id	sid	tid	token	lemma	pos
ejpam-4862	1	1	european	european	PROPN
ejpam-4862	1	2	journal	journal	PROPN
ejpam-4862	1	3	of	of	ADP
ejpam-4862	1	4	pure	pure	ADJ
ejpam-4862	1	5	and	and	CCONJ
ejpam-4862	1	6	applied	apply	VERB
ejpam-4862	1	7	mathematics	mathematic	NOUN
ejpam-4862	1	8	vol	vol	NOUN
ejpam-4862	1	9	.	.	PUNCT
ejpam-4862	2	1	16	16	NUM
ejpam-4862	2	2	,	,	PUNCT
ejpam-4862	2	3	no	no	INTJ
ejpam-4862	2	4	.	.	NOUN
ejpam-4862	2	5	4	4	NUM
ejpam-4862	2	6	,	,	PUNCT
ejpam-4862	2	7	2023	2023	NUM
ejpam-4862	2	8	,	,	PUNCT
ejpam-4862	2	9	2035	2035	NUM
ejpam-4862	2	10	-	-	SYM
ejpam-4862	2	11	2048	2048	NUM
ejpam-4862	2	12	issn	issn	PROPN
ejpam-4862	2	13	1307	1307	NUM
ejpam-4862	2	14	-	-	SYM
ejpam-4862	2	15	5543	5543	NUM
ejpam-4862	2	16	–	–	PUNCT
ejpam-4862	2	17	ejpam.com	ejpam.com	X
ejpam-4862	2	18	published	publish	VERB
ejpam-4862	2	19	by	by	ADP
ejpam-4862	2	20	new	new	PROPN
ejpam-4862	2	21	york	york	PROPN
ejpam-4862	2	22	business	business	PROPN
ejpam-4862	2	23	global	global	ADJ
ejpam-4862	2	24	outer	outer	ADJ
ejpam-4862	2	25	-	-	PUNCT
ejpam-4862	2	26	convex	convex	NOUN
ejpam-4862	2	27	hop	hop	NOUN
ejpam-4862	2	28	domination	domination	NOUN
ejpam-4862	2	29	in	in	ADP
ejpam-4862	2	30	graphs	graph	NOUN
ejpam-4862	2	31	under	under	ADP
ejpam-4862	2	32	some	some	DET
ejpam-4862	2	33	binary	binary	ADJ
ejpam-4862	2	34	operations	operation	NOUN
ejpam-4862	2	35	al	al	PROPN
ejpam-4862	2	36	-	-	PROPN
ejpam-4862	2	37	amin	amin	PROPN
ejpam-4862	2	38	y.	y.	PROPN
ejpam-4862	2	39	isahac1	isahac1	PROPN
ejpam-4862	2	40	,	,	PUNCT
ejpam-4862	2	41	javier	javier	PROPN
ejpam-4862	2	42	a.	a.	PROPN
ejpam-4862	2	43	hassan1,∗	hassan1,∗	PROPN
ejpam-4862	2	44	,	,	PUNCT
ejpam-4862	2	45	ladznar	ladznar	ADJ
ejpam-4862	2	46	s.	s.	PROPN
ejpam-4862	2	47	laja1	laja1	PROPN
ejpam-4862	2	48	,	,	PUNCT
ejpam-4862	2	49	hounam	hounam	PROPN
ejpam-4862	2	50	b.	b.	PROPN
ejpam-4862	2	51	copel1	copel1	PROPN
ejpam-4862	2	52	1	1	NUM
ejpam-4862	2	53	mathematics	mathematic	NOUN
ejpam-4862	2	54	and	and	CCONJ
ejpam-4862	2	55	sciences	sciences	PROPN
ejpam-4862	2	56	department	department	PROPN
ejpam-4862	2	57	,	,	PUNCT
ejpam-4862	2	58	college	college	NOUN
ejpam-4862	2	59	of	of	ADP
ejpam-4862	2	60	arts	art	NOUN
ejpam-4862	2	61	and	and	CCONJ
ejpam-4862	2	62	sciences	science	NOUN
ejpam-4862	2	63	,	,	PUNCT
ejpam-4862	2	64	msu	msu	PROPN
ejpam-4862	2	65	tawi	tawi	PROPN
ejpam-4862	2	66	-	-	PUNCT
ejpam-4862	2	67	tawi	tawi	PROPN
ejpam-4862	2	68	college	college	PROPN
ejpam-4862	2	69	of	of	ADP
ejpam-4862	2	70	technology	technology	NOUN
ejpam-4862	2	71	and	and	CCONJ
ejpam-4862	2	72	oceanography	oceanography	NOUN
ejpam-4862	2	73	,	,	PUNCT
ejpam-4862	2	74	bongao	bongao	NOUN
ejpam-4862	2	75	,	,	PUNCT
ejpam-4862	2	76	tawi	tawi	NOUN
ejpam-4862	2	77	-	-	PUNCT
ejpam-4862	2	78	tawi	tawi	NOUN
ejpam-4862	2	79	,	,	PUNCT
ejpam-4862	2	80	philippines	philippine	NOUN
ejpam-4862	2	81	abstract	abstract	ADJ
ejpam-4862	2	82	.	.	PUNCT
ejpam-4862	3	1	let	let	VERB
ejpam-4862	3	2	g	g	PRON
ejpam-4862	3	3	be	be	AUX
ejpam-4862	3	4	a	a	DET
ejpam-4862	3	5	graph	graph	NOUN
ejpam-4862	3	6	with	with	ADP
ejpam-4862	3	7	vertex	vertex	NOUN
ejpam-4862	3	8	and	and	CCONJ
ejpam-4862	3	9	edge	edge	NOUN
ejpam-4862	3	10	sets	set	NOUN
ejpam-4862	3	11	v	v	ADP
ejpam-4862	3	12	(	(	PUNCT
ejpam-4862	3	13	g	g	NOUN
ejpam-4862	3	14	)	)	PUNCT
ejpam-4862	3	15	and	and	CCONJ
ejpam-4862	3	16	e(g	e(g	PROPN
ejpam-4862	3	17	)	)	PUNCT
ejpam-4862	3	18	,	,	PUNCT
ejpam-4862	3	19	respectively	respectively	ADV
ejpam-4862	3	20	.	.	PUNCT
ejpam-4862	4	1	a	a	DET
ejpam-4862	4	2	set	set	NOUN
ejpam-4862	4	3	c	c	NOUN
ejpam-4862	4	4	⊆	⊆	NUM
ejpam-4862	4	5	v	v	NOUN
ejpam-4862	4	6	(	(	PUNCT
ejpam-4862	4	7	g	g	NOUN
ejpam-4862	4	8	)	)	PUNCT
ejpam-4862	4	9	is	be	AUX
ejpam-4862	4	10	called	call	VERB
ejpam-4862	4	11	an	an	DET
ejpam-4862	4	12	outer	outer	ADJ
ejpam-4862	4	13	-	-	PUNCT
ejpam-4862	4	14	convex	convex	NOUN
ejpam-4862	4	15	hop	hop	NOUN
ejpam-4862	4	16	dominating	dominating	NOUN
ejpam-4862	4	17	if	if	SCONJ
ejpam-4862	4	18	for	for	ADP
ejpam-4862	4	19	every	every	DET
ejpam-4862	4	20	two	two	NUM
ejpam-4862	4	21	vertices	vertex	NOUN
ejpam-4862	4	22	x	x	X
ejpam-4862	4	23	,	,	PUNCT
ejpam-4862	4	24	y	y	PROPN
ejpam-4862	4	25	∈	∈	PROPN
ejpam-4862	4	26	v	v	ADP
ejpam-4862	4	27	(	(	PUNCT
ejpam-4862	4	28	g	g	NOUN
ejpam-4862	4	29	)	)	PUNCT
ejpam-4862	4	30	\	\	PUNCT
ejpam-4862	5	1	c	c	X
ejpam-4862	5	2	,	,	PUNCT
ejpam-4862	5	3	the	the	DET
ejpam-4862	5	4	vertex	vertex	NOUN
ejpam-4862	5	5	set	set	NOUN
ejpam-4862	5	6	of	of	ADP
ejpam-4862	5	7	every	every	DET
ejpam-4862	5	8	x−	x−	PROPN
ejpam-4862	5	9	y	y	PROPN
ejpam-4862	5	10	geodesic	geodesic	NOUN
ejpam-4862	5	11	is	be	AUX
ejpam-4862	5	12	contained	contain	VERB
ejpam-4862	5	13	in	in	ADP
ejpam-4862	5	14	v	v	NUM
ejpam-4862	5	15	(	(	PUNCT
ejpam-4862	5	16	g	g	NOUN
ejpam-4862	5	17	)	)	PUNCT
ejpam-4862	5	18	\c	\c	NOUN
ejpam-4862	5	19	and	and	CCONJ
ejpam-4862	5	20	for	for	ADP
ejpam-4862	5	21	every	every	DET
ejpam-4862	5	22	a	a	DET
ejpam-4862	5	23	∈	∈	PROPN
ejpam-4862	5	24	v	v	NOUN
ejpam-4862	5	25	(	(	PUNCT
ejpam-4862	5	26	g	g	NOUN
ejpam-4862	5	27	)	)	PUNCT
ejpam-4862	5	28	\c	\c	NOUN
ejpam-4862	5	29	,	,	PUNCT
ejpam-4862	5	30	there	there	PRON
ejpam-4862	5	31	exists	exist	VERB
ejpam-4862	5	32	b	b	PROPN
ejpam-4862	5	33	∈	∈	PROPN
ejpam-4862	5	34	c	c	NOUN
ejpam-4862	5	35	such	such	ADJ
ejpam-4862	5	36	that	that	PRON
ejpam-4862	6	1	dg(a	dg(a	PROPN
ejpam-4862	6	2	,	,	PUNCT
ejpam-4862	6	3	b	b	X
ejpam-4862	6	4	)	)	PUNCT
ejpam-4862	6	5	=	=	SYM
ejpam-4862	6	6	2	2	X
ejpam-4862	6	7	.	.	PUNCT
ejpam-4862	7	1	the	the	DET
ejpam-4862	7	2	minimum	minimum	ADJ
ejpam-4862	7	3	cardinality	cardinality	NOUN
ejpam-4862	7	4	of	of	ADP
ejpam-4862	7	5	an	an	DET
ejpam-4862	7	6	outer	outer	ADJ
ejpam-4862	7	7	-	-	PUNCT
ejpam-4862	7	8	convex	convex	NOUN
ejpam-4862	7	9	hop	hop	NOUN
ejpam-4862	7	10	dominating	dominating	NOUN
ejpam-4862	7	11	set	set	NOUN
ejpam-4862	7	12	of	of	ADP
ejpam-4862	7	13	g	g	NOUN
ejpam-4862	7	14	,	,	PUNCT
ejpam-4862	7	15	denoted	denote	VERB
ejpam-4862	7	16	by	by	ADP
ejpam-4862	7	17	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	7	18	)	)	PUNCT
ejpam-4862	7	19	,	,	PUNCT
ejpam-4862	7	20	is	be	AUX
ejpam-4862	7	21	called	call	VERB
ejpam-4862	7	22	the	the	DET
ejpam-4862	7	23	outer	outer	ADJ
ejpam-4862	7	24	-	-	PUNCT
ejpam-4862	7	25	convex	convex	NOUN
ejpam-4862	7	26	hop	hop	NOUN
ejpam-4862	7	27	domination	domination	NOUN
ejpam-4862	7	28	number	number	NOUN
ejpam-4862	7	29	of	of	ADP
ejpam-4862	7	30	g.	g.	PROPN
ejpam-4862	7	31	in	in	ADP
ejpam-4862	7	32	this	this	DET
ejpam-4862	7	33	paper	paper	NOUN
ejpam-4862	7	34	,	,	PUNCT
ejpam-4862	7	35	we	we	PRON
ejpam-4862	7	36	generate	generate	VERB
ejpam-4862	7	37	some	some	DET
ejpam-4862	7	38	formulas	formula	NOUN
ejpam-4862	7	39	for	for	ADP
ejpam-4862	7	40	the	the	DET
ejpam-4862	7	41	parameters	parameter	NOUN
ejpam-4862	7	42	of	of	ADP
ejpam-4862	7	43	some	some	DET
ejpam-4862	7	44	special	special	ADJ
ejpam-4862	7	45	graphs	graph	NOUN
ejpam-4862	7	46	and	and	CCONJ
ejpam-4862	7	47	graphs	graph	NOUN
ejpam-4862	7	48	under	under	ADP
ejpam-4862	7	49	some	some	DET
ejpam-4862	7	50	binary	binary	ADJ
ejpam-4862	7	51	operations	operation	NOUN
ejpam-4862	7	52	by	by	ADP
ejpam-4862	7	53	characterizing	characterize	VERB
ejpam-4862	7	54	first	first	ADV
ejpam-4862	7	55	the	the	DET
ejpam-4862	7	56	outer	outer	ADJ
ejpam-4862	7	57	-	-	PUNCT
ejpam-4862	7	58	convex	convex	NOUN
ejpam-4862	7	59	hop	hop	NOUN
ejpam-4862	7	60	dominating	dominating	NOUN
ejpam-4862	7	61	sets	set	NOUN
ejpam-4862	7	62	of	of	ADP
ejpam-4862	7	63	each	each	PRON
ejpam-4862	7	64	of	of	ADP
ejpam-4862	7	65	these	these	DET
ejpam-4862	7	66	graphs	graph	NOUN
ejpam-4862	7	67	.	.	PUNCT
ejpam-4862	8	1	moreover	moreover	ADV
ejpam-4862	8	2	,	,	PUNCT
ejpam-4862	8	3	we	we	PRON
ejpam-4862	8	4	establish	establish	VERB
ejpam-4862	8	5	realization	realization	NOUN
ejpam-4862	8	6	result	result	NOUN
ejpam-4862	8	7	that	that	SCONJ
ejpam-4862	8	8	identifies	identify	VERB
ejpam-4862	8	9	and	and	CCONJ
ejpam-4862	8	10	determines	determine	VERB
ejpam-4862	8	11	the	the	DET
ejpam-4862	8	12	connection	connection	NOUN
ejpam-4862	8	13	of	of	ADP
ejpam-4862	8	14	this	this	DET
ejpam-4862	8	15	parameter	parameter	NOUN
ejpam-4862	8	16	with	with	ADP
ejpam-4862	8	17	the	the	DET
ejpam-4862	8	18	standard	standard	ADJ
ejpam-4862	8	19	hop	hop	PROPN
ejpam-4862	8	20	domination	domination	NOUN
ejpam-4862	8	21	parameter	parameter	NOUN
ejpam-4862	8	22	.	.	PUNCT
ejpam-4862	9	1	it	it	PRON
ejpam-4862	9	2	shows	show	VERB
ejpam-4862	9	3	that	that	SCONJ
ejpam-4862	9	4	given	give	VERB
ejpam-4862	9	5	any	any	DET
ejpam-4862	9	6	graph	graph	NOUN
ejpam-4862	9	7	,	,	PUNCT
ejpam-4862	9	8	this	this	DET
ejpam-4862	9	9	new	new	ADJ
ejpam-4862	9	10	parameter	parameter	NOUN
ejpam-4862	9	11	is	be	AUX
ejpam-4862	9	12	always	always	ADV
ejpam-4862	9	13	greater	great	ADJ
ejpam-4862	9	14	than	than	ADP
ejpam-4862	9	15	or	or	CCONJ
ejpam-4862	9	16	equal	equal	ADJ
ejpam-4862	9	17	to	to	ADP
ejpam-4862	9	18	the	the	DET
ejpam-4862	9	19	standard	standard	ADJ
ejpam-4862	9	20	hop	hop	PROPN
ejpam-4862	9	21	domination	domination	NOUN
ejpam-4862	9	22	parameter	parameter	NOUN
ejpam-4862	9	23	.	.	PUNCT
ejpam-4862	10	1	2020	2020	NUM
ejpam-4862	10	2	mathematics	mathematic	NOUN
ejpam-4862	10	3	subject	subject	NOUN
ejpam-4862	10	4	classifications	classification	NOUN
ejpam-4862	10	5	:	:	PUNCT
ejpam-4862	10	6	05c69	05c69	X
ejpam-4862	10	7	key	key	ADJ
ejpam-4862	10	8	words	word	NOUN
ejpam-4862	10	9	and	and	CCONJ
ejpam-4862	10	10	phrases	phrase	NOUN
ejpam-4862	10	11	:	:	PUNCT
ejpam-4862	10	12	outer	outer	ADJ
ejpam-4862	10	13	-	-	PUNCT
ejpam-4862	10	14	convex	convex	NOUN
ejpam-4862	10	15	set	set	NOUN
ejpam-4862	10	16	,	,	PUNCT
ejpam-4862	10	17	outer	outer	ADJ
ejpam-4862	10	18	-	-	PUNCT
ejpam-4862	10	19	convex	convex	NOUN
ejpam-4862	10	20	hop	hop	NOUN
ejpam-4862	10	21	dominating	dominating	NOUN
ejpam-4862	10	22	set	set	NOUN
ejpam-4862	10	23	,	,	PUNCT
ejpam-4862	10	24	outer	outer	ADJ
ejpam-4862	10	25	-	-	PUNCT
ejpam-4862	10	26	convex	convex	NOUN
ejpam-4862	10	27	hop	hop	NOUN
ejpam-4862	10	28	domination	domination	NOUN
ejpam-4862	10	29	number	number	NOUN
ejpam-4862	10	30	1	1	NUM
ejpam-4862	10	31	.	.	PUNCT
ejpam-4862	10	32	introduction	introduction	NOUN
ejpam-4862	10	33	a	a	DET
ejpam-4862	10	34	subset	subset	NOUN
ejpam-4862	10	35	s	s	NOUN
ejpam-4862	10	36	of	of	ADP
ejpam-4862	10	37	a	a	DET
ejpam-4862	10	38	vertex	vertex	NOUN
ejpam-4862	10	39	set	set	NOUN
ejpam-4862	10	40	of	of	ADP
ejpam-4862	10	41	a	a	DET
ejpam-4862	10	42	simple	simple	ADJ
ejpam-4862	10	43	graph	graph	NOUN
ejpam-4862	10	44	g	g	NOUN
ejpam-4862	10	45	is	be	AUX
ejpam-4862	10	46	called	call	VERB
ejpam-4862	10	47	a	a	DET
ejpam-4862	10	48	hop	hop	NOUN
ejpam-4862	10	49	dominating	dominating	NOUN
ejpam-4862	10	50	in	in	ADP
ejpam-4862	10	51	g	g	PROPN
ejpam-4862	10	52	if	if	SCONJ
ejpam-4862	10	53	n2	n2	ADJ
ejpam-4862	10	54	g[s	g[s	PROPN
ejpam-4862	10	55	]	]	X
ejpam-4862	10	56	=	=	SYM
ejpam-4862	10	57	v	v	NOUN
ejpam-4862	10	58	(	(	PUNCT
ejpam-4862	10	59	g	g	NOUN
ejpam-4862	10	60	)	)	PUNCT
ejpam-4862	10	61	,	,	PUNCT
ejpam-4862	10	62	that	that	ADV
ejpam-4862	10	63	is	is	ADV
ejpam-4862	10	64	,	,	PUNCT
ejpam-4862	10	65	for	for	ADP
ejpam-4862	10	66	every	every	PRON
ejpam-4862	10	67	v	v	NUM
ejpam-4862	10	68	∈	∈	PROPN
ejpam-4862	10	69	v	v	NOUN
ejpam-4862	10	70	(	(	PUNCT
ejpam-4862	10	71	g	g	NOUN
ejpam-4862	10	72	)	)	PUNCT
ejpam-4862	10	73	\	\	PROPN
ejpam-4862	11	1	s	s	X
ejpam-4862	11	2	,	,	PUNCT
ejpam-4862	11	3	there	there	PRON
ejpam-4862	11	4	exists	exist	VERB
ejpam-4862	11	5	u	u	PROPN
ejpam-4862	11	6	∈	∈	PROPN
ejpam-4862	11	7	s	s	VERB
ejpam-4862	11	8	such	such	ADJ
ejpam-4862	11	9	that	that	DET
ejpam-4862	11	10	dg(u	dg(u	ADJ
ejpam-4862	11	11	,	,	PUNCT
ejpam-4862	11	12	v	v	NOUN
ejpam-4862	11	13	)	)	PUNCT
ejpam-4862	11	14	=	=	SYM
ejpam-4862	11	15	2	2	X
ejpam-4862	11	16	.	.	PUNCT
ejpam-4862	11	17	the	the	DET
ejpam-4862	11	18	minimum	minimum	ADJ
ejpam-4862	11	19	cardinality	cardinality	NOUN
ejpam-4862	11	20	among	among	ADP
ejpam-4862	11	21	all	all	DET
ejpam-4862	11	22	hop	hop	NOUN
ejpam-4862	11	23	dominating	dominating	NOUN
ejpam-4862	11	24	sets	set	NOUN
ejpam-4862	11	25	in	in	ADP
ejpam-4862	11	26	g	g	NOUN
ejpam-4862	11	27	,	,	PUNCT
ejpam-4862	11	28	denoted	denote	VERB
ejpam-4862	11	29	by	by	ADP
ejpam-4862	11	30	γh(g	γh(g	NOUN
ejpam-4862	11	31	)	)	PUNCT
ejpam-4862	11	32	,	,	PUNCT
ejpam-4862	11	33	is	be	AUX
ejpam-4862	11	34	called	call	VERB
ejpam-4862	11	35	the	the	DET
ejpam-4862	11	36	hop	hop	NOUN
ejpam-4862	11	37	domination	domination	NOUN
ejpam-4862	11	38	number	number	NOUN
ejpam-4862	11	39	of	of	ADP
ejpam-4862	11	40	g.	g.	PROPN
ejpam-4862	11	41	this	this	DET
ejpam-4862	11	42	concept	concept	NOUN
ejpam-4862	11	43	was	be	AUX
ejpam-4862	11	44	introduced	introduce	VERB
ejpam-4862	11	45	and	and	CCONJ
ejpam-4862	11	46	investigated	investigate	VERB
ejpam-4862	11	47	by	by	ADP
ejpam-4862	11	48	natarajan	natarajan	PROPN
ejpam-4862	11	49	et	et	PROPN
ejpam-4862	11	50	al	al	PROPN
ejpam-4862	11	51	.	.	PUNCT
ejpam-4862	12	1	in	in	ADP
ejpam-4862	12	2	[	[	X
ejpam-4862	12	3	11	11	NUM
ejpam-4862	12	4	]	]	PUNCT
ejpam-4862	12	5	.	.	PUNCT
ejpam-4862	13	1	they	they	PRON
ejpam-4862	13	2	have	have	AUX
ejpam-4862	13	3	studied	study	VERB
ejpam-4862	13	4	this	this	DET
ejpam-4862	13	5	concept	concept	NOUN
ejpam-4862	13	6	on	on	ADP
ejpam-4862	13	7	some	some	DET
ejpam-4862	13	8	types	type	NOUN
ejpam-4862	13	9	of	of	ADP
ejpam-4862	13	10	graphs	graph	NOUN
ejpam-4862	13	11	and	and	CCONJ
ejpam-4862	13	12	generated	generate	VERB
ejpam-4862	13	13	some	some	DET
ejpam-4862	13	14	interesting	interesting	ADJ
ejpam-4862	13	15	results	result	NOUN
ejpam-4862	13	16	.	.	PUNCT
ejpam-4862	14	1	some	some	DET
ejpam-4862	14	2	extreme	extreme	ADJ
ejpam-4862	14	3	values	value	NOUN
ejpam-4862	14	4	and	and	CCONJ
ejpam-4862	14	5	properties	property	NOUN
ejpam-4862	14	6	of	of	ADP
ejpam-4862	14	7	the	the	DET
ejpam-4862	14	8	said	say	VERB
ejpam-4862	14	9	parameter	parameter	NOUN
ejpam-4862	14	10	can	can	AUX
ejpam-4862	14	11	be	be	AUX
ejpam-4862	14	12	found	find	VERB
ejpam-4862	14	13	in	in	ADP
ejpam-4862	14	14	[	[	X
ejpam-4862	14	15	1	1	NUM
ejpam-4862	14	16	,	,	PUNCT
ejpam-4862	14	17	2	2	NUM
ejpam-4862	14	18	,	,	PUNCT
ejpam-4862	14	19	11	11	NUM
ejpam-4862	14	20	]	]	PUNCT
ejpam-4862	14	21	.	.	PUNCT
ejpam-4862	15	1	recently	recently	ADV
ejpam-4862	15	2	,	,	PUNCT
ejpam-4862	15	3	canoy	canoy	PROPN
ejpam-4862	15	4	et	et	PROPN
ejpam-4862	15	5	al	al	PROPN
ejpam-4862	15	6	.	.	PUNCT
ejpam-4862	16	1	[	[	X
ejpam-4862	16	2	9	9	NUM
ejpam-4862	16	3	]	]	PUNCT
ejpam-4862	16	4	investigated	investigate	VERB
ejpam-4862	16	5	hop	hop	NOUN
ejpam-4862	16	6	domination	domination	NOUN
ejpam-4862	16	7	parameter	parameter	NOUN
ejpam-4862	16	8	on	on	ADP
ejpam-4862	16	9	graphs	graph	NOUN
ejpam-4862	16	10	under	under	ADP
ejpam-4862	16	11	some	some	DET
ejpam-4862	16	12	binary	binary	ADJ
ejpam-4862	16	13	operations	operation	NOUN
ejpam-4862	16	14	.	.	PUNCT
ejpam-4862	17	1	∗corresponding	∗corresponde	VERB
ejpam-4862	17	2	author	author	NOUN
ejpam-4862	17	3	.	.	PUNCT
ejpam-4862	18	1	doi	doi	NOUN
ejpam-4862	18	2	:	:	PUNCT
ejpam-4862	18	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4862	https://doi.org/10.29020/nybg.ejpam.v16i4.4862	NOUN
ejpam-4862	18	4	email	email	NOUN
ejpam-4862	18	5	addresses	address	VERB
ejpam-4862	18	6	:	:	PUNCT
ejpam-4862	18	7	al-aminisahac@msutawi-tawi.edu.ph	al-aminisahac@msutawi-tawi.edu.ph	PROPN
ejpam-4862	18	8	(	(	PUNCT
ejpam-4862	18	9	a.	a.	NOUN
ejpam-4862	18	10	isahac	isahac	PROPN
ejpam-4862	18	11	)	)	PUNCT
ejpam-4862	19	1	javierhassan@msutawi-tawi.edu.ph	javierhassan@msutawi-tawi.edu.ph	PROPN
ejpam-4862	19	2	(	(	PUNCT
ejpam-4862	19	3	j.	j.	PROPN
ejpam-4862	19	4	hassan	hassan	PROPN
ejpam-4862	19	5	)	)	PUNCT
ejpam-4862	19	6	,	,	PUNCT
ejpam-4862	19	7	ladznarlaja@msutawi-tawi.edu.ph	ladznarlaja@msutawi-tawi.edu.ph	PROPN
ejpam-4862	19	8	(	(	PUNCT
ejpam-4862	19	9	l.	l.	PROPN
ejpam-4862	19	10	laja	laja	PROPN
ejpam-4862	19	11	)	)	PUNCT
ejpam-4862	19	12	hounamcopel@msutawi-tawi.edu.ph	hounamcopel@msutawi-tawi.edu.ph	PROPN
ejpam-4862	19	13	(	(	PUNCT
ejpam-4862	19	14	h.	h.	PROPN
ejpam-4862	19	15	copel	copel	PROPN
ejpam-4862	19	16	)	)	PUNCT
ejpam-4862	19	17	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4862	19	18	2035	2035	NUM
ejpam-4862	19	19	©	©	ADP
ejpam-4862	19	20	2023	2023	NUM
ejpam-4862	19	21	ejpam	ejpam	NOUN
ejpam-4862	19	22	all	all	DET
ejpam-4862	19	23	rights	right	NOUN
ejpam-4862	19	24	reserved	reserve	VERB
ejpam-4862	19	25	.	.	PUNCT
ejpam-4862	20	1	j.	j.	PROPN
ejpam-4862	20	2	a.	a.	PROPN
ejpam-4862	20	3	hassan	hassan	PROPN
ejpam-4862	20	4	et	et	PROPN
ejpam-4862	20	5	al	al	PROPN
ejpam-4862	20	6	.	.	PUNCT
ejpam-4862	20	7	/	/	SYM
ejpam-4862	20	8	eur	eur	PROPN
ejpam-4862	20	9	.	.	PUNCT
ejpam-4862	21	1	j.	j.	PROPN
ejpam-4862	21	2	pure	pure	PROPN
ejpam-4862	21	3	appl	appl	PROPN
ejpam-4862	21	4	.	.	PROPN
ejpam-4862	21	5	math	math	PROPN
ejpam-4862	21	6	,	,	PUNCT
ejpam-4862	21	7	16	16	NUM
ejpam-4862	21	8	(	(	PUNCT
ejpam-4862	21	9	4	4	NUM
ejpam-4862	21	10	)	)	PUNCT
ejpam-4862	21	11	(	(	PUNCT
ejpam-4862	21	12	2023	2023	NUM
ejpam-4862	21	13	)	)	PUNCT
ejpam-4862	21	14	,	,	PUNCT
ejpam-4862	21	15	2035	2035	NUM
ejpam-4862	21	16	-	-	SYM
ejpam-4862	21	17	2048	2048	NUM
ejpam-4862	21	18	2036	2036	NUM
ejpam-4862	21	19	because	because	SCONJ
ejpam-4862	21	20	of	of	ADP
ejpam-4862	21	21	its	its	PRON
ejpam-4862	21	22	nice	nice	ADJ
ejpam-4862	21	23	application	application	NOUN
ejpam-4862	21	24	in	in	ADP
ejpam-4862	21	25	networks	network	NOUN
ejpam-4862	21	26	and	and	CCONJ
ejpam-4862	21	27	different	different	ADJ
ejpam-4862	21	28	fields	field	NOUN
ejpam-4862	22	1	,	,	PUNCT
ejpam-4862	22	2	researchers	researcher	NOUN
ejpam-4862	22	3	have	have	AUX
ejpam-4862	22	4	introduced	introduce	VERB
ejpam-4862	22	5	variants	variant	NOUN
ejpam-4862	22	6	of	of	ADP
ejpam-4862	22	7	hop	hop	NOUN
ejpam-4862	22	8	domination	domination	NOUN
ejpam-4862	22	9	and	and	CCONJ
ejpam-4862	22	10	they	they	PRON
ejpam-4862	22	11	studied	study	VERB
ejpam-4862	22	12	these	these	DET
ejpam-4862	22	13	variants	variant	NOUN
ejpam-4862	22	14	for	for	ADP
ejpam-4862	22	15	some	some	DET
ejpam-4862	22	16	special	special	ADJ
ejpam-4862	22	17	graphs	graph	NOUN
ejpam-4862	22	18	and	and	CCONJ
ejpam-4862	22	19	graphs	graph	NOUN
ejpam-4862	22	20	under	under	ADP
ejpam-4862	22	21	some	some	DET
ejpam-4862	22	22	operations	operation	NOUN
ejpam-4862	22	23	.	.	PUNCT
ejpam-4862	23	1	(	(	PUNCT
ejpam-4862	23	2	see	see	VERB
ejpam-4862	23	3	[	[	X
ejpam-4862	23	4	3–7	3–7	NOUN
ejpam-4862	23	5	,	,	PUNCT
ejpam-4862	23	6	10	10	NUM
ejpam-4862	23	7	,	,	PUNCT
ejpam-4862	23	8	12	12	NUM
ejpam-4862	23	9	]	]	PUNCT
ejpam-4862	23	10	)	)	PUNCT
ejpam-4862	23	11	.	.	PUNCT
ejpam-4862	24	1	in	in	ADP
ejpam-4862	24	2	this	this	DET
ejpam-4862	24	3	paper	paper	NOUN
ejpam-4862	24	4	,	,	PUNCT
ejpam-4862	24	5	we	we	PRON
ejpam-4862	24	6	will	will	AUX
ejpam-4862	24	7	introduce	introduce	VERB
ejpam-4862	24	8	new	new	ADJ
ejpam-4862	24	9	variant	variant	NOUN
ejpam-4862	24	10	of	of	ADP
ejpam-4862	24	11	hop	hop	NOUN
ejpam-4862	24	12	domination	domination	NOUN
ejpam-4862	24	13	called	call	VERB
ejpam-4862	24	14	outer	outer	ADJ
ejpam-4862	24	15	-	-	PUNCT
ejpam-4862	24	16	convex	convex	ADJ
ejpam-4862	24	17	hop	hop	NOUN
ejpam-4862	24	18	domination	domination	NOUN
ejpam-4862	24	19	.	.	PUNCT
ejpam-4862	25	1	this	this	DET
ejpam-4862	25	2	study	study	NOUN
ejpam-4862	25	3	is	be	AUX
ejpam-4862	25	4	motivated	motivate	VERB
ejpam-4862	25	5	by	by	ADP
ejpam-4862	25	6	the	the	DET
ejpam-4862	25	7	introduction	introduction	NOUN
ejpam-4862	25	8	of	of	ADP
ejpam-4862	25	9	convex	convex	PROPN
ejpam-4862	25	10	hop	hop	NOUN
ejpam-4862	25	11	domination	domination	NOUN
ejpam-4862	25	12	in	in	ADP
ejpam-4862	25	13	[	[	X
ejpam-4862	25	14	5	5	NUM
ejpam-4862	25	15	]	]	PUNCT
ejpam-4862	25	16	.	.	PUNCT
ejpam-4862	26	1	we	we	PRON
ejpam-4862	26	2	will	will	AUX
ejpam-4862	26	3	investigate	investigate	VERB
ejpam-4862	26	4	this	this	DET
ejpam-4862	26	5	concept	concept	NOUN
ejpam-4862	26	6	on	on	ADP
ejpam-4862	26	7	some	some	DET
ejpam-4862	26	8	classes	class	NOUN
ejpam-4862	26	9	of	of	ADP
ejpam-4862	26	10	graphs	graph	NOUN
ejpam-4862	26	11	,	,	PUNCT
ejpam-4862	26	12	and	and	CCONJ
ejpam-4862	26	13	join	join	VERB
ejpam-4862	26	14	and	and	CCONJ
ejpam-4862	26	15	corona	corona	NOUN
ejpam-4862	26	16	of	of	ADP
ejpam-4862	26	17	two	two	NUM
ejpam-4862	26	18	graphs	graph	NOUN
ejpam-4862	26	19	.	.	PUNCT
ejpam-4862	27	1	we	we	PRON
ejpam-4862	27	2	believe	believe	VERB
ejpam-4862	27	3	that	that	SCONJ
ejpam-4862	27	4	this	this	DET
ejpam-4862	27	5	new	new	ADJ
ejpam-4862	27	6	parameter	parameter	NOUN
ejpam-4862	27	7	and	and	CCONJ
ejpam-4862	27	8	its	its	PRON
ejpam-4862	27	9	results	result	NOUN
ejpam-4862	27	10	can	can	AUX
ejpam-4862	27	11	lead	lead	VERB
ejpam-4862	27	12	to	to	ADP
ejpam-4862	27	13	other	other	ADJ
ejpam-4862	27	14	interesting	interesting	ADJ
ejpam-4862	27	15	research	research	NOUN
ejpam-4862	27	16	directions	direction	NOUN
ejpam-4862	27	17	in	in	ADP
ejpam-4862	27	18	the	the	DET
ejpam-4862	27	19	future	future	NOUN
ejpam-4862	27	20	.	.	PUNCT
ejpam-4862	28	1	2	2	X
ejpam-4862	28	2	.	.	X
ejpam-4862	28	3	terminology	terminology	NOUN
ejpam-4862	28	4	and	and	CCONJ
ejpam-4862	28	5	notation	notation	NOUN
ejpam-4862	28	6	let	let	VERB
ejpam-4862	28	7	g	g	PROPN
ejpam-4862	28	8	=	=	SYM
ejpam-4862	28	9	v	v	PROPN
ejpam-4862	28	10	(	(	PUNCT
ejpam-4862	28	11	g	g	NOUN
ejpam-4862	28	12	)	)	PUNCT
ejpam-4862	28	13	,	,	PUNCT
ejpam-4862	28	14	e(g	e(g	PROPN
ejpam-4862	28	15	)	)	PUNCT
ejpam-4862	28	16	)	)	PUNCT
ejpam-4862	28	17	be	be	AUX
ejpam-4862	28	18	an	an	DET
ejpam-4862	28	19	undirected	undirected	ADJ
ejpam-4862	28	20	graph	graph	NOUN
ejpam-4862	28	21	.	.	PUNCT
ejpam-4862	29	1	given	give	VERB
ejpam-4862	29	2	two	two	NUM
ejpam-4862	29	3	vertices	vertex	NOUN
ejpam-4862	29	4	u	u	NOUN
ejpam-4862	29	5	and	and	CCONJ
ejpam-4862	29	6	v	v	NOUN
ejpam-4862	29	7	of	of	ADP
ejpam-4862	29	8	g	g	NOUN
ejpam-4862	29	9	,	,	PUNCT
ejpam-4862	29	10	the	the	DET
ejpam-4862	29	11	distance	distance	NOUN
ejpam-4862	29	12	dg(u	dg(u	X
ejpam-4862	29	13	,	,	PUNCT
ejpam-4862	29	14	v	v	NOUN
ejpam-4862	29	15	)	)	PUNCT
ejpam-4862	29	16	is	be	AUX
ejpam-4862	29	17	the	the	DET
ejpam-4862	29	18	length	length	NOUN
ejpam-4862	29	19	of	of	ADP
ejpam-4862	29	20	a	a	DET
ejpam-4862	29	21	shortest	short	ADJ
ejpam-4862	29	22	path	path	NOUN
ejpam-4862	29	23	joining	join	VERB
ejpam-4862	29	24	u	u	NOUN
ejpam-4862	29	25	and	and	CCONJ
ejpam-4862	29	26	v.	v.	ADP
ejpam-4862	29	27	any	any	DET
ejpam-4862	29	28	u	u	NOUN
ejpam-4862	29	29	-	-	NOUN
ejpam-4862	29	30	v	v	ADJ
ejpam-4862	29	31	path	path	NOUN
ejpam-4862	29	32	of	of	ADP
ejpam-4862	29	33	length	length	NOUN
ejpam-4862	29	34	dg(u	dg(u	PROPN
ejpam-4862	29	35	,	,	PUNCT
ejpam-4862	29	36	v	v	NOUN
ejpam-4862	29	37	)	)	PUNCT
ejpam-4862	29	38	is	be	AUX
ejpam-4862	29	39	called	call	VERB
ejpam-4862	29	40	a	a	DET
ejpam-4862	29	41	u	u	NOUN
ejpam-4862	29	42	-	-	NOUN
ejpam-4862	29	43	v	v	ADJ
ejpam-4862	29	44	geodesic	geodesic	NOUN
ejpam-4862	29	45	.	.	PUNCT
ejpam-4862	30	1	the	the	DET
ejpam-4862	30	2	interval	interval	NOUN
ejpam-4862	30	3	ig	ig	PROPN
ejpam-4862	31	1	[	[	X
ejpam-4862	31	2	u	u	NOUN
ejpam-4862	31	3	,	,	PUNCT
ejpam-4862	31	4	v	v	NOUN
ejpam-4862	31	5	]	]	PUNCT
ejpam-4862	31	6	consists	consist	VERB
ejpam-4862	31	7	of	of	ADP
ejpam-4862	31	8	u	u	NOUN
ejpam-4862	31	9	,	,	PUNCT
ejpam-4862	31	10	v	v	NOUN
ejpam-4862	31	11	,	,	PUNCT
ejpam-4862	31	12	and	and	CCONJ
ejpam-4862	31	13	all	all	DET
ejpam-4862	31	14	vertices	vertex	NOUN
ejpam-4862	31	15	lying	lie	VERB
ejpam-4862	31	16	on	on	ADP
ejpam-4862	31	17	a	a	DET
ejpam-4862	31	18	u	u	NOUN
ejpam-4862	31	19	-	-	NOUN
ejpam-4862	31	20	v	v	ADJ
ejpam-4862	31	21	geodesic	geodesic	NOUN
ejpam-4862	31	22	.	.	PUNCT
ejpam-4862	32	1	the	the	DET
ejpam-4862	32	2	interval	interval	NOUN
ejpam-4862	32	3	ig(u	ig(u	NOUN
ejpam-4862	32	4	,	,	PUNCT
ejpam-4862	32	5	v	v	NOUN
ejpam-4862	32	6	)	)	PUNCT
ejpam-4862	32	7	=	=	PUNCT
ejpam-4862	33	1	ig	ig	PROPN
ejpam-4862	34	1	[	[	X
ejpam-4862	34	2	u	u	NOUN
ejpam-4862	34	3	,	,	PUNCT
ejpam-4862	34	4	v	v	ADP
ejpam-4862	34	5	]	]	PUNCT
ejpam-4862	34	6	\	\	NOUN
ejpam-4862	34	7	{	{	PUNCT
ejpam-4862	34	8	u	u	NOUN
ejpam-4862	34	9	,	,	PUNCT
ejpam-4862	34	10	v	v	NOUN
ejpam-4862	34	11	}	}	PUNCT
ejpam-4862	34	12	.	.	PUNCT
ejpam-4862	35	1	let	let	VERB
ejpam-4862	35	2	g	g	PRON
ejpam-4862	35	3	be	be	AUX
ejpam-4862	35	4	a	a	DET
ejpam-4862	35	5	graph	graph	NOUN
ejpam-4862	35	6	.	.	PUNCT
ejpam-4862	36	1	a	a	DET
ejpam-4862	36	2	set	set	NOUN
ejpam-4862	36	3	c	c	NOUN
ejpam-4862	36	4	⊆	⊆	NUM
ejpam-4862	36	5	v	v	NOUN
ejpam-4862	36	6	(	(	PUNCT
ejpam-4862	36	7	g	g	NOUN
ejpam-4862	36	8	)	)	PUNCT
ejpam-4862	36	9	is	be	AUX
ejpam-4862	36	10	called	call	VERB
ejpam-4862	36	11	a	a	DET
ejpam-4862	36	12	convex	convex	NOUN
ejpam-4862	36	13	if	if	SCONJ
ejpam-4862	36	14	for	for	ADP
ejpam-4862	36	15	every	every	DET
ejpam-4862	36	16	two	two	NUM
ejpam-4862	36	17	vertices	vertex	NOUN
ejpam-4862	36	18	x	x	X
ejpam-4862	36	19	,	,	PUNCT
ejpam-4862	36	20	y	y	PROPN
ejpam-4862	36	21	∈	∈	PROPN
ejpam-4862	36	22	c	c	PROPN
