id	sid	tid	token	lemma	pos
ejpam-4656	1	1	european	european	PROPN
ejpam-4656	1	2	journal	journal	PROPN
ejpam-4656	1	3	of	of	ADP
ejpam-4656	1	4	pure	pure	ADJ
ejpam-4656	1	5	and	and	CCONJ
ejpam-4656	1	6	applied	apply	VERB
ejpam-4656	1	7	mathematics	mathematic	NOUN
ejpam-4656	1	8	vol	vol	NOUN
ejpam-4656	1	9	.	.	PUNCT
ejpam-4656	2	1	16	16	NUM
ejpam-4656	2	2	,	,	PUNCT
ejpam-4656	2	3	no	no	INTJ
ejpam-4656	2	4	.	.	NOUN
ejpam-4656	2	5	1	1	NUM
ejpam-4656	2	6	,	,	PUNCT
ejpam-4656	2	7	2023	2023	NUM
ejpam-4656	2	8	,	,	PUNCT
ejpam-4656	2	9	319	319	NUM
ejpam-4656	2	10	-	-	SYM
ejpam-4656	2	11	335	335	NUM
ejpam-4656	2	12	issn	issn	PROPN
ejpam-4656	2	13	1307	1307	NUM
ejpam-4656	2	14	-	-	SYM
ejpam-4656	2	15	5543	5543	NUM
ejpam-4656	2	16	–	–	PUNCT
ejpam-4656	2	17	ejpam.com	ejpam.com	X
ejpam-4656	2	18	published	publish	VERB
ejpam-4656	2	19	by	by	ADP
ejpam-4656	2	20	new	new	PROPN
ejpam-4656	2	21	york	york	PROPN
ejpam-4656	2	22	business	business	PROPN
ejpam-4656	2	23	global	global	PROPN
ejpam-4656	2	24	convex	convex	PROPN
ejpam-4656	2	25	hop	hop	NOUN
ejpam-4656	2	26	domination	domination	NOUN
ejpam-4656	2	27	in	in	ADP
ejpam-4656	2	28	graphs	graph	NOUN
ejpam-4656	2	29	javier	javier	PROPN
ejpam-4656	2	30	a.	a.	PROPN
ejpam-4656	2	31	hassan1,∗	hassan1,∗	PROPN
ejpam-4656	2	32	,	,	PUNCT
ejpam-4656	2	33	sergio	sergio	PROPN
ejpam-4656	2	34	r.	r.	PROPN
ejpam-4656	2	35	canoy	canoy	PROPN
ejpam-4656	2	36	,	,	PUNCT
ejpam-4656	2	37	jr.2	jr.2	PROPN
ejpam-4656	2	38	,	,	PUNCT
ejpam-4656	2	39	chrisley	chrisley	NOUN
ejpam-4656	2	40	jade	jade	PROPN
ejpam-4656	2	41	saromines2	saromines2	PROPN
ejpam-4656	2	42	1	1	NUM
ejpam-4656	2	43	mathematics	mathematic	NOUN
ejpam-4656	2	44	and	and	CCONJ
ejpam-4656	2	45	sciences	sciences	PROPN
ejpam-4656	2	46	department	department	PROPN
ejpam-4656	2	47	,	,	PUNCT
ejpam-4656	2	48	college	college	NOUN
ejpam-4656	2	49	of	of	ADP
ejpam-4656	2	50	arts	art	NOUN
ejpam-4656	2	51	and	and	CCONJ
ejpam-4656	2	52	sciences	science	NOUN
ejpam-4656	2	53	,	,	PUNCT
ejpam-4656	2	54	msu	msu	PROPN
ejpam-4656	2	55	tawi	tawi	PROPN
ejpam-4656	2	56	-	-	PUNCT
ejpam-4656	2	57	tawi	tawi	PROPN
ejpam-4656	2	58	college	college	PROPN
ejpam-4656	2	59	of	of	ADP
ejpam-4656	2	60	technology	technology	NOUN
ejpam-4656	2	61	and	and	CCONJ
ejpam-4656	2	62	oceanography	oceanography	NOUN
ejpam-4656	2	63	,	,	PUNCT
ejpam-4656	2	64	bongao	bongao	NOUN
ejpam-4656	2	65	,	,	PUNCT
ejpam-4656	2	66	tawi	tawi	NOUN
ejpam-4656	2	67	-	-	PUNCT
ejpam-4656	2	68	tawi	tawi	NOUN
ejpam-4656	2	69	,	,	PUNCT
ejpam-4656	2	70	philippines	philippines	PROPN
ejpam-4656	2	71	2	2	NUM
ejpam-4656	2	72	department	department	NOUN
ejpam-4656	2	73	of	of	ADP
ejpam-4656	2	74	mathematics	mathematic	NOUN
ejpam-4656	2	75	and	and	CCONJ
ejpam-4656	2	76	statistics	statistic	NOUN
ejpam-4656	2	77	,	,	PUNCT
ejpam-4656	2	78	college	college	NOUN
ejpam-4656	2	79	of	of	ADP
ejpam-4656	2	80	science	science	NOUN
ejpam-4656	2	81	and	and	CCONJ
ejpam-4656	2	82	mathematics	mathematic	NOUN
ejpam-4656	2	83	,	,	PUNCT
ejpam-4656	2	84	center	center	NOUN
ejpam-4656	2	85	for	for	ADP
ejpam-4656	2	86	graph	graph	NOUN
ejpam-4656	2	87	theory	theory	NOUN
ejpam-4656	2	88	,	,	PUNCT
ejpam-4656	2	89	algebra	algebra	NOUN
ejpam-4656	2	90	,	,	PUNCT
ejpam-4656	2	91	and	and	CCONJ
ejpam-4656	2	92	analysisprism	analysisprism	NOUN
ejpam-4656	2	93	,	,	PUNCT
ejpam-4656	2	94	msu	msu	PROPN
ejpam-4656	2	95	-	-	PUNCT
ejpam-4656	2	96	iligan	iligan	PROPN
ejpam-4656	2	97	institute	institute	PROPN
ejpam-4656	2	98	of	of	ADP
ejpam-4656	2	99	technology	technology	PROPN
ejpam-4656	2	100	,	,	PUNCT
ejpam-4656	2	101	9200	9200	NUM
ejpam-4656	2	102	iligan	iligan	ADJ
ejpam-4656	2	103	city	city	NOUN
ejpam-4656	2	104	,	,	PUNCT
ejpam-4656	2	105	philippines	philippine	NOUN
ejpam-4656	2	106	abstract	abstract	ADJ
ejpam-4656	2	107	.	.	PUNCT
ejpam-4656	3	1	let	let	VERB
ejpam-4656	3	2	g	g	PRON
ejpam-4656	3	3	be	be	AUX
ejpam-4656	3	4	an	an	DET
ejpam-4656	3	5	undirected	undirected	ADJ
ejpam-4656	3	6	connected	connected	ADJ
ejpam-4656	3	7	graph	graph	NOUN
ejpam-4656	3	8	with	with	ADP
ejpam-4656	3	9	vertex	vertex	NOUN
ejpam-4656	3	10	and	and	CCONJ
ejpam-4656	3	11	edge	edge	NOUN
ejpam-4656	3	12	sets	set	NOUN
ejpam-4656	3	13	v	v	ADP
ejpam-4656	3	14	(	(	PUNCT
ejpam-4656	3	15	g	g	NOUN
ejpam-4656	3	16	)	)	PUNCT
ejpam-4656	3	17	and	and	CCONJ
ejpam-4656	3	18	e(g	e(g	PROPN
ejpam-4656	3	19	)	)	PUNCT
ejpam-4656	3	20	,	,	PUNCT
ejpam-4656	3	21	respectively	respectively	ADV
ejpam-4656	3	22	.	.	PUNCT
ejpam-4656	4	1	a	a	DET
ejpam-4656	4	2	set	set	NOUN
ejpam-4656	4	3	c	c	NOUN
ejpam-4656	4	4	⊆	⊆	NUM
ejpam-4656	4	5	v	v	NOUN
ejpam-4656	4	6	(	(	PUNCT
ejpam-4656	4	7	g	g	NOUN
ejpam-4656	4	8	)	)	PUNCT
ejpam-4656	4	9	is	be	AUX
ejpam-4656	4	10	called	call	VERB
ejpam-4656	4	11	convex	convex	ADJ
ejpam-4656	4	12	hop	hop	NOUN
ejpam-4656	4	13	dominating	dominate	VERB
ejpam-4656	4	14	if	if	SCONJ
ejpam-4656	4	15	for	for	ADP
ejpam-4656	4	16	every	every	DET
ejpam-4656	4	17	two	two	NUM
ejpam-4656	4	18	vertices	vertex	NOUN
ejpam-4656	4	19	x	x	X
ejpam-4656	4	20	,	,	PUNCT
ejpam-4656	4	21	y	y	PROPN
ejpam-4656	4	22	∈	∈	PROPN
ejpam-4656	4	23	c	c	PROPN
ejpam-4656	4	24	,	,	PUNCT
ejpam-4656	4	25	the	the	DET
ejpam-4656	4	26	vertex	vertex	NOUN
ejpam-4656	4	27	set	set	NOUN
ejpam-4656	4	28	of	of	ADP
ejpam-4656	4	29	every	every	DET
ejpam-4656	4	30	x	x	PROPN
ejpam-4656	4	31	-	-	PROPN
ejpam-4656	4	32	y	y	ADJ
ejpam-4656	4	33	geodesic	geodesic	NOUN
ejpam-4656	4	34	is	be	AUX
ejpam-4656	4	35	contained	contain	VERB
ejpam-4656	4	36	in	in	ADP
ejpam-4656	4	37	c	c	PROPN
ejpam-4656	4	38	and	and	CCONJ
ejpam-4656	4	39	for	for	ADP
ejpam-4656	4	40	every	every	PRON
ejpam-4656	4	41	v	v	NUM
ejpam-4656	4	42	∈	∈	PROPN
ejpam-4656	4	43	v	v	NOUN
ejpam-4656	4	44	(	(	PUNCT
ejpam-4656	4	45	g	g	NOUN
ejpam-4656	4	46	)	)	PUNCT
ejpam-4656	4	47	\	\	PUNCT
ejpam-4656	5	1	c	c	X
ejpam-4656	5	2	,	,	PUNCT
ejpam-4656	5	3	there	there	PRON
ejpam-4656	5	4	exists	exist	VERB
ejpam-4656	5	5	w	w	PROPN
ejpam-4656	5	6	∈	∈	PROPN
ejpam-4656	5	7	c	c	NOUN
ejpam-4656	5	8	such	such	ADJ
ejpam-4656	5	9	that	that	DET
ejpam-4656	5	10	dg(v	dg(v	ADJ
ejpam-4656	5	11	,	,	PUNCT
ejpam-4656	5	12	w	w	NOUN
ejpam-4656	5	13	)	)	PUNCT
ejpam-4656	6	1	=	=	SYM
ejpam-4656	6	2	2	2	X
ejpam-4656	6	3	.	.	PUNCT
ejpam-4656	7	1	the	the	DET
ejpam-4656	7	2	minimum	minimum	ADJ
ejpam-4656	7	3	cardinality	cardinality	NOUN
ejpam-4656	7	4	of	of	ADP
ejpam-4656	7	5	convex	convex	PROPN
ejpam-4656	7	6	hop	hop	NOUN
ejpam-4656	7	7	dominating	dominating	NOUN
ejpam-4656	7	8	set	set	NOUN
ejpam-4656	7	9	of	of	ADP
ejpam-4656	7	10	g	g	NOUN
ejpam-4656	7	11	,	,	PUNCT
ejpam-4656	7	12	denoted	denote	VERB
ejpam-4656	7	13	by	by	ADP
ejpam-4656	7	14	γconh(g	γconh(g	NOUN
ejpam-4656	7	15	)	)	PUNCT
ejpam-4656	7	16	,	,	PUNCT
ejpam-4656	7	17	is	be	AUX
ejpam-4656	7	18	called	call	VERB
ejpam-4656	7	19	the	the	DET
ejpam-4656	7	20	convex	convex	ADJ
ejpam-4656	7	21	hop	hop	NOUN
ejpam-4656	7	22	domination	domination	NOUN
ejpam-4656	7	23	number	number	NOUN
ejpam-4656	7	24	of	of	ADP
ejpam-4656	7	25	g.	g.	PROPN
ejpam-4656	7	26	in	in	ADP
ejpam-4656	7	27	this	this	DET
ejpam-4656	7	28	paper	paper	NOUN
ejpam-4656	7	29	,	,	PUNCT
ejpam-4656	7	30	we	we	PRON
ejpam-4656	7	31	show	show	VERB
ejpam-4656	7	32	that	that	SCONJ
ejpam-4656	7	33	every	every	DET
ejpam-4656	7	34	two	two	NUM
ejpam-4656	7	35	positive	positive	ADJ
ejpam-4656	7	36	integers	integer	NOUN
ejpam-4656	7	37	a	a	PRON
ejpam-4656	7	38	and	and	CCONJ
ejpam-4656	7	39	b	b	NOUN
ejpam-4656	7	40	,	,	PUNCT
ejpam-4656	7	41	where	where	SCONJ
ejpam-4656	7	42	2	2	NUM
ejpam-4656	7	43	≤	≤	NOUN
ejpam-4656	7	44	a	a	DET
ejpam-4656	7	45	≤	≤	NUM
ejpam-4656	7	46	b	b	NOUN
ejpam-4656	7	47	,	,	PUNCT
ejpam-4656	7	48	are	be	AUX
ejpam-4656	7	49	realizable	realizable	ADJ
ejpam-4656	7	50	as	as	ADP
ejpam-4656	7	51	the	the	DET
ejpam-4656	7	52	connected	connected	ADJ
ejpam-4656	7	53	hop	hop	NOUN
ejpam-4656	7	54	domination	domination	NOUN
ejpam-4656	7	55	number	number	NOUN
ejpam-4656	7	56	and	and	CCONJ
ejpam-4656	7	57	convex	convex	VERB
ejpam-4656	7	58	hop	hop	NOUN
ejpam-4656	7	59	domination	domination	NOUN
ejpam-4656	7	60	number	number	NOUN
ejpam-4656	7	61	,	,	PUNCT
ejpam-4656	7	62	respectively	respectively	ADV
ejpam-4656	7	63	,	,	PUNCT
ejpam-4656	7	64	of	of	ADP
ejpam-4656	7	65	a	a	DET
ejpam-4656	7	66	connected	connected	ADJ
ejpam-4656	7	67	graph	graph	NOUN
ejpam-4656	7	68	.	.	PUNCT
ejpam-4656	8	1	we	we	PRON
ejpam-4656	8	2	also	also	ADV
ejpam-4656	8	3	characterize	characterize	VERB
ejpam-4656	8	4	the	the	DET
ejpam-4656	8	5	convex	convex	ADJ
ejpam-4656	8	6	hop	hop	NOUN
ejpam-4656	8	7	dominating	dominating	NOUN
ejpam-4656	8	8	sets	set	NOUN
ejpam-4656	8	9	in	in	ADP
ejpam-4656	8	10	some	some	DET
ejpam-4656	8	11	graphs	graph	NOUN
ejpam-4656	8	12	and	and	CCONJ
ejpam-4656	8	13	determine	determine	VERB
ejpam-4656	8	14	their	their	PRON
ejpam-4656	8	15	convex	convex	ADJ
ejpam-4656	8	16	hop	hop	NOUN
ejpam-4656	8	17	domination	domination	NOUN
ejpam-4656	8	18	numbers	number	NOUN
ejpam-4656	8	19	.	.	PUNCT
ejpam-4656	9	1	2020	2020	NUM
ejpam-4656	9	2	mathematics	mathematic	NOUN
ejpam-4656	9	3	subject	subject	NOUN
ejpam-4656	9	4	classifications	classification	NOUN
ejpam-4656	9	5	:	:	PUNCT
ejpam-4656	9	6	05c69	05c69	X
ejpam-4656	9	7	key	key	ADJ
ejpam-4656	9	8	words	word	NOUN
ejpam-4656	9	9	and	and	CCONJ
ejpam-4656	9	10	phrases	phrase	NOUN
ejpam-4656	9	11	:	:	PUNCT
ejpam-4656	9	12	hop	hop	NOUN
ejpam-4656	9	13	domination	domination	NOUN
ejpam-4656	9	14	,	,	PUNCT
ejpam-4656	9	15	hop	hop	NOUN
ejpam-4656	9	16	domination	domination	NOUN
ejpam-4656	9	17	number	number	NOUN
ejpam-4656	9	18	,	,	PUNCT
ejpam-4656	9	19	convex	convex	NOUN
ejpam-4656	9	20	set	set	NOUN
ejpam-4656	9	21	,	,	PUNCT
ejpam-4656	9	22	convex	convex	VERB
ejpam-4656	9	23	hop	hop	NOUN
ejpam-4656	9	24	dominating	dominating	NOUN
ejpam-4656	9	25	set	set	NOUN
ejpam-4656	9	26	,	,	PUNCT
ejpam-4656	9	27	convex	convex	VERB
ejpam-4656	9	28	hop	hop	NOUN
ejpam-4656	9	29	domination	domination	NOUN
ejpam-4656	9	30	number	number	NOUN
ejpam-4656	9	31	1	1	NUM
ejpam-4656	9	32	.	.	PUNCT
ejpam-4656	10	1	introduction	introduction	NOUN
ejpam-4656	10	2	hop	hop	PROPN
ejpam-4656	10	3	domination	domination	PROPN
ejpam-4656	10	4	,	,	PUNCT
ejpam-4656	10	5	a	a	DET
ejpam-4656	10	6	concept	concept	NOUN
ejpam-4656	10	7	introduced	introduce	VERB
ejpam-4656	10	8	and	and	CCONJ
ejpam-4656	10	9	initially	initially	ADV
ejpam-4656	10	10	studied	study	VERB
ejpam-4656	10	11	by	by	ADP
ejpam-4656	10	12	natarajan	natarajan	PROPN
ejpam-4656	10	13	et	et	PROPN
ejpam-4656	10	14	al	al	PROPN
ejpam-4656	10	15	.	.	PUNCT
ejpam-4656	11	1	in	in	ADP
ejpam-4656	11	2	[	[	X
ejpam-4656	11	3	18	18	NUM
ejpam-4656	11	4	]	]	PUNCT
ejpam-4656	11	5	,	,	PUNCT
ejpam-4656	11	6	has	have	AUX
ejpam-4656	11	7	become	become	VERB
ejpam-4656	11	8	one	one	NUM
ejpam-4656	11	9	of	of	ADP
ejpam-4656	11	10	the	the	DET
ejpam-4656	11	11	topics	topic	NOUN
ejpam-4656	11	12	of	of	ADP
ejpam-4656	11	13	investigation	investigation	NOUN
ejpam-4656	11	14	recently	recently	ADV
ejpam-4656	11	15	.	.	PUNCT
ejpam-4656	12	1	so	so	ADV
ejpam-4656	12	2	far	far	ADV
ejpam-4656	12	3	,	,	PUNCT
ejpam-4656	12	4	there	there	PRON
ejpam-4656	12	5	is	be	VERB
ejpam-4656	12	6	a	a	DET
ejpam-4656	12	7	significant	significant	ADJ
ejpam-4656	12	8	number	number	NOUN
ejpam-4656	12	9	of	of	ADP
ejpam-4656	12	10	variants	variant	NOUN
ejpam-4656	12	11	of	of	ADP
ejpam-4656	12	12	hop	hop	NOUN
ejpam-4656	12	13	domination	domination	NOUN
ejpam-4656	12	14	that	that	PRON
ejpam-4656	12	15	have	have	AUX
ejpam-4656	12	16	been	be	AUX
ejpam-4656	12	17	defined	define	VERB
ejpam-4656	12	18	and	and	CCONJ
ejpam-4656	12	19	investigated	investigate	VERB
ejpam-4656	12	20	.	.	PUNCT
ejpam-4656	13	1	some	some	DET
ejpam-4656	13	2	studies	study	NOUN
ejpam-4656	13	3	on	on	ADP
ejpam-4656	13	4	hop	hop	PROPN
ejpam-4656	13	5	domination	domination	NOUN
ejpam-4656	13	6	,	,	PUNCT
ejpam-4656	13	7	its	its	PRON
ejpam-4656	13	8	variants	variant	NOUN
ejpam-4656	13	9	,	,	PUNCT
ejpam-4656	13	10	and	and	CCONJ
ejpam-4656	13	11	related	related	ADJ
ejpam-4656	13	12	concepts	concept	NOUN
ejpam-4656	13	13	can	can	AUX
ejpam-4656	13	14	be	be	AUX
ejpam-4656	13	15	found	find	VERB
ejpam-4656	13	16	in	in	ADP
ejpam-4656	13	17	[	[	X
ejpam-4656	13	18	1	1	NUM
ejpam-4656	13	19	]	]	PUNCT
ejpam-4656	13	20	,	,	PUNCT
ejpam-4656	13	21	[	[	X
ejpam-4656	13	22	2	2	NUM
ejpam-4656	13	23	]	]	PUNCT
ejpam-4656	13	24	,	,	PUNCT
ejpam-4656	13	25	[	[	X
ejpam-4656	13	26	5	5	NUM
ejpam-4656	13	27	]	]	PUNCT
ejpam-4656	13	28	,	,	PUNCT
ejpam-4656	13	29	[	[	X
ejpam-4656	13	30	8	8	NUM
ejpam-4656	13	31	]	]	PUNCT
ejpam-4656	13	32	,	,	PUNCT
ejpam-4656	13	33	[	[	X
ejpam-4656	13	34	7	7	NUM
ejpam-4656	13	35	]	]	PUNCT
ejpam-4656	13	36	,	,	PUNCT
ejpam-4656	13	37	[	[	X
ejpam-4656	13	38	9	9	NUM
ejpam-4656	13	39	]	]	PUNCT
ejpam-4656	13	40	,	,	PUNCT
ejpam-4656	13	41	[	[	X
ejpam-4656	13	42	13	13	NUM
ejpam-4656	13	43	]	]	PUNCT
ejpam-4656	13	44	,	,	PUNCT
ejpam-4656	13	45	[	[	X
ejpam-4656	13	46	14	14	NUM
ejpam-4656	13	47	]	]	PUNCT
ejpam-4656	13	48	,	,	PUNCT
ejpam-4656	13	49	[	[	X
ejpam-4656	13	50	15	15	NUM
ejpam-4656	13	51	]	]	PUNCT
ejpam-4656	13	52	,	,	PUNCT
ejpam-4656	13	53	[	[	X
ejpam-4656	13	54	19	19	NUM
ejpam-4656	13	55	]	]	PUNCT
ejpam-4656	13	56	,	,	PUNCT
ejpam-4656	13	57	[	[	X
ejpam-4656	13	58	20	20	NUM
ejpam-4656	13	59	]	]	PUNCT
ejpam-4656	13	60	,	,	PUNCT
ejpam-4656	13	61	and	and	CCONJ
ejpam-4656	13	62	[	[	X
ejpam-4656	13	63	21	21	NUM
ejpam-4656	13	64	]	]	PUNCT
ejpam-4656	13	65	.	.	PUNCT
ejpam-4656	14	1	another	another	DET
ejpam-4656	14	2	interesting	interesting	ADJ
ejpam-4656	14	3	topic	topic	NOUN
ejpam-4656	14	4	that	that	PRON
ejpam-4656	14	5	had	have	AUX
ejpam-4656	14	6	caught	catch	VERB
ejpam-4656	14	7	the	the	DET
ejpam-4656	14	8	attention	attention	NOUN
ejpam-4656	14	9	of	of	ADP
ejpam-4656	14	10	several	several	ADJ
ejpam-4656	14	11	researchers	researcher	NOUN
ejpam-4656	14	12	is	be	AUX
ejpam-4656	14	13	convexity	convexity	NOUN
ejpam-4656	14	14	.	.	PUNCT
ejpam-4656	15	1	convexity	convexity	NOUN
ejpam-4656	15	2	is	be	AUX
ejpam-4656	15	3	a	a	DET
ejpam-4656	15	4	concept	concept	NOUN
ejpam-4656	15	5	that	that	PRON
ejpam-4656	15	6	appears	appear	VERB
ejpam-4656	15	7	in	in	ADP
ejpam-4656	15	8	many	many	ADJ
ejpam-4656	15	9	areas	area	NOUN
ejpam-4656	15	10	of	of	ADP
ejpam-4656	15	11	mathematics	mathematic	NOUN
ejpam-4656	15	12	(	(	PUNCT
ejpam-4656	15	13	e.g.	e.g.	ADV
ejpam-4656	15	14	real	real	ADJ
ejpam-4656	15	15	analysis	analysis	NOUN
ejpam-4656	15	16	,	,	PUNCT
ejpam-4656	15	17	topology	topology	NOUN
ejpam-4656	15	18	,	,	PUNCT
ejpam-4656	15	19	geometry	geometry	NOUN
ejpam-4656	15	20	,	,	PUNCT
ejpam-4656	15	21	functional	functional	ADJ
ejpam-4656	15	22	analysis	analysis	NOUN
ejpam-4656	15	23	)	)	PUNCT
ejpam-4656	15	24	.	.	PUNCT
ejpam-4656	16	1	in	in	ADP
ejpam-4656	16	2	graph	graph	NOUN
ejpam-4656	16	3	theory	theory	NOUN
ejpam-4656	16	4	,	,	PUNCT
ejpam-4656	16	5	the	the	DET
ejpam-4656	16	6	concept	concept	NOUN
ejpam-4656	16	7	can	can	AUX
ejpam-4656	16	8	easily	easily	ADV
ejpam-4656	16	9	find	find	VERB
ejpam-4656	16	10	a	a	DET
ejpam-4656	16	11	graph	graph	NOUN
ejpam-4656	16	12	-	-	PUNCT
ejpam-4656	16	13	theoretic	theoretic	NOUN
ejpam-4656	16	14	formulation	formulation	NOUN
ejpam-4656	16	15	.	.	PUNCT
ejpam-4656	17	1	convexity	convexity	NOUN
ejpam-4656	17	2	in	in	ADP
ejpam-4656	17	3	graphs	graph	NOUN
ejpam-4656	17	4	is	be	AUX
ejpam-4656	17	5	discussed	discuss	VERB
ejpam-4656	17	6	in	in	ADP
ejpam-4656	17	7	the	the	DET
ejpam-4656	17	8	book	book	NOUN
ejpam-4656	17	9	by	by	ADP
ejpam-4656	17	10	∗corresponding	∗corresponde	VERB
ejpam-4656	17	11	author	author	NOUN
ejpam-4656	17	12	.	.	PUNCT
ejpam-4656	18	1	doi	doi	NOUN
ejpam-4656	18	2	:	:	PUNCT
ejpam-4656	18	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4656	https://doi.org/10.29020/nybg.ejpam.v16i1.4656	X
ejpam-4656	18	4	email	email	NOUN
ejpam-4656	18	5	addresses	address	NOUN
ejpam-4656	18	6	:	:	PUNCT
ejpam-4656	19	1	javier.hassan@g.msuiit.edu.ph	javier.hassan@g.msuiit.edu.ph	PROPN
ejpam-4656	19	2	(	(	PUNCT
ejpam-4656	19	3	j.	j.	PROPN
ejpam-4656	19	4	hassan	hassan	PROPN
ejpam-4656	19	5	)	)	PUNCT
ejpam-4656	19	6	,	,	PUNCT
ejpam-4656	19	7	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4656	19	8	(	(	PUNCT
ejpam-4656	19	9	s.	s.	PROPN
ejpam-4656	19	10	canoy	canoy	PROPN
ejpam-4656	19	11	)	)	PUNCT
ejpam-4656	19	12	,	,	PUNCT
ejpam-4656	19	13	chrisley.saromines@g.msuiit.edu.ph	chrisley.saromines@g.msuiit.edu.ph	PROPN
ejpam-4656	19	14	(	(	PUNCT
ejpam-4656	19	15	c.	c.	PROPN
ejpam-4656	19	16	saromines	saromines	PROPN
ejpam-4656	19	17	)	)	PUNCT
ejpam-4656	19	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4656	19	19	319	319	NUM
ejpam-4656	20	1	©	©	ADP
ejpam-4656	20	2	2023	2023	NUM
ejpam-4656	20	3	ejpam	ejpam	NOUN
ejpam-4656	20	4	all	all	DET
ejpam-4656	20	5	rights	right	NOUN
ejpam-4656	20	6	reserved	reserve	VERB
ejpam-4656	20	7	.	.	PUNCT
ejpam-4656	21	1	j.	j.	PROPN
ejpam-4656	21	2	hassan	hassan	PROPN
ejpam-4656	21	3	,	,	PUNCT
ejpam-4656	21	4	s.	s.	PROPN
ejpam-4656	21	5	canoy	canoy	PROPN
ejpam-4656	21	6	jr	jr	PROPN
ejpam-4656	21	7	.	.	PROPN
ejpam-4656	21	8	,	,	PUNCT
ejpam-4656	21	9	c.	c.	PROPN
ejpam-4656	21	10	saromines	saromine	VERB
ejpam-4656	21	11	/	/	SYM
ejpam-4656	21	12	eur	eur	PROPN
ejpam-4656	21	13	.	.	PUNCT
ejpam-4656	22	1	j.	j.	PROPN
ejpam-4656	22	2	pure	pure	PROPN
ejpam-4656	22	3	appl	appl	PROPN
ejpam-4656	22	4	.	.	PROPN
ejpam-4656	22	5	math	math	PROPN
ejpam-4656	22	6	,	,	PUNCT
ejpam-4656	22	7	16	16	NUM
ejpam-4656	22	8	(	(	PUNCT
ejpam-4656	22	9	1	1	NUM
ejpam-4656	22	10	)	)	PUNCT
ejpam-4656	22	11	(	(	PUNCT
ejpam-4656	22	12	2023	2023	NUM
ejpam-4656	22	13	)	)	PUNCT
ejpam-4656	22	14	,	,	PUNCT
ejpam-4656	22	15	319	319	NUM
ejpam-4656	22	16	-	-	SYM
ejpam-4656	22	17	335	335	NUM
ejpam-4656	22	18	320	320	NUM
ejpam-4656	22	19	buckley	buckley	NOUN
ejpam-4656	22	20	and	and	CCONJ
ejpam-4656	22	21	harary	harary	NOUN
ejpam-4656	23	1	[	[	X
ejpam-4656	23	2	3	3	NUM
ejpam-4656	23	3	]	]	PUNCT
ejpam-4656	23	4	.	.	PUNCT
ejpam-4656	24	1	the	the	DET
ejpam-4656	24	2	concept	concept	NOUN
ejpam-4656	24	3	and	and	CCONJ
ejpam-4656	24	4	other	other	ADJ
ejpam-4656	24	5	types	type	NOUN
ejpam-4656	24	6	of	of	ADP
ejpam-4656	24	7	convexity	convexity	NOUN
ejpam-4656	24	8	are	be	AUX
ejpam-4656	24	9	studied	study	VERB
ejpam-4656	24	10	in	in	ADP
ejpam-4656	24	11	[	[	X
ejpam-4656	24	12	4	4	NUM
ejpam-4656	24	13	]	]	PUNCT
ejpam-4656	24	14	,	,	PUNCT
ejpam-4656	24	15	[	[	X
ejpam-4656	24	16	6	6	NUM
ejpam-4656	24	17	]	]	PUNCT
ejpam-4656	24	18	,	,	PUNCT
ejpam-4656	24	19	and	and	CCONJ
ejpam-4656	24	20	[	[	X
ejpam-4656	24	21	11	11	NUM
ejpam-4656	24	22	]	]	PUNCT
ejpam-4656	24	23	.	.	PUNCT
ejpam-4656	25	1	the	the	DET
ejpam-4656	25	2	concept	concept	NOUN
ejpam-4656	25	3	is	be	AUX
ejpam-4656	25	4	also	also	ADV
ejpam-4656	25	5	combined	combine	VERB
ejpam-4656	25	6	with	with	ADP
ejpam-4656	25	7	many	many	ADJ
ejpam-4656	25	8	other	other	ADJ
ejpam-4656	25	9	parameters	parameter	NOUN
ejpam-4656	25	10	.	.	PUNCT
ejpam-4656	26	1	one	one	NUM
ejpam-4656	26	2	well	well	ADV
ejpam-4656	26	3	-	-	PUNCT
ejpam-4656	26	4	known	know	VERB
ejpam-4656	26	5	formed	form	VERB
ejpam-4656	26	6	combination	combination	NOUN
ejpam-4656	26	7	is	be	AUX
ejpam-4656	26	8	convex	convex	ADJ
ejpam-4656	26	9	domination	domination	NOUN
ejpam-4656	26	10	.	.	PUNCT
ejpam-4656	27	1	this	this	DET
ejpam-4656	27	2	variation	variation	NOUN
ejpam-4656	27	3	of	of	ADP
ejpam-4656	27	4	domination	domination	NOUN
ejpam-4656	27	5	is	be	AUX
ejpam-4656	27	6	studied	study	VERB
ejpam-4656	27	7	in	in	ADP
ejpam-4656	27	8	[	[	X
ejpam-4656	27	9	4	4	NUM
ejpam-4656	27	10	]	]	PUNCT
ejpam-4656	27	11	,	,	PUNCT
ejpam-4656	27	12	[	[	X
ejpam-4656	27	13	10	10	NUM
ejpam-4656	27	14	]	]	PUNCT
ejpam-4656	27	15	,	,	PUNCT
ejpam-4656	27	16	[	[	X
ejpam-4656	27	17	16	16	NUM
ejpam-4656	27	18	]	]	PUNCT
ejpam-4656	27	19	,	,	PUNCT
ejpam-4656	27	20	and	and	CCONJ
ejpam-4656	27	21	[	[	X
ejpam-4656	27	22	17	17	NUM
ejpam-4656	27	23	]	]	PUNCT
ejpam-4656	27	24	.	.	PUNCT
ejpam-4656	28	1	in	in	ADP
ejpam-4656	28	2	this	this	DET
ejpam-4656	28	3	paper	paper	NOUN
ejpam-4656	28	4	,	,	PUNCT
ejpam-4656	28	5	we	we	PRON
ejpam-4656	28	6	introduce	introduce	VERB
ejpam-4656	28	7	and	and	CCONJ
ejpam-4656	28	8	study	study	VERB
ejpam-4656	28	9	convex	convex	NOUN
ejpam-4656	28	10	hop	hop	NOUN
ejpam-4656	28	11	domination	domination	NOUN
ejpam-4656	28	12	.	.	PUNCT
ejpam-4656	29	1	this	this	DET
ejpam-4656	29	2	study	study	NOUN
ejpam-4656	29	3	is	be	AUX
ejpam-4656	29	4	motivated	motivate	VERB
ejpam-4656	29	5	by	by	ADP
ejpam-4656	29	6	the	the	DET
ejpam-4656	29	7	introduction	introduction	NOUN
ejpam-4656	29	8	of	of	ADP
ejpam-4656	29	9	hop	hop	NOUN
ejpam-4656	29	10	domination	domination	NOUN
ejpam-4656	29	11	and	and	CCONJ
ejpam-4656	29	12	convex	convex	ADJ
ejpam-4656	29	13	domination	domination	NOUN
ejpam-4656	29	14	.	.	PUNCT
ejpam-4656	30	1	just	just	ADV
ejpam-4656	30	2	like	like	ADP
ejpam-4656	30	3	convex	convex	PROPN
ejpam-4656	30	4	domination	domination	NOUN
ejpam-4656	30	5	,	,	PUNCT
ejpam-4656	30	6	we	we	PRON
ejpam-4656	30	7	believe	believe	VERB
ejpam-4656	30	8	that	that	SCONJ
ejpam-4656	30	9	this	this	DET
ejpam-4656	30	10	new	new	ADJ
ejpam-4656	30	11	parameter	parameter	NOUN
ejpam-4656	30	12	will	will	AUX
ejpam-4656	30	13	yield	yield	VERB
ejpam-4656	30	14	significant	significant	ADJ
ejpam-4656	30	15	results	result	NOUN
ejpam-4656	30	16	in	in	ADP
ejpam-4656	30	17	the	the	DET
ejpam-4656	30	18	topic	topic	NOUN
ejpam-4656	30	19	of	of	ADP
ejpam-4656	30	20	domination	domination	NOUN
ejpam-4656	30	21	and	and	CCONJ
ejpam-4656	30	22	can	can	AUX
ejpam-4656	30	23	lead	lead	VERB
ejpam-4656	30	24	to	to	ADP
ejpam-4656	30	25	other	other	ADJ
ejpam-4656	30	26	interesting	interesting	ADJ
ejpam-4656	30	27	research	research	NOUN
ejpam-4656	30	28	directions	direction	NOUN
ejpam-4656	30	29	in	in	ADP
ejpam-4656	30	30	the	the	DET
ejpam-4656	30	31	future	future	NOUN
ejpam-4656	30	32	.	.	PUNCT
ejpam-4656	31	1	2	2	X
ejpam-4656	31	2	.	.	X
ejpam-4656	31	3	terminology	terminology	NOUN
ejpam-4656	31	4	and	and	CCONJ
ejpam-4656	31	5	notation	notation	NOUN
ejpam-4656	31	6	let	let	VERB
ejpam-4656	31	7	g	g	PROPN
ejpam-4656	31	8	=	=	SYM
ejpam-4656	31	9	v	v	PROPN
ejpam-4656	31	10	(	(	PUNCT
ejpam-4656	31	11	g	g	NOUN
ejpam-4656	31	12	)	)	PUNCT
ejpam-4656	31	13	,	,	PUNCT
ejpam-4656	31	14	e(g	e(g	PROPN
ejpam-4656	31	15	)	)	PUNCT
ejpam-4656	31	16	)	)	PUNCT
ejpam-4656	31	17	be	be	AUX
ejpam-4656	31	18	an	an	DET
ejpam-4656	31	19	undirected	undirected	ADJ
ejpam-4656	31	20	graph	graph	NOUN
ejpam-4656	31	21	.	.	PUNCT
ejpam-4656	32	1	for	for	ADP
ejpam-4656	32	2	any	any	DET
ejpam-4656	32	3	two	two	NUM
ejpam-4656	32	4	vertices	vertex	NOUN
ejpam-4656	32	5	u	u	NOUN
ejpam-4656	32	6	and	and	CCONJ
ejpam-4656	32	7	v	v	NOUN
ejpam-4656	32	8	of	of	ADP
ejpam-4656	32	9	g	g	NOUN
ejpam-4656	32	10	,	,	PUNCT
ejpam-4656	32	11	the	the	DET
ejpam-4656	32	12	distance	distance	NOUN
ejpam-4656	32	13	dg(u	dg(u	X
ejpam-4656	32	14	,	,	PUNCT
ejpam-4656	32	15	v	v	NOUN
ejpam-4656	32	16	)	)	PUNCT
ejpam-4656	32	17	is	be	AUX
ejpam-4656	32	18	the	the	DET
ejpam-4656	32	19	length	length	NOUN
ejpam-4656	32	20	of	of	ADP
ejpam-4656	32	21	a	a	DET
ejpam-4656	32	22	shortest	short	ADJ
ejpam-4656	32	23	path	path	NOUN
ejpam-4656	32	24	joining	join	VERB
ejpam-4656	32	25	u	u	NOUN
ejpam-4656	32	26	and	and	CCONJ
ejpam-4656	32	27	v.	v.	ADP
ejpam-4656	32	28	any	any	DET
ejpam-4656	32	29	u	u	NOUN
ejpam-4656	32	30	-	-	NOUN
ejpam-4656	32	31	v	v	ADJ
ejpam-4656	32	32	path	path	NOUN
ejpam-4656	32	33	of	of	ADP
ejpam-4656	32	34	length	length	NOUN
ejpam-4656	32	35	dg(u	dg(u	PROPN
ejpam-4656	32	36	,	,	PUNCT
ejpam-4656	32	37	v	v	NOUN
ejpam-4656	32	38	)	)	PUNCT
ejpam-4656	32	39	is	be	AUX
ejpam-4656	32	40	called	call	VERB
ejpam-4656	32	41	a	a	DET
ejpam-4656	32	42	u	u	NOUN
ejpam-4656	32	43	-	-	NOUN
ejpam-4656	32	44	v	v	ADJ
ejpam-4656	32	45	geodesic	geodesic	NOUN
ejpam-4656	32	46	.	.	PUNCT
ejpam-4656	33	1	the	the	DET
ejpam-4656	33	2	interval	interval	NOUN
ejpam-4656	33	3	ig	ig	PROPN
ejpam-4656	34	1	[	[	X
ejpam-4656	34	2	u	u	NOUN
ejpam-4656	34	3	,	,	PUNCT
ejpam-4656	34	4	v	v	NOUN
ejpam-4656	34	5	]	]	PUNCT
ejpam-4656	34	6	consists	consist	VERB
ejpam-4656	34	7	of	of	ADP
ejpam-4656	34	8	u	u	NOUN
ejpam-4656	34	9	,	,	PUNCT
ejpam-4656	34	10	v	v	NOUN
ejpam-4656	34	11	,	,	PUNCT
ejpam-4656	34	12	and	and	CCONJ
ejpam-4656	34	13	all	all	DET
ejpam-4656	34	14	vertices	vertex	NOUN
ejpam-4656	34	15	lying	lie	VERB
ejpam-4656	34	16	on	on	ADP
ejpam-4656	34	17	a	a	DET
ejpam-4656	34	18	u	u	NOUN
ejpam-4656	34	19	-	-	NOUN
ejpam-4656	34	20	v	v	ADJ
ejpam-4656	34	21	geodesic	geodesic	NOUN
ejpam-4656	34	22	.	.	PUNCT
ejpam-4656	35	1	the	the	DET
ejpam-4656	35	2	interval	interval	NOUN
ejpam-4656	35	3	ig(u	ig(u	NOUN
ejpam-4656	35	4	,	,	PUNCT
ejpam-4656	35	5	v	v	NOUN
ejpam-4656	35	6	)	)	PUNCT
ejpam-4656	35	7	=	=	PUNCT
ejpam-4656	36	1	ig	ig	PROPN
ejpam-4656	37	1	[	[	X
ejpam-4656	37	2	u	u	NOUN
ejpam-4656	37	3	,	,	PUNCT
ejpam-4656	37	4	v	v	ADP
ejpam-4656	37	5	]	]	PUNCT
ejpam-4656	37	6	\	\	NOUN
ejpam-4656	37	7	{	{	PUNCT
ejpam-4656	37	8	u	u	NOUN
ejpam-4656	37	9	,	,	PUNCT
ejpam-4656	37	10	v	v	NOUN
ejpam-4656	37	11	}	}	PUNCT
ejpam-4656	37	12	.	.	PUNCT
ejpam-4656	38	1	vertices	vertice	VERB
ejpam-4656	38	2	u	u	NOUN
ejpam-4656	38	3	and	and	CCONJ
ejpam-4656	38	4	v	v	NOUN
ejpam-4656	38	5	are	be	AUX
ejpam-4656	38	6	adjacent	adjacent	ADJ
ejpam-4656	38	7	(	(	PUNCT
ejpam-4656	38	8	or	or	CCONJ
ejpam-4656	38	9	neighbors	neighbor	NOUN
ejpam-4656	38	10	)	)	PUNCT
ejpam-4656	38	11	if	if	SCONJ
ejpam-4656	38	12	uv	uv	PROPN
ejpam-4656	38	13	∈	∈	PROPN
ejpam-4656	38	14	e(g	e(g	PROPN
ejpam-4656	38	15	)	)	PUNCT
ejpam-4656	38	16	.	.	PUNCT
ejpam-4656	39	1	the	the	DET
ejpam-4656	39	2	set	set	NOUN
ejpam-4656	39	3	of	of	ADP
ejpam-4656	39	4	neighbors	neighbor	NOUN
ejpam-4656	39	5	of	of	ADP
ejpam-4656	39	6	a	a	DET
ejpam-4656	39	7	vertex	vertex	NOUN
ejpam-4656	39	8	u	u	NOUN
ejpam-4656	39	9	in	in	ADP
ejpam-4656	39	10	g	g	NOUN
ejpam-4656	39	11	,	,	PUNCT
ejpam-4656	39	12	denoted	denote	VERB
ejpam-4656	39	13	by	by	ADP
ejpam-4656	39	14	ng(u	ng(u	NOUN
ejpam-4656	39	15	)	)	PUNCT
ejpam-4656	39	16	,	,	PUNCT
ejpam-4656	39	17	is	be	AUX
ejpam-4656	39	18	called	call	VERB
ejpam-4656	39	19	the	the	DET
ejpam-4656	39	20	open	open	ADJ
ejpam-4656	39	21	neighborhood	neighborhood	NOUN
ejpam-4656	39	22	of	of	ADP
ejpam-4656	39	23	u.	u.	VERB
ejpam-4656	39	24	the	the	DET
ejpam-4656	39	25	closed	closed	ADJ
ejpam-4656	39	26	neighborhood	neighborhood	NOUN
ejpam-4656	39	27	of	of	ADP
ejpam-4656	39	28	u	u	NOUN
ejpam-4656	39	29	is	be	AUX
ejpam-4656	39	30	the	the	DET
ejpam-4656	39	31	set	set	NOUN
ejpam-4656	39	32	ng[u	ng[u	PROPN
ejpam-4656	39	33	]	]	X
ejpam-4656	39	34	=	=	SYM
ejpam-4656	39	35	ng(u	ng(u	PROPN
ejpam-4656	39	36	)	)	PUNCT
ejpam-4656	39	37	∪	∪	NOUN
ejpam-4656	39	38	{	{	PUNCT
ejpam-4656	39	39	u	u	NOUN
ejpam-4656	39	40	}	}	PUNCT
ejpam-4656	39	41	.	.	PUNCT
ejpam-4656	40	1	if	if	SCONJ
ejpam-4656	40	2	x	x	PROPN
ejpam-4656	40	3	⊆	⊆	NUM
ejpam-4656	40	4	v	v	X
ejpam-4656	40	5	(	(	PUNCT
ejpam-4656	40	6	g	g	NOUN
ejpam-4656	40	7	)	)	PUNCT
ejpam-4656	40	8	,	,	PUNCT
ejpam-4656	40	9	the	the	DET
ejpam-4656	40	10	open	open	ADJ
ejpam-4656	40	11	neighborhood	neighborhood	NOUN
ejpam-4656	40	12	of	of	ADP
ejpam-4656	40	13	x	x	SYM
ejpam-4656	40	14	is	be	AUX
ejpam-4656	40	15	the	the	DET
ejpam-4656	40	16	set	set	NOUN
ejpam-4656	40	17	ng(x	ng(x	NUM
ejpam-4656	40	18	)	)	PUNCT
ejpam-4656	41	1	=	=	SYM
ejpam-4656	41	2	⋃	⋃	NOUN
ejpam-4656	41	3	u∈x	u∈x	NOUN
ejpam-4656	41	4	ng(u	ng(u	NOUN
ejpam-4656	41	5	)	)	PUNCT
ejpam-4656	41	6	.	.	PUNCT
ejpam-4656	42	1	the	the	DET
ejpam-4656	42	2	closed	closed	ADJ
ejpam-4656	42	3	neighborhood	neighborhood	NOUN
ejpam-4656	42	4	of	of	ADP
ejpam-4656	42	5	x	x	SYM
ejpam-4656	42	6	is	be	AUX
ejpam-4656	42	7	the	the	DET
ejpam-4656	42	8	set	set	NOUN
ejpam-4656	42	9	ng[x	ng[x	PROPN
ejpam-4656	42	10	]	]	X
ejpam-4656	42	11	=	=	PUNCT
ejpam-4656	42	12	ng(x	ng(x	X
ejpam-4656	42	13	)	)	PUNCT
ejpam-4656	43	1	∪x	∪x	PROPN
ejpam-4656	43	2	.	.	PUNCT
ejpam-4656	44	1	a	a	DET
ejpam-4656	44	2	set	set	NOUN
ejpam-4656	44	3	d	d	NOUN
ejpam-4656	44	4	⊆	⊆	NUM
ejpam-4656	44	5	v	v	ADP
ejpam-4656	44	6	(	(	PUNCT
ejpam-4656	44	7	g	g	NOUN
ejpam-4656	44	8	)	)	PUNCT
ejpam-4656	44	9	is	be	AUX
ejpam-4656	44	10	a	a	DET
ejpam-4656	44	11	dominating	dominating	NOUN
ejpam-4656	44	12	set	set	NOUN
ejpam-4656	44	13	(	(	PUNCT
ejpam-4656	44	14	resp	resp	NOUN
ejpam-4656	44	15	.	.	PUNCT
ejpam-4656	45	1	total	total	ADJ
ejpam-4656	45	2	dominating	dominating	NOUN
ejpam-4656	45	3	set	set	NOUN
ejpam-4656	45	4	)	)	PUNCT
ejpam-4656	45	5	of	of	ADP
ejpam-4656	45	6	g	g	PROPN
ejpam-4656	45	7	if	if	SCONJ
ejpam-4656	45	8	for	for	ADP
ejpam-4656	45	9	every	every	PRON
ejpam-4656	45	10	v	v	NUM
ejpam-4656	45	11	∈	∈	NOUN
ejpam-4656	45	12	v	v	NOUN
ejpam-4656	45	13	(	(	PUNCT
ejpam-4656	45	14	g	g	NOUN
ejpam-4656	45	15	)	)	PUNCT
ejpam-4656	45	16	\	\	PUNCT
ejpam-4656	46	1	d	d	X
ejpam-4656	46	2	(	(	PUNCT
ejpam-4656	46	3	resp	resp	NOUN
ejpam-4656	46	4	.	.	PUNCT
ejpam-4656	47	1	v	v	ADP
ejpam-4656	47	2	∈	∈	PROPN
ejpam-4656	47	3	v	v	NOUN
ejpam-4656	47	4	(	(	PUNCT
ejpam-4656	47	5	g	g	NOUN
ejpam-4656	47	6	)	)	PUNCT
ejpam-4656	47	7	)	)	PUNCT
ejpam-4656	48	1	,	,	PUNCT
ejpam-4656	48	2	there	there	PRON
ejpam-4656	48	3	exists	exist	VERB
ejpam-4656	48	4	u	u	NOUN
ejpam-4656	48	5	∈	∈	PROPN
ejpam-4656	48	6	d	d	ADP
ejpam-4656	48	7	such	such	ADJ
ejpam-4656	48	8	that	that	DET
ejpam-4656	48	9	uv	uv	PROPN
ejpam-4656	48	10	∈	∈	PROPN
ejpam-4656	48	11	e(g	e(g	PROPN
ejpam-4656	48	12	)	)	PUNCT
ejpam-4656	48	13	,	,	PUNCT
ejpam-4656	48	14	that	that	ADV
ejpam-4656	48	15	is	is	ADV
ejpam-4656	48	16	,	,	PUNCT
ejpam-4656	48	17	ng[d	ng[d	PROPN
ejpam-4656	48	18	]	]	PUNCT
ejpam-4656	48	19	=	=	SYM
ejpam-4656	48	20	v	v	X
ejpam-4656	48	21	(	(	PUNCT
ejpam-4656	48	22	g	g	NOUN
ejpam-4656	48	23	)	)	PUNCT
ejpam-4656	48	24	(	(	PUNCT
ejpam-4656	48	25	resp	resp	NOUN
ejpam-4656	48	26	.	.	PUNCT
ejpam-4656	48	27	ng(d	ng(d	PUNCT
ejpam-4656	48	28	)	)	PUNCT
ejpam-4656	48	29	=	=	SYM
ejpam-4656	48	30	v	v	X
ejpam-4656	48	31	(	(	PUNCT
ejpam-4656	48	32	g	g	NOUN
ejpam-4656	48	33	)	)	PUNCT
ejpam-4656	48	34	)	)	PUNCT
ejpam-4656	48	35	.	.	PUNCT
ejpam-4656	49	1	the	the	DET
ejpam-4656	49	2	domination	domination	NOUN
ejpam-4656	49	3	number	number	NOUN
ejpam-4656	49	4	(	(	PUNCT
ejpam-4656	49	5	resp	resp	NOUN
ejpam-4656	49	6	.	.	PUNCT
ejpam-4656	50	1	total	total	ADJ
ejpam-4656	50	2	domination	domination	NOUN
ejpam-4656	50	3	number	number	NOUN
ejpam-4656	50	4	)	)	PUNCT
ejpam-4656	50	5	of	of	ADP
ejpam-4656	50	6	g	g	NOUN
ejpam-4656	50	7	,	,	PUNCT
ejpam-4656	50	8	denoted	denote	VERB
ejpam-4656	50	9	by	by	ADP
ejpam-4656	50	10	γ(g	γ(g	PROPN
ejpam-4656	50	11	)	)	PUNCT
ejpam-4656	50	12	(	(	PUNCT
ejpam-4656	50	13	resp	resp	NOUN
ejpam-4656	50	14	.	.	PUNCT
ejpam-4656	50	15	γt(g	γt(g	PUNCT
ejpam-4656	50	16	)	)	PUNCT
ejpam-4656	50	17	)	)	PUNCT
ejpam-4656	50	18	,	,	PUNCT
ejpam-4656	50	19	is	be	AUX
ejpam-4656	50	20	the	the	DET
ejpam-4656	50	21	minimum	minimum	ADJ
ejpam-4656	50	22	cardinality	cardinality	NOUN
ejpam-4656	50	23	of	of	ADP
ejpam-4656	50	24	a	a	DET
ejpam-4656	50	25	dominating	dominating	NOUN
ejpam-4656	50	26	(	(	PUNCT
ejpam-4656	50	27	resp	resp	NOUN
ejpam-4656	50	28	.	.	PUNCT
ejpam-4656	51	1	total	total	ADJ
ejpam-4656	51	2	dominating	dominating	NOUN
ejpam-4656	51	3	)	)	PUNCT
ejpam-4656	51	4	set	set	VERB
ejpam-4656	51	5	in	in	ADP
ejpam-4656	51	6	g.	g.	PROPN
ejpam-4656	51	7	any	any	DET
ejpam-4656	51	8	dominating	dominating	NOUN
ejpam-4656	51	9	(	(	PUNCT
ejpam-4656	51	10	resp	resp	NOUN
ejpam-4656	51	11	.	.	PUNCT
ejpam-4656	52	1	total	total	ADJ
ejpam-4656	52	2	dominating	dominating	NOUN
ejpam-4656	52	3	)	)	PUNCT
ejpam-4656	52	4	set	set	VERB
ejpam-4656	52	5	in	in	ADP
ejpam-4656	52	6	g	g	PROPN
ejpam-4656	52	7	with	with	ADP
ejpam-4656	52	8	cardinality	cardinality	PROPN
ejpam-4656	52	9	γ(g	γ(g	PROPN
ejpam-4656	52	10	)	)	PUNCT
ejpam-4656	52	11	(	(	PUNCT
ejpam-4656	52	12	resp	resp	NOUN
ejpam-4656	52	13	.	.	PUNCT
ejpam-4656	52	14	γt(g	γt(g	PUNCT
ejpam-4656	52	15	)	)	PUNCT
ejpam-4656	52	16	)	)	PUNCT
ejpam-4656	52	17	,	,	PUNCT
ejpam-4656	52	18	is	be	AUX
ejpam-4656	52	19	called	call	VERB
ejpam-4656	52	20	a	a	DET
ejpam-4656	52	21	γ	γ	NOUN
ejpam-4656	52	22	-	-	PUNCT
ejpam-4656	52	23	set	set	ADJ
ejpam-4656	52	24	(	(	PUNCT
ejpam-4656	52	25	resp	resp	NOUN
ejpam-4656	52	26	.	.	PUNCT
ejpam-4656	53	1	γt	γt	NOUN
ejpam-4656	53	2	-	-	PUNCT
ejpam-4656	53	3	set	set	NOUN
ejpam-4656	53	4	)	)	PUNCT
ejpam-4656	53	5	in	in	ADP
ejpam-4656	53	6	g.	g.	PROPN
ejpam-4656	54	1	if	if	SCONJ
ejpam-4656	54	2	γ(g	γ(g	PROPN
ejpam-4656	54	3	)	)	PUNCT
ejpam-4656	54	4	=	=	SYM
ejpam-4656	54	5	1	1	NUM
ejpam-4656	54	6	and	and	CCONJ
ejpam-4656	54	7	{	{	PUNCT
ejpam-4656	54	8	v	v	NOUN
ejpam-4656	54	9	}	}	PUNCT
ejpam-4656	54	10	is	be	AUX
ejpam-4656	54	11	a	a	DET
ejpam-4656	54	12	dominating	dominating	NOUN
ejpam-4656	54	13	set	set	NOUN
ejpam-4656	54	14	in	in	ADP
ejpam-4656	54	15	g	g	PROPN
ejpam-4656	54	16	,	,	PUNCT
ejpam-4656	54	17	then	then	ADV
ejpam-4656	54	18	we	we	PRON
ejpam-4656	54	19	call	call	VERB
ejpam-4656	54	20	v	v	ADP
ejpam-4656	54	21	a	a	DET
ejpam-4656	54	22	dominating	dominating	NOUN
ejpam-4656	54	23	vertex	vertex	NOUN
ejpam-4656	54	24	in	in	ADP
ejpam-4656	54	25	g.	g.	PROPN
ejpam-4656	54	26	a	a	DET
ejpam-4656	54	27	vertex	vertex	NOUN
ejpam-4656	54	28	v	v	NOUN
ejpam-4656	54	29	in	in	ADP
ejpam-4656	54	30	g	g	PROPN
ejpam-4656	54	31	is	be	AUX
ejpam-4656	54	32	a	a	DET
ejpam-4656	54	33	hop	hop	NOUN
ejpam-4656	54	34	neighbor	neighbor	NOUN
ejpam-4656	54	35	of	of	ADP
ejpam-4656	54	36	vertex	vertex	NOUN
ejpam-4656	54	37	u	u	NOUN
ejpam-4656	54	38	in	in	ADP
ejpam-4656	54	39	g	g	PROPN
ejpam-4656	54	40	if	if	SCONJ
ejpam-4656	54	41	dg(u	dg(u	NOUN
ejpam-4656	54	42	,	,	PUNCT
ejpam-4656	54	43	v	v	NOUN
ejpam-4656	54	44	)	)	PUNCT
ejpam-4656	54	45	=	=	SYM
ejpam-4656	55	1	2	2	X
ejpam-4656	55	2	.	.	X
ejpam-4656	55	3	the	the	DET
ejpam-4656	55	4	set	set	ADJ
ejpam-4656	55	5	n2	n2	ADJ
ejpam-4656	55	6	g(u	g(u	PROPN
ejpam-4656	55	7	)	)	PUNCT
ejpam-4656	55	8	=	=	PRON
ejpam-4656	55	9	{	{	PUNCT
ejpam-4656	55	10	v	v	NUM
ejpam-4656	55	11	∈	∈	NOUN
ejpam-4656	55	12	v	v	NOUN
ejpam-4656	55	13	(	(	PUNCT
ejpam-4656	55	14	g	g	NOUN
ejpam-4656	55	15	)	)	PUNCT
ejpam-4656	55	16	:	:	PUNCT
ejpam-4656	55	17	dg(v	dg(v	X
ejpam-4656	55	18	,	,	PUNCT
ejpam-4656	55	19	u	u	NOUN
ejpam-4656	55	20	)	)	PUNCT
ejpam-4656	55	21	=	=	SYM
ejpam-4656	55	22	2	2	X
ejpam-4656	55	23	}	}	PUNCT
ejpam-4656	55	24	is	be	AUX
ejpam-4656	55	25	called	call	VERB
ejpam-4656	55	26	the	the	DET
ejpam-4656	55	27	open	open	ADJ
ejpam-4656	55	28	hop	hop	NOUN
ejpam-4656	55	29	neighborhood	neighborhood	NOUN
ejpam-4656	55	30	of	of	ADP
ejpam-4656	55	31	u.	u.	PROPN
ejpam-4656	55	32	the	the	DET
ejpam-4656	55	33	closed	closed	ADJ
ejpam-4656	55	34	hop	hop	NOUN
ejpam-4656	55	35	neighborhood	neighborhood	NOUN
ejpam-4656	55	36	of	of	ADP
ejpam-4656	55	37	u	u	NOUN
ejpam-4656	55	38	is	be	AUX
ejpam-4656	55	39	given	give	VERB
ejpam-4656	55	40	by	by	ADP
ejpam-4656	55	41	n2	n2	PROPN
ejpam-4656	55	42	g[u	g[u	PROPN
ejpam-4656	55	43	]	]	X
ejpam-4656	55	44	=	=	SYM
ejpam-4656	55	45	n2	n2	ADJ
ejpam-4656	55	46	g(u	g(u	PROPN
ejpam-4656	55	47	)	)	PUNCT
ejpam-4656	55	48	∪	∪	NOUN
ejpam-4656	55	49	{	{	PUNCT
ejpam-4656	55	50	u	u	NOUN
ejpam-4656	55	51	}	}	PUNCT
ejpam-4656	55	52	.	.	PUNCT
ejpam-4656	56	1	the	the	DET
ejpam-4656	56	2	open	open	ADJ
ejpam-4656	56	3	hop	hop	NOUN
ejpam-4656	56	4	neighborhood	neighborhood	NOUN
ejpam-4656	56	5	of	of	ADP
ejpam-4656	56	6	x	x	PROPN
ejpam-4656	56	7	⊆	⊆	NUM
ejpam-4656	56	8	v	v	ADP
ejpam-4656	56	9	(	(	PUNCT
ejpam-4656	56	10	g	g	NOUN
ejpam-4656	56	11	)	)	PUNCT
ejpam-4656	56	12	is	be	AUX
ejpam-4656	56	13	the	the	DET
ejpam-4656	56	14	set	set	ADJ
ejpam-4656	56	15	n2	n2	ADJ
ejpam-4656	56	16	g(x	g(x	NOUN
ejpam-4656	56	17	)	)	PUNCT
ejpam-4656	57	1	=	=	SYM
ejpam-4656	57	2	⋃	⋃	NOUN
ejpam-4656	57	3	u∈x	u∈x	ADJ
ejpam-4656	57	4	n2	n2	NOUN
ejpam-4656	57	5	g(u	g(u	PROPN
ejpam-4656	57	6	)	)	PUNCT
ejpam-4656	57	7	.	.	PUNCT
ejpam-4656	58	1	the	the	DET
ejpam-4656	58	2	closed	closed	ADJ
ejpam-4656	58	3	hop	hop	NOUN
ejpam-4656	58	4	neighborhood	neighborhood	NOUN
ejpam-4656	58	5	of	of	ADP
ejpam-4656	58	6	x	x	SYM
ejpam-4656	58	7	is	be	AUX
ejpam-4656	58	8	the	the	DET
ejpam-4656	58	9	set	set	ADJ
ejpam-4656	58	10	n2	n2	NOUN
ejpam-4656	58	11	g[x	g[x	PROPN
ejpam-4656	58	12	]	]	X
ejpam-4656	58	13	=	=	SYM
ejpam-4656	58	14	n2	n2	PROPN
ejpam-4656	58	15	g(x	g(x	NOUN
ejpam-4656	58	16	)	)	PUNCT
ejpam-4656	58	17	∪x	∪x	NUM
ejpam-4656	58	18	.	.	PUNCT
ejpam-4656	59	1	a	a	DET
ejpam-4656	59	2	set	set	NOUN
ejpam-4656	59	3	s	s	NOUN
ejpam-4656	59	4	⊆	⊆	NUM
ejpam-4656	59	5	v	v	NOUN
ejpam-4656	59	6	(	(	PUNCT
ejpam-4656	59	7	g	g	NOUN
ejpam-4656	59	8	)	)	PUNCT
ejpam-4656	59	9	is	be	AUX
ejpam-4656	59	10	a	a	DET
ejpam-4656	59	11	hop	hop	NOUN
ejpam-4656	59	12	dominating	dominating	NOUN
ejpam-4656	59	13	set	set	VERB
ejpam-4656	59	14	in	in	ADP
ejpam-4656	59	15	g	g	PROPN
ejpam-4656	59	16	if	if	SCONJ
ejpam-4656	59	17	n2	n2	ADJ
ejpam-4656	59	18	g[s	g[s	PROPN
ejpam-4656	59	19	]	]	X
ejpam-4656	59	20	=	=	SYM
ejpam-4656	59	21	v	v	NOUN
ejpam-4656	59	22	(	(	PUNCT
ejpam-4656	59	23	g	g	NOUN
ejpam-4656	59	24	)	)	PUNCT
ejpam-4656	59	25	,	,	PUNCT
ejpam-4656	59	26	that	that	ADV
ejpam-4656	59	27	is	is	ADV
ejpam-4656	59	28	,	,	PUNCT
ejpam-4656	59	29	for	for	ADP
ejpam-4656	59	30	every	every	DET
ejpam-4656	59	31	v	v	NUM
ejpam-4656	59	32	∈	∈	NOUN
ejpam-4656	59	33	v	v	NOUN
ejpam-4656	59	34	(	(	PUNCT
ejpam-4656	59	35	g)\s	g)\s	NOUN
ejpam-4656	59	36	,	,	PUNCT
ejpam-4656	59	37	there	there	PRON
ejpam-4656	59	38	exists	exist	VERB
ejpam-4656	59	39	u	u	PROPN
ejpam-4656	59	40	∈	∈	PROPN
ejpam-4656	59	41	s	s	VERB
ejpam-4656	59	42	such	such	ADJ
ejpam-4656	59	43	that	that	DET
ejpam-4656	59	44	dg(u	dg(u	ADJ
ejpam-4656	59	45	,	,	PUNCT
ejpam-4656	59	46	v	v	NOUN
ejpam-4656	59	47	)	)	PUNCT
ejpam-4656	60	1	=	=	SYM
ejpam-4656	60	2	2	2	X
ejpam-4656	60	3	.	.	PUNCT
ejpam-4656	61	1	the	the	DET
ejpam-4656	61	2	minimum	minimum	ADJ
ejpam-4656	61	3	cardinality	cardinality	NOUN
ejpam-4656	61	4	among	among	ADP
ejpam-4656	61	5	all	all	DET
ejpam-4656	61	6	hop	hop	NOUN
ejpam-4656	61	7	dominating	dominating	NOUN
ejpam-4656	61	8	sets	set	NOUN
ejpam-4656	61	9	in	in	ADP
ejpam-4656	61	10	g	g	NOUN
ejpam-4656	61	11	,	,	PUNCT
ejpam-4656	61	12	denoted	denote	VERB
ejpam-4656	61	13	by	by	ADP
ejpam-4656	61	14	γh(g	γh(g	NOUN
ejpam-4656	61	15	)	)	PUNCT
ejpam-4656	61	16	,	,	PUNCT
ejpam-4656	61	17	is	be	AUX
ejpam-4656	61	18	called	call	VERB
ejpam-4656	61	19	the	the	DET
ejpam-4656	61	20	hop	hop	NOUN
ejpam-4656	61	21	domination	domination	NOUN
ejpam-4656	61	22	number	number	NOUN
ejpam-4656	61	23	of	of	ADP
ejpam-4656	61	24	g.	g.	PROPN
ejpam-4656	61	25	any	any	DET
ejpam-4656	61	26	hop	hop	NOUN
ejpam-4656	61	27	dominating	dominating	NOUN
ejpam-4656	61	28	set	set	VERB
ejpam-4656	61	29	with	with	ADP
ejpam-4656	61	30	cardinality	cardinality	NOUN
ejpam-4656	61	31	equal	equal	ADJ
ejpam-4656	61	32	to	to	ADP
ejpam-4656	61	33	γh(g	γh(g	NOUN
ejpam-4656	61	34	)	)	PUNCT
ejpam-4656	61	35	is	be	AUX
ejpam-4656	61	36	called	call	VERB
ejpam-4656	61	37	a	a	DET
ejpam-4656	61	38	γh	γh	ADV
ejpam-4656	61	39	-	-	PUNCT
ejpam-4656	61	40	set	set	NOUN
ejpam-4656	61	41	.	.	PUNCT
ejpam-4656	62	1	a	a	DET
ejpam-4656	62	2	hop	hop	NOUN
ejpam-4656	62	3	dominating	dominating	NOUN
ejpam-4656	62	4	set	set	NOUN
ejpam-4656	62	5	s	s	VERB
ejpam-4656	62	6	is	be	AUX
ejpam-4656	62	7	connected	connect	VERB
ejpam-4656	62	8	hop	hop	NOUN
ejpam-4656	62	9	dominating	dominating	NOUN
ejpam-4656	62	10	if	if	SCONJ
ejpam-4656	62	11	⟨s⟩	⟨s⟩	PROPN
ejpam-4656	62	12	is	be	AUX
ejpam-4656	62	13	connected	connect	VERB
ejpam-4656	62	14	.	.	PUNCT
ejpam-4656	63	1	the	the	DET
ejpam-4656	63	2	minimum	minimum	ADJ
ejpam-4656	63	3	cardinality	cardinality	NOUN
ejpam-4656	63	4	among	among	ADP
ejpam-4656	63	5	all	all	DET
ejpam-4656	63	6	connected	connect	VERB
ejpam-4656	63	7	hop	hop	NOUN
ejpam-4656	63	8	dominating	dominating	NOUN
ejpam-4656	63	9	sets	set	NOUN
ejpam-4656	63	10	of	of	ADP
ejpam-4656	63	11	g	g	NOUN
ejpam-4656	63	12	,	,	PUNCT
ejpam-4656	63	13	denoted	denote	VERB
ejpam-4656	63	14	by	by	ADP
ejpam-4656	63	15	γch(g	γch(g	NOUN
ejpam-4656	63	16	)	)	PUNCT
ejpam-4656	63	17	,	,	PUNCT
ejpam-4656	63	18	is	be	AUX
ejpam-4656	63	19	called	call	VERB
ejpam-4656	63	20	the	the	DET
ejpam-4656	63	21	connected	connect	VERB
ejpam-4656	63	22	hop	hop	NOUN
ejpam-4656	63	23	domination	domination	NOUN
ejpam-4656	63	24	number	number	NOUN
ejpam-4656	63	25	of	of	ADP
ejpam-4656	63	26	g.	g.	PROPN
ejpam-4656	63	27	any	any	DET
ejpam-4656	63	28	connected	connect	VERB
ejpam-4656	63	29	hop	hop	NOUN
ejpam-4656	63	30	dominating	dominating	NOUN
ejpam-4656	63	31	set	set	VERB
ejpam-4656	63	32	with	with	ADP
ejpam-4656	63	33	cardinality	cardinality	NOUN
ejpam-4656	63	34	equal	equal	ADJ
ejpam-4656	63	35	to	to	ADP
ejpam-4656	63	36	γch(g	γch(g	NOUN
ejpam-4656	63	37	)	)	PUNCT
ejpam-4656	63	38	is	be	AUX
ejpam-4656	63	39	called	call	VERB
ejpam-4656	63	40	a	a	DET
ejpam-4656	63	41	γch	γch	NOUN
ejpam-4656	63	42	-	-	PUNCT
ejpam-4656	63	43	set	set	NOUN
ejpam-4656	63	44	.	.	PUNCT
ejpam-4656	64	1	a	a	DET
ejpam-4656	64	2	set	set	NOUN
ejpam-4656	64	3	c	c	NOUN
ejpam-4656	64	4	⊆	⊆	NUM
ejpam-4656	64	5	v	v	NOUN
ejpam-4656	64	6	(	(	PUNCT
ejpam-4656	64	7	g	g	NOUN
ejpam-4656	64	8	)	)	PUNCT
ejpam-4656	64	9	is	be	AUX
ejpam-4656	64	10	convex	convex	NOUN
ejpam-4656	64	11	set	set	VERB
ejpam-4656	64	12	if	if	SCONJ
ejpam-4656	64	13	for	for	ADP
ejpam-4656	64	14	every	every	DET
ejpam-4656	64	15	two	two	NUM
ejpam-4656	64	16	vertices	vertex	NOUN
ejpam-4656	64	17	x	x	X
ejpam-4656	64	18	,	,	PUNCT
ejpam-4656	64	19	y	y	PROPN
ejpam-4656	64	20	∈	∈	PROPN
ejpam-4656	64	21	c	c	PROPN
ejpam-4656	64	22	,	,	PUNCT
ejpam-4656	64	23	the	the	DET
ejpam-4656	64	24	vertex	vertex	NOUN
ejpam-4656	64	25	set	set	NOUN
ejpam-4656	64	26	of	of	ADP
ejpam-4656	64	27	every	every	DET
ejpam-4656	64	28	x	x	PROPN
ejpam-4656	64	29	-	-	PROPN
ejpam-4656	64	30	y	y	ADJ
ejpam-4656	64	31	geodesic	geodesic	NOUN
ejpam-4656	64	32	is	be	AUX
ejpam-4656	64	33	contained	contain	VERB
ejpam-4656	64	34	in	in	ADP
ejpam-4656	64	35	c	c	NOUN
ejpam-4656	64	36	,	,	PUNCT
ejpam-4656	64	37	that	that	ADV
ejpam-4656	64	38	is	is	ADV
ejpam-4656	64	39	,	,	PUNCT
ejpam-4656	64	40	ig[x	ig[x	PROPN
ejpam-4656	64	41	,	,	PUNCT
ejpam-4656	64	42	y	y	PROPN
ejpam-4656	64	43	]	]	X
ejpam-4656	64	44	⊆	⊆	NUM
ejpam-4656	64	45	c.	c.	NOUN
ejpam-4656	64	46	the	the	DET
ejpam-4656	64	47	largest	large	ADJ
ejpam-4656	64	48	cardinality	cardinality	NOUN
ejpam-4656	64	49	of	of	ADP
ejpam-4656	64	50	a	a	DET
ejpam-4656	64	51	proper	proper	ADJ
ejpam-4656	64	52	convex	convex	NOUN
ejpam-4656	64	53	set	set	VERB
ejpam-4656	64	54	in	in	ADP
ejpam-4656	64	55	g	g	NOUN
ejpam-4656	64	56	,	,	PUNCT
ejpam-4656	64	57	denoted	denote	VERB
ejpam-4656	64	58	by	by	ADP
ejpam-4656	64	59	con(g	con(g	NOUN
ejpam-4656	64	60	)	)	PUNCT
ejpam-4656	64	61	,	,	PUNCT
ejpam-4656	64	62	is	be	AUX
ejpam-4656	64	63	called	call	VERB
ejpam-4656	64	64	the	the	DET
ejpam-4656	64	65	convexity	convexity	NOUN
ejpam-4656	64	66	number	number	NOUN
ejpam-4656	64	67	of	of	ADP
ejpam-4656	64	68	g.	g.	PROPN
ejpam-4656	64	69	a	a	DET
ejpam-4656	64	70	set	set	NOUN
ejpam-4656	64	71	c	c	NOUN
ejpam-4656	64	72	⊆	⊆	NUM
ejpam-4656	64	73	v	v	NOUN
ejpam-4656	64	74	(	(	PUNCT
ejpam-4656	64	75	g	g	NOUN
ejpam-4656	64	76	)	)	PUNCT
ejpam-4656	64	77	j.	j.	PROPN
ejpam-4656	64	78	hassan	hassan	PROPN
ejpam-4656	64	79	,	,	PUNCT
ejpam-4656	64	80	s.	s.	PROPN
ejpam-4656	64	81	canoy	canoy	PROPN
ejpam-4656	64	82	jr	jr	PROPN
ejpam-4656	64	83	.	.	PROPN
ejpam-4656	64	84	,	,	PUNCT
ejpam-4656	64	85	c.	c.	PROPN
ejpam-4656	64	86	saromines	saromine	VERB
ejpam-4656	64	87	/	/	SYM
ejpam-4656	64	88	eur	eur	PROPN
ejpam-4656	64	89	.	.	PUNCT
ejpam-4656	65	1	j.	j.	PROPN
ejpam-4656	65	2	pure	pure	PROPN
ejpam-4656	65	3	appl	appl	PROPN
ejpam-4656	65	4	.	.	PROPN
ejpam-4656	65	5	math	math	PROPN
ejpam-4656	65	6	,	,	PUNCT
ejpam-4656	65	7	16	16	NUM
ejpam-4656	65	8	(	(	PUNCT
ejpam-4656	65	9	1	1	NUM
ejpam-4656	65	10	)	)	PUNCT
ejpam-4656	65	11	(	(	PUNCT
ejpam-4656	65	12	2023	2023	NUM
ejpam-4656	65	13	)	)	PUNCT
