id	sid	tid	token	lemma	pos
ejpam-5978	1	1	european	european	PROPN
ejpam-5978	1	2	journal	journal	PROPN
ejpam-5978	1	3	of	of	ADP
ejpam-5978	1	4	pure	pure	ADJ
ejpam-5978	1	5	and	and	CCONJ
ejpam-5978	1	6	applied	applied	ADJ
ejpam-5978	1	7	mathematics	mathematic	NOUN
ejpam-5978	1	8	2025	2025	NUM
ejpam-5978	1	9	,	,	PUNCT
ejpam-5978	1	10	vol	vol	NOUN
ejpam-5978	1	11	.	.	PROPN
ejpam-5978	1	12	18	18	NUM
ejpam-5978	1	13	,	,	PUNCT
ejpam-5978	1	14	issue	issue	NOUN
ejpam-5978	1	15	2	2	NUM
ejpam-5978	1	16	,	,	PUNCT
ejpam-5978	1	17	article	article	NOUN
ejpam-5978	1	18	number	number	NOUN
ejpam-5978	1	19	5978	5978	NUM
ejpam-5978	1	20	issn	issn	VERB
ejpam-5978	1	21	1307	1307	NUM
ejpam-5978	1	22	-	-	SYM
ejpam-5978	1	23	5543	5543	NUM
ejpam-5978	1	24	–	–	PUNCT
ejpam-5978	1	25	ejpam.com	ejpam.com	X
ejpam-5978	1	26	published	publish	VERB
ejpam-5978	1	27	by	by	ADP
ejpam-5978	1	28	new	new	PROPN
ejpam-5978	1	29	york	york	PROPN
ejpam-5978	1	30	business	business	PROPN
ejpam-5978	1	31	global	global	ADJ
ejpam-5978	1	32	convex	convex	PROPN
ejpam-5978	1	33	independent	independent	ADJ
ejpam-5978	1	34	neighborhood	neighborhood	NOUN
ejpam-5978	1	35	polynomial	polynomial	NOUN
ejpam-5978	1	36	of	of	ADP
ejpam-5978	1	37	some	some	DET
ejpam-5978	1	38	special	special	ADJ
ejpam-5978	1	39	graphs	graph	NOUN
ejpam-5978	1	40	edison	edison	PROPN
ejpam-5978	1	41	john	john	PROPN
ejpam-5978	1	42	b.	b.	PROPN
ejpam-5978	1	43	aguilon1	aguilon1	PROPN
ejpam-5978	1	44	,	,	PUNCT
ejpam-5978	1	45	susan	susan	PROPN
ejpam-5978	1	46	c.	c.	PROPN
ejpam-5978	1	47	dagondon2	dagondon2	PROPN
ejpam-5978	1	48	,	,	PUNCT
ejpam-5978	1	49	rosalio	rosalio	PROPN
ejpam-5978	1	50	g.	g.	PROPN
ejpam-5978	1	51	artes	artes	PROPN
ejpam-5978	1	52	,	,	PUNCT
ejpam-5978	1	53	jr.3	jr.3	PROPN
ejpam-5978	1	54	1	1	NUM
ejpam-5978	1	55	department	department	NOUN
ejpam-5978	1	56	of	of	ADP
ejpam-5978	1	57	mathematics	mathematic	NOUN
ejpam-5978	1	58	and	and	CCONJ
ejpam-5978	1	59	statistics	statistic	NOUN
ejpam-5978	1	60	,	,	PUNCT
ejpam-5978	1	61	college	college	NOUN
ejpam-5978	1	62	of	of	ADP
ejpam-5978	1	63	science	science	NOUN
ejpam-5978	1	64	and	and	CCONJ
ejpam-5978	1	65	mathematics	mathematic	NOUN
ejpam-5978	1	66	,	,	PUNCT
ejpam-5978	1	67	mindanao	mindanao	PROPN
ejpam-5978	1	68	state	state	PROPN
ejpam-5978	1	69	university	university	PROPN
ejpam-5978	1	70	-	-	PUNCT
ejpam-5978	1	71	iligan	iligan	PROPN
ejpam-5978	1	72	institute	institute	PROPN
ejpam-5978	1	73	of	of	ADP
ejpam-5978	1	74	technology	technology	PROPN
ejpam-5978	1	75	,	,	PUNCT
ejpam-5978	1	76	9200	9200	NUM
ejpam-5978	1	77	iligan	iligan	ADJ
ejpam-5978	1	78	city	city	NOUN
ejpam-5978	1	79	,	,	PUNCT
ejpam-5978	1	80	philippines	philippines	PROPN
ejpam-5978	1	81	2	2	NUM
ejpam-5978	1	82	department	department	NOUN
ejpam-5978	1	83	of	of	ADP
ejpam-5978	1	84	mathematics	mathematic	NOUN
ejpam-5978	1	85	and	and	CCONJ
ejpam-5978	1	86	statistics	statistic	NOUN
ejpam-5978	1	87	,	,	PUNCT
ejpam-5978	1	88	college	college	NOUN
ejpam-5978	1	89	of	of	ADP
ejpam-5978	1	90	science	science	NOUN
ejpam-5978	1	91	and	and	CCONJ
ejpam-5978	1	92	mathematics	mathematic	NOUN
ejpam-5978	1	93	,	,	PUNCT
ejpam-5978	1	94	center	center	NOUN
ejpam-5978	1	95	of	of	ADP
ejpam-5978	1	96	graph	graph	NOUN
ejpam-5978	1	97	theory	theory	NOUN
ejpam-5978	1	98	,	,	PUNCT
ejpam-5978	1	99	algebra	algebra	NOUN
ejpam-5978	1	100	,	,	PUNCT
ejpam-5978	1	101	and	and	CCONJ
ejpam-5978	1	102	analysis	analysis	NOUN
ejpam-5978	1	103	-	-	PUNCT
ejpam-5978	1	104	premier	premier	NOUN
ejpam-5978	1	105	research	research	NOUN
ejpam-5978	1	106	institute	institute	PROPN
ejpam-5978	1	107	of	of	ADP
ejpam-5978	1	108	science	science	NOUN
ejpam-5978	1	109	and	and	CCONJ
ejpam-5978	1	110	mathematics	mathematic	NOUN
ejpam-5978	1	111	,	,	PUNCT
ejpam-5978	1	112	mindanao	mindanao	PROPN
ejpam-5978	1	113	state	state	PROPN
ejpam-5978	1	114	university	university	PROPN
ejpam-5978	1	115	-	-	PUNCT
ejpam-5978	1	116	iligan	iligan	PROPN
ejpam-5978	1	117	institute	institute	PROPN
ejpam-5978	1	118	of	of	ADP
ejpam-5978	1	119	technology	technology	PROPN
ejpam-5978	1	120	,	,	PUNCT
ejpam-5978	1	121	9200	9200	NUM
ejpam-5978	1	122	iligan	iligan	ADJ
ejpam-5978	1	123	city	city	NOUN
ejpam-5978	1	124	,	,	PUNCT
ejpam-5978	1	125	philippines	philippine	VERB
ejpam-5978	1	126	3	3	NUM
ejpam-5978	1	127	mathematics	mathematic	NOUN
ejpam-5978	1	128	and	and	CCONJ
ejpam-5978	1	129	sciences	sciences	PROPN
ejpam-5978	1	130	department	department	PROPN
ejpam-5978	1	131	,	,	PUNCT
ejpam-5978	1	132	college	college	NOUN
ejpam-5978	1	133	of	of	ADP
ejpam-5978	1	134	arts	art	NOUN
ejpam-5978	1	135	and	and	CCONJ
ejpam-5978	1	136	sciences	science	NOUN
ejpam-5978	1	137	,	,	PUNCT
ejpam-5978	1	138	mindanao	mindanao	PROPN
ejpam-5978	1	139	state	state	PROPN
ejpam-5978	1	140	university	university	PROPN
ejpam-5978	1	141	tawi	tawi	PROPN
ejpam-5978	1	142	-	-	PUNCT
ejpam-5978	1	143	tawi	tawi	PROPN
ejpam-5978	1	144	college	college	PROPN
ejpam-5978	1	145	of	of	ADP
ejpam-5978	1	146	technology	technology	NOUN
ejpam-5978	1	147	and	and	CCONJ
ejpam-5978	1	148	oceanography	oceanography	NOUN
ejpam-5978	1	149	,	,	PUNCT
ejpam-5978	1	150	sanga	sanga	NOUN
ejpam-5978	1	151	-	-	PUNCT
ejpam-5978	1	152	sanga	sanga	PROPN
ejpam-5978	1	153	,	,	PUNCT
ejpam-5978	1	154	7500	7500	NUM
ejpam-5978	1	155	bongao	bongao	NOUN
ejpam-5978	1	156	,	,	PUNCT
ejpam-5978	1	157	philippines	philippine	NOUN
ejpam-5978	1	158	abstract	abstract	ADJ
ejpam-5978	1	159	.	.	PUNCT
ejpam-5978	2	1	in	in	ADP
ejpam-5978	2	2	this	this	DET
ejpam-5978	2	3	paper	paper	NOUN
ejpam-5978	2	4	,	,	PUNCT
ejpam-5978	2	5	we	we	PRON
ejpam-5978	2	6	introduced	introduce	VERB
ejpam-5978	2	7	the	the	DET
ejpam-5978	2	8	notion	notion	NOUN
ejpam-5978	2	9	of	of	ADP
ejpam-5978	2	10	convex	convex	ADJ
ejpam-5978	2	11	independent	independent	ADJ
ejpam-5978	2	12	neighborhood	neighborhood	NOUN
ejpam-5978	2	13	polynomial	polynomial	NOUN
ejpam-5978	2	14	for	for	ADP
ejpam-5978	2	15	a	a	DET
ejpam-5978	2	16	graph	graph	NOUN
ejpam-5978	2	17	.	.	PUNCT
ejpam-5978	3	1	we	we	PRON
ejpam-5978	3	2	further	far	ADV
ejpam-5978	3	3	explored	explore	VERB
ejpam-5978	3	4	the	the	DET
ejpam-5978	3	5	convex	convex	ADJ
ejpam-5978	3	6	independent	independent	ADJ
ejpam-5978	3	7	neighborhood	neighborhood	NOUN
ejpam-5978	3	8	polynomial	polynomial	NOUN
ejpam-5978	3	9	for	for	ADP
ejpam-5978	3	10	some	some	DET
ejpam-5978	3	11	special	special	ADJ
ejpam-5978	3	12	graphs	graph	NOUN
ejpam-5978	3	13	such	such	ADJ
ejpam-5978	3	14	as	as	ADP
ejpam-5978	3	15	paths	path	NOUN
ejpam-5978	3	16	,	,	PUNCT
ejpam-5978	3	17	cycles	cycle	NOUN
ejpam-5978	3	18	,	,	PUNCT
ejpam-5978	3	19	complete	complete	ADJ
ejpam-5978	3	20	graphs	graph	NOUN
ejpam-5978	3	21	,	,	PUNCT
ejpam-5978	3	22	and	and	CCONJ
ejpam-5978	3	23	star	star	NOUN
ejpam-5978	3	24	graphs	graph	NOUN
ejpam-5978	3	25	.	.	PUNCT
ejpam-5978	4	1	we	we	PRON
ejpam-5978	4	2	generated	generate	VERB
ejpam-5978	4	3	these	these	DET
ejpam-5978	4	4	polynomials	polynomial	NOUN
ejpam-5978	4	5	by	by	ADP
ejpam-5978	4	6	counting	count	VERB
ejpam-5978	4	7	the	the	DET
ejpam-5978	4	8	number	number	NOUN
ejpam-5978	4	9	of	of	ADP
ejpam-5978	4	10	convex	convex	ADJ
ejpam-5978	4	11	subsets	subset	NOUN
ejpam-5978	4	12	of	of	ADP
ejpam-5978	4	13	a	a	DET
ejpam-5978	4	14	graph	graph	NOUN
ejpam-5978	4	15	with	with	ADP
ejpam-5978	4	16	corresponding	correspond	VERB
ejpam-5978	4	17	maximum	maximum	ADJ
ejpam-5978	4	18	independent	independent	ADJ
ejpam-5978	4	19	set	set	NOUN
ejpam-5978	4	20	in	in	ADP
ejpam-5978	4	21	the	the	DET
ejpam-5978	4	22	neighborhood	neighborhood	NOUN
ejpam-5978	4	23	system	system	NOUN
ejpam-5978	4	24	.	.	PUNCT
ejpam-5978	5	1	2020	2020	NUM
ejpam-5978	5	2	mathematics	mathematic	NOUN
ejpam-5978	5	3	subject	subject	NOUN
ejpam-5978	5	4	classifications	classification	NOUN
ejpam-5978	5	5	:	:	PUNCT
ejpam-5978	5	6	05c31	05c31	NUM
ejpam-5978	5	7	,	,	PUNCT
ejpam-5978	5	8	05c69	05c69	NOUN
ejpam-5978	5	9	key	key	ADJ
ejpam-5978	5	10	words	word	NOUN
ejpam-5978	5	11	and	and	CCONJ
ejpam-5978	5	12	phrases	phrase	NOUN
ejpam-5978	5	13	:	:	PUNCT
ejpam-5978	5	14	convex	convex	NOUN
ejpam-5978	5	15	sets	set	NOUN
ejpam-5978	5	16	,	,	PUNCT
ejpam-5978	5	17	convex	convex	NOUN
ejpam-5978	5	18	subgraph	subgraph	NOUN
ejpam-5978	5	19	,	,	PUNCT
ejpam-5978	5	20	independent	independent	ADJ
ejpam-5978	5	21	neighborhood	neighborhood	NOUN
ejpam-5978	5	22	system	system	NOUN
ejpam-5978	5	23	,	,	PUNCT
ejpam-5978	5	24	independent	independent	ADJ
ejpam-5978	5	25	set	set	NOUN
ejpam-5978	5	26	,	,	PUNCT
ejpam-5978	5	27	convex	convex	VERB
ejpam-5978	5	28	independent	independent	ADJ
ejpam-5978	5	29	neighborhood	neighborhood	NOUN
ejpam-5978	5	30	polynomial	polynomial	ADJ
ejpam-5978	5	31	1	1	NUM
ejpam-5978	5	32	.	.	PUNCT
ejpam-5978	6	1	introduction	introduction	NOUN
ejpam-5978	6	2	graph	graph	NOUN
ejpam-5978	6	3	theory	theory	NOUN
ejpam-5978	6	4	offers	offer	VERB
ejpam-5978	6	5	a	a	DET
ejpam-5978	6	6	broad	broad	ADJ
ejpam-5978	6	7	foundation	foundation	NOUN
ejpam-5978	6	8	for	for	ADP
ejpam-5978	6	9	studying	study	VERB
ejpam-5978	6	10	various	various	ADJ
ejpam-5978	6	11	mathematical	mathematical	ADJ
ejpam-5978	6	12	structures	structure	NOUN
ejpam-5978	6	13	,	,	PUNCT
ejpam-5978	6	14	such	such	ADJ
ejpam-5978	6	15	as	as	ADP
ejpam-5978	6	16	graph	graph	NOUN
ejpam-5978	6	17	polynomials	polynomial	NOUN
ejpam-5978	6	18	and	and	CCONJ
ejpam-5978	6	19	convexity	convexity	NOUN
ejpam-5978	6	20	in	in	ADP
ejpam-5978	6	21	graphs	graph	NOUN
ejpam-5978	6	22	.	.	PUNCT
ejpam-5978	7	1	graph	graph	NOUN
ejpam-5978	7	2	polynomials	polynomial	NOUN
ejpam-5978	7	3	have	have	AUX
ejpam-5978	7	4	been	be	AUX
ejpam-5978	7	5	the	the	DET
ejpam-5978	7	6	focus	focus	NOUN
ejpam-5978	7	7	of	of	ADP
ejpam-5978	7	8	interest	interest	NOUN
ejpam-5978	7	9	in	in	ADP
ejpam-5978	7	10	recent	recent	ADJ
ejpam-5978	7	11	developments	development	NOUN
ejpam-5978	7	12	in	in	ADP
ejpam-5978	7	13	graph	graph	NOUN
ejpam-5978	7	14	theory	theory	NOUN
ejpam-5978	7	15	.	.	PUNCT
ejpam-5978	8	1	the	the	DET
ejpam-5978	8	2	use	use	NOUN
ejpam-5978	8	3	of	of	ADP
ejpam-5978	8	4	polynomials	polynomial	NOUN
ejpam-5978	8	5	to	to	PART
ejpam-5978	8	6	represent	represent	VERB
ejpam-5978	8	7	graphs	graph	NOUN
ejpam-5978	8	8	has	have	AUX
ejpam-5978	8	9	recently	recently	ADV
ejpam-5978	8	10	become	become	VERB
ejpam-5978	8	11	a	a	DET
ejpam-5978	8	12	significant	significant	ADJ
ejpam-5978	8	13	area	area	NOUN
ejpam-5978	8	14	of	of	ADP
ejpam-5978	8	15	study	study	NOUN
ejpam-5978	8	16	,	,	PUNCT
ejpam-5978	8	17	driven	drive	VERB
ejpam-5978	8	18	by	by	ADP
ejpam-5978	8	19	its	its	PRON
ejpam-5978	8	20	practical	practical	ADJ
ejpam-5978	8	21	applications	application	NOUN
ejpam-5978	8	22	in	in	ADP
ejpam-5978	8	23	various	various	ADJ
ejpam-5978	8	24	scientific	scientific	ADJ
ejpam-5978	8	25	fields	field	NOUN
ejpam-5978	8	26	[	[	X
ejpam-5978	8	27	1	1	NUM
ejpam-5978	8	28	]	]	PUNCT
ejpam-5978	8	29	.	.	PUNCT
ejpam-5978	9	1	as	as	ADP
ejpam-5978	9	2	a	a	DET
ejpam-5978	9	3	result	result	NOUN
ejpam-5978	9	4	,	,	PUNCT
ejpam-5978	9	5	several	several	ADJ
ejpam-5978	9	6	graph	graph	NOUN
ejpam-5978	9	7	polynomials	polynomial	NOUN
ejpam-5978	9	8	have	have	AUX
ejpam-5978	9	9	been	be	AUX
ejpam-5978	9	10	formulated	formulate	VERB
ejpam-5978	9	11	,	,	PUNCT
ejpam-5978	9	12	and	and	CCONJ
ejpam-5978	9	13	substantial	substantial	ADJ
ejpam-5978	9	14	results	result	NOUN
ejpam-5978	9	15	have	have	AUX
ejpam-5978	9	16	been	be	AUX
ejpam-5978	9	17	obtained	obtain	VERB
ejpam-5978	9	18	such	such	ADJ
ejpam-5978	9	19	as	as	ADP
ejpam-5978	9	20	neighborhood	neighborhood	NOUN
ejpam-5978	9	21	polynomial	polynomial	NOUN
ejpam-5978	9	22	which	which	PRON
ejpam-5978	9	23	was	be	AUX
ejpam-5978	9	24	introduced	introduce	VERB
ejpam-5978	9	25	in	in	ADP
ejpam-5978	9	26	2008	2008	NUM
ejpam-5978	9	27	by	by	ADP
ejpam-5978	9	28	brown	brown	NOUN
ejpam-5978	9	29	and	and	CCONJ
ejpam-5978	9	30	nowakowski	nowakowski	ADJ
ejpam-5978	10	1	[	[	X
ejpam-5978	10	2	2	2	NUM
ejpam-5978	10	3	]	]	PUNCT
ejpam-5978	10	4	and	and	CCONJ
ejpam-5978	10	5	independent	independent	ADJ
ejpam-5978	10	6	neighborhood	neighborhood	NOUN
ejpam-5978	10	7	polynomial	polynomial	NOUN
ejpam-5978	10	8	which	which	PRON
ejpam-5978	10	9	was	be	AUX
ejpam-5978	10	10	studied	study	VERB
ejpam-5978	10	11	by	by	ADP
ejpam-5978	10	12	abdulcarim	abdulcarim	NOUN
ejpam-5978	10	13	et	et	PROPN
ejpam-5978	10	14	al	al	PROPN
ejpam-5978	10	15	.	.	PROPN
ejpam-5978	11	1	in	in	ADP
ejpam-5978	11	2	2021	2021	NUM
ejpam-5978	11	3	[	[	X
ejpam-5978	11	4	3	3	NUM
ejpam-5978	11	5	]	]	PUNCT
ejpam-5978	11	6	.	.	PUNCT
ejpam-5978	12	1	on	on	ADP
ejpam-5978	12	2	the	the	DET
ejpam-5978	12	3	other	other	ADJ
ejpam-5978	12	4	doi	doi	NOUN
ejpam-5978	12	5	:	:	PUNCT
ejpam-5978	12	6	https://doi.org/10.29020/nybg.ejpam.v18i2.5978	https://doi.org/10.29020/nybg.ejpam.v18i2.5978	DET
ejpam-5978	12	7	email	email	NOUN
ejpam-5978	12	8	addresses	address	NOUN
ejpam-5978	12	9	:	:	PUNCT
ejpam-5978	12	10	edisonjohn.aguilon@g.msuiit.edu.ph	edisonjohn.aguilon@g.msuiit.edu.ph	PROPN
ejpam-5978	12	11	(	(	PUNCT
ejpam-5978	12	12	e.j	e.j	PROPN
ejpam-5978	12	13	.	.	PROPN
ejpam-5978	12	14	aguilon	aguilon	NOUN
ejpam-5978	12	15	)	)	PUNCT
ejpam-5978	12	16	,	,	PUNCT
ejpam-5978	12	17	susan.dagondon@g.msuiit.edu.ph	susan.dagondon@g.msuiit.edu.ph	PROPN
ejpam-5978	12	18	(	(	PUNCT
ejpam-5978	12	19	s.	s.	PROPN
ejpam-5978	12	20	dagondon	dagondon	PROPN
ejpam-5978	12	21	)	)	PUNCT
ejpam-5978	12	22	,	,	PUNCT
ejpam-5978	12	23	rosalioartes@msutawi-tawi.edu.ph	rosalioartes@msutawi-tawi.edu.ph	PROPN
ejpam-5978	12	24	(	(	PUNCT
ejpam-5978	12	25	r.	r.	PROPN
ejpam-5978	12	26	artes	artes	PROPN
ejpam-5978	12	27	,	,	PUNCT
ejpam-5978	12	28	jr	jr	PROPN
ejpam-5978	12	29	.	.	PUNCT
ejpam-5978	12	30	)	)	PUNCT
ejpam-5978	12	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5978	13	1	1	1	NUM
ejpam-5978	13	2	copyright	copyright	NOUN
ejpam-5978	13	3	:	:	PUNCT
ejpam-5978	13	4	©	©	PROPN
ejpam-5978	13	5	2025	2025	NUM
ejpam-5978	13	6	the	the	DET
ejpam-5978	13	7	author(s	author(s	NOUN
ejpam-5978	13	8	)	)	PUNCT
ejpam-5978	13	9	.	.	PUNCT
ejpam-5978	14	1	(	(	PUNCT
ejpam-5978	14	2	cc	cc	NOUN
ejpam-5978	14	3	by	by	ADP
ejpam-5978	14	4	-	-	PUNCT
ejpam-5978	14	5	nc	nc	PROPN
ejpam-5978	14	6	4.0	4.0	NUM
ejpam-5978	14	7	)	)	PUNCT
ejpam-5978	14	8	e.j	e.j	PROPN
ejpam-5978	14	9	.	.	PROPN
ejpam-5978	14	10	aguilon	aguilon	PROPN
ejpam-5978	14	11	,	,	PUNCT
ejpam-5978	14	12	s.	s.	PROPN
ejpam-5978	14	13	dagondon	dagondon	PROPN
ejpam-5978	14	14	,	,	PUNCT
ejpam-5978	14	15	r.	r.	PROPN
ejpam-5978	14	16	artes	artes	PROPN
ejpam-5978	14	17	/	/	SYM
ejpam-5978	14	18	eur	eur	PROPN
ejpam-5978	14	19	.	.	PUNCT
ejpam-5978	15	1	j.	j.	PROPN
ejpam-5978	15	2	pure	pure	PROPN
ejpam-5978	15	3	appl	appl	PROPN
ejpam-5978	15	4	.	.	PROPN
ejpam-5978	15	5	math	math	PROPN
ejpam-5978	15	6	,	,	PUNCT
ejpam-5978	15	7	18	18	NUM
ejpam-5978	15	8	(	(	PUNCT
ejpam-5978	15	9	2	2	NUM
ejpam-5978	15	10	)	)	PUNCT
ejpam-5978	15	11	(	(	PUNCT
ejpam-5978	15	12	2025	2025	NUM
ejpam-5978	15	13	)	)	PUNCT
ejpam-5978	15	14	,	,	PUNCT
ejpam-5978	15	15	5978	5978	NUM
ejpam-5978	15	16	2	2	NUM
ejpam-5978	15	17	of	of	ADP
ejpam-5978	15	18	18	18	NUM
ejpam-5978	15	19	hand	hand	NOUN
ejpam-5978	15	20	,	,	PUNCT
ejpam-5978	15	21	convexity	convexity	NOUN
ejpam-5978	15	22	in	in	ADP
ejpam-5978	15	23	a	a	DET
ejpam-5978	15	24	graph	graph	NOUN
ejpam-5978	15	25	is	be	AUX
ejpam-5978	15	26	defined	define	VERB
ejpam-5978	15	27	based	base	VERB
ejpam-5978	15	28	on	on	ADP
ejpam-5978	15	29	specific	specific	ADJ
ejpam-5978	15	30	path	path	NOUN
ejpam-5978	15	31	-	-	PUNCT
ejpam-5978	15	32	based	base	VERB
ejpam-5978	15	33	properties	property	NOUN
ejpam-5978	15	34	.	.	PUNCT
ejpam-5978	16	1	a	a	DET
ejpam-5978	16	2	set	set	NOUN
ejpam-5978	16	3	of	of	ADP
ejpam-5978	16	4	vertices	vertex	NOUN
ejpam-5978	16	5	is	be	AUX
ejpam-5978	16	6	considered	consider	VERB
ejpam-5978	16	7	convex	convex	ADJ
ejpam-5978	16	8	if	if	SCONJ
ejpam-5978	16	9	,	,	PUNCT
ejpam-5978	16	10	for	for	ADP
ejpam-5978	16	11	any	any	DET
ejpam-5978	16	12	two	two	NUM
ejpam-5978	16	13	vertices	vertex	NOUN
ejpam-5978	16	14	within	within	ADP
ejpam-5978	16	15	the	the	DET
ejpam-5978	16	16	set	set	NOUN
ejpam-5978	16	17	,	,	PUNCT
ejpam-5978	16	18	all	all	DET
ejpam-5978	16	19	shortest	short	ADJ
ejpam-5978	16	20	paths	path	NOUN
ejpam-5978	16	21	between	between	ADP
ejpam-5978	16	22	them	they	PRON
ejpam-5978	16	23	remain	remain	VERB
ejpam-5978	16	24	entirely	entirely	ADV
ejpam-5978	16	25	within	within	ADP
ejpam-5978	16	26	the	the	DET
ejpam-5978	16	27	set	set	NOUN
ejpam-5978	16	28	.	.	PUNCT
ejpam-5978	17	1	further	far	ADV
ejpam-5978	17	2	,	,	PUNCT
ejpam-5978	17	3	convexity	convexity	NOUN
ejpam-5978	17	4	is	be	AUX
ejpam-5978	17	5	gaining	gain	VERB
ejpam-5978	17	6	its	its	PRON
ejpam-5978	17	7	resurgence	resurgence	NOUN
ejpam-5978	17	8	due	due	ADP
ejpam-5978	17	9	to	to	ADP
ejpam-5978	17	10	its	its	PRON
ejpam-5978	17	11	various	various	ADJ
ejpam-5978	17	12	current	current	ADJ
ejpam-5978	17	13	applications	application	NOUN
ejpam-5978	17	14	.	.	PUNCT
ejpam-5978	18	1	several	several	ADJ
ejpam-5978	18	2	authors	author	NOUN
ejpam-5978	18	3	studied	study	VERB
ejpam-5978	18	4	graph	graph	NOUN
ejpam-5978	18	5	convexity	convexity	NOUN
ejpam-5978	18	6	in	in	ADP
ejpam-5978	18	7	various	various	ADJ
ejpam-5978	18	8	perspectives	perspective	NOUN
ejpam-5978	18	9	and	and	CCONJ
ejpam-5978	18	10	some	some	DET
ejpam-5978	18	11	explored	explore	VERB
ejpam-5978	18	12	convexity	convexity	NOUN
ejpam-5978	18	13	in	in	ADP
ejpam-5978	18	14	rn	rn	PROPN
ejpam-5978	18	15	[	[	X
ejpam-5978	18	16	4	4	NUM
ejpam-5978	18	17	]	]	PUNCT
ejpam-5978	18	18	.	.	PUNCT
ejpam-5978	19	1	in	in	ADP
ejpam-5978	19	2	particular	particular	ADJ
ejpam-5978	19	3	,	,	PUNCT
ejpam-5978	19	4	studies	study	NOUN
ejpam-5978	19	5	in	in	ADP
ejpam-5978	19	6	[	[	X
ejpam-5978	19	7	5	5	NUM
ejpam-5978	19	8	]	]	PUNCT
ejpam-5978	19	9	[	[	X
ejpam-5978	19	10	6	6	NUM
ejpam-5978	19	11	]	]	X
ejpam-5978	19	12	[	[	X
ejpam-5978	19	13	7	7	X
ejpam-5978	19	14	]	]	PUNCT
ejpam-5978	19	15	considered	consider	VERB
ejpam-5978	19	16	applying	apply	VERB
ejpam-5978	19	17	the	the	DET
ejpam-5978	19	18	concept	concept	NOUN
ejpam-5978	19	19	of	of	ADP
ejpam-5978	19	20	convexity	convexity	NOUN
ejpam-5978	19	21	to	to	PART
ejpam-5978	19	22	graphs	graph	NOUN
ejpam-5978	19	23	and	and	CCONJ
ejpam-5978	19	24	to	to	ADP
ejpam-5978	19	25	its	its	PRON
ejpam-5978	19	26	polynomials	polynomial	NOUN
ejpam-5978	19	27	.	.	PUNCT
ejpam-5978	20	1	furthermore	furthermore	ADV
ejpam-5978	20	2	,	,	PUNCT
ejpam-5978	20	3	in	in	ADP
ejpam-5978	20	4	the	the	DET
ejpam-5978	20	5	studies	study	NOUN
ejpam-5978	20	6	of	of	ADP
ejpam-5978	20	7	r.	r.	PROPN
ejpam-5978	20	8	artes	artes	PROPN
ejpam-5978	20	9	jr	jr	PROPN
ejpam-5978	20	10	.	.	PROPN
ejpam-5978	20	11	et	et	PROPN
ejpam-5978	20	12	al	al	PROPN
ejpam-5978	20	13	.	.	PROPN
ejpam-5978	20	14	,	,	PUNCT
ejpam-5978	20	15	they	they	PRON
ejpam-5978	20	16	integrated	integrate	VERB
ejpam-5978	20	17	the	the	DET
ejpam-5978	20	18	concept	concept	NOUN
ejpam-5978	20	19	of	of	ADP
ejpam-5978	20	20	convexity	convexity	NOUN
ejpam-5978	20	21	with	with	ADP
ejpam-5978	20	22	graph	graph	NOUN
ejpam-5978	20	23	polynomial	polynomial	ADJ
ejpam-5978	20	24	which	which	PRON
ejpam-5978	20	25	involve	involve	VERB
ejpam-5978	20	26	counting	count	VERB
ejpam-5978	20	27	the	the	DET
ejpam-5978	20	28	number	number	NOUN
ejpam-5978	20	29	of	of	ADP
ejpam-5978	20	30	substructures	substructure	NOUN
ejpam-5978	20	31	with	with	ADP
ejpam-5978	20	32	corresponding	correspond	VERB
ejpam-5978	20	33	neighborhood	neighborhood	NOUN
ejpam-5978	20	34	system	system	NOUN
ejpam-5978	20	35	cardinality	cardinality	NOUN
ejpam-5978	20	36	of	of	ADP
ejpam-5978	20	37	some	some	DET
ejpam-5978	20	38	property	property	NOUN
ejpam-5978	20	39	[	[	X
ejpam-5978	20	40	8][9	8][9	NOUN
ejpam-5978	20	41	]	]	X
ejpam-5978	20	42	.	.	PUNCT
ejpam-5978	21	1	with	with	ADP
ejpam-5978	21	2	this	this	DET
ejpam-5978	21	3	development	development	NOUN
ejpam-5978	21	4	in	in	ADP
ejpam-5978	21	5	the	the	DET
ejpam-5978	21	6	study	study	NOUN
ejpam-5978	21	7	of	of	ADP
ejpam-5978	21	8	convex	convex	ADJ
ejpam-5978	21	9	subsets	subset	NOUN
ejpam-5978	21	10	and	and	CCONJ
ejpam-5978	21	11	polynomials	polynomial	NOUN
ejpam-5978	21	12	in	in	ADP
ejpam-5978	21	13	graph	graph	NOUN
ejpam-5978	21	14	,	,	PUNCT
ejpam-5978	21	15	this	this	DET
ejpam-5978	21	16	paper	paper	NOUN
ejpam-5978	21	17	aims	aim	VERB
ejpam-5978	21	18	to	to	PART
ejpam-5978	21	19	investigate	investigate	VERB
ejpam-5978	21	20	another	another	DET
ejpam-5978	21	21	type	type	NOUN
ejpam-5978	21	22	of	of	ADP
ejpam-5978	21	23	graph	graph	NOUN
ejpam-5978	21	24	polynomial	polynomial	NOUN
ejpam-5978	21	25	called	call	VERB
ejpam-5978	21	26	the	the	DET
ejpam-5978	21	27	convex	convex	ADJ
ejpam-5978	21	28	independent	independent	ADJ
ejpam-5978	21	29	neighborhood	neighborhood	NOUN
ejpam-5978	21	30	polynomial	polynomial	NOUN
ejpam-5978	21	31	and	and	CCONJ
ejpam-5978	21	32	considers	consider	VERB
ejpam-5978	21	33	applying	apply	VERB
ejpam-5978	21	34	it	it	PRON
ejpam-5978	21	35	to	to	ADP
ejpam-5978	21	36	some	some	DET
ejpam-5978	21	37	special	special	ADJ
ejpam-5978	21	38	graphs	graph	NOUN
ejpam-5978	21	39	.	.	PUNCT
ejpam-5978	22	1	2	2	X
ejpam-5978	22	2	.	.	NOUN
ejpam-5978	22	3	terminologies	terminology	NOUN
ejpam-5978	22	4	and	and	CCONJ
ejpam-5978	22	5	notations	notation	NOUN
ejpam-5978	22	6	a	a	DET
ejpam-5978	22	7	graph	graph	NOUN
ejpam-5978	22	8	g	g	PROPN
ejpam-5978	22	9	is	be	AUX
ejpam-5978	22	10	a	a	DET
ejpam-5978	22	11	finite	finite	NOUN
ejpam-5978	22	12	nonempty	nonempty	ADV
ejpam-5978	22	13	set	set	VERB
ejpam-5978	22	14	v	v	NOUN
ejpam-5978	22	15	(	(	PUNCT
ejpam-5978	22	16	g	g	NOUN
ejpam-5978	22	17	)	)	PUNCT
ejpam-5978	22	18	of	of	ADP
ejpam-5978	22	19	objects	object	NOUN
ejpam-5978	22	20	called	call	VERB
ejpam-5978	22	21	vertices	vertex	NOUN
ejpam-5978	22	22	together	together	ADV
ejpam-5978	22	23	with	with	ADP
ejpam-5978	22	24	a	a	DET
ejpam-5978	22	25	possibly	possibly	ADV
ejpam-5978	22	26	empty	empty	ADJ
ejpam-5978	22	27	set	set	VERB
ejpam-5978	22	28	e(g	e(g	NOUN
ejpam-5978	22	29	)	)	PUNCT
ejpam-5978	22	30	of	of	ADP
ejpam-5978	22	31	2	2	NUM
ejpam-5978	22	32	-	-	PUNCT
ejpam-5978	22	33	element	element	NOUN
ejpam-5978	22	34	subsets	subset	NOUN
ejpam-5978	22	35	of	of	ADP
ejpam-5978	22	36	v	v	NOUN
ejpam-5978	22	37	(	(	PUNCT
ejpam-5978	22	38	g	g	NOUN
ejpam-5978	22	39	)	)	PUNCT
ejpam-5978	22	40	called	call	VERB
ejpam-5978	22	41	edges	edge	NOUN
ejpam-5978	22	42	.	.	PUNCT
ejpam-5978	23	1	vertices	vertex	NOUN
ejpam-5978	23	2	are	be	AUX
ejpam-5978	23	3	sometimes	sometimes	ADV
ejpam-5978	23	4	called	call	VERB
ejpam-5978	23	5	points	point	NOUN
ejpam-5978	23	6	or	or	CCONJ
ejpam-5978	23	7	nodes	node	NOUN
ejpam-5978	23	8	,	,	PUNCT
ejpam-5978	23	9	while	while	SCONJ
ejpam-5978	23	10	edges	edge	NOUN
ejpam-5978	23	11	are	be	AUX
ejpam-5978	23	12	sometimes	sometimes	ADV
ejpam-5978	23	13	called	call	VERB
ejpam-5978	23	14	lines	line	NOUN
ejpam-5978	23	15	or	or	CCONJ
ejpam-5978	23	16	links	link	NOUN
ejpam-5978	23	17	.	.	PUNCT
ejpam-5978	24	1	given	give	VERB
ejpam-5978	24	2	a	a	DET
ejpam-5978	24	3	graph	graph	NOUN
ejpam-5978	24	4	g	g	NOUN
ejpam-5978	24	5	=	=	PUNCT
ejpam-5978	24	6	⟨v	⟨v	PUNCT
ejpam-5978	24	7	(	(	PUNCT
ejpam-5978	24	8	g	g	NOUN
ejpam-5978	24	9	)	)	PUNCT
ejpam-5978	24	10	,	,	PUNCT
ejpam-5978	24	11	e(g)⟩	e(g)⟩	PROPN
ejpam-5978	24	12	,	,	PUNCT
ejpam-5978	24	13	where	where	SCONJ
ejpam-5978	24	14	v	v	X
ejpam-5978	24	15	(	(	PUNCT
ejpam-5978	24	16	g	g	NOUN
ejpam-5978	24	17	)	)	PUNCT
ejpam-5978	24	18	is	be	AUX
ejpam-5978	24	19	the	the	DET
ejpam-5978	24	20	vertex	vertex	NOUN
ejpam-5978	24	21	-	-	PUNCT
ejpam-5978	24	22	set	set	NOUN
ejpam-5978	24	23	of	of	ADP
ejpam-5978	24	24	g	g	PROPN
ejpam-5978	24	25	and	and	CCONJ
ejpam-5978	24	26	e(g	e(g	PROPN
ejpam-5978	24	27	)	)	PUNCT
ejpam-5978	24	28	is	be	AUX
ejpam-5978	24	29	the	the	DET
ejpam-5978	24	30	edge	edge	NOUN
ejpam-5978	24	31	-	-	PUNCT
ejpam-5978	24	32	set	set	NOUN
ejpam-5978	24	33	of	of	ADP
ejpam-5978	24	34	g	g	NOUN
ejpam-5978	24	35	,	,	PUNCT
ejpam-5978	24	36	the	the	DET
ejpam-5978	24	37	number	number	NOUN
ejpam-5978	24	38	of	of	ADP
ejpam-5978	24	39	vertices	vertex	NOUN
ejpam-5978	24	40	in	in	ADP
ejpam-5978	24	41	a	a	DET
ejpam-5978	24	42	graph	graph	NOUN
ejpam-5978	24	43	g	g	NOUN
ejpam-5978	24	44	is	be	AUX
ejpam-5978	24	45	the	the	DET
ejpam-5978	24	46	order	order	NOUN
ejpam-5978	24	47	of	of	ADP
ejpam-5978	24	48	g	g	NOUN
ejpam-5978	24	49	and	and	CCONJ
ejpam-5978	24	50	the	the	DET
ejpam-5978	24	51	number	number	NOUN
ejpam-5978	24	52	of	of	ADP
ejpam-5978	24	53	edges	edge	NOUN
ejpam-5978	24	54	is	be	AUX
ejpam-5978	24	55	the	the	DET
ejpam-5978	24	56	size	size	NOUN
ejpam-5978	24	57	of	of	ADP
ejpam-5978	24	58	g.	g.	PROPN
ejpam-5978	24	59	a	a	DET
ejpam-5978	24	60	subset	subset	NOUN
ejpam-5978	24	61	s	s	NOUN
ejpam-5978	24	62	of	of	ADP
ejpam-5978	24	63	v	v	NOUN
ejpam-5978	24	64	(	(	PUNCT
ejpam-5978	24	65	g	g	NOUN
ejpam-5978	24	66	)	)	PUNCT
ejpam-5978	24	67	is	be	AUX
ejpam-5978	24	68	said	say	VERB
ejpam-5978	24	69	to	to	PART
ejpam-5978	24	70	be	be	AUX
ejpam-5978	24	71	independent	independent	ADJ
ejpam-5978	24	72	in	in	ADP
ejpam-5978	24	73	g	g	PROPN
ejpam-5978	24	74	if	if	SCONJ
ejpam-5978	24	75	no	no	DET
ejpam-5978	24	76	two	two	NUM
ejpam-5978	24	77	vertices	vertex	NOUN
ejpam-5978	24	78	in	in	ADP
ejpam-5978	24	79	the	the	DET
ejpam-5978	24	80	set	set	NOUN
ejpam-5978	24	81	are	be	AUX
ejpam-5978	24	82	adjacent	adjacent	ADJ
ejpam-5978	24	83	in	in	ADP
ejpam-5978	24	84	g.	g.	PROPN
ejpam-5978	24	85	in	in	ADP
ejpam-5978	24	86	other	other	ADJ
ejpam-5978	24	87	words	word	NOUN
ejpam-5978	24	88	,	,	PUNCT
ejpam-5978	24	89	for	for	SCONJ
ejpam-5978	24	90	any	any	DET
ejpam-5978	24	91	two	two	NUM
ejpam-5978	24	92	vertices	vertex	NOUN
ejpam-5978	24	93	u	u	NOUN
ejpam-5978	24	94	,	,	PUNCT
ejpam-5978	24	95	v	v	ADP
ejpam-5978	24	96	∈	∈	PROPN
ejpam-5978	24	97	s	s	NOUN
ejpam-5978	24	98	,	,	PUNCT
ejpam-5978	24	99	uv	uv	PROPN
ejpam-5978	24	100	/∈	/∈	PUNCT
ejpam-5978	24	101	e(g	e(g	PROPN
ejpam-5978	24	102	)	)	PUNCT
ejpam-5978	24	103	.	.	PUNCT
ejpam-5978	25	1	the	the	DET
ejpam-5978	25	2	cardinality	cardinality	NOUN
ejpam-5978	25	3	of	of	ADP
ejpam-5978	25	4	a	a	DET
ejpam-5978	25	5	maximum	maximum	ADJ
ejpam-5978	25	6	independent	independent	ADJ
ejpam-5978	25	7	set	set	NOUN
ejpam-5978	25	8	is	be	AUX
ejpam-5978	25	9	called	call	VERB
ejpam-5978	25	10	independence	independence	NOUN
ejpam-5978	25	11	number	number	NOUN
ejpam-5978	25	12	of	of	ADP
ejpam-5978	25	13	g.	g.	PROPN
ejpam-5978	25	14	a	a	DET
ejpam-5978	25	15	path	path	NOUN
ejpam-5978	25	16	consists	consist	VERB
ejpam-5978	25	17	of	of	ADP
ejpam-5978	25	18	a	a	DET
ejpam-5978	25	19	sequence	sequence	NOUN
ejpam-5978	25	20	of	of	ADP
ejpam-5978	25	21	edges	edge	NOUN
ejpam-5978	25	22	,	,	PUNCT
ejpam-5978	25	23	one	one	NUM
ejpam-5978	25	24	following	follow	VERB
ejpam-5978	25	25	another	another	PRON
ejpam-5978	25	26	in	in	ADP
ejpam-5978	25	27	which	which	PRON
ejpam-5978	25	28	no	no	DET
ejpam-5978	25	29	vertex	vertex	NOUN
ejpam-5978	25	30	appears	appear	VERB
ejpam-5978	25	31	more	more	ADJ
ejpam-5978	25	32	than	than	ADP
ejpam-5978	25	33	once	once	ADV
ejpam-5978	25	34	.	.	PUNCT
ejpam-5978	26	1	a	a	DET
ejpam-5978	26	2	path	path	NOUN
ejpam-5978	26	3	of	of	ADP
ejpam-5978	26	4	order	order	NOUN
ejpam-5978	26	5	n	n	NOUN
ejpam-5978	26	6	with	with	ADP
ejpam-5978	26	7	vertices	vertex	NOUN
ejpam-5978	26	8	v1	v1	NOUN
ejpam-5978	26	9	,	,	PUNCT
ejpam-5978	26	10	v2	v2	NOUN
ejpam-5978	26	11	,	,	PUNCT
ejpam-5978	26	12	.	.	PUNCT
ejpam-5978	26	13	.	.	PUNCT
ejpam-5978	26	14	.	.	PUNCT
ejpam-5978	27	1	,	,	PUNCT
ejpam-5978	27	2	vn	vn	INTJ
ejpam-5978	27	3	(	(	PUNCT
ejpam-5978	27	4	in	in	ADP
ejpam-5978	27	5	order	order	NOUN
ejpam-5978	27	6	)	)	PUNCT
ejpam-5978	27	7	is	be	AUX
ejpam-5978	27	8	denoted	denote	VERB
ejpam-5978	27	9	by	by	ADP
ejpam-5978	27	10	pn	pn	PROPN
ejpam-5978	27	11	.	.	PUNCT
ejpam-5978	27	12	a	a	DET
ejpam-5978	27	13	graph	graph	NOUN
ejpam-5978	27	14	g	g	NOUN
ejpam-5978	27	15	is	be	AUX
ejpam-5978	27	16	connected	connect	VERB
ejpam-5978	27	17	if	if	SCONJ
ejpam-5978	27	18	every	every	DET
ejpam-5978	27	19	pair	pair	NOUN
ejpam-5978	27	20	of	of	ADP
ejpam-5978	27	21	vertices	vertex	NOUN
ejpam-5978	27	22	in	in	ADP
ejpam-5978	27	23	the	the	DET
ejpam-5978	27	24	vertex	vertex	NOUN
ejpam-5978	27	25	-	-	PUNCT
ejpam-5978	27	26	set	set	NOUN
ejpam-5978	27	27	of	of	ADP
ejpam-5978	27	28	g	g	PROPN
ejpam-5978	27	29	is	be	AUX
ejpam-5978	27	30	connected	connect	VERB
ejpam-5978	27	31	by	by	ADP
ejpam-5978	27	32	a	a	DET
ejpam-5978	27	33	path	path	NOUN
ejpam-5978	27	34	.	.	PUNCT
ejpam-5978	28	1	a	a	DET
ejpam-5978	28	2	cycle	cycle	NOUN
ejpam-5978	28	3	is	be	AUX
ejpam-5978	28	4	a	a	DET
ejpam-5978	28	5	closed	closed	ADJ
ejpam-5978	28	6	path	path	NOUN
ejpam-5978	28	7	of	of	ADP
ejpam-5978	28	8	order	order	NOUN
ejpam-5978	28	9	n	n	NOUN
ejpam-5978	28	10	and	and	CCONJ
ejpam-5978	28	11	is	be	AUX
ejpam-5978	28	12	denoted	denote	VERB
ejpam-5978	28	13	by	by	ADP
ejpam-5978	28	14	cn	cn	PROPN
ejpam-5978	28	15	.	.	PUNCT
ejpam-5978	28	16	a	a	DET
ejpam-5978	28	17	graph	graph	NOUN
ejpam-5978	28	18	g	g	NOUN
ejpam-5978	28	19	is	be	AUX
ejpam-5978	28	20	called	call	VERB
ejpam-5978	28	21	bipartite	bipartite	ADJ
ejpam-5978	28	22	if	if	SCONJ
ejpam-5978	28	23	v	v	NOUN
ejpam-5978	28	24	(	(	PUNCT
ejpam-5978	28	25	g	g	NOUN
ejpam-5978	28	26	)	)	PUNCT
ejpam-5978	28	27	can	can	AUX
ejpam-5978	28	28	be	be	AUX
ejpam-5978	28	29	partitioned	partition	VERB
ejpam-5978	28	30	into	into	ADP
ejpam-5978	28	31	two	two	NUM
ejpam-5978	28	32	nonempty	nonempty	ADJ
ejpam-5978	28	33	independent	independent	ADJ
ejpam-5978	28	34	subsets	subset	NOUN
ejpam-5978	28	35	a	a	PRON
ejpam-5978	28	36	and	and	CCONJ
ejpam-5978	28	37	b	b	PROPN
ejpam-5978	28	38	of	of	ADP
ejpam-5978	28	39	v	v	NOUN
ejpam-5978	28	40	(	(	PUNCT
ejpam-5978	28	41	g	g	NOUN
ejpam-5978	28	42	)	)	PUNCT
ejpam-5978	28	43	(	(	PUNCT
ejpam-5978	28	44	called	call	VERB
ejpam-5978	28	45	partite	partite	ADJ
ejpam-5978	28	46	sets	set	NOUN
ejpam-5978	28	47	)	)	PUNCT
ejpam-5978	28	48	.	.	PUNCT
ejpam-5978	29	1	a	a	DET
ejpam-5978	29	2	complete	complete	ADJ
ejpam-5978	29	3	bipartite	bipartite	NOUN
ejpam-5978	29	4	graph	graph	NOUN
ejpam-5978	29	5	is	be	AUX
ejpam-5978	29	6	a	a	DET
ejpam-5978	29	7	bipartite	bipartite	ADJ
ejpam-5978	29	8	graph	graph	NOUN
ejpam-5978	29	9	in	in	ADP
ejpam-5978	29	10	which	which	PRON
ejpam-5978	29	11	each	each	DET
ejpam-5978	29	12	vertex	vertex	NOUN
ejpam-5978	29	13	in	in	ADP
ejpam-5978	29	14	a	a	PRON
ejpam-5978	29	15	is	be	AUX
ejpam-5978	29	16	joined	join	VERB
ejpam-5978	29	17	to	to	ADP
ejpam-5978	29	18	each	each	DET
ejpam-5978	29	19	vertex	vertex	NOUN
ejpam-5978	29	20	in	in	ADP
ejpam-5978	29	21	b	b	NOUN
ejpam-5978	29	22	and	and	CCONJ
ejpam-5978	29	23	is	be	AUX
ejpam-5978	29	24	denoted	denote	VERB
ejpam-5978	29	25	by	by	ADP
ejpam-5978	29	26	km	km	PROPN
ejpam-5978	29	27	,	,	PUNCT
ejpam-5978	29	28	n	n	PRON
ejpam-5978	29	29	where	where	SCONJ
ejpam-5978	29	30	m	m	VERB
ejpam-5978	29	31	and	and	CCONJ
ejpam-5978	29	32	n	n	PRON
ejpam-5978	29	33	are	be	AUX
ejpam-5978	29	34	the	the	DET
ejpam-5978	29	35	order	order	NOUN
ejpam-5978	29	36	of	of	ADP
ejpam-5978	29	37	a	a	PRON
ejpam-5978	29	38	and	and	CCONJ
ejpam-5978	29	39	b	b	NOUN
ejpam-5978	29	40	,	,	PUNCT
ejpam-5978	29	41	respectively	respectively	ADV
ejpam-5978	29	42	.	.	PUNCT
ejpam-5978	30	1	the	the	DET
ejpam-5978	30	2	complete	complete	ADJ
ejpam-5978	30	3	bipartite	bipartite	PROPN
ejpam-5978	30	4	graph	graph	NOUN
ejpam-5978	30	5	k1,n	k1,n	PROPN
ejpam-5978	30	6	of	of	ADP
ejpam-5978	30	7	order	order	NOUN
ejpam-5978	30	8	n	n	NOUN
ejpam-5978	30	9	+	+	CCONJ
ejpam-5978	30	10	1	1	NUM
ejpam-5978	30	11	is	be	AUX
ejpam-5978	30	12	called	call	VERB
ejpam-5978	30	13	a	a	DET
ejpam-5978	30	14	star	star	NOUN
ejpam-5978	30	15	graph	graph	NOUN
ejpam-5978	30	16	.	.	PUNCT
ejpam-5978	31	1	a	a	DET
ejpam-5978	31	2	graph	graph	NOUN
