id	sid	tid	token	lemma	pos
ejpam-6046	1	1	european	european	PROPN
ejpam-6046	1	2	journal	journal	PROPN
ejpam-6046	1	3	of	of	ADP
ejpam-6046	1	4	pure	pure	ADJ
ejpam-6046	1	5	and	and	CCONJ
ejpam-6046	1	6	applied	applied	ADJ
ejpam-6046	1	7	mathematics	mathematic	NOUN
ejpam-6046	1	8	2025	2025	NUM
ejpam-6046	1	9	,	,	PUNCT
ejpam-6046	1	10	vol	vol	NOUN
ejpam-6046	1	11	.	.	PROPN
ejpam-6046	1	12	18	18	NUM
ejpam-6046	1	13	,	,	PUNCT
ejpam-6046	1	14	issue	issue	NOUN
ejpam-6046	1	15	2	2	NUM
ejpam-6046	1	16	,	,	PUNCT
ejpam-6046	1	17	article	article	NOUN
ejpam-6046	1	18	number	number	NOUN
ejpam-6046	1	19	6046	6046	NUM
ejpam-6046	1	20	issn	issn	PROPN
ejpam-6046	1	21	1307	1307	NUM
ejpam-6046	1	22	-	-	SYM
ejpam-6046	1	23	5543	5543	NUM
ejpam-6046	1	24	–	–	PUNCT
ejpam-6046	1	25	ejpam.com	ejpam.com	X
ejpam-6046	1	26	published	publish	VERB
ejpam-6046	1	27	by	by	ADP
ejpam-6046	1	28	new	new	PROPN
ejpam-6046	1	29	york	york	PROPN
ejpam-6046	1	30	business	business	PROPN
ejpam-6046	1	31	global	global	ADJ
ejpam-6046	1	32	independent	independent	ADJ
ejpam-6046	1	33	edge	edge	NOUN
ejpam-6046	1	34	domination	domination	NOUN
ejpam-6046	1	35	topology	topology	NOUN
ejpam-6046	1	36	of	of	ADP
ejpam-6046	1	37	some	some	DET
ejpam-6046	1	38	graph	graph	NOUN
ejpam-6046	1	39	families	family	NOUN
ejpam-6046	1	40	jhon	jhon	PROPN
ejpam-6046	1	41	neceir	neceir	PROPN
ejpam-6046	1	42	s.	s.	PROPN
ejpam-6046	1	43	ontulan1,∗	ontulan1,∗	PROPN
ejpam-6046	1	44	,	,	PUNCT
ejpam-6046	1	45	cherry	cherry	PROPN
ejpam-6046	1	46	mae	mae	PROPN
ejpam-6046	1	47	r.	r.	PROPN
ejpam-6046	1	48	balingit1	balingit1	PROPN
ejpam-6046	1	49	1	1	NUM
ejpam-6046	1	50	department	department	NOUN
ejpam-6046	1	51	of	of	ADP
ejpam-6046	1	52	mathematics	mathematic	NOUN
ejpam-6046	1	53	,	,	PUNCT
ejpam-6046	1	54	college	college	NOUN
ejpam-6046	1	55	of	of	ADP
ejpam-6046	1	56	arts	art	NOUN
ejpam-6046	1	57	and	and	CCONJ
ejpam-6046	1	58	sciences	science	NOUN
ejpam-6046	1	59	,	,	PUNCT
ejpam-6046	1	60	central	central	ADJ
ejpam-6046	1	61	mindanao	mindanao	PROPN
ejpam-6046	1	62	university	university	PROPN
ejpam-6046	1	63	,	,	PUNCT
ejpam-6046	1	64	university	university	NOUN
ejpam-6046	1	65	town	town	NOUN
ejpam-6046	1	66	,	,	PUNCT
ejpam-6046	1	67	musuan	musuan	PROPN
ejpam-6046	1	68	,	,	PUNCT
ejpam-6046	1	69	8710	8710	NUM
ejpam-6046	1	70	maramag	maramag	NOUN
ejpam-6046	1	71	,	,	PUNCT
ejpam-6046	1	72	bukidnon	bukidnon	NOUN
ejpam-6046	1	73	,	,	PUNCT
ejpam-6046	1	74	philippines	philippine	NOUN
ejpam-6046	1	75	abstract	abstract	ADJ
ejpam-6046	1	76	.	.	PUNCT
ejpam-6046	2	1	let	let	VERB
ejpam-6046	2	2	g	g	PROPN
ejpam-6046	2	3	=	=	SYM
ejpam-6046	2	4	(	(	PUNCT
ejpam-6046	2	5	v	v	NOUN
ejpam-6046	2	6	(	(	PUNCT
ejpam-6046	2	7	g	g	NOUN
ejpam-6046	2	8	)	)	PUNCT
ejpam-6046	2	9	,	,	PUNCT
ejpam-6046	2	10	e(g	e(g	PROPN
ejpam-6046	2	11	)	)	PUNCT
ejpam-6046	2	12	)	)	PUNCT
ejpam-6046	3	1	be	be	AUX
ejpam-6046	3	2	a	a	DET
ejpam-6046	3	3	nonempty	nonempty	ADJ
ejpam-6046	3	4	graph	graph	NOUN
ejpam-6046	3	5	.	.	PUNCT
ejpam-6046	4	1	an	an	DET
ejpam-6046	4	2	independent	independent	ADJ
ejpam-6046	4	3	edge	edge	NOUN
ejpam-6046	4	4	dominating	dominating	NOUN
ejpam-6046	4	5	set	set	NOUN
ejpam-6046	4	6	is	be	AUX
ejpam-6046	4	7	an	an	DET
ejpam-6046	4	8	independent	independent	ADJ
ejpam-6046	4	9	set	set	NOUN
ejpam-6046	4	10	of	of	ADP
ejpam-6046	4	11	edges	edge	NOUN
ejpam-6046	4	12	of	of	ADP
ejpam-6046	4	13	g	g	NOUN
ejpam-6046	4	14	which	which	PRON
ejpam-6046	4	15	is	be	AUX
ejpam-6046	4	16	also	also	ADV
ejpam-6046	4	17	an	an	DET
ejpam-6046	4	18	edge	edge	NOUN
ejpam-6046	4	19	dominating	dominating	NOUN
ejpam-6046	4	20	set	set	NOUN
ejpam-6046	4	21	of	of	ADP
ejpam-6046	4	22	g.	g.	PROPN
ejpam-6046	4	23	the	the	DET
ejpam-6046	4	24	family	family	NOUN
ejpam-6046	4	25	of	of	ADP
ejpam-6046	4	26	independent	independent	ADJ
ejpam-6046	4	27	edge	edge	NOUN
ejpam-6046	4	28	dominating	dominating	NOUN
ejpam-6046	4	29	sets	set	NOUN
ejpam-6046	4	30	of	of	ADP
ejpam-6046	4	31	g	g	PROPN
ejpam-6046	4	32	generates	generate	VERB
ejpam-6046	4	33	a	a	DET
ejpam-6046	4	34	unique	unique	ADJ
ejpam-6046	4	35	topology	topology	NOUN
ejpam-6046	4	36	.	.	PUNCT
ejpam-6046	5	1	in	in	ADP
ejpam-6046	5	2	this	this	DET
ejpam-6046	5	3	paper	paper	NOUN
ejpam-6046	5	4	,	,	PUNCT
ejpam-6046	5	5	we	we	PRON
ejpam-6046	5	6	formally	formally	ADV
ejpam-6046	5	7	define	define	VERB
ejpam-6046	5	8	the	the	DET
ejpam-6046	5	9	new	new	ADJ
ejpam-6046	5	10	notion	notion	NOUN
ejpam-6046	5	11	of	of	ADP
ejpam-6046	5	12	this	this	DET
ejpam-6046	5	13	topology	topology	NOUN
ejpam-6046	5	14	generated	generate	VERB
ejpam-6046	5	15	by	by	ADP
ejpam-6046	5	16	the	the	DET
ejpam-6046	5	17	family	family	NOUN
ejpam-6046	5	18	of	of	ADP
ejpam-6046	5	19	independent	independent	ADJ
ejpam-6046	5	20	edge	edge	NOUN
ejpam-6046	5	21	dominating	dominating	NOUN
ejpam-6046	5	22	sets	set	NOUN
ejpam-6046	5	23	(	(	PUNCT
ejpam-6046	5	24	ieds	ied	NOUN
ejpam-6046	5	25	)	)	PUNCT
ejpam-6046	5	26	in	in	ADP
ejpam-6046	5	27	a	a	DET
ejpam-6046	5	28	graph	graph	NOUN
ejpam-6046	5	29	called	call	VERB
ejpam-6046	5	30	the	the	DET
ejpam-6046	5	31	independent	independent	ADJ
ejpam-6046	5	32	edge	edge	NOUN
ejpam-6046	5	33	domination	domination	NOUN
ejpam-6046	5	34	topology	topology	NOUN
ejpam-6046	5	35	on	on	ADP
ejpam-6046	5	36	e(g	e(g	PROPN
ejpam-6046	5	37	)	)	PUNCT
ejpam-6046	5	38	,	,	PUNCT
ejpam-6046	5	39	herein	herein	NOUN
ejpam-6046	5	40	denoted	denote	VERB
ejpam-6046	5	41	as	as	ADP
ejpam-6046	5	42	τeid(g	τeid(g	PROPN
ejpam-6046	5	43	)	)	PUNCT
ejpam-6046	5	44	.	.	PUNCT
ejpam-6046	6	1	moreover	moreover	ADV
ejpam-6046	6	2	,	,	PUNCT
ejpam-6046	6	3	we	we	PRON
ejpam-6046	6	4	characterize	characterize	VERB
ejpam-6046	6	5	the	the	DET
ejpam-6046	6	6	subbasic	subbasic	ADJ
ejpam-6046	6	7	sets	set	NOUN
ejpam-6046	6	8	generated	generate	VERB
ejpam-6046	6	9	from	from	ADP
ejpam-6046	6	10	the	the	DET
ejpam-6046	6	11	family	family	NOUN
ejpam-6046	6	12	of	of	ADP
ejpam-6046	6	13	independent	independent	ADJ
ejpam-6046	6	14	edge	edge	NOUN
ejpam-6046	6	15	dominating	dominating	NOUN
ejpam-6046	6	16	sets	set	NOUN
ejpam-6046	6	17	and	and	CCONJ
ejpam-6046	6	18	the	the	DET
ejpam-6046	6	19	independent	independent	ADJ
ejpam-6046	6	20	edge	edge	NOUN
ejpam-6046	6	21	domination	domination	NOUN
ejpam-6046	6	22	topology	topology	NOUN
ejpam-6046	6	23	of	of	ADP
ejpam-6046	6	24	some	some	DET
ejpam-6046	6	25	graph	graph	NOUN
ejpam-6046	6	26	families	family	NOUN
ejpam-6046	6	27	.	.	PUNCT
ejpam-6046	7	1	2020	2020	NUM
ejpam-6046	7	2	mathematics	mathematic	NOUN
ejpam-6046	7	3	subject	subject	NOUN
ejpam-6046	7	4	classifications	classification	NOUN
ejpam-6046	7	5	:	:	PUNCT
ejpam-6046	7	6	05c70	05c70	NUM
ejpam-6046	7	7	,	,	PUNCT
ejpam-6046	7	8	54a05	54a05	NUM
ejpam-6046	7	9	,	,	PUNCT
ejpam-6046	7	10	54a25	54a25	NUM
ejpam-6046	7	11	,	,	PUNCT
ejpam-6046	7	12	05c75	05c75	NUM
ejpam-6046	7	13	key	key	ADJ
ejpam-6046	7	14	words	word	NOUN
ejpam-6046	7	15	and	and	CCONJ
ejpam-6046	7	16	phrases	phrase	NOUN
ejpam-6046	7	17	:	:	PUNCT
ejpam-6046	7	18	independent	independent	ADJ
ejpam-6046	7	19	edge	edge	NOUN
ejpam-6046	7	20	domination	domination	NOUN
ejpam-6046	7	21	topology	topology	NOUN
ejpam-6046	7	22	,	,	PUNCT
ejpam-6046	7	23	independent	independent	ADJ
ejpam-6046	7	24	edge	edge	NOUN
ejpam-6046	7	25	dominating	dominating	NOUN
ejpam-6046	7	26	sets	set	NOUN
ejpam-6046	7	27	,	,	PUNCT
ejpam-6046	7	28	complete	complete	ADJ
ejpam-6046	7	29	graph	graph	NOUN
ejpam-6046	7	30	,	,	PUNCT
ejpam-6046	7	31	friendship	friendship	NOUN
ejpam-6046	7	32	graph	graph	NOUN
ejpam-6046	7	33	,	,	PUNCT
ejpam-6046	7	34	complete	complete	ADJ
ejpam-6046	7	35	bipartite	bipartite	NOUN
ejpam-6046	7	36	graph	graph	NOUN
ejpam-6046	7	37	1	1	NUM
ejpam-6046	7	38	.	.	PUNCT
ejpam-6046	7	39	introduction	introduction	NOUN
ejpam-6046	7	40	topology	topology	NOUN
ejpam-6046	7	41	and	and	CCONJ
ejpam-6046	7	42	graph	graph	NOUN
ejpam-6046	7	43	theory	theory	NOUN
ejpam-6046	7	44	are	be	AUX
ejpam-6046	7	45	two	two	NUM
ejpam-6046	7	46	practically	practically	ADV
ejpam-6046	7	47	integrated	integrate	VERB
ejpam-6046	7	48	branches	branch	NOUN
ejpam-6046	7	49	of	of	ADP
ejpam-6046	7	50	mathematics	mathematic	NOUN
ejpam-6046	7	51	that	that	PRON
ejpam-6046	7	52	overlap	overlap	VERB
ejpam-6046	7	53	in	in	ADP
ejpam-6046	7	54	the	the	DET
ejpam-6046	7	55	structural	structural	ADJ
ejpam-6046	7	56	analysis	analysis	NOUN
ejpam-6046	7	57	of	of	ADP
ejpam-6046	7	58	spaces	space	NOUN
ejpam-6046	7	59	and	and	CCONJ
ejpam-6046	7	60	the	the	DET
ejpam-6046	7	61	study	study	NOUN
ejpam-6046	7	62	of	of	ADP
ejpam-6046	7	63	networks	network	NOUN
ejpam-6046	7	64	and	and	CCONJ
ejpam-6046	7	65	connections	connection	NOUN
ejpam-6046	7	66	.	.	PUNCT
ejpam-6046	8	1	from	from	ADP
ejpam-6046	8	2	the	the	DET
ejpam-6046	8	3	point	point	NOUN
ejpam-6046	8	4	of	of	ADP
ejpam-6046	8	5	view	view	NOUN
ejpam-6046	8	6	of	of	ADP
ejpam-6046	8	7	topological	topological	ADJ
ejpam-6046	8	8	ideas	idea	NOUN
ejpam-6046	8	9	connected	connect	VERB
ejpam-6046	8	10	with	with	ADP
ejpam-6046	8	11	various	various	ADJ
ejpam-6046	8	12	graph	graph	NOUN
ejpam-6046	8	13	models	model	NOUN
ejpam-6046	8	14	,	,	PUNCT
ejpam-6046	8	15	it	it	PRON
ejpam-6046	8	16	could	could	AUX
ejpam-6046	8	17	look	look	VERB
ejpam-6046	8	18	at	at	ADP
ejpam-6046	8	19	network	network	NOUN
ejpam-6046	8	20	properties	property	NOUN
ejpam-6046	8	21	like	like	ADP
ejpam-6046	8	22	continuity	continuity	NOUN
ejpam-6046	8	23	,	,	PUNCT
ejpam-6046	8	24	connectedness	connectedness	NOUN
ejpam-6046	8	25	,	,	PUNCT
ejpam-6046	8	26	and	and	CCONJ
ejpam-6046	8	27	space	space	NOUN
ejpam-6046	8	28	-	-	PUNCT
ejpam-6046	8	29	containing	contain	VERB
ejpam-6046	8	30	networks	network	NOUN
ejpam-6046	8	31	.	.	PUNCT
ejpam-6046	9	1	this	this	PRON
ejpam-6046	9	2	lets	let	VERB
ejpam-6046	9	3	researchers	researcher	NOUN
ejpam-6046	9	4	in	in	ADP
ejpam-6046	9	5	both	both	DET
ejpam-6046	9	6	directions	direction	NOUN
ejpam-6046	9	7	make	make	VERB
ejpam-6046	9	8	new	new	ADJ
ejpam-6046	9	9	tools	tool	NOUN
ejpam-6046	9	10	or	or	CCONJ
ejpam-6046	9	11	programs	program	NOUN
ejpam-6046	9	12	[	[	X
ejpam-6046	9	13	1	1	NUM
ejpam-6046	9	14	]	]	PUNCT
ejpam-6046	9	15	.	.	PUNCT
ejpam-6046	10	1	there	there	PRON
ejpam-6046	10	2	are	be	VERB
ejpam-6046	10	3	many	many	ADJ
ejpam-6046	10	4	ways	way	NOUN
ejpam-6046	10	5	of	of	ADP
ejpam-6046	10	6	constructing	construct	VERB
ejpam-6046	10	7	a	a	DET
ejpam-6046	10	8	topological	topological	ADJ
ejpam-6046	10	9	space	space	NOUN
ejpam-6046	10	10	from	from	ADP
ejpam-6046	10	11	a	a	DET
ejpam-6046	10	12	given	give	VERB
ejpam-6046	10	13	graph	graph	NOUN
ejpam-6046	10	14	−	−	PROPN
ejpam-6046	10	15	undirected	undirected	ADJ
ejpam-6046	10	16	or	or	CCONJ
ejpam-6046	10	17	directed	directed	ADJ
ejpam-6046	10	18	graphs	graph	NOUN
ejpam-6046	10	19	−	−	ADP
ejpam-6046	10	20	or	or	CCONJ
ejpam-6046	10	21	devising	devise	VERB
ejpam-6046	10	22	a	a	DET
ejpam-6046	10	23	method	method	NOUN
ejpam-6046	10	24	of	of	ADP
ejpam-6046	10	25	generating	generate	VERB
ejpam-6046	10	26	a	a	DET
ejpam-6046	10	27	graph	graph	NOUN
ejpam-6046	10	28	from	from	ADP
ejpam-6046	10	29	a	a	DET
ejpam-6046	10	30	given	give	VERB
ejpam-6046	10	31	(	(	PUNCT
ejpam-6046	10	32	finite	finite	ADJ
ejpam-6046	10	33	)	)	PUNCT
ejpam-6046	10	34	topological	topological	ADJ
ejpam-6046	10	35	space	space	NOUN
ejpam-6046	10	36	.	.	PUNCT
ejpam-6046	11	1	some	some	DET
ejpam-6046	11	2	construct	construct	NOUN
ejpam-6046	11	3	models	model	NOUN
ejpam-6046	11	4	solely	solely	ADV
ejpam-6046	11	5	based	base	VERB
ejpam-6046	11	6	on	on	ADP
ejpam-6046	11	7	the	the	DET
ejpam-6046	11	8	set	set	NOUN
ejpam-6046	11	9	of	of	ADP
ejpam-6046	11	10	vertices	vertex	NOUN
ejpam-6046	11	11	,	,	PUNCT
ejpam-6046	11	12	while	while	SCONJ
ejpam-6046	11	13	others	other	NOUN
ejpam-6046	11	14	base	base	VERB
ejpam-6046	11	15	their	their	PRON
ejpam-6046	11	16	models	model	NOUN
ejpam-6046	11	17	on	on	ADP
ejpam-6046	11	18	the	the	DET
ejpam-6046	11	19	set	set	NOUN
ejpam-6046	11	20	of	of	ADP
ejpam-6046	11	21	edges	edge	NOUN
ejpam-6046	11	22	.	.	PUNCT
ejpam-6046	12	1	however	however	ADV
ejpam-6046	12	2	,	,	PUNCT
ejpam-6046	12	3	the	the	DET
ejpam-6046	12	4	most	most	ADV
ejpam-6046	12	5	common	common	ADJ
ejpam-6046	12	6	approach	approach	NOUN
ejpam-6046	12	7	relies	rely	VERB
ejpam-6046	12	8	solely	solely	ADV
ejpam-6046	12	9	on	on	ADP
ejpam-6046	12	10	the	the	DET
ejpam-6046	12	11	set	set	NOUN
ejpam-6046	12	12	of	of	ADP
ejpam-6046	12	13	vertices	vertex	NOUN
ejpam-6046	12	14	.	.	PUNCT
ejpam-6046	13	1	in	in	ADP
ejpam-6046	13	2	the	the	DET
ejpam-6046	13	3	study	study	NOUN
ejpam-6046	13	4	by	by	ADP
ejpam-6046	13	5	macaso	macaso	NOUN
ejpam-6046	13	6	and	and	CCONJ
ejpam-6046	13	7	balingit	balingit	ADJ
ejpam-6046	13	8	[	[	X
ejpam-6046	13	9	2	2	NUM
ejpam-6046	13	10	]	]	PUNCT
ejpam-6046	13	11	,	,	PUNCT
ejpam-6046	13	12	they	they	PRON
ejpam-6046	13	13	introduced	introduce	VERB
ejpam-6046	13	14	a	a	DET
ejpam-6046	13	15	new	new	ADJ
ejpam-6046	13	16	topology	topology	NOUN
ejpam-6046	13	17	called	call	VERB
ejpam-6046	13	18	the	the	DET
ejpam-6046	13	19	block	block	NOUN
ejpam-6046	13	20	topology	topology	NOUN
ejpam-6046	13	21	,	,	PUNCT
ejpam-6046	13	22	generated	generate	VERB
ejpam-6046	13	23	by	by	ADP
ejpam-6046	13	24	the	the	DET
ejpam-6046	13	25	family	family	NOUN
ejpam-6046	13	26	of	of	ADP
ejpam-6046	13	27	the	the	DET
ejpam-6046	13	28	vertex	vertex	NOUN
ejpam-6046	13	29	sets	set	NOUN
ejpam-6046	13	30	of	of	ADP
ejpam-6046	13	31	the	the	DET
ejpam-6046	13	32	blocks	block	NOUN
ejpam-6046	13	33	of	of	ADP
ejpam-6046	13	34	the	the	DET
ejpam-6046	13	35	graph	graph	NOUN
ejpam-6046	13	36	.	.	PUNCT
ejpam-6046	14	1	in	in	ADP
ejpam-6046	14	2	2018	2018	NUM
ejpam-6046	14	3	,	,	PUNCT
ejpam-6046	14	4	abdu	abdu	PROPN
ejpam-6046	14	5	and	and	CCONJ
ejpam-6046	14	6	kilicman	kilicman	PROPN
ejpam-6046	14	7	introduced	introduce	VERB
ejpam-6046	14	8	new	new	ADJ
ejpam-6046	14	9	topologies	topology	NOUN
ejpam-6046	14	10	generated	generate	VERB
ejpam-6046	14	11	by	by	ADP
ejpam-6046	14	12	edges	edge	NOUN
ejpam-6046	14	13	.	.	PUNCT
ejpam-6046	15	1	these	these	DET
ejpam-6046	15	2	two	two	NUM
ejpam-6046	15	3	types	type	NOUN
ejpam-6046	15	4	of	of	ADP
ejpam-6046	15	5	topologies	topology	NOUN
ejpam-6046	15	6	are	be	AUX
ejpam-6046	15	7	called	call	VERB
ejpam-6046	15	8	edge	edge	NOUN
ejpam-6046	15	9	-	-	PUNCT
ejpam-6046	15	10	compatible	compatible	ADJ
ejpam-6046	15	11	topology	topology	NOUN
ejpam-6046	15	12	and	and	CCONJ
ejpam-6046	15	13	edge	edge	NOUN
ejpam-6046	15	14	-	-	PUNCT
ejpam-6046	15	15	incompatible	incompatible	ADJ
ejpam-6046	15	16	topology	topology	NOUN
ejpam-6046	15	17	.	.	PUNCT
ejpam-6046	16	1	∗corresponding	∗corresponde	VERB
ejpam-6046	16	2	author	author	NOUN
ejpam-6046	16	3	.	.	PUNCT
ejpam-6046	17	1	doi	doi	NOUN
ejpam-6046	17	2	:	:	PUNCT
ejpam-6046	17	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6046	https://doi.org/10.29020/nybg.ejpam.v18i2.6046	PROPN
ejpam-6046	17	4	email	email	NOUN
ejpam-6046	17	5	addresses	address	NOUN
ejpam-6046	17	6	:	:	PUNCT
ejpam-6046	17	7	ontulanjhonneceir@gmail.com	ontulanjhonneceir@gmail.com	X
ejpam-6046	17	8	(	(	PUNCT
ejpam-6046	17	9	j.	j.	PROPN
ejpam-6046	17	10	n.	n.	PROPN
ejpam-6046	17	11	ontulan	ontulan	PROPN
ejpam-6046	17	12	)	)	PUNCT
ejpam-6046	17	13	,	,	PUNCT
ejpam-6046	17	14	f.cherrymae.balingit@cmu.edu.ph	f.cherrymae.balingit@cmu.edu.ph	PROPN
ejpam-6046	17	15	(	(	PUNCT
ejpam-6046	17	16	c.	c.	PROPN
ejpam-6046	17	17	m.	m.	NOUN
ejpam-6046	17	18	balingit	balingit	PROPN
ejpam-6046	17	19	)	)	PUNCT
ejpam-6046	17	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6046	18	1	1	1	NUM
ejpam-6046	18	2	copyright	copyright	NOUN
ejpam-6046	18	3	:	:	PUNCT
ejpam-6046	18	4	©	©	PROPN
ejpam-6046	18	5	2025	2025	NUM
ejpam-6046	18	6	the	the	DET
ejpam-6046	18	7	author(s	author(s	NOUN
ejpam-6046	18	8	)	)	PUNCT
ejpam-6046	18	9	.	.	PUNCT
ejpam-6046	19	1	(	(	PUNCT
ejpam-6046	19	2	cc	cc	NOUN
ejpam-6046	19	3	by	by	ADP
ejpam-6046	19	4	-	-	PUNCT
ejpam-6046	19	5	nc	nc	PROPN
ejpam-6046	19	6	4.0	4.0	NUM
ejpam-6046	19	7	)	)	PUNCT
ejpam-6046	19	8	j.	j.	PROPN
ejpam-6046	19	9	n.	n.	PROPN
ejpam-6046	19	10	ontulan	ontulan	PROPN
ejpam-6046	19	11	,	,	PUNCT
ejpam-6046	19	12	c.	c.	PROPN
ejpam-6046	19	13	m.	m.	NOUN
ejpam-6046	19	14	balingit	balingit	PROPN
ejpam-6046	19	15	/	/	SYM
ejpam-6046	19	16	eur	eur	PROPN
ejpam-6046	19	17	.	.	PUNCT
ejpam-6046	20	1	j.	j.	PROPN
ejpam-6046	20	2	pure	pure	PROPN
ejpam-6046	20	3	appl	appl	PROPN
ejpam-6046	20	4	.	.	PROPN
ejpam-6046	20	5	math	math	PROPN
ejpam-6046	20	6	,	,	PUNCT
ejpam-6046	20	7	18	18	NUM
ejpam-6046	20	8	(	(	PUNCT
ejpam-6046	20	9	2	2	NUM
ejpam-6046	20	10	)	)	PUNCT
ejpam-6046	20	11	(	(	PUNCT
ejpam-6046	20	12	2025	2025	NUM
ejpam-6046	20	13	)	)	PUNCT
ejpam-6046	20	14	,	,	PUNCT
ejpam-6046	20	15	6046	6046	NUM
ejpam-6046	20	16	2	2	NUM
ejpam-6046	20	17	of	of	ADP
ejpam-6046	20	18	14	14	NUM
ejpam-6046	20	19	they	they	PRON
ejpam-6046	20	20	are	be	AUX
ejpam-6046	20	21	generated	generate	VERB
ejpam-6046	20	22	by	by	ADP
ejpam-6046	20	23	the	the	DET
ejpam-6046	20	24	edge	edge	NOUN
ejpam-6046	20	25	-	-	PUNCT
ejpam-6046	20	26	compatible	compatible	ADJ
ejpam-6046	20	27	sets	set	NOUN
ejpam-6046	20	28	of	of	ADP
ejpam-6046	20	29	directed	direct	VERB
ejpam-6046	20	30	graphs	graph	NOUN
ejpam-6046	20	31	and	and	CCONJ
ejpam-6046	20	32	edge	edge	NOUN
ejpam-6046	20	33	-	-	PUNCT
ejpam-6046	20	34	incompatible	incompatible	ADJ
ejpam-6046	20	35	sets	set	NOUN
ejpam-6046	20	36	of	of	ADP
ejpam-6046	20	37	directed	direct	VERB
ejpam-6046	20	38	graphs	graph	NOUN
ejpam-6046	20	39	[	[	X
ejpam-6046	20	40	3	3	NUM
ejpam-6046	20	41	]	]	PUNCT
ejpam-6046	20	42	.	.	PUNCT
ejpam-6046	21	1	the	the	DET
ejpam-6046	21	2	same	same	ADJ
ejpam-6046	21	3	association	association	NOUN
ejpam-6046	21	4	of	of	ADP
ejpam-6046	21	5	edge	edge	NOUN
ejpam-6046	21	6	sets	set	NOUN
ejpam-6046	21	7	is	be	AUX
ejpam-6046	21	8	the	the	DET
ejpam-6046	21	9	study	study	NOUN
ejpam-6046	21	10	of	of	ADP
ejpam-6046	21	11	alsinaia	alsinaia	PROPN
ejpam-6046	21	12	et	et	PROPN
ejpam-6046	21	13	al	al	PROPN
ejpam-6046	21	14	.	.	PUNCT
ejpam-6046	22	1	[	[	X
ejpam-6046	22	2	4	4	NUM
ejpam-6046	22	3	]	]	PUNCT
ejpam-6046	22	4	,	,	PUNCT
ejpam-6046	22	5	where	where	SCONJ
ejpam-6046	22	6	they	they	PRON
ejpam-6046	22	7	associated	associate	VERB
ejpam-6046	22	8	a	a	DET
ejpam-6046	22	9	new	new	ADJ
ejpam-6046	22	10	method	method	NOUN
ejpam-6046	22	11	of	of	ADP
ejpam-6046	22	12	topologizing	topologize	VERB
ejpam-6046	22	13	,	,	PUNCT
ejpam-6046	22	14	in	in	ADP
ejpam-6046	22	15	which	which	PRON
ejpam-6046	22	16	the	the	DET
ejpam-6046	22	17	topology	topology	NOUN
ejpam-6046	22	18	is	be	AUX
ejpam-6046	22	19	generated	generate	VERB
ejpam-6046	22	20	by	by	ADP
ejpam-6046	22	21	the	the	DET
ejpam-6046	22	22	edge	edge	NOUN
ejpam-6046	22	23	neighborhoods	neighborhood	NOUN
ejpam-6046	22	24	of	of	ADP
ejpam-6046	22	25	the	the	DET
ejpam-6046	22	26	discrete	discrete	ADJ
ejpam-6046	22	27	topological	topological	ADJ
ejpam-6046	22	28	graphs	graph	NOUN
ejpam-6046	22	29	.	.	PUNCT
ejpam-6046	23	1	in	in	ADP
ejpam-6046	23	2	a	a	DET
ejpam-6046	23	3	vertex	vertex	NOUN
ejpam-6046	23	4	dominating	dominating	NOUN
ejpam-6046	23	5	set	set	NOUN
ejpam-6046	23	6	of	of	ADP
ejpam-6046	23	7	a	a	DET
ejpam-6046	23	8	graph	graph	NOUN
ejpam-6046	23	9	,	,	PUNCT
ejpam-6046	23	10	every	every	DET
ejpam-6046	23	11	vertex	vertex	NOUN
ejpam-6046	23	12	in	in	ADP
ejpam-6046	23	13	the	the	DET
ejpam-6046	23	14	graph	graph	NOUN
ejpam-6046	23	15	is	be	AUX
ejpam-6046	23	16	either	either	DET
ejpam-6046	23	17	part	part	NOUN
ejpam-6046	23	18	of	of	ADP
ejpam-6046	23	19	the	the	DET
ejpam-6046	23	20	subset	subset	NOUN
ejpam-6046	23	21	or	or	CCONJ
ejpam-6046	23	22	adjacent	adjacent	ADJ
ejpam-6046	23	23	to	to	ADP
ejpam-6046	23	24	at	at	ADV
ejpam-6046	23	25	least	least	ADV
ejpam-6046	23	26	one	one	NUM
ejpam-6046	23	27	vertex	vertex	NOUN
ejpam-6046	23	28	,	,	PUNCT
ejpam-6046	23	29	ensuring	ensure	VERB
ejpam-6046	23	30	that	that	SCONJ
ejpam-6046	23	31	the	the	DET
ejpam-6046	23	32	set	set	NOUN
ejpam-6046	23	33	dominates	dominate	VERB
ejpam-6046	23	34	or	or	CCONJ
ejpam-6046	23	35	covers	cover	VERB
ejpam-6046	23	36	every	every	DET
ejpam-6046	23	37	vertex	vertex	NOUN
ejpam-6046	23	38	through	through	ADP
ejpam-6046	23	39	an	an	DET
ejpam-6046	23	40	edge	edge	NOUN
ejpam-6046	23	41	.	.	PUNCT
ejpam-6046	24	1	this	this	DET
ejpam-6046	24	2	idea	idea	NOUN
ejpam-6046	24	3	is	be	AUX
ejpam-6046	24	4	crucial	crucial	ADJ
ejpam-6046	24	5	in	in	ADP
ejpam-6046	24	6	network	network	NOUN
ejpam-6046	24	7	design	design	NOUN
ejpam-6046	24	8	since	since	SCONJ
ejpam-6046	24	9	the	the	DET
ejpam-6046	24	10	nodes	node	NOUN
ejpam-6046	24	11	in	in	ADP
ejpam-6046	24	12	the	the	DET
ejpam-6046	24	13	dominant	dominant	ADJ
ejpam-6046	24	14	set	set	NOUN
ejpam-6046	24	15	function	function	NOUN
ejpam-6046	24	16	as	as	ADP
ejpam-6046	24	17	control	control	NOUN
ejpam-6046	24	18	points	point	NOUN
ejpam-6046	24	19	or	or	CCONJ
ejpam-6046	24	20	access	access	NOUN
ejpam-6046	24	21	nodes	node	NOUN
ejpam-6046	24	22	that	that	PRON
ejpam-6046	24	23	efficiently	efficiently	ADV
ejpam-6046	24	24	govern	govern	VERB
ejpam-6046	24	25	or	or	CCONJ
ejpam-6046	24	26	interact	interact	VERB
ejpam-6046	24	27	with	with	ADP
ejpam-6046	24	28	the	the	DET
ejpam-6046	24	29	whole	whole	ADJ
ejpam-6046	24	30	network	network	NOUN
ejpam-6046	24	31	[	[	X
ejpam-6046	24	32	1	1	NUM
ejpam-6046	24	33	]	]	PUNCT
ejpam-6046	24	34	.	.	PUNCT
ejpam-6046	25	1	meanwhile	meanwhile	ADV
ejpam-6046	25	2	,	,	PUNCT
ejpam-6046	25	3	an	an	DET
ejpam-6046	25	4	independent	independent	ADJ
ejpam-6046	25	5	set	set	NOUN
ejpam-6046	25	6	is	be	AUX
ejpam-6046	25	7	a	a	DET
ejpam-6046	25	8	collection	collection	NOUN
ejpam-6046	25	9	of	of	ADP
ejpam-6046	25	10	vertices	vertex	NOUN
ejpam-6046	25	11	in	in	ADP
ejpam-6046	25	12	which	which	PRON
ejpam-6046	25	13	no	no	DET
ejpam-6046	25	14	two	two	NUM
ejpam-6046	25	15	vertices	vertex	NOUN
ejpam-6046	25	16	are	be	AUX
ejpam-6046	25	17	adjacent	adjacent	ADJ
ejpam-6046	25	18	,	,	PUNCT
ejpam-6046	25	19	indicating	indicate	VERB
ejpam-6046	25	20	the	the	DET
ejpam-6046	25	21	absence	absence	NOUN
ejpam-6046	25	22	of	of	ADP
ejpam-6046	25	23	common	common	ADJ
ejpam-6046	25	24	edges	edge	NOUN
ejpam-6046	25	25	and	and	CCONJ
ejpam-6046	25	26	direct	direct	ADJ
ejpam-6046	25	27	connections	connection	NOUN
ejpam-6046	25	28	.	.	PUNCT
ejpam-6046	26	1	independent	independent	ADJ
ejpam-6046	26	2	sets	set	NOUN
ejpam-6046	26	3	are	be	AUX
ejpam-6046	26	4	important	important	ADJ
ejpam-6046	26	5	because	because	SCONJ
ejpam-6046	26	6	they	they	PRON
ejpam-6046	26	7	address	address	VERB
ejpam-6046	26	8	issues	issue	NOUN
ejpam-6046	26	9	requiring	require	VERB
ejpam-6046	26	10	non	non	ADJ
ejpam-6046	26	11	-	-	NOUN
ejpam-6046	26	12	interference	interference	NOUN
ejpam-6046	26	13	,	,	PUNCT
ejpam-6046	26	14	such	such	ADJ
ejpam-6046	26	15	as	as	ADP
ejpam-6046	26	16	the	the	DET
ejpam-6046	26	17	allocation	allocation	NOUN
ejpam-6046	26	18	of	of	ADP
ejpam-6046	26	19	shared	share	VERB
ejpam-6046	26	20	resources	resource	NOUN
ejpam-6046	26	21	[	[	X
ejpam-6046	26	22	5	5	NUM
ejpam-6046	26	23	]	]	PUNCT
ejpam-6046	26	24	.	.	PUNCT
ejpam-6046	27	1	in	in	ADP
ejpam-6046	27	2	2020	2020	NUM
ejpam-6046	27	3	,	,	PUNCT
ejpam-6046	27	4	hassan	hassan	PROPN
ejpam-6046	27	5	and	and	CCONJ
ejpam-6046	27	6	abed	abed	PROPN
ejpam-6046	27	7	presented	present	VERB
ejpam-6046	27	8	another	another	DET
ejpam-6046	27	9	intriguing	intriguing	ADJ
ejpam-6046	27	10	way	way	NOUN
ejpam-6046	27	11	of	of	ADP
ejpam-6046	27	12	constructing	construct	VERB
ejpam-6046	27	13	a	a	DET
ejpam-6046	27	14	topological	topological	ADJ
ejpam-6046	27	15	space	space	NOUN
ejpam-6046	27	16	from	from	ADP
ejpam-6046	27	17	the	the	DET
ejpam-6046	27	18	graph	graph	NOUN
ejpam-6046	27	19	that	that	PRON
ejpam-6046	27	20	permits	permit	VERB
ejpam-6046	27	21	isolated	isolated	ADJ
ejpam-6046	27	22	vertices	vertex	NOUN
ejpam-6046	27	23	.	.	PUNCT
ejpam-6046	28	1	this	this	DET
ejpam-6046	28	2	topology	topology	NOUN
ejpam-6046	28	3	is	be	AUX
ejpam-6046	28	4	called	call	VERB
ejpam-6046	28	5	the	the	DET
ejpam-6046	28	6	independent	independent	ADJ
ejpam-6046	28	7	topology	topology	NOUN
ejpam-6046	28	8	and	and	CCONJ
ejpam-6046	28	9	is	be	AUX
ejpam-6046	28	10	generated	generate	VERB
ejpam-6046	28	11	by	by	ADP
ejpam-6046	28	12	the	the	DET
ejpam-6046	28	13	family	family	NOUN
ejpam-6046	28	14	of	of	ADP
ejpam-6046	28	15	independent	independent	ADJ
ejpam-6046	28	16	sets	set	NOUN
ejpam-6046	28	17	of	of	ADP
ejpam-6046	28	18	vertices	vertex	NOUN
ejpam-6046	28	19	of	of	ADP
ejpam-6046	28	20	the	the	DET
ejpam-6046	28	21	graph	graph	NOUN
ejpam-6046	28	22	[	[	X
ejpam-6046	28	23	6	6	NUM
ejpam-6046	28	24	]	]	PUNCT
ejpam-6046	28	25	.	.	PUNCT
ejpam-6046	29	1	on	on	ADP
ejpam-6046	29	2	the	the	DET
ejpam-6046	29	3	other	other	ADJ
ejpam-6046	29	4	hand	hand	NOUN
ejpam-6046	29	5	,	,	PUNCT
ejpam-6046	29	6	an	an	DET
ejpam-6046	29	7	edge	edge	NOUN
ejpam-6046	29	8	-	-	PUNCT
ejpam-6046	29	9	dominating	dominating	NOUN
ejpam-6046	29	10	set	set	NOUN
ejpam-6046	29	11	is	be	AUX
ejpam-6046	29	12	a	a	DET
ejpam-6046	29	13	subset	subset	NOUN
ejpam-6046	29	14	of	of	ADP
ejpam-6046	29	15	edges	edge	NOUN
ejpam-6046	29	16	that	that	PRON
ejpam-6046	29	17	covers	cover	VERB
ejpam-6046	29	18	all	all	DET
ejpam-6046	29	19	edges	edge	NOUN
ejpam-6046	29	20	in	in	ADP
ejpam-6046	29	21	a	a	DET
ejpam-6046	29	22	graph	graph	NOUN
ejpam-6046	29	23	,	,	PUNCT
ejpam-6046	29	24	either	either	CCONJ
ejpam-6046	29	25	by	by	ADP
ejpam-6046	29	26	inclusion	inclusion	NOUN
ejpam-6046	29	27	in	in	ADP
ejpam-6046	29	28	the	the	DET
ejpam-6046	29	29	subset	subset	NOUN
ejpam-6046	29	30	or	or	CCONJ
ejpam-6046	29	31	by	by	ADP
ejpam-6046	29	32	adjacency	adjacency	NOUN
ejpam-6046	29	33	,	,	PUNCT
ejpam-6046	29	34	thereby	thereby	ADV
ejpam-6046	29	35	ensuring	ensure	VERB
ejpam-6046	29	36	complete	complete	ADJ
ejpam-6046	29	37	domination	domination	NOUN
ejpam-6046	29	38	of	of	ADP
ejpam-6046	29	39	the	the	DET
ejpam-6046	29	40	edges	edge	NOUN
ejpam-6046	29	41	.	.	PUNCT
ejpam-6046	30	1	this	this	DET
ejpam-6046	30	2	concept	concept	NOUN
ejpam-6046	30	3	is	be	AUX
ejpam-6046	30	4	especially	especially	ADV
ejpam-6046	30	5	relevant	relevant	ADJ
ejpam-6046	30	6	in	in	ADP
ejpam-6046	30	7	situations	situation	NOUN
ejpam-6046	30	8	requiring	require	VERB
ejpam-6046	30	9	the	the	DET
ejpam-6046	30	10	management	management	NOUN
ejpam-6046	30	11	or	or	CCONJ
ejpam-6046	30	12	observation	observation	NOUN
ejpam-6046	30	13	of	of	ADP
ejpam-6046	30	14	relationships	relationship	NOUN
ejpam-6046	30	15	among	among	ADP
ejpam-6046	30	16	nodes	node	NOUN
ejpam-6046	30	17	with	with	ADP
ejpam-6046	30	18	a	a	DET
ejpam-6046	30	19	limited	limited	ADJ
ejpam-6046	30	20	number	number	NOUN
ejpam-6046	30	21	of	of	ADP
ejpam-6046	30	22	connections	connection	NOUN
ejpam-6046	30	23	,	,	PUNCT
ejpam-6046	30	24	such	such	ADJ
ejpam-6046	30	25	as	as	ADP
ejpam-6046	30	26	enhancing	enhance	VERB
ejpam-6046	30	27	network	network	NOUN
ejpam-6046	30	28	coverage	coverage	NOUN
ejpam-6046	30	29	or	or	CCONJ
ejpam-6046	30	30	ensuring	ensure	VERB
ejpam-6046	30	31	efficient	efficient	ADJ
ejpam-6046	30	32	oversight	oversight	NOUN
ejpam-6046	30	33	of	of	ADP
ejpam-6046	30	34	infrastructure	infrastructure	NOUN
ejpam-6046	30	35	systems	system	NOUN
ejpam-6046	30	36	[	[	X
ejpam-6046	30	37	7	7	NUM
ejpam-6046	30	38	]	]	PUNCT
ejpam-6046	30	39	.	.	PUNCT
ejpam-6046	31	1	the	the	DET
ejpam-6046	31	2	notion	notion	NOUN
ejpam-6046	31	3	of	of	ADP
ejpam-6046	31	4	an	an	DET
ejpam-6046	31	5	independent	independent	ADJ
ejpam-6046	31	6	set	set	NOUN
ejpam-6046	31	7	of	of	ADP
ejpam-6046	31	8	edges	edge	NOUN
ejpam-6046	31	9	,	,	PUNCT
ejpam-6046	31	10	referred	refer	VERB
ejpam-6046	31	11	to	to	ADP
ejpam-6046	31	12	as	as	ADP
ejpam-6046	31	13	matching	matching	NOUN
ejpam-6046	31	14	,	,	PUNCT
ejpam-6046	31	15	is	be	AUX
ejpam-6046	31	16	closely	closely	ADV
ejpam-6046	31	17	associated	associate	VERB
ejpam-6046	31	18	.	.	PUNCT
ejpam-6046	32	1	a	a	DET
ejpam-6046	32	2	matching	matching	NOUN
ejpam-6046	32	3	is	be	AUX
ejpam-6046	32	4	a	a	DET
ejpam-6046	32	5	set	set	NOUN
ejpam-6046	32	6	of	of	ADP
ejpam-6046	32	7	edges	edge	NOUN
ejpam-6046	32	8	that	that	PRON
ejpam-6046	32	9	do	do	AUX
ejpam-6046	32	10	not	not	PART
ejpam-6046	32	11	share	share	VERB
ejpam-6046	32	12	any	any	DET
ejpam-6046	32	13	common	common	ADJ
ejpam-6046	32	14	vertices	vertex	NOUN
ejpam-6046	32	15	.	.	PUNCT
ejpam-6046	33	1	matchings	matching	NOUN
ejpam-6046	33	2	are	be	AUX
ejpam-6046	33	3	fundamental	fundamental	ADJ
ejpam-6046	33	4	in	in	ADP
ejpam-6046	33	5	solving	solve	VERB
ejpam-6046	33	6	a	a	DET
ejpam-6046	33	7	wide	wide	ADJ
ejpam-6046	33	8	variety	variety	NOUN
ejpam-6046	33	9	of	of	ADP
ejpam-6046	33	10	real	real	ADJ
ejpam-6046	33	11	-	-	PUNCT
ejpam-6046	33	12	world	world	NOUN
ejpam-6046	33	13	problems	problem	NOUN
ejpam-6046	33	14	,	,	PUNCT
ejpam-6046	33	15	such	such	ADJ
ejpam-6046	33	16	as	as	ADP
ejpam-6046	33	17	job	job	NOUN
ejpam-6046	33	18	assignments	assignment	NOUN
ejpam-6046	33	19	where	where	SCONJ
ejpam-6046	33	20	tasks	task	NOUN
ejpam-6046	33	21	need	need	VERB
ejpam-6046	33	22	to	to	PART
ejpam-6046	33	23	be	be	AUX
ejpam-6046	33	24	assigned	assign	VERB
ejpam-6046	33	25	to	to	ADP
ejpam-6046	33	26	workers	worker	NOUN
ejpam-6046	33	27	,	,	PUNCT
ejpam-6046	33	28	ensuring	ensure	VERB
ejpam-6046	33	29	that	that	SCONJ
ejpam-6046	33	30	no	no	DET
ejpam-6046	33	31	worker	worker	NOUN
ejpam-6046	33	32	is	be	AUX
ejpam-6046	33	33	assigned	assign	VERB
ejpam-6046	33	34	more	more	ADJ
ejpam-6046	33	35	than	than	ADP
ejpam-6046	33	36	one	one	NUM
ejpam-6046	33	37	task	task	NOUN
ejpam-6046	33	38	at	at	ADP
ejpam-6046	33	39	a	a	DET
ejpam-6046	33	40	time	time	NOUN
ejpam-6046	33	41	[	[	X
ejpam-6046	33	42	5	5	NUM
ejpam-6046	33	43	]	]	PUNCT
ejpam-6046	33	44	.	.	PUNCT
ejpam-6046	34	1	moreover	moreover	ADV
ejpam-6046	34	2	,	,	PUNCT
ejpam-6046	34	3	an	an	DET
ejpam-6046	34	4	independent	independent	ADJ
ejpam-6046	34	5	edge	edge	NOUN
ejpam-6046	34	6	-	-	PUNCT
ejpam-6046	34	7	dominating	dominating	NOUN
ejpam-6046	34	8	set	set	NOUN
ejpam-6046	34	9	exemplifies	exemplify	VERB
ejpam-6046	34	10	a	a	DET
ejpam-6046	34	11	noteworthy	noteworthy	ADJ
ejpam-6046	34	12	integration	integration	NOUN
ejpam-6046	34	13	of	of	ADP
ejpam-6046	34	14	edge	edge	NOUN
ejpam-6046	34	15	domination	domination	NOUN
ejpam-6046	34	16	and	and	CCONJ
ejpam-6046	34	17	independence	independence	NOUN
ejpam-6046	34	18	characteristics	characteristic	NOUN
ejpam-6046	34	19	.	.	PUNCT
ejpam-6046	35	1	one	one	NUM
ejpam-6046	35	2	set	set	NOUN
ejpam-6046	35	3	of	of	ADP
ejpam-6046	35	4	edges	edge	NOUN
ejpam-6046	35	5	dominates	dominate	VERB
ejpam-6046	35	6	the	the	DET
ejpam-6046	35	7	graph	graph	NOUN
ejpam-6046	35	8	and	and	CCONJ
ejpam-6046	35	9	maintains	maintain	VERB
ejpam-6046	35	10	its	its	PRON
ejpam-6046	35	11	independence	independence	NOUN