ejpam-4862	36	23	,	,	PUNCT
ejpam-4862	36	24	the	the	DET
ejpam-4862	36	25	vertex	vertex	NOUN
ejpam-4862	36	26	set	set	NOUN
ejpam-4862	36	27	of	of	ADP
ejpam-4862	36	28	every	every	DET
ejpam-4862	36	29	x−	x−	PROPN
ejpam-4862	36	30	y	y	PROPN
ejpam-4862	36	31	geodesic	geodesic	NOUN
ejpam-4862	36	32	is	be	AUX
ejpam-4862	36	33	contained	contain	VERB
ejpam-4862	36	34	in	in	ADP
ejpam-4862	36	35	c.	c.	PROPN
ejpam-4862	37	1	a	a	DET
ejpam-4862	37	2	set	set	NOUN
ejpam-4862	37	3	c	c	NOUN
ejpam-4862	37	4	′	′	NOUN
ejpam-4862	37	5	⊆	⊆	NUM
ejpam-4862	37	6	v	v	ADP
ejpam-4862	37	7	(	(	PUNCT
ejpam-4862	37	8	g	g	NOUN
ejpam-4862	37	9	)	)	PUNCT
ejpam-4862	37	10	is	be	AUX
ejpam-4862	37	11	a	a	DET
ejpam-4862	37	12	clique	clique	NOUN
ejpam-4862	37	13	if	if	SCONJ
ejpam-4862	37	14	the	the	DET
ejpam-4862	37	15	subgraph	subgraph	NOUN
ejpam-4862	37	16	⟨c	⟨c	NOUN
ejpam-4862	37	17	′⟩	′⟩	NOUN
ejpam-4862	37	18	induced	induce	VERB
ejpam-4862	37	19	by	by	ADP
ejpam-4862	37	20	c	c	PROPN
ejpam-4862	37	21	′	′	NOUN
ejpam-4862	37	22	is	be	AUX
ejpam-4862	37	23	complete	complete	ADJ
ejpam-4862	37	24	.	.	PUNCT
ejpam-4862	38	1	the	the	DET
ejpam-4862	38	2	maximum	maximum	PROPN
ejpam-4862	38	3	cardinality	cardinality	NOUN
ejpam-4862	38	4	among	among	ADP
ejpam-4862	38	5	all	all	DET
ejpam-4862	38	6	clique	clique	NOUN
ejpam-4862	38	7	sets	set	NOUN
ejpam-4862	38	8	of	of	ADP
ejpam-4862	38	9	g	g	NOUN
ejpam-4862	38	10	,	,	PUNCT
ejpam-4862	38	11	denoted	denote	VERB
ejpam-4862	38	12	by	by	ADP
ejpam-4862	38	13	ω(g	ω(g	NOUN
ejpam-4862	38	14	)	)	PUNCT
ejpam-4862	38	15	,	,	PUNCT
ejpam-4862	38	16	is	be	AUX
ejpam-4862	38	17	called	call	VERB
ejpam-4862	38	18	the	the	DET
ejpam-4862	38	19	clique	clique	ADJ
ejpam-4862	38	20	number	number	NOUN
ejpam-4862	38	21	of	of	ADP
ejpam-4862	38	22	g.	g.	PROPN
ejpam-4862	38	23	two	two	NUM
ejpam-4862	38	24	vertices	vertice	VERB
ejpam-4862	38	25	x	x	X
ejpam-4862	38	26	,	,	PUNCT
ejpam-4862	38	27	y	y	PROPN
ejpam-4862	38	28	of	of	ADP
ejpam-4862	38	29	g	g	PROPN
ejpam-4862	38	30	are	be	AUX
ejpam-4862	38	31	adjacent	adjacent	ADJ
ejpam-4862	38	32	,	,	PUNCT
ejpam-4862	38	33	or	or	CCONJ
ejpam-4862	38	34	neighbors	neighbor	NOUN
ejpam-4862	38	35	,	,	PUNCT
ejpam-4862	38	36	if	if	SCONJ
ejpam-4862	38	37	xy	xy	PROPN
ejpam-4862	38	38	is	be	AUX
ejpam-4862	38	39	an	an	DET
ejpam-4862	38	40	edge	edge	NOUN
ejpam-4862	38	41	of	of	ADP
ejpam-4862	38	42	g.	g.	PROPN
ejpam-4862	38	43	the	the	DET
ejpam-4862	38	44	open	open	ADJ
ejpam-4862	38	45	neighborhood	neighborhood	NOUN
ejpam-4862	38	46	of	of	ADP
ejpam-4862	38	47	x	x	PUNCT
ejpam-4862	38	48	in	in	ADP
ejpam-4862	38	49	g	g	PROPN
ejpam-4862	38	50	is	be	AUX
ejpam-4862	38	51	the	the	DET
ejpam-4862	38	52	set	set	NOUN
ejpam-4862	38	53	ng(x	ng(x	NUM
ejpam-4862	38	54	)	)	PUNCT
ejpam-4862	39	1	=	=	PRON
ejpam-4862	39	2	{	{	PUNCT
ejpam-4862	39	3	y	y	PROPN
ejpam-4862	39	4	∈	∈	PROPN
ejpam-4862	39	5	v	v	NOUN
ejpam-4862	39	6	(	(	PUNCT
ejpam-4862	39	7	g	g	NOUN
ejpam-4862	39	8	)	)	PUNCT
ejpam-4862	39	9	:	:	PUNCT
ejpam-4862	39	10	xy	xy	PROPN
ejpam-4862	39	11	∈	∈	PROPN
ejpam-4862	39	12	e(g	e(g	PROPN
ejpam-4862	39	13	)	)	PUNCT
ejpam-4862	39	14	}	}	PUNCT
ejpam-4862	39	15	.	.	PUNCT
ejpam-4862	40	1	the	the	DET
ejpam-4862	40	2	closed	closed	ADJ
ejpam-4862	40	3	neighborhood	neighborhood	NOUN
ejpam-4862	40	4	of	of	ADP
ejpam-4862	40	5	x	x	SYM
ejpam-4862	40	6	ing	ing	NOUN
ejpam-4862	40	7	is	be	AUX
ejpam-4862	40	8	the	the	DET
ejpam-4862	40	9	setng[x	setng[x	NOUN
ejpam-4862	40	10	]	]	X
ejpam-4862	40	11	=	=	SYM
ejpam-4862	40	12	ng(x)∪{x	ng(x)∪{x	NOUN
ejpam-4862	40	13	}	}	PUNCT
ejpam-4862	40	14	.	.	PUNCT
ejpam-4862	41	1	ifx	ifx	PROPN
ejpam-4862	41	2	⊆	⊆	NUM
ejpam-4862	41	3	v	v	NOUN
ejpam-4862	41	4	(	(	PUNCT
ejpam-4862	41	5	g	g	NOUN
ejpam-4862	41	6	)	)	PUNCT
ejpam-4862	41	7	,	,	PUNCT
ejpam-4862	41	8	the	the	DET
ejpam-4862	41	9	open	open	ADJ
ejpam-4862	41	10	neighborhood	neighborhood	NOUN
ejpam-4862	41	11	of	of	ADP
ejpam-4862	41	12	x	x	PUNCT
ejpam-4862	41	13	in	in	ADP
ejpam-4862	41	14	g	g	PROPN
ejpam-4862	41	15	is	be	AUX
ejpam-4862	41	16	the	the	DET
ejpam-4862	41	17	set	set	NOUN
ejpam-4862	41	18	ng(x	ng(x	NUM
ejpam-4862	41	19	)	)	PUNCT
ejpam-4862	42	1	=	=	SYM
ejpam-4862	42	2	⋃	⋃	NOUN
ejpam-4862	42	3	x∈x	x∈x	NOUN
ejpam-4862	42	4	ng(x	ng(x	NUM
ejpam-4862	42	5	)	)	PUNCT
ejpam-4862	42	6	.	.	PUNCT
ejpam-4862	43	1	the	the	DET
ejpam-4862	43	2	closed	closed	ADJ
ejpam-4862	43	3	neighborhood	neighborhood	NOUN
ejpam-4862	43	4	of	of	ADP
ejpam-4862	43	5	x	x	PUNCT
ejpam-4862	43	6	in	in	ADP
ejpam-4862	43	7	g	g	PROPN
ejpam-4862	43	8	is	be	AUX
ejpam-4862	43	9	the	the	DET
ejpam-4862	43	10	set	set	NOUN
ejpam-4862	43	11	ng[x	ng[x	PROPN
ejpam-4862	43	12	]	]	X
ejpam-4862	43	13	=	=	PUNCT
ejpam-4862	43	14	ng(x	ng(x	X
ejpam-4862	43	15	)	)	PUNCT
ejpam-4862	44	1	∪x	∪x	PROPN
ejpam-4862	44	2	.	.	PUNCT
ejpam-4862	45	1	a	a	DET
ejpam-4862	45	2	set	set	NOUN
ejpam-4862	45	3	p	p	NOUN
ejpam-4862	45	4	⊆	⊆	NUM
ejpam-4862	45	5	v	v	NOUN
ejpam-4862	45	6	(	(	PUNCT
ejpam-4862	45	7	g	g	NOUN
ejpam-4862	45	8	)	)	PUNCT
ejpam-4862	45	9	is	be	AUX
ejpam-4862	45	10	a	a	DET
ejpam-4862	45	11	pointwise	pointwise	ADJ
ejpam-4862	45	12	non	non	ADJ
ejpam-4862	45	13	-	-	ADJ
ejpam-4862	45	14	dominating	dominating	ADJ
ejpam-4862	45	15	set	set	NOUN
ejpam-4862	45	16	if	if	SCONJ
ejpam-4862	45	17	for	for	ADP
ejpam-4862	45	18	every	every	DET
ejpam-4862	45	19	v	v	NUM
ejpam-4862	45	20	∈	∈	NOUN
ejpam-4862	45	21	v	v	NOUN
ejpam-4862	45	22	(	(	PUNCT
ejpam-4862	45	23	g)\p	g)\p	NOUN
ejpam-4862	45	24	,	,	PUNCT
ejpam-4862	45	25	there	there	PRON
ejpam-4862	45	26	exists	exist	VERB
ejpam-4862	45	27	u	u	PROPN
ejpam-4862	45	28	∈	∈	PROPN
ejpam-4862	45	29	p	p	NOUN
ejpam-4862	45	30	such	such	ADJ
ejpam-4862	45	31	that	that	DET
ejpam-4862	45	32	v	v	NOUN
ejpam-4862	45	33	/∈	/∈	PUNCT
ejpam-4862	45	34	ng(u	ng(u	NOUN
ejpam-4862	45	35	)	)	PUNCT
ejpam-4862	45	36	.	.	PUNCT
ejpam-4862	46	1	the	the	DET
ejpam-4862	46	2	minimum	minimum	ADJ
ejpam-4862	46	3	cardinality	cardinality	NOUN
ejpam-4862	46	4	of	of	ADP
ejpam-4862	46	5	a	a	DET
ejpam-4862	46	6	pointwise	pointwise	ADJ
ejpam-4862	46	7	non	non	ADJ
ejpam-4862	46	8	-	-	ADJ
ejpam-4862	46	9	dominating	dominating	ADJ
ejpam-4862	46	10	set	set	NOUN
ejpam-4862	46	11	of	of	ADP
ejpam-4862	46	12	g	g	NOUN
ejpam-4862	46	13	,	,	PUNCT
ejpam-4862	46	14	denoted	denote	VERB
ejpam-4862	46	15	by	by	ADP
ejpam-4862	46	16	pnd(g	pnd(g	PROPN
ejpam-4862	46	17	)	)	PUNCT
ejpam-4862	46	18	,	,	PUNCT
ejpam-4862	46	19	is	be	AUX
ejpam-4862	46	20	called	call	VERB
ejpam-4862	46	21	a	a	DET
ejpam-4862	46	22	pointwise	pointwise	ADJ
ejpam-4862	46	23	non	non	ADJ
ejpam-4862	46	24	-	-	ADJ
ejpam-4862	46	25	domination	domination	ADJ
ejpam-4862	46	26	number	number	NOUN
ejpam-4862	46	27	of	of	ADP
ejpam-4862	46	28	g.	g.	PROPN
ejpam-4862	46	29	a	a	DET
ejpam-4862	46	30	path	path	NOUN
ejpam-4862	46	31	graph	graph	NOUN
ejpam-4862	46	32	is	be	AUX
ejpam-4862	46	33	a	a	DET
ejpam-4862	46	34	non	non	ADJ
ejpam-4862	46	35	-	-	ADJ
ejpam-4862	46	36	empty	empty	ADJ
ejpam-4862	46	37	graph	graph	NOUN
ejpam-4862	46	38	with	with	ADP
ejpam-4862	46	39	vertex	vertex	NOUN
ejpam-4862	46	40	-	-	PUNCT
ejpam-4862	46	41	set	set	VERB
ejpam-4862	46	42	{	{	PUNCT
ejpam-4862	46	43	x1	x1	PROPN
ejpam-4862	46	44	,	,	PUNCT
ejpam-4862	46	45	x2	x2	PROPN
ejpam-4862	46	46	,	,	PUNCT
ejpam-4862	46	47	...	...	PUNCT
ejpam-4862	46	48	,	,	PUNCT
ejpam-4862	46	49	xn	xn	PROPN
ejpam-4862	46	50	}	}	PUNCT
ejpam-4862	46	51	and	and	CCONJ
ejpam-4862	46	52	edge	edge	NOUN
ejpam-4862	46	53	-	-	PUNCT
ejpam-4862	46	54	set	set	NOUN
ejpam-4862	46	55	{	{	PUNCT
ejpam-4862	46	56	x1x2	x1x2	NOUN
ejpam-4862	46	57	,	,	PUNCT
ejpam-4862	46	58	x2x3	x2x3	PROPN
ejpam-4862	46	59	,	,	PUNCT
ejpam-4862	46	60	...	...	PUNCT
ejpam-4862	46	61	,	,	PUNCT
ejpam-4862	46	62	xn−1xn	xn−1xn	NUM
ejpam-4862	46	63	}	}	PUNCT
ejpam-4862	46	64	,	,	PUNCT
ejpam-4862	46	65	where	where	SCONJ
ejpam-4862	46	66	the	the	DET
ejpam-4862	46	67	x	x	NOUN
ejpam-4862	46	68	′	′	NOUN
ejpam-4862	46	69	is	be	AUX
ejpam-4862	46	70	are	be	AUX
ejpam-4862	46	71	all	all	ADV
ejpam-4862	46	72	distinct	distinct	ADJ
ejpam-4862	46	73	.	.	PUNCT
ejpam-4862	47	1	the	the	DET
ejpam-4862	47	2	path	path	NOUN
ejpam-4862	47	3	of	of	ADP
ejpam-4862	47	4	order	order	NOUN
ejpam-4862	47	5	n	n	NOUN
ejpam-4862	47	6	is	be	AUX
ejpam-4862	47	7	denoted	denote	VERB
ejpam-4862	47	8	by	by	ADP
ejpam-4862	47	9	pn	pn	PROPN
ejpam-4862	47	10	.	.	PUNCT
ejpam-4862	48	1	if	if	SCONJ
ejpam-4862	48	2	g	g	PROPN
ejpam-4862	48	3	is	be	AUX
ejpam-4862	48	4	a	a	DET
ejpam-4862	48	5	graph	graph	NOUN
ejpam-4862	48	6	and	and	CCONJ
ejpam-4862	48	7	u	u	NOUN
ejpam-4862	48	8	and	and	CCONJ
ejpam-4862	48	9	v	v	NOUN
ejpam-4862	48	10	are	be	AUX
ejpam-4862	48	11	vertices	vertex	NOUN
ejpam-4862	48	12	of	of	ADP
ejpam-4862	48	13	g	g	NOUN
ejpam-4862	48	14	,	,	PUNCT
ejpam-4862	48	15	then	then	ADV
ejpam-4862	48	16	a	a	DET
ejpam-4862	48	17	path	path	NOUN
ejpam-4862	48	18	from	from	ADP
ejpam-4862	48	19	vertex	vertex	NOUN
ejpam-4862	48	20	u	u	NOUN
ejpam-4862	48	21	to	to	PART
ejpam-4862	48	22	vertex	vertex	NOUN
ejpam-4862	48	23	v	v	NOUN
ejpam-4862	48	24	is	be	AUX
ejpam-4862	48	25	sometimes	sometimes	ADV
ejpam-4862	48	26	called	call	VERB
ejpam-4862	48	27	a	a	DET
ejpam-4862	48	28	u	u	NOUN
ejpam-4862	48	29	-	-	NOUN
ejpam-4862	48	30	v	v	ADJ
ejpam-4862	48	31	path	path	NOUN
ejpam-4862	48	32	.	.	PUNCT
ejpam-4862	49	1	the	the	DET
ejpam-4862	49	2	cycle	cycle	NOUN
ejpam-4862	49	3	graph	graph	NOUN
ejpam-4862	49	4	cn	cn	NOUN
ejpam-4862	50	1	=	=	PUNCT
ejpam-4862	51	1	[	[	X
ejpam-4862	51	2	x1	x1	PROPN
ejpam-4862	51	3	,	,	PUNCT
ejpam-4862	51	4	x2	x2	PROPN
ejpam-4862	51	5	,	,	PUNCT
ejpam-4862	51	6	.	.	PUNCT
ejpam-4862	51	7	.	.	PUNCT
ejpam-4862	52	1	.	.	PUNCT
ejpam-4862	53	1	,	,	PUNCT
ejpam-4862	53	2	xn	xn	PROPN
ejpam-4862	53	3	,	,	PUNCT
ejpam-4862	53	4	x1	x1	PROPN
ejpam-4862	53	5	]	]	PUNCT
ejpam-4862	53	6	is	be	AUX
ejpam-4862	53	7	the	the	DET
ejpam-4862	53	8	graph	graph	NOUN
ejpam-4862	53	9	of	of	ADP
ejpam-4862	53	10	order	order	NOUN
ejpam-4862	53	11	n	n	PRON
ejpam-4862	53	12	≥	≥	NOUN
ejpam-4862	53	13	3	3	NUM
ejpam-4862	53	14	with	with	ADP
ejpam-4862	53	15	vertex	vertex	NOUN
ejpam-4862	53	16	-	-	PUNCT
ejpam-4862	53	17	set	set	VERB
ejpam-4862	53	18	{	{	PUNCT
ejpam-4862	53	19	x1	x1	PROPN
ejpam-4862	53	20	,	,	PUNCT
ejpam-4862	53	21	x2	x2	PROPN
ejpam-4862	53	22	,	,	PUNCT
ejpam-4862	53	23	...	...	PUNCT
ejpam-4862	53	24	,	,	PUNCT
ejpam-4862	53	25	xn	xn	PROPN
ejpam-4862	53	26	}	}	PUNCT
ejpam-4862	53	27	and	and	CCONJ
ejpam-4862	53	28	edge	edge	NOUN
ejpam-4862	53	29	-	-	PUNCT
ejpam-4862	53	30	set	set	NOUN
ejpam-4862	53	31	{	{	PUNCT
ejpam-4862	53	32	x1x2	x1x2	NOUN
ejpam-4862	53	33	,	,	PUNCT
ejpam-4862	53	34	x2x3	x2x3	PROPN
ejpam-4862	53	35	,	,	PUNCT
ejpam-4862	53	36	...	...	PUNCT
ejpam-4862	53	37	,	,	PUNCT
ejpam-4862	53	38	xn−1xn	xn−1xn	PROPN
ejpam-4862	53	39	,	,	PUNCT
ejpam-4862	53	40	xnx1	xnx1	PROPN
ejpam-4862	53	41	}	}	PUNCT
ejpam-4862	53	42	.	.	PUNCT
ejpam-4862	54	1	let	let	VERB
ejpam-4862	54	2	g	g	NOUN
ejpam-4862	54	3	and	and	CCONJ
ejpam-4862	54	4	h	h	NOUN
ejpam-4862	54	5	be	be	VERB
ejpam-4862	54	6	any	any	DET
ejpam-4862	54	7	two	two	NUM
ejpam-4862	54	8	graphs	graph	NOUN
ejpam-4862	54	9	.	.	PUNCT
ejpam-4862	55	1	the	the	DET
ejpam-4862	55	2	join	join	NOUN
ejpam-4862	55	3	g	g	PROPN
ejpam-4862	55	4	+	+	CCONJ
ejpam-4862	55	5	h	h	NOUN
ejpam-4862	55	6	is	be	AUX
ejpam-4862	55	7	the	the	DET
ejpam-4862	55	8	graph	graph	NOUN
ejpam-4862	55	9	with	with	ADP
ejpam-4862	55	10	vertex	vertex	NOUN
ejpam-4862	55	11	set	set	VERB
ejpam-4862	55	12	v	v	NOUN
ejpam-4862	55	13	(	(	PUNCT
ejpam-4862	55	14	g+h	g+h	NOUN
ejpam-4862	55	15	)	)	PUNCT
ejpam-4862	55	16	=	=	SYM
ejpam-4862	55	17	v	v	X
ejpam-4862	55	18	(	(	PUNCT
ejpam-4862	55	19	g	g	NOUN
ejpam-4862	55	20	)	)	PUNCT
ejpam-4862	55	21	∪	∪	NOUN
ejpam-4862	55	22	v	v	NOUN
ejpam-4862	55	23	(	(	PUNCT
ejpam-4862	55	24	h	h	NOUN
ejpam-4862	55	25	)	)	PUNCT
ejpam-4862	55	26	and	and	CCONJ
ejpam-4862	55	27	edge	edge	NOUN
ejpam-4862	55	28	set	set	VERB
ejpam-4862	55	29	e(g+h	e(g+h	NUM
ejpam-4862	55	30	)	)	PUNCT
ejpam-4862	55	31	=	=	SYM
ejpam-4862	55	32	e(g	e(g	NOUN
ejpam-4862	55	33	)	)	PUNCT
ejpam-4862	55	34	∪	∪	ADP
ejpam-4862	55	35	e(h	e(h	PROPN
ejpam-4862	55	36	)	)	PUNCT
ejpam-4862	55	37	∪	∪	NOUN
ejpam-4862	55	38	{	{	PUNCT
ejpam-4862	55	39	uv	uv	NOUN
ejpam-4862	55	40	:	:	PUNCT
ejpam-4862	55	41	u	u	PROPN
ejpam-4862	55	42	∈	∈	PROPN
ejpam-4862	55	43	v	v	ADP
ejpam-4862	55	44	(	(	PUNCT
ejpam-4862	55	45	g	g	NOUN
ejpam-4862	55	46	)	)	PUNCT
ejpam-4862	55	47	,	,	PUNCT
ejpam-4862	55	48	v	v	X
ejpam-4862	55	49	∈	∈	PROPN
ejpam-4862	55	50	v	v	NOUN
ejpam-4862	55	51	(	(	PUNCT
ejpam-4862	55	52	h	h	NOUN
ejpam-4862	55	53	)	)	PUNCT
ejpam-4862	55	54	}	}	PUNCT
ejpam-4862	55	55	.	.	PUNCT
ejpam-4862	56	1	the	the	DET
ejpam-4862	56	2	corona	corona	NOUN
ejpam-4862	56	3	g	g	PROPN
ejpam-4862	56	4	◦	◦	NOUN
ejpam-4862	56	5	h	h	NOUN
ejpam-4862	56	6	is	be	AUX
ejpam-4862	56	7	the	the	DET
ejpam-4862	56	8	graph	graph	NOUN
ejpam-4862	56	9	obtained	obtain	VERB
ejpam-4862	56	10	by	by	ADP
ejpam-4862	56	11	taking	take	VERB
ejpam-4862	56	12	one	one	NUM
ejpam-4862	56	13	copy	copy	NOUN
ejpam-4862	56	14	of	of	ADP
ejpam-4862	56	15	g	g	PROPN
ejpam-4862	56	16	and	and	CCONJ
ejpam-4862	56	17	|v	|v	PROPN
ejpam-4862	56	18	(	(	PUNCT
ejpam-4862	56	19	g)|	g)|	NOUN
ejpam-4862	56	20	copies	copy	NOUN
ejpam-4862	56	21	of	of	ADP
ejpam-4862	56	22	h	h	NOUN
ejpam-4862	56	23	,	,	PUNCT
ejpam-4862	56	24	and	and	CCONJ
ejpam-4862	56	25	then	then	ADV
ejpam-4862	56	26	joining	join	VERB
ejpam-4862	56	27	the	the	DET
ejpam-4862	56	28	ith	ith	PROPN
ejpam-4862	56	29	vertex	vertex	NOUN
ejpam-4862	56	30	of	of	ADP
ejpam-4862	56	31	g	g	NOUN
ejpam-4862	56	32	to	to	ADP
ejpam-4862	56	33	every	every	DET
ejpam-4862	56	34	vertex	vertex	NOUN
ejpam-4862	56	35	of	of	ADP
ejpam-4862	56	36	the	the	DET
ejpam-4862	56	37	ith	ith	PROPN
ejpam-4862	56	38	copy	copy	NOUN
ejpam-4862	56	39	of	of	ADP
ejpam-4862	56	40	h.	h.	PROPN
ejpam-4862	56	41	we	we	PRON
ejpam-4862	56	42	denote	denote	VERB
ejpam-4862	56	43	by	by	ADP
ejpam-4862	56	44	hv	hv	PROPN
ejpam-4862	56	45	the	the	DET
ejpam-4862	56	46	copy	copy	NOUN
ejpam-4862	56	47	of	of	ADP
ejpam-4862	56	48	h	h	NOUN
ejpam-4862	56	49	in	in	ADP
ejpam-4862	56	50	g	g	PROPN
ejpam-4862	56	51	◦	◦	NOUN
ejpam-4862	56	52	h	h	NOUN
ejpam-4862	56	53	corresponding	correspond	VERB
ejpam-4862	56	54	to	to	ADP
ejpam-4862	56	55	the	the	DET
ejpam-4862	56	56	vertex	vertex	NOUN
ejpam-4862	56	57	v	v	ADP
ejpam-4862	56	58	∈	∈	PROPN
ejpam-4862	56	59	g	g	NOUN
ejpam-4862	56	60	and	and	CCONJ
ejpam-4862	56	61	write	write	VERB
ejpam-4862	56	62	v	v	ADP
ejpam-4862	56	63	+	+	CCONJ
ejpam-4862	56	64	hv	hv	NOUN
ejpam-4862	56	65	for	for	ADP
ejpam-4862	56	66	⟨{v}⟩+hv	⟨{v}⟩+hv	PROPN
ejpam-4862	56	67	.	.	PUNCT
ejpam-4862	57	1	j.	j.	PROPN
ejpam-4862	57	2	a.	a.	PROPN
ejpam-4862	57	3	hassan	hassan	PROPN
ejpam-4862	57	4	et	et	PROPN
ejpam-4862	57	5	al	al	PROPN
ejpam-4862	57	6	.	.	PUNCT
ejpam-4862	57	7	/	/	SYM
ejpam-4862	57	8	eur	eur	PROPN
ejpam-4862	57	9	.	.	PUNCT
ejpam-4862	58	1	j.	j.	PROPN
ejpam-4862	58	2	pure	pure	PROPN
ejpam-4862	58	3	appl	appl	PROPN
ejpam-4862	58	4	.	.	PROPN
ejpam-4862	58	5	math	math	PROPN
ejpam-4862	58	6	,	,	PUNCT
ejpam-4862	58	7	16	16	NUM
ejpam-4862	58	8	(	(	PUNCT
ejpam-4862	58	9	4	4	NUM
ejpam-4862	58	10	)	)	PUNCT
ejpam-4862	58	11	(	(	PUNCT
ejpam-4862	58	12	2023	2023	NUM
ejpam-4862	58	13	)	)	PUNCT
ejpam-4862	58	14	,	,	PUNCT
ejpam-4862	58	15	2035	2035	NUM
ejpam-4862	58	16	-	-	SYM
ejpam-4862	58	17	2048	2048	NUM
ejpam-4862	58	18	2037	2037	NUM
ejpam-4862	58	19	the	the	DET
ejpam-4862	58	20	distance	distance	NOUN
ejpam-4862	58	21	dg(u	dg(u	X
ejpam-4862	58	22	,	,	PUNCT
ejpam-4862	58	23	v	v	NOUN
ejpam-4862	58	24	)	)	PUNCT
ejpam-4862	58	25	in	in	ADP
ejpam-4862	58	26	g	g	NOUN
ejpam-4862	58	27	of	of	ADP
ejpam-4862	58	28	two	two	NUM
ejpam-4862	58	29	vertices	vertex	NOUN
ejpam-4862	58	30	u	u	NOUN
ejpam-4862	58	31	,	,	PUNCT
ejpam-4862	58	32	v	v	PROPN
ejpam-4862	58	33	is	be	AUX
ejpam-4862	58	34	the	the	DET
ejpam-4862	58	35	length	length	NOUN
ejpam-4862	58	36	of	of	ADP
ejpam-4862	58	37	a	a	DET
ejpam-4862	58	38	shortest	short	ADJ
ejpam-4862	58	39	u	u	NOUN
ejpam-4862	58	40	-	-	NOUN
ejpam-4862	58	41	v	v	ADJ
ejpam-4862	58	42	path	path	NOUN
ejpam-4862	58	43	in	in	ADP
ejpam-4862	58	44	g.	g.	PROPN
ejpam-4862	58	45	the	the	DET
ejpam-4862	58	46	greatest	great	ADJ
ejpam-4862	58	47	distance	distance	NOUN
ejpam-4862	58	48	between	between	ADP
ejpam-4862	58	49	any	any	DET
ejpam-4862	58	50	two	two	NUM
ejpam-4862	58	51	vertices	vertex	NOUN
ejpam-4862	58	52	in	in	ADP
ejpam-4862	58	53	g	g	NOUN
ejpam-4862	58	54	,	,	PUNCT
ejpam-4862	58	55	denoted	denote	VERB
ejpam-4862	58	56	by	by	ADP
ejpam-4862	58	57	diam(g	diam(g	PROPN
ejpam-4862	58	58	)	)	PUNCT
ejpam-4862	58	59	,	,	PUNCT
ejpam-4862	58	60	is	be	AUX
ejpam-4862	58	61	called	call	VERB
ejpam-4862	58	62	the	the	DET
ejpam-4862	58	63	diameter	diameter	NOUN
ejpam-4862	58	64	of	of	ADP
ejpam-4862	58	65	g.	g.	PROPN
ejpam-4862	58	66	a	a	DET
ejpam-4862	58	67	vertex	vertex	NOUN
ejpam-4862	58	68	v	v	NOUN
ejpam-4862	58	69	in	in	ADP
ejpam-4862	58	70	g	g	PROPN
ejpam-4862	58	71	is	be	AUX
ejpam-4862	58	72	a	a	DET
ejpam-4862	58	73	hop	hop	NOUN
ejpam-4862	58	74	neighbor	neighbor	NOUN
ejpam-4862	58	75	of	of	ADP
ejpam-4862	58	76	vertex	vertex	NOUN
ejpam-4862	58	77	u	u	NOUN
ejpam-4862	58	78	in	in	ADP
ejpam-4862	58	79	g	g	PROPN
ejpam-4862	58	80	if	if	SCONJ
ejpam-4862	58	81	dg(u	dg(u	NOUN
ejpam-4862	58	82	,	,	PUNCT
ejpam-4862	58	83	v	v	NOUN
ejpam-4862	58	84	)	)	PUNCT
ejpam-4862	58	85	=	=	SYM
ejpam-4862	58	86	2	2	X
ejpam-4862	58	87	.	.	X
ejpam-4862	59	1	the	the	DET
ejpam-4862	59	2	set	set	ADJ
ejpam-4862	59	3	n2	n2	ADJ
ejpam-4862	59	4	g(u	g(u	PROPN
ejpam-4862	59	5	)	)	PUNCT
ejpam-4862	59	6	=	=	PRON
ejpam-4862	59	7	{	{	PUNCT
ejpam-4862	59	8	v	v	NUM
ejpam-4862	59	9	∈	∈	NOUN
ejpam-4862	59	10	v	v	NOUN
ejpam-4862	59	11	(	(	PUNCT
ejpam-4862	59	12	g	g	NOUN
ejpam-4862	59	13	)	)	PUNCT
ejpam-4862	59	14	:	:	PUNCT
ejpam-4862	59	15	dg(v	dg(v	X
ejpam-4862	59	16	,	,	PUNCT
ejpam-4862	59	17	u	u	NOUN
ejpam-4862	59	18	)	)	PUNCT
ejpam-4862	59	19	=	=	SYM
ejpam-4862	59	20	2	2	X
ejpam-4862	59	21	}	}	PUNCT
ejpam-4862	59	22	is	be	AUX
ejpam-4862	59	23	called	call	VERB
ejpam-4862	59	24	the	the	DET
ejpam-4862	59	25	open	open	ADJ
ejpam-4862	59	26	hop	hop	NOUN
ejpam-4862	59	27	neighborhood	neighborhood	NOUN
ejpam-4862	59	28	of	of	ADP
ejpam-4862	59	29	u.	u.	PROPN
ejpam-4862	59	30	the	the	DET
ejpam-4862	59	31	closed	closed	ADJ
ejpam-4862	59	32	hop	hop	NOUN
ejpam-4862	59	33	neighborhood	neighborhood	NOUN
ejpam-4862	59	34	of	of	ADP
ejpam-4862	59	35	u	u	PROPN
ejpam-4862	59	36	in	in	ADP
ejpam-4862	59	37	g	g	PROPN
ejpam-4862	59	38	is	be	AUX
ejpam-4862	59	39	given	give	VERB
ejpam-4862	59	40	by	by	ADP
ejpam-4862	59	41	n2	n2	PROPN
ejpam-4862	59	42	g[u	g[u	PROPN
ejpam-4862	59	43	]	]	X
ejpam-4862	59	44	=	=	SYM
ejpam-4862	59	45	n2	n2	PROPN
ejpam-4862	59	46	g(u)∪	g(u)∪	PROPN
ejpam-4862	59	47	{	{	PUNCT
ejpam-4862	59	48	u	u	NOUN
ejpam-4862	59	49	}	}	PUNCT
ejpam-4862	59	50	.	.	PUNCT
ejpam-4862	60	1	the	the	DET
ejpam-4862	60	2	open	open	ADJ
ejpam-4862	60	3	hop	hop	NOUN
ejpam-4862	60	4	neighborhood	neighborhood	NOUN
ejpam-4862	60	5	of	of	ADP
ejpam-4862	60	6	x	x	PROPN
ejpam-4862	60	7	⊆	⊆	NUM
ejpam-4862	60	8	v	v	ADP
ejpam-4862	60	9	(	(	PUNCT
ejpam-4862	60	10	g	g	NOUN
ejpam-4862	60	11	)	)	PUNCT
ejpam-4862	60	12	is	be	AUX
ejpam-4862	60	13	the	the	DET
ejpam-4862	60	14	set	set	ADJ
ejpam-4862	60	15	n2	n2	ADJ
ejpam-4862	60	16	g(x	g(x	NOUN
ejpam-4862	60	17	)	)	PUNCT
ejpam-4862	61	1	=	=	SYM
ejpam-4862	61	2	⋃	⋃	NOUN
ejpam-4862	61	3	u∈x	u∈x	ADJ
ejpam-4862	61	4	n2	n2	NOUN
ejpam-4862	61	5	g(u	g(u	PROPN
ejpam-4862	61	6	)	)	PUNCT
ejpam-4862	61	7	.	.	PUNCT
ejpam-4862	62	1	the	the	DET
ejpam-4862	62	2	closed	closed	ADJ
ejpam-4862	62	3	hop	hop	NOUN
ejpam-4862	62	4	neighborhood	neighborhood	NOUN
ejpam-4862	62	5	of	of	ADP
ejpam-4862	62	6	x	x	PUNCT
ejpam-4862	62	7	in	in	ADP
ejpam-4862	62	8	g	g	PROPN
ejpam-4862	62	9	is	be	AUX
ejpam-4862	62	10	the	the	DET
ejpam-4862	62	11	set	set	ADJ
ejpam-4862	62	12	n2	n2	NOUN
ejpam-4862	62	13	g[x	g[x	PROPN
ejpam-4862	62	14	]	]	X
ejpam-4862	62	15	=	=	SYM
ejpam-4862	62	16	n2	n2	PROPN
ejpam-4862	62	17	g(x	g(x	NOUN
ejpam-4862	62	18	)	)	PUNCT
ejpam-4862	62	19	∪x	∪x	NUM
ejpam-4862	62	20	.	.	PUNCT
ejpam-4862	63	1	a	a	DET
ejpam-4862	63	2	set	set	NOUN
ejpam-4862	63	3	s	s	NOUN
ejpam-4862	63	4	⊆	⊆	NUM
ejpam-4862	63	5	v	v	NOUN
ejpam-4862	63	6	(	(	PUNCT
ejpam-4862	63	7	g	g	NOUN
ejpam-4862	63	8	)	)	PUNCT
ejpam-4862	63	9	is	be	AUX
ejpam-4862	63	10	a	a	DET
ejpam-4862	63	11	hop	hop	NOUN
ejpam-4862	63	12	dominating	dominating	NOUN
ejpam-4862	63	13	set	set	NOUN
ejpam-4862	63	14	of	of	ADP
ejpam-4862	63	15	g	g	PROPN
ejpam-4862	63	16	if	if	SCONJ
ejpam-4862	63	17	n2	n2	ADJ
ejpam-4862	63	18	g[s	g[s	PROPN
ejpam-4862	63	19	]	]	X
ejpam-4862	63	20	=	=	SYM
ejpam-4862	63	21	v	v	NOUN
ejpam-4862	63	22	(	(	PUNCT
ejpam-4862	63	23	g	g	NOUN
ejpam-4862	63	24	)	)	PUNCT
ejpam-4862	63	25	,	,	PUNCT
ejpam-4862	63	26	that	that	ADV
ejpam-4862	63	27	is	is	ADV
ejpam-4862	63	28	,	,	PUNCT
ejpam-4862	63	29	for	for	ADP
ejpam-4862	63	30	every	every	DET
ejpam-4862	63	31	v	v	NUM
ejpam-4862	63	32	∈	∈	NOUN
ejpam-4862	63	33	v	v	NOUN
ejpam-4862	63	34	(	(	PUNCT
ejpam-4862	63	35	g)\s	g)\s	NOUN
ejpam-4862	63	36	,	,	PUNCT
ejpam-4862	63	37	there	there	PRON
ejpam-4862	63	38	exists	exist	VERB
ejpam-4862	63	39	u	u	PROPN
ejpam-4862	63	40	∈	∈	PROPN
ejpam-4862	63	41	s	s	VERB
ejpam-4862	63	42	such	such	ADJ
ejpam-4862	63	43	that	that	DET
ejpam-4862	63	44	dg(u	dg(u	ADJ
ejpam-4862	63	45	,	,	PUNCT
ejpam-4862	63	46	v	v	NOUN
ejpam-4862	63	47	)	)	PUNCT
ejpam-4862	64	1	=	=	SYM
ejpam-4862	64	2	2	2	X
ejpam-4862	64	3	.	.	PUNCT
ejpam-4862	65	1	the	the	DET
ejpam-4862	65	2	minimum	minimum	ADJ
ejpam-4862	65	3	cardinality	cardinality	NOUN
ejpam-4862	65	4	among	among	ADP
ejpam-4862	65	5	all	all	DET
ejpam-4862	65	6	hop	hop	NOUN
ejpam-4862	65	7	dominating	dominating	NOUN
ejpam-4862	65	8	sets	set	NOUN
ejpam-4862	65	9	of	of	ADP
ejpam-4862	65	10	g	g	NOUN
ejpam-4862	65	11	,	,	PUNCT
ejpam-4862	65	12	denoted	denote	VERB
ejpam-4862	65	13	by	by	ADP
ejpam-4862	65	14	γh(g	γh(g	NOUN
ejpam-4862	65	15	)	)	PUNCT
ejpam-4862	65	16	,	,	PUNCT
ejpam-4862	65	17	is	be	AUX
ejpam-4862	65	18	called	call	VERB
ejpam-4862	65	19	the	the	DET
ejpam-4862	65	20	hop	hop	NOUN
ejpam-4862	65	21	domination	domination	NOUN
ejpam-4862	65	22	number	number	NOUN
ejpam-4862	65	23	of	of	ADP
ejpam-4862	65	24	g.	g.	PROPN
ejpam-4862	65	25	any	any	DET
ejpam-4862	65	26	hop	hop	NOUN
ejpam-4862	65	27	dominating	dominating	NOUN
ejpam-4862	65	28	set	set	VERB
ejpam-4862	65	29	with	with	ADP
ejpam-4862	65	30	cardinality	cardinality	NOUN
ejpam-4862	65	31	equal	equal	ADJ
ejpam-4862	65	32	to	to	ADP
ejpam-4862	65	33	γh(g	γh(g	NOUN
ejpam-4862	65	34	)	)	PUNCT
ejpam-4862	65	35	is	be	AUX
ejpam-4862	65	36	called	call	VERB
ejpam-4862	65	37	a	a	DET
ejpam-4862	65	38	γh	γh	ADV
ejpam-4862	65	39	-	-	PUNCT
ejpam-4862	65	40	set	set	NOUN
ejpam-4862	65	41	of	of	ADP
ejpam-4862	65	42	g.	g.	PROPN
ejpam-4862	65	43	3	3	NUM
ejpam-4862	65	44	.	.	PUNCT
ejpam-4862	66	1	results	result	NOUN
ejpam-4862	66	2	we	we	PRON
ejpam-4862	66	3	begin	begin	VERB
ejpam-4862	66	4	this	this	DET
ejpam-4862	66	5	section	section	NOUN
ejpam-4862	66	6	by	by	ADP
ejpam-4862	66	7	defining	define	VERB
ejpam-4862	66	8	the	the	DET
ejpam-4862	66	9	new	new	ADJ
ejpam-4862	66	10	concept	concept	NOUN
ejpam-4862	66	11	called	call	VERB
ejpam-4862	66	12	outer	outer	ADJ
ejpam-4862	66	13	-	-	PUNCT
ejpam-4862	66	14	convex	convex	NOUN
ejpam-4862	66	15	hop	hop	NOUN
ejpam-4862	66	16	domination	domination	NOUN
ejpam-4862	66	17	in	in	ADP
ejpam-4862	66	18	a	a	DET
ejpam-4862	66	19	graph	graph	NOUN
ejpam-4862	66	20	.	.	PUNCT
ejpam-4862	67	1	definition	definition	NOUN
ejpam-4862	67	2	1	1	NUM
ejpam-4862	67	3	.	.	PUNCT
ejpam-4862	68	1	let	let	VERB
ejpam-4862	68	2	g	g	PRON
ejpam-4862	68	3	be	be	AUX
ejpam-4862	68	4	a	a	DET
ejpam-4862	68	5	simple	simple	ADJ
ejpam-4862	68	6	graph	graph	NOUN
ejpam-4862	68	7	with	with	ADP
ejpam-4862	68	8	vertex	vertex	NOUN
ejpam-4862	68	9	and	and	CCONJ
ejpam-4862	68	10	edge	edge	NOUN
ejpam-4862	68	11	-	-	PUNCT
ejpam-4862	68	12	sets	set	NOUN
ejpam-4862	68	13	v	v	NOUN
ejpam-4862	68	14	(	(	PUNCT
ejpam-4862	68	15	g	g	NOUN
ejpam-4862	68	16	)	)	PUNCT
ejpam-4862	68	17	and	and	CCONJ
ejpam-4862	68	18	e(g	e(g	PROPN
ejpam-4862	68	19	)	)	PUNCT
ejpam-4862	68	20	,	,	PUNCT
ejpam-4862	68	21	respectively	respectively	ADV
ejpam-4862	68	22	.	.	PUNCT
ejpam-4862	69	1	then	then	ADV
ejpam-4862	69	2	c	c	PROPN
ejpam-4862	69	3	⊆	⊆	NUM
ejpam-4862	69	4	v	v	X
ejpam-4862	69	5	(	(	PUNCT
ejpam-4862	69	6	g	g	NOUN
ejpam-4862	69	7	)	)	PUNCT
ejpam-4862	69	8	is	be	AUX
ejpam-4862	69	9	called	call	VERB
ejpam-4862	69	10	an	an	DET
ejpam-4862	69	11	outer	outer	ADJ
ejpam-4862	69	12	-	-	PUNCT
ejpam-4862	69	13	convex	convex	NOUN
ejpam-4862	69	14	hop	hop	NOUN
ejpam-4862	69	15	dominating	dominating	NOUN
ejpam-4862	69	16	set	set	NOUN
ejpam-4862	69	17	if	if	SCONJ
ejpam-4862	69	18	c	c	PROPN
ejpam-4862	69	19	is	be	AUX
ejpam-4862	69	20	hop	hop	NOUN
ejpam-4862	69	21	dominating	dominating	NOUN
ejpam-4862	69	22	and	and	CCONJ
ejpam-4862	69	23	v	v	NOUN
ejpam-4862	69	24	(	(	PUNCT
ejpam-4862	69	25	g	g	NOUN