ejpam-5978	31	3	in	in	ADP
ejpam-5978	31	4	which	which	PRON
ejpam-5978	31	5	each	each	DET
ejpam-5978	31	6	pair	pair	NOUN
ejpam-5978	31	7	of	of	ADP
ejpam-5978	31	8	distinct	distinct	ADJ
ejpam-5978	31	9	vertices	vertex	NOUN
ejpam-5978	31	10	are	be	AUX
ejpam-5978	31	11	adjacent	adjacent	ADJ
ejpam-5978	31	12	is	be	AUX
ejpam-5978	31	13	called	call	VERB
ejpam-5978	31	14	a	a	DET
ejpam-5978	31	15	complete	complete	ADJ
ejpam-5978	31	16	graph	graph	NOUN
ejpam-5978	31	17	and	and	CCONJ
ejpam-5978	31	18	denoted	denote	VERB
ejpam-5978	31	19	by	by	ADP
ejpam-5978	31	20	kn	kn	PROPN
ejpam-5978	31	21	where	where	SCONJ
ejpam-5978	31	22	n	n	PROPN
ejpam-5978	31	23	is	be	AUX
ejpam-5978	31	24	the	the	DET
ejpam-5978	31	25	number	number	NOUN
ejpam-5978	31	26	of	of	ADP
ejpam-5978	31	27	vertices	vertex	NOUN
ejpam-5978	31	28	.	.	PUNCT
ejpam-5978	32	1	if	if	SCONJ
ejpam-5978	32	2	v	v	NUM
ejpam-5978	32	3	∈	∈	PROPN
ejpam-5978	32	4	v	v	NOUN
ejpam-5978	32	5	(	(	PUNCT
ejpam-5978	32	6	g	g	NOUN
ejpam-5978	32	7	)	)	PUNCT
ejpam-5978	32	8	,	,	PUNCT
ejpam-5978	32	9	the	the	DET
ejpam-5978	32	10	open	open	ADJ
ejpam-5978	32	11	neighborhood	neighborhood	NOUN
ejpam-5978	32	12	or	or	CCONJ
ejpam-5978	32	13	simply	simply	ADV
ejpam-5978	32	14	neighborhood	neighborhood	NOUN
ejpam-5978	32	15	of	of	ADP
ejpam-5978	32	16	v	v	NOUN
ejpam-5978	32	17	in	in	ADP
ejpam-5978	32	18	g	g	PROPN
ejpam-5978	32	19	is	be	AUX
ejpam-5978	32	20	the	the	DET
ejpam-5978	32	21	set	set	NOUN
ejpam-5978	32	22	ng(v	ng(v	PUNCT
ejpam-5978	32	23	)	)	PUNCT
ejpam-5978	32	24	=	=	SYM
ejpam-5978	33	1	{	{	PUNCT
ejpam-5978	33	2	u	u	NOUN
ejpam-5978	33	3	∈	∈	PROPN
ejpam-5978	33	4	v	v	NOUN
ejpam-5978	33	5	(	(	PUNCT
ejpam-5978	33	6	g	g	NOUN
ejpam-5978	33	7	)	)	PUNCT
ejpam-5978	33	8	:	:	PUNCT
ejpam-5978	33	9	uv	uv	PROPN
ejpam-5978	33	10	∈	∈	PROPN
ejpam-5978	33	11	e(g	e(g	PROPN
ejpam-5978	33	12	)	)	PUNCT
ejpam-5978	33	13	}	}	PUNCT
ejpam-5978	33	14	.	.	PUNCT
ejpam-5978	34	1	for	for	ADP
ejpam-5978	34	2	the	the	DET
ejpam-5978	34	3	subset	subset	NOUN
ejpam-5978	34	4	s	s	PROPN
ejpam-5978	34	5	of	of	ADP
ejpam-5978	34	6	v	v	NOUN
ejpam-5978	34	7	(	(	PUNCT
ejpam-5978	34	8	g	g	NOUN
ejpam-5978	34	9	)	)	PUNCT
ejpam-5978	34	10	,	,	PUNCT
ejpam-5978	34	11	the	the	DET
ejpam-5978	34	12	neighborhood	neighborhood	NOUN
ejpam-5978	34	13	system	system	NOUN
ejpam-5978	34	14	of	of	ADP
ejpam-5978	34	15	s	s	PRON
ejpam-5978	34	16	in	in	ADP
ejpam-5978	34	17	g	g	PROPN
ejpam-5978	34	18	is	be	AUX
ejpam-5978	34	19	the	the	DET
ejpam-5978	34	20	set	set	NOUN
ejpam-5978	34	21	ng(s	ng(s	NOUN
ejpam-5978	34	22	)	)	PUNCT
ejpam-5978	34	23	=	=	SYM
ejpam-5978	34	24	(	(	PUNCT
ejpam-5978	34	25	⋃	⋃	ADP
ejpam-5978	34	26	s∈s	s∈s	NOUN
ejpam-5978	34	27	ng(s	ng(s	NOUN
ejpam-5978	34	28	)	)	PUNCT
ejpam-5978	34	29	)	)	PUNCT
ejpam-5978	35	1	\s	\s	NOUN
ejpam-5978	35	2	.	.	PUNCT
ejpam-5978	36	1	the	the	DET
ejpam-5978	36	2	independent	independent	ADJ
ejpam-5978	36	3	neighborhood	neighborhood	NOUN
ejpam-5978	36	4	system	system	NOUN
ejpam-5978	36	5	of	of	ADP
ejpam-5978	36	6	a	a	DET
ejpam-5978	36	7	subset	subset	NOUN
ejpam-5978	36	8	s	s	NOUN
ejpam-5978	36	9	of	of	ADP
ejpam-5978	36	10	v	v	NOUN
ejpam-5978	36	11	(	(	PUNCT
ejpam-5978	36	12	g	g	NOUN
ejpam-5978	36	13	)	)	PUNCT
ejpam-5978	36	14	is	be	AUX
ejpam-5978	36	15	a	a	DET
ejpam-5978	36	16	subset	subset	NOUN
ejpam-5978	36	17	of	of	ADP
ejpam-5978	36	18	the	the	DET
ejpam-5978	36	19	neighborhood	neighborhood	NOUN
ejpam-5978	36	20	system	system	NOUN
ejpam-5978	36	21	of	of	ADP
ejpam-5978	36	22	s	s	PRON
ejpam-5978	36	23	in	in	ADP
ejpam-5978	36	24	v	v	NOUN
ejpam-5978	36	25	(	(	PUNCT
ejpam-5978	36	26	g	g	NOUN
ejpam-5978	36	27	)	)	PUNCT
ejpam-5978	36	28	which	which	PRON
ejpam-5978	36	29	is	be	AUX
ejpam-5978	36	30	independent	independent	ADJ
ejpam-5978	36	31	.	.	PUNCT
ejpam-5978	37	1	if	if	SCONJ
ejpam-5978	37	2	the	the	DET
ejpam-5978	37	3	independent	independent	ADJ
ejpam-5978	37	4	neighborhood	neighborhood	NOUN
ejpam-5978	37	5	system	system	NOUN
ejpam-5978	37	6	of	of	ADP
ejpam-5978	37	7	a	a	DET
ejpam-5978	37	8	subset	subset	NOUN
ejpam-5978	37	9	s	s	NOUN
ejpam-5978	37	10	of	of	ADP
ejpam-5978	37	11	v	v	NOUN
ejpam-5978	37	12	(	(	PUNCT
ejpam-5978	37	13	g	g	NOUN
ejpam-5978	37	14	)	)	PUNCT
ejpam-5978	37	15	is	be	AUX
ejpam-5978	37	16	maximum	maximum	ADJ
ejpam-5978	37	17	,	,	PUNCT
ejpam-5978	37	18	then	then	ADV
ejpam-5978	37	19	we	we	PRON
ejpam-5978	37	20	say	say	VERB
ejpam-5978	37	21	that	that	SCONJ
ejpam-5978	37	22	it	it	PRON
ejpam-5978	37	23	is	be	AUX
ejpam-5978	37	24	the	the	DET
ejpam-5978	37	25	maximum	maximum	ADJ
ejpam-5978	37	26	independent	independent	ADJ
ejpam-5978	37	27	neighborhood	neighborhood	NOUN
ejpam-5978	37	28	system	system	NOUN
ejpam-5978	37	29	of	of	ADP
ejpam-5978	37	30	s	s	PROPN
ejpam-5978	37	31	,	,	PUNCT
ejpam-5978	37	32	denoted	denote	VERB
ejpam-5978	37	33	by	by	ADP
ejpam-5978	37	34	γin	γin	NOUN
ejpam-5978	37	35	-	-	PUNCT
ejpam-5978	37	36	sets	set	NOUN
ejpam-5978	37	37	.	.	PUNCT
ejpam-5978	38	1	given	give	VERB
ejpam-5978	38	2	a	a	DET
ejpam-5978	38	3	connected	connected	ADJ
ejpam-5978	38	4	graph	graph	NOUN
ejpam-5978	38	5	g	g	NOUN
ejpam-5978	38	6	and	and	CCONJ
ejpam-5978	38	7	vertices	vertice	VERB
ejpam-5978	38	8	u	u	NOUN
ejpam-5978	38	9	,	,	PUNCT
ejpam-5978	38	10	v	v	NOUN
ejpam-5978	38	11	∈	∈	PROPN
ejpam-5978	38	12	v	v	NOUN
ejpam-5978	38	13	(	(	PUNCT
ejpam-5978	38	14	g	g	NOUN
ejpam-5978	38	15	)	)	PUNCT
ejpam-5978	38	16	,	,	PUNCT
ejpam-5978	38	17	the	the	DET
ejpam-5978	38	18	distance	distance	NOUN
ejpam-5978	38	19	dg(u	dg(u	NOUN
ejpam-5978	38	20	,	,	PUNCT
ejpam-5978	38	21	v	v	NOUN
ejpam-5978	38	22	)	)	PUNCT
ejpam-5978	38	23	from	from	ADP
ejpam-5978	38	24	a	a	DET
ejpam-5978	38	25	vertex	vertex	NOUN
ejpam-5978	38	26	u	u	NOUN
ejpam-5978	38	27	to	to	PART
ejpam-5978	38	28	vertex	vertex	NOUN
ejpam-5978	38	29	v	v	NOUN
ejpam-5978	38	30	is	be	AUX
ejpam-5978	38	31	the	the	DET
ejpam-5978	38	32	smallest	small	ADJ
ejpam-5978	38	33	length	length	NOUN
ejpam-5978	38	34	of	of	ADP
ejpam-5978	38	35	a	a	DET
ejpam-5978	38	36	u−v	u−v	X
ejpam-5978	38	37	path	path	NOUN
ejpam-5978	38	38	in	in	ADP
ejpam-5978	38	39	g.	g.	PROPN
ejpam-5978	38	40	a	a	DET
ejpam-5978	38	41	u−	u−	PROPN
ejpam-5978	38	42	v	v	ADP
ejpam-5978	38	43	path	path	NOUN
ejpam-5978	38	44	of	of	ADP
ejpam-5978	38	45	length	length	NOUN
ejpam-5978	38	46	dg(u	dg(u	PROPN
ejpam-5978	38	47	,	,	PUNCT
ejpam-5978	38	48	v	v	NOUN
ejpam-5978	38	49	)	)	PUNCT
ejpam-5978	38	50	is	be	AUX
ejpam-5978	38	51	called	call	VERB
ejpam-5978	38	52	a	a	DET
ejpam-5978	38	53	u−	u−	PROPN
ejpam-5978	38	54	v	v	NOUN
ejpam-5978	38	55	geodesic	geodesic	NOUN
ejpam-5978	38	56	.	.	PUNCT
ejpam-5978	39	1	the	the	DET
ejpam-5978	39	2	geodesic	geodesic	ADJ
ejpam-5978	39	3	closure	closure	NOUN
ejpam-5978	39	4	of	of	ADP
ejpam-5978	39	5	{	{	PUNCT
ejpam-5978	39	6	u	u	NOUN
ejpam-5978	39	7	,	,	PUNCT
ejpam-5978	39	8	v	v	NOUN
ejpam-5978	39	9	}	}	PUNCT
ejpam-5978	39	10	is	be	AUX
ejpam-5978	39	11	the	the	DET
ejpam-5978	39	12	set	set	NOUN
ejpam-5978	39	13	consists	consist	VERB
ejpam-5978	39	14	of	of	ADP
ejpam-5978	39	15	all	all	DET
ejpam-5978	39	16	vertices	vertex	NOUN
ejpam-5978	39	17	lies	lie	VERB
ejpam-5978	39	18	in	in	ADP
ejpam-5978	39	19	any	any	DET
ejpam-5978	39	20	u−v	u−v	PUNCT
ejpam-5978	39	21	geodesic	geodesic	NOUN
ejpam-5978	39	22	including	include	VERB
ejpam-5978	39	23	u	u	NOUN
ejpam-5978	39	24	and	and	CCONJ
ejpam-5978	39	25	v	v	NOUN
ejpam-5978	39	26	and	and	CCONJ
ejpam-5978	39	27	is	be	AUX
ejpam-5978	39	28	e.j	e.j	PROPN
ejpam-5978	39	29	.	.	PROPN
ejpam-5978	39	30	aguilon	aguilon	PROPN
ejpam-5978	39	31	,	,	PUNCT
ejpam-5978	39	32	s.	s.	PROPN
ejpam-5978	39	33	dagondon	dagondon	PROPN
ejpam-5978	39	34	,	,	PUNCT
ejpam-5978	39	35	r.	r.	PROPN
ejpam-5978	39	36	artes	artes	PROPN
ejpam-5978	39	37	/	/	SYM
ejpam-5978	39	38	eur	eur	PROPN
ejpam-5978	39	39	.	.	PUNCT
ejpam-5978	40	1	j.	j.	PROPN
ejpam-5978	40	2	pure	pure	PROPN
ejpam-5978	40	3	appl	appl	PROPN
ejpam-5978	40	4	.	.	PROPN
ejpam-5978	40	5	math	math	PROPN
ejpam-5978	40	6	,	,	PUNCT
ejpam-5978	40	7	18	18	NUM
ejpam-5978	40	8	(	(	PUNCT
ejpam-5978	40	9	2	2	NUM
ejpam-5978	40	10	)	)	PUNCT
ejpam-5978	40	11	(	(	PUNCT
ejpam-5978	40	12	2025	2025	NUM
ejpam-5978	40	13	)	)	PUNCT
ejpam-5978	40	14	,	,	PUNCT
ejpam-5978	40	15	5978	5978	NUM
ejpam-5978	40	16	3	3	NUM
ejpam-5978	40	17	of	of	ADP
ejpam-5978	40	18	18	18	NUM
ejpam-5978	40	19	denoted	denote	VERB
ejpam-5978	40	20	by	by	ADP
ejpam-5978	40	21	ig[u	ig[u	PROPN
ejpam-5978	40	22	,	,	PUNCT
ejpam-5978	40	23	v	v	NOUN
ejpam-5978	40	24	]	]	PUNCT
ejpam-5978	40	25	.	.	PUNCT
ejpam-5978	41	1	in	in	ADP
ejpam-5978	41	2	other	other	ADJ
ejpam-5978	41	3	words	word	NOUN
ejpam-5978	41	4	,	,	PUNCT
ejpam-5978	41	5	ig[u	ig[u	PROPN
ejpam-5978	41	6	,	,	PUNCT
ejpam-5978	41	7	v	v	NOUN
ejpam-5978	41	8	]	]	X
ejpam-5978	41	9	=	=	SYM
ejpam-5978	41	10	{	{	PUNCT
ejpam-5978	41	11	u	u	NOUN
ejpam-5978	41	12	,	,	PUNCT
ejpam-5978	41	13	v	v	NOUN
ejpam-5978	41	14	}	}	PUNCT
ejpam-5978	41	15	∪	∪	X
ejpam-5978	41	16	{	{	PUNCT
ejpam-5978	41	17	x	x	NOUN
ejpam-5978	41	18	:	:	PUNCT
ejpam-5978	41	19	x	x	X
ejpam-5978	41	20	lies	lie	VERB
ejpam-5978	41	21	in	in	ADP
ejpam-5978	41	22	u−	u−	PROPN
ejpam-5978	41	23	v	v	ADJ
ejpam-5978	41	24	geodesic	geodesic	NOUN
ejpam-5978	41	25	in	in	ADP
ejpam-5978	41	26	g	g	NOUN
ejpam-5978	41	27	}	}	PUNCT
ejpam-5978	41	28	.	.	PUNCT
ejpam-5978	42	1	the	the	DET
ejpam-5978	42	2	geodesic	geodesic	ADJ
ejpam-5978	42	3	closure	closure	NOUN
ejpam-5978	42	4	of	of	ADP
ejpam-5978	42	5	a	a	DET
ejpam-5978	42	6	subset	subset	NOUN
ejpam-5978	42	7	s	s	NOUN
ejpam-5978	42	8	of	of	ADP
ejpam-5978	42	9	v	v	NOUN
ejpam-5978	42	10	(	(	PUNCT
ejpam-5978	42	11	g	g	NOUN
ejpam-5978	42	12	)	)	PUNCT
ejpam-5978	42	13	is	be	AUX
ejpam-5978	42	14	the	the	DET
ejpam-5978	42	15	set	set	VERB
ejpam-5978	42	16	ig[s	ig[	NOUN
ejpam-5978	42	17	]	]	X
ejpam-5978	42	18	=	=	SYM
ejpam-5978	42	19	⋃	⋃	NOUN
ejpam-5978	42	20	u	u	NOUN
ejpam-5978	42	21	,	,	PUNCT
ejpam-5978	42	22	v∈s	v∈s	ADJ
ejpam-5978	42	23	ig[u	ig[u	PROPN
ejpam-5978	42	24	,	,	PUNCT
ejpam-5978	42	25	v	v	NOUN
ejpam-5978	42	26	]	]	PUNCT
ejpam-5978	42	27	.	.	PUNCT
ejpam-5978	43	1	a	a	DET
ejpam-5978	43	2	subset	subset	NOUN
ejpam-5978	43	3	s	s	X
ejpam-5978	43	4	of	of	ADP
ejpam-5978	43	5	v	v	NOUN
ejpam-5978	43	6	(	(	PUNCT
ejpam-5978	43	7	g	g	NOUN
ejpam-5978	43	8	)	)	PUNCT
ejpam-5978	43	9	is	be	AUX
ejpam-5978	43	10	convex	convex	ADJ
ejpam-5978	43	11	if	if	SCONJ
ejpam-5978	43	12	for	for	ADP
ejpam-5978	43	13	every	every	DET
ejpam-5978	43	14	u	u	NOUN
ejpam-5978	43	15	,	,	PUNCT
ejpam-5978	43	16	v	v	ADP
ejpam-5978	43	17	∈	∈	PROPN
ejpam-5978	43	18	s	s	NOUN
ejpam-5978	43	19	,	,	PUNCT
ejpam-5978	43	20	the	the	DET
ejpam-5978	43	21	vertex	vertex	NOUN
ejpam-5978	43	22	-	-	PUNCT
ejpam-5978	43	23	set	set	NOUN
ejpam-5978	43	24	of	of	ADP
ejpam-5978	43	25	every	every	DET
ejpam-5978	43	26	u−	u−	PROPN
ejpam-5978	43	27	v	v	PRON
ejpam-5978	43	28	geodesic	geodesic	NOUN
ejpam-5978	43	29	is	be	AUX
ejpam-5978	43	30	contained	contain	VERB
ejpam-5978	43	31	entirely	entirely	ADV
ejpam-5978	43	32	in	in	ADP
ejpam-5978	43	33	s.	s.	PROPN
ejpam-5978	43	34	a	a	DET
ejpam-5978	43	35	convex	convex	PROPN
ejpam-5978	43	36	subset	subset	NOUN
ejpam-5978	43	37	of	of	ADP
ejpam-5978	43	38	cardinality	cardinality	NOUN
ejpam-5978	43	39	i	i	PRON
ejpam-5978	43	40	is	be	AUX
ejpam-5978	43	41	called	call	VERB
ejpam-5978	43	42	i	i	PRON
ejpam-5978	43	43	−	−	PROPN
ejpam-5978	43	44	convex	convex	PROPN
ejpam-5978	43	45	.	.	PUNCT
ejpam-5978	44	1	a	a	DET
ejpam-5978	44	2	subgraph	subgraph	NOUN
ejpam-5978	44	3	h	h	NOUN
ejpam-5978	44	4	of	of	ADP
ejpam-5978	44	5	g	g	PROPN
ejpam-5978	44	6	induced	induce	VERB
ejpam-5978	44	7	by	by	ADP
ejpam-5978	44	8	a	a	DET
ejpam-5978	44	9	convex	convex	NOUN
ejpam-5978	44	10	subset	subset	NOUN
ejpam-5978	44	11	of	of	ADP
ejpam-5978	44	12	v	v	NOUN
ejpam-5978	44	13	(	(	PUNCT
ejpam-5978	44	14	g	g	NOUN
ejpam-5978	44	15	)	)	PUNCT
ejpam-5978	44	16	is	be	AUX
ejpam-5978	44	17	called	call	VERB
ejpam-5978	44	18	a	a	DET
ejpam-5978	44	19	convex	convex	NOUN
ejpam-5978	44	20	subgraph	subgraph	NOUN
ejpam-5978	44	21	.	.	PUNCT
ejpam-5978	45	1	the	the	DET
ejpam-5978	45	2	convex	convex	ADJ
ejpam-5978	45	3	independent	independent	ADJ
ejpam-5978	45	4	neighborhood	neighborhood	NOUN
ejpam-5978	45	5	polynomial	polynomial	NOUN
ejpam-5978	45	6	of	of	ADP
ejpam-5978	45	7	a	a	DET
ejpam-5978	45	8	graph	graph	NOUN
ejpam-5978	45	9	g	g	NOUN
ejpam-5978	45	10	of	of	ADP
ejpam-5978	45	11	order	order	NOUN
ejpam-5978	45	12	n	n	CCONJ
ejpam-5978	45	13	,	,	PUNCT
ejpam-5978	45	14	denoted	denote	VERB
ejpam-5978	45	15	by	by	ADP
ejpam-5978	45	16	γcin(g;x	γcin(g;x	PROPN
ejpam-5978	45	17	,	,	PUNCT
ejpam-5978	45	18	y	y	NOUN
ejpam-5978	45	19	)	)	PUNCT
ejpam-5978	45	20	in	in	ADP
ejpam-5978	45	21	x	x	SYM
ejpam-5978	45	22	and	and	CCONJ
ejpam-5978	45	23	y	y	PROPN
ejpam-5978	45	24	indeterminates	indeterminate	NOUN
ejpam-5978	45	25	,	,	PUNCT
ejpam-5978	45	26	is	be	AUX
ejpam-5978	45	27	given	give	VERB
ejpam-5978	45	28	by	by	ADP
ejpam-5978	45	29	γcin(g;x	γcin(g;x	PROPN
ejpam-5978	45	30	,	,	PUNCT
ejpam-5978	45	31	y	y	NOUN
ejpam-5978	45	32	)	)	PUNCT
ejpam-5978	45	33	=	=	PUNCT
ejpam-5978	45	34	n−i∑	n−i∑	DET
ejpam-5978	45	35	j=0	j=0	PROPN
ejpam-5978	45	36	n∑	n∑	PROPN
ejpam-5978	45	37	i=1	i=1	PROPN
ejpam-5978	45	38	cij(g)xiyj	cij(g)xiyj	NOUN
ejpam-5978	45	39	,	,	PUNCT
ejpam-5978	45	40	where	where	SCONJ
ejpam-5978	45	41	cij(g	cij(g	NOUN
ejpam-5978	45	42	)	)	PUNCT
ejpam-5978	45	43	is	be	AUX
ejpam-5978	45	44	the	the	DET
ejpam-5978	45	45	number	number	NOUN
ejpam-5978	45	46	of	of	ADP
ejpam-5978	45	47	i	i	NOUN
ejpam-5978	45	48	-	-	PUNCT
ejpam-5978	45	49	convex	convex	ADJ
ejpam-5978	45	50	subsets	subset	NOUN
ejpam-5978	45	51	of	of	ADP
ejpam-5978	45	52	g	g	NOUN
ejpam-5978	45	53	with	with	ADP
ejpam-5978	45	54	maximum	maximum	ADJ
ejpam-5978	45	55	independent	independent	ADJ
ejpam-5978	45	56	neighborhood	neighborhood	NOUN
ejpam-5978	45	57	system	system	NOUN
ejpam-5978	45	58	of	of	ADP
ejpam-5978	45	59	cardinality	cardinality	NOUN
ejpam-5978	45	60	equal	equal	ADJ
ejpam-5978	45	61	to	to	ADP
ejpam-5978	45	62	j.	j.	PROPN
ejpam-5978	45	63	the	the	DET
ejpam-5978	45	64	degree	degree	NOUN
ejpam-5978	45	65	of	of	ADP
ejpam-5978	45	66	an	an	DET
ejpam-5978	45	67	algebraic	algebraic	ADJ
ejpam-5978	45	68	polynomial	polynomial	NOUN
ejpam-5978	45	69	is	be	AUX
ejpam-5978	45	70	equal	equal	ADJ
ejpam-5978	45	71	to	to	ADP
ejpam-5978	45	72	the	the	DET
ejpam-5978	45	73	degree	degree	NOUN
ejpam-5978	45	74	of	of	ADP
ejpam-5978	45	75	the	the	DET
ejpam-5978	45	76	term	term	NOUN
ejpam-5978	45	77	that	that	PRON
ejpam-5978	45	78	has	have	VERB
ejpam-5978	45	79	the	the	DET
ejpam-5978	45	80	highest	high	ADJ
ejpam-5978	45	81	exponent	exponent	NOUN
ejpam-5978	45	82	.	.	PUNCT
ejpam-5978	46	1	if	if	SCONJ
ejpam-5978	46	2	,	,	PUNCT
ejpam-5978	46	3	in	in	ADP
ejpam-5978	46	4	additon	additon	PROPN
ejpam-5978	46	5	,	,	PUNCT
ejpam-5978	46	6	the	the	DET
ejpam-5978	46	7	polynomial	polynomial	NOUN
ejpam-5978	46	8	is	be	AUX
ejpam-5978	46	9	defined	define	VERB
ejpam-5978	46	10	by	by	ADP
ejpam-5978	46	11	several	several	ADJ
ejpam-5978	46	12	variables	variable	NOUN
ejpam-5978	46	13	then	then	ADV
ejpam-5978	46	14	two	two	NUM
ejpam-5978	46	15	or	or	CCONJ
ejpam-5978	46	16	more	more	ADJ
ejpam-5978	46	17	variables	variable	NOUN
ejpam-5978	46	18	are	be	AUX
ejpam-5978	46	19	in	in	ADP
ejpam-5978	46	20	a	a	DET
ejpam-5978	46	21	term	term	NOUN
ejpam-5978	46	22	as	as	ADP
ejpam-5978	46	23	factors	factor	NOUN
ejpam-5978	46	24	,	,	PUNCT
ejpam-5978	46	25	wherein	wherein	SCONJ
ejpam-5978	46	26	the	the	DET
ejpam-5978	46	27	degree	degree	NOUN
ejpam-5978	46	28	of	of	ADP
ejpam-5978	46	29	the	the	DET
ejpam-5978	46	30	term	term	NOUN
ejpam-5978	46	31	is	be	AUX
ejpam-5978	46	32	the	the	DET
ejpam-5978	46	33	sum	sum	NOUN
ejpam-5978	46	34	of	of	ADP
ejpam-5978	46	35	the	the	DET
ejpam-5978	46	36	exponents	exponent	NOUN
ejpam-5978	46	37	of	of	ADP
ejpam-5978	46	38	the	the	DET
ejpam-5978	46	39	variables	variable	NOUN
ejpam-5978	46	40	;	;	PUNCT
ejpam-5978	46	41	and	and	CCONJ
ejpam-5978	46	42	the	the	DET
ejpam-5978	46	43	degree	degree	NOUN
ejpam-5978	46	44	of	of	ADP
ejpam-5978	46	45	the	the	DET
ejpam-5978	46	46	polynomial	polynomial	NOUN
ejpam-5978	46	47	will	will	AUX
ejpam-5978	46	48	be	be	AUX
ejpam-5978	46	49	determined	determine	VERB
ejpam-5978	46	50	by	by	ADP
ejpam-5978	46	51	the	the	DET
ejpam-5978	46	52	highest	high	ADJ
ejpam-5978	46	53	degree	degree	NOUN
ejpam-5978	46	54	in	in	ADP
ejpam-5978	46	55	their	their	PRON
ejpam-5978	46	56	terms	term	NOUN
ejpam-5978	46	57	[	[	X
ejpam-5978	46	58	10	10	NUM
ejpam-5978	46	59	]	]	PUNCT
ejpam-5978	46	60	.	.	PUNCT
ejpam-5978	47	1	3	3	X
ejpam-5978	47	2	.	.	X
ejpam-5978	47	3	preliminary	preliminary	ADJ
ejpam-5978	47	4	results	result	NOUN
ejpam-5978	47	5	this	this	DET
ejpam-5978	47	6	section	section	NOUN
ejpam-5978	47	7	illustrates	illustrate	VERB
ejpam-5978	47	8	the	the	DET
ejpam-5978	47	9	definition	definition	NOUN
ejpam-5978	47	10	of	of	ADP
ejpam-5978	47	11	convex	convex	ADJ
ejpam-5978	47	12	independent	independent	ADJ
ejpam-5978	47	13	neighborhood	neighborhood	NOUN
ejpam-5978	47	14	polynomial	polynomial	NOUN
ejpam-5978	47	15	of	of	ADP
ejpam-5978	47	16	a	a	DET
ejpam-5978	47	17	graph	graph	NOUN
ejpam-5978	47	18	.	.	PUNCT
ejpam-5978	48	1	this	this	DET
ejpam-5978	48	2	illustration	illustration	NOUN
ejpam-5978	48	3	form	form	VERB
ejpam-5978	48	4	the	the	DET
ejpam-5978	48	5	basis	basis	NOUN
ejpam-5978	48	6	for	for	ADP
ejpam-5978	48	7	the	the	DET
ejpam-5978	48	8	more	more	ADV
ejpam-5978	48	9	comprehensive	comprehensive	ADJ
ejpam-5978	48	10	analyses	analysis	NOUN
ejpam-5978	48	11	and	and	CCONJ
ejpam-5978	48	12	conclusions	conclusion	NOUN
ejpam-5978	48	13	for	for	ADP
ejpam-5978	48	14	the	the	DET
ejpam-5978	48	15	following	follow	VERB
ejpam-5978	48	16	sections	section	NOUN
ejpam-5978	48	17	.	.	PUNCT
ejpam-5978	49	1	consider	consider	VERB
ejpam-5978	49	2	the	the	DET
ejpam-5978	49	3	graph	graph	NOUN
ejpam-5978	49	4	g	g	NOUN
ejpam-5978	49	5	in	in	ADP
ejpam-5978	49	6	figure	figure	NOUN
ejpam-5978	49	7	1	1	NUM
ejpam-5978	49	8	.	.	PUNCT
ejpam-5978	49	9	v1	v1	PROPN
ejpam-5978	49	10	v2	v2	PROPN
ejpam-5978	49	11	v3	v3	PROPN
ejpam-5978	49	12	v5	v5	PROPN
ejpam-5978	49	13	v4	v4	PROPN
ejpam-5978	49	14	figure	figure	NOUN
ejpam-5978	49	15	1	1	NUM
ejpam-5978	49	16	:	:	PUNCT
ejpam-5978	49	17	a	a	DET
ejpam-5978	49	18	graph	graph	NOUN
ejpam-5978	49	19	g	g	NOUN
ejpam-5978	49	20	of	of	ADP
ejpam-5978	49	21	order	order	NOUN
ejpam-5978	49	22	5	5	NUM
ejpam-5978	49	23	and	and	CCONJ
ejpam-5978	49	24	size	size	NOUN
ejpam-5978	49	25	5	5	NUM
ejpam-5978	49	26	the	the	DET
ejpam-5978	49	27	convex	convex	ADJ
ejpam-5978	49	28	subsets	subset	NOUN
ejpam-5978	49	29	of	of	ADP
ejpam-5978	49	30	v	v	NOUN
ejpam-5978	49	31	(	(	PUNCT
ejpam-5978	49	32	g	g	NOUN
ejpam-5978	49	33	)	)	PUNCT
ejpam-5978	49	34	with	with	ADP
ejpam-5978	49	35	corresponding	correspond	VERB
ejpam-5978	49	36	maximum	maximum	ADJ
ejpam-5978	49	37	independent	independent	ADJ
ejpam-5978	49	38	neighborhood	neighborhood	NOUN
ejpam-5978	49	39	systems	system	NOUN
ejpam-5978	49	40	(	(	PUNCT
ejpam-5978	49	41	γin	γin	NOUN
ejpam-5978	49	42	-	-	PUNCT
ejpam-5978	49	43	sets	set	NOUN
ejpam-5978	49	44	)	)	PUNCT
ejpam-5978	49	45	are	be	AUX
ejpam-5978	49	46	enumerated	enumerate	VERB
ejpam-5978	49	47	in	in	ADP
ejpam-5978	49	48	the	the	DET
ejpam-5978	49	49	following	follow	VERB
ejpam-5978	49	50	tables	table	NOUN
ejpam-5978	49	51	1	1	NUM
ejpam-5978	49	52	,	,	PUNCT
ejpam-5978	49	53	2	2	NUM
ejpam-5978	49	54	and	and	CCONJ
ejpam-5978	49	55	3	3	NUM
ejpam-5978	49	56	:	:	SYM
ejpam-5978	49	57	1	1	NUM
ejpam-5978	49	58	-	-	PUNCT
ejpam-5978	49	59	convex	convex	VERB
ejpam-5978	49	60	γin	γin	NOUN
ejpam-5978	49	61	-	-	PUNCT
ejpam-5978	49	62	sets	set	NOUN
ejpam-5978	49	63	{	{	PUNCT
ejpam-5978	49	64	v1	v1	NOUN
ejpam-5978	49	65	}	}	PUNCT
ejpam-5978	49	66	{	{	PUNCT
ejpam-5978	49	67	v2	v2	NOUN
ejpam-5978	49	68	}	}	PUNCT
ejpam-5978	49	69	{	{	PUNCT
ejpam-5978	49	70	v2	v2	NOUN
ejpam-5978	49	71	}	}	PUNCT
ejpam-5978	49	72	{	{	PUNCT
ejpam-5978	49	73	v1	v1	NOUN
ejpam-5978	49	74	,	,	PUNCT
ejpam-5978	49	75	v3	v3	PROPN
ejpam-5978	49	76	}	}	PUNCT
ejpam-5978	49	77	and	and	CCONJ
ejpam-5978	49	78	{	{	PUNCT
ejpam-5978	49	79	v1	v1	NOUN
ejpam-5978	49	80	,	,	PUNCT
ejpam-5978	49	81	v4	v4	NOUN
ejpam-5978	49	82	}	}	PUNCT
ejpam-5978	49	83	{	{	PUNCT
ejpam-5978	49	84	v3	v3	PROPN
ejpam-5978	49	85	}	}	PUNCT
ejpam-5978	49	86	{	{	PUNCT
ejpam-5978	49	87	v2	v2	PROPN
ejpam-5978	49	88	,	,	PUNCT
ejpam-5978	49	89	v5	v5	NOUN
ejpam-5978	49	90	}	}	PUNCT
ejpam-5978	49	91	and	and	CCONJ
ejpam-5978	49	92	{	{	PUNCT
ejpam-5978	49	93	v4	v4	NOUN
ejpam-5978	49	94	,	,	PUNCT
ejpam-5978	49	95	v5	v5	PROPN
ejpam-5978	49	96	}	}	PUNCT
ejpam-5978	49	97	{	{	PUNCT
ejpam-5978	49	98	v4	v4	NOUN
ejpam-5978	49	99	}	}	PUNCT
ejpam-5978	49	100	{	{	PUNCT
ejpam-5978	49	101	v2	v2	NOUN
ejpam-5978	49	102	}	}	PUNCT
ejpam-5978	49	103	and	and	CCONJ
ejpam-5978	49	104	{	{	PUNCT
ejpam-5978	49	105	v3	v3	PROPN
ejpam-5978	49	106	}	}	PUNCT
ejpam-5978	49	107	{	{	PUNCT
ejpam-5978	49	108	v5	v5	PROPN
ejpam-5978	49	109	}	}	PUNCT
ejpam-5978	49	110	{	{	PUNCT
ejpam-5978	49	111	v3	v3	PROPN
ejpam-5978	49	112	}	}	PUNCT
ejpam-5978	49	113	table	table	NOUN
ejpam-5978	49	114	1	1	NUM
ejpam-5978	49	115	:	:	SYM
ejpam-5978	49	116	1	1	NUM
ejpam-5978	49	117	-	-	PUNCT
ejpam-5978	49	118	convex	convex	NOUN
ejpam-5978	49	119	subsets	subset	NOUN
ejpam-5978	49	120	of	of	ADP
ejpam-5978	49	121	v	v	NOUN
ejpam-5978	49	122	(	(	PUNCT
ejpam-5978	49	123	g	g	NOUN
ejpam-5978	49	124	)	)	PUNCT
ejpam-5978	49	125	and	and	CCONJ
ejpam-5978	49	126	its	its	PRON
ejpam-5978	49	127	corresponding	corresponding	ADJ
ejpam-5978	49	128	γin	γin	NOUN
ejpam-5978	49	129	-	-	PUNCT
ejpam-5978	49	130	sets	set	NOUN
ejpam-5978	49	131	.	.	PUNCT
ejpam-5978	50	1	from	from	ADP
ejpam-5978	50	2	table	table	NOUN
ejpam-5978	50	3	1	1	NUM
ejpam-5978	50	4	,	,	PUNCT
ejpam-5978	50	5	observe	observe	VERB
ejpam-5978	50	6	that	that	SCONJ
ejpam-5978	50	7	there	there	PRON
ejpam-5978	50	8	are	be	VERB
ejpam-5978	50	9	3	3	NUM
ejpam-5978	50	10	1	1	NUM
ejpam-5978	50	11	-	-	PUNCT
ejpam-5978	50	12	convex	convex	NOUN
ejpam-5978	50	13	subset	subset	NOUN
ejpam-5978	50	14	of	of	ADP
ejpam-5978	50	15	v	v	NOUN
ejpam-5978	50	16	(	(	PUNCT
ejpam-5978	50	17	g	g	NOUN
ejpam-5978	50	18	)	)	PUNCT
ejpam-5978	50	19	with	with	ADP
ejpam-5978	50	20	maximum	maximum	PROPN
ejpam-5978	50	21	e.j	e.j	PROPN
ejpam-5978	50	22	.	.	PROPN
ejpam-5978	50	23	aguilon	aguilon	PROPN
ejpam-5978	50	24	,	,	PUNCT
ejpam-5978	50	25	s.	s.	PROPN
ejpam-5978	50	26	dagondon	dagondon	PROPN
ejpam-5978	50	27	,	,	PUNCT
ejpam-5978	50	28	r.	r.	PROPN
ejpam-5978	50	29	artes	artes	PROPN
ejpam-5978	50	30	/	/	SYM
ejpam-5978	50	31	eur	eur	PROPN
ejpam-5978	50	32	.	.	PUNCT
ejpam-5978	51	1	j.	j.	PROPN
ejpam-5978	51	2	pure	pure	PROPN
ejpam-5978	51	3	appl	appl	PROPN
ejpam-5978	51	4	.	.	PROPN
ejpam-5978	51	5	math	math	PROPN
ejpam-5978	51	6	,	,	PUNCT
ejpam-5978	51	7	18	18	NUM
ejpam-5978	51	8	(	(	PUNCT
ejpam-5978	51	9	2	2	NUM
ejpam-5978	51	10	)	)	PUNCT
ejpam-5978	51	11	(	(	PUNCT
ejpam-5978	51	12	2025	2025	NUM
ejpam-5978	51	13	)	)	PUNCT
ejpam-5978	51	14	,	,	PUNCT
ejpam-5978	51	15	5978	5978	NUM
ejpam-5978	51	16	4	4	NUM
ejpam-5978	51	17	of	of	ADP
ejpam-5978	51	18	18	18	NUM
ejpam-5978	51	19	independent	independent	ADJ
ejpam-5978	51	20	neighborhood	neighborhood	NOUN
ejpam-5978	51	21	systems	system	NOUN
ejpam-5978	51	22	(	(	PUNCT
ejpam-5978	51	23	γin	γin	NOUN
ejpam-5978	51	24	-	-	PUNCT
ejpam-5978	51	25	sets	set	NOUN
ejpam-5978	51	26	)	)	PUNCT
ejpam-5978	51	27	cardinality	cardinality	NOUN
ejpam-5978	51	28	equal	equal	ADJ
ejpam-5978	51	29	to	to	ADP
ejpam-5978	51	30	1	1	NUM
ejpam-5978	51	31	,	,	PUNCT
ejpam-5978	51	32	and	and	CCONJ
ejpam-5978	51	33	2	2	NUM
ejpam-5978	51	34	1	1	NUM
ejpam-5978	51	35	-	-	PUNCT
ejpam-5978	51	36	convex	convex	NOUN
ejpam-5978	51	37	subsets	subset	NOUN
ejpam-5978	51	38	of	of	ADP
ejpam-5978	51	39	v	v	NOUN
ejpam-5978	51	40	(	(	PUNCT
ejpam-5978	51	41	g	g	NOUN
ejpam-5978	51	42	)	)	PUNCT
ejpam-5978	51	43	with	with	ADP
ejpam-5978	51	44	maximum	maximum	ADJ
ejpam-5978	51	45	independent	independent	ADJ
ejpam-5978	51	46	neighborhood	neighborhood	NOUN
ejpam-5978	51	47	systems	system	NOUN
ejpam-5978	51	48	(	(	PUNCT
ejpam-5978	51	49	γin	γin	NOUN
ejpam-5978	51	50	-	-	PUNCT
ejpam-5978	51	51	sets	set	NOUN
ejpam-5978	51	52	)	)	PUNCT
ejpam-5978	51	53	cardinality	cardinality	NOUN
ejpam-5978	51	54	equal	equal	ADJ
ejpam-5978	51	55	to	to	ADP
ejpam-5978	51	56	2	2	NUM
ejpam-5978	51	57	.	.	PUNCT
ejpam-5978	52	1	this	this	PRON
ejpam-5978	52	2	contributes	contribute	VERB
ejpam-5978	52	3	to	to	ADP
ejpam-5978	52	4	the	the	DET
ejpam-5978	52	5	convex	convex	ADJ
ejpam-5978	52	6	independent	independent	ADJ
ejpam-5978	52	7	neighborhood	neighborhood	NOUN
ejpam-5978	52	8	polynomial	polynomial	NOUN
ejpam-5978	52	9	of	of	ADP
ejpam-5978	52	10	g	g	PROPN
ejpam-5978	52	11	as	as	ADP
ejpam-5978	52	12	3xy	3xy	PROPN
ejpam-5978	52	13	+	+	NOUN
ejpam-5978	52	14	2xy2	2xy2	NUM
ejpam-5978	52	15	.	.	NOUN
ejpam-5978	52	16	2	2	NUM
ejpam-5978	52	17	-	-	NUM
ejpam-5978	52	18	convex	convex	VERB
ejpam-5978	52	19	γin	γin	NOUN
ejpam-5978	52	20	-	-	PUNCT
ejpam-5978	52	21	sets	set	NOUN
ejpam-5978	52	22	{	{	PUNCT
ejpam-5978	52	23	v1	v1	NOUN
ejpam-5978	52	24	,	,	PUNCT
ejpam-5978	52	25	v2	v2	PROPN
ejpam-5978	52	26	}	}	PUNCT
ejpam-5978	52	27	{	{	PUNCT
ejpam-5978	52	28	v3	v3	PROPN
ejpam-5978	52	29	}	}	PUNCT
ejpam-5978	52	30	,	,	PUNCT
ejpam-5978	52	31	{	{	PUNCT
ejpam-5978	52	32	v4	v4	NOUN
ejpam-5978	52	33	}	}	PUNCT
ejpam-5978	52	34	{	{	PUNCT
ejpam-5978	52	35	v2	v2	PROPN
ejpam-5978	52	36	,	,	PUNCT
ejpam-5978	52	37	v3	v3	PROPN
ejpam-5978	52	38	}	}	PUNCT
ejpam-5978	52	39	{	{	PUNCT
ejpam-5978	52	40	v1	v1	NOUN
ejpam-5978	52	41	,	,	PUNCT
ejpam-5978	52	42	v4	v4	NOUN
ejpam-5978	52	43	,	,	PUNCT
ejpam-5978	52	44	v5	v5	PROPN
ejpam-5978	52	45	}	}	PUNCT
ejpam-5978	52	46	{	{	PUNCT
ejpam-5978	52	47	v2	v2	PROPN
ejpam-5978	52	48	,	,	PUNCT
ejpam-5978	52	49	v4	v4	PROPN
ejpam-5978	52	50	}	}	PUNCT
ejpam-5978	52	51	{	{	PUNCT
ejpam-5978	52	52	v1	v1	NOUN
ejpam-5978	52	53	,	,	PUNCT
ejpam-5978	52	54	v3	v3	PROPN
ejpam-5978	52	55	}	}	PUNCT
ejpam-5978	52	56	{	{	PUNCT
ejpam-5978	52	57	v3	v3	PROPN
ejpam-5978	52	58	,	,	PUNCT
ejpam-5978	52	59	v4	v4	PROPN
ejpam-5978	52	60	}	}	PUNCT
ejpam-5978	52	61	{	{	PUNCT
ejpam-5978	52	62	v2	v2	PROPN
ejpam-5978	52	63	,	,	PUNCT
ejpam-5978	52	64	v5	v5	PROPN
ejpam-5978	52	65	}	}	PUNCT
ejpam-5978	52	66	{	{	PUNCT
ejpam-5978	52	67	v3	v3	PROPN
ejpam-5978	52	68	,	,	PUNCT
ejpam-5978	52	69	v5	v5	PROPN
ejpam-5978	52	70	}	}	PUNCT
ejpam-5978	52	71	{	{	PUNCT
ejpam-5978	52	72	v2	v2	NOUN
ejpam-5978	52	73	}	}	PUNCT
ejpam-5978	52	74	,	,	PUNCT
ejpam-5978	52	75	{	{	PUNCT
ejpam-5978	52	76	v4	v4	NOUN
ejpam-5978	52	77	}	}	PUNCT
ejpam-5978	52	78	table	table	NOUN
ejpam-5978	52	79	2	2	NUM
ejpam-5978	52	80	:	:	SYM
ejpam-5978	52	81	2	2	NUM
ejpam-5978	52	82	-	-	PUNCT
ejpam-5978	52	83	convex	convex	NOUN
ejpam-5978	52	84	subsets	subset	NOUN
ejpam-5978	52	85	of	of	ADP
ejpam-5978	52	86	v	v	NOUN
ejpam-5978	52	87	(	(	PUNCT
ejpam-5978	52	88	g	g	NOUN
ejpam-5978	52	89	)	)	PUNCT
ejpam-5978	52	90	and	and	CCONJ
ejpam-5978	52	91	its	its	PRON
ejpam-5978	52	92	corresponding	corresponding	ADJ
ejpam-5978	52	93	γin	γin	NOUN
ejpam-5978	52	94	-	-	PUNCT
ejpam-5978	52	95	sets	set	NOUN
ejpam-5978	52	96	.	.	PUNCT
ejpam-5978	53	1	from	from	ADP
ejpam-5978	53	2	table	table	NOUN
ejpam-5978	53	3	2	2	NUM
ejpam-5978	53	4	,	,	PUNCT
ejpam-5978	53	5	observe	observe	VERB
ejpam-5978	53	6	that	that	SCONJ
ejpam-5978	53	7	there	there	PRON
ejpam-5978	53	8	are	be	VERB
ejpam-5978	53	9	2	2	NUM
ejpam-5978	53	10	2	2	NUM
ejpam-5978	53	11	-	-	PUNCT
ejpam-5978	53	12	convex	convex	NOUN
ejpam-5978	53	13	subsets	subset	NOUN
ejpam-5978	53	14	of	of	ADP
ejpam-5978	53	15	v	v	NOUN
ejpam-5978	53	16	(	(	PUNCT
ejpam-5978	53	17	g	g	NOUN
ejpam-5978	53	18	)	)	PUNCT
ejpam-5978	53	19	with	with	ADP
ejpam-5978	53	20	maximum	maximum	ADJ
ejpam-5978	53	21	independent	independent	ADJ
ejpam-5978	53	22	neighborhood	neighborhood	NOUN
ejpam-5978	53	23	systems	system	NOUN
ejpam-5978	53	24	(	(	PUNCT
ejpam-5978	53	25	γin	γin	NOUN
ejpam-5978	53	26	-	-	PUNCT
ejpam-5978	53	27	sets	set	NOUN
ejpam-5978	53	28	)	)	PUNCT
ejpam-5978	53	29	cardinality	cardinality	NOUN
ejpam-5978	53	30	equal	equal	ADJ
ejpam-5978	53	31	to	to	ADP
ejpam-5978	53	32	1	1	NUM
ejpam-5978	53	33	,	,	PUNCT
ejpam-5978	53	34	2	2	NUM
ejpam-5978	53	35	2	2	NUM
ejpam-5978	53	36	-	-	PUNCT
ejpam-5978	53	37	convex	convex	NOUN
ejpam-5978	53	38	subsets	subset	NOUN
ejpam-5978	53	39	of	of	ADP
ejpam-5978	53	40	v	v	NOUN
ejpam-5978	53	41	(	(	PUNCT
ejpam-5978	53	42	g	g	NOUN
ejpam-5978	53	43	)	)	PUNCT
ejpam-5978	53	44	with	with	ADP
ejpam-5978	53	45	maximum	maximum	ADJ
ejpam-5978	53	46	independent	independent	ADJ
ejpam-5978	53	47	neighborhood	neighborhood	NOUN
ejpam-5978	53	48	systems	system	NOUN
ejpam-5978	53	49	(	(	PUNCT
ejpam-5978	53	50	γin	γin	NOUN
ejpam-5978	53	51	-	-	PUNCT
ejpam-5978	53	52	sets	set	NOUN
ejpam-5978	53	53	)	)	PUNCT
ejpam-5978	53	54	cardinality	cardinality	NOUN
ejpam-5978	53	55	equal	equal	ADJ
ejpam-5978	53	56	to	to	ADP
ejpam-5978	53	57	2	2	NUM
ejpam-5978	53	58	,	,	PUNCT
ejpam-5978	53	59	and	and	CCONJ
ejpam-5978	53	60	1	1	NUM
ejpam-5978	53	61	2	2	NUM
ejpam-5978	53	62	-	-	PUNCT
ejpam-5978	53	63	convex	convex	NOUN
ejpam-5978	53	64	subset	subset	NOUN
ejpam-5978	53	65	of	of	ADP
ejpam-5978	53	66	v	v	NOUN
ejpam-5978	53	67	(	(	PUNCT
ejpam-5978	53	68	g	g	NOUN
ejpam-5978	53	69	)	)	PUNCT
ejpam-5978	53	70	with	with	ADP
ejpam-5978	53	71	maximum	maximum	ADJ
ejpam-5978	53	72	independent	independent	ADJ
ejpam-5978	53	73	neighborhood	neighborhood	NOUN
ejpam-5978	53	74	systems	system	NOUN
ejpam-5978	53	75	(	(	PUNCT
ejpam-5978	53	76	γin	γin	NOUN
ejpam-5978	53	77	-	-	PUNCT
ejpam-5978	53	78	sets	set	NOUN
ejpam-5978	53	79	)	)	PUNCT
ejpam-5978	53	80	cardinality	cardinality	NOUN
ejpam-5978	53	81	equal	equal	ADJ
ejpam-5978	53	82	to	to	ADP
ejpam-5978	53	83	3	3	NUM
ejpam-5978	53	84	.	.	PUNCT
ejpam-5978	54	1	this	this	PRON
ejpam-5978	54	2	contributes	contribute	VERB
ejpam-5978	54	3	to	to	ADP
ejpam-5978	54	4	the	the	DET
ejpam-5978	54	5	convex	convex	ADJ
ejpam-5978	54	6	independent	independent	ADJ
ejpam-5978	54	7	neighborhood	neighborhood	NOUN
ejpam-5978	54	8	polynomial	polynomial	NOUN
ejpam-5978	54	9	of	of	ADP
ejpam-5978	54	10	g	g	PROPN
ejpam-5978	54	11	as	as	ADP
ejpam-5978	54	12	2x2y	2x2y	NUM
ejpam-5978	54	13	+	+	CCONJ
ejpam-5978	54	14	2x2y2	2x2y2	NUM
ejpam-5978	54	15	+	+	X
ejpam-5978	55	1	x2y3	x2y3	X
ejpam-5978	55	2	.	.	NOUN
ejpam-5978	55	3	3	3	X
ejpam-5978	55	4	-	-	NUM
ejpam-5978	55	5	convex	convex	ADJ
ejpam-5978	55	6	γin	γin	NOUN
ejpam-5978	55	7	-	-	PUNCT
ejpam-5978	55	8	sets	set	NOUN
ejpam-5978	55	9	{	{	PUNCT
ejpam-5978	55	10	v1	v1	NOUN
ejpam-5978	55	11	,	,	PUNCT
ejpam-5978	55	12	v2	v2	PROPN
ejpam-5978	55	13	,	,	PUNCT
ejpam-5978	55	14	v3	v3	PROPN
ejpam-5978	55	15	}	}	PUNCT
ejpam-5978	55	16	{	{	PUNCT
ejpam-5978	55	17	v4	v4	NOUN
ejpam-5978	55	18	,	,	PUNCT
ejpam-5978	55	19	v5	v5	PROPN
ejpam-5978	55	20	}	}	PUNCT
ejpam-5978	55	21	{	{	PUNCT
ejpam-5978	55	22	v1	v1	NOUN
ejpam-5978	55	23	,	,	PUNCT
ejpam-5978	55	24	v2	v2	PROPN
ejpam-5978	55	25	,	,	PUNCT
ejpam-5978	55	26	v4	v4	PROPN
ejpam-5978	55	27	}	}	PUNCT
ejpam-5978	55	28	{	{	PUNCT
ejpam-5978	55	29	v3	v3	PROPN
ejpam-5978	55	30	}	}	PUNCT
ejpam-5978	55	31	{	{	PUNCT
ejpam-5978	55	32	v2	v2	PROPN
ejpam-5978	55	33	,	,	PUNCT
ejpam-5978	55	34	v3	v3	PROPN
ejpam-5978	55	35	,	,	PUNCT
ejpam-5978	55	36	v4	v4	PROPN
ejpam-5978	55	37	}	}	PUNCT
ejpam-5978	55	38	{	{	PUNCT
ejpam-5978	55	39	v1	v1	NOUN
ejpam-5978	55	40	,	,	PUNCT
ejpam-5978	55	41	v5	v5	PROPN
ejpam-5978	55	42	}	}	PUNCT
ejpam-5978	55	43	{	{	PUNCT
ejpam-5978	55	44	v2	v2	PROPN
ejpam-5978	55	45	,	,	PUNCT
ejpam-5978	55	46	v3	v3	PROPN
ejpam-5978	55	47	,	,	PUNCT
ejpam-5978	55	48	v5	v5	PROPN
ejpam-5978	55	49	}	}	PUNCT
ejpam-5978	55	50	{	{	PUNCT
