id	sid	tid	token	lemma	pos
ejpam-5332	1	1	european	european	PROPN
ejpam-5332	1	2	journal	journal	PROPN
ejpam-5332	1	3	of	of	ADP
ejpam-5332	1	4	pure	pure	ADJ
ejpam-5332	1	5	and	and	CCONJ
ejpam-5332	1	6	applied	apply	VERB
ejpam-5332	1	7	mathematics	mathematic	NOUN
ejpam-5332	1	8	vol	vol	NOUN
ejpam-5332	1	9	.	.	PROPN
ejpam-5332	2	1	17	17	NUM
ejpam-5332	2	2	,	,	PUNCT
ejpam-5332	2	3	no	no	INTJ
ejpam-5332	2	4	.	.	NOUN
ejpam-5332	2	5	4	4	NUM
ejpam-5332	2	6	,	,	PUNCT
ejpam-5332	2	7	2024	2024	NUM
ejpam-5332	2	8	,	,	PUNCT
ejpam-5332	2	9	2930	2930	NUM
ejpam-5332	2	10	-	-	SYM
ejpam-5332	2	11	2938	2938	NUM
ejpam-5332	2	12	issn	issn	PROPN
ejpam-5332	2	13	1307	1307	NUM
ejpam-5332	2	14	-	-	SYM
ejpam-5332	2	15	5543	5543	NUM
ejpam-5332	2	16	–	–	PUNCT
ejpam-5332	2	17	ejpam.com	ejpam.com	X
ejpam-5332	2	18	published	publish	VERB
ejpam-5332	2	19	by	by	ADP
ejpam-5332	2	20	new	new	PROPN
ejpam-5332	2	21	york	york	PROPN
ejpam-5332	2	22	business	business	PROPN
ejpam-5332	2	23	global	global	ADJ
ejpam-5332	2	24	convex	convex	NOUN
ejpam-5332	2	25	accessibility	accessibility	NOUN
ejpam-5332	2	26	number	number	NOUN
ejpam-5332	2	27	of	of	ADP
ejpam-5332	2	28	the	the	DET
ejpam-5332	2	29	complements	complement	NOUN
ejpam-5332	2	30	and	and	CCONJ
ejpam-5332	2	31	some	some	DET
ejpam-5332	2	32	binary	binary	ADJ
ejpam-5332	2	33	operations	operation	NOUN
ejpam-5332	2	34	of	of	ADP
ejpam-5332	2	35	graphs	graph	NOUN
ejpam-5332	2	36	harold	harold	PROPN
ejpam-5332	2	37	b.	b.	PROPN
ejpam-5332	2	38	samson1,∗	samson1,∗	PROPN
ejpam-5332	2	39	,	,	PUNCT
ejpam-5332	2	40	imelda	imelda	PROPN
ejpam-5332	2	41	s.	s.	PROPN
ejpam-5332	2	42	aniversario2	aniversario2	PROPN
ejpam-5332	2	43	,	,	PUNCT
ejpam-5332	2	44	mary	mary	PROPN
ejpam-5332	2	45	joy	joy	PROPN
ejpam-5332	2	46	f.	f.	PROPN
ejpam-5332	2	47	luga3	luga3	PROPN
ejpam-5332	2	48	1	1	NUM
ejpam-5332	2	49	mindanao	mindanao	PROPN
ejpam-5332	2	50	state	state	PROPN
ejpam-5332	2	51	university	university	PROPN
ejpam-5332	2	52	-	-	PUNCT
ejpam-5332	2	53	iligan	iligan	PROPN
ejpam-5332	2	54	institute	institute	PROPN
ejpam-5332	2	55	of	of	ADP
ejpam-5332	2	56	technology	technology	PROPN
ejpam-5332	2	57	,	,	PUNCT
ejpam-5332	2	58	9200	9200	NUM
ejpam-5332	2	59	iligan	iligan	ADJ
ejpam-5332	2	60	city	city	NOUN
ejpam-5332	2	61	,	,	PUNCT
ejpam-5332	2	62	philippines	philippines	PROPN
ejpam-5332	2	63	2	2	NUM
ejpam-5332	2	64	department	department	NOUN
ejpam-5332	2	65	of	of	ADP
ejpam-5332	2	66	mathematics	mathematic	NOUN
ejpam-5332	2	67	and	and	CCONJ
ejpam-5332	2	68	statistics	statistic	NOUN
ejpam-5332	2	69	,	,	PUNCT
ejpam-5332	2	70	college	college	NOUN
ejpam-5332	2	71	of	of	ADP
ejpam-5332	2	72	science	science	NOUN
ejpam-5332	2	73	and	and	CCONJ
ejpam-5332	2	74	mathematics	mathematic	NOUN
ejpam-5332	2	75	,	,	PUNCT
ejpam-5332	2	76	mindanao	mindanao	PROPN
ejpam-5332	2	77	state	state	PROPN
ejpam-5332	2	78	university	university	PROPN
ejpam-5332	2	79	-	-	PUNCT
ejpam-5332	2	80	iligan	iligan	PROPN
ejpam-5332	2	81	institute	institute	PROPN
ejpam-5332	2	82	of	of	ADP
ejpam-5332	2	83	technology	technology	PROPN
ejpam-5332	2	84	,	,	PUNCT
ejpam-5332	2	85	9200	9200	NUM
ejpam-5332	2	86	iligan	iligan	ADJ
ejpam-5332	2	87	city	city	NOUN
ejpam-5332	2	88	,	,	PUNCT
ejpam-5332	2	89	philippines	philippine	NOUN
ejpam-5332	2	90	3	3	NUM
ejpam-5332	2	91	integrated	integrate	VERB
ejpam-5332	2	92	developmental	developmental	ADJ
ejpam-5332	2	93	school	school	NOUN
ejpam-5332	2	94	,	,	PUNCT
ejpam-5332	2	95	college	college	NOUN
ejpam-5332	2	96	of	of	ADP
ejpam-5332	2	97	education	education	NOUN
ejpam-5332	2	98	,	,	PUNCT
ejpam-5332	2	99	mindanao	mindanao	PROPN
ejpam-5332	2	100	state	state	PROPN
ejpam-5332	2	101	university	university	PROPN
ejpam-5332	2	102	-	-	PUNCT
ejpam-5332	2	103	iligan	iligan	PROPN
ejpam-5332	2	104	institute	institute	PROPN
ejpam-5332	2	105	of	of	ADP
ejpam-5332	2	106	technology	technology	PROPN
ejpam-5332	2	107	,	,	PUNCT
ejpam-5332	2	108	9200	9200	NUM
ejpam-5332	2	109	iligan	iligan	ADJ
ejpam-5332	2	110	city	city	NOUN
ejpam-5332	2	111	,	,	PUNCT
ejpam-5332	2	112	philippines	philippine	NOUN
ejpam-5332	2	113	abstract	abstract	ADJ
ejpam-5332	2	114	.	.	PUNCT
ejpam-5332	3	1	this	this	DET
ejpam-5332	3	2	study	study	NOUN
ejpam-5332	3	3	explores	explore	VERB
ejpam-5332	3	4	various	various	ADJ
ejpam-5332	3	5	aspects	aspect	NOUN
ejpam-5332	3	6	of	of	ADP
ejpam-5332	3	7	the	the	DET
ejpam-5332	3	8	convex	convex	NOUN
ejpam-5332	3	9	accessibility	accessibility	NOUN
ejpam-5332	3	10	number	number	NOUN
ejpam-5332	3	11	in	in	ADP
ejpam-5332	3	12	graph	graph	NOUN
ejpam-5332	3	13	theory	theory	NOUN
ejpam-5332	3	14	,	,	PUNCT
ejpam-5332	3	15	focusing	focus	VERB
ejpam-5332	3	16	on	on	ADP
ejpam-5332	3	17	some	some	DET
ejpam-5332	3	18	binary	binary	ADJ
ejpam-5332	3	19	operations	operation	NOUN
ejpam-5332	3	20	namely	namely	ADV
ejpam-5332	3	21	cartesian	cartesian	ADJ
ejpam-5332	3	22	product	product	NOUN
ejpam-5332	3	23	and	and	CCONJ
ejpam-5332	3	24	strong	strong	ADJ
ejpam-5332	3	25	product	product	NOUN
ejpam-5332	3	26	and	and	CCONJ
ejpam-5332	3	27	complements	complement	NOUN
ejpam-5332	3	28	of	of	ADP
ejpam-5332	3	29	graphs	graph	NOUN
ejpam-5332	3	30	.	.	PUNCT
ejpam-5332	4	1	the	the	DET
ejpam-5332	4	2	computation	computation	NOUN
ejpam-5332	4	3	of	of	ADP
ejpam-5332	4	4	the	the	DET
ejpam-5332	4	5	convex	convex	NOUN
ejpam-5332	4	6	accessibility	accessibility	NOUN
ejpam-5332	4	7	number	number	NOUN
ejpam-5332	4	8	of	of	ADP
ejpam-5332	4	9	cartesian	cartesian	ADJ
ejpam-5332	4	10	product	product	NOUN
ejpam-5332	4	11	and	and	CCONJ
ejpam-5332	4	12	strong	strong	ADJ
ejpam-5332	4	13	product	product	NOUN
ejpam-5332	4	14	of	of	ADP
ejpam-5332	4	15	graphs	graph	NOUN
ejpam-5332	4	16	is	be	AUX
ejpam-5332	4	17	examined	examine	VERB
ejpam-5332	4	18	.	.	PUNCT
ejpam-5332	5	1	also	also	ADV
ejpam-5332	5	2	,	,	PUNCT
ejpam-5332	5	3	the	the	DET
ejpam-5332	5	4	convex	convex	NOUN
ejpam-5332	5	5	accessibility	accessibility	NOUN
ejpam-5332	5	6	number	number	NOUN
ejpam-5332	5	7	of	of	ADP
ejpam-5332	5	8	the	the	DET
ejpam-5332	5	9	complement	complement	NOUN
ejpam-5332	5	10	of	of	ADP
ejpam-5332	5	11	some	some	DET
ejpam-5332	5	12	known	know	VERB
ejpam-5332	5	13	graphs	graph	NOUN
ejpam-5332	5	14	is	be	AUX
ejpam-5332	5	15	explored	explore	VERB
ejpam-5332	5	16	.	.	PUNCT
ejpam-5332	6	1	through	through	ADP
ejpam-5332	6	2	these	these	DET
ejpam-5332	6	3	investigations	investigation	NOUN
ejpam-5332	6	4	,	,	PUNCT
ejpam-5332	6	5	this	this	DET
ejpam-5332	6	6	study	study	NOUN
ejpam-5332	6	7	contributes	contribute	VERB
ejpam-5332	6	8	to	to	ADP
ejpam-5332	6	9	a	a	DET
ejpam-5332	6	10	deeper	deep	ADJ
ejpam-5332	6	11	understanding	understanding	NOUN
ejpam-5332	6	12	of	of	ADP
ejpam-5332	6	13	the	the	DET
ejpam-5332	6	14	convex	convex	NOUN
ejpam-5332	6	15	accessibility	accessibility	NOUN
ejpam-5332	6	16	number	number	NOUN
ejpam-5332	6	17	in	in	ADP
ejpam-5332	6	18	graph	graph	NOUN
ejpam-5332	6	19	theory	theory	NOUN
ejpam-5332	6	20	,	,	PUNCT
ejpam-5332	6	21	offering	offer	VERB
ejpam-5332	6	22	insights	insight	NOUN
ejpam-5332	6	23	into	into	ADP
ejpam-5332	6	24	its	its	PRON
ejpam-5332	6	25	behavior	behavior	NOUN
ejpam-5332	6	26	under	under	ADP
ejpam-5332	6	27	different	different	ADJ
ejpam-5332	6	28	graph	graph	NOUN
ejpam-5332	6	29	operations	operation	NOUN
ejpam-5332	6	30	and	and	CCONJ
ejpam-5332	6	31	complementation	complementation	NOUN
ejpam-5332	6	32	scenarios	scenario	NOUN
ejpam-5332	6	33	.	.	PUNCT
ejpam-5332	7	1	2020	2020	NUM
ejpam-5332	7	2	mathematics	mathematic	NOUN
ejpam-5332	7	3	subject	subject	NOUN
ejpam-5332	7	4	classifications	classification	NOUN
ejpam-5332	7	5	:	:	PUNCT
ejpam-5332	7	6	05c12	05c12	X
ejpam-5332	7	7	key	key	ADJ
ejpam-5332	7	8	words	word	NOUN
ejpam-5332	7	9	and	and	CCONJ
ejpam-5332	7	10	phrases	phrase	NOUN
ejpam-5332	7	11	:	:	PUNCT
ejpam-5332	7	12	h	h	ADJ
ejpam-5332	7	13	-	-	PUNCT
ejpam-5332	7	14	convex	convex	NOUN
ejpam-5332	7	15	accessibility	accessibility	NOUN
ejpam-5332	7	16	number	number	NOUN
ejpam-5332	7	17	,	,	PUNCT
ejpam-5332	7	18	convex	convex	NOUN
ejpam-5332	7	19	subgraph	subgraph	NOUN
ejpam-5332	7	20	,	,	PUNCT
ejpam-5332	7	21	strong	strong	ADJ
ejpam-5332	7	22	product	product	NOUN
ejpam-5332	7	23	,	,	PUNCT
ejpam-5332	7	24	cartesian	cartesian	ADJ
ejpam-5332	7	25	product	product	NOUN
ejpam-5332	7	26	,	,	PUNCT
ejpam-5332	7	27	complement	complement	NOUN
ejpam-5332	7	28	of	of	ADP
ejpam-5332	7	29	a	a	DET
ejpam-5332	7	30	graph	graph	NOUN
ejpam-5332	7	31	,	,	PUNCT
ejpam-5332	7	32	accessibility	accessibility	NOUN
ejpam-5332	7	33	number	number	NOUN
ejpam-5332	7	34	1	1	NUM
ejpam-5332	7	35	.	.	PUNCT
ejpam-5332	7	36	introduction	introduction	NOUN
ejpam-5332	7	37	the	the	DET
ejpam-5332	7	38	concept	concept	NOUN
ejpam-5332	7	39	of	of	ADP
ejpam-5332	7	40	h	h	NOUN
ejpam-5332	7	41	-	-	PUNCT
ejpam-5332	7	42	convex	convex	NOUN
ejpam-5332	7	43	accessibility	accessibility	NOUN
ejpam-5332	7	44	number	number	NOUN
ejpam-5332	7	45	was	be	AUX
ejpam-5332	7	46	introduced	introduce	VERB
ejpam-5332	7	47	by	by	ADP
ejpam-5332	7	48	r.	r.	PROPN
ejpam-5332	7	49	g.	g.	PROPN
ejpam-5332	7	50	artes	artes	PROPN
ejpam-5332	7	51	,	,	PUNCT
ejpam-5332	7	52	jr	jr	PROPN
ejpam-5332	7	53	.	.	PROPN
ejpam-5332	7	54	and	and	CCONJ
ejpam-5332	7	55	m.j	m.j	PROPN
ejpam-5332	7	56	.	.	PROPN
ejpam-5332	7	57	f.	f.	PROPN
ejpam-5332	7	58	luga	luga	PROPN
ejpam-5332	8	1	[	[	X
ejpam-5332	8	2	3	3	X
ejpam-5332	8	3	]	]	X
ejpam-5332	8	4	[	[	X
ejpam-5332	8	5	2	2	NUM
ejpam-5332	8	6	]	]	PUNCT
ejpam-5332	8	7	in	in	ADP
ejpam-5332	8	8	2014	2014	NUM
ejpam-5332	8	9	,	,	PUNCT
ejpam-5332	8	10	it	it	PRON
ejpam-5332	8	11	was	be	AUX
ejpam-5332	8	12	about	about	ADP
ejpam-5332	8	13	the	the	DET
ejpam-5332	8	14	h	h	NOUN
ejpam-5332	8	15	-	-	PUNCT
ejpam-5332	8	16	convex	convex	NOUN
ejpam-5332	8	17	accessibility	accessibility	NOUN
ejpam-5332	8	18	number	number	NOUN
ejpam-5332	8	19	of	of	ADP
ejpam-5332	8	20	some	some	DET
ejpam-5332	8	21	graphs	graph	NOUN
ejpam-5332	8	22	and	and	CCONJ
ejpam-5332	8	23	graphs	graph	NOUN
ejpam-5332	8	24	under	under	ADP
ejpam-5332	8	25	binary	binary	ADJ
ejpam-5332	8	26	operations	operation	NOUN
ejpam-5332	8	27	join	join	VERB
ejpam-5332	8	28	,	,	PUNCT
ejpam-5332	8	29	corona	corona	NOUN
ejpam-5332	8	30	and	and	CCONJ
ejpam-5332	8	31	composition	composition	NOUN
ejpam-5332	8	32	.	.	PUNCT
ejpam-5332	9	1	this	this	DET
ejpam-5332	9	2	paper	paper	NOUN
ejpam-5332	9	3	presents	present	VERB
ejpam-5332	9	4	the	the	DET
ejpam-5332	9	5	h	h	NOUN
ejpam-5332	9	6	-	-	PUNCT
ejpam-5332	9	7	convex	convex	NOUN
ejpam-5332	9	8	accessibility	accessibility	NOUN
ejpam-5332	9	9	number	number	NOUN
ejpam-5332	9	10	for	for	ADP
ejpam-5332	9	11	various	various	ADJ
ejpam-5332	9	12	graph	graph	NOUN
ejpam-5332	9	13	operations	operation	NOUN
ejpam-5332	9	14	such	such	ADJ
ejpam-5332	9	15	as	as	ADP
ejpam-5332	9	16	cartesian	cartesian	ADJ
ejpam-5332	9	17	products	product	NOUN
ejpam-5332	9	18	,	,	PUNCT
ejpam-5332	9	19	strong	strong	ADJ
ejpam-5332	9	20	products	product	NOUN
ejpam-5332	9	21	,	,	PUNCT
ejpam-5332	9	22	and	and	CCONJ
ejpam-5332	9	23	complements	complement	NOUN
ejpam-5332	9	24	was	be	AUX
ejpam-5332	9	25	determined	determine	VERB
ejpam-5332	9	26	by	by	ADP
ejpam-5332	9	27	analyzing	analyze	VERB
ejpam-5332	9	28	how	how	SCONJ
ejpam-5332	9	29	the	the	DET
ejpam-5332	9	30	proper	proper	ADJ
ejpam-5332	9	31	convex	convex	NOUN
ejpam-5332	9	32	subgraphs	subgraphs	NOUN
ejpam-5332	9	33	influence	influence	VERB
ejpam-5332	9	34	the	the	DET
ejpam-5332	9	35	accessibility	accessibility	NOUN
ejpam-5332	9	36	number	number	NOUN
ejpam-5332	9	37	.	.	PUNCT
ejpam-5332	10	1	as	as	ADP
ejpam-5332	10	2	the	the	DET
ejpam-5332	10	3	size	size	NOUN
ejpam-5332	10	4	of	of	ADP
ejpam-5332	10	5	these	these	DET
ejpam-5332	10	6	proper	proper	ADJ
ejpam-5332	10	7	convex	convex	NOUN
ejpam-5332	10	8	subgraphs	subgraphs	NOUN
ejpam-5332	10	9	increases	increase	NOUN
ejpam-5332	10	10	,	,	PUNCT
ejpam-5332	10	11	the	the	DET
ejpam-5332	10	12	convex	convex	NOUN
ejpam-5332	10	13	accessibility	accessibility	NOUN
ejpam-5332	10	14	number	number	NOUN
ejpam-5332	10	15	tends	tend	VERB
ejpam-5332	10	16	to	to	PART
ejpam-5332	10	17	approach	approach	VERB
ejpam-5332	10	18	1	1	NUM
ejpam-5332	10	19	.	.	PUNCT
ejpam-5332	11	1	therefore	therefore	ADV
ejpam-5332	11	2	,	,	PUNCT
ejpam-5332	11	3	by	by	ADP
ejpam-5332	11	4	starting	start	VERB
ejpam-5332	11	5	with	with	ADP
ejpam-5332	11	6	smaller	small	ADJ
ejpam-5332	11	7	convex	convex	NOUN
ejpam-5332	11	8	subgraphs	subgraph	NOUN
ejpam-5332	11	9	and	and	CCONJ
ejpam-5332	11	10	progressively	progressively	ADV
ejpam-5332	11	11	expanding	expand	VERB
ejpam-5332	11	12	their	their	PRON
ejpam-5332	11	13	size	size	NOUN
ejpam-5332	11	14	,	,	PUNCT
ejpam-5332	11	15	the	the	DET
ejpam-5332	11	16	study	study	NOUN
ejpam-5332	11	17	aimed	aim	VERB
ejpam-5332	11	18	to	to	PART
ejpam-5332	11	19	derive	derive	VERB
ejpam-5332	11	20	a	a	DET
ejpam-5332	11	21	general	general	ADJ
ejpam-5332	11	22	formula	formula	NOUN
ejpam-5332	11	23	by	by	ADP
ejpam-5332	11	24	comparing	compare	VERB
ejpam-5332	11	25	the	the	DET
ejpam-5332	11	26	convex	convex	NOUN
ejpam-5332	11	27	accessibility	accessibility	NOUN
ejpam-5332	11	28	numbers	number	NOUN
ejpam-5332	11	29	across	across	ADP
ejpam-5332	11	30	different	different	ADJ
ejpam-5332	11	31	graph	graph	NOUN
ejpam-5332	11	32	configurations	configuration	NOUN
ejpam-5332	11	33	.	.	PUNCT
ejpam-5332	12	1	the	the	DET
ejpam-5332	12	2	distance	distance	NOUN
ejpam-5332	12	3	from	from	ADP
ejpam-5332	12	4	a	a	DET
ejpam-5332	12	5	vertex	vertex	NOUN
ejpam-5332	12	6	∗corresponding	∗corresponde	VERB
ejpam-5332	12	7	author	author	NOUN
ejpam-5332	12	8	.	.	PUNCT
ejpam-5332	13	1	doi	doi	NOUN
ejpam-5332	13	2	:	:	PUNCT
ejpam-5332	13	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5332	https://doi.org/10.29020/nybg.ejpam.v17i4.5332	NUM
ejpam-5332	13	4	email	email	NOUN
ejpam-5332	13	5	addresses	address	NOUN
ejpam-5332	13	6	:	:	PUNCT
ejpam-5332	13	7	harold.samson@g.msuiit.edu.ph	harold.samson@g.msuiit.edu.ph	PROPN
ejpam-5332	13	8	(	(	PUNCT
ejpam-5332	13	9	h.	h.	PROPN
ejpam-5332	13	10	samson	samson	PROPN
ejpam-5332	13	11	)	)	PUNCT
ejpam-5332	13	12	,	,	PUNCT
ejpam-5332	13	13	imelda.aniverario@g.msuiit.edu.ph	imelda.aniverario@g.msuiit.edu.ph	PROPN
ejpam-5332	13	14	(	(	PUNCT
ejpam-5332	13	15	i.	i.	PROPN
ejpam-5332	13	16	aniversario	aniversario	PROPN
ejpam-5332	13	17	)	)	PUNCT
ejpam-5332	13	18	,	,	PUNCT
ejpam-5332	13	19	maryjoy.luga@g.msuiit.edu.ph	maryjoy.luga@g.msuiit.edu.ph	PROPN
ejpam-5332	13	20	(	(	PUNCT
ejpam-5332	13	21	m.j	m.j	PROPN
ejpam-5332	13	22	.	.	PROPN
ejpam-5332	13	23	luga	luga	PROPN
ejpam-5332	13	24	)	)	PUNCT
ejpam-5332	13	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5332	14	1	2930	2930	NUM
ejpam-5332	15	1	copyright	copyright	NOUN
ejpam-5332	15	2	:	:	PUNCT
ejpam-5332	15	3	©	©	PROPN
ejpam-5332	15	4	2024	2024	NUM
ejpam-5332	15	5	the	the	DET
ejpam-5332	15	6	author(s	author(s	NOUN
ejpam-5332	15	7	)	)	PUNCT
ejpam-5332	15	8	.	.	PUNCT
ejpam-5332	16	1	(	(	PUNCT
ejpam-5332	16	2	cc	cc	NOUN
ejpam-5332	16	3	by	by	ADP
ejpam-5332	16	4	-	-	PUNCT
ejpam-5332	16	5	nc	nc	PROPN
ejpam-5332	16	6	4.0	4.0	NUM
ejpam-5332	16	7	)	)	PUNCT
ejpam-5332	16	8	h.	h.	PROPN
ejpam-5332	16	9	b.	b.	PROPN
ejpam-5332	16	10	samson	samson	PROPN
ejpam-5332	16	11	,	,	PUNCT
ejpam-5332	16	12	i.	i.	PROPN
ejpam-5332	16	13	s.	s.	PROPN
ejpam-5332	16	14	aniversario	aniversario	PROPN
ejpam-5332	16	15	,	,	PUNCT
ejpam-5332	16	16	m.	m.	PROPN
ejpam-5332	16	17	j.	j.	PROPN
ejpam-5332	16	18	f.	f.	PROPN
ejpam-5332	16	19	luga	luga	PROPN
ejpam-5332	16	20	/	/	SYM
ejpam-5332	16	21	eur	eur	PROPN
ejpam-5332	16	22	.	.	PUNCT
ejpam-5332	17	1	j.	j.	PROPN
ejpam-5332	17	2	pure	pure	PROPN
ejpam-5332	17	3	appl	appl	PROPN
ejpam-5332	17	4	.	.	PROPN
ejpam-5332	17	5	math	math	PROPN
ejpam-5332	17	6	,	,	PUNCT
ejpam-5332	17	7	17	17	NUM
ejpam-5332	17	8	(	(	PUNCT
ejpam-5332	17	9	4	4	NUM
ejpam-5332	17	10	)	)	PUNCT
ejpam-5332	17	11	(	(	PUNCT
ejpam-5332	17	12	2024	2024	NUM
ejpam-5332	17	13	)	)	PUNCT
ejpam-5332	17	14	,	,	PUNCT
ejpam-5332	17	15	2930	2930	NUM
ejpam-5332	17	16	-	-	SYM
ejpam-5332	17	17	2938	2938	NUM
ejpam-5332	17	18	2931	2931	NUM
ejpam-5332	17	19	u	u	NOUN
ejpam-5332	17	20	to	to	ADP
ejpam-5332	17	21	a	a	DET
ejpam-5332	17	22	subgraph	subgraph	NOUN
ejpam-5332	17	23	h	h	NOUN
ejpam-5332	17	24	is	be	AUX
ejpam-5332	17	25	defined	define	VERB
ejpam-5332	17	26	as	as	ADP
ejpam-5332	17	27	the	the	DET
ejpam-5332	17	28	shortest	short	ADJ
ejpam-5332	17	29	path	path	NOUN
ejpam-5332	17	30	between	between	ADP
ejpam-5332	17	31	u	u	NOUN
ejpam-5332	17	32	and	and	CCONJ
ejpam-5332	17	33	any	any	DET
ejpam-5332	17	34	vertex	vertex	NOUN
ejpam-5332	17	35	v	v	ADP
ejpam-5332	17	36	∈	∈	PROPN
ejpam-5332	17	37	h.	h.	NOUN
ejpam-5332	17	38	in	in	ADP
ejpam-5332	17	39	this	this	DET
ejpam-5332	17	40	paper	paper	NOUN
ejpam-5332	17	41	,	,	PUNCT
ejpam-5332	17	42	the	the	DET
ejpam-5332	17	43	subgraph	subgraph	NOUN
ejpam-5332	17	44	h	h	NOUN
ejpam-5332	17	45	is	be	AUX
ejpam-5332	17	46	required	require	VERB
ejpam-5332	17	47	to	to	PART
ejpam-5332	17	48	be	be	AUX
ejpam-5332	17	49	a	a	DET
ejpam-5332	17	50	proper	proper	ADJ
ejpam-5332	17	51	convex	convex	NOUN
ejpam-5332	17	52	subgraph	subgraph	NOUN
ejpam-5332	17	53	of	of	ADP
ejpam-5332	17	54	a	a	DET
ejpam-5332	17	55	graph	graph	NOUN
ejpam-5332	17	56	g.	g.	NOUN
ejpam-5332	17	57	the	the	DET
ejpam-5332	17	58	accessibility	accessibility	NOUN
ejpam-5332	17	59	number	number	NOUN
ejpam-5332	17	60	is	be	AUX
ejpam-5332	17	61	defined	define	VERB
ejpam-5332	17	62	as	as	ADP
ejpam-5332	17	63	the	the	DET
ejpam-5332	17	64	minimum	minimum	NOUN
ejpam-5332	17	65	k	k	NOUN
ejpam-5332	17	66	for	for	ADP
ejpam-5332	17	67	which	which	PRON
ejpam-5332	17	68	g	g	NOUN
ejpam-5332	17	69	is	be	AUX
ejpam-5332	17	70	h	h	NOUN
ejpam-5332	17	71	-	-	PUNCT
ejpam-5332	17	72	convex	convex	ADJ
ejpam-5332	17	73	kaccessible	kaccessible	NOUN
ejpam-5332	17	74	.	.	PUNCT
ejpam-5332	18	1	the	the	DET
ejpam-5332	18	2	convex	convex	ADJ
ejpam-5332	18	3	accessibility	accessibility	NOUN
ejpam-5332	18	4	number	number	NOUN
ejpam-5332	18	5	of	of	ADP
ejpam-5332	18	6	a	a	DET
ejpam-5332	18	7	graph	graph	NOUN
ejpam-5332	18	8	helps	help	VERB
ejpam-5332	18	9	in	in	ADP
ejpam-5332	18	10	covering	cover	VERB
ejpam-5332	18	11	all	all	DET
ejpam-5332	18	12	points	point	NOUN
ejpam-5332	18	13	with	with	ADP