ejpam-4862	69	26	)	)	PUNCT
ejpam-4862	69	27	\	\	PUNCT
ejpam-4862	70	1	c	c	NOUN
ejpam-4862	70	2	is	be	AUX
ejpam-4862	70	3	convex	convex	ADJ
ejpam-4862	70	4	in	in	ADP
ejpam-4862	70	5	g.	g.	PROPN
ejpam-4862	70	6	the	the	DET
ejpam-4862	70	7	minimum	minimum	ADJ
ejpam-4862	70	8	cardinality	cardinality	NOUN
ejpam-4862	70	9	among	among	ADP
ejpam-4862	70	10	all	all	DET
ejpam-4862	70	11	outer	outer	ADJ
ejpam-4862	70	12	-	-	PUNCT
ejpam-4862	70	13	convex	convex	NOUN
ejpam-4862	70	14	hop	hop	NOUN
ejpam-4862	70	15	dominating	dominating	NOUN
ejpam-4862	70	16	sets	set	NOUN
ejpam-4862	70	17	of	of	ADP
ejpam-4862	70	18	g	g	NOUN
ejpam-4862	70	19	,	,	PUNCT
ejpam-4862	70	20	denoted	denote	VERB
ejpam-4862	70	21	by	by	ADP
ejpam-4862	70	22	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	70	23	)	)	PUNCT
ejpam-4862	70	24	,	,	PUNCT
ejpam-4862	70	25	is	be	AUX
ejpam-4862	70	26	called	call	VERB
ejpam-4862	70	27	the	the	DET
ejpam-4862	70	28	outer	outer	ADJ
ejpam-4862	70	29	-	-	PUNCT
ejpam-4862	70	30	convex	convex	NOUN
ejpam-4862	70	31	hop	hop	NOUN
ejpam-4862	70	32	domination	domination	NOUN
ejpam-4862	70	33	number	number	NOUN
ejpam-4862	70	34	of	of	ADP
ejpam-4862	70	35	g.	g.	PROPN
ejpam-4862	70	36	any	any	DET
ejpam-4862	70	37	outer	outer	ADJ
ejpam-4862	70	38	-	-	PUNCT
ejpam-4862	70	39	convex	convex	NOUN
ejpam-4862	70	40	hop	hop	NOUN
ejpam-4862	70	41	dominating	dominating	NOUN
ejpam-4862	70	42	set	set	NOUN
ejpam-4862	70	43	c	c	PROPN
ejpam-4862	70	44	satisfying	satisfy	VERB
ejpam-4862	70	45	|c|	|c|	PROPN
ejpam-4862	70	46	=	=	SYM
ejpam-4862	70	47	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	70	48	)	)	PUNCT
ejpam-4862	70	49	,	,	PUNCT
ejpam-4862	70	50	is	be	AUX
ejpam-4862	70	51	called	call	VERB
ejpam-4862	70	52	a	a	DET
ejpam-4862	70	53	γ̃conh	γ̃conh	NOUN
ejpam-4862	70	54	-	-	NOUN
ejpam-4862	70	55	set	set	NOUN
ejpam-4862	70	56	of	of	ADP
ejpam-4862	70	57	g.	g.	PROPN
ejpam-4862	70	58	example	example	NOUN
ejpam-4862	70	59	1	1	X
ejpam-4862	70	60	.	.	X
ejpam-4862	70	61	consider	consider	VERB
ejpam-4862	70	62	the	the	DET
ejpam-4862	70	63	graph	graph	NOUN
ejpam-4862	70	64	g	g	NOUN
ejpam-4862	70	65	given	give	VERB
ejpam-4862	70	66	in	in	ADP
ejpam-4862	70	67	figure	figure	NOUN
ejpam-4862	70	68	1	1	NUM
ejpam-4862	70	69	.	.	PUNCT
ejpam-4862	71	1	let	let	VERB
ejpam-4862	71	2	c	c	NOUN
ejpam-4862	71	3	=	=	SYM
ejpam-4862	71	4	{	{	PUNCT
ejpam-4862	71	5	a5	a5	PROPN
ejpam-4862	71	6	,	,	PUNCT
ejpam-4862	71	7	a6	a6	NOUN
ejpam-4862	71	8	,	,	PUNCT
ejpam-4862	71	9	.	.	PUNCT
ejpam-4862	71	10	.	.	PUNCT
ejpam-4862	72	1	.	.	PUNCT
ejpam-4862	73	1	,	,	PUNCT
ejpam-4862	73	2	a13	a13	PROPN
ejpam-4862	73	3	}	}	PUNCT
ejpam-4862	73	4	.	.	PUNCT
ejpam-4862	74	1	then	then	ADV
ejpam-4862	74	2	n2	n2	PROPN
ejpam-4862	74	3	g[c	g[c	PROPN
ejpam-4862	74	4	]	]	X
ejpam-4862	74	5	=	=	SYM
ejpam-4862	74	6	v	v	X
ejpam-4862	74	7	(	(	PUNCT
ejpam-4862	74	8	g	g	NOUN
ejpam-4862	74	9	)	)	PUNCT
ejpam-4862	74	10	and	and	CCONJ
ejpam-4862	74	11	so	so	ADV
ejpam-4862	74	12	c	c	PROPN
ejpam-4862	74	13	is	be	AUX
ejpam-4862	74	14	a	a	DET
ejpam-4862	74	15	hop	hop	NOUN
ejpam-4862	74	16	dominating	dominating	NOUN
ejpam-4862	74	17	set	set	NOUN
ejpam-4862	74	18	of	of	ADP
ejpam-4862	74	19	g.	g.	PROPN
ejpam-4862	74	20	observe	observe	VERB
ejpam-4862	74	21	that	that	SCONJ
ejpam-4862	74	22	v	v	NOUN
ejpam-4862	74	23	(	(	PUNCT
ejpam-4862	74	24	g	g	NOUN
ejpam-4862	74	25	)	)	PUNCT
ejpam-4862	74	26	\	\	NOUN
ejpam-4862	75	1	c	c	NOUN
ejpam-4862	75	2	=	=	SYM
ejpam-4862	75	3	{	{	PUNCT
ejpam-4862	75	4	a1	a1	PROPN
ejpam-4862	75	5	,	,	PUNCT
ejpam-4862	75	6	a2	a2	PROPN
ejpam-4862	75	7	,	,	PUNCT
ejpam-4862	75	8	a3	a3	NOUN
ejpam-4862	75	9	,	,	PUNCT
ejpam-4862	75	10	a4	a4	PROPN
ejpam-4862	75	11	}	}	PUNCT
ejpam-4862	75	12	is	be	AUX
ejpam-4862	75	13	convex	convex	ADJ
ejpam-4862	75	14	in	in	ADP
ejpam-4862	75	15	g.	g.	PROPN
ejpam-4862	75	16	hence	hence	ADV
ejpam-4862	75	17	,	,	PUNCT
ejpam-4862	75	18	c	c	PROPN
ejpam-4862	75	19	is	be	AUX
ejpam-4862	75	20	an	an	DET
ejpam-4862	75	21	outer	outer	ADJ
ejpam-4862	75	22	-	-	PUNCT
ejpam-4862	75	23	convex	convex	NOUN
ejpam-4862	75	24	hop	hop	NOUN
ejpam-4862	75	25	dominating	dominating	NOUN
ejpam-4862	75	26	set	set	NOUN
ejpam-4862	75	27	of	of	ADP
ejpam-4862	75	28	g.	g.	PROPN
ejpam-4862	75	29	next	next	ADV
ejpam-4862	75	30	,	,	PUNCT
ejpam-4862	75	31	consider	consider	VERB
ejpam-4862	75	32	c	c	NOUN
ejpam-4862	75	33	′	′	NOUN
ejpam-4862	75	34	=	=	SYM
ejpam-4862	75	35	{	{	PUNCT
ejpam-4862	75	36	a5	a5	NOUN
ejpam-4862	75	37	,	,	PUNCT
ejpam-4862	75	38	a6	a6	PROPN
ejpam-4862	75	39	,	,	PUNCT
ejpam-4862	75	40	a7	a7	PROPN
ejpam-4862	75	41	,	,	PUNCT
ejpam-4862	75	42	a11	a11	PROPN
ejpam-4862	75	43	,	,	PUNCT
ejpam-4862	75	44	a12	a12	NOUN
ejpam-4862	75	45	}	}	PUNCT
ejpam-4862	75	46	.	.	PUNCT
ejpam-4862	76	1	then	then	ADV
ejpam-4862	76	2	c	c	X
ejpam-4862	76	3	′	′	PROPN
ejpam-4862	76	4	is	be	AUX
ejpam-4862	76	5	a	a	DET
ejpam-4862	76	6	hop	hop	NOUN
ejpam-4862	76	7	dominating	dominating	NOUN
ejpam-4862	76	8	set	set	VERB
ejpam-4862	76	9	in	in	ADP
ejpam-4862	76	10	g.	g.	PROPN
ejpam-4862	76	11	however	however	ADV
ejpam-4862	76	12	,	,	PUNCT
ejpam-4862	76	13	c	c	NOUN
ejpam-4862	76	14	′	′	NOUN
ejpam-4862	76	15	is	be	AUX
ejpam-4862	76	16	not	not	PART
ejpam-4862	76	17	an	an	DET
ejpam-4862	76	18	outer	outer	ADJ
ejpam-4862	76	19	-	-	PUNCT
ejpam-4862	76	20	convex	convex	NOUN
ejpam-4862	76	21	hop	hop	NOUN
ejpam-4862	76	22	dominating	dominating	NOUN
ejpam-4862	76	23	set	set	VERB
ejpam-4862	76	24	in	in	ADP
ejpam-4862	76	25	g	g	PROPN
ejpam-4862	76	26	since	since	SCONJ
ejpam-4862	76	27	v	v	NOUN
ejpam-4862	76	28	(	(	PUNCT
ejpam-4862	76	29	g	g	NOUN
ejpam-4862	76	30	)	)	PUNCT
ejpam-4862	76	31	\c	\c	NOUN
ejpam-4862	76	32	′	′	NUM
ejpam-4862	76	33	is	be	AUX
ejpam-4862	76	34	not	not	PART
ejpam-4862	76	35	convex	convex	ADJ
ejpam-4862	76	36	in	in	ADP
ejpam-4862	76	37	g.	g.	PROPN
ejpam-4862	76	38	moreover	moreover	ADV
ejpam-4862	76	39	,	,	PUNCT
ejpam-4862	76	40	it	it	PRON
ejpam-4862	76	41	can	can	AUX
ejpam-4862	76	42	be	be	AUX
ejpam-4862	76	43	verified	verify	VERB
ejpam-4862	76	44	that	that	SCONJ
ejpam-4862	76	45	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	76	46	)	)	PUNCT
ejpam-4862	76	47	=	=	SYM
ejpam-4862	76	48	9	9	X
ejpam-4862	76	49	.	.	PUNCT
ejpam-4862	76	50	j.	j.	PROPN
ejpam-4862	76	51	a.	a.	PROPN
ejpam-4862	76	52	hassan	hassan	PROPN
ejpam-4862	76	53	et	et	PROPN
ejpam-4862	76	54	al	al	PROPN
ejpam-4862	76	55	.	.	PUNCT
ejpam-4862	76	56	/	/	SYM
ejpam-4862	76	57	eur	eur	PROPN
ejpam-4862	76	58	.	.	PUNCT
ejpam-4862	77	1	j.	j.	PROPN
ejpam-4862	77	2	pure	pure	PROPN
ejpam-4862	77	3	appl	appl	PROPN
ejpam-4862	77	4	.	.	PROPN
ejpam-4862	77	5	math	math	PROPN
ejpam-4862	77	6	,	,	PUNCT
ejpam-4862	77	7	16	16	NUM
ejpam-4862	77	8	(	(	PUNCT
ejpam-4862	77	9	4	4	NUM
ejpam-4862	77	10	)	)	PUNCT
ejpam-4862	77	11	(	(	PUNCT
ejpam-4862	77	12	2023	2023	NUM
ejpam-4862	77	13	)	)	PUNCT
ejpam-4862	77	14	,	,	PUNCT
ejpam-4862	77	15	2035	2035	NUM
ejpam-4862	77	16	-	-	SYM
ejpam-4862	77	17	2048	2048	NUM
ejpam-4862	77	18	2038	2038	NUM
ejpam-4862	77	19	a1	a1	NOUN
ejpam-4862	77	20	a2	a2	PROPN
ejpam-4862	77	21	a3	a3	NOUN
ejpam-4862	77	22	a4	a4	PROPN
ejpam-4862	77	23	g	g	NOUN
ejpam-4862	77	24	:	:	PUNCT
ejpam-4862	77	25	a5	a5	PROPN
ejpam-4862	77	26	a6	a6	PROPN
ejpam-4862	77	27	a7	a7	PROPN
ejpam-4862	77	28	a8	a8	PROPN
ejpam-4862	77	29	a9	a9	PROPN
ejpam-4862	77	30	a10	a10	PROPN
ejpam-4862	77	31	a11	a11	PROPN
ejpam-4862	77	32	a12	a12	PROPN
ejpam-4862	77	33	a13	a13	PROPN
ejpam-4862	77	34	figure	figure	NOUN
ejpam-4862	77	35	1	1	NUM
ejpam-4862	77	36	:	:	PUNCT
ejpam-4862	77	37	graph	graph	VERB
ejpam-4862	77	38	g	g	NOUN
ejpam-4862	77	39	with	with	ADP
ejpam-4862	77	40	γ̃conh(g)=9	γ̃conh(g)=9	PROPN
ejpam-4862	77	41	remark	remark	NOUN
ejpam-4862	77	42	1	1	NUM
ejpam-4862	77	43	.	.	PUNCT
ejpam-4862	78	1	(	(	PUNCT
ejpam-4862	78	2	i	i	NOUN
ejpam-4862	78	3	)	)	PUNCT
ejpam-4862	78	4	any	any	DET
ejpam-4862	78	5	graph	graph	NOUN
ejpam-4862	78	6	g	g	PROPN
ejpam-4862	78	7	admits	admit	VERB
ejpam-4862	78	8	an	an	DET
ejpam-4862	78	9	outer	outer	ADJ
ejpam-4862	78	10	-	-	PUNCT
ejpam-4862	78	11	convex	convex	ADJ
ejpam-4862	78	12	hop	hop	NOUN
ejpam-4862	78	13	domination	domination	NOUN
ejpam-4862	78	14	.	.	PUNCT
ejpam-4862	79	1	(	(	PUNCT
ejpam-4862	79	2	ii	ii	NOUN
ejpam-4862	79	3	)	)	PUNCT
ejpam-4862	79	4	if	if	SCONJ
ejpam-4862	79	5	s	s	NOUN
ejpam-4862	79	6	is	be	AUX
ejpam-4862	79	7	an	an	DET
ejpam-4862	79	8	outer	outer	ADJ
ejpam-4862	79	9	-	-	PUNCT
ejpam-4862	79	10	convex	convex	NOUN
ejpam-4862	79	11	hop	hop	NOUN
ejpam-4862	79	12	dominating	dominating	NOUN
ejpam-4862	79	13	set	set	NOUN
ejpam-4862	79	14	of	of	ADP
ejpam-4862	79	15	g	g	NOUN
ejpam-4862	79	16	,	,	PUNCT
ejpam-4862	79	17	then	then	ADV
ejpam-4862	79	18	s	s	X
ejpam-4862	79	19	and	and	CCONJ
ejpam-4862	79	20	v	v	NOUN
ejpam-4862	79	21	(	(	PUNCT
ejpam-4862	79	22	g	g	NOUN
ejpam-4862	79	23	)	)	PUNCT
ejpam-4862	79	24	\	\	PROPN
ejpam-4862	80	1	c	c	NOUN
ejpam-4862	80	2	are	be	AUX
ejpam-4862	80	3	not	not	PART
ejpam-4862	80	4	necessarily	necessarily	ADV
ejpam-4862	80	5	convex	convex	ADJ
ejpam-4862	80	6	and	and	CCONJ
ejpam-4862	80	7	hop	hop	NOUN
ejpam-4862	80	8	dominating	dominating	NOUN
ejpam-4862	80	9	sets	set	NOUN
ejpam-4862	80	10	in	in	ADP
ejpam-4862	80	11	g	g	NOUN
ejpam-4862	80	12	,	,	PUNCT
ejpam-4862	80	13	respectively	respectively	ADV
ejpam-4862	80	14	.	.	PUNCT
ejpam-4862	81	1	remark	remark	PROPN
ejpam-4862	81	2	2	2	NUM
ejpam-4862	81	3	.	.	PUNCT
ejpam-4862	82	1	let	let	VERB
ejpam-4862	82	2	g	g	NOUN
ejpam-4862	82	3	be	be	AUX
ejpam-4862	82	4	any	any	DET
ejpam-4862	82	5	graph	graph	NOUN
ejpam-4862	82	6	.	.	PUNCT
ejpam-4862	83	1	then	then	ADV
ejpam-4862	83	2	every	every	DET
ejpam-4862	83	3	outer	outer	ADJ
ejpam-4862	83	4	-	-	PUNCT
ejpam-4862	83	5	convex	convex	NOUN
ejpam-4862	83	6	hop	hop	NOUN
ejpam-4862	83	7	dominating	dominating	NOUN
ejpam-4862	83	8	set	set	NOUN
ejpam-4862	83	9	c	c	NOUN
ejpam-4862	83	10	in	in	ADP
ejpam-4862	83	11	g	g	PROPN
ejpam-4862	83	12	is	be	AUX
ejpam-4862	83	13	hop	hop	NOUN
ejpam-4862	83	14	dominating	dominating	NOUN
ejpam-4862	84	1	but	but	CCONJ
ejpam-4862	84	2	the	the	DET
ejpam-4862	84	3	converse	converse	NOUN
ejpam-4862	84	4	is	be	AUX
ejpam-4862	84	5	not	not	PART
ejpam-4862	84	6	always	always	ADV
ejpam-4862	84	7	true	true	ADJ
ejpam-4862	84	8	.	.	PUNCT
ejpam-4862	85	1	the	the	DET
ejpam-4862	85	2	converse	converse	NOUN
ejpam-4862	85	3	part	part	NOUN
ejpam-4862	85	4	can	can	AUX
ejpam-4862	85	5	be	be	AUX
ejpam-4862	85	6	seen	see	VERB
ejpam-4862	85	7	by	by	ADP
ejpam-4862	85	8	considering	consider	VERB
ejpam-4862	85	9	c	c	NOUN
ejpam-4862	85	10	′	′	NOUN
ejpam-4862	85	11	in	in	ADP
ejpam-4862	85	12	the	the	DET
ejpam-4862	85	13	previous	previous	ADJ
ejpam-4862	85	14	example	example	NOUN
ejpam-4862	85	15	.	.	PUNCT
ejpam-4862	86	1	proposition	proposition	NOUN
ejpam-4862	86	2	1	1	NUM
ejpam-4862	86	3	.	.	PUNCT
ejpam-4862	87	1	let	let	VERB
ejpam-4862	87	2	g	g	NOUN
ejpam-4862	87	3	be	be	AUX
ejpam-4862	87	4	any	any	DET
ejpam-4862	87	5	graph	graph	NOUN
ejpam-4862	87	6	.	.	PUNCT
ejpam-4862	88	1	then	then	ADV
ejpam-4862	88	2	γh(g	γh(g	PUNCT
ejpam-4862	88	3	)	)	PUNCT
ejpam-4862	88	4	≤	≤	NOUN
ejpam-4862	88	5	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	88	6	)	)	PUNCT
ejpam-4862	88	7	.	.	PUNCT
ejpam-4862	89	1	proof	proof	NOUN
ejpam-4862	89	2	.	.	PUNCT
ejpam-4862	90	1	let	let	VERB
ejpam-4862	90	2	g	g	NOUN
ejpam-4862	90	3	be	be	AUX
ejpam-4862	90	4	any	any	DET
ejpam-4862	90	5	graph	graph	NOUN
ejpam-4862	90	6	and	and	CCONJ
ejpam-4862	90	7	let	let	VERB
ejpam-4862	90	8	s	s	PRON
ejpam-4862	90	9	be	be	AUX
ejpam-4862	90	10	a	a	DET
ejpam-4862	90	11	minimum	minimum	ADJ
ejpam-4862	90	12	outer	outer	ADJ
ejpam-4862	90	13	-	-	PUNCT
ejpam-4862	90	14	convex	convex	NOUN
ejpam-4862	90	15	hop	hop	NOUN
ejpam-4862	90	16	dominating	dominating	NOUN
ejpam-4862	90	17	set	set	NOUN
ejpam-4862	90	18	of	of	ADP
ejpam-4862	90	19	g.	g.	PROPN
ejpam-4862	90	20	then	then	ADV
ejpam-4862	90	21	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	90	22	)	)	PUNCT
ejpam-4862	90	23	=	=	SYM
ejpam-4862	90	24	|s|	|s|	PROPN
ejpam-4862	90	25	.	.	PUNCT
ejpam-4862	91	1	by	by	ADP
ejpam-4862	91	2	remark	remark	NOUN
ejpam-4862	91	3	2	2	NUM
ejpam-4862	91	4	,	,	PUNCT
ejpam-4862	91	5	s	s	VERB
ejpam-4862	91	6	is	be	AUX
ejpam-4862	91	7	a	a	DET
ejpam-4862	91	8	hop	hop	NOUN
ejpam-4862	91	9	dominating	dominating	NOUN
ejpam-4862	91	10	set	set	NOUN
ejpam-4862	91	11	of	of	ADP
ejpam-4862	91	12	g.	g.	PROPN
ejpam-4862	91	13	it	it	PRON
ejpam-4862	91	14	follows	follow	VERB
ejpam-4862	91	15	that	that	SCONJ
ejpam-4862	91	16	γh(g	γh(g	NOUN
ejpam-4862	91	17	)	)	PUNCT
ejpam-4862	91	18	≤	≤	NUM
ejpam-4862	91	19	|s|	|s|	PROPN
ejpam-4862	91	20	=	=	PUNCT
ejpam-4862	91	21	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	91	22	)	)	PUNCT
ejpam-4862	91	23	.	.	PUNCT
ejpam-4862	92	1	remark	remark	PROPN
ejpam-4862	92	2	3	3	NUM
ejpam-4862	92	3	.	.	PUNCT
ejpam-4862	93	1	the	the	DET
ejpam-4862	93	2	bound	bind	VERB
ejpam-4862	93	3	given	give	VERB
ejpam-4862	93	4	in	in	ADP
ejpam-4862	93	5	proposition	proposition	NOUN
ejpam-4862	93	6	1	1	NUM
ejpam-4862	93	7	is	be	AUX
ejpam-4862	93	8	sharp	sharp	ADJ
ejpam-4862	93	9	.	.	PUNCT
ejpam-4862	94	1	moreover	moreover	ADV
ejpam-4862	94	2	,	,	PUNCT
ejpam-4862	94	3	strict	strict	ADJ
ejpam-4862	94	4	inequality	inequality	NOUN
ejpam-4862	94	5	can	can	AUX
ejpam-4862	94	6	also	also	ADV
ejpam-4862	94	7	be	be	AUX
ejpam-4862	94	8	attained	attain	VERB
ejpam-4862	94	9	.	.	PUNCT
ejpam-4862	95	1	to	to	PART
ejpam-4862	95	2	see	see	VERB
ejpam-4862	95	3	this	this	PRON
ejpam-4862	95	4	,	,	PUNCT
ejpam-4862	95	5	consider	consider	VERB
ejpam-4862	95	6	the	the	DET
ejpam-4862	95	7	graph	graph	NOUN
ejpam-4862	95	8	g1	g1	NOUN
ejpam-4862	95	9	in	in	ADP
ejpam-4862	95	10	figure	figure	NOUN
ejpam-4862	95	11	2	2	NUM
ejpam-4862	95	12	.	.	PUNCT
ejpam-4862	96	1	let	let	VERB
ejpam-4862	96	2	c	c	NOUN
ejpam-4862	96	3	=	=	PUNCT
ejpam-4862	96	4	{	{	PUNCT
ejpam-4862	96	5	f	f	X
ejpam-4862	96	6	,	,	PUNCT
ejpam-4862	96	7	g	g	NOUN
ejpam-4862	96	8	}	}	PUNCT
ejpam-4862	96	9	.	.	PUNCT
ejpam-4862	97	1	then	then	ADV
ejpam-4862	97	2	c	c	PROPN
ejpam-4862	97	3	is	be	AUX
ejpam-4862	97	4	both	both	CCONJ
ejpam-4862	97	5	a	a	DET
ejpam-4862	97	6	γh	γh	ADV
ejpam-4862	97	7	-	-	PUNCT
ejpam-4862	97	8	set	set	NOUN
ejpam-4862	97	9	and	and	CCONJ
ejpam-4862	97	10	a	a	DET
ejpam-4862	97	11	γ̃conh	γ̃conh	NOUN
ejpam-4862	97	12	-	-	NOUN
ejpam-4862	97	13	set	set	NOUN
ejpam-4862	97	14	of	of	ADP
ejpam-4862	97	15	g1	g1	NOUN
ejpam-4862	97	16	.	.	PUNCT
ejpam-4862	98	1	hence	hence	ADV
ejpam-4862	98	2	,	,	PUNCT
ejpam-4862	98	3	γh(g1	γh(g1	NOUN
ejpam-4862	98	4	)	)	PUNCT
ejpam-4862	98	5	=	=	SYM
ejpam-4862	98	6	2	2	NUM
ejpam-4862	98	7	=	=	SYM
ejpam-4862	98	8	γ̃conh(g1	γ̃conh(g1	NUM
ejpam-4862	98	9	)	)	PUNCT
ejpam-4862	98	10	.	.	PUNCT
ejpam-4862	99	1	j.	j.	PROPN
ejpam-4862	99	2	a.	a.	PROPN
ejpam-4862	99	3	hassan	hassan	PROPN
ejpam-4862	99	4	et	et	PROPN
ejpam-4862	99	5	al	al	PROPN
ejpam-4862	99	6	.	.	PUNCT
ejpam-4862	99	7	/	/	SYM
ejpam-4862	99	8	eur	eur	PROPN
ejpam-4862	99	9	.	.	PUNCT
ejpam-4862	100	1	j.	j.	PROPN
ejpam-4862	100	2	pure	pure	PROPN
ejpam-4862	100	3	appl	appl	PROPN
ejpam-4862	100	4	.	.	PROPN
ejpam-4862	100	5	math	math	PROPN
ejpam-4862	100	6	,	,	PUNCT
ejpam-4862	100	7	16	16	NUM
ejpam-4862	100	8	(	(	PUNCT
ejpam-4862	100	9	4	4	NUM
ejpam-4862	100	10	)	)	PUNCT
ejpam-4862	100	11	(	(	PUNCT
ejpam-4862	100	12	2023	2023	NUM
ejpam-4862	100	13	)	)	PUNCT
ejpam-4862	100	14	,	,	PUNCT
ejpam-4862	100	15	2035	2035	NUM
ejpam-4862	100	16	-	-	SYM
ejpam-4862	100	17	2048	2048	NUM
ejpam-4862	100	18	2039	2039	NUM
ejpam-4862	100	19	g1	g1	NOUN
ejpam-4862	100	20	:	:	PUNCT
ejpam-4862	101	1	c	c	PROPN
ejpam-4862	101	2	d	d	X
ejpam-4862	101	3	b	b	X
ejpam-4862	101	4	e	e	PROPN
ejpam-4862	101	5	a	a	DET
ejpam-4862	101	6	f	f	NOUN
ejpam-4862	101	7	g	g	PROPN
ejpam-4862	101	8	figure	figure	NOUN
ejpam-4862	101	9	2	2	NUM
ejpam-4862	101	10	:	:	PUNCT
ejpam-4862	101	11	graph	graph	NOUN
ejpam-4862	101	12	g1	g1	NOUN
ejpam-4862	101	13	with	with	ADP
ejpam-4862	101	14	γh(g1	γh(g1	NOUN
ejpam-4862	101	15	)	)	PUNCT
ejpam-4862	101	16	=	=	SYM
ejpam-4862	101	17	γ̃conh(g1	γ̃conh(g1	NOUN
ejpam-4862	101	18	)	)	PUNCT
ejpam-4862	101	19	for	for	ADP
ejpam-4862	101	20	strict	strict	ADJ
ejpam-4862	101	21	inequality	inequality	NOUN
ejpam-4862	101	22	,	,	PUNCT
ejpam-4862	101	23	consider	consider	VERB
ejpam-4862	101	24	the	the	DET
ejpam-4862	101	25	graph	graph	NOUN
ejpam-4862	101	26	g2	g2	PROPN
ejpam-4862	101	27	in	in	ADP
ejpam-4862	101	28	figure	figure	NOUN
ejpam-4862	101	29	3	3	NUM
ejpam-4862	101	30	.	.	PUNCT
ejpam-4862	102	1	let	let	VERB
ejpam-4862	102	2	c	c	NOUN
ejpam-4862	102	3	′	′	VERB
ejpam-4862	102	4	=	=	PUNCT
ejpam-4862	102	5	{	{	PUNCT
ejpam-4862	102	6	e	e	NOUN
ejpam-4862	102	7	,	,	PUNCT
ejpam-4862	102	8	f	f	NOUN
ejpam-4862	102	9	}	}	PUNCT
ejpam-4862	102	10	and	and	CCONJ
ejpam-4862	102	11	c	c	X
ejpam-4862	102	12	′′	′′	NOUN
ejpam-4862	102	13	=	=	PRON
ejpam-4862	102	14	{	{	PUNCT
ejpam-4862	102	15	e	e	PROPN
ejpam-4862	102	16	,	,	PUNCT
ejpam-4862	102	17	f	f	PROPN
ejpam-4862	102	18	,	,	PUNCT
ejpam-4862	102	19	g	g	PROPN
ejpam-4862	102	20	,	,	PUNCT
ejpam-4862	102	21	h	h	NOUN
ejpam-4862	102	22	,	,	PUNCT
ejpam-4862	102	23	i	i	NOUN
ejpam-4862	102	24	}	}	PUNCT
ejpam-4862	102	25	.	.	PUNCT
ejpam-4862	103	1	then	then	ADV
ejpam-4862	103	2	c	c	NOUN
ejpam-4862	103	3	′	′	NOUN
ejpam-4862	103	4	and	and	CCONJ
ejpam-4862	103	5	c	c	X
ejpam-4862	104	1	′′	′′	PROPN
ejpam-4862	104	2	are	be	AUX
ejpam-4862	104	3	γh	γh	ADV
ejpam-4862	104	4	-	-	PUNCT
ejpam-4862	104	5	set	set	VERB
ejpam-4862	104	6	and	and	CCONJ
ejpam-4862	104	7	γ̃conh	γ̃conh	NOUN
ejpam-4862	104	8	-	-	PUNCT
ejpam-4862	104	9	set	set	NOUN
ejpam-4862	104	10	of	of	ADP
ejpam-4862	104	11	g2	g2	PROPN
ejpam-4862	104	12	,	,	PUNCT
ejpam-4862	104	13	respectively	respectively	ADV
ejpam-4862	104	14	.	.	PUNCT
ejpam-4862	105	1	thus	thus	ADV
ejpam-4862	105	2	,	,	PUNCT
ejpam-4862	105	3	γh(g2	γh(g2	ADV
ejpam-4862	105	4	)	)	PUNCT
ejpam-4862	105	5	=	=	SYM
ejpam-4862	105	6	2	2	NUM
ejpam-4862	105	7	<	<	SYM
ejpam-4862	105	8	5	5	NUM
ejpam-4862	105	9	=	=	SYM
ejpam-4862	105	10	γ̃conh(g2	γ̃conh(g2	NUM
ejpam-4862	105	11	)	)	PUNCT
ejpam-4862	105	12	.	.	PUNCT
ejpam-4862	106	1	g2	g2	PROPN
ejpam-4862	106	2	:	:	PUNCT
ejpam-4862	107	1	a	a	DET
ejpam-4862	107	2	b	b	X
ejpam-4862	107	3	c	c	NOUN
ejpam-4862	107	4	d	d	X
ejpam-4862	107	5	e	e	X
ejpam-4862	107	6	f	f	PROPN
ejpam-4862	107	7	g	g	PROPN
ejpam-4862	107	8	h	h	NOUN
ejpam-4862	108	1	i	i	PRON
ejpam-4862	108	2	figure	figure	VERB
ejpam-4862	108	3	3	3	NUM
ejpam-4862	108	4	:	:	PUNCT
ejpam-4862	108	5	graph	graph	NOUN
ejpam-4862	108	6	g2	g2	PROPN
ejpam-4862	108	7	with	with	ADP
ejpam-4862	108	8	γh(g2	γh(g2	NOUN
ejpam-4862	108	9	)	)	PUNCT
ejpam-4862	108	10	<	<	X
ejpam-4862	108	11	γ̃conh(g2	γ̃conh(g2	X
ejpam-4862	108	12	)	)	PUNCT
ejpam-4862	108	13	theorem	theorem	VERB
ejpam-4862	108	14	1	1	NUM
ejpam-4862	108	15	.	.	PUNCT
ejpam-4862	109	1	let	let	VERB
ejpam-4862	109	2	g	g	NOUN
ejpam-4862	109	3	be	be	AUX
ejpam-4862	109	4	any	any	DET
ejpam-4862	109	5	graph	graph	NOUN
ejpam-4862	109	6	.	.	PUNCT
ejpam-4862	110	1	then	then	ADV
ejpam-4862	110	2	1	1	NUM
ejpam-4862	110	3	≤	≤	NOUN
ejpam-4862	110	4	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	110	5	)	)	PUNCT
ejpam-4862	110	6	≤	≤	NUM
ejpam-4862	110	7	|v	|v	X
ejpam-4862	110	8	(	(	PUNCT
ejpam-4862	110	9	g)|	g)|	PROPN
ejpam-4862	110	10	.	.	PUNCT
ejpam-4862	111	1	moreover	moreover	ADV
ejpam-4862	111	2	,	,	PUNCT
ejpam-4862	111	3	(	(	PUNCT
ejpam-4862	111	4	i	i	NOUN
ejpam-4862	111	5	)	)	PUNCT
ejpam-4862	111	6	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	111	7	)	)	PUNCT
ejpam-4862	111	8	=	=	SYM
ejpam-4862	111	9	1	1	NUM
ejpam-4862	111	10	if	if	SCONJ
ejpam-4862	111	11	and	and	CCONJ
ejpam-4862	111	12	only	only	ADV
ejpam-4862	111	13	if	if	SCONJ
ejpam-4862	111	14	g	g	PROPN
ejpam-4862	111	15	is	be	AUX
ejpam-4862	111	16	trivial	trivial	ADJ
ejpam-4862	111	17	.	.	PUNCT
ejpam-4862	112	1	(	(	PUNCT
ejpam-4862	112	2	ii	ii	NOUN
ejpam-4862	112	3	)	)	PUNCT
ejpam-4862	112	4	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	112	5	)	)	PUNCT
ejpam-4862	112	6	=	=	SYM
ejpam-4862	112	7	2	2	NUM
ejpam-4862	112	8	if	if	SCONJ
ejpam-4862	112	9	and	and	CCONJ
ejpam-4862	112	10	only	only	ADV
ejpam-4862	112	11	if	if	SCONJ
ejpam-4862	112	12	g	g	PROPN
ejpam-4862	112	13	has	have	AUX
ejpam-4862	112	14	γh	γh	ADV
ejpam-4862	112	15	-	-	PUNCT
ejpam-4862	112	16	set	set	VERB
ejpam-4862	112	17	c	c	NOUN
ejpam-4862	112	18	=	=	SYM
ejpam-4862	112	19	{	{	PUNCT
ejpam-4862	112	20	x	x	PROPN
ejpam-4862	112	21	,	,	PUNCT
ejpam-4862	112	22	y	y	NOUN
ejpam-4862	112	23	}	}	PUNCT
ejpam-4862	112	24	such	such	ADJ
ejpam-4862	112	25	that	that	PRON
ejpam-4862	112	26	v	v	NOUN
ejpam-4862	112	27	(	(	PUNCT
ejpam-4862	112	28	g	g	NOUN
ejpam-4862	112	29	)	)	PUNCT
ejpam-4862	112	30	\	\	PUNCT
ejpam-4862	113	1	c	c	NOUN
ejpam-4862	113	2	is	be	AUX
ejpam-4862	113	3	convex	convex	ADJ
ejpam-4862	113	4	set	set	NOUN
ejpam-4862	113	5	of	of	ADP
ejpam-4862	113	6	g.	g.	PROPN
ejpam-4862	113	7	(	(	PUNCT
ejpam-4862	113	8	iii	iii	PROPN
ejpam-4862	113	9	)	)	PUNCT
ejpam-4862	113	10	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	113	11	)	)	PUNCT
ejpam-4862	113	12	=	=	SYM
ejpam-4862	113	13	|v	|v	X
ejpam-4862	113	14	(	(	PUNCT
ejpam-4862	113	15	g)|	g)|	VERB
ejpam-4862	113	16	if	if	SCONJ
ejpam-4862	113	17	and	and	CCONJ
ejpam-4862	113	18	only	only	ADV
ejpam-4862	113	19	if	if	SCONJ
ejpam-4862	113	20	every	every	DET
ejpam-4862	113	21	component	component	NOUN
ejpam-4862	113	22	of	of	ADP
ejpam-4862	113	23	g	g	PROPN
ejpam-4862	113	24	is	be	AUX
ejpam-4862	113	25	complete	complete	ADJ
ejpam-4862	113	26	.	.	PUNCT
ejpam-4862	114	1	proof	proof	NOUN
ejpam-4862	114	2	.	.	PUNCT
ejpam-4862	115	1	clearly	clearly	ADV
ejpam-4862	115	2	,	,	PUNCT
ejpam-4862	115	3	1	1	NUM
ejpam-4862	115	4	≤	≤	NOUN
ejpam-4862	115	5	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	115	6	)	)	PUNCT
ejpam-4862	115	7	≤	≤	NUM
ejpam-4862	115	8	|v	|v	X
ejpam-4862	115	9	(	(	PUNCT
ejpam-4862	115	10	g)|	g)|	NOUN
ejpam-4862	115	11	.	.	PUNCT
ejpam-4862	116	1	(	(	PUNCT
ejpam-4862	116	2	i	i	NOUN
ejpam-4862	116	3	)	)	PUNCT
ejpam-4862	116	4	suppose	suppose	VERB
ejpam-4862	116	5	that	that	SCONJ
ejpam-4862	116	6	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	116	7	)	)	PUNCT
ejpam-4862	116	8	=	=	SYM
ejpam-4862	116	9	1	1	X
ejpam-4862	116	10	.	.	PUNCT
ejpam-4862	116	11	then	then	ADV
ejpam-4862	116	12	γh(g	γh(g	NOUN
ejpam-4862	116	13	)	)	PUNCT
ejpam-4862	116	14	=	=	SYM
ejpam-4862	116	15	1	1	NUM
ejpam-4862	116	16	by	by	ADP
ejpam-4862	116	17	proposition	proposition	NOUN
ejpam-4862	116	18	1	1	NUM
ejpam-4862	116	19	.	.	PUNCT
ejpam-4862	117	1	it	it	PRON
ejpam-4862	117	2	follows	follow	VERB
ejpam-4862	117	3	that	that	SCONJ
ejpam-4862	117	4	g	g	PROPN
ejpam-4862	117	5	=	=	PROPN
ejpam-4862	117	6	k1	k1	NOUN
ejpam-4862	117	7	which	which	PRON
ejpam-4862	117	8	is	be	AUX
ejpam-4862	117	9	a	a	DET
ejpam-4862	117	10	trivial	trivial	ADJ
ejpam-4862	117	11	graph	graph	NOUN
ejpam-4862	117	12	.	.	PUNCT
ejpam-4862	118	1	the	the	DET
ejpam-4862	118	2	converse	converse	NOUN
ejpam-4862	118	3	is	be	AUX
ejpam-4862	118	4	clear	clear	ADJ
ejpam-4862	118	5	.	.	PUNCT
ejpam-4862	119	1	j.	j.	PROPN
ejpam-4862	119	2	a.	a.	PROPN
ejpam-4862	119	3	hassan	hassan	PROPN
ejpam-4862	119	4	et	et	PROPN
ejpam-4862	119	5	al	al	PROPN
ejpam-4862	119	6	.	.	PUNCT
ejpam-4862	119	7	/	/	SYM
ejpam-4862	119	8	eur	eur	PROPN
ejpam-4862	119	9	.	.	PUNCT
ejpam-4862	120	1	j.	j.	PROPN
ejpam-4862	120	2	pure	pure	PROPN
ejpam-4862	120	3	appl	appl	PROPN
ejpam-4862	120	4	.	.	PROPN
ejpam-4862	120	5	math	math	PROPN
ejpam-4862	120	6	,	,	PUNCT
ejpam-4862	120	7	16	16	NUM
ejpam-4862	120	8	(	(	PUNCT
ejpam-4862	120	9	4	4	NUM
ejpam-4862	120	10	)	)	PUNCT
ejpam-4862	120	11	(	(	PUNCT
ejpam-4862	120	12	2023	2023	NUM
ejpam-4862	120	13	)	)	PUNCT
ejpam-4862	120	14	,	,	PUNCT
ejpam-4862	120	15	2035	2035	NUM
ejpam-4862	120	16	-	-	SYM
ejpam-4862	120	17	2048	2048	NUM
ejpam-4862	120	18	2040	2040	NUM
ejpam-4862	120	19	(	(	PUNCT
ejpam-4862	120	20	ii	ii	NOUN
ejpam-4862	120	21	)	)	PUNCT
ejpam-4862	120	22	suppose	suppose	VERB
ejpam-4862	120	23	that	that	SCONJ
ejpam-4862	120	24	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	120	25	)	)	PUNCT
ejpam-4862	120	26	=	=	SYM
ejpam-4862	120	27	2	2	NUM
ejpam-4862	120	28	,	,	PUNCT
ejpam-4862	120	29	say	say	VERB
ejpam-4862	120	30	c	c	NOUN
ejpam-4862	120	31	=	=	SYM
ejpam-4862	120	32	{	{	PUNCT
ejpam-4862	120	33	x	x	PROPN
ejpam-4862	120	34	,	,	PUNCT
ejpam-4862	120	35	y	y	PRON
ejpam-4862	120	36	}	}	PUNCT
ejpam-4862	120	37	is	be	AUX
ejpam-4862	120	38	a	a	DET
ejpam-4862	120	39	γ̃conh	γ̃conh	NOUN
ejpam-4862	120	40	-	-	NOUN
ejpam-4862	120	41	set	set	NOUN
ejpam-4862	120	42	of	of	ADP
ejpam-4862	120	43	g.	g.	PROPN
ejpam-4862	120	44	then	then	ADV
ejpam-4862	120	45	g	g	PROPN
ejpam-4862	120	46	is	be	AUX
ejpam-4862	120	47	non	non	ADJ
ejpam-4862	120	48	-	-	ADJ
ejpam-4862	120	49	trivial	trivial	ADJ
ejpam-4862	120	50	by	by	ADP
ejpam-4862	120	51	(	(	PUNCT
ejpam-4862	120	52	i	i	NOUN
ejpam-4862	120	53	)	)	PUNCT
ejpam-4862	120	54	and	and	CCONJ
ejpam-4862	120	55	so	so	ADV
ejpam-4862	120	56	γh(g	γh(g	PUNCT