ejpam-5978	55	51	v1	v1	NOUN
ejpam-5978	55	52	,	,	PUNCT
ejpam-5978	55	53	v4	v4	NOUN
ejpam-5978	55	54	}	}	PUNCT
ejpam-5978	55	55	{	{	PUNCT
ejpam-5978	55	56	v4	v4	PROPN
ejpam-5978	55	57	,	,	PUNCT
ejpam-5978	55	58	v3	v3	PROPN
ejpam-5978	55	59	,	,	PUNCT
ejpam-5978	55	60	v5	v5	PROPN
ejpam-5978	55	61	}	}	PUNCT
ejpam-5978	55	62	{	{	PUNCT
ejpam-5978	55	63	v2	v2	NOUN
ejpam-5978	55	64	}	}	PUNCT
ejpam-5978	55	65	table	table	NOUN
ejpam-5978	55	66	3	3	NUM
ejpam-5978	55	67	:	:	SYM
ejpam-5978	55	68	3	3	NUM
ejpam-5978	55	69	-	-	PUNCT
ejpam-5978	55	70	convex	convex	ADJ
ejpam-5978	55	71	subsets	subset	NOUN
ejpam-5978	55	72	of	of	ADP
ejpam-5978	55	73	v	v	NOUN
ejpam-5978	55	74	(	(	PUNCT
ejpam-5978	55	75	g	g	NOUN
ejpam-5978	55	76	)	)	PUNCT
ejpam-5978	55	77	and	and	CCONJ
ejpam-5978	55	78	its	its	PRON
ejpam-5978	55	79	corresponding	corresponding	ADJ
ejpam-5978	55	80	γin	γin	NOUN
ejpam-5978	55	81	-	-	PUNCT
ejpam-5978	55	82	sets	set	NOUN
ejpam-5978	55	83	.	.	PUNCT
ejpam-5978	56	1	from	from	ADP
ejpam-5978	56	2	table	table	NOUN
ejpam-5978	56	3	3	3	NUM
ejpam-5978	56	4	,	,	PUNCT
ejpam-5978	56	5	observe	observe	VERB
ejpam-5978	56	6	that	that	SCONJ
ejpam-5978	56	7	there	there	PRON
ejpam-5978	56	8	are	be	VERB
ejpam-5978	56	9	2	2	NUM
ejpam-5978	56	10	3	3	NUM
ejpam-5978	56	11	-	-	PUNCT
ejpam-5978	56	12	convex	convex	NOUN
ejpam-5978	56	13	subsets	subset	NOUN
ejpam-5978	56	14	of	of	ADP
ejpam-5978	56	15	v	v	NOUN
ejpam-5978	56	16	(	(	PUNCT
ejpam-5978	56	17	g	g	NOUN
ejpam-5978	56	18	)	)	PUNCT
ejpam-5978	56	19	that	that	PRON
ejpam-5978	56	20	has	have	VERB
ejpam-5978	56	21	maximum	maximum	ADJ
ejpam-5978	56	22	independent	independent	ADJ
ejpam-5978	56	23	neighborhood	neighborhood	NOUN
ejpam-5978	56	24	systems	system	NOUN
ejpam-5978	56	25	(	(	PUNCT
ejpam-5978	56	26	γin	γin	NOUN
ejpam-5978	56	27	-	-	PUNCT
ejpam-5978	56	28	sets	set	NOUN
ejpam-5978	56	29	)	)	PUNCT
ejpam-5978	56	30	cardinality	cardinality	NOUN
ejpam-5978	56	31	equal	equal	ADJ
ejpam-5978	56	32	to	to	ADP
ejpam-5978	56	33	1	1	NUM
ejpam-5978	56	34	,	,	PUNCT
ejpam-5978	56	35	and	and	CCONJ
ejpam-5978	56	36	3	3	NUM
ejpam-5978	56	37	3	3	NUM
ejpam-5978	56	38	-	-	PUNCT
ejpam-5978	56	39	convex	convex	NOUN
ejpam-5978	56	40	subsets	subset	NOUN
ejpam-5978	56	41	of	of	ADP
ejpam-5978	56	42	v	v	NOUN
ejpam-5978	56	43	(	(	PUNCT
ejpam-5978	56	44	g	g	NOUN
ejpam-5978	56	45	)	)	PUNCT
ejpam-5978	56	46	that	that	PRON
ejpam-5978	56	47	has	have	VERB
ejpam-5978	56	48	maximum	maximum	ADJ
ejpam-5978	56	49	independent	independent	ADJ
ejpam-5978	56	50	neighborhood	neighborhood	NOUN
ejpam-5978	56	51	systems	system	NOUN
ejpam-5978	56	52	(	(	PUNCT
ejpam-5978	56	53	γin	γin	NOUN
ejpam-5978	56	54	-	-	PUNCT
ejpam-5978	56	55	sets	set	NOUN
ejpam-5978	56	56	)	)	PUNCT
ejpam-5978	56	57	cardinality	cardinality	NOUN
ejpam-5978	56	58	equal	equal	ADJ
ejpam-5978	56	59	to	to	ADP
ejpam-5978	56	60	2	2	NUM
ejpam-5978	56	61	.	.	PUNCT
ejpam-5978	57	1	this	this	PRON
ejpam-5978	57	2	contributes	contribute	VERB
ejpam-5978	57	3	to	to	ADP
ejpam-5978	57	4	the	the	DET
ejpam-5978	57	5	convex	convex	ADJ
ejpam-5978	57	6	independent	independent	ADJ
ejpam-5978	57	7	neighborhood	neighborhood	NOUN
ejpam-5978	57	8	polynomial	polynomial	NOUN
ejpam-5978	57	9	of	of	ADP
ejpam-5978	57	10	g	g	PROPN
ejpam-5978	57	11	as	as	ADP
ejpam-5978	57	12	2x3y	2x3y	PROPN
ejpam-5978	57	13	+	+	CCONJ
ejpam-5978	57	14	3x3y2	3x3y2	NOUN
ejpam-5978	57	15	.	.	PUNCT
ejpam-5978	58	1	for	for	ADP
ejpam-5978	58	2	4	4	NUM
ejpam-5978	58	3	-	-	PUNCT
ejpam-5978	58	4	convex	convex	NOUN
ejpam-5978	58	5	subsets	subset	NOUN
ejpam-5978	58	6	of	of	ADP
ejpam-5978	58	7	v	v	NOUN
ejpam-5978	58	8	(	(	PUNCT
ejpam-5978	58	9	g	g	NOUN
ejpam-5978	58	10	)	)	PUNCT
ejpam-5978	58	11	,	,	PUNCT
ejpam-5978	58	12	it	it	PRON
ejpam-5978	58	13	can	can	AUX
ejpam-5978	58	14	be	be	AUX
ejpam-5978	58	15	verified	verify	VERB
ejpam-5978	58	16	that	that	SCONJ
ejpam-5978	58	17	there	there	PRON
ejpam-5978	58	18	are	be	VERB
ejpam-5978	58	19	3	3	NUM
ejpam-5978	58	20	4	4	NUM
ejpam-5978	58	21	-	-	PUNCT
ejpam-5978	58	22	convex	convex	NOUN
ejpam-5978	58	23	subset	subset	NOUN
ejpam-5978	58	24	with	with	ADP
ejpam-5978	58	25	maximum	maximum	ADJ
ejpam-5978	58	26	independent	independent	ADJ
ejpam-5978	58	27	neighborhood	neighborhood	NOUN
ejpam-5978	58	28	systems	system	NOUN
ejpam-5978	58	29	(	(	PUNCT
ejpam-5978	58	30	γin)-sets	γin)-set	NOUN
ejpam-5978	58	31	cardinality	cardinality	NOUN
ejpam-5978	58	32	equal	equal	ADJ
ejpam-5978	58	33	to	to	ADP
ejpam-5978	58	34	1	1	NUM
ejpam-5978	58	35	.	.	PUNCT
ejpam-5978	59	1	this	this	PRON
ejpam-5978	59	2	contributes	contribute	VERB
ejpam-5978	59	3	to	to	PART
ejpam-5978	59	4	convex	convex	VERB
ejpam-5978	59	5	independent	independent	ADJ
ejpam-5978	59	6	neighborhood	neighborhood	NOUN
ejpam-5978	59	7	polynomial	polynomial	NOUN
ejpam-5978	59	8	of	of	ADP
ejpam-5978	59	9	g	g	PROPN
ejpam-5978	59	10	as	as	ADP
ejpam-5978	59	11	3x4y	3x4y	NUM
ejpam-5978	59	12	.	.	PUNCT
ejpam-5978	60	1	for	for	ADP
ejpam-5978	60	2	5	5	NUM
ejpam-5978	60	3	-	-	PUNCT
ejpam-5978	60	4	convex	convex	NOUN
ejpam-5978	60	5	subsets	subset	NOUN
ejpam-5978	60	6	of	of	ADP
ejpam-5978	60	7	v	v	NOUN
ejpam-5978	60	8	(	(	PUNCT
ejpam-5978	60	9	g	g	NOUN
ejpam-5978	60	10	)	)	PUNCT
ejpam-5978	60	11	,	,	PUNCT
ejpam-5978	60	12	it	it	PRON
ejpam-5978	60	13	can	can	AUX
ejpam-5978	60	14	be	be	AUX
ejpam-5978	60	15	verified	verify	VERB
ejpam-5978	60	16	that	that	SCONJ
ejpam-5978	60	17	there	there	PRON
ejpam-5978	60	18	is	be	VERB
ejpam-5978	60	19	only	only	ADV
ejpam-5978	60	20	1	1	NUM
ejpam-5978	60	21	5	5	NUM
ejpam-5978	60	22	-	-	PUNCT
ejpam-5978	60	23	convex	convex	NOUN
ejpam-5978	60	24	subset	subset	NOUN
ejpam-5978	60	25	with	with	ADP
ejpam-5978	60	26	empty	empty	ADJ
ejpam-5978	60	27	(	(	PUNCT
ejpam-5978	60	28	zero	zero	NUM
ejpam-5978	60	29	cardinality	cardinality	NOUN
ejpam-5978	60	30	)	)	PUNCT
ejpam-5978	60	31	maximum	maximum	ADJ
ejpam-5978	60	32	independent	independent	ADJ
ejpam-5978	60	33	neighborhood	neighborhood	NOUN
ejpam-5978	60	34	systems	system	NOUN
ejpam-5978	60	35	(	(	PUNCT
ejpam-5978	60	36	γin)-set	γin)-set	PROPN
ejpam-5978	60	37	.	.	PUNCT
ejpam-5978	61	1	this	this	PRON
ejpam-5978	61	2	contributes	contribute	VERB
ejpam-5978	61	3	to	to	PART
ejpam-5978	61	4	convex	convex	VERB
ejpam-5978	61	5	independent	independent	ADJ
ejpam-5978	61	6	neighborhood	neighborhood	NOUN
ejpam-5978	61	7	polynomial	polynomial	NOUN
ejpam-5978	61	8	of	of	ADP
ejpam-5978	61	9	g	g	PROPN
ejpam-5978	61	10	as	as	ADP
ejpam-5978	61	11	x5	x5	PROPN
ejpam-5978	61	12	.	.	PUNCT
ejpam-5978	61	13	e.j	e.j	PROPN
ejpam-5978	61	14	.	.	PROPN
ejpam-5978	61	15	aguilon	aguilon	PROPN
ejpam-5978	61	16	,	,	PUNCT
ejpam-5978	61	17	s.	s.	PROPN
ejpam-5978	61	18	dagondon	dagondon	PROPN
ejpam-5978	61	19	,	,	PUNCT
ejpam-5978	61	20	r.	r.	PROPN
ejpam-5978	61	21	artes	artes	PROPN
ejpam-5978	61	22	/	/	SYM
ejpam-5978	61	23	eur	eur	PROPN
ejpam-5978	61	24	.	.	PUNCT
ejpam-5978	62	1	j.	j.	PROPN
ejpam-5978	62	2	pure	pure	PROPN
ejpam-5978	62	3	appl	appl	PROPN
ejpam-5978	62	4	.	.	PROPN
ejpam-5978	62	5	math	math	PROPN
ejpam-5978	62	6	,	,	PUNCT
ejpam-5978	62	7	18	18	NUM
ejpam-5978	62	8	(	(	PUNCT
ejpam-5978	62	9	2	2	NUM
ejpam-5978	62	10	)	)	PUNCT
ejpam-5978	62	11	(	(	PUNCT
ejpam-5978	62	12	2025	2025	NUM
ejpam-5978	62	13	)	)	PUNCT
ejpam-5978	62	14	,	,	PUNCT
ejpam-5978	62	15	5978	5978	NUM
ejpam-5978	62	16	5	5	NUM
ejpam-5978	62	17	of	of	ADP
ejpam-5978	62	18	18	18	NUM
ejpam-5978	62	19	therefore	therefore	ADV
ejpam-5978	62	20	,	,	PUNCT
ejpam-5978	62	21	by	by	ADP
ejpam-5978	62	22	combining	combine	VERB
ejpam-5978	62	23	all	all	DET
ejpam-5978	62	24	the	the	DET
ejpam-5978	62	25	terms	term	NOUN
ejpam-5978	62	26	,	,	PUNCT
ejpam-5978	62	27	we	we	PRON
ejpam-5978	62	28	have	have	VERB
ejpam-5978	62	29	γcin(g;x	γcin(g;x	NUM
ejpam-5978	62	30	,	,	PUNCT
ejpam-5978	62	31	y	y	NOUN
ejpam-5978	62	32	)	)	PUNCT
ejpam-5978	62	33	=	=	SYM
ejpam-5978	62	34	x5	x5	PROPN
ejpam-5978	62	35	+	+	CCONJ
ejpam-5978	62	36	3x4y	3x4y	NOUN
ejpam-5978	63	1	+	+	CCONJ
ejpam-5978	64	1	2x3y	2x3y	PROPN
ejpam-5978	64	2	+	+	NUM
ejpam-5978	64	3	3x3y2	3x3y2	NUM
ejpam-5978	64	4	+	+	NUM
ejpam-5978	64	5	2x2y	2x2y	NUM
ejpam-5978	64	6	+	+	CCONJ
ejpam-5978	64	7	2x2y2	2x2y2	NUM
ejpam-5978	64	8	+	+	X
ejpam-5978	64	9	x2y3	x2y3	PUNCT
ejpam-5978	65	1	+	+	CCONJ
ejpam-5978	65	2	3xy	3xy	ADJ
ejpam-5978	65	3	+	+	CCONJ
ejpam-5978	65	4	2xy2	2xy2	NUM
ejpam-5978	65	5	.	.	NOUN
ejpam-5978	65	6	remark	remark	PROPN
ejpam-5978	65	7	3.1	3.1	NUM
ejpam-5978	65	8	.	.	PUNCT
ejpam-5978	66	1	the	the	DET
ejpam-5978	66	2	following	follow	VERB
ejpam-5978	66	3	properties	property	NOUN
ejpam-5978	66	4	of	of	ADP
ejpam-5978	66	5	the	the	DET
ejpam-5978	66	6	convex	convex	ADJ
ejpam-5978	66	7	independent	independent	ADJ
ejpam-5978	66	8	neighborhood	neighborhood	NOUN
ejpam-5978	66	9	polynomial	polynomial	NOUN
ejpam-5978	66	10	of	of	ADP
ejpam-5978	66	11	a	a	DET
ejpam-5978	66	12	graph	graph	NOUN
ejpam-5978	66	13	g	g	NOUN
ejpam-5978	66	14	are	be	AUX
ejpam-5978	66	15	noted	note	VERB
ejpam-5978	66	16	:	:	PUNCT
ejpam-5978	66	17	i	i	X
ejpam-5978	66	18	)	)	PUNCT
ejpam-5978	66	19	the	the	DET
ejpam-5978	66	20	degree	degree	NOUN
ejpam-5978	66	21	of	of	ADP
ejpam-5978	66	22	the	the	DET
ejpam-5978	66	23	convex	convex	ADJ
ejpam-5978	66	24	independent	independent	ADJ
ejpam-5978	66	25	neighborhood	neighborhood	NOUN
ejpam-5978	66	26	polynomial	polynomial	NOUN
ejpam-5978	66	27	of	of	ADP
ejpam-5978	66	28	a	a	DET
ejpam-5978	66	29	connected	connected	ADJ
ejpam-5978	66	30	graph	graph	NOUN
ejpam-5978	66	31	is	be	AUX
ejpam-5978	66	32	n.	n.	ADJ
ejpam-5978	66	33	moreover	moreover	ADV
ejpam-5978	66	34	,	,	PUNCT
ejpam-5978	66	35	it	it	PRON
ejpam-5978	66	36	is	be	AUX
ejpam-5978	66	37	a	a	DET
ejpam-5978	66	38	monic	monic	ADJ
ejpam-5978	66	39	polynomial	polynomial	NOUN
ejpam-5978	66	40	.	.	PUNCT
ejpam-5978	66	41	ii	ii	PROPN
ejpam-5978	66	42	)	)	PUNCT
ejpam-5978	66	43	the	the	DET
ejpam-5978	66	44	convex	convex	ADJ
ejpam-5978	66	45	independent	independent	ADJ
ejpam-5978	66	46	neighborhood	neighborhood	NOUN
ejpam-5978	66	47	polynomial	polynomial	NOUN
ejpam-5978	66	48	of	of	ADP
ejpam-5978	66	49	a	a	DET
ejpam-5978	66	50	disconnected	disconnected	ADJ
ejpam-5978	66	51	graph	graph	NOUN
ejpam-5978	66	52	with	with	ADP
ejpam-5978	66	53	isolated	isolate	VERB
ejpam-5978	66	54	n	n	PRON
ejpam-5978	66	55	vertices	vertex	NOUN
ejpam-5978	66	56	is	be	AUX
ejpam-5978	66	57	nx	nx	NOUN
ejpam-5978	66	58	.	.	PROPN
ejpam-5978	66	59	4	4	NUM
ejpam-5978	66	60	.	.	NOUN
ejpam-5978	66	61	paths	path	NOUN
ejpam-5978	66	62	and	and	CCONJ
ejpam-5978	66	63	cycles	cycle	NOUN
ejpam-5978	66	64	this	this	DET
ejpam-5978	66	65	section	section	NOUN
ejpam-5978	66	66	discusses	discuss	VERB
ejpam-5978	66	67	the	the	DET
ejpam-5978	66	68	convex	convex	ADJ
ejpam-5978	66	69	independent	independent	ADJ
ejpam-5978	66	70	neighborhood	neighborhood	NOUN
ejpam-5978	66	71	polynomial	polynomial	NOUN
ejpam-5978	66	72	of	of	ADP
ejpam-5978	66	73	paths	path	NOUN
ejpam-5978	66	74	(	(	PUNCT
ejpam-5978	66	75	pn	pn	NOUN
ejpam-5978	66	76	)	)	PUNCT
ejpam-5978	66	77	and	and	CCONJ
ejpam-5978	66	78	cycles	cycle	NOUN
ejpam-5978	66	79	(	(	PUNCT
ejpam-5978	66	80	cn	cn	NOUN
ejpam-5978	66	81	)	)	PUNCT
ejpam-5978	66	82	.	.	PUNCT
ejpam-5978	67	1	theorem	theorem	VERB
ejpam-5978	67	2	4.1	4.1	NUM
ejpam-5978	67	3	.	.	PUNCT
ejpam-5978	68	1	let	let	VERB
ejpam-5978	68	2	pn	pn	PART
ejpam-5978	68	3	be	be	AUX
ejpam-5978	68	4	a	a	DET
ejpam-5978	68	5	path	path	NOUN
ejpam-5978	68	6	of	of	ADP
ejpam-5978	68	7	order	order	NOUN
ejpam-5978	68	8	n.	n.	NOUN
ejpam-5978	68	9	then	then	ADV
ejpam-5978	68	10	,	,	PUNCT
ejpam-5978	68	11	for	for	ADP
ejpam-5978	68	12	n	n	PRON
ejpam-5978	68	13	≥	≥	NUM
ejpam-5978	68	14	2	2	NUM
ejpam-5978	68	15	,	,	PUNCT
ejpam-5978	68	16	the	the	DET
ejpam-5978	68	17	convex	convex	ADJ
ejpam-5978	68	18	independent	independent	ADJ
ejpam-5978	68	19	neighborhood	neighborhood	NOUN
ejpam-5978	68	20	polynomial	polynomial	NOUN
ejpam-5978	68	21	of	of	ADP
ejpam-5978	68	22	pn	pn	PROPN
ejpam-5978	68	23	is	be	AUX
ejpam-5978	68	24	given	give	VERB
ejpam-5978	68	25	by	by	ADP
ejpam-5978	68	26	γcin(pn;x	γcin(pn;x	PROPN
ejpam-5978	68	27	,	,	PUNCT
ejpam-5978	68	28	y	y	NOUN
ejpam-5978	68	29	)	)	PUNCT
ejpam-5978	68	30	=	=	SYM
ejpam-5978	69	1	xn	xn	PROPN
ejpam-5978	70	1	+	+	NUM
ejpam-5978	70	2	n−1∑	n−1∑	NUM
ejpam-5978	70	3	i=1	i=1	PROPN
ejpam-5978	70	4	2xiy	2xiy	NUM
ejpam-5978	70	5	+	+	CCONJ
ejpam-5978	70	6	n−2∑	n−2∑	NUM
ejpam-5978	70	7	i=1	i=1	PROPN
ejpam-5978	70	8	(	(	PUNCT
ejpam-5978	70	9	n−	n−	NOUN
ejpam-5978	70	10	1−	1−	NUM
ejpam-5978	70	11	i)xiy2	i)xiy2	PROPN
ejpam-5978	70	12	.	.	PUNCT
ejpam-5978	70	13	proof	proof	NOUN
ejpam-5978	70	14	.	.	PUNCT
ejpam-5978	71	1	let	let	VERB
ejpam-5978	71	2	v	v	X
ejpam-5978	71	3	(	(	PUNCT
ejpam-5978	71	4	pn	pn	NOUN
ejpam-5978	71	5	)	)	PUNCT
ejpam-5978	71	6	=	=	SYM
ejpam-5978	71	7	{	{	PUNCT
ejpam-5978	71	8	v1	v1	PROPN
ejpam-5978	71	9	,	,	PUNCT
ejpam-5978	71	10	v2	v2	PROPN
ejpam-5978	71	11	,	,	PUNCT
ejpam-5978	71	12	.	.	PUNCT
ejpam-5978	71	13	.	.	PUNCT
ejpam-5978	72	1	.	.	PUNCT
ejpam-5978	73	1	,	,	PUNCT
ejpam-5978	73	2	vn	vn	AUX
ejpam-5978	73	3	}	}	PUNCT
ejpam-5978	73	4	be	be	AUX
ejpam-5978	73	5	the	the	DET
ejpam-5978	73	6	vertex	vertex	NOUN
ejpam-5978	73	7	set	set	NOUN
ejpam-5978	73	8	of	of	ADP
ejpam-5978	73	9	pn	pn	PROPN
ejpam-5978	73	10	.	.	PROPN
ejpam-5978	73	11	note	note	VERB
ejpam-5978	73	12	that	that	SCONJ
ejpam-5978	73	13	for	for	ADP
ejpam-5978	73	14	n	n	CCONJ
ejpam-5978	73	15	-	-	PUNCT
ejpam-5978	73	16	convex	convex	NOUN
ejpam-5978	73	17	subset	subset	NOUN
ejpam-5978	73	18	of	of	ADP
ejpam-5978	73	19	v	v	PROPN
ejpam-5978	73	20	(	(	PUNCT
ejpam-5978	73	21	pn	pn	NOUN
ejpam-5978	73	22	)	)	PUNCT
ejpam-5978	73	23	there	there	PRON
ejpam-5978	73	24	is	be	VERB
ejpam-5978	73	25	only	only	ADV
ejpam-5978	73	26	one	one	NUM
ejpam-5978	73	27	set	set	NOUN
ejpam-5978	73	28	that	that	PRON
ejpam-5978	73	29	is	be	AUX
ejpam-5978	73	30	{	{	PUNCT
ejpam-5978	73	31	v1	v1	NOUN
ejpam-5978	73	32	,	,	PUNCT
ejpam-5978	73	33	v2	v2	NOUN
ejpam-5978	73	34	,	,	PUNCT
ejpam-5978	73	35	.	.	PUNCT
ejpam-5978	73	36	.	.	PUNCT
ejpam-5978	74	1	.	.	PUNCT
ejpam-5978	75	1	,	,	PUNCT
ejpam-5978	75	2	vn	vn	VERB
ejpam-5978	75	3	}	}	PUNCT
ejpam-5978	75	4	with	with	ADP
ejpam-5978	75	5	empty	empty	ADJ
ejpam-5978	75	6	(	(	PUNCT
ejpam-5978	75	7	zero	zero	NUM
ejpam-5978	75	8	cardinality	cardinality	NOUN
ejpam-5978	75	9	)	)	PUNCT
ejpam-5978	75	10	γin	γin	NOUN
ejpam-5978	75	11	-	-	PUNCT
ejpam-5978	75	12	set	set	NOUN
ejpam-5978	75	13	.	.	PUNCT
ejpam-5978	76	1	this	this	PRON
ejpam-5978	76	2	contributes	contribute	VERB
ejpam-5978	76	3	to	to	ADP
ejpam-5978	76	4	the	the	DET
ejpam-5978	76	5	term	term	NOUN
ejpam-5978	76	6	xn	xn	PROPN
ejpam-5978	76	7	of	of	ADP
ejpam-5978	76	8	the	the	DET
ejpam-5978	76	9	polynomial	polynomial	NOUN
ejpam-5978	76	10	.	.	PUNCT
ejpam-5978	77	1	next	next	ADV
ejpam-5978	77	2	,	,	PUNCT
ejpam-5978	77	3	for	for	ADP
ejpam-5978	77	4	i	i	NOUN
ejpam-5978	77	5	-	-	PUNCT
ejpam-5978	77	6	convex	convex	NOUN
ejpam-5978	77	7	subset	subset	NOUN
ejpam-5978	77	8	of	of	ADP
ejpam-5978	77	9	v	v	PROPN
ejpam-5978	77	10	(	(	PUNCT
ejpam-5978	77	11	pn	pn	NOUN
ejpam-5978	77	12	)	)	PUNCT
ejpam-5978	77	13	,	,	PUNCT
ejpam-5978	77	14	i	i	PRON
ejpam-5978	77	15	=	=	NOUN
ejpam-5978	77	16	1	1	NUM
ejpam-5978	77	17	,	,	PUNCT
ejpam-5978	77	18	2	2	NUM
ejpam-5978	77	19	,	,	PUNCT
ejpam-5978	77	20	...	...	PUNCT
ejpam-5978	77	21	,	,	PUNCT
ejpam-5978	77	22	n−	n−	NOUN
ejpam-5978	77	23	1	1	NUM
ejpam-5978	77	24	.	.	PUNCT
ejpam-5978	78	1	we	we	PRON
ejpam-5978	78	2	consider	consider	VERB
ejpam-5978	78	3	two	two	NUM
ejpam-5978	78	4	cases	case	NOUN
ejpam-5978	78	5	in	in	ADP
ejpam-5978	78	6	choosing	choose	VERB
ejpam-5978	78	7	the	the	DET
ejpam-5978	78	8	i	i	NOUN
ejpam-5978	78	9	-	-	PUNCT
ejpam-5978	78	10	convex	convex	NOUN
ejpam-5978	78	11	subset	subset	NOUN
ejpam-5978	78	12	of	of	ADP
ejpam-5978	78	13	v	v	PROPN
ejpam-5978	78	14	(	(	PUNCT
ejpam-5978	78	15	pn	pn	NOUN
ejpam-5978	78	16	)	)	PUNCT
ejpam-5978	78	17	,	,	PUNCT
ejpam-5978	78	18	the	the	DET
ejpam-5978	78	19	first	first	ADJ
ejpam-5978	78	20	case	case	NOUN
ejpam-5978	78	21	is	be	AUX
ejpam-5978	78	22	choosing	choose	VERB
ejpam-5978	78	23	set	set	VERB
ejpam-5978	78	24	of	of	ADP
ejpam-5978	78	25	vertices	vertex	NOUN
ejpam-5978	78	26	which	which	PRON
ejpam-5978	78	27	include	include	VERB
ejpam-5978	78	28	exactly	exactly	ADV
ejpam-5978	78	29	one	one	NUM
ejpam-5978	78	30	of	of	ADP
ejpam-5978	78	31	the	the	DET
ejpam-5978	78	32	end	end	NOUN
ejpam-5978	78	33	vertices	vertex	NOUN
ejpam-5978	78	34	and	and	CCONJ
ejpam-5978	78	35	for	for	ADP
ejpam-5978	78	36	the	the	DET
ejpam-5978	78	37	second	second	ADJ
ejpam-5978	78	38	case	case	NOUN
ejpam-5978	78	39	choosing	choose	VERB
ejpam-5978	78	40	set	set	NOUN
ejpam-5978	78	41	of	of	ADP
ejpam-5978	78	42	vertices	vertex	NOUN
ejpam-5978	78	43	which	which	PRON
ejpam-5978	78	44	does	do	AUX
ejpam-5978	78	45	not	not	PART
ejpam-5978	78	46	include	include	VERB
ejpam-5978	78	47	the	the	DET
ejpam-5978	78	48	end	end	NOUN
ejpam-5978	78	49	vertices	vertex	NOUN
ejpam-5978	78	50	.	.	PUNCT
ejpam-5978	79	1	for	for	ADP
ejpam-5978	79	2	the	the	DET
ejpam-5978	79	3	first	first	ADJ
ejpam-5978	79	4	case	case	NOUN
ejpam-5978	79	5	,	,	PUNCT
ejpam-5978	79	6	for	for	ADP
ejpam-5978	79	7	1	1	NUM
ejpam-5978	79	8	-	-	PUNCT
ejpam-5978	79	9	convex	convex	NOUN
ejpam-5978	79	10	subset	subset	NOUN
ejpam-5978	79	11	of	of	ADP
ejpam-5978	79	12	subset	subset	NOUN
ejpam-5978	79	13	of	of	ADP
ejpam-5978	79	14	v	v	PROPN
ejpam-5978	79	15	(	(	PUNCT
ejpam-5978	79	16	pn	pn	NOUN
ejpam-5978	79	17	)	)	PUNCT
ejpam-5978	79	18	,	,	PUNCT
ejpam-5978	79	19	consider	consider	VERB
ejpam-5978	79	20	the	the	DET
ejpam-5978	79	21	vertex	vertex	NOUN
ejpam-5978	79	22	sets	set	NOUN
ejpam-5978	79	23	{	{	PUNCT
ejpam-5978	79	24	v1	v1	NOUN
ejpam-5978	79	25	}	}	PUNCT
ejpam-5978	79	26	and	and	CCONJ
ejpam-5978	79	27	{	{	PUNCT
ejpam-5978	79	28	vn	vn	NOUN
ejpam-5978	79	29	}	}	PUNCT
ejpam-5978	79	30	,	,	PUNCT
ejpam-5978	79	31	both	both	PRON
ejpam-5978	79	32	of	of	ADP
ejpam-5978	79	33	these	these	DET
ejpam-5978	79	34	convex	convex	ADJ
ejpam-5978	79	35	vertex	vertex	NOUN
ejpam-5978	79	36	sets	set	NOUN
ejpam-5978	79	37	contains	contain	VERB
ejpam-5978	79	38	only	only	ADV
ejpam-5978	79	39	one	one	NUM
ejpam-5978	79	40	γin	γin	NOUN
ejpam-5978	79	41	-	-	PUNCT
ejpam-5978	79	42	sets	set	NOUN
ejpam-5978	79	43	namely	namely	ADV
ejpam-5978	79	44	{	{	PUNCT
ejpam-5978	79	45	v2	v2	NOUN
ejpam-5978	79	46	}	}	PUNCT
ejpam-5978	79	47	and	and	CCONJ
ejpam-5978	79	48	{	{	PUNCT
ejpam-5978	79	49	vn−1	vn−1	PROPN
ejpam-5978	79	50	}	}	PUNCT
ejpam-5978	79	51	,	,	PUNCT
ejpam-5978	79	52	respectively	respectively	ADV
ejpam-5978	79	53	.	.	PUNCT
ejpam-5978	80	1	for	for	ADP
ejpam-5978	80	2	2	2	NUM
ejpam-5978	80	3	-	-	PUNCT
ejpam-5978	80	4	convex	convex	NOUN
ejpam-5978	80	5	subset	subset	NOUN
ejpam-5978	80	6	of	of	ADP
ejpam-5978	80	7	v	v	PROPN
ejpam-5978	80	8	(	(	PUNCT
ejpam-5978	80	9	pn	pn	NOUN
ejpam-5978	80	10	)	)	PUNCT
ejpam-5978	80	11	,	,	PUNCT
ejpam-5978	80	12	consider	consider	VERB
ejpam-5978	80	13	the	the	DET
ejpam-5978	80	14	vertex	vertex	NOUN
ejpam-5978	80	15	set	set	NOUN
ejpam-5978	80	16	{	{	PUNCT
ejpam-5978	80	17	v1	v1	NOUN
ejpam-5978	80	18	,	,	PUNCT
ejpam-5978	80	19	v2	v2	NOUN
ejpam-5978	80	20	}	}	PUNCT
ejpam-5978	80	21	and	and	CCONJ
ejpam-5978	80	22	{	{	PUNCT
ejpam-5978	80	23	vn−1	vn−1	PROPN
ejpam-5978	80	24	,	,	PUNCT
ejpam-5978	80	25	vn	vn	NOUN
ejpam-5978	80	26	}	}	PUNCT
ejpam-5978	80	27	,	,	PUNCT
ejpam-5978	80	28	both	both	PRON
ejpam-5978	80	29	of	of	ADP
ejpam-5978	80	30	these	these	DET
ejpam-5978	80	31	convex	convex	ADJ
ejpam-5978	80	32	vertex	vertex	NOUN
ejpam-5978	80	33	sets	set	NOUN
ejpam-5978	80	34	contains	contain	VERB
ejpam-5978	80	35	only	only	ADV
ejpam-5978	80	36	one	one	NUM
ejpam-5978	80	37	γin	γin	NOUN
ejpam-5978	80	38	-	-	PUNCT
ejpam-5978	80	39	sets	set	NOUN
ejpam-5978	80	40	namely	namely	ADV
ejpam-5978	80	41	{	{	PUNCT
ejpam-5978	80	42	v3	v3	NOUN
ejpam-5978	80	43	}	}	PUNCT
ejpam-5978	80	44	and	and	CCONJ
ejpam-5978	80	45	{	{	PUNCT
ejpam-5978	80	46	vn−2	vn−2	PROPN
ejpam-5978	80	47	}	}	PUNCT
ejpam-5978	80	48	,	,	PUNCT
ejpam-5978	80	49	respectively	respectively	ADV
ejpam-5978	80	50	.	.	PUNCT
ejpam-5978	81	1	since	since	SCONJ
ejpam-5978	81	2	v	v	NOUN
ejpam-5978	81	3	(	(	PUNCT
ejpam-5978	81	4	pn	pn	NOUN
ejpam-5978	81	5	)	)	PUNCT
ejpam-5978	81	6	is	be	AUX
ejpam-5978	81	7	finite	finite	ADJ
ejpam-5978	81	8	,	,	PUNCT
ejpam-5978	81	9	it	it	PRON
ejpam-5978	81	10	follows	follow	VERB
ejpam-5978	81	11	that	that	SCONJ
ejpam-5978	81	12	i	i	PRON
ejpam-5978	81	13	-	-	PUNCT
ejpam-5978	81	14	convex	convex	ADJ
ejpam-5978	81	15	subsets	subset	NOUN
ejpam-5978	81	16	of	of	ADP
ejpam-5978	81	17	v	v	NOUN
ejpam-5978	81	18	(	(	PUNCT
ejpam-5978	81	19	pn	pn	NOUN
ejpam-5978	81	20	)	)	PUNCT
ejpam-5978	81	21	is	be	AUX
ejpam-5978	81	22	also	also	ADV
ejpam-5978	81	23	finite	finite	ADJ
ejpam-5978	81	24	.	.	PUNCT
ejpam-5978	82	1	this	this	PRON
ejpam-5978	82	2	means	mean	VERB
ejpam-5978	82	3	that	that	SCONJ
ejpam-5978	82	4	we	we	PRON
ejpam-5978	82	5	may	may	AUX
ejpam-5978	82	6	continue	continue	VERB
ejpam-5978	82	7	this	this	DET
ejpam-5978	82	8	process	process	NOUN
ejpam-5978	82	9	up	up	ADP
ejpam-5978	82	10	to	to	ADP
ejpam-5978	82	11	(	(	PUNCT
ejpam-5978	82	12	n	n	CCONJ
ejpam-5978	82	13	−	−	PROPN
ejpam-5978	82	14	1)-convex	1)-convex	NUM
ejpam-5978	82	15	subsets	subset	NOUN
ejpam-5978	82	16	of	of	ADP
ejpam-5978	82	17	pn	pn	PROPN
ejpam-5978	82	18	.	.	PUNCT
ejpam-5978	83	1	all	all	PRON
ejpam-5978	83	2	of	of	ADP
ejpam-5978	83	3	these	these	DET
ejpam-5978	83	4	i	i	NOUN
ejpam-5978	83	5	-	-	PUNCT
ejpam-5978	83	6	convex	convex	ADJ
ejpam-5978	83	7	subsets	subset	NOUN
ejpam-5978	83	8	has	have	VERB
ejpam-5978	83	9	γin	γin	NOUN
ejpam-5978	83	10	-	-	PUNCT
ejpam-5978	83	11	sets	set	NOUN
ejpam-5978	83	12	cardinality	cardinality	NOUN
ejpam-5978	83	13	equal	equal	ADJ
ejpam-5978	83	14	to	to	ADP
ejpam-5978	83	15	one	one	NUM
ejpam-5978	83	16	.	.	PUNCT
ejpam-5978	84	1	thus	thus	ADV
ejpam-5978	84	2	,	,	PUNCT
ejpam-5978	84	3	by	by	ADP
ejpam-5978	84	4	combining	combine	VERB
ejpam-5978	84	5	all	all	PRON
ejpam-5978	84	6	of	of	ADP
ejpam-5978	84	7	these	these	DET
ejpam-5978	84	8	i	i	NOUN
ejpam-5978	84	9	-	-	PUNCT
ejpam-5978	84	10	convex	convex	ADJ
ejpam-5978	84	11	subsets	subset	NOUN
ejpam-5978	84	12	with	with	ADP
ejpam-5978	84	13	γin	γin	NOUN
ejpam-5978	84	14	-	-	PUNCT
ejpam-5978	84	15	sets	set	NOUN
ejpam-5978	84	16	cardinality	cardinality	NOUN
ejpam-5978	84	17	equal	equal	ADJ
ejpam-5978	84	18	to	to	ADP
ejpam-5978	84	19	one	one	NUM
ejpam-5978	84	20	.	.	PUNCT
ejpam-5978	85	1	we	we	PRON
ejpam-5978	85	2	have	have	VERB
ejpam-5978	85	3	2xy	2xy	ADJ
ejpam-5978	86	1	+	+	CCONJ
ejpam-5978	86	2	2x2y	2x2y	NUM
ejpam-5978	86	3	+	+	CCONJ
ejpam-5978	86	4	2x3y	2x3y	ADJ
ejpam-5978	86	5	+	+	X
ejpam-5978	86	6	·	·	PUNCT
ejpam-5978	86	7	·	·	PUNCT
ejpam-5978	86	8	·	·	PUNCT
ejpam-5978	86	9	+	+	NUM
ejpam-5978	86	10	2xn−1y	2xn−1y	NOUN
ejpam-5978	86	11	=	=	SYM
ejpam-5978	87	1	n−1∑	n−1∑	PROPN
ejpam-5978	87	2	i=1	i=1	PROPN
ejpam-5978	87	3	2xiy	2xiy	NUM
ejpam-5978	87	4	.	.	PUNCT
ejpam-5978	88	1	for	for	ADP
ejpam-5978	88	2	the	the	DET
ejpam-5978	88	3	second	second	ADJ
ejpam-5978	88	4	case	case	NOUN
ejpam-5978	88	5	,	,	PUNCT
ejpam-5978	88	6	choosing	choose	VERB
ejpam-5978	88	7	i	i	PRON
ejpam-5978	88	8	-	-	PUNCT
ejpam-5978	88	9	convex	convex	NOUN
ejpam-5978	88	10	subset	subset	NOUN
ejpam-5978	88	11	of	of	ADP
ejpam-5978	88	12	v	v	PROPN
ejpam-5978	88	13	(	(	PUNCT
ejpam-5978	88	14	pn	pn	NOUN
ejpam-5978	88	15	)	)	PUNCT
ejpam-5978	88	16	which	which	PRON
ejpam-5978	88	17	does	do	AUX
ejpam-5978	88	18	not	not	PART
ejpam-5978	88	19	include	include	VERB
ejpam-5978	88	20	the	the	DET
ejpam-5978	88	21	end	end	NOUN
ejpam-5978	88	22	vertices	vertex	NOUN
ejpam-5978	88	23	.	.	PUNCT
ejpam-5978	89	1	for	for	ADP
ejpam-5978	89	2	1	1	NUM
ejpam-5978	89	3	-	-	PUNCT
ejpam-5978	89	4	convex	convex	NOUN
ejpam-5978	89	5	subsets	subset	NOUN
ejpam-5978	89	6	of	of	ADP
ejpam-5978	89	7	v	v	NOUN
ejpam-5978	89	8	(	(	PUNCT
ejpam-5978	89	9	pn	pn	NOUN
ejpam-5978	89	10	)	)	PUNCT
ejpam-5978	89	11	,	,	PUNCT
ejpam-5978	89	12	consider	consider	VERB
ejpam-5978	89	13	the	the	DET
ejpam-5978	89	14	vertices	vertex	NOUN
ejpam-5978	89	15	{	{	PUNCT
ejpam-5978	89	16	v2	v2	NOUN
ejpam-5978	89	17	}	}	PUNCT
ejpam-5978	89	18	,	,	PUNCT
ejpam-5978	89	19	{	{	PUNCT
ejpam-5978	89	20	v3	v3	NOUN
ejpam-5978	89	21	}	}	PUNCT
ejpam-5978	89	22	,	,	PUNCT
ejpam-5978	89	23	.	.	PUNCT
ejpam-5978	89	24	.	.	PUNCT
ejpam-5978	90	1	.	.	PUNCT
ejpam-5978	91	1	,	,	PUNCT
ejpam-5978	91	2	{	{	PUNCT
ejpam-5978	91	3	vn−1	vn−1	ADJ
ejpam-5978	91	4	}	}	PUNCT
ejpam-5978	91	5	.	.	PUNCT
ejpam-5978	92	1	then	then	ADV
ejpam-5978	92	2	e.j	e.j	PROPN
ejpam-5978	92	3	.	.	PROPN
ejpam-5978	92	4	aguilon	aguilon	PROPN
ejpam-5978	92	5	,	,	PUNCT
ejpam-5978	92	6	s.	s.	PROPN
ejpam-5978	92	7	dagondon	dagondon	PROPN
ejpam-5978	92	8	,	,	PUNCT
ejpam-5978	92	9	r.	r.	PROPN
ejpam-5978	92	10	artes	artes	PROPN
ejpam-5978	92	11	/	/	SYM
ejpam-5978	92	12	eur	eur	PROPN
ejpam-5978	92	13	.	.	PUNCT
ejpam-5978	93	1	j.	j.	PROPN
ejpam-5978	93	2	pure	pure	PROPN
ejpam-5978	93	3	appl	appl	PROPN
ejpam-5978	93	4	.	.	PROPN
ejpam-5978	93	5	math	math	PROPN
ejpam-5978	93	6	,	,	PUNCT
ejpam-5978	93	7	18	18	NUM
ejpam-5978	93	8	(	(	PUNCT
ejpam-5978	93	9	2	2	NUM
ejpam-5978	93	10	)	)	PUNCT
ejpam-5978	93	11	(	(	PUNCT
ejpam-5978	93	12	2025	2025	NUM
ejpam-5978	93	13	)	)	PUNCT
ejpam-5978	93	14	,	,	PUNCT
ejpam-5978	93	15	5978	5978	NUM
ejpam-5978	93	16	6	6	NUM
ejpam-5978	93	17	of	of	ADP
ejpam-5978	93	18	18	18	NUM
ejpam-5978	93	19	there	there	PRON
ejpam-5978	93	20	are	be	VERB
ejpam-5978	93	21	(	(	PUNCT
ejpam-5978	93	22	n−2	n−2	PROPN
ejpam-5978	93	23	)	)	PUNCT
ejpam-5978	93	24	1	1	NUM
ejpam-5978	93	25	-	-	PUNCT
ejpam-5978	93	26	convex	convex	NOUN
ejpam-5978	93	27	subsets	subset	NOUN
ejpam-5978	93	28	of	of	ADP
ejpam-5978	93	29	v	v	NOUN
ejpam-5978	93	30	(	(	PUNCT
ejpam-5978	93	31	pn	pn	NOUN
ejpam-5978	93	32	)	)	PUNCT
ejpam-5978	93	33	whose	whose	DET
ejpam-5978	93	34	γin	γin	NOUN
ejpam-5978	93	35	-	-	PUNCT
ejpam-5978	93	36	sets	set	NOUN
ejpam-5978	93	37	contains	contain	VERB
ejpam-5978	93	38	two	two	NUM
ejpam-5978	93	39	elements	element	NOUN
ejpam-5978	93	40	.	.	PUNCT
ejpam-5978	94	1	next	next	ADV
ejpam-5978	94	2	,	,	PUNCT
ejpam-5978	94	3	for	for	ADP
ejpam-5978	94	4	2	2	NUM
ejpam-5978	94	5	-	-	PUNCT
ejpam-5978	94	6	convex	convex	NOUN
ejpam-5978	94	7	subsets	subset	NOUN
ejpam-5978	94	8	of	of	ADP
ejpam-5978	94	9	v	v	NOUN
ejpam-5978	94	10	(	(	PUNCT
ejpam-5978	94	11	pn	pn	NOUN
ejpam-5978	94	12	)	)	PUNCT
ejpam-5978	94	13	,	,	PUNCT
ejpam-5978	94	14	consider	consider	VERB
ejpam-5978	94	15	the	the	DET
ejpam-5978	94	16	sets	set	NOUN
ejpam-5978	94	17	{	{	PUNCT
ejpam-5978	94	18	v2	v2	NOUN
ejpam-5978	94	19	,	,	PUNCT
ejpam-5978	94	20	v3	v3	PROPN
ejpam-5978	94	21	}	}	PUNCT
ejpam-5978	94	22	,	,	PUNCT
ejpam-5978	94	23	{	{	PUNCT
ejpam-5978	94	24	v3	v3	PROPN
ejpam-5978	94	25	,	,	PUNCT
ejpam-5978	94	26	v4	v4	PROPN
ejpam-5978	94	27	}	}	PUNCT
ejpam-5978	94	28	,	,	PUNCT
ejpam-5978	94	29	{	{	PUNCT
ejpam-5978	94	30	v4	v4	NOUN
ejpam-5978	94	31	,	,	PUNCT
ejpam-5978	94	32	v5	v5	PROPN
ejpam-5978	94	33	}	}	PUNCT
ejpam-5978	94	34	,	,	PUNCT
ejpam-5978	94	35	.	.	PUNCT
ejpam-5978	94	36	.	.	PUNCT
ejpam-5978	95	1	.	.	PUNCT
ejpam-5978	96	1	,	,	PUNCT
ejpam-5978	96	2	{	{	PUNCT
ejpam-5978	96	3	vn−2	vn−2	PROPN
ejpam-5978	96	4	,	,	PUNCT
ejpam-5978	96	5	vn−1	vn−1	ADJ
ejpam-5978	96	6	}	}	PUNCT
ejpam-5978	96	7	.	.	PUNCT
ejpam-5978	97	1	this	this	PRON
ejpam-5978	97	2	means	mean	VERB
ejpam-5978	97	3	that	that	SCONJ
ejpam-5978	97	4	there	there	PRON
ejpam-5978	97	5	are	be	VERB
ejpam-5978	97	6	(	(	PUNCT
ejpam-5978	97	7	n	n	CCONJ
ejpam-5978	97	8	−	−	PROPN
ejpam-5978	97	9	3	3	NUM
ejpam-5978	97	10	)	)	PUNCT
ejpam-5978	97	11	2	2	NUM
ejpam-5978	97	12	-	-	PUNCT
ejpam-5978	97	13	convex	convex	NOUN
ejpam-5978	97	14	subsets	subset	NOUN
ejpam-5978	97	15	of	of	ADP
ejpam-5978	97	16	v	v	NOUN
ejpam-5978	97	17	(	(	PUNCT
ejpam-5978	97	18	pn	pn	NOUN
ejpam-5978	97	19	)	)	PUNCT
ejpam-5978	97	20	with	with	ADP
ejpam-5978	97	21	γin	γin	NOUN
ejpam-5978	97	22	-	-	PUNCT
ejpam-5978	97	23	sets	set	NOUN
ejpam-5978	97	24	equal	equal	ADJ
ejpam-5978	97	25	to	to	ADP
ejpam-5978	97	26	two	two	NUM
ejpam-5978	97	27	.	.	PUNCT
ejpam-5978	98	1	since	since	SCONJ
ejpam-5978	98	2	v	v	NOUN
ejpam-5978	98	3	(	(	PUNCT
ejpam-5978	98	4	pn	pn	NOUN
ejpam-5978	98	5	)	)	PUNCT
ejpam-5978	98	6	is	be	AUX
ejpam-5978	98	7	finite	finite	ADJ
ejpam-5978	98	8	,	,	PUNCT
ejpam-5978	98	9	similarly	similarly	ADV
ejpam-5978	98	10	we	we	PRON
ejpam-5978	98	11	can	can	AUX
ejpam-5978	98	12	continue	continue	VERB
ejpam-5978	98	13	this	this	DET
ejpam-5978	98	14	process	process	NOUN
ejpam-5978	98	15	till	till	SCONJ
ejpam-5978	98	16	we	we	PRON
ejpam-5978	98	17	choose	choose	VERB
ejpam-5978	98	18	the	the	DET
ejpam-5978	98	19	set	set	NOUN
ejpam-5978	98	20	{	{	PUNCT
ejpam-5978	98	21	v2	v2	PROPN
ejpam-5978	98	22	,	,	PUNCT
ejpam-5978	98	23	v3	v3	PROPN
ejpam-5978	98	24	,	,	PUNCT
ejpam-5978	98	25	...	...	PUNCT
ejpam-5978	98	26	,	,	PUNCT
ejpam-5978	98	27	vn−1	vn−1	ADJ
ejpam-5978	98	28	}	}	PUNCT
ejpam-5978	98	29	.	.	PUNCT
ejpam-5978	99	1	all	all	PRON
ejpam-5978	99	2	of	of	ADP
ejpam-5978	99	3	these	these	DET
ejpam-5978	99	4	i	i	NOUN
ejpam-5978	99	5	-	-	PUNCT
ejpam-5978	99	6	convex	convex	ADJ
ejpam-5978	99	7	subsets	subset	NOUN
ejpam-5978	99	8	have	have	VERB
ejpam-5978	99	9	γin	γin	NOUN
ejpam-5978	99	10	-	-	PUNCT
ejpam-5978	99	11	sets	set	NOUN
ejpam-5978	99	12	with	with	ADP
ejpam-5978	99	13	cardinality	cardinality	NOUN
ejpam-5978	99	14	equal	equal	ADJ
ejpam-5978	99	15	to	to	ADP
ejpam-5978	99	16	two	two	NUM
ejpam-5978	99	17	.	.	PUNCT
ejpam-5978	100	1	thus	thus	ADV
ejpam-5978	100	2	,	,	PUNCT
ejpam-5978	100	3	by	by	ADP
ejpam-5978	100	4	combining	combine	VERB
ejpam-5978	100	5	all	all	PRON
ejpam-5978	100	6	of	of	ADP
ejpam-5978	100	7	these	these	DET
ejpam-5978	100	8	i	i	NOUN
ejpam-5978	100	9	-	-	PUNCT
ejpam-5978	100	10	convex	convex	ADJ
ejpam-5978	100	11	subsets	subset	NOUN
ejpam-5978	100	12	of	of	ADP
ejpam-5978	100	13	v	v	NOUN
ejpam-5978	100	14	(	(	PUNCT
ejpam-5978	100	15	pn	pn	NOUN
ejpam-5978	100	16	)	)	PUNCT
ejpam-5978	100	17	with	with	ADP
ejpam-5978	100	18	γin	γin	NOUN
ejpam-5978	100	19	-	-	PUNCT
ejpam-5978	100	20	sets	set	NOUN
ejpam-5978	100	21	cardinality	cardinality	NOUN
ejpam-5978	100	22	equal	equal	ADJ
ejpam-5978	100	23	to	to	ADP
ejpam-5978	100	24	two	two	NUM
ejpam-5978	100	25	,	,	PUNCT
ejpam-5978	100	26	we	we	PRON
ejpam-5978	100	27	have	have	VERB
ejpam-5978	100	28	(	(	PUNCT
ejpam-5978	100	29	n−	n−	NOUN
ejpam-5978	100	30	2)x1y2	2)x1y2	PROPN
ejpam-5978	100	31	+	+	CCONJ
ejpam-5978	100	32	(	(	PUNCT
ejpam-5978	100	33	n−	n−	NOUN
ejpam-5978	100	34	3)x2y2	3)x2y2	PROPN
ejpam-5978	100	35	+	+	CCONJ
ejpam-5978	100	36	(	(	PUNCT
ejpam-5978	100	37	n−	n−	PROPN
ejpam-5978	100	38	4)x3y2	4)x3y2	NOUN
ejpam-5978	100	39	+	+	CCONJ
ejpam-5978	100	40	·	·	PUNCT
ejpam-5978	100	41	·	·	PUNCT
ejpam-5978	100	42	·	·	PUNCT
ejpam-5978	101	1	+	+	NUM
ejpam-5978	101	2	xn−2y2	xn−2y2	NOUN
ejpam-5978	101	3	=	=	SYM
ejpam-5978	101	4	n−2∑	n−2∑	NUM
ejpam-5978	101	5	i=1	i=1	PROPN
ejpam-5978	101	6	(	(	PUNCT
ejpam-5978	101	7	n−	n−	NOUN
ejpam-5978	101	8	1−	1−	NUM
ejpam-5978	101	9	i)xiy2	i)xiy2	PROPN
ejpam-5978	101	10	.	.	PUNCT
ejpam-5978	102	1	therefore	therefore	ADV
ejpam-5978	102	2	,	,	PUNCT
ejpam-5978	102	3	by	by	ADP
ejpam-5978	102	4	combining	combine	VERB
ejpam-5978	102	5	all	all	DET
ejpam-5978	102	6	the	the	DET
ejpam-5978	102	7	above	above	ADJ
ejpam-5978	102	8	scenarios	scenario	NOUN
ejpam-5978	102	9	,	,	PUNCT
ejpam-5978	102	10	the	the	DET
ejpam-5978	102	11	convex	convex	ADJ
ejpam-5978	102	12	independent	independent	ADJ
ejpam-5978	102	13	neighborhood	neighborhood	NOUN
ejpam-5978	102	14	polynomial	polynomial	NOUN
ejpam-5978	102	15	of	of	ADP
ejpam-5978	102	16	pn	pn	PROPN
ejpam-5978	102	17	is	be	AUX
