id	sid	tid	token	lemma	pos
ejpam-4828	1	1	european	european	PROPN
ejpam-4828	1	2	journal	journal	PROPN
ejpam-4828	1	3	of	of	ADP
ejpam-4828	1	4	pure	pure	ADJ
ejpam-4828	1	5	and	and	CCONJ
ejpam-4828	1	6	applied	apply	VERB
ejpam-4828	1	7	mathematics	mathematic	NOUN
ejpam-4828	1	8	vol	vol	NOUN
ejpam-4828	1	9	.	.	PUNCT
ejpam-4828	2	1	16	16	NUM
ejpam-4828	2	2	,	,	PUNCT
ejpam-4828	2	3	no	no	INTJ
ejpam-4828	2	4	.	.	NOUN
ejpam-4828	2	5	3	3	NUM
ejpam-4828	2	6	,	,	PUNCT
ejpam-4828	2	7	2023	2023	NUM
ejpam-4828	2	8	,	,	PUNCT
ejpam-4828	2	9	1705	1705	NUM
ejpam-4828	2	10	-	-	SYM
ejpam-4828	2	11	1716	1716	NUM
ejpam-4828	2	12	issn	issn	VERB
ejpam-4828	2	13	1307	1307	NUM
ejpam-4828	2	14	-	-	SYM
ejpam-4828	2	15	5543	5543	NUM
ejpam-4828	2	16	–	–	PUNCT
ejpam-4828	2	17	ejpam.com	ejpam.com	X
ejpam-4828	2	18	published	publish	VERB
ejpam-4828	2	19	by	by	ADP
ejpam-4828	2	20	new	new	PROPN
ejpam-4828	2	21	york	york	PROPN
ejpam-4828	2	22	business	business	PROPN
ejpam-4828	2	23	global	global	ADJ
ejpam-4828	2	24	convex	convex	PROPN
ejpam-4828	2	25	roman	roman	ADJ
ejpam-4828	2	26	dominating	dominating	NOUN
ejpam-4828	2	27	functions	function	NOUN
ejpam-4828	2	28	in	in	ADP
ejpam-4828	2	29	a	a	DET
ejpam-4828	2	30	graph	graph	NOUN
ejpam-4828	2	31	rona	rona	PROPN
ejpam-4828	2	32	jane	jane	PROPN
ejpam-4828	2	33	g.	g.	PROPN
ejpam-4828	2	34	fortosa1,∗	fortosa1,∗	PROPN
ejpam-4828	2	35	,	,	PUNCT
ejpam-4828	2	36	sergio	sergio	PROPN
ejpam-4828	2	37	r.	r.	PROPN
ejpam-4828	2	38	canoy	canoy	PROPN
ejpam-4828	2	39	,	,	PUNCT
ejpam-4828	2	40	jr.1,2	jr.1,2	ADJ
ejpam-4828	2	41	1	1	NUM
ejpam-4828	2	42	department	department	NOUN
ejpam-4828	2	43	of	of	ADP
ejpam-4828	2	44	mathematics	mathematic	NOUN
ejpam-4828	2	45	and	and	CCONJ
ejpam-4828	2	46	statistics	statistic	NOUN
ejpam-4828	2	47	,	,	PUNCT
ejpam-4828	2	48	college	college	NOUN
ejpam-4828	2	49	of	of	ADP
ejpam-4828	2	50	science	science	NOUN
ejpam-4828	2	51	and	and	CCONJ
ejpam-4828	2	52	mathematics	mathematic	NOUN
ejpam-4828	2	53	,	,	PUNCT
ejpam-4828	2	54	msuiligan	msuiligan	PROPN
ejpam-4828	2	55	institute	institute	PROPN
ejpam-4828	2	56	of	of	ADP
ejpam-4828	2	57	technology	technology	PROPN
ejpam-4828	2	58	,	,	PUNCT
ejpam-4828	2	59	9200	9200	NUM
ejpam-4828	2	60	iligan	iligan	ADJ
ejpam-4828	2	61	city	city	NOUN
ejpam-4828	2	62	,	,	PUNCT
ejpam-4828	2	63	philippines	philippine	NOUN
ejpam-4828	2	64	1	1	NUM
ejpam-4828	2	65	center	center	NOUN
ejpam-4828	2	66	for	for	ADP
ejpam-4828	2	67	mathematical	mathematical	ADJ
ejpam-4828	2	68	and	and	CCONJ
ejpam-4828	2	69	theoretical	theoretical	ADJ
ejpam-4828	2	70	physical	physical	ADJ
ejpam-4828	2	71	sciences	science	NOUN
ejpam-4828	2	72	prism	prism	NOUN
ejpam-4828	2	73	,	,	PUNCT
ejpam-4828	2	74	msu	msu	PROPN
ejpam-4828	2	75	-	-	PUNCT
ejpam-4828	2	76	iligan	iligan	PROPN
ejpam-4828	2	77	institute	institute	PROPN
ejpam-4828	2	78	of	of	ADP
ejpam-4828	2	79	technology	technology	PROPN
ejpam-4828	2	80	,	,	PUNCT
ejpam-4828	2	81	9200	9200	NUM
ejpam-4828	2	82	iligan	iligan	ADJ
ejpam-4828	2	83	city	city	NOUN
ejpam-4828	2	84	,	,	PUNCT
ejpam-4828	2	85	philippines	philippine	NOUN
ejpam-4828	2	86	abstract	abstract	ADJ
ejpam-4828	2	87	.	.	PUNCT
ejpam-4828	3	1	let	let	VERB
ejpam-4828	3	2	g	g	PRON
ejpam-4828	3	3	be	be	AUX
ejpam-4828	3	4	a	a	DET
ejpam-4828	3	5	connected	connected	ADJ
ejpam-4828	3	6	graph	graph	NOUN
ejpam-4828	3	7	.	.	PUNCT
ejpam-4828	4	1	a	a	DET
ejpam-4828	4	2	function	function	NOUN
ejpam-4828	4	3	f	f	NOUN
ejpam-4828	4	4	:	:	PUNCT
ejpam-4828	4	5	v	v	X
ejpam-4828	4	6	(	(	PUNCT
ejpam-4828	4	7	g	g	NOUN
ejpam-4828	4	8	)	)	PUNCT
ejpam-4828	4	9	→	→	SYM
ejpam-4828	4	10	{	{	PUNCT
ejpam-4828	4	11	0	0	NUM
ejpam-4828	4	12	,	,	PUNCT
ejpam-4828	4	13	1	1	NUM
ejpam-4828	4	14	,	,	PUNCT
ejpam-4828	4	15	2	2	NUM
ejpam-4828	4	16	}	}	PUNCT
ejpam-4828	4	17	is	be	AUX
ejpam-4828	4	18	a	a	DET
ejpam-4828	4	19	convex	convex	ADJ
ejpam-4828	4	20	roman	roman	ADJ
ejpam-4828	4	21	dominating	dominating	NOUN
ejpam-4828	4	22	function	function	NOUN
ejpam-4828	4	23	(	(	PUNCT
ejpam-4828	4	24	or	or	CCONJ
ejpam-4828	4	25	cvrdf	cvrdf	NOUN
ejpam-4828	4	26	)	)	PUNCT
ejpam-4828	4	27	if	if	SCONJ
ejpam-4828	4	28	every	every	DET
ejpam-4828	4	29	vertex	vertex	NOUN
ejpam-4828	4	30	u	u	NOUN
ejpam-4828	4	31	for	for	ADP
ejpam-4828	4	32	which	which	PRON
ejpam-4828	4	33	f(u	f(u	PROPN
ejpam-4828	4	34	)	)	PUNCT
ejpam-4828	5	1	=	=	SYM
ejpam-4828	5	2	0	0	NUM
ejpam-4828	5	3	is	be	AUX
ejpam-4828	5	4	adjacent	adjacent	ADJ
ejpam-4828	5	5	to	to	ADP
ejpam-4828	5	6	at	at	ADV
ejpam-4828	5	7	least	least	ADV
ejpam-4828	5	8	one	one	NUM
ejpam-4828	5	9	vertex	vertex	NOUN
ejpam-4828	5	10	v	v	NOUN
ejpam-4828	5	11	for	for	ADP
ejpam-4828	5	12	which	which	PRON
ejpam-4828	5	13	f(v	f(v	NOUN
ejpam-4828	5	14	)	)	PUNCT
ejpam-4828	5	15	=	=	SYM
ejpam-4828	5	16	2	2	NUM
ejpam-4828	5	17	and	and	CCONJ
ejpam-4828	5	18	v1	v1	VERB
ejpam-4828	5	19	∪	∪	NOUN
ejpam-4828	5	20	v2	v2	NOUN
ejpam-4828	5	21	is	be	AUX
ejpam-4828	5	22	convex	convex	NOUN
ejpam-4828	5	23	.	.	PUNCT
ejpam-4828	6	1	the	the	DET
ejpam-4828	6	2	weight	weight	NOUN
ejpam-4828	6	3	of	of	ADP
ejpam-4828	6	4	a	a	DET
ejpam-4828	6	5	convex	convex	ADJ
ejpam-4828	6	6	roman	roman	ADJ
ejpam-4828	6	7	dominating	dominating	NOUN
ejpam-4828	6	8	function	function	NOUN
ejpam-4828	6	9	f	f	PROPN
ejpam-4828	6	10	,	,	PUNCT
ejpam-4828	6	11	denoted	denote	VERB
ejpam-4828	6	12	by	by	ADP
ejpam-4828	6	13	ωcvr	ωcvr	PROPN
ejpam-4828	6	14	g	g	PROPN
ejpam-4828	6	15	(	(	PUNCT
ejpam-4828	6	16	f	f	PROPN
ejpam-4828	6	17	)	)	PUNCT
ejpam-4828	6	18	,	,	PUNCT
ejpam-4828	6	19	is	be	AUX
ejpam-4828	6	20	given	give	VERB
ejpam-4828	6	21	by	by	ADP
ejpam-4828	6	22	ωcvr	ωcvr	PROPN
ejpam-4828	6	23	g	g	PROPN
ejpam-4828	6	24	(	(	PUNCT
ejpam-4828	6	25	f	f	X
ejpam-4828	6	26	)	)	PUNCT
ejpam-4828	6	27	=	=	SYM
ejpam-4828	6	28	∑	∑	PUNCT
ejpam-4828	6	29	v∈v	v∈v	PROPN
ejpam-4828	6	30	(	(	PUNCT
ejpam-4828	6	31	g	g	NOUN
ejpam-4828	6	32	)	)	PUNCT
ejpam-4828	6	33	f(v	f(v	NOUN
ejpam-4828	6	34	)	)	PUNCT
ejpam-4828	6	35	.	.	PUNCT
ejpam-4828	7	1	the	the	DET
ejpam-4828	7	2	minimum	minimum	ADJ
ejpam-4828	7	3	weight	weight	NOUN
ejpam-4828	7	4	of	of	ADP
ejpam-4828	7	5	a	a	DET
ejpam-4828	7	6	cvrdf	cvrdf	NOUN
ejpam-4828	7	7	on	on	ADP
ejpam-4828	7	8	g	g	NOUN
ejpam-4828	7	9	,	,	PUNCT
ejpam-4828	7	10	denoted	denote	VERB
ejpam-4828	7	11	by	by	ADP
ejpam-4828	7	12	γcvr(g	γcvr(g	PROPN
ejpam-4828	7	13	)	)	PUNCT
ejpam-4828	7	14	,	,	PUNCT
ejpam-4828	7	15	is	be	AUX
ejpam-4828	7	16	called	call	VERB
ejpam-4828	7	17	the	the	DET
ejpam-4828	7	18	convex	convex	ADJ
ejpam-4828	7	19	roman	roman	ADJ
ejpam-4828	7	20	domination	domination	NOUN
ejpam-4828	7	21	number	number	NOUN
ejpam-4828	7	22	of	of	ADP
ejpam-4828	7	23	g.	g.	PROPN
ejpam-4828	7	24	in	in	ADP
ejpam-4828	7	25	this	this	DET
ejpam-4828	7	26	paper	paper	NOUN
ejpam-4828	7	27	,	,	PUNCT
ejpam-4828	7	28	we	we	PRON
ejpam-4828	7	29	determine	determine	VERB
ejpam-4828	7	30	the	the	DET
ejpam-4828	7	31	convex	convex	ADJ
ejpam-4828	7	32	roman	roman	ADJ
ejpam-4828	7	33	domination	domination	NOUN
ejpam-4828	7	34	numbers	number	NOUN
ejpam-4828	7	35	of	of	ADP
ejpam-4828	7	36	some	some	DET
ejpam-4828	7	37	graphs	graph	NOUN
ejpam-4828	7	38	and	and	CCONJ
ejpam-4828	7	39	give	give	VERB
ejpam-4828	7	40	some	some	DET
ejpam-4828	7	41	realization	realization	NOUN
ejpam-4828	7	42	results	result	NOUN
ejpam-4828	7	43	involving	involve	VERB
ejpam-4828	7	44	convex	convex	ADJ
ejpam-4828	7	45	roman	roman	ADJ
ejpam-4828	7	46	domination	domination	NOUN
ejpam-4828	7	47	,	,	PUNCT
ejpam-4828	7	48	connected	connect	VERB
ejpam-4828	7	49	roman	roman	ADJ
ejpam-4828	7	50	domination	domination	NOUN
ejpam-4828	7	51	,	,	PUNCT
ejpam-4828	7	52	and	and	CCONJ
ejpam-4828	7	53	convex	convex	NOUN
ejpam-4828	7	54	domination	domination	NOUN
ejpam-4828	7	55	numbers	number	NOUN
ejpam-4828	7	56	.	.	PUNCT
ejpam-4828	8	1	2020	2020	NUM
ejpam-4828	8	2	mathematics	mathematic	NOUN
ejpam-4828	8	3	subject	subject	NOUN
ejpam-4828	8	4	classifications	classification	NOUN
ejpam-4828	8	5	:	:	PUNCT
ejpam-4828	8	6	05c69	05c69	X
ejpam-4828	8	7	key	key	ADJ
ejpam-4828	8	8	words	word	NOUN
ejpam-4828	8	9	and	and	CCONJ
ejpam-4828	8	10	phrases	phrase	NOUN
ejpam-4828	8	11	:	:	PUNCT
ejpam-4828	8	12	convex	convex	PROPN
ejpam-4828	8	13	set	set	NOUN
ejpam-4828	8	14	,	,	PUNCT
ejpam-4828	8	15	roman	roman	ADJ
ejpam-4828	8	16	dominating	dominating	NOUN
ejpam-4828	8	17	function	function	NOUN
ejpam-4828	8	18	,	,	PUNCT
ejpam-4828	8	19	roman	roman	ADJ
ejpam-4828	8	20	domination	domination	NOUN
ejpam-4828	8	21	number	number	NOUN
ejpam-4828	8	22	,	,	PUNCT
ejpam-4828	8	23	convex	convex	ADJ
ejpam-4828	8	24	roman	roman	ADJ
ejpam-4828	8	25	dominating	dominating	NOUN
ejpam-4828	8	26	function	function	NOUN
ejpam-4828	8	27	,	,	PUNCT
ejpam-4828	8	28	convex	convex	VERB
ejpam-4828	8	29	roman	roman	ADJ
ejpam-4828	8	30	domination	domination	NOUN
ejpam-4828	8	31	number	number	NOUN
ejpam-4828	8	32	1	1	NUM
ejpam-4828	8	33	.	.	PUNCT
ejpam-4828	8	34	introduction	introduction	NOUN
ejpam-4828	8	35	the	the	DET
ejpam-4828	8	36	concept	concept	NOUN
ejpam-4828	8	37	roman	roman	ADJ
ejpam-4828	8	38	domination	domination	NOUN
ejpam-4828	8	39	was	be	AUX
ejpam-4828	8	40	first	first	ADV
ejpam-4828	8	41	introduced	introduce	VERB
ejpam-4828	8	42	by	by	ADP
ejpam-4828	8	43	cockayne	cockayne	NOUN
ejpam-4828	8	44	,	,	PUNCT
ejpam-4828	8	45	dreyer	dreyer	PROPN
ejpam-4828	8	46	and	and	CCONJ
ejpam-4828	8	47	hedetnieme	hedetnieme	NOUN
ejpam-4828	8	48	in	in	ADP
ejpam-4828	8	49	2004	2004	NUM
ejpam-4828	9	1	[	[	X
ejpam-4828	9	2	11	11	NUM
ejpam-4828	9	3	]	]	PUNCT
ejpam-4828	9	4	as	as	ADP
ejpam-4828	9	5	a	a	DET
ejpam-4828	9	6	variant	variant	NOUN
ejpam-4828	9	7	of	of	ADP
ejpam-4828	9	8	dominating	dominate	VERB
ejpam-4828	9	9	set	set	NOUN
ejpam-4828	9	10	problem	problem	NOUN
ejpam-4828	9	11	in	in	ADP
ejpam-4828	9	12	graph	graph	NOUN
ejpam-4828	9	13	theory	theory	NOUN
ejpam-4828	9	14	.	.	PUNCT
ejpam-4828	10	1	roman	roman	ADJ
ejpam-4828	10	2	domination	domination	NOUN
ejpam-4828	10	3	is	be	AUX
ejpam-4828	10	4	inspired	inspire	VERB
ejpam-4828	10	5	by	by	ADP
ejpam-4828	10	6	the	the	DET
ejpam-4828	10	7	ancient	ancient	ADJ
ejpam-4828	10	8	roman	roman	ADJ
ejpam-4828	10	9	empire	empire	NOUN
ejpam-4828	10	10	’s	’s	PART
ejpam-4828	10	11	military	military	ADJ
ejpam-4828	10	12	strategy	strategy	NOUN
ejpam-4828	10	13	,	,	PUNCT
ejpam-4828	10	14	where	where	SCONJ
ejpam-4828	10	15	soldiers	soldier	NOUN
ejpam-4828	10	16	would	would	AUX
ejpam-4828	10	17	be	be	AUX
ejpam-4828	10	18	stationed	station	VERB
ejpam-4828	10	19	at	at	ADP
ejpam-4828	10	20	strategic	strategic	ADJ
ejpam-4828	10	21	points	point	NOUN
ejpam-4828	10	22	throughout	throughout	ADP
ejpam-4828	10	23	a	a	DET
ejpam-4828	10	24	location	location	NOUN
ejpam-4828	10	25	to	to	PART
ejpam-4828	10	26	ensure	ensure	VERB
ejpam-4828	10	27	its	its	PRON
ejpam-4828	10	28	protection	protection	NOUN
ejpam-4828	10	29	.	.	PUNCT
ejpam-4828	11	1	in	in	ADP
ejpam-4828	11	2	the	the	DET
ejpam-4828	11	3	roman	roman	ADJ
ejpam-4828	11	4	domination	domination	NOUN
ejpam-4828	11	5	strategy	strategy	NOUN
ejpam-4828	11	6	,	,	PUNCT
ejpam-4828	11	7	an	an	DET
ejpam-4828	11	8	unsecured	unsecured	ADJ
ejpam-4828	11	9	location	location	NOUN
ejpam-4828	11	10	can	can	AUX
ejpam-4828	11	11	be	be	AUX
ejpam-4828	11	12	secured	secure	VERB
ejpam-4828	11	13	by	by	ADP
ejpam-4828	11	14	sending	send	VERB
ejpam-4828	11	15	an	an	DET
ejpam-4828	11	16	army	army	NOUN
ejpam-4828	11	17	to	to	ADP
ejpam-4828	11	18	the	the	DET
ejpam-4828	11	19	location	location	NOUN
ejpam-4828	11	20	from	from	ADP
ejpam-4828	11	21	an	an	DET
ejpam-4828	11	22	adjacent	adjacent	ADJ
ejpam-4828	11	23	secured	secure	VERB
ejpam-4828	11	24	location	location	NOUN
ejpam-4828	11	25	subject	subject	NOUN
ejpam-4828	11	26	to	to	ADP
ejpam-4828	11	27	the	the	DET
ejpam-4828	11	28	constraint	constraint	NOUN
ejpam-4828	11	29	that	that	PRON
ejpam-4828	11	30	one	one	NUM
ejpam-4828	11	31	army	army	NOUN
ejpam-4828	11	32	must	must	AUX
ejpam-4828	11	33	be	be	AUX
ejpam-4828	11	34	left	leave	VERB
ejpam-4828	11	35	behind	behind	ADP
ejpam-4828	11	36	the	the	DET
ejpam-4828	11	37	secured	secure	VERB
ejpam-4828	11	38	location	location	NOUN
ejpam-4828	11	39	.	.	PUNCT
ejpam-4828	12	1	specifically	specifically	ADV
ejpam-4828	12	2	,	,	PUNCT
ejpam-4828	12	3	in	in	ADP
ejpam-4828	12	4	this	this	DET
ejpam-4828	12	5	protection	protection	NOUN
ejpam-4828	12	6	strategy	strategy	NOUN
ejpam-4828	12	7	,	,	PUNCT
ejpam-4828	12	8	a	a	DET
ejpam-4828	12	9	vertex	vertex	NOUN
ejpam-4828	12	10	with	with	ADP
ejpam-4828	12	11	label	label	NOUN
ejpam-4828	12	12	(	(	PUNCT
ejpam-4828	12	13	or	or	CCONJ
ejpam-4828	12	14	image	image	NOUN
ejpam-4828	12	15	under	under	ADP
ejpam-4828	12	16	a	a	DET
ejpam-4828	12	17	function	function	NOUN
ejpam-4828	12	18	)	)	PUNCT
ejpam-4828	12	19	1	1	NUM
ejpam-4828	12	20	or	or	CCONJ
ejpam-4828	12	21	2	2	NUM
ejpam-4828	12	22	may	may	AUX
ejpam-4828	12	23	be	be	AUX
ejpam-4828	12	24	viewed	view	VERB
ejpam-4828	12	25	as	as	ADP
ejpam-4828	12	26	one	one	NUM
ejpam-4828	12	27	or	or	CCONJ
ejpam-4828	12	28	two	two	NUM
ejpam-4828	12	29	armies	army	NOUN
ejpam-4828	12	30	,	,	PUNCT
ejpam-4828	12	31	respectively	respectively	ADV
ejpam-4828	12	32	,	,	PUNCT
ejpam-4828	12	33	stationed	station	VERB
ejpam-4828	12	34	at	at	ADP
ejpam-4828	12	35	the	the	DET
ejpam-4828	12	36	given	give	VERB
ejpam-4828	12	37	location	location	NOUN
ejpam-4828	12	38	or	or	CCONJ
ejpam-4828	12	39	vertex	vertex	NOUN
ejpam-4828	12	40	.	.	PUNCT
ejpam-4828	13	1	a	a	DET
ejpam-4828	13	2	nearby	nearby	ADJ
ejpam-4828	13	3	location	location	NOUN
ejpam-4828	13	4	(	(	PUNCT
ejpam-4828	13	5	an	an	DET
ejpam-4828	13	6	adjacent	adjacent	ADJ
ejpam-4828	13	7	vertex	vertex	NOUN
ejpam-4828	13	8	)	)	PUNCT
ejpam-4828	13	9	is	be	AUX
ejpam-4828	13	10	considered	consider	VERB
ejpam-4828	13	11	to	to	PART
ejpam-4828	13	12	be	be	AUX
ejpam-4828	13	13	unsecured	unsecured	ADJ
ejpam-4828	13	14	if	if	SCONJ
ejpam-4828	13	15	no	no	DET
ejpam-4828	13	16	armies	army	NOUN
ejpam-4828	13	17	are	be	AUX
ejpam-4828	13	18	stationed	station	VERB
ejpam-4828	13	19	there	there	ADV
ejpam-4828	13	20	,	,	PUNCT
ejpam-4828	13	21	that	that	PRON
ejpam-4828	13	22	is	be	AUX
ejpam-4828	13	23	if	if	SCONJ
ejpam-4828	13	24	the	the	DET
ejpam-4828	13	25	label	label	NOUN
ejpam-4828	13	26	of	of	ADP
ejpam-4828	13	27	the	the	DET
ejpam-4828	13	28	vertex	vertex	NOUN
ejpam-4828	13	29	is	be	AUX
ejpam-4828	13	30	0	0	NUM
ejpam-4828	13	31	.	.	PUNCT
ejpam-4828	14	1	the	the	DET
ejpam-4828	14	2	convex	convex	ADJ
ejpam-4828	14	3	roman	roman	ADJ
ejpam-4828	14	4	domination	domination	NOUN
ejpam-4828	14	5	strategy	strategy	NOUN
ejpam-4828	14	6	in	in	ADP
ejpam-4828	14	7	addition	addition	NOUN
ejpam-4828	14	8	ensures	ensure	VERB
ejpam-4828	14	9	that	that	SCONJ
ejpam-4828	14	10	all	all	DET
ejpam-4828	14	11	locations	location	NOUN
ejpam-4828	14	12	that	that	PRON
ejpam-4828	14	13	lie	lie	VERB
ejpam-4828	14	14	along	along	ADP
ejpam-4828	14	15	shortest	short	ADJ
ejpam-4828	14	16	paths	path	NOUN
ejpam-4828	14	17	between	between	ADP
ejpam-4828	14	18	any	any	DET
ejpam-4828	14	19	two	two	NUM
ejpam-4828	14	20	secured	secure	VERB
ejpam-4828	14	21	locations	location	NOUN
ejpam-4828	14	22	are	be	AUX
ejpam-4828	14	23	also	also	ADV
ejpam-4828	14	24	secured	secure	VERB
ejpam-4828	14	25	.	.	PUNCT
ejpam-4828	15	1	∗corresponding	∗corresponde	VERB
ejpam-4828	15	2	author	author	NOUN
ejpam-4828	15	3	.	.	PUNCT
ejpam-4828	16	1	doi	doi	NOUN
ejpam-4828	16	2	:	:	PUNCT
ejpam-4828	16	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4828	https://doi.org/10.29020/nybg.ejpam.v16i3.4828	NOUN
ejpam-4828	16	4	email	email	NOUN
ejpam-4828	16	5	addresses	address	NOUN
ejpam-4828	16	6	:	:	PUNCT
ejpam-4828	17	1	ronajane.fortosa@g.msuiit.edu.ph	ronajane.fortosa@g.msuiit.edu.ph	PROPN
ejpam-4828	17	2	(	(	PUNCT
ejpam-4828	17	3	r.j	r.j	PROPN
ejpam-4828	17	4	.	.	PROPN
ejpam-4828	17	5	fortosa	fortosa	PROPN
ejpam-4828	17	6	)	)	PUNCT
ejpam-4828	17	7	,	,	PUNCT
ejpam-4828	17	8	sergio.canoy@g.msuiit.edu.ph	sergio.canoy@g.msuiit.edu.ph	PROPN
ejpam-4828	17	9	(	(	PUNCT
ejpam-4828	17	10	s.	s.	PROPN
ejpam-4828	17	11	canoy	canoy	PROPN
ejpam-4828	17	12	)	)	PUNCT
ejpam-4828	17	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4828	17	14	1705	1705	NUM
ejpam-4828	17	15	©	©	PROPN
ejpam-4828	17	16	2023	2023	NUM
ejpam-4828	17	17	ejpam	ejpam	NOUN
ejpam-4828	17	18	all	all	DET
ejpam-4828	17	19	rights	right	NOUN
ejpam-4828	17	20	reserved	reserve	VERB
ejpam-4828	17	21	.	.	PUNCT
ejpam-4828	18	1	r.	r.	PROPN
ejpam-4828	18	2	fortosa	fortosa	PROPN
ejpam-4828	18	3	,	,	PUNCT
ejpam-4828	18	4	s.	s.	PROPN
ejpam-4828	18	5	canoy	canoy	PROPN
ejpam-4828	18	6	jr	jr	PROPN
ejpam-4828	18	7	.	.	PROPN
ejpam-4828	18	8	/	/	SYM
ejpam-4828	18	9	eur	eur	PROPN
ejpam-4828	18	10	.	.	PUNCT
ejpam-4828	19	1	j.	j.	PROPN
ejpam-4828	19	2	pure	pure	PROPN
ejpam-4828	19	3	appl	appl	PROPN
ejpam-4828	19	4	.	.	PROPN
ejpam-4828	19	5	math	math	PROPN
ejpam-4828	19	6	,	,	PUNCT
ejpam-4828	19	7	16	16	NUM
ejpam-4828	19	8	(	(	PUNCT
ejpam-4828	19	9	3	3	NUM
ejpam-4828	19	10	)	)	PUNCT
ejpam-4828	19	11	(	(	PUNCT
ejpam-4828	19	12	2023	2023	NUM
ejpam-4828	19	13	)	)	PUNCT
ejpam-4828	19	14	,	,	PUNCT
ejpam-4828	19	15	1705	1705	NUM
ejpam-4828	19	16	-	-	SYM
ejpam-4828	19	17	1716	1716	NUM
ejpam-4828	19	18	1706	1706	NUM
ejpam-4828	19	19	since	since	SCONJ
ejpam-4828	19	20	then	then	ADV
ejpam-4828	19	21	,	,	PUNCT
ejpam-4828	19	22	roman	roman	ADJ
ejpam-4828	19	23	domination	domination	NOUN
ejpam-4828	19	24	function	function	NOUN
ejpam-4828	19	25	has	have	AUX
ejpam-4828	19	26	become	become	VERB
ejpam-4828	19	27	a	a	DET
ejpam-4828	19	28	popular	popular	ADJ
ejpam-4828	19	29	topic	topic	NOUN
ejpam-4828	19	30	of	of	ADP
ejpam-4828	19	31	study	study	NOUN
ejpam-4828	19	32	in	in	ADP
ejpam-4828	19	33	graph	graph	NOUN
ejpam-4828	19	34	theory	theory	NOUN
ejpam-4828	19	35	,	,	PUNCT
ejpam-4828	19	36	and	and	CCONJ
ejpam-4828	19	37	several	several	ADJ
ejpam-4828	19	38	variations	variation	NOUN
ejpam-4828	19	39	and	and	CCONJ
ejpam-4828	19	40	related	related	ADJ
ejpam-4828	19	41	concepts	concept	NOUN
ejpam-4828	19	42	have	have	AUX
ejpam-4828	19	43	been	be	AUX
ejpam-4828	19	44	studied	study	VERB
ejpam-4828	19	45	.	.	PUNCT
ejpam-4828	20	1	some	some	DET
ejpam-4828	20	2	variations	variation	NOUN
ejpam-4828	20	3	can	can	AUX
ejpam-4828	20	4	be	be	AUX
ejpam-4828	20	5	found	find	VERB
ejpam-4828	20	6	in	in	ADP
ejpam-4828	20	7	[	[	X
ejpam-4828	20	8	1	1	NUM
ejpam-4828	20	9	]	]	PUNCT
ejpam-4828	20	10	,	,	PUNCT
ejpam-4828	20	11	[	[	X
ejpam-4828	20	12	2	2	NUM
ejpam-4828	20	13	]	]	PUNCT
ejpam-4828	20	14	,	,	PUNCT
ejpam-4828	20	15	[	[	X
ejpam-4828	20	16	3	3	NUM
ejpam-4828	20	17	]	]	PUNCT
ejpam-4828	20	18	,	,	PUNCT
ejpam-4828	20	19	[	[	X
ejpam-4828	20	20	4	4	NUM
ejpam-4828	20	21	]	]	PUNCT
ejpam-4828	20	22	,	,	PUNCT
ejpam-4828	20	23	[	[	X
ejpam-4828	20	24	5	5	NUM
ejpam-4828	20	25	]	]	PUNCT
ejpam-4828	20	26	,	,	PUNCT
ejpam-4828	20	27	[	[	X
ejpam-4828	20	28	10	10	NUM
ejpam-4828	20	29	]	]	PUNCT
ejpam-4828	20	30	,	,	PUNCT
ejpam-4828	20	31	[	[	X
ejpam-4828	20	32	11	11	NUM
ejpam-4828	20	33	]	]	PUNCT
ejpam-4828	20	34	,	,	PUNCT
ejpam-4828	20	35	[	[	X
ejpam-4828	20	36	13	13	NUM
ejpam-4828	20	37	]	]	PUNCT
ejpam-4828	20	38	,	,	PUNCT
ejpam-4828	20	39	[	[	X
ejpam-4828	20	40	14	14	NUM
ejpam-4828	20	41	]	]	PUNCT
ejpam-4828	20	42	,	,	PUNCT
ejpam-4828	20	43	[	[	X
ejpam-4828	20	44	18	18	NUM
ejpam-4828	20	45	]	]	PUNCT
ejpam-4828	20	46	,	,	PUNCT
ejpam-4828	20	47	and	and	CCONJ
ejpam-4828	20	48	[	[	X
ejpam-4828	20	49	17	17	NUM
ejpam-4828	20	50	]	]	PUNCT
ejpam-4828	20	51	.	.	PUNCT
ejpam-4828	21	1	one	one	NUM
ejpam-4828	21	2	of	of	ADP
ejpam-4828	21	3	the	the	DET
ejpam-4828	21	4	fundamental	fundamental	ADJ
ejpam-4828	21	5	concepts	concept	NOUN
ejpam-4828	21	6	in	in	ADP
ejpam-4828	21	7	mathematics	mathematic	NOUN
ejpam-4828	21	8	that	that	PRON
ejpam-4828	21	9	has	have	AUX
ejpam-4828	21	10	been	be	AUX
ejpam-4828	21	11	studied	study	VERB
ejpam-4828	21	12	extensively	extensively	ADV
ejpam-4828	21	13	in	in	ADP
ejpam-4828	21	14	geometry	geometry	NOUN
ejpam-4828	21	15	and	and	CCONJ
ejpam-4828	21	16	has	have	AUX
ejpam-4828	21	17	been	be	AUX
ejpam-4828	21	18	extended	extend	VERB
ejpam-4828	21	19	to	to	ADP
ejpam-4828	21	20	graphs	graph	NOUN
ejpam-4828	21	21	is	be	AUX
ejpam-4828	21	22	convexity	convexity	NOUN
ejpam-4828	21	23	.	.	PUNCT
ejpam-4828	22	1	convexity	convexity	NOUN
ejpam-4828	22	2	in	in	ADP
ejpam-4828	22	3	graphs	graph	NOUN
ejpam-4828	22	4	is	be	AUX
ejpam-4828	22	5	discussed	discuss	VERB
ejpam-4828	22	6	in	in	ADP
ejpam-4828	22	7	the	the	DET
ejpam-4828	22	8	book	book	NOUN
ejpam-4828	22	9	of	of	ADP
ejpam-4828	22	10	buckley	buckley	NOUN
ejpam-4828	22	11	and	and	CCONJ
ejpam-4828	22	12	harary	harary	NOUN
ejpam-4828	22	13	[	[	X
ejpam-4828	22	14	6	6	NUM
ejpam-4828	22	15	]	]	PUNCT
ejpam-4828	22	16	.	.	PUNCT
ejpam-4828	23	1	some	some	DET
ejpam-4828	23	2	studies	study	NOUN
ejpam-4828	23	3	on	on	ADP
ejpam-4828	23	4	convexity	convexity	NOUN
ejpam-4828	23	5	in	in	ADP
ejpam-4828	23	6	graphs	graph	NOUN
ejpam-4828	23	7	and	and	CCONJ
ejpam-4828	23	8	its	its	PRON
ejpam-4828	23	9	related	related	ADJ
ejpam-4828	23	10	concepts	concept	NOUN
ejpam-4828	23	11	can	can	AUX
ejpam-4828	23	12	be	be	AUX
ejpam-4828	23	13	found	find	VERB
ejpam-4828	23	14	in	in	ADP
ejpam-4828	23	15	[	[	X
ejpam-4828	23	16	7	7	NUM
ejpam-4828	23	17	]	]	PUNCT
ejpam-4828	23	18	,	,	PUNCT
ejpam-4828	23	19	[	[	X
ejpam-4828	23	20	8	8	NUM
ejpam-4828	23	21	]	]	PUNCT
ejpam-4828	23	22	,	,	PUNCT
ejpam-4828	23	23	[	[	X
ejpam-4828	23	24	9	9	NUM
ejpam-4828	23	25	]	]	PUNCT
ejpam-4828	23	26	,	,	PUNCT
ejpam-4828	23	27	[	[	X
ejpam-4828	23	28	12	12	NUM
ejpam-4828	23	29	]	]	PUNCT
ejpam-4828	23	30	,	,	PUNCT
ejpam-4828	23	31	[	[	X
ejpam-4828	23	32	15	15	NUM
ejpam-4828	23	33	]	]	PUNCT
ejpam-4828	23	34	,	,	PUNCT
ejpam-4828	23	35	[	[	X
ejpam-4828	23	36	16	16	NUM
ejpam-4828	23	37	]	]	PUNCT
ejpam-4828	23	38	,	,	PUNCT
ejpam-4828	23	39	and	and	CCONJ
ejpam-4828	23	40	[	[	X
ejpam-4828	23	41	19	19	NUM
ejpam-4828	23	42	]	]	PUNCT
ejpam-4828	23	43	.	.	PUNCT
ejpam-4828	24	1	in	in	ADP
ejpam-4828	24	2	this	this	DET
ejpam-4828	24	3	paper	paper	NOUN
ejpam-4828	24	4	,	,	PUNCT
ejpam-4828	24	5	we	we	PRON
ejpam-4828	24	6	introduce	introduce	VERB
ejpam-4828	24	7	the	the	DET
ejpam-4828	24	8	concept	concept	NOUN
ejpam-4828	24	9	of	of	ADP
ejpam-4828	24	10	convex	convex	ADJ
ejpam-4828	24	11	roman	roman	ADJ
ejpam-4828	24	12	domination	domination	NOUN
ejpam-4828	24	13	on	on	ADP
ejpam-4828	24	14	which	which	PRON
ejpam-4828	24	15	we	we	PRON
ejpam-4828	24	16	combine	combine	VERB
ejpam-4828	24	17	the	the	DET
ejpam-4828	24	18	notions	notion	NOUN
ejpam-4828	24	19	of	of	ADP
ejpam-4828	24	20	convexity	convexity	NOUN
ejpam-4828	24	21	and	and	CCONJ
ejpam-4828	24	22	roman	roman	ADJ
ejpam-4828	24	23	domination	domination	NOUN
ejpam-4828	24	24	.	.	PUNCT
ejpam-4828	25	1	let	let	VERB
ejpam-4828	25	2	g	g	PRON
ejpam-4828	25	3	be	be	AUX
ejpam-4828	25	4	a	a	DET
ejpam-4828	25	5	connected	connected	ADJ
ejpam-4828	25	6	graph	graph	NOUN
ejpam-4828	25	7	.	.	PUNCT
ejpam-4828	26	1	for	for	ADP
ejpam-4828	26	2	vertices	vertex	NOUN
ejpam-4828	26	3	u	u	NOUN
ejpam-4828	26	4	and	and	CCONJ
ejpam-4828	26	5	v	v	NOUN
ejpam-4828	26	6	in	in	ADP
ejpam-4828	26	7	g	g	PROPN
ejpam-4828	26	8	,	,	PUNCT
ejpam-4828	26	9	a	a	DET
ejpam-4828	26	10	u	u	NOUN
ejpam-4828	26	11	-	-	NOUN
ejpam-4828	26	12	v	v	ADJ
ejpam-4828	26	13	geodesic	geodesic	NOUN
ejpam-4828	26	14	is	be	AUX
ejpam-4828	26	15	any	any	DET
ejpam-4828	26	16	shortest	short	ADJ
ejpam-4828	26	17	path	path	NOUN
ejpam-4828	26	18	in	in	ADP
ejpam-4828	26	19	g	g	NOUN
ejpam-4828	26	20	joining	join	VERB
ejpam-4828	26	21	u	u	NOUN
ejpam-4828	26	22	and	and	CCONJ
ejpam-4828	26	23	v.	v.	ADP
ejpam-4828	26	24	the	the	DET
ejpam-4828	26	25	length	length	NOUN
ejpam-4828	26	26	of	of	ADP
ejpam-4828	26	27	a	a	DET
ejpam-4828	26	28	u	u	NOUN
ejpam-4828	26	29	-	-	NOUN
ejpam-4828	26	30	v	v	ADJ
ejpam-4828	26	31	geodesic	geodesic	NOUN
ejpam-4828	26	32	is	be	AUX
ejpam-4828	26	33	called	call	VERB
ejpam-4828	26	34	the	the	DET
ejpam-4828	26	35	distance	distance	NOUN
ejpam-4828	26	36	dg(u	dg(u	X
ejpam-4828	26	37	,	,	PUNCT
ejpam-4828	26	38	v	v	NOUN
ejpam-4828	26	39	)	)	PUNCT
ejpam-4828	26	40	between	between	ADP
ejpam-4828	26	41	u	u	PROPN
ejpam-4828	26	42	and	and	CCONJ
ejpam-4828	26	43	v.	v.	NOUN
ejpam-4828	26	44	for	for	ADP
ejpam-4828	26	45	every	every	DET
ejpam-4828	26	46	two	two	NUM
ejpam-4828	26	47	vertices	vertex	NOUN
ejpam-4828	26	48	u	u	NOUN
ejpam-4828	26	49	and	and	CCONJ
ejpam-4828	26	50	v	v	NOUN
ejpam-4828	26	51	of	of	ADP
ejpam-4828	26	52	g	g	NOUN
ejpam-4828	26	53	,	,	PUNCT
ejpam-4828	26	54	the	the	DET
ejpam-4828	26	55	symbol	symbol	NOUN
ejpam-4828	26	56	ig[u	ig[u	PROPN
ejpam-4828	26	57	,	,	PUNCT
ejpam-4828	26	58	v	v	NOUN
ejpam-4828	26	59	]	]	PUNCT
ejpam-4828	26	60	is	be	AUX
ejpam-4828	26	61	used	use	VERB
ejpam-4828	26	62	to	to	PART
ejpam-4828	26	63	denote	denote	VERB
ejpam-4828	26	64	the	the	DET
ejpam-4828	26	65	set	set	NOUN
ejpam-4828	26	66	of	of	ADP
ejpam-4828	26	67	vertices	vertex	NOUN
ejpam-4828	26	68	lying	lie	VERB
ejpam-4828	26	69	on	on	ADP
ejpam-4828	26	70	any	any	PRON
ejpam-4828	26	71	of	of	ADP
ejpam-4828	26	72	the	the	DET
ejpam-4828	26	73	u	u	NOUN
ejpam-4828	26	74	-	-	NOUN
ejpam-4828	26	75	v	v	ADJ
ejpam-4828	26	76	geodesics	geodesic	NOUN
ejpam-4828	26	77	.	.	PUNCT
ejpam-4828	27	1	the	the	DET
ejpam-4828	27	2	set	set	NOUN
ejpam-4828	27	3	of	of	ADP
ejpam-4828	27	4	neighbors	neighbor	NOUN
ejpam-4828	27	5	of	of	ADP
ejpam-4828	27	6	a	a	DET
ejpam-4828	27	7	vertex	vertex	NOUN
ejpam-4828	27	8	u	u	NOUN
ejpam-4828	27	9	∈	∈	PROPN
ejpam-4828	27	10	g	g	NOUN
ejpam-4828	27	11	,	,	PUNCT
ejpam-4828	27	12	denoted	denote	VERB
ejpam-4828	27	13	by	by	ADP
ejpam-4828	27	14	ng(u	ng(u	NOUN
ejpam-4828	27	15	)	)	PUNCT
ejpam-4828	27	16	,	,	PUNCT
ejpam-4828	27	17	is	be	AUX
ejpam-4828	27	18	called	call	VERB
ejpam-4828	27	19	the	the	DET
ejpam-4828	27	20	open	open	ADJ
ejpam-4828	27	21	neighborhood	neighborhood	NOUN
ejpam-4828	27	22	of	of	ADP
ejpam-4828	27	23	u.	u.	VERB
ejpam-4828	27	24	the	the	DET
ejpam-4828	27	25	closed	closed	ADJ
ejpam-4828	27	26	neighborhood	neighborhood	NOUN
ejpam-4828	27	27	of	of	ADP
ejpam-4828	27	28	u	u	NOUN
ejpam-4828	27	29	is	be	AUX
ejpam-4828	27	30	the	the	DET
ejpam-4828	27	31	set	set	NOUN
ejpam-4828	27	32	ng[u	ng[u	PROPN
ejpam-4828	27	33	]	]	X
ejpam-4828	27	34	=	=	SYM
ejpam-4828	27	35	ng(u	ng(u	PROPN
ejpam-4828	27	36	)	)	PUNCT
ejpam-4828	27	37	∪	∪	NOUN
ejpam-4828	27	38	{	{	PUNCT
ejpam-4828	27	39	u	u	NOUN
ejpam-4828	27	40	}	}	PUNCT
ejpam-4828	27	41	.	.	PUNCT
ejpam-4828	28	1	the	the	DET
ejpam-4828	28	2	degree	degree	NOUN
ejpam-4828	28	3	of	of	ADP
ejpam-4828	28	4	a	a	DET
ejpam-4828	28	5	vertex	vertex	NOUN
ejpam-4828	28	6	v	v	ADP
ejpam-4828	28	7	denoted	denote	VERB
ejpam-4828	28	8	degg(v	degg(v	PROPN
ejpam-4828	28	9	)	)	PUNCT
ejpam-4828	28	10	in	in	ADP
ejpam-4828	28	11	a	a	DET
ejpam-4828	28	12	graph	graph	NOUN
ejpam-4828	28	13	g	g	NOUN
ejpam-4828	28	14	is	be	AUX
ejpam-4828	28	15	the	the	DET
ejpam-4828	28	16	number	number	NOUN
ejpam-4828	28	17	of	of	ADP
ejpam-4828	28	18	vertices	vertex	NOUN
ejpam-4828	28	19	in	in	ADP
ejpam-4828	28	20	g	g	PROPN
ejpam-4828	28	21	that	that	PRON
ejpam-4828	28	22	are	be	AUX
ejpam-4828	28	23	adjacent	adjacent	ADJ
ejpam-4828	28	24	to	to	ADP
ejpam-4828	28	25	v.	v.	ADP
ejpam-4828	28	26	hence	hence	ADV
ejpam-4828	28	27	,	,	PUNCT
ejpam-4828	28	28	degg(v	degg(v	PROPN
ejpam-4828	28	29	)	)	PUNCT
ejpam-4828	28	30	=	=	SYM
ejpam-4828	28	31	|n(v)|	|n(v)|	PROPN
ejpam-4828	28	32	.	.	PUNCT
ejpam-4828	29	1	the	the	DET
ejpam-4828	29	2	largest	large	ADJ
ejpam-4828	29	3	degree	degree	NOUN
ejpam-4828	29	4	among	among	ADP
ejpam-4828	29	5	the	the	DET
ejpam-4828	29	6	vertices	vertex	NOUN
ejpam-4828	29	7	of	of	ADP
ejpam-4828	29	8	g	g	PROPN
ejpam-4828	29	9	is	be	AUX
ejpam-4828	29	10	called	call	VERB
ejpam-4828	29	11	the	the	DET
ejpam-4828	29	12	maximum	maximum	ADJ
ejpam-4828	29	13	degree	degree	NOUN
ejpam-4828	29	14	of	of	ADP
ejpam-4828	29	15	g	g	NOUN
ejpam-4828	29	16	and	and	CCONJ
ejpam-4828	29	17	is	be	AUX
ejpam-4828	29	18	denoted	denote	VERB
ejpam-4828	29	19	by	by	ADP
ejpam-4828	29	20	△	△	PROPN
ejpam-4828	29	21	(	(	PUNCT
ejpam-4828	29	22	g	g	NOUN
ejpam-4828	29	23	)	)	PUNCT
ejpam-4828	29	24	.	.	PUNCT
ejpam-4828	30	1	the	the	DET
ejpam-4828	30	2	minimum	minimum	NOUN
ejpam-4828	30	3	degree	degree	NOUN
ejpam-4828	30	4	of	of	ADP
ejpam-4828	30	5	g	g	PROPN
ejpam-4828	30	6	is	be	AUX
ejpam-4828	30	7	denoted	denote	VERB
ejpam-4828	30	8	by	by	ADP
ejpam-4828	30	9	δ(g	δ(g	NOUN
ejpam-4828	30	10	)	)	PUNCT
ejpam-4828	30	11	.	.	PUNCT