ejpam-6046	35	12	,	,	PUNCT
ejpam-6046	35	13	meaning	mean	VERB
ejpam-6046	35	14	no	no	DET
ejpam-6046	35	15	two	two	NUM
ejpam-6046	35	16	edges	edge	NOUN
ejpam-6046	35	17	are	be	AUX
ejpam-6046	35	18	adjacent	adjacent	ADJ
ejpam-6046	35	19	.	.	PUNCT
ejpam-6046	36	1	this	this	DET
ejpam-6046	36	2	idea	idea	NOUN
ejpam-6046	36	3	makes	make	VERB
ejpam-6046	36	4	sure	sure	ADJ
ejpam-6046	36	5	that	that	SCONJ
ejpam-6046	36	6	the	the	DET
ejpam-6046	36	7	chosen	choose	VERB
ejpam-6046	36	8	edges	edge	NOUN
ejpam-6046	36	9	cover	cover	VERB
ejpam-6046	36	10	or	or	CCONJ
ejpam-6046	36	11	dominate	dominate	VERB
ejpam-6046	36	12	the	the	DET
ejpam-6046	36	13	graph	graph	NOUN
ejpam-6046	36	14	efficiently	efficiently	ADV
ejpam-6046	36	15	and	and	CCONJ
ejpam-6046	36	16	do	do	AUX
ejpam-6046	36	17	not	not	PART
ejpam-6046	36	18	overlap	overlap	VERB
ejpam-6046	36	19	.	.	PUNCT
ejpam-6046	37	1	this	this	DET
ejpam-6046	37	2	notion	notion	NOUN
ejpam-6046	37	3	is	be	AUX
ejpam-6046	37	4	useful	useful	ADJ
ejpam-6046	37	5	when	when	SCONJ
ejpam-6046	37	6	the	the	DET
ejpam-6046	37	7	need	need	NOUN
ejpam-6046	37	8	arises	arise	VERB
ejpam-6046	37	9	to	to	PART
ejpam-6046	37	10	monitor	monitor	VERB
ejpam-6046	37	11	or	or	CCONJ
ejpam-6046	37	12	control	control	VERB
ejpam-6046	37	13	edges	edge	NOUN
ejpam-6046	37	14	without	without	ADP
ejpam-6046	37	15	having	have	VERB
ejpam-6046	37	16	any	any	DET
ejpam-6046	37	17	extra	extra	ADJ
ejpam-6046	37	18	or	or	CCONJ
ejpam-6046	37	19	direct	direct	ADJ
ejpam-6046	37	20	links	link	NOUN
ejpam-6046	37	21	between	between	ADP
ejpam-6046	37	22	them	they	PRON
ejpam-6046	37	23	,	,	PUNCT
ejpam-6046	37	24	such	such	ADJ
ejpam-6046	37	25	as	as	ADP
ejpam-6046	37	26	in	in	ADP
ejpam-6046	37	27	power	power	NOUN
ejpam-6046	37	28	grid	grid	NOUN
ejpam-6046	37	29	optimization	optimization	NOUN
ejpam-6046	37	30	or	or	CCONJ
ejpam-6046	37	31	routing	route	VERB
ejpam-6046	37	32	protocols	protocol	NOUN
ejpam-6046	37	33	in	in	ADP
ejpam-6046	37	34	telecommunications	telecommunications	NOUN
ejpam-6046	37	35	networks	network	NOUN
ejpam-6046	37	36	[	[	X
ejpam-6046	37	37	8	8	NUM
ejpam-6046	37	38	]	]	SYM
ejpam-6046	37	39	.	.	PUNCT
ejpam-6046	38	1	2	2	X
ejpam-6046	38	2	.	.	X
ejpam-6046	38	3	preliminaries	preliminary	NOUN
ejpam-6046	38	4	definition	definition	NOUN
ejpam-6046	38	5	1	1	NUM
ejpam-6046	38	6	.	.	PUNCT
ejpam-6046	39	1	[	[	X
ejpam-6046	39	2	9	9	NUM
ejpam-6046	39	3	]	]	X
ejpam-6046	39	4	a	a	DET
ejpam-6046	39	5	graph	graph	NOUN
ejpam-6046	39	6	g	g	PROPN
ejpam-6046	39	7	=	=	PUNCT
ejpam-6046	39	8	(	(	PUNCT
ejpam-6046	39	9	v	v	NOUN
ejpam-6046	39	10	(	(	PUNCT
ejpam-6046	39	11	g	g	NOUN
ejpam-6046	39	12	)	)	PUNCT
ejpam-6046	39	13	,	,	PUNCT
ejpam-6046	39	14	e(g	e(g	PROPN
ejpam-6046	39	15	)	)	PUNCT
ejpam-6046	39	16	)	)	PUNCT
ejpam-6046	39	17	is	be	AUX
ejpam-6046	39	18	a	a	DET
ejpam-6046	39	19	finite	finite	NOUN
ejpam-6046	39	20	nonempty	nonempty	ADV
ejpam-6046	39	21	set	set	VERB
ejpam-6046	39	22	v	v	NOUN
ejpam-6046	39	23	(	(	PUNCT
ejpam-6046	39	24	g	g	NOUN
ejpam-6046	39	25	)	)	PUNCT
ejpam-6046	39	26	of	of	ADP
ejpam-6046	39	27	objects	object	NOUN
ejpam-6046	39	28	called	call	VERB
ejpam-6046	39	29	vertices	vertex	NOUN
ejpam-6046	39	30	(	(	PUNCT
ejpam-6046	39	31	the	the	DET
ejpam-6046	39	32	singular	singular	NOUN
ejpam-6046	39	33	is	be	AUX
ejpam-6046	39	34	vertex	vertex	NOUN
ejpam-6046	39	35	)	)	PUNCT
ejpam-6046	39	36	together	together	ADV
ejpam-6046	39	37	with	with	ADP
ejpam-6046	39	38	a	a	DET
ejpam-6046	39	39	possibly	possibly	ADV
ejpam-6046	39	40	empty	empty	ADJ
ejpam-6046	39	41	set	set	VERB
ejpam-6046	39	42	e(g	e(g	NOUN
ejpam-6046	39	43	)	)	PUNCT
ejpam-6046	39	44	of	of	ADP
ejpam-6046	39	45	2element	2element	NUM
ejpam-6046	39	46	subsets	subset	NOUN
ejpam-6046	39	47	of	of	ADP
ejpam-6046	39	48	v	v	NOUN
ejpam-6046	39	49	(	(	PUNCT
ejpam-6046	39	50	g	g	NOUN
ejpam-6046	39	51	)	)	PUNCT
ejpam-6046	39	52	called	call	VERB
ejpam-6046	39	53	edges	edge	NOUN
ejpam-6046	39	54	.	.	PUNCT
ejpam-6046	40	1	here	here	ADV
ejpam-6046	40	2	,	,	PUNCT
ejpam-6046	40	3	v	v	X
ejpam-6046	40	4	(	(	PUNCT
ejpam-6046	40	5	g	g	NOUN
ejpam-6046	40	6	)	)	PUNCT
ejpam-6046	40	7	is	be	AUX
ejpam-6046	40	8	the	the	DET
ejpam-6046	40	9	vertex	vertex	NOUN
ejpam-6046	40	10	set	set	NOUN
ejpam-6046	40	11	of	of	ADP
ejpam-6046	40	12	a	a	DET
ejpam-6046	40	13	graph	graph	NOUN
ejpam-6046	40	14	g	g	NOUN
ejpam-6046	40	15	while	while	SCONJ
ejpam-6046	40	16	e(g	e(g	PROPN
ejpam-6046	40	17	)	)	PUNCT
ejpam-6046	40	18	is	be	AUX
ejpam-6046	40	19	the	the	DET
ejpam-6046	40	20	edge	edge	NOUN
ejpam-6046	40	21	set	set	NOUN
ejpam-6046	40	22	of	of	ADP
ejpam-6046	40	23	the	the	DET
ejpam-6046	40	24	graph	graph	NOUN
ejpam-6046	40	25	g.	g.	VERB
ejpam-6046	40	26	the	the	DET
ejpam-6046	40	27	order	order	NOUN
ejpam-6046	40	28	of	of	ADP
ejpam-6046	40	29	a	a	DET
ejpam-6046	40	30	graph	graph	NOUN
ejpam-6046	40	31	g	g	NOUN
ejpam-6046	40	32	refers	refer	VERB
ejpam-6046	40	33	to	to	ADP
ejpam-6046	40	34	the	the	DET
ejpam-6046	40	35	number	number	NOUN
ejpam-6046	40	36	of	of	ADP
ejpam-6046	40	37	vertices	vertex	NOUN
ejpam-6046	40	38	in	in	ADP
ejpam-6046	40	39	g	g	NOUN
ejpam-6046	40	40	,	,	PUNCT
ejpam-6046	40	41	while	while	SCONJ
ejpam-6046	40	42	the	the	DET
ejpam-6046	40	43	size	size	NOUN
ejpam-6046	40	44	(	(	PUNCT
ejpam-6046	40	45	or	or	CCONJ
ejpam-6046	40	46	length	length	NOUN
ejpam-6046	40	47	)	)	PUNCT
ejpam-6046	40	48	of	of	ADP
ejpam-6046	40	49	a	a	DET
ejpam-6046	40	50	graph	graph	NOUN
ejpam-6046	40	51	g	g	NOUN
ejpam-6046	40	52	refers	refer	VERB
ejpam-6046	40	53	to	to	ADP
ejpam-6046	40	54	the	the	DET
ejpam-6046	40	55	number	number	NOUN
ejpam-6046	40	56	of	of	ADP
ejpam-6046	40	57	edges	edge	NOUN
ejpam-6046	40	58	in	in	ADP
ejpam-6046	40	59	g.	g.	PROPN
ejpam-6046	40	60	two	two	NUM
ejpam-6046	40	61	distinct	distinct	ADJ
ejpam-6046	40	62	vertices	vertex	NOUN
ejpam-6046	40	63	v1	v1	VERB
ejpam-6046	40	64	and	and	CCONJ
ejpam-6046	40	65	v2	v2	NOUN
ejpam-6046	40	66	are	be	AUX
ejpam-6046	40	67	adjacent	adjacent	ADJ
ejpam-6046	40	68	if	if	SCONJ
ejpam-6046	40	69	v1	v1	NOUN
ejpam-6046	40	70	,	,	PUNCT
ejpam-6046	40	71	v2	v2	PROPN
ejpam-6046	40	72	∈	∈	PROPN
ejpam-6046	40	73	g	g	NOUN
ejpam-6046	40	74	and	and	CCONJ
ejpam-6046	40	75	two	two	NUM
ejpam-6046	40	76	edges	edge	NOUN
ejpam-6046	40	77	are	be	AUX
ejpam-6046	40	78	adjacent	adjacent	ADJ
ejpam-6046	40	79	if	if	SCONJ
ejpam-6046	40	80	they	they	PRON
ejpam-6046	40	81	have	have	VERB
ejpam-6046	40	82	a	a	DET
ejpam-6046	40	83	common	common	ADJ
ejpam-6046	40	84	vertex	vertex	NOUN
ejpam-6046	40	85	.	.	PUNCT
ejpam-6046	41	1	a	a	DET
ejpam-6046	41	2	graph	graph	NOUN
ejpam-6046	41	3	of	of	ADP
ejpam-6046	41	4	size	size	NOUN
ejpam-6046	41	5	0	0	NUM
ejpam-6046	41	6	is	be	AUX
ejpam-6046	41	7	called	call	VERB
ejpam-6046	41	8	an	an	DET
ejpam-6046	41	9	empty	empty	ADJ
ejpam-6046	41	10	graph	graph	NOUN
ejpam-6046	41	11	.	.	PUNCT
ejpam-6046	42	1	in	in	ADP
ejpam-6046	42	2	any	any	DET
ejpam-6046	42	3	empty	empty	ADJ
ejpam-6046	42	4	graph	graph	NOUN
ejpam-6046	42	5	,	,	PUNCT
ejpam-6046	42	6	no	no	DET
ejpam-6046	42	7	two	two	NUM
ejpam-6046	42	8	vertices	vertex	NOUN
ejpam-6046	42	9	are	be	AUX
ejpam-6046	42	10	adjacent	adjacent	ADJ
ejpam-6046	42	11	.	.	PUNCT
ejpam-6046	43	1	a	a	DET
ejpam-6046	43	2	nonempty	nonempty	ADJ
ejpam-6046	43	3	graph	graph	NOUN
ejpam-6046	43	4	then	then	ADV
ejpam-6046	43	5	has	have	VERB
ejpam-6046	43	6	one	one	NUM
ejpam-6046	43	7	or	or	CCONJ
ejpam-6046	43	8	more	more	ADJ
ejpam-6046	43	9	edges	edge	NOUN
ejpam-6046	43	10	.	.	PUNCT
ejpam-6046	44	1	a	a	DET
ejpam-6046	44	2	graph	graph	NOUN
ejpam-6046	44	3	g	g	NOUN
ejpam-6046	44	4	is	be	AUX
ejpam-6046	44	5	connected	connect	VERB
ejpam-6046	44	6	if	if	SCONJ
ejpam-6046	44	7	every	every	DET
ejpam-6046	44	8	two	two	NUM
ejpam-6046	44	9	vertices	vertex	NOUN
ejpam-6046	44	10	of	of	ADP
ejpam-6046	44	11	g	g	NOUN
ejpam-6046	44	12	are	be	AUX
ejpam-6046	44	13	adjacent	adjacent	ADJ
ejpam-6046	44	14	,	,	PUNCT
ejpam-6046	44	15	that	that	ADV
ejpam-6046	44	16	is	is	ADV
ejpam-6046	44	17	,	,	PUNCT
ejpam-6046	44	18	if	if	SCONJ
ejpam-6046	44	19	g	g	PROPN
ejpam-6046	44	20	contains	contain	VERB
ejpam-6046	44	21	a	a	DET
ejpam-6046	44	22	j.	j.	PROPN
ejpam-6046	44	23	n.	n.	PROPN
ejpam-6046	44	24	ontulan	ontulan	PROPN
ejpam-6046	44	25	,	,	PUNCT
ejpam-6046	44	26	c.	c.	PROPN
ejpam-6046	44	27	m.	m.	NOUN
ejpam-6046	44	28	balingit	balingit	PROPN
ejpam-6046	44	29	/	/	SYM
ejpam-6046	44	30	eur	eur	PROPN
ejpam-6046	44	31	.	.	PUNCT
ejpam-6046	45	1	j.	j.	PROPN
ejpam-6046	45	2	pure	pure	PROPN
ejpam-6046	45	3	appl	appl	PROPN
ejpam-6046	45	4	.	.	PROPN
ejpam-6046	45	5	math	math	PROPN
ejpam-6046	45	6	,	,	PUNCT
ejpam-6046	45	7	18	18	NUM
ejpam-6046	45	8	(	(	PUNCT
ejpam-6046	45	9	2	2	NUM
ejpam-6046	45	10	)	)	PUNCT
ejpam-6046	45	11	(	(	PUNCT
ejpam-6046	45	12	2025	2025	NUM
ejpam-6046	45	13	)	)	PUNCT
ejpam-6046	45	14	,	,	PUNCT
ejpam-6046	45	15	6046	6046	NUM
ejpam-6046	45	16	3	3	NUM
ejpam-6046	45	17	of	of	ADP
ejpam-6046	45	18	14	14	NUM
ejpam-6046	45	19	u	u	NOUN
ejpam-6046	45	20	−	−	PROPN
ejpam-6046	45	21	v	v	ADP
ejpam-6046	45	22	path	path	NOUN
ejpam-6046	45	23	for	for	ADP
ejpam-6046	45	24	every	every	DET
ejpam-6046	45	25	pair	pair	NOUN
ejpam-6046	45	26	u	u	NOUN
ejpam-6046	45	27	,	,	PUNCT
ejpam-6046	45	28	v	v	NOUN
ejpam-6046	45	29	of	of	ADP
ejpam-6046	45	30	vertices	vertex	NOUN
ejpam-6046	45	31	of	of	ADP
ejpam-6046	45	32	g.	g.	PROPN
ejpam-6046	45	33	a	a	DET
ejpam-6046	45	34	graph	graph	NOUN
ejpam-6046	45	35	g	g	NOUN
ejpam-6046	45	36	that	that	PRON
ejpam-6046	45	37	is	be	AUX
ejpam-6046	45	38	not	not	PART
ejpam-6046	45	39	connected	connect	VERB
ejpam-6046	45	40	is	be	AUX
ejpam-6046	45	41	called	call	VERB
ejpam-6046	45	42	disconnected	disconnected	ADJ
ejpam-6046	45	43	.	.	PUNCT
ejpam-6046	46	1	notation	notation	NOUN
ejpam-6046	46	2	:	:	PUNCT
ejpam-6046	46	3	let	let	VERB
ejpam-6046	46	4	g	g	PROPN
ejpam-6046	46	5	=	=	SYM
ejpam-6046	46	6	(	(	PUNCT
ejpam-6046	46	7	v	v	NOUN
ejpam-6046	46	8	(	(	PUNCT
ejpam-6046	46	9	g	g	NOUN
ejpam-6046	46	10	)	)	PUNCT
ejpam-6046	46	11	,	,	PUNCT
ejpam-6046	46	12	e(g	e(g	PROPN
ejpam-6046	46	13	)	)	PUNCT
ejpam-6046	46	14	)	)	PUNCT
ejpam-6046	46	15	be	be	AUX
ejpam-6046	46	16	a	a	DET
ejpam-6046	46	17	simple	simple	ADJ
ejpam-6046	46	18	graph	graph	NOUN
ejpam-6046	46	19	of	of	ADP
ejpam-6046	46	20	order	order	NOUN
ejpam-6046	46	21	n	n	CCONJ
ejpam-6046	46	22	∈	∈	PROPN
ejpam-6046	46	23	n	n	CCONJ
ejpam-6046	46	24	,	,	PUNCT
ejpam-6046	46	25	where	where	SCONJ
ejpam-6046	46	26	v	v	X
ejpam-6046	46	27	(	(	PUNCT
ejpam-6046	46	28	g	g	NOUN
ejpam-6046	46	29	)	)	PUNCT
ejpam-6046	46	30	=	=	PRON
ejpam-6046	46	31	{	{	PUNCT
ejpam-6046	46	32	vα1	vα1	NOUN
ejpam-6046	46	33	,	,	PUNCT
ejpam-6046	46	34	vα2	vα2	NOUN
ejpam-6046	46	35	,	,	PUNCT
ejpam-6046	46	36	.	.	PUNCT
ejpam-6046	46	37	.	.	PUNCT
ejpam-6046	46	38	.	.	PUNCT
ejpam-6046	47	1	,	,	PUNCT
ejpam-6046	47	2	vαn	vαn	NOUN
ejpam-6046	47	3	}	}	PUNCT
ejpam-6046	47	4	for	for	ADP
ejpam-6046	47	5	some	some	DET
ejpam-6046	47	6	indices	index	NOUN
ejpam-6046	47	7	α1	α1	PROPN
ejpam-6046	47	8	,	,	PUNCT
ejpam-6046	47	9	.	.	PUNCT
ejpam-6046	47	10	.	.	PUNCT
ejpam-6046	48	1	.	.	PUNCT
ejpam-6046	49	1	,	,	PUNCT
ejpam-6046	49	2	αn	αn	X
ejpam-6046	49	3	.	.	PUNCT
ejpam-6046	50	1	henceforth	henceforth	ADV
ejpam-6046	50	2	,	,	PUNCT
ejpam-6046	50	3	as	as	ADP
ejpam-6046	50	4	a	a	DET
ejpam-6046	50	5	convention	convention	NOUN
ejpam-6046	50	6	for	for	ADP
ejpam-6046	50	7	n	n	X
ejpam-6046	50	8	≥	≥	NUM
ejpam-6046	50	9	1	1	NUM
ejpam-6046	50	10	,	,	PUNCT
ejpam-6046	50	11	we	we	PRON
ejpam-6046	50	12	denote	denote	VERB
ejpam-6046	50	13	[	[	X
ejpam-6046	50	14	n	n	X
ejpam-6046	50	15	]	]	X
ejpam-6046	50	16	=	=	PUNCT
ejpam-6046	50	17	{	{	PUNCT
ejpam-6046	50	18	1	1	NUM
ejpam-6046	50	19	,	,	PUNCT
ejpam-6046	50	20	2	2	NUM
ejpam-6046	50	21	,	,	PUNCT
ejpam-6046	50	22	.	.	PUNCT
ejpam-6046	50	23	.	.	PUNCT
ejpam-6046	51	1	.	.	PUNCT
ejpam-6046	52	1	,	,	PUNCT
ejpam-6046	52	2	n	n	CCONJ
ejpam-6046	52	3	}	}	PUNCT
ejpam-6046	52	4	and	and	CCONJ
ejpam-6046	52	5	the	the	DET
ejpam-6046	52	6	edge	edge	NOUN
ejpam-6046	52	7	vαivαj	vαivαj	NOUN
ejpam-6046	52	8	=	=	SYM
ejpam-6046	52	9	ei	ei	PROPN
ejpam-6046	52	10	,	,	PUNCT
ejpam-6046	52	11	j	j	PROPN
ejpam-6046	52	12	,	,	PUNCT
ejpam-6046	52	13	for	for	ADP
ejpam-6046	52	14	i	i	PRON
ejpam-6046	52	15	,	,	PUNCT
ejpam-6046	52	16	j	j	PROPN
ejpam-6046	52	17	∈	∈	PROPN
ejpam-6046	53	1	[	[	X
ejpam-6046	53	2	n	n	X
ejpam-6046	53	3	]	]	PUNCT
ejpam-6046	53	4	.	.	PUNCT
ejpam-6046	54	1	observe	observe	VERB
ejpam-6046	54	2	that	that	SCONJ
ejpam-6046	54	3	the	the	DET
ejpam-6046	54	4	two	two	NUM
ejpam-6046	54	5	edges	edge	NOUN
ejpam-6046	54	6	are	be	AUX
ejpam-6046	54	7	adjacent	adjacent	ADJ
ejpam-6046	54	8	if	if	SCONJ
ejpam-6046	54	9	they	they	PRON
ejpam-6046	54	10	have	have	VERB
ejpam-6046	54	11	a	a	DET
ejpam-6046	54	12	common	common	ADJ
ejpam-6046	54	13	vertex	vertex	NOUN
ejpam-6046	54	14	.	.	PUNCT
ejpam-6046	55	1	with	with	ADP
ejpam-6046	55	2	the	the	DET
ejpam-6046	55	3	above	above	ADJ
ejpam-6046	55	4	notation	notation	NOUN
ejpam-6046	55	5	,	,	PUNCT
ejpam-6046	55	6	the	the	DET
ejpam-6046	55	7	following	follow	VERB
ejpam-6046	55	8	remark	remark	NOUN
ejpam-6046	55	9	is	be	AUX
ejpam-6046	55	10	immediate	immediate	ADJ
ejpam-6046	55	11	.	.	PUNCT
ejpam-6046	56	1	remark	remark	PROPN
ejpam-6046	56	2	1	1	NUM
ejpam-6046	56	3	.	.	PUNCT
ejpam-6046	57	1	let	let	VERB
ejpam-6046	57	2	g	g	PROPN
ejpam-6046	57	3	=	=	SYM
ejpam-6046	57	4	(	(	PUNCT
ejpam-6046	57	5	v	v	NOUN
ejpam-6046	57	6	(	(	PUNCT
ejpam-6046	57	7	g	g	NOUN
ejpam-6046	57	8	)	)	PUNCT
ejpam-6046	57	9	,	,	PUNCT
ejpam-6046	57	10	e(g	e(g	PROPN
ejpam-6046	57	11	)	)	PUNCT
ejpam-6046	57	12	)	)	PUNCT
ejpam-6046	58	1	be	be	AUX
ejpam-6046	58	2	a	a	DET
ejpam-6046	58	3	simple	simple	ADJ
ejpam-6046	58	4	graph	graph	NOUN
ejpam-6046	58	5	.	.	PUNCT
ejpam-6046	59	1	two	two	NUM
ejpam-6046	59	2	edges	edge	NOUN
ejpam-6046	59	3	ei1,j1	ei1,j1	NOUN
ejpam-6046	59	4	and	and	CCONJ
ejpam-6046	59	5	ei2,j2	ei2,j2	NOUN
ejpam-6046	59	6	of	of	ADP
ejpam-6046	59	7	g	g	NOUN
ejpam-6046	59	8	are	be	AUX
ejpam-6046	59	9	adjacent	adjacent	ADJ
ejpam-6046	59	10	if	if	SCONJ
ejpam-6046	59	11	and	and	CCONJ
ejpam-6046	59	12	only	only	ADV
ejpam-6046	59	13	if	if	SCONJ
ejpam-6046	59	14	{	{	PUNCT
ejpam-6046	59	15	i1	i1	PROPN
ejpam-6046	59	16	,	,	PUNCT
ejpam-6046	59	17	j1	j1	PROPN
ejpam-6046	59	18	}	}	PUNCT
ejpam-6046	59	19	∩	∩	NOUN
ejpam-6046	59	20	{	{	PUNCT
ejpam-6046	59	21	i2	i2	PROPN
ejpam-6046	59	22	,	,	PUNCT
ejpam-6046	59	23	j2	j2	PROPN
ejpam-6046	59	24	}	}	PUNCT
ejpam-6046	59	25	=	=	PROPN
ejpam-6046	59	26	̸	̸	X
ejpam-6046	59	27	∅.	∅.	PRON
ejpam-6046	59	28	illustration	illustration	NOUN
ejpam-6046	59	29	:	:	PUNCT
ejpam-6046	59	30	the	the	DET
ejpam-6046	59	31	graph	graph	NOUN
ejpam-6046	59	32	g	g	PROPN
ejpam-6046	59	33	in	in	ADP
ejpam-6046	59	34	figure	figure	NOUN
ejpam-6046	59	35	1	1	NUM
ejpam-6046	59	36	is	be	AUX
ejpam-6046	59	37	labeled	label	VERB
ejpam-6046	59	38	considering	consider	VERB
ejpam-6046	59	39	the	the	DET
ejpam-6046	59	40	convention	convention	NOUN
ejpam-6046	59	41	for	for	ADP
ejpam-6046	59	42	denoting	denote	VERB
ejpam-6046	59	43	the	the	DET
ejpam-6046	59	44	vertices	vertex	NOUN
ejpam-6046	59	45	and	and	CCONJ
ejpam-6046	59	46	edges	edge	NOUN
ejpam-6046	59	47	.	.	PUNCT
ejpam-6046	60	1	observably	observably	ADV
ejpam-6046	60	2	,	,	PUNCT
ejpam-6046	60	3	two	two	NUM
ejpam-6046	60	4	edges	edge	NOUN
ejpam-6046	60	5	are	be	AUX
ejpam-6046	60	6	adjacent	adjacent	ADJ
ejpam-6046	60	7	if	if	SCONJ
ejpam-6046	60	8	they	they	PRON
ejpam-6046	60	9	share	share	VERB
ejpam-6046	60	10	a	a	DET
ejpam-6046	60	11	common	common	ADJ
ejpam-6046	60	12	subscript	subscript	NOUN
ejpam-6046	60	13	.	.	PUNCT
ejpam-6046	61	1	v1	v1	PROPN
ejpam-6046	61	2	v2	v2	PROPN
ejpam-6046	61	3	v3	v3	PROPN
ejpam-6046	61	4	v4	v4	PROPN
ejpam-6046	61	5	v5	v5	PROPN
ejpam-6046	61	6	v6	v6	PROPN
ejpam-6046	61	7	g	g	NOUN
ejpam-6046	61	8	:	:	PUNCT
ejpam-6046	61	9	e1,2	e1,2	PROPN
ejpam-6046	61	10	e2,3e3,4	e2,3e3,4	NUM
ejpam-6046	61	11	e1,4	e1,4	PROPN
ejpam-6046	61	12	e4,5	e4,5	PROPN
ejpam-6046	61	13	e1,5	e1,5	PROPN
ejpam-6046	61	14	e3,5	e3,5	PROPN
ejpam-6046	61	15	e2,6	e2,6	PROPN
ejpam-6046	61	16	figure	figure	VERB
ejpam-6046	61	17	1	1	NUM
ejpam-6046	61	18	:	:	PUNCT
ejpam-6046	61	19	graph	graph	VERB
ejpam-6046	61	20	g	g	NOUN
ejpam-6046	61	21	definition	definition	NOUN
ejpam-6046	61	22	2	2	NUM
ejpam-6046	61	23	.	.	PUNCT
ejpam-6046	62	1	[	[	X
ejpam-6046	62	2	9	9	NUM
ejpam-6046	62	3	]	]	PUNCT
ejpam-6046	62	4	a	a	DET
ejpam-6046	62	5	connected	connected	ADJ
ejpam-6046	62	6	subgraph	subgraph	NOUN
ejpam-6046	62	7	h	h	NOUN
ejpam-6046	62	8	of	of	ADP
ejpam-6046	62	9	a	a	DET
ejpam-6046	62	10	graph	graph	NOUN
ejpam-6046	62	11	g	g	NOUN
ejpam-6046	62	12	is	be	AUX
ejpam-6046	62	13	a	a	DET
ejpam-6046	62	14	component	component	NOUN
ejpam-6046	62	15	of	of	ADP
ejpam-6046	62	16	g	g	PROPN
ejpam-6046	62	17	if	if	SCONJ
ejpam-6046	62	18	h	h	NOUN
ejpam-6046	62	19	is	be	AUX
ejpam-6046	62	20	not	not	PART
ejpam-6046	62	21	a	a	DET
ejpam-6046	62	22	proper	proper	ADJ
ejpam-6046	62	23	subgraph	subgraph	NOUN
ejpam-6046	62	24	of	of	ADP
ejpam-6046	62	25	any	any	DET
ejpam-6046	62	26	connected	connected	ADJ
ejpam-6046	62	27	subgraph	subgraph	NOUN
ejpam-6046	62	28	of	of	ADP
ejpam-6046	62	29	g.	g.	PROPN
ejpam-6046	62	30	the	the	DET
ejpam-6046	62	31	number	number	NOUN
ejpam-6046	62	32	of	of	ADP
ejpam-6046	62	33	components	component	NOUN
ejpam-6046	62	34	in	in	ADP
ejpam-6046	62	35	a	a	DET
ejpam-6046	62	36	graph	graph	NOUN
ejpam-6046	62	37	g	g	NOUN
ejpam-6046	62	38	is	be	AUX
ejpam-6046	62	39	denoted	denote	VERB
ejpam-6046	62	40	by	by	ADP
ejpam-6046	62	41	k(g	k(g	NOUN
ejpam-6046	62	42	)	)	PUNCT
ejpam-6046	62	43	.	.	PUNCT
ejpam-6046	63	1	therefore	therefore	ADV
ejpam-6046	63	2	,	,	PUNCT
ejpam-6046	63	3	g	g	PROPN
ejpam-6046	63	4	is	be	AUX
ejpam-6046	63	5	connected	connect	VERB
ejpam-6046	63	6	if	if	SCONJ
ejpam-6046	63	7	and	and	CCONJ
ejpam-6046	63	8	only	only	ADV
ejpam-6046	63	9	if	if	SCONJ
ejpam-6046	63	10	k(g	k(g	NOUN
ejpam-6046	63	11	)	)	PUNCT
ejpam-6046	64	1	=	=	SYM
ejpam-6046	64	2	1	1	X
ejpam-6046	64	3	.	.	X
ejpam-6046	64	4	illustration	illustration	NOUN
ejpam-6046	64	5	:	:	PUNCT
ejpam-6046	64	6	the	the	DET
ejpam-6046	64	7	graph	graph	NOUN
ejpam-6046	64	8	h	h	NOUN
ejpam-6046	64	9	in	in	ADP
ejpam-6046	64	10	figure	figure	NOUN
ejpam-6046	64	11	2	2	NUM
ejpam-6046	64	12	has	have	VERB
ejpam-6046	64	13	a	a	DET
ejpam-6046	64	14	total	total	NOUN
ejpam-6046	64	15	of	of	ADP
ejpam-6046	64	16	3	3	NUM
ejpam-6046	64	17	components	component	NOUN
ejpam-6046	64	18	;	;	PUNCT
ejpam-6046	64	19	hence	hence	ADV
ejpam-6046	64	20	,	,	PUNCT
ejpam-6046	64	21	k(h	k(h	PROPN
ejpam-6046	64	22	)	)	PUNCT
ejpam-6046	64	23	=	=	SYM
ejpam-6046	65	1	3	3	X
ejpam-6046	65	2	.	.	X
ejpam-6046	65	3	v3	v3	PROPN
ejpam-6046	65	4	v1	v1	PROPN
ejpam-6046	65	5	v2	v2	PROPN
ejpam-6046	65	6	v4	v4	NOUN
ejpam-6046	65	7	v5	v5	PROPN
ejpam-6046	65	8	v6	v6	PROPN
ejpam-6046	65	9	h	h	NOUN
ejpam-6046	65	10	:	:	PUNCT
ejpam-6046	65	11	figure	figure	VERB
ejpam-6046	65	12	2	2	NUM
ejpam-6046	65	13	:	:	PUNCT
ejpam-6046	65	14	a	a	DET
ejpam-6046	65	15	graph	graph	NOUN
ejpam-6046	65	16	h	h	NOUN
ejpam-6046	65	17	with	with	ADP
ejpam-6046	65	18	k(h	k(h	PROPN
ejpam-6046	65	19	)	)	PUNCT
ejpam-6046	65	20	=	=	SYM
ejpam-6046	65	21	3	3	NUM
ejpam-6046	65	22	definition	definition	NOUN
ejpam-6046	65	23	3	3	NUM
ejpam-6046	65	24	.	.	PUNCT
ejpam-6046	66	1	[	[	X
ejpam-6046	66	2	9	9	NUM
ejpam-6046	66	3	]	]	SYM
ejpam-6046	66	4	two	two	NUM
ejpam-6046	66	5	graphs	graph	NOUN
ejpam-6046	66	6	g	g	NOUN
ejpam-6046	66	7	and	and	CCONJ
ejpam-6046	66	8	h	h	NOUN
ejpam-6046	66	9	are	be	AUX
ejpam-6046	66	10	isomorphic	isomorphic	ADJ
ejpam-6046	66	11	,	,	PUNCT
ejpam-6046	66	12	denoted	denote	VERB
ejpam-6046	66	13	by	by	ADP
ejpam-6046	66	14	g	g	PROPN
ejpam-6046	66	15	∼=	∼=	PROPN
ejpam-6046	66	16	h	h	NOUN
ejpam-6046	66	17	,	,	PUNCT
ejpam-6046	66	18	if	if	SCONJ
ejpam-6046	66	19	there	there	PRON
ejpam-6046	66	20	exists	exist	VERB
ejpam-6046	66	21	a	a	DET
ejpam-6046	66	22	bijective	bijective	ADJ
ejpam-6046	66	23	function	function	NOUN
ejpam-6046	66	24	ϕ	ϕ	NOUN
ejpam-6046	66	25	:	:	PUNCT
ejpam-6046	66	26	v	v	NOUN
ejpam-6046	66	27	(	(	PUNCT
ejpam-6046	66	28	g	g	NOUN
ejpam-6046	66	29	)	)	PUNCT
ejpam-6046	66	30	→	→	SYM
ejpam-6046	66	31	v	v	X
ejpam-6046	66	32	(	(	PUNCT
ejpam-6046	66	33	h	h	NOUN
ejpam-6046	66	34	)	)	PUNCT
ejpam-6046	66	35	such	such	ADJ
ejpam-6046	66	36	that	that	SCONJ
ejpam-6046	66	37	two	two	NUM
ejpam-6046	66	38	vertices	vertex	NOUN
ejpam-6046	66	39	u	u	NOUN
ejpam-6046	66	40	and	and	CCONJ
ejpam-6046	66	41	v	v	NOUN
ejpam-6046	66	42	are	be	AUX
ejpam-6046	66	43	adjacent	adjacent	ADJ
ejpam-6046	66	44	in	in	ADP
ejpam-6046	66	45	g	g	PROPN
ejpam-6046	66	46	if	if	SCONJ
ejpam-6046	66	47	j.	j.	PROPN
ejpam-6046	66	48	n.	n.	PROPN
ejpam-6046	66	49	ontulan	ontulan	PROPN
ejpam-6046	66	50	,	,	PUNCT
ejpam-6046	66	51	c.	c.	PROPN
ejpam-6046	66	52	m.	m.	NOUN
ejpam-6046	66	53	balingit	balingit	PROPN
ejpam-6046	66	54	/	/	SYM
ejpam-6046	66	55	eur	eur	PROPN
ejpam-6046	66	56	.	.	PUNCT
ejpam-6046	67	1	j.	j.	PROPN
ejpam-6046	67	2	pure	pure	PROPN
ejpam-6046	67	3	appl	appl	PROPN
ejpam-6046	67	4	.	.	PROPN
ejpam-6046	67	5	math	math	PROPN
ejpam-6046	67	6	,	,	PUNCT
ejpam-6046	67	7	18	18	NUM
ejpam-6046	67	8	(	(	PUNCT
ejpam-6046	67	9	2	2	NUM
ejpam-6046	67	10	)	)	PUNCT
ejpam-6046	67	11	(	(	PUNCT
ejpam-6046	67	12	2025	2025	NUM
ejpam-6046	67	13	)	)	PUNCT
ejpam-6046	67	14	,	,	PUNCT
ejpam-6046	67	15	6046	6046	NUM
ejpam-6046	67	16	4	4	NUM
ejpam-6046	67	17	of	of	ADP
ejpam-6046	67	18	14	14	NUM
ejpam-6046	67	19	and	and	CCONJ
ejpam-6046	67	20	only	only	ADV
ejpam-6046	67	21	if	if	SCONJ
ejpam-6046	67	22	ϕ(u	ϕ(u	NUM
ejpam-6046	67	23	)	)	PUNCT
ejpam-6046	67	24	and	and	CCONJ
ejpam-6046	67	25	ϕ(v	ϕ(v	PROPN
ejpam-6046	67	26	)	)	PUNCT
ejpam-6046	67	27	are	be	AUX
ejpam-6046	67	28	adjacent	adjacent	ADJ
ejpam-6046	67	29	in	in	ADP
ejpam-6046	67	30	h.	h.	PROPN
ejpam-6046	68	1	the	the	DET
ejpam-6046	68	2	function	function	NOUN
ejpam-6046	68	3	ϕ	ϕ	PROPN
ejpam-6046	68	4	is	be	AUX
ejpam-6046	68	5	called	call	VERB
ejpam-6046	68	6	an	an	DET
ejpam-6046	68	7	isomorphism	isomorphism	NOUN
ejpam-6046	68	8	from	from	ADP
ejpam-6046	68	9	g	g	PROPN
ejpam-6046	68	10	to	to	ADP
ejpam-6046	68	11	h.	h.	PROPN
ejpam-6046	68	12	illustration	illustration	NOUN
ejpam-6046	68	13	:	:	PUNCT
ejpam-6046	68	14	the	the	DET
ejpam-6046	68	15	graphs	graph	NOUN
ejpam-6046	68	16	g	g	NOUN
ejpam-6046	68	17	and	and	CCONJ
ejpam-6046	68	18	h	h	NOUN
ejpam-6046	68	19	shown	show	VERB
ejpam-6046	68	20	in	in	ADP
ejpam-6046	68	21	figure	figure	NOUN
ejpam-6046	68	22	3	3	NUM
ejpam-6046	68	23	are	be	AUX
ejpam-6046	68	24	isomorphic	isomorphic	ADJ
ejpam-6046	68	25	,	,	PUNCT
ejpam-6046	68	26	via	via	ADP
ejpam-6046	68	27	the	the	DET
ejpam-6046	68	28	isomorphism	isomorphism	NOUN
ejpam-6046	68	29	ϕ	ϕ	NOUN
ejpam-6046	68	30	:	:	PUNCT
ejpam-6046	68	31	v	v	NOUN
ejpam-6046	68	32	(	(	PUNCT
ejpam-6046	68	33	g	g	NOUN
ejpam-6046	68	34	)	)	PUNCT
ejpam-6046	68	35	→	→	SYM
ejpam-6046	68	36	v	v	X
ejpam-6046	68	37	(	(	PUNCT
ejpam-6046	68	38	h	h	NOUN
ejpam-6046	68	39	)	)	PUNCT
ejpam-6046	68	40	defined	define	VERB
ejpam-6046	68	41	by	by	ADP
ejpam-6046	68	42	,	,	PUNCT
ejpam-6046	68	43	ϕ(u1	ϕ(u1	NOUN
ejpam-6046	68	44	)	)	PUNCT
ejpam-6046	69	1	=	=	SYM
ejpam-6046	69	2	v2	v2	PROPN
ejpam-6046	69	3	,	,	PUNCT
ejpam-6046	69	4	ϕ(u2	ϕ(u2	ADJ
ejpam-6046	69	5	)	)	PUNCT
ejpam-6046	70	1	=	=	SYM
ejpam-6046	70	2	v3	v3	PROPN
ejpam-6046	70	3	,	,	PUNCT
ejpam-6046	70	4	ϕ(u3	ϕ(u3	X
ejpam-6046	70	5	)	)	PUNCT
ejpam-6046	70	6	=	=	SYM
ejpam-6046	70	7	v1	v1	NOUN
ejpam-6046	70	8	,	,	PUNCT
ejpam-6046	70	9	ϕ(u4	ϕ(u4	NOUN
ejpam-6046	70	10	)	)	PUNCT
ejpam-6046	70	11	=	=	SYM
ejpam-6046	70	12	v4	v4	PROPN
ejpam-6046	70	13	,	,	PUNCT
ejpam-6046	70	14	ϕ(u5	ϕ(u5	NOUN
ejpam-6046	70	15	)	)	PUNCT
ejpam-6046	70	16	=	=	SYM
ejpam-6046	71	1	v5	v5	PROPN
ejpam-6046	71	2	,	,	PUNCT
ejpam-6046	71	3	ϕ(u6	ϕ(u6	NUM
ejpam-6046	71	4	)	)	PUNCT
ejpam-6046	71	5	=	=	SYM
ejpam-6046	71	6	v6	v6	NOUN
ejpam-6046	71	7	,	,	PUNCT
ejpam-6046	71	8	and	and	CCONJ
ejpam-6046	71	9	ϕ(u7	ϕ(u7	NOUN
ejpam-6046	71	10	)	)	PUNCT
ejpam-6046	72	1	=	=	SYM
ejpam-6046	72	2	v7	v7	VERB
ejpam-6046	72	3	.	.	PUNCT
ejpam-6046	73	1	u1	u1	PROPN
ejpam-6046	73	2	u2	u2	PROPN
ejpam-6046	73	3	u3	u3	PROPN
ejpam-6046	73	4	u4u5	u4u5	PROPN
ejpam-6046	73	5	u6	u6	PROPN
ejpam-6046	73	6	u7	u7	PROPN
ejpam-6046	73	7	g	g	PROPN
ejpam-6046	73	8	:	:	PUNCT
ejpam-6046	73	9	v1	v1	VERB
ejpam-6046	73	10	v2	v2	PROPN
ejpam-6046	73	11	v3	v3	PROPN
ejpam-6046	73	12	v4	v4	PROPN
ejpam-6046	73	13	v5	v5	PROPN
ejpam-6046	73	14	v6	v6	NOUN
ejpam-6046	73	15	v7	v7	PROPN
ejpam-6046	73	16	h	h	NOUN
ejpam-6046	73	17	:	:	PUNCT
ejpam-6046	73	18	figure	figure	VERB
ejpam-6046	73	19	3	3	NUM
ejpam-6046	73	20	:	:	PUNCT
ejpam-6046	73	21	the	the	DET
ejpam-6046	73	22	graph	graph	NOUN
ejpam-6046	73	23	g	g	PROPN
ejpam-6046	73	24	is	be	AUX
ejpam-6046	73	25	isomorphic	isomorphic	ADJ
ejpam-6046	73	26	to	to	PART
ejpam-6046	73	27	graph	graph	VERB
ejpam-6046	73	28	h	h	NOUN
ejpam-6046	73	29	definition	definition	NOUN
ejpam-6046	73	30	4	4	NUM
ejpam-6046	73	31	.	.	PUNCT
ejpam-6046	74	1	[	[	X
ejpam-6046	74	2	10	10	NUM
ejpam-6046	74	3	]	]	X
ejpam-6046	74	4	a	a	DET
ejpam-6046	74	5	set	set	NOUN
ejpam-6046	74	6	f	f	NOUN
ejpam-6046	74	7	of	of	ADP
ejpam-6046	74	8	edges	edge	NOUN
ejpam-6046	74	9	in	in	ADP
ejpam-6046	74	10	a	a	DET
ejpam-6046	74	11	graph	graph	NOUN
ejpam-6046	74	12	g	g	NOUN
ejpam-6046	74	13	is	be	AUX
ejpam-6046	74	14	an	an	DET
ejpam-6046	74	15	edge	edge	NOUN
ejpam-6046	74	16	dominating	dominating	NOUN
ejpam-6046	74	17	set	set	NOUN
ejpam-6046	74	18	if	if	SCONJ
ejpam-6046	74	19	every	every	DET
ejpam-6046	74	20	edge	edge	NOUN
ejpam-6046	74	21	not	not	PART
ejpam-6046	74	22	in	in	ADP
ejpam-6046	74	23	f	f	PROPN
ejpam-6046	74	24	is	be	AUX
ejpam-6046	74	25	adjacent	adjacent	ADJ
ejpam-6046	74	26	to	to	ADP
ejpam-6046	74	27	some	some	DET
ejpam-6046	74	28	edge	edge	NOUN
ejpam-6046	74	29	in	in	ADP
ejpam-6046	74	30	f	f	PROPN
ejpam-6046	74	31	.	.	PUNCT
ejpam-6046	75	1	a	a	DET
ejpam-6046	75	2	set	set	ADJ
ejpam-6046	75	3	f	f	NOUN
ejpam-6046	75	4	of	of	ADP
ejpam-6046	75	5	edges	edge	NOUN
ejpam-6046	75	6	is	be	AUX
ejpam-6046	75	7	an	an	DET
ejpam-6046	75	8	independent	independent	ADJ
ejpam-6046	75	9	edge	edge	NOUN
ejpam-6046	75	10	set	set	VERB
ejpam-6046	75	11	if	if	SCONJ
ejpam-6046	75	12	no	no	DET
ejpam-6046	75	13	two	two	NUM
ejpam-6046	75	14	edges	edge	NOUN
ejpam-6046	75	15	in	in	ADP
ejpam-6046	75	16	f	f	PROPN
ejpam-6046	75	17	are	be	AUX
ejpam-6046	75	18	adjacent	adjacent	ADJ
ejpam-6046	75	19	.	.	PUNCT
ejpam-6046	76	1	consequently	consequently	ADV
ejpam-6046	76	2	,	,	PUNCT
ejpam-6046	76	3	an	an	DET
ejpam-6046	76	4	independent	independent	ADJ
ejpam-6046	76	5	edge	edge	NOUN
ejpam-6046	76	6	dominating	dominating	NOUN
ejpam-6046	76	7	set	set	NOUN
ejpam-6046	76	8	(	(	PUNCT
ejpam-6046	76	9	ieds	ied	NOUN
ejpam-6046	76	10	)	)	PUNCT
ejpam-6046	76	11	of	of	ADP
ejpam-6046	76	12	g	g	PROPN
ejpam-6046	76	13	is	be	AUX
ejpam-6046	76	14	an	an	DET
ejpam-6046	76	15	independent	independent	ADJ
ejpam-6046	76	16	set	set	NOUN
ejpam-6046	76	17	of	of	ADP
ejpam-6046	76	18	edges	edge	NOUN
ejpam-6046	76	19	which	which	PRON
ejpam-6046	76	20	is	be	AUX
ejpam-6046	76	21	also	also	ADV
ejpam-6046	76	22	an	an	DET
ejpam-6046	76	23	edge	edge	NOUN
ejpam-6046	76	24	dominating	dominating	NOUN
ejpam-6046	76	25	set	set	NOUN
ejpam-6046	76	26	.	.	PUNCT
ejpam-6046	77	1	(	(	PUNCT
ejpam-6046	77	2	the	the	DET
ejpam-6046	77	3	family	family	NOUN
ejpam-6046	77	4	of	of	ADP
ejpam-6046	77	5	all	all	DET
ejpam-6046	77	6	ieds	ied	NOUN
ejpam-6046	77	7	of	of	ADP
ejpam-6046	77	8	g	g	PROPN
ejpam-6046	77	9	is	be	AUX
ejpam-6046	77	10	denoted	denote	VERB
ejpam-6046	77	11	by	by	ADP
ejpam-6046	77	12	ide	ide	NOUN
ejpam-6046	77	13	g	g	NOUN
ejpam-6046	77	14	)	)	PUNCT
ejpam-6046	77	15	.	.	PUNCT
ejpam-6046	78	1	definition	definition	NOUN
ejpam-6046	78	2	5	5	NUM
ejpam-6046	78	3	.	.	PUNCT
ejpam-6046	79	1	[	[	X
ejpam-6046	79	2	11	11	NUM
ejpam-6046	79	3	]	]	PUNCT
ejpam-6046	79	4	let	let	VERB
ejpam-6046	79	5	x	x	PRON
ejpam-6046	79	6	be	be	AUX
ejpam-6046	79	7	a	a	DET
ejpam-6046	79	8	set	set	NOUN
ejpam-6046	79	9	.	.	PUNCT
ejpam-6046	80	1	a	a	DET
ejpam-6046	80	2	topology	topology	NOUN
ejpam-6046	80	3	on	on	ADP
ejpam-6046	80	4	a	a	DET
ejpam-6046	80	5	point	point	NOUN
ejpam-6046	80	6	set	set	NOUN
ejpam-6046	80	7	x	x	PUNCT
ejpam-6046	80	8	is	be	AUX
ejpam-6046	80	9	a	a	DET
ejpam-6046	80	10	collection	collection	NOUN
ejpam-6046	80	11	τ	τ	PROPN
ejpam-6046	80	12	of	of	ADP
ejpam-6046	80	13	subsets	subset	NOUN
ejpam-6046	80	14	of	of	ADP
ejpam-6046	80	15	x	x	PUNCT
ejpam-6046	80	16	having	have	VERB
ejpam-6046	80	17	the	the	DET
ejpam-6046	80	18	following	follow	VERB
ejpam-6046	80	19	properties	property	NOUN
ejpam-6046	80	20	:	:	PUNCT
ejpam-6046	80	21	i.	i.	NOUN
ejpam-6046	80	22	∅	∅	NOUN
ejpam-6046	80	23	and	and	CCONJ
ejpam-6046	80	24	x	x	NOUN
ejpam-6046	80	25	are	be	AUX
ejpam-6046	80	26	in	in	ADP
ejpam-6046	80	27	τ	τ	PROPN
ejpam-6046	80	28	.	.	PUNCT
ejpam-6046	80	29	ii	ii	PROPN
ejpam-6046	80	30	.	.	PUNCT
ejpam-6046	81	1	the	the	DET
ejpam-6046	81	2	union	union	NOUN
ejpam-6046	81	3	of	of	ADP
ejpam-6046	81	4	the	the	DET
ejpam-6046	81	5	elements	element	NOUN
ejpam-6046	81	6	of	of	ADP
ejpam-6046	81	7	any	any	DET
ejpam-6046	81	8	subcollection	subcollection	NOUN
ejpam-6046	81	9	of	of	ADP
ejpam-6046	81	10	τ	τ	PROPN
ejpam-6046	81	11	is	be	AUX
ejpam-6046	81	12	in	in	ADP
ejpam-6046	81	13	τ	τ	PROPN
ejpam-6046	81	14	;	;	PUNCT
ejpam-6046	81	15	that	that	PRON
ejpam-6046	81	16	is	is	ADV
ejpam-6046	81	17	,	,	PUNCT
ejpam-6046	81	18	if	if	SCONJ
ejpam-6046	81	19	{	{	PUNCT
ejpam-6046	81	20	uα}α∈a	uα}α∈a	NUM
ejpam-6046	81	21	⊂	⊂	PROPN
ejpam-6046	81	22	τ	τ	PROPN
ejpam-6046	81	23	then	then	ADV
ejpam-6046	81	24	⋃	⋃	PROPN
ejpam-6046	81	25	α∈a	α∈a	X
ejpam-6046	81	26	uα	uα	PROPN
ejpam-6046	81	27	∈	∈	PROPN
ejpam-6046	81	28	τ	τ	X
ejpam-6046	81	29	.	.	PUNCT
ejpam-6046	82	1	iii	iii	X
ejpam-6046	82	2	.	.	PUNCT
ejpam-6046	83	1	the	the	DET
ejpam-6046	83	2	intersection	intersection	NOUN
ejpam-6046	83	3	of	of	ADP
ejpam-6046	83	4	the	the	DET
ejpam-6046	83	5	elements	element	NOUN
ejpam-6046	83	6	of	of	ADP
ejpam-6046	83	7	any	any	DET
ejpam-6046	83	8	finite	finite	ADJ
ejpam-6046	83	9	subcollection	subcollection	NOUN
ejpam-6046	83	10	of	of	ADP
ejpam-6046	83	11	τ	τ	PROPN
ejpam-6046	83	12	is	be	AUX
ejpam-6046	83	13	in	in	ADP
ejpam-6046	83	14	τ	τ	PROPN
ejpam-6046	83	15	;	;	PUNCT
ejpam-6046	83	16	that	that	PRON
ejpam-6046	83	17	is	is	ADV
ejpam-6046	83	18	,	,	PUNCT
ejpam-6046	83	19	if	if	SCONJ
ejpam-6046	83	20	u1	u1	NOUN
ejpam-6046	83	21	,	,	PUNCT
ejpam-6046	83	22	u2	u2	NOUN
ejpam-6046	83	23	,	,	PUNCT
ejpam-6046	83	24	.	.	PUNCT
ejpam-6046	83	25	.	.	PUNCT
ejpam-6046	83	26	.	.	PUNCT
ejpam-6046	84	1	,	,	PUNCT
ejpam-6046	84	2	un	un	PROPN
ejpam-6046	84	3	∈	∈	PROPN
ejpam-6046	84	4	τ	τ	X