ejpam-5978	102	18	γcin(pn;x	γcin(pn;x	PROPN
ejpam-5978	102	19	,	,	PUNCT
ejpam-5978	102	20	y	y	NOUN
ejpam-5978	102	21	)	)	PUNCT
ejpam-5978	102	22	=	=	SYM
ejpam-5978	103	1	xn	xn	PROPN
ejpam-5978	104	1	+	+	NUM
ejpam-5978	104	2	n−1∑	n−1∑	NUM
ejpam-5978	104	3	i=1	i=1	PROPN
ejpam-5978	104	4	2xiy	2xiy	NUM
ejpam-5978	104	5	+	+	CCONJ
ejpam-5978	104	6	n−2∑	n−2∑	NUM
ejpam-5978	104	7	i=1	i=1	PROPN
ejpam-5978	104	8	(	(	PUNCT
ejpam-5978	104	9	n−	n−	NOUN
ejpam-5978	104	10	1−	1−	NUM
ejpam-5978	104	11	i)xiy2	i)xiy2	PROPN
ejpam-5978	104	12	.	.	PUNCT
ejpam-5978	105	1	■	■	PUNCT
ejpam-5978	105	2	let	let	VERB
ejpam-5978	105	3	v	v	X
ejpam-5978	105	4	(	(	PUNCT
ejpam-5978	105	5	pn	pn	NOUN
ejpam-5978	105	6	)	)	PUNCT
ejpam-5978	105	7	=	=	SYM
ejpam-5978	105	8	{	{	PUNCT
ejpam-5978	105	9	v1	v1	PROPN
ejpam-5978	105	10	,	,	PUNCT
ejpam-5978	105	11	.	.	PUNCT
ejpam-5978	105	12	.	.	PUNCT
ejpam-5978	106	1	.	.	PUNCT
ejpam-5978	107	1	,	,	PUNCT
ejpam-5978	107	2	vn	vn	AUX
ejpam-5978	107	3	}	}	PUNCT
ejpam-5978	107	4	be	be	AUX
ejpam-5978	107	5	vertex	vertex	NOUN
ejpam-5978	107	6	set	set	NOUN
ejpam-5978	107	7	of	of	ADP
ejpam-5978	107	8	pn	pn	PROPN
ejpam-5978	107	9	.	.	PROPN
ejpam-5978	107	10	note	note	VERB
ejpam-5978	107	11	that	that	SCONJ
ejpam-5978	107	12	when	when	SCONJ
ejpam-5978	107	13	i	i	PRON
ejpam-5978	107	14	=	=	SYM
ejpam-5978	107	15	n	n	CCONJ
ejpam-5978	107	16	,	,	PUNCT
ejpam-5978	107	17	there	there	PRON
ejpam-5978	107	18	is	be	VERB
ejpam-5978	107	19	only	only	ADV
ejpam-5978	107	20	1	1	NUM
ejpam-5978	107	21	n	n	CCONJ
ejpam-5978	107	22	-	-	PUNCT
ejpam-5978	107	23	convex	convex	NOUN
ejpam-5978	107	24	subset	subset	NOUN
ejpam-5978	107	25	of	of	ADP
ejpam-5978	107	26	v	v	PROPN
ejpam-5978	107	27	(	(	PUNCT
ejpam-5978	107	28	pn	pn	NOUN
ejpam-5978	107	29	)	)	PUNCT
ejpam-5978	107	30	with	with	ADP
ejpam-5978	107	31	empty	empty	ADJ
ejpam-5978	107	32	(	(	PUNCT
ejpam-5978	107	33	zero	zero	NUM
ejpam-5978	107	34	cardinality	cardinality	NOUN
ejpam-5978	107	35	)	)	PUNCT
ejpam-5978	107	36	maximum	maximum	ADJ
ejpam-5978	107	37	independent	independent	ADJ
ejpam-5978	107	38	neighborhood	neighborhood	NOUN
ejpam-5978	107	39	system	system	NOUN
ejpam-5978	107	40	(	(	PUNCT
ejpam-5978	107	41	γin	γin	NOUN
ejpam-5978	107	42	)	)	PUNCT
ejpam-5978	107	43	.	.	PUNCT
ejpam-5978	108	1	now	now	ADV
ejpam-5978	108	2	,	,	PUNCT
ejpam-5978	108	3	for	for	ADP
ejpam-5978	108	4	i	i	PROPN
ejpam-5978	108	5	=	=	SYM
ejpam-5978	108	6	1	1	NUM
ejpam-5978	108	7	,	,	PUNCT
ejpam-5978	108	8	2	2	NUM
ejpam-5978	108	9	,	,	PUNCT
ejpam-5978	108	10	...	...	PUNCT
ejpam-5978	108	11	,	,	PUNCT
ejpam-5978	108	12	(	(	PUNCT
ejpam-5978	108	13	n−1	n−1	PROPN
ejpam-5978	108	14	)	)	PUNCT
ejpam-5978	108	15	,	,	PUNCT
ejpam-5978	108	16	there	there	PRON
ejpam-5978	108	17	are	be	VERB
ejpam-5978	108	18	(	(	PUNCT
ejpam-5978	108	19	n−1	n−1	PROPN
ejpam-5978	108	20	)	)	PUNCT
ejpam-5978	108	21	i	i	NOUN
ejpam-5978	108	22	-	-	PUNCT
ejpam-5978	108	23	convex	convex	ADJ
ejpam-5978	108	24	subsets	subset	NOUN
ejpam-5978	108	25	of	of	ADP
ejpam-5978	108	26	v	v	NOUN
ejpam-5978	108	27	(	(	PUNCT
ejpam-5978	108	28	pn	pn	NOUN
ejpam-5978	108	29	)	)	PUNCT
ejpam-5978	108	30	with	with	ADP
ejpam-5978	108	31	maximum	maximum	ADJ
ejpam-5978	108	32	independent	independent	ADJ
ejpam-5978	108	33	neighborhood	neighborhood	NOUN
ejpam-5978	108	34	system	system	NOUN
ejpam-5978	108	35	(	(	PUNCT
ejpam-5978	108	36	γin)-set	γin)-set	PROPN
ejpam-5978	108	37	cardinality	cardinality	PROPN
ejpam-5978	108	38	equal	equal	ADJ
ejpam-5978	108	39	to	to	ADP
ejpam-5978	108	40	1	1	NUM
ejpam-5978	108	41	.	.	PUNCT
ejpam-5978	109	1	moreover	moreover	ADV
ejpam-5978	109	2	,	,	PUNCT
ejpam-5978	109	3	there	there	PRON
ejpam-5978	109	4	are	be	VERB
ejpam-5978	109	5	(	(	PUNCT
ejpam-5978	109	6	n	n	CCONJ
ejpam-5978	109	7	−	−	PROPN
ejpam-5978	109	8	2	2	NUM
ejpam-5978	109	9	)	)	PUNCT
ejpam-5978	109	10	i	i	NOUN
ejpam-5978	109	11	-	-	PUNCT
ejpam-5978	109	12	convex	convex	ADJ
ejpam-5978	109	13	subsets	subset	NOUN
ejpam-5978	109	14	of	of	ADP
ejpam-5978	109	15	v	v	NOUN
ejpam-5978	109	16	(	(	PUNCT
ejpam-5978	109	17	pn	pn	NOUN
ejpam-5978	109	18	)	)	PUNCT
ejpam-5978	109	19	with	with	ADP
ejpam-5978	109	20	maximum	maximum	ADJ
ejpam-5978	109	21	independent	independent	ADJ
ejpam-5978	109	22	neighborhood	neighborhood	NOUN
ejpam-5978	109	23	system	system	NOUN
ejpam-5978	109	24	(	(	PUNCT
ejpam-5978	109	25	γin)-sets	γin)-set	NOUN
ejpam-5978	109	26	.	.	PUNCT
ejpam-5978	110	1	thus	thus	ADV
ejpam-5978	110	2	,	,	PUNCT
ejpam-5978	110	3	by	by	ADP
ejpam-5978	110	4	combining	combine	VERB
ejpam-5978	110	5	all	all	DET
ejpam-5978	110	6	the	the	DET
ejpam-5978	110	7	vertices	vertex	NOUN
ejpam-5978	110	8	,	,	PUNCT
ejpam-5978	110	9	we	we	PRON
ejpam-5978	110	10	have	have	VERB
ejpam-5978	110	11	1	1	NUM
ejpam-5978	110	12	+	+	CCONJ
ejpam-5978	110	13	(	(	PUNCT
ejpam-5978	110	14	n−	n−	NOUN
ejpam-5978	110	15	1	1	NUM
ejpam-5978	110	16	)	)	PUNCT
ejpam-5978	110	17	+	+	CCONJ
ejpam-5978	110	18	(	(	PUNCT
ejpam-5978	110	19	n−	n−	NOUN
ejpam-5978	110	20	2	2	NUM
ejpam-5978	110	21	)	)	PUNCT
ejpam-5978	110	22	=	=	PUNCT
ejpam-5978	111	1	2n−	2n−	NUM
ejpam-5978	111	2	2	2	NUM
ejpam-5978	111	3	number	number	NOUN
ejpam-5978	111	4	of	of	ADP
ejpam-5978	111	5	terms	term	NOUN
ejpam-5978	111	6	of	of	ADP
ejpam-5978	111	7	the	the	DET
ejpam-5978	111	8	convex	convex	ADJ
ejpam-5978	111	9	independent	independent	ADJ
ejpam-5978	111	10	neighborhood	neighborhood	NOUN
ejpam-5978	111	11	polynomial	polynomial	NOUN
ejpam-5978	111	12	of	of	ADP
ejpam-5978	111	13	pn	pn	PROPN
ejpam-5978	111	14	.	.	PUNCT
ejpam-5978	112	1	thus	thus	ADV
ejpam-5978	112	2	,	,	PUNCT
ejpam-5978	112	3	we	we	PRON
ejpam-5978	112	4	have	have	VERB
ejpam-5978	112	5	this	this	DET
ejpam-5978	112	6	corollary	corollary	ADJ
ejpam-5978	112	7	corollary	corollary	ADJ
ejpam-5978	112	8	4.2	4.2	NUM
ejpam-5978	112	9	.	.	PUNCT
ejpam-5978	113	1	for	for	ADP
ejpam-5978	113	2	n	n	PRON
ejpam-5978	113	3	≥	≥	NUM
ejpam-5978	113	4	2	2	NUM
ejpam-5978	113	5	,	,	PUNCT
ejpam-5978	113	6	the	the	DET
ejpam-5978	113	7	number	number	NOUN
ejpam-5978	113	8	of	of	ADP
ejpam-5978	113	9	terms	term	NOUN
ejpam-5978	113	10	for	for	ADP
ejpam-5978	113	11	the	the	DET
ejpam-5978	113	12	convex	convex	ADJ
ejpam-5978	113	13	independent	independent	ADJ
ejpam-5978	113	14	neighborhood	neighborhood	NOUN
ejpam-5978	113	15	polynomial	polynomial	NOUN
ejpam-5978	113	16	of	of	ADP
ejpam-5978	113	17	pn	pn	PROPN
ejpam-5978	113	18	is	be	AUX
ejpam-5978	113	19	given	give	VERB
ejpam-5978	113	20	by	by	ADP
ejpam-5978	113	21	2n−	2n−	PROPN
ejpam-5978	113	22	2	2	NUM
ejpam-5978	113	23	.	.	PUNCT
ejpam-5978	113	24	illustration	illustration	NOUN
ejpam-5978	113	25	4.3	4.3	NUM
ejpam-5978	113	26	.	.	PUNCT
ejpam-5978	114	1	consider	consider	VERB
ejpam-5978	114	2	p5	p5	ADJ
ejpam-5978	114	3	be	be	AUX
ejpam-5978	114	4	a	a	DET
ejpam-5978	114	5	path	path	NOUN
ejpam-5978	114	6	of	of	ADP
ejpam-5978	114	7	order	order	NOUN
ejpam-5978	114	8	5	5	NUM
ejpam-5978	114	9	.	.	PUNCT
ejpam-5978	114	10	v1	v1	PROPN
ejpam-5978	114	11	v2	v2	PROPN
ejpam-5978	114	12	v3	v3	PROPN
ejpam-5978	114	13	v4	v4	PROPN
ejpam-5978	114	14	v5	v5	PROPN
ejpam-5978	114	15	figure	figure	NOUN
ejpam-5978	114	16	2	2	NUM
ejpam-5978	114	17	:	:	PUNCT
ejpam-5978	114	18	a	a	DET
ejpam-5978	114	19	path	path	NOUN
ejpam-5978	114	20	p5	p5	ADJ
ejpam-5978	114	21	of	of	ADP
ejpam-5978	114	22	order	order	NOUN
ejpam-5978	114	23	5	5	NUM
ejpam-5978	114	24	then	then	ADV
ejpam-5978	114	25	,	,	PUNCT
ejpam-5978	114	26	by	by	ADP
ejpam-5978	114	27	using	use	VERB
ejpam-5978	114	28	theorem	theorem	NOUN
ejpam-5978	114	29	4.1	4.1	NUM
ejpam-5978	114	30	,	,	PUNCT
ejpam-5978	114	31	γcin(p5;x	γcin(p5;x	NOUN
ejpam-5978	114	32	,	,	PUNCT
ejpam-5978	114	33	y	y	NOUN
ejpam-5978	114	34	)	)	PUNCT
ejpam-5978	114	35	=	=	SYM
ejpam-5978	114	36	x5	x5	NOUN
ejpam-5978	114	37	+	+	CCONJ
ejpam-5978	114	38	5−1∑	5−1∑	NUM
ejpam-5978	114	39	i=1	i=1	PROPN
ejpam-5978	114	40	2xiy	2xiy	NUM
ejpam-5978	115	1	+	+	CCONJ
ejpam-5978	116	1	5−2∑	5−2∑	NUM
ejpam-5978	116	2	i=1	i=1	PROPN
ejpam-5978	116	3	(	(	PUNCT
ejpam-5978	116	4	5−	5−	NUM
ejpam-5978	116	5	1−	1−	NUM
ejpam-5978	116	6	i)xiy2	i)xiy2	PROPN
ejpam-5978	116	7	=	=	SYM
ejpam-5978	116	8	x5	x5	PROPN
ejpam-5978	117	1	+	+	CCONJ
ejpam-5978	117	2	4∑	4∑	NOUN
ejpam-5978	117	3	i=1	i=1	PROPN
ejpam-5978	117	4	2xiy	2xiy	NUM
ejpam-5978	118	1	+	+	NOUN
ejpam-5978	119	1	3∑	3∑	NUM
ejpam-5978	119	2	i=1	i=1	PROPN
ejpam-5978	120	1	(	(	PUNCT
ejpam-5978	120	2	4−	4−	NUM
ejpam-5978	120	3	i)xiy2	i)xiy2	PROPN
ejpam-5978	120	4	e.j	e.j	PROPN
ejpam-5978	120	5	.	.	PROPN
ejpam-5978	120	6	aguilon	aguilon	PROPN
ejpam-5978	120	7	,	,	PUNCT
ejpam-5978	120	8	s.	s.	PROPN
ejpam-5978	120	9	dagondon	dagondon	PROPN
ejpam-5978	120	10	,	,	PUNCT
ejpam-5978	120	11	r.	r.	PROPN
ejpam-5978	120	12	artes	artes	PROPN
ejpam-5978	120	13	/	/	SYM
ejpam-5978	120	14	eur	eur	PROPN
ejpam-5978	120	15	.	.	PUNCT
ejpam-5978	121	1	j.	j.	PROPN
ejpam-5978	121	2	pure	pure	PROPN
ejpam-5978	121	3	appl	appl	PROPN
ejpam-5978	121	4	.	.	PROPN
ejpam-5978	121	5	math	math	PROPN
ejpam-5978	121	6	,	,	PUNCT
ejpam-5978	121	7	18	18	NUM
ejpam-5978	121	8	(	(	PUNCT
ejpam-5978	121	9	2	2	NUM
ejpam-5978	121	10	)	)	PUNCT
ejpam-5978	121	11	(	(	PUNCT
ejpam-5978	121	12	2025	2025	NUM
ejpam-5978	121	13	)	)	PUNCT
ejpam-5978	121	14	,	,	PUNCT
ejpam-5978	121	15	5978	5978	NUM
ejpam-5978	121	16	7	7	NUM
ejpam-5978	121	17	of	of	ADP
ejpam-5978	121	18	18	18	NUM
ejpam-5978	121	19	=	=	SYM
ejpam-5978	121	20	x5	x5	PROPN
ejpam-5978	121	21	+	+	CCONJ
ejpam-5978	121	22	(	(	PUNCT
ejpam-5978	121	23	2xy	2xy	ADJ
ejpam-5978	121	24	+	+	NUM
ejpam-5978	121	25	2x2y	2x2y	NOUN
ejpam-5978	121	26	+	+	CCONJ
ejpam-5978	121	27	2x3y	2x3y	ADJ
ejpam-5978	121	28	+	+	CCONJ
ejpam-5978	121	29	2x4y	2x4y	NOUN
ejpam-5978	121	30	)	)	PUNCT
ejpam-5978	122	1	+	+	CCONJ
ejpam-5978	122	2	(	(	PUNCT
ejpam-5978	123	1	3xy2	3xy2	NUM
ejpam-5978	123	2	+	+	NUM
ejpam-5978	123	3	2x2y2	2x2y2	NUM
ejpam-5978	123	4	+	+	CCONJ
ejpam-5978	123	5	x3y2	x3y2	NOUN
ejpam-5978	123	6	)	)	PUNCT
ejpam-5978	123	7	=	=	SYM
ejpam-5978	123	8	x5	x5	NOUN
ejpam-5978	123	9	+	+	CCONJ
ejpam-5978	123	10	2x4y	2x4y	ADJ
ejpam-5978	123	11	+	+	CCONJ
ejpam-5978	123	12	2x3y	2x3y	ADJ
ejpam-5978	123	13	+	+	X
ejpam-5978	123	14	x3y2	x3y2	NOUN
ejpam-5978	123	15	+	+	NUM
ejpam-5978	123	16	2x2y	2x2y	NUM
ejpam-5978	123	17	+	+	CCONJ
ejpam-5978	123	18	2x2y2	2x2y2	NUM
ejpam-5978	123	19	+	+	CCONJ
ejpam-5978	123	20	2xy	2xy	ADJ
ejpam-5978	123	21	+	+	CCONJ
ejpam-5978	123	22	3xy2	3xy2	NUM
ejpam-5978	123	23	.	.	PUNCT
ejpam-5978	124	1	and	and	CCONJ
ejpam-5978	124	2	by	by	ADP
ejpam-5978	124	3	corollary	corollary	ADJ
ejpam-5978	124	4	4.2	4.2	NUM
ejpam-5978	124	5	,	,	PUNCT
ejpam-5978	124	6	there	there	PRON
ejpam-5978	124	7	are	be	VERB
ejpam-5978	124	8	[	[	X
ejpam-5978	124	9	2(5)−	2(5)−	NUM
ejpam-5978	124	10	2	2	NUM
ejpam-5978	124	11	]	]	PUNCT
ejpam-5978	124	12	=	=	SYM
ejpam-5978	124	13	8	8	NUM
ejpam-5978	124	14	terms	term	NOUN
ejpam-5978	124	15	in	in	ADP
ejpam-5978	124	16	convex	convex	ADJ
ejpam-5978	124	17	independent	independent	ADJ
ejpam-5978	124	18	neighborhood	neighborhood	NOUN
ejpam-5978	124	19	polynomial	polynomial	NOUN
ejpam-5978	124	20	of	of	ADP
ejpam-5978	124	21	p5	p5	PROPN
ejpam-5978	124	22	.	.	PUNCT
ejpam-5978	125	1	to	to	PART
ejpam-5978	125	2	see	see	VERB
ejpam-5978	125	3	the	the	DET
ejpam-5978	125	4	convex	convex	ADJ
ejpam-5978	125	5	subsets	subset	NOUN
ejpam-5978	125	6	of	of	ADP
ejpam-5978	125	7	v	v	NOUN
ejpam-5978	125	8	(	(	PUNCT
ejpam-5978	125	9	p5	p5	ADJ
ejpam-5978	125	10	)	)	PUNCT
ejpam-5978	125	11	and	and	CCONJ
ejpam-5978	125	12	its	its	PRON
ejpam-5978	125	13	corresponding	corresponding	ADJ
ejpam-5978	125	14	γin	γin	NOUN
ejpam-5978	125	15	-	-	PUNCT
ejpam-5978	125	16	sets	set	NOUN
ejpam-5978	125	17	of	of	ADP
ejpam-5978	125	18	p5	p5	NOUN
ejpam-5978	125	19	,	,	PUNCT
ejpam-5978	125	20	refer	refer	VERB
ejpam-5978	125	21	to	to	ADP
ejpam-5978	125	22	the	the	DET
ejpam-5978	125	23	tables	table	NOUN
ejpam-5978	125	24	4	4	NUM
ejpam-5978	125	25	,	,	PUNCT
ejpam-5978	125	26	5	5	NUM
ejpam-5978	125	27	,	,	PUNCT
ejpam-5978	125	28	and	and	CCONJ
ejpam-5978	125	29	6	6	NUM
ejpam-5978	125	30	:	:	SYM
ejpam-5978	125	31	1	1	NUM
ejpam-5978	125	32	-	-	PUNCT
ejpam-5978	125	33	convex	convex	VERB
ejpam-5978	125	34	γin	γin	NOUN
ejpam-5978	125	35	-	-	PUNCT
ejpam-5978	125	36	sets	set	NOUN
ejpam-5978	125	37	{	{	PUNCT
ejpam-5978	125	38	v1	v1	NOUN
ejpam-5978	125	39	}	}	PUNCT
ejpam-5978	125	40	{	{	PUNCT
ejpam-5978	125	41	v2	v2	NOUN
ejpam-5978	125	42	}	}	PUNCT
ejpam-5978	125	43	{	{	PUNCT
ejpam-5978	125	44	v2	v2	NOUN
ejpam-5978	125	45	}	}	PUNCT
ejpam-5978	125	46	{	{	PUNCT
ejpam-5978	125	47	v1	v1	NOUN
ejpam-5978	125	48	,	,	PUNCT
ejpam-5978	125	49	v3	v3	PROPN
ejpam-5978	125	50	}	}	PUNCT
ejpam-5978	125	51	{	{	PUNCT
ejpam-5978	125	52	v3	v3	PROPN
ejpam-5978	125	53	}	}	PUNCT
ejpam-5978	125	54	{	{	PUNCT
ejpam-5978	125	55	v2	v2	PROPN
ejpam-5978	125	56	,	,	PUNCT
ejpam-5978	125	57	v4	v4	PROPN
ejpam-5978	125	58	}	}	PUNCT
ejpam-5978	125	59	{	{	PUNCT
ejpam-5978	125	60	v4	v4	NOUN
ejpam-5978	125	61	}	}	PUNCT
ejpam-5978	125	62	{	{	PUNCT
ejpam-5978	125	63	v3	v3	PROPN
ejpam-5978	125	64	,	,	PUNCT
ejpam-5978	125	65	v5	v5	PROPN
ejpam-5978	125	66	}	}	PUNCT
ejpam-5978	125	67	{	{	PUNCT
ejpam-5978	125	68	v5	v5	PROPN
ejpam-5978	125	69	}	}	PUNCT
ejpam-5978	125	70	{	{	PUNCT
ejpam-5978	125	71	v4	v4	NOUN
ejpam-5978	125	72	}	}	PUNCT
ejpam-5978	125	73	table	table	NOUN
ejpam-5978	125	74	4	4	NUM
ejpam-5978	125	75	:	:	SYM
ejpam-5978	125	76	1	1	NUM
ejpam-5978	125	77	-	-	PUNCT
ejpam-5978	125	78	convex	convex	NOUN
ejpam-5978	125	79	subsets	subset	NOUN
ejpam-5978	125	80	of	of	ADP
ejpam-5978	125	81	v	v	NOUN
ejpam-5978	125	82	(	(	PUNCT
ejpam-5978	125	83	p5	p5	ADJ
ejpam-5978	125	84	)	)	PUNCT
ejpam-5978	125	85	and	and	CCONJ
ejpam-5978	125	86	its	its	PRON
ejpam-5978	125	87	corresponding	corresponding	ADJ
ejpam-5978	125	88	γin	γin	NOUN
ejpam-5978	125	89	-	-	PUNCT
ejpam-5978	125	90	sets	set	NOUN
ejpam-5978	125	91	.	.	PUNCT
ejpam-5978	126	1	table	table	NOUN
ejpam-5978	126	2	4	4	NUM
ejpam-5978	126	3	shows	show	VERB
ejpam-5978	126	4	that	that	SCONJ
ejpam-5978	126	5	there	there	PRON
ejpam-5978	126	6	are	be	VERB
ejpam-5978	126	7	2	2	NUM
ejpam-5978	126	8	1	1	NUM
ejpam-5978	126	9	-	-	PUNCT
ejpam-5978	126	10	convex	convex	NOUN
ejpam-5978	126	11	subsets	subset	NOUN
ejpam-5978	126	12	of	of	ADP
ejpam-5978	126	13	v	v	NOUN
ejpam-5978	126	14	(	(	PUNCT
ejpam-5978	126	15	p5	p5	PROPN
ejpam-5978	126	16	)	)	PUNCT
ejpam-5978	126	17	with	with	ADP
ejpam-5978	126	18	γin	γin	NOUN
ejpam-5978	126	19	-	-	PUNCT
ejpam-5978	126	20	sets	set	NOUN
ejpam-5978	126	21	cardinality	cardinality	NOUN
ejpam-5978	126	22	equal	equal	ADJ
ejpam-5978	126	23	to	to	ADP
ejpam-5978	126	24	1	1	NUM
ejpam-5978	126	25	,	,	PUNCT
ejpam-5978	126	26	and	and	CCONJ
ejpam-5978	126	27	3	3	NUM
ejpam-5978	126	28	1	1	NUM
ejpam-5978	126	29	-	-	PUNCT
ejpam-5978	126	30	convex	convex	NOUN
ejpam-5978	126	31	subsets	subset	NOUN
ejpam-5978	126	32	of	of	ADP
ejpam-5978	126	33	v	v	NOUN
ejpam-5978	126	34	(	(	PUNCT
ejpam-5978	126	35	p5	p5	PROPN
ejpam-5978	126	36	)	)	PUNCT
ejpam-5978	126	37	with	with	ADP
ejpam-5978	126	38	γin	γin	NOUN
ejpam-5978	126	39	-	-	PUNCT
ejpam-5978	126	40	sets	set	NOUN
ejpam-5978	126	41	cardinality	cardinality	NOUN
ejpam-5978	126	42	equal	equal	ADJ
ejpam-5978	126	43	to	to	ADP
ejpam-5978	126	44	2	2	NUM
ejpam-5978	126	45	.	.	PUNCT
ejpam-5978	127	1	this	this	PRON
ejpam-5978	127	2	contributes	contribute	VERB
ejpam-5978	127	3	to	to	ADP
ejpam-5978	127	4	the	the	DET
ejpam-5978	127	5	convex	convex	ADJ
ejpam-5978	127	6	independent	independent	ADJ
ejpam-5978	127	7	neighborhood	neighborhood	NOUN
ejpam-5978	127	8	polynomial	polynomial	NOUN
ejpam-5978	127	9	of	of	ADP
ejpam-5978	127	10	p5	p5	ADJ
ejpam-5978	127	11	as	as	ADP
ejpam-5978	127	12	2xy	2xy	ADJ
ejpam-5978	127	13	+	+	CCONJ
ejpam-5978	127	14	3xy2	3xy2	NUM
ejpam-5978	127	15	.	.	X
ejpam-5978	128	1	2	2	NUM
ejpam-5978	128	2	-	-	NUM
ejpam-5978	128	3	convex	convex	VERB
ejpam-5978	128	4	γin	γin	NOUN
ejpam-5978	128	5	-	-	PUNCT
ejpam-5978	128	6	sets	set	NOUN
ejpam-5978	128	7	{	{	PUNCT
ejpam-5978	128	8	v1	v1	NOUN
ejpam-5978	128	9	,	,	PUNCT
ejpam-5978	128	10	v2	v2	PROPN
ejpam-5978	128	11	}	}	PUNCT
ejpam-5978	128	12	{	{	PUNCT
ejpam-5978	128	13	v3	v3	PROPN
ejpam-5978	128	14	}	}	PUNCT
ejpam-5978	128	15	{	{	PUNCT
ejpam-5978	128	16	v2	v2	PROPN
ejpam-5978	128	17	,	,	PUNCT
ejpam-5978	128	18	v3	v3	PROPN
ejpam-5978	128	19	}	}	PUNCT
ejpam-5978	128	20	{	{	PUNCT
ejpam-5978	128	21	v1	v1	NOUN
ejpam-5978	128	22	,	,	PUNCT
ejpam-5978	128	23	v4	v4	NOUN
ejpam-5978	128	24	}	}	PUNCT
ejpam-5978	128	25	{	{	PUNCT
ejpam-5978	128	26	v3	v3	PROPN
ejpam-5978	128	27	,	,	PUNCT
ejpam-5978	128	28	v4	v4	PROPN
ejpam-5978	128	29	}	}	PUNCT
ejpam-5978	128	30	{	{	PUNCT
ejpam-5978	128	31	v2	v2	PROPN
ejpam-5978	128	32	,	,	PUNCT
ejpam-5978	128	33	v5	v5	PROPN
ejpam-5978	128	34	}	}	PUNCT
ejpam-5978	128	35	{	{	PUNCT
ejpam-5978	128	36	v4	v4	NOUN
ejpam-5978	128	37	,	,	PUNCT
ejpam-5978	128	38	v5	v5	PROPN
ejpam-5978	128	39	}	}	PUNCT
ejpam-5978	128	40	{	{	PUNCT
ejpam-5978	128	41	v3	v3	PROPN
ejpam-5978	128	42	}	}	PUNCT
ejpam-5978	128	43	table	table	NOUN
ejpam-5978	128	44	5	5	NUM
ejpam-5978	128	45	:	:	SYM
ejpam-5978	128	46	2	2	NUM
ejpam-5978	128	47	-	-	PUNCT
ejpam-5978	128	48	convex	convex	NOUN
ejpam-5978	128	49	subsets	subset	NOUN
ejpam-5978	128	50	of	of	ADP
ejpam-5978	128	51	v	v	NOUN
ejpam-5978	128	52	(	(	PUNCT
ejpam-5978	128	53	p5	p5	ADJ
ejpam-5978	128	54	)	)	PUNCT
ejpam-5978	128	55	and	and	CCONJ
ejpam-5978	128	56	its	its	PRON
ejpam-5978	128	57	corresponding	corresponding	ADJ
ejpam-5978	128	58	γin	γin	NOUN
ejpam-5978	128	59	-	-	PUNCT
ejpam-5978	128	60	sets	set	NOUN
ejpam-5978	128	61	.	.	PUNCT
ejpam-5978	129	1	table	table	NOUN
ejpam-5978	129	2	5	5	NUM
ejpam-5978	129	3	shows	show	VERB
ejpam-5978	129	4	that	that	SCONJ
ejpam-5978	129	5	there	there	PRON
ejpam-5978	129	6	are	be	VERB
ejpam-5978	129	7	2	2	NUM
ejpam-5978	129	8	2	2	NUM
ejpam-5978	129	9	-	-	PUNCT
ejpam-5978	129	10	convex	convex	NOUN
ejpam-5978	129	11	subsets	subset	NOUN
ejpam-5978	129	12	of	of	ADP
ejpam-5978	129	13	v	v	NOUN
ejpam-5978	129	14	(	(	PUNCT
ejpam-5978	129	15	p5	p5	PROPN
ejpam-5978	129	16	)	)	PUNCT
ejpam-5978	129	17	with	with	ADP
ejpam-5978	129	18	γin	γin	NOUN
ejpam-5978	129	19	-	-	PUNCT
ejpam-5978	129	20	sets	set	NOUN
ejpam-5978	129	21	cardinality	cardinality	NOUN
ejpam-5978	129	22	equal	equal	ADJ
ejpam-5978	129	23	to	to	ADP
ejpam-5978	129	24	1	1	NUM
ejpam-5978	129	25	,	,	PUNCT
ejpam-5978	129	26	and	and	CCONJ
ejpam-5978	129	27	2	2	NUM
ejpam-5978	129	28	2	2	NUM
ejpam-5978	129	29	-	-	PUNCT
ejpam-5978	129	30	convex	convex	NOUN
ejpam-5978	129	31	subsets	subset	NOUN
ejpam-5978	129	32	of	of	ADP
ejpam-5978	129	33	v	v	NOUN
ejpam-5978	129	34	(	(	PUNCT
ejpam-5978	129	35	p5	p5	PROPN
ejpam-5978	129	36	)	)	PUNCT
ejpam-5978	129	37	with	with	ADP
ejpam-5978	129	38	γin	γin	NOUN
ejpam-5978	129	39	-	-	PUNCT
ejpam-5978	129	40	sets	set	NOUN
ejpam-5978	129	41	cardinality	cardinality	NOUN
ejpam-5978	129	42	equal	equal	ADJ
ejpam-5978	129	43	to	to	ADP
ejpam-5978	129	44	2	2	NUM
ejpam-5978	129	45	.	.	PUNCT
ejpam-5978	130	1	this	this	PRON
ejpam-5978	130	2	contributes	contribute	VERB
ejpam-5978	130	3	to	to	ADP
ejpam-5978	130	4	the	the	DET
ejpam-5978	130	5	convex	convex	ADJ
ejpam-5978	130	6	independent	independent	ADJ
ejpam-5978	130	7	neighborhood	neighborhood	NOUN
ejpam-5978	130	8	polynomial	polynomial	NOUN
ejpam-5978	130	9	of	of	ADP
ejpam-5978	130	10	p5	p5	ADJ
ejpam-5978	130	11	as	as	ADP
ejpam-5978	130	12	2x2y	2x2y	NUM
ejpam-5978	130	13	+	+	CCONJ
ejpam-5978	130	14	2x2y2	2x2y2	NUM
ejpam-5978	130	15	.	.	PUNCT
ejpam-5978	131	1	3	3	NUM
ejpam-5978	131	2	-	-	NUM
ejpam-5978	131	3	convex	convex	VERB
ejpam-5978	131	4	γin	γin	NOUN
ejpam-5978	131	5	-	-	PUNCT
ejpam-5978	131	6	sets	set	NOUN
ejpam-5978	131	7	{	{	PUNCT
ejpam-5978	131	8	v1	v1	NOUN
ejpam-5978	131	9	,	,	PUNCT
ejpam-5978	131	10	v2	v2	PROPN
ejpam-5978	131	11	,	,	PUNCT
ejpam-5978	131	12	v3	v3	PROPN
ejpam-5978	131	13	}	}	PUNCT
ejpam-5978	131	14	{	{	PUNCT
ejpam-5978	131	15	v4	v4	NOUN
ejpam-5978	131	16	}	}	PUNCT
ejpam-5978	131	17	{	{	PUNCT
ejpam-5978	131	18	v2	v2	PROPN
ejpam-5978	131	19	,	,	PUNCT
ejpam-5978	131	20	v3	v3	PROPN
ejpam-5978	131	21	,	,	PUNCT
ejpam-5978	131	22	v4	v4	PROPN
ejpam-5978	131	23	}	}	PUNCT
ejpam-5978	131	24	{	{	PUNCT
ejpam-5978	131	25	v1	v1	NOUN
ejpam-5978	131	26	,	,	PUNCT
ejpam-5978	131	27	v5	v5	PROPN
ejpam-5978	131	28	}	}	PUNCT
ejpam-5978	131	29	{	{	PUNCT
ejpam-5978	131	30	v3	v3	PROPN
ejpam-5978	131	31	,	,	PUNCT
ejpam-5978	131	32	v4	v4	PROPN
ejpam-5978	131	33	,	,	PUNCT
ejpam-5978	131	34	v5	v5	PROPN
ejpam-5978	131	35	}	}	PUNCT
ejpam-5978	131	36	{	{	PUNCT
ejpam-5978	131	37	v2	v2	NOUN
ejpam-5978	131	38	}	}	PUNCT
ejpam-5978	131	39	table	table	NOUN
ejpam-5978	131	40	6	6	NUM
ejpam-5978	131	41	:	:	SYM
ejpam-5978	131	42	3	3	NUM
ejpam-5978	131	43	-	-	PUNCT
ejpam-5978	131	44	convex	convex	ADJ
ejpam-5978	131	45	subsets	subset	NOUN
ejpam-5978	131	46	of	of	ADP
ejpam-5978	131	47	v	v	NOUN
ejpam-5978	131	48	(	(	PUNCT
ejpam-5978	131	49	p5	p5	ADJ
ejpam-5978	131	50	)	)	PUNCT
ejpam-5978	131	51	and	and	CCONJ
ejpam-5978	131	52	its	its	PRON
ejpam-5978	131	53	corresponding	corresponding	ADJ
ejpam-5978	131	54	γin	γin	NOUN
ejpam-5978	131	55	-	-	PUNCT
ejpam-5978	131	56	sets	set	NOUN
ejpam-5978	131	57	.	.	PUNCT
ejpam-5978	132	1	table	table	NOUN
ejpam-5978	132	2	6	6	NUM
ejpam-5978	132	3	shows	show	VERB
ejpam-5978	132	4	that	that	SCONJ
ejpam-5978	132	5	there	there	PRON
ejpam-5978	132	6	are	be	VERB
ejpam-5978	132	7	2	2	NUM
ejpam-5978	132	8	3	3	NUM
ejpam-5978	132	9	-	-	PUNCT
ejpam-5978	132	10	convex	convex	NOUN
ejpam-5978	132	11	subsets	subset	NOUN
ejpam-5978	132	12	of	of	ADP
ejpam-5978	132	13	v	v	NOUN
ejpam-5978	132	14	(	(	PUNCT
ejpam-5978	132	15	p5	p5	PROPN
ejpam-5978	132	16	)	)	PUNCT
ejpam-5978	132	17	with	with	ADP
ejpam-5978	132	18	γin	γin	NOUN
ejpam-5978	132	19	-	-	PUNCT
ejpam-5978	132	20	sets	set	NOUN
ejpam-5978	132	21	cardinality	cardinality	NOUN
ejpam-5978	132	22	equal	equal	ADJ
ejpam-5978	132	23	to	to	ADP
ejpam-5978	132	24	1	1	NUM
ejpam-5978	132	25	,	,	PUNCT
ejpam-5978	132	26	and	and	CCONJ
ejpam-5978	132	27	1	1	NUM
ejpam-5978	132	28	3	3	NUM
ejpam-5978	132	29	-	-	PUNCT
ejpam-5978	132	30	convex	convex	NOUN
ejpam-5978	132	31	subsets	subset	NOUN
ejpam-5978	132	32	of	of	ADP
ejpam-5978	132	33	v	v	NOUN
ejpam-5978	132	34	(	(	PUNCT
ejpam-5978	132	35	p5	p5	PROPN
ejpam-5978	132	36	)	)	PUNCT
ejpam-5978	132	37	with	with	ADP
ejpam-5978	132	38	γin	γin	NOUN
ejpam-5978	132	39	-	-	PUNCT
ejpam-5978	132	40	sets	set	NOUN
ejpam-5978	132	41	cardinality	cardinality	NOUN
ejpam-5978	132	42	equal	equal	ADJ
ejpam-5978	132	43	to	to	ADP
ejpam-5978	132	44	2	2	NUM
ejpam-5978	132	45	.	.	PUNCT
ejpam-5978	133	1	this	this	PRON
ejpam-5978	133	2	contributes	contribute	VERB
ejpam-5978	133	3	e.j	e.j	PROPN
ejpam-5978	133	4	.	.	PROPN
ejpam-5978	133	5	aguilon	aguilon	PROPN
ejpam-5978	133	6	,	,	PUNCT
ejpam-5978	133	7	s.	s.	PROPN
ejpam-5978	133	8	dagondon	dagondon	PROPN
ejpam-5978	133	9	,	,	PUNCT
ejpam-5978	133	10	r.	r.	PROPN
ejpam-5978	133	11	artes	artes	PROPN
ejpam-5978	133	12	/	/	SYM
ejpam-5978	133	13	eur	eur	PROPN
ejpam-5978	133	14	.	.	PUNCT
ejpam-5978	134	1	j.	j.	PROPN
ejpam-5978	134	2	pure	pure	PROPN
ejpam-5978	134	3	appl	appl	PROPN
ejpam-5978	134	4	.	.	PROPN
ejpam-5978	134	5	math	math	PROPN
ejpam-5978	134	6	,	,	PUNCT
ejpam-5978	134	7	18	18	NUM
ejpam-5978	134	8	(	(	PUNCT
ejpam-5978	134	9	2	2	NUM
ejpam-5978	134	10	)	)	PUNCT
ejpam-5978	134	11	(	(	PUNCT
ejpam-5978	134	12	2025	2025	NUM
ejpam-5978	134	13	)	)	PUNCT
ejpam-5978	134	14	,	,	PUNCT
ejpam-5978	134	15	5978	5978	NUM
ejpam-5978	134	16	8	8	NUM
ejpam-5978	134	17	of	of	ADP
ejpam-5978	134	18	18	18	NUM
ejpam-5978	134	19	to	to	ADP
ejpam-5978	134	20	the	the	DET
ejpam-5978	134	21	convex	convex	ADJ
ejpam-5978	134	22	independent	independent	ADJ
ejpam-5978	134	23	neighborhood	neighborhood	NOUN
ejpam-5978	134	24	polynomial	polynomial	NOUN
ejpam-5978	134	25	of	of	ADP
ejpam-5978	134	26	p5	p5	ADJ
ejpam-5978	134	27	as	as	ADP
ejpam-5978	134	28	2x3y	2x3y	PROPN
ejpam-5978	134	29	+	+	CCONJ
ejpam-5978	134	30	x3y2	x3y2	NOUN
ejpam-5978	134	31	.	.	NOUN
ejpam-5978	135	1	for	for	ADP
ejpam-5978	135	2	4	4	NUM
ejpam-5978	135	3	-	-	PUNCT
ejpam-5978	135	4	convex	convex	NOUN
ejpam-5978	135	5	subsets	subset	NOUN
ejpam-5978	135	6	of	of	ADP
ejpam-5978	135	7	v	v	NOUN
ejpam-5978	135	8	(	(	PUNCT
ejpam-5978	135	9	p5	p5	PROPN
ejpam-5978	135	10	)	)	PUNCT
ejpam-5978	135	11	,	,	PUNCT
ejpam-5978	135	12	it	it	PRON
ejpam-5978	135	13	can	can	AUX
ejpam-5978	135	14	be	be	AUX
ejpam-5978	135	15	verified	verify	VERB
ejpam-5978	135	16	that	that	SCONJ
ejpam-5978	135	17	there	there	PRON
ejpam-5978	135	18	are	be	VERB
ejpam-5978	135	19	2	2	NUM
ejpam-5978	135	20	4	4	NUM
ejpam-5978	135	21	-	-	PUNCT
ejpam-5978	135	22	convex	convex	NOUN
ejpam-5978	135	23	subset	subset	NOUN
ejpam-5978	135	24	with	with	ADP
ejpam-5978	135	25	γin	γin	NOUN
ejpam-5978	135	26	-	-	PUNCT
ejpam-5978	135	27	sets	set	NOUN
ejpam-5978	135	28	cardinality	cardinality	NOUN
ejpam-5978	135	29	equal	equal	ADJ
ejpam-5978	135	30	to	to	ADP
ejpam-5978	135	31	one	one	NUM
ejpam-5978	135	32	.	.	PUNCT
ejpam-5978	136	1	this	this	PRON
ejpam-5978	136	2	contributes	contribute	VERB
ejpam-5978	136	3	to	to	ADP
ejpam-5978	136	4	the	the	DET
ejpam-5978	136	5	convex	convex	ADJ
ejpam-5978	136	6	independent	independent	ADJ
ejpam-5978	136	7	neighborhood	neighborhood	NOUN
ejpam-5978	136	8	polynomial	polynomial	NOUN
ejpam-5978	136	9	of	of	ADP
ejpam-5978	136	10	p5	p5	ADJ
ejpam-5978	136	11	as	as	ADP
ejpam-5978	136	12	2x4y	2x4y	NOUN
ejpam-5978	136	13	.	.	PUNCT
ejpam-5978	137	1	for	for	ADP
ejpam-5978	137	2	5	5	NUM
ejpam-5978	137	3	-	-	PUNCT
ejpam-5978	137	4	convex	convex	NOUN
ejpam-5978	137	5	subsets	subset	NOUN
ejpam-5978	137	6	of	of	ADP
ejpam-5978	137	7	v	v	NOUN
ejpam-5978	137	8	(	(	PUNCT
ejpam-5978	137	9	p5	p5	PROPN
ejpam-5978	137	10	)	)	PUNCT
ejpam-5978	137	11	,	,	PUNCT
ejpam-5978	137	12	it	it	PRON
ejpam-5978	137	13	can	can	AUX
ejpam-5978	137	14	be	be	AUX
ejpam-5978	137	15	verified	verify	VERB
ejpam-5978	137	16	that	that	SCONJ
ejpam-5978	137	17	there	there	PRON
ejpam-5978	137	18	is	be	VERB
ejpam-5978	137	19	only	only	ADV
ejpam-5978	137	20	1	1	NUM
ejpam-5978	137	21	5	5	NUM
ejpam-5978	137	22	-	-	PUNCT
ejpam-5978	137	23	convex	convex	NOUN
ejpam-5978	137	24	subset	subset	NOUN
ejpam-5978	137	25	with	with	ADP
ejpam-5978	137	26	empty	empty	ADJ
ejpam-5978	137	27	(	(	PUNCT
ejpam-5978	137	28	zero	zero	NUM
ejpam-5978	137	29	cardinality	cardinality	NOUN
ejpam-5978	137	30	)	)	PUNCT
ejpam-5978	137	31	γin	γin	NOUN
ejpam-5978	137	32	-	-	PUNCT
ejpam-5978	137	33	set	set	NOUN
ejpam-5978	137	34	.	.	PUNCT
ejpam-5978	138	1	this	this	PRON
ejpam-5978	138	2	contributes	contribute	VERB
ejpam-5978	138	3	to	to	ADP
ejpam-5978	138	4	the	the	DET
ejpam-5978	138	5	convex	convex	ADJ
ejpam-5978	138	6	independent	independent	ADJ
ejpam-5978	138	7	neighborhood	neighborhood	NOUN
ejpam-5978	138	8	polynomial	polynomial	NOUN
ejpam-5978	138	9	of	of	ADP
ejpam-5978	138	10	p5	p5	ADJ
ejpam-5978	138	11	as	as	ADP
ejpam-5978	138	12	x5	x5	PROPN
ejpam-5978	138	13	.	.	PUNCT
ejpam-5978	138	14	theorem	theorem	PROPN
ejpam-5978	138	15	4.4	4.4	NUM
ejpam-5978	138	16	.	.	PUNCT
ejpam-5978	139	1	let	let	VERB
ejpam-5978	139	2	cn	cn	PROPN
ejpam-5978	139	3	be	be	AUX
ejpam-5978	139	4	a	a	DET
ejpam-5978	139	5	cycle	cycle	NOUN
ejpam-5978	139	6	of	of	ADP
ejpam-5978	139	7	order	order	NOUN
ejpam-5978	139	8	n.	n.	NOUN
ejpam-5978	139	9	then	then	ADV
ejpam-5978	139	10	,	,	PUNCT
ejpam-5978	139	11	for	for	ADP
ejpam-5978	139	12	n	n	PRON
ejpam-5978	139	13	≥	≥	NUM
ejpam-5978	139	14	6	6	NUM
ejpam-5978	139	15	,	,	PUNCT
ejpam-5978	139	16	the	the	DET
ejpam-5978	139	17	convex	convex	ADJ
ejpam-5978	139	18	independent	independent	ADJ
ejpam-5978	139	19	neighborhood	neighborhood	NOUN
ejpam-5978	139	20	polynomial	polynomial	NOUN
ejpam-5978	139	21	of	of	ADP
ejpam-5978	139	22	cn	cn	PROPN
ejpam-5978	139	23	is	be	AUX
ejpam-5978	139	24	γcin(cn;x	γcin(cn;x	PROPN
ejpam-5978	139	25	,	,	PUNCT
ejpam-5978	139	26	y	y	NOUN
ejpam-5978	139	27	)	)	PUNCT
ejpam-5978	140	1	=	=	SYM
ejpam-5978	140	2	xn	xn	NOUN
ejpam-5978	140	3	+	+	CCONJ
ejpam-5978	141	1	n	n	CCONJ
ejpam-5978	141	2	∑n+1	∑n+1	NOUN
ejpam-5978	141	3	2	2	X
ejpam-5978	141	4	i=1	i=1	PROPN
ejpam-5978	141	5	xiy2	xiy2	PROPN
ejpam-5978	141	6	,	,	PUNCT
ejpam-5978	141	7	if	if	SCONJ
ejpam-5978	141	8	n	n	PRON
ejpam-5978	141	9	is	be	AUX
ejpam-5978	141	10	odd	odd	ADJ
ejpam-5978	141	11	xn	xn	PROPN
ejpam-5978	142	1	+	+	CCONJ
ejpam-5978	142	2	n	n	CCONJ
ejpam-5978	142	3	∑n	∑n	PROPN
ejpam-5978	142	4	2	2	NUM
ejpam-5978	142	5	i=1	i=1	NOUN
ejpam-5978	142	6	x	x	SYM
ejpam-5978	142	7	iy2	iy2	PROPN
ejpam-5978	142	8	,	,	PUNCT
ejpam-5978	142	9	if	if	SCONJ
ejpam-5978	142	10	n	n	PRON
ejpam-5978	142	11	is	be	AUX
ejpam-5978	142	12	even	even	ADV
ejpam-5978	142	13	.	.	PUNCT
ejpam-5978	143	1	proof	proof	NOUN
ejpam-5978	143	2	.	.	PUNCT
ejpam-5978	144	1	let	let	VERB
ejpam-5978	144	2	v	v	X
ejpam-5978	144	3	(	(	PUNCT
ejpam-5978	144	4	cn	cn	PROPN
ejpam-5978	144	5	)	)	PUNCT
ejpam-5978	144	6	=	=	SYM
ejpam-5978	144	7	{	{	PUNCT
ejpam-5978	144	8	v1	v1	PROPN
ejpam-5978	144	9	,	,	PUNCT
ejpam-5978	144	10	v2	v2	PROPN
ejpam-5978	144	11	,	,	PUNCT
ejpam-5978	144	12	.	.	PUNCT
ejpam-5978	144	13	.	.	PUNCT
ejpam-5978	145	1	.	.	PUNCT
ejpam-5978	146	1	,	,	PUNCT
ejpam-5978	146	2	vn	vn	AUX
ejpam-5978	146	3	}	}	PUNCT
ejpam-5978	146	4	be	be	AUX
ejpam-5978	146	5	the	the	DET
ejpam-5978	146	6	vertex	vertex	NOUN
ejpam-5978	146	7	set	set	NOUN
ejpam-5978	146	8	of	of	ADP
ejpam-5978	146	9	cn	cn	PROPN
ejpam-5978	146	10	.	.	PUNCT
ejpam-5978	147	1	we	we	PRON
ejpam-5978	147	2	consider	consider	VERB
ejpam-5978	147	3	the	the	DET
ejpam-5978	147	4	following	follow	VERB
ejpam-5978	147	5	cases	case	NOUN
ejpam-5978	147	6	:	:	PUNCT
ejpam-5978	147	7	case	case	NOUN
ejpam-5978	147	8	1	1	NUM
ejpam-5978	147	9	:	:	PUNCT
ejpam-5978	147	10	let	let	VERB
ejpam-5978	147	11	n	n	PRON
ejpam-5978	147	12	be	be	AUX
ejpam-5978	147	13	odd	odd	ADJ
ejpam-5978	147	14	.	.	PUNCT
ejpam-5978	148	1	first	first	ADV
ejpam-5978	148	2	,	,	PUNCT
ejpam-5978	148	3	there	there	PRON
ejpam-5978	148	4	is	be	VERB
ejpam-5978	148	5	only	only	ADV
ejpam-5978	148	6	one	one	NUM
ejpam-5978	148	7	n	n	CCONJ
ejpam-5978	148	8	-	-	PUNCT
ejpam-5978	148	9	convex	convex	NOUN
ejpam-5978	148	10	subset	subset	NOUN
ejpam-5978	148	11	of	of	ADP
ejpam-5978	148	12	v	v	NOUN
ejpam-5978	148	13	(	(	PUNCT
ejpam-5978	148	14	cn	cn	PROPN
ejpam-5978	148	15	)	)	PUNCT
ejpam-5978	148	16	with	with	ADP
ejpam-5978	148	17	empty	empty	ADJ
ejpam-5978	148	18	(	(	PUNCT
ejpam-5978	148	19	zero	zero	NUM
ejpam-5978	148	20	cardinality	cardinality	NOUN
ejpam-5978	148	21	)	)	PUNCT
ejpam-5978	148	22	γin	γin	NOUN
ejpam-5978	148	23	-	-	PUNCT
ejpam-5978	148	24	sets	set	NOUN
ejpam-5978	148	25	and	and	CCONJ
ejpam-5978	148	26	this	this	PRON
ejpam-5978	148	27	contributes	contribute	VERB
ejpam-5978	148	28	to	to	ADP
ejpam-5978	148	29	the	the	DET
ejpam-5978	148	30	term	term	NOUN
ejpam-5978	148	31	xn	xn	PROPN
ejpam-5978	148	32	of	of	ADP
ejpam-5978	148	33	the	the	DET
ejpam-5978	148	34	polynomial	polynomial	NOUN
ejpam-5978	148	35	.	.	PUNCT
ejpam-5978	149	1	next	next	ADV
ejpam-5978	149	2	,	,	PUNCT
ejpam-5978	149	3	we	we	PRON
ejpam-5978	149	4	consider	consider	VERB
ejpam-5978	149	5	the	the	DET
ejpam-5978	149	6	i	i	NOUN
ejpam-5978	149	7	-	-	PUNCT
ejpam-5978	149	8	convex	convex	ADJ
ejpam-5978	149	9	subsets	subset	NOUN
ejpam-5978	149	10	of	of	ADP
ejpam-5978	149	11	v	v	NOUN
ejpam-5978	149	12	(	(	PUNCT
ejpam-5978	149	13	cn	cn	PROPN
ejpam-5978	149	14	)	)	PUNCT
ejpam-5978	149	15	for	for	ADP
ejpam-5978	149	16	i	i	PROPN
ejpam-5978	149	17	=	=	NOUN
ejpam-5978	149	18	1	1	NUM
ejpam-5978	149	19	,	,	PUNCT
ejpam-5978	149	20	2	2	NUM
ejpam-5978	149	21	,	,	PUNCT
ejpam-5978	149	22	...	...	PUNCT
ejpam-5978	149	23	,	,	PUNCT
ejpam-5978	149	24	n+1	n+1	PROPN
ejpam-5978	149	25	2	2	NUM
ejpam-5978	149	26	.	.	PUNCT