ejpam-5332	18	14	the	the	DET
ejpam-5332	18	15	minimum	minimum	ADJ
ejpam-5332	18	16	number	number	NOUN
ejpam-5332	18	17	of	of	ADP
ejpam-5332	18	18	surveillance	surveillance	NOUN
ejpam-5332	18	19	cameras	camera	NOUN
ejpam-5332	18	20	,	,	PUNCT
ejpam-5332	18	21	which	which	PRON
ejpam-5332	18	22	is	be	AUX
ejpam-5332	18	23	essential	essential	ADJ
ejpam-5332	18	24	for	for	ADP
ejpam-5332	18	25	secure	secure	ADJ
ejpam-5332	18	26	network	network	NOUN
ejpam-5332	18	27	design	design	NOUN
ejpam-5332	18	28	.	.	PUNCT
ejpam-5332	19	1	it	it	PRON
ejpam-5332	19	2	also	also	ADV
ejpam-5332	19	3	aids	aid	VERB
ejpam-5332	19	4	in	in	ADP
ejpam-5332	19	5	placing	place	VERB
ejpam-5332	19	6	key	key	ADJ
ejpam-5332	19	7	facilities	facility	NOUN
ejpam-5332	19	8	like	like	ADP
ejpam-5332	19	9	hospitals	hospital	NOUN
ejpam-5332	19	10	or	or	CCONJ
ejpam-5332	19	11	fire	fire	NOUN
ejpam-5332	19	12	stations	station	NOUN
ejpam-5332	19	13	to	to	PART
ejpam-5332	19	14	improve	improve	VERB
ejpam-5332	19	15	emergency	emergency	NOUN
ejpam-5332	19	16	response	response	NOUN
ejpam-5332	19	17	times	time	NOUN
ejpam-5332	19	18	.	.	PUNCT
ejpam-5332	20	1	in	in	ADP
ejpam-5332	20	2	wireless	wireless	ADJ
ejpam-5332	20	3	sensor	sensor	NOUN
ejpam-5332	20	4	networks	network	NOUN
ejpam-5332	20	5	,	,	PUNCT
ejpam-5332	20	6	it	it	PRON
ejpam-5332	20	7	determines	determine	VERB
ejpam-5332	20	8	the	the	DET
ejpam-5332	20	9	optimal	optimal	ADJ
ejpam-5332	20	10	sensor	sensor	NOUN
ejpam-5332	20	11	placement	placement	NOUN
ejpam-5332	20	12	for	for	ADP
ejpam-5332	20	13	full	full	ADJ
ejpam-5332	20	14	coverage	coverage	NOUN
ejpam-5332	20	15	,	,	PUNCT
ejpam-5332	20	16	ensuring	ensure	VERB
ejpam-5332	20	17	efficient	efficient	ADJ
ejpam-5332	20	18	resource	resource	NOUN
ejpam-5332	20	19	use	use	NOUN
ejpam-5332	20	20	.	.	PUNCT
ejpam-5332	21	1	all	all	DET
ejpam-5332	21	2	the	the	DET
ejpam-5332	21	3	graphs	graph	NOUN
ejpam-5332	21	4	considered	consider	VERB
ejpam-5332	21	5	in	in	ADP
ejpam-5332	21	6	this	this	DET
ejpam-5332	21	7	study	study	NOUN
ejpam-5332	21	8	are	be	AUX
ejpam-5332	21	9	finite	finite	ADJ
ejpam-5332	21	10	,	,	PUNCT
ejpam-5332	21	11	undirected	undirected	ADJ
ejpam-5332	21	12	and	and	CCONJ
ejpam-5332	21	13	connected	connected	ADJ
ejpam-5332	21	14	.	.	PUNCT
ejpam-5332	22	1	most	most	ADJ
ejpam-5332	22	2	of	of	ADP
ejpam-5332	22	3	the	the	DET
ejpam-5332	22	4	definitions	definition	NOUN
ejpam-5332	22	5	are	be	AUX
ejpam-5332	22	6	from	from	ADP
ejpam-5332	22	7	[	[	X
ejpam-5332	22	8	1	1	NUM
ejpam-5332	22	9	]	]	PUNCT
ejpam-5332	22	10	.	.	PUNCT
ejpam-5332	23	1	those	those	PRON
ejpam-5332	23	2	that	that	PRON
ejpam-5332	23	3	are	be	AUX
ejpam-5332	23	4	not	not	PART
ejpam-5332	23	5	from	from	ADP
ejpam-5332	23	6	the	the	DET
ejpam-5332	23	7	said	say	VERB
ejpam-5332	23	8	source	source	NOUN
ejpam-5332	23	9	are	be	AUX
ejpam-5332	23	10	so	so	ADV
ejpam-5332	23	11	indicated	indicate	VERB
ejpam-5332	23	12	.	.	PUNCT
ejpam-5332	24	1	the	the	DET
ejpam-5332	24	2	symbols	symbol	NOUN
ejpam-5332	24	3	v	v	ADP
ejpam-5332	24	4	(	(	PUNCT
ejpam-5332	24	5	g	g	NOUN
ejpam-5332	24	6	)	)	PUNCT
ejpam-5332	24	7	and	and	CCONJ
ejpam-5332	24	8	e(g	e(g	PROPN
ejpam-5332	24	9	)	)	PUNCT
ejpam-5332	24	10	denote	denote	VERB
ejpam-5332	24	11	the	the	DET
ejpam-5332	24	12	vertex	vertex	NOUN
ejpam-5332	24	13	set	set	NOUN
ejpam-5332	24	14	and	and	CCONJ
ejpam-5332	24	15	edge	edge	NOUN
ejpam-5332	24	16	set	set	NOUN
ejpam-5332	24	17	of	of	ADP
ejpam-5332	24	18	g.	g.	PROPN
ejpam-5332	24	19	an	an	DET
ejpam-5332	24	20	edge	edge	NOUN
ejpam-5332	24	21	joining	join	VERB
ejpam-5332	24	22	vertices	vertice	VERB
ejpam-5332	24	23	u	u	NOUN
ejpam-5332	24	24	,	,	PUNCT
ejpam-5332	24	25	v	v	PROPN
ejpam-5332	24	26	∈	∈	PROPN
ejpam-5332	24	27	g	g	NOUN
ejpam-5332	24	28	is	be	AUX
ejpam-5332	24	29	denoted	denote	VERB
ejpam-5332	24	30	by	by	ADP
ejpam-5332	24	31	[	[	X
ejpam-5332	24	32	u	u	NOUN
ejpam-5332	24	33	,	,	PUNCT
ejpam-5332	24	34	v	v	ADP
ejpam-5332	24	35	]	]	PUNCT
ejpam-5332	24	36	.	.	PUNCT
ejpam-5332	25	1	in	in	ADP
ejpam-5332	25	2	this	this	DET
ejpam-5332	25	3	case	case	NOUN
ejpam-5332	25	4	,	,	PUNCT
ejpam-5332	25	5	u	u	NOUN
ejpam-5332	25	6	and	and	CCONJ
ejpam-5332	25	7	v	v	NOUN
ejpam-5332	25	8	are	be	AUX
ejpam-5332	25	9	adjacent	adjacent	ADJ
ejpam-5332	25	10	.	.	PUNCT
ejpam-5332	26	1	a	a	DET
ejpam-5332	26	2	graph	graph	NOUN
ejpam-5332	26	3	h	h	NOUN
ejpam-5332	26	4	is	be	AUX
ejpam-5332	26	5	a	a	DET
ejpam-5332	26	6	subgraph	subgraph	NOUN
ejpam-5332	26	7	of	of	ADP
ejpam-5332	26	8	a	a	DET
ejpam-5332	26	9	graph	graph	NOUN
ejpam-5332	26	10	g	g	NOUN
ejpam-5332	26	11	,	,	PUNCT
ejpam-5332	26	12	denoted	denote	VERB
ejpam-5332	26	13	by	by	ADP
ejpam-5332	26	14	h	h	PROPN
ejpam-5332	26	15	⪯	⪯	PROPN
ejpam-5332	26	16	g	g	NOUN
ejpam-5332	26	17	,	,	PUNCT
ejpam-5332	26	18	if	if	SCONJ
ejpam-5332	26	19	v	v	X
ejpam-5332	26	20	(	(	PUNCT
ejpam-5332	26	21	h	h	NOUN
ejpam-5332	26	22	)	)	PUNCT
ejpam-5332	26	23	⊆	⊆	NUM
ejpam-5332	26	24	v	v	NOUN
ejpam-5332	26	25	(	(	PUNCT
ejpam-5332	26	26	g	g	NOUN
ejpam-5332	26	27	)	)	PUNCT
ejpam-5332	26	28	and	and	CCONJ
ejpam-5332	26	29	e(h	e(h	NOUN
ejpam-5332	26	30	)	)	PUNCT
ejpam-5332	26	31	⊆	⊆	NUM
ejpam-5332	26	32	e(g	e(g	PROPN
ejpam-5332	26	33	)	)	PUNCT
ejpam-5332	26	34	.	.	PUNCT
ejpam-5332	27	1	a	a	DET
ejpam-5332	27	2	graph	graph	NOUN
ejpam-5332	27	3	h	h	NOUN
ejpam-5332	27	4	=	=	PUNCT
ejpam-5332	27	5	⟨v	⟨v	PROPN
ejpam-5332	27	6	(	(	PUNCT
ejpam-5332	27	7	h)⟩	h)⟩	PROPN
ejpam-5332	27	8	is	be	AUX
ejpam-5332	27	9	an	an	DET
ejpam-5332	27	10	induced	induced	ADJ
ejpam-5332	27	11	subgraph	subgraph	NOUN
ejpam-5332	27	12	of	of	ADP
ejpam-5332	27	13	a	a	DET
ejpam-5332	27	14	graph	graph	NOUN
ejpam-5332	27	15	g	g	NOUN
ejpam-5332	27	16	if	if	SCONJ
ejpam-5332	27	17	h	h	NOUN
ejpam-5332	27	18	⪯	⪯	VERB
ejpam-5332	27	19	g	g	PROPN
ejpam-5332	27	20	and	and	CCONJ
ejpam-5332	27	21	two	two	NUM
ejpam-5332	27	22	vertices	vertex	NOUN
ejpam-5332	27	23	in	in	ADP
ejpam-5332	27	24	h	h	NOUN
ejpam-5332	27	25	are	be	AUX
ejpam-5332	27	26	adjacent	adjacent	ADJ
ejpam-5332	27	27	whenever	whenever	SCONJ
ejpam-5332	27	28	they	they	PRON
ejpam-5332	27	29	are	be	AUX
ejpam-5332	27	30	adjacent	adjacent	ADJ
ejpam-5332	27	31	in	in	ADP
ejpam-5332	27	32	g.	g.	PROPN
ejpam-5332	27	33	a	a	DET
ejpam-5332	27	34	graph	graph	NOUN
ejpam-5332	27	35	h	h	NOUN
ejpam-5332	27	36	is	be	AUX
ejpam-5332	27	37	a	a	DET
ejpam-5332	27	38	proper	proper	ADJ
ejpam-5332	27	39	subgraph	subgraph	NOUN
ejpam-5332	27	40	of	of	ADP
ejpam-5332	27	41	g	g	PROPN
ejpam-5332	27	42	if	if	SCONJ
ejpam-5332	27	43	e(g	e(g	PROPN
ejpam-5332	27	44	)	)	PUNCT
ejpam-5332	27	45	\	\	PROPN
ejpam-5332	28	1	e(h	e(h	PROPN
ejpam-5332	28	2	)	)	PUNCT
ejpam-5332	28	3	̸=	̸=	PROPN
ejpam-5332	28	4	∅.	∅.	ADV
ejpam-5332	28	5	given	give	VERB
ejpam-5332	28	6	a	a	DET
ejpam-5332	28	7	connected	connected	ADJ
ejpam-5332	28	8	graph	graph	NOUN
ejpam-5332	28	9	g	g	NOUN
ejpam-5332	28	10	,	,	PUNCT
ejpam-5332	28	11	the	the	DET
ejpam-5332	28	12	distance	distance	NOUN
ejpam-5332	28	13	between	between	ADP
ejpam-5332	28	14	two	two	NUM
ejpam-5332	28	15	vertices	vertex	NOUN
ejpam-5332	28	16	u	u	NOUN
ejpam-5332	28	17	and	and	CCONJ
ejpam-5332	28	18	v	v	NOUN
ejpam-5332	28	19	in	in	ADP
ejpam-5332	28	20	g	g	NOUN
ejpam-5332	28	21	,	,	PUNCT
ejpam-5332	28	22	denoted	denote	VERB
ejpam-5332	28	23	by	by	ADP
ejpam-5332	28	24	dg(u	dg(u	PROPN
ejpam-5332	28	25	,	,	PUNCT
ejpam-5332	28	26	v	v	NOUN
ejpam-5332	28	27	)	)	PUNCT
ejpam-5332	28	28	is	be	AUX
ejpam-5332	28	29	the	the	DET
ejpam-5332	28	30	length	length	NOUN
ejpam-5332	28	31	of	of	ADP
ejpam-5332	28	32	the	the	DET
ejpam-5332	28	33	shortest	short	ADJ
ejpam-5332	28	34	path	path	NOUN
ejpam-5332	28	35	joining	join	VERB
ejpam-5332	28	36	u	u	NOUN
ejpam-5332	28	37	and	and	CCONJ
ejpam-5332	28	38	v[1	v[1	NOUN
ejpam-5332	28	39	]	]	PUNCT
ejpam-5332	28	40	.	.	PUNCT
ejpam-5332	29	1	the	the	DET
ejpam-5332	29	2	distance	distance	NOUN
ejpam-5332	29	3	between	between	ADP
ejpam-5332	29	4	a	a	DET
ejpam-5332	29	5	vertex	vertex	NOUN
ejpam-5332	29	6	u	u	NOUN
ejpam-5332	29	7	∈	∈	PROPN
ejpam-5332	29	8	v	v	ADP
ejpam-5332	29	9	(	(	PUNCT
ejpam-5332	29	10	g	g	NOUN
ejpam-5332	29	11	)	)	PUNCT
ejpam-5332	29	12	and	and	CCONJ
ejpam-5332	29	13	a	a	DET
ejpam-5332	29	14	subgraph	subgraph	NOUN
ejpam-5332	29	15	h	h	NOUN
ejpam-5332	29	16	of	of	ADP
ejpam-5332	29	17	g	g	PROPN
ejpam-5332	29	18	is	be	AUX
ejpam-5332	29	19	defined	define	VERB
ejpam-5332	29	20	as	as	ADP
ejpam-5332	29	21	dg(u	dg(u	NOUN
ejpam-5332	29	22	,	,	PUNCT
ejpam-5332	29	23	h	h	NOUN
ejpam-5332	29	24	)	)	PUNCT
ejpam-5332	30	1	=	=	SYM
ejpam-5332	30	2	min	min	NOUN
ejpam-5332	30	3	{	{	PUNCT
ejpam-5332	30	4	dg(u	dg(u	X
ejpam-5332	30	5	,	,	PUNCT
ejpam-5332	30	6	v	v	NOUN
ejpam-5332	30	7	)	)	PUNCT
ejpam-5332	30	8	:	:	PUNCT
ejpam-5332	30	9	v	v	X
ejpam-5332	30	10	∈	∈	PROPN
ejpam-5332	30	11	v	v	NOUN
ejpam-5332	30	12	(	(	PUNCT
ejpam-5332	30	13	h	h	NOUN
ejpam-5332	30	14	)	)	PUNCT
ejpam-5332	30	15	}	}	PUNCT
ejpam-5332	30	16	.	.	PUNCT
ejpam-5332	31	1	for	for	ADP
ejpam-5332	31	2	vertices	vertex	NOUN
ejpam-5332	31	3	u	u	NOUN
ejpam-5332	31	4	and	and	CCONJ
ejpam-5332	31	5	v	v	NOUN
ejpam-5332	31	6	of	of	ADP
ejpam-5332	31	7	a	a	DET
ejpam-5332	31	8	graph	graph	NOUN
ejpam-5332	31	9	g	g	NOUN
ejpam-5332	31	10	,	,	PUNCT
ejpam-5332	31	11	a	a	DET
ejpam-5332	31	12	u	u	NOUN
ejpam-5332	31	13	-	-	NOUN
ejpam-5332	31	14	v	v	ADJ
ejpam-5332	31	15	geodesic	geodesic	NOUN
ejpam-5332	31	16	is	be	AUX
ejpam-5332	31	17	any	any	DET
ejpam-5332	31	18	shortest	short	ADJ
ejpam-5332	31	19	path	path	NOUN
ejpam-5332	31	20	in	in	ADP
ejpam-5332	31	21	g	g	NOUN
ejpam-5332	31	22	joining	join	VERB
ejpam-5332	31	23	u	u	PROPN
ejpam-5332	31	24	and	and	CCONJ
ejpam-5332	31	25	v.	v.	ADP
ejpam-5332	31	26	the	the	DET
ejpam-5332	31	27	closed	closed	ADJ
ejpam-5332	31	28	interval	interval	NOUN
ejpam-5332	31	29	ig[u	ig[u	PROPN
ejpam-5332	31	30	,	,	PUNCT
ejpam-5332	31	31	v	v	NOUN
ejpam-5332	31	32	]	]	PUNCT
ejpam-5332	31	33	is	be	AUX
ejpam-5332	31	34	the	the	DET
ejpam-5332	31	35	set	set	NOUN
ejpam-5332	31	36	of	of	ADP
ejpam-5332	31	37	vertices	vertex	NOUN
ejpam-5332	31	38	lying	lie	VERB
ejpam-5332	31	39	in	in	ADP
ejpam-5332	31	40	any	any	DET
ejpam-5332	31	41	u	u	NOUN
ejpam-5332	31	42	-	-	NOUN
ejpam-5332	31	43	v	v	ADJ
ejpam-5332	31	44	geodesics	geodesic	NOUN
ejpam-5332	31	45	of	of	ADP
ejpam-5332	31	46	g	g	PROPN
ejpam-5332	31	47	and	and	CCONJ
ejpam-5332	31	48	the	the	DET
ejpam-5332	31	49	set	set	NOUN
ejpam-5332	31	50	ig[u	ig[u	PROPN
ejpam-5332	31	51	,	,	PUNCT
ejpam-5332	31	52	v	v	AUX
ejpam-5332	31	53	]	]	PUNCT
ejpam-5332	31	54	consist	consist	VERB
ejpam-5332	31	55	all	all	DET
ejpam-5332	31	56	the	the	DET
ejpam-5332	31	57	vertices	vertex	NOUN
ejpam-5332	31	58	in	in	ADP
ejpam-5332	31	59	any	any	DET
ejpam-5332	31	60	u	u	NOUN
ejpam-5332	31	61	-	-	NOUN
ejpam-5332	31	62	v	v	ADJ
ejpam-5332	31	63	geodesic	geodesic	NOUN
ejpam-5332	31	64	including	include	VERB
ejpam-5332	31	65	u	u	NOUN
ejpam-5332	31	66	and	and	CCONJ
ejpam-5332	31	67	v.	v.	ADP
ejpam-5332	31	68	a	a	DET
ejpam-5332	31	69	subset	subset	NOUN
ejpam-5332	31	70	c	c	NOUN
ejpam-5332	31	71	of	of	ADP
ejpam-5332	31	72	v	v	PROPN
ejpam-5332	31	73	(	(	PUNCT
ejpam-5332	31	74	g	g	NOUN
ejpam-5332	31	75	)	)	PUNCT
ejpam-5332	31	76	is	be	AUX
ejpam-5332	31	77	convex	convex	ADJ
ejpam-5332	31	78	if	if	SCONJ
ejpam-5332	31	79	for	for	SCONJ
ejpam-5332	31	80	every	every	DET
ejpam-5332	31	81	u	u	NOUN
ejpam-5332	31	82	,	,	PUNCT
ejpam-5332	31	83	v	v	NOUN
ejpam-5332	31	84	∈	∈	ADJ
ejpam-5332	31	85	c	c	NOUN
ejpam-5332	31	86	,	,	PUNCT
ejpam-5332	31	87	the	the	DET
ejpam-5332	31	88	vertex	vertex	NOUN
ejpam-5332	31	89	set	set	NOUN
ejpam-5332	31	90	of	of	ADP
ejpam-5332	31	91	every	every	DET
ejpam-5332	31	92	u	u	NOUN
ejpam-5332	31	93	-	-	NOUN
ejpam-5332	31	94	v	v	ADJ
ejpam-5332	31	95	geodesic	geodesic	NOUN
ejpam-5332	31	96	is	be	AUX
ejpam-5332	31	97	contained	contain	VERB
ejpam-5332	31	98	in	in	ADP
ejpam-5332	31	99	c.	c.	PROPN
ejpam-5332	31	100	equivalently	equivalently	PROPN
ejpam-5332	31	101	,	,	PUNCT
ejpam-5332	31	102	c	c	PROPN
ejpam-5332	31	103	is	be	AUX
ejpam-5332	31	104	convex	convex	ADJ
ejpam-5332	31	105	if	if	SCONJ
ejpam-5332	31	106	for	for	ADP
ejpam-5332	31	107	every	every	DET
ejpam-5332	31	108	u	u	NOUN
ejpam-5332	31	109	,	,	PUNCT
ejpam-5332	31	110	v	v	NOUN
ejpam-5332	31	111	∈	∈	ADJ
ejpam-5332	31	112	c	c	NOUN
ejpam-5332	31	113	,	,	PUNCT
ejpam-5332	31	114	the	the	DET
ejpam-5332	31	115	closed	closed	ADJ
ejpam-5332	31	116	interval	interval	NOUN
ejpam-5332	31	117	ig[u	ig[u	PROPN
ejpam-5332	31	118	,	,	PUNCT
ejpam-5332	31	119	v	v	NOUN
ejpam-5332	31	120	]	]	PUNCT
ejpam-5332	31	121	is	be	AUX
ejpam-5332	31	122	a	a	DET
ejpam-5332	31	123	subset	subset	NOUN
ejpam-5332	31	124	of	of	ADP
ejpam-5332	31	125	c.	c.	PROPN
ejpam-5332	31	126	a	a	DET
ejpam-5332	31	127	convex	convex	NOUN
ejpam-5332	31	128	subgraph	subgraph	NOUN
ejpam-5332	31	129	h	h	NOUN
ejpam-5332	31	130	of	of	ADP
ejpam-5332	31	131	a	a	DET
ejpam-5332	31	132	graph	graph	NOUN
ejpam-5332	31	133	g	g	NOUN
ejpam-5332	31	134	is	be	AUX
ejpam-5332	31	135	a	a	DET
ejpam-5332	31	136	subgraph	subgraph	NOUN
ejpam-5332	31	137	of	of	ADP
ejpam-5332	31	138	g	g	NOUN
ejpam-5332	31	139	induced	induce	VERB
ejpam-5332	31	140	by	by	ADP
ejpam-5332	31	141	a	a	DET
ejpam-5332	31	142	convex	convex	NOUN
ejpam-5332	31	143	subset	subset	NOUN
ejpam-5332	31	144	of	of	ADP
ejpam-5332	31	145	v	v	NOUN
ejpam-5332	31	146	(	(	PUNCT
ejpam-5332	31	147	g	g	NOUN
ejpam-5332	31	148	)	)	PUNCT
ejpam-5332	31	149	.	.	PUNCT
ejpam-5332	32	1	a	a	DET
ejpam-5332	32	2	proper	proper	ADJ
ejpam-5332	32	3	convex	convex	NOUN
ejpam-5332	32	4	subgraph	subgraph	NOUN
ejpam-5332	32	5	h	h	PROPN
ejpam-5332	32	6	of	of	ADP
ejpam-5332	32	7	g.	g.	PROPN
ejpam-5332	32	8	subgraph	subgraph	PROPN
ejpam-5332	32	9	h	h	PROPN
ejpam-5332	32	10	is	be	AUX
ejpam-5332	32	11	said	say	VERB
ejpam-5332	32	12	to	to	PART
ejpam-5332	32	13	be	be	AUX
ejpam-5332	32	14	the	the	DET
ejpam-5332	32	15	maximum	maximum	ADJ
ejpam-5332	32	16	proper	proper	ADJ
ejpam-5332	32	17	convex	convex	NOUN
ejpam-5332	32	18	subgraph	subgraph	NOUN
ejpam-5332	32	19	of	of	ADP
ejpam-5332	32	20	g	g	PROPN
ejpam-5332	32	21	if	if	SCONJ
ejpam-5332	32	22	for	for	ADP
ejpam-5332	32	23	any	any	DET
ejpam-5332	32	24	proper	proper	ADJ
ejpam-5332	32	25	convex	convex	NOUN
ejpam-5332	32	26	subgraph	subgraph	NOUN
ejpam-5332	32	27	h∗	h∗	PROPN
ejpam-5332	32	28	with	with	ADP
ejpam-5332	32	29	h	h	PROPN
ejpam-5332	32	30	⪯	⪯	PROPN
ejpam-5332	32	31	h∗	h∗	PROPN
ejpam-5332	32	32	⪯	⪯	PROPN
ejpam-5332	32	33	g	g	PROPN
ejpam-5332	32	34	,	,	PUNCT
ejpam-5332	32	35	then	then	ADV
ejpam-5332	32	36	h	h	NOUN
ejpam-5332	32	37	=	=	PRON
ejpam-5332	32	38	h∗.	h∗.	VERB
ejpam-5332	32	39	a	a	DET
ejpam-5332	32	40	graph	graph	NOUN
ejpam-5332	32	41	g	g	NOUN
ejpam-5332	32	42	is	be	AUX
ejpam-5332	32	43	h	h	NOUN
ejpam-5332	32	44	-	-	ADJ
ejpam-5332	32	45	convex	convex	ADJ
ejpam-5332	32	46	k	k	NOUN
ejpam-5332	32	47	-	-	ADJ
ejpam-5332	32	48	accessible	accessible	ADJ
ejpam-5332	32	49	if	if	SCONJ
ejpam-5332	32	50	there	there	PRON
ejpam-5332	32	51	exists	exist	VERB
ejpam-5332	32	52	a	a	DET
ejpam-5332	32	53	proper	proper	ADJ
ejpam-5332	32	54	convex	convex	NOUN
ejpam-5332	32	55	subgraph	subgraph	NOUN
ejpam-5332	32	56	h	h	NOUN
ejpam-5332	32	57	of	of	ADP
ejpam-5332	32	58	g	g	PROPN
ejpam-5332	32	59	such	such	ADJ
ejpam-5332	32	60	that	that	PRON
ejpam-5332	32	61	for	for	ADP
ejpam-5332	32	62	every	every	PRON
ejpam-5332	32	63	v	v	NUM
ejpam-5332	32	64	∈	∈	PROPN
ejpam-5332	32	65	v	v	NOUN
ejpam-5332	32	66	(	(	PUNCT
ejpam-5332	32	67	g	g	NOUN
ejpam-5332	32	68	)	)	PUNCT
ejpam-5332	32	69	\	\	PROPN
ejpam-5332	32	70	v	v	X
ejpam-5332	32	71	(	(	PUNCT
ejpam-5332	32	72	h	h	NOUN
ejpam-5332	32	73	)	)	PUNCT
ejpam-5332	32	74	,	,	PUNCT
ejpam-5332	32	75	there	there	PRON
ejpam-5332	32	76	exists	exist	VERB
ejpam-5332	32	77	u	u	PROPN
ejpam-5332	32	78	∈	∈	PROPN
ejpam-5332	32	79	v	v	ADP
ejpam-5332	32	80	(	(	PUNCT
ejpam-5332	32	81	h	h	NOUN
ejpam-5332	32	82	)	)	PUNCT
ejpam-5332	32	83	satisfying	satisfy	VERB
ejpam-5332	32	84	dg(u	dg(u	ADJ
ejpam-5332	32	85	,	,	PUNCT
ejpam-5332	32	86	v	v	NOUN
ejpam-5332	32	87	)	)	PUNCT
ejpam-5332	32	88	≤	≤	NOUN
ejpam-5332	33	1	k	k	PROPN
ejpam-5332	33	2	,	,	PUNCT
ejpam-5332	33	3	k	k	PROPN
ejpam-5332	33	4	∈	∈	PROPN
ejpam-5332	33	5	n.	n.	NOUN
ejpam-5332	33	6	for	for	ADP
ejpam-5332	33	7	a	a	DET
ejpam-5332	33	8	proper	proper	ADJ
ejpam-5332	33	9	convex	convex	NOUN
ejpam-5332	33	10	subgraph	subgraph	NOUN
ejpam-5332	33	11	h	h	NOUN
ejpam-5332	33	12	of	of	ADP
ejpam-5332	33	13	g	g	PROPN
ejpam-5332	33	14	,	,	PUNCT
ejpam-5332	33	15	we	we	PRON
ejpam-5332	33	16	define	define	VERB
ejpam-5332	33	17	the	the	DET
ejpam-5332	33	18	h	h	NOUN
ejpam-5332	33	19	-	-	PUNCT
ejpam-5332	33	20	convex	convex	ADJ
ejpam-5332	33	21	accessbility	accessbility	NOUN
ejpam-5332	33	22	number	number	NOUN
ejpam-5332	33	23	of	of	ADP
ejpam-5332	33	24	g	g	NOUN
ejpam-5332	33	25	as	as	ADP
ejpam-5332	33	26	γh(g	γh(g	NOUN
ejpam-5332	33	27	)	)	PUNCT
ejpam-5332	34	1	=	=	SYM
ejpam-5332	34	2	min{k	min{k	NOUN
ejpam-5332	34	3	:	:	PUNCT
ejpam-5332	34	4	g	g	PROPN
ejpam-5332	34	5	is	be	AUX
ejpam-5332	34	6	h	h	PROPN
ejpam-5332	34	7	convex	convex	PROPN
ejpam-5332	34	8	k	k	PROPN
ejpam-5332	34	9	accessible	accessible	ADJ
ejpam-5332	34	10	}	}	PUNCT
ejpam-5332	34	11	.	.	PUNCT
ejpam-5332	35	1	the	the	DET
ejpam-5332	35	2	complement	complement	NOUN
ejpam-5332	35	3	of	of	ADP
ejpam-5332	35	4	a	a	DET
ejpam-5332	35	5	graph	graph	NOUN
ejpam-5332	35	6	g	g	NOUN
ejpam-5332	35	7	is	be	AUX
ejpam-5332	35	8	a	a	DET
ejpam-5332	35	9	graph	graph	NOUN
ejpam-5332	35	10	ḡ	ḡ	VERB
ejpam-5332	35	11	,	,	PUNCT
ejpam-5332	35	12	with	with	ADP
ejpam-5332	35	13	vertex	vertex	NOUN
ejpam-5332	35	14	set	set	VERB
ejpam-5332	35	15	same	same	ADJ
ejpam-5332	35	16	as	as	ADP
ejpam-5332	35	17	g	g	NOUN
ejpam-5332	35	18	and	and	CCONJ
ejpam-5332	35	19	two	two	NUM
ejpam-5332	35	20	vertices	vertex	NOUN
ejpam-5332	35	21	in	in	ADP
ejpam-5332	35	22	ḡ	ḡ	VERB
ejpam-5332	35	23	are	be	AUX
ejpam-5332	35	24	adjacent	adjacent	ADJ
ejpam-5332	35	25	if	if	SCONJ
ejpam-5332	35	26	and	and	CCONJ
ejpam-5332	35	27	only	only	ADV
ejpam-5332	35	28	if	if	SCONJ
ejpam-5332	35	29	they	they	PRON
ejpam-5332	35	30	are	be	AUX
ejpam-5332	35	31	not	not	PART
ejpam-5332	35	32	adjacent	adjacent	ADJ
ejpam-5332	35	33	in	in	ADP
ejpam-5332	35	34	g.	g.	PROPN
