id	sid	tid	token	lemma	pos
ejpam-5734	1	1	european	european	PROPN
ejpam-5734	1	2	journal	journal	PROPN
ejpam-5734	1	3	of	of	ADP
ejpam-5734	1	4	pure	pure	ADJ
ejpam-5734	1	5	and	and	CCONJ
ejpam-5734	1	6	applied	applied	ADJ
ejpam-5734	1	7	mathematics	mathematic	NOUN
ejpam-5734	1	8	2025	2025	NUM
ejpam-5734	1	9	,	,	PUNCT
ejpam-5734	1	10	vol	vol	NOUN
ejpam-5734	1	11	.	.	PROPN
ejpam-5734	1	12	18	18	NUM
ejpam-5734	1	13	,	,	PUNCT
ejpam-5734	1	14	issue	issue	NOUN
ejpam-5734	1	15	2	2	NUM
ejpam-5734	1	16	,	,	PUNCT
ejpam-5734	1	17	article	article	NOUN
ejpam-5734	1	18	number	number	NOUN
ejpam-5734	1	19	5734	5734	NUM
ejpam-5734	1	20	issn	issn	VERB
ejpam-5734	1	21	1307	1307	NUM
ejpam-5734	1	22	-	-	SYM
ejpam-5734	1	23	5543	5543	NUM
ejpam-5734	1	24	–	–	PUNCT
ejpam-5734	1	25	ejpam.com	ejpam.com	X
ejpam-5734	1	26	published	publish	VERB
ejpam-5734	1	27	by	by	ADP
ejpam-5734	1	28	new	new	PROPN
ejpam-5734	1	29	york	york	PROPN
ejpam-5734	1	30	business	business	PROPN
ejpam-5734	1	31	global	global	ADJ
ejpam-5734	1	32	distance-2	distance-2	NUM
ejpam-5734	1	33	chromatic	chromatic	ADJ
ejpam-5734	1	34	number	number	NOUN
ejpam-5734	1	35	of	of	ADP
ejpam-5734	1	36	the	the	DET
ejpam-5734	1	37	central	central	ADJ
ejpam-5734	1	38	and	and	CCONJ
ejpam-5734	1	39	shadow	shadow	NOUN
ejpam-5734	1	40	graphs	graph	NOUN
ejpam-5734	1	41	of	of	ADP
ejpam-5734	1	42	a	a	DET
ejpam-5734	1	43	cycle	cycle	NOUN
ejpam-5734	1	44	and	and	CCONJ
ejpam-5734	1	45	its	its	PRON
ejpam-5734	1	46	application	application	NOUN
ejpam-5734	1	47	to	to	ADP
ejpam-5734	1	48	computer	computer	NOUN
ejpam-5734	1	49	science	science	NOUN
ejpam-5734	1	50	merliza	merliza	PROPN
ejpam-5734	1	51	f.	f.	PROPN
ejpam-5734	1	52	libao1,∗	libao1,∗	PROPN
ejpam-5734	1	53	,	,	PUNCT
ejpam-5734	1	54	kyla	kyla	PROPN
ejpam-5734	1	55	b.	b.	PROPN
ejpam-5734	1	56	abarca1	abarca1	NOUN
ejpam-5734	1	57	1	1	NUM
ejpam-5734	1	58	mathematics	mathematics	PROPN
ejpam-5734	1	59	department	department	NOUN
ejpam-5734	1	60	,	,	PUNCT
ejpam-5734	1	61	caraga	caraga	PROPN
ejpam-5734	1	62	state	state	PROPN
ejpam-5734	1	63	university	university	PROPN
ejpam-5734	1	64	,	,	PUNCT
ejpam-5734	1	65	butuan	butuan	PROPN
ejpam-5734	1	66	city	city	PROPN
ejpam-5734	1	67	,	,	PUNCT
ejpam-5734	1	68	philippines	philippine	NOUN
ejpam-5734	1	69	abstract	abstract	ADJ
ejpam-5734	1	70	.	.	PUNCT
ejpam-5734	2	1	let	let	VERB
ejpam-5734	2	2	g	g	PROPN
ejpam-5734	2	3	=	=	SYM
ejpam-5734	2	4	(	(	PUNCT
ejpam-5734	2	5	v	v	NOUN
ejpam-5734	2	6	(	(	PUNCT
ejpam-5734	2	7	g	g	NOUN
ejpam-5734	2	8	)	)	PUNCT
ejpam-5734	2	9	,	,	PUNCT
ejpam-5734	2	10	e(g	e(g	PROPN
ejpam-5734	2	11	)	)	PUNCT
ejpam-5734	2	12	)	)	PUNCT
ejpam-5734	3	1	be	be	AUX
ejpam-5734	3	2	a	a	DET
ejpam-5734	3	3	graph	graph	NOUN
ejpam-5734	3	4	.	.	PUNCT
ejpam-5734	4	1	the	the	DET
ejpam-5734	4	2	chromatic	chromatic	ADJ
ejpam-5734	4	3	number	number	NOUN
ejpam-5734	4	4	of	of	ADP
ejpam-5734	4	5	a	a	DET
ejpam-5734	4	6	graph	graph	NOUN
ejpam-5734	4	7	g	g	NOUN
ejpam-5734	4	8	,	,	PUNCT
ejpam-5734	4	9	χ(g	χ(g	PROPN
ejpam-5734	4	10	)	)	PUNCT
ejpam-5734	4	11	,	,	PUNCT
ejpam-5734	4	12	is	be	AUX
ejpam-5734	4	13	the	the	DET
ejpam-5734	4	14	minimum	minimum	ADJ
ejpam-5734	4	15	number	number	NOUN
ejpam-5734	4	16	of	of	ADP
ejpam-5734	4	17	colors	color	NOUN
ejpam-5734	4	18	needed	need	VERB
ejpam-5734	4	19	to	to	PART
ejpam-5734	4	20	color	color	VERB
ejpam-5734	4	21	the	the	DET
ejpam-5734	4	22	vertices	vertex	NOUN
ejpam-5734	4	23	such	such	ADJ
ejpam-5734	4	24	that	that	SCONJ
ejpam-5734	4	25	no	no	DET
ejpam-5734	4	26	two	two	NUM
ejpam-5734	4	27	adjacent	adjacent	ADJ
ejpam-5734	4	28	vertices	vertex	NOUN
ejpam-5734	4	29	share	share	VERB
ejpam-5734	4	30	the	the	DET
ejpam-5734	4	31	same	same	ADJ
ejpam-5734	4	32	color	color	NOUN
ejpam-5734	4	33	.	.	PUNCT
ejpam-5734	5	1	the	the	DET
ejpam-5734	5	2	distance-2	distance-2	CCONJ
ejpam-5734	5	3	chromatic	chromatic	ADJ
ejpam-5734	5	4	number	number	NOUN
ejpam-5734	5	5	of	of	ADP
ejpam-5734	5	6	g	g	NOUN
ejpam-5734	5	7	,	,	PUNCT
ejpam-5734	5	8	χ2(g	χ2(g	NUM
ejpam-5734	5	9	)	)	PUNCT
ejpam-5734	5	10	,	,	PUNCT
ejpam-5734	5	11	extends	extend	VERB
ejpam-5734	5	12	this	this	PRON
ejpam-5734	5	13	by	by	ADP
ejpam-5734	5	14	ensuring	ensure	VERB
ejpam-5734	5	15	that	that	SCONJ
ejpam-5734	5	16	no	no	DET
ejpam-5734	5	17	two	two	NUM
ejpam-5734	5	18	vertices	vertex	NOUN
ejpam-5734	5	19	within	within	ADP
ejpam-5734	5	20	distance	distance	NOUN
ejpam-5734	5	21	2	2	NUM
ejpam-5734	5	22	share	share	NOUN
ejpam-5734	5	23	the	the	DET
ejpam-5734	5	24	same	same	ADJ
ejpam-5734	5	25	color	color	NOUN
ejpam-5734	5	26	in	in	ADP
ejpam-5734	5	27	g.	g.	PROPN
ejpam-5734	5	28	this	this	DET
ejpam-5734	5	29	study	study	NOUN
ejpam-5734	5	30	investigates	investigate	VERB
ejpam-5734	5	31	χ2(g	χ2(g	NOUN
ejpam-5734	5	32	)	)	PUNCT
ejpam-5734	5	33	for	for	ADP
ejpam-5734	5	34	the	the	DET
ejpam-5734	5	35	shadow	shadow	NOUN
ejpam-5734	5	36	and	and	CCONJ
ejpam-5734	5	37	central	central	ADJ
ejpam-5734	5	38	graphs	graph	NOUN
ejpam-5734	5	39	of	of	ADP
ejpam-5734	5	40	cycles	cycle	NOUN
ejpam-5734	5	41	.	.	PUNCT
ejpam-5734	6	1	while	while	SCONJ
ejpam-5734	6	2	previous	previous	ADJ
ejpam-5734	6	3	research	research	NOUN
ejpam-5734	6	4	has	have	AUX
ejpam-5734	6	5	focused	focus	VERB
ejpam-5734	6	6	on	on	ADP
ejpam-5734	6	7	certain	certain	ADJ
ejpam-5734	6	8	graphs	graph	NOUN
ejpam-5734	6	9	,	,	PUNCT
ejpam-5734	6	10	we	we	PRON
ejpam-5734	6	11	expand	expand	VERB
ejpam-5734	6	12	the	the	DET
ejpam-5734	6	13	analysis	analysis	NOUN
ejpam-5734	6	14	to	to	ADP
ejpam-5734	6	15	the	the	DET
ejpam-5734	6	16	shadow	shadow	NOUN
ejpam-5734	6	17	and	and	CCONJ
ejpam-5734	6	18	central	central	ADJ
ejpam-5734	6	19	graphs	graph	NOUN
ejpam-5734	6	20	of	of	ADP
ejpam-5734	6	21	cycles	cycle	NOUN
ejpam-5734	6	22	,	,	PUNCT
ejpam-5734	6	23	with	with	ADP
ejpam-5734	6	24	potential	potential	ADJ
ejpam-5734	6	25	applications	application	NOUN
ejpam-5734	6	26	in	in	ADP
ejpam-5734	6	27	computer	computer	NOUN
ejpam-5734	6	28	science	science	NOUN
ejpam-5734	6	29	,	,	PUNCT
ejpam-5734	6	30	particularly	particularly	ADV
ejpam-5734	6	31	in	in	ADP
ejpam-5734	6	32	network	network	NOUN
ejpam-5734	6	33	topology	topology	NOUN
ejpam-5734	6	34	and	and	CCONJ
ejpam-5734	6	35	resource	resource	NOUN
ejpam-5734	6	36	allocation	allocation	NOUN
ejpam-5734	6	37	.	.	PUNCT
ejpam-5734	7	1	2020	2020	NUM
ejpam-5734	7	2	mathematics	mathematic	NOUN
ejpam-5734	7	3	subject	subject	NOUN
ejpam-5734	7	4	classifications	classification	NOUN
ejpam-5734	7	5	:	:	PUNCT
ejpam-5734	7	6	05c15	05c15	NUM
ejpam-5734	7	7	,	,	PUNCT
ejpam-5734	7	8	05c90	05c90	NUM
ejpam-5734	7	9	,	,	PUNCT
ejpam-5734	7	10	68r10	68r10	NUM
ejpam-5734	7	11	key	key	ADJ
ejpam-5734	7	12	words	word	NOUN
ejpam-5734	7	13	and	and	CCONJ
ejpam-5734	7	14	phrases	phrase	NOUN
ejpam-5734	7	15	:	:	PUNCT
ejpam-5734	7	16	distance-2	distance-2	PRON
ejpam-5734	7	17	chromatic	chromatic	ADJ
ejpam-5734	7	18	number	number	NOUN
ejpam-5734	7	19	,	,	PUNCT
ejpam-5734	7	20	graph	graph	NOUN
ejpam-5734	7	21	coloring	coloring	NOUN
ejpam-5734	7	22	,	,	PUNCT
ejpam-5734	7	23	shadow	shadow	NOUN
ejpam-5734	7	24	graphs	graph	NOUN
ejpam-5734	7	25	,	,	PUNCT
ejpam-5734	7	26	central	central	ADJ
ejpam-5734	7	27	graphs	graph	NOUN
ejpam-5734	7	28	,	,	PUNCT
ejpam-5734	7	29	cycle	cycle	NOUN
ejpam-5734	7	30	graphs	graph	NOUN
ejpam-5734	7	31	,	,	PUNCT
ejpam-5734	7	32	graph	graph	NOUN
ejpam-5734	7	33	theory	theory	NOUN
ejpam-5734	7	34	,	,	PUNCT
ejpam-5734	7	35	computer	computer	NOUN
ejpam-5734	7	36	science	science	NOUN
ejpam-5734	7	37	applications	application	NOUN
ejpam-5734	7	38	,	,	PUNCT
ejpam-5734	7	39	network	network	NOUN
ejpam-5734	7	40	topology	topology	NOUN
ejpam-5734	7	41	,	,	PUNCT
ejpam-5734	7	42	resource	resource	NOUN
ejpam-5734	7	43	allocation	allocation	NOUN
ejpam-5734	7	44	1	1	NUM
ejpam-5734	7	45	.	.	PUNCT
ejpam-5734	8	1	introduction	introduction	NOUN
ejpam-5734	8	2	graph	graph	NOUN
ejpam-5734	8	3	coloring	coloring	NOUN
ejpam-5734	8	4	is	be	AUX
ejpam-5734	8	5	a	a	DET
ejpam-5734	8	6	fundamental	fundamental	ADJ
ejpam-5734	8	7	problem	problem	NOUN
ejpam-5734	8	8	in	in	ADP
ejpam-5734	8	9	graph	graph	NOUN
ejpam-5734	8	10	theory	theory	NOUN
ejpam-5734	8	11	,	,	PUNCT
ejpam-5734	8	12	with	with	ADP
ejpam-5734	8	13	deep	deep	ADJ
ejpam-5734	8	14	historical	historical	ADJ
ejpam-5734	8	15	roots	root	NOUN
ejpam-5734	8	16	and	and	CCONJ
ejpam-5734	8	17	numerous	numerous	ADJ
ejpam-5734	8	18	modern	modern	ADJ
ejpam-5734	8	19	applications	application	NOUN
ejpam-5734	8	20	in	in	ADP
ejpam-5734	8	21	scheduling	scheduling	NOUN
ejpam-5734	8	22	,	,	PUNCT
ejpam-5734	8	23	frequency	frequency	NOUN
ejpam-5734	8	24	assignment	assignment	NOUN
ejpam-5734	8	25	,	,	PUNCT
ejpam-5734	8	26	and	and	CCONJ
ejpam-5734	8	27	register	register	VERB
ejpam-5734	8	28	allocation	allocation	NOUN
ejpam-5734	8	29	.	.	PUNCT
ejpam-5734	9	1	the	the	DET
ejpam-5734	9	2	problem	problem	NOUN
ejpam-5734	9	3	was	be	AUX
ejpam-5734	9	4	first	first	ADV
ejpam-5734	9	5	formulated	formulate	VERB
ejpam-5734	9	6	by	by	ADP
ejpam-5734	9	7	the	the	DET
ejpam-5734	9	8	mathematician	mathematician	ADJ
ejpam-5734	9	9	francis	francis	PROPN
ejpam-5734	9	10	guthrie	guthrie	PROPN
ejpam-5734	9	11	in	in	ADP
ejpam-5734	9	12	1852	1852	NUM
ejpam-5734	9	13	,	,	PUNCT
ejpam-5734	9	14	when	when	SCONJ
ejpam-5734	9	15	he	he	PRON
ejpam-5734	9	16	posed	pose	VERB
ejpam-5734	9	17	the	the	DET
ejpam-5734	9	18	challenge	challenge	NOUN
ejpam-5734	9	19	of	of	ADP
ejpam-5734	9	20	coloring	color	VERB
ejpam-5734	9	21	the	the	DET
ejpam-5734	9	22	countries	country	NOUN
ejpam-5734	9	23	on	on	ADP
ejpam-5734	9	24	a	a	DET
ejpam-5734	9	25	map	map	NOUN
ejpam-5734	9	26	of	of	ADP
ejpam-5734	9	27	england	england	NOUN
ejpam-5734	9	28	using	use	VERB
ejpam-5734	9	29	four	four	NUM
ejpam-5734	9	30	or	or	CCONJ
ejpam-5734	9	31	fewer	few	ADJ
ejpam-5734	9	32	colors	color	NOUN
ejpam-5734	9	33	,	,	PUNCT
ejpam-5734	9	34	such	such	ADJ
ejpam-5734	9	35	that	that	SCONJ
ejpam-5734	9	36	no	no	DET
ejpam-5734	9	37	two	two	NUM
ejpam-5734	9	38	adjacent	adjacent	ADJ
ejpam-5734	9	39	regions	region	NOUN
ejpam-5734	9	40	shared	share	VERB
ejpam-5734	9	41	the	the	DET
ejpam-5734	9	42	same	same	ADJ
ejpam-5734	9	43	color	color	NOUN
ejpam-5734	10	1	[	[	X
ejpam-5734	10	2	1	1	NUM
ejpam-5734	10	3	]	]	PUNCT
ejpam-5734	10	4	.	.	PUNCT
ejpam-5734	11	1	guthrie	guthrie	PROPN
ejpam-5734	11	2	’s	’s	PART
ejpam-5734	11	3	brother	brother	PROPN
ejpam-5734	11	4	,	,	PUNCT
ejpam-5734	11	5	frederick	frederick	PROPN
ejpam-5734	11	6	guthrie	guthrie	PROPN
ejpam-5734	11	7	,	,	PUNCT
ejpam-5734	11	8	intrigued	intrigue	VERB
ejpam-5734	11	9	by	by	ADP
ejpam-5734	11	10	the	the	DET
ejpam-5734	11	11	problem	problem	NOUN
ejpam-5734	11	12	,	,	PUNCT
ejpam-5734	11	13	sought	seek	VERB
ejpam-5734	11	14	the	the	DET
ejpam-5734	11	15	help	help	NOUN
ejpam-5734	11	16	of	of	ADP
ejpam-5734	11	17	his	his	PRON
ejpam-5734	11	18	professor	professor	NOUN
ejpam-5734	11	19	,	,	PUNCT
ejpam-5734	11	20	augustus	augustus	PROPN
ejpam-5734	11	21	de	de	PROPN
ejpam-5734	11	22	morgan	morgan	PROPN
ejpam-5734	11	23	,	,	PUNCT
ejpam-5734	11	24	to	to	PART
ejpam-5734	11	25	prove	prove	VERB
ejpam-5734	11	26	the	the	DET
ejpam-5734	11	27	concept	concept	NOUN
ejpam-5734	11	28	.	.	PUNCT
ejpam-5734	12	1	de	de	X
ejpam-5734	12	2	morgan	morgan	PROPN
ejpam-5734	12	3	,	,	PUNCT
ejpam-5734	12	4	captivated	captivate	VERB
ejpam-5734	12	5	by	by	ADP
ejpam-5734	12	6	the	the	DET
ejpam-5734	12	7	challenge	challenge	NOUN
ejpam-5734	12	8	,	,	PUNCT
ejpam-5734	12	9	introduced	introduce	VERB
ejpam-5734	12	10	the	the	DET
ejpam-5734	12	11	concept	concept	NOUN
ejpam-5734	12	12	of	of	ADP
ejpam-5734	12	13	graph	graph	NOUN
ejpam-5734	12	14	coloring	color	VERB
ejpam-5734	12	15	to	to	ADP
ejpam-5734	12	16	the	the	DET
ejpam-5734	12	17	academic	academic	ADJ
ejpam-5734	12	18	community	community	NOUN
ejpam-5734	12	19	,	,	PUNCT
ejpam-5734	12	20	thus	thus	ADV
ejpam-5734	12	21	marking	mark	VERB
ejpam-5734	12	22	the	the	DET
ejpam-5734	12	23	inception	inception	NOUN
ejpam-5734	12	24	of	of	ADP
ejpam-5734	12	25	graph	graph	NOUN
ejpam-5734	12	26	theory	theory	NOUN
ejpam-5734	12	27	as	as	ADP
ejpam-5734	12	28	a	a	DET
ejpam-5734	12	29	formal	formal	ADJ
ejpam-5734	12	30	area	area	NOUN
ejpam-5734	12	31	of	of	ADP
ejpam-5734	12	32	study	study	NOUN
ejpam-5734	12	33	[	[	X
ejpam-5734	12	34	2	2	NUM
ejpam-5734	12	35	]	]	PUNCT
ejpam-5734	12	36	.	.	PUNCT
ejpam-5734	13	1	the	the	DET
ejpam-5734	13	2	classical	classical	ADJ
ejpam-5734	13	3	vertex	vertex	NOUN
ejpam-5734	13	4	coloring	coloring	NOUN
ejpam-5734	13	5	problem	problem	NOUN
ejpam-5734	13	6	[	[	X
ejpam-5734	13	7	3	3	NUM
ejpam-5734	13	8	]	]	PUNCT
ejpam-5734	13	9	,	,	PUNCT
ejpam-5734	13	10	where	where	SCONJ
ejpam-5734	13	11	the	the	DET
ejpam-5734	13	12	goal	goal	NOUN
ejpam-5734	13	13	is	be	AUX
ejpam-5734	13	14	to	to	PART
ejpam-5734	13	15	assign	assign	VERB
ejpam-5734	13	16	colors	color	NOUN
ejpam-5734	13	17	to	to	ADP
ejpam-5734	13	18	the	the	DET
ejpam-5734	13	19	vertices	vertex	NOUN
ejpam-5734	13	20	of	of	ADP
ejpam-5734	13	21	a	a	DET
ejpam-5734	13	22	graph	graph	NOUN
ejpam-5734	13	23	such	such	ADJ
ejpam-5734	13	24	that	that	SCONJ
ejpam-5734	13	25	no	no	DET
ejpam-5734	13	26	two	two	NUM
ejpam-5734	13	27	adjacent	adjacent	ADJ
ejpam-5734	13	28	vertices	vertex	NOUN
ejpam-5734	13	29	share	share	VERB
ejpam-5734	13	30	the	the	DET
ejpam-5734	13	31	same	same	ADJ
ejpam-5734	13	32	color	color	NOUN
ejpam-5734	13	33	,	,	PUNCT
ejpam-5734	13	34	has	have	AUX
ejpam-5734	13	35	since	since	SCONJ
ejpam-5734	13	36	become	become	VERB
ejpam-5734	13	37	a	a	DET
ejpam-5734	13	38	central	central	ADJ
ejpam-5734	13	39	topic	topic	NOUN
ejpam-5734	13	40	of	of	ADP
ejpam-5734	13	41	study	study	NOUN
ejpam-5734	13	42	.	.	PUNCT
ejpam-5734	14	1	the	the	DET
ejpam-5734	14	2	minimum	minimum	ADJ
ejpam-5734	14	3	number	number	NOUN
ejpam-5734	14	4	of	of	ADP
ejpam-5734	14	5	colors	color	NOUN
ejpam-5734	14	6	required	require	VERB
ejpam-5734	14	7	to	to	PART
ejpam-5734	14	8	achieve	achieve	VERB
ejpam-5734	14	9	such	such	ADJ
ejpam-5734	14	10	∗corresponding	∗corresponde	VERB
ejpam-5734	14	11	author	author	NOUN
ejpam-5734	14	12	.	.	PUNCT
ejpam-5734	15	1	doi	doi	NOUN
ejpam-5734	15	2	:	:	PUNCT
ejpam-5734	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5734	https://doi.org/10.29020/nybg.ejpam.v18i2.5734	PROPN
ejpam-5734	15	4	email	email	NOUN
ejpam-5734	15	5	addresses	address	NOUN
ejpam-5734	15	6	:	:	PUNCT
ejpam-5734	15	7	mflibao@carsu.edu.ph	mflibao@carsu.edu.ph	PROPN
ejpam-5734	15	8	(	(	PUNCT
ejpam-5734	15	9	m.	m.	PROPN
ejpam-5734	15	10	f.	f.	PROPN
ejpam-5734	15	11	libao	libao	PROPN
ejpam-5734	15	12	)	)	PUNCT
ejpam-5734	15	13	,	,	PUNCT
ejpam-5734	15	14	kyla.abarca@carsu.edu.ph	kyla.abarca@carsu.edu.ph	PROPN
ejpam-5734	15	15	(	(	PUNCT
ejpam-5734	15	16	k.	k.	PROPN
ejpam-5734	15	17	b.	b.	PROPN
ejpam-5734	15	18	abarca	abarca	PROPN
ejpam-5734	15	19	)	)	PUNCT
ejpam-5734	15	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5734	16	1	1	1	NUM
ejpam-5734	16	2	copyright	copyright	NOUN
ejpam-5734	16	3	:	:	PUNCT
ejpam-5734	16	4	©	©	PROPN
ejpam-5734	16	5	2025	2025	NUM
ejpam-5734	16	6	the	the	DET
ejpam-5734	16	7	author(s	author(s	NOUN
ejpam-5734	16	8	)	)	PUNCT
ejpam-5734	16	9	.	.	PUNCT
ejpam-5734	17	1	(	(	PUNCT
ejpam-5734	17	2	cc	cc	NOUN
ejpam-5734	17	3	by	by	ADP
ejpam-5734	17	4	-	-	PUNCT
ejpam-5734	17	5	nc	nc	PROPN
ejpam-5734	17	6	4.0	4.0	NUM
ejpam-5734	17	7	)	)	PUNCT
ejpam-5734	17	8	m.	m.	NOUN
ejpam-5734	17	9	f.	f.	PROPN
ejpam-5734	17	10	libao	libao	PROPN
ejpam-5734	17	11	,	,	PUNCT
ejpam-5734	17	12	k.	k.	PROPN
ejpam-5734	17	13	b.	b.	PROPN
ejpam-5734	17	14	abarca	abarca	PROPN
ejpam-5734	17	15	/	/	SYM
ejpam-5734	17	16	eur	eur	PROPN
ejpam-5734	17	17	.	.	PUNCT
ejpam-5734	18	1	j.	j.	PROPN
ejpam-5734	18	2	pure	pure	PROPN
ejpam-5734	18	3	appl	appl	PROPN
ejpam-5734	18	4	.	.	PROPN
ejpam-5734	18	5	math	math	PROPN
ejpam-5734	18	6	,	,	PUNCT
ejpam-5734	18	7	18	18	NUM
ejpam-5734	18	8	(	(	PUNCT
ejpam-5734	18	9	2	2	NUM
ejpam-5734	18	10	)	)	PUNCT
ejpam-5734	18	11	(	(	PUNCT
ejpam-5734	18	12	2025	2025	NUM
ejpam-5734	18	13	)	)	PUNCT
ejpam-5734	18	14	,	,	PUNCT
ejpam-5734	18	15	5734	5734	NUM
ejpam-5734	18	16	2	2	NUM
ejpam-5734	18	17	of	of	ADP
ejpam-5734	18	18	25	25	NUM
ejpam-5734	18	19	a	a	DET
ejpam-5734	18	20	coloring	coloring	NOUN
ejpam-5734	18	21	is	be	AUX
ejpam-5734	18	22	known	know	VERB
ejpam-5734	18	23	as	as	ADP
ejpam-5734	18	24	the	the	DET
ejpam-5734	18	25	chromatic	chromatic	ADJ
ejpam-5734	18	26	number	number	NOUN
ejpam-5734	18	27	,	,	PUNCT
ejpam-5734	18	28	denoted	denote	VERB
ejpam-5734	18	29	by	by	ADP
ejpam-5734	18	30	χ(g	χ(g	PROPN
ejpam-5734	18	31	)	)	PUNCT
ejpam-5734	18	32	.	.	PUNCT
ejpam-5734	19	1	one	one	NUM
ejpam-5734	19	2	of	of	ADP
ejpam-5734	19	3	the	the	DET
ejpam-5734	19	4	most	most	ADV
ejpam-5734	19	5	celebrated	celebrate	VERB
ejpam-5734	19	6	results	result	NOUN
ejpam-5734	19	7	in	in	ADP
ejpam-5734	19	8	this	this	DET
ejpam-5734	19	9	area	area	NOUN
ejpam-5734	19	10	is	be	AUX
ejpam-5734	19	11	the	the	DET
ejpam-5734	19	12	four	four	NUM
ejpam-5734	19	13	color	color	NOUN
ejpam-5734	19	14	theorem	theorem	NOUN
ejpam-5734	19	15	,	,	PUNCT
ejpam-5734	19	16	which	which	PRON
ejpam-5734	19	17	asserts	assert	VERB
ejpam-5734	19	18	that	that	SCONJ
ejpam-5734	19	19	any	any	DET
ejpam-5734	19	20	planar	planar	ADJ
ejpam-5734	19	21	graph	graph	NOUN
ejpam-5734	19	22	can	can	AUX
ejpam-5734	19	23	be	be	AUX
ejpam-5734	19	24	colored	color	VERB
ejpam-5734	19	25	with	with	ADP
ejpam-5734	19	26	no	no	DET
ejpam-5734	19	27	more	more	ADJ
ejpam-5734	19	28	than	than	ADP
ejpam-5734	19	29	four	four	NUM
ejpam-5734	19	30	colors	color	NOUN
ejpam-5734	19	31	,	,	PUNCT
ejpam-5734	19	32	a	a	DET
ejpam-5734	19	33	result	result	NOUN
ejpam-5734	19	34	that	that	PRON
ejpam-5734	19	35	was	be	AUX
ejpam-5734	19	36	finally	finally	ADV
ejpam-5734	19	37	proven	prove	VERB
ejpam-5734	19	38	in	in	ADP
ejpam-5734	19	39	1976	1976	NUM
ejpam-5734	19	40	by	by	ADP
ejpam-5734	19	41	appel	appel	PROPN
ejpam-5734	19	42	and	and	CCONJ
ejpam-5734	19	43	haken	haken	PROPN
ejpam-5734	20	1	[	[	X
ejpam-5734	20	2	4	4	NUM
ejpam-5734	20	3	]	]	PUNCT
ejpam-5734	20	4	.	.	PUNCT
ejpam-5734	21	1	the	the	DET
ejpam-5734	21	2	square	square	ADJ
ejpam-5734	21	3	coloring	coloring	NOUN
ejpam-5734	21	4	problem	problem	NOUN
ejpam-5734	21	5	in	in	ADP
ejpam-5734	21	6	graph	graph	NOUN
ejpam-5734	21	7	theory	theory	NOUN
ejpam-5734	21	8	[	[	X
ejpam-5734	21	9	5	5	NUM
ejpam-5734	21	10	]	]	PUNCT
ejpam-5734	21	11	,	,	PUNCT
ejpam-5734	21	12	which	which	PRON
ejpam-5734	21	13	involves	involve	VERB
ejpam-5734	21	14	coloring	coloring	NOUN
ejpam-5734	21	15	vertices	vertex	NOUN
ejpam-5734	21	16	so	so	SCONJ
ejpam-5734	21	17	that	that	SCONJ
ejpam-5734	21	18	no	no	DET
ejpam-5734	21	19	two	two	NUM
ejpam-5734	21	20	vertices	vertex	NOUN
ejpam-5734	21	21	within	within	ADP
ejpam-5734	21	22	a	a	DET
ejpam-5734	21	23	distance	distance	NOUN
ejpam-5734	21	24	of	of	ADP
ejpam-5734	21	25	two	two	NUM
ejpam-5734	21	26	receive	receive	VERB
ejpam-5734	21	27	the	the	DET
ejpam-5734	21	28	same	same	ADJ
ejpam-5734	21	29	color	color	NOUN
ejpam-5734	21	30	,	,	PUNCT
ejpam-5734	21	31	has	have	VERB
ejpam-5734	21	32	its	its	PRON
ejpam-5734	21	33	origins	origin	NOUN
ejpam-5734	21	34	in	in	ADP
ejpam-5734	21	35	general	general	ADJ
ejpam-5734	21	36	graph	graph	NOUN
ejpam-5734	21	37	coloring	coloring	NOUN
ejpam-5734	21	38	and	and	CCONJ
ejpam-5734	21	39	has	have	AUX
ejpam-5734	21	40	been	be	AUX
ejpam-5734	21	41	explored	explore	VERB
ejpam-5734	21	42	extensively	extensively	ADV
ejpam-5734	21	43	over	over	ADP
ejpam-5734	21	44	the	the	DET
ejpam-5734	21	45	years	year	NOUN
ejpam-5734	21	46	.	.	PUNCT
ejpam-5734	22	1	the	the	DET
ejpam-5734	22	2	complexity	complexity	NOUN
ejpam-5734	22	3	of	of	ADP
ejpam-5734	22	4	square	square	ADJ
ejpam-5734	22	5	coloring	coloring	NOUN
ejpam-5734	22	6	varies	vary	VERB
ejpam-5734	22	7	significantly	significantly	ADV
ejpam-5734	22	8	:	:	PUNCT
ejpam-5734	22	9	it	it	PRON
ejpam-5734	22	10	is	be	AUX
ejpam-5734	22	11	polynomial	polynomial	ADJ
ejpam-5734	22	12	-	-	PUNCT
ejpam-5734	22	13	time	time	NOUN
ejpam-5734	22	14	solvable	solvable	NOUN
ejpam-5734	22	15	for	for	ADP
ejpam-5734	22	16	graphs	graph	NOUN
ejpam-5734	22	17	with	with	ADP
ejpam-5734	22	18	bounded	bounded	ADJ
ejpam-5734	22	19	treewidth	treewidth	NOUN
ejpam-5734	22	20	,	,	PUNCT
ejpam-5734	22	21	but	but	CCONJ
ejpam-5734	22	22	np	np	X
ejpam-5734	22	23	-	-	PUNCT
ejpam-5734	22	24	hard	hard	ADJ
ejpam-5734	22	25	for	for	ADP
ejpam-5734	22	26	planar	planar	ADJ
ejpam-5734	22	27	graphs	graph	NOUN
ejpam-5734	22	28	with	with	ADP
ejpam-5734	22	29	four	four	NUM
ejpam-5734	22	30	or	or	CCONJ
ejpam-5734	22	31	more	more	ADJ
ejpam-5734	22	32	colors	color	NOUN
ejpam-5734	22	33	(	(	PUNCT
ejpam-5734	22	34	agrawal	agrawal	PROPN
ejpam-5734	22	35	et	et	PROPN
ejpam-5734	22	36	al	al	PROPN
ejpam-5734	22	37	.	.	PROPN
ejpam-5734	22	38	,	,	PUNCT
ejpam-5734	22	39	2023	2023	NUM
ejpam-5734	22	40	)	)	PUNCT
ejpam-5734	23	1	[	[	X
ejpam-5734	23	2	6	6	NUM
ejpam-5734	23	3	]	]	PUNCT
ejpam-5734	23	4	.	.	PUNCT
ejpam-5734	24	1	interestingly	interestingly	ADV
ejpam-5734	24	2	,	,	PUNCT
ejpam-5734	24	3	planar	planar	ADJ
ejpam-5734	24	4	graphs	graph	NOUN
ejpam-5734	24	5	with	with	ADP
ejpam-5734	24	6	square	square	ADJ
ejpam-5734	24	7	or	or	CCONJ
ejpam-5734	24	8	cube	cube	NOUN
ejpam-5734	24	9	roots	root	NOUN
ejpam-5734	24	10	are	be	AUX
ejpam-5734	24	11	four	four	NUM
ejpam-5734	24	12	-	-	PUNCT
ejpam-5734	24	13	colorable	colorable	ADJ
ejpam-5734	24	14	,	,	PUNCT
ejpam-5734	24	15	as	as	SCONJ
ejpam-5734	24	16	shown	show	VERB
ejpam-5734	24	17	by	by	ADP
ejpam-5734	24	18	ramachandran	ramachandran	PROPN
ejpam-5734	24	19	(	(	PUNCT
ejpam-5734	24	20	1978	1978	NUM
ejpam-5734	24	21	)	)	PUNCT
ejpam-5734	25	1	[	[	X
ejpam-5734	25	2	7	7	NUM
ejpam-5734	25	3	]	]	PUNCT
ejpam-5734	25	4	.	.	PUNCT
ejpam-5734	26	1	the	the	DET
ejpam-5734	26	2	square	square	ADJ
ejpam-5734	26	3	coloring	coloring	NOUN
ejpam-5734	26	4	problem	problem	NOUN
ejpam-5734	26	5	has	have	AUX
ejpam-5734	26	6	also	also	ADV
ejpam-5734	26	7	stimulated	stimulate	VERB
ejpam-5734	26	8	research	research	NOUN
ejpam-5734	26	9	in	in	ADP
ejpam-5734	26	10	various	various	ADJ
ejpam-5734	26	11	areas	area	NOUN
ejpam-5734	26	12	of	of	ADP
ejpam-5734	26	13	graph	graph	NOUN
ejpam-5734	26	14	theory	theory	NOUN
ejpam-5734	26	15	,	,	PUNCT
ejpam-5734	26	16	including	include	VERB
ejpam-5734	26	17	vertex	vertex	NOUN
ejpam-5734	26	18	colorings	coloring	NOUN
ejpam-5734	26	19	,	,	PUNCT
ejpam-5734	26	20	edge	edge	NOUN
ejpam-5734	26	21	colorings	coloring	NOUN
ejpam-5734	26	22	,	,	PUNCT
ejpam-5734	26	23	and	and	CCONJ
ejpam-5734	26	24	distance	distance	NOUN
ejpam-5734	26	25	-	-	PUNCT
ejpam-5734	26	26	related	relate	VERB
ejpam-5734	26	27	colorings	coloring	NOUN
ejpam-5734	26	28	[	[	X
ejpam-5734	26	29	3	3	NUM
ejpam-5734	26	30	]	]	PUNCT
ejpam-5734	26	31	.	.	PUNCT
ejpam-5734	27	1	while	while	SCONJ
ejpam-5734	27	2	the	the	DET
ejpam-5734	27	3	original	original	ADJ
ejpam-5734	27	4	four	four	NUM
ejpam-5734	27	5	-	-	PUNCT
ejpam-5734	27	6	color	color	NOUN
ejpam-5734	27	7	problem	problem	NOUN
ejpam-5734	27	8	was	be	AUX
ejpam-5734	27	9	eventually	eventually	ADV
ejpam-5734	27	10	solved	solve	VERB
ejpam-5734	27	11	using	use	VERB
ejpam-5734	27	12	computer	computer	NOUN
ejpam-5734	27	13	-	-	PUNCT
ejpam-5734	27	14	assisted	assist	VERB
ejpam-5734	27	15	proofs	proof	NOUN
ejpam-5734	27	16	,	,	PUNCT
ejpam-5734	27	17	it	it	PRON
ejpam-5734	27	18	highlighted	highlight	VERB
ejpam-5734	27	19	the	the	DET
ejpam-5734	27	20	increasing	increase	VERB
ejpam-5734	27	21	complexity	complexity	NOUN
ejpam-5734	27	22	of	of	ADP
ejpam-5734	27	23	graph	graph	NOUN
ejpam-5734	27	24	coloring	coloring	NOUN
ejpam-5734	27	25	problems	problem	NOUN
ejpam-5734	27	26	,	,	PUNCT
ejpam-5734	27	27	ranging	range	VERB
ejpam-5734	27	28	from	from	ADP
ejpam-5734	27	29	simpler	simple	ADJ
ejpam-5734	27	30	proofs	proof	NOUN
ejpam-5734	27	31	for	for	ADP
ejpam-5734	27	32	six	six	NUM
ejpam-5734	27	33	colors	color	NOUN
ejpam-5734	27	34	to	to	ADP
ejpam-5734	27	35	highly	highly	ADV
ejpam-5734	27	36	complex	complex	ADJ
ejpam-5734	27	37	ones	one	NOUN
ejpam-5734	27	38	for	for	ADP
ejpam-5734	27	39	four	four	NUM
ejpam-5734	27	40	colors	color	NOUN
ejpam-5734	27	41	[	[	X
ejpam-5734	27	42	8	8	NUM
ejpam-5734	27	43	]	]	PUNCT
ejpam-5734	27	44	.	.	PUNCT
ejpam-5734	28	1	a	a	DET
ejpam-5734	28	2	closely	closely	ADV
ejpam-5734	28	3	related	relate	VERB
ejpam-5734	28	4	concept	concept	NOUN
ejpam-5734	28	5	is	be	AUX
ejpam-5734	28	6	the	the	DET
ejpam-5734	28	7	distance-2	distance-2	NUM
ejpam-5734	28	8	chromatic	chromatic	ADJ
ejpam-5734	28	9	number	number	NOUN
ejpam-5734	28	10	,	,	PUNCT
ejpam-5734	28	11	introduced	introduce	VERB
ejpam-5734	28	12	by	by	ADP
ejpam-5734	28	13	borodin	borodin	NOUN
ejpam-5734	28	14	and	and	CCONJ
ejpam-5734	28	15	ivanova	ivanova	PROPN
ejpam-5734	28	16	in	in	ADP
ejpam-5734	28	17	2009	2009	NUM
ejpam-5734	28	18	[	[	X
ejpam-5734	28	19	9	9	NUM
ejpam-5734	28	20	]	]	PUNCT
ejpam-5734	28	21	.	.	PUNCT
ejpam-5734	29	1	this	this	DET
ejpam-5734	29	2	concept	concept	NOUN
ejpam-5734	29	3	extends	extend	VERB
ejpam-5734	29	4	the	the	DET
ejpam-5734	29	5	idea	idea	NOUN
ejpam-5734	29	6	of	of	ADP
ejpam-5734	29	7	square	square	ADJ
ejpam-5734	29	8	coloring	coloring	NOUN
ejpam-5734	29	9	by	by	ADP
ejpam-5734	29	10	requiring	require	VERB
ejpam-5734	29	11	that	that	SCONJ
ejpam-5734	29	12	vertices	vertex	NOUN
ejpam-5734	29	13	within	within	ADP
ejpam-5734	29	14	a	a	DET
ejpam-5734	29	15	distance	distance	NOUN
ejpam-5734	29	16	of	of	ADP
ejpam-5734	29	17	2	2	NUM
ejpam-5734	29	18	from	from	ADP
ejpam-5734	29	19	each	each	DET
ejpam-5734	29	20	other	other	ADJ
ejpam-5734	29	21	(	(	PUNCT
ejpam-5734	29	22	i.e.	i.e.	X
ejpam-5734	29	23	,	,	PUNCT
ejpam-5734	29	24	vertices	vertice	VERB
ejpam-5734	29	25	that	that	PRON
ejpam-5734	29	26	are	be	AUX
ejpam-5734	29	27	either	either	CCONJ
ejpam-5734	29	28	adjacent	adjacent	ADJ
ejpam-5734	29	29	or	or	CCONJ
ejpam-5734	29	30	share	share	VERB
ejpam-5734	29	31	a	a	DET
ejpam-5734	29	32	common	common	ADJ
ejpam-5734	29	33	neighbor	neighbor	NOUN
ejpam-5734	29	34	)	)	PUNCT
ejpam-5734	29	35	must	must	AUX
ejpam-5734	29	36	receive	receive	VERB
ejpam-5734	29	37	different	different	ADJ
ejpam-5734	29	38	colors	color	NOUN
ejpam-5734	29	39	.	.	PUNCT
ejpam-5734	30	1	the	the	DET
ejpam-5734	30	2	minimum	minimum	ADJ
ejpam-5734	30	3	number	number	NOUN
ejpam-5734	30	4	of	of	ADP
ejpam-5734	30	5	colors	color	NOUN
ejpam-5734	30	6	required	require	VERB
ejpam-5734	30	7	to	to	PART
ejpam-5734	30	8	satisfy	satisfy	VERB
ejpam-5734	30	9	this	this	DET
ejpam-5734	30	10	condition	condition	NOUN
ejpam-5734	30	11	is	be	AUX
ejpam-5734	30	12	denoted	denote	VERB
ejpam-5734	30	13	by	by	ADP
ejpam-5734	30	14	χ2(g	χ2(g	NOUN
ejpam-5734	30	15	)	)	PUNCT
ejpam-5734	30	16	.	.	PUNCT
ejpam-5734	31	1	this	this	DET
ejpam-5734	31	2	form	form	NOUN
ejpam-5734	31	3	of	of	ADP
ejpam-5734	31	4	coloring	coloring	NOUN
ejpam-5734	31	5	is	be	AUX
ejpam-5734	31	6	particularly	particularly	ADV
ejpam-5734	31	7	relevant	relevant	ADJ
ejpam-5734	31	8	in	in	ADP
ejpam-5734	31	9	scenarios	scenario	NOUN
ejpam-5734	31	10	where	where	SCONJ
ejpam-5734	31	11	interference	interference	NOUN
ejpam-5734	31	12	or	or	CCONJ
ejpam-5734	31	13	conflict	conflict	NOUN
ejpam-5734	31	14	extends	extend	VERB
ejpam-5734	31	15	beyond	beyond	ADP
ejpam-5734	31	16	immediate	immediate	ADJ
ejpam-5734	31	17	neighbors	neighbor	NOUN
ejpam-5734	31	18	,	,	PUNCT
ejpam-5734	31	19	such	such	ADJ
ejpam-5734	31	20	as	as	ADP
ejpam-5734	31	21	in	in	ADP
ejpam-5734	31	22	wireless	wireless	ADJ
ejpam-5734	31	23	network	network	NOUN
ejpam-5734	31	24	frequency	frequency	NOUN
ejpam-5734	31	25	assignment	assignment	NOUN
ejpam-5734	31	26	.	.	PUNCT
ejpam-5734	32	1	related	relate	VERB
ejpam-5734	32	2	to	to	ADP
ejpam-5734	32	3	distance-2	distance-2	PRON
ejpam-5734	32	4	coloring	coloring	NOUN
ejpam-5734	32	5	is	be	AUX
ejpam-5734	32	6	the	the	DET
ejpam-5734	32	7	l(2,1)-labeling	l(2,1)-labele	VERB
ejpam-5734	32	8	problem	problem	NOUN
ejpam-5734	32	9	,	,	PUNCT
ejpam-5734	32	10	introduced	introduce	VERB
ejpam-5734	32	11	by	by	ADP
ejpam-5734	32	12	griggs	griggs	PROPN
ejpam-5734	32	13	and	and	CCONJ
ejpam-5734	32	14	yeh	yeh	PROPN
ejpam-5734	32	15	in	in	ADP
ejpam-5734	32	16	1992	1992	NUM
ejpam-5734	33	1	[	[	X
ejpam-5734	33	2	10	10	NUM
ejpam-5734	33	3	]	]	PUNCT
ejpam-5734	33	4	.	.	PUNCT
ejpam-5734	34	1	in	in	ADP
ejpam-5734	34	2	this	this	DET
ejpam-5734	34	3	labeling	labeling	NOUN
ejpam-5734	34	4	scheme	scheme	NOUN
ejpam-5734	34	5	,	,	PUNCT
ejpam-5734	34	6	vertices	vertex	NOUN
ejpam-5734	34	7	are	be	AUX
ejpam-5734	34	8	assigned	assign	VERB
ejpam-5734	34	9	labels	label	NOUN
ejpam-5734	34	10	(	(	PUNCT
ejpam-5734	34	11	which	which	PRON
ejpam-5734	34	12	can	can	AUX
ejpam-5734	34	13	be	be	AUX
ejpam-5734	34	14	thought	think	VERB
ejpam-5734	34	15	of	of	ADP
ejpam-5734	34	16	as	as	ADP
ejpam-5734	34	17	colors	color	NOUN
ejpam-5734	34	18	)	)	PUNCT
ejpam-5734	34	19	such	such	ADJ
ejpam-5734	34	20	that	that	SCONJ
ejpam-5734	34	21	adjacent	adjacent	ADJ
ejpam-5734	34	22	vertices	vertex	NOUN
ejpam-5734	34	23	receive	receive	VERB
ejpam-5734	34	24	labels	label	NOUN
ejpam-5734	34	25	differing	differ	VERB
ejpam-5734	34	26	by	by	ADP
ejpam-5734	34	27	at	at	ADV
ejpam-5734	34	28	least	least	ADV
ejpam-5734	34	29	2	2	NUM
ejpam-5734	34	30	,	,	PUNCT
ejpam-5734	34	31	and	and	CCONJ
ejpam-5734	34	32	vertices	vertice	VERB
ejpam-5734	34	33	at	at	ADP
ejpam-5734	34	34	distance	distance	NOUN
ejpam-5734	34	35	2	2	NUM
ejpam-5734	34	36	receive	receive	VERB
ejpam-5734	34	37	labels	label	NOUN
ejpam-5734	34	38	differing	differ	VERB
ejpam-5734	34	39	by	by	ADP
ejpam-5734	34	40	at	at	ADV
ejpam-5734	34	41	least	least	ADV
ejpam-5734	34	42	1	1	NUM
ejpam-5734	34	43	.	.	PUNCT
ejpam-5734	35	1	this	this	DET
ejpam-5734	35	2	problem	problem	NOUN
ejpam-5734	35	3	is	be	AUX
ejpam-5734	35	4	particularly	particularly	ADV
ejpam-5734	35	5	relevant	relevant	ADJ
ejpam-5734	35	6	in	in	ADP
ejpam-5734	35	7	frequency	frequency	NOUN
ejpam-5734	35	8	assignment	assignment	NOUN
ejpam-5734	35	9	for	for	ADP
ejpam-5734	35	10	wireless	wireless	ADJ
ejpam-5734	35	11	networks	network	NOUN
ejpam-5734	35	12	,	,	PUNCT
ejpam-5734	35	13	where	where	SCONJ
ejpam-5734	35	14	minimizing	minimize	VERB