ejpam-4828	31	1	a	a	DET
ejpam-4828	31	2	graph	graph	NOUN
ejpam-4828	31	3	g	g	NOUN
ejpam-4828	31	4	is	be	AUX
ejpam-4828	31	5	connected	connect	VERB
ejpam-4828	31	6	if	if	SCONJ
ejpam-4828	31	7	every	every	DET
ejpam-4828	31	8	pair	pair	NOUN
ejpam-4828	31	9	of	of	ADP
ejpam-4828	31	10	its	its	PRON
ejpam-4828	31	11	vertices	vertex	NOUN
ejpam-4828	31	12	can	can	AUX
ejpam-4828	31	13	be	be	AUX
ejpam-4828	31	14	joined	join	VERB
ejpam-4828	31	15	by	by	ADP
ejpam-4828	31	16	a	a	DET
ejpam-4828	31	17	path	path	NOUN
ejpam-4828	31	18	.	.	PUNCT
ejpam-4828	32	1	a	a	DET
ejpam-4828	32	2	vertex	vertex	NOUN
ejpam-4828	32	3	of	of	ADP
ejpam-4828	32	4	a	a	DET
ejpam-4828	32	5	connected	connected	ADJ
ejpam-4828	32	6	graph	graph	NOUN
ejpam-4828	32	7	g	g	PROPN
ejpam-4828	32	8	is	be	AUX
ejpam-4828	32	9	an	an	DET
ejpam-4828	32	10	extreme	extreme	ADJ
ejpam-4828	32	11	vertex	vertex	NOUN
ejpam-4828	32	12	or	or	CCONJ
ejpam-4828	32	13	simplicial	simplicial	NOUN
ejpam-4828	32	14	if	if	SCONJ
ejpam-4828	32	15	its	its	PRON
ejpam-4828	32	16	open	open	ADJ
ejpam-4828	32	17	neighborhood	neighborhood	NOUN
ejpam-4828	32	18	induces	induce	VERB
ejpam-4828	32	19	a	a	DET
ejpam-4828	32	20	complete	complete	ADJ
ejpam-4828	32	21	subgraph	subgraph	NOUN
ejpam-4828	32	22	of	of	ADP
ejpam-4828	32	23	g.	g.	PROPN
ejpam-4828	32	24	the	the	DET
ejpam-4828	32	25	set	set	NOUN
ejpam-4828	32	26	of	of	ADP
ejpam-4828	32	27	extreme	extreme	ADJ
ejpam-4828	32	28	vertices	vertex	NOUN
ejpam-4828	32	29	of	of	ADP
ejpam-4828	32	30	g	g	PROPN
ejpam-4828	32	31	is	be	AUX
ejpam-4828	32	32	denoted	denote	VERB
ejpam-4828	32	33	by	by	ADP
ejpam-4828	32	34	ext(g	ext(g	PROPN
ejpam-4828	32	35	)	)	PUNCT
ejpam-4828	32	36	.	.	PUNCT
ejpam-4828	33	1	a	a	DET
ejpam-4828	33	2	set	set	NOUN
ejpam-4828	33	3	s	s	NOUN
ejpam-4828	33	4	⊆	⊆	NUM
ejpam-4828	33	5	v	v	NOUN
ejpam-4828	33	6	(	(	PUNCT
ejpam-4828	33	7	g	g	NOUN
ejpam-4828	33	8	)	)	PUNCT
ejpam-4828	33	9	is	be	AUX
ejpam-4828	33	10	said	say	VERB
ejpam-4828	33	11	to	to	PART
ejpam-4828	33	12	be	be	AUX
ejpam-4828	33	13	a	a	DET
ejpam-4828	33	14	dominating	dominating	NOUN
ejpam-4828	33	15	set	set	NOUN
ejpam-4828	33	16	of	of	ADP
ejpam-4828	33	17	a	a	DET
ejpam-4828	33	18	graph	graph	NOUN
ejpam-4828	33	19	g	g	NOUN
ejpam-4828	33	20	if	if	SCONJ
ejpam-4828	33	21	every	every	DET
ejpam-4828	33	22	vertex	vertex	NOUN
ejpam-4828	33	23	v	v	ADP
ejpam-4828	33	24	∈	∈	PROPN
ejpam-4828	33	25	v	v	NOUN
ejpam-4828	33	26	(	(	PUNCT
ejpam-4828	33	27	g	g	NOUN
ejpam-4828	33	28	)	)	PUNCT
ejpam-4828	33	29	is	be	AUX
ejpam-4828	33	30	either	either	CCONJ
ejpam-4828	33	31	an	an	DET
ejpam-4828	33	32	element	element	NOUN
ejpam-4828	33	33	of	of	ADP
ejpam-4828	33	34	s	s	PRON
ejpam-4828	33	35	or	or	CCONJ
ejpam-4828	33	36	is	be	AUX
ejpam-4828	33	37	adjacent	adjacent	ADJ
ejpam-4828	33	38	to	to	ADP
ejpam-4828	33	39	an	an	DET
ejpam-4828	33	40	element	element	NOUN
ejpam-4828	33	41	of	of	ADP
ejpam-4828	33	42	s.	s.	PROPN
ejpam-4828	33	43	thus	thus	ADV
ejpam-4828	33	44	,	,	PUNCT
ejpam-4828	33	45	n	n	X
ejpam-4828	33	46	[	[	X
ejpam-4828	33	47	s	s	X
ejpam-4828	33	48	]	]	X
ejpam-4828	33	49	=	=	SYM
ejpam-4828	33	50	v	v	NOUN
ejpam-4828	33	51	(	(	PUNCT
ejpam-4828	33	52	g	g	NOUN
ejpam-4828	33	53	)	)	PUNCT
ejpam-4828	33	54	.	.	PUNCT
ejpam-4828	34	1	the	the	DET
ejpam-4828	34	2	smallest	small	ADJ
ejpam-4828	34	3	cardinality	cardinality	NOUN
ejpam-4828	34	4	of	of	ADP
ejpam-4828	34	5	a	a	DET
ejpam-4828	34	6	dominating	dominating	NOUN
ejpam-4828	34	7	set	set	NOUN
ejpam-4828	34	8	s	s	PART
ejpam-4828	34	9	is	be	AUX
ejpam-4828	34	10	called	call	VERB
ejpam-4828	34	11	the	the	DET
ejpam-4828	34	12	domination	domination	NOUN
ejpam-4828	34	13	number	number	NOUN
ejpam-4828	34	14	of	of	ADP
ejpam-4828	34	15	g	g	NOUN
ejpam-4828	34	16	and	and	CCONJ
ejpam-4828	34	17	is	be	AUX
ejpam-4828	34	18	denoted	denote	VERB
ejpam-4828	34	19	by	by	ADP
ejpam-4828	34	20	γ(g	γ(g	PROPN
ejpam-4828	34	21	)	)	PUNCT
ejpam-4828	34	22	.	.	PUNCT
ejpam-4828	35	1	that	that	PRON
ejpam-4828	35	2	is	be	AUX
ejpam-4828	35	3	γ(g	γ(g	PROPN
ejpam-4828	35	4	)	)	PUNCT
ejpam-4828	36	1	=	=	NOUN
ejpam-4828	36	2	min{|s|	min{|s|	NOUN
ejpam-4828	36	3	:	:	PUNCT
ejpam-4828	36	4	s	s	VERB
ejpam-4828	36	5	is	be	AUX
ejpam-4828	36	6	a	a	DET
ejpam-4828	36	7	dominating	dominating	NOUN
ejpam-4828	36	8	set	set	NOUN
ejpam-4828	36	9	of	of	ADP
ejpam-4828	36	10	g	g	NOUN
ejpam-4828	36	11	}	}	PUNCT
ejpam-4828	36	12	.	.	PUNCT
ejpam-4828	37	1	any	any	DET
ejpam-4828	37	2	dominating	dominating	NOUN
ejpam-4828	37	3	set	set	NOUN
ejpam-4828	37	4	s	s	NOUN
ejpam-4828	37	5	of	of	ADP
ejpam-4828	37	6	g	g	NOUN
ejpam-4828	37	7	with	with	ADP
ejpam-4828	37	8	|s|	|s|	PROPN
ejpam-4828	37	9	=	=	SYM
ejpam-4828	37	10	γ(g	γ(g	PROPN
ejpam-4828	37	11	)	)	PUNCT
ejpam-4828	37	12	is	be	AUX
ejpam-4828	37	13	called	call	VERB
ejpam-4828	37	14	a	a	DET
ejpam-4828	37	15	γ	γ	NOUN
ejpam-4828	37	16	-	-	PUNCT
ejpam-4828	37	17	set	set	NOUN
ejpam-4828	37	18	of	of	ADP
ejpam-4828	37	19	g.	g.	PROPN
ejpam-4828	37	20	a	a	DET
ejpam-4828	37	21	set	set	NOUN
ejpam-4828	37	22	s	s	PROPN
ejpam-4828	37	23	⊆	⊆	NUM
ejpam-4828	37	24	v	v	NOUN
ejpam-4828	37	25	(	(	PUNCT
ejpam-4828	37	26	g	g	NOUN
ejpam-4828	37	27	)	)	PUNCT
ejpam-4828	37	28	is	be	AUX
ejpam-4828	37	29	convex	convex	ADJ
ejpam-4828	37	30	if	if	SCONJ
ejpam-4828	37	31	for	for	ADP
ejpam-4828	37	32	every	every	DET
ejpam-4828	37	33	two	two	NUM
ejpam-4828	37	34	vertices	vertex	NOUN
ejpam-4828	37	35	x	x	X
ejpam-4828	37	36	,	,	PUNCT
ejpam-4828	37	37	y	y	PROPN
ejpam-4828	37	38	∈	∈	PROPN
ejpam-4828	37	39	s	s	PROPN
ejpam-4828	37	40	,	,	PUNCT
ejpam-4828	37	41	ig[x	ig[x	PROPN
ejpam-4828	37	42	,	,	PUNCT
ejpam-4828	37	43	y	y	PROPN
ejpam-4828	37	44	]	]	X
ejpam-4828	37	45	⊆	⊆	NUM
ejpam-4828	37	46	s.	s.	PROPN
ejpam-4828	37	47	the	the	DET
ejpam-4828	37	48	largest	large	ADJ
ejpam-4828	37	49	cardinality	cardinality	NOUN
ejpam-4828	37	50	of	of	ADP
ejpam-4828	37	51	a	a	DET
ejpam-4828	37	52	proper	proper	ADJ
ejpam-4828	37	53	convex	convex	NOUN
ejpam-4828	37	54	set	set	VERB
ejpam-4828	37	55	in	in	ADP
ejpam-4828	37	56	g	g	NOUN
ejpam-4828	37	57	,	,	PUNCT
ejpam-4828	37	58	denoted	denote	VERB
ejpam-4828	37	59	by	by	ADP
ejpam-4828	37	60	con(g	con(g	NOUN
ejpam-4828	37	61	)	)	PUNCT
ejpam-4828	37	62	,	,	PUNCT
ejpam-4828	37	63	is	be	AUX
ejpam-4828	37	64	called	call	VERB
ejpam-4828	37	65	the	the	DET
ejpam-4828	37	66	convexity	convexity	NOUN
ejpam-4828	37	67	number	number	NOUN
ejpam-4828	37	68	of	of	ADP
ejpam-4828	37	69	g.	g.	PROPN
ejpam-4828	37	70	a	a	DET
ejpam-4828	37	71	set	set	NOUN
ejpam-4828	37	72	s	s	PROPN
ejpam-4828	37	73	⊆	⊆	NUM
ejpam-4828	37	74	v	v	NOUN
ejpam-4828	37	75	(	(	PUNCT
ejpam-4828	37	76	g	g	NOUN
ejpam-4828	37	77	)	)	PUNCT
ejpam-4828	37	78	is	be	AUX
ejpam-4828	37	79	convex	convex	VERB
ejpam-4828	37	80	dominating	dominate	VERB
ejpam-4828	37	81	if	if	SCONJ
ejpam-4828	37	82	s	s	VERB
ejpam-4828	37	83	is	be	AUX
ejpam-4828	37	84	both	both	PRON
ejpam-4828	37	85	convex	convex	ADJ
ejpam-4828	37	86	and	and	CCONJ
ejpam-4828	37	87	dominating	dominating	NOUN
ejpam-4828	37	88	.	.	PUNCT
ejpam-4828	38	1	the	the	DET
ejpam-4828	38	2	minimum	minimum	ADJ
ejpam-4828	38	3	cardinality	cardinality	NOUN
ejpam-4828	38	4	among	among	ADP
ejpam-4828	38	5	all	all	DET
ejpam-4828	38	6	convex	convex	ADJ
ejpam-4828	38	7	dominating	dominating	NOUN
ejpam-4828	38	8	sets	set	NOUN
ejpam-4828	38	9	in	in	ADP
ejpam-4828	38	10	g	g	NOUN
ejpam-4828	38	11	,	,	PUNCT
ejpam-4828	38	12	denoted	denote	VERB
ejpam-4828	38	13	by	by	ADP
ejpam-4828	38	14	γcon(g	γcon(g	NOUN
ejpam-4828	38	15	)	)	PUNCT
ejpam-4828	38	16	is	be	AUX
ejpam-4828	38	17	called	call	VERB
ejpam-4828	38	18	the	the	DET
ejpam-4828	38	19	convex	convex	ADJ
ejpam-4828	38	20	domination	domination	NOUN
ejpam-4828	38	21	number	number	NOUN
ejpam-4828	38	22	of	of	ADP
ejpam-4828	38	23	g.	g.	PROPN
ejpam-4828	38	24	a	a	DET
ejpam-4828	38	25	function	function	NOUN
ejpam-4828	38	26	f	f	NOUN
ejpam-4828	38	27	:	:	PUNCT
ejpam-4828	38	28	v	v	X
ejpam-4828	38	29	(	(	PUNCT
ejpam-4828	38	30	g	g	NOUN
ejpam-4828	38	31	)	)	PUNCT
ejpam-4828	38	32	→	→	SYM
ejpam-4828	38	33	{	{	PUNCT
ejpam-4828	38	34	0	0	NUM
ejpam-4828	38	35	,	,	PUNCT
ejpam-4828	38	36	1	1	NUM
ejpam-4828	38	37	,	,	PUNCT
ejpam-4828	38	38	2	2	NUM
ejpam-4828	38	39	}	}	PUNCT
ejpam-4828	38	40	is	be	AUX
ejpam-4828	38	41	a	a	DET
ejpam-4828	38	42	roman	roman	ADJ
ejpam-4828	38	43	dominating	dominating	NOUN
ejpam-4828	38	44	function	function	NOUN
ejpam-4828	38	45	(	(	PUNCT
ejpam-4828	38	46	or	or	CCONJ
ejpam-4828	38	47	just	just	ADV
ejpam-4828	38	48	rdf	rdf	VERB
ejpam-4828	38	49	)	)	PUNCT
ejpam-4828	38	50	if	if	SCONJ
ejpam-4828	38	51	every	every	DET
ejpam-4828	38	52	vertex	vertex	NOUN
ejpam-4828	38	53	u	u	NOUN
ejpam-4828	38	54	for	for	ADP
ejpam-4828	38	55	which	which	PRON
ejpam-4828	38	56	f(u	f(u	PROPN
ejpam-4828	38	57	)	)	PUNCT
ejpam-4828	39	1	=	=	SYM
ejpam-4828	39	2	0	0	NUM
ejpam-4828	39	3	is	be	AUX
ejpam-4828	39	4	adjacent	adjacent	ADJ
ejpam-4828	39	5	to	to	ADP
ejpam-4828	39	6	at	at	ADV
ejpam-4828	39	7	least	least	ADV
ejpam-4828	39	8	one	one	NUM
ejpam-4828	39	9	vertex	vertex	NOUN
ejpam-4828	39	10	v	v	NOUN
ejpam-4828	39	11	for	for	ADP
ejpam-4828	39	12	which	which	PRON
ejpam-4828	39	13	f(v	f(v	NOUN
ejpam-4828	39	14	)	)	PUNCT
ejpam-4828	39	15	=	=	SYM
ejpam-4828	40	1	2	2	X
ejpam-4828	40	2	.	.	PUNCT
ejpam-4828	40	3	the	the	DET
ejpam-4828	40	4	weight	weight	NOUN
ejpam-4828	40	5	of	of	ADP
ejpam-4828	40	6	an	an	DET
ejpam-4828	40	7	rdf	rdf	NOUN
ejpam-4828	40	8	f	f	NOUN
ejpam-4828	40	9	is	be	AUX
ejpam-4828	40	10	given	give	VERB
ejpam-4828	40	11	by	by	ADP
ejpam-4828	40	12	ωg(f	ωg(f	NOUN
ejpam-4828	40	13	)	)	PUNCT
ejpam-4828	40	14	=	=	SYM
ejpam-4828	40	15	∑	∑	PUNCT
ejpam-4828	40	16	v∈v	v∈v	PROPN
ejpam-4828	40	17	(	(	PUNCT
ejpam-4828	40	18	g	g	NOUN
ejpam-4828	40	19	)	)	PUNCT
ejpam-4828	40	20	f(v	f(v	NOUN
ejpam-4828	40	21	)	)	PUNCT
ejpam-4828	40	22	.	.	PUNCT
ejpam-4828	41	1	the	the	DET
ejpam-4828	41	2	roman	roman	ADJ
ejpam-4828	41	3	domination	domination	NOUN
ejpam-4828	41	4	number	number	NOUN
ejpam-4828	41	5	of	of	ADP
ejpam-4828	41	6	a	a	DET
ejpam-4828	41	7	graph	graph	NOUN
ejpam-4828	41	8	g	g	NOUN
ejpam-4828	41	9	,	,	PUNCT
ejpam-4828	41	10	denoted	denote	VERB
ejpam-4828	41	11	by	by	ADP
ejpam-4828	41	12	γr(g	γr(g	PROPN
ejpam-4828	41	13	)	)	PUNCT
ejpam-4828	41	14	,	,	PUNCT
ejpam-4828	41	15	is	be	AUX
ejpam-4828	41	16	the	the	DET
ejpam-4828	41	17	minimum	minimum	ADJ
ejpam-4828	41	18	weight	weight	NOUN
ejpam-4828	41	19	of	of	ADP
ejpam-4828	41	20	an	an	DET
ejpam-4828	41	21	rdf	rdf	NOUN
ejpam-4828	41	22	in	in	ADP
ejpam-4828	41	23	g.	g.	PROPN
ejpam-4828	41	24	any	any	DET
ejpam-4828	41	25	rdf	rdf	VERB
ejpam-4828	41	26	f	f	NOUN
ejpam-4828	41	27	on	on	ADP
ejpam-4828	41	28	g	g	NOUN
ejpam-4828	41	29	with	with	ADP
ejpam-4828	41	30	ωg(f	ωg(f	NOUN
ejpam-4828	41	31	)	)	PUNCT
ejpam-4828	41	32	=	=	SYM
ejpam-4828	41	33	γr(g	γr(g	NOUN
ejpam-4828	41	34	)	)	PUNCT
ejpam-4828	41	35	is	be	AUX
ejpam-4828	41	36	called	call	VERB
ejpam-4828	41	37	a	a	DET
ejpam-4828	41	38	γr	γr	PROPN
ejpam-4828	41	39	-	-	NOUN
ejpam-4828	41	40	function	function	NOUN
ejpam-4828	41	41	.	.	PUNCT
ejpam-4828	42	1	if	if	SCONJ
ejpam-4828	42	2	f	f	PROPN
ejpam-4828	42	3	=	=	SYM
ejpam-4828	42	4	(	(	PUNCT
ejpam-4828	42	5	v0	v0	PROPN
ejpam-4828	42	6	,	,	PUNCT
ejpam-4828	42	7	v1	v1	NOUN
ejpam-4828	42	8	,	,	PUNCT
ejpam-4828	42	9	v2	v2	PROPN
ejpam-4828	42	10	)	)	PUNCT
ejpam-4828	42	11	is	be	AUX
ejpam-4828	42	12	an	an	DET
ejpam-4828	42	13	rdf	rdf	NOUN
ejpam-4828	42	14	in	in	ADP
ejpam-4828	42	15	g	g	NOUN
ejpam-4828	42	16	,	,	PUNCT
ejpam-4828	42	17	then	then	ADV
ejpam-4828	42	18	ωg(f	ωg(f	NOUN
ejpam-4828	42	19	)	)	PUNCT
ejpam-4828	42	20	=	=	PUNCT
ejpam-4828	42	21	|v1|+	|v1|+	DET
ejpam-4828	42	22	2|v2|	2|v2|	NUM
ejpam-4828	42	23	.	.	PUNCT
ejpam-4828	43	1	a	a	DET
ejpam-4828	43	2	function	function	NOUN
ejpam-4828	43	3	f	f	X
ejpam-4828	43	4	=	=	SYM
ejpam-4828	43	5	(	(	PUNCT
ejpam-4828	43	6	v0	v0	PROPN
ejpam-4828	43	7	,	,	PUNCT
ejpam-4828	43	8	v1	v1	NOUN
ejpam-4828	43	9	,	,	PUNCT
ejpam-4828	43	10	v2	v2	PROPN
ejpam-4828	43	11	)	)	PUNCT
ejpam-4828	43	12	is	be	AUX
ejpam-4828	43	13	called	call	VERB
ejpam-4828	43	14	connected	connected	ADJ
ejpam-4828	43	15	roman	roman	ADJ
ejpam-4828	43	16	dominating	dominating	NOUN
ejpam-4828	43	17	function	function	NOUN
ejpam-4828	43	18	(	(	PUNCT
ejpam-4828	43	19	crdf	crdf	NOUN
ejpam-4828	43	20	)	)	PUNCT
ejpam-4828	43	21	in	in	ADP
ejpam-4828	43	22	g	g	PROPN
ejpam-4828	43	23	if	if	SCONJ
ejpam-4828	43	24	⟨v1	⟨v1	PROPN
ejpam-4828	43	25	∪	∪	ADP
ejpam-4828	43	26	v2⟩	v2⟩	PROPN
ejpam-4828	43	27	is	be	AUX
ejpam-4828	43	28	connected	connect	VERB
ejpam-4828	43	29	.	.	PUNCT
ejpam-4828	44	1	the	the	DET
ejpam-4828	44	2	weight	weight	NOUN
ejpam-4828	44	3	of	of	ADP
ejpam-4828	44	4	a	a	DET
ejpam-4828	44	5	connected	connected	ADJ
ejpam-4828	44	6	roman	roman	ADJ
ejpam-4828	44	7	dominating	dominating	NOUN
ejpam-4828	44	8	function	function	NOUN
ejpam-4828	44	9	f	f	PROPN
ejpam-4828	44	10	=	=	SYM
ejpam-4828	44	11	(	(	PUNCT
ejpam-4828	44	12	v0	v0	PROPN
ejpam-4828	44	13	,	,	PUNCT
ejpam-4828	44	14	v1	v1	NOUN
ejpam-4828	44	15	,	,	PUNCT
ejpam-4828	44	16	v2	v2	PROPN
ejpam-4828	44	17	)	)	PUNCT
ejpam-4828	44	18	in	in	ADP
ejpam-4828	44	19	g	g	PROPN
ejpam-4828	44	20	is	be	AUX
ejpam-4828	44	21	given	give	VERB
ejpam-4828	44	22	by	by	ADP
ejpam-4828	44	23	ωcr	ωcr	PRON
ejpam-4828	44	24	g	g	PROPN
ejpam-4828	44	25	(	(	PUNCT
ejpam-4828	44	26	f	f	X
ejpam-4828	44	27	)	)	PUNCT
ejpam-4828	44	28	=	=	PUNCT
ejpam-4828	44	29	|v1|+2|v2|	|v1|+2|v2|	NOUN
ejpam-4828	44	30	.	.	PUNCT
ejpam-4828	45	1	the	the	DET
ejpam-4828	45	2	connected	connect	VERB
ejpam-4828	45	3	roman	roman	ADJ
ejpam-4828	45	4	domination	domination	NOUN
ejpam-4828	45	5	number	number	NOUN
ejpam-4828	45	6	γcr(g	γcr(g	PROPN
ejpam-4828	45	7	)	)	PUNCT
ejpam-4828	45	8	is	be	AUX
ejpam-4828	45	9	the	the	DET
ejpam-4828	45	10	minimum	minimum	ADJ
ejpam-4828	45	11	weight	weight	NOUN
ejpam-4828	45	12	of	of	ADP
ejpam-4828	45	13	a	a	DET
ejpam-4828	45	14	crdf	crdf	NOUN
ejpam-4828	45	15	in	in	ADP
ejpam-4828	45	16	g.	g.	PROPN
ejpam-4828	45	17	any	any	DET
ejpam-4828	45	18	crdf	crdf	NOUN
ejpam-4828	45	19	f	f	X
ejpam-4828	45	20	in	in	ADP
ejpam-4828	45	21	g	g	PROPN
ejpam-4828	45	22	with	with	ADP
ejpam-4828	45	23	ωcr	ωcr	PROPN
ejpam-4828	45	24	g	g	PROPN
ejpam-4828	45	25	(	(	PUNCT
ejpam-4828	45	26	f	f	X
ejpam-4828	45	27	)	)	PUNCT
ejpam-4828	45	28	=	=	SYM
ejpam-4828	45	29	γcr(g	γcr(g	PROPN
ejpam-4828	45	30	)	)	PUNCT
ejpam-4828	45	31	is	be	AUX
ejpam-4828	45	32	called	call	VERB
ejpam-4828	45	33	a	a	DET
ejpam-4828	45	34	γcr	γcr	ADJ
ejpam-4828	45	35	-	-	PUNCT
ejpam-4828	45	36	function	function	NOUN
ejpam-4828	45	37	.	.	PUNCT
ejpam-4828	46	1	r.	r.	PROPN
ejpam-4828	46	2	fortosa	fortosa	PROPN
ejpam-4828	46	3	,	,	PUNCT
ejpam-4828	46	4	s.	s.	PROPN
ejpam-4828	46	5	canoy	canoy	PROPN
ejpam-4828	46	6	jr	jr	PROPN
ejpam-4828	46	7	.	.	PROPN
ejpam-4828	46	8	/	/	SYM
ejpam-4828	46	9	eur	eur	PROPN
ejpam-4828	46	10	.	.	PUNCT
ejpam-4828	47	1	j.	j.	PROPN
ejpam-4828	47	2	pure	pure	PROPN
ejpam-4828	47	3	appl	appl	PROPN
ejpam-4828	47	4	.	.	PROPN
ejpam-4828	47	5	math	math	PROPN
ejpam-4828	47	6	,	,	PUNCT
ejpam-4828	47	7	16	16	NUM
ejpam-4828	47	8	(	(	PUNCT
ejpam-4828	47	9	3	3	NUM
ejpam-4828	47	10	)	)	PUNCT
ejpam-4828	47	11	(	(	PUNCT
ejpam-4828	47	12	2023	2023	NUM
ejpam-4828	47	13	)	)	PUNCT
ejpam-4828	47	14	,	,	PUNCT
ejpam-4828	47	15	1705	1705	NUM
ejpam-4828	47	16	-	-	SYM
ejpam-4828	47	17	1716	1716	NUM
ejpam-4828	47	18	1707	1707	NUM
ejpam-4828	47	19	a	a	DET
ejpam-4828	47	20	roman	roman	ADJ
ejpam-4828	47	21	dominating	dominating	NOUN
ejpam-4828	47	22	function	function	NOUN
ejpam-4828	47	23	f	f	PROPN
ejpam-4828	47	24	=	=	SYM
ejpam-4828	47	25	(	(	PUNCT
ejpam-4828	47	26	v0	v0	PROPN
ejpam-4828	47	27	,	,	PUNCT
ejpam-4828	47	28	v1	v1	NOUN
ejpam-4828	47	29	,	,	PUNCT
ejpam-4828	47	30	v2	v2	PROPN
ejpam-4828	47	31	)	)	PUNCT
ejpam-4828	47	32	on	on	ADP
ejpam-4828	47	33	g	g	PROPN
ejpam-4828	47	34	is	be	AUX
ejpam-4828	47	35	a	a	DET
ejpam-4828	47	36	convex	convex	ADJ
ejpam-4828	47	37	roman	roman	ADJ
ejpam-4828	47	38	dominating	dominating	NOUN
ejpam-4828	47	39	function	function	NOUN
ejpam-4828	47	40	(	(	PUNCT
ejpam-4828	47	41	or	or	CCONJ
ejpam-4828	47	42	cvrdf	cvrdf	NOUN
ejpam-4828	47	43	)	)	PUNCT
ejpam-4828	47	44	if	if	SCONJ
ejpam-4828	47	45	v1	v1	NOUN
ejpam-4828	47	46	∪	∪	VERB
ejpam-4828	47	47	v2	v2	PROPN
ejpam-4828	47	48	is	be	AUX
ejpam-4828	47	49	convex	convex	NOUN
ejpam-4828	47	50	.	.	PUNCT
ejpam-4828	48	1	the	the	DET
ejpam-4828	48	2	weight	weight	NOUN
ejpam-4828	48	3	of	of	ADP
ejpam-4828	48	4	a	a	DET
ejpam-4828	48	5	convex	convex	ADJ
ejpam-4828	48	6	roman	roman	ADJ
ejpam-4828	48	7	dominating	dominating	NOUN
ejpam-4828	48	8	function	function	NOUN
ejpam-4828	48	9	f	f	PROPN
ejpam-4828	48	10	=	=	SYM
ejpam-4828	48	11	(	(	PUNCT
ejpam-4828	48	12	v0	v0	PROPN
ejpam-4828	48	13	,	,	PUNCT
ejpam-4828	48	14	v1	v1	NOUN
ejpam-4828	48	15	,	,	PUNCT
ejpam-4828	48	16	v2	v2	PROPN
ejpam-4828	48	17	)	)	PUNCT
ejpam-4828	48	18	in	in	ADP
ejpam-4828	48	19	g	g	PROPN
ejpam-4828	48	20	is	be	AUX
ejpam-4828	48	21	given	give	VERB
ejpam-4828	48	22	by	by	ADP
ejpam-4828	48	23	ωcvr	ωcvr	PROPN
ejpam-4828	48	24	g	g	PROPN
ejpam-4828	48	25	(	(	PUNCT
ejpam-4828	48	26	f	f	X
ejpam-4828	48	27	)	)	PUNCT
ejpam-4828	48	28	=	=	PUNCT
ejpam-4828	48	29	|v1|+2|v2|	|v1|+2|v2|	NOUN
ejpam-4828	48	30	.	.	PUNCT
ejpam-4828	49	1	the	the	DET
ejpam-4828	49	2	minimum	minimum	ADJ
ejpam-4828	49	3	weight	weight	NOUN
ejpam-4828	49	4	of	of	ADP
ejpam-4828	49	5	a	a	DET
ejpam-4828	49	6	cvrdf	cvrdf	NOUN
ejpam-4828	49	7	on	on	ADP
ejpam-4828	49	8	g	g	NOUN
ejpam-4828	49	9	,	,	PUNCT
ejpam-4828	49	10	denoted	denote	VERB
ejpam-4828	49	11	by	by	ADP
ejpam-4828	49	12	γcvr(g	γcvr(g	PROPN
ejpam-4828	49	13	)	)	PUNCT
ejpam-4828	49	14	,	,	PUNCT
ejpam-4828	49	15	is	be	AUX
ejpam-4828	49	16	called	call	VERB
ejpam-4828	49	17	the	the	DET
ejpam-4828	49	18	convex	convex	ADJ
ejpam-4828	49	19	roman	roman	ADJ
ejpam-4828	49	20	domination	domination	NOUN
ejpam-4828	49	21	number	number	NOUN
ejpam-4828	49	22	of	of	ADP
ejpam-4828	49	23	g.	g.	PROPN
ejpam-4828	49	24	any	any	DET
ejpam-4828	49	25	cvrdf	cvrdf	NOUN
ejpam-4828	49	26	f	f	PROPN
ejpam-4828	49	27	in	in	ADP
ejpam-4828	49	28	g	g	PROPN
ejpam-4828	49	29	with	with	ADP
ejpam-4828	49	30	ωcvr	ωcvr	PROPN
ejpam-4828	49	31	g	g	PROPN
ejpam-4828	49	32	(	(	PUNCT
ejpam-4828	49	33	f	f	X
ejpam-4828	49	34	)	)	PUNCT
ejpam-4828	49	35	=	=	SYM
ejpam-4828	49	36	γcvr(g	γcvr(g	NOUN
ejpam-4828	49	37	)	)	PUNCT
ejpam-4828	49	38	is	be	AUX
ejpam-4828	49	39	called	call	VERB
ejpam-4828	49	40	a	a	DET
ejpam-4828	49	41	γcvr	γcvr	NOUN
ejpam-4828	49	42	-	-	PUNCT
ejpam-4828	49	43	function	function	NOUN
ejpam-4828	49	44	.	.	PUNCT
ejpam-4828	50	1	a	a	DET
ejpam-4828	50	2	complete	complete	ADJ
ejpam-4828	50	3	k	k	ADJ
ejpam-4828	50	4	-	-	ADJ
ejpam-4828	50	5	partite	partite	ADJ
ejpam-4828	50	6	graph	graph	NOUN
ejpam-4828	50	7	g	g	PROPN
ejpam-4828	50	8	is	be	AUX
ejpam-4828	50	9	a	a	DET
ejpam-4828	50	10	k	k	ADJ
ejpam-4828	50	11	-	-	ADJ
ejpam-4828	50	12	partite	partite	ADJ
ejpam-4828	50	13	graph	graph	NOUN
ejpam-4828	50	14	with	with	ADP
ejpam-4828	50	15	partite	partite	ADJ
ejpam-4828	50	16	sets	set	NOUN
ejpam-4828	50	17	sn1	sn1	PROPN
ejpam-4828	50	18	,	,	PUNCT
ejpam-4828	50	19	sn2	sn2	PROPN
ejpam-4828	50	20	,	,	PUNCT
ejpam-4828	50	21	.	.	PUNCT
ejpam-4828	50	22	.	.	PUNCT
ejpam-4828	51	1	.	.	PUNCT
ejpam-4828	52	1	,	,	PUNCT
ejpam-4828	52	2	snk	snk	PROPN
ejpam-4828	52	3	having	have	VERB
ejpam-4828	52	4	the	the	DET
ejpam-4828	52	5	added	add	VERB
ejpam-4828	52	6	property	property	NOUN
ejpam-4828	52	7	that	that	SCONJ
ejpam-4828	52	8	if	if	SCONJ
ejpam-4828	52	9	u	u	PROPN
ejpam-4828	52	10	∈	∈	PROPN
ejpam-4828	52	11	sni	sni	PROPN
ejpam-4828	52	12	and	and	CCONJ
ejpam-4828	52	13	v	v	ADP
ejpam-4828	52	14	∈	∈	PROPN
ejpam-4828	52	15	snj	snj	NOUN
ejpam-4828	52	16	,	,	PUNCT
ejpam-4828	52	17	i	i	PRON
ejpam-4828	52	18	̸=	̸=	PROPN
ejpam-4828	52	19	j	j	PROPN
ejpam-4828	52	20	,	,	PUNCT
ejpam-4828	52	21	then	then	ADV
ejpam-4828	52	22	uv	uv	PROPN
ejpam-4828	52	23	∈	∈	PROPN
ejpam-4828	52	24	e(g	e(g	PROPN
ejpam-4828	52	25	)	)	PUNCT
ejpam-4828	52	26	.	.	PUNCT
ejpam-4828	53	1	if	if	SCONJ
ejpam-4828	53	2	|sni	|sni	NOUN
ejpam-4828	53	3	|	|	NOUN
ejpam-4828	53	4	=	=	SYM
ejpam-4828	53	5	ni	ni	PROPN
ejpam-4828	53	6	,	,	PUNCT
ejpam-4828	53	7	then	then	ADV
ejpam-4828	53	8	this	this	DET
ejpam-4828	53	9	graph	graph	NOUN
ejpam-4828	53	10	is	be	AUX
ejpam-4828	53	11	denoted	denote	VERB
ejpam-4828	53	12	by	by	ADP
ejpam-4828	53	13	kn1,n2,	kn1,n2,	NOUN
ejpam-4828	53	14	...	...	PUNCT
ejpam-4828	53	15	,nk	,nk	PUNCT
ejpam-4828	53	16	.	.	PUNCT
ejpam-4828	54	1	the	the	DET
ejpam-4828	54	2	join	join	NOUN
ejpam-4828	54	3	of	of	ADP
ejpam-4828	54	4	two	two	NUM
ejpam-4828	54	5	graphs	graph	NOUN
ejpam-4828	54	6	g	g	NOUN
ejpam-4828	54	7	and	and	CCONJ
ejpam-4828	54	8	h	h	NOUN
ejpam-4828	54	9	,	,	PUNCT
ejpam-4828	54	10	denoted	denote	VERB
ejpam-4828	54	11	by	by	ADP
ejpam-4828	54	12	g	g	PROPN
ejpam-4828	54	13	+	+	PROPN
ejpam-4828	54	14	h	h	NOUN
ejpam-4828	54	15	,	,	PUNCT
ejpam-4828	54	16	is	be	AUX
ejpam-4828	54	17	the	the	DET
ejpam-4828	54	18	graph	graph	NOUN
ejpam-4828	54	19	with	with	ADP
ejpam-4828	54	20	v	v	NOUN
ejpam-4828	54	21	(	(	PUNCT
ejpam-4828	54	22	g+h	g+h	NOUN
ejpam-4828	54	23	)	)	PUNCT
ejpam-4828	54	24	=	=	SYM
ejpam-4828	54	25	v	v	X
ejpam-4828	54	26	(	(	PUNCT
ejpam-4828	54	27	g)∪v	g)∪v	NOUN
ejpam-4828	54	28	(	(	PUNCT
ejpam-4828	54	29	h	h	NOUN
ejpam-4828	54	30	)	)	PUNCT
ejpam-4828	54	31	and	and	CCONJ
ejpam-4828	54	32	e(g+h	e(g+h	NUM
ejpam-4828	54	33	)	)	PUNCT
ejpam-4828	55	1	=	=	PUNCT
ejpam-4828	55	2	e(g)∪e(h)∪{uv	e(g)∪e(h)∪{uv	X
ejpam-4828	55	3	:	:	PUNCT
ejpam-4828	55	4	u	u	PROPN
ejpam-4828	55	5	∈	∈	PROPN
ejpam-4828	55	6	v	v	ADP
ejpam-4828	55	7	(	(	PUNCT
ejpam-4828	55	8	g	g	NOUN
ejpam-4828	55	9	)	)	PUNCT
ejpam-4828	55	10	and	and	CCONJ
ejpam-4828	55	11	v	v	ADP
ejpam-4828	55	12	∈	∈	NOUN
ejpam-4828	55	13	v	v	NOUN
ejpam-4828	55	14	(	(	PUNCT
ejpam-4828	55	15	g	g	NOUN
ejpam-4828	55	16	)	)	PUNCT
ejpam-4828	55	17	}	}	PUNCT
ejpam-4828	55	18	,	,	PUNCT
ejpam-4828	55	19	where	where	SCONJ
ejpam-4828	55	20	“	"	PUNCT
ejpam-4828	55	21	∪	∪	NOUN
ejpam-4828	55	22	”	"	PUNCT
ejpam-4828	55	23	refers	refer	VERB
ejpam-4828	55	24	to	to	ADP
ejpam-4828	55	25	a	a	DET
ejpam-4828	55	26	disjoint	disjoint	NOUN
ejpam-4828	55	27	union	union	NOUN
ejpam-4828	55	28	of	of	ADP
ejpam-4828	55	29	sets	set	NOUN
ejpam-4828	55	30	.	.	PUNCT
ejpam-4828	56	1	2	2	X
ejpam-4828	56	2	.	.	X
ejpam-4828	56	3	known	know	VERB
ejpam-4828	56	4	results	result	NOUN
ejpam-4828	56	5	cyman	cyman	NOUN
ejpam-4828	56	6	et	et	PROPN
ejpam-4828	56	7	al	al	PROPN
ejpam-4828	56	8	.	.	PUNCT
ejpam-4828	57	1	[	[	X
ejpam-4828	57	2	19	19	NUM
ejpam-4828	57	3	]	]	PUNCT
ejpam-4828	57	4	investigated	investigate	VERB
ejpam-4828	57	5	those	those	DET
ejpam-4828	57	6	graphs	graph	NOUN
ejpam-4828	57	7	which	which	PRON
ejpam-4828	57	8	have	have	VERB
ejpam-4828	57	9	convex	convex	NOUN
ejpam-4828	57	10	domination	domination	NOUN
ejpam-4828	57	11	number	number	NOUN
ejpam-4828	57	12	close	close	ADJ
ejpam-4828	57	13	to	to	ADP
ejpam-4828	57	14	their	their	PRON
ejpam-4828	57	15	orders	order	NOUN
ejpam-4828	57	16	.	.	PUNCT
ejpam-4828	58	1	they	they	PRON
ejpam-4828	58	2	generated	generate	VERB
ejpam-4828	58	3	the	the	DET
ejpam-4828	58	4	following	follow	VERB
ejpam-4828	58	5	results	result	NOUN
ejpam-4828	58	6	which	which	PRON
ejpam-4828	58	7	will	will	AUX
ejpam-4828	58	8	be	be	AUX
ejpam-4828	58	9	used	use	VERB
ejpam-4828	58	10	in	in	ADP
ejpam-4828	58	11	this	this	DET
ejpam-4828	58	12	study	study	NOUN
ejpam-4828	58	13	.	.	PUNCT
ejpam-4828	59	1	theorem	theorem	NOUN
ejpam-4828	59	2	1	1	X
ejpam-4828	59	3	.	.	PUNCT
ejpam-4828	60	1	let	let	VERB
ejpam-4828	60	2	g	g	PRON
ejpam-4828	60	3	be	be	AUX
ejpam-4828	60	4	a	a	DET
ejpam-4828	60	5	connected	connected	ADJ
ejpam-4828	60	6	graph	graph	NOUN
ejpam-4828	60	7	with	with	ADP
ejpam-4828	60	8	n	n	NUM
ejpam-4828	60	9	≥	≥	NUM
ejpam-4828	60	10	5	5	NUM
ejpam-4828	60	11	.	.	PUNCT
ejpam-4828	61	1	if	if	SCONJ
ejpam-4828	61	2	γcon(g	γcon(g	PROPN
ejpam-4828	61	3	)	)	PUNCT
ejpam-4828	61	4	=	=	SYM
ejpam-4828	62	1	n	n	CCONJ
ejpam-4828	62	2	,	,	PUNCT
ejpam-4828	62	3	then	then	ADV
ejpam-4828	62	4	△	△	X
ejpam-4828	62	5	(	(	PUNCT
ejpam-4828	62	6	g	g	NOUN
ejpam-4828	62	7	)	)	PUNCT
ejpam-4828	62	8	≤	≤	NUM
ejpam-4828	62	9	n−	n−	NOUN
ejpam-4828	62	10	4	4	NUM
ejpam-4828	62	11	.	.	PUNCT
ejpam-4828	62	12	corollary	corollary	ADJ
ejpam-4828	63	1	1	1	NUM
ejpam-4828	63	2	.	.	PUNCT
ejpam-4828	64	1	if	if	SCONJ
ejpam-4828	64	2	γcon(g	γcon(g	PROPN
ejpam-4828	64	3	)	)	PUNCT
ejpam-4828	64	4	=	=	SYM
ejpam-4828	65	1	n	n	PROPN
ejpam-4828	65	2	and	and	CCONJ
ejpam-4828	65	3	g	g	PROPN
ejpam-4828	65	4	̸=	̸=	PROPN
ejpam-4828	65	5	k1	k1	NOUN
ejpam-4828	65	6	,	,	PUNCT
ejpam-4828	65	7	then	then	ADV
ejpam-4828	65	8	2	2	NUM
ejpam-4828	65	9	≤	≤	NUM
ejpam-4828	65	10	δ(g	δ(g	ADP
ejpam-4828	65	11	)	)	PUNCT
ejpam-4828	65	12	≤	≤	NUM
ejpam-4828	65	13	△	△	X
ejpam-4828	65	14	(	(	PUNCT
ejpam-4828	65	15	g	g	NOUN
ejpam-4828	65	16	)	)	PUNCT
ejpam-4828	65	17	≤	≤	NUM
ejpam-4828	65	18	n−	n−	NOUN
ejpam-4828	65	19	4	4	NUM
ejpam-4828	65	20	.	.	PUNCT
ejpam-4828	65	21	corollary	corollary	ADJ
ejpam-4828	66	1	2	2	NUM
ejpam-4828	66	2	.	.	PUNCT
ejpam-4828	67	1	if	if	SCONJ
ejpam-4828	67	2	γcon(g	γcon(g	PROPN
ejpam-4828	67	3	)	)	PUNCT
ejpam-4828	67	4	=	=	SYM
ejpam-4828	68	1	n	n	PROPN
ejpam-4828	68	2	and	and	CCONJ
ejpam-4828	68	3	g	g	PROPN
ejpam-4828	68	4	̸=	̸=	PROPN
ejpam-4828	68	5	k1	k1	NOUN
ejpam-4828	68	6	,	,	PUNCT
ejpam-4828	68	7	then	then	ADV
ejpam-4828	68	8	n	n	PRON
ejpam-4828	68	9	≥	≥	NOUN
ejpam-4828	68	10	6	6	NUM
ejpam-4828	68	11	.	.	NOUN
ejpam-4828	68	12	3	3	NUM
ejpam-4828	68	13	.	.	NOUN
ejpam-4828	68	14	results	result	NOUN
ejpam-4828	68	15	it	it	PRON
ejpam-4828	68	16	is	be	AUX
ejpam-4828	68	17	well	well	ADV
ejpam-4828	68	18	-	-	PUNCT
ejpam-4828	68	19	known	know	VERB
ejpam-4828	68	20	that	that	SCONJ
ejpam-4828	68	21	every	every	DET
ejpam-4828	68	22	convex	convex	NOUN
ejpam-4828	68	23	set	set	VERB
ejpam-4828	68	24	in	in	ADP
ejpam-4828	68	25	a	a	DET
ejpam-4828	68	26	connected	connected	ADJ
ejpam-4828	68	27	graph	graph	NOUN
ejpam-4828	68	28	induces	induce	VERB
ejpam-4828	68	29	a	a	DET
ejpam-4828	68	30	connected	connected	ADJ
ejpam-4828	68	31	graph	graph	NOUN
ejpam-4828	68	32	.	.	PUNCT
ejpam-4828	69	1	remark	remark	NOUN
ejpam-4828	69	2	1	1	NUM
ejpam-4828	69	3	.	.	PUNCT
ejpam-4828	70	1	every	every	DET
ejpam-4828	70	2	convex	convex	ADJ
ejpam-4828	70	3	roman	roman	ADJ
ejpam-4828	70	4	dominating	dominating	NOUN
ejpam-4828	70	5	function	function	NOUN
ejpam-4828	70	6	is	be	AUX
ejpam-4828	70	7	a	a	DET
ejpam-4828	70	8	connected	connected	ADJ
ejpam-4828	70	9	roman	roman	ADJ
ejpam-4828	70	10	dominating	dominating	NOUN
ejpam-4828	70	11	function	function	NOUN
ejpam-4828	70	12	.	.	PUNCT
ejpam-4828	71	1	hence	hence	ADV
ejpam-4828	71	2	,	,	PUNCT
ejpam-4828	71	3	γcvr(g	γcvr(g	PROPN
ejpam-4828	71	4	)	)	PUNCT
ejpam-4828	71	5	≥	≥	NOUN
ejpam-4828	71	6	γcr(g	γcr(g	PROPN
ejpam-4828	71	7	)	)	PUNCT
ejpam-4828	71	8	.	.	PUNCT
ejpam-4828	72	1	the	the	DET
ejpam-4828	72	2	next	next	ADJ
ejpam-4828	72	3	result	result	NOUN
ejpam-4828	72	4	shows	show	VERB
ejpam-4828	72	5	that	that	SCONJ
ejpam-4828	72	6	every	every	DET
ejpam-4828	72	7	pair	pair	NOUN
ejpam-4828	72	8	of	of	ADP
ejpam-4828	72	9	positive	positive	ADJ
ejpam-4828	72	10	integers	integer	NOUN
ejpam-4828	72	11	are	be	AUX
ejpam-4828	72	12	realizable	realizable	ADJ
ejpam-4828	72	13	as	as	ADP
ejpam-4828	72	14	the	the	DET
ejpam-4828	72	15	connected	connected	ADJ
ejpam-4828	72	16	roman	roman	ADJ
ejpam-4828	72	17	domination	domination	NOUN
ejpam-4828	72	18	number	number	NOUN
ejpam-4828	72	19	and	and	CCONJ
ejpam-4828	72	20	convex	convex	VERB
ejpam-4828	72	21	roman	roman	ADJ
ejpam-4828	72	22	domination	domination	NOUN
ejpam-4828	72	23	number	number	NOUN
ejpam-4828	72	24	of	of	ADP
ejpam-4828	72	25	a	a	DET
ejpam-4828	72	26	connected	connected	ADJ
ejpam-4828	72	27	graph	graph	NOUN
ejpam-4828	72	28	.	.	PUNCT
ejpam-4828	73	1	theorem	theorem	NOUN
ejpam-4828	73	2	2	2	NUM
ejpam-4828	73	3	.	.	PUNCT
ejpam-4828	73	4	let	let	VERB
ejpam-4828	73	5	a	a	PRON
ejpam-4828	73	6	and	and	CCONJ
ejpam-4828	73	7	b	b	NOUN
ejpam-4828	73	8	be	be	AUX
ejpam-4828	73	9	positive	positive	ADJ
ejpam-4828	73	10	integers	integer	NOUN
ejpam-4828	73	11	such	such	ADJ
ejpam-4828	73	12	that	that	SCONJ
ejpam-4828	73	13	4	4	NUM
ejpam-4828	73	14	≤	≤	NUM
ejpam-4828	73	15	a	a	DET
ejpam-4828	73	16	≤	≤	PROPN
ejpam-4828	73	17	b.	b.	NOUN
ejpam-4828	74	1	then	then	ADV
ejpam-4828	74	2	there	there	PRON