ejpam-6046	84	5	then	then	ADV
ejpam-6046	84	6	⋂n	⋂n	VERB
ejpam-6046	84	7	i=1	i=1	PROPN
ejpam-6046	85	1	ui	ui	PROPN
ejpam-6046	86	1	∈	∈	PROPN
ejpam-6046	87	1	τ	τ	X
ejpam-6046	87	2	.	.	PUNCT
ejpam-6046	88	1	a	a	DET
ejpam-6046	88	2	set	set	NOUN
ejpam-6046	88	3	x	x	PUNCT
ejpam-6046	88	4	for	for	ADP
ejpam-6046	88	5	which	which	PRON
ejpam-6046	88	6	a	a	DET
ejpam-6046	88	7	topology	topology	NOUN
ejpam-6046	88	8	τ	τ	PROPN
ejpam-6046	88	9	has	have	AUX
ejpam-6046	88	10	been	be	AUX
ejpam-6046	88	11	specified	specify	VERB
ejpam-6046	88	12	is	be	AUX
ejpam-6046	88	13	a	a	DET
ejpam-6046	88	14	topological	topological	ADJ
ejpam-6046	88	15	space	space	NOUN
ejpam-6046	88	16	,	,	PUNCT
ejpam-6046	88	17	denoted	denote	VERB
ejpam-6046	88	18	as	as	ADP
ejpam-6046	88	19	the	the	DET
ejpam-6046	88	20	pair	pair	NOUN
ejpam-6046	88	21	(	(	PUNCT
ejpam-6046	88	22	x	x	X
ejpam-6046	88	23	,	,	PUNCT
ejpam-6046	88	24	τ	τ	PROPN
ejpam-6046	88	25	)	)	PUNCT
ejpam-6046	88	26	.	.	PUNCT
ejpam-6046	89	1	a	a	DET
ejpam-6046	89	2	subset	subset	NOUN
ejpam-6046	89	3	of	of	ADP
ejpam-6046	89	4	x	x	PRON
ejpam-6046	89	5	which	which	PRON
ejpam-6046	89	6	is	be	AUX
ejpam-6046	89	7	in	in	ADP
ejpam-6046	89	8	τ	τ	PROPN
ejpam-6046	89	9	is	be	AUX
ejpam-6046	89	10	called	call	VERB
ejpam-6046	89	11	a	a	DET
ejpam-6046	89	12	τ	τ	NOUN
ejpam-6046	89	13	-	-	ADJ
ejpam-6046	89	14	open	open	ADJ
ejpam-6046	89	15	set	set	NOUN
ejpam-6046	89	16	.	.	PUNCT
ejpam-6046	90	1	if	if	SCONJ
ejpam-6046	90	2	x	x	PRON
ejpam-6046	90	3	is	be	AUX
ejpam-6046	90	4	any	any	DET
ejpam-6046	90	5	set	set	NOUN
ejpam-6046	90	6	and	and	CCONJ
ejpam-6046	90	7	τ1	τ1	NOUN
ejpam-6046	90	8	is	be	AUX
ejpam-6046	90	9	the	the	DET
ejpam-6046	90	10	collection	collection	NOUN
ejpam-6046	90	11	of	of	ADP
ejpam-6046	90	12	all	all	DET
ejpam-6046	90	13	subsets	subset	NOUN
ejpam-6046	90	14	of	of	ADP
ejpam-6046	90	15	x	x	X
ejpam-6046	90	16	(	(	PUNCT
ejpam-6046	90	17	that	that	PRON
ejpam-6046	90	18	is	is	ADV
ejpam-6046	90	19	,	,	PUNCT
ejpam-6046	90	20	τ1	τ1	NOUN
ejpam-6046	90	21	is	be	AUX
ejpam-6046	90	22	the	the	DET
ejpam-6046	90	23	power	power	NOUN
ejpam-6046	90	24	set	set	NOUN
ejpam-6046	90	25	of	of	ADP
ejpam-6046	90	26	x	x	PROPN
ejpam-6046	90	27	,	,	PUNCT
ejpam-6046	90	28	τ1	τ1	NOUN
ejpam-6046	90	29	=	=	SYM
ejpam-6046	90	30	p(x	p(x	PROPN
ejpam-6046	90	31	)	)	PUNCT
ejpam-6046	90	32	)	)	PUNCT
ejpam-6046	91	1	then	then	ADV
ejpam-6046	91	2	this	this	PRON
ejpam-6046	91	3	is	be	AUX
ejpam-6046	91	4	a	a	DET
ejpam-6046	91	5	topological	topological	ADJ
ejpam-6046	91	6	space	space	NOUN
ejpam-6046	91	7	.	.	PUNCT
ejpam-6046	92	1	τ1	τ1	NOUN
ejpam-6046	92	2	is	be	AUX
ejpam-6046	92	3	called	call	VERB
ejpam-6046	92	4	the	the	DET
ejpam-6046	92	5	discrete	discrete	ADJ
ejpam-6046	92	6	topology	topology	NOUN
ejpam-6046	92	7	on	on	ADP
ejpam-6046	92	8	x.	x.	NOUN
ejpam-6046	92	9	at	at	ADP
ejpam-6046	92	10	the	the	DET
ejpam-6046	92	11	other	other	ADJ
ejpam-6046	92	12	extreme	extreme	NOUN
ejpam-6046	92	13	is	be	AUX
ejpam-6046	92	14	the	the	DET
ejpam-6046	92	15	topology	topology	NOUN
ejpam-6046	92	16	τ2	τ2	NOUN
ejpam-6046	92	17	=	=	SYM
ejpam-6046	92	18	{	{	PUNCT
ejpam-6046	92	19	∅	∅	NOUN
ejpam-6046	92	20	,	,	PUNCT
ejpam-6046	92	21	x	x	NOUN
ejpam-6046	92	22	}	}	PUNCT
ejpam-6046	92	23	,	,	PUNCT
ejpam-6046	92	24	called	call	VERB
ejpam-6046	92	25	the	the	DET
ejpam-6046	92	26	indiscrete	indiscrete	ADJ
ejpam-6046	92	27	topology	topology	NOUN
ejpam-6046	92	28	or	or	CCONJ
ejpam-6046	92	29	trivial	trivial	ADJ
ejpam-6046	92	30	topology	topology	NOUN
ejpam-6046	92	31	on	on	ADP
ejpam-6046	92	32	x.	x.	NOUN
ejpam-6046	92	33	theorem	theorem	VERB
ejpam-6046	92	34	1	1	NUM
ejpam-6046	92	35	.	.	PUNCT
ejpam-6046	93	1	[	[	X
ejpam-6046	93	2	11	11	NUM
ejpam-6046	93	3	]	]	PUNCT
ejpam-6046	93	4	in	in	ADP
ejpam-6046	93	5	a	a	DET
ejpam-6046	93	6	discrete	discrete	ADJ
ejpam-6046	93	7	topological	topological	ADJ
ejpam-6046	93	8	space	space	NOUN
ejpam-6046	93	9	(	(	PUNCT
ejpam-6046	93	10	x	x	NOUN
ejpam-6046	93	11	,	,	PUNCT
ejpam-6046	93	12	p(x	p(x	PROPN
ejpam-6046	93	13	)	)	PUNCT
ejpam-6046	93	14	)	)	PUNCT
ejpam-6046	93	15	,	,	PUNCT
ejpam-6046	93	16	every	every	DET
ejpam-6046	93	17	singleton	singleton	NOUN
ejpam-6046	93	18	set	set	NOUN
ejpam-6046	93	19	{	{	PUNCT
ejpam-6046	93	20	x	x	NOUN
ejpam-6046	93	21	}	}	PUNCT
ejpam-6046	93	22	is	be	AUX
ejpam-6046	93	23	both	both	CCONJ
ejpam-6046	93	24	open	open	ADJ
ejpam-6046	93	25	and	and	CCONJ
ejpam-6046	93	26	closed	closed	ADJ
ejpam-6046	93	27	.	.	PUNCT
ejpam-6046	94	1	j.	j.	PROPN
ejpam-6046	94	2	n.	n.	PROPN
ejpam-6046	94	3	ontulan	ontulan	PROPN
ejpam-6046	94	4	,	,	PUNCT
ejpam-6046	94	5	c.	c.	PROPN
ejpam-6046	94	6	m.	m.	NOUN
ejpam-6046	94	7	balingit	balingit	PROPN
ejpam-6046	94	8	/	/	SYM
ejpam-6046	94	9	eur	eur	PROPN
ejpam-6046	94	10	.	.	PUNCT
ejpam-6046	95	1	j.	j.	PROPN
ejpam-6046	95	2	pure	pure	PROPN
ejpam-6046	95	3	appl	appl	PROPN
ejpam-6046	95	4	.	.	PROPN
ejpam-6046	95	5	math	math	PROPN
ejpam-6046	95	6	,	,	PUNCT
ejpam-6046	95	7	18	18	NUM
ejpam-6046	95	8	(	(	PUNCT
ejpam-6046	95	9	2	2	NUM
ejpam-6046	95	10	)	)	PUNCT
ejpam-6046	95	11	(	(	PUNCT
ejpam-6046	95	12	2025	2025	NUM
ejpam-6046	95	13	)	)	PUNCT
ejpam-6046	95	14	,	,	PUNCT
ejpam-6046	95	15	6046	6046	NUM
ejpam-6046	95	16	5	5	NUM
ejpam-6046	95	17	of	of	ADP
ejpam-6046	95	18	14	14	NUM
ejpam-6046	95	19	definition	definition	NOUN
ejpam-6046	95	20	6	6	NUM
ejpam-6046	95	21	.	.	PUNCT
ejpam-6046	96	1	[	[	X
ejpam-6046	96	2	12	12	NUM
ejpam-6046	96	3	]	]	PUNCT
ejpam-6046	96	4	given	give	VERB
ejpam-6046	96	5	any	any	DET
ejpam-6046	96	6	family	family	NOUN
ejpam-6046	96	7	σ	σ	NOUN
ejpam-6046	96	8	=	=	PUNCT
ejpam-6046	96	9	{	{	PUNCT
ejpam-6046	96	10	aα	aα	NOUN
ejpam-6046	96	11	:	:	PUNCT
ejpam-6046	97	1	α	α	PROPN
ejpam-6046	97	2	∈	∈	PROPN
ejpam-6046	97	3	a	a	PRON
ejpam-6046	97	4	}	}	PUNCT
ejpam-6046	97	5	of	of	ADP
ejpam-6046	97	6	subsets	subset	NOUN
ejpam-6046	97	7	of	of	ADP
ejpam-6046	97	8	x	x	PRON
ejpam-6046	97	9	,	,	PUNCT
ejpam-6046	97	10	there	there	PRON
ejpam-6046	97	11	always	always	ADV
ejpam-6046	97	12	exists	exist	VERB
ejpam-6046	97	13	a	a	DET
ejpam-6046	97	14	unique	unique	ADJ
ejpam-6046	97	15	,	,	PUNCT
ejpam-6046	97	16	smallest	small	ADJ
ejpam-6046	97	17	topology	topology	NOUN
ejpam-6046	97	18	τ(σ	τ(σ	PROPN
ejpam-6046	97	19	)	)	PUNCT
ejpam-6046	97	20	⊃	⊃	PROPN
ejpam-6046	97	21	σ	σ	PROPN
ejpam-6046	97	22	.	.	PUNCT
ejpam-6046	98	1	the	the	DET
ejpam-6046	98	2	family	family	NOUN
ejpam-6046	98	3	τ(σ	τ(σ	PROPN
ejpam-6046	98	4	)	)	PUNCT
ejpam-6046	98	5	can	can	AUX
ejpam-6046	98	6	be	be	AUX
ejpam-6046	98	7	described	describe	VERB
ejpam-6046	98	8	as	as	SCONJ
ejpam-6046	98	9	follows	follow	VERB
ejpam-6046	98	10	:	:	PUNCT
ejpam-6046	98	11	it	it	PRON
ejpam-6046	98	12	consists	consist	VERB
ejpam-6046	98	13	of	of	ADP
ejpam-6046	98	14	∅	∅	NOUN
ejpam-6046	98	15	,	,	PUNCT
ejpam-6046	98	16	x	x	PRON
ejpam-6046	98	17	,	,	PUNCT
ejpam-6046	98	18	all	all	DET
ejpam-6046	98	19	finite	finite	ADJ
ejpam-6046	98	20	intersections	intersection	NOUN
ejpam-6046	98	21	of	of	ADP
ejpam-6046	98	22	the	the	DET
ejpam-6046	98	23	aα	aα	NOUN
ejpam-6046	98	24	and	and	CCONJ
ejpam-6046	98	25	all	all	DET
ejpam-6046	98	26	arbitrary	arbitrary	ADJ
ejpam-6046	98	27	unions	union	NOUN
ejpam-6046	98	28	of	of	ADP
ejpam-6046	98	29	these	these	DET
ejpam-6046	98	30	finite	finite	ADJ
ejpam-6046	98	31	intersections	intersection	NOUN
ejpam-6046	98	32	.	.	PUNCT
ejpam-6046	99	1	σ	σ	NOUN
ejpam-6046	99	2	is	be	AUX
ejpam-6046	99	3	called	call	VERB
ejpam-6046	99	4	a	a	DET
ejpam-6046	99	5	subbasis	subbasis	NOUN
ejpam-6046	99	6	for	for	ADP
ejpam-6046	99	7	τ(σ	τ(σ	PROPN
ejpam-6046	99	8	)	)	PUNCT
ejpam-6046	99	9	,	,	PUNCT
ejpam-6046	99	10	and	and	CCONJ
ejpam-6046	99	11	τ(σ	τ(σ	PROPN
ejpam-6046	99	12	)	)	PUNCT
ejpam-6046	99	13	is	be	AUX
ejpam-6046	99	14	said	say	VERB
ejpam-6046	99	15	to	to	PART
ejpam-6046	99	16	be	be	AUX
ejpam-6046	99	17	generated	generate	VERB
ejpam-6046	99	18	by	by	ADP
ejpam-6046	99	19	σ	σ	PROPN
ejpam-6046	99	20	.	.	PROPN
ejpam-6046	99	21	example	example	NOUN
ejpam-6046	100	1	1	1	NUM
ejpam-6046	100	2	.	.	PUNCT
ejpam-6046	100	3	let	let	VERB
ejpam-6046	100	4	x	x	PUNCT
ejpam-6046	100	5	=	=	PRON
ejpam-6046	100	6	{	{	PUNCT
ejpam-6046	100	7	a	a	PRON
ejpam-6046	100	8	,	,	PUNCT
ejpam-6046	100	9	b	b	NOUN
ejpam-6046	100	10	,	,	PUNCT
ejpam-6046	100	11	c	c	NOUN
ejpam-6046	100	12	,	,	PUNCT
ejpam-6046	100	13	d	d	NOUN
ejpam-6046	100	14	}	}	PUNCT
ejpam-6046	100	15	and	and	CCONJ
ejpam-6046	100	16	σ	σ	NUM
ejpam-6046	100	17	=	=	SYM
ejpam-6046	100	18	{	{	PUNCT
ejpam-6046	100	19	{	{	PUNCT
ejpam-6046	100	20	a	a	PROPN
ejpam-6046	100	21	,	,	PUNCT
ejpam-6046	100	22	b	b	NOUN
ejpam-6046	100	23	}	}	PUNCT
ejpam-6046	100	24	,	,	PUNCT
ejpam-6046	100	25	{	{	PUNCT
ejpam-6046	100	26	a	a	X
ejpam-6046	100	27	,	,	PUNCT
ejpam-6046	100	28	c	c	NOUN
ejpam-6046	100	29	}	}	PUNCT
ejpam-6046	100	30	,	,	PUNCT
ejpam-6046	100	31	{	{	PUNCT
ejpam-6046	100	32	b	b	X
ejpam-6046	100	33	,	,	PUNCT
ejpam-6046	100	34	d	d	NOUN
ejpam-6046	100	35	}	}	PUNCT
ejpam-6046	100	36	,	,	PUNCT
ejpam-6046	100	37	{	{	PUNCT
ejpam-6046	100	38	c	c	X
ejpam-6046	100	39	,	,	PUNCT
ejpam-6046	100	40	d	d	NOUN
ejpam-6046	100	41	}	}	PUNCT
ejpam-6046	100	42	}	}	PUNCT
ejpam-6046	100	43	.	.	PUNCT
ejpam-6046	101	1	by	by	ADP
ejpam-6046	101	2	direct	direct	ADJ
ejpam-6046	101	3	application	application	NOUN
ejpam-6046	101	4	of	of	ADP
ejpam-6046	101	5	definition	definition	NOUN
ejpam-6046	101	6	6	6	NUM
ejpam-6046	101	7	,	,	PUNCT
ejpam-6046	101	8	τ(σ	τ(σ	PROPN
ejpam-6046	101	9	)	)	PUNCT
ejpam-6046	101	10	=	=	PRON
ejpam-6046	101	11	{	{	PUNCT
ejpam-6046	101	12	∅	∅	NOUN
ejpam-6046	101	13	,	,	PUNCT
ejpam-6046	101	14	{	{	PUNCT
ejpam-6046	101	15	a	a	X
ejpam-6046	101	16	}	}	PUNCT
ejpam-6046	101	17	,	,	PUNCT
ejpam-6046	101	18	{	{	PUNCT
ejpam-6046	101	19	b	b	NOUN
ejpam-6046	101	20	}	}	PUNCT
ejpam-6046	101	21	,	,	PUNCT
ejpam-6046	101	22	{	{	PUNCT
ejpam-6046	101	23	c	c	X
ejpam-6046	101	24	}	}	PUNCT
ejpam-6046	101	25	,	,	PUNCT
ejpam-6046	101	26	{	{	PUNCT
ejpam-6046	101	27	d	d	X
ejpam-6046	101	28	}	}	PUNCT
ejpam-6046	101	29	,	,	PUNCT
ejpam-6046	101	30	{	{	PUNCT
ejpam-6046	101	31	a	a	DET
ejpam-6046	101	32	,	,	PUNCT
ejpam-6046	101	33	b	b	NOUN
ejpam-6046	101	34	}	}	PUNCT
ejpam-6046	101	35	,	,	PUNCT
ejpam-6046	101	36	{	{	PUNCT
ejpam-6046	101	37	a	a	X
ejpam-6046	101	38	,	,	PUNCT
ejpam-6046	101	39	c	c	NOUN
ejpam-6046	101	40	}	}	PUNCT
ejpam-6046	101	41	,	,	PUNCT
ejpam-6046	101	42	{	{	PUNCT
ejpam-6046	101	43	a	a	DET
ejpam-6046	101	44	,	,	PUNCT
ejpam-6046	101	45	d	d	NOUN
ejpam-6046	101	46	}	}	PUNCT
ejpam-6046	101	47	,	,	PUNCT
ejpam-6046	101	48	{	{	PUNCT
ejpam-6046	101	49	b	b	X
ejpam-6046	101	50	,	,	PUNCT
ejpam-6046	101	51	c	c	NOUN
ejpam-6046	101	52	}	}	PUNCT
ejpam-6046	101	53	,	,	PUNCT
ejpam-6046	101	54	{	{	PUNCT
ejpam-6046	101	55	b	b	X
ejpam-6046	101	56	,	,	PUNCT
ejpam-6046	101	57	d	d	NOUN
ejpam-6046	101	58	}	}	PUNCT
ejpam-6046	101	59	,	,	PUNCT
ejpam-6046	101	60	{	{	PUNCT
ejpam-6046	101	61	c	c	X
ejpam-6046	101	62	,	,	PUNCT
ejpam-6046	101	63	d	d	NOUN
ejpam-6046	101	64	}	}	PUNCT
ejpam-6046	101	65	,	,	PUNCT
ejpam-6046	101	66	{	{	PUNCT
ejpam-6046	101	67	a	a	DET
ejpam-6046	101	68	,	,	PUNCT
ejpam-6046	101	69	b	b	NOUN
ejpam-6046	101	70	,	,	PUNCT
ejpam-6046	101	71	c	c	NOUN
ejpam-6046	101	72	}	}	PUNCT
ejpam-6046	101	73	,	,	PUNCT
ejpam-6046	101	74	{	{	PUNCT
ejpam-6046	101	75	a	a	DET
ejpam-6046	101	76	,	,	PUNCT
ejpam-6046	101	77	b	b	NOUN
ejpam-6046	101	78	,	,	PUNCT
ejpam-6046	101	79	d	d	NOUN
ejpam-6046	101	80	}	}	PUNCT
ejpam-6046	101	81	,	,	PUNCT
ejpam-6046	101	82	{	{	PUNCT
ejpam-6046	101	83	a	a	PRON
ejpam-6046	101	84	,	,	PUNCT
ejpam-6046	101	85	c	c	NOUN
ejpam-6046	101	86	,	,	PUNCT
ejpam-6046	101	87	d	d	NOUN
ejpam-6046	101	88	}	}	PUNCT
ejpam-6046	101	89	,	,	PUNCT
ejpam-6046	101	90	{	{	PUNCT
ejpam-6046	101	91	b	b	X
ejpam-6046	101	92	,	,	PUNCT
ejpam-6046	101	93	c	c	NOUN
ejpam-6046	101	94	,	,	PUNCT
ejpam-6046	101	95	d	d	NOUN
ejpam-6046	101	96	}	}	PUNCT
ejpam-6046	101	97	,	,	PUNCT
ejpam-6046	101	98	x	x	NOUN
ejpam-6046	101	99	}	}	PUNCT
ejpam-6046	101	100	=	=	SYM
ejpam-6046	101	101	p(x	p(x	PROPN
ejpam-6046	101	102	)	)	PUNCT
ejpam-6046	101	103	.	.	PUNCT
ejpam-6046	102	1	this	this	PRON
ejpam-6046	102	2	means	mean	VERB
ejpam-6046	102	3	that	that	SCONJ
ejpam-6046	102	4	τ(σ	τ(σ	PROPN
ejpam-6046	102	5	)	)	PUNCT
ejpam-6046	102	6	is	be	AUX
ejpam-6046	102	7	the	the	DET
ejpam-6046	102	8	discrete	discrete	ADJ
ejpam-6046	102	9	topology	topology	NOUN
ejpam-6046	102	10	on	on	ADP
ejpam-6046	102	11	x.	x.	NOUN
ejpam-6046	102	12	3	3	X
ejpam-6046	102	13	.	.	PUNCT
ejpam-6046	102	14	independent	independent	ADJ
ejpam-6046	102	15	edge	edge	PROPN
ejpam-6046	102	16	domination	domination	NOUN
ejpam-6046	102	17	topology	topology	NOUN
ejpam-6046	102	18	definition	definition	NOUN
ejpam-6046	102	19	7	7	NUM
ejpam-6046	102	20	.	.	PUNCT
ejpam-6046	103	1	let	let	VERB
ejpam-6046	103	2	g	g	PRON
ejpam-6046	103	3	be	be	AUX
ejpam-6046	103	4	a	a	DET
ejpam-6046	103	5	nonempty	nonempty	ADJ
ejpam-6046	103	6	graph	graph	NOUN
ejpam-6046	103	7	.	.	PUNCT
ejpam-6046	104	1	the	the	DET
ejpam-6046	104	2	independent	independent	ADJ
ejpam-6046	104	3	edge	edge	NOUN
ejpam-6046	104	4	domination	domination	NOUN
ejpam-6046	104	5	topology	topology	NOUN
ejpam-6046	104	6	of	of	ADP
ejpam-6046	104	7	g	g	NOUN
ejpam-6046	104	8	,	,	PUNCT
ejpam-6046	104	9	denoted	denote	VERB
ejpam-6046	104	10	by	by	ADP
ejpam-6046	104	11	τeid(g	τeid(g	PROPN
ejpam-6046	104	12	)	)	PUNCT
ejpam-6046	104	13	is	be	AUX
ejpam-6046	104	14	the	the	DET
ejpam-6046	104	15	topology	topology	NOUN
ejpam-6046	104	16	generated	generate	VERB
ejpam-6046	104	17	by	by	ADP
ejpam-6046	104	18	the	the	DET
ejpam-6046	104	19	family	family	NOUN
ejpam-6046	104	20	ide	ide	NOUN
ejpam-6046	104	21	g	g	NOUN
ejpam-6046	104	22	of	of	ADP
ejpam-6046	104	23	all	all	DET
ejpam-6046	104	24	independent	independent	ADJ
ejpam-6046	104	25	edge	edge	NOUN
ejpam-6046	104	26	dominating	dominating	NOUN
ejpam-6046	104	27	sets	set	NOUN
ejpam-6046	104	28	of	of	ADP
ejpam-6046	104	29	g.	g.	PROPN
ejpam-6046	104	30	the	the	DET
ejpam-6046	104	31	pair	pair	NOUN
ejpam-6046	104	32	(	(	PUNCT
ejpam-6046	104	33	e(g	e(g	PROPN
ejpam-6046	104	34	)	)	PUNCT
ejpam-6046	104	35	,	,	PUNCT
ejpam-6046	104	36	τeid(g	τeid(g	PROPN
ejpam-6046	104	37	)	)	PUNCT
ejpam-6046	104	38	)	)	PUNCT
ejpam-6046	105	1	is	be	AUX
ejpam-6046	105	2	called	call	VERB
ejpam-6046	105	3	the	the	DET
ejpam-6046	105	4	independent	independent	ADJ
ejpam-6046	105	5	edge	edge	NOUN
ejpam-6046	105	6	domination	domination	NOUN
ejpam-6046	105	7	topological	topological	ADJ
ejpam-6046	105	8	space	space	NOUN
ejpam-6046	105	9	of	of	ADP
ejpam-6046	105	10	g.	g.	PROPN
ejpam-6046	105	11	example	example	NOUN
ejpam-6046	105	12	2	2	X
ejpam-6046	105	13	.	.	X
ejpam-6046	105	14	consider	consider	VERB
ejpam-6046	105	15	the	the	DET
ejpam-6046	105	16	graph	graph	NOUN
ejpam-6046	105	17	g	g	NOUN
ejpam-6046	105	18	in	in	ADP
ejpam-6046	105	19	figure	figure	NOUN
ejpam-6046	105	20	4	4	NUM
ejpam-6046	105	21	with	with	ADP
ejpam-6046	105	22	e(g	e(g	NOUN
ejpam-6046	105	23	)	)	PUNCT
ejpam-6046	106	1	=	=	PRON
ejpam-6046	106	2	{	{	PUNCT
ejpam-6046	106	3	e1,2	e1,2	PROPN
ejpam-6046	106	4	,	,	PUNCT
ejpam-6046	106	5	e1,3	e1,3	PROPN
ejpam-6046	106	6	,	,	PUNCT
ejpam-6046	106	7	e1,4	e1,4	PROPN
ejpam-6046	106	8	,	,	PUNCT
ejpam-6046	106	9	e2,3	e2,3	PROPN
ejpam-6046	106	10	,	,	PUNCT
ejpam-6046	106	11	e3,4	e3,4	ADJ
ejpam-6046	106	12	}	}	PUNCT
ejpam-6046	106	13	.	.	PUNCT
ejpam-6046	107	1	the	the	DET
ejpam-6046	107	2	family	family	NOUN
ejpam-6046	107	3	of	of	ADP
ejpam-6046	107	4	all	all	DET
ejpam-6046	107	5	independent	independent	ADJ
ejpam-6046	107	6	edge	edge	NOUN
ejpam-6046	107	7	dominating	dominating	NOUN
ejpam-6046	107	8	sets	set	NOUN
ejpam-6046	107	9	of	of	ADP
ejpam-6046	107	10	g	g	NOUN
ejpam-6046	107	11	is	be	AUX
ejpam-6046	107	12	given	give	VERB
ejpam-6046	107	13	by	by	ADP
ejpam-6046	107	14	ide	ide	NOUN
ejpam-6046	107	15	g	g	NOUN
ejpam-6046	107	16	=	=	PUNCT
ejpam-6046	107	17	{	{	PUNCT
ejpam-6046	107	18	{	{	PUNCT
ejpam-6046	107	19	e1,3	e1,3	PROPN
ejpam-6046	107	20	}	}	PUNCT
ejpam-6046	107	21	,	,	PUNCT
ejpam-6046	107	22	{	{	PUNCT
ejpam-6046	107	23	e1,2	e1,2	ADJ
ejpam-6046	107	24	,	,	PUNCT
ejpam-6046	107	25	e3,4	e3,4	ADJ
ejpam-6046	107	26	}	}	PUNCT
ejpam-6046	107	27	,	,	PUNCT
ejpam-6046	107	28	{	{	PUNCT
ejpam-6046	107	29	e1,4	e1,4	ADV
ejpam-6046	107	30	,	,	PUNCT
ejpam-6046	107	31	e2,3	e2,3	NOUN
ejpam-6046	107	32	}	}	PUNCT
ejpam-6046	107	33	}	}	PUNCT
ejpam-6046	107	34	,	,	PUNCT
ejpam-6046	107	35	and	and	CCONJ
ejpam-6046	107	36	so	so	ADV
ejpam-6046	107	37	,	,	PUNCT
ejpam-6046	107	38	by	by	ADP
ejpam-6046	107	39	definition	definition	NOUN
ejpam-6046	107	40	6	6	NUM
ejpam-6046	107	41	and	and	CCONJ
ejpam-6046	107	42	definition	definition	NOUN
ejpam-6046	107	43	7	7	NUM
ejpam-6046	107	44	,	,	PUNCT
ejpam-6046	107	45	τeid(g	τeid(g	PROPN
ejpam-6046	107	46	)	)	PUNCT
ejpam-6046	107	47	=	=	SYM
ejpam-6046	107	48	{	{	PUNCT
ejpam-6046	107	49	∅	∅	NOUN
ejpam-6046	107	50	,	,	PUNCT
ejpam-6046	107	51	{	{	PUNCT
ejpam-6046	107	52	e1,3	e1,3	NOUN
ejpam-6046	107	53	}	}	PUNCT
ejpam-6046	107	54	,	,	PUNCT
ejpam-6046	107	55	{	{	PUNCT
ejpam-6046	107	56	e1,2	e1,2	ADJ
ejpam-6046	107	57	,	,	PUNCT
ejpam-6046	107	58	e3,4	e3,4	ADJ
ejpam-6046	107	59	}	}	PUNCT
ejpam-6046	107	60	,	,	PUNCT
ejpam-6046	107	61	{	{	PUNCT
ejpam-6046	107	62	e1,4	e1,4	ADV
ejpam-6046	107	63	,	,	PUNCT
ejpam-6046	107	64	e2,3	e2,3	NOUN
ejpam-6046	107	65	}	}	PUNCT
ejpam-6046	107	66	,	,	PUNCT
ejpam-6046	107	67	{	{	PUNCT
ejpam-6046	107	68	e1,2	e1,2	ADJ
ejpam-6046	107	69	,	,	PUNCT
ejpam-6046	107	70	e1,3	e1,3	PROPN
ejpam-6046	107	71	,	,	PUNCT
ejpam-6046	107	72	e3,4	e3,4	ADJ
ejpam-6046	107	73	}	}	PUNCT
ejpam-6046	107	74	,	,	PUNCT
ejpam-6046	107	75	{	{	PUNCT
ejpam-6046	107	76	e1,3	e1,3	PROPN
ejpam-6046	107	77	,	,	PUNCT
ejpam-6046	107	78	e1,4	e1,4	PROPN
ejpam-6046	107	79	,	,	PUNCT
ejpam-6046	107	80	e2,3	e2,3	NOUN
ejpam-6046	107	81	}	}	PUNCT
ejpam-6046	107	82	,	,	PUNCT
ejpam-6046	107	83	{	{	PUNCT
ejpam-6046	107	84	e1,2	e1,2	ADJ
ejpam-6046	107	85	,	,	PUNCT
ejpam-6046	107	86	e1,4	e1,4	PROPN
ejpam-6046	107	87	,	,	PUNCT
ejpam-6046	107	88	e2,3	e2,3	PROPN
ejpam-6046	107	89	,	,	PUNCT
ejpam-6046	107	90	e3,4	e3,4	ADJ
ejpam-6046	107	91	}	}	PUNCT
ejpam-6046	107	92	,	,	PUNCT
ejpam-6046	107	93	e(g	e(g	PROPN
ejpam-6046	107	94	)	)	PUNCT
ejpam-6046	107	95	}	}	PUNCT
ejpam-6046	107	96	.	.	PUNCT
ejpam-6046	108	1	v1	v1	PROPN
ejpam-6046	108	2	v2	v2	PROPN
ejpam-6046	108	3	v3	v3	PROPN
ejpam-6046	108	4	v4	v4	PROPN
ejpam-6046	108	5	g	g	PROPN
ejpam-6046	108	6	:	:	PUNCT
ejpam-6046	108	7	e	e	NOUN
ejpam-6046	108	8	1,2	1,2	NUM
ejpam-6046	108	9	e	e	X
ejpam-6046	108	10	2	2	NUM
ejpam-6046	108	11	,	,	PUNCT
ejpam-6046	108	12	3	3	NUM
ejpam-6046	108	13	e	e	NOUN
ejpam-6046	108	14	3,4	3,4	NUM
ejpam-6046	108	15	e	e	SYM
ejpam-6046	108	16	1	1	NUM
ejpam-6046	108	17	,	,	PUNCT
ejpam-6046	108	18	4	4	NUM
ejpam-6046	108	19	e	e	NOUN
ejpam-6046	108	20	1	1	NUM
ejpam-6046	108	21	,	,	PUNCT
ejpam-6046	108	22	3	3	NUM
ejpam-6046	108	23	figure	figure	NOUN
ejpam-6046	108	24	4	4	NUM
ejpam-6046	108	25	:	:	PUNCT
ejpam-6046	108	26	graph	graph	NOUN
ejpam-6046	108	27	g	g	NOUN
ejpam-6046	108	28	theorem	theorem	NOUN
ejpam-6046	108	29	2	2	X
ejpam-6046	108	30	.	.	PUNCT
ejpam-6046	109	1	let	let	VERB
ejpam-6046	109	2	g	g	PRON
ejpam-6046	109	3	be	be	AUX
ejpam-6046	109	4	a	a	DET
ejpam-6046	109	5	nonempty	nonempty	ADJ
ejpam-6046	109	6	graph	graph	NOUN
ejpam-6046	109	7	.	.	PUNCT
ejpam-6046	110	1	the	the	DET
ejpam-6046	110	2	topology	topology	NOUN
ejpam-6046	110	3	τeid(g	τeid(g	NOUN
ejpam-6046	110	4	)	)	PUNCT
ejpam-6046	110	5	is	be	AUX
ejpam-6046	110	6	the	the	DET
ejpam-6046	110	7	indiscrete	indiscrete	ADJ
ejpam-6046	110	8	topology	topology	NOUN
ejpam-6046	110	9	on	on	ADP
ejpam-6046	110	10	e(g	e(g	PROPN
ejpam-6046	110	11	)	)	PUNCT
ejpam-6046	111	1	if	if	SCONJ
ejpam-6046	111	2	and	and	CCONJ
ejpam-6046	111	3	only	only	ADV
ejpam-6046	111	4	if	if	SCONJ
ejpam-6046	111	5	g	g	PROPN
ejpam-6046	111	6	has	have	VERB
ejpam-6046	111	7	k	k	PROPN
ejpam-6046	111	8	≥	≥	NUM
ejpam-6046	111	9	1	1	NUM
ejpam-6046	111	10	components	component	NOUN
ejpam-6046	111	11	,	,	PUNCT
ejpam-6046	111	12	where	where	SCONJ
ejpam-6046	111	13	each	each	DET
ejpam-6046	111	14	component	component	NOUN
ejpam-6046	111	15	is	be	AUX
ejpam-6046	111	16	isomorphic	isomorphic	ADJ
ejpam-6046	111	17	to	to	ADP
ejpam-6046	111	18	either	either	CCONJ
ejpam-6046	111	19	p1	p1	PROPN
ejpam-6046	111	20	or	or	CCONJ
ejpam-6046	111	21	p2	p2	NOUN
ejpam-6046	111	22	.	.	PUNCT
ejpam-6046	112	1	proof	proof	NOUN
ejpam-6046	112	2	.	.	PUNCT
ejpam-6046	113	1	suppose	suppose	VERB
ejpam-6046	113	2	g	g	PROPN
ejpam-6046	113	3	has	have	VERB
ejpam-6046	113	4	a	a	DET
ejpam-6046	113	5	component	component	NOUN
ejpam-6046	113	6	h	h	NOUN
ejpam-6046	113	7	that	that	PRON
ejpam-6046	113	8	has	have	VERB
ejpam-6046	113	9	at	at	ADV
ejpam-6046	113	10	least	least	ADJ
ejpam-6046	113	11	2	2	NUM
ejpam-6046	113	12	adjacent	adjacent	ADJ
ejpam-6046	113	13	edges	edge	NOUN
ejpam-6046	113	14	ei1,j	ei1,j	ADP
ejpam-6046	113	15	and	and	CCONJ
ejpam-6046	113	16	ei2,j	ei2,j	ADJ
ejpam-6046	113	17	.	.	PUNCT
ejpam-6046	114	1	then	then	ADV
ejpam-6046	114	2	for	for	ADP
ejpam-6046	114	3	any	any	DET
ejpam-6046	114	4	ieds	ied	NOUN
ejpam-6046	114	5	s	s	VERB
ejpam-6046	114	6	of	of	ADP
ejpam-6046	114	7	g	g	NOUN
ejpam-6046	114	8	either	either	CCONJ
ejpam-6046	114	9	ei1,j	ei1,j	NOUN
ejpam-6046	114	10	,	,	PUNCT
ejpam-6046	114	11	ei2,j	ei2,j	ADJ
ejpam-6046	114	12	/∈	/∈	PUNCT
ejpam-6046	114	13	s	s	PART
ejpam-6046	114	14	or	or	CCONJ
ejpam-6046	114	15	exactly	exactly	ADV
ejpam-6046	114	16	one	one	NUM
ejpam-6046	114	17	of	of	ADP
ejpam-6046	114	18	them	they	PRON
ejpam-6046	114	19	belongs	belong	VERB
ejpam-6046	114	20	to	to	ADP
ejpam-6046	114	21	s.	s.	PROPN
ejpam-6046	114	22	both	both	DET
ejpam-6046	114	23	cases	case	NOUN
ejpam-6046	114	24	imply	imply	VERB
ejpam-6046	114	25	that	that	SCONJ
ejpam-6046	114	26	there	there	PRON
ejpam-6046	114	27	exists	exist	VERB
ejpam-6046	114	28	s	s	PROPN
ejpam-6046	114	29	∈	∈	PROPN
ejpam-6046	114	30	ide	ide	NOUN
ejpam-6046	114	31	g	g	PROPN
ejpam-6046	114	32	⊆	⊆	NUM
ejpam-6046	114	33	τeid(g	τeid(g	NUM
ejpam-6046	114	34	)	)	PUNCT
ejpam-6046	114	35	such	such	ADJ
ejpam-6046	114	36	that	that	PRON
ejpam-6046	114	37	s	s	VERB
ejpam-6046	114	38	̸=	̸=	PROPN
ejpam-6046	114	39	e(g	e(g	PROPN
ejpam-6046	114	40	)	)	PUNCT
ejpam-6046	114	41	.	.	PUNCT
ejpam-6046	115	1	therefore	therefore	ADV
ejpam-6046	115	2	,	,	PUNCT
ejpam-6046	115	3	τeid(g	τeid(g	PROPN
ejpam-6046	115	4	)	)	PUNCT
ejpam-6046	115	5	is	be	AUX
ejpam-6046	115	6	not	not	PART
ejpam-6046	115	7	the	the	DET
ejpam-6046	115	8	indiscrete	indiscrete	ADJ
ejpam-6046	115	9	topology	topology	NOUN
ejpam-6046	115	10	on	on	ADP
ejpam-6046	115	11	e(g	e(g	PROPN
ejpam-6046	115	12	)	)	PUNCT
ejpam-6046	115	13	.	.	PUNCT
ejpam-6046	116	1	j.	j.	PROPN
ejpam-6046	116	2	n.	n.	PROPN
ejpam-6046	116	3	ontulan	ontulan	PROPN
ejpam-6046	116	4	,	,	PUNCT
ejpam-6046	116	5	c.	c.	PROPN
ejpam-6046	116	6	m.	m.	NOUN
ejpam-6046	116	7	balingit	balingit	PROPN
ejpam-6046	116	8	/	/	SYM
ejpam-6046	116	9	eur	eur	PROPN
ejpam-6046	116	10	.	.	PUNCT
ejpam-6046	117	1	j.	j.	PROPN
ejpam-6046	117	2	pure	pure	PROPN
ejpam-6046	117	3	appl	appl	PROPN
ejpam-6046	117	4	.	.	PROPN
ejpam-6046	117	5	math	math	PROPN
ejpam-6046	117	6	,	,	PUNCT
ejpam-6046	117	7	18	18	NUM
ejpam-6046	117	8	(	(	PUNCT
ejpam-6046	117	9	2	2	NUM
ejpam-6046	117	10	)	)	PUNCT
ejpam-6046	117	11	(	(	PUNCT
ejpam-6046	117	12	2025	2025	NUM
ejpam-6046	117	13	)	)	PUNCT
ejpam-6046	117	14	,	,	PUNCT
ejpam-6046	117	15	6046	6046	NUM
ejpam-6046	117	16	6	6	NUM
ejpam-6046	117	17	of	of	ADP
ejpam-6046	117	18	14	14	NUM
ejpam-6046	117	19	conversely	conversely	ADV
ejpam-6046	117	20	,	,	PUNCT
ejpam-6046	117	21	it	it	PRON
ejpam-6046	117	22	is	be	AUX
ejpam-6046	117	23	easy	easy	ADJ
ejpam-6046	117	24	to	to	PART
ejpam-6046	117	25	see	see	VERB
ejpam-6046	117	26	that	that	SCONJ
ejpam-6046	117	27	if	if	SCONJ
ejpam-6046	117	28	g	g	PROPN
ejpam-6046	117	29	is	be	AUX
ejpam-6046	117	30	nonempty	nonempty	ADJ
ejpam-6046	117	31	and	and	CCONJ
ejpam-6046	117	32	its	its	PRON
ejpam-6046	117	33	components	component	NOUN
ejpam-6046	117	34	are	be	AUX
ejpam-6046	117	35	either	either	CCONJ
ejpam-6046	117	36	p1	p1	NOUN
ejpam-6046	117	37	or	or	CCONJ
ejpam-6046	117	38	p2	p2	NOUN
ejpam-6046	117	39	,	,	PUNCT
ejpam-6046	117	40	then	then	ADV
ejpam-6046	117	41	e(g	e(g	PROPN
ejpam-6046	117	42	)	)	PUNCT
ejpam-6046	117	43	is	be	AUX
ejpam-6046	117	44	an	an	DET
ejpam-6046	117	45	ieds	ied	NOUN
ejpam-6046	117	46	of	of	ADP
ejpam-6046	117	47	g	g	NOUN
ejpam-6046	117	48	,	,	PUNCT
ejpam-6046	117	49	and	and	CCONJ
ejpam-6046	117	50	any	any	DET
ejpam-6046	117	51	proper	proper	ADJ
ejpam-6046	117	52	subset	subset	NOUN
ejpam-6046	117	53	of	of	ADP
ejpam-6046	117	54	e(g	e(g	PROPN
ejpam-6046	117	55	)	)	PUNCT
ejpam-6046	117	56	is	be	AUX
ejpam-6046	117	57	not	not	PART
ejpam-6046	117	58	an	an	DET
ejpam-6046	117	59	edge	edge	NOUN
ejpam-6046	117	60	dominating	dominating	NOUN
ejpam-6046	117	61	set	set	NOUN
ejpam-6046	117	62	of	of	ADP
ejpam-6046	117	63	g.	g.	PROPN
ejpam-6046	117	64	thus	thus	ADV
ejpam-6046	117	65	,	,	PUNCT
ejpam-6046	117	66	ide	ide	ADJ
ejpam-6046	117	67	g	g	PROPN
ejpam-6046	117	68	contains	contain	VERB
ejpam-6046	117	69	only	only	ADV
ejpam-6046	117	70	e(g	e(g	PROPN
ejpam-6046	117	71	)	)	PUNCT
ejpam-6046	117	72	.	.	PUNCT
ejpam-6046	118	1	consequently	consequently	ADV
ejpam-6046	118	2	,	,	PUNCT
ejpam-6046	118	3	τeid(g	τeid(g	PROPN
ejpam-6046	118	4	)	)	PUNCT
ejpam-6046	118	5	is	be	AUX
ejpam-6046	118	6	the	the	DET
ejpam-6046	118	7	indiscrete	indiscrete	ADJ
ejpam-6046	118	8	topology	topology	NOUN
ejpam-6046	118	9	on	on	ADP
ejpam-6046	118	10	e(g	e(g	PROPN
ejpam-6046	118	11	)	)	PUNCT
ejpam-6046	118	12	.	.	PUNCT
ejpam-6046	119	1	■	■	PUNCT
ejpam-6046	119	2	example	example	NOUN
ejpam-6046	119	3	3	3	X
ejpam-6046	119	4	.	.	X
ejpam-6046	119	5	consider	consider	VERB
ejpam-6046	119	6	the	the	DET
ejpam-6046	119	7	graph	graph	NOUN
ejpam-6046	119	8	h	h	NOUN
ejpam-6046	119	9	in	in	ADP
ejpam-6046	119	10	figure	figure	NOUN
ejpam-6046	119	11	5	5	NUM
ejpam-6046	119	12	with	with	ADP
ejpam-6046	119	13	e(h	e(h	PROPN
ejpam-6046	119	14	)	)	PUNCT
ejpam-6046	119	15	=	=	PRON
ejpam-6046	119	16	{	{	PUNCT
ejpam-6046	119	17	e1,2	e1,2	ADJ
ejpam-6046	119	18	,	,	PUNCT
ejpam-6046	119	19	e4,5	e4,5	NOUN
ejpam-6046	119	20	}	}	PUNCT
ejpam-6046	119	21	.	.	PUNCT
ejpam-6046	120	1	observe	observe	VERB
ejpam-6046	120	2	that	that	DET
ejpam-6046	120	3	ide	ide	NOUN
ejpam-6046	120	4	h	h	NOUN
ejpam-6046	120	5	=	=	PRON
ejpam-6046	120	6	{	{	PUNCT
ejpam-6046	120	7	{	{	PUNCT
ejpam-6046	120	8	e1,2	e1,2	ADJ
ejpam-6046	120	9	,	,	PUNCT
ejpam-6046	120	10	e4,5	e4,5	NOUN
ejpam-6046	120	11	}	}	PUNCT
ejpam-6046	120	12	}	}	PUNCT
ejpam-6046	120	13	,	,	PUNCT
ejpam-6046	120	14	and	and	CCONJ
ejpam-6046	120	15	so	so	ADV
ejpam-6046	120	16	,	,	PUNCT
ejpam-6046	120	17	by	by	ADP
ejpam-6046	120	18	theorem	theorem	NOUN
ejpam-6046	120	19	2	2	NUM
ejpam-6046	120	20	,	,	PUNCT
ejpam-6046	120	21	τeid(h	τeid(h	NUM
ejpam-6046	120	22	)	)	PUNCT
ejpam-6046	121	1	=	=	SYM
ejpam-6046	121	2	{	{	PUNCT
ejpam-6046	121	3	∅	∅	NOUN
ejpam-6046	121	4	,	,	PUNCT
ejpam-6046	121	5	e(h	e(h	PROPN
ejpam-6046	121	6	)	)	PUNCT
ejpam-6046	121	7	}	}	PUNCT
ejpam-6046	121	8	is	be	AUX
ejpam-6046	121	9	the	the	DET
ejpam-6046	121	10	indiscrete	indiscrete	ADJ
ejpam-6046	121	11	topology	topology	NOUN
ejpam-6046	121	12	on	on	ADP
ejpam-6046	121	13	e(h	e(h	PROPN
ejpam-6046	121	14	)	)	PUNCT
ejpam-6046	121	15	.	.	PUNCT
ejpam-6046	122	1	v1	v1	PROPN
ejpam-6046	122	2	v2	v2	PROPN
ejpam-6046	122	3	v3	v3	PROPN
ejpam-6046	122	4	v4	v4	PROPN
ejpam-6046	122	5	v5	v5	PROPN
ejpam-6046	122	6	h	h	NOUN
ejpam-6046	122	7	:	:	PUNCT
ejpam-6046	122	8	e	e	NOUN
ejpam-6046	122	9	1	1	NUM
ejpam-6046	122	10	,	,	PUNCT
ejpam-6046	122	11	2	2	NUM
ejpam-6046	122	12	e	e	SYM
ejpam-6046	122	13	4	4	NUM
ejpam-6046	122	14	,	,	PUNCT
ejpam-6046	122	15	5	5	NUM
ejpam-6046	122	16	figure	figure	NOUN
ejpam-6046	122	17	5	5	NUM
ejpam-6046	122	18	:	:	PUNCT
ejpam-6046	122	19	the	the	DET
ejpam-6046	122	20	component	component	NOUN
ejpam-6046	122	21	of	of	ADP
ejpam-6046	122	22	graph	graph	NOUN
ejpam-6046	122	23	h	h	NOUN
ejpam-6046	122	24	4	4	NUM
ejpam-6046	122	25	.	.	PUNCT
ejpam-6046	122	26	independent	independent	ADJ
ejpam-6046	122	27	edge	edge	PROPN
ejpam-6046	122	28	domination	domination	NOUN
ejpam-6046	122	29	topology	topology	NOUN
ejpam-6046	122	30	of	of	ADP
ejpam-6046	122	31	complete	complete	ADJ
ejpam-6046	122	32	graphs	graph	NOUN
ejpam-6046	122	33	definition	definition	NOUN
ejpam-6046	122	34	8	8	NUM
ejpam-6046	122	35	.	.	PUNCT
ejpam-6046	123	1	[	[	X
ejpam-6046	123	2	9	9	NUM
ejpam-6046	123	3	]	]	X
ejpam-6046	123	4	a	a	DET
ejpam-6046	123	5	graph	graph	NOUN
ejpam-6046	123	6	g	g	NOUN
ejpam-6046	123	7	is	be	AUX
ejpam-6046	123	8	complete	complete	ADJ
ejpam-6046	123	9	if	if	SCONJ
ejpam-6046	123	10	every	every	DET
ejpam-6046	123	11	two	two	NUM
ejpam-6046	123	12	distinct	distinct	ADJ
ejpam-6046	123	13	vertices	vertex	NOUN
ejpam-6046	123	14	of	of	ADP
ejpam-6046	123	15	g	g	NOUN
ejpam-6046	123	16	are	be	AUX
ejpam-6046	123	17	adjacent	adjacent	ADJ
ejpam-6046	123	18	.	.	PUNCT
ejpam-6046	124	1	a	a	DET
ejpam-6046	124	2	complete	complete	ADJ
ejpam-6046	124	3	graph	graph	NOUN
ejpam-6046	124	4	of	of	ADP
ejpam-6046	124	5	order	order	NOUN
ejpam-6046	124	6	n	n	NOUN
ejpam-6046	124	7	is	be	AUX
ejpam-6046	124	8	denoted	denote	VERB
ejpam-6046	124	9	by	by	ADP
ejpam-6046	124	10	kn	kn	PROPN
ejpam-6046	124	11	.	.	PUNCT
ejpam-6046	125	1	therefore	therefore	ADV
ejpam-6046	125	2	,	,	PUNCT
ejpam-6046	125	3	kn	kn	PROPN
ejpam-6046	125	4	has	have	VERB
ejpam-6046	125	5	the	the	DET
ejpam-6046	125	6	maximum	maximum	ADJ
ejpam-6046	125	7	possible	possible	ADJ
ejpam-6046	125	8	size	size	NOUN
ejpam-6046	125	9	of	of	ADP
ejpam-6046	125	10	a	a	DET
ejpam-6046	125	11	graph	graph	NOUN
ejpam-6046	125	12	with	with	ADP
ejpam-6046	125	13	n	n	ADP
ejpam-6046	125	14	vertices	vertex	NOUN
ejpam-6046	125	15	.	.	PUNCT
ejpam-6046	126	1	since	since	SCONJ
ejpam-6046	126	2	every	every	DET
ejpam-6046	126	3	two	two	NUM
ejpam-6046	126	4	distinct	distinct	ADJ
ejpam-6046	126	5	vertices	vertex	NOUN
ejpam-6046	126	6	of	of	ADP
ejpam-6046	126	7	kn	kn	PROPN
ejpam-6046	126	8	are	be	AUX
ejpam-6046	126	9	joined	join	VERB
ejpam-6046	126	10	by	by	ADP
ejpam-6046	126	11	an	an	DET
ejpam-6046	126	12	edge	edge	NOUN
ejpam-6046	126	13	,	,	PUNCT
ejpam-6046	126	14	the	the	DET
ejpam-6046	126	15	number	number	NOUN
ejpam-6046	126	16	of	of	ADP
ejpam-6046	126	17	pairs	pair	NOUN
ejpam-6046	126	18	of	of	ADP
ejpam-6046	126	19	vertices	vertex	NOUN
ejpam-6046	126	20	in	in	ADP
ejpam-6046	126	21	kn	kn	PROPN
ejpam-6046	126	22	is	be	AUX
ejpam-6046	126	23	n(n−	n(n−	PROPN
ejpam-6046	126	24	1	1	NUM
ejpam-6046	126	25	)	)	PUNCT
ejpam-6046	126	26	2	2	NUM
ejpam-6046	126	27	.	.	PUNCT
ejpam-6046	127	1	notation	notation	NOUN
ejpam-6046	127	2	:	:	PUNCT