ejpam-5332	35	35	the	the	DET
ejpam-5332	35	36	cartesian	cartesian	ADJ
ejpam-5332	35	37	product	product	NOUN
ejpam-5332	35	38	g	g	NOUN
ejpam-5332	35	39	□	□	PROPN
ejpam-5332	35	40	h	h	NOUN
ejpam-5332	35	41	of	of	ADP
ejpam-5332	35	42	graphs	graph	NOUN
ejpam-5332	35	43	g	g	NOUN
ejpam-5332	35	44	and	and	CCONJ
ejpam-5332	35	45	h	h	NOUN
ejpam-5332	35	46	is	be	AUX
ejpam-5332	35	47	a	a	DET
ejpam-5332	35	48	graph	graph	NOUN
ejpam-5332	35	49	such	such	ADJ
ejpam-5332	35	50	that	that	SCONJ
ejpam-5332	35	51	the	the	DET
ejpam-5332	35	52	vertex	vertex	NOUN
ejpam-5332	35	53	set	set	VERB
ejpam-5332	35	54	g	g	PROPN
ejpam-5332	35	55	□	□	PROPN
ejpam-5332	35	56	h	h	NOUN
ejpam-5332	35	57	is	be	AUX
ejpam-5332	35	58	the	the	DET
ejpam-5332	35	59	cartesian	cartesian	ADJ
ejpam-5332	35	60	product	product	NOUN
ejpam-5332	35	61	v	v	NOUN
ejpam-5332	35	62	(	(	PUNCT
ejpam-5332	35	63	g	g	NOUN
ejpam-5332	35	64	)	)	PUNCT
ejpam-5332	35	65	×	×	NOUN
ejpam-5332	35	66	v	v	NOUN
ejpam-5332	35	67	(	(	PUNCT
ejpam-5332	35	68	h	h	NOUN
ejpam-5332	35	69	)	)	PUNCT
ejpam-5332	35	70	and	and	CCONJ
ejpam-5332	35	71	vertices	vertice	VERB
ejpam-5332	35	72	(	(	PUNCT
ejpam-5332	35	73	u	u	NOUN
ejpam-5332	35	74	,	,	PUNCT
ejpam-5332	35	75	v	v	NOUN
ejpam-5332	35	76	)	)	PUNCT
ejpam-5332	35	77	and	and	CCONJ
ejpam-5332	35	78	(	(	PUNCT
ejpam-5332	35	79	u′	u′	PROPN
ejpam-5332	35	80	,	,	PUNCT
ejpam-5332	35	81	v′	v′	PROPN
ejpam-5332	35	82	)	)	PUNCT
ejpam-5332	35	83	are	be	AUX
ejpam-5332	35	84	adjacent	adjacent	ADJ
ejpam-5332	35	85	in	in	ADP
ejpam-5332	35	86	g	g	PROPN
ejpam-5332	35	87	□	□	PROPN
ejpam-5332	35	88	h	h	NOUN
ejpam-5332	35	89	if	if	SCONJ
ejpam-5332	36	1	and	and	CCONJ
ejpam-5332	36	2	only	only	ADV
ejpam-5332	36	3	if	if	SCONJ
ejpam-5332	36	4	u	u	NOUN
ejpam-5332	36	5	is	be	AUX
ejpam-5332	36	6	adjacent	adjacent	ADJ
ejpam-5332	36	7	to	to	ADP
ejpam-5332	36	8	u′	u′	PROPN
ejpam-5332	36	9	in	in	ADP
ejpam-5332	36	10	g	g	PROPN
ejpam-5332	36	11	or	or	CCONJ
ejpam-5332	36	12	,	,	PUNCT
ejpam-5332	36	13	v	v	NOUN
ejpam-5332	36	14	is	be	AUX
ejpam-5332	36	15	adjacent	adjacent	ADJ
ejpam-5332	36	16	to	to	ADP
ejpam-5332	36	17	v′	v′	NOUN
ejpam-5332	36	18	in	in	ADP
ejpam-5332	36	19	h.	h.	PROPN
ejpam-5332	36	20	the	the	DET
ejpam-5332	36	21	strong	strong	ADJ
ejpam-5332	36	22	product	product	NOUN
ejpam-5332	36	23	g	g	PROPN
ejpam-5332	36	24	⊠h	⊠h	PROPN
ejpam-5332	36	25	of	of	ADP
ejpam-5332	36	26	graphs	graph	NOUN
ejpam-5332	36	27	g	g	PROPN
ejpam-5332	36	28	and	and	CCONJ
ejpam-5332	36	29	h	h	NOUN
ejpam-5332	36	30	is	be	AUX
ejpam-5332	36	31	a	a	DET
ejpam-5332	36	32	graph	graph	NOUN
ejpam-5332	36	33	such	such	ADJ
ejpam-5332	36	34	that	that	SCONJ
ejpam-5332	36	35	the	the	DET
ejpam-5332	36	36	vertex	vertex	NOUN
ejpam-5332	36	37	set	set	NOUN
ejpam-5332	36	38	of	of	ADP
ejpam-5332	36	39	g⊠h	g⊠h	NOUN
ejpam-5332	36	40	is	be	AUX
ejpam-5332	36	41	the	the	DET
ejpam-5332	36	42	cartesian	cartesian	ADJ
ejpam-5332	36	43	product	product	NOUN
ejpam-5332	36	44	v	v	NOUN
ejpam-5332	36	45	(	(	PUNCT
ejpam-5332	36	46	g)×v	g)×v	PROPN
ejpam-5332	36	47	(	(	PUNCT
ejpam-5332	36	48	h	h	NOUN
ejpam-5332	36	49	)	)	PUNCT
ejpam-5332	36	50	and	and	CCONJ
ejpam-5332	36	51	distinct	distinct	ADJ
ejpam-5332	36	52	vertices	vertex	NOUN
ejpam-5332	36	53	(	(	PUNCT
ejpam-5332	36	54	u	u	NOUN
ejpam-5332	36	55	,	,	PUNCT
ejpam-5332	36	56	u′	u′	PROPN
ejpam-5332	36	57	)	)	PUNCT
ejpam-5332	36	58	and	and	CCONJ
ejpam-5332	36	59	(	(	PUNCT
ejpam-5332	36	60	v	v	NOUN
ejpam-5332	36	61	,	,	PUNCT
ejpam-5332	36	62	v′	v′	PROPN
ejpam-5332	36	63	)	)	PUNCT
ejpam-5332	36	64	are	be	AUX
ejpam-5332	36	65	adjacent	adjacent	ADJ
ejpam-5332	36	66	in	in	ADP
ejpam-5332	36	67	g⊠h	g⊠h	NOUN
ejpam-5332	36	68	if	if	SCONJ
ejpam-5332	36	69	and	and	CCONJ
ejpam-5332	36	70	only	only	ADV
ejpam-5332	36	71	if	if	SCONJ
ejpam-5332	36	72	u	u	PROPN
ejpam-5332	36	73	=	=	SYM
ejpam-5332	36	74	v	v	NOUN
ejpam-5332	36	75	and	and	CCONJ
ejpam-5332	36	76	u′	u′	PRON
ejpam-5332	36	77	is	be	AUX
ejpam-5332	36	78	adjacent	adjacent	ADJ
ejpam-5332	36	79	to	to	ADP
ejpam-5332	36	80	v′	v′	NOUN
ejpam-5332	36	81	in	in	ADP
ejpam-5332	36	82	h	h	NOUN
ejpam-5332	36	83	or	or	CCONJ
ejpam-5332	36	84	,	,	PUNCT
ejpam-5332	36	85	u′	u′	PROPN
ejpam-5332	36	86	=	=	SYM
ejpam-5332	36	87	v′	v′	PROPN
ejpam-5332	36	88	and	and	CCONJ
ejpam-5332	36	89	uis	uis	PROPN
ejpam-5332	36	90	adjacent	adjacent	ADJ
ejpam-5332	36	91	to	to	ADP
ejpam-5332	36	92	v	v	NOUN
ejpam-5332	36	93	in	in	ADP
ejpam-5332	36	94	g	g	PROPN
ejpam-5332	36	95	or	or	CCONJ
ejpam-5332	36	96	,	,	PUNCT
ejpam-5332	36	97	u	u	NOUN
ejpam-5332	36	98	is	be	AUX
ejpam-5332	36	99	adjacent	adjacent	ADJ
ejpam-5332	36	100	to	to	ADP
ejpam-5332	36	101	v	v	NOUN
ejpam-5332	36	102	in	in	ADP
ejpam-5332	36	103	g	g	PROPN
ejpam-5332	36	104	and	and	CCONJ
ejpam-5332	36	105	u′	u′	PROPN
ejpam-5332	36	106	is	be	AUX
ejpam-5332	36	107	adjacent	adjacent	ADJ
ejpam-5332	36	108	to	to	ADP
ejpam-5332	36	109	v′	v′	NOUN
ejpam-5332	36	110	in	in	ADP
ejpam-5332	36	111	h.	h.	PROPN
ejpam-5332	36	112	for	for	ADP
ejpam-5332	36	113	a	a	DET
ejpam-5332	36	114	set	set	NOUN
ejpam-5332	36	115	c	c	PROPN
ejpam-5332	36	116	⊂	⊂	PROPN
ejpam-5332	36	117	v	v	X
ejpam-5332	36	118	(	(	PUNCT
ejpam-5332	36	119	g	g	PROPN
ejpam-5332	36	120	×h	×h	PROPN
ejpam-5332	36	121	)	)	PUNCT
ejpam-5332	36	122	,	,	PUNCT
ejpam-5332	36	123	we	we	PRON
ejpam-5332	36	124	denote	denote	VERB
ejpam-5332	36	125	,	,	PUNCT
ejpam-5332	36	126	cg	cg	NOUN
ejpam-5332	36	127	=	=	SYM
ejpam-5332	36	128	{	{	PUNCT
ejpam-5332	36	129	u	u	NOUN
ejpam-5332	36	130	:	:	PUNCT
ejpam-5332	36	131	(	(	PUNCT
ejpam-5332	36	132	u	u	NOUN
ejpam-5332	36	133	,	,	PUNCT
ejpam-5332	36	134	v	v	NOUN
ejpam-5332	36	135	)	)	PUNCT
ejpam-5332	36	136	∈	∈	PROPN
ejpam-5332	36	137	c	c	NOUN
ejpam-5332	36	138	for	for	ADP
ejpam-5332	36	139	some	some	DET
ejpam-5332	36	140	v	v	ADP
ejpam-5332	36	141	∈	∈	PROPN
ejpam-5332	36	142	v	v	NOUN
ejpam-5332	36	143	(	(	PUNCT
ejpam-5332	36	144	h	h	NOUN
ejpam-5332	36	145	)	)	PUNCT
ejpam-5332	36	146	}	}	PUNCT
ejpam-5332	36	147	and	and	CCONJ
ejpam-5332	36	148	ch	ch	NOUN
ejpam-5332	36	149	=	=	SYM
ejpam-5332	36	150	{	{	PUNCT
ejpam-5332	36	151	v	v	NOUN
ejpam-5332	36	152	:	:	PUNCT
ejpam-5332	36	153	(	(	PUNCT
ejpam-5332	36	154	u	u	NOUN
ejpam-5332	36	155	,	,	PUNCT
ejpam-5332	36	156	v	v	NOUN
ejpam-5332	36	157	)	)	PUNCT
ejpam-5332	36	158	∈	∈	PROPN
ejpam-5332	36	159	c	c	NOUN
ejpam-5332	36	160	for	for	ADP
ejpam-5332	36	161	some	some	DET
ejpam-5332	36	162	u	u	NOUN
ejpam-5332	36	163	∈	∈	PROPN
ejpam-5332	36	164	v	v	NOUN
ejpam-5332	36	165	(	(	PUNCT
ejpam-5332	36	166	g	g	NOUN
ejpam-5332	36	167	)	)	PUNCT
ejpam-5332	36	168	}	}	PUNCT
ejpam-5332	36	169	.	.	PUNCT
ejpam-5332	37	1	a	a	DET
ejpam-5332	37	2	set	set	NOUN
ejpam-5332	37	3	c	c	PROPN
ejpam-5332	37	4	∈	∈	PROPN
ejpam-5332	37	5	v	v	NOUN
ejpam-5332	37	6	(	(	PUNCT
ejpam-5332	37	7	g	g	NOUN
ejpam-5332	37	8	□	□	NOUN
ejpam-5332	37	9	h	h	NOUN
ejpam-5332	37	10	)	)	PUNCT
ejpam-5332	37	11	is	be	AUX
ejpam-5332	37	12	a	a	DET
ejpam-5332	37	13	convex	convex	NOUN
ejpam-5332	37	14	set	set	VERB
ejpam-5332	37	15	in	in	ADP
ejpam-5332	37	16	g	g	PROPN
ejpam-5332	37	17	□	□	PROPN
ejpam-5332	37	18	h	h	NOUN
ejpam-5332	37	19	if	if	SCONJ
ejpam-5332	38	1	and	and	CCONJ
ejpam-5332	38	2	only	only	ADV
ejpam-5332	38	3	if	if	SCONJ
ejpam-5332	38	4	c	c	NOUN
ejpam-5332	38	5	=	=	SYM
ejpam-5332	38	6	cg	cg	NOUN
ejpam-5332	38	7	□	□	PROPN
ejpam-5332	38	8	ch	ch	NOUN
ejpam-5332	38	9	,	,	PUNCT
ejpam-5332	38	10	where	where	SCONJ
ejpam-5332	38	11	cg	cg	NOUN
ejpam-5332	38	12	and	and	CCONJ
ejpam-5332	38	13	ch	ch	PROPN
ejpam-5332	38	14	are	be	AUX
ejpam-5332	38	15	convex	convex	NOUN
ejpam-5332	38	16	sets	set	NOUN
ejpam-5332	38	17	in	in	ADP
ejpam-5332	38	18	g	g	PROPN
ejpam-5332	38	19	and	and	CCONJ
ejpam-5332	38	20	h	h	NOUN
ejpam-5332	38	21	respectively	respectively	ADV
ejpam-5332	38	22	,	,	PUNCT
ejpam-5332	38	23	h.	h.	PROPN
ejpam-5332	38	24	b.	b.	PROPN
ejpam-5332	38	25	samson	samson	PROPN
ejpam-5332	38	26	,	,	PUNCT
ejpam-5332	38	27	i.	i.	PROPN
ejpam-5332	38	28	s.	s.	PROPN
ejpam-5332	38	29	aniversario	aniversario	PROPN
ejpam-5332	38	30	,	,	PUNCT
ejpam-5332	38	31	m.	m.	PROPN
ejpam-5332	38	32	j.	j.	PROPN
ejpam-5332	38	33	f.	f.	PROPN
ejpam-5332	38	34	luga	luga	PROPN
ejpam-5332	38	35	/	/	SYM
ejpam-5332	38	36	eur	eur	PROPN
ejpam-5332	38	37	.	.	PUNCT
ejpam-5332	39	1	j.	j.	PROPN
ejpam-5332	39	2	pure	pure	PROPN
ejpam-5332	39	3	appl	appl	PROPN
ejpam-5332	39	4	.	.	PROPN
ejpam-5332	39	5	math	math	PROPN
ejpam-5332	39	6	,	,	PUNCT
ejpam-5332	39	7	17	17	NUM
ejpam-5332	39	8	(	(	PUNCT
ejpam-5332	39	9	4	4	NUM
ejpam-5332	39	10	)	)	PUNCT
ejpam-5332	39	11	(	(	PUNCT
ejpam-5332	39	12	2024	2024	NUM
ejpam-5332	39	13	)	)	PUNCT
ejpam-5332	39	14	,	,	PUNCT
ejpam-5332	39	15	2930	2930	NUM
ejpam-5332	39	16	-	-	SYM
ejpam-5332	39	17	2938	2938	NUM
ejpam-5332	39	18	2932	2932	NUM
ejpam-5332	39	19	where	where	SCONJ
ejpam-5332	39	20	g	g	PROPN
ejpam-5332	39	21	and	and	CCONJ
ejpam-5332	39	22	h	h	NOUN
ejpam-5332	39	23	are	be	AUX
ejpam-5332	39	24	connected	connect	VERB
ejpam-5332	39	25	graphs	graph	NOUN
ejpam-5332	39	26	[	[	X
ejpam-5332	39	27	5	5	NUM
ejpam-5332	39	28	]	]	PUNCT
ejpam-5332	39	29	.	.	PUNCT
ejpam-5332	40	1	the	the	DET
ejpam-5332	40	2	distance	distance	NOUN
ejpam-5332	40	3	between	between	ADP
ejpam-5332	40	4	vertices	vertex	NOUN
ejpam-5332	40	5	(	(	PUNCT
ejpam-5332	40	6	g	g	NOUN
ejpam-5332	40	7	,	,	PUNCT
ejpam-5332	40	8	h	h	NOUN
ejpam-5332	40	9	)	)	PUNCT
ejpam-5332	40	10	and	and	CCONJ
ejpam-5332	40	11	(	(	PUNCT
ejpam-5332	40	12	g′	g′	NOUN
ejpam-5332	40	13	,	,	PUNCT
ejpam-5332	40	14	h′	h′	PROPN
ejpam-5332	40	15	)	)	PUNCT
ejpam-5332	40	16	in	in	ADP
ejpam-5332	40	17	the	the	DET
ejpam-5332	40	18	cartesian	cartesian	ADJ
ejpam-5332	40	19	product	product	NOUN
ejpam-5332	40	20	g	g	NOUN
ejpam-5332	40	21	□	□	PROPN
ejpam-5332	40	22	h	h	NOUN
ejpam-5332	40	23	is	be	AUX
ejpam-5332	40	24	equal	equal	ADJ
ejpam-5332	40	25	to	to	ADP
ejpam-5332	40	26	dg	dg	PROPN
ejpam-5332	40	27	□	□	SYM
ejpam-5332	40	28	h((g	h((g	ADJ
ejpam-5332	40	29	,	,	PUNCT
ejpam-5332	40	30	h	h	NOUN
ejpam-5332	40	31	)	)	PUNCT
ejpam-5332	40	32	,	,	PUNCT
ejpam-5332	40	33	(	(	PUNCT
ejpam-5332	40	34	g′	g′	NOUN
ejpam-5332	40	35	,	,	PUNCT
ejpam-5332	40	36	h′	h′	PROPN
ejpam-5332	40	37	)	)	PUNCT
ejpam-5332	40	38	)	)	PUNCT
ejpam-5332	41	1	=	=	PUNCT
ejpam-5332	41	2	dg(g	dg(g	PROPN
ejpam-5332	41	3	,	,	PUNCT
ejpam-5332	41	4	g	g	PROPN
ejpam-5332	41	5	′	′	NUM
ejpam-5332	41	6	)	)	PUNCT
ejpam-5332	42	1	+	+	CCONJ
ejpam-5332	42	2	dh(h	dh(h	NUM
ejpam-5332	42	3	,	,	PUNCT
ejpam-5332	42	4	h′	h′	PROPN
ejpam-5332	42	5	)	)	PUNCT
ejpam-5332	43	1	[	[	X
ejpam-5332	43	2	4	4	NUM
ejpam-5332	43	3	]	]	PUNCT
ejpam-5332	43	4	.	.	PUNCT
ejpam-5332	44	1	the	the	DET
ejpam-5332	44	2	distance	distance	NOUN
ejpam-5332	44	3	between	between	ADP
ejpam-5332	44	4	vertices	vertex	NOUN
ejpam-5332	44	5	(	(	PUNCT
ejpam-5332	44	6	u	u	NOUN
ejpam-5332	44	7	,	,	PUNCT
ejpam-5332	44	8	v	v	NOUN
ejpam-5332	44	9	)	)	PUNCT
ejpam-5332	44	10	and	and	CCONJ
ejpam-5332	44	11	(	(	PUNCT
ejpam-5332	44	12	u′	u′	PROPN
ejpam-5332	44	13	,	,	PUNCT
ejpam-5332	44	14	v′	v′	PROPN
ejpam-5332	44	15	)	)	PUNCT
ejpam-5332	44	16	in	in	ADP
ejpam-5332	44	17	the	the	DET
ejpam-5332	44	18	strong	strong	ADJ
ejpam-5332	44	19	product	product	NOUN
ejpam-5332	44	20	g	g	PROPN
ejpam-5332	44	21	⊠	⊠	PROPN
ejpam-5332	44	22	h	h	NOUN
ejpam-5332	44	23	is	be	AUX
ejpam-5332	44	24	equal	equal	ADJ
ejpam-5332	44	25	to	to	ADP
ejpam-5332	44	26	dg⊠h((u	dg⊠h((u	PROPN
ejpam-5332	44	27	,	,	PUNCT
ejpam-5332	44	28	v	v	NOUN
ejpam-5332	44	29	)	)	PUNCT
ejpam-5332	44	30	,	,	PUNCT
ejpam-5332	44	31	(	(	PUNCT
ejpam-5332	44	32	u′	u′	PROPN
ejpam-5332	44	33	,	,	PUNCT
ejpam-5332	44	34	v′	v′	NOUN
ejpam-5332	44	35	)	)	PUNCT
ejpam-5332	44	36	)	)	PUNCT
ejpam-5332	45	1	=	=	SYM
ejpam-5332	45	2	max{dg(u	max{dg(u	X
ejpam-5332	45	3	,	,	PUNCT
ejpam-5332	45	4	u′	u′	PROPN
ejpam-5332	45	5	)	)	PUNCT
ejpam-5332	45	6	,	,	PUNCT
ejpam-5332	45	7	dh(v	dh(v	NOUN
ejpam-5332	45	8	,	,	PUNCT
ejpam-5332	45	9	v′	v′	NOUN
ejpam-5332	45	10	)	)	PUNCT
ejpam-5332	45	11	}	}	PUNCT
ejpam-5332	46	1	[	[	X
ejpam-5332	46	2	4	4	NUM
ejpam-5332	46	3	]	]	PUNCT
ejpam-5332	46	4	.	.	PUNCT
ejpam-5332	47	1	2	2	X
ejpam-5332	47	2	.	.	X
ejpam-5332	47	3	h	h	NOUN
ejpam-5332	47	4	convex	convex	PROPN
ejpam-5332	47	5	accessibility	accessibility	NOUN
ejpam-5332	47	6	number	number	NOUN
ejpam-5332	47	7	of	of	ADP
ejpam-5332	47	8	the	the	DET
ejpam-5332	47	9	complement	complement	NOUN
ejpam-5332	47	10	of	of	ADP
ejpam-5332	47	11	some	some	DET
ejpam-5332	47	12	known	know	VERB
ejpam-5332	47	13	graphs	graph	NOUN
ejpam-5332	47	14	in	in	ADP
ejpam-5332	47	15	this	this	DET
ejpam-5332	47	16	section	section	NOUN
ejpam-5332	47	17	,	,	PUNCT
ejpam-5332	47	18	we	we	PRON
ejpam-5332	47	19	established	establish	VERB
ejpam-5332	47	20	the	the	DET
ejpam-5332	47	21	h	h	NOUN
ejpam-5332	47	22	-	-	PUNCT
ejpam-5332	47	23	convex	convex	NOUN
ejpam-5332	47	24	accessibility	accessibility	NOUN
ejpam-5332	47	25	number	number	NOUN
ejpam-5332	47	26	of	of	ADP
ejpam-5332	47	27	the	the	DET
ejpam-5332	47	28	complement	complement	NOUN
ejpam-5332	47	29	of	of	ADP
ejpam-5332	47	30	some	some	DET
ejpam-5332	47	31	known	know	VERB
ejpam-5332	47	32	graphs	graph	NOUN
ejpam-5332	47	33	.	.	PUNCT
ejpam-5332	48	1	theorem	theorem	NOUN
ejpam-5332	48	2	1	1	NUM
ejpam-5332	48	3	.	.	PUNCT
ejpam-5332	49	1	let	let	VERB
ejpam-5332	49	2	g	g	PRON
ejpam-5332	49	3	be	be	AUX
ejpam-5332	49	4	a	a	DET
ejpam-5332	49	5	graph	graph	NOUN
ejpam-5332	50	1	such	such	ADJ
ejpam-5332	50	2	that	that	SCONJ
ejpam-5332	50	3	g	g	NOUN
ejpam-5332	50	4	=	=	PUNCT
ejpam-5332	50	5	pn	pn	PROPN
ejpam-5332	50	6	=	=	PUNCT
ejpam-5332	51	1	[	[	X
ejpam-5332	51	2	x1	x1	PROPN
ejpam-5332	51	3	,	,	PUNCT
ejpam-5332	51	4	x2	x2	PROPN
ejpam-5332	51	5	,	,	PUNCT
ejpam-5332	51	6	.	.	PUNCT
ejpam-5332	51	7	.	.	PUNCT
ejpam-5332	52	1	.	.	PUNCT
ejpam-5332	53	1	,	,	PUNCT
ejpam-5332	53	2	xn	xn	PROPN
ejpam-5332	53	3	]	]	X
ejpam-5332	53	4	for	for	ADP
ejpam-5332	53	5	n	n	X
ejpam-5332	53	6	≥	≥	NOUN
ejpam-5332	53	7	4	4	NUM
ejpam-5332	53	8	and	and	CCONJ
ejpam-5332	53	9	h	h	NOUN
ejpam-5332	53	10	be	be	VERB
ejpam-5332	53	11	a	a	DET
ejpam-5332	53	12	proper	proper	ADJ
ejpam-5332	53	13	convex	convex	NOUN
ejpam-5332	53	14	subgraph	subgraph	NOUN
ejpam-5332	53	15	of	of	ADP
ejpam-5332	53	16	g.	g.	PROPN
ejpam-5332	53	17	then	then	ADV
ejpam-5332	53	18	γh(g	γh(g	NOUN
ejpam-5332	53	19	)	)	PUNCT
ejpam-5332	54	1	=	=	PRON
ejpam-5332	54	2	{	{	PUNCT
ejpam-5332	54	3	2	2	NUM
ejpam-5332	54	4	,	,	PUNCT
ejpam-5332	54	5	if	if	SCONJ
ejpam-5332	54	6	h	h	NOUN
ejpam-5332	54	7	=	=	SYM
ejpam-5332	54	8	k1	k1	PROPN
ejpam-5332	54	9	or	or	CCONJ
ejpam-5332	54	10	h	h	NOUN
ejpam-5332	54	11	=	=	NOUN
ejpam-5332	54	12	p2	p2	PROPN
ejpam-5332	54	13	=	=	PUNCT
ejpam-5332	55	1	[	[	X
ejpam-5332	55	2	xi	xi	X
ejpam-5332	55	3	,	,	PUNCT
ejpam-5332	55	4	xi+2	xi+2	PROPN
ejpam-5332	55	5	]	]	X
ejpam-5332	55	6	1	1	NUM
ejpam-5332	55	7	,	,	PUNCT
ejpam-5332	55	8	otherwise	otherwise	ADV
ejpam-5332	55	9	.	.	PUNCT
ejpam-5332	56	1	proof	proof	NOUN
ejpam-5332	56	2	.	.	PUNCT
ejpam-5332	57	1	let	let	VERB
ejpam-5332	57	2	g	g	NOUN
ejpam-5332	57	3	=	=	VERB
ejpam-5332	57	4	pn	pn	AUX
ejpam-5332	57	5	be	be	AUX
ejpam-5332	57	6	a	a	DET
ejpam-5332	57	7	connected	connected	ADJ
ejpam-5332	57	8	path	path	NOUN
ejpam-5332	57	9	graph	graph	NOUN
ejpam-5332	57	10	where	where	SCONJ
ejpam-5332	57	11	the	the	DET
ejpam-5332	57	12	vertices	vertex	NOUN
ejpam-5332	57	13	are	be	AUX
ejpam-5332	57	14	x1	x1	PROPN
ejpam-5332	57	15	,	,	PUNCT
ejpam-5332	57	16	x2	x2	PROPN
ejpam-5332	57	17	,	,	PUNCT
ejpam-5332	57	18	x3	x3	ADJ
ejpam-5332	57	19	,	,	PUNCT
ejpam-5332	57	20	.	.	PUNCT
ejpam-5332	57	21	.	.	PUNCT
ejpam-5332	58	1	.	.	PUNCT
ejpam-5332	59	1	,	,	PUNCT
ejpam-5332	59	2	xn	xn	PROPN
ejpam-5332	59	3	and	and	CCONJ
ejpam-5332	59	4	the	the	DET
ejpam-5332	59	5	edges	edge	NOUN
ejpam-5332	59	6	are	be	AUX
ejpam-5332	59	7	[	[	X
ejpam-5332	59	8	x1	x1	PROPN
ejpam-5332	59	9	,	,	PUNCT
ejpam-5332	59	10	x2][x2	x2][x2	PROPN
ejpam-5332	59	11	,	,	PUNCT
ejpam-5332	59	12	x3	x3	ADJ
ejpam-5332	59	13	]	]	PUNCT
ejpam-5332	59	14	,	,	PUNCT
ejpam-5332	60	1	[	[	X
ejpam-5332	60	2	x3	x3	ADJ
ejpam-5332	60	3	,	,	PUNCT
ejpam-5332	60	4	x4	x4	PROPN
ejpam-5332	60	5	]	]	X
ejpam-5332	60	6	,	,	PUNCT
ejpam-5332	60	7	.	.	PUNCT
ejpam-5332	60	8	.	.	PUNCT
ejpam-5332	61	1	.	.	PUNCT
ejpam-5332	62	1	,	,	PUNCT
ejpam-5332	63	1	[	[	X
ejpam-5332	63	2	xn−1	xn−1	PROPN
ejpam-5332	63	3	,	,	PUNCT
ejpam-5332	63	4	xn	xn	PROPN
ejpam-5332	63	5	]	]	X
ejpam-5332	63	6	∈	∈	PROPN
ejpam-5332	63	7	e(g	e(g	PROPN
ejpam-5332	63	8	)	)	PUNCT
ejpam-5332	63	9	.	.	PUNCT
ejpam-5332	64	1	consider	consider	VERB
ejpam-5332	64	2	the	the	DET
ejpam-5332	64	3	following	follow	VERB
ejpam-5332	64	4	cases	case	NOUN
ejpam-5332	64	5	for	for	ADP
ejpam-5332	64	6	the	the	DET
ejpam-5332	64	7	graph	graph	NOUN
ejpam-5332	64	8	g	g	NOUN
ejpam-5332	64	9	and	and	CCONJ
ejpam-5332	64	10	its	its	PRON
ejpam-5332	64	11	complement	complement	NOUN
ejpam-5332	64	12	g.	g.	NOUN
ejpam-5332	64	13	case	case	NOUN
ejpam-5332	64	14	1	1	NUM
ejpam-5332	64	15	:	:	PUNCT
ejpam-5332	64	16	h	h	PROPN
ejpam-5332	64	17	=	=	SYM
ejpam-5332	64	18	k1	k1	PROPN
ejpam-5332	64	19	.	.	PUNCT
ejpam-5332	65	1	let	let	VERB
ejpam-5332	65	2	h	h	NOUN
ejpam-5332	65	3	=	=	NOUN
ejpam-5332	65	4	k1	k1	PROPN
ejpam-5332	65	5	where	where	SCONJ
ejpam-5332	65	6	v	v	NOUN
ejpam-5332	65	7	(	(	PUNCT
ejpam-5332	65	8	h	h	NOUN
ejpam-5332	65	9	)	)	PUNCT
ejpam-5332	66	1	=	=	PRON
ejpam-5332	66	2	{	{	PUNCT
ejpam-5332	66	3	xi	xi	NOUN
ejpam-5332	66	4	}	}	PUNCT
ejpam-5332	66	5	and	and	CCONJ
ejpam-5332	66	6	xi	xi	X
ejpam-5332	66	7	is	be	AUX
ejpam-5332	66	8	not	not	PART
ejpam-5332	66	9	an	an	DET
ejpam-5332	66	10	end	end	NOUN
ejpam-5332	66	11	vertex	vertex	NOUN
ejpam-5332	66	12	of	of	ADP
ejpam-5332	66	13	g.	g.	PROPN
ejpam-5332	67	1	this	this	PRON
ejpam-5332	67	2	means	mean	VERB
ejpam-5332	67	3	that	that	SCONJ
ejpam-5332	67	4	xi	xi	PROPN
ejpam-5332	67	5	is	be	AUX
ejpam-5332	67	6	connected	connect	VERB
ejpam-5332	67	7	to	to	ADP
ejpam-5332	67	8	xi−1	xi−1	PROPN
ejpam-5332	67	9	and	and	CCONJ
ejpam-5332	67	10	xi+1	xi+1	PROPN
ejpam-5332	67	11	in	in	ADP
ejpam-5332	67	12	g.	g.	PROPN
ejpam-5332	67	13	consequently	consequently	ADV
ejpam-5332	67	14	,	,	PUNCT
ejpam-5332	67	15	in	in	ADP
ejpam-5332	67	16	the	the	DET
ejpam-5332	67	17	complement	complement	NOUN
ejpam-5332	67	18	g	g	NOUN