ejpam-5734	35	15	interference	interference	NOUN
ejpam-5734	35	16	between	between	ADP
ejpam-5734	35	17	channels	channel	NOUN
ejpam-5734	35	18	is	be	AUX
ejpam-5734	35	19	critical	critical	ADJ
ejpam-5734	35	20	.	.	PUNCT
ejpam-5734	36	1	in	in	ADP
ejpam-5734	36	2	addition	addition	NOUN
ejpam-5734	36	3	to	to	ADP
ejpam-5734	36	4	chromatic	chromatic	ADJ
ejpam-5734	36	5	and	and	CCONJ
ejpam-5734	36	6	distance-2	distance-2	PRON
ejpam-5734	36	7	chromatic	chromatic	ADJ
ejpam-5734	36	8	numbers	number	NOUN
ejpam-5734	36	9	,	,	PUNCT
ejpam-5734	36	10	graph	graph	NOUN
ejpam-5734	36	11	theorists	theorist	NOUN
ejpam-5734	36	12	have	have	AUX
ejpam-5734	36	13	also	also	ADV
ejpam-5734	36	14	explored	explore	VERB
ejpam-5734	36	15	the	the	DET
ejpam-5734	36	16	properties	property	NOUN
ejpam-5734	36	17	of	of	ADP
ejpam-5734	36	18	more	more	ADJ
ejpam-5734	36	19	complex	complex	ADJ
ejpam-5734	36	20	graph	graph	NOUN
ejpam-5734	36	21	structures	structure	NOUN
ejpam-5734	36	22	,	,	PUNCT
ejpam-5734	36	23	such	such	ADJ
ejpam-5734	36	24	as	as	ADP
ejpam-5734	36	25	shadow	shadow	NOUN
ejpam-5734	36	26	graphs	graph	NOUN
ejpam-5734	36	27	and	and	CCONJ
ejpam-5734	36	28	central	central	ADJ
ejpam-5734	36	29	graphs	graph	NOUN
ejpam-5734	36	30	.	.	PUNCT
ejpam-5734	37	1	the	the	DET
ejpam-5734	37	2	concept	concept	NOUN
ejpam-5734	37	3	of	of	ADP
ejpam-5734	37	4	shadow	shadow	NOUN
ejpam-5734	37	5	graphs	graph	NOUN
ejpam-5734	37	6	was	be	AUX
ejpam-5734	37	7	introduced	introduce	VERB
ejpam-5734	37	8	by	by	ADP
ejpam-5734	37	9	harary	harary	NOUN
ejpam-5734	37	10	and	and	CCONJ
ejpam-5734	37	11	hedetniemi	hedetniemi	ADV
ejpam-5734	37	12	in	in	ADP
ejpam-5734	37	13	1970	1970	NUM
ejpam-5734	38	1	[	[	X
ejpam-5734	38	2	11	11	NUM
ejpam-5734	38	3	]	]	PUNCT
ejpam-5734	38	4	,	,	PUNCT
ejpam-5734	38	5	where	where	SCONJ
ejpam-5734	38	6	a	a	DET
ejpam-5734	38	7	shadow	shadow	NOUN
ejpam-5734	38	8	graph	graph	NOUN
ejpam-5734	38	9	is	be	AUX
ejpam-5734	38	10	constructed	construct	VERB
ejpam-5734	38	11	by	by	ADP
ejpam-5734	38	12	taking	take	VERB
ejpam-5734	38	13	a	a	DET
ejpam-5734	38	14	copy	copy	NOUN
ejpam-5734	38	15	of	of	ADP
ejpam-5734	38	16	the	the	DET
ejpam-5734	38	17	original	original	ADJ
ejpam-5734	38	18	graph	graph	NOUN
ejpam-5734	38	19	and	and	CCONJ
ejpam-5734	38	20	adding	add	VERB
ejpam-5734	38	21	edges	edge	NOUN
ejpam-5734	38	22	between	between	ADP
ejpam-5734	38	23	corresponding	corresponding	ADJ
ejpam-5734	38	24	vertices	vertex	NOUN
ejpam-5734	38	25	of	of	ADP
ejpam-5734	38	26	the	the	DET
ejpam-5734	38	27	two	two	NUM
ejpam-5734	38	28	copies	copy	NOUN
ejpam-5734	38	29	.	.	PUNCT
ejpam-5734	39	1	central	central	ADJ
ejpam-5734	39	2	graphs	graph	NOUN
ejpam-5734	39	3	,	,	PUNCT
ejpam-5734	39	4	first	first	ADV
ejpam-5734	39	5	studied	study	VERB
ejpam-5734	39	6	by	by	ADP
ejpam-5734	39	7	sampathkumar	sampathkumar	PROPN
ejpam-5734	39	8	and	and	CCONJ
ejpam-5734	39	9	walikar	walikar	NOUN
ejpam-5734	39	10	in	in	ADP
ejpam-5734	39	11	1974	1974	NUM
ejpam-5734	39	12	[	[	X
ejpam-5734	39	13	12	12	NUM
ejpam-5734	39	14	]	]	PUNCT
ejpam-5734	39	15	,	,	PUNCT
ejpam-5734	39	16	are	be	AUX
ejpam-5734	39	17	created	create	VERB
ejpam-5734	39	18	by	by	ADP
ejpam-5734	39	19	adding	add	VERB
ejpam-5734	39	20	new	new	ADJ
ejpam-5734	39	21	vertices	vertex	NOUN
ejpam-5734	39	22	corresponding	correspond	VERB
ejpam-5734	39	23	to	to	ADP
ejpam-5734	39	24	each	each	DET
ejpam-5734	39	25	edge	edge	NOUN
ejpam-5734	39	26	of	of	ADP
ejpam-5734	39	27	the	the	DET
ejpam-5734	39	28	original	original	ADJ
ejpam-5734	39	29	graph	graph	NOUN
ejpam-5734	39	30	,	,	PUNCT
ejpam-5734	39	31	with	with	ADP
ejpam-5734	39	32	each	each	DET
ejpam-5734	39	33	new	new	ADJ
ejpam-5734	39	34	vertex	vertex	NOUN
ejpam-5734	39	35	adjacent	adjacent	ADJ
ejpam-5734	39	36	to	to	ADP
ejpam-5734	39	37	the	the	DET
ejpam-5734	39	38	endpoints	endpoint	NOUN
ejpam-5734	39	39	of	of	ADP
ejpam-5734	39	40	its	its	PRON
ejpam-5734	39	41	corresponding	corresponding	ADJ
ejpam-5734	39	42	edge	edge	NOUN
ejpam-5734	39	43	.	.	PUNCT
ejpam-5734	40	1	this	this	DET
ejpam-5734	40	2	study	study	NOUN
ejpam-5734	40	3	builds	build	VERB
ejpam-5734	40	4	on	on	ADP
ejpam-5734	40	5	these	these	DET
ejpam-5734	40	6	established	establish	VERB
ejpam-5734	40	7	concepts	concept	NOUN
ejpam-5734	40	8	by	by	ADP
ejpam-5734	40	9	examining	examine	VERB
ejpam-5734	40	10	the	the	DET
ejpam-5734	40	11	distance-2	distance-2	CCONJ
ejpam-5734	40	12	chromatic	chromatic	ADJ
ejpam-5734	40	13	number	number	NOUN
ejpam-5734	40	14	in	in	ADP
ejpam-5734	40	15	the	the	DET
ejpam-5734	40	16	context	context	NOUN
ejpam-5734	40	17	of	of	ADP
ejpam-5734	40	18	specific	specific	ADJ
ejpam-5734	40	19	graph	graph	NOUN
ejpam-5734	40	20	families	family	NOUN
ejpam-5734	40	21	.	.	PUNCT
ejpam-5734	41	1	while	while	SCONJ
ejpam-5734	41	2	previous	previous	ADJ
ejpam-5734	41	3	research	research	NOUN
ejpam-5734	41	4	has	have	AUX
ejpam-5734	41	5	extensively	extensively	ADV
ejpam-5734	41	6	explored	explore	VERB
ejpam-5734	41	7	the	the	DET
ejpam-5734	41	8	distance-2	distance-2	NUM
ejpam-5734	41	9	chromatic	chromatic	ADJ
ejpam-5734	41	10	number	number	NOUN
ejpam-5734	41	11	for	for	ADP
ejpam-5734	41	12	various	various	ADJ
ejpam-5734	41	13	graph	graph	NOUN
ejpam-5734	41	14	types	type	NOUN
ejpam-5734	41	15	,	,	PUNCT
ejpam-5734	41	16	this	this	DET
ejpam-5734	41	17	paper	paper	NOUN
ejpam-5734	41	18	extends	extend	VERB
ejpam-5734	41	19	the	the	DET
ejpam-5734	41	20	analysis	analysis	NOUN
ejpam-5734	41	21	of	of	ADP
ejpam-5734	41	22	cycle	cycle	NOUN
ejpam-5734	41	23	graphs	graph	NOUN
ejpam-5734	41	24	by	by	ADP
ejpam-5734	41	25	investigating	investigate	VERB
ejpam-5734	41	26	the	the	DET
ejpam-5734	41	27	shadow	shadow	NOUN
ejpam-5734	41	28	and	and	CCONJ
ejpam-5734	41	29	central	central	ADJ
ejpam-5734	41	30	graphs	graph	NOUN
ejpam-5734	41	31	of	of	ADP
ejpam-5734	41	32	cycles	cycle	NOUN
ejpam-5734	41	33	,	,	PUNCT
ejpam-5734	41	34	providing	provide	VERB
ejpam-5734	41	35	a	a	DET
ejpam-5734	41	36	more	more	ADV
ejpam-5734	41	37	comprehensive	comprehensive	ADJ
ejpam-5734	41	38	understanding	understanding	NOUN
ejpam-5734	41	39	of	of	ADP
ejpam-5734	41	40	these	these	DET
ejpam-5734	41	41	structures	structure	NOUN
ejpam-5734	41	42	under	under	ADP
ejpam-5734	41	43	the	the	DET
ejpam-5734	41	44	distance-2	distance-2	NUM
ejpam-5734	41	45	coloring	coloring	NOUN
ejpam-5734	41	46	framework	framework	NOUN
ejpam-5734	41	47	.	.	PUNCT
ejpam-5734	42	1	m.	m.	NOUN
ejpam-5734	42	2	f.	f.	PROPN
ejpam-5734	42	3	libao	libao	PROPN
ejpam-5734	42	4	,	,	PUNCT
ejpam-5734	42	5	k.	k.	PROPN
ejpam-5734	42	6	b.	b.	PROPN
ejpam-5734	42	7	abarca	abarca	PROPN
ejpam-5734	42	8	/	/	SYM
ejpam-5734	42	9	eur	eur	PROPN
ejpam-5734	42	10	.	.	PUNCT
ejpam-5734	43	1	j.	j.	PROPN
ejpam-5734	43	2	pure	pure	PROPN
ejpam-5734	43	3	appl	appl	PROPN
ejpam-5734	43	4	.	.	PROPN
ejpam-5734	43	5	math	math	PROPN
ejpam-5734	43	6	,	,	PUNCT
ejpam-5734	43	7	18	18	NUM
ejpam-5734	43	8	(	(	PUNCT
ejpam-5734	43	9	2	2	NUM
ejpam-5734	43	10	)	)	PUNCT
ejpam-5734	43	11	(	(	PUNCT
ejpam-5734	43	12	2025	2025	NUM
ejpam-5734	43	13	)	)	PUNCT
ejpam-5734	43	14	,	,	PUNCT
ejpam-5734	43	15	5734	5734	NUM
ejpam-5734	43	16	3	3	NUM
ejpam-5734	43	17	of	of	ADP
ejpam-5734	43	18	25	25	NUM
ejpam-5734	43	19	moreover	moreover	ADV
ejpam-5734	43	20	,	,	PUNCT
ejpam-5734	43	21	graph	graph	NOUN
ejpam-5734	43	22	coloring	coloring	NOUN
ejpam-5734	43	23	has	have	AUX
ejpam-5734	43	24	found	find	VERB
ejpam-5734	43	25	extensive	extensive	ADJ
ejpam-5734	43	26	applications	application	NOUN
ejpam-5734	43	27	in	in	ADP
ejpam-5734	43	28	various	various	ADJ
ejpam-5734	43	29	fields	field	NOUN
ejpam-5734	43	30	of	of	ADP
ejpam-5734	43	31	computer	computer	NOUN
ejpam-5734	43	32	science	science	NOUN
ejpam-5734	43	33	,	,	PUNCT
ejpam-5734	43	34	from	from	ADP
ejpam-5734	43	35	scheduling	schedule	VERB
ejpam-5734	43	36	to	to	ADP
ejpam-5734	43	37	network	network	NOUN
ejpam-5734	43	38	optimization	optimization	NOUN
ejpam-5734	43	39	,	,	PUNCT
ejpam-5734	43	40	as	as	SCONJ
ejpam-5734	43	41	highlighted	highlight	VERB
ejpam-5734	43	42	by	by	ADP
ejpam-5734	43	43	shamim	shamim	PROPN
ejpam-5734	43	44	ahmed	ahme	VERB
ejpam-5734	43	45	in	in	ADP
ejpam-5734	43	46	2012	2012	NUM
ejpam-5734	43	47	in	in	ADP
ejpam-5734	43	48	applications	application	NOUN
ejpam-5734	43	49	of	of	ADP
ejpam-5734	43	50	graph	graph	NOUN
ejpam-5734	43	51	coloring	coloring	NOUN
ejpam-5734	43	52	in	in	ADP
ejpam-5734	43	53	modern	modern	ADJ
ejpam-5734	43	54	computer	computer	NOUN
ejpam-5734	43	55	science	science	NOUN
ejpam-5734	43	56	.	.	PUNCT
ejpam-5734	44	1	ahmed	ahmed	PROPN
ejpam-5734	44	2	[	[	PUNCT
ejpam-5734	44	3	13	13	NUM
ejpam-5734	44	4	]	]	PUNCT
ejpam-5734	44	5	explores	explore	VERB
ejpam-5734	44	6	how	how	SCONJ
ejpam-5734	44	7	traditional	traditional	ADJ
ejpam-5734	44	8	graph	graph	NOUN
ejpam-5734	44	9	coloring	coloring	NOUN
ejpam-5734	44	10	techniques	technique	NOUN
ejpam-5734	44	11	are	be	AUX
ejpam-5734	44	12	used	use	VERB
ejpam-5734	44	13	to	to	PART
ejpam-5734	44	14	solve	solve	VERB
ejpam-5734	44	15	complex	complex	ADJ
ejpam-5734	44	16	problems	problem	NOUN
ejpam-5734	44	17	in	in	ADP
ejpam-5734	44	18	areas	area	NOUN
ejpam-5734	44	19	like	like	ADP
ejpam-5734	44	20	resource	resource	NOUN
ejpam-5734	44	21	allocation	allocation	NOUN
ejpam-5734	44	22	and	and	CCONJ
ejpam-5734	44	23	efficient	efficient	ADJ
ejpam-5734	44	24	communication	communication	NOUN
ejpam-5734	44	25	in	in	ADP
ejpam-5734	44	26	networks	network	NOUN
ejpam-5734	44	27	.	.	PUNCT
ejpam-5734	45	1	recent	recent	ADJ
ejpam-5734	45	2	studies	study	NOUN
ejpam-5734	45	3	further	far	ADV
ejpam-5734	45	4	extend	extend	VERB
ejpam-5734	45	5	these	these	DET
ejpam-5734	45	6	applications	application	NOUN
ejpam-5734	45	7	.	.	PUNCT
ejpam-5734	46	1	jain	jain	PROPN
ejpam-5734	46	2	and	and	CCONJ
ejpam-5734	46	3	jain	jain	PROPN
ejpam-5734	46	4	[	[	X
ejpam-5734	46	5	14	14	NUM
ejpam-5734	46	6	]	]	PUNCT
ejpam-5734	46	7	highlight	highlight	VERB
ejpam-5734	46	8	the	the	DET
ejpam-5734	46	9	role	role	NOUN
ejpam-5734	46	10	of	of	ADP
ejpam-5734	46	11	graph	graph	NOUN
ejpam-5734	46	12	theory	theory	NOUN
ejpam-5734	46	13	in	in	ADP
ejpam-5734	46	14	areas	area	NOUN
ejpam-5734	46	15	such	such	ADJ
ejpam-5734	46	16	as	as	ADP
ejpam-5734	46	17	network	network	NOUN
ejpam-5734	46	18	optimization	optimization	NOUN
ejpam-5734	46	19	,	,	PUNCT
ejpam-5734	46	20	spanning	span	VERB
ejpam-5734	46	21	trees	tree	NOUN
ejpam-5734	46	22	,	,	PUNCT
ejpam-5734	46	23	and	and	CCONJ
ejpam-5734	46	24	vlsi	vlsi	PROPN
ejpam-5734	46	25	design	design	NOUN
ejpam-5734	46	26	,	,	PUNCT
ejpam-5734	46	27	demonstrating	demonstrate	VERB
ejpam-5734	46	28	its	its	PRON
ejpam-5734	46	29	ability	ability	NOUN
ejpam-5734	46	30	to	to	PART
ejpam-5734	46	31	tackle	tackle	VERB
ejpam-5734	46	32	challenges	challenge	NOUN
ejpam-5734	46	33	like	like	ADP
ejpam-5734	46	34	the	the	DET
ejpam-5734	46	35	traveling	travel	VERB
ejpam-5734	46	36	salesman	salesman	ADJ
ejpam-5734	46	37	problem	problem	NOUN
ejpam-5734	46	38	.	.	PUNCT
ejpam-5734	47	1	similarly	similarly	ADV
ejpam-5734	47	2	,	,	PUNCT
ejpam-5734	47	3	majeed	majeed	PROPN
ejpam-5734	47	4	and	and	CCONJ
ejpam-5734	47	5	rauf	rauf	PROPN
ejpam-5734	48	1	[	[	X
ejpam-5734	48	2	5	5	NUM
ejpam-5734	48	3	]	]	PUNCT
ejpam-5734	48	4	emphasize	emphasize	VERB
ejpam-5734	48	5	its	its	PRON
ejpam-5734	48	6	relevance	relevance	NOUN
ejpam-5734	48	7	in	in	ADP
ejpam-5734	48	8	social	social	ADJ
ejpam-5734	48	9	networks	network	NOUN
ejpam-5734	48	10	and	and	CCONJ
ejpam-5734	48	11	cryptography	cryptography	NOUN
ejpam-5734	48	12	,	,	PUNCT
ejpam-5734	48	13	where	where	SCONJ
ejpam-5734	48	14	graph	graph	NOUN
ejpam-5734	48	15	-	-	PUNCT
ejpam-5734	48	16	based	base	VERB
ejpam-5734	48	17	models	model	NOUN
ejpam-5734	48	18	ensure	ensure	VERB
ejpam-5734	48	19	secure	secure	ADJ
ejpam-5734	48	20	communication	communication	NOUN
ejpam-5734	48	21	and	and	CCONJ
ejpam-5734	48	22	effective	effective	ADJ
ejpam-5734	48	23	data	datum	NOUN
ejpam-5734	48	24	organization	organization	NOUN
ejpam-5734	48	25	.	.	PUNCT
ejpam-5734	49	1	however	however	ADV
ejpam-5734	49	2	,	,	PUNCT
ejpam-5734	49	3	while	while	SCONJ
ejpam-5734	49	4	graph	graph	NOUN
ejpam-5734	49	5	theory	theory	NOUN
ejpam-5734	49	6	has	have	AUX
ejpam-5734	49	7	been	be	AUX
ejpam-5734	49	8	widely	widely	ADV
ejpam-5734	49	9	applied	apply	VERB
ejpam-5734	49	10	in	in	ADP
ejpam-5734	49	11	network	network	NOUN
ejpam-5734	49	12	topology	topology	NOUN
ejpam-5734	49	13	and	and	CCONJ
ejpam-5734	49	14	optimization	optimization	NOUN
ejpam-5734	49	15	[	[	X
ejpam-5734	49	16	5	5	NUM
ejpam-5734	49	17	,	,	PUNCT
ejpam-5734	49	18	14	14	NUM
ejpam-5734	49	19	]	]	PUNCT
ejpam-5734	49	20	,	,	PUNCT
ejpam-5734	49	21	the	the	DET
ejpam-5734	49	22	existing	exist	VERB
ejpam-5734	49	23	literature	literature	NOUN
ejpam-5734	49	24	does	do	AUX
ejpam-5734	49	25	not	not	PART
ejpam-5734	49	26	explicitly	explicitly	ADV
ejpam-5734	49	27	introduce	introduce	VERB
ejpam-5734	49	28	twin	twin	ADJ
ejpam-5734	49	29	building	building	NOUN
ejpam-5734	49	30	and	and	CCONJ
ejpam-5734	49	31	office	office	NOUN
ejpam-5734	49	32	building	building	NOUN
ejpam-5734	49	33	analogies	analogy	NOUN
ejpam-5734	49	34	.	.	PUNCT
ejpam-5734	50	1	similar	similar	ADJ
ejpam-5734	50	2	approaches	approach	NOUN
ejpam-5734	50	3	using	use	VERB
ejpam-5734	50	4	physical	physical	ADJ
ejpam-5734	50	5	structures	structure	NOUN
ejpam-5734	50	6	to	to	ADP
ejpam-5734	50	7	model	model	NOUN
ejpam-5734	50	8	graph	graph	NOUN
ejpam-5734	50	9	behaviors	behavior	NOUN
ejpam-5734	50	10	have	have	AUX
ejpam-5734	50	11	been	be	AUX
ejpam-5734	50	12	explored	explore	VERB
ejpam-5734	50	13	in	in	ADP
ejpam-5734	50	14	network	network	NOUN
ejpam-5734	50	15	modeling	modeling	NOUN
ejpam-5734	50	16	[	[	X
ejpam-5734	50	17	2	2	NUM
ejpam-5734	50	18	]	]	PUNCT
ejpam-5734	50	19	.	.	PUNCT
ejpam-5734	51	1	this	this	DET
ejpam-5734	51	2	study	study	NOUN
ejpam-5734	51	3	extends	extend	VERB
ejpam-5734	51	4	these	these	DET
ejpam-5734	51	5	concepts	concept	NOUN
ejpam-5734	51	6	by	by	ADP
ejpam-5734	51	7	introducing	introduce	VERB
ejpam-5734	51	8	new	new	ADJ
ejpam-5734	51	9	analogies	analogy	NOUN
ejpam-5734	51	10	that	that	PRON
ejpam-5734	51	11	align	align	VERB
ejpam-5734	51	12	with	with	ADP
ejpam-5734	51	13	established	establish	VERB
ejpam-5734	51	14	applications	application	NOUN
ejpam-5734	51	15	of	of	ADP
ejpam-5734	51	16	the	the	DET
ejpam-5734	51	17	distance-2	distance-2	NUM
ejpam-5734	51	18	chromatic	chromatic	ADJ
ejpam-5734	51	19	number	number	NOUN
ejpam-5734	51	20	in	in	ADP
ejpam-5734	51	21	network	network	NOUN
ejpam-5734	51	22	communication	communication	NOUN
ejpam-5734	51	23	and	and	CCONJ
ejpam-5734	51	24	resource	resource	NOUN
ejpam-5734	51	25	allocation	allocation	NOUN
ejpam-5734	51	26	.	.	PUNCT
ejpam-5734	52	1	2	2	X
ejpam-5734	52	2	.	.	X
ejpam-5734	52	3	preliminaries	preliminary	NOUN
ejpam-5734	52	4	in	in	ADP
ejpam-5734	52	5	this	this	DET
ejpam-5734	52	6	section	section	NOUN
ejpam-5734	52	7	,	,	PUNCT
ejpam-5734	52	8	the	the	DET
ejpam-5734	52	9	definitions	definition	NOUN
ejpam-5734	52	10	[	[	X
ejpam-5734	52	11	2	2	NUM
ejpam-5734	52	12	]	]	PUNCT
ejpam-5734	52	13	and	and	CCONJ
ejpam-5734	52	14	results	result	NOUN
ejpam-5734	52	15	necessary	necessary	ADJ
ejpam-5734	52	16	for	for	SCONJ
ejpam-5734	52	17	this	this	DET
ejpam-5734	52	18	study	study	NOUN
ejpam-5734	52	19	are	be	AUX
ejpam-5734	52	20	discussed	discuss	VERB
ejpam-5734	52	21	.	.	PUNCT
ejpam-5734	53	1	definition	definition	NOUN
ejpam-5734	53	2	2.1	2.1	NUM
ejpam-5734	53	3	(	(	PUNCT
ejpam-5734	53	4	graph	graph	NOUN
ejpam-5734	53	5	)	)	PUNCT
ejpam-5734	53	6	.	.	PUNCT
ejpam-5734	54	1	a	a	DET
ejpam-5734	54	2	graph	graph	NOUN
ejpam-5734	54	3	g	g	PROPN
ejpam-5734	54	4	=	=	PUNCT
ejpam-5734	54	5	(	(	PUNCT
ejpam-5734	54	6	v	v	NOUN
ejpam-5734	54	7	(	(	PUNCT
ejpam-5734	54	8	g	g	NOUN
ejpam-5734	54	9	)	)	PUNCT
ejpam-5734	54	10	,	,	PUNCT
ejpam-5734	54	11	e(g	e(g	PROPN
ejpam-5734	54	12	)	)	PUNCT
ejpam-5734	54	13	)	)	PUNCT
ejpam-5734	54	14	is	be	AUX
ejpam-5734	54	15	an	an	DET
ejpam-5734	54	16	ordered	ordered	ADJ
ejpam-5734	54	17	pair	pair	NOUN
ejpam-5734	54	18	,	,	PUNCT
ejpam-5734	54	19	where	where	SCONJ
ejpam-5734	54	20	v	v	X
ejpam-5734	54	21	(	(	PUNCT
ejpam-5734	54	22	g	g	NOUN
ejpam-5734	54	23	)	)	PUNCT
ejpam-5734	54	24	is	be	AUX
ejpam-5734	54	25	a	a	DET
ejpam-5734	54	26	finite	finite	NOUN
ejpam-5734	54	27	nonempty	nonempty	ADV
ejpam-5734	54	28	set	set	VERB
ejpam-5734	54	29	known	know	VERB
ejpam-5734	54	30	as	as	ADP
ejpam-5734	54	31	the	the	DET
ejpam-5734	54	32	vertex	vertex	NOUN
ejpam-5734	54	33	set	set	NOUN
ejpam-5734	54	34	of	of	ADP
ejpam-5734	54	35	g.	g.	PROPN
ejpam-5734	54	36	the	the	DET
ejpam-5734	54	37	elements	element	NOUN
ejpam-5734	54	38	of	of	ADP
ejpam-5734	54	39	v	v	NOUN
ejpam-5734	54	40	(	(	PUNCT
ejpam-5734	54	41	g	g	NOUN
ejpam-5734	54	42	)	)	PUNCT
ejpam-5734	54	43	are	be	AUX
ejpam-5734	54	44	referred	refer	VERB
ejpam-5734	54	45	to	to	ADP
ejpam-5734	54	46	as	as	ADP
ejpam-5734	54	47	vertices	vertex	NOUN
ejpam-5734	54	48	,	,	PUNCT
ejpam-5734	54	49	and	and	CCONJ
ejpam-5734	54	50	the	the	DET
ejpam-5734	54	51	cardinality	cardinality	NOUN
ejpam-5734	54	52	of	of	ADP
ejpam-5734	54	53	g	g	NOUN
ejpam-5734	54	54	,	,	PUNCT
ejpam-5734	54	55	denoted	denote	VERB
ejpam-5734	54	56	as	as	ADP
ejpam-5734	54	57	|v	|v	PROPN
ejpam-5734	54	58	(	(	PUNCT
ejpam-5734	54	59	g)|	g)|	PROPN
ejpam-5734	54	60	,	,	PUNCT
ejpam-5734	54	61	represents	represent	VERB
ejpam-5734	54	62	the	the	DET
ejpam-5734	54	63	order	order	NOUN
ejpam-5734	54	64	of	of	ADP
ejpam-5734	54	65	g.	g.	PROPN
ejpam-5734	54	66	similarly	similarly	ADV
ejpam-5734	54	67	,	,	PUNCT
ejpam-5734	54	68	the	the	DET
ejpam-5734	54	69	set	set	PROPN
ejpam-5734	54	70	e(g	e(g	PROPN
ejpam-5734	54	71	)	)	PUNCT
ejpam-5734	54	72	is	be	AUX
ejpam-5734	54	73	called	call	VERB
ejpam-5734	54	74	the	the	DET
ejpam-5734	54	75	edge	edge	NOUN
ejpam-5734	54	76	set	set	NOUN
ejpam-5734	54	77	of	of	ADP
ejpam-5734	54	78	g	g	NOUN
ejpam-5734	54	79	,	,	PUNCT
ejpam-5734	54	80	with	with	ADP
ejpam-5734	54	81	elements	element	NOUN
ejpam-5734	54	82	called	call	VERB
ejpam-5734	54	83	edges	edge	NOUN
ejpam-5734	54	84	,	,	PUNCT
ejpam-5734	54	85	and	and	CCONJ
ejpam-5734	54	86	the	the	DET
ejpam-5734	54	87	cardinality	cardinality	NOUN
ejpam-5734	54	88	of	of	ADP
ejpam-5734	54	89	e(g	e(g	PROPN
ejpam-5734	54	90	)	)	PUNCT
ejpam-5734	54	91	,	,	PUNCT
ejpam-5734	54	92	denoted	denote	VERB
ejpam-5734	54	93	as	as	ADP
ejpam-5734	54	94	|e(g)|	|e(g)|	NOUN
ejpam-5734	54	95	,	,	PUNCT
ejpam-5734	54	96	represents	represent	VERB
ejpam-5734	54	97	the	the	DET
ejpam-5734	54	98	size	size	NOUN
ejpam-5734	54	99	of	of	ADP
ejpam-5734	54	100	g.	g.	PROPN
ejpam-5734	54	101	g	g	PROPN
ejpam-5734	55	1	:	:	PUNCT
ejpam-5734	55	2	p	p	X
ejpam-5734	55	3	q	q	X
ejpam-5734	55	4	r	r	NOUN
ejpam-5734	55	5	st	st	PROPN
ejpam-5734	55	6	figure	figure	NOUN
ejpam-5734	55	7	1	1	NUM
ejpam-5734	55	8	:	:	PUNCT
ejpam-5734	55	9	a	a	DET
ejpam-5734	55	10	graph	graph	NOUN
ejpam-5734	55	11	g	g	NOUN
ejpam-5734	55	12	of	of	ADP
ejpam-5734	55	13	order	order	NOUN
ejpam-5734	55	14	5	5	NUM
ejpam-5734	55	15	and	and	CCONJ
ejpam-5734	55	16	size	size	NOUN
ejpam-5734	55	17	8	8	NUM
ejpam-5734	55	18	example	example	NOUN
ejpam-5734	55	19	1	1	NUM
ejpam-5734	55	20	.	.	PUNCT
ejpam-5734	55	21	figure	figure	NOUN
ejpam-5734	55	22	1	1	NUM
ejpam-5734	55	23	is	be	AUX
ejpam-5734	55	24	an	an	DET
ejpam-5734	55	25	example	example	NOUN
ejpam-5734	55	26	of	of	ADP
ejpam-5734	55	27	a	a	DET
ejpam-5734	55	28	graph	graph	NOUN
ejpam-5734	55	29	with	with	ADP
ejpam-5734	55	30	the	the	DET
ejpam-5734	55	31	set	set	NOUN
ejpam-5734	55	32	of	of	ADP
ejpam-5734	55	33	vertices	vertex	NOUN
ejpam-5734	55	34	v	v	X
ejpam-5734	55	35	(	(	PUNCT
ejpam-5734	55	36	g	g	NOUN
ejpam-5734	55	37	)	)	PUNCT
ejpam-5734	55	38	=	=	PUNCT
ejpam-5734	56	1	{	{	PUNCT
ejpam-5734	56	2	p	p	X
ejpam-5734	56	3	,	,	PUNCT
ejpam-5734	56	4	q	q	ADJ
ejpam-5734	56	5	,	,	PUNCT
ejpam-5734	56	6	r	r	NOUN
ejpam-5734	56	7	,	,	PUNCT
ejpam-5734	56	8	s	s	PROPN
ejpam-5734	56	9	,	,	PUNCT
ejpam-5734	56	10	t	t	PROPN
ejpam-5734	56	11	}	}	PUNCT
ejpam-5734	56	12	and	and	CCONJ
ejpam-5734	56	13	set	set	VERB
ejpam-5734	56	14	of	of	ADP
ejpam-5734	56	15	edges	edge	NOUN
ejpam-5734	56	16	e(g	e(g	PROPN
ejpam-5734	56	17	)	)	PUNCT
ejpam-5734	57	1	=	=	PRON
ejpam-5734	57	2	{	{	PUNCT
ejpam-5734	57	3	pq	pq	INTJ
ejpam-5734	57	4	,	,	PUNCT
ejpam-5734	57	5	qr	qr	NOUN
ejpam-5734	57	6	,	,	PUNCT
ejpam-5734	57	7	rs	rs	ADJ
ejpam-5734	57	8	,	,	PUNCT
ejpam-5734	57	9	qs	qs	PROPN
ejpam-5734	57	10	,	,	PUNCT
ejpam-5734	57	11	st	st	PROPN
ejpam-5734	57	12	,	,	PUNCT
ejpam-5734	57	13	pt	pt	PROPN
ejpam-5734	57	14	,	,	PUNCT
ejpam-5734	57	15	ps	ps	NOUN
ejpam-5734	57	16	}	}	PUNCT
ejpam-5734	57	17	.	.	PUNCT
ejpam-5734	58	1	moreover	moreover	ADV
ejpam-5734	58	2	,	,	PUNCT
ejpam-5734	58	3	g	g	PROPN
ejpam-5734	58	4	is	be	AUX
ejpam-5734	58	5	a	a	DET
ejpam-5734	58	6	graph	graph	NOUN
ejpam-5734	58	7	of	of	ADP
ejpam-5734	58	8	order	order	NOUN
ejpam-5734	58	9	5	5	NUM
ejpam-5734	58	10	and	and	CCONJ
ejpam-5734	58	11	size	size	NOUN
ejpam-5734	58	12	8	8	NUM
ejpam-5734	58	13	.	.	PUNCT
ejpam-5734	59	1	definition	definition	NOUN
ejpam-5734	59	2	2.2	2.2	NUM
ejpam-5734	59	3	(	(	PUNCT
ejpam-5734	59	4	cycle	cycle	NOUN
ejpam-5734	59	5	)	)	PUNCT
ejpam-5734	59	6	.	.	PUNCT
ejpam-5734	60	1	the	the	DET
ejpam-5734	60	2	cycle	cycle	NOUN
ejpam-5734	60	3	cn	cn	PROPN
ejpam-5734	60	4	is	be	AUX
ejpam-5734	60	5	the	the	DET
ejpam-5734	60	6	graph	graph	NOUN
ejpam-5734	60	7	of	of	ADP
ejpam-5734	60	8	order	order	NOUN
ejpam-5734	60	9	n	n	PRON
ejpam-5734	60	10	≥	≥	NOUN
ejpam-5734	60	11	3	3	NUM
ejpam-5734	60	12	containing	contain	VERB
ejpam-5734	60	13	the	the	DET
ejpam-5734	60	14	vertex	vertex	NOUN
ejpam-5734	60	15	set	set	NOUN
ejpam-5734	60	16	{	{	PUNCT
ejpam-5734	60	17	vi	vi	NOUN
ejpam-5734	60	18	|	|	ADV
ejpam-5734	60	19	1	1	NUM
ejpam-5734	60	20	≤	≤	NUM
ejpam-5734	60	21	i	i	PRON
ejpam-5734	60	22	≤	≤	NOUN
ejpam-5734	60	23	n	n	CCONJ
ejpam-5734	60	24	}	}	PUNCT
ejpam-5734	60	25	.	.	PUNCT
ejpam-5734	61	1	the	the	DET
ejpam-5734	61	2	edges	edge	NOUN
ejpam-5734	61	3	include	include	VERB
ejpam-5734	61	4	{	{	PUNCT
ejpam-5734	61	5	vivi+1	vivi+1	ADJ
ejpam-5734	61	6	|	|	NOUN
ejpam-5734	61	7	1	1	NUM
ejpam-5734	61	8	≤	≤	NUM
ejpam-5734	62	1	i	i	PRON
ejpam-5734	62	2	≤	≤	ADJ
ejpam-5734	62	3	n−	n−	NOUN
ejpam-5734	62	4	1	1	NUM
ejpam-5734	62	5	}	}	PUNCT
ejpam-5734	62	6	∪	∪	ADJ
ejpam-5734	62	7	{	{	PUNCT
ejpam-5734	62	8	vnv1	vnv1	NOUN
ejpam-5734	62	9	}	}	PUNCT
ejpam-5734	62	10	.	.	PUNCT
ejpam-5734	63	1	example	example	NOUN
ejpam-5734	64	1	2	2	NUM
ejpam-5734	64	2	.	.	X
ejpam-5734	65	1	in	in	ADP
ejpam-5734	65	2	figure	figure	NOUN
ejpam-5734	65	3	2	2	NUM
ejpam-5734	65	4	,	,	PUNCT
ejpam-5734	65	5	a	a	DET
ejpam-5734	65	6	graph	graph	NOUN
ejpam-5734	65	7	c4	c4	NOUN
ejpam-5734	65	8	is	be	AUX
ejpam-5734	65	9	a	a	DET
ejpam-5734	65	10	cycle	cycle	NOUN
ejpam-5734	65	11	of	of	ADP
ejpam-5734	65	12	order	order	NOUN
ejpam-5734	65	13	4	4	NUM
ejpam-5734	65	14	with	with	ADP
ejpam-5734	65	15	the	the	DET
ejpam-5734	65	16	set	set	NOUN
ejpam-5734	65	17	of	of	ADP
ejpam-5734	65	18	vertices	vertex	NOUN
ejpam-5734	65	19	v	v	NOUN
ejpam-5734	65	20	(	(	PUNCT
ejpam-5734	65	21	c4	c4	NOUN
ejpam-5734	65	22	)	)	PUNCT
ejpam-5734	65	23	=	=	SYM
ejpam-5734	65	24	{	{	PUNCT
ejpam-5734	65	25	v1	v1	PROPN
ejpam-5734	65	26	,	,	PUNCT
ejpam-5734	65	27	v2	v2	PROPN
ejpam-5734	65	28	,	,	PUNCT
ejpam-5734	65	29	v3	v3	PROPN
ejpam-5734	65	30	,	,	PUNCT
ejpam-5734	65	31	v4	v4	NOUN
ejpam-5734	65	32	}	}	PUNCT
ejpam-5734	65	33	and	and	CCONJ
ejpam-5734	65	34	set	set	VERB
ejpam-5734	65	35	of	of	ADP
ejpam-5734	65	36	edges	edge	NOUN
ejpam-5734	65	37	e(c4	e(c4	ADV
ejpam-5734	65	38	)	)	PUNCT
ejpam-5734	66	1	=	=	PRON
ejpam-5734	66	2	{	{	PUNCT
ejpam-5734	66	3	v1v2	v1v2	PROPN
ejpam-5734	66	4	,	,	PUNCT
ejpam-5734	66	5	v2v3	v2v3	PROPN
ejpam-5734	66	6	,	,	PUNCT
ejpam-5734	66	7	v3v4	v3v4	NOUN
ejpam-5734	66	8	,	,	PUNCT
ejpam-5734	66	9	v4v1	v4v1	ADJ
ejpam-5734	66	10	}	}	PUNCT
ejpam-5734	66	11	.	.	PUNCT
ejpam-5734	67	1	m.	m.	PROPN
ejpam-5734	67	2	f.	f.	PROPN
ejpam-5734	67	3	libao	libao	PROPN
ejpam-5734	67	4	,	,	PUNCT
ejpam-5734	67	5	k.	k.	PROPN
ejpam-5734	67	6	b.	b.	PROPN
ejpam-5734	67	7	abarca	abarca	PROPN
ejpam-5734	67	8	/	/	SYM
ejpam-5734	67	9	eur	eur	PROPN
ejpam-5734	67	10	.	.	PUNCT
ejpam-5734	68	1	j.	j.	PROPN
ejpam-5734	68	2	pure	pure	PROPN
ejpam-5734	68	3	appl	appl	PROPN
ejpam-5734	68	4	.	.	PROPN
ejpam-5734	68	5	math	math	PROPN
ejpam-5734	68	6	,	,	PUNCT
ejpam-5734	68	7	18	18	NUM
ejpam-5734	68	8	(	(	PUNCT
ejpam-5734	68	9	2	2	NUM
ejpam-5734	68	10	)	)	PUNCT
ejpam-5734	68	11	(	(	PUNCT
ejpam-5734	68	12	2025	2025	NUM
ejpam-5734	68	13	)	)	PUNCT
ejpam-5734	68	14	,	,	PUNCT
ejpam-5734	68	15	5734	5734	NUM
ejpam-5734	68	16	4	4	NUM
ejpam-5734	68	17	of	of	ADP
ejpam-5734	68	18	25	25	NUM
ejpam-5734	68	19	c4	c4	NOUN
ejpam-5734	68	20	:	:	PUNCT
ejpam-5734	68	21	v1	v1	VERB
ejpam-5734	68	22	v2	v2	PROPN
ejpam-5734	68	23	v3v4	v3v4	PUNCT
ejpam-5734	68	24	figure	figure	NOUN
ejpam-5734	68	25	2	2	NUM
ejpam-5734	68	26	:	:	PUNCT
ejpam-5734	68	27	a	a	DET
ejpam-5734	68	28	graph	graph	NOUN
ejpam-5734	68	29	of	of	ADP
ejpam-5734	68	30	c4	c4	NOUN
ejpam-5734	68	31	definition	definition	NOUN
ejpam-5734	68	32	2.3	2.3	NUM
ejpam-5734	68	33	(	(	PUNCT
ejpam-5734	68	34	graph	graph	NOUN
ejpam-5734	68	35	coloring	coloring	NOUN
ejpam-5734	68	36	)	)	PUNCT
ejpam-5734	68	37	.	.	PUNCT
ejpam-5734	69	1	graph	graph	NOUN
ejpam-5734	69	2	coloring	coloring	NOUN
ejpam-5734	69	3	is	be	AUX
ejpam-5734	69	4	a	a	DET
ejpam-5734	69	5	way	way	NOUN
ejpam-5734	69	6	of	of	ADP
ejpam-5734	69	7	coloring	color	VERB
ejpam-5734	69	8	the	the	DET
ejpam-5734	69	9	vertices	vertex	NOUN
ejpam-5734	69	10	of	of	ADP
ejpam-5734	69	11	a	a	DET
ejpam-5734	69	12	graph	graph	NOUN
ejpam-5734	69	13	such	such	ADJ
ejpam-5734	69	14	that	that	SCONJ
ejpam-5734	69	15	no	no	DET
ejpam-5734	69	16	two	two	NUM
ejpam-5734	69	17	adjacent	adjacent	ADJ
ejpam-5734	69	18	vertices	vertex	NOUN
ejpam-5734	69	19	have	have	VERB
ejpam-5734	69	20	the	the	DET
ejpam-5734	69	21	same	same	ADJ
ejpam-5734	69	22	color	color	NOUN
ejpam-5734	69	23	;	;	PUNCT
ejpam-5734	69	24	this	this	PRON
ejpam-5734	69	25	is	be	AUX
ejpam-5734	69	26	called	call	VERB
ejpam-5734	69	27	proper	proper	ADJ
ejpam-5734	69	28	coloring	coloring	NOUN
ejpam-5734	69	29	.	.	PUNCT
ejpam-5734	70	1	g	g	NOUN
ejpam-5734	70	2	:	:	PUNCT
ejpam-5734	70	3	v6	v6	PROPN
ejpam-5734	70	4	v1	v1	PROPN
ejpam-5734	70	5	v4	v4	PROPN
ejpam-5734	70	6	v3	v3	PROPN
ejpam-5734	70	7	v5	v5	PROPN
ejpam-5734	70	8	v2	v2	PROPN
ejpam-5734	70	9	figure	figure	NOUN
ejpam-5734	70	10	3	3	NUM
ejpam-5734	70	11	:	:	PUNCT
ejpam-5734	70	12	a	a	DET
ejpam-5734	70	13	graph	graph	NOUN
ejpam-5734	70	14	with	with	ADP
ejpam-5734	70	15	proper	proper	ADJ
ejpam-5734	70	16	coloring	coloring	NOUN
ejpam-5734	70	17	definition	definition	NOUN
ejpam-5734	70	18	2.4	2.4	NUM
ejpam-5734	70	19	(	(	PUNCT
ejpam-5734	70	20	distance	distance	NOUN
ejpam-5734	70	21	)	)	PUNCT
ejpam-5734	70	22	.	.	PUNCT
ejpam-5734	71	1	the	the	DET
ejpam-5734	71	2	distance	distance	NOUN
ejpam-5734	71	3	between	between	ADP
ejpam-5734	71	4	vertices	vertex	NOUN
ejpam-5734	71	5	u	u	NOUN
ejpam-5734	71	6	and	and	CCONJ
ejpam-5734	71	7	v	v	NOUN
ejpam-5734	71	8	,	,	PUNCT
ejpam-5734	71	9	denoted	denote	VERB
ejpam-5734	71	10	as	as	ADP
ejpam-5734	71	11	d(u	d(u	PROPN
ejpam-5734	71	12	,	,	PUNCT
ejpam-5734	71	13	v	v	NOUN
ejpam-5734	71	14	)	)	PUNCT
ejpam-5734	71	15	,	,	PUNCT
ejpam-5734	71	16	in	in	ADP
ejpam-5734	71	17	a	a	DET
ejpam-5734	71	18	connected	connected	ADJ
ejpam-5734	71	19	graph	graph	NOUN
ejpam-5734	71	20	g	g	PROPN
ejpam-5734	71	21	is	be	AUX
ejpam-5734	71	22	the	the	DET
ejpam-5734	71	23	length	length	NOUN
ejpam-5734	71	24	of	of	ADP
ejpam-5734	71	25	a	a	DET
ejpam-5734	71	26	shortest	short	ADJ
ejpam-5734	71	27	u	u	NOUN
ejpam-5734	71	28	-	-	NOUN
ejpam-5734	71	29	v	v	ADJ
ejpam-5734	71	30	path	path	NOUN
ejpam-5734	71	31	in	in	ADP
ejpam-5734	71	32	g.	g.	PROPN
ejpam-5734	71	33	example	example	NOUN
ejpam-5734	72	1	3	3	X
ejpam-5734	72	2	.	.	PUNCT
ejpam-5734	73	1	in	in	ADP
ejpam-5734	73	2	figure	figure	NOUN
ejpam-5734	73	3	3	3	NUM
ejpam-5734	73	4	,	,	PUNCT
ejpam-5734	73	5	d(v1	d(v1	NOUN
ejpam-5734	73	6	,	,	PUNCT
ejpam-5734	73	7	v3	v3	PROPN
ejpam-5734	73	8	)	)	PUNCT
ejpam-5734	73	9	=	=	SYM
ejpam-5734	73	10	2	2	NUM
ejpam-5734	73	11	definition	definition	NOUN
ejpam-5734	73	12	2.5	2.5	NUM
ejpam-5734	73	13	(	(	PUNCT
ejpam-5734	73	14	chromatic	chromatic	ADJ
ejpam-5734	73	15	number	number	NOUN
ejpam-5734	73	16	)	)	PUNCT
ejpam-5734	73	17	.	.	PUNCT
ejpam-5734	74	1	the	the	DET
ejpam-5734	74	2	chromatic	chromatic	ADJ
ejpam-5734	74	3	number	number	NOUN
ejpam-5734	74	4	of	of	ADP
ejpam-5734	74	5	a	a	DET
ejpam-5734	74	6	graph	graph	NOUN
ejpam-5734	74	7	g	g	NOUN
ejpam-5734	74	8	is	be	AUX
ejpam-5734	74	9	the	the	DET
ejpam-5734	74	10	minimum	minimum	ADJ
ejpam-5734	74	11	number	number	NOUN
ejpam-5734	74	12	of	of	ADP
ejpam-5734	74	13	colors	color	NOUN
ejpam-5734	74	14	required	require	VERB
ejpam-5734	74	15	to	to	PART
ejpam-5734	74	16	color	color	VERB
ejpam-5734	74	17	every	every	DET
ejpam-5734	74	18	vertex	vertex	NOUN
ejpam-5734	74	19	of	of	ADP
ejpam-5734	74	20	g	g	NOUN
ejpam-5734	74	21	so	so	SCONJ
ejpam-5734	74	22	that	that	SCONJ
ejpam-5734	74	23	no	no	DET
ejpam-5734	74	24	two	two	NUM
ejpam-5734	74	25	adjacent	adjacent	ADJ
ejpam-5734	74	26	vertices	vertex	NOUN
ejpam-5734	74	27	share	share	VERB
ejpam-5734	74	28	the	the	DET
ejpam-5734	74	29	same	same	ADJ
ejpam-5734	74	30	color	color	NOUN
ejpam-5734	74	31	.	.	PUNCT
ejpam-5734	75	1	example	example	NOUN
ejpam-5734	76	1	4	4	NUM
ejpam-5734	76	2	.	.	PUNCT
ejpam-5734	77	1	in	in	ADP
ejpam-5734	77	2	figure	figure	NOUN
ejpam-5734	77	3	2	2	NUM
ejpam-5734	77	4	,	,	PUNCT
ejpam-5734	77	5	vertices	vertice	VERB
ejpam-5734	77	6	v1	v1	NOUN
ejpam-5734	77	7	and	and	CCONJ
ejpam-5734	77	8	v3	v3	PROPN
ejpam-5734	77	9	may	may	AUX
ejpam-5734	77	10	be	be	AUX
ejpam-5734	77	11	assigned	assign	VERB
ejpam-5734	77	12	the	the	DET
ejpam-5734	77	13	same	same	ADJ
ejpam-5734	77	14	color	color	NOUN
ejpam-5734	77	15	,	,	PUNCT
ejpam-5734	77	16	say	say	VERB
ejpam-5734	77	17	red	red	ADJ
ejpam-5734	77	18	,	,	PUNCT
ejpam-5734	77	19	while	while	SCONJ
ejpam-5734	77	20	v2	v2	PROPN