ejpam-5978	150	1	we	we	PRON
ejpam-5978	150	2	only	only	ADV
ejpam-5978	150	3	consider	consider	VERB
ejpam-5978	150	4	subsets	subset	NOUN
ejpam-5978	150	5	less	less	ADJ
ejpam-5978	150	6	than	than	ADP
ejpam-5978	150	7	or	or	CCONJ
ejpam-5978	150	8	equal	equal	ADJ
ejpam-5978	150	9	to	to	ADP
ejpam-5978	150	10	n+1	n+1	PROPN
ejpam-5978	150	11	2	2	NUM
ejpam-5978	150	12	because	because	SCONJ
ejpam-5978	150	13	these	these	PRON
ejpam-5978	150	14	are	be	AUX
ejpam-5978	150	15	the	the	DET
ejpam-5978	150	16	only	only	ADJ
ejpam-5978	150	17	convex	convex	ADJ
ejpam-5978	150	18	subsets	subset	NOUN
ejpam-5978	150	19	of	of	ADP
ejpam-5978	150	20	v	v	NOUN
ejpam-5978	150	21	(	(	PUNCT
ejpam-5978	150	22	cn	cn	PROPN
ejpam-5978	150	23	)	)	PUNCT
ejpam-5978	150	24	.	.	PUNCT
ejpam-5978	151	1	subsets	subset	NOUN
ejpam-5978	151	2	more	more	ADJ
ejpam-5978	151	3	than	than	ADP
ejpam-5978	151	4	n+1	n+1	PROPN
ejpam-5978	151	5	2	2	NUM
ejpam-5978	151	6	are	be	AUX
ejpam-5978	151	7	no	no	ADV
ejpam-5978	151	8	longer	long	ADV
ejpam-5978	151	9	convex	convex	VERB
ejpam-5978	151	10	subsets	subset	NOUN
ejpam-5978	151	11	.	.	PUNCT
ejpam-5978	152	1	now	now	ADV
ejpam-5978	152	2	,	,	PUNCT
ejpam-5978	152	3	for	for	ADP
ejpam-5978	152	4	i	i	NOUN
ejpam-5978	152	5	-	-	PUNCT
ejpam-5978	152	6	convex	convex	ADJ
ejpam-5978	152	7	subsets	subset	NOUN
ejpam-5978	152	8	of	of	ADP
ejpam-5978	152	9	cn	cn	PROPN
ejpam-5978	152	10	such	such	ADJ
ejpam-5978	152	11	that	that	SCONJ
ejpam-5978	152	12	i	i	PRON
ejpam-5978	152	13	=	=	NOUN
ejpam-5978	152	14	1	1	NUM
ejpam-5978	152	15	,	,	PUNCT
ejpam-5978	152	16	2	2	NUM
ejpam-5978	152	17	,	,	PUNCT
ejpam-5978	152	18	...	...	PUNCT
ejpam-5978	152	19	,	,	PUNCT
ejpam-5978	152	20	n+1	n+1	PROPN
ejpam-5978	152	21	2	2	NUM
ejpam-5978	152	22	,	,	PUNCT
ejpam-5978	152	23	all	all	PRON
ejpam-5978	152	24	of	of	ADP
ejpam-5978	152	25	these	these	PRON
ejpam-5978	152	26	contains	contain	VERB
ejpam-5978	152	27	γin	γin	NUM
ejpam-5978	152	28	-	-	PUNCT
ejpam-5978	152	29	sets	set	NOUN
ejpam-5978	152	30	equal	equal	ADJ
ejpam-5978	152	31	to	to	ADP
ejpam-5978	152	32	two	two	NUM
ejpam-5978	152	33	and	and	CCONJ
ejpam-5978	152	34	each	each	PRON
ejpam-5978	152	35	of	of	ADP
ejpam-5978	152	36	these	these	DET
ejpam-5978	152	37	i	i	NOUN
ejpam-5978	152	38	-	-	PUNCT
ejpam-5978	152	39	convex	convex	ADJ
ejpam-5978	152	40	subsets	subset	NOUN
ejpam-5978	152	41	has	have	VERB
ejpam-5978	152	42	n	n	DET
ejpam-5978	152	43	choices	choice	NOUN
ejpam-5978	152	44	.	.	PUNCT
ejpam-5978	153	1	thus	thus	ADV
ejpam-5978	153	2	,	,	PUNCT
ejpam-5978	153	3	we	we	PRON
ejpam-5978	153	4	have	have	VERB
ejpam-5978	153	5	the	the	DET
ejpam-5978	153	6	following	follow	VERB
ejpam-5978	153	7	polynomial	polynomial	ADJ
ejpam-5978	153	8	nxy2	nxy2	PROPN
ejpam-5978	153	9	+	+	CCONJ
ejpam-5978	153	10	nx2y2	nx2y2	PROPN
ejpam-5978	153	11	+	+	X
ejpam-5978	153	12	·	·	PUNCT
ejpam-5978	153	13	·	·	PUNCT
ejpam-5978	153	14	·	·	PUNCT
ejpam-5978	154	1	+	+	NUM
ejpam-5978	154	2	nx	nx	NUM
ejpam-5978	154	3	n+1	n+1	NUM
ejpam-5978	154	4	2	2	NUM
ejpam-5978	154	5	y2	y2	NOUN
ejpam-5978	154	6	=	=	SYM
ejpam-5978	154	7	n	n	PROPN
ejpam-5978	154	8	n+1	n+1	PROPN
ejpam-5978	154	9	2∑	2∑	NUM
ejpam-5978	154	10	i=1	i=1	PROPN
ejpam-5978	154	11	xiy2	xiy2	PROPN
ejpam-5978	154	12	.	.	PUNCT
ejpam-5978	155	1	hence	hence	ADV
ejpam-5978	155	2	,	,	PUNCT
ejpam-5978	155	3	the	the	DET
ejpam-5978	155	4	convex	convex	ADJ
ejpam-5978	155	5	independent	independent	ADJ
ejpam-5978	155	6	neighborhood	neighborhood	NOUN
ejpam-5978	155	7	polynomial	polynomial	NOUN
ejpam-5978	155	8	of	of	ADP
ejpam-5978	155	9	cn	cn	PROPN
ejpam-5978	155	10	if	if	SCONJ
ejpam-5978	155	11	n	n	NOUN
ejpam-5978	155	12	is	be	AUX
ejpam-5978	155	13	odd	odd	ADJ
ejpam-5978	155	14	is	be	AUX
ejpam-5978	155	15	given	give	VERB
ejpam-5978	155	16	by	by	ADP
ejpam-5978	155	17	γcin(cn;x	γcin(cn;x	PROPN
ejpam-5978	155	18	,	,	PUNCT
ejpam-5978	155	19	y	y	NOUN
ejpam-5978	155	20	)	)	PUNCT
ejpam-5978	155	21	=	=	PUNCT
ejpam-5978	156	1	xn	xn	PROPN
ejpam-5978	157	1	+	+	CCONJ
ejpam-5978	157	2	n	n	PROPN
ejpam-5978	157	3	n+1	n+1	PROPN
ejpam-5978	157	4	2∑	2∑	NUM
ejpam-5978	157	5	i=1	i=1	PROPN
ejpam-5978	157	6	xiy2	xiy2	PROPN
ejpam-5978	157	7	.	.	PUNCT
ejpam-5978	158	1	case	case	NOUN
ejpam-5978	158	2	2	2	NUM
ejpam-5978	158	3	:	:	PUNCT
ejpam-5978	158	4	let	let	VERB
ejpam-5978	158	5	n	n	PRON
ejpam-5978	158	6	be	be	AUX
ejpam-5978	158	7	even	even	ADV
ejpam-5978	158	8	.	.	PUNCT
ejpam-5978	159	1	by	by	ADP
ejpam-5978	159	2	similar	similar	ADJ
ejpam-5978	159	3	argument	argument	NOUN
ejpam-5978	159	4	as	as	SCONJ
ejpam-5978	159	5	case	case	NOUN
ejpam-5978	159	6	1	1	NUM
ejpam-5978	159	7	and	and	CCONJ
ejpam-5978	159	8	integer	integer	NOUN
ejpam-5978	159	9	i	i	NOUN
ejpam-5978	159	10	=	=	NOUN
ejpam-5978	159	11	1	1	NUM
ejpam-5978	159	12	,	,	PUNCT
ejpam-5978	159	13	2	2	NUM
ejpam-5978	159	14	,	,	PUNCT
ejpam-5978	159	15	...	...	PUNCT
ejpam-5978	159	16	,	,	PUNCT
ejpam-5978	159	17	n2	n2	PROPN
ejpam-5978	159	18	,	,	PUNCT
ejpam-5978	159	19	we	we	PRON
ejpam-5978	159	20	will	will	AUX
ejpam-5978	159	21	obtain	obtain	VERB
ejpam-5978	159	22	the	the	DET
ejpam-5978	159	23	convex	convex	ADJ
ejpam-5978	159	24	neighborhood	neighborhood	NOUN
ejpam-5978	159	25	polynomial	polynomial	NOUN
ejpam-5978	159	26	of	of	ADP
ejpam-5978	159	27	cn	cn	PROPN
ejpam-5978	159	28	,	,	PUNCT
ejpam-5978	159	29	i.e.	i.e.	X
ejpam-5978	159	30	,	,	PUNCT
ejpam-5978	159	31	γcin(cn;x	γcin(cn;x	PROPN
ejpam-5978	159	32	,	,	PUNCT
ejpam-5978	159	33	y	y	NOUN
ejpam-5978	159	34	)	)	PUNCT
ejpam-5978	159	35	=	=	PUNCT
ejpam-5978	160	1	xn	xn	PROPN
ejpam-5978	161	1	+	+	CCONJ
ejpam-5978	161	2	n	n	CCONJ
ejpam-5978	161	3	n	n	PRON
ejpam-5978	161	4	2∑	2∑	NUM
ejpam-5978	161	5	i=1	i=1	X
ejpam-5978	161	6	xiy2	xiy2	PROPN
ejpam-5978	161	7	.	.	PUNCT
ejpam-5978	162	1	e.j	e.j	PROPN
ejpam-5978	162	2	.	.	PROPN
ejpam-5978	162	3	aguilon	aguilon	PROPN
ejpam-5978	162	4	,	,	PUNCT
ejpam-5978	162	5	s.	s.	PROPN
ejpam-5978	162	6	dagondon	dagondon	PROPN
ejpam-5978	162	7	,	,	PUNCT
ejpam-5978	162	8	r.	r.	PROPN
ejpam-5978	162	9	artes	artes	PROPN
ejpam-5978	162	10	/	/	SYM
ejpam-5978	162	11	eur	eur	PROPN
ejpam-5978	162	12	.	.	PUNCT
ejpam-5978	163	1	j.	j.	PROPN
ejpam-5978	163	2	pure	pure	PROPN
ejpam-5978	163	3	appl	appl	PROPN
ejpam-5978	163	4	.	.	PROPN
ejpam-5978	163	5	math	math	PROPN
ejpam-5978	163	6	,	,	PUNCT
ejpam-5978	163	7	18	18	NUM
ejpam-5978	163	8	(	(	PUNCT
ejpam-5978	163	9	2	2	NUM
ejpam-5978	163	10	)	)	PUNCT
ejpam-5978	163	11	(	(	PUNCT
ejpam-5978	163	12	2025	2025	NUM
ejpam-5978	163	13	)	)	PUNCT
ejpam-5978	163	14	,	,	PUNCT
ejpam-5978	163	15	5978	5978	NUM
ejpam-5978	163	16	9	9	NUM
ejpam-5978	163	17	of	of	ADP
ejpam-5978	163	18	18	18	NUM
ejpam-5978	163	19	this	this	PRON
ejpam-5978	163	20	complete	complete	ADJ
ejpam-5978	163	21	the	the	DET
ejpam-5978	163	22	proof	proof	NOUN
ejpam-5978	163	23	.	.	PUNCT
ejpam-5978	164	1	■	■	PUNCT
ejpam-5978	164	2	let	let	VERB
ejpam-5978	164	3	v	v	X
ejpam-5978	164	4	(	(	PUNCT
ejpam-5978	164	5	cn	cn	PROPN
ejpam-5978	164	6	)	)	PUNCT
ejpam-5978	164	7	=	=	SYM
ejpam-5978	164	8	{	{	PUNCT
ejpam-5978	164	9	v1	v1	PROPN
ejpam-5978	164	10	,	,	PUNCT
ejpam-5978	164	11	v2	v2	PROPN
ejpam-5978	164	12	,	,	PUNCT
ejpam-5978	164	13	...	...	PUNCT
ejpam-5978	164	14	,	,	PUNCT
ejpam-5978	164	15	vn	vn	PART
ejpam-5978	164	16	}	}	PUNCT
ejpam-5978	164	17	be	be	AUX
ejpam-5978	164	18	vertex	vertex	NOUN
ejpam-5978	164	19	set	set	NOUN
ejpam-5978	164	20	of	of	ADP
ejpam-5978	164	21	cn	cn	PROPN
ejpam-5978	164	22	.	.	PROPN
ejpam-5978	164	23	note	note	VERB
ejpam-5978	164	24	that	that	SCONJ
ejpam-5978	164	25	the	the	DET
ejpam-5978	164	26	vertices	vertex	NOUN
ejpam-5978	164	27	{	{	PUNCT
ejpam-5978	164	28	v1	v1	NOUN
ejpam-5978	164	29	,	,	PUNCT
ejpam-5978	164	30	v2	v2	PROPN
ejpam-5978	164	31	,	,	PUNCT
ejpam-5978	164	32	...	...	PUNCT
ejpam-5978	164	33	,	,	PUNCT
ejpam-5978	164	34	vn	vn	PART
ejpam-5978	164	35	}	}	PUNCT
ejpam-5978	164	36	convex	convex	PROPN
ejpam-5978	164	37	subset	subset	NOUN
ejpam-5978	164	38	of	of	ADP
ejpam-5978	164	39	v	v	NOUN
ejpam-5978	164	40	(	(	PUNCT
ejpam-5978	164	41	cn	cn	PROPN
ejpam-5978	164	42	)	)	PUNCT
ejpam-5978	164	43	is	be	AUX
ejpam-5978	164	44	the	the	DET
ejpam-5978	164	45	only	only	ADJ
ejpam-5978	164	46	subset	subset	NOUN
ejpam-5978	164	47	that	that	PRON
ejpam-5978	164	48	has	have	AUX
ejpam-5978	164	49	empty	empty	ADJ
ejpam-5978	164	50	(	(	PUNCT
ejpam-5978	164	51	zero	zero	NUM
ejpam-5978	164	52	cardinality	cardinality	NOUN
ejpam-5978	164	53	)	)	PUNCT
ejpam-5978	164	54	γin	γin	ADV
ejpam-5978	164	55	-	-	PUNCT
ejpam-5978	164	56	set	set	NOUN
ejpam-5978	164	57	which	which	PRON
ejpam-5978	164	58	is	be	AUX
ejpam-5978	164	59	the	the	DET
ejpam-5978	164	60	leading	lead	VERB
ejpam-5978	164	61	term	term	NOUN
ejpam-5978	164	62	of	of	ADP
ejpam-5978	164	63	the	the	DET
ejpam-5978	164	64	convex	convex	ADJ
ejpam-5978	164	65	independent	independent	ADJ
ejpam-5978	164	66	neighborhood	neighborhood	NOUN
ejpam-5978	164	67	polynomial	polynomial	NOUN
ejpam-5978	164	68	of	of	ADP
ejpam-5978	164	69	cn	cn	PROPN
ejpam-5978	164	70	.	.	PUNCT
ejpam-5978	165	1	now	now	ADV
ejpam-5978	165	2	,	,	PUNCT
ejpam-5978	165	3	consider	consider	VERB
ejpam-5978	165	4	the	the	DET
ejpam-5978	165	5	following	follow	VERB
ejpam-5978	165	6	cases	case	NOUN
ejpam-5978	165	7	,	,	PUNCT
ejpam-5978	165	8	if	if	SCONJ
ejpam-5978	165	9	n	n	PRON
ejpam-5978	165	10	is	be	AUX
ejpam-5978	165	11	odd	odd	ADJ
ejpam-5978	165	12	,	,	PUNCT
ejpam-5978	165	13	then	then	ADV
ejpam-5978	165	14	there	there	PRON
ejpam-5978	165	15	are	be	VERB
ejpam-5978	165	16	n+1	n+1	NUM
ejpam-5978	165	17	2	2	NUM
ejpam-5978	165	18	terms	term	NOUN
ejpam-5978	165	19	with	with	ADP
ejpam-5978	165	20	γin	γin	ADV
ejpam-5978	165	21	-	-	PUNCT
ejpam-5978	165	22	set	set	VERB
ejpam-5978	165	23	cardinality	cardinality	NOUN
ejpam-5978	165	24	equal	equal	ADJ
ejpam-5978	165	25	to	to	ADP
ejpam-5978	165	26	two	two	NUM
ejpam-5978	165	27	.	.	PUNCT
ejpam-5978	166	1	this	this	PRON
ejpam-5978	166	2	means	mean	VERB
ejpam-5978	166	3	that	that	SCONJ
ejpam-5978	166	4	,	,	PUNCT
ejpam-5978	166	5	for	for	ADP
ejpam-5978	166	6	n	n	NUM
ejpam-5978	166	7	≥	≥	NOUN
ejpam-5978	166	8	6	6	NUM
ejpam-5978	166	9	when	when	SCONJ
ejpam-5978	166	10	n	n	X
ejpam-5978	166	11	is	be	AUX
ejpam-5978	166	12	odd	odd	ADJ
ejpam-5978	166	13	,	,	PUNCT
ejpam-5978	166	14	there	there	PRON
ejpam-5978	166	15	are	be	VERB
ejpam-5978	166	16	1	1	NUM
ejpam-5978	166	17	+	+	CCONJ
ejpam-5978	166	18	n+	n+	NUM
ejpam-5978	166	19	1	1	NUM
ejpam-5978	166	20	2	2	NUM
ejpam-5978	166	21	=	=	SYM
ejpam-5978	166	22	n+	n+	NUM
ejpam-5978	166	23	3	3	NUM
ejpam-5978	166	24	2	2	NUM
ejpam-5978	166	25	terms	term	NOUN
ejpam-5978	166	26	for	for	ADP
ejpam-5978	166	27	the	the	DET
ejpam-5978	166	28	convex	convex	ADJ
ejpam-5978	166	29	independent	independent	ADJ
ejpam-5978	166	30	neighborhood	neighborhood	NOUN
ejpam-5978	166	31	polynomial	polynomial	NOUN
ejpam-5978	166	32	of	of	ADP
ejpam-5978	166	33	cn	cn	PROPN
ejpam-5978	166	34	.	.	PROPN
ejpam-5978	167	1	on	on	ADP
ejpam-5978	167	2	the	the	DET
ejpam-5978	167	3	other	other	ADJ
ejpam-5978	167	4	hand	hand	NOUN
ejpam-5978	167	5	,	,	PUNCT
ejpam-5978	167	6	if	if	SCONJ
ejpam-5978	167	7	n	n	PRON
ejpam-5978	167	8	is	be	AUX
ejpam-5978	167	9	even	even	ADV
ejpam-5978	167	10	,	,	PUNCT
ejpam-5978	167	11	then	then	ADV
ejpam-5978	167	12	there	there	PRON
ejpam-5978	167	13	are	be	VERB
ejpam-5978	167	14	n	n	PRON
ejpam-5978	167	15	2	2	NUM
ejpam-5978	167	16	terms	term	NOUN
ejpam-5978	167	17	with	with	ADP
ejpam-5978	167	18	γin	γin	ADV
ejpam-5978	167	19	-	-	PUNCT
ejpam-5978	167	20	set	set	VERB
ejpam-5978	167	21	cardinality	cardinality	NOUN
ejpam-5978	167	22	equal	equal	ADJ
ejpam-5978	167	23	to	to	ADP
ejpam-5978	167	24	two	two	NUM
ejpam-5978	167	25	.	.	PUNCT
ejpam-5978	168	1	this	this	PRON
ejpam-5978	168	2	means	mean	VERB
ejpam-5978	168	3	that	that	SCONJ
ejpam-5978	168	4	,	,	PUNCT
ejpam-5978	168	5	for	for	ADP
ejpam-5978	168	6	n	n	NUM
ejpam-5978	168	7	≥	≥	NOUN
ejpam-5978	168	8	6	6	NUM
ejpam-5978	168	9	when	when	SCONJ
ejpam-5978	168	10	n	n	X
ejpam-5978	168	11	is	be	AUX
ejpam-5978	168	12	even	even	ADV
ejpam-5978	168	13	,	,	PUNCT
ejpam-5978	168	14	there	there	PRON
ejpam-5978	168	15	are	be	VERB
ejpam-5978	168	16	1	1	NUM
ejpam-5978	168	17	+	+	CCONJ
ejpam-5978	168	18	n	n	PRON
ejpam-5978	168	19	2	2	NUM
ejpam-5978	168	20	=	=	SYM
ejpam-5978	168	21	n+	n+	NUM
ejpam-5978	168	22	2	2	NUM
ejpam-5978	168	23	2	2	NUM
ejpam-5978	168	24	terms	term	NOUN
ejpam-5978	168	25	for	for	ADP
ejpam-5978	168	26	the	the	DET
ejpam-5978	168	27	convex	convex	ADJ
ejpam-5978	168	28	independent	independent	ADJ
ejpam-5978	168	29	neighborhood	neighborhood	NOUN
ejpam-5978	168	30	polynomial	polynomial	NOUN
ejpam-5978	168	31	of	of	ADP
ejpam-5978	168	32	cn	cn	PROPN
ejpam-5978	168	33	.	.	PUNCT
ejpam-5978	169	1	thus	thus	ADV
ejpam-5978	169	2	,	,	PUNCT
ejpam-5978	169	3	we	we	PRON
ejpam-5978	169	4	have	have	VERB
ejpam-5978	169	5	the	the	DET
ejpam-5978	169	6	following	follow	VERB
ejpam-5978	169	7	corollary	corollary	ADJ
ejpam-5978	169	8	corollary	corollary	ADJ
ejpam-5978	169	9	4.5	4.5	NUM
ejpam-5978	169	10	.	.	PUNCT
ejpam-5978	170	1	for	for	ADP
ejpam-5978	170	2	n	n	X
ejpam-5978	170	3	≥	≥	NUM
ejpam-5978	170	4	6	6	NUM
ejpam-5978	170	5	,	,	PUNCT
ejpam-5978	170	6	the	the	DET
ejpam-5978	170	7	number	number	NOUN
ejpam-5978	170	8	of	of	ADP
ejpam-5978	170	9	terms	term	NOUN
ejpam-5978	170	10	of	of	ADP
ejpam-5978	170	11	the	the	DET
ejpam-5978	170	12	convex	convex	ADJ
ejpam-5978	170	13	independent	independent	ADJ
ejpam-5978	170	14	neighborhood	neighborhood	NOUN
ejpam-5978	170	15	polynomial	polynomial	NOUN
ejpam-5978	170	16	of	of	ADP
ejpam-5978	170	17	cn	cn	PROPN
ejpam-5978	170	18	in	in	ADP
ejpam-5978	170	19	terms	term	NOUN
ejpam-5978	170	20	of	of	ADP
ejpam-5978	170	21	n	n	NUM
ejpam-5978	170	22	is	be	AUX
ejpam-5978	170	23	given	give	VERB
ejpam-5978	170	24	by	by	ADP
ejpam-5978	170	25	,	,	PUNCT
ejpam-5978	170	26	{	{	PUNCT
ejpam-5978	170	27	n+3	n+3	PROPN
ejpam-5978	170	28	2	2	NUM
ejpam-5978	170	29	,	,	PUNCT
ejpam-5978	170	30	if	if	SCONJ
ejpam-5978	170	31	n	n	PRON
ejpam-5978	170	32	is	be	AUX
ejpam-5978	170	33	odd	odd	ADJ
ejpam-5978	170	34	n+2	n+2	ADV
ejpam-5978	170	35	2	2	NUM
ejpam-5978	170	36	,	,	PUNCT
ejpam-5978	170	37	if	if	SCONJ
ejpam-5978	170	38	n	n	PRON
ejpam-5978	170	39	is	be	AUX
ejpam-5978	170	40	even	even	ADV
ejpam-5978	170	41	.	.	PUNCT
ejpam-5978	171	1	illustration	illustration	NOUN
ejpam-5978	171	2	4.6	4.6	NUM
ejpam-5978	171	3	.	.	PUNCT
ejpam-5978	172	1	consider	consider	VERB
ejpam-5978	172	2	the	the	DET
ejpam-5978	172	3	cycle	cycle	NOUN
ejpam-5978	172	4	c6	c6	PROPN
ejpam-5978	172	5	.	.	PUNCT
ejpam-5978	173	1	v1	v1	PROPN
ejpam-5978	173	2	v2	v2	PROPN
ejpam-5978	173	3	v3	v3	PROPN
ejpam-5978	173	4	v6	v6	PROPN
ejpam-5978	173	5	v5	v5	PROPN
ejpam-5978	173	6	v4	v4	PROPN
ejpam-5978	173	7	figure	figure	NOUN
ejpam-5978	173	8	3	3	NUM
ejpam-5978	173	9	:	:	PUNCT
ejpam-5978	173	10	a	a	DET
ejpam-5978	173	11	cycle	cycle	NOUN
ejpam-5978	173	12	c6	c6	NOUN
ejpam-5978	173	13	of	of	ADP
ejpam-5978	173	14	order	order	NOUN
ejpam-5978	173	15	6	6	NUM
ejpam-5978	173	16	then	then	ADV
ejpam-5978	173	17	,	,	PUNCT
ejpam-5978	173	18	by	by	ADP
ejpam-5978	173	19	using	use	VERB
ejpam-5978	173	20	theorem	theorem	ADJ
ejpam-5978	173	21	4.4	4.4	NUM
ejpam-5978	173	22	when	when	SCONJ
ejpam-5978	173	23	n	n	X
ejpam-5978	173	24	is	be	AUX
ejpam-5978	173	25	even	even	ADV
ejpam-5978	173	26	,	,	PUNCT
ejpam-5978	173	27	γcin(c6;x	γcin(c6;x	NOUN
ejpam-5978	173	28	,	,	PUNCT
ejpam-5978	173	29	y	y	NOUN
ejpam-5978	173	30	)	)	PUNCT
ejpam-5978	173	31	=	=	SYM
ejpam-5978	173	32	x6	x6	PROPN
ejpam-5978	174	1	+	+	CCONJ
ejpam-5978	174	2	6	6	NUM
ejpam-5978	174	3	6	6	NUM
ejpam-5978	174	4	2∑	2∑	NUM
ejpam-5978	174	5	i=1	i=1	X
ejpam-5978	174	6	xiy2	xiy2	PROPN
ejpam-5978	175	1	=	=	PUNCT
ejpam-5978	175	2	x6	x6	PROPN
ejpam-5978	175	3	+	+	CCONJ
ejpam-5978	175	4	6	6	NUM
ejpam-5978	175	5	3∑	3∑	NUM
ejpam-5978	175	6	i=1	i=1	NOUN
ejpam-5978	175	7	xiy2	xiy2	NOUN
ejpam-5978	176	1	=	=	PUNCT
ejpam-5978	176	2	x6	x6	PROPN
ejpam-5978	176	3	+	+	CCONJ
ejpam-5978	176	4	6(xy2	6(xy2	NUM
ejpam-5978	177	1	+	+	CCONJ
ejpam-5978	177	2	x2y2	x2y2	X
ejpam-5978	177	3	+	+	CCONJ
ejpam-5978	177	4	x3y2	x3y2	NOUN
ejpam-5978	177	5	)	)	PUNCT
ejpam-5978	177	6	e.j	e.j	PROPN
ejpam-5978	177	7	.	.	PROPN
ejpam-5978	177	8	aguilon	aguilon	PROPN
ejpam-5978	177	9	,	,	PUNCT
ejpam-5978	177	10	s.	s.	PROPN
ejpam-5978	177	11	dagondon	dagondon	PROPN
ejpam-5978	177	12	,	,	PUNCT
ejpam-5978	177	13	r.	r.	PROPN
ejpam-5978	177	14	artes	artes	PROPN
ejpam-5978	177	15	/	/	SYM
ejpam-5978	177	16	eur	eur	PROPN
ejpam-5978	177	17	.	.	PUNCT
ejpam-5978	178	1	j.	j.	PROPN
ejpam-5978	178	2	pure	pure	PROPN
ejpam-5978	178	3	appl	appl	PROPN
ejpam-5978	178	4	.	.	PROPN
ejpam-5978	178	5	math	math	PROPN
ejpam-5978	178	6	,	,	PUNCT
ejpam-5978	178	7	18	18	NUM
ejpam-5978	178	8	(	(	PUNCT
ejpam-5978	178	9	2	2	NUM
ejpam-5978	178	10	)	)	PUNCT
ejpam-5978	178	11	(	(	PUNCT
ejpam-5978	178	12	2025	2025	NUM
ejpam-5978	178	13	)	)	PUNCT
ejpam-5978	178	14	,	,	PUNCT
ejpam-5978	178	15	5978	5978	NUM
ejpam-5978	178	16	10	10	NUM
ejpam-5978	178	17	of	of	ADP
ejpam-5978	178	18	18	18	NUM
ejpam-5978	178	19	=	=	SYM
ejpam-5978	178	20	x6	x6	PROPN
ejpam-5978	178	21	+	+	CCONJ
ejpam-5978	178	22	6x3y2	6x3y2	NUM
ejpam-5978	178	23	+	+	CCONJ
ejpam-5978	178	24	6x2y2	6x2y2	NUM
ejpam-5978	178	25	+	+	X
ejpam-5978	178	26	6xy2	6xy2	NUM
ejpam-5978	178	27	.	.	PUNCT
ejpam-5978	179	1	and	and	CCONJ
ejpam-5978	179	2	by	by	ADP
ejpam-5978	179	3	corollary	corollary	ADJ
ejpam-5978	179	4	4.5	4.5	NUM
ejpam-5978	179	5	,	,	PUNCT
ejpam-5978	179	6	there	there	PRON
ejpam-5978	179	7	are	be	VERB
ejpam-5978	179	8	6	6	NUM
ejpam-5978	179	9	+	+	SYM
ejpam-5978	179	10	2	2	NUM
ejpam-5978	179	11	2	2	NUM
ejpam-5978	179	12	=	=	SYM
ejpam-5978	179	13	4	4	NUM
ejpam-5978	179	14	terms	term	NOUN
ejpam-5978	179	15	in	in	ADP
ejpam-5978	179	16	the	the	DET
ejpam-5978	179	17	convex	convex	ADJ
ejpam-5978	179	18	independent	independent	ADJ
ejpam-5978	179	19	neighborhood	neighborhood	NOUN
ejpam-5978	179	20	polynomial	polynomial	NOUN
ejpam-5978	179	21	of	of	ADP
ejpam-5978	179	22	c6	c6	PROPN
ejpam-5978	179	23	.	.	PUNCT
ejpam-5978	180	1	to	to	PART
ejpam-5978	180	2	see	see	VERB
ejpam-5978	180	3	the	the	DET
ejpam-5978	180	4	convex	convex	ADJ
ejpam-5978	180	5	subsets	subset	NOUN
ejpam-5978	180	6	of	of	ADP
ejpam-5978	180	7	v	v	NOUN
ejpam-5978	180	8	(	(	PUNCT
ejpam-5978	180	9	c6	c6	PROPN
ejpam-5978	180	10	)	)	PUNCT
ejpam-5978	180	11	and	and	CCONJ
ejpam-5978	180	12	its	its	PRON
ejpam-5978	180	13	corresponding	corresponding	ADJ
ejpam-5978	180	14	γin	γin	NOUN
ejpam-5978	180	15	-	-	PUNCT
ejpam-5978	180	16	sets	set	NOUN
ejpam-5978	180	17	,	,	PUNCT
ejpam-5978	180	18	refer	refer	VERB
ejpam-5978	180	19	to	to	ADP
ejpam-5978	180	20	the	the	DET
ejpam-5978	180	21	tables	table	NOUN
ejpam-5978	180	22	7	7	NUM
ejpam-5978	180	23	,	,	PUNCT
ejpam-5978	180	24	8	8	NUM
ejpam-5978	180	25	,	,	PUNCT
ejpam-5978	180	26	and	and	CCONJ
ejpam-5978	180	27	9	9	NUM
ejpam-5978	180	28	:	:	SYM
ejpam-5978	180	29	1	1	NUM
ejpam-5978	180	30	-	-	PUNCT
ejpam-5978	180	31	convex	convex	VERB
ejpam-5978	180	32	γin	γin	NOUN
ejpam-5978	180	33	-	-	PUNCT
ejpam-5978	180	34	sets	set	NOUN
ejpam-5978	180	35	{	{	PUNCT
ejpam-5978	180	36	v1	v1	NOUN
ejpam-5978	180	37	}	}	PUNCT
ejpam-5978	180	38	{	{	PUNCT
ejpam-5978	180	39	v6	v6	NOUN
ejpam-5978	180	40	,	,	PUNCT
ejpam-5978	180	41	v2	v2	PROPN
ejpam-5978	180	42	}	}	PUNCT
ejpam-5978	180	43	{	{	PUNCT
ejpam-5978	180	44	v2	v2	NOUN
ejpam-5978	180	45	}	}	PUNCT
ejpam-5978	180	46	{	{	PUNCT
ejpam-5978	180	47	v1	v1	NOUN
ejpam-5978	180	48	,	,	PUNCT
ejpam-5978	180	49	v3	v3	PROPN
ejpam-5978	180	50	}	}	PUNCT
ejpam-5978	180	51	{	{	PUNCT
ejpam-5978	180	52	v3	v3	PROPN
ejpam-5978	180	53	}	}	PUNCT
ejpam-5978	180	54	{	{	PUNCT
ejpam-5978	180	55	v2	v2	PROPN
ejpam-5978	180	56	,	,	PUNCT
ejpam-5978	180	57	v4	v4	PROPN
ejpam-5978	180	58	}	}	PUNCT
ejpam-5978	180	59	{	{	PUNCT
ejpam-5978	180	60	v4	v4	NOUN
ejpam-5978	180	61	}	}	PUNCT
ejpam-5978	180	62	{	{	PUNCT
ejpam-5978	180	63	v3	v3	PROPN
ejpam-5978	180	64	,	,	PUNCT
ejpam-5978	180	65	v5	v5	PROPN
ejpam-5978	180	66	}	}	PUNCT
ejpam-5978	180	67	{	{	PUNCT
ejpam-5978	180	68	v5	v5	PROPN
ejpam-5978	180	69	}	}	PUNCT
ejpam-5978	180	70	{	{	PUNCT
ejpam-5978	180	71	v4	v4	NOUN
ejpam-5978	180	72	,	,	PUNCT
ejpam-5978	180	73	v6	v6	PROPN
ejpam-5978	180	74	}	}	PUNCT
ejpam-5978	180	75	{	{	PUNCT
ejpam-5978	180	76	v6	v6	NOUN
ejpam-5978	180	77	}	}	PUNCT
ejpam-5978	180	78	{	{	PUNCT
ejpam-5978	180	79	v5	v5	PROPN
ejpam-5978	180	80	,	,	PUNCT
ejpam-5978	180	81	v1	v1	NOUN
ejpam-5978	180	82	}	}	PUNCT
ejpam-5978	180	83	table	table	NOUN
ejpam-5978	180	84	7	7	NUM
ejpam-5978	180	85	:	:	SYM
ejpam-5978	180	86	1	1	NUM
ejpam-5978	180	87	-	-	PUNCT
ejpam-5978	180	88	convex	convex	NOUN
ejpam-5978	180	89	subsets	subset	NOUN
ejpam-5978	180	90	of	of	ADP
ejpam-5978	180	91	v	v	NOUN
ejpam-5978	180	92	(	(	PUNCT
ejpam-5978	180	93	c6	c6	PROPN
ejpam-5978	180	94	)	)	PUNCT
ejpam-5978	180	95	and	and	CCONJ
ejpam-5978	180	96	its	its	PRON
ejpam-5978	180	97	corresponding	corresponding	ADJ
ejpam-5978	180	98	γin	γin	NOUN
ejpam-5978	180	99	-	-	PUNCT
ejpam-5978	180	100	sets	set	NOUN
ejpam-5978	180	101	.	.	PUNCT
ejpam-5978	181	1	table	table	NOUN
ejpam-5978	181	2	7	7	NUM
ejpam-5978	181	3	shows	show	VERB
ejpam-5978	181	4	that	that	SCONJ
ejpam-5978	181	5	there	there	PRON
ejpam-5978	181	6	are	be	VERB
ejpam-5978	181	7	6	6	NUM
ejpam-5978	181	8	1	1	NUM
ejpam-5978	181	9	-	-	PUNCT
ejpam-5978	181	10	convex	convex	NOUN
ejpam-5978	181	11	subsets	subset	NOUN
ejpam-5978	181	12	of	of	ADP
ejpam-5978	181	13	v	v	NOUN
ejpam-5978	181	14	(	(	PUNCT
ejpam-5978	181	15	c6	c6	PROPN
ejpam-5978	181	16	)	)	PUNCT
ejpam-5978	181	17	with	with	ADP
ejpam-5978	181	18	γin	γin	NOUN
ejpam-5978	181	19	-	-	PUNCT
ejpam-5978	181	20	sets	set	NOUN
ejpam-5978	181	21	cardinality	cardinality	NOUN
ejpam-5978	181	22	equal	equal	ADJ
ejpam-5978	181	23	to	to	ADP
ejpam-5978	181	24	2	2	NUM
ejpam-5978	181	25	.	.	PUNCT
ejpam-5978	182	1	this	this	PRON
ejpam-5978	182	2	contributes	contribute	VERB
ejpam-5978	182	3	to	to	ADP
ejpam-5978	182	4	the	the	DET
ejpam-5978	182	5	convex	convex	ADJ
ejpam-5978	182	6	independent	independent	ADJ
ejpam-5978	182	7	neighborhood	neighborhood	NOUN
ejpam-5978	182	8	polynomial	polynomial	NOUN
ejpam-5978	182	9	of	of	ADP
ejpam-5978	182	10	c6	c6	PROPN
ejpam-5978	182	11	as	as	ADP
ejpam-5978	182	12	6xy2	6xy2	NUM
ejpam-5978	182	13	.	.	PUNCT
ejpam-5978	183	1	2	2	NUM
ejpam-5978	183	2	-	-	NUM
ejpam-5978	183	3	convex	convex	VERB
ejpam-5978	183	4	γin	γin	NOUN
ejpam-5978	183	5	-	-	PUNCT
ejpam-5978	183	6	sets	set	NOUN
ejpam-5978	183	7	{	{	PUNCT
ejpam-5978	183	8	v1	v1	NOUN
ejpam-5978	183	9	,	,	PUNCT
ejpam-5978	183	10	v2	v2	PROPN
ejpam-5978	183	11	}	}	PUNCT
ejpam-5978	183	12	{	{	PUNCT
ejpam-5978	183	13	v6	v6	NOUN
ejpam-5978	183	14	,	,	PUNCT
ejpam-5978	183	15	v3	v3	PROPN
ejpam-5978	183	16	}	}	PUNCT
ejpam-5978	183	17	{	{	PUNCT
ejpam-5978	183	18	v2	v2	PROPN
ejpam-5978	183	19	,	,	PUNCT
ejpam-5978	183	20	v3	v3	PROPN
ejpam-5978	183	21	}	}	PUNCT
ejpam-5978	183	22	{	{	PUNCT
ejpam-5978	183	23	v1	v1	NOUN
ejpam-5978	183	24	,	,	PUNCT
ejpam-5978	183	25	v4	v4	NOUN
ejpam-5978	183	26	}	}	PUNCT
ejpam-5978	183	27	{	{	PUNCT
ejpam-5978	183	28	v3	v3	PROPN
ejpam-5978	183	29	,	,	PUNCT
ejpam-5978	183	30	v4	v4	PROPN
ejpam-5978	183	31	}	}	PUNCT
ejpam-5978	183	32	{	{	PUNCT
ejpam-5978	183	33	v2	v2	PROPN
ejpam-5978	183	34	,	,	PUNCT
ejpam-5978	183	35	v5	v5	PROPN
ejpam-5978	183	36	}	}	PUNCT
ejpam-5978	183	37	{	{	PUNCT
ejpam-5978	183	38	v4	v4	NOUN
ejpam-5978	183	39	,	,	PUNCT
ejpam-5978	183	40	v5	v5	PROPN
ejpam-5978	183	41	}	}	PUNCT
ejpam-5978	183	42	{	{	PUNCT
ejpam-5978	183	43	v3	v3	PROPN
ejpam-5978	183	44	,	,	PUNCT
ejpam-5978	183	45	v6	v6	PROPN
ejpam-5978	183	46	}	}	PUNCT
ejpam-5978	183	47	{	{	PUNCT
ejpam-5978	183	48	v5	v5	PROPN
ejpam-5978	183	49	,	,	PUNCT
ejpam-5978	183	50	v6	v6	NOUN
ejpam-5978	183	51	}	}	PUNCT
ejpam-5978	183	52	{	{	PUNCT
ejpam-5978	183	53	v4	v4	NOUN
ejpam-5978	183	54	,	,	PUNCT
ejpam-5978	183	55	v1	v1	NOUN
ejpam-5978	183	56	}	}	PUNCT
ejpam-5978	183	57	{	{	PUNCT
ejpam-5978	183	58	v6	v6	NOUN
ejpam-5978	183	59	,	,	PUNCT
ejpam-5978	183	60	v1	v1	PROPN
ejpam-5978	183	61	}	}	PUNCT
ejpam-5978	183	62	{	{	PUNCT
ejpam-5978	183	63	v5	v5	PROPN
ejpam-5978	183	64	,	,	PUNCT
ejpam-5978	183	65	v2	v2	NOUN
ejpam-5978	183	66	}	}	PUNCT
ejpam-5978	183	67	table	table	NOUN
ejpam-5978	183	68	8	8	NUM
ejpam-5978	183	69	:	:	SYM
ejpam-5978	183	70	2	2	NUM
ejpam-5978	183	71	-	-	PUNCT
ejpam-5978	183	72	convex	convex	NOUN
ejpam-5978	183	73	subsets	subset	NOUN
ejpam-5978	183	74	of	of	ADP
ejpam-5978	183	75	v	v	NOUN
ejpam-5978	183	76	(	(	PUNCT
ejpam-5978	183	77	c6	c6	PROPN
ejpam-5978	183	78	)	)	PUNCT
ejpam-5978	183	79	and	and	CCONJ
ejpam-5978	183	80	its	its	PRON
ejpam-5978	183	81	corresponding	corresponding	ADJ
ejpam-5978	183	82	γin	γin	NOUN
ejpam-5978	183	83	-	-	PUNCT
ejpam-5978	183	84	sets	set	NOUN
ejpam-5978	183	85	.	.	PUNCT
ejpam-5978	184	1	table	table	NOUN
ejpam-5978	184	2	8	8	NUM
ejpam-5978	184	3	shows	show	VERB
ejpam-5978	184	4	that	that	SCONJ
ejpam-5978	184	5	there	there	PRON
ejpam-5978	184	6	are	be	VERB
ejpam-5978	184	7	6	6	NUM
ejpam-5978	184	8	2	2	NUM
ejpam-5978	184	9	-	-	PUNCT
ejpam-5978	184	10	convex	convex	NOUN
ejpam-5978	184	11	subsets	subset	NOUN
ejpam-5978	184	12	of	of	ADP
ejpam-5978	184	13	v	v	NOUN
ejpam-5978	184	14	(	(	PUNCT
ejpam-5978	184	15	c6	c6	PROPN
ejpam-5978	184	16	)	)	PUNCT
ejpam-5978	184	17	with	with	ADP
ejpam-5978	184	18	γin	γin	NOUN
ejpam-5978	184	19	-	-	PUNCT
ejpam-5978	184	20	sets	set	NOUN
ejpam-5978	184	21	cardinality	cardinality	NOUN
ejpam-5978	184	22	equal	equal	ADJ
ejpam-5978	184	23	to	to	ADP
ejpam-5978	184	24	2	2	NUM
ejpam-5978	184	25	.	.	PUNCT
ejpam-5978	185	1	this	this	PRON
ejpam-5978	185	2	contributes	contribute	VERB
ejpam-5978	185	3	to	to	ADP
ejpam-5978	185	4	the	the	DET
ejpam-5978	185	5	convex	convex	ADJ
ejpam-5978	185	6	independent	independent	ADJ
ejpam-5978	185	7	neighborhood	neighborhood	NOUN
ejpam-5978	185	8	polynomial	polynomial	NOUN
ejpam-5978	185	9	of	of	ADP
ejpam-5978	185	10	c6	c6	PROPN
ejpam-5978	185	11	as	as	ADP
ejpam-5978	185	12	6x2y2	6x2y2	NUM
ejpam-5978	185	13	.	.	PUNCT
ejpam-5978	186	1	e.j	e.j	PROPN
ejpam-5978	186	2	.	.	PROPN
ejpam-5978	186	3	aguilon	aguilon	PROPN
ejpam-5978	186	4	,	,	PUNCT
ejpam-5978	186	5	s.	s.	PROPN
ejpam-5978	186	6	dagondon	dagondon	PROPN
ejpam-5978	186	7	,	,	PUNCT
ejpam-5978	186	8	r.	r.	PROPN
ejpam-5978	186	9	artes	artes	PROPN
ejpam-5978	186	10	/	/	SYM
ejpam-5978	186	11	eur	eur	PROPN
ejpam-5978	186	12	.	.	PUNCT
ejpam-5978	187	1	j.	j.	PROPN
ejpam-5978	187	2	pure	pure	PROPN
ejpam-5978	187	3	appl	appl	PROPN
ejpam-5978	187	4	.	.	PROPN
ejpam-5978	187	5	math	math	PROPN
ejpam-5978	187	6	,	,	PUNCT
ejpam-5978	187	7	18	18	NUM
ejpam-5978	187	8	(	(	PUNCT
ejpam-5978	187	9	2	2	NUM
ejpam-5978	187	10	)	)	PUNCT
ejpam-5978	187	11	(	(	PUNCT
ejpam-5978	187	12	2025	2025	NUM
ejpam-5978	187	13	)	)	PUNCT
ejpam-5978	187	14	,	,	PUNCT
ejpam-5978	187	15	5978	5978	NUM
ejpam-5978	187	16	11	11	NUM
ejpam-5978	187	17	of	of	ADP
ejpam-5978	187	18	18	18	NUM
ejpam-5978	187	19	3	3	NUM
ejpam-5978	187	20	-	-	PUNCT
ejpam-5978	187	21	convex	convex	ADJ
ejpam-5978	187	22	γin	γin	NOUN
ejpam-5978	187	23	-	-	PUNCT
ejpam-5978	187	24	sets	set	NOUN
ejpam-5978	187	25	{	{	PUNCT
ejpam-5978	187	26	v1	v1	NOUN
ejpam-5978	187	27	,	,	PUNCT
ejpam-5978	187	28	v2	v2	PROPN
ejpam-5978	187	29	,	,	PUNCT
ejpam-5978	187	30	v3	v3	PROPN
ejpam-5978	187	31	}	}	PUNCT
ejpam-5978	187	32	{	{	PUNCT
ejpam-5978	187	33	v6	v6	NOUN
ejpam-5978	187	34	,	,	PUNCT
ejpam-5978	187	35	v4	v4	PROPN
ejpam-5978	187	36	}	}	PUNCT
ejpam-5978	187	37	{	{	PUNCT
ejpam-5978	187	38	v2	v2	PROPN
ejpam-5978	187	39	,	,	PUNCT
ejpam-5978	187	40	v3	v3	PROPN
ejpam-5978	187	41	,	,	PUNCT
ejpam-5978	187	42	v4	v4	PROPN
ejpam-5978	187	43	}	}	PUNCT
ejpam-5978	187	44	{	{	PUNCT
ejpam-5978	187	45	v1	v1	NOUN
ejpam-5978	187	46	,	,	PUNCT
ejpam-5978	187	47	v5	v5	PROPN
ejpam-5978	187	48	}	}	PUNCT
ejpam-5978	187	49	{	{	PUNCT
ejpam-5978	187	50	v3	v3	PROPN
ejpam-5978	187	51	,	,	PUNCT
ejpam-5978	187	52	v4	v4	PROPN
ejpam-5978	187	53	,	,	PUNCT
ejpam-5978	187	54	v5	v5	PROPN
ejpam-5978	187	55	}	}	PUNCT
ejpam-5978	187	56	{	{	PUNCT
ejpam-5978	187	57	v2	v2	PROPN
ejpam-5978	187	58	,	,	PUNCT
ejpam-5978	187	59	v6	v6	NOUN
ejpam-5978	187	60	}	}	PUNCT
ejpam-5978	187	61	{	{	PUNCT
ejpam-5978	187	62	v4	v4	NOUN
ejpam-5978	187	63	,	,	PUNCT
ejpam-5978	187	64	v5	v5	PROPN
ejpam-5978	187	65	,	,	PUNCT
ejpam-5978	187	66	v6	v6	NOUN
ejpam-5978	187	67	}	}	PUNCT
ejpam-5978	187	68	{	{	PUNCT
ejpam-5978	187	69	v3	v3	PROPN
ejpam-5978	187	70	,	,	PUNCT
ejpam-5978	187	71	v1	v1	PROPN
ejpam-5978	187	72	}	}	PUNCT
ejpam-5978	187	73	{	{	PUNCT
ejpam-5978	187	74	v5	v5	PROPN
ejpam-5978	187	75	,	,	PUNCT
ejpam-5978	187	76	v6	v6	NOUN
ejpam-5978	187	77	,	,	PUNCT
ejpam-5978	187	78	v1	v1	PROPN
ejpam-5978	187	79	}	}	PUNCT
ejpam-5978	187	80	{	{	PUNCT
ejpam-5978	187	81	v4	v4	NOUN
ejpam-5978	187	82	,	,	PUNCT
ejpam-5978	187	83	v2	v2	PROPN
ejpam-5978	187	84	}	}	PUNCT
ejpam-5978	187	85	{	{	PUNCT
ejpam-5978	187	86	v6	v6	NOUN
ejpam-5978	187	87	,	,	PUNCT
ejpam-5978	187	88	v1	v1	NOUN
ejpam-5978	187	89	,	,	PUNCT
ejpam-5978	187	90	v2	v2	PROPN
ejpam-5978	187	91	}	}	PUNCT
ejpam-5978	187	92	{	{	PUNCT
ejpam-5978	187	93	v5	v5	PROPN
ejpam-5978	187	94	,	,	PUNCT
ejpam-5978	187	95	v3	v3	PROPN
ejpam-5978	187	96	}	}	PUNCT
ejpam-5978	187	97	table	table	NOUN
ejpam-5978	187	98	9	9	NUM
ejpam-5978	187	99	:	:	SYM
ejpam-5978	187	100	3	3	NUM
ejpam-5978	187	101	-	-	PUNCT
ejpam-5978	187	102	convex	convex	ADJ
ejpam-5978	187	103	subsets	subset	NOUN
ejpam-5978	187	104	of	of	ADP
ejpam-5978	187	105	v	v	NOUN
ejpam-5978	187	106	(	(	PUNCT
ejpam-5978	187	107	c6	c6	PROPN
ejpam-5978	187	108	)	)	PUNCT
ejpam-5978	187	109	and	and	CCONJ
ejpam-5978	187	110	its	its	PRON
ejpam-5978	187	111	corresponding	corresponding	ADJ
ejpam-5978	187	112	γin	γin	NOUN
ejpam-5978	187	113	-	-	PUNCT
ejpam-5978	187	114	sets	set	NOUN
ejpam-5978	187	115	.	.	PUNCT
ejpam-5978	188	1	table	table	NOUN
ejpam-5978	188	2	9	9	NUM
ejpam-5978	188	3	shows	show	VERB
ejpam-5978	188	4	that	that	SCONJ
ejpam-5978	188	5	there	there	PRON
ejpam-5978	188	6	are	be	VERB
ejpam-5978	188	7	6	6	NUM
ejpam-5978	188	8	3	3	NUM
ejpam-5978	188	9	-	-	PUNCT
ejpam-5978	188	10	convex	convex	NOUN
ejpam-5978	188	11	subsets	subset	NOUN
ejpam-5978	188	12	of	of	ADP
ejpam-5978	188	13	v	v	NOUN
ejpam-5978	188	14	(	(	PUNCT
ejpam-5978	188	15	c6	c6	PROPN
ejpam-5978	188	16	)	)	PUNCT
ejpam-5978	188	17	with	with	ADP
ejpam-5978	188	18	γin	γin	NOUN
ejpam-5978	188	19	-	-	PUNCT
ejpam-5978	188	20	sets	set	NOUN
ejpam-5978	188	21	cardinality	cardinality	NOUN
ejpam-5978	188	22	equal	equal	ADJ
ejpam-5978	188	23	to	to	ADP
ejpam-5978	188	24	2	2	NUM
ejpam-5978	188	25	.	.	PUNCT
ejpam-5978	189	1	this	this	PRON
ejpam-5978	189	2	contributes	contribute	VERB
ejpam-5978	189	3	to	to	ADP
ejpam-5978	189	4	the	the	DET
ejpam-5978	189	5	convex	convex	ADJ
ejpam-5978	189	6	independent	independent	ADJ
ejpam-5978	189	7	neighborhood	neighborhood	NOUN
ejpam-5978	189	8	polynomial	polynomial	NOUN
ejpam-5978	189	9	of	of	ADP
ejpam-5978	189	10	c6	c6	PROPN
ejpam-5978	189	11	as	as	ADP
ejpam-5978	189	12	6x	6x	NOUN
ejpam-5978	189	13	3y2	3y2	NOUN
ejpam-5978	189	14	.	.	PUNCT
ejpam-5978	190	1	for	for	ADP
ejpam-5978	190	2	both	both	DET
ejpam-5978	190	3	4	4	NUM
ejpam-5978	190	4	-	-	NOUN
ejpam-5978	190	5	convex	convex	NOUN
ejpam-5978	190	6	and	and	CCONJ
ejpam-5978	190	7	5	5	NUM
ejpam-5978	190	8	-	-	PUNCT
ejpam-5978	190	9	convex	convex	ADJ
ejpam-5978	190	10	subsets	subset	NOUN
ejpam-5978	190	11	of	of	ADP
ejpam-5978	190	12	v	v	NOUN
ejpam-5978	190	13	(	(	PUNCT
ejpam-5978	190	14	c6	c6	PROPN
ejpam-5978	190	15	)	)	PUNCT
ejpam-5978	190	16	,	,	PUNCT
ejpam-5978	190	17	it	it	PRON
ejpam-5978	190	18	can	can	AUX
ejpam-5978	190	19	be	be	AUX
ejpam-5978	190	20	verified	verify	VERB
ejpam-5978	190	21	that	that	SCONJ
ejpam-5978	190	22	there	there	PRON