ejpam-5332	67	19	,	,	PUNCT
ejpam-5332	67	20	xi	xi	X
ejpam-5332	67	21	is	be	AUX
ejpam-5332	67	22	adjacent	adjacent	ADJ
ejpam-5332	67	23	to	to	ADP
ejpam-5332	67	24	all	all	DET
ejpam-5332	67	25	vertices	vertex	NOUN
ejpam-5332	67	26	except	except	SCONJ
ejpam-5332	67	27	xi−1	xi−1	PROPN
ejpam-5332	67	28	and	and	CCONJ
ejpam-5332	67	29	xi+1	xi+1	PROPN
ejpam-5332	67	30	.	.	PUNCT
ejpam-5332	68	1	therefore	therefore	ADV
ejpam-5332	68	2	,	,	PUNCT
ejpam-5332	68	3	the	the	DET
ejpam-5332	68	4	distance	distance	NOUN
ejpam-5332	68	5	from	from	ADP
ejpam-5332	68	6	xi	xi	PRON
ejpam-5332	68	7	to	to	ADP
ejpam-5332	68	8	any	any	DET
ejpam-5332	68	9	vertex	vertex	NOUN
ejpam-5332	68	10	u	u	NOUN
ejpam-5332	68	11	∈	∈	PROPN
ejpam-5332	68	12	v	v	ADP
ejpam-5332	68	13	(	(	PUNCT
ejpam-5332	68	14	g	g	NOUN
ejpam-5332	68	15	)	)	PUNCT
ejpam-5332	68	16	\	\	NOUN
ejpam-5332	68	17	{	{	PUNCT
ejpam-5332	68	18	xi−1	xi−1	PROPN
ejpam-5332	68	19	,	,	PUNCT
ejpam-5332	68	20	xi+1	xi+1	NOUN
ejpam-5332	68	21	}	}	PUNCT
ejpam-5332	68	22	is	be	AUX
ejpam-5332	68	23	1	1	NUM
ejpam-5332	68	24	.	.	PUNCT
ejpam-5332	69	1	for	for	ADP
ejpam-5332	69	2	xi−1	xi−1	PROPN
ejpam-5332	69	3	and	and	CCONJ
ejpam-5332	69	4	xi+1	xi+1	PROPN
ejpam-5332	69	5	,	,	PUNCT
ejpam-5332	69	6	the	the	DET
ejpam-5332	69	7	distance	distance	NOUN
ejpam-5332	69	8	is	be	AUX
ejpam-5332	69	9	2	2	NUM
ejpam-5332	69	10	.	.	PUNCT
ejpam-5332	70	1	thus	thus	ADV
ejpam-5332	70	2	,	,	PUNCT
ejpam-5332	70	3	dg(u	dg(u	X
ejpam-5332	70	4	,	,	PUNCT
ejpam-5332	70	5	xi	xi	ADJ
ejpam-5332	70	6	)	)	PUNCT
ejpam-5332	70	7	≤	≤	NUM
ejpam-5332	70	8	2	2	NUM
ejpam-5332	70	9	for	for	ADP
ejpam-5332	70	10	all	all	PRON
ejpam-5332	70	11	u	u	NOUN
ejpam-5332	70	12	∈	∈	PROPN
ejpam-5332	70	13	v	v	NOUN
ejpam-5332	70	14	(	(	PUNCT
ejpam-5332	70	15	g	g	NOUN
ejpam-5332	70	16	)	)	PUNCT
ejpam-5332	70	17	\	\	NOUN
ejpam-5332	70	18	{	{	PUNCT
ejpam-5332	70	19	xi	xi	X
ejpam-5332	70	20	}	}	PUNCT
ejpam-5332	70	21	.	.	PUNCT
ejpam-5332	71	1	hence	hence	ADV
ejpam-5332	71	2	,	,	PUNCT
ejpam-5332	71	3	g	g	PROPN
ejpam-5332	71	4	is	be	AUX
ejpam-5332	71	5	k1	k1	NOUN
ejpam-5332	71	6	-	-	PUNCT
ejpam-5332	71	7	convex	convex	ADJ
ejpam-5332	71	8	2	2	NUM
ejpam-5332	71	9	-	-	PUNCT
ejpam-5332	71	10	accessible	accessible	ADJ
ejpam-5332	71	11	,	,	PUNCT
ejpam-5332	71	12	i.e.	i.e.	X
ejpam-5332	71	13	,	,	PUNCT
ejpam-5332	71	14	γk1(g	γk1(g	INTJ
ejpam-5332	71	15	)	)	PUNCT
ejpam-5332	72	1	=	=	SYM
ejpam-5332	72	2	2	2	X
ejpam-5332	72	3	.	.	X
ejpam-5332	72	4	case	case	NOUN
ejpam-5332	72	5	2	2	NUM
ejpam-5332	72	6	:	:	PUNCT
ejpam-5332	72	7	h	h	NOUN
ejpam-5332	72	8	=	=	PUNCT
ejpam-5332	72	9	p2	p2	PROPN
ejpam-5332	72	10	.	.	PUNCT
ejpam-5332	73	1	let	let	VERB
ejpam-5332	73	2	h	h	NOUN
ejpam-5332	73	3	=	=	PUNCT
ejpam-5332	73	4	p2	p2	PROPN
ejpam-5332	73	5	in	in	ADP
ejpam-5332	73	6	g.	g.	PROPN
ejpam-5332	73	7	without	without	ADP
ejpam-5332	73	8	loss	loss	NOUN
ejpam-5332	73	9	of	of	ADP
ejpam-5332	73	10	generality	generality	NOUN
ejpam-5332	73	11	,	,	PUNCT
ejpam-5332	73	12	assume	assume	VERB
ejpam-5332	73	13	that	that	SCONJ
ejpam-5332	73	14	v	v	X
ejpam-5332	73	15	(	(	PUNCT
ejpam-5332	73	16	h	h	NOUN
ejpam-5332	73	17	)	)	PUNCT
ejpam-5332	73	18	=	=	PRON
ejpam-5332	73	19	{	{	PUNCT
ejpam-5332	73	20	xi	xi	PROPN
ejpam-5332	73	21	,	,	PUNCT
ejpam-5332	73	22	xi+2	xi+2	NUM
ejpam-5332	73	23	}	}	PUNCT
ejpam-5332	73	24	.	.	PUNCT
ejpam-5332	74	1	since	since	SCONJ
ejpam-5332	74	2	[	[	X
ejpam-5332	74	3	xi	xi	X
ejpam-5332	74	4	,	,	PUNCT
ejpam-5332	74	5	xi+2	xi+2	NUM
ejpam-5332	74	6	]	]	X
ejpam-5332	74	7	∈	∈	PROPN
ejpam-5332	74	8	e(g	e(g	PROPN
ejpam-5332	74	9	)	)	PUNCT
ejpam-5332	74	10	,	,	PUNCT
ejpam-5332	74	11	the	the	DET
ejpam-5332	74	12	distance	distance	NOUN
ejpam-5332	74	13	dg(u	dg(u	NOUN
ejpam-5332	74	14	,	,	PUNCT
ejpam-5332	74	15	p2	p2	X
ejpam-5332	74	16	)	)	PUNCT
ejpam-5332	74	17	=	=	SYM
ejpam-5332	74	18	1	1	NUM
ejpam-5332	74	19	if	if	SCONJ
ejpam-5332	74	20	and	and	CCONJ
ejpam-5332	74	21	only	only	ADV
ejpam-5332	74	22	if	if	SCONJ
ejpam-5332	74	23	u	u	PROPN
ejpam-5332	74	24	̸=	̸=	PROPN
ejpam-5332	74	25	xi−1	xi−1	PROPN
ejpam-5332	74	26	and	and	CCONJ
ejpam-5332	74	27	u	u	PROPN
ejpam-5332	74	28	̸=	̸=	PROPN
ejpam-5332	74	29	xi+1	xi+1	NUM
ejpam-5332	74	30	.	.	PUNCT
ejpam-5332	75	1	however	however	ADV
ejpam-5332	75	2	,	,	PUNCT
ejpam-5332	75	3	dg(xi−1	dg(xi−1	PROPN
ejpam-5332	75	4	,	,	PUNCT
ejpam-5332	75	5	p2	p2	X
ejpam-5332	75	6	)	)	PUNCT
ejpam-5332	75	7	=	=	SYM
ejpam-5332	75	8	2	2	NUM
ejpam-5332	75	9	and	and	CCONJ
ejpam-5332	75	10	dg(xi+1	dg(xi+1	PROPN
ejpam-5332	75	11	,	,	PUNCT
ejpam-5332	75	12	p2	p2	X
ejpam-5332	75	13	)	)	PUNCT
ejpam-5332	75	14	=	=	SYM
ejpam-5332	76	1	2	2	X
ejpam-5332	76	2	.	.	PUNCT
ejpam-5332	76	3	therefore	therefore	ADV
ejpam-5332	76	4	,	,	PUNCT
ejpam-5332	76	5	for	for	ADP
ejpam-5332	76	6	any	any	DET
ejpam-5332	76	7	u	u	PROPN
ejpam-5332	76	8	∈	∈	PROPN
ejpam-5332	76	9	v	v	NOUN
ejpam-5332	76	10	(	(	PUNCT
ejpam-5332	76	11	g	g	NOUN
ejpam-5332	76	12	)	)	PUNCT
ejpam-5332	76	13	\	\	PROPN
ejpam-5332	76	14	v	v	X
ejpam-5332	76	15	(	(	PUNCT
ejpam-5332	76	16	p2	p2	PROPN
ejpam-5332	76	17	)	)	PUNCT
ejpam-5332	76	18	,	,	PUNCT
ejpam-5332	76	19	dg(u	dg(u	X
ejpam-5332	76	20	,	,	PUNCT
ejpam-5332	76	21	p2	p2	X
ejpam-5332	76	22	)	)	PUNCT
ejpam-5332	76	23	≤	≤	NUM
ejpam-5332	76	24	2	2	NUM
ejpam-5332	76	25	.	.	PUNCT
ejpam-5332	77	1	therefore	therefore	ADV
ejpam-5332	77	2	,	,	PUNCT
ejpam-5332	77	3	g	g	PROPN
ejpam-5332	77	4	is	be	AUX
ejpam-5332	77	5	p2	p2	NOUN
ejpam-5332	77	6	-	-	PUNCT
ejpam-5332	77	7	convex	convex	ADJ
ejpam-5332	77	8	2	2	NUM
ejpam-5332	77	9	-	-	PUNCT
ejpam-5332	77	10	accessible	accessible	ADJ
ejpam-5332	77	11	,	,	PUNCT
ejpam-5332	77	12	i.e.	i.e.	X
ejpam-5332	77	13	,γp2(g	,γp2(g	PUNCT
ejpam-5332	77	14	)	)	PUNCT
ejpam-5332	77	15	=	=	SYM
ejpam-5332	77	16	2	2	X
ejpam-5332	77	17	.	.	X
ejpam-5332	77	18	case	case	NOUN
ejpam-5332	77	19	3	3	NUM
ejpam-5332	77	20	:	:	PUNCT
ejpam-5332	77	21	the	the	DET
ejpam-5332	77	22	degree	degree	NOUN
ejpam-5332	77	23	of	of	ADP
ejpam-5332	77	24	x1	x1	PROPN
ejpam-5332	77	25	and	and	CCONJ
ejpam-5332	77	26	xn	xn	PROPN
ejpam-5332	77	27	in	in	ADP
ejpam-5332	77	28	g	g	PROPN
ejpam-5332	77	29	are	be	AUX
ejpam-5332	77	30	both	both	PRON
ejpam-5332	77	31	1	1	NUM
ejpam-5332	77	32	.	.	PUNCT
ejpam-5332	78	1	in	in	ADP
ejpam-5332	78	2	this	this	DET
ejpam-5332	78	3	case	case	NOUN
ejpam-5332	78	4	,	,	PUNCT
ejpam-5332	78	5	x1	x1	PROPN
ejpam-5332	78	6	and	and	CCONJ
ejpam-5332	78	7	xn	xn	PROPN
ejpam-5332	78	8	are	be	AUX
ejpam-5332	78	9	the	the	DET
ejpam-5332	78	10	start	start	NOUN
ejpam-5332	78	11	and	and	CCONJ
ejpam-5332	78	12	end	end	VERB
ejpam-5332	78	13	vertices	vertex	NOUN
ejpam-5332	78	14	of	of	ADP
ejpam-5332	78	15	the	the	DET
ejpam-5332	78	16	path	path	NOUN
ejpam-5332	78	17	g	g	NOUN
ejpam-5332	78	18	,	,	PUNCT
ejpam-5332	78	19	respectively	respectively	ADV
ejpam-5332	78	20	,	,	PUNCT
ejpam-5332	78	21	meaning	mean	VERB
ejpam-5332	78	22	they	they	PRON
ejpam-5332	78	23	are	be	AUX
ejpam-5332	78	24	not	not	PART
ejpam-5332	78	25	directly	directly	ADV
ejpam-5332	78	26	connected	connect	VERB
ejpam-5332	78	27	in	in	ADP
ejpam-5332	78	28	g.	g.	PROPN
ejpam-5332	78	29	therefore	therefore	ADV
ejpam-5332	78	30	,	,	PUNCT
ejpam-5332	78	31	there	there	PRON
ejpam-5332	78	32	exists	exist	VERB
ejpam-5332	78	33	and	and	CCONJ
ejpam-5332	78	34	edge	edge	VERB
ejpam-5332	78	35	[	[	X
ejpam-5332	78	36	x1	x1	PROPN
ejpam-5332	78	37	,	,	PUNCT
ejpam-5332	78	38	xn	xn	PROPN
ejpam-5332	78	39	]	]	X
ejpam-5332	78	40	∈	∈	PROPN
ejpam-5332	78	41	e(g	e(g	PROPN
ejpam-5332	78	42	)	)	PUNCT
ejpam-5332	78	43	connecting	connect	VERB
ejpam-5332	78	44	x1	x1	PROPN
ejpam-5332	78	45	and	and	CCONJ
ejpam-5332	78	46	xn	xn	NUM
ejpam-5332	78	47	.	.	PUNCT
ejpam-5332	79	1	considering	consider	VERB
ejpam-5332	79	2	this	this	DET
ejpam-5332	79	3	path	path	NOUN
ejpam-5332	79	4	as	as	ADP
ejpam-5332	79	5	the	the	DET
ejpam-5332	79	6	proper	proper	ADJ
ejpam-5332	79	7	convex	convex	NOUN
ejpam-5332	79	8	subgraph	subgraph	NOUN
ejpam-5332	79	9	in	in	ADP
ejpam-5332	79	10	g	g	PROPN
ejpam-5332	79	11	,	,	PUNCT
ejpam-5332	79	12	g	g	PROPN
ejpam-5332	79	13	is	be	AUX
ejpam-5332	79	14	p2	p2	NOUN
ejpam-5332	79	15	-	-	PUNCT
ejpam-5332	79	16	convex	convex	ADJ
ejpam-5332	79	17	1	1	NUM
ejpam-5332	79	18	-	-	PUNCT
ejpam-5332	79	19	accessible	accessible	ADJ
ejpam-5332	79	20	,	,	PUNCT
ejpam-5332	79	21	i.e.	i.e.	X
ejpam-5332	79	22	,	,	PUNCT
ejpam-5332	79	23	γp2(g	γp2(g	NUM
ejpam-5332	79	24	)	)	PUNCT
ejpam-5332	79	25	=	=	SYM
ejpam-5332	79	26	1	1	X
ejpam-5332	79	27	.	.	PUNCT
ejpam-5332	80	1	■	■	PUNCT
ejpam-5332	80	2	consider	consider	VERB
ejpam-5332	80	3	the	the	DET
ejpam-5332	80	4	complement	complement	NOUN
ejpam-5332	80	5	of	of	ADP
ejpam-5332	80	6	p5	p5	NOUN
ejpam-5332	80	7	,	,	PUNCT
ejpam-5332	80	8	that	that	PRON
ejpam-5332	80	9	is	be	AUX
ejpam-5332	80	10	p5	p5	ADJ
ejpam-5332	80	11	.	.	PUNCT
ejpam-5332	81	1	if	if	SCONJ
ejpam-5332	81	2	h1	h1	PROPN
ejpam-5332	81	3	=	=	SYM
ejpam-5332	81	4	k1	k1	PROPN
ejpam-5332	81	5	,	,	PUNCT
ejpam-5332	81	6	then	then	ADV
ejpam-5332	81	7	γh1(p5	γh1(p5	NUM
ejpam-5332	81	8	)	)	PUNCT
ejpam-5332	81	9	=	=	SYM
ejpam-5332	81	10	2	2	X
ejpam-5332	81	11	.	.	X
ejpam-5332	82	1	if	if	SCONJ
ejpam-5332	82	2	h2	h2	NOUN
ejpam-5332	82	3	=	=	PUNCT
ejpam-5332	83	1	[	[	X
ejpam-5332	83	2	a	a	X
ejpam-5332	83	3	,	,	PUNCT
ejpam-5332	83	4	c	c	NOUN
ejpam-5332	83	5	]	]	X
ejpam-5332	83	6	,	,	PUNCT
ejpam-5332	83	7	then	then	ADV
ejpam-5332	83	8	γh2(p5	γh2(p5	NUM
ejpam-5332	83	9	)	)	PUNCT
ejpam-5332	83	10	=	=	SYM
ejpam-5332	84	1	2	2	X
ejpam-5332	84	2	.	.	X
ejpam-5332	84	3	if	if	SCONJ
ejpam-5332	84	4	h3	h3	NOUN
ejpam-5332	84	5	=	=	PUNCT
ejpam-5332	85	1	[	[	X
ejpam-5332	85	2	a	a	X
ejpam-5332	85	3	,	,	PUNCT
ejpam-5332	85	4	e	e	NOUN
ejpam-5332	85	5	]	]	X
ejpam-5332	85	6	,	,	PUNCT
ejpam-5332	85	7	then	then	ADV
ejpam-5332	85	8	γh3(p5	γh3(p5	NOUN
ejpam-5332	85	9	)	)	PUNCT
ejpam-5332	85	10	=	=	SYM
ejpam-5332	86	1	1	1	X
ejpam-5332	86	2	.	.	PUNCT
ejpam-5332	87	1	if	if	SCONJ
ejpam-5332	87	2	h4	h4	PROPN
ejpam-5332	87	3	=	=	PUNCT
ejpam-5332	87	4	{	{	PUNCT
ejpam-5332	87	5	a	a	X
ejpam-5332	87	6	,	,	PUNCT
ejpam-5332	87	7	c	c	NOUN
ejpam-5332	87	8	,	,	PUNCT
ejpam-5332	87	9	e	e	NOUN
ejpam-5332	87	10	}	}	PUNCT
ejpam-5332	87	11	,	,	PUNCT
ejpam-5332	87	12	then	then	ADV
ejpam-5332	87	13	γh4(p5	γh4(p5	X
ejpam-5332	87	14	)	)	PUNCT
ejpam-5332	87	15	=	=	SYM
ejpam-5332	87	16	1	1	X
ejpam-5332	87	17	.	.	PUNCT
ejpam-5332	87	18	h.	h.	PROPN
ejpam-5332	87	19	b.	b.	PROPN
ejpam-5332	87	20	samson	samson	PROPN
ejpam-5332	87	21	,	,	PUNCT
ejpam-5332	87	22	i.	i.	PROPN
ejpam-5332	87	23	s.	s.	PROPN
ejpam-5332	87	24	aniversario	aniversario	PROPN
ejpam-5332	87	25	,	,	PUNCT
ejpam-5332	87	26	m.	m.	PROPN
ejpam-5332	87	27	j.	j.	PROPN
ejpam-5332	87	28	f.	f.	PROPN
ejpam-5332	87	29	luga	luga	PROPN
ejpam-5332	87	30	/	/	SYM
ejpam-5332	87	31	eur	eur	PROPN
ejpam-5332	87	32	.	.	PUNCT
ejpam-5332	88	1	j.	j.	PROPN
ejpam-5332	88	2	pure	pure	PROPN
ejpam-5332	88	3	appl	appl	PROPN
ejpam-5332	88	4	.	.	PROPN
ejpam-5332	88	5	math	math	PROPN
ejpam-5332	88	6	,	,	PUNCT
ejpam-5332	88	7	17	17	NUM
ejpam-5332	88	8	(	(	PUNCT
ejpam-5332	88	9	4	4	NUM
ejpam-5332	88	10	)	)	PUNCT
ejpam-5332	88	11	(	(	PUNCT
ejpam-5332	88	12	2024	2024	NUM
ejpam-5332	88	13	)	)	PUNCT
ejpam-5332	88	14	,	,	PUNCT
ejpam-5332	88	15	2930	2930	NUM
ejpam-5332	88	16	-	-	SYM
ejpam-5332	88	17	2938	2938	NUM
ejpam-5332	88	18	2933	2933	NUM
ejpam-5332	88	19	figure	figure	NOUN
ejpam-5332	88	20	1	1	NUM
ejpam-5332	88	21	:	:	PUNCT
ejpam-5332	88	22	p5	p5	ADJ
ejpam-5332	88	23	theorem	theorem	NOUN
ejpam-5332	88	24	2	2	X
ejpam-5332	88	25	.	.	PUNCT
ejpam-5332	89	1	let	let	VERB
ejpam-5332	89	2	g	g	PRON
ejpam-5332	89	3	be	be	AUX
ejpam-5332	89	4	a	a	DET
ejpam-5332	89	5	graph	graph	NOUN
ejpam-5332	89	6	such	such	ADJ
ejpam-5332	89	7	that	that	SCONJ
ejpam-5332	89	8	g	g	PROPN
ejpam-5332	89	9	=	=	SYM
ejpam-5332	89	10	cn	cn	PROPN
ejpam-5332	89	11	for	for	ADP
ejpam-5332	89	12	n	n	X
ejpam-5332	89	13	≥	≥	NUM
ejpam-5332	89	14	5	5	NUM
ejpam-5332	89	15	and	and	CCONJ
ejpam-5332	89	16	h	h	NOUN
ejpam-5332	89	17	be	be	VERB
ejpam-5332	89	18	a	a	DET
ejpam-5332	89	19	proper	proper	ADJ
ejpam-5332	89	20	convex	convex	NOUN
ejpam-5332	89	21	subgraph	subgraph	NOUN
ejpam-5332	89	22	of	of	ADP
ejpam-5332	89	23	g.	g.	PROPN
ejpam-5332	89	24	then	then	ADV
ejpam-5332	89	25	γh(g	γh(g	NOUN
ejpam-5332	89	26	)	)	PUNCT
ejpam-5332	90	1	=	=	PRON
ejpam-5332	90	2	{	{	PUNCT
ejpam-5332	90	3	2	2	NUM
ejpam-5332	90	4	,	,	PUNCT
ejpam-5332	90	5	if	if	SCONJ
ejpam-5332	90	6	h	h	NOUN
ejpam-5332	90	7	=	=	NOUN
ejpam-5332	90	8	p2	p2	PROPN
ejpam-5332	90	9	or	or	CCONJ
ejpam-5332	90	10	h	h	NOUN
ejpam-5332	90	11	=	=	SYM
ejpam-5332	90	12	k1	k1	PROPN
ejpam-5332	90	13	1	1	NUM
ejpam-5332	90	14	,	,	PUNCT
ejpam-5332	90	15	otherwise	otherwise	ADV
ejpam-5332	90	16	.	.	PUNCT
ejpam-5332	91	1	proof	proof	NOUN
ejpam-5332	91	2	.	.	PUNCT
ejpam-5332	92	1	let	let	VERB
ejpam-5332	92	2	cn	cn	PROPN
ejpam-5332	92	3	be	be	AUX
ejpam-5332	92	4	a	a	DET
ejpam-5332	92	5	cycle	cycle	NOUN
ejpam-5332	92	6	graph	graph	NOUN
ejpam-5332	92	7	defined	define	VERB
ejpam-5332	92	8	by	by	ADP
ejpam-5332	92	9	the	the	DET
ejpam-5332	92	10	sequence	sequence	NOUN
ejpam-5332	92	11	of	of	ADP
ejpam-5332	92	12	vertices	vertex	NOUN
ejpam-5332	92	13	[	[	X
ejpam-5332	92	14	u1	u1	NOUN
ejpam-5332	92	15	,	,	PUNCT
ejpam-5332	92	16	u2	u2	NOUN
ejpam-5332	92	17	,	,	PUNCT
ejpam-5332	92	18	.	.	PUNCT
ejpam-5332	92	19	.	.	PUNCT
ejpam-5332	93	1	.	.	PUNCT
ejpam-5332	94	1	,	,	PUNCT
ejpam-5332	94	2	un	un	PROPN
ejpam-5332	94	3	,	,	PUNCT
ejpam-5332	94	4	u1	u1	NOUN
ejpam-5332	94	5	]	]	PUNCT
ejpam-5332	94	6	where	where	SCONJ
ejpam-5332	94	7	the	the	DET
ejpam-5332	94	8	edges	edge	NOUN
ejpam-5332	94	9	are	be	AUX
ejpam-5332	94	10	[	[	X
ejpam-5332	94	11	u1	u1	NOUN
ejpam-5332	94	12	,	,	PUNCT
ejpam-5332	94	13	u2	u2	NOUN
ejpam-5332	94	14	]	]	PUNCT
ejpam-5332	94	15	,	,	PUNCT
ejpam-5332	95	1	[	[	X
ejpam-5332	95	2	u2	u2	NOUN
ejpam-5332	95	3	,	,	PUNCT
ejpam-5332	95	4	u3	u3	NOUN
ejpam-5332	95	5	]	]	PUNCT
ejpam-5332	95	6	,	,	PUNCT
ejpam-5332	95	7	.	.	PUNCT
ejpam-5332	95	8	.	.	PUNCT
ejpam-5332	95	9	.	.	PUNCT
ejpam-5332	96	1	,	,	PUNCT
ejpam-5332	97	1	[	[	X
ejpam-5332	97	2	un−1	un−1	PROPN
ejpam-5332	97	3	,	,	PUNCT
ejpam-5332	97	4	un	un	ADJ
ejpam-5332	97	5	]	]	X
ejpam-5332	97	6	,	,	PUNCT
ejpam-5332	97	7	[	[	X
ejpam-5332	97	8	un	un	ADJ
ejpam-5332	97	9	,	,	PUNCT
ejpam-5332	97	10	u1	u1	NOUN
ejpam-5332	97	11	]	]	PUNCT
ejpam-5332	97	12	∈	∈	PROPN
ejpam-5332	97	13	e(cn	e(cn	NOUN
ejpam-5332	97	14	)	)	PUNCT
ejpam-5332	97	15	.	.	PUNCT
ejpam-5332	98	1	in	in	ADP
ejpam-5332	98	2	this	this	DET
ejpam-5332	98	3	cycle	cycle	NOUN
ejpam-5332	98	4	graph	graph	NOUN
ejpam-5332	98	5	,	,	PUNCT
ejpam-5332	98	6	observe	observe	VERB
ejpam-5332	98	7	that	that	SCONJ
ejpam-5332	98	8	[	[	X
ejpam-5332	98	9	ui−1	ui−1	PROPN
ejpam-5332	98	10	,	,	PUNCT
ejpam-5332	98	11	ui	ui	NOUN
ejpam-5332	98	12	]	]	PUNCT
ejpam-5332	98	13	and	and	CCONJ
ejpam-5332	98	14	[	[	X
ejpam-5332	98	15	ui	ui	PROPN
ejpam-5332	98	16	,	,	PUNCT
ejpam-5332	98	17	ui+1	ui+1	PROPN
ejpam-5332	98	18	]	]	PUNCT
ejpam-5332	98	19	are	be	AUX
ejpam-5332	98	20	edges	edge	NOUN
ejpam-5332	98	21	of	of	ADP
ejpam-5332	98	22	cn	cn	PROPN
ejpam-5332	98	23	.	.	PUNCT
ejpam-5332	99	1	this	this	PRON
ejpam-5332	99	2	implies	imply	VERB
ejpam-5332	99	3	that	that	SCONJ
ejpam-5332	99	4	[	[	X
ejpam-5332	99	5	ui−1	ui−1	PROPN
ejpam-5332	99	6	,	,	PUNCT
ejpam-5332	99	7	ui	ui	NOUN
ejpam-5332	99	8	]	]	PUNCT
ejpam-5332	99	9	and	and	CCONJ
ejpam-5332	99	10	[	[	X
ejpam-5332	99	11	ui	ui	PROPN
ejpam-5332	99	12	,	,	PUNCT
ejpam-5332	99	13	ui+1	ui+1	PROPN
ejpam-5332	99	14	]	]	PUNCT
ejpam-5332	99	15	can	can	AUX
ejpam-5332	99	16	not	not	PART
ejpam-5332	99	17	be	be	AUX
ejpam-5332	99	18	edges	edge	NOUN
ejpam-5332	99	19	in	in	ADP
ejpam-5332	99	20	the	the	DET
ejpam-5332	99	21	complement	complement	NOUN
ejpam-5332	99	22	graph	graph	NOUN
ejpam-5332	99	23	cn	cn	PROPN
ejpam-5332	99	24	.	.	PROPN
ejpam-5332	100	1	without	without	ADP
ejpam-5332	100	2	loss	loss	NOUN
ejpam-5332	100	3	of	of	ADP
ejpam-5332	100	4	generality	generality	NOUN
ejpam-5332	100	5	,	,	PUNCT
ejpam-5332	100	6	let	let	VERB
ejpam-5332	100	7	p2	p2	X
ejpam-5332	100	8	=	=	SYM
ejpam-5332	100	9	{	{	PUNCT
ejpam-5332	100	10	ui	ui	PROPN
ejpam-5332	100	11	,	,	PUNCT
ejpam-5332	100	12	ui+2	ui+2	PROPN
ejpam-5332	100	13	}	}	PUNCT
ejpam-5332	100	14	where	where	SCONJ
ejpam-5332	100	15	[	[	X
ejpam-5332	100	16	ui	ui	NOUN
ejpam-5332	100	17	,	,	PUNCT
ejpam-5332	100	18	ui+2	ui+2	PROPN
ejpam-5332	100	19	]	]	X
ejpam-5332	100	20	∈	∈	PROPN
ejpam-5332	100	21	ecn	ecn	PROPN
ejpam-5332	100	22	.	.	PUNCT
ejpam-5332	101	1	for	for	ADP
ejpam-5332	101	2	any	any	DET
ejpam-5332	101	3	vertex	vertex	NOUN
ejpam-5332	101	4	v	v	NOUN
ejpam-5332	101	5	in	in	ADP
ejpam-5332	101	6	cn	cn	PROPN
ejpam-5332	101	7	,	,	PUNCT
ejpam-5332	101	8	the	the	DET
ejpam-5332	101	9	distance	distance	NOUN
ejpam-5332	101	10	dcn	dcn	PROPN
ejpam-5332	101	11	(	(	PUNCT
ejpam-5332	101	12	v	v	NOUN
ejpam-5332	101	13	,	,	PUNCT
ejpam-5332	101	14	p2	p2	PROPN
ejpam-5332	101	15	)	)	PUNCT
ejpam-5332	101	16	is	be	AUX
ejpam-5332	101	17	defined	define	VERB
ejpam-5332	101	18	as	as	ADP
ejpam-5332	101	19	the	the	DET
ejpam-5332	101	20	minimum	minimum	ADJ
ejpam-5332	101	21	distance	distance	NOUN
ejpam-5332	101	22	from	from	ADP
ejpam-5332	101	23	v	v	PRON
ejpam-5332	101	24	to	to	ADP
ejpam-5332	101	25	either	either	CCONJ
ejpam-5332	101	26	ui	ui	PROPN
ejpam-5332	101	27	or	or	CCONJ
ejpam-5332	101	28	ui−2	ui−2	NOUN
ejpam-5332	101	29	.	.	PUNCT
ejpam-5332	102	1	this	this	PRON
ejpam-5332	102	2	means	mean	VERB
ejpam-5332	102	3	that	that	SCONJ
ejpam-5332	102	4	for	for	ADP
ejpam-5332	102	5	v	v	NOUN
ejpam-5332	102	6	=	=	SYM
ejpam-5332	102	7	ui−1	ui−1	PROPN
ejpam-5332	102	8	or	or	CCONJ
ejpam-5332	102	9	v	v	NOUN
ejpam-5332	102	10	=	=	SYM
ejpam-5332	102	11	ui+1	ui+1	PROPN
ejpam-5332	102	12	,	,	PUNCT
ejpam-5332	102	13	dcn	dcn	PROPN
ejpam-5332	102	14	(	(	PUNCT
ejpam-5332	102	15	v	v	NOUN
ejpam-5332	102	16	,	,	PUNCT
ejpam-5332	102	17	p2	p2	X
ejpam-5332	102	18	)	)	PUNCT
ejpam-5332	102	19	=	=	SYM
ejpam-5332	102	20	2	2	NUM
ejpam-5332	102	21	and	and	CCONJ
ejpam-5332	102	22	for	for	ADP
ejpam-5332	102	23	any	any	DET
ejpam-5332	102	24	other	other	ADJ
ejpam-5332	102	25	vertex	vertex	NOUN
ejpam-5332	102	26	v	v	NOUN
ejpam-5332	102	27	,	,	PUNCT