ejpam-4828	74	3	exists	exist	VERB
ejpam-4828	74	4	a	a	DET
ejpam-4828	74	5	connected	connected	ADJ
ejpam-4828	74	6	graph	graph	NOUN
ejpam-4828	74	7	g	g	ADP
ejpam-4828	74	8	such	such	ADJ
ejpam-4828	74	9	that	that	PRON
ejpam-4828	74	10	γcr(g	γcr(g	NOUN
ejpam-4828	74	11	)	)	PUNCT
ejpam-4828	74	12	=	=	PUNCT
ejpam-4828	74	13	a	a	PRON
ejpam-4828	74	14	and	and	CCONJ
ejpam-4828	74	15	γcvr(g	γcvr(g	ADJ
ejpam-4828	74	16	)	)	PUNCT
ejpam-4828	74	17	=	=	SYM
ejpam-4828	74	18	b.	b.	PROPN
ejpam-4828	74	19	proof	proof	NOUN
ejpam-4828	74	20	.	.	PUNCT
ejpam-4828	75	1	consider	consider	VERB
ejpam-4828	75	2	the	the	DET
ejpam-4828	75	3	following	follow	VERB
ejpam-4828	75	4	cases	case	NOUN
ejpam-4828	75	5	:	:	PUNCT
ejpam-4828	75	6	case	case	NOUN
ejpam-4828	75	7	1	1	NUM
ejpam-4828	75	8	.	.	PUNCT
ejpam-4828	76	1	a	a	DET
ejpam-4828	76	2	=	=	X
ejpam-4828	76	3	b.	b.	PROPN
ejpam-4828	76	4	let	let	VERB
ejpam-4828	76	5	g	g	NOUN
ejpam-4828	76	6	=	=	VERB
ejpam-4828	76	7	ca	can	AUX
ejpam-4828	76	8	.	.	PUNCT
ejpam-4828	77	1	then	then	ADV
ejpam-4828	77	2	γcr(g	γcr(g	NUM
ejpam-4828	77	3	)	)	PUNCT
ejpam-4828	78	1	=	=	PUNCT
ejpam-4828	78	2	γcvr(g	γcvr(g	NOUN
ejpam-4828	78	3	)	)	PUNCT
ejpam-4828	78	4	=	=	NOUN
ejpam-4828	78	5	a.	a.	NOUN
ejpam-4828	78	6	case	case	NOUN
ejpam-4828	78	7	2	2	NUM
ejpam-4828	78	8	.	.	PUNCT
ejpam-4828	78	9	a	a	DET
ejpam-4828	78	10	<	<	X
ejpam-4828	78	11	b.	b.	NOUN
ejpam-4828	78	12	letm	letm	PROPN
ejpam-4828	78	13	=	=	SYM
ejpam-4828	78	14	b−a	b−a	PROPN
ejpam-4828	78	15	.	.	PUNCT
ejpam-4828	79	1	consider	consider	VERB
ejpam-4828	79	2	the	the	DET
ejpam-4828	79	3	graphg	graphg	NOUN
ejpam-4828	79	4	in	in	ADP
ejpam-4828	79	5	figure	figure	NOUN
ejpam-4828	79	6	1	1	NUM
ejpam-4828	79	7	.	.	PUNCT
ejpam-4828	80	1	let	let	VERB
ejpam-4828	80	2	v0	v0	NOUN
ejpam-4828	80	3	=	=	SYM
ejpam-4828	80	4	{	{	PUNCT
ejpam-4828	80	5	x1	x1	PROPN
ejpam-4828	80	6	,	,	PUNCT
ejpam-4828	80	7	x2	x2	PROPN
ejpam-4828	80	8	,	,	PUNCT
ejpam-4828	80	9	.	.	PUNCT
ejpam-4828	80	10	.	.	PUNCT
ejpam-4828	81	1	.	.	PUNCT
ejpam-4828	82	1	,	,	PUNCT
ejpam-4828	82	2	xm	xm	PROPN
ejpam-4828	82	3	}	}	PUNCT
ejpam-4828	82	4	,	,	PUNCT
ejpam-4828	82	5	v1	v1	NOUN
ejpam-4828	82	6	=	=	SYM
ejpam-4828	82	7	{	{	PUNCT
ejpam-4828	82	8	v1	v1	PROPN
ejpam-4828	82	9	,	,	PUNCT
ejpam-4828	82	10	v2	v2	PROPN
ejpam-4828	82	11	,	,	PUNCT
ejpam-4828	82	12	.	.	PUNCT
ejpam-4828	82	13	.	.	PUNCT
ejpam-4828	82	14	.	.	PUNCT
ejpam-4828	83	1	,	,	PUNCT
ejpam-4828	83	2	va−2	va−2	PROPN
ejpam-4828	83	3	}	}	PUNCT
ejpam-4828	83	4	,	,	PUNCT
ejpam-4828	83	5	v2	v2	PROPN
ejpam-4828	83	6	=	=	SYM
ejpam-4828	83	7	{	{	PUNCT
ejpam-4828	83	8	va−1	va−1	NOUN
ejpam-4828	83	9	}	}	PUNCT
ejpam-4828	83	10	,	,	PUNCT
ejpam-4828	83	11	v	v	X
ejpam-4828	83	12	′	′	NOUN
ejpam-4828	83	13	0	0	NUM
ejpam-4828	84	1	=	=	NOUN
ejpam-4828	84	2	∅	∅	NOUN
ejpam-4828	84	3	,	,	PUNCT
ejpam-4828	84	4	v1	v1	NOUN
ejpam-4828	84	5	=	=	SYM
ejpam-4828	84	6	{	{	PUNCT
ejpam-4828	84	7	x1	x1	PROPN
ejpam-4828	84	8	,	,	PUNCT
ejpam-4828	84	9	x2	x2	PROPN
ejpam-4828	84	10	,	,	PUNCT
ejpam-4828	84	11	.	.	PUNCT
ejpam-4828	84	12	.	.	PUNCT
ejpam-4828	84	13	.	.	PUNCT
ejpam-4828	85	1	,	,	PUNCT
ejpam-4828	85	2	xm	xm	PROPN
ejpam-4828	85	3	,	,	PUNCT
ejpam-4828	85	4	v1	v1	PROPN
ejpam-4828	85	5	,	,	PUNCT
ejpam-4828	85	6	v2	v2	NOUN
ejpam-4828	85	7	,	,	PUNCT
ejpam-4828	85	8	.	.	PUNCT
ejpam-4828	85	9	.	.	PUNCT
ejpam-4828	86	1	.	.	PUNCT
ejpam-4828	86	2	,	,	PUNCT
ejpam-4828	86	3	va−2	va−2	PROPN
ejpam-4828	86	4	}	}	PUNCT
ejpam-4828	86	5	,	,	PUNCT
ejpam-4828	86	6	v2	v2	PROPN
ejpam-4828	86	7	=	=	SYM
ejpam-4828	86	8	{	{	PUNCT
ejpam-4828	86	9	va−1	va−1	NOUN
ejpam-4828	86	10	}	}	PUNCT
ejpam-4828	86	11	.	.	PUNCT
ejpam-4828	87	1	then	then	ADV
ejpam-4828	87	2	f	f	X
ejpam-4828	87	3	=	=	SYM
ejpam-4828	87	4	(	(	PUNCT
ejpam-4828	87	5	v0	v0	PROPN
ejpam-4828	87	6	,	,	PUNCT
ejpam-4828	87	7	v1	v1	NOUN
ejpam-4828	87	8	,	,	PUNCT
ejpam-4828	87	9	v2	v2	PROPN
ejpam-4828	87	10	)	)	PUNCT
ejpam-4828	87	11	is	be	AUX
ejpam-4828	87	12	a	a	DET
ejpam-4828	87	13	γcr	γcr	ADJ
ejpam-4828	87	14	-	-	PUNCT
ejpam-4828	87	15	function	function	NOUN
ejpam-4828	87	16	and	and	CCONJ
ejpam-4828	87	17	g	g	NOUN
ejpam-4828	87	18	=	=	SYM
ejpam-4828	87	19	(	(	PUNCT
ejpam-4828	87	20	v	v	NUM
ejpam-4828	87	21	′	′	NUM
ejpam-4828	87	22	0	0	NUM
ejpam-4828	87	23	,	,	PUNCT
ejpam-4828	87	24	v	v	NOUN
ejpam-4828	87	25	′	′	NUM
ejpam-4828	87	26	1	1	NUM
ejpam-4828	87	27	,	,	PUNCT
ejpam-4828	87	28	v	v	NOUN
ejpam-4828	87	29	′	′	NUM
ejpam-4828	87	30	2	2	NUM
ejpam-4828	87	31	)	)	PUNCT
ejpam-4828	87	32	is	be	AUX
ejpam-4828	87	33	a	a	DET
ejpam-4828	87	34	γcvrfunction	γcvrfunction	NOUN
ejpam-4828	87	35	on	on	ADP
ejpam-4828	87	36	g.	g.	PROPN
ejpam-4828	87	37	hence	hence	ADV
ejpam-4828	87	38	,	,	PUNCT
ejpam-4828	87	39	γcr(g	γcr(g	PROPN
ejpam-4828	87	40	)	)	PUNCT
ejpam-4828	88	1	=	=	SYM
ejpam-4828	88	2	ωcr	ωcr	PRON
ejpam-4828	88	3	g	g	PROPN
ejpam-4828	88	4	(	(	PUNCT
ejpam-4828	88	5	g	g	NOUN
ejpam-4828	88	6	)	)	PUNCT
ejpam-4828	88	7	=	=	PUNCT
ejpam-4828	88	8	|v1|+	|v1|+	PRON
ejpam-4828	88	9	2|v2|	2|v2|	NUM
ejpam-4828	88	10	=	=	SYM
ejpam-4828	88	11	a−	a−	X
ejpam-4828	88	12	2	2	NUM
ejpam-4828	88	13	+	+	CCONJ
ejpam-4828	88	14	2(1	2(1	NUM
ejpam-4828	88	15	)	)	PUNCT
ejpam-4828	88	16	=	=	PUNCT
ejpam-4828	89	1	a	a	PRON
ejpam-4828	89	2	and	and	CCONJ
ejpam-4828	89	3	γcvr(g	γcvr(g	ADJ
ejpam-4828	89	4	)	)	PUNCT
ejpam-4828	90	1	=	=	PUNCT
ejpam-4828	90	2	ωcvr	ωcvr	PROPN
ejpam-4828	90	3	g	g	PROPN
ejpam-4828	90	4	(	(	PUNCT
ejpam-4828	90	5	g	g	NOUN
ejpam-4828	90	6	)	)	PUNCT
ejpam-4828	90	7	=	=	PUNCT
ejpam-4828	90	8	|v	|v	PROPN
ejpam-4828	90	9	′	′	NUM
ejpam-4828	90	10	1	1	NUM
ejpam-4828	90	11	|+	|+	NOUN
ejpam-4828	90	12	2|v	2|v	NOUN
ejpam-4828	91	1	′	′	NOUN
ejpam-4828	91	2	2	2	NUM
ejpam-4828	92	1	|	|	ADV
ejpam-4828	92	2	=	=	SYM
ejpam-4828	92	3	m+	m+	NUM
ejpam-4828	92	4	(	(	PUNCT
ejpam-4828	92	5	a−	a−	PROPN
ejpam-4828	92	6	2	2	NUM
ejpam-4828	92	7	)	)	PUNCT
ejpam-4828	92	8	+	+	NUM
ejpam-4828	92	9	2(1	2(1	NUM
ejpam-4828	92	10	)	)	PUNCT
ejpam-4828	92	11	=	=	SYM
ejpam-4828	92	12	b.	b.	PROPN
ejpam-4828	92	13	r.	r.	PROPN
ejpam-4828	92	14	fortosa	fortosa	PROPN
ejpam-4828	92	15	,	,	PUNCT
ejpam-4828	92	16	s.	s.	PROPN
ejpam-4828	92	17	canoy	canoy	PROPN
ejpam-4828	92	18	jr	jr	PROPN
ejpam-4828	92	19	.	.	PROPN
ejpam-4828	92	20	/	/	SYM
ejpam-4828	92	21	eur	eur	PROPN
ejpam-4828	92	22	.	.	PUNCT
ejpam-4828	93	1	j.	j.	PROPN
ejpam-4828	93	2	pure	pure	PROPN
ejpam-4828	93	3	appl	appl	PROPN
ejpam-4828	93	4	.	.	PROPN
ejpam-4828	93	5	math	math	PROPN
ejpam-4828	93	6	,	,	PUNCT
ejpam-4828	93	7	16	16	NUM
ejpam-4828	93	8	(	(	PUNCT
ejpam-4828	93	9	3	3	NUM
ejpam-4828	93	10	)	)	PUNCT
ejpam-4828	93	11	(	(	PUNCT
ejpam-4828	93	12	2023	2023	NUM
ejpam-4828	93	13	)	)	PUNCT
ejpam-4828	93	14	,	,	PUNCT
ejpam-4828	93	15	1705	1705	NUM
ejpam-4828	93	16	-	-	SYM
ejpam-4828	93	17	1716	1716	NUM
ejpam-4828	93	18	1708	1708	NUM
ejpam-4828	93	19	v1	v1	PROPN
ejpam-4828	93	20	v2	v2	PROPN
ejpam-4828	93	21	v3	v3	PROPN
ejpam-4828	93	22	·	·	PUNCT
ejpam-4828	93	23	·	·	PUNCT
ejpam-4828	93	24	·	·	PUNCT
ejpam-4828	94	1	va−4	va−4	NOUN
ejpam-4828	94	2	va−3	va−3	PROPN
ejpam-4828	94	3	va−2	va−2	PROPN
ejpam-4828	94	4	va−1	va−1	NOUN
ejpam-4828	95	1	x1	x1	PROPN
ejpam-4828	96	1	x2	x2	INTJ
ejpam-4828	96	2	...	...	PUNCT
ejpam-4828	97	1	xm	xm	PROPN
ejpam-4828	97	2	figure	figure	NOUN
ejpam-4828	97	3	1	1	NUM
ejpam-4828	97	4	:	:	PUNCT
ejpam-4828	97	5	a	a	DET
ejpam-4828	97	6	graph	graph	NOUN
ejpam-4828	97	7	with	with	ADP
ejpam-4828	97	8	γcr(g	γcr(g	PROPN
ejpam-4828	97	9	)	)	PUNCT
ejpam-4828	97	10	=	=	PUNCT
ejpam-4828	98	1	a	a	PRON
ejpam-4828	98	2	and	and	CCONJ
ejpam-4828	98	3	γcvr(g	γcvr(g	ADJ
ejpam-4828	98	4	)	)	PUNCT
ejpam-4828	99	1	=	=	SYM
ejpam-4828	99	2	b	b	PROPN
ejpam-4828	99	3	this	this	PRON
ejpam-4828	99	4	proves	prove	VERB
ejpam-4828	99	5	the	the	DET
ejpam-4828	99	6	assertion	assertion	NOUN
ejpam-4828	99	7	.	.	PUNCT
ejpam-4828	100	1	corollary	corollary	ADJ
ejpam-4828	100	2	3	3	X
ejpam-4828	100	3	.	.	PUNCT
ejpam-4828	101	1	let	let	VERB
ejpam-4828	101	2	n	n	PRON
ejpam-4828	101	3	be	be	AUX
ejpam-4828	101	4	a	a	DET
ejpam-4828	101	5	positive	positive	ADJ
ejpam-4828	101	6	integer	integer	NOUN
ejpam-4828	101	7	.	.	PUNCT
ejpam-4828	102	1	then	then	ADV
ejpam-4828	102	2	there	there	PRON
ejpam-4828	102	3	exists	exist	VERB
ejpam-4828	102	4	a	a	DET
ejpam-4828	102	5	connected	connected	ADJ
ejpam-4828	102	6	graph	graph	NOUN
ejpam-4828	102	7	g	g	ADP
ejpam-4828	102	8	such	such	ADJ
ejpam-4828	102	9	that	that	DET
ejpam-4828	102	10	γcvr(g	γcvr(g	NOUN
ejpam-4828	102	11	)	)	PUNCT
ejpam-4828	102	12	−	−	PROPN
ejpam-4828	102	13	γcr(g	γcr(g	NOUN
ejpam-4828	102	14	)	)	PUNCT
ejpam-4828	103	1	=	=	VERB
ejpam-4828	103	2	n.	n.	NOUN
ejpam-4828	103	3	in	in	ADP
ejpam-4828	103	4	other	other	ADJ
ejpam-4828	103	5	words	word	NOUN
ejpam-4828	103	6	,	,	PUNCT
ejpam-4828	103	7	the	the	DET
ejpam-4828	103	8	difference	difference	NOUN
ejpam-4828	103	9	γcvr(g	γcvr(g	NOUN
ejpam-4828	103	10	)	)	PUNCT
ejpam-4828	103	11	−	−	PROPN
ejpam-4828	103	12	γcr(g	γcr(g	NOUN
ejpam-4828	103	13	)	)	PUNCT
ejpam-4828	103	14	can	can	AUX
ejpam-4828	103	15	be	be	AUX
ejpam-4828	103	16	made	make	VERB
ejpam-4828	103	17	arbitrarily	arbitrarily	ADV
ejpam-4828	103	18	large	large	ADJ
ejpam-4828	103	19	.	.	PUNCT
ejpam-4828	104	1	remark	remark	NOUN
ejpam-4828	104	2	2	2	NUM
ejpam-4828	104	3	.	.	PUNCT
ejpam-4828	105	1	if	if	SCONJ
ejpam-4828	105	2	f	f	PROPN
ejpam-4828	105	3	=	=	SYM
ejpam-4828	105	4	(	(	PUNCT
ejpam-4828	105	5	v0	v0	PROPN
ejpam-4828	105	6	,	,	PUNCT
ejpam-4828	105	7	v1	v1	NOUN
ejpam-4828	105	8	,	,	PUNCT
ejpam-4828	105	9	v2	v2	PROPN
ejpam-4828	105	10	)	)	PUNCT
ejpam-4828	105	11	is	be	AUX
ejpam-4828	105	12	a	a	DET
ejpam-4828	105	13	γcvr	γcvr	NOUN
ejpam-4828	105	14	-	-	PUNCT
ejpam-4828	105	15	function	function	NOUN
ejpam-4828	105	16	,	,	PUNCT
ejpam-4828	105	17	then	then	ADV
ejpam-4828	105	18	v1	v1	VERB
ejpam-4828	105	19	∪	∪	NOUN
ejpam-4828	105	20	v2	v2	NOUN
ejpam-4828	105	21	need	need	AUX
ejpam-4828	105	22	not	not	PART
ejpam-4828	105	23	be	be	AUX
ejpam-4828	105	24	a	a	DET
ejpam-4828	105	25	γcon	γcon	NOUN
ejpam-4828	105	26	-	-	PUNCT
ejpam-4828	105	27	set	set	NOUN
ejpam-4828	105	28	.	.	PUNCT
ejpam-4828	106	1	to	to	PART
ejpam-4828	106	2	see	see	VERB
ejpam-4828	106	3	this	this	PRON
ejpam-4828	106	4	,	,	PUNCT
ejpam-4828	106	5	consider	consider	VERB
ejpam-4828	106	6	p4	p4	ADJ
ejpam-4828	106	7	=	=	PUNCT
ejpam-4828	106	8	[	[	X
ejpam-4828	106	9	v1	v1	NOUN
ejpam-4828	106	10	,	,	PUNCT
ejpam-4828	106	11	v2	v2	PROPN
ejpam-4828	106	12	,	,	PUNCT
ejpam-4828	106	13	v3	v3	PROPN
ejpam-4828	106	14	,	,	PUNCT
ejpam-4828	106	15	v4	v4	PROPN
ejpam-4828	106	16	]	]	PUNCT
ejpam-4828	106	17	.	.	PUNCT
ejpam-4828	107	1	let	let	VERB
ejpam-4828	107	2	v0	v0	NOUN
ejpam-4828	107	3	=	=	SYM
ejpam-4828	107	4	{	{	PUNCT
ejpam-4828	107	5	v1	v1	NOUN
ejpam-4828	107	6	}	}	PUNCT
ejpam-4828	107	7	,	,	PUNCT
ejpam-4828	107	8	v1	v1	NOUN
ejpam-4828	107	9	=	=	SYM
ejpam-4828	107	10	{	{	PUNCT
ejpam-4828	107	11	v3	v3	PROPN
ejpam-4828	107	12	,	,	PUNCT
ejpam-4828	107	13	v4	v4	PROPN
ejpam-4828	107	14	}	}	PUNCT
ejpam-4828	107	15	,	,	PUNCT
ejpam-4828	107	16	and	and	CCONJ
ejpam-4828	107	17	v2	v2	NOUN
ejpam-4828	107	18	=	=	SYM
ejpam-4828	107	19	{	{	PUNCT
ejpam-4828	107	20	v2	v2	NOUN
ejpam-4828	107	21	}	}	PUNCT
ejpam-4828	107	22	.	.	PUNCT
ejpam-4828	108	1	then	then	ADV
ejpam-4828	108	2	f	f	X
ejpam-4828	108	3	=	=	SYM
ejpam-4828	108	4	(	(	PUNCT
ejpam-4828	108	5	v0	v0	PROPN
ejpam-4828	108	6	,	,	PUNCT
ejpam-4828	108	7	v1	v1	NOUN
ejpam-4828	108	8	,	,	PUNCT
ejpam-4828	108	9	v2	v2	PROPN
ejpam-4828	108	10	)	)	PUNCT
ejpam-4828	108	11	is	be	AUX
ejpam-4828	108	12	a	a	DET
ejpam-4828	108	13	γcvr	γcvr	NOUN
ejpam-4828	108	14	-	-	PUNCT
ejpam-4828	108	15	function	function	NOUN
ejpam-4828	108	16	on	on	ADP
ejpam-4828	108	17	p4	p4	ADJ
ejpam-4828	108	18	.	.	PUNCT
ejpam-4828	109	1	clearly	clearly	ADV
ejpam-4828	109	2	,	,	PUNCT
ejpam-4828	109	3	v1	v1	VERB
ejpam-4828	109	4	∪	∪	NOUN
ejpam-4828	109	5	v2	v2	NOUN
ejpam-4828	109	6	is	be	AUX
ejpam-4828	109	7	not	not	PART
ejpam-4828	109	8	a	a	DET
ejpam-4828	109	9	γcon	γcon	NOUN
ejpam-4828	109	10	-	-	PUNCT
ejpam-4828	109	11	set	set	NOUN
ejpam-4828	109	12	in	in	ADP
ejpam-4828	109	13	p4	p4	ADJ
ejpam-4828	109	14	.	.	PUNCT
ejpam-4828	110	1	proposition	proposition	NOUN
ejpam-4828	110	2	1	1	NUM
ejpam-4828	110	3	.	.	PUNCT
ejpam-4828	111	1	for	for	ADP
ejpam-4828	111	2	any	any	DET
ejpam-4828	111	3	connected	connected	ADJ
ejpam-4828	111	4	graph	graph	NOUN
ejpam-4828	111	5	g	g	NOUN
ejpam-4828	111	6	of	of	ADP
ejpam-4828	111	7	order	order	NOUN
ejpam-4828	111	8	n	n	CCONJ
ejpam-4828	111	9	,	,	PUNCT
ejpam-4828	111	10	1	1	NUM
ejpam-4828	111	11	≤	≤	NUM
ejpam-4828	111	12	γcon(g	γcon(g	PROPN
ejpam-4828	111	13	)	)	PUNCT
ejpam-4828	111	14	≤	≤	NOUN
ejpam-4828	111	15	γcvr(g	γcvr(g	PROPN
ejpam-4828	111	16	)	)	PUNCT
ejpam-4828	111	17	≤	≤	NUM
ejpam-4828	111	18	min{n	min{n	NOUN
ejpam-4828	111	19	,	,	PUNCT
ejpam-4828	111	20	2γcon(g	2γcon(g	NUM
ejpam-4828	111	21	)	)	PUNCT
ejpam-4828	111	22	}	}	PUNCT
ejpam-4828	111	23	.	.	PUNCT
ejpam-4828	112	1	proof	proof	NOUN
ejpam-4828	112	2	.	.	PUNCT
ejpam-4828	113	1	let	let	VERB
ejpam-4828	113	2	f	f	PROPN
ejpam-4828	113	3	=	=	SYM
ejpam-4828	113	4	(	(	PUNCT
ejpam-4828	113	5	v0	v0	PROPN
ejpam-4828	113	6	,	,	PUNCT
ejpam-4828	113	7	v1	v1	NOUN
ejpam-4828	113	8	,	,	PUNCT
ejpam-4828	113	9	v2	v2	PROPN
ejpam-4828	113	10	)	)	PUNCT
ejpam-4828	113	11	be	be	AUX
ejpam-4828	113	12	a	a	DET
ejpam-4828	113	13	γcvr	γcvr	NOUN
ejpam-4828	113	14	-	-	PUNCT
ejpam-4828	113	15	function	function	NOUN
ejpam-4828	113	16	.	.	PUNCT
ejpam-4828	114	1	then	then	ADV
ejpam-4828	114	2	v1	v1	VERB
ejpam-4828	114	3	∪	∪	ADJ
ejpam-4828	114	4	v2	v2	NOUN
ejpam-4828	114	5	is	be	AUX
ejpam-4828	114	6	a	a	DET
ejpam-4828	114	7	convex	convex	NOUN
ejpam-4828	114	8	dominating	dominating	NOUN
ejpam-4828	114	9	set	set	VERB
ejpam-4828	114	10	in	in	ADP
ejpam-4828	114	11	g.	g.	PROPN
ejpam-4828	114	12	hence	hence	ADV
ejpam-4828	114	13	,	,	PUNCT
ejpam-4828	114	14	1	1	NUM
ejpam-4828	114	15	≤	≤	NUM
ejpam-4828	114	16	γcon(g	γcon(g	PROPN
ejpam-4828	114	17	)	)	PUNCT
ejpam-4828	114	18	≤	≤	NOUN
ejpam-4828	114	19	|v1|+	|v1|+	PUNCT
ejpam-4828	114	20	|v2|	|v2|	ADV
ejpam-4828	114	21	≤	≤	NUM
ejpam-4828	114	22	|v1|+	|v1|+	PRON
ejpam-4828	114	23	2|v2|	2|v2|	NUM
ejpam-4828	114	24	=	=	SYM
ejpam-4828	114	25	γcvr(g	γcvr(g	NOUN
ejpam-4828	114	26	)	)	PUNCT
ejpam-4828	114	27	.	.	PUNCT
ejpam-4828	115	1	now	now	ADV
ejpam-4828	115	2	,	,	PUNCT
ejpam-4828	115	3	let	let	VERB
ejpam-4828	115	4	v	v	NOUN
ejpam-4828	115	5	′	′	NOUN
ejpam-4828	115	6	0	0	NUM
ejpam-4828	116	1	=	=	SYM
ejpam-4828	116	2	v	v	NUM
ejpam-4828	116	3	′	′	NUM
ejpam-4828	116	4	2	2	NUM
ejpam-4828	116	5	=	=	NOUN
ejpam-4828	116	6	∅	∅	NOUN
ejpam-4828	116	7	and	and	CCONJ
ejpam-4828	116	8	v	v	NOUN
ejpam-4828	116	9	′	′	NUM
ejpam-4828	116	10	1	1	NUM
ejpam-4828	116	11	=	=	SYM
ejpam-4828	116	12	v	v	NOUN
ejpam-4828	116	13	(	(	PUNCT
ejpam-4828	116	14	g	g	NOUN
ejpam-4828	116	15	)	)	PUNCT
ejpam-4828	116	16	.	.	PUNCT
ejpam-4828	117	1	then	then	ADV
ejpam-4828	117	2	g	g	PROPN
ejpam-4828	117	3	=	=	PUNCT
ejpam-4828	117	4	(	(	PUNCT
ejpam-4828	117	5	v	v	NUM
ejpam-4828	117	6	′	′	NUM
ejpam-4828	117	7	0	0	NUM
ejpam-4828	117	8	,	,	PUNCT
ejpam-4828	117	9	v	v	NOUN
ejpam-4828	117	10	′	′	NUM
ejpam-4828	117	11	1	1	NUM
ejpam-4828	117	12	,	,	PUNCT
ejpam-4828	117	13	v	v	NOUN
ejpam-4828	117	14	′	′	NUM
ejpam-4828	117	15	2	2	NUM
ejpam-4828	117	16	)	)	PUNCT
ejpam-4828	117	17	is	be	AUX
ejpam-4828	117	18	a	a	DET
ejpam-4828	117	19	cvrdf	cvrdf	NOUN
ejpam-4828	117	20	and	and	CCONJ
ejpam-4828	117	21	γcvr(g	γcvr(g	NOUN
ejpam-4828	117	22	)	)	PUNCT
ejpam-4828	117	23	≤	≤	NOUN
ejpam-4828	117	24	|v	|v	ADV
ejpam-4828	117	25	′	′	NOUN
ejpam-4828	117	26	1	1	NUM
ejpam-4828	117	27	|	|	ADV
ejpam-4828	117	28	=	=	SYM
ejpam-4828	117	29	|v	|v	X
ejpam-4828	117	30	(	(	PUNCT
ejpam-4828	117	31	g)|	g)|	NOUN
ejpam-4828	117	32	=	=	PROPN
ejpam-4828	117	33	n.	n.	PROPN
ejpam-4828	117	34	next	next	ADV
ejpam-4828	117	35	,	,	PUNCT
ejpam-4828	117	36	let	let	VERB
ejpam-4828	117	37	s	s	PRON
ejpam-4828	117	38	be	be	AUX
ejpam-4828	117	39	a	a	DET
ejpam-4828	117	40	γcon	γcon	NOUN
ejpam-4828	117	41	-	-	PUNCT
ejpam-4828	117	42	set	set	NOUN
ejpam-4828	117	43	of	of	ADP
ejpam-4828	117	44	g.	g.	PROPN
ejpam-4828	117	45	define	define	VERB
ejpam-4828	117	46	h	h	NOUN
ejpam-4828	117	47	=	=	SYM
ejpam-4828	117	48	(	(	PUNCT
ejpam-4828	117	49	v	v	NUM
ejpam-4828	117	50	′′	′′	PROPN
ejpam-4828	117	51	0	0	NUM
ejpam-4828	117	52	,	,	PUNCT
ejpam-4828	117	53	v	v	ADP
ejpam-4828	117	54	′′	′′	PROPN
ejpam-4828	117	55	1	1	NUM
ejpam-4828	117	56	,	,	PUNCT
ejpam-4828	117	57	v	v	ADP
ejpam-4828	117	58	′′	′′	PROPN
ejpam-4828	117	59	2	2	NUM
ejpam-4828	117	60	)	)	PUNCT
ejpam-4828	117	61	by	by	ADP
ejpam-4828	117	62	setting	set	VERB
ejpam-4828	117	63	v	v	ADP
ejpam-4828	117	64	′′	′′	PROPN
ejpam-4828	117	65	2	2	NUM
ejpam-4828	117	66	=	=	SYM
ejpam-4828	117	67	s	s	PROPN
ejpam-4828	117	68	,	,	PUNCT
ejpam-4828	117	69	v	v	ADP
ejpam-4828	117	70	′′	′′	PROPN
ejpam-4828	117	71	0	0	NUM
ejpam-4828	118	1	=	=	SYM
ejpam-4828	118	2	v	v	NOUN
ejpam-4828	118	3	(	(	PUNCT
ejpam-4828	118	4	g	g	NOUN
ejpam-4828	118	5	)	)	PUNCT
ejpam-4828	118	6	\	\	PROPN
ejpam-4828	119	1	s	s	PROPN
ejpam-4828	119	2	,	,	PUNCT
ejpam-4828	119	3	and	and	CCONJ
ejpam-4828	119	4	v	v	ADP
ejpam-4828	119	5	′′	′′	PROPN
ejpam-4828	119	6	1	1	NUM
ejpam-4828	119	7	=	=	SYM
ejpam-4828	119	8	∅.	∅.	NOUN
ejpam-4828	119	9	then	then	ADV
ejpam-4828	119	10	h	h	PROPN
ejpam-4828	119	11	is	be	AUX
ejpam-4828	119	12	a	a	DET
ejpam-4828	119	13	cvrdf	cvrdf	NOUN
ejpam-4828	119	14	on	on	ADP
ejpam-4828	119	15	g.	g.	PROPN
ejpam-4828	119	16	hence	hence	ADV
ejpam-4828	119	17	,	,	PUNCT
ejpam-4828	119	18	γcvr(g	γcvr(g	PROPN
ejpam-4828	119	19	)	)	PUNCT
ejpam-4828	119	20	≤	≤	NOUN
ejpam-4828	119	21	ωcvr	ωcvr	ADP
ejpam-4828	119	22	g	g	PROPN
ejpam-4828	119	23	(	(	PUNCT
ejpam-4828	119	24	g	g	NOUN
ejpam-4828	119	25	)	)	PUNCT
ejpam-4828	119	26	=	=	SYM
ejpam-4828	119	27	2|s|	2|s|	NUM
ejpam-4828	119	28	=	=	SYM
ejpam-4828	119	29	2γcon(g	2γcon(g	NUM
ejpam-4828	119	30	)	)	PUNCT
ejpam-4828	119	31	.	.	PUNCT
ejpam-4828	120	1	therefore	therefore	ADV
ejpam-4828	120	2	,	,	PUNCT
ejpam-4828	120	3	γcvr(g	γcvr(g	NOUN
ejpam-4828	120	4	)	)	PUNCT
ejpam-4828	120	5	≤	≤	NUM
ejpam-4828	120	6	min{n	min{n	NOUN
ejpam-4828	120	7	,	,	PUNCT
ejpam-4828	120	8	2γcon(g	2γcon(g	NUM
ejpam-4828	120	9	)	)	PUNCT
ejpam-4828	120	10	}	}	PUNCT
ejpam-4828	120	11	.	.	PUNCT
ejpam-4828	121	1	theorem	theorem	NOUN
ejpam-4828	121	2	3	3	X
ejpam-4828	121	3	.	.	PUNCT
ejpam-4828	122	1	let	let	VERB
ejpam-4828	122	2	g	g	PRON
ejpam-4828	122	3	be	be	AUX
ejpam-4828	122	4	a	a	DET
ejpam-4828	122	5	connected	connected	ADJ
ejpam-4828	122	6	graph	graph	NOUN
ejpam-4828	122	7	on	on	ADP
ejpam-4828	122	8	n	n	DET
ejpam-4828	122	9	vertices	vertex	NOUN
ejpam-4828	122	10	.	.	PUNCT
ejpam-4828	123	1	then	then	ADV
ejpam-4828	123	2	each	each	PRON
ejpam-4828	123	3	of	of	ADP
ejpam-4828	123	4	the	the	DET
ejpam-4828	123	5	the	the	DET
ejpam-4828	123	6	following	following	ADJ
ejpam-4828	123	7	statements	statement	NOUN
ejpam-4828	123	8	holds	hold	VERB
ejpam-4828	123	9	.	.	PUNCT
ejpam-4828	124	1	(	(	PUNCT
ejpam-4828	124	2	i	i	NOUN
ejpam-4828	124	3	)	)	PUNCT
ejpam-4828	124	4	γcvr(g	γcvr(g	PROPN
ejpam-4828	124	5	)	)	PUNCT
ejpam-4828	124	6	=	=	SYM
ejpam-4828	124	7	1	1	NUM
ejpam-4828	124	8	if	if	SCONJ
ejpam-4828	124	9	and	and	CCONJ
ejpam-4828	124	10	only	only	ADV
ejpam-4828	124	11	if	if	SCONJ
ejpam-4828	124	12	g	g	PROPN
ejpam-4828	124	13	=	=	SYM
ejpam-4828	124	14	k1	k1	PROPN
ejpam-4828	124	15	(	(	PUNCT
ejpam-4828	124	16	ii	ii	NOUN
ejpam-4828	124	17	)	)	PUNCT
ejpam-4828	124	18	γcvr(g	γcvr(g	NOUN
ejpam-4828	124	19	)	)	PUNCT
ejpam-4828	124	20	=	=	SYM
ejpam-4828	124	21	2	2	NUM
ejpam-4828	124	22	if	if	SCONJ
ejpam-4828	124	23	and	and	CCONJ
ejpam-4828	124	24	only	only	ADV
ejpam-4828	124	25	if	if	SCONJ
ejpam-4828	124	26	g	g	NOUN
ejpam-4828	124	27	=	=	PROPN
ejpam-4828	124	28	k1	k1	PROPN
ejpam-4828	125	1	+	+	NOUN
ejpam-4828	125	2	h	h	NOUN
ejpam-4828	125	3	for	for	ADP
ejpam-4828	125	4	some	some	DET
ejpam-4828	125	5	graph	graph	NOUN
ejpam-4828	125	6	h	h	NOUN
ejpam-4828	125	7	proof	proof	NOUN
ejpam-4828	125	8	.	.	PUNCT
ejpam-4828	126	1	(	(	PUNCT
ejpam-4828	126	2	i	i	NOUN
ejpam-4828	126	3	)	)	PUNCT
ejpam-4828	126	4	assume	assume	VERB
ejpam-4828	126	5	that	that	SCONJ
ejpam-4828	126	6	γcvr(g	γcvr(g	NOUN
ejpam-4828	126	7	)	)	PUNCT
ejpam-4828	126	8	=	=	SYM
ejpam-4828	126	9	1	1	NUM
ejpam-4828	126	10	and	and	CCONJ
ejpam-4828	126	11	let	let	VERB
ejpam-4828	126	12	f	f	PROPN
ejpam-4828	126	13	=	=	SYM
ejpam-4828	126	14	(	(	PUNCT
ejpam-4828	126	15	v0	v0	PROPN
ejpam-4828	126	16	,	,	PUNCT
ejpam-4828	126	17	v1	v1	NOUN
ejpam-4828	126	18	,	,	PUNCT
ejpam-4828	126	19	v2	v2	PROPN
ejpam-4828	126	20	)	)	PUNCT
ejpam-4828	126	21	be	be	AUX
ejpam-4828	126	22	a	a	DET
ejpam-4828	126	23	γcvr	γcvr	NOUN
ejpam-4828	126	24	-	-	PUNCT
ejpam-4828	126	25	function	function	NOUN
ejpam-4828	126	26	on	on	ADP
ejpam-4828	126	27	g.	g.	PROPN
ejpam-4828	126	28	then	then	ADV
ejpam-4828	126	29	|v1|	|v1|	VERB
ejpam-4828	126	30	=	=	SYM
ejpam-4828	126	31	1	1	NUM
ejpam-4828	126	32	and	and	CCONJ
ejpam-4828	126	33	|v2|	|v2|	NOUN
ejpam-4828	126	34	=	=	SYM
ejpam-4828	127	1	0	0	X
ejpam-4828	127	2	.	.	PUNCT
ejpam-4828	128	1	hence	hence	ADV
ejpam-4828	128	2	g	g	PROPN
ejpam-4828	128	3	=	=	SYM
ejpam-4828	128	4	k1	k1	PROPN
ejpam-4828	128	5	.	.	PUNCT
ejpam-4828	129	1	the	the	DET
ejpam-4828	129	2	converse	converse	NOUN
ejpam-4828	129	3	is	be	AUX
ejpam-4828	129	4	clear	clear	ADJ
ejpam-4828	129	5	.	.	PUNCT
ejpam-4828	130	1	r.	r.	PROPN
ejpam-4828	130	2	fortosa	fortosa	PROPN
ejpam-4828	130	3	,	,	PUNCT
ejpam-4828	130	4	s.	s.	PROPN
ejpam-4828	130	5	canoy	canoy	PROPN
ejpam-4828	130	6	jr	jr	PROPN
ejpam-4828	130	7	.	.	PROPN
ejpam-4828	130	8	/	/	SYM
ejpam-4828	130	9	eur	eur	PROPN
ejpam-4828	130	10	.	.	PUNCT
ejpam-4828	131	1	j.	j.	PROPN
ejpam-4828	131	2	pure	pure	PROPN
ejpam-4828	131	3	appl	appl	PROPN
ejpam-4828	131	4	.	.	PROPN
ejpam-4828	131	5	math	math	PROPN
ejpam-4828	131	6	,	,	PUNCT
ejpam-4828	131	7	16	16	NUM
ejpam-4828	131	8	(	(	PUNCT
ejpam-4828	131	9	3	3	NUM
ejpam-4828	131	10	)	)	PUNCT
ejpam-4828	131	11	(	(	PUNCT
ejpam-4828	131	12	2023	2023	NUM
ejpam-4828	131	13	)	)	PUNCT
ejpam-4828	131	14	,	,	PUNCT
ejpam-4828	131	15	1705	1705	NUM
ejpam-4828	131	16	-	-	SYM
ejpam-4828	131	17	1716	1716	NUM
ejpam-4828	131	18	1709	1709	NUM
ejpam-4828	131	19	(	(	PUNCT
ejpam-4828	131	20	ii	ii	NOUN
ejpam-4828	131	21	)	)	PUNCT
ejpam-4828	131	22	suppose	suppose	VERB
ejpam-4828	131	23	that	that	SCONJ
ejpam-4828	131	24	γcvr(g	γcvr(g	NOUN
ejpam-4828	131	25	)	)	PUNCT
ejpam-4828	131	26	=	=	SYM
ejpam-4828	131	27	2	2	NUM
ejpam-4828	131	28	and	and	CCONJ
ejpam-4828	131	29	let	let	VERB
ejpam-4828	131	30	f	f	PROPN
ejpam-4828	131	31	=	=	SYM
ejpam-4828	131	32	(	(	PUNCT
ejpam-4828	131	33	v0	v0	PROPN
ejpam-4828	131	34	,	,	PUNCT
ejpam-4828	131	35	v1	v1	NOUN
ejpam-4828	131	36	,	,	PUNCT
ejpam-4828	131	37	v2	v2	PROPN
ejpam-4828	131	38	)	)	PUNCT
ejpam-4828	131	39	be	be	AUX
ejpam-4828	131	40	a	a	DET
ejpam-4828	131	41	γcvr	γcvr	NOUN
ejpam-4828	131	42	-	-	PUNCT
ejpam-4828	131	43	function	function	NOUN
ejpam-4828	131	44	on	on	ADP
ejpam-4828	131	45	g.	g.	PROPN
ejpam-4828	131	46	then	then	ADV
ejpam-4828	131	47	ωcvr	ωcvr	PROPN
ejpam-4828	131	48	g	g	PROPN
ejpam-4828	131	49	(	(	PUNCT
ejpam-4828	131	50	f	f	X
ejpam-4828	131	51	)	)	PUNCT
ejpam-4828	131	52	=	=	PUNCT
ejpam-4828	131	53	|v1|+	|v1|+	PRON
ejpam-4828	131	54	2|v2|	2|v2|	NUM
ejpam-4828	131	55	=	=	SYM
ejpam-4828	131	56	2	2	X
ejpam-4828	131	57	.	.	X
ejpam-4828	131	58	consider	consider	VERB
ejpam-4828	131	59	the	the	DET
ejpam-4828	131	60	following	follow	VERB
ejpam-4828	131	61	cases	case	NOUN
ejpam-4828	131	62	:	:	PUNCT
ejpam-4828	131	63	case	case	NOUN
ejpam-4828	131	64	1	1	NUM
ejpam-4828	131	65	.	.	PUNCT
ejpam-4828	131	66	|v1|	|v1|	NOUN
ejpam-4828	131	67	=	=	NOUN
ejpam-4828	131	68	̸	̸	NUM
ejpam-4828	131	69	0	0	PUNCT
ejpam-4828	131	70	then	then	ADV
ejpam-4828	131	71	|v2|	|v2|	ADV
ejpam-4828	131	72	=	=	SYM
ejpam-4828	131	73	0	0	NUM
ejpam-4828	131	74	and	and	CCONJ
ejpam-4828	131	75	|v1|	|v1|	NOUN
ejpam-4828	131	76	=	=	SYM
ejpam-4828	131	77	2	2	NUM
ejpam-4828	131	78	,	,	PUNCT
ejpam-4828	131	79	say	say	VERB
ejpam-4828	131	80	v1	v1	NOUN
ejpam-4828	131	81	=	=	SYM
ejpam-4828	131	82	{	{	PUNCT
ejpam-4828	131	83	a	a	DET
ejpam-4828	131	84	,	,	PUNCT
ejpam-4828	131	85	b	b	NOUN
ejpam-4828	131	86	}	}	PUNCT
ejpam-4828	131	87	.	.	PUNCT
ejpam-4828	132	1	since	since	SCONJ
ejpam-4828	132	2	v1	v1	NOUN
ejpam-4828	132	3	is	be	AUX
ejpam-4828	132	4	convex	convex	PROPN
ejpam-4828	132	5	,	,	PUNCT
ejpam-4828	132	6	ab	ab	PROPN
ejpam-4828	132	7	∈	∈	PROPN
ejpam-4828	132	8	e(g	e(g	PROPN
ejpam-4828	132	9	)	)	PUNCT
ejpam-4828	132	10	.	.	PUNCT
ejpam-4828	133	1	since	since	SCONJ
ejpam-4828	133	2	|v2|	|v2|	NOUN
ejpam-4828	133	3	=	=	SYM
ejpam-4828	133	4	0	0	NUM
ejpam-4828	133	5	,	,	PUNCT
ejpam-4828	133	6	|v0|	|v0|	NOUN
ejpam-4828	133	7	=	=	SYM
ejpam-4828	133	8	0	0	X
ejpam-4828	133	9	.	.	PUNCT
ejpam-4828	134	1	hence	hence	ADV
ejpam-4828	134	2	,	,	PUNCT
ejpam-4828	134	3	v	v	X
ejpam-4828	134	4	(	(	PUNCT
ejpam-4828	134	5	g	g	NOUN
ejpam-4828	134	6	)	)	PUNCT
ejpam-4828	134	7	=	=	SYM
ejpam-4828	134	8	v1	v1	NOUN
ejpam-4828	134	9	,	,	PUNCT
ejpam-4828	134	10	that	that	PRON
ejpam-4828	134	11	is	be	AUX
ejpam-4828	134	12	g	g	PROPN
ejpam-4828	134	13	=	=	SYM
ejpam-4828	134	14	k2	k2	PROPN
ejpam-4828	134	15	=	=	PROPN
ejpam-4828	134	16	k1	k1	PROPN
ejpam-4828	134	17	+	+	NOUN
ejpam-4828	134	18	k1	k1	NOUN
ejpam-4828	134	19	.	.	PUNCT
ejpam-4828	135	1	case	case	NOUN
ejpam-4828	135	2	2	2	NUM
ejpam-4828	135	3	.	.	PUNCT
ejpam-4828	135	4	|v1|	|v1|	NOUN
ejpam-4828	136	1	=	=	SYM
ejpam-4828	136	2	0	0	PUNCT
ejpam-4828	136	3	then	then	ADV
ejpam-4828	136	4	|v2|	|v2|	ADV
ejpam-4828	136	5	=	=	PUNCT
ejpam-4828	137	1	1	1	NUM
ejpam-4828	137	2	since	since	SCONJ
ejpam-4828	137	3	2|v2|	2|v2|	NUM
ejpam-4828	137	4	=	=	SYM
ejpam-4828	137	5	2	2	X
ejpam-4828	137	6	.	.	PUNCT
ejpam-4828	138	1	if	if	SCONJ
ejpam-4828	138	2	n	n	NOUN
ejpam-4828	138	3	=	=	SYM
ejpam-4828	138	4	2	2	NUM
ejpam-4828	138	5	,	,	PUNCT
ejpam-4828	138	6	then	then	ADV
ejpam-4828	138	7	g	g	PROPN
ejpam-4828	138	8	=	=	PROPN
ejpam-4828	138	9	k2	k2	PROPN
ejpam-4828	138	10	.	.	PUNCT
ejpam-4828	139	1	suppose	suppose	VERB
ejpam-4828	139	2	n	n	PRON
ejpam-4828	139	3	≥	≥	NUM
ejpam-4828	139	4	3	3	NUM
ejpam-4828	139	5	.	.	PUNCT
ejpam-4828	140	1	let	let	VERB
ejpam-4828	140	2	v2	v2	VERB
ejpam-4828	140	3	=	=	SYM
ejpam-4828	140	4	{	{	PUNCT
ejpam-4828	140	5	u	u	NOUN
ejpam-4828	140	6	}	}	PUNCT
ejpam-4828	140	7	and	and	CCONJ
ejpam-4828	140	8	let	let	VERB
ejpam-4828	140	9	w	w	PROPN
ejpam-4828	140	10	∈	∈	PROPN
ejpam-4828	140	11	v	v	ADP
ejpam-4828	140	12	(	(	PUNCT
ejpam-4828	140	13	g	g	NOUN
ejpam-4828	140	14	)	)	PUNCT
ejpam-4828	140	15	\	\	PROPN
ejpam-4828	140	16	v2	v2	PROPN
ejpam-4828	140	17	.	.	PUNCT
ejpam-4828	141	1	then	then	ADV
ejpam-4828	141	2	w	w	PROPN
ejpam-4828	141	3	∈	∈	PROPN
ejpam-4828	141	4	v0	v0	NOUN
ejpam-4828	141	5	,	,	PUNCT
ejpam-4828	141	6	that	that	PRON
ejpam-4828	141	7	is	be	AUX
ejpam-4828	141	8	v0	v0	NOUN
ejpam-4828	141	9	=	=	SYM
ejpam-4828	141	10	v	v	PROPN
ejpam-4828	141	11	(	(	PUNCT
ejpam-4828	141	12	g	g	NOUN
ejpam-4828	141	13	)	)	PUNCT
ejpam-4828	141	14	\	\	PROPN
ejpam-4828	142	1	v2	v2	NOUN
ejpam-4828	142	2	.	.	PUNCT
ejpam-4828	143	1	this	this	PRON
ejpam-4828	143	2	implies	imply	VERB
ejpam-4828	143	3	that	that	SCONJ
ejpam-4828	143	4	uw	uw	PROPN
ejpam-4828	143	5	∈	∈	PROPN
ejpam-4828	143	6	e(g	e(g	PROPN
ejpam-4828	143	7	)	)	PUNCT
ejpam-4828	143	8	for	for	ADP
ejpam-4828	143	9	all	all	DET
ejpam-4828	143	10	w	w	PROPN
ejpam-4828	143	11	∈	∈	PROPN
ejpam-4828	143	12	v	v	ADP
ejpam-4828	143	13	(	(	PUNCT
ejpam-4828	143	14	g	g	NOUN
ejpam-4828	143	15	)	)	PUNCT
ejpam-4828	143	16	\	\	PROPN
ejpam-4828	143	17	v2	v2	PROPN
ejpam-4828	143	18	.	.	PUNCT
ejpam-4828	144	1	hence	hence	ADV
ejpam-4828	144	2	,	,	PUNCT
ejpam-4828	144	3	g	g	PROPN
ejpam-4828	144	4	=	=	PUNCT
ejpam-4828	144	5	⟨{u}⟩	⟨{u}⟩	NOUN
ejpam-4828	144	6	+	+	CCONJ
ejpam-4828	144	7	⟨v	⟨v	X
ejpam-4828	144	8	(	(	PUNCT
ejpam-4828	144	9	g	g	NOUN
ejpam-4828	144	10	)	)	PUNCT
ejpam-4828	144	11	\	\	NOUN
ejpam-4828	145	1	{	{	PUNCT
ejpam-4828	145	2	u}⟩.	u}⟩.	NOUN
ejpam-4828	145	3	let	let	VERB
ejpam-4828	145	4	h	h	NOUN
ejpam-4828	145	5	=	=	PUNCT
ejpam-4828	145	6	⟨v	⟨v	PUNCT
ejpam-4828	145	7	(	(	PUNCT
ejpam-4828	145	8	g	g	NOUN
ejpam-4828	145	9	)	)	PUNCT
ejpam-4828	145	10	\	\	NOUN
ejpam-4828	145	11	{	{	PUNCT
ejpam-4828	145	12	u}⟩.	u}⟩.	NOUN
ejpam-4828	145	13	then	then	ADV