ejpam-6046	127	3	let	let	VERB
ejpam-6046	127	4	kn	kn	PROPN
ejpam-6046	127	5	be	be	AUX
ejpam-6046	127	6	a	a	DET
ejpam-6046	127	7	complete	complete	ADJ
ejpam-6046	127	8	graph	graph	NOUN
ejpam-6046	127	9	of	of	ADP
ejpam-6046	127	10	order	order	NOUN
ejpam-6046	127	11	n.	n.	NOUN
ejpam-6046	127	12	we	we	PRON
ejpam-6046	127	13	use	use	VERB
ejpam-6046	127	14	the	the	DET
ejpam-6046	127	15	following	following	ADJ
ejpam-6046	127	16	notations	notation	NOUN
ejpam-6046	127	17	:	:	PUNCT
ejpam-6046	127	18	i.	i.	PROPN
ejpam-6046	127	19	v	v	PROPN
ejpam-6046	127	20	(	(	PUNCT
ejpam-6046	127	21	kn	kn	PROPN
ejpam-6046	127	22	)	)	PUNCT
ejpam-6046	127	23	=	=	SYM
ejpam-6046	127	24	{	{	PUNCT
ejpam-6046	127	25	v1	v1	PROPN
ejpam-6046	127	26	,	,	PUNCT
ejpam-6046	127	27	v2	v2	PROPN
ejpam-6046	127	28	,	,	PUNCT
ejpam-6046	127	29	.	.	PUNCT
ejpam-6046	127	30	.	.	PUNCT
ejpam-6046	127	31	.	.	PUNCT
ejpam-6046	128	1	,	,	PUNCT
ejpam-6046	128	2	vn	vn	PROPN
ejpam-6046	128	3	}	}	PUNCT
ejpam-6046	128	4	;	;	PUNCT
ejpam-6046	128	5	and	and	CCONJ
ejpam-6046	128	6	ii	ii	X
ejpam-6046	128	7	.	.	PUNCT
ejpam-6046	128	8	e(kn	e(kn	NUM
ejpam-6046	128	9	)	)	PUNCT
ejpam-6046	129	1	=	=	PRON
ejpam-6046	129	2	{	{	PUNCT
ejpam-6046	129	3	ei	ei	PROPN
ejpam-6046	129	4	,	,	PUNCT
ejpam-6046	129	5	j	j	NOUN
ejpam-6046	129	6	=	=	PUNCT
ejpam-6046	129	7	vivj	vivj	NOUN
ejpam-6046	129	8	:	:	PUNCT
ejpam-6046	129	9	vi	vi	ADJ
ejpam-6046	129	10	,	,	PUNCT
ejpam-6046	129	11	vj	vj	X
ejpam-6046	129	12	∈	∈	PROPN
ejpam-6046	129	13	v	v	PROPN
ejpam-6046	129	14	(	(	PUNCT
ejpam-6046	129	15	kn	kn	PROPN
ejpam-6046	129	16	)	)	PUNCT
ejpam-6046	129	17	}	}	PUNCT
ejpam-6046	129	18	.	.	PUNCT
ejpam-6046	130	1	illustration	illustration	NOUN
ejpam-6046	130	2	:	:	PUNCT
ejpam-6046	130	3	the	the	DET
ejpam-6046	130	4	complete	complete	ADJ
ejpam-6046	130	5	graph	graph	NOUN
ejpam-6046	130	6	k5	k5	PROPN
ejpam-6046	130	7	in	in	ADP
ejpam-6046	130	8	figure	figure	NOUN
ejpam-6046	130	9	6	6	NUM
ejpam-6046	130	10	is	be	AUX
ejpam-6046	130	11	labeled	label	VERB
ejpam-6046	130	12	using	use	VERB
ejpam-6046	130	13	the	the	DET
ejpam-6046	130	14	abovementioned	abovementioned	ADJ
ejpam-6046	130	15	notation	notation	NOUN
ejpam-6046	130	16	convention	convention	NOUN
ejpam-6046	130	17	.	.	PUNCT
ejpam-6046	131	1	v1	v1	PROPN
ejpam-6046	131	2	v2	v2	PROPN
ejpam-6046	131	3	v3v4	v3v4	PUNCT
ejpam-6046	131	4	v5	v5	PROPN
ejpam-6046	131	5	k5	k5	PROPN
ejpam-6046	131	6	:	:	PUNCT
ejpam-6046	131	7	e	e	X
ejpam-6046	131	8	1,2	1,2	NUM
ejpam-6046	131	9	e	e	X
ejpam-6046	131	10	1	1	NUM
ejpam-6046	131	11	,	,	PUNCT
ejpam-6046	131	12	3e	3e	X
ejpam-6046	131	13	1	1	NUM
ejpam-6046	131	14	,	,	PUNCT
ejpam-6046	131	15	4	4	NUM
ejpam-6046	131	16	e1,5	e1,5	NUM
ejpam-6046	131	17	e	e	NOUN
ejpam-6046	131	18	2	2	NUM
ejpam-6046	131	19	,	,	PUNCT
ejpam-6046	131	20	3	3	NUM
ejpam-6046	131	21	e	e	SYM
ejpam-6046	131	22	2	2	NUM
ejpam-6046	131	23	,	,	PUNCT
ejpam-6046	131	24	4	4	NUM
ejpam-6046	131	25	e2,5	e2,5	PROPN
ejpam-6046	131	26	e3,4	e3,4	ADJ
ejpam-6046	131	27	e	e	NOUN
ejpam-6046	131	28	3,5	3,5	NUM
ejpam-6046	131	29	e	e	NOUN
ejpam-6046	131	30	4,5	4,5	NUM
ejpam-6046	131	31	figure	figure	NOUN
ejpam-6046	131	32	6	6	NUM
ejpam-6046	131	33	:	:	PUNCT
ejpam-6046	131	34	the	the	DET
ejpam-6046	131	35	complete	complete	ADJ
ejpam-6046	131	36	graph	graph	NOUN
ejpam-6046	131	37	k5	k5	PROPN
ejpam-6046	131	38	j.	j.	PROPN
ejpam-6046	131	39	n.	n.	PROPN
ejpam-6046	131	40	ontulan	ontulan	PROPN
ejpam-6046	131	41	,	,	PUNCT
ejpam-6046	131	42	c.	c.	PROPN
ejpam-6046	131	43	m.	m.	NOUN
ejpam-6046	131	44	balingit	balingit	PROPN
ejpam-6046	131	45	/	/	SYM
ejpam-6046	131	46	eur	eur	PROPN
ejpam-6046	131	47	.	.	PUNCT
ejpam-6046	132	1	j.	j.	PROPN
ejpam-6046	132	2	pure	pure	PROPN
ejpam-6046	132	3	appl	appl	PROPN
ejpam-6046	132	4	.	.	PROPN
ejpam-6046	132	5	math	math	PROPN
ejpam-6046	132	6	,	,	PUNCT
ejpam-6046	132	7	18	18	NUM
ejpam-6046	132	8	(	(	PUNCT
ejpam-6046	132	9	2	2	NUM
ejpam-6046	132	10	)	)	PUNCT
ejpam-6046	132	11	(	(	PUNCT
ejpam-6046	132	12	2025	2025	NUM
ejpam-6046	132	13	)	)	PUNCT
ejpam-6046	132	14	,	,	PUNCT
ejpam-6046	132	15	6046	6046	NUM
ejpam-6046	132	16	7	7	NUM
ejpam-6046	132	17	of	of	ADP
ejpam-6046	132	18	14	14	NUM
ejpam-6046	132	19	theorem	theorem	NOUN
ejpam-6046	132	20	3	3	X
ejpam-6046	132	21	.	.	PUNCT
ejpam-6046	133	1	let	let	VERB
ejpam-6046	133	2	kn	kn	PROPN
ejpam-6046	133	3	be	be	AUX
ejpam-6046	133	4	a	a	DET
ejpam-6046	133	5	complete	complete	ADJ
ejpam-6046	133	6	graph	graph	NOUN
ejpam-6046	133	7	with	with	ADP
ejpam-6046	133	8	n	n	PRON
ejpam-6046	133	9	≥	≥	NUM
ejpam-6046	133	10	2	2	NUM
ejpam-6046	133	11	and	and	CCONJ
ejpam-6046	133	12	s	s	VERB
ejpam-6046	133	13	⊆	⊆	NUM
ejpam-6046	133	14	e(kn	e(kn	NUM
ejpam-6046	133	15	)	)	PUNCT
ejpam-6046	133	16	.	.	PUNCT
ejpam-6046	134	1	s	s	PROPN
ejpam-6046	135	1	∈	∈	PROPN
ejpam-6046	135	2	ide	ide	NOUN
ejpam-6046	135	3	kn	kn	PROPN
ejpam-6046	135	4	if	if	SCONJ
ejpam-6046	135	5	and	and	CCONJ
ejpam-6046	135	6	only	only	ADV
ejpam-6046	135	7	if	if	SCONJ
ejpam-6046	135	8	s	s	VERB
ejpam-6046	135	9	=	=	PUNCT
ejpam-6046	135	10	{	{	PUNCT
ejpam-6046	135	11	ei1,j1	ei1,j1	NOUN
ejpam-6046	135	12	,	,	PUNCT
ejpam-6046	135	13	.	.	PUNCT
ejpam-6046	135	14	.	.	PUNCT
ejpam-6046	135	15	.	.	PUNCT
ejpam-6046	136	1	,	,	PUNCT
ejpam-6046	136	2	eik	eik	PROPN
ejpam-6046	136	3	,	,	PUNCT
ejpam-6046	136	4	jk	jk	PROPN
ejpam-6046	136	5	}	}	PUNCT
ejpam-6046	136	6	such	such	ADJ
ejpam-6046	136	7	that	that	SCONJ
ejpam-6046	136	8	k	k	PROPN
ejpam-6046	136	9	=	=	PUNCT
ejpam-6046	136	10	|s|	|s|	PROPN
ejpam-6046	136	11	=	=	SYM
ejpam-6046	136	12	⌊	⌊	PROPN
ejpam-6046	136	13	n	n	ADV
ejpam-6046	136	14	2	2	NUM
ejpam-6046	136	15	⌋	⌋	NOUN
ejpam-6046	136	16	and	and	CCONJ
ejpam-6046	136	17	i1	i1	PROPN
ejpam-6046	136	18	̸=	̸=	PROPN
ejpam-6046	136	19	.	.	PUNCT
ejpam-6046	136	20	.	.	PUNCT
ejpam-6046	136	21	.	.	PUNCT
ejpam-6046	137	1	̸=	̸=	PROPN
ejpam-6046	137	2	ik	ik	PROPN
ejpam-6046	137	3	̸=	̸=	PROPN
ejpam-6046	137	4	j1	j1	PROPN
ejpam-6046	137	5	̸=	̸=	PROPN
ejpam-6046	137	6	.	.	PUNCT
ejpam-6046	137	7	.	.	PUNCT
ejpam-6046	137	8	.	.	PUNCT
ejpam-6046	138	1	̸=	̸=	PROPN
ejpam-6046	138	2	jk	jk	PROPN
ejpam-6046	138	3	.	.	PUNCT
ejpam-6046	139	1	proof	proof	NOUN
ejpam-6046	139	2	.	.	PUNCT
ejpam-6046	140	1	if	if	SCONJ
ejpam-6046	140	2	s	s	VERB
ejpam-6046	140	3	=	=	SYM
ejpam-6046	140	4	{	{	PUNCT
ejpam-6046	140	5	ei1,j1	ei1,j1	NOUN
ejpam-6046	140	6	,	,	PUNCT
ejpam-6046	140	7	.	.	PUNCT
ejpam-6046	140	8	.	.	PUNCT
ejpam-6046	141	1	.	.	PUNCT
ejpam-6046	142	1	,	,	PUNCT
ejpam-6046	142	2	eik	eik	PROPN
ejpam-6046	142	3	,	,	PUNCT
ejpam-6046	142	4	jk	jk	PROPN
ejpam-6046	142	5	}	}	PUNCT
ejpam-6046	142	6	is	be	AUX
ejpam-6046	142	7	as	as	SCONJ
ejpam-6046	142	8	described	describe	VERB
ejpam-6046	142	9	,	,	PUNCT
ejpam-6046	142	10	then	then	ADV
ejpam-6046	142	11	the	the	DET
ejpam-6046	142	12	condition	condition	NOUN
ejpam-6046	142	13	i1	i1	PROPN
ejpam-6046	142	14	̸=	̸=	PROPN
ejpam-6046	142	15	.	.	PUNCT
ejpam-6046	142	16	.	.	PUNCT
ejpam-6046	142	17	.	.	PUNCT
ejpam-6046	143	1	̸=	̸=	PROPN
ejpam-6046	143	2	ik	ik	PROPN
ejpam-6046	143	3	̸=	̸=	PROPN
ejpam-6046	143	4	j1	j1	PROPN
ejpam-6046	143	5	̸=	̸=	PROPN
ejpam-6046	143	6	.	.	PUNCT
ejpam-6046	143	7	.	.	PUNCT
ejpam-6046	143	8	.	.	PUNCT
ejpam-6046	144	1	̸=	̸=	PROPN
ejpam-6046	144	2	jk	jk	PROPN
ejpam-6046	144	3	implies	imply	VERB
ejpam-6046	144	4	that	that	SCONJ
ejpam-6046	144	5	s	s	VERB
ejpam-6046	144	6	is	be	AUX
ejpam-6046	144	7	independent	independent	ADJ
ejpam-6046	144	8	,	,	PUNCT
ejpam-6046	144	9	by	by	ADP
ejpam-6046	144	10	remark	remark	NOUN
ejpam-6046	144	11	1	1	NUM
ejpam-6046	144	12	.	.	PUNCT
ejpam-6046	145	1	now	now	ADV
ejpam-6046	145	2	,	,	PUNCT
ejpam-6046	145	3	let	let	VERB
ejpam-6046	145	4	ep	ep	PROPN
ejpam-6046	145	5	,	,	PUNCT
ejpam-6046	145	6	q	q	PROPN
ejpam-6046	145	7	∈	∈	PROPN
ejpam-6046	145	8	e(kn	e(kn	NUM
ejpam-6046	145	9	)	)	PUNCT
ejpam-6046	145	10	\	\	PUNCT
ejpam-6046	146	1	s.	s.	PROPN
ejpam-6046	146	2	if	if	SCONJ
ejpam-6046	146	3	n	n	PROPN
ejpam-6046	146	4	is	be	AUX
ejpam-6046	146	5	odd	odd	ADJ
ejpam-6046	146	6	,	,	PUNCT
ejpam-6046	146	7	then	then	ADV
ejpam-6046	146	8	k	k	PROPN
ejpam-6046	146	9	=	=	PUNCT
ejpam-6046	146	10	n−	n−	NOUN
ejpam-6046	146	11	1	1	NUM
ejpam-6046	146	12	2	2	NUM
ejpam-6046	146	13	and	and	CCONJ
ejpam-6046	146	14	so	so	ADV
ejpam-6046	146	15	|{i1	|{i1	PROPN
ejpam-6046	146	16	,	,	PUNCT
ejpam-6046	146	17	.	.	PUNCT
ejpam-6046	146	18	.	.	PUNCT
ejpam-6046	147	1	.	.	PUNCT
ejpam-6046	148	1	,	,	PUNCT
ejpam-6046	148	2	ik	ik	PROPN
ejpam-6046	148	3	,	,	PUNCT
ejpam-6046	148	4	j1	j1	PROPN
ejpam-6046	148	5	,	,	PUNCT
ejpam-6046	148	6	.	.	PUNCT
ejpam-6046	148	7	.	.	PUNCT
ejpam-6046	149	1	.	.	PUNCT
ejpam-6046	150	1	,	,	PUNCT
ejpam-6046	150	2	jk}|	jk}|	X
ejpam-6046	150	3	=	=	SYM
ejpam-6046	150	4	2k	2k	NUM
ejpam-6046	150	5	=	=	SYM
ejpam-6046	150	6	n	n	CCONJ
ejpam-6046	150	7	−	−	NOUN
ejpam-6046	150	8	1	1	NUM
ejpam-6046	150	9	.	.	PUNCT
ejpam-6046	151	1	this	this	PRON
ejpam-6046	151	2	means	mean	VERB
ejpam-6046	151	3	that	that	SCONJ
ejpam-6046	151	4	,	,	PUNCT
ejpam-6046	151	5	if	if	SCONJ
ejpam-6046	151	6	p	p	PROPN
ejpam-6046	151	7	∈	∈	PROPN
ejpam-6046	151	8	{	{	PUNCT
ejpam-6046	151	9	i1	i1	NOUN
ejpam-6046	151	10	,	,	PUNCT
ejpam-6046	151	11	.	.	PUNCT
ejpam-6046	151	12	.	.	PUNCT
ejpam-6046	152	1	.	.	PUNCT
ejpam-6046	153	1	,	,	PUNCT
ejpam-6046	153	2	ik	ik	PROPN
ejpam-6046	153	3	,	,	PUNCT
ejpam-6046	153	4	j1	j1	PROPN
ejpam-6046	153	5	,	,	PUNCT
ejpam-6046	153	6	.	.	PUNCT
ejpam-6046	153	7	.	.	PUNCT
ejpam-6046	154	1	.	.	PUNCT
ejpam-6046	155	1	,	,	PUNCT
ejpam-6046	155	2	jk	jk	PROPN
ejpam-6046	155	3	}	}	PUNCT
ejpam-6046	155	4	,	,	PUNCT
ejpam-6046	155	5	then	then	ADV
ejpam-6046	155	6	ep	ep	PROPN
ejpam-6046	155	7	,	,	PUNCT
ejpam-6046	155	8	q	q	PROPN
ejpam-6046	155	9	is	be	AUX
ejpam-6046	155	10	adjacent	adjacent	ADJ
ejpam-6046	155	11	to	to	ADP
ejpam-6046	155	12	one	one	NUM
ejpam-6046	155	13	of	of	ADP
ejpam-6046	155	14	the	the	DET
ejpam-6046	155	15	edges	edge	NOUN
ejpam-6046	155	16	in	in	ADP
ejpam-6046	155	17	s.	s.	PROPN
ejpam-6046	155	18	also	also	ADV
ejpam-6046	155	19	,	,	PUNCT
ejpam-6046	155	20	if	if	SCONJ
ejpam-6046	155	21	p	p	X
ejpam-6046	155	22	/∈	/∈	PUNCT
ejpam-6046	155	23	{	{	PUNCT
ejpam-6046	155	24	i1	i1	PROPN
ejpam-6046	155	25	,	,	PUNCT
ejpam-6046	155	26	.	.	PUNCT
ejpam-6046	155	27	.	.	PUNCT
ejpam-6046	156	1	.	.	PUNCT
ejpam-6046	157	1	,	,	PUNCT
ejpam-6046	157	2	ik	ik	PROPN
ejpam-6046	157	3	,	,	PUNCT
ejpam-6046	157	4	j1	j1	PROPN
ejpam-6046	157	5	,	,	PUNCT
ejpam-6046	157	6	.	.	PUNCT
ejpam-6046	157	7	.	.	PUNCT
ejpam-6046	158	1	.	.	PUNCT
ejpam-6046	159	1	,	,	PUNCT
ejpam-6046	159	2	jk	jk	PROPN
ejpam-6046	159	3	}	}	PUNCT
ejpam-6046	159	4	,	,	PUNCT
ejpam-6046	159	5	then	then	ADV
ejpam-6046	159	6	p	p	PROPN
ejpam-6046	159	7	is	be	AUX
ejpam-6046	159	8	the	the	DET
ejpam-6046	159	9	remaining	remain	VERB
ejpam-6046	159	10	element	element	NOUN
ejpam-6046	159	11	of	of	ADP
ejpam-6046	159	12	[	[	X
ejpam-6046	159	13	n	n	X
ejpam-6046	159	14	]	]	PUNCT
ejpam-6046	159	15	not	not	PART
ejpam-6046	159	16	in	in	ADP
ejpam-6046	159	17	{	{	PUNCT
ejpam-6046	159	18	i1	i1	NOUN
ejpam-6046	159	19	,	,	PUNCT
ejpam-6046	159	20	.	.	PUNCT
ejpam-6046	159	21	.	.	PUNCT
ejpam-6046	160	1	.	.	PUNCT
ejpam-6046	161	1	,	,	PUNCT
ejpam-6046	161	2	ik	ik	PROPN
ejpam-6046	161	3	,	,	PUNCT
ejpam-6046	161	4	j1	j1	PROPN
ejpam-6046	161	5	,	,	PUNCT
ejpam-6046	161	6	.	.	PUNCT
ejpam-6046	161	7	.	.	PUNCT
ejpam-6046	161	8	.	.	PUNCT
ejpam-6046	162	1	,	,	PUNCT
ejpam-6046	162	2	jk	jk	PROPN
ejpam-6046	162	3	}	}	PUNCT
ejpam-6046	162	4	,	,	PUNCT
ejpam-6046	162	5	implying	imply	VERB
ejpam-6046	162	6	that	that	SCONJ
ejpam-6046	162	7	q	q	PUNCT
ejpam-6046	162	8	∈	∈	PROPN
ejpam-6046	162	9	{	{	PUNCT
ejpam-6046	162	10	i1	i1	NOUN
ejpam-6046	162	11	,	,	PUNCT
ejpam-6046	162	12	.	.	PUNCT
ejpam-6046	162	13	.	.	PUNCT
ejpam-6046	163	1	.	.	PUNCT
ejpam-6046	164	1	,	,	PUNCT
ejpam-6046	164	2	ik	ik	PROPN
ejpam-6046	164	3	,	,	PUNCT
ejpam-6046	164	4	j1	j1	PROPN
ejpam-6046	164	5	,	,	PUNCT
ejpam-6046	164	6	.	.	PUNCT
ejpam-6046	164	7	.	.	PUNCT
ejpam-6046	164	8	.	.	PUNCT
ejpam-6046	165	1	,	,	PUNCT
ejpam-6046	165	2	jk	jk	PROPN
ejpam-6046	165	3	}	}	PUNCT
ejpam-6046	165	4	since	since	SCONJ
ejpam-6046	165	5	p	p	PROPN
ejpam-6046	165	6	̸=	̸=	PROPN
ejpam-6046	165	7	q.	q.	NOUN
ejpam-6046	165	8	therefore	therefore	ADV
ejpam-6046	165	9	,	,	PUNCT
ejpam-6046	165	10	by	by	ADP
ejpam-6046	165	11	remark	remark	NOUN
ejpam-6046	165	12	1	1	NUM
ejpam-6046	165	13	ep	ep	PROPN
ejpam-6046	165	14	,	,	PUNCT
ejpam-6046	165	15	q	q	X
ejpam-6046	165	16	is	be	AUX
ejpam-6046	165	17	adjacent	adjacent	ADJ
ejpam-6046	165	18	to	to	ADP
ejpam-6046	165	19	an	an	DET
ejpam-6046	165	20	edge	edge	NOUN
ejpam-6046	165	21	in	in	ADP
ejpam-6046	165	22	s.	s.	PROPN
ejpam-6046	165	23	if	if	SCONJ
ejpam-6046	165	24	n	n	PRON
ejpam-6046	165	25	is	be	AUX
ejpam-6046	165	26	even	even	ADV
ejpam-6046	165	27	,	,	PUNCT
ejpam-6046	165	28	then	then	ADV
ejpam-6046	165	29	k	k	PROPN
ejpam-6046	165	30	=	=	PUNCT
ejpam-6046	165	31	n	n	PRON
ejpam-6046	165	32	2	2	NUM
ejpam-6046	165	33	and	and	CCONJ
ejpam-6046	165	34	|{i1	|{i1	PROPN
ejpam-6046	165	35	,	,	PUNCT
ejpam-6046	165	36	.	.	PUNCT
ejpam-6046	165	37	.	.	PUNCT
ejpam-6046	165	38	.	.	PUNCT
ejpam-6046	166	1	,	,	PUNCT
ejpam-6046	166	2	ik	ik	PROPN
ejpam-6046	166	3	,	,	PUNCT
ejpam-6046	166	4	j1	j1	PROPN
ejpam-6046	166	5	,	,	PUNCT
ejpam-6046	166	6	.	.	PUNCT
ejpam-6046	166	7	.	.	PUNCT
ejpam-6046	167	1	.	.	PUNCT
ejpam-6046	168	1	,	,	PUNCT
ejpam-6046	168	2	jk}|	jk}|	X
ejpam-6046	168	3	=	=	SYM
ejpam-6046	168	4	2k	2k	NUM
ejpam-6046	168	5	=	=	SYM
ejpam-6046	169	1	n	n	CCONJ
ejpam-6046	169	2	this	this	PRON
ejpam-6046	169	3	imply	imply	VERB
ejpam-6046	169	4	that	that	DET
ejpam-6046	169	5	|{i1	|{i1	NOUN
ejpam-6046	169	6	,	,	PUNCT
ejpam-6046	169	7	.	.	PUNCT
ejpam-6046	169	8	.	.	PUNCT
ejpam-6046	170	1	.	.	PUNCT
ejpam-6046	171	1	,	,	PUNCT
ejpam-6046	171	2	ik	ik	PROPN
ejpam-6046	171	3	,	,	PUNCT
ejpam-6046	171	4	j1	j1	PROPN
ejpam-6046	171	5	,	,	PUNCT
ejpam-6046	171	6	.	.	PUNCT
ejpam-6046	171	7	.	.	PUNCT
ejpam-6046	172	1	.	.	PUNCT
ejpam-6046	173	1	,	,	PUNCT
ejpam-6046	173	2	jk}|	jk}|	X
ejpam-6046	174	1	=	=	PUNCT
ejpam-6046	175	1	[	[	X
ejpam-6046	175	2	n	n	X
ejpam-6046	175	3	]	]	PUNCT
ejpam-6046	175	4	.	.	PUNCT
ejpam-6046	176	1	thus	thus	ADV
ejpam-6046	176	2	,	,	PUNCT
ejpam-6046	176	3	if	if	SCONJ
ejpam-6046	176	4	p	p	X
ejpam-6046	176	5	,	,	PUNCT
ejpam-6046	176	6	q	q	PROPN
ejpam-6046	176	7	∈	∈	PROPN
ejpam-6046	176	8	{	{	PUNCT
ejpam-6046	176	9	i1	i1	NOUN
ejpam-6046	176	10	,	,	PUNCT
ejpam-6046	176	11	.	.	PUNCT
ejpam-6046	176	12	.	.	PUNCT
ejpam-6046	176	13	.	.	PUNCT
ejpam-6046	176	14	,	,	PUNCT
ejpam-6046	176	15	ik	ik	PROPN
ejpam-6046	176	16	,	,	PUNCT
ejpam-6046	176	17	j1	j1	PROPN
ejpam-6046	176	18	,	,	PUNCT
ejpam-6046	176	19	.	.	PUNCT
ejpam-6046	176	20	.	.	PUNCT
ejpam-6046	176	21	.	.	PUNCT
ejpam-6046	177	1	,	,	PUNCT
ejpam-6046	177	2	jk	jk	NOUN
ejpam-6046	177	3	}	}	PUNCT
ejpam-6046	177	4	.	.	PUNCT
ejpam-6046	178	1	by	by	ADP
ejpam-6046	178	2	remark	remark	NOUN
ejpam-6046	178	3	1	1	NUM
ejpam-6046	178	4	,	,	PUNCT
ejpam-6046	178	5	ep	ep	PROPN
ejpam-6046	178	6	,	,	PUNCT
ejpam-6046	178	7	q	q	PROPN
ejpam-6046	178	8	is	be	AUX
ejpam-6046	178	9	adjacent	adjacent	ADJ
ejpam-6046	178	10	to	to	ADP
ejpam-6046	178	11	one	one	NUM
ejpam-6046	178	12	of	of	ADP
ejpam-6046	178	13	the	the	DET
ejpam-6046	178	14	edges	edge	NOUN
ejpam-6046	178	15	in	in	ADP
ejpam-6046	178	16	s.	s.	PROPN
ejpam-6046	178	17	hence	hence	ADV
ejpam-6046	178	18	,	,	PUNCT
ejpam-6046	178	19	s	s	VERB
ejpam-6046	178	20	is	be	AUX
ejpam-6046	178	21	an	an	DET
ejpam-6046	178	22	edge	edge	NOUN
ejpam-6046	178	23	dominating	dominating	NOUN
ejpam-6046	178	24	set	set	NOUN
ejpam-6046	178	25	of	of	ADP
ejpam-6046	178	26	kn	kn	PROPN
ejpam-6046	178	27	.	.	PUNCT
ejpam-6046	179	1	therefore	therefore	ADV
ejpam-6046	179	2	,	,	PUNCT
ejpam-6046	179	3	s	s	PROPN
ejpam-6046	179	4	∈	∈	PROPN
ejpam-6046	179	5	ide	ide	NOUN
ejpam-6046	179	6	kn	kn	PROPN
ejpam-6046	179	7	.	.	PUNCT
ejpam-6046	180	1	conversely	conversely	ADV
ejpam-6046	180	2	,	,	PUNCT
ejpam-6046	180	3	suppose	suppose	VERB
ejpam-6046	180	4	s	s	NOUN
ejpam-6046	180	5	is	be	AUX
ejpam-6046	180	6	not	not	PART
ejpam-6046	180	7	as	as	SCONJ
ejpam-6046	180	8	described	describe	VERB
ejpam-6046	180	9	.	.	PUNCT
ejpam-6046	181	1	if	if	SCONJ
ejpam-6046	181	2	|s|	|s|	NOUN
ejpam-6046	181	3	>	>	X
ejpam-6046	181	4	⌊	⌊	PROPN
ejpam-6046	181	5	n	n	ADV
ejpam-6046	181	6	2	2	NUM
ejpam-6046	181	7	⌋	⌋	NOUN
ejpam-6046	181	8	,	,	PUNCT
ejpam-6046	181	9	then	then	ADV
ejpam-6046	181	10	|{i1	|{i1	PROPN
ejpam-6046	181	11	,	,	PUNCT
ejpam-6046	181	12	.	.	PUNCT
ejpam-6046	181	13	.	.	PUNCT
ejpam-6046	181	14	.	.	PUNCT
ejpam-6046	181	15	,	,	PUNCT
ejpam-6046	181	16	ik	ik	PROPN
ejpam-6046	181	17	,	,	PUNCT
ejpam-6046	181	18	j1	j1	PROPN
ejpam-6046	181	19	,	,	PUNCT
ejpam-6046	181	20	.	.	PUNCT
ejpam-6046	181	21	.	.	PUNCT
ejpam-6046	181	22	.	.	PUNCT
ejpam-6046	182	1	,	,	PUNCT
ejpam-6046	182	2	jk}|	jk}|	X
ejpam-6046	182	3	=	=	SYM
ejpam-6046	182	4	2k	2k	PROPN
ejpam-6046	182	5	≥	≥	NOUN
ejpam-6046	182	6	n+1	n+1	NUM
ejpam-6046	182	7	implying	imply	VERB
ejpam-6046	182	8	that	that	SCONJ
ejpam-6046	182	9	two	two	NUM
ejpam-6046	182	10	of	of	ADP
ejpam-6046	182	11	the	the	DET
ejpam-6046	182	12	subscripts	subscript	NOUN
ejpam-6046	182	13	in	in	ADP
ejpam-6046	182	14	s	s	NOUN
ejpam-6046	182	15	are	be	AUX
ejpam-6046	182	16	equal	equal	ADJ
ejpam-6046	182	17	.	.	PUNCT
ejpam-6046	183	1	by	by	ADP
ejpam-6046	183	2	remark	remark	NOUN
ejpam-6046	183	3	1	1	NUM
ejpam-6046	183	4	,	,	PUNCT
ejpam-6046	183	5	there	there	PRON
ejpam-6046	183	6	exists	exist	VERB
ejpam-6046	183	7	an	an	DET
ejpam-6046	183	8	edge	edge	NOUN
ejpam-6046	183	9	in	in	ADP
ejpam-6046	183	10	s	s	PRON
ejpam-6046	183	11	that	that	PRON
ejpam-6046	183	12	share	share	VERB
ejpam-6046	183	13	a	a	DET
ejpam-6046	183	14	common	common	ADJ
ejpam-6046	183	15	vertex	vertex	NOUN
ejpam-6046	183	16	,	,	PUNCT
ejpam-6046	183	17	and	and	CCONJ
ejpam-6046	183	18	so	so	ADV
ejpam-6046	183	19	s	s	VERB
ejpam-6046	183	20	is	be	AUX
ejpam-6046	183	21	not	not	PART
ejpam-6046	183	22	independent	independent	ADJ
ejpam-6046	183	23	.	.	PUNCT
ejpam-6046	184	1	also	also	ADV
ejpam-6046	184	2	,	,	PUNCT
ejpam-6046	184	3	if	if	SCONJ
ejpam-6046	184	4	|s|	|s|	NOUN
ejpam-6046	184	5	<	<	X
ejpam-6046	184	6	⌊	⌊	PROPN
ejpam-6046	184	7	n	n	PRON
ejpam-6046	184	8	2	2	NUM
ejpam-6046	184	9	⌋	⌋	NOUN
ejpam-6046	184	10	,	,	PUNCT
ejpam-6046	184	11	then	then	ADV
ejpam-6046	184	12	|{i1	|{i1	PROPN
ejpam-6046	184	13	,	,	PUNCT
ejpam-6046	184	14	.	.	PUNCT
ejpam-6046	184	15	.	.	PUNCT
ejpam-6046	184	16	.	.	PUNCT
ejpam-6046	185	1	,	,	PUNCT
ejpam-6046	185	2	ik	ik	PROPN
ejpam-6046	185	3	,	,	PUNCT
ejpam-6046	185	4	j1	j1	PROPN
ejpam-6046	185	5	,	,	PUNCT
ejpam-6046	185	6	.	.	PUNCT
ejpam-6046	185	7	.	.	PUNCT
ejpam-6046	186	1	.	.	PUNCT
ejpam-6046	187	1	,	,	PUNCT
ejpam-6046	187	2	jk}|	jk}|	X
ejpam-6046	187	3	=	=	PUNCT
ejpam-6046	187	4	2k	2k	PROPN
ejpam-6046	187	5	≤	≤	NOUN
ejpam-6046	187	6	n	n	CCONJ
ejpam-6046	187	7	−	−	PROPN
ejpam-6046	187	8	2	2	NUM
ejpam-6046	187	9	.	.	PUNCT
ejpam-6046	188	1	this	this	PRON
ejpam-6046	188	2	means	mean	VERB
ejpam-6046	188	3	that	that	SCONJ
ejpam-6046	188	4	there	there	PRON
ejpam-6046	188	5	exist	exist	VERB
ejpam-6046	188	6	p	p	PRON
ejpam-6046	188	7	,	,	PUNCT
ejpam-6046	188	8	q	q	NOUN
ejpam-6046	188	9	∈	∈	PROPN
ejpam-6046	189	1	[	[	X
ejpam-6046	189	2	n	n	CCONJ
ejpam-6046	189	3	]	]	PUNCT
ejpam-6046	189	4	not	not	PART
ejpam-6046	189	5	appearing	appear	VERB
ejpam-6046	189	6	in	in	ADP
ejpam-6046	189	7	{	{	PUNCT
ejpam-6046	189	8	ei1,j1	ei1,j1	NOUN
ejpam-6046	189	9	,	,	PUNCT
ejpam-6046	189	10	.	.	PUNCT
ejpam-6046	189	11	.	.	PUNCT
ejpam-6046	190	1	.	.	PUNCT
ejpam-6046	191	1	,	,	PUNCT
ejpam-6046	191	2	eik	eik	PROPN
ejpam-6046	191	3	,	,	PUNCT
ejpam-6046	191	4	jk	jk	PROPN
ejpam-6046	191	5	}	}	PUNCT
ejpam-6046	191	6	.	.	PUNCT
ejpam-6046	192	1	so	so	ADV
ejpam-6046	192	2	,	,	PUNCT
ejpam-6046	192	3	there	there	PRON
ejpam-6046	192	4	exists	exist	VERB
ejpam-6046	192	5	an	an	DET
ejpam-6046	192	6	edge	edge	NOUN
ejpam-6046	192	7	ep	ep	NOUN
ejpam-6046	192	8	,	,	PUNCT
ejpam-6046	192	9	q	q	NOUN
ejpam-6046	192	10	in	in	ADP
ejpam-6046	192	11	e(kn	e(kn	NUM
ejpam-6046	192	12	)	)	PUNCT
ejpam-6046	192	13	\	\	PUNCT
ejpam-6046	193	1	s	s	PART
ejpam-6046	194	1	which	which	PRON
ejpam-6046	194	2	is	be	AUX
ejpam-6046	194	3	not	not	PART
ejpam-6046	194	4	adjacent	adjacent	ADJ
ejpam-6046	194	5	to	to	ADP
ejpam-6046	194	6	any	any	PRON
ejpam-6046	194	7	of	of	ADP
ejpam-6046	194	8	the	the	DET
ejpam-6046	194	9	edges	edge	NOUN
ejpam-6046	194	10	in	in	ADP
ejpam-6046	194	11	s.	s.	PROPN
ejpam-6046	194	12	therefore	therefore	ADV
ejpam-6046	194	13	,	,	PUNCT
ejpam-6046	194	14	s	s	VERB
ejpam-6046	194	15	is	be	AUX
ejpam-6046	194	16	not	not	PART
ejpam-6046	194	17	an	an	DET
ejpam-6046	194	18	edge	edge	NOUN
ejpam-6046	194	19	dominating	dominating	NOUN
ejpam-6046	194	20	set	set	NOUN
ejpam-6046	194	21	of	of	ADP
ejpam-6046	194	22	kn	kn	PROPN
ejpam-6046	194	23	.	.	PUNCT
ejpam-6046	194	24	suppose	suppose	VERB
ejpam-6046	194	25	that	that	SCONJ
ejpam-6046	194	26	s	s	VERB
ejpam-6046	194	27	contains	contain	VERB
ejpam-6046	194	28	elements	element	NOUN
ejpam-6046	194	29	ei1,j1	ei1,j1	NOUN
ejpam-6046	194	30	and	and	CCONJ
ejpam-6046	194	31	ei2,j2	ei2,j2	NOUN
ejpam-6046	194	32	such	such	ADJ
ejpam-6046	194	33	that	that	SCONJ
ejpam-6046	194	34	{	{	PUNCT
ejpam-6046	194	35	i1	i1	PROPN
ejpam-6046	194	36	,	,	PUNCT
ejpam-6046	194	37	j1	j1	PROPN
ejpam-6046	194	38	}	}	PUNCT
ejpam-6046	194	39	∩	∩	NOUN
ejpam-6046	194	40	{	{	PUNCT
ejpam-6046	194	41	i2	i2	PROPN
ejpam-6046	194	42	,	,	PUNCT
ejpam-6046	194	43	j2	j2	PROPN
ejpam-6046	194	44	}	}	PUNCT
ejpam-6046	194	45	̸=	̸=	PROPN
ejpam-6046	194	46	∅.	∅.	VERB
ejpam-6046	194	47	then	then	ADV
ejpam-6046	194	48	s	s	VERB
ejpam-6046	194	49	is	be	AUX
ejpam-6046	194	50	not	not	PART
ejpam-6046	194	51	an	an	DET
ejpam-6046	194	52	independent	independent	ADJ
ejpam-6046	194	53	set	set	NOUN
ejpam-6046	194	54	.	.	PUNCT
ejpam-6046	195	1	■	■	PUNCT
ejpam-6046	195	2	theorem	theorem	ADJ
ejpam-6046	195	3	4	4	NUM
ejpam-6046	195	4	.	.	PUNCT
ejpam-6046	195	5	for	for	ADP
ejpam-6046	195	6	the	the	DET
ejpam-6046	195	7	complete	complete	ADJ
ejpam-6046	195	8	graph	graph	NOUN
ejpam-6046	195	9	kn	kn	PROPN
ejpam-6046	195	10	with	with	ADP
ejpam-6046	195	11	n	n	PRON
ejpam-6046	195	12	≥	≥	NUM
ejpam-6046	195	13	2	2	NUM
ejpam-6046	195	14	,	,	PUNCT
ejpam-6046	195	15	|ide	|ide	SCONJ
ejpam-6046	195	16	kn	kn	PROPN
ejpam-6046	195	17	|	|	ADV
ejpam-6046	195	18	=	=	SYM
ejpam-6046	195	19	n	n	X
ejpam-6046	195	20	!	!	X
ejpam-6046	195	21	2k	2k	NUM
ejpam-6046	195	22	·	·	PUNCT
ejpam-6046	196	1	k	k	X
ejpam-6046	196	2	!	!	PUNCT
ejpam-6046	196	3	,	,	PUNCT
ejpam-6046	196	4	where	where	SCONJ
ejpam-6046	196	5	k	k	NOUN
ejpam-6046	196	6	=	=	SYM
ejpam-6046	196	7	⌊	⌊	PROPN
ejpam-6046	196	8	n	n	ADV
ejpam-6046	196	9	2	2	NUM
ejpam-6046	196	10	⌋	⌋	NOUN
ejpam-6046	196	11	.	.	PUNCT
ejpam-6046	197	1	proof	proof	NOUN
ejpam-6046	197	2	.	.	PUNCT
ejpam-6046	198	1	in	in	ADP
ejpam-6046	198	2	view	view	NOUN
ejpam-6046	198	3	of	of	ADP
ejpam-6046	198	4	theorem	theorem	NOUN
ejpam-6046	198	5	3	3	NUM
ejpam-6046	198	6	,	,	PUNCT
ejpam-6046	198	7	an	an	DET
ejpam-6046	198	8	ieds	ied	NOUN
ejpam-6046	198	9	of	of	ADP
ejpam-6046	198	10	kn	kn	PROPN
ejpam-6046	198	11	is	be	AUX
ejpam-6046	198	12	formed	form	VERB
ejpam-6046	198	13	by	by	ADP
ejpam-6046	198	14	choosing	choose	VERB
ejpam-6046	198	15	the	the	DET
ejpam-6046	198	16	k	k	PROPN
ejpam-6046	198	17	pairwise	pairwise	PROPN
ejpam-6046	198	18	disjoint	disjoint	NOUN
ejpam-6046	198	19	2	2	NUM
ejpam-6046	198	20	-	-	PUNCT
ejpam-6046	198	21	element	element	NOUN
ejpam-6046	198	22	subsets	subset	NOUN
ejpam-6046	198	23	{	{	PUNCT
ejpam-6046	198	24	i1	i1	PROPN
ejpam-6046	198	25	,	,	PUNCT
ejpam-6046	198	26	j1	j1	PROPN
ejpam-6046	198	27	}	}	PUNCT
ejpam-6046	198	28	,	,	PUNCT
ejpam-6046	198	29	{	{	PUNCT
ejpam-6046	198	30	i2	i2	PROPN
ejpam-6046	198	31	,	,	PUNCT
ejpam-6046	198	32	j2	j2	PROPN
ejpam-6046	198	33	}	}	PUNCT
ejpam-6046	198	34	,	,	PUNCT
ejpam-6046	198	35	.	.	PUNCT
ejpam-6046	198	36	.	.	PUNCT
ejpam-6046	198	37	.	.	PUNCT
ejpam-6046	199	1	,	,	PUNCT
ejpam-6046	199	2	{	{	PUNCT
ejpam-6046	199	3	ik	ik	PROPN
ejpam-6046	199	4	,	,	PUNCT
ejpam-6046	199	5	jk	jk	PROPN
ejpam-6046	199	6	}	}	PUNCT
ejpam-6046	199	7	of	of	ADP
ejpam-6046	199	8	[	[	X
ejpam-6046	199	9	n	n	X
ejpam-6046	199	10	]	]	X
ejpam-6046	199	11	where	where	SCONJ
ejpam-6046	199	12	k	k	NOUN
ejpam-6046	199	13	=	=	SYM
ejpam-6046	199	14	⌊	⌊	PROPN
ejpam-6046	199	15	n	n	ADV
ejpam-6046	199	16	2	2	NUM
ejpam-6046	199	17	⌋	⌋	NOUN
ejpam-6046	199	18	.	.	PUNCT
ejpam-6046	200	1	there	there	PRON
ejpam-6046	200	2	are	be	VERB
ejpam-6046	200	3	(	(	PUNCT
ejpam-6046	200	4	n	n	PROPN
ejpam-6046	200	5	2	2	NUM
ejpam-6046	200	6	)	)	PUNCT
ejpam-6046	200	7	ways	way	NOUN
ejpam-6046	200	8	to	to	PART
ejpam-6046	200	9	choose	choose	VERB
ejpam-6046	200	10	2	2	NUM
ejpam-6046	200	11	elements	element	NOUN
ejpam-6046	200	12	from	from	ADP
ejpam-6046	200	13	n	n	PRON
ejpam-6046	200	14	objects	object	NOUN
ejpam-6046	200	15	,	,	PUNCT
ejpam-6046	200	16	(	(	PUNCT
ejpam-6046	200	17	n−	n−	NOUN
ejpam-6046	200	18	2	2	NUM
ejpam-6046	200	19	2	2	NUM
ejpam-6046	200	20	)	)	PUNCT
ejpam-6046	200	21	ways	way	NOUN
ejpam-6046	200	22	to	to	PART
ejpam-6046	200	23	choose	choose	VERB
ejpam-6046	200	24	2	2	NUM
ejpam-6046	200	25	elements	element	NOUN
ejpam-6046	200	26	from	from	ADP
ejpam-6046	200	27	n−2	n−2	PROPN
ejpam-6046	200	28	objects	object	NOUN
ejpam-6046	200	29	,	,	PUNCT
ejpam-6046	200	30	.	.	PUNCT
ejpam-6046	200	31	.	.	PUNCT
ejpam-6046	200	32	.	.	PUNCT
ejpam-6046	201	1	,	,	PUNCT
ejpam-6046	202	1	and	and	CCONJ
ejpam-6046	202	2	(	(	PUNCT
ejpam-6046	202	3	n−	n−	NOUN
ejpam-6046	202	4	2k	2k	NOUN
ejpam-6046	202	5	+	+	CCONJ
ejpam-6046	202	6	2	2	NUM
ejpam-6046	202	7	2	2	NUM
ejpam-6046	202	8	)	)	PUNCT
ejpam-6046	202	9	ways	way	NOUN
ejpam-6046	202	10	to	to	PART
ejpam-6046	202	11	select	select	VERB
ejpam-6046	202	12	the	the	DET
ejpam-6046	202	13	last	last	ADJ
ejpam-6046	202	14	2	2	NUM
ejpam-6046	202	15	elements	element	NOUN
ejpam-6046	202	16	from	from	ADP
ejpam-6046	202	17	the	the	DET
ejpam-6046	202	18	remaining	remain	VERB
ejpam-6046	202	19	n−	n−	NOUN
ejpam-6046	202	20	2k	2k	NOUN
ejpam-6046	202	21	+	+	CCONJ
ejpam-6046	202	22	2	2	NUM
ejpam-6046	202	23	objects	object	NOUN
ejpam-6046	202	24	.	.	PUNCT
ejpam-6046	203	1	in	in	ADP
ejpam-6046	203	2	total	total	NOUN
ejpam-6046	203	3	,	,	PUNCT
ejpam-6046	203	4	given	give	VERB
ejpam-6046	203	5	that	that	SCONJ
ejpam-6046	203	6	n−	n−	PROPN
ejpam-6046	203	7	2k	2k	NOUN
ejpam-6046	203	8	is	be	AUX
ejpam-6046	203	9	either	either	CCONJ
ejpam-6046	203	10	0	0	NUM
ejpam-6046	203	11	or	or	CCONJ
ejpam-6046	203	12	1	1	NUM
ejpam-6046	203	13	,	,	PUNCT
ejpam-6046	203	14	(	(	PUNCT
ejpam-6046	203	15	n	n	ADV
ejpam-6046	203	16	2	2	NUM
ejpam-6046	203	17	)	)	PUNCT
ejpam-6046	203	18	(	(	PUNCT
ejpam-6046	203	19	n−	n−	NOUN
ejpam-6046	203	20	2	2	NUM
ejpam-6046	203	21	2	2	NUM
ejpam-6046	203	22	)	)	PUNCT
ejpam-6046	203	23	(	(	PUNCT
ejpam-6046	203	24	n−	n−	NOUN
ejpam-6046	203	25	2−	2−	NUM
ejpam-6046	203	26	2	2	NUM
ejpam-6046	203	27	2	2	NUM
ejpam-6046	203	28	)	)	PUNCT
ejpam-6046	203	29	·	·	PUNCT
ejpam-6046	203	30	·	·	PUNCT
ejpam-6046	203	31	·	·	PUNCT
ejpam-6046	203	32	(	(	PUNCT
ejpam-6046	203	33	n−	n−	NOUN
ejpam-6046	203	34	2k	2k	NOUN
ejpam-6046	203	35	+	+	CCONJ
ejpam-6046	203	36	2	2	NUM
ejpam-6046	203	37	2	2	NUM
ejpam-6046	203	38	)	)	PUNCT
ejpam-6046	203	39	︸	︸	X
ejpam-6046	204	1	︷︷	︷︷	PROPN
ejpam-6046	204	2	︸	︸	X
ejpam-6046	205	1	k	k	PROPN
ejpam-6046	205	2	factors	factor	NOUN
ejpam-6046	205	3	=	=	SYM
ejpam-6046	205	4	n	n	X
ejpam-6046	205	5	!	!	NOUN
ejpam-6046	205	6	2k(n−	2k(n−	NUM
ejpam-6046	205	7	2k	2k	NUM
ejpam-6046	205	8	)	)	PUNCT
ejpam-6046	205	9	!	!	PUNCT
ejpam-6046	206	1	=	=	PUNCT
ejpam-6046	207	1	n	n	X
ejpam-6046	207	2	!	!	PUNCT
ejpam-6046	207	3	2k	2k	PROPN
ejpam-6046	207	4	.	.	PUNCT
ejpam-6046	208	1	j.	j.	PROPN
ejpam-6046	208	2	n.	n.	PROPN
ejpam-6046	208	3	ontulan	ontulan	PROPN
ejpam-6046	208	4	,	,	PUNCT
ejpam-6046	208	5	c.	c.	PROPN
ejpam-6046	208	6	m.	m.	NOUN
ejpam-6046	208	7	balingit	balingit	PROPN
ejpam-6046	208	8	/	/	SYM
ejpam-6046	208	9	eur	eur	PROPN
ejpam-6046	208	10	.	.	PUNCT
ejpam-6046	209	1	j.	j.	PROPN
ejpam-6046	209	2	pure	pure	PROPN
ejpam-6046	209	3	appl	appl	PROPN
ejpam-6046	209	4	.	.	PROPN
ejpam-6046	209	5	math	math	PROPN
ejpam-6046	209	6	,	,	PUNCT
ejpam-6046	209	7	18	18	NUM
ejpam-6046	209	8	(	(	PUNCT
ejpam-6046	209	9	2	2	NUM
ejpam-6046	209	10	)	)	PUNCT
ejpam-6046	209	11	(	(	PUNCT
ejpam-6046	209	12	2025	2025	NUM
ejpam-6046	209	13	)	)	PUNCT
ejpam-6046	209	14	,	,	PUNCT
ejpam-6046	209	15	6046	6046	NUM
ejpam-6046	209	16	8	8	NUM
ejpam-6046	209	17	of	of	ADP
ejpam-6046	209	18	14	14	NUM
ejpam-6046	209	19	since	since	SCONJ
ejpam-6046	209	20	the	the	DET
ejpam-6046	209	21	order	order	NOUN
ejpam-6046	209	22	of	of	ADP
ejpam-6046	209	23	the	the	DET
ejpam-6046	209	24	elements	element	NOUN
ejpam-6046	209	25	in	in	ADP
ejpam-6046	209	26	s	s	VERB
ejpam-6046	209	27	does	do	AUX
ejpam-6046	209	28	not	not	PART
ejpam-6046	209	29	matter	matter	VERB
ejpam-6046	209	30	,	,	PUNCT
ejpam-6046	209	31	we	we	PRON
ejpam-6046	209	32	divide	divide	VERB
ejpam-6046	209	33	this	this	DET
ejpam-6046	209	34	quantity	quantity	NOUN
ejpam-6046	209	35	by	by	ADP
ejpam-6046	209	36	k	k	PROPN
ejpam-6046	209	37	!	!	PUNCT
ejpam-6046	209	38	.	.	PUNCT
ejpam-6046	210	1	hence	hence	ADV
ejpam-6046	210	2	,	,	PUNCT
ejpam-6046	210	3	|ide	|ide	SCONJ
ejpam-6046	210	4	kn	kn	PROPN
ejpam-6046	210	5	|	|	ADV
ejpam-6046	210	6	=	=	SYM
ejpam-6046	210	7	n	n	X
ejpam-6046	210	8	!	!	X
ejpam-6046	210	9	2k	2k	NUM
ejpam-6046	210	10	·	·	PUNCT
ejpam-6046	210	11	k	k	X
ejpam-6046	210	12	!	!	PUNCT
ejpam-6046	210	13	.	.	PUNCT
ejpam-6046	211	1	■	■	PUNCT
ejpam-6046	211	2	example	example	NOUN
ejpam-6046	211	3	4	4	X
ejpam-6046	211	4	.	.	PUNCT
ejpam-6046	211	5	consider	consider	VERB
ejpam-6046	211	6	the	the	DET
ejpam-6046	211	7	complete	complete	ADJ
ejpam-6046	211	8	graph	graph	NOUN
ejpam-6046	211	9	k5	k5	PROPN
ejpam-6046	211	10	in	in	ADP
ejpam-6046	211	11	figure	figure	NOUN
ejpam-6046	211	12	6	6	NUM
ejpam-6046	211	13	with	with	ADP
ejpam-6046	211	14	e(k5	e(k5	NOUN
ejpam-6046	211	15	)	)	PUNCT
ejpam-6046	212	1	=	=	PRON
ejpam-6046	212	2	{	{	PUNCT
ejpam-6046	212	3	e1,2	e1,2	PROPN
ejpam-6046	212	4	,	,	PUNCT
ejpam-6046	212	5	e1,3	e1,3	PROPN
ejpam-6046	212	6	,	,	PUNCT
ejpam-6046	212	7	e1,4	e1,4	ADV
ejpam-6046	212	8	,	,	PUNCT
ejpam-6046	212	9	e1,5	e1,5	PROPN
ejpam-6046	212	10	,	,	PUNCT
ejpam-6046	212	11	e2,3	e2,3	PROPN
ejpam-6046	212	12	,	,	PUNCT
ejpam-6046	212	13	e2,4	e2,4	PROPN
ejpam-6046	212	14	,	,	PUNCT
ejpam-6046	212	15	e2,5	e2,5	NOUN
ejpam-6046	212	16	,	,	PUNCT
ejpam-6046	212	17	e3,4	e3,4	PROPN
ejpam-6046	212	18	,	,	PUNCT
ejpam-6046	212	19	e3,5	e3,5	NOUN
ejpam-6046	212	20	,	,	PUNCT
ejpam-6046	212	21	e4,5	e4,5	NOUN