ejpam-5332	102	28	which	which	PRON
ejpam-5332	102	29	is	be	AUX
ejpam-5332	102	30	neither	neither	CCONJ
ejpam-5332	102	31	v	v	NOUN
ejpam-5332	102	32	=	=	SYM
ejpam-5332	102	33	ui−1	ui−1	PROPN
ejpam-5332	102	34	nor	nor	CCONJ
ejpam-5332	102	35	v	v	NOUN
ejpam-5332	102	36	=	=	SYM
ejpam-5332	102	37	ui+1	ui+1	PROPN
ejpam-5332	102	38	,	,	PUNCT
ejpam-5332	102	39	dcn	dcn	PROPN
ejpam-5332	102	40	(	(	PUNCT
ejpam-5332	102	41	v	v	NOUN
ejpam-5332	102	42	,	,	PUNCT
ejpam-5332	102	43	p2	p2	X
ejpam-5332	102	44	)	)	PUNCT
ejpam-5332	102	45	=	=	SYM
ejpam-5332	102	46	2	2	NUM
ejpam-5332	102	47	as	as	ADV
ejpam-5332	102	48	well	well	ADV
ejpam-5332	102	49	.	.	PUNCT
ejpam-5332	103	1	thus	thus	ADV
ejpam-5332	103	2	,	,	PUNCT
ejpam-5332	103	3	the	the	DET
ejpam-5332	103	4	distance	distance	NOUN
ejpam-5332	103	5	from	from	ADP
ejpam-5332	103	6	any	any	DET
ejpam-5332	103	7	vertex	vertex	NOUN
ejpam-5332	103	8	to	to	ADP
ejpam-5332	103	9	p2	p2	PROPN
ejpam-5332	103	10	is	be	AUX
ejpam-5332	103	11	atmost	atmost	PROPN
ejpam-5332	103	12	2	2	NUM
ejpam-5332	103	13	,	,	PUNCT
ejpam-5332	103	14	showing	show	VERB
ejpam-5332	103	15	that	that	SCONJ
ejpam-5332	103	16	cn	cn	PROPN
ejpam-5332	103	17	is	be	AUX
ejpam-5332	103	18	p2	p2	NOUN
ejpam-5332	103	19	-	-	PUNCT
ejpam-5332	103	20	convex	convex	ADJ
ejpam-5332	103	21	2	2	NUM
ejpam-5332	103	22	-	-	PUNCT
ejpam-5332	103	23	accessible	accessible	ADJ
ejpam-5332	103	24	.	.	PUNCT
ejpam-5332	104	1	■	■	PUNCT
ejpam-5332	104	2	remark	remark	NOUN
ejpam-5332	104	3	1	1	NUM
ejpam-5332	104	4	.	.	PUNCT
ejpam-5332	104	5	for	for	ADP
ejpam-5332	104	6	the	the	DET
ejpam-5332	104	7	star	star	NOUN
ejpam-5332	104	8	,	,	PUNCT
ejpam-5332	104	9	wheel	wheel	NOUN
ejpam-5332	104	10	,	,	PUNCT
ejpam-5332	104	11	fan	fan	PROPN
ejpam-5332	104	12	,	,	PUNCT
ejpam-5332	104	13	complete	complete	ADJ
ejpam-5332	104	14	graph	graph	NOUN
ejpam-5332	104	15	,	,	PUNCT
ejpam-5332	104	16	complete	complete	ADJ
ejpam-5332	104	17	bipartite	bipartite	NOUN
ejpam-5332	104	18	and	and	CCONJ
ejpam-5332	104	19	join	join	VERB
ejpam-5332	104	20	,	,	PUNCT
ejpam-5332	104	21	the	the	DET
ejpam-5332	104	22	complement	complement	NOUN
ejpam-5332	104	23	of	of	ADP
ejpam-5332	104	24	these	these	DET
ejpam-5332	104	25	graphs	graph	NOUN
ejpam-5332	104	26	have	have	VERB
ejpam-5332	104	27	isolated	isolate	VERB
ejpam-5332	104	28	vertices	vertex	NOUN
ejpam-5332	104	29	.	.	PUNCT
ejpam-5332	105	1	this	this	PRON
ejpam-5332	105	2	means	mean	VERB
ejpam-5332	105	3	that	that	SCONJ
ejpam-5332	105	4	it	it	PRON
ejpam-5332	105	5	is	be	AUX
ejpam-5332	105	6	not	not	PART
ejpam-5332	105	7	possible	possible	ADJ
ejpam-5332	105	8	to	to	PART
ejpam-5332	105	9	get	get	VERB
ejpam-5332	105	10	the	the	DET
ejpam-5332	105	11	h	h	NOUN
ejpam-5332	105	12	convex	convex	NOUN
ejpam-5332	105	13	accessibility	accessibility	NOUN
ejpam-5332	105	14	number	number	NOUN
ejpam-5332	105	15	of	of	ADP
ejpam-5332	105	16	these	these	DET
ejpam-5332	105	17	graphs	graph	NOUN
ejpam-5332	105	18	.	.	PUNCT
ejpam-5332	106	1	3	3	X
ejpam-5332	106	2	.	.	X
ejpam-5332	106	3	h	h	PROPN
ejpam-5332	106	4	convex	convex	PROPN
ejpam-5332	106	5	accessibility	accessibility	NOUN
ejpam-5332	106	6	number	number	NOUN
ejpam-5332	106	7	of	of	ADP
ejpam-5332	106	8	the	the	DET
ejpam-5332	106	9	cartesian	cartesian	ADJ
ejpam-5332	106	10	product	product	NOUN
ejpam-5332	106	11	of	of	ADP
ejpam-5332	106	12	graphs	graph	NOUN
ejpam-5332	106	13	in	in	ADP
ejpam-5332	106	14	this	this	DET
ejpam-5332	106	15	section	section	NOUN
ejpam-5332	106	16	,	,	PUNCT
ejpam-5332	106	17	we	we	PRON
ejpam-5332	106	18	established	establish	VERB
ejpam-5332	106	19	the	the	DET
ejpam-5332	106	20	h	h	NOUN
ejpam-5332	106	21	-	-	PUNCT
ejpam-5332	106	22	convex	convex	NOUN
ejpam-5332	106	23	accessibility	accessibility	NOUN
ejpam-5332	106	24	number	number	NOUN
ejpam-5332	106	25	of	of	ADP
ejpam-5332	106	26	the	the	DET
ejpam-5332	106	27	cartesian	cartesian	ADJ
ejpam-5332	106	28	product	product	NOUN
ejpam-5332	106	29	of	of	ADP
ejpam-5332	106	30	graphs	graph	NOUN
ejpam-5332	106	31	.	.	PUNCT
ejpam-5332	107	1	theorem	theorem	NOUN
ejpam-5332	107	2	3	3	X
ejpam-5332	107	3	.	.	PUNCT
ejpam-5332	108	1	let	let	VERB
ejpam-5332	108	2	g1	g1	PROPN
ejpam-5332	108	3	and	and	CCONJ
ejpam-5332	108	4	g2	g2	PROPN
ejpam-5332	108	5	be	be	AUX
ejpam-5332	108	6	connected	connect	VERB
ejpam-5332	108	7	graphs	graph	NOUN
ejpam-5332	108	8	and	and	CCONJ
ejpam-5332	108	9	h	h	NOUN
ejpam-5332	108	10	=	=	SYM
ejpam-5332	108	11	h1	h1	PROPN
ejpam-5332	108	12	□	□	PUNCT
ejpam-5332	108	13	h2	h2	NOUN
ejpam-5332	108	14	be	be	AUX
ejpam-5332	108	15	a	a	DET
ejpam-5332	108	16	proper	proper	ADJ
ejpam-5332	108	17	convex	convex	NOUN
ejpam-5332	108	18	subgraph	subgraph	NOUN
ejpam-5332	108	19	of	of	ADP
ejpam-5332	108	20	v	v	NOUN
ejpam-5332	108	21	(	(	PUNCT
ejpam-5332	108	22	g1	g1	PROPN
ejpam-5332	108	23	□	□	PROPN
ejpam-5332	108	24	g2	g2	PROPN
ejpam-5332	108	25	)	)	PUNCT
ejpam-5332	108	26	,	,	PUNCT
ejpam-5332	108	27	where	where	SCONJ
ejpam-5332	108	28	h1	h1	NOUN
ejpam-5332	108	29	and	and	CCONJ
ejpam-5332	108	30	h2	h2	NOUN
ejpam-5332	108	31	are	be	AUX
ejpam-5332	108	32	proper	proper	ADJ
ejpam-5332	108	33	convex	convex	ADJ
ejpam-5332	108	34	subgraphs	subgraph	NOUN
ejpam-5332	108	35	of	of	ADP
ejpam-5332	108	36	g1	g1	NOUN
ejpam-5332	108	37	and	and	CCONJ
ejpam-5332	108	38	g2	g2	PROPN
ejpam-5332	108	39	respectively	respectively	ADV
ejpam-5332	108	40	.	.	PUNCT
ejpam-5332	109	1	then	then	ADV
ejpam-5332	109	2	,	,	PUNCT
ejpam-5332	109	3	γh(g1	γh(g1	PROPN
ejpam-5332	109	4	□	□	SYM
ejpam-5332	109	5	g2	g2	NOUN
ejpam-5332	109	6	)	)	PUNCT
ejpam-5332	109	7	=	=	PUNCT
ejpam-5332	109	8	γh1(g1	γh1(g1	X
ejpam-5332	109	9	)	)	PUNCT
ejpam-5332	109	10	+	+	NUM
ejpam-5332	109	11	γh2(g2	γh2(g2	NOUN
ejpam-5332	109	12	)	)	PUNCT
ejpam-5332	109	13	proof	proof	NOUN
ejpam-5332	109	14	.	.	PUNCT
ejpam-5332	109	15	suppose	suppose	VERB
ejpam-5332	109	16	that	that	SCONJ
ejpam-5332	109	17	g1	g1	PROPN
ejpam-5332	109	18	and	and	CCONJ
ejpam-5332	109	19	g2	g2	PROPN
ejpam-5332	109	20	are	be	AUX
ejpam-5332	109	21	connected	connect	VERB
ejpam-5332	109	22	graphs	graph	NOUN
ejpam-5332	109	23	and	and	CCONJ
ejpam-5332	109	24	h	h	NOUN
ejpam-5332	109	25	=	=	SYM
ejpam-5332	109	26	h1	h1	PROPN
ejpam-5332	109	27	□	□	PUNCT
ejpam-5332	109	28	h2	h2	NOUN
ejpam-5332	109	29	is	be	AUX
ejpam-5332	109	30	a	a	DET
ejpam-5332	109	31	convex	convex	NOUN
ejpam-5332	109	32	set	set	VERB
ejpam-5332	109	33	in	in	ADP
ejpam-5332	109	34	g1	g1	NOUN
ejpam-5332	109	35	□	□	PROPN
ejpam-5332	109	36	g2	g2	PROPN
ejpam-5332	109	37	.	.	PUNCT
ejpam-5332	110	1	by	by	ADP
ejpam-5332	110	2	[	[	X
ejpam-5332	110	3	5	5	NUM
ejpam-5332	110	4	]	]	PUNCT
ejpam-5332	110	5	,	,	PUNCT
ejpam-5332	110	6	h1	h1	PROPN
ejpam-5332	110	7	and	and	CCONJ
ejpam-5332	110	8	h2	h2	NOUN
ejpam-5332	110	9	are	be	AUX
ejpam-5332	110	10	convex	convex	NOUN
ejpam-5332	110	11	sets	set	NOUN
ejpam-5332	110	12	in	in	ADP
ejpam-5332	110	13	g1	g1	PROPN
ejpam-5332	110	14	and	and	CCONJ
ejpam-5332	110	15	g2	g2	PROPN
ejpam-5332	110	16	respectively	respectively	ADV
ejpam-5332	110	17	.	.	PUNCT
ejpam-5332	111	1	h.	h.	PROPN
ejpam-5332	111	2	b.	b.	PROPN
ejpam-5332	111	3	samson	samson	PROPN
ejpam-5332	111	4	,	,	PUNCT
ejpam-5332	111	5	i.	i.	PROPN
ejpam-5332	111	6	s.	s.	PROPN
ejpam-5332	111	7	aniversario	aniversario	PROPN
ejpam-5332	111	8	,	,	PUNCT
ejpam-5332	111	9	m.	m.	PROPN
ejpam-5332	111	10	j.	j.	PROPN
ejpam-5332	111	11	f.	f.	PROPN
ejpam-5332	111	12	luga	luga	PROPN
ejpam-5332	111	13	/	/	SYM
ejpam-5332	111	14	eur	eur	PROPN
ejpam-5332	111	15	.	.	PUNCT
ejpam-5332	112	1	j.	j.	PROPN
ejpam-5332	112	2	pure	pure	PROPN
ejpam-5332	112	3	appl	appl	PROPN
ejpam-5332	112	4	.	.	PROPN
ejpam-5332	112	5	math	math	PROPN
ejpam-5332	112	6	,	,	PUNCT
ejpam-5332	112	7	17	17	NUM
ejpam-5332	112	8	(	(	PUNCT
ejpam-5332	112	9	4	4	NUM
ejpam-5332	112	10	)	)	PUNCT
ejpam-5332	112	11	(	(	PUNCT
ejpam-5332	112	12	2024	2024	NUM
ejpam-5332	112	13	)	)	PUNCT
ejpam-5332	112	14	,	,	PUNCT
ejpam-5332	112	15	2930	2930	NUM
ejpam-5332	112	16	-	-	SYM
ejpam-5332	112	17	2938	2938	NUM
ejpam-5332	112	18	2934	2934	NUM
ejpam-5332	112	19	consider	consider	VERB
ejpam-5332	112	20	any	any	DET
ejpam-5332	112	21	vertex	vertex	NOUN
ejpam-5332	112	22	(	(	PUNCT
ejpam-5332	112	23	u	u	NOUN
ejpam-5332	112	24	,	,	PUNCT
ejpam-5332	112	25	v	v	NOUN
ejpam-5332	112	26	)	)	PUNCT
ejpam-5332	112	27	∈	∈	NOUN
ejpam-5332	112	28	v	v	NOUN
ejpam-5332	112	29	(	(	PUNCT
ejpam-5332	112	30	g1	g1	PROPN
ejpam-5332	112	31	□	□	SYM
ejpam-5332	112	32	g2	g2	PROPN
ejpam-5332	112	33	)	)	PUNCT
ejpam-5332	112	34	\	\	PROPN
ejpam-5332	113	1	v	v	X
ejpam-5332	113	2	(	(	PUNCT
ejpam-5332	113	3	h1	h1	PROPN
ejpam-5332	113	4	□	□	PUNCT
ejpam-5332	113	5	h2	h2	NOUN
ejpam-5332	113	6	)	)	PUNCT
ejpam-5332	113	7	and	and	CCONJ
ejpam-5332	113	8	any	any	DET
ejpam-5332	113	9	vertex	vertex	NOUN
ejpam-5332	113	10	(	(	PUNCT
ejpam-5332	113	11	x	x	NOUN
ejpam-5332	113	12	,	,	PUNCT
ejpam-5332	113	13	y	y	NOUN
ejpam-5332	113	14	)	)	PUNCT
ejpam-5332	113	15	∈	∈	PROPN
ejpam-5332	113	16	v	v	X
ejpam-5332	113	17	(	(	PUNCT
ejpam-5332	113	18	h1	h1	PROPN
ejpam-5332	113	19	□	□	PUNCT
ejpam-5332	113	20	h2	h2	NOUN
ejpam-5332	113	21	)	)	PUNCT
ejpam-5332	113	22	.	.	PUNCT
ejpam-5332	114	1	then	then	ADV
ejpam-5332	114	2	the	the	DET
ejpam-5332	114	3	distance	distance	NOUN
ejpam-5332	114	4	between	between	ADP
ejpam-5332	114	5	these	these	DET
ejpam-5332	114	6	vertices	vertex	NOUN
ejpam-5332	114	7	in	in	ADP
ejpam-5332	114	8	g1	g1	NOUN
ejpam-5332	114	9	□	□	SYM
ejpam-5332	114	10	g2	g2	PROPN
ejpam-5332	114	11	is	be	AUX
ejpam-5332	114	12	given	give	VERB
ejpam-5332	114	13	by	by	ADP
ejpam-5332	114	14	,	,	PUNCT
ejpam-5332	114	15	dg1	dg1	PROPN
ejpam-5332	114	16	□	□	PUNCT
ejpam-5332	114	17	g2((u	g2((u	NOUN
ejpam-5332	114	18	,	,	PUNCT
ejpam-5332	114	19	v	v	NOUN
ejpam-5332	114	20	)	)	PUNCT
ejpam-5332	114	21	,	,	PUNCT
ejpam-5332	114	22	(	(	PUNCT
ejpam-5332	114	23	x	x	X
ejpam-5332	114	24	,	,	PUNCT
ejpam-5332	114	25	y	y	NOUN
ejpam-5332	114	26	)	)	PUNCT
ejpam-5332	114	27	)	)	PUNCT
ejpam-5332	115	1	=	=	SYM
ejpam-5332	115	2	dg1(u	dg1(u	NOUN
ejpam-5332	115	3	,	,	PUNCT
ejpam-5332	115	4	x	x	PRON
ejpam-5332	115	5	)	)	PUNCT
ejpam-5332	115	6	+	+	CCONJ
ejpam-5332	115	7	dg2(v	dg2(v	PROPN
ejpam-5332	115	8	,	,	PUNCT
ejpam-5332	115	9	y	y	PROPN
ejpam-5332	115	10	)	)	PUNCT
ejpam-5332	115	11	.	.	PUNCT
ejpam-5332	116	1	since	since	SCONJ
ejpam-5332	116	2	h1	h1	PROPN
ejpam-5332	116	3	is	be	AUX
ejpam-5332	116	4	a	a	DET
ejpam-5332	116	5	proper	proper	ADJ
ejpam-5332	116	6	convex	convex	NOUN
ejpam-5332	116	7	subgraph	subgraph	NOUN
ejpam-5332	116	8	of	of	ADP
ejpam-5332	116	9	g1	g1	PROPN
ejpam-5332	116	10	and	and	CCONJ
ejpam-5332	116	11	h2	h2	NOUN
ejpam-5332	116	12	is	be	AUX
ejpam-5332	116	13	also	also	ADV
ejpam-5332	116	14	a	a	DET
ejpam-5332	116	15	proper	proper	ADJ
ejpam-5332	116	16	convex	convex	NOUN
ejpam-5332	116	17	subgraph	subgraph	NOUN
ejpam-5332	116	18	of	of	ADP
ejpam-5332	116	19	g2	g2	PROPN
ejpam-5332	116	20	,	,	PUNCT
ejpam-5332	116	21	we	we	PRON
ejpam-5332	116	22	have	have	VERB
ejpam-5332	116	23	γh1(g1	γh1(g1	NOUN
ejpam-5332	116	24	)	)	PUNCT
ejpam-5332	116	25	≤	≤	NUM
ejpam-5332	116	26	dg1(u	dg1(u	NOUN
ejpam-5332	116	27	,	,	PUNCT
ejpam-5332	116	28	h1	h1	NOUN
ejpam-5332	116	29	)	)	PUNCT
ejpam-5332	116	30	γh2(g2	γh2(g2	NOUN
ejpam-5332	116	31	)	)	PUNCT
ejpam-5332	116	32	≤	≤	NUM
ejpam-5332	116	33	dg2(v	dg2(v	PROPN
ejpam-5332	116	34	,	,	PUNCT
ejpam-5332	116	35	h2	h2	PROPN
ejpam-5332	116	36	)	)	PUNCT
ejpam-5332	116	37	.	.	PUNCT
ejpam-5332	117	1	adding	add	VERB
ejpam-5332	117	2	these	these	DET
ejpam-5332	117	3	inequalities	inequality	NOUN
ejpam-5332	117	4	,	,	PUNCT
ejpam-5332	117	5	we	we	PRON
ejpam-5332	117	6	have	have	VERB
ejpam-5332	117	7	γh1(g1	γh1(g1	NOUN
ejpam-5332	117	8	)	)	PUNCT
ejpam-5332	118	1	+	+	NUM
ejpam-5332	118	2	γh2(g2	γh2(g2	NOUN
ejpam-5332	118	3	)	)	PUNCT
ejpam-5332	118	4	≤	≤	NUM
ejpam-5332	118	5	dg1(u	dg1(u	NOUN
ejpam-5332	118	6	,	,	PUNCT
ejpam-5332	118	7	h1	h1	NOUN
ejpam-5332	118	8	)	)	PUNCT
ejpam-5332	118	9	+	+	NUM
ejpam-5332	118	10	dg2(v	dg2(v	PROPN
ejpam-5332	118	11	,	,	PUNCT
ejpam-5332	118	12	h2	h2	NOUN
ejpam-5332	118	13	)	)	PUNCT
ejpam-5332	118	14	γh1(g1	γh1(g1	NOUN
ejpam-5332	118	15	)	)	PUNCT
ejpam-5332	118	16	+	+	NUM
ejpam-5332	118	17	γh2(g2	γh2(g2	NOUN
ejpam-5332	118	18	)	)	PUNCT
ejpam-5332	118	19	≤	≤	PUNCT
ejpam-5332	118	20	dg1	dg1	PROPN
ejpam-5332	118	21	□	□	PUNCT
ejpam-5332	118	22	g2((u	g2((u	NOUN
ejpam-5332	118	23	,	,	PUNCT
ejpam-5332	118	24	v),h1	v),h1	NOUN
ejpam-5332	118	25	□	□	SYM
ejpam-5332	118	26	h2	h2	NOUN
ejpam-5332	118	27	)	)	PUNCT
ejpam-5332	118	28	.	.	PUNCT
ejpam-5332	119	1	since	since	SCONJ
ejpam-5332	119	2	(	(	PUNCT
ejpam-5332	119	3	u	u	NOUN
ejpam-5332	119	4	,	,	PUNCT
ejpam-5332	119	5	v	v	NOUN
ejpam-5332	119	6	)	)	PUNCT
ejpam-5332	119	7	and	and	CCONJ
ejpam-5332	119	8	(	(	PUNCT
ejpam-5332	119	9	x	x	X
ejpam-5332	119	10	,	,	PUNCT
ejpam-5332	119	11	y	y	NOUN
ejpam-5332	119	12	)	)	PUNCT
ejpam-5332	119	13	are	be	AUX
ejpam-5332	119	14	arbitrarily	arbitrarily	ADV
ejpam-5332	119	15	chosen	choose	VERB
ejpam-5332	119	16	vertices	vertex	NOUN
ejpam-5332	119	17	in	in	ADP
ejpam-5332	119	18	g1	g1	NOUN
ejpam-5332	119	19	□	□	PROPN
ejpam-5332	119	20	g2	g2	PROPN
ejpam-5332	119	21	and	and	CCONJ
ejpam-5332	119	22	h1	h1	PROPN
ejpam-5332	119	23	□	□	PUNCT
ejpam-5332	119	24	h2	h2	NOUN
ejpam-5332	119	25	,	,	PUNCT
ejpam-5332	119	26	respectively	respectively	ADV
ejpam-5332	119	27	,	,	PUNCT
ejpam-5332	119	28	the	the	DET
ejpam-5332	119	29	distance	distance	NOUN
ejpam-5332	119	30	dg1	dg1	PROPN
ejpam-5332	119	31	□	□	PROPN
ejpam-5332	119	32	g2	g2	PROPN
ejpam-5332	119	33	=	=	SYM
ejpam-5332	119	34	(	(	PUNCT
ejpam-5332	119	35	(	(	PUNCT
ejpam-5332	119	36	u	u	NOUN
ejpam-5332	119	37	,	,	PUNCT
ejpam-5332	119	38	v	v	NOUN
ejpam-5332	119	39	)	)	PUNCT
ejpam-5332	119	40	,	,	PUNCT
ejpam-5332	119	41	(	(	PUNCT
ejpam-5332	119	42	x	x	X
ejpam-5332	119	43	,	,	PUNCT
ejpam-5332	119	44	y	y	NOUN
ejpam-5332	119	45	)	)	PUNCT
ejpam-5332	119	46	)	)	PUNCT
ejpam-5332	119	47	represents	represent	VERB
ejpam-5332	119	48	the	the	DET
ejpam-5332	119	49	shortest	short	ADJ
ejpam-5332	119	50	path	path	NOUN
ejpam-5332	119	51	distance	distance	NOUN
ejpam-5332	119	52	between	between	ADP
ejpam-5332	119	53	(	(	PUNCT
ejpam-5332	119	54	u	u	NOUN
ejpam-5332	119	55	,	,	PUNCT
ejpam-5332	119	56	v	v	NOUN
ejpam-5332	119	57	)	)	PUNCT
ejpam-5332	119	58	and	and	CCONJ
ejpam-5332	119	59	(	(	PUNCT
ejpam-5332	119	60	x	x	X
ejpam-5332	119	61	,	,	PUNCT
ejpam-5332	119	62	y	y	PROPN
ejpam-5332	119	63	)	)	PUNCT
ejpam-5332	119	64	.	.	PUNCT
ejpam-5332	120	1	therefore	therefore	ADV
ejpam-5332	120	2	,	,	PUNCT
ejpam-5332	120	3	dg1	dg1	PROPN
ejpam-5332	120	4	□	□	PUNCT
ejpam-5332	120	5	g2((u	g2((u	NOUN
ejpam-5332	120	6	,	,	PUNCT
ejpam-5332	120	7	v),h1	v),h1	NOUN
ejpam-5332	120	8	□	□	SYM
ejpam-5332	120	9	h2	h2	NOUN
ejpam-5332	120	10	)	)	PUNCT
ejpam-5332	120	11	=	=	SYM
ejpam-5332	121	1	γh(g1	γh(g1	X
ejpam-5332	121	2	□	□	X
ejpam-5332	121	3	g2	g2	NOUN
ejpam-5332	121	4	)	)	PUNCT
ejpam-5332	121	5	.	.	PUNCT
ejpam-5332	122	1	substituting	substitute	VERB
ejpam-5332	122	2	this	this	DET
ejpam-5332	122	3	result	result	NOUN
ejpam-5332	122	4	,	,	PUNCT
ejpam-5332	122	5	we	we	PRON
ejpam-5332	122	6	have	have	VERB
ejpam-5332	122	7	γh1(g1	γh1(g1	NOUN
ejpam-5332	122	8	)	)	PUNCT
ejpam-5332	123	1	+	+	NUM
ejpam-5332	123	2	γh2(g2	γh2(g2	NOUN
ejpam-5332	123	3	)	)	PUNCT
ejpam-5332	123	4	≤	≤	NOUN
ejpam-5332	123	5	γh(g1	γh(g1	NOUN
ejpam-5332	123	6	□	□	SYM
ejpam-5332	123	7	g2	g2	NOUN
ejpam-5332	123	8	)	)	PUNCT
ejpam-5332	123	9	.	.	PUNCT
ejpam-5332	124	1	by	by	ADP
ejpam-5332	124	2	the	the	DET
ejpam-5332	124	3	definition	definition	NOUN
ejpam-5332	124	4	of	of	ADP
ejpam-5332	124	5	convex	convex	ADJ
ejpam-5332	124	6	accessibility	accessibility	NOUN
ejpam-5332	124	7	number	number	NOUN
ejpam-5332	124	8	,	,	PUNCT
ejpam-5332	124	9	we	we	PRON
ejpam-5332	124	10	also	also	ADV
ejpam-5332	124	11	have	have	VERB
ejpam-5332	124	12	γh(g1	γh(g1	NOUN
ejpam-5332	124	13	□	□	SYM
ejpam-5332	124	14	g2	g2	NOUN
ejpam-5332	124	15	)	)	PUNCT
ejpam-5332	124	16	≤	≤	NOUN
ejpam-5332	124	17	γh1(g1	γh1(g1	ADV
ejpam-5332	124	18	)	)	PUNCT
ejpam-5332	124	19	+	+	NUM
ejpam-5332	124	20	γh2(g2	γh2(g2	NOUN
ejpam-5332	124	21	)	)	PUNCT
ejpam-5332	124	22	.	.	PUNCT
ejpam-5332	125	1	combining	combine	VERB
ejpam-5332	125	2	these	these	DET
ejpam-5332	125	3	inequalities	inequality	NOUN
ejpam-5332	125	4	,	,	PUNCT
ejpam-5332	125	5	we	we	PRON
ejpam-5332	125	6	obtain	obtain	VERB
ejpam-5332	125	7	,	,	PUNCT
ejpam-5332	125	8	γh(g1	γh(g1	NOUN
ejpam-5332	125	9	□	□	SYM
ejpam-5332	125	10	g2	g2	NOUN
ejpam-5332	125	11	)	)	PUNCT
ejpam-5332	125	12	=	=	PUNCT
ejpam-5332	126	1	γh1(g1	γh1(g1	X
ejpam-5332	126	2	)	)	PUNCT
ejpam-5332	127	1	+	+	NUM
ejpam-5332	127	2	γh2(g2	γh2(g2	NOUN
ejpam-5332	127	3	)	)	PUNCT
ejpam-5332	127	4	.	.	PUNCT
ejpam-5332	128	1	■	■	PUNCT
ejpam-5332	128	2	consider	consider	VERB
ejpam-5332	128	3	the	the	DET
ejpam-5332	128	4	cartesian	cartesian	ADJ
ejpam-5332	128	5	product	product	NOUN
ejpam-5332	128	6	of	of	ADP
ejpam-5332	128	7	p6	p6	PROPN
ejpam-5332	128	8	and	and	CCONJ
ejpam-5332	128	9	p6	p6	PROPN
ejpam-5332	128	10	,	,	PUNCT
ejpam-5332	128	11	that	that	PRON
ejpam-5332	128	12	is	is	AUX
ejpam-5332	128	13	p6	p6	PROPN
ejpam-5332	128	14	□	□	PUNCT
ejpam-5332	128	15	p6	p6	NOUN
ejpam-5332	128	16	is	be	AUX
ejpam-5332	128	17	as	as	SCONJ
ejpam-5332	128	18	shown	show	VERB
ejpam-5332	128	19	in	in	ADP
ejpam-5332	128	20	figure	figure	NOUN
ejpam-5332	128	21	2	2	NUM
ejpam-5332	128	22	and	and	CCONJ
ejpam-5332	128	23	a	a	DET
ejpam-5332	128	24	proper	proper	ADJ
ejpam-5332	128	25	convex	convex	NOUN
ejpam-5332	128	26	subgraph	subgraph	NOUN
ejpam-5332	128	27	h	h	NOUN
ejpam-5332	128	28	=	=	PUNCT
ejpam-5332	128	29	p2	p2	X
ejpam-5332	128	30	□	□	NUM
ejpam-5332	128	31	p2	p2	NOUN
ejpam-5332	128	32	,	,	PUNCT
ejpam-5332	128	33	where	where	SCONJ
ejpam-5332	128	34	p2	p2	PROPN
ejpam-5332	128	35	is	be	AUX
ejpam-5332	128	36	a	a	DET
ejpam-5332	128	37	convex	convex	ADJ
ejpam-5332	128	38	subgraph	subgraph	NOUN
ejpam-5332	128	39	of	of	ADP
ejpam-5332	128	40	p6	p6	PROPN
ejpam-5332	128	41	.	.	PUNCT
ejpam-5332	129	1	for	for	ADP
ejpam-5332	129	2	this	this	DET
ejpam-5332	129	3	graph	graph	NOUN
ejpam-5332	129	4	,	,	PUNCT
ejpam-5332	129	5	γh(p6	γh(p6	NUM
ejpam-5332	129	6	□	□	SYM
ejpam-5332	129	7	p6	p6	NOUN