ejpam-5978	190	23	are	be	VERB
ejpam-5978	190	24	no	no	DET
ejpam-5978	190	25	4	4	NUM
ejpam-5978	190	26	-	-	PUNCT
ejpam-5978	190	27	convex	convex	NOUN
ejpam-5978	190	28	and	and	CCONJ
ejpam-5978	190	29	5	5	NUM
ejpam-5978	190	30	-	-	PUNCT
ejpam-5978	190	31	convex	convex	ADJ
ejpam-5978	190	32	subsets	subset	NOUN
ejpam-5978	190	33	of	of	ADP
ejpam-5978	190	34	v	v	NOUN
ejpam-5978	190	35	(	(	PUNCT
ejpam-5978	190	36	c6	c6	PROPN
ejpam-5978	190	37	)	)	PUNCT
ejpam-5978	190	38	since	since	SCONJ
ejpam-5978	190	39	any	any	DET
ejpam-5978	190	40	subsets	subset	NOUN
ejpam-5978	190	41	of	of	ADP
ejpam-5978	190	42	c6	c6	PROPN
ejpam-5978	190	43	that	that	PRON
ejpam-5978	190	44	contains	contain	VERB
ejpam-5978	190	45	four	four	NUM
ejpam-5978	190	46	or	or	CCONJ
ejpam-5978	190	47	more	more	ADJ
ejpam-5978	190	48	elements	element	NOUN
ejpam-5978	190	49	is	be	AUX
ejpam-5978	190	50	no	no	ADV
ejpam-5978	190	51	longer	long	ADV
ejpam-5978	190	52	convex	convex	NOUN
ejpam-5978	190	53	sets	set	NOUN
ejpam-5978	190	54	.	.	PUNCT
ejpam-5978	191	1	for	for	ADP
ejpam-5978	191	2	6	6	NUM
ejpam-5978	191	3	-	-	PUNCT
ejpam-5978	191	4	convex	convex	NOUN
ejpam-5978	191	5	subsets	subset	NOUN
ejpam-5978	191	6	of	of	ADP
ejpam-5978	191	7	v	v	NOUN
ejpam-5978	191	8	(	(	PUNCT
ejpam-5978	191	9	c6	c6	PROPN
ejpam-5978	191	10	)	)	PUNCT
ejpam-5978	191	11	,	,	PUNCT
ejpam-5978	191	12	it	it	PRON
ejpam-5978	191	13	can	can	AUX
ejpam-5978	191	14	be	be	AUX
ejpam-5978	191	15	verified	verify	VERB
ejpam-5978	191	16	that	that	SCONJ
ejpam-5978	191	17	there	there	PRON
ejpam-5978	191	18	is	be	VERB
ejpam-5978	191	19	only	only	ADV
ejpam-5978	191	20	1	1	NUM
ejpam-5978	191	21	6	6	NUM
ejpam-5978	191	22	-	-	PUNCT
ejpam-5978	191	23	convex	convex	NOUN
ejpam-5978	191	24	subset	subset	NOUN
ejpam-5978	191	25	of	of	ADP
ejpam-5978	191	26	v	v	PROPN
ejpam-5978	191	27	(	(	PUNCT
ejpam-5978	191	28	c6	c6	PROPN
ejpam-5978	191	29	)	)	PUNCT
ejpam-5978	191	30	with	with	ADP
ejpam-5978	191	31	empty	empty	ADJ
ejpam-5978	191	32	(	(	PUNCT
ejpam-5978	191	33	zero	zero	NUM
ejpam-5978	191	34	cardinality	cardinality	NOUN
ejpam-5978	191	35	)	)	PUNCT
ejpam-5978	191	36	γin	γin	NOUN
ejpam-5978	191	37	-	-	PUNCT
ejpam-5978	191	38	set	set	NOUN
ejpam-5978	191	39	.	.	PUNCT
ejpam-5978	192	1	this	this	PRON
ejpam-5978	192	2	contributes	contribute	VERB
ejpam-5978	192	3	to	to	ADP
ejpam-5978	192	4	the	the	DET
ejpam-5978	192	5	convex	convex	ADJ
ejpam-5978	192	6	independent	independent	ADJ
ejpam-5978	192	7	neighborhood	neighborhood	NOUN
ejpam-5978	192	8	polynomial	polynomial	NOUN
ejpam-5978	192	9	of	of	ADP
ejpam-5978	192	10	c6	c6	PROPN
ejpam-5978	192	11	as	as	ADP
ejpam-5978	192	12	x6	x6	PROPN
ejpam-5978	192	13	.	.	PUNCT
ejpam-5978	193	1	5	5	NUM
ejpam-5978	193	2	.	.	PUNCT
ejpam-5978	193	3	complete	complete	ADJ
ejpam-5978	193	4	graph	graph	NOUN
ejpam-5978	193	5	and	and	CCONJ
ejpam-5978	193	6	star	star	NOUN
ejpam-5978	193	7	graph	graph	NOUN
ejpam-5978	193	8	this	this	DET
ejpam-5978	193	9	section	section	NOUN
ejpam-5978	193	10	discusses	discuss	VERB
ejpam-5978	193	11	the	the	DET
ejpam-5978	193	12	convex	convex	ADJ
ejpam-5978	193	13	independent	independent	ADJ
ejpam-5978	193	14	neighborhood	neighborhood	NOUN
ejpam-5978	193	15	polynomial	polynomial	NOUN
ejpam-5978	193	16	of	of	ADP
ejpam-5978	193	17	complete	complete	ADJ
ejpam-5978	193	18	graph	graph	NOUN
ejpam-5978	193	19	(	(	PUNCT
ejpam-5978	193	20	kn	kn	PROPN
ejpam-5978	193	21	)	)	PUNCT
ejpam-5978	193	22	and	and	CCONJ
ejpam-5978	193	23	star	star	NOUN
ejpam-5978	193	24	graph	graph	NOUN
ejpam-5978	193	25	(	(	PUNCT
ejpam-5978	193	26	k1,n	k1,n	PROPN
ejpam-5978	193	27	)	)	PUNCT
ejpam-5978	193	28	.	.	PUNCT
ejpam-5978	194	1	theorem	theorem	VERB
ejpam-5978	194	2	5.1	5.1	NUM
ejpam-5978	194	3	.	.	PUNCT
ejpam-5978	195	1	let	let	VERB
ejpam-5978	195	2	kn	kn	PROPN
ejpam-5978	195	3	be	be	AUX
ejpam-5978	195	4	a	a	DET
ejpam-5978	195	5	complete	complete	ADJ
ejpam-5978	195	6	graph	graph	NOUN
ejpam-5978	195	7	of	of	ADP
ejpam-5978	195	8	order	order	NOUN
ejpam-5978	195	9	n.	n.	NOUN
ejpam-5978	195	10	then	then	ADV
ejpam-5978	195	11	,	,	PUNCT
ejpam-5978	195	12	the	the	DET
ejpam-5978	195	13	convex	convex	ADJ
ejpam-5978	195	14	independent	independent	ADJ
ejpam-5978	195	15	neighborhood	neighborhood	NOUN
ejpam-5978	195	16	polynomial	polynomial	NOUN
ejpam-5978	195	17	of	of	ADP
ejpam-5978	195	18	kn	kn	PROPN
ejpam-5978	195	19	is	be	AUX
ejpam-5978	195	20	γcin(kn;x	γcin(kn;x	PROPN
ejpam-5978	195	21	,	,	PUNCT
ejpam-5978	195	22	y	y	NOUN
ejpam-5978	195	23	)	)	PUNCT
ejpam-5978	195	24	=	=	SYM
ejpam-5978	196	1	xn	xn	PROPN
ejpam-5978	197	1	+	+	NUM
ejpam-5978	197	2	n−1∑	n−1∑	PROPN
ejpam-5978	197	3	i=1	i=1	PROPN
ejpam-5978	198	1	(	(	PUNCT
ejpam-5978	198	2	n	n	X
ejpam-5978	198	3	i	i	PRON
ejpam-5978	198	4	)	)	PUNCT
ejpam-5978	198	5	xiy	xiy	PROPN
ejpam-5978	198	6	where	where	SCONJ
ejpam-5978	198	7	n	n	PRON
ejpam-5978	198	8	≥	≥	NOUN
ejpam-5978	198	9	3	3	NUM
ejpam-5978	198	10	,	,	PUNCT
ejpam-5978	198	11	(	(	PUNCT
ejpam-5978	198	12	n	n	X
ejpam-5978	198	13	i	i	NOUN
ejpam-5978	198	14	)	)	PUNCT
ejpam-5978	198	15	is	be	AUX
ejpam-5978	198	16	the	the	DET
ejpam-5978	198	17	number	number	NOUN
ejpam-5978	198	18	of	of	ADP
ejpam-5978	198	19	i	i	NOUN
ejpam-5978	198	20	-	-	PUNCT
ejpam-5978	198	21	convex	convex	ADJ
ejpam-5978	198	22	subsets	subset	NOUN
ejpam-5978	198	23	of	of	ADP
ejpam-5978	198	24	v	v	NOUN
ejpam-5978	198	25	(	(	PUNCT
ejpam-5978	198	26	kn	kn	PROPN
ejpam-5978	198	27	)	)	PUNCT
ejpam-5978	198	28	with	with	ADP
ejpam-5978	198	29	maximum	maximum	ADJ
ejpam-5978	198	30	independent	independent	ADJ
ejpam-5978	198	31	neighborhood	neighborhood	NOUN
ejpam-5978	198	32	system	system	NOUN
ejpam-5978	198	33	cardinality	cardinality	NOUN
ejpam-5978	198	34	equal	equal	ADJ
ejpam-5978	198	35	to	to	ADP
ejpam-5978	198	36	1	1	NUM
ejpam-5978	198	37	which	which	PRON
ejpam-5978	198	38	is	be	AUX
ejpam-5978	198	39	the	the	DET
ejpam-5978	198	40	combination	combination	NOUN
ejpam-5978	198	41	of	of	ADP
ejpam-5978	198	42	n	n	PRON
ejpam-5978	198	43	vertices	vertex	NOUN
ejpam-5978	198	44	taken	take	VERB
ejpam-5978	198	45	i	i	PRON
ejpam-5978	198	46	at	at	ADP
ejpam-5978	198	47	a	a	DET
ejpam-5978	198	48	time	time	NOUN
ejpam-5978	198	49	.	.	PUNCT
ejpam-5978	199	1	proof	proof	NOUN
ejpam-5978	199	2	.	.	PUNCT
ejpam-5978	200	1	let	let	VERB
ejpam-5978	200	2	v	v	X
ejpam-5978	200	3	(	(	PUNCT
ejpam-5978	200	4	kn	kn	PROPN
ejpam-5978	200	5	)	)	PUNCT
ejpam-5978	200	6	=	=	SYM
ejpam-5978	200	7	{	{	PUNCT
ejpam-5978	200	8	v1	v1	PROPN
ejpam-5978	200	9	,	,	PUNCT
ejpam-5978	200	10	v2	v2	PROPN
ejpam-5978	200	11	,	,	PUNCT
ejpam-5978	200	12	.	.	PUNCT
ejpam-5978	200	13	.	.	PUNCT
ejpam-5978	201	1	.	.	PUNCT
ejpam-5978	202	1	,	,	PUNCT
ejpam-5978	202	2	vn	vn	AUX
ejpam-5978	202	3	}	}	PUNCT
ejpam-5978	202	4	be	be	AUX
ejpam-5978	202	5	vertex	vertex	NOUN
ejpam-5978	202	6	set	set	NOUN
ejpam-5978	202	7	of	of	ADP
ejpam-5978	202	8	kn	kn	PROPN
ejpam-5978	202	9	.	.	PUNCT
ejpam-5978	203	1	first	first	ADV
ejpam-5978	203	2	,	,	PUNCT
ejpam-5978	203	3	note	note	VERB
ejpam-5978	203	4	that	that	SCONJ
ejpam-5978	203	5	there	there	PRON
ejpam-5978	203	6	is	be	VERB
ejpam-5978	203	7	only	only	ADV
ejpam-5978	203	8	one	one	NUM
ejpam-5978	203	9	n	n	CCONJ
ejpam-5978	203	10	-	-	PUNCT
ejpam-5978	203	11	convex	convex	NOUN
ejpam-5978	203	12	subset	subset	NOUN
ejpam-5978	203	13	of	of	ADP
ejpam-5978	203	14	v	v	PROPN
ejpam-5978	203	15	(	(	PUNCT
ejpam-5978	203	16	kn	kn	PROPN
ejpam-5978	203	17	)	)	PUNCT
ejpam-5978	203	18	which	which	PRON
ejpam-5978	203	19	has	have	VERB
ejpam-5978	203	20	empty	empty	ADJ
ejpam-5978	203	21	(	(	PUNCT
ejpam-5978	203	22	zero	zero	NUM
ejpam-5978	203	23	cardinality	cardinality	NOUN
ejpam-5978	203	24	)	)	PUNCT
ejpam-5978	203	25	γin	γin	NOUN
ejpam-5978	203	26	-	-	PUNCT
ejpam-5978	203	27	sets	set	NOUN
ejpam-5978	203	28	.	.	PUNCT
ejpam-5978	204	1	this	this	PRON
ejpam-5978	204	2	contributes	contribute	VERB
ejpam-5978	204	3	to	to	ADP
ejpam-5978	204	4	xn	xn	PROPN
ejpam-5978	204	5	.	.	PUNCT
ejpam-5978	205	1	now	now	ADV
ejpam-5978	205	2	,	,	PUNCT
ejpam-5978	205	3	for	for	ADP
ejpam-5978	205	4	integer	integer	NOUN
ejpam-5978	205	5	i	i	NOUN
ejpam-5978	205	6	=	=	NOUN
ejpam-5978	205	7	1	1	NUM
ejpam-5978	205	8	,	,	PUNCT
ejpam-5978	205	9	2	2	NUM
ejpam-5978	205	10	,	,	PUNCT
ejpam-5978	205	11	...	...	PUNCT
ejpam-5978	205	12	,	,	PUNCT
ejpam-5978	205	13	n	n	CCONJ
ejpam-5978	205	14	−	−	PROPN
ejpam-5978	205	15	1	1	NUM
ejpam-5978	205	16	,	,	PUNCT
ejpam-5978	205	17	there	there	PRON
ejpam-5978	205	18	always	always	ADV
ejpam-5978	205	19	exist	exist	VERB
ejpam-5978	205	20	an	an	DET
ejpam-5978	205	21	i	i	NOUN
ejpam-5978	205	22	-	-	PUNCT
ejpam-5978	205	23	convex	convex	ADJ
ejpam-5978	205	24	subsets	subset	NOUN
ejpam-5978	205	25	of	of	ADP
ejpam-5978	205	26	v	v	NOUN
ejpam-5978	205	27	(	(	PUNCT
ejpam-5978	205	28	kn	kn	PROPN
ejpam-5978	205	29	)	)	PUNCT
ejpam-5978	205	30	.	.	PUNCT
ejpam-5978	206	1	this	this	PRON
ejpam-5978	206	2	means	mean	VERB
ejpam-5978	206	3	that	that	SCONJ
ejpam-5978	206	4	the	the	DET
ejpam-5978	206	5	γin	γin	NOUN
ejpam-5978	206	6	-	-	PUNCT
ejpam-5978	206	7	sets	set	NOUN
ejpam-5978	206	8	of	of	ADP
ejpam-5978	206	9	i	i	NOUN
ejpam-5978	206	10	-	-	PUNCT
ejpam-5978	206	11	convex	convex	ADJ
ejpam-5978	206	12	subsets	subset	NOUN
ejpam-5978	206	13	of	of	ADP
ejpam-5978	206	14	v	v	NOUN
ejpam-5978	206	15	(	(	PUNCT
ejpam-5978	206	16	kn	kn	PROPN
ejpam-5978	206	17	)	)	PUNCT
ejpam-5978	206	18	contains	contain	VERB
ejpam-5978	206	19	exactly	exactly	ADV
ejpam-5978	206	20	one	one	NUM
ejpam-5978	206	21	element	element	NOUN
ejpam-5978	206	22	,	,	PUNCT
ejpam-5978	206	23	for	for	ADP
ejpam-5978	206	24	all	all	DET
ejpam-5978	206	25	i	i	PRON
ejpam-5978	206	26	=	=	NOUN
ejpam-5978	206	27	1	1	NUM
ejpam-5978	206	28	,	,	PUNCT
ejpam-5978	206	29	2	2	NUM
ejpam-5978	206	30	,	,	PUNCT
ejpam-5978	206	31	...	...	PUNCT
ejpam-5978	206	32	,	,	PUNCT
ejpam-5978	206	33	n	n	CCONJ
ejpam-5978	206	34	−	−	PROPN
ejpam-5978	206	35	1	1	NUM
ejpam-5978	206	36	since	since	SCONJ
ejpam-5978	206	37	every	every	DET
ejpam-5978	206	38	vertices	vertex	NOUN
ejpam-5978	206	39	are	be	AUX
ejpam-5978	206	40	connected	connect	VERB
ejpam-5978	206	41	to	to	ADP
ejpam-5978	206	42	each	each	DET
ejpam-5978	206	43	other	other	ADJ
ejpam-5978	206	44	.	.	PUNCT
ejpam-5978	207	1	moreover	moreover	ADV
ejpam-5978	207	2	,	,	PUNCT
ejpam-5978	207	3	there	there	PRON
ejpam-5978	207	4	are	be	VERB
ejpam-5978	207	5	(	(	PUNCT
ejpam-5978	207	6	n	n	X
ejpam-5978	207	7	i	i	NOUN
ejpam-5978	207	8	)	)	PUNCT
ejpam-5978	208	1	i	i	PRON
ejpam-5978	208	2	-	-	PUNCT
ejpam-5978	208	3	convex	convex	ADJ
ejpam-5978	208	4	subsets	subset	NOUN
ejpam-5978	208	5	of	of	ADP
ejpam-5978	208	6	v	v	NOUN
ejpam-5978	208	7	(	(	PUNCT
ejpam-5978	208	8	kn	kn	PROPN
ejpam-5978	208	9	)	)	PUNCT
ejpam-5978	208	10	whose	whose	DET
ejpam-5978	208	11	γin	γin	NOUN
ejpam-5978	208	12	-	-	PUNCT
ejpam-5978	208	13	sets	set	NOUN
ejpam-5978	208	14	contain	contain	VERB
ejpam-5978	208	15	exactly	exactly	ADV
ejpam-5978	208	16	one	one	NUM
ejpam-5978	208	17	element	element	NOUN
ejpam-5978	208	18	.	.	PUNCT
ejpam-5978	209	1	e.j	e.j	PROPN
ejpam-5978	209	2	.	.	PROPN
ejpam-5978	209	3	aguilon	aguilon	PROPN
ejpam-5978	209	4	,	,	PUNCT
ejpam-5978	209	5	s.	s.	PROPN
ejpam-5978	209	6	dagondon	dagondon	PROPN
ejpam-5978	209	7	,	,	PUNCT
ejpam-5978	209	8	r.	r.	PROPN
ejpam-5978	209	9	artes	artes	PROPN
ejpam-5978	209	10	/	/	SYM
ejpam-5978	209	11	eur	eur	PROPN
ejpam-5978	209	12	.	.	PUNCT
ejpam-5978	210	1	j.	j.	PROPN
ejpam-5978	210	2	pure	pure	PROPN
ejpam-5978	210	3	appl	appl	PROPN
ejpam-5978	210	4	.	.	PROPN
ejpam-5978	210	5	math	math	PROPN
ejpam-5978	210	6	,	,	PUNCT
ejpam-5978	210	7	18	18	NUM
ejpam-5978	210	8	(	(	PUNCT
ejpam-5978	210	9	2	2	NUM
ejpam-5978	210	10	)	)	PUNCT
ejpam-5978	210	11	(	(	PUNCT
ejpam-5978	210	12	2025	2025	NUM
ejpam-5978	210	13	)	)	PUNCT
ejpam-5978	210	14	,	,	PUNCT
ejpam-5978	210	15	5978	5978	NUM
ejpam-5978	210	16	12	12	NUM
ejpam-5978	210	17	of	of	ADP
ejpam-5978	210	18	18	18	NUM
ejpam-5978	210	19	therefore	therefore	ADV
ejpam-5978	210	20	,	,	PUNCT
ejpam-5978	210	21	the	the	DET
ejpam-5978	210	22	convex	convex	ADJ
ejpam-5978	210	23	independent	independent	ADJ
ejpam-5978	210	24	neighborhood	neighborhood	NOUN
ejpam-5978	210	25	polynomial	polynomial	NOUN
ejpam-5978	210	26	of	of	ADP
ejpam-5978	210	27	kn	kn	PROPN
ejpam-5978	210	28	is	be	AUX
ejpam-5978	210	29	γcin(kn;x	γcin(kn;x	PROPN
ejpam-5978	210	30	,	,	PUNCT
ejpam-5978	210	31	y	y	NOUN
ejpam-5978	210	32	)	)	PUNCT
ejpam-5978	210	33	=	=	SYM
ejpam-5978	211	1	xn	xn	PROPN
ejpam-5978	212	1	+	+	NUM
ejpam-5978	212	2	n−1∑	n−1∑	PROPN
ejpam-5978	212	3	i=1	i=1	PROPN
ejpam-5978	213	1	(	(	PUNCT
ejpam-5978	213	2	n	n	X
ejpam-5978	213	3	i	i	PRON
ejpam-5978	213	4	)	)	PUNCT
ejpam-5978	213	5	xiy	xiy	PROPN
ejpam-5978	213	6	.	.	PUNCT
ejpam-5978	214	1	■	■	PUNCT
ejpam-5978	214	2	let	let	VERB
ejpam-5978	214	3	v	v	X
ejpam-5978	214	4	(	(	PUNCT
ejpam-5978	214	5	kn	kn	PROPN
ejpam-5978	214	6	)	)	PUNCT
ejpam-5978	214	7	=	=	SYM
ejpam-5978	214	8	{	{	PUNCT
ejpam-5978	214	9	v1	v1	PROPN
ejpam-5978	214	10	,	,	PUNCT
ejpam-5978	214	11	v2	v2	PROPN
ejpam-5978	214	12	,	,	PUNCT
ejpam-5978	214	13	...	...	PUNCT
ejpam-5978	214	14	,	,	PUNCT
ejpam-5978	214	15	vn	vn	PART
ejpam-5978	214	16	}	}	PUNCT
ejpam-5978	214	17	be	be	AUX
ejpam-5978	214	18	vertex	vertex	NOUN
ejpam-5978	214	19	set	set	NOUN
ejpam-5978	214	20	of	of	ADP
ejpam-5978	214	21	complete	complete	ADJ
ejpam-5978	214	22	graph	graph	NOUN
ejpam-5978	214	23	kn	kn	PROPN
ejpam-5978	214	24	.	.	PUNCT
ejpam-5978	214	25	note	note	VERB
ejpam-5978	214	26	that	that	SCONJ
ejpam-5978	214	27	the	the	DET
ejpam-5978	214	28	vertices	vertex	NOUN
ejpam-5978	214	29	{	{	PUNCT
ejpam-5978	214	30	v1	v1	NOUN
ejpam-5978	214	31	,	,	PUNCT
ejpam-5978	214	32	v2	v2	PROPN
ejpam-5978	214	33	,	,	PUNCT
ejpam-5978	214	34	...	...	PUNCT
ejpam-5978	214	35	,	,	PUNCT
ejpam-5978	214	36	vn	vn	PROPN
ejpam-5978	214	37	}	}	PUNCT
ejpam-5978	214	38	is	be	AUX
ejpam-5978	214	39	the	the	DET
ejpam-5978	214	40	n	n	ADV
ejpam-5978	214	41	-	-	PUNCT
ejpam-5978	214	42	convex	convex	NOUN
ejpam-5978	214	43	subset	subset	NOUN
ejpam-5978	214	44	of	of	ADP
ejpam-5978	214	45	v	v	PROPN
ejpam-5978	214	46	(	(	PUNCT
ejpam-5978	214	47	kn	kn	PROPN
ejpam-5978	214	48	)	)	PUNCT
ejpam-5978	214	49	which	which	PRON
ejpam-5978	214	50	contributes	contribute	VERB
ejpam-5978	214	51	to	to	ADP
ejpam-5978	214	52	the	the	DET
ejpam-5978	214	53	leading	lead	VERB
ejpam-5978	214	54	term	term	NOUN
ejpam-5978	214	55	of	of	ADP
ejpam-5978	214	56	the	the	DET
ejpam-5978	214	57	convex	convex	ADJ
ejpam-5978	214	58	independent	independent	ADJ
ejpam-5978	214	59	neighborhood	neighborhood	NOUN
ejpam-5978	214	60	polynomial	polynomial	NOUN
ejpam-5978	214	61	of	of	ADP
ejpam-5978	214	62	kn	kn	PROPN
ejpam-5978	214	63	.	.	PUNCT
ejpam-5978	215	1	now	now	ADV
ejpam-5978	215	2	,	,	PUNCT
ejpam-5978	215	3	for	for	ADP
ejpam-5978	215	4	i	i	PROPN
ejpam-5978	215	5	=	=	NOUN
ejpam-5978	215	6	1	1	NUM
ejpam-5978	215	7	,	,	PUNCT
ejpam-5978	215	8	...	...	PUNCT
ejpam-5978	215	9	,	,	PUNCT
ejpam-5978	215	10	n	n	CCONJ
ejpam-5978	215	11	−	−	PROPN
ejpam-5978	215	12	1	1	NUM
ejpam-5978	215	13	,	,	PUNCT
ejpam-5978	215	14	the	the	DET
ejpam-5978	215	15	i	i	NOUN
ejpam-5978	215	16	-	-	PUNCT
ejpam-5978	215	17	convex	convex	ADJ
ejpam-5978	215	18	subsets	subset	NOUN
ejpam-5978	215	19	of	of	ADP
ejpam-5978	215	20	v	v	NOUN
ejpam-5978	215	21	(	(	PUNCT
ejpam-5978	215	22	kn	kn	PROPN
ejpam-5978	215	23	)	)	PUNCT
ejpam-5978	215	24	has	have	VERB
ejpam-5978	215	25	γin	γin	NOUN
ejpam-5978	215	26	-	-	PUNCT
ejpam-5978	215	27	sets	set	NOUN
ejpam-5978	215	28	cardinality	cardinality	NOUN
ejpam-5978	215	29	equal	equal	ADJ
ejpam-5978	215	30	to	to	ADP
ejpam-5978	215	31	one	one	NUM
ejpam-5978	215	32	.	.	PUNCT
ejpam-5978	216	1	this	this	PRON
ejpam-5978	216	2	means	mean	VERB
ejpam-5978	216	3	that	that	SCONJ
ejpam-5978	216	4	for	for	ADP
ejpam-5978	216	5	n	n	PRON
ejpam-5978	216	6	≥	≥	NOUN
ejpam-5978	216	7	3	3	NUM
ejpam-5978	216	8	,	,	PUNCT
ejpam-5978	216	9	there	there	PRON
ejpam-5978	216	10	are	be	VERB
ejpam-5978	216	11	1	1	NUM
ejpam-5978	216	12	+	+	CCONJ
ejpam-5978	216	13	(	(	PUNCT
ejpam-5978	216	14	n−	n−	NOUN
ejpam-5978	216	15	1	1	NUM
ejpam-5978	216	16	)	)	PUNCT
ejpam-5978	216	17	=	=	SYM
ejpam-5978	217	1	n	n	NOUN
ejpam-5978	217	2	terms	term	NOUN
ejpam-5978	217	3	for	for	ADP
ejpam-5978	217	4	the	the	DET
ejpam-5978	217	5	convex	convex	ADJ
ejpam-5978	217	6	independent	independent	ADJ
ejpam-5978	217	7	neighborhood	neighborhood	NOUN
ejpam-5978	217	8	polynomial	polynomial	NOUN
ejpam-5978	217	9	of	of	ADP
ejpam-5978	217	10	kn	kn	PROPN
ejpam-5978	217	11	.	.	PUNCT
ejpam-5978	218	1	thus	thus	ADV
ejpam-5978	218	2	,	,	PUNCT
ejpam-5978	218	3	we	we	PRON
ejpam-5978	218	4	have	have	VERB
ejpam-5978	218	5	the	the	DET
ejpam-5978	218	6	following	follow	VERB
ejpam-5978	218	7	corollary	corollary	ADJ
ejpam-5978	218	8	corollary	corollary	ADJ
ejpam-5978	218	9	5.2	5.2	NUM
ejpam-5978	218	10	.	.	PUNCT
ejpam-5978	219	1	for	for	ADP
ejpam-5978	219	2	n	n	PRON
ejpam-5978	219	3	≥	≥	NUM
ejpam-5978	219	4	3	3	NUM
ejpam-5978	219	5	,	,	PUNCT
ejpam-5978	219	6	the	the	DET
ejpam-5978	219	7	number	number	NOUN
ejpam-5978	219	8	of	of	ADP
ejpam-5978	219	9	terms	term	NOUN
ejpam-5978	219	10	of	of	ADP
ejpam-5978	219	11	the	the	DET
ejpam-5978	219	12	convex	convex	ADJ
ejpam-5978	219	13	independent	independent	ADJ
ejpam-5978	219	14	neighborhood	neighborhood	NOUN
ejpam-5978	219	15	polynomial	polynomial	NOUN
ejpam-5978	219	16	of	of	ADP
ejpam-5978	219	17	kn	kn	PROPN
ejpam-5978	219	18	is	be	AUX
ejpam-5978	219	19	n.	n.	NOUN
ejpam-5978	219	20	illustration	illustration	NOUN
ejpam-5978	219	21	5.3	5.3	NUM
ejpam-5978	219	22	.	.	PUNCT
ejpam-5978	220	1	consider	consider	VERB
ejpam-5978	220	2	k4	k4	PROPN
ejpam-5978	220	3	be	be	AUX
ejpam-5978	220	4	a	a	DET
ejpam-5978	220	5	complete	complete	ADJ
ejpam-5978	220	6	graph	graph	NOUN
ejpam-5978	220	7	of	of	ADP
ejpam-5978	220	8	order	order	NOUN
ejpam-5978	220	9	4	4	NUM
ejpam-5978	220	10	.	.	PUNCT
ejpam-5978	221	1	v1	v1	PROPN
ejpam-5978	221	2	v2	v2	PROPN
ejpam-5978	221	3	v3v4	v3v4	PUNCT
ejpam-5978	221	4	figure	figure	VERB
ejpam-5978	221	5	4	4	NUM
ejpam-5978	221	6	:	:	PUNCT
ejpam-5978	221	7	a	a	DET
ejpam-5978	221	8	complete	complete	ADJ
ejpam-5978	221	9	graph	graph	NOUN
ejpam-5978	221	10	k4	k4	NOUN
ejpam-5978	221	11	of	of	ADP
ejpam-5978	221	12	order	order	NOUN
ejpam-5978	221	13	4	4	NUM
ejpam-5978	221	14	then	then	ADV
ejpam-5978	221	15	,	,	PUNCT
ejpam-5978	221	16	by	by	ADP
ejpam-5978	221	17	using	use	VERB
ejpam-5978	221	18	theorem	theorem	ADJ
ejpam-5978	221	19	5.1	5.1	NUM
ejpam-5978	221	20	,	,	PUNCT
ejpam-5978	221	21	γcin(k4;x	γcin(k4;x	NUM
ejpam-5978	221	22	,	,	PUNCT
ejpam-5978	221	23	y	y	NOUN
ejpam-5978	221	24	)	)	PUNCT
ejpam-5978	221	25	=	=	PUNCT
ejpam-5978	222	1	x4	x4	PROPN
ejpam-5978	223	1	+	+	CCONJ
ejpam-5978	224	1	4−1∑	4−1∑	NUM
ejpam-5978	224	2	i=1	i=1	X
ejpam-5978	224	3	(	(	PUNCT
ejpam-5978	224	4	4	4	NUM
ejpam-5978	224	5	i	i	NOUN
ejpam-5978	224	6	)	)	PUNCT
ejpam-5978	224	7	xiy	xiy	PROPN
ejpam-5978	225	1	=	=	PUNCT
ejpam-5978	225	2	x4	x4	PROPN
ejpam-5978	226	1	+	+	NOUN
ejpam-5978	226	2	3∑	3∑	NUM
ejpam-5978	226	3	i=1	i=1	NOUN
ejpam-5978	226	4	(	(	PUNCT
ejpam-5978	226	5	4	4	NUM
ejpam-5978	226	6	i	i	NOUN
ejpam-5978	226	7	)	)	PUNCT
ejpam-5978	226	8	xiy	xiy	PROPN
ejpam-5978	227	1	=	=	PUNCT
ejpam-5978	227	2	x4	x4	PROPN
ejpam-5978	228	1	+	+	X
ejpam-5978	228	2	[	[	X
ejpam-5978	228	3	(	(	PUNCT
ejpam-5978	228	4	4	4	NUM
ejpam-5978	228	5	1	1	NUM
ejpam-5978	228	6	)	)	PUNCT
ejpam-5978	228	7	xy	xy	PROPN
ejpam-5978	229	1	+	+	CCONJ
ejpam-5978	229	2	(	(	PUNCT
ejpam-5978	229	3	4	4	NUM
ejpam-5978	229	4	2	2	NUM
ejpam-5978	229	5	)	)	PUNCT
ejpam-5978	229	6	x2y	x2y	NOUN
ejpam-5978	230	1	+	+	CCONJ
ejpam-5978	230	2	(	(	PUNCT
ejpam-5978	230	3	4	4	NUM
ejpam-5978	230	4	3	3	NUM
ejpam-5978	230	5	)	)	PUNCT
ejpam-5978	230	6	x3y	x3y	PUNCT
ejpam-5978	230	7	]	]	PUNCT
ejpam-5978	231	1	=	=	PUNCT
ejpam-5978	231	2	x4	x4	PROPN
ejpam-5978	231	3	+	+	X
ejpam-5978	231	4	4x3y	4x3y	ADJ
ejpam-5978	231	5	+	+	CCONJ
ejpam-5978	231	6	6x2y	6x2y	NOUN
ejpam-5978	231	7	+	+	X
ejpam-5978	231	8	4x3y	4x3y	NUM
ejpam-5978	231	9	.	.	PUNCT
ejpam-5978	232	1	and	and	CCONJ
ejpam-5978	232	2	by	by	ADP
ejpam-5978	232	3	corollary	corollary	ADJ
ejpam-5978	232	4	5.2	5.2	NUM
ejpam-5978	232	5	,	,	PUNCT
ejpam-5978	232	6	there	there	PRON
ejpam-5978	232	7	are	be	VERB
ejpam-5978	232	8	n	n	DET
ejpam-5978	232	9	=	=	SYM
ejpam-5978	232	10	4	4	NUM
ejpam-5978	232	11	terms	term	NOUN
ejpam-5978	232	12	in	in	ADP
ejpam-5978	232	13	the	the	DET
ejpam-5978	232	14	convex	convex	ADJ
ejpam-5978	232	15	independent	independent	ADJ
ejpam-5978	232	16	neighborhood	neighborhood	NOUN
ejpam-5978	232	17	polynomial	polynomial	NOUN
ejpam-5978	232	18	of	of	ADP
ejpam-5978	232	19	k4	k4	PROPN
ejpam-5978	232	20	.	.	PUNCT
ejpam-5978	233	1	e.j	e.j	PROPN
ejpam-5978	233	2	.	.	PROPN
ejpam-5978	233	3	aguilon	aguilon	PROPN
ejpam-5978	233	4	,	,	PUNCT
ejpam-5978	233	5	s.	s.	PROPN
ejpam-5978	233	6	dagondon	dagondon	PROPN
ejpam-5978	233	7	,	,	PUNCT
ejpam-5978	233	8	r.	r.	PROPN
ejpam-5978	233	9	artes	artes	PROPN
ejpam-5978	233	10	/	/	SYM
ejpam-5978	233	11	eur	eur	PROPN
ejpam-5978	233	12	.	.	PUNCT
ejpam-5978	234	1	j.	j.	PROPN
ejpam-5978	234	2	pure	pure	PROPN
ejpam-5978	234	3	appl	appl	PROPN
ejpam-5978	234	4	.	.	PROPN
ejpam-5978	234	5	math	math	PROPN
ejpam-5978	234	6	,	,	PUNCT
ejpam-5978	234	7	18	18	NUM
ejpam-5978	234	8	(	(	PUNCT
ejpam-5978	234	9	2	2	NUM
ejpam-5978	234	10	)	)	PUNCT
ejpam-5978	234	11	(	(	PUNCT
ejpam-5978	234	12	2025	2025	NUM
ejpam-5978	234	13	)	)	PUNCT
ejpam-5978	234	14	,	,	PUNCT
ejpam-5978	234	15	5978	5978	NUM
ejpam-5978	234	16	13	13	NUM
ejpam-5978	234	17	of	of	ADP
ejpam-5978	234	18	18	18	NUM
ejpam-5978	234	19	to	to	PART
ejpam-5978	234	20	see	see	VERB
ejpam-5978	234	21	the	the	DET
ejpam-5978	234	22	convex	convex	ADJ
ejpam-5978	234	23	subsets	subset	NOUN
ejpam-5978	234	24	of	of	ADP
ejpam-5978	234	25	v	v	NOUN
ejpam-5978	234	26	(	(	PUNCT
ejpam-5978	234	27	k4	k4	NOUN
ejpam-5978	234	28	)	)	PUNCT
ejpam-5978	234	29	and	and	CCONJ
ejpam-5978	234	30	its	its	PRON
ejpam-5978	234	31	corresponding	corresponding	ADJ
ejpam-5978	234	32	γin	γin	NOUN
ejpam-5978	234	33	-	-	PUNCT
ejpam-5978	234	34	sets	set	NOUN
ejpam-5978	234	35	,	,	PUNCT
ejpam-5978	234	36	refer	refer	VERB
ejpam-5978	234	37	to	to	ADP
ejpam-5978	234	38	the	the	DET
ejpam-5978	234	39	tables	table	NOUN
ejpam-5978	234	40	10	10	NUM
ejpam-5978	234	41	,	,	PUNCT
ejpam-5978	234	42	11	11	NUM
ejpam-5978	234	43	,	,	PUNCT
ejpam-5978	234	44	and	and	CCONJ
ejpam-5978	234	45	12	12	NUM
ejpam-5978	234	46	:	:	SYM
ejpam-5978	234	47	1	1	NUM
ejpam-5978	234	48	-	-	PUNCT
ejpam-5978	234	49	convex	convex	VERB
ejpam-5978	234	50	γin	γin	NOUN
ejpam-5978	234	51	-	-	PUNCT
ejpam-5978	234	52	sets	set	NOUN
ejpam-5978	234	53	{	{	PUNCT
ejpam-5978	234	54	v1	v1	NOUN
ejpam-5978	234	55	}	}	PUNCT
ejpam-5978	234	56	{	{	PUNCT
ejpam-5978	234	57	v2	v2	NOUN
ejpam-5978	234	58	}	}	PUNCT
ejpam-5978	234	59	,	,	PUNCT
ejpam-5978	234	60	{	{	PUNCT
ejpam-5978	234	61	v3	v3	NOUN
ejpam-5978	234	62	}	}	PUNCT
ejpam-5978	234	63	,	,	PUNCT
ejpam-5978	234	64	{	{	PUNCT
ejpam-5978	234	65	v4	v4	NOUN
ejpam-5978	234	66	}	}	PUNCT
ejpam-5978	234	67	{	{	PUNCT
ejpam-5978	234	68	v2	v2	NOUN
ejpam-5978	234	69	}	}	PUNCT
ejpam-5978	234	70	{	{	PUNCT
ejpam-5978	234	71	v1	v1	NOUN
ejpam-5978	234	72	}	}	PUNCT
ejpam-5978	234	73	,	,	PUNCT
ejpam-5978	234	74	{	{	PUNCT
ejpam-5978	234	75	v3	v3	NOUN
ejpam-5978	234	76	}	}	PUNCT
ejpam-5978	234	77	,	,	PUNCT
ejpam-5978	234	78	{	{	PUNCT
ejpam-5978	234	79	v4	v4	NOUN
ejpam-5978	234	80	}	}	PUNCT
ejpam-5978	234	81	{	{	PUNCT
ejpam-5978	234	82	v3	v3	PROPN
ejpam-5978	234	83	}	}	PUNCT
ejpam-5978	234	84	{	{	PUNCT
ejpam-5978	234	85	v1	v1	NOUN
ejpam-5978	234	86	}	}	PUNCT
ejpam-5978	234	87	,	,	PUNCT
ejpam-5978	234	88	{	{	PUNCT
ejpam-5978	234	89	v2	v2	NOUN
ejpam-5978	234	90	}	}	PUNCT
ejpam-5978	234	91	,	,	PUNCT
ejpam-5978	234	92	{	{	PUNCT
ejpam-5978	234	93	v4	v4	NOUN
ejpam-5978	234	94	}	}	PUNCT
ejpam-5978	234	95	{	{	PUNCT
ejpam-5978	234	96	v4	v4	NOUN
ejpam-5978	234	97	}	}	PUNCT
ejpam-5978	234	98	{	{	PUNCT
ejpam-5978	234	99	v1	v1	NOUN
ejpam-5978	234	100	}	}	PUNCT
ejpam-5978	234	101	,	,	PUNCT
ejpam-5978	234	102	{	{	PUNCT
ejpam-5978	234	103	v2	v2	NOUN
ejpam-5978	234	104	}	}	PUNCT
ejpam-5978	234	105	,	,	PUNCT
ejpam-5978	234	106	{	{	PUNCT
ejpam-5978	234	107	v3	v3	NOUN
ejpam-5978	234	108	}	}	PUNCT
ejpam-5978	234	109	table	table	NOUN
ejpam-5978	234	110	10	10	NUM
ejpam-5978	234	111	:	:	SYM
ejpam-5978	234	112	1	1	NUM
ejpam-5978	234	113	-	-	PUNCT
ejpam-5978	234	114	convex	convex	NOUN
ejpam-5978	234	115	subsets	subset	NOUN
ejpam-5978	234	116	of	of	ADP
ejpam-5978	234	117	v	v	NOUN
ejpam-5978	234	118	(	(	PUNCT
ejpam-5978	234	119	k4	k4	NOUN
ejpam-5978	234	120	)	)	PUNCT
ejpam-5978	234	121	and	and	CCONJ
ejpam-5978	234	122	its	its	PRON
ejpam-5978	234	123	corresponding	corresponding	ADJ
ejpam-5978	234	124	γin	γin	NOUN
ejpam-5978	234	125	-	-	PUNCT
ejpam-5978	234	126	sets	set	NOUN
ejpam-5978	234	127	.	.	PUNCT
ejpam-5978	235	1	table	table	NOUN
ejpam-5978	235	2	10	10	NUM
ejpam-5978	235	3	shows	show	VERB
ejpam-5978	235	4	that	that	SCONJ
ejpam-5978	235	5	there	there	PRON
ejpam-5978	235	6	are	be	VERB
ejpam-5978	235	7	4	4	NUM
ejpam-5978	235	8	1	1	NUM
ejpam-5978	235	9	-	-	PUNCT
ejpam-5978	235	10	convex	convex	NOUN
ejpam-5978	235	11	subsets	subset	NOUN
ejpam-5978	235	12	of	of	ADP
ejpam-5978	235	13	v	v	NOUN
ejpam-5978	235	14	(	(	PUNCT
ejpam-5978	235	15	k4	k4	PROPN
ejpam-5978	235	16	)	)	PUNCT
ejpam-5978	235	17	with	with	ADP
ejpam-5978	235	18	γin	γin	NOUN
ejpam-5978	235	19	-	-	PUNCT
ejpam-5978	235	20	sets	set	NOUN
ejpam-5978	235	21	cardinality	cardinality	NOUN
ejpam-5978	235	22	equal	equal	ADJ
ejpam-5978	235	23	to	to	ADP
ejpam-5978	235	24	1	1	NUM
ejpam-5978	235	25	.	.	PUNCT
ejpam-5978	236	1	this	this	PRON
ejpam-5978	236	2	contributes	contribute	VERB
ejpam-5978	236	3	to	to	ADP
ejpam-5978	236	4	the	the	DET
ejpam-5978	236	5	convex	convex	ADJ
ejpam-5978	236	6	independent	independent	ADJ
ejpam-5978	236	7	neighborhood	neighborhood	NOUN
ejpam-5978	236	8	polynomial	polynomial	NOUN
ejpam-5978	236	9	of	of	ADP
ejpam-5978	236	10	k4	k4	NOUN
ejpam-5978	236	11	as	as	ADP
ejpam-5978	236	12	4xy	4xy	ADJ
ejpam-5978	236	13	.	.	PUNCT
ejpam-5978	237	1	2	2	NUM
ejpam-5978	237	2	-	-	NUM
ejpam-5978	237	3	convex	convex	VERB
ejpam-5978	237	4	γin	γin	NOUN
ejpam-5978	237	5	-	-	PUNCT
ejpam-5978	237	6	sets	set	NOUN
ejpam-5978	237	7	{	{	PUNCT
ejpam-5978	237	8	v1	v1	NOUN
ejpam-5978	237	9	,	,	PUNCT
ejpam-5978	237	10	v2	v2	PROPN
ejpam-5978	237	11	}	}	PUNCT
ejpam-5978	237	12	{	{	PUNCT
ejpam-5978	237	13	v3	v3	PROPN
ejpam-5978	237	14	}	}	PUNCT
ejpam-5978	237	15	,	,	PUNCT
ejpam-5978	237	16	{	{	PUNCT
ejpam-5978	237	17	v4	v4	NOUN
ejpam-5978	237	18	}	}	PUNCT
ejpam-5978	237	19	{	{	PUNCT
ejpam-5978	237	20	v2	v2	PROPN
ejpam-5978	237	21	,	,	PUNCT
ejpam-5978	237	22	v3	v3	PROPN
ejpam-5978	237	23	}	}	PUNCT
ejpam-5978	237	24	{	{	PUNCT
ejpam-5978	237	25	v1	v1	NOUN
ejpam-5978	237	26	}	}	PUNCT
ejpam-5978	237	27	,	,	PUNCT
ejpam-5978	237	28	{	{	PUNCT
ejpam-5978	237	29	v4	v4	NOUN
ejpam-5978	237	30	}	}	PUNCT
ejpam-5978	237	31	{	{	PUNCT
ejpam-5978	237	32	v3	v3	PROPN
ejpam-5978	237	33	,	,	PUNCT
ejpam-5978	237	34	v4	v4	PROPN
ejpam-5978	237	35	}	}	PUNCT
ejpam-5978	237	36	{	{	PUNCT
ejpam-5978	237	37	v1	v1	NOUN
ejpam-5978	237	38	}	}	PUNCT
ejpam-5978	237	39	,	,	PUNCT
ejpam-5978	237	40	{	{	PUNCT
ejpam-5978	237	41	v2	v2	NOUN
ejpam-5978	237	42	}	}	PUNCT
ejpam-5978	237	43	{	{	PUNCT
ejpam-5978	237	44	v4	v4	NOUN
ejpam-5978	237	45	,	,	PUNCT
ejpam-5978	237	46	v1	v1	NOUN
ejpam-5978	237	47	}	}	PUNCT
ejpam-5978	237	48	{	{	PUNCT
ejpam-5978	237	49	v2	v2	NOUN
ejpam-5978	237	50	}	}	PUNCT
ejpam-5978	237	51	,	,	PUNCT
ejpam-5978	237	52	{	{	PUNCT
ejpam-5978	237	53	v3	v3	NOUN
ejpam-5978	237	54	}	}	PUNCT
ejpam-5978	237	55	{	{	PUNCT
ejpam-5978	237	56	v1	v1	NOUN
ejpam-5978	237	57	,	,	PUNCT
ejpam-5978	237	58	v3	v3	PROPN
ejpam-5978	237	59	}	}	PUNCT
ejpam-5978	237	60	{	{	PUNCT
ejpam-5978	237	61	v2	v2	PROPN
ejpam-5978	237	62	}	}	PUNCT
ejpam-5978	237	63	,	,	PUNCT
ejpam-5978	237	64	{	{	PUNCT
ejpam-5978	237	65	v4	v4	NOUN
ejpam-5978	237	66	}	}	PUNCT
ejpam-5978	237	67	{	{	PUNCT
ejpam-5978	237	68	v2	v2	PROPN
ejpam-5978	237	69	,	,	PUNCT
ejpam-5978	237	70	v4	v4	PROPN
ejpam-5978	237	71	}	}	PUNCT
ejpam-5978	237	72	{	{	PUNCT
ejpam-5978	237	73	v1	v1	NOUN
ejpam-5978	237	74	}	}	PUNCT
ejpam-5978	237	75	,	,	PUNCT
ejpam-5978	237	76	{	{	PUNCT
ejpam-5978	237	77	v3	v3	NOUN
ejpam-5978	237	78	}	}	PUNCT
ejpam-5978	237	79	table	table	NOUN
ejpam-5978	237	80	11	11	NUM
ejpam-5978	237	81	:	:	SYM
ejpam-5978	237	82	2	2	NUM
ejpam-5978	237	83	-	-	PUNCT
ejpam-5978	237	84	convex	convex	NOUN
ejpam-5978	237	85	subsets	subset	NOUN
ejpam-5978	237	86	of	of	ADP
ejpam-5978	237	87	v	v	NOUN
ejpam-5978	237	88	(	(	PUNCT
ejpam-5978	237	89	k4	k4	NOUN
ejpam-5978	237	90	)	)	PUNCT
ejpam-5978	237	91	and	and	CCONJ
ejpam-5978	237	92	its	its	PRON
ejpam-5978	237	93	corresponding	corresponding	ADJ
ejpam-5978	237	94	γin	γin	NOUN
ejpam-5978	237	95	-	-	PUNCT
ejpam-5978	237	96	sets	set	NOUN
ejpam-5978	237	97	.	.	PUNCT
ejpam-5978	238	1	table	table	NOUN
ejpam-5978	238	2	11	11	NUM
ejpam-5978	238	3	shows	show	VERB
ejpam-5978	238	4	that	that	SCONJ
ejpam-5978	238	5	there	there	PRON
ejpam-5978	238	6	are	be	VERB
ejpam-5978	238	7	6	6	NUM
ejpam-5978	238	8	2	2	NUM
ejpam-5978	238	9	-	-	PUNCT
ejpam-5978	238	10	convex	convex	NOUN
ejpam-5978	238	11	subsets	subset	NOUN
ejpam-5978	238	12	of	of	ADP
ejpam-5978	238	13	v	v	NOUN
ejpam-5978	238	14	(	(	PUNCT
ejpam-5978	238	15	k4	k4	PROPN
ejpam-5978	238	16	)	)	PUNCT
ejpam-5978	238	17	with	with	ADP
ejpam-5978	238	18	γin	γin	NOUN
ejpam-5978	238	19	-	-	PUNCT
ejpam-5978	238	20	sets	set	NOUN
ejpam-5978	238	21	cardinality	cardinality	NOUN
ejpam-5978	238	22	equal	equal	ADJ
ejpam-5978	238	23	to	to	ADP
ejpam-5978	238	24	1	1	NUM
ejpam-5978	238	25	.	.	PUNCT
ejpam-5978	239	1	this	this	PRON
ejpam-5978	239	2	contributes	contribute	VERB
ejpam-5978	239	3	to	to	ADP
ejpam-5978	239	4	the	the	DET
ejpam-5978	239	5	convex	convex	ADJ
ejpam-5978	239	6	independent	independent	ADJ
ejpam-5978	239	7	neighborhood	neighborhood	NOUN
ejpam-5978	239	8	polynomial	polynomial	NOUN
ejpam-5978	239	9	of	of	ADP
ejpam-5978	239	10	k4	k4	NOUN
ejpam-5978	239	11	as	as	ADP
ejpam-5978	239	12	6x2y	6x2y	NOUN
ejpam-5978	239	13	.	.	PUNCT
ejpam-5978	240	1	3	3	NUM
ejpam-5978	240	2	-	-	NUM
ejpam-5978	240	3	convex	convex	ADJ
ejpam-5978	240	4	γin	γin	NOUN
ejpam-5978	240	5	-	-	PUNCT
ejpam-5978	240	6	sets	set	NOUN
ejpam-5978	240	7	{	{	PUNCT
ejpam-5978	240	8	v1	v1	NOUN
ejpam-5978	240	9	,	,	PUNCT
ejpam-5978	240	10	v2	v2	PROPN
ejpam-5978	240	11	,	,	PUNCT
ejpam-5978	240	12	v3	v3	PROPN
ejpam-5978	240	13	}	}	PUNCT
ejpam-5978	240	14	{	{	PUNCT
ejpam-5978	240	15	v4	v4	NOUN
ejpam-5978	240	16	}	}	PUNCT
ejpam-5978	240	17	{	{	PUNCT
ejpam-5978	240	18	v2	v2	PROPN
ejpam-5978	240	19	,	,	PUNCT
ejpam-5978	240	20	v3	v3	PROPN
ejpam-5978	240	21	,	,	PUNCT
ejpam-5978	240	22	v4	v4	PROPN
ejpam-5978	240	23	}	}	PUNCT
ejpam-5978	240	24	{	{	PUNCT
ejpam-5978	240	25	v1	v1	NOUN
ejpam-5978	240	26	}	}	PUNCT
ejpam-5978	240	27	{	{	PUNCT
ejpam-5978	240	28	v1	v1	NOUN
ejpam-5978	240	29	,	,	PUNCT
ejpam-5978	240	30	v2	v2	PROPN
ejpam-5978	240	31	,	,	PUNCT
ejpam-5978	240	32	v4	v4	PROPN
ejpam-5978	240	33	}	}	PUNCT
ejpam-5978	240	34	{	{	PUNCT
ejpam-5978	240	35	v3	v3	PROPN
ejpam-5978	240	36	}	}	PUNCT
ejpam-5978	240	37	{	{	PUNCT
ejpam-5978	240	38	v1	v1	PROPN
ejpam-5978	240	39	,	,	PUNCT
ejpam-5978	240	40	v3	v3	PROPN
ejpam-5978	240	41	,	,	PUNCT
ejpam-5978	240	42	v4	v4	PROPN
ejpam-5978	240	43	}	}	PUNCT
ejpam-5978	240	44	{	{	PUNCT
ejpam-5978	240	45	v2	v2	NOUN
ejpam-5978	240	46	}	}	PUNCT
ejpam-5978	240	47	table	table	NOUN
ejpam-5978	240	48	12	12	NUM
ejpam-5978	240	49	:	:	PUNCT
ejpam-5978	240	50	3	3	NUM
ejpam-5978	240	51	-	-	PUNCT
ejpam-5978	240	52	convex	convex	ADJ
ejpam-5978	240	53	subsets	subset	NOUN
ejpam-5978	240	54	of	of	ADP