ejpam-6046	212	22	}	}	PUNCT
ejpam-6046	212	23	.	.	PUNCT
ejpam-6046	213	1	observe	observe	VERB
ejpam-6046	213	2	that	that	DET
ejpam-6046	213	3	ide	ide	NOUN
ejpam-6046	213	4	k5	k5	PROPN
ejpam-6046	213	5	=	=	PUNCT
ejpam-6046	213	6	{	{	PUNCT
ejpam-6046	213	7	{	{	PUNCT
ejpam-6046	213	8	e1,2	e1,2	ADJ
ejpam-6046	213	9	,	,	PUNCT
ejpam-6046	213	10	e3,4	e3,4	ADJ
ejpam-6046	213	11	}	}	PUNCT
ejpam-6046	213	12	,	,	PUNCT
ejpam-6046	213	13	{	{	PUNCT
ejpam-6046	213	14	e1,2	e1,2	ADJ
ejpam-6046	213	15	,	,	PUNCT
ejpam-6046	213	16	e3,5	e3,5	NOUN
ejpam-6046	213	17	}	}	PUNCT
ejpam-6046	213	18	,	,	PUNCT
ejpam-6046	213	19	{	{	PUNCT
ejpam-6046	213	20	e1,2	e1,2	ADJ
ejpam-6046	213	21	,	,	PUNCT
ejpam-6046	213	22	e4,5	e4,5	NOUN
ejpam-6046	213	23	}	}	PUNCT
ejpam-6046	213	24	,	,	PUNCT
ejpam-6046	213	25	{	{	PUNCT
ejpam-6046	213	26	e1,3	e1,3	PROPN
ejpam-6046	213	27	,	,	PUNCT
ejpam-6046	213	28	e2,4	e2,4	PROPN
ejpam-6046	213	29	}	}	PUNCT
ejpam-6046	213	30	,	,	PUNCT
ejpam-6046	213	31	{	{	PUNCT
ejpam-6046	213	32	e1,3	e1,3	PROPN
ejpam-6046	213	33	,	,	PUNCT
ejpam-6046	213	34	e2,5	e2,5	PROPN
ejpam-6046	213	35	}	}	PUNCT
ejpam-6046	213	36	,	,	PUNCT
ejpam-6046	213	37	{	{	PUNCT
ejpam-6046	213	38	e1,3	e1,3	PROPN
ejpam-6046	213	39	,	,	PUNCT
ejpam-6046	213	40	e4,5	e4,5	NOUN
ejpam-6046	213	41	}	}	PUNCT
ejpam-6046	213	42	,	,	PUNCT
ejpam-6046	213	43	{	{	PUNCT
ejpam-6046	213	44	e1,4	e1,4	ADV
ejpam-6046	213	45	,	,	PUNCT
ejpam-6046	213	46	e2,3	e2,3	NOUN
ejpam-6046	213	47	}	}	PUNCT
ejpam-6046	213	48	,	,	PUNCT
ejpam-6046	213	49	{	{	PUNCT
ejpam-6046	213	50	e1,4	e1,4	ADV
ejpam-6046	213	51	,	,	PUNCT
ejpam-6046	213	52	e2,5	e2,5	PROPN
ejpam-6046	213	53	}	}	PUNCT
ejpam-6046	213	54	,	,	PUNCT
ejpam-6046	213	55	{	{	PUNCT
ejpam-6046	213	56	e1,4	e1,4	ADV
ejpam-6046	213	57	,	,	PUNCT
ejpam-6046	213	58	e3,5	e3,5	PROPN
ejpam-6046	213	59	}	}	PUNCT
ejpam-6046	213	60	,	,	PUNCT
ejpam-6046	213	61	{	{	PUNCT
ejpam-6046	213	62	e1,5	e1,5	PROPN
ejpam-6046	213	63	,	,	PUNCT
ejpam-6046	213	64	e2,3	e2,3	NOUN
ejpam-6046	213	65	}	}	PUNCT
ejpam-6046	213	66	,	,	PUNCT
ejpam-6046	213	67	{	{	PUNCT
ejpam-6046	213	68	e1,5	e1,5	ADJ
ejpam-6046	213	69	,	,	PUNCT
ejpam-6046	213	70	e2,4	e2,4	PROPN
ejpam-6046	213	71	}	}	PUNCT
ejpam-6046	213	72	,	,	PUNCT
ejpam-6046	213	73	{	{	PUNCT
ejpam-6046	213	74	e1,5	e1,5	ADJ
ejpam-6046	213	75	,	,	PUNCT
ejpam-6046	213	76	e3,4	e3,4	ADJ
ejpam-6046	213	77	}	}	PUNCT
ejpam-6046	213	78	,	,	PUNCT
ejpam-6046	213	79	{	{	PUNCT
ejpam-6046	213	80	e2,3	e2,3	NOUN
ejpam-6046	213	81	,	,	PUNCT
ejpam-6046	213	82	e4,5	e4,5	NOUN
ejpam-6046	213	83	}	}	PUNCT
ejpam-6046	213	84	,	,	PUNCT
ejpam-6046	213	85	{	{	PUNCT
ejpam-6046	213	86	e2,4	e2,4	PROPN
ejpam-6046	213	87	,	,	PUNCT
ejpam-6046	213	88	e3,5	e3,5	PROPN
ejpam-6046	213	89	}	}	PUNCT
ejpam-6046	213	90	,	,	PUNCT
ejpam-6046	213	91	{	{	PUNCT
ejpam-6046	213	92	e2,5	e2,5	NOUN
ejpam-6046	213	93	,	,	PUNCT
ejpam-6046	213	94	e3,4	e3,4	ADJ
ejpam-6046	213	95	}	}	PUNCT
ejpam-6046	213	96	}	}	PUNCT
ejpam-6046	213	97	.	.	PUNCT
ejpam-6046	214	1	indeed	indeed	ADV
ejpam-6046	214	2	,	,	PUNCT
ejpam-6046	214	3	with	with	ADP
ejpam-6046	214	4	k	k	PROPN
ejpam-6046	214	5	=	=	PUNCT
ejpam-6046	214	6	⌊5	⌊5	X
ejpam-6046	214	7	2	2	NUM
ejpam-6046	214	8	⌋	⌋	NOUN
ejpam-6046	214	9	=	=	SYM
ejpam-6046	214	10	2	2	NUM
ejpam-6046	214	11	,	,	PUNCT
ejpam-6046	214	12	|ide	|ide	VERB
ejpam-6046	214	13	k4	k4	NOUN
ejpam-6046	214	14	|	|	NOUN
ejpam-6046	214	15	=	=	SYM
ejpam-6046	214	16	5	5	NUM
ejpam-6046	214	17	!	!	NOUN
ejpam-6046	214	18	22	22	NUM
ejpam-6046	214	19	·	·	PUNCT
ejpam-6046	214	20	2	2	X
ejpam-6046	214	21	!	!	PUNCT
ejpam-6046	214	22	=	=	SYM
ejpam-6046	215	1	15	15	NUM
ejpam-6046	215	2	.	.	PUNCT
ejpam-6046	215	3	remark	remark	NOUN
ejpam-6046	215	4	2	2	NUM
ejpam-6046	215	5	.	.	PUNCT
ejpam-6046	216	1	in	in	ADP
ejpam-6046	216	2	view	view	NOUN
ejpam-6046	216	3	of	of	ADP
ejpam-6046	216	4	theorem	theorem	ADJ
ejpam-6046	216	5	2	2	NUM
ejpam-6046	216	6	,	,	PUNCT
ejpam-6046	216	7	τeid(k2	τeid(k2	NOUN
ejpam-6046	216	8	)	)	PUNCT
ejpam-6046	216	9	is	be	AUX
ejpam-6046	216	10	the	the	DET
ejpam-6046	216	11	indiscrete	indiscrete	ADJ
ejpam-6046	216	12	topology	topology	NOUN
ejpam-6046	216	13	on	on	ADP
ejpam-6046	216	14	e(k2	e(k2	NOUN
ejpam-6046	216	15	)	)	PUNCT
ejpam-6046	216	16	.	.	PUNCT
ejpam-6046	217	1	furthermore	furthermore	ADV
ejpam-6046	217	2	,	,	PUNCT
ejpam-6046	217	3	τeid(k3	τeid(k3	NOUN
ejpam-6046	217	4	)	)	PUNCT
ejpam-6046	217	5	is	be	AUX
ejpam-6046	217	6	the	the	DET
ejpam-6046	217	7	discrete	discrete	ADJ
ejpam-6046	217	8	topology	topology	NOUN
ejpam-6046	217	9	on	on	ADP
ejpam-6046	217	10	e(k3	e(k3	NOUN
ejpam-6046	217	11	)	)	PUNCT
ejpam-6046	217	12	,	,	PUNCT
ejpam-6046	217	13	given	give	VERB
ejpam-6046	217	14	that	that	DET
ejpam-6046	217	15	ide	ide	NOUN
ejpam-6046	217	16	k3	k3	NOUN
ejpam-6046	217	17	=	=	SYM
ejpam-6046	217	18	{	{	PUNCT
ejpam-6046	217	19	{	{	PUNCT
ejpam-6046	217	20	e1,2	e1,2	NOUN
ejpam-6046	217	21	}	}	PUNCT
ejpam-6046	217	22	,	,	PUNCT
ejpam-6046	217	23	{	{	PUNCT
ejpam-6046	217	24	e1,3	e1,3	NOUN
ejpam-6046	217	25	}	}	PUNCT
ejpam-6046	217	26	,	,	PUNCT
ejpam-6046	217	27	{	{	PUNCT
ejpam-6046	217	28	e2,3	e2,3	NOUN
ejpam-6046	217	29	}	}	PUNCT
ejpam-6046	217	30	}	}	PUNCT
ejpam-6046	217	31	⊆	⊆	NUM
ejpam-6046	217	32	τeid(k3	τeid(k3	NOUN
ejpam-6046	217	33	)	)	PUNCT
ejpam-6046	217	34	,	,	PUNCT
ejpam-6046	217	35	by	by	ADP
ejpam-6046	217	36	theorem	theorem	NOUN
ejpam-6046	217	37	1	1	NUM
ejpam-6046	217	38	.	.	PUNCT
ejpam-6046	218	1	however	however	ADV
ejpam-6046	218	2	,	,	PUNCT
ejpam-6046	218	3	τeid(k4	τeid(k4	PROPN
ejpam-6046	218	4	)	)	PUNCT
ejpam-6046	218	5	is	be	AUX
ejpam-6046	218	6	neither	neither	CCONJ
ejpam-6046	218	7	the	the	DET
ejpam-6046	218	8	discrete	discrete	NOUN
ejpam-6046	218	9	nor	nor	CCONJ
ejpam-6046	218	10	the	the	DET
ejpam-6046	218	11	indiscrete	indiscrete	ADJ
ejpam-6046	218	12	topology	topology	NOUN
ejpam-6046	218	13	on	on	ADP
ejpam-6046	218	14	e(k4	e(k4	NOUN
ejpam-6046	218	15	)	)	PUNCT
ejpam-6046	218	16	.	.	PUNCT
ejpam-6046	219	1	to	to	PART
ejpam-6046	219	2	see	see	VERB
ejpam-6046	219	3	this	this	PRON
ejpam-6046	219	4	,	,	PUNCT
ejpam-6046	219	5	observe	observe	VERB
ejpam-6046	219	6	that	that	SCONJ
ejpam-6046	219	7	e(g	e(g	NOUN
ejpam-6046	219	8	)	)	PUNCT
ejpam-6046	220	1	=	=	PRON
ejpam-6046	220	2	{	{	PUNCT
ejpam-6046	220	3	e1,2	e1,2	ADJ
ejpam-6046	220	4	,	,	PUNCT
ejpam-6046	220	5	e1,4	e1,4	PROPN
ejpam-6046	220	6	,	,	PUNCT
ejpam-6046	220	7	e1,3	e1,3	PROPN
ejpam-6046	220	8	,	,	PUNCT
ejpam-6046	220	9	e2,3	e2,3	PROPN
ejpam-6046	220	10	,	,	PUNCT
ejpam-6046	220	11	e2,4	e2,4	PROPN
ejpam-6046	220	12	,	,	PUNCT
ejpam-6046	220	13	e3,4	e3,4	ADJ
ejpam-6046	220	14	}	}	PUNCT
ejpam-6046	220	15	,	,	PUNCT
ejpam-6046	220	16	ide	ide	NOUN
ejpam-6046	220	17	k4	k4	NOUN
ejpam-6046	220	18	=	=	NOUN
ejpam-6046	220	19	{	{	PUNCT
ejpam-6046	220	20	{	{	PUNCT
ejpam-6046	220	21	e1,2	e1,2	ADJ
ejpam-6046	220	22	,	,	PUNCT
ejpam-6046	220	23	e3,4	e3,4	ADJ
ejpam-6046	220	24	}	}	PUNCT
ejpam-6046	220	25	,	,	PUNCT
ejpam-6046	220	26	{	{	PUNCT
ejpam-6046	220	27	e1,4	e1,4	ADV
ejpam-6046	220	28	,	,	PUNCT
ejpam-6046	220	29	e2,3	e2,3	NOUN
ejpam-6046	220	30	}	}	PUNCT
ejpam-6046	220	31	,	,	PUNCT
ejpam-6046	220	32	{	{	PUNCT
ejpam-6046	220	33	e1,3	e1,3	PROPN
ejpam-6046	220	34	,	,	PUNCT
ejpam-6046	220	35	e2,4	e2,4	PROPN
ejpam-6046	220	36	}	}	PUNCT
ejpam-6046	220	37	}	}	PUNCT
ejpam-6046	220	38	and	and	CCONJ
ejpam-6046	220	39	so	so	ADV
ejpam-6046	220	40	,	,	PUNCT
ejpam-6046	220	41	τeid(k4	τeid(k4	PROPN
ejpam-6046	220	42	)	)	PUNCT
ejpam-6046	220	43	=	=	PRON
ejpam-6046	221	1	{	{	PUNCT
ejpam-6046	221	2	∅	∅	NOUN
ejpam-6046	221	3	,	,	PUNCT
ejpam-6046	221	4	{	{	PUNCT
ejpam-6046	221	5	e1,2	e1,2	ADJ
ejpam-6046	221	6	,	,	PUNCT
ejpam-6046	221	7	e3,4	e3,4	ADJ
ejpam-6046	221	8	}	}	PUNCT
ejpam-6046	221	9	,	,	PUNCT
ejpam-6046	221	10	{	{	PUNCT
ejpam-6046	221	11	e1,4	e1,4	ADV
ejpam-6046	221	12	,	,	PUNCT
ejpam-6046	221	13	e2,3	e2,3	NOUN
ejpam-6046	221	14	}	}	PUNCT
ejpam-6046	221	15	,	,	PUNCT
ejpam-6046	221	16	{	{	PUNCT
ejpam-6046	221	17	e1,3	e1,3	PROPN
ejpam-6046	221	18	,	,	PUNCT
ejpam-6046	221	19	e2,4	e2,4	PROPN
ejpam-6046	221	20	}	}	PUNCT
ejpam-6046	221	21	,	,	PUNCT
ejpam-6046	221	22	{	{	PUNCT
ejpam-6046	221	23	e1,2	e1,2	ADJ
ejpam-6046	221	24	,	,	PUNCT
ejpam-6046	221	25	e3,4	e3,4	ADJ
ejpam-6046	221	26	,	,	PUNCT
ejpam-6046	221	27	e1,4	e1,4	ADV
ejpam-6046	221	28	,	,	PUNCT
ejpam-6046	221	29	e2,3	e2,3	NOUN
ejpam-6046	221	30	}	}	PUNCT
ejpam-6046	221	31	,	,	PUNCT
ejpam-6046	221	32	{	{	PUNCT
ejpam-6046	221	33	e1,2	e1,2	ADJ
ejpam-6046	221	34	,	,	PUNCT
ejpam-6046	221	35	e3,4	e3,4	ADJ
ejpam-6046	221	36	,	,	PUNCT
ejpam-6046	221	37	e1,3	e1,3	PROPN
ejpam-6046	221	38	,	,	PUNCT
ejpam-6046	221	39	e2,4	e2,4	PROPN
ejpam-6046	221	40	}	}	PUNCT
ejpam-6046	221	41	,	,	PUNCT
ejpam-6046	221	42	{	{	PUNCT
ejpam-6046	221	43	e1,4	e1,4	ADV
ejpam-6046	221	44	,	,	PUNCT
ejpam-6046	221	45	e2,3	e2,3	PROPN
ejpam-6046	221	46	,	,	PUNCT
ejpam-6046	221	47	e1,3	e1,3	PROPN
ejpam-6046	221	48	,	,	PUNCT
ejpam-6046	221	49	e2,4	e2,4	PROPN
ejpam-6046	221	50	}	}	PUNCT
ejpam-6046	221	51	,	,	PUNCT
ejpam-6046	221	52	e(k4	e(k4	NOUN
ejpam-6046	221	53	)	)	PUNCT
ejpam-6046	221	54	}	}	PUNCT
ejpam-6046	221	55	.	.	PUNCT
ejpam-6046	222	1	theorem	theorem	NOUN
ejpam-6046	222	2	5	5	NUM
ejpam-6046	222	3	.	.	PUNCT
ejpam-6046	223	1	let	let	VERB
ejpam-6046	223	2	kn	kn	PROPN
ejpam-6046	223	3	be	be	AUX
ejpam-6046	223	4	a	a	DET
ejpam-6046	223	5	complete	complete	ADJ
ejpam-6046	223	6	graph	graph	NOUN
ejpam-6046	223	7	where	where	SCONJ
ejpam-6046	223	8	n	n	PRON
ejpam-6046	223	9	≥	≥	NUM
ejpam-6046	223	10	5	5	NUM
ejpam-6046	223	11	.	.	PUNCT
ejpam-6046	223	12	then	then	ADV
ejpam-6046	223	13	τeid(kn	τeid(kn	PROPN
ejpam-6046	223	14	)	)	PUNCT
ejpam-6046	223	15	is	be	AUX
ejpam-6046	223	16	the	the	DET
ejpam-6046	223	17	discrete	discrete	ADJ
ejpam-6046	223	18	topology	topology	NOUN
ejpam-6046	223	19	on	on	ADP
ejpam-6046	223	20	e(kn	e(kn	NUM
ejpam-6046	223	21	)	)	PUNCT
ejpam-6046	223	22	.	.	PUNCT
ejpam-6046	224	1	proof	proof	NOUN
ejpam-6046	224	2	.	.	PUNCT
ejpam-6046	225	1	let	let	VERB
ejpam-6046	225	2	ep	ep	PROPN
ejpam-6046	225	3	,	,	PUNCT
ejpam-6046	225	4	q	q	PROPN
ejpam-6046	225	5	∈	∈	PROPN
ejpam-6046	225	6	e(kn	e(kn	NUM
ejpam-6046	225	7	)	)	PUNCT
ejpam-6046	225	8	where	where	SCONJ
ejpam-6046	225	9	n	n	X
ejpam-6046	225	10	>	>	X
ejpam-6046	225	11	5	5	NUM
ejpam-6046	225	12	.	.	PUNCT
ejpam-6046	226	1	then	then	ADV
ejpam-6046	226	2	,	,	PUNCT
ejpam-6046	226	3	by	by	ADP
ejpam-6046	226	4	theorem	theorem	NOUN
ejpam-6046	226	5	3	3	NUM
ejpam-6046	226	6	,	,	PUNCT
ejpam-6046	226	7	and	and	CCONJ
ejpam-6046	226	8	since	since	SCONJ
ejpam-6046	226	9	k	k	PROPN
ejpam-6046	226	10	=	=	PUNCT
ejpam-6046	226	11	⌊	⌊	PROPN
ejpam-6046	226	12	n	n	PRON
ejpam-6046	226	13	2	2	NUM
ejpam-6046	226	14	⌋	⌋	NOUN
ejpam-6046	226	15	≥	≥	NOUN
ejpam-6046	226	16	3	3	NUM
ejpam-6046	226	17	,	,	PUNCT
ejpam-6046	226	18	s	s	PART
ejpam-6046	226	19	=	=	PUNCT
ejpam-6046	226	20	{	{	PUNCT
ejpam-6046	226	21	ep	ep	PROPN
ejpam-6046	226	22	,	,	PUNCT
ejpam-6046	226	23	q	q	NOUN
ejpam-6046	226	24	,	,	PUNCT
ejpam-6046	226	25	ei1,j1	ei1,j1	NOUN
ejpam-6046	226	26	,	,	PUNCT
ejpam-6046	226	27	.	.	PUNCT
ejpam-6046	226	28	.	.	PUNCT
ejpam-6046	226	29	.	.	PUNCT
ejpam-6046	227	1	,	,	PUNCT
ejpam-6046	227	2	eik−1,jk−1	eik−1,jk−1	AUX
ejpam-6046	227	3	}	}	PUNCT
ejpam-6046	227	4	where	where	SCONJ
ejpam-6046	227	5	k	k	NOUN
ejpam-6046	227	6	=	=	SYM
ejpam-6046	227	7	⌊	⌊	PROPN
ejpam-6046	227	8	n	n	ADV
ejpam-6046	227	9	2	2	NUM
ejpam-6046	227	10	⌋	⌋	NOUN
ejpam-6046	227	11	and	and	CCONJ
ejpam-6046	227	12	i1	i1	PROPN
ejpam-6046	227	13	̸=	̸=	PROPN
ejpam-6046	227	14	ik−1	ik−1	PROPN
ejpam-6046	227	15	̸=	̸=	PROPN
ejpam-6046	227	16	j1	j1	PROPN
ejpam-6046	227	17	̸=	̸=	PROPN
ejpam-6046	227	18	.	.	PUNCT
ejpam-6046	227	19	.	.	PUNCT
ejpam-6046	227	20	.	.	PUNCT
ejpam-6046	228	1	̸=	̸=	PROPN
ejpam-6046	228	2	jk−1	jk−1	PROPN
ejpam-6046	228	3	̸=	̸=	PROPN
ejpam-6046	228	4	p	p	PROPN
ejpam-6046	228	5	̸=	̸=	PROPN
ejpam-6046	228	6	q	q	NOUN
ejpam-6046	228	7	is	be	AUX
ejpam-6046	228	8	an	an	DET
ejpam-6046	228	9	ieds	ied	NOUN
ejpam-6046	228	10	of	of	ADP
ejpam-6046	228	11	kn	kn	PROPN
ejpam-6046	228	12	.	.	PROPN
ejpam-6046	228	13	observe	observe	VERB
ejpam-6046	228	14	that	that	SCONJ
ejpam-6046	228	15	s′	s′	ADJ
ejpam-6046	228	16	=	=	PUNCT
ejpam-6046	228	17	{	{	PUNCT
ejpam-6046	228	18	ep	ep	NOUN
ejpam-6046	228	19	,	,	PUNCT
ejpam-6046	228	20	q	q	NOUN
ejpam-6046	228	21	,	,	PUNCT
ejpam-6046	228	22	ei1,jk−1	ei1,jk−1	NOUN
ejpam-6046	228	23	,	,	PUNCT
ejpam-6046	228	24	ei1,jk−2	ei1,jk−2	PROPN
ejpam-6046	228	25	,	,	PUNCT
ejpam-6046	228	26	.	.	PUNCT
ejpam-6046	228	27	.	.	PUNCT
ejpam-6046	228	28	.	.	PUNCT
ejpam-6046	229	1	,	,	PUNCT
ejpam-6046	229	2	eik−1,j1	eik−1,j1	X
ejpam-6046	229	3	}	}	PUNCT
ejpam-6046	229	4	is	be	AUX
ejpam-6046	229	5	an	an	DET
ejpam-6046	229	6	ieds	ied	NOUN
ejpam-6046	229	7	of	of	ADP
ejpam-6046	229	8	kn	kn	PROPN
ejpam-6046	229	9	such	such	ADJ
ejpam-6046	229	10	that	that	DET
ejpam-6046	229	11	s	s	NOUN
ejpam-6046	229	12	∩	∩	NOUN
ejpam-6046	229	13	s′	s′	PUNCT
ejpam-6046	229	14	=	=	PUNCT
ejpam-6046	229	15	{	{	PUNCT
ejpam-6046	229	16	ep	ep	NOUN
ejpam-6046	229	17	,	,	PUNCT
ejpam-6046	229	18	q	q	ADJ
ejpam-6046	229	19	}	}	PUNCT
ejpam-6046	229	20	∈	∈	PROPN
ejpam-6046	229	21	τeid(kn	τeid(kn	NOUN
ejpam-6046	229	22	)	)	PUNCT
ejpam-6046	229	23	.	.	PUNCT
ejpam-6046	230	1	if	if	SCONJ
ejpam-6046	230	2	n	n	NOUN
ejpam-6046	230	3	=	=	SYM
ejpam-6046	230	4	5	5	NUM
ejpam-6046	230	5	,	,	PUNCT
ejpam-6046	230	6	s	s	PART
ejpam-6046	230	7	=	=	PUNCT
ejpam-6046	230	8	{	{	PUNCT
ejpam-6046	230	9	ep	ep	PROPN
ejpam-6046	230	10	,	,	PUNCT
ejpam-6046	230	11	q	q	NOUN
ejpam-6046	230	12	,	,	PUNCT
ejpam-6046	230	13	ei1,j2	ei1,j2	NOUN
ejpam-6046	230	14	}	}	PUNCT
ejpam-6046	230	15	is	be	AUX
ejpam-6046	230	16	an	an	DET
ejpam-6046	230	17	ieds	ied	NOUN
ejpam-6046	230	18	,	,	PUNCT
ejpam-6046	230	19	for	for	ADP
ejpam-6046	230	20	any	any	DET
ejpam-6046	230	21	distinct	distinct	PROPN
ejpam-6046	230	22	i1	i1	PROPN
ejpam-6046	230	23	,	,	PUNCT
ejpam-6046	230	24	j1	j1	PROPN
ejpam-6046	230	25	∈	∈	PROPN
ejpam-6046	231	1	[	[	X
ejpam-6046	231	2	5	5	NUM
ejpam-6046	231	3	]	]	PUNCT
ejpam-6046	231	4	\	\	PUNCT
ejpam-6046	231	5	{	{	PUNCT
ejpam-6046	231	6	p	p	X
ejpam-6046	231	7	,	,	PUNCT
ejpam-6046	231	8	q	q	NOUN
ejpam-6046	231	9	}	}	PUNCT
ejpam-6046	231	10	.	.	PUNCT
ejpam-6046	232	1	putting	put	VERB
ejpam-6046	232	2	r	r	NOUN
ejpam-6046	232	3	=	=	PUNCT
ejpam-6046	233	1	[	[	X
ejpam-6046	233	2	5	5	NUM
ejpam-6046	233	3	]	]	PUNCT
ejpam-6046	233	4	\	\	PROPN
ejpam-6046	233	5	{	{	PUNCT
ejpam-6046	233	6	i1	i1	PROPN
ejpam-6046	233	7	,	,	PUNCT
ejpam-6046	233	8	j1	j1	PROPN
ejpam-6046	233	9	,	,	PUNCT
ejpam-6046	233	10	p	p	X
ejpam-6046	233	11	,	,	PUNCT
ejpam-6046	233	12	q	q	NOUN
ejpam-6046	233	13	}	}	PUNCT
ejpam-6046	233	14	,	,	PUNCT
ejpam-6046	233	15	s′	s′	PUNCT
ejpam-6046	233	16	=	=	PUNCT
ejpam-6046	233	17	{	{	PUNCT
ejpam-6046	233	18	ep	ep	NOUN
ejpam-6046	233	19	,	,	PUNCT
ejpam-6046	233	20	q	q	NOUN
ejpam-6046	233	21	,	,	PUNCT
ejpam-6046	233	22	ei1,r	ei1,r	PROPN
ejpam-6046	233	23	}	}	PUNCT
ejpam-6046	233	24	is	be	AUX
ejpam-6046	233	25	an	an	DET
ejpam-6046	233	26	ieds	ied	NOUN
ejpam-6046	233	27	of	of	ADP
ejpam-6046	233	28	k5	k5	PROPN
ejpam-6046	233	29	with	with	ADP
ejpam-6046	233	30	s	s	PROPN
ejpam-6046	233	31	∩	∩	NOUN
ejpam-6046	233	32	s′	s′	PUNCT
ejpam-6046	233	33	=	=	PUNCT
ejpam-6046	233	34	{	{	PUNCT
ejpam-6046	233	35	ep	ep	NOUN
ejpam-6046	233	36	,	,	PUNCT
ejpam-6046	233	37	q	q	ADJ
ejpam-6046	233	38	}	}	PUNCT
ejpam-6046	233	39	∈	∈	NOUN
ejpam-6046	233	40	τeid(k5	τeid(k5	NOUN
ejpam-6046	233	41	)	)	PUNCT
ejpam-6046	233	42	,	,	PUNCT
ejpam-6046	233	43	by	by	ADP
ejpam-6046	233	44	theorem	theorem	NOUN
ejpam-6046	233	45	1	1	NUM
ejpam-6046	233	46	.	.	PUNCT
ejpam-6046	234	1	in	in	ADP
ejpam-6046	234	2	both	both	DET
ejpam-6046	234	3	cases	case	NOUN
ejpam-6046	234	4	,	,	PUNCT
ejpam-6046	234	5	{	{	PUNCT
ejpam-6046	234	6	ep	ep	NOUN
ejpam-6046	234	7	,	,	PUNCT
ejpam-6046	234	8	q	q	ADJ
ejpam-6046	234	9	}	}	PUNCT
ejpam-6046	234	10	∈	∈	PROPN
ejpam-6046	234	11	τeid(kn	τeid(kn	NOUN
ejpam-6046	234	12	)	)	PUNCT
ejpam-6046	234	13	for	for	ADP
ejpam-6046	234	14	all	all	DET
ejpam-6046	234	15	ep	ep	NOUN
ejpam-6046	234	16	,	,	PUNCT
ejpam-6046	234	17	q	q	PROPN
ejpam-6046	234	18	∈	∈	PROPN
ejpam-6046	234	19	e(kn	e(kn	NUM
ejpam-6046	234	20	)	)	PUNCT
ejpam-6046	234	21	.	.	PUNCT
ejpam-6046	235	1	thus	thus	ADV
ejpam-6046	235	2	,	,	PUNCT
ejpam-6046	235	3	by	by	ADP
ejpam-6046	235	4	theorem	theorem	NOUN
ejpam-6046	235	5	1	1	NUM
ejpam-6046	235	6	,	,	PUNCT
ejpam-6046	235	7	τeid(kn	τeid(kn	NOUN
ejpam-6046	235	8	)	)	PUNCT
ejpam-6046	235	9	is	be	AUX
ejpam-6046	235	10	the	the	DET
ejpam-6046	235	11	discrete	discrete	ADJ
ejpam-6046	235	12	topology	topology	NOUN
ejpam-6046	235	13	on	on	ADP
ejpam-6046	235	14	e(kn	e(kn	NUM
ejpam-6046	235	15	)	)	PUNCT
ejpam-6046	235	16	for	for	ADP
ejpam-6046	235	17	all	all	DET
ejpam-6046	235	18	n	n	PRON
ejpam-6046	235	19	≥	≥	NOUN
ejpam-6046	235	20	5	5	NUM
ejpam-6046	235	21	.	.	PUNCT
ejpam-6046	236	1	■	■	PUNCT
ejpam-6046	236	2	corollary	corollary	ADJ
ejpam-6046	236	3	1	1	NUM
ejpam-6046	236	4	.	.	PUNCT
ejpam-6046	237	1	for	for	ADP
ejpam-6046	237	2	a	a	DET
ejpam-6046	237	3	complete	complete	ADJ
ejpam-6046	237	4	graph	graph	NOUN
ejpam-6046	237	5	kn	kn	NOUN
ejpam-6046	237	6	of	of	ADP
ejpam-6046	237	7	order	order	NOUN
ejpam-6046	237	8	n	n	PRON
ejpam-6046	237	9	≥	≥	NOUN
ejpam-6046	237	10	2	2	NUM
ejpam-6046	237	11	,	,	PUNCT
ejpam-6046	237	12	|τeid(kn)|	|τeid(kn)|	ADV
ejpam-6046	237	13	=	=	SYM
ejpam-6046	238	1			NOUN
ejpam-6046	238	2	2	2	NUM
ejpam-6046	238	3	,	,	PUNCT
ejpam-6046	238	4	if	if	SCONJ
ejpam-6046	238	5	n	n	NOUN
ejpam-6046	238	6	=	=	SYM
ejpam-6046	238	7	2	2	NUM
ejpam-6046	238	8	8	8	NUM
ejpam-6046	238	9	,	,	PUNCT
ejpam-6046	238	10	if	if	SCONJ
ejpam-6046	238	11	n	n	CCONJ
ejpam-6046	238	12	=	=	SYM
ejpam-6046	238	13	3	3	NUM
ejpam-6046	238	14	,	,	PUNCT
ejpam-6046	238	15	4	4	NUM
ejpam-6046	238	16	2	2	NUM
ejpam-6046	238	17	n(n−1	n(n−1	NUM
ejpam-6046	238	18	)	)	PUNCT
ejpam-6046	238	19	2	2	NUM
ejpam-6046	238	20	,	,	PUNCT
ejpam-6046	238	21	if	if	SCONJ
ejpam-6046	238	22	n	n	PRON
ejpam-6046	238	23	≥	≥	NOUN
ejpam-6046	238	24	5	5	NUM
ejpam-6046	238	25	5	5	NUM
ejpam-6046	238	26	.	.	PUNCT
ejpam-6046	238	27	independent	independent	ADJ
ejpam-6046	238	28	edge	edge	PROPN
ejpam-6046	238	29	domination	domination	NOUN
ejpam-6046	238	30	topology	topology	NOUN
ejpam-6046	238	31	of	of	ADP
ejpam-6046	238	32	friendship	friendship	NOUN
ejpam-6046	238	33	graphs	graph	NOUN
ejpam-6046	238	34	definition	definition	NOUN
ejpam-6046	238	35	9	9	NUM
ejpam-6046	238	36	.	.	PUNCT
ejpam-6046	239	1	[	[	X
ejpam-6046	239	2	13	13	NUM
ejpam-6046	239	3	]	]	PUNCT
ejpam-6046	239	4	the	the	DET
ejpam-6046	239	5	friendship	friendship	NOUN
ejpam-6046	239	6	graph	graph	NOUN
ejpam-6046	239	7	of	of	ADP
ejpam-6046	239	8	order	order	NOUN
ejpam-6046	239	9	n	n	PRON
ejpam-6046	239	10	≥	≥	NOUN
ejpam-6046	239	11	2	2	NUM
ejpam-6046	239	12	,	,	PUNCT
ejpam-6046	239	13	denoted	denote	VERB
ejpam-6046	239	14	by	by	ADP
ejpam-6046	239	15	frn	frn	PROPN
ejpam-6046	239	16	,	,	PUNCT
ejpam-6046	239	17	is	be	AUX
ejpam-6046	239	18	a	a	DET
ejpam-6046	239	19	set	set	NOUN
ejpam-6046	239	20	of	of	ADP
ejpam-6046	239	21	n	n	NOUN
ejpam-6046	239	22	copies	copy	NOUN
ejpam-6046	239	23	of	of	ADP
ejpam-6046	239	24	cycle	cycle	NOUN
ejpam-6046	239	25	c3	c3	PROPN
ejpam-6046	239	26	having	have	VERB
ejpam-6046	239	27	a	a	DET
ejpam-6046	239	28	common	common	ADJ
ejpam-6046	239	29	vertex	vertex	NOUN
ejpam-6046	239	30	v0	v0	NOUN
ejpam-6046	239	31	.	.	PUNCT
ejpam-6046	240	1	j.	j.	PROPN
ejpam-6046	240	2	n.	n.	PROPN
ejpam-6046	240	3	ontulan	ontulan	PROPN
ejpam-6046	240	4	,	,	PUNCT
ejpam-6046	240	5	c.	c.	PROPN
ejpam-6046	240	6	m.	m.	NOUN
ejpam-6046	240	7	balingit	balingit	PROPN
ejpam-6046	240	8	/	/	SYM
ejpam-6046	240	9	eur	eur	PROPN
ejpam-6046	240	10	.	.	PUNCT
ejpam-6046	241	1	j.	j.	PROPN
ejpam-6046	241	2	pure	pure	PROPN
ejpam-6046	241	3	appl	appl	PROPN
ejpam-6046	241	4	.	.	PROPN
ejpam-6046	241	5	math	math	PROPN
ejpam-6046	241	6	,	,	PUNCT
ejpam-6046	241	7	18	18	NUM
ejpam-6046	241	8	(	(	PUNCT
ejpam-6046	241	9	2	2	NUM
ejpam-6046	241	10	)	)	PUNCT
ejpam-6046	241	11	(	(	PUNCT
ejpam-6046	241	12	2025	2025	NUM
ejpam-6046	241	13	)	)	PUNCT
ejpam-6046	241	14	,	,	PUNCT
ejpam-6046	241	15	6046	6046	NUM
ejpam-6046	241	16	9	9	NUM
ejpam-6046	241	17	of	of	ADP
ejpam-6046	241	18	14	14	NUM
ejpam-6046	241	19	notation	notation	NOUN
ejpam-6046	241	20	:	:	PUNCT
ejpam-6046	241	21	for	for	ADP
ejpam-6046	241	22	the	the	DET
ejpam-6046	241	23	friendship	friendship	NOUN
ejpam-6046	241	24	graph	graph	NOUN
ejpam-6046	241	25	frn	frn	PROPN
ejpam-6046	241	26	of	of	ADP
ejpam-6046	241	27	order	order	NOUN
ejpam-6046	241	28	n	n	PRON
ejpam-6046	241	29	≥	≥	NOUN
ejpam-6046	241	30	2	2	NUM
ejpam-6046	241	31	,	,	PUNCT
ejpam-6046	241	32	we	we	PRON
ejpam-6046	241	33	use	use	VERB
ejpam-6046	241	34	the	the	DET
ejpam-6046	241	35	following	following	ADJ
ejpam-6046	241	36	notations	notation	NOUN
ejpam-6046	241	37	:	:	PUNCT
ejpam-6046	241	38	i.	i.	PROPN
ejpam-6046	241	39	v	v	PROPN
ejpam-6046	241	40	(	(	PUNCT
ejpam-6046	241	41	frn	frn	PROPN
ejpam-6046	241	42	)	)	PUNCT
ejpam-6046	241	43	=	=	SYM
ejpam-6046	241	44	{	{	PUNCT
ejpam-6046	241	45	v0	v0	NOUN
ejpam-6046	241	46	,	,	PUNCT
ejpam-6046	241	47	v1a	v1a	X
ejpam-6046	241	48	,	,	PUNCT
ejpam-6046	241	49	v1b	v1b	NOUN
ejpam-6046	241	50	,	,	PUNCT
ejpam-6046	241	51	v2a	v2a	NOUN
ejpam-6046	241	52	,	,	PUNCT
ejpam-6046	241	53	v2b	v2b	PROPN
ejpam-6046	241	54	,	,	PUNCT
ejpam-6046	241	55	.	.	PUNCT
ejpam-6046	241	56	.	.	PUNCT
ejpam-6046	241	57	.	.	PUNCT
ejpam-6046	242	1	,	,	PUNCT
ejpam-6046	242	2	vna	vna	PROPN
ejpam-6046	242	3	,	,	PUNCT
ejpam-6046	242	4	vnb	vnb	VERB
ejpam-6046	242	5	}	}	PUNCT
ejpam-6046	242	6	,	,	PUNCT
ejpam-6046	242	7	where	where	SCONJ
ejpam-6046	242	8	via	via	ADP
ejpam-6046	242	9	is	be	AUX
ejpam-6046	242	10	the	the	DET
ejpam-6046	242	11	first	first	ADJ
ejpam-6046	242	12	vertex	vertex	NOUN
ejpam-6046	242	13	of	of	ADP
ejpam-6046	242	14	the	the	DET
ejpam-6046	242	15	ith	ith	PROPN
ejpam-6046	242	16	copy	copy	NOUN
ejpam-6046	242	17	of	of	ADP
ejpam-6046	242	18	c3	c3	PROPN
ejpam-6046	242	19	;	;	PUNCT
ejpam-6046	242	20	vib	vib	PROPN
ejpam-6046	242	21	is	be	AUX
ejpam-6046	242	22	the	the	DET
ejpam-6046	242	23	second	second	ADJ
ejpam-6046	242	24	vertex	vertex	NOUN
ejpam-6046	242	25	of	of	ADP
ejpam-6046	242	26	the	the	DET
ejpam-6046	242	27	ith	ith	PROPN
ejpam-6046	242	28	copy	copy	NOUN
ejpam-6046	242	29	of	of	ADP
ejpam-6046	242	30	c3	c3	PROPN
ejpam-6046	242	31	;	;	PUNCT
ejpam-6046	242	32	and	and	CCONJ
ejpam-6046	242	33	v0	v0	NOUN
ejpam-6046	242	34	is	be	AUX
ejpam-6046	242	35	the	the	DET
ejpam-6046	242	36	common	common	ADJ
ejpam-6046	242	37	vertex	vertex	NOUN
ejpam-6046	242	38	of	of	ADP
ejpam-6046	242	39	all	all	DET
ejpam-6046	242	40	copies	copy	NOUN
ejpam-6046	242	41	of	of	ADP
ejpam-6046	242	42	c3	c3	PROPN
ejpam-6046	242	43	ii	ii	PROPN
ejpam-6046	242	44	.	.	PUNCT
ejpam-6046	243	1	e(frn	e(frn	PROPN
ejpam-6046	243	2	)	)	PUNCT
ejpam-6046	244	1	=	=	PRON
ejpam-6046	244	2	{	{	PUNCT
ejpam-6046	244	3	e0,1a	e0,1a	PROPN
ejpam-6046	244	4	,	,	PUNCT
ejpam-6046	244	5	e0,1b	e0,1b	PROPN
ejpam-6046	244	6	,	,	PUNCT
ejpam-6046	244	7	e1a,1b	e1a,1b	NOUN
ejpam-6046	244	8	,	,	PUNCT
ejpam-6046	244	9	e0,2a	e0,2a	PROPN
ejpam-6046	244	10	,	,	PUNCT
ejpam-6046	244	11	e0,2b	e0,2b	PROPN
ejpam-6046	244	12	,	,	PUNCT
ejpam-6046	244	13	e2a,2b	e2a,2b	ADV
ejpam-6046	244	14	,	,	PUNCT
ejpam-6046	244	15	.	.	PUNCT
ejpam-6046	244	16	.	.	PUNCT
ejpam-6046	245	1	.	.	PUNCT
ejpam-6046	246	1	,	,	PUNCT
ejpam-6046	246	2	e0,na	e0,na	NOUN
ejpam-6046	246	3	,	,	PUNCT
ejpam-6046	246	4	e0,nb	e0,nb	NOUN
ejpam-6046	246	5	,	,	PUNCT
ejpam-6046	246	6	ena	ena	PROPN
ejpam-6046	246	7	,	,	PUNCT
ejpam-6046	246	8	nb	nb	PROPN
ejpam-6046	246	9	}	}	PUNCT
ejpam-6046	246	10	,	,	PUNCT
ejpam-6046	246	11	where	where	SCONJ
ejpam-6046	246	12	e0,ia	e0,ia	PROPN
ejpam-6046	246	13	=	=	SYM
ejpam-6046	246	14	v0via	v0via	PROPN
ejpam-6046	246	15	,	,	PUNCT
ejpam-6046	246	16	e0,ib	e0,ib	ADV
ejpam-6046	246	17	=	=	SYM
ejpam-6046	246	18	v0vib	v0vib	PROPN
ejpam-6046	246	19	,	,	PUNCT
ejpam-6046	246	20	and	and	CCONJ
ejpam-6046	246	21	eia	eia	PROPN
ejpam-6046	246	22	,	,	PUNCT
ejpam-6046	246	23	ib	ib	NOUN
ejpam-6046	246	24	=	=	PUNCT
ejpam-6046	246	25	viavib	viavib	PROPN
ejpam-6046	246	26	.	.	PUNCT
ejpam-6046	247	1	illustration	illustration	NOUN
ejpam-6046	247	2	:	:	PUNCT
ejpam-6046	247	3	the	the	DET
ejpam-6046	247	4	friendship	friendship	NOUN
ejpam-6046	247	5	graph	graph	NOUN
ejpam-6046	247	6	fr3	fr3	PROPN
ejpam-6046	247	7	in	in	ADP
ejpam-6046	247	8	figure	figure	NOUN
ejpam-6046	247	9	7	7	NUM
ejpam-6046	247	10	is	be	AUX
ejpam-6046	247	11	labeled	label	VERB
ejpam-6046	247	12	using	use	VERB
ejpam-6046	247	13	the	the	DET
ejpam-6046	247	14	notation	notation	NOUN
ejpam-6046	247	15	convention	convention	NOUN
ejpam-6046	247	16	.	.	PUNCT
ejpam-6046	248	1	v0	v0	PROPN
ejpam-6046	248	2	v1a	v1a	NUM
ejpam-6046	248	3	v1b	v1b	X
ejpam-6046	248	4	v3b	v3b	ADJ
ejpam-6046	248	5	v3a	v3a	ADV
ejpam-6046	248	6	v4b	v4b	ADP
ejpam-6046	248	7	v4a	v4a	VERB
ejpam-6046	248	8	v2a	v2a	NOUN
ejpam-6046	248	9	v2b	v2b	PROPN
ejpam-6046	248	10	fr4	fr4	PROPN
ejpam-6046	248	11	:	:	PUNCT
ejpam-6046	249	1	e0,1a	e0,1a	PUNCT
ejpam-6046	249	2	e0,1b	e0,1b	SYM
ejpam-6046	249	3	e0,2a	e0,2a	PROPN
ejpam-6046	249	4	e0,2b	e0,2b	PROPN
ejpam-6046	249	5	e0,3ae0,3b	e0,3ae0,3b	PRON
ejpam-6046	249	6	e0,4a	e0,4a	PROPN
ejpam-6046	249	7	e0,4b	e0,4b	PROPN
ejpam-6046	249	8	e1a,1b	e1a,1b	NOUN
ejpam-6046	249	9	e2a,2b	e2a,2b	DET
ejpam-6046	249	10	e3a,3b	e3a,3b	NOUN
ejpam-6046	249	11	e4a,4b	e4a,4b	X
ejpam-6046	249	12	figure	figure	VERB
ejpam-6046	249	13	7	7	NUM
ejpam-6046	249	14	:	:	PUNCT
ejpam-6046	249	15	the	the	DET
ejpam-6046	249	16	friendship	friendship	NOUN
ejpam-6046	249	17	graph	graph	NOUN
ejpam-6046	249	18	fr4	fr4	PROPN
ejpam-6046	249	19	theorem	theorem	VERB
ejpam-6046	249	20	6	6	NUM
ejpam-6046	249	21	.	.	PUNCT
ejpam-6046	250	1	let	let	VERB
ejpam-6046	250	2	frn	frn	PROPN
ejpam-6046	250	3	be	be	AUX
ejpam-6046	250	4	a	a	DET
ejpam-6046	250	5	friendship	friendship	NOUN
ejpam-6046	250	6	graph	graph	NOUN
ejpam-6046	250	7	with	with	ADP
ejpam-6046	250	8	n	n	PRON
ejpam-6046	250	9	≥	≥	NUM
ejpam-6046	250	10	2	2	NUM
ejpam-6046	250	11	and	and	CCONJ
ejpam-6046	250	12	s	s	VERB
ejpam-6046	250	13	⊆	⊆	NUM
ejpam-6046	250	14	e(frn	e(frn	PROPN
ejpam-6046	250	15	)	)	PUNCT
ejpam-6046	250	16	.	.	PUNCT
ejpam-6046	251	1	s	s	PROPN
ejpam-6046	252	1	∈	∈	PROPN
ejpam-6046	252	2	ide	ide	NOUN
ejpam-6046	252	3	frn	frn	PROPN
ejpam-6046	252	4	if	if	SCONJ
ejpam-6046	252	5	and	and	CCONJ
ejpam-6046	252	6	only	only	ADV
ejpam-6046	252	7	if	if	SCONJ
ejpam-6046	252	8	s	s	NOUN
ejpam-6046	252	9	takes	take	VERB
ejpam-6046	252	10	one	one	NUM
ejpam-6046	252	11	of	of	ADP
ejpam-6046	252	12	the	the	DET
ejpam-6046	252	13	following	follow	VERB
ejpam-6046	252	14	forms	form	NOUN
ejpam-6046	252	15	:	:	PUNCT
ejpam-6046	252	16	i.	i.	NOUN
ejpam-6046	252	17	s1	s1	PROPN
ejpam-6046	252	18	=	=	PUNCT
ejpam-6046	252	19	{	{	PUNCT
ejpam-6046	252	20	e1a,1b	e1a,1b	NOUN
ejpam-6046	252	21	,	,	PUNCT
ejpam-6046	252	22	e2a,2b	e2a,2b	ADV
ejpam-6046	252	23	,	,	PUNCT
ejpam-6046	252	24	.	.	PUNCT
ejpam-6046	252	25	.	.	PUNCT
ejpam-6046	253	1	.	.	PUNCT
ejpam-6046	254	1	,	,	PUNCT
ejpam-6046	254	2	ena	ena	PROPN
ejpam-6046	254	3	,	,	PUNCT
ejpam-6046	254	4	nb	nb	PROPN
ejpam-6046	254	5	}	}	PUNCT
ejpam-6046	254	6	ii	ii	PROPN
ejpam-6046	254	7	.	.	PUNCT
ejpam-6046	254	8	sk	sk	VERB
ejpam-6046	254	9	a	a	DET
ejpam-6046	254	10	=	=	X
ejpam-6046	254	11	[	[	X
ejpam-6046	254	12	{	{	PUNCT
ejpam-6046	254	13	e1a,1b	e1a,1b	NOUN
ejpam-6046	254	14	,	,	PUNCT
ejpam-6046	254	15	e2a,2b	e2a,2b	ADV
ejpam-6046	254	16	,	,	PUNCT
ejpam-6046	254	17	.	.	PUNCT
ejpam-6046	254	18	.	.	PUNCT
ejpam-6046	255	1	.	.	PUNCT
ejpam-6046	256	1	,	,	PUNCT
ejpam-6046	256	2	ena	ena	PROPN
ejpam-6046	256	3	,	,	PUNCT
ejpam-6046	256	4	nb	nb	INTJ
ejpam-6046	256	5	}	}	PUNCT
ejpam-6046	256	6	\	\	NOUN
ejpam-6046	256	7	{	{	PUNCT
ejpam-6046	256	8	eka	eka	PROPN
ejpam-6046	256	9	,	,	PUNCT
ejpam-6046	256	10	kb	kb	PROPN
ejpam-6046	256	11	}	}	PUNCT
ejpam-6046	256	12	]	]	PUNCT
ejpam-6046	256	13	∪	∪	X
ejpam-6046	256	14	{	{	PUNCT
ejpam-6046	256	15	e0,ka	e0,ka	NOUN
ejpam-6046	256	16	}	}	PUNCT
ejpam-6046	256	17	for	for	ADP
ejpam-6046	256	18	some	some	DET
ejpam-6046	256	19	k	k	PROPN
ejpam-6046	256	20	∈	∈	PROPN
ejpam-6046	256	21	[	[	X
ejpam-6046	256	22	n	n	X
ejpam-6046	256	23	]	]	X
ejpam-6046	256	24	iii	iii	X
ejpam-6046	256	25	.	.	PUNCT
ejpam-6046	257	1	sk	sk	PROPN
ejpam-6046	257	2	b	b	NOUN
ejpam-6046	257	3	=	=	SYM
ejpam-6046	258	1	[	[	X
ejpam-6046	258	2	{	{	PUNCT
ejpam-6046	258	3	e1a,1b	e1a,1b	NOUN
ejpam-6046	258	4	,	,	PUNCT
ejpam-6046	258	5	e2a,2b	e2a,2b	ADV
ejpam-6046	258	6	,	,	PUNCT
ejpam-6046	258	7	.	.	PUNCT
ejpam-6046	258	8	.	.	PUNCT
ejpam-6046	259	1	.	.	PUNCT
ejpam-6046	260	1	,	,	PUNCT
ejpam-6046	260	2	ena	ena	PROPN
ejpam-6046	260	3	,	,	PUNCT
ejpam-6046	260	4	nb	nb	INTJ
ejpam-6046	260	5	}	}	PUNCT
ejpam-6046	260	6	\	\	NOUN
ejpam-6046	260	7	{	{	PUNCT
ejpam-6046	260	8	eka	eka	PROPN
ejpam-6046	260	9	,	,	PUNCT
ejpam-6046	260	10	kb	kb	PROPN
ejpam-6046	260	11	}	}	PUNCT
ejpam-6046	260	12	]	]	PUNCT
ejpam-6046	260	13	∪	∪	X
ejpam-6046	260	14	{	{	PUNCT
ejpam-6046	260	15	e0,kb	e0,kb	NOUN
ejpam-6046	260	16	}	}	PUNCT
ejpam-6046	260	17	for	for	ADP
ejpam-6046	260	18	some	some	DET
ejpam-6046	260	19	k	k	PROPN
ejpam-6046	260	20	∈	∈	PROPN
ejpam-6046	261	1	[	[	X
ejpam-6046	261	2	n	n	X
ejpam-6046	261	3	]	]	PUNCT
ejpam-6046	261	4	.	.	PUNCT
ejpam-6046	262	1	proof	proof	NOUN
ejpam-6046	262	2	.	.	PUNCT
ejpam-6046	263	1	by	by	ADP
ejpam-6046	263	2	remark	remark	NOUN
ejpam-6046	263	3	1	1	NUM
ejpam-6046	263	4	,	,	PUNCT
ejpam-6046	263	5	s1	s1	NOUN
ejpam-6046	263	6	=	=	PUNCT
ejpam-6046	263	7	{	{	PUNCT
ejpam-6046	263	8	e1a,1b	e1a,1b	NOUN
ejpam-6046	263	9	,	,	PUNCT
ejpam-6046	263	10	e2a,2b	e2a,2b	ADV
ejpam-6046	263	11	,	,	PUNCT
ejpam-6046	263	12	.	.	PUNCT
ejpam-6046	263	13	.	.	PUNCT
ejpam-6046	263	14	.	.	PUNCT
ejpam-6046	264	1	,	,	PUNCT
ejpam-6046	264	2	ena	ena	PROPN
ejpam-6046	264	3	,	,	PUNCT
ejpam-6046	264	4	nb	nb	PROPN
ejpam-6046	264	5	}	}	PUNCT
ejpam-6046	264	6	is	be	AUX
ejpam-6046	264	7	an	an	DET
ejpam-6046	264	8	independent	independent	ADJ
ejpam-6046	264	9	edge	edge	NOUN
ejpam-6046	264	10	set	set	NOUN
ejpam-6046	264	11	.	.	PUNCT
ejpam-6046	265	1	let	let	VERB
ejpam-6046	265	2	ep	ep	PROPN
ejpam-6046	265	3	,	,	PUNCT
ejpam-6046	265	4	q	q	PROPN
ejpam-6046	265	5	∈	∈	PROPN
ejpam-6046	265	6	e(frn	e(frn	PROPN
ejpam-6046	265	7	)	)	PUNCT
ejpam-6046	265	8	\	\	NOUN
ejpam-6046	265	9	s1	s1	NOUN
ejpam-6046	265	10	.	.	PUNCT
ejpam-6046	266	1	then	then	ADV
ejpam-6046	266	2	p	p	X
ejpam-6046	266	3	=	=	NOUN
ejpam-6046	266	4	0	0	NUM
ejpam-6046	266	5	and	and	CCONJ
ejpam-6046	266	6	q	q	NOUN
ejpam-6046	266	7	is	be	AUX
ejpam-6046	266	8	either	either	PRON