ejpam-5734	77	21	and	and	CCONJ
ejpam-5734	77	22	v4	v4	NOUN
ejpam-5734	77	23	can	can	AUX
ejpam-5734	77	24	be	be	AUX
ejpam-5734	77	25	colored	color	VERB
ejpam-5734	77	26	blue	blue	ADJ
ejpam-5734	77	27	.	.	PUNCT
ejpam-5734	78	1	however	however	ADV
ejpam-5734	78	2	,	,	PUNCT
ejpam-5734	78	3	assigning	assign	VERB
ejpam-5734	78	4	only	only	ADV
ejpam-5734	78	5	one	one	NUM
ejpam-5734	78	6	color	color	NOUN
ejpam-5734	78	7	to	to	ADP
ejpam-5734	78	8	all	all	DET
ejpam-5734	78	9	four	four	NUM
ejpam-5734	78	10	vertices	vertex	NOUN
ejpam-5734	78	11	would	would	AUX
ejpam-5734	78	12	violate	violate	VERB
ejpam-5734	78	13	the	the	DET
ejpam-5734	78	14	graph	graph	NOUN
ejpam-5734	78	15	coloring	coloring	NOUN
ejpam-5734	78	16	rule	rule	NOUN
ejpam-5734	78	17	,	,	PUNCT
ejpam-5734	78	18	which	which	PRON
ejpam-5734	78	19	requires	require	VERB
ejpam-5734	78	20	adjacent	adjacent	ADJ
ejpam-5734	78	21	vertices	vertex	NOUN
ejpam-5734	78	22	to	to	PART
ejpam-5734	78	23	receive	receive	VERB
ejpam-5734	78	24	different	different	ADJ
ejpam-5734	78	25	colors	color	NOUN
ejpam-5734	78	26	.	.	PUNCT
ejpam-5734	79	1	thus	thus	ADV
ejpam-5734	79	2	,	,	PUNCT
ejpam-5734	79	3	the	the	DET
ejpam-5734	79	4	chromatic	chromatic	ADJ
ejpam-5734	79	5	number	number	NOUN
ejpam-5734	79	6	of	of	ADP
ejpam-5734	79	7	c4	c4	NOUN
ejpam-5734	79	8	is	be	AUX
ejpam-5734	79	9	χ(c4	χ(c4	NOUN
ejpam-5734	79	10	)	)	PUNCT
ejpam-5734	80	1	=	=	SYM
ejpam-5734	80	2	2	2	X
ejpam-5734	80	3	.	.	X
ejpam-5734	80	4	definition	definition	NOUN
ejpam-5734	80	5	2.6	2.6	NUM
ejpam-5734	80	6	(	(	PUNCT
ejpam-5734	80	7	color	color	NOUN
ejpam-5734	80	8	class	class	NOUN
ejpam-5734	80	9	)	)	PUNCT
ejpam-5734	80	10	.	.	PUNCT
ejpam-5734	81	1	a	a	DET
ejpam-5734	81	2	color	color	NOUN
ejpam-5734	81	3	class	class	NOUN
ejpam-5734	81	4	,	,	PUNCT
ejpam-5734	81	5	a	a	PRON
ejpam-5734	81	6	,	,	PUNCT
ejpam-5734	81	7	is	be	AUX
ejpam-5734	81	8	the	the	DET
ejpam-5734	81	9	set	set	NOUN
ejpam-5734	81	10	of	of	ADP
ejpam-5734	81	11	all	all	DET
ejpam-5734	81	12	vertices	vertex	NOUN
ejpam-5734	81	13	having	have	VERB
ejpam-5734	81	14	the	the	DET
ejpam-5734	81	15	same	same	ADJ
ejpam-5734	81	16	color	color	NOUN
ejpam-5734	81	17	.	.	PUNCT
ejpam-5734	81	18	example	example	NOUN
ejpam-5734	82	1	5	5	NUM
ejpam-5734	82	2	.	.	PUNCT
ejpam-5734	83	1	in	in	ADP
ejpam-5734	83	2	example	example	NOUN
ejpam-5734	83	3	4	4	NUM
ejpam-5734	83	4	,	,	PUNCT
ejpam-5734	83	5	we	we	PRON
ejpam-5734	83	6	may	may	AUX
ejpam-5734	83	7	assign	assign	VERB
ejpam-5734	83	8	a1	a1	NOUN
ejpam-5734	83	9	as	as	ADP
ejpam-5734	83	10	red	red	ADJ
ejpam-5734	83	11	,	,	PUNCT
ejpam-5734	83	12	and	and	CCONJ
ejpam-5734	83	13	a2	a2	PROPN
ejpam-5734	83	14	as	as	ADP
ejpam-5734	83	15	blue	blue	ADJ
ejpam-5734	83	16	.	.	PUNCT
ejpam-5734	84	1	a1	a1	NOUN
ejpam-5734	84	2	and	and	CCONJ
ejpam-5734	84	3	a2	a2	PROPN
ejpam-5734	84	4	are	be	AUX
ejpam-5734	84	5	called	call	VERB
ejpam-5734	84	6	color	color	NOUN
ejpam-5734	84	7	classes	class	NOUN
ejpam-5734	84	8	.	.	PUNCT
ejpam-5734	85	1	definition	definition	NOUN
ejpam-5734	85	2	2.7	2.7	NUM
ejpam-5734	85	3	(	(	PUNCT
ejpam-5734	85	4	shadow	shadow	NOUN
ejpam-5734	85	5	graph	graph	NOUN
ejpam-5734	85	6	)	)	PUNCT
ejpam-5734	85	7	.	.	PUNCT
ejpam-5734	86	1	the	the	DET
ejpam-5734	86	2	shadow	shadow	NOUN
ejpam-5734	86	3	graph	graph	NOUN
ejpam-5734	86	4	,	,	PUNCT
ejpam-5734	86	5	d2(g	d2(g	PROPN
ejpam-5734	86	6	)	)	PUNCT
ejpam-5734	86	7	,	,	PUNCT
ejpam-5734	86	8	is	be	AUX
ejpam-5734	86	9	constructed	construct	VERB
ejpam-5734	86	10	by	by	ADP
ejpam-5734	86	11	taking	take	VERB
ejpam-5734	86	12	two	two	NUM
ejpam-5734	86	13	copies	copy	NOUN
ejpam-5734	86	14	of	of	ADP
ejpam-5734	86	15	g	g	NOUN
ejpam-5734	86	16	,	,	PUNCT
ejpam-5734	86	17	namely	namely	ADV
ejpam-5734	86	18	g	g	ADP
ejpam-5734	86	19	itself	itself	PRON
ejpam-5734	86	20	and	and	CCONJ
ejpam-5734	86	21	g′	g′	NOUN
ejpam-5734	86	22	,	,	PUNCT
ejpam-5734	86	23	and	and	CCONJ
ejpam-5734	86	24	by	by	ADP
ejpam-5734	86	25	joining	join	VERB
ejpam-5734	86	26	each	each	DET
ejpam-5734	86	27	vertex	vertex	NOUN
ejpam-5734	86	28	u	u	NOUN
ejpam-5734	86	29	in	in	ADP
ejpam-5734	86	30	g	g	NOUN
ejpam-5734	86	31	to	to	ADP
ejpam-5734	86	32	the	the	DET
ejpam-5734	86	33	neighbors	neighbor	NOUN
ejpam-5734	86	34	of	of	ADP
ejpam-5734	86	35	the	the	DET
ejpam-5734	86	36	corresponding	corresponding	ADJ
ejpam-5734	86	37	vertex	vertex	NOUN
ejpam-5734	86	38	u′	u′	X
ejpam-5734	86	39	in	in	ADP
ejpam-5734	86	40	g′.	g′.	ADP
ejpam-5734	86	41	m.	m.	PROPN
ejpam-5734	86	42	f.	f.	PROPN
ejpam-5734	86	43	libao	libao	PROPN
ejpam-5734	86	44	,	,	PUNCT
ejpam-5734	86	45	k.	k.	PROPN
ejpam-5734	86	46	b.	b.	PROPN
ejpam-5734	86	47	abarca	abarca	PROPN
ejpam-5734	86	48	/	/	SYM
ejpam-5734	86	49	eur	eur	PROPN
ejpam-5734	86	50	.	.	PUNCT
ejpam-5734	87	1	j.	j.	PROPN
ejpam-5734	87	2	pure	pure	PROPN
ejpam-5734	87	3	appl	appl	PROPN
ejpam-5734	87	4	.	.	PROPN
ejpam-5734	87	5	math	math	PROPN
ejpam-5734	87	6	,	,	PUNCT
ejpam-5734	87	7	18	18	NUM
ejpam-5734	87	8	(	(	PUNCT
ejpam-5734	87	9	2	2	NUM
ejpam-5734	87	10	)	)	PUNCT
ejpam-5734	87	11	(	(	PUNCT
ejpam-5734	87	12	2025	2025	NUM
ejpam-5734	87	13	)	)	PUNCT
ejpam-5734	87	14	,	,	PUNCT
ejpam-5734	87	15	5734	5734	NUM
ejpam-5734	87	16	5	5	NUM
ejpam-5734	87	17	of	of	ADP
ejpam-5734	87	18	25	25	NUM
ejpam-5734	87	19	g′gg	g′gg	NOUN
ejpam-5734	87	20	v1	v1	PROPN
ejpam-5734	87	21	v3	v3	PROPN
ejpam-5734	87	22	v2	v2	PROPN
ejpam-5734	87	23	v1	v1	PROPN
ejpam-5734	87	24	v2	v2	PROPN
ejpam-5734	87	25	v3	v3	PROPN
ejpam-5734	87	26	v′1	v′1	PROPN
ejpam-5734	87	27	v′2	v′2	PROPN
ejpam-5734	87	28	v′3	v′3	PROPN
ejpam-5734	87	29	figure	figure	NOUN
ejpam-5734	87	30	4	4	NUM
ejpam-5734	87	31	:	:	PUNCT
ejpam-5734	87	32	graph	graph	NOUN
ejpam-5734	87	33	g	g	PROPN
ejpam-5734	87	34	and	and	CCONJ
ejpam-5734	87	35	its	its	PRON
ejpam-5734	87	36	shadow	shadow	NOUN
ejpam-5734	87	37	graph	graph	NOUN
ejpam-5734	87	38	example	example	NOUN
ejpam-5734	87	39	6	6	NUM
ejpam-5734	87	40	.	.	PUNCT
ejpam-5734	88	1	in	in	ADP
ejpam-5734	88	2	the	the	DET
ejpam-5734	88	3	shadow	shadow	NOUN
ejpam-5734	88	4	graph	graph	NOUN
ejpam-5734	88	5	of	of	ADP
ejpam-5734	88	6	g	g	NOUN
ejpam-5734	88	7	(	(	PUNCT
ejpam-5734	88	8	figure	figure	NOUN
ejpam-5734	88	9	4	4	NUM
ejpam-5734	88	10	)	)	PUNCT
ejpam-5734	88	11	,	,	PUNCT
ejpam-5734	88	12	v1	v1	NOUN
ejpam-5734	88	13	is	be	AUX
ejpam-5734	88	14	adjacent	adjacent	ADJ
ejpam-5734	88	15	to	to	ADP
ejpam-5734	88	16	the	the	DET
ejpam-5734	88	17	vertex	vertex	NOUN
ejpam-5734	88	18	v′2	v′2	NOUN
ejpam-5734	88	19	,	,	PUNCT
ejpam-5734	88	20	v2	v2	PROPN
ejpam-5734	88	21	is	be	AUX
ejpam-5734	88	22	adjacent	adjacent	ADJ
ejpam-5734	88	23	to	to	ADP
ejpam-5734	88	24	v′1	v′1	PROPN
ejpam-5734	88	25	and	and	CCONJ
ejpam-5734	88	26	v′3	v′3	NOUN
ejpam-5734	88	27	,	,	PUNCT
ejpam-5734	88	28	v3	v3	PROPN
ejpam-5734	88	29	is	be	AUX
ejpam-5734	88	30	adjacent	adjacent	ADJ
ejpam-5734	88	31	to	to	ADP
ejpam-5734	88	32	the	the	DET
ejpam-5734	88	33	vertex	vertex	NOUN
ejpam-5734	88	34	v′2	v′2	NOUN
ejpam-5734	88	35	.	.	PUNCT
ejpam-5734	89	1	definition	definition	NOUN
ejpam-5734	89	2	2.8	2.8	NUM
ejpam-5734	89	3	(	(	PUNCT
ejpam-5734	89	4	shadow	shadow	NOUN
ejpam-5734	89	5	vertex	vertex	PROPN
ejpam-5734	89	6	)	)	PUNCT
ejpam-5734	89	7	.	.	PUNCT
ejpam-5734	90	1	a	a	DET
ejpam-5734	90	2	shadow	shadow	NOUN
ejpam-5734	90	3	vertex	vertex	NOUN
ejpam-5734	90	4	is	be	AUX
ejpam-5734	90	5	the	the	DET
ejpam-5734	90	6	vertex	vertex	NOUN
ejpam-5734	90	7	u′	u′	PROPN
ejpam-5734	90	8	in	in	ADP
ejpam-5734	90	9	g′	g′	NOUN
ejpam-5734	90	10	that	that	PRON
ejpam-5734	90	11	corresponds	correspond	VERB
ejpam-5734	90	12	to	to	ADP
ejpam-5734	90	13	a	a	DET
ejpam-5734	90	14	vertex	vertex	NOUN
ejpam-5734	90	15	u	u	NOUN
ejpam-5734	90	16	in	in	ADP
ejpam-5734	90	17	g	g	NOUN
ejpam-5734	90	18	or	or	CCONJ
ejpam-5734	90	19	vice	vice	NOUN
ejpam-5734	90	20	versa	versa	ADV
ejpam-5734	90	21	.	.	PUNCT
ejpam-5734	91	1	example	example	NOUN
ejpam-5734	91	2	7	7	NUM
ejpam-5734	91	3	.	.	PUNCT
ejpam-5734	92	1	also	also	ADV
ejpam-5734	92	2	in	in	ADP
ejpam-5734	92	3	figure	figure	NOUN
ejpam-5734	92	4	4	4	NUM
ejpam-5734	92	5	,	,	PUNCT
ejpam-5734	92	6	the	the	DET
ejpam-5734	92	7	shadow	shadow	NOUN
ejpam-5734	92	8	vertex	vertex	NOUN
ejpam-5734	92	9	of	of	ADP
ejpam-5734	92	10	v1	v1	NOUN
ejpam-5734	92	11	is	be	AUX
ejpam-5734	92	12	v′1	v′1	ADJ
ejpam-5734	92	13	,	,	PUNCT
ejpam-5734	92	14	the	the	DET
ejpam-5734	92	15	shadow	shadow	NOUN
ejpam-5734	92	16	vertex	vertex	NOUN
ejpam-5734	92	17	of	of	ADP
ejpam-5734	92	18	v2	v2	PROPN
ejpam-5734	92	19	is	be	AUX
ejpam-5734	92	20	v′2	v′2	ADJ
ejpam-5734	92	21	,	,	PUNCT
ejpam-5734	92	22	the	the	DET
ejpam-5734	92	23	shadow	shadow	NOUN
ejpam-5734	92	24	vertex	vertex	NOUN
ejpam-5734	92	25	of	of	ADP
ejpam-5734	92	26	v3	v3	PROPN
ejpam-5734	92	27	is	be	AUX
ejpam-5734	92	28	v′3	v′3	NOUN
ejpam-5734	92	29	.	.	PUNCT
ejpam-5734	93	1	definition	definition	NOUN
ejpam-5734	93	2	2.9	2.9	NUM
ejpam-5734	93	3	(	(	PUNCT
ejpam-5734	93	4	central	central	ADJ
ejpam-5734	93	5	graph	graph	NOUN
ejpam-5734	93	6	)	)	PUNCT
ejpam-5734	93	7	.	.	PUNCT
ejpam-5734	94	1	the	the	DET
ejpam-5734	94	2	central	central	ADJ
ejpam-5734	94	3	graph	graph	NOUN
ejpam-5734	94	4	of	of	ADP
ejpam-5734	94	5	g	g	NOUN
ejpam-5734	94	6	,	,	PUNCT
ejpam-5734	94	7	denoted	denote	VERB
ejpam-5734	94	8	as	as	ADP
ejpam-5734	94	9	c(g	c(g	PROPN
ejpam-5734	94	10	)	)	PUNCT
ejpam-5734	94	11	,	,	PUNCT
ejpam-5734	94	12	is	be	AUX
ejpam-5734	94	13	obtained	obtain	VERB
ejpam-5734	94	14	by	by	ADP
ejpam-5734	94	15	subdividing	subdivide	VERB
ejpam-5734	94	16	each	each	DET
ejpam-5734	94	17	edge	edge	NOUN
ejpam-5734	94	18	of	of	ADP
ejpam-5734	94	19	g	g	NOUN
ejpam-5734	94	20	exactly	exactly	ADV
ejpam-5734	94	21	once	once	ADV
ejpam-5734	94	22	and	and	CCONJ
ejpam-5734	94	23	joining	join	VERB
ejpam-5734	94	24	all	all	DET
ejpam-5734	94	25	the	the	DET
ejpam-5734	94	26	non	non	ADJ
ejpam-5734	94	27	-	-	ADJ
ejpam-5734	94	28	adjacent	adjacent	ADJ
ejpam-5734	94	29	vertices	vertex	NOUN
ejpam-5734	94	30	of	of	ADP
ejpam-5734	94	31	g	g	NOUN
ejpam-5734	94	32	in	in	ADP
ejpam-5734	94	33	c(g	c(g	PROPN
ejpam-5734	94	34	)	)	PUNCT
ejpam-5734	94	35	.	.	PUNCT
ejpam-5734	95	1	the	the	DET
ejpam-5734	95	2	resulting	result	VERB
ejpam-5734	95	3	vertices	vertex	NOUN
ejpam-5734	95	4	created	create	VERB
ejpam-5734	95	5	by	by	ADP
ejpam-5734	95	6	the	the	DET
ejpam-5734	95	7	subdivisions	subdivision	NOUN
ejpam-5734	95	8	are	be	AUX
ejpam-5734	95	9	referred	refer	VERB
ejpam-5734	95	10	to	to	ADP
ejpam-5734	95	11	as	as	ADP
ejpam-5734	95	12	central	central	ADJ
ejpam-5734	95	13	vertices	vertex	NOUN
ejpam-5734	95	14	(	(	PUNCT
ejpam-5734	95	15	denoted	denote	VERB
ejpam-5734	95	16	by	by	ADP
ejpam-5734	95	17	ci	ci	NOUN
ejpam-5734	95	18	)	)	PUNCT
ejpam-5734	95	19	.	.	PUNCT
ejpam-5734	96	1	c(g)g	c(g)g	PROPN
ejpam-5734	96	2	v2	v2	PROPN
ejpam-5734	96	3	v4	v4	PROPN
ejpam-5734	96	4	v3	v3	PROPN
ejpam-5734	96	5	v2	v2	PROPN
ejpam-5734	96	6	v3	v3	PROPN
ejpam-5734	96	7	v4	v4	PROPN
ejpam-5734	96	8	v1	v1	PROPN
ejpam-5734	96	9	v1	v1	PROPN
ejpam-5734	96	10	c1	c1	NOUN
ejpam-5734	96	11	c2	c2	PROPN
ejpam-5734	96	12	c3	c3	PROPN
ejpam-5734	96	13	figure	figure	NOUN
ejpam-5734	96	14	5	5	NUM
ejpam-5734	96	15	:	:	PUNCT
ejpam-5734	96	16	graph	graph	NOUN
ejpam-5734	96	17	g	g	PROPN
ejpam-5734	96	18	and	and	CCONJ
ejpam-5734	96	19	its	its	PRON
ejpam-5734	96	20	central	central	ADJ
ejpam-5734	96	21	graph	graph	NOUN
ejpam-5734	96	22	,	,	PUNCT
ejpam-5734	96	23	c(g	c(g	PROPN
ejpam-5734	96	24	)	)	PUNCT
ejpam-5734	96	25	example	example	NOUN
ejpam-5734	96	26	8	8	NUM
ejpam-5734	96	27	.	.	PUNCT
ejpam-5734	97	1	in	in	ADP
ejpam-5734	97	2	figure	figure	NOUN
ejpam-5734	97	3	5	5	NUM
ejpam-5734	97	4	,	,	PUNCT
ejpam-5734	97	5	the	the	DET
ejpam-5734	97	6	central	central	ADJ
ejpam-5734	97	7	graph	graph	NOUN
ejpam-5734	97	8	of	of	ADP
ejpam-5734	97	9	g	g	PROPN
ejpam-5734	97	10	has	have	VERB
ejpam-5734	97	11	the	the	DET
ejpam-5734	97	12	following	follow	VERB
ejpam-5734	97	13	vertices	vertex	NOUN
ejpam-5734	97	14	:	:	PUNCT
ejpam-5734	97	15	c1	c1	NOUN
ejpam-5734	97	16	between	between	ADP
ejpam-5734	97	17	v1	v1	PROPN
ejpam-5734	97	18	and	and	CCONJ
ejpam-5734	97	19	v2	v2	NOUN
ejpam-5734	97	20	,	,	PUNCT
ejpam-5734	97	21	c2	c2	PROPN
ejpam-5734	97	22	between	between	ADP
ejpam-5734	97	23	v2	v2	PROPN
ejpam-5734	97	24	and	and	CCONJ
ejpam-5734	97	25	v3	v3	PROPN
ejpam-5734	97	26	,	,	PUNCT
ejpam-5734	97	27	here	here	ADV
ejpam-5734	97	28	,	,	PUNCT
ejpam-5734	97	29	v1	v1	NOUN
ejpam-5734	97	30	is	be	AUX
ejpam-5734	97	31	now	now	ADV
ejpam-5734	97	32	connected	connect	VERB
ejpam-5734	97	33	to	to	ADP
ejpam-5734	97	34	v3	v3	PROPN
ejpam-5734	97	35	and	and	CCONJ
ejpam-5734	97	36	v4	v4	PROPN
ejpam-5734	97	37	,	,	PUNCT
ejpam-5734	97	38	v2	v2	PROPN
ejpam-5734	97	39	is	be	AUX
ejpam-5734	97	40	now	now	ADV
ejpam-5734	97	41	connected	connect	VERB
ejpam-5734	97	42	to	to	ADP
ejpam-5734	97	43	v4	v4	NOUN
ejpam-5734	97	44	,	,	PUNCT
ejpam-5734	97	45	and	and	CCONJ
ejpam-5734	97	46	v3	v3	PROPN
ejpam-5734	97	47	is	be	AUX
ejpam-5734	97	48	now	now	ADV
ejpam-5734	97	49	connected	connect	VERB
ejpam-5734	97	50	to	to	PART
ejpam-5734	97	51	v1	v1	VERB
ejpam-5734	97	52	.	.	PUNCT
ejpam-5734	98	1	m.	m.	PROPN
ejpam-5734	98	2	f.	f.	PROPN
ejpam-5734	98	3	libao	libao	PROPN
ejpam-5734	98	4	,	,	PUNCT
ejpam-5734	98	5	k.	k.	PROPN
ejpam-5734	98	6	b.	b.	PROPN
ejpam-5734	98	7	abarca	abarca	PROPN
ejpam-5734	98	8	/	/	SYM
ejpam-5734	98	9	eur	eur	PROPN
ejpam-5734	98	10	.	.	PUNCT
ejpam-5734	99	1	j.	j.	PROPN
ejpam-5734	99	2	pure	pure	PROPN
ejpam-5734	99	3	appl	appl	PROPN
ejpam-5734	99	4	.	.	PROPN
ejpam-5734	99	5	math	math	PROPN
ejpam-5734	99	6	,	,	PUNCT
ejpam-5734	99	7	18	18	NUM
ejpam-5734	99	8	(	(	PUNCT
ejpam-5734	99	9	2	2	NUM
ejpam-5734	99	10	)	)	PUNCT
ejpam-5734	99	11	(	(	PUNCT
ejpam-5734	99	12	2025	2025	NUM
ejpam-5734	99	13	)	)	PUNCT
ejpam-5734	99	14	,	,	PUNCT
ejpam-5734	99	15	5734	5734	NUM
ejpam-5734	99	16	6	6	NUM
ejpam-5734	99	17	of	of	ADP
ejpam-5734	99	18	25	25	NUM
ejpam-5734	99	19	3	3	NUM
ejpam-5734	99	20	.	.	PUNCT
ejpam-5734	100	1	distance-2	distance-2	VERB
ejpam-5734	100	2	chromatic	chromatic	ADJ
ejpam-5734	100	3	concepts	concept	NOUN
ejpam-5734	100	4	one	one	NUM
ejpam-5734	100	5	extension	extension	NOUN
ejpam-5734	100	6	of	of	ADP
ejpam-5734	100	7	traditional	traditional	ADJ
ejpam-5734	100	8	vertex	vertex	NOUN
ejpam-5734	100	9	coloring	coloring	NOUN
ejpam-5734	100	10	is	be	AUX
ejpam-5734	100	11	the	the	DET
ejpam-5734	100	12	concept	concept	NOUN
ejpam-5734	100	13	of	of	ADP
ejpam-5734	100	14	distance-2	distance-2	PRON
ejpam-5734	100	15	coloring	coloring	NOUN
ejpam-5734	100	16	,	,	PUNCT
ejpam-5734	100	17	which	which	PRON
ejpam-5734	100	18	focuses	focus	VERB
ejpam-5734	100	19	on	on	ADP
ejpam-5734	100	20	ensuring	ensure	VERB
ejpam-5734	100	21	that	that	SCONJ
ejpam-5734	100	22	vertices	vertex	NOUN
ejpam-5734	100	23	within	within	ADP
ejpam-5734	100	24	a	a	DET
ejpam-5734	100	25	distance	distance	NOUN
ejpam-5734	100	26	of	of	ADP
ejpam-5734	100	27	two	two	NUM
ejpam-5734	100	28	from	from	ADP
ejpam-5734	100	29	each	each	DET
ejpam-5734	100	30	other	other	ADJ
ejpam-5734	100	31	do	do	AUX
ejpam-5734	100	32	not	not	PART
ejpam-5734	100	33	share	share	VERB
ejpam-5734	100	34	the	the	DET
ejpam-5734	100	35	same	same	ADJ
ejpam-5734	100	36	color	color	NOUN
ejpam-5734	100	37	.	.	PUNCT
ejpam-5734	101	1	this	this	DET
ejpam-5734	101	2	concept	concept	NOUN
ejpam-5734	101	3	is	be	AUX
ejpam-5734	101	4	particularly	particularly	ADV
ejpam-5734	101	5	relevant	relevant	ADJ
ejpam-5734	101	6	in	in	ADP
ejpam-5734	101	7	scenarios	scenario	NOUN
ejpam-5734	101	8	where	where	SCONJ
ejpam-5734	101	9	interactions	interaction	NOUN
ejpam-5734	101	10	or	or	CCONJ
ejpam-5734	101	11	conflicts	conflict	NOUN
ejpam-5734	101	12	extend	extend	VERB
ejpam-5734	101	13	beyond	beyond	ADP
ejpam-5734	101	14	immediate	immediate	ADJ
ejpam-5734	101	15	neighbors	neighbor	NOUN
ejpam-5734	101	16	,	,	PUNCT
ejpam-5734	101	17	such	such	ADJ
ejpam-5734	101	18	as	as	ADP
ejpam-5734	101	19	in	in	ADP
ejpam-5734	101	20	network	network	NOUN
ejpam-5734	101	21	design	design	NOUN
ejpam-5734	101	22	or	or	CCONJ
ejpam-5734	101	23	scheduling	scheduling	NOUN
ejpam-5734	101	24	problems	problem	NOUN
ejpam-5734	101	25	.	.	PUNCT
ejpam-5734	102	1	we	we	PRON
ejpam-5734	102	2	formally	formally	ADV
ejpam-5734	102	3	explore	explore	VERB
ejpam-5734	102	4	this	this	DET
ejpam-5734	102	5	concept	concept	NOUN
ejpam-5734	102	6	by	by	ADP
ejpam-5734	102	7	introducing	introduce	VERB
ejpam-5734	102	8	the	the	DET
ejpam-5734	102	9	definitions	definition	NOUN
ejpam-5734	102	10	of	of	ADP
ejpam-5734	102	11	some	some	DET
ejpam-5734	102	12	related	related	ADJ
ejpam-5734	102	13	terms	term	NOUN
ejpam-5734	102	14	.	.	PUNCT
ejpam-5734	103	1	definition	definition	NOUN
ejpam-5734	103	2	3.1	3.1	NUM
ejpam-5734	103	3	(	(	PUNCT
ejpam-5734	103	4	distance-2	distance-2	NUM
ejpam-5734	103	5	coloring	coloring	NOUN
ejpam-5734	103	6	)	)	PUNCT
ejpam-5734	103	7	.	.	PUNCT
ejpam-5734	104	1	let	let	VERB
ejpam-5734	104	2	g	g	PRON
ejpam-5734	104	3	be	be	AUX
ejpam-5734	104	4	a	a	DET
ejpam-5734	104	5	connected	connected	ADJ
ejpam-5734	104	6	graph	graph	NOUN
ejpam-5734	104	7	of	of	ADP
ejpam-5734	104	8	order	order	NOUN
ejpam-5734	104	9	n	n	PRON
ejpam-5734	104	10	≥	≥	NOUN
ejpam-5734	104	11	3	3	NUM
ejpam-5734	104	12	.	.	PUNCT
ejpam-5734	105	1	a	a	DET
ejpam-5734	105	2	subset	subset	NOUN
ejpam-5734	105	3	a	a	DET
ejpam-5734	105	4	⊆	⊆	NUM
ejpam-5734	105	5	v	v	NOUN
ejpam-5734	105	6	(	(	PUNCT
ejpam-5734	105	7	g	g	NOUN
ejpam-5734	105	8	)	)	PUNCT
ejpam-5734	105	9	is	be	AUX
ejpam-5734	105	10	called	call	VERB
ejpam-5734	105	11	a	a	DET
ejpam-5734	105	12	distance-2	distance-2	NUM
ejpam-5734	105	13	coloring	coloring	NOUN
ejpam-5734	105	14	if	if	SCONJ
ejpam-5734	105	15	for	for	ADP
ejpam-5734	105	16	every	every	DET
ejpam-5734	105	17	u	u	NOUN
ejpam-5734	105	18	,	,	PUNCT
ejpam-5734	105	19	v	v	ADP
ejpam-5734	105	20	∈	∈	PROPN
ejpam-5734	105	21	a	a	PRON
ejpam-5734	105	22	,	,	PUNCT
ejpam-5734	105	23	d(u	d(u	PROPN
ejpam-5734	105	24	,	,	PUNCT
ejpam-5734	105	25	v	v	NOUN
ejpam-5734	105	26	)	)	PUNCT
ejpam-5734	105	27	≥	≥	NOUN
ejpam-5734	105	28	3	3	NUM
ejpam-5734	105	29	.	.	PUNCT
ejpam-5734	106	1	this	this	DET
ejpam-5734	106	2	condition	condition	NOUN
ejpam-5734	106	3	ensures	ensure	VERB
ejpam-5734	106	4	that	that	SCONJ
ejpam-5734	106	5	no	no	DET
ejpam-5734	106	6	two	two	NUM
ejpam-5734	106	7	vertices	vertex	NOUN
ejpam-5734	106	8	in	in	ADP
ejpam-5734	106	9	the	the	DET
ejpam-5734	106	10	same	same	ADJ
ejpam-5734	106	11	class	class	NOUN
ejpam-5734	106	12	are	be	AUX
ejpam-5734	106	13	within	within	ADP
ejpam-5734	106	14	a	a	DET
ejpam-5734	106	15	distance	distance	NOUN
ejpam-5734	106	16	of	of	ADP
ejpam-5734	106	17	two	two	NUM
ejpam-5734	106	18	from	from	ADP
ejpam-5734	106	19	each	each	DET
ejpam-5734	106	20	other	other	ADJ
ejpam-5734	106	21	,	,	PUNCT
ejpam-5734	106	22	thereby	thereby	ADV
ejpam-5734	106	23	satisfying	satisfy	VERB
ejpam-5734	106	24	the	the	DET
ejpam-5734	106	25	distance-2	distance-2	NUM
ejpam-5734	106	26	coloring	coloring	NOUN
ejpam-5734	106	27	constraint	constraint	NOUN
ejpam-5734	106	28	.	.	PUNCT
ejpam-5734	107	1	g	g	NOUN
ejpam-5734	107	2	:	:	PUNCT
ejpam-5734	107	3	v1	v1	VERB
ejpam-5734	107	4	v4	v4	PROPN
ejpam-5734	107	5	v3v2	v3v2	PUNCT
ejpam-5734	107	6	v5	v5	PROPN
ejpam-5734	107	7	figure	figure	NOUN
ejpam-5734	107	8	6	6	NUM
ejpam-5734	107	9	:	:	PUNCT
ejpam-5734	107	10	a	a	DET
ejpam-5734	107	11	graph	graph	NOUN
ejpam-5734	107	12	g	g	NOUN
ejpam-5734	107	13	with	with	ADP
ejpam-5734	107	14	a	a	DET
ejpam-5734	107	15	distance	distance	NOUN
ejpam-5734	107	16	2	2	NUM
ejpam-5734	107	17	coloring	coloring	NOUN
ejpam-5734	107	18	example	example	NOUN
ejpam-5734	107	19	9	9	NUM
ejpam-5734	107	20	.	.	X
ejpam-5734	107	21	figure	figure	NOUN
ejpam-5734	107	22	6	6	NUM
ejpam-5734	107	23	shows	show	VERB
ejpam-5734	107	24	a	a	DET
ejpam-5734	107	25	graph	graph	NOUN
ejpam-5734	107	26	g	g	NOUN
ejpam-5734	107	27	with	with	ADP
ejpam-5734	107	28	vertices	vertex	NOUN
ejpam-5734	107	29	v1	v1	NOUN
ejpam-5734	107	30	,	,	PUNCT
ejpam-5734	107	31	v2	v2	PROPN
ejpam-5734	107	32	,	,	PUNCT
ejpam-5734	107	33	v3	v3	PROPN
ejpam-5734	107	34	,	,	PUNCT
ejpam-5734	107	35	v4	v4	PROPN
ejpam-5734	107	36	and	and	CCONJ
ejpam-5734	107	37	v5	v5	PROPN
ejpam-5734	107	38	.	.	PUNCT
ejpam-5734	108	1	here	here	ADV
ejpam-5734	108	2	,	,	PUNCT
ejpam-5734	108	3	the	the	DET
ejpam-5734	108	4	color	color	NOUN
ejpam-5734	108	5	classes	class	NOUN
ejpam-5734	108	6	are	be	AUX
ejpam-5734	108	7	a1={v1	a1={v1	NOUN
ejpam-5734	108	8	}	}	PUNCT
ejpam-5734	108	9	(	(	PUNCT
ejpam-5734	108	10	red	red	ADJ
ejpam-5734	108	11	)	)	PUNCT
ejpam-5734	108	12	,	,	PUNCT
ejpam-5734	108	13	a2={v2	a2={v2	PROPN
ejpam-5734	108	14	,	,	PUNCT
ejpam-5734	108	15	v5}(blue	v5}(blue	PROPN
ejpam-5734	108	16	)	)	PUNCT
ejpam-5734	108	17	,	,	PUNCT
ejpam-5734	108	18	a3	a3	NOUN
ejpam-5734	108	19	=	=	NOUN
ejpam-5734	108	20	{	{	PUNCT
ejpam-5734	108	21	v3}(yellow	v3}(yellow	NOUN
ejpam-5734	108	22	)	)	PUNCT
ejpam-5734	108	23	,	,	PUNCT
ejpam-5734	108	24	a4={v4}(green	a4={v4}(green	NUM
ejpam-5734	108	25	)	)	PUNCT
ejpam-5734	108	26	.	.	PUNCT
ejpam-5734	109	1	note	note	VERB
ejpam-5734	109	2	that	that	DET
ejpam-5734	109	3	d(v2	d(v2	NOUN
ejpam-5734	109	4	,	,	PUNCT
ejpam-5734	109	5	v5	v5	PROPN
ejpam-5734	109	6	)	)	PUNCT
ejpam-5734	109	7	=	=	SYM
ejpam-5734	109	8	3	3	X
ejpam-5734	109	9	.	.	X
ejpam-5734	109	10	definition	definition	NOUN
ejpam-5734	109	11	3.2	3.2	NUM
ejpam-5734	109	12	(	(	PUNCT
ejpam-5734	109	13	distance-2	distance-2	NUM
ejpam-5734	109	14	chromatic	chromatic	ADJ
ejpam-5734	109	15	set	set	NOUN
ejpam-5734	109	16	)	)	PUNCT
ejpam-5734	109	17	.	.	PUNCT
ejpam-5734	110	1	a	a	DET
ejpam-5734	110	2	distance-2	distance-2	CCONJ
ejpam-5734	110	3	chromatic	chromatic	ADJ
ejpam-5734	110	4	set	set	NOUN
ejpam-5734	110	5	,	,	PUNCT
ejpam-5734	110	6	denoted	denote	VERB
ejpam-5734	110	7	as	as	ADP
ejpam-5734	110	8	c	c	PROPN
ejpam-5734	110	9	,	,	PUNCT
ejpam-5734	110	10	is	be	AUX
ejpam-5734	110	11	a	a	DET
ejpam-5734	110	12	collection	collection	NOUN
ejpam-5734	110	13	of	of	ADP
ejpam-5734	110	14	distance-2	distance-2	NUM
ejpam-5734	110	15	color	color	NOUN
ejpam-5734	110	16	classes	class	NOUN
ejpam-5734	110	17	that	that	PRON
ejpam-5734	110	18	collectively	collectively	ADV
ejpam-5734	110	19	cover	cover	VERB
ejpam-5734	110	20	all	all	DET
ejpam-5734	110	21	vertices	vertex	NOUN
ejpam-5734	110	22	in	in	ADP
ejpam-5734	110	23	the	the	DET
ejpam-5734	110	24	graph	graph	NOUN
ejpam-5734	110	25	g.	g.	PROPN
ejpam-5734	110	26	formally	formally	ADV
ejpam-5734	110	27	,	,	PUNCT
ejpam-5734	110	28	the	the	DET
ejpam-5734	110	29	set	set	NOUN
ejpam-5734	110	30	c	c	NOUN
ejpam-5734	110	31	=	=	PRON
ejpam-5734	110	32	{	{	PUNCT
ejpam-5734	110	33	a	a	DET
ejpam-5734	110	34	|	|	NOUN
ejpam-5734	110	35	a	a	PRON
ejpam-5734	110	36	is	be	AUX
ejpam-5734	110	37	a	a	DET
ejpam-5734	110	38	distance-2	distance-2	NUM
ejpam-5734	110	39	color	color	NOUN
ejpam-5734	110	40	class	class	NOUN
ejpam-5734	110	41	}	}	PUNCT
ejpam-5734	110	42	must	must	AUX
ejpam-5734	110	43	satisfy	satisfy	VERB
ejpam-5734	110	44	the	the	DET
ejpam-5734	110	45	following	follow	VERB
ejpam-5734	110	46	conditions	condition	NOUN
ejpam-5734	110	47	:	:	PUNCT
ejpam-5734	110	48	(	(	PUNCT
ejpam-5734	110	49	i	i	NOUN
ejpam-5734	110	50	)	)	PUNCT
ejpam-5734	111	1	⋃	⋃	VERB
ejpam-5734	111	2	a∈c	a∈c	NOUN
ejpam-5734	111	3	a	a	DET
ejpam-5734	111	4	=	=	SYM
ejpam-5734	111	5	v	v	NOUN
ejpam-5734	111	6	(	(	PUNCT
ejpam-5734	111	7	g	g	NOUN
ejpam-5734	111	8	)	)	PUNCT
ejpam-5734	111	9	,	,	PUNCT
ejpam-5734	111	10	meaning	mean	VERB
ejpam-5734	111	11	every	every	DET
ejpam-5734	111	12	vertex	vertex	NOUN
ejpam-5734	111	13	in	in	ADP
ejpam-5734	111	14	the	the	DET
ejpam-5734	111	15	graph	graph	NOUN
ejpam-5734	111	16	belongs	belong	VERB
ejpam-5734	111	17	to	to	ADP
ejpam-5734	111	18	exactly	exactly	ADV
ejpam-5734	111	19	one	one	NUM
ejpam-5734	111	20	color	color	NOUN
ejpam-5734	111	21	class	class	NOUN
ejpam-5734	111	22	,	,	PUNCT
ejpam-5734	111	23	and	and	CCONJ
ejpam-5734	111	24	(	(	PUNCT
ejpam-5734	111	25	ii	ii	NOUN
ejpam-5734	111	26	)	)	PUNCT
ejpam-5734	111	27	a∩a′	a∩a′	NOUN
ejpam-5734	111	28	=	=	NOUN
ejpam-5734	111	29	∅	∅	NOUN
ejpam-5734	111	30	,	,	PUNCT
ejpam-5734	111	31	for	for	ADP
ejpam-5734	111	32	every	every	DET
ejpam-5734	111	33	a	a	NOUN
ejpam-5734	111	34	,	,	PUNCT
ejpam-5734	111	35	a′	a′	PROPN
ejpam-5734	111	36	∈	∈	PROPN
ejpam-5734	111	37	c	c	PROPN
ejpam-5734	111	38	,	,	PUNCT
ejpam-5734	111	39	ensuring	ensure	VERB
ejpam-5734	111	40	that	that	SCONJ
ejpam-5734	111	41	color	color	NOUN
ejpam-5734	111	42	classes	class	NOUN
ejpam-5734	111	43	are	be	AUX
ejpam-5734	111	44	mutually	mutually	ADV
ejpam-5734	111	45	exclusive	exclusive	ADJ
ejpam-5734	111	46	.	.	PUNCT
ejpam-5734	112	1	lemma	lemma	PROPN
ejpam-5734	112	2	1	1	X
ejpam-5734	112	3	.	.	PUNCT
ejpam-5734	113	1	let	let	VERB
ejpam-5734	113	2	c	c	NOUN
ejpam-5734	113	3	=	=	PUNCT
ejpam-5734	113	4	{	{	PUNCT
ejpam-5734	113	5	a1	a1	PROPN
ejpam-5734	113	6	,	,	PUNCT
ejpam-5734	113	7	a2	a2	PROPN
ejpam-5734	113	8	,	,	PUNCT
ejpam-5734	113	9	.	.	PUNCT
ejpam-5734	113	10	.	.	PUNCT
ejpam-5734	114	1	.	.	PUNCT
ejpam-5734	115	1	,	,	PUNCT
ejpam-5734	115	2	ak	ak	AUX
ejpam-5734	115	3	}	}	PUNCT
ejpam-5734	115	4	be	be	AUX
ejpam-5734	115	5	a	a	DET
ejpam-5734	115	6	collection	collection	NOUN
ejpam-5734	115	7	of	of	ADP
ejpam-5734	115	8	color	color	NOUN
ejpam-5734	115	9	classes	class	NOUN
ejpam-5734	115	10	over	over	ADP
ejpam-5734	115	11	a	a	DET
ejpam-5734	115	12	graph	graph	NOUN
ejpam-5734	115	13	g	g	NOUN
ejpam-5734	115	14	,	,	PUNCT
ejpam-5734	115	15	where	where	SCONJ
ejpam-5734	115	16	each	each	PRON
ejpam-5734	115	17	ai	ai	VERB
ejpam-5734	115	18	is	be	AUX
ejpam-5734	115	19	a	a	DET
ejpam-5734	115	20	subset	subset	NOUN
ejpam-5734	115	21	of	of	ADP
ejpam-5734	115	22	v	v	NOUN
ejpam-5734	115	23	(	(	PUNCT
ejpam-5734	115	24	g	g	NOUN
ejpam-5734	115	25	)	)	PUNCT
ejpam-5734	115	26	.	.	PUNCT
ejpam-5734	116	1	then	then	ADV
ejpam-5734	116	2	the	the	DET
ejpam-5734	116	3	following	follow	VERB
ejpam-5734	116	4	are	be	AUX
ejpam-5734	116	5	equivalent	equivalent	ADJ
ejpam-5734	116	6	:	:	PUNCT
ejpam-5734	116	7	1	1	X
ejpam-5734	116	8	.	.	X
ejpam-5734	117	1	⋃	⋃	VERB
ejpam-5734	117	2	a∈c	a∈c	VERB
ejpam-5734	117	3	a	a	DET
ejpam-5734	117	4	=	=	SYM
ejpam-5734	117	5	v	v	NOUN
ejpam-5734	117	6	(	(	PUNCT
ejpam-5734	117	7	g	g	NOUN
ejpam-5734	117	8	)	)	PUNCT
ejpam-5734	117	9	and	and	CCONJ
ejpam-5734	117	10	∑	∑	ADP
ejpam-5734	117	11	a∈c	a∈c	PROPN
ejpam-5734	117	12	|a|	|a|	PROPN
ejpam-5734	117	13	=	=	PROPN
ejpam-5734	117	14	|v	|v	PROPN
ejpam-5734	117	15	(	(	PUNCT
ejpam-5734	117	16	g)|	g)|	PROPN
ejpam-5734	117	17	,	,	PUNCT
ejpam-5734	117	18	2	2	NUM
ejpam-5734	117	19	.	.	X
ejpam-5734	117	20	a	a	DET
ejpam-5734	117	21	∩a′	∩a′	NOUN
ejpam-5734	117	22	=	=	NOUN
ejpam-5734	117	23	∅	∅	NOUN
ejpam-5734	117	24	for	for	ADP
ejpam-5734	117	25	every	every	DET
ejpam-5734	117	26	a	a	NOUN
ejpam-5734	117	27	,	,	PUNCT
ejpam-5734	117	28	a′	a′	PROPN
ejpam-5734	117	29	∈	∈	PROPN
ejpam-5734	117	30	c	c	PROPN
ejpam-5734	117	31	,	,	PUNCT
ejpam-5734	117	32	a	a	DET
ejpam-5734	117	33	=	=	NOUN
ejpam-5734	117	34	̸	̸	NUM
ejpam-5734	117	35	a′.	a′.	NOUN
ejpam-5734	117	36	m.	m.	NOUN
ejpam-5734	117	37	f.	f.	PROPN
ejpam-5734	117	38	libao	libao	PROPN
ejpam-5734	117	39	,	,	PUNCT
ejpam-5734	117	40	k.	k.	PROPN
ejpam-5734	117	41	b.	b.	PROPN
ejpam-5734	117	42	abarca	abarca	PROPN
ejpam-5734	117	43	/	/	SYM
ejpam-5734	117	44	eur	eur	PROPN
ejpam-5734	117	45	.	.	PUNCT
ejpam-5734	118	1	j.	j.	PROPN
ejpam-5734	118	2	pure	pure	PROPN
ejpam-5734	118	3	appl	appl	PROPN
ejpam-5734	118	4	.	.	PROPN
ejpam-5734	118	5	math	math	PROPN
ejpam-5734	118	6	,	,	PUNCT
ejpam-5734	118	7	18	18	NUM
ejpam-5734	118	8	(	(	PUNCT
ejpam-5734	118	9	2	2	NUM
ejpam-5734	118	10	)	)	PUNCT
ejpam-5734	118	11	(	(	PUNCT
ejpam-5734	118	12	2025	2025	NUM
ejpam-5734	118	13	)	)	PUNCT
ejpam-5734	118	14	,	,	PUNCT
ejpam-5734	118	15	5734	5734	NUM
ejpam-5734	118	16	7	7	NUM
ejpam-5734	118	17	of	of	ADP
ejpam-5734	118	18	25	25	NUM
ejpam-5734	118	19	proof	proof	NOUN
ejpam-5734	118	20	.	.	PUNCT
ejpam-5734	119	1	(	(	PUNCT
ejpam-5734	119	2	⇒	⇒	PROPN
ejpam-5734	119	3	)	)	PUNCT
ejpam-5734	119	4	assume	assume	VERB
ejpam-5734	120	1	that⋃	that⋃	PROPN
ejpam-5734	120	2	a∈c	a∈c	PROPN
ejpam-5734	120	3	a	a	DET
ejpam-5734	120	4	=	=	SYM
ejpam-5734	120	5	v	v	X
ejpam-5734	120	6	(	(	PUNCT
ejpam-5734	120	7	g	g	NOUN
ejpam-5734	120	8	)	)	PUNCT
ejpam-5734	120	9	and	and	CCONJ
ejpam-5734	120	10	∑	∑	ADP
ejpam-5734	120	11	a∈c	a∈c	PROPN
ejpam-5734	120	12	|a|	|a|	PROPN
ejpam-5734	120	13	=	=	PROPN
ejpam-5734	120	14	|v	|v	PROPN
ejpam-5734	120	15	(	(	PUNCT
ejpam-5734	120	16	g)|	g)|	NOUN
ejpam-5734	120	17	.	.	PUNCT
ejpam-5734	121	1	if	if	SCONJ
ejpam-5734	121	2	there	there	PRON
ejpam-5734	121	3	exists	exist	VERB
ejpam-5734	121	4	a	a	PRON
ejpam-5734	121	5	,	,	PUNCT
ejpam-5734	121	6	a′	a′	PROPN
ejpam-5734	121	7	∈	∈	PROPN
ejpam-5734	121	8	c	c	PROPN
ejpam-5734	121	9	,	,	PUNCT
ejpam-5734	121	10	a	a	DET
ejpam-5734	121	11	̸=	̸=	PROPN
ejpam-5734	121	12	a′	a′	VERB
ejpam-5734	121	13	such	such	DET
ejpam-5734	121	14	that	that	SCONJ
ejpam-5734	121	15	a	a	DET
ejpam-5734	121	16	∩	∩	NOUN
ejpam-5734	121	17	a′	a′	PROPN
ejpam-5734	121	18	̸=	̸=	PROPN
ejpam-5734	121	19	∅	∅	NOUN
ejpam-5734	121	20	,	,	PUNCT
ejpam-5734	121	21	then	then	ADV
ejpam-5734	121	22	at	at	ADV
ejpam-5734	121	23	least	least	ADV
ejpam-5734	121	24	one	one	NUM
ejpam-5734	121	25	vertex	vertex	NOUN
ejpam-5734	121	26	is	be	AUX
ejpam-5734	121	27	counted	count	VERB
ejpam-5734	121	28	more	more	ADJ
ejpam-5734	121	29	than	than	ADP
ejpam-5734	121	30	once	once	ADV
ejpam-5734	121	31	in	in	ADP
ejpam-5734	121	32	the	the	DET
ejpam-5734	121	33	sum	sum	NOUN
ejpam-5734	121	34	∑	∑	PUNCT
ejpam-5734	121	35	|a|	|a|	PROPN
ejpam-5734	121	36	,	,	PUNCT
ejpam-5734	121	37	contradicting	contradict	VERB
ejpam-5734	121	38	the	the	DET
ejpam-5734	121	39	assumption	assumption	NOUN
ejpam-5734	121	40	that	that	SCONJ
ejpam-5734	121	41	this	this	DET
ejpam-5734	121	42	sum	sum	NOUN
ejpam-5734	121	43	equals	equal	VERB
ejpam-5734	121	44	|v	|v	PROPN
ejpam-5734	121	45	(	(	PUNCT
ejpam-5734	121	46	g)|	g)|	PROPN
ejpam-5734	121	47	.	.	PUNCT
ejpam-5734	122	1	therefore	therefore	ADV
ejpam-5734	122	2	,	,	PUNCT