ejpam-5978	240	55	v	v	NOUN
ejpam-5978	240	56	(	(	PUNCT
ejpam-5978	240	57	k4	k4	NOUN
ejpam-5978	240	58	)	)	PUNCT
ejpam-5978	240	59	and	and	CCONJ
ejpam-5978	240	60	its	its	PRON
ejpam-5978	240	61	corresponding	corresponding	ADJ
ejpam-5978	240	62	γin	γin	NOUN
ejpam-5978	240	63	-	-	PUNCT
ejpam-5978	240	64	sets	set	NOUN
ejpam-5978	240	65	.	.	PUNCT
ejpam-5978	241	1	table	table	NOUN
ejpam-5978	241	2	12	12	NUM
ejpam-5978	241	3	shows	show	VERB
ejpam-5978	241	4	that	that	SCONJ
ejpam-5978	241	5	there	there	PRON
ejpam-5978	241	6	are	be	VERB
ejpam-5978	241	7	4	4	NUM
ejpam-5978	241	8	3	3	NUM
ejpam-5978	241	9	-	-	PUNCT
ejpam-5978	241	10	convex	convex	NOUN
ejpam-5978	241	11	subsets	subset	NOUN
ejpam-5978	241	12	of	of	ADP
ejpam-5978	241	13	v	v	NOUN
ejpam-5978	241	14	(	(	PUNCT
ejpam-5978	241	15	k4	k4	PROPN
ejpam-5978	241	16	)	)	PUNCT
ejpam-5978	241	17	with	with	ADP
ejpam-5978	241	18	γin	γin	NOUN
ejpam-5978	241	19	-	-	PUNCT
ejpam-5978	241	20	sets	set	NOUN
ejpam-5978	241	21	cardinality	cardinality	NOUN
ejpam-5978	241	22	equal	equal	ADJ
ejpam-5978	241	23	to	to	ADP
ejpam-5978	241	24	1	1	NUM
ejpam-5978	241	25	.	.	PUNCT
ejpam-5978	242	1	this	this	PRON
ejpam-5978	242	2	contributes	contribute	VERB
ejpam-5978	242	3	to	to	ADP
ejpam-5978	242	4	the	the	DET
ejpam-5978	242	5	convex	convex	ADJ
ejpam-5978	242	6	independent	independent	ADJ
ejpam-5978	242	7	neighborhood	neighborhood	NOUN
ejpam-5978	242	8	polynomial	polynomial	NOUN
ejpam-5978	242	9	of	of	ADP
ejpam-5978	242	10	k4	k4	NOUN
ejpam-5978	242	11	as	as	ADP
ejpam-5978	242	12	4x3y	4x3y	NUM
ejpam-5978	242	13	.	.	PUNCT
ejpam-5978	243	1	for	for	ADP
ejpam-5978	243	2	the	the	DET
ejpam-5978	243	3	4	4	NUM
ejpam-5978	243	4	-	-	PUNCT
ejpam-5978	243	5	convex	convex	ADJ
ejpam-5978	243	6	subsets	subset	NOUN
ejpam-5978	243	7	of	of	ADP
ejpam-5978	243	8	v	v	NOUN
ejpam-5978	243	9	(	(	PUNCT
ejpam-5978	243	10	k4	k4	PROPN
ejpam-5978	243	11	)	)	PUNCT
ejpam-5978	243	12	,	,	PUNCT
ejpam-5978	243	13	it	it	PRON
ejpam-5978	243	14	can	can	AUX
ejpam-5978	243	15	be	be	AUX
ejpam-5978	243	16	verified	verify	VERB
ejpam-5978	243	17	that	that	SCONJ
ejpam-5978	243	18	there	there	PRON
ejpam-5978	243	19	is	be	VERB
ejpam-5978	243	20	only	only	ADV
ejpam-5978	243	21	1	1	NUM
ejpam-5978	243	22	4	4	NUM
ejpam-5978	243	23	-	-	PUNCT
ejpam-5978	243	24	convex	convex	NOUN
ejpam-5978	243	25	subset	subset	NOUN
ejpam-5978	243	26	of	of	ADP
ejpam-5978	243	27	v	v	PROPN
ejpam-5978	243	28	(	(	PUNCT
ejpam-5978	243	29	k4	k4	PROPN
ejpam-5978	243	30	)	)	PUNCT
ejpam-5978	243	31	with	with	ADP
ejpam-5978	243	32	empty	empty	ADJ
ejpam-5978	243	33	(	(	PUNCT
ejpam-5978	243	34	zero	zero	NUM
ejpam-5978	243	35	cardinality	cardinality	NOUN
ejpam-5978	243	36	)	)	PUNCT
ejpam-5978	243	37	γin	γin	NOUN
ejpam-5978	243	38	-	-	PUNCT
ejpam-5978	243	39	set	set	NOUN
ejpam-5978	243	40	.	.	PUNCT
ejpam-5978	244	1	this	this	PRON
ejpam-5978	244	2	contributes	contribute	VERB
ejpam-5978	244	3	to	to	ADP
ejpam-5978	244	4	the	the	DET
ejpam-5978	244	5	convex	convex	ADJ
ejpam-5978	244	6	independent	independent	ADJ
ejpam-5978	244	7	neighborhood	neighborhood	NOUN
ejpam-5978	244	8	polynomial	polynomial	NOUN
ejpam-5978	244	9	of	of	ADP
ejpam-5978	244	10	k4	k4	NOUN
ejpam-5978	244	11	as	as	ADP
ejpam-5978	244	12	x4	x4	PROPN
ejpam-5978	244	13	.	.	PUNCT
ejpam-5978	245	1	e.j	e.j	PROPN
ejpam-5978	245	2	.	.	PROPN
ejpam-5978	245	3	aguilon	aguilon	PROPN
ejpam-5978	245	4	,	,	PUNCT
ejpam-5978	245	5	s.	s.	PROPN
ejpam-5978	245	6	dagondon	dagondon	PROPN
ejpam-5978	245	7	,	,	PUNCT
ejpam-5978	245	8	r.	r.	PROPN
ejpam-5978	245	9	artes	artes	PROPN
ejpam-5978	245	10	/	/	SYM
ejpam-5978	245	11	eur	eur	PROPN
ejpam-5978	245	12	.	.	PUNCT
ejpam-5978	246	1	j.	j.	PROPN
ejpam-5978	246	2	pure	pure	PROPN
ejpam-5978	246	3	appl	appl	PROPN
ejpam-5978	246	4	.	.	PROPN
ejpam-5978	246	5	math	math	PROPN
ejpam-5978	246	6	,	,	PUNCT
ejpam-5978	246	7	18	18	NUM
ejpam-5978	246	8	(	(	PUNCT
ejpam-5978	246	9	2	2	NUM
ejpam-5978	246	10	)	)	PUNCT
ejpam-5978	246	11	(	(	PUNCT
ejpam-5978	246	12	2025	2025	NUM
ejpam-5978	246	13	)	)	PUNCT
ejpam-5978	246	14	,	,	PUNCT
ejpam-5978	246	15	5978	5978	NUM
ejpam-5978	246	16	14	14	NUM
ejpam-5978	246	17	of	of	ADP
ejpam-5978	246	18	18	18	NUM
ejpam-5978	246	19	theorem	theorem	NOUN
ejpam-5978	246	20	5.4	5.4	NUM
ejpam-5978	246	21	.	.	PUNCT
ejpam-5978	247	1	let	let	VERB
ejpam-5978	247	2	k1,n	k1,n	PROPN
ejpam-5978	247	3	be	be	AUX
ejpam-5978	247	4	a	a	DET
ejpam-5978	247	5	star	star	NOUN
ejpam-5978	247	6	graph	graph	NOUN
ejpam-5978	247	7	of	of	ADP
ejpam-5978	247	8	order	order	NOUN
ejpam-5978	247	9	n	n	X
ejpam-5978	248	1	+	+	NOUN
ejpam-5978	248	2	1	1	X
ejpam-5978	248	3	.	.	PUNCT
ejpam-5978	249	1	then	then	ADV
ejpam-5978	249	2	,	,	PUNCT
ejpam-5978	249	3	the	the	DET
ejpam-5978	249	4	convex	convex	ADJ
ejpam-5978	249	5	independent	independent	ADJ
ejpam-5978	249	6	neighborhood	neighborhood	NOUN
ejpam-5978	249	7	polynomial	polynomial	NOUN
ejpam-5978	249	8	of	of	ADP
ejpam-5978	249	9	k1,n	k1,n	PROPN
ejpam-5978	249	10	is	be	AUX
ejpam-5978	249	11	γcin(k1,n;x	γcin(k1,n;x	PROPN
ejpam-5978	249	12	,	,	PUNCT
ejpam-5978	249	13	y	y	NOUN
ejpam-5978	249	14	)	)	PUNCT
ejpam-5978	249	15	=	=	PUNCT
ejpam-5978	250	1	xn+1	xn+1	PROPN
ejpam-5978	251	1	+	+	CCONJ
ejpam-5978	251	2	n∑	n∑	ADJ
ejpam-5978	251	3	i=2	i=2	PROPN
ejpam-5978	251	4	(	(	PUNCT
ejpam-5978	251	5	n	n	X
ejpam-5978	251	6	i−	i−	PROPN
ejpam-5978	251	7	1	1	NUM
ejpam-5978	251	8	)	)	PUNCT
ejpam-5978	251	9	xiy[n−(i−1	xiy[n−(i−1	PROPN
ejpam-5978	251	10	)	)	PUNCT
ejpam-5978	251	11	]	]	PUNCT
ejpam-5978	252	1	+	+	CCONJ
ejpam-5978	252	2	xyn	xyn	PROPN
ejpam-5978	252	3	+	+	CCONJ
ejpam-5978	252	4	nxy	nxy	ADJ
ejpam-5978	252	5	,	,	PUNCT
ejpam-5978	252	6	where	where	SCONJ
ejpam-5978	252	7	n	n	PRON
ejpam-5978	252	8	≥	≥	NOUN
ejpam-5978	252	9	3	3	NUM
ejpam-5978	252	10	,	,	PUNCT
ejpam-5978	252	11	(	(	PUNCT
ejpam-5978	252	12	n	n	X
ejpam-5978	252	13	i−1	i−1	PROPN
ejpam-5978	252	14	)	)	PUNCT
ejpam-5978	252	15	is	be	AUX
ejpam-5978	252	16	the	the	DET
ejpam-5978	252	17	number	number	NOUN
ejpam-5978	252	18	of	of	ADP
ejpam-5978	252	19	i	i	NOUN
ejpam-5978	252	20	-	-	PUNCT
ejpam-5978	252	21	convex	convex	ADJ
ejpam-5978	252	22	subsets	subset	NOUN
ejpam-5978	252	23	of	of	ADP
ejpam-5978	252	24	v	v	NOUN
ejpam-5978	252	25	(	(	PUNCT
ejpam-5978	252	26	k1,n	k1,n	PROPN
ejpam-5978	252	27	)	)	PUNCT
ejpam-5978	252	28	with	with	ADP
ejpam-5978	252	29	maximum	maximum	ADJ
ejpam-5978	252	30	independent	independent	ADJ
ejpam-5978	252	31	neighborhood	neighborhood	NOUN
ejpam-5978	252	32	system	system	NOUN
ejpam-5978	252	33	cardinality	cardinality	NOUN
ejpam-5978	252	34	equal	equal	ADJ
ejpam-5978	252	35	to	to	ADP
ejpam-5978	252	36	[	[	X
ejpam-5978	252	37	n−	n−	PROPN
ejpam-5978	252	38	(	(	PUNCT
ejpam-5978	252	39	i−1	i−1	PROPN
ejpam-5978	252	40	)	)	PUNCT
ejpam-5978	252	41	]	]	PUNCT
ejpam-5978	252	42	which	which	PRON
ejpam-5978	252	43	is	be	AUX
ejpam-5978	252	44	the	the	DET
ejpam-5978	252	45	combination	combination	NOUN
ejpam-5978	252	46	of	of	ADP
ejpam-5978	252	47	n	n	PRON
ejpam-5978	252	48	vertices	vertex	NOUN
ejpam-5978	252	49	taken	take	VERB
ejpam-5978	252	50	(	(	PUNCT
ejpam-5978	252	51	i−	i−	PROPN
ejpam-5978	252	52	1	1	NUM
ejpam-5978	252	53	)	)	PUNCT
ejpam-5978	252	54	at	at	ADP
ejpam-5978	252	55	a	a	DET
ejpam-5978	252	56	time	time	NOUN
ejpam-5978	252	57	.	.	PUNCT
ejpam-5978	253	1	proof	proof	NOUN
ejpam-5978	253	2	.	.	PUNCT
ejpam-5978	254	1	let	let	VERB
ejpam-5978	254	2	v	v	X
ejpam-5978	254	3	(	(	PUNCT
ejpam-5978	254	4	k1,n	k1,n	PROPN
ejpam-5978	254	5	)	)	PUNCT
ejpam-5978	254	6	=	=	PRON
ejpam-5978	254	7	{	{	PUNCT
ejpam-5978	254	8	u1	u1	NOUN
ejpam-5978	254	9	,	,	PUNCT
ejpam-5978	254	10	v1	v1	NOUN
ejpam-5978	254	11	,	,	PUNCT
ejpam-5978	254	12	v2	v2	PROPN
ejpam-5978	254	13	,	,	PUNCT
ejpam-5978	254	14	...	...	PUNCT
ejpam-5978	254	15	,	,	PUNCT
ejpam-5978	254	16	vn	vn	PART
ejpam-5978	254	17	}	}	PUNCT
ejpam-5978	254	18	be	be	AUX
ejpam-5978	254	19	a	a	DET
ejpam-5978	254	20	vertex	vertex	NOUN
ejpam-5978	254	21	set	set	NOUN
ejpam-5978	254	22	of	of	ADP
ejpam-5978	254	23	star	star	NOUN
ejpam-5978	254	24	graph	graph	NOUN
ejpam-5978	254	25	of	of	ADP
ejpam-5978	254	26	order	order	NOUN
ejpam-5978	254	27	k1,n	k1,n	PROPN
ejpam-5978	254	28	and	and	CCONJ
ejpam-5978	254	29	let	let	VERB
ejpam-5978	254	30	u1	u1	NOUN
ejpam-5978	254	31	be	be	AUX
ejpam-5978	254	32	the	the	DET
ejpam-5978	254	33	center	center	ADJ
ejpam-5978	254	34	vertex	vertex	NOUN
ejpam-5978	254	35	.	.	PUNCT
ejpam-5978	255	1	first	first	ADV
ejpam-5978	255	2	,	,	PUNCT
ejpam-5978	255	3	note	note	VERB
ejpam-5978	255	4	that	that	SCONJ
ejpam-5978	255	5	every	every	DET
ejpam-5978	255	6	n	n	NOUN
ejpam-5978	255	7	vertices	vertex	NOUN
ejpam-5978	255	8	are	be	AUX
ejpam-5978	255	9	all	all	ADV
ejpam-5978	255	10	adjacent	adjacent	ADJ
ejpam-5978	255	11	only	only	ADV
ejpam-5978	255	12	to	to	ADP
ejpam-5978	255	13	the	the	DET
ejpam-5978	255	14	center	center	ADJ
ejpam-5978	255	15	vertex	vertex	NOUN
ejpam-5978	255	16	,	,	PUNCT
ejpam-5978	255	17	namely	namely	ADV
ejpam-5978	255	18	,	,	PUNCT
ejpam-5978	255	19	u1	u1	NOUN
ejpam-5978	255	20	.	.	PUNCT
ejpam-5978	256	1	this	this	PRON
ejpam-5978	256	2	means	mean	VERB
ejpam-5978	256	3	that	that	SCONJ
ejpam-5978	256	4	there	there	PRON
ejpam-5978	256	5	are	be	VERB
ejpam-5978	256	6	exactly	exactly	ADV
ejpam-5978	256	7	n	n	DET
ejpam-5978	256	8	1	1	NUM
ejpam-5978	256	9	-	-	PUNCT
ejpam-5978	256	10	convex	convex	NOUN
ejpam-5978	256	11	subset	subset	NOUN
ejpam-5978	256	12	of	of	ADP
ejpam-5978	256	13	v	v	PROPN
ejpam-5978	256	14	(	(	PUNCT
ejpam-5978	256	15	k1,n	k1,n	PROPN
ejpam-5978	256	16	)	)	PUNCT
ejpam-5978	256	17	with	with	ADP
ejpam-5978	256	18	γin	γin	ADV
ejpam-5978	256	19	-	-	PUNCT
ejpam-5978	256	20	set	set	VERB
ejpam-5978	256	21	contain	contain	VERB
ejpam-5978	256	22	only	only	ADV
ejpam-5978	256	23	one	one	NUM
ejpam-5978	256	24	element	element	NOUN
ejpam-5978	256	25	,	,	PUNCT
ejpam-5978	256	26	namely	namely	ADV
ejpam-5978	256	27	u1	u1	NOUN
ejpam-5978	256	28	.	.	PUNCT
ejpam-5978	257	1	this	this	PRON
ejpam-5978	257	2	contribute	contribute	VERB
ejpam-5978	257	3	to	to	ADP
ejpam-5978	257	4	the	the	DET
ejpam-5978	257	5	convex	convex	ADJ
ejpam-5978	257	6	independent	independent	ADJ
ejpam-5978	257	7	neighborhood	neighborhood	NOUN
ejpam-5978	257	8	polynomial	polynomial	NOUN
ejpam-5978	257	9	of	of	ADP
ejpam-5978	257	10	k1,n	k1,n	PROPN
ejpam-5978	257	11	as	as	ADP
ejpam-5978	257	12	nxy	nxy	PROPN
ejpam-5978	257	13	.	.	PUNCT
ejpam-5978	258	1	also	also	ADV
ejpam-5978	258	2	,	,	PUNCT
ejpam-5978	258	3	there	there	PRON
ejpam-5978	258	4	is	be	VERB
ejpam-5978	258	5	only	only	ADV
ejpam-5978	258	6	1	1	NUM
ejpam-5978	258	7	1	1	NUM
ejpam-5978	258	8	-	-	PUNCT
ejpam-5978	258	9	convex	convex	NOUN
ejpam-5978	258	10	subset	subset	NOUN
ejpam-5978	258	11	of	of	ADP
ejpam-5978	258	12	v	v	PROPN
ejpam-5978	258	13	(	(	PUNCT
ejpam-5978	258	14	k1,n	k1,n	PROPN
ejpam-5978	258	15	)	)	PUNCT
ejpam-5978	258	16	with	with	ADP
ejpam-5978	258	17	γin	γin	ADV
ejpam-5978	258	18	-	-	PUNCT
ejpam-5978	258	19	set	set	VERB
ejpam-5978	258	20	contain	contain	NOUN
ejpam-5978	258	21	n	n	DET
ejpam-5978	258	22	elements	element	NOUN
ejpam-5978	258	23	,	,	PUNCT
ejpam-5978	258	24	namely	namely	ADV
ejpam-5978	258	25	u1	u1	NOUN
ejpam-5978	258	26	,	,	PUNCT
ejpam-5978	258	27	the	the	DET
ejpam-5978	258	28	center	center	NOUN
ejpam-5978	258	29	vertex	vertex	NOUN
ejpam-5978	258	30	.	.	PUNCT
ejpam-5978	259	1	this	this	PRON
ejpam-5978	259	2	contribute	contribute	VERB
ejpam-5978	259	3	to	to	ADP
ejpam-5978	259	4	the	the	DET
ejpam-5978	259	5	polynomial	polynomial	NOUN
ejpam-5978	259	6	as	as	ADP
ejpam-5978	259	7	xyn	xyn	PROPN
ejpam-5978	259	8	.	.	PUNCT
ejpam-5978	260	1	now	now	ADV
ejpam-5978	260	2	,	,	PUNCT
ejpam-5978	260	3	for	for	ADP
ejpam-5978	260	4	(	(	PUNCT
ejpam-5978	260	5	n	n	X
ejpam-5978	260	6	+	+	CCONJ
ejpam-5978	260	7	1)-convex	1)-convex	NUM
ejpam-5978	260	8	subset	subset	NOUN
ejpam-5978	260	9	of	of	ADP
ejpam-5978	260	10	v	v	PROPN
ejpam-5978	260	11	(	(	PUNCT
ejpam-5978	260	12	k1,n	k1,n	PROPN
ejpam-5978	260	13	)	)	PUNCT
ejpam-5978	260	14	,	,	PUNCT
ejpam-5978	260	15	there	there	PRON
ejpam-5978	260	16	is	be	VERB
ejpam-5978	260	17	exactly	exactly	ADV
ejpam-5978	260	18	one	one	NUM
ejpam-5978	260	19	(	(	PUNCT
ejpam-5978	260	20	n	n	X
ejpam-5978	260	21	+	+	CCONJ
ejpam-5978	260	22	1)-convex	1)-convex	NUM
ejpam-5978	260	23	with	with	ADP
ejpam-5978	260	24	empty	empty	ADJ
ejpam-5978	260	25	(	(	PUNCT
ejpam-5978	260	26	zero	zero	NUM
ejpam-5978	260	27	cardinality	cardinality	NOUN
ejpam-5978	260	28	)	)	PUNCT
ejpam-5978	260	29	γin	γin	ADV
ejpam-5978	260	30	-	-	PUNCT
ejpam-5978	260	31	set	set	NOUN
ejpam-5978	260	32	which	which	PRON
ejpam-5978	260	33	contributes	contribute	VERB
ejpam-5978	260	34	as	as	ADP
ejpam-5978	260	35	xn+1	xn+1	NUM
ejpam-5978	260	36	to	to	ADP
ejpam-5978	260	37	the	the	DET
ejpam-5978	260	38	polynomial	polynomial	NOUN
ejpam-5978	260	39	.	.	PUNCT
ejpam-5978	261	1	now	now	ADV
ejpam-5978	261	2	,	,	PUNCT
ejpam-5978	261	3	for	for	ADP
ejpam-5978	261	4	i	i	NOUN
ejpam-5978	261	5	-	-	PUNCT
ejpam-5978	261	6	convex	convex	ADJ
ejpam-5978	261	7	subsets	subset	NOUN
ejpam-5978	261	8	of	of	ADP
ejpam-5978	261	9	v	v	NOUN
ejpam-5978	261	10	(	(	PUNCT
ejpam-5978	261	11	k1,n	k1,n	PROPN
ejpam-5978	261	12	)	)	PUNCT
ejpam-5978	261	13	where	where	SCONJ
ejpam-5978	261	14	i	i	PRON
ejpam-5978	261	15	=	=	NOUN
ejpam-5978	261	16	2	2	NUM
ejpam-5978	261	17	,	,	PUNCT
ejpam-5978	261	18	...	...	PUNCT
ejpam-5978	261	19	,	,	PUNCT
ejpam-5978	261	20	n	n	CCONJ
ejpam-5978	261	21	,	,	PUNCT
ejpam-5978	261	22	there	there	PRON
ejpam-5978	261	23	are	be	VERB
ejpam-5978	261	24	(	(	PUNCT
ejpam-5978	261	25	n	n	X
ejpam-5978	261	26	i−1	i−1	PROPN
ejpam-5978	261	27	)	)	PUNCT
ejpam-5978	262	1	i	i	PRON
ejpam-5978	262	2	-	-	PUNCT
ejpam-5978	262	3	convex	convex	ADJ
ejpam-5978	262	4	subsets	subset	NOUN
ejpam-5978	262	5	of	of	ADP
ejpam-5978	262	6	v	v	NOUN
ejpam-5978	262	7	(	(	PUNCT
ejpam-5978	262	8	k1,n	k1,n	PROPN
ejpam-5978	262	9	)	)	PUNCT
ejpam-5978	262	10	with	with	ADP
ejpam-5978	262	11	γin	γin	NOUN
ejpam-5978	262	12	-	-	PUNCT
ejpam-5978	262	13	sets	set	NOUN
ejpam-5978	262	14	contain	contain	VERB
ejpam-5978	262	15	[	[	X
ejpam-5978	262	16	n	n	X
ejpam-5978	262	17	−	−	PROPN
ejpam-5978	263	1	(	(	PUNCT
ejpam-5978	263	2	i	i	PRON
ejpam-5978	263	3	−	−	PROPN
ejpam-5978	263	4	1	1	NUM
ejpam-5978	263	5	)	)	PUNCT
ejpam-5978	263	6	]	]	PUNCT
ejpam-5978	263	7	elements	element	NOUN
ejpam-5978	263	8	.	.	PUNCT
ejpam-5978	264	1	thus	thus	ADV
ejpam-5978	264	2	,	,	PUNCT
ejpam-5978	264	3	by	by	ADP
ejpam-5978	264	4	combining	combine	VERB
ejpam-5978	264	5	all	all	DET
ejpam-5978	264	6	i	i	PRON
ejpam-5978	264	7	-	-	NOUN
ejpam-5978	264	8	convex	convex	ADJ
ejpam-5978	264	9	with	with	ADP
ejpam-5978	264	10	γin	γin	NOUN
ejpam-5978	264	11	-	-	PUNCT
ejpam-5978	264	12	sets	set	NOUN
ejpam-5978	264	13	cardinality	cardinality	NOUN
ejpam-5978	264	14	equal	equal	ADJ
ejpam-5978	264	15	to	to	ADP
ejpam-5978	264	16	[	[	X
ejpam-5978	264	17	n−	n−	PROPN
ejpam-5978	264	18	(	(	PUNCT
ejpam-5978	264	19	i−	i−	PROPN
ejpam-5978	264	20	1	1	NUM
ejpam-5978	264	21	)	)	PUNCT
ejpam-5978	264	22	]	]	PUNCT
ejpam-5978	264	23	we	we	PRON
ejpam-5978	264	24	have	have	VERB
ejpam-5978	264	25	(	(	PUNCT
ejpam-5978	264	26	n	n	ADV
ejpam-5978	264	27	1	1	NUM
ejpam-5978	264	28	)	)	PUNCT
ejpam-5978	264	29	x2yn−1	x2yn−1	PROPN
ejpam-5978	265	1	+	+	CCONJ
ejpam-5978	265	2	(	(	PUNCT
ejpam-5978	265	3	n	n	PRON
ejpam-5978	265	4	2	2	NUM
ejpam-5978	265	5	)	)	PUNCT
ejpam-5978	265	6	x3yn−2	x3yn−2	PROPN
ejpam-5978	265	7	+	+	CCONJ
ejpam-5978	265	8	·	·	PUNCT
ejpam-5978	265	9	·	·	PUNCT
ejpam-5978	265	10	·	·	PUNCT
ejpam-5978	266	1	+	+	CCONJ
ejpam-5978	266	2	(	(	PUNCT
ejpam-5978	266	3	n	n	NUM
ejpam-5978	266	4	n−	n−	NOUN
ejpam-5978	266	5	1	1	NUM
ejpam-5978	266	6	)	)	PUNCT
ejpam-5978	266	7	xny	xny	X
ejpam-5978	266	8	=	=	PUNCT
ejpam-5978	267	1	n∑	n∑	X
ejpam-5978	267	2	i=2	i=2	PROPN
ejpam-5978	267	3	(	(	PUNCT
ejpam-5978	267	4	n	n	X
ejpam-5978	267	5	i−	i−	PROPN
ejpam-5978	267	6	1	1	NUM
ejpam-5978	267	7	)	)	PUNCT
ejpam-5978	267	8	xiyn−(i−1	xiyn−(i−1	PROPN
ejpam-5978	267	9	)	)	PUNCT
ejpam-5978	267	10	therefore	therefore	ADV
ejpam-5978	267	11	,	,	PUNCT
ejpam-5978	267	12	the	the	DET
ejpam-5978	267	13	convex	convex	ADJ
ejpam-5978	267	14	independent	independent	ADJ
ejpam-5978	267	15	neighborhood	neighborhood	NOUN
ejpam-5978	267	16	polynomial	polynomial	NOUN
ejpam-5978	267	17	of	of	ADP
ejpam-5978	267	18	k1,n	k1,n	PROPN
ejpam-5978	267	19	is	be	AUX
ejpam-5978	267	20	γcin(k1,n;x	γcin(k1,n;x	PROPN
ejpam-5978	267	21	,	,	PUNCT
ejpam-5978	267	22	y	y	NOUN
ejpam-5978	267	23	)	)	PUNCT
ejpam-5978	267	24	=	=	PUNCT
ejpam-5978	268	1	xn+1	xn+1	PROPN
ejpam-5978	269	1	+	+	CCONJ
ejpam-5978	269	2	n∑	n∑	ADJ
ejpam-5978	269	3	i=2	i=2	PROPN
ejpam-5978	269	4	(	(	PUNCT
ejpam-5978	269	5	n	n	X
ejpam-5978	269	6	i−	i−	PROPN
ejpam-5978	269	7	1	1	NUM
ejpam-5978	269	8	)	)	PUNCT
ejpam-5978	269	9	xiy[n−(i−1	xiy[n−(i−1	PROPN
ejpam-5978	269	10	)	)	PUNCT
ejpam-5978	269	11	]	]	PUNCT
ejpam-5978	270	1	+	+	CCONJ
ejpam-5978	270	2	xyn	xyn	X
ejpam-5978	270	3	+	+	CCONJ
ejpam-5978	270	4	nxy	nxy	ADJ
ejpam-5978	270	5	.	.	PUNCT
ejpam-5978	271	1	■	■	PUNCT
ejpam-5978	271	2	let	let	VERB
ejpam-5978	271	3	v	v	X
ejpam-5978	271	4	(	(	PUNCT
ejpam-5978	271	5	k1,n	k1,n	PROPN
ejpam-5978	271	6	)	)	PUNCT
ejpam-5978	271	7	=	=	PRON
ejpam-5978	271	8	{	{	PUNCT
ejpam-5978	271	9	u1	u1	NOUN
ejpam-5978	271	10	,	,	PUNCT
ejpam-5978	271	11	v1	v1	NOUN
ejpam-5978	271	12	,	,	PUNCT
ejpam-5978	271	13	v2	v2	PROPN
ejpam-5978	271	14	,	,	PUNCT
ejpam-5978	271	15	...	...	PUNCT
ejpam-5978	271	16	,	,	PUNCT
ejpam-5978	271	17	vn	vn	PART
ejpam-5978	271	18	}	}	PUNCT
ejpam-5978	271	19	be	be	AUX
ejpam-5978	271	20	a	a	DET
ejpam-5978	271	21	vertex	vertex	NOUN
ejpam-5978	271	22	-	-	PUNCT
ejpam-5978	271	23	set	set	NOUN
ejpam-5978	271	24	of	of	ADP
ejpam-5978	271	25	star	star	NOUN
ejpam-5978	271	26	graph	graph	NOUN
ejpam-5978	271	27	of	of	ADP
ejpam-5978	271	28	order	order	NOUN
ejpam-5978	271	29	k1,n	k1,n	PROPN
ejpam-5978	271	30	and	and	CCONJ
ejpam-5978	271	31	let	let	VERB
ejpam-5978	271	32	u1	u1	NOUN
ejpam-5978	271	33	be	be	AUX
ejpam-5978	271	34	the	the	DET
ejpam-5978	271	35	center	center	ADJ
ejpam-5978	271	36	vertex	vertex	NOUN
ejpam-5978	271	37	.	.	PUNCT
ejpam-5978	272	1	note	note	VERB
ejpam-5978	272	2	that	that	SCONJ
ejpam-5978	272	3	every	every	DET
ejpam-5978	272	4	n	n	NOUN
ejpam-5978	272	5	vertices	vertex	NOUN
ejpam-5978	272	6	are	be	AUX
ejpam-5978	272	7	all	all	ADV
ejpam-5978	272	8	adjacent	adjacent	ADJ
ejpam-5978	272	9	only	only	ADV
ejpam-5978	272	10	to	to	ADP
ejpam-5978	272	11	the	the	DET
ejpam-5978	272	12	center	center	ADJ
ejpam-5978	272	13	vertex	vertex	NOUN
ejpam-5978	272	14	,	,	PUNCT
ejpam-5978	272	15	namely	namely	ADV
ejpam-5978	272	16	,	,	PUNCT
ejpam-5978	272	17	u1	u1	NOUN
ejpam-5978	272	18	.	.	PUNCT
ejpam-5978	273	1	this	this	PRON
ejpam-5978	273	2	means	mean	VERB
ejpam-5978	273	3	that	that	SCONJ
ejpam-5978	273	4	the	the	DET
ejpam-5978	273	5	n	n	ADJ
ejpam-5978	273	6	1	1	NUM
ejpam-5978	273	7	-	-	PUNCT
ejpam-5978	273	8	convex	convex	NOUN
ejpam-5978	273	9	subsets	subset	NOUN
ejpam-5978	273	10	of	of	ADP
ejpam-5978	273	11	v	v	NOUN
ejpam-5978	273	12	(	(	PUNCT
ejpam-5978	273	13	k1,n	k1,n	PROPN
ejpam-5978	273	14	)	)	PUNCT
ejpam-5978	273	15	with	with	ADP
ejpam-5978	273	16	γin	γin	NOUN
ejpam-5978	273	17	-	-	PUNCT
ejpam-5978	273	18	sets	set	NOUN
ejpam-5978	273	19	cardinality	cardinality	NOUN
ejpam-5978	273	20	equal	equal	ADJ
ejpam-5978	273	21	to	to	ADP
ejpam-5978	273	22	one	one	NUM
ejpam-5978	273	23	contribute	contribute	NOUN
ejpam-5978	273	24	as	as	ADP
ejpam-5978	273	25	the	the	DET
ejpam-5978	273	26	nxy	nxy	ADJ
ejpam-5978	273	27	term	term	NOUN
ejpam-5978	273	28	in	in	ADP
ejpam-5978	273	29	the	the	DET
ejpam-5978	273	30	polynomial	polynomial	NOUN
ejpam-5978	273	31	.	.	PUNCT
ejpam-5978	274	1	moreover	moreover	ADV
ejpam-5978	274	2	,	,	PUNCT
ejpam-5978	274	3	there	there	PRON
ejpam-5978	274	4	is	be	VERB
ejpam-5978	274	5	only	only	ADV
ejpam-5978	274	6	1	1	NUM
ejpam-5978	274	7	1	1	NUM
ejpam-5978	274	8	-	-	PUNCT
ejpam-5978	274	9	convex	convex	NOUN
ejpam-5978	274	10	subset	subset	NOUN
ejpam-5978	274	11	of	of	ADP
ejpam-5978	274	12	v	v	PROPN
ejpam-5978	274	13	(	(	PUNCT
ejpam-5978	274	14	k1,n	k1,n	PROPN
ejpam-5978	274	15	)	)	PUNCT
ejpam-5978	274	16	with	with	ADP
ejpam-5978	274	17	γin	γin	NOUN
ejpam-5978	274	18	-	-	PUNCT
ejpam-5978	274	19	sets	set	NOUN
ejpam-5978	274	20	cardinality	cardinality	NOUN
ejpam-5978	274	21	equal	equal	ADJ
ejpam-5978	274	22	to	to	ADP
ejpam-5978	274	23	n	n	CCONJ
ejpam-5978	274	24	,	,	PUNCT
ejpam-5978	274	25	i.e.	i.e.	X
ejpam-5978	274	26	,	,	PUNCT
ejpam-5978	274	27	u1	u1	NOUN
ejpam-5978	274	28	which	which	PRON
ejpam-5978	274	29	contribute	contribute	VERB
ejpam-5978	274	30	to	to	ADP
ejpam-5978	274	31	the	the	DET
ejpam-5978	274	32	polynomial	polynomial	NOUN
ejpam-5978	274	33	as	as	ADP
ejpam-5978	274	34	xyn	xyn	PROPN
ejpam-5978	274	35	.	.	PUNCT
ejpam-5978	275	1	now	now	ADV
ejpam-5978	275	2	,	,	PUNCT
ejpam-5978	275	3	the	the	DET
ejpam-5978	275	4	vertices	vertex	NOUN
ejpam-5978	275	5	{	{	PUNCT
ejpam-5978	275	6	u1	u1	NOUN
ejpam-5978	275	7	,	,	PUNCT
ejpam-5978	275	8	v1	v1	NOUN
ejpam-5978	275	9	,	,	PUNCT
ejpam-5978	275	10	...	...	PUNCT
ejpam-5978	275	11	,	,	PUNCT
ejpam-5978	275	12	vn	vn	PROPN
ejpam-5978	275	13	}	}	PUNCT
ejpam-5978	275	14	is	be	AUX
ejpam-5978	275	15	the	the	DET
ejpam-5978	275	16	(	(	PUNCT
ejpam-5978	275	17	n+1)-convex	n+1)-convex	PROPN
ejpam-5978	275	18	subset	subset	NOUN
ejpam-5978	275	19	of	of	ADP
ejpam-5978	275	20	v	v	PROPN
ejpam-5978	275	21	(	(	PUNCT
ejpam-5978	275	22	k1,n	k1,n	PROPN
ejpam-5978	275	23	)	)	PUNCT
ejpam-5978	275	24	which	which	PRON
ejpam-5978	275	25	contributes	contribute	VERB
ejpam-5978	275	26	to	to	ADP
ejpam-5978	275	27	the	the	DET
ejpam-5978	275	28	leading	lead	VERB
ejpam-5978	275	29	term	term	NOUN
ejpam-5978	275	30	of	of	ADP
ejpam-5978	275	31	the	the	DET
ejpam-5978	275	32	convex	convex	ADJ
ejpam-5978	275	33	independent	independent	ADJ
ejpam-5978	275	34	neighborhood	neighborhood	NOUN
ejpam-5978	275	35	polynomial	polynomial	NOUN
ejpam-5978	275	36	of	of	ADP
ejpam-5978	275	37	k1,n	k1,n	PROPN
ejpam-5978	275	38	,	,	PUNCT
ejpam-5978	275	39	i.e.	i.e.	X
ejpam-5978	275	40	,	,	PUNCT
ejpam-5978	275	41	xn+1	xn+1	X
ejpam-5978	275	42	.	.	PUNCT
ejpam-5978	276	1	now	now	ADV
ejpam-5978	276	2	,	,	PUNCT
ejpam-5978	276	3	for	for	ADP
ejpam-5978	276	4	i	i	PROPN
ejpam-5978	276	5	=	=	NOUN
ejpam-5978	276	6	2	2	NUM
ejpam-5978	276	7	,	,	PUNCT
ejpam-5978	276	8	...	...	PUNCT
ejpam-5978	276	9	,	,	PUNCT
ejpam-5978	276	10	n	n	CCONJ
ejpam-5978	276	11	,	,	PUNCT
ejpam-5978	276	12	the	the	DET
ejpam-5978	276	13	i	i	NOUN
ejpam-5978	276	14	-	-	PUNCT
ejpam-5978	276	15	convex	convex	ADJ
ejpam-5978	276	16	subsets	subset	NOUN
ejpam-5978	276	17	of	of	ADP
ejpam-5978	276	18	v	v	NOUN
ejpam-5978	276	19	(	(	PUNCT
ejpam-5978	276	20	k1,n	k1,n	PROPN
ejpam-5978	276	21	)	)	PUNCT
ejpam-5978	276	22	contains	contain	VERB
ejpam-5978	276	23	γin	γin	NOUN
ejpam-5978	276	24	-	-	PUNCT
ejpam-5978	276	25	sets	set	NOUN
ejpam-5978	276	26	[	[	X
ejpam-5978	276	27	n−	n−	NOUN
ejpam-5978	276	28	(	(	PUNCT
ejpam-5978	276	29	i−	i−	PROPN
ejpam-5978	276	30	1	1	NUM
ejpam-5978	276	31	)	)	PUNCT
ejpam-5978	276	32	]	]	PUNCT
ejpam-5978	276	33	elements	element	NOUN
ejpam-5978	276	34	.	.	PUNCT
ejpam-5978	277	1	this	this	PRON
ejpam-5978	277	2	means	mean	VERB
ejpam-5978	277	3	that	that	SCONJ
ejpam-5978	277	4	for	for	ADP
ejpam-5978	277	5	n	n	PRON
ejpam-5978	277	6	≥	≥	NOUN
ejpam-5978	277	7	3	3	NUM
ejpam-5978	277	8	,	,	PUNCT
ejpam-5978	277	9	there	there	PRON
ejpam-5978	277	10	are	be	VERB
ejpam-5978	277	11	1	1	NUM
ejpam-5978	277	12	+	+	CCONJ
ejpam-5978	277	13	1	1	NUM
ejpam-5978	277	14	+	+	NUM
ejpam-5978	277	15	1	1	NUM
ejpam-5978	277	16	+	+	CCONJ
ejpam-5978	277	17	(	(	PUNCT
ejpam-5978	277	18	n−	n−	NOUN
ejpam-5978	277	19	1	1	NUM
ejpam-5978	277	20	)	)	PUNCT
ejpam-5978	277	21	=	=	SYM
ejpam-5978	277	22	n+	n+	ADP
ejpam-5978	277	23	2	2	NUM
ejpam-5978	277	24	terms	term	NOUN
ejpam-5978	277	25	for	for	ADP
ejpam-5978	277	26	the	the	DET
ejpam-5978	277	27	convex	convex	ADJ
ejpam-5978	277	28	independent	independent	ADJ
ejpam-5978	277	29	neighborhood	neighborhood	NOUN
ejpam-5978	277	30	polynomial	polynomial	NOUN
ejpam-5978	277	31	of	of	ADP
ejpam-5978	277	32	k1,n	k1,n	PROPN
ejpam-5978	277	33	.	.	PUNCT
ejpam-5978	278	1	thus	thus	ADV
ejpam-5978	278	2	,	,	PUNCT
ejpam-5978	278	3	we	we	PRON
ejpam-5978	278	4	have	have	VERB
ejpam-5978	278	5	the	the	DET
ejpam-5978	278	6	following	follow	VERB
ejpam-5978	278	7	corollary	corollary	PROPN
ejpam-5978	278	8	e.j	e.j	PROPN
ejpam-5978	278	9	.	.	PROPN
ejpam-5978	278	10	aguilon	aguilon	PROPN
ejpam-5978	278	11	,	,	PUNCT
ejpam-5978	278	12	s.	s.	PROPN
ejpam-5978	278	13	dagondon	dagondon	PROPN
ejpam-5978	278	14	,	,	PUNCT
ejpam-5978	278	15	r.	r.	PROPN
ejpam-5978	278	16	artes	artes	PROPN
ejpam-5978	278	17	/	/	SYM
ejpam-5978	278	18	eur	eur	PROPN
ejpam-5978	278	19	.	.	PUNCT
ejpam-5978	279	1	j.	j.	PROPN
ejpam-5978	279	2	pure	pure	PROPN
ejpam-5978	279	3	appl	appl	PROPN
ejpam-5978	279	4	.	.	PROPN
ejpam-5978	279	5	math	math	PROPN
ejpam-5978	279	6	,	,	PUNCT
ejpam-5978	279	7	18	18	NUM
ejpam-5978	279	8	(	(	PUNCT
ejpam-5978	279	9	2	2	NUM
ejpam-5978	279	10	)	)	PUNCT
ejpam-5978	279	11	(	(	PUNCT
ejpam-5978	279	12	2025	2025	NUM
ejpam-5978	279	13	)	)	PUNCT
ejpam-5978	279	14	,	,	PUNCT
ejpam-5978	279	15	5978	5978	NUM
ejpam-5978	279	16	15	15	NUM
ejpam-5978	279	17	of	of	ADP
ejpam-5978	279	18	18	18	NUM
ejpam-5978	279	19	corollary	corollary	ADJ
ejpam-5978	279	20	5.5	5.5	NUM
ejpam-5978	279	21	.	.	PUNCT
ejpam-5978	280	1	for	for	ADP
ejpam-5978	280	2	n	n	X
ejpam-5978	280	3	≥	≥	NUM
ejpam-5978	280	4	3	3	NUM
ejpam-5978	280	5	,	,	PUNCT
ejpam-5978	280	6	the	the	DET
ejpam-5978	280	7	number	number	NOUN
ejpam-5978	280	8	of	of	ADP
ejpam-5978	280	9	terms	term	NOUN
ejpam-5978	280	10	of	of	ADP
ejpam-5978	280	11	the	the	DET
ejpam-5978	280	12	convex	convex	ADJ
ejpam-5978	280	13	independent	independent	ADJ
ejpam-5978	280	14	neighborhood	neighborhood	NOUN
ejpam-5978	280	15	polynomial	polynomial	NOUN
ejpam-5978	280	16	of	of	ADP
ejpam-5978	280	17	k1,n	k1,n	PROPN
ejpam-5978	280	18	is	be	AUX
ejpam-5978	280	19	(	(	PUNCT
ejpam-5978	280	20	n+	n+	NOUN
ejpam-5978	280	21	2	2	NUM
ejpam-5978	280	22	)	)	PUNCT
ejpam-5978	280	23	.	.	PUNCT
ejpam-5978	281	1	illustration	illustration	NOUN
ejpam-5978	281	2	5.6	5.6	NUM
ejpam-5978	281	3	.	.	PUNCT
ejpam-5978	282	1	consider	consider	VERB
ejpam-5978	282	2	k1,4	k1,4	ADV
ejpam-5978	282	3	be	be	AUX
ejpam-5978	282	4	a	a	DET
ejpam-5978	282	5	star	star	NOUN
ejpam-5978	282	6	graph	graph	NOUN
ejpam-5978	282	7	of	of	ADP
ejpam-5978	282	8	order	order	NOUN
ejpam-5978	282	9	5	5	NUM
ejpam-5978	282	10	.	.	PUNCT
ejpam-5978	282	11	u1	u1	PROPN
ejpam-5978	282	12	v1	v1	PROPN
ejpam-5978	282	13	v2	v2	PROPN
ejpam-5978	282	14	v4	v4	PROPN
ejpam-5978	282	15	v3	v3	PROPN
ejpam-5978	282	16	figure	figure	NOUN
ejpam-5978	282	17	5	5	NUM
ejpam-5978	282	18	:	:	PUNCT
ejpam-5978	282	19	a	a	DET
ejpam-5978	282	20	star	star	NOUN
ejpam-5978	282	21	graph	graph	NOUN
ejpam-5978	282	22	k1,4	k1,4	ADV
ejpam-5978	282	23	of	of	ADP
ejpam-5978	282	24	order	order	NOUN
ejpam-5978	282	25	5	5	NUM
ejpam-5978	282	26	then	then	ADV
ejpam-5978	282	27	,	,	PUNCT
ejpam-5978	282	28	by	by	ADP
ejpam-5978	282	29	using	use	VERB
ejpam-5978	282	30	theorem	theorem	ADJ
ejpam-5978	282	31	5.4	5.4	NUM
ejpam-5978	282	32	,	,	PUNCT
ejpam-5978	282	33	γcin(k1,4;x	γcin(k1,4;x	PROPN
ejpam-5978	282	34	,	,	PUNCT
ejpam-5978	282	35	y	y	NOUN
ejpam-5978	282	36	)	)	PUNCT
ejpam-5978	282	37	=	=	PUNCT
ejpam-5978	283	1	x4	x4	PROPN
ejpam-5978	283	2	+	+	PROPN
ejpam-5978	283	3	1	1	NUM
ejpam-5978	283	4	+	+	SYM
ejpam-5978	283	5	4∑	4∑	NOUN
ejpam-5978	283	6	i=2	i=2	NOUN
ejpam-5978	283	7	(	(	PUNCT
ejpam-5978	283	8	4	4	NUM
ejpam-5978	283	9	i−	i−	PROPN
ejpam-5978	283	10	1	1	NUM
ejpam-5978	283	11	)	)	PUNCT
ejpam-5978	283	12	xiy[4−(i−1	xiy[4−(i−1	PROPN
ejpam-5978	283	13	)	)	PUNCT
ejpam-5978	283	14	]	]	PUNCT
ejpam-5978	284	1	+	+	CCONJ
ejpam-5978	284	2	xy4	xy4	PROPN
ejpam-5978	284	3	+	+	NUM
ejpam-5978	284	4	4xy	4xy	ADJ
ejpam-5978	284	5	=	=	SYM
ejpam-5978	284	6	x5	x5	NOUN
ejpam-5978	284	7	+	+	CCONJ
ejpam-5978	285	1	[	[	X
ejpam-5978	285	2	(	(	PUNCT
ejpam-5978	285	3	4	4	NUM
ejpam-5978	285	4	1	1	NUM
ejpam-5978	285	5	)	)	PUNCT
ejpam-5978	285	6	x2y3	x2y3	PUNCT
ejpam-5978	286	1	+	+	CCONJ
ejpam-5978	286	2	(	(	PUNCT
ejpam-5978	286	3	4	4	NUM
ejpam-5978	286	4	2	2	NUM
ejpam-5978	286	5	)	)	PUNCT
ejpam-5978	286	6	x3y2	x3y2	PUNCT
ejpam-5978	287	1	+	+	CCONJ
ejpam-5978	287	2	(	(	PUNCT
ejpam-5978	287	3	4	4	NUM
ejpam-5978	287	4	3	3	NUM
ejpam-5978	287	5	)	)	PUNCT
ejpam-5978	288	1	x4y	x4y	PRON
ejpam-5978	288	2	]	]	PUNCT
ejpam-5978	289	1	+	+	ADJ
ejpam-5978	289	2	xy4	xy4	PROPN
ejpam-5978	289	3	+	+	X
ejpam-5978	289	4	4xy	4xy	ADJ
ejpam-5978	289	5	=	=	SYM
ejpam-5978	289	6	x5	x5	NOUN
ejpam-5978	289	7	+	+	NUM
ejpam-5978	289	8	4x2y3	4x2y3	NUM
ejpam-5978	289	9	+	+	CCONJ
ejpam-5978	289	10	6x3y2	6x3y2	NOUN
ejpam-5978	289	11	+	+	NUM
ejpam-5978	289	12	4x4y	4x4y	NOUN
ejpam-5978	289	13	+	+	CCONJ
ejpam-5978	289	14	xy4	xy4	PROPN
ejpam-5978	289	15	+	+	NUM
ejpam-5978	289	16	4xy	4xy	ADJ
ejpam-5978	289	17	=	=	SYM
ejpam-5978	289	18	x5	x5	PROPN
ejpam-5978	289	19	+	+	CCONJ
ejpam-5978	289	20	4x4y	4x4y	NOUN
ejpam-5978	289	21	+	+	CCONJ
ejpam-5978	289	22	6x3y2	6x3y2	NOUN
ejpam-5978	289	23	+	+	CCONJ
ejpam-5978	289	24	4x2y3	4x2y3	NUM
ejpam-5978	289	25	+	+	CCONJ
ejpam-5978	289	26	xy4	xy4	PROPN
ejpam-5978	289	27	+	+	NUM
ejpam-5978	289	28	4xy	4xy	ADJ
ejpam-5978	289	29	.	.	PUNCT
ejpam-5978	290	1	and	and	CCONJ
ejpam-5978	290	2	by	by	ADP
ejpam-5978	290	3	corollary	corollary	ADJ
ejpam-5978	290	4	5.5	5.5	NUM
ejpam-5978	290	5	,	,	PUNCT
ejpam-5978	290	6	there	there	PRON
ejpam-5978	290	7	are	be	VERB
ejpam-5978	290	8	4	4	NUM
ejpam-5978	290	9	+	+	SYM
ejpam-5978	290	10	2	2	NUM
ejpam-5978	290	11	=	=	SYM
ejpam-5978	290	12	6	6	NUM
ejpam-5978	290	13	terms	term	NOUN
ejpam-5978	290	14	in	in	ADP
ejpam-5978	290	15	the	the	DET
ejpam-5978	290	16	convex	convex	ADJ
ejpam-5978	290	17	independent	independent	ADJ
ejpam-5978	290	18	neighborhood	neighborhood	NOUN
ejpam-5978	290	19	polynomial	polynomial	NOUN
ejpam-5978	290	20	of	of	ADP
ejpam-5978	290	21	k1,4	k1,4	PROPN
ejpam-5978	290	22	.	.	PUNCT
ejpam-5978	291	1	to	to	PART
ejpam-5978	291	2	see	see	VERB
ejpam-5978	291	3	the	the	DET
ejpam-5978	291	4	convex	convex	ADJ
ejpam-5978	291	5	subsets	subset	NOUN
ejpam-5978	291	6	of	of	ADP
ejpam-5978	291	7	v	v	NOUN
ejpam-5978	291	8	(	(	PUNCT
ejpam-5978	291	9	k1,4)and	k1,4)and	VERB
ejpam-5978	291	10	its	its	PRON
ejpam-5978	291	11	corresponding	corresponding	ADJ
ejpam-5978	291	12	γin	γin	NOUN
ejpam-5978	291	13	-	-	PUNCT
ejpam-5978	291	14	sets	set	NOUN
ejpam-5978	291	15	,	,	PUNCT
ejpam-5978	291	16	refer	refer	VERB
ejpam-5978	291	17	to	to	ADP
ejpam-5978	291	18	the	the	DET
ejpam-5978	291	19	following	follow	VERB
ejpam-5978	291	20	tables	table	NOUN
ejpam-5978	291	21	13	13	NUM
ejpam-5978	291	22	,	,	PUNCT
ejpam-5978	291	23	14	14	NUM
ejpam-5978	291	24	,	,	PUNCT
ejpam-5978	291	25	and	and	CCONJ
ejpam-5978	291	26	15	15	NUM
ejpam-5978	291	27	:	:	PUNCT
ejpam-5978	291	28	e.j	e.j	PROPN
ejpam-5978	291	29	.	.	PROPN
ejpam-5978	291	30	aguilon	aguilon	PROPN
ejpam-5978	291	31	,	,	PUNCT
ejpam-5978	291	32	s.	s.	PROPN
ejpam-5978	291	33	dagondon	dagondon	PROPN
ejpam-5978	291	34	,	,	PUNCT
ejpam-5978	291	35	r.	r.	PROPN
ejpam-5978	291	36	artes	artes	PROPN
ejpam-5978	291	37	/	/	SYM
ejpam-5978	291	38	eur	eur	PROPN
ejpam-5978	291	39	.	.	PUNCT
ejpam-5978	292	1	j.	j.	PROPN
ejpam-5978	292	2	pure	pure	PROPN
ejpam-5978	292	3	appl	appl	PROPN
ejpam-5978	292	4	.	.	PROPN
ejpam-5978	292	5	math	math	PROPN
ejpam-5978	292	6	,	,	PUNCT
ejpam-5978	292	7	18	18	NUM
ejpam-5978	292	8	(	(	PUNCT
ejpam-5978	292	9	2	2	NUM
ejpam-5978	292	10	)	)	PUNCT
ejpam-5978	292	11	(	(	PUNCT
ejpam-5978	292	12	2025	2025	NUM
ejpam-5978	292	13	)	)	PUNCT
ejpam-5978	292	14	,	,	PUNCT