ejpam-5332	129	8	)	)	PUNCT
ejpam-5332	129	9	=	=	PUNCT
ejpam-5332	129	10	γp2(p6	γp2(p6	NUM
ejpam-5332	129	11	)	)	PUNCT
ejpam-5332	129	12	+	+	CCONJ
ejpam-5332	129	13	γp2(p6	γp2(p6	NUM
ejpam-5332	129	14	)	)	PUNCT
ejpam-5332	129	15	=	=	SYM
ejpam-5332	129	16	2	2	NUM
ejpam-5332	129	17	+	+	NUM
ejpam-5332	129	18	2	2	NUM
ejpam-5332	129	19	=	=	SYM
ejpam-5332	129	20	4	4	NUM
ejpam-5332	129	21	.	.	NOUN
ejpam-5332	129	22	4	4	NUM
ejpam-5332	129	23	.	.	X
ejpam-5332	129	24	h	h	NOUN
ejpam-5332	129	25	-	-	PUNCT
ejpam-5332	129	26	convex	convex	NOUN
ejpam-5332	129	27	accessibility	accessibility	NOUN
ejpam-5332	129	28	number	number	NOUN
ejpam-5332	129	29	of	of	ADP
ejpam-5332	129	30	the	the	DET
ejpam-5332	129	31	strong	strong	ADJ
ejpam-5332	129	32	product	product	NOUN
ejpam-5332	129	33	of	of	ADP
ejpam-5332	129	34	graphs	graph	NOUN
ejpam-5332	129	35	in	in	ADP
ejpam-5332	129	36	this	this	DET
ejpam-5332	129	37	section	section	NOUN
ejpam-5332	129	38	,	,	PUNCT
ejpam-5332	129	39	we	we	PRON
ejpam-5332	129	40	established	establish	VERB
ejpam-5332	129	41	the	the	DET
ejpam-5332	129	42	h	h	NOUN
ejpam-5332	129	43	-	-	PUNCT
ejpam-5332	129	44	convex	convex	NOUN
ejpam-5332	129	45	accessibility	accessibility	NOUN
ejpam-5332	129	46	number	number	NOUN
ejpam-5332	129	47	of	of	ADP
ejpam-5332	129	48	the	the	DET
ejpam-5332	129	49	strong	strong	ADJ
ejpam-5332	129	50	product	product	NOUN
ejpam-5332	129	51	of	of	ADP
ejpam-5332	129	52	graphs	graph	NOUN
ejpam-5332	129	53	.	.	PUNCT
ejpam-5332	130	1	h.	h.	PROPN
ejpam-5332	130	2	b.	b.	PROPN
ejpam-5332	130	3	samson	samson	PROPN
ejpam-5332	130	4	,	,	PUNCT
ejpam-5332	130	5	i.	i.	PROPN
ejpam-5332	130	6	s.	s.	PROPN
ejpam-5332	130	7	aniversario	aniversario	PROPN
ejpam-5332	130	8	,	,	PUNCT
ejpam-5332	130	9	m.	m.	PROPN
ejpam-5332	130	10	j.	j.	PROPN
ejpam-5332	130	11	f.	f.	PROPN
ejpam-5332	130	12	luga	luga	PROPN
ejpam-5332	130	13	/	/	SYM
ejpam-5332	130	14	eur	eur	PROPN
ejpam-5332	130	15	.	.	PUNCT
ejpam-5332	131	1	j.	j.	PROPN
ejpam-5332	131	2	pure	pure	PROPN
ejpam-5332	131	3	appl	appl	PROPN
ejpam-5332	131	4	.	.	PROPN
ejpam-5332	131	5	math	math	PROPN
ejpam-5332	131	6	,	,	PUNCT
ejpam-5332	131	7	17	17	NUM
ejpam-5332	131	8	(	(	PUNCT
ejpam-5332	131	9	4	4	NUM
ejpam-5332	131	10	)	)	PUNCT
ejpam-5332	131	11	(	(	PUNCT
ejpam-5332	131	12	2024	2024	NUM
ejpam-5332	131	13	)	)	PUNCT
ejpam-5332	131	14	,	,	PUNCT
ejpam-5332	131	15	2930	2930	NUM
ejpam-5332	131	16	-	-	SYM
ejpam-5332	131	17	2938	2938	NUM
ejpam-5332	131	18	2935	2935	NUM
ejpam-5332	131	19	figure	figure	NOUN
ejpam-5332	131	20	2	2	NUM
ejpam-5332	131	21	:	:	PUNCT
ejpam-5332	131	22	the	the	DET
ejpam-5332	131	23	cartesian	cartesian	ADJ
ejpam-5332	131	24	product	product	NOUN
ejpam-5332	131	25	of	of	ADP
ejpam-5332	131	26	p6	p6	PROPN
ejpam-5332	131	27	and	and	CCONJ
ejpam-5332	131	28	p6	p6	PROPN
ejpam-5332	131	29	theorem	theorem	VERB
ejpam-5332	131	30	4	4	NUM
ejpam-5332	131	31	.	.	PUNCT
ejpam-5332	132	1	let	let	VERB
ejpam-5332	132	2	g	g	NOUN
ejpam-5332	132	3	and	and	CCONJ
ejpam-5332	132	4	h	h	NOUN
ejpam-5332	132	5	be	be	AUX
ejpam-5332	132	6	connected	connect	VERB
ejpam-5332	132	7	graphs	graph	NOUN
ejpam-5332	132	8	.	.	PUNCT
ejpam-5332	133	1	if	if	SCONJ
ejpam-5332	133	2	c	c	NOUN
ejpam-5332	133	3	=	=	SYM
ejpam-5332	133	4	cg⊠ch	cg⊠ch	PROPN
ejpam-5332	133	5	,	,	PUNCT
ejpam-5332	133	6	then	then	ADV
ejpam-5332	133	7	a	a	DET
ejpam-5332	133	8	set	set	NOUN
ejpam-5332	133	9	c	c	PROPN
ejpam-5332	133	10	⊂	⊂	PROPN
ejpam-5332	133	11	v	v	X
ejpam-5332	133	12	(	(	PUNCT
ejpam-5332	133	13	g⊠h	g⊠h	NOUN
ejpam-5332	133	14	)	)	PUNCT
ejpam-5332	133	15	is	be	AUX
ejpam-5332	133	16	a	a	DET
ejpam-5332	133	17	convex	convex	NOUN
ejpam-5332	133	18	set	set	VERB
ejpam-5332	133	19	in	in	ADP
ejpam-5332	133	20	g⊠h	g⊠h	NOUN
ejpam-5332	133	21	,	,	PUNCT
ejpam-5332	133	22	where	where	SCONJ
ejpam-5332	133	23	cg	cg	NOUN
ejpam-5332	133	24	and	and	CCONJ
ejpam-5332	133	25	ch	ch	PROPN
ejpam-5332	133	26	are	be	AUX
ejpam-5332	133	27	convex	convex	NOUN
ejpam-5332	133	28	sets	set	NOUN
ejpam-5332	133	29	in	in	ADP
ejpam-5332	133	30	g	g	PROPN
ejpam-5332	133	31	and	and	CCONJ
ejpam-5332	133	32	h	h	NOUN
ejpam-5332	133	33	respectively	respectively	ADV
ejpam-5332	133	34	.	.	PUNCT
ejpam-5332	134	1	proof	proof	NOUN
ejpam-5332	134	2	.	.	PUNCT
ejpam-5332	135	1	let	let	VERB
ejpam-5332	135	2	g	g	NOUN
ejpam-5332	135	3	and	and	CCONJ
ejpam-5332	135	4	h	h	NOUN
ejpam-5332	135	5	be	be	VERB
ejpam-5332	135	6	a	a	DET
ejpam-5332	135	7	connected	connected	ADJ
ejpam-5332	135	8	graph	graph	NOUN
ejpam-5332	135	9	and	and	CCONJ
ejpam-5332	135	10	let	let	VERB
ejpam-5332	135	11	c	c	NOUN
ejpam-5332	135	12	=	=	PUNCT
ejpam-5332	135	13	cg	cg	NOUN
ejpam-5332	135	14	⊠	⊠	PROPN
ejpam-5332	135	15	ch	ch	NOUN
ejpam-5332	135	16	,	,	PUNCT
ejpam-5332	135	17	where	where	SCONJ
ejpam-5332	135	18	cg	cg	NOUN
ejpam-5332	135	19	⊂	⊂	PROPN
ejpam-5332	135	20	v	v	X
ejpam-5332	135	21	(	(	PUNCT
ejpam-5332	135	22	g	g	NOUN
ejpam-5332	135	23	)	)	PUNCT
ejpam-5332	135	24	and	and	CCONJ
ejpam-5332	136	1	ch	ch	PROPN
ejpam-5332	136	2	⊂	⊂	PROPN
ejpam-5332	136	3	v	v	X
ejpam-5332	136	4	(	(	PUNCT
ejpam-5332	136	5	h	h	NOUN
ejpam-5332	136	6	)	)	PUNCT
ejpam-5332	136	7	.	.	PUNCT
ejpam-5332	137	1	we	we	PRON
ejpam-5332	137	2	aim	aim	VERB
ejpam-5332	137	3	to	to	PART
ejpam-5332	137	4	show	show	VERB
ejpam-5332	137	5	that	that	SCONJ
ejpam-5332	137	6	c	c	PROPN
ejpam-5332	137	7	is	be	AUX
ejpam-5332	137	8	convex	convex	ADJ
ejpam-5332	137	9	in	in	ADP
ejpam-5332	137	10	g⊠h	g⊠h	NOUN
ejpam-5332	137	11	.	.	PUNCT
ejpam-5332	138	1	consider	consider	VERB
ejpam-5332	138	2	any	any	DET
ejpam-5332	138	3	two	two	NUM
ejpam-5332	138	4	vertices	vertex	NOUN
ejpam-5332	138	5	(	(	PUNCT
ejpam-5332	138	6	u	u	NOUN
ejpam-5332	138	7	,	,	PUNCT
ejpam-5332	138	8	v	v	NOUN
ejpam-5332	138	9	)	)	PUNCT
ejpam-5332	138	10	,	,	PUNCT
ejpam-5332	138	11	(	(	PUNCT
ejpam-5332	138	12	u′	u′	PROPN
ejpam-5332	138	13	,	,	PUNCT
ejpam-5332	138	14	v′	v′	NOUN
ejpam-5332	138	15	)	)	PUNCT
ejpam-5332	138	16	∈	∈	PROPN
ejpam-5332	138	17	c.	c.	NOUN
ejpam-5332	138	18	let	let	VERB
ejpam-5332	138	19	(	(	PUNCT
ejpam-5332	138	20	x	x	NOUN
ejpam-5332	138	21	,	,	PUNCT
ejpam-5332	138	22	y	y	NOUN
ejpam-5332	138	23	)	)	PUNCT
ejpam-5332	138	24	be	be	AUX
ejpam-5332	138	25	a	a	DET
ejpam-5332	138	26	vertex	vertex	NOUN
ejpam-5332	138	27	on	on	ADP
ejpam-5332	138	28	a	a	DET
ejpam-5332	138	29	(	(	PUNCT
ejpam-5332	138	30	u	u	NOUN
ejpam-5332	138	31	,	,	PUNCT
ejpam-5332	138	32	v	v	NOUN
ejpam-5332	138	33	)	)	PUNCT
ejpam-5332	138	34	(	(	PUNCT
ejpam-5332	138	35	u′	u′	PROPN
ejpam-5332	138	36	,	,	PUNCT
ejpam-5332	138	37	v′	v′	PROPN
ejpam-5332	138	38	)	)	PUNCT
ejpam-5332	138	39	geodesic	geodesic	NOUN
ejpam-5332	138	40	in	in	ADP
ejpam-5332	138	41	g⊠h	g⊠h	NOUN
ejpam-5332	138	42	.	.	PUNCT
ejpam-5332	139	1	then	then	ADV
ejpam-5332	139	2	,	,	PUNCT
ejpam-5332	139	3	by	by	ADP
ejpam-5332	139	4	definition	definition	NOUN
ejpam-5332	139	5	of	of	ADP
ejpam-5332	139	6	strong	strong	ADJ
ejpam-5332	139	7	product	product	NOUN
ejpam-5332	139	8	,	,	PUNCT
ejpam-5332	139	9	one	one	NUM
ejpam-5332	139	10	of	of	ADP
ejpam-5332	139	11	the	the	DET
ejpam-5332	139	12	following	following	NOUN
ejpam-5332	139	13	must	must	AUX
ejpam-5332	139	14	hold	hold	VERB
ejpam-5332	139	15	,	,	PUNCT
ejpam-5332	139	16	u	u	NOUN
ejpam-5332	139	17	=	=	PROPN
ejpam-5332	139	18	x	x	X
ejpam-5332	139	19	and	and	CCONJ
ejpam-5332	139	20	v	v	NOUN
ejpam-5332	139	21	is	be	AUX
ejpam-5332	139	22	adjacent	adjacent	ADJ
ejpam-5332	139	23	to	to	ADP
ejpam-5332	139	24	y	y	PROPN
ejpam-5332	139	25	in	in	ADP
ejpam-5332	139	26	h	h	NOUN
ejpam-5332	139	27	,	,	PUNCT
ejpam-5332	139	28	or	or	CCONJ
ejpam-5332	139	29	,	,	PUNCT
ejpam-5332	139	30	v	v	X
ejpam-5332	139	31	=	=	SYM
ejpam-5332	139	32	y	y	PROPN
ejpam-5332	139	33	and	and	CCONJ
ejpam-5332	139	34	u	u	NOUN
ejpam-5332	139	35	is	be	AUX
ejpam-5332	139	36	adjacent	adjacent	ADJ
ejpam-5332	139	37	to	to	ADP
ejpam-5332	139	38	x	x	PUNCT
ejpam-5332	139	39	in	in	ADP
ejpam-5332	139	40	g	g	NOUN
ejpam-5332	139	41	or	or	CCONJ
ejpam-5332	139	42	u	u	NOUN
ejpam-5332	139	43	is	be	AUX
ejpam-5332	139	44	adjacent	adjacent	ADJ
ejpam-5332	139	45	to	to	ADP
ejpam-5332	139	46	x	x	PUNCT
ejpam-5332	139	47	in	in	ADP
ejpam-5332	139	48	g	g	PROPN
ejpam-5332	139	49	and	and	CCONJ
ejpam-5332	139	50	v	v	NOUN
ejpam-5332	139	51	is	be	AUX
ejpam-5332	139	52	adjacent	adjacent	ADJ
ejpam-5332	139	53	to	to	ADP
ejpam-5332	139	54	y	y	PROPN
ejpam-5332	139	55	in	in	ADP
ejpam-5332	139	56	h.	h.	PROPN
ejpam-5332	139	57	case	case	NOUN
ejpam-5332	139	58	1	1	NUM
ejpam-5332	139	59	:	:	PUNCT
ejpam-5332	139	60	u	u	NOUN
ejpam-5332	139	61	=	=	NOUN
ejpam-5332	139	62	x	x	X
ejpam-5332	139	63	and	and	CCONJ
ejpam-5332	139	64	v	v	NOUN
ejpam-5332	139	65	is	be	AUX
ejpam-5332	139	66	adjacent	adjacent	ADJ
ejpam-5332	139	67	to	to	ADP
ejpam-5332	139	68	y	y	PROPN
ejpam-5332	139	69	in	in	ADP
ejpam-5332	139	70	h.	h.	PROPN
ejpam-5332	139	71	suppose	suppose	VERB
ejpam-5332	139	72	that	that	SCONJ
ejpam-5332	139	73	u	u	PRON
ejpam-5332	139	74	=	=	PUNCT
ejpam-5332	139	75	x	x	X
ejpam-5332	139	76	and	and	CCONJ
ejpam-5332	139	77	v	v	NOUN
ejpam-5332	139	78	is	be	AUX
ejpam-5332	139	79	adjacent	adjacent	ADJ
ejpam-5332	139	80	to	to	ADP
ejpam-5332	139	81	y	y	PROPN
ejpam-5332	139	82	in	in	ADP
ejpam-5332	139	83	h.	h.	PROPN
ejpam-5332	139	84	by	by	ADP
ejpam-5332	139	85	assumption	assumption	NOUN
ejpam-5332	139	86	,	,	PUNCT
ejpam-5332	139	87	there	there	PRON
ejpam-5332	139	88	exist	exist	VERB
ejpam-5332	139	89	the	the	DET
ejpam-5332	139	90	u	u	NOUN
ejpam-5332	139	91	-	-	ADJ
ejpam-5332	139	92	u′	u′	ADJ
ejpam-5332	139	93	path	path	NOUN
ejpam-5332	139	94	joining	join	VERB
ejpam-5332	139	95	vertices	vertice	VERB
ejpam-5332	139	96	u	u	NOUN
ejpam-5332	139	97	and	and	CCONJ
ejpam-5332	139	98	u′	u′	PROPN
ejpam-5332	139	99	in	in	ADP
ejpam-5332	139	100	g.	g.	PROPN
ejpam-5332	139	101	hence	hence	ADV
ejpam-5332	139	102	,	,	PUNCT
ejpam-5332	139	103	u	u	PROPN
ejpam-5332	139	104	=	=	PROPN
ejpam-5332	139	105	x	x	VERB
ejpam-5332	139	106	must	must	AUX
ejpam-5332	139	107	be	be	AUX
ejpam-5332	139	108	in	in	ADP
ejpam-5332	139	109	cg	cg	NOUN
ejpam-5332	139	110	.	.	PUNCT
ejpam-5332	140	1	similarly	similarly	ADV
ejpam-5332	140	2	,	,	PUNCT
ejpam-5332	140	3	y	y	PROPN
ejpam-5332	140	4	is	be	AUX
ejpam-5332	140	5	also	also	ADV
ejpam-5332	140	6	contained	contain	VERB
ejpam-5332	140	7	in	in	ADP
ejpam-5332	140	8	ch	ch	NOUN
ejpam-5332	140	9	because	because	SCONJ
ejpam-5332	140	10	ch	ch	PROPN
ejpam-5332	140	11	is	be	AUX
ejpam-5332	140	12	convex	convex	NOUN
ejpam-5332	140	13	.	.	PUNCT
ejpam-5332	141	1	case	case	NOUN
ejpam-5332	141	2	2	2	NUM
ejpam-5332	141	3	:	:	SYM
ejpam-5332	141	4	v	v	NOUN
ejpam-5332	141	5	=	=	SYM
ejpam-5332	141	6	y	y	PROPN
ejpam-5332	141	7	and	and	CCONJ
ejpam-5332	141	8	u	u	NOUN
ejpam-5332	141	9	is	be	AUX
ejpam-5332	141	10	adjacent	adjacent	ADJ
ejpam-5332	141	11	to	to	ADP
ejpam-5332	141	12	x	x	PUNCT
ejpam-5332	141	13	in	in	ADP
ejpam-5332	141	14	g.	g.	PROPN
ejpam-5332	141	15	assume	assume	VERB
ejpam-5332	141	16	that	that	SCONJ
ejpam-5332	141	17	v	v	X
ejpam-5332	141	18	=	=	SYM
ejpam-5332	141	19	y	y	PROPN
ejpam-5332	141	20	and	and	CCONJ
ejpam-5332	141	21	u	u	NOUN
ejpam-5332	141	22	is	be	AUX
ejpam-5332	141	23	adjacent	adjacent	ADJ
ejpam-5332	141	24	to	to	ADP
ejpam-5332	141	25	x	x	PROPN
ejpam-5332	141	26	in	in	ADP
ejpam-5332	141	27	g.	g.	PROPN
ejpam-5332	141	28	then	then	ADV
ejpam-5332	141	29	,	,	PUNCT
ejpam-5332	141	30	x	x	PRON
ejpam-5332	141	31	must	must	AUX
ejpam-5332	141	32	be	be	AUX
ejpam-5332	141	33	in	in	ADP
ejpam-5332	141	34	cg	cg	NOUN
ejpam-5332	141	35	because	because	SCONJ
ejpam-5332	141	36	cg	cg	NOUN
ejpam-5332	141	37	is	be	AUX
ejpam-5332	141	38	convex	convex	PROPN
ejpam-5332	141	39	.	.	PUNCT
ejpam-5332	142	1	analogously	analogously	ADV
ejpam-5332	142	2	,	,	PUNCT
ejpam-5332	142	3	there	there	PRON
ejpam-5332	142	4	exist	exist	VERB
ejpam-5332	142	5	a	a	DET
ejpam-5332	142	6	v	v	NOUN
ejpam-5332	142	7	-	-	PUNCT
ejpam-5332	142	8	v′	v′	NOUN
ejpam-5332	142	9	path	path	NOUN
ejpam-5332	142	10	joining	join	VERB
ejpam-5332	142	11	vertices	vertex	NOUN
ejpam-5332	142	12	v	v	ADP
ejpam-5332	142	13	and	and	CCONJ
ejpam-5332	142	14	v′	v′	NOUN
ejpam-5332	142	15	in	in	ADP
ejpam-5332	142	16	h.	h.	PROPN
ejpam-5332	142	17	thus	thus	ADV
ejpam-5332	142	18	,	,	PUNCT
ejpam-5332	142	19	y	y	PROPN
ejpam-5332	142	20	=	=	PUNCT
ejpam-5332	142	21	v	v	PROPN
ejpam-5332	142	22	is	be	AUX
ejpam-5332	142	23	in	in	ADP
ejpam-5332	142	24	ch	ch	NOUN
ejpam-5332	142	25	.	.	PUNCT
ejpam-5332	143	1	case	case	NOUN
ejpam-5332	143	2	3	3	NUM
ejpam-5332	143	3	:	:	PUNCT
ejpam-5332	143	4	u	u	NOUN
ejpam-5332	143	5	is	be	AUX
ejpam-5332	143	6	adjacent	adjacent	ADJ
ejpam-5332	143	7	to	to	ADP
ejpam-5332	143	8	x	x	PUNCT
ejpam-5332	143	9	in	in	ADP
ejpam-5332	143	10	g	g	PROPN
ejpam-5332	143	11	and	and	CCONJ
ejpam-5332	143	12	v	v	NOUN
ejpam-5332	143	13	is	be	AUX
ejpam-5332	143	14	adjacent	adjacent	ADJ
ejpam-5332	143	15	to	to	ADP
ejpam-5332	143	16	y	y	PROPN
ejpam-5332	143	17	in	in	ADP
ejpam-5332	143	18	h.	h.	PROPN
ejpam-5332	143	19	let	let	VERB
ejpam-5332	143	20	u	u	PRON
ejpam-5332	143	21	is	be	AUX
ejpam-5332	143	22	adjacent	adjacent	ADJ
ejpam-5332	143	23	to	to	ADP
ejpam-5332	143	24	x	x	PUNCT
ejpam-5332	143	25	in	in	ADP
ejpam-5332	143	26	g	g	PROPN
ejpam-5332	143	27	and	and	CCONJ
ejpam-5332	143	28	v	v	NOUN
ejpam-5332	143	29	is	be	AUX
ejpam-5332	143	30	adjacent	adjacent	ADJ
ejpam-5332	143	31	to	to	ADP
ejpam-5332	143	32	y	y	PROPN
ejpam-5332	143	33	in	in	ADP
ejpam-5332	143	34	h.	h.	PROPN
ejpam-5332	144	1	this	this	PRON
ejpam-5332	144	2	must	must	AUX
ejpam-5332	144	3	mean	mean	VERB
ejpam-5332	144	4	that	that	SCONJ
ejpam-5332	144	5	x	x	PRON
ejpam-5332	144	6	is	be	AUX
ejpam-5332	144	7	contained	contain	VERB
ejpam-5332	144	8	in	in	ADP
ejpam-5332	144	9	cg	cg	NOUN
ejpam-5332	144	10	since	since	SCONJ
ejpam-5332	144	11	cg	cg	NOUN
ejpam-5332	144	12	is	be	AUX
ejpam-5332	144	13	convex	convex	ADJ
ejpam-5332	144	14	.	.	PUNCT
ejpam-5332	145	1	in	in	ADP
ejpam-5332	145	2	a	a	DET
ejpam-5332	145	3	similar	similar	ADJ
ejpam-5332	145	4	fashion	fashion	NOUN
ejpam-5332	145	5	,	,	PUNCT
ejpam-5332	145	6	y	y	PROPN
ejpam-5332	145	7	is	be	AUX
ejpam-5332	145	8	also	also	ADV
ejpam-5332	145	9	contained	contain	VERB
ejpam-5332	145	10	in	in	ADP
ejpam-5332	145	11	ch	ch	NOUN
ejpam-5332	145	12	since	since	SCONJ
ejpam-5332	145	13	ch	ch	PROPN
ejpam-5332	145	14	is	be	AUX
ejpam-5332	145	15	convex	convex	ADJ
ejpam-5332	145	16	.	.	PUNCT
ejpam-5332	146	1	in	in	ADP
ejpam-5332	146	2	all	all	DET
ejpam-5332	146	3	cases	case	NOUN
ejpam-5332	146	4	,	,	PUNCT
ejpam-5332	146	5	(	(	PUNCT
ejpam-5332	146	6	x	x	X
ejpam-5332	146	7	,	,	PUNCT
ejpam-5332	146	8	y	y	NOUN
ejpam-5332	146	9	)	)	PUNCT
ejpam-5332	146	10	is	be	AUX
ejpam-5332	146	11	contained	contain	VERB
ejpam-5332	146	12	in	in	ADP
ejpam-5332	146	13	c	c	NOUN
ejpam-5332	146	14	=	=	PUNCT
ejpam-5332	146	15	cg	cg	NOUN
ejpam-5332	146	16	⊠	⊠	PROPN
ejpam-5332	146	17	ch	ch	NOUN
ejpam-5332	146	18	.	.	PUNCT
ejpam-5332	147	1	therefore	therefore	ADV
ejpam-5332	147	2	,	,	PUNCT
ejpam-5332	147	3	c	c	PROPN
ejpam-5332	147	4	is	be	AUX
ejpam-5332	147	5	convex	convex	ADJ
ejpam-5332	147	6	in	in	ADP
ejpam-5332	147	7	g⊠h	g⊠h	NOUN
ejpam-5332	147	8	.	.	PUNCT
ejpam-5332	148	1	■	■	PUNCT
ejpam-5332	148	2	theorem	theorem	ADJ
ejpam-5332	148	3	5	5	NUM
ejpam-5332	148	4	.	.	PUNCT
ejpam-5332	149	1	let	let	VERB
ejpam-5332	149	2	g	g	NOUN
ejpam-5332	149	3	and	and	CCONJ
ejpam-5332	149	4	h	h	NOUN
ejpam-5332	149	5	be	be	AUX
ejpam-5332	149	6	connected	connect	VERB
ejpam-5332	149	7	graphs	graph	NOUN
ejpam-5332	149	8	.	.	PUNCT
ejpam-5332	150	1	if	if	SCONJ
ejpam-5332	150	2	a	a	DET
ejpam-5332	150	3	set	set	NOUN
ejpam-5332	150	4	c	c	PROPN
ejpam-5332	150	5	⊂	⊂	PROPN
ejpam-5332	150	6	v	v	X
ejpam-5332	150	7	(	(	PUNCT
ejpam-5332	150	8	g⊠h	g⊠h	NOUN
ejpam-5332	150	9	)	)	PUNCT
ejpam-5332	150	10	is	be	AUX
ejpam-5332	150	11	a	a	DET
ejpam-5332	150	12	convex	convex	NOUN
ejpam-5332	150	13	set	set	VERB
ejpam-5332	150	14	in	in	ADP
ejpam-5332	150	15	g⊠h	g⊠h	NOUN
ejpam-5332	150	16	,	,	PUNCT
ejpam-5332	150	17	then	then	ADV
ejpam-5332	150	18	c	c	X
ejpam-5332	150	19	=	=	PUNCT
ejpam-5332	150	20	cg	cg	NOUN
ejpam-5332	150	21	⊠	⊠	PROPN
ejpam-5332	150	22	ch	ch	NOUN
ejpam-5332	150	23	,	,	PUNCT
ejpam-5332	150	24	where	where	SCONJ
ejpam-5332	150	25	cg	cg	NOUN
ejpam-5332	150	26	and	and	CCONJ
ejpam-5332	150	27	ch	ch	PROPN
ejpam-5332	150	28	are	be	AUX
ejpam-5332	150	29	convex	convex	NOUN
ejpam-5332	150	30	sets	set	NOUN
ejpam-5332	150	31	in	in	ADP
ejpam-5332	150	32	g	g	PROPN
ejpam-5332	150	33	and	and	CCONJ
ejpam-5332	150	34	h	h	NOUN
ejpam-5332	150	35	respectively	respectively	ADV
ejpam-5332	150	36	.	.	PUNCT
ejpam-5332	151	1	proof	proof	NOUN
ejpam-5332	151	2	.	.	PUNCT
ejpam-5332	152	1	suppose	suppose	VERB
ejpam-5332	152	2	a	a	DET
ejpam-5332	152	3	set	set	NOUN
ejpam-5332	152	4	c	c	PROPN
ejpam-5332	152	5	∈	∈	PROPN
ejpam-5332	152	6	v	v	NOUN
ejpam-5332	152	7	(	(	PUNCT
ejpam-5332	152	8	g	g	PROPN
ejpam-5332	152	9	⊠	⊠	PROPN
ejpam-5332	152	10	h	h	NOUN
ejpam-5332	152	11	)	)	PUNCT
ejpam-5332	152	12	is	be	AUX
ejpam-5332	152	13	a	a	DET
ejpam-5332	152	14	convex	convex	NOUN
ejpam-5332	152	15	set	set	VERB
ejpam-5332	152	16	in	in	ADP
ejpam-5332	152	17	g	g	PROPN
ejpam-5332	152	18	⊠	⊠	PROPN
ejpam-5332	152	19	h.	h.	PROPN
ejpam-5332	152	20	let	let	VERB
ejpam-5332	152	21	(	(	PUNCT
ejpam-5332	152	22	u	u	NOUN
ejpam-5332	152	23	,	,	PUNCT
ejpam-5332	152	24	u′	u′	PROPN
ejpam-5332	152	25	)	)	PUNCT
ejpam-5332	152	26	∈	∈	PROPN
ejpam-5332	152	27	cg	cg	NOUN
ejpam-5332	152	28	and	and	CCONJ
ejpam-5332	152	29	x	x	AUX
ejpam-5332	152	30	be	be	AUX
ejpam-5332	152	31	a	a	DET
ejpam-5332	152	32	vertex	vertex	NOUN
ejpam-5332	152	33	in	in	ADP
ejpam-5332	152	34	a	a	DET
ejpam-5332	152	35	u	u	NOUN
ejpam-5332	152	36	u′	u′	PROPN
ejpam-5332	152	37	geodesic	geodesic	NOUN
ejpam-5332	152	38	in	in	ADP
ejpam-5332	152	39	g.	g.	PROPN
ejpam-5332	152	40	by	by	ADP
ejpam-5332	152	41	definition	definition	NOUN
ejpam-5332	152	42	of	of	ADP
ejpam-5332	152	43	strong	strong	ADJ
ejpam-5332	152	44	product	product	NOUN
ejpam-5332	152	45	,	,	PUNCT
ejpam-5332	152	46	there	there	PRON
ejpam-5332	152	47	exists	exist	VERB
ejpam-5332	152	48	(	(	PUNCT
ejpam-5332	152	49	v	v	NOUN
ejpam-5332	152	50	,	,	PUNCT
ejpam-5332	152	51	v′	v′	NOUN
ejpam-5332	152	52	)	)	PUNCT