ejpam-4828	145	14	g	g	PROPN
ejpam-4828	145	15	=	=	PROPN
ejpam-4828	145	16	k1	k1	PROPN
ejpam-4828	146	1	+	+	NOUN
ejpam-4828	146	2	h.	h.	NOUN
ejpam-4828	146	3	conversely	conversely	ADV
ejpam-4828	146	4	,	,	PUNCT
ejpam-4828	146	5	suppose	suppose	VERB
ejpam-4828	146	6	that	that	SCONJ
ejpam-4828	146	7	g	g	PROPN
ejpam-4828	146	8	=	=	PROPN
ejpam-4828	146	9	k1	k1	PROPN
ejpam-4828	147	1	+	+	NOUN
ejpam-4828	147	2	h	h	NOUN
ejpam-4828	147	3	for	for	ADP
ejpam-4828	147	4	some	some	DET
ejpam-4828	147	5	graph	graph	NOUN
ejpam-4828	147	6	h.	h.	NOUN
ejpam-4828	147	7	define	define	VERB
ejpam-4828	147	8	g	g	PROPN
ejpam-4828	147	9	=	=	PUNCT
ejpam-4828	147	10	(	(	PUNCT
ejpam-4828	147	11	v	v	NUM
ejpam-4828	147	12	′	′	NUM
ejpam-4828	147	13	0	0	NUM
ejpam-4828	147	14	,	,	PUNCT
ejpam-4828	147	15	v	v	NOUN
ejpam-4828	147	16	′	′	NUM
ejpam-4828	147	17	1	1	NUM
ejpam-4828	147	18	,	,	PUNCT
ejpam-4828	147	19	v	v	NOUN
ejpam-4828	147	20	′	′	NUM
ejpam-4828	147	21	2	2	NUM
ejpam-4828	147	22	)	)	PUNCT
ejpam-4828	147	23	by	by	ADP
ejpam-4828	147	24	setting	set	VERB
ejpam-4828	147	25	v	v	NUM
ejpam-4828	147	26	′	′	NUM
ejpam-4828	147	27	0	0	NUM
ejpam-4828	148	1	=	=	SYM
ejpam-4828	148	2	v	v	ADJ
ejpam-4828	148	3	(	(	PUNCT
ejpam-4828	148	4	h	h	NOUN
ejpam-4828	148	5	)	)	PUNCT
ejpam-4828	148	6	,	,	PUNCT
ejpam-4828	148	7	v	v	X
ejpam-4828	148	8	′	′	NOUN
ejpam-4828	148	9	1	1	NUM
ejpam-4828	148	10	=	=	NOUN
ejpam-4828	148	11	∅	∅	NOUN
ejpam-4828	148	12	and	and	CCONJ
ejpam-4828	148	13	v	v	NOUN
ejpam-4828	148	14	′	′	NUM
ejpam-4828	148	15	2	2	NUM
ejpam-4828	148	16	=	=	SYM
ejpam-4828	148	17	v	v	PROPN
ejpam-4828	148	18	(	(	PUNCT
ejpam-4828	148	19	k1	k1	NOUN
ejpam-4828	148	20	)	)	PUNCT
ejpam-4828	148	21	.	.	PUNCT
ejpam-4828	149	1	then	then	ADV
ejpam-4828	149	2	g	g	PROPN
ejpam-4828	149	3	is	be	AUX
ejpam-4828	149	4	a	a	DET
ejpam-4828	149	5	γcvr	γcvr	NOUN
ejpam-4828	149	6	-	-	PUNCT
ejpam-4828	149	7	function	function	NOUN
ejpam-4828	149	8	on	on	ADP
ejpam-4828	149	9	g	g	PROPN
ejpam-4828	149	10	and	and	CCONJ
ejpam-4828	149	11	ωcvr	ωcvr	PROPN
ejpam-4828	149	12	g	g	PROPN
ejpam-4828	149	13	(	(	PUNCT
ejpam-4828	149	14	g	g	NOUN
ejpam-4828	149	15	)	)	PUNCT
ejpam-4828	149	16	=	=	SYM
ejpam-4828	149	17	γcvr(g	γcvr(g	NOUN
ejpam-4828	149	18	)	)	PUNCT
ejpam-4828	149	19	=	=	PUNCT
ejpam-4828	149	20	|v1|+	|v1|+	PRON
ejpam-4828	149	21	2|v2|	2|v2|	NUM
ejpam-4828	149	22	=	=	SYM
ejpam-4828	149	23	2	2	X
ejpam-4828	149	24	.	.	PUNCT
ejpam-4828	149	25	theorem	theorem	VERB
ejpam-4828	149	26	3(ii	3(ii	NUM
ejpam-4828	149	27	)	)	PUNCT
ejpam-4828	149	28	can	can	AUX
ejpam-4828	149	29	be	be	AUX
ejpam-4828	149	30	rephrased	rephrase	VERB
ejpam-4828	149	31	as	as	SCONJ
ejpam-4828	149	32	follows	follow	VERB
ejpam-4828	149	33	:	:	PUNCT
ejpam-4828	149	34	corollary	corollary	ADJ
ejpam-4828	149	35	4	4	NUM
ejpam-4828	149	36	.	.	PUNCT
ejpam-4828	150	1	for	for	ADP
ejpam-4828	150	2	any	any	DET
ejpam-4828	150	3	connected	connected	ADJ
ejpam-4828	150	4	graph	graph	NOUN
ejpam-4828	150	5	g	g	NOUN
ejpam-4828	150	6	of	of	ADP
ejpam-4828	150	7	order	order	NOUN
ejpam-4828	150	8	n	n	CCONJ
ejpam-4828	150	9	,	,	PUNCT
ejpam-4828	150	10	γcvr(g	γcvr(g	PROPN
ejpam-4828	150	11	)	)	PUNCT
ejpam-4828	150	12	=	=	SYM
ejpam-4828	150	13	2	2	NUM
ejpam-4828	150	14	if	if	SCONJ
ejpam-4828	150	15	and	and	CCONJ
ejpam-4828	150	16	only	only	ADV
ejpam-4828	150	17	if	if	SCONJ
ejpam-4828	150	18	g	g	PROPN
ejpam-4828	150	19	̸=	̸=	PROPN
ejpam-4828	150	20	k1	k1	PROPN
ejpam-4828	150	21	and	and	CCONJ
ejpam-4828	150	22	γ(g	γ(g	PROPN
ejpam-4828	150	23	)	)	PUNCT
ejpam-4828	151	1	=	=	PUNCT
ejpam-4828	151	2	1	1	X
ejpam-4828	151	3	.	.	PUNCT
ejpam-4828	152	1	in	in	ADP
ejpam-4828	152	2	particular	particular	ADJ
ejpam-4828	152	3	,	,	PUNCT
ejpam-4828	152	4	(	(	PUNCT
ejpam-4828	152	5	i	i	NOUN
ejpam-4828	152	6	)	)	PUNCT
ejpam-4828	152	7	γcvr(kn	γcvr(kn	NOUN
ejpam-4828	152	8	)	)	PUNCT
ejpam-4828	152	9	=	=	SYM
ejpam-4828	152	10	2	2	NUM
ejpam-4828	152	11	for	for	ADP
ejpam-4828	152	12	n	n	X
ejpam-4828	152	13	≥	≥	NOUN
ejpam-4828	152	14	2	2	NUM
ejpam-4828	152	15	;	;	PUNCT
ejpam-4828	152	16	(	(	PUNCT
ejpam-4828	152	17	ii	ii	NOUN
ejpam-4828	152	18	)	)	PUNCT
ejpam-4828	152	19	γcvr(fn	γcvr(fn	NOUN
ejpam-4828	152	20	)	)	PUNCT
ejpam-4828	152	21	=	=	SYM
ejpam-4828	152	22	2	2	NUM
ejpam-4828	152	23	for	for	ADP
ejpam-4828	152	24	n	n	X
ejpam-4828	152	25	≥	≥	NOUN
ejpam-4828	152	26	1	1	NUM
ejpam-4828	152	27	;	;	PUNCT
ejpam-4828	152	28	(	(	PUNCT
ejpam-4828	152	29	iii	iii	X
ejpam-4828	152	30	)	)	PUNCT
ejpam-4828	152	31	γcvr(wn	γcvr(wn	NOUN
ejpam-4828	152	32	)	)	PUNCT
ejpam-4828	152	33	=	=	SYM
ejpam-4828	152	34	2	2	NUM
ejpam-4828	152	35	for	for	ADP
ejpam-4828	152	36	n	n	X
ejpam-4828	152	37	≥	≥	NOUN
ejpam-4828	152	38	3	3	NUM
ejpam-4828	152	39	;	;	PUNCT
ejpam-4828	152	40	and	and	CCONJ
ejpam-4828	152	41	(	(	PUNCT
ejpam-4828	152	42	iv	iv	X
ejpam-4828	152	43	)	)	PUNCT
ejpam-4828	152	44	γcvr(sn	γcvr(sn	ADJ
ejpam-4828	152	45	)	)	PUNCT
ejpam-4828	152	46	=	=	SYM
ejpam-4828	152	47	γcvr(k1,n−1	γcvr(k1,n−1	NOUN
ejpam-4828	152	48	)	)	PUNCT
ejpam-4828	152	49	=	=	SYM
ejpam-4828	152	50	2	2	NUM
ejpam-4828	152	51	for	for	ADP
ejpam-4828	152	52	n	n	X
ejpam-4828	152	53	≥	≥	NUM
ejpam-4828	152	54	2	2	NUM
ejpam-4828	152	55	.	.	PUNCT
ejpam-4828	152	56	proposition	proposition	NOUN
ejpam-4828	152	57	2	2	NUM
ejpam-4828	152	58	.	.	PUNCT
ejpam-4828	153	1	there	there	PRON
ejpam-4828	153	2	exists	exist	VERB
ejpam-4828	153	3	no	no	DET
ejpam-4828	153	4	connected	connected	ADJ
ejpam-4828	153	5	graph	graph	NOUN
ejpam-4828	153	6	g	g	NOUN
ejpam-4828	153	7	with	with	ADP
ejpam-4828	153	8	γcvr(g	γcvr(g	NOUN
ejpam-4828	153	9	)	)	PUNCT
ejpam-4828	153	10	=	=	SYM
ejpam-4828	153	11	3	3	X
ejpam-4828	153	12	.	.	PUNCT
ejpam-4828	153	13	proof	proof	NOUN
ejpam-4828	153	14	.	.	PUNCT
ejpam-4828	154	1	suppose	suppose	VERB
ejpam-4828	154	2	g	g	PROPN
ejpam-4828	154	3	is	be	AUX
ejpam-4828	154	4	a	a	DET
ejpam-4828	154	5	connected	connected	ADJ
ejpam-4828	154	6	graph	graph	NOUN
ejpam-4828	154	7	with	with	ADP
ejpam-4828	154	8	γcvr(g	γcvr(g	NOUN
ejpam-4828	154	9	)	)	PUNCT
ejpam-4828	154	10	=	=	SYM
ejpam-4828	155	1	3	3	X
ejpam-4828	155	2	.	.	X
ejpam-4828	155	3	let	let	VERB
ejpam-4828	155	4	f	f	PROPN
ejpam-4828	155	5	=	=	SYM
ejpam-4828	155	6	(	(	PUNCT
ejpam-4828	155	7	v0	v0	PROPN
ejpam-4828	155	8	,	,	PUNCT
ejpam-4828	155	9	v1	v1	NOUN
ejpam-4828	155	10	,	,	PUNCT
ejpam-4828	155	11	v2	v2	PROPN
ejpam-4828	155	12	)	)	PUNCT
ejpam-4828	155	13	be	be	AUX
ejpam-4828	155	14	a	a	DET
ejpam-4828	155	15	γcvr	γcvr	NOUN
ejpam-4828	155	16	-	-	PUNCT
ejpam-4828	155	17	function	function	NOUN
ejpam-4828	155	18	on	on	ADP
ejpam-4828	155	19	g.	g.	PROPN
ejpam-4828	155	20	then	then	ADV
ejpam-4828	155	21	γcvr(g	γcvr(g	VERB
ejpam-4828	155	22	)	)	PUNCT
ejpam-4828	155	23	=	=	NOUN
ejpam-4828	155	24	|v1|	|v1|	NOUN
ejpam-4828	155	25	+	+	CCONJ
ejpam-4828	155	26	2|v2|	2|v2|	NUM
ejpam-4828	155	27	=	=	SYM
ejpam-4828	155	28	3	3	X
ejpam-4828	155	29	.	.	PUNCT
ejpam-4828	156	1	this	this	PRON
ejpam-4828	156	2	implies	imply	VERB
ejpam-4828	156	3	that	that	DET
ejpam-4828	156	4	|v2|	|v2|	NOUN
ejpam-4828	156	5	≤	≤	NOUN
ejpam-4828	156	6	1	1	NUM
ejpam-4828	156	7	.	.	PUNCT
ejpam-4828	156	8	suppose	suppose	VERB
ejpam-4828	156	9	|v2|	|v2|	NOUN
ejpam-4828	156	10	=	=	SYM
ejpam-4828	157	1	0	0	X
ejpam-4828	157	2	.	.	PUNCT
ejpam-4828	157	3	then	then	ADV
ejpam-4828	157	4	|v0|	|v0|	NOUN
ejpam-4828	157	5	=	=	SYM
ejpam-4828	157	6	0	0	NUM
ejpam-4828	157	7	and	and	CCONJ
ejpam-4828	157	8	|v1|	|v1|	NOUN
ejpam-4828	157	9	=	=	SYM
ejpam-4828	157	10	|v	|v	PROPN
ejpam-4828	157	11	(	(	PUNCT
ejpam-4828	157	12	g)|	g)|	NOUN
ejpam-4828	157	13	=	=	SYM
ejpam-4828	157	14	3	3	NUM
ejpam-4828	157	15	.	.	PUNCT
ejpam-4828	158	1	hence	hence	ADV
ejpam-4828	158	2	,	,	PUNCT
ejpam-4828	158	3	g	g	NOUN
ejpam-4828	158	4	=	=	PUNCT
ejpam-4828	158	5	k3	k3	X
ejpam-4828	158	6	or	or	CCONJ
ejpam-4828	158	7	g	g	PROPN
ejpam-4828	158	8	=	=	PROPN
ejpam-4828	158	9	p3	p3	PROPN
ejpam-4828	158	10	.	.	PUNCT
ejpam-4828	159	1	however	however	ADV
ejpam-4828	159	2	,	,	PUNCT
ejpam-4828	159	3	γcvr(k3	γcvr(k3	PROPN
ejpam-4828	159	4	)	)	PUNCT
ejpam-4828	159	5	=	=	SYM
ejpam-4828	159	6	γcvr(p3	γcvr(p3	ADJ
ejpam-4828	159	7	)	)	PUNCT
ejpam-4828	159	8	=	=	SYM
ejpam-4828	159	9	2	2	NUM
ejpam-4828	159	10	,	,	PUNCT
ejpam-4828	159	11	a	a	DET
ejpam-4828	159	12	contradiction	contradiction	NOUN
ejpam-4828	159	13	.	.	PUNCT
ejpam-4828	160	1	next	next	ADV
ejpam-4828	160	2	,	,	PUNCT
ejpam-4828	160	3	suppose	suppose	VERB
ejpam-4828	160	4	that	that	SCONJ
ejpam-4828	160	5	|v2|	|v2|	NOUN
ejpam-4828	160	6	=	=	SYM
ejpam-4828	160	7	1	1	X
ejpam-4828	160	8	.	.	PUNCT
ejpam-4828	160	9	then	then	ADV
ejpam-4828	160	10	|v1|	|v1|	NOUN
ejpam-4828	160	11	=	=	SYM
ejpam-4828	160	12	1	1	X
ejpam-4828	160	13	.	.	PUNCT
ejpam-4828	161	1	let	let	VERB
ejpam-4828	161	2	v1	v1	VERB
ejpam-4828	161	3	=	=	SYM
ejpam-4828	161	4	{	{	PUNCT
ejpam-4828	161	5	w	w	NOUN
ejpam-4828	161	6	}	}	PUNCT
ejpam-4828	161	7	and	and	CCONJ
ejpam-4828	161	8	v2	v2	NOUN
ejpam-4828	161	9	=	=	SYM
ejpam-4828	161	10	{	{	PUNCT
ejpam-4828	161	11	v	v	NOUN
ejpam-4828	161	12	}	}	PUNCT
ejpam-4828	161	13	.	.	PUNCT
ejpam-4828	162	1	since	since	SCONJ
ejpam-4828	162	2	v1	v1	NOUN
ejpam-4828	162	3	∪	∪	NOUN
ejpam-4828	162	4	v2	v2	NOUN
ejpam-4828	162	5	is	be	AUX
ejpam-4828	162	6	convex	convex	PROPN
ejpam-4828	162	7	,	,	PUNCT
ejpam-4828	162	8	vw	vw	PROPN
ejpam-4828	162	9	∈	∈	PROPN
ejpam-4828	162	10	e(g	e(g	PROPN
ejpam-4828	162	11	)	)	PUNCT
ejpam-4828	162	12	.	.	PUNCT
ejpam-4828	163	1	also	also	ADV
ejpam-4828	163	2	,	,	PUNCT
ejpam-4828	163	3	since	since	SCONJ
ejpam-4828	163	4	v0	v0	NOUN
ejpam-4828	163	5	⊆	⊆	NUM
ejpam-4828	163	6	ng(v	ng(v	NOUN
ejpam-4828	163	7	)	)	PUNCT
ejpam-4828	163	8	,	,	PUNCT
ejpam-4828	163	9	v2	v2	PROPN
ejpam-4828	163	10	is	be	AUX
ejpam-4828	163	11	a	a	DET
ejpam-4828	163	12	dominating	dominating	NOUN
ejpam-4828	163	13	set	set	VERB
ejpam-4828	163	14	in	in	ADP
ejpam-4828	163	15	g.	g.	PROPN
ejpam-4828	163	16	hence	hence	ADV
ejpam-4828	163	17	,	,	PUNCT
ejpam-4828	163	18	γ(g	γ(g	PROPN
ejpam-4828	163	19	)	)	PUNCT
ejpam-4828	164	1	=	=	SYM
ejpam-4828	164	2	1	1	NUM
ejpam-4828	164	3	,	,	PUNCT
ejpam-4828	164	4	implying	imply	VERB
ejpam-4828	164	5	that	that	SCONJ
ejpam-4828	164	6	γcvr(g	γcvr(g	NOUN
ejpam-4828	164	7	)	)	PUNCT
ejpam-4828	164	8	=	=	SYM
ejpam-4828	164	9	2	2	NUM
ejpam-4828	164	10	,	,	PUNCT
ejpam-4828	164	11	a	a	DET
ejpam-4828	164	12	contradiction	contradiction	NOUN
ejpam-4828	164	13	.	.	PUNCT
ejpam-4828	165	1	this	this	PRON
ejpam-4828	165	2	proves	prove	VERB
ejpam-4828	165	3	the	the	DET
ejpam-4828	165	4	claim	claim	NOUN
ejpam-4828	165	5	.	.	PUNCT
ejpam-4828	166	1	proposition	proposition	NOUN
ejpam-4828	166	2	3	3	X
ejpam-4828	166	3	.	.	PUNCT
ejpam-4828	167	1	let	let	VERB
ejpam-4828	167	2	g	g	PRON
ejpam-4828	167	3	be	be	AUX
ejpam-4828	167	4	a	a	DET
ejpam-4828	167	5	nontrivial	nontrivial	ADJ
ejpam-4828	167	6	connected	connect	VERB
ejpam-4828	167	7	graph	graph	NOUN
ejpam-4828	167	8	and	and	CCONJ
ejpam-4828	167	9	let	let	VERB
ejpam-4828	167	10	f	f	PROPN
ejpam-4828	167	11	=	=	SYM
ejpam-4828	167	12	(	(	PUNCT
ejpam-4828	167	13	v0	v0	PROPN
ejpam-4828	167	14	,	,	PUNCT
ejpam-4828	167	15	v1	v1	NOUN
ejpam-4828	167	16	,	,	PUNCT
ejpam-4828	167	17	v2	v2	PROPN
ejpam-4828	167	18	)	)	PUNCT
ejpam-4828	167	19	be	be	AUX
ejpam-4828	167	20	a	a	DET
ejpam-4828	167	21	γcvrfunction	γcvrfunction	NOUN
ejpam-4828	167	22	on	on	ADP
ejpam-4828	167	23	g.	g.	PROPN
ejpam-4828	167	24	then	then	ADV
ejpam-4828	167	25	the	the	DET
ejpam-4828	167	26	following	follow	VERB
ejpam-4828	167	27	hold	hold	NOUN
ejpam-4828	167	28	:	:	PUNCT
ejpam-4828	167	29	(	(	PUNCT
ejpam-4828	167	30	i	i	NOUN
ejpam-4828	167	31	)	)	PUNCT
ejpam-4828	168	1	if	if	SCONJ
ejpam-4828	168	2	|v0|	|v0|	NOUN
ejpam-4828	168	3	=	=	SYM
ejpam-4828	168	4	0	0	NUM
ejpam-4828	168	5	,	,	PUNCT
ejpam-4828	168	6	then	then	ADV
ejpam-4828	168	7	|v2|	|v2|	ADV
ejpam-4828	168	8	=	=	SYM
ejpam-4828	168	9	0	0	X
ejpam-4828	168	10	.	.	PUNCT
ejpam-4828	168	11	(	(	PUNCT
ejpam-4828	168	12	ii	ii	NOUN
ejpam-4828	168	13	)	)	PUNCT
ejpam-4828	168	14	if	if	SCONJ
ejpam-4828	168	15	|v0|	|v0|	NOUN
ejpam-4828	168	16	=	=	SYM
ejpam-4828	168	17	1	1	NUM
ejpam-4828	168	18	,	,	PUNCT
ejpam-4828	168	19	then	then	ADV
ejpam-4828	168	20	|v2|	|v2|	ADV
ejpam-4828	168	21	=	=	SYM
ejpam-4828	169	1	1	1	X
ejpam-4828	169	2	.	.	PUNCT
ejpam-4828	169	3	(	(	PUNCT
ejpam-4828	169	4	iii	iii	NOUN
ejpam-4828	169	5	)	)	PUNCT
ejpam-4828	169	6	|v1|	|v1|	NOUN
ejpam-4828	169	7	=	=	SYM
ejpam-4828	169	8	0	0	PUNCT
ejpam-4828	170	1	if	if	SCONJ
ejpam-4828	170	2	and	and	CCONJ
ejpam-4828	170	3	only	only	ADV
ejpam-4828	170	4	if	if	SCONJ
ejpam-4828	170	5	v2	v2	PROPN
ejpam-4828	170	6	is	be	AUX
ejpam-4828	170	7	a	a	DET
ejpam-4828	170	8	γcon	γcon	NOUN
ejpam-4828	170	9	-	-	PUNCT
ejpam-4828	170	10	set	set	NOUN
ejpam-4828	170	11	in	in	ADP
ejpam-4828	170	12	g	g	PROPN
ejpam-4828	170	13	(	(	PUNCT
ejpam-4828	170	14	hence	hence	ADV
ejpam-4828	170	15	,	,	PUNCT
ejpam-4828	170	16	γcvr(g	γcvr(g	PROPN
ejpam-4828	170	17	)	)	PUNCT
ejpam-4828	170	18	=	=	SYM
ejpam-4828	170	19	2γcon(g	2γcon(g	NUM
ejpam-4828	170	20	)	)	PUNCT
ejpam-4828	170	21	)	)	PUNCT
ejpam-4828	170	22	.	.	PUNCT
ejpam-4828	171	1	r.	r.	PROPN
ejpam-4828	171	2	fortosa	fortosa	PROPN
ejpam-4828	171	3	,	,	PUNCT
ejpam-4828	171	4	s.	s.	PROPN
ejpam-4828	171	5	canoy	canoy	PROPN
ejpam-4828	171	6	jr	jr	PROPN
ejpam-4828	171	7	.	.	PROPN
ejpam-4828	171	8	/	/	SYM
ejpam-4828	171	9	eur	eur	PROPN
ejpam-4828	171	10	.	.	PUNCT
ejpam-4828	172	1	j.	j.	PROPN
ejpam-4828	172	2	pure	pure	PROPN
ejpam-4828	172	3	appl	appl	PROPN
ejpam-4828	172	4	.	.	PROPN
ejpam-4828	172	5	math	math	PROPN
ejpam-4828	172	6	,	,	PUNCT
ejpam-4828	172	7	16	16	NUM
ejpam-4828	172	8	(	(	PUNCT
ejpam-4828	172	9	3	3	NUM
ejpam-4828	172	10	)	)	PUNCT
ejpam-4828	172	11	(	(	PUNCT
ejpam-4828	172	12	2023	2023	NUM
ejpam-4828	172	13	)	)	PUNCT
ejpam-4828	172	14	,	,	PUNCT
ejpam-4828	172	15	1705	1705	NUM
ejpam-4828	172	16	-	-	SYM
ejpam-4828	172	17	1716	1716	NUM
ejpam-4828	172	18	1710	1710	NUM
ejpam-4828	172	19	proof	proof	NOUN
ejpam-4828	172	20	.	.	PUNCT
ejpam-4828	173	1	(	(	PUNCT
ejpam-4828	173	2	i	i	NOUN
ejpam-4828	173	3	)	)	PUNCT
ejpam-4828	173	4	suppose	suppose	VERB
ejpam-4828	173	5	|v2|	|v2|	ADV
ejpam-4828	173	6	̸=	̸=	PROPN
ejpam-4828	173	7	0	0	NUM
ejpam-4828	173	8	.	.	PUNCT
ejpam-4828	174	1	let	let	VERB
ejpam-4828	174	2	v	v	NOUN
ejpam-4828	174	3	′	′	NOUN
ejpam-4828	174	4	0	0	NUM
ejpam-4828	175	1	=	=	SYM
ejpam-4828	175	2	v0	v0	PROPN
ejpam-4828	175	3	,	,	PUNCT
ejpam-4828	175	4	v	v	NOUN
ejpam-4828	175	5	′	′	NUM
ejpam-4828	175	6	1	1	NUM
ejpam-4828	175	7	=	=	SYM
ejpam-4828	175	8	v1	v1	VERB
ejpam-4828	175	9	∪	∪	NOUN
ejpam-4828	175	10	v2	v2	NOUN
ejpam-4828	175	11	and	and	CCONJ
ejpam-4828	175	12	v	v	NOUN
ejpam-4828	175	13	′	′	NUM
ejpam-4828	175	14	2	2	NUM
ejpam-4828	175	15	=	=	PUNCT
ejpam-4828	175	16	∅.	∅.	NOUN
ejpam-4828	175	17	then	then	ADV
ejpam-4828	175	18	g	g	PROPN
ejpam-4828	175	19	=	=	PUNCT
ejpam-4828	175	20	(	(	PUNCT
ejpam-4828	175	21	v	v	NUM
ejpam-4828	175	22	′	′	NUM
ejpam-4828	175	23	0	0	NUM
ejpam-4828	175	24	,	,	PUNCT
ejpam-4828	175	25	v	v	NOUN
ejpam-4828	175	26	′	′	NUM
ejpam-4828	175	27	1	1	NUM
ejpam-4828	175	28	,	,	PUNCT
ejpam-4828	175	29	v	v	NOUN
ejpam-4828	175	30	′	′	NUM
ejpam-4828	175	31	2	2	NUM
ejpam-4828	175	32	)	)	PUNCT
ejpam-4828	175	33	is	be	AUX
ejpam-4828	175	34	a	a	DET
ejpam-4828	175	35	cvrdf	cvrdf	NOUN
ejpam-4828	175	36	on	on	ADP
ejpam-4828	175	37	g	g	PROPN
ejpam-4828	175	38	and	and	CCONJ
ejpam-4828	175	39	ωcvr	ωcvr	PROPN
ejpam-4828	175	40	g	g	PROPN
ejpam-4828	175	41	(	(	PUNCT
ejpam-4828	175	42	g	g	NOUN
ejpam-4828	175	43	)	)	PUNCT
ejpam-4828	175	44	=	=	PUNCT
ejpam-4828	176	1	|v	|v	PROPN
ejpam-4828	176	2	′	′	NOUN
ejpam-4828	176	3	1	1	NUM
ejpam-4828	177	1	|	|	ADV
ejpam-4828	177	2	=	=	PUNCT
ejpam-4828	177	3	|v1|	|v1|	NOUN
ejpam-4828	177	4	+	+	CCONJ
ejpam-4828	177	5	|v2|	|v2|	X
ejpam-4828	177	6	<	<	X
ejpam-4828	177	7	|v1|	|v1|	NOUN
ejpam-4828	177	8	+	+	CCONJ
ejpam-4828	177	9	2|v2|	2|v2|	NUM
ejpam-4828	177	10	=	=	SYM
ejpam-4828	177	11	ωcvr	ωcvr	PROPN
ejpam-4828	177	12	g	g	PROPN
ejpam-4828	177	13	(	(	PUNCT
ejpam-4828	177	14	f	f	PROPN
ejpam-4828	177	15	)	)	PUNCT
ejpam-4828	177	16	,	,	PUNCT
ejpam-4828	177	17	a	a	DET
ejpam-4828	177	18	contradiction	contradiction	NOUN
ejpam-4828	177	19	.	.	PUNCT
ejpam-4828	178	1	(	(	PUNCT
ejpam-4828	178	2	ii	ii	NOUN
ejpam-4828	178	3	)	)	PUNCT
ejpam-4828	178	4	suppose	suppose	VERB
ejpam-4828	178	5	|v0|	|v0|	NOUN
ejpam-4828	178	6	=	=	SYM
ejpam-4828	178	7	1	1	NUM
ejpam-4828	178	8	,	,	PUNCT
ejpam-4828	178	9	say	say	VERB
ejpam-4828	178	10	v0	v0	NOUN
ejpam-4828	178	11	=	=	SYM
ejpam-4828	178	12	{	{	PUNCT
ejpam-4828	178	13	v0	v0	NOUN
ejpam-4828	178	14	}	}	PUNCT
ejpam-4828	178	15	.	.	PUNCT
ejpam-4828	179	1	suppose	suppose	VERB
ejpam-4828	179	2	further	far	ADV
ejpam-4828	179	3	that	that	PRON
ejpam-4828	179	4	|v2|	|v2|	ADV
ejpam-4828	179	5	≥	≥	NOUN
ejpam-4828	179	6	2	2	NUM
ejpam-4828	179	7	.	.	PUNCT
ejpam-4828	180	1	then	then	ADV
ejpam-4828	180	2	v	v	X
ejpam-4828	180	3	(	(	PUNCT
ejpam-4828	180	4	g	g	NOUN
ejpam-4828	180	5	)	)	PUNCT
ejpam-4828	180	6	\	\	NOUN
ejpam-4828	180	7	{	{	PUNCT
ejpam-4828	180	8	v0	v0	NOUN
ejpam-4828	180	9	}	}	PUNCT
ejpam-4828	180	10	is	be	AUX
ejpam-4828	180	11	a	a	DET
ejpam-4828	180	12	convex	convex	NOUN
ejpam-4828	180	13	dominating	dominating	NOUN
ejpam-4828	180	14	set	set	VERB
ejpam-4828	180	15	in	in	ADP
ejpam-4828	180	16	g.	g.	PROPN
ejpam-4828	180	17	let	let	VERB
ejpam-4828	180	18	v	v	NUM
ejpam-4828	180	19	∈	∈	PROPN
ejpam-4828	180	20	v2	v2	NOUN
ejpam-4828	181	1	such	such	ADJ
ejpam-4828	181	2	that	that	SCONJ
ejpam-4828	181	3	v0v	v0v	PUNCT
ejpam-4828	181	4	∈	∈	PROPN
ejpam-4828	181	5	e(g	e(g	PROPN
ejpam-4828	181	6	)	)	PUNCT
ejpam-4828	181	7	.	.	PUNCT
ejpam-4828	182	1	let	let	VERB
ejpam-4828	182	2	w	w	PROPN
ejpam-4828	182	3	∈	∈	PROPN
ejpam-4828	182	4	v2	v2	PROPN
ejpam-4828	182	5	\{v	\{v	PROPN
ejpam-4828	182	6	}	}	PUNCT
ejpam-4828	182	7	.	.	PUNCT
ejpam-4828	183	1	let	let	VERB
ejpam-4828	183	2	h	h	NOUN
ejpam-4828	183	3	=	=	SYM
ejpam-4828	183	4	(	(	PUNCT
ejpam-4828	183	5	v0	v0	PROPN
ejpam-4828	183	6	,	,	PUNCT
ejpam-4828	183	7	v	v	NOUN
ejpam-4828	183	8	′	′	NUM
ejpam-4828	183	9	1	1	NUM
ejpam-4828	183	10	,	,	PUNCT
ejpam-4828	183	11	v	v	NOUN
ejpam-4828	183	12	′	′	NUM
ejpam-4828	183	13	2	2	NUM
ejpam-4828	183	14	)	)	PUNCT
ejpam-4828	183	15	,	,	PUNCT
ejpam-4828	183	16	where	where	SCONJ
ejpam-4828	183	17	v	v	X
ejpam-4828	183	18	′	′	NOUN
ejpam-4828	183	19	1	1	NUM
ejpam-4828	183	20	=	=	SYM
ejpam-4828	183	21	v1∪{w	v1∪{w	ADV
ejpam-4828	183	22	}	}	PUNCT
ejpam-4828	183	23	and	and	CCONJ
ejpam-4828	183	24	v	v	X
ejpam-4828	183	25	′	′	NUM
ejpam-4828	183	26	2	2	NUM
ejpam-4828	183	27	=	=	SYM
ejpam-4828	183	28	v2\{w	v2\{w	NOUN
ejpam-4828	183	29	}	}	PUNCT
ejpam-4828	183	30	.	.	PUNCT
ejpam-4828	184	1	since	since	SCONJ
ejpam-4828	184	2	v	v	NUM
ejpam-4828	184	3	′	′	NUM
ejpam-4828	184	4	1∪v	1∪v	NUM
ejpam-4828	184	5	′	′	NUM
ejpam-4828	184	6	2	2	NUM
ejpam-4828	184	7	=	=	SYM
ejpam-4828	184	8	v1∪v2	v1∪v2	PROPN
ejpam-4828	184	9	,	,	PUNCT
ejpam-4828	184	10	h	h	PROPN
ejpam-4828	184	11	is	be	AUX
ejpam-4828	184	12	a	a	DET
ejpam-4828	184	13	convex	convex	ADJ
ejpam-4828	184	14	roman	roman	ADJ
ejpam-4828	184	15	dominating	dominating	NOUN
ejpam-4828	184	16	function	function	NOUN
ejpam-4828	184	17	on	on	ADP
ejpam-4828	184	18	g	g	PROPN
ejpam-4828	184	19	and	and	CCONJ
ejpam-4828	184	20	ωcvr	ωcvr	PROPN
ejpam-4828	184	21	g	g	PROPN
ejpam-4828	184	22	(	(	PUNCT
ejpam-4828	184	23	h	h	NOUN
ejpam-4828	184	24	)	)	PUNCT
ejpam-4828	184	25	=	=	SYM
ejpam-4828	184	26	|v	|v	PROPN
ejpam-4828	184	27	′	′	NUM
ejpam-4828	184	28	1	1	NUM
ejpam-4828	184	29	|+	|+	NOUN
ejpam-4828	185	1	2|v	2|v	NOUN
ejpam-4828	186	1	′	′	NOUN
ejpam-4828	186	2	2	2	NUM
ejpam-4828	186	3	|	|	NOUN
ejpam-4828	186	4	=	=	SYM
ejpam-4828	186	5	|v1|+	|v1|+	PRON
ejpam-4828	186	6	1	1	NUM
ejpam-4828	186	7	+	+	SYM
ejpam-4828	186	8	2(|v2|	2(|v2|	NUM
ejpam-4828	186	9	−	−	NUM
ejpam-4828	186	10	1	1	NUM
ejpam-4828	186	11	)	)	PUNCT
ejpam-4828	186	12	=	=	PUNCT
ejpam-4828	186	13	|v1|+	|v1|+	PRON
ejpam-4828	186	14	2|v2|	2|v2|	NUM
ejpam-4828	186	15	−	−	NOUN
ejpam-4828	186	16	1	1	NUM
ejpam-4828	186	17	<	<	X
ejpam-4828	186	18	ωcvr	ωcvr	PROPN
ejpam-4828	186	19	g	g	PROPN
ejpam-4828	186	20	(	(	PUNCT
ejpam-4828	186	21	f	f	PROPN
ejpam-4828	186	22	)	)	PUNCT
ejpam-4828	186	23	,	,	PUNCT
ejpam-4828	186	24	a	a	DET
ejpam-4828	186	25	contradiction	contradiction	NOUN
ejpam-4828	186	26	.	.	PUNCT
ejpam-4828	187	1	thus	thus	ADV
ejpam-4828	187	2	,	,	PUNCT
ejpam-4828	187	3	|v2|	|v2|	NOUN
ejpam-4828	187	4	=	=	SYM
ejpam-4828	187	5	1	1	X
ejpam-4828	187	6	.	.	PUNCT
ejpam-4828	187	7	(	(	PUNCT
ejpam-4828	187	8	iii	iii	NOUN
ejpam-4828	187	9	)	)	PUNCT
ejpam-4828	187	10	suppose	suppose	VERB
ejpam-4828	187	11	|v1|	|v1|	NOUN
ejpam-4828	187	12	=	=	SYM
ejpam-4828	187	13	0	0	X
ejpam-4828	187	14	.	.	PUNCT
ejpam-4828	187	15	suppose	suppose	VERB
ejpam-4828	187	16	further	far	ADV
ejpam-4828	187	17	that	that	SCONJ
ejpam-4828	187	18	v2	v2	PROPN
ejpam-4828	187	19	is	be	AUX
ejpam-4828	187	20	not	not	PART
ejpam-4828	187	21	a	a	DET
ejpam-4828	187	22	γcon	γcon	NOUN
ejpam-4828	187	23	-	-	PUNCT
ejpam-4828	187	24	set	set	NOUN
ejpam-4828	187	25	in	in	ADP
ejpam-4828	187	26	g.	g.	PROPN
ejpam-4828	187	27	then	then	ADV
ejpam-4828	187	28	there	there	PRON
ejpam-4828	187	29	exists	exist	VERB
ejpam-4828	187	30	v	v	NOUN
ejpam-4828	187	31	′	′	NUM
ejpam-4828	187	32	2	2	NUM
ejpam-4828	187	33	⊆	⊆	NUM
ejpam-4828	187	34	v	v	NOUN
ejpam-4828	187	35	(	(	PUNCT
ejpam-4828	187	36	g	g	NOUN
ejpam-4828	187	37	)	)	PUNCT
ejpam-4828	187	38	such	such	ADJ
ejpam-4828	187	39	that	that	DET
ejpam-4828	187	40	v	v	NOUN
ejpam-4828	187	41	′	′	NUM
ejpam-4828	187	42	2	2	NUM
ejpam-4828	187	43	is	be	AUX
ejpam-4828	187	44	a	a	DET
ejpam-4828	187	45	convex	convex	NOUN
ejpam-4828	187	46	dominating	dominating	NOUN
ejpam-4828	187	47	set	set	VERB
ejpam-4828	187	48	in	in	ADP
ejpam-4828	187	49	g	g	NOUN
ejpam-4828	187	50	with	with	ADP
ejpam-4828	187	51	|v	|v	PROPN
ejpam-4828	188	1	′	′	NUM
ejpam-4828	188	2	2	2	NUM
ejpam-4828	189	1	|	|	ADV
ejpam-4828	189	2	<	<	X
ejpam-4828	189	3	|v2|	|v2|	NOUN
ejpam-4828	189	4	.	.	PUNCT
ejpam-4828	190	1	let	let	VERB
ejpam-4828	190	2	h	h	NOUN
ejpam-4828	190	3	=	=	PUNCT
ejpam-4828	190	4	(	(	PUNCT
ejpam-4828	190	5	v	v	NOUN
ejpam-4828	190	6	∗	∗	NOUN
ejpam-4828	190	7	0	0	NUM
ejpam-4828	190	8	,	,	PUNCT
ejpam-4828	190	9	v	v	NOUN
ejpam-4828	190	10	∗	∗	NOUN
ejpam-4828	190	11	1	1	NUM
ejpam-4828	190	12	,	,	PUNCT
ejpam-4828	190	13	v	v	NOUN
ejpam-4828	190	14	∗	∗	NOUN
ejpam-4828	190	15	2	2	NUM
ejpam-4828	190	16	)	)	PUNCT
ejpam-4828	190	17	,	,	PUNCT
ejpam-4828	190	18	where	where	SCONJ
ejpam-4828	190	19	v	v	NOUN
ejpam-4828	190	20	∗	∗	X
ejpam-4828	190	21	1	1	NUM
ejpam-4828	190	22	=	=	NOUN
ejpam-4828	190	23	∅	∅	NOUN
ejpam-4828	190	24	,	,	PUNCT
ejpam-4828	190	25	v	v	NOUN
ejpam-4828	190	26	∗	∗	NOUN
ejpam-4828	190	27	2	2	NUM
ejpam-4828	190	28	=	=	SYM
ejpam-4828	190	29	v	v	NOUN
ejpam-4828	190	30	′	′	NUM
ejpam-4828	190	31	2	2	NUM
ejpam-4828	190	32	,	,	PUNCT
ejpam-4828	190	33	and	and	CCONJ
ejpam-4828	190	34	v	v	ADP
ejpam-4828	190	35	∗	∗	NOUN
ejpam-4828	190	36	0	0	NUM
ejpam-4828	191	1	=	=	SYM
ejpam-4828	191	2	v	v	NOUN
ejpam-4828	191	3	(	(	PUNCT
ejpam-4828	191	4	g)\v	g)\v	NOUN
ejpam-4828	191	5	′	′	NOUN
ejpam-4828	191	6	2	2	NUM
ejpam-4828	191	7	.	.	PUNCT
ejpam-4828	192	1	then	then	ADV
ejpam-4828	192	2	h	h	PROPN
ejpam-4828	192	3	is	be	AUX
ejpam-4828	192	4	a	a	DET
ejpam-4828	192	5	convex	convex	ADJ
ejpam-4828	192	6	roman	roman	ADJ
ejpam-4828	192	7	dominating	dominating	NOUN
ejpam-4828	192	8	function	function	NOUN
ejpam-4828	192	9	on	on	ADP
ejpam-4828	192	10	g	g	PROPN
ejpam-4828	192	11	and	and	CCONJ
ejpam-4828	192	12	ωcvr	ωcvr	PROPN
ejpam-4828	193	1	g	g	PROPN
ejpam-4828	193	2	(	(	PUNCT
ejpam-4828	193	3	h	h	NOUN
ejpam-4828	193	4	)	)	PUNCT
ejpam-4828	193	5	=	=	SYM
ejpam-4828	193	6	2|v	2|v	NUM
ejpam-4828	193	7	∗	∗	NOUN
ejpam-4828	193	8	2	2	NUM
ejpam-4828	193	9	|	|	ADV
ejpam-4828	193	10	<	<	X
ejpam-4828	193	11	2|v2|	2|v2|	NUM
ejpam-4828	193	12	,	,	PUNCT
ejpam-4828	193	13	a	a	DET
ejpam-4828	193	14	contradiction	contradiction	NOUN
ejpam-4828	193	15	.	.	PUNCT
ejpam-4828	194	1	thus	thus	ADV
ejpam-4828	194	2	,	,	PUNCT
ejpam-4828	194	3	v2	v2	PROPN
ejpam-4828	194	4	is	be	AUX
ejpam-4828	194	5	a	a	DET
ejpam-4828	194	6	γcon	γcon	NOUN
ejpam-4828	194	7	-	-	PUNCT
ejpam-4828	194	8	set	set	NOUN
ejpam-4828	194	9	in	in	ADP
ejpam-4828	194	10	g.	g.	NOUN
ejpam-4828	194	11	conversely	conversely	ADV
ejpam-4828	194	12	,	,	PUNCT
ejpam-4828	194	13	suppose	suppose	VERB
ejpam-4828	194	14	that	that	SCONJ
ejpam-4828	194	15	v2	v2	PROPN
ejpam-4828	194	16	is	be	AUX
ejpam-4828	194	17	a	a	DET
ejpam-4828	194	18	γcon	γcon	NOUN
ejpam-4828	194	19	-	-	PUNCT
ejpam-4828	194	20	set	set	VERB
ejpam-4828	194	21	in	in	ADP
ejpam-4828	194	22	g.	g.	PROPN
ejpam-4828	194	23	suppose	suppose	VERB
ejpam-4828	194	24	|v1|	|v1|	NOUN
ejpam-4828	194	25	=	=	NOUN
ejpam-4828	194	26	̸	̸	NUM
ejpam-4828	194	27	0	0	NUM
ejpam-4828	194	28	.	.	PUNCT
ejpam-4828	195	1	then	then	ADV
ejpam-4828	195	2	γcvr(g	γcvr(g	VERB
ejpam-4828	195	3	)	)	PUNCT
ejpam-4828	195	4	=	=	NOUN
ejpam-4828	195	5	|v1|	|v1|	NOUN
ejpam-4828	195	6	+	+	CCONJ
ejpam-4828	195	7	2|v2|	2|v2|	NUM
ejpam-4828	195	8	>	>	PUNCT
ejpam-4828	195	9	2|v2|	2|v2|	NUM
ejpam-4828	195	10	.	.	PUNCT
ejpam-4828	196	1	let	let	VERB
ejpam-4828	196	2	v	v	VERB
ejpam-4828	196	3	′′	′′	PROPN
ejpam-4828	196	4	0	0	PUNCT
ejpam-4828	197	1	=	=	SYM
ejpam-4828	197	2	v0	v0	NOUN
ejpam-4828	197	3	∪	∪	NOUN
ejpam-4828	197	4	v1	v1	PROPN
ejpam-4828	197	5	,	,	PUNCT
ejpam-4828	197	6	v	v	ADP
ejpam-4828	197	7	′′	′′	PROPN
ejpam-4828	197	8	1	1	NUM
ejpam-4828	197	9	=	=	NOUN
ejpam-4828	197	10	∅	∅	NOUN
ejpam-4828	197	11	,	,	PUNCT
ejpam-4828	197	12	and	and	CCONJ
ejpam-4828	197	13	v	v	ADP
ejpam-4828	197	14	′′	′′	PROPN
ejpam-4828	197	15	2	2	NUM
ejpam-4828	197	16	=	=	SYM
ejpam-4828	197	17	v2	v2	PROPN
ejpam-4828	197	18	.	.	PUNCT
ejpam-4828	198	1	then	then	ADV
ejpam-4828	198	2	v	v	ADP
ejpam-4828	198	3	′′	′′	PROPN
ejpam-4828	198	4	0	0	NUM
ejpam-4828	199	1	⊆	⊆	NUM
ejpam-4828	199	2	ng(v	ng(v	PUNCT
ejpam-4828	199	3	′′	′′	PROPN
ejpam-4828	199	4	2	2	NUM
ejpam-4828	199	5	)	)	PUNCT
ejpam-4828	199	6	and	and	CCONJ
ejpam-4828	199	7	v	v	ADP
ejpam-4828	199	8	′′	′′	PROPN
ejpam-4828	199	9	1	1	NUM
ejpam-4828	199	10	∪	∪	X
ejpam-4828	199	11	v	v	ADP
ejpam-4828	199	12	′′	′′	PROPN
ejpam-4828	199	13	2	2	NUM
ejpam-4828	199	14	=	=	SYM
ejpam-4828	199	15	v2	v2	NOUN
ejpam-4828	199	16	is	be	AUX
ejpam-4828	199	17	a	a	DET
ejpam-4828	199	18	convex	convex	NOUN
ejpam-4828	199	19	dominating	dominating	NOUN
ejpam-4828	199	20	set	set	VERB
ejpam-4828	199	21	in	in	ADP
ejpam-4828	199	22	g.	g.	PROPN
ejpam-4828	199	23	thus	thus	ADV
ejpam-4828	199	24	,	,	PUNCT
ejpam-4828	199	25	h	h	NOUN
ejpam-4828	199	26	=	=	PRON
ejpam-4828	199	27	(	(	PUNCT
ejpam-4828	199	28	v	v	NUM
ejpam-4828	199	29	′′	′′	PROPN
ejpam-4828	199	30	0	0	NUM
ejpam-4828	199	31	,	,	PUNCT
ejpam-4828	199	32	v	v	ADP
ejpam-4828	199	33	′′	′′	PROPN
ejpam-4828	199	34	1	1	NUM
ejpam-4828	199	35	,	,	PUNCT
ejpam-4828	199	36	v	v	ADP
ejpam-4828	199	37	′′	′′	PROPN
ejpam-4828	199	38	2	2	NUM
ejpam-4828	199	39	)	)	PUNCT
ejpam-4828	199	40	is	be	AUX
ejpam-4828	199	41	a	a	DET
ejpam-4828	199	42	cvrdf	cvrdf	NOUN
ejpam-4828	199	43	on	on	ADP
ejpam-4828	199	44	g	g	PROPN
ejpam-4828	199	45	and	and	CCONJ
ejpam-4828	199	46	ωcvr	ωcvr	PROPN
ejpam-4828	199	47	g	g	PROPN
ejpam-4828	199	48	(	(	PUNCT
ejpam-4828	199	49	h	h	NOUN
ejpam-4828	199	50	)	)	PUNCT
ejpam-4828	199	51	=	=	SYM
ejpam-4828	199	52	2|v2|	2|v2|	NUM
ejpam-4828	199	53	<	<	X
ejpam-4828	199	54	ωcvr	ωcvr	PROPN
ejpam-4828	199	55	g	g	PROPN
ejpam-4828	199	56	(	(	PUNCT
ejpam-4828	199	57	f	f	PROPN
ejpam-4828	199	58	)	)	PUNCT
ejpam-4828	199	59	,	,	PUNCT
ejpam-4828	199	60	contrary	contrary	ADV
ejpam-4828	199	61	to	to	ADP
ejpam-4828	199	62	our	our	PRON
ejpam-4828	199	63	assumption	assumption	NOUN
ejpam-4828	199	64	of	of	ADP
ejpam-4828	199	65	f	f	PROPN
ejpam-4828	199	66	.	.	PUNCT
ejpam-4828	200	1	we	we	PRON
ejpam-4828	200	2	now	now	ADV
ejpam-4828	200	3	show	show	VERB
ejpam-4828	200	4	that	that	SCONJ
ejpam-4828	200	5	every	every	DET
ejpam-4828	200	6	pair	pair	NOUN
ejpam-4828	200	7	of	of	ADP
ejpam-4828	200	8	positive	positive	ADJ
ejpam-4828	200	9	integers	integer	NOUN
ejpam-4828	200	10	under	under	ADP
ejpam-4828	200	11	some	some	DET
ejpam-4828	200	12	restrictions	restriction	NOUN
ejpam-4828	200	13	are	be	AUX
ejpam-4828	200	14	realizable	realizable	ADJ
ejpam-4828	200	15	as	as	ADP
ejpam-4828	200	16	the	the	DET
ejpam-4828	200	17	convex	convex	NOUN