ejpam-4656	65	14	,	,	PUNCT
ejpam-4656	65	15	319	319	NUM
ejpam-4656	65	16	-	-	SYM
ejpam-4656	65	17	335	335	NUM
ejpam-4656	65	18	321	321	NUM
ejpam-4656	65	19	is	be	AUX
ejpam-4656	65	20	called	call	VERB
ejpam-4656	65	21	a	a	DET
ejpam-4656	65	22	convex	convex	NOUN
ejpam-4656	65	23	dominating	dominating	NOUN
ejpam-4656	65	24	set	set	NOUN
ejpam-4656	65	25	(	(	PUNCT
ejpam-4656	65	26	resp	resp	NOUN
ejpam-4656	65	27	.	.	PUNCT
ejpam-4656	66	1	convex	convex	VERB
ejpam-4656	66	2	hop	hop	NOUN
ejpam-4656	66	3	dominating	dominating	NOUN
ejpam-4656	66	4	set	set	NOUN
ejpam-4656	66	5	)	)	PUNCT
ejpam-4656	66	6	if	if	SCONJ
ejpam-4656	66	7	c	c	PROPN
ejpam-4656	66	8	is	be	AUX
ejpam-4656	66	9	both	both	PRON
ejpam-4656	66	10	convex	convex	ADJ
ejpam-4656	66	11	and	and	CCONJ
ejpam-4656	66	12	dominating	dominating	NOUN
ejpam-4656	66	13	(	(	PUNCT
ejpam-4656	66	14	resp	resp	NOUN
ejpam-4656	66	15	.	.	PUNCT
ejpam-4656	67	1	convex	convex	PROPN
ejpam-4656	67	2	and	and	CCONJ
ejpam-4656	67	3	hop	hop	NOUN
ejpam-4656	67	4	dominating	dominating	NOUN
ejpam-4656	67	5	)	)	PUNCT
ejpam-4656	67	6	.	.	PUNCT
ejpam-4656	68	1	the	the	DET
ejpam-4656	68	2	minimum	minimum	ADJ
ejpam-4656	68	3	cardinality	cardinality	NOUN
ejpam-4656	68	4	among	among	ADP
ejpam-4656	68	5	all	all	DET
ejpam-4656	68	6	convex	convex	ADJ
ejpam-4656	68	7	dominating	dominating	NOUN
ejpam-4656	68	8	(	(	PUNCT
ejpam-4656	68	9	resp	resp	NOUN
ejpam-4656	68	10	.	.	PUNCT
ejpam-4656	69	1	convex	convex	VERB
ejpam-4656	69	2	hop	hop	NOUN
ejpam-4656	69	3	dominating	dominating	NOUN
ejpam-4656	69	4	)	)	PUNCT
ejpam-4656	69	5	sets	set	NOUN
ejpam-4656	69	6	in	in	ADP
ejpam-4656	69	7	g	g	NOUN
ejpam-4656	69	8	,	,	PUNCT
ejpam-4656	69	9	denoted	denote	VERB
ejpam-4656	69	10	by	by	ADP
ejpam-4656	69	11	γcon(g	γcon(g	PROPN
ejpam-4656	69	12	)	)	PUNCT
ejpam-4656	69	13	(	(	PUNCT
ejpam-4656	69	14	resp	resp	NOUN
ejpam-4656	69	15	.	.	PUNCT
ejpam-4656	70	1	γconh(g	γconh(g	NOUN
ejpam-4656	70	2	)	)	PUNCT
ejpam-4656	70	3	)	)	PUNCT
ejpam-4656	70	4	,	,	PUNCT
ejpam-4656	70	5	is	be	AUX
ejpam-4656	70	6	called	call	VERB
ejpam-4656	70	7	the	the	DET
ejpam-4656	70	8	convex	convex	ADJ
ejpam-4656	70	9	domination	domination	NOUN
ejpam-4656	70	10	number	number	NOUN
ejpam-4656	70	11	(	(	PUNCT
ejpam-4656	70	12	resp	resp	NOUN
ejpam-4656	70	13	.	.	PUNCT
ejpam-4656	71	1	convex	convex	VERB
ejpam-4656	71	2	hop	hop	NOUN
ejpam-4656	71	3	domination	domination	NOUN
ejpam-4656	71	4	number	number	NOUN
ejpam-4656	71	5	)	)	PUNCT
ejpam-4656	71	6	of	of	ADP
ejpam-4656	71	7	g.	g.	PROPN
ejpam-4656	71	8	any	any	DET
ejpam-4656	71	9	convex	convex	NOUN
ejpam-4656	71	10	dominating	dominating	NOUN
ejpam-4656	71	11	(	(	PUNCT
ejpam-4656	71	12	resp	resp	NOUN
ejpam-4656	71	13	.	.	PUNCT
ejpam-4656	72	1	convex	convex	VERB
ejpam-4656	72	2	hop	hop	NOUN
ejpam-4656	72	3	dominating	dominating	NOUN
ejpam-4656	72	4	set	set	NOUN
ejpam-4656	72	5	)	)	PUNCT
ejpam-4656	72	6	with	with	ADP
ejpam-4656	72	7	cardinality	cardinality	NOUN
ejpam-4656	72	8	equal	equal	ADJ
ejpam-4656	72	9	to	to	ADP
ejpam-4656	72	10	γcon(g	γcon(g	PROPN
ejpam-4656	72	11	)	)	PUNCT
ejpam-4656	72	12	(	(	PUNCT
ejpam-4656	72	13	resp	resp	NOUN
ejpam-4656	72	14	.	.	PUNCT
ejpam-4656	73	1	γconh(g	γconh(g	NOUN
ejpam-4656	73	2	)	)	PUNCT
ejpam-4656	73	3	)	)	PUNCT
ejpam-4656	73	4	is	be	AUX
ejpam-4656	73	5	called	call	VERB
ejpam-4656	73	6	a	a	DET
ejpam-4656	73	7	γcon	γcon	NOUN
ejpam-4656	73	8	-	-	PUNCT
ejpam-4656	73	9	set	set	VERB
ejpam-4656	73	10	(	(	PUNCT
ejpam-4656	73	11	resp	resp	NOUN
ejpam-4656	73	12	.	.	PUNCT
ejpam-4656	74	1	γconh	γconh	NOUN
ejpam-4656	74	2	-	-	PUNCT
ejpam-4656	74	3	set	set	NOUN
ejpam-4656	74	4	)	)	PUNCT
ejpam-4656	74	5	.	.	PUNCT
ejpam-4656	75	1	a	a	DET
ejpam-4656	75	2	nonempty	nonempty	ADV
ejpam-4656	75	3	set	set	VERB
ejpam-4656	75	4	s	s	PROPN
ejpam-4656	75	5	⊆	⊆	NUM
ejpam-4656	75	6	v	v	NOUN
ejpam-4656	75	7	(	(	PUNCT
ejpam-4656	75	8	g	g	NOUN
ejpam-4656	75	9	)	)	PUNCT
ejpam-4656	75	10	is	be	AUX
ejpam-4656	75	11	non	non	ADJ
ejpam-4656	75	12	-	-	ADJ
ejpam-4656	75	13	connecting	connecting	ADJ
ejpam-4656	75	14	if	if	SCONJ
ejpam-4656	75	15	for	for	ADP
ejpam-4656	75	16	each	each	DET
ejpam-4656	75	17	pair	pair	NOUN
ejpam-4656	75	18	of	of	ADP
ejpam-4656	75	19	vertices	vertex	NOUN
ejpam-4656	75	20	v	v	ADP
ejpam-4656	75	21	,	,	PUNCT
ejpam-4656	75	22	w	w	PROPN
ejpam-4656	75	23	∈	∈	PROPN
ejpam-4656	75	24	v	v	NOUN
ejpam-4656	75	25	(	(	PUNCT
ejpam-4656	75	26	g)\s	g)\s	NOUN
ejpam-4656	75	27	with	with	ADP
ejpam-4656	75	28	dg(v	dg(v	NOUN
ejpam-4656	75	29	,	,	PUNCT
ejpam-4656	75	30	w	w	NOUN
ejpam-4656	75	31	)	)	PUNCT
ejpam-4656	75	32	=	=	SYM
ejpam-4656	75	33	2	2	NUM
ejpam-4656	75	34	,	,	PUNCT
ejpam-4656	75	35	it	it	PRON
ejpam-4656	75	36	holds	hold	VERB
ejpam-4656	75	37	that	that	SCONJ
ejpam-4656	75	38	ng(v	ng(v	NOUN
ejpam-4656	75	39	)	)	PUNCT
ejpam-4656	75	40	∩ng(w	∩ng(w	ADJ
ejpam-4656	75	41	)	)	PUNCT
ejpam-4656	75	42	∩	∩	NOUN
ejpam-4656	75	43	s	s	PART
ejpam-4656	75	44	=	=	PUNCT
ejpam-4656	75	45	∅.	∅.	VERB
ejpam-4656	75	46	a	a	DET
ejpam-4656	75	47	set	set	NOUN
ejpam-4656	75	48	s	s	NOUN
ejpam-4656	75	49	⊆	⊆	NUM
ejpam-4656	75	50	v	v	NOUN
ejpam-4656	75	51	(	(	PUNCT
ejpam-4656	75	52	g	g	NOUN
ejpam-4656	75	53	)	)	PUNCT
ejpam-4656	75	54	is	be	AUX
ejpam-4656	75	55	a	a	DET
ejpam-4656	75	56	clique	clique	NOUN
ejpam-4656	75	57	if	if	SCONJ
ejpam-4656	75	58	the	the	DET
ejpam-4656	75	59	subgraph	subgraph	NOUN
ejpam-4656	75	60	⟨s⟩	⟨s⟩	PROPN
ejpam-4656	75	61	induced	induce	VERB
ejpam-4656	75	62	by	by	ADP
ejpam-4656	75	63	s	s	PROPN
ejpam-4656	75	64	is	be	AUX
ejpam-4656	75	65	a	a	DET
ejpam-4656	75	66	complete	complete	ADJ
ejpam-4656	75	67	graph	graph	NOUN
ejpam-4656	75	68	.	.	PUNCT
ejpam-4656	76	1	the	the	DET
ejpam-4656	76	2	maximum	maximum	ADJ
ejpam-4656	76	3	cardinality	cardinality	NOUN
ejpam-4656	76	4	of	of	ADP
ejpam-4656	76	5	a	a	DET
ejpam-4656	76	6	clique	clique	NOUN
ejpam-4656	76	7	in	in	ADP
ejpam-4656	76	8	g	g	NOUN
ejpam-4656	76	9	,	,	PUNCT
ejpam-4656	76	10	denoted	denote	VERB
ejpam-4656	76	11	by	by	ADP
ejpam-4656	76	12	ω(g	ω(g	NOUN
ejpam-4656	76	13	)	)	PUNCT
ejpam-4656	76	14	,	,	PUNCT
ejpam-4656	76	15	is	be	AUX
ejpam-4656	76	16	called	call	VERB
ejpam-4656	76	17	the	the	DET
ejpam-4656	76	18	clique	clique	ADJ
ejpam-4656	76	19	number	number	NOUN
ejpam-4656	76	20	of	of	ADP
ejpam-4656	76	21	g.	g.	PROPN
ejpam-4656	76	22	a	a	DET
ejpam-4656	76	23	clique	clique	NOUN
ejpam-4656	76	24	s	s	X
ejpam-4656	76	25	which	which	PRON
ejpam-4656	76	26	is	be	AUX
ejpam-4656	76	27	also	also	ADV
ejpam-4656	76	28	hop	hop	NOUN
ejpam-4656	76	29	dominating	dominate	VERB
ejpam-4656	76	30	in	in	ADP
ejpam-4656	76	31	g	g	PROPN
ejpam-4656	76	32	is	be	AUX
ejpam-4656	76	33	called	call	VERB
ejpam-4656	76	34	clique	clique	ADJ
ejpam-4656	76	35	hop	hop	PROPN
ejpam-4656	76	36	dominating	dominating	NOUN
ejpam-4656	76	37	.	.	PUNCT
ejpam-4656	77	1	whenever	whenever	SCONJ
ejpam-4656	77	2	g	g	PROPN
ejpam-4656	77	3	admits	admit	VERB
ejpam-4656	77	4	a	a	DET
ejpam-4656	77	5	clique	clique	NOUN
ejpam-4656	77	6	hop	hop	NOUN
ejpam-4656	77	7	dominating	dominating	NOUN
ejpam-4656	77	8	set	set	NOUN
ejpam-4656	77	9	,	,	PUNCT
ejpam-4656	77	10	we	we	PRON
ejpam-4656	77	11	call	call	VERB
ejpam-4656	77	12	the	the	DET
ejpam-4656	77	13	smallest	small	ADJ
ejpam-4656	77	14	cardinality	cardinality	NOUN
ejpam-4656	77	15	of	of	ADP
ejpam-4656	77	16	a	a	DET
ejpam-4656	77	17	clique	clique	NOUN
ejpam-4656	77	18	hop	hop	NOUN
ejpam-4656	77	19	dominating	dominating	NOUN
ejpam-4656	77	20	set	set	VERB
ejpam-4656	77	21	in	in	ADP
ejpam-4656	77	22	g	g	NOUN
ejpam-4656	77	23	,	,	PUNCT
ejpam-4656	77	24	denoted	denote	VERB
ejpam-4656	77	25	by	by	ADP
ejpam-4656	77	26	γclh(g	γclh(g	NOUN
ejpam-4656	77	27	)	)	PUNCT
ejpam-4656	77	28	,	,	PUNCT
ejpam-4656	77	29	the	the	DET
ejpam-4656	77	30	clique	clique	NOUN
ejpam-4656	77	31	hop	hop	PROPN
ejpam-4656	77	32	domination	domination	NOUN
ejpam-4656	77	33	number	number	NOUN
ejpam-4656	77	34	of	of	ADP
ejpam-4656	77	35	g.	g.	PROPN
ejpam-4656	77	36	a	a	DET
ejpam-4656	77	37	set	set	NOUN
ejpam-4656	77	38	c	c	NOUN
ejpam-4656	77	39	⊆	⊆	NUM
ejpam-4656	77	40	v	v	NOUN
ejpam-4656	77	41	(	(	PUNCT
ejpam-4656	77	42	g	g	NOUN
ejpam-4656	77	43	)	)	PUNCT
ejpam-4656	77	44	is	be	AUX
ejpam-4656	77	45	a	a	DET
ejpam-4656	77	46	pointwise	pointwise	ADJ
ejpam-4656	77	47	non	non	ADJ
ejpam-4656	77	48	-	-	ADJ
ejpam-4656	77	49	dominating	dominating	ADJ
ejpam-4656	77	50	set	set	NOUN
ejpam-4656	77	51	if	if	SCONJ
ejpam-4656	77	52	for	for	ADP
ejpam-4656	77	53	every	every	DET
ejpam-4656	77	54	v	v	NUM
ejpam-4656	77	55	∈	∈	NOUN
ejpam-4656	77	56	v	v	NOUN
ejpam-4656	77	57	(	(	PUNCT
ejpam-4656	77	58	g)\c	g)\c	NOUN
ejpam-4656	77	59	,	,	PUNCT
ejpam-4656	77	60	there	there	PRON
ejpam-4656	77	61	exists	exist	VERB
ejpam-4656	77	62	u	u	PROPN
ejpam-4656	77	63	∈	∈	PROPN
ejpam-4656	77	64	c	c	NOUN
ejpam-4656	77	65	such	such	ADJ
ejpam-4656	77	66	that	that	DET
ejpam-4656	77	67	v	v	NOUN
ejpam-4656	77	68	/∈	/∈	PUNCT
ejpam-4656	77	69	ng(u	ng(u	NOUN
ejpam-4656	77	70	)	)	PUNCT
ejpam-4656	77	71	.	.	PUNCT
ejpam-4656	78	1	the	the	DET
ejpam-4656	78	2	minimum	minimum	ADJ
ejpam-4656	78	3	cardinality	cardinality	NOUN
ejpam-4656	78	4	of	of	ADP
ejpam-4656	78	5	a	a	DET
ejpam-4656	78	6	pointwise	pointwise	ADJ
ejpam-4656	78	7	non	non	ADJ
ejpam-4656	78	8	-	-	ADJ
ejpam-4656	78	9	dominating	dominating	ADJ
ejpam-4656	78	10	set	set	NOUN
ejpam-4656	78	11	in	in	ADP
ejpam-4656	78	12	g	g	NOUN
ejpam-4656	78	13	,	,	PUNCT
ejpam-4656	78	14	denoted	denote	VERB
ejpam-4656	78	15	by	by	ADP
ejpam-4656	78	16	pnd(g	pnd(g	PROPN
ejpam-4656	78	17	)	)	PUNCT
ejpam-4656	78	18	,	,	PUNCT
ejpam-4656	78	19	is	be	AUX
ejpam-4656	78	20	called	call	VERB
ejpam-4656	78	21	a	a	DET
ejpam-4656	78	22	pointwise	pointwise	ADJ
ejpam-4656	78	23	non	non	ADJ
ejpam-4656	78	24	-	-	ADJ
ejpam-4656	78	25	domination	domination	ADJ
ejpam-4656	78	26	number	number	NOUN
ejpam-4656	78	27	of	of	ADP
ejpam-4656	78	28	g.	g.	PROPN
ejpam-4656	78	29	a	a	DET
ejpam-4656	78	30	set	set	NOUN
ejpam-4656	78	31	s	s	PROPN
ejpam-4656	78	32	⊆	⊆	NUM
ejpam-4656	78	33	v	v	NOUN
ejpam-4656	78	34	(	(	PUNCT
ejpam-4656	78	35	g	g	NOUN
ejpam-4656	78	36	)	)	PUNCT
ejpam-4656	78	37	is	be	AUX
ejpam-4656	78	38	a	a	DET
ejpam-4656	78	39	clique	clique	NOUN
ejpam-4656	78	40	pointwise	pointwise	PROPN
ejpam-4656	78	41	non	non	ADJ
ejpam-4656	78	42	-	-	ADJ
ejpam-4656	78	43	dominating	dominating	ADJ
ejpam-4656	78	44	set	set	NOUN
ejpam-4656	78	45	if	if	SCONJ
ejpam-4656	78	46	s	s	VERB
ejpam-4656	78	47	is	be	AUX
ejpam-4656	78	48	both	both	PRON
ejpam-4656	78	49	a	a	DET
ejpam-4656	78	50	clique	clique	NOUN
ejpam-4656	78	51	and	and	CCONJ
ejpam-4656	78	52	a	a	DET
ejpam-4656	78	53	pointwise	pointwise	ADJ
ejpam-4656	78	54	non	non	ADJ
ejpam-4656	78	55	-	-	ADJ
ejpam-4656	78	56	dominating	dominating	ADJ
ejpam-4656	78	57	set	set	NOUN
ejpam-4656	78	58	in	in	ADP
ejpam-4656	78	59	g.	g.	PROPN
ejpam-4656	78	60	the	the	DET
ejpam-4656	78	61	smallest	small	ADJ
ejpam-4656	78	62	cardinality	cardinality	NOUN
ejpam-4656	78	63	of	of	ADP
ejpam-4656	78	64	a	a	DET
ejpam-4656	78	65	clique	clique	NOUN
ejpam-4656	79	1	pointwise	pointwise	NOUN
ejpam-4656	79	2	nondominating	nondominate	VERB
ejpam-4656	79	3	set	set	NOUN
ejpam-4656	79	4	in	in	ADP
ejpam-4656	79	5	g	g	NOUN
ejpam-4656	79	6	,	,	PUNCT
ejpam-4656	79	7	denoted	denote	VERB
ejpam-4656	79	8	by	by	ADP
ejpam-4656	79	9	cpnd(g	cpnd(g	PROPN
ejpam-4656	79	10	)	)	PUNCT
ejpam-4656	79	11	,	,	PUNCT
ejpam-4656	79	12	is	be	AUX
ejpam-4656	79	13	called	call	VERB
ejpam-4656	79	14	the	the	DET
ejpam-4656	79	15	clique	clique	NOUN
ejpam-4656	79	16	pointwise	pointwise	PROPN
ejpam-4656	79	17	non	non	ADJ
ejpam-4656	79	18	-	-	ADJ
ejpam-4656	79	19	domination	domination	ADJ
ejpam-4656	79	20	number	number	NOUN
ejpam-4656	79	21	of	of	ADP
ejpam-4656	79	22	g.	g.	PROPN
ejpam-4656	79	23	any	any	DET
ejpam-4656	79	24	clique	clique	NOUN
ejpam-4656	79	25	pointwise	pointwise	PROPN
ejpam-4656	79	26	non	non	ADJ
ejpam-4656	79	27	-	-	ADJ
ejpam-4656	79	28	dominating	dominating	ADJ
ejpam-4656	79	29	set	set	NOUN
ejpam-4656	79	30	in	in	ADP
ejpam-4656	79	31	g	g	NOUN
ejpam-4656	79	32	with	with	ADP
ejpam-4656	79	33	cardinality	cardinality	NOUN
ejpam-4656	79	34	cpnd(g	cpnd(g	PROPN
ejpam-4656	79	35	)	)	PUNCT
ejpam-4656	79	36	is	be	AUX
ejpam-4656	79	37	called	call	VERB
ejpam-4656	79	38	a	a	DET
ejpam-4656	79	39	cpnd	cpnd	NOUN
ejpam-4656	79	40	-	-	PUNCT
ejpam-4656	79	41	set	set	NOUN
ejpam-4656	79	42	in	in	ADP
ejpam-4656	79	43	g.	g.	PROPN
ejpam-4656	79	44	the	the	DET
ejpam-4656	79	45	shadow	shadow	NOUN
ejpam-4656	79	46	graph	graph	NOUN
ejpam-4656	79	47	s(g	s(g	PROPN
ejpam-4656	79	48	)	)	PUNCT
ejpam-4656	79	49	of	of	ADP
ejpam-4656	79	50	graph	graph	NOUN
ejpam-4656	79	51	g	g	PROPN
ejpam-4656	79	52	is	be	AUX
ejpam-4656	79	53	constructed	construct	VERB
ejpam-4656	79	54	by	by	ADP
ejpam-4656	79	55	taking	take	VERB
ejpam-4656	79	56	two	two	NUM
ejpam-4656	79	57	copies	copy	NOUN
ejpam-4656	79	58	of	of	ADP
ejpam-4656	79	59	g	g	NOUN
ejpam-4656	79	60	,	,	PUNCT
ejpam-4656	79	61	say	say	VERB
ejpam-4656	79	62	g1	g1	PROPN
ejpam-4656	79	63	and	and	CCONJ
ejpam-4656	79	64	g2	g2	PROPN
ejpam-4656	79	65	,	,	PUNCT
ejpam-4656	79	66	and	and	CCONJ
ejpam-4656	79	67	then	then	ADV
ejpam-4656	79	68	joining	join	VERB
ejpam-4656	79	69	each	each	DET
ejpam-4656	79	70	vertex	vertex	NOUN
ejpam-4656	79	71	u	u	NOUN
ejpam-4656	79	72	∈	∈	PROPN
ejpam-4656	79	73	v	v	NOUN
ejpam-4656	79	74	(	(	PUNCT
ejpam-4656	79	75	g1	g1	PROPN
ejpam-4656	79	76	)	)	PUNCT
ejpam-4656	79	77	to	to	ADP
ejpam-4656	79	78	the	the	DET
ejpam-4656	79	79	neighbors	neighbor	NOUN
ejpam-4656	79	80	of	of	ADP
ejpam-4656	79	81	its	its	PRON
ejpam-4656	79	82	corresponding	correspond	VERB
ejpam-4656	79	83	vertex	vertex	NOUN
ejpam-4656	79	84	u′	u′	PROPN
ejpam-4656	79	85	∈	∈	PROPN
ejpam-4656	79	86	v	v	NOUN
ejpam-4656	79	87	(	(	PUNCT
ejpam-4656	79	88	g2	g2	PROPN
ejpam-4656	79	89	)	)	PUNCT
ejpam-4656	79	90	.	.	PUNCT
ejpam-4656	80	1	for	for	ADP
ejpam-4656	80	2	a	a	DET
ejpam-4656	80	3	graph	graph	NOUN
ejpam-4656	80	4	g	g	NOUN
ejpam-4656	80	5	,	,	PUNCT
ejpam-4656	80	6	the	the	DET
ejpam-4656	80	7	complementary	complementary	ADJ
ejpam-4656	80	8	prism	prism	NOUN
ejpam-4656	80	9	,	,	PUNCT
ejpam-4656	80	10	denoted	denote	VERB
ejpam-4656	80	11	by	by	ADP
ejpam-4656	80	12	gg	gg	PROPN
ejpam-4656	80	13	,	,	PUNCT
ejpam-4656	80	14	is	be	AUX
ejpam-4656	80	15	formed	form	VERB
ejpam-4656	80	16	from	from	ADP
ejpam-4656	80	17	the	the	DET
ejpam-4656	80	18	disjoint	disjoint	PROPN
ejpam-4656	80	19	union	union	NOUN
ejpam-4656	80	20	of	of	ADP
ejpam-4656	80	21	g	g	PROPN
ejpam-4656	80	22	and	and	CCONJ
ejpam-4656	80	23	its	its	PRON
ejpam-4656	80	24	complement	complement	NOUN
ejpam-4656	80	25	g	g	NOUN
ejpam-4656	80	26	by	by	ADP
ejpam-4656	80	27	adding	add	VERB
ejpam-4656	80	28	a	a	DET
ejpam-4656	80	29	perfect	perfect	ADJ
ejpam-4656	80	30	matching	matching	NOUN
ejpam-4656	80	31	between	between	ADP
ejpam-4656	80	32	corresponding	corresponding	ADJ
ejpam-4656	80	33	vertices	vertex	NOUN
ejpam-4656	80	34	of	of	ADP
ejpam-4656	80	35	g	g	PROPN
ejpam-4656	80	36	and	and	CCONJ
ejpam-4656	80	37	g.	g.	NOUN
ejpam-4656	80	38	for	for	ADP
ejpam-4656	80	39	each	each	DET
ejpam-4656	80	40	v	v	NUM
ejpam-4656	80	41	∈	∈	PROPN
ejpam-4656	80	42	v	v	NOUN
ejpam-4656	80	43	(	(	PUNCT
ejpam-4656	80	44	g	g	NOUN
ejpam-4656	80	45	)	)	PUNCT
ejpam-4656	80	46	,	,	PUNCT
ejpam-4656	80	47	let	let	VERB
ejpam-4656	80	48	v	v	PART
ejpam-4656	80	49	denote	denote	VERB
ejpam-4656	80	50	the	the	DET
ejpam-4656	80	51	vertex	vertex	NOUN
ejpam-4656	80	52	in	in	ADP
ejpam-4656	80	53	g	g	NOUN
ejpam-4656	80	54	corresponding	correspond	VERB
ejpam-4656	80	55	to	to	ADP
ejpam-4656	80	56	v.	v.	PROPN
ejpam-4656	80	57	in	in	ADP
ejpam-4656	80	58	simple	simple	ADJ
ejpam-4656	80	59	terms	term	NOUN
ejpam-4656	80	60	,	,	PUNCT
ejpam-4656	80	61	the	the	DET
ejpam-4656	80	62	graph	graph	NOUN
ejpam-4656	80	63	gg	gg	NOUN
ejpam-4656	80	64	is	be	AUX
ejpam-4656	80	65	form	form	NOUN
ejpam-4656	80	66	from	from	ADP
ejpam-4656	80	67	g∪g	g∪g	NOUN
ejpam-4656	80	68	by	by	ADP
ejpam-4656	80	69	adding	add	VERB
ejpam-4656	80	70	the	the	DET
ejpam-4656	80	71	edge	edge	NOUN
ejpam-4656	80	72	vv	vv	NOUN
ejpam-4656	80	73	for	for	ADP
ejpam-4656	80	74	every	every	DET
ejpam-4656	80	75	vertex	vertex	NOUN
ejpam-4656	80	76	v	v	ADP
ejpam-4656	80	77	∈	∈	NOUN
ejpam-4656	80	78	v	v	NOUN
ejpam-4656	80	79	(	(	PUNCT
ejpam-4656	80	80	g	g	NOUN
ejpam-4656	80	81	)	)	PUNCT
ejpam-4656	80	82	.	.	PUNCT
ejpam-4656	81	1	let	let	VERB
ejpam-4656	81	2	g	g	NOUN
ejpam-4656	81	3	and	and	CCONJ
ejpam-4656	81	4	h	h	NOUN
ejpam-4656	81	5	be	be	VERB
ejpam-4656	81	6	any	any	DET
ejpam-4656	81	7	two	two	NUM
ejpam-4656	81	8	graphs	graph	NOUN
ejpam-4656	81	9	.	.	PUNCT
ejpam-4656	82	1	the	the	DET
ejpam-4656	82	2	join	join	NOUN
ejpam-4656	82	3	g	g	PROPN
ejpam-4656	82	4	+	+	CCONJ
ejpam-4656	82	5	h	h	NOUN
ejpam-4656	82	6	is	be	AUX
ejpam-4656	82	7	the	the	DET
ejpam-4656	82	8	graph	graph	NOUN
ejpam-4656	82	9	with	with	ADP
ejpam-4656	82	10	vertex	vertex	NOUN
ejpam-4656	82	11	set	set	VERB
ejpam-4656	82	12	v	v	NOUN
ejpam-4656	82	13	(	(	PUNCT
ejpam-4656	82	14	g+h	g+h	NOUN
ejpam-4656	82	15	)	)	PUNCT
ejpam-4656	82	16	=	=	SYM
ejpam-4656	82	17	v	v	NOUN
ejpam-4656	82	18	(	(	PUNCT
ejpam-4656	82	19	g)∪	g)∪	VERB
ejpam-4656	82	20	v	v	NUM
ejpam-4656	82	21	(	(	PUNCT
ejpam-4656	82	22	h	h	NOUN
ejpam-4656	82	23	)	)	PUNCT
ejpam-4656	82	24	and	and	CCONJ
ejpam-4656	82	25	edge	edge	NOUN
ejpam-4656	82	26	set	set	VERB
ejpam-4656	82	27	e(g+h	e(g+h	NUM
ejpam-4656	82	28	)	)	PUNCT
ejpam-4656	83	1	=	=	SYM
ejpam-4656	83	2	e(g)∪e(h)∪	e(g)∪e(h)∪	NOUN
ejpam-4656	83	3	{	{	PUNCT
ejpam-4656	83	4	uv	uv	NOUN
ejpam-4656	83	5	:	:	PUNCT
ejpam-4656	83	6	u	u	PROPN
ejpam-4656	83	7	∈	∈	PROPN
ejpam-4656	83	8	v	v	ADP
ejpam-4656	83	9	(	(	PUNCT
ejpam-4656	83	10	g	g	NOUN
ejpam-4656	83	11	)	)	PUNCT
ejpam-4656	83	12	,	,	PUNCT
ejpam-4656	83	13	v	v	X
ejpam-4656	83	14	∈	∈	PROPN
ejpam-4656	83	15	v	v	NOUN
ejpam-4656	83	16	(	(	PUNCT
ejpam-4656	83	17	h	h	NOUN
ejpam-4656	83	18	)	)	PUNCT
ejpam-4656	83	19	}	}	PUNCT
ejpam-4656	83	20	.	.	PUNCT
ejpam-4656	84	1	the	the	DET
ejpam-4656	84	2	corona	corona	NOUN
ejpam-4656	84	3	g	g	PROPN
ejpam-4656	84	4	◦	◦	NOUN
ejpam-4656	84	5	h	h	NOUN
ejpam-4656	84	6	is	be	AUX
ejpam-4656	84	7	the	the	DET
ejpam-4656	84	8	graph	graph	NOUN
ejpam-4656	84	9	obtained	obtain	VERB
ejpam-4656	84	10	by	by	ADP
ejpam-4656	84	11	taking	take	VERB
ejpam-4656	84	12	one	one	NUM
ejpam-4656	84	13	copy	copy	NOUN
ejpam-4656	84	14	of	of	ADP
ejpam-4656	84	15	g	g	PROPN
ejpam-4656	84	16	and	and	CCONJ
ejpam-4656	84	17	|v	|v	PROPN
ejpam-4656	84	18	(	(	PUNCT
ejpam-4656	84	19	g)|	g)|	NOUN
ejpam-4656	84	20	copies	copy	NOUN
ejpam-4656	84	21	of	of	ADP
ejpam-4656	84	22	h	h	NOUN
ejpam-4656	84	23	,	,	PUNCT
ejpam-4656	84	24	and	and	CCONJ
ejpam-4656	84	25	then	then	ADV
ejpam-4656	84	26	joining	join	VERB
ejpam-4656	84	27	the	the	DET
ejpam-4656	84	28	ith	ith	PROPN
ejpam-4656	84	29	vertex	vertex	NOUN
ejpam-4656	84	30	of	of	ADP
ejpam-4656	84	31	g	g	NOUN
ejpam-4656	84	32	to	to	ADP
ejpam-4656	84	33	every	every	DET
ejpam-4656	84	34	vertex	vertex	NOUN
ejpam-4656	84	35	of	of	ADP
ejpam-4656	84	36	the	the	DET
ejpam-4656	84	37	ith	ith	PROPN
ejpam-4656	84	38	copy	copy	NOUN
ejpam-4656	84	39	of	of	ADP
ejpam-4656	84	40	h.	h.	PROPN
ejpam-4656	84	41	we	we	PRON
ejpam-4656	84	42	denote	denote	VERB
ejpam-4656	84	43	by	by	ADP
ejpam-4656	84	44	hv	hv	PROPN
ejpam-4656	85	1	the	the	DET
ejpam-4656	85	2	copy	copy	NOUN
ejpam-4656	85	3	of	of	ADP
ejpam-4656	85	4	h	h	NOUN
ejpam-4656	85	5	in	in	ADP
ejpam-4656	85	6	g	g	PROPN
ejpam-4656	85	7	◦	◦	NOUN
ejpam-4656	85	8	h	h	NOUN
ejpam-4656	85	9	corresponding	correspond	VERB
ejpam-4656	85	10	to	to	ADP
ejpam-4656	85	11	the	the	DET
ejpam-4656	85	12	vertex	vertex	NOUN
ejpam-4656	85	13	v	v	ADP
ejpam-4656	85	14	∈	∈	PROPN
ejpam-4656	85	15	g	g	NOUN
ejpam-4656	85	16	and	and	CCONJ
ejpam-4656	85	17	write	write	VERB
ejpam-4656	85	18	v	v	ADP
ejpam-4656	85	19	+	+	CCONJ
ejpam-4656	85	20	hv	hv	NOUN
ejpam-4656	85	21	for	for	ADP
ejpam-4656	85	22	⟨{v}⟩	⟨{v}⟩	NOUN
ejpam-4656	85	23	+	+	X
ejpam-4656	85	24	hv	hv	X
ejpam-4656	85	25	.	.	PUNCT
ejpam-4656	86	1	the	the	DET
ejpam-4656	86	2	lexicographic	lexicographic	ADJ
ejpam-4656	86	3	product	product	NOUN
ejpam-4656	86	4	g[h	g[h	PROPN
ejpam-4656	86	5	]	]	PUNCT
ejpam-4656	86	6	is	be	AUX
ejpam-4656	86	7	the	the	DET
ejpam-4656	86	8	graph	graph	NOUN
ejpam-4656	86	9	with	with	ADP
ejpam-4656	86	10	vertex	vertex	NOUN
ejpam-4656	86	11	set	set	VERB
ejpam-4656	86	12	v	v	NOUN
ejpam-4656	86	13	(	(	PUNCT
ejpam-4656	86	14	g[h	g[h	PROPN
ejpam-4656	86	15	]	]	PUNCT
ejpam-4656	86	16	)	)	PUNCT
ejpam-4656	86	17	=	=	SYM
ejpam-4656	86	18	v	v	X
ejpam-4656	86	19	(	(	PUNCT
ejpam-4656	86	20	g	g	NOUN
ejpam-4656	86	21	)	)	PUNCT
ejpam-4656	86	22	×	×	NOUN
ejpam-4656	86	23	v	v	NOUN
ejpam-4656	86	24	(	(	PUNCT
ejpam-4656	86	25	h	h	NOUN
ejpam-4656	86	26	)	)	PUNCT
ejpam-4656	86	27	and	and	CCONJ
ejpam-4656	86	28	(	(	PUNCT
ejpam-4656	86	29	v	v	NOUN
ejpam-4656	86	30	,	,	PUNCT
ejpam-4656	86	31	a)(u	a)(u	ADJ
ejpam-4656	86	32	,	,	PUNCT
ejpam-4656	86	33	b	b	X
ejpam-4656	86	34	)	)	PUNCT
ejpam-4656	86	35	∈	∈	NOUN
ejpam-4656	86	36	e(g[h	e(g[h	NOUN
ejpam-4656	86	37	]	]	PUNCT
ejpam-4656	86	38	)	)	PUNCT
ejpam-4656	86	39	if	if	SCONJ
ejpam-4656	86	40	and	and	CCONJ
ejpam-4656	86	41	only	only	ADV
ejpam-4656	86	42	if	if	SCONJ
ejpam-4656	86	43	either	either	DET
ejpam-4656	86	44	uv	uv	PROPN
ejpam-4656	86	45	∈	∈	PROPN
ejpam-4656	86	46	e(g	e(g	PROPN
ejpam-4656	86	47	)	)	PUNCT
ejpam-4656	86	48	or	or	CCONJ
ejpam-4656	86	49	u	u	X
ejpam-4656	86	50	=	=	PROPN
ejpam-4656	86	51	v	v	PROPN
ejpam-4656	86	52	and	and	CCONJ
ejpam-4656	86	53	ab	ab	PROPN
ejpam-4656	86	54	∈	∈	PROPN
ejpam-4656	86	55	e(h	e(h	PROPN
ejpam-4656	86	56	)	)	PUNCT
ejpam-4656	86	57	.	.	PUNCT
ejpam-4656	87	1	any	any	DET
ejpam-4656	87	2	non	non	ADJ
ejpam-4656	87	3	-	-	ADJ
ejpam-4656	87	4	empty	empty	ADJ
ejpam-4656	87	5	set	set	NOUN
ejpam-4656	87	6	c	c	NOUN
ejpam-4656	87	7	⊆	⊆	NUM
ejpam-4656	87	8	v	v	NOUN
ejpam-4656	87	9	(	(	PUNCT
ejpam-4656	87	10	g	g	NOUN
ejpam-4656	87	11	)	)	PUNCT
ejpam-4656	87	12	×	×	NOUN
ejpam-4656	87	13	v	v	NOUN
ejpam-4656	87	14	(	(	PUNCT
ejpam-4656	87	15	h	h	NOUN
ejpam-4656	87	16	)	)	PUNCT
ejpam-4656	87	17	can	can	AUX
ejpam-4656	87	18	be	be	AUX
ejpam-4656	87	19	expressed	express	VERB
ejpam-4656	87	20	as	as	ADP
ejpam-4656	87	21	c	c	NOUN
ejpam-4656	87	22	=	=	PUNCT
ejpam-4656	87	23	⋃	⋃	PROPN
ejpam-4656	87	24	x∈s	x∈s	NOUN
ejpam-4656	88	1	[	[	X
ejpam-4656	88	2	{	{	PUNCT
ejpam-4656	88	3	x	x	NOUN
ejpam-4656	88	4	}	}	PUNCT
ejpam-4656	88	5	×	×	PROPN
ejpam-4656	88	6	tx	tx	PROPN
ejpam-4656	88	7	]	]	X
ejpam-4656	88	8	,	,	PUNCT
ejpam-4656	88	9	where	where	SCONJ
ejpam-4656	88	10	s	s	VERB
ejpam-4656	88	11	⊆	⊆	NUM
ejpam-4656	88	12	v	v	NOUN
ejpam-4656	88	13	(	(	PUNCT
ejpam-4656	88	14	g	g	NOUN
ejpam-4656	88	15	)	)	PUNCT
ejpam-4656	88	16	and	and	CCONJ
ejpam-4656	88	17	tx	tx	VERB
ejpam-4656	88	18	⊆	⊆	NUM
ejpam-4656	88	19	v	v	NOUN
ejpam-4656	88	20	(	(	PUNCT
ejpam-4656	88	21	h	h	NOUN
ejpam-4656	88	22	)	)	PUNCT
ejpam-4656	88	23	for	for	ADP
ejpam-4656	88	24	each	each	DET
ejpam-4656	88	25	x	x	PROPN
ejpam-4656	88	26	∈	∈	PROPN
ejpam-4656	88	27	s.	s.	PROPN
ejpam-4656	88	28	specifically	specifically	ADV
ejpam-4656	88	29	,	,	PUNCT
ejpam-4656	88	30	tx	tx	PROPN
ejpam-4656	88	31	=	=	PUNCT
ejpam-4656	88	32	{	{	PUNCT
ejpam-4656	88	33	a	a	DET
ejpam-4656	88	34	∈	∈	PROPN
ejpam-4656	88	35	v	v	ADP
ejpam-4656	88	36	(	(	PUNCT
ejpam-4656	88	37	h	h	NOUN
ejpam-4656	88	38	)	)	PUNCT
ejpam-4656	88	39	:	:	PUNCT
ejpam-4656	88	40	(	(	PUNCT
ejpam-4656	88	41	x	x	X
ejpam-4656	88	42	,	,	PUNCT
ejpam-4656	88	43	a	a	PRON
ejpam-4656	88	44	)	)	PUNCT
ejpam-4656	88	45	∈	∈	PROPN
ejpam-4656	88	46	c	c	NOUN
ejpam-4656	88	47	}	}	PUNCT
ejpam-4656	88	48	for	for	ADP
ejpam-4656	88	49	each	each	DET
ejpam-4656	88	50	x	x	PROPN
ejpam-4656	88	51	∈	∈	PROPN
ejpam-4656	88	52	s.	s.	PROPN
ejpam-4656	88	53	j.	j.	PROPN
ejpam-4656	88	54	hassan	hassan	PROPN
ejpam-4656	88	55	,	,	PUNCT
ejpam-4656	88	56	s.	s.	PROPN
ejpam-4656	88	57	canoy	canoy	PROPN
ejpam-4656	88	58	jr	jr	PROPN
ejpam-4656	88	59	.	.	PROPN
ejpam-4656	88	60	,	,	PUNCT
ejpam-4656	88	61	c.	c.	PROPN
ejpam-4656	88	62	saromines	saromine	VERB
ejpam-4656	88	63	/	/	SYM
ejpam-4656	88	64	eur	eur	PROPN
ejpam-4656	88	65	.	.	PUNCT
ejpam-4656	89	1	j.	j.	PROPN
ejpam-4656	89	2	pure	pure	PROPN
ejpam-4656	89	3	appl	appl	PROPN
ejpam-4656	89	4	.	.	PROPN
ejpam-4656	89	5	math	math	PROPN
ejpam-4656	89	6	,	,	PUNCT
ejpam-4656	89	7	16	16	NUM
ejpam-4656	89	8	(	(	PUNCT
ejpam-4656	89	9	1	1	NUM
ejpam-4656	89	10	)	)	PUNCT
ejpam-4656	89	11	(	(	PUNCT
ejpam-4656	89	12	2023	2023	NUM
ejpam-4656	89	13	)	)	PUNCT
ejpam-4656	89	14	,	,	PUNCT
ejpam-4656	89	15	319	319	NUM
ejpam-4656	89	16	-	-	SYM
ejpam-4656	89	17	335	335	NUM
ejpam-4656	89	18	322	322	NUM
ejpam-4656	89	19	3	3	NUM
ejpam-4656	89	20	.	.	PUNCT
ejpam-4656	89	21	results	result	NOUN
ejpam-4656	89	22	since	since	SCONJ
ejpam-4656	89	23	every	every	DET
ejpam-4656	89	24	convex	convex	NOUN
ejpam-4656	89	25	set	set	VERB
ejpam-4656	89	26	in	in	ADP
ejpam-4656	89	27	a	a	DET
ejpam-4656	89	28	connected	connected	ADJ
ejpam-4656	89	29	graph	graph	NOUN
ejpam-4656	89	30	induces	induce	VERB
ejpam-4656	89	31	a	a	DET
ejpam-4656	89	32	connected	connected	ADJ
ejpam-4656	89	33	graph	graph	NOUN
ejpam-4656	89	34	,	,	PUNCT
ejpam-4656	89	35	every	every	DET
ejpam-4656	89	36	convex	convex	NOUN
ejpam-4656	89	37	hop	hop	NOUN
ejpam-4656	89	38	dominating	dominating	NOUN
ejpam-4656	89	39	set	set	NOUN
ejpam-4656	89	40	is	be	AUX
ejpam-4656	89	41	connected	connect	VERB
ejpam-4656	89	42	hop	hop	NOUN
ejpam-4656	89	43	dominating	dominating	NOUN
ejpam-4656	89	44	.	.	PUNCT
ejpam-4656	90	1	we	we	PRON
ejpam-4656	90	2	formally	formally	ADV
ejpam-4656	90	3	state	state	VERB
ejpam-4656	90	4	a	a	DET
ejpam-4656	90	5	consequence	consequence	NOUN
ejpam-4656	90	6	of	of	ADP
ejpam-4656	90	7	this	this	DET
ejpam-4656	90	8	fact	fact	NOUN
ejpam-4656	90	9	here	here	ADV
ejpam-4656	90	10	.	.	PUNCT
ejpam-4656	91	1	remark	remark	VERB
ejpam-4656	91	2	1	1	NUM
ejpam-4656	91	3	.	.	PUNCT
ejpam-4656	92	1	let	let	VERB
ejpam-4656	92	2	g	g	NOUN
ejpam-4656	92	3	be	be	AUX
ejpam-4656	92	4	any	any	DET
ejpam-4656	92	5	connected	connected	ADJ
ejpam-4656	92	6	graph	graph	NOUN
ejpam-4656	92	7	on	on	ADP
ejpam-4656	92	8	n	n	DET
ejpam-4656	92	9	vertices	vertex	NOUN
ejpam-4656	92	10	.	.	PUNCT
ejpam-4656	93	1	then	then	ADV
ejpam-4656	93	2	γch(g	γch(g	NOUN
ejpam-4656	93	3	)	)	PUNCT
ejpam-4656	93	4	≤	≤	NUM
ejpam-4656	93	5	γconh(g	γconh(g	NOUN
ejpam-4656	93	6	)	)	PUNCT
ejpam-4656	93	7	.	.	PUNCT
ejpam-4656	94	1	remark	remark	PROPN
ejpam-4656	94	2	2	2	NUM
ejpam-4656	94	3	.	.	PUNCT
ejpam-4656	95	1	the	the	DET
ejpam-4656	95	2	bound	bind	VERB
ejpam-4656	95	3	given	give	VERB
ejpam-4656	95	4	in	in	ADP
ejpam-4656	95	5	remark	remark	NOUN
ejpam-4656	95	6	1	1	NUM
ejpam-4656	95	7	is	be	AUX
ejpam-4656	95	8	tight	tight	ADJ
ejpam-4656	95	9	.	.	PUNCT
ejpam-4656	96	1	moreover	moreover	ADV
ejpam-4656	96	2	,	,	PUNCT
ejpam-4656	96	3	strict	strict	ADJ
ejpam-4656	96	4	inequality	inequality	NOUN
ejpam-4656	96	5	can	can	AUX
ejpam-4656	96	6	also	also	ADV
ejpam-4656	96	7	be	be	AUX
ejpam-4656	96	8	attained	attain	VERB
ejpam-4656	96	9	.	.	PUNCT
ejpam-4656	97	1	for	for	ADP
ejpam-4656	97	2	tightness	tightness	NOUN
ejpam-4656	97	3	,	,	PUNCT
ejpam-4656	97	4	consider	consider	VERB
ejpam-4656	97	5	g	g	NOUN
ejpam-4656	97	6	=	=	PUNCT
ejpam-4656	97	7	k1,5	k1,5	PROPN
ejpam-4656	97	8	.	.	PUNCT
ejpam-4656	98	1	then	then	ADV
ejpam-4656	98	2	γch(g	γch(g	NOUN
ejpam-4656	98	3	)	)	PUNCT
ejpam-4656	98	4	=	=	SYM
ejpam-4656	98	5	γconh(g	γconh(g	NOUN
ejpam-4656	98	6	)	)	PUNCT
ejpam-4656	98	7	=	=	SYM
ejpam-4656	99	1	2	2	X
ejpam-4656	99	2	.	.	PUNCT
ejpam-4656	100	1	next	next	ADV
ejpam-4656	100	2	,	,	PUNCT
ejpam-4656	100	3	consider	consider	VERB
ejpam-4656	100	4	the	the	DET
ejpam-4656	100	5	graph	graph	NOUN
ejpam-4656	100	6	g	g	NOUN
ejpam-4656	100	7	in	in	ADP
ejpam-4656	100	8	figure	figure	NOUN
ejpam-4656	100	9	1	1	NUM
ejpam-4656	100	10	.	.	PUNCT
ejpam-4656	101	1	let	let	VERB
ejpam-4656	101	2	c	c	NOUN
ejpam-4656	101	3	=	=	PUNCT
ejpam-4656	101	4	{	{	PUNCT
ejpam-4656	101	5	c	c	NOUN
ejpam-4656	101	6	,	,	PUNCT
ejpam-4656	101	7	d	d	NOUN
ejpam-4656	101	8	,	,	PUNCT
ejpam-4656	101	9	f	f	NOUN
ejpam-4656	101	10	}	}	PUNCT
ejpam-4656	101	11	and	and	CCONJ
ejpam-4656	101	12	c	c	NOUN
ejpam-4656	101	13	′	′	NUM
ejpam-4656	102	1	=	=	PUNCT
ejpam-4656	103	1	{	{	PUNCT
ejpam-4656	103	2	c	c	X
ejpam-4656	103	3	,	,	PUNCT
ejpam-4656	103	4	d	d	NOUN
ejpam-4656	103	5	,	,	PUNCT
ejpam-4656	103	6	e	e	NOUN
ejpam-4656	103	7	,	,	PUNCT
ejpam-4656	103	8	f	f	NOUN
ejpam-4656	103	9	}	}	PUNCT
ejpam-4656	103	10	.	.	PUNCT
ejpam-4656	104	1	then	then	ADV
ejpam-4656	104	2	c	c	PROPN
ejpam-4656	104	3	and	and	CCONJ
ejpam-4656	104	4	c	c	PROPN
ejpam-4656	104	5	′	′	NOUN
ejpam-4656	104	6	are	be	AUX
ejpam-4656	104	7	γch	γch	VERB
ejpam-4656	104	8	-	-	PUNCT
ejpam-4656	104	9	set	set	VERB
ejpam-4656	104	10	and	and	CCONJ
ejpam-4656	104	11	γconh	γconh	NOUN
ejpam-4656	104	12	-	-	PUNCT
ejpam-4656	104	13	set	set	NOUN
ejpam-4656	104	14	in	in	ADP
ejpam-4656	104	15	g	g	NOUN
ejpam-4656	104	16	,	,	PUNCT
ejpam-4656	104	17	respectively	respectively	ADV
ejpam-4656	104	18	.	.	PUNCT
ejpam-4656	105	1	hence	hence	ADV
ejpam-4656	105	2	,	,	PUNCT
ejpam-4656	105	3	γch(g	γch(g	NOUN
ejpam-4656	105	4	)	)	PUNCT
ejpam-4656	105	5	=	=	PUNCT
ejpam-4656	105	6	3	3	NUM
ejpam-4656	105	7	<	<	SYM
ejpam-4656	105	8	4	4	NUM
ejpam-4656	105	9	=	=	SYM
ejpam-4656	105	10	γconh(g	γconh(g	NOUN
ejpam-4656	105	11	)	)	PUNCT
ejpam-4656	105	12	.	.	PUNCT
ejpam-4656	106	1	....................................	....................................	PUNCT
ejpam-4656	106	2	....................................	....................................	PUNCT
ejpam-4656	107	1	....................................	....................................	PUNCT
ejpam-4656	107	2	....................................	....................................	PUNCT
ejpam-4656	108	1	....................................	....................................	PUNCT
ejpam-4656	108	2	....................................	....................................	PUNCT
ejpam-4656	109	1	....................................	....................................	PUNCT
ejpam-4656	109	2	....................................	....................................	PUNCT
ejpam-4656	110	1	...........	...........	PUNCT
ejpam-4656	110	2	..........	..........	PUNCT
ejpam-4656	111	1	..........	..........	PUNCT
ejpam-4656	111	2	..........	..........	PUNCT
ejpam-4656	112	1	..........	..........	PUNCT
ejpam-4656	112	2	..........	..........	PUNCT
ejpam-4656	113	1	..........	..........	PUNCT
ejpam-4656	113	2	..........	..........	PUNCT
ejpam-4656	114	1	..........	..........	PUNCT
ejpam-4656	114	2	..........	..........	PUNCT
ejpam-4656	115	1	..........	..........	PUNCT
ejpam-4656	115	2	..........	..........	PUNCT
ejpam-4656	116	1	..........	..........	PUNCT
ejpam-4656	116	2	..........	..........	PUNCT
ejpam-4656	117	1	..........	..........	PUNCT
ejpam-4656	117	2	..........	..........	PUNCT
ejpam-4656	118	1	..........	..........	PUNCT
ejpam-4656	118	2	..........	..........	PUNCT
ejpam-4656	119	1	..........	..........	PUNCT
ejpam-4656	119	2	..........	..........	PUNCT
ejpam-4656	120	1	..........	..........	PUNCT
ejpam-4656	120	2	..........	..........	PUNCT
ejpam-4656	121	1	..........	..........	PUNCT
ejpam-4656	121	2	......	......	PUNCT
ejpam-4656	122	1	......................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................	PUNCT
ejpam-4656	122	2	........	........	PUNCT
ejpam-4656	122	3	........	........	PUNCT
ejpam-4656	122	4	........	........	PUNCT
ejpam-4656	122	5	........	........	PUNCT
ejpam-4656	122	6	........	........	PUNCT
ejpam-4656	122	7	........	........	PUNCT
ejpam-4656	122	8	........	........	PUNCT
ejpam-4656	122	9	........	........	PUNCT
ejpam-4656	122	10	........	........	PUNCT
ejpam-4656	122	11	........	........	PUNCT
ejpam-4656	122	12	........	........	PUNCT
ejpam-4656	122	13	........	........	PUNCT
ejpam-4656	122	14	........	........	PUNCT
ejpam-4656	122	15	........	........	PUNCT
ejpam-4656	122	16	........	........	PUNCT
ejpam-4656	122	17	........	........	PUNCT
ejpam-4656	122	18	........	........	PUNCT
ejpam-4656	122	19	........	........	PUNCT
ejpam-4656	122	20	........	........	PUNCT
ejpam-4656	122	21	........	........	PUNCT
ejpam-4656	122	22	........	........	PUNCT
ejpam-4656	122	23	........	........	PUNCT
ejpam-4656	123	1	......	......	PUNCT
ejpam-4656	123	2	....................................	....................................	PUNCT
ejpam-4656	124	1	.........................................................................................................................................................................	.........................................................................................................................................................................	INTJ
ejpam-4656	124	2	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-4656	125	1	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-4656	125	2	.........................................................................................................................................................................	.........................................................................................................................................................................	PUNCT
ejpam-4656	125	3	.........	.........	PUNCT
ejpam-4656	125	4	........	........	PUNCT
ejpam-4656	125	5	........	........	PUNCT
ejpam-4656	125	6	........	........	PUNCT
ejpam-4656	125	7	........	........	PUNCT
ejpam-4656	125	8	........	........	PUNCT
ejpam-4656	125	9	........	........	PUNCT
ejpam-4656	125	10	........	........	PUNCT
ejpam-4656	125	11	........	........	PUNCT
ejpam-4656	125	12	........	........	PUNCT
ejpam-4656	125	13	........	........	PUNCT
ejpam-4656	125	14	........	........	PUNCT
ejpam-4656	125	15	........	........	PUNCT
ejpam-4656	125	16	........	........	PUNCT
ejpam-4656	125	17	........	........	PUNCT
ejpam-4656	125	18	........	........	PUNCT
ejpam-4656	125	19	........	........	PUNCT
ejpam-4656	125	20	........	........	PUNCT
ejpam-4656	125	21	........	........	PUNCT
ejpam-4656	125	22	........	........	PUNCT
ejpam-4656	125	23	........	........	PUNCT
ejpam-4656	125	24	........	........	PUNCT
ejpam-4656	125	25	........	........	PUNCT
ejpam-4656	126	1	......	......	PUNCT
ejpam-4656	126	2	....................................	....................................	PUNCT
ejpam-4656	127	1	....................................	....................................	PUNCT
ejpam-4656	128	1	g	g	NOUN
ejpam-4656	128	2	:	:	PUNCT
ejpam-4656	128	3	•	•	NUM
ejpam-4656	128	4	•	•	NUM
ejpam-4656	128	5	•	•	NOUN
ejpam-4656	128	6	•	•	NOUN
ejpam-4656	128	7	c	c	NOUN
ejpam-4656	129	1	d	d	X
ejpam-4656	129	2	f	f	X
ejpam-4656	129	3	e	e	NOUN
ejpam-4656	129	4	figure	figure	NOUN
ejpam-4656	129	5	1	1	NUM
ejpam-4656	129	6	:	:	PUNCT
ejpam-4656	129	7	a	a	DET
ejpam-4656	129	8	graph	graph	NOUN
ejpam-4656	129	9	g	g	NOUN
ejpam-4656	129	10	with	with	ADP
ejpam-4656	129	11	γch(g	γch(g	NOUN
ejpam-4656	129	12	)	)	PUNCT
ejpam-4656	129	13	<	<	X
ejpam-4656	129	14	γconh(g	γconh(g	PROPN
ejpam-4656	129	15	)	)	PUNCT
ejpam-4656	129	16	.	.	PUNCT
ejpam-4656	130	1	theorem	theorem	NOUN
ejpam-4656	130	2	1	1	X
ejpam-4656	130	3	.	.	PUNCT
ejpam-4656	131	1	let	let	VERB
ejpam-4656	131	2	g	g	NOUN
ejpam-4656	131	3	be	be	AUX
ejpam-4656	131	4	any	any	DET
ejpam-4656	131	5	connected	connected	ADJ
ejpam-4656	131	6	graph	graph	NOUN
ejpam-4656	131	7	on	on	ADP
ejpam-4656	131	8	n	n	PRON
ejpam-4656	131	9	≥	≥	NUM
ejpam-4656	131	10	2	2	NUM
ejpam-4656	131	11	vertices	vertex	NOUN
ejpam-4656	131	12	.	.	PUNCT
ejpam-4656	132	1	then	then	ADV
ejpam-4656	132	2	2	2	NUM
ejpam-4656	132	3	≤	≤	NUM
ejpam-4656	132	4	γconh(g	γconh(g	NOUN
ejpam-4656	132	5	)	)	PUNCT
ejpam-4656	132	6	≤	≤	PROPN
ejpam-4656	132	7	n.	n.	NOUN
ejpam-4656	132	8	moreover	moreover	ADV
ejpam-4656	132	9	,	,	PUNCT
ejpam-4656	132	10	γconh(g	γconh(g	INTJ
ejpam-4656	132	11	)	)	PUNCT
ejpam-4656	132	12	=	=	SYM
ejpam-4656	132	13	2	2	NUM
ejpam-4656	133	1	if	if	SCONJ
ejpam-4656	133	2	and	and	CCONJ
ejpam-4656	133	3	only	only	ADV
ejpam-4656	133	4	if	if	SCONJ
ejpam-4656	133	5	γch(g	γch(g	NOUN
ejpam-4656	133	6	)	)	PUNCT
ejpam-4656	133	7	=	=	SYM
ejpam-4656	133	8	2	2	X
ejpam-4656	133	9	.	.	PUNCT
ejpam-4656	133	10	proof	proof	NOUN
ejpam-4656	133	11	.	.	PUNCT
ejpam-4656	134	1	clearly	clearly	ADV
ejpam-4656	134	2	,	,	PUNCT
ejpam-4656	134	3	2	2	NUM
ejpam-4656	134	4	≤	≤	NUM
ejpam-4656	134	5	γconh(g	γconh(g	PROPN
ejpam-4656	134	6	)	)	PUNCT
ejpam-4656	134	7	≤	≤	PROPN
ejpam-4656	134	8	n.	n.	NOUN
ejpam-4656	134	9	suppose	suppose	VERB
ejpam-4656	134	10	γconh(g	γconh(g	NOUN
ejpam-4656	134	11	)	)	PUNCT
ejpam-4656	134	12	=	=	SYM
ejpam-4656	135	1	2	2	X
ejpam-4656	135	2	.	.	PUNCT
ejpam-4656	135	3	by	by	ADP
ejpam-4656	135	4	remark	remark	NOUN
ejpam-4656	135	5	1	1	NUM
ejpam-4656	135	6	,	,	PUNCT
ejpam-4656	135	7	γch(g	γch(g	NOUN
ejpam-4656	135	8	)	)	PUNCT
ejpam-4656	135	9	≤	≤	NUM
ejpam-4656	135	10	γconh(g	γconh(g	NOUN
ejpam-4656	135	11	)	)	PUNCT
ejpam-4656	135	12	=	=	SYM
ejpam-4656	135	13	2	2	X
ejpam-4656	135	14	.	.	PUNCT
ejpam-4656	135	15	since	since	SCONJ
ejpam-4656	135	16	γch(g	γch(g	NOUN
ejpam-4656	135	17	)	)	PUNCT
ejpam-4656	135	18	≥	≥	NOUN
ejpam-4656	135	19	2	2	NUM
ejpam-4656	135	20	for	for	ADP
ejpam-4656	135	21	any	any	DET
ejpam-4656	135	22	connected	connected	ADJ
ejpam-4656	135	23	graph	graph	NOUN
ejpam-4656	135	24	of	of	ADP
ejpam-4656	135	25	order	order	NOUN
ejpam-4656	135	26	n	n	PRON
ejpam-4656	135	27	≥	≥	NOUN
ejpam-4656	135	28	2	2	NUM
ejpam-4656	135	29	,	,	PUNCT
ejpam-4656	135	30	it	it	PRON
ejpam-4656	135	31	follows	follow	VERB
ejpam-4656	135	32	that	that	SCONJ
ejpam-4656	135	33	γch(g	γch(g	NOUN
ejpam-4656	135	34	)	)	PUNCT
ejpam-4656	135	35	=	=	SYM
ejpam-4656	136	1	2	2	X
ejpam-4656	136	2	.	.	PUNCT
ejpam-4656	136	3	conversely	conversely	ADV
ejpam-4656	136	4	,	,	PUNCT
ejpam-4656	136	5	suppose	suppose	VERB
ejpam-4656	136	6	γch(g	γch(g	NOUN
ejpam-4656	136	7	)	)	PUNCT
ejpam-4656	136	8	=	=	SYM
ejpam-4656	136	9	2	2	NUM
ejpam-4656	136	10	,	,	PUNCT
ejpam-4656	136	11	say	say	VERB
ejpam-4656	136	12	,	,	PUNCT
ejpam-4656	136	13	s	s	PART
ejpam-4656	136	14	=	=	PUNCT
ejpam-4656	136	15	{	{	PUNCT
ejpam-4656	136	16	x	x	PROPN
ejpam-4656	136	17	,	,	PUNCT
ejpam-4656	136	18	y	y	PRON
ejpam-4656	136	19	}	}	PUNCT
ejpam-4656	136	20	is	be	AUX
ejpam-4656	136	21	a	a	DET
ejpam-4656	136	22	γch	γch	NOUN
ejpam-4656	136	23	-	-	PUNCT
ejpam-4656	136	24	set	set	NOUN
ejpam-4656	136	25	of	of	ADP
ejpam-4656	136	26	g.	g.	PROPN
ejpam-4656	136	27	since	since	SCONJ
ejpam-4656	136	28	the	the	DET
ejpam-4656	136	29	graph	graph	NOUN
ejpam-4656	136	30	induced	induce	VERB
ejpam-4656	136	31	by	by	ADP
ejpam-4656	136	32	s	s	PROPN
ejpam-4656	136	33	is	be	AUX
ejpam-4656	136	34	k2	k2	ADJ
ejpam-4656	136	35	,	,	PUNCT
ejpam-4656	136	36	s	s	PART
ejpam-4656	136	37	is	be	AUX
ejpam-4656	136	38	convex	convex	NOUN
ejpam-4656	136	39	.	.	PUNCT
ejpam-4656	137	1	thus	thus	ADV
ejpam-4656	137	2	,	,	PUNCT
ejpam-4656	137	3	s	s	VERB
ejpam-4656	137	4	is	be	AUX
ejpam-4656	137	5	a	a	DET
ejpam-4656	137	6	convex	convex	ADJ
ejpam-4656	137	7	hop	hop	NOUN
ejpam-4656	137	8	dominating	dominating	NOUN
ejpam-4656	137	9	set	set	VERB
ejpam-4656	137	10	in	in	ADP
ejpam-4656	137	11	g	g	PROPN
ejpam-4656	137	12	and	and	CCONJ
ejpam-4656	137	13	γconh(g	γconh(g	PROPN
ejpam-4656	137	14	)	)	PUNCT
ejpam-4656	137	15	≤	≤	NUM
ejpam-4656	137	16	2	2	NUM
ejpam-4656	137	17	.	.	PUNCT
ejpam-4656	137	18	by	by	ADP
ejpam-4656	137	19	remark	remark	NOUN
ejpam-4656	137	20	1	1	NUM
ejpam-4656	137	21	,	,	PUNCT
ejpam-4656	137	22	γconh(g	γconh(g	NOUN
ejpam-4656	137	23	)	)	PUNCT
ejpam-4656	137	24	=	=	SYM
ejpam-4656	138	1	2	2	X
ejpam-4656	138	2	.	.	X
ejpam-4656	138	3	theorem	theorem	NOUN
ejpam-4656	138	4	2	2	NUM
ejpam-4656	138	5	.	.	PUNCT
ejpam-4656	139	1	let	let	VERB
ejpam-4656	139	2	a	a	PRON
ejpam-4656	139	3	and	and	CCONJ
ejpam-4656	139	4	b	b	NOUN
ejpam-4656	139	5	be	be	AUX
ejpam-4656	139	6	positive	positive	ADJ
ejpam-4656	139	7	integers	integer	NOUN
ejpam-4656	139	8	such	such	ADJ
ejpam-4656	139	9	that	that	SCONJ
ejpam-4656	139	10	3	3	NUM
ejpam-4656	139	11	≤	≤	NOUN
ejpam-4656	139	12	a	a	DET
ejpam-4656	139	13	≤	≤	PROPN
ejpam-4656	139	14	b.	b.	NOUN
ejpam-4656	140	1	then	then	ADV
ejpam-4656	140	2	there	there	PRON
ejpam-4656	140	3	exists	exist	VERB
ejpam-4656	140	4	a	a	DET
ejpam-4656	140	5	connected	connected	ADJ
ejpam-4656	140	6	graph	graph	NOUN
ejpam-4656	140	7	g	g	ADP
ejpam-4656	140	8	such	such	ADJ
ejpam-4656	140	9	that	that	DET
ejpam-4656	140	10	γch(g	γch(g	NOUN
ejpam-4656	140	11	)	)	PUNCT
ejpam-4656	140	12	=	=	SYM
ejpam-4656	140	13	a	a	PRON
ejpam-4656	140	14	and	and	CCONJ
ejpam-4656	140	15	γconh(g	γconh(g	NOUN
ejpam-4656	140	16	)	)	PUNCT
ejpam-4656	140	17	=	=	SYM
ejpam-4656	140	18	b.	b.	NOUN
ejpam-4656	140	19	proof	proof	NOUN
ejpam-4656	140	20	.	.	PUNCT
ejpam-4656	141	1	for	for	ADP
ejpam-4656	141	2	a	a	DET
ejpam-4656	141	3	=	=	SYM
ejpam-4656	141	4	b	b	NOUN
ejpam-4656	141	5	,	,	PUNCT
ejpam-4656	141	6	consider	consider	VERB
ejpam-4656	141	7	g	g	PROPN
ejpam-4656	141	8	=	=	SYM
ejpam-4656	141	9	ka	ka	PROPN
ejpam-4656	141	10	.	.	PUNCT
ejpam-4656	142	1	then	then	ADV
ejpam-4656	142	2	γch(g	γch(g	NOUN
ejpam-4656	142	3	)	)	PUNCT
ejpam-4656	142	4	=	=	PUNCT
ejpam-4656	143	1	a	a	DET
ejpam-4656	143	2	=	=	NOUN
ejpam-4656	143	3	γconh(g	γconh(g	NOUN
ejpam-4656	143	4	)	)	PUNCT
ejpam-4656	143	5	.	.	PUNCT
ejpam-4656	143	6	suppose	suppose	VERB
ejpam-4656	143	7	a	a	DET
ejpam-4656	143	8	<	<	X
ejpam-4656	143	9	b.	b.	NOUN
ejpam-4656	143	10	consider	consider	VERB
ejpam-4656	143	11	the	the	DET
ejpam-4656	143	12	following	follow	VERB
ejpam-4656	143	13	two	two	NUM
ejpam-4656	143	14	cases	case	NOUN
ejpam-4656	143	15	:	:	PUNCT
ejpam-4656	143	16	j.	j.	PROPN
ejpam-4656	143	17	hassan	hassan	PROPN
ejpam-4656	143	18	,	,	PUNCT
ejpam-4656	143	19	s.	s.	PROPN
ejpam-4656	143	20	canoy	canoy	PROPN
ejpam-4656	143	21	jr	jr	PROPN
ejpam-4656	143	22	.	.	PROPN
ejpam-4656	143	23	,	,	PUNCT
ejpam-4656	143	24	c.	c.	PROPN
ejpam-4656	143	25	saromines	saromine	VERB
ejpam-4656	143	26	/	/	SYM
ejpam-4656	143	27	eur	eur	PROPN
ejpam-4656	143	28	.	.	PUNCT
ejpam-4656	144	1	j.	j.	PROPN
ejpam-4656	144	2	pure	pure	PROPN
ejpam-4656	144	3	appl	appl	PROPN
ejpam-4656	144	4	.	.	PROPN
ejpam-4656	144	5	math	math	PROPN
ejpam-4656	144	6	,	,	PUNCT
ejpam-4656	144	7	16	16	NUM
ejpam-4656	144	8	(	(	PUNCT
ejpam-4656	144	9	1	1	NUM
ejpam-4656	144	10	)	)	PUNCT
ejpam-4656	144	11	(	(	PUNCT
ejpam-4656	144	12	2023	2023	NUM
ejpam-4656	144	13	)	)	PUNCT
ejpam-4656	144	14	,	,	PUNCT
ejpam-4656	144	15	319	319	NUM
ejpam-4656	144	16	-	-	SYM
ejpam-4656	144	17	335	335	NUM
ejpam-4656	144	18	323	323	NUM
ejpam-4656	144	19	case	case	NOUN
ejpam-4656	144	20	1	1	NUM
ejpam-4656	144	21	:	:	PUNCT
ejpam-4656	144	22	a	a	PRON
ejpam-4656	144	23	=	=	ADJ
ejpam-4656	144	24	3	3	X
ejpam-4656	144	25	.	.	PUNCT
ejpam-4656	145	1	let	let	VERB
ejpam-4656	145	2	m	m	VERB
ejpam-4656	145	3	=	=	VERB
ejpam-4656	146	1	b	b	X
ejpam-4656	146	2	−	−	PROPN
ejpam-4656	146	3	a	a	PRON
ejpam-4656	147	1	and	and	CCONJ
ejpam-4656	147	2	consider	consider	VERB
ejpam-4656	147	3	the	the	DET
ejpam-4656	147	4	graph	graph	NOUN
ejpam-4656	147	5	g	g	NOUN
ejpam-4656	147	6	in	in	ADP
ejpam-4656	147	7	figure	figure	NOUN
ejpam-4656	147	8	2	2	NUM
ejpam-4656	147	9	.	.	PUNCT
ejpam-4656	148	1	let	let	VERB
ejpam-4656	148	2	c	c	NOUN
ejpam-4656	148	3	=	=	PUNCT
ejpam-4656	148	4	{	{	PUNCT
ejpam-4656	148	5	x1	x1	PROPN
ejpam-4656	148	6	,	,	PUNCT
ejpam-4656	148	7	x2	x2	PROPN
ejpam-4656	148	8	,	,	PUNCT
ejpam-4656	148	9	x3	x3	ADJ
ejpam-4656	148	10	}	}	PUNCT
ejpam-4656	148	11	and	and	CCONJ
ejpam-4656	148	12	c	c	NOUN
ejpam-4656	148	13	′	′	NUM
ejpam-4656	149	1	=	=	PUNCT
ejpam-4656	149	2	{	{	PUNCT
ejpam-4656	149	3	x1	x1	PROPN
ejpam-4656	149	4	,	,	PUNCT
ejpam-4656	149	5	x2	x2	PROPN
ejpam-4656	149	6	,	,	PUNCT
ejpam-4656	149	7	x3	x3	ADJ
ejpam-4656	149	8	,	,	PUNCT
ejpam-4656	149	9	y1	y1	NOUN
ejpam-4656	149	10	,	,	PUNCT
ejpam-4656	149	11	y2	y2	PROPN