ejpam-5734	122	3	the	the	DET
ejpam-5734	122	4	color	color	NOUN
ejpam-5734	122	5	classes	class	NOUN
ejpam-5734	122	6	must	must	AUX
ejpam-5734	122	7	be	be	AUX
ejpam-5734	122	8	pairwise	pairwise	NOUN
ejpam-5734	122	9	disjoint	disjoint	NOUN
ejpam-5734	122	10	:	:	PUNCT
ejpam-5734	122	11	a	a	DET
ejpam-5734	122	12	∩a′	∩a′	X
ejpam-5734	122	13	=	=	X
ejpam-5734	122	14	∅.	∅.	X
ejpam-5734	122	15	(	(	PUNCT
ejpam-5734	122	16	⇐	⇐	ADJ
ejpam-5734	122	17	)	)	PUNCT
ejpam-5734	122	18	assume	assume	VERB
ejpam-5734	122	19	that	that	SCONJ
ejpam-5734	122	20	a	a	DET
ejpam-5734	122	21	∩	∩	NOUN
ejpam-5734	122	22	a′	a′	NOUN
ejpam-5734	122	23	=	=	SYM
ejpam-5734	122	24	∅	∅	NOUN
ejpam-5734	122	25	for	for	ADP
ejpam-5734	122	26	all	all	DET
ejpam-5734	122	27	a	a	DET
ejpam-5734	122	28	=	=	NOUN
ejpam-5734	122	29	̸	̸	NUM
ejpam-5734	122	30	a′	a′	PROPN
ejpam-5734	122	31	,	,	PUNCT
ejpam-5734	122	32	and	and	CCONJ
ejpam-5734	122	33	that	that	SCONJ
ejpam-5734	122	34	⋃	⋃	PUNCT
ejpam-5734	122	35	a∈c	a∈c	NOUN
ejpam-5734	122	36	a	a	DET
ejpam-5734	122	37	=	=	SYM
ejpam-5734	122	38	v	v	NOUN
ejpam-5734	122	39	(	(	PUNCT
ejpam-5734	122	40	g	g	NOUN
ejpam-5734	122	41	)	)	PUNCT
ejpam-5734	122	42	.	.	PUNCT
ejpam-5734	123	1	since	since	SCONJ
ejpam-5734	123	2	the	the	DET
ejpam-5734	123	3	color	color	NOUN
ejpam-5734	123	4	classes	class	NOUN
ejpam-5734	123	5	are	be	AUX
ejpam-5734	123	6	disjoint	disjoint	ADJ
ejpam-5734	123	7	,	,	PUNCT
ejpam-5734	123	8	each	each	DET
ejpam-5734	123	9	vertex	vertex	NOUN
ejpam-5734	123	10	in	in	ADP
ejpam-5734	123	11	v	v	NOUN
ejpam-5734	123	12	(	(	PUNCT
ejpam-5734	123	13	g	g	NOUN
ejpam-5734	123	14	)	)	PUNCT
ejpam-5734	123	15	appears	appear	VERB
ejpam-5734	123	16	exactly	exactly	ADV
ejpam-5734	123	17	once	once	ADV
ejpam-5734	123	18	across	across	ADV
ejpam-5734	123	19	all	all	PRON
ejpam-5734	123	20	ai	ai	VERB
ejpam-5734	123	21	,	,	PUNCT
ejpam-5734	123	22	so	so	ADV
ejpam-5734	123	23	|v	|v	PROPN
ejpam-5734	123	24	(	(	PUNCT
ejpam-5734	123	25	g)|	g)|	NOUN
ejpam-5734	123	26	=	=	PUNCT
ejpam-5734	123	27	∑	∑	PROPN
ejpam-5734	123	28	a∈c	a∈c	PROPN
ejpam-5734	123	29	|a|	|a|	PROPN
ejpam-5734	123	30	.	.	PROPN
ejpam-5734	123	31	thus	thus	ADV
ejpam-5734	123	32	,	,	PUNCT
ejpam-5734	123	33	the	the	DET
ejpam-5734	123	34	two	two	NUM
ejpam-5734	123	35	conditions	condition	NOUN
ejpam-5734	123	36	are	be	AUX
ejpam-5734	123	37	equivalent	equivalent	ADJ
ejpam-5734	123	38	.	.	PUNCT
ejpam-5734	124	1	example	example	NOUN
ejpam-5734	125	1	10	10	NUM
ejpam-5734	125	2	.	.	PUNCT
ejpam-5734	126	1	from	from	ADP
ejpam-5734	126	2	example	example	NOUN
ejpam-5734	126	3	8	8	NUM
ejpam-5734	126	4	,	,	PUNCT
ejpam-5734	126	5	let	let	VERB
ejpam-5734	126	6	c={a1	c={a1	NOUN
ejpam-5734	126	7	,	,	PUNCT
ejpam-5734	126	8	a2	a2	PROPN
ejpam-5734	126	9	,	,	PUNCT
ejpam-5734	126	10	a3	a3	NOUN
ejpam-5734	126	11	,	,	PUNCT
ejpam-5734	126	12	a4	a4	PROPN
ejpam-5734	126	13	}	}	PUNCT
ejpam-5734	126	14	.	.	PUNCT
ejpam-5734	127	1	i.	i.	PROPN
ejpam-5734	127	2	to	to	PART
ejpam-5734	127	3	check	check	VERB
ejpam-5734	127	4	whether	whether	SCONJ
ejpam-5734	127	5	every	every	DET
ejpam-5734	127	6	vertex	vertex	NOUN
ejpam-5734	127	7	in	in	ADP
ejpam-5734	127	8	the	the	DET
ejpam-5734	127	9	graph	graph	NOUN
ejpam-5734	127	10	belongs	belong	VERB
ejpam-5734	127	11	to	to	ADP
ejpam-5734	127	12	exactly	exactly	ADV
ejpam-5734	127	13	one	one	NUM
ejpam-5734	127	14	color	color	NOUN
ejpam-5734	127	15	class,⋃	class,⋃	NOUN
ejpam-5734	127	16	a∈c	a∈c	VERB
ejpam-5734	127	17	a	a	PRON
ejpam-5734	127	18	=	=	X
ejpam-5734	127	19	{	{	PUNCT
ejpam-5734	127	20	a1,a2,a3,a4	a1,a2,a3,a4	PROPN
ejpam-5734	127	21	}	}	PUNCT
ejpam-5734	127	22	=	=	SYM
ejpam-5734	127	23	{	{	PUNCT
ejpam-5734	127	24	a1	a1	PROPN
ejpam-5734	127	25	}	}	PUNCT
ejpam-5734	127	26	∪	∪	ADJ
ejpam-5734	127	27	{	{	PUNCT
ejpam-5734	127	28	a2	a2	NOUN
ejpam-5734	127	29	}	}	PUNCT
ejpam-5734	127	30	∪	∪	NOUN
ejpam-5734	127	31	{	{	PUNCT
ejpam-5734	127	32	a3	a3	NOUN
ejpam-5734	127	33	}	}	PUNCT
ejpam-5734	127	34	∪	∪	NOUN
ejpam-5734	127	35	{	{	PUNCT
ejpam-5734	127	36	a4	a4	NOUN
ejpam-5734	127	37	}	}	PUNCT
ejpam-5734	127	38	=	=	SYM
ejpam-5734	127	39	{	{	PUNCT
ejpam-5734	127	40	v1	v1	NOUN
ejpam-5734	127	41	}	}	PUNCT
ejpam-5734	127	42	∪	∪	X
ejpam-5734	127	43	{	{	PUNCT
ejpam-5734	127	44	v2	v2	NOUN
ejpam-5734	127	45	,	,	PUNCT
ejpam-5734	127	46	v5	v5	NOUN
ejpam-5734	127	47	}	}	PUNCT
ejpam-5734	127	48	∪	∪	NOUN
ejpam-5734	127	49	{	{	PUNCT
ejpam-5734	127	50	v3	v3	PROPN
ejpam-5734	127	51	}	}	PUNCT
ejpam-5734	127	52	∪	∪	NOUN
ejpam-5734	127	53	{	{	PUNCT
ejpam-5734	127	54	v4	v4	NOUN
ejpam-5734	127	55	}	}	PUNCT
ejpam-5734	127	56	=	=	SYM
ejpam-5734	127	57	{	{	PUNCT
ejpam-5734	127	58	v1	v1	PROPN
ejpam-5734	127	59	,	,	PUNCT
ejpam-5734	127	60	v2	v2	PROPN
ejpam-5734	127	61	,	,	PUNCT
ejpam-5734	127	62	v3	v3	PROPN
ejpam-5734	127	63	,	,	PUNCT
ejpam-5734	127	64	v4	v4	PROPN
ejpam-5734	127	65	,	,	PUNCT
ejpam-5734	127	66	v5	v5	NOUN
ejpam-5734	127	67	}	}	PUNCT
ejpam-5734	127	68	=	=	SYM
ejpam-5734	127	69	v	v	NOUN
ejpam-5734	127	70	(	(	PUNCT
ejpam-5734	127	71	d2(cn	d2(cn	NOUN
ejpam-5734	127	72	)	)	PUNCT
ejpam-5734	127	73	)	)	PUNCT
ejpam-5734	127	74	ii	ii	PROPN
ejpam-5734	127	75	.	.	PUNCT
ejpam-5734	128	1	to	to	PART
ejpam-5734	128	2	verify	verify	VERB
ejpam-5734	128	3	that	that	SCONJ
ejpam-5734	128	4	the	the	DET
ejpam-5734	128	5	color	color	NOUN
ejpam-5734	128	6	classes	class	NOUN
ejpam-5734	128	7	ak	ak	PROPN
ejpam-5734	128	8	are	be	AUX
ejpam-5734	128	9	mutually	mutually	ADV
ejpam-5734	128	10	exclusive	exclusive	ADJ
ejpam-5734	128	11	,	,	PUNCT
ejpam-5734	128	12	we	we	PRON
ejpam-5734	128	13	examine	examine	VERB
ejpam-5734	128	14	the	the	DET
ejpam-5734	128	15	total	total	ADJ
ejpam-5734	128	16	number	number	NOUN
ejpam-5734	128	17	of	of	ADP
ejpam-5734	128	18	assigned	assign	VERB
ejpam-5734	128	19	vertices	vertex	NOUN
ejpam-5734	128	20	.	.	PUNCT
ejpam-5734	129	1	the	the	DET
ejpam-5734	129	2	following	follow	VERB
ejpam-5734	129	3	equations	equation	NOUN
ejpam-5734	129	4	confirm	confirm	VERB
ejpam-5734	129	5	that	that	SCONJ
ejpam-5734	129	6	each	each	DET
ejpam-5734	129	7	vertex	vertex	NOUN
ejpam-5734	129	8	in	in	ADP
ejpam-5734	129	9	v	v	NOUN
ejpam-5734	129	10	[	[	X
ejpam-5734	129	11	g	g	X
ejpam-5734	129	12	]	]	PUNCT
ejpam-5734	129	13	is	be	AUX
ejpam-5734	129	14	uniquely	uniquely	ADV
ejpam-5734	129	15	assigned	assign	VERB
ejpam-5734	129	16	to	to	ADP
ejpam-5734	129	17	one	one	NUM
ejpam-5734	129	18	color	color	NOUN
ejpam-5734	129	19	class	class	NOUN
ejpam-5734	129	20	,	,	PUNCT
ejpam-5734	129	21	ensuring	ensure	VERB
ejpam-5734	129	22	a	a	DET
ejpam-5734	129	23	proper	proper	ADJ
ejpam-5734	129	24	partition	partition	NOUN
ejpam-5734	129	25	of	of	ADP
ejpam-5734	129	26	the	the	DET
ejpam-5734	129	27	graph.∑	graph.∑	NOUN
ejpam-5734	129	28	a∈c	a∈c	PROPN
ejpam-5734	129	29	|a|	|a|	PROPN
ejpam-5734	129	30	=	=	PUNCT
ejpam-5734	129	31	|a1|+	|a1|+	PROPN
ejpam-5734	129	32	|a2|+	|a2|+	X
ejpam-5734	129	33	|a3|+	|a3|+	X
ejpam-5734	129	34	|a4|	|a4|	NOUN
ejpam-5734	129	35	=	=	SYM
ejpam-5734	129	36	1	1	NUM
ejpam-5734	129	37	+	+	NUM
ejpam-5734	129	38	2	2	NUM
ejpam-5734	129	39	+	+	SYM
ejpam-5734	129	40	1	1	NUM
ejpam-5734	129	41	+	+	SYM
ejpam-5734	129	42	1	1	NUM
ejpam-5734	129	43	=	=	SYM
ejpam-5734	129	44	5	5	NUM
ejpam-5734	129	45	=	=	SYM
ejpam-5734	129	46	|v	|v	X
ejpam-5734	129	47	(	(	PUNCT
ejpam-5734	129	48	g)|	g)|	VERB
ejpam-5734	129	49	by	by	ADP
ejpam-5734	129	50	lemma	lemma	PROPN
ejpam-5734	129	51	1	1	NUM
ejpam-5734	129	52	,	,	PUNCT
ejpam-5734	129	53	a	a	DET
ejpam-5734	129	54	∩a′	∩a′	X
ejpam-5734	129	55	=	=	X
ejpam-5734	129	56	∅.	∅.	NOUN
ejpam-5734	129	57	thus	thus	ADV
ejpam-5734	129	58	,	,	PUNCT
ejpam-5734	129	59	c	c	PROPN
ejpam-5734	129	60	is	be	AUX
ejpam-5734	129	61	a	a	DET
ejpam-5734	129	62	distance-2	distance-2	CCONJ
ejpam-5734	129	63	chromatic	chromatic	ADJ
ejpam-5734	129	64	set	set	NOUN
ejpam-5734	129	65	.	.	PUNCT
ejpam-5734	130	1	m.	m.	PROPN
ejpam-5734	130	2	f.	f.	PROPN
ejpam-5734	130	3	libao	libao	PROPN
ejpam-5734	130	4	,	,	PUNCT
ejpam-5734	130	5	k.	k.	PROPN
ejpam-5734	130	6	b.	b.	PROPN
ejpam-5734	130	7	abarca	abarca	PROPN
ejpam-5734	130	8	/	/	SYM
ejpam-5734	130	9	eur	eur	PROPN
ejpam-5734	130	10	.	.	PUNCT
ejpam-5734	131	1	j.	j.	PROPN
ejpam-5734	131	2	pure	pure	PROPN
ejpam-5734	131	3	appl	appl	PROPN
ejpam-5734	131	4	.	.	PROPN
ejpam-5734	131	5	math	math	PROPN
ejpam-5734	131	6	,	,	PUNCT
ejpam-5734	131	7	18	18	NUM
ejpam-5734	131	8	(	(	PUNCT
ejpam-5734	131	9	2	2	NUM
ejpam-5734	131	10	)	)	PUNCT
ejpam-5734	131	11	(	(	PUNCT
ejpam-5734	131	12	2025	2025	NUM
ejpam-5734	131	13	)	)	PUNCT
ejpam-5734	131	14	,	,	PUNCT
ejpam-5734	131	15	5734	5734	NUM
ejpam-5734	131	16	8	8	NUM
ejpam-5734	131	17	of	of	ADP
ejpam-5734	131	18	25	25	NUM
ejpam-5734	131	19	definition	definition	NOUN
ejpam-5734	131	20	3.3	3.3	NUM
ejpam-5734	131	21	(	(	PUNCT
ejpam-5734	131	22	distance-2	distance-2	VERB
ejpam-5734	131	23	chromatic	chromatic	ADJ
ejpam-5734	131	24	number	number	NOUN
ejpam-5734	131	25	)	)	PUNCT
ejpam-5734	131	26	.	.	PUNCT
ejpam-5734	132	1	the	the	DET
ejpam-5734	132	2	distance-2	distance-2	NUM
ejpam-5734	132	3	chromatic	chromatic	ADJ
ejpam-5734	132	4	number	number	NOUN
ejpam-5734	132	5	,	,	PUNCT
ejpam-5734	132	6	denoted	denote	VERB
ejpam-5734	132	7	by	by	ADP
ejpam-5734	132	8	χ2(g	χ2(g	NOUN
ejpam-5734	132	9	)	)	PUNCT
ejpam-5734	132	10	,	,	PUNCT
ejpam-5734	132	11	is	be	AUX
ejpam-5734	132	12	the	the	DET
ejpam-5734	132	13	minimum	minimum	ADJ
ejpam-5734	132	14	cardinality	cardinality	NOUN
ejpam-5734	132	15	of	of	ADP
ejpam-5734	132	16	a	a	DET
ejpam-5734	132	17	distance-2	distance-2	CCONJ
ejpam-5734	132	18	chromatic	chromatic	ADJ
ejpam-5734	132	19	set	set	NOUN
ejpam-5734	132	20	for	for	ADP
ejpam-5734	132	21	the	the	DET
ejpam-5734	132	22	graph	graph	NOUN
ejpam-5734	132	23	g.	g.	NOUN
ejpam-5734	132	24	in	in	ADP
ejpam-5734	132	25	other	other	ADJ
ejpam-5734	132	26	words	word	NOUN
ejpam-5734	132	27	,	,	PUNCT
ejpam-5734	132	28	χ2(g	χ2(g	NUM
ejpam-5734	132	29	)	)	PUNCT
ejpam-5734	132	30	represents	represent	VERB
ejpam-5734	132	31	the	the	DET
ejpam-5734	132	32	smallest	small	ADJ
ejpam-5734	132	33	number	number	NOUN
ejpam-5734	132	34	of	of	ADP
ejpam-5734	132	35	colors	color	NOUN
ejpam-5734	132	36	needed	need	VERB
ejpam-5734	132	37	to	to	PART
ejpam-5734	132	38	achieve	achieve	VERB
ejpam-5734	132	39	a	a	DET
ejpam-5734	132	40	valid	valid	ADJ
ejpam-5734	132	41	distance-2	distance-2	ADJ
ejpam-5734	132	42	coloring	coloring	NOUN
ejpam-5734	132	43	of	of	ADP
ejpam-5734	132	44	the	the	DET
ejpam-5734	132	45	graph	graph	NOUN
ejpam-5734	132	46	,	,	PUNCT
ejpam-5734	132	47	that	that	ADV
ejpam-5734	132	48	is	is	ADV
ejpam-5734	132	49	,	,	PUNCT
ejpam-5734	132	50	χ2(g	χ2(g	NUM
ejpam-5734	132	51	)	)	PUNCT
ejpam-5734	133	1	=	=	SYM
ejpam-5734	133	2	min{|c	min{|c	PROPN
ejpam-5734	134	1	|	|	ADV
ejpam-5734	134	2	:	:	PUNCT
ejpam-5734	134	3	c	c	NOUN
ejpam-5734	134	4	is	be	AUX
ejpam-5734	134	5	a	a	DET
ejpam-5734	134	6	distance-2	distance-2	CCONJ
ejpam-5734	134	7	chromatic	chromatic	ADJ
ejpam-5734	134	8	set	set	NOUN
ejpam-5734	134	9	}	}	PUNCT
ejpam-5734	134	10	.	.	PUNCT
ejpam-5734	135	1	example	example	NOUN
ejpam-5734	136	1	11	11	NUM
ejpam-5734	136	2	.	.	PUNCT
ejpam-5734	137	1	in	in	ADP
ejpam-5734	137	2	the	the	DET
ejpam-5734	137	3	previous	previous	ADJ
ejpam-5734	137	4	example	example	NOUN
ejpam-5734	137	5	,	,	PUNCT
ejpam-5734	137	6	|c	|c	ADJ
ejpam-5734	137	7	|	|	NOUN
ejpam-5734	137	8	=	=	NOUN
ejpam-5734	137	9	4	4	X
ejpam-5734	137	10	.	.	PUNCT
ejpam-5734	137	11	to	to	PART
ejpam-5734	137	12	determine	determine	VERB
ejpam-5734	137	13	whether	whether	SCONJ
ejpam-5734	137	14	χ2(g	χ2(g	NOUN
ejpam-5734	137	15	)	)	PUNCT
ejpam-5734	137	16	=	=	SYM
ejpam-5734	137	17	4	4	NUM
ejpam-5734	137	18	,	,	PUNCT
ejpam-5734	137	19	we	we	PRON
ejpam-5734	137	20	must	must	AUX
ejpam-5734	137	21	show	show	VERB
ejpam-5734	137	22	that	that	SCONJ
ejpam-5734	137	23	there	there	PRON
ejpam-5734	137	24	is	be	VERB
ejpam-5734	137	25	no	no	DET
ejpam-5734	137	26	|c	|c	ADJ
ejpam-5734	137	27	|	|	NOUN
ejpam-5734	137	28	<	<	X
ejpam-5734	137	29	4	4	NUM
ejpam-5734	137	30	.	.	PUNCT
ejpam-5734	138	1	let	let	VERB
ejpam-5734	138	2	us	we	PRON
ejpam-5734	138	3	try	try	VERB
ejpam-5734	138	4	a	a	DET
ejpam-5734	138	5	set	set	NOUN
ejpam-5734	138	6	of	of	ADP
ejpam-5734	138	7	3	3	NUM
ejpam-5734	138	8	color	color	NOUN
ejpam-5734	138	9	classes	class	NOUN
ejpam-5734	138	10	,	,	PUNCT
ejpam-5734	138	11	say	say	VERB
ejpam-5734	138	12	c={a1	c={a1	NOUN
ejpam-5734	138	13	,	,	PUNCT
ejpam-5734	138	14	a2	a2	PROPN
ejpam-5734	138	15	,	,	PUNCT
ejpam-5734	138	16	a3	a3	NOUN
ejpam-5734	138	17	}	}	PUNCT
ejpam-5734	138	18	.	.	PUNCT
ejpam-5734	139	1	assign	assign	VERB
ejpam-5734	139	2	a1	a1	NOUN
ejpam-5734	139	3	to	to	ADP
ejpam-5734	139	4	v4	v4	NOUN
ejpam-5734	139	5	,	,	PUNCT
ejpam-5734	139	6	d(v4	d(v4	NOUN
ejpam-5734	139	7	,	,	PUNCT
ejpam-5734	139	8	v1)=1	v1)=1	PROPN
ejpam-5734	139	9	,	,	PUNCT
ejpam-5734	139	10	a	a	DET
ejpam-5734	139	11	violation	violation	NOUN
ejpam-5734	139	12	.	.	PUNCT
ejpam-5734	140	1	next	next	ADV
ejpam-5734	140	2	,	,	PUNCT
ejpam-5734	140	3	we	we	PRON
ejpam-5734	140	4	try	try	VERB
ejpam-5734	140	5	to	to	PART
ejpam-5734	140	6	assign	assign	VERB
ejpam-5734	140	7	a2	a2	PROPN
ejpam-5734	140	8	to	to	ADP
ejpam-5734	140	9	v4	v4	PROPN
ejpam-5734	140	10	,	,	PUNCT
ejpam-5734	140	11	d(v4	d(v4	NOUN
ejpam-5734	140	12	,	,	PUNCT
ejpam-5734	140	13	v2	v2	PROPN
ejpam-5734	140	14	)	)	PUNCT
ejpam-5734	140	15	=	=	SYM
ejpam-5734	140	16	2	2	NUM
ejpam-5734	140	17	and	and	CCONJ
ejpam-5734	140	18	d(v4	d(v4	NOUN
ejpam-5734	140	19	,	,	PUNCT
ejpam-5734	140	20	v5)=1	v5)=1	ADV
ejpam-5734	140	21	,	,	PUNCT
ejpam-5734	140	22	also	also	ADV
ejpam-5734	140	23	a	a	DET
ejpam-5734	140	24	violation	violation	NOUN
ejpam-5734	140	25	.	.	PUNCT
ejpam-5734	141	1	we	we	PRON
ejpam-5734	141	2	can	can	AUX
ejpam-5734	141	3	not	not	PART
ejpam-5734	141	4	assign	assign	VERB
ejpam-5734	141	5	a3	a3	NOUN
ejpam-5734	141	6	to	to	ADP
ejpam-5734	141	7	v4	v4	PROPN
ejpam-5734	141	8	since	since	SCONJ
ejpam-5734	141	9	d(v4	d(v4	NOUN
ejpam-5734	141	10	,	,	PUNCT
ejpam-5734	141	11	v3	v3	PROPN
ejpam-5734	141	12	)	)	PUNCT
ejpam-5734	141	13	=	=	SYM
ejpam-5734	142	1	1	1	X
ejpam-5734	142	2	.	.	X
ejpam-5734	142	3	note	note	VERB
ejpam-5734	142	4	that	that	SCONJ
ejpam-5734	142	5	to	to	PART
ejpam-5734	142	6	satisfy	satisfy	VERB
ejpam-5734	142	7	the	the	DET
ejpam-5734	142	8	distance	distance	NOUN
ejpam-5734	142	9	2	2	NUM
ejpam-5734	142	10	coloring	coloring	NOUN
ejpam-5734	142	11	,	,	PUNCT
ejpam-5734	142	12	every	every	DET
ejpam-5734	142	13	u	u	NOUN
ejpam-5734	142	14	,	,	PUNCT
ejpam-5734	142	15	v	v	ADP
ejpam-5734	142	16	∈	∈	PROPN
ejpam-5734	142	17	a	a	PRON
ejpam-5734	142	18	,	,	PUNCT
ejpam-5734	142	19	d(u	d(u	PROPN
ejpam-5734	142	20	,	,	PUNCT
ejpam-5734	142	21	v	v	NOUN
ejpam-5734	142	22	)	)	PUNCT
ejpam-5734	142	23	≥	≥	NOUN
ejpam-5734	142	24	3	3	NUM
ejpam-5734	142	25	.	.	PUNCT
ejpam-5734	142	26	thus	thus	ADV
ejpam-5734	142	27	,	,	PUNCT
ejpam-5734	142	28	χ2(g	χ2(g	NUM
ejpam-5734	142	29	)	)	PUNCT
ejpam-5734	142	30	=	=	SYM
ejpam-5734	142	31	4	4	X
ejpam-5734	142	32	.	.	PUNCT
ejpam-5734	143	1	these	these	DET
ejpam-5734	143	2	definitions	definition	NOUN
ejpam-5734	143	3	,	,	PUNCT
ejpam-5734	143	4	along	along	ADP
ejpam-5734	143	5	with	with	ADP
ejpam-5734	143	6	the	the	DET
ejpam-5734	143	7	supporting	support	VERB
ejpam-5734	143	8	lemma	lemma	PROPN
ejpam-5734	143	9	on	on	ADP
ejpam-5734	143	10	the	the	DET
ejpam-5734	143	11	distance-2	distance-2	NUM
ejpam-5734	143	12	chromatic	chromatic	ADJ
ejpam-5734	143	13	set	set	NOUN
ejpam-5734	143	14	,	,	PUNCT
ejpam-5734	143	15	provide	provide	VERB
ejpam-5734	143	16	the	the	DET
ejpam-5734	143	17	necessary	necessary	ADJ
ejpam-5734	143	18	foundation	foundation	NOUN
ejpam-5734	143	19	for	for	ADP
ejpam-5734	143	20	analyzing	analyze	VERB
ejpam-5734	143	21	and	and	CCONJ
ejpam-5734	143	22	proving	prove	VERB
ejpam-5734	143	23	results	result	NOUN
ejpam-5734	143	24	involving	involve	VERB
ejpam-5734	143	25	the	the	DET
ejpam-5734	143	26	distance2	distance2	NOUN
ejpam-5734	143	27	chromatic	chromatic	ADJ
ejpam-5734	143	28	number	number	NOUN
ejpam-5734	143	29	of	of	ADP
ejpam-5734	143	30	graphs	graph	NOUN
ejpam-5734	143	31	.	.	PUNCT
ejpam-5734	144	1	by	by	ADP
ejpam-5734	144	2	formally	formally	ADV
ejpam-5734	144	3	introducing	introduce	VERB
ejpam-5734	144	4	the	the	DET
ejpam-5734	144	5	concepts	concept	NOUN
ejpam-5734	144	6	of	of	ADP
ejpam-5734	144	7	distance-2	distance-2	NUM
ejpam-5734	144	8	color	color	NOUN
ejpam-5734	144	9	class	class	NOUN
ejpam-5734	144	10	,	,	PUNCT
ejpam-5734	144	11	distance-2	distance-2	NUM
ejpam-5734	144	12	chromatic	chromatic	ADJ
ejpam-5734	144	13	set	set	NOUN
ejpam-5734	144	14	,	,	PUNCT
ejpam-5734	144	15	and	and	CCONJ
ejpam-5734	144	16	distance-2	distance-2	PRON
ejpam-5734	144	17	chromatic	chromatic	ADJ
ejpam-5734	144	18	number	number	NOUN
ejpam-5734	144	19	,	,	PUNCT
ejpam-5734	144	20	we	we	PRON
ejpam-5734	144	21	build	build	VERB
ejpam-5734	144	22	a	a	DET
ejpam-5734	144	23	coherent	coherent	ADJ
ejpam-5734	144	24	framework	framework	NOUN
ejpam-5734	144	25	that	that	PRON
ejpam-5734	144	26	captures	capture	VERB
ejpam-5734	144	27	vertex	vertex	NOUN
ejpam-5734	144	28	interactions	interaction	NOUN
ejpam-5734	144	29	beyond	beyond	ADP
ejpam-5734	144	30	immediate	immediate	ADJ
ejpam-5734	144	31	adjacency	adjacency	NOUN
ejpam-5734	144	32	.	.	PUNCT
ejpam-5734	145	1	this	this	DET
ejpam-5734	145	2	framework	framework	NOUN
ejpam-5734	145	3	is	be	AUX
ejpam-5734	145	4	essential	essential	ADJ
ejpam-5734	145	5	in	in	ADP
ejpam-5734	145	6	guiding	guide	VERB
ejpam-5734	145	7	the	the	DET
ejpam-5734	145	8	construction	construction	NOUN
ejpam-5734	145	9	of	of	ADP
ejpam-5734	145	10	proofs	proof	NOUN
ejpam-5734	145	11	,	,	PUNCT
ejpam-5734	145	12	particularly	particularly	ADV
ejpam-5734	145	13	in	in	ADP
ejpam-5734	145	14	ensuring	ensure	VERB
ejpam-5734	145	15	that	that	SCONJ
ejpam-5734	145	16	no	no	DET
ejpam-5734	145	17	two	two	NUM
ejpam-5734	145	18	vertices	vertex	NOUN
ejpam-5734	145	19	within	within	ADP
ejpam-5734	145	20	a	a	DET
ejpam-5734	145	21	distance	distance	NOUN
ejpam-5734	145	22	of	of	ADP
ejpam-5734	145	23	two	two	NUM
ejpam-5734	145	24	share	share	NOUN
ejpam-5734	145	25	the	the	DET
ejpam-5734	145	26	same	same	ADJ
ejpam-5734	145	27	color	color	NOUN
ejpam-5734	145	28	,	,	PUNCT
ejpam-5734	145	29	aa	aa	PROPN
ejpam-5734	145	30	critical	critical	ADJ
ejpam-5734	145	31	requirement	requirement	NOUN
ejpam-5734	145	32	in	in	ADP
ejpam-5734	145	33	distance2	distance2	NOUN
ejpam-5734	145	34	coloring	color	VERB
ejpam-5734	145	35	that	that	SCONJ
ejpam-5734	145	36	traditional	traditional	ADJ
ejpam-5734	145	37	vertex	vertex	NOUN
ejpam-5734	145	38	coloring	coloring	NOUN
ejpam-5734	145	39	does	do	AUX
ejpam-5734	145	40	not	not	PART
ejpam-5734	145	41	address	address	VERB
ejpam-5734	145	42	.	.	PUNCT
ejpam-5734	146	1	4	4	X
ejpam-5734	146	2	.	.	X
ejpam-5734	146	3	main	main	ADJ
ejpam-5734	146	4	results	result	NOUN
ejpam-5734	146	5	4.1	4.1	NUM
ejpam-5734	146	6	.	.	PUNCT
ejpam-5734	147	1	distance-2	distance-2	VERB
ejpam-5734	147	2	chromatic	chromatic	ADJ
ejpam-5734	147	3	number	number	NOUN
ejpam-5734	147	4	of	of	ADP
ejpam-5734	147	5	the	the	DET
ejpam-5734	147	6	shadow	shadow	NOUN
ejpam-5734	147	7	graph	graph	NOUN
ejpam-5734	147	8	of	of	ADP
ejpam-5734	147	9	cycle	cycle	NOUN
ejpam-5734	147	10	graphs	graph	NOUN
ejpam-5734	147	11	,	,	PUNCT
ejpam-5734	147	12	d2(cn	d2(cn	PROPN
ejpam-5734	147	13	)	)	PUNCT
ejpam-5734	147	14	theorem	theorem	VERB
ejpam-5734	147	15	4.1.1	4.1.1	X
ejpam-5734	147	16	.	.	PUNCT
ejpam-5734	148	1	let	let	VERB
ejpam-5734	148	2	g	g	PRON
ejpam-5734	148	3	be	be	AUX
ejpam-5734	148	4	a	a	DET
ejpam-5734	148	5	cycle	cycle	NOUN
ejpam-5734	148	6	graph	graph	NOUN
ejpam-5734	148	7	,	,	PUNCT
ejpam-5734	148	8	cn	cn	PROPN
ejpam-5734	148	9	,	,	PUNCT
ejpam-5734	148	10	with	with	ADP
ejpam-5734	148	11	3	3	NUM
ejpam-5734	148	12	≤	≤	NOUN
ejpam-5734	148	13	n	n	PRON
ejpam-5734	148	14	≤	≤	NOUN
ejpam-5734	148	15	5	5	NUM
ejpam-5734	148	16	.	.	PUNCT
ejpam-5734	149	1	then	then	ADV
ejpam-5734	149	2	,	,	PUNCT
ejpam-5734	149	3	χ2[d2(cn	χ2[d2(cn	PROPN
ejpam-5734	149	4	)	)	PUNCT
ejpam-5734	149	5	]	]	PUNCT
ejpam-5734	150	1	=	=	SYM
ejpam-5734	150	2	2n	2n	NUM
ejpam-5734	150	3	.	.	PUNCT
ejpam-5734	151	1	proof	proof	NOUN
ejpam-5734	151	2	.	.	PUNCT
ejpam-5734	152	1	consider	consider	VERB
ejpam-5734	152	2	the	the	DET
ejpam-5734	152	3	cycle	cycle	NOUN
ejpam-5734	152	4	graph	graph	NOUN
ejpam-5734	152	5	cn	cn	VERB
ejpam-5734	152	6	with	with	ADP
ejpam-5734	152	7	3	3	NUM
ejpam-5734	152	8	≤	≤	NOUN
ejpam-5734	153	1	n	n	PRON
ejpam-5734	153	2	≤	≤	NOUN
ejpam-5734	153	3	5	5	NUM
ejpam-5734	153	4	.	.	PUNCT
ejpam-5734	154	1	let	let	VERB
ejpam-5734	154	2	v	v	X
ejpam-5734	154	3	(	(	PUNCT
ejpam-5734	154	4	cn	cn	PROPN
ejpam-5734	154	5	)	)	PUNCT
ejpam-5734	154	6	=	=	PRON
ejpam-5734	154	7	{	{	PUNCT
ejpam-5734	154	8	vi	vi	NOUN
ejpam-5734	154	9	|	|	ADV
ejpam-5734	154	10	1	1	NUM
ejpam-5734	154	11	≤	≤	NUM
ejpam-5734	154	12	i	i	PRON
ejpam-5734	154	13	≤	≤	PROPN
ejpam-5734	154	14	n	n	CCONJ
ejpam-5734	154	15	}	}	PUNCT
ejpam-5734	154	16	be	be	AUX
ejpam-5734	154	17	the	the	DET
ejpam-5734	154	18	set	set	NOUN
ejpam-5734	154	19	of	of	ADP
ejpam-5734	154	20	vertices	vertex	NOUN
ejpam-5734	154	21	of	of	ADP
ejpam-5734	154	22	g	g	NOUN
ejpam-5734	154	23	,	,	PUNCT
ejpam-5734	154	24	and	and	CCONJ
ejpam-5734	154	25	let	let	VERB
ejpam-5734	154	26	v	v	PART
ejpam-5734	154	27	′(cn	′(cn	VERB
ejpam-5734	154	28	)	)	PUNCT
ejpam-5734	155	1	=	=	PRON
ejpam-5734	155	2	{	{	PUNCT
ejpam-5734	155	3	v′i	v′i	INTJ
ejpam-5734	155	4	|	|	ADV
ejpam-5734	155	5	1	1	NUM
ejpam-5734	155	6	≤	≤	NUM
ejpam-5734	155	7	i	i	PRON
ejpam-5734	155	8	≤	≤	PROPN
ejpam-5734	155	9	n	n	CCONJ
ejpam-5734	155	10	}	}	PUNCT
ejpam-5734	155	11	be	be	AUX
ejpam-5734	155	12	the	the	DET
ejpam-5734	155	13	vertices	vertex	NOUN
ejpam-5734	155	14	of	of	ADP
ejpam-5734	155	15	the	the	DET
ejpam-5734	155	16	copy	copy	NOUN
ejpam-5734	155	17	of	of	ADP
ejpam-5734	155	18	g.	g.	PROPN
ejpam-5734	155	19	then	then	ADV
ejpam-5734	155	20	,	,	PUNCT
ejpam-5734	155	21	v	v	X
ejpam-5734	155	22	[	[	X
ejpam-5734	155	23	d2(cn	d2(cn	NOUN
ejpam-5734	155	24	)	)	PUNCT
ejpam-5734	155	25	]	]	PUNCT
ejpam-5734	156	1	=	=	PUNCT
ejpam-5734	156	2	{	{	PUNCT
ejpam-5734	156	3	vi	vi	NOUN
ejpam-5734	156	4	|	|	ADV
ejpam-5734	156	5	1	1	NUM
ejpam-5734	156	6	≤	≤	NUM
ejpam-5734	156	7	i	i	PRON
ejpam-5734	156	8	≤	≤	NOUN
ejpam-5734	156	9	n	n	CCONJ
ejpam-5734	156	10	}	}	PUNCT
ejpam-5734	156	11	∪	∪	ADJ
ejpam-5734	156	12	{	{	PUNCT
ejpam-5734	156	13	v′i	v′i	NOUN
ejpam-5734	156	14	|	|	ADV
ejpam-5734	156	15	1	1	NUM
ejpam-5734	156	16	≤	≤	NUM
ejpam-5734	156	17	i	i	PRON
ejpam-5734	156	18	≤	≤	NOUN
ejpam-5734	156	19	n	n	CCONJ
ejpam-5734	156	20	}	}	PUNCT
ejpam-5734	156	21	.	.	PUNCT
ejpam-5734	157	1	it	it	PRON
ejpam-5734	157	2	is	be	AUX
ejpam-5734	157	3	easy	easy	ADJ
ejpam-5734	157	4	to	to	PART
ejpam-5734	157	5	determine	determine	VERB
ejpam-5734	157	6	that	that	PRON
ejpam-5734	157	7	χ2(cn	χ2(cn	PROPN
ejpam-5734	157	8	)	)	PUNCT
ejpam-5734	157	9	=	=	PROPN
ejpam-5734	158	1	n	n	PROPN
ejpam-5734	158	2	for	for	ADP
ejpam-5734	158	3	3	3	NUM
ejpam-5734	158	4	≤	≤	NOUN
ejpam-5734	158	5	n	n	PRON
ejpam-5734	158	6	≤	≤	NOUN
ejpam-5734	158	7	5	5	NUM
ejpam-5734	158	8	,	,	PUNCT
ejpam-5734	158	9	and	and	CCONJ
ejpam-5734	158	10	this	this	PRON
ejpam-5734	158	11	is	be	AUX
ejpam-5734	158	12	also	also	ADV
ejpam-5734	158	13	true	true	ADJ
ejpam-5734	158	14	for	for	ADP
ejpam-5734	158	15	the	the	DET
ejpam-5734	158	16	copy	copy	NOUN
ejpam-5734	158	17	of	of	ADP
ejpam-5734	158	18	cn	cn	PROPN
ejpam-5734	158	19	in	in	ADP
ejpam-5734	158	20	d2(cn	d2(cn	PROPN
ejpam-5734	158	21	)	)	PUNCT
ejpam-5734	158	22	.	.	PUNCT
ejpam-5734	159	1	by	by	ADP
ejpam-5734	159	2	definition	definition	NOUN
ejpam-5734	159	3	of	of	ADP
ejpam-5734	159	4	d2(cn	d2(cn	PROPN
ejpam-5734	159	5	)	)	PUNCT
ejpam-5734	159	6	,	,	PUNCT
ejpam-5734	159	7	for	for	ADP
ejpam-5734	159	8	every	every	DET
ejpam-5734	159	9	vi	vi	PROPN
ejpam-5734	159	10	∈	∈	PROPN
ejpam-5734	159	11	v	v	NOUN
ejpam-5734	159	12	(	(	PUNCT
ejpam-5734	159	13	cn	cn	PROPN
ejpam-5734	159	14	)	)	PUNCT
ejpam-5734	159	15	where	where	SCONJ
ejpam-5734	159	16	1	1	NUM
ejpam-5734	159	17	≤	≤	NUM
ejpam-5734	159	18	i	i	NOUN
ejpam-5734	159	19	≤	≤	ADJ
ejpam-5734	159	20	n−	n−	PROPN
ejpam-5734	159	21	1	1	NUM
ejpam-5734	159	22	,	,	PUNCT
ejpam-5734	159	23	vi	vi	PROPN
ejpam-5734	159	24	is	be	AUX
ejpam-5734	159	25	adjacent	adjacent	ADJ
ejpam-5734	159	26	to	to	ADP
ejpam-5734	159	27	v′i+1	v′i+1	NOUN
ejpam-5734	159	28	and	and	CCONJ
ejpam-5734	159	29	v′i−1	v′i−1	PROPN
ejpam-5734	159	30	∈	∈	PROPN
ejpam-5734	159	31	v	v	ADP
ejpam-5734	159	32	′(cn	′(cn	NOUN
ejpam-5734	159	33	)	)	PUNCT
ejpam-5734	159	34	.	.	PUNCT
ejpam-5734	160	1	this	this	PRON
ejpam-5734	160	2	implies	imply	VERB
ejpam-5734	160	3	that	that	SCONJ
ejpam-5734	160	4	distinct	distinct	ADJ
ejpam-5734	160	5	color	color	NOUN
ejpam-5734	160	6	classes	class	NOUN
ejpam-5734	160	7	are	be	AUX
ejpam-5734	160	8	assigned	assign	VERB
ejpam-5734	160	9	to	to	ADP
ejpam-5734	160	10	these	these	DET
ejpam-5734	160	11	vertices	vertex	NOUN
ejpam-5734	160	12	since	since	SCONJ
ejpam-5734	160	13	m.	m.	PROPN
ejpam-5734	160	14	f.	f.	PROPN
ejpam-5734	160	15	libao	libao	PROPN
ejpam-5734	160	16	,	,	PUNCT
ejpam-5734	160	17	k.	k.	PROPN
ejpam-5734	160	18	b.	b.	PROPN
ejpam-5734	160	19	abarca	abarca	PROPN
ejpam-5734	160	20	/	/	SYM
ejpam-5734	160	21	eur	eur	PROPN
ejpam-5734	160	22	.	.	PUNCT
ejpam-5734	161	1	j.	j.	PROPN
ejpam-5734	161	2	pure	pure	PROPN
ejpam-5734	161	3	appl	appl	PROPN
ejpam-5734	161	4	.	.	PROPN
ejpam-5734	161	5	math	math	PROPN
ejpam-5734	161	6	,	,	PUNCT
ejpam-5734	161	7	18	18	NUM
ejpam-5734	161	8	(	(	PUNCT
ejpam-5734	161	9	2	2	NUM
ejpam-5734	161	10	)	)	PUNCT
ejpam-5734	161	11	(	(	PUNCT
ejpam-5734	161	12	2025	2025	NUM
ejpam-5734	161	13	)	)	PUNCT
ejpam-5734	161	14	,	,	PUNCT
ejpam-5734	161	15	5734	5734	NUM
ejpam-5734	161	16	9	9	NUM
ejpam-5734	161	17	of	of	ADP
ejpam-5734	161	18	25	25	NUM
ejpam-5734	161	19	d(vi	d(vi	NOUN
ejpam-5734	161	20	,	,	PUNCT
ejpam-5734	161	21	v	v	NOUN
ejpam-5734	161	22	′	′	NUM
ejpam-5734	161	23	n	n	CCONJ
ejpam-5734	161	24	)	)	PUNCT
ejpam-5734	161	25	≤	≤	NUM
ejpam-5734	162	1	2	2	NUM
ejpam-5734	162	2	.	.	PUNCT
ejpam-5734	163	1	then	then	ADV
ejpam-5734	163	2	,	,	PUNCT
ejpam-5734	163	3	the	the	DET
ejpam-5734	163	4	following	follow	VERB
ejpam-5734	163	5	are	be	AUX
ejpam-5734	163	6	color	color	NOUN
ejpam-5734	163	7	classes	class	NOUN
ejpam-5734	163	8	in	in	ADP
ejpam-5734	163	9	d2(cn	d2(cn	PROPN
ejpam-5734	163	10	)	)	PUNCT
ejpam-5734	163	11	are	be	AUX
ejpam-5734	163	12	:	:	PUNCT
ejpam-5734	163	13	a1	a1	NOUN
ejpam-5734	163	14	=	=	SYM
ejpam-5734	163	15	{	{	PUNCT
ejpam-5734	163	16	v1	v1	NOUN
ejpam-5734	163	17	}	}	PUNCT
ejpam-5734	163	18	a2	a2	NOUN
ejpam-5734	163	19	=	=	PUNCT
ejpam-5734	163	20	{	{	PUNCT
ejpam-5734	163	21	v2	v2	PROPN
ejpam-5734	163	22	}	}	PUNCT
ejpam-5734	163	23	...	...	PUNCT
ejpam-5734	164	1	an	an	DET
ejpam-5734	164	2	=	=	SYM
ejpam-5734	164	3	{	{	PUNCT
ejpam-5734	164	4	vn	vn	NOUN
ejpam-5734	164	5	}	}	PUNCT
ejpam-5734	164	6	an+1	an+1	PROPN
ejpam-5734	164	7	=	=	SYM
ejpam-5734	164	8	{	{	PUNCT
ejpam-5734	164	9	v′1	v′1	ADJ
ejpam-5734	164	10	}	}	PUNCT
ejpam-5734	165	1	...	...	PUNCT
ejpam-5734	165	2	a2n	a2n	PROPN
ejpam-5734	165	3	=	=	PRON
ejpam-5734	165	4	{	{	PUNCT
ejpam-5734	165	5	v′n	v′n	NOUN
ejpam-5734	165	6	}	}	PUNCT
ejpam-5734	165	7	note	note	NOUN
ejpam-5734	165	8	that	that	SCONJ
ejpam-5734	165	9	⋃2n	⋃2n	PROPN
ejpam-5734	165	10	k=1ak	k=1ak	NOUN
ejpam-5734	165	11	=	=	SYM
ejpam-5734	165	12	v	v	PROPN
ejpam-5734	165	13	[	[	X
ejpam-5734	165	14	d2(cn	d2(cn	PROPN
ejpam-5734	165	15	)	)	PUNCT
ejpam-5734	165	16	]	]	PUNCT
ejpam-5734	165	17	and	and	CCONJ
ejpam-5734	165	18	∑	∑	ADP
ejpam-5734	165	19	a∈c	a∈c	PROPN
ejpam-5734	165	20	|a|	|a|	PROPN
ejpam-5734	165	21	=	=	PROPN
ejpam-5734	165	22	|v	|v	PROPN
ejpam-5734	166	1	[	[	X
ejpam-5734	166	2	d2(cn)]|	d2(cn)]|	NOUN
ejpam-5734	166	3	.	.	VERB
ejpam-5734	166	4	by	by	ADP
ejpam-5734	166	5	lemma	lemma	PROPN
ejpam-5734	166	6	1	1	NUM
ejpam-5734	166	7	,	,	PUNCT
ejpam-5734	166	8	the	the	DET
ejpam-5734	166	9	color	color	NOUN
ejpam-5734	166	10	classes	class	NOUN
ejpam-5734	166	11	are	be	AUX
ejpam-5734	166	12	disjoint	disjoint	ADJ
ejpam-5734	166	13	.	.	PUNCT
ejpam-5734	167	1	therefore	therefore	ADV
ejpam-5734	167	2	,	,	PUNCT
ejpam-5734	167	3	c	c	PROPN
ejpam-5734	167	4	=	=	PRON
ejpam-5734	167	5	{	{	PUNCT
ejpam-5734	167	6	ak	ak	PROPN
ejpam-5734	167	7	|	|	ADV
ejpam-5734	167	8	1	1	NUM
ejpam-5734	167	9	≤	≤	NUM
ejpam-5734	167	10	k	k	X
ejpam-5734	167	11	≤	≤	NUM
ejpam-5734	167	12	2n	2n	NUM
ejpam-5734	167	13	}	}	PUNCT
ejpam-5734	167	14	is	be	AUX
ejpam-5734	167	15	a	a	DET
ejpam-5734	167	16	distance-2	distance-2	CCONJ
ejpam-5734	167	17	chromatic	chromatic	ADJ
ejpam-5734	167	18	set	set	NOUN
ejpam-5734	167	19	.	.	PUNCT
ejpam-5734	168	1	hence	hence	ADV
ejpam-5734	168	2	,	,	PUNCT
ejpam-5734	168	3	χ2[d2(cn	χ2[d2(cn	PROPN
ejpam-5734	168	4	)	)	PUNCT
ejpam-5734	168	5	]	]	PUNCT
ejpam-5734	168	6	≤	≤	NUM
ejpam-5734	168	7	2n	2n	NUM
ejpam-5734	168	8	.	.	PUNCT
ejpam-5734	169	1	suppose	suppose	VERB
ejpam-5734	169	2	∃c	∃c	PROPN
ejpam-5734	169	3	′	′	NOUN
ejpam-5734	169	4	is	be	AUX
ejpam-5734	169	5	such	such	ADJ
ejpam-5734	169	6	that	that	SCONJ
ejpam-5734	169	7	|c	|c	ADJ
ejpam-5734	169	8	′|	′|	NUM
ejpam-5734	169	9	≤	≤	NOUN
ejpam-5734	169	10	2n	2n	NUM
ejpam-5734	169	11	−	−	ADP
ejpam-5734	169	12	1	1	NUM
ejpam-5734	169	13	,	,	PUNCT
ejpam-5734	169	14	which	which	PRON
ejpam-5734	169	15	implies	imply	VERB
ejpam-5734	169	16	that	that	SCONJ
ejpam-5734	169	17	v′1	v′1	NOUN
ejpam-5734	169	18	is	be	AUX
ejpam-5734	169	19	colored	color	VERB
ejpam-5734	169	20	with	with	ADP
ejpam-5734	169	21	a1	a1	NOUN
ejpam-5734	169	22	.	.	PUNCT
ejpam-5734	170	1	this	this	PRON
ejpam-5734	170	2	is	be	AUX
ejpam-5734	170	3	a	a	DET
ejpam-5734	170	4	contradiction	contradiction	NOUN
ejpam-5734	170	5	since	since	SCONJ
ejpam-5734	170	6	d(v1	d(v1	NOUN
ejpam-5734	170	7	,	,	PUNCT
ejpam-5734	170	8	v	v	NOUN
ejpam-5734	170	9	′	′	NUM
ejpam-5734	170	10	1	1	NUM
ejpam-5734	170	11	)	)	PUNCT
ejpam-5734	170	12	=	=	SYM
ejpam-5734	170	13	2	2	X
ejpam-5734	170	14	.	.	PUNCT
ejpam-5734	170	15	accordingly	accordingly	ADV