ejpam-4828	200	18	domination	domination	NOUN
ejpam-4828	200	19	number	number	NOUN
ejpam-4828	200	20	and	and	CCONJ
ejpam-4828	200	21	convex	convex	VERB
ejpam-4828	200	22	roman	roman	ADJ
ejpam-4828	200	23	domination	domination	NOUN
ejpam-4828	200	24	number	number	NOUN
ejpam-4828	200	25	of	of	ADP
ejpam-4828	200	26	a	a	DET
ejpam-4828	200	27	connected	connected	ADJ
ejpam-4828	200	28	graph	graph	NOUN
ejpam-4828	200	29	.	.	PUNCT
ejpam-4828	201	1	theorem	theorem	NOUN
ejpam-4828	201	2	4	4	NUM
ejpam-4828	201	3	.	.	PUNCT
ejpam-4828	202	1	let	let	VERB
ejpam-4828	202	2	a	a	PRON
ejpam-4828	202	3	and	and	CCONJ
ejpam-4828	202	4	b	b	NOUN
ejpam-4828	202	5	be	be	AUX
ejpam-4828	202	6	positive	positive	ADJ
ejpam-4828	202	7	integers	integer	NOUN
ejpam-4828	202	8	such	such	ADJ
ejpam-4828	202	9	that	that	SCONJ
ejpam-4828	202	10	4	4	NUM
ejpam-4828	202	11	≤	≤	NOUN
ejpam-4828	202	12	a	a	DET
ejpam-4828	202	13	+	+	NUM
ejpam-4828	202	14	2	2	NUM
ejpam-4828	202	15	≤	≤	NUM
ejpam-4828	202	16	b	b	NOUN
ejpam-4828	202	17	≤	≤	NUM
ejpam-4828	202	18	2a	2a	NUM
ejpam-4828	202	19	.	.	PUNCT
ejpam-4828	203	1	then	then	ADV
ejpam-4828	203	2	there	there	PRON
ejpam-4828	203	3	exists	exist	VERB
ejpam-4828	203	4	a	a	DET
ejpam-4828	203	5	connected	connected	ADJ
ejpam-4828	203	6	graph	graph	NOUN
ejpam-4828	203	7	g	g	ADP
ejpam-4828	203	8	such	such	ADJ
ejpam-4828	203	9	that	that	DET
ejpam-4828	203	10	γcon(g	γcon(g	NOUN
ejpam-4828	203	11	)	)	PUNCT
ejpam-4828	203	12	=	=	SYM
ejpam-4828	203	13	a	a	PRON
ejpam-4828	203	14	and	and	CCONJ
ejpam-4828	203	15	γcvr(g	γcvr(g	ADJ
ejpam-4828	203	16	)	)	PUNCT
ejpam-4828	203	17	=	=	SYM
ejpam-4828	203	18	b.	b.	PROPN
ejpam-4828	203	19	proof	proof	NOUN
ejpam-4828	203	20	.	.	PUNCT
ejpam-4828	204	1	suppose	suppose	VERB
ejpam-4828	204	2	b	b	NOUN
ejpam-4828	204	3	=	=	SYM
ejpam-4828	204	4	2a	2a	NUM
ejpam-4828	204	5	.	.	PUNCT
ejpam-4828	205	1	consider	consider	VERB
ejpam-4828	205	2	the	the	DET
ejpam-4828	205	3	graph	graph	NOUN
ejpam-4828	205	4	g′	g′	NOUN
ejpam-4828	205	5	in	in	ADP
ejpam-4828	205	6	figure	figure	NOUN
ejpam-4828	205	7	2	2	NUM
ejpam-4828	205	8	.	.	PUNCT
ejpam-4828	206	1	let	let	VERB
ejpam-4828	206	2	s	s	VERB
ejpam-4828	206	3	=	=	NOUN
ejpam-4828	206	4	{	{	PUNCT
ejpam-4828	206	5	v1	v1	PROPN
ejpam-4828	206	6	,	,	PUNCT
ejpam-4828	206	7	v2	v2	PROPN
ejpam-4828	206	8	,	,	PUNCT
ejpam-4828	206	9	v3	v3	PROPN
ejpam-4828	206	10	,	,	PUNCT
ejpam-4828	206	11	.	.	PUNCT
ejpam-4828	206	12	.	.	PUNCT
ejpam-4828	207	1	.	.	PUNCT
ejpam-4828	208	1	,	,	PUNCT
ejpam-4828	208	2	va	va	NOUN
ejpam-4828	208	3	}	}	PUNCT
ejpam-4828	208	4	.	.	PUNCT
ejpam-4828	209	1	put	put	VERB
ejpam-4828	209	2	v2	v2	NOUN
ejpam-4828	209	3	=	=	SYM
ejpam-4828	209	4	s	s	NOUN
ejpam-4828	209	5	,	,	PUNCT
ejpam-4828	209	6	v1	v1	NOUN
ejpam-4828	209	7	=	=	SYM
ejpam-4828	209	8	∅	∅	NOUN
ejpam-4828	209	9	,	,	PUNCT
ejpam-4828	209	10	and	and	CCONJ
ejpam-4828	209	11	v0	v0	PROPN
ejpam-4828	209	12	=	=	SYM
ejpam-4828	209	13	v	v	PROPN
ejpam-4828	209	14	(	(	PUNCT
ejpam-4828	209	15	g′	g′	NOUN
ejpam-4828	209	16	)	)	PUNCT
ejpam-4828	209	17	\	\	PROPN
ejpam-4828	210	1	v2	v2	PROPN
ejpam-4828	210	2	.	.	PUNCT
ejpam-4828	211	1	clearly	clearly	ADV
ejpam-4828	211	2	,	,	PUNCT
ejpam-4828	211	3	s	s	VERB
ejpam-4828	211	4	is	be	AUX
ejpam-4828	211	5	γcon	γcon	NOUN
ejpam-4828	211	6	-	-	PUNCT
ejpam-4828	211	7	set	set	VERB
ejpam-4828	211	8	and	and	CCONJ
ejpam-4828	211	9	f	f	NOUN
ejpam-4828	211	10	=	=	SYM
ejpam-4828	211	11	(	(	PUNCT
ejpam-4828	211	12	v0	v0	PROPN
ejpam-4828	211	13	,	,	PUNCT
ejpam-4828	211	14	v1	v1	NOUN
ejpam-4828	211	15	,	,	PUNCT
ejpam-4828	211	16	v2	v2	PROPN
ejpam-4828	211	17	)	)	PUNCT
ejpam-4828	211	18	is	be	AUX
ejpam-4828	211	19	a	a	DET
ejpam-4828	211	20	γcvr	γcvr	NOUN
ejpam-4828	211	21	-	-	PUNCT
ejpam-4828	211	22	function	function	NOUN
ejpam-4828	211	23	on	on	ADP
ejpam-4828	211	24	g′.	g′.	X
ejpam-4828	211	25	thus	thus	ADV
ejpam-4828	211	26	,	,	PUNCT
ejpam-4828	211	27	γcon(g	γcon(g	PROPN
ejpam-4828	211	28	′	′	NOUN
ejpam-4828	211	29	)	)	PUNCT
ejpam-4828	211	30	=	=	PUNCT
ejpam-4828	211	31	|s|	|s|	PROPN
ejpam-4828	211	32	=	=	PUNCT
ejpam-4828	211	33	a	a	PROPN
ejpam-4828	211	34	and	and	CCONJ
ejpam-4828	211	35	γcvr(g	γcvr(g	ADV
ejpam-4828	211	36	′	′	NUM
ejpam-4828	211	37	)	)	PUNCT
ejpam-4828	211	38	=	=	SYM
ejpam-4828	211	39	2|v2|	2|v2|	NUM
ejpam-4828	211	40	=	=	SYM
ejpam-4828	211	41	2a	2a	NUM
ejpam-4828	211	42	=	=	SYM
ejpam-4828	211	43	b.	b.	PROPN
ejpam-4828	211	44	v1	v1	PROPN
ejpam-4828	211	45	v2	v2	PROPN
ejpam-4828	211	46	v3	v3	PROPN
ejpam-4828	211	47	·	·	PUNCT
ejpam-4828	211	48	·	·	PUNCT
ejpam-4828	211	49	·	·	PUNCT
ejpam-4828	211	50	va−1	va−1	NOUN
ejpam-4828	211	51	va	va	NOUN
ejpam-4828	211	52	figure	figure	NOUN
ejpam-4828	211	53	2	2	NUM
ejpam-4828	211	54	:	:	PUNCT
ejpam-4828	211	55	a	a	DET
ejpam-4828	211	56	graph	graph	NOUN
ejpam-4828	211	57	g′	g′	NOUN
ejpam-4828	211	58	with	with	ADP
ejpam-4828	211	59	γcon(g	γcon(g	PROPN
ejpam-4828	211	60	′	′	NUM
ejpam-4828	211	61	)	)	PUNCT
ejpam-4828	211	62	=	=	PUNCT
ejpam-4828	212	1	a	a	PRON
ejpam-4828	212	2	and	and	CCONJ
ejpam-4828	212	3	γcvr(g	γcvr(g	ADV
ejpam-4828	212	4	′	′	NUM
ejpam-4828	212	5	)	)	PUNCT
ejpam-4828	213	1	=	=	PUNCT
ejpam-4828	213	2	2a	2a	PROPN
ejpam-4828	213	3	r.	r.	PROPN
ejpam-4828	213	4	fortosa	fortosa	PROPN
ejpam-4828	213	5	,	,	PUNCT
ejpam-4828	213	6	s.	s.	PROPN
ejpam-4828	213	7	canoy	canoy	PROPN
ejpam-4828	213	8	jr	jr	PROPN
ejpam-4828	213	9	.	.	PROPN
ejpam-4828	213	10	/	/	SYM
ejpam-4828	213	11	eur	eur	PROPN
ejpam-4828	213	12	.	.	PUNCT
ejpam-4828	214	1	j.	j.	PROPN
ejpam-4828	214	2	pure	pure	PROPN
ejpam-4828	214	3	appl	appl	PROPN
ejpam-4828	214	4	.	.	PROPN
ejpam-4828	214	5	math	math	PROPN
ejpam-4828	214	6	,	,	PUNCT
ejpam-4828	214	7	16	16	NUM
ejpam-4828	214	8	(	(	PUNCT
ejpam-4828	214	9	3	3	NUM
ejpam-4828	214	10	)	)	PUNCT
ejpam-4828	214	11	(	(	PUNCT
ejpam-4828	214	12	2023	2023	NUM
ejpam-4828	214	13	)	)	PUNCT
ejpam-4828	214	14	,	,	PUNCT
ejpam-4828	214	15	1705	1705	NUM
ejpam-4828	214	16	-	-	SYM
ejpam-4828	214	17	1716	1716	NUM
ejpam-4828	214	18	1711	1711	NUM
ejpam-4828	214	19	next	next	ADV
ejpam-4828	214	20	,	,	PUNCT
ejpam-4828	214	21	let	let	VERB
ejpam-4828	214	22	b	b	PRON
ejpam-4828	214	23	<	<	X
ejpam-4828	214	24	2a	2a	NUM
ejpam-4828	214	25	.	.	PUNCT
ejpam-4828	215	1	then	then	ADV
ejpam-4828	215	2	2	2	NUM
ejpam-4828	215	3	≤	≤	NOUN
ejpam-4828	215	4	m	m	VERB
ejpam-4828	215	5	=	=	SYM
ejpam-4828	216	1	b	b	X
ejpam-4828	216	2	−	−	NOUN
ejpam-4828	216	3	a	a	DET
ejpam-4828	216	4	<	<	X
ejpam-4828	216	5	a.	a.	NOUN
ejpam-4828	216	6	consider	consider	VERB
ejpam-4828	216	7	the	the	DET
ejpam-4828	216	8	graph	graph	NOUN
ejpam-4828	216	9	g	g	NOUN
ejpam-4828	216	10	in	in	ADP
ejpam-4828	216	11	figure	figure	NOUN
ejpam-4828	216	12	3	3	NUM
ejpam-4828	216	13	.	.	PUNCT
ejpam-4828	217	1	let	let	VERB
ejpam-4828	217	2	s∗	s∗	PROPN
ejpam-4828	217	3	=	=	SYM
ejpam-4828	217	4	{	{	PUNCT
ejpam-4828	217	5	v1	v1	PROPN
ejpam-4828	217	6	,	,	PUNCT
ejpam-4828	217	7	v2	v2	PROPN
ejpam-4828	217	8	,	,	PUNCT
ejpam-4828	217	9	.	.	PUNCT
ejpam-4828	217	10	.	.	PUNCT
ejpam-4828	218	1	.	.	PUNCT
ejpam-4828	219	1	,	,	PUNCT
ejpam-4828	219	2	va	va	NOUN
ejpam-4828	219	3	}	}	PUNCT
ejpam-4828	219	4	.	.	PUNCT
ejpam-4828	220	1	then	then	ADV
ejpam-4828	220	2	s∗	s∗	PROPN
ejpam-4828	220	3	is	be	AUX
ejpam-4828	220	4	a	a	DET
ejpam-4828	220	5	γcon	γcon	NOUN
ejpam-4828	220	6	-	-	PUNCT
ejpam-4828	220	7	set	set	NOUN
ejpam-4828	220	8	in	in	ADP
ejpam-4828	220	9	g.	g.	PROPN
ejpam-4828	220	10	it	it	PRON
ejpam-4828	220	11	follows	follow	VERB
ejpam-4828	220	12	that	that	SCONJ
ejpam-4828	220	13	γcon(g	γcon(g	NOUN
ejpam-4828	220	14	)	)	PUNCT
ejpam-4828	220	15	=	=	SYM
ejpam-4828	220	16	a.	a.	NOUN
ejpam-4828	220	17	set	set	VERB
ejpam-4828	220	18	v2	v2	NOUN
ejpam-4828	220	19	=	=	PUNCT
ejpam-4828	220	20	{	{	PUNCT
ejpam-4828	220	21	v1	v1	PROPN
ejpam-4828	220	22	,	,	PUNCT
ejpam-4828	220	23	v2	v2	PROPN
ejpam-4828	220	24	,	,	PUNCT
ejpam-4828	220	25	.	.	PUNCT
ejpam-4828	220	26	.	.	PUNCT
ejpam-4828	221	1	.	.	PUNCT
ejpam-4828	222	1	,	,	PUNCT
ejpam-4828	222	2	vm−1	vm−1	NOUN
ejpam-4828	222	3	,	,	PUNCT
ejpam-4828	222	4	va	va	NOUN
ejpam-4828	222	5	}	}	PUNCT
ejpam-4828	222	6	,	,	PUNCT
ejpam-4828	222	7	v1	v1	NOUN
ejpam-4828	222	8	=	=	SYM
ejpam-4828	222	9	{	{	PUNCT
ejpam-4828	222	10	vm	vm	PROPN
ejpam-4828	222	11	,	,	PUNCT
ejpam-4828	222	12	vm+1	vm+1	NOUN
ejpam-4828	222	13	,	,	PUNCT
ejpam-4828	222	14	.	.	PUNCT
ejpam-4828	222	15	.	.	PUNCT
ejpam-4828	222	16	.	.	PUNCT
ejpam-4828	223	1	,	,	PUNCT
ejpam-4828	223	2	va−1	va−1	NOUN
ejpam-4828	223	3	}	}	PUNCT
ejpam-4828	223	4	,	,	PUNCT
ejpam-4828	223	5	and	and	CCONJ
ejpam-4828	223	6	v0	v0	PROPN
ejpam-4828	223	7	=	=	SYM
ejpam-4828	223	8	v	v	PROPN
ejpam-4828	223	9	(	(	PUNCT
ejpam-4828	223	10	g)\(v1∪v2	g)\(v1∪v2	PROPN
ejpam-4828	223	11	)	)	PUNCT
ejpam-4828	223	12	.	.	PUNCT
ejpam-4828	224	1	clearly	clearly	ADV
ejpam-4828	224	2	,	,	PUNCT
ejpam-4828	224	3	g	g	PROPN
ejpam-4828	224	4	=	=	SYM
ejpam-4828	224	5	(	(	PUNCT
ejpam-4828	224	6	v0	v0	PROPN
ejpam-4828	224	7	,	,	PUNCT
ejpam-4828	224	8	v1	v1	NOUN
ejpam-4828	224	9	,	,	PUNCT
ejpam-4828	224	10	v2	v2	PROPN
ejpam-4828	224	11	)	)	PUNCT
ejpam-4828	224	12	is	be	AUX
ejpam-4828	224	13	a	a	DET
ejpam-4828	224	14	γcvr	γcvr	NOUN
ejpam-4828	224	15	-	-	PUNCT
ejpam-4828	224	16	function	function	NOUN
ejpam-4828	224	17	on	on	ADP
ejpam-4828	224	18	g.	g.	PROPN
ejpam-4828	224	19	therefore	therefore	ADV
ejpam-4828	224	20	,	,	PUNCT
ejpam-4828	224	21	γcvr(g	γcvr(g	NOUN
ejpam-4828	224	22	)	)	PUNCT
ejpam-4828	224	23	=	=	PUNCT
ejpam-4828	224	24	|v1|+	|v1|+	PRON
ejpam-4828	224	25	2|v2|	2|v2|	NUM
ejpam-4828	224	26	=	=	SYM
ejpam-4828	224	27	(	(	PUNCT
ejpam-4828	224	28	a−m	a−m	NOUN
ejpam-4828	224	29	)	)	PUNCT
ejpam-4828	225	1	+	+	CCONJ
ejpam-4828	225	2	2	2	NUM
ejpam-4828	225	3	m	m	VERB
ejpam-4828	225	4	=	=	NOUN
ejpam-4828	225	5	m+	m+	NUM
ejpam-4828	225	6	a	a	DET
ejpam-4828	225	7	=	=	X
ejpam-4828	225	8	b.	b.	PROPN
ejpam-4828	225	9	v1	v1	PROPN
ejpam-4828	225	10	v2	v2	PROPN
ejpam-4828	225	11	v3	v3	PROPN
ejpam-4828	225	12	·	·	PUNCT
ejpam-4828	225	13	·	·	PUNCT
ejpam-4828	225	14	·	·	PUNCT
ejpam-4828	226	1	vm−1	vm−1	NOUN
ejpam-4828	226	2	vm	vm	PROPN
ejpam-4828	226	3	·	·	PUNCT
ejpam-4828	226	4	·	·	PUNCT
ejpam-4828	226	5	·	·	PUNCT
ejpam-4828	226	6	va−1	va−1	NOUN
ejpam-4828	226	7	va	va	NOUN
ejpam-4828	226	8	figure	figure	NOUN
ejpam-4828	226	9	3	3	NUM
ejpam-4828	226	10	:	:	PUNCT
ejpam-4828	226	11	a	a	DET
ejpam-4828	226	12	graph	graph	NOUN
ejpam-4828	226	13	g	g	NOUN
ejpam-4828	226	14	with	with	ADP
ejpam-4828	226	15	γcon(g	γcon(g	NOUN
ejpam-4828	226	16	)	)	PUNCT
ejpam-4828	226	17	=	=	SYM
ejpam-4828	226	18	a	a	PRON
ejpam-4828	226	19	and	and	CCONJ
ejpam-4828	226	20	γcvr(g	γcvr(g	ADJ
ejpam-4828	226	21	)	)	PUNCT
ejpam-4828	226	22	=	=	SYM
ejpam-4828	227	1	b	b	X
ejpam-4828	227	2	<	<	X
ejpam-4828	227	3	2a	2a	NUM
ejpam-4828	227	4	this	this	PRON
ejpam-4828	227	5	proves	prove	VERB
ejpam-4828	227	6	the	the	DET
ejpam-4828	227	7	assertion	assertion	NOUN
ejpam-4828	227	8	.	.	PUNCT
ejpam-4828	228	1	corollary	corollary	ADJ
ejpam-4828	228	2	5	5	NUM
ejpam-4828	228	3	.	.	PUNCT
ejpam-4828	229	1	let	let	VERB
ejpam-4828	229	2	n	n	PRON
ejpam-4828	229	3	be	be	AUX
ejpam-4828	229	4	a	a	DET
ejpam-4828	229	5	positive	positive	ADJ
ejpam-4828	229	6	integer	integer	NOUN
ejpam-4828	229	7	with	with	ADP
ejpam-4828	229	8	n	n	PRON
ejpam-4828	229	9	≥	≥	NUM
ejpam-4828	229	10	2	2	NUM
ejpam-4828	229	11	.	.	PUNCT
ejpam-4828	230	1	then	then	ADV
ejpam-4828	230	2	there	there	PRON
ejpam-4828	230	3	exists	exist	VERB
ejpam-4828	230	4	a	a	DET
ejpam-4828	230	5	connected	connected	ADJ
ejpam-4828	230	6	graph	graph	NOUN
ejpam-4828	230	7	g	g	ADP
ejpam-4828	230	8	such	such	ADJ
ejpam-4828	230	9	that	that	PRON
ejpam-4828	230	10	γcvr(g	γcvr(g	NOUN
ejpam-4828	230	11	)	)	PUNCT
ejpam-4828	230	12	−	−	PROPN
ejpam-4828	230	13	γcon(g	γcon(g	PROPN
ejpam-4828	230	14	)	)	PUNCT
ejpam-4828	230	15	=	=	VERB
ejpam-4828	231	1	n.	n.	NOUN
ejpam-4828	231	2	in	in	ADP
ejpam-4828	231	3	other	other	ADJ
ejpam-4828	231	4	words	word	NOUN
ejpam-4828	231	5	,	,	PUNCT
ejpam-4828	231	6	the	the	DET
ejpam-4828	231	7	difference	difference	NOUN
ejpam-4828	231	8	γcvr(g	γcvr(g	NOUN
ejpam-4828	231	9	)	)	PUNCT
ejpam-4828	231	10	−	−	PROPN
ejpam-4828	231	11	γcon(g	γcon(g	PROPN
ejpam-4828	231	12	)	)	PUNCT
ejpam-4828	231	13	can	can	AUX
ejpam-4828	231	14	be	be	AUX
ejpam-4828	231	15	made	make	VERB
ejpam-4828	231	16	arbitrarily	arbitrarily	ADV
ejpam-4828	231	17	large	large	ADJ
ejpam-4828	231	18	.	.	PUNCT
ejpam-4828	232	1	proposition	proposition	NOUN
ejpam-4828	232	2	4	4	NUM
ejpam-4828	232	3	.	.	PUNCT
ejpam-4828	233	1	let	let	VERB
ejpam-4828	233	2	n	n	PRON
ejpam-4828	233	3	be	be	AUX
ejpam-4828	233	4	a	a	DET
ejpam-4828	233	5	positive	positive	ADJ
ejpam-4828	233	6	integer	integer	NOUN
ejpam-4828	233	7	.	.	PUNCT
ejpam-4828	234	1	then	then	ADV
ejpam-4828	234	2	γcvr(pn	γcvr(pn	ADJ
ejpam-4828	234	3	)	)	PUNCT
ejpam-4828	234	4	=	=	PUNCT
ejpam-4828	235	1			NOUN
ejpam-4828	235	2	1	1	NUM
ejpam-4828	235	3	if	if	SCONJ
ejpam-4828	235	4	n	n	NOUN
ejpam-4828	235	5	=	=	SYM
ejpam-4828	235	6	1	1	NUM
ejpam-4828	235	7	2	2	NUM
ejpam-4828	235	8	if	if	SCONJ
ejpam-4828	235	9	n	n	NOUN
ejpam-4828	235	10	=	=	SYM
ejpam-4828	235	11	2	2	NUM
ejpam-4828	235	12	,	,	PUNCT
ejpam-4828	235	13	3	3	NUM
ejpam-4828	235	14	n	n	NOUN
ejpam-4828	235	15	if	if	SCONJ
ejpam-4828	235	16	n	n	PRON
ejpam-4828	235	17	≥	≥	NOUN
ejpam-4828	235	18	4	4	NUM
ejpam-4828	235	19	.	.	PUNCT
ejpam-4828	236	1	proof	proof	NOUN
ejpam-4828	236	2	.	.	PUNCT
ejpam-4828	237	1	clearly	clearly	ADV
ejpam-4828	237	2	,	,	PUNCT
ejpam-4828	237	3	γcvr(p1	γcvr(p1	NOUN
ejpam-4828	237	4	)	)	PUNCT
ejpam-4828	237	5	=	=	SYM
ejpam-4828	237	6	1	1	NUM
ejpam-4828	237	7	and	and	CCONJ
ejpam-4828	237	8	γcvr(pn	γcvr(pn	ADJ
ejpam-4828	237	9	)	)	PUNCT
ejpam-4828	237	10	=	=	SYM
ejpam-4828	237	11	2	2	NUM
ejpam-4828	237	12	for	for	ADP
ejpam-4828	237	13	n	n	NOUN
ejpam-4828	237	14	=	=	SYM
ejpam-4828	237	15	2	2	NUM
ejpam-4828	237	16	,	,	PUNCT
ejpam-4828	237	17	3	3	NUM
ejpam-4828	237	18	.	.	PUNCT
ejpam-4828	237	19	suppose	suppose	VERB
ejpam-4828	237	20	n	n	PRON
ejpam-4828	237	21	≥	≥	NUM
ejpam-4828	237	22	4	4	NUM
ejpam-4828	237	23	.	.	PUNCT
ejpam-4828	238	1	let	let	VERB
ejpam-4828	238	2	pn	pn	VERB
ejpam-4828	238	3	=	=	PUNCT
ejpam-4828	239	1	[	[	X
ejpam-4828	239	2	v1	v1	NOUN
ejpam-4828	239	3	,	,	PUNCT
ejpam-4828	239	4	v2	v2	NOUN
ejpam-4828	239	5	,	,	PUNCT
ejpam-4828	239	6	.	.	PUNCT
ejpam-4828	239	7	.	.	PUNCT
ejpam-4828	239	8	.	.	PUNCT
ejpam-4828	240	1	,	,	PUNCT
ejpam-4828	240	2	vn	vn	X
ejpam-4828	240	3	]	]	PUNCT
ejpam-4828	240	4	and	and	CCONJ
ejpam-4828	240	5	let	let	VERB
ejpam-4828	240	6	f	f	PROPN
ejpam-4828	240	7	=	=	SYM
ejpam-4828	240	8	(	(	PUNCT
ejpam-4828	240	9	v0	v0	PROPN
ejpam-4828	240	10	,	,	PUNCT
ejpam-4828	240	11	v1	v1	NOUN
ejpam-4828	240	12	,	,	PUNCT
ejpam-4828	240	13	v2	v2	PROPN
ejpam-4828	240	14	)	)	PUNCT
ejpam-4828	240	15	be	be	AUX
ejpam-4828	240	16	a	a	DET
ejpam-4828	240	17	γcvr	γcvr	NOUN
ejpam-4828	240	18	-	-	PUNCT
ejpam-4828	240	19	function	function	NOUN
ejpam-4828	240	20	on	on	ADP
ejpam-4828	240	21	pn	pn	PROPN
ejpam-4828	240	22	.	.	PUNCT
ejpam-4828	241	1	if	if	SCONJ
ejpam-4828	241	2	|v0|	|v0|	NOUN
ejpam-4828	241	3	=	=	SYM
ejpam-4828	241	4	0	0	NUM
ejpam-4828	241	5	,	,	PUNCT
ejpam-4828	241	6	|v2|	|v2|	NOUN
ejpam-4828	241	7	=	=	SYM
ejpam-4828	241	8	0	0	NUM
ejpam-4828	241	9	by	by	ADP
ejpam-4828	241	10	proposition	proposition	NOUN
ejpam-4828	241	11	3(i	3(i	NUM
ejpam-4828	241	12	)	)	PUNCT
ejpam-4828	241	13	.	.	PUNCT
ejpam-4828	242	1	it	it	PRON
ejpam-4828	242	2	follows	follow	VERB
ejpam-4828	242	3	that	that	PRON
ejpam-4828	242	4	v1	v1	NOUN
ejpam-4828	242	5	=	=	SYM
ejpam-4828	242	6	v	v	NOUN
ejpam-4828	242	7	(	(	PUNCT
ejpam-4828	242	8	pn	pn	NOUN
ejpam-4828	242	9	)	)	PUNCT
ejpam-4828	242	10	and	and	CCONJ
ejpam-4828	242	11	γcvr(pn	γcvr(pn	ADJ
ejpam-4828	242	12	)	)	PUNCT
ejpam-4828	242	13	=	=	PUNCT
ejpam-4828	242	14	ωcvr	ωcvr	PROPN
ejpam-4828	242	15	pn	pn	PROPN
ejpam-4828	242	16	(	(	PUNCT
ejpam-4828	242	17	f	f	X
ejpam-4828	242	18	)	)	PUNCT
ejpam-4828	242	19	=	=	NOUN
ejpam-4828	242	20	|v1|	|v1|	NOUN
ejpam-4828	242	21	=	=	SYM
ejpam-4828	242	22	n.	n.	PROPN
ejpam-4828	242	23	suppose	suppose	VERB
ejpam-4828	242	24	there	there	PRON
ejpam-4828	242	25	exists	exist	VERB
ejpam-4828	242	26	vj	vj	PROPN
ejpam-4828	242	27	∈	∈	PROPN
ejpam-4828	242	28	v0	v0	NOUN
ejpam-4828	242	29	such	such	ADJ
ejpam-4828	242	30	that	that	SCONJ
ejpam-4828	242	31	j	j	PROPN
ejpam-4828	242	32	̸=	̸=	PROPN
ejpam-4828	242	33	1	1	NUM
ejpam-4828	242	34	,	,	PUNCT
ejpam-4828	242	35	n.	n.	NOUN
ejpam-4828	242	36	then	then	ADV
ejpam-4828	242	37	vj−1	vj−1	PROPN
ejpam-4828	242	38	∈	∈	PROPN
ejpam-4828	242	39	v2	v2	PROPN
ejpam-4828	242	40	or	or	CCONJ
ejpam-4828	242	41	vj+1	vj+1	NUM
ejpam-4828	242	42	∈	∈	PROPN
ejpam-4828	242	43	v2	v2	NOUN
ejpam-4828	242	44	.	.	PUNCT
ejpam-4828	243	1	if	if	SCONJ
ejpam-4828	243	2	vj−1	vj−1	PROPN
ejpam-4828	243	3	∈	∈	PROPN
ejpam-4828	243	4	v2	v2	PROPN
ejpam-4828	243	5	,	,	PUNCT
ejpam-4828	243	6	then	then	ADV
ejpam-4828	243	7	vk	vk	NOUN
ejpam-4828	243	8	∈	∈	PROPN
ejpam-4828	243	9	v0	v0	NOUN
ejpam-4828	243	10	for	for	ADP
ejpam-4828	243	11	all	all	PRON
ejpam-4828	243	12	k	k	PROPN
ejpam-4828	243	13	>	>	X
ejpam-4828	243	14	j	j	PROPN
ejpam-4828	243	15	since	since	SCONJ
ejpam-4828	243	16	v1	v1	PROPN
ejpam-4828	243	17	∪	∪	NOUN
ejpam-4828	243	18	v2	v2	NOUN
ejpam-4828	243	19	is	be	AUX
ejpam-4828	243	20	convex	convex	NOUN
ejpam-4828	243	21	.	.	PUNCT
ejpam-4828	244	1	again	again	ADV
ejpam-4828	244	2	,	,	PUNCT
ejpam-4828	244	3	by	by	ADP
ejpam-4828	244	4	convexity	convexity	NOUN
ejpam-4828	244	5	in	in	ADP
ejpam-4828	244	6	v1	v1	PROPN
ejpam-4828	244	7	∪	∪	X
ejpam-4828	244	8	v2	v2	NOUN
ejpam-4828	244	9	,	,	PUNCT
ejpam-4828	244	10	vs	vs	ADP
ejpam-4828	244	11	∈	∈	PROPN
ejpam-4828	244	12	v0	v0	NOUN
ejpam-4828	244	13	for	for	ADP
ejpam-4828	244	14	all	all	PRON
ejpam-4828	244	15	s	s	PART
ejpam-4828	244	16	<	<	X
ejpam-4828	244	17	j	j	X
ejpam-4828	244	18	whenever	whenever	SCONJ
ejpam-4828	244	19	vj+1	vj+1	DET
ejpam-4828	244	20	∈	∈	PROPN
ejpam-4828	244	21	v2	v2	NOUN
ejpam-4828	244	22	.	.	PUNCT
ejpam-4828	245	1	in	in	ADP
ejpam-4828	245	2	either	either	DET
ejpam-4828	245	3	case	case	NOUN
ejpam-4828	245	4	,	,	PUNCT
ejpam-4828	245	5	f	f	PROPN
ejpam-4828	245	6	is	be	AUX
ejpam-4828	245	7	not	not	PART
ejpam-4828	245	8	an	an	DET
ejpam-4828	245	9	rdf	rdf	NOUN
ejpam-4828	245	10	in	in	ADP
ejpam-4828	245	11	g	g	NOUN
ejpam-4828	245	12	,	,	PUNCT
ejpam-4828	245	13	a	a	DET
ejpam-4828	245	14	contradiction	contradiction	NOUN
ejpam-4828	245	15	.	.	PUNCT
ejpam-4828	246	1	therefore	therefore	ADV
ejpam-4828	246	2	,	,	PUNCT
ejpam-4828	246	3	v0	v0	PROPN
ejpam-4828	246	4	⊆	⊆	NUM
ejpam-4828	246	5	{	{	PUNCT
ejpam-4828	246	6	v1	v1	NOUN
ejpam-4828	246	7	,	,	PUNCT
ejpam-4828	246	8	vn	vn	NOUN
ejpam-4828	246	9	}	}	PUNCT
ejpam-4828	246	10	.	.	PUNCT
ejpam-4828	247	1	suppose	suppose	VERB
ejpam-4828	247	2	v0	v0	NOUN
ejpam-4828	247	3	=	=	SYM
ejpam-4828	247	4	{	{	PUNCT
ejpam-4828	247	5	v1	v1	NOUN
ejpam-4828	247	6	}	}	PUNCT
ejpam-4828	247	7	(	(	PUNCT
ejpam-4828	247	8	or	or	CCONJ
ejpam-4828	247	9	{	{	PUNCT
ejpam-4828	247	10	vn	vn	NOUN
ejpam-4828	247	11	}	}	PUNCT
ejpam-4828	247	12	)	)	PUNCT
ejpam-4828	247	13	.	.	PUNCT
ejpam-4828	248	1	since	since	SCONJ
ejpam-4828	248	2	f	f	PROPN
ejpam-4828	248	3	is	be	AUX
ejpam-4828	248	4	a	a	DET
ejpam-4828	248	5	γcvr	γcvr	NOUN
ejpam-4828	248	6	-	-	PUNCT
ejpam-4828	248	7	function	function	NOUN
ejpam-4828	248	8	,	,	PUNCT
ejpam-4828	248	9	v2	v2	PROPN
ejpam-4828	248	10	=	=	SYM
ejpam-4828	248	11	{	{	PUNCT
ejpam-4828	248	12	v2	v2	NOUN
ejpam-4828	248	13	}	}	PUNCT
ejpam-4828	248	14	(	(	PUNCT
ejpam-4828	248	15	resp	resp	NOUN
ejpam-4828	248	16	.	.	PUNCT
ejpam-4828	249	1	{	{	PUNCT
ejpam-4828	249	2	vn−1	vn−1	ADJ
ejpam-4828	249	3	}	}	PUNCT
ejpam-4828	249	4	)	)	PUNCT
ejpam-4828	249	5	and	and	CCONJ
ejpam-4828	249	6	v1	v1	NOUN
ejpam-4828	249	7	=	=	SYM
ejpam-4828	249	8	v	v	NOUN
ejpam-4828	249	9	(	(	PUNCT
ejpam-4828	249	10	pn	pn	NOUN
ejpam-4828	249	11	)	)	PUNCT
ejpam-4828	249	12	\	\	NOUN
ejpam-4828	249	13	{	{	PUNCT
ejpam-4828	249	14	v1	v1	NOUN
ejpam-4828	249	15	,	,	PUNCT
ejpam-4828	249	16	v2	v2	PROPN
ejpam-4828	249	17	}	}	PUNCT
ejpam-4828	249	18	(	(	PUNCT
ejpam-4828	249	19	resp	resp	NOUN
ejpam-4828	249	20	.	.	PUNCT
ejpam-4828	250	1	v	v	X
ejpam-4828	250	2	(	(	PUNCT
ejpam-4828	250	3	pn	pn	NOUN
ejpam-4828	250	4	)	)	PUNCT
ejpam-4828	250	5	\	\	NOUN
ejpam-4828	250	6	{	{	PUNCT
ejpam-4828	250	7	vn−1	vn−1	PROPN
ejpam-4828	250	8	,	,	PUNCT
ejpam-4828	250	9	vn	vn	NOUN
ejpam-4828	250	10	}	}	PUNCT
ejpam-4828	250	11	)	)	PUNCT
ejpam-4828	250	12	.	.	PUNCT
ejpam-4828	251	1	hence	hence	ADV
ejpam-4828	251	2	,	,	PUNCT
ejpam-4828	251	3	γcvr(pn	γcvr(pn	ADJ
ejpam-4828	251	4	)	)	PUNCT
ejpam-4828	251	5	=	=	PUNCT
ejpam-4828	252	1	ωcvr	ωcvr	PROPN
ejpam-4828	252	2	pn	pn	PROPN
ejpam-4828	252	3	(	(	PUNCT
ejpam-4828	252	4	f	f	X
ejpam-4828	252	5	)	)	PUNCT
ejpam-4828	252	6	=	=	NOUN
ejpam-4828	252	7	|v1|	|v1|	NOUN
ejpam-4828	252	8	+	+	CCONJ
ejpam-4828	252	9	2|v2|	2|v2|	NUM
ejpam-4828	252	10	=	=	SYM
ejpam-4828	252	11	n.	n.	NOUN
ejpam-4828	252	12	suppose	suppose	VERB
ejpam-4828	252	13	v0	v0	NOUN
ejpam-4828	252	14	=	=	SYM
ejpam-4828	252	15	{	{	PUNCT
ejpam-4828	252	16	v1	v1	PROPN
ejpam-4828	252	17	,	,	PUNCT
ejpam-4828	252	18	vn	vn	NOUN
ejpam-4828	252	19	}	}	PUNCT
ejpam-4828	252	20	.	.	PUNCT
ejpam-4828	253	1	then	then	ADV
ejpam-4828	253	2	v2	v2	VERB
ejpam-4828	253	3	=	=	SYM
ejpam-4828	253	4	{	{	PUNCT
ejpam-4828	253	5	v2	v2	PROPN
ejpam-4828	253	6	,	,	PUNCT
ejpam-4828	253	7	vn−1	vn−1	ADJ
ejpam-4828	253	8	}	}	PUNCT
ejpam-4828	253	9	and	and	CCONJ
ejpam-4828	253	10	v1	v1	PROPN
ejpam-4828	253	11	=	=	SYM
ejpam-4828	253	12	v	v	NOUN
ejpam-4828	253	13	(	(	PUNCT
ejpam-4828	253	14	pn	pn	NOUN
ejpam-4828	253	15	)	)	PUNCT
ejpam-4828	253	16	\	\	NOUN
ejpam-4828	253	17	{	{	PUNCT
ejpam-4828	253	18	v1	v1	NOUN
ejpam-4828	253	19	,	,	PUNCT
ejpam-4828	253	20	v2	v2	PROPN
ejpam-4828	253	21	,	,	PUNCT
ejpam-4828	253	22	vn−1	vn−1	PROPN
ejpam-4828	253	23	,	,	PUNCT
ejpam-4828	253	24	vn	vn	NOUN
ejpam-4828	253	25	}	}	PUNCT
ejpam-4828	253	26	.	.	PUNCT
ejpam-4828	254	1	hence	hence	ADV
ejpam-4828	254	2	γcvr(pn	γcvr(pn	ADJ
ejpam-4828	254	3	)	)	PUNCT
ejpam-4828	254	4	=	=	PUNCT
ejpam-4828	254	5	ωcvr	ωcvr	PROPN
ejpam-4828	254	6	pn	pn	X
ejpam-4828	254	7	=	=	PUNCT
ejpam-4828	254	8	|v1|+	|v1|+	PRON
ejpam-4828	254	9	2|v2|	2|v2|	NUM
ejpam-4828	254	10	=	=	SYM
ejpam-4828	254	11	n.	n.	NOUN
ejpam-4828	254	12	proposition	proposition	NOUN
ejpam-4828	254	13	5	5	NUM
ejpam-4828	254	14	.	.	PUNCT
ejpam-4828	255	1	let	let	VERB
ejpam-4828	255	2	n	n	PRON
ejpam-4828	255	3	be	be	AUX
ejpam-4828	255	4	a	a	DET
ejpam-4828	255	5	positive	positive	ADJ
ejpam-4828	255	6	integer	integer	NOUN
ejpam-4828	255	7	with	with	ADP
ejpam-4828	255	8	n	n	PRON
ejpam-4828	255	9	≥	≥	NUM
ejpam-4828	255	10	3	3	NUM
ejpam-4828	255	11	.	.	PUNCT
ejpam-4828	255	12	then	then	ADV
ejpam-4828	255	13	γcvr(cn	γcvr(cn	VERB
ejpam-4828	255	14	)	)	PUNCT
ejpam-4828	255	15	=	=	PUNCT
ejpam-4828	255	16	{	{	PUNCT
ejpam-4828	255	17	2	2	NUM
ejpam-4828	255	18	if	if	SCONJ
ejpam-4828	255	19	n	n	ADV
ejpam-4828	255	20	=	=	SYM
ejpam-4828	255	21	3	3	NUM
ejpam-4828	255	22	n	n	NOUN
ejpam-4828	255	23	if	if	SCONJ
ejpam-4828	255	24	n	n	PRON
ejpam-4828	255	25	≥	≥	NOUN
ejpam-4828	255	26	4	4	NUM
ejpam-4828	255	27	.	.	PUNCT
ejpam-4828	255	28	r.	r.	PROPN
ejpam-4828	255	29	fortosa	fortosa	PROPN
ejpam-4828	255	30	,	,	PUNCT
ejpam-4828	255	31	s.	s.	PROPN
ejpam-4828	255	32	canoy	canoy	PROPN
ejpam-4828	255	33	jr	jr	PROPN
ejpam-4828	255	34	.	.	PROPN
ejpam-4828	255	35	/	/	SYM
ejpam-4828	255	36	eur	eur	PROPN
ejpam-4828	255	37	.	.	PUNCT
ejpam-4828	256	1	j.	j.	PROPN
ejpam-4828	256	2	pure	pure	PROPN
ejpam-4828	256	3	appl	appl	PROPN
ejpam-4828	256	4	.	.	PROPN
ejpam-4828	256	5	math	math	PROPN
ejpam-4828	256	6	,	,	PUNCT
ejpam-4828	256	7	16	16	NUM
ejpam-4828	256	8	(	(	PUNCT
ejpam-4828	256	9	3	3	NUM
ejpam-4828	256	10	)	)	PUNCT
ejpam-4828	256	11	(	(	PUNCT
ejpam-4828	256	12	2023	2023	NUM
ejpam-4828	256	13	)	)	PUNCT
ejpam-4828	256	14	,	,	PUNCT
ejpam-4828	256	15	1705	1705	NUM
ejpam-4828	256	16	-	-	SYM
ejpam-4828	256	17	1716	1716	NUM
ejpam-4828	256	18	1712	1712	NUM
ejpam-4828	256	19	proof	proof	NOUN
ejpam-4828	256	20	.	.	PUNCT
ejpam-4828	257	1	clearly	clearly	ADV
ejpam-4828	257	2	,	,	PUNCT
ejpam-4828	257	3	γcvr(c3	γcvr(c3	NOUN
ejpam-4828	257	4	)	)	PUNCT
ejpam-4828	257	5	=	=	SYM
ejpam-4828	258	1	2	2	X
ejpam-4828	258	2	.	.	PUNCT
ejpam-4828	258	3	suppose	suppose	VERB
ejpam-4828	258	4	that	that	SCONJ
ejpam-4828	258	5	n	n	PROPN
ejpam-4828	258	6	≥	≥	NUM
ejpam-4828	258	7	4	4	NUM
ejpam-4828	258	8	.	.	PUNCT
ejpam-4828	259	1	let	let	VERB
ejpam-4828	259	2	cn	cn	PROPN
ejpam-4828	259	3	=	=	PUNCT
ejpam-4828	260	1	[	[	X
ejpam-4828	260	2	v1	v1	NOUN
ejpam-4828	260	3	,	,	PUNCT
ejpam-4828	260	4	v2	v2	NOUN
ejpam-4828	260	5	,	,	PUNCT
ejpam-4828	260	6	.	.	PUNCT
ejpam-4828	260	7	.	.	PUNCT
ejpam-4828	260	8	.	.	PUNCT
ejpam-4828	261	1	,	,	PUNCT
ejpam-4828	261	2	vn	vn	X
ejpam-4828	261	3	,	,	PUNCT
ejpam-4828	261	4	v1	v1	PROPN
ejpam-4828	261	5	]	]	PUNCT
ejpam-4828	261	6	and	and	CCONJ
ejpam-4828	261	7	let	let	VERB
ejpam-4828	261	8	g	g	PROPN
ejpam-4828	261	9	=	=	SYM
ejpam-4828	261	10	(	(	PUNCT
ejpam-4828	261	11	v0	v0	PROPN
ejpam-4828	261	12	,	,	PUNCT
ejpam-4828	261	13	v1	v1	NOUN
ejpam-4828	261	14	,	,	PUNCT
ejpam-4828	261	15	v2	v2	PROPN
ejpam-4828	261	16	)	)	PUNCT
ejpam-4828	261	17	be	be	AUX
ejpam-4828	261	18	a	a	DET
ejpam-4828	261	19	γcvr	γcvr	NOUN
ejpam-4828	261	20	-	-	PUNCT
ejpam-4828	261	21	function	function	NOUN
ejpam-4828	261	22	on	on	ADP
ejpam-4828	261	23	cn	cn	PROPN
ejpam-4828	261	24	.	.	PUNCT
ejpam-4828	262	1	if	if	SCONJ
ejpam-4828	262	2	v0	v0	NOUN
ejpam-4828	262	3	=	=	SYM
ejpam-4828	262	4	∅	∅	NOUN
ejpam-4828	262	5	,	,	PUNCT
ejpam-4828	262	6	then	then	ADV
ejpam-4828	262	7	v2	v2	NOUN
ejpam-4828	262	8	=	=	NOUN
ejpam-4828	262	9	∅	∅	NOUN
ejpam-4828	262	10	,	,	PUNCT
ejpam-4828	262	11	by	by	ADP
ejpam-4828	262	12	proposition	proposition	NOUN
ejpam-4828	262	13	3(i	3(i	NUM
ejpam-4828	262	14	)	)	PUNCT
ejpam-4828	262	15	.	.	PUNCT
ejpam-4828	263	1	hence	hence	ADV
ejpam-4828	263	2	,	,	PUNCT
ejpam-4828	263	3	γcvr(cn	γcvr(cn	NOUN
ejpam-4828	263	4	)	)	PUNCT
ejpam-4828	263	5	=	=	VERB
ejpam-4828	264	1	n.	n.	NOUN
ejpam-4828	264	2	suppose	suppose	VERB
ejpam-4828	264	3	v0	v0	PROPN
ejpam-4828	264	4	̸=	̸=	PROPN
ejpam-4828	264	5	∅.	∅.	ADV
ejpam-4828	264	6	since	since	SCONJ
ejpam-4828	264	7	v1	v1	NOUN
ejpam-4828	264	8	∪	∪	NOUN
ejpam-4828	264	9	v2	v2	NOUN
ejpam-4828	264	10	is	be	AUX
ejpam-4828	264	11	convex	convex	NOUN
ejpam-4828	264	12	,	,	PUNCT
ejpam-4828	264	13	⟨v0⟩	⟨v0⟩	NOUN
ejpam-4828	264	14	is	be	AUX
ejpam-4828	264	15	connected	connect	VERB
ejpam-4828	264	16	.	.	PUNCT
ejpam-4828	265	1	hence	hence	ADV
ejpam-4828	265	2	,	,	PUNCT
ejpam-4828	265	3	|v0|	|v0|	NOUN
ejpam-4828	265	4	≤	≤	NUM
ejpam-4828	265	5	2	2	NUM
ejpam-4828	265	6	.	.	PUNCT
ejpam-4828	266	1	let	let	VERB
ejpam-4828	266	2	n	n	NOUN
ejpam-4828	266	3	=	=	SYM
ejpam-4828	266	4	4	4	X
ejpam-4828	266	5	.	.	PUNCT
ejpam-4828	266	6	suppose	suppose	VERB
ejpam-4828	266	7	|v0|	|v0|	NOUN
ejpam-4828	266	8	=	=	SYM
ejpam-4828	266	9	1	1	X
ejpam-4828	266	10	.	.	X
ejpam-4828	266	11	assume	assume	VERB
ejpam-4828	266	12	without	without	ADP
ejpam-4828	266	13	loss	loss	NOUN
ejpam-4828	266	14	in	in	ADP
ejpam-4828	266	15	generality	generality	NOUN
ejpam-4828	266	16	that	that	PRON
ejpam-4828	266	17	v0	v0	NOUN
ejpam-4828	266	18	=	=	SYM
ejpam-4828	266	19	{	{	PUNCT
ejpam-4828	266	20	v1	v1	NOUN
ejpam-4828	266	21	}	}	PUNCT
ejpam-4828	266	22	.	.	PUNCT
ejpam-4828	267	1	then	then	ADV
ejpam-4828	267	2	v1	v1	VERB
ejpam-4828	267	3	∪	∪	ADJ
ejpam-4828	267	4	v2	v2	NOUN
ejpam-4828	267	5	=	=	SYM
ejpam-4828	267	6	{	{	PUNCT
ejpam-4828	267	7	v2	v2	PROPN
ejpam-4828	267	8	,	,	PUNCT
ejpam-4828	267	9	v3	v3	PROPN
ejpam-4828	267	10	,	,	PUNCT
ejpam-4828	267	11	v4	v4	PROPN
ejpam-4828	267	12	}	}	PUNCT
ejpam-4828	267	13	which	which	PRON
ejpam-4828	267	14	is	be	AUX
ejpam-4828	267	15	not	not	PART
ejpam-4828	267	16	convex	convex	ADJ
ejpam-4828	267	17	,	,	PUNCT
ejpam-4828	267	18	a	a	DET
ejpam-4828	267	19	contradiction	contradiction	NOUN
ejpam-4828	267	20	.	.	PUNCT
ejpam-4828	268	1	hence	hence	ADV
ejpam-4828	268	2	|v0|	|v0|	NOUN
ejpam-4828	268	3	=	=	SYM
ejpam-4828	268	4	2	2	X
ejpam-4828	268	5	.	.	PUNCT
ejpam-4828	268	6	again	again	ADV
ejpam-4828	268	7	,	,	PUNCT
ejpam-4828	268	8	we	we	PRON
ejpam-4828	268	9	may	may	AUX
ejpam-4828	268	10	assume	assume	VERB
ejpam-4828	268	11	that	that	SCONJ
ejpam-4828	268	12	v0	v0	NOUN
ejpam-4828	268	13	=	=	SYM