ejpam-4656	149	12	,	,	PUNCT
ejpam-4656	149	13	.	.	PUNCT
ejpam-4656	149	14	.	.	PUNCT
ejpam-4656	150	1	.	.	PUNCT
ejpam-4656	151	1	,	,	PUNCT
ejpam-4656	151	2	ym	ym	PROPN
ejpam-4656	151	3	}	}	PUNCT
ejpam-4656	151	4	.	.	PUNCT
ejpam-4656	152	1	then	then	ADV
ejpam-4656	152	2	c	c	PROPN
ejpam-4656	152	3	and	and	CCONJ
ejpam-4656	152	4	c	c	PROPN
ejpam-4656	152	5	′	′	NOUN
ejpam-4656	152	6	are	be	AUX
ejpam-4656	152	7	γch	γch	VERB
ejpam-4656	152	8	-	-	PUNCT
ejpam-4656	152	9	set	set	VERB
ejpam-4656	152	10	and	and	CCONJ
ejpam-4656	152	11	γconh	γconh	NOUN
ejpam-4656	152	12	-	-	PUNCT
ejpam-4656	152	13	set	set	NOUN
ejpam-4656	152	14	in	in	ADP
ejpam-4656	152	15	g	g	NOUN
ejpam-4656	152	16	,	,	PUNCT
ejpam-4656	152	17	respectively	respectively	ADV
ejpam-4656	152	18	.	.	PUNCT
ejpam-4656	153	1	thus	thus	ADV
ejpam-4656	153	2	,	,	PUNCT
ejpam-4656	153	3	γch(g	γch(g	NOUN
ejpam-4656	153	4	)	)	PUNCT
ejpam-4656	153	5	=	=	SYM
ejpam-4656	154	1	a	a	PRON
ejpam-4656	154	2	and	and	CCONJ
ejpam-4656	154	3	γconh(g	γconh(g	NOUN
ejpam-4656	154	4	)	)	PUNCT
ejpam-4656	154	5	=	=	PUNCT
ejpam-4656	154	6	a+m	a+m	NUM
ejpam-4656	155	1	=	=	SYM
ejpam-4656	155	2	b.	b.	PROPN
ejpam-4656	155	3	....................................	....................................	PUNCT
ejpam-4656	155	4	....................................	....................................	PUNCT
ejpam-4656	156	1	....................................	....................................	PUNCT
ejpam-4656	156	2	....................................	....................................	PUNCT
ejpam-4656	157	1	....................................	....................................	PUNCT
ejpam-4656	157	2	....................................	....................................	PUNCT
ejpam-4656	158	1	....................................	....................................	PUNCT
ejpam-4656	158	2	....................................	....................................	PUNCT
ejpam-4656	159	1	....................................	....................................	PUNCT
ejpam-4656	159	2	............................................................................	............................................................................	PUNCT
ejpam-4656	159	3	............................................................................	............................................................................	PUNCT
ejpam-4656	159	4	............................................................................	............................................................................	PUNCT
ejpam-4656	159	5	............................................................................	............................................................................	PUNCT
ejpam-4656	159	6	............................................................................	............................................................................	PUNCT
ejpam-4656	159	7	............................................................................	............................................................................	PUNCT
ejpam-4656	160	1	....................................	....................................	PUNCT
ejpam-4656	160	2	....................................	....................................	PUNCT
ejpam-4656	161	1	....................................	....................................	PUNCT
ejpam-4656	161	2	.........	.........	PUNCT
ejpam-4656	161	3	........	........	PUNCT
ejpam-4656	161	4	........	........	PUNCT
ejpam-4656	161	5	........	........	PUNCT
ejpam-4656	161	6	........	........	PUNCT
ejpam-4656	161	7	........	........	PUNCT
ejpam-4656	161	8	........	........	PUNCT
ejpam-4656	161	9	........	........	PUNCT
ejpam-4656	161	10	........	........	PUNCT
ejpam-4656	162	1	..................................................................................................................	..................................................................................................................	PUNCT
ejpam-4656	162	2	......................................................................................................................................................................................	......................................................................................................................................................................................	PUNCT
ejpam-4656	162	3	.............................................................................................................................................................................................................................................................................................................................	.............................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4656	162	4	.........	.........	PUNCT
ejpam-4656	162	5	........	........	PUNCT
ejpam-4656	162	6	........	........	PUNCT
ejpam-4656	162	7	........	........	PUNCT
ejpam-4656	162	8	........	........	PUNCT
ejpam-4656	162	9	........	........	PUNCT
ejpam-4656	162	10	........	........	PUNCT
ejpam-4656	162	11	........	........	PUNCT
ejpam-4656	162	12	........	........	PUNCT
ejpam-4656	162	13	...	...	PUNCT
ejpam-4656	162	14	............	............	PUNCT
ejpam-4656	162	15	...........	...........	PUNCT
ejpam-4656	162	16	...........	...........	PUNCT
ejpam-4656	162	17	...........	...........	PUNCT
ejpam-4656	162	18	...........	...........	PUNCT
ejpam-4656	162	19	...........	...........	PUNCT
ejpam-4656	162	20	...........	...........	PUNCT
ejpam-4656	162	21	...........	...........	PUNCT
ejpam-4656	162	22	...........	...........	PUNCT
ejpam-4656	162	23	...........	...........	PUNCT
ejpam-4656	162	24	...................	...................	PUNCT
ejpam-4656	162	25	..................	..................	PUNCT
ejpam-4656	162	26	..................	..................	PUNCT
ejpam-4656	163	1	..................	..................	PUNCT
ejpam-4656	163	2	..................	..................	PUNCT
ejpam-4656	164	1	..................	..................	PUNCT
ejpam-4656	164	2	..................	..................	PUNCT
ejpam-4656	165	1	..................	..................	PUNCT
ejpam-4656	165	2	..................	..................	PUNCT
ejpam-4656	165	3	..................	..................	PUNCT
ejpam-4656	165	4	.	.	PUNCT
ejpam-4656	165	5	...............................	...............................	PUNCT
ejpam-4656	165	6	..............................	..............................	PUNCT
ejpam-4656	165	7	..............................	..............................	PUNCT
ejpam-4656	165	8	..............................	..............................	PUNCT
ejpam-4656	165	9	..............................	..............................	PUNCT
ejpam-4656	165	10	..............................	..............................	PUNCT
ejpam-4656	165	11	..............................	..............................	PUNCT
ejpam-4656	165	12	..............................	..............................	PUNCT
ejpam-4656	165	13	..............................	..............................	PUNCT
ejpam-4656	165	14	..............................	..............................	PUNCT
ejpam-4656	166	1	................	................	PUNCT
ejpam-4656	167	1	x1	x1	NUM
ejpam-4656	168	1	x2	x2	NUM
ejpam-4656	168	2	x3	x3	ADJ
ejpam-4656	168	3	y1	y1	NOUN
ejpam-4656	168	4	y2	y2	INTJ
ejpam-4656	168	5	.	.	PUNCT
ejpam-4656	168	6	.	.	PUNCT
ejpam-4656	168	7	.	.	PUNCT
ejpam-4656	169	1	ym	ym	INTJ
ejpam-4656	170	1	g	g	NOUN
ejpam-4656	170	2	:	:	PUNCT
ejpam-4656	170	3	•	•	NUM
ejpam-4656	170	4	•	•	NUM
ejpam-4656	170	5	•	•	NUM
ejpam-4656	170	6	•	•	NUM
ejpam-4656	170	7	•	•	NOUN
ejpam-4656	170	8	•	•	NUM
ejpam-4656	170	9	figure	figure	NOUN
ejpam-4656	170	10	2	2	NUM
ejpam-4656	170	11	:	:	PUNCT
ejpam-4656	170	12	a	a	DET
ejpam-4656	170	13	graph	graph	NOUN
ejpam-4656	170	14	g	g	NOUN
ejpam-4656	170	15	with	with	ADP
ejpam-4656	170	16	γch(g	γch(g	NOUN
ejpam-4656	170	17	)	)	PUNCT
ejpam-4656	170	18	<	<	X
ejpam-4656	170	19	γconh(g	γconh(g	PROPN
ejpam-4656	170	20	)	)	PUNCT
ejpam-4656	170	21	.	.	PUNCT
ejpam-4656	171	1	case	case	NOUN
ejpam-4656	171	2	2	2	NUM
ejpam-4656	171	3	:	:	PUNCT
ejpam-4656	171	4	a	a	DET
ejpam-4656	171	5	≥	≥	NOUN
ejpam-4656	171	6	4	4	NUM
ejpam-4656	171	7	.	.	PUNCT
ejpam-4656	172	1	let	let	VERB
ejpam-4656	172	2	m	m	VERB
ejpam-4656	172	3	=	=	VERB
ejpam-4656	173	1	b	b	X
ejpam-4656	173	2	−	−	PROPN
ejpam-4656	173	3	a	a	PRON
ejpam-4656	174	1	and	and	CCONJ
ejpam-4656	174	2	consider	consider	VERB
ejpam-4656	174	3	the	the	DET
ejpam-4656	174	4	graph	graph	NOUN
ejpam-4656	174	5	g′	g′	NOUN
ejpam-4656	174	6	in	in	ADP
ejpam-4656	174	7	figure	figure	NOUN
ejpam-4656	174	8	3	3	NUM
ejpam-4656	174	9	.	.	PUNCT
ejpam-4656	175	1	let	let	VERB
ejpam-4656	175	2	d	d	NOUN
ejpam-4656	175	3	=	=	PRON
ejpam-4656	175	4	{	{	PUNCT
ejpam-4656	175	5	x1	x1	PROPN
ejpam-4656	175	6	,	,	PUNCT
ejpam-4656	175	7	x2	x2	PROPN
ejpam-4656	175	8	,	,	PUNCT
ejpam-4656	175	9	.	.	PUNCT
ejpam-4656	175	10	.	.	PUNCT
ejpam-4656	176	1	.	.	PUNCT
ejpam-4656	177	1	,	,	PUNCT
ejpam-4656	177	2	xa	xa	PROPN
ejpam-4656	177	3	}	}	PUNCT
ejpam-4656	177	4	and	and	CCONJ
ejpam-4656	177	5	d′	d′	NUM
ejpam-4656	177	6	=	=	SYM
ejpam-4656	177	7	{	{	PUNCT
ejpam-4656	177	8	x1	x1	PROPN
ejpam-4656	177	9	,	,	PUNCT
ejpam-4656	177	10	x2	x2	PROPN
ejpam-4656	177	11	,	,	PUNCT
ejpam-4656	177	12	.	.	PUNCT
ejpam-4656	177	13	.	.	PUNCT
ejpam-4656	177	14	.	.	PUNCT
ejpam-4656	178	1	,	,	PUNCT
ejpam-4656	178	2	xa	xa	PROPN
ejpam-4656	178	3	,	,	PUNCT
ejpam-4656	178	4	y1	y1	PROPN
ejpam-4656	178	5	,	,	PUNCT
ejpam-4656	178	6	y2	y2	PROPN
ejpam-4656	178	7	,	,	PUNCT
ejpam-4656	178	8	.	.	PUNCT
ejpam-4656	178	9	.	.	PUNCT
ejpam-4656	178	10	.	.	PUNCT
ejpam-4656	179	1	,	,	PUNCT
ejpam-4656	179	2	ym	ym	PROPN
ejpam-4656	179	3	}	}	PUNCT
ejpam-4656	179	4	.	.	PUNCT
ejpam-4656	180	1	then	then	ADV
ejpam-4656	180	2	d	d	PROPN
ejpam-4656	180	3	and	and	CCONJ
ejpam-4656	180	4	d′	d′	PRON
ejpam-4656	180	5	are	be	AUX
ejpam-4656	180	6	γch	γch	VERB
ejpam-4656	180	7	-	-	PUNCT
ejpam-4656	180	8	set	set	VERB
ejpam-4656	180	9	and	and	CCONJ
ejpam-4656	180	10	γconh	γconh	NOUN
ejpam-4656	180	11	-	-	PUNCT
ejpam-4656	180	12	set	set	NOUN
ejpam-4656	180	13	in	in	ADP
ejpam-4656	180	14	g′	g′	NOUN
ejpam-4656	180	15	,	,	PUNCT
ejpam-4656	180	16	respectively	respectively	ADV
ejpam-4656	180	17	.	.	PUNCT
ejpam-4656	181	1	thus	thus	ADV
ejpam-4656	181	2	,	,	PUNCT
ejpam-4656	181	3	γch(g	γch(g	NOUN
ejpam-4656	181	4	′	′	NUM
ejpam-4656	181	5	)	)	PUNCT
ejpam-4656	181	6	=	=	PUNCT
ejpam-4656	181	7	a	a	PROPN
ejpam-4656	181	8	and	and	CCONJ
ejpam-4656	181	9	γconh(g	γconh(g	NOUN
ejpam-4656	181	10	′	′	NUM
ejpam-4656	181	11	)	)	PUNCT
ejpam-4656	181	12	=	=	PUNCT
ejpam-4656	182	1	a+m	a+m	NUM
ejpam-4656	182	2	=	=	SYM
ejpam-4656	182	3	b.	b.	PROPN
ejpam-4656	182	4	....................................	....................................	PUNCT
ejpam-4656	182	5	....................................	....................................	PUNCT
ejpam-4656	182	6	....................................	....................................	PUNCT
ejpam-4656	182	7	....................................	....................................	PUNCT
ejpam-4656	182	8	....................................	....................................	PUNCT
ejpam-4656	182	9	....................................	....................................	PUNCT
ejpam-4656	182	10	....................................	....................................	PUNCT
ejpam-4656	182	11	....................................	....................................	PUNCT
ejpam-4656	182	12	....................................	....................................	PUNCT
ejpam-4656	182	13	.........	.........	PUNCT
ejpam-4656	182	14	........	........	PUNCT
ejpam-4656	182	15	........	........	PUNCT
ejpam-4656	182	16	........	........	PUNCT
ejpam-4656	182	17	........	........	PUNCT
ejpam-4656	182	18	........	........	PUNCT
ejpam-4656	182	19	........	........	PUNCT
ejpam-4656	182	20	........	........	PUNCT
ejpam-4656	182	21	........	........	PUNCT
ejpam-4656	182	22	...	...	PUNCT
ejpam-4656	182	23	.........	.........	PUNCT
ejpam-4656	182	24	........	........	PUNCT
ejpam-4656	182	25	........	........	PUNCT
ejpam-4656	182	26	........	........	PUNCT
ejpam-4656	182	27	........	........	PUNCT
ejpam-4656	182	28	........	........	PUNCT
ejpam-4656	182	29	........	........	PUNCT
ejpam-4656	182	30	........	........	PUNCT
ejpam-4656	182	31	........	........	PUNCT
ejpam-4656	182	32	...	...	PUNCT
ejpam-4656	182	33	.........	.........	PUNCT
ejpam-4656	182	34	........	........	PUNCT
ejpam-4656	182	35	........	........	PUNCT
ejpam-4656	182	36	........	........	PUNCT
ejpam-4656	182	37	........	........	PUNCT
ejpam-4656	182	38	........	........	PUNCT
ejpam-4656	182	39	........	........	PUNCT
ejpam-4656	182	40	........	........	PUNCT
ejpam-4656	182	41	........	........	PUNCT
ejpam-4656	182	42	...	...	PUNCT
ejpam-4656	182	43	.........	.........	PUNCT
ejpam-4656	182	44	........	........	PUNCT
ejpam-4656	182	45	........	........	PUNCT
ejpam-4656	182	46	........	........	PUNCT
ejpam-4656	182	47	........	........	PUNCT
ejpam-4656	182	48	........	........	PUNCT
ejpam-4656	182	49	........	........	PUNCT
ejpam-4656	182	50	........	........	PUNCT
ejpam-4656	182	51	........	........	PUNCT
ejpam-4656	182	52	...	...	PUNCT
ejpam-4656	182	53	.........	.........	PUNCT
ejpam-4656	182	54	........	........	PUNCT
ejpam-4656	182	55	........	........	PUNCT
ejpam-4656	182	56	........	........	PUNCT
ejpam-4656	182	57	........	........	PUNCT
ejpam-4656	182	58	........	........	PUNCT
ejpam-4656	182	59	........	........	PUNCT
ejpam-4656	182	60	........	........	PUNCT
ejpam-4656	182	61	........	........	PUNCT
ejpam-4656	182	62	...	...	PUNCT
ejpam-4656	182	63	.........	.........	PUNCT
ejpam-4656	182	64	........	........	PUNCT
ejpam-4656	182	65	........	........	PUNCT
ejpam-4656	182	66	........	........	PUNCT
ejpam-4656	182	67	........	........	PUNCT
ejpam-4656	182	68	........	........	PUNCT
ejpam-4656	182	69	........	........	PUNCT
ejpam-4656	182	70	........	........	PUNCT
ejpam-4656	182	71	........	........	PUNCT
ejpam-4656	182	72	...	...	PUNCT
ejpam-4656	182	73	............................................................................	............................................................................	PUNCT
ejpam-4656	182	74	............................................................................	............................................................................	PUNCT
ejpam-4656	182	75	.	.	PUNCT
ejpam-4656	182	76	.	.	PUNCT
ejpam-4656	182	77	.	.	PUNCT
ejpam-4656	182	78	.	.	PUNCT
ejpam-4656	182	79	.	.	PUNCT
ejpam-4656	182	80	.	.	PUNCT
ejpam-4656	182	81	.	.	PUNCT
ejpam-4656	182	82	.	.	PUNCT
ejpam-4656	182	83	.	.	PUNCT
ejpam-4656	183	1	....................................	....................................	PUNCT
ejpam-4656	183	2	....................................	....................................	PUNCT
ejpam-4656	184	1	....................................	....................................	PUNCT
ejpam-4656	184	2	....................................	....................................	PUNCT
ejpam-4656	185	1	....................................	....................................	PUNCT
ejpam-4656	185	2	....................................	....................................	PUNCT
ejpam-4656	186	1	.........	.........	PUNCT
ejpam-4656	186	2	........	........	PUNCT
ejpam-4656	186	3	........	........	PUNCT
ejpam-4656	186	4	........	........	PUNCT
ejpam-4656	186	5	........	........	PUNCT
ejpam-4656	186	6	........	........	PUNCT
ejpam-4656	186	7	........	........	PUNCT
ejpam-4656	186	8	........	........	PUNCT
ejpam-4656	186	9	........	........	PUNCT
ejpam-4656	186	10	...	...	PUNCT
ejpam-4656	186	11	.........	.........	PUNCT
ejpam-4656	187	1	........	........	PUNCT
ejpam-4656	187	2	........	........	PUNCT
ejpam-4656	187	3	........	........	PUNCT
ejpam-4656	187	4	........	........	PUNCT
ejpam-4656	187	5	........	........	PUNCT
ejpam-4656	187	6	........	........	PUNCT
ejpam-4656	187	7	........	........	PUNCT
ejpam-4656	187	8	........	........	PUNCT
ejpam-4656	187	9	...	...	PUNCT
ejpam-4656	187	10	.........	.........	PUNCT
ejpam-4656	187	11	........	........	PUNCT
ejpam-4656	187	12	........	........	PUNCT
ejpam-4656	187	13	........	........	PUNCT
ejpam-4656	187	14	........	........	PUNCT
ejpam-4656	187	15	........	........	PUNCT
ejpam-4656	187	16	........	........	PUNCT
ejpam-4656	187	17	........	........	PUNCT
ejpam-4656	187	18	........	........	PUNCT
ejpam-4656	187	19	...	...	PUNCT
ejpam-4656	187	20	.........	.........	PUNCT
ejpam-4656	187	21	........	........	PUNCT
ejpam-4656	187	22	........	........	PUNCT
ejpam-4656	187	23	........	........	PUNCT
ejpam-4656	187	24	........	........	PUNCT
ejpam-4656	187	25	........	........	PUNCT
ejpam-4656	187	26	........	........	PUNCT
ejpam-4656	187	27	........	........	PUNCT
ejpam-4656	187	28	........	........	PUNCT
ejpam-4656	187	29	...	...	PUNCT
ejpam-4656	187	30	............................................................................	............................................................................	PUNCT
ejpam-4656	188	1	....................................	....................................	PUNCT
ejpam-4656	188	2	....................................	....................................	PUNCT
ejpam-4656	189	1	....................................	....................................	PUNCT
ejpam-4656	189	2	..............	..............	PUNCT
ejpam-4656	189	3	.............	.............	PUNCT
ejpam-4656	189	4	.............	.............	PUNCT
ejpam-4656	189	5	.............	.............	PUNCT
ejpam-4656	189	6	.............	.............	PUNCT
ejpam-4656	189	7	.............	.............	PUNCT
ejpam-4656	189	8	.............	.............	PUNCT
ejpam-4656	189	9	.............	.............	PUNCT
ejpam-4656	189	10	.............	.............	PUNCT
ejpam-4656	189	11	.............	.............	PUNCT
ejpam-4656	189	12	.............	.............	PUNCT
ejpam-4656	189	13	.............	.............	PUNCT
ejpam-4656	189	14	.............	.............	PUNCT
ejpam-4656	189	15	.............	.............	PUNCT
ejpam-4656	189	16	.............	.............	PUNCT
ejpam-4656	189	17	.............	.............	PUNCT
ejpam-4656	190	1	.....	.....	PUNCT
ejpam-4656	190	2	...................	...................	PUNCT
ejpam-4656	190	3	..................	..................	PUNCT
ejpam-4656	190	4	..................	..................	PUNCT
ejpam-4656	190	5	..................	..................	PUNCT
ejpam-4656	191	1	..................	..................	PUNCT
ejpam-4656	191	2	..................	..................	PUNCT
ejpam-4656	192	1	..................	..................	PUNCT
ejpam-4656	192	2	..................	..................	PUNCT
ejpam-4656	193	1	..................	..................	PUNCT
ejpam-4656	193	2	..................	..................	PUNCT
ejpam-4656	193	3	.	.	PUNCT
ejpam-4656	193	4	.................................	.................................	PUNCT
ejpam-4656	194	1	................................	................................	PUNCT
ejpam-4656	194	2	................................	................................	PUNCT
ejpam-4656	194	3	................................	................................	PUNCT
ejpam-4656	194	4	................................	................................	PUNCT
ejpam-4656	195	1	......	......	PUNCT
ejpam-4656	195	2	....................................	....................................	PUNCT
ejpam-4656	196	1	....................................	....................................	PUNCT
ejpam-4656	196	2	...........................................................................................................................................................................	...........................................................................................................................................................................	PUNCT
ejpam-4656	197	1	.....................................................................................................................................................................................................	.....................................................................................................................................................................................................	PUNCT
ejpam-4656	197	2	....................................	....................................	PUNCT
ejpam-4656	198	1	......................................................................................................................................................................................................................	......................................................................................................................................................................................................................	PUNCT
ejpam-4656	198	2	......................................................................................................................................................................................	......................................................................................................................................................................................	PUNCT
ejpam-4656	199	1	.......................................................................................................................................................................	.......................................................................................................................................................................	PUNCT
ejpam-4656	199	2	..........................	..........................	PUNCT
ejpam-4656	200	1	.........................	.........................	PUNCT
ejpam-4656	200	2	.........................	.........................	PUNCT
ejpam-4656	200	3	.........................	.........................	PUNCT
ejpam-4656	200	4	.........................	.........................	PUNCT
ejpam-4656	200	5	.........................	.........................	PUNCT
ejpam-4656	200	6	....................	....................	PUNCT
ejpam-4656	200	7	...............	...............	PUNCT
ejpam-4656	200	8	..............	..............	PUNCT
ejpam-4656	201	1	..............	..............	PUNCT
ejpam-4656	201	2	..............	..............	PUNCT
ejpam-4656	202	1	..............	..............	PUNCT
ejpam-4656	202	2	..............	..............	PUNCT
ejpam-4656	203	1	..............	..............	PUNCT
ejpam-4656	203	2	..............	..............	PUNCT
ejpam-4656	204	1	..............	..............	PUNCT
ejpam-4656	204	2	..............	..............	PUNCT
ejpam-4656	205	1	..............	..............	PUNCT
ejpam-4656	205	2	..............	..............	PUNCT
ejpam-4656	206	1	..............	..............	PUNCT
ejpam-4656	206	2	..............	..............	PUNCT
ejpam-4656	207	1	....................................	....................................	PUNCT
ejpam-4656	207	2	................................................................................................................	................................................................................................................	PUNCT
ejpam-4656	207	3	............................................................................	............................................................................	PUNCT
ejpam-4656	207	4	.........	.........	PUNCT
ejpam-4656	207	5	........	........	PUNCT
ejpam-4656	207	6	........	........	PUNCT
ejpam-4656	207	7	........	........	PUNCT
ejpam-4656	207	8	........	........	PUNCT
ejpam-4656	208	1	......	......	PUNCT
ejpam-4656	208	2	....................................	....................................	PUNCT
ejpam-4656	209	1	.........	.........	PUNCT
ejpam-4656	209	2	........	........	PUNCT
ejpam-4656	209	3	........	........	PUNCT
ejpam-4656	209	4	........	........	PUNCT
ejpam-4656	210	1	....................................	....................................	PUNCT
ejpam-4656	210	2	....................................	....................................	PUNCT
ejpam-4656	210	3	.........	.........	PUNCT
ejpam-4656	210	4	........	........	PUNCT
ejpam-4656	210	5	........	........	PUNCT
ejpam-4656	210	6	........	........	PUNCT
ejpam-4656	211	1	........	........	PUNCT
ejpam-4656	211	2	......	......	PUNCT
ejpam-4656	212	1	...	...	PUNCT
ejpam-4656	213	1	g	g	NOUN
ejpam-4656	213	2	′	′	NUM
ejpam-4656	213	3	:	:	PUNCT
ejpam-4656	214	1	x1	x1	PROPN
ejpam-4656	214	2	x2	x2	NOUN
ejpam-4656	214	3	x3	x3	PROPN
ejpam-4656	215	1	xa−3	xa−3	PROPN
ejpam-4656	215	2	xa−2	xa−2	PROPN
ejpam-4656	215	3	xa−1	xa−1	PROPN
ejpam-4656	216	1	y1	y1	PROPN
ejpam-4656	216	2	y2	y2	PROPN
ejpam-4656	216	3	y3	y3	NOUN
ejpam-4656	216	4	ym	ym	PROPN
ejpam-4656	216	5	xa	xa	PROPN
ejpam-4656	217	1	•	•	NUM
ejpam-4656	217	2	•	•	NUM
ejpam-4656	217	3	•	•	NUM
ejpam-4656	217	4	•	•	NUM
ejpam-4656	217	5	•	•	NUM
ejpam-4656	217	6	•	•	NUM
ejpam-4656	217	7	•	•	NUM
ejpam-4656	217	8	•	•	NUM
ejpam-4656	217	9	•	•	NUM
ejpam-4656	217	10	•	•	NOUN
ejpam-4656	217	11	•	•	NUM
ejpam-4656	217	12	figure	figure	NOUN
ejpam-4656	217	13	3	3	NUM
ejpam-4656	217	14	:	:	PUNCT
ejpam-4656	217	15	a	a	DET
ejpam-4656	217	16	graph	graph	NOUN
ejpam-4656	217	17	g′	g′	NOUN
ejpam-4656	217	18	with	with	ADP
ejpam-4656	217	19	γch(g	γch(g	NOUN
ejpam-4656	217	20	′	′	NUM
ejpam-4656	217	21	)	)	PUNCT
ejpam-4656	217	22	<	<	X
ejpam-4656	217	23	γconh(g	γconh(g	PROPN
ejpam-4656	217	24	′	′	PROPN
ejpam-4656	217	25	)	)	PUNCT
ejpam-4656	217	26	.	.	PUNCT
ejpam-4656	218	1	this	this	PRON
ejpam-4656	218	2	proves	prove	VERB
ejpam-4656	218	3	the	the	DET
ejpam-4656	218	4	assertion	assertion	NOUN
ejpam-4656	218	5	.	.	PUNCT
ejpam-4656	219	1	corollary	corollary	ADJ
ejpam-4656	219	2	1	1	NUM
ejpam-4656	219	3	.	.	PUNCT
ejpam-4656	220	1	let	let	VERB
ejpam-4656	220	2	n	n	PRON
ejpam-4656	220	3	be	be	AUX
ejpam-4656	220	4	a	a	DET
ejpam-4656	220	5	positive	positive	ADJ
ejpam-4656	220	6	integer	integer	NOUN
ejpam-4656	220	7	.	.	PUNCT
ejpam-4656	221	1	then	then	ADV
ejpam-4656	221	2	there	there	PRON
ejpam-4656	221	3	exists	exist	VERB
ejpam-4656	221	4	a	a	DET
ejpam-4656	221	5	connected	connected	ADJ
ejpam-4656	221	6	graph	graph	NOUN
ejpam-4656	221	7	g	g	ADP
ejpam-4656	221	8	such	such	ADJ
ejpam-4656	221	9	that	that	SCONJ
ejpam-4656	221	10	γconh(g)−	γconh(g)−	NOUN
ejpam-4656	221	11	γch(g	γch(g	NOUN
ejpam-4656	221	12	)	)	PUNCT
ejpam-4656	221	13	=	=	VERB
ejpam-4656	221	14	n.	n.	NOUN
ejpam-4656	221	15	in	in	ADP
ejpam-4656	221	16	other	other	ADJ
ejpam-4656	221	17	words	word	NOUN
ejpam-4656	221	18	,	,	PUNCT
ejpam-4656	221	19	γconh	γconh	NOUN
ejpam-4656	221	20	−	−	PROPN
ejpam-4656	221	21	γch	γch	VERB
ejpam-4656	221	22	can	can	AUX
ejpam-4656	221	23	be	be	AUX
ejpam-4656	221	24	made	make	VERB
ejpam-4656	221	25	arbitrarily	arbitrarily	ADV
ejpam-4656	221	26	large	large	ADJ
ejpam-4656	221	27	.	.	PUNCT
ejpam-4656	222	1	proposition	proposition	NOUN
ejpam-4656	222	2	1	1	NUM
ejpam-4656	222	3	.	.	PUNCT
ejpam-4656	223	1	let	let	VERB
ejpam-4656	223	2	n	n	PRON
ejpam-4656	223	3	be	be	AUX
ejpam-4656	223	4	any	any	DET
ejpam-4656	223	5	positive	positive	ADJ
ejpam-4656	223	6	integer	integer	NOUN
ejpam-4656	223	7	.	.	PUNCT
ejpam-4656	224	1	then	then	ADV
ejpam-4656	224	2	each	each	PRON
ejpam-4656	224	3	of	of	ADP
ejpam-4656	224	4	the	the	DET
ejpam-4656	224	5	following	follow	VERB
ejpam-4656	224	6	holds	hold	NOUN
ejpam-4656	224	7	.	.	PUNCT
ejpam-4656	225	1	(	(	PUNCT
ejpam-4656	225	2	i	i	NOUN
ejpam-4656	225	3	)	)	PUNCT
ejpam-4656	225	4	γconh(pn	γconh(pn	NOUN
ejpam-4656	225	5	)	)	PUNCT
ejpam-4656	225	6	=	=	SYM
ejpam-4656	225	7	{	{	PUNCT
ejpam-4656	225	8	2	2	NUM
ejpam-4656	225	9	if	if	SCONJ
ejpam-4656	225	10	n	n	X
ejpam-4656	225	11	=	=	SYM
ejpam-4656	225	12	2	2	NUM
ejpam-4656	225	13	,	,	PUNCT
ejpam-4656	225	14	3	3	NUM
ejpam-4656	225	15	,	,	PUNCT
ejpam-4656	225	16	4	4	NUM
ejpam-4656	225	17	,	,	PUNCT
ejpam-4656	225	18	5	5	NUM
ejpam-4656	225	19	n−	n−	NOUN
ejpam-4656	225	20	4	4	NUM
ejpam-4656	225	21	if	if	SCONJ
ejpam-4656	225	22	n	n	PRON
ejpam-4656	225	23	≥	≥	NOUN
ejpam-4656	225	24	6	6	NUM
ejpam-4656	225	25	.	.	PUNCT
ejpam-4656	226	1	j.	j.	PROPN
ejpam-4656	226	2	hassan	hassan	PROPN
ejpam-4656	226	3	,	,	PUNCT
ejpam-4656	226	4	s.	s.	PROPN
ejpam-4656	226	5	canoy	canoy	PROPN
ejpam-4656	226	6	jr	jr	PROPN
ejpam-4656	226	7	.	.	PROPN
ejpam-4656	226	8	,	,	PUNCT
ejpam-4656	226	9	c.	c.	PROPN
ejpam-4656	226	10	saromines	saromine	VERB
ejpam-4656	226	11	/	/	SYM
ejpam-4656	226	12	eur	eur	PROPN
ejpam-4656	226	13	.	.	PUNCT
ejpam-4656	227	1	j.	j.	PROPN
ejpam-4656	227	2	pure	pure	PROPN
ejpam-4656	227	3	appl	appl	PROPN
ejpam-4656	227	4	.	.	PROPN
ejpam-4656	227	5	math	math	PROPN
ejpam-4656	227	6	,	,	PUNCT
ejpam-4656	227	7	16	16	NUM
ejpam-4656	227	8	(	(	PUNCT
ejpam-4656	227	9	1	1	NUM
ejpam-4656	227	10	)	)	PUNCT
ejpam-4656	227	11	(	(	PUNCT
ejpam-4656	227	12	2023	2023	NUM
ejpam-4656	227	13	)	)	PUNCT
ejpam-4656	227	14	,	,	PUNCT
ejpam-4656	227	15	319	319	NUM
ejpam-4656	227	16	-	-	SYM
ejpam-4656	227	17	335	335	NUM
ejpam-4656	227	18	324	324	NUM
ejpam-4656	227	19	(	(	PUNCT
ejpam-4656	227	20	ii	ii	NOUN
ejpam-4656	227	21	)	)	PUNCT
ejpam-4656	227	22	γconh(cn	γconh(cn	NOUN
ejpam-4656	227	23	)	)	PUNCT
ejpam-4656	227	24	=	=	PUNCT
ejpam-4656	228	1			NUM
ejpam-4656	228	2	2	2	NUM
ejpam-4656	228	3	if	if	SCONJ
ejpam-4656	228	4	n	n	X
ejpam-4656	228	5	=	=	SYM
ejpam-4656	228	6	4	4	NUM
ejpam-4656	228	7	,	,	PUNCT
ejpam-4656	228	8	5	5	NUM
ejpam-4656	228	9	3	3	NUM
ejpam-4656	228	10	if	if	SCONJ
ejpam-4656	228	11	n	n	NOUN
ejpam-4656	228	12	=	=	SYM
ejpam-4656	228	13	3	3	NUM
ejpam-4656	228	14	n−	n−	NOUN
ejpam-4656	228	15	4	4	NUM
ejpam-4656	228	16	if	if	SCONJ
ejpam-4656	228	17	n	n	NUM
ejpam-4656	228	18	≥	≥	VERB
ejpam-4656	229	1	6	6	NUM
ejpam-4656	229	2	n−	n−	NOUN
ejpam-4656	229	3	4if6	4if6	NUM
ejpam-4656	229	4	≤	≤	NUM
ejpam-4656	229	5	n	n	PRON
ejpam-4656	229	6	≤	≤	NOUN
ejpam-4656	229	7	9	9	NUM
ejpam-4656	229	8	nifn	nifn	NOUN
ejpam-4656	229	9	≥	≥	NOUN
ejpam-4656	229	10	10	10	NUM
ejpam-4656	229	11	.	.	PUNCT
ejpam-4656	230	1	(	(	PUNCT
ejpam-4656	230	2	iii	iii	X
ejpam-4656	230	3	)	)	PUNCT
ejpam-4656	230	4	γconh(kn	γconh(kn	NOUN
ejpam-4656	230	5	)	)	PUNCT
ejpam-4656	230	6	=	=	SYM
ejpam-4656	231	1	n	n	PROPN
ejpam-4656	231	2	for	for	ADP
ejpam-4656	231	3	all	all	DET
ejpam-4656	231	4	n	n	PRON
ejpam-4656	231	5	≥	≥	NOUN
ejpam-4656	231	6	1	1	NUM
ejpam-4656	231	7	.	.	PUNCT
ejpam-4656	232	1	proof	proof	NOUN
ejpam-4656	232	2	.	.	PUNCT
ejpam-4656	233	1	(	(	PUNCT
ejpam-4656	233	2	i	i	NOUN
ejpam-4656	233	3	)	)	PUNCT
ejpam-4656	233	4	clearly	clearly	ADV
ejpam-4656	233	5	,	,	PUNCT
ejpam-4656	233	6	γconh(pn	γconh(pn	NOUN
ejpam-4656	233	7	)	)	PUNCT
ejpam-4656	233	8	=	=	SYM
ejpam-4656	233	9	2	2	NUM
ejpam-4656	233	10	for	for	ADP
ejpam-4656	233	11	n	n	PRON
ejpam-4656	233	12	∈	∈	NOUN
ejpam-4656	233	13	{	{	PUNCT
ejpam-4656	233	14	2	2	NUM
ejpam-4656	233	15	,	,	PUNCT
ejpam-4656	233	16	3	3	NUM
ejpam-4656	233	17	,	,	PUNCT
ejpam-4656	233	18	4	4	NUM
ejpam-4656	233	19	,	,	PUNCT
ejpam-4656	233	20	5	5	NUM
ejpam-4656	233	21	}	}	PUNCT
ejpam-4656	233	22	.	.	PUNCT
ejpam-4656	234	1	suppose	suppose	VERB
ejpam-4656	234	2	n	n	PRON
ejpam-4656	234	3	≥	≥	NUM
ejpam-4656	234	4	6	6	NUM
ejpam-4656	234	5	.	.	PUNCT
ejpam-4656	235	1	let	let	VERB
ejpam-4656	235	2	pn	pn	VERB
ejpam-4656	235	3	=	=	PUNCT
ejpam-4656	236	1	[	[	X
ejpam-4656	236	2	v1	v1	NOUN
ejpam-4656	236	3	,	,	PUNCT
ejpam-4656	236	4	v2	v2	NOUN
ejpam-4656	236	5	,	,	PUNCT
ejpam-4656	236	6	.	.	PUNCT
ejpam-4656	236	7	.	.	PUNCT
ejpam-4656	236	8	.	.	PUNCT
ejpam-4656	237	1	,	,	PUNCT
ejpam-4656	237	2	vn	vn	X
ejpam-4656	237	3	]	]	PUNCT
ejpam-4656	237	4	and	and	CCONJ
ejpam-4656	237	5	consider	consider	VERB
ejpam-4656	237	6	c	c	NOUN
ejpam-4656	237	7	=	=	SYM
ejpam-4656	237	8	{	{	PUNCT
ejpam-4656	237	9	v3	v3	PROPN
ejpam-4656	237	10	,	,	PUNCT
ejpam-4656	237	11	v4	v4	PROPN
ejpam-4656	237	12	,	,	PUNCT
ejpam-4656	237	13	.	.	PUNCT
ejpam-4656	237	14	.	.	PUNCT
ejpam-4656	238	1	.	.	PUNCT
ejpam-4656	239	1	,	,	PUNCT
ejpam-4656	239	2	vn−3	vn−3	PROPN
ejpam-4656	239	3	,	,	PUNCT
ejpam-4656	239	4	vn−2	vn−2	PROPN
ejpam-4656	239	5	}	}	PUNCT
ejpam-4656	239	6	.	.	PUNCT
ejpam-4656	240	1	then	then	ADV
ejpam-4656	240	2	c	c	PROPN
ejpam-4656	240	3	is	be	AUX
ejpam-4656	240	4	a	a	DET
ejpam-4656	240	5	convex	convex	ADJ
ejpam-4656	240	6	hop	hop	NOUN
ejpam-4656	240	7	dominating	dominating	NOUN
ejpam-4656	240	8	set	set	VERB
ejpam-4656	240	9	in	in	ADP
ejpam-4656	240	10	pn	pn	PROPN
ejpam-4656	240	11	.	.	PUNCT
ejpam-4656	241	1	since	since	SCONJ
ejpam-4656	241	2	every	every	DET
ejpam-4656	241	3	convex	convex	NOUN
ejpam-4656	241	4	hop	hop	NOUN
ejpam-4656	241	5	dominating	dominating	NOUN
ejpam-4656	241	6	set	set	VERB
ejpam-4656	241	7	in	in	ADP
ejpam-4656	241	8	pn	pn	PROPN
ejpam-4656	241	9	contains	contain	VERB
ejpam-4656	241	10	c	c	PROPN
ejpam-4656	241	11	,	,	PUNCT
ejpam-4656	241	12	it	it	PRON
ejpam-4656	241	13	follows	follow	VERB
ejpam-4656	241	14	that	that	SCONJ
ejpam-4656	241	15	c	c	PROPN
ejpam-4656	241	16	is	be	AUX
ejpam-4656	241	17	a	a	DET
ejpam-4656	241	18	γconh	γconh	NOUN
ejpam-4656	241	19	-	-	PUNCT
ejpam-4656	241	20	set	set	NOUN
ejpam-4656	241	21	of	of	ADP
ejpam-4656	241	22	pn	pn	PROPN
ejpam-4656	241	23	.	.	PUNCT
ejpam-4656	242	1	thus	thus	ADV
ejpam-4656	242	2	,	,	PUNCT
ejpam-4656	242	3	γconh(pn	γconh(pn	NOUN
ejpam-4656	242	4	)	)	PUNCT
ejpam-4656	242	5	=	=	PUNCT
ejpam-4656	243	1	n−	n−	NOUN
ejpam-4656	243	2	4	4	NUM
ejpam-4656	243	3	for	for	ADP
ejpam-4656	243	4	all	all	DET
ejpam-4656	243	5	n	n	PRON
ejpam-4656	243	6	≥	≥	NOUN
ejpam-4656	243	7	6	6	NUM
ejpam-4656	243	8	.	.	PUNCT
ejpam-4656	243	9	(	(	PUNCT
ejpam-4656	243	10	ii	ii	NOUN
ejpam-4656	243	11	)	)	PUNCT
ejpam-4656	243	12	clearly	clearly	ADV
ejpam-4656	243	13	,	,	PUNCT
ejpam-4656	243	14	γconh(cn	γconh(cn	NOUN
ejpam-4656	243	15	)	)	PUNCT
ejpam-4656	243	16	=	=	SYM
ejpam-4656	243	17	2	2	NUM
ejpam-4656	243	18	for	for	ADP
ejpam-4656	243	19	n	n	PRON
ejpam-4656	243	20	∈	∈	NOUN
ejpam-4656	243	21	{	{	PUNCT
ejpam-4656	243	22	4	4	NUM
ejpam-4656	243	23	,	,	PUNCT
ejpam-4656	243	24	5	5	NUM
ejpam-4656	243	25	}	}	PUNCT
ejpam-4656	243	26	and	and	CCONJ
ejpam-4656	243	27	γconh(cn	γconh(cn	NOUN
ejpam-4656	243	28	)	)	PUNCT
ejpam-4656	243	29	=	=	SYM
ejpam-4656	243	30	3	3	NUM
ejpam-4656	243	31	for	for	ADP
ejpam-4656	243	32	n	n	NOUN
ejpam-4656	243	33	=	=	SYM
ejpam-4656	243	34	3	3	X
ejpam-4656	243	35	.	.	PUNCT
ejpam-4656	243	36	suppose	suppose	VERB
ejpam-4656	243	37	6	6	NUM
ejpam-4656	243	38	≤	≤	NOUN
ejpam-4656	243	39	n	n	PRON
ejpam-4656	243	40	≤	≤	NOUN
ejpam-4656	243	41	9	9	NUM
ejpam-4656	243	42	..	..	PUNCT
ejpam-4656	243	43	let	let	VERB
ejpam-4656	243	44	cn	cn	PROPN
ejpam-4656	243	45	=	=	PUNCT
ejpam-4656	244	1	[	[	X
ejpam-4656	244	2	v1	v1	NOUN
ejpam-4656	244	3	,	,	PUNCT
ejpam-4656	244	4	v2	v2	NOUN
ejpam-4656	244	5	,	,	PUNCT
ejpam-4656	244	6	.	.	PUNCT
ejpam-4656	244	7	.	.	PUNCT
ejpam-4656	244	8	.	.	PUNCT
ejpam-4656	245	1	,	,	PUNCT
ejpam-4656	245	2	vn	vn	X
ejpam-4656	245	3	,	,	PUNCT
ejpam-4656	245	4	v1	v1	PROPN
ejpam-4656	245	5	]	]	PUNCT
ejpam-4656	245	6	and	and	CCONJ
ejpam-4656	245	7	let	let	VERB
ejpam-4656	245	8	c	c	NOUN
ejpam-4656	245	9	′	′	VERB
ejpam-4656	245	10	be	be	AUX
ejpam-4656	245	11	a	a	DET
ejpam-4656	245	12	γconh	γconh	NOUN
ejpam-4656	245	13	-	-	PUNCT
ejpam-4656	245	14	set	set	NOUN
ejpam-4656	245	15	of	of	ADP
ejpam-4656	245	16	cn	cn	PROPN
ejpam-4656	245	17	.	.	PUNCT
ejpam-4656	246	1	we	we	PRON
ejpam-4656	246	2	may	may	AUX
ejpam-4656	246	3	assume	assume	VERB
ejpam-4656	246	4	that	that	SCONJ
ejpam-4656	246	5	v1	v1	NOUN
ejpam-4656	246	6	∈	∈	PROPN
ejpam-4656	246	7	c	c	NOUN
ejpam-4656	246	8	′	′	NOUN
ejpam-4656	247	1	and	and	CCONJ
ejpam-4656	247	2	vn	vn	PROPN
ejpam-4656	247	3	/∈	/∈	PUNCT
ejpam-4656	248	1	c.	c.	NOUN
ejpam-4656	249	1	then	then	ADV
ejpam-4656	249	2	c	c	NOUN
ejpam-4656	249	3	′	′	NOUN
ejpam-4656	250	1	=	=	SYM
ejpam-4656	250	2	{	{	PUNCT
ejpam-4656	250	3	v1	v1	NOUN
ejpam-4656	250	4	,	,	PUNCT
ejpam-4656	250	5	v2	v2	PROPN
ejpam-4656	250	6	,	,	PUNCT
ejpam-4656	250	7	.	.	PUNCT
ejpam-4656	250	8	.	.	PUNCT
ejpam-4656	250	9	.	.	PUNCT
ejpam-4656	251	1	,	,	PUNCT
ejpam-4656	251	2	vn−5	vn−5	NOUN
ejpam-4656	251	3	,	,	PUNCT
ejpam-4656	251	4	vn−4	vn−4	NOUN
ejpam-4656	251	5	}	}	PUNCT
ejpam-4656	251	6	.	.	PUNCT
ejpam-4656	252	1	it	it	PRON
ejpam-4656	252	2	follows	follow	VERB
ejpam-4656	252	3	that	that	SCONJ
ejpam-4656	252	4	γconh(cn	γconh(cn	NOUN
ejpam-4656	252	5	)	)	PUNCT
ejpam-4656	252	6	=	=	PUNCT
ejpam-4656	252	7	n−	n−	NOUN
ejpam-4656	252	8	4	4	NUM
ejpam-4656	252	9	for	for	ADP
ejpam-4656	252	10	all	all	DET
ejpam-4656	252	11	6	6	NUM
ejpam-4656	252	12	≤	≤	NOUN
ejpam-4656	252	13	n	n	PRON
ejpam-4656	252	14	≤	≤	NOUN
ejpam-4656	252	15	9	9	NUM
ejpam-4656	252	16	.	.	PUNCT
ejpam-4656	253	1	next	next	ADV
ejpam-4656	253	2	,	,	PUNCT
ejpam-4656	253	3	suppose	suppose	VERB
ejpam-4656	253	4	that	that	SCONJ
ejpam-4656	253	5	n	n	PROPN
ejpam-4656	253	6	≥	≥	NOUN
ejpam-4656	253	7	10.ifs’isaγconh	10.ifs’isaγconh	NUM
ejpam-4656	253	8	-	-	PUNCT
ejpam-4656	253	9	set	set	NOUN
ejpam-4656	253	10	of	of	ADP
ejpam-4656	253	11	cn	cn	PROPN
ejpam-4656	253	12	,	,	PUNCT
ejpam-4656	253	13	then	then	ADV
ejpam-4656	253	14	|s′|	|s′|	NOUN
ejpam-4656	253	15	≥	≥	VERB
ejpam-4656	253	16	n	n	CCONJ
ejpam-4656	253	17	−	−	PROPN
ejpam-4656	253	18	4	4	NUM
ejpam-4656	253	19	since	since	SCONJ
ejpam-4656	253	20	s′	s′	ADJ
ejpam-4656	253	21	is	be	AUX
ejpam-4656	253	22	a	a	DET
ejpam-4656	253	23	connected	connected	ADJ
ejpam-4656	253	24	hop	hop	NOUN
ejpam-4656	253	25	dominating	dominating	NOUN
ejpam-4656	253	26	set	set	NOUN
ejpam-4656	253	27	.	.	PUNCT
ejpam-4656	254	1	we	we	PRON
ejpam-4656	254	2	may	may	AUX
ejpam-4656	254	3	assume	assume	VERB
ejpam-4656	254	4	that	that	SCONJ
ejpam-4656	254	5	v1	v1	NOUN
ejpam-4656	254	6	,	,	PUNCT
ejpam-4656	254	7	v2	v2	PROPN
ejpam-4656	254	8	,	,	PUNCT
ejpam-4656	254	9	...	...	PUNCT
ejpam-4656	254	10	,	,	PUNCT
ejpam-4656	254	11	vn−5	vn−5	PROPN
ejpam-4656	254	12	,	,	PUNCT
ejpam-4656	254	13	vn−4	vn−4	NOUN
ejpam-4656	254	14	∈	∈	PROPN
ejpam-4656	255	1	s′.	s′.	PROPN
ejpam-4656	255	2	then	then	ADV
ejpam-4656	255	3	dcn(v1	dcn(v1	PROPN
ejpam-4656	255	4	,	,	PUNCT
ejpam-4656	255	5	vn−4	vn−4	NOUN
ejpam-4656	255	6	)	)	PUNCT
ejpam-4656	255	7	≤	≤	NUM
ejpam-4656	255	8	n−	n−	NOUN
ejpam-4656	255	9	5	5	NUM
ejpam-4656	255	10	.	.	PUNCT
ejpam-4656	256	1	it	it	PRON
ejpam-4656	256	2	follows	follow	VERB
ejpam-4656	256	3	that	that	SCONJ
ejpam-4656	256	4	vn−3	vn−3	PROPN
ejpam-4656	256	5	,	,	PUNCT
ejpam-4656	256	6	vn−2	vn−2	PROPN
ejpam-4656	256	7	,	,	PUNCT
ejpam-4656	256	8	vn−1	vn−1	ADJ
ejpam-4656	256	9	,	,	PUNCT
ejpam-4656	256	10	vnlieinthev1vn−4	vnlieinthev1vn−4	NOUN
ejpam-4656	256	11	geodesic	geodesic	NOUN
ejpam-4656	256	12	.	.	PUNCT
ejpam-4656	257	1	since	since	SCONJ
ejpam-4656	257	2	s	s	NOUN
ejpam-4656	257	3	’	'	PUNCT
ejpam-4656	257	4	is	be	AUX
ejpam-4656	257	5	convex	convex	NOUN
ejpam-4656	257	6	,	,	PUNCT
ejpam-4656	257	7	s′	s′	ADJ
ejpam-4656	257	8	=	=	SYM
ejpam-4656	257	9	v	v	NOUN
ejpam-4656	257	10	(	(	PUNCT
ejpam-4656	257	11	cn	cn	PROPN
ejpam-4656	257	12	)	)	PUNCT
ejpam-4656	257	13	and	and	CCONJ
ejpam-4656	257	14	γconh(cn	γconh(cn	NOUN
ejpam-4656	257	15	)	)	PUNCT
ejpam-4656	257	16	=	=	SYM
ejpam-4656	257	17	n.	n.	NOUN
ejpam-4656	257	18	(	(	PUNCT
ejpam-4656	257	19	iii	iii	NOUN
ejpam-4656	257	20	)	)	PUNCT
ejpam-4656	257	21	since	since	SCONJ
ejpam-4656	257	22	γch(kn	γch(kn	NOUN
ejpam-4656	257	23	)	)	PUNCT
ejpam-4656	257	24	=	=	SYM
ejpam-4656	258	1	n	n	CCONJ
ejpam-4656	258	2	for	for	ADP
ejpam-4656	258	3	all	all	DET
ejpam-4656	258	4	n	n	PRON
ejpam-4656	258	5	≥	≥	NOUN
ejpam-4656	258	6	1	1	NUM
ejpam-4656	258	7	,	,	PUNCT
ejpam-4656	258	8	it	it	PRON
ejpam-4656	258	9	follows	follow	VERB
ejpam-4656	258	10	from	from	ADP
ejpam-4656	258	11	remark	remark	NOUN
ejpam-4656	258	12	1	1	NUM
ejpam-4656	258	13	that	that	DET
ejpam-4656	258	14	γconh(kn	γconh(kn	NOUN
ejpam-4656	258	15	)	)	PUNCT
ejpam-4656	258	16	=	=	SYM
ejpam-4656	259	1	n	n	PROPN
ejpam-4656	259	2	for	for	ADP
ejpam-4656	259	3	all	all	DET
ejpam-4656	259	4	n	n	PRON
ejpam-4656	259	5	≥	≥	NUM
ejpam-4656	259	6	1	1	NUM
ejpam-4656	259	7	.	.	PUNCT
ejpam-4656	259	8	theorem	theorem	NOUN
ejpam-4656	259	9	3	3	X
ejpam-4656	259	10	.	.	PUNCT
ejpam-4656	260	1	let	let	VERB
ejpam-4656	260	2	g	g	PRON
ejpam-4656	260	3	be	be	AUX
ejpam-4656	260	4	a	a	DET
ejpam-4656	260	5	connected	connected	ADJ
ejpam-4656	260	6	graph	graph	NOUN
ejpam-4656	260	7	of	of	ADP
ejpam-4656	260	8	order	order	NOUN
ejpam-4656	260	9	n.	n.	NOUN
ejpam-4656	260	10	then	then	ADV
ejpam-4656	260	11	γconh(gg	γconh(gg	NOUN
ejpam-4656	260	12	)	)	PUNCT
ejpam-4656	260	13	=	=	SYM
ejpam-4656	261	1	2	2	X
ejpam-4656	261	2	.	.	X
ejpam-4656	261	3	in	in	ADP
ejpam-4656	261	4	particular	particular	ADJ
ejpam-4656	261	5	,	,	PUNCT
ejpam-4656	261	6	{	{	PUNCT
ejpam-4656	261	7	u	u	NOUN
ejpam-4656	261	8	,	,	PUNCT
ejpam-4656	261	9	u	u	NOUN
ejpam-4656	261	10	}	}	PUNCT
ejpam-4656	261	11	is	be	AUX
ejpam-4656	261	12	a	a	DET
ejpam-4656	261	13	γconh	γconh	NOUN
ejpam-4656	261	14	-	-	PUNCT
ejpam-4656	261	15	set	set	NOUN
ejpam-4656	261	16	of	of	ADP
ejpam-4656	261	17	gg	gg	NOUN
ejpam-4656	261	18	for	for	ADP
ejpam-4656	261	19	any	any	DET
ejpam-4656	261	20	u	u	PROPN
ejpam-4656	261	21	∈	∈	PROPN
ejpam-4656	261	22	v	v	NOUN
ejpam-4656	261	23	(	(	PUNCT
ejpam-4656	261	24	g	g	NOUN
ejpam-4656	261	25	)	)	PUNCT
ejpam-4656	261	26	.	.	PUNCT
ejpam-4656	262	1	proof	proof	NOUN
ejpam-4656	262	2	.	.	PUNCT
ejpam-4656	263	1	clearly	clearly	ADV
ejpam-4656	263	2	,	,	PUNCT
ejpam-4656	263	3	γconh(gg	γconh(gg	NOUN
ejpam-4656	263	4	)	)	PUNCT
ejpam-4656	263	5	=	=	SYM
ejpam-4656	263	6	2	2	NUM
ejpam-4656	263	7	if	if	SCONJ
ejpam-4656	263	8	n	n	NOUN
ejpam-4656	263	9	=	=	SYM
ejpam-4656	263	10	1	1	X
ejpam-4656	263	11	.	.	PUNCT
ejpam-4656	263	12	suppose	suppose	VERB
ejpam-4656	263	13	n	n	PRON
ejpam-4656	263	14	≥	≥	NOUN
ejpam-4656	263	15	2	2	NUM
ejpam-4656	263	16	.	.	PUNCT
ejpam-4656	264	1	let	let	VERB
ejpam-4656	264	2	s	s	VERB
ejpam-4656	264	3	=	=	PUNCT
ejpam-4656	264	4	{	{	PUNCT
ejpam-4656	264	5	u	u	NOUN
ejpam-4656	264	6	,	,	PUNCT
ejpam-4656	264	7	u	u	NOUN
ejpam-4656	264	8	}	}	PUNCT
ejpam-4656	264	9	where	where	SCONJ
ejpam-4656	264	10	u	u	PROPN
ejpam-4656	264	11	∈	∈	PROPN
ejpam-4656	264	12	v	v	ADP
ejpam-4656	264	13	(	(	PUNCT
ejpam-4656	264	14	g	g	NOUN
ejpam-4656	264	15	)	)	PUNCT
ejpam-4656	264	16	and	and	CCONJ
ejpam-4656	264	17	u	u	PROPN
ejpam-4656	264	18	∈	∈	PROPN
ejpam-4656	264	19	v	v	NOUN
ejpam-4656	264	20	(	(	PUNCT
ejpam-4656	264	21	g	g	NOUN
ejpam-4656	264	22	)	)	PUNCT
ejpam-4656	264	23	.	.	PUNCT
ejpam-4656	265	1	clearly	clearly	ADV
ejpam-4656	265	2	,	,	PUNCT
ejpam-4656	265	3	s	s	VERB
ejpam-4656	265	4	is	be	AUX
ejpam-4656	265	5	a	a	DET
ejpam-4656	265	6	convex	convex	NOUN
ejpam-4656	265	7	set	set	NOUN
ejpam-4656	265	8	.	.	PUNCT
ejpam-4656	266	1	let	let	VERB
ejpam-4656	266	2	w	w	NOUN
ejpam-4656	266	3	∈	∈	PROPN
ejpam-4656	266	4	v	v	X
ejpam-4656	266	5	(	(	PUNCT
ejpam-4656	266	6	gg	gg	NOUN
ejpam-4656	266	7	)	)	PUNCT
ejpam-4656	266	8	\	\	PROPN
ejpam-4656	266	9	s	s	PART
ejpam-4656	266	10	and	and	CCONJ
ejpam-4656	266	11	consider	consider	VERB
ejpam-4656	266	12	the	the	DET
ejpam-4656	266	13	following	follow	VERB
ejpam-4656	266	14	two	two	NUM
ejpam-4656	266	15	cases	case	NOUN
ejpam-4656	266	16	:	:	PUNCT
ejpam-4656	266	17	case	case	NOUN
ejpam-4656	266	18	1	1	NUM
ejpam-4656	266	19	:	:	PUNCT
ejpam-4656	266	20	w	w	PROPN
ejpam-4656	266	21	∈	∈	PROPN
ejpam-4656	266	22	v	v	ADP
ejpam-4656	266	23	(	(	PUNCT
ejpam-4656	266	24	g	g	NOUN
ejpam-4656	266	25	)	)	PUNCT
ejpam-4656	266	26	.	.	PUNCT
ejpam-4656	267	1	if	if	SCONJ
ejpam-4656	267	2	uw	uw	PROPN
ejpam-4656	267	3	∈	∈	PROPN
ejpam-4656	267	4	e(g	e(g	PROPN
ejpam-4656	267	5	)	)	PUNCT
ejpam-4656	267	6	,	,	PUNCT