ejpam-6046	266	9	ka	ka	PROPN
ejpam-6046	266	10	or	or	CCONJ
ejpam-6046	266	11	kb	kb	PROPN
ejpam-6046	266	12	for	for	ADP
ejpam-6046	266	13	some	some	DET
ejpam-6046	266	14	k	k	PROPN
ejpam-6046	266	15	∈	∈	PROPN
ejpam-6046	267	1	[	[	X
ejpam-6046	267	2	n	n	X
ejpam-6046	267	3	]	]	PUNCT
ejpam-6046	267	4	.	.	PUNCT
ejpam-6046	268	1	now	now	ADV
ejpam-6046	268	2	,	,	PUNCT
ejpam-6046	268	3	observe	observe	VERB
ejpam-6046	268	4	that	that	SCONJ
ejpam-6046	268	5	,	,	PUNCT
ejpam-6046	268	6	eka	eka	PROPN
ejpam-6046	268	7	,	,	PUNCT
ejpam-6046	268	8	kb	kb	PROPN
ejpam-6046	268	9	∈	∈	PROPN
ejpam-6046	268	10	s1	s1	PROPN
ejpam-6046	268	11	and	and	CCONJ
ejpam-6046	268	12	is	be	AUX
ejpam-6046	268	13	adjacent	adjacent	ADJ
ejpam-6046	268	14	to	to	ADP
ejpam-6046	268	15	ep	ep	PROPN
ejpam-6046	268	16	,	,	PUNCT
ejpam-6046	268	17	q	q	X
ejpam-6046	268	18	,	,	PUNCT
ejpam-6046	268	19	by	by	ADP
ejpam-6046	268	20	remark	remark	NOUN
ejpam-6046	268	21	1	1	NUM
ejpam-6046	268	22	.	.	PUNCT
ejpam-6046	269	1	since	since	SCONJ
ejpam-6046	269	2	ep	ep	PROPN
ejpam-6046	269	3	,	,	PUNCT
ejpam-6046	269	4	q	q	PROPN
ejpam-6046	269	5	is	be	AUX
ejpam-6046	269	6	arbitrary	arbitrary	ADJ
ejpam-6046	269	7	,	,	PUNCT
ejpam-6046	269	8	s1	s1	PROPN
ejpam-6046	269	9	is	be	AUX
ejpam-6046	269	10	an	an	DET
ejpam-6046	269	11	edge	edge	NOUN
ejpam-6046	269	12	dominating	dominating	NOUN
ejpam-6046	269	13	set	set	NOUN
ejpam-6046	269	14	of	of	ADP
ejpam-6046	269	15	e(frn	e(frn	PROPN
ejpam-6046	269	16	)	)	PUNCT
ejpam-6046	269	17	,	,	PUNCT
ejpam-6046	269	18	and	and	CCONJ
ejpam-6046	269	19	consequently	consequently	ADV
ejpam-6046	269	20	,	,	PUNCT
ejpam-6046	269	21	s1	s1	PROPN
ejpam-6046	269	22	∈	∈	PROPN
ejpam-6046	269	23	ide	ide	NOUN
ejpam-6046	269	24	frn	frn	PROPN
ejpam-6046	269	25	.	.	PUNCT
ejpam-6046	270	1	in	in	ADP
ejpam-6046	270	2	sk	sk	ADP
ejpam-6046	270	3	a	a	DET
ejpam-6046	270	4	=	=	X
ejpam-6046	270	5	{	{	PUNCT
ejpam-6046	270	6	e1a,1b	e1a,1b	NOUN
ejpam-6046	270	7	,	,	PUNCT
ejpam-6046	270	8	e2a,2b	e2a,2b	ADV
ejpam-6046	270	9	,	,	PUNCT
ejpam-6046	270	10	.	.	PUNCT
ejpam-6046	270	11	.	.	PUNCT
ejpam-6046	270	12	.	.	PUNCT
ejpam-6046	271	1	,	,	PUNCT
ejpam-6046	271	2	ena	ena	PROPN
ejpam-6046	271	3	,	,	PUNCT
ejpam-6046	271	4	nb	nb	INTJ
ejpam-6046	271	5	}	}	PUNCT
ejpam-6046	271	6	\	\	NOUN
ejpam-6046	271	7	{	{	PUNCT
ejpam-6046	271	8	eka	eka	PROPN
ejpam-6046	271	9	,	,	PUNCT
ejpam-6046	271	10	kb	kb	PROPN
ejpam-6046	271	11	}	}	PUNCT
ejpam-6046	271	12	,	,	PUNCT
ejpam-6046	271	13	note	note	VERB
ejpam-6046	271	14	that	that	SCONJ
ejpam-6046	271	15	by	by	ADP
ejpam-6046	271	16	removing	remove	VERB
ejpam-6046	271	17	eka	eka	NOUN
ejpam-6046	271	18	,	,	PUNCT
ejpam-6046	271	19	kb	kb	PROPN
ejpam-6046	271	20	and	and	CCONJ
ejpam-6046	271	21	replacing	replace	VERB
ejpam-6046	271	22	it	it	PRON
ejpam-6046	271	23	with	with	ADP
ejpam-6046	271	24	e0,ka	e0,ka	NOUN
ejpam-6046	271	25	,	,	PUNCT
ejpam-6046	271	26	which	which	PRON
ejpam-6046	271	27	is	be	AUX
ejpam-6046	271	28	adjacent	adjacent	ADJ
ejpam-6046	271	29	only	only	ADV
ejpam-6046	271	30	to	to	ADP
ejpam-6046	271	31	eka	eka	PROPN
ejpam-6046	271	32	,	,	PUNCT
ejpam-6046	271	33	kb	kb	PROPN
ejpam-6046	271	34	,	,	PUNCT
ejpam-6046	271	35	s	s	PART
ejpam-6046	271	36	k	k	PROPN
ejpam-6046	271	37	a	a	PRON
ejpam-6046	271	38	is	be	AUX
ejpam-6046	271	39	an	an	DET
ejpam-6046	271	40	independent	independent	ADJ
ejpam-6046	271	41	edge	edge	NOUN
ejpam-6046	271	42	set	set	NOUN
ejpam-6046	271	43	.	.	PUNCT
ejpam-6046	272	1	let	let	VERB
ejpam-6046	272	2	ep	ep	PROPN
ejpam-6046	272	3	,	,	PUNCT
ejpam-6046	272	4	q	q	PROPN
ejpam-6046	272	5	∈	∈	PROPN
ejpam-6046	272	6	e(frn	e(frn	PROPN
ejpam-6046	272	7	)	)	PUNCT
ejpam-6046	272	8	\	\	PROPN
ejpam-6046	272	9	sk	sk	VERB
ejpam-6046	272	10	a	a	PRON
ejpam-6046	272	11	.	.	PUNCT
ejpam-6046	273	1	then	then	ADV
ejpam-6046	273	2	either	either	CCONJ
ejpam-6046	273	3	p	p	X
ejpam-6046	273	4	=	=	SYM
ejpam-6046	273	5	0	0	NUM
ejpam-6046	273	6	and	and	CCONJ
ejpam-6046	273	7	q	q	PROPN
ejpam-6046	273	8	∈	∈	PROPN
ejpam-6046	273	9	{	{	PUNCT
ejpam-6046	273	10	ra	ra	PROPN
ejpam-6046	273	11	,	,	PUNCT
ejpam-6046	273	12	rb	rb	VERB
ejpam-6046	273	13	}	}	PUNCT
ejpam-6046	273	14	for	for	ADP
ejpam-6046	273	15	some	some	DET
ejpam-6046	273	16	r	r	NOUN
ejpam-6046	273	17	∈	∈	PROPN
ejpam-6046	274	1	[	[	X
ejpam-6046	274	2	n	n	X
ejpam-6046	274	3	]	]	PUNCT
ejpam-6046	274	4	\	\	PUNCT
ejpam-6046	274	5	{	{	PUNCT
ejpam-6046	274	6	k	k	NOUN
ejpam-6046	274	7	}	}	PUNCT
ejpam-6046	274	8	,	,	PUNCT
ejpam-6046	274	9	or	or	CCONJ
ejpam-6046	274	10	ep	ep	PROPN
ejpam-6046	274	11	,	,	PUNCT
ejpam-6046	274	12	q	q	NOUN
ejpam-6046	274	13	=	=	SYM
ejpam-6046	274	14	eka	eka	PROPN
ejpam-6046	274	15	,	,	PUNCT
ejpam-6046	274	16	kb	kb	PROPN
ejpam-6046	274	17	,	,	PUNCT
ejpam-6046	274	18	and	and	CCONJ
ejpam-6046	274	19	so	so	ADV
ejpam-6046	274	20	ep	ep	PROPN
ejpam-6046	274	21	,	,	PUNCT
ejpam-6046	274	22	q	q	X
ejpam-6046	274	23	is	be	AUX
ejpam-6046	274	24	either	either	CCONJ
ejpam-6046	274	25	adjacent	adjacent	ADJ
ejpam-6046	274	26	to	to	ADP
ejpam-6046	274	27	era	era	NOUN
ejpam-6046	274	28	,	,	PUNCT
ejpam-6046	274	29	rb	rb	NOUN
ejpam-6046	274	30	or	or	CCONJ
ejpam-6046	274	31	to	to	PART
ejpam-6046	274	32	e0,ka	e0,ka	NOUN
ejpam-6046	274	33	which	which	PRON
ejpam-6046	274	34	are	be	AUX
ejpam-6046	274	35	in	in	ADP
ejpam-6046	274	36	sk	sk	PROPN
ejpam-6046	274	37	a	a	PRON
ejpam-6046	274	38	.	.	PUNCT
ejpam-6046	275	1	hence	hence	ADV
ejpam-6046	275	2	,	,	PUNCT
ejpam-6046	275	3	sk	sk	VERB
ejpam-6046	275	4	a	a	PRON
ejpam-6046	275	5	is	be	AUX
ejpam-6046	275	6	an	an	DET
ejpam-6046	275	7	edge	edge	NOUN
ejpam-6046	275	8	dominating	dominating	NOUN
ejpam-6046	275	9	set	set	NOUN
ejpam-6046	275	10	.	.	PUNCT
ejpam-6046	276	1	therefore	therefore	ADV
ejpam-6046	276	2	,	,	PUNCT
ejpam-6046	276	3	sk	sk	VERB
ejpam-6046	276	4	a	a	DET
ejpam-6046	276	5	∈	∈	PROPN
ejpam-6046	276	6	ide	ide	NOUN
ejpam-6046	276	7	frn	frn	PROPN
ejpam-6046	276	8	.	.	PUNCT
ejpam-6046	277	1	j.	j.	PROPN
ejpam-6046	277	2	n.	n.	PROPN
ejpam-6046	277	3	ontulan	ontulan	PROPN
ejpam-6046	277	4	,	,	PUNCT
ejpam-6046	277	5	c.	c.	PROPN
ejpam-6046	277	6	m.	m.	NOUN
ejpam-6046	277	7	balingit	balingit	PROPN
ejpam-6046	277	8	/	/	SYM
ejpam-6046	277	9	eur	eur	PROPN
ejpam-6046	277	10	.	.	PUNCT
ejpam-6046	278	1	j.	j.	PROPN
ejpam-6046	278	2	pure	pure	PROPN
ejpam-6046	278	3	appl	appl	PROPN
ejpam-6046	278	4	.	.	PROPN
ejpam-6046	278	5	math	math	PROPN
ejpam-6046	278	6	,	,	PUNCT
ejpam-6046	278	7	18	18	NUM
ejpam-6046	278	8	(	(	PUNCT
ejpam-6046	278	9	2	2	NUM
ejpam-6046	278	10	)	)	PUNCT
ejpam-6046	278	11	(	(	PUNCT
ejpam-6046	278	12	2025	2025	NUM
ejpam-6046	278	13	)	)	PUNCT
ejpam-6046	278	14	,	,	PUNCT
ejpam-6046	278	15	6046	6046	NUM
ejpam-6046	278	16	10	10	NUM
ejpam-6046	278	17	of	of	ADP
ejpam-6046	278	18	14	14	NUM
ejpam-6046	278	19	similarly	similarly	ADV
ejpam-6046	278	20	,	,	PUNCT
ejpam-6046	278	21	sk	sk	PROPN
ejpam-6046	278	22	b	b	PROPN
ejpam-6046	278	23	∈	∈	PROPN
ejpam-6046	278	24	ide	ide	NOUN
ejpam-6046	278	25	frn	frn	PROPN
ejpam-6046	278	26	.	.	PUNCT
ejpam-6046	279	1	conversely	conversely	ADV
ejpam-6046	279	2	,	,	PUNCT
ejpam-6046	279	3	let	let	VERB
ejpam-6046	279	4	s	s	PRON
ejpam-6046	279	5	⊆	⊆	NUM
ejpam-6046	279	6	e(frn	e(frn	PROPN
ejpam-6046	279	7	)	)	PUNCT
ejpam-6046	279	8	such	such	ADJ
ejpam-6046	279	9	that	that	SCONJ
ejpam-6046	279	10	s	s	VERB
ejpam-6046	279	11	is	be	AUX
ejpam-6046	279	12	not	not	PART
ejpam-6046	279	13	one	one	NUM
ejpam-6046	279	14	of	of	ADP
ejpam-6046	279	15	the	the	DET
ejpam-6046	279	16	given	give	VERB
ejpam-6046	279	17	forms	form	NOUN
ejpam-6046	279	18	.	.	PUNCT
ejpam-6046	280	1	if	if	SCONJ
ejpam-6046	280	2	|s|	|s|	NOUN
ejpam-6046	280	3	>	>	SYM
ejpam-6046	280	4	n	n	CCONJ
ejpam-6046	280	5	,	,	PUNCT
ejpam-6046	280	6	then	then	ADV
ejpam-6046	280	7	there	there	PRON
ejpam-6046	280	8	exists	exist	VERB
ejpam-6046	280	9	k	k	PROPN
ejpam-6046	280	10	∈	∈	PROPN
ejpam-6046	281	1	[	[	X
ejpam-6046	281	2	n	n	X
ejpam-6046	281	3	]	]	X
ejpam-6046	281	4	such	such	ADJ
ejpam-6046	281	5	that	that	SCONJ
ejpam-6046	281	6	two	two	NUM
ejpam-6046	281	7	of	of	ADP
ejpam-6046	281	8	eka	eka	PROPN
ejpam-6046	281	9	,	,	PUNCT
ejpam-6046	281	10	kb	kb	PROPN
ejpam-6046	281	11	,	,	PUNCT
ejpam-6046	281	12	e0,ka	e0,ka	NOUN
ejpam-6046	281	13	,	,	PUNCT
ejpam-6046	281	14	or	or	CCONJ
ejpam-6046	281	15	e0,kb	e0,kb	PROPN
ejpam-6046	281	16	are	be	AUX
ejpam-6046	281	17	in	in	ADP
ejpam-6046	281	18	s	s	PROPN
ejpam-6046	281	19	,	,	PUNCT
ejpam-6046	281	20	so	so	SCONJ
ejpam-6046	281	21	that	that	SCONJ
ejpam-6046	281	22	s	s	VERB
ejpam-6046	281	23	is	be	AUX
ejpam-6046	281	24	not	not	PART
ejpam-6046	281	25	independent	independent	ADJ
ejpam-6046	281	26	.	.	PUNCT
ejpam-6046	282	1	if	if	SCONJ
ejpam-6046	282	2	|s|	|s|	NOUN
ejpam-6046	282	3	<	<	X
ejpam-6046	282	4	n	n	CCONJ
ejpam-6046	282	5	,	,	PUNCT
ejpam-6046	282	6	then	then	ADV
ejpam-6046	282	7	there	there	PRON
ejpam-6046	282	8	exists	exist	VERB
ejpam-6046	282	9	k	k	PROPN
ejpam-6046	282	10	∈	∈	PROPN
ejpam-6046	283	1	[	[	X
ejpam-6046	283	2	n	n	X
ejpam-6046	283	3	]	]	X
ejpam-6046	283	4	such	such	ADJ
ejpam-6046	283	5	that	that	SCONJ
ejpam-6046	283	6	eka	eka	PROPN
ejpam-6046	283	7	,	,	PUNCT
ejpam-6046	283	8	kb	kb	PROPN
ejpam-6046	283	9	,	,	PUNCT
ejpam-6046	283	10	e0,ka	e0,ka	NOUN
ejpam-6046	283	11	,	,	PUNCT
ejpam-6046	283	12	e0,kb	e0,kb	PROPN
ejpam-6046	283	13	/∈	/∈	PUNCT
ejpam-6046	284	1	s.	s.	PROPN
ejpam-6046	284	2	this	this	PRON
ejpam-6046	284	3	means	mean	VERB
ejpam-6046	284	4	that	that	SCONJ
ejpam-6046	284	5	eka	eka	PROPN
ejpam-6046	284	6	,	,	PUNCT
ejpam-6046	284	7	kb	kb	PROPN
ejpam-6046	284	8	is	be	AUX
ejpam-6046	284	9	not	not	PART
ejpam-6046	284	10	dominated	dominate	VERB
ejpam-6046	284	11	by	by	ADP
ejpam-6046	284	12	s	s	PROPN
ejpam-6046	284	13	,	,	PUNCT
ejpam-6046	284	14	and	and	CCONJ
ejpam-6046	284	15	so	so	ADV
ejpam-6046	284	16	s	s	VERB
ejpam-6046	284	17	is	be	AUX
ejpam-6046	284	18	not	not	PART
ejpam-6046	284	19	an	an	DET
ejpam-6046	284	20	edge	edge	NOUN
ejpam-6046	284	21	dominating	dominating	NOUN
ejpam-6046	284	22	set	set	NOUN
ejpam-6046	284	23	of	of	ADP
ejpam-6046	284	24	frn	frn	PROPN
ejpam-6046	284	25	.	.	PUNCT
ejpam-6046	285	1	now	now	ADV
ejpam-6046	285	2	,	,	PUNCT
ejpam-6046	285	3	if	if	SCONJ
ejpam-6046	285	4	|s|	|s|	PROPN
ejpam-6046	285	5	=	=	SYM
ejpam-6046	285	6	n	n	NOUN
ejpam-6046	285	7	and	and	CCONJ
ejpam-6046	285	8	there	there	PRON
ejpam-6046	285	9	exist	exist	VERB
ejpam-6046	285	10	distinct	distinct	ADJ
ejpam-6046	285	11	k	k	NOUN
ejpam-6046	285	12	,	,	PUNCT
ejpam-6046	285	13	k′	k′	PROPN
ejpam-6046	285	14	∈	∈	PROPN
ejpam-6046	286	1	[	[	X
ejpam-6046	286	2	n	n	X
ejpam-6046	286	3	]	]	X
ejpam-6046	286	4	such	such	ADJ
ejpam-6046	286	5	that	that	DET
ejpam-6046	286	6	e0,kx	e0,kx	NOUN
ejpam-6046	286	7	,	,	PUNCT
ejpam-6046	286	8	e0,k′y	e0,k′y	PROPN
ejpam-6046	286	9	∈	∈	NOUN
ejpam-6046	286	10	s	s	NOUN
ejpam-6046	286	11	with	with	ADP
ejpam-6046	286	12	x	x	PROPN
ejpam-6046	286	13	,	,	PUNCT
ejpam-6046	286	14	y	y	PROPN
ejpam-6046	286	15	∈	∈	PROPN
ejpam-6046	286	16	{	{	PUNCT
ejpam-6046	286	17	a	a	PROPN
ejpam-6046	286	18	,	,	PUNCT
ejpam-6046	286	19	b	b	NOUN
ejpam-6046	286	20	}	}	PUNCT
ejpam-6046	286	21	,	,	PUNCT
ejpam-6046	286	22	s	s	VERB
ejpam-6046	286	23	is	be	AUX
ejpam-6046	286	24	not	not	PART
ejpam-6046	286	25	an	an	DET
ejpam-6046	286	26	independent	independent	ADJ
ejpam-6046	286	27	edge	edge	NOUN
ejpam-6046	286	28	set	set	VERB
ejpam-6046	286	29	by	by	ADP
ejpam-6046	286	30	remark	remark	NOUN
ejpam-6046	286	31	1	1	NUM
ejpam-6046	286	32	.	.	PUNCT
ejpam-6046	287	1	■	■	PUNCT
ejpam-6046	287	2	corollary	corollary	ADJ
ejpam-6046	287	3	2	2	NUM
ejpam-6046	287	4	.	.	PUNCT
ejpam-6046	288	1	for	for	ADP
ejpam-6046	288	2	the	the	DET
ejpam-6046	288	3	friendship	friendship	NOUN
ejpam-6046	288	4	graph	graph	NOUN
ejpam-6046	288	5	frn	frn	PROPN
ejpam-6046	288	6	,	,	PUNCT
ejpam-6046	288	7	n	n	PRON
ejpam-6046	288	8	≥	≥	NOUN
ejpam-6046	288	9	2	2	NUM
ejpam-6046	288	10	,	,	PUNCT
ejpam-6046	288	11	|ide	|ide	ADJ
ejpam-6046	288	12	frn	frn	PROPN
ejpam-6046	288	13	|	|	NOUN
ejpam-6046	289	1	=	=	SYM
ejpam-6046	289	2	2n+	2n+	NUM
ejpam-6046	289	3	1	1	NUM
ejpam-6046	289	4	.	.	PUNCT
ejpam-6046	289	5	example	example	NOUN
ejpam-6046	289	6	5	5	NUM
ejpam-6046	289	7	.	.	PUNCT
ejpam-6046	289	8	consider	consider	VERB
ejpam-6046	289	9	the	the	DET
ejpam-6046	289	10	friendship	friendship	NOUN
ejpam-6046	289	11	graph	graph	NOUN
ejpam-6046	289	12	fr4	fr4	PROPN
ejpam-6046	289	13	in	in	ADP
ejpam-6046	289	14	figure	figure	NOUN
ejpam-6046	289	15	7	7	NUM
ejpam-6046	289	16	with	with	ADP
ejpam-6046	289	17	e(fr4	e(fr4	NOUN
ejpam-6046	289	18	)	)	PUNCT
ejpam-6046	289	19	=	=	SYM
ejpam-6046	289	20	{	{	PUNCT
ejpam-6046	289	21	e0,1a	e0,1a	PROPN
ejpam-6046	289	22	,	,	PUNCT
ejpam-6046	289	23	e0,1b	e0,1b	PROPN
ejpam-6046	289	24	,	,	PUNCT
ejpam-6046	289	25	e1a,1b	e1a,1b	NOUN
ejpam-6046	289	26	,	,	PUNCT
ejpam-6046	289	27	e0,2a	e0,2a	PROPN
ejpam-6046	289	28	,	,	PUNCT
ejpam-6046	289	29	e0,2b	e0,2b	PROPN
ejpam-6046	289	30	,	,	PUNCT
ejpam-6046	289	31	e2a,2b	e2a,2b	ADV
ejpam-6046	289	32	,	,	PUNCT
ejpam-6046	289	33	e0,3a	e0,3a	PROPN
ejpam-6046	289	34	,	,	PUNCT
ejpam-6046	289	35	e0,3b	e0,3b	PROPN
ejpam-6046	289	36	,	,	PUNCT
ejpam-6046	289	37	e3a,3b	e3a,3b	NOUN
ejpam-6046	289	38	,	,	PUNCT
ejpam-6046	289	39	e0,4a	e0,4a	PROPN
ejpam-6046	289	40	,	,	PUNCT
ejpam-6046	289	41	e0,4b	e0,4b	PROPN
ejpam-6046	289	42	,	,	PUNCT
ejpam-6046	289	43	e4a,4b	e4a,4b	ADV
ejpam-6046	289	44	,	,	PUNCT
ejpam-6046	289	45	}	}	PUNCT
ejpam-6046	289	46	.	.	PUNCT
ejpam-6046	290	1	by	by	ADP
ejpam-6046	290	2	theorem	theorem	NOUN
ejpam-6046	290	3	6	6	NUM
ejpam-6046	290	4	,	,	PUNCT
ejpam-6046	290	5	observe	observe	VERB
ejpam-6046	290	6	that	that	DET
ejpam-6046	290	7	ide	ide	NOUN
ejpam-6046	290	8	fr4	fr4	PROPN
ejpam-6046	290	9	=	=	PUNCT
ejpam-6046	290	10	{	{	PUNCT
ejpam-6046	290	11	{	{	PUNCT
ejpam-6046	290	12	e1a,1b	e1a,1b	NOUN
ejpam-6046	290	13	,	,	PUNCT
ejpam-6046	290	14	e2a,2b	e2a,2b	ADV
ejpam-6046	290	15	,	,	PUNCT
ejpam-6046	290	16	e3a,3b	e3a,3b	NOUN
ejpam-6046	290	17	,	,	PUNCT
ejpam-6046	290	18	e4a,4b	e4a,4b	X
ejpam-6046	290	19	}	}	PUNCT
ejpam-6046	290	20	,	,	PUNCT
ejpam-6046	290	21	{	{	PUNCT
ejpam-6046	290	22	e2a,2b	e2a,2b	ADV
ejpam-6046	290	23	,	,	PUNCT
ejpam-6046	290	24	e3a,3b	e3a,3b	NOUN
ejpam-6046	290	25	,	,	PUNCT
ejpam-6046	290	26	e4a,4b	e4a,4b	NOUN
ejpam-6046	290	27	,	,	PUNCT
ejpam-6046	290	28	e0,1a	e0,1a	PROPN
ejpam-6046	290	29	}	}	PUNCT
ejpam-6046	290	30	,	,	PUNCT
ejpam-6046	290	31	{	{	PUNCT
ejpam-6046	290	32	e1a,1b	e1a,1b	NOUN
ejpam-6046	290	33	,	,	PUNCT
ejpam-6046	290	34	e3a,3b	e3a,3b	NOUN
ejpam-6046	290	35	,	,	PUNCT
ejpam-6046	290	36	e4a,4b	e4a,4b	NOUN
ejpam-6046	290	37	,	,	PUNCT
ejpam-6046	290	38	e0,2a	e0,2a	PROPN
ejpam-6046	290	39	}	}	PUNCT
ejpam-6046	290	40	,	,	PUNCT
ejpam-6046	290	41	{	{	PUNCT
ejpam-6046	290	42	e1a,1b	e1a,1b	NOUN
ejpam-6046	290	43	,	,	PUNCT
ejpam-6046	290	44	e2a,2b	e2a,2b	ADV
ejpam-6046	290	45	,	,	PUNCT
ejpam-6046	290	46	e4a,4b	e4a,4b	PROPN
ejpam-6046	290	47	,	,	PUNCT
ejpam-6046	290	48	e0,3a	e0,3a	PROPN
ejpam-6046	290	49	}	}	PUNCT
ejpam-6046	290	50	,	,	PUNCT
ejpam-6046	290	51	{	{	PUNCT
ejpam-6046	290	52	e1a,1b	e1a,1b	NOUN
ejpam-6046	290	53	,	,	PUNCT
ejpam-6046	290	54	e2a,2b	e2a,2b	ADV
ejpam-6046	290	55	,	,	PUNCT
ejpam-6046	290	56	e3a,3b	e3a,3b	NOUN
ejpam-6046	290	57	,	,	PUNCT
ejpam-6046	290	58	e0,4a	e0,4a	PROPN
ejpam-6046	290	59	}	}	PUNCT
ejpam-6046	290	60	,	,	PUNCT
ejpam-6046	290	61	{	{	PUNCT
ejpam-6046	290	62	e2a,2b	e2a,2b	ADV
ejpam-6046	290	63	,	,	PUNCT
ejpam-6046	290	64	e3a,3b	e3a,3b	NOUN
ejpam-6046	290	65	,	,	PUNCT
ejpam-6046	290	66	e4a,4b	e4a,4b	NOUN
ejpam-6046	290	67	,	,	PUNCT
ejpam-6046	290	68	e0,1b	e0,1b	NOUN
ejpam-6046	290	69	}	}	PUNCT
ejpam-6046	290	70	,	,	PUNCT
ejpam-6046	290	71	{	{	PUNCT
ejpam-6046	290	72	e1a,1b	e1a,1b	NOUN
ejpam-6046	290	73	,	,	PUNCT
ejpam-6046	290	74	e3a,3b	e3a,3b	NOUN
ejpam-6046	290	75	,	,	PUNCT
ejpam-6046	290	76	e4a,4b	e4a,4b	X
ejpam-6046	290	77	,	,	PUNCT
ejpam-6046	290	78	e0,2b	e0,2b	NOUN
ejpam-6046	290	79	}	}	PUNCT
ejpam-6046	290	80	,	,	PUNCT
ejpam-6046	290	81	{	{	PUNCT
ejpam-6046	290	82	e1a,1b	e1a,1b	NOUN
ejpam-6046	290	83	,	,	PUNCT
ejpam-6046	290	84	e2a,2b	e2a,2b	ADV
ejpam-6046	290	85	,	,	PUNCT
ejpam-6046	290	86	e4a,4b	e4a,4b	ADV
ejpam-6046	290	87	,	,	PUNCT
ejpam-6046	290	88	e0,3b	e0,3b	PROPN
ejpam-6046	290	89	}	}	PUNCT
ejpam-6046	290	90	,	,	PUNCT
ejpam-6046	290	91	{	{	PUNCT
ejpam-6046	290	92	e1a,1b	e1a,1b	NOUN
ejpam-6046	290	93	,	,	PUNCT
ejpam-6046	290	94	e2a,2b	e2a,2b	ADV
ejpam-6046	290	95	,	,	PUNCT
ejpam-6046	290	96	e3a,3b	e3a,3b	NOUN
ejpam-6046	290	97	,	,	PUNCT
ejpam-6046	290	98	e0,4b	e0,4b	PROPN
ejpam-6046	290	99	}	}	PUNCT
ejpam-6046	290	100	}	}	PUNCT
ejpam-6046	290	101	.	.	PUNCT
ejpam-6046	291	1	indeed	indeed	ADV
ejpam-6046	291	2	,	,	PUNCT
ejpam-6046	291	3	|ide	|ide	ADP
ejpam-6046	291	4	fr4	fr4	PROPN
ejpam-6046	291	5	|	|	PROPN
ejpam-6046	291	6	=	=	PROPN
ejpam-6046	291	7	2(4	2(4	NUM
ejpam-6046	291	8	)	)	PUNCT
ejpam-6046	292	1	+	+	CCONJ
ejpam-6046	292	2	1	1	NUM
ejpam-6046	292	3	=	=	SYM
ejpam-6046	292	4	9	9	NUM
ejpam-6046	292	5	.	.	PUNCT
ejpam-6046	292	6	theorem	theorem	NOUN
ejpam-6046	292	7	7	7	NUM
ejpam-6046	292	8	.	.	PUNCT
ejpam-6046	293	1	let	let	VERB
ejpam-6046	293	2	frn	frn	PROPN
ejpam-6046	293	3	be	be	AUX
ejpam-6046	293	4	a	a	DET
ejpam-6046	293	5	friendship	friendship	NOUN
ejpam-6046	293	6	graph	graph	NOUN
ejpam-6046	293	7	and	and	CCONJ
ejpam-6046	293	8	s1	s1	NOUN
ejpam-6046	293	9	=	=	PUNCT
ejpam-6046	293	10	{	{	PUNCT
ejpam-6046	293	11	e1a,1b	e1a,1b	NOUN
ejpam-6046	293	12	,	,	PUNCT
ejpam-6046	293	13	e2a,2b	e2a,2b	ADV
ejpam-6046	293	14	,	,	PUNCT
ejpam-6046	293	15	.	.	PUNCT
ejpam-6046	293	16	.	.	PUNCT
ejpam-6046	294	1	.	.	PUNCT
ejpam-6046	295	1	,	,	PUNCT
ejpam-6046	295	2	ena	ena	PROPN
ejpam-6046	295	3	,	,	PUNCT
ejpam-6046	295	4	nb	nb	NOUN
ejpam-6046	295	5	}	}	PUNCT
ejpam-6046	295	6	.	.	PUNCT
ejpam-6046	296	1	a	a	DET
ejpam-6046	296	2	set	set	NOUN
ejpam-6046	296	3	s	s	NOUN
ejpam-6046	296	4	⊆	⊆	NUM
ejpam-6046	296	5	e(frn	e(frn	PROPN
ejpam-6046	296	6	)	)	PUNCT
ejpam-6046	296	7	is	be	AUX
ejpam-6046	296	8	τeid(frn)-open	τeid(frn)-open	VERB
ejpam-6046	296	9	if	if	SCONJ
ejpam-6046	296	10	and	and	CCONJ
ejpam-6046	296	11	only	only	ADV
ejpam-6046	296	12	if	if	SCONJ
ejpam-6046	296	13	s	s	X
ejpam-6046	296	14	satisfies	satisfy	VERB
ejpam-6046	296	15	any	any	PRON
ejpam-6046	296	16	of	of	ADP
ejpam-6046	296	17	the	the	DET
ejpam-6046	296	18	following	follow	VERB
ejpam-6046	296	19	forms	form	NOUN
ejpam-6046	296	20	:	:	PUNCT
ejpam-6046	296	21	i.	i.	PROPN
ejpam-6046	296	22	s	s	PART
ejpam-6046	296	23	⊆	⊆	NUM
ejpam-6046	296	24	s1	s1	NOUN
ejpam-6046	296	25	;	;	PUNCT
ejpam-6046	296	26	ii	ii	X
ejpam-6046	296	27	.	.	PUNCT
ejpam-6046	296	28	s	s	PART
ejpam-6046	297	1	=	=	NOUN
ejpam-6046	297	2	s1	s1	PROPN
ejpam-6046	297	3	∪	∪	X
ejpam-6046	297	4	{	{	PUNCT
ejpam-6046	297	5	e0,ia	e0,ia	PROPN
ejpam-6046	297	6	:	:	PUNCT
ejpam-6046	297	7	i	i	PRON
ejpam-6046	297	8	∈	∈	VERB
ejpam-6046	297	9	a	a	DET
ejpam-6046	297	10	}	}	PUNCT
ejpam-6046	297	11	∪	∪	X
ejpam-6046	297	12	{	{	PUNCT
ejpam-6046	297	13	e0,ib	e0,ib	ADV
ejpam-6046	297	14	:	:	PUNCT
ejpam-6046	297	15	i	i	PROPN
ejpam-6046	297	16	∈	∈	PROPN
ejpam-6046	297	17	b	b	AUX
ejpam-6046	297	18	}	}	PUNCT
ejpam-6046	297	19	such	such	ADJ
ejpam-6046	297	20	that	that	SCONJ
ejpam-6046	297	21	a	a	DET
ejpam-6046	297	22	,	,	PUNCT
ejpam-6046	297	23	b	b	PROPN
ejpam-6046	297	24	∈	∈	PROPN
ejpam-6046	297	25	[	[	X
ejpam-6046	297	26	n	n	X
ejpam-6046	297	27	]	]	X
ejpam-6046	297	28	;	;	PUNCT
ejpam-6046	297	29	and	and	CCONJ
ejpam-6046	297	30	iii	iii	X
ejpam-6046	297	31	.	.	PUNCT
ejpam-6046	297	32	s	s	PART
ejpam-6046	298	1	=	=	PUNCT
ejpam-6046	298	2	[	[	X
ejpam-6046	298	3	s1	s1	X
ejpam-6046	298	4	\	\	PROPN
ejpam-6046	298	5	{	{	PUNCT
ejpam-6046	298	6	eka	eka	PROPN
ejpam-6046	298	7	,	,	PUNCT
ejpam-6046	298	8	kb	kb	PROPN
ejpam-6046	298	9	}	}	PUNCT
ejpam-6046	298	10	]	]	PUNCT
ejpam-6046	298	11	∪	∪	ADP
ejpam-6046	298	12	s∗	s∗	PROPN
ejpam-6046	298	13	such	such	ADJ
ejpam-6046	298	14	that	that	DET
ejpam-6046	298	15	s∗	s∗	PROPN
ejpam-6046	298	16	⊆	⊆	NUM
ejpam-6046	298	17	{	{	PUNCT
ejpam-6046	298	18	e0,ka	e0,ka	NOUN
ejpam-6046	298	19	,	,	PUNCT
ejpam-6046	298	20	e0,kb	e0,kb	PROPN
ejpam-6046	298	21	}	}	PUNCT
ejpam-6046	298	22	for	for	ADP
ejpam-6046	298	23	all	all	DET
ejpam-6046	298	24	k	k	PROPN
ejpam-6046	298	25	∈	∈	PROPN
ejpam-6046	298	26	[	[	X
ejpam-6046	298	27	n	n	X
ejpam-6046	298	28	]	]	PUNCT
ejpam-6046	298	29	.	.	PUNCT
ejpam-6046	299	1	proof	proof	NOUN
ejpam-6046	299	2	.	.	PUNCT
ejpam-6046	300	1	let	let	VERB
ejpam-6046	300	2	s	s	PRON
ejpam-6046	300	3	⊆	⊆	NUM
ejpam-6046	300	4	e(frn	e(frn	PROPN
ejpam-6046	300	5	)	)	PUNCT
ejpam-6046	300	6	.	.	PUNCT
ejpam-6046	301	1	if	if	SCONJ
ejpam-6046	301	2	s	s	VERB
ejpam-6046	301	3	⊆	⊆	NUM
ejpam-6046	301	4	s1	s1	NOUN
ejpam-6046	301	5	,	,	PUNCT
ejpam-6046	301	6	then	then	ADV
ejpam-6046	301	7	for	for	ADP
ejpam-6046	301	8	some	some	DET
ejpam-6046	301	9	a	a	DET
ejpam-6046	301	10	⊆	⊆	NUM
ejpam-6046	301	11	[	[	X
ejpam-6046	301	12	n	n	X
ejpam-6046	301	13	]	]	X
ejpam-6046	301	14	,	,	PUNCT
ejpam-6046	301	15	s	s	NOUN
ejpam-6046	301	16	=	=	PUNCT
ejpam-6046	301	17	{	{	PUNCT
ejpam-6046	301	18	eia	eia	PROPN
ejpam-6046	301	19	,	,	PUNCT
ejpam-6046	301	20	ib	ib	X
ejpam-6046	301	21	:	:	PUNCT
ejpam-6046	301	22	i	i	PRON
ejpam-6046	301	23	∈	∈	VERB
ejpam-6046	301	24	a	a	DET
ejpam-6046	301	25	}	}	PUNCT
ejpam-6046	301	26	=	=	SYM
ejpam-6046	301	27	⋂	⋂	PROPN
ejpam-6046	301	28	i/∈a	i/∈a	VERB
ejpam-6046	301	29	sk	sk	VERB
ejpam-6046	301	30	a	a	DET
ejpam-6046	301	31	∈	∈	PROPN
ejpam-6046	301	32	τeid(frn	τeid(frn	NOUN
ejpam-6046	301	33	)	)	PUNCT
ejpam-6046	301	34	.	.	PUNCT
ejpam-6046	302	1	let	let	VERB
ejpam-6046	302	2	a	a	PRON
ejpam-6046	302	3	,	,	PUNCT
ejpam-6046	302	4	b	b	NOUN
ejpam-6046	302	5	⊆	⊆	NUM
ejpam-6046	302	6	[	[	X
ejpam-6046	302	7	n	n	X
ejpam-6046	302	8	]	]	PUNCT
ejpam-6046	302	9	.	.	PUNCT
ejpam-6046	303	1	then	then	ADV
ejpam-6046	303	2	,	,	PUNCT
ejpam-6046	303	3	s	s	NOUN
ejpam-6046	303	4	=	=	NOUN
ejpam-6046	303	5	s1	s1	PROPN
ejpam-6046	303	6	∪	∪	X
ejpam-6046	303	7	{	{	PUNCT
ejpam-6046	303	8	e0,ia	e0,ia	PROPN
ejpam-6046	303	9	:	:	PUNCT
ejpam-6046	303	10	i	i	PRON
ejpam-6046	303	11	∈	∈	VERB
ejpam-6046	303	12	a	a	DET
ejpam-6046	303	13	}	}	PUNCT
ejpam-6046	303	14	∪	∪	X
ejpam-6046	303	15	{	{	PUNCT
ejpam-6046	303	16	e0,ib	e0,ib	ADV
ejpam-6046	303	17	:	:	PUNCT
ejpam-6046	304	1	i	i	PROPN
ejpam-6046	304	2	∈	∈	PROPN
ejpam-6046	304	3	b	b	AUX
ejpam-6046	304	4	}	}	PUNCT
ejpam-6046	304	5	=	=	SYM
ejpam-6046	304	6	s1	s1	NOUN
ejpam-6046	304	7	∪	∪	ADP
ejpam-6046	304	8	[	[	PUNCT
ejpam-6046	304	9	⋃	⋃	NOUN
ejpam-6046	304	10	i∈a	i∈a	ADJ
ejpam-6046	304	11	si	si	PROPN
ejpam-6046	304	12	a	a	X
ejpam-6046	304	13	]	]	X
ejpam-6046	304	14	∪	∪	X
ejpam-6046	304	15	[	[	PUNCT
ejpam-6046	304	16	⋃	⋃	PROPN
ejpam-6046	304	17	i∈b	i∈b	ADJ
ejpam-6046	304	18	si	si	PROPN
ejpam-6046	304	19	b	b	X
ejpam-6046	304	20	]	]	X
ejpam-6046	304	21	∈	∈	PROPN
ejpam-6046	304	22	τeid(frn	τeid(frn	NOUN
ejpam-6046	304	23	)	)	PUNCT
ejpam-6046	304	24	.	.	PUNCT
ejpam-6046	305	1	if	if	SCONJ
ejpam-6046	305	2	k	k	PROPN
ejpam-6046	305	3	∈	∈	PROPN
ejpam-6046	305	4	[	[	X
ejpam-6046	305	5	n	n	X
ejpam-6046	305	6	]	]	PUNCT
ejpam-6046	305	7	and	and	CCONJ
ejpam-6046	305	8	s	s	NOUN
ejpam-6046	305	9	=	=	PUNCT
ejpam-6046	306	1	[	[	X
ejpam-6046	306	2	s1	s1	X
ejpam-6046	306	3	\	\	PROPN
ejpam-6046	306	4	{	{	PUNCT
ejpam-6046	306	5	eka	eka	PROPN
ejpam-6046	306	6	,	,	PUNCT
ejpam-6046	306	7	kb	kb	PROPN
ejpam-6046	306	8	}	}	PUNCT
ejpam-6046	306	9	]	]	PUNCT
ejpam-6046	306	10	∪	∪	ADP
ejpam-6046	306	11	s∗	s∗	PROPN
ejpam-6046	306	12	where	where	SCONJ
ejpam-6046	306	13	s∗	s∗	PROPN
ejpam-6046	306	14	=	=	SYM
ejpam-6046	306	15	∅	∅	NOUN
ejpam-6046	306	16	,	,	PUNCT
ejpam-6046	306	17	then	then	ADV
ejpam-6046	306	18	s	s	VERB
ejpam-6046	306	19	⊆	⊆	NUM
ejpam-6046	306	20	s1	s1	NOUN
ejpam-6046	306	21	.	.	PUNCT
ejpam-6046	307	1	if	if	SCONJ
ejpam-6046	307	2	s∗	s∗	PROPN
ejpam-6046	307	3	is	be	AUX
ejpam-6046	307	4	either	either	CCONJ
ejpam-6046	307	5	{	{	PUNCT
ejpam-6046	307	6	e0,ka	e0,ka	NOUN
ejpam-6046	307	7	}	}	PUNCT
ejpam-6046	307	8	or	or	CCONJ
ejpam-6046	307	9	{	{	PUNCT
ejpam-6046	307	10	e0,kb	e0,kb	PROPN
ejpam-6046	307	11	}	}	PUNCT
ejpam-6046	307	12	,	,	PUNCT
ejpam-6046	307	13	then	then	ADV
ejpam-6046	307	14	s	s	VERB
ejpam-6046	307	15	is	be	AUX
ejpam-6046	307	16	also	also	ADV
ejpam-6046	307	17	either	either	CCONJ
ejpam-6046	307	18	sk	sk	VERB
ejpam-6046	307	19	a	a	PRON
ejpam-6046	307	20	or	or	CCONJ
ejpam-6046	307	21	sk	sk	PROPN
ejpam-6046	307	22	b	b	PROPN
ejpam-6046	307	23	.	.	PUNCT
ejpam-6046	308	1	if	if	SCONJ
ejpam-6046	308	2	s	s	VERB
ejpam-6046	308	3	∗	∗	NOUN
ejpam-6046	308	4	=	=	SYM
ejpam-6046	308	5	{	{	PUNCT
ejpam-6046	308	6	e0,ka	e0,ka	NOUN
ejpam-6046	308	7	,	,	PUNCT
ejpam-6046	308	8	e0,kb	e0,kb	PROPN
ejpam-6046	308	9	}	}	PUNCT
ejpam-6046	308	10	,	,	PUNCT
ejpam-6046	308	11	then	then	ADV
ejpam-6046	308	12	s	s	AUX
ejpam-6046	308	13	=	=	PUNCT
ejpam-6046	308	14	sk	sk	VERB
ejpam-6046	308	15	a	a	DET
ejpam-6046	308	16	∪	∪	NOUN
ejpam-6046	308	17	sk	sk	X
ejpam-6046	308	18	b	b	PROPN
ejpam-6046	308	19	.	.	PUNCT
ejpam-6046	309	1	in	in	ADP
ejpam-6046	309	2	all	all	DET
ejpam-6046	309	3	cases	case	NOUN
ejpam-6046	309	4	,	,	PUNCT
ejpam-6046	309	5	s	s	VERB
ejpam-6046	309	6	is	be	AUX
ejpam-6046	309	7	τeid(frn)-open	τeid(frn)-open	NOUN
ejpam-6046	309	8	,	,	PUNCT
ejpam-6046	309	9	by	by	ADP
ejpam-6046	309	10	definition	definition	NOUN
ejpam-6046	309	11	6	6	NUM
ejpam-6046	309	12	.	.	PUNCT
ejpam-6046	310	1	conversely	conversely	ADV
ejpam-6046	310	2	,	,	PUNCT
ejpam-6046	310	3	suppose	suppose	VERB
ejpam-6046	310	4	s	s	VERB
ejpam-6046	310	5	⊆	⊆	NUM
ejpam-6046	310	6	e(frn	e(frn	PROPN
ejpam-6046	310	7	)	)	PUNCT
ejpam-6046	310	8	does	do	AUX
ejpam-6046	310	9	not	not	PART
ejpam-6046	310	10	take	take	VERB
ejpam-6046	310	11	any	any	PRON
ejpam-6046	310	12	of	of	ADP
ejpam-6046	310	13	the	the	DET
ejpam-6046	310	14	given	give	VERB
ejpam-6046	310	15	forms	form	NOUN
ejpam-6046	310	16	.	.	PUNCT
ejpam-6046	311	1	then	then	ADV
ejpam-6046	311	2	there	there	PRON
ejpam-6046	311	3	exist	exist	VERB
ejpam-6046	311	4	k	k	PROPN
ejpam-6046	311	5	,	,	PUNCT
ejpam-6046	311	6	k′	k′	PROPN
ejpam-6046	311	7	,	,	PUNCT
ejpam-6046	311	8	k∗	k∗	PROPN
ejpam-6046	311	9	∈	∈	PROPN
ejpam-6046	312	1	[	[	X
ejpam-6046	312	2	n	n	X
ejpam-6046	312	3	]	]	X
ejpam-6046	312	4	such	such	ADJ
ejpam-6046	312	5	that	that	SCONJ
ejpam-6046	312	6	eka	eka	PROPN
ejpam-6046	312	7	,	,	PUNCT
ejpam-6046	312	8	kb	kb	PROPN
ejpam-6046	312	9	,	,	PUNCT
ejpam-6046	312	10	ek′a	ek′a	PROPN
ejpam-6046	312	11	,	,	PUNCT
ejpam-6046	312	12	k′b	k′b	VERB
ejpam-6046	312	13	/∈	/∈	INTJ
ejpam-6046	312	14	s	s	X
ejpam-6046	312	15	and	and	CCONJ
ejpam-6046	312	16	either	either	CCONJ
ejpam-6046	312	17	e0,k∗a	e0,k∗a	NOUN
ejpam-6046	312	18	∈	∈	PROPN
ejpam-6046	312	19	s	s	PART
ejpam-6046	312	20	or	or	CCONJ
ejpam-6046	312	21	e0,k∗b	e0,k∗b	VERB
ejpam-6046	312	22	∈	∈	PROPN
ejpam-6046	312	23	s.	s.	PROPN
ejpam-6046	312	24	if	if	SCONJ
ejpam-6046	312	25	s	s	PROPN
ejpam-6046	312	26	is	be	AUX
ejpam-6046	312	27	a	a	DET
ejpam-6046	312	28	τeid(frn)-open	τeid(frn)-open	NOUN
ejpam-6046	312	29	set	set	VERB
ejpam-6046	312	30	,	,	PUNCT
ejpam-6046	312	31	s	s	VERB
ejpam-6046	312	32	can	can	AUX
ejpam-6046	312	33	be	be	AUX
ejpam-6046	312	34	generated	generate	VERB
ejpam-6046	312	35	out	out	ADP
ejpam-6046	312	36	of	of	ADP
ejpam-6046	312	37	the	the	DET
ejpam-6046	312	38	sets	set	NOUN
ejpam-6046	312	39	in	in	ADP
ejpam-6046	312	40	ide	ide	ADJ
ejpam-6046	312	41	frn	frn	NOUN
ejpam-6046	312	42	given	give	VERB
ejpam-6046	312	43	in	in	ADP
ejpam-6046	312	44	the	the	DET
ejpam-6046	312	45	theorem	theorem	NOUN
ejpam-6046	312	46	6	6	NUM
ejpam-6046	312	47	.	.	PUNCT
ejpam-6046	313	1	necessarily	necessarily	ADV
ejpam-6046	313	2	,	,	PUNCT
ejpam-6046	313	3	either	either	CCONJ
ejpam-6046	313	4	sk∗	sk∗	VERB
ejpam-6046	313	5	a	a	DET
ejpam-6046	313	6	⊆	⊆	NUM
ejpam-6046	313	7	s	s	NOUN
ejpam-6046	313	8	⊆	⊆	NUM
ejpam-6046	313	9	sk	sk	NOUN
ejpam-6046	313	10	x	x	PROPN
ejpam-6046	313	11	∩	∩	ADJ
ejpam-6046	313	12	sk′	sk′	ADJ
ejpam-6046	313	13	y	y	NOUN
ejpam-6046	313	14	or	or	CCONJ
ejpam-6046	313	15	sk∗	sk∗	VERB
ejpam-6046	313	16	b	b	PROPN
ejpam-6046	313	17	⊆	⊆	NUM
ejpam-6046	313	18	s	s	NOUN
ejpam-6046	313	19	⊆	⊆	NUM
ejpam-6046	313	20	sk	sk	NOUN
ejpam-6046	313	21	x	x	PROPN
ejpam-6046	313	22	∩	∩	ADJ
ejpam-6046	313	23	sk′	sk′	NOUN
ejpam-6046	313	24	y	y	PROPN
ejpam-6046	313	25	where	where	SCONJ
ejpam-6046	313	26	x	x	X
ejpam-6046	313	27	,	,	PUNCT
ejpam-6046	313	28	y	y	PROPN
ejpam-6046	313	29	∈	∈	PROPN
ejpam-6046	313	30	{	{	PUNCT
ejpam-6046	313	31	a	a	PROPN
ejpam-6046	313	32	,	,	PUNCT
ejpam-6046	313	33	b	b	NOUN
ejpam-6046	313	34	}	}	PUNCT
ejpam-6046	313	35	,	,	PUNCT
ejpam-6046	313	36	which	which	PRON
ejpam-6046	313	37	are	be	AUX
ejpam-6046	313	38	both	both	ADV
ejpam-6046	313	39	impossible	impossible	ADJ
ejpam-6046	313	40	.	.	PUNCT
ejpam-6046	314	1	thus	thus	ADV
ejpam-6046	314	2	,	,	PUNCT
ejpam-6046	314	3	s	s	VERB
ejpam-6046	314	4	can	can	AUX
ejpam-6046	314	5	not	not	PART
ejpam-6046	314	6	be	be	AUX
ejpam-6046	314	7	τeid(frn)-open	τeid(frn)-open	NOUN
ejpam-6046	314	8	.	.	PUNCT
ejpam-6046	315	1	■	■	PUNCT
ejpam-6046	315	2	remark	remark	NOUN
ejpam-6046	315	3	3	3	NUM
ejpam-6046	315	4	.	.	PUNCT
ejpam-6046	316	1	let	let	VERB
ejpam-6046	316	2	frn	frn	PROPN
ejpam-6046	316	3	be	be	AUX
ejpam-6046	316	4	a	a	DET
ejpam-6046	316	5	friendship	friendship	NOUN
ejpam-6046	316	6	graph	graph	NOUN
ejpam-6046	316	7	and	and	CCONJ
ejpam-6046	316	8	s	s	VERB
ejpam-6046	316	9	⊆	⊆	NUM
ejpam-6046	316	10	e(frn	e(frn	PROPN
ejpam-6046	316	11	)	)	PUNCT
ejpam-6046	316	12	with	with	ADP
ejpam-6046	316	13	n	n	PRON
ejpam-6046	316	14	≥	≥	NUM
ejpam-6046	316	15	2	2	NUM
ejpam-6046	316	16	.	.	PUNCT
ejpam-6046	317	1	then	then	ADV
ejpam-6046	317	2	τeid(frn	τeid(frn	PROPN
ejpam-6046	317	3	)	)	PUNCT
ejpam-6046	317	4	is	be	AUX
ejpam-6046	317	5	not	not	PART
ejpam-6046	317	6	the	the	DET
ejpam-6046	317	7	indiscrete	indiscrete	ADJ
ejpam-6046	317	8	nor	nor	CCONJ
ejpam-6046	317	9	the	the	DET
ejpam-6046	317	10	discrete	discrete	ADJ
ejpam-6046	317	11	topology	topology	NOUN
ejpam-6046	317	12	.	.	PUNCT
ejpam-6046	318	1	corollary	corollary	ADJ
ejpam-6046	318	2	3	3	NUM
ejpam-6046	318	3	.	.	PUNCT
ejpam-6046	319	1	for	for	ADP
ejpam-6046	319	2	the	the	DET
ejpam-6046	319	3	friendship	friendship	NOUN
ejpam-6046	319	4	graph	graph	NOUN
ejpam-6046	319	5	frn	frn	PROPN
ejpam-6046	319	6	with	with	ADP
ejpam-6046	319	7	n	n	PROPN
ejpam-6046	319	8	≥	≥	NUM
ejpam-6046	319	9	2	2	NUM
ejpam-6046	319	10	,	,	PUNCT
ejpam-6046	319	11	|τeid(frn)|	|τeid(frn)|	ADV
ejpam-6046	319	12	=	=	SYM
ejpam-6046	319	13	22n	22n	X
ejpam-6046	319	14	+	+	X
ejpam-6046	319	15	2n	2n	NUM
ejpam-6046	320	1	+	+	PUNCT
ejpam-6046	320	2	3n−	3n−	NUM
ejpam-6046	320	3	1	1	NUM
ejpam-6046	320	4	.	.	PUNCT
ejpam-6046	320	5	j.	j.	PROPN
ejpam-6046	320	6	n.	n.	PROPN