ejpam-5734	170	16	,	,	PUNCT
ejpam-5734	170	17	χ2[d2(cn	χ2[d2(cn	PROPN
ejpam-5734	170	18	)	)	PUNCT
ejpam-5734	170	19	]	]	PUNCT
ejpam-5734	171	1	=	=	PUNCT
ejpam-5734	171	2	χ2(cn	χ2(cn	PROPN
ejpam-5734	171	3	)	)	PUNCT
ejpam-5734	172	1	+	+	CCONJ
ejpam-5734	172	2	χ2(c	χ2(c	NUM
ejpam-5734	172	3	′	′	NUM
ejpam-5734	172	4	n	n	CCONJ
ejpam-5734	172	5	)	)	PUNCT
ejpam-5734	172	6	=	=	SYM
ejpam-5734	172	7	n+	n+	PUNCT
ejpam-5734	172	8	n	n	NOUN
ejpam-5734	172	9	=	=	SYM
ejpam-5734	172	10	2n	2n	NUM
ejpam-5734	172	11	thus	thus	ADV
ejpam-5734	172	12	,	,	PUNCT
ejpam-5734	172	13	χ2[d2(cn	χ2[d2(cn	PROPN
ejpam-5734	172	14	)	)	PUNCT
ejpam-5734	172	15	]	]	PUNCT
ejpam-5734	173	1	=	=	SYM
ejpam-5734	173	2	2n	2n	X
ejpam-5734	173	3	.	.	PUNCT
ejpam-5734	174	1	theorem	theorem	PROPN
ejpam-5734	174	2	4.1.2	4.1.2	NUM
ejpam-5734	174	3	.	.	PUNCT
ejpam-5734	175	1	let	let	VERB
ejpam-5734	175	2	g	g	PRON
ejpam-5734	175	3	be	be	AUX
ejpam-5734	175	4	a	a	DET
ejpam-5734	175	5	cycle	cycle	NOUN
ejpam-5734	175	6	graph	graph	NOUN
ejpam-5734	175	7	cn	cn	VERB
ejpam-5734	175	8	with	with	ADP
ejpam-5734	175	9	n	n	NUM
ejpam-5734	175	10	≥	≥	NUM
ejpam-5734	175	11	6	6	NUM
ejpam-5734	175	12	.	.	PUNCT
ejpam-5734	176	1	then	then	ADV
ejpam-5734	176	2	,	,	PUNCT
ejpam-5734	176	3	the	the	DET
ejpam-5734	176	4	distance-2	distance-2	NUM
ejpam-5734	176	5	chromatic	chromatic	ADJ
ejpam-5734	176	6	number	number	NOUN
ejpam-5734	176	7	of	of	ADP
ejpam-5734	176	8	the	the	DET
ejpam-5734	176	9	shadow	shadow	NOUN
ejpam-5734	176	10	graph	graph	NOUN
ejpam-5734	176	11	of	of	ADP
ejpam-5734	176	12	the	the	DET
ejpam-5734	176	13	cycle	cycle	NOUN
ejpam-5734	176	14	graph	graph	NOUN
ejpam-5734	176	15	,	,	PUNCT
ejpam-5734	176	16	denoted	denote	VERB
ejpam-5734	176	17	as	as	ADP
ejpam-5734	176	18	χ2[d2(cn	χ2[d2(cn	PROPN
ejpam-5734	176	19	)	)	PUNCT
ejpam-5734	176	20	]	]	PUNCT
ejpam-5734	176	21	,	,	PUNCT
ejpam-5734	176	22	is	be	AUX
ejpam-5734	176	23	given	give	VERB
ejpam-5734	176	24	by	by	ADP
ejpam-5734	176	25	:	:	PUNCT
ejpam-5734	176	26	χ2[d2(cn	χ2[d2(cn	PROPN
ejpam-5734	176	27	)	)	PUNCT
ejpam-5734	176	28	]	]	PUNCT
ejpam-5734	177	1	=	=	PUNCT
ejpam-5734	177	2			NOUN
ejpam-5734	177	3	6	6	NUM
ejpam-5734	177	4	;	;	PUNCT
ejpam-5734	177	5	n	n	NUM
ejpam-5734	177	6	≡	≡	PROPN
ejpam-5734	177	7	0	0	PUNCT
ejpam-5734	178	1	(	(	PUNCT
ejpam-5734	178	2	mod	mod	NOUN
ejpam-5734	178	3	3	3	NUM
ejpam-5734	178	4	)	)	PUNCT
ejpam-5734	178	5	7	7	NUM
ejpam-5734	178	6	;	;	PUNCT
ejpam-5734	178	7	n	n	NUM
ejpam-5734	178	8	≡	≡	PROPN
ejpam-5734	178	9	1	1	NUM
ejpam-5734	178	10	(	(	PUNCT
ejpam-5734	178	11	mod	mod	NOUN
ejpam-5734	178	12	3	3	NUM
ejpam-5734	178	13	)	)	PUNCT
ejpam-5734	178	14	8	8	NUM
ejpam-5734	178	15	;	;	PUNCT
ejpam-5734	178	16	n	n	NUM
ejpam-5734	178	17	≡	≡	PROPN
ejpam-5734	178	18	2	2	NUM
ejpam-5734	178	19	(	(	PUNCT
ejpam-5734	178	20	mod	mod	NOUN
ejpam-5734	178	21	3	3	NUM
ejpam-5734	178	22	)	)	PUNCT
ejpam-5734	178	23	.	.	PUNCT
ejpam-5734	179	1	proof	proof	NOUN
ejpam-5734	179	2	.	.	PUNCT
ejpam-5734	180	1	consider	consider	VERB
ejpam-5734	180	2	the	the	DET
ejpam-5734	180	3	cycle	cycle	NOUN
ejpam-5734	180	4	cn	cn	NOUN
ejpam-5734	180	5	of	of	ADP
ejpam-5734	180	6	order	order	NOUN
ejpam-5734	180	7	n	n	PRON
ejpam-5734	180	8	≥	≥	NUM
ejpam-5734	180	9	6	6	NUM
ejpam-5734	180	10	.	.	PUNCT
ejpam-5734	181	1	let	let	VERB
ejpam-5734	181	2	v	v	X
ejpam-5734	181	3	(	(	PUNCT
ejpam-5734	181	4	cn	cn	PROPN
ejpam-5734	181	5	)	)	PUNCT
ejpam-5734	181	6	=	=	PRON
ejpam-5734	181	7	{	{	PUNCT
ejpam-5734	181	8	vi	vi	NOUN
ejpam-5734	181	9	|	|	ADV
ejpam-5734	181	10	1	1	NUM
ejpam-5734	181	11	≤	≤	NUM
ejpam-5734	181	12	i	i	PRON
ejpam-5734	181	13	≤	≤	PROPN
ejpam-5734	181	14	n	n	CCONJ
ejpam-5734	181	15	}	}	PUNCT
ejpam-5734	181	16	be	be	AUX
ejpam-5734	181	17	the	the	DET
ejpam-5734	181	18	set	set	NOUN
ejpam-5734	181	19	of	of	ADP
ejpam-5734	181	20	vertices	vertex	NOUN
ejpam-5734	181	21	of	of	ADP
ejpam-5734	181	22	cn	cn	PROPN
ejpam-5734	181	23	,	,	PUNCT
ejpam-5734	181	24	and	and	CCONJ
ejpam-5734	181	25	v	v	ADP
ejpam-5734	181	26	′(cn	′(cn	NOUN
ejpam-5734	181	27	)	)	PUNCT
ejpam-5734	182	1	=	=	PRON
ejpam-5734	182	2	{	{	PUNCT
ejpam-5734	182	3	v′i	v′i	INTJ
ejpam-5734	182	4	|	|	ADV
ejpam-5734	182	5	1	1	NUM
ejpam-5734	182	6	≤	≤	NUM
ejpam-5734	182	7	i	i	PRON
ejpam-5734	182	8	≤	≤	PROPN
ejpam-5734	182	9	n	n	CCONJ
ejpam-5734	182	10	}	}	PUNCT
ejpam-5734	182	11	denote	denote	VERB
ejpam-5734	182	12	the	the	DET
ejpam-5734	182	13	vertices	vertex	NOUN
ejpam-5734	182	14	of	of	ADP
ejpam-5734	182	15	the	the	DET
ejpam-5734	182	16	copy	copy	NOUN
ejpam-5734	182	17	of	of	ADP
ejpam-5734	182	18	cn	cn	PROPN
ejpam-5734	182	19	.	.	PUNCT
ejpam-5734	183	1	then	then	ADV
ejpam-5734	183	2	,	,	PUNCT
ejpam-5734	183	3	v	v	X
ejpam-5734	183	4	[	[	X
ejpam-5734	183	5	d2(cn	d2(cn	NOUN
ejpam-5734	183	6	)	)	PUNCT
ejpam-5734	183	7	]	]	PUNCT
ejpam-5734	184	1	=	=	PUNCT
ejpam-5734	184	2	{	{	PUNCT
ejpam-5734	184	3	vi	vi	NOUN
ejpam-5734	184	4	|	|	ADV
ejpam-5734	184	5	1	1	NUM
ejpam-5734	184	6	≤	≤	NUM
ejpam-5734	184	7	i	i	PRON
ejpam-5734	184	8	≤	≤	NOUN
ejpam-5734	184	9	n	n	CCONJ
ejpam-5734	184	10	}	}	PUNCT
ejpam-5734	184	11	∪	∪	ADJ
ejpam-5734	184	12	{	{	PUNCT
ejpam-5734	184	13	v′i	v′i	NOUN
ejpam-5734	184	14	|	|	ADV
ejpam-5734	184	15	1	1	NUM
ejpam-5734	184	16	≤	≤	NUM
ejpam-5734	184	17	i	i	PRON
ejpam-5734	184	18	≤	≤	NOUN
ejpam-5734	184	19	n	n	CCONJ
ejpam-5734	184	20	}	}	PUNCT
ejpam-5734	184	21	.	.	PUNCT
ejpam-5734	185	1	case	case	NOUN
ejpam-5734	185	2	1	1	NUM
ejpam-5734	185	3	.	.	PUNCT
ejpam-5734	186	1	n	n	X
ejpam-5734	186	2	≡	≡	PROPN
ejpam-5734	186	3	0	0	PUNCT
ejpam-5734	186	4	(	(	PUNCT
ejpam-5734	186	5	mod	mod	NOUN
ejpam-5734	186	6	3	3	X
ejpam-5734	186	7	)	)	PUNCT
ejpam-5734	186	8	the	the	DET
ejpam-5734	186	9	color	color	NOUN
ejpam-5734	186	10	classes	class	NOUN
ejpam-5734	186	11	in	in	ADP
ejpam-5734	186	12	d2(cn	d2(cn	PROPN
ejpam-5734	186	13	)	)	PUNCT
ejpam-5734	186	14	are	be	AUX
ejpam-5734	186	15	:	:	PUNCT
ejpam-5734	186	16	a1	a1	NOUN
ejpam-5734	186	17	=	=	PUNCT
ejpam-5734	186	18	{	{	PUNCT
ejpam-5734	186	19	v3i−2	v3i−2	NOUN
ejpam-5734	186	20	|	|	ADV
ejpam-5734	186	21	1	1	NUM
ejpam-5734	186	22	≤	≤	NUM
ejpam-5734	186	23	i	i	PRON
ejpam-5734	186	24	≤	≤	ADV
ejpam-5734	186	25	⌊n	⌊n	X
ejpam-5734	186	26	3	3	NUM
ejpam-5734	186	27	⌋	⌋	NOUN
ejpam-5734	186	28	}	}	PUNCT
ejpam-5734	186	29	a2	a2	PROPN
ejpam-5734	186	30	=	=	PUNCT
ejpam-5734	186	31	{	{	PUNCT
ejpam-5734	186	32	v3i−1	v3i−1	PROPN
ejpam-5734	186	33	|	|	ADV
ejpam-5734	186	34	1	1	NUM
ejpam-5734	186	35	≤	≤	NUM
ejpam-5734	187	1	i	i	PRON
ejpam-5734	187	2	≤	≤	ADV
ejpam-5734	187	3	⌊n	⌊n	X
ejpam-5734	187	4	3	3	NUM
ejpam-5734	187	5	⌋	⌋	NOUN
ejpam-5734	187	6	}	}	PUNCT
ejpam-5734	187	7	m.	m.	NOUN
ejpam-5734	187	8	f.	f.	PROPN
ejpam-5734	187	9	libao	libao	PROPN
ejpam-5734	187	10	,	,	PUNCT
ejpam-5734	187	11	k.	k.	PROPN
ejpam-5734	187	12	b.	b.	PROPN
ejpam-5734	187	13	abarca	abarca	PROPN
ejpam-5734	187	14	/	/	SYM
ejpam-5734	187	15	eur	eur	PROPN
ejpam-5734	187	16	.	.	PUNCT
ejpam-5734	188	1	j.	j.	PROPN
ejpam-5734	188	2	pure	pure	PROPN
ejpam-5734	188	3	appl	appl	PROPN
ejpam-5734	188	4	.	.	PROPN
ejpam-5734	188	5	math	math	PROPN
ejpam-5734	188	6	,	,	PUNCT
ejpam-5734	188	7	18	18	NUM
ejpam-5734	188	8	(	(	PUNCT
ejpam-5734	188	9	2	2	NUM
ejpam-5734	188	10	)	)	PUNCT
ejpam-5734	188	11	(	(	PUNCT
ejpam-5734	188	12	2025	2025	NUM
ejpam-5734	188	13	)	)	PUNCT
ejpam-5734	188	14	,	,	PUNCT
ejpam-5734	188	15	5734	5734	NUM
ejpam-5734	188	16	10	10	NUM
ejpam-5734	188	17	of	of	ADP
ejpam-5734	188	18	25	25	NUM
ejpam-5734	188	19	a3	a3	NOUN
ejpam-5734	188	20	=	=	PRON
ejpam-5734	188	21	{	{	PUNCT
ejpam-5734	188	22	v3i	v3i	NOUN
ejpam-5734	188	23	|	|	ADV
ejpam-5734	188	24	1	1	NUM
ejpam-5734	188	25	≤	≤	NUM
ejpam-5734	189	1	i	i	PRON
ejpam-5734	189	2	≤	≤	ADV
ejpam-5734	189	3	⌊n	⌊n	X
ejpam-5734	189	4	3	3	NUM
ejpam-5734	189	5	⌋	⌋	NOUN
ejpam-5734	189	6	}	}	PUNCT
ejpam-5734	189	7	a4	a4	NOUN
ejpam-5734	189	8	=	=	SYM
ejpam-5734	189	9	{	{	PUNCT
ejpam-5734	189	10	v′3i−2	v′3i−2	NOUN
ejpam-5734	189	11	|	|	ADV
ejpam-5734	189	12	1	1	NUM
ejpam-5734	189	13	≤	≤	NUM
ejpam-5734	189	14	i	i	PRON
ejpam-5734	189	15	≤	≤	ADV
ejpam-5734	189	16	⌊n	⌊n	X
ejpam-5734	189	17	3	3	NUM
ejpam-5734	189	18	⌋	⌋	NOUN
ejpam-5734	189	19	}	}	PUNCT
ejpam-5734	189	20	a5	a5	PROPN
ejpam-5734	189	21	=	=	PUNCT
ejpam-5734	189	22	{	{	PUNCT
ejpam-5734	189	23	v′3i−1	v′3i−1	PROPN
ejpam-5734	189	24	|	|	CCONJ
ejpam-5734	189	25	1	1	NUM
ejpam-5734	189	26	≤	≤	NUM
ejpam-5734	190	1	i	i	PRON
ejpam-5734	190	2	≤	≤	ADV
ejpam-5734	190	3	⌊n	⌊n	X
ejpam-5734	190	4	3	3	NUM
ejpam-5734	190	5	⌋	⌋	NOUN
ejpam-5734	190	6	}	}	PUNCT
ejpam-5734	190	7	a6	a6	NOUN
ejpam-5734	190	8	=	=	PUNCT
ejpam-5734	190	9	{	{	PUNCT
ejpam-5734	190	10	v′3i	v′3i	PROPN
ejpam-5734	190	11	|	|	CCONJ
ejpam-5734	190	12	1	1	NUM
ejpam-5734	190	13	≤	≤	NUM
ejpam-5734	190	14	i	i	PRON
ejpam-5734	190	15	≤	≤	ADV
ejpam-5734	190	16	⌊n	⌊n	X
ejpam-5734	190	17	3	3	NUM
ejpam-5734	190	18	⌋	⌋	NOUN
ejpam-5734	190	19	}	}	PUNCT
ejpam-5734	190	20	.	.	PUNCT
ejpam-5734	191	1	i.	i.	PROPN
ejpam-5734	191	2	to	to	PART
ejpam-5734	191	3	check	check	VERB
ejpam-5734	191	4	whether	whether	SCONJ
ejpam-5734	191	5	every	every	DET
ejpam-5734	191	6	vertex	vertex	NOUN
ejpam-5734	191	7	in	in	ADP
ejpam-5734	191	8	the	the	DET
ejpam-5734	191	9	graph	graph	NOUN
ejpam-5734	191	10	belongs	belong	VERB
ejpam-5734	191	11	to	to	ADP
ejpam-5734	191	12	exactly	exactly	ADV
ejpam-5734	191	13	one	one	NUM
ejpam-5734	191	14	color	color	NOUN
ejpam-5734	191	15	class	class	NOUN
ejpam-5734	191	16	,	,	PUNCT
ejpam-5734	191	17	⋃	⋃	PUNCT
ejpam-5734	191	18	a∈c	a∈c	NOUN
ejpam-5734	191	19	a	a	DET
ejpam-5734	191	20	=	=	X
ejpam-5734	191	21	{	{	PUNCT
ejpam-5734	191	22	a1,a2,a3,a4,a5,a6	a1,a2,a3,a4,a5,a6	NOUN
ejpam-5734	191	23	}	}	PUNCT
ejpam-5734	191	24	=	=	SYM
ejpam-5734	191	25	{	{	PUNCT
ejpam-5734	191	26	v3i−2	v3i−2	PROPN
ejpam-5734	191	27	,	,	PUNCT
ejpam-5734	191	28	v3i−1	v3i−1	PROPN
ejpam-5734	191	29	,	,	PUNCT
ejpam-5734	191	30	v3i	v3i	NOUN
ejpam-5734	191	31	,	,	PUNCT
ejpam-5734	191	32	v	v	X
ejpam-5734	191	33	′	′	NUM
ejpam-5734	191	34	3i−2	3i−2	NUM
ejpam-5734	191	35	,	,	PUNCT
ejpam-5734	191	36	v	v	NOUN
ejpam-5734	191	37	′	′	NUM
ejpam-5734	191	38	3i−1	3i−1	NUM
ejpam-5734	191	39	,	,	PUNCT
ejpam-5734	191	40	v	v	NOUN
ejpam-5734	191	41	′	′	NUM
ejpam-5734	191	42	3i	3i	NOUN
ejpam-5734	191	43	|	|	ADP
ejpam-5734	191	44	1	1	NUM
ejpam-5734	191	45	≤	≤	NUM
ejpam-5734	192	1	i	i	PRON
ejpam-5734	192	2	≤	≤	ADV
ejpam-5734	192	3	⌊n	⌊n	X
ejpam-5734	192	4	3	3	NUM
ejpam-5734	192	5	⌋	⌋	NOUN
ejpam-5734	192	6	}	}	PUNCT
ejpam-5734	192	7	=	=	SYM
ejpam-5734	192	8	{	{	PUNCT
ejpam-5734	192	9	v1	v1	PROPN
ejpam-5734	192	10	,	,	PUNCT
ejpam-5734	192	11	v2	v2	PROPN
ejpam-5734	192	12	,	,	PUNCT
ejpam-5734	192	13	v3	v3	PROPN
ejpam-5734	192	14	,	,	PUNCT
ejpam-5734	192	15	.	.	PUNCT
ejpam-5734	192	16	.	.	PUNCT
ejpam-5734	193	1	.	.	PUNCT
ejpam-5734	194	1	,	,	PUNCT
ejpam-5734	194	2	vn−2	vn−2	PROPN
ejpam-5734	194	3	,	,	PUNCT
ejpam-5734	194	4	vn−1	vn−1	PROPN
ejpam-5734	194	5	,	,	PUNCT
ejpam-5734	194	6	vn	vn	NOUN
ejpam-5734	194	7	,	,	PUNCT
ejpam-5734	194	8	v	v	ADJ
ejpam-5734	194	9	′	′	NUM
ejpam-5734	194	10	1	1	NUM
ejpam-5734	194	11	,	,	PUNCT
ejpam-5734	194	12	v	v	NOUN
ejpam-5734	194	13	′	′	NUM
ejpam-5734	194	14	2	2	NUM
ejpam-5734	194	15	,	,	PUNCT
ejpam-5734	194	16	v	v	NOUN
ejpam-5734	194	17	′	′	NUM
ejpam-5734	194	18	3	3	NUM
ejpam-5734	194	19	,	,	PUNCT
ejpam-5734	194	20	.	.	PUNCT
ejpam-5734	194	21	.	.	PUNCT
ejpam-5734	195	1	.	.	PUNCT
ejpam-5734	196	1	,	,	PUNCT
ejpam-5734	196	2	v	v	X
ejpam-5734	196	3	′	′	NUM
ejpam-5734	197	1	n−2	n−2	PROPN
ejpam-5734	197	2	,	,	PUNCT
ejpam-5734	197	3	v	v	NOUN
ejpam-5734	197	4	′	′	NUM
ejpam-5734	197	5	n−1	n−1	PROPN
ejpam-5734	197	6	,	,	PUNCT
ejpam-5734	197	7	v	v	NOUN
ejpam-5734	197	8	′	′	NUM
ejpam-5734	197	9	n	n	CCONJ
ejpam-5734	197	10	}	}	PUNCT
ejpam-5734	197	11	=	=	SYM
ejpam-5734	197	12	v	v	NOUN
ejpam-5734	197	13	(	(	PUNCT
ejpam-5734	197	14	d2(cn	d2(cn	NOUN
ejpam-5734	197	15	)	)	PUNCT
ejpam-5734	197	16	)	)	PUNCT
ejpam-5734	197	17	ii	ii	PROPN
ejpam-5734	197	18	.	.	PUNCT
ejpam-5734	198	1	to	to	PART
ejpam-5734	198	2	verify	verify	VERB
ejpam-5734	198	3	that	that	SCONJ
ejpam-5734	198	4	the	the	DET
ejpam-5734	198	5	color	color	NOUN
ejpam-5734	198	6	classes	class	NOUN
ejpam-5734	198	7	are	be	AUX
ejpam-5734	198	8	disjoint	disjoint	ADJ
ejpam-5734	198	9	,	,	PUNCT
ejpam-5734	198	10	we	we	PRON
ejpam-5734	198	11	also	also	ADV
ejpam-5734	198	12	have	have	VERB
ejpam-5734	198	13	to	to	PART
ejpam-5734	198	14	show	show	VERB
ejpam-5734	198	15	that	that	SCONJ
ejpam-5734	198	16	∑	∑	PROPN
ejpam-5734	198	17	a∈c	a∈c	PROPN
ejpam-5734	198	18	|a|	|a|	PROPN
ejpam-5734	198	19	=	=	PROPN
ejpam-5734	198	20	|v	|v	NOUN
ejpam-5734	199	1	[	[	X
ejpam-5734	199	2	d2(cn)]|	d2(cn)]|	ADP
ejpam-5734	199	3	in	in	ADP
ejpam-5734	199	4	addition	addition	NOUN
ejpam-5734	199	5	to	to	ADP
ejpam-5734	199	6	the	the	DET
ejpam-5734	199	7	above	above	ADJ
ejpam-5734	199	8	condition	condition	NOUN
ejpam-5734	199	9	.	.	PUNCT
ejpam-5734	200	1	∑	∑	PROPN
ejpam-5734	200	2	a∈c	a∈c	PROPN
ejpam-5734	200	3	|a|	|a|	PROPN
ejpam-5734	200	4	=	=	PUNCT
ejpam-5734	200	5	|a1|+	|a1|+	PRON
ejpam-5734	200	6	|a2|+	|a2|+	ADJ
ejpam-5734	200	7	|a3|+	|a3|+	ADP
ejpam-5734	200	8	|a4|+	|a4|+	NOUN
ejpam-5734	200	9	|a5|+	|a5|+	NOUN
ejpam-5734	200	10	|a6|	|a6|	NOUN
ejpam-5734	200	11	=	=	SYM
ejpam-5734	200	12	⌊n	⌊n	NUM
ejpam-5734	200	13	3	3	NUM
ejpam-5734	200	14	⌋+	⌋+	X
ejpam-5734	200	15	⌊n	⌊n	NUM
ejpam-5734	200	16	3	3	NUM
ejpam-5734	200	17	⌋+	⌋+	X
ejpam-5734	200	18	⌊n	⌊n	NUM
ejpam-5734	200	19	3	3	NUM
ejpam-5734	200	20	⌋+	⌋+	X
ejpam-5734	200	21	⌊n	⌊n	NUM
ejpam-5734	200	22	3	3	NUM
ejpam-5734	200	23	⌋+	⌋+	X
ejpam-5734	200	24	⌊n	⌊n	NUM
ejpam-5734	200	25	3	3	NUM
ejpam-5734	200	26	⌋+	⌋+	X
ejpam-5734	200	27	⌊n	⌊n	X
ejpam-5734	200	28	3	3	NUM
ejpam-5734	200	29	⌋	⌋	NOUN
ejpam-5734	200	30	=	=	PUNCT
ejpam-5734	200	31	n	n	PRON
ejpam-5734	200	32	3	3	NUM
ejpam-5734	200	33	+	+	CCONJ
ejpam-5734	200	34	n	n	PRON
ejpam-5734	200	35	3	3	NUM
ejpam-5734	200	36	+	+	CCONJ
ejpam-5734	200	37	n	n	PRON
ejpam-5734	200	38	3	3	NUM
ejpam-5734	200	39	+	+	CCONJ
ejpam-5734	200	40	n	n	PRON
ejpam-5734	200	41	3	3	NUM
ejpam-5734	200	42	+	+	CCONJ
ejpam-5734	200	43	n	n	PRON
ejpam-5734	200	44	3	3	NUM
ejpam-5734	200	45	+	+	CCONJ
ejpam-5734	200	46	n	n	NUM
ejpam-5734	200	47	3	3	NUM
ejpam-5734	200	48	,	,	PUNCT
ejpam-5734	200	49	since	since	SCONJ
ejpam-5734	200	50	n	n	X
ejpam-5734	200	51	≡	≡	PROPN
ejpam-5734	200	52	0	0	PUNCT
ejpam-5734	200	53	(	(	PUNCT
ejpam-5734	200	54	mod	mod	NOUN
ejpam-5734	200	55	3	3	NUM
ejpam-5734	200	56	)	)	PUNCT
ejpam-5734	200	57	=	=	SYM
ejpam-5734	200	58	6	6	NUM
ejpam-5734	200	59	(	(	PUNCT
ejpam-5734	200	60	n	n	NOUN
ejpam-5734	200	61	3	3	NUM
ejpam-5734	200	62	)	)	PUNCT
ejpam-5734	200	63	=	=	SYM
ejpam-5734	200	64	2n	2n	NUM
ejpam-5734	200	65	.	.	PUNCT
ejpam-5734	201	1	=	=	PRON
ejpam-5734	201	2	|v	|v	X
ejpam-5734	202	1	[	[	X
ejpam-5734	202	2	d2(cn)]|	d2(cn)]|	VERB
ejpam-5734	202	3	by	by	ADP
ejpam-5734	202	4	lemma	lemma	PROPN
ejpam-5734	202	5	1	1	NUM
ejpam-5734	202	6	,	,	PUNCT
ejpam-5734	202	7	all	all	DET
ejpam-5734	202	8	color	color	NOUN
ejpam-5734	202	9	classes	class	NOUN
ejpam-5734	202	10	are	be	AUX
ejpam-5734	202	11	mutually	mutually	ADV
ejpam-5734	202	12	exclusive	exclusive	ADJ
ejpam-5734	202	13	,	,	PUNCT
ejpam-5734	202	14	that	that	ADV
ejpam-5734	202	15	is	is	ADV
ejpam-5734	202	16	,	,	PUNCT
ejpam-5734	202	17	ak	ak	PROPN
ejpam-5734	202	18	∩aj	∩aj	NOUN
ejpam-5734	202	19	=	=	PUNCT
ejpam-5734	202	20	∅	∅	NOUN
ejpam-5734	202	21	for	for	ADP
ejpam-5734	202	22	k	k	PROPN
ejpam-5734	202	23	̸=	̸=	PROPN
ejpam-5734	202	24	j.	j.	PROPN
ejpam-5734	202	25	next	next	PROPN
ejpam-5734	202	26	,	,	PUNCT
ejpam-5734	202	27	note	note	VERB
ejpam-5734	202	28	that	that	SCONJ
ejpam-5734	202	29	for	for	ADP
ejpam-5734	202	30	each	each	DET
ejpam-5734	202	31	vi	vi	NOUN
ejpam-5734	202	32	,	,	PUNCT
ejpam-5734	202	33	vj	vj	PROPN
ejpam-5734	202	34	∈	∈	PROPN
ejpam-5734	202	35	ak	ak	PROPN
ejpam-5734	202	36	,	,	PUNCT
ejpam-5734	202	37	1	1	NUM
ejpam-5734	202	38	≤	≤	NUM
ejpam-5734	202	39	k	k	X
ejpam-5734	202	40	≤	≤	NUM
ejpam-5734	202	41	6	6	NUM
ejpam-5734	202	42	,	,	PUNCT
ejpam-5734	202	43	where	where	SCONJ
ejpam-5734	202	44	d(vi	d(vi	PROPN
ejpam-5734	202	45	,	,	PUNCT
ejpam-5734	202	46	vj	vj	ADJ
ejpam-5734	202	47	)	)	PUNCT
ejpam-5734	202	48	=	=	SYM
ejpam-5734	203	1	3	3	X
ejpam-5734	203	2	.	.	X
ejpam-5734	204	1	hence	hence	ADV
ejpam-5734	204	2	,	,	PUNCT
ejpam-5734	204	3	c	c	PROPN
ejpam-5734	204	4	=	=	PRON
ejpam-5734	204	5	{	{	PUNCT
ejpam-5734	204	6	a1,a2,a3,a4,a5,a6	a1,a2,a3,a4,a5,a6	NOUN
ejpam-5734	204	7	}	}	PUNCT
ejpam-5734	204	8	is	be	AUX
ejpam-5734	204	9	a	a	DET
ejpam-5734	204	10	distance-2	distance-2	CCONJ
ejpam-5734	204	11	chromatic	chromatic	ADJ
ejpam-5734	204	12	set	set	VERB
ejpam-5734	204	13	ofd2(cn	ofd2(cn	PROPN
ejpam-5734	204	14	)	)	PUNCT
ejpam-5734	204	15	,	,	PUNCT
ejpam-5734	204	16	and	and	CCONJ
ejpam-5734	204	17	χ2	χ2	PROPN
ejpam-5734	204	18	[	[	PUNCT
ejpam-5734	204	19	d2(cn	d2(cn	PROPN
ejpam-5734	204	20	)	)	PUNCT
ejpam-5734	204	21	]	]	PUNCT
ejpam-5734	204	22	≤	≤	NUM
ejpam-5734	204	23	6	6	NUM
ejpam-5734	204	24	.	.	PUNCT
ejpam-5734	205	1	suppose	suppose	VERB
ejpam-5734	205	2	χ2	χ2	PROPN
ejpam-5734	205	3	[	[	PUNCT
ejpam-5734	205	4	d2(cn	d2(cn	PROPN
ejpam-5734	205	5	)	)	PUNCT
ejpam-5734	205	6	]	]	PUNCT
ejpam-5734	205	7	<	<	X
ejpam-5734	205	8	6	6	NUM
ejpam-5734	205	9	,	,	PUNCT
ejpam-5734	205	10	say	say	VERB
ejpam-5734	205	11	the	the	DET
ejpam-5734	205	12	color	color	NOUN
ejpam-5734	205	13	class	class	NOUN
ejpam-5734	205	14	assigned	assign	VERB
ejpam-5734	205	15	to	to	ADP
ejpam-5734	205	16	v′3i	v′3i	PROPN
ejpam-5734	205	17	is	be	AUX
ejpam-5734	205	18	a1	a1	NOUN
ejpam-5734	205	19	,	,	PUNCT
ejpam-5734	205	20	then	then	ADV
ejpam-5734	205	21	d(v3i−2	d(v3i−2	PROPN
ejpam-5734	205	22	,	,	PUNCT
ejpam-5734	205	23	v	v	ADJ
ejpam-5734	205	24	′	′	NUM
ejpam-5734	205	25	3i	3i	NOUN
ejpam-5734	205	26	)	)	PUNCT
ejpam-5734	205	27	=	=	SYM
ejpam-5734	205	28	2	2	NUM
ejpam-5734	205	29	,	,	PUNCT
ejpam-5734	205	30	a	a	DET
ejpam-5734	205	31	contradiction	contradiction	NOUN
ejpam-5734	205	32	.	.	PUNCT
ejpam-5734	206	1	if	if	SCONJ
ejpam-5734	206	2	the	the	DET
ejpam-5734	206	3	color	color	NOUN
ejpam-5734	206	4	class	class	NOUN
ejpam-5734	206	5	assigned	assign	VERB
ejpam-5734	206	6	to	to	ADP
ejpam-5734	206	7	v′3i	v′3i	PROPN
ejpam-5734	206	8	is	be	AUX
ejpam-5734	206	9	a2	a2	PROPN
ejpam-5734	206	10	,	,	PUNCT
ejpam-5734	206	11	then	then	ADV
ejpam-5734	206	12	d(v3i−2	d(v3i−2	PROPN
ejpam-5734	206	13	,	,	PUNCT
ejpam-5734	206	14	v	v	ADJ
ejpam-5734	206	15	′	′	NUM
ejpam-5734	206	16	3i	3i	NOUN
ejpam-5734	206	17	)	)	PUNCT
ejpam-5734	206	18	=	=	SYM
ejpam-5734	206	19	1	1	NUM
ejpam-5734	206	20	,	,	PUNCT
ejpam-5734	206	21	still	still	ADV
ejpam-5734	206	22	a	a	DET
ejpam-5734	206	23	contradiction	contradiction	NOUN
ejpam-5734	206	24	.	.	PUNCT
ejpam-5734	207	1	if	if	SCONJ
ejpam-5734	207	2	v′3i	v′3i	NOUN
ejpam-5734	207	3	is	be	AUX
ejpam-5734	207	4	assigned	assign	VERB
ejpam-5734	207	5	with	with	ADP
ejpam-5734	207	6	a3	a3	NOUN
ejpam-5734	207	7	,	,	PUNCT
ejpam-5734	207	8	then	then	ADV
ejpam-5734	207	9	d(v3i−2	d(v3i−2	PROPN
ejpam-5734	207	10	,	,	PUNCT
ejpam-5734	207	11	v	v	ADJ
ejpam-5734	207	12	′	′	NUM
ejpam-5734	207	13	3i	3i	NOUN
ejpam-5734	207	14	)	)	PUNCT
ejpam-5734	207	15	=	=	SYM
ejpam-5734	207	16	2	2	NUM
ejpam-5734	207	17	,	,	PUNCT
ejpam-5734	207	18	also	also	ADV
ejpam-5734	207	19	a	a	DET
ejpam-5734	207	20	contradiction	contradiction	NOUN
ejpam-5734	207	21	.	.	PUNCT
ejpam-5734	208	1	if	if	SCONJ
ejpam-5734	208	2	v′3i	v′3i	NOUN
ejpam-5734	208	3	is	be	AUX
ejpam-5734	208	4	assigned	assign	VERB
ejpam-5734	208	5	with	with	ADP
ejpam-5734	208	6	a4	a4	NUM
ejpam-5734	208	7	,	,	PUNCT
ejpam-5734	208	8	then	then	ADV
ejpam-5734	208	9	d(v′3i−2	d(v′3i−2	NOUN
ejpam-5734	208	10	,	,	PUNCT
ejpam-5734	208	11	v	v	ADJ
ejpam-5734	208	12	′	′	NUM
ejpam-5734	208	13	3i	3i	NOUN
ejpam-5734	208	14	)	)	PUNCT
ejpam-5734	208	15	=	=	SYM
ejpam-5734	208	16	2	2	NUM
ejpam-5734	208	17	,	,	PUNCT
ejpam-5734	208	18	another	another	DET
ejpam-5734	208	19	contradiction	contradiction	NOUN
ejpam-5734	208	20	.	.	PUNCT
ejpam-5734	209	1	lastly	lastly	ADV
ejpam-5734	209	2	,	,	PUNCT
ejpam-5734	209	3	if	if	SCONJ
ejpam-5734	209	4	v′3i	v′3i	PROPN
ejpam-5734	209	5	is	be	AUX
ejpam-5734	209	6	assigned	assign	VERB
ejpam-5734	209	7	with	with	ADP
ejpam-5734	209	8	a5	a5	PROPN
ejpam-5734	209	9	,	,	PUNCT
ejpam-5734	209	10	then	then	ADV
ejpam-5734	209	11	d(v′3i−1	d(v′3i−1	PROPN
ejpam-5734	209	12	,	,	PUNCT
ejpam-5734	209	13	v	v	ADJ
ejpam-5734	209	14	′	′	NUM
ejpam-5734	209	15	3i	3i	NOUN
ejpam-5734	209	16	)	)	PUNCT
ejpam-5734	209	17	=	=	SYM
ejpam-5734	209	18	1	1	NUM
ejpam-5734	209	19	,	,	PUNCT
ejpam-5734	209	20	which	which	PRON
ejpam-5734	209	21	is	be	AUX
ejpam-5734	209	22	again	again	ADV
ejpam-5734	209	23	a	a	DET
ejpam-5734	209	24	contradiction	contradiction	NOUN
ejpam-5734	209	25	.	.	PUNCT
ejpam-5734	210	1	thus	thus	ADV
ejpam-5734	210	2	,	,	PUNCT
ejpam-5734	210	3	x2[d2(cn	x2[d2(cn	NUM
ejpam-5734	210	4	)	)	PUNCT
ejpam-5734	210	5	]	]	PUNCT
ejpam-5734	210	6	≮	≮	VERB
ejpam-5734	210	7	6	6	NUM
ejpam-5734	210	8	.	.	PUNCT
ejpam-5734	211	1	therefore	therefore	ADV
ejpam-5734	211	2	,	,	PUNCT
ejpam-5734	211	3	χ2	χ2	PROPN
ejpam-5734	211	4	[	[	PUNCT
ejpam-5734	211	5	d2(cn	d2(cn	PROPN
ejpam-5734	211	6	)	)	PUNCT
ejpam-5734	211	7	]	]	PUNCT
ejpam-5734	211	8	=	=	PUNCT
ejpam-5734	211	9	6	6	X
ejpam-5734	211	10	.	.	PUNCT
ejpam-5734	211	11	below	below	ADV
ejpam-5734	211	12	is	be	AUX
ejpam-5734	211	13	an	an	DET
ejpam-5734	211	14	example	example	NOUN
ejpam-5734	211	15	of	of	ADP
ejpam-5734	211	16	a	a	DET
ejpam-5734	211	17	shadow	shadow	NOUN
ejpam-5734	211	18	graph	graph	NOUN
ejpam-5734	211	19	of	of	ADP
ejpam-5734	211	20	c6	c6	PROPN
ejpam-5734	211	21	,	,	PUNCT
ejpam-5734	211	22	d2(c6	d2(c6	PROPN
ejpam-5734	211	23	)	)	PUNCT
ejpam-5734	211	24	with	with	ADP
ejpam-5734	211	25	a	a	DET
ejpam-5734	211	26	distance	distance	NOUN
ejpam-5734	211	27	-2	-2	INTJ
ejpam-5734	211	28	chromatic	chromatic	ADJ
ejpam-5734	211	29	number	number	NOUN
ejpam-5734	211	30	of	of	ADP
ejpam-5734	211	31	6	6	NUM
ejpam-5734	211	32	,	,	PUNCT
ejpam-5734	211	33	where	where	SCONJ
ejpam-5734	211	34	c	c	NOUN
ejpam-5734	211	35	=	=	PRON
ejpam-5734	211	36	{	{	PUNCT
ejpam-5734	211	37	red	red	PROPN
ejpam-5734	211	38	(	(	PUNCT
ejpam-5734	211	39	v1	v1	NOUN
ejpam-5734	211	40	,	,	PUNCT
ejpam-5734	211	41	v4),blue	v4),blue	NOUN
ejpam-5734	211	42	(	(	PUNCT
ejpam-5734	211	43	v2	v2	NOUN
ejpam-5734	211	44	,	,	PUNCT
ejpam-5734	211	45	v5),green	v5),green	X
ejpam-5734	211	46	(	(	PUNCT
ejpam-5734	211	47	v3	v3	PROPN
ejpam-5734	211	48	,	,	PUNCT
ejpam-5734	211	49	v6),orange	v6),orange	ADV
ejpam-5734	211	50	(	(	PUNCT
ejpam-5734	211	51	v′1	v′1	ADJ
ejpam-5734	211	52	,	,	PUNCT
ejpam-5734	211	53	v	v	NOUN
ejpam-5734	211	54	′	′	NUM
ejpam-5734	211	55	4),pink	4),pink	NUM
ejpam-5734	211	56	(	(	PUNCT
ejpam-5734	211	57	v′2	v′2	INTJ
ejpam-5734	211	58	,	,	PUNCT
ejpam-5734	211	59	v	v	ADJ
ejpam-5734	211	60	′	′	NUM
ejpam-5734	211	61	5),yellow	5),yellow	PROPN
ejpam-5734	211	62	(	(	PUNCT
ejpam-5734	211	63	v′3	v′3	NOUN
ejpam-5734	211	64	,	,	PUNCT
ejpam-5734	211	65	v	v	ADJ
ejpam-5734	211	66	′	′	NUM
ejpam-5734	211	67	6	6	NUM
ejpam-5734	211	68	)	)	PUNCT
ejpam-5734	211	69	}	}	PUNCT
ejpam-5734	211	70	.	.	PUNCT
ejpam-5734	212	1	m.	m.	PROPN
ejpam-5734	212	2	f.	f.	PROPN
ejpam-5734	212	3	libao	libao	PROPN
ejpam-5734	212	4	,	,	PUNCT
ejpam-5734	212	5	k.	k.	PROPN
ejpam-5734	212	6	b.	b.	PROPN
ejpam-5734	212	7	abarca	abarca	PROPN
ejpam-5734	212	8	/	/	SYM
ejpam-5734	212	9	eur	eur	PROPN
ejpam-5734	212	10	.	.	PUNCT
ejpam-5734	213	1	j.	j.	PROPN
ejpam-5734	213	2	pure	pure	PROPN
ejpam-5734	213	3	appl	appl	PROPN
ejpam-5734	213	4	.	.	PROPN
ejpam-5734	213	5	math	math	PROPN
ejpam-5734	213	6	,	,	PUNCT
ejpam-5734	213	7	18	18	NUM
ejpam-5734	213	8	(	(	PUNCT
ejpam-5734	213	9	2	2	NUM
ejpam-5734	213	10	)	)	PUNCT
ejpam-5734	213	11	(	(	PUNCT
ejpam-5734	213	12	2025	2025	NUM
ejpam-5734	213	13	)	)	PUNCT
ejpam-5734	213	14	,	,	PUNCT
ejpam-5734	213	15	5734	5734	NUM
ejpam-5734	213	16	11	11	NUM
ejpam-5734	213	17	of	of	ADP
ejpam-5734	213	18	25	25	NUM
ejpam-5734	213	19	d2(c6	d2(c6	NOUN
ejpam-5734	213	20	)	)	PUNCT
ejpam-5734	213	21	:	:	PUNCT
ejpam-5734	214	1	v1	v1	VERB
ejpam-5734	214	2	v2	v2	PROPN
ejpam-5734	214	3	v3	v3	PROPN
ejpam-5734	214	4	v′	v′	NOUN
ejpam-5734	214	5	1	1	NUM
ejpam-5734	214	6	v′	v′	NUM
ejpam-5734	214	7	2	2	NUM
ejpam-5734	214	8	v′	v′	NOUN
ejpam-5734	214	9	3	3	NUM
ejpam-5734	214	10	v6	v6	NOUN
ejpam-5734	214	11	v5	v5	PROPN
ejpam-5734	214	12	v4	v4	PROPN
ejpam-5734	214	13	v′	v′	NOUN
ejpam-5734	214	14	6	6	NUM
ejpam-5734	214	15	v′	v′	NOUN
ejpam-5734	214	16	5	5	NUM
ejpam-5734	214	17	v′	v′	NOUN
ejpam-5734	214	18	4	4	NUM
ejpam-5734	214	19	figure	figure	NOUN
ejpam-5734	214	20	7	7	NUM
ejpam-5734	214	21	:	:	PUNCT
ejpam-5734	214	22	shadow	shadow	NOUN
ejpam-5734	214	23	graph	graph	NOUN
ejpam-5734	214	24	of	of	ADP
ejpam-5734	214	25	cycle	cycle	NOUN
ejpam-5734	214	26	graph	graph	NOUN
ejpam-5734	214	27	c6	c6	PROPN
ejpam-5734	214	28	with	with	ADP
ejpam-5734	214	29	χ2[d2(c6	χ2[d2(c6	PROPN
ejpam-5734	214	30	)	)	PUNCT
ejpam-5734	214	31	]	]	PUNCT
ejpam-5734	215	1	=	=	PUNCT
ejpam-5734	215	2	6	6	X
ejpam-5734	215	3	.	.	PUNCT
ejpam-5734	215	4	case	case	NOUN
ejpam-5734	215	5	2	2	NUM
ejpam-5734	215	6	.	.	X
ejpam-5734	216	1	n	n	NUM
ejpam-5734	216	2	≡	≡	PROPN
ejpam-5734	216	3	1	1	NUM
ejpam-5734	216	4	(	(	PUNCT
ejpam-5734	216	5	mod	mod	NOUN
ejpam-5734	216	6	3	3	X
ejpam-5734	216	7	)	)	PUNCT
ejpam-5734	216	8	consider	consider	VERB
ejpam-5734	216	9	the	the	DET
ejpam-5734	216	10	following	follow	VERB
ejpam-5734	216	11	color	color	NOUN
ejpam-5734	216	12	classes	class	NOUN
ejpam-5734	216	13	in	in	ADP
ejpam-5734	216	14	d2(cn	d2(cn	PROPN
ejpam-5734	216	15	):	):	PUNCT
ejpam-5734	216	16	a1	a1	NOUN
ejpam-5734	216	17	=	=	PUNCT
ejpam-5734	216	18	{	{	PUNCT
ejpam-5734	216	19	v3i−2	v3i−2	NOUN
ejpam-5734	216	20	|	|	ADV
ejpam-5734	216	21	1	1	NUM
ejpam-5734	216	22	≤	≤	NUM
ejpam-5734	217	1	i	i	PRON
ejpam-5734	217	2	≤	≤	ADV
ejpam-5734	217	3	⌊n	⌊n	X
ejpam-5734	217	4	3	3	NUM
ejpam-5734	217	5	⌋	⌋	NOUN
ejpam-5734	217	6	}	}	PUNCT
ejpam-5734	217	7	a2	a2	PROPN
ejpam-5734	217	8	=	=	PUNCT
ejpam-5734	217	9	{	{	PUNCT
ejpam-5734	217	10	v3i−1	v3i−1	PROPN
ejpam-5734	217	11	|	|	ADV
ejpam-5734	217	12	1	1	NUM
ejpam-5734	217	13	≤	≤	NUM
ejpam-5734	217	14	i	i	PRON
ejpam-5734	217	15	≤	≤	ADV
ejpam-5734	217	16	⌊n	⌊n	X
ejpam-5734	217	17	3	3	NUM
ejpam-5734	217	18	⌋	⌋	NOUN
ejpam-5734	217	19	}	}	PUNCT
ejpam-5734	217	20	a3	a3	NOUN
ejpam-5734	217	21	=	=	PRON
ejpam-5734	217	22	{	{	PUNCT
ejpam-5734	217	23	v3i	v3i	NOUN
ejpam-5734	217	24	|	|	ADV
ejpam-5734	217	25	1	1	NUM
ejpam-5734	217	26	≤	≤	NUM
ejpam-5734	217	27	i	i	PRON
ejpam-5734	217	28	≤	≤	ADV
ejpam-5734	217	29	⌊n	⌊n	X
ejpam-5734	217	30	3	3	NUM
ejpam-5734	217	31	⌋	⌋	NOUN
ejpam-5734	217	32	}	}	PUNCT
ejpam-5734	217	33	a4	a4	NOUN
ejpam-5734	217	34	=	=	SYM
ejpam-5734	217	35	{	{	PUNCT
ejpam-5734	217	36	vn	vn	NOUN
ejpam-5734	217	37	}	}	PUNCT
ejpam-5734	217	38	∪	∪	X
ejpam-5734	217	39	{	{	PUNCT
ejpam-5734	217	40	v′3i	v′3i	NUM
ejpam-5734	217	41	|	|	CCONJ
ejpam-5734	217	42	1	1	NUM
ejpam-5734	217	43	≤	≤	NUM
ejpam-5734	217	44	i	i	PRON
ejpam-5734	217	45	≤	≤	ADV
ejpam-5734	217	46	⌊n	⌊n	X
ejpam-5734	217	47	3	3	NUM
ejpam-5734	217	48	⌋	⌋	NOUN
ejpam-5734	217	49	−	−	NOUN
ejpam-5734	217	50	1	1	NUM
ejpam-5734	217	51	}	}	PUNCT
ejpam-5734	217	52	a5	a5	NOUN
ejpam-5734	217	53	=	=	PUNCT
ejpam-5734	217	54	{	{	PUNCT
ejpam-5734	217	55	v′3i+1	v′3i+1	NOUN
ejpam-5734	217	56	|	|	ADV
ejpam-5734	217	57	1	1	NUM
ejpam-5734	217	58	≤	≤	NUM
ejpam-5734	217	59	i	i	PRON
ejpam-5734	217	60	≤	≤	ADV
ejpam-5734	217	61	⌊n	⌊n	X
ejpam-5734	217	62	3	3	NUM
ejpam-5734	217	63	⌋	⌋	NOUN
ejpam-5734	217	64	}	}	PUNCT
ejpam-5734	217	65	a6	a6	NOUN
ejpam-5734	217	66	=	=	PRON
ejpam-5734	217	67	{	{	PUNCT
ejpam-5734	217	68	v′3i+2	v′3i+2	X
ejpam-5734	217	69	|	|	NOUN
ejpam-5734	217	70	1	1	X
ejpam-5734	217	71	≤	≤	NUM
ejpam-5734	217	72	i	i	PRON
ejpam-5734	217	73	≤	≤	ADV
ejpam-5734	217	74	⌊n	⌊n	X
ejpam-5734	217	75	3	3	NUM
ejpam-5734	217	76	⌋	⌋	NOUN
ejpam-5734	217	77	−	−	NOUN
ejpam-5734	217	78	1	1	NUM
ejpam-5734	217	79	}	}	PUNCT
ejpam-5734	217	80	∪	∪	X
ejpam-5734	217	81	{	{	PUNCT
ejpam-5734	217	82	v′1	v′1	ADJ
ejpam-5734	217	83	}	}	PUNCT
ejpam-5734	217	84	a7	a7	NOUN
ejpam-5734	217	85	=	=	PUNCT
ejpam-5734	217	86	{	{	PUNCT
ejpam-5734	217	87	v′2	v′2	X
ejpam-5734	217	88	∪	∪	ADP
ejpam-5734	217	89	v′n−1	v′n−1	PROPN
ejpam-5734	217	90	}	}	PUNCT
ejpam-5734	217	91	i.	i.	NOUN
ejpam-5734	217	92	to	to	PART
ejpam-5734	217	93	check	check	VERB
ejpam-5734	217	94	whether	whether	SCONJ
ejpam-5734	217	95	the	the	DET
ejpam-5734	217	96	vertices	vertex	NOUN
ejpam-5734	217	97	belongs	belong	VERB
ejpam-5734	217	98	to	to	ADP
ejpam-5734	217	99	exactly	exactly	ADV
ejpam-5734	217	100	one	one	NUM
ejpam-5734	217	101	color	color	NOUN
ejpam-5734	217	102	class	class	NOUN
ejpam-5734	217	103	,	,	PUNCT
ejpam-5734	217	104	we	we	PRON
ejpam-5734	217	105	have⋃	have⋃	VERB
ejpam-5734	217	106	a∈c	a∈c	VERB
ejpam-5734	217	107	a	a	PRON
ejpam-5734	217	108	=	=	X
ejpam-5734	217	109	{	{	PUNCT
ejpam-5734	217	110	a1,a2,a3,a4,a5,a6,a7	a1,a2,a3,a4,a5,a6,a7	NOUN
ejpam-5734	217	111	}	}	PUNCT
ejpam-5734	217	112	to	to	PART
ejpam-5734	217	113	avoid	avoid	VERB
ejpam-5734	217	114	complication	complication	NOUN
ejpam-5734	217	115	,	,	PUNCT
ejpam-5734	217	116	we	we	PRON
ejpam-5734	217	117	group	group	VERB
ejpam-5734	217	118	the	the	DET
ejpam-5734	217	119	color	color	NOUN
ejpam-5734	217	120	classes	class	NOUN
ejpam-5734	217	121	as	as	SCONJ
ejpam-5734	217	122	follows	follow	VERB
ejpam-5734	217	123	:	:	PUNCT
ejpam-5734	217	124	m.	m.	PROPN
ejpam-5734	217	125	f.	f.	PROPN
ejpam-5734	217	126	libao	libao	PROPN
ejpam-5734	217	127	,	,	PUNCT
ejpam-5734	217	128	k.	k.	PROPN
ejpam-5734	217	129	b.	b.	PROPN
ejpam-5734	217	130	abarca	abarca	PROPN
ejpam-5734	217	131	/	/	SYM
ejpam-5734	217	132	eur	eur	PROPN
ejpam-5734	217	133	.	.	PUNCT
ejpam-5734	218	1	j.	j.	PROPN
ejpam-5734	218	2	pure	pure	PROPN
ejpam-5734	218	3	appl	appl	PROPN
ejpam-5734	218	4	.	.	PROPN
ejpam-5734	218	5	math	math	PROPN
ejpam-5734	218	6	,	,	PUNCT
ejpam-5734	218	7	18	18	NUM
ejpam-5734	218	8	(	(	PUNCT
ejpam-5734	218	9	2	2	NUM
ejpam-5734	218	10	)	)	PUNCT