ejpam-4828	268	14	{	{	PUNCT
ejpam-4828	268	15	v1	v1	PROPN
ejpam-4828	268	16	,	,	PUNCT
ejpam-4828	268	17	v2	v2	PROPN
ejpam-4828	268	18	}	}	PUNCT
ejpam-4828	268	19	.	.	PUNCT
ejpam-4828	269	1	then	then	ADV
ejpam-4828	269	2	v2	v2	VERB
ejpam-4828	269	3	=	=	SYM
ejpam-4828	269	4	{	{	PUNCT
ejpam-4828	269	5	v3	v3	PROPN
ejpam-4828	269	6	,	,	PUNCT
ejpam-4828	269	7	v4	v4	PROPN
ejpam-4828	269	8	}	}	PUNCT
ejpam-4828	269	9	.	.	PUNCT
ejpam-4828	270	1	it	it	PRON
ejpam-4828	270	2	follows	follow	VERB
ejpam-4828	270	3	that	that	DET
ejpam-4828	270	4	γcvr(c4	γcvr(c4	NOUN
ejpam-4828	270	5	)	)	PUNCT
ejpam-4828	270	6	=	=	SYM
ejpam-4828	270	7	2|v2|	2|v2|	NUM
ejpam-4828	270	8	=	=	SYM
ejpam-4828	270	9	4	4	X
ejpam-4828	270	10	.	.	PUNCT
ejpam-4828	271	1	let	let	VERB
ejpam-4828	271	2	n	n	NOUN
ejpam-4828	271	3	=	=	SYM
ejpam-4828	271	4	5	5	X
ejpam-4828	271	5	.	.	PUNCT
ejpam-4828	271	6	by	by	ADP
ejpam-4828	271	7	convexity	convexity	NOUN
ejpam-4828	271	8	in	in	ADP
ejpam-4828	271	9	v1∪v2	v1∪v2	PROPN
ejpam-4828	271	10	,	,	PUNCT
ejpam-4828	271	11	it	it	PRON
ejpam-4828	271	12	can	can	AUX
ejpam-4828	271	13	be	be	AUX
ejpam-4828	271	14	verified	verify	VERB
ejpam-4828	272	1	that	that	SCONJ
ejpam-4828	272	2	|v0|	|v0|	NOUN
ejpam-4828	272	3	=	=	SYM
ejpam-4828	272	4	2	2	X
ejpam-4828	272	5	.	.	PUNCT
ejpam-4828	273	1	this	this	PRON
ejpam-4828	273	2	implies	imply	VERB
ejpam-4828	273	3	that	that	DET
ejpam-4828	273	4	|v2|	|v2|	NOUN
ejpam-4828	273	5	=	=	SYM
ejpam-4828	273	6	2	2	NUM
ejpam-4828	273	7	and	and	CCONJ
ejpam-4828	273	8	|v1|	|v1|	NOUN
ejpam-4828	273	9	=	=	SYM
ejpam-4828	273	10	1	1	X
ejpam-4828	273	11	.	.	PUNCT
ejpam-4828	273	12	thus	thus	ADV
ejpam-4828	273	13	,	,	PUNCT
ejpam-4828	273	14	γcvr(c5	γcvr(c5	NOUN
ejpam-4828	273	15	)	)	PUNCT
ejpam-4828	273	16	=	=	NOUN
ejpam-4828	273	17	|v1|	|v1|	NOUN
ejpam-4828	273	18	+	+	CCONJ
ejpam-4828	273	19	2|v2|	2|v2|	NUM
ejpam-4828	273	20	=	=	SYM
ejpam-4828	273	21	5	5	X
ejpam-4828	273	22	.	.	PUNCT
ejpam-4828	273	23	suppose	suppose	VERB
ejpam-4828	273	24	n	n	PRON
ejpam-4828	273	25	≥	≥	NUM
ejpam-4828	273	26	6	6	NUM
ejpam-4828	273	27	.	.	PUNCT
ejpam-4828	273	28	suppose	suppose	VERB
ejpam-4828	273	29	|v0|	|v0|	NOUN
ejpam-4828	273	30	=	=	SYM
ejpam-4828	273	31	2	2	NUM
ejpam-4828	273	32	,	,	PUNCT
ejpam-4828	273	33	say	say	VERB
ejpam-4828	273	34	v0	v0	NOUN
ejpam-4828	273	35	=	=	SYM
ejpam-4828	273	36	{	{	PUNCT
ejpam-4828	273	37	v1	v1	PROPN
ejpam-4828	273	38	,	,	PUNCT
ejpam-4828	273	39	v2	v2	PROPN
ejpam-4828	273	40	}	}	PUNCT
ejpam-4828	273	41	.	.	PUNCT
ejpam-4828	274	1	then	then	ADV
ejpam-4828	274	2	[	[	X
ejpam-4828	274	3	v3	v3	PROPN
ejpam-4828	274	4	,	,	PUNCT
ejpam-4828	274	5	v2	v2	PROPN
ejpam-4828	274	6	,	,	PUNCT
ejpam-4828	274	7	v1	v1	NOUN
ejpam-4828	274	8	,	,	PUNCT
ejpam-4828	274	9	vn	vn	X
ejpam-4828	274	10	]	]	X
ejpam-4828	274	11	is	be	AUX
ejpam-4828	274	12	a	a	DET
ejpam-4828	274	13	v3	v3	PROPN
ejpam-4828	274	14	-	-	PUNCT
ejpam-4828	274	15	vn	vn	PROPN
ejpam-4828	274	16	geodesic	geodesic	NOUN
ejpam-4828	274	17	in	in	ADP
ejpam-4828	274	18	cn	cn	PROPN
ejpam-4828	274	19	,	,	PUNCT
ejpam-4828	274	20	implying	imply	VERB
ejpam-4828	274	21	that	that	SCONJ
ejpam-4828	274	22	v1	v1	NOUN
ejpam-4828	274	23	∪	∪	NOUN
ejpam-4828	274	24	v2	v2	NOUN
ejpam-4828	274	25	is	be	AUX
ejpam-4828	274	26	not	not	PART
ejpam-4828	274	27	convex	convex	ADJ
ejpam-4828	274	28	.	.	PUNCT
ejpam-4828	275	1	this	this	PRON
ejpam-4828	275	2	is	be	AUX
ejpam-4828	275	3	a	a	DET
ejpam-4828	275	4	contradiction	contradiction	NOUN
ejpam-4828	275	5	to	to	ADP
ejpam-4828	275	6	the	the	DET
ejpam-4828	275	7	assumption	assumption	NOUN
ejpam-4828	275	8	that	that	SCONJ
ejpam-4828	275	9	g	g	PROPN
ejpam-4828	275	10	is	be	AUX
ejpam-4828	275	11	a	a	DET
ejpam-4828	275	12	cvrdf	cvrdf	NOUN
ejpam-4828	275	13	.	.	PUNCT
ejpam-4828	276	1	therefore	therefore	ADV
ejpam-4828	276	2	,	,	PUNCT
ejpam-4828	276	3	|v0|	|v0|	NOUN
ejpam-4828	276	4	=	=	SYM
ejpam-4828	276	5	1	1	X
ejpam-4828	276	6	.	.	PUNCT
ejpam-4828	277	1	since	since	SCONJ
ejpam-4828	277	2	g	g	PROPN
ejpam-4828	277	3	is	be	AUX
ejpam-4828	277	4	a	a	DET
ejpam-4828	277	5	γcvr	γcvr	NOUN
ejpam-4828	277	6	-	-	PUNCT
ejpam-4828	277	7	function	function	NOUN
ejpam-4828	277	8	,	,	PUNCT
ejpam-4828	277	9	|v2|	|v2|	NOUN
ejpam-4828	277	10	=	=	SYM
ejpam-4828	277	11	1	1	NUM
ejpam-4828	277	12	and	and	CCONJ
ejpam-4828	277	13	|v1|	|v1|	NOUN
ejpam-4828	277	14	=	=	SYM
ejpam-4828	277	15	n−	n−	NOUN
ejpam-4828	277	16	2	2	NUM
ejpam-4828	277	17	.	.	PUNCT
ejpam-4828	278	1	thus	thus	ADV
ejpam-4828	278	2	,	,	PUNCT
ejpam-4828	278	3	γcvr(cn	γcvr(cn	NOUN
ejpam-4828	278	4	)	)	PUNCT
ejpam-4828	278	5	=	=	PUNCT
ejpam-4828	278	6	n.	n.	NOUN
ejpam-4828	278	7	proposition	proposition	NOUN
ejpam-4828	278	8	6	6	NUM
ejpam-4828	278	9	.	.	PUNCT
ejpam-4828	279	1	let	let	VERB
ejpam-4828	279	2	g	g	PROPN
ejpam-4828	279	3	=	=	SYM
ejpam-4828	279	4	kn1,	kn1,	X
ejpam-4828	279	5	...	...	PUNCT
ejpam-4828	279	6	,nk	,nk	PUNCT
ejpam-4828	279	7	be	be	VERB
ejpam-4828	279	8	the	the	DET
ejpam-4828	279	9	complete	complete	ADJ
ejpam-4828	279	10	k	k	ADJ
ejpam-4828	279	11	-	-	ADJ
ejpam-4828	279	12	partite	partite	ADJ
ejpam-4828	279	13	graph	graph	NOUN
ejpam-4828	279	14	with	with	ADP
ejpam-4828	279	15	2	2	NUM
ejpam-4828	279	16	≤	≤	NUM
ejpam-4828	279	17	n1	n1	ADJ
ejpam-4828	279	18	≤	≤	NOUN
ejpam-4828	279	19	n2	n2	NOUN
ejpam-4828	279	20	.	.	PUNCT
ejpam-4828	279	21	.	.	PUNCT
ejpam-4828	279	22	.	.	PUNCT
ejpam-4828	280	1	≤	≤	PROPN
ejpam-4828	280	2	nk	nk	PROPN
ejpam-4828	280	3	where	where	SCONJ
ejpam-4828	280	4	k	k	PROPN
ejpam-4828	280	5	≥	≥	NUM
ejpam-4828	280	6	2	2	NUM
ejpam-4828	280	7	.	.	PUNCT
ejpam-4828	280	8	then	then	ADV
ejpam-4828	280	9	γcvr(g	γcvr(g	VERB
ejpam-4828	280	10	)	)	PUNCT
ejpam-4828	280	11	=	=	SYM
ejpam-4828	281	1	4	4	X
ejpam-4828	281	2	.	.	X
ejpam-4828	281	3	proof	proof	NOUN
ejpam-4828	281	4	.	.	PUNCT
ejpam-4828	282	1	let	let	VERB
ejpam-4828	282	2	sn1	sn1	PROPN
ejpam-4828	282	3	,	,	PUNCT
ejpam-4828	282	4	sn2	sn2	PROPN
ejpam-4828	282	5	,	,	PUNCT
ejpam-4828	282	6	.	.	PUNCT
ejpam-4828	282	7	.	.	PUNCT
ejpam-4828	283	1	.	.	PUNCT
ejpam-4828	284	1	,	,	PUNCT
ejpam-4828	284	2	snk	snk	PROPN
ejpam-4828	284	3	be	be	AUX
ejpam-4828	284	4	the	the	DET
ejpam-4828	284	5	partite	partite	ADJ
ejpam-4828	284	6	sets	set	NOUN
ejpam-4828	284	7	in	in	ADP
ejpam-4828	284	8	g.	g.	PROPN
ejpam-4828	284	9	let	let	VERB
ejpam-4828	284	10	i	i	PRON
ejpam-4828	284	11	,	,	PUNCT
ejpam-4828	284	12	j	j	PROPN
ejpam-4828	284	13	∈	∈	PROPN
ejpam-4828	284	14	{	{	PUNCT
ejpam-4828	284	15	1	1	NUM
ejpam-4828	284	16	,	,	PUNCT
ejpam-4828	284	17	2	2	NUM
ejpam-4828	284	18	,	,	PUNCT
ejpam-4828	284	19	.	.	PUNCT
ejpam-4828	284	20	.	.	PUNCT
ejpam-4828	285	1	.	.	PUNCT
ejpam-4828	286	1	,	,	PUNCT
ejpam-4828	286	2	k	k	X
ejpam-4828	286	3	}	}	PUNCT
ejpam-4828	286	4	with	with	ADP
ejpam-4828	286	5	i	i	PROPN
ejpam-4828	286	6	̸=	̸=	PROPN
ejpam-4828	286	7	j.	j.	PROPN
ejpam-4828	286	8	choose	choose	VERB
ejpam-4828	286	9	any	any	DET
ejpam-4828	286	10	u	u	PROPN
ejpam-4828	286	11	∈	∈	PROPN
ejpam-4828	286	12	sni	sni	PROPN
ejpam-4828	286	13	and	and	CCONJ
ejpam-4828	286	14	w	w	PROPN
ejpam-4828	286	15	∈	∈	PROPN
ejpam-4828	286	16	snj	snj	NOUN
ejpam-4828	286	17	.	.	PUNCT
ejpam-4828	287	1	put	put	VERB
ejpam-4828	287	2	v2	v2	NOUN
ejpam-4828	287	3	=	=	PUNCT
ejpam-4828	287	4	{	{	PUNCT
ejpam-4828	287	5	u	u	NOUN
ejpam-4828	287	6	,	,	PUNCT
ejpam-4828	287	7	w	w	NOUN
ejpam-4828	287	8	}	}	PUNCT
ejpam-4828	287	9	,	,	PUNCT
ejpam-4828	287	10	v0	v0	NOUN
ejpam-4828	287	11	=	=	SYM
ejpam-4828	287	12	v	v	PROPN
ejpam-4828	287	13	(	(	PUNCT
ejpam-4828	287	14	g	g	NOUN
ejpam-4828	287	15	)	)	PUNCT
ejpam-4828	287	16	\	\	PROPN
ejpam-4828	287	17	v2	v2	PROPN
ejpam-4828	287	18	,	,	PUNCT
ejpam-4828	287	19	and	and	CCONJ
ejpam-4828	287	20	v1	v1	NOUN
ejpam-4828	287	21	=	=	SYM
ejpam-4828	287	22	∅.	∅.	NOUN
ejpam-4828	287	23	then	then	ADV
ejpam-4828	287	24	f	f	PROPN
ejpam-4828	288	1	=	=	SYM
ejpam-4828	289	1	(	(	PUNCT
ejpam-4828	289	2	v0	v0	PROPN
ejpam-4828	289	3	,	,	PUNCT
ejpam-4828	289	4	v1	v1	NOUN
ejpam-4828	289	5	,	,	PUNCT
ejpam-4828	289	6	v2	v2	PROPN
ejpam-4828	289	7	)	)	PUNCT
ejpam-4828	289	8	is	be	AUX
ejpam-4828	289	9	a	a	DET
ejpam-4828	289	10	cvrdf	cvrdf	NOUN
ejpam-4828	289	11	on	on	ADP
ejpam-4828	289	12	g.	g.	PROPN
ejpam-4828	289	13	thus	thus	ADV
ejpam-4828	289	14	,	,	PUNCT
ejpam-4828	289	15	γcvr(g	γcvr(g	NOUN
ejpam-4828	289	16	)	)	PUNCT
ejpam-4828	289	17	≤	≤	NOUN
ejpam-4828	289	18	ωcvr	ωcvr	ADP
ejpam-4828	290	1	g	g	PROPN
ejpam-4828	290	2	(	(	PUNCT
ejpam-4828	290	3	f	f	X
ejpam-4828	290	4	)	)	PUNCT
ejpam-4828	290	5	=	=	SYM
ejpam-4828	290	6	2|v2|	2|v2|	NUM
ejpam-4828	290	7	=	=	SYM
ejpam-4828	290	8	4	4	X
ejpam-4828	290	9	.	.	PUNCT
ejpam-4828	290	10	suppose	suppose	VERB
ejpam-4828	290	11	γcvr(g	γcvr(g	NUM
ejpam-4828	290	12	)	)	PUNCT
ejpam-4828	290	13	<	<	X
ejpam-4828	291	1	4	4	X
ejpam-4828	291	2	.	.	PUNCT
ejpam-4828	291	3	let	let	VERB
ejpam-4828	291	4	g	g	NOUN
ejpam-4828	291	5	=	=	PUNCT
ejpam-4828	291	6	(	(	PUNCT
ejpam-4828	291	7	v	v	NUM
ejpam-4828	291	8	′	′	NUM
ejpam-4828	291	9	0	0	NUM
ejpam-4828	291	10	,	,	PUNCT
ejpam-4828	291	11	v	v	NOUN
ejpam-4828	291	12	′	′	NUM
ejpam-4828	291	13	1	1	NUM
ejpam-4828	291	14	,	,	PUNCT
ejpam-4828	291	15	v	v	NOUN
ejpam-4828	291	16	′	′	NUM
ejpam-4828	291	17	2	2	NUM
ejpam-4828	291	18	)	)	PUNCT
ejpam-4828	291	19	be	be	AUX
ejpam-4828	291	20	a	a	DET
ejpam-4828	291	21	γcvr	γcvr	NOUN
ejpam-4828	291	22	-	-	PUNCT
ejpam-4828	291	23	function	function	NOUN
ejpam-4828	291	24	on	on	ADP
ejpam-4828	291	25	g.	g.	PROPN
ejpam-4828	291	26	then	then	ADV
ejpam-4828	291	27	γcvr(g	γcvr(g	VERB
ejpam-4828	291	28	)	)	PUNCT
ejpam-4828	292	1	=	=	PUNCT
ejpam-4828	292	2	ωcvr	ωcvr	PROPN
ejpam-4828	292	3	g	g	PROPN
ejpam-4828	292	4	(	(	PUNCT
ejpam-4828	292	5	g	g	NOUN
ejpam-4828	292	6	)	)	PUNCT
ejpam-4828	292	7	=	=	PUNCT
ejpam-4828	292	8	|v	|v	PROPN
ejpam-4828	292	9	′	′	NOUN
ejpam-4828	292	10	1	1	NUM
ejpam-4828	293	1	|	|	ADV
ejpam-4828	294	1	+	+	CCONJ
ejpam-4828	294	2	2|v	2|v	NUM
ejpam-4828	295	1	′	′	NUM
ejpam-4828	295	2	2	2	NUM
ejpam-4828	296	1	|	|	ADV
ejpam-4828	296	2	<	<	X
ejpam-4828	296	3	4	4	NUM
ejpam-4828	296	4	.	.	PUNCT
ejpam-4828	297	1	this	this	PRON
ejpam-4828	297	2	implies	imply	VERB
ejpam-4828	297	3	that	that	SCONJ
ejpam-4828	297	4	|v	|v	PROPN
ejpam-4828	297	5	′	′	NUM
ejpam-4828	297	6	2	2	NUM
ejpam-4828	297	7	|	|	ADV
ejpam-4828	297	8	≤	≤	NUM
ejpam-4828	297	9	1	1	NUM
ejpam-4828	297	10	.	.	PUNCT
ejpam-4828	298	1	if	if	SCONJ
ejpam-4828	298	2	|v	|v	PROPN
ejpam-4828	298	3	′	′	NOUN
ejpam-4828	298	4	2	2	NUM
ejpam-4828	298	5	|	|	NOUN
ejpam-4828	298	6	=	=	SYM
ejpam-4828	298	7	0	0	NUM
ejpam-4828	298	8	,	,	PUNCT
ejpam-4828	298	9	then	then	ADV
ejpam-4828	298	10	|v	|v	VERB
ejpam-4828	298	11	′	′	NOUN
ejpam-4828	298	12	0	0	PUNCT
ejpam-4828	299	1	|	|	ADV
ejpam-4828	299	2	=	=	SYM
ejpam-4828	299	3	0	0	NUM
ejpam-4828	299	4	and	and	CCONJ
ejpam-4828	299	5	|v	|v	PROPN
ejpam-4828	299	6	′	′	NUM
ejpam-4828	299	7	1	1	NUM
ejpam-4828	299	8	|	|	ADV
ejpam-4828	299	9	=	=	SYM
ejpam-4828	299	10	|v	|v	PROPN
ejpam-4828	299	11	(	(	PUNCT
ejpam-4828	299	12	g)|	g)|	X
ejpam-4828	299	13	≥	≥	NOUN
ejpam-4828	299	14	4	4	NUM
ejpam-4828	299	15	,	,	PUNCT
ejpam-4828	299	16	a	a	DET
ejpam-4828	299	17	contradiction	contradiction	NOUN
ejpam-4828	299	18	.	.	PUNCT
ejpam-4828	300	1	thus	thus	ADV
ejpam-4828	300	2	,	,	PUNCT
ejpam-4828	300	3	|v	|v	ADJ
ejpam-4828	300	4	′	′	NOUN
ejpam-4828	300	5	2	2	NUM
ejpam-4828	300	6	|	|	ADV
ejpam-4828	300	7	=	=	NOUN
ejpam-4828	300	8	1	1	X
ejpam-4828	300	9	.	.	PUNCT
ejpam-4828	301	1	if	if	SCONJ
ejpam-4828	301	2	ωcvr	ωcvr	PROPN
ejpam-4828	301	3	g	g	PROPN
ejpam-4828	301	4	(	(	PUNCT
ejpam-4828	301	5	g	g	NOUN
ejpam-4828	301	6	)	)	PUNCT
ejpam-4828	301	7	=	=	SYM
ejpam-4828	301	8	2	2	NUM
ejpam-4828	301	9	,	,	PUNCT
ejpam-4828	301	10	then	then	ADV
ejpam-4828	301	11	|v	|v	VERB
ejpam-4828	301	12	′	′	NOUN
ejpam-4828	301	13	1	1	NUM
ejpam-4828	301	14	|	|	ADV
ejpam-4828	301	15	=	=	NOUN
ejpam-4828	301	16	0	0	X
ejpam-4828	301	17	.	.	PUNCT
ejpam-4828	302	1	let	let	VERB
ejpam-4828	302	2	v	v	NOUN
ejpam-4828	302	3	′	′	NOUN
ejpam-4828	302	4	2	2	NUM
ejpam-4828	302	5	=	=	SYM
ejpam-4828	302	6	{	{	PUNCT
ejpam-4828	302	7	p	p	X
ejpam-4828	302	8	}	}	PUNCT
ejpam-4828	302	9	,	,	PUNCT
ejpam-4828	302	10	where	where	SCONJ
ejpam-4828	302	11	p	p	PROPN
ejpam-4828	302	12	∈	∈	PROPN
ejpam-4828	302	13	snj	snj	NOUN
ejpam-4828	302	14	for	for	ADP
ejpam-4828	302	15	j	j	PROPN
ejpam-4828	302	16	∈	∈	PROPN
ejpam-4828	302	17	{	{	PUNCT
ejpam-4828	302	18	1	1	NUM
ejpam-4828	302	19	,	,	PUNCT
ejpam-4828	302	20	2	2	NUM
ejpam-4828	302	21	,	,	PUNCT
ejpam-4828	302	22	.	.	PUNCT
ejpam-4828	302	23	.	.	PUNCT
ejpam-4828	303	1	.	.	PUNCT
ejpam-4828	304	1	,	,	PUNCT
ejpam-4828	304	2	k	k	X
ejpam-4828	304	3	}	}	PUNCT
ejpam-4828	304	4	.	.	PUNCT
ejpam-4828	305	1	pick	pick	VERB
ejpam-4828	305	2	any	any	DET
ejpam-4828	305	3	q	q	PROPN
ejpam-4828	305	4	∈	∈	PROPN
ejpam-4828	305	5	snj	snj	NOUN
ejpam-4828	305	6	\	\	PUNCT
ejpam-4828	305	7	{	{	PUNCT
ejpam-4828	305	8	p	p	X
ejpam-4828	305	9	}	}	PUNCT
ejpam-4828	305	10	.	.	PUNCT
ejpam-4828	306	1	since	since	SCONJ
ejpam-4828	306	2	|v	|v	PROPN
ejpam-4828	306	3	′	′	NUM
ejpam-4828	306	4	2	2	NUM
ejpam-4828	306	5	|	|	NOUN
ejpam-4828	306	6	=	=	NOUN
ejpam-4828	306	7	1	1	NUM
ejpam-4828	306	8	,	,	PUNCT
ejpam-4828	306	9	q	q	PROPN
ejpam-4828	306	10	∈	∈	PROPN
ejpam-4828	306	11	v0	v0	NOUN
ejpam-4828	306	12	.	.	PUNCT
ejpam-4828	307	1	this	this	PRON
ejpam-4828	307	2	is	be	AUX
ejpam-4828	307	3	not	not	PART
ejpam-4828	307	4	possible	possible	ADJ
ejpam-4828	307	5	because	because	SCONJ
ejpam-4828	307	6	pq	pq	PROPN
ejpam-4828	307	7	/∈	/∈	PUNCT
ejpam-4828	307	8	e(g	e(g	PROPN
ejpam-4828	307	9	)	)	PUNCT
ejpam-4828	307	10	.	.	PUNCT
ejpam-4828	308	1	this	this	DET
ejpam-4828	308	2	forces	force	NOUN
ejpam-4828	308	3	ωcvr	ωcvr	NOUN
ejpam-4828	308	4	g	g	PROPN
ejpam-4828	308	5	(	(	PUNCT
ejpam-4828	308	6	g	g	NOUN
ejpam-4828	308	7	)	)	PUNCT
ejpam-4828	308	8	=	=	SYM
ejpam-4828	308	9	3	3	NUM
ejpam-4828	308	10	which	which	PRON
ejpam-4828	308	11	is	be	AUX
ejpam-4828	308	12	also	also	ADV
ejpam-4828	308	13	not	not	PART
ejpam-4828	308	14	possible	possible	ADJ
ejpam-4828	308	15	by	by	ADP
ejpam-4828	308	16	proposition	proposition	NOUN
ejpam-4828	308	17	2	2	NUM
ejpam-4828	308	18	.	.	PUNCT
ejpam-4828	308	19	therefore	therefore	ADV
ejpam-4828	308	20	,	,	PUNCT
ejpam-4828	308	21	γcvr(g	γcvr(g	NOUN
ejpam-4828	308	22	)	)	PUNCT
ejpam-4828	308	23	=	=	SYM
ejpam-4828	308	24	4	4	X
ejpam-4828	308	25	.	.	X
ejpam-4828	308	26	proposition	proposition	NOUN
ejpam-4828	308	27	7	7	NUM
ejpam-4828	308	28	.	.	PUNCT
ejpam-4828	309	1	let	let	VERB
ejpam-4828	309	2	g	g	PRON
ejpam-4828	309	3	be	be	AUX
ejpam-4828	309	4	a	a	DET
ejpam-4828	309	5	connected	connected	ADJ
ejpam-4828	309	6	non	non	ADJ
ejpam-4828	309	7	-	-	ADJ
ejpam-4828	309	8	complete	complete	ADJ
ejpam-4828	309	9	graph	graph	NOUN
ejpam-4828	309	10	and	and	CCONJ
ejpam-4828	309	11	let	let	VERB
ejpam-4828	309	12	f	f	PROPN
ejpam-4828	309	13	=	=	SYM
ejpam-4828	309	14	(	(	PUNCT
ejpam-4828	309	15	v0	v0	PROPN
ejpam-4828	309	16	,	,	PUNCT
ejpam-4828	309	17	v1	v1	NOUN
ejpam-4828	309	18	,	,	PUNCT
ejpam-4828	309	19	v2	v2	PROPN
ejpam-4828	309	20	)	)	PUNCT
ejpam-4828	309	21	be	be	AUX
ejpam-4828	309	22	a	a	DET
ejpam-4828	309	23	γcvr	γcvr	NOUN
ejpam-4828	309	24	-	-	PUNCT
ejpam-4828	309	25	function	function	NOUN
ejpam-4828	309	26	on	on	ADP
ejpam-4828	309	27	g.	g.	PROPN
ejpam-4828	309	28	if	if	SCONJ
ejpam-4828	309	29	|v1|	|v1|	NUM
ejpam-4828	309	30	=	=	SYM
ejpam-4828	309	31	0	0	NUM
ejpam-4828	309	32	,	,	PUNCT
ejpam-4828	309	33	then	then	ADV
ejpam-4828	309	34	the	the	DET
ejpam-4828	309	35	following	follow	VERB
ejpam-4828	309	36	hold	hold	NOUN
ejpam-4828	309	37	:	:	PUNCT
ejpam-4828	309	38	(	(	PUNCT
ejpam-4828	309	39	i	i	NOUN
ejpam-4828	309	40	)	)	PUNCT
ejpam-4828	309	41	every	every	DET
ejpam-4828	309	42	cut	cut	VERB
ejpam-4828	309	43	-	-	PUNCT
ejpam-4828	309	44	vertex	vertex	NOUN
ejpam-4828	309	45	belongs	belong	VERB
ejpam-4828	309	46	to	to	ADP
ejpam-4828	309	47	v2	v2	PROPN
ejpam-4828	309	48	,	,	PUNCT
ejpam-4828	309	49	(	(	PUNCT
ejpam-4828	309	50	ii	ii	NOUN
ejpam-4828	309	51	)	)	PUNCT
ejpam-4828	309	52	no	no	DET
ejpam-4828	309	53	extreme	extreme	ADJ
ejpam-4828	309	54	vertex	vertex	NOUN
ejpam-4828	309	55	belongs	belong	VERB
ejpam-4828	309	56	to	to	ADP
ejpam-4828	309	57	v2	v2	VERB
ejpam-4828	309	58	,	,	PUNCT
ejpam-4828	309	59	and	and	CCONJ
ejpam-4828	309	60	(	(	PUNCT
ejpam-4828	309	61	iii	iii	NOUN
ejpam-4828	309	62	)	)	PUNCT
ejpam-4828	309	63	for	for	ADP
ejpam-4828	309	64	any	any	DET
ejpam-4828	309	65	u	u	NOUN
ejpam-4828	309	66	,	,	PUNCT
ejpam-4828	309	67	v	v	PROPN
ejpam-4828	309	68	∈	∈	NOUN
ejpam-4828	309	69	v2	v2	NOUN
ejpam-4828	309	70	such	such	ADJ
ejpam-4828	309	71	that	that	DET
ejpam-4828	309	72	dg(u	dg(u	ADJ
ejpam-4828	309	73	,	,	PUNCT
ejpam-4828	309	74	v	v	NOUN
ejpam-4828	309	75	)	)	PUNCT
ejpam-4828	309	76	≥	≥	NOUN
ejpam-4828	309	77	2	2	NUM
ejpam-4828	309	78	,	,	PUNCT
ejpam-4828	309	79	ng(u	ng(u	NUM
ejpam-4828	309	80	)	)	PUNCT
ejpam-4828	309	81	∩ng(v	∩ng(v	PROPN
ejpam-4828	309	82	)	)	PUNCT
ejpam-4828	309	83	⊆	⊆	NUM
ejpam-4828	309	84	v2	v2	NOUN
ejpam-4828	309	85	.	.	PUNCT
ejpam-4828	310	1	proof	proof	NOUN
ejpam-4828	310	2	.	.	PUNCT
ejpam-4828	311	1	since	since	SCONJ
ejpam-4828	311	2	|v1|	|v1|	NOUN
ejpam-4828	311	3	=	=	SYM
ejpam-4828	311	4	0	0	NUM
ejpam-4828	311	5	,	,	PUNCT
ejpam-4828	311	6	v2	v2	PROPN
ejpam-4828	311	7	is	be	AUX
ejpam-4828	311	8	a	a	DET
ejpam-4828	311	9	γcon	γcon	NOUN
ejpam-4828	311	10	-	-	PUNCT
ejpam-4828	311	11	set	set	NOUN
ejpam-4828	311	12	in	in	ADP
ejpam-4828	311	13	g	g	NOUN
ejpam-4828	311	14	by	by	ADP
ejpam-4828	311	15	proposition	proposition	NOUN
ejpam-4828	311	16	3(iii	3(iii	NUM
ejpam-4828	311	17	)	)	PUNCT
ejpam-4828	311	18	.	.	PUNCT
ejpam-4828	312	1	suppose	suppose	VERB
ejpam-4828	312	2	there	there	PRON
ejpam-4828	312	3	exists	exist	VERB
ejpam-4828	312	4	a	a	DET
ejpam-4828	312	5	cut	cut	NOUN
ejpam-4828	312	6	-	-	PUNCT
ejpam-4828	312	7	vetex	vetex	NOUN
ejpam-4828	312	8	v	v	NOUN
ejpam-4828	312	9	of	of	ADP
ejpam-4828	312	10	g	g	NOUN
ejpam-4828	312	11	such	such	ADJ
ejpam-4828	312	12	that	that	PRON
ejpam-4828	312	13	v	v	NOUN
ejpam-4828	312	14	/∈	/∈	PUNCT
ejpam-4828	313	1	v2	v2	INTJ
ejpam-4828	313	2	.	.	PUNCT
ejpam-4828	314	1	let	let	VERB
ejpam-4828	314	2	g1	g1	PROPN
ejpam-4828	314	3	and	and	CCONJ
ejpam-4828	314	4	g2	g2	PROPN
ejpam-4828	314	5	be	be	AUX
ejpam-4828	314	6	distinct	distinct	ADJ
ejpam-4828	314	7	components	component	NOUN
ejpam-4828	314	8	of	of	ADP
ejpam-4828	314	9	g	g	NOUN
ejpam-4828	314	10	\	\	PUNCT
ejpam-4828	315	1	v.	v.	ADP
ejpam-4828	315	2	pick	pick	VERB
ejpam-4828	315	3	any	any	DET
ejpam-4828	315	4	p	p	PROPN
ejpam-4828	315	5	∈	∈	PROPN
ejpam-4828	315	6	v2∩v	v2∩v	NOUN
ejpam-4828	315	7	(	(	PUNCT
ejpam-4828	315	8	g1	g1	PROPN
ejpam-4828	315	9	)	)	PUNCT
ejpam-4828	315	10	and	and	CCONJ
ejpam-4828	315	11	q	q	NOUN
ejpam-4828	315	12	∈	∈	PROPN
ejpam-4828	315	13	v2∩v	v2∩v	NOUN
ejpam-4828	315	14	(	(	PUNCT
ejpam-4828	315	15	g2	g2	PROPN
ejpam-4828	315	16	)	)	PUNCT
ejpam-4828	315	17	.	.	PUNCT
ejpam-4828	316	1	since	since	SCONJ
ejpam-4828	316	2	every	every	DET
ejpam-4828	316	3	p	p	NOUN
ejpam-4828	316	4	-	-	PUNCT
ejpam-4828	316	5	q	q	NOUN
ejpam-4828	316	6	geodesic	geodesic	NOUN
ejpam-4828	316	7	contains	contain	VERB
ejpam-4828	316	8	v	v	ADP
ejpam-4828	316	9	,	,	PUNCT
ejpam-4828	316	10	it	it	PRON
ejpam-4828	316	11	follows	follow	VERB
ejpam-4828	316	12	that	that	SCONJ
ejpam-4828	316	13	v2	v2	PROPN
ejpam-4828	316	14	is	be	AUX
ejpam-4828	316	15	not	not	PART
ejpam-4828	316	16	convex	convex	ADJ
ejpam-4828	316	17	,	,	PUNCT
ejpam-4828	316	18	a	a	DET
ejpam-4828	316	19	contradiction	contradiction	NOUN
ejpam-4828	316	20	.	.	PUNCT
ejpam-4828	317	1	hence	hence	ADV
ejpam-4828	317	2	,	,	PUNCT
ejpam-4828	317	3	(	(	PUNCT
ejpam-4828	317	4	i	i	NOUN
ejpam-4828	317	5	)	)	PUNCT
ejpam-4828	317	6	holds	hold	VERB
ejpam-4828	317	7	.	.	PUNCT
ejpam-4828	318	1	suppose	suppose	VERB
ejpam-4828	318	2	there	there	PRON
ejpam-4828	318	3	exists	exist	VERB
ejpam-4828	318	4	w	w	PROPN
ejpam-4828	318	5	∈	∈	PROPN
ejpam-4828	318	6	ext(g)∩v2	ext(g)∩v2	NOUN
ejpam-4828	318	7	.	.	PUNCT
ejpam-4828	319	1	since	since	SCONJ
ejpam-4828	319	2	g	g	PROPN
ejpam-4828	319	3	̸=	̸=	PROPN
ejpam-4828	319	4	kn	kn	PROPN
ejpam-4828	319	5	,	,	PUNCT
ejpam-4828	319	6	there	there	PRON
ejpam-4828	319	7	exists	exist	VERB
ejpam-4828	319	8	z	z	PROPN
ejpam-4828	319	9	∈	∈	PROPN
ejpam-4828	319	10	ng(w	ng(w	NOUN
ejpam-4828	319	11	)	)	PUNCT
ejpam-4828	319	12	such	such	ADJ
ejpam-4828	319	13	that	that	SCONJ
ejpam-4828	319	14	y	y	PROPN
ejpam-4828	319	15	∈	∈	PROPN
ejpam-4828	319	16	ng(z	ng(z	PROPN
ejpam-4828	319	17	)	)	PUNCT
ejpam-4828	319	18	\	\	NOUN
ejpam-4828	319	19	ng(w	ng(w	NOUN
ejpam-4828	319	20	)	)	PUNCT
ejpam-4828	319	21	.	.	PUNCT
ejpam-4828	320	1	suppose	suppose	VERB
ejpam-4828	320	2	z	z	PROPN
ejpam-4828	320	3	∈	∈	PROPN
ejpam-4828	320	4	v0	v0	NOUN
ejpam-4828	320	5	.	.	PUNCT
ejpam-4828	321	1	then	then	ADV
ejpam-4828	321	2	there	there	PRON
ejpam-4828	321	3	exists	exist	VERB
ejpam-4828	321	4	x	x	X
ejpam-4828	321	5	∈	∈	PROPN
ejpam-4828	321	6	ng(z	ng(z	NUM
ejpam-4828	321	7	)	)	PUNCT
ejpam-4828	321	8	∩	∩	NOUN
ejpam-4828	321	9	v2	v2	PROPN
ejpam-4828	321	10	.	.	PUNCT
ejpam-4828	322	1	since	since	SCONJ
ejpam-4828	322	2	v2	v2	PROPN
ejpam-4828	322	3	is	be	AUX
ejpam-4828	322	4	γcon	γcon	NOUN
ejpam-4828	322	5	-	-	PUNCT
ejpam-4828	322	6	set	set	VERB
ejpam-4828	322	7	,	,	PUNCT
ejpam-4828	322	8	x	x	X
ejpam-4828	322	9	/∈	/∈	PUNCT
ejpam-4828	322	10	ng(w	ng(w	NOUN
ejpam-4828	322	11	)	)	PUNCT
ejpam-4828	322	12	.	.	PUNCT
ejpam-4828	323	1	hence	hence	ADV
ejpam-4828	323	2	,	,	PUNCT
ejpam-4828	323	3	[	[	X
ejpam-4828	323	4	x	x	X
ejpam-4828	323	5	,	,	PUNCT
ejpam-4828	323	6	z	z	PROPN
ejpam-4828	323	7	,	,	PUNCT
ejpam-4828	323	8	w	w	PROPN
ejpam-4828	323	9	]	]	X
ejpam-4828	323	10	is	be	AUX
ejpam-4828	323	11	a	a	DET
ejpam-4828	323	12	x	x	ADJ
ejpam-4828	323	13	-	-	NOUN
ejpam-4828	323	14	w	w	NOUN
ejpam-4828	323	15	geodesic	geodesic	NOUN
ejpam-4828	323	16	,	,	PUNCT
ejpam-4828	323	17	contrary	contrary	ADV
ejpam-4828	323	18	to	to	ADP
ejpam-4828	323	19	the	the	DET
ejpam-4828	323	20	fact	fact	NOUN
ejpam-4828	323	21	that	that	SCONJ
ejpam-4828	323	22	v2	v2	PROPN
ejpam-4828	323	23	is	be	AUX
ejpam-4828	323	24	convex	convex	NOUN
ejpam-4828	323	25	.	.	PUNCT
ejpam-4828	324	1	hence	hence	ADV
ejpam-4828	324	2	,	,	PUNCT
ejpam-4828	324	3	z	z	PROPN
ejpam-4828	324	4	∈	∈	PROPN
ejpam-4828	324	5	v2	v2	PROPN
ejpam-4828	324	6	.	.	PUNCT
ejpam-4828	325	1	again	again	ADV
ejpam-4828	325	2	,	,	PUNCT
ejpam-4828	325	3	this	this	PRON
ejpam-4828	325	4	is	be	AUX
ejpam-4828	325	5	not	not	PART
ejpam-4828	325	6	possible	possible	ADJ
ejpam-4828	325	7	because	because	SCONJ
ejpam-4828	325	8	v2	v2	PROPN
ejpam-4828	325	9	is	be	AUX
ejpam-4828	325	10	a	a	DET
ejpam-4828	325	11	γcon	γcon	NOUN
ejpam-4828	325	12	-	-	PUNCT
ejpam-4828	325	13	set	set	NOUN
ejpam-4828	325	14	.	.	PUNCT
ejpam-4828	326	1	therefore	therefore	ADV
ejpam-4828	326	2	,	,	PUNCT
ejpam-4828	326	3	w	w	PROPN
ejpam-4828	326	4	/∈	/∈	PUNCT
ejpam-4828	326	5	v2	v2	PROPN
ejpam-4828	326	6	.	.	PUNCT
ejpam-4828	327	1	thus	thus	ADV
ejpam-4828	327	2	,	,	PUNCT
ejpam-4828	327	3	(	(	PUNCT
ejpam-4828	327	4	ii	ii	NOUN
ejpam-4828	327	5	)	)	PUNCT
ejpam-4828	327	6	holds	hold	VERB
ejpam-4828	327	7	.	.	PUNCT
ejpam-4828	328	1	next	next	ADV
ejpam-4828	328	2	,	,	PUNCT
ejpam-4828	328	3	let	let	VERB
ejpam-4828	328	4	u	u	NOUN
ejpam-4828	328	5	,	,	PUNCT
ejpam-4828	328	6	v	v	PROPN
ejpam-4828	328	7	∈	∈	NOUN
ejpam-4828	328	8	v2	v2	NOUN
ejpam-4828	328	9	such	such	ADJ
ejpam-4828	328	10	that	that	DET
ejpam-4828	328	11	dg(u	dg(u	ADJ
ejpam-4828	328	12	,	,	PUNCT
ejpam-4828	328	13	v	v	NOUN
ejpam-4828	328	14	)	)	PUNCT
ejpam-4828	328	15	≥	≥	NOUN
ejpam-4828	328	16	2	2	NUM
ejpam-4828	328	17	.	.	PUNCT
ejpam-4828	329	1	if	if	SCONJ
ejpam-4828	329	2	dg(u	dg(u	NOUN
ejpam-4828	329	3	,	,	PUNCT
ejpam-4828	329	4	v	v	NOUN
ejpam-4828	329	5	)	)	PUNCT
ejpam-4828	329	6	>	>	X
ejpam-4828	329	7	2	2	NUM
ejpam-4828	329	8	,	,	PUNCT
ejpam-4828	329	9	then	then	ADV
ejpam-4828	329	10	ng(u	ng(u	NOUN
ejpam-4828	329	11	)	)	PUNCT
ejpam-4828	329	12	∩ng(v	∩ng(v	PROPN
ejpam-4828	329	13	)	)	PUNCT
ejpam-4828	329	14	=	=	NOUN
ejpam-4828	330	1	∅	∅	NOUN
ejpam-4828	330	2	,	,	PUNCT
ejpam-4828	330	3	then	then	ADV
ejpam-4828	330	4	we	we	PRON
ejpam-4828	330	5	are	be	AUX
ejpam-4828	330	6	done	do	VERB
ejpam-4828	330	7	.	.	PUNCT
ejpam-4828	331	1	suppose	suppose	VERB
ejpam-4828	331	2	dg(u	dg(u	NOUN
ejpam-4828	331	3	,	,	PUNCT
ejpam-4828	331	4	v	v	NOUN
ejpam-4828	331	5	)	)	PUNCT
ejpam-4828	331	6	=	=	SYM
ejpam-4828	331	7	2	2	NUM
ejpam-4828	331	8	and	and	CCONJ
ejpam-4828	331	9	let	let	VERB
ejpam-4828	331	10	a	a	DET
ejpam-4828	331	11	∈	∈	PROPN
ejpam-4828	331	12	ng(u	ng(u	NOUN
ejpam-4828	331	13	)	)	PUNCT
ejpam-4828	331	14	∩ng(v	∩ng(v	PROPN
ejpam-4828	331	15	)	)	PUNCT
ejpam-4828	331	16	.	.	PUNCT
ejpam-4828	332	1	by	by	ADP
ejpam-4828	332	2	convexity	convexity	NOUN
ejpam-4828	332	3	of	of	ADP
ejpam-4828	332	4	v2	v2	NOUN
ejpam-4828	332	5	,	,	PUNCT
ejpam-4828	332	6	it	it	PRON
ejpam-4828	332	7	follows	follow	VERB
ejpam-4828	332	8	that	that	SCONJ
ejpam-4828	332	9	a	a	DET
ejpam-4828	332	10	∈	∈	PROPN
ejpam-4828	332	11	v2	v2	NOUN
ejpam-4828	332	12	,	,	PUNCT
ejpam-4828	332	13	showing	show	VERB
ejpam-4828	332	14	that	that	SCONJ
ejpam-4828	332	15	ng(u)∩ng(v	ng(u)∩ng(v	NOUN
ejpam-4828	332	16	)	)	PUNCT
ejpam-4828	332	17	⊆	⊆	NUM
ejpam-4828	332	18	v2	v2	NOUN
ejpam-4828	332	19	.	.	PUNCT
ejpam-4828	333	1	this	this	PRON
ejpam-4828	333	2	shows	show	VERB
ejpam-4828	333	3	that	that	SCONJ
ejpam-4828	333	4	(	(	PUNCT
ejpam-4828	333	5	iii	iii	NOUN
ejpam-4828	333	6	)	)	PUNCT
ejpam-4828	333	7	holds	hold	VERB
ejpam-4828	333	8	.	.	PUNCT
ejpam-4828	334	1	r.	r.	PROPN
ejpam-4828	334	2	fortosa	fortosa	PROPN
ejpam-4828	334	3	,	,	PUNCT
ejpam-4828	334	4	s.	s.	PROPN
ejpam-4828	334	5	canoy	canoy	PROPN
ejpam-4828	334	6	jr	jr	PROPN
ejpam-4828	334	7	.	.	PROPN
ejpam-4828	334	8	/	/	SYM
ejpam-4828	334	9	eur	eur	PROPN
ejpam-4828	334	10	.	.	PUNCT
ejpam-4828	335	1	j.	j.	PROPN
ejpam-4828	335	2	pure	pure	PROPN
ejpam-4828	335	3	appl	appl	PROPN
ejpam-4828	335	4	.	.	PROPN
ejpam-4828	335	5	math	math	PROPN
ejpam-4828	335	6	,	,	PUNCT
ejpam-4828	335	7	16	16	NUM
ejpam-4828	335	8	(	(	PUNCT
ejpam-4828	335	9	3	3	NUM
ejpam-4828	335	10	)	)	PUNCT
ejpam-4828	335	11	(	(	PUNCT
ejpam-4828	335	12	2023	2023	NUM
ejpam-4828	335	13	)	)	PUNCT
ejpam-4828	335	14	,	,	PUNCT
ejpam-4828	335	15	1705	1705	NUM
ejpam-4828	335	16	-	-	SYM
ejpam-4828	335	17	1716	1716	NUM
ejpam-4828	335	18	1713	1713	NUM
ejpam-4828	335	19	proposition	proposition	NOUN
ejpam-4828	335	20	8	8	NUM
ejpam-4828	335	21	.	.	PUNCT
ejpam-4828	336	1	let	let	VERB
ejpam-4828	336	2	g	g	PRON
ejpam-4828	336	3	be	be	AUX
ejpam-4828	336	4	a	a	DET
ejpam-4828	336	5	conneted	connete	VERB
ejpam-4828	336	6	graph	graph	NOUN
ejpam-4828	336	7	of	of	ADP
ejpam-4828	336	8	order	order	NOUN
ejpam-4828	336	9	n.	n.	NOUN
ejpam-4828	336	10	then	then	ADV
ejpam-4828	336	11	γcon(g	γcon(g	PROPN
ejpam-4828	336	12	)	)	PUNCT
ejpam-4828	337	1	=	=	SYM
ejpam-4828	338	1	γcvr(g	γcvr(g	PROPN
ejpam-4828	338	2	)	)	PUNCT
ejpam-4828	338	3	if	if	SCONJ
ejpam-4828	338	4	and	and	CCONJ
ejpam-4828	338	5	only	only	ADV
ejpam-4828	338	6	if	if	SCONJ
ejpam-4828	338	7	γcon(g	γcon(g	PROPN
ejpam-4828	338	8	)	)	PUNCT
ejpam-4828	338	9	=	=	SYM
ejpam-4828	339	1	n.	n.	NOUN
ejpam-4828	339	2	proof	proof	NOUN
ejpam-4828	339	3	.	.	PUNCT
ejpam-4828	340	1	if	if	SCONJ
ejpam-4828	340	2	γcon(g	γcon(g	PROPN
ejpam-4828	340	3	)	)	PUNCT
ejpam-4828	340	4	=	=	SYM
ejpam-4828	341	1	n	n	CCONJ
ejpam-4828	341	2	,	,	PUNCT
ejpam-4828	341	3	then	then	ADV
ejpam-4828	341	4	γcvr(g	γcvr(g	ADJ
ejpam-4828	341	5	)	)	PUNCT
ejpam-4828	341	6	=	=	SYM
ejpam-4828	342	1	n	n	X
ejpam-4828	342	2	by	by	ADP
ejpam-4828	342	3	proposition	proposition	NOUN
ejpam-4828	342	4	1	1	NUM
ejpam-4828	342	5	.	.	PUNCT
ejpam-4828	343	1	for	for	ADP
ejpam-4828	343	2	the	the	DET
ejpam-4828	343	3	converse	converse	NOUN
ejpam-4828	343	4	,	,	PUNCT
ejpam-4828	343	5	suppose	suppose	VERB
ejpam-4828	343	6	that	that	SCONJ
ejpam-4828	343	7	γcon(g	γcon(g	NOUN
ejpam-4828	343	8	)	)	PUNCT
ejpam-4828	343	9	=	=	SYM
ejpam-4828	343	10	γcvr(g	γcvr(g	PROPN
ejpam-4828	343	11	)	)	PUNCT
ejpam-4828	343	12	.	.	PUNCT
ejpam-4828	344	1	let	let	VERB
ejpam-4828	344	2	f	f	PROPN
ejpam-4828	344	3	=	=	SYM
ejpam-4828	344	4	(	(	PUNCT
ejpam-4828	344	5	v0	v0	PROPN
ejpam-4828	344	6	,	,	PUNCT
ejpam-4828	344	7	v1	v1	NOUN
ejpam-4828	344	8	,	,	PUNCT
ejpam-4828	344	9	v2	v2	PROPN
ejpam-4828	344	10	)	)	PUNCT
ejpam-4828	344	11	be	be	AUX
ejpam-4828	344	12	a	a	DET