ejpam-5332	152	53	∈	∈	PROPN
ejpam-5332	152	54	ch	ch	NOUN
ejpam-5332	152	55	such	such	ADJ
ejpam-5332	152	56	that	that	SCONJ
ejpam-5332	152	57	the	the	DET
ejpam-5332	152	58	either	either	CCONJ
ejpam-5332	152	59	u	u	NOUN
ejpam-5332	152	60	=	=	PROPN
ejpam-5332	152	61	x	x	X
ejpam-5332	152	62	and	and	CCONJ
ejpam-5332	152	63	v	v	NOUN
ejpam-5332	152	64	is	be	AUX
ejpam-5332	152	65	adjacent	adjacent	ADJ
ejpam-5332	152	66	to	to	ADP
ejpam-5332	152	67	v′	v′	NOUN
ejpam-5332	152	68	in	in	ADP
ejpam-5332	152	69	h	h	NOUN
ejpam-5332	152	70	,	,	PUNCT
ejpam-5332	152	71	oru	oru	PROPN
ejpam-5332	152	72	is	be	AUX
ejpam-5332	152	73	adjacent	adjacent	ADJ
ejpam-5332	152	74	to	to	ADP
ejpam-5332	152	75	x	x	PUNCT
ejpam-5332	152	76	in	in	ADP
ejpam-5332	152	77	g	g	PROPN
ejpam-5332	152	78	and	and	CCONJ
ejpam-5332	152	79	v	v	NOUN
ejpam-5332	152	80	is	be	AUX
ejpam-5332	152	81	adjacent	adjacent	ADJ
ejpam-5332	152	82	to	to	ADP
ejpam-5332	152	83	v′	v′	NOUN
ejpam-5332	152	84	in	in	ADP
ejpam-5332	152	85	h.	h.	PROPN
ejpam-5332	152	86	in	in	ADP
ejpam-5332	152	87	either	either	DET
ejpam-5332	152	88	cases	case	NOUN
ejpam-5332	152	89	,	,	PUNCT
ejpam-5332	152	90	(	(	PUNCT
ejpam-5332	152	91	x	x	NOUN
ejpam-5332	152	92	,	,	PUNCT
ejpam-5332	152	93	v	v	NOUN
ejpam-5332	152	94	)	)	PUNCT
ejpam-5332	152	95	and	and	CCONJ
ejpam-5332	152	96	(	(	PUNCT
ejpam-5332	152	97	x	x	NOUN
ejpam-5332	152	98	,	,	PUNCT
ejpam-5332	152	99	v′	v′	NOUN
ejpam-5332	152	100	)	)	PUNCT
ejpam-5332	152	101	∈	∈	PROPN
ejpam-5332	152	102	c.	c.	NOUN
ejpam-5332	152	103	hence	hence	ADV
ejpam-5332	152	104	,	,	PUNCT
ejpam-5332	152	105	x	x	PUNCT
ejpam-5332	152	106	∈	∈	PROPN
ejpam-5332	152	107	cg	cg	NOUN
ejpam-5332	152	108	thus	thus	ADV
ejpam-5332	152	109	.	.	PUNCT
ejpam-5332	153	1	cg	cg	NOUN
ejpam-5332	153	2	is	be	AUX
ejpam-5332	153	3	convex	convex	ADJ
ejpam-5332	153	4	in	in	ADP
ejpam-5332	153	5	g.	g.	PROPN
ejpam-5332	153	6	similarly	similarly	ADV
ejpam-5332	153	7	,	,	PUNCT
ejpam-5332	153	8	let	let	VERB
ejpam-5332	153	9	a	a	PRON
ejpam-5332	153	10	,	,	PUNCT
ejpam-5332	153	11	a′	a′	PROPN
ejpam-5332	153	12	∈	∈	PROPN
ejpam-5332	153	13	ch	ch	NOUN
ejpam-5332	153	14	and	and	CCONJ
ejpam-5332	153	15	y	y	PROPN
ejpam-5332	153	16	be	be	AUX
ejpam-5332	153	17	a	a	DET
ejpam-5332	153	18	vertex	vertex	NOUN
ejpam-5332	153	19	set	set	VERB
ejpam-5332	153	20	in	in	ADP
ejpam-5332	153	21	a	a	DET
ejpam-5332	153	22	a	a	DET
ejpam-5332	153	23	-	-	PUNCT
ejpam-5332	153	24	a′	a′	NOUN
ejpam-5332	153	25	geodesic	geodesic	NOUN
ejpam-5332	153	26	in	in	ADP
ejpam-5332	153	27	h.	h.	NOUN
ejpam-5332	153	28	by	by	ADP
ejpam-5332	153	29	definition	definition	NOUN
ejpam-5332	153	30	of	of	ADP
ejpam-5332	153	31	strong	strong	ADJ
ejpam-5332	153	32	product	product	NOUN
ejpam-5332	153	33	,	,	PUNCT
ejpam-5332	153	34	there	there	PRON
ejpam-5332	153	35	exist	exist	VERB
ejpam-5332	153	36	(	(	PUNCT
ejpam-5332	153	37	b	b	NOUN
ejpam-5332	153	38	,	,	PUNCT
ejpam-5332	153	39	b′	b′	NUM
ejpam-5332	153	40	)	)	PUNCT
ejpam-5332	153	41	∈	∈	PROPN
ejpam-5332	153	42	cg	cg	NOUN
ejpam-5332	153	43	such	such	ADJ
ejpam-5332	153	44	that	that	SCONJ
ejpam-5332	153	45	a	a	DET
ejpam-5332	153	46	=	=	SYM
ejpam-5332	153	47	y	y	PROPN
ejpam-5332	153	48	and	and	CCONJ
ejpam-5332	153	49	b	b	PROPN
ejpam-5332	153	50	is	be	AUX
ejpam-5332	153	51	h.	h.	PROPN
ejpam-5332	153	52	b.	b.	PROPN
ejpam-5332	153	53	samson	samson	PROPN
ejpam-5332	153	54	,	,	PUNCT
ejpam-5332	153	55	i.	i.	PROPN
ejpam-5332	153	56	s.	s.	PROPN
ejpam-5332	153	57	aniversario	aniversario	PROPN
ejpam-5332	153	58	,	,	PUNCT
ejpam-5332	153	59	m.	m.	PROPN
ejpam-5332	153	60	j.	j.	PROPN
ejpam-5332	153	61	f.	f.	PROPN
ejpam-5332	153	62	luga	luga	PROPN
ejpam-5332	153	63	/	/	SYM
ejpam-5332	153	64	eur	eur	PROPN
ejpam-5332	153	65	.	.	PUNCT
ejpam-5332	154	1	j.	j.	PROPN
ejpam-5332	154	2	pure	pure	PROPN
ejpam-5332	154	3	appl	appl	PROPN
ejpam-5332	154	4	.	.	PROPN
ejpam-5332	154	5	math	math	PROPN
ejpam-5332	154	6	,	,	PUNCT
ejpam-5332	154	7	17	17	NUM
ejpam-5332	154	8	(	(	PUNCT
ejpam-5332	154	9	4	4	NUM
ejpam-5332	154	10	)	)	PUNCT
ejpam-5332	154	11	(	(	PUNCT
ejpam-5332	154	12	2024	2024	NUM
ejpam-5332	154	13	)	)	PUNCT
ejpam-5332	154	14	,	,	PUNCT
ejpam-5332	154	15	2930	2930	NUM
ejpam-5332	154	16	-	-	SYM
ejpam-5332	154	17	2938	2938	NUM
ejpam-5332	154	18	2936	2936	NUM
ejpam-5332	154	19	adjacent	adjacent	ADJ
ejpam-5332	154	20	to	to	ADP
ejpam-5332	154	21	b′	b′	NUM
ejpam-5332	154	22	in	in	ADP
ejpam-5332	154	23	g	g	PROPN
ejpam-5332	154	24	,	,	PUNCT
ejpam-5332	154	25	or	or	CCONJ
ejpam-5332	154	26	b	b	NOUN
ejpam-5332	154	27	is	be	AUX
ejpam-5332	154	28	adjacent	adjacent	ADJ
ejpam-5332	154	29	to	to	ADP
ejpam-5332	154	30	b′	b′	NUM
ejpam-5332	154	31	in	in	ADP
ejpam-5332	154	32	g	g	PROPN
ejpam-5332	154	33	and	and	CCONJ
ejpam-5332	154	34	a	a	PRON
ejpam-5332	154	35	is	be	AUX
ejpam-5332	154	36	adjacent	adjacent	ADJ
ejpam-5332	154	37	to	to	ADP
ejpam-5332	154	38	y	y	PROPN
ejpam-5332	154	39	in	in	ADP
ejpam-5332	154	40	h.	h.	PROPN
ejpam-5332	154	41	in	in	ADP
ejpam-5332	154	42	both	both	DET
ejpam-5332	154	43	cases	case	NOUN
ejpam-5332	154	44	,	,	PUNCT
ejpam-5332	154	45	(	(	PUNCT
ejpam-5332	154	46	b	b	X
ejpam-5332	154	47	,	,	PUNCT
ejpam-5332	154	48	y	y	PROPN
ejpam-5332	154	49	)	)	PUNCT
ejpam-5332	154	50	and	and	CCONJ
ejpam-5332	154	51	(	(	PUNCT
ejpam-5332	154	52	b′	b′	NUM
ejpam-5332	154	53	,	,	PUNCT
ejpam-5332	154	54	y	y	NOUN
ejpam-5332	154	55	)	)	PUNCT
ejpam-5332	154	56	∈	∈	PROPN
ejpam-5332	154	57	c.	c.	PROPN
ejpam-5332	154	58	thus	thus	ADV
ejpam-5332	154	59	,	,	PUNCT
ejpam-5332	154	60	y	y	PROPN
ejpam-5332	154	61	∈	∈	PROPN
ejpam-5332	154	62	ch	ch	NOUN
ejpam-5332	154	63	and	and	CCONJ
ejpam-5332	154	64	ch	ch	NOUN
ejpam-5332	154	65	is	be	AUX
ejpam-5332	154	66	convex	convex	ADJ
ejpam-5332	154	67	in	in	ADP
ejpam-5332	154	68	h.	h.	PROPN
ejpam-5332	154	69	the	the	DET
ejpam-5332	154	70	assumption	assumption	NOUN
ejpam-5332	154	71	implies	imply	VERB
ejpam-5332	154	72	that	that	SCONJ
ejpam-5332	154	73	c	c	PROPN
ejpam-5332	154	74	⊆	⊆	NUM
ejpam-5332	154	75	cg	cg	NOUN
ejpam-5332	154	76	⊠	⊠	PROPN
ejpam-5332	154	77	ch	ch	NOUN
ejpam-5332	154	78	.	.	PUNCT
ejpam-5332	155	1	assume	assume	VERB
ejpam-5332	155	2	that	that	SCONJ
ejpam-5332	155	3	(	(	PUNCT
ejpam-5332	155	4	i	i	PRON
ejpam-5332	155	5	,	,	PUNCT
ejpam-5332	155	6	j	j	PROPN
ejpam-5332	155	7	)	)	PUNCT
ejpam-5332	155	8	∈	∈	PROPN
ejpam-5332	155	9	cg	cg	NOUN
ejpam-5332	155	10	⊠	⊠	PROPN
ejpam-5332	155	11	ch	ch	NOUN
ejpam-5332	155	12	.	.	PUNCT
ejpam-5332	156	1	then	then	ADV
ejpam-5332	156	2	,	,	PUNCT
ejpam-5332	156	3	there	there	PRON
ejpam-5332	156	4	exists	exist	VERB
ejpam-5332	156	5	m	m	VERB
ejpam-5332	156	6	∈	∈	PROPN
ejpam-5332	156	7	v	v	ADP
ejpam-5332	156	8	(	(	PUNCT
ejpam-5332	156	9	g	g	NOUN
ejpam-5332	156	10	)	)	PUNCT
ejpam-5332	156	11	and	and	CCONJ
ejpam-5332	157	1	n	n	PRON
ejpam-5332	157	2	∈	∈	NOUN
ejpam-5332	157	3	v	v	NOUN
ejpam-5332	157	4	(	(	PUNCT
ejpam-5332	157	5	h	h	NOUN
ejpam-5332	157	6	)	)	PUNCT
ejpam-5332	157	7	such	such	ADJ
ejpam-5332	157	8	that	that	SCONJ
ejpam-5332	157	9	either	either	CCONJ
ejpam-5332	157	10	i	i	PRON
ejpam-5332	157	11	=	=	VERB
ejpam-5332	157	12	m	m	PROPN
ejpam-5332	157	13	and	and	CCONJ
ejpam-5332	157	14	j	j	PROPN
ejpam-5332	157	15	is	be	AUX
ejpam-5332	157	16	adjacent	adjacent	ADJ
ejpam-5332	157	17	to	to	ADP
ejpam-5332	157	18	n	n	PROPN
ejpam-5332	157	19	in	in	ADP
ejpam-5332	157	20	h	h	NOUN
ejpam-5332	157	21	,	,	PUNCT
ejpam-5332	157	22	or	or	CCONJ
ejpam-5332	157	23	,	,	PUNCT
ejpam-5332	157	24	j	j	PROPN
ejpam-5332	157	25	=	=	SYM
ejpam-5332	157	26	n	n	PROPN
ejpam-5332	158	1	and	and	CCONJ
ejpam-5332	158	2	i	i	PRON
ejpam-5332	158	3	is	be	AUX
ejpam-5332	158	4	adjacent	adjacent	ADJ
ejpam-5332	158	5	to	to	ADP
ejpam-5332	158	6	m	m	PROPN
ejpam-5332	158	7	in	in	ADP
ejpam-5332	158	8	g	g	PROPN
ejpam-5332	158	9	,	,	PUNCT
ejpam-5332	158	10	or	or	CCONJ
ejpam-5332	158	11	i	i	PRON
ejpam-5332	158	12	is	be	AUX
ejpam-5332	158	13	adjacent	adjacent	ADJ
ejpam-5332	158	14	to	to	ADP
ejpam-5332	158	15	m	m	PROPN
ejpam-5332	158	16	in	in	ADP
ejpam-5332	158	17	g	g	PROPN
ejpam-5332	158	18	and	and	CCONJ
ejpam-5332	158	19	j	j	PROPN
ejpam-5332	158	20	is	be	AUX
ejpam-5332	158	21	adjacent	adjacent	ADJ
ejpam-5332	158	22	to	to	ADP
ejpam-5332	158	23	n	n	PROPN
ejpam-5332	158	24	in	in	ADP
ejpam-5332	158	25	h.	h.	PROPN
ejpam-5332	158	26	note	note	NOUN
ejpam-5332	158	27	that	that	SCONJ
ejpam-5332	158	28	c	c	PROPN
ejpam-5332	158	29	is	be	AUX
ejpam-5332	158	30	convex	convex	PROPN
ejpam-5332	158	31	,	,	PUNCT
ejpam-5332	158	32	it	it	PRON
ejpam-5332	158	33	follows	follow	VERB
ejpam-5332	158	34	that	that	SCONJ
ejpam-5332	158	35	(	(	PUNCT
ejpam-5332	158	36	i	i	PRON
ejpam-5332	158	37	,	,	PUNCT
ejpam-5332	158	38	j	j	PROPN
ejpam-5332	158	39	)	)	PUNCT
ejpam-5332	158	40	∈	∈	PROPN
ejpam-5332	158	41	c.thus	c.thus	NOUN
ejpam-5332	158	42	,	,	PUNCT
ejpam-5332	158	43	cg	cg	NOUN
ejpam-5332	158	44	⊠	⊠	PROPN
ejpam-5332	158	45	ch	ch	NOUN
ejpam-5332	158	46	⊆	⊆	NUM
ejpam-5332	158	47	c.	c.	NOUN
ejpam-5332	158	48	consequently	consequently	ADV
ejpam-5332	158	49	,	,	PUNCT
ejpam-5332	158	50	c	c	PROPN
ejpam-5332	158	51	=	=	PUNCT
ejpam-5332	158	52	cg	cg	NOUN
ejpam-5332	158	53	⊠	⊠	PROPN
ejpam-5332	158	54	ch	ch	NOUN
ejpam-5332	158	55	.	.	PUNCT
ejpam-5332	159	1	■	■	PUNCT
ejpam-5332	159	2	corollary	corollary	ADJ
ejpam-5332	159	3	1	1	NUM
ejpam-5332	159	4	.	.	PUNCT
ejpam-5332	160	1	let	let	VERB
ejpam-5332	160	2	g	g	NOUN
ejpam-5332	160	3	and	and	CCONJ
ejpam-5332	160	4	h	h	NOUN
ejpam-5332	160	5	be	be	AUX
ejpam-5332	160	6	connected	connect	VERB
ejpam-5332	160	7	graphs	graph	NOUN
ejpam-5332	160	8	.	.	PUNCT
ejpam-5332	161	1	a	a	DET
ejpam-5332	161	2	set	set	NOUN
ejpam-5332	161	3	c	c	PROPN
ejpam-5332	161	4	∈	∈	PROPN
ejpam-5332	161	5	v	v	NOUN
ejpam-5332	161	6	(	(	PUNCT
ejpam-5332	161	7	g	g	PROPN
ejpam-5332	161	8	⊠	⊠	PROPN
ejpam-5332	161	9	h	h	NOUN
ejpam-5332	161	10	)	)	PUNCT
ejpam-5332	161	11	is	be	AUX
ejpam-5332	161	12	a	a	DET
ejpam-5332	161	13	convex	convex	NOUN
ejpam-5332	161	14	set	set	VERB
ejpam-5332	161	15	in	in	ADP
ejpam-5332	161	16	g	g	PROPN
ejpam-5332	161	17	⊠	⊠	PROPN
ejpam-5332	161	18	h	h	NOUN
ejpam-5332	161	19	if	if	SCONJ
ejpam-5332	162	1	and	and	CCONJ
ejpam-5332	162	2	only	only	ADV
ejpam-5332	162	3	if	if	SCONJ
ejpam-5332	162	4	c	c	NOUN
ejpam-5332	162	5	=	=	VERB
ejpam-5332	162	6	cg	cg	NOUN
ejpam-5332	162	7	⊠	⊠	PROPN
ejpam-5332	162	8	ch	ch	NOUN
ejpam-5332	162	9	,	,	PUNCT
ejpam-5332	162	10	where	where	SCONJ
ejpam-5332	162	11	cg	cg	NOUN
ejpam-5332	162	12	and	and	CCONJ
ejpam-5332	162	13	ch	ch	PROPN
ejpam-5332	162	14	are	be	AUX
ejpam-5332	162	15	convex	convex	NOUN
ejpam-5332	162	16	sets	set	NOUN
ejpam-5332	162	17	in	in	ADP
ejpam-5332	162	18	g	g	PROPN
ejpam-5332	162	19	and	and	CCONJ
ejpam-5332	162	20	h	h	NOUN
ejpam-5332	162	21	respectively	respectively	ADV
ejpam-5332	162	22	.	.	PUNCT
ejpam-5332	163	1	proof	proof	NOUN
ejpam-5332	163	2	.	.	PUNCT
ejpam-5332	164	1	notice	notice	VERB
ejpam-5332	164	2	that	that	SCONJ
ejpam-5332	164	3	the	the	DET
ejpam-5332	164	4	preceding	precede	VERB
ejpam-5332	164	5	two	two	NUM
ejpam-5332	164	6	theorems	theorem	NOUN
ejpam-5332	164	7	have	have	AUX
ejpam-5332	164	8	established	establish	VERB
ejpam-5332	164	9	both	both	CCONJ
ejpam-5332	164	10	the	the	DET
ejpam-5332	164	11	sufficiency	sufficiency	NOUN
ejpam-5332	164	12	and	and	CCONJ
ejpam-5332	164	13	necessity	necessity	NOUN
ejpam-5332	164	14	conditions	condition	NOUN
ejpam-5332	164	15	required	require	VERB
ejpam-5332	164	16	for	for	ADP
ejpam-5332	164	17	this	this	DET
ejpam-5332	164	18	corollary	corollary	NOUN
ejpam-5332	164	19	.	.	PUNCT
ejpam-5332	165	1	thus	thus	ADV
ejpam-5332	165	2	,	,	PUNCT
ejpam-5332	165	3	this	this	PRON
ejpam-5332	165	4	directly	directly	ADV
ejpam-5332	165	5	follows	follow	VERB
ejpam-5332	165	6	from	from	ADP
ejpam-5332	165	7	theorem	theorem	ADJ
ejpam-5332	165	8	4	4	NUM
ejpam-5332	165	9	and	and	CCONJ
ejpam-5332	165	10	theorem	theorem	VERB
ejpam-5332	165	11	5	5	NUM
ejpam-5332	165	12	.	.	PUNCT
ejpam-5332	165	13	theorem	theorem	NOUN
ejpam-5332	165	14	6	6	NUM
ejpam-5332	165	15	.	.	PUNCT
ejpam-5332	166	1	let	let	VERB
ejpam-5332	166	2	g1	g1	PROPN
ejpam-5332	166	3	and	and	CCONJ
ejpam-5332	166	4	g2	g2	PROPN
ejpam-5332	166	5	be	be	AUX
ejpam-5332	166	6	connected	connect	VERB
ejpam-5332	166	7	graphs	graph	NOUN
ejpam-5332	166	8	and	and	CCONJ
ejpam-5332	166	9	h	h	NOUN
ejpam-5332	166	10	=	=	NOUN
ejpam-5332	166	11	h1	h1	PROPN
ejpam-5332	166	12	⊠h2	⊠h2	PROPN
ejpam-5332	166	13	be	be	AUX
ejpam-5332	166	14	a	a	DET
ejpam-5332	166	15	proper	proper	ADJ
ejpam-5332	166	16	convex	convex	NOUN
ejpam-5332	166	17	subgraph	subgraph	NOUN
ejpam-5332	166	18	of	of	ADP
ejpam-5332	166	19	v	v	NOUN
ejpam-5332	166	20	(	(	PUNCT
ejpam-5332	166	21	g1	g1	PROPN
ejpam-5332	166	22	⊠	⊠	PROPN
ejpam-5332	166	23	g2	g2	PROPN
ejpam-5332	166	24	)	)	PUNCT
ejpam-5332	166	25	,	,	PUNCT
ejpam-5332	166	26	where	where	SCONJ
ejpam-5332	166	27	h1	h1	NOUN
ejpam-5332	166	28	and	and	CCONJ
ejpam-5332	166	29	h2	h2	NOUN
ejpam-5332	166	30	are	be	AUX
ejpam-5332	166	31	proper	proper	ADJ
ejpam-5332	166	32	convex	convex	ADJ
ejpam-5332	166	33	subgraphs	subgraph	NOUN
ejpam-5332	166	34	of	of	ADP
ejpam-5332	166	35	g1	g1	NOUN
ejpam-5332	166	36	and	and	CCONJ
ejpam-5332	166	37	g2	g2	PROPN
ejpam-5332	166	38	respectively	respectively	ADV
ejpam-5332	166	39	.	.	PUNCT
ejpam-5332	167	1	then	then	ADV
ejpam-5332	167	2	,	,	PUNCT
ejpam-5332	167	3	γh(g1	γh(g1	ADP
ejpam-5332	167	4	⊠g2	⊠g2	PROPN
ejpam-5332	167	5	)	)	PUNCT
ejpam-5332	167	6	=	=	SYM
ejpam-5332	167	7	max{γh1(g1),γh2(g2	max{γh1(g1),γh2(g2	X
ejpam-5332	167	8	)	)	PUNCT
ejpam-5332	167	9	}	}	PUNCT
ejpam-5332	167	10	proof	proof	NOUN
ejpam-5332	167	11	.	.	PUNCT
ejpam-5332	168	1	let	let	VERB
ejpam-5332	168	2	g1	g1	PROPN
ejpam-5332	168	3	and	and	CCONJ
ejpam-5332	168	4	g2	g2	PROPN
ejpam-5332	168	5	be	be	AUX
ejpam-5332	168	6	connected	connect	VERB
ejpam-5332	168	7	graphs	graph	NOUN
ejpam-5332	168	8	and	and	CCONJ
ejpam-5332	168	9	h	h	NOUN
ejpam-5332	168	10	=	=	PRON
ejpam-5332	168	11	h1	h1	PROPN
ejpam-5332	168	12	⊠	⊠	PROPN
ejpam-5332	168	13	h2	h2	NOUN
ejpam-5332	168	14	be	be	AUX
ejpam-5332	168	15	a	a	DET
ejpam-5332	168	16	proper	proper	ADJ
ejpam-5332	168	17	convex	convex	NOUN
ejpam-5332	168	18	subgraph	subgraph	NOUN
ejpam-5332	168	19	of	of	ADP
ejpam-5332	168	20	g1	g1	PROPN
ejpam-5332	168	21	and	and	CCONJ
ejpam-5332	168	22	g2	g2	PROPN
ejpam-5332	168	23	.	.	PUNCT
ejpam-5332	169	1	we	we	PRON
ejpam-5332	169	2	aim	aim	VERB
ejpam-5332	169	3	to	to	PART
ejpam-5332	169	4	show	show	VERB
ejpam-5332	169	5	that	that	SCONJ
ejpam-5332	169	6	the	the	DET
ejpam-5332	169	7	graph	graph	NOUN
ejpam-5332	169	8	g1⊠g2	g1⊠g2	PROPN
ejpam-5332	169	9	has	have	VERB
ejpam-5332	169	10	a	a	DET
ejpam-5332	169	11	certain	certain	ADJ
ejpam-5332	169	12	relationship	relationship	NOUN
ejpam-5332	169	13	with	with	ADP
ejpam-5332	169	14	the	the	DET
ejpam-5332	169	15	convexity	convexity	NOUN
ejpam-5332	169	16	parameters	parameter	NOUN
ejpam-5332	169	17	of	of	ADP
ejpam-5332	169	18	g1	g1	PROPN
ejpam-5332	169	19	and	and	CCONJ
ejpam-5332	169	20	g2	g2	PROPN
ejpam-5332	169	21	.	.	PUNCT
ejpam-5332	170	1	consider	consider	VERB
ejpam-5332	170	2	an	an	DET
ejpam-5332	170	3	arbitrary	arbitrary	ADJ
ejpam-5332	170	4	vertex	vertex	NOUN
ejpam-5332	170	5	(	(	PUNCT
ejpam-5332	170	6	u	u	NOUN
ejpam-5332	170	7	,	,	PUNCT
ejpam-5332	170	8	v	v	NOUN
ejpam-5332	170	9	)	)	PUNCT
ejpam-5332	170	10	∈	∈	NOUN
ejpam-5332	170	11	v	v	NOUN
ejpam-5332	170	12	(	(	PUNCT
ejpam-5332	170	13	g1	g1	PROPN
ejpam-5332	170	14	⊠g2	⊠g2	PROPN
ejpam-5332	170	15	)	)	PUNCT
ejpam-5332	170	16	\	\	PROPN
ejpam-5332	170	17	v	v	X
ejpam-5332	170	18	(	(	PUNCT
ejpam-5332	170	19	h	h	NOUN
ejpam-5332	170	20	)	)	PUNCT
ejpam-5332	170	21	.	.	PUNCT
ejpam-5332	171	1	without	without	ADP
ejpam-5332	171	2	loss	loss	NOUN
ejpam-5332	171	3	of	of	ADP
ejpam-5332	171	4	generality	generality	NOUN
ejpam-5332	171	5	,	,	PUNCT
ejpam-5332	171	6	let	let	VERB
ejpam-5332	171	7	(	(	PUNCT
ejpam-5332	171	8	u′	u′	PROPN
ejpam-5332	171	9	,	,	PUNCT
ejpam-5332	171	10	v′	v′	NOUN
ejpam-5332	171	11	)	)	PUNCT
ejpam-5332	171	12	∈	∈	PROPN
ejpam-5332	171	13	v	v	ADP
ejpam-5332	171	14	(	(	PUNCT
ejpam-5332	171	15	h	h	NOUN
ejpam-5332	171	16	)	)	PUNCT
ejpam-5332	171	17	.	.	PUNCT
ejpam-5332	172	1	according	accord	VERB
ejpam-5332	172	2	to	to	ADP
ejpam-5332	172	3	[	[	X
ejpam-5332	172	4	4	4	NUM
ejpam-5332	172	5	]	]	PUNCT
ejpam-5332	172	6	,	,	PUNCT
ejpam-5332	172	7	the	the	DET
ejpam-5332	172	8	distance	distance	NOUN
ejpam-5332	172	9	in	in	ADP
ejpam-5332	172	10	the	the	DET
ejpam-5332	172	11	strong	strong	ADJ
ejpam-5332	172	12	product	product	NOUN
ejpam-5332	172	13	graph	graph	NOUN
ejpam-5332	172	14	g1	g1	NOUN
ejpam-5332	172	15	⊠g2	⊠g2	PROPN
ejpam-5332	172	16	is	be	AUX
ejpam-5332	172	17	given	give	VERB
ejpam-5332	172	18	by	by	ADP
ejpam-5332	172	19	,	,	PUNCT
ejpam-5332	172	20	dg1⊠g2((u	dg1⊠g2((u	NOUN
ejpam-5332	172	21	,	,	PUNCT
ejpam-5332	172	22	v	v	NOUN
ejpam-5332	172	23	)	)	PUNCT
ejpam-5332	172	24	,	,	PUNCT
ejpam-5332	172	25	(	(	PUNCT
ejpam-5332	172	26	u	u	NOUN
ejpam-5332	172	27	′	′	NOUN
ejpam-5332	172	28	,	,	PUNCT
ejpam-5332	172	29	v′	v′	NOUN
ejpam-5332	172	30	)	)	PUNCT
ejpam-5332	172	31	)	)	PUNCT
ejpam-5332	173	1	=	=	SYM
ejpam-5332	173	2	max	max	PROPN
ejpam-5332	173	3	{	{	PUNCT
ejpam-5332	173	4	dg1(u	dg1(u	PROPN
ejpam-5332	173	5	,	,	PUNCT
ejpam-5332	173	6	u	u	NOUN
ejpam-5332	173	7	′	′	NOUN
ejpam-5332	173	8	)	)	PUNCT
ejpam-5332	173	9	,	,	PUNCT
ejpam-5332	173	10	dg2(v	dg2(v	PROPN
ejpam-5332	173	11	,	,	PUNCT
ejpam-5332	173	12	v	v	NOUN
ejpam-5332	173	13	′	′	NOUN
ejpam-5332	173	14	)	)	PUNCT
ejpam-5332	173	15	}	}	PUNCT
ejpam-5332	173	16	.	.	PUNCT
ejpam-5332	174	1	by	by	ADP
ejpam-5332	174	2	[	[	X
ejpam-5332	174	3	3	3	NUM
ejpam-5332	174	4	]	]	PUNCT
ejpam-5332	174	5	,	,	PUNCT
ejpam-5332	174	6	we	we	PRON
ejpam-5332	174	7	know	know	VERB
ejpam-5332	174	8	that	that	SCONJ
ejpam-5332	174	9	,	,	PUNCT
ejpam-5332	174	10	γh1(g1	γh1(g1	NOUN
ejpam-5332	174	11	)	)	PUNCT
ejpam-5332	174	12	≤	≤	NUM
ejpam-5332	174	13	dg1(u	dg1(u	NOUN
ejpam-5332	174	14	,	,	PUNCT
ejpam-5332	174	15	u	u	NOUN
ejpam-5332	174	16	′	′	NOUN
ejpam-5332	174	17	)	)	PUNCT
ejpam-5332	174	18	and	and	CCONJ
ejpam-5332	174	19	γh2(g2	γh2(g2	NOUN
ejpam-5332	174	20	)	)	PUNCT
ejpam-5332	174	21	≤	≤	NUM
ejpam-5332	174	22	dg2(v	dg2(v	PROPN
ejpam-5332	174	23	,	,	PUNCT
ejpam-5332	174	24	v	v	NOUN