ejpam-4656	267	7	then	then	ADV
ejpam-4656	267	8	dgg(u	dgg(u	PROPN
ejpam-4656	267	9	,	,	PUNCT
ejpam-4656	267	10	w	w	NOUN
ejpam-4656	267	11	)	)	PUNCT
ejpam-4656	267	12	=	=	SYM
ejpam-4656	267	13	2	2	X
ejpam-4656	267	14	.	.	PUNCT
ejpam-4656	267	15	suppose	suppose	VERB
ejpam-4656	267	16	that	that	SCONJ
ejpam-4656	267	17	uw	uw	PROPN
ejpam-4656	267	18	/∈	/∈	PROPN
ejpam-4656	267	19	e(g	e(g	PROPN
ejpam-4656	267	20	)	)	PUNCT
ejpam-4656	267	21	,	,	PUNCT
ejpam-4656	267	22	then	then	ADV
ejpam-4656	267	23	u	u	PROPN
ejpam-4656	267	24	w	w	PROPN
ejpam-4656	267	25	∈	∈	PROPN
ejpam-4656	267	26	e(g	e(g	PROPN
ejpam-4656	267	27	)	)	PUNCT
ejpam-4656	267	28	.	.	PUNCT
ejpam-4656	268	1	this	this	PRON
ejpam-4656	268	2	implies	imply	VERB
ejpam-4656	268	3	that	that	SCONJ
ejpam-4656	268	4	dgg(u	dgg(u	NOUN
ejpam-4656	268	5	,	,	PUNCT
ejpam-4656	268	6	w	w	NOUN
ejpam-4656	268	7	)	)	PUNCT
ejpam-4656	268	8	=	=	SYM
ejpam-4656	268	9	2	2	X
ejpam-4656	268	10	.	.	X
ejpam-4656	268	11	case	case	NOUN
ejpam-4656	268	12	2	2	NUM
ejpam-4656	268	13	:	:	PUNCT
ejpam-4656	268	14	w	w	PROPN
ejpam-4656	268	15	∈	∈	PROPN
ejpam-4656	268	16	v	v	ADP
ejpam-4656	268	17	(	(	PUNCT
ejpam-4656	268	18	g	g	NOUN
ejpam-4656	268	19	)	)	PUNCT
ejpam-4656	268	20	.	.	PUNCT
ejpam-4656	269	1	let	let	VERB
ejpam-4656	269	2	w	w	NOUN
ejpam-4656	269	3	=	=	SYM
ejpam-4656	269	4	z	z	NOUN
ejpam-4656	269	5	,	,	PUNCT
ejpam-4656	269	6	where	where	SCONJ
ejpam-4656	269	7	z	z	PROPN
ejpam-4656	269	8	∈	∈	PROPN
ejpam-4656	269	9	v	v	ADP
ejpam-4656	269	10	(	(	PUNCT
ejpam-4656	269	11	g	g	NOUN
ejpam-4656	269	12	)	)	PUNCT
ejpam-4656	269	13	.	.	PUNCT
ejpam-4656	270	1	if	if	SCONJ
ejpam-4656	270	2	u	u	PROPN
ejpam-4656	270	3	z	z	PROPN
ejpam-4656	270	4	∈	∈	PROPN
ejpam-4656	270	5	e(g	e(g	PROPN
ejpam-4656	270	6	)	)	PUNCT
ejpam-4656	270	7	,	,	PUNCT
ejpam-4656	270	8	then	then	ADV
ejpam-4656	270	9	dgg(u	dgg(u	PROPN
ejpam-4656	270	10	,	,	PUNCT
ejpam-4656	270	11	w	w	NOUN
ejpam-4656	270	12	)	)	PUNCT
ejpam-4656	270	13	=	=	SYM
ejpam-4656	270	14	2	2	X
ejpam-4656	270	15	.	.	X
ejpam-4656	271	1	if	if	SCONJ
ejpam-4656	271	2	u	u	PROPN
ejpam-4656	271	3	z	z	PROPN
ejpam-4656	271	4	/∈	/∈	PUNCT
ejpam-4656	271	5	e(g	e(g	PROPN
ejpam-4656	271	6	)	)	PUNCT
ejpam-4656	271	7	,	,	PUNCT
ejpam-4656	271	8	then	then	ADV
ejpam-4656	271	9	uz	uz	PROPN
ejpam-4656	271	10	∈	∈	PROPN
ejpam-4656	271	11	e(g	e(g	PROPN
ejpam-4656	271	12	)	)	PUNCT
ejpam-4656	271	13	.	.	PUNCT
ejpam-4656	272	1	this	this	PRON
ejpam-4656	272	2	means	mean	VERB
ejpam-4656	272	3	that	that	SCONJ
ejpam-4656	272	4	dgg(u	dgg(u	NOUN
ejpam-4656	272	5	,	,	PUNCT
ejpam-4656	272	6	w	w	NOUN
ejpam-4656	272	7	)	)	PUNCT
ejpam-4656	272	8	=	=	SYM
ejpam-4656	272	9	2	2	X
ejpam-4656	272	10	.	.	X
ejpam-4656	272	11	therefore	therefore	ADV
ejpam-4656	272	12	,	,	PUNCT
ejpam-4656	272	13	s	s	VERB
ejpam-4656	272	14	is	be	AUX
ejpam-4656	272	15	a	a	DET
ejpam-4656	272	16	convex	convex	ADJ
ejpam-4656	272	17	hop	hop	NOUN
ejpam-4656	272	18	dominating	dominating	NOUN
ejpam-4656	272	19	set	set	VERB
ejpam-4656	272	20	in	in	ADP
ejpam-4656	272	21	gg	gg	PROPN
ejpam-4656	272	22	.	.	PUNCT
ejpam-4656	273	1	since	since	SCONJ
ejpam-4656	273	2	gg	gg	PROPN
ejpam-4656	273	3	is	be	AUX
ejpam-4656	273	4	non	non	ADJ
ejpam-4656	273	5	-	-	ADJ
ejpam-4656	273	6	trivial	trivial	ADJ
ejpam-4656	273	7	,	,	PUNCT
ejpam-4656	273	8	it	it	PRON
ejpam-4656	273	9	follows	follow	VERB
ejpam-4656	273	10	that	that	SCONJ
ejpam-4656	273	11	γconh(gg	γconh(gg	NOUN
ejpam-4656	273	12	)	)	PUNCT
ejpam-4656	273	13	=	=	SYM
ejpam-4656	274	1	2	2	X
ejpam-4656	274	2	.	.	X
ejpam-4656	274	3	if	if	SCONJ
ejpam-4656	274	4	g1	g1	PROPN
ejpam-4656	274	5	and	and	CCONJ
ejpam-4656	274	6	g2	g2	PROPN
ejpam-4656	274	7	are	be	AUX
ejpam-4656	274	8	the	the	DET
ejpam-4656	274	9	copies	copy	NOUN
ejpam-4656	274	10	of	of	ADP
ejpam-4656	274	11	graph	graph	NOUN
ejpam-4656	274	12	g	g	PROPN
ejpam-4656	274	13	in	in	ADP
ejpam-4656	274	14	the	the	DET
ejpam-4656	274	15	definition	definition	NOUN
ejpam-4656	274	16	of	of	ADP
ejpam-4656	274	17	the	the	DET
ejpam-4656	274	18	shadow	shadow	NOUN
ejpam-4656	274	19	graph	graph	NOUN
ejpam-4656	274	20	s(g	s(g	PROPN
ejpam-4656	274	21	)	)	PUNCT
ejpam-4656	274	22	and	and	CCONJ
ejpam-4656	274	23	if	if	SCONJ
ejpam-4656	274	24	sg1	sg1	PROPN
ejpam-4656	274	25	⊆	⊆	PROPN
ejpam-4656	274	26	v	v	NOUN
ejpam-4656	274	27	(	(	PUNCT
ejpam-4656	274	28	g1	g1	PROPN
ejpam-4656	274	29	)	)	PUNCT
ejpam-4656	274	30	and	and	CCONJ
ejpam-4656	274	31	sg2	sg2	PROPN
ejpam-4656	274	32	⊆	⊆	NUM
ejpam-4656	274	33	v	v	PROPN
ejpam-4656	274	34	(	(	PUNCT
ejpam-4656	274	35	g2	g2	PROPN
ejpam-4656	274	36	)	)	PUNCT
ejpam-4656	274	37	,	,	PUNCT
ejpam-4656	274	38	then	then	ADV
ejpam-4656	274	39	the	the	DET
ejpam-4656	274	40	sets	set	NOUN
ejpam-4656	274	41	s′	s′	VERB
ejpam-4656	274	42	g1	g1	NOUN
ejpam-4656	274	43	and	and	CCONJ
ejpam-4656	274	44	s′	s′	ADJ
ejpam-4656	274	45	g2	g2	PROPN
ejpam-4656	274	46	are	be	AUX
ejpam-4656	274	47	the	the	DET
ejpam-4656	274	48	sets	set	NOUN
ejpam-4656	274	49	given	give	VERB
ejpam-4656	274	50	by	by	ADP
ejpam-4656	274	51	s′	s′	ADJ
ejpam-4656	274	52	g1	g1	NOUN
ejpam-4656	274	53	=	=	PUNCT
ejpam-4656	274	54	{	{	PUNCT
ejpam-4656	274	55	a′	a′	PROPN
ejpam-4656	274	56	∈	∈	PROPN
ejpam-4656	274	57	v	v	ADP
ejpam-4656	274	58	(	(	PUNCT
ejpam-4656	274	59	g2	g2	PROPN
ejpam-4656	274	60	)	)	PUNCT
ejpam-4656	274	61	:	:	PUNCT
ejpam-4656	274	62	a	a	DET
ejpam-4656	274	63	∈	∈	NOUN
ejpam-4656	274	64	sg1	sg1	NOUN
ejpam-4656	274	65	}	}	PUNCT
ejpam-4656	274	66	and	and	CCONJ
ejpam-4656	274	67	s′	s′	ADJ
ejpam-4656	274	68	g2	g2	PROPN
ejpam-4656	274	69	=	=	PRON
ejpam-4656	274	70	{	{	PUNCT
ejpam-4656	274	71	a	a	DET
ejpam-4656	274	72	∈	∈	PROPN
ejpam-4656	274	73	v	v	NOUN
ejpam-4656	274	74	(	(	PUNCT
ejpam-4656	274	75	g1	g1	PROPN
ejpam-4656	274	76	)	)	PUNCT
ejpam-4656	274	77	:	:	PUNCT
ejpam-4656	274	78	a	a	DET
ejpam-4656	274	79	′	′	NUM
ejpam-4656	274	80	∈	∈	PROPN
ejpam-4656	274	81	sg2	sg2	PROPN
ejpam-4656	274	82	}	}	PUNCT
ejpam-4656	274	83	.	.	PUNCT
ejpam-4656	275	1	j.	j.	PROPN
ejpam-4656	275	2	hassan	hassan	PROPN
ejpam-4656	275	3	,	,	PUNCT
ejpam-4656	275	4	s.	s.	PROPN
ejpam-4656	275	5	canoy	canoy	PROPN
ejpam-4656	275	6	jr	jr	PROPN
ejpam-4656	275	7	.	.	PROPN
ejpam-4656	275	8	,	,	PUNCT
ejpam-4656	275	9	c.	c.	PROPN
ejpam-4656	275	10	saromines	saromine	VERB
ejpam-4656	275	11	/	/	SYM
ejpam-4656	275	12	eur	eur	PROPN
ejpam-4656	275	13	.	.	PUNCT
ejpam-4656	276	1	j.	j.	PROPN
ejpam-4656	276	2	pure	pure	PROPN
ejpam-4656	276	3	appl	appl	PROPN
ejpam-4656	276	4	.	.	PROPN
ejpam-4656	276	5	math	math	PROPN
ejpam-4656	276	6	,	,	PUNCT
ejpam-4656	276	7	16	16	NUM
ejpam-4656	276	8	(	(	PUNCT
ejpam-4656	276	9	1	1	NUM
ejpam-4656	276	10	)	)	PUNCT
ejpam-4656	276	11	(	(	PUNCT
ejpam-4656	276	12	2023	2023	NUM
ejpam-4656	276	13	)	)	PUNCT
ejpam-4656	276	14	,	,	PUNCT
ejpam-4656	276	15	319	319	NUM
ejpam-4656	276	16	-	-	SYM
ejpam-4656	276	17	335	335	NUM
ejpam-4656	276	18	325	325	NUM
ejpam-4656	276	19	theorem	theorem	NOUN
ejpam-4656	276	20	4	4	NUM
ejpam-4656	276	21	.	.	PUNCT
ejpam-4656	277	1	let	let	VERB
ejpam-4656	277	2	g	g	PRON
ejpam-4656	277	3	be	be	AUX
ejpam-4656	277	4	a	a	DET
ejpam-4656	277	5	non	non	ADJ
ejpam-4656	277	6	-	-	ADJ
ejpam-4656	277	7	trivial	trivial	ADJ
ejpam-4656	277	8	connected	connected	ADJ
ejpam-4656	277	9	graph	graph	NOUN
ejpam-4656	277	10	.	.	PUNCT
ejpam-4656	278	1	then	then	ADV
ejpam-4656	278	2	a	a	DET
ejpam-4656	278	3	proper	proper	ADJ
ejpam-4656	278	4	subset	subset	NOUN
ejpam-4656	278	5	s	s	NOUN
ejpam-4656	278	6	of	of	ADP
ejpam-4656	278	7	v	v	NOUN
ejpam-4656	278	8	(	(	PUNCT
ejpam-4656	278	9	s(g	s(g	PROPN
ejpam-4656	278	10	)	)	PUNCT
ejpam-4656	278	11	)	)	PUNCT
ejpam-4656	278	12	is	be	AUX
ejpam-4656	278	13	convex	convex	ADJ
ejpam-4656	278	14	in	in	ADP
ejpam-4656	278	15	s(g	s(g	PROPN
ejpam-4656	278	16	)	)	PUNCT
ejpam-4656	278	17	if	if	SCONJ
ejpam-4656	278	18	and	and	CCONJ
ejpam-4656	278	19	only	only	ADV
ejpam-4656	278	20	if	if	SCONJ
ejpam-4656	278	21	one	one	NUM
ejpam-4656	278	22	of	of	ADP
ejpam-4656	278	23	the	the	DET
ejpam-4656	278	24	following	follow	VERB
ejpam-4656	278	25	conditions	condition	NOUN
ejpam-4656	278	26	holds	hold	VERB
ejpam-4656	278	27	:	:	PUNCT
ejpam-4656	278	28	(	(	PUNCT
ejpam-4656	278	29	i	i	NOUN
ejpam-4656	278	30	)	)	PUNCT
ejpam-4656	278	31	s	s	VERB
ejpam-4656	278	32	is	be	AUX
ejpam-4656	278	33	clique	clique	ADJ
ejpam-4656	278	34	in	in	ADP
ejpam-4656	278	35	g1	g1	PROPN
ejpam-4656	278	36	.	.	PUNCT
ejpam-4656	279	1	(	(	PUNCT
ejpam-4656	279	2	ii	ii	NOUN
ejpam-4656	279	3	)	)	PUNCT
ejpam-4656	279	4	s	s	VERB
ejpam-4656	279	5	is	be	AUX
ejpam-4656	279	6	clique	clique	ADJ
ejpam-4656	279	7	in	in	ADP
ejpam-4656	279	8	g2	g2	PROPN
ejpam-4656	279	9	.	.	PUNCT
ejpam-4656	280	1	(	(	PUNCT
ejpam-4656	280	2	iii	iii	X
ejpam-4656	280	3	)	)	PUNCT
ejpam-4656	280	4	s	s	PART
ejpam-4656	280	5	=	=	NOUN
ejpam-4656	280	6	sg1	sg1	NOUN
ejpam-4656	280	7	∪	∪	VERB
ejpam-4656	280	8	sg2	sg2	PROPN
ejpam-4656	280	9	and	and	CCONJ
ejpam-4656	280	10	satisfies	satisfy	VERB
ejpam-4656	280	11	the	the	DET
ejpam-4656	280	12	following	follow	VERB
ejpam-4656	280	13	conditions	condition	NOUN
ejpam-4656	280	14	:	:	PUNCT
ejpam-4656	280	15	(	(	PUNCT
ejpam-4656	280	16	a	a	X
ejpam-4656	280	17	)	)	PUNCT
ejpam-4656	280	18	sg1	sg1	NOUN
ejpam-4656	280	19	∩	∩	NOUN
ejpam-4656	280	20	s′	s′	VERB
ejpam-4656	280	21	g2	g2	PROPN
ejpam-4656	280	22	=	=	PUNCT
ejpam-4656	280	23	∅	∅	NOUN
ejpam-4656	280	24	and	and	CCONJ
ejpam-4656	280	25	s′	s′	ADJ
ejpam-4656	280	26	g1	g1	PROPN
ejpam-4656	280	27	∩	∩	PROPN
ejpam-4656	280	28	sg2	sg2	PROPN
ejpam-4656	280	29	=	=	PROPN
ejpam-4656	280	30	∅.	∅.	PROPN
ejpam-4656	280	31	(	(	PUNCT
ejpam-4656	280	32	b	b	NOUN
ejpam-4656	280	33	)	)	PUNCT
ejpam-4656	280	34	sg1	sg1	NOUN
ejpam-4656	280	35	and	and	CCONJ
ejpam-4656	280	36	sg2	sg2	PROPN
ejpam-4656	280	37	are	be	AUX
ejpam-4656	280	38	cliques	clique	NOUN
ejpam-4656	280	39	in	in	ADP
ejpam-4656	280	40	g1	g1	PROPN
ejpam-4656	280	41	and	and	CCONJ
ejpam-4656	280	42	g2	g2	PROPN
ejpam-4656	280	43	,	,	PUNCT
ejpam-4656	280	44	respectively	respectively	ADV
ejpam-4656	280	45	.	.	PUNCT
ejpam-4656	281	1	(	(	PUNCT
ejpam-4656	281	2	c	c	X
ejpam-4656	281	3	)	)	PUNCT
ejpam-4656	281	4	sg1	sg1	NOUN
ejpam-4656	281	5	∪	∪	ADP
ejpam-4656	281	6	s′	s′	ADJ
ejpam-4656	281	7	g2	g2	PROPN
ejpam-4656	281	8	and	and	CCONJ
ejpam-4656	281	9	s′	s′	ADJ
ejpam-4656	281	10	g1	g1	PROPN
ejpam-4656	281	11	∪	∪	ADP
ejpam-4656	281	12	sg2	sg2	PROPN
ejpam-4656	281	13	are	be	AUX
ejpam-4656	281	14	cliques	clique	NOUN
ejpam-4656	281	15	in	in	ADP
ejpam-4656	281	16	g1	g1	PROPN
ejpam-4656	281	17	and	and	CCONJ
ejpam-4656	281	18	g2	g2	PROPN
ejpam-4656	281	19	,	,	PUNCT
ejpam-4656	281	20	respectively	respectively	ADV
ejpam-4656	281	21	.	.	PUNCT
ejpam-4656	282	1	proof	proof	NOUN
ejpam-4656	282	2	.	.	PUNCT
ejpam-4656	283	1	suppose	suppose	VERB
ejpam-4656	283	2	s	s	NOUN
ejpam-4656	283	3	is	be	AUX
ejpam-4656	283	4	convex	convex	ADJ
ejpam-4656	283	5	in	in	ADP
ejpam-4656	283	6	s(g	s(g	PROPN
ejpam-4656	283	7	)	)	PUNCT
ejpam-4656	283	8	.	.	PUNCT
ejpam-4656	284	1	if	if	SCONJ
ejpam-4656	284	2	sg2	sg2	PROPN
ejpam-4656	284	3	=	=	SYM
ejpam-4656	284	4	∅	∅	NOUN
ejpam-4656	284	5	,	,	PUNCT
ejpam-4656	284	6	then	then	ADV
ejpam-4656	284	7	s	s	PART
ejpam-4656	284	8	=	=	NOUN
ejpam-4656	284	9	sg1	sg1	NOUN
ejpam-4656	284	10	.	.	PUNCT
ejpam-4656	285	1	suppose	suppose	VERB
ejpam-4656	285	2	s	s	PRON
ejpam-4656	285	3	is	be	AUX
ejpam-4656	285	4	not	not	PART
ejpam-4656	285	5	a	a	DET
ejpam-4656	285	6	clique	clique	NOUN
ejpam-4656	285	7	in	in	ADP
ejpam-4656	285	8	g1	g1	PROPN
ejpam-4656	285	9	.	.	PUNCT
ejpam-4656	286	1	then	then	ADV
ejpam-4656	286	2	there	there	PRON
ejpam-4656	286	3	exist	exist	VERB
ejpam-4656	286	4	a	a	DET
ejpam-4656	286	5	,	,	PUNCT
ejpam-4656	286	6	b	b	X
ejpam-4656	286	7	∈	∈	NOUN
ejpam-4656	286	8	s	s	VERB
ejpam-4656	286	9	such	such	ADJ
ejpam-4656	286	10	that	that	SCONJ
ejpam-4656	286	11	dg1(a	dg1(a	PROPN
ejpam-4656	286	12	,	,	PUNCT
ejpam-4656	286	13	b	b	NOUN
ejpam-4656	286	14	)	)	PUNCT
ejpam-4656	286	15	=	=	SYM
ejpam-4656	286	16	2	2	NUM
ejpam-4656	286	17	=	=	SYM
ejpam-4656	286	18	ds(g)(a	ds(g)(a	PROPN
ejpam-4656	286	19	,	,	PUNCT
ejpam-4656	286	20	b	b	NOUN
ejpam-4656	286	21	)	)	PUNCT
ejpam-4656	286	22	.	.	PUNCT
ejpam-4656	287	1	it	it	PRON
ejpam-4656	287	2	follows	follow	VERB
ejpam-4656	287	3	that	that	SCONJ
ejpam-4656	287	4	x	x	PUNCT
ejpam-4656	287	5	∈	∈	NOUN
ejpam-4656	287	6	s	s	X
ejpam-4656	287	7	for	for	ADP
ejpam-4656	287	8	all	all	PRON
ejpam-4656	287	9	x	x	SYM
ejpam-4656	287	10	∈	∈	PROPN
ejpam-4656	287	11	ng1(a	ng1(a	PROPN
ejpam-4656	287	12	)	)	PUNCT
ejpam-4656	287	13	∩ng1(b	∩ng1(b	NOUN
ejpam-4656	287	14	)	)	PUNCT
ejpam-4656	287	15	.	.	PUNCT
ejpam-4656	288	1	hence	hence	ADV
ejpam-4656	288	2	,	,	PUNCT
ejpam-4656	288	3	x′	x′	PROPN
ejpam-4656	288	4	∈	∈	PROPN
ejpam-4656	288	5	s	s	VERB
ejpam-4656	288	6	for	for	ADP
ejpam-4656	288	7	all	all	DET
ejpam-4656	288	8	x	x	SYM
ejpam-4656	288	9	∈	∈	PROPN
ejpam-4656	288	10	ng1(a	ng1(a	PROPN
ejpam-4656	288	11	)	)	PUNCT
ejpam-4656	288	12	∩ng1(b	∩ng1(b	NOUN
ejpam-4656	288	13	)	)	PUNCT
ejpam-4656	288	14	.	.	PUNCT
ejpam-4656	289	1	this	this	PRON
ejpam-4656	289	2	contradicts	contradict	VERB
ejpam-4656	289	3	the	the	DET
ejpam-4656	289	4	assumption	assumption	NOUN
ejpam-4656	289	5	that	that	SCONJ
ejpam-4656	289	6	sg2	sg2	PROPN
ejpam-4656	289	7	=	=	PROPN
ejpam-4656	289	8	∅.	∅.	VERB
ejpam-4656	289	9	therefore	therefore	ADV
ejpam-4656	289	10	,	,	PUNCT
ejpam-4656	289	11	s	s	PART
ejpam-4656	289	12	is	be	AUX
ejpam-4656	289	13	a	a	DET
ejpam-4656	289	14	clique	clique	NOUN
ejpam-4656	289	15	in	in	ADP
ejpam-4656	289	16	g1	g1	PROPN
ejpam-4656	289	17	.	.	PUNCT
ejpam-4656	290	1	similarly	similarly	ADV
ejpam-4656	290	2	,	,	PUNCT
ejpam-4656	290	3	if	if	SCONJ
ejpam-4656	290	4	cg1	cg1	NOUN
ejpam-4656	290	5	=	=	NOUN
ejpam-4656	290	6	∅	∅	NOUN
ejpam-4656	290	7	,	,	PUNCT
ejpam-4656	290	8	then	then	ADV
ejpam-4656	290	9	s	s	VERB
ejpam-4656	290	10	is	be	AUX
ejpam-4656	290	11	a	a	DET
ejpam-4656	290	12	clique	clique	NOUN
ejpam-4656	290	13	in	in	ADP
ejpam-4656	290	14	g2	g2	PROPN
ejpam-4656	290	15	.	.	PUNCT
ejpam-4656	291	1	hence	hence	ADV
ejpam-4656	291	2	,	,	PUNCT
ejpam-4656	291	3	(	(	PUNCT
ejpam-4656	291	4	i	i	NOUN
ejpam-4656	291	5	)	)	PUNCT
ejpam-4656	291	6	and	and	CCONJ
ejpam-4656	291	7	(	(	PUNCT
ejpam-4656	291	8	ii	ii	NOUN
ejpam-4656	291	9	)	)	PUNCT
ejpam-4656	291	10	hold	hold	VERB
ejpam-4656	291	11	.	.	PUNCT
ejpam-4656	292	1	next	next	ADV
ejpam-4656	292	2	,	,	PUNCT
ejpam-4656	292	3	suppose	suppose	VERB
ejpam-4656	292	4	sg1	sg1	PROPN
ejpam-4656	292	5	and	and	CCONJ
ejpam-4656	292	6	sg2	sg2	PROPN
ejpam-4656	292	7	are	be	AUX
ejpam-4656	292	8	both	both	PRON
ejpam-4656	292	9	non	non	ADJ
ejpam-4656	292	10	-	-	ADJ
ejpam-4656	292	11	empty	empty	ADJ
ejpam-4656	292	12	.	.	PUNCT
ejpam-4656	293	1	then	then	ADV
ejpam-4656	293	2	s	s	VERB
ejpam-4656	293	3	=	=	PUNCT
ejpam-4656	293	4	sg1	sg1	PROPN
ejpam-4656	293	5	∪	∪	PROPN
ejpam-4656	293	6	sg2	sg2	PROPN
ejpam-4656	293	7	.	.	PUNCT
ejpam-4656	294	1	suppose	suppose	VERB
ejpam-4656	294	2	sg1	sg1	NOUN
ejpam-4656	294	3	∩	∩	NOUN
ejpam-4656	294	4	s′	s′	VERB
ejpam-4656	294	5	g2	g2	PROPN
ejpam-4656	294	6	̸=	̸=	PROPN
ejpam-4656	294	7	∅	∅	NOUN
ejpam-4656	294	8	,	,	PUNCT
ejpam-4656	294	9	say	say	VERB
ejpam-4656	294	10	v	v	NUM
ejpam-4656	294	11	∈	∈	PROPN
ejpam-4656	294	12	sg1	sg1	NOUN
ejpam-4656	294	13	∩	∩	NOUN
ejpam-4656	294	14	s′	s′	ADJ
ejpam-4656	294	15	g2	g2	PROPN
ejpam-4656	294	16	.	.	PUNCT
ejpam-4656	295	1	then	then	ADV
ejpam-4656	295	2	v	v	X
ejpam-4656	295	3	,	,	PUNCT
ejpam-4656	295	4	v′	v′	PROPN
ejpam-4656	295	5	∈	∈	PROPN
ejpam-4656	295	6	s.	s.	PROPN
ejpam-4656	295	7	by	by	ADP
ejpam-4656	295	8	convexity	convexity	NOUN
ejpam-4656	295	9	of	of	ADP
ejpam-4656	295	10	s	s	PROPN
ejpam-4656	295	11	,	,	PUNCT
ejpam-4656	295	12	x	x	PRON
ejpam-4656	295	13	,	,	PUNCT
ejpam-4656	296	1	x′	x′	PROPN
ejpam-4656	296	2	∈	∈	PROPN
ejpam-4656	296	3	s	s	VERB
ejpam-4656	296	4	for	for	ADP
ejpam-4656	296	5	all	all	DET
ejpam-4656	296	6	x	x	SYM
ejpam-4656	296	7	∈	∈	NOUN
ejpam-4656	296	8	ng(v	ng(v	NOUN
ejpam-4656	296	9	)	)	PUNCT
ejpam-4656	296	10	.	.	PUNCT
ejpam-4656	297	1	this	this	PRON
ejpam-4656	297	2	implies	imply	VERB
ejpam-4656	297	3	that	that	SCONJ
ejpam-4656	297	4	s	s	VERB
ejpam-4656	297	5	=	=	SYM
ejpam-4656	297	6	v	v	PROPN
ejpam-4656	297	7	(	(	PUNCT
ejpam-4656	297	8	s(g	s(g	PROPN
ejpam-4656	297	9	)	)	PUNCT
ejpam-4656	297	10	)	)	PUNCT
ejpam-4656	297	11	,	,	PUNCT
ejpam-4656	297	12	a	a	DET
ejpam-4656	297	13	contradiction	contradiction	NOUN
ejpam-4656	297	14	.	.	PUNCT
ejpam-4656	298	1	therefore	therefore	ADV
ejpam-4656	298	2	,	,	PUNCT
ejpam-4656	298	3	sg1	sg1	PROPN
ejpam-4656	298	4	∩	∩	NOUN
ejpam-4656	298	5	s′	s′	VERB
ejpam-4656	298	6	g2	g2	PROPN
ejpam-4656	298	7	=	=	PUNCT
ejpam-4656	298	8	∅.	∅.	PRON
ejpam-4656	298	9	similarly	similarly	ADV
ejpam-4656	298	10	,	,	PUNCT
ejpam-4656	298	11	s′	s′	ADJ
ejpam-4656	298	12	g1	g1	PROPN
ejpam-4656	298	13	∩	∩	PROPN
ejpam-4656	298	14	sg2	sg2	PROPN
ejpam-4656	298	15	=	=	SYM
ejpam-4656	298	16	∅	∅	NOUN
ejpam-4656	298	17	,	,	PUNCT
ejpam-4656	298	18	showing	show	VERB
ejpam-4656	298	19	that	that	SCONJ
ejpam-4656	298	20	(	(	PUNCT
ejpam-4656	298	21	a	a	X
ejpam-4656	298	22	)	)	PUNCT
ejpam-4656	298	23	holds	hold	NOUN
ejpam-4656	298	24	.	.	PUNCT
ejpam-4656	299	1	now	now	ADV
ejpam-4656	299	2	,	,	PUNCT
ejpam-4656	299	3	suppose	suppose	VERB
ejpam-4656	299	4	sg1	sg1	NOUN
ejpam-4656	299	5	is	be	AUX
ejpam-4656	299	6	not	not	PART
ejpam-4656	299	7	clique	clique	ADJ
ejpam-4656	299	8	.	.	PUNCT
ejpam-4656	300	1	then	then	ADV
ejpam-4656	300	2	there	there	PRON
ejpam-4656	300	3	exist	exist	VERB
ejpam-4656	300	4	a	a	DET
ejpam-4656	300	5	,	,	PUNCT
ejpam-4656	300	6	b	b	X
ejpam-4656	300	7	∈	∈	NOUN
ejpam-4656	300	8	sg1	sg1	NOUN
ejpam-4656	300	9	such	such	ADJ
ejpam-4656	300	10	that	that	SCONJ
ejpam-4656	300	11	dg1(a	dg1(a	PROPN
ejpam-4656	300	12	,	,	PUNCT
ejpam-4656	300	13	b	b	NOUN
ejpam-4656	300	14	)	)	PUNCT
ejpam-4656	300	15	=	=	SYM
ejpam-4656	300	16	2	2	NUM
ejpam-4656	300	17	=	=	SYM
ejpam-4656	300	18	ds(g)(a	ds(g)(a	PROPN
ejpam-4656	300	19	,	,	PUNCT
ejpam-4656	300	20	b	b	NOUN
ejpam-4656	300	21	)	)	PUNCT
ejpam-4656	300	22	.	.	PUNCT
ejpam-4656	301	1	again	again	ADV
ejpam-4656	301	2	,	,	PUNCT
ejpam-4656	301	3	by	by	ADP
ejpam-4656	301	4	convexity	convexity	NOUN
ejpam-4656	301	5	of	of	ADP
ejpam-4656	301	6	s	s	PROPN
ejpam-4656	301	7	,	,	PUNCT
ejpam-4656	301	8	it	it	PRON
ejpam-4656	301	9	follows	follow	VERB
ejpam-4656	301	10	that	that	SCONJ
ejpam-4656	301	11	x	x	SYM
ejpam-4656	301	12	,	,	PUNCT
ejpam-4656	301	13	x′	x′	PROPN
ejpam-4656	301	14	∈	∈	PROPN
ejpam-4656	301	15	s	s	VERB
ejpam-4656	301	16	for	for	ADP
ejpam-4656	301	17	all	all	DET
ejpam-4656	301	18	x	x	SYM
ejpam-4656	301	19	∈	∈	PROPN
ejpam-4656	301	20	ng1(a	ng1(a	NOUN
ejpam-4656	301	21	)	)	PUNCT
ejpam-4656	301	22	∩	∩	PROPN
ejpam-4656	301	23	ng1(b	ng1(b	NOUN
ejpam-4656	301	24	)	)	PUNCT
ejpam-4656	301	25	.	.	PUNCT
ejpam-4656	302	1	this	this	PRON
ejpam-4656	302	2	implies	imply	VERB
ejpam-4656	302	3	that	that	SCONJ
ejpam-4656	302	4	s	s	VERB
ejpam-4656	302	5	=	=	SYM
ejpam-4656	302	6	v	v	PROPN
ejpam-4656	302	7	(	(	PUNCT
ejpam-4656	302	8	s(g	s(g	PROPN
ejpam-4656	302	9	)	)	PUNCT
ejpam-4656	302	10	)	)	PUNCT
ejpam-4656	302	11	,	,	PUNCT
ejpam-4656	302	12	a	a	DET
ejpam-4656	302	13	contradiction	contradiction	NOUN
ejpam-4656	302	14	.	.	PUNCT
ejpam-4656	303	1	therefore	therefore	ADV
ejpam-4656	303	2	,	,	PUNCT
ejpam-4656	303	3	sg1	sg1	PROPN
ejpam-4656	303	4	is	be	AUX
ejpam-4656	303	5	a	a	DET
ejpam-4656	303	6	clique	clique	NOUN
ejpam-4656	303	7	in	in	ADP
ejpam-4656	303	8	g1	g1	PROPN
ejpam-4656	303	9	.	.	PUNCT
ejpam-4656	304	1	similarly	similarly	ADV
ejpam-4656	304	2	,	,	PUNCT
ejpam-4656	304	3	sg2	sg2	PROPN
ejpam-4656	304	4	is	be	AUX
ejpam-4656	304	5	a	a	DET
ejpam-4656	304	6	clique	clique	NOUN
ejpam-4656	304	7	in	in	ADP
ejpam-4656	304	8	g2	g2	PROPN
ejpam-4656	304	9	,	,	PUNCT
ejpam-4656	304	10	showing	show	VERB
ejpam-4656	304	11	that	that	SCONJ
ejpam-4656	304	12	(	(	PUNCT
ejpam-4656	304	13	b	b	X
ejpam-4656	304	14	)	)	PUNCT
ejpam-4656	304	15	holds	hold	NOUN
ejpam-4656	304	16	.	.	PUNCT
ejpam-4656	305	1	suppose	suppose	VERB
ejpam-4656	305	2	sg1	sg1	NOUN
ejpam-4656	305	3	∪s′	∪s′	PROPN
ejpam-4656	305	4	g2	g2	PROPN
ejpam-4656	305	5	is	be	AUX
ejpam-4656	305	6	not	not	PART
ejpam-4656	305	7	a	a	DET
ejpam-4656	305	8	clique	clique	NOUN
ejpam-4656	305	9	in	in	ADP
ejpam-4656	305	10	g1	g1	PROPN
ejpam-4656	305	11	.	.	PUNCT
ejpam-4656	306	1	then	then	ADV
ejpam-4656	306	2	there	there	PRON
ejpam-4656	306	3	exist	exist	VERB
ejpam-4656	306	4	x	x	NOUN
ejpam-4656	306	5	,	,	PUNCT
ejpam-4656	306	6	y	y	PROPN
ejpam-4656	306	7	∈	∈	PROPN
ejpam-4656	306	8	sg1	sg1	PROPN
ejpam-4656	306	9	∪s′	∪s′	PROPN
ejpam-4656	306	10	g2	g2	PROPN
ejpam-4656	306	11	such	such	ADJ
ejpam-4656	306	12	that	that	DET
ejpam-4656	306	13	dg1(x	dg1(x	PROPN
ejpam-4656	306	14	,	,	PUNCT
ejpam-4656	306	15	y	y	NOUN
ejpam-4656	306	16	)	)	PUNCT
ejpam-4656	307	1	=	=	SYM
ejpam-4656	307	2	2	2	X
ejpam-4656	307	3	.	.	PUNCT
ejpam-4656	307	4	since	since	SCONJ
ejpam-4656	307	5	sg1	sg1	PROPN
ejpam-4656	307	6	and	and	CCONJ
ejpam-4656	307	7	sg2	sg2	PROPN
ejpam-4656	307	8	are	be	AUX
ejpam-4656	307	9	cliques	clique	NOUN
ejpam-4656	307	10	,	,	PUNCT
ejpam-4656	307	11	we	we	PRON
ejpam-4656	307	12	may	may	AUX
ejpam-4656	307	13	assume	assume	VERB
ejpam-4656	307	14	that	that	SCONJ
ejpam-4656	307	15	x	x	SYM
ejpam-4656	307	16	∈	∈	NOUN
ejpam-4656	307	17	sg1	sg1	NOUN
ejpam-4656	307	18	and	and	CCONJ
ejpam-4656	307	19	y	y	PROPN
ejpam-4656	307	20	∈	∈	PROPN
ejpam-4656	307	21	s′	s′	PUNCT
ejpam-4656	307	22	g2	g2	PROPN
ejpam-4656	307	23	.	.	PUNCT
ejpam-4656	308	1	then	then	ADV
ejpam-4656	308	2	y′	y′	NOUN
ejpam-4656	308	3	∈	∈	PROPN
ejpam-4656	308	4	sg2	sg2	PROPN
ejpam-4656	308	5	.	.	PUNCT
ejpam-4656	309	1	let	let	VERB
ejpam-4656	309	2	z	z	NOUN
ejpam-4656	309	3	∈	∈	PROPN
ejpam-4656	309	4	ng(x	ng(x	NUM
ejpam-4656	309	5	)	)	PUNCT
ejpam-4656	309	6	∩	∩	NOUN
ejpam-4656	309	7	ng(y	ng(y	NOUN
ejpam-4656	309	8	)	)	PUNCT
ejpam-4656	309	9	.	.	PUNCT
ejpam-4656	310	1	then	then	ADV
ejpam-4656	310	2	z	z	X
ejpam-4656	310	3	,	,	PUNCT
ejpam-4656	310	4	z′	z′	PROPN
ejpam-4656	310	5	∈	∈	PROPN
ejpam-4656	310	6	ns(g)(x	ns(g)(x	PROPN
ejpam-4656	310	7	)	)	PUNCT
ejpam-4656	310	8	∩	∩	PROPN
ejpam-4656	310	9	ns(g)(y	ns(g)(y	PROPN
ejpam-4656	310	10	′	′	NUM
ejpam-4656	310	11	)	)	PUNCT
ejpam-4656	310	12	.	.	PUNCT
ejpam-4656	311	1	since	since	SCONJ
ejpam-4656	311	2	s	s	PROPN
ejpam-4656	311	3	is	be	AUX
ejpam-4656	311	4	convex	convex	NOUN
ejpam-4656	311	5	,	,	PUNCT
ejpam-4656	311	6	z	z	PROPN
ejpam-4656	311	7	,	,	PUNCT
ejpam-4656	311	8	z′	z′	PROPN
ejpam-4656	311	9	∈	∈	PROPN
ejpam-4656	311	10	s.	s.	PROPN
ejpam-4656	311	11	since	since	SCONJ
ejpam-4656	311	12	yz	yz	PROPN
ejpam-4656	311	13	,	,	PUNCT
ejpam-4656	311	14	yz′	yz′	PROPN
ejpam-4656	311	15	∈	∈	PROPN
ejpam-4656	311	16	e(s(g	e(s(g	PROPN
ejpam-4656	311	17	)	)	PUNCT
ejpam-4656	311	18	)	)	PUNCT
ejpam-4656	311	19	,	,	PUNCT
ejpam-4656	311	20	y	y	PROPN
ejpam-4656	311	21	∈	∈	PROPN
ejpam-4656	311	22	s	s	PART
ejpam-4656	311	23	by	by	ADP
ejpam-4656	311	24	convexity	convexity	NOUN
ejpam-4656	311	25	of	of	ADP
ejpam-4656	311	26	s.	s.	PROPN
ejpam-4656	311	27	this	this	PRON
ejpam-4656	311	28	would	would	AUX
ejpam-4656	311	29	imply	imply	VERB
ejpam-4656	311	30	that	that	PRON
ejpam-4656	311	31	s	s	VERB
ejpam-4656	311	32	=	=	SYM
ejpam-4656	311	33	v	v	PROPN
ejpam-4656	311	34	(	(	PUNCT
ejpam-4656	311	35	s(g	s(g	PROPN
ejpam-4656	311	36	)	)	PUNCT
ejpam-4656	311	37	)	)	PUNCT
ejpam-4656	311	38	,	,	PUNCT
ejpam-4656	311	39	a	a	DET
ejpam-4656	311	40	contradiction	contradiction	NOUN
ejpam-4656	311	41	.	.	PUNCT
ejpam-4656	312	1	therefore	therefore	ADV
ejpam-4656	312	2	,	,	PUNCT
ejpam-4656	312	3	sg1	sg1	PROPN
ejpam-4656	312	4	∪	∪	ADP
ejpam-4656	312	5	s′	s′	ADJ
ejpam-4656	312	6	g2	g2	PROPN
ejpam-4656	312	7	is	be	AUX
ejpam-4656	312	8	a	a	DET
ejpam-4656	312	9	clique	clique	NOUN
ejpam-4656	312	10	in	in	ADP
ejpam-4656	312	11	g1	g1	PROPN
ejpam-4656	312	12	.	.	PUNCT
ejpam-4656	313	1	similarly	similarly	ADV
ejpam-4656	313	2	,	,	PUNCT
ejpam-4656	313	3	s′	s′	ADJ
ejpam-4656	313	4	g1	g1	PROPN
ejpam-4656	313	5	∪	∪	ADP
ejpam-4656	313	6	sg2	sg2	PROPN
ejpam-4656	313	7	is	be	AUX
ejpam-4656	313	8	a	a	DET
ejpam-4656	313	9	clique	clique	NOUN
ejpam-4656	313	10	in	in	ADP
ejpam-4656	313	11	g2	g2	PROPN
ejpam-4656	313	12	.	.	PUNCT
ejpam-4656	314	1	thus	thus	ADV
ejpam-4656	314	2	,	,	PUNCT
ejpam-4656	314	3	(	(	PUNCT
ejpam-4656	314	4	c	c	X
ejpam-4656	314	5	)	)	PUNCT
ejpam-4656	314	6	holds	hold	NOUN
ejpam-4656	314	7	.	.	PUNCT
ejpam-4656	315	1	the	the	DET
ejpam-4656	315	2	converse	converse	NOUN
ejpam-4656	315	3	is	be	AUX
ejpam-4656	315	4	clear	clear	ADJ
ejpam-4656	315	5	.	.	PUNCT
ejpam-4656	316	1	corollary	corollary	ADJ
ejpam-4656	316	2	2	2	NUM
ejpam-4656	316	3	.	.	PUNCT
ejpam-4656	317	1	let	let	VERB
ejpam-4656	317	2	g	g	PRON
ejpam-4656	317	3	be	be	AUX
ejpam-4656	317	4	a	a	DET
ejpam-4656	317	5	non	non	ADJ
ejpam-4656	317	6	-	-	ADJ
ejpam-4656	317	7	trivial	trivial	ADJ
ejpam-4656	317	8	connected	connected	ADJ
ejpam-4656	317	9	graph	graph	NOUN
ejpam-4656	317	10	.	.	PUNCT
ejpam-4656	318	1	then	then	ADV
ejpam-4656	318	2	con(s(g	con(s(g	PROPN
ejpam-4656	318	3	)	)	PUNCT
ejpam-4656	318	4	)	)	PUNCT
ejpam-4656	319	1	=	=	SYM
ejpam-4656	319	2	ω(g	ω(g	NOUN
ejpam-4656	319	3	)	)	PUNCT
ejpam-4656	319	4	.	.	PUNCT
ejpam-4656	320	1	theorem	theorem	NOUN
ejpam-4656	320	2	5	5	NUM
ejpam-4656	320	3	.	.	PUNCT
ejpam-4656	321	1	let	let	VERB
ejpam-4656	321	2	g	g	PRON
ejpam-4656	321	3	be	be	AUX
ejpam-4656	321	4	a	a	DET
ejpam-4656	321	5	non	non	ADJ
ejpam-4656	321	6	-	-	ADJ
ejpam-4656	321	7	trivial	trivial	ADJ
ejpam-4656	321	8	connected	connected	ADJ
ejpam-4656	321	9	graph	graph	NOUN
ejpam-4656	321	10	.	.	PUNCT
ejpam-4656	322	1	then	then	ADV
ejpam-4656	322	2	s	s	VERB
ejpam-4656	322	3	is	be	AUX
ejpam-4656	322	4	a	a	DET
ejpam-4656	322	5	hop	hop	NOUN
ejpam-4656	322	6	dominating	dominating	NOUN
ejpam-4656	322	7	set	set	NOUN
ejpam-4656	322	8	in	in	ADP
ejpam-4656	322	9	s(g	s(g	PROPN
ejpam-4656	322	10	)	)	PUNCT
ejpam-4656	322	11	if	if	SCONJ
ejpam-4656	322	12	and	and	CCONJ
ejpam-4656	322	13	only	only	ADV
ejpam-4656	322	14	if	if	SCONJ
ejpam-4656	322	15	one	one	NUM
ejpam-4656	322	16	of	of	ADP
ejpam-4656	322	17	the	the	DET
ejpam-4656	322	18	following	follow	VERB
ejpam-4656	322	19	conditions	condition	NOUN
ejpam-4656	322	20	holds	hold	VERB
ejpam-4656	322	21	:	:	PUNCT
ejpam-4656	322	22	(	(	PUNCT
ejpam-4656	322	23	i	i	NOUN
ejpam-4656	322	24	)	)	PUNCT
ejpam-4656	322	25	s	s	VERB
ejpam-4656	322	26	is	be	AUX
ejpam-4656	322	27	a	a	DET
ejpam-4656	322	28	hop	hop	NOUN
ejpam-4656	322	29	dominating	dominating	NOUN
ejpam-4656	322	30	set	set	VERB
ejpam-4656	322	31	in	in	ADP
ejpam-4656	322	32	g1	g1	PROPN
ejpam-4656	322	33	.	.	PUNCT
ejpam-4656	323	1	(	(	PUNCT
ejpam-4656	323	2	ii	ii	X
ejpam-4656	323	3	)	)	PUNCT
ejpam-4656	323	4	s	s	VERB
ejpam-4656	323	5	is	be	AUX
ejpam-4656	323	6	a	a	DET
ejpam-4656	323	7	hop	hop	NOUN
ejpam-4656	323	8	dominating	dominating	NOUN
ejpam-4656	323	9	set	set	VERB
ejpam-4656	323	10	in	in	ADP
ejpam-4656	323	11	g2	g2	PROPN
ejpam-4656	323	12	.	.	PUNCT
ejpam-4656	324	1	(	(	PUNCT
ejpam-4656	324	2	iii	iii	X
ejpam-4656	324	3	)	)	PUNCT
ejpam-4656	324	4	s	s	PART
ejpam-4656	324	5	=	=	NOUN
ejpam-4656	324	6	sg1	sg1	NOUN
ejpam-4656	324	7	∪	∪	VERB
ejpam-4656	324	8	sg2	sg2	PROPN
ejpam-4656	324	9	such	such	ADJ
ejpam-4656	324	10	that	that	SCONJ
ejpam-4656	324	11	sg1	sg1	NOUN
ejpam-4656	324	12	∪	∪	ADP
ejpam-4656	324	13	s′	s′	ADJ
ejpam-4656	324	14	g2	g2	PROPN
ejpam-4656	324	15	and	and	CCONJ
ejpam-4656	324	16	s′	s′	ADJ
ejpam-4656	324	17	g1	g1	PROPN
ejpam-4656	324	18	∪	∪	ADP
ejpam-4656	324	19	sg2	sg2	PROPN
ejpam-4656	324	20	are	be	AUX
ejpam-4656	324	21	hop	hop	NOUN
ejpam-4656	324	22	dominating	dominating	NOUN
ejpam-4656	324	23	sets	set	NOUN
ejpam-4656	324	24	in	in	ADP
ejpam-4656	324	25	g1	g1	PROPN
ejpam-4656	324	26	and	and	CCONJ
ejpam-4656	324	27	g2	g2	PROPN
ejpam-4656	324	28	.	.	PUNCT
ejpam-4656	325	1	j.	j.	PROPN
ejpam-4656	325	2	hassan	hassan	PROPN
ejpam-4656	325	3	,	,	PUNCT
ejpam-4656	325	4	s.	s.	PROPN
ejpam-4656	325	5	canoy	canoy	PROPN
ejpam-4656	325	6	jr	jr	PROPN
ejpam-4656	325	7	.	.	PROPN
ejpam-4656	325	8	,	,	PUNCT
ejpam-4656	325	9	c.	c.	PROPN
ejpam-4656	325	10	saromines	saromine	VERB
ejpam-4656	325	11	/	/	SYM
ejpam-4656	325	12	eur	eur	PROPN
ejpam-4656	325	13	.	.	PUNCT
ejpam-4656	326	1	j.	j.	PROPN
ejpam-4656	326	2	pure	pure	PROPN
ejpam-4656	326	3	appl	appl	PROPN
ejpam-4656	326	4	.	.	PROPN
ejpam-4656	326	5	math	math	PROPN
ejpam-4656	326	6	,	,	PUNCT
ejpam-4656	326	7	16	16	NUM
ejpam-4656	326	8	(	(	PUNCT
ejpam-4656	326	9	1	1	NUM
ejpam-4656	326	10	)	)	PUNCT
ejpam-4656	326	11	(	(	PUNCT
ejpam-4656	326	12	2023	2023	NUM
ejpam-4656	326	13	)	)	PUNCT
ejpam-4656	326	14	,	,	PUNCT
ejpam-4656	326	15	319	319	NUM
ejpam-4656	326	16	-	-	SYM
ejpam-4656	326	17	335	335	NUM
ejpam-4656	326	18	326	326	NUM
ejpam-4656	326	19	proof	proof	NOUN
ejpam-4656	326	20	.	.	PUNCT
ejpam-4656	327	1	let	let	VERB
ejpam-4656	327	2	s	s	PRON
ejpam-4656	327	3	be	be	AUX
ejpam-4656	327	4	a	a	DET
ejpam-4656	327	5	hop	hop	NOUN
ejpam-4656	327	6	dominating	dominating	NOUN
ejpam-4656	327	7	set	set	NOUN
ejpam-4656	327	8	in	in	ADP
ejpam-4656	327	9	s(g	s(g	PROPN
ejpam-4656	327	10	)	)	PUNCT
ejpam-4656	327	11	.	.	PUNCT
ejpam-4656	328	1	set	set	VERB
ejpam-4656	328	2	sg1	sg1	NOUN
ejpam-4656	328	3	=	=	SYM
ejpam-4656	328	4	s	s	PROPN
ejpam-4656	328	5	∩	∩	ADJ
ejpam-4656	328	6	v	v	X
ejpam-4656	328	7	(	(	PUNCT
ejpam-4656	328	8	g1	g1	PROPN
ejpam-4656	328	9	)	)	PUNCT
ejpam-4656	328	10	and	and	CCONJ
ejpam-4656	328	11	sg2	sg2	PROPN
ejpam-4656	328	12	=	=	PROPN
ejpam-4656	328	13	s	s	PROPN
ejpam-4656	328	14	∩	∩	ADJ
ejpam-4656	328	15	v	v	X
ejpam-4656	328	16	(	(	PUNCT
ejpam-4656	328	17	g2	g2	PROPN
ejpam-4656	328	18	)	)	PUNCT
ejpam-4656	328	19	.	.	PUNCT
ejpam-4656	329	1	if	if	SCONJ
ejpam-4656	329	2	sg2	sg2	PROPN
ejpam-4656	329	3	=	=	SYM
ejpam-4656	329	4	∅	∅	NOUN
ejpam-4656	329	5	,	,	PUNCT
ejpam-4656	329	6	then	then	ADV
ejpam-4656	329	7	s	s	PART
ejpam-4656	329	8	=	=	NOUN
ejpam-4656	329	9	sg1	sg1	PROPN
ejpam-4656	329	10	is	be	AUX
ejpam-4656	329	11	a	a	DET
ejpam-4656	329	12	hop	hop	NOUN
ejpam-4656	329	13	dominating	dominating	NOUN
ejpam-4656	329	14	set	set	VERB
ejpam-4656	329	15	in	in	ADP
ejpam-4656	329	16	g1	g1	NOUN
ejpam-4656	329	17	.	.	PUNCT
ejpam-4656	330	1	if	if	SCONJ
ejpam-4656	330	2	sg1	sg1	NOUN
ejpam-4656	330	3	=	=	SYM
ejpam-4656	330	4	∅	∅	NOUN
ejpam-4656	330	5	,	,	PUNCT
ejpam-4656	330	6	then	then	ADV
ejpam-4656	330	7	s	s	PART
ejpam-4656	330	8	=	=	PUNCT
ejpam-4656	330	9	sg2	sg2	PROPN
ejpam-4656	330	10	is	be	AUX
ejpam-4656	330	11	a	a	DET
ejpam-4656	330	12	hop	hop	NOUN
ejpam-4656	330	13	dominating	dominating	NOUN
ejpam-4656	330	14	set	set	NOUN
ejpam-4656	330	15	in	in	ADP
ejpam-4656	330	16	g2	g2	PROPN
ejpam-4656	330	17	.	.	PUNCT
ejpam-4656	331	1	hence	hence	ADV
ejpam-4656	331	2	,	,	PUNCT
ejpam-4656	331	3	(	(	PUNCT
ejpam-4656	331	4	i	i	NOUN
ejpam-4656	331	5	)	)	PUNCT
ejpam-4656	331	6	or	or	CCONJ
ejpam-4656	331	7	(	(	PUNCT
ejpam-4656	331	8	ii	ii	NOUN
ejpam-4656	331	9	)	)	PUNCT
ejpam-4656	331	10	holds	hold	VERB
ejpam-4656	331	11	.	.	PUNCT
ejpam-4656	332	1	next	next	ADV
ejpam-4656	332	2	,	,	PUNCT
ejpam-4656	332	3	suppose	suppose	VERB
ejpam-4656	332	4	sg1	sg1	NOUN
ejpam-4656	332	5	̸=	̸=	PROPN
ejpam-4656	332	6	∅	∅	NOUN
ejpam-4656	332	7	and	and	CCONJ
ejpam-4656	332	8	sg2	sg2	PROPN
ejpam-4656	332	9	̸=	̸=	PROPN
ejpam-4656	332	10	∅.	∅.	ADV
ejpam-4656	332	11	let	let	VERB
ejpam-4656	332	12	x	x	SYM
ejpam-4656	332	13	∈	∈	PROPN
ejpam-4656	332	14	v	v	X
ejpam-4656	332	15	(	(	PUNCT
ejpam-4656	332	16	g1	g1	PROPN
ejpam-4656	332	17	)	)	PUNCT
ejpam-4656	332	18	\	\	PROPN
ejpam-4656	332	19	sg1	sg1	NOUN
ejpam-4656	332	20	∪	∪	ADP
ejpam-4656	332	21	s′	s′	ADJ
ejpam-4656	332	22	g2	g2	PROPN
ejpam-4656	332	23	.	.	PUNCT
ejpam-4656	333	1	then	then	ADV
ejpam-4656	333	2	x	x	SYM
ejpam-4656	333	3	∈	∈	PROPN
ejpam-4656	333	4	v	v	X
ejpam-4656	333	5	(	(	PUNCT
ejpam-4656	333	6	s(g	s(g	PROPN
ejpam-4656	333	7	)	)	PUNCT
ejpam-4656	333	8	)	)	PUNCT
ejpam-4656	333	9	\	\	PROPN
ejpam-4656	334	1	s.	s.	PROPN
ejpam-4656	334	2	since	since	SCONJ
ejpam-4656	334	3	s	s	PROPN
ejpam-4656	334	4	is	be	AUX
ejpam-4656	334	5	a	a	DET
ejpam-4656	334	6	hop	hop	NOUN
ejpam-4656	334	7	dominating	dominating	NOUN
ejpam-4656	334	8	set	set	NOUN
ejpam-4656	334	9	in	in	ADP
ejpam-4656	334	10	s(g	s(g	PROPN
ejpam-4656	334	11	)	)	PUNCT
ejpam-4656	334	12	,	,	PUNCT
ejpam-4656	334	13	there	there	PRON
ejpam-4656	334	14	exists	exist	VERB
ejpam-4656	334	15	y	y	PROPN
ejpam-4656	334	16	∈	∈	PROPN
ejpam-4656	334	17	s	s	VERB
ejpam-4656	334	18	such	such	ADJ
ejpam-4656	334	19	that	that	DET
ejpam-4656	334	20	ds(g)(x	ds(g)(x	NOUN
ejpam-4656	334	21	,	,	PUNCT
ejpam-4656	334	22	y	y	NOUN
ejpam-4656	334	23	)	)	PUNCT
ejpam-4656	334	24	=	=	SYM
ejpam-4656	335	1	2	2	X
ejpam-4656	335	2	.	.	X
ejpam-4656	336	1	if	if	SCONJ
ejpam-4656	336	2	y	y	PROPN
ejpam-4656	336	3	∈	∈	PROPN
ejpam-4656	336	4	sg1	sg1	NOUN
ejpam-4656	336	5	,	,	PUNCT
ejpam-4656	336	6	then	then	ADV
ejpam-4656	336	7	we	we	PRON
ejpam-4656	336	8	are	be	AUX
ejpam-4656	336	9	done	do	VERB
ejpam-4656	336	10	.	.	PUNCT
ejpam-4656	337	1	suppose	suppose	VERB
ejpam-4656	337	2	y	y	PROPN
ejpam-4656	337	3	∈	∈	PROPN
ejpam-4656	337	4	sg2	sg2	PROPN
ejpam-4656	337	5	,	,	PUNCT
ejpam-4656	337	6	say	say	VERB
ejpam-4656	337	7	y	y	PROPN
ejpam-4656	337	8	=	=	SYM
ejpam-4656	337	9	z′	z′	PROPN
ejpam-4656	337	10	,	,	PUNCT
ejpam-4656	337	11	where	where	SCONJ
ejpam-4656	337	12	z	z	PROPN
ejpam-4656	337	13	∈	∈	PROPN
ejpam-4656	337	14	v	v	NOUN
ejpam-4656	337	15	(	(	PUNCT
ejpam-4656	337	16	g1	g1	PROPN
ejpam-4656	337	17	)	)	PUNCT
ejpam-4656	337	18	.	.	PUNCT
ejpam-4656	338	1	then	then	ADV
ejpam-4656	338	2	z	z	PROPN
ejpam-4656	338	3	∈	∈	PROPN
ejpam-4656	338	4	s′	s′	VERB
ejpam-4656	338	5	g2	g2	PROPN
ejpam-4656	338	6	and	and	CCONJ
ejpam-4656	338	7	ds(g)(x	ds(g)(x	PROPN
ejpam-4656	338	8	,	,	PUNCT
ejpam-4656	338	9	z	z	NOUN
ejpam-4656	338	10	)	)	PUNCT
ejpam-4656	338	11	=	=	SYM
ejpam-4656	338	12	dg1(x	dg1(x	PROPN
ejpam-4656	338	13	,	,	PUNCT
ejpam-4656	338	14	z	z	NOUN
ejpam-4656	338	15	)	)	PUNCT
ejpam-4656	338	16	=	=	SYM
ejpam-4656	338	17	2	2	X
ejpam-4656	338	18	.	.	X
ejpam-4656	338	19	therefore	therefore	ADV
ejpam-4656	338	20	,	,	PUNCT
ejpam-4656	338	21	sg1	sg1	PROPN
ejpam-4656	338	22	∪s′	∪s′	PROPN
ejpam-4656	338	23	g2	g2	PROPN
ejpam-4656	338	24	is	be	AUX
ejpam-4656	338	25	a	a	DET
ejpam-4656	338	26	hop	hop	NOUN
ejpam-4656	338	27	dominating	dominating	NOUN
ejpam-4656	338	28	set	set	VERB
ejpam-4656	338	29	in	in	ADP
ejpam-4656	338	30	g1	g1	PROPN
ejpam-4656	338	31	.	.	PUNCT
ejpam-4656	339	1	similarly	similarly	ADV
ejpam-4656	339	2	,	,	PUNCT
ejpam-4656	339	3	s′	s′	ADJ
ejpam-4656	339	4	g1	g1	PROPN
ejpam-4656	339	5	∪	∪	ADP
ejpam-4656	339	6	sg2	sg2	PROPN
ejpam-4656	339	7	is	be	AUX
ejpam-4656	339	8	a	a	DET
ejpam-4656	339	9	hop	hop	NOUN
ejpam-4656	339	10	dominating	dominating	NOUN
ejpam-4656	339	11	set	set	NOUN
ejpam-4656	339	12	in	in	ADP
ejpam-4656	339	13	g2	g2	PROPN
ejpam-4656	339	14	.	.	PUNCT
ejpam-4656	340	1	hence	hence	ADV
ejpam-4656	340	2	,	,	PUNCT
ejpam-4656	340	3	(	(	PUNCT
ejpam-4656	340	4	iii	iii	NOUN
ejpam-4656	340	5	)	)	PUNCT
ejpam-4656	340	6	holds	hold	VERB
ejpam-4656	340	7	.	.	PUNCT
ejpam-4656	341	1	for	for	ADP
ejpam-4656	341	2	the	the	DET
ejpam-4656	341	3	converse	converse	NOUN
ejpam-4656	341	4	,	,	PUNCT
ejpam-4656	341	5	suppose	suppose	VERB
ejpam-4656	341	6	(	(	PUNCT
ejpam-4656	341	7	i	i	NOUN
ejpam-4656	341	8	)	)	PUNCT
ejpam-4656	341	9	holds	hold	VERB
ejpam-4656	341	10	.	.	PUNCT
ejpam-4656	342	1	let	let	VERB
ejpam-4656	342	2	a	a	DET
ejpam-4656	342	3	∈	∈	PROPN
ejpam-4656	342	4	v	v	NOUN
ejpam-4656	342	5	(	(	PUNCT
ejpam-4656	342	6	s(g	s(g	PROPN
ejpam-4656	342	7	)	)	PUNCT
ejpam-4656	342	8	)	)	PUNCT
ejpam-4656	343	1	\	\	PUNCT
ejpam-4656	343	2	s.	s.	PROPN
ejpam-4656	343	3	if	if	SCONJ
ejpam-4656	343	4	a	a	DET
ejpam-4656	343	5	∈	∈	PROPN
ejpam-4656	343	6	v	v	NOUN
ejpam-4656	343	7	(	(	PUNCT
ejpam-4656	343	8	g1	g1	PROPN
ejpam-4656	343	9	)	)	PUNCT
ejpam-4656	343	10	\	\	PROPN
ejpam-4656	343	11	s	s	X
ejpam-4656	343	12	,	,	PUNCT
ejpam-4656	343	13	then	then	ADV
ejpam-4656	343	14	there	there	PRON
ejpam-4656	343	15	exists	exist	VERB
ejpam-4656	343	16	b	b	PROPN
ejpam-4656	343	17	∈	∈	PROPN
ejpam-4656	343	18	s	s	VERB
ejpam-4656	343	19	such	such	ADJ
ejpam-4656	343	20	that	that	SCONJ
ejpam-4656	343	21	dg1(a	dg1(a	PROPN
ejpam-4656	343	22	,	,	PUNCT
ejpam-4656	343	23	b	b	NOUN
ejpam-4656	343	24	)	)	PUNCT
ejpam-4656	343	25	=	=	PUNCT
ejpam-4656	343	26	ds(g)(a	ds(g)(a	PROPN
ejpam-4656	343	27	,	,	PUNCT
ejpam-4656	343	28	b	b	NOUN
ejpam-4656	343	29	)	)	PUNCT
ejpam-4656	343	30	=	=	SYM
ejpam-4656	343	31	2	2	X
ejpam-4656	343	32	.	.	PUNCT
ejpam-4656	343	33	suppose	suppose	VERB
ejpam-4656	343	34	a	a	DET
ejpam-4656	343	35	∈	∈	PROPN
ejpam-4656	343	36	v	v	NOUN
ejpam-4656	343	37	(	(	PUNCT
ejpam-4656	343	38	g2	g2	PROPN
ejpam-4656	343	39	)	)	PUNCT
ejpam-4656	343	40	,	,	PUNCT
ejpam-4656	343	41	say	say	VERB
ejpam-4656	343	42	a	a	DET
ejpam-4656	343	43	=	=	NOUN
ejpam-4656	343	44	v′	v′	NOUN
ejpam-4656	343	45	,	,	PUNCT
ejpam-4656	343	46	where	where	SCONJ
ejpam-4656	343	47	v	v	X
ejpam-4656	343	48	∈	∈	PROPN
ejpam-4656	343	49	v	v	NOUN
ejpam-4656	343	50	(	(	PUNCT
ejpam-4656	343	51	g1	g1	PROPN
ejpam-4656	343	52	)	)	PUNCT
ejpam-4656	343	53	.	.	PUNCT
ejpam-4656	344	1	if	if	SCONJ
ejpam-4656	344	2	v	v	NUM
ejpam-4656	344	3	∈	∈	PROPN
ejpam-4656	344	4	s	s	NOUN
ejpam-4656	344	5	,	,	PUNCT
ejpam-4656	344	6	then	then	ADV
ejpam-4656	344	7	dg1(a	dg1(a	PROPN
ejpam-4656	344	8	,	,	PUNCT
ejpam-4656	344	9	v	v	NOUN
ejpam-4656	344	10	)	)	PUNCT
ejpam-4656	344	11	=	=	PUNCT
ejpam-4656	344	12	ds(g)(a	ds(g)(a	PROPN
ejpam-4656	344	13	,	,	PUNCT
ejpam-4656	344	14	v	v	NOUN
ejpam-4656	344	15	)	)	PUNCT
ejpam-4656	344	16	=	=	SYM
ejpam-4656	344	17	2	2	X
ejpam-4656	344	18	.	.	X
ejpam-4656	345	1	if	if	SCONJ
ejpam-4656	345	2	v	v	NUM
ejpam-4656	345	3	/∈	/∈	SYM
ejpam-4656	346	1	s	s	X
ejpam-4656	346	2	,	,	PUNCT
ejpam-4656	346	3	then	then	ADV
ejpam-4656	346	4	there	there	PRON
ejpam-4656	346	5	exists	exist	VERB
ejpam-4656	346	6	w	w	PROPN
ejpam-4656	346	7	∈	∈	PROPN
ejpam-4656	346	8	s	s	VERB
ejpam-4656	346	9	such	such	ADJ
ejpam-4656	347	1	that	that	PRON
ejpam-4656	347	2	dg1(v	dg1(v	PROPN
ejpam-4656	347	3	,	,	PUNCT
ejpam-4656	347	4	w	w	PROPN
ejpam-4656	347	5	)	)	PUNCT
ejpam-4656	347	6	=	=	SYM
ejpam-4656	347	7	2	2	X
ejpam-4656	347	8	.	.	PUNCT
ejpam-4656	347	9	it	it	PRON
ejpam-4656	347	10	follows	follow	VERB
ejpam-4656	347	11	that	that	SCONJ
ejpam-4656	347	12	ds(g)(a	ds(g)(a	NOUN
ejpam-4656	347	13	,	,	PUNCT
ejpam-4656	347	14	w	w	NOUN
ejpam-4656	347	15	)	)	PUNCT
ejpam-4656	347	16	=	=	SYM
ejpam-4656	347	17	ds(g)(v	ds(g)(v	NOUN
ejpam-4656	347	18	′	′	NOUN
ejpam-4656	347	19	,	,	PUNCT
ejpam-4656	347	20	w	w	NOUN
ejpam-4656	347	21	)	)	PUNCT
ejpam-4656	347	22	=	=	SYM
ejpam-4656	347	23	2	2	X
ejpam-4656	347	24	.	.	X
ejpam-4656	347	25	therefore	therefore	ADV
ejpam-4656	347	26	,	,	PUNCT
ejpam-4656	347	27	s	s	VERB
ejpam-4656	347	28	is	be	AUX
ejpam-4656	347	29	a	a	DET
ejpam-4656	347	30	hop	hop	NOUN
ejpam-4656	347	31	dominating	dominating	NOUN
ejpam-4656	347	32	set	set	NOUN
ejpam-4656	347	33	in	in	ADP
ejpam-4656	347	34	s(g	s(g	PROPN
ejpam-4656	347	35	)	)	PUNCT
ejpam-4656	347	36	.	.	PUNCT
ejpam-4656	348	1	similarly	similarly	ADV
ejpam-4656	348	2	,	,	PUNCT
ejpam-4656	348	3	if	if	SCONJ
ejpam-4656	348	4	(	(	PUNCT
ejpam-4656	348	5	ii	ii	NOUN
ejpam-4656	348	6	)	)	PUNCT
ejpam-4656	348	7	holds	hold	VERB
ejpam-4656	348	8	,	,	PUNCT
ejpam-4656	348	9	then	then	ADV
ejpam-4656	348	10	s	s	VERB
ejpam-4656	348	11	is	be	AUX
ejpam-4656	348	12	a	a	DET
ejpam-4656	348	13	hop	hop	NOUN
ejpam-4656	348	14	dominating	dominating	NOUN
ejpam-4656	348	15	set	set	NOUN
ejpam-4656	348	16	in	in	ADP
ejpam-4656	348	17	s(g	s(g	PROPN
ejpam-4656	348	18	)	)	PUNCT
ejpam-4656	348	19	.	.	PUNCT
ejpam-4656	349	1	now	now	ADV
ejpam-4656	349	2	,	,	PUNCT
ejpam-4656	349	3	suppose	suppose	VERB
ejpam-4656	349	4	(	(	PUNCT
ejpam-4656	349	5	iii	iii	NOUN
ejpam-4656	349	6	)	)	PUNCT
ejpam-4656	349	7	holds	hold	VERB
ejpam-4656	349	8	.	.	PUNCT
ejpam-4656	350	1	let	let	VERB
ejpam-4656	350	2	y	y	PROPN
ejpam-4656	350	3	∈	∈	PROPN
ejpam-4656	350	4	v	v	X
ejpam-4656	350	5	(	(	PUNCT
ejpam-4656	350	6	s(g	s(g	PROPN
ejpam-4656	350	7	)	)	PUNCT
ejpam-4656	350	8	)	)	PUNCT
ejpam-4656	350	9	\	\	PUNCT
ejpam-4656	351	1	s.	s.	PROPN
ejpam-4656	351	2	then	then	ADV
ejpam-4656	351	3	y	y	PROPN
ejpam-4656	351	4	/∈	/∈	PUNCT
ejpam-4656	351	5	sg1	sg1	PROPN
ejpam-4656	351	6	∪	∪	ADP
ejpam-4656	351	7	sg2	sg2	PROPN
ejpam-4656	351	8	.	.	PUNCT
ejpam-4656	352	1	suppose	suppose	VERB
ejpam-4656	352	2	y	y	PROPN
ejpam-4656	352	3	∈	∈	PROPN
ejpam-4656	352	4	v	v	PROPN
ejpam-4656	352	5	(	(	PUNCT
ejpam-4656	352	6	g2	g2	PROPN
ejpam-4656	352	7	)	)	PUNCT
ejpam-4656	352	8	\	\	PROPN
ejpam-4656	353	1	sg2	sg2	PROPN
ejpam-4656	353	2	,	,	PUNCT
ejpam-4656	353	3	say	say	VERB
ejpam-4656	353	4	y	y	PROPN
ejpam-4656	353	5	=	=	SYM
ejpam-4656	353	6	z′	z′	PROPN
ejpam-4656	353	7	,	,	PUNCT
ejpam-4656	353	8	where	where	SCONJ
ejpam-4656	353	9	z	z	PROPN
ejpam-4656	353	10	∈	∈	PROPN
ejpam-4656	353	11	v	v	NOUN
ejpam-4656	353	12	(	(	PUNCT
ejpam-4656	353	13	g1	g1	PROPN
ejpam-4656	353	14	)	)	PUNCT
ejpam-4656	353	15	.	.	PUNCT
ejpam-4656	354	1	then	then	ADV
ejpam-4656	354	2	z	z	PROPN
ejpam-4656	354	3	/∈	/∈	PUNCT
ejpam-4656	354	4	s′	s′	VERB
ejpam-4656	354	5	g2	g2	PROPN
ejpam-4656	354	6	.	.	PUNCT
ejpam-4656	355	1	if	if	SCONJ
ejpam-4656	355	2	z	z	NOUN
ejpam-4656	355	3	∈	∈	PROPN
ejpam-4656	355	4	sg1	sg1	NOUN
ejpam-4656	355	5	,	,	PUNCT
ejpam-4656	355	6	then	then	ADV
ejpam-4656	355	7	ds(g)(y	ds(g)(y	ADJ
ejpam-4656	355	8	,	,	PUNCT
ejpam-4656	355	9	z	z	NOUN
ejpam-4656	355	10	)	)	PUNCT
ejpam-4656	355	11	=	=	VERB
ejpam-4656	355	12	ds(g)(z	ds(g)(z	VERB
ejpam-4656	355	13	′	′	NUM
ejpam-4656	355	14	,	,	PUNCT
ejpam-4656	355	15	z	z	NOUN
ejpam-4656	355	16	)	)	PUNCT
ejpam-4656	355	17	=	=	SYM
ejpam-4656	355	18	2	2	X
ejpam-4656	355	19	.	.	X
ejpam-4656	355	20	suppose	suppose	VERB
ejpam-4656	355	21	z	z	NOUN
ejpam-4656	355	22	/∈	/∈	PUNCT
ejpam-4656	355	23	sg1	sg1	PROPN
ejpam-4656	355	24	.	.	PUNCT
ejpam-4656	356	1	since	since	SCONJ
ejpam-4656	356	2	sg1∪s′	sg1∪s′	PROPN
ejpam-4656	356	3	g2	g2	PROPN
ejpam-4656	356	4	is	be	AUX
ejpam-4656	356	5	a	a	DET
ejpam-4656	356	6	hop	hop	NOUN
ejpam-4656	356	7	dominating	dominating	NOUN
ejpam-4656	356	8	set	set	VERB
ejpam-4656	356	9	in	in	ADP
ejpam-4656	356	10	g1	g1	PROPN
ejpam-4656	356	11	,	,	PUNCT
ejpam-4656	356	12	there	there	PRON
ejpam-4656	356	13	exists	exist	VERB
ejpam-4656	356	14	p	p	PROPN
ejpam-4656	356	15	∈	∈	PROPN
ejpam-4656	356	16	sg1∪s′	sg1∪s′	NOUN
ejpam-4656	356	17	g2	g2	PROPN
ejpam-4656	356	18	such	such	ADJ
ejpam-4656	356	19	that	that	SCONJ
ejpam-4656	356	20	dg1(p	dg1(p	PROPN
ejpam-4656	356	21	,	,	PUNCT
ejpam-4656	356	22	z	z	NOUN
ejpam-4656	356	23	)	)	PUNCT
ejpam-4656	356	24	=	=	SYM
ejpam-4656	356	25	2	2	NUM
ejpam-4656	356	26	=	=	SYM
ejpam-4656	356	27	ds(g)(p	ds(g)(p	NUM
ejpam-4656	356	28	,	,	PUNCT
ejpam-4656	356	29	z	z	NOUN
ejpam-4656	356	30	)	)	PUNCT
ejpam-4656	356	31	.	.	PUNCT
ejpam-4656	357	1	if	if	SCONJ
ejpam-4656	357	2	p	p	PROPN
ejpam-4656	357	3	∈	∈	PROPN
ejpam-4656	357	4	sg1	sg1	NOUN
ejpam-4656	357	5	,	,	PUNCT
ejpam-4656	357	6	then	then	ADV
ejpam-4656	357	7	p	p	PROPN
ejpam-4656	357	8	∈	∈	PROPN
ejpam-4656	357	9	s	s	X
ejpam-4656	357	10	and	and	CCONJ
ejpam-4656	357	11	ds(g)(p	ds(g)(p	NOUN
ejpam-4656	357	12	,	,	PUNCT
ejpam-4656	357	13	z	z	NOUN
ejpam-4656	357	14	′	′	NOUN
ejpam-4656	357	15	)	)	PUNCT
ejpam-4656	357	16	=	=	SYM
ejpam-4656	358	1	2	2	X
ejpam-4656	358	2	.	.	X
ejpam-4656	359	1	if	if	SCONJ
ejpam-4656	359	2	p	p	PROPN
ejpam-4656	359	3	∈	∈	PROPN
ejpam-4656	359	4	s′	s′	ADJ
ejpam-4656	359	5	g2	g2	PROPN
ejpam-4656	359	6	,	,	PUNCT
ejpam-4656	359	7	then	then	ADV
ejpam-4656	359	8	p′	p′	PROPN
ejpam-4656	359	9	∈	∈	PROPN
ejpam-4656	359	10	sg2	sg2	PROPN
ejpam-4656	359	11	⊆	⊆	NUM
ejpam-4656	359	12	s	s	NOUN
ejpam-4656	359	13	and	and	CCONJ
ejpam-4656	359	14	dg2(p	dg2(p	PROPN
ejpam-4656	359	15	′	′	NUM
ejpam-4656	359	16	,	,	PUNCT
ejpam-4656	359	17	z′	z′	NUM