ejpam-5734	218	11	(	(	PUNCT
ejpam-5734	218	12	2025	2025	NUM
ejpam-5734	218	13	)	)	PUNCT
ejpam-5734	218	14	,	,	PUNCT
ejpam-5734	218	15	5734	5734	NUM
ejpam-5734	218	16	12	12	NUM
ejpam-5734	218	17	of	of	ADP
ejpam-5734	218	18	25	25	NUM
ejpam-5734	218	19	⋃	⋃	PUNCT
ejpam-5734	218	20	a∈c	a∈c	NOUN
ejpam-5734	218	21	a	a	DET
ejpam-5734	218	22	=	=	X
ejpam-5734	218	23	{	{	PUNCT
ejpam-5734	218	24	a1,a2,a3	a1,a2,a3	PROPN
ejpam-5734	218	25	}	}	PUNCT
ejpam-5734	218	26	∪	∪	ADJ
ejpam-5734	218	27	{	{	PUNCT
ejpam-5734	218	28	a4	a4	NOUN
ejpam-5734	218	29	}	}	PUNCT
ejpam-5734	218	30	∪	∪	NOUN
ejpam-5734	218	31	{	{	PUNCT
ejpam-5734	218	32	a5	a5	NOUN
ejpam-5734	218	33	}	}	PUNCT
ejpam-5734	218	34	∪	∪	NOUN
ejpam-5734	218	35	{	{	PUNCT
ejpam-5734	218	36	a6	a6	NOUN
ejpam-5734	218	37	}	}	PUNCT
ejpam-5734	218	38	∪	∪	NOUN
ejpam-5734	218	39	{	{	PUNCT
ejpam-5734	218	40	a7	a7	NOUN
ejpam-5734	218	41	}	}	PUNCT
ejpam-5734	218	42	=	=	SYM
ejpam-5734	218	43	{	{	PUNCT
ejpam-5734	218	44	v3i−2	v3i−2	PROPN
ejpam-5734	218	45	,	,	PUNCT
ejpam-5734	218	46	v3i−1	v3i−1	PROPN
ejpam-5734	218	47	,	,	PUNCT
ejpam-5734	218	48	v3i	v3i	NOUN
ejpam-5734	218	49	|	|	ADV
ejpam-5734	218	50	1	1	NUM
ejpam-5734	218	51	≤	≤	NUM
ejpam-5734	218	52	i	i	PRON
ejpam-5734	218	53	≤	≤	NOUN
ejpam-5734	218	54	⌊n/3⌋	⌊n/3⌋	NOUN
ejpam-5734	218	55	}	}	PUNCT
ejpam-5734	218	56	∪	∪	X
ejpam-5734	218	57	{	{	PUNCT
ejpam-5734	218	58	vn	vn	NOUN
ejpam-5734	218	59	,	,	PUNCT
ejpam-5734	218	60	v′3i	v′3i	PROPN
ejpam-5734	218	61	|	|	CCONJ
ejpam-5734	218	62	1	1	NUM
ejpam-5734	218	63	≤	≤	NUM
ejpam-5734	218	64	i	i	PRON
ejpam-5734	218	65	≤	≤	NOUN
ejpam-5734	218	66	⌊n/3⌋	⌊n/3⌋	PUNCT
ejpam-5734	218	67	−	−	PROPN
ejpam-5734	218	68	1	1	NUM
ejpam-5734	218	69	}	}	PUNCT
ejpam-5734	218	70	∪	∪	NOUN
ejpam-5734	218	71	{	{	PUNCT
ejpam-5734	218	72	v′3i+1	v′3i+1	NOUN
ejpam-5734	218	73	|	|	NOUN
ejpam-5734	218	74	1	1	NUM
ejpam-5734	218	75	≤	≤	NUM
ejpam-5734	218	76	i	i	PRON
ejpam-5734	218	77	≤	≤	NOUN
ejpam-5734	218	78	⌊n/3⌋	⌊n/3⌋	NOUN
ejpam-5734	218	79	}	}	PUNCT
ejpam-5734	218	80	∪	∪	X
ejpam-5734	218	81	{	{	PUNCT
ejpam-5734	218	82	v′1	v′1	ADJ
ejpam-5734	218	83	,	,	PUNCT
ejpam-5734	218	84	v′3i+2	v′3i+2	PRON
ejpam-5734	218	85	|	|	NOUN
ejpam-5734	218	86	1	1	X
ejpam-5734	218	87	≤	≤	NUM
ejpam-5734	218	88	i	i	PRON
ejpam-5734	218	89	≤	≤	NOUN
ejpam-5734	218	90	⌊n/3⌋	⌊n/3⌋	PUNCT
ejpam-5734	218	91	−	−	PROPN
ejpam-5734	218	92	1	1	NUM
ejpam-5734	218	93	}	}	PUNCT
ejpam-5734	218	94	∪	∪	ADJ
ejpam-5734	218	95	{	{	PUNCT
ejpam-5734	218	96	v′2	v′2	ADJ
ejpam-5734	218	97	,	,	PUNCT
ejpam-5734	218	98	v′n−1	v′n−1	PROPN
ejpam-5734	218	99	}	}	PUNCT
ejpam-5734	218	100	=	=	SYM
ejpam-5734	218	101	{	{	PUNCT
ejpam-5734	218	102	v1	v1	PROPN
ejpam-5734	218	103	,	,	PUNCT
ejpam-5734	218	104	v2	v2	PROPN
ejpam-5734	218	105	,	,	PUNCT
ejpam-5734	218	106	v3	v3	PROPN
ejpam-5734	218	107	,	,	PUNCT
ejpam-5734	218	108	.	.	PUNCT
ejpam-5734	218	109	.	.	PUNCT
ejpam-5734	219	1	.	.	PUNCT
ejpam-5734	220	1	,	,	PUNCT
ejpam-5734	220	2	vn−2	vn−2	PROPN
ejpam-5734	220	3	,	,	PUNCT
ejpam-5734	220	4	vn−1	vn−1	ADJ
ejpam-5734	220	5	}	}	PUNCT
ejpam-5734	220	6	∪	∪	ADJ
ejpam-5734	220	7	{	{	PUNCT
ejpam-5734	220	8	vn	vn	NOUN
ejpam-5734	220	9	,	,	PUNCT
ejpam-5734	220	10	v′3	v′3	NOUN
ejpam-5734	220	11	,	,	PUNCT
ejpam-5734	220	12	v′6	v′6	NOUN
ejpam-5734	220	13	,	,	PUNCT
ejpam-5734	220	14	.	.	PUNCT
ejpam-5734	220	15	.	.	PUNCT
ejpam-5734	221	1	.	.	PUNCT
ejpam-5734	222	1	,	,	PUNCT
ejpam-5734	222	2	v′n−7	v′n−7	NOUN
ejpam-5734	222	3	,	,	PUNCT
ejpam-5734	222	4	v	v	NOUN
ejpam-5734	222	5	′	′	NUM
ejpam-5734	222	6	n−4	n−4	NOUN
ejpam-5734	222	7	}	}	PUNCT
ejpam-5734	222	8	∪	∪	ADJ
ejpam-5734	222	9	{	{	PUNCT
ejpam-5734	222	10	v′4	v′4	NOUN
ejpam-5734	222	11	,	,	PUNCT
ejpam-5734	222	12	v′7	v′7	ADJ
ejpam-5734	222	13	,	,	PUNCT
ejpam-5734	222	14	.	.	PUNCT
ejpam-5734	222	15	.	.	PUNCT
ejpam-5734	223	1	.	.	PUNCT
ejpam-5734	224	1	,	,	PUNCT
ejpam-5734	224	2	v′n−3	v′n−3	PROPN
ejpam-5734	224	3	,	,	PUNCT
ejpam-5734	224	4	v	v	NOUN
ejpam-5734	224	5	′	′	NUM
ejpam-5734	224	6	n	n	CCONJ
ejpam-5734	224	7	}	}	PUNCT
ejpam-5734	224	8	∪	∪	X
ejpam-5734	224	9	{	{	PUNCT
ejpam-5734	224	10	v′1	v′1	ADJ
ejpam-5734	224	11	,	,	PUNCT
ejpam-5734	224	12	v′5	v′5	NOUN
ejpam-5734	224	13	,	,	PUNCT
ejpam-5734	224	14	v′8	v′8	VERB
ejpam-5734	224	15	,	,	PUNCT
ejpam-5734	224	16	.	.	PUNCT
ejpam-5734	224	17	.	.	PUNCT
ejpam-5734	225	1	.	.	PUNCT
ejpam-5734	226	1	,	,	PUNCT
ejpam-5734	227	1	v′n−5	v′n−5	ADV
ejpam-5734	227	2	,	,	PUNCT
ejpam-5734	227	3	v	v	ADP
ejpam-5734	227	4	′	′	NUM
ejpam-5734	227	5	n−2	n−2	PROPN
ejpam-5734	227	6	}	}	PUNCT
ejpam-5734	227	7	∪	∪	X
ejpam-5734	227	8	{	{	PUNCT
ejpam-5734	227	9	v′2	v′2	ADJ
ejpam-5734	227	10	,	,	PUNCT
ejpam-5734	227	11	v′n−1	v′n−1	PROPN
ejpam-5734	227	12	}	}	PUNCT
ejpam-5734	227	13	=	=	SYM
ejpam-5734	227	14	{	{	PUNCT
ejpam-5734	227	15	v1	v1	PROPN
ejpam-5734	227	16	,	,	PUNCT
ejpam-5734	227	17	v2	v2	PROPN
ejpam-5734	227	18	,	,	PUNCT
ejpam-5734	227	19	v3	v3	PROPN
ejpam-5734	227	20	,	,	PUNCT
ejpam-5734	227	21	.	.	PUNCT
ejpam-5734	227	22	.	.	PUNCT
ejpam-5734	227	23	.	.	PUNCT
ejpam-5734	228	1	,	,	PUNCT
ejpam-5734	228	2	vn−1	vn−1	PROPN
ejpam-5734	228	3	,	,	PUNCT
ejpam-5734	228	4	vn	vn	NOUN
ejpam-5734	228	5	,	,	PUNCT
ejpam-5734	228	6	v	v	ADJ
ejpam-5734	228	7	′	′	NUM
ejpam-5734	228	8	1	1	NUM
ejpam-5734	228	9	,	,	PUNCT
ejpam-5734	228	10	v	v	NOUN
ejpam-5734	228	11	′	′	NUM
ejpam-5734	228	12	2	2	NUM
ejpam-5734	228	13	,	,	PUNCT
ejpam-5734	228	14	v	v	NOUN
ejpam-5734	228	15	′	′	NUM
ejpam-5734	228	16	3	3	NUM
ejpam-5734	228	17	,	,	PUNCT
ejpam-5734	228	18	.	.	PUNCT
ejpam-5734	228	19	.	.	PUNCT
ejpam-5734	229	1	.	.	PUNCT
ejpam-5734	230	1	,	,	PUNCT
ejpam-5734	230	2	v	v	X
ejpam-5734	230	3	′	′	NUM
ejpam-5734	231	1	n−2	n−2	PROPN
ejpam-5734	231	2	,	,	PUNCT
ejpam-5734	231	3	v	v	NOUN
ejpam-5734	231	4	′	′	NUM
ejpam-5734	231	5	n−1	n−1	PROPN
ejpam-5734	231	6	,	,	PUNCT
ejpam-5734	231	7	v	v	NOUN
ejpam-5734	231	8	′	′	NUM
ejpam-5734	231	9	n	n	CCONJ
ejpam-5734	231	10	}	}	PUNCT
ejpam-5734	231	11	=	=	SYM
ejpam-5734	231	12	v	v	NOUN
ejpam-5734	231	13	(	(	PUNCT
ejpam-5734	231	14	d2(cn	d2(cn	NOUN
ejpam-5734	231	15	)	)	PUNCT
ejpam-5734	231	16	)	)	PUNCT
ejpam-5734	231	17	ii	ii	PROPN
ejpam-5734	231	18	.	.	PUNCT
ejpam-5734	232	1	to	to	PART
ejpam-5734	232	2	verify	verify	VERB
ejpam-5734	232	3	that	that	SCONJ
ejpam-5734	232	4	the	the	DET
ejpam-5734	232	5	color	color	NOUN
ejpam-5734	232	6	classes	class	NOUN
ejpam-5734	232	7	are	be	AUX
ejpam-5734	232	8	disjoint	disjoint	ADJ
ejpam-5734	232	9	,	,	PUNCT
ejpam-5734	232	10	we	we	PRON
ejpam-5734	232	11	also	also	ADV
ejpam-5734	232	12	have	have	VERB
ejpam-5734	232	13	to	to	PART
ejpam-5734	232	14	show	show	VERB
ejpam-5734	232	15	that	that	SCONJ
ejpam-5734	232	16	∑	∑	PROPN
ejpam-5734	232	17	a∈c	a∈c	PROPN
ejpam-5734	232	18	|a|	|a|	PROPN
ejpam-5734	232	19	=	=	PROPN
ejpam-5734	232	20	|v	|v	NOUN
ejpam-5734	233	1	[	[	X
ejpam-5734	233	2	d2(cn)]|	d2(cn)]|	ADP
ejpam-5734	233	3	in	in	ADP
ejpam-5734	233	4	addition	addition	NOUN
ejpam-5734	233	5	to	to	ADP
ejpam-5734	233	6	the	the	DET
ejpam-5734	233	7	above	above	ADJ
ejpam-5734	233	8	condition.∑	condition.∑	NOUN
ejpam-5734	233	9	a∈c	a∈c	PROPN
ejpam-5734	233	10	|a|	|a|	PROPN
ejpam-5734	233	11	=	=	PUNCT
ejpam-5734	233	12	|a1|+	|a1|+	PRON
ejpam-5734	233	13	|a2|+	|a2|+	ADJ
ejpam-5734	233	14	|a3|+	|a3|+	ADP
ejpam-5734	233	15	|a4|+	|a4|+	NOUN
ejpam-5734	233	16	|a5|+	|a5|+	NOUN
ejpam-5734	233	17	|a6|	|a6|	NOUN
ejpam-5734	233	18	=	=	SYM
ejpam-5734	233	19	⌊n	⌊n	NUM
ejpam-5734	233	20	3	3	NUM
ejpam-5734	233	21	⌋+	⌋+	X
ejpam-5734	233	22	⌊n	⌊n	NUM
ejpam-5734	233	23	3	3	NUM
ejpam-5734	233	24	⌋+	⌋+	X
ejpam-5734	233	25	⌊n	⌊n	NUM
ejpam-5734	233	26	3	3	NUM
ejpam-5734	233	27	⌋+	⌋+	X
ejpam-5734	233	28	(	(	PUNCT
ejpam-5734	233	29	1	1	NUM
ejpam-5734	233	30	+	+	CCONJ
ejpam-5734	233	31	⌊n	⌊n	ADJ
ejpam-5734	233	32	3	3	NUM
ejpam-5734	233	33	⌋	⌋	NOUN
ejpam-5734	233	34	−	−	NOUN
ejpam-5734	233	35	1	1	NUM
ejpam-5734	233	36	)	)	PUNCT
ejpam-5734	234	1	+	+	CCONJ
ejpam-5734	234	2	⌊n	⌊n	SYM
ejpam-5734	234	3	3	3	NUM
ejpam-5734	234	4	⌋+	⌋+	X
ejpam-5734	234	5	(	(	PUNCT
ejpam-5734	234	6	⌊n	⌊n	X
ejpam-5734	234	7	3	3	NUM
ejpam-5734	234	8	⌋	⌋	NOUN
ejpam-5734	234	9	−	−	NOUN
ejpam-5734	234	10	1	1	NUM
ejpam-5734	234	11	+	+	NUM
ejpam-5734	234	12	1	1	NUM
ejpam-5734	234	13	)	)	PUNCT
ejpam-5734	234	14	+	+	CCONJ
ejpam-5734	234	15	2	2	NUM
ejpam-5734	234	16	=	=	SYM
ejpam-5734	234	17	6	6	NUM
ejpam-5734	234	18	n−	n−	NOUN
ejpam-5734	234	19	1	1	NUM
ejpam-5734	234	20	3	3	NUM
ejpam-5734	234	21	+	+	NUM
ejpam-5734	234	22	2	2	NUM
ejpam-5734	234	23	since	since	SCONJ
ejpam-5734	234	24	n	n	X
ejpam-5734	234	25	≡	≡	PROPN
ejpam-5734	234	26	1	1	NUM
ejpam-5734	234	27	(	(	PUNCT
ejpam-5734	234	28	mod	mod	NOUN
ejpam-5734	234	29	3	3	NUM
ejpam-5734	234	30	)	)	PUNCT
ejpam-5734	234	31	=	=	SYM
ejpam-5734	234	32	2n	2n	NUM
ejpam-5734	234	33	=	=	SYM
ejpam-5734	234	34	|v	|v	X
ejpam-5734	235	1	[	[	X
ejpam-5734	235	2	d2(cn)]|	d2(cn)]|	VERB
ejpam-5734	235	3	by	by	ADP
ejpam-5734	235	4	lemma	lemma	PROPN
ejpam-5734	235	5	1	1	NUM
ejpam-5734	235	6	,	,	PUNCT
ejpam-5734	235	7	color	color	NOUN
ejpam-5734	235	8	classes	class	NOUN
ejpam-5734	235	9	are	be	AUX
ejpam-5734	235	10	mutually	mutually	ADV
ejpam-5734	235	11	exclusive	exclusive	ADJ
ejpam-5734	235	12	,	,	PUNCT
ejpam-5734	235	13	that	that	ADV
ejpam-5734	235	14	is	is	ADV
ejpam-5734	235	15	,	,	PUNCT
ejpam-5734	235	16	ak	ak	PROPN
ejpam-5734	235	17	∩	∩	PROPN
ejpam-5734	235	18	aj	aj	PROPN
ejpam-5734	235	19	=	=	PROPN
ejpam-5734	235	20	∅	∅	NOUN
ejpam-5734	235	21	for	for	ADP
ejpam-5734	235	22	k	k	PROPN
ejpam-5734	235	23	̸=	̸=	PROPN
ejpam-5734	235	24	j.	j.	PROPN
ejpam-5734	235	25	subsequently	subsequently	ADV
ejpam-5734	235	26	,	,	PUNCT
ejpam-5734	235	27	for	for	ADP
ejpam-5734	235	28	each	each	DET
ejpam-5734	235	29	vi	vi	NOUN
ejpam-5734	235	30	,	,	PUNCT
ejpam-5734	235	31	vj	vj	PROPN
ejpam-5734	235	32	∈	∈	PROPN
ejpam-5734	235	33	ak	ak	PROPN
ejpam-5734	235	34	,	,	PUNCT
ejpam-5734	235	35	1	1	NUM
ejpam-5734	235	36	≤	≤	NUM
ejpam-5734	235	37	k	k	X
ejpam-5734	235	38	≤	≤	NUM
ejpam-5734	235	39	7	7	NUM
ejpam-5734	235	40	,	,	PUNCT
ejpam-5734	235	41	we	we	PRON
ejpam-5734	235	42	have	have	VERB
ejpam-5734	235	43	d(vi	d(vi	PROPN
ejpam-5734	235	44	,	,	PUNCT
ejpam-5734	235	45	vj	vj	PROPN
ejpam-5734	235	46	)	)	PUNCT
ejpam-5734	235	47	≥	≥	NOUN
ejpam-5734	235	48	3	3	NUM
ejpam-5734	235	49	.	.	PUNCT
ejpam-5734	236	1	hence	hence	ADV
ejpam-5734	236	2	,	,	PUNCT
ejpam-5734	236	3	c	c	PROPN
ejpam-5734	236	4	=	=	PRON
ejpam-5734	236	5	{	{	PUNCT
ejpam-5734	236	6	a1,a2,a3,a4,a5,a6,a7	a1,a2,a3,a4,a5,a6,a7	PROPN
ejpam-5734	236	7	}	}	PUNCT
ejpam-5734	236	8	is	be	AUX
ejpam-5734	236	9	a	a	DET
ejpam-5734	236	10	distance-2	distance-2	CCONJ
ejpam-5734	236	11	chromatic	chromatic	ADJ
ejpam-5734	236	12	set	set	NOUN
ejpam-5734	236	13	of	of	ADP
ejpam-5734	236	14	d2(cn	d2(cn	PROPN
ejpam-5734	236	15	)	)	PUNCT
ejpam-5734	236	16	,	,	PUNCT
ejpam-5734	236	17	and	and	CCONJ
ejpam-5734	236	18	χ2	χ2	PROPN
ejpam-5734	236	19	[	[	PUNCT
ejpam-5734	236	20	d2(cn	d2(cn	PROPN
ejpam-5734	236	21	)	)	PUNCT
ejpam-5734	236	22	]	]	PUNCT
ejpam-5734	236	23	≤	≤	NUM
ejpam-5734	236	24	7	7	NUM
ejpam-5734	236	25	.	.	PUNCT
ejpam-5734	237	1	suppose	suppose	VERB
ejpam-5734	238	1	χ2	χ2	PROPN
ejpam-5734	238	2	[	[	PUNCT
ejpam-5734	238	3	d2(cn	d2(cn	PROPN
ejpam-5734	238	4	)	)	PUNCT
ejpam-5734	238	5	]	]	PUNCT
ejpam-5734	238	6	<	<	X
ejpam-5734	238	7	7	7	NUM
ejpam-5734	238	8	,	,	PUNCT
ejpam-5734	238	9	say	say	VERB
ejpam-5734	238	10	6	6	NUM
ejpam-5734	238	11	(	(	PUNCT
ejpam-5734	238	12	there	there	PRON
ejpam-5734	238	13	is	be	VERB
ejpam-5734	238	14	no	no	DET
ejpam-5734	238	15	a7	a7	PROPN
ejpam-5734	238	16	)	)	PUNCT
ejpam-5734	238	17	.	.	PUNCT
ejpam-5734	239	1	choose	choose	VERB
ejpam-5734	239	2	one	one	NUM
ejpam-5734	239	3	of	of	ADP
ejpam-5734	239	4	the	the	DET
ejpam-5734	239	5	other	other	ADJ
ejpam-5734	239	6	classes	class	NOUN
ejpam-5734	239	7	,	,	PUNCT
ejpam-5734	239	8	say	say	VERB
ejpam-5734	239	9	a1	a1	PROPN
ejpam-5734	239	10	,	,	PUNCT
ejpam-5734	239	11	to	to	PART
ejpam-5734	239	12	absorb	absorb	VERB
ejpam-5734	239	13	v′2	v′2	NOUN
ejpam-5734	239	14	and	and	CCONJ
ejpam-5734	239	15	v′n−1	v′n−1	NOUN
ejpam-5734	239	16	,	,	PUNCT
ejpam-5734	239	17	but	but	CCONJ
ejpam-5734	239	18	d(v	d(v	ADJ
ejpam-5734	239	19	′	′	NOUN
ejpam-5734	239	20	2	2	NUM
ejpam-5734	239	21	,	,	PUNCT
ejpam-5734	239	22	v3i−2	v3i−2	PROPN
ejpam-5734	239	23	)	)	PUNCT
ejpam-5734	239	24	=	=	SYM
ejpam-5734	240	1	1	1	NUM
ejpam-5734	240	2	when	when	SCONJ
ejpam-5734	240	3	i	i	PRON
ejpam-5734	240	4	=	=	NOUN
ejpam-5734	240	5	1	1	NUM
ejpam-5734	240	6	,	,	PUNCT
ejpam-5734	240	7	a	a	DET
ejpam-5734	240	8	contradiction	contradiction	NOUN
ejpam-5734	240	9	.	.	PUNCT
ejpam-5734	241	1	this	this	DET
ejpam-5734	241	2	contradiction	contradiction	NOUN
ejpam-5734	241	3	is	be	AUX
ejpam-5734	241	4	also	also	ADV
ejpam-5734	241	5	true	true	ADJ
ejpam-5734	241	6	for	for	ADP
ejpam-5734	241	7	the	the	DET
ejpam-5734	241	8	other	other	ADJ
ejpam-5734	241	9	classes	class	NOUN
ejpam-5734	241	10	:	:	PUNCT
ejpam-5734	241	11	m.	m.	PROPN
ejpam-5734	241	12	f.	f.	PROPN
ejpam-5734	241	13	libao	libao	PROPN
ejpam-5734	241	14	,	,	PUNCT
ejpam-5734	241	15	k.	k.	PROPN
ejpam-5734	241	16	b.	b.	PROPN
ejpam-5734	241	17	abarca	abarca	PROPN
ejpam-5734	241	18	/	/	SYM
ejpam-5734	241	19	eur	eur	PROPN
ejpam-5734	241	20	.	.	PUNCT
ejpam-5734	242	1	j.	j.	PROPN
ejpam-5734	242	2	pure	pure	PROPN
ejpam-5734	242	3	appl	appl	PROPN
ejpam-5734	242	4	.	.	PROPN
ejpam-5734	242	5	math	math	PROPN
ejpam-5734	242	6	,	,	PUNCT
ejpam-5734	242	7	18	18	NUM
ejpam-5734	242	8	(	(	PUNCT
ejpam-5734	242	9	2	2	NUM
ejpam-5734	242	10	)	)	PUNCT
ejpam-5734	242	11	(	(	PUNCT
ejpam-5734	242	12	2025	2025	NUM
ejpam-5734	242	13	)	)	PUNCT
ejpam-5734	242	14	,	,	PUNCT
ejpam-5734	242	15	5734	5734	NUM
ejpam-5734	242	16	13	13	NUM
ejpam-5734	242	17	of	of	ADP
ejpam-5734	242	18	25	25	NUM
ejpam-5734	242	19	a2	a2	PROPN
ejpam-5734	242	20	:	:	PUNCT
ejpam-5734	242	21	d(v′2	d(v′2	PROPN
ejpam-5734	242	22	,	,	PUNCT
ejpam-5734	242	23	v3i−1	v3i−1	PROPN
ejpam-5734	242	24	)	)	PUNCT
ejpam-5734	242	25	=	=	SYM
ejpam-5734	242	26	2	2	NUM
ejpam-5734	242	27	when	when	SCONJ
ejpam-5734	242	28	i	i	PRON
ejpam-5734	242	29	=	=	SYM
ejpam-5734	242	30	1	1	NUM
ejpam-5734	242	31	a3	a3	NOUN
ejpam-5734	242	32	:	:	PUNCT
ejpam-5734	242	33	d(v′2	d(v′2	PROPN
ejpam-5734	242	34	,	,	PUNCT
ejpam-5734	242	35	v3i	v3i	NOUN
ejpam-5734	242	36	)	)	PUNCT
ejpam-5734	242	37	=	=	SYM
ejpam-5734	243	1	1	1	NUM
ejpam-5734	243	2	when	when	SCONJ
ejpam-5734	243	3	i	i	PRON
ejpam-5734	243	4	=	=	SYM
ejpam-5734	243	5	1	1	NUM
ejpam-5734	243	6	a4	a4	NUM
ejpam-5734	243	7	:	:	PUNCT
ejpam-5734	243	8	d(v′2	d(v′2	NOUN
ejpam-5734	243	9	,	,	PUNCT
ejpam-5734	243	10	v	v	ADJ
ejpam-5734	243	11	′	′	NUM
ejpam-5734	243	12	3i	3i	NOUN
ejpam-5734	243	13	)	)	PUNCT
ejpam-5734	243	14	=	=	SYM
ejpam-5734	244	1	1	1	NUM
ejpam-5734	244	2	when	when	SCONJ
ejpam-5734	244	3	i	i	PRON
ejpam-5734	244	4	=	=	VERB
ejpam-5734	244	5	1	1	NUM
ejpam-5734	244	6	a5	a5	NOUN
ejpam-5734	244	7	:	:	PUNCT
ejpam-5734	244	8	d(v′2	d(v′2	PROPN
ejpam-5734	244	9	,	,	PUNCT
ejpam-5734	244	10	v	v	NOUN
ejpam-5734	244	11	′	′	NUM
ejpam-5734	244	12	4	4	NUM
ejpam-5734	244	13	)	)	PUNCT
ejpam-5734	244	14	=	=	SYM
ejpam-5734	244	15	2	2	NUM
ejpam-5734	244	16	a6	a6	NOUN
ejpam-5734	244	17	:	:	PUNCT
ejpam-5734	244	18	d(v′2	d(v′2	PROPN
ejpam-5734	244	19	,	,	PUNCT
ejpam-5734	244	20	v	v	NOUN
ejpam-5734	244	21	′	′	NUM
ejpam-5734	244	22	1	1	NUM
ejpam-5734	244	23	)	)	PUNCT
ejpam-5734	244	24	=	=	SYM
ejpam-5734	244	25	1	1	NUM
ejpam-5734	244	26	a1	a1	NOUN
ejpam-5734	244	27	:	:	PUNCT
ejpam-5734	244	28	d(v′n−1	d(v′n−1	PROPN
ejpam-5734	244	29	,	,	PUNCT
ejpam-5734	244	30	vn−3	vn−3	PROPN
ejpam-5734	244	31	)	)	PUNCT
ejpam-5734	244	32	=	=	SYM
ejpam-5734	244	33	2	2	NUM
ejpam-5734	244	34	a2	a2	NOUN
ejpam-5734	244	35	:	:	PUNCT
ejpam-5734	244	36	d(v′n−1	d(v′n−1	PROPN
ejpam-5734	244	37	,	,	PUNCT
ejpam-5734	244	38	vn−2	vn−2	PROPN
ejpam-5734	244	39	)	)	PUNCT
ejpam-5734	244	40	=	=	SYM
ejpam-5734	244	41	1	1	NUM
ejpam-5734	244	42	a3	a3	NOUN
ejpam-5734	244	43	:	:	PUNCT
ejpam-5734	244	44	d(v′n−1	d(v′n−1	PROPN
ejpam-5734	244	45	,	,	PUNCT
ejpam-5734	244	46	vn−1	vn−1	ADJ
ejpam-5734	244	47	)	)	PUNCT
ejpam-5734	244	48	=	=	SYM
ejpam-5734	244	49	2	2	NUM
ejpam-5734	244	50	a4	a4	NOUN
ejpam-5734	244	51	:	:	PUNCT
ejpam-5734	244	52	d(v′n−1	d(v′n−1	PROPN
ejpam-5734	244	53	,	,	PUNCT
ejpam-5734	244	54	vn	vn	NOUN
ejpam-5734	244	55	)	)	PUNCT
ejpam-5734	244	56	=	=	SYM
ejpam-5734	244	57	1	1	NUM
ejpam-5734	244	58	a5	a5	NOUN
ejpam-5734	244	59	:	:	PUNCT
ejpam-5734	244	60	d(v′n−1	d(v′n−1	PROPN
ejpam-5734	244	61	,	,	PUNCT
ejpam-5734	244	62	v	v	NOUN
ejpam-5734	244	63	′	′	NUM
ejpam-5734	244	64	n	n	CCONJ
ejpam-5734	244	65	)	)	PUNCT
ejpam-5734	244	66	=	=	SYM
ejpam-5734	244	67	1	1	NUM
ejpam-5734	244	68	a6	a6	NOUN
ejpam-5734	244	69	:	:	PUNCT
ejpam-5734	244	70	d(v′n−1	d(v′n−1	ADJ
ejpam-5734	244	71	,	,	PUNCT
ejpam-5734	244	72	v	v	ADP
ejpam-5734	244	73	′	′	NUM
ejpam-5734	244	74	n−2	n−2	PROPN
ejpam-5734	244	75	)	)	PUNCT
ejpam-5734	244	76	=	=	PUNCT
ejpam-5734	244	77	1	1	NUM
ejpam-5734	244	78	this	this	PRON
ejpam-5734	244	79	gives	give	VERB
ejpam-5734	244	80	us	we	PRON
ejpam-5734	244	81	the	the	DET
ejpam-5734	244	82	conclusion	conclusion	NOUN
ejpam-5734	244	83	that	that	SCONJ
ejpam-5734	244	84	χ2	χ2	PROPN
ejpam-5734	244	85	[	[	PUNCT
ejpam-5734	244	86	d2(cn	d2(cn	PROPN
ejpam-5734	244	87	)	)	PUNCT
ejpam-5734	244	88	]	]	PUNCT
ejpam-5734	244	89	̸	̸	X
ejpam-5734	244	90	<	<	X
ejpam-5734	244	91	7	7	NUM
ejpam-5734	244	92	.	.	PUNCT
ejpam-5734	244	93	thus	thus	ADV
ejpam-5734	244	94	,	,	PUNCT
ejpam-5734	244	95	χ2	χ2	PROPN
ejpam-5734	244	96	[	[	PUNCT
ejpam-5734	244	97	d2(cn	d2(cn	PROPN
ejpam-5734	244	98	)	)	PUNCT
ejpam-5734	244	99	]	]	PUNCT
ejpam-5734	245	1	=	=	PUNCT
ejpam-5734	245	2	7	7	NUM
ejpam-5734	245	3	when	when	SCONJ
ejpam-5734	245	4	n	n	X
ejpam-5734	245	5	≡	≡	PROPN
ejpam-5734	245	6	1	1	NUM
ejpam-5734	245	7	(	(	PUNCT
ejpam-5734	245	8	mod	mod	NOUN
ejpam-5734	245	9	3	3	NUM
ejpam-5734	245	10	)	)	PUNCT
ejpam-5734	245	11	.	.	PUNCT
ejpam-5734	246	1	below	below	ADV
ejpam-5734	246	2	is	be	AUX
ejpam-5734	246	3	an	an	DET
ejpam-5734	246	4	example	example	NOUN
ejpam-5734	246	5	of	of	ADP
ejpam-5734	246	6	a	a	DET
ejpam-5734	246	7	shadow	shadow	NOUN
ejpam-5734	246	8	graph	graph	NOUN
ejpam-5734	246	9	of	of	ADP
ejpam-5734	246	10	c7	c7	PROPN
ejpam-5734	246	11	,	,	PUNCT
ejpam-5734	246	12	d2(c7	d2(c7	PROPN
ejpam-5734	246	13	)	)	PUNCT
ejpam-5734	246	14	,	,	PUNCT
ejpam-5734	246	15	with	with	ADP
ejpam-5734	246	16	a	a	DET
ejpam-5734	246	17	distance-2	distance-2	CCONJ
ejpam-5734	246	18	chromatic	chromatic	ADJ
ejpam-5734	246	19	number	number	NOUN
ejpam-5734	246	20	of	of	ADP
ejpam-5734	246	21	7	7	NUM
ejpam-5734	246	22	.	.	PUNCT
ejpam-5734	247	1	here	here	ADV
ejpam-5734	247	2	,	,	PUNCT
ejpam-5734	247	3	c	c	NOUN
ejpam-5734	247	4	=	=	PRON
ejpam-5734	247	5	{	{	PUNCT
ejpam-5734	247	6	red	red	ADJ
ejpam-5734	247	7	(	(	PUNCT
ejpam-5734	247	8	v1	v1	NOUN
ejpam-5734	247	9	,	,	PUNCT
ejpam-5734	247	10	v4),blue	v4),blue	NOUN
ejpam-5734	247	11	(	(	PUNCT
ejpam-5734	247	12	v2	v2	NOUN
ejpam-5734	247	13	,	,	PUNCT
ejpam-5734	247	14	v5),green	v5),green	X
ejpam-5734	247	15	(	(	PUNCT
ejpam-5734	247	16	v3	v3	PROPN
ejpam-5734	247	17	,	,	PUNCT
ejpam-5734	247	18	v6),black	v6),black	NOUN
ejpam-5734	247	19	(	(	PUNCT
ejpam-5734	247	20	v7	v7	VERB
ejpam-5734	247	21	,	,	PUNCT
ejpam-5734	247	22	v	v	NOUN
ejpam-5734	247	23	′	′	NUM
ejpam-5734	247	24	3),orange	3),orange	NUM
ejpam-5734	247	25	(	(	PUNCT
ejpam-5734	247	26	v′4	v′4	NOUN
ejpam-5734	247	27	,	,	PUNCT
ejpam-5734	247	28	v	v	NOUN
ejpam-5734	247	29	′	′	NUM
ejpam-5734	247	30	7),pink	7),pink	NUM
ejpam-5734	247	31	(	(	PUNCT
ejpam-5734	247	32	v′1	v′1	NOUN
ejpam-5734	247	33	,	,	PUNCT
ejpam-5734	247	34	v	v	NOUN
ejpam-5734	247	35	′	′	NUM
ejpam-5734	247	36	5),purple	5),purple	NUM
ejpam-5734	247	37	(	(	PUNCT
ejpam-5734	247	38	v	v	NOUN
ejpam-5734	247	39	′	′	NUM
ejpam-5734	247	40	2	2	NUM
ejpam-5734	247	41	,	,	PUNCT
ejpam-5734	247	42	v	v	NOUN
ejpam-5734	247	43	′	′	NUM
ejpam-5734	247	44	6	6	NUM
ejpam-5734	247	45	)	)	PUNCT
ejpam-5734	247	46	}	}	PUNCT
ejpam-5734	247	47	.	.	PUNCT
ejpam-5734	248	1	d2(c7	d2(c7	VERB
ejpam-5734	248	2	)	)	PUNCT
ejpam-5734	248	3	:	:	PUNCT
ejpam-5734	248	4	v1	v1	VERB
ejpam-5734	248	5	v2	v2	PROPN
ejpam-5734	248	6	v3	v3	PROPN
ejpam-5734	248	7	v4	v4	PROPN
ejpam-5734	248	8	v5v6v7	v5v6v7	NOUN
ejpam-5734	248	9	v′	v′	PROPN
ejpam-5734	248	10	1	1	NUM
ejpam-5734	248	11	v′	v′	NUM
ejpam-5734	248	12	2	2	NUM
ejpam-5734	248	13	v′	v′	NOUN
ejpam-5734	248	14	3	3	NUM
ejpam-5734	248	15	v′	v′	NOUN
ejpam-5734	248	16	4	4	NUM
ejpam-5734	248	17	v′	v′	NOUN
ejpam-5734	248	18	5v′	5v′	NUM
ejpam-5734	248	19	6v′	6v′	NUM
ejpam-5734	248	20	7	7	NUM
ejpam-5734	248	21	figure	figure	NOUN
ejpam-5734	248	22	8	8	NUM
ejpam-5734	248	23	:	:	PUNCT
ejpam-5734	248	24	the	the	DET
ejpam-5734	248	25	shadow	shadow	NOUN
ejpam-5734	248	26	graph	graph	NOUN
ejpam-5734	248	27	of	of	ADP
ejpam-5734	248	28	a	a	DET
ejpam-5734	248	29	cycle	cycle	NOUN
ejpam-5734	248	30	graph	graph	NOUN
ejpam-5734	248	31	c7	c7	PROPN
ejpam-5734	248	32	with	with	ADP
ejpam-5734	248	33	χ2[d2(c7	χ2[d2(c7	NOUN
ejpam-5734	248	34	)	)	PUNCT
ejpam-5734	248	35	]	]	PUNCT
ejpam-5734	249	1	=	=	SYM
ejpam-5734	249	2	7	7	NUM
ejpam-5734	249	3	m.	m.	NOUN
ejpam-5734	249	4	f.	f.	PROPN
ejpam-5734	249	5	libao	libao	PROPN
ejpam-5734	249	6	,	,	PUNCT
ejpam-5734	249	7	k.	k.	PROPN
ejpam-5734	249	8	b.	b.	PROPN
ejpam-5734	249	9	abarca	abarca	PROPN
ejpam-5734	249	10	/	/	SYM
ejpam-5734	249	11	eur	eur	PROPN
ejpam-5734	249	12	.	.	PUNCT
ejpam-5734	250	1	j.	j.	PROPN
ejpam-5734	250	2	pure	pure	PROPN
ejpam-5734	250	3	appl	appl	PROPN
ejpam-5734	250	4	.	.	PROPN
ejpam-5734	250	5	math	math	PROPN
ejpam-5734	250	6	,	,	PUNCT
ejpam-5734	250	7	18	18	NUM
ejpam-5734	250	8	(	(	PUNCT
ejpam-5734	250	9	2	2	NUM
ejpam-5734	250	10	)	)	PUNCT
ejpam-5734	250	11	(	(	PUNCT
ejpam-5734	250	12	2025	2025	NUM
ejpam-5734	250	13	)	)	PUNCT
ejpam-5734	250	14	,	,	PUNCT
ejpam-5734	250	15	5734	5734	NUM
ejpam-5734	250	16	14	14	NUM
ejpam-5734	250	17	of	of	ADP
ejpam-5734	250	18	25	25	NUM
ejpam-5734	250	19	case	case	NOUN
ejpam-5734	250	20	3	3	NUM
ejpam-5734	250	21	.	.	X
ejpam-5734	250	22	n	n	NUM
ejpam-5734	250	23	≡	≡	PROPN
ejpam-5734	250	24	2	2	NUM
ejpam-5734	250	25	(	(	PUNCT
ejpam-5734	250	26	mod	mod	NOUN
ejpam-5734	250	27	3	3	NUM
ejpam-5734	250	28	)	)	PUNCT
ejpam-5734	250	29	consider	consider	VERB
ejpam-5734	250	30	the	the	DET
ejpam-5734	250	31	following	follow	VERB
ejpam-5734	250	32	color	color	NOUN
ejpam-5734	250	33	classes	class	NOUN
ejpam-5734	250	34	in	in	ADP
ejpam-5734	250	35	d2(cn	d2(cn	NOUN
ejpam-5734	250	36	)	)	PUNCT
ejpam-5734	250	37	a1	a1	NOUN
ejpam-5734	250	38	=	=	SYM
ejpam-5734	250	39	{	{	PUNCT
ejpam-5734	250	40	v1	v1	PROPN
ejpam-5734	250	41	,	,	PUNCT
ejpam-5734	250	42	v5	v5	NOUN
ejpam-5734	250	43	}	}	PUNCT
ejpam-5734	250	44	∪	∪	NOUN
ejpam-5734	250	45	{	{	PUNCT
ejpam-5734	250	46	v3i	v3i	NOUN
ejpam-5734	250	47	|	|	ADV
ejpam-5734	250	48	3	3	NUM
ejpam-5734	250	49	≤	≤	NUM
ejpam-5734	251	1	i	i	PRON
ejpam-5734	251	2	≤	≤	ADV
ejpam-5734	251	3	⌊n	⌊n	X
ejpam-5734	251	4	3	3	NUM
ejpam-5734	251	5	⌋	⌋	NOUN
ejpam-5734	251	6	}	}	PUNCT
ejpam-5734	251	7	a2	a2	PROPN
ejpam-5734	251	8	=	=	PUNCT
ejpam-5734	251	9	{	{	PUNCT
ejpam-5734	251	10	v2	v2	PROPN
ejpam-5734	251	11	,	,	PUNCT
ejpam-5734	251	12	v6	v6	NOUN
ejpam-5734	251	13	}	}	PUNCT
ejpam-5734	251	14	∪	∪	X
ejpam-5734	251	15	{	{	PUNCT
ejpam-5734	251	16	v3i+1	v3i+1	NOUN
ejpam-5734	251	17	|	|	ADV
ejpam-5734	251	18	3	3	NUM
ejpam-5734	251	19	≤	≤	NUM
ejpam-5734	251	20	i	i	PRON
ejpam-5734	251	21	≤	≤	ADV
ejpam-5734	251	22	⌊n	⌊n	X
ejpam-5734	251	23	3	3	NUM
ejpam-5734	251	24	⌋	⌋	NOUN
ejpam-5734	251	25	}	}	PUNCT
ejpam-5734	251	26	a3	a3	NOUN
ejpam-5734	251	27	=	=	SYM
ejpam-5734	251	28	{	{	PUNCT
ejpam-5734	251	29	v3	v3	PROPN
ejpam-5734	251	30	,	,	PUNCT
ejpam-5734	251	31	v7	v7	VERB
ejpam-5734	251	32	}	}	PUNCT
ejpam-5734	251	33	∪	∪	X
ejpam-5734	251	34	{	{	PUNCT
ejpam-5734	251	35	v3i+2	v3i+2	ADV
ejpam-5734	251	36	|	|	ADV
ejpam-5734	251	37	3	3	X
ejpam-5734	251	38	≤	≤	NUM
ejpam-5734	252	1	i	i	PRON
ejpam-5734	252	2	≤	≤	ADV
ejpam-5734	252	3	⌊n	⌊n	X
ejpam-5734	252	4	3	3	NUM
ejpam-5734	252	5	⌋	⌋	NOUN
ejpam-5734	252	6	}	}	PUNCT
ejpam-5734	252	7	a4	a4	NOUN
ejpam-5734	252	8	=	=	SYM
ejpam-5734	252	9	{	{	PUNCT
ejpam-5734	252	10	v4	v4	NOUN
ejpam-5734	252	11	,	,	PUNCT
ejpam-5734	252	12	v8	v8	PROPN
ejpam-5734	252	13	}	}	PUNCT
ejpam-5734	252	14	a5	a5	PROPN
ejpam-5734	252	15	=	=	PUNCT
ejpam-5734	252	16	{	{	PUNCT
ejpam-5734	252	17	v′1	v′1	ADJ
ejpam-5734	252	18	,	,	PUNCT
ejpam-5734	252	19	v′5	v′5	NOUN
ejpam-5734	252	20	}	}	PUNCT
ejpam-5734	252	21	∪	∪	X
ejpam-5734	252	22	{	{	PUNCT
ejpam-5734	252	23	v′3i	v′3i	PROPN
ejpam-5734	252	24	|	|	CCONJ
ejpam-5734	252	25	3	3	NUM
ejpam-5734	252	26	≤	≤	NUM
ejpam-5734	253	1	i	i	PRON
ejpam-5734	253	2	≤	≤	ADV
ejpam-5734	253	3	⌊n	⌊n	X
ejpam-5734	253	4	3	3	NUM
ejpam-5734	253	5	⌋	⌋	NOUN
ejpam-5734	253	6	}	}	PUNCT
ejpam-5734	253	7	a6	a6	NOUN
ejpam-5734	253	8	=	=	SYM
ejpam-5734	253	9	{	{	PUNCT
ejpam-5734	253	10	v′2	v′2	NOUN
ejpam-5734	253	11	,	,	PUNCT
ejpam-5734	253	12	v′6	v′6	NOUN
ejpam-5734	253	13	}	}	PUNCT
ejpam-5734	253	14	∪	∪	NOUN
ejpam-5734	253	15	{	{	PUNCT
ejpam-5734	253	16	v′3i+1	v′3i+1	NOUN
ejpam-5734	253	17	|	|	ADV
ejpam-5734	253	18	3	3	NUM
ejpam-5734	253	19	≤	≤	NUM
ejpam-5734	253	20	i	i	PRON
ejpam-5734	253	21	≤	≤	ADV
ejpam-5734	253	22	⌊n	⌊n	X
ejpam-5734	253	23	3	3	NUM
ejpam-5734	253	24	⌋	⌋	NOUN
ejpam-5734	253	25	}	}	PUNCT
ejpam-5734	253	26	a7	a7	PROPN
ejpam-5734	253	27	=	=	SYM
ejpam-5734	253	28	{	{	PUNCT
ejpam-5734	253	29	v′3	v′3	NOUN
ejpam-5734	253	30	,	,	PUNCT
ejpam-5734	253	31	v′7	v′7	CCONJ
ejpam-5734	253	32	}	}	PUNCT
ejpam-5734	253	33	∪	∪	NOUN
ejpam-5734	253	34	{	{	PUNCT
ejpam-5734	253	35	v3i+2	v3i+2	ADV
ejpam-5734	253	36	|	|	ADV
ejpam-5734	253	37	3	3	X
ejpam-5734	253	38	≤	≤	NUM
ejpam-5734	253	39	i	i	PRON
ejpam-5734	253	40	≤	≤	NOUN
ejpam-5734	253	41	⌊a⌋	⌊a⌋	VERB
ejpam-5734	253	42	}	}	PUNCT
ejpam-5734	253	43	a8	a8	PROPN
ejpam-5734	253	44	=	=	SYM
ejpam-5734	253	45	{	{	PUNCT
ejpam-5734	253	46	v′4	v′4	NOUN
ejpam-5734	253	47	,	,	PUNCT
ejpam-5734	253	48	v′8	v′8	VERB
ejpam-5734	253	49	}	}	PUNCT
ejpam-5734	253	50	.	.	PUNCT
ejpam-5734	254	1	i.	i.	PROPN
ejpam-5734	254	2	to	to	PART
ejpam-5734	254	3	ensure	ensure	VERB
ejpam-5734	254	4	that	that	SCONJ
ejpam-5734	254	5	every	every	DET
ejpam-5734	254	6	vertex	vertex	NOUN
ejpam-5734	254	7	in	in	ADP
ejpam-5734	254	8	the	the	DET
ejpam-5734	254	9	graph	graph	NOUN
ejpam-5734	254	10	belongs	belong	VERB
ejpam-5734	254	11	to	to	ADP
ejpam-5734	254	12	exactly	exactly	ADV
ejpam-5734	254	13	one	one	NUM
ejpam-5734	254	14	color	color	NOUN
ejpam-5734	254	15	class	class	NOUN
ejpam-5734	254	16	:	:	PUNCT
ejpam-5734	254	17	⋃	⋃	PUNCT
ejpam-5734	254	18	a∈c	a∈c	NOUN
ejpam-5734	254	19	a	a	PRON
ejpam-5734	254	20	=	=	X
ejpam-5734	254	21	{	{	PUNCT
ejpam-5734	254	22	a1,a2,a3,a4,a5,a6,a7	a1,a2,a3,a4,a5,a6,a7	NOUN
ejpam-5734	254	23	}	}	PUNCT
ejpam-5734	254	24	to	to	PART
ejpam-5734	254	25	avoid	avoid	VERB
ejpam-5734	254	26	confusion	confusion	NOUN
ejpam-5734	254	27	,	,	PUNCT
ejpam-5734	254	28	we	we	PRON
ejpam-5734	254	29	group	group	VERB
ejpam-5734	254	30	the	the	DET
ejpam-5734	254	31	color	color	NOUN
ejpam-5734	254	32	classes	class	NOUN
ejpam-5734	254	33	as	as	SCONJ
ejpam-5734	254	34	follows	follow	VERB
ejpam-5734	254	35	:	:	PUNCT
ejpam-5734	254	36	⋃	⋃	PUNCT
ejpam-5734	254	37	a∈c	a∈c	VERB
ejpam-5734	254	38	a	a	PRON
ejpam-5734	254	39	=	=	PUNCT
ejpam-5734	254	40	{	{	PUNCT
ejpam-5734	254	41	a1	a1	PROPN
ejpam-5734	254	42	}	}	PUNCT
ejpam-5734	254	43	∪	∪	ADJ
ejpam-5734	254	44	{	{	PUNCT
ejpam-5734	254	45	a2	a2	NOUN
ejpam-5734	254	46	}	}	PUNCT
ejpam-5734	254	47	∪	∪	NOUN
ejpam-5734	254	48	{	{	PUNCT
ejpam-5734	254	49	a3	a3	NOUN
ejpam-5734	254	50	}	}	PUNCT
ejpam-5734	254	51	∪	∪	X
ejpam-5734	254	52	{	{	PUNCT
ejpam-5734	254	53	a4	a4	NOUN
ejpam-5734	254	54	}	}	PUNCT
ejpam-5734	254	55	∪	∪	NOUN
ejpam-5734	254	56	{	{	PUNCT
ejpam-5734	254	57	a5	a5	NOUN
ejpam-5734	254	58	}	}	PUNCT
ejpam-5734	254	59	∪	∪	NOUN
ejpam-5734	254	60	{	{	PUNCT
ejpam-5734	254	61	a6	a6	NOUN
ejpam-5734	254	62	}	}	PUNCT
ejpam-5734	254	63	∪	∪	NOUN
ejpam-5734	254	64	{	{	PUNCT
ejpam-5734	254	65	a7	a7	PROPN
ejpam-5734	254	66	}	}	PUNCT
ejpam-5734	254	67	∪	∪	ADJ
ejpam-5734	254	68	{	{	PUNCT
ejpam-5734	254	69	a8	a8	PROPN
ejpam-5734	254	70	}	}	PUNCT
ejpam-5734	254	71	=	=	SYM
ejpam-5734	254	72	{	{	PUNCT
ejpam-5734	254	73	{	{	PUNCT
ejpam-5734	254	74	v1	v1	NOUN
ejpam-5734	254	75	,	,	PUNCT
ejpam-5734	254	76	v5	v5	NOUN
ejpam-5734	254	77	}	}	PUNCT
ejpam-5734	254	78	∪	∪	NOUN
ejpam-5734	254	79	{	{	PUNCT
ejpam-5734	254	80	v3i	v3i	NOUN
ejpam-5734	254	81	|	|	ADV
ejpam-5734	254	82	3	3	NUM
ejpam-5734	254	83	≤	≤	NUM
ejpam-5734	255	1	i	i	PRON
ejpam-5734	255	2	≤	≤	ADV
ejpam-5734	255	3	⌊n	⌊n	X
ejpam-5734	255	4	3	3	NUM
ejpam-5734	255	5	⌋	⌋	NOUN
ejpam-5734	255	6	}	}	PUNCT
ejpam-5734	255	7	}	}	PUNCT
ejpam-5734	255	8	∪	∪	X
ejpam-5734	255	9	{	{	PUNCT
ejpam-5734	255	10	{	{	PUNCT
ejpam-5734	255	11	v2	v2	PROPN
ejpam-5734	255	12	,	,	PUNCT
ejpam-5734	255	13	v6	v6	NOUN
ejpam-5734	255	14	}	}	PUNCT
ejpam-5734	255	15	∪	∪	X
ejpam-5734	255	16	{	{	PUNCT
ejpam-5734	255	17	v3i+1	v3i+1	NOUN
ejpam-5734	255	18	|	|	ADV
ejpam-5734	255	19	3	3	NUM
ejpam-5734	255	20	≤	≤	NUM
ejpam-5734	256	1	i	i	PRON
ejpam-5734	256	2	≤	≤	ADV
ejpam-5734	256	3	⌊n	⌊n	X
ejpam-5734	256	4	3	3	NUM
ejpam-5734	256	5	⌋	⌋	NOUN
ejpam-5734	256	6	}	}	PUNCT
ejpam-5734	256	7	}	}	PUNCT
ejpam-5734	256	8	∪	∪	X
ejpam-5734	256	9	{	{	PUNCT
ejpam-5734	256	10	{	{	PUNCT
ejpam-5734	256	11	v3	v3	PROPN
ejpam-5734	256	12	,	,	PUNCT
ejpam-5734	256	13	v7	v7	VERB
ejpam-5734	256	14	}	}	PUNCT
ejpam-5734	256	15	∪	∪	X
ejpam-5734	256	16	{	{	PUNCT
ejpam-5734	256	17	v3i+2	v3i+2	ADV
ejpam-5734	256	18	|	|	ADV
ejpam-5734	256	19	3	3	X
ejpam-5734	256	20	≤	≤	NUM
ejpam-5734	256	21	i	i	PRON
ejpam-5734	256	22	≤	≤	ADV
ejpam-5734	256	23	⌊n	⌊n	X
ejpam-5734	256	24	3	3	NUM
ejpam-5734	256	25	⌋	⌋	NOUN
ejpam-5734	256	26	}	}	PUNCT
ejpam-5734	256	27	}	}	PUNCT
ejpam-5734	256	28	∪	∪	X
ejpam-5734	256	29	{	{	PUNCT
ejpam-5734	256	30	{	{	PUNCT
ejpam-5734	256	31	v4	v4	NOUN
ejpam-5734	256	32	,	,	PUNCT
ejpam-5734	256	33	v8	v8	PROPN
ejpam-5734	256	34	}	}	PUNCT