ejpam-5332	174	25	′	′	NOUN
ejpam-5332	174	26	)	)	PUNCT
ejpam-5332	174	27	.	.	PUNCT
ejpam-5332	175	1	thus	thus	ADV
ejpam-5332	175	2	,	,	PUNCT
ejpam-5332	175	3	we	we	PRON
ejpam-5332	175	4	have	have	VERB
ejpam-5332	175	5	max	max	PROPN
ejpam-5332	175	6	{	{	PUNCT
ejpam-5332	175	7	γh1(g1),γh2(g2	γh1(g1),γh2(g2	NOUN
ejpam-5332	175	8	)	)	PUNCT
ejpam-5332	175	9	}	}	PUNCT
ejpam-5332	175	10	≤	≤	NUM
ejpam-5332	175	11	max	max	PROPN
ejpam-5332	175	12	{	{	PUNCT
ejpam-5332	175	13	dg1(u	dg1(u	PROPN
ejpam-5332	175	14	,	,	PUNCT
ejpam-5332	175	15	u	u	NOUN
ejpam-5332	175	16	′	′	NOUN
ejpam-5332	175	17	)	)	PUNCT
ejpam-5332	175	18	,	,	PUNCT
ejpam-5332	175	19	dg2(v	dg2(v	PROPN
ejpam-5332	175	20	,	,	PUNCT
ejpam-5332	175	21	v	v	NOUN
ejpam-5332	175	22	′	′	NOUN
ejpam-5332	175	23	)	)	PUNCT
ejpam-5332	175	24	}	}	PUNCT
ejpam-5332	175	25	.	.	PUNCT
ejpam-5332	176	1	this	this	DET
ejpam-5332	176	2	simplifies	simplifie	NOUN
ejpam-5332	176	3	to	to	ADP
ejpam-5332	176	4	max	max	PROPN
ejpam-5332	176	5	{	{	PUNCT
ejpam-5332	176	6	γh1(g1),γh2(g2	γh1(g1),γh2(g2	PROPN
ejpam-5332	176	7	)	)	PUNCT
ejpam-5332	176	8	}	}	PUNCT
ejpam-5332	176	9	≤	≤	NUM
ejpam-5332	176	10	dg1⊠g2((u	dg1⊠g2((u	NOUN
ejpam-5332	176	11	,	,	PUNCT
ejpam-5332	176	12	v	v	NOUN
ejpam-5332	176	13	)	)	PUNCT
ejpam-5332	176	14	,	,	PUNCT
ejpam-5332	176	15	(	(	PUNCT
ejpam-5332	176	16	u	u	NOUN
ejpam-5332	176	17	′	′	NOUN
ejpam-5332	176	18	,	,	PUNCT
ejpam-5332	176	19	v′	v′	NOUN
ejpam-5332	176	20	)	)	PUNCT
ejpam-5332	176	21	)	)	PUNCT
ejpam-5332	176	22	.	.	PUNCT
ejpam-5332	177	1	since	since	SCONJ
ejpam-5332	177	2	(	(	PUNCT
ejpam-5332	177	3	u	u	NOUN
ejpam-5332	177	4	,	,	PUNCT
ejpam-5332	177	5	v	v	NOUN
ejpam-5332	177	6	)	)	PUNCT
ejpam-5332	177	7	and	and	CCONJ
ejpam-5332	177	8	(	(	PUNCT
ejpam-5332	177	9	u′	u′	PROPN
ejpam-5332	177	10	,	,	PUNCT
ejpam-5332	177	11	v′	v′	PROPN
ejpam-5332	177	12	)	)	PUNCT
ejpam-5332	177	13	are	be	AUX
ejpam-5332	177	14	arbitrarily	arbitrarily	ADV
ejpam-5332	177	15	chosen	choose	VERB
ejpam-5332	177	16	vertices	vertex	NOUN
ejpam-5332	177	17	,	,	PUNCT
ejpam-5332	177	18	the	the	DET
ejpam-5332	177	19	distance	distance	NOUN
ejpam-5332	177	20	dg1⊠g2((u	dg1⊠g2((u	NOUN
ejpam-5332	177	21	,	,	PUNCT
ejpam-5332	177	22	v	v	NOUN
ejpam-5332	177	23	)	)	PUNCT
ejpam-5332	177	24	,	,	PUNCT
ejpam-5332	177	25	(	(	PUNCT
ejpam-5332	177	26	u	u	NOUN
ejpam-5332	177	27	′	′	NOUN
ejpam-5332	177	28	,	,	PUNCT
ejpam-5332	177	29	v′	v′	PROPN
ejpam-5332	177	30	)	)	PUNCT
ejpam-5332	177	31	)	)	PUNCT
ejpam-5332	177	32	represents	represent	VERB
ejpam-5332	177	33	the	the	DET
ejpam-5332	177	34	shortest	short	ADJ
ejpam-5332	177	35	path	path	NOUN
ejpam-5332	177	36	between	between	ADP
ejpam-5332	177	37	these	these	DET
ejpam-5332	177	38	vertices	vertex	NOUN
ejpam-5332	177	39	.	.	PUNCT
ejpam-5332	178	1	therefore	therefore	ADV
ejpam-5332	178	2	dg1⊠g2((u	dg1⊠g2((u	NOUN
ejpam-5332	178	3	,	,	PUNCT
ejpam-5332	178	4	v	v	NOUN
ejpam-5332	178	5	)	)	PUNCT
ejpam-5332	178	6	,	,	PUNCT
ejpam-5332	178	7	(	(	PUNCT
ejpam-5332	178	8	u	u	NOUN
ejpam-5332	178	9	′	′	NOUN
ejpam-5332	178	10	,	,	PUNCT
ejpam-5332	178	11	v′	v′	NOUN
ejpam-5332	178	12	)	)	PUNCT
ejpam-5332	178	13	)	)	PUNCT
ejpam-5332	179	1	=	=	SYM
ejpam-5332	179	2	γh(g1	γh(g1	ADP
ejpam-5332	179	3	⊠g2	⊠g2	NOUN
ejpam-5332	179	4	)	)	PUNCT
ejpam-5332	179	5	.	.	PUNCT
ejpam-5332	180	1	substituting	substitute	VERB
ejpam-5332	180	2	this	this	PRON
ejpam-5332	180	3	to	to	ADP
ejpam-5332	180	4	our	our	PRON
ejpam-5332	180	5	inequality	inequality	NOUN
ejpam-5332	180	6	we	we	PRON
ejpam-5332	180	7	get	get	VERB
ejpam-5332	180	8	max{γh1(g1),γh2(g2	max{γh1(g1),γh2(g2	ADJ
ejpam-5332	180	9	)	)	PUNCT
ejpam-5332	180	10	}	}	PUNCT
ejpam-5332	180	11	≤	≤	NOUN
ejpam-5332	180	12	γh(g1	γh(g1	ADP
ejpam-5332	180	13	⊠g2	⊠g2	PROPN
ejpam-5332	180	14	)	)	PUNCT
ejpam-5332	180	15	.	.	PUNCT
ejpam-5332	181	1	h.	h.	PROPN
ejpam-5332	181	2	b.	b.	PROPN
ejpam-5332	181	3	samson	samson	PROPN
ejpam-5332	181	4	,	,	PUNCT
ejpam-5332	181	5	i.	i.	PROPN
ejpam-5332	181	6	s.	s.	PROPN
ejpam-5332	181	7	aniversario	aniversario	PROPN
ejpam-5332	181	8	,	,	PUNCT
ejpam-5332	181	9	m.	m.	PROPN
ejpam-5332	181	10	j.	j.	PROPN
ejpam-5332	181	11	f.	f.	PROPN
ejpam-5332	181	12	luga	luga	PROPN
ejpam-5332	181	13	/	/	SYM
ejpam-5332	181	14	eur	eur	PROPN
ejpam-5332	181	15	.	.	PUNCT
ejpam-5332	182	1	j.	j.	PROPN
ejpam-5332	182	2	pure	pure	PROPN
ejpam-5332	182	3	appl	appl	PROPN
ejpam-5332	182	4	.	.	PROPN
ejpam-5332	182	5	math	math	PROPN
ejpam-5332	182	6	,	,	PUNCT
ejpam-5332	182	7	17	17	NUM
ejpam-5332	182	8	(	(	PUNCT
ejpam-5332	182	9	4	4	NUM
ejpam-5332	182	10	)	)	PUNCT
ejpam-5332	182	11	(	(	PUNCT
ejpam-5332	182	12	2024	2024	NUM
ejpam-5332	182	13	)	)	PUNCT
ejpam-5332	182	14	,	,	PUNCT
ejpam-5332	182	15	2930	2930	NUM
ejpam-5332	182	16	-	-	SYM
ejpam-5332	182	17	2938	2938	NUM
ejpam-5332	182	18	2937	2937	NUM
ejpam-5332	182	19	from	from	ADP
ejpam-5332	182	20	[	[	X
ejpam-5332	182	21	3	3	NUM
ejpam-5332	182	22	]	]	PUNCT
ejpam-5332	182	23	,	,	PUNCT
ejpam-5332	182	24	we	we	PRON
ejpam-5332	182	25	also	also	ADV
ejpam-5332	182	26	have	have	AUX
ejpam-5332	182	27	,	,	PUNCT
ejpam-5332	182	28	γh(g1	γh(g1	PUNCT
ejpam-5332	182	29	⊠g2	⊠g2	ADJ
ejpam-5332	182	30	)	)	PUNCT
ejpam-5332	182	31	≤	≤	NUM
ejpam-5332	182	32	max{γh1(g1),γh2(g2	max{γh1(g1),γh2(g2	NOUN
ejpam-5332	182	33	)	)	PUNCT
ejpam-5332	182	34	}	}	PUNCT
ejpam-5332	182	35	.	.	PUNCT
ejpam-5332	183	1	combining	combine	VERB
ejpam-5332	183	2	these	these	DET
ejpam-5332	183	3	results	result	NOUN
ejpam-5332	183	4	,	,	PUNCT
ejpam-5332	183	5	we	we	PRON
ejpam-5332	183	6	conclude	conclude	VERB
ejpam-5332	183	7	γh(g1	γh(g1	ADP
ejpam-5332	183	8	⊠g2	⊠g2	ADJ
ejpam-5332	183	9	)	)	PUNCT
ejpam-5332	183	10	=	=	SYM
ejpam-5332	183	11	max{γh1(g1),γh2(g2	max{γh1(g1),γh2(g2	X
ejpam-5332	183	12	)	)	PUNCT
ejpam-5332	183	13	}	}	PUNCT
ejpam-5332	183	14	.	.	PUNCT
ejpam-5332	184	1	■	■	PUNCT
ejpam-5332	184	2	consider	consider	VERB
ejpam-5332	184	3	the	the	DET
ejpam-5332	184	4	strong	strong	ADJ
ejpam-5332	184	5	product	product	NOUN
ejpam-5332	184	6	of	of	ADP
ejpam-5332	184	7	p8	p8	PROPN
ejpam-5332	184	8	and	and	CCONJ
ejpam-5332	184	9	p6	p6	PROPN
ejpam-5332	184	10	,	,	PUNCT
ejpam-5332	184	11	that	that	PRON
ejpam-5332	184	12	is	be	AUX
ejpam-5332	184	13	p8⊠p6	p8⊠p6	VERB
ejpam-5332	184	14	is	be	AUX
ejpam-5332	184	15	as	as	SCONJ
ejpam-5332	184	16	shown	show	VERB
ejpam-5332	184	17	in	in	ADP
ejpam-5332	184	18	figure	figure	NOUN
ejpam-5332	184	19	3	3	NUM
ejpam-5332	184	20	and	and	CCONJ
ejpam-5332	184	21	a	a	DET
ejpam-5332	184	22	proper	proper	ADJ
ejpam-5332	184	23	convex	convex	NOUN
ejpam-5332	184	24	subgraph	subgraph	NOUN
ejpam-5332	184	25	h	h	NOUN
ejpam-5332	184	26	=	=	PUNCT
ejpam-5332	184	27	p2	p2	PROPN
ejpam-5332	184	28	⊠	⊠	PROPN
ejpam-5332	184	29	p2	p2	NOUN
ejpam-5332	184	30	,	,	PUNCT
ejpam-5332	184	31	where	where	SCONJ
ejpam-5332	184	32	p2	p2	PROPN
ejpam-5332	184	33	is	be	AUX
ejpam-5332	184	34	a	a	DET
ejpam-5332	184	35	convex	convex	ADJ
ejpam-5332	184	36	subgraph	subgraph	NOUN
ejpam-5332	184	37	of	of	ADP
ejpam-5332	184	38	p8	p8	PROPN
ejpam-5332	184	39	and	and	CCONJ
ejpam-5332	184	40	p2	p2	PROPN
ejpam-5332	184	41	is	be	AUX
ejpam-5332	184	42	a	a	DET
ejpam-5332	184	43	proper	proper	ADJ
ejpam-5332	184	44	convex	convex	NOUN
ejpam-5332	184	45	subgraph	subgraph	NOUN
ejpam-5332	184	46	of	of	ADP
ejpam-5332	184	47	p6	p6	PROPN
ejpam-5332	184	48	.	.	PUNCT
ejpam-5332	185	1	for	for	ADP
ejpam-5332	185	2	this	this	DET
ejpam-5332	185	3	graph	graph	NOUN
ejpam-5332	185	4	,	,	PUNCT
ejpam-5332	185	5	γh(p8	γh(p8	NOUN
ejpam-5332	185	6	⊠	⊠	PROPN
ejpam-5332	185	7	p6	p6	PROPN
ejpam-5332	185	8	)	)	PUNCT
ejpam-5332	186	1	=	=	SYM
ejpam-5332	186	2	max	max	PROPN
ejpam-5332	186	3	{	{	PUNCT
ejpam-5332	186	4	γp2(p8),γp2(p6	γp2(p8),γp2(p6	NOUN
ejpam-5332	186	5	)	)	PUNCT
ejpam-5332	186	6	}	}	PUNCT
ejpam-5332	186	7	=	=	SYM
ejpam-5332	186	8	max{3	max{3	NOUN
ejpam-5332	186	9	,	,	PUNCT
ejpam-5332	186	10	2	2	X
ejpam-5332	186	11	}	}	PUNCT
ejpam-5332	186	12	=	=	SYM
ejpam-5332	186	13	3	3	X
ejpam-5332	186	14	.	.	X
ejpam-5332	186	15	figure	figure	NOUN
ejpam-5332	186	16	3	3	NUM
ejpam-5332	186	17	:	:	PUNCT
ejpam-5332	186	18	the	the	DET
ejpam-5332	186	19	strong	strong	ADJ
ejpam-5332	186	20	product	product	NOUN
ejpam-5332	186	21	of	of	ADP
ejpam-5332	186	22	p8	p8	ADJ
ejpam-5332	186	23	and	and	CCONJ
ejpam-5332	186	24	p6	p6	ADJ
ejpam-5332	186	25	conclusion	conclusion	NOUN
ejpam-5332	186	26	this	this	DET
ejpam-5332	186	27	study	study	NOUN
ejpam-5332	186	28	has	have	AUX
ejpam-5332	186	29	advanced	advance	VERB
ejpam-5332	186	30	the	the	DET
ejpam-5332	186	31	understanding	understanding	NOUN
ejpam-5332	186	32	of	of	ADP
ejpam-5332	186	33	the	the	DET
ejpam-5332	186	34	convex	convex	NOUN
ejpam-5332	186	35	accessibility	accessibility	NOUN
ejpam-5332	186	36	number	number	NOUN
ejpam-5332	186	37	by	by	ADP
ejpam-5332	186	38	investigating	investigate	VERB
ejpam-5332	186	39	its	its	PRON
ejpam-5332	186	40	behavior	behavior	NOUN
ejpam-5332	186	41	under	under	ADP
ejpam-5332	186	42	various	various	ADJ
ejpam-5332	186	43	graph	graph	NOUN
ejpam-5332	186	44	operations	operation	NOUN
ejpam-5332	186	45	and	and	CCONJ
ejpam-5332	186	46	complementation	complementation	NOUN
ejpam-5332	186	47	.	.	PUNCT
ejpam-5332	187	1	the	the	DET
ejpam-5332	187	2	analysis	analysis	NOUN
ejpam-5332	187	3	of	of	ADP
ejpam-5332	187	4	the	the	DET
ejpam-5332	187	5	cartesian	cartesian	ADJ
ejpam-5332	187	6	and	and	CCONJ
ejpam-5332	187	7	strong	strong	ADJ
ejpam-5332	187	8	products	product	NOUN
ejpam-5332	187	9	revealed	reveal	VERB
ejpam-5332	187	10	distinct	distinct	ADJ
ejpam-5332	187	11	patterns	pattern	NOUN
ejpam-5332	187	12	in	in	ADP
ejpam-5332	187	13	the	the	DET
ejpam-5332	187	14	convex	convex	NOUN
ejpam-5332	187	15	accessibility	accessibility	NOUN
ejpam-5332	187	16	number	number	NOUN
ejpam-5332	187	17	,	,	PUNCT
ejpam-5332	187	18	offering	offer	VERB
ejpam-5332	187	19	valuable	valuable	ADJ
ejpam-5332	187	20	insights	insight	NOUN
ejpam-5332	187	21	into	into	ADP
ejpam-5332	187	22	how	how	SCONJ
ejpam-5332	187	23	these	these	DET
ejpam-5332	187	24	binary	binary	ADJ
ejpam-5332	187	25	operations	operation	NOUN
ejpam-5332	187	26	impact	impact	NOUN
ejpam-5332	187	27	graph	graph	NOUN
ejpam-5332	187	28	properties	property	NOUN
ejpam-5332	187	29	.	.	PUNCT
ejpam-5332	188	1	additionally	additionally	ADV
ejpam-5332	188	2	,	,	PUNCT
ejpam-5332	188	3	exploring	explore	VERB
ejpam-5332	188	4	the	the	DET
ejpam-5332	188	5	convex	convex	NOUN
ejpam-5332	188	6	accessibility	accessibility	NOUN
ejpam-5332	188	7	number	number	NOUN
ejpam-5332	188	8	of	of	ADP
ejpam-5332	188	9	graph	graph	NOUN
ejpam-5332	188	10	complements	complement	NOUN
ejpam-5332	188	11	has	have	AUX
ejpam-5332	188	12	provided	provide	VERB
ejpam-5332	188	13	further	further	ADJ
ejpam-5332	188	14	clarity	clarity	NOUN
ejpam-5332	188	15	on	on	ADP
ejpam-5332	188	16	its	its	PRON
ejpam-5332	188	17	interaction	interaction	NOUN
ejpam-5332	188	18	with	with	ADP
ejpam-5332	188	19	graph	graph	NOUN
ejpam-5332	188	20	structures	structure	NOUN
ejpam-5332	188	21	.	.	PUNCT
ejpam-5332	189	1	these	these	DET
ejpam-5332	189	2	findings	finding	NOUN
ejpam-5332	189	3	not	not	PART
ejpam-5332	189	4	only	only	ADV
ejpam-5332	189	5	enhance	enhance	VERB
ejpam-5332	189	6	theoretical	theoretical	ADJ
ejpam-5332	189	7	knowledge	knowledge	NOUN
ejpam-5332	189	8	but	but	CCONJ
ejpam-5332	189	9	also	also	ADV
ejpam-5332	189	10	pave	pave	VERB
ejpam-5332	189	11	the	the	DET
ejpam-5332	189	12	way	way	NOUN
ejpam-5332	189	13	for	for	ADP
ejpam-5332	189	14	future	future	ADJ
ejpam-5332	189	15	research	research	NOUN
ejpam-5332	189	16	in	in	ADP
ejpam-5332	189	17	graph	graph	NOUN
ejpam-5332	189	18	theory	theory	NOUN
ejpam-5332	189	19	,	,	PUNCT
ejpam-5332	189	20	particularly	particularly	ADV
ejpam-5332	189	21	in	in	ADP
ejpam-5332	189	22	understanding	understand	VERB
ejpam-5332	189	23	how	how	SCONJ
ejpam-5332	189	24	different	different	ADJ
ejpam-5332	189	25	operations	operation	NOUN
ejpam-5332	189	26	affect	affect	VERB
ejpam-5332	189	27	convex	convex	NOUN
ejpam-5332	189	28	accessibility	accessibility	NOUN
ejpam-5332	189	29	.	.	PUNCT
ejpam-5332	190	1	by	by	ADP
ejpam-5332	190	2	bridging	bridge	VERB
ejpam-5332	190	3	gaps	gap	NOUN
ejpam-5332	190	4	in	in	ADP
ejpam-5332	190	5	the	the	DET
ejpam-5332	190	6	existing	exist	VERB
ejpam-5332	190	7	literature	literature	NOUN
ejpam-5332	190	8	and	and	CCONJ
ejpam-5332	190	9	presenting	present	VERB
ejpam-5332	190	10	new	new	ADJ
ejpam-5332	190	11	perspectives	perspective	NOUN
ejpam-5332	190	12	,	,	PUNCT
ejpam-5332	190	13	this	this	DET
ejpam-5332	190	14	study	study	NOUN
ejpam-5332	190	15	contributes	contribute	VERB
ejpam-5332	190	16	significantly	significantly	ADV
ejpam-5332	190	17	to	to	ADP
ejpam-5332	190	18	the	the	DET
ejpam-5332	190	19	broader	broad	ADJ
ejpam-5332	190	20	field	field	NOUN
ejpam-5332	190	21	of	of	ADP
ejpam-5332	190	22	graph	graph	NOUN
ejpam-5332	190	23	theory	theory	NOUN
ejpam-5332	190	24	and	and	CCONJ
ejpam-5332	190	25	its	its	PRON
ejpam-5332	190	26	applications	application	NOUN
ejpam-5332	190	27	.	.	PUNCT
ejpam-5332	191	1	acknowledgements	acknowledgement	NOUN
ejpam-5332	191	2	the	the	DET
ejpam-5332	191	3	authors	author	NOUN
ejpam-5332	191	4	are	be	AUX
ejpam-5332	191	5	grateful	grateful	ADJ
ejpam-5332	191	6	to	to	ADP
ejpam-5332	191	7	the	the	DET
ejpam-5332	191	8	department	department	NOUN
ejpam-5332	191	9	of	of	ADP
ejpam-5332	191	10	science	science	NOUN
ejpam-5332	191	11	and	and	CCONJ
ejpam-5332	191	12	technology	technology	NOUN
ejpam-5332	191	13	accelerated	accelerate	VERB
ejpam-5332	191	14	science	science	NOUN
ejpam-5332	191	15	and	and	CCONJ
ejpam-5332	191	16	technology	technology	NOUN
ejpam-5332	191	17	human	human	ADJ
ejpam-5332	191	18	resource	resource	NOUN
ejpam-5332	191	19	development	development	NOUN
ejpam-5332	191	20	program	program	NOUN
ejpam-5332	191	21	(	(	PUNCT
ejpam-5332	191	22	dost	dost	NOUN
ejpam-5332	191	23	-	-	PUNCT
ejpam-5332	191	24	asthrdp)philippines	asthrdp)philippine	NOUN
ejpam-5332	191	25	and	and	CCONJ
ejpam-5332	191	26	msu	msu	PROPN
ejpam-5332	191	27	-	-	PUNCT
ejpam-5332	191	28	iligan	iligan	PROPN
ejpam-5332	191	29	institute	institute	PROPN
ejpam-5332	191	30	of	of	ADP
ejpam-5332	191	31	technology	technology	NOUN
ejpam-5332	191	32	for	for	ADP
ejpam-5332	191	33	funding	fund	VERB
ejpam-5332	191	34	this	this	DET
ejpam-5332	191	35	research	research	NOUN
ejpam-5332	191	36	.	.	PUNCT
ejpam-5332	192	1	references	reference	NOUN
ejpam-5332	192	2	2938	2938	NUM
ejpam-5332	192	3	references	reference	NOUN
ejpam-5332	192	4	[	[	X
ejpam-5332	192	5	1	1	NUM
ejpam-5332	192	6	]	]	PUNCT
ejpam-5332	192	7	f	f	PROPN
ejpam-5332	192	8	harary	harary	NOUN
ejpam-5332	192	9	.	.	PUNCT
ejpam-5332	193	1	graph	graph	NOUN
ejpam-5332	193	2	theory	theory	NOUN
ejpam-5332	193	3	.	.	PUNCT
ejpam-5332	194	1	addison	addison	PROPN
ejpam-5332	194	2	-	-	PUNCT
ejpam-5332	194	3	weasley	weasley	PROPN
ejpam-5332	194	4	publishing	publishing	PROPN
ejpam-5332	194	5	company	company	NOUN
ejpam-5332	194	6	,	,	PUNCT
ejpam-5332	194	7	boston	boston	PROPN
ejpam-5332	194	8	,	,	PUNCT
ejpam-5332	194	9	usa	usa	PROPN
ejpam-5332	194	10	,	,	PUNCT
ejpam-5332	194	11	1969	1969	NUM
ejpam-5332	194	12	.	.	PUNCT
ejpam-5332	195	1	[	[	X
ejpam-5332	195	2	2	2	NUM
ejpam-5332	195	3	]	]	PUNCT
ejpam-5332	195	4	jr	jr	PROPN
ejpam-5332	195	5	r	r	NOUN
ejpam-5332	195	6	artes	arte	NOUN
ejpam-5332	195	7	and	and	CCONJ
ejpam-5332	195	8	mj	mj	PROPN
ejpam-5332	195	9	luga	luga	PROPN
ejpam-5332	195	10	.	.	PUNCT
ejpam-5332	196	1	convex	convex	PROPN
ejpam-5332	196	2	accessibility	accessibility	NOUN
ejpam-5332	196	3	in	in	ADP
ejpam-5332	196	4	graph	graph	NOUN
ejpam-5332	196	5	operation	operation	NOUN
ejpam-5332	196	6	.	.	PUNCT
ejpam-5332	197	1	hikari	hikari	PROPN
ejpam-5332	197	2	ltd	ltd	PROPN
ejpam-5332	197	3	,	,	PUNCT
ejpam-5332	197	4	8(116):5763–5770	8(116):5763–5770	NOUN
ejpam-5332	197	5	,	,	PUNCT
ejpam-5332	197	6	2014	2014	NUM
ejpam-5332	197	7	.	.	PUNCT
ejpam-5332	198	1	[	[	X
ejpam-5332	198	2	3	3	X
ejpam-5332	198	3	]	]	X
ejpam-5332	198	4	jr	jr	PROPN
ejpam-5332	198	5	r	r	NOUN
ejpam-5332	198	6	artes	arte	NOUN
ejpam-5332	198	7	and	and	CCONJ
ejpam-5332	198	8	mj	mj	PROPN
ejpam-5332	198	9	luga	luga	PROPN
ejpam-5332	198	10	.	.	PUNCT
ejpam-5332	199	1	convex	convex	PROPN
ejpam-5332	199	2	accessibility	accessibility	NOUN
ejpam-5332	199	3	in	in	ADP
ejpam-5332	199	4	graphs	graph	NOUN
ejpam-5332	199	5	.	.	PUNCT
ejpam-5332	200	1	hikari	hikari	PROPN
ejpam-5332	200	2	ltd	ltd	PROPN
ejpam-5332	200	3	,	,	PUNCT
ejpam-5332	200	4	8(88):4361–4366	8(88):4361–4366	NUM
ejpam-5332	200	5	,	,	PUNCT
ejpam-5332	200	6	2014	2014	NUM
ejpam-5332	200	7	.	.	PUNCT
ejpam-5332	201	1	[	[	X
ejpam-5332	201	2	4	4	X
ejpam-5332	201	3	]	]	PUNCT
ejpam-5332	201	4	w	w	NOUN
ejpam-5332	201	5	imrich	imrich	NOUN
ejpam-5332	201	6	r	r	NOUN
ejpam-5332	201	7	hammack	hammack	NOUN
ejpam-5332	201	8	and	and	CCONJ
ejpam-5332	201	9	s	s	PROPN
ejpam-5332	201	10	klavzar	klavzar	PROPN
ejpam-5332	201	11	.	.	PUNCT
ejpam-5332	202	1	handbook	handbook	NOUN
ejpam-5332	202	2	on	on	ADP
ejpam-5332	202	3	product	product	NOUN
ejpam-5332	202	4	graphs	graph	NOUN
ejpam-5332	202	5	.	.	PUNCT
ejpam-5332	203	1	taylor	taylor	PROPN
ejpam-5332	203	2	and	and	CCONJ
ejpam-5332	203	3	francis	francis	PROPN
ejpam-5332	203	4	group	group	PROPN
ejpam-5332	203	5	,	,	PUNCT
ejpam-5332	203	6	england	england	PROPN
ejpam-5332	203	7	,	,	PUNCT
ejpam-5332	203	8	united	united	ADJ
ejpam-5332	203	9	kingdom	kingdom	PROPN
ejpam-5332	203	10	,	,	PUNCT
ejpam-5332	203	11	2011	2011	NUM
ejpam-5332	203	12	.	.	PUNCT
ejpam-5332	204	1	[	[	X
ejpam-5332	204	2	5	5	NUM
ejpam-5332	204	3	]	]	X
ejpam-5332	204	4	jr	jr	PROPN
ejpam-5332	204	5	s	s	PROPN
ejpam-5332	204	6	canoy	canoy	PROPN
ejpam-5332	204	7	and	and	CCONJ
ejpam-5332	204	8	ijl	ijl	PROPN
ejpam-5332	204	9	garces	garce	NOUN
ejpam-5332	204	10	.	.	PUNCT
ejpam-5332	205	1	convex	convex	VERB
ejpam-5332	205	2	under	under	ADP
ejpam-5332	205	3	some	some	DET
ejpam-5332	205	4	graph	graph	NOUN
ejpam-5332	205	5	operations	operation	NOUN
ejpam-5332	205	6	.	.	PUNCT
ejpam-5332	206	1	graphs	graph	NOUN
ejpam-5332	206	2	and	and	CCONJ
ejpam-5332	206	3	combinatorics	combinatoric	NOUN
ejpam-5332	206	4	,	,	PUNCT
ejpam-5332	206	5	18:787–793	18:787–793	PROPN
ejpam-5332	206	6	,	,	PUNCT
ejpam-5332	206	7	2002	2002	NUM
ejpam-5332	206	8	.	.	PUNCT