ejpam-6046	320	7	ontulan	ontulan	PROPN
ejpam-6046	320	8	,	,	PUNCT
ejpam-6046	320	9	c.	c.	PROPN
ejpam-6046	320	10	m.	m.	NOUN
ejpam-6046	320	11	balingit	balingit	PROPN
ejpam-6046	320	12	/	/	SYM
ejpam-6046	320	13	eur	eur	PROPN
ejpam-6046	320	14	.	.	PUNCT
ejpam-6046	321	1	j.	j.	PROPN
ejpam-6046	321	2	pure	pure	PROPN
ejpam-6046	321	3	appl	appl	PROPN
ejpam-6046	321	4	.	.	PROPN
ejpam-6046	321	5	math	math	PROPN
ejpam-6046	321	6	,	,	PUNCT
ejpam-6046	321	7	18	18	NUM
ejpam-6046	321	8	(	(	PUNCT
ejpam-6046	321	9	2	2	NUM
ejpam-6046	321	10	)	)	PUNCT
ejpam-6046	321	11	(	(	PUNCT
ejpam-6046	321	12	2025	2025	NUM
ejpam-6046	321	13	)	)	PUNCT
ejpam-6046	321	14	,	,	PUNCT
ejpam-6046	321	15	6046	6046	NUM
ejpam-6046	321	16	11	11	NUM
ejpam-6046	321	17	of	of	ADP
ejpam-6046	321	18	14	14	NUM
ejpam-6046	321	19	proof	proof	NOUN
ejpam-6046	321	20	.	.	PUNCT
ejpam-6046	322	1	the	the	DET
ejpam-6046	322	2	proof	proof	NOUN
ejpam-6046	322	3	immediately	immediately	ADV
ejpam-6046	322	4	follows	follow	VERB
ejpam-6046	322	5	by	by	ADP
ejpam-6046	322	6	counting	count	VERB
ejpam-6046	322	7	the	the	DET
ejpam-6046	322	8	numbers	number	NOUN
ejpam-6046	322	9	of	of	ADP
ejpam-6046	322	10	τeid(frn)-open	τeid(frn)-open	NOUN
ejpam-6046	322	11	sets	set	NOUN
ejpam-6046	322	12	in	in	ADP
ejpam-6046	322	13	theorem	theorem	NOUN
ejpam-6046	322	14	7	7	NUM
ejpam-6046	322	15	.	.	PUNCT
ejpam-6046	323	1	■	■	PUNCT
ejpam-6046	323	2	6	6	X
ejpam-6046	323	3	.	.	PUNCT
ejpam-6046	323	4	independent	independent	ADJ
ejpam-6046	323	5	edge	edge	PROPN
ejpam-6046	323	6	domination	domination	NOUN
ejpam-6046	323	7	topology	topology	NOUN
ejpam-6046	323	8	of	of	ADP
ejpam-6046	323	9	complete	complete	ADJ
ejpam-6046	323	10	bipartite	bipartite	NOUN
ejpam-6046	323	11	graphs	graph	NOUN
ejpam-6046	323	12	definition	definition	NOUN
ejpam-6046	323	13	10	10	NUM
ejpam-6046	323	14	.	.	PUNCT
ejpam-6046	324	1	[	[	X
ejpam-6046	324	2	14	14	NUM
ejpam-6046	324	3	]	]	X
ejpam-6046	324	4	a	a	DET
ejpam-6046	324	5	complete	complete	ADJ
ejpam-6046	324	6	bipartite	bipartite	NOUN
ejpam-6046	324	7	is	be	AUX
ejpam-6046	324	8	a	a	DET
ejpam-6046	324	9	graph	graph	NOUN
ejpam-6046	324	10	whose	whose	DET
ejpam-6046	324	11	vertex	vertex	NOUN
ejpam-6046	324	12	set	set	NOUN
ejpam-6046	324	13	can	can	AUX
ejpam-6046	324	14	be	be	AUX
ejpam-6046	324	15	partitioned	partition	VERB
ejpam-6046	324	16	into	into	ADP
ejpam-6046	324	17	two	two	NUM
ejpam-6046	324	18	disjoint	disjoint	NOUN
ejpam-6046	324	19	nonempty	nonempty	NOUN
ejpam-6046	324	20	sets	set	NOUN
ejpam-6046	324	21	va	va	NOUN
ejpam-6046	324	22	and	and	CCONJ
ejpam-6046	324	23	vb	vb	VERB
ejpam-6046	324	24	such	such	ADJ
ejpam-6046	324	25	that	that	SCONJ
ejpam-6046	324	26	two	two	NUM
ejpam-6046	324	27	vertices	vertex	NOUN
ejpam-6046	324	28	via	via	ADP
ejpam-6046	324	29	and	and	CCONJ
ejpam-6046	324	30	vib	vib	PROPN
ejpam-6046	324	31	are	be	AUX
ejpam-6046	324	32	adjacent	adjacent	ADJ
ejpam-6046	324	33	if	if	SCONJ
ejpam-6046	324	34	and	and	CCONJ
ejpam-6046	324	35	only	only	ADV
ejpam-6046	324	36	if	if	SCONJ
ejpam-6046	324	37	via	via	ADP
ejpam-6046	324	38	∈	∈	PROPN
ejpam-6046	324	39	va	va	PROPN
ejpam-6046	324	40	and	and	CCONJ
ejpam-6046	324	41	vib	vib	PROPN
ejpam-6046	324	42	∈	∈	PROPN
ejpam-6046	324	43	vb	vb	PROPN
ejpam-6046	324	44	.	.	PUNCT
ejpam-6046	325	1	if	if	SCONJ
ejpam-6046	325	2	|va|	|va|	PROPN
ejpam-6046	325	3	=	=	SYM
ejpam-6046	325	4	m	m	PROPN
ejpam-6046	325	5	and	and	CCONJ
ejpam-6046	325	6	|vb|	|vb|	NUM
ejpam-6046	325	7	=	=	SYM
ejpam-6046	325	8	n	n	CCONJ
ejpam-6046	325	9	,	,	PUNCT
ejpam-6046	325	10	then	then	ADV
ejpam-6046	325	11	such	such	DET
ejpam-6046	325	12	a	a	DET
ejpam-6046	325	13	graph	graph	NOUN
ejpam-6046	325	14	is	be	AUX
ejpam-6046	325	15	denoted	denote	VERB
ejpam-6046	325	16	km	km	NOUN
ejpam-6046	325	17	,	,	PUNCT
ejpam-6046	325	18	n.	n.	NOUN
ejpam-6046	325	19	notation	notation	NOUN
ejpam-6046	325	20	:	:	PUNCT
ejpam-6046	325	21	for	for	ADP
ejpam-6046	325	22	the	the	DET
ejpam-6046	325	23	complete	complete	ADJ
ejpam-6046	325	24	bipartite	bipartite	PROPN
ejpam-6046	325	25	graph	graph	NOUN
ejpam-6046	325	26	km	km	PROPN
ejpam-6046	325	27	,	,	PUNCT
ejpam-6046	325	28	n	n	CCONJ
ejpam-6046	325	29	,	,	PUNCT
ejpam-6046	325	30	the	the	DET
ejpam-6046	325	31	two	two	NUM
ejpam-6046	325	32	partite	partite	ADJ
ejpam-6046	325	33	sets	set	NOUN
ejpam-6046	325	34	are	be	AUX
ejpam-6046	325	35	labeled	label	VERB
ejpam-6046	325	36	as	as	ADP
ejpam-6046	325	37	i.	i.	PROPN
ejpam-6046	325	38	va(km	va(km	PROPN
ejpam-6046	325	39	,	,	PUNCT
ejpam-6046	325	40	n	n	CCONJ
ejpam-6046	325	41	)	)	PUNCT
ejpam-6046	325	42	=	=	PRON
ejpam-6046	325	43	{	{	PUNCT
ejpam-6046	325	44	v1a	v1a	NOUN
ejpam-6046	325	45	,	,	PUNCT
ejpam-6046	325	46	v2a	v2a	INTJ
ejpam-6046	325	47	,	,	PUNCT
ejpam-6046	325	48	.	.	PUNCT
ejpam-6046	325	49	.	.	PUNCT
ejpam-6046	326	1	.	.	PUNCT
ejpam-6046	327	1	,	,	PUNCT
ejpam-6046	327	2	vma	vma	NOUN
ejpam-6046	327	3	}	}	PUNCT
ejpam-6046	327	4	;	;	PUNCT
ejpam-6046	327	5	and	and	CCONJ
ejpam-6046	327	6	ii	ii	PROPN
ejpam-6046	327	7	.	.	PUNCT
ejpam-6046	328	1	vb(km	vb(km	PROPN
ejpam-6046	328	2	,	,	PUNCT
ejpam-6046	328	3	n	n	CCONJ
ejpam-6046	328	4	)	)	PUNCT
ejpam-6046	328	5	=	=	SYM
ejpam-6046	328	6	{	{	PUNCT
ejpam-6046	328	7	v1b	v1b	NOUN
ejpam-6046	328	8	,	,	PUNCT
ejpam-6046	328	9	v2b	v2b	PROPN
ejpam-6046	328	10	,	,	PUNCT
ejpam-6046	328	11	.	.	PUNCT
ejpam-6046	328	12	.	.	PUNCT
ejpam-6046	329	1	.	.	PUNCT
ejpam-6046	330	1	,	,	PUNCT
ejpam-6046	330	2	vnb	vnb	VERB
ejpam-6046	330	3	}	}	PUNCT
ejpam-6046	330	4	,	,	PUNCT
ejpam-6046	330	5	so	so	SCONJ
ejpam-6046	330	6	that	that	SCONJ
ejpam-6046	330	7	e(km	e(km	NOUN
ejpam-6046	330	8	,	,	PUNCT
ejpam-6046	330	9	n	n	CCONJ
ejpam-6046	330	10	)	)	PUNCT
ejpam-6046	330	11	=	=	PRON
ejpam-6046	330	12	{	{	PUNCT
ejpam-6046	330	13	ei	ei	PROPN
ejpam-6046	330	14	,	,	PUNCT
ejpam-6046	330	15	j	j	PROPN
ejpam-6046	330	16	=	=	PROPN
ejpam-6046	330	17	viavjb	viavjb	PROPN
ejpam-6046	330	18	:	:	PUNCT
ejpam-6046	330	19	via	via	ADP
ejpam-6046	330	20	∈	∈	PROPN
ejpam-6046	330	21	va(km	va(km	PROPN
ejpam-6046	330	22	,	,	PUNCT
ejpam-6046	330	23	n	n	CCONJ
ejpam-6046	330	24	)	)	PUNCT
ejpam-6046	330	25	,	,	PUNCT
ejpam-6046	330	26	vjb	vjb	PROPN
ejpam-6046	330	27	∈	∈	PROPN
ejpam-6046	330	28	vb(km	vb(km	PROPN
ejpam-6046	330	29	,	,	PUNCT
ejpam-6046	330	30	n	n	CCONJ
ejpam-6046	330	31	)	)	PUNCT
ejpam-6046	330	32	}	}	PUNCT
ejpam-6046	330	33	.	.	PUNCT
ejpam-6046	331	1	illustration	illustration	NOUN
ejpam-6046	331	2	:	:	PUNCT
ejpam-6046	331	3	the	the	DET
ejpam-6046	331	4	complete	complete	ADJ
ejpam-6046	331	5	bipartite	bipartite	PROPN
ejpam-6046	331	6	graph	graph	NOUN
ejpam-6046	331	7	k2,3	k2,3	PROPN
ejpam-6046	331	8	in	in	ADP
ejpam-6046	331	9	figure	figure	NOUN
ejpam-6046	331	10	8	8	NUM
ejpam-6046	331	11	is	be	AUX
ejpam-6046	331	12	labeled	label	VERB
ejpam-6046	331	13	using	use	VERB
ejpam-6046	331	14	the	the	DET
ejpam-6046	331	15	notation	notation	NOUN
ejpam-6046	331	16	convention	convention	NOUN
ejpam-6046	331	17	.	.	PUNCT
ejpam-6046	332	1	v1a	v1a	VERB
ejpam-6046	332	2	v2a	v2a	NOUN
ejpam-6046	332	3	v1b	v1b	NOUN
ejpam-6046	332	4	v2b	v2b	ADV
ejpam-6046	332	5	v3b	v3b	PROPN
ejpam-6046	332	6	k2,3	k2,3	PROPN
ejpam-6046	332	7	:	:	PUNCT
ejpam-6046	332	8	e1a,1b	e1a,1b	NOUN
ejpam-6046	332	9	e	e	PROPN
ejpam-6046	332	10	2a	2a	NUM
ejpam-6046	332	11	,	,	PUNCT
ejpam-6046	332	12	1	1	NUM
ejpam-6046	332	13	b	b	NOUN
ejpam-6046	332	14	e1a	e1a	PRON
ejpam-6046	332	15	,	,	PUNCT
ejpam-6046	332	16	2b	2b	X
ejpam-6046	332	17	e	e	ADP
ejpam-6046	332	18	1	1	NUM
ejpam-6046	332	19	a	a	PRON
ejpam-6046	332	20	,	,	PUNCT
ejpam-6046	332	21	3	3	NUM
ejpam-6046	332	22	b	b	NOUN
ejpam-6046	332	23	e2a,2b	e2a,2b	ADV
ejpam-6046	332	24	e2a	e2a	PROPN
ejpam-6046	332	25	,	,	PUNCT
ejpam-6046	332	26	3b	3b	NUM
ejpam-6046	332	27	figure	figure	NOUN
ejpam-6046	332	28	8	8	NUM
ejpam-6046	332	29	:	:	PUNCT
ejpam-6046	332	30	the	the	DET
ejpam-6046	332	31	complete	complete	ADJ
ejpam-6046	332	32	bipartite	bipartite	PROPN
ejpam-6046	332	33	graph	graph	NOUN
ejpam-6046	332	34	k2,3	k2,3	PROPN
ejpam-6046	332	35	theorem	theorem	NOUN
ejpam-6046	332	36	8	8	NUM
ejpam-6046	332	37	.	.	PUNCT
ejpam-6046	333	1	let	let	VERB
ejpam-6046	333	2	km	km	PROPN
ejpam-6046	333	3	,	,	PUNCT
ejpam-6046	333	4	n	n	PRON
ejpam-6046	333	5	be	be	VERB
ejpam-6046	333	6	a	a	DET
ejpam-6046	333	7	complete	complete	ADJ
ejpam-6046	333	8	bipartite	bipartite	NOUN
ejpam-6046	333	9	graph	graph	NOUN
ejpam-6046	333	10	and	and	CCONJ
ejpam-6046	333	11	s	s	VERB
ejpam-6046	333	12	⊆	⊆	NUM
ejpam-6046	333	13	e(km	e(km	NUM
ejpam-6046	333	14	,	,	PUNCT
ejpam-6046	333	15	n	n	CCONJ
ejpam-6046	333	16	)	)	PUNCT
ejpam-6046	333	17	.	.	PUNCT
ejpam-6046	334	1	s	s	PROPN
ejpam-6046	335	1	∈	∈	PROPN
ejpam-6046	335	2	ide	ide	NOUN
ejpam-6046	335	3	km	km	NOUN
ejpam-6046	335	4	,	,	PUNCT
ejpam-6046	335	5	n	n	CCONJ
ejpam-6046	335	6	if	if	SCONJ
ejpam-6046	335	7	and	and	CCONJ
ejpam-6046	335	8	only	only	ADV
ejpam-6046	335	9	if	if	SCONJ
ejpam-6046	335	10	s	s	VERB
ejpam-6046	335	11	=	=	PUNCT
ejpam-6046	335	12	{	{	PUNCT
ejpam-6046	335	13	ei1,j1	ei1,j1	NOUN
ejpam-6046	335	14	,	,	PUNCT
ejpam-6046	335	15	.	.	PUNCT
ejpam-6046	335	16	.	.	PUNCT
ejpam-6046	335	17	.	.	PUNCT
ejpam-6046	336	1	,	,	PUNCT
ejpam-6046	336	2	eik	eik	PROPN
ejpam-6046	336	3	,	,	PUNCT
ejpam-6046	336	4	jk	jk	PROPN
ejpam-6046	336	5	}	}	PUNCT
ejpam-6046	336	6	such	such	ADJ
ejpam-6046	336	7	that	that	SCONJ
ejpam-6046	336	8	|s|	|s|	PROPN
ejpam-6046	336	9	=	=	SYM
ejpam-6046	336	10	k	k	PROPN
ejpam-6046	336	11	=	=	SYM
ejpam-6046	336	12	min{m	min{m	PROPN
ejpam-6046	336	13	,	,	PUNCT
ejpam-6046	336	14	n	n	CCONJ
ejpam-6046	336	15	}	}	PUNCT
ejpam-6046	336	16	and	and	CCONJ
ejpam-6046	336	17	i1	i1	PROPN
ejpam-6046	336	18	̸=	̸=	PROPN
ejpam-6046	336	19	.	.	PUNCT
ejpam-6046	336	20	.	.	PUNCT
ejpam-6046	336	21	.	.	PUNCT
ejpam-6046	337	1	̸=	̸=	PROPN
ejpam-6046	337	2	ik	ik	PROPN
ejpam-6046	337	3	,	,	PUNCT
ejpam-6046	337	4	j1	j1	PROPN
ejpam-6046	337	5	̸=	̸=	PROPN
ejpam-6046	337	6	.	.	PUNCT
ejpam-6046	337	7	.	.	PUNCT
ejpam-6046	337	8	.	.	PUNCT
ejpam-6046	338	1	̸=	̸=	PROPN
ejpam-6046	338	2	jk	jk	PROPN
ejpam-6046	338	3	where	where	SCONJ
ejpam-6046	338	4	i1	i1	PROPN
ejpam-6046	338	5	,	,	PUNCT
ejpam-6046	338	6	.	.	PUNCT
ejpam-6046	338	7	.	.	PUNCT
ejpam-6046	339	1	.	.	PUNCT
ejpam-6046	340	1	,	,	PUNCT
ejpam-6046	340	2	ik	ik	PROPN
ejpam-6046	340	3	∈	∈	PROPN
ejpam-6046	340	4	{	{	PUNCT
ejpam-6046	340	5	1a	1a	NOUN
ejpam-6046	340	6	,	,	PUNCT
ejpam-6046	340	7	.	.	PUNCT
ejpam-6046	340	8	.	.	PUNCT
ejpam-6046	340	9	.	.	PUNCT
ejpam-6046	341	1	,	,	PUNCT
ejpam-6046	341	2	ma	ma	PROPN
ejpam-6046	341	3	}	}	PUNCT
ejpam-6046	341	4	and	and	CCONJ
ejpam-6046	341	5	j1	j1	PROPN
ejpam-6046	341	6	,	,	PUNCT
ejpam-6046	341	7	.	.	PUNCT
ejpam-6046	341	8	.	.	PUNCT
ejpam-6046	342	1	.	.	PUNCT
ejpam-6046	343	1	,	,	PUNCT
ejpam-6046	343	2	jk	jk	PROPN
ejpam-6046	343	3	∈	∈	PROPN
ejpam-6046	343	4	{	{	PUNCT
ejpam-6046	343	5	1b	1b	NUM
ejpam-6046	343	6	,	,	PUNCT
ejpam-6046	343	7	.	.	PUNCT
ejpam-6046	343	8	.	.	PUNCT
ejpam-6046	343	9	.	.	PUNCT
ejpam-6046	343	10	,	,	PUNCT
ejpam-6046	343	11	nb	nb	INTJ
ejpam-6046	343	12	}	}	PUNCT
ejpam-6046	343	13	.	.	PUNCT
ejpam-6046	344	1	proof	proof	NOUN
ejpam-6046	344	2	.	.	PUNCT
ejpam-6046	345	1	independence	independence	NOUN
ejpam-6046	345	2	follows	follow	VERB
ejpam-6046	345	3	immediately	immediately	ADV
ejpam-6046	345	4	by	by	ADP
ejpam-6046	345	5	remark	remark	NOUN
ejpam-6046	345	6	1	1	NUM
ejpam-6046	345	7	and	and	CCONJ
ejpam-6046	345	8	by	by	ADP
ejpam-6046	345	9	the	the	DET
ejpam-6046	345	10	definition	definition	NOUN
ejpam-6046	345	11	of	of	ADP
ejpam-6046	345	12	s.	s.	PROPN
ejpam-6046	345	13	let	let	VERB
ejpam-6046	345	14	ep	ep	PROPN
ejpam-6046	345	15	,	,	PUNCT
ejpam-6046	345	16	q	q	PROPN
ejpam-6046	345	17	∈	∈	PROPN
ejpam-6046	345	18	e(km	e(km	NOUN
ejpam-6046	345	19	,	,	PUNCT
ejpam-6046	345	20	n	n	CCONJ
ejpam-6046	345	21	)	)	PUNCT
ejpam-6046	345	22	\	\	PROPN
ejpam-6046	346	1	s	s	PROPN
ejpam-6046	346	2	,	,	PUNCT
ejpam-6046	346	3	and	and	CCONJ
ejpam-6046	346	4	assume	assume	VERB
ejpam-6046	346	5	that	that	SCONJ
ejpam-6046	346	6	k	k	PROPN
ejpam-6046	346	7	=	=	SYM
ejpam-6046	346	8	min{m	min{m	PROPN
ejpam-6046	346	9	,	,	PUNCT
ejpam-6046	346	10	n	n	CCONJ
ejpam-6046	346	11	}	}	PUNCT
ejpam-6046	346	12	=	=	SYM
ejpam-6046	346	13	m.	m.	NOUN
ejpam-6046	346	14	since	since	SCONJ
ejpam-6046	346	15	|s|	|s|	PROPN
ejpam-6046	346	16	=	=	SYM
ejpam-6046	346	17	k	k	PROPN
ejpam-6046	346	18	and	and	CCONJ
ejpam-6046	346	19	s	s	VERB
ejpam-6046	346	20	is	be	AUX
ejpam-6046	346	21	independent	independent	ADJ
ejpam-6046	346	22	,	,	PUNCT
ejpam-6046	346	23	all	all	DET
ejpam-6046	346	24	the	the	DET
ejpam-6046	346	25	subscripts	subscript	NOUN
ejpam-6046	346	26	1a	1a	NOUN
ejpam-6046	346	27	,	,	PUNCT
ejpam-6046	346	28	.	.	PUNCT
ejpam-6046	346	29	.	.	PUNCT
ejpam-6046	346	30	.	.	PUNCT
ejpam-6046	347	1	,	,	PUNCT
ejpam-6046	347	2	ma	ma	PROPN
ejpam-6046	347	3	appear	appear	VERB
ejpam-6046	347	4	in	in	ADP
ejpam-6046	347	5	s.	s.	PROPN
ejpam-6046	347	6	hence	hence	PROPN
ejpam-6046	347	7	,	,	PUNCT
ejpam-6046	347	8	p	p	PROPN
ejpam-6046	347	9	∈	∈	PROPN
ejpam-6046	347	10	{	{	PUNCT
ejpam-6046	347	11	1a	1a	NOUN
ejpam-6046	347	12	,	,	PUNCT
ejpam-6046	347	13	.	.	PUNCT
ejpam-6046	347	14	.	.	PUNCT
ejpam-6046	347	15	.	.	PUNCT
ejpam-6046	348	1	,	,	PUNCT
ejpam-6046	348	2	ma	ma	PROPN
ejpam-6046	348	3	}	}	PUNCT
ejpam-6046	348	4	.	.	PUNCT
ejpam-6046	349	1	this	this	PRON
ejpam-6046	349	2	means	mean	VERB
ejpam-6046	349	3	that	that	SCONJ
ejpam-6046	349	4	there	there	PRON
ejpam-6046	349	5	exist	exist	VERB
ejpam-6046	349	6	c	c	PROPN
ejpam-6046	349	7	∈	∈	PROPN
ejpam-6046	350	1	[	[	X
ejpam-6046	350	2	m	m	X
ejpam-6046	350	3	]	]	X
ejpam-6046	350	4	and	and	CCONJ
ejpam-6046	350	5	d	d	X
ejpam-6046	350	6	∈	∈	PROPN
ejpam-6046	350	7	[	[	X
ejpam-6046	350	8	n	n	X
ejpam-6046	350	9	]	]	X
ejpam-6046	350	10	such	such	ADJ
ejpam-6046	350	11	that	that	SCONJ
ejpam-6046	350	12	eca	eca	NOUN
ejpam-6046	350	13	,	,	PUNCT
ejpam-6046	350	14	db	db	PROPN
ejpam-6046	350	15	∈	∈	PROPN
ejpam-6046	350	16	s	s	NOUN
ejpam-6046	350	17	and	and	CCONJ
ejpam-6046	350	18	ca	ca	NOUN
ejpam-6046	350	19	=	=	SYM
ejpam-6046	350	20	p.	p.	NOUN
ejpam-6046	350	21	by	by	ADP
ejpam-6046	350	22	remark	remark	NOUN
ejpam-6046	350	23	1	1	NUM
ejpam-6046	350	24	,	,	PUNCT
ejpam-6046	350	25	eca	eca	NOUN
ejpam-6046	350	26	,	,	PUNCT
ejpam-6046	350	27	db	db	PROPN
ejpam-6046	350	28	is	be	AUX
ejpam-6046	350	29	adjacent	adjacent	ADJ
ejpam-6046	350	30	to	to	ADP
ejpam-6046	350	31	ep	ep	PROPN
ejpam-6046	350	32	,	,	PUNCT
ejpam-6046	350	33	q.	q.	PROPN
ejpam-6046	350	34	since	since	SCONJ
ejpam-6046	350	35	ep	ep	PROPN
ejpam-6046	350	36	,	,	PUNCT
ejpam-6046	350	37	q	q	PROPN
ejpam-6046	350	38	is	be	AUX
ejpam-6046	350	39	arbitrary	arbitrary	ADJ
ejpam-6046	350	40	,	,	PUNCT
ejpam-6046	350	41	s	s	PART
ejpam-6046	350	42	is	be	AUX
ejpam-6046	350	43	an	an	DET
ejpam-6046	350	44	edge	edge	NOUN
ejpam-6046	350	45	dominating	dominating	NOUN
ejpam-6046	350	46	set	set	NOUN
ejpam-6046	350	47	of	of	ADP
ejpam-6046	350	48	km	km	PROPN
ejpam-6046	350	49	,	,	PUNCT
ejpam-6046	350	50	n.	n.	PROPN
ejpam-6046	350	51	j.	j.	PROPN
ejpam-6046	350	52	n.	n.	PROPN
ejpam-6046	350	53	ontulan	ontulan	PROPN
ejpam-6046	350	54	,	,	PUNCT
ejpam-6046	350	55	c.	c.	PROPN
ejpam-6046	350	56	m.	m.	NOUN
ejpam-6046	350	57	balingit	balingit	PROPN
ejpam-6046	350	58	/	/	SYM
ejpam-6046	350	59	eur	eur	PROPN
ejpam-6046	350	60	.	.	PUNCT
ejpam-6046	351	1	j.	j.	PROPN
ejpam-6046	351	2	pure	pure	PROPN
ejpam-6046	351	3	appl	appl	PROPN
ejpam-6046	351	4	.	.	PROPN
ejpam-6046	351	5	math	math	PROPN
ejpam-6046	351	6	,	,	PUNCT
ejpam-6046	351	7	18	18	NUM
ejpam-6046	351	8	(	(	PUNCT
ejpam-6046	351	9	2	2	NUM
ejpam-6046	351	10	)	)	PUNCT
ejpam-6046	351	11	(	(	PUNCT
ejpam-6046	351	12	2025	2025	NUM
ejpam-6046	351	13	)	)	PUNCT
ejpam-6046	351	14	,	,	PUNCT
ejpam-6046	351	15	6046	6046	NUM
ejpam-6046	351	16	12	12	NUM
ejpam-6046	351	17	of	of	ADP
ejpam-6046	351	18	14	14	NUM
ejpam-6046	351	19	conversely	conversely	ADV
ejpam-6046	351	20	,	,	PUNCT
ejpam-6046	351	21	assume	assume	VERB
ejpam-6046	351	22	wlog	wlog	NOUN
ejpam-6046	351	23	that	that	SCONJ
ejpam-6046	351	24	k	k	PROPN
ejpam-6046	351	25	=	=	SYM
ejpam-6046	351	26	min{m	min{m	PROPN
ejpam-6046	351	27	,	,	PUNCT
ejpam-6046	351	28	n	n	CCONJ
ejpam-6046	351	29	}	}	PUNCT
ejpam-6046	351	30	=	=	SYM
ejpam-6046	351	31	m.	m.	NOUN
ejpam-6046	351	32	if	if	SCONJ
ejpam-6046	351	33	|s|	|s|	NOUN
ejpam-6046	351	34	>	>	PUNCT
ejpam-6046	351	35	k	k	PROPN
ejpam-6046	352	1	=	=	PUNCT
ejpam-6046	352	2	m	m	PROPN
ejpam-6046	352	3	,	,	PUNCT
ejpam-6046	352	4	then	then	ADV
ejpam-6046	352	5	by	by	ADP
ejpam-6046	352	6	the	the	DET
ejpam-6046	352	7	pigeonhole	pigeonhole	NOUN
ejpam-6046	352	8	principle	principle	NOUN
ejpam-6046	352	9	applied	apply	VERB
ejpam-6046	352	10	to	to	ADP
ejpam-6046	352	11	the	the	DET
ejpam-6046	352	12	subscript	subscript	NOUN
ejpam-6046	352	13	p	p	PROPN
ejpam-6046	352	14	of	of	ADP
ejpam-6046	352	15	the	the	DET
ejpam-6046	352	16	edges	edge	NOUN
ejpam-6046	352	17	ep	ep	PROPN
ejpam-6046	352	18	,	,	PUNCT
ejpam-6046	352	19	q	q	NOUN
ejpam-6046	352	20	in	in	ADP
ejpam-6046	352	21	s	s	PROPN
ejpam-6046	352	22	,	,	PUNCT
ejpam-6046	352	23	there	there	PRON
ejpam-6046	352	24	exist	exist	VERB
ejpam-6046	352	25	at	at	ADV
ejpam-6046	352	26	least	least	ADV
ejpam-6046	352	27	two	two	NUM
ejpam-6046	352	28	edges	edge	NOUN
ejpam-6046	352	29	in	in	ADP
ejpam-6046	352	30	s	s	VERB
ejpam-6046	352	31	sharing	share	VERB
ejpam-6046	352	32	the	the	DET
ejpam-6046	352	33	same	same	ADJ
ejpam-6046	352	34	first	first	ADJ
ejpam-6046	352	35	subscripts	subscript	NOUN
ejpam-6046	352	36	.	.	PUNCT
ejpam-6046	353	1	by	by	ADP
ejpam-6046	353	2	remark	remark	NOUN
ejpam-6046	353	3	1	1	NUM
ejpam-6046	353	4	,	,	PUNCT
ejpam-6046	353	5	s	s	VERB
ejpam-6046	353	6	is	be	AUX
ejpam-6046	353	7	not	not	PART
ejpam-6046	353	8	independent	independent	ADJ
ejpam-6046	353	9	.	.	PUNCT
ejpam-6046	354	1	if	if	SCONJ
ejpam-6046	354	2	|s|	|s|	NOUN
ejpam-6046	354	3	<	<	X
ejpam-6046	354	4	k	k	X
ejpam-6046	355	1	=	=	PUNCT
ejpam-6046	355	2	m	m	VERB
ejpam-6046	355	3	<	<	X
ejpam-6046	355	4	n	n	CCONJ
ejpam-6046	355	5	,	,	PUNCT
ejpam-6046	355	6	then	then	ADV
ejpam-6046	355	7	there	there	PRON
ejpam-6046	355	8	exists	exist	VERB
ejpam-6046	355	9	an	an	DET
ejpam-6046	355	10	edge	edge	NOUN
ejpam-6046	355	11	ep	ep	NOUN
ejpam-6046	355	12	,	,	PUNCT
ejpam-6046	355	13	q	q	PROPN
ejpam-6046	355	14	∈	∈	PROPN
ejpam-6046	355	15	e(km	e(km	NOUN
ejpam-6046	355	16	,	,	PUNCT
ejpam-6046	355	17	n	n	CCONJ
ejpam-6046	355	18	)	)	PUNCT
ejpam-6046	355	19	\	\	PROPN
ejpam-6046	356	1	s	s	VERB
ejpam-6046	356	2	such	such	ADJ
ejpam-6046	356	3	that	that	SCONJ
ejpam-6046	356	4	p	p	PROPN
ejpam-6046	356	5	and	and	CCONJ
ejpam-6046	356	6	q	q	NOUN
ejpam-6046	356	7	do	do	AUX
ejpam-6046	356	8	not	not	PART
ejpam-6046	356	9	appear	appear	VERB
ejpam-6046	356	10	as	as	ADP
ejpam-6046	356	11	subscripts	subscript	NOUN
ejpam-6046	356	12	of	of	ADP
ejpam-6046	356	13	the	the	DET
ejpam-6046	356	14	edges	edge	NOUN
ejpam-6046	356	15	in	in	ADP
ejpam-6046	356	16	s.	s.	PROPN
ejpam-6046	356	17	hence	hence	PROPN
ejpam-6046	356	18	,	,	PUNCT
ejpam-6046	356	19	ep	ep	PROPN
ejpam-6046	356	20	,	,	PUNCT
ejpam-6046	356	21	q	q	X
ejpam-6046	356	22	is	be	AUX
ejpam-6046	356	23	not	not	PART
ejpam-6046	356	24	adjacent	adjacent	ADJ
ejpam-6046	356	25	to	to	ADP
ejpam-6046	356	26	any	any	DET
ejpam-6046	356	27	element	element	NOUN
ejpam-6046	356	28	of	of	ADP
ejpam-6046	356	29	s	s	PROPN
ejpam-6046	356	30	,	,	PUNCT
ejpam-6046	356	31	by	by	ADP
ejpam-6046	356	32	remark	remark	NOUN
ejpam-6046	356	33	1	1	NUM
ejpam-6046	356	34	.	.	PUNCT
ejpam-6046	357	1	therefore	therefore	ADV
ejpam-6046	357	2	,	,	PUNCT
ejpam-6046	357	3	s	s	VERB
ejpam-6046	357	4	is	be	AUX
ejpam-6046	357	5	not	not	PART
ejpam-6046	357	6	an	an	DET
ejpam-6046	357	7	edge	edge	NOUN
ejpam-6046	357	8	dominating	dominating	NOUN
ejpam-6046	357	9	set	set	NOUN
ejpam-6046	357	10	of	of	ADP
ejpam-6046	357	11	km	km	PROPN
ejpam-6046	357	12	,	,	PUNCT
ejpam-6046	357	13	n.	n.	NOUN
ejpam-6046	357	14	if	if	SCONJ
ejpam-6046	357	15	|s|	|s|	PROPN
ejpam-6046	357	16	=	=	SYM
ejpam-6046	357	17	k	k	PROPN
ejpam-6046	357	18	but	but	CCONJ
ejpam-6046	357	19	fails	fail	VERB
ejpam-6046	357	20	to	to	PART
ejpam-6046	357	21	satisfy	satisfy	VERB
ejpam-6046	357	22	the	the	DET
ejpam-6046	357	23	condition	condition	NOUN
ejpam-6046	357	24	i1	i1	PROPN
ejpam-6046	357	25	̸=	̸=	PROPN
ejpam-6046	357	26	.	.	PUNCT
ejpam-6046	357	27	.	.	PUNCT
ejpam-6046	357	28	.	.	PUNCT
ejpam-6046	358	1	̸=	̸=	PROPN
ejpam-6046	358	2	ik	ik	PROPN
ejpam-6046	358	3	,	,	PUNCT
ejpam-6046	358	4	j1	j1	PROPN
ejpam-6046	358	5	̸=	̸=	PROPN
ejpam-6046	358	6	.	.	PUNCT
ejpam-6046	358	7	.	.	PUNCT
ejpam-6046	358	8	.	.	PUNCT
ejpam-6046	359	1	̸=	̸=	PROPN
ejpam-6046	359	2	jk	jk	PROPN
ejpam-6046	359	3	,	,	PUNCT
ejpam-6046	359	4	then	then	ADV
ejpam-6046	359	5	,	,	PUNCT
ejpam-6046	359	6	by	by	ADP
ejpam-6046	359	7	remark	remark	NOUN
ejpam-6046	359	8	1	1	NUM
ejpam-6046	359	9	,	,	PUNCT
ejpam-6046	359	10	s	s	VERB
ejpam-6046	359	11	is	be	AUX
ejpam-6046	359	12	not	not	PART
ejpam-6046	359	13	an	an	DET
ejpam-6046	359	14	independent	independent	ADJ
ejpam-6046	359	15	nor	nor	CCONJ
ejpam-6046	359	16	an	an	DET
ejpam-6046	359	17	edge	edge	NOUN
ejpam-6046	359	18	dominating	dominating	NOUN
ejpam-6046	359	19	set	set	NOUN
ejpam-6046	359	20	of	of	ADP
ejpam-6046	359	21	km	km	PROPN
ejpam-6046	359	22	,	,	PUNCT
ejpam-6046	359	23	n.	n.	NOUN
ejpam-6046	359	24	■	■	PUNCT
ejpam-6046	359	25	theorem	theorem	VERB
ejpam-6046	359	26	9	9	NUM
ejpam-6046	359	27	.	.	PUNCT
ejpam-6046	360	1	for	for	ADP
ejpam-6046	360	2	the	the	DET
ejpam-6046	360	3	complete	complete	ADJ
ejpam-6046	360	4	bipartite	bipartite	PROPN
ejpam-6046	360	5	graph	graph	NOUN
ejpam-6046	360	6	km	km	PROPN
ejpam-6046	360	7	,	,	PUNCT
ejpam-6046	360	8	n	n	NOUN
ejpam-6046	360	9	with	with	ADP
ejpam-6046	360	10	m	m	PROPN
ejpam-6046	360	11	≤	≤	NOUN
ejpam-6046	360	12	n	n	CCONJ
ejpam-6046	360	13	|ide	|ide	ADJ
ejpam-6046	360	14	km	km	PROPN
ejpam-6046	360	15	,	,	PUNCT
ejpam-6046	360	16	n	n	CCONJ
ejpam-6046	360	17	|	|	NOUN
ejpam-6046	360	18	=	=	SYM
ejpam-6046	360	19	n	n	X
ejpam-6046	360	20	!	!	PUNCT
ejpam-6046	360	21	(	(	PUNCT
ejpam-6046	360	22	n−m	n−m	PROPN
ejpam-6046	360	23	)	)	PUNCT
ejpam-6046	360	24	!	!	PUNCT
ejpam-6046	360	25	.	.	PUNCT
ejpam-6046	361	1	proof	proof	NOUN
ejpam-6046	361	2	.	.	PUNCT
ejpam-6046	362	1	assume	assume	VERB
ejpam-6046	362	2	that	that	SCONJ
ejpam-6046	362	3	m	m	VERB
ejpam-6046	362	4	≤	≤	PROPN
ejpam-6046	362	5	n.	n.	NOUN
ejpam-6046	362	6	observe	observe	VERB
ejpam-6046	362	7	that	that	SCONJ
ejpam-6046	362	8	by	by	ADP
ejpam-6046	362	9	theorem	theorem	NOUN
ejpam-6046	362	10	8	8	NUM
ejpam-6046	362	11	,	,	PUNCT
ejpam-6046	362	12	all	all	PRON
ejpam-6046	362	13	subscripts	subscript	NOUN
ejpam-6046	362	14	1a	1a	NOUN
ejpam-6046	362	15	,	,	PUNCT
ejpam-6046	362	16	2a	2a	NUM
ejpam-6046	362	17	,	,	PUNCT
ejpam-6046	362	18	.	.	PUNCT
ejpam-6046	362	19	.	.	PUNCT
ejpam-6046	363	1	.	.	PUNCT
ejpam-6046	364	1	,	,	PUNCT
ejpam-6046	364	2	ma	ma	PROPN
ejpam-6046	364	3	appear	appear	VERB
ejpam-6046	364	4	in	in	ADP
ejpam-6046	364	5	every	every	DET
ejpam-6046	364	6	independent	independent	ADJ
ejpam-6046	364	7	edge	edge	NOUN
ejpam-6046	364	8	dominating	dominating	NOUN
ejpam-6046	364	9	set	set	NOUN
ejpam-6046	364	10	s	s	PROPN
ejpam-6046	364	11	of	of	ADP
ejpam-6046	364	12	km	km	PROPN
ejpam-6046	364	13	,	,	PUNCT
ejpam-6046	364	14	n.	n.	NOUN
ejpam-6046	364	15	each	each	PRON
ejpam-6046	364	16	of	of	ADP
ejpam-6046	364	17	these	these	DET
ejpam-6046	364	18	subscripts	subscript	NOUN
ejpam-6046	364	19	is	be	AUX
ejpam-6046	364	20	paired	pair	VERB
ejpam-6046	364	21	to	to	ADP
ejpam-6046	364	22	one	one	NUM
ejpam-6046	364	23	of	of	ADP
ejpam-6046	364	24	the	the	DET
ejpam-6046	364	25	subscripts	subscript	NOUN
ejpam-6046	364	26	1b	1b	NUM
ejpam-6046	364	27	,	,	PUNCT
ejpam-6046	364	28	.	.	PUNCT
ejpam-6046	364	29	.	.	PUNCT
ejpam-6046	365	1	.	.	PUNCT
ejpam-6046	366	1	,	,	PUNCT
ejpam-6046	366	2	nb	nb	INTJ
ejpam-6046	366	3	,	,	PUNCT
ejpam-6046	366	4	where	where	SCONJ
ejpam-6046	366	5	the	the	DET
ejpam-6046	366	6	chosen	choose	VERB
ejpam-6046	366	7	subscripts	subscript	NOUN
ejpam-6046	366	8	are	be	AUX
ejpam-6046	366	9	all	all	ADV
ejpam-6046	366	10	distinct	distinct	ADJ
ejpam-6046	366	11	.	.	PUNCT
ejpam-6046	367	1	there	there	PRON
ejpam-6046	367	2	are	be	VERB
ejpam-6046	367	3	n	n	PRON
ejpam-6046	367	4	choices	choice	NOUN
ejpam-6046	367	5	for	for	ADP
ejpam-6046	367	6	the	the	DET
ejpam-6046	367	7	subscript	subscript	NOUN
ejpam-6046	367	8	paired	pair	VERB
ejpam-6046	367	9	to	to	ADP
ejpam-6046	367	10	1a	1a	NUM
ejpam-6046	367	11	,	,	PUNCT
ejpam-6046	367	12	n	n	CCONJ
ejpam-6046	367	13	−	−	PROPN
ejpam-6046	367	14	1	1	NUM
ejpam-6046	367	15	choices	choice	NOUN
ejpam-6046	367	16	for	for	ADP
ejpam-6046	367	17	the	the	DET
ejpam-6046	367	18	subscript	subscript	NOUN
ejpam-6046	367	19	paired	pair	VERB
ejpam-6046	367	20	to	to	ADP
ejpam-6046	367	21	2a	2a	NUM
ejpam-6046	367	22	,	,	PUNCT
ejpam-6046	367	23	.	.	PUNCT
ejpam-6046	367	24	.	.	PUNCT
ejpam-6046	368	1	.	.	PUNCT
ejpam-6046	369	1	,	,	PUNCT
ejpam-6046	369	2	and	and	CCONJ
ejpam-6046	369	3	n	n	PRON
ejpam-6046	369	4	−m	−m	NOUN
ejpam-6046	369	5	+	+	CCONJ
ejpam-6046	369	6	1	1	NUM
ejpam-6046	369	7	choices	choice	NOUN
ejpam-6046	369	8	for	for	ADP
ejpam-6046	369	9	the	the	DET
ejpam-6046	369	10	subscript	subscript	NOUN
ejpam-6046	369	11	paired	pair	VERB
ejpam-6046	369	12	to	to	ADP
ejpam-6046	369	13	ma	ma	PROPN
ejpam-6046	369	14	.	.	PUNCT
ejpam-6046	370	1	this	this	PRON
ejpam-6046	370	2	means	mean	VERB
ejpam-6046	370	3	that	that	SCONJ
ejpam-6046	370	4	there	there	PRON
ejpam-6046	370	5	are	be	VERB
ejpam-6046	370	6	n(n−	n(n−	ADJ
ejpam-6046	370	7	1)(n−	1)(n−	PROPN
ejpam-6046	370	8	2	2	NUM
ejpam-6046	370	9	)	)	PUNCT
ejpam-6046	370	10	.	.	PUNCT
ejpam-6046	370	11	.	.	PUNCT
ejpam-6046	370	12	.	.	PUNCT
ejpam-6046	371	1	(	(	PUNCT
ejpam-6046	371	2	n−m+1	n−m+1	NOUN
ejpam-6046	371	3	)	)	PUNCT
ejpam-6046	371	4	=	=	SYM
ejpam-6046	371	5	n	n	X
ejpam-6046	371	6	!	!	PUNCT
ejpam-6046	371	7	(	(	PUNCT
ejpam-6046	371	8	n−m	n−m	PROPN
ejpam-6046	371	9	)	)	PUNCT
ejpam-6046	371	10	!	!	PUNCT
ejpam-6046	372	1	such	such	ADJ
ejpam-6046	372	2	pairs	pair	NOUN
ejpam-6046	372	3	and	and	CCONJ
ejpam-6046	372	4	so	so	ADV
ejpam-6046	372	5	|ide	|ide	SCONJ
ejpam-6046	372	6	km	km	PROPN
ejpam-6046	372	7	,	,	PUNCT
ejpam-6046	372	8	n	n	CCONJ
ejpam-6046	372	9	|	|	NOUN
ejpam-6046	372	10	=	=	SYM
ejpam-6046	372	11	n	n	X
ejpam-6046	372	12	!	!	PUNCT
ejpam-6046	372	13	(	(	PUNCT
ejpam-6046	372	14	n−m	n−m	PROPN
ejpam-6046	372	15	)	)	PUNCT
ejpam-6046	372	16	!	!	PUNCT
ejpam-6046	372	17	.	.	PUNCT
ejpam-6046	373	1	■	■	PUNCT
ejpam-6046	373	2	example	example	NOUN
ejpam-6046	373	3	6	6	NUM
ejpam-6046	373	4	.	.	PUNCT
ejpam-6046	374	1	consider	consider	VERB
ejpam-6046	374	2	the	the	DET
ejpam-6046	374	3	complete	complete	ADJ
ejpam-6046	374	4	bipartite	bipartite	NOUN
ejpam-6046	374	5	graph	graph	NOUN
ejpam-6046	374	6	k2,3	k2,3	PROPN
ejpam-6046	374	7	in	in	ADP
ejpam-6046	374	8	figure	figure	NOUN
ejpam-6046	374	9	8	8	NUM
ejpam-6046	374	10	with	with	ADP
ejpam-6046	374	11	e(k2,3	e(k2,3	NOUN
ejpam-6046	374	12	)	)	PUNCT
ejpam-6046	374	13	=	=	SYM
ejpam-6046	374	14	{	{	PUNCT
ejpam-6046	374	15	e1a,1b	e1a,1b	NOUN
ejpam-6046	374	16	,	,	PUNCT
ejpam-6046	374	17	e1a,2b	e1a,2b	NOUN
ejpam-6046	374	18	,	,	PUNCT
ejpam-6046	374	19	e1a,3b	e1a,3b	X
ejpam-6046	374	20	,	,	PUNCT
ejpam-6046	374	21	e2a,1b	e2a,1b	NOUN
ejpam-6046	374	22	,	,	PUNCT
ejpam-6046	374	23	e2a,2b	e2a,2b	ADV
ejpam-6046	374	24	,	,	PUNCT
ejpam-6046	374	25	e2a,3b	e2a,3b	PROPN
ejpam-6046	374	26	}	}	PUNCT
ejpam-6046	374	27	.	.	PUNCT
ejpam-6046	375	1	observe	observe	VERB
ejpam-6046	375	2	that	that	DET
ejpam-6046	375	3	ide	ide	NOUN
ejpam-6046	375	4	k2,3	k2,3	NOUN
ejpam-6046	375	5	=	=	PUNCT
ejpam-6046	375	6	{	{	PUNCT
ejpam-6046	375	7	{	{	PUNCT
ejpam-6046	375	8	e1a,1b	e1a,1b	NOUN
ejpam-6046	375	9	,	,	PUNCT
ejpam-6046	375	10	e2a,2b	e2a,2b	PROPN
ejpam-6046	375	11	}	}	PUNCT
ejpam-6046	375	12	,	,	PUNCT
ejpam-6046	375	13	{	{	PUNCT
ejpam-6046	375	14	e1a,1b	e1a,1b	NOUN
ejpam-6046	375	15	,	,	PUNCT
ejpam-6046	375	16	e2a,3b	e2a,3b	PROPN
ejpam-6046	375	17	}	}	PUNCT
ejpam-6046	375	18	,	,	PUNCT
ejpam-6046	375	19	{	{	PUNCT
ejpam-6046	375	20	e1a,2b	e1a,2b	NOUN
ejpam-6046	375	21	,	,	PUNCT
ejpam-6046	375	22	e2a,1b	e2a,1b	PROPN
ejpam-6046	375	23	}	}	PUNCT
ejpam-6046	375	24	,	,	PUNCT
ejpam-6046	375	25	{	{	PUNCT
ejpam-6046	375	26	e1a,2b	e1a,2b	NOUN
ejpam-6046	375	27	,	,	PUNCT
ejpam-6046	375	28	e2a,3b	e2a,3b	PROPN
ejpam-6046	375	29	}	}	PUNCT
ejpam-6046	375	30	,	,	PUNCT
ejpam-6046	375	31	{	{	PUNCT
ejpam-6046	375	32	e1a,3b	e1a,3b	NOUN
ejpam-6046	375	33	,	,	PUNCT
ejpam-6046	375	34	e2a,1a	e2a,1a	PROPN
ejpam-6046	375	35	}	}	PUNCT
ejpam-6046	375	36	,	,	PUNCT
ejpam-6046	375	37	{	{	PUNCT
ejpam-6046	375	38	e1a,3b	e1a,3b	NOUN
ejpam-6046	375	39	,	,	PUNCT
ejpam-6046	375	40	e2a,2b	e2a,2b	PROPN
ejpam-6046	375	41	}	}	PUNCT
ejpam-6046	375	42	}	}	PUNCT
ejpam-6046	375	43	.	.	PUNCT
ejpam-6046	376	1	indeed	indeed	ADV
ejpam-6046	376	2	,	,	PUNCT
ejpam-6046	376	3	|ide	|ide	ADJ
ejpam-6046	376	4	km	km	PROPN
ejpam-6046	376	5	,	,	PUNCT
ejpam-6046	376	6	n	n	CCONJ
ejpam-6046	376	7	|	|	NOUN
ejpam-6046	376	8	=	=	SYM
ejpam-6046	376	9	6	6	NUM
ejpam-6046	376	10	.	.	PUNCT
ejpam-6046	376	11	remark	remark	PROPN
ejpam-6046	376	12	4	4	NUM
ejpam-6046	376	13	.	.	PUNCT
ejpam-6046	376	14	i.	i.	PROPN
ejpam-6046	376	15	τeid(k1,1	τeid(k1,1	PROPN
ejpam-6046	376	16	)	)	PUNCT
ejpam-6046	376	17	is	be	AUX
ejpam-6046	376	18	the	the	DET
ejpam-6046	376	19	indiscrete	indiscrete	ADJ
ejpam-6046	376	20	topology	topology	NOUN
ejpam-6046	376	21	on	on	ADP
ejpam-6046	376	22	e(k1,1	e(k1,1	NOUN
ejpam-6046	376	23	)	)	PUNCT
ejpam-6046	376	24	,	,	PUNCT
ejpam-6046	376	25	by	by	ADP
ejpam-6046	376	26	theorem	theorem	NOUN
ejpam-6046	376	27	2	2	NUM
ejpam-6046	376	28	.	.	X
ejpam-6046	376	29	ii	ii	PROPN
ejpam-6046	376	30	.	.	PUNCT
ejpam-6046	377	1	τeid(k2,2	τeid(k2,2	X
ejpam-6046	377	2	)	)	PUNCT
ejpam-6046	378	1	is	be	AUX
ejpam-6046	378	2	neither	neither	CCONJ
ejpam-6046	378	3	the	the	DET
ejpam-6046	378	4	discrete	discrete	NOUN
ejpam-6046	378	5	nor	nor	CCONJ
ejpam-6046	378	6	the	the	DET
ejpam-6046	378	7	indiscrete	indiscrete	ADJ
ejpam-6046	378	8	topology	topology	NOUN
ejpam-6046	378	9	on	on	ADP
ejpam-6046	378	10	e(k2,2	e(k2,2	PROPN
ejpam-6046	378	11	)	)	PUNCT
ejpam-6046	378	12	.	.	PUNCT
ejpam-6046	379	1	to	to	PART
ejpam-6046	379	2	see	see	VERB
ejpam-6046	379	3	this	this	PRON
ejpam-6046	379	4	,	,	PUNCT
ejpam-6046	379	5	observe	observe	VERB
ejpam-6046	379	6	that	that	DET
ejpam-6046	379	7	ide	ide	NOUN
ejpam-6046	379	8	k2,2	k2,2	PROPN
ejpam-6046	379	9	=	=	PUNCT
ejpam-6046	379	10	{	{	PUNCT
ejpam-6046	379	11	{	{	PUNCT
ejpam-6046	379	12	e1a,1b	e1a,1b	NOUN
ejpam-6046	379	13	,	,	PUNCT
ejpam-6046	379	14	e2a,2b	e2a,2b	PROPN
ejpam-6046	379	15	}	}	PUNCT
ejpam-6046	379	16	,	,	PUNCT