ejpam-4828	344	13	γcvr	γcvr	NOUN
ejpam-4828	344	14	-	-	PUNCT
ejpam-4828	344	15	function	function	NOUN
ejpam-4828	344	16	on	on	ADP
ejpam-4828	344	17	g.	g.	PROPN
ejpam-4828	344	18	then	then	ADV
ejpam-4828	344	19	γcon(g	γcon(g	PROPN
ejpam-4828	344	20	)	)	PUNCT
ejpam-4828	344	21	≤	≤	NOUN
ejpam-4828	344	22	|v1|+	|v1|+	PUNCT
ejpam-4828	344	23	|v2|	|v2|	ADV
ejpam-4828	344	24	≤	≤	NUM
ejpam-4828	344	25	|v1|+	|v1|+	PRON
ejpam-4828	344	26	2|v2|	2|v2|	NUM
ejpam-4828	344	27	=	=	SYM
ejpam-4828	344	28	γcvr(g	γcvr(g	NOUN
ejpam-4828	344	29	)	)	PUNCT
ejpam-4828	344	30	.	.	PUNCT
ejpam-4828	345	1	by	by	ADP
ejpam-4828	345	2	assumption	assumption	NOUN
ejpam-4828	345	3	,	,	PUNCT
ejpam-4828	345	4	this	this	PRON
ejpam-4828	345	5	implies	imply	VERB
ejpam-4828	345	6	that	that	DET
ejpam-4828	345	7	|v2|	|v2|	NOUN
ejpam-4828	345	8	=	=	SYM
ejpam-4828	345	9	0	0	X
ejpam-4828	345	10	.	.	PUNCT
ejpam-4828	346	1	hence	hence	ADV
ejpam-4828	346	2	,	,	PUNCT
ejpam-4828	346	3	|v0|	|v0|	NOUN
ejpam-4828	346	4	=	=	SYM
ejpam-4828	346	5	0	0	NUM
ejpam-4828	346	6	,	,	PUNCT
ejpam-4828	346	7	implying	imply	VERB
ejpam-4828	346	8	that	that	SCONJ
ejpam-4828	346	9	γcon(g	γcon(g	NOUN
ejpam-4828	346	10	)	)	PUNCT
ejpam-4828	346	11	=	=	NOUN
ejpam-4828	346	12	|v1|	|v1|	NOUN
ejpam-4828	346	13	=	=	SYM
ejpam-4828	346	14	n	n	PROPN
ejpam-4828	346	15	=	=	SYM
ejpam-4828	346	16	γcvr(g	γcvr(g	PROPN
ejpam-4828	346	17	)	)	PUNCT
ejpam-4828	346	18	.	.	PUNCT
ejpam-4828	347	1	the	the	DET
ejpam-4828	347	2	next	next	ADJ
ejpam-4828	347	3	two	two	NUM
ejpam-4828	347	4	results	result	NOUN
ejpam-4828	347	5	follow	follow	VERB
ejpam-4828	347	6	from	from	ADP
ejpam-4828	347	7	proposition	proposition	NOUN
ejpam-4828	347	8	8	8	NUM
ejpam-4828	347	9	,	,	PUNCT
ejpam-4828	347	10	theorem	theorem	VERB
ejpam-4828	347	11	1	1	NUM
ejpam-4828	347	12	,	,	PUNCT
ejpam-4828	347	13	corollary	corollary	ADJ
ejpam-4828	347	14	1	1	NUM
ejpam-4828	347	15	,	,	PUNCT
ejpam-4828	347	16	and	and	CCONJ
ejpam-4828	347	17	corollary	corollary	ADJ
ejpam-4828	347	18	2	2	NUM
ejpam-4828	347	19	.	.	PUNCT
ejpam-4828	347	20	corollary	corollary	ADJ
ejpam-4828	347	21	6	6	NUM
ejpam-4828	347	22	.	.	PUNCT
ejpam-4828	348	1	let	let	VERB
ejpam-4828	348	2	g	g	PRON
ejpam-4828	348	3	be	be	AUX
ejpam-4828	348	4	a	a	DET
ejpam-4828	348	5	connected	connected	ADJ
ejpam-4828	348	6	graph	graph	NOUN
ejpam-4828	348	7	of	of	ADP
ejpam-4828	348	8	order	order	NOUN
ejpam-4828	348	9	n.	n.	NOUN
ejpam-4828	348	10	if	if	SCONJ
ejpam-4828	348	11	γcon(g	γcon(g	PROPN
ejpam-4828	348	12	)	)	PUNCT
ejpam-4828	349	1	=	=	SYM
ejpam-4828	349	2	γcvr(g	γcvr(g	NOUN
ejpam-4828	349	3	)	)	PUNCT
ejpam-4828	349	4	and	and	CCONJ
ejpam-4828	349	5	g	g	PROPN
ejpam-4828	349	6	̸=	̸=	PROPN
ejpam-4828	349	7	k1	k1	NOUN
ejpam-4828	349	8	,	,	PUNCT
ejpam-4828	349	9	then	then	ADV
ejpam-4828	349	10	2	2	NUM
ejpam-4828	349	11	≤	≤	NUM
ejpam-4828	349	12	δ(g	δ(g	ADP
ejpam-4828	349	13	)	)	PUNCT
ejpam-4828	349	14	≤	≤	NUM
ejpam-4828	349	15	△	△	X
ejpam-4828	349	16	(	(	PUNCT
ejpam-4828	349	17	g	g	NOUN
ejpam-4828	349	18	)	)	PUNCT
ejpam-4828	349	19	≤	≤	NUM
ejpam-4828	349	20	n−	n−	NOUN
ejpam-4828	349	21	4	4	NUM
ejpam-4828	349	22	.	.	PUNCT
ejpam-4828	349	23	corollary	corollary	ADJ
ejpam-4828	349	24	7	7	NUM
ejpam-4828	349	25	.	.	PUNCT
ejpam-4828	350	1	let	let	VERB
ejpam-4828	350	2	g	g	PRON
ejpam-4828	350	3	be	be	AUX
ejpam-4828	350	4	a	a	DET
ejpam-4828	350	5	nontrivial	nontrivial	ADJ
ejpam-4828	350	6	connected	connect	VERB
ejpam-4828	350	7	graph	graph	NOUN
ejpam-4828	350	8	of	of	ADP
ejpam-4828	350	9	order	order	NOUN
ejpam-4828	350	10	n.	n.	NOUN
ejpam-4828	350	11	if	if	SCONJ
ejpam-4828	350	12	γcon(g	γcon(g	PROPN
ejpam-4828	350	13	)	)	PUNCT
ejpam-4828	351	1	=	=	SYM
ejpam-4828	351	2	γcvr(g	γcvr(g	PROPN
ejpam-4828	351	3	)	)	PUNCT
ejpam-4828	351	4	,	,	PUNCT
ejpam-4828	351	5	then	then	ADV
ejpam-4828	351	6	n	n	PRON
ejpam-4828	351	7	≥	≥	NOUN
ejpam-4828	351	8	6	6	NUM
ejpam-4828	351	9	.	.	PUNCT
ejpam-4828	352	1	theorem	theorem	NOUN
ejpam-4828	352	2	5	5	NUM
ejpam-4828	352	3	.	.	PUNCT
ejpam-4828	353	1	let	let	VERB
ejpam-4828	353	2	g	g	PRON
ejpam-4828	353	3	be	be	AUX
ejpam-4828	353	4	a	a	DET
ejpam-4828	353	5	nontrivial	nontrivial	ADJ
ejpam-4828	353	6	connected	connect	VERB
ejpam-4828	353	7	graph	graph	NOUN
ejpam-4828	353	8	on	on	ADP
ejpam-4828	353	9	n	n	PRON
ejpam-4828	353	10	vertices	vertex	NOUN
ejpam-4828	353	11	such	such	ADJ
ejpam-4828	353	12	that	that	SCONJ
ejpam-4828	353	13	γcon(g	γcon(g	NOUN
ejpam-4828	353	14	)	)	PUNCT
ejpam-4828	353	15	<	<	X
ejpam-4828	353	16	γcvr(g	γcvr(g	PROPN
ejpam-4828	353	17	)	)	PUNCT
ejpam-4828	353	18	.	.	PUNCT
ejpam-4828	354	1	then	then	ADV
ejpam-4828	354	2	γcvr(g	γcvr(g	VERB
ejpam-4828	354	3	)	)	PUNCT
ejpam-4828	355	1	=	=	SYM
ejpam-4828	355	2	γcon(g	γcon(g	NOUN
ejpam-4828	355	3	)	)	PUNCT
ejpam-4828	356	1	+	+	CCONJ
ejpam-4828	356	2	1	1	NUM
ejpam-4828	356	3	if	if	SCONJ
ejpam-4828	356	4	and	and	CCONJ
ejpam-4828	356	5	only	only	ADV
ejpam-4828	356	6	if	if	SCONJ
ejpam-4828	356	7	there	there	PRON
ejpam-4828	356	8	exist	exist	VERB
ejpam-4828	356	9	a	a	DET
ejpam-4828	356	10	vertex	vertex	NOUN
ejpam-4828	356	11	v	v	NOUN
ejpam-4828	356	12	and	and	CCONJ
ejpam-4828	357	1	a	a	DET
ejpam-4828	357	2	set	set	NOUN
ejpam-4828	357	3	s	s	NOUN
ejpam-4828	357	4	⊆	⊆	NUM
ejpam-4828	357	5	v	v	NOUN
ejpam-4828	357	6	(	(	PUNCT
ejpam-4828	357	7	g	g	NOUN
ejpam-4828	357	8	)	)	PUNCT
ejpam-4828	357	9	such	such	ADJ
ejpam-4828	357	10	that	that	PRON
ejpam-4828	357	11	s	s	VERB
ejpam-4828	357	12	⊆	⊆	NUM
ejpam-4828	357	13	ng(v	ng(v	PUNCT
ejpam-4828	357	14	)	)	PUNCT
ejpam-4828	357	15	and	and	CCONJ
ejpam-4828	357	16	v	v	NOUN
ejpam-4828	357	17	(	(	PUNCT
ejpam-4828	357	18	g	g	NOUN
ejpam-4828	357	19	)	)	PUNCT
ejpam-4828	357	20	\	\	PROPN
ejpam-4828	358	1	s	s	PART
ejpam-4828	358	2	is	be	AUX
ejpam-4828	358	3	a	a	DET
ejpam-4828	358	4	γcon	γcon	NOUN
ejpam-4828	358	5	-	-	PUNCT
ejpam-4828	358	6	set	set	VERB
ejpam-4828	358	7	in	in	ADP
ejpam-4828	358	8	g.	g.	PROPN
ejpam-4828	358	9	proof	proof	PROPN
ejpam-4828	358	10	.	.	PUNCT
ejpam-4828	359	1	suppose	suppose	VERB
ejpam-4828	359	2	γcvr(g	γcvr(g	ADP
ejpam-4828	359	3	)	)	PUNCT
ejpam-4828	359	4	=	=	SYM
ejpam-4828	359	5	γcon(g	γcon(g	NOUN
ejpam-4828	359	6	)	)	PUNCT
ejpam-4828	359	7	+	+	NOUN
ejpam-4828	360	1	1	1	X
ejpam-4828	360	2	.	.	X
ejpam-4828	360	3	let	let	VERB
ejpam-4828	360	4	f	f	PROPN
ejpam-4828	360	5	=	=	SYM
ejpam-4828	360	6	(	(	PUNCT
ejpam-4828	360	7	v0	v0	PROPN
ejpam-4828	360	8	,	,	PUNCT
ejpam-4828	360	9	v1	v1	NOUN
ejpam-4828	360	10	,	,	PUNCT
ejpam-4828	360	11	v2	v2	PROPN
ejpam-4828	360	12	)	)	PUNCT
ejpam-4828	360	13	be	be	AUX
ejpam-4828	360	14	a	a	DET
ejpam-4828	360	15	γcvr	γcvr	NOUN
ejpam-4828	360	16	-	-	PUNCT
ejpam-4828	360	17	function	function	NOUN
ejpam-4828	360	18	on	on	ADP
ejpam-4828	360	19	g.	g.	PROPN
ejpam-4828	360	20	since	since	SCONJ
ejpam-4828	360	21	v1	v1	PROPN
ejpam-4828	360	22	∪	∪	NOUN
ejpam-4828	360	23	v2	v2	NOUN
ejpam-4828	360	24	is	be	AUX
ejpam-4828	360	25	a	a	DET
ejpam-4828	360	26	convex	convex	NOUN
ejpam-4828	360	27	dominating	dominating	NOUN
ejpam-4828	360	28	set	set	VERB
ejpam-4828	360	29	in	in	ADP
ejpam-4828	360	30	g	g	PROPN
ejpam-4828	360	31	,	,	PUNCT
ejpam-4828	360	32	γcon(g	γcon(g	PROPN
ejpam-4828	360	33	)	)	PUNCT
ejpam-4828	360	34	≤	≤	NOUN
ejpam-4828	360	35	|v1|	|v1|	NOUN
ejpam-4828	360	36	+	+	CCONJ
ejpam-4828	360	37	|v2|	|v2|	ADV
ejpam-4828	360	38	.	.	PUNCT
ejpam-4828	361	1	consider	consider	VERB
ejpam-4828	361	2	the	the	DET
ejpam-4828	361	3	following	follow	VERB
ejpam-4828	361	4	cases	case	NOUN
ejpam-4828	361	5	:	:	PUNCT
ejpam-4828	361	6	case	case	NOUN
ejpam-4828	361	7	1	1	NUM
ejpam-4828	361	8	.	.	PUNCT
ejpam-4828	362	1	γcon(g	γcon(g	NOUN
ejpam-4828	362	2	)	)	PUNCT
ejpam-4828	362	3	=	=	SYM
ejpam-4828	362	4	|v1|+	|v1|+	PRON
ejpam-4828	362	5	|v2|	|v2|	NOUN
ejpam-4828	362	6	.	.	PUNCT
ejpam-4828	363	1	then	then	ADV
ejpam-4828	363	2	γcon(g	γcon(g	PROPN
ejpam-4828	363	3	)	)	PUNCT
ejpam-4828	364	1	+	+	CCONJ
ejpam-4828	364	2	1	1	NUM
ejpam-4828	364	3	=	=	NOUN
ejpam-4828	364	4	|v1|	|v1|	NOUN
ejpam-4828	364	5	+	+	CCONJ
ejpam-4828	364	6	|v2|	|v2|	ADV
ejpam-4828	364	7	+	+	NOUN
ejpam-4828	364	8	1	1	X
ejpam-4828	364	9	.	.	PUNCT
ejpam-4828	364	10	by	by	ADP
ejpam-4828	364	11	assumption	assumption	NOUN
ejpam-4828	364	12	,	,	PUNCT
ejpam-4828	364	13	|v1|	|v1|	NOUN
ejpam-4828	364	14	+	+	CCONJ
ejpam-4828	364	15	|v2|	|v2|	ADV
ejpam-4828	364	16	+	+	CCONJ
ejpam-4828	364	17	1	1	NUM
ejpam-4828	364	18	=	=	NOUN
ejpam-4828	364	19	|v1|	|v1|	NOUN
ejpam-4828	364	20	+	+	CCONJ
ejpam-4828	364	21	2|v2|	2|v2|	NUM
ejpam-4828	364	22	.	.	PUNCT
ejpam-4828	365	1	this	this	PRON
ejpam-4828	365	2	implies	imply	VERB
ejpam-4828	365	3	that	that	DET
ejpam-4828	365	4	|v2|	|v2|	NOUN
ejpam-4828	365	5	=	=	SYM
ejpam-4828	365	6	1	1	NUM
ejpam-4828	365	7	and	and	CCONJ
ejpam-4828	365	8	|v1|	|v1|	NOUN
ejpam-4828	365	9	=	=	SYM
ejpam-4828	365	10	γcon(g)−	γcon(g)−	PROPN
ejpam-4828	365	11	1	1	NUM
ejpam-4828	365	12	.	.	PUNCT
ejpam-4828	366	1	let	let	VERB
ejpam-4828	366	2	v2	v2	VERB
ejpam-4828	366	3	=	=	PUNCT
ejpam-4828	366	4	{	{	PUNCT
ejpam-4828	366	5	v	v	NOUN
ejpam-4828	366	6	}	}	PUNCT
ejpam-4828	366	7	and	and	CCONJ
ejpam-4828	366	8	s	s	NOUN
ejpam-4828	366	9	=	=	PROPN
ejpam-4828	366	10	v0	v0	PROPN
ejpam-4828	366	11	.	.	PUNCT
ejpam-4828	367	1	then	then	ADV
ejpam-4828	367	2	s	s	VERB
ejpam-4828	367	3	⊆	⊆	NUM
ejpam-4828	367	4	ng(v	ng(v	NUM
ejpam-4828	367	5	)	)	PUNCT
ejpam-4828	367	6	.	.	PUNCT
ejpam-4828	368	1	since	since	SCONJ
ejpam-4828	368	2	v1	v1	NOUN
ejpam-4828	368	3	∪	∪	NOUN
ejpam-4828	368	4	v2	v2	NOUN
ejpam-4828	368	5	is	be	AUX
ejpam-4828	368	6	a	a	DET
ejpam-4828	368	7	convex	convex	NOUN
ejpam-4828	368	8	dominating	dominating	NOUN
ejpam-4828	368	9	set	set	VERB
ejpam-4828	368	10	in	in	ADP
ejpam-4828	368	11	g	g	PROPN
ejpam-4828	368	12	and	and	CCONJ
ejpam-4828	368	13	|v1	|v1	PROPN
ejpam-4828	368	14	∪	∪	X
ejpam-4828	368	15	v2|	v2|	X
ejpam-4828	368	16	=	=	SYM
ejpam-4828	368	17	γcon(g	γcon(g	PROPN
ejpam-4828	368	18	)	)	PUNCT
ejpam-4828	368	19	,	,	PUNCT
ejpam-4828	368	20	it	it	PRON
ejpam-4828	368	21	follows	follow	VERB
ejpam-4828	368	22	that	that	SCONJ
ejpam-4828	368	23	v	v	X
ejpam-4828	368	24	(	(	PUNCT
ejpam-4828	368	25	g	g	NOUN
ejpam-4828	368	26	)	)	PUNCT
ejpam-4828	368	27	\	\	PROPN
ejpam-4828	369	1	s	s	PART
ejpam-4828	369	2	=	=	SYM
ejpam-4828	369	3	v1	v1	NOUN
ejpam-4828	369	4	∪	∪	NOUN
ejpam-4828	369	5	v2	v2	NOUN
ejpam-4828	369	6	is	be	AUX
ejpam-4828	369	7	a	a	DET
ejpam-4828	369	8	γcon	γcon	NOUN
ejpam-4828	369	9	-	-	PUNCT
ejpam-4828	369	10	set	set	VERB
ejpam-4828	369	11	in	in	ADP
ejpam-4828	369	12	g.	g.	NOUN
ejpam-4828	369	13	case	case	NOUN
ejpam-4828	369	14	2	2	NUM
ejpam-4828	370	1	.	.	X
ejpam-4828	370	2	γcon(g	γcon(g	NOUN
ejpam-4828	370	3	)	)	PUNCT
ejpam-4828	370	4	<	<	X
ejpam-4828	370	5	|v1|+	|v1|+	PRON
ejpam-4828	370	6	|v2|	|v2|	NOUN
ejpam-4828	370	7	.	.	PUNCT
ejpam-4828	371	1	then	then	ADV
ejpam-4828	371	2	γcon(g)+1	γcon(g)+1	VERB
ejpam-4828	371	3	≤	≤	NOUN
ejpam-4828	371	4	|v1|+	|v1|+	CCONJ
ejpam-4828	371	5	|v2|	|v2|	NOUN
ejpam-4828	371	6	.	.	PUNCT
ejpam-4828	372	1	the	the	DET
ejpam-4828	372	2	assumption	assumption	NOUN
ejpam-4828	372	3	γcvr(g	γcvr(g	PROPN
ejpam-4828	372	4	)	)	PUNCT
ejpam-4828	372	5	=	=	NOUN
ejpam-4828	372	6	γcon(g)+1	γcon(g)+1	NOUN
ejpam-4828	372	7	forces	force	VERB
ejpam-4828	372	8	the	the	DET
ejpam-4828	372	9	equality	equality	NOUN
ejpam-4828	372	10	|v1|	|v1|	NOUN
ejpam-4828	372	11	+	+	X
ejpam-4828	372	12	|v2|	|v2|	NOUN
ejpam-4828	372	13	=	=	SYM
ejpam-4828	372	14	|v1|	|v1|	NOUN
ejpam-4828	372	15	+	+	CCONJ
ejpam-4828	372	16	2|v2|	2|v2|	NUM
ejpam-4828	372	17	.	.	PUNCT
ejpam-4828	373	1	hence	hence	ADV
ejpam-4828	373	2	,	,	PUNCT
ejpam-4828	373	3	|v2|	|v2|	NOUN
ejpam-4828	373	4	=	=	SYM
ejpam-4828	373	5	0	0	NUM
ejpam-4828	373	6	,	,	PUNCT
ejpam-4828	373	7	|v0|	|v0|	NOUN
ejpam-4828	373	8	=	=	SYM
ejpam-4828	373	9	0	0	NUM
ejpam-4828	373	10	,	,	PUNCT
ejpam-4828	373	11	and	and	CCONJ
ejpam-4828	373	12	|v1|	|v1|	NOUN
ejpam-4828	373	13	=	=	SYM
ejpam-4828	373	14	n.	n.	PROPN
ejpam-4828	373	15	consequently	consequently	ADV
ejpam-4828	373	16	,	,	PUNCT
ejpam-4828	373	17	γcon(g	γcon(g	PROPN
ejpam-4828	373	18	)	)	PUNCT
ejpam-4828	373	19	=	=	SYM
ejpam-4828	373	20	n	n	CCONJ
ejpam-4828	373	21	−	−	NOUN
ejpam-4828	374	1	1	1	X
ejpam-4828	374	2	.	.	PUNCT
ejpam-4828	375	1	let	let	AUX
ejpam-4828	375	2	d	d	NOUN
ejpam-4828	375	3	=	=	SYM
ejpam-4828	375	4	v	v	X
ejpam-4828	375	5	(	(	PUNCT
ejpam-4828	375	6	g	g	NOUN
ejpam-4828	375	7	)	)	PUNCT
ejpam-4828	375	8	\	\	NOUN
ejpam-4828	375	9	{	{	PUNCT
ejpam-4828	375	10	w	w	AUX
ejpam-4828	375	11	}	}	PUNCT
ejpam-4828	375	12	be	be	AUX
ejpam-4828	375	13	a	a	DET
ejpam-4828	375	14	γcon	γcon	NOUN
ejpam-4828	375	15	-	-	PUNCT
ejpam-4828	375	16	set	set	NOUN
ejpam-4828	375	17	in	in	ADP
ejpam-4828	375	18	g	g	NOUN
ejpam-4828	375	19	and	and	CCONJ
ejpam-4828	375	20	set	set	VERB
ejpam-4828	375	21	s	s	PART
ejpam-4828	375	22	=	=	PUNCT
ejpam-4828	375	23	{	{	PUNCT
ejpam-4828	375	24	w	w	NOUN
ejpam-4828	375	25	}	}	PUNCT
ejpam-4828	375	26	.	.	PUNCT
ejpam-4828	376	1	since	since	SCONJ
ejpam-4828	376	2	d	d	PROPN
ejpam-4828	376	3	is	be	AUX
ejpam-4828	376	4	a	a	DET
ejpam-4828	376	5	dominating	dominating	NOUN
ejpam-4828	376	6	set	set	NOUN
ejpam-4828	376	7	and	and	CCONJ
ejpam-4828	376	8	g	g	NOUN
ejpam-4828	376	9	is	be	AUX
ejpam-4828	376	10	non	non	ADJ
ejpam-4828	376	11	-	-	ADJ
ejpam-4828	376	12	trivial	trivial	ADJ
ejpam-4828	376	13	,	,	PUNCT
ejpam-4828	376	14	there	there	PRON
ejpam-4828	376	15	exists	exist	VERB
ejpam-4828	376	16	v	v	ADP
ejpam-4828	376	17	∈	∈	PROPN
ejpam-4828	376	18	d	d	NOUN
ejpam-4828	376	19	such	such	ADJ
ejpam-4828	376	20	that	that	PRON
ejpam-4828	376	21	s	s	NOUN
ejpam-4828	376	22	⊆	⊆	NUM
ejpam-4828	376	23	ng(v	ng(v	NUM
ejpam-4828	376	24	)	)	PUNCT
ejpam-4828	376	25	.	.	PUNCT
ejpam-4828	377	1	in	in	ADP
ejpam-4828	377	2	either	either	DET
ejpam-4828	377	3	case	case	NOUN
ejpam-4828	377	4	,	,	PUNCT
ejpam-4828	377	5	the	the	DET
ejpam-4828	377	6	desired	desire	VERB
ejpam-4828	377	7	properties	property	NOUN
ejpam-4828	377	8	hold	hold	VERB
ejpam-4828	377	9	.	.	PUNCT
ejpam-4828	378	1	for	for	ADP
ejpam-4828	378	2	the	the	DET
ejpam-4828	378	3	converse	converse	NOUN
ejpam-4828	378	4	,	,	PUNCT
ejpam-4828	378	5	suppose	suppose	VERB
ejpam-4828	378	6	that	that	SCONJ
ejpam-4828	378	7	there	there	PRON
ejpam-4828	378	8	exist	exist	VERB
ejpam-4828	378	9	a	a	DET
ejpam-4828	378	10	vertex	vertex	NOUN
ejpam-4828	378	11	v	v	NOUN
ejpam-4828	378	12	and	and	CCONJ
ejpam-4828	378	13	a	a	DET
ejpam-4828	378	14	set	set	NOUN
ejpam-4828	378	15	s	s	NOUN
ejpam-4828	378	16	⊆	⊆	NUM
ejpam-4828	378	17	v	v	NOUN
ejpam-4828	378	18	(	(	PUNCT
ejpam-4828	378	19	g	g	NOUN
ejpam-4828	378	20	)	)	PUNCT
ejpam-4828	378	21	such	such	ADJ
ejpam-4828	378	22	that	that	PRON
ejpam-4828	378	23	s	s	VERB
ejpam-4828	378	24	⊆	⊆	NUM
ejpam-4828	378	25	ng(v	ng(v	PUNCT
ejpam-4828	378	26	)	)	PUNCT
ejpam-4828	378	27	and	and	CCONJ
ejpam-4828	378	28	v	v	NOUN
ejpam-4828	378	29	(	(	PUNCT
ejpam-4828	378	30	g	g	NOUN
ejpam-4828	378	31	)	)	PUNCT
ejpam-4828	378	32	\	\	PROPN
ejpam-4828	379	1	s	s	PART
ejpam-4828	379	2	is	be	AUX
ejpam-4828	379	3	a	a	DET
ejpam-4828	379	4	γcon	γcon	NOUN
ejpam-4828	379	5	-	-	PUNCT
ejpam-4828	379	6	set	set	NOUN
ejpam-4828	379	7	in	in	ADP
ejpam-4828	379	8	g.	g.	PROPN
ejpam-4828	379	9	let	let	VERB
ejpam-4828	379	10	v2	v2	VERB
ejpam-4828	379	11	=	=	PUNCT
ejpam-4828	379	12	{	{	PUNCT
ejpam-4828	379	13	v	v	NOUN
ejpam-4828	379	14	}	}	PUNCT
ejpam-4828	379	15	,	,	PUNCT
ejpam-4828	379	16	v1	v1	NOUN
ejpam-4828	379	17	=	=	SYM
ejpam-4828	379	18	v	v	NOUN
ejpam-4828	379	19	(	(	PUNCT
ejpam-4828	379	20	g	g	NOUN
ejpam-4828	379	21	)	)	PUNCT
ejpam-4828	379	22	\	\	PUNCT
ejpam-4828	380	1	(	(	PUNCT
ejpam-4828	380	2	s	s	X
ejpam-4828	380	3	∪	∪	X
ejpam-4828	380	4	v2	v2	NOUN
ejpam-4828	380	5	)	)	PUNCT
ejpam-4828	380	6	,	,	PUNCT
ejpam-4828	380	7	and	and	CCONJ
ejpam-4828	380	8	v0	v0	PROPN
ejpam-4828	380	9	=	=	SYM
ejpam-4828	380	10	v	v	PROPN
ejpam-4828	380	11	(	(	PUNCT
ejpam-4828	380	12	g	g	NOUN
ejpam-4828	380	13	)	)	PUNCT
ejpam-4828	380	14	\	\	PUNCT
ejpam-4828	380	15	(	(	PUNCT
ejpam-4828	380	16	v1	v1	VERB
ejpam-4828	380	17	∪	∪	X
ejpam-4828	380	18	v2	v2	NOUN
ejpam-4828	380	19	)	)	PUNCT
ejpam-4828	380	20	=	=	PUNCT
ejpam-4828	381	1	s.	s.	PROPN
ejpam-4828	381	2	then	then	ADV
ejpam-4828	381	3	,	,	PUNCT
ejpam-4828	381	4	by	by	ADP
ejpam-4828	381	5	assumption	assumption	NOUN
ejpam-4828	381	6	,	,	PUNCT
ejpam-4828	381	7	v	v	NOUN
ejpam-4828	381	8	(	(	PUNCT
ejpam-4828	381	9	g	g	NOUN
ejpam-4828	381	10	)	)	PUNCT
ejpam-4828	381	11	\	\	PROPN
ejpam-4828	381	12	s	s	PART
ejpam-4828	381	13	=	=	SYM
ejpam-4828	381	14	v1	v1	NOUN
ejpam-4828	381	15	∪	∪	NOUN
ejpam-4828	381	16	v2	v2	NOUN
ejpam-4828	381	17	is	be	AUX
ejpam-4828	381	18	convex	convex	NOUN
ejpam-4828	381	19	and	and	CCONJ
ejpam-4828	381	20	v0	v0	NOUN
ejpam-4828	381	21	⊆	⊆	NUM
ejpam-4828	381	22	ng(v	ng(v	NOUN
ejpam-4828	381	23	)	)	PUNCT
ejpam-4828	381	24	.	.	PUNCT
ejpam-4828	382	1	therefore	therefore	ADV
ejpam-4828	382	2	,	,	PUNCT
ejpam-4828	382	3	g	g	PROPN
ejpam-4828	382	4	=	=	SYM
ejpam-4828	382	5	(	(	PUNCT
ejpam-4828	382	6	v0	v0	PROPN
ejpam-4828	382	7	,	,	PUNCT
ejpam-4828	382	8	v1	v1	NOUN
ejpam-4828	382	9	,	,	PUNCT
ejpam-4828	382	10	v2	v2	PROPN
ejpam-4828	382	11	)	)	PUNCT
ejpam-4828	382	12	is	be	AUX
ejpam-4828	382	13	cvrdf	cvrdf	NOUN
ejpam-4828	382	14	on	on	ADP
ejpam-4828	382	15	g	g	PROPN
ejpam-4828	382	16	and	and	CCONJ
ejpam-4828	382	17	γcvr(g	γcvr(g	NOUN
ejpam-4828	382	18	)	)	PUNCT
ejpam-4828	382	19	≤	≤	NOUN
ejpam-4828	382	20	wcvr	wcvr	NOUN
ejpam-4828	382	21	g	g	PROPN
ejpam-4828	382	22	(	(	PUNCT
ejpam-4828	382	23	g	g	NOUN
ejpam-4828	382	24	)	)	PUNCT
ejpam-4828	382	25	=	=	PUNCT
ejpam-4828	382	26	|v1|+	|v1|+	PRON
ejpam-4828	382	27	2|v2|	2|v2|	NUM
ejpam-4828	382	28	=	=	PUNCT
ejpam-4828	383	1	[	[	X
ejpam-4828	383	2	n−	n−	NOUN
ejpam-4828	383	3	(	(	PUNCT
ejpam-4828	383	4	n−	n−	NOUN
ejpam-4828	383	5	γcon(g	γcon(g	NOUN
ejpam-4828	383	6	)	)	PUNCT
ejpam-4828	383	7	+	+	CCONJ
ejpam-4828	383	8	1	1	NUM
ejpam-4828	383	9	)	)	PUNCT
ejpam-4828	383	10	]	]	PUNCT
ejpam-4828	384	1	+	+	CCONJ
ejpam-4828	384	2	2	2	NUM
ejpam-4828	384	3	r.	r.	NOUN
ejpam-4828	384	4	fortosa	fortosa	PROPN
ejpam-4828	384	5	,	,	PUNCT
ejpam-4828	384	6	s.	s.	PROPN
ejpam-4828	384	7	canoy	canoy	PROPN
ejpam-4828	384	8	jr	jr	PROPN
ejpam-4828	384	9	.	.	PROPN
ejpam-4828	384	10	/	/	SYM
ejpam-4828	384	11	eur	eur	PROPN
ejpam-4828	384	12	.	.	PUNCT
ejpam-4828	385	1	j.	j.	PROPN
ejpam-4828	385	2	pure	pure	PROPN
ejpam-4828	385	3	appl	appl	PROPN
ejpam-4828	385	4	.	.	PROPN
ejpam-4828	385	5	math	math	PROPN
ejpam-4828	385	6	,	,	PUNCT
ejpam-4828	385	7	16	16	NUM
ejpam-4828	385	8	(	(	PUNCT
ejpam-4828	385	9	3	3	NUM
ejpam-4828	385	10	)	)	PUNCT
ejpam-4828	385	11	(	(	PUNCT
ejpam-4828	385	12	2023	2023	NUM
ejpam-4828	385	13	)	)	PUNCT
ejpam-4828	385	14	,	,	PUNCT
ejpam-4828	385	15	1705	1705	NUM
ejpam-4828	385	16	-	-	SYM
ejpam-4828	385	17	1716	1716	NUM
ejpam-4828	385	18	1714	1714	NUM
ejpam-4828	385	19	=	=	SYM
ejpam-4828	385	20	γcon(g	γcon(g	NOUN
ejpam-4828	385	21	)	)	PUNCT
ejpam-4828	385	22	+	+	PROPN
ejpam-4828	386	1	1	1	X
ejpam-4828	386	2	.	.	PUNCT
ejpam-4828	386	3	since	since	SCONJ
ejpam-4828	386	4	γcon(g	γcon(g	PROPN
ejpam-4828	386	5	)	)	PUNCT
ejpam-4828	386	6	<	<	X
ejpam-4828	386	7	γcvr(g	γcvr(g	PROPN
ejpam-4828	386	8	)	)	PUNCT
ejpam-4828	386	9	,	,	PUNCT
ejpam-4828	386	10	γcon(g)+1	γcon(g)+1	ADJ
ejpam-4828	386	11	≤	≤	NOUN
ejpam-4828	386	12	γcvr(g	γcvr(g	PROPN
ejpam-4828	386	13	)	)	PUNCT
ejpam-4828	386	14	.	.	PUNCT
ejpam-4828	387	1	therefore	therefore	ADV
ejpam-4828	387	2	,	,	PUNCT
ejpam-4828	387	3	γcvr(g	γcvr(g	NOUN
ejpam-4828	387	4	)	)	PUNCT
ejpam-4828	387	5	=	=	NOUN
ejpam-4828	387	6	γcon(g)+1	γcon(g)+1	NOUN
ejpam-4828	387	7	.	.	PUNCT
ejpam-4828	388	1	graphs	graph	VERB
ejpam-4828	388	2	g	g	ADP
ejpam-4828	388	3	such	such	ADJ
ejpam-4828	388	4	that	that	DET
ejpam-4828	388	5	γcvr(g	γcvr(g	NOUN
ejpam-4828	388	6	)	)	PUNCT
ejpam-4828	388	7	=	=	SYM
ejpam-4828	388	8	2γcon(g	2γcon(g	NUM
ejpam-4828	388	9	)	)	PUNCT
ejpam-4828	388	10	are	be	AUX
ejpam-4828	388	11	called	call	VERB
ejpam-4828	388	12	convex	convex	ADJ
ejpam-4828	388	13	roman	roman	ADJ
ejpam-4828	388	14	graphs	graph	NOUN
ejpam-4828	388	15	.	.	PUNCT
ejpam-4828	389	1	theorem	theorem	ADJ
ejpam-4828	389	2	6	6	NUM
ejpam-4828	389	3	.	.	PUNCT
ejpam-4828	390	1	let	let	VERB
ejpam-4828	390	2	g	g	PRON
ejpam-4828	390	3	be	be	AUX
ejpam-4828	390	4	a	a	DET
ejpam-4828	390	5	nontrivial	nontrivial	ADJ
ejpam-4828	390	6	connected	connect	VERB
ejpam-4828	390	7	graph	graph	NOUN
ejpam-4828	390	8	.	.	PUNCT
ejpam-4828	391	1	the	the	DET
ejpam-4828	391	2	following	follow	VERB
ejpam-4828	391	3	statements	statement	NOUN
ejpam-4828	391	4	are	be	AUX
ejpam-4828	391	5	equivalent	equivalent	ADJ
ejpam-4828	391	6	.	.	PUNCT
ejpam-4828	392	1	(	(	PUNCT
ejpam-4828	392	2	i	i	NOUN
ejpam-4828	392	3	)	)	PUNCT
ejpam-4828	392	4	g	g	NOUN
ejpam-4828	392	5	is	be	AUX
ejpam-4828	392	6	a	a	DET
ejpam-4828	392	7	convex	convex	ADJ
ejpam-4828	392	8	roman	roman	ADJ
ejpam-4828	392	9	graph	graph	NOUN
ejpam-4828	392	10	.	.	PUNCT
ejpam-4828	393	1	(	(	PUNCT
ejpam-4828	393	2	ii	ii	NOUN
ejpam-4828	393	3	)	)	PUNCT
ejpam-4828	393	4	g	g	PROPN
ejpam-4828	393	5	has	have	VERB
ejpam-4828	393	6	a	a	DET
ejpam-4828	393	7	γcvr	γcvr	NOUN
ejpam-4828	393	8	-	-	PUNCT
ejpam-4828	393	9	function	function	NOUN
ejpam-4828	393	10	f	f	NOUN
ejpam-4828	393	11	=	=	SYM
ejpam-4828	393	12	(	(	PUNCT
ejpam-4828	393	13	v0	v0	PROPN
ejpam-4828	393	14	,	,	PUNCT
ejpam-4828	393	15	v1	v1	NOUN
ejpam-4828	393	16	,	,	PUNCT
ejpam-4828	393	17	v2	v2	NOUN
ejpam-4828	393	18	)	)	PUNCT
ejpam-4828	393	19	such	such	ADJ
ejpam-4828	393	20	that	that	DET
ejpam-4828	393	21	|v1|	|v1|	NOUN
ejpam-4828	393	22	=	=	SYM
ejpam-4828	393	23	0	0	X
ejpam-4828	393	24	.	.	PUNCT
ejpam-4828	394	1	(	(	PUNCT
ejpam-4828	394	2	iii	iii	X
ejpam-4828	394	3	)	)	PUNCT
ejpam-4828	394	4	g	g	NOUN
ejpam-4828	394	5	has	have	VERB
ejpam-4828	394	6	a	a	DET
ejpam-4828	394	7	γcvr	γcvr	NOUN
ejpam-4828	394	8	-	-	PUNCT
ejpam-4828	394	9	function	function	NOUN
ejpam-4828	394	10	f	f	NOUN
ejpam-4828	394	11	=	=	SYM
ejpam-4828	394	12	(	(	PUNCT
ejpam-4828	394	13	v0	v0	PROPN
ejpam-4828	394	14	,	,	PUNCT
ejpam-4828	394	15	v1	v1	NOUN
ejpam-4828	394	16	,	,	PUNCT
ejpam-4828	394	17	v2	v2	NOUN
ejpam-4828	394	18	)	)	PUNCT
ejpam-4828	394	19	such	such	ADJ
ejpam-4828	394	20	that	that	SCONJ
ejpam-4828	394	21	v2	v2	PROPN
ejpam-4828	394	22	is	be	AUX
ejpam-4828	394	23	a	a	DET
ejpam-4828	394	24	γcon	γcon	NOUN
ejpam-4828	394	25	-	-	PUNCT
ejpam-4828	394	26	set	set	VERB
ejpam-4828	394	27	in	in	ADP
ejpam-4828	394	28	g.	g.	PROPN
ejpam-4828	394	29	proof	proof	PROPN
ejpam-4828	394	30	.	.	PUNCT
ejpam-4828	395	1	let	let	VERB
ejpam-4828	395	2	g	g	PRON
ejpam-4828	395	3	be	be	AUX
ejpam-4828	395	4	a	a	DET
ejpam-4828	395	5	convex	convex	ADJ
ejpam-4828	395	6	roman	roman	ADJ
ejpam-4828	395	7	graph	graph	NOUN
ejpam-4828	395	8	and	and	CCONJ
ejpam-4828	395	9	let	let	VERB
ejpam-4828	395	10	f	f	PROPN
ejpam-4828	395	11	=	=	SYM
ejpam-4828	395	12	(	(	PUNCT
ejpam-4828	395	13	v0	v0	PROPN
ejpam-4828	395	14	,	,	PUNCT
ejpam-4828	395	15	v1	v1	NOUN
ejpam-4828	395	16	,	,	PUNCT
ejpam-4828	395	17	v2	v2	PROPN
ejpam-4828	395	18	)	)	PUNCT
ejpam-4828	395	19	be	be	AUX
ejpam-4828	395	20	a	a	DET
ejpam-4828	395	21	γcvr	γcvr	NOUN
ejpam-4828	395	22	-	-	PUNCT
ejpam-4828	395	23	function	function	NOUN
ejpam-4828	395	24	on	on	ADP
ejpam-4828	395	25	g.	g.	PROPN
ejpam-4828	395	26	then	then	ADV
ejpam-4828	395	27	2γcon(g	2γcon(g	NUM
ejpam-4828	395	28	)	)	PUNCT
ejpam-4828	395	29	=	=	PUNCT
ejpam-4828	396	1	2|v1|	2|v1|	NUM
ejpam-4828	397	1	+	+	CCONJ
ejpam-4828	397	2	2|v2|	2|v2|	NUM
ejpam-4828	397	3	=	=	SYM
ejpam-4828	397	4	|v1|	|v1|	NOUN
ejpam-4828	397	5	+	+	CCONJ
ejpam-4828	397	6	2|v2|	2|v2|	NUM
ejpam-4828	397	7	=	=	SYM
ejpam-4828	397	8	γcvr(g	γcvr(g	NOUN
ejpam-4828	397	9	)	)	PUNCT
ejpam-4828	397	10	.	.	PUNCT
ejpam-4828	398	1	this	this	PRON
ejpam-4828	398	2	implies	imply	VERB
ejpam-4828	398	3	that	that	SCONJ
ejpam-4828	398	4	|v1|	|v1|	NOUN
ejpam-4828	398	5	=	=	SYM
ejpam-4828	398	6	0	0	X
ejpam-4828	398	7	.	.	PUNCT
ejpam-4828	399	1	hence	hence	ADV
ejpam-4828	399	2	(	(	PUNCT
ejpam-4828	399	3	i	i	NOUN
ejpam-4828	399	4	)	)	PUNCT
ejpam-4828	399	5	implies	imply	VERB
ejpam-4828	399	6	(	(	PUNCT
ejpam-4828	399	7	ii	ii	NOUN
ejpam-4828	399	8	)	)	PUNCT
ejpam-4828	399	9	.	.	PUNCT
ejpam-4828	400	1	next	next	ADV
ejpam-4828	400	2	,	,	PUNCT
ejpam-4828	400	3	let	let	VERB
ejpam-4828	400	4	f	f	PROPN
ejpam-4828	400	5	=	=	SYM
ejpam-4828	400	6	(	(	PUNCT
ejpam-4828	400	7	v0	v0	PROPN
ejpam-4828	400	8	,	,	PUNCT
ejpam-4828	400	9	v1	v1	NOUN
ejpam-4828	400	10	,	,	PUNCT
ejpam-4828	400	11	v2	v2	PROPN
ejpam-4828	400	12	)	)	PUNCT
ejpam-4828	400	13	be	be	AUX
ejpam-4828	400	14	a	a	DET
ejpam-4828	400	15	γcvr	γcvr	NOUN
ejpam-4828	400	16	-	-	PUNCT
ejpam-4828	400	17	function	function	NOUN
ejpam-4828	400	18	on	on	ADP
ejpam-4828	400	19	g	g	PROPN
ejpam-4828	400	20	with	with	ADP
ejpam-4828	400	21	|v1|	|v1|	NOUN
ejpam-4828	400	22	=	=	SYM
ejpam-4828	400	23	0	0	X
ejpam-4828	400	24	.	.	PUNCT
ejpam-4828	401	1	by	by	ADP
ejpam-4828	401	2	proposition	proposition	NOUN
ejpam-4828	401	3	3(iii	3(iii	NUM
ejpam-4828	401	4	)	)	PUNCT
ejpam-4828	401	5	,	,	PUNCT
ejpam-4828	401	6	v2	v2	PROPN
ejpam-4828	401	7	is	be	AUX
ejpam-4828	401	8	a	a	DET
ejpam-4828	401	9	γcon	γcon	NOUN
ejpam-4828	401	10	-	-	PUNCT
ejpam-4828	401	11	set	set	NOUN
ejpam-4828	401	12	in	in	ADP
ejpam-4828	401	13	g	g	PROPN
ejpam-4828	401	14	and	and	CCONJ
ejpam-4828	401	15	γcvr(g	γcvr(g	NOUN
ejpam-4828	401	16	)	)	PUNCT
ejpam-4828	402	1	=	=	SYM
ejpam-4828	402	2	2|v2|	2|v2|	NUM
ejpam-4828	402	3	=	=	SYM
ejpam-4828	402	4	2γcon(g	2γcon(g	NUM
ejpam-4828	402	5	)	)	PUNCT
ejpam-4828	402	6	.	.	PUNCT
ejpam-4828	403	1	thus	thus	ADV
ejpam-4828	403	2	(	(	PUNCT
ejpam-4828	403	3	ii	ii	NOUN
ejpam-4828	403	4	)	)	PUNCT
ejpam-4828	403	5	implies	imply	VERB
ejpam-4828	403	6	(	(	PUNCT
ejpam-4828	403	7	i	i	NOUN
ejpam-4828	403	8	)	)	PUNCT
ejpam-4828	403	9	.	.	PUNCT
ejpam-4828	404	1	the	the	DET
ejpam-4828	404	2	equivalence	equivalence	NOUN
ejpam-4828	404	3	of	of	ADP
ejpam-4828	404	4	statements	statement	NOUN
ejpam-4828	404	5	(	(	PUNCT
ejpam-4828	404	6	ii	ii	NOUN
ejpam-4828	404	7	)	)	PUNCT
ejpam-4828	404	8	and	and	CCONJ
ejpam-4828	404	9	(	(	PUNCT
ejpam-4828	404	10	iii	iii	NOUN
ejpam-4828	404	11	)	)	PUNCT
ejpam-4828	404	12	follows	follow	VERB
ejpam-4828	404	13	from	from	ADP
ejpam-4828	404	14	proposition	proposition	NOUN
ejpam-4828	404	15	3(iii	3(iii	NUM
ejpam-4828	404	16	)	)	PUNCT
ejpam-4828	404	17	.	.	PUNCT
ejpam-4828	405	1	corollary	corollary	ADJ
ejpam-4828	405	2	8	8	NUM
ejpam-4828	405	3	.	.	PUNCT
ejpam-4828	406	1	let	let	VERB
ejpam-4828	406	2	g	g	PRON
ejpam-4828	406	3	be	be	AUX
ejpam-4828	406	4	a	a	DET
ejpam-4828	406	5	nontrivial	nontrivial	ADJ
ejpam-4828	406	6	connected	connect	VERB
ejpam-4828	406	7	graph	graph	NOUN
ejpam-4828	406	8	.	.	PUNCT
ejpam-4828	407	1	if	if	SCONJ
ejpam-4828	407	2	γ(g	γ(g	PROPN
ejpam-4828	407	3	)	)	PUNCT
ejpam-4828	407	4	=	=	SYM
ejpam-4828	407	5	1	1	NUM
ejpam-4828	407	6	,	,	PUNCT
ejpam-4828	407	7	then	then	ADV
ejpam-4828	407	8	g	g	PROPN
ejpam-4828	407	9	is	be	AUX
ejpam-4828	407	10	a	a	DET
ejpam-4828	407	11	convex	convex	ADJ
ejpam-4828	407	12	roman	roman	ADJ
ejpam-4828	407	13	graph	graph	NOUN
ejpam-4828	407	14	.	.	PUNCT
ejpam-4828	408	1	theorem	theorem	ADJ
ejpam-4828	408	2	7	7	NUM
ejpam-4828	408	3	.	.	PUNCT
ejpam-4828	409	1	let	let	VERB
ejpam-4828	409	2	g	g	NOUN
ejpam-4828	410	1	and	and	CCONJ
ejpam-4828	410	2	h	h	NOUN
ejpam-4828	410	3	be	be	VERB
ejpam-4828	410	4	any	any	DET
ejpam-4828	410	5	connected	connected	ADJ
ejpam-4828	410	6	graphs	graph	NOUN
ejpam-4828	410	7	.	.	PUNCT
ejpam-4828	411	1	then	then	ADV
ejpam-4828	411	2	γcvr(g+h	γcvr(g+h	VERB
ejpam-4828	411	3	)	)	PUNCT
ejpam-4828	411	4	=	=	PRON
ejpam-4828	411	5	{	{	PUNCT
ejpam-4828	411	6	2	2	NUM
ejpam-4828	411	7	if	if	SCONJ
ejpam-4828	411	8	γ(g	γ(g	NOUN
ejpam-4828	411	9	)	)	PUNCT
ejpam-4828	411	10	=	=	SYM
ejpam-4828	411	11	1	1	NUM
ejpam-4828	411	12	or	or	CCONJ
ejpam-4828	411	13	γ(h	γ(h	NOUN
ejpam-4828	411	14	)	)	PUNCT
ejpam-4828	411	15	=	=	SYM
ejpam-4828	412	1	1	1	NUM
ejpam-4828	412	2	4	4	NUM
ejpam-4828	412	3	otherwise	otherwise	ADV
ejpam-4828	412	4	.	.	PUNCT
ejpam-4828	413	1	proof	proof	NOUN
ejpam-4828	413	2	.	.	PUNCT
ejpam-4828	414	1	since	since	SCONJ
ejpam-4828	414	2	g+h	g+h	PROPN
ejpam-4828	414	3	̸=	̸=	PROPN
ejpam-4828	414	4	k1	k1	PROPN
ejpam-4828	414	5	,	,	PUNCT
ejpam-4828	414	6	γcvr(g+h	γcvr(g+h	NOUN
ejpam-4828	414	7	)	)	PUNCT
ejpam-4828	414	8	≥	≥	NOUN
ejpam-4828	414	9	2	2	NUM