ejpam-4656	359	18	)	)	PUNCT
ejpam-4656	359	19	=	=	SYM
ejpam-4656	359	20	ds(g)(p	ds(g)(p	NOUN
ejpam-4656	359	21	′	′	NUM
ejpam-4656	359	22	,	,	PUNCT
ejpam-4656	359	23	z′	z′	NUM
ejpam-4656	359	24	)	)	PUNCT
ejpam-4656	359	25	=	=	SYM
ejpam-4656	360	1	2	2	X
ejpam-4656	360	2	.	.	X
ejpam-4656	360	3	therefore	therefore	ADV
ejpam-4656	360	4	,	,	PUNCT
ejpam-4656	360	5	s	s	VERB
ejpam-4656	360	6	is	be	AUX
ejpam-4656	360	7	a	a	DET
ejpam-4656	360	8	hop	hop	NOUN
ejpam-4656	360	9	dominating	dominating	NOUN
ejpam-4656	360	10	set	set	NOUN
ejpam-4656	360	11	in	in	ADP
ejpam-4656	360	12	s(g	s(g	PROPN
ejpam-4656	360	13	)	)	PUNCT
ejpam-4656	360	14	.	.	PUNCT
ejpam-4656	361	1	corollary	corollary	ADJ
ejpam-4656	361	2	3	3	X
ejpam-4656	361	3	.	.	PUNCT
ejpam-4656	362	1	let	let	VERB
ejpam-4656	362	2	g	g	PRON
ejpam-4656	362	3	be	be	AUX
ejpam-4656	362	4	a	a	DET
ejpam-4656	362	5	non	non	ADJ
ejpam-4656	362	6	-	-	ADJ
ejpam-4656	362	7	trivial	trivial	ADJ
ejpam-4656	362	8	connected	connected	ADJ
ejpam-4656	362	9	graph	graph	NOUN
ejpam-4656	362	10	.	.	PUNCT
ejpam-4656	363	1	then	then	ADV
ejpam-4656	363	2	γh(s(g	γh(s(g	NOUN
ejpam-4656	363	3	)	)	PUNCT
ejpam-4656	363	4	)	)	PUNCT
ejpam-4656	364	1	=	=	NOUN
ejpam-4656	364	2	γh(g	γh(g	NOUN
ejpam-4656	364	3	)	)	PUNCT
ejpam-4656	364	4	.	.	PUNCT
ejpam-4656	365	1	theorem	theorem	NOUN
ejpam-4656	365	2	6	6	NUM
ejpam-4656	365	3	.	.	PUNCT
ejpam-4656	366	1	let	let	VERB
ejpam-4656	366	2	g	g	PRON
ejpam-4656	366	3	be	be	AUX
ejpam-4656	366	4	a	a	DET
ejpam-4656	366	5	non	non	ADJ
ejpam-4656	366	6	-	-	ADJ
ejpam-4656	366	7	trivial	trivial	ADJ
ejpam-4656	366	8	connected	connected	ADJ
ejpam-4656	366	9	graph	graph	NOUN
ejpam-4656	366	10	.	.	PUNCT
ejpam-4656	367	1	then	then	ADV
ejpam-4656	367	2	s	s	VERB
ejpam-4656	367	3	is	be	AUX
ejpam-4656	367	4	a	a	DET
ejpam-4656	367	5	convex	convex	ADJ
ejpam-4656	367	6	hop	hop	NOUN
ejpam-4656	367	7	dominating	dominating	NOUN
ejpam-4656	367	8	set	set	NOUN
ejpam-4656	367	9	in	in	ADP
ejpam-4656	367	10	s(g	s(g	PROPN
ejpam-4656	367	11	)	)	PUNCT
ejpam-4656	367	12	if	if	SCONJ
ejpam-4656	367	13	and	and	CCONJ
ejpam-4656	367	14	only	only	ADV
ejpam-4656	367	15	if	if	SCONJ
ejpam-4656	367	16	one	one	NUM
ejpam-4656	367	17	of	of	ADP
ejpam-4656	367	18	the	the	DET
ejpam-4656	367	19	following	follow	VERB
ejpam-4656	367	20	conditions	condition	NOUN
ejpam-4656	367	21	holds	hold	VERB
ejpam-4656	367	22	:	:	PUNCT
ejpam-4656	367	23	(	(	PUNCT
ejpam-4656	367	24	i	i	NOUN
ejpam-4656	367	25	)	)	PUNCT
ejpam-4656	367	26	s	s	VERB
ejpam-4656	367	27	is	be	AUX
ejpam-4656	367	28	clique	clique	ADJ
ejpam-4656	367	29	hop	hop	PROPN
ejpam-4656	367	30	dominating	dominating	NOUN
ejpam-4656	367	31	set	set	VERB
ejpam-4656	367	32	in	in	ADP
ejpam-4656	367	33	g1	g1	PROPN
ejpam-4656	367	34	.	.	PUNCT
ejpam-4656	368	1	(	(	PUNCT
ejpam-4656	368	2	ii	ii	NOUN
ejpam-4656	368	3	)	)	PUNCT
ejpam-4656	368	4	s	s	AUX
ejpam-4656	368	5	is	be	AUX
ejpam-4656	368	6	clique	clique	ADJ
ejpam-4656	368	7	hop	hop	PROPN
ejpam-4656	368	8	dominating	dominating	NOUN
ejpam-4656	368	9	set	set	VERB
ejpam-4656	368	10	in	in	ADP
ejpam-4656	368	11	g2	g2	PROPN
ejpam-4656	368	12	.	.	PUNCT
ejpam-4656	369	1	(	(	PUNCT
ejpam-4656	369	2	iii	iii	X
ejpam-4656	369	3	)	)	PUNCT
ejpam-4656	369	4	s	s	PART
ejpam-4656	369	5	=	=	NOUN
ejpam-4656	369	6	sg1	sg1	NOUN
ejpam-4656	369	7	∪	∪	ADP
ejpam-4656	369	8	sg2	sg2	PROPN
ejpam-4656	369	9	where	where	SCONJ
ejpam-4656	369	10	(	(	PUNCT
ejpam-4656	369	11	a	a	X
ejpam-4656	369	12	)	)	PUNCT
ejpam-4656	369	13	sg1	sg1	NOUN
ejpam-4656	369	14	∩	∩	NOUN
ejpam-4656	369	15	s′	s′	VERB
ejpam-4656	369	16	g2	g2	PROPN
ejpam-4656	369	17	=	=	PUNCT
ejpam-4656	369	18	∅	∅	NOUN
ejpam-4656	369	19	and	and	CCONJ
ejpam-4656	369	20	s′	s′	ADJ
ejpam-4656	369	21	g1	g1	PROPN
ejpam-4656	369	22	∩	∩	PROPN
ejpam-4656	369	23	sg2	sg2	PROPN
ejpam-4656	369	24	=	=	PROPN
ejpam-4656	369	25	∅.	∅.	PROPN
ejpam-4656	369	26	(	(	PUNCT
ejpam-4656	369	27	b	b	NOUN
ejpam-4656	369	28	)	)	PUNCT
ejpam-4656	369	29	sg1	sg1	NOUN
ejpam-4656	369	30	and	and	CCONJ
ejpam-4656	369	31	sg2	sg2	PROPN
ejpam-4656	369	32	are	be	AUX
ejpam-4656	369	33	cliques	clique	NOUN
ejpam-4656	369	34	in	in	ADP
ejpam-4656	369	35	sg1	sg1	PROPN
ejpam-4656	369	36	and	and	CCONJ
ejpam-4656	369	37	sg2	sg2	PROPN
ejpam-4656	369	38	,	,	PUNCT
ejpam-4656	369	39	respectively	respectively	ADV
ejpam-4656	369	40	.	.	PUNCT
ejpam-4656	370	1	(	(	PUNCT
ejpam-4656	370	2	c	c	X
ejpam-4656	370	3	)	)	PUNCT
ejpam-4656	370	4	sg1	sg1	NOUN
ejpam-4656	370	5	∪	∪	ADP
ejpam-4656	370	6	s′	s′	ADJ
ejpam-4656	370	7	g2	g2	PROPN
ejpam-4656	370	8	and	and	CCONJ
ejpam-4656	370	9	s′	s′	ADJ
ejpam-4656	370	10	g1	g1	PROPN
ejpam-4656	370	11	∪	∪	ADP
ejpam-4656	370	12	sg2	sg2	PROPN
ejpam-4656	370	13	are	be	AUX
ejpam-4656	370	14	clique	clique	ADJ
ejpam-4656	370	15	hop	hop	PROPN
ejpam-4656	370	16	dominating	dominating	NOUN
ejpam-4656	370	17	sets	set	NOUN
ejpam-4656	370	18	in	in	ADP
ejpam-4656	370	19	sg1	sg1	PROPN
ejpam-4656	370	20	and	and	CCONJ
ejpam-4656	370	21	sg2	sg2	PROPN
ejpam-4656	370	22	,	,	PUNCT
ejpam-4656	370	23	respectively	respectively	ADV
ejpam-4656	370	24	.	.	PUNCT
ejpam-4656	371	1	proof	proof	NOUN
ejpam-4656	371	2	.	.	PUNCT
ejpam-4656	372	1	follows	follow	VERB
ejpam-4656	372	2	from	from	ADP
ejpam-4656	372	3	theorem	theorem	ADJ
ejpam-4656	372	4	4	4	NUM
ejpam-4656	372	5	and	and	CCONJ
ejpam-4656	372	6	theorem	theorem	VERB
ejpam-4656	372	7	5	5	NUM
ejpam-4656	372	8	.	.	PUNCT
ejpam-4656	372	9	consider	consider	VERB
ejpam-4656	372	10	the	the	DET
ejpam-4656	372	11	following	follow	VERB
ejpam-4656	372	12	family	family	NOUN
ejpam-4656	372	13	of	of	ADP
ejpam-4656	372	14	graphs	graph	NOUN
ejpam-4656	372	15	:	:	PUNCT
ejpam-4656	372	16	b	b	X
ejpam-4656	372	17	=	=	SYM
ejpam-4656	372	18	{	{	PUNCT
ejpam-4656	372	19	g	g	NOUN
ejpam-4656	372	20	:	:	PUNCT
ejpam-4656	372	21	g	g	PROPN
ejpam-4656	372	22	admits	admit	VERB
ejpam-4656	372	23	a	a	DET
ejpam-4656	372	24	clique	clique	NOUN
ejpam-4656	372	25	hop	hop	PROPN
ejpam-4656	372	26	domination	domination	PROPN
ejpam-4656	372	27	}	}	PUNCT
ejpam-4656	372	28	.	.	PUNCT
ejpam-4656	373	1	then	then	ADV
ejpam-4656	373	2	the	the	DET
ejpam-4656	373	3	following	following	ADJ
ejpam-4656	373	4	result	result	NOUN
ejpam-4656	373	5	follows	follow	VERB
ejpam-4656	373	6	from	from	ADP
ejpam-4656	373	7	theorem	theorem	ADJ
ejpam-4656	373	8	6	6	NUM
ejpam-4656	373	9	.	.	PUNCT
ejpam-4656	373	10	corollary	corollary	ADJ
ejpam-4656	373	11	4	4	NUM
ejpam-4656	373	12	.	.	PUNCT
ejpam-4656	374	1	let	let	VERB
ejpam-4656	374	2	g	g	PRON
ejpam-4656	374	3	be	be	AUX
ejpam-4656	374	4	a	a	DET
ejpam-4656	374	5	non	non	ADJ
ejpam-4656	374	6	-	-	ADJ
ejpam-4656	374	7	trivial	trivial	ADJ
ejpam-4656	374	8	connected	connected	ADJ
ejpam-4656	374	9	graph	graph	NOUN
ejpam-4656	374	10	.	.	PUNCT
ejpam-4656	375	1	then	then	ADV
ejpam-4656	375	2	γconh(s(g	γconh(s(g	PUNCT
ejpam-4656	375	3	)	)	PUNCT
ejpam-4656	375	4	)	)	PUNCT
ejpam-4656	376	1	=	=	PRON
ejpam-4656	376	2	{	{	PUNCT
ejpam-4656	376	3	γclh(g	γclh(g	NOUN
ejpam-4656	376	4	)	)	PUNCT
ejpam-4656	376	5	if	if	SCONJ
ejpam-4656	376	6	g	g	PROPN
ejpam-4656	376	7	∈	∈	PROPN
ejpam-4656	376	8	b	b	PROPN
ejpam-4656	376	9	|v	|v	X
ejpam-4656	376	10	(	(	PUNCT
ejpam-4656	376	11	s(g))|	s(g))|	PROPN
ejpam-4656	376	12	if	if	SCONJ
ejpam-4656	376	13	g	g	PROPN
ejpam-4656	376	14	/∈	/∈	PROPN
ejpam-4656	376	15	b.	b.	PROPN
ejpam-4656	376	16	j.	j.	PROPN
ejpam-4656	376	17	hassan	hassan	PROPN
ejpam-4656	376	18	,	,	PUNCT
ejpam-4656	376	19	s.	s.	PROPN
ejpam-4656	376	20	canoy	canoy	PROPN
ejpam-4656	376	21	jr	jr	PROPN
ejpam-4656	376	22	.	.	PROPN
ejpam-4656	376	23	,	,	PUNCT
ejpam-4656	376	24	c.	c.	PROPN
ejpam-4656	376	25	saromines	saromine	VERB
ejpam-4656	376	26	/	/	SYM
ejpam-4656	376	27	eur	eur	PROPN
ejpam-4656	376	28	.	.	PUNCT
ejpam-4656	377	1	j.	j.	PROPN
ejpam-4656	377	2	pure	pure	PROPN
ejpam-4656	377	3	appl	appl	PROPN
ejpam-4656	377	4	.	.	PROPN
ejpam-4656	377	5	math	math	PROPN
ejpam-4656	377	6	,	,	PUNCT
ejpam-4656	377	7	16	16	NUM
ejpam-4656	377	8	(	(	PUNCT
ejpam-4656	377	9	1	1	NUM
ejpam-4656	377	10	)	)	PUNCT
ejpam-4656	377	11	(	(	PUNCT
ejpam-4656	377	12	2023	2023	NUM
ejpam-4656	377	13	)	)	PUNCT
ejpam-4656	377	14	,	,	PUNCT
ejpam-4656	377	15	319	319	NUM
ejpam-4656	377	16	-	-	SYM
ejpam-4656	377	17	335	335	NUM
ejpam-4656	377	18	327	327	NUM
ejpam-4656	377	19	theorem	theorem	NOUN
ejpam-4656	377	20	7	7	NUM
ejpam-4656	377	21	.	.	PUNCT
ejpam-4656	378	1	[	[	X
ejpam-4656	378	2	7	7	X
ejpam-4656	378	3	]	]	PUNCT
ejpam-4656	378	4	let	let	VERB
ejpam-4656	378	5	g	g	PRON
ejpam-4656	378	6	be	be	AUX
ejpam-4656	378	7	a	a	DET
ejpam-4656	378	8	graph	graph	NOUN
ejpam-4656	378	9	of	of	ADP
ejpam-4656	378	10	order	order	NOUN
ejpam-4656	378	11	n.	n.	NOUN
ejpam-4656	378	12	then	then	ADV
ejpam-4656	378	13	1	1	NUM
ejpam-4656	378	14	≤	≤	NUM
ejpam-4656	378	15	cpnd(g	cpnd(g	NOUN
ejpam-4656	378	16	)	)	PUNCT
ejpam-4656	378	17	≤	≤	NOUN
ejpam-4656	378	18	n.	n.	NOUN
ejpam-4656	378	19	moreover	moreover	ADV
ejpam-4656	378	20	,	,	PUNCT
ejpam-4656	378	21	(	(	PUNCT
ejpam-4656	378	22	i	i	NOUN
ejpam-4656	378	23	)	)	PUNCT
ejpam-4656	378	24	cpnd(g	cpnd(g	NOUN
ejpam-4656	378	25	)	)	PUNCT
ejpam-4656	379	1	=	=	SYM
ejpam-4656	379	2	1	1	NUM
ejpam-4656	379	3	if	if	SCONJ
ejpam-4656	379	4	and	and	CCONJ
ejpam-4656	379	5	only	only	ADV
ejpam-4656	379	6	if	if	SCONJ
ejpam-4656	379	7	g	g	PROPN
ejpam-4656	379	8	has	have	VERB
ejpam-4656	379	9	an	an	DET
ejpam-4656	379	10	isolated	isolated	ADJ
ejpam-4656	379	11	vertex	vertex	NOUN
ejpam-4656	379	12	.	.	PUNCT
ejpam-4656	380	1	(	(	PUNCT
ejpam-4656	380	2	ii	ii	NOUN
ejpam-4656	380	3	)	)	PUNCT
ejpam-4656	380	4	cpnd(g	cpnd(g	NOUN
ejpam-4656	380	5	)	)	PUNCT
ejpam-4656	380	6	=	=	SYM
ejpam-4656	381	1	n	n	NOUN
ejpam-4656	381	2	if	if	SCONJ
ejpam-4656	381	3	and	and	CCONJ
ejpam-4656	381	4	only	only	ADV
ejpam-4656	381	5	if	if	SCONJ
ejpam-4656	381	6	g	g	PROPN
ejpam-4656	381	7	is	be	AUX
ejpam-4656	381	8	a	a	DET
ejpam-4656	381	9	complete	complete	ADJ
ejpam-4656	381	10	graph	graph	NOUN
ejpam-4656	381	11	.	.	PUNCT
ejpam-4656	382	1	corollary	corollary	ADJ
ejpam-4656	382	2	5	5	NUM
ejpam-4656	382	3	.	.	PUNCT
ejpam-4656	383	1	[	[	X
ejpam-4656	383	2	7	7	X
ejpam-4656	383	3	]	]	X
ejpam-4656	383	4	let	let	VERB
ejpam-4656	383	5	n	n	PRON
ejpam-4656	383	6	be	be	AUX
ejpam-4656	383	7	any	any	DET
ejpam-4656	383	8	positive	positive	ADJ
ejpam-4656	383	9	integer	integer	NOUN
ejpam-4656	383	10	.	.	PUNCT
ejpam-4656	384	1	then	then	ADV
ejpam-4656	384	2	(	(	PUNCT
ejpam-4656	384	3	i	i	NOUN
ejpam-4656	384	4	)	)	PUNCT
ejpam-4656	384	5	cpnd(pn	cpnd(pn	PROPN
ejpam-4656	384	6	)	)	PUNCT
ejpam-4656	384	7	=	=	SYM
ejpam-4656	384	8	2	2	NUM
ejpam-4656	384	9	for	for	ADP
ejpam-4656	384	10	any	any	DET
ejpam-4656	384	11	n	n	PRON
ejpam-4656	384	12	≥	≥	NOUN
ejpam-4656	384	13	2	2	NUM
ejpam-4656	384	14	.	.	PUNCT
ejpam-4656	384	15	(	(	PUNCT
ejpam-4656	384	16	ii	ii	NOUN
ejpam-4656	384	17	)	)	PUNCT
ejpam-4656	384	18	cpnd(cn	cpnd(cn	NOUN
ejpam-4656	384	19	)	)	PUNCT
ejpam-4656	384	20	=	=	SYM
ejpam-4656	384	21	2	2	NUM
ejpam-4656	384	22	for	for	ADP
ejpam-4656	384	23	any	any	DET
ejpam-4656	384	24	n	n	PRON
ejpam-4656	384	25	≥	≥	NOUN
ejpam-4656	384	26	4	4	NUM
ejpam-4656	384	27	.	.	PUNCT
ejpam-4656	385	1	the	the	DET
ejpam-4656	385	2	next	next	ADJ
ejpam-4656	385	3	result	result	NOUN
ejpam-4656	385	4	is	be	AUX
ejpam-4656	385	5	found	find	VERB
ejpam-4656	385	6	in	in	ADP
ejpam-4656	385	7	[	[	X
ejpam-4656	385	8	13	13	NUM
ejpam-4656	385	9	]	]	PUNCT
ejpam-4656	385	10	.	.	PUNCT
ejpam-4656	386	1	theorem	theorem	ADJ
ejpam-4656	386	2	8	8	NUM
ejpam-4656	386	3	.	.	PUNCT
ejpam-4656	387	1	let	let	VERB
ejpam-4656	387	2	g	g	NOUN
ejpam-4656	387	3	and	and	CCONJ
ejpam-4656	387	4	h	h	NOUN
ejpam-4656	387	5	be	be	VERB
ejpam-4656	387	6	any	any	DET
ejpam-4656	387	7	two	two	NUM
ejpam-4656	387	8	graphs	graph	NOUN
ejpam-4656	387	9	.	.	PUNCT
ejpam-4656	388	1	a	a	DET
ejpam-4656	388	2	set	set	NOUN
ejpam-4656	388	3	s	s	NOUN
ejpam-4656	388	4	⊆	⊆	NUM
ejpam-4656	388	5	v	v	NOUN
ejpam-4656	388	6	(	(	PUNCT
ejpam-4656	388	7	g	g	PROPN
ejpam-4656	388	8	+	+	NOUN
ejpam-4656	388	9	h	h	NOUN
ejpam-4656	388	10	)	)	PUNCT
ejpam-4656	388	11	is	be	AUX
ejpam-4656	388	12	hop	hop	NOUN
ejpam-4656	388	13	dominating	dominating	NOUN
ejpam-4656	388	14	set	set	VERB
ejpam-4656	388	15	in	in	ADP
ejpam-4656	388	16	g+h	g+h	PROPN
ejpam-4656	388	17	if	if	SCONJ
ejpam-4656	388	18	and	and	CCONJ
ejpam-4656	388	19	only	only	ADV
ejpam-4656	388	20	if	if	SCONJ
ejpam-4656	388	21	s	s	NOUN
ejpam-4656	388	22	=	=	PUNCT
ejpam-4656	388	23	sg	sg	PROPN
ejpam-4656	388	24	∪sh	∪sh	NOUN
ejpam-4656	388	25	,	,	PUNCT
ejpam-4656	388	26	where	where	SCONJ
ejpam-4656	388	27	sg	sg	PROPN
ejpam-4656	388	28	and	and	CCONJ
ejpam-4656	388	29	sh	sh	PROPN
ejpam-4656	388	30	are	be	AUX
ejpam-4656	388	31	pointwise	pointwise	PROPN
ejpam-4656	388	32	non	non	ADJ
ejpam-4656	388	33	-	-	ADJ
ejpam-4656	388	34	dominating	dominating	ADJ
ejpam-4656	388	35	sets	set	NOUN
ejpam-4656	388	36	in	in	ADP
ejpam-4656	388	37	g	g	PROPN
ejpam-4656	388	38	and	and	CCONJ
ejpam-4656	388	39	h	h	NOUN
ejpam-4656	388	40	,	,	PUNCT
ejpam-4656	388	41	respectively	respectively	ADV
ejpam-4656	388	42	.	.	PUNCT
ejpam-4656	389	1	the	the	DET
ejpam-4656	389	2	following	follow	VERB
ejpam-4656	389	3	two	two	NUM
ejpam-4656	389	4	results	result	NOUN
ejpam-4656	389	5	are	be	AUX
ejpam-4656	389	6	obtained	obtain	VERB
ejpam-4656	389	7	in	in	ADP
ejpam-4656	389	8	[	[	X
ejpam-4656	389	9	12	12	NUM
ejpam-4656	389	10	]	]	PUNCT
ejpam-4656	389	11	.	.	PUNCT
ejpam-4656	390	1	theorem	theorem	NOUN
ejpam-4656	390	2	9	9	NUM
ejpam-4656	390	3	.	.	PUNCT
ejpam-4656	391	1	let	let	VERB
ejpam-4656	391	2	g	g	PRON
ejpam-4656	391	3	be	be	AUX
ejpam-4656	391	4	a	a	DET
ejpam-4656	391	5	connected	connected	ADJ
ejpam-4656	391	6	graph	graph	NOUN
ejpam-4656	391	7	and	and	CCONJ
ejpam-4656	391	8	kn	kn	PROPN
ejpam-4656	391	9	the	the	DET
ejpam-4656	391	10	complete	complete	ADJ
ejpam-4656	391	11	graph	graph	NOUN
ejpam-4656	391	12	of	of	ADP
ejpam-4656	391	13	order	order	NOUN
ejpam-4656	391	14	n.	n.	NOUN
ejpam-4656	391	15	then	then	ADV
ejpam-4656	391	16	a	a	DET
ejpam-4656	391	17	proper	proper	ADJ
ejpam-4656	391	18	subset	subset	NOUN
ejpam-4656	391	19	c	c	NOUN
ejpam-4656	391	20	=	=	SYM
ejpam-4656	391	21	s1	s1	PROPN
ejpam-4656	391	22	∪	∪	X
ejpam-4656	391	23	s2	s2	NOUN
ejpam-4656	391	24	of	of	ADP
ejpam-4656	391	25	v	v	NOUN
ejpam-4656	391	26	(	(	PUNCT
ejpam-4656	391	27	g	g	PROPN
ejpam-4656	391	28	+	+	PROPN
ejpam-4656	391	29	kn	kn	PROPN
ejpam-4656	391	30	)	)	PUNCT
ejpam-4656	391	31	,	,	PUNCT
ejpam-4656	391	32	where	where	SCONJ
ejpam-4656	391	33	s1	s1	PROPN
ejpam-4656	391	34	⊆	⊆	NUM
ejpam-4656	391	35	v	v	NOUN
ejpam-4656	391	36	(	(	PUNCT
ejpam-4656	391	37	g	g	NOUN
ejpam-4656	391	38	)	)	PUNCT
ejpam-4656	391	39	and	and	CCONJ
ejpam-4656	391	40	s2	s2	VERB
ejpam-4656	391	41	⊆	⊆	NUM
ejpam-4656	391	42	v	v	NOUN
ejpam-4656	391	43	(	(	PUNCT
ejpam-4656	391	44	kn	kn	PROPN
ejpam-4656	391	45	)	)	PUNCT
ejpam-4656	391	46	,	,	PUNCT
ejpam-4656	391	47	is	be	AUX
ejpam-4656	391	48	a	a	DET
ejpam-4656	391	49	convex	convex	NOUN
ejpam-4656	391	50	set	set	VERB
ejpam-4656	391	51	in	in	ADP
ejpam-4656	391	52	g+h	g+h	PROPN
ejpam-4656	392	1	if	if	SCONJ
ejpam-4656	392	2	and	and	CCONJ
ejpam-4656	392	3	only	only	ADV
ejpam-4656	392	4	if	if	SCONJ
ejpam-4656	392	5	s1	s1	NOUN
ejpam-4656	392	6	induces	induce	VERB
ejpam-4656	392	7	a	a	DET
ejpam-4656	392	8	complete	complete	ADJ
ejpam-4656	392	9	subgraph	subgraph	NOUN
ejpam-4656	392	10	of	of	ADP
ejpam-4656	392	11	g	g	PROPN
ejpam-4656	392	12	or	or	CCONJ
ejpam-4656	392	13	v	v	NOUN
ejpam-4656	392	14	(	(	PUNCT
ejpam-4656	392	15	g	g	NOUN
ejpam-4656	392	16	)	)	PUNCT
ejpam-4656	392	17	\	\	NOUN
ejpam-4656	393	1	s1	s1	NOUN
ejpam-4656	393	2	is	be	AUX
ejpam-4656	393	3	a	a	DET
ejpam-4656	393	4	non	non	ADJ
ejpam-4656	393	5	-	-	ADJ
ejpam-4656	393	6	connecting	connecting	ADJ
ejpam-4656	393	7	set	set	NOUN
ejpam-4656	393	8	and	and	CCONJ
ejpam-4656	393	9	s2	s2	PROPN
ejpam-4656	393	10	=	=	SYM
ejpam-4656	393	11	v	v	PROPN
ejpam-4656	393	12	(	(	PUNCT
ejpam-4656	393	13	kn	kn	PROPN
ejpam-4656	393	14	)	)	PUNCT
ejpam-4656	393	15	.	.	PUNCT
ejpam-4656	394	1	theorem	theorem	ADJ
ejpam-4656	394	2	10	10	NUM
ejpam-4656	394	3	.	.	PUNCT
ejpam-4656	395	1	let	let	VERB
ejpam-4656	395	2	g	g	NOUN
ejpam-4656	395	3	and	and	CCONJ
ejpam-4656	395	4	h	h	NOUN
ejpam-4656	395	5	be	be	VERB
ejpam-4656	395	6	two	two	NUM
ejpam-4656	395	7	non	non	ADJ
ejpam-4656	395	8	-	-	ADJ
ejpam-4656	395	9	complete	complete	ADJ
ejpam-4656	395	10	connected	connected	ADJ
ejpam-4656	395	11	graphs	graph	NOUN
ejpam-4656	395	12	.	.	PUNCT
ejpam-4656	396	1	then	then	ADV
ejpam-4656	396	2	a	a	DET
ejpam-4656	396	3	proper	proper	ADJ
ejpam-4656	396	4	subset	subset	NOUN
ejpam-4656	396	5	c	c	NOUN
ejpam-4656	396	6	=	=	SYM
ejpam-4656	396	7	s1	s1	PROPN
ejpam-4656	396	8	∪	∪	X
ejpam-4656	396	9	s2	s2	NOUN
ejpam-4656	396	10	of	of	ADP
ejpam-4656	396	11	v	v	NOUN
ejpam-4656	396	12	(	(	PUNCT
ejpam-4656	396	13	g+h	g+h	PROPN
ejpam-4656	396	14	)	)	PUNCT
ejpam-4656	396	15	,	,	PUNCT
ejpam-4656	396	16	where	where	SCONJ
ejpam-4656	396	17	s1	s1	PROPN
ejpam-4656	396	18	⊆	⊆	NUM
ejpam-4656	396	19	v	v	NOUN
ejpam-4656	396	20	(	(	PUNCT
ejpam-4656	396	21	g	g	NOUN
ejpam-4656	396	22	)	)	PUNCT
ejpam-4656	396	23	and	and	CCONJ
ejpam-4656	396	24	s2	s2	VERB
ejpam-4656	396	25	⊆	⊆	NUM
ejpam-4656	396	26	v	v	NOUN
ejpam-4656	396	27	(	(	PUNCT
ejpam-4656	396	28	h	h	NOUN
ejpam-4656	396	29	)	)	PUNCT
ejpam-4656	396	30	,	,	PUNCT
ejpam-4656	396	31	is	be	AUX
ejpam-4656	396	32	a	a	DET
ejpam-4656	396	33	convex	convex	NOUN
ejpam-4656	396	34	set	set	VERB
ejpam-4656	396	35	in	in	ADP
ejpam-4656	396	36	g+h	g+h	PROPN
ejpam-4656	397	1	if	if	SCONJ
ejpam-4656	397	2	and	and	CCONJ
ejpam-4656	397	3	only	only	ADV
ejpam-4656	397	4	if	if	SCONJ
ejpam-4656	397	5	s1	s1	PROPN
ejpam-4656	397	6	and	and	CCONJ
ejpam-4656	397	7	s2	s2	NOUN
ejpam-4656	397	8	induce	induce	VERB
ejpam-4656	397	9	complete	complete	ADJ
ejpam-4656	397	10	subgraphs	subgraph	NOUN
ejpam-4656	397	11	of	of	ADP
ejpam-4656	397	12	g	g	NOUN
ejpam-4656	397	13	and	and	CCONJ
ejpam-4656	397	14	h	h	NOUN
ejpam-4656	397	15	,	,	PUNCT
ejpam-4656	397	16	respectively	respectively	ADV
ejpam-4656	397	17	,	,	PUNCT
ejpam-4656	397	18	where	where	SCONJ
ejpam-4656	397	19	it	it	PRON
ejpam-4656	397	20	may	may	AUX
ejpam-4656	397	21	occur	occur	VERB
ejpam-4656	397	22	that	that	DET
ejpam-4656	397	23	s1	s1	NOUN
ejpam-4656	397	24	=	=	PUNCT
ejpam-4656	397	25	∅	∅	NOUN
ejpam-4656	397	26	or	or	CCONJ
ejpam-4656	397	27	s2	s2	VERB
ejpam-4656	397	28	=	=	PUNCT
ejpam-4656	397	29	∅.	∅.	NOUN
ejpam-4656	397	30	theorem	theorem	VERB
ejpam-4656	397	31	11	11	NUM
ejpam-4656	397	32	.	.	PUNCT
ejpam-4656	398	1	let	let	VERB
ejpam-4656	398	2	g	g	NOUN
ejpam-4656	398	3	and	and	CCONJ
ejpam-4656	398	4	h	h	NOUN
ejpam-4656	398	5	be	be	VERB
ejpam-4656	398	6	two	two	NUM
ejpam-4656	398	7	non	non	ADJ
ejpam-4656	398	8	-	-	ADJ
ejpam-4656	398	9	complete	complete	ADJ
ejpam-4656	398	10	connected	connected	ADJ
ejpam-4656	398	11	graphs	graph	NOUN
ejpam-4656	398	12	.	.	PUNCT
ejpam-4656	399	1	a	a	DET
ejpam-4656	399	2	set	set	NOUN
ejpam-4656	399	3	s	s	NOUN
ejpam-4656	399	4	⊆	⊆	NUM
ejpam-4656	399	5	v	v	NOUN
ejpam-4656	399	6	(	(	PUNCT
ejpam-4656	399	7	g+h	g+h	PROPN
ejpam-4656	399	8	)	)	PUNCT
ejpam-4656	399	9	is	be	AUX
ejpam-4656	399	10	a	a	DET
ejpam-4656	399	11	convex	convex	ADJ
ejpam-4656	399	12	hop	hop	NOUN
ejpam-4656	399	13	dominating	dominating	NOUN
ejpam-4656	399	14	set	set	VERB
ejpam-4656	399	15	in	in	ADP
ejpam-4656	399	16	g	g	PROPN
ejpam-4656	400	1	+	+	NOUN
ejpam-4656	400	2	h	h	NOUN
ejpam-4656	400	3	if	if	SCONJ
ejpam-4656	400	4	and	and	CCONJ
ejpam-4656	400	5	only	only	ADV
ejpam-4656	400	6	if	if	SCONJ
ejpam-4656	400	7	s	s	VERB
ejpam-4656	400	8	=	=	PUNCT
ejpam-4656	400	9	sg	sg	X
ejpam-4656	400	10	∪	∪	ADJ
ejpam-4656	400	11	sh	sh	PROPN
ejpam-4656	400	12	,	,	PUNCT
ejpam-4656	400	13	where	where	SCONJ
ejpam-4656	400	14	sg	sg	PROPN
ejpam-4656	400	15	and	and	CCONJ
ejpam-4656	400	16	sh	sh	PROPN
ejpam-4656	400	17	are	be	AUX
ejpam-4656	400	18	clique	clique	PROPN
ejpam-4656	400	19	pointwise	pointwise	PROPN
ejpam-4656	400	20	non	non	ADJ
ejpam-4656	400	21	-	-	ADJ
ejpam-4656	400	22	dominating	dominating	ADJ
ejpam-4656	400	23	sets	set	NOUN
ejpam-4656	400	24	in	in	ADP
ejpam-4656	400	25	g	g	PROPN
ejpam-4656	400	26	and	and	CCONJ
ejpam-4656	400	27	h	h	NOUN
ejpam-4656	400	28	,	,	PUNCT
ejpam-4656	400	29	respectively	respectively	ADV
ejpam-4656	400	30	.	.	PUNCT
ejpam-4656	401	1	proof	proof	NOUN
ejpam-4656	401	2	.	.	PUNCT
ejpam-4656	402	1	suppose	suppose	VERB
ejpam-4656	402	2	s	s	PRON
ejpam-4656	402	3	is	be	AUX
ejpam-4656	402	4	a	a	DET
ejpam-4656	402	5	convex	convex	ADJ
ejpam-4656	402	6	hop	hop	NOUN
ejpam-4656	402	7	dominating	dominating	NOUN
ejpam-4656	402	8	set	set	VERB
ejpam-4656	402	9	in	in	ADP
ejpam-4656	402	10	g+h	g+h	PROPN
ejpam-4656	402	11	.	.	PUNCT
ejpam-4656	403	1	then	then	ADV
ejpam-4656	403	2	sg	sg	PROPN
ejpam-4656	403	3	and	and	CCONJ
ejpam-4656	403	4	sh	sh	PROPN
ejpam-4656	403	5	are	be	AUX
ejpam-4656	403	6	both	both	PRON
ejpam-4656	403	7	non	non	ADJ
ejpam-4656	403	8	-	-	ADJ
ejpam-4656	403	9	empty	empty	ADJ
ejpam-4656	403	10	.	.	PUNCT
ejpam-4656	404	1	since	since	SCONJ
ejpam-4656	404	2	s	s	PROPN
ejpam-4656	404	3	is	be	AUX
ejpam-4656	404	4	a	a	DET
ejpam-4656	404	5	hop	hop	NOUN
ejpam-4656	404	6	dominating	dominating	NOUN
ejpam-4656	404	7	set	set	NOUN
ejpam-4656	404	8	,	,	PUNCT
ejpam-4656	404	9	sg	sg	PROPN
ejpam-4656	404	10	and	and	CCONJ
ejpam-4656	404	11	sh	sh	PROPN
ejpam-4656	404	12	are	be	AUX
ejpam-4656	404	13	pointwise	pointwise	PROPN
ejpam-4656	404	14	non	non	ADJ
ejpam-4656	404	15	-	-	ADJ
ejpam-4656	404	16	dominating	dominating	ADJ
ejpam-4656	404	17	sets	set	NOUN
ejpam-4656	404	18	in	in	ADP
ejpam-4656	404	19	g	g	PROPN
ejpam-4656	404	20	and	and	CCONJ
ejpam-4656	404	21	h	h	NOUN
ejpam-4656	404	22	,	,	PUNCT
ejpam-4656	404	23	respectively	respectively	ADV
ejpam-4656	404	24	by	by	ADP
ejpam-4656	404	25	theorem	theorem	NOUN
ejpam-4656	404	26	8	8	NUM
ejpam-4656	404	27	.	.	PUNCT
ejpam-4656	405	1	since	since	SCONJ
ejpam-4656	405	2	s	s	PROPN
ejpam-4656	405	3	is	be	AUX
ejpam-4656	405	4	a	a	DET
ejpam-4656	405	5	convex	convex	NOUN
ejpam-4656	405	6	set	set	NOUN
ejpam-4656	405	7	,	,	PUNCT
ejpam-4656	405	8	sg	sg	PROPN
ejpam-4656	405	9	and	and	CCONJ
ejpam-4656	405	10	sh	sh	PROPN
ejpam-4656	405	11	are	be	AUX
ejpam-4656	405	12	cliques	clique	NOUN
ejpam-4656	405	13	in	in	ADP
ejpam-4656	405	14	g	g	PROPN
ejpam-4656	405	15	and	and	CCONJ
ejpam-4656	405	16	h	h	NOUN
ejpam-4656	405	17	,	,	PUNCT
ejpam-4656	405	18	respectively	respectively	ADV
ejpam-4656	405	19	,	,	PUNCT
ejpam-4656	405	20	by	by	ADP
ejpam-4656	405	21	theorem	theorem	NOUN
ejpam-4656	405	22	10	10	NUM
ejpam-4656	405	23	.	.	PUNCT
ejpam-4656	406	1	therefore	therefore	ADV
ejpam-4656	406	2	,	,	PUNCT
ejpam-4656	406	3	sg	sg	PROPN
ejpam-4656	406	4	and	and	CCONJ
ejpam-4656	406	5	sh	sh	PROPN
ejpam-4656	406	6	are	be	AUX
ejpam-4656	406	7	clique	clique	PROPN
ejpam-4656	406	8	pointwise	pointwise	PROPN
ejpam-4656	406	9	non	non	ADJ
ejpam-4656	406	10	-	-	ADJ
ejpam-4656	406	11	dominating	dominating	ADJ
ejpam-4656	406	12	sets	set	NOUN
ejpam-4656	406	13	in	in	ADP
ejpam-4656	406	14	g	g	PROPN
ejpam-4656	406	15	and	and	CCONJ
ejpam-4656	406	16	h	h	NOUN
ejpam-4656	406	17	,	,	PUNCT
ejpam-4656	406	18	respectively	respectively	ADV
ejpam-4656	406	19	.	.	PUNCT
ejpam-4656	407	1	conversely	conversely	ADV
ejpam-4656	407	2	,	,	PUNCT
ejpam-4656	407	3	suppose	suppose	VERB
ejpam-4656	407	4	that	that	SCONJ
ejpam-4656	407	5	s	s	VERB
ejpam-4656	407	6	=	=	PUNCT
ejpam-4656	407	7	sg	sg	X
ejpam-4656	407	8	∪	∪	ADJ
ejpam-4656	407	9	sh	sh	PROPN
ejpam-4656	407	10	,	,	PUNCT
ejpam-4656	407	11	where	where	SCONJ
ejpam-4656	407	12	sg	sg	PROPN
ejpam-4656	407	13	and	and	CCONJ
ejpam-4656	407	14	sh	sh	PROPN
ejpam-4656	407	15	are	be	AUX
ejpam-4656	407	16	clique	clique	ADJ
ejpam-4656	407	17	pointwise	pointwise	PROPN
ejpam-4656	407	18	nondominating	nondominate	VERB
ejpam-4656	407	19	sets	set	NOUN
ejpam-4656	407	20	in	in	ADP
ejpam-4656	407	21	g	g	PROPN
ejpam-4656	407	22	and	and	CCONJ
ejpam-4656	407	23	h	h	NOUN
ejpam-4656	407	24	,	,	PUNCT
ejpam-4656	407	25	respectively	respectively	ADV
ejpam-4656	407	26	.	.	PUNCT
ejpam-4656	408	1	since	since	SCONJ
ejpam-4656	408	2	sg	sg	PROPN
ejpam-4656	408	3	and	and	CCONJ
ejpam-4656	408	4	sh	sh	PROPN
ejpam-4656	408	5	are	be	AUX
ejpam-4656	408	6	pointwise	pointwise	PROPN
ejpam-4656	408	7	non	non	ADJ
ejpam-4656	408	8	-	-	ADJ
ejpam-4656	408	9	dominating	dominating	ADJ
ejpam-4656	408	10	sets	set	NOUN
ejpam-4656	408	11	,	,	PUNCT
ejpam-4656	408	12	s	s	PART
ejpam-4656	408	13	=	=	PUNCT
ejpam-4656	408	14	sg	sg	PROPN
ejpam-4656	408	15	∪	∪	NOUN
ejpam-4656	408	16	sh	sh	PROPN
ejpam-4656	408	17	is	be	AUX
ejpam-4656	408	18	a	a	DET
ejpam-4656	408	19	hop	hop	NOUN
ejpam-4656	408	20	dominating	dominating	NOUN
ejpam-4656	408	21	set	set	VERB
ejpam-4656	408	22	in	in	ADP
ejpam-4656	408	23	g+h	g+h	PROPN
ejpam-4656	408	24	by	by	ADP
ejpam-4656	408	25	theorem	theorem	NOUN
ejpam-4656	408	26	8	8	NUM
ejpam-4656	408	27	.	.	PUNCT
ejpam-4656	409	1	since	since	SCONJ
ejpam-4656	409	2	sg	sg	PROPN
ejpam-4656	409	3	and	and	CCONJ
ejpam-4656	409	4	sh	sh	PROPN
ejpam-4656	409	5	are	be	AUX
ejpam-4656	409	6	cliques	clique	NOUN
ejpam-4656	409	7	,	,	PUNCT
ejpam-4656	409	8	it	it	PRON
ejpam-4656	409	9	follows	follow	VERB
ejpam-4656	409	10	that	that	SCONJ
ejpam-4656	409	11	s	s	VERB
ejpam-4656	409	12	=	=	ADJ
ejpam-4656	409	13	sg∪sh	sg∪sh	PROPN
ejpam-4656	409	14	is	be	AUX
ejpam-4656	409	15	a	a	DET
ejpam-4656	409	16	convex	convex	NOUN
ejpam-4656	409	17	set	set	VERB
ejpam-4656	409	18	in	in	ADP
ejpam-4656	409	19	g+h	g+h	PROPN
ejpam-4656	409	20	by	by	ADP
ejpam-4656	409	21	theorem	theorem	NOUN
ejpam-4656	409	22	10	10	NUM
ejpam-4656	409	23	.	.	PUNCT
ejpam-4656	410	1	consequently	consequently	ADV
ejpam-4656	410	2	,	,	PUNCT
ejpam-4656	410	3	s	s	VERB
ejpam-4656	410	4	=	=	PUNCT
ejpam-4656	410	5	sg	sg	PROPN
ejpam-4656	410	6	∪	∪	NOUN
ejpam-4656	410	7	sh	sh	PROPN
ejpam-4656	410	8	is	be	AUX
ejpam-4656	410	9	a	a	DET
ejpam-4656	410	10	convex	convex	ADJ
ejpam-4656	410	11	hop	hop	NOUN
ejpam-4656	410	12	dominating	dominating	NOUN
ejpam-4656	410	13	set	set	VERB
ejpam-4656	410	14	in	in	ADP
ejpam-4656	410	15	g+h	g+h	PROPN
ejpam-4656	410	16	.	.	PUNCT
ejpam-4656	411	1	the	the	DET
ejpam-4656	411	2	next	next	ADJ
ejpam-4656	411	3	result	result	NOUN
ejpam-4656	411	4	follows	follow	VERB
ejpam-4656	411	5	from	from	ADP
ejpam-4656	411	6	theorem	theorem	ADJ
ejpam-4656	411	7	7	7	NUM
ejpam-4656	411	8	,	,	PUNCT
ejpam-4656	411	9	corollary	corollary	ADJ
ejpam-4656	411	10	5	5	NUM
ejpam-4656	411	11	and	and	CCONJ
ejpam-4656	411	12	theorem	theorem	VERB
ejpam-4656	411	13	11	11	NUM
ejpam-4656	411	14	.	.	PUNCT
ejpam-4656	412	1	corollary	corollary	ADJ
ejpam-4656	412	2	6	6	NUM
ejpam-4656	412	3	.	.	PUNCT
ejpam-4656	413	1	let	let	VERB
ejpam-4656	413	2	g	g	NOUN
ejpam-4656	413	3	and	and	CCONJ
ejpam-4656	413	4	h	h	NOUN
ejpam-4656	413	5	be	be	VERB
ejpam-4656	413	6	two	two	NUM
ejpam-4656	413	7	non	non	ADJ
ejpam-4656	413	8	-	-	ADJ
ejpam-4656	413	9	complete	complete	ADJ
ejpam-4656	413	10	connected	connected	ADJ
ejpam-4656	413	11	graphs	graph	NOUN
ejpam-4656	413	12	.	.	PUNCT
ejpam-4656	414	1	then	then	ADV
ejpam-4656	414	2	γconh(g+h	γconh(g+h	NOUN
ejpam-4656	414	3	)	)	PUNCT
ejpam-4656	415	1	=	=	PUNCT
ejpam-4656	415	2	cpnd(g	cpnd(g	NOUN
ejpam-4656	415	3	)	)	PUNCT
ejpam-4656	415	4	+	+	CCONJ
ejpam-4656	415	5	cpnd(h	cpnd(h	NOUN
ejpam-4656	415	6	)	)	PUNCT
ejpam-4656	415	7	.	.	PUNCT
ejpam-4656	416	1	in	in	ADP
ejpam-4656	416	2	particular	particular	ADJ
ejpam-4656	416	3	,	,	PUNCT
ejpam-4656	416	4	we	we	PRON
ejpam-4656	416	5	have	have	VERB
ejpam-4656	416	6	j.	j.	PROPN
ejpam-4656	416	7	hassan	hassan	PROPN
ejpam-4656	416	8	,	,	PUNCT
ejpam-4656	416	9	s.	s.	PROPN
ejpam-4656	416	10	canoy	canoy	PROPN
ejpam-4656	416	11	jr	jr	PROPN
ejpam-4656	416	12	.	.	PROPN
ejpam-4656	416	13	,	,	PUNCT
ejpam-4656	416	14	c.	c.	PROPN
ejpam-4656	416	15	saromines	saromine	VERB
ejpam-4656	416	16	/	/	SYM
ejpam-4656	416	17	eur	eur	PROPN
ejpam-4656	416	18	.	.	PUNCT
ejpam-4656	417	1	j.	j.	PROPN
ejpam-4656	417	2	pure	pure	PROPN
ejpam-4656	417	3	appl	appl	PROPN
ejpam-4656	417	4	.	.	PROPN
ejpam-4656	417	5	math	math	PROPN
ejpam-4656	417	6	,	,	PUNCT
ejpam-4656	417	7	16	16	NUM
ejpam-4656	417	8	(	(	PUNCT
ejpam-4656	417	9	1	1	NUM
ejpam-4656	417	10	)	)	PUNCT
ejpam-4656	417	11	(	(	PUNCT
ejpam-4656	417	12	2023	2023	NUM
ejpam-4656	417	13	)	)	PUNCT
ejpam-4656	417	14	,	,	PUNCT
ejpam-4656	417	15	319	319	NUM
ejpam-4656	417	16	-	-	SYM
ejpam-4656	417	17	335	335	NUM
ejpam-4656	417	18	328	328	NUM
ejpam-4656	417	19	(	(	PUNCT
ejpam-4656	417	20	i	i	NOUN
ejpam-4656	417	21	)	)	PUNCT
ejpam-4656	417	22	γconh(pn	γconh(pn	NOUN
ejpam-4656	417	23	+	+	CCONJ
ejpam-4656	417	24	pm	pm	NOUN
ejpam-4656	417	25	)	)	PUNCT
ejpam-4656	417	26	=	=	SYM
ejpam-4656	417	27	4	4	NUM
ejpam-4656	417	28	for	for	ADP
ejpam-4656	417	29	all	all	DET
ejpam-4656	417	30	n	n	CCONJ
ejpam-4656	417	31	,	,	PUNCT
ejpam-4656	417	32	m	m	VERB
ejpam-4656	417	33	≥	≥	NOUN
ejpam-4656	417	34	3	3	NUM
ejpam-4656	417	35	,	,	PUNCT
ejpam-4656	417	36	and	and	CCONJ
ejpam-4656	417	37	(	(	PUNCT
ejpam-4656	417	38	ii	ii	NOUN
ejpam-4656	417	39	)	)	PUNCT
ejpam-4656	417	40	γconh(cn	γconh(cn	NOUN
ejpam-4656	417	41	+	+	CCONJ
ejpam-4656	417	42	cm	cm	NOUN
ejpam-4656	417	43	)	)	PUNCT
ejpam-4656	417	44	=	=	SYM
ejpam-4656	417	45	4	4	NUM
ejpam-4656	417	46	for	for	ADP
ejpam-4656	417	47	all	all	DET
ejpam-4656	417	48	n	n	CCONJ
ejpam-4656	417	49	,	,	PUNCT
ejpam-4656	417	50	m	m	VERB
ejpam-4656	417	51	≥	≥	NOUN
ejpam-4656	417	52	4	4	NUM
ejpam-4656	417	53	.	.	PUNCT
ejpam-4656	417	54	theorem	theorem	NOUN
ejpam-4656	417	55	12	12	NUM
ejpam-4656	417	56	.	.	PUNCT
ejpam-4656	418	1	let	let	VERB
ejpam-4656	418	2	g	g	PRON
ejpam-4656	418	3	be	be	AUX
ejpam-4656	418	4	a	a	DET
ejpam-4656	418	5	connected	connected	ADJ
ejpam-4656	418	6	graph	graph	NOUN
ejpam-4656	418	7	and	and	CCONJ
ejpam-4656	418	8	kn	kn	PROPN
ejpam-4656	418	9	the	the	DET
ejpam-4656	418	10	complete	complete	ADJ
ejpam-4656	418	11	graph	graph	NOUN
ejpam-4656	418	12	of	of	ADP
ejpam-4656	418	13	order	order	NOUN
ejpam-4656	418	14	n.	n.	VERB
ejpam-4656	418	15	a	a	DET
ejpam-4656	418	16	set	set	NOUN
ejpam-4656	418	17	s	s	PROPN
ejpam-4656	418	18	⊆	⊆	NUM
ejpam-4656	418	19	v	v	NOUN
ejpam-4656	418	20	(	(	PUNCT
ejpam-4656	418	21	g+kn	g+kn	NOUN
ejpam-4656	418	22	)	)	PUNCT
ejpam-4656	418	23	is	be	AUX
ejpam-4656	418	24	a	a	DET
ejpam-4656	418	25	convex	convex	ADJ
ejpam-4656	418	26	hop	hop	NOUN
ejpam-4656	418	27	dominating	dominating	NOUN
ejpam-4656	418	28	set	set	VERB
ejpam-4656	418	29	in	in	ADP
ejpam-4656	418	30	g+kn	g+kn	NOUN
ejpam-4656	418	31	if	if	SCONJ
ejpam-4656	419	1	and	and	CCONJ
ejpam-4656	419	2	only	only	ADV
ejpam-4656	419	3	if	if	SCONJ
ejpam-4656	419	4	s	s	VERB
ejpam-4656	419	5	=	=	SYM
ejpam-4656	419	6	v	v	PROPN
ejpam-4656	419	7	(	(	PUNCT
ejpam-4656	419	8	kn)∪sg	kn)∪sg	PROPN
ejpam-4656	419	9	where	where	SCONJ
ejpam-4656	419	10	v	v	X
ejpam-4656	419	11	(	(	PUNCT
ejpam-4656	419	12	g	g	NOUN
ejpam-4656	419	13	)	)	PUNCT
ejpam-4656	419	14	\	\	PROPN
ejpam-4656	420	1	sg	sg	PROPN
ejpam-4656	420	2	is	be	AUX
ejpam-4656	420	3	a	a	DET
ejpam-4656	420	4	non	non	ADJ
ejpam-4656	420	5	-	-	ADJ
ejpam-4656	420	6	connecting	connecting	ADJ
ejpam-4656	420	7	set	set	NOUN
ejpam-4656	420	8	and	and	CCONJ
ejpam-4656	420	9	sg	sg	PROPN
ejpam-4656	420	10	is	be	AUX
ejpam-4656	420	11	a	a	DET
ejpam-4656	420	12	pointwise	pointwise	ADJ
ejpam-4656	420	13	non	non	ADJ
ejpam-4656	420	14	-	-	ADJ
ejpam-4656	420	15	dominating	dominating	ADJ
ejpam-4656	420	16	set	set	NOUN
ejpam-4656	420	17	in	in	ADP
ejpam-4656	420	18	g.	g.	PROPN
ejpam-4656	420	19	proof	proof	PROPN
ejpam-4656	420	20	.	.	PUNCT
ejpam-4656	421	1	suppose	suppose	VERB
ejpam-4656	421	2	s	s	X
ejpam-4656	421	3	=	=	ADJ
ejpam-4656	421	4	skn	skn	PROPN
ejpam-4656	421	5	∪sg	∪sg	VERB
ejpam-4656	421	6	is	be	AUX
ejpam-4656	421	7	a	a	DET
ejpam-4656	421	8	convex	convex	ADJ
ejpam-4656	421	9	hop	hop	NOUN
ejpam-4656	421	10	dominating	dominating	NOUN
ejpam-4656	421	11	set	set	NOUN
ejpam-4656	421	12	of	of	ADP
ejpam-4656	421	13	g+kn	g+kn	NOUN
ejpam-4656	421	14	.	.	PUNCT
ejpam-4656	422	1	by	by	ADP
ejpam-4656	422	2	theorem	theorem	NOUN
ejpam-4656	422	3	8	8	NUM
ejpam-4656	422	4	,	,	PUNCT
ejpam-4656	422	5	skn	skn	PRON
ejpam-4656	422	6	and	and	CCONJ
ejpam-4656	422	7	sg	sg	PROPN
ejpam-4656	422	8	are	be	AUX
ejpam-4656	422	9	pointwise	pointwise	PROPN
ejpam-4656	422	10	non	non	ADJ
ejpam-4656	422	11	-	-	ADJ
ejpam-4656	422	12	dominating	dominating	ADJ
ejpam-4656	422	13	sets	set	NOUN
ejpam-4656	422	14	of	of	ADP
ejpam-4656	422	15	kn	kn	PROPN
ejpam-4656	422	16	and	and	CCONJ
ejpam-4656	422	17	g	g	NOUN
ejpam-4656	422	18	,	,	PUNCT
ejpam-4656	422	19	respectively	respectively	ADV
ejpam-4656	422	20	.	.	PUNCT
ejpam-4656	423	1	hence	hence	ADV
ejpam-4656	423	2	,	,	PUNCT
ejpam-4656	423	3	skn	skn	PROPN
ejpam-4656	423	4	=	=	SYM
ejpam-4656	423	5	v	v	PROPN
ejpam-4656	423	6	(	(	PUNCT
ejpam-4656	423	7	kn	kn	PROPN
ejpam-4656	423	8	)	)	PUNCT
ejpam-4656	423	9	.	.	PUNCT
ejpam-4656	424	1	moreover	moreover	ADV
ejpam-4656	424	2	,	,	PUNCT
ejpam-4656	424	3	by	by	ADP
ejpam-4656	424	4	theorem	theorem	NOUN
ejpam-4656	424	5	9	9	NUM
ejpam-4656	424	6	,	,	PUNCT
ejpam-4656	424	7	v	v	NOUN
ejpam-4656	424	8	(	(	PUNCT
ejpam-4656	424	9	g	g	NOUN
ejpam-4656	424	10	)	)	PUNCT
ejpam-4656	424	11	\	\	PROPN
ejpam-4656	424	12	sg	sg	PROPN
ejpam-4656	424	13	is	be	AUX
ejpam-4656	424	14	a	a	DET
ejpam-4656	424	15	non	non	ADJ
ejpam-4656	424	16	-	-	ADJ
ejpam-4656	424	17	connecting	connecting	ADJ
ejpam-4656	424	18	set	set	NOUN
ejpam-4656	424	19	in	in	ADP
ejpam-4656	424	20	g.	g.	NOUN
ejpam-4656	424	21	conversely	conversely	ADV
ejpam-4656	424	22	,	,	PUNCT
ejpam-4656	424	23	suppose	suppose	VERB
ejpam-4656	424	24	that	that	SCONJ
ejpam-4656	424	25	s	s	VERB
ejpam-4656	424	26	=	=	SYM
ejpam-4656	424	27	v	v	PROPN
ejpam-4656	424	28	(	(	PUNCT
ejpam-4656	424	29	kn	kn	PROPN
ejpam-4656	424	30	)	)	PUNCT
ejpam-4656	424	31	∪	∪	ADP
ejpam-4656	424	32	sg	sg	ADP
ejpam-4656	424	33	such	such	ADJ
ejpam-4656	424	34	that	that	PRON
ejpam-4656	424	35	v	v	NOUN
ejpam-4656	424	36	(	(	PUNCT
ejpam-4656	424	37	g	g	NOUN
ejpam-4656	424	38	)	)	PUNCT
ejpam-4656	424	39	\	\	PROPN
ejpam-4656	424	40	sg	sg	PROPN
ejpam-4656	424	41	is	be	AUX
ejpam-4656	424	42	a	a	DET
ejpam-4656	424	43	non	non	ADJ
ejpam-4656	424	44	-	-	ADJ
ejpam-4656	424	45	connecting	connecting	ADJ
ejpam-4656	424	46	set	set	NOUN
ejpam-4656	424	47	and	and	CCONJ
ejpam-4656	424	48	sg	sg	PROPN
ejpam-4656	424	49	is	be	AUX
ejpam-4656	424	50	a	a	DET
ejpam-4656	424	51	pointwise	pointwise	ADJ
ejpam-4656	424	52	non	non	ADJ
ejpam-4656	424	53	-	-	ADJ
ejpam-4656	424	54	dominating	dominating	ADJ
ejpam-4656	424	55	set	set	NOUN
ejpam-4656	424	56	in	in	ADP
ejpam-4656	424	57	g.	g.	PROPN
ejpam-4656	424	58	then	then	ADV
ejpam-4656	424	59	,	,	PUNCT
ejpam-4656	424	60	by	by	ADP
ejpam-4656	424	61	theorem	theorem	NOUN
ejpam-4656	424	62	8	8	NUM
ejpam-4656	424	63	and	and	CCONJ
ejpam-4656	424	64	theorem	theorem	VERB
ejpam-4656	424	65	9	9	NUM
ejpam-4656	424	66	,	,	PUNCT
ejpam-4656	424	67	s	s	VERB
ejpam-4656	424	68	is	be	AUX
ejpam-4656	424	69	a	a	DET
ejpam-4656	424	70	convex	convex	ADJ
ejpam-4656	424	71	hop	hop	NOUN
ejpam-4656	424	72	dominating	dominating	NOUN
ejpam-4656	424	73	set	set	NOUN
ejpam-4656	424	74	of	of	ADP
ejpam-4656	424	75	g+kn	g+kn	NOUN
ejpam-4656	424	76	.	.	PUNCT
ejpam-4656	425	1	the	the	DET
ejpam-4656	425	2	next	next	ADJ
ejpam-4656	425	3	result	result	NOUN
ejpam-4656	425	4	follows	follow	VERB
ejpam-4656	425	5	from	from	ADP
ejpam-4656	425	6	theorem	theorem	ADJ
ejpam-4656	425	7	12	12	NUM
ejpam-4656	425	8	.	.	PUNCT
ejpam-4656	426	1	corollary	corollary	ADJ
ejpam-4656	426	2	7	7	NUM
ejpam-4656	426	3	.	.	PUNCT
ejpam-4656	427	1	let	let	VERB
ejpam-4656	427	2	g	g	PROPN
ejpam-4656	427	3	a	a	DET
ejpam-4656	427	4	connected	connected	ADJ
ejpam-4656	427	5	graph	graph	NOUN
ejpam-4656	427	6	and	and	CCONJ
ejpam-4656	427	7	kn	kn	PROPN
ejpam-4656	427	8	the	the	DET
ejpam-4656	427	9	complete	complete	ADJ
ejpam-4656	427	10	graph	graph	NOUN
ejpam-4656	427	11	of	of	ADP
ejpam-4656	427	12	order	order	NOUN
ejpam-4656	427	13	n.	n.	NOUN
ejpam-4656	427	14	then	then	ADV
ejpam-4656	427	15	γconh(g+kn	γconh(g+kn	PROPN
ejpam-4656	427	16	)	)	PUNCT
ejpam-4656	427	17	=	=	SYM
ejpam-4656	427	18	n+	n+	NUM
ejpam-4656	427	19	rg	rg	NOUN
ejpam-4656	427	20	,	,	PUNCT
ejpam-4656	427	21	where	where	SCONJ
ejpam-4656	427	22	rg	rg	PROPN
ejpam-4656	427	23	=	=	PUNCT
ejpam-4656	427	24	min{|s|	min{|s|	NOUN
ejpam-4656	427	25	:	:	PUNCT
ejpam-4656	427	26	v	v	X
ejpam-4656	427	27	(	(	PUNCT
ejpam-4656	427	28	g)\s	g)\s	NOUN
ejpam-4656	427	29	is	be	AUX
ejpam-4656	427	30	non	non	ADJ
ejpam-4656	427	31	-	-	ADJ
ejpam-4656	427	32	connecting	connect	VERB
ejpam-4656	427	33	and	and	CCONJ
ejpam-4656	427	34	s	s	NOUN
ejpam-4656	427	35	is	be	AUX
ejpam-4656	427	36	a	a	DET
ejpam-4656	427	37	pointwise	pointwise	ADJ
ejpam-4656	427	38	non	non	ADJ
ejpam-4656	427	39	-	-	ADJ
ejpam-4656	427	40	dominating	dominating	ADJ
ejpam-4656	427	41	set	set	NOUN
ejpam-4656	427	42	in	in	ADP
ejpam-4656	427	43	g	g	NOUN
ejpam-4656	427	44	}	}	PUNCT
ejpam-4656	427	45	.	.	PUNCT
ejpam-4656	428	1	in	in	ADP
ejpam-4656	428	2	particular	particular	ADJ
ejpam-4656	428	3	,	,	PUNCT
ejpam-4656	428	4	the	the	DET
ejpam-4656	428	5	following	follow	VERB
ejpam-4656	428	6	hold	hold	NOUN
ejpam-4656	428	7	:	:	PUNCT
ejpam-4656	428	8	(	(	PUNCT
ejpam-4656	428	9	i	i	NOUN
ejpam-4656	428	10	)	)	PUNCT
ejpam-4656	428	11	γconh(kn	γconh(kn	NOUN
ejpam-4656	428	12	+	+	CCONJ
ejpam-4656	428	13	cn	cn	ADJ
ejpam-4656	428	14	)	)	PUNCT
ejpam-4656	428	15	=	=	SYM
ejpam-4656	428	16	{	{	PUNCT
ejpam-4656	429	1	n+	n+	ADP
ejpam-4656	429	2	3	3	NUM
ejpam-4656	429	3	if	if	SCONJ
ejpam-4656	429	4	n	n	NOUN
ejpam-4656	429	5	=	=	SYM
ejpam-4656	429	6	3	3	NUM
ejpam-4656	429	7	n+	n+	SYM
ejpam-4656	429	8	2	2	NUM
ejpam-4656	430	1	if	if	SCONJ
ejpam-4656	430	2	n	n	PRON
ejpam-4656	430	3	≥	≥	NOUN
ejpam-4656	430	4	4	4	NUM
ejpam-4656	430	5	.	.	PUNCT
ejpam-4656	430	6	(	(	PUNCT
ejpam-4656	430	7	ii	ii	NOUN
ejpam-4656	430	8	)	)	PUNCT
ejpam-4656	430	9	γconh(kn	γconh(kn	NOUN
ejpam-4656	431	1	+	+	CCONJ
ejpam-4656	431	2	pn	pn	NOUN
ejpam-4656	431	3	)	)	PUNCT
ejpam-4656	431	4	=	=	PUNCT
ejpam-4656	432	1	n+	n+	ADP
ejpam-4656	432	2	2	2	NUM
ejpam-4656	432	3	for	for	ADP
ejpam-4656	432	4	all	all	DET
ejpam-4656	432	5	n	n	PRON
ejpam-4656	432	6	≥	≥	NOUN
ejpam-4656	432	7	2	2	NUM
ejpam-4656	432	8	.	.	PUNCT
ejpam-4656	433	1	the	the	DET
ejpam-4656	433	2	result	result	NOUN
ejpam-4656	433	3	that	that	PRON
ejpam-4656	433	4	follows	follow	VERB
ejpam-4656	433	5	is	be	AUX
ejpam-4656	433	6	a	a	DET
ejpam-4656	433	7	restatement	restatement	NOUN
ejpam-4656	433	8	of	of	ADP
ejpam-4656	433	9	a	a	DET
ejpam-4656	433	10	result	result	NOUN
ejpam-4656	433	11	in	in	ADP
ejpam-4656	433	12	[	[	X
ejpam-4656	433	13	13	13	NUM
ejpam-4656	433	14	]	]	PUNCT
ejpam-4656	433	15	.	.	PUNCT
ejpam-4656	434	1	theorem	theorem	NOUN
ejpam-4656	434	2	13	13	NUM
ejpam-4656	434	3	.	.	PUNCT
ejpam-4656	435	1	let	let	VERB
ejpam-4656	435	2	g	g	NOUN
ejpam-4656	435	3	and	and	CCONJ
ejpam-4656	435	4	h	h	NOUN
ejpam-4656	435	5	be	be	VERB
ejpam-4656	435	6	any	any	DET
ejpam-4656	435	7	two	two	NUM
ejpam-4656	435	8	graphs	graph	NOUN
ejpam-4656	435	9	.	.	PUNCT
ejpam-4656	436	1	a	a	DET
ejpam-4656	436	2	set	set	NOUN
ejpam-4656	436	3	c	c	NOUN
ejpam-4656	436	4	⊆	⊆	NUM
ejpam-4656	436	5	v	v	NOUN
ejpam-4656	436	6	(	(	PUNCT
ejpam-4656	436	7	g	g	NOUN
ejpam-4656	436	8	)	)	PUNCT
ejpam-4656	436	9	is	be	AUX
ejpam-4656	436	10	a	a	DET
ejpam-4656	436	11	hop	hop	NOUN
ejpam-4656	436	12	dominating	dominating	NOUN
ejpam-4656	436	13	set	set	VERB
ejpam-4656	436	14	in	in	ADP
ejpam-4656	436	15	g	g	PROPN
ejpam-4656	436	16	◦	◦	NOUN
ejpam-4656	436	17	h	h	NOUN
ejpam-4656	436	18	if	if	SCONJ
ejpam-4656	437	1	and	and	CCONJ
ejpam-4656	437	2	only	only	ADV
ejpam-4656	437	3	if	if	SCONJ
ejpam-4656	437	4	c	c	PROPN
ejpam-4656	437	5	=	=	SYM
ejpam-4656	437	6	a∪	a∪	PROPN
ejpam-4656	437	7	(	(	PUNCT
ejpam-4656	437	8	∪v∈v	∪v∈v	X
ejpam-4656	437	9	(	(	PUNCT
ejpam-4656	437	10	g)cv	g)cv	PROPN
ejpam-4656	437	11	)	)	PUNCT
ejpam-4656	437	12	,	,	PUNCT
ejpam-4656	437	13	where	where	SCONJ
ejpam-4656	437	14	a	a	DET
ejpam-4656	437	15	⊆	⊆	NUM
ejpam-4656	437	16	v	v	NOUN
ejpam-4656	437	17	(	(	PUNCT
ejpam-4656	437	18	g	g	NOUN
ejpam-4656	437	19	)	)	PUNCT
ejpam-4656	437	20	and	and	CCONJ
ejpam-4656	437	21	cv	cv	PROPN
ejpam-4656	437	22	⊆	⊆	NUM
ejpam-4656	437	23	v	v	PROPN
ejpam-4656	437	24	(	(	PUNCT
ejpam-4656	437	25	hv	hv	PROPN
ejpam-4656	437	26	)	)	PUNCT
ejpam-4656	437	27	for	for	ADP
ejpam-4656	437	28	each	each	DET
ejpam-4656	437	29	v	v	NUM
ejpam-4656	437	30	∈	∈	PROPN
ejpam-4656	437	31	v	v	NOUN
ejpam-4656	437	32	(	(	PUNCT
ejpam-4656	437	33	g	g	NOUN
ejpam-4656	437	34	)	)	PUNCT
ejpam-4656	437	35	,	,	PUNCT
ejpam-4656	437	36	and	and	CCONJ
ejpam-4656	437	37	satisfies	satisfy	VERB
ejpam-4656	437	38	the	the	DET
ejpam-4656	437	39	following	follow	VERB
ejpam-4656	437	40	conditions	condition	NOUN
ejpam-4656	437	41	:	:	PUNCT
ejpam-4656	437	42	(	(	PUNCT
ejpam-4656	437	43	i	i	NOUN
ejpam-4656	437	44	)	)	PUNCT
ejpam-4656	437	45	for	for	ADP
ejpam-4656	437	46	each	each	DET
ejpam-4656	437	47	w	w	PROPN
ejpam-4656	437	48	∈	∈	PROPN
ejpam-4656	437	49	v	v	ADP
ejpam-4656	437	50	(	(	PUNCT
ejpam-4656	437	51	g	g	NOUN
ejpam-4656	437	52	)	)	PUNCT
ejpam-4656	437	53	\	\	PROPN
ejpam-4656	437	54	a	a	PRON
ejpam-4656	437	55	,	,	PUNCT
ejpam-4656	437	56	there	there	PRON
ejpam-4656	437	57	exists	exist	VERB
ejpam-4656	437	58	x	x	X
ejpam-4656	437	59	∈	∈	PROPN
ejpam-4656	437	60	a	a	PRON
ejpam-4656	437	61	with	with	ADP
ejpam-4656	437	62	dg(w	dg(w	NOUN
ejpam-4656	437	63	,	,	PUNCT
ejpam-4656	437	64	x	x	X
ejpam-4656	437	65	)	)	PUNCT
ejpam-4656	437	66	=	=	SYM
ejpam-4656	437	67	2	2	NUM
ejpam-4656	437	68	or	or	CCONJ
ejpam-4656	437	69	there	there	PRON
ejpam-4656	437	70	exists	exist	VERB
ejpam-4656	437	71	y	y	PROPN
ejpam-4656	437	72	∈	∈	PROPN
ejpam-4656	437	73	ng(w	ng(w	NOUN
ejpam-4656	437	74	)	)	PUNCT
ejpam-4656	437	75	with	with	ADP
ejpam-4656	437	76	cy	cy	PROPN
ejpam-4656	437	77	̸=	̸=	PROPN
ejpam-4656	437	78	∅.	∅.	ADP
ejpam-4656	437	79	(	(	PUNCT
ejpam-4656	437	80	ii	ii	NOUN
ejpam-4656	437	81	)	)	PUNCT
ejpam-4656	437	82	cw	cw	NOUN
ejpam-4656	437	83	is	be	AUX
ejpam-4656	437	84	a	a	DET
ejpam-4656	437	85	pointwise	pointwise	ADJ
ejpam-4656	437	86	non	non	ADJ
ejpam-4656	437	87	-	-	ADJ
ejpam-4656	437	88	dominating	dominating	ADJ
ejpam-4656	437	89	set	set	NOUN
ejpam-4656	437	90	in	in	ADP
ejpam-4656	437	91	hw	hw	PRON
ejpam-4656	437	92	for	for	ADP
ejpam-4656	437	93	each	each	DET
ejpam-4656	437	94	w	w	PROPN
ejpam-4656	437	95	∈	∈	PROPN
ejpam-4656	437	96	v	v	ADP
ejpam-4656	437	97	(	(	PUNCT
ejpam-4656	437	98	g	g	NOUN
ejpam-4656	437	99	)	)	PUNCT
ejpam-4656	437	100	\ng(a	\ng(a	PROPN
ejpam-4656	437	101	)	)	PUNCT
ejpam-4656	437	102	.	.	PUNCT
ejpam-4656	438	1	theorem	theorem	VERB
ejpam-4656	438	2	14	14	NUM
ejpam-4656	438	3	.	.	PUNCT
ejpam-4656	439	1	let	let	VERB
ejpam-4656	439	2	g	g	PRON
ejpam-4656	439	3	be	be	AUX
ejpam-4656	439	4	a	a	DET
ejpam-4656	439	5	non	non	ADJ
ejpam-4656	439	6	-	-	ADJ
ejpam-4656	439	7	trivial	trivial	ADJ
ejpam-4656	439	8	connected	connected	ADJ
ejpam-4656	439	9	graph	graph	NOUN
ejpam-4656	439	10	and	and	CCONJ
ejpam-4656	439	11	let	let	VERB
ejpam-4656	439	12	h	h	NOUN
ejpam-4656	439	13	be	be	AUX
ejpam-4656	439	14	any	any	DET
ejpam-4656	439	15	graph	graph	NOUN
ejpam-4656	439	16	.	.	PUNCT
ejpam-4656	440	1	then	then	ADV
ejpam-4656	440	2	c	c	PROPN
ejpam-4656	440	3	is	be	AUX
ejpam-4656	440	4	a	a	DET
ejpam-4656	440	5	convex	convex	ADJ
ejpam-4656	440	6	hop	hop	NOUN
ejpam-4656	440	7	dominating	dominating	NOUN
ejpam-4656	440	8	set	set	VERB
ejpam-4656	440	9	in	in	ADP
ejpam-4656	440	10	g	g	PROPN
ejpam-4656	440	11	◦	◦	NOUN
ejpam-4656	440	12	h	h	NOUN
ejpam-4656	440	13	if	if	SCONJ
ejpam-4656	441	1	and	and	CCONJ
ejpam-4656	441	2	only	only	ADV
ejpam-4656	441	3	if	if	SCONJ
ejpam-4656	441	4	c	c	PROPN
ejpam-4656	441	5	=	=	SYM
ejpam-4656	441	6	a∪	a∪	PROPN
ejpam-4656	441	7	(	(	PUNCT
ejpam-4656	441	8	∪v∈v	∪v∈v	X
ejpam-4656	441	9	(	(	PUNCT
ejpam-4656	441	10	g)cv	g)cv	PROPN
ejpam-4656	441	11	)	)	PUNCT