ejpam-4862	120	57	)	)	PUNCT
ejpam-4862	120	58	≥	≥	NOUN
ejpam-4862	120	59	2	2	NUM
ejpam-4862	120	60	.	.	PUNCT
ejpam-4862	120	61	by	by	ADP
ejpam-4862	120	62	assumption	assumption	NOUN
ejpam-4862	120	63	and	and	CCONJ
ejpam-4862	120	64	proposition	proposition	NOUN
ejpam-4862	120	65	1	1	NUM
ejpam-4862	120	66	,	,	PUNCT
ejpam-4862	120	67	γh(g	γh(g	NOUN
ejpam-4862	120	68	)	)	PUNCT
ejpam-4862	120	69	≤	≤	NUM
ejpam-4862	120	70	2	2	NUM
ejpam-4862	120	71	.	.	PUNCT
ejpam-4862	120	72	thus	thus	ADV
ejpam-4862	120	73	,	,	PUNCT
ejpam-4862	120	74	γh(g	γh(g	NOUN
ejpam-4862	120	75	)	)	PUNCT
ejpam-4862	120	76	=	=	SYM
ejpam-4862	121	1	2	2	X
ejpam-4862	121	2	.	.	X
ejpam-4862	121	3	in	in	ADP
ejpam-4862	121	4	particular	particular	ADJ
ejpam-4862	121	5	,	,	PUNCT
ejpam-4862	121	6	c	c	PROPN
ejpam-4862	121	7	is	be	AUX
ejpam-4862	121	8	a	a	DET
ejpam-4862	121	9	γh	γh	ADV
ejpam-4862	121	10	-	-	PUNCT
ejpam-4862	121	11	set	set	NOUN
ejpam-4862	121	12	of	of	ADP
ejpam-4862	121	13	g.	g.	PROPN
ejpam-4862	121	14	moreover	moreover	ADV
ejpam-4862	121	15	,	,	PUNCT
ejpam-4862	121	16	v	v	INTJ
ejpam-4862	121	17	(	(	PUNCT
ejpam-4862	121	18	g	g	NOUN
ejpam-4862	121	19	)	)	PUNCT
ejpam-4862	121	20	\c	\c	NOUN
ejpam-4862	121	21	is	be	AUX
ejpam-4862	121	22	a	a	DET
ejpam-4862	121	23	convex	convex	NOUN
ejpam-4862	121	24	set	set	NOUN
ejpam-4862	121	25	of	of	ADP
ejpam-4862	121	26	g	g	NOUN
ejpam-4862	121	27	by	by	ADP
ejpam-4862	121	28	assumption	assumption	NOUN
ejpam-4862	121	29	.	.	PUNCT
ejpam-4862	122	1	conversely	conversely	ADV
ejpam-4862	122	2	,	,	PUNCT
ejpam-4862	122	3	suppose	suppose	VERB
ejpam-4862	122	4	that	that	SCONJ
ejpam-4862	122	5	g	g	PROPN
ejpam-4862	122	6	has	have	AUX
ejpam-4862	122	7	γh	γh	ADV
ejpam-4862	122	8	-	-	PUNCT
ejpam-4862	122	9	set	set	VERB
ejpam-4862	122	10	c	c	NOUN
ejpam-4862	122	11	=	=	SYM
ejpam-4862	122	12	{	{	PUNCT
ejpam-4862	122	13	x	x	PROPN
ejpam-4862	122	14	,	,	PUNCT
ejpam-4862	122	15	y	y	NOUN
ejpam-4862	122	16	}	}	PUNCT
ejpam-4862	122	17	of	of	ADP
ejpam-4862	122	18	g	g	PROPN
ejpam-4862	122	19	such	such	ADJ
ejpam-4862	122	20	that	that	PRON
ejpam-4862	122	21	v	v	NOUN
ejpam-4862	122	22	(	(	PUNCT
ejpam-4862	122	23	g	g	NOUN
ejpam-4862	122	24	)	)	PUNCT
ejpam-4862	122	25	\	\	PUNCT
ejpam-4862	123	1	c	c	NOUN
ejpam-4862	123	2	is	be	AUX
ejpam-4862	123	3	convex	convex	ADJ
ejpam-4862	123	4	set	set	NOUN
ejpam-4862	123	5	of	of	ADP
ejpam-4862	123	6	g.	g.	PROPN
ejpam-4862	123	7	then	then	ADV
ejpam-4862	123	8	c	c	PROPN
ejpam-4862	123	9	is	be	AUX
ejpam-4862	123	10	an	an	DET
ejpam-4862	123	11	outer	outer	ADJ
ejpam-4862	123	12	-	-	PUNCT
ejpam-4862	123	13	convex	convex	NOUN
ejpam-4862	123	14	hop	hop	NOUN
ejpam-4862	123	15	dominating	dominating	NOUN
ejpam-4862	123	16	set	set	NOUN
ejpam-4862	123	17	of	of	ADP
ejpam-4862	123	18	g.	g.	PROPN
ejpam-4862	123	19	thus	thus	ADV
ejpam-4862	123	20	,	,	PUNCT
ejpam-4862	123	21	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	123	22	)	)	PUNCT
ejpam-4862	123	23	≤	≤	NUM
ejpam-4862	123	24	2	2	NUM
ejpam-4862	123	25	.	.	PUNCT
ejpam-4862	123	26	since	since	SCONJ
ejpam-4862	123	27	γh(g	γh(g	NOUN
ejpam-4862	123	28	)	)	PUNCT
ejpam-4862	123	29	=	=	SYM
ejpam-4862	123	30	2	2	NUM
ejpam-4862	123	31	,	,	PUNCT
ejpam-4862	123	32	it	it	PRON
ejpam-4862	123	33	follows	follow	VERB
ejpam-4862	123	34	that	that	SCONJ
ejpam-4862	123	35	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	123	36	)	)	PUNCT
ejpam-4862	123	37	=	=	SYM
ejpam-4862	123	38	2	2	NUM
ejpam-4862	123	39	by	by	ADP
ejpam-4862	123	40	proposition	proposition	NOUN
ejpam-4862	123	41	1	1	NUM
ejpam-4862	123	42	.	.	PUNCT
ejpam-4862	124	1	(	(	PUNCT
ejpam-4862	124	2	iii	iii	NOUN
ejpam-4862	124	3	)	)	PUNCT
ejpam-4862	124	4	assume	assume	VERB
ejpam-4862	124	5	that	that	SCONJ
ejpam-4862	124	6	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	124	7	)	)	PUNCT
ejpam-4862	124	8	=	=	SYM
ejpam-4862	124	9	|v	|v	PROPN
ejpam-4862	124	10	(	(	PUNCT
ejpam-4862	124	11	g)|	g)|	PROPN
ejpam-4862	124	12	.	.	PUNCT
ejpam-4862	124	13	suppose	suppose	VERB
ejpam-4862	124	14	that	that	SCONJ
ejpam-4862	124	15	there	there	PRON
ejpam-4862	124	16	is	be	VERB
ejpam-4862	124	17	a	a	DET
ejpam-4862	124	18	component	component	NOUN
ejpam-4862	124	19	c	c	NOUN
ejpam-4862	124	20	of	of	ADP
ejpam-4862	124	21	g	g	NOUN
ejpam-4862	124	22	which	which	PRON
ejpam-4862	124	23	is	be	AUX
ejpam-4862	124	24	non	non	ADJ
ejpam-4862	124	25	-	-	ADJ
ejpam-4862	124	26	complete	complete	ADJ
ejpam-4862	124	27	.	.	PUNCT
ejpam-4862	125	1	then	then	ADV
ejpam-4862	125	2	there	there	PRON
ejpam-4862	125	3	exist	exist	VERB
ejpam-4862	125	4	u	u	NOUN
ejpam-4862	125	5	,	,	PUNCT
ejpam-4862	125	6	v	v	NOUN
ejpam-4862	125	7	∈	∈	PROPN
ejpam-4862	125	8	v	v	NOUN
ejpam-4862	125	9	(	(	PUNCT
ejpam-4862	125	10	c	c	NOUN
ejpam-4862	125	11	)	)	PUNCT
ejpam-4862	125	12	⊆	⊆	NUM
ejpam-4862	125	13	v	v	NOUN
ejpam-4862	125	14	(	(	PUNCT
ejpam-4862	125	15	g	g	NOUN
ejpam-4862	125	16	)	)	PUNCT
ejpam-4862	125	17	such	such	ADJ
ejpam-4862	125	18	that	that	PRON
ejpam-4862	125	19	dc(u	dc(u	PROPN
ejpam-4862	125	20	,	,	PUNCT
ejpam-4862	125	21	v	v	NOUN
ejpam-4862	125	22	)	)	PUNCT
ejpam-4862	125	23	=	=	SYM
ejpam-4862	125	24	2	2	NUM
ejpam-4862	125	25	=	=	SYM
ejpam-4862	125	26	dg(u	dg(u	X
ejpam-4862	125	27	,	,	PUNCT
ejpam-4862	125	28	v	v	NOUN
ejpam-4862	125	29	)	)	PUNCT
ejpam-4862	125	30	.	.	PUNCT
ejpam-4862	126	1	let	let	VERB
ejpam-4862	126	2	s∗	s∗	PROPN
ejpam-4862	126	3	=	=	SYM
ejpam-4862	126	4	v	v	PROPN
ejpam-4862	126	5	(	(	PUNCT
ejpam-4862	126	6	g	g	NOUN
ejpam-4862	126	7	)	)	PUNCT
ejpam-4862	126	8	\	\	NOUN
ejpam-4862	126	9	{	{	PUNCT
ejpam-4862	126	10	u	u	NOUN
ejpam-4862	126	11	}	}	PUNCT
ejpam-4862	126	12	.	.	PUNCT
ejpam-4862	127	1	then	then	ADV
ejpam-4862	127	2	s∗	s∗	PROPN
ejpam-4862	127	3	is	be	AUX
ejpam-4862	127	4	an	an	DET
ejpam-4862	127	5	outer	outer	ADJ
ejpam-4862	127	6	-	-	PUNCT
ejpam-4862	127	7	convex	convex	NOUN
ejpam-4862	127	8	hop	hop	NOUN
ejpam-4862	127	9	dominating	dominating	NOUN
ejpam-4862	127	10	set	set	VERB
ejpam-4862	127	11	in	in	ADP
ejpam-4862	127	12	g.	g.	PROPN
ejpam-4862	127	13	hence	hence	ADV
ejpam-4862	127	14	,	,	PUNCT
ejpam-4862	127	15	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	127	16	)	)	PUNCT
ejpam-4862	127	17	≤	≤	NUM
ejpam-4862	127	18	|v	|v	X
ejpam-4862	127	19	(	(	PUNCT
ejpam-4862	127	20	g)|	g)|	INTJ
ejpam-4862	127	21	−	−	PROPN
ejpam-4862	127	22	1	1	NUM
ejpam-4862	127	23	,	,	PUNCT
ejpam-4862	127	24	a	a	DET
ejpam-4862	127	25	contradiction	contradiction	NOUN
ejpam-4862	127	26	.	.	PUNCT
ejpam-4862	128	1	therefore	therefore	ADV
ejpam-4862	128	2	,	,	PUNCT
ejpam-4862	128	3	every	every	DET
ejpam-4862	128	4	component	component	NOUN
ejpam-4862	128	5	of	of	ADP
ejpam-4862	128	6	g	g	PROPN
ejpam-4862	128	7	is	be	AUX
ejpam-4862	128	8	complete	complete	ADJ
ejpam-4862	128	9	.	.	PUNCT
ejpam-4862	129	1	conversely	conversely	ADV
ejpam-4862	129	2	,	,	PUNCT
ejpam-4862	129	3	suppose	suppose	VERB
ejpam-4862	129	4	every	every	DET
ejpam-4862	129	5	component	component	NOUN
ejpam-4862	129	6	of	of	ADP
ejpam-4862	129	7	g	g	PROPN
ejpam-4862	129	8	is	be	AUX
ejpam-4862	129	9	complete	complete	ADJ
ejpam-4862	129	10	.	.	PUNCT
ejpam-4862	130	1	then	then	ADV
ejpam-4862	130	2	v	v	X
ejpam-4862	130	3	(	(	PUNCT
ejpam-4862	130	4	g	g	NOUN
ejpam-4862	130	5	)	)	PUNCT
ejpam-4862	130	6	is	be	AUX
ejpam-4862	130	7	the	the	DET
ejpam-4862	130	8	minimum	minimum	ADJ
ejpam-4862	130	9	outer	outer	ADJ
ejpam-4862	130	10	-	-	PUNCT
ejpam-4862	130	11	convex	convex	NOUN
ejpam-4862	130	12	hop	hop	NOUN
ejpam-4862	130	13	dominating	dominating	NOUN
ejpam-4862	130	14	set	set	NOUN
ejpam-4862	130	15	of	of	ADP
ejpam-4862	130	16	g.	g.	PROPN
ejpam-4862	130	17	therefore	therefore	ADV
ejpam-4862	130	18	,	,	PUNCT
ejpam-4862	130	19	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	130	20	)	)	PUNCT
ejpam-4862	130	21	=	=	SYM
ejpam-4862	130	22	|v	|v	PROPN
ejpam-4862	130	23	(	(	PUNCT
ejpam-4862	130	24	g)|	g)|	NOUN
ejpam-4862	130	25	.	.	PUNCT
ejpam-4862	131	1	the	the	DET
ejpam-4862	131	2	next	next	ADJ
ejpam-4862	131	3	result	result	NOUN
ejpam-4862	131	4	is	be	AUX
ejpam-4862	131	5	a	a	DET
ejpam-4862	131	6	direct	direct	ADJ
ejpam-4862	131	7	consequence	consequence	NOUN
ejpam-4862	131	8	of	of	ADP
ejpam-4862	131	9	theorem	theorem	NOUN
ejpam-4862	131	10	1	1	NUM
ejpam-4862	131	11	.	.	PUNCT
ejpam-4862	131	12	corollary	corollary	ADJ
ejpam-4862	131	13	1	1	NUM
ejpam-4862	131	14	.	.	PUNCT
ejpam-4862	132	1	let	let	VERB
ejpam-4862	132	2	g	g	NOUN
ejpam-4862	132	3	be	be	AUX
ejpam-4862	132	4	any	any	DET
ejpam-4862	132	5	graph	graph	NOUN
ejpam-4862	132	6	of	of	ADP
ejpam-4862	132	7	order	order	NOUN
ejpam-4862	132	8	k	k	PROPN
ejpam-4862	132	9	≥	≥	NUM
ejpam-4862	132	10	1	1	NUM
ejpam-4862	132	11	.	.	PUNCT
ejpam-4862	133	1	then	then	ADV
ejpam-4862	133	2	each	each	PRON
ejpam-4862	133	3	of	of	ADP
ejpam-4862	133	4	the	the	DET
ejpam-4862	133	5	following	following	ADJ
ejpam-4862	133	6	statements	statement	NOUN
ejpam-4862	133	7	holds	hold	VERB
ejpam-4862	133	8	.	.	PUNCT
ejpam-4862	134	1	(	(	PUNCT
ejpam-4862	134	2	i	i	NOUN
ejpam-4862	134	3	)	)	PUNCT
ejpam-4862	134	4	γ̃conh(g	γ̃conh(g	ADV
ejpam-4862	134	5	)	)	PUNCT
ejpam-4862	135	1	=	=	SYM
ejpam-4862	135	2	k	k	NOUN
ejpam-4862	135	3	if	if	SCONJ
ejpam-4862	135	4	g	g	PROPN
ejpam-4862	135	5	is	be	AUX
ejpam-4862	135	6	complete	complete	ADJ
ejpam-4862	135	7	.	.	PUNCT
ejpam-4862	136	1	(	(	PUNCT
ejpam-4862	136	2	ii	ii	NOUN
ejpam-4862	136	3	)	)	PUNCT
ejpam-4862	136	4	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	136	5	)	)	PUNCT
ejpam-4862	136	6	≤	≤	PUNCT
ejpam-4862	137	1	k	k	X
ejpam-4862	137	2	−	−	NOUN
ejpam-4862	137	3	1	1	NUM
ejpam-4862	137	4	if	if	SCONJ
ejpam-4862	137	5	g	g	PROPN
ejpam-4862	137	6	is	be	AUX
ejpam-4862	137	7	non	non	ADJ
ejpam-4862	137	8	-	-	ADJ
ejpam-4862	137	9	complete	complete	ADJ
ejpam-4862	137	10	.	.	PUNCT
ejpam-4862	138	1	the	the	DET
ejpam-4862	138	2	following	following	ADJ
ejpam-4862	138	3	result	result	NOUN
ejpam-4862	138	4	is	be	AUX
ejpam-4862	138	5	a	a	DET
ejpam-4862	138	6	realization	realization	NOUN
ejpam-4862	138	7	result	result	NOUN
ejpam-4862	138	8	involving	involve	VERB
ejpam-4862	138	9	outer	outer	ADJ
ejpam-4862	138	10	-	-	PUNCT
ejpam-4862	138	11	convex	convex	NOUN
ejpam-4862	138	12	hop	hop	NOUN
ejpam-4862	138	13	domination	domination	NOUN
ejpam-4862	138	14	and	and	CCONJ
ejpam-4862	138	15	hop	hop	NOUN
ejpam-4862	138	16	domination	domination	NOUN
ejpam-4862	138	17	.	.	PUNCT
ejpam-4862	139	1	theorem	theorem	NOUN
ejpam-4862	139	2	2	2	NUM
ejpam-4862	139	3	.	.	PUNCT
ejpam-4862	139	4	let	let	VERB
ejpam-4862	139	5	a	a	PRON
ejpam-4862	139	6	and	and	CCONJ
ejpam-4862	139	7	b	b	NOUN
ejpam-4862	139	8	be	be	AUX
ejpam-4862	139	9	positive	positive	ADJ
ejpam-4862	139	10	integers	integer	NOUN
ejpam-4862	139	11	such	such	ADJ
ejpam-4862	139	12	that	that	SCONJ
ejpam-4862	139	13	2	2	NUM
ejpam-4862	139	14	≤	≤	NUM
ejpam-4862	139	15	a	a	DET
ejpam-4862	139	16	≤	≤	PROPN
ejpam-4862	139	17	b.	b.	NOUN
ejpam-4862	140	1	then	then	ADV
ejpam-4862	140	2	there	there	PRON
ejpam-4862	140	3	exists	exist	VERB
ejpam-4862	140	4	a	a	DET
ejpam-4862	140	5	connected	connected	ADJ
ejpam-4862	140	6	graph	graph	NOUN
ejpam-4862	140	7	g	g	ADP
ejpam-4862	140	8	such	such	ADJ
ejpam-4862	140	9	that	that	PRON
ejpam-4862	140	10	γh(g	γh(g	NOUN
ejpam-4862	140	11	)	)	PUNCT
ejpam-4862	140	12	=	=	SYM
ejpam-4862	140	13	a	a	PRON
ejpam-4862	140	14	and	and	CCONJ
ejpam-4862	140	15	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	140	16	)	)	PUNCT
ejpam-4862	140	17	=	=	SYM
ejpam-4862	140	18	b.	b.	NOUN
ejpam-4862	140	19	proof	proof	NOUN
ejpam-4862	140	20	.	.	PUNCT
ejpam-4862	141	1	for	for	ADP
ejpam-4862	141	2	a	a	DET
ejpam-4862	141	3	=	=	SYM
ejpam-4862	141	4	b	b	NOUN
ejpam-4862	141	5	,	,	PUNCT
ejpam-4862	141	6	consider	consider	VERB
ejpam-4862	141	7	the	the	DET
ejpam-4862	141	8	graph	graph	NOUN
ejpam-4862	141	9	g	g	NOUN
ejpam-4862	141	10	in	in	ADP
ejpam-4862	141	11	figure	figure	NOUN
ejpam-4862	141	12	4	4	NUM
ejpam-4862	141	13	.	.	PUNCT
ejpam-4862	142	1	let	let	VERB
ejpam-4862	142	2	c	c	NOUN
ejpam-4862	142	3	=	=	SYM
ejpam-4862	142	4	{	{	PUNCT
ejpam-4862	142	5	v1	v1	PROPN
ejpam-4862	142	6	,	,	PUNCT
ejpam-4862	142	7	v2	v2	PROPN
ejpam-4862	142	8	,	,	PUNCT
ejpam-4862	142	9	.	.	PUNCT
ejpam-4862	142	10	.	.	PUNCT
ejpam-4862	143	1	.	.	PUNCT
ejpam-4862	144	1	,	,	PUNCT
ejpam-4862	144	2	va	va	NOUN
ejpam-4862	144	3	}	}	PUNCT
ejpam-4862	144	4	.	.	PUNCT
ejpam-4862	145	1	then	then	ADV
ejpam-4862	145	2	c	c	PROPN
ejpam-4862	145	3	is	be	AUX
ejpam-4862	145	4	both	both	DET
ejpam-4862	145	5	γh	γh	ADV
ejpam-4862	145	6	-	-	PUNCT
ejpam-4862	145	7	set	set	VERB
ejpam-4862	145	8	and	and	CCONJ
ejpam-4862	145	9	γ̃conh	γ̃conh	NOUN
ejpam-4862	145	10	-	-	PUNCT
ejpam-4862	145	11	set	set	NOUN
ejpam-4862	145	12	of	of	ADP
ejpam-4862	145	13	g	g	NOUN
ejpam-4862	145	14	,	,	PUNCT
ejpam-4862	145	15	respectively	respectively	ADV
ejpam-4862	145	16	.	.	PUNCT
ejpam-4862	146	1	hence	hence	ADV
ejpam-4862	146	2	,	,	PUNCT
ejpam-4862	146	3	γh(g	γh(g	NOUN
ejpam-4862	146	4	)	)	PUNCT
ejpam-4862	146	5	=	=	SYM
ejpam-4862	146	6	a	a	DET
ejpam-4862	146	7	=	=	NOUN
ejpam-4862	146	8	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	146	9	)	)	PUNCT
ejpam-4862	146	10	.	.	PUNCT
ejpam-4862	146	11	.	.	PUNCT
ejpam-4862	146	12	.	.	PUNCT
ejpam-4862	146	13	.	.	PUNCT
ejpam-4862	147	1	v1	v1	VERB
ejpam-4862	147	2	v2	v2	PROPN
ejpam-4862	147	3	va	va	PROPN
ejpam-4862	147	4	g	g	PROPN
ejpam-4862	147	5	:	:	PUNCT
ejpam-4862	147	6	v3	v3	PROPN
ejpam-4862	147	7	va−1va−2	va−1va−2	PROPN
ejpam-4862	147	8	figure	figure	NOUN
ejpam-4862	147	9	4	4	NUM
ejpam-4862	147	10	:	:	PUNCT
ejpam-4862	147	11	graph	graph	VERB
ejpam-4862	147	12	g	g	NOUN
ejpam-4862	147	13	with	with	ADP
ejpam-4862	147	14	γh(g	γh(g	NOUN
ejpam-4862	147	15	)	)	PUNCT
ejpam-4862	147	16	=	=	SYM
ejpam-4862	147	17	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	147	18	)	)	PUNCT
ejpam-4862	147	19	suppose	suppose	VERB
ejpam-4862	147	20	that	that	SCONJ
ejpam-4862	147	21	a	a	DET
ejpam-4862	147	22	<	<	X
ejpam-4862	147	23	b.	b.	NOUN
ejpam-4862	147	24	for	for	ADP
ejpam-4862	147	25	a	a	DET
ejpam-4862	147	26	=	=	SYM
ejpam-4862	147	27	2	2	NUM
ejpam-4862	147	28	,	,	PUNCT
ejpam-4862	147	29	let	let	VERB
ejpam-4862	147	30	s	s	NOUN
ejpam-4862	147	31	=	=	VERB
ejpam-4862	147	32	b	b	NOUN
ejpam-4862	147	33	−	−	PROPN
ejpam-4862	147	34	2	2	NUM
ejpam-4862	147	35	and	and	CCONJ
ejpam-4862	147	36	consider	consider	VERB
ejpam-4862	147	37	the	the	DET
ejpam-4862	147	38	graph	graph	NOUN
ejpam-4862	147	39	h	h	NOUN
ejpam-4862	147	40	given	give	VERB
ejpam-4862	147	41	in	in	ADP
ejpam-4862	147	42	figure	figure	NOUN
ejpam-4862	147	43	5	5	NUM
ejpam-4862	147	44	.	.	PUNCT
ejpam-4862	148	1	let	let	VERB
ejpam-4862	148	2	c	c	NOUN
ejpam-4862	148	3	=	=	SYM
ejpam-4862	148	4	{	{	PUNCT
ejpam-4862	148	5	v1	v1	PROPN
ejpam-4862	148	6	,	,	PUNCT
ejpam-4862	148	7	v2	v2	NOUN
ejpam-4862	148	8	}	}	PUNCT
ejpam-4862	148	9	and	and	CCONJ
ejpam-4862	148	10	c	c	NOUN
ejpam-4862	148	11	′	′	NUM
ejpam-4862	148	12	=	=	SYM
ejpam-4862	148	13	{	{	PUNCT
ejpam-4862	148	14	v1	v1	NOUN
ejpam-4862	148	15	,	,	PUNCT
ejpam-4862	148	16	v2	v2	PROPN
ejpam-4862	148	17	,	,	PUNCT
ejpam-4862	148	18	y1	y1	NOUN
ejpam-4862	148	19	,	,	PUNCT
ejpam-4862	148	20	y2	y2	PROPN
ejpam-4862	148	21	,	,	PUNCT
ejpam-4862	148	22	.	.	PUNCT
ejpam-4862	148	23	.	.	PUNCT
ejpam-4862	149	1	.	.	PUNCT
ejpam-4862	150	1	,	,	PUNCT
ejpam-4862	150	2	ys	ys	VERB
ejpam-4862	150	3	}	}	PUNCT
ejpam-4862	150	4	.	.	PUNCT
ejpam-4862	151	1	then	then	ADV
ejpam-4862	151	2	c	c	PROPN
ejpam-4862	151	3	and	and	CCONJ
ejpam-4862	151	4	c	c	PROPN
ejpam-4862	151	5	′	′	NOUN
ejpam-4862	151	6	are	be	AUX
ejpam-4862	151	7	γh	γh	ADV
ejpam-4862	151	8	-	-	PUNCT
ejpam-4862	151	9	set	set	VERB
ejpam-4862	151	10	and	and	CCONJ
ejpam-4862	151	11	γ̃conh	γ̃conh	NOUN
ejpam-4862	151	12	-	-	PUNCT
ejpam-4862	151	13	set	set	NOUN
ejpam-4862	151	14	of	of	ADP
ejpam-4862	151	15	h	h	NOUN
ejpam-4862	151	16	,	,	PUNCT
ejpam-4862	151	17	respectively	respectively	ADV
ejpam-4862	151	18	.	.	PUNCT
ejpam-4862	152	1	therefore	therefore	ADV
ejpam-4862	152	2	,	,	PUNCT
ejpam-4862	152	3	γh(h	γh(h	PUNCT
ejpam-4862	152	4	)	)	PUNCT
ejpam-4862	152	5	=	=	SYM
ejpam-4862	152	6	2	2	NUM
ejpam-4862	152	7	and	and	CCONJ
ejpam-4862	152	8	γ̃conh(h	γ̃conh(h	NUM
ejpam-4862	152	9	)	)	PUNCT
ejpam-4862	153	1	=	=	PUNCT
ejpam-4862	153	2	s+	s+	PUNCT
ejpam-4862	153	3	2	2	X
ejpam-4862	153	4	=	=	SYM
ejpam-4862	153	5	b.	b.	PROPN
ejpam-4862	153	6	j.	j.	PROPN
ejpam-4862	153	7	a.	a.	PROPN
ejpam-4862	153	8	hassan	hassan	PROPN
ejpam-4862	153	9	et	et	PROPN
ejpam-4862	153	10	al	al	PROPN
ejpam-4862	153	11	.	.	PUNCT
ejpam-4862	153	12	/	/	SYM
ejpam-4862	153	13	eur	eur	PROPN
ejpam-4862	153	14	.	.	PUNCT
ejpam-4862	154	1	j.	j.	PROPN
ejpam-4862	154	2	pure	pure	PROPN
ejpam-4862	154	3	appl	appl	PROPN
ejpam-4862	154	4	.	.	PROPN
ejpam-4862	154	5	math	math	PROPN
ejpam-4862	154	6	,	,	PUNCT
ejpam-4862	154	7	16	16	NUM
ejpam-4862	154	8	(	(	PUNCT
ejpam-4862	154	9	4	4	NUM
ejpam-4862	154	10	)	)	PUNCT
ejpam-4862	154	11	(	(	PUNCT
ejpam-4862	154	12	2023	2023	NUM
ejpam-4862	154	13	)	)	PUNCT
ejpam-4862	154	14	,	,	PUNCT
ejpam-4862	154	15	2035	2035	NUM
ejpam-4862	154	16	-	-	SYM
ejpam-4862	154	17	2048	2048	NUM
ejpam-4862	154	18	2041	2041	NUM
ejpam-4862	154	19	v1	v1	NOUN
ejpam-4862	154	20	v2	v2	NOUN
ejpam-4862	154	21	y1	y1	NOUN
ejpam-4862	154	22	y2	y2	NOUN
ejpam-4862	154	23	ys	ys	INTJ
ejpam-4862	154	24	.	.	PUNCT
ejpam-4862	154	25	.	.	PUNCT
ejpam-4862	154	26	.	.	PUNCT
ejpam-4862	155	1	u	u	PRON
ejpam-4862	155	2	h	h	NOUN
ejpam-4862	155	3	:	:	PUNCT
ejpam-4862	155	4	figure	figure	VERB
ejpam-4862	155	5	5	5	NUM
ejpam-4862	155	6	:	:	PUNCT
ejpam-4862	155	7	graph	graph	VERB
ejpam-4862	155	8	g	g	NOUN
ejpam-4862	155	9	with	with	ADP
ejpam-4862	155	10	γh(g	γh(g	NOUN
ejpam-4862	155	11	)	)	PUNCT
ejpam-4862	155	12	<	<	X
ejpam-4862	155	13	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	155	14	)	)	PUNCT
ejpam-4862	155	15	for	for	ADP
ejpam-4862	155	16	a	a	DET
ejpam-4862	155	17	≥	≥	NOUN
ejpam-4862	155	18	3	3	NUM
ejpam-4862	155	19	,	,	PUNCT
ejpam-4862	155	20	let	let	VERB
ejpam-4862	155	21	s	s	PRON
ejpam-4862	155	22	=	=	NOUN
ejpam-4862	155	23	b−a	b−a	X
ejpam-4862	155	24	and	and	CCONJ
ejpam-4862	155	25	consider	consider	VERB
ejpam-4862	155	26	the	the	DET
ejpam-4862	155	27	graphg′	graphg′	NOUN
ejpam-4862	155	28	in	in	ADP
ejpam-4862	155	29	figure	figure	NOUN
ejpam-4862	155	30	6	6	NUM
ejpam-4862	155	31	.	.	PUNCT
ejpam-4862	156	1	let	let	VERB
ejpam-4862	156	2	c	c	NOUN
ejpam-4862	156	3	′	′	VERB
ejpam-4862	157	1	=	=	PUNCT
ejpam-4862	157	2	{	{	PUNCT
ejpam-4862	157	3	v1	v1	NOUN
ejpam-4862	157	4	,	,	PUNCT
ejpam-4862	157	5	v2	v2	PROPN
ejpam-4862	157	6	,	,	PUNCT
ejpam-4862	157	7	.	.	PUNCT
ejpam-4862	157	8	.	.	PUNCT
ejpam-4862	158	1	.	.	PUNCT
ejpam-4862	159	1	,	,	PUNCT
ejpam-4862	159	2	va−2	va−2	PROPN
ejpam-4862	159	3	,	,	PUNCT
ejpam-4862	159	4	u	u	NOUN
ejpam-4862	159	5	,	,	PUNCT
ejpam-4862	159	6	va	va	NOUN
ejpam-4862	159	7	}	}	PUNCT
ejpam-4862	159	8	and	and	CCONJ
ejpam-4862	159	9	c	c	X
ejpam-4862	159	10	′′	′′	NOUN
ejpam-4862	159	11	=	=	SYM
ejpam-4862	159	12	{	{	PUNCT
ejpam-4862	159	13	v1	v1	PROPN
ejpam-4862	159	14	,	,	PUNCT
ejpam-4862	159	15	v2	v2	PROPN
ejpam-4862	159	16	,	,	PUNCT
ejpam-4862	159	17	.	.	PUNCT
ejpam-4862	159	18	.	.	PUNCT
ejpam-4862	160	1	.	.	PUNCT
ejpam-4862	161	1	,	,	PUNCT
ejpam-4862	161	2	va	va	NOUN
ejpam-4862	161	3	,	,	PUNCT
ejpam-4862	161	4	y1	y1	PROPN
ejpam-4862	161	5	,	,	PUNCT
ejpam-4862	161	6	y2	y2	PROPN
ejpam-4862	161	7	,	,	PUNCT
ejpam-4862	161	8	.	.	PUNCT
ejpam-4862	161	9	.	.	PUNCT
ejpam-4862	161	10	.	.	PUNCT
ejpam-4862	162	1	,	,	PUNCT
ejpam-4862	162	2	ys	ys	VERB
ejpam-4862	162	3	}	}	PUNCT
ejpam-4862	162	4	.	.	PUNCT
ejpam-4862	163	1	then	then	ADV
ejpam-4862	163	2	c	c	NOUN
ejpam-4862	163	3	′	′	NOUN
ejpam-4862	163	4	and	and	CCONJ
ejpam-4862	163	5	c	c	X
ejpam-4862	164	1	′′	′′	PROPN
ejpam-4862	164	2	are	be	AUX
ejpam-4862	164	3	γh	γh	ADV
ejpam-4862	164	4	-	-	PUNCT
ejpam-4862	164	5	set	set	VERB
ejpam-4862	164	6	and	and	CCONJ
ejpam-4862	164	7	γ̃conh	γ̃conh	NOUN
ejpam-4862	164	8	-	-	PUNCT
ejpam-4862	164	9	set	set	NOUN
ejpam-4862	164	10	of	of	ADP
ejpam-4862	164	11	g′	g′	NOUN
ejpam-4862	164	12	,	,	PUNCT
ejpam-4862	164	13	respectively	respectively	ADV
ejpam-4862	164	14	.	.	PUNCT
ejpam-4862	165	1	therefore	therefore	ADV
ejpam-4862	165	2	,	,	PUNCT
ejpam-4862	165	3	γh(g	γh(g	PUNCT
ejpam-4862	165	4	′	′	NUM
ejpam-4862	165	5	)	)	PUNCT
ejpam-4862	165	6	=	=	PUNCT
ejpam-4862	166	1	a	a	PRON
ejpam-4862	166	2	and	and	CCONJ
ejpam-4862	166	3	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	166	4	′	′	NOUN
ejpam-4862	166	5	)	)	PUNCT
ejpam-4862	167	1	=	=	PUNCT
ejpam-4862	167	2	s+	s+	PUNCT
ejpam-4862	167	3	a	a	DET
ejpam-4862	167	4	=	=	X
ejpam-4862	167	5	b.	b.	PROPN
ejpam-4862	167	6	.	.	PUNCT
ejpam-4862	167	7	.	.	PUNCT
ejpam-4862	167	8	.	.	PUNCT
ejpam-4862	168	1	v1	v1	PROPN
ejpam-4862	168	2	v2	v2	PROPN
ejpam-4862	168	3	v3	v3	PROPN
ejpam-4862	168	4	va−2	va−2	PROPN
ejpam-4862	168	5	va−1	va−1	PROPN
ejpam-4862	168	6	va	va	PROPN
ejpam-4862	168	7	y1	y1	ADJ
ejpam-4862	168	8	y2	y2	NOUN
ejpam-4862	168	9	ys	ys	INTJ
ejpam-4862	168	10	.	.	PUNCT
ejpam-4862	168	11	.	.	PUNCT
ejpam-4862	168	12	.	.	PUNCT
ejpam-4862	169	1	u	u	PRON
ejpam-4862	169	2	g′	g′	NOUN
ejpam-4862	169	3	:	:	PUNCT
ejpam-4862	169	4	figure	figure	VERB
ejpam-4862	169	5	6	6	NUM
ejpam-4862	169	6	:	:	PUNCT
ejpam-4862	169	7	graph	graph	NOUN
ejpam-4862	169	8	g′	g′	NOUN
ejpam-4862	169	9	with	with	ADP
ejpam-4862	169	10	γh(g	γh(g	X
ejpam-4862	169	11	′	′	NUM
ejpam-4862	169	12	)	)	PUNCT
ejpam-4862	169	13	<	<	X
ejpam-4862	169	14	γ̃conh(g	γ̃conh(g	ADP
ejpam-4862	169	15	′	′	NOUN
ejpam-4862	169	16	)	)	PUNCT
ejpam-4862	169	17	corollary	corollary	ADJ
ejpam-4862	169	18	2	2	NUM
ejpam-4862	169	19	.	.	PUNCT
ejpam-4862	170	1	let	let	VERB
ejpam-4862	170	2	n	n	PRON
ejpam-4862	170	3	be	be	AUX
ejpam-4862	170	4	a	a	DET
ejpam-4862	170	5	positive	positive	ADJ
ejpam-4862	170	6	integer	integer	NOUN
ejpam-4862	170	7	.	.	PUNCT
ejpam-4862	171	1	then	then	ADV
ejpam-4862	171	2	there	there	PRON
ejpam-4862	171	3	exists	exist	VERB
ejpam-4862	171	4	a	a	DET
ejpam-4862	171	5	connected	connected	ADJ
ejpam-4862	171	6	graph	graph	NOUN
ejpam-4862	171	7	g	g	ADP
ejpam-4862	171	8	such	such	ADJ
ejpam-4862	171	9	that	that	DET
ejpam-4862	171	10	γ̃conh(g)−	γ̃conh(g)−	NOUN
ejpam-4862	171	11	γh(g	γh(g	NOUN
ejpam-4862	171	12	)	)	PUNCT
ejpam-4862	171	13	=	=	VERB
ejpam-4862	172	1	n.	n.	NOUN
ejpam-4862	172	2	in	in	ADP
ejpam-4862	172	3	other	other	ADJ
ejpam-4862	172	4	words	word	NOUN
ejpam-4862	172	5	,	,	PUNCT
ejpam-4862	172	6	γ̃conh(g)−	γ̃conh(g)−	NOUN
ejpam-4862	172	7	γh(g	γh(g	NOUN
ejpam-4862	172	8	)	)	PUNCT
ejpam-4862	172	9	can	can	AUX
ejpam-4862	172	10	be	be	AUX
ejpam-4862	172	11	made	make	VERB
ejpam-4862	172	12	arbitrarily	arbitrarily	ADV
ejpam-4862	172	13	large	large	ADJ
ejpam-4862	172	14	.	.	PUNCT
ejpam-4862	173	1	proposition	proposition	NOUN
ejpam-4862	173	2	2	2	NUM
ejpam-4862	173	3	.	.	PUNCT
ejpam-4862	174	1	let	let	VERB
ejpam-4862	174	2	n	n	PRON
ejpam-4862	174	3	be	be	AUX
ejpam-4862	174	4	any	any	DET
ejpam-4862	174	5	positive	positive	ADJ
ejpam-4862	174	6	integer	integer	NOUN
ejpam-4862	174	7	.	.	PUNCT
ejpam-4862	175	1	then	then	ADV
ejpam-4862	175	2	each	each	PRON
ejpam-4862	175	3	of	of	ADP
ejpam-4862	175	4	the	the	DET
ejpam-4862	175	5	following	follow	VERB
ejpam-4862	175	6	holds	hold	NOUN
ejpam-4862	175	7	.	.	PUNCT
ejpam-4862	176	1	(	(	PUNCT
ejpam-4862	176	2	i	i	NOUN
ejpam-4862	176	3	)	)	PUNCT
ejpam-4862	176	4	γ̃conh(pn	γ̃conh(pn	NOUN
ejpam-4862	176	5	)	)	PUNCT
ejpam-4862	176	6	=	=	PRON
ejpam-4862	176	7	{	{	PUNCT
ejpam-4862	176	8	2	2	NUM
ejpam-4862	176	9	if	if	SCONJ
ejpam-4862	176	10	n	n	X
ejpam-4862	176	11	=	=	SYM
ejpam-4862	176	12	2	2	NUM
ejpam-4862	176	13	,	,	PUNCT
ejpam-4862	176	14	3	3	NUM
ejpam-4862	176	15	n−	n−	NOUN
ejpam-4862	176	16	2	2	NUM
ejpam-4862	176	17	if	if	SCONJ
ejpam-4862	176	18	n	n	PRON
ejpam-4862	176	19	≥	≥	NOUN
ejpam-4862	176	20	4	4	NUM
ejpam-4862	176	21	.	.	PUNCT
ejpam-4862	177	1	j.	j.	PROPN
ejpam-4862	177	2	a.	a.	PROPN
ejpam-4862	177	3	hassan	hassan	PROPN
ejpam-4862	177	4	et	et	PROPN
ejpam-4862	177	5	al	al	PROPN
ejpam-4862	177	6	.	.	PUNCT
ejpam-4862	177	7	/	/	SYM
ejpam-4862	177	8	eur	eur	PROPN
ejpam-4862	177	9	.	.	PUNCT
ejpam-4862	178	1	j.	j.	PROPN
ejpam-4862	178	2	pure	pure	PROPN
ejpam-4862	178	3	appl	appl	PROPN
ejpam-4862	178	4	.	.	PROPN
ejpam-4862	178	5	math	math	PROPN
ejpam-4862	178	6	,	,	PUNCT
ejpam-4862	178	7	16	16	NUM
ejpam-4862	178	8	(	(	PUNCT
ejpam-4862	178	9	4	4	NUM
ejpam-4862	178	10	)	)	PUNCT
ejpam-4862	178	11	(	(	PUNCT
ejpam-4862	178	12	2023	2023	NUM
ejpam-4862	178	13	)	)	PUNCT
ejpam-4862	178	14	,	,	PUNCT
ejpam-4862	178	15	2035	2035	NUM
ejpam-4862	178	16	-	-	SYM
ejpam-4862	178	17	2048	2048	NUM
ejpam-4862	178	18	2042	2042	NUM
ejpam-4862	178	19	(	(	PUNCT
ejpam-4862	178	20	ii	ii	NOUN
ejpam-4862	178	21	)	)	PUNCT
ejpam-4862	178	22	γ̃conh(cn	γ̃conh(cn	NOUN
ejpam-4862	178	23	)	)	PUNCT
ejpam-4862	178	24	=	=	PUNCT
ejpam-4862	179	1			NOUN
ejpam-4862	179	2	2	2	NUM
ejpam-4862	179	3	if	if	SCONJ
ejpam-4862	179	4	n	n	NOUN
ejpam-4862	179	5	=	=	SYM
ejpam-4862	179	6	4	4	NUM
ejpam-4862	179	7	,	,	PUNCT
ejpam-4862	179	8	5	5	NUM
ejpam-4862	179	9	3	3	NUM
ejpam-4862	179	10	if	if	SCONJ