ejpam-4828	414	10	,	,	PUNCT
ejpam-4828	414	11	by	by	ADP
ejpam-4828	414	12	theorem	theorem	NOUN
ejpam-4828	414	13	3(i	3(i	NUM
ejpam-4828	414	14	)	)	PUNCT
ejpam-4828	414	15	.	.	PUNCT
ejpam-4828	415	1	suppose	suppose	VERB
ejpam-4828	415	2	γ(g	γ(g	NOUN
ejpam-4828	415	3	)	)	PUNCT
ejpam-4828	415	4	=	=	SYM
ejpam-4828	415	5	1	1	NUM
ejpam-4828	415	6	or	or	CCONJ
ejpam-4828	415	7	γ(h	γ(h	NOUN
ejpam-4828	415	8	)	)	PUNCT
ejpam-4828	415	9	=	=	SYM
ejpam-4828	416	1	1	1	X
ejpam-4828	416	2	.	.	PUNCT
ejpam-4828	416	3	then	then	ADV
ejpam-4828	416	4	γ(g+h	γ(g+h	NUM
ejpam-4828	416	5	)	)	PUNCT
ejpam-4828	416	6	=	=	SYM
ejpam-4828	417	1	1	1	X
ejpam-4828	417	2	.	.	PUNCT
ejpam-4828	417	3	by	by	ADP
ejpam-4828	417	4	corollary	corollary	ADJ
ejpam-4828	417	5	4	4	NUM
ejpam-4828	417	6	,	,	PUNCT
ejpam-4828	417	7	γcvr(g+h	γcvr(g+h	NOUN
ejpam-4828	417	8	)	)	PUNCT
ejpam-4828	417	9	=	=	SYM
ejpam-4828	418	1	2	2	X
ejpam-4828	418	2	.	.	PUNCT
ejpam-4828	418	3	suppose	suppose	VERB
ejpam-4828	418	4	γ(g	γ(g	NOUN
ejpam-4828	418	5	)	)	PUNCT
ejpam-4828	418	6	̸=	̸=	PROPN
ejpam-4828	418	7	1	1	NUM
ejpam-4828	418	8	and	and	CCONJ
ejpam-4828	418	9	γ(h	γ(h	NOUN
ejpam-4828	418	10	)	)	PUNCT
ejpam-4828	418	11	̸=	̸=	PROPN
ejpam-4828	418	12	1	1	NUM
ejpam-4828	418	13	.	.	PUNCT
ejpam-4828	419	1	by	by	ADP
ejpam-4828	419	2	proposition	proposition	NOUN
ejpam-4828	419	3	2	2	NUM
ejpam-4828	419	4	,	,	PUNCT
ejpam-4828	419	5	γcvr(g	γcvr(g	PROPN
ejpam-4828	419	6	+	+	ADJ
ejpam-4828	419	7	h	h	NOUN
ejpam-4828	419	8	)	)	PUNCT
ejpam-4828	419	9	≥	≥	NOUN
ejpam-4828	419	10	4	4	NUM
ejpam-4828	419	11	.	.	PUNCT
ejpam-4828	419	12	pick	pick	VERB
ejpam-4828	419	13	any	any	DET
ejpam-4828	419	14	x	x	SYM
ejpam-4828	419	15	∈	∈	PROPN
ejpam-4828	419	16	v	v	NOUN
ejpam-4828	419	17	(	(	PUNCT
ejpam-4828	419	18	g	g	NOUN
ejpam-4828	419	19	)	)	PUNCT
ejpam-4828	419	20	and	and	CCONJ
ejpam-4828	419	21	y	y	PROPN
ejpam-4828	419	22	∈	∈	PROPN
ejpam-4828	419	23	v	v	ADP
ejpam-4828	419	24	(	(	PUNCT
ejpam-4828	419	25	h	h	NOUN
ejpam-4828	419	26	)	)	PUNCT
ejpam-4828	419	27	.	.	PUNCT
ejpam-4828	420	1	let	let	VERB
ejpam-4828	420	2	v2	v2	VERB
ejpam-4828	420	3	=	=	SYM
ejpam-4828	420	4	{	{	PUNCT
ejpam-4828	420	5	x	x	PROPN
ejpam-4828	420	6	,	,	PUNCT
ejpam-4828	420	7	y	y	NOUN
ejpam-4828	420	8	}	}	PUNCT
ejpam-4828	420	9	,	,	PUNCT
ejpam-4828	420	10	v0	v0	NOUN
ejpam-4828	420	11	=	=	SYM
ejpam-4828	420	12	v	v	PROPN
ejpam-4828	420	13	(	(	PUNCT
ejpam-4828	420	14	g	g	NOUN
ejpam-4828	420	15	)	)	PUNCT
ejpam-4828	420	16	\	\	PROPN
ejpam-4828	420	17	v2	v2	PROPN
ejpam-4828	420	18	,	,	PUNCT
ejpam-4828	420	19	and	and	CCONJ
ejpam-4828	420	20	v1	v1	NOUN
ejpam-4828	420	21	=	=	SYM
ejpam-4828	420	22	∅.	∅.	NOUN
ejpam-4828	420	23	then	then	ADV
ejpam-4828	420	24	f	f	PROPN
ejpam-4828	420	25	=	=	SYM
ejpam-4828	420	26	(	(	PUNCT
ejpam-4828	420	27	v0	v0	PROPN
ejpam-4828	420	28	,	,	PUNCT
ejpam-4828	420	29	v1	v1	NOUN
ejpam-4828	420	30	,	,	PUNCT
ejpam-4828	420	31	v2	v2	PROPN
ejpam-4828	420	32	)	)	PUNCT
ejpam-4828	420	33	is	be	AUX
ejpam-4828	420	34	a	a	DET
ejpam-4828	420	35	cvrdf	cvrdf	NOUN
ejpam-4828	420	36	on	on	ADP
ejpam-4828	420	37	g	g	PROPN
ejpam-4828	420	38	+	+	NOUN
ejpam-4828	420	39	h	h	NOUN
ejpam-4828	420	40	and	and	CCONJ
ejpam-4828	420	41	ωcvr	ωcvr	NOUN
ejpam-4828	420	42	g+h(f	g+h(f	NOUN
ejpam-4828	420	43	)	)	PUNCT
ejpam-4828	420	44	=	=	SYM
ejpam-4828	421	1	4	4	X
ejpam-4828	421	2	.	.	X
ejpam-4828	421	3	therefore	therefore	ADV
ejpam-4828	421	4	,	,	PUNCT
ejpam-4828	421	5	γcvr(g+h	γcvr(g+h	NOUN
ejpam-4828	421	6	)	)	PUNCT
ejpam-4828	421	7	=	=	SYM
ejpam-4828	422	1	4	4	X
ejpam-4828	422	2	.	.	PUNCT
ejpam-4828	423	1	this	this	PRON
ejpam-4828	423	2	proves	prove	VERB
ejpam-4828	423	3	the	the	DET
ejpam-4828	423	4	assertion	assertion	NOUN
ejpam-4828	423	5	.	.	PUNCT
ejpam-4828	424	1	4	4	X
ejpam-4828	424	2	.	.	X
ejpam-4828	424	3	conclusion	conclusion	VERB
ejpam-4828	424	4	the	the	DET
ejpam-4828	424	5	concept	concept	NOUN
ejpam-4828	424	6	of	of	ADP
ejpam-4828	424	7	convex	convex	ADJ
ejpam-4828	424	8	roman	roman	ADJ
ejpam-4828	424	9	domination	domination	NOUN
ejpam-4828	424	10	was	be	AUX
ejpam-4828	424	11	introduced	introduce	VERB
ejpam-4828	424	12	and	and	CCONJ
ejpam-4828	424	13	initially	initially	ADV
ejpam-4828	424	14	investigated	investigate	VERB
ejpam-4828	424	15	in	in	ADP
ejpam-4828	424	16	this	this	DET
ejpam-4828	424	17	study	study	NOUN
ejpam-4828	424	18	.	.	PUNCT
ejpam-4828	425	1	the	the	DET
ejpam-4828	425	2	convex	convex	ADJ
ejpam-4828	425	3	roman	roman	ADJ
ejpam-4828	425	4	domination	domination	NOUN
ejpam-4828	425	5	numbers	number	NOUN
ejpam-4828	425	6	of	of	ADP
ejpam-4828	425	7	some	some	DET
ejpam-4828	425	8	graphs	graph	NOUN
ejpam-4828	425	9	and	and	CCONJ
ejpam-4828	425	10	the	the	DET
ejpam-4828	425	11	join	join	NOUN
ejpam-4828	425	12	of	of	ADP
ejpam-4828	425	13	two	two	NUM
ejpam-4828	425	14	graphs	graph	NOUN
ejpam-4828	425	15	were	be	AUX
ejpam-4828	425	16	determined	determine	VERB
ejpam-4828	425	17	.	.	PUNCT
ejpam-4828	426	1	it	it	PRON
ejpam-4828	426	2	was	be	AUX
ejpam-4828	426	3	shown	show	VERB
ejpam-4828	426	4	that	that	SCONJ
ejpam-4828	426	5	every	every	DET
ejpam-4828	426	6	pair	pair	NOUN
ejpam-4828	426	7	of	of	ADP
ejpam-4828	426	8	positive	positive	ADJ
ejpam-4828	426	9	integers	integer	NOUN
ejpam-4828	426	10	(	(	PUNCT
ejpam-4828	426	11	with	with	ADP
ejpam-4828	426	12	some	some	DET
ejpam-4828	426	13	restrictions	restriction	NOUN
ejpam-4828	426	14	)	)	PUNCT
ejpam-4828	426	15	are	be	AUX
ejpam-4828	426	16	realizable	realizable	ADJ
ejpam-4828	426	17	as	as	ADP
ejpam-4828	426	18	the	the	DET
ejpam-4828	426	19	connected	connected	ADJ
ejpam-4828	426	20	roman	roman	ADJ
ejpam-4828	426	21	domination	domination	NOUN
ejpam-4828	426	22	number	number	NOUN
ejpam-4828	426	23	and	and	CCONJ
ejpam-4828	426	24	convex	convex	VERB
ejpam-4828	426	25	roman	roman	ADJ
ejpam-4828	426	26	domination	domination	NOUN
ejpam-4828	426	27	number	number	NOUN
ejpam-4828	426	28	of	of	ADP
ejpam-4828	426	29	some	some	DET
ejpam-4828	426	30	connected	connect	VERB
ejpam-4828	426	31	graph	graph	NOUN
ejpam-4828	426	32	.	.	PUNCT
ejpam-4828	427	1	a	a	DET
ejpam-4828	427	2	realization	realization	NOUN
ejpam-4828	427	3	result	result	NOUN
ejpam-4828	427	4	involving	involve	VERB
ejpam-4828	427	5	convex	convex	ADJ
ejpam-4828	427	6	domination	domination	NOUN
ejpam-4828	427	7	number	number	NOUN
ejpam-4828	427	8	and	and	CCONJ
ejpam-4828	427	9	convex	convex	VERB
ejpam-4828	427	10	roman	roman	ADJ
ejpam-4828	427	11	domination	domination	NOUN
ejpam-4828	427	12	number	number	NOUN
ejpam-4828	427	13	was	be	AUX
ejpam-4828	427	14	also	also	ADV
ejpam-4828	427	15	obtained	obtain	VERB
ejpam-4828	427	16	.	.	PUNCT
ejpam-4828	428	1	the	the	DET
ejpam-4828	428	2	newly	newly	ADV
ejpam-4828	428	3	defined	define	VERB
ejpam-4828	428	4	variant	variant	NOUN
ejpam-4828	428	5	of	of	ADP
ejpam-4828	428	6	roman	roman	ADJ
ejpam-4828	428	7	domination	domination	NOUN
ejpam-4828	428	8	in	in	ADP
ejpam-4828	428	9	this	this	DET
ejpam-4828	428	10	study	study	NOUN
ejpam-4828	428	11	can	can	AUX
ejpam-4828	428	12	be	be	AUX
ejpam-4828	428	13	studied	study	VERB
ejpam-4828	428	14	for	for	ADP
ejpam-4828	428	15	other	other	ADJ
ejpam-4828	428	16	graphs	graph	NOUN
ejpam-4828	428	17	including	include	VERB
ejpam-4828	428	18	those	those	DET
ejpam-4828	428	19	ones	one	NOUN
ejpam-4828	428	20	under	under	ADP
ejpam-4828	428	21	some	some	DET
ejpam-4828	428	22	binary	binary	ADJ
ejpam-4828	428	23	operations	operation	NOUN
ejpam-4828	428	24	.	.	PUNCT
ejpam-4828	429	1	references	reference	NOUN
ejpam-4828	429	2	1715	1715	NUM
ejpam-4828	429	3	acknowledgements	acknowledgement	NOUN
ejpam-4828	429	4	the	the	DET
ejpam-4828	429	5	authors	author	NOUN
ejpam-4828	429	6	would	would	AUX
ejpam-4828	429	7	like	like	VERB
ejpam-4828	429	8	to	to	PART
ejpam-4828	429	9	thank	thank	VERB
ejpam-4828	429	10	the	the	DET
ejpam-4828	429	11	referees	referee	NOUN
ejpam-4828	429	12	for	for	ADP
ejpam-4828	429	13	the	the	DET
ejpam-4828	429	14	invaluable	invaluable	ADJ
ejpam-4828	429	15	assistance	assistance	NOUN
ejpam-4828	429	16	they	they	PRON
ejpam-4828	429	17	gave	give	VERB
ejpam-4828	429	18	us	we	PRON
ejpam-4828	429	19	through	through	ADP
ejpam-4828	429	20	their	their	PRON
ejpam-4828	429	21	comments	comment	NOUN
ejpam-4828	429	22	and	and	CCONJ
ejpam-4828	429	23	suggestions	suggestion	NOUN
ejpam-4828	429	24	which	which	PRON
ejpam-4828	429	25	led	lead	VERB
ejpam-4828	429	26	to	to	ADP
ejpam-4828	429	27	the	the	DET
ejpam-4828	429	28	improvement	improvement	NOUN
ejpam-4828	429	29	of	of	ADP
ejpam-4828	429	30	the	the	DET
ejpam-4828	429	31	paper	paper	NOUN
ejpam-4828	429	32	.	.	PUNCT
ejpam-4828	430	1	the	the	DET
ejpam-4828	430	2	authors	author	NOUN
ejpam-4828	430	3	are	be	AUX
ejpam-4828	430	4	also	also	ADV
ejpam-4828	430	5	grateful	grateful	ADJ
ejpam-4828	430	6	to	to	ADP
ejpam-4828	430	7	the	the	DET
ejpam-4828	430	8	department	department	NOUN
ejpam-4828	430	9	of	of	ADP
ejpam-4828	430	10	science	science	NOUN
ejpam-4828	430	11	and	and	CCONJ
ejpam-4828	430	12	technology	technology	NOUN
ejpam-4828	430	13	accelerated	accelerate	VERB
ejpam-4828	430	14	science	science	NOUN
ejpam-4828	430	15	and	and	CCONJ
ejpam-4828	430	16	technology	technology	NOUN
ejpam-4828	430	17	human	human	ADJ
ejpam-4828	430	18	resource	resource	NOUN
ejpam-4828	430	19	development	development	NOUN
ejpam-4828	430	20	program	program	NOUN
ejpam-4828	430	21	(	(	PUNCT
ejpam-4828	430	22	dost	dost	NOUN
ejpam-4828	430	23	-	-	PUNCT
ejpam-4828	430	24	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-4828	430	25	and	and	CCONJ
ejpam-4828	430	26	msu	msu	PROPN
ejpam-4828	430	27	-	-	PUNCT
ejpam-4828	430	28	iligan	iligan	PROPN
ejpam-4828	430	29	institute	institute	PROPN
ejpam-4828	430	30	of	of	ADP
ejpam-4828	430	31	technology	technology	NOUN
ejpam-4828	430	32	for	for	ADP
ejpam-4828	430	33	funding	fund	VERB
ejpam-4828	430	34	this	this	DET
ejpam-4828	430	35	research	research	NOUN
ejpam-4828	430	36	.	.	PUNCT
ejpam-4828	431	1	references	reference	NOUN
ejpam-4828	431	2	[	[	X
ejpam-4828	431	3	1	1	NUM
ejpam-4828	431	4	]	]	PUNCT
ejpam-4828	431	5	m.	m.	NOUN
ejpam-4828	431	6	adabi	adabi	PROPN
ejpam-4828	431	7	,	,	PUNCT
ejpam-4828	431	8	e.	e.	PROPN
ejpam-4828	431	9	ebrahimi	ebrahimi	PROPN
ejpam-4828	431	10	targhi	targhi	PROPN
ejpam-4828	431	11	,	,	PUNCT
ejpam-4828	431	12	n.	n.	PROPN
ejpam-4828	431	13	jafari	jafari	PROPN
ejpam-4828	431	14	rad	rad	PROPN
ejpam-4828	431	15	,	,	PUNCT
ejpam-4828	431	16	and	and	CCONJ
ejpam-4828	431	17	m.	m.	NOUN
ejpam-4828	431	18	saied	saie	VERB
ejpam-4828	431	19	moradi	moradi	NOUN
ejpam-4828	431	20	.	.	PUNCT
ejpam-4828	432	1	properties	property	NOUN
ejpam-4828	432	2	of	of	ADP
ejpam-4828	432	3	independent	independent	ADJ
ejpam-4828	432	4	roman	roman	ADJ
ejpam-4828	432	5	domination	domination	NOUN
ejpam-4828	432	6	in	in	ADP
ejpam-4828	432	7	graphs	graph	NOUN
ejpam-4828	432	8	.	.	PUNCT
ejpam-4828	433	1	australasian	australasian	ADJ
ejpam-4828	433	2	journal	journal	NOUN
ejpam-4828	433	3	of	of	ADP
ejpam-4828	433	4	combinatorics	combinatoric	NOUN
ejpam-4828	433	5	,	,	PUNCT
ejpam-4828	433	6	52:11–18	52:11–18	NUM
ejpam-4828	433	7	,	,	PUNCT
ejpam-4828	433	8	2012	2012	NUM
ejpam-4828	433	9	.	.	PUNCT
ejpam-4828	434	1	[	[	X
ejpam-4828	434	2	2	2	NUM
ejpam-4828	434	3	]	]	X
ejpam-4828	434	4	h.a	h.a	PROPN
ejpam-4828	434	5	.	.	PROPN
ejpam-4828	434	6	ahangar	ahangar	PROPN
ejpam-4828	434	7	,	,	PUNCT
ejpam-4828	434	8	m.a	m.a	PROPN
ejpam-4828	434	9	.	.	PROPN
ejpam-4828	434	10	henning	henning	PROPN
ejpam-4828	434	11	,	,	PUNCT
ejpam-4828	434	12	v.	v.	ADP
ejpam-4828	434	13	samodivkin	samodivkin	NOUN
ejpam-4828	434	14	,	,	PUNCT
ejpam-4828	434	15	and	and	CCONJ
ejpam-4828	434	16	i.g	i.g	PROPN
ejpam-4828	434	17	.	.	PROPN
ejpam-4828	434	18	yero	yero	PROPN
ejpam-4828	434	19	.	.	PUNCT
ejpam-4828	434	20	total	total	ADJ
ejpam-4828	434	21	roman	roman	ADJ
ejpam-4828	434	22	domination	domination	NOUN
ejpam-4828	434	23	in	in	ADP
ejpam-4828	434	24	graphs	graph	NOUN
ejpam-4828	434	25	.	.	PUNCT
ejpam-4828	435	1	applicable	applicable	ADJ
ejpam-4828	435	2	analysis	analysis	NOUN
ejpam-4828	435	3	and	and	CCONJ
ejpam-4828	435	4	discrete	discrete	ADJ
ejpam-4828	435	5	mathematics	mathematic	NOUN
ejpam-4828	435	6	,	,	PUNCT
ejpam-4828	435	7	10(2):501–517	10(2):501–517	PROPN
ejpam-4828	435	8	,	,	PUNCT
ejpam-4828	435	9	2016	2016	NUM
ejpam-4828	435	10	.	.	PUNCT
ejpam-4828	436	1	[	[	X
ejpam-4828	436	2	3	3	X
ejpam-4828	436	3	]	]	X
ejpam-4828	436	4	m.p	m.p	PROPN
ejpam-4828	436	5	.	.	PROPN
ejpam-4828	436	6	alvarez	alvarez	PROPN
ejpam-4828	436	7	-	-	PUNCT
ejpam-4828	436	8	ruiz	ruiz	PROPN
ejpam-4828	436	9	,	,	PUNCT
ejpam-4828	436	10	t.	t.	PROPN
ejpam-4828	436	11	mediavilla	mediavilla	PROPN
ejpam-4828	436	12	-	-	PUNCT
ejpam-4828	436	13	gradolph	gradolph	NOUN
ejpam-4828	436	14	,	,	PUNCT
ejpam-4828	436	15	s.m	s.m	PROPN
ejpam-4828	436	16	.	.	PROPN
ejpam-4828	436	17	sheikholeslami	sheikholeslami	PROPN
ejpam-4828	436	18	,	,	PUNCT
ejpam-4828	436	19	j.c	j.c	PROPN
ejpam-4828	436	20	.	.	PROPN
ejpam-4828	436	21	valenzuelatripodoro	valenzuelatripodoro	PROPN
ejpam-4828	436	22	,	,	PUNCT
ejpam-4828	436	23	and	and	CCONJ
ejpam-4828	436	24	i.g	i.g	PROPN
ejpam-4828	436	25	.	.	PROPN
ejpam-4828	436	26	yero	yero	PROPN
ejpam-4828	436	27	.	.	PUNCT
ejpam-4828	437	1	on	on	ADP
ejpam-4828	437	2	the	the	DET
ejpam-4828	437	3	strong	strong	ADJ
ejpam-4828	437	4	roman	roman	ADJ
ejpam-4828	437	5	domination	domination	NOUN
ejpam-4828	437	6	number	number	NOUN
ejpam-4828	437	7	of	of	ADP
ejpam-4828	437	8	graphs	graph	NOUN
ejpam-4828	437	9	.	.	PUNCT
ejpam-4828	438	1	discrete	discrete	ADJ
ejpam-4828	438	2	applied	apply	VERB
ejpam-4828	438	3	mathematics	mathematic	NOUN
ejpam-4828	438	4	,	,	PUNCT
ejpam-4828	438	5	231:44–59	231:44–59	NUM
ejpam-4828	438	6	,	,	PUNCT
ejpam-4828	438	7	2017	2017	NUM
ejpam-4828	438	8	.	.	PUNCT
ejpam-4828	439	1	[	[	X
ejpam-4828	439	2	4	4	X
ejpam-4828	439	3	]	]	PUNCT
ejpam-4828	439	4	s.	s.	PROPN
ejpam-4828	439	5	banerjee	banerjee	PROPN
ejpam-4828	439	6	,	,	PUNCT
ejpam-4828	439	7	j.m	j.m	PROPN
ejpam-4828	439	8	.	.	PROPN
ejpam-4828	439	9	keil	keil	PROPN
ejpam-4828	439	10	,	,	PUNCT
ejpam-4828	439	11	and	and	CCONJ
ejpam-4828	439	12	d.	d.	PROPN
ejpam-4828	439	13	pradhan	pradhan	PROPN
ejpam-4828	439	14	.	.	PUNCT
ejpam-4828	440	1	perfect	perfect	ADJ
ejpam-4828	440	2	roman	roman	ADJ
ejpam-4828	440	3	domination	domination	NOUN
ejpam-4828	440	4	in	in	ADP
ejpam-4828	440	5	graphs	graph	NOUN
ejpam-4828	440	6	.	.	PUNCT
ejpam-4828	441	1	theoretical	theoretical	ADJ
ejpam-4828	441	2	computer	computer	NOUN
ejpam-4828	441	3	science	science	NOUN
ejpam-4828	441	4	,	,	PUNCT
ejpam-4828	441	5	796:1–21	796:1–21	NUM
ejpam-4828	441	6	,	,	PUNCT
ejpam-4828	441	7	2019	2019	NUM
ejpam-4828	441	8	.	.	PUNCT
ejpam-4828	442	1	[	[	X
ejpam-4828	442	2	5	5	NUM
ejpam-4828	442	3	]	]	X
ejpam-4828	442	4	r.a	r.a	PROPN
ejpam-4828	442	5	.	.	PROPN
ejpam-4828	442	6	beeler	beeler	PROPN
ejpam-4828	442	7	,	,	PUNCT
ejpam-4828	442	8	t.w	t.w	PROPN
ejpam-4828	442	9	.	.	PROPN
ejpam-4828	442	10	haynes	haynes	PROPN
ejpam-4828	442	11	,	,	PUNCT
ejpam-4828	442	12	and	and	CCONJ
ejpam-4828	442	13	s.t	s.t	PROPN
ejpam-4828	442	14	.	.	PROPN
ejpam-4828	442	15	hedetnieme	hedetnieme	PROPN
ejpam-4828	442	16	.	.	PUNCT
ejpam-4828	443	1	double	double	ADJ
ejpam-4828	443	2	roman	roman	ADJ
ejpam-4828	443	3	domination	domination	NOUN
ejpam-4828	443	4	.	.	PUNCT
ejpam-4828	444	1	discrete	discrete	ADJ
ejpam-4828	444	2	applied	apply	VERB
ejpam-4828	444	3	mathematics	mathematic	NOUN
ejpam-4828	444	4	,	,	PUNCT
ejpam-4828	444	5	211:23–29	211:23–29	NUM
ejpam-4828	444	6	,	,	PUNCT
ejpam-4828	444	7	2016	2016	NUM
ejpam-4828	444	8	.	.	PUNCT
ejpam-4828	445	1	[	[	X
ejpam-4828	445	2	6	6	NUM
ejpam-4828	445	3	]	]	PUNCT
ejpam-4828	445	4	f.	f.	PROPN
ejpam-4828	445	5	buckey	buckey	PROPN
ejpam-4828	445	6	and	and	CCONJ
ejpam-4828	445	7	f.	f.	PROPN
ejpam-4828	445	8	harary	harary	PROPN
ejpam-4828	445	9	.	.	PUNCT
ejpam-4828	446	1	distance	distance	NOUN
ejpam-4828	446	2	in	in	ADP
ejpam-4828	446	3	graphs	graph	NOUN
ejpam-4828	446	4	.	.	PUNCT
ejpam-4828	447	1	addison	addison	PROPN
ejpam-4828	447	2	-	-	PUNCT
ejpam-4828	447	3	wesley	wesley	PROPN
ejpam-4828	447	4	,	,	PUNCT
ejpam-4828	447	5	redwood	redwood	NOUN
ejpam-4828	447	6	city	city	NOUN
ejpam-4828	447	7	,	,	PUNCT
ejpam-4828	447	8	california	california	PROPN
ejpam-4828	447	9	,	,	PUNCT
ejpam-4828	447	10	1990	1990	NUM
ejpam-4828	447	11	.	.	PUNCT
ejpam-4828	448	1	[	[	X
ejpam-4828	448	2	7	7	X
ejpam-4828	448	3	]	]	X
ejpam-4828	448	4	s.r	s.r	PROPN
ejpam-4828	448	5	.	.	PROPN
ejpam-4828	448	6	canoy	canoy	PROPN
ejpam-4828	448	7	.	.	PUNCT
ejpam-4828	449	1	a	a	DET
ejpam-4828	449	2	short	short	ADJ
ejpam-4828	449	3	note	note	NOUN
ejpam-4828	449	4	on	on	ADP
ejpam-4828	449	5	convexity	convexity	NOUN
ejpam-4828	449	6	and	and	CCONJ
ejpam-4828	449	7	convex	convex	NOUN
ejpam-4828	449	8	domination	domination	NOUN
ejpam-4828	449	9	in	in	ADP
ejpam-4828	449	10	g[km	g[km	PROPN
ejpam-4828	449	11	]	]	PUNCT
ejpam-4828	449	12	.	.	PUNCT
ejpam-4828	450	1	applied	apply	VERB
ejpam-4828	450	2	mathematical	mathematical	ADJ
ejpam-4828	450	3	sciences	science	NOUN
ejpam-4828	450	4	,	,	PUNCT
ejpam-4828	450	5	8(115):5737–5741	8(115):5737–5741	NUM
ejpam-4828	450	6	,	,	PUNCT
ejpam-4828	450	7	2014	2014	NUM
ejpam-4828	450	8	.	.	PUNCT
ejpam-4828	451	1	[	[	X
ejpam-4828	451	2	8	8	NUM
ejpam-4828	451	3	]	]	X
ejpam-4828	451	4	s.r	s.r	PROPN
ejpam-4828	451	5	.	.	PROPN
ejpam-4828	451	6	canoy	canoy	PROPN
ejpam-4828	451	7	and	and	CCONJ
ejpam-4828	451	8	i.j.l	i.j.l	NOUN
ejpam-4828	451	9	.	.	PROPN
ejpam-4828	451	10	garces	garces	PROPN
ejpam-4828	451	11	.	.	PUNCT
ejpam-4828	452	1	convex	convex	PROPN
ejpam-4828	452	2	sets	set	NOUN
ejpam-4828	452	3	under	under	ADP
ejpam-4828	452	4	some	some	DET
ejpam-4828	452	5	graph	graph	NOUN
ejpam-4828	452	6	operations	operation	NOUN
ejpam-4828	452	7	.	.	PUNCT
ejpam-4828	453	1	graphs	graph	NOUN
ejpam-4828	453	2	and	and	CCONJ
ejpam-4828	453	3	combinatorics	combinatoric	NOUN
ejpam-4828	453	4	,	,	PUNCT
ejpam-4828	453	5	18(4):787–793	18(4):787–793	NUM
ejpam-4828	453	6	,	,	PUNCT
ejpam-4828	453	7	2002	2002	NUM
ejpam-4828	453	8	.	.	PUNCT
ejpam-4828	454	1	[	[	X
ejpam-4828	454	2	9	9	NUM
ejpam-4828	454	3	]	]	X
ejpam-4828	454	4	g.	g.	PROPN
ejpam-4828	454	5	chartrand	chartrand	PROPN
ejpam-4828	454	6	,	,	PUNCT
ejpam-4828	454	7	j.	j.	PROPN
ejpam-4828	454	8	fink	fink	PROPN
ejpam-4828	454	9	,	,	PUNCT
ejpam-4828	454	10	and	and	CCONJ
ejpam-4828	454	11	p.	p.	PROPN
ejpam-4828	454	12	zhang	zhang	PROPN
ejpam-4828	454	13	.	.	PUNCT
ejpam-4828	455	1	convexity	convexity	NOUN
ejpam-4828	455	2	in	in	ADP
ejpam-4828	455	3	graphs	graph	NOUN
ejpam-4828	455	4	.	.	PUNCT
ejpam-4828	456	1	discrete	discrete	ADJ
ejpam-4828	456	2	applied	apply	VERB
ejpam-4828	456	3	mathematics	mathematic	NOUN
ejpam-4828	456	4	,	,	PUNCT
ejpam-4828	456	5	(	(	PUNCT
ejpam-4828	456	6	116):115–126	116):115–126	NOUN
ejpam-4828	456	7	,	,	PUNCT
ejpam-4828	456	8	2002	2002	NUM
ejpam-4828	456	9	.	.	PUNCT
ejpam-4828	457	1	[	[	X
ejpam-4828	457	2	10	10	NUM
ejpam-4828	457	3	]	]	X
ejpam-4828	457	4	m.	m.	NOUN
ejpam-4828	457	5	chellali	chellali	PROPN
ejpam-4828	457	6	,	,	PUNCT
ejpam-4828	457	7	t.w	t.w	PROPN
ejpam-4828	457	8	.	.	PROPN
ejpam-4828	457	9	haynes	haynes	PROPN
ejpam-4828	457	10	,	,	PUNCT
ejpam-4828	457	11	and	and	CCONJ
ejpam-4828	457	12	s.t	s.t	PROPN
ejpam-4828	457	13	.	.	PROPN
ejpam-4828	457	14	hedetnieme	hedetnieme	PROPN
ejpam-4828	457	15	.	.	PUNCT
ejpam-4828	458	1	roman	roman	NOUN
ejpam-4828	458	2	{	{	PUNCT
ejpam-4828	458	3	2	2	NUM
ejpam-4828	458	4	}	}	PUNCT
ejpam-4828	458	5	domination	domination	NOUN
ejpam-4828	458	6	.	.	PUNCT
ejpam-4828	459	1	discrete	discrete	ADJ
ejpam-4828	459	2	applied	apply	VERB
ejpam-4828	459	3	math	math	NOUN
ejpam-4828	459	4	,	,	PUNCT
ejpam-4828	459	5	204:22–28	204:22–28	NUM
ejpam-4828	459	6	,	,	PUNCT
ejpam-4828	459	7	2016	2016	NUM
ejpam-4828	459	8	.	.	PUNCT
ejpam-4828	460	1	[	[	X
ejpam-4828	460	2	11	11	NUM
ejpam-4828	460	3	]	]	X
ejpam-4828	460	4	e.j	e.j	PROPN
ejpam-4828	460	5	.	.	PROPN
ejpam-4828	460	6	cockayne	cockayne	PROPN
ejpam-4828	460	7	,	,	PUNCT
ejpam-4828	460	8	p.a	p.a	PROPN
ejpam-4828	460	9	.	.	PROPN
ejpam-4828	460	10	deryer	deryer	PROPN
ejpam-4828	460	11	,	,	PUNCT
ejpam-4828	460	12	s.m	s.m	PROPN
ejpam-4828	460	13	.	.	PROPN
ejpam-4828	460	14	hedetnieme	hedetnieme	PROPN
ejpam-4828	460	15	,	,	PUNCT
ejpam-4828	460	16	and	and	CCONJ
ejpam-4828	460	17	s.t	s.t	PROPN
ejpam-4828	460	18	.	.	PROPN
ejpam-4828	460	19	hedetnieme	hedetnieme	PROPN
ejpam-4828	460	20	.	.	PUNCT
ejpam-4828	461	1	roman	roman	ADJ
ejpam-4828	461	2	domination	domination	NOUN
ejpam-4828	461	3	in	in	ADP
ejpam-4828	461	4	graphs	graph	NOUN
ejpam-4828	461	5	.	.	PUNCT
ejpam-4828	462	1	discrete	discrete	ADJ
ejpam-4828	462	2	mathematics	mathematic	NOUN
ejpam-4828	462	3	,	,	PUNCT
ejpam-4828	462	4	278(13):11–22	278(13):11–22	NUM
ejpam-4828	462	5	,	,	PUNCT
ejpam-4828	462	6	2004	2004	NUM
ejpam-4828	462	7	.	.	PUNCT
ejpam-4828	463	1	[	[	X
ejpam-4828	463	2	12	12	NUM
ejpam-4828	463	3	]	]	X
ejpam-4828	463	4	e.l	e.l	PROPN
ejpam-4828	463	5	.	.	PROPN
ejpam-4828	463	6	enriquez	enriquez	PROPN
ejpam-4828	463	7	and	and	CCONJ
ejpam-4828	463	8	s.r	s.r	PROPN
ejpam-4828	463	9	.	.	PROPN
ejpam-4828	463	10	canoy	canoy	PROPN
ejpam-4828	463	11	.	.	PUNCT
ejpam-4828	464	1	on	on	ADP
ejpam-4828	464	2	a	a	DET
ejpam-4828	464	3	variant	variant	NOUN
ejpam-4828	464	4	of	of	ADP
ejpam-4828	464	5	convex	convex	ADJ
ejpam-4828	464	6	domination	domination	NOUN
ejpam-4828	464	7	in	in	ADP
ejpam-4828	464	8	a	a	DET
ejpam-4828	464	9	graph	graph	NOUN
ejpam-4828	464	10	.	.	PUNCT
ejpam-4828	465	1	international	international	ADJ
ejpam-4828	465	2	journal	journal	PROPN
ejpam-4828	465	3	of	of	ADP
ejpam-4828	465	4	mathematical	mathematical	ADJ
ejpam-4828	465	5	analysis	analysis	NOUN
ejpam-4828	465	6	,	,	PUNCT
ejpam-4828	465	7	9(32):1585–1592	9(32):1585–1592	NUM
ejpam-4828	465	8	,	,	PUNCT
ejpam-4828	465	9	2015	2015	NUM
ejpam-4828	465	10	.	.	PUNCT
ejpam-4828	466	1	references	reference	NOUN
ejpam-4828	466	2	1716	1716	NUM
ejpam-4828	466	3	[	[	SYM
ejpam-4828	466	4	13	13	NUM
ejpam-4828	466	5	]	]	X
ejpam-4828	466	6	m.a	m.a	PROPN
ejpam-4828	466	7	.	.	PROPN
ejpam-4828	466	8	henning	henning	PROPN
ejpam-4828	466	9	,	,	PUNCT
ejpam-4828	466	10	w.f	w.f	PROPN
ejpam-4828	466	11	.	.	PROPN
ejpam-4828	466	12	klostermeyer	klostermeyer	PROPN
ejpam-4828	466	13	,	,	PUNCT
ejpam-4828	466	14	and	and	CCONJ
ejpam-4828	466	15	g.	g.	PROPN
ejpam-4828	466	16	macgillivray	macgillivray	PROPN
ejpam-4828	466	17	.	.	PUNCT
ejpam-4828	467	1	perfect	perfect	ADJ
ejpam-4828	467	2	roman	roman	ADJ
ejpam-4828	467	3	domination	domination	NOUN
ejpam-4828	467	4	in	in	ADP
ejpam-4828	467	5	trees	tree	NOUN
ejpam-4828	467	6	.	.	PUNCT
ejpam-4828	468	1	discrete	discrete	ADJ
ejpam-4828	468	2	applied	apply	VERB
ejpam-4828	468	3	mathematics	mathematic	NOUN
ejpam-4828	468	4	,	,	PUNCT
ejpam-4828	468	5	236:235–245	236:235–245	NUM
ejpam-4828	468	6	,	,	PUNCT
ejpam-4828	468	7	2018	2018	NUM
ejpam-4828	468	8	.	.	PUNCT
ejpam-4828	469	1	[	[	X
ejpam-4828	469	2	14	14	NUM
ejpam-4828	469	3	]	]	X
ejpam-4828	469	4	k.	k.	PROPN
ejpam-4828	469	5	kammerling	kammerling	PROPN
ejpam-4828	469	6	and	and	CCONJ
ejpam-4828	469	7	l.	l.	PROPN
ejpam-4828	469	8	volkman	volkman	PROPN
ejpam-4828	469	9	.	.	PUNCT
ejpam-4828	470	1	roman	roman	ADJ
ejpam-4828	470	2	k	k	NOUN
ejpam-4828	470	3	-	-	PUNCT
ejpam-4828	470	4	domination	domination	NOUN
ejpam-4828	470	5	in	in	ADP
ejpam-4828	470	6	graphs	graph	NOUN
ejpam-4828	470	7	.	.	PUNCT
ejpam-4828	471	1	journal	journal	NOUN
ejpam-4828	471	2	of	of	ADP
ejpam-4828	471	3	the	the	DET
ejpam-4828	471	4	korean	korean	PROPN
ejpam-4828	471	5	mathematical	mathematical	ADJ
ejpam-4828	471	6	society	society	NOUN
ejpam-4828	471	7	,	,	PUNCT
ejpam-4828	471	8	46(6):1309–1318	46(6):1309–1318	PROPN
ejpam-4828	471	9	,	,	PUNCT
ejpam-4828	471	10	2009	2009	NUM
ejpam-4828	471	11	.	.	PUNCT
ejpam-4828	472	1	[	[	X
ejpam-4828	472	2	15	15	NUM
ejpam-4828	472	3	]	]	X
ejpam-4828	472	4	m.a	m.a	PROPN
ejpam-4828	472	5	.	.	PROPN
ejpam-4828	472	6	labendia	labendia	PROPN
ejpam-4828	472	7	and	and	CCONJ
ejpam-4828	472	8	s.r	s.r	PROPN
ejpam-4828	472	9	.	.	PROPN
ejpam-4828	472	10	canoy	canoy	PROPN
ejpam-4828	472	11	.	.	PUNCT
ejpam-4828	473	1	convex	convex	PROPN
ejpam-4828	473	2	dominatioin	dominatioin	NOUN
ejpam-4828	473	3	in	in	ADP
ejpam-4828	473	4	the	the	DET
ejpam-4828	473	5	composition	composition	NOUN
ejpam-4828	473	6	and	and	CCONJ
ejpam-4828	473	7	cartesian	cartesian	ADJ
ejpam-4828	473	8	product	product	NOUN
ejpam-4828	473	9	of	of	ADP
ejpam-4828	473	10	graphs	graph	NOUN
ejpam-4828	473	11	.	.	PUNCT
ejpam-4828	474	1	czechoslovak	czechoslovak	ADJ
ejpam-4828	474	2	mathematical	mathematical	PROPN
ejpam-4828	474	3	journal	journal	PROPN
ejpam-4828	474	4	,	,	PUNCT
ejpam-4828	474	5	62:1003–1009	62:1003–1009	NUM
ejpam-4828	474	6	,	,	PUNCT
ejpam-4828	474	7	2012	2012	NUM
ejpam-4828	474	8	.	.	PUNCT
ejpam-4828	475	1	[	[	X
ejpam-4828	475	2	16	16	NUM
ejpam-4828	475	3	]	]	PUNCT
ejpam-4828	475	4	m.	m.	NOUN
ejpam-4828	475	5	lemanska	lemanska	PROPN
ejpam-4828	475	6	.	.	PUNCT
ejpam-4828	476	1	weakly	weakly	ADJ
ejpam-4828	476	2	convex	convex	NOUN
ejpam-4828	476	3	and	and	CCONJ
ejpam-4828	476	4	convex	convex	ADJ
ejpam-4828	476	5	domination	domination	NOUN
ejpam-4828	476	6	numbers	number	NOUN
ejpam-4828	476	7	.	.	PUNCT
ejpam-4828	477	1	opuscula	opuscula	PROPN
ejpam-4828	477	2	mathematica	mathematica	PROPN
ejpam-4828	477	3	,	,	PUNCT
ejpam-4828	477	4	24(2):181–188	24(2):181–188	PROPN
ejpam-4828	477	5	,	,	PUNCT
ejpam-4828	477	6	2004	2004	NUM
ejpam-4828	477	7	.	.	PUNCT
ejpam-4828	478	1	[	[	X
ejpam-4828	478	2	17	17	NUM
ejpam-4828	478	3	]	]	X
ejpam-4828	478	4	m.h	m.h	PROPN
ejpam-4828	478	5	.	.	PROPN
ejpam-4828	478	6	muddebiha	muddebiha	PROPN
ejpam-4828	478	7	and	and	CCONJ
ejpam-4828	478	8	sumangaladevi	sumangaladevi	ADJ
ejpam-4828	478	9	.	.	PUNCT
ejpam-4828	479	1	connected	connect	VERB
ejpam-4828	479	2	roman	roman	ADJ
ejpam-4828	479	3	domination	domination	NOUN
ejpam-4828	479	4	in	in	ADP
ejpam-4828	479	5	graphs	graph	NOUN
ejpam-4828	479	6	.	.	PUNCT
ejpam-4828	480	1	international	international	ADJ
ejpam-4828	480	2	journal	journal	PROPN
ejpam-4828	480	3	of	of	ADP
ejpam-4828	480	4	research	research	NOUN
ejpam-4828	480	5	and	and	CCONJ
ejpam-4828	480	6	engineering	engineering	NOUN
ejpam-4828	480	7	technology	technology	NOUN
ejpam-4828	480	8	,	,	PUNCT
ejpam-4828	480	9	2(10):333–340	2(10):333–340	NUM
ejpam-4828	480	10	,	,	PUNCT
ejpam-4828	480	11	2013	2013	NUM
ejpam-4828	480	12	.	.	PUNCT
ejpam-4828	481	1	[	[	X
ejpam-4828	481	2	18	18	NUM
ejpam-4828	481	3	]	]	PUNCT
ejpam-4828	481	4	p.r.l	p.r.l	NOUN
ejpam-4828	481	5	.	.	PUNCT
ejpam-4828	482	1	pushpam	pushpam	NOUN
ejpam-4828	482	2	and	and	CCONJ
ejpam-4828	482	3	t.n.m	t.n.m	NOUN
ejpam-4828	482	4	.	.	PUNCT
ejpam-4828	483	1	malini	malini	PROPN
ejpam-4828	483	2	mai	mai	PROPN
ejpam-4828	483	3	.	.	PROPN
ejpam-4828	483	4	edge	edge	PROPN
ejpam-4828	483	5	roman	roman	ADJ
ejpam-4828	483	6	domination	domination	NOUN
ejpam-4828	483	7	in	in	ADP
ejpam-4828	483	8	graphs	graph	NOUN
ejpam-4828	483	9	.	.	PUNCT
ejpam-4828	484	1	journal	journal	NOUN
ejpam-4828	484	2	of	of	ADP
ejpam-4828	484	3	combinatorial	combinatorial	ADJ
ejpam-4828	484	4	mathematics	mathematic	NOUN
ejpam-4828	484	5	and	and	CCONJ
ejpam-4828	484	6	combinatorial	combinatorial	ADJ
ejpam-4828	484	7	computing	computing	NOUN
ejpam-4828	484	8	,	,	PUNCT
ejpam-4828	484	9	69:175–182	69:175–182	NOUN
ejpam-4828	484	10	,	,	PUNCT
ejpam-4828	484	11	2009	2009	NUM
ejpam-4828	484	12	.	.	PUNCT
ejpam-4828	485	1	[	[	X
ejpam-4828	485	2	19	19	NUM
ejpam-4828	485	3	]	]	X
ejpam-4828	485	4	j.	j.	PROPN
ejpam-4828	485	5	cyman	cyman	PROPN
ejpam-4828	485	6	snd	snd	PROPN
ejpam-4828	485	7	m.	m.	PROPN
ejpam-4828	485	8	lemańska	lemańska	PROPN
ejpam-4828	485	9	and	and	CCONJ
ejpam-4828	485	10	j.	j.	PROPN
ejpam-4828	485	11	raczek	raczek	PROPN
ejpam-4828	485	12	.	.	PUNCT
ejpam-4828	486	1	graphs	graph	NOUN
ejpam-4828	486	2	with	with	ADP
ejpam-4828	486	3	convex	convex	ADJ
ejpam-4828	486	4	domination	domination	NOUN
ejpam-4828	486	5	number	number	NOUN
ejpam-4828	486	6	close	close	ADJ
ejpam-4828	486	7	to	to	ADP
ejpam-4828	486	8	their	their	PRON
ejpam-4828	486	9	order	order	NOUN
ejpam-4828	486	10	.	.	PUNCT
ejpam-4828	487	1	discussiones	discussione	NOUN
ejpam-4828	487	2	mathematicae	mathematicae	PROPN
ejpam-4828	487	3	graph	graph	NOUN
ejpam-4828	487	4	theory	theory	NOUN
ejpam-4828	487	5	,	,	PUNCT
ejpam-4828	487	6	26(2):307–316	26(2):307–316	NUM
ejpam-4828	487	7	,	,	PUNCT
ejpam-4828	487	8	2006	2006	NUM
ejpam-4828	487	9	.	.	PUNCT