ejpam-5734	256	35	∪	∪	X
ejpam-5734	256	36	{	{	PUNCT
ejpam-5734	256	37	v′1	v′1	ADJ
ejpam-5734	256	38	,	,	PUNCT
ejpam-5734	256	39	v′5	v′5	NOUN
ejpam-5734	256	40	}	}	PUNCT
ejpam-5734	256	41	∪	∪	X
ejpam-5734	256	42	{	{	PUNCT
ejpam-5734	256	43	v′3i	v′3i	PROPN
ejpam-5734	256	44	|	|	CCONJ
ejpam-5734	256	45	3	3	NUM
ejpam-5734	256	46	≤	≤	NUM
ejpam-5734	256	47	i	i	PRON
ejpam-5734	256	48	≤	≤	ADV
ejpam-5734	256	49	⌊n	⌊n	X
ejpam-5734	256	50	3	3	NUM
ejpam-5734	256	51	⌋	⌋	NOUN
ejpam-5734	256	52	}	}	PUNCT
ejpam-5734	256	53	}	}	PUNCT
ejpam-5734	256	54	∪	∪	X
ejpam-5734	256	55	{	{	PUNCT
ejpam-5734	256	56	{	{	PUNCT
ejpam-5734	256	57	v′2	v′2	ADJ
ejpam-5734	256	58	,	,	PUNCT
ejpam-5734	256	59	v′6	v′6	NOUN
ejpam-5734	256	60	}	}	PUNCT
ejpam-5734	256	61	∪	∪	NOUN
ejpam-5734	256	62	{	{	PUNCT
ejpam-5734	256	63	v′3i+1	v′3i+1	NOUN
ejpam-5734	256	64	|	|	ADV
ejpam-5734	256	65	3	3	NUM
ejpam-5734	256	66	≤	≤	NUM
ejpam-5734	256	67	i	i	PRON
ejpam-5734	256	68	≤	≤	NOUN
ejpam-5734	256	69	⌊n/3⌋	⌊n/3⌋	NOUN
ejpam-5734	256	70	}	}	PUNCT
ejpam-5734	256	71	}	}	PUNCT
ejpam-5734	256	72	∪	∪	X
ejpam-5734	256	73	{	{	PUNCT
ejpam-5734	256	74	{	{	PUNCT
ejpam-5734	256	75	v′3	v′3	NOUN
ejpam-5734	256	76	,	,	PUNCT
ejpam-5734	256	77	v′7	v′7	CCONJ
ejpam-5734	256	78	}	}	PUNCT
ejpam-5734	256	79	∪	∪	X
ejpam-5734	256	80	{	{	PUNCT
ejpam-5734	256	81	v′3i+2	v′3i+2	X
ejpam-5734	256	82	|	|	NOUN
ejpam-5734	256	83	3	3	NUM
ejpam-5734	256	84	≤	≤	NUM
ejpam-5734	256	85	i	i	PRON
ejpam-5734	256	86	≤	≤	NOUN
ejpam-5734	256	87	⌊n/3⌋	⌊n/3⌋	NOUN
ejpam-5734	256	88	}	}	PUNCT
ejpam-5734	256	89	}	}	PUNCT
ejpam-5734	256	90	∪	∪	ADJ
ejpam-5734	256	91	{	{	PUNCT
ejpam-5734	256	92	v′4	v′4	NOUN
ejpam-5734	256	93	,	,	PUNCT
ejpam-5734	256	94	v′8	v′8	ADJ
ejpam-5734	256	95	}	}	PUNCT
ejpam-5734	256	96	=	=	SYM
ejpam-5734	256	97	{	{	PUNCT
ejpam-5734	256	98	{	{	PUNCT
ejpam-5734	256	99	v1	v1	NOUN
ejpam-5734	256	100	,	,	PUNCT
ejpam-5734	256	101	v5	v5	NOUN
ejpam-5734	256	102	}	}	PUNCT
ejpam-5734	256	103	∪	∪	NOUN
ejpam-5734	256	104	{	{	PUNCT
ejpam-5734	256	105	v9	v9	PROPN
ejpam-5734	256	106	,	,	PUNCT
ejpam-5734	256	107	v12	v12	VERB
ejpam-5734	256	108	,	,	PUNCT
ejpam-5734	256	109	.	.	PUNCT
ejpam-5734	256	110	.	.	PUNCT
ejpam-5734	256	111	.	.	PUNCT
ejpam-5734	257	1	,	,	PUNCT
ejpam-5734	257	2	vn−5	vn−5	PROPN
ejpam-5734	257	3	,	,	PUNCT
ejpam-5734	257	4	vn−2	vn−2	PROPN
ejpam-5734	257	5	}	}	PUNCT
ejpam-5734	257	6	}	}	PUNCT
ejpam-5734	257	7	∪	∪	X
ejpam-5734	257	8	{	{	PUNCT
ejpam-5734	257	9	{	{	PUNCT
ejpam-5734	257	10	v2	v2	PROPN
ejpam-5734	257	11	,	,	PUNCT
ejpam-5734	257	12	v6	v6	NOUN
ejpam-5734	257	13	}	}	PUNCT
ejpam-5734	257	14	∪	∪	NOUN
ejpam-5734	257	15	{	{	PUNCT
ejpam-5734	257	16	v10	v10	PROPN
ejpam-5734	257	17	,	,	PUNCT
ejpam-5734	257	18	v13	v13	NOUN
ejpam-5734	257	19	,	,	PUNCT
ejpam-5734	257	20	.	.	PUNCT
ejpam-5734	257	21	.	.	PUNCT
ejpam-5734	258	1	.	.	PUNCT
ejpam-5734	259	1	,	,	PUNCT
ejpam-5734	259	2	vn−4	vn−4	NOUN
ejpam-5734	259	3	,	,	PUNCT
ejpam-5734	259	4	vn−1	vn−1	ADJ
ejpam-5734	259	5	}	}	PUNCT
ejpam-5734	259	6	}	}	PUNCT
ejpam-5734	259	7	∪	∪	X
ejpam-5734	259	8	{	{	PUNCT
ejpam-5734	259	9	{	{	PUNCT
ejpam-5734	259	10	v3	v3	PROPN
ejpam-5734	259	11	,	,	PUNCT
ejpam-5734	259	12	v7	v7	VERB
ejpam-5734	259	13	}	}	PUNCT
ejpam-5734	259	14	∪	∪	NOUN
ejpam-5734	259	15	{	{	PUNCT
ejpam-5734	259	16	v11	v11	NOUN
ejpam-5734	259	17	,	,	PUNCT
ejpam-5734	259	18	v14	v14	PROPN
ejpam-5734	259	19	,	,	PUNCT
ejpam-5734	259	20	.	.	PUNCT
ejpam-5734	259	21	.	.	PUNCT
ejpam-5734	260	1	.	.	PUNCT
ejpam-5734	261	1	,	,	PUNCT
ejpam-5734	261	2	vn−3	vn−3	PROPN
ejpam-5734	261	3	,	,	PUNCT
ejpam-5734	261	4	vn	vn	NOUN
ejpam-5734	261	5	}	}	PUNCT
ejpam-5734	261	6	}	}	PUNCT
ejpam-5734	261	7	∪	∪	ADJ
ejpam-5734	261	8	{	{	PUNCT
ejpam-5734	261	9	v4	v4	NOUN
ejpam-5734	261	10	,	,	PUNCT
ejpam-5734	261	11	v8	v8	PROPN
ejpam-5734	261	12	}	}	PUNCT
ejpam-5734	261	13	∪	∪	X
ejpam-5734	261	14	{	{	PUNCT
ejpam-5734	261	15	v′1	v′1	ADJ
ejpam-5734	261	16	,	,	PUNCT
ejpam-5734	261	17	v′5	v′5	NOUN
ejpam-5734	261	18	}	}	PUNCT
ejpam-5734	261	19	∪	∪	NOUN
ejpam-5734	261	20	{	{	PUNCT
ejpam-5734	261	21	v′9	v′9	ADJ
ejpam-5734	261	22	,	,	PUNCT
ejpam-5734	261	23	v′12	v′12	NOUN
ejpam-5734	261	24	,	,	PUNCT
ejpam-5734	261	25	.	.	PUNCT
ejpam-5734	261	26	.	.	PUNCT
ejpam-5734	262	1	.	.	PUNCT
ejpam-5734	263	1	,	,	PUNCT
ejpam-5734	264	1	v′n−5	v′n−5	ADV
ejpam-5734	264	2	,	,	PUNCT
ejpam-5734	264	3	v	v	ADP
ejpam-5734	264	4	′	′	NUM
ejpam-5734	264	5	n−2	n−2	PROPN
ejpam-5734	264	6	}	}	PUNCT
ejpam-5734	264	7	∪	∪	X
ejpam-5734	264	8	{	{	PUNCT
ejpam-5734	264	9	{	{	PUNCT
ejpam-5734	264	10	v′2	v′2	ADJ
ejpam-5734	264	11	,	,	PUNCT
ejpam-5734	264	12	v′6	v′6	NOUN
ejpam-5734	264	13	}	}	PUNCT
ejpam-5734	264	14	∪	∪	NOUN
ejpam-5734	264	15	{	{	PUNCT
ejpam-5734	264	16	v′10	v′10	NOUN
ejpam-5734	264	17	,	,	PUNCT
ejpam-5734	264	18	v′13	v′13	NOUN
ejpam-5734	264	19	,	,	PUNCT
ejpam-5734	264	20	.	.	PUNCT
ejpam-5734	264	21	.	.	PUNCT
ejpam-5734	264	22	.	.	PUNCT
ejpam-5734	265	1	,	,	PUNCT
ejpam-5734	265	2	v′n−4	v′n−4	PROPN
ejpam-5734	265	3	,	,	PUNCT
ejpam-5734	265	4	v	v	NOUN
ejpam-5734	265	5	′	′	NUM
ejpam-5734	265	6	n−1	n−1	ADJ
ejpam-5734	265	7	}	}	PUNCT
ejpam-5734	265	8	}	}	PUNCT
ejpam-5734	265	9	m.	m.	NOUN
ejpam-5734	265	10	f.	f.	PROPN
ejpam-5734	265	11	libao	libao	PROPN
ejpam-5734	265	12	,	,	PUNCT
ejpam-5734	265	13	k.	k.	PROPN
ejpam-5734	265	14	b.	b.	PROPN
ejpam-5734	265	15	abarca	abarca	PROPN
ejpam-5734	265	16	/	/	SYM
ejpam-5734	265	17	eur	eur	PROPN
ejpam-5734	265	18	.	.	PUNCT
ejpam-5734	266	1	j.	j.	PROPN
ejpam-5734	266	2	pure	pure	PROPN
ejpam-5734	266	3	appl	appl	PROPN
ejpam-5734	266	4	.	.	PROPN
ejpam-5734	266	5	math	math	PROPN
ejpam-5734	266	6	,	,	PUNCT
ejpam-5734	266	7	18	18	NUM
ejpam-5734	266	8	(	(	PUNCT
ejpam-5734	266	9	2	2	NUM
ejpam-5734	266	10	)	)	PUNCT
ejpam-5734	266	11	(	(	PUNCT
ejpam-5734	266	12	2025	2025	NUM
ejpam-5734	266	13	)	)	PUNCT
ejpam-5734	266	14	,	,	PUNCT
ejpam-5734	266	15	5734	5734	NUM
ejpam-5734	266	16	15	15	NUM
ejpam-5734	266	17	of	of	ADP
ejpam-5734	266	18	25	25	NUM
ejpam-5734	266	19	∪	∪	X
ejpam-5734	266	20	{	{	PUNCT
ejpam-5734	266	21	{	{	PUNCT
ejpam-5734	266	22	v′3	v′3	NOUN
ejpam-5734	266	23	,	,	PUNCT
ejpam-5734	266	24	v′7	v′7	CCONJ
ejpam-5734	266	25	}	}	PUNCT
ejpam-5734	266	26	∪	∪	ADJ
ejpam-5734	266	27	{	{	PUNCT
ejpam-5734	266	28	v′11	v′11	NOUN
ejpam-5734	266	29	,	,	PUNCT
ejpam-5734	266	30	v′14	v′14	NOUN
ejpam-5734	266	31	,	,	PUNCT
ejpam-5734	266	32	.	.	PUNCT
ejpam-5734	266	33	.	.	PUNCT
ejpam-5734	266	34	.	.	PUNCT
ejpam-5734	267	1	,	,	PUNCT
ejpam-5734	267	2	v′n−3	v′n−3	PROPN
ejpam-5734	267	3	,	,	PUNCT
ejpam-5734	267	4	v	v	NOUN
ejpam-5734	267	5	′	′	NUM
ejpam-5734	267	6	n	n	CCONJ
ejpam-5734	267	7	}	}	PUNCT
ejpam-5734	267	8	}	}	PUNCT
ejpam-5734	267	9	∪	∪	ADJ
ejpam-5734	267	10	{	{	PUNCT
ejpam-5734	267	11	v′4	v′4	NOUN
ejpam-5734	267	12	,	,	PUNCT
ejpam-5734	267	13	v′8	v′8	ADJ
ejpam-5734	267	14	}	}	PUNCT
ejpam-5734	267	15	=	=	SYM
ejpam-5734	267	16	{	{	PUNCT
ejpam-5734	267	17	v1	v1	PROPN
ejpam-5734	267	18	,	,	PUNCT
ejpam-5734	267	19	v2	v2	PROPN
ejpam-5734	267	20	,	,	PUNCT
ejpam-5734	267	21	v3	v3	PROPN
ejpam-5734	267	22	,	,	PUNCT
ejpam-5734	267	23	.	.	PUNCT
ejpam-5734	267	24	.	.	PUNCT
ejpam-5734	268	1	.	.	PUNCT
ejpam-5734	269	1	,	,	PUNCT
ejpam-5734	269	2	vn−1	vn−1	PROPN
ejpam-5734	269	3	,	,	PUNCT
ejpam-5734	269	4	vn	vn	NOUN
ejpam-5734	269	5	,	,	PUNCT
ejpam-5734	269	6	v	v	ADJ
ejpam-5734	269	7	′	′	NUM
ejpam-5734	269	8	1	1	NUM
ejpam-5734	269	9	,	,	PUNCT
ejpam-5734	269	10	v	v	NOUN
ejpam-5734	269	11	′	′	NUM
ejpam-5734	269	12	2	2	NUM
ejpam-5734	269	13	,	,	PUNCT
ejpam-5734	269	14	v	v	NOUN
ejpam-5734	269	15	′	′	NUM
ejpam-5734	269	16	3	3	NUM
ejpam-5734	269	17	,	,	PUNCT
ejpam-5734	269	18	.	.	PUNCT
ejpam-5734	269	19	.	.	PUNCT
ejpam-5734	270	1	.	.	PUNCT
ejpam-5734	271	1	,	,	PUNCT
ejpam-5734	271	2	v	v	X
ejpam-5734	271	3	′	′	NUM
ejpam-5734	272	1	n−2	n−2	PROPN
ejpam-5734	272	2	,	,	PUNCT
ejpam-5734	272	3	v	v	NOUN
ejpam-5734	272	4	′	′	NUM
ejpam-5734	272	5	n−1	n−1	PROPN
ejpam-5734	272	6	,	,	PUNCT
ejpam-5734	272	7	v	v	NOUN
ejpam-5734	272	8	′	′	NUM
ejpam-5734	272	9	n	n	CCONJ
ejpam-5734	272	10	}	}	PUNCT
ejpam-5734	272	11	=	=	PUNCT
ejpam-5734	272	12	v	v	ADP
ejpam-5734	272	13	[	[	X
ejpam-5734	272	14	d2(cn	d2(cn	PROPN
ejpam-5734	272	15	)	)	PUNCT
ejpam-5734	272	16	]	]	X
ejpam-5734	272	17	ii	ii	X
ejpam-5734	272	18	.	.	PUNCT
ejpam-5734	273	1	to	to	PART
ejpam-5734	273	2	verify	verify	VERB
ejpam-5734	273	3	that	that	SCONJ
ejpam-5734	273	4	the	the	DET
ejpam-5734	273	5	color	color	NOUN
ejpam-5734	273	6	classes	class	NOUN
ejpam-5734	273	7	are	be	AUX
ejpam-5734	273	8	disjoint	disjoint	ADJ
ejpam-5734	273	9	,	,	PUNCT
ejpam-5734	273	10	we	we	PRON
ejpam-5734	273	11	also	also	ADV
ejpam-5734	273	12	have	have	VERB
ejpam-5734	273	13	to	to	PART
ejpam-5734	273	14	show	show	VERB
ejpam-5734	273	15	that	that	SCONJ
ejpam-5734	273	16	∑	∑	PROPN
ejpam-5734	273	17	a∈c	a∈c	PROPN
ejpam-5734	273	18	|a|	|a|	PROPN
ejpam-5734	273	19	=	=	PROPN
ejpam-5734	273	20	|v	|v	NOUN
ejpam-5734	274	1	[	[	X
ejpam-5734	274	2	d2(cn)]|	d2(cn)]|	ADP
ejpam-5734	274	3	in	in	ADP
ejpam-5734	274	4	addition	addition	NOUN
ejpam-5734	274	5	to	to	ADP
ejpam-5734	274	6	the	the	DET
ejpam-5734	274	7	above	above	ADJ
ejpam-5734	274	8	condition	condition	NOUN
ejpam-5734	274	9	.	.	PUNCT
ejpam-5734	275	1	∑	∑	PROPN
ejpam-5734	275	2	a∈c	a∈c	PROPN
ejpam-5734	275	3	|a|	|a|	PROPN
ejpam-5734	275	4	=	=	PUNCT
ejpam-5734	275	5	|a1|+	|a1|+	PRON
ejpam-5734	275	6	|a2|+	|a2|+	ADJ
ejpam-5734	275	7	|a3|+	|a3|+	ADP
ejpam-5734	275	8	|a4|+	|a4|+	NOUN
ejpam-5734	275	9	|a5|+	|a5|+	ADP
ejpam-5734	275	10	|a6|+	|a6|+	NOUN
ejpam-5734	275	11	|a7|+	|a7|+	NOUN
ejpam-5734	275	12	|a8|	|a8|	NOUN
ejpam-5734	275	13	=	=	SYM
ejpam-5734	275	14	(	(	PUNCT
ejpam-5734	275	15	2	2	NUM
ejpam-5734	275	16	+	+	CCONJ
ejpam-5734	275	17	⌊n	⌊n	ADJ
ejpam-5734	275	18	3	3	NUM
ejpam-5734	275	19	⌋	⌋	NOUN
ejpam-5734	275	20	−	−	PROPN
ejpam-5734	275	21	2	2	NUM
ejpam-5734	275	22	)	)	PUNCT
ejpam-5734	275	23	+	+	CCONJ
ejpam-5734	275	24	(	(	PUNCT
ejpam-5734	275	25	2	2	NUM
ejpam-5734	275	26	+	+	CCONJ
ejpam-5734	275	27	⌊n	⌊n	ADJ
ejpam-5734	275	28	3	3	NUM
ejpam-5734	275	29	⌋	⌋	NOUN
ejpam-5734	275	30	−	−	PROPN
ejpam-5734	275	31	2	2	NUM
ejpam-5734	275	32	)	)	PUNCT
ejpam-5734	275	33	+	+	CCONJ
ejpam-5734	275	34	(	(	PUNCT
ejpam-5734	275	35	2	2	NUM
ejpam-5734	275	36	+	+	CCONJ
ejpam-5734	275	37	⌊n	⌊n	ADJ
ejpam-5734	275	38	3	3	NUM
ejpam-5734	275	39	⌋	⌋	NOUN
ejpam-5734	275	40	−	−	NOUN
ejpam-5734	275	41	2	2	NUM
ejpam-5734	275	42	)	)	PUNCT
ejpam-5734	275	43	+	+	CCONJ
ejpam-5734	275	44	2	2	NUM
ejpam-5734	275	45	+	+	CCONJ
ejpam-5734	275	46	(	(	PUNCT
ejpam-5734	275	47	2	2	NUM
ejpam-5734	275	48	+	+	CCONJ
ejpam-5734	275	49	⌊n	⌊n	ADJ
ejpam-5734	275	50	3	3	NUM
ejpam-5734	275	51	⌋	⌋	NOUN
ejpam-5734	275	52	−	−	PROPN
ejpam-5734	275	53	2	2	NUM
ejpam-5734	275	54	)	)	PUNCT
ejpam-5734	275	55	+	+	CCONJ
ejpam-5734	275	56	(	(	PUNCT
ejpam-5734	275	57	2	2	NUM
ejpam-5734	275	58	+	+	CCONJ
ejpam-5734	275	59	⌊n	⌊n	ADJ
ejpam-5734	275	60	3	3	NUM
ejpam-5734	275	61	⌋	⌋	NOUN
ejpam-5734	275	62	−	−	PROPN
ejpam-5734	275	63	2	2	NUM
ejpam-5734	275	64	)	)	PUNCT
ejpam-5734	275	65	+	+	CCONJ
ejpam-5734	275	66	(	(	PUNCT
ejpam-5734	275	67	2	2	NUM
ejpam-5734	275	68	+	+	CCONJ
ejpam-5734	275	69	⌊n	⌊n	ADJ
ejpam-5734	275	70	3	3	NUM
ejpam-5734	275	71	⌋	⌋	NOUN
ejpam-5734	275	72	−	−	NOUN
ejpam-5734	275	73	2	2	NUM
ejpam-5734	275	74	)	)	PUNCT
ejpam-5734	275	75	+	+	CCONJ
ejpam-5734	275	76	2	2	NUM
ejpam-5734	275	77	=	=	SYM
ejpam-5734	275	78	6	6	NUM
ejpam-5734	275	79	(	(	PUNCT
ejpam-5734	275	80	n−	n−	NOUN
ejpam-5734	275	81	2	2	NUM
ejpam-5734	275	82	3	3	NUM
ejpam-5734	275	83	)	)	PUNCT
ejpam-5734	275	84	+	+	CCONJ
ejpam-5734	275	85	4	4	NUM
ejpam-5734	275	86	,	,	PUNCT
ejpam-5734	275	87	since	since	SCONJ
ejpam-5734	275	88	n	n	X
ejpam-5734	275	89	≡	≡	PROPN
ejpam-5734	275	90	2	2	NUM
ejpam-5734	275	91	(	(	PUNCT
ejpam-5734	275	92	mod	mod	NOUN
ejpam-5734	275	93	3	3	NUM
ejpam-5734	275	94	)	)	PUNCT
ejpam-5734	275	95	=	=	SYM
ejpam-5734	275	96	2n	2n	NUM
ejpam-5734	275	97	=	=	SYM
ejpam-5734	275	98	|v	|v	X
ejpam-5734	276	1	[	[	X
ejpam-5734	276	2	d2(cn)]|	d2(cn)]|	ADV
ejpam-5734	276	3	thus	thus	ADV
ejpam-5734	276	4	,	,	PUNCT
ejpam-5734	276	5	by	by	ADP
ejpam-5734	276	6	lemma	lemma	PROPN
ejpam-5734	276	7	1	1	NUM
ejpam-5734	276	8	,	,	PUNCT
ejpam-5734	276	9	color	color	NOUN
ejpam-5734	276	10	classes	class	NOUN
ejpam-5734	276	11	are	be	AUX
ejpam-5734	276	12	mutually	mutually	ADV
ejpam-5734	276	13	exclusive	exclusive	ADJ
ejpam-5734	276	14	,	,	PUNCT
ejpam-5734	276	15	that	that	ADV
ejpam-5734	276	16	is	is	ADV
ejpam-5734	276	17	,	,	PUNCT
ejpam-5734	276	18	ak	ak	PROPN
ejpam-5734	276	19	∩	∩	PROPN
ejpam-5734	276	20	aj	aj	PROPN
ejpam-5734	276	21	=	=	PROPN
ejpam-5734	276	22	∅	∅	NOUN
ejpam-5734	276	23	for	for	ADP
ejpam-5734	276	24	k	k	PROPN
ejpam-5734	276	25	̸=	̸=	PROPN
ejpam-5734	276	26	j.	j.	PROPN
ejpam-5734	276	27	now	now	ADV
ejpam-5734	276	28	,	,	PUNCT
ejpam-5734	276	29	we	we	PRON
ejpam-5734	276	30	can	can	AUX
ejpam-5734	276	31	say	say	VERB
ejpam-5734	276	32	that	that	PRON
ejpam-5734	276	33	c	c	PROPN
ejpam-5734	276	34	=	=	PRON
ejpam-5734	276	35	{	{	PUNCT
ejpam-5734	276	36	a1,a2,a3,a4,a5,a6,a7,a8	a1,a2,a3,a4,a5,a6,a7,a8	X
ejpam-5734	276	37	}	}	PUNCT
ejpam-5734	276	38	is	be	AUX
ejpam-5734	276	39	a	a	DET
ejpam-5734	276	40	distance-2	distance-2	CCONJ
ejpam-5734	276	41	chromatic	chromatic	ADJ
ejpam-5734	276	42	set	set	NOUN
ejpam-5734	276	43	since	since	SCONJ
ejpam-5734	276	44	for	for	ADP
ejpam-5734	276	45	any	any	DET
ejpam-5734	276	46	pair	pair	NOUN
ejpam-5734	276	47	of	of	ADP
ejpam-5734	276	48	vertices	vertex	NOUN
ejpam-5734	276	49	vi	vi	PROPN
ejpam-5734	276	50	,	,	PUNCT
ejpam-5734	276	51	vj	vj	PROPN
ejpam-5734	276	52	∈	∈	PROPN
ejpam-5734	276	53	ak	ak	PROPN
ejpam-5734	276	54	,	,	PUNCT
ejpam-5734	276	55	1	1	NUM
ejpam-5734	276	56	≤	≤	NUM
ejpam-5734	276	57	k	k	X
ejpam-5734	276	58	≤	≤	NUM
ejpam-5734	276	59	8	8	NUM
ejpam-5734	276	60	,	,	PUNCT
ejpam-5734	276	61	in	in	ADP
ejpam-5734	276	62	c	c	NOUN
ejpam-5734	276	63	,	,	PUNCT
ejpam-5734	276	64	d(vi	d(vi	PROPN
ejpam-5734	276	65	,	,	PUNCT
ejpam-5734	276	66	vj	vj	PROPN
ejpam-5734	276	67	)	)	PUNCT
ejpam-5734	276	68	≥	≥	NOUN
ejpam-5734	276	69	3	3	NUM
ejpam-5734	276	70	.	.	PUNCT
ejpam-5734	277	1	thus	thus	ADV
ejpam-5734	277	2	,	,	PUNCT
ejpam-5734	277	3	χ2	χ2	PROPN
ejpam-5734	277	4	[	[	PUNCT
ejpam-5734	277	5	d2(cn	d2(cn	PROPN
ejpam-5734	277	6	)	)	PUNCT
ejpam-5734	277	7	]	]	PUNCT
ejpam-5734	277	8	≤	≤	NUM
ejpam-5734	277	9	8	8	NUM
ejpam-5734	277	10	.	.	PUNCT
ejpam-5734	277	11	suppose	suppose	VERB
ejpam-5734	277	12	χ2	χ2	PROPN
ejpam-5734	277	13	[	[	PUNCT
ejpam-5734	277	14	d2(cn	d2(cn	PROPN
ejpam-5734	277	15	)	)	PUNCT
ejpam-5734	277	16	]	]	PUNCT
ejpam-5734	277	17	<	<	X
ejpam-5734	277	18	8	8	NUM
ejpam-5734	277	19	,	,	PUNCT
ejpam-5734	277	20	say	say	VERB
ejpam-5734	277	21	7	7	NUM
ejpam-5734	277	22	.	.	PUNCT
ejpam-5734	278	1	this	this	PRON
ejpam-5734	278	2	means	mean	VERB
ejpam-5734	278	3	that	that	SCONJ
ejpam-5734	278	4	the	the	DET
ejpam-5734	278	5	vertices	vertex	NOUN
ejpam-5734	278	6	assigned	assign	VERB
ejpam-5734	278	7	with	with	ADP
ejpam-5734	278	8	a8	a8	PROPN
ejpam-5734	278	9	will	will	AUX
ejpam-5734	278	10	be	be	AUX
ejpam-5734	278	11	assigned	assign	VERB
ejpam-5734	278	12	to	to	ADP
ejpam-5734	278	13	another	another	DET
ejpam-5734	278	14	color	color	NOUN
ejpam-5734	278	15	class	class	NOUN
ejpam-5734	278	16	.	.	PUNCT
ejpam-5734	279	1	consider	consider	VERB
ejpam-5734	279	2	v′4	v′4	NOUN
ejpam-5734	279	3	:	:	PUNCT
ejpam-5734	279	4	a1	a1	NOUN
ejpam-5734	279	5	:	:	PUNCT
ejpam-5734	279	6	d(v	d(v	ADJ
ejpam-5734	279	7	′	′	NOUN
ejpam-5734	279	8	4	4	NUM
ejpam-5734	279	9	,	,	PUNCT
ejpam-5734	279	10	v5	v5	NOUN
ejpam-5734	279	11	)	)	PUNCT
ejpam-5734	279	12	=	=	SYM
ejpam-5734	279	13	1	1	NUM
ejpam-5734	279	14	a2	a2	NOUN
ejpam-5734	279	15	:	:	PUNCT
ejpam-5734	280	1	d(v	d(v	ADJ
ejpam-5734	280	2	′	′	NOUN
ejpam-5734	280	3	4	4	NUM
ejpam-5734	280	4	,	,	PUNCT
ejpam-5734	280	5	v2	v2	NOUN
ejpam-5734	280	6	)	)	PUNCT
ejpam-5734	280	7	=	=	SYM
ejpam-5734	280	8	2	2	NUM
ejpam-5734	280	9	a3	a3	NOUN
ejpam-5734	280	10	:	:	PUNCT
ejpam-5734	280	11	d(v	d(v	ADJ
ejpam-5734	280	12	′	′	NOUN
ejpam-5734	280	13	4	4	NUM
ejpam-5734	280	14	,	,	PUNCT
ejpam-5734	280	15	v3	v3	PROPN
ejpam-5734	280	16	)	)	PUNCT
ejpam-5734	280	17	=	=	SYM
ejpam-5734	280	18	1	1	NUM
ejpam-5734	280	19	a4	a4	NOUN
ejpam-5734	280	20	:	:	PUNCT
ejpam-5734	280	21	d(v	d(v	ADJ
ejpam-5734	280	22	′	′	NOUN
ejpam-5734	280	23	4	4	NUM
ejpam-5734	280	24	,	,	PUNCT
ejpam-5734	280	25	v4	v4	NOUN
ejpam-5734	280	26	)	)	PUNCT
ejpam-5734	280	27	=	=	SYM
ejpam-5734	280	28	2	2	NUM
ejpam-5734	280	29	a5	a5	NOUN
ejpam-5734	280	30	:	:	PUNCT
ejpam-5734	280	31	d(v	d(v	ADJ
ejpam-5734	280	32	′	′	NOUN
ejpam-5734	280	33	4	4	NUM
ejpam-5734	280	34	,	,	PUNCT
ejpam-5734	280	35	v	v	NOUN
ejpam-5734	280	36	′	′	NUM
ejpam-5734	280	37	5	5	NUM
ejpam-5734	280	38	)	)	PUNCT
ejpam-5734	280	39	=	=	SYM
ejpam-5734	280	40	1	1	NUM
ejpam-5734	280	41	a6	a6	NOUN
ejpam-5734	280	42	:	:	PUNCT
ejpam-5734	280	43	d(v	d(v	ADJ
ejpam-5734	280	44	′	′	NOUN
ejpam-5734	280	45	4	4	NUM
ejpam-5734	280	46	,	,	PUNCT
ejpam-5734	280	47	v	v	NOUN
ejpam-5734	280	48	′	′	NUM
ejpam-5734	280	49	2	2	NUM
ejpam-5734	280	50	)	)	PUNCT
ejpam-5734	280	51	=	=	SYM
ejpam-5734	280	52	2	2	NUM
ejpam-5734	280	53	a7	a7	NOUN
ejpam-5734	280	54	:	:	PUNCT
ejpam-5734	281	1	d(v	d(v	ADJ
ejpam-5734	281	2	′	′	NOUN
ejpam-5734	281	3	4	4	NUM
ejpam-5734	281	4	,	,	PUNCT
ejpam-5734	281	5	v	v	NOUN
ejpam-5734	281	6	′	′	NUM
ejpam-5734	281	7	1	1	NUM
ejpam-5734	281	8	)	)	PUNCT
ejpam-5734	281	9	=	=	SYM
ejpam-5734	281	10	1	1	NUM
ejpam-5734	281	11	m.	m.	NOUN
ejpam-5734	281	12	f.	f.	PROPN
ejpam-5734	281	13	libao	libao	PROPN
ejpam-5734	281	14	,	,	PUNCT
ejpam-5734	281	15	k.	k.	PROPN
ejpam-5734	281	16	b.	b.	PROPN
ejpam-5734	281	17	abarca	abarca	PROPN
ejpam-5734	281	18	/	/	SYM
ejpam-5734	281	19	eur	eur	PROPN
ejpam-5734	281	20	.	.	PUNCT
ejpam-5734	282	1	j.	j.	PROPN
ejpam-5734	282	2	pure	pure	PROPN
ejpam-5734	282	3	appl	appl	PROPN
ejpam-5734	282	4	.	.	PROPN
ejpam-5734	282	5	math	math	PROPN
ejpam-5734	282	6	,	,	PUNCT
ejpam-5734	282	7	18	18	NUM
ejpam-5734	282	8	(	(	PUNCT
ejpam-5734	282	9	2	2	NUM
ejpam-5734	282	10	)	)	PUNCT
ejpam-5734	282	11	(	(	PUNCT
ejpam-5734	282	12	2025	2025	NUM
ejpam-5734	282	13	)	)	PUNCT
ejpam-5734	282	14	,	,	PUNCT
ejpam-5734	282	15	5734	5734	NUM
ejpam-5734	282	16	16	16	NUM
ejpam-5734	282	17	of	of	ADP
ejpam-5734	282	18	25	25	NUM
ejpam-5734	282	19	likewise	likewise	ADV
ejpam-5734	282	20	,	,	PUNCT
ejpam-5734	282	21	for	for	ADP
ejpam-5734	282	22	v′8	v′8	ADJ
ejpam-5734	282	23	:	:	PUNCT
ejpam-5734	282	24	a1	a1	NOUN
ejpam-5734	282	25	:	:	PUNCT
ejpam-5734	282	26	d(v	d(v	ADJ
ejpam-5734	282	27	′	′	NOUN
ejpam-5734	282	28	8	8	NUM
ejpam-5734	282	29	,	,	PUNCT
ejpam-5734	282	30	v3i	v3i	NOUN
ejpam-5734	282	31	)	)	PUNCT
ejpam-5734	282	32	=	=	SYM
ejpam-5734	283	1	1	1	NUM
ejpam-5734	283	2	when	when	SCONJ
ejpam-5734	283	3	i	i	PRON
ejpam-5734	283	4	=	=	SYM
ejpam-5734	283	5	1	1	NUM
ejpam-5734	283	6	a2	a2	NOUN
ejpam-5734	283	7	:	:	PUNCT
ejpam-5734	284	1	d(v	d(v	ADJ
ejpam-5734	284	2	′	′	NOUN
ejpam-5734	284	3	8	8	NUM
ejpam-5734	284	4	,	,	PUNCT
ejpam-5734	284	5	v3i+1	v3i+1	NOUN
ejpam-5734	284	6	)	)	PUNCT
ejpam-5734	284	7	=	=	SYM
ejpam-5734	284	8	2	2	NUM
ejpam-5734	284	9	when	when	SCONJ
ejpam-5734	284	10	i	i	PRON
ejpam-5734	284	11	=	=	SYM
ejpam-5734	284	12	1	1	NUM
ejpam-5734	284	13	a3	a3	NOUN
ejpam-5734	284	14	:	:	PUNCT
ejpam-5734	285	1	d(v	d(v	ADJ
ejpam-5734	285	2	′	′	NOUN
ejpam-5734	285	3	8	8	NUM
ejpam-5734	285	4	,	,	PUNCT
ejpam-5734	285	5	v7	v7	NUM
ejpam-5734	285	6	)	)	PUNCT
ejpam-5734	285	7	=	=	SYM
ejpam-5734	285	8	1	1	NUM
ejpam-5734	285	9	a4	a4	NOUN
ejpam-5734	285	10	:	:	PUNCT
ejpam-5734	285	11	d(v	d(v	ADJ
ejpam-5734	285	12	′	′	NOUN
ejpam-5734	285	13	8	8	NUM
ejpam-5734	285	14	,	,	PUNCT
ejpam-5734	285	15	v6	v6	NOUN
ejpam-5734	285	16	)	)	PUNCT
ejpam-5734	285	17	=	=	SYM
ejpam-5734	285	18	2	2	NUM
ejpam-5734	285	19	a5	a5	NOUN
ejpam-5734	285	20	:	:	PUNCT
ejpam-5734	285	21	d(v	d(v	ADJ
ejpam-5734	285	22	′	′	NOUN
ejpam-5734	285	23	8	8	NUM
ejpam-5734	285	24	,	,	PUNCT
ejpam-5734	285	25	v	v	ADJ
ejpam-5734	285	26	′	′	NUM
ejpam-5734	285	27	3i	3i	NOUN
ejpam-5734	285	28	)	)	PUNCT
ejpam-5734	285	29	=	=	SYM
ejpam-5734	285	30	1	1	NUM
ejpam-5734	285	31	when	when	SCONJ
ejpam-5734	285	32	i	i	PRON
ejpam-5734	285	33	=	=	NOUN
ejpam-5734	285	34	1	1	NUM
ejpam-5734	285	35	a6	a6	NOUN
ejpam-5734	285	36	:	:	PUNCT
ejpam-5734	285	37	d(v	d(v	ADJ
ejpam-5734	285	38	′	′	NOUN
ejpam-5734	285	39	8	8	NUM
ejpam-5734	285	40	,	,	PUNCT
ejpam-5734	285	41	v	v	NOUN
ejpam-5734	285	42	′	′	NUM
ejpam-5734	285	43	3i+1	3i+1	NUM
ejpam-5734	285	44	)	)	PUNCT
ejpam-5734	285	45	=	=	SYM
ejpam-5734	285	46	2	2	NUM
ejpam-5734	286	1	when	when	SCONJ
ejpam-5734	286	2	i	i	PRON
ejpam-5734	286	3	=	=	VERB
ejpam-5734	286	4	1	1	NUM
ejpam-5734	286	5	a7	a7	NOUN
ejpam-5734	286	6	:	:	PUNCT
ejpam-5734	286	7	d(v	d(v	ADJ
ejpam-5734	286	8	′	′	NOUN
ejpam-5734	286	9	8	8	NUM
ejpam-5734	286	10	,	,	PUNCT
ejpam-5734	286	11	v	v	NOUN
ejpam-5734	286	12	′	′	NUM
ejpam-5734	286	13	7	7	NUM
ejpam-5734	286	14	)	)	PUNCT
ejpam-5734	286	15	=	=	SYM
ejpam-5734	286	16	1	1	NUM
ejpam-5734	286	17	these	these	PRON
ejpam-5734	286	18	would	would	AUX
ejpam-5734	286	19	violate	violate	VERB
ejpam-5734	286	20	the	the	DET
ejpam-5734	286	21	distance-2	distance-2	NUM
ejpam-5734	286	22	coloring	coloring	NOUN
ejpam-5734	286	23	.	.	PUNCT
ejpam-5734	287	1	thus	thus	ADV
ejpam-5734	287	2	,	,	PUNCT
ejpam-5734	287	3	χ2	χ2	PROPN
ejpam-5734	287	4	[	[	PUNCT
ejpam-5734	287	5	d2(cn	d2(cn	PROPN
ejpam-5734	287	6	)	)	PUNCT
ejpam-5734	287	7	]	]	PUNCT
ejpam-5734	288	1	̸	̸	PUNCT
ejpam-5734	288	2	<	<	X
ejpam-5734	288	3	8	8	NUM
ejpam-5734	288	4	.	.	PUNCT
ejpam-5734	289	1	this	this	PRON
ejpam-5734	289	2	leads	lead	VERB
ejpam-5734	289	3	us	we	PRON
ejpam-5734	289	4	to	to	ADP
ejpam-5734	289	5	the	the	DET
ejpam-5734	289	6	conclusion	conclusion	NOUN
ejpam-5734	289	7	that	that	SCONJ
ejpam-5734	289	8	χ2	χ2	PROPN
ejpam-5734	289	9	[	[	PUNCT
ejpam-5734	289	10	d2(cn	d2(cn	PROPN
ejpam-5734	289	11	)	)	PUNCT
ejpam-5734	289	12	]	]	PUNCT
ejpam-5734	290	1	=	=	PUNCT
ejpam-5734	290	2	8	8	NUM
ejpam-5734	290	3	when	when	SCONJ
ejpam-5734	290	4	n	n	X
ejpam-5734	290	5	≡	≡	PROPN
ejpam-5734	290	6	2	2	NUM
ejpam-5734	290	7	(	(	PUNCT
ejpam-5734	290	8	mod	mod	NOUN
ejpam-5734	290	9	3	3	NUM
ejpam-5734	290	10	)	)	PUNCT
ejpam-5734	290	11	.	.	PUNCT
ejpam-5734	291	1	below	below	ADV
ejpam-5734	291	2	is	be	AUX
ejpam-5734	291	3	an	an	DET
ejpam-5734	291	4	example	example	NOUN
ejpam-5734	291	5	of	of	ADP
ejpam-5734	291	6	a	a	DET
ejpam-5734	291	7	shadow	shadow	NOUN
ejpam-5734	291	8	graph	graph	NOUN
ejpam-5734	291	9	of	of	ADP
ejpam-5734	291	10	c8	c8	PROPN
ejpam-5734	291	11	,	,	PUNCT
ejpam-5734	291	12	d2(c8	d2(c8	NOUN
ejpam-5734	291	13	)	)	PUNCT
ejpam-5734	291	14	with	with	ADP
ejpam-5734	291	15	a	a	DET
ejpam-5734	291	16	distance-2	distance-2	CCONJ
ejpam-5734	291	17	chromatic	chromatic	ADJ
ejpam-5734	291	18	number	number	NOUN
ejpam-5734	291	19	of	of	ADP
ejpam-5734	291	20	8	8	NUM
ejpam-5734	291	21	.	.	PUNCT
ejpam-5734	292	1	here	here	ADV
ejpam-5734	292	2	,	,	PUNCT
ejpam-5734	292	3	c	c	X
ejpam-5734	292	4	=	=	PRON
ejpam-5734	292	5	{	{	PUNCT
ejpam-5734	292	6	red	red	ADJ
ejpam-5734	292	7	(	(	PUNCT
ejpam-5734	292	8	v1	v1	NOUN
ejpam-5734	292	9	,	,	PUNCT
ejpam-5734	292	10	v5),blue	v5),blue	NOUN
ejpam-5734	292	11	(	(	PUNCT
ejpam-5734	292	12	v2	v2	PROPN
ejpam-5734	292	13	,	,	PUNCT
ejpam-5734	292	14	v6),green	v6),green	NUM
ejpam-5734	292	15	(	(	PUNCT
ejpam-5734	292	16	v3	v3	PROPN
ejpam-5734	292	17	,	,	PUNCT
ejpam-5734	292	18	v7),gray	v7),gray	X
ejpam-5734	292	19	(	(	PUNCT
ejpam-5734	292	20	v4	v4	NOUN
ejpam-5734	292	21	,	,	PUNCT
ejpam-5734	292	22	v8),orange	v8),orange	NOUN
ejpam-5734	292	23	(	(	PUNCT
ejpam-5734	292	24	v′1	v′1	NOUN
ejpam-5734	292	25	,	,	PUNCT
ejpam-5734	292	26	v	v	NOUN
ejpam-5734	292	27	′	′	NUM
ejpam-5734	292	28	5),pink	5),pink	NUM
ejpam-5734	292	29	(	(	PUNCT
ejpam-5734	292	30	v′2	v′2	PROPN
ejpam-5734	292	31	,	,	PUNCT
ejpam-5734	292	32	v	v	ADJ
ejpam-5734	292	33	′	′	NUM
ejpam-5734	292	34	6),yellow	6),yellow	PROPN
ejpam-5734	292	35	(	(	PUNCT
ejpam-5734	292	36	v′3	v′3	NOUN
ejpam-5734	292	37	,	,	PUNCT
ejpam-5734	292	38	v	v	NOUN
ejpam-5734	292	39	′	′	NUM
ejpam-5734	292	40	7),purple	7),purple	NUM
ejpam-5734	292	41	(	(	PUNCT
ejpam-5734	292	42	v	v	NUM
ejpam-5734	292	43	′	′	NUM
ejpam-5734	292	44	4	4	NUM
ejpam-5734	292	45	,	,	PUNCT
ejpam-5734	292	46	v	v	ADJ
ejpam-5734	292	47	′	′	NUM
ejpam-5734	292	48	8)	8)	NUM
ejpam-5734	292	49	}	}	PUNCT
ejpam-5734	292	50	.	.	PUNCT
ejpam-5734	293	1	d2(c8	d2(c8	NOUN
ejpam-5734	293	2	)	)	PUNCT
ejpam-5734	293	3	:	:	PUNCT
ejpam-5734	293	4	v1	v1	VERB
ejpam-5734	293	5	v2	v2	PROPN
ejpam-5734	293	6	v3	v3	PROPN
ejpam-5734	293	7	v4	v4	PROPN
ejpam-5734	293	8	v′	v′	NOUN
ejpam-5734	293	9	1	1	NUM
ejpam-5734	293	10	v′	v′	NUM
ejpam-5734	293	11	2	2	NUM
ejpam-5734	293	12	v′	v′	NOUN
ejpam-5734	293	13	3	3	NUM
ejpam-5734	293	14	v′	v′	NOUN
ejpam-5734	293	15	4	4	NUM
ejpam-5734	293	16	v8	v8	NOUN
ejpam-5734	293	17	v7	v7	VERB
ejpam-5734	293	18	v6	v6	NOUN
ejpam-5734	293	19	v5	v5	PROPN
ejpam-5734	293	20	v′	v′	PROPN
ejpam-5734	293	21	8	8	NUM
ejpam-5734	293	22	v′	v′	NOUN
ejpam-5734	293	23	7	7	NUM
ejpam-5734	293	24	v′	v′	NOUN
ejpam-5734	293	25	6	6	NUM
ejpam-5734	293	26	v′	v′	NOUN
ejpam-5734	293	27	5	5	NUM
ejpam-5734	293	28	figure	figure	NOUN
ejpam-5734	293	29	9	9	NUM
ejpam-5734	293	30	:	:	PUNCT
ejpam-5734	293	31	a	a	DET
ejpam-5734	293	32	shadow	shadow	NOUN
ejpam-5734	293	33	graph	graph	NOUN
ejpam-5734	293	34	of	of	ADP
ejpam-5734	293	35	cycle	cycle	NOUN
ejpam-5734	293	36	graph	graph	NOUN
ejpam-5734	293	37	c8	c8	PROPN
ejpam-5734	293	38	with	with	ADP
ejpam-5734	293	39	χ2[d2(c8	χ2[d2(c8	PROPN
ejpam-5734	293	40	)	)	PUNCT
ejpam-5734	293	41	]	]	PUNCT
ejpam-5734	294	1	=	=	PUNCT
ejpam-5734	294	2	8	8	NUM
ejpam-5734	294	3	4.2	4.2	NUM
ejpam-5734	294	4	.	.	PUNCT
ejpam-5734	295	1	distance-2	distance-2	VERB
ejpam-5734	295	2	chromatic	chromatic	ADJ
ejpam-5734	295	3	number	number	NOUN
ejpam-5734	295	4	of	of	ADP
ejpam-5734	295	5	the	the	DET
ejpam-5734	295	6	central	central	ADJ
ejpam-5734	295	7	graph	graph	NOUN
ejpam-5734	295	8	of	of	ADP
ejpam-5734	295	9	cycle	cycle	NOUN
ejpam-5734	295	10	graphs	graph	NOUN
ejpam-5734	295	11	,	,	PUNCT
ejpam-5734	295	12	c(cn	c(cn	NOUN
ejpam-5734	295	13	)	)	PUNCT
ejpam-5734	295	14	theorem	theorem	VERB
ejpam-5734	295	15	4.2.1	4.2.1	NUM
ejpam-5734	295	16	.	.	PUNCT
ejpam-5734	296	1	let	let	VERB
ejpam-5734	296	2	cn	cn	PROPN
ejpam-5734	296	3	be	be	AUX
ejpam-5734	296	4	a	a	DET
ejpam-5734	296	5	cycle	cycle	NOUN
ejpam-5734	296	6	graph	graph	NOUN
ejpam-5734	296	7	of	of	ADP
ejpam-5734	296	8	order	order	NOUN
ejpam-5734	296	9	n	n	PRON
ejpam-5734	296	10	≥	≥	NOUN
ejpam-5734	296	11	4	4	NUM
ejpam-5734	296	12	.	.	PUNCT
ejpam-5734	297	1	then	then	ADV
ejpam-5734	297	2	the	the	DET
ejpam-5734	297	3	distance-2	distance-2	NUM
ejpam-5734	297	4	chromatic	chromatic	ADJ
ejpam-5734	297	5	number	number	NOUN
ejpam-5734	297	6	of	of	ADP
ejpam-5734	297	7	the	the	DET
ejpam-5734	297	8	central	central	ADJ
ejpam-5734	297	9	graph	graph	NOUN
ejpam-5734	297	10	of	of	ADP
ejpam-5734	297	11	cn	cn	PROPN
ejpam-5734	297	12	is	be	AUX
ejpam-5734	297	13	χ2[c(cn	χ2[c(cn	PROPN
ejpam-5734	297	14	)	)	PUNCT
ejpam-5734	297	15	]	]	PUNCT
ejpam-5734	298	1	=	=	PUNCT
ejpam-5734	298	2	{	{	PUNCT
ejpam-5734	298	3	n+	n+	ADP
ejpam-5734	298	4	2	2	NUM
ejpam-5734	298	5	if	if	SCONJ
ejpam-5734	298	6	n	n	PRON
ejpam-5734	298	7	is	be	AUX
ejpam-5734	298	8	even	even	ADV
ejpam-5734	298	9	n+	n+	ADP
ejpam-5734	298	10	3	3	NUM
ejpam-5734	298	11	if	if	SCONJ
ejpam-5734	298	12	n	n	NOUN
ejpam-5734	298	13	is	be	AUX
ejpam-5734	298	14	odd	odd	ADJ
ejpam-5734	298	15	proof	proof	NOUN
ejpam-5734	298	16	.	.	PUNCT
ejpam-5734	299	1	let	let	VERB
ejpam-5734	299	2	v	v	X
ejpam-5734	299	3	(	(	PUNCT
ejpam-5734	299	4	cn	cn	PROPN
ejpam-5734	299	5	)	)	PUNCT
ejpam-5734	299	6	=	=	PRON
ejpam-5734	299	7	{	{	PUNCT
ejpam-5734	299	8	vi	vi	NOUN
ejpam-5734	299	9	|	|	ADV
ejpam-5734	299	10	1	1	NUM
ejpam-5734	299	11	≤	≤	NUM
ejpam-5734	299	12	i	i	PRON
ejpam-5734	299	13	≤	≤	NOUN
ejpam-5734	299	14	n	n	CCONJ
ejpam-5734	299	15	}	}	PUNCT
ejpam-5734	299	16	and	and	CCONJ
ejpam-5734	299	17	e(cn	e(cn	NOUN
ejpam-5734	299	18	)	)	PUNCT
ejpam-5734	299	19	=	=	PRON
ejpam-5734	299	20	{	{	PUNCT
ejpam-5734	299	21	ep	ep	NOUN
ejpam-5734	299	22	|	|	ADV
ejpam-5734	299	23	1	1	NUM
ejpam-5734	299	24	≤	≤	NOUN
ejpam-5734	299	25	p	p	NOUN
ejpam-5734	299	26	≤	≤	NOUN
ejpam-5734	299	27	n	n	CCONJ
ejpam-5734	299	28	−	−	PROPN
ejpam-5734	299	29	1	1	NUM
ejpam-5734	299	30	}	}	PUNCT
ejpam-5734	299	31	∪	∪	X
ejpam-5734	299	32	{	{	PUNCT
ejpam-5734	299	33	en	en	NOUN
ejpam-5734	299	34	}	}	PUNCT
ejpam-5734	299	35	such	such	ADJ
ejpam-5734	299	36	that	that	SCONJ
ejpam-5734	299	37	ep	ep	PROPN
ejpam-5734	299	38	=	=	PUNCT
ejpam-5734	299	39	vivi+1	vivi+1	PROPN
ejpam-5734	299	40	for	for	ADP
ejpam-5734	299	41	1	1	NUM
ejpam-5734	299	42	≤	≤	NUM
ejpam-5734	299	43	i	i	PRON
ejpam-5734	299	44	≤	≤	NOUN
ejpam-5734	299	45	n	n	CCONJ
ejpam-5734	299	46	−	−	PROPN
ejpam-5734	299	47	1	1	NUM
ejpam-5734	299	48	and	and	CCONJ
ejpam-5734	299	49	en	en	X
ejpam-5734	299	50	=	=	SYM
ejpam-5734	299	51	v1vn	v1vn	PROPN
ejpam-5734	299	52	.	.	PUNCT
ejpam-5734	300	1	by	by	ADP
ejpam-5734	300	2	the	the	DET
ejpam-5734	300	3	definition	definition	NOUN
ejpam-5734	300	4	of	of	ADP
ejpam-5734	300	5	a	a	DET
ejpam-5734	300	6	central	central	ADJ
ejpam-5734	300	7	m.	m.	NOUN
ejpam-5734	300	8	f.	f.	PROPN
ejpam-5734	300	9	libao	libao	PROPN
ejpam-5734	300	10	,	,	PUNCT
ejpam-5734	300	11	k.	k.	PROPN
ejpam-5734	300	12	b.	b.	PROPN
ejpam-5734	300	13	abarca	abarca	PROPN
ejpam-5734	300	14	/	/	SYM
ejpam-5734	300	15	eur	eur	PROPN
ejpam-5734	300	16	.	.	PUNCT
ejpam-5734	301	1	j.	j.	PROPN
ejpam-5734	301	2	pure	pure	PROPN
ejpam-5734	301	3	appl	appl	PROPN
ejpam-5734	301	4	.	.	PROPN
ejpam-5734	301	5	math	math	PROPN
ejpam-5734	301	6	,	,	PUNCT
ejpam-5734	301	7	18	18	NUM
ejpam-5734	301	8	(	(	PUNCT
ejpam-5734	301	9	2	2	NUM
ejpam-5734	301	10	)	)	PUNCT
ejpam-5734	301	11	(	(	PUNCT
ejpam-5734	301	12	2025	2025	NUM
ejpam-5734	301	13	)	)	PUNCT
ejpam-5734	301	14	,	,	PUNCT
ejpam-5734	301	15	5734	5734	NUM
ejpam-5734	301	16	17	17	NUM
ejpam-5734	301	17	of	of	ADP
