PUNCT
ejpam-5189	499	11	2023	2023	NUM
ejpam-5189	499	12	.	.	PUNCT
ejpam-5189	500	1	[	[	X
ejpam-5189	500	2	22	22	NUM
ejpam-5189	500	3	]	]	X
ejpam-5189	500	4	f.	f.	PROPN
ejpam-5189	500	5	harary	harary	PROPN
ejpam-5189	500	6	and	and	CCONJ
ejpam-5189	500	7	j.	j.	PROPN
ejpam-5189	500	8	nieminen	nieminen	PROPN
ejpam-5189	500	9	.	.	PUNCT
ejpam-5189	501	1	convexity	convexity	NOUN
ejpam-5189	501	2	in	in	ADP
ejpam-5189	501	3	graphs	graph	NOUN
ejpam-5189	501	4	.	.	PUNCT
ejpam-5189	502	1	journal	journal	PROPN
ejpam-5189	502	2	of	of	ADP
ejpam-5189	502	3	differential	differential	ADJ
ejpam-5189	502	4	geometry	geometry	NOUN
ejpam-5189	502	5	,	,	PUNCT
ejpam-5189	502	6	16(2):185–190	16(2):185–190	NUM
ejpam-5189	502	7	,	,	PUNCT
ejpam-5189	502	8	1981	1981	NUM
ejpam-5189	502	9	.	.	PUNCT
ejpam-5189	503	1	[	[	X
ejpam-5189	503	2	23	23	NUM
ejpam-5189	503	3	]	]	X
ejpam-5189	503	4	t.w	t.w	PROPN
ejpam-5189	503	5	.	.	PROPN
ejpam-5189	503	6	haynes	haynes	PROPN
ejpam-5189	503	7	,	,	PUNCT
ejpam-5189	503	8	s.	s.	PROPN
ejpam-5189	503	9	hedetniemi	hedetniemi	PROPN
ejpam-5189	503	10	,	,	PUNCT
ejpam-5189	503	11	and	and	CCONJ
ejpam-5189	503	12	p.	p.	PROPN
ejpam-5189	503	13	slater	slater	PROPN
ejpam-5189	503	14	.	.	PUNCT
ejpam-5189	504	1	fundamentals	fundamental	NOUN
ejpam-5189	504	2	of	of	ADP
ejpam-5189	504	3	domination	domination	NOUN
ejpam-5189	504	4	in	in	ADP
ejpam-5189	504	5	graphs	graph	NOUN
ejpam-5189	504	6	.	.	PUNCT
ejpam-5189	505	1	crc	crc	PROPN
ejpam-5189	505	2	press	press	PROPN
ejpam-5189	505	3	,	,	PUNCT
ejpam-5189	505	4	2013	2013	NUM
ejpam-5189	505	5	.	.	PUNCT
ejpam-5189	506	1	[	[	X
ejpam-5189	506	2	24	24	NUM
ejpam-5189	506	3	]	]	PUNCT
ejpam-5189	506	4	m.	m.	NOUN
ejpam-5189	506	5	lemanska	lemanska	PROPN
ejpam-5189	506	6	.	.	PUNCT
ejpam-5189	507	1	weakly	weakly	ADJ
ejpam-5189	507	2	convex	convex	NOUN
ejpam-5189	507	3	and	and	CCONJ
ejpam-5189	507	4	convex	convex	ADJ
ejpam-5189	507	5	domination	domination	NOUN
ejpam-5189	507	6	numbers	number	NOUN
ejpam-5189	507	7	.	.	PUNCT
ejpam-5189	508	1	opuscula	opuscula	PROPN
ejpam-5189	508	2	mathematica	mathematica	PROPN
ejpam-5189	508	3	,	,	PUNCT
ejpam-5189	508	4	24(2):181–188	24(2):181–188	PROPN
ejpam-5189	508	5	,	,	PUNCT
ejpam-5189	508	6	2004	2004	NUM
ejpam-5189	508	7	.	.	PUNCT
ejpam-5189	509	1	[	[	X
ejpam-5189	509	2	25	25	NUM
ejpam-5189	509	3	]	]	PUNCT
ejpam-5189	509	4	b.	b.	PROPN
ejpam-5189	509	5	omamalin	omamalin	PROPN
ejpam-5189	509	6	,	,	PUNCT
ejpam-5189	509	7	s.r	s.r	PROPN
ejpam-5189	509	8	.	.	PROPN
ejpam-5189	509	9	canoy	canoy	PROPN
ejpam-5189	509	10	jr	jr	PROPN
ejpam-5189	509	11	.	.	PROPN
ejpam-5189	509	12	,	,	PUNCT
ejpam-5189	509	13	and	and	CCONJ
ejpam-5189	509	14	h.	h.	PROPN
ejpam-5189	509	15	rara	rara	PROPN
ejpam-5189	509	16	.	.	PUNCT
ejpam-5189	510	1	locating	locate	VERB
ejpam-5189	510	2	total	total	ADJ
ejpam-5189	510	3	dominating	dominating	NOUN
ejpam-5189	510	4	sets	set	NOUN
ejpam-5189	510	5	in	in	ADP
ejpam-5189	510	6	the	the	DET
ejpam-5189	510	7	join	join	NOUN
ejpam-5189	510	8	,	,	PUNCT
ejpam-5189	510	9	corona	corona	NOUN