ejpam-4862	179	11	n	n	NOUN
ejpam-4862	179	12	=	=	SYM
ejpam-4862	179	13	3	3	NUM
ejpam-4862	179	14	,	,	PUNCT
ejpam-4862	179	15	6	6	NUM
ejpam-4862	179	16	n−	n−	NOUN
ejpam-4862	179	17	4	4	NUM
ejpam-4862	179	18	if	if	SCONJ
ejpam-4862	179	19	n	n	PRON
ejpam-4862	179	20	≥	≥	NOUN
ejpam-4862	179	21	7	7	NUM
ejpam-4862	179	22	.	.	PUNCT
ejpam-4862	180	1	proof	proof	NOUN
ejpam-4862	180	2	.	.	PUNCT
ejpam-4862	181	1	(	(	PUNCT
ejpam-4862	181	2	i	i	NOUN
ejpam-4862	181	3	)	)	PUNCT
ejpam-4862	181	4	clearly	clearly	ADV
ejpam-4862	181	5	,	,	PUNCT
ejpam-4862	181	6	γ̃conh(pn	γ̃conh(pn	ADJ
ejpam-4862	181	7	)	)	PUNCT
ejpam-4862	181	8	=	=	SYM
ejpam-4862	181	9	2	2	NUM
ejpam-4862	181	10	for	for	ADP
ejpam-4862	181	11	n	n	NOUN
ejpam-4862	181	12	=	=	SYM
ejpam-4862	181	13	2	2	NUM
ejpam-4862	181	14	,	,	PUNCT
ejpam-4862	181	15	3	3	NUM
ejpam-4862	181	16	.	.	PUNCT
ejpam-4862	181	17	suppose	suppose	VERB
ejpam-4862	181	18	that	that	SCONJ
ejpam-4862	181	19	n	n	PROPN
ejpam-4862	181	20	≥	≥	NUM
ejpam-4862	181	21	4	4	NUM
ejpam-4862	181	22	.	.	PUNCT
ejpam-4862	182	1	let	let	VERB
ejpam-4862	182	2	pn	pn	VERB
ejpam-4862	182	3	=	=	PUNCT
ejpam-4862	183	1	[	[	X
ejpam-4862	183	2	v1	v1	NOUN
ejpam-4862	183	3	,	,	PUNCT
ejpam-4862	183	4	v2	v2	NOUN
ejpam-4862	183	5	,	,	PUNCT
ejpam-4862	183	6	.	.	PUNCT
ejpam-4862	183	7	.	.	PUNCT
ejpam-4862	183	8	.	.	PUNCT
ejpam-4862	184	1	,	,	PUNCT
ejpam-4862	184	2	vn	vn	X
ejpam-4862	184	3	]	]	PUNCT
ejpam-4862	184	4	and	and	CCONJ
ejpam-4862	184	5	consider	consider	VERB
ejpam-4862	184	6	s	s	PRON
ejpam-4862	184	7	=	=	NOUN
ejpam-4862	184	8	{	{	PUNCT
ejpam-4862	184	9	v1	v1	PROPN
ejpam-4862	184	10	,	,	PUNCT
ejpam-4862	184	11	v2	v2	PROPN
ejpam-4862	184	12	,	,	PUNCT
ejpam-4862	184	13	.	.	PUNCT
ejpam-4862	184	14	.	.	PUNCT
ejpam-4862	185	1	.	.	PUNCT
ejpam-4862	186	1	,	,	PUNCT
ejpam-4862	186	2	vn−3	vn−3	PROPN
ejpam-4862	186	3	,	,	PUNCT
ejpam-4862	186	4	vn−2	vn−2	PROPN
ejpam-4862	186	5	}	}	PUNCT
ejpam-4862	186	6	.	.	PUNCT
ejpam-4862	187	1	clearly	clearly	ADV
ejpam-4862	187	2	,	,	PUNCT
ejpam-4862	187	3	s	s	VERB
ejpam-4862	187	4	is	be	AUX
ejpam-4862	187	5	a	a	DET
ejpam-4862	187	6	hop	hop	NOUN
ejpam-4862	187	7	dominating	dominating	NOUN
ejpam-4862	187	8	set	set	NOUN
ejpam-4862	187	9	of	of	ADP
ejpam-4862	187	10	pn	pn	PROPN
ejpam-4862	187	11	.	.	PROPN
ejpam-4862	187	12	observe	observe	VERB
ejpam-4862	187	13	that	that	DET
ejpam-4862	187	14	v	v	NOUN
ejpam-4862	187	15	(	(	PUNCT
ejpam-4862	187	16	pn	pn	NOUN
ejpam-4862	187	17	)	)	PUNCT
ejpam-4862	187	18	\	\	PROPN
ejpam-4862	187	19	s	s	PART
ejpam-4862	187	20	=	=	PUNCT
ejpam-4862	187	21	{	{	PUNCT
ejpam-4862	187	22	vn−1	vn−1	PROPN
ejpam-4862	187	23	,	,	PUNCT
ejpam-4862	187	24	vn	vn	VERB
ejpam-4862	187	25	}	}	PUNCT
ejpam-4862	187	26	is	be	AUX
ejpam-4862	187	27	convex	convex	ADJ
ejpam-4862	187	28	set	set	NOUN
ejpam-4862	187	29	of	of	ADP
ejpam-4862	187	30	pn	pn	PROPN
ejpam-4862	187	31	.	.	PUNCT
ejpam-4862	188	1	it	it	PRON
ejpam-4862	188	2	follows	follow	VERB
ejpam-4862	188	3	that	that	SCONJ
ejpam-4862	188	4	s	s	VERB
ejpam-4862	188	5	is	be	AUX
ejpam-4862	188	6	an	an	DET
ejpam-4862	188	7	outer	outer	ADJ
ejpam-4862	188	8	-	-	PUNCT
ejpam-4862	188	9	convex	convex	NOUN
ejpam-4862	188	10	hop	hop	NOUN
ejpam-4862	188	11	dominating	dominating	NOUN
ejpam-4862	188	12	set	set	NOUN
ejpam-4862	188	13	of	of	ADP
ejpam-4862	188	14	pn	pn	PROPN
ejpam-4862	188	15	.	.	PUNCT
ejpam-4862	189	1	since	since	SCONJ
ejpam-4862	189	2	the	the	DET
ejpam-4862	189	3	induced	induced	ADJ
ejpam-4862	189	4	subgraph	subgraph	NOUN
ejpam-4862	189	5	of	of	ADP
ejpam-4862	189	6	a	a	DET
ejpam-4862	189	7	convex	convex	NOUN
ejpam-4862	189	8	set	set	NOUN
ejpam-4862	189	9	is	be	AUX
ejpam-4862	189	10	always	always	ADV
ejpam-4862	189	11	connected	connect	VERB
ejpam-4862	189	12	,	,	PUNCT
ejpam-4862	189	13	it	it	PRON
ejpam-4862	189	14	follows	follow	VERB
ejpam-4862	189	15	that	that	SCONJ
ejpam-4862	189	16	s	s	VERB
ejpam-4862	189	17	is	be	AUX
ejpam-4862	189	18	a	a	DET
ejpam-4862	189	19	minimum	minimum	ADJ
ejpam-4862	189	20	outer	outer	ADJ
ejpam-4862	189	21	-	-	PUNCT
ejpam-4862	189	22	convex	convex	NOUN
ejpam-4862	189	23	hop	hop	NOUN
ejpam-4862	189	24	dominating	dominating	NOUN
ejpam-4862	189	25	set	set	NOUN
ejpam-4862	189	26	of	of	ADP
ejpam-4862	189	27	pn	pn	PROPN
ejpam-4862	189	28	.	.	PUNCT
ejpam-4862	190	1	thus	thus	ADV
ejpam-4862	190	2	,	,	PUNCT
ejpam-4862	190	3	γ̃conh(pn	γ̃conh(pn	ADJ
ejpam-4862	190	4	)	)	PUNCT
ejpam-4862	190	5	=	=	SYM
ejpam-4862	190	6	n−	n−	NOUN
ejpam-4862	190	7	2	2	NUM
ejpam-4862	190	8	for	for	ADP
ejpam-4862	190	9	all	all	DET
ejpam-4862	190	10	n	n	PRON
ejpam-4862	190	11	≥	≥	NOUN
ejpam-4862	190	12	4	4	NUM
ejpam-4862	190	13	.	.	PUNCT
ejpam-4862	190	14	(	(	PUNCT
ejpam-4862	190	15	ii	ii	NOUN
ejpam-4862	190	16	)	)	PUNCT
ejpam-4862	190	17	clearly	clearly	ADV
ejpam-4862	190	18	,	,	PUNCT
ejpam-4862	190	19	γ̃conh(c4	γ̃conh(c4	NOUN
ejpam-4862	190	20	)	)	PUNCT
ejpam-4862	190	21	=	=	SYM
ejpam-4862	190	22	2	2	NUM
ejpam-4862	190	23	=	=	SYM
ejpam-4862	190	24	γ̃conh(c5	γ̃conh(c5	NOUN
ejpam-4862	190	25	)	)	PUNCT
ejpam-4862	190	26	and	and	CCONJ
ejpam-4862	190	27	γ̃conh(c3	γ̃conh(c3	NOUN
ejpam-4862	190	28	)	)	PUNCT
ejpam-4862	191	1	=	=	SYM
ejpam-4862	191	2	3	3	NUM
ejpam-4862	191	3	=	=	SYM
ejpam-4862	191	4	γ̃conh(c6	γ̃conh(c6	PROPN
ejpam-4862	191	5	)	)	PUNCT
ejpam-4862	191	6	.	.	PUNCT
ejpam-4862	192	1	suppose	suppose	VERB
ejpam-4862	192	2	that	that	SCONJ
ejpam-4862	192	3	n	n	PROPN
ejpam-4862	192	4	≥	≥	NUM
ejpam-4862	192	5	7	7	NUM
ejpam-4862	192	6	.	.	PUNCT
ejpam-4862	193	1	let	let	VERB
ejpam-4862	193	2	cn	cn	PROPN
ejpam-4862	193	3	=	=	PUNCT
ejpam-4862	194	1	[	[	X
ejpam-4862	194	2	v1	v1	NOUN
ejpam-4862	194	3	,	,	PUNCT
ejpam-4862	194	4	v2	v2	NOUN
ejpam-4862	194	5	,	,	PUNCT
ejpam-4862	194	6	.	.	PUNCT
ejpam-4862	194	7	.	.	PUNCT
ejpam-4862	194	8	.	.	PUNCT
ejpam-4862	195	1	,	,	PUNCT
ejpam-4862	195	2	vn	vn	X
ejpam-4862	195	3	,	,	PUNCT
ejpam-4862	195	4	v1	v1	PROPN
ejpam-4862	195	5	]	]	PUNCT
ejpam-4862	195	6	and	and	CCONJ
ejpam-4862	195	7	consider	consider	VERB
ejpam-4862	195	8	s∗	s∗	PROPN
ejpam-4862	195	9	=	=	SYM
ejpam-4862	195	10	{	{	PUNCT
ejpam-4862	195	11	v1	v1	PROPN
ejpam-4862	195	12	,	,	PUNCT
ejpam-4862	195	13	v2	v2	PROPN
ejpam-4862	195	14	,	,	PUNCT
ejpam-4862	195	15	.	.	PUNCT
ejpam-4862	195	16	.	.	PUNCT
ejpam-4862	196	1	.	.	PUNCT
ejpam-4862	197	1	,	,	PUNCT
ejpam-4862	197	2	vn−5	vn−5	NOUN
ejpam-4862	197	3	,	,	PUNCT
ejpam-4862	197	4	vn−4	vn−4	NOUN
ejpam-4862	197	5	}	}	PUNCT
ejpam-4862	197	6	.	.	PUNCT
ejpam-4862	198	1	clearly	clearly	ADV
ejpam-4862	198	2	,	,	PUNCT
ejpam-4862	198	3	s∗	s∗	PROPN
ejpam-4862	198	4	is	be	AUX
ejpam-4862	198	5	hop	hop	NOUN
ejpam-4862	198	6	dominating	dominate	VERB
ejpam-4862	198	7	set	set	NOUN
ejpam-4862	198	8	of	of	ADP
ejpam-4862	198	9	cn	cn	PROPN
ejpam-4862	198	10	.	.	PROPN
ejpam-4862	198	11	notice	notice	VERB
ejpam-4862	198	12	that	that	SCONJ
ejpam-4862	198	13	v	v	X
ejpam-4862	198	14	(	(	PUNCT
ejpam-4862	198	15	cn	cn	PROPN
ejpam-4862	198	16	)	)	PUNCT
ejpam-4862	198	17	\	\	PROPN
ejpam-4862	198	18	s∗	s∗	PROPN
ejpam-4862	198	19	=	=	SYM
ejpam-4862	198	20	{	{	PUNCT
ejpam-4862	198	21	vn−3	vn−3	PROPN
ejpam-4862	198	22	,	,	PUNCT
ejpam-4862	198	23	vn−2	vn−2	PROPN
ejpam-4862	198	24	,	,	PUNCT
ejpam-4862	198	25	vn−1	vn−1	PROPN
ejpam-4862	198	26	,	,	PUNCT
ejpam-4862	198	27	vn	vn	VERB
ejpam-4862	198	28	}	}	PUNCT
ejpam-4862	198	29	is	be	AUX
ejpam-4862	198	30	a	a	DET
ejpam-4862	198	31	convex	convex	NOUN
ejpam-4862	198	32	set	set	NOUN
ejpam-4862	198	33	of	of	ADP
ejpam-4862	198	34	cn	cn	PROPN
ejpam-4862	198	35	.	.	PUNCT
ejpam-4862	199	1	it	it	PRON
ejpam-4862	199	2	follows	follow	VERB
ejpam-4862	199	3	that	that	SCONJ
ejpam-4862	199	4	s∗	s∗	PROPN
ejpam-4862	199	5	is	be	AUX
ejpam-4862	199	6	an	an	DET
ejpam-4862	199	7	outer	outer	ADJ
ejpam-4862	199	8	-	-	PUNCT
ejpam-4862	199	9	convex	convex	NOUN
ejpam-4862	199	10	hop	hop	NOUN
ejpam-4862	199	11	dominating	dominating	NOUN
ejpam-4862	199	12	set	set	NOUN
ejpam-4862	199	13	of	of	ADP
ejpam-4862	199	14	cn	cn	PROPN
ejpam-4862	199	15	.	.	PUNCT
ejpam-4862	200	1	since	since	SCONJ
ejpam-4862	200	2	the	the	DET
ejpam-4862	200	3	induced	induced	ADJ
ejpam-4862	200	4	subgraph	subgraph	NOUN
ejpam-4862	200	5	of	of	ADP
ejpam-4862	200	6	any	any	DET
ejpam-4862	200	7	convex	convex	NOUN
ejpam-4862	200	8	set	set	NOUN
ejpam-4862	200	9	is	be	AUX
ejpam-4862	200	10	connected	connect	VERB
ejpam-4862	200	11	,	,	PUNCT
ejpam-4862	200	12	it	it	PRON
ejpam-4862	200	13	follows	follow	VERB
ejpam-4862	200	14	that	that	SCONJ
ejpam-4862	200	15	s∗	s∗	PROPN
ejpam-4862	200	16	is	be	AUX
ejpam-4862	200	17	a	a	DET
ejpam-4862	200	18	minimum	minimum	ADJ
ejpam-4862	200	19	outer	outer	ADJ
ejpam-4862	200	20	-	-	PUNCT
ejpam-4862	200	21	convex	convex	NOUN
ejpam-4862	200	22	hop	hop	NOUN
ejpam-4862	200	23	dominating	dominating	NOUN
ejpam-4862	200	24	set	set	NOUN
ejpam-4862	200	25	of	of	ADP
ejpam-4862	200	26	cn	cn	PROPN
ejpam-4862	200	27	.	.	PUNCT
ejpam-4862	200	28	therefore	therefore	ADV
ejpam-4862	200	29	,	,	PUNCT
ejpam-4862	200	30	γ̃conh(cn	γ̃conh(cn	NOUN
ejpam-4862	200	31	)	)	PUNCT
ejpam-4862	201	1	=	=	NUM
ejpam-4862	201	2	n−	n−	NOUN
ejpam-4862	201	3	4	4	NUM
ejpam-4862	201	4	for	for	ADP
ejpam-4862	201	5	all	all	DET
ejpam-4862	201	6	n	n	PRON
ejpam-4862	201	7	≥	≥	NOUN
ejpam-4862	201	8	7	7	NUM
ejpam-4862	201	9	.	.	PUNCT
ejpam-4862	201	10	proposition	proposition	NOUN
ejpam-4862	201	11	3	3	X
ejpam-4862	201	12	.	.	PUNCT
ejpam-4862	202	1	let	let	VERB
ejpam-4862	202	2	g	g	NOUN
ejpam-4862	202	3	be	be	AUX
ejpam-4862	202	4	any	any	DET
ejpam-4862	202	5	graph	graph	NOUN
ejpam-4862	202	6	on	on	ADP
ejpam-4862	202	7	n	n	PRON
ejpam-4862	202	8	≥	≥	NUM
ejpam-4862	202	9	2	2	NUM
ejpam-4862	202	10	vertices	vertex	NOUN
ejpam-4862	202	11	.	.	PUNCT
ejpam-4862	203	1	if	if	SCONJ
ejpam-4862	203	2	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	203	3	)	)	PUNCT
ejpam-4862	203	4	=	=	SYM
ejpam-4862	203	5	2	2	NUM
ejpam-4862	203	6	,	,	PUNCT
ejpam-4862	203	7	then	then	ADV
ejpam-4862	203	8	γh(g	γh(g	PUNCT
ejpam-4862	203	9	)	)	PUNCT
ejpam-4862	203	10	=	=	SYM
ejpam-4862	204	1	2	2	X
ejpam-4862	204	2	.	.	PUNCT
ejpam-4862	205	1	however	however	ADV
ejpam-4862	205	2	,	,	PUNCT
ejpam-4862	205	3	the	the	DET
ejpam-4862	205	4	converse	converse	NOUN
ejpam-4862	205	5	is	be	AUX
ejpam-4862	205	6	not	not	PART
ejpam-4862	205	7	always	always	ADV
ejpam-4862	205	8	true	true	ADJ
ejpam-4862	205	9	.	.	PUNCT
ejpam-4862	206	1	proof	proof	NOUN
ejpam-4862	206	2	.	.	PUNCT
ejpam-4862	207	1	suppose	suppose	VERB
ejpam-4862	207	2	γ̃conh(g	γ̃conh(g	NOUN
ejpam-4862	207	3	)	)	PUNCT
ejpam-4862	207	4	=	=	SYM
ejpam-4862	207	5	2	2	X
ejpam-4862	207	6	.	.	PUNCT
ejpam-4862	207	7	then	then	ADV
ejpam-4862	207	8	γh(g	γh(g	PUNCT
ejpam-4862	207	9	)	)	PUNCT
ejpam-4862	207	10	≤	≤	NUM
ejpam-4862	207	11	2	2	NUM
ejpam-4862	207	12	by	by	ADP
ejpam-4862	207	13	remark	remark	NOUN
ejpam-4862	207	14	1	1	NUM
ejpam-4862	207	15	.	.	PUNCT
ejpam-4862	207	16	since	since	SCONJ
ejpam-4862	207	17	γh(g	γh(g	NOUN
ejpam-4862	207	18	)	)	PUNCT
ejpam-4862	207	19	≥	≥	NOUN
ejpam-4862	207	20	2	2	NUM
ejpam-4862	207	21	for	for	ADP
ejpam-4862	207	22	any	any	DET
ejpam-4862	207	23	graph	graph	NOUN
ejpam-4862	207	24	of	of	ADP
ejpam-4862	207	25	order	order	NOUN
ejpam-4862	207	26	n	n	PRON
ejpam-4862	207	27	≥	≥	NOUN
ejpam-4862	207	28	2	2	NUM
ejpam-4862	207	29	,	,	PUNCT
ejpam-4862	207	30	it	it	PRON
ejpam-4862	207	31	follows	follow	VERB
ejpam-4862	207	32	that	that	PRON
ejpam-4862	207	33	γh(g	γh(g	PUNCT
ejpam-4862	207	34	)	)	PUNCT
ejpam-4862	207	35	=	=	SYM
ejpam-4862	207	36	2	2	X
ejpam-4862	207	37	.	.	PUNCT
ejpam-4862	207	38	to	to	PART
ejpam-4862	207	39	see	see	VERB
ejpam-4862	207	40	the	the	DET
ejpam-4862	207	41	converse	converse	NOUN
ejpam-4862	207	42	is	be	AUX
ejpam-4862	207	43	not	not	PART
ejpam-4862	207	44	necessarily	necessarily	ADV
ejpam-4862	207	45	true	true	ADJ
ejpam-4862	207	46	,	,	PUNCT
ejpam-4862	207	47	consider	consider	VERB
ejpam-4862	207	48	p5	p5	ADJ
ejpam-4862	207	49	=	=	PUNCT
ejpam-4862	208	1	[	[	X
ejpam-4862	208	2	v1	v1	NOUN
ejpam-4862	208	3	,	,	PUNCT
ejpam-4862	208	4	v2	v2	PROPN
ejpam-4862	208	5	,	,	PUNCT
ejpam-4862	208	6	v3	v3	PROPN
ejpam-4862	208	7	,	,	PUNCT
ejpam-4862	208	8	v4	v4	PROPN
ejpam-4862	208	9	,	,	PUNCT
ejpam-4862	208	10	v5	v5	PROPN
ejpam-4862	208	11	]	]	PUNCT
ejpam-4862	208	12	.	.	PUNCT
ejpam-4862	209	1	let	let	VERB
ejpam-4862	209	2	c	c	NOUN
ejpam-4862	209	3	=	=	PUNCT
ejpam-4862	209	4	{	{	PUNCT
ejpam-4862	209	5	v2	v2	PROPN
ejpam-4862	209	6	,	,	PUNCT
ejpam-4862	209	7	v3	v3	PROPN
ejpam-4862	209	8	}	}	PUNCT
ejpam-4862	209	9	.	.	PUNCT
ejpam-4862	210	1	then	then	ADV
ejpam-4862	210	2	c	c	PROPN
ejpam-4862	210	3	is	be	AUX
ejpam-4862	210	4	a	a	DET
ejpam-4862	210	5	γh	γh	ADV
ejpam-4862	210	6	-	-	PUNCT
ejpam-4862	210	7	set	set	NOUN
ejpam-4862	210	8	of	of	ADP
ejpam-4862	210	9	p5	p5	NOUN
ejpam-4862	210	10	.	.	PUNCT
ejpam-4862	211	1	hence	hence	ADV
ejpam-4862	211	2	,	,	PUNCT
ejpam-4862	211	3	γh(p5	γh(p5	NOUN
ejpam-4862	211	4	)	)	PUNCT
ejpam-4862	211	5	=	=	SYM
ejpam-4862	211	6	2	2	X
ejpam-4862	211	7	.	.	PUNCT
ejpam-4862	211	8	however	however	ADV
ejpam-4862	211	9	,	,	PUNCT
ejpam-4862	211	10	γ̃conh(p5	γ̃conh(p5	NOUN
ejpam-4862	211	11	)	)	PUNCT
ejpam-4862	211	12	=	=	SYM
ejpam-4862	211	13	3	3	NUM
ejpam-4862	211	14	by	by	ADP
ejpam-4862	211	15	proposition	proposition	NOUN
ejpam-4862	211	16	2	2	NUM
ejpam-4862	211	17	.	.	PUNCT
ejpam-4862	212	1	the	the	DET
ejpam-4862	212	2	following	follow	VERB
ejpam-4862	212	3	concept	concept	NOUN
ejpam-4862	212	4	can	can	AUX
ejpam-4862	212	5	be	be	AUX
ejpam-4862	212	6	found	find	VERB
ejpam-4862	212	7	in	in	ADP
ejpam-4862	212	8	[	[	X
ejpam-4862	212	9	6	6	NUM
ejpam-4862	212	10	]	]	PUNCT
ejpam-4862	212	11	and	and	CCONJ
ejpam-4862	212	12	it	it	PRON
ejpam-4862	212	13	will	will	AUX
ejpam-4862	212	14	be	be	AUX
ejpam-4862	212	15	used	use	VERB
ejpam-4862	212	16	to	to	PART
ejpam-4862	212	17	characterize	characterize	VERB
ejpam-4862	212	18	outerconvex	outerconvex	NOUN
ejpam-4862	212	19	hop	hop	NOUN
ejpam-4862	212	20	dominating	dominating	NOUN
ejpam-4862	212	21	sets	set	NOUN
ejpam-4862	212	22	in	in	ADP
ejpam-4862	212	23	the	the	DET
ejpam-4862	212	24	join	join	NOUN
ejpam-4862	212	25	of	of	ADP
ejpam-4862	212	26	two	two	NUM
ejpam-4862	212	27	graphs	graph	NOUN
ejpam-4862	212	28	.	.	PUNCT
ejpam-4862	213	1	definition	definition	NOUN
ejpam-4862	213	2	2	2	NUM
ejpam-4862	213	3	.	.	PUNCT
ejpam-4862	214	1	let	let	VERB
ejpam-4862	214	2	g	g	PRON
ejpam-4862	214	3	be	be	AUX
ejpam-4862	214	4	a	a	DET
ejpam-4862	214	5	non	non	ADJ
ejpam-4862	214	6	-	-	ADJ
ejpam-4862	214	7	complete	complete	ADJ
ejpam-4862	214	8	graph	graph	NOUN
ejpam-4862	214	9	.	.	PUNCT
ejpam-4862	215	1	then	then	ADV
ejpam-4862	215	2	d	d	PROPN
ejpam-4862	215	3	⊆	⊆	NUM
ejpam-4862	215	4	v	v	ADP
ejpam-4862	215	5	(	(	PUNCT
ejpam-4862	215	6	g	g	NOUN
ejpam-4862	215	7	)	)	PUNCT
ejpam-4862	215	8	is	be	AUX
ejpam-4862	215	9	called	call	VERB
ejpam-4862	215	10	an	an	DET
ejpam-4862	215	11	outer	outer	ADJ
ejpam-4862	215	12	-	-	PUNCT
ejpam-4862	215	13	clique	clique	NOUN
ejpam-4862	215	14	pointwise	pointwise	PROPN
ejpam-4862	215	15	non	non	ADJ
ejpam-4862	215	16	-	-	ADJ
ejpam-4862	215	17	dominating	dominating	ADJ
ejpam-4862	215	18	set	set	NOUN
ejpam-4862	215	19	in	in	ADP
ejpam-4862	215	20	g	g	PROPN
ejpam-4862	215	21	if	if	SCONJ
ejpam-4862	215	22	d	d	PROPN
ejpam-4862	215	23	is	be	AUX
ejpam-4862	215	24	pointwise	pointwise	PROPN
ejpam-4862	215	25	non	non	ADJ
ejpam-4862	215	26	-	-	ADJ
ejpam-4862	215	27	dominating	dominating	ADJ
ejpam-4862	215	28	set	set	NOUN
ejpam-4862	215	29	and	and	CCONJ
ejpam-4862	215	30	v	v	NOUN
ejpam-4862	215	31	(	(	PUNCT
ejpam-4862	215	32	g	g	NOUN
ejpam-4862	215	33	)	)	PUNCT
ejpam-4862	215	34	\d	\d	NOUN
ejpam-4862	215	35	is	be	AUX
ejpam-4862	215	36	clique	clique	NOUN
ejpam-4862	215	37	set	set	NOUN
ejpam-4862	215	38	in	in	ADP
ejpam-4862	215	39	g.	g.	PROPN
ejpam-4862	215	40	the	the	DET
ejpam-4862	215	41	smallest	small	ADJ
ejpam-4862	215	42	cardinality	cardinality	NOUN
ejpam-4862	215	43	of	of	ADP
ejpam-4862	215	44	an	an	DET
ejpam-4862	215	45	outer	outer	ADJ
ejpam-4862	215	46	-	-	PUNCT
ejpam-4862	215	47	clique	clique	NOUN
ejpam-4862	215	48	pointwise	pointwise	PROPN
ejpam-4862	215	49	non	non	ADJ
ejpam-4862	215	50	-	-	ADJ
ejpam-4862	215	51	dominating	dominating	ADJ
ejpam-4862	215	52	set	set	NOUN
ejpam-4862	215	53	of	of	ADP
ejpam-4862	215	54	g	g	NOUN
ejpam-4862	215	55	,	,	PUNCT
ejpam-4862	215	56	denoted	denote	VERB
ejpam-4862	215	57	by	by	ADP
ejpam-4862	215	58	ocpnd(g	ocpnd(g	NOUN
ejpam-4862	215	59	)	)	PUNCT
ejpam-4862	215	60	,	,	PUNCT
ejpam-4862	215	61	is	be	AUX
ejpam-4862	215	62	called	call	VERB
ejpam-4862	215	63	the	the	DET
ejpam-4862	215	64	outer	outer	ADJ
ejpam-4862	215	65	-	-	PUNCT
ejpam-4862	215	66	clique	clique	NOUN
ejpam-4862	215	67	pointwise	pointwise	PROPN
ejpam-4862	215	68	non	non	ADJ
ejpam-4862	215	69	-	-	ADJ
ejpam-4862	215	70	domination	domination	ADJ
ejpam-4862	215	71	number	number	NOUN
ejpam-4862	215	72	of	of	ADP
ejpam-4862	215	73	g.	g.	PROPN
ejpam-4862	215	74	any	any	DET
ejpam-4862	215	75	outer	outer	ADJ
ejpam-4862	215	76	-	-	PUNCT
ejpam-4862	215	77	clique	clique	NOUN
ejpam-4862	215	78	pointwise	pointwise	PROPN
ejpam-4862	215	79	non	non	ADJ
ejpam-4862	215	80	-	-	ADJ
ejpam-4862	215	81	dominating	dominating	ADJ
ejpam-4862	215	82	set	set	NOUN
ejpam-4862	215	83	d	d	NOUN
ejpam-4862	215	84	of	of	ADP
ejpam-4862	215	85	g	g	NOUN
ejpam-4862	215	86	with	with	ADP
ejpam-4862	215	87	|d|	|d|	PROPN
ejpam-4862	215	88	=	=	SYM
ejpam-4862	215	89	ocpnd(g	ocpnd(g	PROPN
ejpam-4862	215	90	)	)	PUNCT
ejpam-4862	215	91	,	,	PUNCT
ejpam-4862	215	92	is	be	AUX
ejpam-4862	215	93	called	call	VERB
ejpam-4862	215	94	an	an	DET
ejpam-4862	215	95	ocpnd	ocpnd	NOUN
ejpam-4862	215	96	-	-	PUNCT
ejpam-4862	215	97	set	set	NOUN
ejpam-4862	215	98	of	of	ADP
ejpam-4862	215	99	g.	g.	PROPN
ejpam-4862	215	100	the	the	DET
ejpam-4862	215	101	following	follow	VERB
ejpam-4862	215	102	results	result	NOUN
ejpam-4862	215	103	will	will	AUX
ejpam-4862	215	104	be	be	AUX
ejpam-4862	215	105	used	use	VERB
ejpam-4862	215	106	to	to	PART
ejpam-4862	215	107	calculate	calculate	VERB
ejpam-4862	215	108	the	the	DET
ejpam-4862	215	109	exact	exact	ADJ
ejpam-4862	215	110	values	value	NOUN
ejpam-4862	215	111	of	of	ADP
ejpam-4862	215	112	the	the	DET
ejpam-4862	215	113	parameter	parameter	NOUN
ejpam-4862	215	114	on	on	ADP
ejpam-4862	215	115	the	the	DET
ejpam-4862	215	116	join	join	NOUN
ejpam-4862	215	117	of	of	ADP
ejpam-4862	215	118	two	two	NUM
ejpam-4862	215	119	graphs	graph	NOUN
ejpam-4862	215	120	.	.	PUNCT
ejpam-4862	216	1	theorem	theorem	NOUN
ejpam-4862	216	2	3	3	X
ejpam-4862	216	3	.	.	PUNCT
ejpam-4862	217	1	let	let	VERB
ejpam-4862	217	2	g	g	PRON
ejpam-4862	217	3	be	be	AUX
ejpam-4862	217	4	a	a	DET
ejpam-4862	217	5	non	non	ADJ
ejpam-4862	217	6	-	-	ADJ
ejpam-4862	217	7	complete	complete	ADJ
ejpam-4862	217	8	graph	graph	NOUN
ejpam-4862	217	9	of	of	ADP
ejpam-4862	217	10	order	order	NOUN
ejpam-4862	217	11	n.	n.	NOUN
ejpam-4862	217	12	then	then	ADV
ejpam-4862	217	13	1	1	NUM
ejpam-4862	217	14	≤	≤	NUM
ejpam-4862	217	15	ocpnd(g	ocpnd(g	ADP
ejpam-4862	217	16	)	)	PUNCT
ejpam-4862	217	17	≤	≤	NOUN
ejpam-4862	218	1	n	n	CCONJ
ejpam-4862	219	1	−	−	PROPN
ejpam-4862	219	2	1	1	NUM
ejpam-4862	219	3	.	.	PUNCT
ejpam-4862	220	1	moreover	moreover	ADV
ejpam-4862	220	2	,	,	PUNCT
ejpam-4862	220	3	(	(	PUNCT
ejpam-4862	220	4	i	i	NOUN
ejpam-4862	220	5	)	)	PUNCT
ejpam-4862	220	6	pnd(g	pnd(g	ADP
ejpam-4862	220	7	)	)	PUNCT
ejpam-4862	220	8	≤	≤	NUM
ejpam-4862	220	9	ocpnd(g	ocpnd(g	ADP
ejpam-4862	220	10	)	)	PUNCT
ejpam-4862	220	11	.	.	PUNCT
ejpam-4862	221	1	j.	j.	PROPN
ejpam-4862	221	2	a.	a.	PROPN
ejpam-4862	221	3	hassan	hassan	PROPN
ejpam-4862	221	4	et	et	PROPN
ejpam-4862	221	5	al	al	PROPN
ejpam-4862	221	6	.	.	PUNCT
ejpam-4862	221	7	/	/	SYM
ejpam-4862	221	8	eur	eur	PROPN
ejpam-4862	221	9	.	.	PUNCT
ejpam-4862	222	1	j.	j.	PROPN
ejpam-4862	222	2	pure	pure	PROPN
ejpam-4862	222	3	appl	appl	PROPN
ejpam-4862	222	4	.	.	PROPN
ejpam-4862	222	5	math	math	PROPN
ejpam-4862	222	6	,	,	PUNCT
ejpam-4862	222	7	16	16	NUM
ejpam-4862	222	8	(	(	PUNCT
ejpam-4862	222	9	4	4	NUM
ejpam-4862	222	10	)	)	PUNCT
ejpam-4862	222	11	(	(	PUNCT
ejpam-4862	222	12	2023	2023	NUM
ejpam-4862	222	13	)	)	PUNCT
ejpam-4862	222	14	,	,	PUNCT
ejpam-4862	222	15	2035	2035	NUM
ejpam-4862	222	16	-	-	SYM
ejpam-4862	222	17	2048	2048	NUM
ejpam-4862	222	18	2043	2043	NUM
ejpam-4862	222	19	(	(	PUNCT
ejpam-4862	222	20	ii	ii	NOUN
ejpam-4862	222	21	)	)	PUNCT
ejpam-4862	222	22	ocpnd(g	ocpnd(g	ADP
ejpam-4862	222	23	)	)	PUNCT
ejpam-4862	222	24	=	=	SYM
ejpam-4862	222	25	1	1	NUM
ejpam-4862	222	26	if	if	SCONJ
ejpam-4862	222	27	and	and	CCONJ
ejpam-4862	222	28	only	only	ADV
ejpam-4862	222	29	if	if	SCONJ
ejpam-4862	222	30	g	g	PROPN
ejpam-4862	222	31	has	have	VERB
ejpam-4862	222	32	an	an	DET
ejpam-4862	222	33	isolated	isolated	ADJ
ejpam-4862	222	34	vertex	vertex	NOUN
ejpam-4862	222	35	v	v	ADP
ejpam-4862	222	36	such	such	ADJ
ejpam-4862	222	37	that	that	PRON
ejpam-4862	222	38	⟨v	⟨v	NOUN
ejpam-4862	222	39	(	(	PUNCT
ejpam-4862	222	40	g	g	NOUN
ejpam-4862	222	41	)	)	PUNCT
ejpam-4862	222	42	\	\	NOUN
ejpam-4862	223	1	{	{	PUNCT
ejpam-4862	223	2	v}⟩	v}⟩	PROPN
ejpam-4862	223	3	is	be	AUX
ejpam-4862	223	4	complete	complete	ADJ
ejpam-4862	223	5	.	.	PUNCT
ejpam-4862	224	1	proof	proof	NOUN
ejpam-4862	224	2	.	.	PUNCT
ejpam-4862	225	1	since	since	SCONJ
ejpam-4862	225	2	∅	∅	NOUN
ejpam-4862	225	3	is	be	AUX
ejpam-4862	225	4	not	not	PART
ejpam-4862	225	5	an	an	DET
ejpam-4862	225	6	outer	outer	ADJ
ejpam-4862	225	7	-	-	PUNCT
ejpam-4862	225	8	clique	clique	NOUN
ejpam-4862	225	9	pointwise	pointwise	PROPN
ejpam-4862	225	10	non	non	ADJ
ejpam-4862	225	11	-	-	ADJ
ejpam-4862	225	12	dominating	dominating	ADJ
ejpam-4862	225	13	set	set	NOUN
ejpam-4862	225	14	of	of	ADP
ejpam-4862	225	15	g	g	PROPN
ejpam-4862	225	16	,	,	PUNCT
ejpam-4862	225	17	it	it	PRON
ejpam-4862	225	18	follows	follow	VERB
ejpam-4862	225	19	that	that	PRON
ejpam-4862	225	20	ocpnd(g	ocpnd(g	ADP
ejpam-4862	225	21	)	)	PUNCT
ejpam-4862	225	22	≥	≥	NOUN
ejpam-4862	225	23	1	1	NUM
ejpam-4862	225	24	.	.	PUNCT
ejpam-4862	226	1	also	also	ADV
ejpam-4862	226	2	,	,	PUNCT
ejpam-4862	226	3	since	since	SCONJ
ejpam-4862	226	4	v	v	NOUN
ejpam-4862	226	5	(	(	PUNCT
ejpam-4862	226	6	g	g	NOUN
ejpam-4862	226	7	)	)	PUNCT
ejpam-4862	226	8	\	\	NOUN
ejpam-4862	226	9	{	{	PUNCT
ejpam-4862	226	10	v	v	NOUN
ejpam-4862	226	11	}	}	PUNCT
ejpam-4862	226	12	is	be	AUX
ejpam-4862	226	13	an	an	DET
ejpam-4862	226	14	outer	outer	ADJ
ejpam-4862	226	15	-	-	PUNCT
ejpam-4862	226	16	clique	clique	NOUN
ejpam-4862	226	17	pointwise	pointwise	PROPN
ejpam-4862	226	18	non	non	ADJ
ejpam-4862	226	19	-	-	ADJ
ejpam-4862	226	20	dominating	dominating	ADJ
ejpam-4862	226	21	set	set	NOUN
ejpam-4862	226	22	of	of	ADP
ejpam-4862	226	23	g	g	NOUN
ejpam-4862	226	24	for	for	ADP
ejpam-4862	226	25	every	every	PRON
ejpam-4862	226	26	v	v	NUM
ejpam-4862	226	27	∈	∈	NOUN
ejpam-4862	226	28	v	v	NOUN
ejpam-4862	226	29	(	(	PUNCT
ejpam-4862	226	30	g	g	NOUN
ejpam-4862	226	31	)	)	PUNCT
ejpam-4862	226	32	,	,	PUNCT
ejpam-4862	226	33	by	by	ADP
ejpam-4862	226	34	definition	definition	NOUN
ejpam-4862	226	35	we	we	PRON
ejpam-4862	226	36	have	have	AUX
ejpam-4862	226	37	ocpnd(g	ocpnd(g	VERB
ejpam-4862	226	38	)	)	PUNCT
ejpam-4862	226	39	≤	≤	NOUN
ejpam-4862	227	1	n	n	CCONJ
ejpam-4862	228	1	−	−	PROPN
ejpam-4862	228	2	1	1	NUM
ejpam-4862	228	3	.	.	PUNCT
ejpam-4862	229	1	consequently	consequently	ADV
ejpam-4862	229	2	,	,	PUNCT
ejpam-4862	229	3	1	1	NUM
ejpam-4862	229	4	≤	≤	NUM
ejpam-4862	229	5	ocpnd(g	ocpnd(g	ADP
ejpam-4862	229	6	)	)	PUNCT
ejpam-4862	229	7	≤	≤	NUM
ejpam-4862	229	8	n−	n−	NOUN
ejpam-4862	229	9	1	1	NUM
ejpam-4862	229	10	.	.	PUNCT
ejpam-4862	230	1	(	(	PUNCT
ejpam-4862	230	2	i	i	NOUN
ejpam-4862	230	3	)	)	PUNCT
ejpam-4862	230	4	since	since	SCONJ
ejpam-4862	230	5	every	every	DET
ejpam-4862	230	6	outer	outer	ADJ
ejpam-4862	230	7	-	-	PUNCT
ejpam-4862	230	8	clique	clique	NOUN
ejpam-4862	230	9	pointwise	pointwise	PROPN
ejpam-4862	230	10	non	non	ADJ
ejpam-4862	230	11	-	-	ADJ
ejpam-4862	230	12	dominating	dominating	ADJ
ejpam-4862	230	13	set	set	NOUN
ejpam-4862	230	14	is	be	AUX
ejpam-4862	230	15	a	a	DET
ejpam-4862	230	16	pointwise	pointwise	ADJ
ejpam-4862	230	17	non	non	ADJ
ejpam-4862	230	18	-	-	ADJ
ejpam-4862	230	19	dominating	dominating	ADJ
ejpam-4862	230	20	set	set	NOUN
ejpam-4862	230	21	,	,	PUNCT
ejpam-4862	230	22	it	it	PRON
ejpam-4862	230	23	follows	follow	VERB
ejpam-4862	230	24	that	that	SCONJ
ejpam-4862	230	25	pnd(g	pnd(g	ADP
ejpam-4862	230	26	)	)	PUNCT
ejpam-4862	230	27	≤	≤	NUM
ejpam-4862	230	28	ocpnd(g	ocpnd(g	ADP
ejpam-4862	230	29	)	)	PUNCT
ejpam-4862	230	30	.	.	PUNCT
ejpam-4862	231	1	(	(	PUNCT
ejpam-4862	231	2	ii	ii	NOUN
ejpam-4862	231	3	)	)	PUNCT
ejpam-4862	231	4	suppose	suppose	VERB
ejpam-4862	231	5	that	that	SCONJ
ejpam-4862	231	6	ocpnd(g	ocpnd(g	ADP
ejpam-4862	231	7	)	)	PUNCT
ejpam-4862	231	8	=	=	SYM
ejpam-4862	231	9	1	1	NUM
ejpam-4862	231	10	,	,	PUNCT
ejpam-4862	231	11	say	say	VERB
ejpam-4862	231	12	{	{	PUNCT
ejpam-4862	231	13	v	v	NOUN
ejpam-4862	231	14	}	}	PUNCT
ejpam-4862	231	15	is	be	AUX
ejpam-4862	231	16	an	an	DET
ejpam-4862	231	17	ocpnd	ocpnd	NOUN
ejpam-4862	231	18	-	-	PUNCT