ejpam-5978	292	15	5978	5978	NUM
ejpam-5978	292	16	16	16	NUM
ejpam-5978	292	17	of	of	ADP
ejpam-5978	292	18	18	18	NUM
ejpam-5978	292	19	1	1	NUM
ejpam-5978	292	20	-	-	PUNCT
ejpam-5978	292	21	convex	convex	NOUN
ejpam-5978	292	22	γin	γin	NOUN
ejpam-5978	292	23	-	-	PUNCT
ejpam-5978	292	24	sets	set	NOUN
ejpam-5978	292	25	{	{	PUNCT
ejpam-5978	292	26	u1	u1	NOUN
ejpam-5978	292	27	}	}	PUNCT
ejpam-5978	292	28	{	{	PUNCT
ejpam-5978	292	29	v1	v1	NOUN
ejpam-5978	292	30	,	,	PUNCT
ejpam-5978	292	31	v2	v2	PROPN
ejpam-5978	292	32	,	,	PUNCT
ejpam-5978	292	33	v3	v3	PROPN
ejpam-5978	292	34	,	,	PUNCT
ejpam-5978	292	35	v4	v4	PROPN
ejpam-5978	292	36	}	}	PUNCT
ejpam-5978	292	37	{	{	PUNCT
ejpam-5978	292	38	v1	v1	NOUN
ejpam-5978	292	39	}	}	PUNCT
ejpam-5978	292	40	{	{	PUNCT
ejpam-5978	292	41	u1	u1	NOUN
ejpam-5978	292	42	}	}	PUNCT
ejpam-5978	292	43	{	{	PUNCT
ejpam-5978	292	44	v2	v2	NOUN
ejpam-5978	292	45	}	}	PUNCT
ejpam-5978	292	46	{	{	PUNCT
ejpam-5978	292	47	u1	u1	NOUN
ejpam-5978	292	48	}	}	PUNCT
ejpam-5978	292	49	{	{	PUNCT
ejpam-5978	292	50	v3	v3	PROPN
ejpam-5978	292	51	}	}	PUNCT
ejpam-5978	292	52	{	{	PUNCT
ejpam-5978	292	53	u1	u1	NOUN
ejpam-5978	292	54	}	}	PUNCT
ejpam-5978	292	55	{	{	PUNCT
ejpam-5978	292	56	v4	v4	NOUN
ejpam-5978	292	57	}	}	PUNCT
ejpam-5978	292	58	{	{	PUNCT
ejpam-5978	292	59	u1	u1	NOUN
ejpam-5978	292	60	}	}	PUNCT
ejpam-5978	292	61	table	table	NOUN
ejpam-5978	292	62	13	13	NUM
ejpam-5978	292	63	:	:	SYM
ejpam-5978	292	64	1	1	NUM
ejpam-5978	292	65	-	-	PUNCT
ejpam-5978	292	66	convex	convex	NOUN
ejpam-5978	292	67	subsets	subset	NOUN
ejpam-5978	292	68	of	of	ADP
ejpam-5978	292	69	v	v	NOUN
ejpam-5978	292	70	(	(	PUNCT
ejpam-5978	292	71	k1,4	k1,4	PROPN
ejpam-5978	292	72	)	)	PUNCT
ejpam-5978	292	73	and	and	CCONJ
ejpam-5978	292	74	its	its	PRON
ejpam-5978	292	75	corresponding	corresponding	ADJ
ejpam-5978	292	76	γin	γin	NOUN
ejpam-5978	292	77	-	-	PUNCT
ejpam-5978	292	78	sets	set	NOUN
ejpam-5978	292	79	.	.	PUNCT
ejpam-5978	293	1	table	table	NOUN
ejpam-5978	293	2	13	13	NUM
ejpam-5978	293	3	shows	show	VERB
ejpam-5978	293	4	that	that	SCONJ
ejpam-5978	293	5	there	there	PRON
ejpam-5978	293	6	are	be	VERB
ejpam-5978	293	7	4	4	NUM
ejpam-5978	293	8	1	1	NUM
ejpam-5978	293	9	-	-	PUNCT
ejpam-5978	293	10	convex	convex	NOUN
ejpam-5978	293	11	subsets	subset	NOUN
ejpam-5978	293	12	of	of	ADP
ejpam-5978	293	13	v	v	NOUN
ejpam-5978	293	14	(	(	PUNCT
ejpam-5978	293	15	k1,4	k1,4	PROPN
ejpam-5978	293	16	)	)	PUNCT
ejpam-5978	293	17	with	with	ADP
ejpam-5978	293	18	γin	γin	ADV
ejpam-5978	293	19	-	-	PUNCT
ejpam-5978	293	20	set	set	VERB
ejpam-5978	293	21	cardinality	cardinality	NOUN
ejpam-5978	293	22	equal	equal	ADJ
ejpam-5978	293	23	to	to	ADP
ejpam-5978	293	24	1	1	NUM
ejpam-5978	293	25	and	and	CCONJ
ejpam-5978	293	26	exactly	exactly	ADV
ejpam-5978	293	27	1	1	NUM
ejpam-5978	293	28	1	1	NUM
ejpam-5978	293	29	-	-	PUNCT
ejpam-5978	293	30	convex	convex	NOUN
ejpam-5978	293	31	subset	subset	NOUN
ejpam-5978	293	32	of	of	ADP
ejpam-5978	293	33	v	v	PROPN
ejpam-5978	293	34	(	(	PUNCT
ejpam-5978	293	35	k1,4	k1,4	PROPN
ejpam-5978	293	36	)	)	PUNCT
ejpam-5978	293	37	with	with	ADP
ejpam-5978	293	38	γin	γin	ADV
ejpam-5978	293	39	-	-	PUNCT
ejpam-5978	293	40	set	set	VERB
ejpam-5978	293	41	cardinality	cardinality	NOUN
ejpam-5978	293	42	equal	equal	ADJ
ejpam-5978	293	43	to	to	ADP
ejpam-5978	293	44	4	4	NUM
ejpam-5978	293	45	.	.	PUNCT
ejpam-5978	294	1	this	this	PRON
ejpam-5978	294	2	contributes	contribute	VERB
ejpam-5978	294	3	to	to	ADP
ejpam-5978	294	4	the	the	DET
ejpam-5978	294	5	convex	convex	ADJ
ejpam-5978	294	6	independent	independent	ADJ
ejpam-5978	294	7	neighborhood	neighborhood	NOUN
ejpam-5978	294	8	polynomial	polynomial	NOUN
ejpam-5978	294	9	of	of	ADP
ejpam-5978	294	10	k1,4	k1,4	ADV
ejpam-5978	294	11	as	as	ADP
ejpam-5978	294	12	xy4	xy4	PROPN
ejpam-5978	294	13	+	+	X
ejpam-5978	294	14	4xy	4xy	ADJ
ejpam-5978	294	15	.	.	PUNCT
ejpam-5978	295	1	2	2	NUM
ejpam-5978	295	2	-	-	NUM
ejpam-5978	295	3	convex	convex	VERB
ejpam-5978	295	4	γin	γin	NOUN
ejpam-5978	295	5	-	-	PUNCT
ejpam-5978	295	6	sets	set	NOUN
ejpam-5978	295	7	{	{	PUNCT
ejpam-5978	295	8	v1	v1	NOUN
ejpam-5978	295	9	,	,	PUNCT
ejpam-5978	295	10	u1	u1	NOUN
ejpam-5978	295	11	}	}	PUNCT
ejpam-5978	295	12	{	{	PUNCT
ejpam-5978	295	13	v2	v2	PROPN
ejpam-5978	295	14	,	,	PUNCT
ejpam-5978	295	15	v3	v3	PROPN
ejpam-5978	295	16	,	,	PUNCT
ejpam-5978	295	17	v4	v4	PROPN
ejpam-5978	295	18	}	}	PUNCT
ejpam-5978	295	19	{	{	PUNCT
ejpam-5978	295	20	v2	v2	NOUN
ejpam-5978	295	21	,	,	PUNCT
ejpam-5978	295	22	u1	u1	NOUN
ejpam-5978	295	23	}	}	PUNCT
ejpam-5978	295	24	{	{	PUNCT
ejpam-5978	295	25	v1	v1	PROPN
ejpam-5978	295	26	,	,	PUNCT
ejpam-5978	295	27	v3	v3	PROPN
ejpam-5978	295	28	,	,	PUNCT
ejpam-5978	295	29	v4	v4	PROPN
ejpam-5978	295	30	}	}	PUNCT
ejpam-5978	295	31	{	{	PUNCT
ejpam-5978	295	32	v3	v3	PROPN
ejpam-5978	295	33	,	,	PUNCT
ejpam-5978	295	34	u1	u1	NOUN
ejpam-5978	295	35	}	}	PUNCT
ejpam-5978	295	36	{	{	PUNCT
ejpam-5978	295	37	v1	v1	NOUN
ejpam-5978	295	38	,	,	PUNCT
ejpam-5978	295	39	v2	v2	PROPN
ejpam-5978	295	40	,	,	PUNCT
ejpam-5978	295	41	v4	v4	NOUN
ejpam-5978	295	42	}	}	PUNCT
ejpam-5978	295	43	{	{	PUNCT
ejpam-5978	295	44	v4	v4	NOUN
ejpam-5978	295	45	,	,	PUNCT
ejpam-5978	295	46	u1	u1	NOUN
ejpam-5978	295	47	}	}	PUNCT
ejpam-5978	295	48	{	{	PUNCT
ejpam-5978	295	49	v1	v1	NOUN
ejpam-5978	295	50	,	,	PUNCT
ejpam-5978	295	51	v2	v2	PROPN
ejpam-5978	295	52	,	,	PUNCT
ejpam-5978	295	53	v3	v3	PROPN
ejpam-5978	295	54	}	}	PUNCT
ejpam-5978	295	55	table	table	NOUN
ejpam-5978	295	56	14	14	NUM
ejpam-5978	295	57	:	:	SYM
ejpam-5978	295	58	2	2	NUM
ejpam-5978	295	59	-	-	PUNCT
ejpam-5978	295	60	convex	convex	NOUN
ejpam-5978	295	61	subsets	subset	NOUN
ejpam-5978	295	62	of	of	ADP
ejpam-5978	295	63	v	v	NOUN
ejpam-5978	295	64	(	(	PUNCT
ejpam-5978	295	65	k1,4	k1,4	PROPN
ejpam-5978	295	66	)	)	PUNCT
ejpam-5978	295	67	and	and	CCONJ
ejpam-5978	295	68	its	its	PRON
ejpam-5978	295	69	corresponding	corresponding	ADJ
ejpam-5978	295	70	γin	γin	NOUN
ejpam-5978	295	71	-	-	PUNCT
ejpam-5978	295	72	sets	set	NOUN
ejpam-5978	295	73	.	.	PUNCT
ejpam-5978	296	1	table	table	NOUN
ejpam-5978	296	2	14	14	NUM
ejpam-5978	296	3	shows	show	VERB
ejpam-5978	296	4	that	that	SCONJ
ejpam-5978	296	5	there	there	PRON
ejpam-5978	296	6	are	be	VERB
ejpam-5978	296	7	4	4	NUM
ejpam-5978	296	8	2	2	NUM
ejpam-5978	296	9	-	-	PUNCT
ejpam-5978	296	10	convex	convex	NOUN
ejpam-5978	296	11	subsets	subset	NOUN
ejpam-5978	296	12	of	of	ADP
ejpam-5978	296	13	v	v	NOUN
ejpam-5978	296	14	(	(	PUNCT
ejpam-5978	296	15	k1,4	k1,4	PROPN
ejpam-5978	296	16	)	)	PUNCT
ejpam-5978	296	17	with	with	ADP
ejpam-5978	296	18	γin	γin	ADV
ejpam-5978	296	19	-	-	PUNCT
ejpam-5978	296	20	set	set	VERB
ejpam-5978	296	21	cardinality	cardinality	NOUN
ejpam-5978	296	22	equal	equal	ADJ
ejpam-5978	296	23	to	to	ADP
ejpam-5978	296	24	3	3	NUM
ejpam-5978	296	25	.	.	PUNCT
ejpam-5978	297	1	this	this	PRON
ejpam-5978	297	2	contributes	contribute	VERB
ejpam-5978	297	3	to	to	ADP
ejpam-5978	297	4	the	the	DET
ejpam-5978	297	5	convex	convex	ADJ
ejpam-5978	297	6	independent	independent	ADJ
ejpam-5978	297	7	neighborhood	neighborhood	NOUN
ejpam-5978	297	8	polynomial	polynomial	NOUN
ejpam-5978	297	9	of	of	ADP
ejpam-5978	297	10	k1,4	k1,4	PROPN
ejpam-5978	297	11	as	as	ADP
ejpam-5978	297	12	4x2y3	4x2y3	NUM
ejpam-5978	297	13	.	.	PUNCT
ejpam-5978	298	1	3	3	X
ejpam-5978	298	2	-	-	NUM
ejpam-5978	298	3	convex	convex	VERB
ejpam-5978	298	4	γin	γin	NOUN
ejpam-5978	298	5	-	-	PUNCT
ejpam-5978	298	6	sets	set	NOUN
ejpam-5978	298	7	{	{	PUNCT
ejpam-5978	298	8	v1	v1	NOUN
ejpam-5978	298	9	,	,	PUNCT
ejpam-5978	298	10	v2	v2	NOUN
ejpam-5978	298	11	,	,	PUNCT
ejpam-5978	298	12	u1	u1	NOUN
ejpam-5978	298	13	}	}	PUNCT
ejpam-5978	298	14	{	{	PUNCT
ejpam-5978	298	15	v3	v3	PROPN
ejpam-5978	298	16	,	,	PUNCT
ejpam-5978	298	17	v4	v4	PROPN
ejpam-5978	298	18	}	}	PUNCT
ejpam-5978	298	19	{	{	PUNCT
ejpam-5978	298	20	v1	v1	PROPN
ejpam-5978	298	21	,	,	PUNCT
ejpam-5978	298	22	v3	v3	PROPN
ejpam-5978	298	23	,	,	PUNCT
ejpam-5978	298	24	u1	u1	PROPN
ejpam-5978	298	25	}	}	PUNCT
ejpam-5978	298	26	{	{	PUNCT
ejpam-5978	298	27	v2	v2	PROPN
ejpam-5978	298	28	,	,	PUNCT
ejpam-5978	298	29	v4	v4	PROPN
ejpam-5978	298	30	}	}	PUNCT
ejpam-5978	298	31	{	{	PUNCT
ejpam-5978	298	32	v1	v1	NOUN
ejpam-5978	298	33	,	,	PUNCT
ejpam-5978	298	34	v4	v4	NOUN
ejpam-5978	298	35	,	,	PUNCT
ejpam-5978	298	36	u1	u1	NOUN
ejpam-5978	298	37	}	}	PUNCT
ejpam-5978	298	38	{	{	PUNCT
ejpam-5978	298	39	v2	v2	PROPN
ejpam-5978	298	40	,	,	PUNCT
ejpam-5978	298	41	v3	v3	PROPN
ejpam-5978	298	42	}	}	PUNCT
ejpam-5978	298	43	{	{	PUNCT
ejpam-5978	298	44	v2	v2	PROPN
ejpam-5978	298	45	,	,	PUNCT
ejpam-5978	298	46	v3	v3	PROPN
ejpam-5978	298	47	,	,	PUNCT
ejpam-5978	298	48	u1	u1	NOUN
ejpam-5978	298	49	}	}	PUNCT
ejpam-5978	298	50	{	{	PUNCT
ejpam-5978	298	51	v1	v1	NOUN
ejpam-5978	298	52	,	,	PUNCT
ejpam-5978	298	53	v4	v4	NOUN
ejpam-5978	298	54	}	}	PUNCT
ejpam-5978	298	55	{	{	PUNCT
ejpam-5978	298	56	v2	v2	PROPN
ejpam-5978	298	57	,	,	PUNCT
ejpam-5978	298	58	v4	v4	NOUN
ejpam-5978	298	59	,	,	PUNCT
ejpam-5978	298	60	u1	u1	NOUN
ejpam-5978	298	61	}	}	PUNCT
ejpam-5978	298	62	{	{	PUNCT
ejpam-5978	298	63	v1	v1	NOUN
ejpam-5978	298	64	,	,	PUNCT
ejpam-5978	298	65	v3	v3	PROPN
ejpam-5978	298	66	}	}	PUNCT
ejpam-5978	298	67	{	{	PUNCT
ejpam-5978	298	68	v3	v3	PROPN
ejpam-5978	298	69	,	,	PUNCT
ejpam-5978	298	70	v4	v4	NOUN
ejpam-5978	298	71	,	,	PUNCT
ejpam-5978	298	72	u1	u1	NOUN
ejpam-5978	298	73	}	}	PUNCT
ejpam-5978	298	74	{	{	PUNCT
ejpam-5978	298	75	v1	v1	NOUN
ejpam-5978	298	76	,	,	PUNCT
ejpam-5978	298	77	v2	v2	NOUN
ejpam-5978	298	78	}	}	PUNCT
ejpam-5978	298	79	table	table	NOUN
ejpam-5978	298	80	15	15	NUM
ejpam-5978	298	81	:	:	SYM
ejpam-5978	298	82	3	3	NUM
ejpam-5978	298	83	-	-	PUNCT
ejpam-5978	298	84	convex	convex	ADJ
ejpam-5978	298	85	subsets	subset	NOUN
ejpam-5978	298	86	of	of	ADP
ejpam-5978	298	87	v	v	NOUN
ejpam-5978	298	88	(	(	PUNCT
ejpam-5978	298	89	k1,4	k1,4	PROPN
ejpam-5978	298	90	)	)	PUNCT
ejpam-5978	298	91	and	and	CCONJ
ejpam-5978	298	92	its	its	PRON
ejpam-5978	298	93	corresponding	corresponding	ADJ
ejpam-5978	298	94	γin	γin	NOUN
ejpam-5978	298	95	-	-	PUNCT
ejpam-5978	298	96	sets	set	NOUN
ejpam-5978	298	97	.	.	PUNCT
ejpam-5978	299	1	table	table	NOUN
ejpam-5978	299	2	15	15	NUM
ejpam-5978	299	3	shows	show	VERB
ejpam-5978	299	4	that	that	SCONJ
ejpam-5978	299	5	there	there	PRON
ejpam-5978	299	6	are	be	VERB
ejpam-5978	299	7	6	6	NUM
ejpam-5978	299	8	3	3	NUM
ejpam-5978	299	9	-	-	PUNCT
ejpam-5978	299	10	convex	convex	NOUN
ejpam-5978	299	11	subsets	subset	NOUN
ejpam-5978	299	12	of	of	ADP
ejpam-5978	299	13	v	v	NOUN
ejpam-5978	299	14	(	(	PUNCT
ejpam-5978	299	15	k1,4	k1,4	PROPN
ejpam-5978	299	16	)	)	PUNCT
ejpam-5978	299	17	with	with	ADP
ejpam-5978	299	18	γin	γin	ADV
ejpam-5978	299	19	-	-	PUNCT
ejpam-5978	299	20	set	set	VERB
ejpam-5978	299	21	cardinality	cardinality	NOUN
ejpam-5978	299	22	equal	equal	ADJ
ejpam-5978	299	23	to	to	ADP
ejpam-5978	299	24	2	2	NUM
ejpam-5978	299	25	.	.	PUNCT
ejpam-5978	300	1	this	this	PRON
ejpam-5978	300	2	contributes	contribute	VERB
ejpam-5978	300	3	to	to	ADP
ejpam-5978	300	4	the	the	DET
ejpam-5978	300	5	convex	convex	ADJ
ejpam-5978	300	6	independent	independent	ADJ
ejpam-5978	300	7	neighborhood	neighborhood	NOUN
ejpam-5978	300	8	polynomial	polynomial	NOUN
ejpam-5978	300	9	of	of	ADP
ejpam-5978	300	10	k1,4	k1,4	PROPN
ejpam-5978	300	11	as	as	ADP
ejpam-5978	300	12	6x3y2	6x3y2	PROPN
ejpam-5978	300	13	.	.	PUNCT
ejpam-5978	301	1	for	for	ADP
ejpam-5978	301	2	4	4	NUM
ejpam-5978	301	3	-	-	PUNCT
ejpam-5978	301	4	convex	convex	NOUN
ejpam-5978	301	5	subsets	subset	NOUN
ejpam-5978	301	6	of	of	ADP
ejpam-5978	301	7	v	v	NOUN
ejpam-5978	301	8	(	(	PUNCT
ejpam-5978	301	9	k1,4	k1,4	PROPN
ejpam-5978	301	10	)	)	PUNCT
ejpam-5978	301	11	,	,	PUNCT
ejpam-5978	301	12	it	it	PRON
ejpam-5978	301	13	can	can	AUX
ejpam-5978	301	14	be	be	AUX
ejpam-5978	301	15	verified	verify	VERB
ejpam-5978	301	16	that	that	SCONJ
ejpam-5978	301	17	there	there	PRON
ejpam-5978	301	18	are	be	VERB
ejpam-5978	301	19	4	4	NUM
ejpam-5978	301	20	4	4	NUM
ejpam-5978	301	21	-	-	PUNCT
ejpam-5978	301	22	convex	convex	NOUN
ejpam-5978	301	23	subsets	subset	NOUN
ejpam-5978	301	24	of	of	ADP
ejpam-5978	301	25	v	v	NOUN
ejpam-5978	301	26	(	(	PUNCT
ejpam-5978	301	27	k1,4	k1,4	PROPN
ejpam-5978	301	28	)	)	PUNCT
ejpam-5978	301	29	with	with	ADP
ejpam-5978	301	30	γin	γin	ADV
ejpam-5978	301	31	-	-	PUNCT
ejpam-5978	301	32	set	set	VERB
ejpam-5978	301	33	cardinality	cardinality	NOUN
ejpam-5978	301	34	equal	equal	ADJ
ejpam-5978	301	35	to	to	ADP
ejpam-5978	301	36	1	1	NUM
ejpam-5978	301	37	.	.	PUNCT
ejpam-5978	302	1	this	this	PRON
ejpam-5978	302	2	contributes	contribute	VERB
ejpam-5978	302	3	to	to	ADP
ejpam-5978	302	4	the	the	DET
ejpam-5978	302	5	convex	convex	ADJ
ejpam-5978	302	6	independent	independent	ADJ
ejpam-5978	302	7	neighborhood	neighborhood	NOUN
ejpam-5978	302	8	polynomial	polynomial	NOUN
ejpam-5978	302	9	of	of	ADP
ejpam-5978	302	10	k1,4	k1,4	PROPN
ejpam-5978	302	11	as	as	ADP
ejpam-5978	302	12	4x4y	4x4y	PROPN
ejpam-5978	302	13	.	.	PUNCT
ejpam-5978	303	1	e.j	e.j	PROPN
ejpam-5978	303	2	.	.	PROPN
ejpam-5978	303	3	aguilon	aguilon	PROPN
ejpam-5978	303	4	,	,	PUNCT
ejpam-5978	303	5	s.	s.	PROPN
ejpam-5978	303	6	dagondon	dagondon	PROPN
ejpam-5978	303	7	,	,	PUNCT
ejpam-5978	303	8	r.	r.	PROPN
ejpam-5978	303	9	artes	artes	PROPN
ejpam-5978	303	10	/	/	SYM
ejpam-5978	303	11	eur	eur	PROPN
ejpam-5978	303	12	.	.	PUNCT
ejpam-5978	304	1	j.	j.	PROPN
ejpam-5978	304	2	pure	pure	PROPN
ejpam-5978	304	3	appl	appl	PROPN
ejpam-5978	304	4	.	.	PROPN
ejpam-5978	304	5	math	math	PROPN
ejpam-5978	304	6	,	,	PUNCT
ejpam-5978	304	7	18	18	NUM
ejpam-5978	304	8	(	(	PUNCT
ejpam-5978	304	9	2	2	NUM
ejpam-5978	304	10	)	)	PUNCT
ejpam-5978	304	11	(	(	PUNCT
ejpam-5978	304	12	2025	2025	NUM
ejpam-5978	304	13	)	)	PUNCT
ejpam-5978	304	14	,	,	PUNCT
ejpam-5978	304	15	5978	5978	NUM
ejpam-5978	304	16	17	17	NUM
ejpam-5978	304	17	of	of	ADP
ejpam-5978	304	18	18	18	NUM
ejpam-5978	304	19	for	for	ADP
ejpam-5978	304	20	5	5	NUM
ejpam-5978	304	21	-	-	PUNCT
ejpam-5978	304	22	convex	convex	NOUN
ejpam-5978	304	23	subset	subset	NOUN
ejpam-5978	304	24	of	of	ADP
ejpam-5978	304	25	v	v	PROPN
ejpam-5978	304	26	(	(	PUNCT
ejpam-5978	304	27	k1,4	k1,4	PROPN
ejpam-5978	304	28	)	)	PUNCT
ejpam-5978	304	29	,	,	PUNCT
ejpam-5978	304	30	there	there	PRON
ejpam-5978	304	31	is	be	VERB
ejpam-5978	304	32	only	only	ADV
ejpam-5978	304	33	1	1	NUM
ejpam-5978	304	34	5	5	NUM
ejpam-5978	304	35	-	-	PUNCT
ejpam-5978	304	36	convex	convex	NOUN
ejpam-5978	304	37	subset	subset	NOUN
ejpam-5978	304	38	of	of	ADP
ejpam-5978	304	39	v	v	PROPN
ejpam-5978	304	40	(	(	PUNCT
ejpam-5978	304	41	k1,4	k1,4	PROPN
ejpam-5978	304	42	)	)	PUNCT
ejpam-5978	304	43	with	with	ADP
ejpam-5978	304	44	empty	empty	ADJ
ejpam-5978	304	45	(	(	PUNCT
ejpam-5978	304	46	zero	zero	NUM
ejpam-5978	304	47	cardinality	cardinality	NOUN
ejpam-5978	304	48	)	)	PUNCT
ejpam-5978	304	49	γin	γin	NOUN
ejpam-5978	304	50	-	-	PUNCT
ejpam-5978	304	51	set	set	NOUN
ejpam-5978	304	52	.	.	PUNCT
ejpam-5978	305	1	this	this	PRON
ejpam-5978	305	2	contributes	contribute	VERB
ejpam-5978	305	3	to	to	ADP
ejpam-5978	305	4	the	the	DET
ejpam-5978	305	5	convex	convex	ADJ
ejpam-5978	305	6	independent	independent	ADJ
ejpam-5978	305	7	neighborhood	neighborhood	NOUN
ejpam-5978	305	8	polynomial	polynomial	NOUN
ejpam-5978	305	9	of	of	ADP
ejpam-5978	305	10	k1,4	k1,4	PROPN
ejpam-5978	305	11	as	as	ADP
ejpam-5978	305	12	x5	x5	PROPN
ejpam-5978	305	13	.	.	PROPN
ejpam-5978	305	14	6	6	NUM
ejpam-5978	305	15	.	.	X
ejpam-5978	305	16	conclusion	conclusion	VERB
ejpam-5978	305	17	the	the	DET
ejpam-5978	305	18	study	study	NOUN
ejpam-5978	305	19	of	of	ADP
ejpam-5978	305	20	graph	graph	NOUN
ejpam-5978	305	21	polynomials	polynomial	NOUN
ejpam-5978	305	22	and	and	CCONJ
ejpam-5978	305	23	convexity	convexity	NOUN
ejpam-5978	305	24	in	in	ADP
ejpam-5978	305	25	graphs	graph	NOUN
ejpam-5978	305	26	continues	continue	VERB
ejpam-5978	305	27	to	to	PART
ejpam-5978	305	28	be	be	AUX
ejpam-5978	305	29	a	a	DET
ejpam-5978	305	30	significant	significant	ADJ
ejpam-5978	305	31	area	area	NOUN
ejpam-5978	305	32	of	of	ADP
ejpam-5978	305	33	research	research	NOUN
ejpam-5978	305	34	in	in	ADP
ejpam-5978	305	35	graph	graph	NOUN
ejpam-5978	305	36	theory	theory	NOUN
ejpam-5978	305	37	,	,	PUNCT
ejpam-5978	305	38	offering	offer	VERB
ejpam-5978	305	39	valuable	valuable	ADJ
ejpam-5978	305	40	insights	insight	NOUN
ejpam-5978	305	41	and	and	CCONJ
ejpam-5978	305	42	applications	application	NOUN
ejpam-5978	305	43	across	across	ADP
ejpam-5978	305	44	various	various	ADJ
ejpam-5978	305	45	scientific	scientific	ADJ
ejpam-5978	305	46	fields	field	NOUN
ejpam-5978	305	47	.	.	PUNCT
ejpam-5978	306	1	researchers	researcher	NOUN
ejpam-5978	306	2	have	have	AUX
ejpam-5978	306	3	investigated	investigate	VERB
ejpam-5978	306	4	new	new	ADJ
ejpam-5978	306	5	approaches	approach	NOUN
ejpam-5978	306	6	to	to	PART
ejpam-5978	306	7	count	count	VERB
ejpam-5978	306	8	and	and	CCONJ
ejpam-5978	306	9	describe	describe	VERB
ejpam-5978	306	10	substructures	substructure	NOUN
ejpam-5978	306	11	based	base	VERB
ejpam-5978	306	12	on	on	ADP
ejpam-5978	306	13	their	their	PRON
ejpam-5978	306	14	neighborhood	neighborhood	NOUN
ejpam-5978	306	15	system	system	NOUN
ejpam-5978	306	16	by	by	ADP
ejpam-5978	306	17	combining	combine	VERB
ejpam-5978	306	18	the	the	DET
ejpam-5978	306	19	ideas	idea	NOUN
ejpam-5978	306	20	of	of	ADP
ejpam-5978	306	21	convexity	convexity	NOUN
ejpam-5978	306	22	with	with	ADP
ejpam-5978	306	23	graph	graph	NOUN
ejpam-5978	306	24	polynomials	polynomial	NOUN
ejpam-5978	306	25	.	.	PUNCT
ejpam-5978	307	1	in	in	ADP
ejpam-5978	307	2	this	this	DET
ejpam-5978	307	3	paper	paper	NOUN
ejpam-5978	307	4	,	,	PUNCT
ejpam-5978	307	5	we	we	PRON
ejpam-5978	307	6	have	have	AUX
ejpam-5978	307	7	extended	extend	VERB
ejpam-5978	307	8	this	this	DET
ejpam-5978	307	9	line	line	NOUN
ejpam-5978	307	10	of	of	ADP
ejpam-5978	307	11	study	study	NOUN
ejpam-5978	307	12	by	by	ADP
ejpam-5978	307	13	considering	consider	VERB
ejpam-5978	307	14	independent	independent	ADJ
ejpam-5978	307	15	neighborhood	neighborhood	NOUN
ejpam-5978	307	16	systems	system	NOUN
ejpam-5978	307	17	of	of	ADP
ejpam-5978	307	18	convex	convex	ADJ
ejpam-5978	307	19	subgraphs	subgraph	NOUN
ejpam-5978	307	20	,	,	PUNCT
ejpam-5978	307	21	which	which	PRON
ejpam-5978	307	22	leads	lead	VERB
ejpam-5978	307	23	to	to	ADP
ejpam-5978	307	24	the	the	DET
ejpam-5978	307	25	introduction	introduction	NOUN
ejpam-5978	307	26	of	of	ADP
ejpam-5978	307	27	the	the	DET
ejpam-5978	307	28	convex	convex	ADJ
ejpam-5978	307	29	independent	independent	ADJ
ejpam-5978	307	30	neighborhood	neighborhood	NOUN
ejpam-5978	307	31	polynomial	polynomial	NOUN
ejpam-5978	307	32	for	for	ADP
ejpam-5978	307	33	paths	path	NOUN
ejpam-5978	307	34	,	,	PUNCT
ejpam-5978	307	35	cycles	cycle	NOUN
ejpam-5978	307	36	,	,	PUNCT
ejpam-5978	307	37	complete	complete	ADJ
ejpam-5978	307	38	and	and	CCONJ
ejpam-5978	307	39	star	star	NOUN
ejpam-5978	307	40	graph	graph	NOUN
ejpam-5978	307	41	.	.	PUNCT
ejpam-5978	308	1	this	this	DET
ejpam-5978	308	2	new	new	ADJ
ejpam-5978	308	3	polynomial	polynomial	NOUN
ejpam-5978	308	4	provides	provide	VERB
ejpam-5978	308	5	a	a	DET
ejpam-5978	308	6	new	new	ADJ
ejpam-5978	308	7	way	way	NOUN
ejpam-5978	308	8	to	to	PART
ejpam-5978	308	9	look	look	VERB
ejpam-5978	308	10	at	at	ADP
ejpam-5978	308	11	how	how	SCONJ
ejpam-5978	308	12	convexity	convexity	NOUN
ejpam-5978	308	13	and	and	CCONJ
ejpam-5978	308	14	neighborhood	neighborhood	NOUN
ejpam-5978	308	15	structures	structure	NOUN
ejpam-5978	308	16	work	work	VERB
ejpam-5978	308	17	together	together	ADV
ejpam-5978	308	18	,	,	PUNCT
ejpam-5978	308	19	creating	create	VERB
ejpam-5978	308	20	a	a	DET
ejpam-5978	308	21	foundation	foundation	NOUN
ejpam-5978	308	22	for	for	ADP
ejpam-5978	308	23	future	future	ADJ
ejpam-5978	308	24	graph	graph	NOUN
ejpam-5978	308	25	theory	theory	NOUN
ejpam-5978	308	26	researches	research	VERB
ejpam-5978	308	27	.	.	PUNCT
ejpam-5978	309	1	acknowledgements	acknowledgement	NOUN
ejpam-5978	309	2	the	the	DET
ejpam-5978	309	3	authors	author	NOUN
ejpam-5978	309	4	would	would	AUX
ejpam-5978	309	5	like	like	VERB
ejpam-5978	309	6	to	to	PART
ejpam-5978	309	7	thank	thank	VERB
ejpam-5978	309	8	department	department	PROPN
ejpam-5978	309	9	of	of	ADP
ejpam-5978	309	10	science	science	NOUN
ejpam-5978	309	11	and	and	CCONJ
ejpam-5978	309	12	technology	technology	NOUN
ejpam-5978	309	13	accelerated	accelerate	VERB
ejpam-5978	309	14	science	science	NOUN
ejpam-5978	309	15	and	and	CCONJ
ejpam-5978	309	16	technology	technology	NOUN
ejpam-5978	309	17	human	human	ADJ
ejpam-5978	309	18	resource	resource	NOUN
ejpam-5978	309	19	development	development	NOUN
ejpam-5978	309	20	program	program	NOUN
ejpam-5978	309	21	(	(	PUNCT
ejpam-5978	309	22	dost	dost	NOUN
ejpam-5978	309	23	-	-	PUNCT
ejpam-5978	309	24	asthrdp	asthrdp	NOUN
ejpam-5978	309	25	)	)	PUNCT
ejpam-5978	309	26	,	,	PUNCT
ejpam-5978	309	27	philippines	philippine	NOUN
ejpam-5978	309	28	and	and	CCONJ
ejpam-5978	309	29	msu	msu	PROPN
ejpam-5978	309	30	-	-	PUNCT
ejpam-5978	309	31	iligan	iligan	PROPN
ejpam-5978	309	32	institute	institute	PROPN
ejpam-5978	309	33	of	of	ADP
ejpam-5978	309	34	technology	technology	PROPN
ejpam-5978	309	35	(	(	PUNCT
ejpam-5978	309	36	iligan	iligan	ADJ
ejpam-5978	309	37	city	city	NOUN
ejpam-5978	309	38	,	,	PUNCT
ejpam-5978	309	39	philippines	philippine	NOUN
ejpam-5978	309	40	)	)	PUNCT
ejpam-5978	309	41	for	for	ADP
ejpam-5978	309	42	funding	fund	VERB
ejpam-5978	309	43	this	this	DET
ejpam-5978	309	44	research	research	NOUN
ejpam-5978	309	45	.	.	PUNCT
ejpam-5978	310	1	references	reference	NOUN
ejpam-5978	310	2	[	[	X
ejpam-5978	310	3	1	1	NUM
ejpam-5978	310	4	]	]	X
ejpam-5978	310	5	j.a	j.a	PROPN
ejpam-5978	310	6	.	.	PROPN
ejpam-5978	310	7	ellis	ellis	PROPN
ejpam-5978	310	8	-	-	PUNCT
ejpam-5978	310	9	monaghan	monaghan	PROPN
ejpam-5978	310	10	and	and	CCONJ
ejpam-5978	310	11	c.	c.	PROPN
ejpam-5978	310	12	merino	merino	PROPN
ejpam-5978	310	13	.	.	PUNCT
ejpam-5978	311	1	graph	graph	NOUN
ejpam-5978	311	2	polynomials	polynomial	NOUN
ejpam-5978	311	3	and	and	CCONJ
ejpam-5978	311	4	their	their	PRON
ejpam-5978	311	5	applications	application	NOUN
ejpam-5978	311	6	ii	ii	NOUN
ejpam-5978	311	7	:	:	PUNCT
ejpam-5978	311	8	interrelations	interrelation	NOUN
ejpam-5978	311	9	and	and	CCONJ
ejpam-5978	311	10	interpretations	interpretation	NOUN
ejpam-5978	311	11	.	.	PUNCT
ejpam-5978	312	1	structural	structural	ADJ
ejpam-5978	312	2	analysis	analysis	NOUN
ejpam-5978	312	3	of	of	ADP
ejpam-5978	312	4	complex	complex	ADJ
ejpam-5978	312	5	networks	network	NOUN
ejpam-5978	312	6	,	,	PUNCT
ejpam-5978	312	7	pages	page	NOUN
ejpam-5978	312	8	257–292	257–292	NUM
ejpam-5978	312	9	,	,	PUNCT
ejpam-5978	312	10	2011	2011	NUM
ejpam-5978	312	11	.	.	PUNCT
ejpam-5978	313	1	[	[	X
ejpam-5978	313	2	2	2	X
ejpam-5978	313	3	]	]	PUNCT
ejpam-5978	313	4	j.	j.	PROPN
ejpam-5978	313	5	brown	brown	PROPN
ejpam-5978	313	6	and	and	CCONJ
ejpam-5978	313	7	r.	r.	PROPN
ejpam-5978	313	8	nowakowski	nowakowski	PROPN
ejpam-5978	313	9	.	.	PUNCT
ejpam-5978	314	1	the	the	DET
ejpam-5978	314	2	neighbourhood	neighbourhood	NOUN
ejpam-5978	314	3	polynomial	polynomial	NOUN
ejpam-5978	314	4	of	of	ADP
ejpam-5978	314	5	a	a	DET
ejpam-5978	314	6	graph	graph	NOUN
ejpam-5978	314	7	.	.	PUNCT
ejpam-5978	315	1	australas	australa	NOUN
ejpam-5978	315	2	.	.	PUNCT
ejpam-5978	316	1	j	j	PROPN
ejpam-5978	316	2	comb	comb	PROPN
ejpam-5978	316	3	.	.	PUNCT
ejpam-5978	316	4	,	,	PUNCT
ejpam-5978	316	5	42:55–68	42:55–68	NUM
ejpam-5978	316	6	,	,	PUNCT
ejpam-5978	316	7	2008	2008	NUM
ejpam-5978	316	8	.	.	PUNCT
ejpam-5978	317	1	[	[	X
ejpam-5978	317	2	3	3	X
ejpam-5978	317	3	]	]	X
ejpam-5978	317	4	s.	s.	PROPN
ejpam-5978	317	5	dagondon	dagondon	VERB
ejpam-5978	317	6	n.s	n.s	PROPN
ejpam-5978	317	7	abdulcarim	abdulcarim	PROPN
ejpam-5978	317	8	and	and	CCONJ
ejpam-5978	317	9	e.	e.	PROPN
ejpam-5978	317	10	chacon	chacon	PROPN
ejpam-5978	317	11	.	.	PUNCT
ejpam-5978	318	1	on	on	ADP
ejpam-5978	318	2	the	the	DET
ejpam-5978	318	3	independent	independent	ADJ
ejpam-5978	318	4	neighborhood	neighborhood	NOUN
ejpam-5978	318	5	polynomial	polynomial	NOUN
ejpam-5978	318	6	of	of	ADP
ejpam-5978	318	7	the	the	DET
ejpam-5978	318	8	cartesian	cartesian	ADJ
ejpam-5978	318	9	product	product	NOUN
ejpam-5978	318	10	of	of	ADP
ejpam-5978	318	11	some	some	DET
ejpam-5978	318	12	special	special	ADJ
ejpam-5978	318	13	graphs	graph	NOUN
ejpam-5978	318	14	.	.	PUNCT
ejpam-5978	319	1	european	european	ADJ
ejpam-5978	319	2	journal	journal	PROPN
ejpam-5978	319	3	of	of	ADP
ejpam-5978	319	4	pure	pure	ADJ
ejpam-5978	319	5	and	and	CCONJ
ejpam-5978	319	6	applied	applied	ADJ
ejpam-5978	319	7	mathematics	mathematic	NOUN
ejpam-5978	319	8	,	,	PUNCT
ejpam-5978	319	9	14(1):173–191	14(1):173–191	PROPN
ejpam-5978	319	10	,	,	PUNCT
ejpam-5978	319	11	2021	2021	NUM
ejpam-5978	319	12	.	.	PUNCT
ejpam-5978	320	1	[	[	X
ejpam-5978	320	2	4	4	NUM
ejpam-5978	320	3	]	]	PUNCT
ejpam-5978	320	4	m.	m.	NOUN
ejpam-5978	320	5	berger	berger	PROPN
ejpam-5978	320	6	.	.	PUNCT
ejpam-5978	321	1	convexity	convexity	PROPN
ejpam-5978	321	2	.	.	PUNCT
ejpam-5978	322	1	the	the	DET
ejpam-5978	322	2	american	american	PROPN
ejpam-5978	322	3	mathematical	mathematical	PROPN
ejpam-5978	322	4	monthly	monthly	ADJ
ejpam-5978	322	5	,	,	PUNCT
ejpam-5978	322	6	97(8):650–678	97(8):650–678	NUM
ejpam-5978	322	7	,	,	PUNCT
ejpam-5978	322	8	1990	1990	NUM
ejpam-5978	322	9	.	.	PUNCT
ejpam-5978	323	1	[	[	X
ejpam-5978	323	2	5	5	X
ejpam-5978	323	3	]	]	PUNCT
ejpam-5978	323	4	f.	f.	PROPN
ejpam-5978	323	5	harary	harary	PROPN
ejpam-5978	323	6	frank	frank	PROPN
ejpam-5978	323	7	and	and	CCONJ
ejpam-5978	323	8	j.	j.	PROPN
ejpam-5978	323	9	nieminen	nieminen	PROPN
ejpam-5978	323	10	.	.	PUNCT
ejpam-5978	324	1	convexity	convexity	NOUN
ejpam-5978	324	2	in	in	ADP
ejpam-5978	324	3	graphs	graph	NOUN
ejpam-5978	324	4	.	.	PUNCT
ejpam-5978	325	1	journal	journal	PROPN
ejpam-5978	325	2	of	of	ADP
ejpam-5978	325	3	differential	differential	ADJ
ejpam-5978	325	4	geometry	geometry	NOUN
ejpam-5978	325	5	,	,	PUNCT
ejpam-5978	325	6	16(2):185–190	16(2):185–190	NUM
ejpam-5978	325	7	,	,	PUNCT
ejpam-5978	325	8	1981	1981	NUM
ejpam-5978	325	9	.	.	PUNCT
ejpam-5978	326	1	[	[	X
ejpam-5978	326	2	6	6	NUM
ejpam-5978	326	3	]	]	PUNCT
ejpam-5978	326	4	l.	l.	PROPN
ejpam-5978	326	5	laja	laja	PROPN
ejpam-5978	326	6	and	and	CCONJ
ejpam-5978	326	7	r.	r.	PROPN
ejpam-5978	326	8	artes	artes	PROPN
ejpam-5978	326	9	jr	jr	PROPN
ejpam-5978	326	10	.	.	PROPN
ejpam-5978	326	11	zeros	zero	NOUN
ejpam-5978	326	12	of	of	ADP
ejpam-5978	326	13	convex	convex	ADJ
ejpam-5978	326	14	subgraph	subgraph	NOUN
ejpam-5978	326	15	polynomials	polynomial	NOUN
ejpam-5978	326	16	.	.	PUNCT
ejpam-5978	327	1	appl	appl	PROPN
ejpam-5978	327	2	.	.	PROPN
ejpam-5978	327	3	math	math	PROPN
ejpam-5978	327	4	.	.	PUNCT
ejpam-5978	328	1	sci	sci	PROPN
ejpam-5978	328	2	,	,	PUNCT
ejpam-5978	328	3	8(59):2917–2923	8(59):2917–2923	NUM
ejpam-5978	328	4	,	,	PUNCT
ejpam-5978	328	5	2014	2014	NUM
ejpam-5978	328	6	.	.	PUNCT
ejpam-5978	329	1	[	[	X
ejpam-5978	329	2	7	7	X
ejpam-5978	329	3	]	]	X
ejpam-5978	329	4	l.	l.	PROPN
ejpam-5978	329	5	laja	laja	PROPN
ejpam-5978	329	6	and	and	CCONJ
ejpam-5978	329	7	r.	r.	PROPN
ejpam-5978	329	8	artes	artes	PROPN
ejpam-5978	329	9	jr	jr	PROPN
ejpam-5978	329	10	.	.	PROPN
ejpam-5978	330	1	convex	convex	PROPN
ejpam-5978	330	2	subgraph	subgraph	NOUN
ejpam-5978	330	3	polynomials	polynomial	NOUN
ejpam-5978	330	4	of	of	ADP
ejpam-5978	330	5	the	the	DET
ejpam-5978	330	6	join	join	NOUN
ejpam-5978	330	7	and	and	CCONJ
ejpam-5978	330	8	the	the	DET
ejpam-5978	330	9	composition	composition	NOUN
ejpam-5978	330	10	of	of	ADP
ejpam-5978	330	11	graphs	graph	NOUN
ejpam-5978	330	12	.	.	PUNCT
ejpam-5978	331	1	international	international	ADJ
ejpam-5978	331	2	journal	journal	PROPN
ejpam-5978	331	3	of	of	ADP
ejpam-5978	331	4	mathematical	mathematical	ADJ
ejpam-5978	331	5	analysis	analysis	NOUN
ejpam-5978	331	6	,	,	PUNCT
ejpam-5978	331	7	10(11):515–529	10(11):515–529	NUM
ejpam-5978	331	8	,	,	PUNCT
ejpam-5978	331	9	2016	2016	NUM
ejpam-5978	331	10	.	.	PUNCT
ejpam-5978	332	1	e.j	e.j	PROPN
ejpam-5978	332	2	.	.	PROPN
ejpam-5978	332	3	aguilon	aguilon	PROPN
ejpam-5978	332	4	,	,	PUNCT
ejpam-5978	332	5	s.	s.	PROPN
ejpam-5978	332	6	dagondon	dagondon	PROPN
ejpam-5978	332	7	,	,	PUNCT
ejpam-5978	332	8	r.	r.	PROPN
ejpam-5978	332	9	artes	artes	PROPN
ejpam-5978	332	10	/	/	SYM
ejpam-5978	332	11	eur	eur	PROPN
ejpam-5978	332	12	.	.	PUNCT
ejpam-5978	333	1	j.	j.	PROPN
ejpam-5978	333	2	pure	pure	PROPN
ejpam-5978	333	3	appl	appl	PROPN
ejpam-5978	333	4	.	.	PROPN
ejpam-5978	333	5	math	math	PROPN
ejpam-5978	333	6	,	,	PUNCT
ejpam-5978	333	7	18	18	NUM
ejpam-5978	333	8	(	(	PUNCT
ejpam-5978	333	9	2	2	NUM
ejpam-5978	333	10	)	)	PUNCT
ejpam-5978	333	11	(	(	PUNCT
ejpam-5978	333	12	2025	2025	NUM
ejpam-5978	333	13	)	)	PUNCT
ejpam-5978	333	14	,	,	PUNCT
ejpam-5978	333	15	5978	5978	NUM
ejpam-5978	333	16	18	18	NUM
ejpam-5978	333	17	of	of	ADP
ejpam-5978	333	18	18	18	NUM
ejpam-5978	333	19	[	[	SYM
ejpam-5978	333	20	8	8	NUM
ejpam-5978	333	21	]	]	PUNCT
ejpam-5978	333	22	a.	a.	NOUN
ejpam-5978	333	23	arriesgado	arriesgado	NOUN
ejpam-5978	333	24	and	and	CCONJ
ejpam-5978	333	25	r.	r.	PROPN
ejpam-5978	333	26	artes	artes	PROPN
ejpam-5978	333	27	jr	jr	PROPN
ejpam-5978	333	28	.	.	PROPN
ejpam-5978	333	29	convex	convex	VERB
ejpam-5978	333	30	independent	independent	ADJ
ejpam-5978	333	31	common	common	ADJ
ejpam-5978	333	32	neighborhood	neighborhood	NOUN
ejpam-5978	333	33	polynomial	polynomial	NOUN
ejpam-5978	333	34	of	of	ADP
ejpam-5978	333	35	a	a	DET
ejpam-5978	333	36	graph	graph	NOUN
ejpam-5978	333	37	.	.	PUNCT
ejpam-5978	334	1	advances	advance	NOUN
ejpam-5978	334	2	and	and	CCONJ
ejpam-5978	334	3	applications	application	NOUN
ejpam-5978	334	4	in	in	ADP
ejpam-5978	334	5	discrete	discrete	ADJ
ejpam-5978	334	6	mathematics	mathematic	NOUN
ejpam-5978	334	7	,	,	PUNCT
ejpam-5978	334	8	38:145–158	38:145–158	PROPN
ejpam-5978	334	9	,	,	PUNCT
ejpam-5978	334	10	04	04	NUM
ejpam-5978	334	11	2023	2023	NUM
ejpam-5978	334	12	.	.	PUNCT
ejpam-5978	335	1	[	[	X
ejpam-5978	335	2	9	9	NUM
ejpam-5978	335	3	]	]	X
ejpam-5978	335	4	j.i	j.i	PROPN
ejpam-5978	335	5	.	.	PROPN
ejpam-5978	335	6	salim	salim	PROPN
ejpam-5978	335	7	s.	s.	PROPN
ejpam-5978	335	8	abdurasid	abdurasid	PROPN
ejpam-5978	335	9	,	,	PUNCT
ejpam-5978	335	10	b.	b.	PROPN
ejpam-5978	335	11	amiruddin	amiruddin	PROPN
ejpam-5978	335	12	and	and	CCONJ
ejpam-5978	335	13	r.	r.	PROPN
ejpam-5978	335	14	artes	artes	PROPN
ejpam-5978	335	15	jr	jr	PROPN
ejpam-5978	335	16	.	.	PROPN
ejpam-5978	336	1	convex	convex	PROPN
ejpam-5978	336	2	neighborhood	neighborhood	NOUN
ejpam-5978	336	3	polynomial	polynomial	NOUN
ejpam-5978	336	4	of	of	ADP
ejpam-5978	336	5	graphs	graph	NOUN
ejpam-5978	336	6	.	.	PUNCT
ejpam-5978	337	1	advances	advance	NOUN
ejpam-5978	337	2	&	&	CCONJ
ejpam-5978	337	3	applications	application	NOUN
ejpam-5978	337	4	in	in	ADP
ejpam-5978	337	5	discrete	discrete	ADJ
ejpam-5978	337	6	mathematics	mathematic	NOUN
ejpam-5978	337	7	,	,	PUNCT
ejpam-5978	337	8	40(1	40(1	NOUN
ejpam-5978	337	9	)	)	PUNCT
ejpam-5978	337	10	,	,	PUNCT
ejpam-5978	337	11	2023	2023	NUM
ejpam-5978	337	12	.	.	PUNCT
ejpam-5978	338	1	[	[	X
ejpam-5978	338	2	10	10	NUM
ejpam-5978	338	3	]	]	PUNCT
ejpam-5978	338	4	a.	a.	NOUN
ejpam-5978	338	5	fuentes	fuentes	PROPN
ejpam-5978	338	6	.	.	PUNCT
ejpam-5978	339	1	algebra	algebra	PROPN
ejpam-5978	339	2	.	.	PUNCT
ejpam-5978	340	1	a	a	DET
ejpam-5978	340	2	mathematical	mathematical	ADJ
ejpam-5978	340	3	analysis	analysis	NOUN
ejpam-5978	340	4	preliminary	preliminary	ADJ
ejpam-5978	340	5	to	to	ADP
ejpam-5978	340	6	calculus	calculus	NOUN
ejpam-5978	340	7	.	.	PUNCT
ejpam-5978	341	1	lulu	lulu	PROPN
ejpam-5978	341	2	.	.	PUNCT
ejpam-5978	341	3	com	com	NOUN
ejpam-5978	341	4	,	,	PUNCT
ejpam-5978	341	5	2016	2016	NUM
ejpam-5978	341	6	.	.	PUNCT