ejpam-6046	379	17	{	{	PUNCT
ejpam-6046	379	18	e1a,2b	e1a,2b	NOUN
ejpam-6046	379	19	,	,	PUNCT
ejpam-6046	379	20	e2a,1b	e2a,1b	PROPN
ejpam-6046	379	21	}	}	PUNCT
ejpam-6046	379	22	}	}	PUNCT
ejpam-6046	379	23	and	and	CCONJ
ejpam-6046	379	24	so	so	ADV
ejpam-6046	379	25	τeid(k2,2	τeid(k2,2	SYM
ejpam-6046	379	26	)	)	PUNCT
ejpam-6046	380	1	=	=	SYM
ejpam-6046	380	2	{	{	PUNCT
ejpam-6046	380	3	∅	∅	NOUN
ejpam-6046	380	4	,	,	PUNCT
ejpam-6046	380	5	{	{	PUNCT
ejpam-6046	380	6	e1a,1b	e1a,1b	NOUN
ejpam-6046	380	7	,	,	PUNCT
ejpam-6046	380	8	e2a,2b	e2a,2b	PROPN
ejpam-6046	380	9	}	}	PUNCT
ejpam-6046	380	10	,	,	PUNCT
ejpam-6046	380	11	{	{	PUNCT
ejpam-6046	380	12	e1a,2b	e1a,2b	NOUN
ejpam-6046	380	13	,	,	PUNCT
ejpam-6046	380	14	e2a,1b	e2a,1b	PROPN
ejpam-6046	380	15	}	}	PUNCT
ejpam-6046	380	16	,	,	PUNCT
ejpam-6046	380	17	e(k2,2	e(k2,2	PROPN
ejpam-6046	380	18	)	)	PUNCT
ejpam-6046	380	19	}	}	PUNCT
ejpam-6046	380	20	.	.	PUNCT
ejpam-6046	381	1	theorem	theorem	ADJ
ejpam-6046	381	2	10	10	NUM
ejpam-6046	381	3	.	.	PUNCT
ejpam-6046	382	1	for	for	ADP
ejpam-6046	382	2	the	the	DET
ejpam-6046	382	3	complete	complete	ADJ
ejpam-6046	382	4	bipartite	bipartite	PROPN
ejpam-6046	382	5	graph	graph	NOUN
ejpam-6046	382	6	k1,n	k1,n	PROPN
ejpam-6046	382	7	(	(	PUNCT
ejpam-6046	382	8	star	star	NOUN
ejpam-6046	382	9	graph	graph	NOUN
ejpam-6046	382	10	)	)	PUNCT
ejpam-6046	382	11	with	with	ADP
ejpam-6046	382	12	n	n	PRON
ejpam-6046	382	13	≥	≥	NOUN
ejpam-6046	382	14	2	2	NUM
ejpam-6046	382	15	,	,	PUNCT
ejpam-6046	382	16	τeid(k1,n	τeid(k1,n	NOUN
ejpam-6046	382	17	)	)	PUNCT
ejpam-6046	382	18	is	be	AUX
ejpam-6046	382	19	the	the	DET
ejpam-6046	382	20	discrete	discrete	ADJ
ejpam-6046	382	21	topology	topology	NOUN
ejpam-6046	382	22	on	on	ADP
ejpam-6046	382	23	e(k1,n	e(k1,n	NOUN
ejpam-6046	382	24	)	)	PUNCT
ejpam-6046	382	25	.	.	PUNCT
ejpam-6046	383	1	proof	proof	NOUN
ejpam-6046	383	2	.	.	PUNCT
ejpam-6046	384	1	let	let	VERB
ejpam-6046	384	2	s	s	PRON
ejpam-6046	384	3	⊆	⊆	NUM
ejpam-6046	384	4	e(k1,n	e(k1,n	NOUN
ejpam-6046	384	5	)	)	PUNCT
ejpam-6046	384	6	where	where	SCONJ
ejpam-6046	384	7	n	n	PRON
ejpam-6046	384	8	≥	≥	NOUN
ejpam-6046	384	9	2	2	NUM
ejpam-6046	384	10	.	.	PUNCT
ejpam-6046	384	11	by	by	ADP
ejpam-6046	384	12	theorem	theorem	ADJ
ejpam-6046	384	13	8	8	NUM
ejpam-6046	384	14	,	,	PUNCT
ejpam-6046	384	15	|s|	|s|	PROPN
ejpam-6046	384	16	=	=	SYM
ejpam-6046	384	17	min{1	min{1	PROPN
ejpam-6046	384	18	,	,	PUNCT
ejpam-6046	384	19	n	n	CCONJ
ejpam-6046	384	20	}	}	PUNCT
ejpam-6046	384	21	=	=	SYM
ejpam-6046	384	22	1	1	NUM
ejpam-6046	384	23	,	,	PUNCT
ejpam-6046	384	24	implying	imply	VERB
ejpam-6046	384	25	that	that	SCONJ
ejpam-6046	384	26	every	every	DET
ejpam-6046	384	27	singleton	singleton	NOUN
ejpam-6046	384	28	subsets	subset	NOUN
ejpam-6046	384	29	of	of	ADP
ejpam-6046	384	30	e(k1,n	e(k1,n	NOUN
ejpam-6046	384	31	)	)	PUNCT
ejpam-6046	384	32	is	be	AUX
ejpam-6046	384	33	an	an	DET
ejpam-6046	384	34	independent	independent	ADJ
ejpam-6046	384	35	edge	edge	NOUN
ejpam-6046	384	36	dominating	dominating	NOUN
ejpam-6046	384	37	set	set	NOUN
ejpam-6046	384	38	.	.	PUNCT
ejpam-6046	385	1	consequently	consequently	ADV
ejpam-6046	385	2	,	,	PUNCT
ejpam-6046	385	3	every	every	DET
ejpam-6046	385	4	subset	subset	NOUN
ejpam-6046	385	5	of	of	ADP
ejpam-6046	385	6	e(km	e(km	PROPN
ejpam-6046	385	7	,	,	PUNCT
ejpam-6046	385	8	n	n	CCONJ
ejpam-6046	385	9	)	)	PUNCT
ejpam-6046	385	10	is	be	AUX
ejpam-6046	385	11	τeid(km	τeid(km	ADJ
ejpam-6046	385	12	,	,	PUNCT
ejpam-6046	385	13	n)-open	n)-open	ADJ
ejpam-6046	385	14	,	,	PUNCT
ejpam-6046	385	15	thus	thus	ADV
ejpam-6046	385	16	,	,	PUNCT
ejpam-6046	385	17	by	by	ADP
ejpam-6046	385	18	theorem	theorem	NOUN
ejpam-6046	385	19	1	1	NUM
ejpam-6046	385	20	,	,	PUNCT
ejpam-6046	385	21	τeid(km	τeid(km	NOUN
ejpam-6046	385	22	,	,	PUNCT
ejpam-6046	385	23	n	n	CCONJ
ejpam-6046	385	24	)	)	PUNCT
ejpam-6046	385	25	is	be	AUX
ejpam-6046	385	26	the	the	DET
ejpam-6046	385	27	discrete	discrete	ADJ
ejpam-6046	385	28	topology	topology	NOUN
ejpam-6046	385	29	.	.	PUNCT
ejpam-6046	386	1	■	■	PUNCT
ejpam-6046	386	2	theorem	theorem	ADJ
ejpam-6046	386	3	11	11	NUM
ejpam-6046	386	4	.	.	PUNCT
ejpam-6046	387	1	let	let	VERB
ejpam-6046	387	2	km	km	PROPN
ejpam-6046	387	3	,	,	PUNCT
ejpam-6046	387	4	n	n	PRON
ejpam-6046	387	5	be	be	VERB
ejpam-6046	387	6	a	a	DET
ejpam-6046	387	7	complete	complete	ADJ
ejpam-6046	387	8	bipartite	bipartite	NOUN
ejpam-6046	387	9	graph	graph	NOUN
ejpam-6046	387	10	with	with	ADP
ejpam-6046	387	11	m	m	PROPN
ejpam-6046	387	12	≤	≤	NOUN
ejpam-6046	387	13	n.	n.	NOUN
ejpam-6046	387	14	if	if	SCONJ
ejpam-6046	387	15	m	m	PROPN
ejpam-6046	387	16	≥	≥	VERB
ejpam-6046	387	17	2	2	NUM
ejpam-6046	387	18	and	and	CCONJ
ejpam-6046	387	19	n	n	PRON
ejpam-6046	387	20	≥	≥	NOUN
ejpam-6046	387	21	3	3	NUM
ejpam-6046	387	22	,	,	PUNCT
ejpam-6046	387	23	then	then	ADV
ejpam-6046	387	24	τeid(km	τeid(km	PROPN
ejpam-6046	387	25	,	,	PUNCT
ejpam-6046	387	26	n	n	CCONJ
ejpam-6046	387	27	)	)	PUNCT
ejpam-6046	387	28	is	be	AUX
ejpam-6046	387	29	the	the	DET
ejpam-6046	387	30	discrete	discrete	ADJ
ejpam-6046	387	31	topology	topology	NOUN
ejpam-6046	387	32	on	on	ADP
ejpam-6046	387	33	e(km	e(km	PROPN
ejpam-6046	387	34	,	,	PUNCT
ejpam-6046	387	35	n	n	CCONJ
ejpam-6046	387	36	)	)	PUNCT
ejpam-6046	387	37	.	.	PUNCT
ejpam-6046	388	1	j.	j.	PROPN
ejpam-6046	388	2	n.	n.	PROPN
ejpam-6046	388	3	ontulan	ontulan	PROPN
ejpam-6046	388	4	,	,	PUNCT
ejpam-6046	388	5	c.	c.	PROPN
ejpam-6046	388	6	m.	m.	NOUN
ejpam-6046	388	7	balingit	balingit	PROPN
ejpam-6046	388	8	/	/	SYM
ejpam-6046	388	9	eur	eur	PROPN
ejpam-6046	388	10	.	.	PUNCT
ejpam-6046	389	1	j.	j.	PROPN
ejpam-6046	389	2	pure	pure	PROPN
ejpam-6046	389	3	appl	appl	PROPN
ejpam-6046	389	4	.	.	PROPN
ejpam-6046	389	5	math	math	PROPN
ejpam-6046	389	6	,	,	PUNCT
ejpam-6046	389	7	18	18	NUM
ejpam-6046	389	8	(	(	PUNCT
ejpam-6046	389	9	2	2	NUM
ejpam-6046	389	10	)	)	PUNCT
ejpam-6046	389	11	(	(	PUNCT
ejpam-6046	389	12	2025	2025	NUM
ejpam-6046	389	13	)	)	PUNCT
ejpam-6046	389	14	,	,	PUNCT
ejpam-6046	389	15	6046	6046	NUM
ejpam-6046	389	16	13	13	NUM
ejpam-6046	389	17	of	of	ADP
ejpam-6046	389	18	14	14	NUM
ejpam-6046	389	19	proof	proof	NOUN
ejpam-6046	389	20	.	.	PUNCT
ejpam-6046	390	1	consider	consider	VERB
ejpam-6046	390	2	the	the	DET
ejpam-6046	390	3	complete	complete	ADJ
ejpam-6046	390	4	bipartite	bipartite	PROPN
ejpam-6046	390	5	graph	graph	NOUN
ejpam-6046	390	6	km	km	PROPN
ejpam-6046	390	7	,	,	PUNCT
ejpam-6046	390	8	n	n	PRON
ejpam-6046	390	9	such	such	ADJ
ejpam-6046	390	10	that	that	SCONJ
ejpam-6046	390	11	m	m	VERB
ejpam-6046	390	12	≤	≤	ADJ
ejpam-6046	390	13	n	n	CCONJ
ejpam-6046	390	14	,	,	PUNCT
ejpam-6046	390	15	m	m	VERB
ejpam-6046	390	16	≥	≥	NOUN
ejpam-6046	390	17	2	2	NUM
ejpam-6046	390	18	and	and	CCONJ
ejpam-6046	390	19	n	n	PRON
ejpam-6046	390	20	≥	≥	NOUN
ejpam-6046	390	21	3	3	X
ejpam-6046	390	22	.	.	PUNCT
ejpam-6046	391	1	let	let	VERB
ejpam-6046	391	2	ep	ep	PROPN
ejpam-6046	391	3	,	,	PUNCT
ejpam-6046	391	4	q	q	PROPN
ejpam-6046	391	5	∈	∈	PROPN
ejpam-6046	391	6	e(km	e(km	NOUN
ejpam-6046	391	7	,	,	PUNCT
ejpam-6046	391	8	n	n	CCONJ
ejpam-6046	391	9	)	)	PUNCT
ejpam-6046	391	10	and	and	CCONJ
ejpam-6046	391	11	s1	s1	PROPN
ejpam-6046	391	12	=	=	SYM
ejpam-6046	391	13	{	{	PUNCT
ejpam-6046	391	14	ep	ep	PROPN
ejpam-6046	391	15	,	,	PUNCT
ejpam-6046	391	16	q	q	NOUN
ejpam-6046	391	17	,	,	PUNCT
ejpam-6046	391	18	ei1,j1	ei1,j1	NOUN
ejpam-6046	391	19	,	,	PUNCT
ejpam-6046	391	20	ei2,j2	ei2,j2	NOUN
ejpam-6046	391	21	,	,	PUNCT
ejpam-6046	391	22	.	.	PUNCT
ejpam-6046	391	23	.	.	PUNCT
ejpam-6046	392	1	.	.	PUNCT
ejpam-6046	393	1	,	,	PUNCT
ejpam-6046	393	2	eim−1,jm−1	eim−1,jm−1	NOUN
ejpam-6046	393	3	}	}	PUNCT
ejpam-6046	393	4	such	such	ADJ
ejpam-6046	393	5	that	that	SCONJ
ejpam-6046	393	6	p	p	PROPN
ejpam-6046	393	7	,	,	PUNCT
ejpam-6046	393	8	i1	i1	PROPN
ejpam-6046	393	9	,	,	PUNCT
ejpam-6046	393	10	.	.	PUNCT
ejpam-6046	393	11	.	.	PUNCT
ejpam-6046	394	1	.	.	PUNCT
ejpam-6046	395	1	,	,	PUNCT
ejpam-6046	395	2	im−1	im−1	PROPN
ejpam-6046	395	3	∈	∈	PROPN
ejpam-6046	395	4	{	{	PUNCT
ejpam-6046	395	5	1a	1a	NOUN
ejpam-6046	395	6	,	,	PUNCT
ejpam-6046	395	7	2a	2a	NUM
ejpam-6046	395	8	,	,	PUNCT
ejpam-6046	395	9	.	.	PUNCT
ejpam-6046	395	10	.	.	PUNCT
ejpam-6046	395	11	.	.	PUNCT
ejpam-6046	396	1	,	,	PUNCT
ejpam-6046	396	2	ma	ma	PROPN
ejpam-6046	396	3	}	}	PUNCT
ejpam-6046	396	4	,	,	PUNCT
ejpam-6046	396	5	q	q	X
ejpam-6046	396	6	,	,	PUNCT
ejpam-6046	396	7	j1	j1	PROPN
ejpam-6046	396	8	,	,	PUNCT
ejpam-6046	396	9	.	.	PUNCT
ejpam-6046	396	10	.	.	PUNCT
ejpam-6046	397	1	.	.	PUNCT
ejpam-6046	398	1	,	,	PUNCT
ejpam-6046	398	2	jm−1	jm−1	PROPN
ejpam-6046	398	3	∈	∈	PROPN
ejpam-6046	398	4	{	{	PUNCT
ejpam-6046	398	5	1b	1b	NUM
ejpam-6046	398	6	,	,	PUNCT
ejpam-6046	398	7	2b	2b	NOUN
ejpam-6046	398	8	,	,	PUNCT
ejpam-6046	398	9	.	.	PUNCT
ejpam-6046	398	10	.	.	PUNCT
ejpam-6046	398	11	.	.	PUNCT
ejpam-6046	399	1	,	,	PUNCT
ejpam-6046	399	2	nb	nb	INTJ
ejpam-6046	399	3	}	}	PUNCT
ejpam-6046	399	4	where	where	SCONJ
ejpam-6046	399	5	p	p	PROPN
ejpam-6046	399	6	̸=	̸=	PROPN
ejpam-6046	399	7	i1	i1	PROPN
ejpam-6046	399	8	̸=	̸=	PROPN
ejpam-6046	399	9	i2	i2	PROPN
ejpam-6046	399	10	̸=	̸=	PROPN
ejpam-6046	399	11	·	·	PUNCT
ejpam-6046	399	12	·	·	PUNCT
ejpam-6046	399	13	·	·	PUNCT
ejpam-6046	400	1	=	=	SYM
ejpam-6046	400	2	̸	̸	ADV
ejpam-6046	400	3	im−1	im−1	PROPN
ejpam-6046	400	4	and	and	CCONJ
ejpam-6046	400	5	q	q	NOUN
ejpam-6046	400	6	̸=	̸=	PROPN
ejpam-6046	400	7	j1	j1	PROPN
ejpam-6046	400	8	̸=	̸=	PROPN
ejpam-6046	400	9	j2	j2	PROPN
ejpam-6046	400	10	̸=	̸=	PROPN
ejpam-6046	400	11	·	·	PUNCT
ejpam-6046	400	12	·	·	PUNCT
ejpam-6046	400	13	·	·	PUNCT
ejpam-6046	401	1	̸=	̸=	PROPN
ejpam-6046	401	2	jm−1	jm−1	PROPN
ejpam-6046	401	3	.	.	PUNCT
ejpam-6046	402	1	by	by	ADP
ejpam-6046	402	2	the	the	DET
ejpam-6046	402	3	preceding	precede	VERB
ejpam-6046	402	4	theorem	theorem	NOUN
ejpam-6046	402	5	,	,	PUNCT
ejpam-6046	402	6	s1	s1	PROPN
ejpam-6046	402	7	∈	∈	PROPN
ejpam-6046	402	8	ide	ide	NOUN
ejpam-6046	402	9	km	km	NOUN
ejpam-6046	402	10	,	,	PUNCT
ejpam-6046	402	11	n	n	NOUN
ejpam-6046	402	12	.	.	PUNCT
ejpam-6046	403	1	now	now	ADV
ejpam-6046	403	2	,	,	PUNCT
ejpam-6046	403	3	if	if	SCONJ
ejpam-6046	403	4	|s1|	|s1|	NOUN
ejpam-6046	403	5	=	=	SYM
ejpam-6046	403	6	m	m	NOUN
ejpam-6046	403	7	=	=	SYM
ejpam-6046	403	8	2	2	NUM
ejpam-6046	403	9	,	,	PUNCT
ejpam-6046	403	10	let	let	VERB
ejpam-6046	403	11	s2	s2	VERB
ejpam-6046	403	12	=	=	PRON
ejpam-6046	403	13	{	{	PUNCT
ejpam-6046	403	14	ep	ep	PROPN
ejpam-6046	403	15	,	,	PUNCT
ejpam-6046	403	16	q	q	NOUN
ejpam-6046	403	17	,	,	PUNCT
ejpam-6046	403	18	ei1,j2	ei1,j2	NOUN
ejpam-6046	403	19	}	}	PUNCT
ejpam-6046	403	20	where	where	SCONJ
ejpam-6046	403	21	j2	j2	PROPN
ejpam-6046	403	22	̸=	̸=	PROPN
ejpam-6046	403	23	q	q	PROPN
ejpam-6046	403	24	̸=	̸=	PROPN
ejpam-6046	403	25	j1	j1	NOUN
ejpam-6046	403	26	;	;	PUNCT
ejpam-6046	403	27	otherwise	otherwise	ADV
ejpam-6046	403	28	,	,	PUNCT
ejpam-6046	403	29	let	let	VERB
ejpam-6046	403	30	s2	s2	VERB
ejpam-6046	403	31	=	=	PRON
ejpam-6046	403	32	{	{	PUNCT
ejpam-6046	403	33	ep	ep	PROPN
ejpam-6046	403	34	,	,	PUNCT
ejpam-6046	403	35	q	q	NOUN
ejpam-6046	403	36	,	,	PUNCT
ejpam-6046	403	37	ei1,jm−1	ei1,jm−1	PROPN
ejpam-6046	403	38	,	,	PUNCT
ejpam-6046	403	39	ei2,jm−2	ei2,jm−2	PROPN
ejpam-6046	403	40	,	,	PUNCT
ejpam-6046	403	41	.	.	PUNCT
ejpam-6046	403	42	.	.	PUNCT
ejpam-6046	404	1	.	.	PUNCT
ejpam-6046	405	1	,	,	PUNCT
ejpam-6046	405	2	eim−1,j1	eim−1,j1	ADV
ejpam-6046	405	3	}	}	PUNCT
ejpam-6046	405	4	.	.	PUNCT
ejpam-6046	406	1	then	then	ADV
ejpam-6046	406	2	s2	s2	VERB
ejpam-6046	406	3	∈	∈	PROPN
ejpam-6046	406	4	ide	ide	NOUN
ejpam-6046	406	5	km	km	NOUN
ejpam-6046	406	6	,	,	PUNCT
ejpam-6046	406	7	n	n	PRON
ejpam-6046	406	8	such	such	ADJ
ejpam-6046	406	9	that	that	SCONJ
ejpam-6046	406	10	s1	s1	PROPN
ejpam-6046	406	11	∩	∩	ADJ
ejpam-6046	406	12	s2	s2	NOUN
ejpam-6046	406	13	=	=	SYM
ejpam-6046	406	14	{	{	PUNCT
ejpam-6046	406	15	ep	ep	PROPN
ejpam-6046	406	16	,	,	PUNCT
ejpam-6046	406	17	q	q	ADJ
ejpam-6046	406	18	}	}	PUNCT
ejpam-6046	406	19	∈	∈	PROPN
ejpam-6046	406	20	τeid(km	τeid(km	PROPN
ejpam-6046	406	21	,	,	PUNCT
ejpam-6046	406	22	n	n	CCONJ
ejpam-6046	406	23	)	)	PUNCT
ejpam-6046	406	24	.	.	PUNCT
ejpam-6046	407	1	by	by	ADP
ejpam-6046	407	2	theorem	theorem	NOUN
ejpam-6046	407	3	1	1	NUM
ejpam-6046	407	4	,	,	PUNCT
ejpam-6046	407	5	τeid(km	τeid(km	NOUN
ejpam-6046	407	6	,	,	PUNCT
ejpam-6046	407	7	n	n	CCONJ
ejpam-6046	407	8	)	)	PUNCT
ejpam-6046	407	9	is	be	AUX
ejpam-6046	407	10	the	the	DET
ejpam-6046	407	11	discrete	discrete	ADJ
ejpam-6046	407	12	topology	topology	NOUN
ejpam-6046	407	13	on	on	ADP
ejpam-6046	407	14	e(km	e(km	PROPN
ejpam-6046	407	15	,	,	PUNCT
ejpam-6046	407	16	n	n	CCONJ
ejpam-6046	407	17	)	)	PUNCT
ejpam-6046	407	18	.	.	PUNCT
ejpam-6046	408	1	■	■	PUNCT
ejpam-6046	408	2	corollary	corollary	ADJ
ejpam-6046	408	3	4	4	NUM
ejpam-6046	408	4	.	.	PUNCT
ejpam-6046	409	1	for	for	ADP
ejpam-6046	409	2	complete	complete	ADJ
ejpam-6046	409	3	bipartite	bipartite	PROPN
ejpam-6046	409	4	graph	graph	NOUN
ejpam-6046	409	5	km	km	PROPN
ejpam-6046	409	6	,	,	PUNCT
ejpam-6046	409	7	n	n	CCONJ
ejpam-6046	409	8	with	with	ADP
ejpam-6046	409	9	m	m	PROPN
ejpam-6046	409	10	≤	≤	NUM
ejpam-6046	409	11	n	n	CCONJ
ejpam-6046	409	12	,	,	PUNCT
ejpam-6046	409	13	|τeid(km	|τeid(km	PROPN
ejpam-6046	409	14	,	,	PUNCT
ejpam-6046	409	15	n)|	n)|	NOUN
ejpam-6046	409	16	=	=	SYM
ejpam-6046	409	17			NOUN
ejpam-6046	409	18	2	2	NUM
ejpam-6046	409	19	,	,	PUNCT
ejpam-6046	409	20	if	if	SCONJ
ejpam-6046	409	21	m	m	ADV
ejpam-6046	409	22	=	=	SYM
ejpam-6046	409	23	1	1	NUM
ejpam-6046	409	24	,	,	PUNCT
ejpam-6046	409	25	n	n	NOUN
ejpam-6046	409	26	=	=	SYM
ejpam-6046	409	27	1	1	NUM
ejpam-6046	409	28	4	4	NUM
ejpam-6046	409	29	,	,	PUNCT
ejpam-6046	409	30	if	if	SCONJ
ejpam-6046	409	31	m	m	ADV
ejpam-6046	409	32	=	=	SYM
ejpam-6046	409	33	2	2	NUM
ejpam-6046	409	34	,	,	PUNCT
ejpam-6046	409	35	n	n	NOUN
ejpam-6046	409	36	=	=	SYM
ejpam-6046	409	37	2	2	NUM
ejpam-6046	409	38	2n	2n	NUM
ejpam-6046	409	39	,	,	PUNCT
ejpam-6046	409	40	if	if	SCONJ
ejpam-6046	409	41	m	m	VERB
ejpam-6046	409	42	=	=	SYM
ejpam-6046	409	43	1	1	NUM
ejpam-6046	409	44	,	,	PUNCT
ejpam-6046	409	45	n	n	PRON
ejpam-6046	409	46	≥	≥	NOUN
ejpam-6046	409	47	2	2	NUM
ejpam-6046	409	48	2mn	2mn	NOUN
ejpam-6046	409	49	,	,	PUNCT
ejpam-6046	409	50	if	if	SCONJ
ejpam-6046	409	51	m	m	PROPN
ejpam-6046	409	52	≥	≥	NOUN
ejpam-6046	409	53	2	2	NUM
ejpam-6046	409	54	,	,	PUNCT
ejpam-6046	409	55	n	n	PRON
ejpam-6046	409	56	≥	≥	NOUN
ejpam-6046	409	57	3	3	NUM
ejpam-6046	409	58	.	.	PUNCT
ejpam-6046	410	1	acknowledgements	acknowledgement	NOUN
ejpam-6046	410	2	the	the	DET
ejpam-6046	410	3	authors	author	NOUN
ejpam-6046	410	4	express	express	VERB
ejpam-6046	410	5	profound	profound	ADJ
ejpam-6046	410	6	gratitude	gratitude	NOUN
ejpam-6046	410	7	and	and	CCONJ
ejpam-6046	410	8	genuine	genuine	ADJ
ejpam-6046	410	9	thanks	thank	NOUN
ejpam-6046	410	10	to	to	ADP
ejpam-6046	410	11	the	the	DET
ejpam-6046	410	12	department	department	PROPN
ejpam-6046	410	13	of	of	ADP
ejpam-6046	410	14	science	science	NOUN
ejpam-6046	410	15	and	and	CCONJ
ejpam-6046	410	16	technology	technology	NOUN
ejpam-6046	410	17	-	-	PUNCT
ejpam-6046	410	18	science	science	NOUN
ejpam-6046	410	19	education	education	PROPN
ejpam-6046	410	20	institute	institute	NOUN
ejpam-6046	410	21	(	(	PUNCT
ejpam-6046	410	22	dost	dost	NOUN
ejpam-6046	410	23	-	-	PUNCT
ejpam-6046	410	24	sei	sei	ADJ
ejpam-6046	410	25	)	)	PUNCT
ejpam-6046	410	26	through	through	ADP
ejpam-6046	410	27	the	the	DET
ejpam-6046	410	28	science	science	NOUN
ejpam-6046	410	29	and	and	CCONJ
ejpam-6046	410	30	technology	technology	NOUN
ejpam-6046	410	31	regional	regional	ADJ
ejpam-6046	410	32	alliance	alliance	NOUN
ejpam-6046	410	33	of	of	ADP
ejpam-6046	410	34	universities	university	NOUN
ejpam-6046	410	35	for	for	ADP
ejpam-6046	410	36	national	national	ADJ
ejpam-6046	410	37	development	development	NOUN
ejpam-6046	410	38	(	(	PUNCT
ejpam-6046	410	39	strand	strand	NOUN
ejpam-6046	410	40	)	)	PUNCT
ejpam-6046	410	41	scholarship	scholarship	NOUN
ejpam-6046	410	42	program	program	NOUN
ejpam-6046	410	43	and	and	CCONJ
ejpam-6046	410	44	the	the	DET
ejpam-6046	410	45	office	office	NOUN
ejpam-6046	410	46	of	of	ADP
ejpam-6046	410	47	admission	admission	NOUN
ejpam-6046	410	48	,	,	PUNCT
ejpam-6046	410	49	scholarships	scholarship	NOUN
ejpam-6046	410	50	,	,	PUNCT
ejpam-6046	410	51	and	and	CCONJ
ejpam-6046	410	52	placement	placement	NOUN
ejpam-6046	410	53	(	(	PUNCT
ejpam-6046	410	54	oasp	oasp	NOUN
ejpam-6046	410	55	)	)	PUNCT
ejpam-6046	410	56	and	and	CCONJ
ejpam-6046	410	57	department	department	NOUN
ejpam-6046	410	58	of	of	ADP
ejpam-6046	410	59	mathematics	mathematic	NOUN
ejpam-6046	410	60	of	of	ADP
ejpam-6046	410	61	central	central	PROPN
ejpam-6046	410	62	mindanao	mindanao	PROPN
ejpam-6046	410	63	university	university	NOUN
ejpam-6046	410	64	,	,	PUNCT
ejpam-6046	410	65	and	and	CCONJ
ejpam-6046	410	66	all	all	DET
ejpam-6046	410	67	others	other	NOUN
ejpam-6046	410	68	who	who	PRON
ejpam-6046	410	69	made	make	VERB
ejpam-6046	410	70	this	this	DET
ejpam-6046	410	71	research	research	NOUN
ejpam-6046	410	72	project	project	NOUN
ejpam-6046	410	73	possible	possible	ADJ
ejpam-6046	410	74	.	.	PUNCT
ejpam-6046	411	1	references	reference	NOUN
ejpam-6046	411	2	[	[	X
ejpam-6046	411	3	1	1	X
ejpam-6046	411	4	]	]	X
ejpam-6046	411	5	j.l	j.l	PROPN
ejpam-6046	411	6	gross	gross	ADJ
ejpam-6046	411	7	and	and	CCONJ
ejpam-6046	411	8	j	j	PROPN
ejpam-6046	411	9	yellen	yellen	PROPN
ejpam-6046	411	10	.	.	PUNCT
ejpam-6046	412	1	graph	graph	NOUN
ejpam-6046	412	2	theory	theory	NOUN
ejpam-6046	412	3	and	and	CCONJ
ejpam-6046	412	4	its	its	PRON
ejpam-6046	412	5	applications	application	NOUN
ejpam-6046	412	6	.	.	PUNCT
ejpam-6046	413	1	crc	crc	PROPN
ejpam-6046	413	2	press	press	PROPN
ejpam-6046	413	3	,	,	PUNCT
ejpam-6046	413	4	2nd	2nd	PROPN
ejpam-6046	413	5	edition	edition	NOUN
ejpam-6046	413	6	,	,	PUNCT
ejpam-6046	413	7	2005	2005	NUM
ejpam-6046	413	8	.	.	PUNCT
ejpam-6046	414	1	[	[	X
ejpam-6046	414	2	2	2	X
ejpam-6046	414	3	]	]	X
ejpam-6046	414	4	j.b	j.b	PROPN
ejpam-6046	414	5	macaso	macaso	PROPN
ejpam-6046	414	6	and	and	CCONJ
ejpam-6046	414	7	c.m	c.m	X
ejpam-6046	414	8	balingit	balingit	ADJ
ejpam-6046	414	9	.	.	PUNCT
ejpam-6046	415	1	the	the	DET
ejpam-6046	415	2	block	block	NOUN
ejpam-6046	415	3	topological	topological	ADJ
ejpam-6046	415	4	space	space	NOUN
ejpam-6046	415	5	and	and	CCONJ
ejpam-6046	415	6	block	block	NOUN
ejpam-6046	415	7	topological	topological	ADJ
ejpam-6046	415	8	graph	graph	NOUN
ejpam-6046	415	9	induced	induce	VERB
ejpam-6046	415	10	by	by	ADP
ejpam-6046	415	11	undirected	undirected	ADJ
ejpam-6046	415	12	graphs	graph	NOUN
ejpam-6046	415	13	.	.	PUNCT
ejpam-6046	416	1	european	european	ADJ
ejpam-6046	416	2	journal	journal	PROPN
ejpam-6046	416	3	of	of	ADP
ejpam-6046	416	4	pure	pure	ADJ
ejpam-6046	416	5	and	and	CCONJ
ejpam-6046	416	6	applied	applied	ADJ
ejpam-6046	416	7	mathematics	mathematic	NOUN
ejpam-6046	416	8	,	,	PUNCT
ejpam-6046	416	9	17(2):663–675	17(2):663–675	NUM
ejpam-6046	416	10	,	,	PUNCT
ejpam-6046	416	11	2024	2024	NUM
ejpam-6046	416	12	.	.	PUNCT
ejpam-6046	417	1	[	[	X
ejpam-6046	417	2	3	3	X
ejpam-6046	417	3	]	]	X
ejpam-6046	417	4	k.a	k.a	PROPN
ejpam-6046	417	5	abdu	abdu	PROPN
ejpam-6046	417	6	and	and	CCONJ
ejpam-6046	417	7	a	a	DET
ejpam-6046	417	8	kilicman	kilicman	NOUN
ejpam-6046	417	9	.	.	PUNCT
ejpam-6046	418	1	topologies	topology	NOUN
ejpam-6046	418	2	on	on	ADP
ejpam-6046	418	3	the	the	DET
ejpam-6046	418	4	edges	edge	NOUN
ejpam-6046	418	5	set	set	VERB
ejpam-6046	418	6	of	of	ADP
ejpam-6046	418	7	directed	direct	VERB
ejpam-6046	418	8	graph	graph	NOUN
ejpam-6046	418	9	.	.	PUNCT
ejpam-6046	419	1	international	international	ADJ
ejpam-6046	419	2	journal	journal	PROPN
ejpam-6046	419	3	of	of	ADP
ejpam-6046	419	4	mathematical	mathematical	ADJ
ejpam-6046	419	5	analysis	analysis	NOUN
ejpam-6046	419	6	,	,	PUNCT
ejpam-6046	419	7	12(2):71–84	12(2):71–84	NUM
ejpam-6046	419	8	,	,	PUNCT
ejpam-6046	419	9	2018	2018	NUM
ejpam-6046	419	10	.	.	PUNCT
ejpam-6046	420	1	[	[	X
ejpam-6046	420	2	4	4	X
ejpam-6046	420	3	]	]	X
ejpam-6046	420	4	a	a	DET
ejpam-6046	420	5	alsinaia	alsinaia	NOUN
ejpam-6046	420	6	,	,	PUNCT
ejpam-6046	420	7	d	d	PROPN
ejpam-6046	420	8	bv	bv	PROPN
ejpam-6046	420	9	,	,	PUNCT
ejpam-6046	420	10	m	m	VERB
ejpam-6046	420	11	abdlhusein	abdlhusein	NOUN
ejpam-6046	420	12	,	,	PUNCT
ejpam-6046	420	13	m	m	PROPN
ejpam-6046	420	14	idan	idan	PROPN
ejpam-6046	420	15	,	,	PUNCT
ejpam-6046	420	16	and	and	CCONJ
ejpam-6046	420	17	m	m	PROPN
ejpam-6046	420	18	cancan	cancan	ADJ
ejpam-6046	420	19	.	.	PUNCT
ejpam-6046	421	1	topological	topological	ADJ
ejpam-6046	421	2	space	space	NOUN
ejpam-6046	421	3	generated	generate	VERB
ejpam-6046	421	4	by	by	ADP
ejpam-6046	421	5	edges	edge	NOUN
ejpam-6046	421	6	neighborhoods	neighborhood	NOUN
ejpam-6046	421	7	of	of	ADP
ejpam-6046	421	8	discrete	discrete	ADJ
ejpam-6046	421	9	topological	topological	ADJ
ejpam-6046	421	10	graphs	graph	NOUN
ejpam-6046	421	11	.	.	PUNCT
ejpam-6046	422	1	eur	eur	ADJ
ejpam-6046	422	2	.	.	PUNCT
ejpam-6046	422	3	chem	chem	PROPN
ejpam-6046	422	4	.	.	PUNCT
ejpam-6046	423	1	bull	bull	NOUN
ejpam-6046	423	2	,	,	PUNCT
ejpam-6046	423	3	12(3):3273–3279	12(3):3273–3279	NOUN
ejpam-6046	423	4	,	,	PUNCT
ejpam-6046	423	5	2023	2023	NUM
ejpam-6046	423	6	.	.	PUNCT
ejpam-6046	424	1	[	[	X
ejpam-6046	424	2	5	5	NUM
ejpam-6046	424	3	]	]	SYM
ejpam-6046	424	4	r	r	NOUN
ejpam-6046	424	5	diestel	diestel	NOUN
ejpam-6046	424	6	.	.	PUNCT
ejpam-6046	425	1	graph	graph	NOUN
ejpam-6046	425	2	theory	theory	NOUN
ejpam-6046	425	3	:	:	PUNCT
ejpam-6046	425	4	graduate	graduate	NOUN
ejpam-6046	425	5	texts	text	NOUN
ejpam-6046	425	6	in	in	ADP
ejpam-6046	425	7	mathematics	mathematic	NOUN
ejpam-6046	425	8	.	.	PUNCT
ejpam-6046	426	1	springer	springer	PROPN
ejpam-6046	426	2	,	,	PUNCT
ejpam-6046	426	3	3rd	3rd	ADJ
ejpam-6046	426	4	edition	edition	NOUN
ejpam-6046	426	5	,	,	PUNCT
ejpam-6046	426	6	2006	2006	NUM
ejpam-6046	426	7	.	.	PUNCT
ejpam-6046	427	1	[	[	X
ejpam-6046	427	2	6	6	NUM
ejpam-6046	427	3	]	]	X
ejpam-6046	427	4	a.f	a.f	PROPN
ejpam-6046	427	5	hassan	hassan	PROPN
ejpam-6046	427	6	and	and	CCONJ
ejpam-6046	427	7	z.i	z.i	PROPN
ejpam-6046	427	8	abed	abe	VERB
ejpam-6046	427	9	.	.	PUNCT
ejpam-6046	428	1	independent	independent	ADJ
ejpam-6046	428	2	(	(	PUNCT
ejpam-6046	428	3	non	non	ADJ
ejpam-6046	428	4	-	-	ADJ
ejpam-6046	428	5	adjacent	adjacent	ADJ
ejpam-6046	428	6	vertices	vertex	NOUN
ejpam-6046	428	7	)	)	PUNCT
ejpam-6046	428	8	topological	topological	ADJ
ejpam-6046	428	9	spaces	space	NOUN
ejpam-6046	428	10	associated	associate	VERB
ejpam-6046	428	11	with	with	ADP
ejpam-6046	428	12	undirected	undirected	ADJ
ejpam-6046	428	13	graphs	graph	NOUN
ejpam-6046	428	14	,	,	PUNCT
ejpam-6046	428	15	with	with	ADP
ejpam-6046	428	16	some	some	DET
ejpam-6046	428	17	applications	application	NOUN
ejpam-6046	428	18	in	in	ADP
ejpam-6046	428	19	biomathematics	biomathematic	NOUN
ejpam-6046	428	20	.	.	PUNCT
ejpam-6046	429	1	journal	journal	PROPN
ejpam-6046	429	2	of	of	ADP
ejpam-6046	429	3	physics	physics	PROPN
ejpam-6046	429	4	:	:	PUNCT
ejpam-6046	429	5	conference	conference	NOUN
ejpam-6046	429	6	series	series	NOUN
ejpam-6046	429	7	,	,	PUNCT
ejpam-6046	429	8	1591(1):1–10	1591(1):1–10	PROPN
ejpam-6046	429	9	,	,	PUNCT
ejpam-6046	429	10	2020	2020	NUM
ejpam-6046	429	11	.	.	PUNCT
ejpam-6046	430	1	[	[	X
ejpam-6046	430	2	7	7	X
ejpam-6046	430	3	]	]	X
ejpam-6046	430	4	t.w	t.w	PROPN
ejpam-6046	430	5	haynes	haynes	PROPN
ejpam-6046	430	6	,	,	PUNCT
ejpam-6046	430	7	s.t	s.t	PROPN
ejpam-6046	430	8	hedetniemi	hedetniemi	ADV
ejpam-6046	430	9	,	,	PUNCT
ejpam-6046	430	10	and	and	CCONJ
ejpam-6046	430	11	p.j	p.j	PROPN
ejpam-6046	430	12	slater	slater	NOUN
ejpam-6046	430	13	.	.	PUNCT
ejpam-6046	431	1	fundamentals	fundamental	NOUN
ejpam-6046	431	2	of	of	ADP
ejpam-6046	431	3	domination	domination	NOUN
ejpam-6046	431	4	in	in	ADP
ejpam-6046	431	5	graphs	graph	NOUN
ejpam-6046	431	6	.	.	PUNCT
ejpam-6046	432	1	marcel	marcel	PROPN
ejpam-6046	432	2	dekker	dekker	PROPN
ejpam-6046	432	3	,	,	PUNCT
ejpam-6046	432	4	inc	inc	PROPN
ejpam-6046	432	5	.	.	PROPN
ejpam-6046	432	6	,	,	PUNCT
ejpam-6046	432	7	1998	1998	NUM
ejpam-6046	432	8	.	.	PUNCT
ejpam-6046	433	1	j.	j.	PROPN
ejpam-6046	433	2	n.	n.	PROPN
ejpam-6046	433	3	ontulan	ontulan	PROPN
ejpam-6046	433	4	,	,	PUNCT
ejpam-6046	433	5	c.	c.	PROPN
ejpam-6046	433	6	m.	m.	NOUN
ejpam-6046	433	7	balingit	balingit	PROPN
ejpam-6046	433	8	/	/	SYM
ejpam-6046	433	9	eur	eur	PROPN
ejpam-6046	433	10	.	.	PUNCT
ejpam-6046	434	1	j.	j.	PROPN
ejpam-6046	434	2	pure	pure	PROPN
ejpam-6046	434	3	appl	appl	PROPN
ejpam-6046	434	4	.	.	PROPN
ejpam-6046	434	5	math	math	PROPN
ejpam-6046	434	6	,	,	PUNCT
ejpam-6046	434	7	18	18	NUM
ejpam-6046	434	8	(	(	PUNCT
ejpam-6046	434	9	2	2	NUM
ejpam-6046	434	10	)	)	PUNCT
ejpam-6046	434	11	(	(	PUNCT
ejpam-6046	434	12	2025	2025	NUM
ejpam-6046	434	13	)	)	PUNCT
ejpam-6046	434	14	,	,	PUNCT
ejpam-6046	434	15	6046	6046	NUM
ejpam-6046	434	16	14	14	NUM
ejpam-6046	434	17	of	of	ADP
ejpam-6046	434	18	14	14	NUM
ejpam-6046	435	1	[	[	SYM
ejpam-6046	435	2	8	8	NUM
ejpam-6046	435	3	]	]	X
ejpam-6046	435	4	t.h	t.h	PROPN
ejpam-6046	435	5	cormen	corman	NOUN
ejpam-6046	435	6	,	,	PUNCT
ejpam-6046	435	7	c.e	c.e	PROPN
ejpam-6046	435	8	leiserson	leiserson	PROPN
ejpam-6046	435	9	,	,	PUNCT
ejpam-6046	435	10	r.l	r.l	PROPN
ejpam-6046	435	11	rivest	riv	ADJ
ejpam-6046	435	12	,	,	PUNCT
ejpam-6046	435	13	and	and	CCONJ
ejpam-6046	435	14	c	c	PROPN
ejpam-6046	435	15	stein	stein	PROPN
ejpam-6046	435	16	.	.	PUNCT
ejpam-6046	436	1	introduction	introduction	NOUN
ejpam-6046	436	2	to	to	ADP
ejpam-6046	436	3	algorithms	algorithm	NOUN
ejpam-6046	436	4	.	.	PUNCT
ejpam-6046	437	1	mit	mit	PROPN
ejpam-6046	437	2	press	press	PROPN
ejpam-6046	437	3	.	.	PUNCT
ejpam-6046	437	4	,	,	PUNCT
ejpam-6046	437	5	3rd	3rd	PROPN
ejpam-6046	437	6	edition	edition	NOUN
ejpam-6046	437	7	,	,	PUNCT
ejpam-6046	437	8	2009	2009	NUM
ejpam-6046	437	9	.	.	PUNCT
ejpam-6046	438	1	[	[	X
ejpam-6046	438	2	9	9	NUM
ejpam-6046	438	3	]	]	PUNCT
ejpam-6046	438	4	g	g	PROPN
ejpam-6046	438	5	chartrand	chartrand	NOUN
ejpam-6046	438	6	,	,	PUNCT
ejpam-6046	438	7	l	l	PROPN
ejpam-6046	438	8	lesniak	lesniak	PROPN
ejpam-6046	438	9	,	,	PUNCT
ejpam-6046	438	10	and	and	CCONJ
ejpam-6046	438	11	p	p	PROPN
ejpam-6046	438	12	zhang	zhang	PROPN
ejpam-6046	438	13	.	.	PUNCT
ejpam-6046	438	14	graphs	graph	NOUN
ejpam-6046	438	15	and	and	CCONJ
ejpam-6046	438	16	digraphs	digraph	NOUN
ejpam-6046	438	17	.	.	PUNCT
ejpam-6046	439	1	crc	crc	NOUN
ejpam-6046	439	2	press	press	PROPN
ejpam-6046	439	3	,	,	PUNCT
ejpam-6046	439	4	6th	6th	ADJ
ejpam-6046	439	5	edition	edition	NOUN
ejpam-6046	439	6	,	,	PUNCT
ejpam-6046	439	7	2015	2015	NUM
ejpam-6046	439	8	.	.	PUNCT
ejpam-6046	440	1	[	[	X
ejpam-6046	440	2	10	10	NUM
ejpam-6046	440	3	]	]	X
ejpam-6046	440	4	d.a	d.a	NOUN
ejpam-6046	440	5	mojdeh	mojdeh	NOUN
ejpam-6046	440	6	and	and	CCONJ
ejpam-6046	440	7	r	r	PROPN
ejpam-6046	440	8	sadeghi	sadeghi	NOUN
ejpam-6046	440	9	.	.	PUNCT
ejpam-6046	441	1	indepedent	indepedent	ADJ
ejpam-6046	441	2	edge	edge	NOUN
ejpam-6046	441	3	dominating	dominate	VERB
ejpam-6046	441	4	set	set	NOUN
ejpam-6046	441	5	of	of	ADP
ejpam-6046	441	6	certain	certain	ADJ
ejpam-6046	441	7	graphs	graph	NOUN
ejpam-6046	441	8	.	.	PUNCT
ejpam-6046	442	1	international	international	ADJ
ejpam-6046	442	2	mathematical	mathematical	PROPN
ejpam-6046	442	3	forum	forum	PROPN
ejpam-6046	442	4	,	,	PUNCT
ejpam-6046	442	5	2(7):315–320	2(7):315–320	NUM
ejpam-6046	442	6	,	,	PUNCT
ejpam-6046	442	7	2007	2007	NUM
ejpam-6046	442	8	.	.	PUNCT
ejpam-6046	443	1	[	[	X
ejpam-6046	443	2	11	11	NUM
ejpam-6046	443	3	]	]	X
ejpam-6046	443	4	j	j	PROPN
ejpam-6046	443	5	munkres	munkre	NOUN
ejpam-6046	443	6	.	.	PUNCT
ejpam-6046	444	1	topology	topology	NOUN
ejpam-6046	444	2	.	.	PUNCT
ejpam-6046	445	1	prentice	prentice	PROPN
ejpam-6046	445	2	hall	hall	PROPN
ejpam-6046	445	3	,	,	PUNCT
ejpam-6046	445	4	inc	inc	PROPN
ejpam-6046	445	5	.	.	PROPN
ejpam-6046	445	6	,	,	PUNCT
ejpam-6046	445	7	2nd	2nd	PROPN
ejpam-6046	445	8	edition	edition	NOUN
ejpam-6046	445	9	,	,	PUNCT
ejpam-6046	445	10	1966	1966	NUM
ejpam-6046	445	11	.	.	PUNCT
ejpam-6046	446	1	[	[	X
ejpam-6046	446	2	12	12	NUM
ejpam-6046	446	3	]	]	X
ejpam-6046	446	4	j	j	PROPN
ejpam-6046	446	5	dugunji	dugunji	PROPN
ejpam-6046	446	6	.	.	PUNCT
ejpam-6046	447	1	topology	topology	PROPN
ejpam-6046	447	2	.	.	PUNCT
ejpam-6046	448	1	allyn	allyn	PROPN
ejpam-6046	448	2	and	and	CCONJ
ejpam-6046	448	3	bacon	bacon	PROPN
ejpam-6046	448	4	,	,	PUNCT
ejpam-6046	448	5	inc	inc	PROPN
ejpam-6046	448	6	.	.	PROPN
ejpam-6046	448	7	,	,	PUNCT
ejpam-6046	448	8	1966	1966	NUM
ejpam-6046	448	9	.	.	PUNCT
ejpam-6046	449	1	[	[	X
ejpam-6046	449	2	13	13	NUM
ejpam-6046	449	3	]	]	X
ejpam-6046	449	4	c.e	c.e	PROPN
ejpam-6046	449	5	sambaan	sambaan	PROPN
ejpam-6046	449	6	,	,	PUNCT
ejpam-6046	449	7	b	b	NOUN
ejpam-6046	449	8	lausa	lausa	NOUN
ejpam-6046	449	9	,	,	PUNCT
ejpam-6046	449	10	and	and	CCONJ
ejpam-6046	449	11	c.m	c.m	AUX
ejpam-6046	449	12	balingit	balingit	ADJ
ejpam-6046	449	13	.	.	PUNCT
ejpam-6046	450	1	independent	independent	ADJ
ejpam-6046	450	2	domination	domination	NOUN
ejpam-6046	450	3	topology	topology	NOUN
ejpam-6046	450	4	of	of	ADP
ejpam-6046	450	5	the	the	DET
ejpam-6046	450	6	friendship	friendship	NOUN
ejpam-6046	450	7	graph	graph	NOUN
ejpam-6046	450	8	and	and	CCONJ
ejpam-6046	450	9	its	its	PRON
ejpam-6046	450	10	line	line	NOUN
ejpam-6046	450	11	graph	graph	NOUN
ejpam-6046	450	12	.	.	PUNCT
ejpam-6046	451	1	asian	asian	ADJ
ejpam-6046	451	2	research	research	PROPN
ejpam-6046	451	3	journal	journal	NOUN
ejpam-6046	451	4	of	of	ADP
ejpam-6046	451	5	mathematics	mathematic	NOUN
ejpam-6046	451	6	,	,	PUNCT
ejpam-6046	451	7	20(10):30–37	20(10):30–37	NOUN
ejpam-6046	451	8	,	,	PUNCT
ejpam-6046	451	9	2024	2024	NUM
ejpam-6046	451	10	.	.	PUNCT
ejpam-6046	452	1	[	[	X
ejpam-6046	452	2	14	14	NUM
ejpam-6046	452	3	]	]	X
ejpam-6046	452	4	r.s	r.s	PROPN
ejpam-6046	452	5	kumar	kumar	PROPN
ejpam-6046	452	6	,	,	PUNCT
ejpam-6046	452	7	b	b	PROPN
ejpam-6046	452	8	kannan	kannan	PROPN
ejpam-6046	452	9	,	,	PUNCT
ejpam-6046	452	10	and	and	CCONJ
ejpam-6046	452	11	m	m	PROPN
ejpam-6046	452	12	jathavedan	jathavedan	PROPN
ejpam-6046	452	13	.	.	PUNCT
ejpam-6046	453	1	betweenness	betweenness	ADJ
ejpam-6046	453	2	centrality	centrality	NOUN
ejpam-6046	453	3	in	in	ADP
ejpam-6046	453	4	some	some	DET
ejpam-6046	453	5	classes	class	NOUN
ejpam-6046	453	6	of	of	ADP
ejpam-6046	453	7	graphs	graph	NOUN
ejpam-6046	453	8	.	.	PUNCT
ejpam-6046	454	1	international	international	ADJ
ejpam-6046	454	2	journal	journal	PROPN
ejpam-6046	454	3	of	of	ADP
ejpam-6046	454	4	combinatorics	combinatoric	NOUN
ejpam-6046	454	5	,	,	PUNCT
ejpam-6046	454	6	pages	page	NOUN
ejpam-6046	454	7	1–12	1–12	PROPN
ejpam-6046	454	8	,	,	PUNCT
ejpam-6046	454	9	2014	2014	NUM
ejpam-6046	454	10	.	.	PUNCT