ejpam-4862	231	19	set	set	NOUN
ejpam-4862	231	20	of	of	ADP
ejpam-4862	231	21	g.	g.	PROPN
ejpam-4862	231	22	then	then	ADV
ejpam-4862	231	23	pnd(g	pnd(g	ADP
ejpam-4862	231	24	)	)	PUNCT
ejpam-4862	231	25	=	=	SYM
ejpam-4862	231	26	1	1	NUM
ejpam-4862	231	27	by	by	ADP
ejpam-4862	231	28	(	(	PUNCT
ejpam-4862	231	29	i	i	NOUN
ejpam-4862	231	30	)	)	PUNCT
ejpam-4862	231	31	.	.	PUNCT
ejpam-4862	232	1	it	it	PRON
ejpam-4862	232	2	follows	follow	VERB
ejpam-4862	232	3	that	that	SCONJ
ejpam-4862	232	4	g	g	PROPN
ejpam-4862	232	5	is	be	AUX
ejpam-4862	232	6	either	either	CCONJ
ejpam-4862	232	7	a	a	DET
ejpam-4862	232	8	trivial	trivial	ADJ
ejpam-4862	232	9	or	or	CCONJ
ejpam-4862	232	10	g	g	NOUN
ejpam-4862	232	11	has	have	VERB
ejpam-4862	232	12	an	an	DET
ejpam-4862	232	13	isolated	isolated	ADJ
ejpam-4862	232	14	vertex	vertex	NOUN
ejpam-4862	232	15	v.	v.	CCONJ
ejpam-4862	232	16	since	since	SCONJ
ejpam-4862	232	17	outer	outer	ADJ
ejpam-4862	232	18	-	-	PUNCT
ejpam-4862	232	19	clique	clique	NOUN
ejpam-4862	232	20	pointwise	pointwise	PROPN
ejpam-4862	232	21	non	non	NOUN
ejpam-4862	232	22	-	-	NOUN
ejpam-4862	232	23	domination	domination	NOUN
ejpam-4862	232	24	is	be	AUX
ejpam-4862	232	25	not	not	PART
ejpam-4862	232	26	defined	define	VERB
ejpam-4862	232	27	on	on	ADP
ejpam-4862	232	28	any	any	DET
ejpam-4862	232	29	complete	complete	ADJ
ejpam-4862	232	30	graph	graph	NOUN
ejpam-4862	232	31	,	,	PUNCT
ejpam-4862	232	32	it	it	PRON
ejpam-4862	232	33	follows	follow	VERB
ejpam-4862	232	34	that	that	SCONJ
ejpam-4862	232	35	g	g	PROPN
ejpam-4862	232	36	has	have	VERB
ejpam-4862	232	37	an	an	DET
ejpam-4862	232	38	isolated	isolated	ADJ
ejpam-4862	232	39	vertex	vertex	NOUN
ejpam-4862	232	40	v.	v.	ADP
ejpam-4862	232	41	moreover	moreover	ADV
ejpam-4862	232	42	,	,	PUNCT
ejpam-4862	232	43	⟨v	⟨v	X
ejpam-4862	232	44	(	(	PUNCT
ejpam-4862	232	45	g	g	NOUN
ejpam-4862	232	46	)	)	PUNCT
ejpam-4862	232	47	\	\	NOUN
ejpam-4862	233	1	{	{	PUNCT
ejpam-4862	233	2	v}⟩	v}⟩	PROPN
ejpam-4862	233	3	is	be	AUX
ejpam-4862	233	4	complete	complete	ADJ
ejpam-4862	233	5	by	by	ADP
ejpam-4862	233	6	assumption	assumption	NOUN
ejpam-4862	233	7	.	.	PUNCT
ejpam-4862	234	1	conversely	conversely	ADV
ejpam-4862	234	2	,	,	PUNCT
ejpam-4862	234	3	supposeg	supposeg	PROPN
ejpam-4862	234	4	has	have	VERB
ejpam-4862	234	5	an	an	DET
ejpam-4862	234	6	isolated	isolated	ADJ
ejpam-4862	234	7	vertex	vertex	NOUN
ejpam-4862	234	8	v	v	ADP
ejpam-4862	234	9	such	such	ADJ
ejpam-4862	234	10	that	that	PRON
ejpam-4862	234	11	⟨v	⟨v	NOUN
ejpam-4862	234	12	(	(	PUNCT
ejpam-4862	234	13	g)\{v}⟩	g)\{v}⟩	VERB
ejpam-4862	234	14	is	be	AUX
ejpam-4862	234	15	complete	complete	ADJ
ejpam-4862	234	16	.	.	PUNCT
ejpam-4862	235	1	then	then	ADV
ejpam-4862	235	2	{	{	PUNCT
ejpam-4862	235	3	v	v	NOUN
ejpam-4862	235	4	}	}	PUNCT
ejpam-4862	235	5	is	be	AUX
ejpam-4862	235	6	an	an	DET
ejpam-4862	235	7	outer	outer	ADJ
ejpam-4862	235	8	-	-	PUNCT
ejpam-4862	235	9	clique	clique	NOUN
ejpam-4862	235	10	pointwise	pointwise	PROPN
ejpam-4862	235	11	non	non	ADJ
ejpam-4862	235	12	-	-	ADJ
ejpam-4862	235	13	dominating	dominating	ADJ
ejpam-4862	235	14	set	set	VERB
ejpam-4862	235	15	ofg	ofg	PROPN
ejpam-4862	235	16	.	.	PUNCT
ejpam-4862	236	1	it	it	PRON
ejpam-4862	236	2	follows	follow	VERB
ejpam-4862	236	3	that	that	PRON
ejpam-4862	236	4	ocpnd(g	ocpnd(g	ADP
ejpam-4862	236	5	)	)	PUNCT
ejpam-4862	236	6	=	=	SYM
ejpam-4862	236	7	1	1	X
ejpam-4862	236	8	.	.	X
ejpam-4862	236	9	proposition	proposition	NOUN
ejpam-4862	236	10	4	4	NUM
ejpam-4862	236	11	.	.	PUNCT
ejpam-4862	237	1	let	let	VERB
ejpam-4862	237	2	n	n	PRON
ejpam-4862	237	3	≥	≥	X
ejpam-4862	237	4	2	2	NUM
ejpam-4862	237	5	be	be	AUX
ejpam-4862	237	6	any	any	DET
ejpam-4862	237	7	positive	positive	ADJ
ejpam-4862	237	8	integer	integer	NOUN
ejpam-4862	237	9	.	.	PUNCT
ejpam-4862	238	1	then	then	ADV
ejpam-4862	238	2	each	each	PRON
ejpam-4862	238	3	of	of	ADP
ejpam-4862	238	4	the	the	DET
ejpam-4862	238	5	following	follow	VERB
ejpam-4862	238	6	holds	hold	VERB
ejpam-4862	238	7	:	:	PUNCT
ejpam-4862	238	8	(	(	PUNCT
ejpam-4862	238	9	i	i	NOUN
ejpam-4862	238	10	)	)	PUNCT
ejpam-4862	238	11	ocpnd(pn	ocpnd(pn	PROPN
ejpam-4862	238	12	)	)	PUNCT
ejpam-4862	238	13	=	=	NOUN
ejpam-4862	238	14	{	{	PUNCT
ejpam-4862	238	15	2	2	NUM
ejpam-4862	238	16	if	if	SCONJ
ejpam-4862	238	17	n	n	NOUN
ejpam-4862	238	18	=	=	SYM
ejpam-4862	238	19	3	3	NUM
ejpam-4862	238	20	n−	n−	NOUN
ejpam-4862	238	21	2	2	NUM
ejpam-4862	238	22	if	if	SCONJ
ejpam-4862	238	23	n	n	PRON
ejpam-4862	238	24	≥	≥	NOUN
ejpam-4862	238	25	4	4	NUM
ejpam-4862	238	26	.	.	PUNCT
ejpam-4862	238	27	(	(	PUNCT
ejpam-4862	238	28	ii	ii	NOUN
ejpam-4862	238	29	)	)	PUNCT
ejpam-4862	238	30	ocpnd(cn	ocpnd(cn	NOUN
ejpam-4862	238	31	)	)	PUNCT
ejpam-4862	238	32	=	=	PUNCT
ejpam-4862	238	33	n−	n−	NOUN
ejpam-4862	238	34	2	2	NUM
ejpam-4862	238	35	for	for	ADP
ejpam-4862	238	36	all	all	DET
ejpam-4862	238	37	n	n	PRON
ejpam-4862	238	38	≥	≥	NOUN
ejpam-4862	238	39	4	4	NUM
ejpam-4862	238	40	.	.	PUNCT
ejpam-4862	239	1	(	(	PUNCT
ejpam-4862	239	2	iii	iii	X
ejpam-4862	239	3	)	)	PUNCT
ejpam-4862	239	4	ocpnd(kn	ocpnd(kn	NOUN
ejpam-4862	239	5	)	)	PUNCT
ejpam-4862	239	6	=	=	PUNCT
ejpam-4862	240	1	n−	n−	NOUN
ejpam-4862	240	2	1	1	NUM
ejpam-4862	240	3	for	for	ADP
ejpam-4862	240	4	all	all	DET
ejpam-4862	240	5	n	n	PRON
ejpam-4862	240	6	≥	≥	NOUN
ejpam-4862	240	7	2	2	NUM
ejpam-4862	240	8	.	.	PUNCT
ejpam-4862	240	9	proof	proof	NOUN
ejpam-4862	240	10	.	.	PUNCT
ejpam-4862	241	1	(	(	PUNCT
ejpam-4862	241	2	i	i	NOUN
ejpam-4862	241	3	)	)	PUNCT
ejpam-4862	241	4	clearly	clearly	ADV
ejpam-4862	241	5	,	,	PUNCT
ejpam-4862	241	6	ocpnd(p3	ocpnd(p3	PROPN
ejpam-4862	241	7	)	)	PUNCT
ejpam-4862	241	8	=	=	SYM
ejpam-4862	241	9	2	2	X
ejpam-4862	241	10	.	.	PUNCT
ejpam-4862	241	11	suppose	suppose	VERB
ejpam-4862	241	12	that	that	SCONJ
ejpam-4862	241	13	n	n	PROPN
ejpam-4862	241	14	≥	≥	NUM
ejpam-4862	241	15	4	4	NUM
ejpam-4862	241	16	.	.	PUNCT
ejpam-4862	242	1	let	let	VERB
ejpam-4862	242	2	pn	pn	VERB
ejpam-4862	242	3	=	=	PUNCT
ejpam-4862	243	1	[	[	X
ejpam-4862	243	2	v1	v1	NOUN
ejpam-4862	243	3	,	,	PUNCT
ejpam-4862	243	4	v2	v2	NOUN
ejpam-4862	243	5	,	,	PUNCT
ejpam-4862	243	6	.	.	PUNCT
ejpam-4862	243	7	.	.	PUNCT
ejpam-4862	243	8	.	.	PUNCT
ejpam-4862	244	1	,	,	PUNCT
ejpam-4862	244	2	vn	vn	X
ejpam-4862	244	3	]	]	PUNCT
ejpam-4862	244	4	and	and	CCONJ
ejpam-4862	244	5	consider	consider	VERB
ejpam-4862	244	6	c	c	NOUN
ejpam-4862	244	7	=	=	SYM
ejpam-4862	244	8	{	{	PUNCT
ejpam-4862	244	9	v1	v1	PROPN
ejpam-4862	244	10	,	,	PUNCT
ejpam-4862	244	11	v2	v2	PROPN
ejpam-4862	244	12	,	,	PUNCT
ejpam-4862	244	13	.	.	PUNCT
ejpam-4862	244	14	.	.	PUNCT
ejpam-4862	245	1	.	.	PUNCT
ejpam-4862	246	1	,	,	PUNCT
ejpam-4862	246	2	vn−3	vn−3	PROPN
ejpam-4862	246	3	,	,	PUNCT
ejpam-4862	246	4	vn−2	vn−2	PROPN
ejpam-4862	246	5	}	}	PUNCT
ejpam-4862	246	6	.	.	PUNCT
ejpam-4862	247	1	observe	observe	VERB
ejpam-4862	247	2	that	that	SCONJ
ejpam-4862	247	3	c	c	PROPN
ejpam-4862	247	4	is	be	AUX
ejpam-4862	247	5	a	a	DET
ejpam-4862	247	6	pointwise	pointwise	ADJ
ejpam-4862	247	7	non	non	ADJ
ejpam-4862	247	8	-	-	ADJ
ejpam-4862	247	9	dominating	dominating	ADJ
ejpam-4862	247	10	set	set	NOUN
ejpam-4862	247	11	of	of	ADP
ejpam-4862	247	12	pn	pn	PROPN
ejpam-4862	247	13	.	.	PUNCT
ejpam-4862	248	1	since	since	SCONJ
ejpam-4862	248	2	⟨v	⟨v	PROPN
ejpam-4862	248	3	(	(	PUNCT
ejpam-4862	248	4	pn	pn	NOUN
ejpam-4862	248	5	)	)	PUNCT
ejpam-4862	248	6	\	\	NOUN
ejpam-4862	248	7	c⟩	c⟩	PUNCT
ejpam-4862	248	8	∼=	∼=	PROPN
ejpam-4862	248	9	k2	k2	NOUN
ejpam-4862	248	10	,	,	PUNCT
ejpam-4862	248	11	it	it	PRON
ejpam-4862	248	12	follows	follow	VERB
ejpam-4862	248	13	that	that	SCONJ
ejpam-4862	248	14	v	v	X
ejpam-4862	248	15	(	(	PUNCT
ejpam-4862	248	16	pn	pn	NOUN
ejpam-4862	248	17	)	)	PUNCT
ejpam-4862	248	18	\	\	PROPN
ejpam-4862	249	1	c	c	NOUN
ejpam-4862	249	2	is	be	AUX
ejpam-4862	249	3	clique	clique	ADJ
ejpam-4862	249	4	in	in	ADP
ejpam-4862	249	5	pn	pn	PROPN
ejpam-4862	249	6	.	.	PROPN
ejpam-4862	250	1	hence	hence	ADV
ejpam-4862	250	2	,	,	PUNCT
ejpam-4862	250	3	c	c	PROPN
ejpam-4862	250	4	is	be	AUX
ejpam-4862	250	5	an	an	DET
ejpam-4862	250	6	outer	outer	ADJ
ejpam-4862	250	7	-	-	PUNCT
ejpam-4862	250	8	clique	clique	NOUN
ejpam-4862	250	9	pointwise	pointwise	PROPN
ejpam-4862	250	10	non	non	ADJ
ejpam-4862	250	11	-	-	ADJ
ejpam-4862	250	12	dominating	dominating	ADJ
ejpam-4862	250	13	set	set	NOUN
ejpam-4862	250	14	in	in	ADP
ejpam-4862	250	15	pn	pn	PROPN
ejpam-4862	250	16	.	.	PUNCT
ejpam-4862	251	1	since	since	SCONJ
ejpam-4862	251	2	k1	k1	NOUN
ejpam-4862	251	3	and	and	CCONJ
ejpam-4862	251	4	k2	k2	PROPN
ejpam-4862	251	5	are	be	AUX
ejpam-4862	251	6	the	the	DET
ejpam-4862	251	7	only	only	ADJ
ejpam-4862	251	8	complete	complete	ADJ
ejpam-4862	251	9	subgraphs	subgraph	NOUN
ejpam-4862	251	10	of	of	ADP
ejpam-4862	251	11	pn	pn	NOUN
ejpam-4862	251	12	for	for	ADP
ejpam-4862	251	13	all	all	DET
ejpam-4862	251	14	n	n	PRON
ejpam-4862	251	15	≥	≥	NOUN
ejpam-4862	251	16	4	4	NUM
ejpam-4862	251	17	,	,	PUNCT
ejpam-4862	251	18	it	it	PRON
ejpam-4862	251	19	follows	follow	VERB
ejpam-4862	251	20	that	that	SCONJ
ejpam-4862	251	21	c	c	PROPN
ejpam-4862	251	22	is	be	AUX
ejpam-4862	251	23	a	a	DET
ejpam-4862	251	24	minimum	minimum	ADJ
ejpam-4862	251	25	outer	outer	ADJ
ejpam-4862	251	26	-	-	PUNCT
ejpam-4862	251	27	clique	clique	NOUN
ejpam-4862	251	28	pointwise	pointwise	NOUN
ejpam-4862	251	29	nondominating	nondominate	VERB
ejpam-4862	251	30	set	set	NOUN
ejpam-4862	251	31	of	of	ADP
ejpam-4862	251	32	pn	pn	PROPN
ejpam-4862	251	33	.	.	PROPN
ejpam-4862	252	1	therefore	therefore	ADV
ejpam-4862	252	2	,	,	PUNCT
ejpam-4862	252	3	ocpnd(g	ocpnd(g	ADV
ejpam-4862	252	4	)	)	PUNCT
ejpam-4862	252	5	=	=	SYM
ejpam-4862	253	1	n−	n−	NOUN
ejpam-4862	253	2	2	2	NUM
ejpam-4862	253	3	for	for	ADP
ejpam-4862	253	4	all	all	DET
ejpam-4862	253	5	n	n	PRON
ejpam-4862	253	6	≥	≥	NOUN
ejpam-4862	253	7	4	4	NUM
ejpam-4862	253	8	.	.	PUNCT
ejpam-4862	253	9	(	(	PUNCT
ejpam-4862	253	10	ii	ii	NOUN
ejpam-4862	253	11	)	)	PUNCT
ejpam-4862	253	12	suppose	suppose	VERB
ejpam-4862	253	13	that	that	SCONJ
ejpam-4862	253	14	n	n	PROPN
ejpam-4862	253	15	≥	≥	NUM
ejpam-4862	253	16	4	4	NUM
ejpam-4862	253	17	.	.	PUNCT
ejpam-4862	253	18	then	then	ADV
ejpam-4862	253	19	applying	apply	VERB
ejpam-4862	253	20	the	the	DET
ejpam-4862	253	21	same	same	ADJ
ejpam-4862	253	22	argument	argument	NOUN
ejpam-4862	253	23	as	as	ADP
ejpam-4862	253	24	in	in	ADP
ejpam-4862	253	25	the	the	DET
ejpam-4862	253	26	proof	proof	NOUN
ejpam-4862	253	27	of	of	ADP
ejpam-4862	253	28	(	(	PUNCT
ejpam-4862	253	29	i	i	PROPN
ejpam-4862	253	30	)	)	PUNCT
ejpam-4862	253	31	,	,	PUNCT
ejpam-4862	253	32	we	we	PRON
ejpam-4862	253	33	have	have	VERB
ejpam-4862	253	34	ocpnd(cn	ocpnd(cn	NOUN
ejpam-4862	253	35	)	)	PUNCT
ejpam-4862	253	36	=	=	PUNCT
ejpam-4862	254	1	n−	n−	NOUN
ejpam-4862	254	2	2	2	NUM
ejpam-4862	254	3	for	for	ADP
ejpam-4862	254	4	all	all	DET
ejpam-4862	254	5	n	n	PRON
ejpam-4862	254	6	≥	≥	NOUN
ejpam-4862	254	7	4	4	NUM
ejpam-4862	254	8	.	.	PUNCT
ejpam-4862	254	9	(	(	PUNCT
ejpam-4862	254	10	iii	iii	X
ejpam-4862	254	11	)	)	PUNCT
ejpam-4862	254	12	let	let	VERB
ejpam-4862	254	13	v	v	NOUN
ejpam-4862	254	14	(	(	PUNCT
ejpam-4862	254	15	kn	kn	PROPN
ejpam-4862	254	16	)	)	PUNCT
ejpam-4862	254	17	=	=	SYM
ejpam-4862	254	18	{	{	PUNCT
ejpam-4862	254	19	v1	v1	PROPN
ejpam-4862	254	20	,	,	PUNCT
ejpam-4862	254	21	v2	v2	PROPN
ejpam-4862	254	22	,	,	PUNCT
ejpam-4862	254	23	.	.	PUNCT
ejpam-4862	254	24	.	.	PUNCT
ejpam-4862	255	1	.	.	PUNCT
ejpam-4862	256	1	,	,	PUNCT
ejpam-4862	256	2	vn	vn	PROPN
ejpam-4862	256	3	}	}	PUNCT
ejpam-4862	256	4	,	,	PUNCT
ejpam-4862	256	5	where	where	SCONJ
ejpam-4862	256	6	n	n	PRON
ejpam-4862	256	7	≥	≥	X
ejpam-4862	256	8	2	2	NUM
ejpam-4862	256	9	and	and	CCONJ
ejpam-4862	256	10	consider	consider	VERB
ejpam-4862	256	11	c∗	c∗	NOUN
ejpam-4862	256	12	=	=	SYM
ejpam-4862	256	13	{	{	PUNCT
ejpam-4862	256	14	v1	v1	PROPN
ejpam-4862	256	15	,	,	PUNCT
ejpam-4862	256	16	v2	v2	PROPN
ejpam-4862	256	17	,	,	PUNCT
ejpam-4862	256	18	.	.	PUNCT
ejpam-4862	256	19	.	.	PUNCT
ejpam-4862	257	1	.	.	PUNCT
ejpam-4862	258	1	,	,	PUNCT
ejpam-4862	258	2	vn−1	vn−1	ADJ
ejpam-4862	258	3	}	}	PUNCT
ejpam-4862	258	4	.	.	PUNCT
ejpam-4862	259	1	then	then	ADV
ejpam-4862	259	2	c∗	c∗	PROPN
ejpam-4862	259	3	is	be	AUX
ejpam-4862	259	4	a	a	DET
ejpam-4862	259	5	minimum	minimum	ADJ
ejpam-4862	259	6	outer	outer	ADJ
ejpam-4862	259	7	-	-	PUNCT
ejpam-4862	259	8	clique	clique	NOUN
ejpam-4862	259	9	pointwise	pointwise	PROPN
ejpam-4862	259	10	non	non	ADJ
ejpam-4862	259	11	-	-	ADJ
ejpam-4862	259	12	dominating	dominating	ADJ
ejpam-4862	259	13	set	set	NOUN
ejpam-4862	259	14	of	of	ADP
ejpam-4862	259	15	kn	kn	PROPN
ejpam-4862	259	16	for	for	ADP
ejpam-4862	259	17	all	all	DET
ejpam-4862	259	18	n	n	PRON
ejpam-4862	259	19	≥	≥	NOUN
ejpam-4862	259	20	2	2	NUM
ejpam-4862	259	21	.	.	PUNCT
ejpam-4862	260	1	hence	hence	ADV
ejpam-4862	260	2	,	,	PUNCT
ejpam-4862	260	3	ocpnd(kn	ocpnd(kn	ADJ
ejpam-4862	260	4	)	)	PUNCT
ejpam-4862	260	5	=	=	PUNCT
ejpam-4862	261	1	n−	n−	NOUN
ejpam-4862	261	2	1	1	NUM
ejpam-4862	261	3	for	for	ADP
ejpam-4862	261	4	all	all	DET
ejpam-4862	261	5	n	n	PRON
ejpam-4862	261	6	≥	≥	NUM
ejpam-4862	261	7	2	2	NUM
ejpam-4862	261	8	.	.	PUNCT
ejpam-4862	261	9	theorem	theorem	VERB
ejpam-4862	261	10	4	4	NUM
ejpam-4862	261	11	.	.	PUNCT
ejpam-4862	262	1	[	[	X
ejpam-4862	262	2	9	9	NUM
ejpam-4862	262	3	]	]	PUNCT
ejpam-4862	262	4	let	let	VERB
ejpam-4862	262	5	g	g	NOUN
ejpam-4862	262	6	and	and	CCONJ
ejpam-4862	262	7	h	h	NOUN
ejpam-4862	262	8	be	be	VERB
ejpam-4862	262	9	any	any	DET
ejpam-4862	262	10	two	two	NUM
ejpam-4862	262	11	graphs	graph	NOUN
ejpam-4862	262	12	.	.	PUNCT
ejpam-4862	263	1	a	a	DET
ejpam-4862	263	2	set	set	NOUN
ejpam-4862	263	3	s	s	NOUN
ejpam-4862	263	4	⊆	⊆	NUM
ejpam-4862	263	5	v	v	NOUN
ejpam-4862	263	6	(	(	PUNCT
ejpam-4862	263	7	g+h	g+h	PROPN
ejpam-4862	263	8	)	)	PUNCT
ejpam-4862	263	9	is	be	AUX
ejpam-4862	263	10	hop	hop	NOUN
ejpam-4862	263	11	dominating	dominate	VERB
ejpam-4862	263	12	set	set	NOUN
ejpam-4862	263	13	of	of	ADP
ejpam-4862	263	14	g+h	g+h	PROPN
ejpam-4862	263	15	if	if	SCONJ
ejpam-4862	264	1	and	and	CCONJ
ejpam-4862	264	2	only	only	ADV
ejpam-4862	264	3	if	if	SCONJ
ejpam-4862	264	4	s	s	NOUN
ejpam-4862	264	5	=	=	PUNCT
ejpam-4862	264	6	sg	sg	PROPN
ejpam-4862	264	7	∪sh	∪sh	NOUN
ejpam-4862	264	8	,	,	PUNCT
ejpam-4862	264	9	where	where	SCONJ
ejpam-4862	264	10	sg	sg	PROPN
ejpam-4862	264	11	and	and	CCONJ
ejpam-4862	264	12	sh	sh	PROPN
ejpam-4862	264	13	are	be	AUX
ejpam-4862	264	14	pointwise	pointwise	PROPN
ejpam-4862	264	15	non	non	ADJ
ejpam-4862	264	16	-	-	ADJ
ejpam-4862	264	17	dominating	dominating	ADJ
ejpam-4862	264	18	sets	set	NOUN
ejpam-4862	264	19	of	of	ADP
ejpam-4862	264	20	g	g	PROPN
ejpam-4862	264	21	and	and	CCONJ
ejpam-4862	264	22	h	h	NOUN
ejpam-4862	264	23	,	,	PUNCT
ejpam-4862	264	24	respectively	respectively	ADV
ejpam-4862	264	25	.	.	PUNCT
ejpam-4862	265	1	j.	j.	PROPN
ejpam-4862	265	2	a.	a.	PROPN
ejpam-4862	265	3	hassan	hassan	PROPN
ejpam-4862	265	4	et	et	PROPN
ejpam-4862	265	5	al	al	PROPN
ejpam-4862	265	6	.	.	PUNCT
ejpam-4862	265	7	/	/	SYM
ejpam-4862	265	8	eur	eur	PROPN
ejpam-4862	265	9	.	.	PUNCT
ejpam-4862	266	1	j.	j.	PROPN
ejpam-4862	266	2	pure	pure	PROPN
ejpam-4862	266	3	appl	appl	PROPN
ejpam-4862	266	4	.	.	PROPN
ejpam-4862	266	5	math	math	PROPN
ejpam-4862	266	6	,	,	PUNCT
ejpam-4862	266	7	16	16	NUM
ejpam-4862	266	8	(	(	PUNCT
ejpam-4862	266	9	4	4	NUM
ejpam-4862	266	10	)	)	PUNCT
ejpam-4862	266	11	(	(	PUNCT
ejpam-4862	266	12	2023	2023	NUM
ejpam-4862	266	13	)	)	PUNCT
ejpam-4862	266	14	,	,	PUNCT
ejpam-4862	266	15	2035	2035	NUM
ejpam-4862	266	16	-	-	SYM
ejpam-4862	266	17	2048	2048	NUM
ejpam-4862	266	18	2044	2044	NUM
ejpam-4862	266	19	theorem	theorem	VERB
ejpam-4862	266	20	5	5	NUM
ejpam-4862	266	21	.	.	PUNCT
ejpam-4862	267	1	[	[	X
ejpam-4862	267	2	8	8	NUM
ejpam-4862	267	3	]	]	PUNCT
ejpam-4862	267	4	let	let	VERB
ejpam-4862	267	5	g	g	NOUN
ejpam-4862	267	6	and	and	CCONJ
ejpam-4862	267	7	h	h	NOUN
ejpam-4862	267	8	be	be	VERB
ejpam-4862	267	9	two	two	NUM
ejpam-4862	267	10	connected	connected	ADJ
ejpam-4862	267	11	graphs	graph	NOUN
ejpam-4862	267	12	.	.	PUNCT
ejpam-4862	268	1	then	then	ADV
ejpam-4862	268	2	a	a	DET
ejpam-4862	268	3	proper	proper	ADJ
ejpam-4862	268	4	subset	subset	NOUN
ejpam-4862	268	5	c	c	NOUN
ejpam-4862	268	6	=	=	PUNCT
ejpam-4862	268	7	s1∪s2	s1∪s2	NUM
ejpam-4862	268	8	of	of	ADP
ejpam-4862	268	9	v	v	NOUN
ejpam-4862	268	10	(	(	PUNCT
ejpam-4862	268	11	g+h	g+h	PROPN
ejpam-4862	268	12	)	)	PUNCT
ejpam-4862	268	13	,	,	PUNCT
ejpam-4862	268	14	where	where	SCONJ
ejpam-4862	268	15	s1	s1	PROPN
ejpam-4862	268	16	⊆	⊆	NUM
ejpam-4862	268	17	v	v	NOUN
ejpam-4862	268	18	(	(	PUNCT
ejpam-4862	268	19	g	g	NOUN
ejpam-4862	268	20	)	)	PUNCT
ejpam-4862	268	21	and	and	CCONJ
ejpam-4862	268	22	s2	s2	VERB
ejpam-4862	268	23	⊆	⊆	NUM
ejpam-4862	268	24	v	v	NOUN
ejpam-4862	268	25	(	(	PUNCT
ejpam-4862	268	26	h	h	NOUN
ejpam-4862	268	27	)	)	PUNCT
ejpam-4862	268	28	,	,	PUNCT
ejpam-4862	268	29	is	be	AUX
ejpam-4862	268	30	a	a	DET
ejpam-4862	268	31	convex	convex	NOUN
ejpam-4862	268	32	set	set	VERB
ejpam-4862	268	33	in	in	ADP
ejpam-4862	268	34	g+h	g+h	PROPN
ejpam-4862	269	1	if	if	SCONJ
ejpam-4862	269	2	and	and	CCONJ
ejpam-4862	269	3	only	only	ADV
ejpam-4862	269	4	if	if	SCONJ
ejpam-4862	269	5	s1	s1	PROPN
ejpam-4862	269	6	and	and	CCONJ
ejpam-4862	269	7	s2	s2	NOUN
ejpam-4862	269	8	induce	induce	VERB
ejpam-4862	269	9	complete	complete	ADJ
ejpam-4862	269	10	subgraphs	subgraph	NOUN
ejpam-4862	269	11	of	of	ADP
ejpam-4862	269	12	g	g	NOUN
ejpam-4862	269	13	and	and	CCONJ
ejpam-4862	269	14	h	h	NOUN
ejpam-4862	269	15	,	,	PUNCT
ejpam-4862	269	16	respectively	respectively	ADV
ejpam-4862	269	17	,	,	PUNCT
ejpam-4862	269	18	where	where	SCONJ
ejpam-4862	269	19	it	it	PRON
ejpam-4862	269	20	may	may	AUX
ejpam-4862	269	21	occur	occur	VERB
ejpam-4862	269	22	that	that	DET
ejpam-4862	269	23	s1	s1	NOUN
ejpam-4862	269	24	=	=	PUNCT
ejpam-4862	269	25	∅	∅	NOUN
ejpam-4862	269	26	or	or	CCONJ
ejpam-4862	269	27	s2	s2	VERB
ejpam-4862	269	28	=	=	PUNCT
ejpam-4862	269	29	∅.	∅.	NOUN
ejpam-4862	269	30	theorem	theorem	VERB
ejpam-4862	269	31	6	6	NUM
ejpam-4862	269	32	.	.	PUNCT
ejpam-4862	270	1	let	let	VERB
ejpam-4862	270	2	g	g	NOUN
ejpam-4862	270	3	and	and	CCONJ
ejpam-4862	270	4	h	h	NOUN
ejpam-4862	270	5	be	be	VERB
ejpam-4862	270	6	two	two	NUM
ejpam-4862	270	7	non	non	ADJ
ejpam-4862	270	8	-	-	ADJ
ejpam-4862	270	9	complete	complete	ADJ
ejpam-4862	270	10	graphs	graph	NOUN
ejpam-4862	270	11	.	.	PUNCT
ejpam-4862	271	1	a	a	DET
ejpam-4862	271	2	set	set	NOUN
ejpam-4862	271	3	c	c	NOUN
ejpam-4862	271	4	⊆	⊆	NUM
ejpam-4862	271	5	v	v	NOUN
ejpam-4862	271	6	(	(	PUNCT
ejpam-4862	271	7	g	g	PROPN
ejpam-4862	271	8	+	+	NOUN
ejpam-4862	271	9	h	h	NOUN
ejpam-4862	271	10	)	)	PUNCT
ejpam-4862	271	11	is	be	AUX
ejpam-4862	271	12	an	an	DET
ejpam-4862	271	13	outer	outer	ADJ
ejpam-4862	271	14	-	-	PUNCT
ejpam-4862	271	15	convex	convex	NOUN
ejpam-4862	271	16	hop	hop	NOUN
ejpam-4862	271	17	dominating	dominating	NOUN
ejpam-4862	271	18	set	set	NOUN
ejpam-4862	271	19	of	of	ADP
ejpam-4862	271	20	g+h	g+h	PROPN
ejpam-4862	272	1	if	if	SCONJ
ejpam-4862	272	2	and	and	CCONJ
ejpam-4862	272	3	only	only	ADV
ejpam-4862	272	4	if	if	SCONJ
ejpam-4862	272	5	c	c	X
ejpam-4862	272	6	=	=	SYM
ejpam-4862	272	7	cg∪ch	cg∪ch	PROPN
ejpam-4862	272	8	,	,	PUNCT
ejpam-4862	272	9	where	where	SCONJ
ejpam-4862	272	10	cg	cg	NOUN
ejpam-4862	272	11	and	and	CCONJ
ejpam-4862	272	12	ch	ch	NOUN
ejpam-4862	272	13	are	be	AUX
ejpam-4862	272	14	outer	outer	ADJ
ejpam-4862	272	15	-	-	PUNCT
ejpam-4862	272	16	clique	clique	NOUN
ejpam-4862	272	17	pointwise	pointwise	PROPN
ejpam-4862	272	18	non	non	ADJ
ejpam-4862	272	19	-	-	ADJ
ejpam-4862	272	20	dominating	dominating	ADJ
ejpam-4862	272	21	sets	set	NOUN
ejpam-4862	272	22	of	of	ADP
ejpam-4862	272	23	g	g	PROPN
ejpam-4862	272	24	and	and	CCONJ
ejpam-4862	272	25	h	h	NOUN
ejpam-4862	272	26	,	,	PUNCT
ejpam-4862	272	27	respectively	respectively	ADV
ejpam-4862	272	28	.	.	PUNCT
ejpam-4862	273	1	proof	proof	NOUN
ejpam-4862	273	2	.	.	PUNCT
ejpam-4862	274	1	suppose	suppose	VERB
ejpam-4862	274	2	that	that	SCONJ
ejpam-4862	274	3	c	c	PROPN
ejpam-4862	274	4	is	be	AUX
ejpam-4862	274	5	an	an	DET
ejpam-4862	274	6	outer	outer	ADJ
ejpam-4862	274	7	-	-	PUNCT
ejpam-4862	274	8	convex	convex	NOUN
ejpam-4862	274	9	hop	hop	NOUN
ejpam-4862	274	10	dominating	dominating	NOUN
ejpam-4862	274	11	set	set	NOUN
ejpam-4862	274	12	ofg+h	ofg+h	PROPN
ejpam-4862	274	13	.	.	PUNCT
ejpam-4862	275	1	if	if	SCONJ
ejpam-4862	275	2	cg	cg	NOUN
ejpam-4862	275	3	=	=	NOUN
ejpam-4862	275	4	∅	∅	NOUN
ejpam-4862	275	5	,	,	PUNCT
ejpam-4862	275	6	then	then	ADV
ejpam-4862	275	7	v	v	X
ejpam-4862	275	8	(	(	PUNCT
ejpam-4862	275	9	g	g	NOUN
ejpam-4862	275	10	)	)	PUNCT
ejpam-4862	275	11	⊈	⊈	PROPN
ejpam-4862	275	12	n2	n2	PROPN
ejpam-4862	275	13	g[c	g[c	PROPN
ejpam-4862	275	14	]	]	PUNCT
ejpam-4862	275	15	.	.	PUNCT
ejpam-4862	276	1	however	however	ADV
ejpam-4862	276	2	,	,	PUNCT
ejpam-4862	276	3	this	this	PRON
ejpam-4862	276	4	is	be	AUX
ejpam-4862	276	5	a	a	DET
ejpam-4862	276	6	contradiction	contradiction	NOUN
ejpam-4862	276	7	to	to	ADP
ejpam-4862	276	8	the	the	DET
ejpam-4862	276	9	fact	fact	NOUN
ejpam-4862	276	10	that	that	SCONJ
ejpam-4862	276	11	c	c	PROPN
ejpam-4862	276	12	is	be	AUX
ejpam-4862	276	13	a	a	DET
ejpam-4862	276	14	hop	hop	NOUN
ejpam-4862	276	15	dominating	dominating	NOUN
ejpam-4862	276	16	set	set	NOUN
ejpam-4862	276	17	of	of	ADP
ejpam-4862	276	18	g	g	PROPN
ejpam-4862	276	19	+	+	PROPN
ejpam-4862	276	20	h.	h.	PROPN
ejpam-4862	276	21	thus	thus	ADV
ejpam-4862	276	22	,	,	PUNCT
ejpam-4862	276	23	cg	cg	PROPN
ejpam-4862	276	24	̸=	̸=	PROPN
ejpam-4862	276	25	∅.	∅.	PRON
ejpam-4862	276	26	similarly	similarly	ADV
ejpam-4862	276	27	,	,	PUNCT
ejpam-4862	276	28	sh	sh	PROPN
ejpam-4862	276	29	̸=	̸=	PROPN
ejpam-4862	276	30	∅.	∅.	VERB
ejpam-4862	276	31	now	now	ADV
ejpam-4862	276	32	,	,	PUNCT
ejpam-4862	276	33	since	since	SCONJ
ejpam-4862	276	34	c	c	PROPN
ejpam-4862	276	35	is	be	AUX
ejpam-4862	276	36	a	a	DET
ejpam-4862	276	37	hop	hop	NOUN
ejpam-4862	276	38	dominating	dominating	NOUN
ejpam-4862	276	39	set	set	NOUN
ejpam-4862	276	40	of	of	ADP
ejpam-4862	276	41	g	g	PROPN
ejpam-4862	276	42	+	+	CCONJ
ejpam-4862	276	43	h	h	NOUN
ejpam-4862	276	44	,	,	PUNCT
ejpam-4862	276	45	it	it	PRON
ejpam-4862	276	46	follows	follow	VERB
ejpam-4862	276	47	that	that	PRON
ejpam-4862	276	48	cg	cg	NOUN
ejpam-4862	276	49	and	and	CCONJ
ejpam-4862	276	50	ch	ch	NOUN
ejpam-4862	276	51	are	be	AUX
ejpam-4862	276	52	pointwise	pointwise	PROPN
ejpam-4862	276	53	non	non	ADJ
ejpam-4862	276	54	-	-	ADJ
ejpam-4862	276	55	dominating	dominating	ADJ
ejpam-4862	276	56	sets	set	NOUN
ejpam-4862	276	57	of	of	ADP
ejpam-4862	276	58	g	g	PROPN
ejpam-4862	276	59	and	and	CCONJ
ejpam-4862	276	60	h	h	NOUN
ejpam-4862	276	61	,	,	PUNCT
ejpam-4862	276	62	respectively	respectively	ADV
ejpam-4862	276	63	by	by	ADP
ejpam-4862	276	64	theorem	theorem	NOUN
ejpam-4862	276	65	4	4	NUM
ejpam-4862	276	66	.	.	PUNCT
ejpam-4862	277	1	moreover	moreover	ADV
ejpam-4862	277	2	,	,	PUNCT
ejpam-4862	277	3	since	since	SCONJ
ejpam-4862	277	4	v	v	NOUN
ejpam-4862	277	5	(	(	PUNCT
ejpam-4862	277	6	g	g	PROPN
ejpam-4862	277	7	+	+	NOUN
ejpam-4862	277	8	h	h	NOUN
ejpam-4862	277	9	)	)	PUNCT
ejpam-4862	277	10	\	\	PUNCT
ejpam-4862	278	1	c	c	NOUN
ejpam-4862	278	2	is	be	AUX
ejpam-4862	278	3	convex	convex	NOUN
ejpam-4862	278	4	set	set	VERB
ejpam-4862	278	5	in	in	ADP
ejpam-4862	278	6	g	g	PROPN
ejpam-4862	278	7	+	+	CCONJ
ejpam-4862	278	8	h	h	NOUN
ejpam-4862	278	9	,	,	PUNCT
ejpam-4862	278	10	v	v	ADJ
ejpam-4862	278	11	(	(	PUNCT
ejpam-4862	278	12	g	g	NOUN
ejpam-4862	278	13	)	)	PUNCT
ejpam-4862	278	14	\cg	\cg	PROPN
ejpam-4862	278	15	and	and	CCONJ
ejpam-4862	278	16	v	v	NOUN
ejpam-4862	278	17	(	(	PUNCT
ejpam-4862	278	18	h	h	NOUN
ejpam-4862	278	19	)	)	PUNCT
ejpam-4862	278	20	\ch	\ch	PROPN
ejpam-4862	278	21	are	be	AUX
ejpam-4862	278	22	cliques	clique	NOUN
ejpam-4862	278	23	in	in	ADP
ejpam-4862	278	24	g	g	PROPN
ejpam-4862	278	25	and	and	CCONJ
ejpam-4862	278	26	h	h	NOUN
ejpam-4862	278	27	,	,	PUNCT
ejpam-4862	278	28	respectively	respectively	ADV
ejpam-4862	278	29	by	by	ADP
ejpam-4862	278	30	theorem	theorem	NOUN
ejpam-4862	278	31	5	5	NUM
ejpam-4862	278	32	.	.	PUNCT
ejpam-4862	278	33	therefore	therefore	ADV
ejpam-4862	278	34	,	,	PUNCT
ejpam-4862	278	35	cg	cg	NOUN
ejpam-4862	278	36	and	and	CCONJ
ejpam-4862	278	37	ch	ch	NOUN
ejpam-4862	278	38	are	be	AUX
ejpam-4862	278	39	outer	outer	ADJ
ejpam-4862	278	40	-	-	PUNCT
ejpam-4862	278	41	clique	clique	NOUN
ejpam-4862	278	42	pointwise	pointwise	PROPN
ejpam-4862	278	43	non	non	ADJ
ejpam-4862	278	44	-	-	ADJ
ejpam-4862	278	45	dominating	dominating	ADJ
ejpam-4862	278	46	sets	set	NOUN
ejpam-4862	278	47	of	of	ADP
ejpam-4862	278	48	g	g	PROPN
ejpam-4862	278	49	and	and	CCONJ
ejpam-4862	278	50	h	h	NOUN
ejpam-4862	278	51	,	,	PUNCT
ejpam-4862	278	52	respectively	respectively	ADV
ejpam-4862	278	53	.	.	PUNCT
ejpam-4862	279	1	conversely	conversely	ADV
ejpam-4862	279	2	,	,	PUNCT
ejpam-4862	279	3	suppose	suppose	VERB
ejpam-4862	279	4	that	that	SCONJ
ejpam-4862	279	5	c	c	AUX
ejpam-4862	279	6	=	=	PUNCT
ejpam-4862	279	7	cg	cg	NOUN
ejpam-4862	279	8	∪	∪	NOUN
ejpam-4862	279	9	ch	ch	NOUN