ejpam-4656	441	12	,	,	PUNCT
ejpam-4656	441	13	where	where	SCONJ
ejpam-4656	441	14	a	a	DET
ejpam-4656	441	15	⊆	⊆	NUM
ejpam-4656	441	16	v	v	NOUN
ejpam-4656	441	17	(	(	PUNCT
ejpam-4656	441	18	g	g	NOUN
ejpam-4656	441	19	)	)	PUNCT
ejpam-4656	441	20	,	,	PUNCT
ejpam-4656	441	21	cv	cv	PROPN
ejpam-4656	441	22	⊆	⊆	NUM
ejpam-4656	441	23	v	v	PROPN
ejpam-4656	441	24	(	(	PUNCT
ejpam-4656	441	25	hv	hv	PROPN
ejpam-4656	441	26	)	)	PUNCT
ejpam-4656	441	27	for	for	ADP
ejpam-4656	441	28	each	each	DET
ejpam-4656	441	29	v	v	NUM
ejpam-4656	441	30	∈	∈	PROPN
ejpam-4656	441	31	v	v	NOUN
ejpam-4656	441	32	(	(	PUNCT
ejpam-4656	441	33	g	g	NOUN
ejpam-4656	441	34	)	)	PUNCT
ejpam-4656	441	35	,	,	PUNCT
ejpam-4656	441	36	and	and	CCONJ
ejpam-4656	441	37	satisfies	satisfy	VERB
ejpam-4656	441	38	the	the	DET
ejpam-4656	441	39	following	follow	VERB
ejpam-4656	441	40	conditions	condition	NOUN
ejpam-4656	441	41	:	:	PUNCT
ejpam-4656	441	42	(	(	PUNCT
ejpam-4656	441	43	i	i	NOUN
ejpam-4656	441	44	)	)	PUNCT
ejpam-4656	441	45	for	for	ADP
ejpam-4656	441	46	each	each	DET
ejpam-4656	441	47	a	a	DET
ejpam-4656	441	48	∈	∈	PROPN
ejpam-4656	441	49	v	v	NOUN
ejpam-4656	441	50	(	(	PUNCT
ejpam-4656	441	51	g	g	NOUN
ejpam-4656	441	52	)	)	PUNCT
ejpam-4656	441	53	\	\	PROPN
ejpam-4656	441	54	a	a	PRON
ejpam-4656	441	55	,	,	PUNCT
ejpam-4656	441	56	there	there	PRON
ejpam-4656	441	57	exists	exist	VERB
ejpam-4656	441	58	b	b	PROPN
ejpam-4656	441	59	∈	∈	PROPN
ejpam-4656	441	60	a	a	PRON
ejpam-4656	441	61	with	with	ADP
ejpam-4656	441	62	dg(a	dg(a	PROPN
ejpam-4656	441	63	,	,	PUNCT
ejpam-4656	441	64	b	b	NOUN
ejpam-4656	441	65	)	)	PUNCT
ejpam-4656	441	66	=	=	SYM
ejpam-4656	441	67	2	2	NUM
ejpam-4656	441	68	or	or	CCONJ
ejpam-4656	441	69	there	there	PRON
ejpam-4656	441	70	exists	exist	VERB
ejpam-4656	441	71	y	y	PROPN
ejpam-4656	441	72	∈	∈	PROPN
ejpam-4656	441	73	a	a	DET
ejpam-4656	441	74	∩ng(a	∩ng(a	NOUN
ejpam-4656	441	75	)	)	PUNCT
ejpam-4656	441	76	with	with	ADP
ejpam-4656	441	77	cy	cy	PROPN
ejpam-4656	441	78	̸=	̸=	PROPN
ejpam-4656	441	79	∅.	∅.	ADP
ejpam-4656	441	80	j.	j.	PROPN
ejpam-4656	441	81	hassan	hassan	PROPN
ejpam-4656	441	82	,	,	PUNCT
ejpam-4656	441	83	s.	s.	PROPN
ejpam-4656	441	84	canoy	canoy	PROPN
ejpam-4656	441	85	jr	jr	PROPN
ejpam-4656	441	86	.	.	PROPN
ejpam-4656	441	87	,	,	PUNCT
ejpam-4656	441	88	c.	c.	PROPN
ejpam-4656	441	89	saromines	saromine	VERB
ejpam-4656	441	90	/	/	SYM
ejpam-4656	441	91	eur	eur	PROPN
ejpam-4656	441	92	.	.	PUNCT
ejpam-4656	442	1	j.	j.	PROPN
ejpam-4656	442	2	pure	pure	PROPN
ejpam-4656	442	3	appl	appl	PROPN
ejpam-4656	442	4	.	.	PROPN
ejpam-4656	442	5	math	math	PROPN
ejpam-4656	442	6	,	,	PUNCT
ejpam-4656	442	7	16	16	NUM
ejpam-4656	442	8	(	(	PUNCT
ejpam-4656	442	9	1	1	NUM
ejpam-4656	442	10	)	)	PUNCT
ejpam-4656	442	11	(	(	PUNCT
ejpam-4656	442	12	2023	2023	NUM
ejpam-4656	442	13	)	)	PUNCT
ejpam-4656	442	14	,	,	PUNCT
ejpam-4656	442	15	319	319	NUM
ejpam-4656	442	16	-	-	SYM
ejpam-4656	442	17	335	335	NUM
ejpam-4656	442	18	329	329	NUM
ejpam-4656	442	19	(	(	PUNCT
ejpam-4656	442	20	ii	ii	NOUN
ejpam-4656	442	21	)	)	PUNCT
ejpam-4656	442	22	a	a	PRON
ejpam-4656	442	23	is	be	AUX
ejpam-4656	442	24	a	a	DET
ejpam-4656	442	25	convex	convex	NOUN
ejpam-4656	442	26	dominating	dominating	NOUN
ejpam-4656	442	27	set	set	VERB
ejpam-4656	442	28	in	in	ADP
ejpam-4656	442	29	g.	g.	PROPN
ejpam-4656	442	30	(	(	PUNCT
ejpam-4656	442	31	iii	iii	PROPN
ejpam-4656	442	32	)	)	PUNCT
ejpam-4656	442	33	cv	cv	NOUN
ejpam-4656	442	34	=	=	NOUN
ejpam-4656	442	35	∅	∅	NOUN
ejpam-4656	442	36	for	for	ADP
ejpam-4656	442	37	each	each	DET
ejpam-4656	442	38	v	v	NUM
ejpam-4656	442	39	∈	∈	PROPN
ejpam-4656	442	40	v	v	NOUN
ejpam-4656	442	41	(	(	PUNCT
ejpam-4656	442	42	g	g	NOUN
ejpam-4656	442	43	)	)	PUNCT
ejpam-4656	442	44	\a	\a	ADJ
ejpam-4656	442	45	.	.	PUNCT
ejpam-4656	443	1	(	(	PUNCT
ejpam-4656	443	2	iv	iv	X
ejpam-4656	443	3	)	)	PUNCT
ejpam-4656	443	4	v	v	NOUN
ejpam-4656	443	5	(	(	PUNCT
ejpam-4656	443	6	hv	hv	PROPN
ejpam-4656	443	7	)	)	PUNCT
ejpam-4656	443	8	\	\	PROPN
ejpam-4656	444	1	cv	cv	PROPN
ejpam-4656	444	2	is	be	AUX
ejpam-4656	444	3	a	a	DET
ejpam-4656	444	4	non	non	ADJ
ejpam-4656	444	5	-	-	ADJ
ejpam-4656	444	6	connecting	connect	VERB
ejpam-4656	444	7	in	in	ADP
ejpam-4656	444	8	hv	hv	PROPN
ejpam-4656	444	9	for	for	ADP
ejpam-4656	444	10	each	each	DET
ejpam-4656	444	11	v	v	ADP
ejpam-4656	444	12	∈	∈	PROPN
ejpam-4656	444	13	a	a	DET
ejpam-4656	444	14	∩ng(a	∩ng(a	NOUN
ejpam-4656	444	15	)	)	PUNCT
ejpam-4656	444	16	.	.	PUNCT
ejpam-4656	445	1	(	(	PUNCT
ejpam-4656	445	2	v	v	NOUN
ejpam-4656	445	3	)	)	PUNCT
ejpam-4656	445	4	v	v	NOUN
ejpam-4656	445	5	(	(	PUNCT
ejpam-4656	445	6	hv	hv	PROPN
ejpam-4656	445	7	)	)	PUNCT
ejpam-4656	445	8	\cv	\cv	PROPN
ejpam-4656	445	9	is	be	AUX
ejpam-4656	445	10	a	a	DET
ejpam-4656	445	11	non	non	ADJ
ejpam-4656	445	12	-	-	ADJ
ejpam-4656	445	13	connecting	connecting	ADJ
ejpam-4656	445	14	set	set	NOUN
ejpam-4656	445	15	and	and	CCONJ
ejpam-4656	445	16	cv	cv	PROPN
ejpam-4656	445	17	is	be	AUX
ejpam-4656	445	18	a	a	DET
ejpam-4656	445	19	pointwise	pointwise	ADJ
ejpam-4656	445	20	non	non	ADJ
ejpam-4656	445	21	-	-	ADJ
ejpam-4656	445	22	dominating	dominating	ADJ
ejpam-4656	445	23	set	set	NOUN
ejpam-4656	445	24	in	in	ADP
ejpam-4656	445	25	hv	hv	PROPN
ejpam-4656	445	26	if	if	SCONJ
ejpam-4656	445	27	a	a	PRON
ejpam-4656	445	28	=	=	X
ejpam-4656	445	29	{	{	PUNCT
ejpam-4656	445	30	v	v	NOUN
ejpam-4656	445	31	}	}	PUNCT
ejpam-4656	445	32	(	(	PUNCT
ejpam-4656	445	33	that	that	PRON
ejpam-4656	445	34	is	is	ADV
ejpam-4656	445	35	,	,	PUNCT
ejpam-4656	445	36	if	if	SCONJ
ejpam-4656	445	37	v	v	NUM
ejpam-4656	445	38	∈	∈	DET
ejpam-4656	445	39	a	a	DET
ejpam-4656	445	40	\ng(a	\ng(a	NOUN
ejpam-4656	445	41	)	)	PUNCT
ejpam-4656	445	42	)	)	PUNCT
ejpam-4656	445	43	.	.	PUNCT
ejpam-4656	446	1	proof	proof	NOUN
ejpam-4656	446	2	.	.	PUNCT
ejpam-4656	447	1	suppose	suppose	VERB
ejpam-4656	447	2	c	c	NOUN
ejpam-4656	447	3	is	be	AUX
ejpam-4656	447	4	a	a	DET
ejpam-4656	447	5	convex	convex	ADJ
ejpam-4656	447	6	hop	hop	NOUN
ejpam-4656	447	7	dominating	dominating	NOUN
ejpam-4656	447	8	set	set	VERB
ejpam-4656	447	9	in	in	ADP
ejpam-4656	447	10	g	g	PROPN
ejpam-4656	447	11	◦	◦	PROPN
ejpam-4656	447	12	h.	h.	NOUN
ejpam-4656	447	13	by	by	ADP
ejpam-4656	447	14	theorem	theorem	NOUN
ejpam-4656	447	15	13(ii	13(ii	NUM
ejpam-4656	447	16	)	)	PUNCT
ejpam-4656	447	17	,	,	PUNCT
ejpam-4656	447	18	statement	statement	NOUN
ejpam-4656	447	19	(	(	PUNCT
ejpam-4656	447	20	i	i	NOUN
ejpam-4656	447	21	)	)	PUNCT
ejpam-4656	447	22	holds	hold	VERB
ejpam-4656	447	23	.	.	PUNCT
ejpam-4656	448	1	let	let	VERB
ejpam-4656	448	2	x	x	PRON
ejpam-4656	448	3	,	,	PUNCT
ejpam-4656	448	4	y	y	PROPN
ejpam-4656	448	5	∈	∈	PROPN
ejpam-4656	448	6	a	a	PRON
ejpam-4656	448	7	with	with	ADP
ejpam-4656	448	8	x	x	PUNCT
ejpam-4656	448	9	̸=	̸=	PROPN
ejpam-4656	448	10	y.	y.	NOUN
ejpam-4656	448	11	then	then	ADV
ejpam-4656	448	12	x	x	SYM
ejpam-4656	448	13	and	and	CCONJ
ejpam-4656	448	14	y	y	PROPN
ejpam-4656	448	15	are	be	AUX
ejpam-4656	448	16	in	in	ADP
ejpam-4656	448	17	c.	c.	NOUN
ejpam-4656	448	18	since	since	SCONJ
ejpam-4656	448	19	c	c	PROPN
ejpam-4656	448	20	is	be	AUX
ejpam-4656	448	21	convex	convex	ADJ
ejpam-4656	448	22	and	and	CCONJ
ejpam-4656	448	23	ig	ig	NOUN
ejpam-4656	448	24	◦	◦	NOUN
ejpam-4656	448	25	h	h	NOUN
ejpam-4656	449	1	[	[	X
ejpam-4656	449	2	x	x	X
ejpam-4656	449	3	,	,	PUNCT
ejpam-4656	449	4	y	y	PROPN
ejpam-4656	449	5	]	]	X
ejpam-4656	449	6	=	=	SYM
ejpam-4656	449	7	ig[x	ig[x	PROPN
ejpam-4656	449	8	,	,	PUNCT
ejpam-4656	449	9	y	y	PROPN
ejpam-4656	449	10	]	]	PUNCT
ejpam-4656	449	11	,	,	PUNCT
ejpam-4656	449	12	it	it	PRON
ejpam-4656	449	13	follows	follow	VERB
ejpam-4656	449	14	that	that	SCONJ
ejpam-4656	449	15	ig[x	ig[x	PROPN
ejpam-4656	449	16	,	,	PUNCT
ejpam-4656	449	17	y	y	PROPN
ejpam-4656	449	18	]	]	X
ejpam-4656	449	19	⊆	⊆	NUM
ejpam-4656	449	20	a.	a.	NOUN
ejpam-4656	449	21	hence	hence	ADV
ejpam-4656	449	22	,	,	PUNCT
ejpam-4656	449	23	a	a	PRON
ejpam-4656	449	24	is	be	AUX
ejpam-4656	449	25	convex	convex	PROPN
ejpam-4656	449	26	.	.	PUNCT
ejpam-4656	450	1	suppose	suppose	VERB
ejpam-4656	450	2	a	a	PRON
ejpam-4656	450	3	is	be	AUX
ejpam-4656	450	4	not	not	PART
ejpam-4656	450	5	a	a	DET
ejpam-4656	450	6	dominating	dominating	NOUN
ejpam-4656	450	7	set	set	VERB
ejpam-4656	450	8	in	in	ADP
ejpam-4656	450	9	g.	g.	PROPN
ejpam-4656	450	10	then	then	ADV
ejpam-4656	450	11	there	there	PRON
ejpam-4656	450	12	exists	exist	VERB
ejpam-4656	450	13	v	v	ADP
ejpam-4656	450	14	∈	∈	PROPN
ejpam-4656	450	15	v	v	NOUN
ejpam-4656	450	16	(	(	PUNCT
ejpam-4656	450	17	g	g	NOUN
ejpam-4656	450	18	)	)	PUNCT
ejpam-4656	450	19	\ng[a	\ng[a	NOUN
ejpam-4656	450	20	]	]	PUNCT
ejpam-4656	450	21	.	.	PUNCT
ejpam-4656	451	1	by	by	ADP
ejpam-4656	451	2	theorem	theorem	NOUN
ejpam-4656	451	3	13(ii	13(ii	NUM
ejpam-4656	451	4	)	)	PUNCT
ejpam-4656	451	5	,	,	PUNCT
ejpam-4656	451	6	cv	cv	PROPN
ejpam-4656	451	7	is	be	AUX
ejpam-4656	451	8	a	a	DET
ejpam-4656	451	9	pointwise	pointwise	ADJ
ejpam-4656	451	10	non	non	ADJ
ejpam-4656	451	11	-	-	ADJ
ejpam-4656	451	12	dominating	dominating	ADJ
ejpam-4656	451	13	set	set	NOUN
ejpam-4656	451	14	in	in	ADP
ejpam-4656	451	15	hv	hv	PROPN
ejpam-4656	451	16	.	.	PUNCT
ejpam-4656	452	1	also	also	ADV
ejpam-4656	452	2	,	,	PUNCT
ejpam-4656	452	3	by	by	ADP
ejpam-4656	452	4	theorem	theorem	NOUN
ejpam-4656	452	5	13(i	13(i	NUM
ejpam-4656	452	6	)	)	PUNCT
ejpam-4656	452	7	,	,	PUNCT
ejpam-4656	452	8	there	there	PRON
ejpam-4656	452	9	exists	exist	VERB
ejpam-4656	452	10	x	x	X
ejpam-4656	452	11	∈	∈	PROPN
ejpam-4656	452	12	a	a	PRON
ejpam-4656	452	13	with	with	ADP
ejpam-4656	452	14	dg(v	dg(v	NOUN
ejpam-4656	452	15	,	,	PUNCT
ejpam-4656	452	16	x	x	X
ejpam-4656	452	17	)	)	PUNCT
ejpam-4656	452	18	=	=	SYM
ejpam-4656	452	19	2	2	NUM
ejpam-4656	452	20	or	or	CCONJ
ejpam-4656	452	21	there	there	PRON
ejpam-4656	452	22	exists	exist	VERB
ejpam-4656	452	23	y	y	PROPN
ejpam-4656	452	24	∈	∈	PROPN
ejpam-4656	452	25	ng(v	ng(v	PUNCT
ejpam-4656	452	26	)	)	PUNCT
ejpam-4656	452	27	with	with	ADP
ejpam-4656	452	28	cy	cy	PROPN
ejpam-4656	452	29	̸=	̸=	PROPN
ejpam-4656	452	30	∅.	∅.	AUX
ejpam-4656	452	31	pick	pick	VERB
ejpam-4656	452	32	any	any	DET
ejpam-4656	452	33	p	p	PROPN
ejpam-4656	452	34	∈	∈	PROPN
ejpam-4656	452	35	cv	cv	NOUN
ejpam-4656	452	36	and	and	CCONJ
ejpam-4656	452	37	let	let	VERB
ejpam-4656	452	38	q	q	PROPN
ejpam-4656	452	39	∈	∈	PROPN
ejpam-4656	452	40	c	c	NOUN
ejpam-4656	452	41	such	such	ADJ
ejpam-4656	452	42	that	that	PRON
ejpam-4656	452	43	dg	dg	AUX
ejpam-4656	452	44	◦	◦	NOUN
ejpam-4656	452	45	h(v	h(v	PROPN
ejpam-4656	452	46	,	,	PUNCT
ejpam-4656	452	47	q	q	NOUN
ejpam-4656	452	48	)	)	PUNCT
ejpam-4656	452	49	=	=	SYM
ejpam-4656	452	50	2	2	NUM
ejpam-4656	452	51	(	(	PUNCT
ejpam-4656	452	52	q	q	NOUN
ejpam-4656	452	53	=	=	PUNCT
ejpam-4656	452	54	x	x	X
ejpam-4656	452	55	or	or	CCONJ
ejpam-4656	452	56	q	q	PROPN
ejpam-4656	452	57	∈	∈	PROPN
ejpam-4656	452	58	cy	cy	PROPN
ejpam-4656	452	59	)	)	PUNCT
ejpam-4656	452	60	.	.	PUNCT
ejpam-4656	453	1	then	then	ADV
ejpam-4656	453	2	v	v	X
ejpam-4656	453	3	∈	∈	PROPN
ejpam-4656	453	4	ig	ig	PROPN
ejpam-4656	453	5	◦	◦	NOUN
ejpam-4656	453	6	h(p	h(p	NOUN
ejpam-4656	453	7	,	,	PUNCT
ejpam-4656	453	8	q	q	NOUN
ejpam-4656	453	9	)	)	PUNCT
ejpam-4656	453	10	.	.	PUNCT
ejpam-4656	454	1	by	by	ADP
ejpam-4656	454	2	convexity	convexity	NOUN
ejpam-4656	454	3	of	of	ADP
ejpam-4656	454	4	c	c	NOUN
ejpam-4656	454	5	,	,	PUNCT
ejpam-4656	454	6	it	it	PRON
ejpam-4656	454	7	follows	follow	VERB
ejpam-4656	454	8	that	that	SCONJ
ejpam-4656	454	9	v	v	X
ejpam-4656	454	10	∈	∈	PROPN
ejpam-4656	454	11	c	c	NOUN
ejpam-4656	454	12	,	,	PUNCT
ejpam-4656	454	13	a	a	DET
ejpam-4656	454	14	contradiction	contradiction	NOUN
ejpam-4656	454	15	.	.	PUNCT
ejpam-4656	455	1	thus	thus	ADV
ejpam-4656	455	2	,	,	PUNCT
ejpam-4656	455	3	a	a	PRON
ejpam-4656	455	4	is	be	AUX
ejpam-4656	455	5	a	a	DET
ejpam-4656	455	6	dominating	dominating	NOUN
ejpam-4656	455	7	set	set	VERB
ejpam-4656	455	8	in	in	ADP
ejpam-4656	455	9	g.	g.	PROPN
ejpam-4656	455	10	this	this	PRON
ejpam-4656	455	11	shows	show	VERB
ejpam-4656	455	12	that	that	SCONJ
ejpam-4656	455	13	(	(	PUNCT
ejpam-4656	455	14	ii	ii	NOUN
ejpam-4656	455	15	)	)	PUNCT
ejpam-4656	455	16	holds	hold	VERB
ejpam-4656	455	17	.	.	PUNCT
ejpam-4656	456	1	next	next	ADV
ejpam-4656	456	2	,	,	PUNCT
ejpam-4656	456	3	let	let	VERB
ejpam-4656	456	4	y	y	PROPN
ejpam-4656	456	5	∈	∈	PROPN
ejpam-4656	456	6	v	v	ADP
ejpam-4656	456	7	(	(	PUNCT
ejpam-4656	456	8	g	g	NOUN
ejpam-4656	456	9	)	)	PUNCT
ejpam-4656	456	10	\a	\a	ADJ
ejpam-4656	456	11	.	.	PUNCT
ejpam-4656	457	1	since	since	SCONJ
ejpam-4656	457	2	a	a	PRON
ejpam-4656	457	3	is	be	AUX
ejpam-4656	457	4	a	a	DET
ejpam-4656	457	5	dominating	dominating	NOUN
ejpam-4656	457	6	set	set	NOUN
ejpam-4656	457	7	in	in	ADP
ejpam-4656	457	8	g	g	PROPN
ejpam-4656	457	9	,	,	PUNCT
ejpam-4656	457	10	y	y	PROPN
ejpam-4656	457	11	∈	∈	PROPN
ejpam-4656	457	12	ng(a	ng(a	NOUN
ejpam-4656	457	13	)	)	PUNCT
ejpam-4656	457	14	.	.	PUNCT
ejpam-4656	458	1	by	by	ADP
ejpam-4656	458	2	convexity	convexity	NOUN
ejpam-4656	458	3	of	of	ADP
ejpam-4656	458	4	c	c	PROPN
ejpam-4656	458	5	,	,	PUNCT
ejpam-4656	458	6	cy	cy	NOUN
ejpam-4656	458	7	=	=	PUNCT
ejpam-4656	458	8	∅.	∅.	ADP
ejpam-4656	458	9	hence	hence	ADV
ejpam-4656	458	10	,	,	PUNCT
ejpam-4656	458	11	(	(	PUNCT
ejpam-4656	458	12	iii	iii	NOUN
ejpam-4656	458	13	)	)	PUNCT
ejpam-4656	458	14	holds	hold	VERB
ejpam-4656	458	15	.	.	PUNCT
ejpam-4656	459	1	let	let	VERB
ejpam-4656	459	2	v	v	NUM
ejpam-4656	459	3	∈	∈	NOUN
ejpam-4656	459	4	a.	a.	NOUN
ejpam-4656	459	5	suppose	suppose	VERB
ejpam-4656	459	6	v	v	X
ejpam-4656	459	7	(	(	PUNCT
ejpam-4656	459	8	hv)\cv	hv)\cv	NOUN
ejpam-4656	459	9	is	be	AUX
ejpam-4656	459	10	not	not	PART
ejpam-4656	459	11	a	a	DET
ejpam-4656	459	12	non	non	ADJ
ejpam-4656	459	13	-	-	ADJ
ejpam-4656	459	14	connecting	connecting	ADJ
ejpam-4656	459	15	set	set	NOUN
ejpam-4656	459	16	in	in	ADP
ejpam-4656	459	17	hv	hv	PROPN
ejpam-4656	459	18	.	.	PUNCT
ejpam-4656	460	1	then	then	ADV
ejpam-4656	460	2	there	there	PRON
ejpam-4656	460	3	exist	exist	VERB
ejpam-4656	460	4	p	p	PRON
ejpam-4656	460	5	,	,	PUNCT
ejpam-4656	460	6	q	q	PROPN
ejpam-4656	460	7	∈	∈	PROPN
ejpam-4656	460	8	cv	cv	NOUN
ejpam-4656	460	9	such	such	ADJ
ejpam-4656	460	10	that	that	SCONJ
ejpam-4656	460	11	p	p	PROPN
ejpam-4656	460	12	̸=	̸=	PROPN
ejpam-4656	460	13	q	q	NOUN
ejpam-4656	460	14	and	and	CCONJ
ejpam-4656	460	15	nhv(p)∩nhv(q)∩	nhv(p)∩nhv(q)∩	PROPN
ejpam-4656	461	1	[	[	X
ejpam-4656	461	2	v	v	X
ejpam-4656	461	3	(	(	PUNCT
ejpam-4656	461	4	hv	hv	NOUN
ejpam-4656	461	5	)	)	PUNCT
ejpam-4656	461	6	\cv	\cv	PROPN
ejpam-4656	461	7	]	]	X
ejpam-4656	461	8	̸=	̸=	PROPN
ejpam-4656	461	9	∅.	∅.	ADP
ejpam-4656	461	10	this	this	PRON
ejpam-4656	461	11	implies	imply	VERB
ejpam-4656	461	12	that	that	SCONJ
ejpam-4656	461	13	c	c	PROPN
ejpam-4656	461	14	is	be	AUX
ejpam-4656	461	15	not	not	PART
ejpam-4656	461	16	convex	convex	ADJ
ejpam-4656	461	17	,	,	PUNCT
ejpam-4656	461	18	a	a	DET
ejpam-4656	461	19	contradiction	contradiction	NOUN
ejpam-4656	461	20	.	.	PUNCT
ejpam-4656	462	1	therefore	therefore	ADV
ejpam-4656	462	2	,	,	PUNCT
ejpam-4656	462	3	v	v	PROPN
ejpam-4656	462	4	(	(	PUNCT
ejpam-4656	462	5	hv	hv	NOUN
ejpam-4656	462	6	)	)	PUNCT
ejpam-4656	462	7	\	\	PROPN
ejpam-4656	462	8	cv	cv	PROPN
ejpam-4656	462	9	is	be	AUX
ejpam-4656	462	10	a	a	DET
ejpam-4656	462	11	nonconnecting	nonconnecting	NOUN
ejpam-4656	462	12	set	set	NOUN
ejpam-4656	462	13	in	in	ADP
ejpam-4656	462	14	hv	hv	PROPN
ejpam-4656	462	15	,	,	PUNCT
ejpam-4656	462	16	showing	show	VERB
ejpam-4656	462	17	that	that	SCONJ
ejpam-4656	462	18	(	(	PUNCT
ejpam-4656	462	19	iv	iv	X
ejpam-4656	462	20	)	)	PUNCT
ejpam-4656	462	21	holds	hold	NOUN
ejpam-4656	462	22	.	.	PUNCT
ejpam-4656	463	1	suppose	suppose	VERB
ejpam-4656	463	2	now	now	ADV
ejpam-4656	463	3	that	that	SCONJ
ejpam-4656	463	4	v	v	ADP
ejpam-4656	463	5	∈	∈	PROPN
ejpam-4656	463	6	a	a	DET
ejpam-4656	463	7	\ng(a	\ng(a	NOUN
ejpam-4656	463	8	)	)	PUNCT
ejpam-4656	463	9	.	.	PUNCT
ejpam-4656	464	1	then	then	ADV
ejpam-4656	464	2	,	,	PUNCT
ejpam-4656	464	3	by	by	ADP
ejpam-4656	464	4	theorem	theorem	NOUN
ejpam-4656	464	5	13(ii	13(ii	NUM
ejpam-4656	464	6	)	)	PUNCT
ejpam-4656	464	7	,	,	PUNCT
ejpam-4656	464	8	cv	cv	PROPN
ejpam-4656	464	9	is	be	AUX
ejpam-4656	464	10	a	a	DET
ejpam-4656	464	11	pointwise	pointwise	ADJ
ejpam-4656	464	12	non	non	ADJ
ejpam-4656	464	13	-	-	ADJ
ejpam-4656	464	14	dominating	dominating	ADJ
ejpam-4656	464	15	set	set	NOUN
ejpam-4656	464	16	in	in	ADP
ejpam-4656	464	17	hv	hv	PROPN
ejpam-4656	464	18	.	.	PUNCT
ejpam-4656	465	1	hence	hence	ADV
ejpam-4656	465	2	,	,	PUNCT
ejpam-4656	465	3	(	(	PUNCT
ejpam-4656	465	4	v	v	NOUN
ejpam-4656	465	5	)	)	PUNCT
ejpam-4656	465	6	also	also	ADV
ejpam-4656	465	7	holds	hold	VERB
ejpam-4656	465	8	.	.	PUNCT
ejpam-4656	466	1	conversely	conversely	ADV
ejpam-4656	466	2	,	,	PUNCT
ejpam-4656	466	3	suppose	suppose	VERB
ejpam-4656	466	4	that	that	SCONJ
ejpam-4656	466	5	c	c	PROPN
ejpam-4656	466	6	has	have	VERB
ejpam-4656	466	7	the	the	DET
ejpam-4656	466	8	given	give	VERB
ejpam-4656	466	9	form	form	NOUN
ejpam-4656	466	10	and	and	CCONJ
ejpam-4656	466	11	satisfies	satisfie	NOUN
ejpam-4656	466	12	(	(	PUNCT
ejpam-4656	466	13	i	i	NOUN
ejpam-4656	466	14	)	)	PUNCT
ejpam-4656	466	15	,	,	PUNCT
ejpam-4656	466	16	(	(	PUNCT
ejpam-4656	466	17	ii	ii	NOUN
ejpam-4656	466	18	)	)	PUNCT
ejpam-4656	466	19	,	,	PUNCT
ejpam-4656	466	20	(	(	PUNCT
ejpam-4656	466	21	iii	iii	X
ejpam-4656	466	22	)	)	PUNCT
ejpam-4656	466	23	(	(	PUNCT
ejpam-4656	466	24	iv	iv	X
ejpam-4656	466	25	)	)	PUNCT
ejpam-4656	466	26	and	and	CCONJ
ejpam-4656	466	27	(	(	PUNCT
ejpam-4656	466	28	v	v	NOUN
ejpam-4656	466	29	)	)	PUNCT
ejpam-4656	466	30	.	.	PUNCT
ejpam-4656	467	1	since	since	SCONJ
ejpam-4656	467	2	(	(	PUNCT
ejpam-4656	467	3	i	i	NOUN
ejpam-4656	467	4	)	)	PUNCT
ejpam-4656	467	5	and	and	CCONJ
ejpam-4656	467	6	(	(	PUNCT
ejpam-4656	467	7	v	v	NOUN
ejpam-4656	467	8	)	)	PUNCT
ejpam-4656	467	9	hold	hold	NOUN
ejpam-4656	467	10	and	and	CCONJ
ejpam-4656	467	11	a	a	PRON
ejpam-4656	467	12	is	be	AUX
ejpam-4656	467	13	a	a	DET
ejpam-4656	467	14	dominating	dominating	NOUN
ejpam-4656	467	15	set	set	NOUN
ejpam-4656	467	16	in	in	ADP
ejpam-4656	467	17	g	g	PROPN
ejpam-4656	467	18	,	,	PUNCT
ejpam-4656	467	19	the	the	DET
ejpam-4656	467	20	conditions	condition	NOUN
ejpam-4656	467	21	(	(	PUNCT
ejpam-4656	467	22	i	i	NOUN
ejpam-4656	467	23	)	)	PUNCT
ejpam-4656	467	24	and	and	CCONJ
ejpam-4656	467	25	(	(	PUNCT
ejpam-4656	467	26	ii	ii	NOUN
ejpam-4656	467	27	)	)	PUNCT
ejpam-4656	467	28	of	of	ADP
ejpam-4656	467	29	theorem	theorem	ADJ
ejpam-4656	467	30	13	13	NUM
ejpam-4656	467	31	hold	hold	NOUN
ejpam-4656	467	32	.	.	PUNCT
ejpam-4656	468	1	thus	thus	ADV
ejpam-4656	468	2	,	,	PUNCT
ejpam-4656	468	3	c	c	PROPN
ejpam-4656	468	4	is	be	AUX
ejpam-4656	468	5	a	a	DET
ejpam-4656	468	6	hop	hop	NOUN
ejpam-4656	468	7	dominating	dominating	NOUN
ejpam-4656	468	8	set	set	VERB
ejpam-4656	468	9	in	in	ADP
ejpam-4656	468	10	g	g	PROPN
ejpam-4656	468	11	◦	◦	NOUN
ejpam-4656	468	12	h.	h.	PROPN
ejpam-4656	468	13	next	next	ADV
ejpam-4656	468	14	,	,	PUNCT
ejpam-4656	468	15	let	let	VERB
ejpam-4656	468	16	x	x	PRON
ejpam-4656	468	17	,	,	PUNCT
ejpam-4656	468	18	y	y	PROPN
ejpam-4656	468	19	∈	∈	PROPN
ejpam-4656	468	20	c	c	NOUN
ejpam-4656	468	21	with	with	ADP
ejpam-4656	468	22	x	x	PUNCT
ejpam-4656	468	23	̸=	̸=	PROPN
ejpam-4656	468	24	y.	y.	NOUN
ejpam-4656	468	25	let	let	VERB
ejpam-4656	468	26	v	v	NOUN
ejpam-4656	468	27	,	,	PUNCT
ejpam-4656	468	28	w	w	PROPN
ejpam-4656	468	29	∈	∈	PROPN
ejpam-4656	468	30	v	v	ADP
ejpam-4656	468	31	(	(	PUNCT
ejpam-4656	468	32	g	g	NOUN
ejpam-4656	468	33	)	)	PUNCT
ejpam-4656	468	34	such	such	ADJ
ejpam-4656	468	35	that	that	SCONJ
ejpam-4656	468	36	x	x	SYM
ejpam-4656	468	37	∈	∈	PROPN
ejpam-4656	468	38	v	v	X
ejpam-4656	468	39	(	(	PUNCT
ejpam-4656	468	40	v+hv	v+hv	NOUN
ejpam-4656	468	41	)	)	PUNCT
ejpam-4656	468	42	and	and	CCONJ
ejpam-4656	468	43	y	y	PROPN
ejpam-4656	468	44	∈	∈	PROPN
ejpam-4656	468	45	v	v	ADP
ejpam-4656	468	46	(	(	PUNCT
ejpam-4656	468	47	w+hw	w+hw	NOUN
ejpam-4656	468	48	)	)	PUNCT
ejpam-4656	468	49	.	.	PUNCT
ejpam-4656	469	1	consider	consider	VERB
ejpam-4656	469	2	the	the	DET
ejpam-4656	469	3	following	follow	VERB
ejpam-4656	469	4	cases	case	NOUN
ejpam-4656	469	5	:	:	PUNCT
ejpam-4656	469	6	case	case	NOUN
ejpam-4656	469	7	1	1	NUM
ejpam-4656	469	8	:	:	SYM
ejpam-4656	469	9	v	v	NOUN
ejpam-4656	469	10	=	=	PUNCT
ejpam-4656	469	11	w.	w.	NOUN
ejpam-4656	469	12	if	if	SCONJ
ejpam-4656	469	13	one	one	NUM
ejpam-4656	469	14	of	of	ADP
ejpam-4656	469	15	x	x	PUNCT
ejpam-4656	469	16	and	and	CCONJ
ejpam-4656	469	17	y	y	PROPN
ejpam-4656	469	18	is	be	AUX
ejpam-4656	469	19	v	v	ADJ
ejpam-4656	469	20	,	,	PUNCT
ejpam-4656	469	21	say	say	VERB
ejpam-4656	469	22	x	x	SYM
ejpam-4656	469	23	=	=	SYM
ejpam-4656	469	24	v	v	NOUN
ejpam-4656	469	25	,	,	PUNCT
ejpam-4656	469	26	then	then	ADV
ejpam-4656	469	27	y	y	PROPN
ejpam-4656	469	28	∈	∈	PROPN
ejpam-4656	469	29	cv	cv	PROPN
ejpam-4656	469	30	and	and	CCONJ
ejpam-4656	469	31	ig	ig	PROPN
ejpam-4656	469	32	◦	◦	NOUN
ejpam-4656	469	33	h	h	NOUN
ejpam-4656	470	1	[	[	X
ejpam-4656	470	2	x	x	X
ejpam-4656	470	3	,	,	PUNCT
ejpam-4656	470	4	y	y	PROPN
ejpam-4656	470	5	]	]	X
ejpam-4656	470	6	=	=	PUNCT
ejpam-4656	470	7	{	{	PUNCT
ejpam-4656	470	8	x	x	PROPN
ejpam-4656	470	9	,	,	PUNCT
ejpam-4656	470	10	y	y	PROPN
ejpam-4656	470	11	}	}	PUNCT
ejpam-4656	470	12	⊆	⊆	NUM
ejpam-4656	470	13	c.	c.	NOUN
ejpam-4656	470	14	suppose	suppose	VERB
ejpam-4656	470	15	x	x	PRON
ejpam-4656	470	16	,	,	PUNCT
ejpam-4656	470	17	y	y	PROPN
ejpam-4656	470	18	∈	∈	PROPN
ejpam-4656	470	19	cv	cv	PROPN
ejpam-4656	470	20	.	.	PROPN
ejpam-4656	471	1	since	since	SCONJ
ejpam-4656	471	2	cv	cv	PROPN
ejpam-4656	471	3	̸=	̸=	PROPN
ejpam-4656	471	4	∅	∅	NOUN
ejpam-4656	471	5	,	,	PUNCT
ejpam-4656	471	6	v	v	ADP
ejpam-4656	471	7	∈	∈	PRON
ejpam-4656	471	8	a	a	PRON
ejpam-4656	471	9	by	by	ADP
ejpam-4656	471	10	(	(	PUNCT
ejpam-4656	471	11	iii	iii	NOUN
ejpam-4656	471	12	)	)	PUNCT
ejpam-4656	471	13	.	.	PUNCT
ejpam-4656	472	1	by	by	ADP
ejpam-4656	472	2	(	(	PUNCT
ejpam-4656	472	3	iv	iv	X
ejpam-4656	472	4	)	)	PUNCT
ejpam-4656	472	5	,	,	PUNCT
ejpam-4656	472	6	v	v	PROPN
ejpam-4656	472	7	(	(	PUNCT
ejpam-4656	472	8	hv	hv	NOUN
ejpam-4656	472	9	)	)	PUNCT
ejpam-4656	472	10	\	\	PROPN
ejpam-4656	472	11	cv	cv	PROPN
ejpam-4656	472	12	is	be	AUX
ejpam-4656	472	13	a	a	DET
ejpam-4656	472	14	non	non	ADJ
ejpam-4656	472	15	-	-	ADJ
ejpam-4656	472	16	connecting	connecting	ADJ
ejpam-4656	472	17	set	set	NOUN
ejpam-4656	472	18	in	in	ADP
ejpam-4656	472	19	hv	hv	PROPN
ejpam-4656	472	20	.	.	PUNCT
ejpam-4656	473	1	hence	hence	ADV
ejpam-4656	473	2	,	,	PUNCT
ejpam-4656	473	3	ig	ig	PROPN
ejpam-4656	473	4	◦	◦	NOUN
ejpam-4656	473	5	h	h	NOUN
ejpam-4656	473	6	[	[	X
ejpam-4656	473	7	x	x	X
ejpam-4656	473	8	,	,	PUNCT
ejpam-4656	473	9	y	y	PROPN
ejpam-4656	473	10	]	]	X
ejpam-4656	473	11	⊆	⊆	NUM
ejpam-4656	473	12	c.	c.	NOUN
ejpam-4656	473	13	case	case	NOUN
ejpam-4656	473	14	2	2	NUM
ejpam-4656	473	15	:	:	PUNCT
ejpam-4656	473	16	v	v	ADP
ejpam-4656	473	17	̸=	̸=	PROPN
ejpam-4656	473	18	w.	w.	NOUN
ejpam-4656	473	19	suppose	suppose	VERB
ejpam-4656	473	20	x	x	SYM
ejpam-4656	473	21	=	=	SYM
ejpam-4656	473	22	v	v	PROPN
ejpam-4656	473	23	and	and	CCONJ
ejpam-4656	473	24	y	y	PROPN
ejpam-4656	473	25	=	=	SYM
ejpam-4656	473	26	w.	w.	PROPN
ejpam-4656	473	27	since	since	SCONJ
ejpam-4656	473	28	a	a	PRON
ejpam-4656	473	29	is	be	AUX
ejpam-4656	473	30	convex	convex	NOUN
ejpam-4656	473	31	,	,	PUNCT
ejpam-4656	473	32	ig[x	ig[x	PROPN
ejpam-4656	473	33	,	,	PUNCT
ejpam-4656	473	34	y	y	PROPN
ejpam-4656	473	35	]	]	X
ejpam-4656	473	36	⊆	⊆	NUM
ejpam-4656	473	37	a.	a.	NOUN
ejpam-4656	473	38	since	since	SCONJ
ejpam-4656	473	39	ig	ig	NOUN
ejpam-4656	473	40	◦	◦	NOUN
ejpam-4656	473	41	h	h	NOUN
ejpam-4656	474	1	[	[	X
ejpam-4656	474	2	x	x	X
ejpam-4656	474	3	,	,	PUNCT
ejpam-4656	474	4	y	y	PROPN
ejpam-4656	474	5	]	]	X
ejpam-4656	474	6	=	=	SYM
ejpam-4656	474	7	ig[x	ig[x	PROPN
ejpam-4656	474	8	,	,	PUNCT
ejpam-4656	474	9	y	y	PROPN
ejpam-4656	474	10	]	]	X
ejpam-4656	474	11	,	,	PUNCT
ejpam-4656	474	12	ig	ig	PROPN
ejpam-4656	474	13	◦	◦	NOUN
ejpam-4656	474	14	h	h	NOUN
ejpam-4656	475	1	[	[	X
ejpam-4656	475	2	x	x	X
ejpam-4656	475	3	,	,	PUNCT
ejpam-4656	475	4	y	y	PROPN
ejpam-4656	475	5	]	]	X
ejpam-4656	475	6	⊆	⊆	NUM
ejpam-4656	475	7	c.	c.	NOUN
ejpam-4656	475	8	suppose	suppose	VERB
ejpam-4656	475	9	x	x	SYM
ejpam-4656	475	10	=	=	SYM
ejpam-4656	475	11	v	v	PROPN
ejpam-4656	475	12	and	and	CCONJ
ejpam-4656	475	13	y	y	PROPN
ejpam-4656	475	14	∈	∈	PROPN
ejpam-4656	475	15	cw	cw	PROPN
ejpam-4656	475	16	.	.	PUNCT
ejpam-4656	476	1	then	then	ADV
ejpam-4656	476	2	w	w	PROPN
ejpam-4656	476	3	∈	∈	PROPN
ejpam-4656	476	4	a	a	PRON
ejpam-4656	476	5	and	and	CCONJ
ejpam-4656	476	6	,	,	PUNCT
ejpam-4656	476	7	by	by	ADP
ejpam-4656	476	8	convexity	convexity	NOUN
ejpam-4656	476	9	of	of	ADP
ejpam-4656	476	10	a	a	DET
ejpam-4656	476	11	,	,	PUNCT
ejpam-4656	476	12	ig[x	ig[x	PROPN
ejpam-4656	476	13	,	,	PUNCT
ejpam-4656	476	14	w	w	PROPN
ejpam-4656	476	15	]	]	X
ejpam-4656	476	16	⊆	⊆	NUM
ejpam-4656	476	17	a.	a.	NOUN
ejpam-4656	476	18	since	since	SCONJ
ejpam-4656	476	19	ig	ig	NOUN
ejpam-4656	476	20	◦	◦	NOUN
ejpam-4656	476	21	h	h	NOUN
ejpam-4656	477	1	[	[	X
ejpam-4656	477	2	x	x	X
ejpam-4656	477	3	,	,	PUNCT
ejpam-4656	477	4	y	y	PROPN
ejpam-4656	477	5	]	]	X
ejpam-4656	477	6	=	=	SYM
ejpam-4656	477	7	ig[x	ig[x	PROPN
ejpam-4656	477	8	,	,	PUNCT
ejpam-4656	477	9	w	w	NOUN
ejpam-4656	477	10	]	]	PUNCT
ejpam-4656	477	11	∪	∪	ADP
ejpam-4656	477	12	ig	ig	PROPN
ejpam-4656	477	13	◦	◦	NOUN
ejpam-4656	477	14	h	h	NOUN
ejpam-4656	478	1	[	[	X
ejpam-4656	478	2	w	w	PROPN
ejpam-4656	478	3	,	,	PUNCT
ejpam-4656	478	4	y	y	PROPN
ejpam-4656	478	5	]	]	X
ejpam-4656	478	6	=	=	SYM
ejpam-4656	478	7	ig	ig	PROPN
ejpam-4656	478	8	◦	◦	NOUN
ejpam-4656	478	9	h	h	NOUN
ejpam-4656	479	1	[	[	X
ejpam-4656	479	2	x	x	X
ejpam-4656	479	3	,	,	PUNCT
ejpam-4656	479	4	w	w	NOUN
ejpam-4656	479	5	]	]	X
ejpam-4656	479	6	∪	∪	X
ejpam-4656	479	7	{	{	PUNCT
ejpam-4656	479	8	y	y	NOUN
ejpam-4656	479	9	}	}	PUNCT
ejpam-4656	479	10	,	,	PUNCT
ejpam-4656	479	11	it	it	PRON
ejpam-4656	479	12	follows	follow	VERB
ejpam-4656	479	13	that	that	SCONJ
ejpam-4656	479	14	ig	ig	PROPN
ejpam-4656	479	15	◦	◦	NOUN
ejpam-4656	479	16	h	h	NOUN
ejpam-4656	479	17	[	[	X
ejpam-4656	479	18	x	x	X
ejpam-4656	479	19	,	,	PUNCT
ejpam-4656	479	20	y	y	PROPN
ejpam-4656	479	21	]	]	X
ejpam-4656	479	22	⊆	⊆	NUM
ejpam-4656	479	23	c.	c.	NOUN
ejpam-4656	479	24	the	the	DET
ejpam-4656	479	25	same	same	ADJ
ejpam-4656	479	26	conclusion	conclusion	NOUN
ejpam-4656	479	27	holds	hold	VERB
ejpam-4656	479	28	when	when	SCONJ
ejpam-4656	479	29	x	x	PROPN
ejpam-4656	479	30	∈	∈	PROPN
ejpam-4656	479	31	cv	cv	PROPN
ejpam-4656	479	32	and	and	CCONJ
ejpam-4656	479	33	y	y	PROPN
ejpam-4656	479	34	=	=	PROPN
ejpam-4656	479	35	w.	w.	PROPN
ejpam-4656	479	36	finally	finally	ADV
ejpam-4656	479	37	,	,	PUNCT
ejpam-4656	479	38	let	let	VERB
ejpam-4656	479	39	x	x	X
ejpam-4656	479	40	∈	∈	PROPN
ejpam-4656	479	41	cv	cv	PROPN
ejpam-4656	479	42	and	and	CCONJ
ejpam-4656	479	43	y	y	PROPN
ejpam-4656	479	44	∈	∈	PROPN
ejpam-4656	479	45	cw	cw	NOUN
ejpam-4656	479	46	.	.	PUNCT
ejpam-4656	480	1	then	then	ADV
ejpam-4656	480	2	,	,	PUNCT
ejpam-4656	480	3	by	by	ADP
ejpam-4656	480	4	(	(	PUNCT
ejpam-4656	480	5	iii	iii	NOUN
ejpam-4656	480	6	)	)	PUNCT
ejpam-4656	480	7	,	,	PUNCT
ejpam-4656	480	8	v	v	NOUN
ejpam-4656	480	9	,	,	PUNCT
ejpam-4656	480	10	w	w	PROPN
ejpam-4656	480	11	∈	∈	PROPN
ejpam-4656	480	12	a.	a.	NOUN
ejpam-4656	480	13	again	again	ADV
ejpam-4656	480	14	,	,	PUNCT
ejpam-4656	480	15	by	by	ADP
ejpam-4656	480	16	convexity	convexity	NOUN
ejpam-4656	480	17	of	of	ADP
ejpam-4656	480	18	a	a	PRON
ejpam-4656	480	19	,	,	PUNCT
ejpam-4656	480	20	ig	ig	PROPN
ejpam-4656	480	21	◦	◦	NOUN
ejpam-4656	480	22	h	h	NOUN
ejpam-4656	481	1	[	[	X
ejpam-4656	481	2	v	v	NOUN
ejpam-4656	481	3	,	,	PUNCT
ejpam-4656	481	4	w	w	NOUN
ejpam-4656	481	5	]	]	X
ejpam-4656	481	6	=	=	SYM
ejpam-4656	481	7	ig[v	ig[v	PROPN
ejpam-4656	481	8	,	,	PUNCT
ejpam-4656	481	9	w	w	PROPN
ejpam-4656	481	10	]	]	PUNCT
ejpam-4656	481	11	is	be	AUX
ejpam-4656	481	12	contained	contain	VERB
ejpam-4656	481	13	in	in	ADP
ejpam-4656	481	14	a	a	DET
ejpam-4656	481	15	⊆	⊆	NUM
ejpam-4656	481	16	c.	c.	NOUN
ejpam-4656	481	17	this	this	PRON
ejpam-4656	481	18	implies	imply	VERB
ejpam-4656	481	19	that	that	SCONJ
ejpam-4656	481	20	ig	ig	PROPN
ejpam-4656	481	21	◦	◦	NOUN
ejpam-4656	481	22	h	h	NOUN
ejpam-4656	481	23	[	[	X
ejpam-4656	481	24	x	x	X
ejpam-4656	481	25	,	,	PUNCT
ejpam-4656	481	26	y	y	PROPN
ejpam-4656	481	27	]	]	X
ejpam-4656	481	28	=	=	SYM
ejpam-4656	481	29	ig	ig	PROPN
ejpam-4656	481	30	◦	◦	NOUN
ejpam-4656	481	31	h	h	NOUN
ejpam-4656	482	1	[	[	X
ejpam-4656	482	2	v	v	NOUN
ejpam-4656	482	3	,	,	PUNCT
ejpam-4656	482	4	w	w	NOUN
ejpam-4656	482	5	]	]	X
ejpam-4656	482	6	∪	∪	ADP
ejpam-4656	482	7	ig	ig	PROPN
ejpam-4656	482	8	◦	◦	NOUN
ejpam-4656	482	9	h	h	NOUN
ejpam-4656	483	1	[	[	X
ejpam-4656	483	2	x	x	X
ejpam-4656	483	3	,	,	PUNCT
ejpam-4656	483	4	v	v	NOUN
ejpam-4656	483	5	]	]	PUNCT
ejpam-4656	483	6	∪	∪	ADP
ejpam-4656	483	7	ig	ig	PROPN
ejpam-4656	483	8	◦	◦	NOUN
ejpam-4656	483	9	h	h	NOUN
ejpam-4656	484	1	[	[	X
ejpam-4656	484	2	y	y	PROPN
ejpam-4656	484	3	,	,	PUNCT
ejpam-4656	484	4	w	w	PROPN
ejpam-4656	484	5	]	]	X
ejpam-4656	484	6	=	=	SYM
ejpam-4656	484	7	ig	ig	PROPN
ejpam-4656	484	8	◦	◦	NOUN
ejpam-4656	484	9	h	h	NOUN
ejpam-4656	485	1	[	[	X
ejpam-4656	485	2	v	v	NOUN
ejpam-4656	485	3	,	,	PUNCT
ejpam-4656	485	4	w	w	NOUN
ejpam-4656	485	5	]	]	X
ejpam-4656	485	6	∪	∪	X
ejpam-4656	485	7	{	{	PUNCT
ejpam-4656	485	8	x	x	NOUN
ejpam-4656	485	9	,	,	PUNCT
ejpam-4656	485	10	y	y	PROPN
ejpam-4656	485	11	}	}	PUNCT
ejpam-4656	485	12	j.	j.	PROPN
ejpam-4656	485	13	hassan	hassan	PROPN
ejpam-4656	485	14	,	,	PUNCT
ejpam-4656	485	15	s.	s.	PROPN
ejpam-4656	485	16	canoy	canoy	PROPN
ejpam-4656	485	17	jr	jr	PROPN
ejpam-4656	485	18	.	.	PROPN
ejpam-4656	485	19	,	,	PUNCT
ejpam-4656	485	20	c.	c.	PROPN
ejpam-4656	485	21	saromines	saromine	VERB
ejpam-4656	485	22	/	/	SYM
ejpam-4656	485	23	eur	eur	PROPN
ejpam-4656	485	24	.	.	PUNCT
ejpam-4656	486	1	j.	j.	PROPN
ejpam-4656	486	2	pure	pure	PROPN
ejpam-4656	486	3	appl	appl	PROPN
ejpam-4656	486	4	.	.	PROPN
ejpam-4656	486	5	math	math	PROPN
ejpam-4656	486	6	,	,	PUNCT
ejpam-4656	486	7	16	16	NUM
ejpam-4656	486	8	(	(	PUNCT
ejpam-4656	486	9	1	1	NUM
ejpam-4656	486	10	)	)	PUNCT
ejpam-4656	486	11	(	(	PUNCT
ejpam-4656	486	12	2023	2023	NUM
ejpam-4656	486	13	)	)	PUNCT
ejpam-4656	486	14	,	,	PUNCT
ejpam-4656	486	15	319	319	NUM
ejpam-4656	486	16	-	-	SYM
ejpam-4656	486	17	335	335	NUM
ejpam-4656	486	18	330	330	NUM
ejpam-4656	486	19	is	be	AUX
ejpam-4656	486	20	contained	contain	VERB
ejpam-4656	486	21	in	in	ADP
ejpam-4656	486	22	c.	c.	PROPN
ejpam-4656	486	23	therefore	therefore	ADV
ejpam-4656	486	24	,	,	PUNCT
ejpam-4656	486	25	c	c	PROPN
ejpam-4656	486	26	is	be	AUX
ejpam-4656	486	27	a	a	DET
ejpam-4656	486	28	convex	convex	NOUN
ejpam-4656	486	29	set	set	VERB
ejpam-4656	486	30	in	in	ADP
ejpam-4656	486	31	g	g	PROPN
ejpam-4656	486	32	◦	◦	NOUN
ejpam-4656	486	33	h.	h.	NOUN
ejpam-4656	486	34	accordingly	accordingly	ADV
ejpam-4656	486	35	,	,	PUNCT
ejpam-4656	486	36	c	c	PROPN
ejpam-4656	486	37	is	be	AUX
ejpam-4656	486	38	a	a	DET
ejpam-4656	486	39	convex	convex	ADJ
ejpam-4656	486	40	hop	hop	NOUN
ejpam-4656	486	41	dominating	dominating	NOUN
ejpam-4656	486	42	set	set	VERB
ejpam-4656	486	43	in	in	ADP
ejpam-4656	486	44	g	g	PROPN
ejpam-4656	486	45	◦	◦	NOUN
ejpam-4656	486	46	h.	h.	NOUN
ejpam-4656	486	47	let	let	VERB
ejpam-4656	486	48	g	g	PRON
ejpam-4656	486	49	be	be	AUX
ejpam-4656	486	50	a	a	DET
ejpam-4656	486	51	graph	graph	NOUN
ejpam-4656	486	52	.	.	PUNCT
ejpam-4656	487	1	we	we	PRON
ejpam-4656	487	2	denote	denote	VERB
ejpam-4656	487	3	by	by	ADP
ejpam-4656	487	4	dg	dg	PROPN
ejpam-4656	487	5	,	,	PUNCT
ejpam-4656	487	6	lg	lg	NOUN
ejpam-4656	487	7	,	,	PUNCT
ejpam-4656	487	8	and	and	CCONJ
ejpam-4656	487	9	ih	ih	PRON
ejpam-4656	487	10	the	the	DET
ejpam-4656	487	11	sets	set	NOUN
ejpam-4656	487	12	containing	contain	VERB
ejpam-4656	487	13	the	the	DET
ejpam-4656	487	14	dominating	dominating	NOUN
ejpam-4656	487	15	vertices	vertex	NOUN
ejpam-4656	487	16	,	,	PUNCT
ejpam-4656	487	17	leaves	leave	NOUN
ejpam-4656	487	18	,	,	PUNCT
ejpam-4656	487	19	and	and	CCONJ
ejpam-4656	487	20	isolated	isolated	ADJ
ejpam-4656	487	21	vertices	vertex	NOUN
ejpam-4656	487	22	of	of	ADP
ejpam-4656	487	23	g	g	NOUN
ejpam-4656	487	24	,	,	PUNCT
ejpam-4656	487	25	respectively	respectively	ADV
ejpam-4656	487	26	.	.	PUNCT
ejpam-4656	488	1	note	note	VERB
ejpam-4656	488	2	that	that	SCONJ
ejpam-4656	488	3	if	if	SCONJ
ejpam-4656	488	4	γ(g	γ(g	PROPN
ejpam-4656	488	5	)	)	PUNCT
ejpam-4656	488	6	=	=	SYM
ejpam-4656	489	1	1	1	NUM
ejpam-4656	489	2	,	,	PUNCT
ejpam-4656	489	3	then	then	ADV
ejpam-4656	489	4	|dg|	|dg|	PROPN
ejpam-4656	489	5	≥	≥	NUM
ejpam-4656	489	6	1	1	NUM
ejpam-4656	489	7	.	.	PUNCT
ejpam-4656	489	8	corollary	corollary	ADJ
ejpam-4656	489	9	8	8	NUM
ejpam-4656	489	10	.	.	PUNCT
ejpam-4656	490	1	let	let	VERB
ejpam-4656	490	2	g	g	PRON
ejpam-4656	490	3	be	be	AUX
ejpam-4656	490	4	a	a	DET
ejpam-4656	490	5	non	non	ADJ
ejpam-4656	490	6	-	-	ADJ
ejpam-4656	490	7	trivial	trivial	ADJ
ejpam-4656	490	8	connected	connected	ADJ
ejpam-4656	490	9	graph	graph	NOUN
ejpam-4656	490	10	with	with	ADP
ejpam-4656	490	11	γ(g	γ(g	PROPN
ejpam-4656	490	12	)	)	PUNCT
ejpam-4656	490	13	=	=	SYM
ejpam-4656	490	14	1	1	NUM
ejpam-4656	490	15	and	and	CCONJ
ejpam-4656	490	16	let	let	VERB
ejpam-4656	490	17	h	h	NOUN
ejpam-4656	490	18	be	be	AUX
ejpam-4656	490	19	any	any	DET
ejpam-4656	490	20	graph	graph	NOUN
ejpam-4656	490	21	.	.	PUNCT
ejpam-4656	491	1	then	then	ADV
ejpam-4656	491	2	γconh(g	γconh(g	ADP
ejpam-4656	491	3	◦	◦	PROPN
ejpam-4656	491	4	h	h	NOUN
ejpam-4656	491	5	)	)	PUNCT
ejpam-4656	492	1	=	=	NOUN
ejpam-4656	492	2	{	{	PUNCT
ejpam-4656	492	3	2	2	NUM
ejpam-4656	492	4	,	,	PUNCT
ejpam-4656	492	5	if	if	SCONJ
ejpam-4656	492	6	|lg|	|lg|	X
ejpam-4656	492	7	≥	≥	NOUN
ejpam-4656	492	8	1	1	NUM
ejpam-4656	492	9	or	or	CCONJ
ejpam-4656	492	10	|ih	|ih	NUM
ejpam-4656	492	11	|	|	ADV
ejpam-4656	492	12	≥	≥	NOUN
ejpam-4656	492	13	1	1	NUM
ejpam-4656	492	14	3	3	NUM
ejpam-4656	492	15	,	,	PUNCT
ejpam-4656	492	16	otherwise	otherwise	ADV
ejpam-4656	492	17	proof	proof	NOUN
ejpam-4656	492	18	.	.	PUNCT
ejpam-4656	493	1	let	let	VERB
ejpam-4656	493	2	v	v	NUM
ejpam-4656	493	3	∈	∈	NOUN
ejpam-4656	493	4	dg	dg	NOUN
ejpam-4656	493	5	.	.	PUNCT
ejpam-4656	494	1	suppose	suppose	VERB
ejpam-4656	494	2	|lg|	|lg|	X
ejpam-4656	494	3	≥	≥	NOUN
ejpam-4656	494	4	1	1	NUM
ejpam-4656	494	5	,	,	PUNCT
ejpam-4656	494	6	say	say	VERB
ejpam-4656	494	7	w	w	PROPN
ejpam-4656	494	8	∈	∈	PROPN
ejpam-4656	494	9	lg	lg	PROPN
ejpam-4656	494	10	.	.	PROPN
ejpam-4656	494	11	set	set	VERB
ejpam-4656	494	12	a1	a1	NOUN
ejpam-4656	494	13	=	=	SYM
ejpam-4656	494	14	{	{	PUNCT
ejpam-4656	494	15	v	v	NOUN
ejpam-4656	494	16	,	,	PUNCT
ejpam-4656	494	17	w	w	NOUN
ejpam-4656	494	18	}	}	PUNCT
ejpam-4656	494	19	.	.	PUNCT
ejpam-4656	495	1	then	then	ADV
ejpam-4656	495	2	a1	a1	NOUN
ejpam-4656	495	3	is	be	AUX
ejpam-4656	495	4	a	a	DET
ejpam-4656	495	5	convex	convex	NOUN
ejpam-4656	495	6	dominating	dominating	NOUN
ejpam-4656	495	7	set	set	VERB
ejpam-4656	495	8	in	in	ADP
ejpam-4656	495	9	g.	g.	PROPN
ejpam-4656	495	10	let	let	VERB
ejpam-4656	495	11	cu	cu	NOUN
ejpam-4656	495	12	=	=	NOUN
ejpam-4656	495	13	∅	∅	NOUN
ejpam-4656	495	14	for	for	ADP
ejpam-4656	495	15	each	each	DET
ejpam-4656	495	16	u	u	NOUN
ejpam-4656	495	17	∈	∈	PROPN
ejpam-4656	495	18	v	v	NOUN
ejpam-4656	495	19	(	(	PUNCT
ejpam-4656	495	20	g	g	NOUN
ejpam-4656	495	21	)	)	PUNCT
ejpam-4656	495	22	.	.	PUNCT
ejpam-4656	496	1	then	then	ADV
ejpam-4656	496	2	c1	c1	PROPN
ejpam-4656	496	3	=	=	PROPN
ejpam-4656	496	4	a1	a1	PROPN
ejpam-4656	496	5	∪	∪	X
ejpam-4656	496	6	(	(	PUNCT
ejpam-4656	496	7	∪u∈v	∪u∈v	PROPN
ejpam-4656	496	8	(	(	PUNCT
ejpam-4656	496	9	g)cu	g)cu	PROPN
ejpam-4656	496	10	)	)	PUNCT
ejpam-4656	496	11	=	=	NOUN
ejpam-4656	496	12	a1	a1	NOUN
ejpam-4656	496	13	is	be	AUX
ejpam-4656	496	14	a	a	DET
ejpam-4656	496	15	convex	convex	ADJ
ejpam-4656	496	16	hop	hop	NOUN
ejpam-4656	496	17	dominating	dominating	NOUN
ejpam-4656	496	18	set	set	VERB
ejpam-4656	496	19	in	in	ADP
ejpam-4656	496	20	g	g	PROPN
ejpam-4656	496	21	◦	◦	NOUN
ejpam-4656	496	22	h	h	NOUN
ejpam-4656	496	23	by	by	ADP
ejpam-4656	496	24	theorem	theorem	NOUN
ejpam-4656	496	25	14	14	NUM
ejpam-4656	496	26	.	.	PUNCT
ejpam-4656	497	1	thus	thus	ADV
ejpam-4656	497	2	,	,	PUNCT
ejpam-4656	497	3	γconh(g	γconh(g	ADP
ejpam-4656	497	4	◦	◦	NOUN
ejpam-4656	497	5	h	h	NOUN
ejpam-4656	497	6	)	)	PUNCT
ejpam-4656	497	7	=	=	SYM
ejpam-4656	497	8	2	2	X
ejpam-4656	497	9	.	.	PUNCT
ejpam-4656	498	1	next	next	ADV
ejpam-4656	498	2	,	,	PUNCT
ejpam-4656	498	3	suppose	suppose	VERB
ejpam-4656	498	4	that	that	SCONJ
ejpam-4656	498	5	|ih	|ih	NUM
ejpam-4656	498	6	|	|	ADV
ejpam-4656	498	7	≥	≥	NOUN
ejpam-4656	498	8	1	1	NUM
ejpam-4656	498	9	.	.	PUNCT
ejpam-4656	498	10	pick	pick	VERB
ejpam-4656	498	11	any	any	DET
ejpam-4656	498	12	p	p	PROPN
ejpam-4656	498	13	∈	∈	PROPN
ejpam-4656	498	14	ihv	ihv	NOUN
ejpam-4656	498	15	.	.	PUNCT
ejpam-4656	499	1	then	then	ADV
ejpam-4656	499	2	a2	a2	PROPN
ejpam-4656	499	3	=	=	PRON
ejpam-4656	499	4	{	{	PUNCT
ejpam-4656	499	5	v	v	NOUN
ejpam-4656	499	6	}	}	PUNCT
ejpam-4656	499	7	is	be	AUX
ejpam-4656	499	8	a	a	DET
ejpam-4656	499	9	convex	convex	NOUN
ejpam-4656	499	10	dominating	dominating	NOUN
ejpam-4656	499	11	set	set	VERB
ejpam-4656	499	12	in	in	ADP
ejpam-4656	499	13	g.	g.	PROPN
ejpam-4656	499	14	set	set	VERB
ejpam-4656	499	15	cv	cv	PROPN
ejpam-4656	500	1	=	=	PUNCT
ejpam-4656	500	2	{	{	PUNCT
ejpam-4656	500	3	p	p	X
ejpam-4656	500	4	}	}	PUNCT
ejpam-4656	500	5	and	and	CCONJ
ejpam-4656	500	6	let	let	VERB
ejpam-4656	500	7	cu	cu	NOUN
ejpam-4656	500	8	=	=	NOUN
ejpam-4656	500	9	∅	∅	NOUN
ejpam-4656	500	10	for	for	ADP
ejpam-4656	500	11	all	all	PRON
ejpam-4656	500	12	u	u	NOUN
ejpam-4656	500	13	∈	∈	PROPN
ejpam-4656	500	14	v	v	NOUN
ejpam-4656	500	15	(	(	PUNCT
ejpam-4656	500	16	g	g	NOUN
ejpam-4656	500	17	)	)	PUNCT
ejpam-4656	500	18	\	\	NOUN
ejpam-4656	500	19	{	{	PUNCT
ejpam-4656	500	20	v	v	NOUN
ejpam-4656	500	21	}	}	PUNCT
ejpam-4656	500	22	.	.	PUNCT
ejpam-4656	501	1	then	then	ADV
ejpam-4656	501	2	v	v	X
ejpam-4656	501	3	(	(	PUNCT
ejpam-4656	501	4	hv)\cv	hv)\cv	NOUN
ejpam-4656	501	5	is	be	AUX
ejpam-4656	501	6	a	a	DET
ejpam-4656	501	7	non	non	ADJ
ejpam-4656	501	8	-	-	ADJ
ejpam-4656	501	9	connecting	connecting	ADJ
ejpam-4656	501	10	set	set	NOUN
ejpam-4656	501	11	and	and	CCONJ
ejpam-4656	501	12	cv	cv	PROPN
ejpam-4656	501	13	is	be	AUX
ejpam-4656	501	14	a	a	DET
ejpam-4656	501	15	pointwise	pointwise	ADJ
ejpam-4656	501	16	non	non	ADJ
ejpam-4656	501	17	-	-	ADJ
ejpam-4656	501	18	dominating	dominating	ADJ
ejpam-4656	501	19	set	set	NOUN
ejpam-4656	501	20	in	in	ADP
ejpam-4656	501	21	hv	hv	PROPN
ejpam-4656	501	22	.	.	PUNCT
ejpam-4656	502	1	hence	hence	ADV
ejpam-4656	502	2	,	,	PUNCT
ejpam-4656	502	3	c2	c2	PROPN
ejpam-4656	502	4	=	=	PROPN
ejpam-4656	502	5	a2	a2	PROPN
ejpam-4656	502	6	∪	∪	ADJ
ejpam-4656	502	7	(	(	PUNCT
ejpam-4656	502	8	∪z∈v	∪z∈v	PUNCT
ejpam-4656	502	9	(	(	PUNCT
ejpam-4656	502	10	g)cz	g)cz	PROPN
ejpam-4656	502	11	)	)	PUNCT
ejpam-4656	502	12	=	=	SYM
ejpam-4656	502	13	a2	a2	PROPN
ejpam-4656	502	14	∪	∪	X
ejpam-4656	502	15	cv	cv	PROPN
ejpam-4656	502	16	is	be	AUX
ejpam-4656	502	17	a	a	DET
ejpam-4656	502	18	convex	convex	ADJ
ejpam-4656	502	19	hop	hop	NOUN
ejpam-4656	502	20	dominating	dominating	NOUN
ejpam-4656	502	21	set	set	VERB
ejpam-4656	502	22	in	in	ADP
ejpam-4656	502	23	g	g	PROPN
ejpam-4656	502	24	◦	◦	NOUN
ejpam-4656	502	25	h	h	NOUN
ejpam-4656	502	26	by	by	ADP
ejpam-4656	502	27	theorem	theorem	NOUN
ejpam-4656	502	28	14	14	NUM
ejpam-4656	502	29	.	.	PUNCT
ejpam-4656	503	1	it	it	PRON
ejpam-4656	503	2	follows	follow	VERB
ejpam-4656	503	3	that	that	SCONJ
ejpam-4656	503	4	γconh(g	γconh(g	ADP
ejpam-4656	503	5	◦	◦	NOUN
ejpam-4656	503	6	h	h	NOUN
ejpam-4656	503	7	)	)	PUNCT
ejpam-4656	503	8	=	=	SYM
ejpam-4656	503	9	2	2	X
ejpam-4656	503	10	.	.	PUNCT
ejpam-4656	503	11	suppose	suppose	VERB
ejpam-4656	503	12	now	now	ADV
ejpam-4656	503	13	that	that	SCONJ
ejpam-4656	503	14	|lg|	|lg|	NOUN
ejpam-4656	503	15	=	=	SYM
ejpam-4656	503	16	0	0	NUM
ejpam-4656	503	17	and	and	CCONJ
ejpam-4656	503	18	|ih	|ih	NUM
ejpam-4656	503	19	|	|	NOUN
ejpam-4656	503	20	=	=	NOUN
ejpam-4656	503	21	0	0	X
ejpam-4656	503	22	.	.	PUNCT
ejpam-4656	504	1	again	again	ADV
ejpam-4656	504	2	,	,	PUNCT
ejpam-4656	504	3	let	let	VERB
ejpam-4656	504	4	v	v	PRON
ejpam-4656	504	5	∈	∈	NOUN
ejpam-4656	504	6	dg	dg	NOUN
ejpam-4656	504	7	.	.	PUNCT
ejpam-4656	505	1	pick	pick	VERB
ejpam-4656	505	2	any	any	DET
ejpam-4656	505	3	z	z	NOUN
ejpam-4656	505	4	∈	∈	PROPN
ejpam-4656	505	5	v	v	ADP
ejpam-4656	505	6	(	(	PUNCT
ejpam-4656	505	7	g	g	NOUN
ejpam-4656	505	8	)	)	PUNCT
ejpam-4656	505	9	\	\	NOUN
ejpam-4656	505	10	{	{	PUNCT
ejpam-4656	505	11	v	v	NOUN
ejpam-4656	505	12	}	}	PUNCT
ejpam-4656	505	13	and	and	CCONJ
ejpam-4656	505	14	let	let	VERB
ejpam-4656	505	15	a	a	DET
ejpam-4656	505	16	=	=	PUNCT
ejpam-4656	505	17	{	{	PUNCT
ejpam-4656	505	18	v	v	NOUN
ejpam-4656	505	19	,	,	PUNCT
ejpam-4656	505	20	z	z	NOUN
ejpam-4656	505	21	}	}	PUNCT
ejpam-4656	505	22	.	.	PUNCT
ejpam-4656	506	1	then	then	ADV
ejpam-4656	506	2	a	a	PRON
ejpam-4656	506	3	is	be	AUX
ejpam-4656	506	4	a	a	DET
ejpam-4656	506	5	convex	convex	NOUN
ejpam-4656	506	6	dominating	dominating	NOUN
ejpam-4656	506	7	set	set	NOUN
ejpam-4656	506	8	of	of	ADP
ejpam-4656	506	9	g.	g.	PROPN
ejpam-4656	506	10	choose	choose	VERB
ejpam-4656	506	11	any	any	DET
ejpam-4656	506	12	q	q	PROPN
ejpam-4656	506	13	∈	∈	PROPN
ejpam-4656	506	14	v	v	ADP
ejpam-4656	506	15	(	(	PUNCT
ejpam-4656	506	16	hv	hv	PROPN
ejpam-4656	506	17	)	)	PUNCT
ejpam-4656	506	18	and	and	CCONJ
ejpam-4656	506	19	let	let	VERB
ejpam-4656	506	20	cv	cv	PROPN
ejpam-4656	506	21	=	=	PUNCT
ejpam-4656	506	22	{	{	PUNCT
ejpam-4656	506	23	q	q	X
ejpam-4656	506	24	}	}	PUNCT
ejpam-4656	506	25	.	.	PUNCT
ejpam-4656	507	1	put	put	VERB
ejpam-4656	507	2	cx	cx	NOUN
ejpam-4656	507	3	=	=	NOUN
ejpam-4656	507	4	∅	∅	NOUN
ejpam-4656	507	5	for	for	ADP
ejpam-4656	507	6	all	all	PRON
ejpam-4656	507	7	x	x	SYM
ejpam-4656	507	8	∈	∈	NOUN
ejpam-4656	507	9	v	v	NOUN
ejpam-4656	507	10	(	(	PUNCT
ejpam-4656	507	11	g	g	NOUN
ejpam-4656	507	12	)	)	PUNCT
ejpam-4656	507	13	\	\	NOUN
ejpam-4656	507	14	{	{	PUNCT
ejpam-4656	507	15	v	v	NOUN
ejpam-4656	507	16	}	}	PUNCT
ejpam-4656	507	17	.	.	PUNCT
ejpam-4656	508	1	then	then	ADV
ejpam-4656	508	2	cz	cz	NOUN
ejpam-4656	508	3	=	=	SYM
ejpam-4656	508	4	∅	∅	NOUN
ejpam-4656	508	5	and	and	CCONJ
ejpam-4656	508	6	v	v	NOUN
ejpam-4656	508	7	(	(	PUNCT
ejpam-4656	508	8	hv	hv	NOUN
ejpam-4656	508	9	)	)	PUNCT
ejpam-4656	508	10	\	\	PROPN
ejpam-4656	509	1	cv	cv	PROPN
ejpam-4656	509	2	and	and	CCONJ
ejpam-4656	509	3	v	v	PROPN
ejpam-4656	509	4	(	(	PUNCT
ejpam-4656	509	5	hz	hz	NOUN
ejpam-4656	509	6	)	)	PUNCT
ejpam-4656	509	7	\	\	NOUN
ejpam-4656	509	8	cz	cz	NOUN
ejpam-4656	509	9	are	be	AUX
ejpam-4656	509	10	non	non	ADJ
ejpam-4656	509	11	-	-	ADJ
ejpam-4656	509	12	connecting	connecting	ADJ
ejpam-4656	509	13	sets	set	NOUN
ejpam-4656	509	14	in	in	ADP
ejpam-4656	509	15	hv	hv	PROPN
ejpam-4656	509	16	and	and	CCONJ
ejpam-4656	509	17	hz	hz	PROPN
ejpam-4656	509	18	,	,	PUNCT
ejpam-4656	509	19	respectively	respectively	ADV
ejpam-4656	509	20	.	.	PUNCT
ejpam-4656	510	1	by	by	ADP
ejpam-4656	510	2	theorem	theorem	NOUN
ejpam-4656	510	3	14	14	NUM
ejpam-4656	510	4	,	,	PUNCT
ejpam-4656	510	5	c	c	X
ejpam-4656	510	6	=	=	PUNCT
ejpam-4656	510	7	a	a	DET
ejpam-4656	510	8	∪	∪	ADJ
ejpam-4656	510	9	(	(	PUNCT
ejpam-4656	510	10	∪y∈v	∪y∈v	PROPN
ejpam-4656	510	11	(	(	PUNCT
ejpam-4656	510	12	g)cy	g)cy	PROPN
ejpam-4656	510	13	)	)	PUNCT
ejpam-4656	510	14	=	=	NOUN
ejpam-4656	510	15	a	a	PRON
ejpam-4656	510	16	∪	∪	X
ejpam-4656	510	17	cv	cv	PROPN
ejpam-4656	510	18	is	be	AUX
ejpam-4656	510	19	a	a	DET
ejpam-4656	510	20	convex	convex	ADJ
ejpam-4656	510	21	hop	hop	NOUN
ejpam-4656	510	22	dominating	dominating	NOUN
ejpam-4656	510	23	set	set	VERB
ejpam-4656	510	24	in	in	ADP
ejpam-4656	510	25	g	g	PROPN