ejpam-5189	510	10	and	and	CCONJ
ejpam-5189	510	11	composition	composition	NOUN
ejpam-5189	510	12	of	of	ADP
ejpam-5189	510	13	graphs	graph	NOUN
ejpam-5189	510	14	.	.	PUNCT
ejpam-5189	511	1	applied	apply	VERB
ejpam-5189	511	2	mathematical	mathematical	ADJ
ejpam-5189	511	3	sciences	science	NOUN
ejpam-5189	511	4	,	,	PUNCT
ejpam-5189	511	5	8(48):2363–2374	8(48):2363–2374	NUM
ejpam-5189	511	6	,	,	PUNCT
ejpam-5189	511	7	2014	2014	NUM
ejpam-5189	511	8	.	.	PUNCT
ejpam-5189	512	1	[	[	X
ejpam-5189	512	2	26	26	NUM
ejpam-5189	512	3	]	]	X
ejpam-5189	512	4	l.m	l.m	PROPN
ejpam-5189	512	5	.	.	PROPN
ejpam-5189	512	6	paleta	paleta	PROPN
ejpam-5189	512	7	and	and	CCONJ
ejpam-5189	512	8	f.p	f.p	PROPN
ejpam-5189	512	9	.	.	PROPN
ejpam-5189	512	10	jamil	jamil	PROPN
ejpam-5189	512	11	.	.	PUNCT
ejpam-5189	513	1	on	on	ADP
ejpam-5189	513	2	perfect	perfect	ADJ
ejpam-5189	513	3	italian	italian	ADJ
ejpam-5189	513	4	domination	domination	NOUN
ejpam-5189	513	5	in	in	ADP
ejpam-5189	513	6	graphs	graph	NOUN
ejpam-5189	513	7	.	.	PUNCT
ejpam-5189	514	1	discrete	discrete	ADJ
ejpam-5189	514	2	mathematics	mathematic	NOUN
ejpam-5189	514	3	,	,	PUNCT
ejpam-5189	514	4	algorithms	algorithm	NOUN
ejpam-5189	514	5	and	and	CCONJ
ejpam-5189	514	6	applications	application	NOUN
ejpam-5189	514	7	,	,	PUNCT
ejpam-5189	514	8	page	page	NOUN
ejpam-5189	514	9	2350085	2350085	NUM
ejpam-5189	514	10	,	,	PUNCT
ejpam-5189	514	11	2023	2023	NUM
ejpam-5189	514	12	.	.	PUNCT
ejpam-5189	515	1	[	[	X
ejpam-5189	515	2	27	27	NUM
ejpam-5189	515	3	]	]	X
ejpam-5189	515	4	c.s	c.s	PROPN
ejpam-5189	515	5	.	.	PROPN
ejpam-5189	515	6	revelle	revelle	PROPN
ejpam-5189	515	7	and	and	CCONJ
ejpam-5189	515	8	k.e	k.e	PROPN
ejpam-5189	515	9	.	.	PUNCT
ejpam-5189	516	1	rosing	rosing	PROPN
ejpam-5189	516	2	.	.	PUNCT
ejpam-5189	517	1	defendens	defenden	VERB
ejpam-5189	517	2	imperium	imperium	NOUN
ejpam-5189	517	3	romanum	romanum	NOUN
ejpam-5189	517	4	:	:	PUNCT
ejpam-5189	517	5	a	a	DET
ejpam-5189	517	6	classical	classical	ADJ
ejpam-5189	517	7	problem	problem	NOUN
ejpam-5189	517	8	in	in	ADP
ejpam-5189	517	9	military	military	ADJ
ejpam-5189	517	10	strategy	strategy	NOUN
ejpam-5189	517	11	.	.	PUNCT
ejpam-5189	518	1	american	american	PROPN
ejpam-5189	518	2	mathematical	mathematical	PROPN
ejpam-5189	518	3	monthly	monthly	PROPN
ejpam-5189	518	4	,	,	PUNCT
ejpam-5189	518	5	107(7):585–594	107(7):585–594	PROPN
ejpam-5189	518	6	,	,	PUNCT
ejpam-5189	518	7	2000	2000	NUM
ejpam-5189	518	8	.	.	PUNCT
ejpam-5189	519	1	[	[	X
ejpam-5189	519	2	28	28	NUM
ejpam-5189	519	3	]	]	X
ejpam-5189	519	4	i.	i.	PROPN
ejpam-5189	519	5	stewart	stewart	PROPN
ejpam-5189	519	6	.	.	PUNCT
ejpam-5189	520	1	defend	defend	VERB
ejpam-5189	520	2	the	the	DET
ejpam-5189	520	3	roman	roman	ADJ
ejpam-5189	520	4	empire	empire	NOUN
ejpam-5189	520	5	!	!	PUNCT
ejpam-5189	521	1	scientific	scientific	ADJ
ejpam-5189	521	2	american	american	PROPN
ejpam-5189	521	3	,	,	PUNCT
ejpam-5189	521	4	281(6):136–138	281(6):136–138	PROPN
ejpam-5189	521	5	,	,	PUNCT
ejpam-5189	521	6	1999	1999	NUM
ejpam-5189	521	7	.	.	PUNCT