ejpam-4862	279	10	,	,	PUNCT
ejpam-4862	279	11	where	where	SCONJ
ejpam-4862	279	12	cg	cg	NOUN
ejpam-4862	279	13	and	and	CCONJ
ejpam-4862	279	14	ch	ch	NOUN
ejpam-4862	279	15	are	be	AUX
ejpam-4862	279	16	outer	outer	ADJ
ejpam-4862	279	17	-	-	PUNCT
ejpam-4862	279	18	clique	clique	NOUN
ejpam-4862	279	19	pointwise	pointwise	PROPN
ejpam-4862	279	20	non	non	ADJ
ejpam-4862	279	21	-	-	ADJ
ejpam-4862	279	22	dominating	dominating	ADJ
ejpam-4862	279	23	sets	set	NOUN
ejpam-4862	279	24	of	of	ADP
ejpam-4862	279	25	g	g	PROPN
ejpam-4862	279	26	and	and	CCONJ
ejpam-4862	279	27	h	h	NOUN
ejpam-4862	279	28	,	,	PUNCT
ejpam-4862	279	29	respectively	respectively	ADV
ejpam-4862	279	30	.	.	PUNCT
ejpam-4862	280	1	then	then	ADV
ejpam-4862	280	2	⟨v	⟨v	X
ejpam-4862	280	3	(	(	PUNCT
ejpam-4862	280	4	g	g	NOUN
ejpam-4862	280	5	)	)	PUNCT
ejpam-4862	280	6	\	\	PROPN
ejpam-4862	280	7	cg⟩	cg⟩	PROPN
ejpam-4862	280	8	and	and	CCONJ
ejpam-4862	280	9	⟨v	⟨v	NUM
ejpam-4862	280	10	(	(	PUNCT
ejpam-4862	280	11	h	h	NOUN
ejpam-4862	280	12	)	)	PUNCT
ejpam-4862	280	13	\	\	NOUN
ejpam-4862	281	1	ch⟩	ch⟩	VERB
ejpam-4862	281	2	are	be	AUX
ejpam-4862	281	3	complete	complete	ADJ
ejpam-4862	281	4	in	in	ADP
ejpam-4862	281	5	g	g	PROPN
ejpam-4862	281	6	and	and	CCONJ
ejpam-4862	281	7	h	h	NOUN
ejpam-4862	281	8	,	,	PUNCT
ejpam-4862	281	9	respectively	respectively	ADV
ejpam-4862	281	10	.	.	PUNCT
ejpam-4862	282	1	hence	hence	ADV
ejpam-4862	282	2	,	,	PUNCT
ejpam-4862	282	3	by	by	ADP
ejpam-4862	282	4	theorem	theorem	NOUN
ejpam-4862	282	5	5	5	NUM
ejpam-4862	282	6	,	,	PUNCT
ejpam-4862	282	7	v	v	NOUN
ejpam-4862	282	8	(	(	PUNCT
ejpam-4862	282	9	g	g	PROPN
ejpam-4862	282	10	+	+	NOUN
ejpam-4862	282	11	h	h	NOUN
ejpam-4862	282	12	)	)	PUNCT
ejpam-4862	282	13	\	\	PUNCT
ejpam-4862	283	1	c	c	NOUN
ejpam-4862	283	2	is	be	AUX
ejpam-4862	283	3	convex	convex	NOUN
ejpam-4862	283	4	set	set	VERB
ejpam-4862	283	5	in	in	ADP
ejpam-4862	283	6	g	g	PROPN
ejpam-4862	283	7	+	+	PROPN
ejpam-4862	283	8	h.	h.	PROPN
ejpam-4862	283	9	since	since	SCONJ
ejpam-4862	283	10	cg	cg	PROPN
ejpam-4862	283	11	and	and	CCONJ
ejpam-4862	283	12	ch	ch	NOUN
ejpam-4862	283	13	are	be	AUX
ejpam-4862	283	14	pointwise	pointwise	PROPN
ejpam-4862	283	15	non	non	ADJ
ejpam-4862	283	16	-	-	ADJ
ejpam-4862	283	17	dominating	dominating	ADJ
ejpam-4862	283	18	sets	set	NOUN
ejpam-4862	283	19	,	,	PUNCT
ejpam-4862	283	20	c	c	NOUN
ejpam-4862	283	21	=	=	PUNCT
ejpam-4862	283	22	cg	cg	NOUN
ejpam-4862	283	23	∪	∪	NOUN
ejpam-4862	283	24	ch	ch	NOUN
ejpam-4862	283	25	is	be	AUX
ejpam-4862	283	26	a	a	DET
ejpam-4862	283	27	hop	hop	NOUN
ejpam-4862	283	28	dominating	dominating	NOUN
ejpam-4862	283	29	set	set	NOUN
ejpam-4862	283	30	of	of	ADP
ejpam-4862	283	31	g+h	g+h	PROPN
ejpam-4862	283	32	by	by	ADP
ejpam-4862	283	33	theorem	theorem	NOUN
ejpam-4862	283	34	4	4	NUM
ejpam-4862	283	35	.	.	PUNCT
ejpam-4862	284	1	therefore	therefore	ADV
ejpam-4862	284	2	,	,	PUNCT
ejpam-4862	284	3	c	c	PROPN
ejpam-4862	284	4	=	=	PUNCT
ejpam-4862	284	5	cg	cg	PROPN
ejpam-4862	284	6	∪ch	∪ch	PROPN
ejpam-4862	284	7	is	be	AUX
ejpam-4862	284	8	an	an	DET
ejpam-4862	284	9	outer	outer	ADJ
ejpam-4862	284	10	-	-	PUNCT
ejpam-4862	284	11	convex	convex	NOUN
ejpam-4862	284	12	hop	hop	NOUN
ejpam-4862	284	13	dominating	dominating	NOUN
ejpam-4862	284	14	set	set	NOUN
ejpam-4862	284	15	of	of	ADP
ejpam-4862	284	16	g+h	g+h	PROPN
ejpam-4862	284	17	.	.	PUNCT
ejpam-4862	285	1	the	the	DET
ejpam-4862	285	2	next	next	ADJ
ejpam-4862	285	3	result	result	NOUN
ejpam-4862	285	4	follows	follow	VERB
ejpam-4862	285	5	from	from	ADP
ejpam-4862	285	6	proposition	proposition	NOUN
ejpam-4862	285	7	4	4	NUM
ejpam-4862	285	8	and	and	CCONJ
ejpam-4862	285	9	theorem	theorem	VERB
ejpam-4862	285	10	6	6	NUM
ejpam-4862	285	11	.	.	PUNCT
ejpam-4862	285	12	corollary	corollary	ADJ
ejpam-4862	285	13	3	3	X
ejpam-4862	285	14	.	.	PUNCT
ejpam-4862	286	1	let	let	VERB
ejpam-4862	286	2	g	g	NOUN
ejpam-4862	286	3	and	and	CCONJ
ejpam-4862	286	4	h	h	NOUN
ejpam-4862	286	5	be	be	VERB
ejpam-4862	286	6	two	two	NUM
ejpam-4862	286	7	non	non	ADJ
ejpam-4862	286	8	-	-	ADJ
ejpam-4862	286	9	complete	complete	ADJ
ejpam-4862	286	10	graphs	graph	NOUN
ejpam-4862	286	11	.	.	PUNCT
ejpam-4862	287	1	then	then	ADV
ejpam-4862	287	2	γ̃conh(g+h	γ̃conh(g+h	NOUN
ejpam-4862	287	3	)	)	PUNCT
ejpam-4862	288	1	=	=	SYM
ejpam-4862	288	2	ocpnd(g	ocpnd(g	X
ejpam-4862	288	3	)	)	PUNCT
ejpam-4862	288	4	+	+	NOUN
ejpam-4862	288	5	ocpnd(h	ocpnd(h	NUM
ejpam-4862	288	6	)	)	PUNCT
ejpam-4862	288	7	.	.	PUNCT
ejpam-4862	289	1	in	in	ADP
ejpam-4862	289	2	particular	particular	ADJ
ejpam-4862	289	3	,	,	PUNCT
ejpam-4862	289	4	given	give	VERB
ejpam-4862	289	5	positive	positive	ADJ
ejpam-4862	289	6	integers	integer	NOUN
ejpam-4862	289	7	n	n	PRON
ejpam-4862	289	8	and	and	CCONJ
ejpam-4862	289	9	m	m	ADV
ejpam-4862	289	10	,	,	PUNCT
ejpam-4862	289	11	we	we	PRON
ejpam-4862	289	12	have	have	VERB
ejpam-4862	289	13	(	(	PUNCT
ejpam-4862	289	14	i	i	NOUN
ejpam-4862	289	15	)	)	PUNCT
ejpam-4862	289	16	γ̃conh(pn	γ̃conh(pn	NOUN
ejpam-4862	289	17	+	+	X
ejpam-4862	289	18	pm	pm	NOUN
ejpam-4862	289	19	)	)	PUNCT
ejpam-4862	289	20	=	=	PUNCT
ejpam-4862	289	21			NOUN
ejpam-4862	289	22	4	4	NUM
ejpam-4862	289	23	if	if	SCONJ
ejpam-4862	289	24	n	n	CCONJ
ejpam-4862	289	25	,	,	PUNCT
ejpam-4862	289	26	m	m	VERB
ejpam-4862	289	27	=	=	NOUN
ejpam-4862	289	28	3	3	NUM
ejpam-4862	289	29	m	m	NOUN
ejpam-4862	289	30	if	if	SCONJ
ejpam-4862	289	31	n	n	ADJ
ejpam-4862	289	32	=	=	SYM
ejpam-4862	289	33	3,m	3,m	NUM
ejpam-4862	289	34	≥	≥	NOUN
ejpam-4862	289	35	4	4	NUM
ejpam-4862	289	36	n	n	NOUN
ejpam-4862	290	1	if	if	SCONJ
ejpam-4862	290	2	n	n	NUM
ejpam-4862	290	3	≥	≥	NOUN
ejpam-4862	290	4	4,m	4,m	NUM
ejpam-4862	290	5	=	=	SYM
ejpam-4862	290	6	3	3	NUM
ejpam-4862	290	7	n+m−	n+m−	NOUN
ejpam-4862	290	8	4	4	NUM
ejpam-4862	290	9	if	if	SCONJ
ejpam-4862	290	10	n	n	CCONJ
ejpam-4862	290	11	,	,	PUNCT
ejpam-4862	290	12	m	m	VERB
ejpam-4862	290	13	≥	≥	NOUN
ejpam-4862	290	14	4	4	NUM
ejpam-4862	290	15	;	;	PUNCT
ejpam-4862	290	16	(	(	PUNCT
ejpam-4862	290	17	ii	ii	NOUN
ejpam-4862	290	18	)	)	PUNCT
ejpam-4862	290	19	γ̃conh(cn	γ̃conh(cn	NOUN
ejpam-4862	291	1	+	+	CCONJ
ejpam-4862	291	2	cm	cm	NOUN
ejpam-4862	291	3	)	)	PUNCT
ejpam-4862	291	4	=	=	PRON
ejpam-4862	291	5	n+m−	n+m−	NOUN
ejpam-4862	291	6	4	4	NUM
ejpam-4862	291	7	for	for	ADP
ejpam-4862	291	8	all	all	DET
ejpam-4862	291	9	n	n	CCONJ
ejpam-4862	291	10	,	,	PUNCT
ejpam-4862	291	11	m	m	VERB
ejpam-4862	291	12	≥	≥	NOUN
ejpam-4862	291	13	4	4	NUM
ejpam-4862	291	14	;	;	PUNCT
ejpam-4862	291	15	and	and	CCONJ
ejpam-4862	291	16	(	(	PUNCT
ejpam-4862	291	17	iii	iii	NOUN
ejpam-4862	291	18	)	)	PUNCT
ejpam-4862	291	19	γ̃conh(pn	γ̃conh(pn	NOUN
ejpam-4862	291	20	+	+	NOUN
ejpam-4862	291	21	cm	cm	NOUN
ejpam-4862	291	22	)	)	PUNCT
ejpam-4862	291	23	=	=	PRON
ejpam-4862	292	1	{	{	PUNCT
ejpam-4862	292	2	m	m	VERB
ejpam-4862	292	3	if	if	SCONJ
ejpam-4862	292	4	n	n	ADJ
ejpam-4862	292	5	=	=	SYM
ejpam-4862	292	6	3,m	3,m	NUM
ejpam-4862	292	7	≥	≥	NOUN
ejpam-4862	292	8	4	4	NUM
ejpam-4862	292	9	n+m−	n+m−	NOUN
ejpam-4862	292	10	4	4	NUM
ejpam-4862	292	11	if	if	SCONJ
ejpam-4862	292	12	n	n	CCONJ
ejpam-4862	292	13	,	,	PUNCT
ejpam-4862	292	14	m	m	VERB
ejpam-4862	292	15	≥	≥	NOUN
ejpam-4862	292	16	4	4	NUM
ejpam-4862	292	17	.	.	PUNCT
ejpam-4862	293	1	theorem	theorem	VERB
ejpam-4862	293	2	7	7	NUM
ejpam-4862	293	3	.	.	PUNCT
ejpam-4862	294	1	let	let	VERB
ejpam-4862	294	2	g	g	NOUN
ejpam-4862	294	3	be	be	AUX
ejpam-4862	294	4	any	any	DET
ejpam-4862	294	5	non	non	ADJ
ejpam-4862	294	6	-	-	ADJ
ejpam-4862	294	7	complete	complete	ADJ
ejpam-4862	294	8	graph	graph	NOUN
ejpam-4862	294	9	and	and	CCONJ
ejpam-4862	294	10	h	h	NOUN
ejpam-4862	294	11	be	be	AUX
ejpam-4862	294	12	any	any	DET
ejpam-4862	294	13	complete	complete	ADJ
ejpam-4862	294	14	graph	graph	NOUN
ejpam-4862	294	15	.	.	PUNCT
ejpam-4862	295	1	then	then	ADV
ejpam-4862	295	2	c	c	PROPN
ejpam-4862	295	3	⊆	⊆	NUM
ejpam-4862	295	4	v	v	NOUN
ejpam-4862	295	5	(	(	PUNCT
ejpam-4862	295	6	g	g	PROPN
ejpam-4862	295	7	+	+	NOUN
ejpam-4862	295	8	h	h	NOUN
ejpam-4862	295	9	)	)	PUNCT
ejpam-4862	295	10	is	be	AUX
ejpam-4862	295	11	an	an	DET
ejpam-4862	295	12	outer	outer	ADJ
ejpam-4862	295	13	-	-	PUNCT
ejpam-4862	295	14	convex	convex	NOUN
ejpam-4862	295	15	hop	hop	NOUN
ejpam-4862	295	16	dominating	dominating	NOUN
ejpam-4862	295	17	set	set	NOUN
ejpam-4862	295	18	of	of	ADP
ejpam-4862	295	19	g	g	PROPN
ejpam-4862	296	1	+	+	CCONJ
ejpam-4862	296	2	h	h	NOUN
ejpam-4862	296	3	if	if	SCONJ
ejpam-4862	296	4	and	and	CCONJ
ejpam-4862	296	5	only	only	ADV
ejpam-4862	296	6	if	if	SCONJ
ejpam-4862	296	7	c	c	NOUN
ejpam-4862	296	8	=	=	NOUN
ejpam-4862	296	9	cg	cg	NOUN
ejpam-4862	296	10	∪	∪	PROPN
ejpam-4862	296	11	v	v	PROPN
ejpam-4862	296	12	(	(	PUNCT
ejpam-4862	296	13	h	h	NOUN
ejpam-4862	296	14	)	)	PUNCT
ejpam-4862	296	15	,	,	PUNCT
ejpam-4862	296	16	where	where	SCONJ
ejpam-4862	296	17	cg	cg	NOUN
ejpam-4862	296	18	is	be	AUX
ejpam-4862	296	19	an	an	DET
ejpam-4862	296	20	outer	outer	ADJ
ejpam-4862	296	21	-	-	PUNCT
ejpam-4862	296	22	clique	clique	NOUN
ejpam-4862	296	23	pointwise	pointwise	PROPN
ejpam-4862	296	24	non	non	ADJ
ejpam-4862	296	25	-	-	ADJ
ejpam-4862	296	26	dominating	dominating	ADJ
ejpam-4862	296	27	set	set	NOUN
ejpam-4862	296	28	of	of	ADP
ejpam-4862	296	29	g.	g.	PROPN
ejpam-4862	296	30	j.	j.	PROPN
ejpam-4862	296	31	a.	a.	PROPN
ejpam-4862	296	32	hassan	hassan	PROPN
ejpam-4862	296	33	et	et	PROPN
ejpam-4862	296	34	al	al	PROPN
ejpam-4862	296	35	.	.	PUNCT
ejpam-4862	296	36	/	/	SYM
ejpam-4862	296	37	eur	eur	PROPN
ejpam-4862	296	38	.	.	PUNCT
ejpam-4862	297	1	j.	j.	PROPN
ejpam-4862	297	2	pure	pure	PROPN
ejpam-4862	297	3	appl	appl	PROPN
ejpam-4862	297	4	.	.	PROPN
ejpam-4862	297	5	math	math	PROPN
ejpam-4862	297	6	,	,	PUNCT
ejpam-4862	297	7	16	16	NUM
ejpam-4862	297	8	(	(	PUNCT
ejpam-4862	297	9	4	4	NUM
ejpam-4862	297	10	)	)	PUNCT
ejpam-4862	297	11	(	(	PUNCT
ejpam-4862	297	12	2023	2023	NUM
ejpam-4862	297	13	)	)	PUNCT
ejpam-4862	297	14	,	,	PUNCT
ejpam-4862	297	15	2035	2035	NUM
ejpam-4862	297	16	-	-	SYM
ejpam-4862	297	17	2048	2048	NUM
ejpam-4862	297	18	2045	2045	NUM
ejpam-4862	297	19	proof	proof	NOUN
ejpam-4862	297	20	.	.	PUNCT
ejpam-4862	297	21	suppose	suppose	VERB
ejpam-4862	297	22	that	that	SCONJ
ejpam-4862	297	23	c	c	PROPN
ejpam-4862	297	24	is	be	AUX
ejpam-4862	297	25	an	an	DET
ejpam-4862	297	26	outer	outer	ADJ
ejpam-4862	297	27	-	-	PUNCT
ejpam-4862	297	28	convex	convex	NOUN
ejpam-4862	297	29	hop	hop	NOUN
ejpam-4862	297	30	dominating	dominating	NOUN
ejpam-4862	297	31	set	set	VERB
ejpam-4862	297	32	in	in	ADP
ejpam-4862	297	33	g	g	PROPN
ejpam-4862	297	34	+	+	CCONJ
ejpam-4862	297	35	h.	h.	PROPN
ejpam-4862	297	36	since	since	SCONJ
ejpam-4862	297	37	h	h	PROPN
ejpam-4862	297	38	is	be	AUX
ejpam-4862	297	39	complete	complete	ADJ
ejpam-4862	297	40	,	,	PUNCT
ejpam-4862	297	41	it	it	PRON
ejpam-4862	297	42	follows	follow	VERB
ejpam-4862	297	43	that	that	PRON
ejpam-4862	297	44	c	c	PROPN
ejpam-4862	297	45	=	=	PUNCT
ejpam-4862	297	46	cg	cg	NOUN
ejpam-4862	297	47	∪	∪	PROPN
ejpam-4862	297	48	v	v	PROPN
ejpam-4862	297	49	(	(	PUNCT
ejpam-4862	297	50	h	h	NOUN
ejpam-4862	297	51	)	)	PUNCT
ejpam-4862	297	52	,	,	PUNCT
ejpam-4862	297	53	where	where	SCONJ
ejpam-4862	297	54	cg	cg	NOUN
ejpam-4862	297	55	̸=	̸=	PROPN
ejpam-4862	297	56	∅.	∅.	ADV
ejpam-4862	297	57	by	by	ADP
ejpam-4862	297	58	theorem	theorem	NOUN
ejpam-4862	297	59	6	6	NUM
ejpam-4862	297	60	,	,	PUNCT
ejpam-4862	297	61	cg	cg	NOUN
ejpam-4862	297	62	is	be	AUX
ejpam-4862	297	63	an	an	DET
ejpam-4862	297	64	outer	outer	ADJ
ejpam-4862	297	65	-	-	PUNCT
ejpam-4862	297	66	clique	clique	NOUN
ejpam-4862	297	67	pointwise	pointwise	PROPN
ejpam-4862	297	68	non	non	ADJ
ejpam-4862	297	69	-	-	ADJ
ejpam-4862	297	70	dominating	dominating	ADJ
ejpam-4862	297	71	set	set	NOUN
ejpam-4862	297	72	of	of	ADP
ejpam-4862	297	73	g.	g.	PROPN
ejpam-4862	297	74	conversely	conversely	ADV
ejpam-4862	297	75	,	,	PUNCT
ejpam-4862	297	76	assume	assume	VERB
ejpam-4862	297	77	that	that	SCONJ
ejpam-4862	297	78	c	c	AUX
ejpam-4862	297	79	=	=	NOUN
ejpam-4862	297	80	cg	cg	NOUN
ejpam-4862	297	81	∪	∪	PROPN
ejpam-4862	297	82	v	v	PROPN
ejpam-4862	297	83	(	(	PUNCT
ejpam-4862	297	84	h	h	NOUN
ejpam-4862	297	85	)	)	PUNCT
ejpam-4862	297	86	,	,	PUNCT
ejpam-4862	297	87	where	where	SCONJ
ejpam-4862	297	88	cg	cg	NOUN
ejpam-4862	297	89	is	be	AUX
ejpam-4862	297	90	an	an	DET
ejpam-4862	297	91	outer	outer	ADJ
ejpam-4862	297	92	-	-	PUNCT
ejpam-4862	297	93	clique	clique	NOUN
ejpam-4862	297	94	pointwise	pointwise	NOUN
ejpam-4862	297	95	nondominating	nondominate	VERB
ejpam-4862	297	96	set	set	NOUN
ejpam-4862	297	97	of	of	ADP
ejpam-4862	297	98	g.	g.	PROPN
ejpam-4862	297	99	then	then	ADV
ejpam-4862	297	100	n2	n2	PROPN
ejpam-4862	297	101	g+h	g+h	PROPN
ejpam-4862	298	1	[	[	X
ejpam-4862	298	2	c	c	X
ejpam-4862	298	3	]	]	X
ejpam-4862	298	4	=	=	SYM
ejpam-4862	298	5	v	v	X
ejpam-4862	298	6	(	(	PUNCT
ejpam-4862	298	7	g+h	g+h	PROPN
ejpam-4862	298	8	)	)	PUNCT
ejpam-4862	298	9	,	,	PUNCT
ejpam-4862	298	10	that	that	ADV
ejpam-4862	298	11	is	is	ADV
ejpam-4862	298	12	,	,	PUNCT
ejpam-4862	298	13	c	c	PROPN
ejpam-4862	298	14	is	be	AUX
ejpam-4862	298	15	a	a	DET
ejpam-4862	298	16	hop	hop	NOUN
ejpam-4862	298	17	dominating	dominating	NOUN
ejpam-4862	298	18	set	set	VERB
ejpam-4862	298	19	in	in	ADP
ejpam-4862	298	20	g	g	PROPN
ejpam-4862	298	21	+	+	CCONJ
ejpam-4862	298	22	h.	h.	PROPN
ejpam-4862	298	23	since	since	SCONJ
ejpam-4862	298	24	cg	cg	PROPN
ejpam-4862	298	25	is	be	AUX
ejpam-4862	298	26	an	an	DET
ejpam-4862	298	27	outer	outer	ADJ
ejpam-4862	298	28	-	-	PUNCT
ejpam-4862	298	29	clique	clique	NOUN
ejpam-4862	298	30	set	set	NOUN
ejpam-4862	298	31	in	in	ADP
ejpam-4862	298	32	g	g	PROPN
ejpam-4862	298	33	,	,	PUNCT
ejpam-4862	298	34	it	it	PRON
ejpam-4862	298	35	follows	follow	VERB
ejpam-4862	298	36	that	that	SCONJ
ejpam-4862	298	37	v	v	ADP
ejpam-4862	298	38	(	(	PUNCT
ejpam-4862	298	39	g	g	PROPN
ejpam-4862	298	40	+	+	NOUN
ejpam-4862	298	41	h	h	NOUN
ejpam-4862	298	42	)	)	PUNCT
ejpam-4862	298	43	\	\	PUNCT
ejpam-4862	299	1	c	c	NOUN
ejpam-4862	299	2	is	be	AUX
ejpam-4862	299	3	clique	clique	ADJ
ejpam-4862	299	4	in	in	ADP
ejpam-4862	299	5	g	g	PROPN
ejpam-4862	299	6	+	+	PROPN
ejpam-4862	299	7	h	h	NOUN
ejpam-4862	299	8	,	,	PUNCT
ejpam-4862	299	9	that	that	ADV
ejpam-4862	299	10	is	is	ADV
ejpam-4862	299	11	,	,	PUNCT
ejpam-4862	299	12	v	v	INTJ
ejpam-4862	299	13	(	(	PUNCT
ejpam-4862	299	14	g	g	PROPN
ejpam-4862	299	15	+	+	NOUN
ejpam-4862	299	16	h	h	NOUN
ejpam-4862	299	17	)	)	PUNCT
ejpam-4862	299	18	\	\	PUNCT
ejpam-4862	300	1	c	c	NOUN
ejpam-4862	300	2	is	be	AUX
ejpam-4862	300	3	convex	convex	ADJ
ejpam-4862	300	4	in	in	ADP
ejpam-4862	300	5	g	g	PROPN
ejpam-4862	300	6	+	+	PROPN
ejpam-4862	300	7	h.	h.	PROPN
ejpam-4862	300	8	therefore	therefore	ADV
ejpam-4862	300	9	,	,	PUNCT
ejpam-4862	300	10	c	c	PROPN
ejpam-4862	300	11	is	be	AUX
ejpam-4862	300	12	an	an	DET
ejpam-4862	300	13	outer	outer	ADJ
ejpam-4862	300	14	-	-	PUNCT
ejpam-4862	300	15	convex	convex	NOUN
ejpam-4862	300	16	hop	hop	NOUN
ejpam-4862	300	17	dominating	dominating	NOUN
ejpam-4862	300	18	set	set	NOUN
ejpam-4862	300	19	of	of	ADP
ejpam-4862	300	20	g+h	g+h	PROPN
ejpam-4862	300	21	.	.	PUNCT
ejpam-4862	301	1	the	the	DET
ejpam-4862	301	2	next	next	ADJ
ejpam-4862	301	3	result	result	NOUN
ejpam-4862	301	4	follows	follow	VERB
ejpam-4862	301	5	from	from	ADP
ejpam-4862	301	6	corollary	corollary	ADJ
ejpam-4862	301	7	1	1	NUM
ejpam-4862	301	8	,	,	PUNCT
ejpam-4862	301	9	theorem	theorem	VERB
ejpam-4862	301	10	3	3	NUM
ejpam-4862	301	11	,	,	PUNCT
ejpam-4862	301	12	proposition	proposition	NOUN
ejpam-4862	301	13	4	4	NUM
ejpam-4862	301	14	,	,	PUNCT
ejpam-4862	301	15	and	and	CCONJ
ejpam-4862	301	16	theorem	theorem	VERB
ejpam-4862	301	17	7	7	NUM
ejpam-4862	301	18	.	.	PUNCT
ejpam-4862	301	19	corollary	corollary	ADJ
ejpam-4862	301	20	4	4	NUM
ejpam-4862	301	21	.	.	PUNCT
ejpam-4862	302	1	let	let	VERB
ejpam-4862	302	2	g	g	NOUN
ejpam-4862	302	3	be	be	AUX
ejpam-4862	302	4	any	any	DET
ejpam-4862	302	5	non	non	ADJ
ejpam-4862	302	6	-	-	ADJ
ejpam-4862	302	7	complete	complete	ADJ
ejpam-4862	302	8	graph	graph	NOUN
ejpam-4862	302	9	and	and	CCONJ
ejpam-4862	302	10	h	h	NOUN
ejpam-4862	302	11	be	be	AUX
ejpam-4862	302	12	any	any	DET
ejpam-4862	302	13	complete	complete	ADJ
ejpam-4862	302	14	graph	graph	NOUN
ejpam-4862	302	15	.	.	PUNCT
ejpam-4862	303	1	then	then	ADV
ejpam-4862	303	2	γ̃conh(g+h	γ̃conh(g+h	NOUN
ejpam-4862	303	3	)	)	PUNCT
ejpam-4862	304	1	=	=	SYM
ejpam-4862	304	2	ocpnd(g	ocpnd(g	X
ejpam-4862	304	3	)	)	PUNCT
ejpam-4862	304	4	+	+	CCONJ
ejpam-4862	304	5	|v	|v	PROPN
ejpam-4862	304	6	(	(	PUNCT
ejpam-4862	304	7	h)|	h)|	PROPN
ejpam-4862	304	8	.	.	PUNCT
ejpam-4862	305	1	in	in	ADP
ejpam-4862	305	2	particular	particular	ADJ
ejpam-4862	305	3	,	,	PUNCT
ejpam-4862	305	4	given	give	VERB
ejpam-4862	305	5	positive	positive	ADJ
ejpam-4862	305	6	integers	integer	NOUN
ejpam-4862	305	7	n	n	PRON
ejpam-4862	305	8	and	and	CCONJ
ejpam-4862	305	9	m	m	ADV
ejpam-4862	305	10	,	,	PUNCT
ejpam-4862	305	11	we	we	PRON
ejpam-4862	305	12	have	have	VERB
ejpam-4862	305	13	(	(	PUNCT
ejpam-4862	305	14	i	i	NOUN
ejpam-4862	305	15	)	)	PUNCT
ejpam-4862	305	16	γ̃conh(pn	γ̃conh(pn	ADJ
ejpam-4862	305	17	+	+	PROPN
ejpam-4862	305	18	km	km	NOUN
ejpam-4862	305	19	)	)	PUNCT
ejpam-4862	305	20	=	=	PRON
ejpam-4862	305	21	{	{	PUNCT
ejpam-4862	306	1	m+	m+	NUM
ejpam-4862	306	2	2	2	NUM
ejpam-4862	306	3	if	if	SCONJ
ejpam-4862	306	4	n	n	PRON
ejpam-4862	306	5	=	=	SYM
ejpam-4862	306	6	3,m	3,m	NUM
ejpam-4862	306	7	≥	≥	NOUN
ejpam-4862	306	8	1	1	NUM
ejpam-4862	306	9	n+m−	n+m−	NOUN
ejpam-4862	306	10	2	2	NUM
ejpam-4862	306	11	if	if	SCONJ
ejpam-4862	306	12	n	n	PRON
ejpam-4862	306	13	≥	≥	NOUN
ejpam-4862	306	14	4	4	NUM
ejpam-4862	306	15	,	,	PUNCT
ejpam-4862	306	16	m	m	VERB
ejpam-4862	306	17	≥	≥	NOUN
ejpam-4862	306	18	1	1	NUM
ejpam-4862	306	19	;	;	PUNCT
ejpam-4862	306	20	(	(	PUNCT
ejpam-4862	306	21	ii	ii	NOUN
ejpam-4862	306	22	)	)	PUNCT
ejpam-4862	306	23	γ̃conh(cn	γ̃conh(cn	NOUN
ejpam-4862	307	1	+	+	NOUN
ejpam-4862	307	2	km	km	NOUN
ejpam-4862	307	3	)	)	PUNCT
ejpam-4862	307	4	=	=	SYM
ejpam-4862	307	5	n+m−	n+m−	NOUN
ejpam-4862	307	6	2	2	NUM
ejpam-4862	307	7	for	for	ADP
ejpam-4862	307	8	all	all	DET
ejpam-4862	307	9	n	n	PRON
ejpam-4862	307	10	≥	≥	NOUN
ejpam-4862	307	11	4,m	4,m	NUM
ejpam-4862	307	12	≥	≥	NUM
ejpam-4862	307	13	1	1	NUM
ejpam-4862	307	14	.	.	PUNCT
ejpam-4862	307	15	theorem	theorem	NOUN
ejpam-4862	307	16	8	8	NUM
ejpam-4862	307	17	.	.	PUNCT
ejpam-4862	308	1	let	let	VERB
ejpam-4862	308	2	g	g	PRON
ejpam-4862	308	3	be	be	AUX
ejpam-4862	308	4	a	a	DET
ejpam-4862	308	5	connected	connected	ADJ
ejpam-4862	308	6	non	non	ADJ
ejpam-4862	308	7	-	-	ADJ
ejpam-4862	308	8	trivial	trivial	ADJ
ejpam-4862	308	9	graph	graph	NOUN
ejpam-4862	308	10	and	and	CCONJ
ejpam-4862	308	11	h	h	NOUN
ejpam-4862	308	12	be	be	AUX
ejpam-4862	308	13	any	any	DET
ejpam-4862	308	14	graph	graph	NOUN
ejpam-4862	308	15	.	.	PUNCT
ejpam-4862	309	1	if	if	SCONJ
ejpam-4862	309	2	c	c	NOUN
ejpam-4862	309	3	=	=	PUNCT
ejpam-4862	309	4	⋃	⋃	PROPN
ejpam-4862	309	5	x∈v	x∈v	PROPN
ejpam-4862	309	6	(	(	PUNCT
ejpam-4862	309	7	g	g	NOUN
ejpam-4862	309	8	)	)	PUNCT
ejpam-4862	309	9	v	v	NOUN
ejpam-4862	309	10	(	(	PUNCT
ejpam-4862	309	11	hx	hx	PROPN
ejpam-4862	309	12	)	)	PUNCT
ejpam-4862	309	13	,	,	PUNCT
ejpam-4862	309	14	then	then	ADV
ejpam-4862	309	15	c	c	PROPN
ejpam-4862	309	16	is	be	AUX
ejpam-4862	309	17	an	an	DET
ejpam-4862	309	18	outer	outer	ADJ
ejpam-4862	309	19	-	-	PUNCT
ejpam-4862	309	20	convex	convex	NOUN
ejpam-4862	309	21	hop	hop	NOUN
ejpam-4862	309	22	dominating	dominating	NOUN
ejpam-4862	309	23	set	set	NOUN
ejpam-4862	309	24	of	of	ADP
ejpam-4862	309	25	g	g	PROPN
ejpam-4862	309	26	◦	◦	PROPN
ejpam-4862	309	27	h.	h.	PROPN
ejpam-4862	309	28	moreover	moreover	ADV
ejpam-4862	309	29	,	,	PUNCT
ejpam-4862	309	30	γ̃conh(g	γ̃conh(g	ADP
ejpam-4862	309	31	◦	◦	NOUN
ejpam-4862	309	32	h	h	NOUN
ejpam-4862	309	33	)	)	PUNCT
ejpam-4862	309	34	≤	≤	NOUN
ejpam-4862	309	35	|v	|v	X
ejpam-4862	309	36	(	(	PUNCT
ejpam-4862	309	37	g)||v	g)||v	PROPN
ejpam-4862	309	38	(	(	PUNCT
ejpam-4862	309	39	h)|	h)|	PROPN
ejpam-4862	309	40	.	.	PUNCT
ejpam-4862	309	41	proof	proof	NOUN
ejpam-4862	309	42	.	.	PUNCT
ejpam-4862	310	1	suppose	suppose	VERB
ejpam-4862	310	2	that	that	SCONJ
ejpam-4862	310	3	c	c	NOUN
ejpam-4862	310	4	=	=	PUNCT
ejpam-4862	310	5	⋃	⋃	PROPN
ejpam-4862	310	6	x∈v	x∈v	PROPN
ejpam-4862	310	7	(	(	PUNCT
ejpam-4862	310	8	g	g	NOUN
ejpam-4862	310	9	)	)	PUNCT
ejpam-4862	310	10	v	v	NOUN
ejpam-4862	310	11	(	(	PUNCT
ejpam-4862	310	12	hx	hx	PROPN
ejpam-4862	310	13	)	)	PUNCT
ejpam-4862	310	14	.	.	PUNCT
ejpam-4862	311	1	let	let	VERB
ejpam-4862	311	2	a	a	DET
ejpam-4862	311	3	∈	∈	PROPN
ejpam-4862	311	4	v	v	NOUN
ejpam-4862	311	5	(	(	PUNCT
ejpam-4862	311	6	g	g	PROPN
ejpam-4862	311	7	◦	◦	NOUN
ejpam-4862	311	8	h	h	NOUN
ejpam-4862	311	9	)	)	PUNCT
ejpam-4862	311	10	\	\	PROPN
ejpam-4862	311	11	c.	c.	NOUN
ejpam-4862	311	12	then	then	ADV
ejpam-4862	311	13	a	a	DET
ejpam-4862	311	14	∈	∈	PROPN
ejpam-4862	311	15	v	v	NOUN
ejpam-4862	311	16	(	(	PUNCT
ejpam-4862	311	17	g	g	NOUN
ejpam-4862	311	18	)	)	PUNCT
ejpam-4862	311	19	.	.	PUNCT
ejpam-4862	312	1	since	since	SCONJ
ejpam-4862	312	2	g	g	PROPN
ejpam-4862	312	3	is	be	AUX
ejpam-4862	312	4	connected	connect	VERB
ejpam-4862	312	5	non	non	ADJ
ejpam-4862	312	6	-	-	ADJ
ejpam-4862	312	7	trivial	trivial	ADJ
ejpam-4862	312	8	graph	graph	NOUN
ejpam-4862	312	9	,	,	PUNCT
ejpam-4862	312	10	there	there	PRON
ejpam-4862	312	11	exists	exist	VERB
ejpam-4862	312	12	b	b	PROPN
ejpam-4862	312	13	∈	∈	PROPN
ejpam-4862	312	14	v	v	PROPN
ejpam-4862	312	15	(	(	PUNCT
ejpam-4862	312	16	hx	hx	PROPN
ejpam-4862	312	17	)	)	PUNCT
ejpam-4862	312	18	for	for	ADP
ejpam-4862	312	19	some	some	PRON
ejpam-4862	312	20	x	x	SYM
ejpam-4862	312	21	∈	∈	PROPN
ejpam-4862	312	22	v	v	ADP
ejpam-4862	312	23	(	(	PUNCT
ejpam-4862	312	24	g	g	NOUN
ejpam-4862	312	25	)	)	PUNCT
ejpam-4862	312	26	such	such	ADJ
ejpam-4862	312	27	that	that	SCONJ
ejpam-4862	312	28	dg	dg	PROPN
ejpam-4862	312	29	◦	◦	PROPN
ejpam-4862	312	30	h(a	h(a	PROPN
ejpam-4862	312	31	,	,	PUNCT
ejpam-4862	312	32	b	b	NOUN
ejpam-4862	312	33	)	)	PUNCT
ejpam-4862	312	34	=	=	SYM
ejpam-4862	312	35	2	2	X
ejpam-4862	312	36	.	.	PUNCT
ejpam-4862	313	1	thus	thus	ADV
ejpam-4862	313	2	,	,	PUNCT
ejpam-4862	313	3	c	c	PROPN
ejpam-4862	313	4	is	be	AUX
ejpam-4862	313	5	a	a	DET
ejpam-4862	313	6	hop	hop	NOUN
ejpam-4862	313	7	dominating	dominating	NOUN
ejpam-4862	313	8	set	set	VERB
ejpam-4862	313	9	in	in	ADP
ejpam-4862	313	10	g	g	PROPN
ejpam-4862	313	11	◦	◦	NOUN
ejpam-4862	313	12	h.	h.	PROPN
ejpam-4862	313	13	clearly	clearly	ADV
ejpam-4862	313	14	,	,	PUNCT
ejpam-4862	313	15	v	v	X
ejpam-4862	313	16	(	(	PUNCT
ejpam-4862	313	17	g	g	PROPN
ejpam-4862	313	18	◦	◦	NOUN
ejpam-4862	313	19	h	h	NOUN
ejpam-4862	313	20	)	)	PUNCT
ejpam-4862	313	21	\	\	PROPN
ejpam-4862	314	1	c	c	NOUN
ejpam-4862	314	2	is	be	AUX
ejpam-4862	314	3	convex	convex	ADJ
ejpam-4862	314	4	in	in	ADP
ejpam-4862	314	5	g	g	PROPN
ejpam-4862	314	6	◦	◦	NOUN
ejpam-4862	314	7	h.	h.	NOUN
ejpam-4862	314	8	therefore	therefore	ADV
ejpam-4862	314	9	,	,	PUNCT
ejpam-4862	314	10	c	c	PROPN
ejpam-4862	314	11	is	be	AUX
ejpam-4862	314	12	an	an	DET
ejpam-4862	314	13	outer	outer	ADJ
ejpam-4862	314	14	-	-	PUNCT
ejpam-4862	314	15	convex	convex	NOUN
ejpam-4862	314	16	hop	hop	NOUN
ejpam-4862	314	17	dominating	dominating	NOUN
ejpam-4862	314	18	set	set	VERB
ejpam-4862	314	19	in	in	ADP
ejpam-4862	314	20	g	g	PROPN
ejpam-4862	314	21	◦	◦	NOUN
ejpam-4862	314	22	h.	h.	NOUN
ejpam-4862	314	23	moreover	moreover	ADV
ejpam-4862	314	24	,	,	PUNCT
ejpam-4862	314	25	since	since	SCONJ
ejpam-4862	314	26	|c|	|c|	PROPN
ejpam-4862	314	27	=	=	SYM
ejpam-4862	314	28	|v	|v	PROPN
ejpam-4862	314	29	(	(	PUNCT
ejpam-4862	314	30	g)||v	g)||v	PROPN
ejpam-4862	314	31	(	(	PUNCT
ejpam-4862	314	32	h)|	h)|	PROPN
ejpam-4862	314	33	,	,	PUNCT
ejpam-4862	314	34	it	it	PRON
ejpam-4862	314	35	follows	follow	VERB
ejpam-4862	314	36	that	that	SCONJ
ejpam-4862	314	37	γ̃conh(g	γ̃conh(g	ADP
ejpam-4862	314	38	◦	◦	NOUN
ejpam-4862	314	39	h	h	NOUN
ejpam-4862	314	40	)	)	PUNCT
ejpam-4862	314	41	≤	≤	NOUN
ejpam-4862	314	42	|v	|v	X
ejpam-4862	314	43	(	(	PUNCT
ejpam-4862	314	44	g)||v	g)||v	PROPN
ejpam-4862	314	45	(	(	PUNCT
ejpam-4862	314	46	h)|	h)|	PROPN
ejpam-4862	314	47	.	.	PUNCT
ejpam-4862	314	48	remark	remark	PROPN
ejpam-4862	314	49	4	4	NUM
ejpam-4862	314	50	.	.	PUNCT
ejpam-4862	315	1	the	the	DET
ejpam-4862	315	2	sharpness	sharpness	NOUN
ejpam-4862	315	3	of	of	ADP
ejpam-4862	315	4	theorem	theorem	ADJ
ejpam-4862	315	5	8	8	NUM
ejpam-4862	315	6	is	be	AUX
ejpam-4862	315	7	attainable	attainable	ADJ
ejpam-4862	315	8	.	.	PUNCT
ejpam-4862	316	1	moreover	moreover	ADV
ejpam-4862	316	2	,	,	PUNCT
ejpam-4862	316	3	strict	strict	ADJ
ejpam-4862	316	4	inequality	inequality	NOUN
ejpam-4862	316	5	can	can	AUX
ejpam-4862	316	6	be	be	AUX
ejpam-4862	316	7	attained	attain	VERB
ejpam-4862	316	8	.	.	PUNCT
ejpam-4862	317	1	for	for	ADP
ejpam-4862	317	2	the	the	DET
ejpam-4862	317	3	sharpness	sharpness	NOUN
ejpam-4862	317	4	,	,	PUNCT
ejpam-4862	317	5	consider	consider	VERB
ejpam-4862	317	6	the	the	DET
ejpam-4862	317	7	graph	graph	NOUN
ejpam-4862	317	8	p4	p4	ADJ
ejpam-4862	317	9	◦	◦	NOUN
ejpam-4862	317	10	p2	p2	NOUN