ejpam-4656	510	26	◦	◦	NOUN
ejpam-4656	510	27	h.	h.	NOUN
ejpam-4656	511	1	it	it	PRON
ejpam-4656	511	2	follows	follow	VERB
ejpam-4656	511	3	that	that	SCONJ
ejpam-4656	511	4	γconh(g	γconh(g	ADP
ejpam-4656	511	5	◦	◦	PROPN
ejpam-4656	511	6	h	h	NOUN
ejpam-4656	511	7	)	)	PUNCT
ejpam-4656	511	8	≤	≤	NOUN
ejpam-4656	511	9	3	3	NUM
ejpam-4656	511	10	.	.	PUNCT
ejpam-4656	511	11	suppose	suppose	VERB
ejpam-4656	511	12	now	now	ADV
ejpam-4656	511	13	that	that	SCONJ
ejpam-4656	511	14	c	c	AUX
ejpam-4656	511	15	=	=	SYM
ejpam-4656	511	16	a0	a0	PROPN
ejpam-4656	511	17	∪	∪	ADV
ejpam-4656	511	18	(	(	PUNCT
ejpam-4656	511	19	∪u∈v	∪u∈v	PROPN
ejpam-4656	511	20	(	(	PUNCT
ejpam-4656	511	21	g)su	g)su	PROPN
ejpam-4656	511	22	)	)	PUNCT
ejpam-4656	511	23	is	be	AUX
ejpam-4656	511	24	a	a	DET
ejpam-4656	511	25	γconh	γconh	NOUN
ejpam-4656	511	26	-	-	PUNCT
ejpam-4656	511	27	set	set	NOUN
ejpam-4656	511	28	of	of	ADP
ejpam-4656	511	29	g	g	PROPN
ejpam-4656	511	30	◦	◦	PROPN
ejpam-4656	511	31	h.	h.	PROPN
ejpam-4656	511	32	suppose	suppose	VERB
ejpam-4656	511	33	first	first	ADV
ejpam-4656	511	34	that	that	SCONJ
ejpam-4656	511	35	|a0|	|a0|	NOUN
ejpam-4656	511	36	=	=	NOUN
ejpam-4656	511	37	1	1	NUM
ejpam-4656	511	38	,	,	PUNCT
ejpam-4656	511	39	say	say	VERB
ejpam-4656	511	40	a0	a0	PROPN
ejpam-4656	511	41	=	=	SYM
ejpam-4656	511	42	{	{	PUNCT
ejpam-4656	511	43	z	z	NOUN
ejpam-4656	511	44	}	}	PUNCT
ejpam-4656	511	45	.	.	PUNCT
ejpam-4656	512	1	then	then	ADV
ejpam-4656	512	2	a0	a0	PROPN
ejpam-4656	512	3	is	be	AUX
ejpam-4656	512	4	(	(	PUNCT
ejpam-4656	512	5	convex	convex	PROPN
ejpam-4656	512	6	)	)	PUNCT
ejpam-4656	512	7	dominating	dominating	NOUN
ejpam-4656	512	8	set	set	VERB
ejpam-4656	512	9	in	in	ADP
ejpam-4656	512	10	g	g	NOUN
ejpam-4656	512	11	by	by	ADP
ejpam-4656	512	12	theorem	theorem	NOUN
ejpam-4656	512	13	14(ii	14(ii	NUM
ejpam-4656	512	14	)	)	PUNCT
ejpam-4656	512	15	.	.	PUNCT
ejpam-4656	513	1	moreover	moreover	ADV
ejpam-4656	513	2	,	,	PUNCT
ejpam-4656	513	3	su	su	NOUN
ejpam-4656	513	4	=	=	NOUN
ejpam-4656	513	5	∅	∅	NOUN
ejpam-4656	513	6	for	for	ADP
ejpam-4656	513	7	all	all	PRON
ejpam-4656	513	8	u	u	NOUN
ejpam-4656	513	9	∈	∈	PROPN
ejpam-4656	513	10	v	v	NOUN
ejpam-4656	513	11	(	(	PUNCT
ejpam-4656	513	12	g	g	NOUN
ejpam-4656	513	13	)	)	PUNCT
ejpam-4656	513	14	\	\	PROPN
ejpam-4656	513	15	a0	a0	NOUN
ejpam-4656	513	16	by	by	ADP
ejpam-4656	513	17	theorem	theorem	PROPN
ejpam-4656	513	18	14(iii	14(iii	NUM
ejpam-4656	513	19	)	)	PUNCT
ejpam-4656	513	20	.	.	PUNCT
ejpam-4656	514	1	since	since	SCONJ
ejpam-4656	514	2	|ih	|ih	NUM
ejpam-4656	514	3	|	|	NOUN
ejpam-4656	514	4	=	=	SYM
ejpam-4656	514	5	0	0	NUM
ejpam-4656	514	6	,	,	PUNCT
ejpam-4656	514	7	any	any	DET
ejpam-4656	514	8	pointwise	pointwise	ADJ
ejpam-4656	514	9	non	non	ADJ
ejpam-4656	514	10	-	-	ADJ
ejpam-4656	514	11	dominating	dominating	ADJ
ejpam-4656	514	12	set	set	NOUN
ejpam-4656	514	13	in	in	ADP
ejpam-4656	514	14	hz	hz	PROPN
ejpam-4656	514	15	contains	contain	VERB
ejpam-4656	514	16	at	at	ADP
ejpam-4656	514	17	least	least	ADV
ejpam-4656	514	18	two	two	NUM
ejpam-4656	514	19	elements	element	NOUN
ejpam-4656	514	20	,	,	PUNCT
ejpam-4656	514	21	that	that	ADV
ejpam-4656	514	22	is	is	ADV
ejpam-4656	514	23	,	,	PUNCT
ejpam-4656	514	24	|sz|	|sz|	VERB
ejpam-4656	514	25	≥	≥	NOUN
ejpam-4656	514	26	2	2	NUM
ejpam-4656	514	27	.	.	PUNCT
ejpam-4656	515	1	it	it	PRON
ejpam-4656	515	2	follows	follow	VERB
ejpam-4656	515	3	that	that	SCONJ
ejpam-4656	515	4	γconh(g	γconh(g	ADP
ejpam-4656	515	5	◦	◦	NOUN
ejpam-4656	515	6	h	h	NOUN
ejpam-4656	515	7	)	)	PUNCT
ejpam-4656	515	8	=	=	NOUN
ejpam-4656	515	9	|c0|	|c0|	NOUN
ejpam-4656	515	10	≥	≥	NOUN
ejpam-4656	515	11	3	3	NUM
ejpam-4656	515	12	.	.	PUNCT
ejpam-4656	515	13	suppose	suppose	VERB
ejpam-4656	515	14	that	that	SCONJ
ejpam-4656	515	15	|a0|	|a0|	NOUN
ejpam-4656	515	16	=	=	SYM
ejpam-4656	515	17	2	2	NUM
ejpam-4656	515	18	,	,	PUNCT
ejpam-4656	515	19	say	say	VERB
ejpam-4656	515	20	a0	a0	PROPN
ejpam-4656	515	21	=	=	SYM
ejpam-4656	515	22	{	{	PUNCT
ejpam-4656	515	23	x	x	PROPN
ejpam-4656	515	24	,	,	PUNCT
ejpam-4656	515	25	y	y	NOUN
ejpam-4656	515	26	}	}	PUNCT
ejpam-4656	515	27	.	.	PUNCT
ejpam-4656	516	1	if	if	SCONJ
ejpam-4656	516	2	x	x	X
ejpam-4656	516	3	,	,	PUNCT
ejpam-4656	516	4	y	y	PROPN
ejpam-4656	516	5	/∈	/∈	PUNCT
ejpam-4656	516	6	dg	dg	PROPN
ejpam-4656	516	7	,	,	PUNCT
ejpam-4656	516	8	then	then	ADV
ejpam-4656	516	9	cx	cx	PROPN
ejpam-4656	516	10	̸=	̸=	PROPN
ejpam-4656	516	11	∅	∅	NOUN
ejpam-4656	516	12	or	or	CCONJ
ejpam-4656	516	13	cy	cy	ADP
ejpam-4656	516	14	̸=	̸=	PROPN
ejpam-4656	516	15	∅	∅	NOUN
ejpam-4656	516	16	(	(	PUNCT
ejpam-4656	516	17	since	since	SCONJ
ejpam-4656	516	18	x	x	X
ejpam-4656	516	19	and	and	CCONJ
ejpam-4656	516	20	y	y	PROPN
ejpam-4656	516	21	are	be	AUX
ejpam-4656	516	22	not	not	PART
ejpam-4656	516	23	hop	hop	ADJ
ejpam-4656	516	24	neighbors	neighbor	NOUN
ejpam-4656	516	25	of	of	ADP
ejpam-4656	516	26	a	a	DET
ejpam-4656	516	27	dominating	dominating	NOUN
ejpam-4656	516	28	vertex	vertex	NOUN
ejpam-4656	516	29	of	of	ADP
ejpam-4656	516	30	g	g	NOUN
ejpam-4656	516	31	)	)	PUNCT
ejpam-4656	516	32	.	.	PUNCT
ejpam-4656	517	1	suppose	suppose	VERB
ejpam-4656	517	2	one	one	NUM
ejpam-4656	517	3	of	of	ADP
ejpam-4656	517	4	x	x	PUNCT
ejpam-4656	517	5	and	and	CCONJ
ejpam-4656	517	6	y	y	PROPN
ejpam-4656	517	7	,	,	PUNCT
ejpam-4656	517	8	say	say	VERB
ejpam-4656	517	9	x	x	X
ejpam-4656	517	10	,	,	PUNCT
ejpam-4656	517	11	is	be	AUX
ejpam-4656	517	12	a	a	DET
ejpam-4656	517	13	dominating	dominating	NOUN
ejpam-4656	517	14	vertex	vertex	NOUN
ejpam-4656	517	15	in	in	ADP
ejpam-4656	517	16	g.	g.	PROPN
ejpam-4656	517	17	since	since	SCONJ
ejpam-4656	517	18	y	y	PROPN
ejpam-4656	517	19	/∈	/∈	PUNCT
ejpam-4656	518	1	lg	lg	NOUN
ejpam-4656	518	2	,	,	PUNCT
ejpam-4656	518	3	there	there	PRON
ejpam-4656	518	4	exists	exist	VERB
ejpam-4656	518	5	a	a	DET
ejpam-4656	518	6	vertex	vertex	NOUN
ejpam-4656	518	7	d	d	X
ejpam-4656	518	8	∈	∈	PROPN
ejpam-4656	518	9	ng(y	ng(y	NOUN
ejpam-4656	518	10	)	)	PUNCT
ejpam-4656	518	11	∩ng(x	∩ng(x	NOUN
ejpam-4656	518	12	)	)	PUNCT
ejpam-4656	518	13	.	.	PUNCT
ejpam-4656	519	1	this	this	PRON
ejpam-4656	519	2	implies	imply	VERB
ejpam-4656	519	3	that	that	SCONJ
ejpam-4656	519	4	cx	cx	PROPN
ejpam-4656	519	5	̸=	̸=	PROPN
ejpam-4656	519	6	∅	∅	NOUN
ejpam-4656	519	7	or	or	CCONJ
ejpam-4656	519	8	cy	cy	ADP
ejpam-4656	519	9	̸=	̸=	PROPN
ejpam-4656	519	10	∅.	∅.	ADV
ejpam-4656	519	11	in	in	ADP
ejpam-4656	519	12	either	either	DET
ejpam-4656	519	13	case	case	NOUN
ejpam-4656	519	14	,	,	PUNCT
ejpam-4656	519	15	γconh(g	γconh(g	PROPN
ejpam-4656	519	16	◦	◦	NOUN
ejpam-4656	519	17	h	h	NOUN
ejpam-4656	519	18	)	)	PUNCT
ejpam-4656	519	19	=	=	NOUN
ejpam-4656	519	20	|c0|	|c0|	NOUN
ejpam-4656	519	21	≥	≥	NOUN
ejpam-4656	519	22	3	3	NUM
ejpam-4656	519	23	.	.	PUNCT
ejpam-4656	520	1	therefore	therefore	ADV
ejpam-4656	520	2	,	,	PUNCT
ejpam-4656	520	3	γconh(g	γconh(g	PROPN
ejpam-4656	520	4	◦	◦	NOUN
ejpam-4656	520	5	h	h	NOUN
ejpam-4656	520	6	)	)	PUNCT
ejpam-4656	520	7	=	=	SYM
ejpam-4656	520	8	3	3	X
ejpam-4656	520	9	.	.	X
ejpam-4656	520	10	for	for	ADP
ejpam-4656	520	11	a	a	DET
ejpam-4656	520	12	connected	connected	ADJ
ejpam-4656	520	13	graph	graph	NOUN
ejpam-4656	520	14	g	g	NOUN
ejpam-4656	520	15	,	,	PUNCT
ejpam-4656	520	16	γhcon(g	γhcon(g	PROPN
ejpam-4656	520	17	)	)	PUNCT
ejpam-4656	520	18	=	=	NOUN
ejpam-4656	520	19	min{|s|	min{|s|	NOUN
ejpam-4656	520	20	:	:	PUNCT
ejpam-4656	520	21	s	s	VERB
ejpam-4656	520	22	is	be	AUX
ejpam-4656	520	23	a	a	DET
ejpam-4656	520	24	convex	convex	NOUN
ejpam-4656	520	25	dominating	dominating	NOUN
ejpam-4656	520	26	and	and	CCONJ
ejpam-4656	520	27	hop	hop	NOUN
ejpam-4656	520	28	dominating	dominating	NOUN
ejpam-4656	520	29	set	set	NOUN
ejpam-4656	520	30	in	in	ADP
ejpam-4656	520	31	g	g	NOUN
ejpam-4656	520	32	}	}	PUNCT
ejpam-4656	520	33	.	.	PUNCT
ejpam-4656	521	1	since	since	SCONJ
ejpam-4656	521	2	v	v	NOUN
ejpam-4656	521	3	(	(	PUNCT
ejpam-4656	521	4	g	g	NOUN
ejpam-4656	521	5	)	)	PUNCT
ejpam-4656	521	6	is	be	AUX
ejpam-4656	521	7	a	a	DET
ejpam-4656	521	8	convex	convex	NOUN
ejpam-4656	521	9	dominating	dominating	NOUN
ejpam-4656	521	10	and	and	CCONJ
ejpam-4656	521	11	hop	hop	NOUN
ejpam-4656	521	12	dominating	dominating	NOUN
ejpam-4656	521	13	set	set	NOUN
ejpam-4656	521	14	,	,	PUNCT
ejpam-4656	521	15	g	g	PROPN
ejpam-4656	521	16	admits	admit	VERB
ejpam-4656	521	17	a	a	DET
ejpam-4656	521	18	convex	convex	NOUN
ejpam-4656	521	19	dominating	dominating	NOUN
ejpam-4656	521	20	and	and	CCONJ
ejpam-4656	521	21	hop	hop	NOUN
ejpam-4656	521	22	dominating	dominating	NOUN
ejpam-4656	521	23	set	set	NOUN
ejpam-4656	521	24	.	.	PUNCT
ejpam-4656	522	1	moreover	moreover	ADV
ejpam-4656	522	2	,	,	PUNCT
ejpam-4656	522	3	γcon(g	γcon(g	PROPN
ejpam-4656	522	4	)	)	PUNCT
ejpam-4656	522	5	≤	≤	NUM
ejpam-4656	522	6	γhcon(g	γhcon(g	PROPN
ejpam-4656	522	7	)	)	PUNCT
ejpam-4656	522	8	.	.	PUNCT
ejpam-4656	523	1	corollary	corollary	ADJ
ejpam-4656	523	2	9	9	NUM
ejpam-4656	523	3	.	.	PUNCT
ejpam-4656	524	1	let	let	VERB
ejpam-4656	524	2	g	g	PRON
ejpam-4656	524	3	be	be	AUX
ejpam-4656	524	4	a	a	DET
ejpam-4656	524	5	non	non	ADJ
ejpam-4656	524	6	-	-	ADJ
ejpam-4656	524	7	trivial	trivial	ADJ
ejpam-4656	524	8	connected	connected	ADJ
ejpam-4656	524	9	graph	graph	NOUN
ejpam-4656	524	10	with	with	ADP
ejpam-4656	524	11	γ(g	γ(g	PROPN
ejpam-4656	524	12	)	)	PUNCT
ejpam-4656	524	13	̸=	̸=	PROPN
ejpam-4656	524	14	1	1	NUM
ejpam-4656	524	15	and	and	CCONJ
ejpam-4656	524	16	let	let	VERB
ejpam-4656	524	17	h	h	NOUN
ejpam-4656	524	18	be	be	AUX
ejpam-4656	524	19	any	any	DET
ejpam-4656	524	20	j.	j.	PROPN
ejpam-4656	524	21	hassan	hassan	PROPN
ejpam-4656	524	22	,	,	PUNCT
ejpam-4656	524	23	s.	s.	PROPN
ejpam-4656	524	24	canoy	canoy	PROPN
ejpam-4656	524	25	jr	jr	PROPN
ejpam-4656	524	26	.	.	PROPN
ejpam-4656	524	27	,	,	PUNCT
ejpam-4656	524	28	c.	c.	PROPN
ejpam-4656	524	29	saromines	saromine	VERB
ejpam-4656	524	30	/	/	SYM
ejpam-4656	524	31	eur	eur	PROPN
ejpam-4656	524	32	.	.	PUNCT
ejpam-4656	525	1	j.	j.	PROPN
ejpam-4656	525	2	pure	pure	PROPN
ejpam-4656	525	3	appl	appl	PROPN
ejpam-4656	525	4	.	.	PROPN
ejpam-4656	525	5	math	math	PROPN
ejpam-4656	525	6	,	,	PUNCT
ejpam-4656	525	7	16	16	NUM
ejpam-4656	525	8	(	(	PUNCT
ejpam-4656	525	9	1	1	NUM
ejpam-4656	525	10	)	)	PUNCT
ejpam-4656	525	11	(	(	PUNCT
ejpam-4656	525	12	2023	2023	NUM
ejpam-4656	525	13	)	)	PUNCT
ejpam-4656	525	14	,	,	PUNCT
ejpam-4656	525	15	319	319	NUM
ejpam-4656	525	16	-	-	SYM
ejpam-4656	525	17	335	335	NUM
ejpam-4656	525	18	331	331	NUM
ejpam-4656	525	19	graph	graph	NOUN
ejpam-4656	525	20	.	.	PUNCT
ejpam-4656	526	1	then	then	ADV
ejpam-4656	526	2	γconh(g	γconh(g	ADP
ejpam-4656	526	3	◦	◦	PROPN
ejpam-4656	526	4	h	h	NOUN
ejpam-4656	526	5	)	)	PUNCT
ejpam-4656	527	1	=	=	PRON
ejpam-4656	527	2	{	{	PUNCT
ejpam-4656	527	3	γcon(g	γcon(g	NOUN
ejpam-4656	527	4	)	)	PUNCT
ejpam-4656	527	5	,	,	PUNCT
ejpam-4656	527	6	if	if	SCONJ
ejpam-4656	527	7	γcon(g	γcon(g	PROPN
ejpam-4656	527	8	)	)	PUNCT
ejpam-4656	527	9	=	=	SYM
ejpam-4656	527	10	γhcon(g	γhcon(g	NOUN
ejpam-4656	527	11	)	)	PUNCT
ejpam-4656	527	12	γcon(g	γcon(g	NOUN
ejpam-4656	527	13	)	)	PUNCT
ejpam-4656	528	1	+	+	CCONJ
ejpam-4656	528	2	1	1	NUM
ejpam-4656	528	3	,	,	PUNCT
ejpam-4656	528	4	otherwise	otherwise	ADV
ejpam-4656	528	5	.	.	PUNCT
ejpam-4656	529	1	proof	proof	NOUN
ejpam-4656	529	2	.	.	PUNCT
ejpam-4656	530	1	suppose	suppose	VERB
ejpam-4656	530	2	γcon(g	γcon(g	NOUN
ejpam-4656	530	3	)	)	PUNCT
ejpam-4656	530	4	=	=	SYM
ejpam-4656	530	5	γhcon(g	γhcon(g	PROPN
ejpam-4656	530	6	)	)	PUNCT
ejpam-4656	530	7	.	.	PUNCT
ejpam-4656	531	1	let	let	VERB
ejpam-4656	531	2	a	a	PRON
ejpam-4656	531	3	be	be	AUX
ejpam-4656	531	4	a	a	DET
ejpam-4656	531	5	γhcon	γhcon	NOUN
ejpam-4656	531	6	-	-	PUNCT
ejpam-4656	531	7	set	set	VERB
ejpam-4656	531	8	ofg	ofg	PROPN
ejpam-4656	531	9	.	.	PUNCT
ejpam-4656	532	1	then	then	ADV
ejpam-4656	532	2	|a|	|a|	PROPN
ejpam-4656	532	3	≥	≥	NOUN
ejpam-4656	532	4	2	2	NUM
ejpam-4656	532	5	.	.	PUNCT
ejpam-4656	532	6	set	set	VERB
ejpam-4656	532	7	cv	cv	NOUN
ejpam-4656	532	8	=	=	NOUN
ejpam-4656	532	9	∅	∅	NOUN
ejpam-4656	532	10	for	for	ADP
ejpam-4656	532	11	all	all	PRON
ejpam-4656	532	12	v	v	ADP
ejpam-4656	532	13	∈	∈	NUM
ejpam-4656	532	14	v	v	NOUN
ejpam-4656	532	15	(	(	PUNCT
ejpam-4656	532	16	g	g	NOUN
ejpam-4656	532	17	)	)	PUNCT
ejpam-4656	532	18	.	.	PUNCT
ejpam-4656	533	1	then	then	ADV
ejpam-4656	533	2	,	,	PUNCT
ejpam-4656	533	3	by	by	ADP
ejpam-4656	533	4	theorem	theorem	NOUN
ejpam-4656	533	5	14	14	NUM
ejpam-4656	533	6	,	,	PUNCT
ejpam-4656	533	7	c	c	X
ejpam-4656	533	8	=	=	PUNCT
ejpam-4656	533	9	a	a	PRON
ejpam-4656	533	10	is	be	AUX
ejpam-4656	533	11	a	a	DET
ejpam-4656	533	12	convex	convex	ADJ
ejpam-4656	533	13	hop	hop	NOUN
ejpam-4656	533	14	dominating	dominating	NOUN
ejpam-4656	533	15	set	set	VERB
ejpam-4656	533	16	in	in	ADP
ejpam-4656	533	17	g	g	PROPN
ejpam-4656	533	18	◦	◦	NOUN
ejpam-4656	533	19	h.	h.	PROPN
ejpam-4656	533	20	hence	hence	ADV
ejpam-4656	533	21	,	,	PUNCT
ejpam-4656	533	22	γconh(g	γconh(g	ADP
ejpam-4656	533	23	◦	◦	NOUN
ejpam-4656	533	24	h	h	NOUN
ejpam-4656	533	25	)	)	PUNCT
ejpam-4656	533	26	≤	≤	NOUN
ejpam-4656	533	27	γcon(g	γcon(g	PROPN
ejpam-4656	533	28	)	)	PUNCT
ejpam-4656	533	29	.	.	PUNCT
ejpam-4656	534	1	by	by	ADP
ejpam-4656	534	2	theorem	theorem	NOUN
ejpam-4656	534	3	14(ii	14(ii	NUM
ejpam-4656	534	4	)	)	PUNCT
ejpam-4656	534	5	,	,	PUNCT
ejpam-4656	534	6	it	it	PRON
ejpam-4656	534	7	follows	follow	VERB
ejpam-4656	534	8	that	that	SCONJ
ejpam-4656	534	9	γconh(g	γconh(g	ADP
ejpam-4656	534	10	◦	◦	NOUN
ejpam-4656	534	11	h	h	NOUN
ejpam-4656	534	12	)	)	PUNCT
ejpam-4656	534	13	=	=	SYM
ejpam-4656	534	14	γcon(g	γcon(g	PROPN
ejpam-4656	534	15	)	)	PUNCT
ejpam-4656	534	16	.	.	PUNCT
ejpam-4656	535	1	next	next	ADV
ejpam-4656	535	2	,	,	PUNCT
ejpam-4656	535	3	suppose	suppose	VERB
ejpam-4656	535	4	that	that	SCONJ
ejpam-4656	535	5	γcon(g	γcon(g	NOUN
ejpam-4656	535	6	)	)	PUNCT
ejpam-4656	535	7	<	<	X
ejpam-4656	535	8	γhcon(g	γhcon(g	PROPN
ejpam-4656	535	9	)	)	PUNCT
ejpam-4656	535	10	.	.	PUNCT
ejpam-4656	536	1	let	let	VERB
ejpam-4656	536	2	a′	a′	NOUN
ejpam-4656	536	3	be	be	AUX
ejpam-4656	536	4	a	a	DET
ejpam-4656	536	5	γcon	γcon	NOUN
ejpam-4656	536	6	-	-	PUNCT
ejpam-4656	536	7	set	set	NOUN
ejpam-4656	536	8	of	of	ADP
ejpam-4656	536	9	g.	g.	PROPN
ejpam-4656	536	10	since	since	SCONJ
ejpam-4656	536	11	γ(g	γ(g	PROPN
ejpam-4656	536	12	)	)	PUNCT
ejpam-4656	536	13	̸=	̸=	PROPN
ejpam-4656	536	14	1	1	NUM
ejpam-4656	536	15	,	,	PUNCT
ejpam-4656	536	16	|a′|	|a′|	NOUN
ejpam-4656	536	17	≥	≥	NOUN
ejpam-4656	536	18	2	2	NUM
ejpam-4656	536	19	.	.	PUNCT
ejpam-4656	537	1	the	the	DET
ejpam-4656	537	2	assumption	assumption	NOUN
ejpam-4656	537	3	that	that	SCONJ
ejpam-4656	537	4	γcon(g	γcon(g	NOUN
ejpam-4656	537	5	)	)	PUNCT
ejpam-4656	537	6	<	<	X
ejpam-4656	537	7	γhcon(g	γhcon(g	PROPN
ejpam-4656	537	8	)	)	PUNCT
ejpam-4656	537	9	implies	imply	VERB
ejpam-4656	537	10	that	that	SCONJ
ejpam-4656	537	11	a′	a′	PROPN
ejpam-4656	537	12	is	be	AUX
ejpam-4656	537	13	not	not	PART
ejpam-4656	537	14	a	a	DET
ejpam-4656	537	15	hop	hop	NOUN
ejpam-4656	537	16	dominating	dominating	NOUN
ejpam-4656	537	17	set	set	VERB
ejpam-4656	537	18	in	in	ADP
ejpam-4656	537	19	g.	g.	PROPN
ejpam-4656	537	20	hence	hence	ADV
ejpam-4656	537	21	,	,	PUNCT
ejpam-4656	537	22	there	there	PRON
ejpam-4656	537	23	exists	exist	VERB
ejpam-4656	537	24	v	v	DET
ejpam-4656	537	25	/∈	/∈	SYM
ejpam-4656	537	26	n2	n2	ADJ
ejpam-4656	537	27	g[a	g[a	PROPN
ejpam-4656	537	28	′	′	NOUN
ejpam-4656	537	29	]	]	PUNCT
ejpam-4656	537	30	.	.	PUNCT
ejpam-4656	538	1	let	let	VERB
ejpam-4656	538	2	x	x	PRON
ejpam-4656	538	3	,	,	PUNCT
ejpam-4656	538	4	y	y	PROPN
ejpam-4656	538	5	∈	∈	PROPN
ejpam-4656	538	6	a′	a′	NOUN
ejpam-4656	538	7	with	with	ADP
ejpam-4656	538	8	x	x	PROPN
ejpam-4656	538	9	̸=	̸=	PROPN
ejpam-4656	538	10	y.	y.	NOUN
ejpam-4656	538	11	since	since	SCONJ
ejpam-4656	538	12	a′	a′	PROPN
ejpam-4656	538	13	is	be	AUX
ejpam-4656	538	14	a	a	DET
ejpam-4656	538	15	dominating	dominating	NOUN
ejpam-4656	538	16	set	set	NOUN
ejpam-4656	538	17	,	,	PUNCT
ejpam-4656	538	18	there	there	PRON
ejpam-4656	538	19	exists	exist	VERB
ejpam-4656	538	20	w	w	PROPN
ejpam-4656	538	21	∈	∈	PROPN
ejpam-4656	538	22	a′	a′	PROPN
ejpam-4656	538	23	∩ng(v	∩ng(v	PROPN
ejpam-4656	538	24	)	)	PUNCT
ejpam-4656	538	25	.	.	PUNCT
ejpam-4656	539	1	because	because	SCONJ
ejpam-4656	539	2	a′	a′	PROPN
ejpam-4656	539	3	is	be	AUX
ejpam-4656	539	4	convex	convex	NOUN
ejpam-4656	539	5	,	,	PUNCT
ejpam-4656	539	6	⟨a′⟩	⟨a′⟩	PROPN
ejpam-4656	539	7	is	be	AUX
ejpam-4656	539	8	connected	connect	VERB
ejpam-4656	539	9	.	.	PUNCT
ejpam-4656	540	1	let	let	VERB
ejpam-4656	541	1	[	[	X
ejpam-4656	541	2	w1	w1	NOUN
ejpam-4656	541	3	,	,	PUNCT
ejpam-4656	541	4	w2	w2	NOUN
ejpam-4656	541	5	,	,	PUNCT
ejpam-4656	541	6	...	...	PUNCT
ejpam-4656	541	7	,	,	PUNCT
ejpam-4656	541	8	wk	wk	PROPN
ejpam-4656	541	9	]	]	PUNCT
ejpam-4656	541	10	,	,	PUNCT
ejpam-4656	541	11	where	where	SCONJ
ejpam-4656	541	12	w1	w1	NOUN
ejpam-4656	541	13	=	=	SYM
ejpam-4656	541	14	w	w	PROPN
ejpam-4656	541	15	and	and	CCONJ
ejpam-4656	541	16	wk	wk	INTJ
ejpam-4656	541	17	=	=	SYM
ejpam-4656	541	18	x	x	NOUN
ejpam-4656	541	19	,	,	PUNCT
ejpam-4656	541	20	be	be	AUX
ejpam-4656	541	21	a	a	DET
ejpam-4656	541	22	w	w	NOUN
ejpam-4656	541	23	-	-	PUNCT
ejpam-4656	541	24	x	x	NOUN
ejpam-4656	541	25	geodesic	geodesic	NOUN
ejpam-4656	541	26	in	in	ADP
ejpam-4656	541	27	⟨a′⟩.	⟨a′⟩.	NOUN
ejpam-4656	541	28	since	since	SCONJ
ejpam-4656	541	29	v	v	NUM
ejpam-4656	541	30	/∈	/∈	SYM
ejpam-4656	541	31	n2	n2	ADJ
ejpam-4656	541	32	g[a	g[a	PROPN
ejpam-4656	541	33	′	′	NOUN
ejpam-4656	541	34	]	]	PUNCT
ejpam-4656	541	35	,	,	PUNCT
ejpam-4656	541	36	vwj	vwj	PROPN
ejpam-4656	541	37	∈	∈	PROPN
ejpam-4656	541	38	e(g	e(g	PROPN
ejpam-4656	541	39	)	)	PUNCT
ejpam-4656	541	40	for	for	ADP
ejpam-4656	541	41	all	all	DET
ejpam-4656	541	42	j	j	PROPN
ejpam-4656	541	43	∈	∈	PROPN
ejpam-4656	541	44	{	{	PUNCT
ejpam-4656	541	45	1	1	NUM
ejpam-4656	541	46	,	,	PUNCT
ejpam-4656	541	47	2	2	NUM
ejpam-4656	541	48	,	,	PUNCT
ejpam-4656	541	49	...	...	PUNCT
ejpam-4656	541	50	,	,	PUNCT
ejpam-4656	541	51	k	k	NOUN
ejpam-4656	541	52	}	}	PUNCT
ejpam-4656	541	53	.	.	PUNCT
ejpam-4656	542	1	in	in	ADP
ejpam-4656	542	2	particular	particular	ADJ
ejpam-4656	542	3	,	,	PUNCT
ejpam-4656	542	4	vx	vx	PROPN
ejpam-4656	542	5	∈	∈	PROPN
ejpam-4656	542	6	e(g	e(g	PROPN
ejpam-4656	542	7	)	)	PUNCT
ejpam-4656	542	8	.	.	PUNCT
ejpam-4656	543	1	let	let	VERB
ejpam-4656	544	1	[	[	X
ejpam-4656	544	2	x1	x1	ADJ
ejpam-4656	544	3	,	,	PUNCT
ejpam-4656	544	4	x2	x2	PROPN
ejpam-4656	544	5	,	,	PUNCT
ejpam-4656	544	6	...	...	PUNCT
ejpam-4656	544	7	,	,	PUNCT
ejpam-4656	544	8	xt	xt	ADP
ejpam-4656	544	9	]	]	X
ejpam-4656	544	10	,	,	PUNCT
ejpam-4656	544	11	where	where	SCONJ
ejpam-4656	544	12	x1	x1	ADJ
ejpam-4656	544	13	=	=	PUNCT
ejpam-4656	544	14	x	x	X
ejpam-4656	544	15	and	and	CCONJ
ejpam-4656	544	16	xt	xt	X
ejpam-4656	544	17	=	=	SYM
ejpam-4656	544	18	y	y	PROPN
ejpam-4656	544	19	,	,	PUNCT
ejpam-4656	544	20	be	be	AUX
ejpam-4656	544	21	an	an	DET
ejpam-4656	544	22	x	x	NOUN
ejpam-4656	544	23	-	-	NOUN
ejpam-4656	544	24	y	y	ADJ
ejpam-4656	544	25	geodesic	geodesic	NOUN
ejpam-4656	544	26	in	in	ADP
ejpam-4656	544	27	⟨a′⟩.	⟨a′⟩.	NOUN
ejpam-4656	544	28	again	again	ADV
ejpam-4656	544	29	,	,	PUNCT
ejpam-4656	544	30	since	since	SCONJ
ejpam-4656	544	31	v	v	NUM
ejpam-4656	544	32	/∈	/∈	SYM
ejpam-4656	545	1	n2	n2	ADJ
ejpam-4656	545	2	g[a	g[a	PROPN
ejpam-4656	545	3	′	′	NOUN
ejpam-4656	545	4	]	]	X
ejpam-4656	545	5	,	,	PUNCT
ejpam-4656	545	6	vxi	vxi	PROPN
ejpam-4656	545	7	∈	∈	PROPN
ejpam-4656	545	8	e(g	e(g	PROPN
ejpam-4656	545	9	)	)	PUNCT
ejpam-4656	546	1	for	for	ADP
ejpam-4656	546	2	all	all	PRON
ejpam-4656	546	3	i	i	PRON
ejpam-4656	546	4	∈	∈	PROPN
ejpam-4656	546	5	{	{	PUNCT
ejpam-4656	546	6	1	1	NUM
ejpam-4656	546	7	,	,	PUNCT
ejpam-4656	546	8	2	2	NUM
ejpam-4656	546	9	,	,	PUNCT
ejpam-4656	546	10	...	...	PUNCT
ejpam-4656	546	11	,	,	PUNCT
ejpam-4656	546	12	t	t	PROPN
ejpam-4656	546	13	}	}	PUNCT
ejpam-4656	546	14	.	.	PUNCT
ejpam-4656	547	1	moreover	moreover	ADV
ejpam-4656	547	2	,	,	PUNCT
ejpam-4656	547	3	by	by	ADP
ejpam-4656	547	4	convexity	convexity	NOUN
ejpam-4656	547	5	of	of	ADP
ejpam-4656	547	6	a′	a′	PROPN
ejpam-4656	547	7	,	,	PUNCT
ejpam-4656	547	8	⟨{x1	⟨{x1	PROPN
ejpam-4656	547	9	,	,	PUNCT
ejpam-4656	547	10	x2	x2	PROPN
ejpam-4656	547	11	,	,	PUNCT
ejpam-4656	547	12	...	...	PUNCT
ejpam-4656	547	13	,	,	PUNCT
ejpam-4656	547	14	xt}⟩	xt}⟩	PROPN
ejpam-4656	547	15	is	be	AUX
ejpam-4656	547	16	complete	complete	ADJ
ejpam-4656	547	17	(	(	PUNCT
ejpam-4656	547	18	otherwise	otherwise	ADV
ejpam-4656	547	19	,	,	PUNCT
ejpam-4656	547	20	v	v	NOUN
ejpam-4656	547	21	∈	∈	PROPN
ejpam-4656	547	22	a′	a′	PROPN
ejpam-4656	547	23	,	,	PUNCT
ejpam-4656	547	24	a	a	DET
ejpam-4656	547	25	contradiction	contradiction	NOUN
ejpam-4656	547	26	)	)	PUNCT
ejpam-4656	547	27	.	.	PUNCT
ejpam-4656	548	1	hence	hence	ADV
ejpam-4656	548	2	,	,	PUNCT
ejpam-4656	548	3	xy	xy	PROPN
ejpam-4656	548	4	∈	∈	PROPN
ejpam-4656	548	5	e(g	e(g	PROPN
ejpam-4656	548	6	)	)	PUNCT
ejpam-4656	548	7	.	.	PUNCT
ejpam-4656	549	1	thus	thus	ADV
ejpam-4656	549	2	,	,	PUNCT
ejpam-4656	549	3	⟨a′⟩	⟨a′⟩	PROPN
ejpam-4656	549	4	is	be	AUX
ejpam-4656	549	5	complete	complete	ADJ
ejpam-4656	549	6	.	.	PUNCT
ejpam-4656	550	1	pick	pick	VERB
ejpam-4656	550	2	any	any	DET
ejpam-4656	550	3	w	w	PROPN
ejpam-4656	550	4	∈	∈	PROPN
ejpam-4656	550	5	a′	a′	NOUN
ejpam-4656	550	6	and	and	CCONJ
ejpam-4656	550	7	p	p	NOUN
ejpam-4656	550	8	∈	∈	PROPN
ejpam-4656	550	9	v	v	ADP
ejpam-4656	550	10	(	(	PUNCT
ejpam-4656	550	11	hw	hw	NOUN
ejpam-4656	550	12	)	)	PUNCT
ejpam-4656	550	13	.	.	PUNCT
ejpam-4656	551	1	set	set	VERB
ejpam-4656	551	2	cw	cw	NOUN
ejpam-4656	551	3	=	=	PRON
ejpam-4656	551	4	{	{	PUNCT
ejpam-4656	551	5	p	p	X
ejpam-4656	551	6	}	}	PUNCT
ejpam-4656	551	7	and	and	CCONJ
ejpam-4656	551	8	cz	cz	NOUN
ejpam-4656	551	9	=	=	NOUN
ejpam-4656	551	10	∅	∅	NOUN
ejpam-4656	551	11	for	for	ADP
ejpam-4656	551	12	all	all	DET
ejpam-4656	551	13	z	z	NOUN
ejpam-4656	551	14	∈	∈	PROPN
ejpam-4656	551	15	v	v	ADP
ejpam-4656	551	16	(	(	PUNCT
ejpam-4656	551	17	g	g	NOUN
ejpam-4656	551	18	)	)	PUNCT
ejpam-4656	551	19	\	\	NOUN
ejpam-4656	551	20	{	{	PUNCT
ejpam-4656	551	21	w	w	NOUN
ejpam-4656	551	22	}	}	PUNCT
ejpam-4656	551	23	.	.	PUNCT
ejpam-4656	552	1	then	then	ADV
ejpam-4656	552	2	c	c	NOUN
ejpam-4656	552	3	′	′	NOUN
ejpam-4656	553	1	=	=	PUNCT
ejpam-4656	553	2	a′	a′	PROPN
ejpam-4656	553	3	∪	∪	ADJ
ejpam-4656	553	4	cw	cw	NOUN
ejpam-4656	553	5	is	be	AUX
ejpam-4656	553	6	a	a	DET
ejpam-4656	553	7	convex	convex	ADJ
ejpam-4656	553	8	hop	hop	NOUN
ejpam-4656	553	9	dominating	dominating	NOUN
ejpam-4656	553	10	set	set	VERB
ejpam-4656	553	11	in	in	ADP
ejpam-4656	553	12	g	g	PROPN
ejpam-4656	553	13	◦	◦	NOUN
ejpam-4656	553	14	h	h	NOUN
ejpam-4656	553	15	by	by	ADP
ejpam-4656	553	16	theorem	theorem	NOUN
ejpam-4656	553	17	14	14	NUM
ejpam-4656	553	18	.	.	PUNCT
ejpam-4656	554	1	hence	hence	ADV
ejpam-4656	554	2	,	,	PUNCT
ejpam-4656	554	3	γconh(g	γconh(g	PROPN
ejpam-4656	554	4	◦	◦	PROPN
ejpam-4656	554	5	h	h	NOUN
ejpam-4656	554	6	)	)	PUNCT
ejpam-4656	554	7	≤	≤	NOUN
ejpam-4656	554	8	|c	|c	VERB
ejpam-4656	554	9	′|	′|	NUM
ejpam-4656	554	10	=	=	SYM
ejpam-4656	554	11	γcon(g)+1	γcon(g)+1	NOUN
ejpam-4656	554	12	.	.	PUNCT
ejpam-4656	555	1	now	now	ADV
ejpam-4656	555	2	let	let	VERB
ejpam-4656	555	3	c∗	c∗	PROPN
ejpam-4656	555	4	=	=	PUNCT
ejpam-4656	555	5	a∗∪	a∗∪	NOUN
ejpam-4656	555	6	(	(	PUNCT
ejpam-4656	555	7	∪v∈v	∪v∈v	X
ejpam-4656	555	8	(	(	PUNCT
ejpam-4656	555	9	g)rv	g)rv	PROPN
ejpam-4656	555	10	)	)	PUNCT
ejpam-4656	555	11	be	be	VERB
ejpam-4656	555	12	a	a	DET
ejpam-4656	555	13	γconh	γconh	NOUN
ejpam-4656	555	14	-	-	PUNCT
ejpam-4656	555	15	set	set	NOUN
ejpam-4656	555	16	of	of	ADP
ejpam-4656	555	17	g	g	PROPN
ejpam-4656	555	18	◦	◦	PROPN
ejpam-4656	555	19	h.	h.	PROPN
ejpam-4656	555	20	then	then	ADV
ejpam-4656	555	21	a∗	a∗	PROPN
ejpam-4656	555	22	is	be	AUX
ejpam-4656	555	23	a	a	DET
ejpam-4656	555	24	convex	convex	NOUN
ejpam-4656	555	25	dominating	dominating	NOUN
ejpam-4656	555	26	set	set	VERB
ejpam-4656	555	27	in	in	ADP
ejpam-4656	555	28	g	g	NOUN
ejpam-4656	555	29	by	by	ADP
ejpam-4656	555	30	theorem	theorem	NOUN
ejpam-4656	555	31	14	14	NUM
ejpam-4656	555	32	.	.	PUNCT
ejpam-4656	556	1	if	if	SCONJ
ejpam-4656	556	2	|a∗|	|a∗|	NUM
ejpam-4656	556	3	>	>	X
ejpam-4656	556	4	γcon(g	γcon(g	NOUN
ejpam-4656	556	5	)	)	PUNCT
ejpam-4656	556	6	,	,	PUNCT
ejpam-4656	556	7	then	then	ADV
ejpam-4656	556	8	|c∗|	|c∗|	VERB
ejpam-4656	556	9	≥	≥	NOUN
ejpam-4656	556	10	|a∗|	|a∗|	PUNCT
ejpam-4656	556	11	≥	≥	X
ejpam-4656	556	12	γcon(g	γcon(g	NOUN
ejpam-4656	556	13	)	)	PUNCT
ejpam-4656	556	14	+	+	NUM
ejpam-4656	556	15	1	1	X
ejpam-4656	556	16	.	.	X
ejpam-4656	556	17	suppose	suppose	VERB
ejpam-4656	556	18	|a∗|	|a∗|	PUNCT
ejpam-4656	557	1	=	=	SYM
ejpam-4656	557	2	γcon(g	γcon(g	NOUN
ejpam-4656	557	3	)	)	PUNCT
ejpam-4656	557	4	.	.	PUNCT
ejpam-4656	558	1	since	since	SCONJ
ejpam-4656	558	2	γcon(g	γcon(g	PROPN
ejpam-4656	558	3	)	)	PUNCT
ejpam-4656	558	4	<	<	X
ejpam-4656	558	5	γhcon(g	γhcon(g	PROPN
ejpam-4656	558	6	)	)	PUNCT
ejpam-4656	558	7	,	,	PUNCT
ejpam-4656	558	8	a∗	a∗	PROPN
ejpam-4656	558	9	is	be	AUX
ejpam-4656	558	10	not	not	PART
ejpam-4656	558	11	a	a	DET
ejpam-4656	558	12	hop	hop	NOUN
ejpam-4656	558	13	dominating	dominating	NOUN
ejpam-4656	558	14	set	set	NOUN
ejpam-4656	558	15	,	,	PUNCT
ejpam-4656	558	16	say	say	VERB
ejpam-4656	558	17	v	v	X
ejpam-4656	558	18	/∈	/∈	SYM
ejpam-4656	558	19	n2	n2	ADJ
ejpam-4656	558	20	g[a	g[a	ADJ
ejpam-4656	558	21	∗	∗	NOUN
ejpam-4656	558	22	]	]	PUNCT
ejpam-4656	558	23	.	.	PUNCT
ejpam-4656	559	1	hence	hence	ADV
ejpam-4656	559	2	,	,	PUNCT
ejpam-4656	559	3	by	by	ADP
ejpam-4656	559	4	theorem	theorem	NOUN
ejpam-4656	559	5	14(i	14(i	NUM
ejpam-4656	559	6	)	)	PUNCT
ejpam-4656	559	7	,	,	PUNCT
ejpam-4656	559	8	there	there	PRON
ejpam-4656	559	9	exists	exist	VERB
ejpam-4656	559	10	y	y	PROPN
ejpam-4656	559	11	∈	∈	PROPN
ejpam-4656	559	12	a∗	a∗	PROPN
ejpam-4656	559	13	∩	∩	NOUN
ejpam-4656	559	14	ng(v	ng(v	NOUN
ejpam-4656	559	15	)	)	PUNCT
ejpam-4656	559	16	with	with	ADP
ejpam-4656	559	17	ry	ry	NOUN
ejpam-4656	559	18	̸=	̸=	PROPN
ejpam-4656	559	19	∅.	∅.	NOUN
ejpam-4656	559	20	it	it	PRON
ejpam-4656	559	21	follows	follow	VERB
ejpam-4656	559	22	that	that	SCONJ
ejpam-4656	559	23	γconh(g	γconh(g	ADP
ejpam-4656	559	24	◦	◦	NOUN
ejpam-4656	559	25	h	h	NOUN
ejpam-4656	559	26	)	)	PUNCT
ejpam-4656	559	27	=	=	SYM
ejpam-4656	559	28	|c∗|	|c∗|	X
ejpam-4656	559	29	≥	≥	X
ejpam-4656	559	30	|a∗|+	|a∗|+	PROPN
ejpam-4656	560	1	|ry|	|ry|	PROPN
ejpam-4656	560	2	≥	≥	NUM
ejpam-4656	560	3	γcon(g	γcon(g	PROPN
ejpam-4656	560	4	)	)	PUNCT
ejpam-4656	561	1	+	+	CCONJ
ejpam-4656	561	2	1	1	X
ejpam-4656	561	3	.	.	X
ejpam-4656	561	4	this	this	PRON
ejpam-4656	561	5	establishes	establish	VERB
ejpam-4656	561	6	the	the	DET
ejpam-4656	561	7	desired	desire	VERB
ejpam-4656	561	8	equality	equality	NOUN
ejpam-4656	561	9	.	.	PUNCT
ejpam-4656	562	1	the	the	DET
ejpam-4656	562	2	next	next	ADJ
ejpam-4656	562	3	result	result	NOUN
ejpam-4656	562	4	is	be	AUX
ejpam-4656	562	5	found	find	VERB
ejpam-4656	562	6	in	in	ADP
ejpam-4656	562	7	[	[	X
ejpam-4656	562	8	13	13	NUM
ejpam-4656	562	9	]	]	PUNCT
ejpam-4656	562	10	.	.	PUNCT
ejpam-4656	563	1	theorem	theorem	NOUN
ejpam-4656	563	2	15	15	NUM
ejpam-4656	563	3	.	.	PUNCT
ejpam-4656	564	1	let	let	VERB
ejpam-4656	564	2	g	g	NOUN
ejpam-4656	564	3	and	and	CCONJ
ejpam-4656	564	4	h	h	NOUN
ejpam-4656	564	5	be	be	AUX
ejpam-4656	564	6	connected	connect	VERB
ejpam-4656	564	7	non	non	ADJ
ejpam-4656	564	8	-	-	ADJ
ejpam-4656	564	9	trivial	trivial	ADJ
ejpam-4656	564	10	graphs	graph	NOUN
ejpam-4656	564	11	.	.	PUNCT
ejpam-4656	565	1	then	then	ADV
ejpam-4656	565	2	c	c	NOUN
ejpam-4656	565	3	=	=	PUNCT
ejpam-4656	565	4	⋃	⋃	PROPN
ejpam-4656	565	5	x∈s	x∈s	NOUN
ejpam-4656	566	1	[	[	X
ejpam-4656	566	2	{	{	PUNCT
ejpam-4656	566	3	x	x	NOUN
ejpam-4656	566	4	}	}	PUNCT
ejpam-4656	566	5	×	×	PROPN
ejpam-4656	566	6	tx	tx	PROPN
ejpam-4656	566	7	]	]	PUNCT
ejpam-4656	566	8	is	be	AUX
ejpam-4656	566	9	a	a	DET
ejpam-4656	566	10	hop	hop	NOUN
ejpam-4656	566	11	dominating	dominating	NOUN
ejpam-4656	566	12	set	set	VERB
ejpam-4656	566	13	in	in	ADP
ejpam-4656	566	14	g[h	g[h	PROPN
ejpam-4656	566	15	]	]	PUNCT
ejpam-4656	566	16	if	if	SCONJ
ejpam-4656	566	17	and	and	CCONJ
ejpam-4656	566	18	only	only	ADV
ejpam-4656	566	19	if	if	SCONJ
ejpam-4656	566	20	the	the	DET
ejpam-4656	566	21	following	follow	VERB
ejpam-4656	566	22	conditions	condition	NOUN
ejpam-4656	566	23	hold	hold	VERB
ejpam-4656	566	24	.	.	PUNCT
ejpam-4656	567	1	(	(	PUNCT
ejpam-4656	567	2	i	i	NOUN
ejpam-4656	567	3	)	)	PUNCT
ejpam-4656	567	4	s	s	VERB
ejpam-4656	567	5	is	be	AUX
ejpam-4656	567	6	a	a	DET
ejpam-4656	567	7	hop	hop	NOUN
ejpam-4656	567	8	dominating	dominating	NOUN
ejpam-4656	567	9	set	set	VERB
ejpam-4656	567	10	in	in	ADP
ejpam-4656	567	11	g.	g.	PROPN
ejpam-4656	567	12	(	(	PUNCT
ejpam-4656	567	13	ii	ii	PROPN
ejpam-4656	567	14	)	)	PUNCT
ejpam-4656	567	15	tx	tx	PROPN
ejpam-4656	567	16	is	be	AUX
ejpam-4656	567	17	a	a	DET
ejpam-4656	567	18	pointwise	pointwise	ADJ
ejpam-4656	567	19	non	non	ADJ
ejpam-4656	567	20	-	-	ADJ
ejpam-4656	567	21	dominating	dominating	ADJ
ejpam-4656	567	22	set	set	NOUN
ejpam-4656	567	23	in	in	ADP
ejpam-4656	567	24	h	h	NOUN
ejpam-4656	567	25	for	for	ADP
ejpam-4656	567	26	each	each	DET
ejpam-4656	567	27	x	x	SYM
ejpam-4656	567	28	∈	∈	PROPN
ejpam-4656	567	29	s	s	PART
ejpam-4656	567	30	\n2	\n2	ADJ
ejpam-4656	567	31	g(s	g(	NOUN
ejpam-4656	567	32	)	)	PUNCT
ejpam-4656	567	33	.	.	PUNCT
ejpam-4656	568	1	the	the	DET
ejpam-4656	568	2	next	next	ADJ
ejpam-4656	568	3	result	result	NOUN
ejpam-4656	568	4	is	be	AUX
ejpam-4656	568	5	a	a	DET
ejpam-4656	568	6	restatement	restatement	NOUN
ejpam-4656	568	7	of	of	ADP
ejpam-4656	568	8	the	the	DET
ejpam-4656	568	9	one	one	NOUN
ejpam-4656	568	10	obtained	obtain	VERB
ejpam-4656	568	11	by	by	ADP
ejpam-4656	568	12	canoy	canoy	NOUN
ejpam-4656	568	13	and	and	CCONJ
ejpam-4656	568	14	garces	garce	NOUN
ejpam-4656	568	15	in	in	ADP
ejpam-4656	568	16	[	[	X
ejpam-4656	568	17	12	12	NUM
ejpam-4656	568	18	]	]	PUNCT
ejpam-4656	568	19	.	.	PUNCT
ejpam-4656	569	1	theorem	theorem	NOUN
ejpam-4656	569	2	16	16	NUM
ejpam-4656	569	3	.	.	PUNCT
ejpam-4656	570	1	let	let	VERB
ejpam-4656	570	2	g	g	NOUN
ejpam-4656	570	3	and	and	CCONJ
ejpam-4656	570	4	h	h	NOUN
ejpam-4656	570	5	be	be	AUX
ejpam-4656	570	6	connected	connect	VERB
ejpam-4656	570	7	non	non	ADJ
ejpam-4656	570	8	-	-	ADJ
ejpam-4656	570	9	complete	complete	ADJ
ejpam-4656	570	10	graphs	graph	NOUN
ejpam-4656	570	11	.	.	PUNCT
ejpam-4656	571	1	then	then	ADV
ejpam-4656	571	2	c	c	X
ejpam-4656	571	3	=	=	SYM
ejpam-4656	571	4	⋃	⋃	PROPN
ejpam-4656	571	5	x∈s({x}×tx	x∈s({x}×tx	PROPN
ejpam-4656	571	6	)	)	PUNCT
ejpam-4656	571	7	is	be	AUX
ejpam-4656	571	8	convex	convex	ADJ
ejpam-4656	571	9	in	in	ADP
ejpam-4656	571	10	g[h	g[h	PROPN
ejpam-4656	571	11	]	]	PUNCT
ejpam-4656	571	12	if	if	SCONJ
ejpam-4656	572	1	and	and	CCONJ
ejpam-4656	572	2	only	only	ADV
ejpam-4656	572	3	if	if	SCONJ
ejpam-4656	572	4	s	s	NOUN
ejpam-4656	572	5	is	be	AUX
ejpam-4656	572	6	a	a	DET
ejpam-4656	572	7	clique	clique	NOUN
ejpam-4656	572	8	in	in	ADP
ejpam-4656	572	9	g	g	PROPN
ejpam-4656	572	10	and	and	CCONJ
ejpam-4656	572	11	tx	tx	PROPN
ejpam-4656	572	12	is	be	AUX
ejpam-4656	572	13	a	a	DET
ejpam-4656	572	14	clique	clique	NOUN
ejpam-4656	572	15	in	in	ADP
ejpam-4656	572	16	h	h	NOUN
ejpam-4656	572	17	for	for	ADP
ejpam-4656	572	18	each	each	DET
ejpam-4656	572	19	x	x	SYM
ejpam-4656	572	20	∈	∈	PROPN
ejpam-4656	572	21	s.	s.	PROPN
ejpam-4656	572	22	theorem	theorem	VERB
ejpam-4656	572	23	17	17	NUM
ejpam-4656	572	24	.	.	PUNCT
ejpam-4656	573	1	let	let	VERB
ejpam-4656	573	2	g	g	NOUN
ejpam-4656	573	3	and	and	CCONJ
ejpam-4656	573	4	h	h	NOUN
ejpam-4656	573	5	be	be	AUX
ejpam-4656	573	6	connected	connect	VERB
ejpam-4656	573	7	non	non	ADJ
ejpam-4656	573	8	-	-	ADJ
ejpam-4656	573	9	complete	complete	ADJ
ejpam-4656	573	10	graphs	graph	NOUN
ejpam-4656	573	11	.	.	PUNCT
ejpam-4656	574	1	then	then	ADV
ejpam-4656	574	2	c	c	X
ejpam-4656	574	3	=	=	PUNCT
ejpam-4656	574	4	⋃	⋃	NOUN
ejpam-4656	574	5	x∈a	x∈a	NOUN
ejpam-4656	574	6	[	[	X
ejpam-4656	574	7	{	{	PUNCT
ejpam-4656	574	8	x}×	x}×	PROPN
ejpam-4656	574	9	tx	tx	PROPN
ejpam-4656	574	10	]	]	X
ejpam-4656	574	11	,	,	PUNCT
ejpam-4656	574	12	where	where	SCONJ
ejpam-4656	574	13	a	a	DET
ejpam-4656	574	14	⊆	⊆	NUM
ejpam-4656	574	15	v	v	NOUN
ejpam-4656	574	16	(	(	PUNCT
ejpam-4656	574	17	g	g	NOUN
ejpam-4656	574	18	)	)	PUNCT
ejpam-4656	574	19	and	and	CCONJ
ejpam-4656	574	20	tx	tx	VERB
ejpam-4656	574	21	⊆	⊆	NUM
ejpam-4656	574	22	v	v	NOUN
ejpam-4656	574	23	(	(	PUNCT
ejpam-4656	574	24	h	h	NOUN
ejpam-4656	574	25	)	)	PUNCT
ejpam-4656	574	26	for	for	ADP
ejpam-4656	574	27	each	each	DET
ejpam-4656	574	28	x	x	SYM
ejpam-4656	574	29	∈	∈	PROPN
ejpam-4656	574	30	a	a	PRON
ejpam-4656	574	31	,	,	PUNCT
ejpam-4656	574	32	is	be	AUX
ejpam-4656	574	33	a	a	DET
ejpam-4656	574	34	convex	convex	ADJ
ejpam-4656	574	35	hop	hop	NOUN
ejpam-4656	574	36	dominating	dominating	NOUN
ejpam-4656	574	37	set	set	VERB
ejpam-4656	574	38	in	in	ADP
ejpam-4656	574	39	g[h	g[h	PROPN
ejpam-4656	574	40	]	]	PUNCT
ejpam-4656	574	41	if	if	SCONJ
ejpam-4656	574	42	and	and	CCONJ
ejpam-4656	574	43	only	only	ADV
ejpam-4656	574	44	if	if	SCONJ
ejpam-4656	574	45	c	c	PROPN
ejpam-4656	574	46	=	=	SYM
ejpam-4656	574	47	v	v	PROPN
ejpam-4656	574	48	(	(	PUNCT
ejpam-4656	574	49	g[h	g[h	PROPN
ejpam-4656	574	50	]	]	PUNCT
ejpam-4656	574	51	)	)	PUNCT
ejpam-4656	574	52	or	or	CCONJ
ejpam-4656	574	53	c	c	NOUN
ejpam-4656	574	54	satisfies	satisfy	VERB
ejpam-4656	574	55	the	the	DET
ejpam-4656	574	56	following	follow	VERB
ejpam-4656	574	57	conditions	condition	NOUN
ejpam-4656	574	58	:	:	PUNCT
ejpam-4656	574	59	(	(	PUNCT
ejpam-4656	574	60	i	i	NOUN
ejpam-4656	574	61	)	)	PUNCT
ejpam-4656	574	62	a	a	PRON
ejpam-4656	574	63	is	be	AUX
ejpam-4656	574	64	a	a	DET
ejpam-4656	574	65	clique	clique	NOUN
ejpam-4656	574	66	hop	hop	NOUN
ejpam-4656	574	67	dominating	dominating	NOUN
ejpam-4656	574	68	set	set	VERB
ejpam-4656	574	69	in	in	ADP
ejpam-4656	574	70	g.	g.	PROPN
ejpam-4656	574	71	(	(	PUNCT
ejpam-4656	574	72	ii	ii	PROPN
ejpam-4656	574	73	)	)	PUNCT
ejpam-4656	574	74	tx	tx	PROPN
ejpam-4656	574	75	is	be	AUX
ejpam-4656	574	76	a	a	DET
ejpam-4656	574	77	clique	clique	NOUN
ejpam-4656	574	78	pointwise	pointwise	PROPN
ejpam-4656	574	79	non	non	ADJ
ejpam-4656	574	80	-	-	ADJ
ejpam-4656	574	81	dominating	dominating	ADJ
ejpam-4656	574	82	set	set	NOUN
ejpam-4656	574	83	in	in	ADP
ejpam-4656	574	84	h	h	NOUN
ejpam-4656	574	85	for	for	ADP
ejpam-4656	574	86	each	each	DET
ejpam-4656	574	87	x	x	SYM
ejpam-4656	574	88	∈	∈	PROPN
ejpam-4656	574	89	a.	a.	NOUN
ejpam-4656	574	90	j.	j.	PROPN
ejpam-4656	574	91	hassan	hassan	PROPN
ejpam-4656	574	92	,	,	PUNCT
ejpam-4656	574	93	s.	s.	PROPN
ejpam-4656	574	94	canoy	canoy	PROPN
ejpam-4656	574	95	jr	jr	PROPN
ejpam-4656	574	96	.	.	PROPN
ejpam-4656	574	97	,	,	PUNCT
ejpam-4656	574	98	c.	c.	PROPN
ejpam-4656	574	99	saromines	saromine	VERB
ejpam-4656	574	100	/	/	SYM
ejpam-4656	574	101	eur	eur	PROPN
ejpam-4656	574	102	.	.	PUNCT
ejpam-4656	575	1	j.	j.	PROPN
ejpam-4656	575	2	pure	pure	PROPN
ejpam-4656	575	3	appl	appl	PROPN
ejpam-4656	575	4	.	.	PROPN
ejpam-4656	575	5	math	math	PROPN
ejpam-4656	575	6	,	,	PUNCT
ejpam-4656	575	7	16	16	NUM
ejpam-4656	575	8	(	(	PUNCT
ejpam-4656	575	9	1	1	NUM
ejpam-4656	575	10	)	)	PUNCT
ejpam-4656	575	11	(	(	PUNCT
ejpam-4656	575	12	2023	2023	NUM
ejpam-4656	575	13	)	)	PUNCT
ejpam-4656	575	14	,	,	PUNCT
ejpam-4656	575	15	319	319	NUM
ejpam-4656	575	16	-	-	SYM
ejpam-4656	575	17	335	335	NUM
ejpam-4656	575	18	332	332	NUM
ejpam-4656	575	19	proof	proof	NOUN
ejpam-4656	575	20	.	.	PUNCT
ejpam-4656	576	1	if	if	SCONJ
ejpam-4656	576	2	c	c	PROPN
ejpam-4656	576	3	=	=	SYM
ejpam-4656	576	4	v	v	PROPN
ejpam-4656	576	5	(	(	PUNCT
ejpam-4656	576	6	g[h	g[h	PROPN
ejpam-4656	576	7	]	]	PUNCT
ejpam-4656	576	8	)	)	PUNCT
ejpam-4656	576	9	,	,	PUNCT
ejpam-4656	576	10	then	then	ADV
ejpam-4656	576	11	we	we	PRON
ejpam-4656	576	12	are	be	AUX
ejpam-4656	576	13	done	do	VERB
ejpam-4656	576	14	.	.	PUNCT
ejpam-4656	577	1	suppose	suppose	VERB
ejpam-4656	577	2	c	c	PROPN
ejpam-4656	577	3	̸=	̸=	PROPN
ejpam-4656	577	4	v	v	NOUN
ejpam-4656	577	5	(	(	PUNCT
ejpam-4656	577	6	g[h	g[h	PROPN
ejpam-4656	577	7	]	]	PUNCT
ejpam-4656	577	8	)	)	PUNCT
ejpam-4656	577	9	.	.	PUNCT
ejpam-4656	578	1	then	then	ADV
ejpam-4656	578	2	a	a	PRON
ejpam-4656	578	3	is	be	AUX
ejpam-4656	578	4	a	a	DET
ejpam-4656	578	5	clique	clique	NOUN
ejpam-4656	578	6	in	in	ADP
ejpam-4656	578	7	g	g	PROPN
ejpam-4656	578	8	and	and	CCONJ
ejpam-4656	578	9	tx	tx	PROPN
ejpam-4656	578	10	is	be	AUX
ejpam-4656	578	11	a	a	DET
ejpam-4656	578	12	clique	clique	NOUN
ejpam-4656	578	13	in	in	ADP
ejpam-4656	578	14	h	h	NOUN
ejpam-4656	578	15	for	for	ADP
ejpam-4656	578	16	each	each	DET
ejpam-4656	578	17	x	x	SYM
ejpam-4656	578	18	∈	∈	PROPN
ejpam-4656	578	19	a	a	PRON
ejpam-4656	578	20	by	by	ADP
ejpam-4656	578	21	theorem	theorem	NOUN
ejpam-4656	578	22	16	16	NUM
ejpam-4656	578	23	.	.	PUNCT
ejpam-4656	579	1	since	since	SCONJ
ejpam-4656	579	2	c	c	PROPN
ejpam-4656	579	3	is	be	AUX
ejpam-4656	579	4	hop	hop	NOUN
ejpam-4656	579	5	dominating	dominating	NOUN
ejpam-4656	579	6	set	set	NOUN
ejpam-4656	579	7	,	,	PUNCT
ejpam-4656	579	8	a	a	PRON
ejpam-4656	579	9	is	be	AUX
ejpam-4656	579	10	a	a	DET
ejpam-4656	579	11	hop	hop	NOUN
ejpam-4656	579	12	dominating	dominating	NOUN
ejpam-4656	579	13	set	set	VERB
ejpam-4656	579	14	in	in	ADP
ejpam-4656	579	15	g	g	NOUN
ejpam-4656	579	16	by	by	ADP
ejpam-4656	579	17	theorem	theorem	NOUN
ejpam-4656	579	18	15	15	NUM
ejpam-4656	579	19	.	.	PUNCT
ejpam-4656	580	1	since	since	SCONJ
ejpam-4656	580	2	a	a	PRON
ejpam-4656	580	3	is	be	AUX
ejpam-4656	580	4	a	a	DET
ejpam-4656	580	5	clique	clique	NOUN
ejpam-4656	580	6	,	,	PUNCT
ejpam-4656	580	7	x	x	PROPN
ejpam-4656	580	8	/∈	/∈	PROPN
ejpam-4656	580	9	n2	n2	PROPN
ejpam-4656	580	10	g(a	g(a	PROPN
ejpam-4656	580	11	)	)	PUNCT
ejpam-4656	580	12	for	for	ADP
ejpam-4656	580	13	all	all	DET
ejpam-4656	580	14	x	x	SYM
ejpam-4656	580	15	∈	∈	NOUN
ejpam-4656	580	16	a.	a.	NOUN
ejpam-4656	580	17	thus	thus	ADV
ejpam-4656	580	18	,	,	PUNCT
ejpam-4656	580	19	tx	tx	PROPN
ejpam-4656	580	20	is	be	AUX
ejpam-4656	580	21	a	a	DET
ejpam-4656	580	22	pointwise	pointwise	ADJ
ejpam-4656	580	23	non	non	ADJ
ejpam-4656	580	24	-	-	ADJ
ejpam-4656	580	25	dominating	dominating	ADJ
ejpam-4656	580	26	set	set	NOUN
ejpam-4656	580	27	in	in	ADP
ejpam-4656	580	28	h	h	NOUN
ejpam-4656	580	29	for	for	ADP
ejpam-4656	580	30	every	every	DET
ejpam-4656	580	31	x	x	PROPN
ejpam-4656	580	32	∈	∈	PROPN
ejpam-4656	580	33	a	a	PRON
ejpam-4656	580	34	by	by	ADP
ejpam-4656	580	35	theorem	theorem	NOUN
ejpam-4656	580	36	15(ii	15(ii	NUM
ejpam-4656	580	37	)	)	PUNCT
ejpam-4656	580	38	.	.	PUNCT
ejpam-4656	581	1	therefore	therefore	ADV
ejpam-4656	581	2	,	,	PUNCT
ejpam-4656	581	3	(	(	PUNCT
ejpam-4656	581	4	i	i	NOUN
ejpam-4656	581	5	)	)	PUNCT
ejpam-4656	581	6	and	and	CCONJ
ejpam-4656	581	7	(	(	PUNCT
ejpam-4656	581	8	ii	ii	NOUN
ejpam-4656	581	9	)	)	PUNCT
ejpam-4656	581	10	hold	hold	VERB
ejpam-4656	581	11	.	.	PUNCT
ejpam-4656	582	1	for	for	ADP
ejpam-4656	582	2	the	the	DET
ejpam-4656	582	3	converse	converse	NOUN
ejpam-4656	582	4	,	,	PUNCT
ejpam-4656	582	5	suppose	suppose	VERB
ejpam-4656	582	6	that	that	SCONJ
ejpam-4656	582	7	c	c	PROPN
ejpam-4656	582	8	=	=	SYM
ejpam-4656	582	9	v	v	PROPN
ejpam-4656	582	10	(	(	PUNCT
ejpam-4656	582	11	g[h	g[h	PROPN
ejpam-4656	582	12	]	]	PUNCT
ejpam-4656	582	13	)	)	PUNCT
ejpam-4656	582	14	.	.	PUNCT
ejpam-4656	583	1	then	then	ADV
ejpam-4656	583	2	c	c	PROPN
ejpam-4656	583	3	is	be	AUX
ejpam-4656	583	4	convex	convex	ADJ
ejpam-4656	583	5	hop	hop	NOUN
ejpam-4656	583	6	dominating	dominating	NOUN
ejpam-4656	583	7	in	in	ADP
ejpam-4656	583	8	g[h	g[h	PROPN
ejpam-4656	583	9	]	]	PUNCT
ejpam-4656	583	10	.	.	PUNCT
ejpam-4656	584	1	next	next	ADV
ejpam-4656	584	2	,	,	PUNCT
ejpam-4656	584	3	suppose	suppose	VERB
ejpam-4656	584	4	c	c	NOUN
ejpam-4656	584	5	satisfies	satisfie	NOUN
ejpam-4656	584	6	i	i	PRON
ejpam-4656	584	7	and	and	CCONJ
ejpam-4656	584	8	(	(	PUNCT
ejpam-4656	584	9	ii	ii	NOUN
ejpam-4656	584	10	)	)	PUNCT
ejpam-4656	584	11	.	.	PUNCT
ejpam-4656	585	1	then	then	ADV
ejpam-4656	585	2	by	by	ADP
ejpam-4656	585	3	theorem	theorem	NOUN
ejpam-4656	585	4	15	15	NUM
ejpam-4656	585	5	,	,	PUNCT
ejpam-4656	585	6	c	c	PROPN
ejpam-4656	585	7	is	be	AUX
ejpam-4656	585	8	a	a	DET
ejpam-4656	585	9	hop	hop	NOUN
ejpam-4656	585	10	dominating	dominating	NOUN
ejpam-4656	585	11	set	set	VERB
ejpam-4656	585	12	in	in	ADP
ejpam-4656	585	13	g[h	g[h	PROPN
ejpam-4656	585	14	]	]	PUNCT
ejpam-4656	585	15	.	.	PUNCT
ejpam-4656	586	1	by	by	ADP
ejpam-4656	586	2	(	(	PUNCT
ejpam-4656	586	3	i	i	NOUN
ejpam-4656	586	4	)	)	PUNCT
ejpam-4656	586	5	,	,	PUNCT
ejpam-4656	586	6	(	(	PUNCT
ejpam-4656	586	7	ii	ii	NOUN
ejpam-4656	586	8	)	)	PUNCT
ejpam-4656	586	9	and	and	CCONJ
ejpam-4656	586	10	theorem	theorem	VERB
ejpam-4656	586	11	16	16	NUM
ejpam-4656	586	12	,	,	PUNCT
ejpam-4656	586	13	c	c	PROPN
ejpam-4656	586	14	is	be	AUX
ejpam-4656	586	15	a	a	DET
ejpam-4656	586	16	convex	convex	NOUN
ejpam-4656	586	17	set	set	VERB
ejpam-4656	586	18	in	in	ADP
ejpam-4656	586	19	g[h	g[h	PROPN
ejpam-4656	586	20	]	]	PUNCT
ejpam-4656	586	21	.	.	PUNCT
ejpam-4656	587	1	hence	hence	ADV
ejpam-4656	587	2	,	,	PUNCT
ejpam-4656	587	3	c	c	PROPN
ejpam-4656	587	4	is	be	AUX
ejpam-4656	587	5	a	a	DET
ejpam-4656	587	6	convex	convex	ADJ
ejpam-4656	587	7	hop	hop	NOUN
ejpam-4656	587	8	dominating	dominating	NOUN
ejpam-4656	587	9	set	set	VERB
ejpam-4656	587	10	in	in	ADP
ejpam-4656	587	11	g[h	g[h	PROPN
ejpam-4656	587	12	]	]	PUNCT
ejpam-4656	587	13	.	.	PUNCT
ejpam-4656	588	1	in	in	ADP
ejpam-4656	588	2	the	the	DET
ejpam-4656	588	3	next	next	ADJ
ejpam-4656	588	4	result	result	NOUN
ejpam-4656	588	5	,	,	PUNCT
ejpam-4656	588	6	we	we	PRON
ejpam-4656	588	7	shall	shall	AUX
ejpam-4656	588	8	consider	consider	VERB
ejpam-4656	588	9	the	the	DET
ejpam-4656	588	10	family	family	NOUN
ejpam-4656	588	11	c	c	NOUN
ejpam-4656	588	12	of	of	ADP
ejpam-4656	588	13	graphs	graph	NOUN
ejpam-4656	588	14	given	give	VERB
ejpam-4656	588	15	by	by	ADP
ejpam-4656	588	16	c	c	NOUN
ejpam-4656	588	17	=	=	SYM
ejpam-4656	588	18	{	{	PUNCT
ejpam-4656	588	19	g	g	NOUN
ejpam-4656	588	20	:	:	PUNCT
ejpam-4656	588	21	g	g	PROPN
ejpam-4656	588	22	is	be	AUX
ejpam-4656	588	23	a	a	DET
ejpam-4656	588	24	connected	connected	ADJ
ejpam-4656	588	25	non	non	ADJ
ejpam-4656	588	26	-	-	ADJ
ejpam-4656	588	27	complete	complete	ADJ
ejpam-4656	588	28	graph	graph	NOUN
ejpam-4656	588	29	that	that	PRON
ejpam-4656	588	30	admits	admit	VERB
ejpam-4656	588	31	a	a	DET
ejpam-4656	588	32	clique	clique	NOUN
ejpam-4656	588	33	hop	hop	NOUN
ejpam-4656	588	34	dominating	dominating	NOUN
ejpam-4656	588	35	set	set	PROPN
ejpam-4656	588	36	}	}	PUNCT
ejpam-4656	588	37	.	.	PUNCT
ejpam-4656	589	1	corollary	corollary	ADJ
ejpam-4656	589	2	10	10	NUM
ejpam-4656	589	3	.	.	PUNCT
ejpam-4656	590	1	let	let	VERB
ejpam-4656	590	2	g	g	NOUN
ejpam-4656	590	3	and	and	CCONJ
ejpam-4656	590	4	h	h	NOUN
ejpam-4656	590	5	be	be	AUX
ejpam-4656	590	6	connected	connect	VERB
ejpam-4656	590	7	non	non	ADJ
ejpam-4656	590	8	-	-	ADJ
ejpam-4656	590	9	complete	complete	ADJ
ejpam-4656	590	10	graphs	graph	NOUN
ejpam-4656	590	11	of	of	ADP
ejpam-4656	590	12	orders	order	NOUN
ejpam-4656	590	13	m	m	VERB
ejpam-4656	590	14	and	and	CCONJ
ejpam-4656	590	15	n	n	CCONJ
ejpam-4656	590	16	,	,	PUNCT
ejpam-4656	590	17	respectively	respectively	ADV
ejpam-4656	590	18	.	.	PUNCT
ejpam-4656	591	1	then	then	ADV
ejpam-4656	591	2	γconh(g[h	γconh(g[h	ADV
ejpam-4656	591	3	]	]	PUNCT
ejpam-4656	591	4	)	)	PUNCT
ejpam-4656	592	1	=	=	SYM
ejpam-4656	592	2	{	{	PUNCT
ejpam-4656	592	3	nm	nm	INTJ
ejpam-4656	592	4	if	if	SCONJ
ejpam-4656	592	5	g	g	PROPN
ejpam-4656	592	6	/∈	/∈	PROPN
ejpam-4656	592	7	c	c	NOUN
ejpam-4656	592	8	γclh(g)cpnd(h	γclh(g)cpnd(h	NOUN
ejpam-4656	592	9	)	)	PUNCT
ejpam-4656	592	10	if	if	SCONJ
ejpam-4656	592	11	g	g	PROPN
ejpam-4656	592	12	∈	∈	PROPN
ejpam-4656	592	13	c.	c.	NOUN
ejpam-4656	592	14	the	the	DET
ejpam-4656	592	15	next	next	ADJ
ejpam-4656	592	16	result	result	NOUN
ejpam-4656	592	17	is	be	AUX