ejpam-4862	317	11	in	in	ADP
ejpam-4862	317	12	figure	figure	NOUN
ejpam-4862	317	13	7	7	NUM
ejpam-4862	317	14	.	.	PUNCT
ejpam-4862	318	1	let	let	VERB
ejpam-4862	318	2	c	c	NOUN
ejpam-4862	318	3	=	=	SYM
ejpam-4862	318	4	{	{	PUNCT
ejpam-4862	318	5	u1	u1	NOUN
ejpam-4862	318	6	,	,	PUNCT
ejpam-4862	318	7	u2	u2	NOUN
ejpam-4862	318	8	,	,	PUNCT
ejpam-4862	318	9	.	.	PUNCT
ejpam-4862	318	10	.	.	PUNCT
ejpam-4862	319	1	.	.	PUNCT
ejpam-4862	320	1	,	,	PUNCT
ejpam-4862	320	2	u8	u8	PROPN
ejpam-4862	320	3	}	}	PUNCT
ejpam-4862	320	4	.	.	PUNCT
ejpam-4862	321	1	then	then	ADV
ejpam-4862	321	2	c	c	PROPN
ejpam-4862	321	3	is	be	AUX
ejpam-4862	321	4	the	the	DET
ejpam-4862	321	5	minimum	minimum	ADJ
ejpam-4862	321	6	outer	outer	ADJ
ejpam-4862	321	7	-	-	PUNCT
ejpam-4862	321	8	convex	convex	NOUN
ejpam-4862	321	9	hop	hop	NOUN
ejpam-4862	321	10	dominating	dominating	NOUN
ejpam-4862	321	11	set	set	NOUN
ejpam-4862	321	12	of	of	ADP
ejpam-4862	321	13	p4	p4	ADJ
ejpam-4862	321	14	◦	◦	NOUN
ejpam-4862	321	15	p2	p2	NOUN
ejpam-4862	321	16	.	.	PUNCT
ejpam-4862	322	1	thus	thus	ADV
ejpam-4862	322	2	,	,	PUNCT
ejpam-4862	322	3	γ̃conh(p4	γ̃conh(p4	NOUN
ejpam-4862	322	4	◦	◦	NOUN
ejpam-4862	322	5	p2	p2	NOUN
ejpam-4862	322	6	)	)	PUNCT
ejpam-4862	322	7	=	=	SYM
ejpam-4862	322	8	4(2	4(2	NUM
ejpam-4862	322	9	)	)	PUNCT
ejpam-4862	323	1	=	=	SYM
ejpam-4862	323	2	|v	|v	PROPN
ejpam-4862	323	3	(	(	PUNCT
ejpam-4862	323	4	g)||v	g)||v	PROPN
ejpam-4862	323	5	(	(	PUNCT
ejpam-4862	323	6	h)|	h)|	PROPN
ejpam-4862	323	7	.	.	PUNCT
ejpam-4862	324	1	j.	j.	PROPN
ejpam-4862	324	2	a.	a.	PROPN
ejpam-4862	324	3	hassan	hassan	PROPN
ejpam-4862	324	4	et	et	PROPN
ejpam-4862	324	5	al	al	PROPN
ejpam-4862	324	6	.	.	PUNCT
ejpam-4862	324	7	/	/	SYM
ejpam-4862	324	8	eur	eur	PROPN
ejpam-4862	324	9	.	.	PUNCT
ejpam-4862	325	1	j.	j.	PROPN
ejpam-4862	325	2	pure	pure	PROPN
ejpam-4862	325	3	appl	appl	PROPN
ejpam-4862	325	4	.	.	PROPN
ejpam-4862	325	5	math	math	PROPN
ejpam-4862	325	6	,	,	PUNCT
ejpam-4862	325	7	16	16	NUM
ejpam-4862	325	8	(	(	PUNCT
ejpam-4862	325	9	4	4	NUM
ejpam-4862	325	10	)	)	PUNCT
ejpam-4862	325	11	(	(	PUNCT
ejpam-4862	325	12	2023	2023	NUM
ejpam-4862	325	13	)	)	PUNCT
ejpam-4862	325	14	,	,	PUNCT
ejpam-4862	325	15	2035	2035	NUM
ejpam-4862	325	16	-	-	SYM
ejpam-4862	325	17	2048	2048	NUM
ejpam-4862	325	18	2046	2046	NUM
ejpam-4862	325	19	p4	p4	ADJ
ejpam-4862	325	20	◦	◦	NOUN
ejpam-4862	325	21	p2	p2	PROPN
ejpam-4862	325	22	:	:	PUNCT
ejpam-4862	325	23	u3	u3	NOUN
ejpam-4862	325	24	u5u1	u5u1	ADP
ejpam-4862	325	25	u2	u2	PROPN
ejpam-4862	325	26	u4	u4	PROPN
ejpam-4862	325	27	u6	u6	PROPN
ejpam-4862	325	28	u7	u7	PROPN
ejpam-4862	325	29	u8	u8	PROPN
ejpam-4862	325	30	u9	u9	PROPN
ejpam-4862	325	31	u10	u10	PROPN
ejpam-4862	325	32	u11	u11	PROPN
ejpam-4862	325	33	u12	u12	PROPN
ejpam-4862	325	34	figure	figure	NOUN
ejpam-4862	325	35	7	7	NUM
ejpam-4862	325	36	:	:	PUNCT
ejpam-4862	325	37	graph	graph	VERB
ejpam-4862	325	38	p4	p4	ADJ
ejpam-4862	325	39	◦	◦	NOUN
ejpam-4862	325	40	p2	p2	NOUN
ejpam-4862	325	41	with	with	ADP
ejpam-4862	325	42	γ̃conh(p4	γ̃conh(p4	NOUN
ejpam-4862	325	43	◦	◦	NOUN
ejpam-4862	325	44	p2	p2	NOUN
ejpam-4862	325	45	)	)	PUNCT
ejpam-4862	325	46	=	=	SYM
ejpam-4862	325	47	|v	|v	X
ejpam-4862	325	48	(	(	PUNCT
ejpam-4862	325	49	p4)||v	p4)||v	NOUN
ejpam-4862	325	50	(	(	PUNCT
ejpam-4862	325	51	p2)|	p2)|	NOUN
ejpam-4862	325	52	for	for	ADP
ejpam-4862	325	53	strict	strict	ADJ
ejpam-4862	325	54	inequality	inequality	NOUN
ejpam-4862	325	55	,	,	PUNCT
ejpam-4862	325	56	consider	consider	VERB
ejpam-4862	325	57	the	the	DET
ejpam-4862	325	58	graph	graph	NOUN
ejpam-4862	325	59	c4	c4	NOUN
ejpam-4862	325	60	◦	◦	NOUN
ejpam-4862	325	61	k3	k3	VERB
ejpam-4862	325	62	given	give	VERB
ejpam-4862	325	63	in	in	ADP
ejpam-4862	325	64	figure	figure	NOUN
ejpam-4862	325	65	8	8	NUM
ejpam-4862	325	66	.	.	PUNCT
ejpam-4862	326	1	let	let	VERB
ejpam-4862	326	2	c	c	NOUN
ejpam-4862	326	3	′	′	VERB
ejpam-4862	327	1	=	=	PUNCT
ejpam-4862	327	2	{	{	PUNCT
ejpam-4862	327	3	a	a	PRON
ejpam-4862	327	4	,	,	PUNCT
ejpam-4862	327	5	b	b	NOUN
ejpam-4862	327	6	,	,	PUNCT
ejpam-4862	327	7	c	c	NOUN
ejpam-4862	327	8	,	,	PUNCT
ejpam-4862	327	9	d	d	NOUN
ejpam-4862	327	10	,	,	PUNCT
ejpam-4862	327	11	e	e	NOUN
ejpam-4862	327	12	,	,	PUNCT
ejpam-4862	327	13	f	f	PROPN
ejpam-4862	327	14	,	,	PUNCT
ejpam-4862	327	15	g	g	PROPN
ejpam-4862	327	16	,	,	PUNCT
ejpam-4862	327	17	h	h	NOUN
ejpam-4862	327	18	}	}	PUNCT
ejpam-4862	327	19	.	.	PUNCT
ejpam-4862	328	1	then	then	ADV
ejpam-4862	328	2	c	c	X
ejpam-4862	328	3	′	′	PROPN
ejpam-4862	328	4	is	be	AUX
ejpam-4862	328	5	a	a	DET
ejpam-4862	328	6	minimum	minimum	ADJ
ejpam-4862	328	7	outer	outer	ADJ
ejpam-4862	328	8	-	-	PUNCT
ejpam-4862	328	9	convex	convex	NOUN
ejpam-4862	328	10	hop	hop	NOUN
ejpam-4862	328	11	dominating	dominating	NOUN
ejpam-4862	328	12	of	of	ADP
ejpam-4862	328	13	c4	c4	NOUN
ejpam-4862	328	14	◦	◦	NOUN
ejpam-4862	328	15	k3	k3	ADJ
ejpam-4862	328	16	.	.	PUNCT
ejpam-4862	329	1	hence	hence	ADV
ejpam-4862	329	2	,	,	PUNCT
ejpam-4862	329	3	γ̃conh(c4	γ̃conh(c4	VERB
ejpam-4862	329	4	◦	◦	NOUN
ejpam-4862	329	5	k3	k3	ADJ
ejpam-4862	329	6	)	)	PUNCT
ejpam-4862	329	7	=	=	SYM
ejpam-4862	329	8	8	8	NUM
ejpam-4862	329	9	<	<	SYM
ejpam-4862	329	10	12	12	NUM
ejpam-4862	329	11	=	=	SYM
ejpam-4862	329	12	|v	|v	X
ejpam-4862	329	13	(	(	PUNCT
ejpam-4862	329	14	c4)||v	c4)||v	PROPN
ejpam-4862	329	15	(	(	PUNCT
ejpam-4862	329	16	k3)|	k3)|	NOUN
ejpam-4862	329	17	.	.	PUNCT
ejpam-4862	330	1	c4	c4	NOUN
ejpam-4862	330	2	◦	◦	NOUN
ejpam-4862	330	3	k3	k3	ADJ
ejpam-4862	330	4	:	:	PUNCT
ejpam-4862	330	5	a	a	DET
ejpam-4862	330	6	b	b	X
ejpam-4862	330	7	c	c	NOUN
ejpam-4862	330	8	d	d	X
ejpam-4862	330	9	e	e	X
ejpam-4862	330	10	f	f	PROPN
ejpam-4862	331	1	g	g	PROPN
ejpam-4862	332	1	h	h	NOUN
ejpam-4862	333	1	i	i	PRON
ejpam-4862	333	2	j	j	PROPN
ejpam-4862	334	1	k	k	PROPN
ejpam-4862	334	2	l	l	PROPN
ejpam-4862	334	3	m	m	VERB
ejpam-4862	334	4	n	n	ADV
ejpam-4862	334	5	o	o	NOUN
ejpam-4862	334	6	p	p	NOUN
ejpam-4862	334	7	figure	figure	NOUN
ejpam-4862	334	8	8	8	NUM
ejpam-4862	334	9	:	:	PUNCT
ejpam-4862	334	10	graph	graph	NOUN
ejpam-4862	334	11	c4	c4	NOUN
ejpam-4862	334	12	◦	◦	NOUN
ejpam-4862	334	13	k3	k3	ADJ
ejpam-4862	334	14	with	with	ADP
ejpam-4862	334	15	γ̃conh(c4	γ̃conh(c4	NOUN
ejpam-4862	334	16	◦	◦	NOUN
ejpam-4862	334	17	k3	k3	ADJ
ejpam-4862	334	18	)	)	PUNCT
ejpam-4862	334	19	<	<	X
ejpam-4862	334	20	|v	|v	X
ejpam-4862	334	21	(	(	PUNCT
ejpam-4862	334	22	c4)||v	c4)||v	PROPN
ejpam-4862	334	23	(	(	PUNCT
ejpam-4862	334	24	k3)|	k3)|	PROPN
ejpam-4862	334	25	4	4	NUM
ejpam-4862	334	26	.	.	PUNCT
ejpam-4862	334	27	conclusion	conclusion	VERB
ejpam-4862	334	28	the	the	DET
ejpam-4862	334	29	concept	concept	NOUN
ejpam-4862	334	30	of	of	ADP
ejpam-4862	334	31	an	an	DET
ejpam-4862	334	32	outer	outer	ADJ
ejpam-4862	334	33	-	-	PUNCT
ejpam-4862	334	34	convex	convex	NOUN
ejpam-4862	334	35	hop	hop	NOUN
ejpam-4862	334	36	domination	domination	NOUN
ejpam-4862	334	37	has	have	AUX
ejpam-4862	334	38	been	be	AUX
ejpam-4862	334	39	introduced	introduce	VERB
ejpam-4862	334	40	and	and	CCONJ
ejpam-4862	334	41	investigated	investigate	VERB
ejpam-4862	334	42	in	in	ADP
ejpam-4862	334	43	this	this	DET
ejpam-4862	334	44	study	study	NOUN
ejpam-4862	334	45	.	.	PUNCT
ejpam-4862	335	1	necessary	necessary	ADJ
ejpam-4862	335	2	and	and	CCONJ
ejpam-4862	335	3	sufficient	sufficient	ADJ
ejpam-4862	335	4	conditions	condition	NOUN
ejpam-4862	335	5	for	for	ADP
ejpam-4862	335	6	sets	set	NOUN
ejpam-4862	335	7	in	in	ADP
ejpam-4862	335	8	some	some	DET
ejpam-4862	335	9	special	special	ADJ
ejpam-4862	335	10	graphs	graph	NOUN
ejpam-4862	335	11	and	and	CCONJ
ejpam-4862	335	12	the	the	DET
ejpam-4862	335	13	join	join	NOUN
ejpam-4862	335	14	of	of	ADP
ejpam-4862	335	15	two	two	NUM
ejpam-4862	335	16	graphs	graph	NOUN
ejpam-4862	335	17	have	have	AUX
ejpam-4862	335	18	been	be	AUX
ejpam-4862	335	19	formulated	formulate	VERB
ejpam-4862	335	20	.	.	PUNCT
ejpam-4862	336	1	these	these	DET
ejpam-4862	336	2	results	result	NOUN
ejpam-4862	336	3	have	have	AUX
ejpam-4862	336	4	been	be	AUX
ejpam-4862	336	5	used	use	VERB
ejpam-4862	336	6	to	to	PART
ejpam-4862	336	7	derive	derive	VERB
ejpam-4862	336	8	bound	bound	ADJ
ejpam-4862	336	9	references	reference	NOUN
ejpam-4862	336	10	2047	2047	NUM
ejpam-4862	336	11	or	or	CCONJ
ejpam-4862	336	12	exact	exact	ADJ
ejpam-4862	336	13	value	value	NOUN
ejpam-4862	336	14	of	of	ADP
ejpam-4862	336	15	outer	outer	ADJ
ejpam-4862	336	16	-	-	PUNCT
ejpam-4862	336	17	convex	convex	NOUN
ejpam-4862	336	18	hop	hop	NOUN
ejpam-4862	336	19	domination	domination	NOUN
ejpam-4862	336	20	number	number	NOUN
ejpam-4862	336	21	of	of	ADP
ejpam-4862	336	22	each	each	PRON
ejpam-4862	336	23	of	of	ADP
ejpam-4862	336	24	these	these	DET
ejpam-4862	336	25	graphs	graph	NOUN
ejpam-4862	336	26	.	.	PUNCT
ejpam-4862	337	1	moreover	moreover	ADV
ejpam-4862	337	2	,	,	PUNCT
ejpam-4862	337	3	we	we	PRON
ejpam-4862	337	4	have	have	AUX
ejpam-4862	337	5	established	establish	VERB
ejpam-4862	337	6	upper	upper	ADJ
ejpam-4862	337	7	bound	bind	VERB
ejpam-4862	337	8	for	for	ADP
ejpam-4862	337	9	the	the	DET
ejpam-4862	337	10	parameter	parameter	NOUN
ejpam-4862	337	11	on	on	ADP
ejpam-4862	337	12	the	the	DET
ejpam-4862	337	13	corona	corona	NOUN
ejpam-4862	337	14	of	of	ADP
ejpam-4862	337	15	two	two	NUM
ejpam-4862	337	16	graphs	graph	NOUN
ejpam-4862	337	17	.	.	PUNCT
ejpam-4862	338	1	other	other	ADJ
ejpam-4862	338	2	interested	interested	ADJ
ejpam-4862	338	3	researchers	researcher	NOUN
ejpam-4862	338	4	may	may	AUX
ejpam-4862	338	5	investigate	investigate	VERB
ejpam-4862	338	6	the	the	DET
ejpam-4862	338	7	concept	concept	NOUN
ejpam-4862	338	8	for	for	ADP
ejpam-4862	338	9	other	other	ADJ
ejpam-4862	338	10	graphs	graph	NOUN
ejpam-4862	338	11	that	that	PRON
ejpam-4862	338	12	were	be	AUX
ejpam-4862	338	13	not	not	PART
ejpam-4862	338	14	considered	consider	VERB
ejpam-4862	338	15	in	in	ADP
ejpam-4862	338	16	this	this	DET
ejpam-4862	338	17	study	study	NOUN
ejpam-4862	338	18	.	.	PUNCT
ejpam-4862	339	1	providing	provide	VERB
ejpam-4862	339	2	a	a	DET
ejpam-4862	339	3	real	real	ADJ
ejpam-4862	339	4	-	-	PUNCT
ejpam-4862	339	5	life	life	NOUN
ejpam-4862	339	6	application	application	NOUN
ejpam-4862	339	7	of	of	ADP
ejpam-4862	339	8	the	the	DET
ejpam-4862	339	9	concept	concept	NOUN
ejpam-4862	339	10	will	will	AUX
ejpam-4862	339	11	be	be	AUX
ejpam-4862	339	12	an	an	DET
ejpam-4862	339	13	interesting	interesting	ADJ
ejpam-4862	339	14	topic	topic	NOUN
ejpam-4862	339	15	to	to	PART
ejpam-4862	339	16	consider	consider	VERB
ejpam-4862	339	17	.	.	PUNCT
ejpam-4862	340	1	acknowledgements	acknowledgement	NOUN
ejpam-4862	340	2	the	the	DET
ejpam-4862	340	3	authors	author	NOUN
ejpam-4862	340	4	would	would	AUX
ejpam-4862	340	5	like	like	VERB
ejpam-4862	340	6	to	to	PART
ejpam-4862	340	7	thank	thank	VERB
ejpam-4862	340	8	the	the	DET
ejpam-4862	340	9	referees	referee	NOUN
ejpam-4862	340	10	for	for	ADP
ejpam-4862	340	11	their	their	PRON
ejpam-4862	340	12	invaluable	invaluable	ADJ
ejpam-4862	340	13	comments	comment	NOUN
ejpam-4862	340	14	and	and	CCONJ
ejpam-4862	340	15	suggestions	suggestion	NOUN
ejpam-4862	340	16	that	that	PRON
ejpam-4862	340	17	led	lead	VERB
ejpam-4862	340	18	to	to	ADP
ejpam-4862	340	19	the	the	DET
ejpam-4862	340	20	improvement	improvement	NOUN
ejpam-4862	340	21	of	of	ADP
ejpam-4862	340	22	the	the	DET
ejpam-4862	340	23	paper	paper	NOUN
ejpam-4862	340	24	.	.	PUNCT
ejpam-4862	341	1	also	also	ADV
ejpam-4862	341	2	,	,	PUNCT
ejpam-4862	341	3	the	the	DET
ejpam-4862	341	4	authors	author	NOUN
ejpam-4862	341	5	are	be	AUX
ejpam-4862	341	6	grateful	grateful	ADJ
ejpam-4862	341	7	to	to	PART
ejpam-4862	341	8	mindanao	mindanao	PROPN
ejpam-4862	341	9	state	state	PROPN
ejpam-4862	341	10	university	university	PROPN
ejpam-4862	341	11	tawi	tawi	PROPN
ejpam-4862	341	12	-	-	PUNCT
ejpam-4862	341	13	tawi	tawi	PROPN
ejpam-4862	341	14	college	college	PROPN
ejpam-4862	341	15	of	of	ADP
ejpam-4862	341	16	technology	technology	NOUN
ejpam-4862	341	17	and	and	CCONJ
ejpam-4862	341	18	oceanography	oceanography	NOUN
ejpam-4862	341	19	for	for	ADP
ejpam-4862	341	20	funding	fund	VERB
ejpam-4862	341	21	this	this	DET
ejpam-4862	341	22	research	research	NOUN
ejpam-4862	341	23	.	.	PUNCT
ejpam-4862	342	1	references	reference	NOUN
ejpam-4862	342	2	[	[	X
ejpam-4862	342	3	1	1	NUM
ejpam-4862	342	4	]	]	PUNCT
ejpam-4862	342	5	s.	s.	PROPN
ejpam-4862	342	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4862	342	7	,	,	PUNCT
ejpam-4862	342	8	b.	b.	PROPN
ejpam-4862	342	9	krishnakumari	krishnakumari	PROPN
ejpam-4862	342	10	,	,	PUNCT
ejpam-4862	342	11	b.	b.	PROPN
ejpam-4862	342	12	natarjan	natarjan	PROPN
ejpam-4862	342	13	,	,	PUNCT
ejpam-4862	342	14	and	and	CCONJ
ejpam-4862	342	15	y.	y.	PROPN
ejpam-4862	342	16	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4862	342	17	.	.	PUNCT
ejpam-4862	343	1	bounds	bound	NOUN
ejpam-4862	343	2	on	on	ADP
ejpam-4862	343	3	the	the	DET
ejpam-4862	343	4	hop	hop	NOUN
ejpam-4862	343	5	domination	domination	NOUN
ejpam-4862	343	6	number	number	NOUN
ejpam-4862	343	7	of	of	ADP
ejpam-4862	343	8	a	a	DET
ejpam-4862	343	9	tree	tree	NOUN
ejpam-4862	343	10	.	.	PUNCT
ejpam-4862	344	1	proceedings	proceeding	NOUN
ejpam-4862	344	2	-	-	PUNCT
ejpam-4862	344	3	mathematical	mathematical	ADJ
ejpam-4862	344	4	sciences	science	NOUN
ejpam-4862	344	5	.	.	PUNCT
ejpam-4862	344	6	,	,	PUNCT
ejpam-4862	344	7	125(4):449–455	125(4):449–455	ADP
ejpam-4862	344	8	,	,	PUNCT
ejpam-4862	344	9	2015	2015	NUM
ejpam-4862	344	10	.	.	PUNCT
ejpam-4862	345	1	[	[	X
ejpam-4862	345	2	2	2	NUM
ejpam-4862	345	3	]	]	PUNCT
ejpam-4862	345	4	s.	s.	PROPN
ejpam-4862	345	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4862	345	6	,	,	PUNCT
ejpam-4862	345	7	c.	c.	PROPN
ejpam-4862	345	8	natarajan	natarajan	PROPN
ejpam-4862	345	9	,	,	PUNCT
ejpam-4862	345	10	and	and	CCONJ
ejpam-4862	345	11	g.	g.	PROPN
ejpam-4862	345	12	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4862	345	13	.	.	PUNCT
ejpam-4862	346	1	a	a	DET
ejpam-4862	346	2	note	note	NOUN
ejpam-4862	346	3	on	on	ADP
ejpam-4862	346	4	hop	hop	NOUN
ejpam-4862	346	5	domination	domination	NOUN
ejpam-4862	346	6	number	number	NOUN
ejpam-4862	346	7	of	of	ADP
ejpam-4862	346	8	some	some	DET
ejpam-4862	346	9	special	special	ADJ
ejpam-4862	346	10	families	family	NOUN
ejpam-4862	346	11	of	of	ADP
ejpam-4862	346	12	graphs	graph	NOUN
ejpam-4862	346	13	.	.	PUNCT
ejpam-4862	347	1	international	international	ADJ
ejpam-4862	347	2	journal	journal	NOUN
ejpam-4862	347	3	of	of	ADP
ejpam-4862	347	4	pure	pure	ADJ
ejpam-4862	347	5	and	and	CCONJ
ejpam-4862	347	6	applied	applied	ADJ
ejpam-4862	347	7	mathematics	mathematic	NOUN
ejpam-4862	347	8	.	.	PUNCT
ejpam-4862	347	9	,	,	PUNCT
ejpam-4862	347	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4862	347	11	,	,	PUNCT
ejpam-4862	347	12	2018	2018	NUM
ejpam-4862	347	13	.	.	PUNCT
ejpam-4862	348	1	[	[	X
ejpam-4862	348	2	3	3	X
ejpam-4862	348	3	]	]	X
ejpam-4862	348	4	j.	j.	PROPN
ejpam-4862	348	5	hassan	hassan	PROPN
ejpam-4862	348	6	and	and	CCONJ
ejpam-4862	348	7	s.	s.	PROPN
ejpam-4862	348	8	canoy	canoy	PROPN
ejpam-4862	348	9	jr	jr	PROPN
ejpam-4862	348	10	.	.	PROPN
ejpam-4862	348	11	hop	hop	PROPN
ejpam-4862	348	12	independent	independent	ADJ
ejpam-4862	348	13	hop	hop	NOUN
ejpam-4862	348	14	domination	domination	NOUN
ejpam-4862	348	15	in	in	ADP
ejpam-4862	348	16	graphs	graph	NOUN
ejpam-4862	348	17	.	.	PUNCT
ejpam-4862	349	1	eur	eur	PROPN
ejpam-4862	349	2	.	.	PUNCT
ejpam-4862	350	1	j.	j.	PROPN
ejpam-4862	350	2	pure	pure	PROPN
ejpam-4862	350	3	appl	appl	PROPN
ejpam-4862	350	4	.	.	PUNCT
ejpam-4862	350	5	math	math	PROPN
ejpam-4862	350	6	.	.	PUNCT
ejpam-4862	350	7	,	,	PUNCT
ejpam-4862	350	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-4862	350	9	,	,	PUNCT
ejpam-4862	350	10	2022	2022	NUM
ejpam-4862	350	11	.	.	PUNCT
ejpam-4862	351	1	[	[	X
ejpam-4862	351	2	4	4	X
ejpam-4862	351	3	]	]	PUNCT
ejpam-4862	351	4	j.	j.	PROPN
ejpam-4862	351	5	hassan	hassan	PROPN
ejpam-4862	351	6	and	and	CCONJ
ejpam-4862	351	7	s.	s.	PROPN
ejpam-4862	351	8	canoy	canoy	PROPN
ejpam-4862	351	9	jr	jr	PROPN
ejpam-4862	351	10	.	.	PROPN
ejpam-4862	351	11	connected	connect	VERB
ejpam-4862	351	12	grundy	grundy	PROPN
ejpam-4862	351	13	hop	hop	NOUN
ejpam-4862	351	14	dominating	dominate	VERB
ejpam-4862	351	15	sequences	sequence	NOUN
ejpam-4862	351	16	in	in	ADP
ejpam-4862	351	17	graphs	graph	NOUN
ejpam-4862	351	18	.	.	PUNCT
ejpam-4862	352	1	eur	eur	PROPN
ejpam-4862	352	2	.	.	PUNCT
ejpam-4862	353	1	j.	j.	PROPN
ejpam-4862	353	2	pure	pure	PROPN
ejpam-4862	353	3	appl	appl	PROPN
ejpam-4862	353	4	.	.	PUNCT
ejpam-4862	353	5	math	math	PROPN
ejpam-4862	353	6	.	.	PUNCT
ejpam-4862	353	7	,	,	PUNCT
ejpam-4862	354	1	16(2):1212–1227	16(2):1212–1227	NUM
ejpam-4862	354	2	,	,	PUNCT
ejpam-4862	354	3	2023	2023	NUM
ejpam-4862	354	4	.	.	PUNCT
ejpam-4862	355	1	[	[	X
ejpam-4862	355	2	5	5	X
ejpam-4862	355	3	]	]	PUNCT
ejpam-4862	355	4	j.	j.	PROPN
ejpam-4862	355	5	hassan	hassan	PROPN
ejpam-4862	355	6	,	,	PUNCT
ejpam-4862	355	7	s.	s.	PROPN
ejpam-4862	355	8	canoy	canoy	PROPN
ejpam-4862	355	9	jr	jr	PROPN
ejpam-4862	355	10	.	.	PROPN
ejpam-4862	355	11	,	,	PUNCT
ejpam-4862	355	12	and	and	CCONJ
ejpam-4862	355	13	chrisley	chrisley	PROPN
ejpam-4862	355	14	jade	jade	NOUN
ejpam-4862	355	15	saromines	saromine	NOUN
ejpam-4862	355	16	.	.	PUNCT
ejpam-4862	356	1	convex	convex	VERB
ejpam-4862	356	2	hop	hop	NOUN
ejpam-4862	356	3	domination	domination	NOUN
ejpam-4862	356	4	in	in	ADP
ejpam-4862	356	5	graphs	graph	NOUN
ejpam-4862	356	6	.	.	PUNCT
ejpam-4862	357	1	eur	eur	PROPN
ejpam-4862	357	2	.	.	PUNCT
ejpam-4862	358	1	j.	j.	PROPN
ejpam-4862	358	2	pure	pure	PROPN
ejpam-4862	358	3	appl	appl	PROPN
ejpam-4862	358	4	.	.	PUNCT
ejpam-4862	358	5	math	math	PROPN
ejpam-4862	358	6	.	.	PUNCT
ejpam-4862	358	7	,	,	PUNCT
ejpam-4862	358	8	16(1):319–335	16(1):319–335	NOUN
ejpam-4862	358	9	,	,	PUNCT
ejpam-4862	358	10	2023	2023	NUM
ejpam-4862	358	11	.	.	PUNCT
ejpam-4862	359	1	[	[	X
ejpam-4862	359	2	6	6	NUM
ejpam-4862	359	3	]	]	PUNCT
ejpam-4862	359	4	j.	j.	PROPN
ejpam-4862	359	5	hassan	hassan	PROPN
ejpam-4862	359	6	,	,	PUNCT
ejpam-4862	359	7	a.	a.	PROPN
ejpam-4862	359	8	lintasan	lintasan	PROPN
ejpam-4862	359	9	,	,	PUNCT
ejpam-4862	359	10	and	and	CCONJ
ejpam-4862	359	11	n.h	n.h	PROPN
ejpam-4862	359	12	.	.	PUNCT
ejpam-4862	360	1	mohammad	mohammad	PROPN
ejpam-4862	360	2	.	.	PUNCT
ejpam-4862	361	1	some	some	DET
ejpam-4862	361	2	properties	property	NOUN
ejpam-4862	361	3	and	and	CCONJ
ejpam-4862	361	4	realization	realization	NOUN
ejpam-4862	361	5	problems	problem	NOUN
ejpam-4862	361	6	involving	involve	VERB
ejpam-4862	361	7	connected	connected	ADJ
ejpam-4862	361	8	outer	outer	ADJ
ejpam-4862	361	9	-	-	PUNCT
ejpam-4862	361	10	hop	hop	NOUN
ejpam-4862	361	11	independent	independent	ADJ
ejpam-4862	361	12	hop	hop	NOUN
ejpam-4862	361	13	domination	domination	NOUN
ejpam-4862	361	14	in	in	ADP
ejpam-4862	361	15	graphs	graph	NOUN
ejpam-4862	361	16	.	.	PUNCT
ejpam-4862	362	1	eur	eur	PROPN
ejpam-4862	362	2	.	.	PUNCT
ejpam-4862	363	1	j.	j.	PROPN
ejpam-4862	363	2	pure	pure	PROPN
ejpam-4862	363	3	appl	appl	PROPN
ejpam-4862	363	4	.	.	PUNCT
ejpam-4862	363	5	math	math	PROPN
ejpam-4862	363	6	.	.	PUNCT
ejpam-4862	363	7	,	,	PUNCT
ejpam-4862	363	8	16(3):1848–1861	16(3):1848–1861	NUM
ejpam-4862	363	9	,	,	PUNCT
ejpam-4862	363	10	2023	2023	NUM
ejpam-4862	363	11	.	.	PUNCT
ejpam-4862	364	1	[	[	X
ejpam-4862	364	2	7	7	X
ejpam-4862	364	3	]	]	X
ejpam-4862	364	4	s.	s.	PROPN
ejpam-4862	364	5	canoy	canoy	PROPN
ejpam-4862	364	6	jr	jr	PROPN
ejpam-4862	364	7	and	and	CCONJ
ejpam-4862	364	8	i.j.l	i.j.l	PROPN
ejpam-4862	364	9	.	.	PROPN
ejpam-4862	364	10	garces	garces	PROPN
ejpam-4862	364	11	.	.	PUNCT
ejpam-4862	365	1	convex	convex	PROPN
ejpam-4862	365	2	sets	set	NOUN
ejpam-4862	365	3	under	under	ADP
ejpam-4862	365	4	some	some	DET
ejpam-4862	365	5	graph	graph	NOUN
ejpam-4862	365	6	operations	operation	NOUN
ejpam-4862	365	7	.	.	PUNCT
ejpam-4862	366	1	graphs	graph	NOUN
ejpam-4862	366	2	and	and	CCONJ
ejpam-4862	366	3	combinatorics	combinatoric	NOUN
ejpam-4862	366	4	,	,	PUNCT
ejpam-4862	366	5	18:787–793	18:787–793	PROPN
ejpam-4862	366	6	,	,	PUNCT
ejpam-4862	366	7	2002	2002	NUM
ejpam-4862	366	8	.	.	PUNCT
ejpam-4862	367	1	[	[	X
ejpam-4862	367	2	8	8	X
ejpam-4862	367	3	]	]	X
ejpam-4862	367	4	s.	s.	PROPN
ejpam-4862	367	5	canoy	canoy	PROPN
ejpam-4862	367	6	jr	jr	PROPN
ejpam-4862	367	7	and	and	CCONJ
ejpam-4862	367	8	j.	j.	PROPN
ejpam-4862	367	9	hassan	hassan	PROPN
ejpam-4862	367	10	.	.	PUNCT
ejpam-4862	368	1	weakly	weakly	ADJ
ejpam-4862	368	2	convex	convex	VERB
ejpam-4862	368	3	hop	hop	NOUN
ejpam-4862	368	4	dominating	dominating	NOUN
ejpam-4862	368	5	sets	set	NOUN
ejpam-4862	368	6	in	in	ADP
ejpam-4862	368	7	graphs	graph	NOUN
ejpam-4862	368	8	.	.	PUNCT
ejpam-4862	369	1	eur	eur	PROPN
ejpam-4862	369	2	.	.	PUNCT
ejpam-4862	370	1	j.	j.	PROPN
ejpam-4862	370	2	pure	pure	PROPN
ejpam-4862	370	3	appl	appl	PROPN
ejpam-4862	370	4	.	.	PUNCT
ejpam-4862	370	5	math	math	PROPN
ejpam-4862	370	6	.	.	PUNCT
ejpam-4862	370	7	,	,	PUNCT
ejpam-4862	370	8	16(2):1196–1211	16(2):1196–1211	NUM
ejpam-4862	370	9	,	,	PUNCT
ejpam-4862	370	10	2023	2023	NUM
ejpam-4862	370	11	.	.	PUNCT
ejpam-4862	371	1	[	[	X
ejpam-4862	371	2	9	9	NUM
ejpam-4862	371	3	]	]	PUNCT
ejpam-4862	371	4	s.	s.	PROPN
ejpam-4862	371	5	canoy	canoy	PROPN
ejpam-4862	371	6	jr	jr	PROPN
ejpam-4862	371	7	.	.	PROPN
ejpam-4862	371	8	,	,	PUNCT
ejpam-4862	371	9	r.	r.	PROPN
ejpam-4862	371	10	mollejon	mollejon	NOUN
ejpam-4862	371	11	,	,	PUNCT
ejpam-4862	371	12	and	and	CCONJ
ejpam-4862	371	13	j.	j.	PROPN
ejpam-4862	371	14	g.	g.	PROPN
ejpam-4862	371	15	canoy	canoy	PROPN
ejpam-4862	371	16	.	.	PUNCT
ejpam-4862	372	1	hop	hop	PROPN
ejpam-4862	372	2	dominating	dominating	NOUN
ejpam-4862	372	3	sets	set	NOUN
ejpam-4862	372	4	in	in	ADP
ejpam-4862	372	5	graphs	graph	NOUN
ejpam-4862	372	6	under	under	ADP
ejpam-4862	372	7	binary	binary	ADJ
ejpam-4862	372	8	operations	operation	NOUN
ejpam-4862	372	9	.	.	PUNCT
ejpam-4862	373	1	eur	eur	PROPN
ejpam-4862	373	2	.	.	PUNCT
ejpam-4862	374	1	j.	j.	PROPN
ejpam-4862	374	2	pure	pure	PROPN
ejpam-4862	374	3	appl	appl	PROPN
ejpam-4862	374	4	.	.	PUNCT
ejpam-4862	374	5	math	math	PROPN
ejpam-4862	374	6	.	.	PUNCT
ejpam-4862	374	7	,	,	PUNCT
ejpam-4862	375	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4862	375	2	,	,	PUNCT
ejpam-4862	375	3	2019	2019	NUM
ejpam-4862	375	4	.	.	PUNCT
ejpam-4862	376	1	[	[	X
ejpam-4862	376	2	10	10	NUM
ejpam-4862	376	3	]	]	X
ejpam-4862	376	4	s.	s.	PROPN
ejpam-4862	376	5	nanding	nanding	PROPN
ejpam-4862	376	6	and	and	CCONJ
ejpam-4862	376	7	h.	h.	PROPN
ejpam-4862	376	8	rara	rara	PROPN
ejpam-4862	376	9	.	.	PUNCT
ejpam-4862	377	1	connected	connect	VERB
ejpam-4862	377	2	outer	outer	ADJ
ejpam-4862	377	3	-	-	PUNCT
ejpam-4862	377	4	independent	independent	ADJ
ejpam-4862	377	5	hop	hop	NOUN
ejpam-4862	377	6	domination	domination	NOUN
ejpam-4862	377	7	in	in	ADP
ejpam-4862	377	8	graphs	graph	NOUN
ejpam-4862	377	9	.	.	PUNCT
ejpam-4862	378	1	eur	eur	PROPN
ejpam-4862	378	2	.	.	PUNCT
ejpam-4862	379	1	j.	j.	PROPN
ejpam-4862	379	2	pure	pure	PROPN
ejpam-4862	379	3	appl	appl	PROPN
ejpam-4862	379	4	.	.	PUNCT
ejpam-4862	379	5	math	math	PROPN
ejpam-4862	379	6	.	.	PUNCT
ejpam-4862	379	7	,	,	PUNCT
ejpam-4862	379	8	14(4):1226–1236	14(4):1226–1236	NUM
ejpam-4862	379	9	,	,	PUNCT
ejpam-4862	379	10	2021	2021	NUM
ejpam-4862	379	11	.	.	PUNCT
ejpam-4862	380	1	references	reference	NOUN
ejpam-4862	380	2	2048	2048	NUM
ejpam-4862	380	3	[	[	X
ejpam-4862	380	4	11	11	NUM
ejpam-4862	380	5	]	]	X
ejpam-4862	380	6	c.	c.	PROPN
ejpam-4862	380	7	natarajan	natarajan	PROPN
ejpam-4862	380	8	and	and	CCONJ
ejpam-4862	380	9	s.	s.	PROPN
ejpam-4862	380	10	ayyaswamy	ayyaswamy	PROPN
ejpam-4862	380	11	.	.	PUNCT
ejpam-4862	381	1	hop	hop	PROPN
ejpam-4862	381	2	domination	domination	NOUN
ejpam-4862	381	3	in	in	ADP
ejpam-4862	381	4	graphs	graphs	PROPN
ejpam-4862	381	5	ii	ii	PROPN
ejpam-4862	381	6	.	.	PUNCT
ejpam-4862	381	7	versita	versita	PROPN
ejpam-4862	381	8	,	,	PUNCT
ejpam-4862	381	9	23(2):187	23(2):187	NUM
ejpam-4862	381	10	–	–	PUNCT
ejpam-4862	381	11	199	199	NUM
ejpam-4862	381	12	,	,	PUNCT
ejpam-4862	381	13	2015	2015	NUM
ejpam-4862	381	14	.	.	PUNCT
ejpam-4862	382	1	[	[	X
ejpam-4862	382	2	12	12	NUM
ejpam-4862	382	3	]	]	X
ejpam-4862	382	4	y.	y.	PROPN
ejpam-4862	382	5	pabilona	pabilona	PROPN
ejpam-4862	382	6	and	and	CCONJ
ejpam-4862	382	7	h.	h.	PROPN
ejpam-4862	382	8	rara	rara	PROPN
ejpam-4862	382	9	.	.	PUNCT
ejpam-4862	383	1	connected	connect	VERB
ejpam-4862	383	2	hop	hop	NOUN
ejpam-4862	383	3	domination	domination	NOUN
ejpam-4862	383	4	in	in	ADP
ejpam-4862	383	5	graphs	graph	NOUN
ejpam-4862	383	6	under	under	ADP
ejpam-4862	383	7	some	some	DET
ejpam-4862	383	8	binary	binary	ADJ
ejpam-4862	383	9	operations	operation	NOUN
ejpam-4862	383	10	.	.	PUNCT
ejpam-4862	384	1	asian	asian	ADJ
ejpam-4862	384	2	-	-	PUNCT
ejpam-4862	384	3	eur	eur	NOUN
ejpam-4862	384	4	.	.	PUNCT
ejpam-4862	385	1	j.	j.	PROPN
ejpam-4862	385	2	math	math	PROPN
ejpam-4862	385	3	.	.	PROPN
ejpam-4862	385	4	,	,	PUNCT
ejpam-4862	385	5	11(5):1850075–1–1850075–11	11(5):1850075–1–1850075–11	NUM
ejpam-4862	385	6	,	,	PUNCT
ejpam-4862	385	7	2018	2018	NUM
ejpam-4862	385	8	.	.	PUNCT