ejpam-4656	592	18	taken	take	VERB
ejpam-4656	592	19	from	from	ADP
ejpam-4656	592	20	[	[	X
ejpam-4656	592	21	10	10	NUM
ejpam-4656	592	22	]	]	PUNCT
ejpam-4656	592	23	.	.	PUNCT
ejpam-4656	593	1	theorem	theorem	NOUN
ejpam-4656	593	2	18	18	NUM
ejpam-4656	593	3	.	.	PUNCT
ejpam-4656	594	1	let	let	VERB
ejpam-4656	594	2	g	g	PRON
ejpam-4656	594	3	be	be	AUX
ejpam-4656	594	4	a	a	DET
ejpam-4656	594	5	connected	connected	ADJ
ejpam-4656	594	6	graph	graph	NOUN
ejpam-4656	594	7	and	and	CCONJ
ejpam-4656	594	8	km	km	VERB
ejpam-4656	594	9	the	the	DET
ejpam-4656	594	10	complete	complete	ADJ
ejpam-4656	594	11	graph	graph	NOUN
ejpam-4656	594	12	of	of	ADP
ejpam-4656	594	13	order	order	NOUN
ejpam-4656	594	14	m.	m.	NOUN
ejpam-4656	594	15	a	a	DET
ejpam-4656	594	16	subset	subset	NOUN
ejpam-4656	594	17	c	c	NOUN
ejpam-4656	595	1	=	=	PUNCT
ejpam-4656	595	2	⋃	⋃	NOUN
ejpam-4656	595	3	x∈s({x	x∈s({x	NOUN
ejpam-4656	595	4	}	}	SYM
ejpam-4656	595	5	×	×	PROPN
ejpam-4656	595	6	tx	tx	PROPN
ejpam-4656	595	7	)	)	PUNCT
ejpam-4656	595	8	of	of	ADP
ejpam-4656	595	9	v	v	PROPN
ejpam-4656	595	10	(	(	PUNCT
ejpam-4656	595	11	g[km	g[km	PROPN
ejpam-4656	595	12	]	]	PUNCT
ejpam-4656	595	13	)	)	PUNCT
ejpam-4656	595	14	is	be	AUX
ejpam-4656	595	15	convex	convex	ADJ
ejpam-4656	595	16	in	in	ADP
ejpam-4656	595	17	g[km	g[km	PROPN
ejpam-4656	595	18	]	]	X
ejpam-4656	595	19	if	if	SCONJ
ejpam-4656	595	20	and	and	CCONJ
ejpam-4656	595	21	only	only	ADV
ejpam-4656	595	22	if	if	SCONJ
ejpam-4656	595	23	s	s	NOUN
ejpam-4656	595	24	is	be	AUX
ejpam-4656	595	25	convex	convex	ADJ
ejpam-4656	595	26	in	in	ADP
ejpam-4656	595	27	g	g	PROPN
ejpam-4656	595	28	and	and	CCONJ
ejpam-4656	595	29	tx	tx	PROPN
ejpam-4656	595	30	=	=	SYM
ejpam-4656	595	31	v	v	PROPN
ejpam-4656	595	32	(	(	PUNCT
ejpam-4656	595	33	km	km	PROPN
ejpam-4656	595	34	)	)	PUNCT
ejpam-4656	595	35	for	for	ADP
ejpam-4656	595	36	each	each	DET
ejpam-4656	595	37	x	x	SYM
ejpam-4656	595	38	∈	∈	PROPN
ejpam-4656	595	39	s	s	PART
ejpam-4656	595	40	∩	∩	NOUN
ejpam-4656	595	41	ig(s	ig(s	NUM
ejpam-4656	595	42	)	)	PUNCT
ejpam-4656	595	43	.	.	PUNCT
ejpam-4656	596	1	theorem	theorem	NOUN
ejpam-4656	596	2	19	19	NUM
ejpam-4656	596	3	.	.	PUNCT
ejpam-4656	597	1	let	let	VERB
ejpam-4656	597	2	g	g	PRON
ejpam-4656	597	3	be	be	AUX
ejpam-4656	597	4	a	a	DET
ejpam-4656	597	5	connected	connected	ADJ
ejpam-4656	597	6	graph	graph	NOUN
ejpam-4656	597	7	and	and	CCONJ
ejpam-4656	597	8	km	km	VERB
ejpam-4656	597	9	the	the	DET
ejpam-4656	597	10	complete	complete	ADJ
ejpam-4656	597	11	graph	graph	NOUN
ejpam-4656	597	12	of	of	ADP
ejpam-4656	597	13	order	order	NOUN
ejpam-4656	597	14	m.	m.	NOUN
ejpam-4656	598	1	then	then	ADV
ejpam-4656	598	2	c	c	NOUN
ejpam-4656	598	3	=	=	SYM
ejpam-4656	598	4	⋃	⋃	NOUN
ejpam-4656	598	5	x∈a	x∈a	NOUN
ejpam-4656	598	6	[	[	X
ejpam-4656	598	7	{	{	PUNCT
ejpam-4656	598	8	x	x	NOUN
ejpam-4656	598	9	}	}	PUNCT
ejpam-4656	598	10	×	×	PROPN
ejpam-4656	598	11	tx	tx	PROPN
ejpam-4656	598	12	]	]	X
ejpam-4656	598	13	,	,	PUNCT
ejpam-4656	598	14	where	where	SCONJ
ejpam-4656	598	15	a	a	DET
ejpam-4656	598	16	⊆	⊆	NUM
ejpam-4656	598	17	v	v	NOUN
ejpam-4656	598	18	(	(	PUNCT
ejpam-4656	598	19	g	g	NOUN
ejpam-4656	598	20	)	)	PUNCT
ejpam-4656	598	21	and	and	CCONJ
ejpam-4656	598	22	tx	tx	VERB
ejpam-4656	598	23	⊆	⊆	NUM
ejpam-4656	598	24	v	v	NOUN
ejpam-4656	598	25	(	(	PUNCT
ejpam-4656	598	26	km	km	PROPN
ejpam-4656	598	27	)	)	PUNCT
ejpam-4656	598	28	for	for	ADP
ejpam-4656	598	29	each	each	DET
ejpam-4656	598	30	x	x	SYM
ejpam-4656	598	31	∈	∈	PROPN
ejpam-4656	598	32	a	a	PRON
ejpam-4656	598	33	,	,	PUNCT
ejpam-4656	598	34	is	be	AUX
ejpam-4656	598	35	a	a	DET
ejpam-4656	598	36	convex	convex	ADJ
ejpam-4656	598	37	hop	hop	NOUN
ejpam-4656	598	38	dominating	dominating	NOUN
ejpam-4656	598	39	set	set	NOUN
ejpam-4656	598	40	in	in	ADP
ejpam-4656	598	41	g[km	g[km	PROPN
ejpam-4656	598	42	]	]	X
ejpam-4656	598	43	if	if	SCONJ
ejpam-4656	598	44	and	and	CCONJ
ejpam-4656	598	45	only	only	ADV
ejpam-4656	598	46	if	if	SCONJ
ejpam-4656	598	47	c	c	PROPN
ejpam-4656	598	48	=	=	SYM
ejpam-4656	598	49	v	v	PROPN
ejpam-4656	598	50	(	(	PUNCT
ejpam-4656	598	51	g[h	g[h	PROPN
ejpam-4656	598	52	]	]	PUNCT
ejpam-4656	598	53	)	)	PUNCT
ejpam-4656	598	54	or	or	CCONJ
ejpam-4656	598	55	c	c	NOUN
ejpam-4656	598	56	satisfies	satisfy	VERB
ejpam-4656	598	57	the	the	DET
ejpam-4656	598	58	following	follow	VERB
ejpam-4656	598	59	conditions	condition	NOUN
ejpam-4656	598	60	:	:	PUNCT
ejpam-4656	598	61	(	(	PUNCT
ejpam-4656	598	62	i	i	NOUN
ejpam-4656	598	63	)	)	PUNCT
ejpam-4656	598	64	a	a	PRON
ejpam-4656	598	65	is	be	AUX
ejpam-4656	598	66	a	a	DET
ejpam-4656	598	67	convex	convex	ADJ
ejpam-4656	598	68	hop	hop	NOUN
ejpam-4656	598	69	dominating	dominating	NOUN
ejpam-4656	598	70	set	set	VERB
ejpam-4656	598	71	in	in	ADP
ejpam-4656	598	72	g.	g.	PROPN
ejpam-4656	598	73	(	(	PUNCT
ejpam-4656	598	74	ii	ii	PROPN
ejpam-4656	598	75	)	)	PUNCT
ejpam-4656	599	1	tx	tx	PROPN
ejpam-4656	599	2	=	=	SYM
ejpam-4656	599	3	v	v	PROPN
ejpam-4656	599	4	(	(	PUNCT
ejpam-4656	599	5	km	km	PROPN
ejpam-4656	599	6	)	)	PUNCT
ejpam-4656	599	7	for	for	ADP
ejpam-4656	599	8	each	each	DET
ejpam-4656	599	9	x	x	SYM
ejpam-4656	599	10	∈	∈	PROPN
ejpam-4656	599	11	(	(	PUNCT
ejpam-4656	599	12	a	a	DET
ejpam-4656	599	13	∩	∩	NOUN
ejpam-4656	599	14	ig(a	ig(a	X
ejpam-4656	599	15	)	)	PUNCT
ejpam-4656	599	16	)	)	PUNCT
ejpam-4656	599	17	∪	∪	NOUN
ejpam-4656	599	18	(	(	PUNCT
ejpam-4656	599	19	a	a	DET
ejpam-4656	599	20	\n2	\n2	ADJ
ejpam-4656	599	21	g(a	g(a	PROPN
ejpam-4656	599	22	)	)	PUNCT
ejpam-4656	599	23	)	)	PUNCT
ejpam-4656	599	24	.	.	PUNCT
ejpam-4656	600	1	proof	proof	NOUN
ejpam-4656	600	2	.	.	PUNCT
ejpam-4656	601	1	suppose	suppose	VERB
ejpam-4656	601	2	c	c	NOUN
ejpam-4656	601	3	is	be	AUX
ejpam-4656	601	4	a	a	DET
ejpam-4656	601	5	convex	convex	ADJ
ejpam-4656	601	6	hop	hop	NOUN
ejpam-4656	601	7	dominating	dominating	NOUN
ejpam-4656	601	8	set	set	NOUN
ejpam-4656	601	9	of	of	ADP
ejpam-4656	601	10	g[km	g[km	PROPN
ejpam-4656	601	11	]	]	PUNCT
ejpam-4656	601	12	.	.	PUNCT
ejpam-4656	602	1	by	by	ADP
ejpam-4656	602	2	theorem	theorem	ADJ
ejpam-4656	602	3	15	15	NUM
ejpam-4656	602	4	and	and	CCONJ
ejpam-4656	602	5	theorem	theorem	VERB
ejpam-4656	602	6	18	18	NUM
ejpam-4656	602	7	,	,	PUNCT
ejpam-4656	602	8	a	a	PRON
ejpam-4656	602	9	is	be	AUX
ejpam-4656	602	10	a	a	DET
ejpam-4656	602	11	convex	convex	ADJ
ejpam-4656	602	12	hop	hop	NOUN
ejpam-4656	602	13	dominating	dominating	NOUN
ejpam-4656	602	14	set	set	VERB
ejpam-4656	602	15	in	in	ADP
ejpam-4656	602	16	g	g	PROPN
ejpam-4656	602	17	and	and	CCONJ
ejpam-4656	602	18	tx	tx	PROPN
ejpam-4656	602	19	=	=	SYM
ejpam-4656	602	20	v	v	PROPN
ejpam-4656	602	21	(	(	PUNCT
ejpam-4656	602	22	km	km	PROPN
ejpam-4656	602	23	)	)	PUNCT
ejpam-4656	602	24	for	for	ADP
ejpam-4656	602	25	each	each	DET
ejpam-4656	602	26	x	x	SYM
ejpam-4656	602	27	∈	∈	PROPN
ejpam-4656	602	28	(	(	PUNCT
ejpam-4656	602	29	a	a	DET
ejpam-4656	602	30	∩	∩	NOUN
ejpam-4656	602	31	ig(a	ig(a	X
ejpam-4656	602	32	)	)	PUNCT
ejpam-4656	602	33	)	)	PUNCT
ejpam-4656	602	34	∪	∪	NOUN
ejpam-4656	602	35	(	(	PUNCT
ejpam-4656	602	36	a	a	DET
ejpam-4656	602	37	\n2	\n2	ADJ
ejpam-4656	602	38	g(a	g(a	PROPN
ejpam-4656	602	39	)	)	PUNCT
ejpam-4656	602	40	)	)	PUNCT
ejpam-4656	602	41	.	.	PUNCT
ejpam-4656	603	1	hence	hence	ADV
ejpam-4656	603	2	,	,	PUNCT
ejpam-4656	603	3	(	(	PUNCT
ejpam-4656	603	4	i	i	NOUN
ejpam-4656	603	5	)	)	PUNCT
ejpam-4656	603	6	and	and	CCONJ
ejpam-4656	603	7	(	(	PUNCT
ejpam-4656	603	8	ii	ii	NOUN
ejpam-4656	603	9	)	)	PUNCT
ejpam-4656	603	10	hold	hold	VERB
ejpam-4656	603	11	.	.	PUNCT
ejpam-4656	604	1	conversely	conversely	ADV
ejpam-4656	604	2	,	,	PUNCT
ejpam-4656	604	3	suppose	suppose	VERB
ejpam-4656	604	4	that	that	SCONJ
ejpam-4656	604	5	(	(	PUNCT
ejpam-4656	604	6	i	i	NOUN
ejpam-4656	604	7	)	)	PUNCT
ejpam-4656	604	8	and	and	CCONJ
ejpam-4656	604	9	(	(	PUNCT
ejpam-4656	604	10	ii	ii	NOUN
ejpam-4656	604	11	)	)	PUNCT
ejpam-4656	604	12	hold	hold	VERB
ejpam-4656	604	13	.	.	PUNCT
ejpam-4656	605	1	then	then	ADV
ejpam-4656	605	2	,	,	PUNCT
ejpam-4656	605	3	by	by	ADP
ejpam-4656	605	4	theorem	theorem	ADJ
ejpam-4656	605	5	15	15	NUM
ejpam-4656	605	6	and	and	CCONJ
ejpam-4656	605	7	theorem	theorem	VERB
ejpam-4656	605	8	18	18	NUM
ejpam-4656	605	9	,	,	PUNCT
ejpam-4656	605	10	c	c	PROPN
ejpam-4656	605	11	is	be	AUX
ejpam-4656	605	12	a	a	DET
ejpam-4656	605	13	convex	convex	ADJ
ejpam-4656	605	14	hop	hop	NOUN
ejpam-4656	605	15	dominating	dominating	NOUN
ejpam-4656	605	16	set	set	VERB
ejpam-4656	605	17	in	in	ADP
ejpam-4656	605	18	g[km	g[km	PROPN
ejpam-4656	605	19	]	]	PUNCT
ejpam-4656	605	20	.	.	PUNCT
ejpam-4656	606	1	corollary	corollary	ADJ
ejpam-4656	606	2	11	11	NUM
ejpam-4656	606	3	.	.	PUNCT
ejpam-4656	607	1	let	let	VERB
ejpam-4656	607	2	g	g	PRON
ejpam-4656	607	3	be	be	AUX
ejpam-4656	607	4	a	a	DET
ejpam-4656	607	5	connected	connected	ADJ
ejpam-4656	607	6	graph	graph	NOUN
ejpam-4656	607	7	and	and	CCONJ
ejpam-4656	607	8	km	km	VERB
ejpam-4656	607	9	the	the	DET
ejpam-4656	607	10	complete	complete	ADJ
ejpam-4656	607	11	graph	graph	NOUN
ejpam-4656	607	12	of	of	ADP
ejpam-4656	607	13	order	order	NOUN
ejpam-4656	607	14	m.	m.	NOUN
ejpam-4656	607	15	then	then	ADV
ejpam-4656	607	16	γconh(g[km	γconh(g[km	NUM
ejpam-4656	607	17	]	]	X
ejpam-4656	607	18	)	)	PUNCT
ejpam-4656	608	1	=	=	SYM
ejpam-4656	608	2	min{|s|+(m−1)|s0∪(s\n2	min{|s|+(m−1)|s0∪(s\n2	PROPN
ejpam-4656	608	3	g(s))|	g(s))|	NOUN
ejpam-4656	608	4	:	:	PUNCT
ejpam-4656	608	5	s	s	VERB
ejpam-4656	608	6	is	be	AUX
ejpam-4656	608	7	a	a	DET
ejpam-4656	608	8	convex	convex	ADJ
ejpam-4656	608	9	hop	hop	NOUN
ejpam-4656	608	10	dominating	dominating	NOUN
ejpam-4656	608	11	set	set	VERB
ejpam-4656	608	12	in	in	ADP
ejpam-4656	608	13	g	g	NOUN
ejpam-4656	608	14	}	}	PUNCT
ejpam-4656	608	15	,	,	PUNCT
ejpam-4656	608	16	where	where	SCONJ
ejpam-4656	608	17	s0	s0	PROPN
ejpam-4656	608	18	=	=	SYM
ejpam-4656	608	19	s	s	PART
ejpam-4656	608	20	∩	∩	NOUN
ejpam-4656	608	21	ig(s	ig(s	NUM
ejpam-4656	608	22	)	)	PUNCT
ejpam-4656	608	23	.	.	PUNCT
ejpam-4656	609	1	references	reference	NOUN
ejpam-4656	609	2	333	333	NUM
ejpam-4656	609	3	proof	proof	NOUN
ejpam-4656	609	4	.	.	PUNCT
ejpam-4656	610	1	let	let	VERB
ejpam-4656	610	2	c	c	NOUN
ejpam-4656	610	3	=	=	PUNCT
ejpam-4656	611	1	⋃	⋃	PROPN
ejpam-4656	611	2	x∈s	x∈s	NOUN
ejpam-4656	612	1	[	[	X
ejpam-4656	612	2	{	{	PUNCT
ejpam-4656	612	3	x	x	NOUN
ejpam-4656	612	4	}	}	PUNCT
ejpam-4656	612	5	×	×	PROPN
ejpam-4656	612	6	tx	tx	PROPN
ejpam-4656	612	7	]	]	PUNCT
ejpam-4656	612	8	be	be	AUX
ejpam-4656	612	9	a	a	DET
ejpam-4656	612	10	γconh	γconh	NOUN
ejpam-4656	612	11	-	-	PUNCT
ejpam-4656	612	12	set	set	NOUN
ejpam-4656	612	13	of	of	ADP
ejpam-4656	612	14	g[km	g[km	PROPN
ejpam-4656	612	15	]	]	PUNCT
ejpam-4656	612	16	.	.	PUNCT
ejpam-4656	613	1	then	then	ADV
ejpam-4656	613	2	s	s	VERB
ejpam-4656	613	3	is	be	AUX
ejpam-4656	613	4	a	a	DET
ejpam-4656	613	5	convex	convex	ADJ
ejpam-4656	613	6	hop	hop	NOUN
ejpam-4656	613	7	dominating	dominating	NOUN
ejpam-4656	613	8	set	set	NOUN
ejpam-4656	613	9	and	and	CCONJ
ejpam-4656	613	10	tx	tx	PROPN
ejpam-4656	613	11	=	=	SYM
ejpam-4656	613	12	v	v	PROPN
ejpam-4656	613	13	(	(	PUNCT
ejpam-4656	613	14	km	km	PROPN
ejpam-4656	613	15	)	)	PUNCT
ejpam-4656	613	16	for	for	ADP
ejpam-4656	613	17	all	all	DET
ejpam-4656	613	18	x	x	SYM
ejpam-4656	613	19	∈	∈	PROPN
ejpam-4656	613	20	s0	s0	NOUN
ejpam-4656	613	21	∪	∪	X
ejpam-4656	613	22	(	(	PUNCT
ejpam-4656	613	23	s	s	NOUN
ejpam-4656	613	24	\n2	\n2	ADJ
ejpam-4656	613	25	g(s	g(s	NOUN
ejpam-4656	613	26	)	)	PUNCT
ejpam-4656	613	27	)	)	PUNCT
ejpam-4656	613	28	by	by	ADP
ejpam-4656	613	29	theorem	theorem	NOUN
ejpam-4656	613	30	19	19	NUM
ejpam-4656	613	31	.	.	PUNCT
ejpam-4656	614	1	since	since	SCONJ
ejpam-4656	614	2	c	c	PROPN
ejpam-4656	614	3	is	be	AUX
ejpam-4656	614	4	a	a	DET
ejpam-4656	614	5	γconh	γconh	NOUN
ejpam-4656	614	6	-	-	PUNCT
ejpam-4656	614	7	set	set	NOUN
ejpam-4656	614	8	,	,	PUNCT
ejpam-4656	614	9	|tx|	|tx|	X
ejpam-4656	614	10	=	=	SYM
ejpam-4656	614	11	1	1	NUM
ejpam-4656	614	12	for	for	ADP
ejpam-4656	614	13	all	all	DET
ejpam-4656	614	14	x	x	PART
ejpam-4656	614	15	∈	∈	PROPN
ejpam-4656	614	16	s	s	PART
ejpam-4656	614	17	\	\	X
ejpam-4656	615	1	[	[	X
ejpam-4656	615	2	s0	s0	PROPN
ejpam-4656	615	3	∪	∪	X
ejpam-4656	615	4	(	(	PUNCT
ejpam-4656	615	5	s	s	NOUN
ejpam-4656	615	6	\n2	\n2	ADJ
ejpam-4656	615	7	g(s	g(	NOUN
ejpam-4656	615	8	)	)	PUNCT
ejpam-4656	615	9	)	)	PUNCT
ejpam-4656	615	10	]	]	PUNCT
ejpam-4656	615	11	.	.	PUNCT
ejpam-4656	616	1	it	it	PRON
ejpam-4656	616	2	follows	follow	VERB
ejpam-4656	616	3	that	that	DET
ejpam-4656	616	4	|c|	|c|	PROPN
ejpam-4656	616	5	=	=	PUNCT
ejpam-4656	616	6	∑	∑	PUNCT
ejpam-4656	616	7	x∈[s0∪(s\n2	x∈[s0∪(s\n2	ADJ
ejpam-4656	616	8	g(s	g(	NOUN
ejpam-4656	616	9	)	)	PUNCT
ejpam-4656	616	10	)	)	PUNCT
ejpam-4656	616	11	]	]	PUNCT
ejpam-4656	616	12	|tx|+	|tx|+	X
ejpam-4656	616	13	∑	∑	INTJ
ejpam-4656	616	14	x∈s\[s0∪(s\n2	x∈s\[s0∪(s\n2	NOUN
ejpam-4656	616	15	g(s	g(	NOUN
ejpam-4656	616	16	)	)	PUNCT
ejpam-4656	616	17	)	)	PUNCT
ejpam-4656	616	18	]	]	PUNCT
ejpam-4656	617	1	|tx|	|tx|	NOUN
ejpam-4656	617	2	=	=	PUNCT
ejpam-4656	617	3	m|s0	m|s0	ADJ
ejpam-4656	617	4	∪	∪	X
ejpam-4656	617	5	(	(	PUNCT
ejpam-4656	617	6	s	s	NOUN
ejpam-4656	617	7	\n2	\n2	PROPN
ejpam-4656	617	8	g(s))|+	g(s))|+	PROPN
ejpam-4656	617	9	|s|	|s|	PROPN
ejpam-4656	617	10	−	−	PROPN
ejpam-4656	617	11	|s0	|s0	ADJ
ejpam-4656	617	12	∪	∪	X
ejpam-4656	617	13	(	(	PUNCT
ejpam-4656	617	14	s	s	NOUN
ejpam-4656	617	15	\n2	\n2	ADJ
ejpam-4656	617	16	g(s))|	g(s))|	PROPN
ejpam-4656	617	17	=	=	SYM
ejpam-4656	617	18	|s|+	|s|+	PROPN
ejpam-4656	617	19	(	(	PUNCT
ejpam-4656	617	20	m−	m−	PROPN
ejpam-4656	617	21	1)|s0	1)|s0	NUM
ejpam-4656	617	22	∪	∪	X
ejpam-4656	617	23	(	(	PUNCT
ejpam-4656	617	24	s	s	NOUN
ejpam-4656	617	25	\n2	\n2	ADJ
ejpam-4656	617	26	g(s))|	g(s))|	NOUN
ejpam-4656	617	27	.	.	PUNCT
ejpam-4656	618	1	this	this	PRON
ejpam-4656	618	2	proves	prove	VERB
ejpam-4656	618	3	the	the	DET
ejpam-4656	618	4	desired	desire	VERB
ejpam-4656	618	5	equality	equality	NOUN
ejpam-4656	618	6	.	.	PUNCT
ejpam-4656	619	1	it	it	PRON
ejpam-4656	619	2	is	be	AUX
ejpam-4656	619	3	worth	worth	ADJ
ejpam-4656	619	4	mentioning	mention	VERB
ejpam-4656	619	5	that	that	SCONJ
ejpam-4656	619	6	the	the	DET
ejpam-4656	619	7	value	value	NOUN
ejpam-4656	619	8	of	of	ADP
ejpam-4656	619	9	the	the	DET
ejpam-4656	619	10	parameter	parameter	NOUN
ejpam-4656	619	11	given	give	VERB
ejpam-4656	619	12	in	in	ADP
ejpam-4656	619	13	corollary	corollary	ADJ
ejpam-4656	619	14	11	11	NUM
ejpam-4656	619	15	is	be	AUX
ejpam-4656	619	16	not	not	PART
ejpam-4656	619	17	necessarily	necessarily	ADV
ejpam-4656	619	18	attained	attain	VERB
ejpam-4656	619	19	when	when	SCONJ
ejpam-4656	619	20	s	s	PROPN
ejpam-4656	619	21	is	be	AUX
ejpam-4656	619	22	a	a	DET
ejpam-4656	619	23	γconh	γconh	NOUN
ejpam-4656	619	24	-	-	PUNCT
ejpam-4656	619	25	set	set	VERB
ejpam-4656	619	26	in	in	ADP
ejpam-4656	619	27	g.	g.	PROPN
ejpam-4656	619	28	to	to	PART
ejpam-4656	619	29	see	see	VERB
ejpam-4656	619	30	this	this	PRON
ejpam-4656	619	31	,	,	PUNCT
ejpam-4656	619	32	consider	consider	VERB
ejpam-4656	619	33	p5[k3	p5[k3	PRON
ejpam-4656	619	34	]	]	X
ejpam-4656	619	35	.	.	PUNCT
ejpam-4656	620	1	it	it	PRON
ejpam-4656	620	2	is	be	AUX
ejpam-4656	620	3	easily	easily	ADV
ejpam-4656	620	4	verified	verify	VERB
ejpam-4656	620	5	that	that	SCONJ
ejpam-4656	620	6	γconh(p5	γconh(p5	NOUN
ejpam-4656	620	7	)	)	PUNCT
ejpam-4656	620	8	=	=	SYM
ejpam-4656	621	1	2	2	X
ejpam-4656	621	2	.	.	X
ejpam-4656	622	1	if	if	SCONJ
ejpam-4656	622	2	s	s	PROPN
ejpam-4656	622	3	is	be	AUX
ejpam-4656	622	4	γconh	γconh	NOUN
ejpam-4656	622	5	-	-	PUNCT
ejpam-4656	622	6	set	set	VERB
ejpam-4656	622	7	in	in	ADP
ejpam-4656	622	8	p5	p5	NOUN
ejpam-4656	622	9	,	,	PUNCT
ejpam-4656	622	10	then	then	ADV
ejpam-4656	622	11	⟨s⟩	⟨s⟩	PROPN
ejpam-4656	622	12	=	=	SYM
ejpam-4656	622	13	k2	k2	PROPN
ejpam-4656	622	14	and	and	CCONJ
ejpam-4656	622	15	s0∪(s\n2	s0∪(s\n2	ADJ
ejpam-4656	622	16	g(s	g(	NOUN
ejpam-4656	622	17	)	)	PUNCT
ejpam-4656	622	18	)	)	PUNCT
ejpam-4656	623	1	=	=	SYM
ejpam-4656	623	2	s.	s.	PROPN
ejpam-4656	623	3	hence	hence	ADV
ejpam-4656	623	4	,	,	PUNCT
ejpam-4656	623	5	|s|	|s|	PROPN
ejpam-4656	623	6	+	+	CCONJ
ejpam-4656	623	7	(	(	PUNCT
ejpam-4656	623	8	3	3	NUM
ejpam-4656	623	9	−	−	NUM
ejpam-4656	623	10	1)|s0	1)|s0	NUM
ejpam-4656	623	11	∪	∪	X
ejpam-4656	623	12	(	(	PUNCT
ejpam-4656	623	13	s	s	NOUN
ejpam-4656	623	14	\	\	PROPN
ejpam-4656	623	15	n2	n2	ADJ
ejpam-4656	623	16	g(s))|	g(s))|	PROPN
ejpam-4656	623	17	=	=	SYM
ejpam-4656	623	18	6	6	NUM
ejpam-4656	623	19	.	.	PUNCT
ejpam-4656	624	1	however	however	ADV
ejpam-4656	624	2	,	,	PUNCT
ejpam-4656	624	3	by	by	ADP
ejpam-4656	624	4	taking	take	VERB
ejpam-4656	624	5	any	any	DET
ejpam-4656	624	6	three	three	NUM
ejpam-4656	624	7	consecutive	consecutive	ADJ
ejpam-4656	624	8	vertices	vertex	NOUN
ejpam-4656	624	9	of	of	ADP
ejpam-4656	624	10	p5	p5	NOUN
ejpam-4656	624	11	,	,	PUNCT
ejpam-4656	624	12	one	one	PRON
ejpam-4656	624	13	can	can	AUX
ejpam-4656	624	14	see	see	VERB
ejpam-4656	624	15	that	that	DET
ejpam-4656	624	16	γconh(p5[k3	γconh(p5[k3	NOUN
ejpam-4656	624	17	]	]	X
ejpam-4656	624	18	)	)	PUNCT
ejpam-4656	624	19	=	=	SYM
ejpam-4656	625	1	5	5	NUM
ejpam-4656	625	2	.	.	NOUN
ejpam-4656	625	3	4	4	NUM
ejpam-4656	625	4	.	.	X
ejpam-4656	625	5	conclusion	conclusion	VERB
ejpam-4656	625	6	the	the	DET
ejpam-4656	625	7	concept	concept	NOUN
ejpam-4656	625	8	of	of	ADP
ejpam-4656	625	9	convex	convex	PROPN
ejpam-4656	625	10	hop	hop	NOUN
ejpam-4656	625	11	domination	domination	NOUN
ejpam-4656	625	12	has	have	AUX
ejpam-4656	625	13	been	be	AUX
ejpam-4656	625	14	introduced	introduce	VERB
ejpam-4656	625	15	and	and	CCONJ
ejpam-4656	625	16	initially	initially	ADV
ejpam-4656	625	17	investigated	investigate	VERB
ejpam-4656	625	18	in	in	ADP
ejpam-4656	625	19	this	this	DET
ejpam-4656	625	20	study	study	NOUN
ejpam-4656	625	21	.	.	PUNCT
ejpam-4656	626	1	graphs	graph	NOUN
ejpam-4656	626	2	which	which	PRON
ejpam-4656	626	3	attained	attain	VERB
ejpam-4656	626	4	some	some	DET
ejpam-4656	626	5	specific	specific	ADJ
ejpam-4656	626	6	convex	convex	NOUN
ejpam-4656	626	7	hop	hop	NOUN
ejpam-4656	626	8	domination	domination	NOUN
ejpam-4656	626	9	number	number	NOUN
ejpam-4656	626	10	have	have	AUX
ejpam-4656	626	11	been	be	AUX
ejpam-4656	626	12	characterized	characterize	VERB
ejpam-4656	626	13	.	.	PUNCT
ejpam-4656	627	1	the	the	DET
ejpam-4656	627	2	convex	convex	PROPN
ejpam-4656	627	3	hop	hop	NOUN
ejpam-4656	627	4	domination	domination	NOUN
ejpam-4656	627	5	number	number	NOUN
ejpam-4656	627	6	of	of	ADP
ejpam-4656	627	7	the	the	DET
ejpam-4656	627	8	complementary	complementary	ADJ
ejpam-4656	627	9	prism	prism	NOUN
ejpam-4656	627	10	has	have	AUX
ejpam-4656	627	11	been	be	AUX
ejpam-4656	627	12	obtained	obtain	VERB
ejpam-4656	627	13	and	and	CCONJ
ejpam-4656	627	14	necessary	necessary	ADJ
ejpam-4656	627	15	and	and	CCONJ
ejpam-4656	627	16	sufficient	sufficient	ADJ
ejpam-4656	627	17	conditions	condition	NOUN
ejpam-4656	627	18	for	for	ADP
ejpam-4656	627	19	a	a	DET
ejpam-4656	627	20	subset	subset	NOUN
ejpam-4656	627	21	to	to	PART
ejpam-4656	627	22	be	be	AUX
ejpam-4656	627	23	convex	convex	ADJ
ejpam-4656	627	24	hop	hop	NOUN
ejpam-4656	627	25	dominating	dominating	NOUN
ejpam-4656	627	26	in	in	ADP
ejpam-4656	627	27	the	the	DET
ejpam-4656	627	28	shadow	shadow	NOUN
ejpam-4656	627	29	graph	graph	NOUN
ejpam-4656	627	30	,	,	PUNCT
ejpam-4656	627	31	join	join	NOUN
ejpam-4656	627	32	,	,	PUNCT
ejpam-4656	627	33	corona	corona	PROPN
ejpam-4656	627	34	,	,	PUNCT
ejpam-4656	627	35	and	and	CCONJ
ejpam-4656	627	36	lexicographic	lexicographic	ADJ
ejpam-4656	627	37	product	product	NOUN
ejpam-4656	627	38	of	of	ADP
ejpam-4656	627	39	two	two	NUM
ejpam-4656	627	40	graphs	graph	NOUN
ejpam-4656	627	41	have	have	AUX
ejpam-4656	627	42	been	be	AUX
ejpam-4656	627	43	obtained	obtain	VERB
ejpam-4656	627	44	.	.	PUNCT
ejpam-4656	628	1	these	these	DET
ejpam-4656	628	2	characterizations	characterization	NOUN
ejpam-4656	628	3	have	have	AUX
ejpam-4656	628	4	been	be	AUX
ejpam-4656	628	5	used	use	VERB
ejpam-4656	628	6	to	to	PART
ejpam-4656	628	7	obtain	obtain	VERB
ejpam-4656	628	8	bounds	bound	NOUN
ejpam-4656	628	9	or	or	CCONJ
ejpam-4656	628	10	exact	exact	ADJ
ejpam-4656	628	11	value	value	NOUN
ejpam-4656	628	12	of	of	ADP
ejpam-4656	628	13	the	the	DET
ejpam-4656	628	14	convex	convex	NOUN
ejpam-4656	628	15	hop	hop	NOUN
ejpam-4656	628	16	domination	domination	NOUN
ejpam-4656	628	17	number	number	NOUN
ejpam-4656	628	18	of	of	ADP
ejpam-4656	628	19	each	each	PRON
ejpam-4656	628	20	of	of	ADP
ejpam-4656	628	21	these	these	DET
ejpam-4656	628	22	graphs	graph	NOUN
ejpam-4656	628	23	.	.	PUNCT
ejpam-4656	629	1	the	the	DET
ejpam-4656	629	2	concept	concept	NOUN
ejpam-4656	629	3	can	can	AUX
ejpam-4656	629	4	be	be	AUX
ejpam-4656	629	5	studied	study	VERB
ejpam-4656	629	6	for	for	ADP
ejpam-4656	629	7	other	other	ADJ
ejpam-4656	629	8	interesting	interesting	ADJ
ejpam-4656	629	9	graphs	graph	NOUN
ejpam-4656	629	10	.	.	PUNCT
ejpam-4656	630	1	moreover	moreover	ADV
ejpam-4656	630	2	,	,	PUNCT
ejpam-4656	630	3	it	it	PRON
ejpam-4656	630	4	is	be	AUX
ejpam-4656	630	5	conjectured	conjecture	VERB
ejpam-4656	630	6	that	that	SCONJ
ejpam-4656	630	7	the	the	DET
ejpam-4656	630	8	convex	convex	PROPN
ejpam-4656	630	9	hop	hop	NOUN
ejpam-4656	630	10	domination	domination	NOUN
ejpam-4656	630	11	problem	problem	NOUN
ejpam-4656	630	12	is	be	AUX
ejpam-4656	630	13	np	np	ADP
ejpam-4656	630	14	-complete	-complete	ADJ
ejpam-4656	630	15	.	.	PUNCT
ejpam-4656	631	1	acknowledgements	acknowledgement	NOUN
ejpam-4656	631	2	the	the	DET
ejpam-4656	631	3	authors	author	NOUN
ejpam-4656	631	4	would	would	AUX
ejpam-4656	631	5	like	like	VERB
ejpam-4656	631	6	to	to	PART
ejpam-4656	631	7	thank	thank	VERB
ejpam-4656	631	8	the	the	DET
ejpam-4656	631	9	referees	referee	NOUN
ejpam-4656	631	10	for	for	ADP
ejpam-4656	631	11	the	the	DET
ejpam-4656	631	12	invaluable	invaluable	ADJ
ejpam-4656	631	13	assistance	assistance	NOUN
ejpam-4656	631	14	they	they	PRON
ejpam-4656	631	15	gave	give	VERB
ejpam-4656	631	16	us	we	PRON
ejpam-4656	631	17	through	through	ADP
ejpam-4656	631	18	their	their	PRON
ejpam-4656	631	19	comments	comment	NOUN
ejpam-4656	631	20	and	and	CCONJ
ejpam-4656	631	21	suggestions	suggestion	NOUN
ejpam-4656	631	22	which	which	PRON
ejpam-4656	631	23	led	lead	VERB
ejpam-4656	631	24	to	to	ADP
ejpam-4656	631	25	the	the	DET
ejpam-4656	631	26	improvement	improvement	NOUN
ejpam-4656	631	27	of	of	ADP
ejpam-4656	631	28	the	the	DET
ejpam-4656	631	29	paper	paper	NOUN
ejpam-4656	631	30	.	.	PUNCT
ejpam-4656	632	1	the	the	DET
ejpam-4656	632	2	authors	author	NOUN
ejpam-4656	632	3	are	be	AUX
ejpam-4656	632	4	also	also	ADV
ejpam-4656	632	5	grateful	grateful	ADJ
ejpam-4656	632	6	to	to	ADP
ejpam-4656	632	7	the	the	DET
ejpam-4656	632	8	department	department	NOUN
ejpam-4656	632	9	of	of	ADP
ejpam-4656	632	10	science	science	NOUN
ejpam-4656	632	11	and	and	CCONJ
ejpam-4656	632	12	technology	technology	NOUN
ejpam-4656	632	13	accelerated	accelerate	VERB
ejpam-4656	632	14	science	science	NOUN
ejpam-4656	632	15	and	and	CCONJ
ejpam-4656	632	16	technology	technology	NOUN
ejpam-4656	632	17	human	human	ADJ
ejpam-4656	632	18	resource	resource	NOUN
ejpam-4656	632	19	development	development	NOUN
ejpam-4656	632	20	program	program	NOUN
ejpam-4656	632	21	(	(	PUNCT
ejpam-4656	632	22	dost	dost	NOUN
ejpam-4656	632	23	-	-	PUNCT
ejpam-4656	632	24	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4656	632	25	and	and	CCONJ
ejpam-4656	632	26	msu	msu	PROPN
ejpam-4656	632	27	-	-	PUNCT
ejpam-4656	632	28	iligan	iligan	PROPN
ejpam-4656	632	29	institute	institute	PROPN
ejpam-4656	632	30	of	of	ADP
ejpam-4656	632	31	technology	technology	NOUN
ejpam-4656	632	32	for	for	ADP
ejpam-4656	632	33	funding	fund	VERB
ejpam-4656	632	34	this	this	DET
ejpam-4656	632	35	research	research	NOUN
ejpam-4656	632	36	.	.	PUNCT
ejpam-4656	633	1	references	reference	NOUN
ejpam-4656	633	2	[	[	X
ejpam-4656	633	3	1	1	NUM
ejpam-4656	633	4	]	]	PUNCT
ejpam-4656	633	5	s.	s.	PROPN
ejpam-4656	633	6	ayyaswamy	ayyaswamy	PROPN
ejpam-4656	633	7	,	,	PUNCT
ejpam-4656	633	8	b.	b.	PROPN
ejpam-4656	633	9	krishnakumari	krishnakumari	PROPN
ejpam-4656	633	10	,	,	PUNCT
ejpam-4656	633	11	b.	b.	PROPN
ejpam-4656	633	12	natarjan	natarjan	PROPN
ejpam-4656	633	13	,	,	PUNCT
ejpam-4656	633	14	and	and	CCONJ
ejpam-4656	633	15	y.	y.	PROPN
ejpam-4656	633	16	venkatakrishnan	venkatakrishnan	PROPN
ejpam-4656	633	17	.	.	PUNCT
ejpam-4656	634	1	bounds	bound	NOUN
ejpam-4656	634	2	on	on	ADP
ejpam-4656	634	3	the	the	DET
ejpam-4656	634	4	hop	hop	NOUN
ejpam-4656	634	5	domination	domination	NOUN
ejpam-4656	634	6	number	number	NOUN
ejpam-4656	634	7	of	of	ADP
ejpam-4656	634	8	a	a	DET
ejpam-4656	634	9	tree	tree	NOUN
ejpam-4656	634	10	.	.	PUNCT
ejpam-4656	635	1	proceedings	proceeding	NOUN
ejpam-4656	635	2	-	-	PUNCT
ejpam-4656	635	3	mathematical	mathematical	ADJ
ejpam-4656	635	4	sciences	science	NOUN
ejpam-4656	635	5	.	.	PUNCT
ejpam-4656	635	6	,	,	PUNCT
ejpam-4656	635	7	125(4):449–455	125(4):449–455	ADP
ejpam-4656	635	8	,	,	PUNCT
ejpam-4656	635	9	2015	2015	NUM
ejpam-4656	635	10	.	.	PUNCT
ejpam-4656	636	1	references	reference	NOUN
ejpam-4656	636	2	334	334	NUM
ejpam-4656	637	1	[	[	X
ejpam-4656	637	2	2	2	NUM
ejpam-4656	637	3	]	]	PUNCT
ejpam-4656	637	4	s.	s.	PROPN
ejpam-4656	637	5	ayyaswamy	ayyaswamy	PROPN
ejpam-4656	637	6	,	,	PUNCT
ejpam-4656	637	7	c.	c.	PROPN
ejpam-4656	637	8	natarajan	natarajan	PROPN
ejpam-4656	637	9	,	,	PUNCT
ejpam-4656	637	10	and	and	CCONJ
ejpam-4656	637	11	g.	g.	PROPN
ejpam-4656	637	12	sathiamoorphy	sathiamoorphy	PROPN
ejpam-4656	637	13	.	.	PUNCT
ejpam-4656	638	1	a	a	DET
ejpam-4656	638	2	note	note	NOUN
ejpam-4656	638	3	on	on	ADP
ejpam-4656	638	4	hop	hop	NOUN
ejpam-4656	638	5	domination	domination	NOUN
ejpam-4656	638	6	number	number	NOUN
ejpam-4656	638	7	of	of	ADP
ejpam-4656	638	8	some	some	DET
ejpam-4656	638	9	special	special	ADJ
ejpam-4656	638	10	families	family	NOUN
ejpam-4656	638	11	of	of	ADP
ejpam-4656	638	12	graphs	graph	NOUN
ejpam-4656	638	13	.	.	PUNCT
ejpam-4656	639	1	international	international	ADJ
ejpam-4656	639	2	journal	journal	NOUN
ejpam-4656	639	3	of	of	ADP
ejpam-4656	639	4	pure	pure	ADJ
ejpam-4656	639	5	and	and	CCONJ
ejpam-4656	639	6	applied	applied	ADJ
ejpam-4656	639	7	mathematics	mathematic	NOUN
ejpam-4656	639	8	.	.	PUNCT
ejpam-4656	639	9	,	,	PUNCT
ejpam-4656	639	10	119(12):11465–14171	119(12):11465–14171	NUM
ejpam-4656	639	11	,	,	PUNCT
ejpam-4656	639	12	2018	2018	NUM
ejpam-4656	639	13	.	.	PUNCT
ejpam-4656	640	1	[	[	X
ejpam-4656	640	2	3	3	NUM
ejpam-4656	640	3	]	]	X
ejpam-4656	640	4	f.	f.	PROPN
ejpam-4656	640	5	buckley	buckley	PROPN
ejpam-4656	640	6	and	and	CCONJ
ejpam-4656	640	7	f.	f.	PROPN
ejpam-4656	640	8	harary	harary	PROPN
ejpam-4656	640	9	.	.	PUNCT
ejpam-4656	641	1	distance	distance	NOUN
ejpam-4656	641	2	in	in	ADP
ejpam-4656	641	3	graphs	graph	NOUN
ejpam-4656	641	4	.	.	PUNCT
ejpam-4656	642	1	addison	addison	PROPN
ejpam-4656	642	2	-	-	PUNCT
ejpam-4656	642	3	wesley	wesley	PROPN
ejpam-4656	642	4	,	,	PUNCT
ejpam-4656	642	5	redwood	redwood	NOUN
ejpam-4656	642	6	city	city	NOUN
ejpam-4656	642	7	,	,	PUNCT
ejpam-4656	642	8	ca	ca	NOUN
ejpam-4656	642	9	,	,	PUNCT
ejpam-4656	642	10	1990	1990	NUM
ejpam-4656	642	11	.	.	PUNCT
ejpam-4656	643	1	[	[	X
ejpam-4656	643	2	4	4	X
ejpam-4656	643	3	]	]	X
ejpam-4656	643	4	g.	g.	PROPN
ejpam-4656	643	5	chartrand	chartrand	PROPN
ejpam-4656	643	6	,	,	PUNCT
ejpam-4656	643	7	j.	j.	PROPN
ejpam-4656	643	8	fink	fink	PROPN
ejpam-4656	643	9	,	,	PUNCT
ejpam-4656	643	10	and	and	CCONJ
ejpam-4656	643	11	p.	p.	PROPN
ejpam-4656	643	12	zhang	zhang	PROPN
ejpam-4656	643	13	.	.	PUNCT
ejpam-4656	644	1	convexity	convexity	NOUN
ejpam-4656	644	2	in	in	ADP
ejpam-4656	644	3	graphs	graph	NOUN
ejpam-4656	644	4	.	.	PUNCT
ejpam-4656	645	1	discrete	discrete	ADJ
ejpam-4656	645	2	applied	applied	ADJ
ejpam-4656	645	3	mathematics	mathematic	NOUN
ejpam-4656	645	4	,	,	PUNCT
ejpam-4656	645	5	116:115–126	116:115–126	NUM
ejpam-4656	645	6	,	,	PUNCT
ejpam-4656	645	7	2002	2002	NUM
ejpam-4656	645	8	.	.	PUNCT
ejpam-4656	646	1	[	[	X
ejpam-4656	646	2	5	5	X
ejpam-4656	646	3	]	]	PUNCT
ejpam-4656	646	4	t.	t.	PROPN
ejpam-4656	646	5	daniel	daniel	PROPN
ejpam-4656	646	6	and	and	CCONJ
ejpam-4656	646	7	s.	s.	PROPN
ejpam-4656	646	8	canoy	canoy	PROPN
ejpam-4656	646	9	jr	jr	PROPN
ejpam-4656	646	10	.	.	PROPN
ejpam-4656	646	11	clique	clique	PROPN
ejpam-4656	646	12	domination	domination	NOUN
ejpam-4656	646	13	in	in	ADP
ejpam-4656	646	14	a	a	DET
ejpam-4656	646	15	graph	graph	NOUN
ejpam-4656	646	16	.	.	PUNCT
ejpam-4656	647	1	applied	apply	VERB
ejpam-4656	647	2	mathematical	mathematical	ADJ
ejpam-4656	647	3	sciences	science	NOUN
ejpam-4656	647	4	,	,	PUNCT
ejpam-4656	647	5	9(116):5749–5755	9(116):5749–5755	NUM
ejpam-4656	647	6	,	,	PUNCT
ejpam-4656	647	7	2015	2015	NUM
ejpam-4656	647	8	.	.	PUNCT
ejpam-4656	648	1	[	[	X
ejpam-4656	648	2	6	6	NUM
ejpam-4656	648	3	]	]	PUNCT
ejpam-4656	648	4	f.	f.	PROPN
ejpam-4656	648	5	harary	harary	PROPN
ejpam-4656	648	6	and	and	CCONJ
ejpam-4656	648	7	j.	j.	PROPN
ejpam-4656	648	8	nieminen	nieminen	PROPN
ejpam-4656	648	9	.	.	PUNCT
ejpam-4656	649	1	convexity	convexity	NOUN
ejpam-4656	649	2	in	in	ADP
ejpam-4656	649	3	graphs	graph	NOUN
ejpam-4656	649	4	.	.	PUNCT
ejpam-4656	650	1	j.	j.	PROPN
ejpam-4656	650	2	differential	differential	PROPN
ejpam-4656	650	3	geom	geom	PROPN
ejpam-4656	650	4	.	.	PROPN
ejpam-4656	650	5	,	,	PUNCT
ejpam-4656	650	6	16:185–190	16:185–190	NUM
ejpam-4656	650	7	,	,	PUNCT
ejpam-4656	650	8	1981	1981	NUM
ejpam-4656	650	9	.	.	PUNCT
ejpam-4656	651	1	[	[	X
ejpam-4656	651	2	7	7	X
ejpam-4656	651	3	]	]	PUNCT
ejpam-4656	651	4	j.	j.	PROPN
ejpam-4656	651	5	hassan	hassan	PROPN
ejpam-4656	651	6	and	and	CCONJ
ejpam-4656	651	7	s.	s.	PROPN
ejpam-4656	651	8	canoy	canoy	PROPN
ejpam-4656	651	9	jr	jr	PROPN
ejpam-4656	651	10	.	.	PROPN
ejpam-4656	651	11	hop	hop	PROPN
ejpam-4656	651	12	independent	independent	ADJ
ejpam-4656	651	13	hop	hop	NOUN
ejpam-4656	651	14	domination	domination	NOUN
ejpam-4656	651	15	in	in	ADP
ejpam-4656	651	16	graphs	graph	NOUN
ejpam-4656	651	17	.	.	PUNCT
ejpam-4656	652	1	eur	eur	PROPN
ejpam-4656	652	2	.	.	PUNCT
ejpam-4656	653	1	j.	j.	PROPN
ejpam-4656	653	2	pure	pure	PROPN
ejpam-4656	653	3	appl	appl	PROPN
ejpam-4656	653	4	.	.	PUNCT
ejpam-4656	653	5	math	math	PROPN
ejpam-4656	653	6	.	.	PUNCT
ejpam-4656	653	7	,	,	PUNCT
ejpam-4656	653	8	15(4):1783–1796	15(4):1783–1796	NUM
ejpam-4656	653	9	,	,	PUNCT
ejpam-4656	653	10	2022	2022	NUM
ejpam-4656	653	11	.	.	PUNCT
ejpam-4656	654	1	[	[	X
ejpam-4656	654	2	8	8	X
ejpam-4656	654	3	]	]	X
ejpam-4656	654	4	j.	j.	PROPN
ejpam-4656	654	5	hassan	hassan	PROPN
ejpam-4656	654	6	,	,	PUNCT
ejpam-4656	654	7	s.	s.	PROPN
ejpam-4656	654	8	canoy	canoy	PROPN
ejpam-4656	654	9	jr	jr	PROPN
ejpam-4656	654	10	.	.	PROPN
ejpam-4656	654	11	,	,	PUNCT
ejpam-4656	654	12	and	and	CCONJ
ejpam-4656	654	13	a.	a.	PROPN
ejpam-4656	654	14	aradais	aradais	PROPN
ejpam-4656	654	15	.	.	PUNCT
ejpam-4656	655	1	hop	hop	PROPN
ejpam-4656	655	2	independent	independent	ADJ
ejpam-4656	655	3	sets	set	NOUN
ejpam-4656	655	4	in	in	ADP
ejpam-4656	655	5	graphs	graph	NOUN
ejpam-4656	655	6	.	.	PUNCT
ejpam-4656	656	1	eur	eur	PROPN
ejpam-4656	656	2	.	.	PUNCT
ejpam-4656	657	1	j.	j.	PROPN
ejpam-4656	657	2	pure	pure	PROPN
ejpam-4656	657	3	appl	appl	PROPN
ejpam-4656	657	4	.	.	PUNCT
ejpam-4656	657	5	math	math	PROPN
ejpam-4656	657	6	.	.	PUNCT
ejpam-4656	657	7	,	,	PUNCT
ejpam-4656	657	8	15(2):467–477	15(2):467–477	PROPN
ejpam-4656	657	9	,	,	PUNCT
ejpam-4656	657	10	2022	2022	NUM
ejpam-4656	657	11	.	.	PUNCT
ejpam-4656	658	1	[	[	X
ejpam-4656	658	2	9	9	NUM
ejpam-4656	658	3	]	]	X
ejpam-4656	658	4	m.	m.	NOUN
ejpam-4656	658	5	henning	henning	PROPN
ejpam-4656	658	6	and	and	CCONJ
ejpam-4656	658	7	n.	n.	PROPN
ejpam-4656	658	8	rad	rad	PROPN
ejpam-4656	658	9	.	.	PROPN
ejpam-4656	659	1	on	on	ADP
ejpam-4656	659	2	2	2	NUM
ejpam-4656	659	3	-	-	PUNCT
ejpam-4656	659	4	step	step	NOUN
ejpam-4656	659	5	and	and	CCONJ
ejpam-4656	659	6	hop	hop	NOUN
ejpam-4656	659	7	dominating	dominating	NOUN
ejpam-4656	659	8	sets	set	NOUN
ejpam-4656	659	9	in	in	ADP
ejpam-4656	659	10	graphs	graph	NOUN
ejpam-4656	659	11	.	.	PUNCT
ejpam-4656	660	1	graphs	graph	NOUN
ejpam-4656	660	2	and	and	CCONJ
ejpam-4656	660	3	combinatorics	combinatoric	NOUN
ejpam-4656	660	4	.	.	PUNCT
ejpam-4656	660	5	,	,	PUNCT
ejpam-4656	660	6	33(4):913–927	33(4):913–927	PROPN
ejpam-4656	660	7	,	,	PUNCT
ejpam-4656	660	8	2017	2017	NUM
ejpam-4656	660	9	.	.	PUNCT
ejpam-4656	661	1	[	[	X
ejpam-4656	661	2	10	10	NUM
ejpam-4656	661	3	]	]	X
ejpam-4656	661	4	s.	s.	PROPN
ejpam-4656	661	5	canoy	canoy	PROPN
ejpam-4656	661	6	jr	jr	PROPN
ejpam-4656	661	7	.	.	PUNCT
ejpam-4656	662	1	a	a	DET
ejpam-4656	662	2	short	short	ADJ
ejpam-4656	662	3	note	note	NOUN
ejpam-4656	662	4	on	on	ADP
ejpam-4656	662	5	convexity	convexity	NOUN
ejpam-4656	662	6	and	and	CCONJ
ejpam-4656	662	7	convex	convex	NOUN
ejpam-4656	662	8	domination	domination	NOUN
ejpam-4656	662	9	in	in	ADP
ejpam-4656	662	10	g[k	g[k	NOUN
ejpam-4656	662	11	m	m	PRON
ejpam-4656	662	12	]	]	PUNCT
ejpam-4656	662	13	.	.	PUNCT
ejpam-4656	663	1	applied	apply	VERB
ejpam-4656	663	2	mathematical	mathematical	ADJ
ejpam-4656	663	3	sciences	science	NOUN
ejpam-4656	663	4	,	,	PUNCT
ejpam-4656	663	5	8(115):5737–5741	8(115):5737–5741	NUM
ejpam-4656	663	6	,	,	PUNCT
ejpam-4656	663	7	2014	2014	NUM
ejpam-4656	663	8	.	.	PUNCT
ejpam-4656	664	1	[	[	X
ejpam-4656	664	2	11	11	NUM
ejpam-4656	664	3	]	]	X
ejpam-4656	664	4	s.	s.	PROPN
ejpam-4656	664	5	canoy	canoy	PROPN
ejpam-4656	664	6	jr	jr	PROPN
ejpam-4656	664	7	.	.	PROPN
ejpam-4656	664	8	,	,	PUNCT
ejpam-4656	664	9	g.	g.	PROPN
ejpam-4656	664	10	cagaanan	cagaanan	PROPN
ejpam-4656	664	11	,	,	PUNCT
ejpam-4656	664	12	and	and	CCONJ
ejpam-4656	664	13	s.	s.	PROPN
ejpam-4656	664	14	gervacio	gervacio	PROPN
ejpam-4656	664	15	.	.	PUNCT
ejpam-4656	665	1	convexity	convexity	PROPN
ejpam-4656	665	2	,	,	PUNCT
ejpam-4656	665	3	geodetic	geodetic	ADJ
ejpam-4656	665	4	,	,	PUNCT
ejpam-4656	665	5	and	and	CCONJ
ejpam-4656	665	6	hull	hull	NOUN
ejpam-4656	665	7	numbers	number	NOUN
ejpam-4656	665	8	of	of	ADP
ejpam-4656	665	9	the	the	DET
ejpam-4656	665	10	join	join	NOUN
ejpam-4656	665	11	of	of	ADP
ejpam-4656	665	12	graphs	graph	NOUN
ejpam-4656	665	13	.	.	PUNCT
ejpam-4656	666	1	utilitas	utilitas	PROPN
ejpam-4656	666	2	mathematica	mathematica	PROPN
ejpam-4656	666	3	,	,	PUNCT
ejpam-4656	666	4	71:143–159	71:143–159	PROPN
ejpam-4656	666	5	,	,	PUNCT
ejpam-4656	666	6	2006	2006	NUM
ejpam-4656	666	7	.	.	PUNCT
ejpam-4656	667	1	[	[	X
ejpam-4656	667	2	12	12	NUM
ejpam-4656	667	3	]	]	X
ejpam-4656	667	4	s.	s.	PROPN
ejpam-4656	667	5	canoy	canoy	PROPN
ejpam-4656	667	6	jr	jr	PROPN
ejpam-4656	667	7	.	.	PROPN
ejpam-4656	667	8	and	and	CCONJ
ejpam-4656	667	9	i.j.l	i.j.l	PROPN
ejpam-4656	667	10	.	.	PROPN
ejpam-4656	667	11	garces	garces	PROPN
ejpam-4656	667	12	.	.	PUNCT
ejpam-4656	668	1	convex	convex	PROPN
ejpam-4656	668	2	sets	set	NOUN
ejpam-4656	668	3	under	under	ADP
ejpam-4656	668	4	some	some	DET
ejpam-4656	668	5	graph	graph	NOUN
ejpam-4656	668	6	operations	operation	NOUN
ejpam-4656	668	7	.	.	PUNCT
ejpam-4656	669	1	graphs	graph	NOUN
ejpam-4656	669	2	and	and	CCONJ
ejpam-4656	669	3	combinatorics	combinatoric	NOUN
ejpam-4656	669	4	,	,	PUNCT
ejpam-4656	669	5	18:787–793	18:787–793	PROPN
ejpam-4656	669	6	,	,	PUNCT
ejpam-4656	669	7	2002	2002	NUM
ejpam-4656	669	8	.	.	PUNCT
ejpam-4656	670	1	[	[	X
ejpam-4656	670	2	13	13	NUM
ejpam-4656	670	3	]	]	PUNCT
ejpam-4656	670	4	s.	s.	PROPN
ejpam-4656	670	5	canoy	canoy	PROPN
ejpam-4656	670	6	jr	jr	PROPN
ejpam-4656	670	7	.	.	PROPN
ejpam-4656	670	8	,	,	PUNCT
ejpam-4656	670	9	r.	r.	PROPN
ejpam-4656	670	10	mollejon	mollejon	NOUN
ejpam-4656	670	11	,	,	PUNCT
ejpam-4656	670	12	and	and	CCONJ
ejpam-4656	670	13	j.	j.	PROPN
ejpam-4656	670	14	g.	g.	PROPN
ejpam-4656	670	15	canoy	canoy	PROPN
ejpam-4656	670	16	.	.	PUNCT
ejpam-4656	671	1	hop	hop	PROPN
ejpam-4656	671	2	dominating	dominating	NOUN
ejpam-4656	671	3	sets	set	NOUN
ejpam-4656	671	4	in	in	ADP
ejpam-4656	671	5	graphs	graph	NOUN
ejpam-4656	671	6	under	under	ADP
ejpam-4656	671	7	binary	binary	ADJ
ejpam-4656	671	8	operations	operation	NOUN
ejpam-4656	671	9	.	.	PUNCT
ejpam-4656	672	1	eur	eur	PROPN
ejpam-4656	672	2	.	.	PUNCT
ejpam-4656	673	1	j.	j.	PROPN
ejpam-4656	673	2	pure	pure	PROPN
ejpam-4656	673	3	appl	appl	PROPN
ejpam-4656	673	4	.	.	PUNCT
ejpam-4656	673	5	math	math	PROPN
ejpam-4656	673	6	.	.	PUNCT
ejpam-4656	673	7	,	,	PUNCT
ejpam-4656	674	1	12(4):1455–1463	12(4):1455–1463	NUM
ejpam-4656	674	2	,	,	PUNCT
ejpam-4656	674	3	2019	2019	NUM
ejpam-4656	674	4	.	.	PUNCT
ejpam-4656	675	1	[	[	X
ejpam-4656	675	2	14	14	NUM
ejpam-4656	675	3	]	]	X
ejpam-4656	675	4	s.	s.	PROPN
ejpam-4656	675	5	canoy	canoy	PROPN
ejpam-4656	675	6	jr	jr	PROPN
ejpam-4656	675	7	.	.	PROPN
ejpam-4656	675	8	and	and	CCONJ
ejpam-4656	675	9	g.	g.	PROPN
ejpam-4656	675	10	salasalan	salasalan	NOUN
ejpam-4656	675	11	.	.	PUNCT
ejpam-4656	676	1	revisiting	revisit	VERB
ejpam-4656	676	2	domination	domination	NOUN
ejpam-4656	676	3	,	,	PUNCT
ejpam-4656	676	4	hop	hop	NOUN
ejpam-4656	676	5	domination	domination	NOUN
ejpam-4656	676	6	,	,	PUNCT
ejpam-4656	676	7	and	and	CCONJ
ejpam-4656	676	8	global	global	ADJ
ejpam-4656	676	9	hop	hop	NOUN
ejpam-4656	676	10	domination	domination	NOUN
ejpam-4656	676	11	in	in	ADP
ejpam-4656	676	12	graphs	graph	NOUN
ejpam-4656	676	13	.	.	PUNCT
ejpam-4656	677	1	eur	eur	PROPN
ejpam-4656	677	2	.	.	PUNCT
ejpam-4656	678	1	j.	j.	PROPN
ejpam-4656	678	2	pure	pure	PROPN
ejpam-4656	678	3	appl	appl	PROPN
ejpam-4656	678	4	.	.	PUNCT
ejpam-4656	678	5	math	math	PROPN
ejpam-4656	678	6	.	.	PUNCT
ejpam-4656	678	7	,	,	PUNCT
ejpam-4656	678	8	14:1415–1428	14:1415–1428	NUM
ejpam-4656	678	9	,	,	PUNCT
ejpam-4656	678	10	2021	2021	NUM
ejpam-4656	678	11	.	.	PUNCT
ejpam-4656	679	1	[	[	X
ejpam-4656	679	2	15	15	NUM
ejpam-4656	679	3	]	]	X
ejpam-4656	679	4	s.	s.	PROPN
ejpam-4656	679	5	canoy	canoy	PROPN
ejpam-4656	679	6	jr	jr	PROPN
ejpam-4656	679	7	.	.	PROPN
ejpam-4656	679	8	and	and	CCONJ
ejpam-4656	679	9	g.	g.	PROPN
ejpam-4656	679	10	salasalan	salasalan	NOUN
ejpam-4656	679	11	.	.	PUNCT
ejpam-4656	680	1	locating	locate	VERB
ejpam-4656	680	2	-	-	PUNCT
ejpam-4656	680	3	hop	hop	NOUN
ejpam-4656	680	4	domination	domination	NOUN
ejpam-4656	680	5	in	in	ADP
ejpam-4656	680	6	graphs	graph	NOUN
ejpam-4656	680	7	.	.	PUNCT
ejpam-4656	681	1	kyungpook	kyungpook	PROPN
ejpam-4656	681	2	mathematical	mathematical	PROPN
ejpam-4656	681	3	journal	journal	PROPN
ejpam-4656	681	4	.	.	PUNCT
ejpam-4656	681	5	,	,	PUNCT
ejpam-4656	681	6	62:193–204	62:193–204	NUM
ejpam-4656	681	7	,	,	PUNCT
ejpam-4656	681	8	2022	2022	NUM
ejpam-4656	681	9	.	.	PUNCT
ejpam-4656	682	1	[	[	X
ejpam-4656	682	2	16	16	NUM
ejpam-4656	682	3	]	]	PUNCT
ejpam-4656	682	4	m.	m.	NOUN
ejpam-4656	682	5	labendia	labendia	PROPN
ejpam-4656	682	6	and	and	CCONJ
ejpam-4656	682	7	s.	s.	PROPN
ejpam-4656	682	8	canoy	canoy	PROPN
ejpam-4656	682	9	jr	jr	PROPN
ejpam-4656	682	10	.	.	PROPN
ejpam-4656	682	11	convex	convex	PROPN
ejpam-4656	682	12	domination	domination	NOUN
ejpam-4656	682	13	in	in	ADP
ejpam-4656	682	14	the	the	DET
ejpam-4656	682	15	composition	composition	NOUN
ejpam-4656	682	16	and	and	CCONJ
ejpam-4656	682	17	cartesian	cartesian	ADJ
ejpam-4656	682	18	product	product	NOUN
ejpam-4656	682	19	of	of	ADP
ejpam-4656	682	20	graphs	graph	NOUN
ejpam-4656	682	21	.	.	PUNCT
ejpam-4656	683	1	czechoslovak	czechoslovak	ADJ
ejpam-4656	683	2	mathematical	mathematical	PROPN
ejpam-4656	683	3	journal	journal	NOUN
ejpam-4656	683	4	,	,	PUNCT
ejpam-4656	683	5	62(4):1003–1009	62(4):1003–1009	NUM
ejpam-4656	683	6	,	,	PUNCT
ejpam-4656	683	7	2012	2012	NUM
ejpam-4656	683	8	.	.	PUNCT
ejpam-4656	684	1	[	[	X
ejpam-4656	684	2	17	17	NUM
ejpam-4656	684	3	]	]	PUNCT
ejpam-4656	684	4	m.	m.	NOUN
ejpam-4656	684	5	lemanska	lemanska	PROPN
ejpam-4656	684	6	.	.	PUNCT
ejpam-4656	685	1	weakly	weakly	ADJ
ejpam-4656	685	2	convex	convex	NOUN
ejpam-4656	685	3	and	and	CCONJ
ejpam-4656	685	4	convex	convex	ADJ
ejpam-4656	685	5	domination	domination	NOUN
ejpam-4656	685	6	numbers	number	NOUN
ejpam-4656	685	7	.	.	PUNCT
ejpam-4656	686	1	opusc	opusc	PROPN
ejpam-4656	686	2	.	.	PUNCT
ejpam-4656	686	3	math	math	NOUN
ejpam-4656	686	4	.	.	PUNCT
ejpam-4656	686	5	,	,	PUNCT
ejpam-4656	686	6	24:181	24:181	NUM
ejpam-4656	686	7	–	–	PUNCT
ejpam-4656	686	8	188	188	NUM
ejpam-4656	686	9	,	,	PUNCT
ejpam-4656	686	10	2004	2004	NUM
ejpam-4656	686	11	.	.	PUNCT
ejpam-4656	687	1	references	reference	NOUN
ejpam-4656	687	2	335	335	NUM
ejpam-4656	687	3	[	[	X
ejpam-4656	687	4	18	18	NUM
ejpam-4656	687	5	]	]	X
ejpam-4656	687	6	c.	c.	PROPN
ejpam-4656	687	7	natarajan	natarajan	PROPN
ejpam-4656	687	8	and	and	CCONJ
ejpam-4656	687	9	s.	s.	PROPN
ejpam-4656	687	10	ayyaswamy	ayyaswamy	PROPN
ejpam-4656	687	11	.	.	PUNCT
ejpam-4656	688	1	hop	hop	PROPN
ejpam-4656	688	2	domination	domination	NOUN
ejpam-4656	688	3	in	in	ADP
ejpam-4656	688	4	graphs	graphs	PROPN
ejpam-4656	688	5	ii	ii	PROPN
ejpam-4656	688	6	.	.	PUNCT
ejpam-4656	688	7	versita	versita	PROPN
ejpam-4656	688	8	,	,	PUNCT
ejpam-4656	688	9	23(2):187	23(2):187	NUM
ejpam-4656	688	10	–	–	PUNCT
ejpam-4656	688	11	199	199	NUM
ejpam-4656	688	12	,	,	PUNCT
ejpam-4656	688	13	2015	2015	NUM
ejpam-4656	688	14	.	.	PUNCT
ejpam-4656	689	1	[	[	X
ejpam-4656	689	2	19	19	NUM
ejpam-4656	689	3	]	]	X
ejpam-4656	689	4	y.	y.	PROPN
ejpam-4656	689	5	pabilona	pabilona	PROPN
ejpam-4656	689	6	and	and	CCONJ
ejpam-4656	689	7	h.	h.	PROPN
ejpam-4656	689	8	rara	rara	PROPN
ejpam-4656	689	9	.	.	PUNCT
ejpam-4656	690	1	connected	connect	VERB
ejpam-4656	690	2	hop	hop	NOUN
ejpam-4656	690	3	domination	domination	NOUN
ejpam-4656	690	4	in	in	ADP
ejpam-4656	690	5	graphs	graph	NOUN
ejpam-4656	690	6	under	under	ADP
ejpam-4656	690	7	some	some	DET
ejpam-4656	690	8	binary	binary	ADJ
ejpam-4656	690	9	operations	operation	NOUN
ejpam-4656	690	10	.	.	PUNCT
ejpam-4656	691	1	asian	asian	ADJ
ejpam-4656	691	2	-	-	PUNCT
ejpam-4656	691	3	eur	eur	NOUN
ejpam-4656	691	4	.	.	PUNCT
ejpam-4656	692	1	j.	j.	PROPN
ejpam-4656	692	2	math	math	PROPN
ejpam-4656	692	3	.	.	PROPN
ejpam-4656	692	4	,	,	PUNCT
ejpam-4656	692	5	11(5):1850075–1–1850075–11	11(5):1850075–1–1850075–11	NUM
ejpam-4656	692	6	,	,	PUNCT
ejpam-4656	692	7	2018	2018	NUM
ejpam-4656	692	8	.	.	PUNCT
ejpam-4656	693	1	[	[	X
ejpam-4656	693	2	20	20	NUM
ejpam-4656	693	3	]	]	PUNCT
ejpam-4656	693	4	r.	r.	PROPN
ejpam-4656	693	5	rakim	rakim	PROPN
ejpam-4656	693	6	,	,	PUNCT
ejpam-4656	693	7	h.	h.	PROPN
ejpam-4656	693	8	rara	rara	PROPN
ejpam-4656	693	9	,	,	PUNCT
ejpam-4656	693	10	and	and	CCONJ
ejpam-4656	693	11	c.j	c.j	PROPN
ejpam-4656	693	12	.	.	PROPN
ejpam-4656	693	13	saromines	saromine	NOUN
ejpam-4656	693	14	.	.	PUNCT
ejpam-4656	694	1	perfect	perfect	ADJ
ejpam-4656	694	2	hop	hop	NOUN
ejpam-4656	694	3	domination	domination	NOUN
ejpam-4656	694	4	in	in	ADP
ejpam-4656	694	5	graphs	graph	NOUN
ejpam-4656	694	6	.	.	PUNCT
ejpam-4656	695	1	applied	apply	VERB
ejpam-4656	695	2	mathematical	mathematical	ADJ
ejpam-4656	695	3	sciences	sciences	PROPN
ejpam-4656	695	4	,	,	PUNCT
ejpam-4656	695	5	12(13):635–649	12(13):635–649	NUM
ejpam-4656	695	6	,	,	PUNCT
ejpam-4656	695	7	2018	2018	NUM
ejpam-4656	695	8	.	.	PUNCT
ejpam-4656	696	1	[	[	X
ejpam-4656	696	2	21	21	NUM
ejpam-4656	696	3	]	]	X
ejpam-4656	696	4	g.	g.	PROPN
ejpam-4656	696	5	salasalan	salasalan	NOUN
ejpam-4656	696	6	and	and	CCONJ
ejpam-4656	696	7	s.	s.	PROPN
ejpam-4656	696	8	canoy	canoy	PROPN
ejpam-4656	696	9	jr	jr	PROPN
ejpam-4656	696	10	.	.	PROPN
ejpam-4656	696	11	global	global	PROPN
ejpam-4656	696	12	hop	hop	PROPN
ejpam-4656	696	13	domination	domination	PROPN
ejpam-4656	696	14	numbers	number	NOUN
ejpam-4656	696	15	of	of	ADP
ejpam-4656	696	16	graphs	graph	NOUN
ejpam-4656	696	17	.	.	PUNCT
ejpam-4656	697	1	eur	eur	PROPN
ejpam-4656	697	2	.	.	PUNCT
ejpam-4656	698	1	j.	j.	PROPN
ejpam-4656	698	2	pure	pure	PROPN
ejpam-4656	698	3	appl	appl	PROPN
ejpam-4656	698	4	.	.	PUNCT
ejpam-4656	698	5	math	math	PROPN
ejpam-4656	698	6	.	.	PUNCT
ejpam-4656	698	7	,	,	PUNCT
ejpam-4656	698	8	14(1):112–125	14(1):112–125	NUM
ejpam-4656	698	9	,	,	PUNCT
ejpam-4656	698	10	2021	2021	NUM
ejpam-4656	698	11	.	.	PUNCT