ejpam-5734	301	18	25	25	NUM
ejpam-5734	301	19	graph	graph	NOUN
ejpam-5734	301	20	,	,	PUNCT
ejpam-5734	301	21	for	for	ADP
ejpam-5734	301	22	each	each	DET
ejpam-5734	301	23	edge	edge	NOUN
ejpam-5734	301	24	ep	ep	PROPN
ejpam-5734	301	25	,	,	PUNCT
ejpam-5734	301	26	en	en	PROPN
ejpam-5734	301	27	∈	∈	PROPN
ejpam-5734	301	28	e(cn	e(cn	NOUN
ejpam-5734	301	29	)	)	PUNCT
ejpam-5734	302	1	,	,	PUNCT
ejpam-5734	302	2	there	there	PRON
ejpam-5734	302	3	exists	exist	VERB
ejpam-5734	302	4	a	a	DET
ejpam-5734	302	5	corresponding	correspond	VERB
ejpam-5734	302	6	central	central	ADJ
ejpam-5734	302	7	vertex	vertex	NOUN
ejpam-5734	302	8	cq	cq	NOUN
ejpam-5734	302	9	,	,	PUNCT
ejpam-5734	302	10	where	where	SCONJ
ejpam-5734	302	11	1	1	NUM
ejpam-5734	302	12	≤	≤	NOUN
ejpam-5734	302	13	q	q	PROPN
ejpam-5734	302	14	≤	≤	NUM
ejpam-5734	302	15	n	n	CCONJ
ejpam-5734	302	16	,	,	PUNCT
ejpam-5734	302	17	that	that	PRON
ejpam-5734	302	18	divides	divide	VERB
ejpam-5734	302	19	the	the	DET
ejpam-5734	302	20	edges	edge	NOUN
ejpam-5734	302	21	in	in	ADP
ejpam-5734	302	22	two	two	NUM
ejpam-5734	302	23	.	.	PUNCT
ejpam-5734	303	1	thus	thus	ADV
ejpam-5734	303	2	,	,	PUNCT
ejpam-5734	303	3	we	we	PRON
ejpam-5734	303	4	have	have	VERB
ejpam-5734	303	5	the	the	DET
ejpam-5734	303	6	set	set	NOUN
ejpam-5734	303	7	of	of	ADP
ejpam-5734	303	8	central	central	ADJ
ejpam-5734	303	9	vertices	vertex	NOUN
ejpam-5734	303	10	as	as	ADP
ejpam-5734	303	11	v	v	NOUN
ejpam-5734	303	12	(	(	PUNCT
ejpam-5734	303	13	cv	cv	PROPN
ejpam-5734	303	14	)	)	PUNCT
ejpam-5734	303	15	=	=	SYM
ejpam-5734	303	16	{	{	PUNCT
ejpam-5734	303	17	c1	c1	PROPN
ejpam-5734	303	18	,	,	PUNCT
ejpam-5734	303	19	c2	c2	PROPN
ejpam-5734	303	20	,	,	PUNCT
ejpam-5734	303	21	.	.	PUNCT
ejpam-5734	303	22	.	.	PUNCT
ejpam-5734	303	23	.	.	PUNCT
ejpam-5734	304	1	,	,	PUNCT
ejpam-5734	304	2	cn	cn	PROPN
ejpam-5734	304	3	}	}	PUNCT
ejpam-5734	304	4	for	for	ADP
ejpam-5734	304	5	corresponding	correspond	VERB
ejpam-5734	304	6	edges	edge	NOUN
ejpam-5734	304	7	e1	e1	NOUN
ejpam-5734	304	8	,	,	PUNCT
ejpam-5734	304	9	e2	e2	PROPN
ejpam-5734	304	10	,	,	PUNCT
ejpam-5734	304	11	...	...	PUNCT
ejpam-5734	304	12	,	,	PUNCT
ejpam-5734	304	13	en	en	X
ejpam-5734	304	14	.	.	PUNCT
ejpam-5734	305	1	therefore	therefore	ADV
ejpam-5734	305	2	,	,	PUNCT
ejpam-5734	305	3	v	v	X
ejpam-5734	305	4	[	[	X
ejpam-5734	305	5	c(cn	c(cn	NOUN
ejpam-5734	305	6	)	)	PUNCT
ejpam-5734	305	7	]	]	PUNCT
ejpam-5734	306	1	=	=	SYM
ejpam-5734	306	2	v	v	X
ejpam-5734	306	3	(	(	PUNCT
ejpam-5734	306	4	cn	cn	NOUN
ejpam-5734	306	5	)	)	PUNCT
ejpam-5734	306	6	∪	∪	NOUN
ejpam-5734	306	7	v	v	PROPN
ejpam-5734	306	8	(	(	PUNCT
ejpam-5734	306	9	cv	cv	PROPN
ejpam-5734	306	10	)	)	PUNCT
ejpam-5734	306	11	.	.	PUNCT
ejpam-5734	307	1	moreover	moreover	ADV
ejpam-5734	307	2	,	,	PUNCT
ejpam-5734	307	3	cq	cq	PROPN
ejpam-5734	307	4	for	for	ADP
ejpam-5734	307	5	1	1	NUM
ejpam-5734	307	6	≤	≤	NUM
ejpam-5734	307	7	q	q	PROPN
ejpam-5734	307	8	≤	≤	NUM
ejpam-5734	307	9	n	n	CCONJ
ejpam-5734	307	10	−	−	PROPN
ejpam-5734	307	11	1	1	NUM
ejpam-5734	307	12	is	be	AUX
ejpam-5734	307	13	adjacent	adjacent	ADJ
ejpam-5734	307	14	to	to	ADP
ejpam-5734	307	15	both	both	DET
ejpam-5734	307	16	vi	vi	PROPN
ejpam-5734	307	17	and	and	CCONJ
ejpam-5734	307	18	vi+1	vi+1	NOUN
ejpam-5734	307	19	and	and	CCONJ
ejpam-5734	307	20	cn	cn	PROPN
ejpam-5734	307	21	is	be	AUX
ejpam-5734	307	22	adjacent	adjacent	ADJ
ejpam-5734	307	23	to	to	ADP
ejpam-5734	307	24	both	both	DET
ejpam-5734	307	25	vn	vn	PROPN
ejpam-5734	307	26	and	and	CCONJ
ejpam-5734	307	27	v1	v1	PROPN
ejpam-5734	307	28	.	.	PUNCT
ejpam-5734	308	1	accordingly	accordingly	ADV
ejpam-5734	308	2	,	,	PUNCT
ejpam-5734	308	3	all	all	DET
ejpam-5734	308	4	the	the	DET
ejpam-5734	308	5	vi	vi	PROPN
ejpam-5734	308	6	∈	∈	PROPN
ejpam-5734	308	7	v	v	NOUN
ejpam-5734	308	8	(	(	PUNCT
ejpam-5734	308	9	cn	cn	NOUN
ejpam-5734	308	10	)	)	PUNCT
ejpam-5734	308	11	are	be	AUX
ejpam-5734	308	12	adjacent	adjacent	ADJ
ejpam-5734	308	13	to	to	ADP
ejpam-5734	308	14	each	each	DET
ejpam-5734	308	15	other	other	ADJ
ejpam-5734	308	16	,	,	PUNCT
ejpam-5734	308	17	which	which	PRON
ejpam-5734	308	18	implies	imply	VERB
ejpam-5734	308	19	that	that	SCONJ
ejpam-5734	308	20	we	we	PRON
ejpam-5734	308	21	must	must	AUX
ejpam-5734	308	22	assign	assign	VERB
ejpam-5734	308	23	a	a	DET
ejpam-5734	308	24	different	different	ADJ
ejpam-5734	308	25	color	color	NOUN
ejpam-5734	308	26	to	to	ADP
ejpam-5734	308	27	each	each	DET
ejpam-5734	308	28	vertex	vertex	NOUN
ejpam-5734	308	29	vi	vi	NOUN
ejpam-5734	308	30	,	,	PUNCT
ejpam-5734	308	31	thus	thus	ADV
ejpam-5734	308	32	assigning	assign	VERB
ejpam-5734	308	33	each	each	DET
ejpam-5734	308	34	color	color	NOUN
ejpam-5734	308	35	class	class	NOUN
ejpam-5734	308	36	ai	ai	VERB
ejpam-5734	308	37	to	to	ADP
ejpam-5734	308	38	vi	vi	NUM
ejpam-5734	308	39	,	,	PUNCT
ejpam-5734	308	40	respectively	respectively	ADV
ejpam-5734	308	41	.	.	PUNCT
ejpam-5734	309	1	we	we	PRON
ejpam-5734	309	2	now	now	ADV
ejpam-5734	309	3	have	have	VERB
ejpam-5734	309	4	the	the	DET
ejpam-5734	309	5	color	color	NOUN
ejpam-5734	309	6	classesa1,a2,a3	classesa1,a2,a3	PROPN
ejpam-5734	309	7	,	,	PUNCT
ejpam-5734	309	8	...	...	PUNCT
ejpam-5734	309	9	,	,	PUNCT
ejpam-5734	309	10	an	an	PRON
ejpam-5734	309	11	for	for	ADP
ejpam-5734	309	12	each	each	DET
ejpam-5734	309	13	vi	vi	PROPN
ejpam-5734	309	14	∈	∈	PROPN
ejpam-5734	309	15	v	v	NOUN
ejpam-5734	309	16	(	(	PUNCT
ejpam-5734	309	17	cn	cn	PROPN
ejpam-5734	309	18	)	)	PUNCT
ejpam-5734	309	19	.	.	PUNCT
ejpam-5734	310	1	next	next	ADV
ejpam-5734	310	2	,	,	PUNCT
ejpam-5734	310	3	consider	consider	VERB
ejpam-5734	310	4	the	the	DET
ejpam-5734	310	5	following	follow	VERB
ejpam-5734	310	6	cases	case	NOUN
ejpam-5734	310	7	for	for	ADP
ejpam-5734	310	8	v	v	NOUN
ejpam-5734	310	9	(	(	PUNCT
ejpam-5734	310	10	cv	cv	PROPN
ejpam-5734	310	11	)	)	PUNCT
ejpam-5734	310	12	.	.	PUNCT
ejpam-5734	311	1	case	case	NOUN
ejpam-5734	311	2	1	1	NUM
ejpam-5734	311	3	:	:	PUNCT
ejpam-5734	311	4	n	n	PRON
ejpam-5734	311	5	is	be	AUX
ejpam-5734	311	6	even	even	ADV
ejpam-5734	311	7	let	let	VERB
ejpam-5734	311	8	v	v	X
ejpam-5734	311	9	(	(	PUNCT
ejpam-5734	311	10	cv	cv	PROPN
ejpam-5734	311	11	)	)	PUNCT
ejpam-5734	311	12	=	=	SYM
ejpam-5734	311	13	{	{	PUNCT
ejpam-5734	311	14	c1	c1	PROPN
ejpam-5734	311	15	,	,	PUNCT
ejpam-5734	311	16	c2	c2	PROPN
ejpam-5734	311	17	,	,	PUNCT
ejpam-5734	311	18	.	.	PUNCT
ejpam-5734	311	19	.	.	PUNCT
ejpam-5734	311	20	.	.	PUNCT
ejpam-5734	312	1	,	,	PUNCT
ejpam-5734	312	2	cn	cn	PROPN
ejpam-5734	312	3	}	}	PUNCT
ejpam-5734	312	4	=	=	SYM
ejpam-5734	312	5	{	{	PUNCT
ejpam-5734	312	6	cs	cs	X
ejpam-5734	312	7	:	:	PUNCT
ejpam-5734	312	8	s	s	X
ejpam-5734	312	9	=	=	SYM
ejpam-5734	312	10	1	1	NUM
ejpam-5734	312	11	,	,	PUNCT
ejpam-5734	312	12	3	3	NUM
ejpam-5734	312	13	,	,	PUNCT
ejpam-5734	312	14	.	.	PUNCT
ejpam-5734	312	15	.	.	PUNCT
ejpam-5734	313	1	.	.	PUNCT
ejpam-5734	314	1	,	,	PUNCT
ejpam-5734	315	1	n	n	CCONJ
ejpam-5734	315	2	−	−	PROPN
ejpam-5734	315	3	1	1	NUM
ejpam-5734	315	4	}	}	PUNCT
ejpam-5734	315	5	∪	∪	NOUN
ejpam-5734	315	6	{	{	PUNCT
ejpam-5734	315	7	ct	ct	NOUN
ejpam-5734	315	8	:	:	PUNCT
ejpam-5734	315	9	t	t	NOUN
ejpam-5734	315	10	=	=	SYM
ejpam-5734	315	11	2	2	NUM
ejpam-5734	315	12	,	,	PUNCT
ejpam-5734	315	13	4	4	NUM
ejpam-5734	315	14	,	,	PUNCT
ejpam-5734	315	15	.	.	PUNCT
ejpam-5734	315	16	.	.	PUNCT
ejpam-5734	315	17	.	.	PUNCT
ejpam-5734	315	18	,	,	PUNCT
ejpam-5734	315	19	n	n	CCONJ
ejpam-5734	315	20	}	}	PUNCT
ejpam-5734	315	21	.	.	PUNCT
ejpam-5734	316	1	observe	observe	VERB
ejpam-5734	316	2	that	that	SCONJ
ejpam-5734	316	3	for	for	SCONJ
ejpam-5734	316	4	any	any	DET
ejpam-5734	316	5	pair	pair	NOUN
ejpam-5734	316	6	of	of	ADP
ejpam-5734	316	7	consecutive	consecutive	ADJ
ejpam-5734	316	8	vertices	vertex	NOUN
ejpam-5734	316	9	ck	ck	PROPN
ejpam-5734	316	10	,	,	PUNCT
ejpam-5734	316	11	cj	cj	PROPN
ejpam-5734	316	12	∈	∈	PROPN
ejpam-5734	316	13	{	{	PUNCT
ejpam-5734	316	14	cs	cs	NOUN
ejpam-5734	316	15	:	:	PUNCT
ejpam-5734	316	16	s	s	X
ejpam-5734	316	17	=	=	SYM
ejpam-5734	316	18	1	1	NUM
ejpam-5734	316	19	,	,	PUNCT
ejpam-5734	316	20	3	3	NUM
ejpam-5734	316	21	,	,	PUNCT
ejpam-5734	316	22	.	.	PUNCT
ejpam-5734	316	23	.	.	PUNCT
ejpam-5734	317	1	.	.	PUNCT
ejpam-5734	318	1	,	,	PUNCT
ejpam-5734	318	2	n−	n−	NOUN
ejpam-5734	318	3	1	1	NUM
ejpam-5734	318	4	}	}	PUNCT
ejpam-5734	318	5	,	,	PUNCT
ejpam-5734	318	6	we	we	PRON
ejpam-5734	318	7	have	have	VERB
ejpam-5734	318	8	d(ck	d(ck	NUM
ejpam-5734	318	9	,	,	PUNCT
ejpam-5734	318	10	cj	cj	X
ejpam-5734	318	11	)	)	PUNCT
ejpam-5734	319	1	=	=	SYM
ejpam-5734	319	2	2	2	NUM
ejpam-5734	319	3	,	,	PUNCT
ejpam-5734	319	4	which	which	PRON
ejpam-5734	319	5	is	be	AUX
ejpam-5734	319	6	also	also	ADV
ejpam-5734	319	7	true	true	ADJ
ejpam-5734	319	8	for	for	ADP
ejpam-5734	319	9	{	{	PUNCT
ejpam-5734	319	10	ct	ct	X
ejpam-5734	319	11	:	:	PUNCT
ejpam-5734	319	12	t	t	NOUN
ejpam-5734	319	13	=	=	SYM
ejpam-5734	319	14	2	2	NUM
ejpam-5734	319	15	,	,	PUNCT
ejpam-5734	319	16	4	4	NUM
ejpam-5734	319	17	,	,	PUNCT
ejpam-5734	319	18	.	.	PUNCT
ejpam-5734	319	19	.	.	PUNCT
ejpam-5734	320	1	.	.	PUNCT
ejpam-5734	320	2	,	,	PUNCT
ejpam-5734	320	3	n	n	CCONJ
ejpam-5734	320	4	}	}	PUNCT
ejpam-5734	320	5	.	.	PUNCT
ejpam-5734	321	1	thus	thus	ADV
ejpam-5734	321	2	,	,	PUNCT
ejpam-5734	321	3	we	we	PRON
ejpam-5734	321	4	have	have	VERB
ejpam-5734	321	5	another	another	DET
ejpam-5734	321	6	color	color	NOUN
ejpam-5734	321	7	classes	class	NOUN
ejpam-5734	321	8	an+1	an+1	AUX
ejpam-5734	322	1	=	=	SYM
ejpam-5734	322	2	{	{	PUNCT
ejpam-5734	322	3	cs	cs	X
ejpam-5734	322	4	:	:	PUNCT
ejpam-5734	322	5	s	s	X
ejpam-5734	322	6	=	=	SYM
ejpam-5734	322	7	1	1	NUM
ejpam-5734	322	8	,	,	PUNCT
ejpam-5734	322	9	3	3	NUM
ejpam-5734	322	10	,	,	PUNCT
ejpam-5734	322	11	.	.	PUNCT
ejpam-5734	322	12	.	.	PUNCT
ejpam-5734	322	13	.	.	PUNCT
ejpam-5734	323	1	,	,	PUNCT
ejpam-5734	324	1	n	n	CCONJ
ejpam-5734	324	2	−	−	PROPN
ejpam-5734	324	3	1	1	NUM
ejpam-5734	324	4	}	}	PUNCT
ejpam-5734	324	5	and	and	CCONJ
ejpam-5734	324	6	an+2	an+2	ADV
ejpam-5734	324	7	=	=	SYM
ejpam-5734	324	8	{	{	PUNCT
ejpam-5734	324	9	ct	ct	X
ejpam-5734	324	10	:	:	PUNCT
ejpam-5734	324	11	t	t	NOUN
ejpam-5734	324	12	=	=	SYM
ejpam-5734	324	13	2	2	NUM
ejpam-5734	324	14	,	,	PUNCT
ejpam-5734	324	15	4	4	NUM
ejpam-5734	324	16	,	,	PUNCT
ejpam-5734	324	17	.	.	PUNCT
ejpam-5734	324	18	.	.	PUNCT
ejpam-5734	324	19	.	.	PUNCT
ejpam-5734	324	20	,	,	PUNCT
ejpam-5734	324	21	n	n	CCONJ
ejpam-5734	324	22	}	}	PUNCT
ejpam-5734	324	23	.	.	PUNCT
ejpam-5734	325	1	therefore	therefore	ADV
ejpam-5734	325	2	,	,	PUNCT
ejpam-5734	325	3	c	c	X
ejpam-5734	325	4	=	=	PRON
ejpam-5734	325	5	{	{	PUNCT
ejpam-5734	325	6	a1,a2	a1,a2	PROPN
ejpam-5734	325	7	,	,	PUNCT
ejpam-5734	325	8	.	.	PUNCT
ejpam-5734	325	9	.	.	PUNCT
ejpam-5734	325	10	.	.	PUNCT
ejpam-5734	326	1	,	,	PUNCT
ejpam-5734	326	2	an	an	PRON
ejpam-5734	326	3	,	,	PUNCT
ejpam-5734	326	4	an+1,an+2	an+1,an+2	NOUN
ejpam-5734	326	5	}	}	PUNCT
ejpam-5734	326	6	.	.	PUNCT
ejpam-5734	327	1	let	let	VERB
ejpam-5734	327	2	us	we	PRON
ejpam-5734	327	3	see	see	VERB
ejpam-5734	327	4	whether	whether	SCONJ
ejpam-5734	327	5	this	this	DET
ejpam-5734	327	6	set	set	NOUN
ejpam-5734	327	7	is	be	AUX
ejpam-5734	327	8	a	a	DET
ejpam-5734	327	9	distance-2	distance-2	CCONJ
ejpam-5734	327	10	chromatic	chromatic	ADJ
ejpam-5734	327	11	set	set	NOUN
ejpam-5734	327	12	.	.	PUNCT
ejpam-5734	328	1	i.	i.	PROPN
ejpam-5734	328	2	to	to	PART
ejpam-5734	328	3	ensure	ensure	VERB
ejpam-5734	328	4	that	that	SCONJ
ejpam-5734	328	5	every	every	DET
ejpam-5734	328	6	vertex	vertex	NOUN
ejpam-5734	328	7	in	in	ADP
ejpam-5734	328	8	the	the	DET
ejpam-5734	328	9	graph	graph	NOUN
ejpam-5734	328	10	belongs	belong	VERB
ejpam-5734	328	11	to	to	ADP
ejpam-5734	328	12	exactly	exactly	ADV
ejpam-5734	328	13	one	one	NUM
ejpam-5734	328	14	color	color	NOUN
ejpam-5734	328	15	class:⋃	class:⋃	PUNCT
ejpam-5734	328	16	a∈c	a∈c	VERB
ejpam-5734	328	17	a	a	PRON
ejpam-5734	328	18	=	=	X
ejpam-5734	328	19	{	{	PUNCT
ejpam-5734	328	20	a1,a2	a1,a2	PROPN
ejpam-5734	328	21	,	,	PUNCT
ejpam-5734	328	22	.	.	PUNCT
ejpam-5734	328	23	.	.	PUNCT
ejpam-5734	329	1	.	.	PUNCT
ejpam-5734	330	1	,	,	PUNCT
ejpam-5734	330	2	an	an	DET
ejpam-5734	330	3	,	,	PUNCT
ejpam-5734	330	4	an+1,an+2	an+1,an+2	NOUN
ejpam-5734	330	5	}	}	PUNCT
ejpam-5734	330	6	=	=	SYM
ejpam-5734	330	7	{	{	PUNCT
ejpam-5734	330	8	a1,a2	a1,a2	PROPN
ejpam-5734	330	9	,	,	PUNCT
ejpam-5734	330	10	.	.	PUNCT
ejpam-5734	330	11	.	.	PUNCT
ejpam-5734	331	1	.	.	PUNCT
ejpam-5734	332	1	,	,	PUNCT
ejpam-5734	332	2	an	an	DET
ejpam-5734	332	3	}	}	PUNCT
ejpam-5734	332	4	∪	∪	ADJ
ejpam-5734	332	5	{	{	PUNCT
ejpam-5734	332	6	an+1	an+1	NOUN
ejpam-5734	332	7	}	}	PUNCT
ejpam-5734	332	8	∪	∪	X
ejpam-5734	332	9	{	{	PUNCT
ejpam-5734	332	10	an+2	an+2	ADV
ejpam-5734	332	11	}	}	PUNCT
ejpam-5734	332	12	=	=	SYM
ejpam-5734	332	13	{	{	PUNCT
ejpam-5734	332	14	v1	v1	NOUN
ejpam-5734	332	15	,	,	PUNCT
ejpam-5734	332	16	v2	v2	PROPN
ejpam-5734	332	17	,	,	PUNCT
ejpam-5734	332	18	.	.	PUNCT
ejpam-5734	332	19	.	.	PUNCT
ejpam-5734	333	1	.	.	PUNCT
ejpam-5734	334	1	,	,	PUNCT
ejpam-5734	334	2	vn	vn	VERB
ejpam-5734	334	3	}	}	PUNCT
ejpam-5734	334	4	∪	∪	ADJ
ejpam-5734	334	5	{	{	PUNCT
ejpam-5734	334	6	c1	c1	NOUN
ejpam-5734	334	7	,	,	PUNCT
ejpam-5734	334	8	c3	c3	PROPN
ejpam-5734	334	9	,	,	PUNCT
ejpam-5734	334	10	.	.	PUNCT
ejpam-5734	334	11	.	.	PUNCT
ejpam-5734	335	1	.	.	PUNCT
ejpam-5734	336	1	,	,	PUNCT
ejpam-5734	336	2	cn−1	cn−1	ADV
ejpam-5734	336	3	}	}	PUNCT
ejpam-5734	336	4	∪	∪	NOUN
ejpam-5734	336	5	{	{	PUNCT
ejpam-5734	336	6	c2	c2	PROPN
ejpam-5734	336	7	,	,	PUNCT
ejpam-5734	336	8	c4	c4	NOUN
ejpam-5734	336	9	,	,	PUNCT
ejpam-5734	336	10	.	.	PUNCT
ejpam-5734	336	11	.	.	PUNCT
ejpam-5734	336	12	.	.	PUNCT
ejpam-5734	337	1	,	,	PUNCT
ejpam-5734	337	2	cn	cn	PROPN
ejpam-5734	337	3	}	}	PUNCT
ejpam-5734	337	4	=	=	SYM
ejpam-5734	337	5	{	{	PUNCT
ejpam-5734	337	6	v1	v1	NOUN
ejpam-5734	337	7	,	,	PUNCT
ejpam-5734	337	8	v2	v2	PROPN
ejpam-5734	337	9	,	,	PUNCT
ejpam-5734	337	10	.	.	PUNCT
ejpam-5734	337	11	.	.	PUNCT
ejpam-5734	338	1	.	.	PUNCT
ejpam-5734	339	1	,	,	PUNCT
ejpam-5734	339	2	vn	vn	VERB
ejpam-5734	339	3	}	}	PUNCT
ejpam-5734	339	4	∪	∪	ADJ
ejpam-5734	339	5	{	{	PUNCT
ejpam-5734	339	6	c1	c1	NOUN
ejpam-5734	339	7	,	,	PUNCT
ejpam-5734	339	8	c2	c2	PROPN
ejpam-5734	339	9	,	,	PUNCT
ejpam-5734	339	10	.	.	PUNCT
ejpam-5734	339	11	.	.	PUNCT
ejpam-5734	340	1	.	.	PUNCT
ejpam-5734	341	1	,	,	PUNCT
ejpam-5734	341	2	cn	cn	PROPN
ejpam-5734	341	3	}	}	PUNCT
ejpam-5734	341	4	=	=	SYM
ejpam-5734	341	5	{	{	PUNCT
ejpam-5734	341	6	vi	vi	NOUN
ejpam-5734	341	7	}	}	PUNCT
ejpam-5734	341	8	∪	∪	ADJ
ejpam-5734	341	9	{	{	PUNCT
ejpam-5734	341	10	ci	ci	NOUN
ejpam-5734	341	11	}	}	PUNCT
ejpam-5734	341	12	,	,	PUNCT
ejpam-5734	342	1	1	1	NUM
ejpam-5734	342	2	≤	≤	NUM
ejpam-5734	342	3	i	i	PRON
ejpam-5734	342	4	≤	≤	ADJ
ejpam-5734	342	5	n	n	CCONJ
ejpam-5734	342	6	=	=	SYM
ejpam-5734	342	7	v	v	NOUN
ejpam-5734	342	8	[	[	X
ejpam-5734	342	9	c(cn	c(cn	NOUN
ejpam-5734	342	10	)	)	PUNCT
ejpam-5734	342	11	]	]	PUNCT
ejpam-5734	342	12	ii	ii	X
ejpam-5734	342	13	.	.	PUNCT
ejpam-5734	342	14	to	to	PART
ejpam-5734	342	15	show	show	VERB
ejpam-5734	342	16	that	that	SCONJ
ejpam-5734	342	17	the	the	DET
ejpam-5734	342	18	color	color	NOUN
ejpam-5734	342	19	classes	class	NOUN
ejpam-5734	342	20	are	be	AUX
ejpam-5734	342	21	disjoint	disjoint	ADJ
ejpam-5734	342	22	,	,	PUNCT
ejpam-5734	342	23	we	we	PRON
ejpam-5734	342	24	also	also	ADV
ejpam-5734	342	25	have	have	VERB
ejpam-5734	342	26	to	to	PART
ejpam-5734	342	27	show	show	VERB
ejpam-5734	342	28	that	that	SCONJ
ejpam-5734	342	29	∑	∑	PROPN
ejpam-5734	342	30	a∈c	a∈c	PROPN
ejpam-5734	342	31	|a|	|a|	PROPN
ejpam-5734	342	32	=	=	PROPN
ejpam-5734	342	33	|v	|v	PROPN
ejpam-5734	343	1	[	[	X
ejpam-5734	343	2	c(cn)]|	c(cn)]|	VERB
ejpam-5734	343	3	in	in	ADP
ejpam-5734	343	4	addition	addition	NOUN
ejpam-5734	343	5	to	to	ADP
ejpam-5734	343	6	the	the	DET
ejpam-5734	343	7	above	above	ADJ
ejpam-5734	343	8	condition	condition	NOUN
ejpam-5734	343	9	.	.	PUNCT
ejpam-5734	344	1	∑	∑	PROPN
ejpam-5734	344	2	a∈c	a∈c	PROPN
ejpam-5734	344	3	|a|	|a|	PROPN
ejpam-5734	344	4	=	=	PUNCT
ejpam-5734	344	5	|a1|+	|a1|+	NOUN
ejpam-5734	344	6	|a2|+	|a2|+	X
ejpam-5734	344	7	...	...	PUNCT
ejpam-5734	344	8	+	+	PUNCT
ejpam-5734	344	9	|an|+	|an|+	NUM
ejpam-5734	344	10	|an+1|+	|an+1|+	PROPN
ejpam-5734	344	11	|an+2|	|an+2|	NOUN
ejpam-5734	344	12	=	=	SYM
ejpam-5734	344	13	1	1	NUM
ejpam-5734	344	14	+	+	NUM
ejpam-5734	344	15	1	1	NUM
ejpam-5734	344	16	+	+	CCONJ
ejpam-5734	344	17	·	·	PUNCT
ejpam-5734	344	18	·	·	PUNCT
ejpam-5734	344	19	·	·	PUNCT
ejpam-5734	345	1	+	+	NUM
ejpam-5734	345	2	1	1	NUM
ejpam-5734	345	3	+	+	CCONJ
ejpam-5734	345	4	n	n	PRON
ejpam-5734	345	5	2	2	NUM
ejpam-5734	345	6	+	+	CCONJ
ejpam-5734	345	7	n	n	PRON
ejpam-5734	345	8	2	2	NUM
ejpam-5734	345	9	=	=	SYM
ejpam-5734	345	10	n+	n+	NOUN
ejpam-5734	345	11	n	n	ADV
ejpam-5734	345	12	2	2	NUM
ejpam-5734	345	13	+	+	CCONJ
ejpam-5734	345	14	n	n	CCONJ
ejpam-5734	345	15	2	2	NUM
ejpam-5734	345	16	=	=	SYM
ejpam-5734	345	17	2n	2n	NUM
ejpam-5734	345	18	m.	m.	PROPN
ejpam-5734	345	19	f.	f.	PROPN
ejpam-5734	345	20	libao	libao	PROPN
ejpam-5734	345	21	,	,	PUNCT
ejpam-5734	345	22	k.	k.	PROPN
ejpam-5734	345	23	b.	b.	PROPN
ejpam-5734	345	24	abarca	abarca	PROPN
ejpam-5734	345	25	/	/	SYM
ejpam-5734	345	26	eur	eur	PROPN
ejpam-5734	345	27	.	.	PUNCT
ejpam-5734	346	1	j.	j.	PROPN
ejpam-5734	346	2	pure	pure	PROPN
ejpam-5734	346	3	appl	appl	PROPN
ejpam-5734	346	4	.	.	PROPN
ejpam-5734	346	5	math	math	PROPN
ejpam-5734	346	6	,	,	PUNCT
ejpam-5734	346	7	18	18	NUM
ejpam-5734	346	8	(	(	PUNCT
ejpam-5734	346	9	2	2	NUM
ejpam-5734	346	10	)	)	PUNCT
ejpam-5734	346	11	(	(	PUNCT
ejpam-5734	346	12	2025	2025	NUM
ejpam-5734	346	13	)	)	PUNCT
ejpam-5734	346	14	,	,	PUNCT
ejpam-5734	346	15	5734	5734	NUM
ejpam-5734	346	16	18	18	NUM
ejpam-5734	346	17	of	of	ADP
ejpam-5734	346	18	25	25	NUM
ejpam-5734	346	19	=	=	SYM
ejpam-5734	346	20	|v	|v	X
ejpam-5734	346	21	[	[	X
ejpam-5734	346	22	c(cn)]|	c(cn)]|	VERB
ejpam-5734	346	23	by	by	ADP
ejpam-5734	346	24	lemma	lemma	PROPN
ejpam-5734	346	25	1	1	NUM
ejpam-5734	346	26	,	,	PUNCT
ejpam-5734	346	27	color	color	NOUN
ejpam-5734	346	28	classes	class	NOUN
ejpam-5734	346	29	are	be	AUX
ejpam-5734	346	30	mutually	mutually	ADV
ejpam-5734	346	31	exclusive	exclusive	ADJ
ejpam-5734	346	32	,	,	PUNCT
ejpam-5734	346	33	that	that	ADV
ejpam-5734	346	34	is	is	ADV
ejpam-5734	346	35	,	,	PUNCT
ejpam-5734	346	36	ai	ai	VERB
ejpam-5734	346	37	∩	∩	ADJ
ejpam-5734	346	38	aj	aj	PROPN
ejpam-5734	346	39	=	=	PROPN
ejpam-5734	346	40	∅	∅	NOUN
ejpam-5734	346	41	for	for	ADP
ejpam-5734	346	42	i	i	PRON
ejpam-5734	346	43	̸=	̸=	PROPN
ejpam-5734	346	44	j.	j.	PROPN
ejpam-5734	346	45	we	we	PRON
ejpam-5734	346	46	have	have	AUX
ejpam-5734	346	47	just	just	ADV
ejpam-5734	346	48	shown	show	VERB
ejpam-5734	346	49	that	that	SCONJ
ejpam-5734	346	50	c	c	NOUN
ejpam-5734	346	51	=	=	PRON
ejpam-5734	346	52	{	{	PUNCT
ejpam-5734	346	53	a1,a2	a1,a2	PROPN
ejpam-5734	346	54	,	,	PUNCT
ejpam-5734	346	55	.	.	PUNCT
ejpam-5734	346	56	.	.	PUNCT
ejpam-5734	347	1	.	.	PUNCT
ejpam-5734	348	1	,	,	PUNCT
ejpam-5734	348	2	an	an	PRON
ejpam-5734	348	3	,	,	PUNCT
ejpam-5734	348	4	an+1,an+2	an+1,an+2	NOUN
ejpam-5734	348	5	}	}	PUNCT
ejpam-5734	348	6	is	be	AUX
ejpam-5734	348	7	a	a	DET
ejpam-5734	348	8	distance-2	distance-2	CCONJ
ejpam-5734	348	9	chromatic	chromatic	ADJ
ejpam-5734	348	10	set	set	NOUN
ejpam-5734	348	11	and	and	CCONJ
ejpam-5734	348	12	|c	|c	NOUN
ejpam-5734	348	13	|	|	NOUN
ejpam-5734	348	14	=	=	SYM
ejpam-5734	348	15	n	n	NOUN
ejpam-5734	348	16	+	+	NOUN
ejpam-5734	348	17	2	2	X
ejpam-5734	348	18	.	.	X
ejpam-5734	349	1	this	this	PRON
ejpam-5734	349	2	means	mean	VERB
ejpam-5734	349	3	that	that	SCONJ
ejpam-5734	349	4	χ2[c(cn	χ2[c(cn	PROPN
ejpam-5734	349	5	)	)	PUNCT
ejpam-5734	349	6	]	]	PUNCT
ejpam-5734	349	7	≤	≤	NUM
ejpam-5734	349	8	n	n	PRON
ejpam-5734	349	9	+	+	NOUN
ejpam-5734	349	10	2	2	X
ejpam-5734	349	11	.	.	X
ejpam-5734	349	12	one	one	PRON
ejpam-5734	349	13	can	can	AUX
ejpam-5734	349	14	simply	simply	ADV
ejpam-5734	349	15	examine	examine	VERB
ejpam-5734	349	16	that	that	SCONJ
ejpam-5734	349	17	χ2[c(cn	χ2[c(cn	PROPN
ejpam-5734	349	18	)	)	PUNCT
ejpam-5734	349	19	]	]	PUNCT
ejpam-5734	349	20	̸	̸	CCONJ
ejpam-5734	349	21	<	<	X
ejpam-5734	349	22	n	n	NOUN
ejpam-5734	349	23	+	+	X
ejpam-5734	349	24	2	2	NUM
ejpam-5734	349	25	since	since	SCONJ
ejpam-5734	349	26	taking	take	VERB
ejpam-5734	349	27	out	out	ADP
ejpam-5734	349	28	any	any	DET
ejpam-5734	349	29	ak	ak	PROPN
ejpam-5734	349	30	∈	∈	PROPN
ejpam-5734	349	31	c	c	NOUN
ejpam-5734	349	32	will	will	AUX
ejpam-5734	349	33	violate	violate	VERB
ejpam-5734	349	34	the	the	DET
ejpam-5734	349	35	distance-2	distance-2	NUM
ejpam-5734	349	36	coloring	coloring	NOUN
ejpam-5734	349	37	rule	rule	NOUN
ejpam-5734	349	38	.	.	PUNCT
ejpam-5734	350	1	for	for	ADP
ejpam-5734	350	2	instance	instance	NOUN
ejpam-5734	350	3	,	,	PUNCT
ejpam-5734	350	4	we	we	PRON
ejpam-5734	350	5	assign	assign	VERB
ejpam-5734	350	6	other	other	ADJ
ejpam-5734	350	7	color	color	NOUN
ejpam-5734	350	8	class	class	NOUN
ejpam-5734	350	9	to	to	PART
ejpam-5734	350	10	v1	v1	VERB
ejpam-5734	350	11	,	,	PUNCT
ejpam-5734	350	12	say	say	VERB
ejpam-5734	350	13	we	we	PRON
ejpam-5734	350	14	choose	choose	VERB
ejpam-5734	350	15	any	any	PRON
ejpam-5734	350	16	of	of	ADP
ejpam-5734	350	17	a2	a2	PROPN
ejpam-5734	350	18	,	,	PUNCT
ejpam-5734	350	19	.	.	PUNCT
ejpam-5734	350	20	.	.	PUNCT
ejpam-5734	351	1	.	.	PUNCT
ejpam-5734	352	1	,	,	PUNCT
ejpam-5734	352	2	an	an	PRON
ejpam-5734	352	3	,	,	PUNCT
ejpam-5734	352	4	but	but	CCONJ
ejpam-5734	352	5	since	since	SCONJ
ejpam-5734	352	6	d(v1	d(v1	NOUN
ejpam-5734	352	7	,	,	PUNCT
ejpam-5734	352	8	vi	vi	NOUN
ejpam-5734	352	9	)	)	PUNCT
ejpam-5734	352	10	=	=	SYM
ejpam-5734	352	11	1	1	NUM
ejpam-5734	352	12	for	for	ADP
ejpam-5734	352	13	i	i	PRON
ejpam-5734	352	14	=	=	SYM
ejpam-5734	352	15	2	2	NUM
ejpam-5734	352	16	,	,	PUNCT
ejpam-5734	352	17	3	3	NUM
ejpam-5734	352	18	,	,	PUNCT
ejpam-5734	352	19	.	.	PUNCT
ejpam-5734	352	20	.	.	PUNCT
ejpam-5734	353	1	.	.	PUNCT
ejpam-5734	354	1	,	,	PUNCT
ejpam-5734	354	2	n	n	CCONJ
ejpam-5734	354	3	,	,	PUNCT
ejpam-5734	354	4	this	this	DET
ejpam-5734	354	5	assignment	assignment	NOUN
ejpam-5734	354	6	does	do	AUX
ejpam-5734	354	7	not	not	PART
ejpam-5734	354	8	follow	follow	VERB
ejpam-5734	354	9	the	the	DET
ejpam-5734	354	10	required	require	VERB
ejpam-5734	354	11	distance-2	distance-2	NUM
ejpam-5734	354	12	constraint	constraint	NOUN
ejpam-5734	354	13	.	.	PUNCT
ejpam-5734	355	1	for	for	ADP
ejpam-5734	355	2	the	the	DET
ejpam-5734	355	3	remaining	remain	VERB
ejpam-5734	355	4	colors	color	NOUN
ejpam-5734	355	5	,	,	PUNCT
ejpam-5734	355	6	an+1	an+1	NOUN
ejpam-5734	355	7	and	and	CCONJ
ejpam-5734	355	8	an+2	an+2	ADV
ejpam-5734	355	9	,	,	PUNCT
ejpam-5734	355	10	one	one	PRON
ejpam-5734	355	11	could	could	AUX
ejpam-5734	355	12	examine	examine	VERB
ejpam-5734	355	13	that	that	DET
ejpam-5734	355	14	d(v1	d(v1	NOUN
ejpam-5734	355	15	,	,	PUNCT
ejpam-5734	355	16	cs	cs	ADJ
ejpam-5734	355	17	)	)	PUNCT
ejpam-5734	355	18	=	=	SYM
ejpam-5734	355	19	1	1	NUM
ejpam-5734	355	20	and	and	CCONJ
ejpam-5734	355	21	d(v1	d(v1	NOUN
ejpam-5734	355	22	,	,	PUNCT
ejpam-5734	355	23	ct	ct	PROPN
ejpam-5734	355	24	)	)	PUNCT
ejpam-5734	355	25	=	=	SYM
ejpam-5734	355	26	1	1	NUM
ejpam-5734	355	27	,	,	PUNCT
ejpam-5734	355	28	respectively	respectively	ADV
ejpam-5734	355	29	.	.	PUNCT
ejpam-5734	356	1	still	still	ADV
ejpam-5734	356	2	,	,	PUNCT
ejpam-5734	356	3	non	non	ADJ
ejpam-5734	356	4	-	-	ADJ
ejpam-5734	356	5	compliant	compliant	ADJ
ejpam-5734	356	6	.	.	PUNCT
ejpam-5734	357	1	therefore	therefore	ADV
ejpam-5734	357	2	,	,	PUNCT
ejpam-5734	357	3	χ2[c(cn	χ2[c(cn	PROPN
ejpam-5734	357	4	)	)	PUNCT
ejpam-5734	357	5	]	]	PUNCT
ejpam-5734	357	6	=	=	SYM
ejpam-5734	357	7	n+	n+	PUNCT
ejpam-5734	357	8	2	2	X
ejpam-5734	357	9	.	.	PUNCT
ejpam-5734	357	10	below	below	ADV
ejpam-5734	357	11	is	be	AUX
ejpam-5734	357	12	an	an	DET
ejpam-5734	357	13	example	example	NOUN
ejpam-5734	357	14	of	of	ADP
ejpam-5734	357	15	a	a	DET
ejpam-5734	357	16	central	central	ADJ
ejpam-5734	357	17	graph	graph	NOUN
ejpam-5734	357	18	of	of	ADP
ejpam-5734	357	19	c6	c6	PROPN
ejpam-5734	357	20	,	,	PUNCT
ejpam-5734	357	21	c(c6	c(c6	NOUN
ejpam-5734	357	22	)	)	PUNCT
ejpam-5734	357	23	,	,	PUNCT
ejpam-5734	357	24	with	with	ADP
ejpam-5734	357	25	χ2[c(c6	χ2[c(c6	PROPN
ejpam-5734	357	26	)	)	PUNCT
ejpam-5734	357	27	]	]	PUNCT
ejpam-5734	358	1	=	=	PUNCT
ejpam-5734	358	2	8	8	X
ejpam-5734	358	3	.	.	PUNCT
ejpam-5734	358	4	c	c	X
ejpam-5734	358	5	=	=	PRON
ejpam-5734	358	6	{	{	PUNCT
ejpam-5734	358	7	red	red	NOUN
ejpam-5734	358	8	(	(	PUNCT
ejpam-5734	358	9	v1),blue	v1),blue	NOUN
ejpam-5734	358	10	(	(	PUNCT
ejpam-5734	358	11	v2),purple	v2),purple	X
ejpam-5734	358	12	(	(	PUNCT
ejpam-5734	358	13	v3),green	v3),green	X
ejpam-5734	358	14	(	(	PUNCT
ejpam-5734	358	15	v4),pink	v4),pink	NOUN
ejpam-5734	358	16	(	(	PUNCT
ejpam-5734	358	17	v5),yellow	v5),yellow	X
ejpam-5734	358	18	(	(	PUNCT
ejpam-5734	358	19	v6),orange	v6),orange	X
ejpam-5734	358	20	(	(	PUNCT
ejpam-5734	358	21	c1	c1	PROPN
ejpam-5734	358	22	,	,	PUNCT
ejpam-5734	358	23	c3	c3	PROPN
ejpam-5734	358	24	,	,	PUNCT
ejpam-5734	358	25	c5),black	c5),black	X
ejpam-5734	358	26	(	(	PUNCT
ejpam-5734	358	27	c2	c2	PROPN
ejpam-5734	358	28	,	,	PUNCT
ejpam-5734	358	29	c4	c4	NOUN
ejpam-5734	358	30	,	,	PUNCT
ejpam-5734	358	31	c6	c6	PROPN
ejpam-5734	358	32	)	)	PUNCT
ejpam-5734	358	33	}	}	PUNCT
ejpam-5734	358	34	.	.	PUNCT
ejpam-5734	359	1	c(c6	c(c6	PROPN
ejpam-5734	359	2	)	)	PUNCT
ejpam-5734	359	3	:	:	PUNCT
ejpam-5734	359	4	v1	v1	VERB
ejpam-5734	359	5	v2	v2	NOUN
ejpam-5734	359	6	v3v6	v3v6	NOUN
ejpam-5734	359	7	v5	v5	PROPN
ejpam-5734	359	8	v4	v4	PROPN
ejpam-5734	359	9	c6	c6	PROPN
ejpam-5734	359	10	c5	c5	PROPN
ejpam-5734	359	11	c4	c4	PROPN
ejpam-5734	359	12	c3	c3	PROPN
ejpam-5734	359	13	c2	c2	PROPN
ejpam-5734	359	14	c1	c1	PROPN
ejpam-5734	359	15	figure	figure	VERB
ejpam-5734	359	16	10	10	NUM
ejpam-5734	359	17	:	:	PUNCT
ejpam-5734	359	18	a	a	DET
ejpam-5734	359	19	central	central	ADJ
ejpam-5734	359	20	graph	graph	NOUN
ejpam-5734	359	21	of	of	ADP
ejpam-5734	359	22	cycle	cycle	NOUN
ejpam-5734	359	23	graph	graph	NOUN
ejpam-5734	359	24	with	with	ADP
ejpam-5734	359	25	c6	c6	PROPN
ejpam-5734	359	26	with	with	ADP
ejpam-5734	359	27	χ2[c(c6	χ2[c(c6	PROPN
ejpam-5734	359	28	)	)	PUNCT
ejpam-5734	359	29	]	]	PUNCT
ejpam-5734	360	1	=	=	SYM
ejpam-5734	360	2	8	8	NUM
ejpam-5734	360	3	case	case	NOUN
ejpam-5734	360	4	2	2	NUM
ejpam-5734	360	5	:	:	PUNCT
ejpam-5734	360	6	n	n	PRON
ejpam-5734	360	7	is	be	AUX
ejpam-5734	360	8	odd	odd	ADJ
ejpam-5734	360	9	let	let	VERB
ejpam-5734	360	10	v	v	X
ejpam-5734	360	11	(	(	PUNCT
ejpam-5734	360	12	cv	cv	PROPN
ejpam-5734	360	13	)	)	PUNCT
ejpam-5734	360	14	=	=	SYM
ejpam-5734	360	15	{	{	PUNCT
ejpam-5734	360	16	c1	c1	PROPN
ejpam-5734	360	17	,	,	PUNCT
ejpam-5734	360	18	c2	c2	PROPN
ejpam-5734	360	19	,	,	PUNCT
ejpam-5734	360	20	.	.	PUNCT
ejpam-5734	360	21	.	.	PUNCT
ejpam-5734	361	1	.	.	PUNCT
ejpam-5734	362	1	,	,	PUNCT
ejpam-5734	362	2	cn	cn	PROPN
ejpam-5734	362	3	}	}	PUNCT
ejpam-5734	362	4	=	=	SYM
ejpam-5734	362	5	{	{	PUNCT
ejpam-5734	362	6	cs	cs	X
ejpam-5734	362	7	:	:	PUNCT
ejpam-5734	362	8	s	s	X
ejpam-5734	362	9	=	=	SYM
ejpam-5734	362	10	1	1	NUM
ejpam-5734	362	11	,	,	PUNCT
ejpam-5734	362	12	3	3	NUM
ejpam-5734	362	13	,	,	PUNCT
ejpam-5734	362	14	.	.	PUNCT
ejpam-5734	362	15	.	.	PUNCT
ejpam-5734	363	1	.	.	PUNCT
ejpam-5734	364	1	,	,	PUNCT
ejpam-5734	364	2	n−2}∪{ct	n−2}∪{ct	NOUN
ejpam-5734	364	3	:	:	PUNCT
ejpam-5734	365	1	t	t	X
ejpam-5734	365	2	=	=	SYM
ejpam-5734	365	3	2	2	NUM
ejpam-5734	365	4	,	,	PUNCT
ejpam-5734	365	5	4	4	NUM
ejpam-5734	365	6	,	,	PUNCT
ejpam-5734	365	7	.	.	PUNCT
ejpam-5734	365	8	.	.	PUNCT
ejpam-5734	365	9	.	.	PUNCT
ejpam-5734	366	1	,	,	PUNCT
ejpam-5734	366	2	n−1}∪{cn	n−1}∪{cn	PROPN
ejpam-5734	366	3	}	}	PUNCT
ejpam-5734	366	4	.	.	PUNCT
ejpam-5734	367	1	similarly	similarly	ADV
ejpam-5734	367	2	,	,	PUNCT
ejpam-5734	367	3	we	we	PRON
ejpam-5734	367	4	have	have	VERB
ejpam-5734	367	5	an+1	an+1	NOUN
ejpam-5734	367	6	=	=	SYM
ejpam-5734	367	7	{	{	PUNCT
ejpam-5734	367	8	cs	cs	X
ejpam-5734	367	9	:	:	PUNCT
ejpam-5734	367	10	s	s	X
ejpam-5734	367	11	=	=	SYM
ejpam-5734	367	12	1	1	NUM
ejpam-5734	367	13	,	,	PUNCT
ejpam-5734	367	14	3	3	NUM
ejpam-5734	367	15	,	,	PUNCT
ejpam-5734	367	16	.	.	PUNCT
ejpam-5734	367	17	.	.	PUNCT
ejpam-5734	368	1	.	.	PUNCT
ejpam-5734	369	1	,	,	PUNCT
ejpam-5734	369	2	n−	n−	NOUN
ejpam-5734	369	3	2	2	NUM
ejpam-5734	369	4	}	}	PUNCT
ejpam-5734	369	5	and	and	CCONJ
ejpam-5734	369	6	an+2	an+2	ADV
ejpam-5734	369	7	=	=	SYM
ejpam-5734	369	8	{	{	PUNCT
ejpam-5734	369	9	ct	ct	X
ejpam-5734	369	10	:	:	PUNCT
ejpam-5734	369	11	t	t	NOUN
ejpam-5734	369	12	=	=	SYM
ejpam-5734	369	13	2	2	NUM
ejpam-5734	369	14	,	,	PUNCT
ejpam-5734	369	15	4	4	NUM
ejpam-5734	369	16	,	,	PUNCT
ejpam-5734	369	17	.	.	PUNCT
ejpam-5734	369	18	.	.	PUNCT
ejpam-5734	370	1	.	.	PUNCT
ejpam-5734	371	1	,	,	PUNCT
ejpam-5734	371	2	n−	n−	NOUN
ejpam-5734	371	3	1	1	NUM
ejpam-5734	371	4	}	}	PUNCT
ejpam-5734	371	5	.	.	PUNCT
ejpam-5734	372	1	however	however	ADV
ejpam-5734	372	2	,	,	PUNCT
ejpam-5734	372	3	cn	cn	PROPN
ejpam-5734	372	4	can	can	AUX
ejpam-5734	372	5	not	not	PART
ejpam-5734	372	6	be	be	AUX
ejpam-5734	372	7	an	an	DET
ejpam-5734	372	8	element	element	NOUN
ejpam-5734	372	9	of	of	ADP
ejpam-5734	372	10	neither	neither	CCONJ
ejpam-5734	372	11	an+1	an+1	NOUN
ejpam-5734	372	12	nor	nor	CCONJ
ejpam-5734	372	13	an+2	an+2	PROPN
ejpam-5734	372	14	since	since	SCONJ
ejpam-5734	372	15	d(cn	d(cn	PROPN
ejpam-5734	372	16	,	,	PUNCT
ejpam-5734	372	17	c1	c1	PROPN
ejpam-5734	372	18	∈	∈	PROPN
ejpam-5734	372	19	an+1	an+1	NOUN
ejpam-5734	372	20	)	)	PUNCT
ejpam-5734	372	21	=	=	SYM
ejpam-5734	372	22	2	2	NUM
ejpam-5734	372	23	,	,	PUNCT
ejpam-5734	372	24	and	and	CCONJ
ejpam-5734	372	25	d(cn	d(cn	PROPN
ejpam-5734	372	26	,	,	PUNCT
ejpam-5734	372	27	cn−1	cn−1	PROPN
ejpam-5734	372	28	∈	∈	PROPN
ejpam-5734	372	29	an+2	an+2	ADV
ejpam-5734	372	30	)	)	PUNCT
ejpam-5734	372	31	=	=	SYM
ejpam-5734	372	32	2	2	X
ejpam-5734	372	33	.	.	X
ejpam-5734	372	34	assign	assign	VERB
ejpam-5734	372	35	another	another	DET
ejpam-5734	372	36	color	color	NOUN
ejpam-5734	372	37	class	class	NOUN
ejpam-5734	372	38	to	to	ADP
ejpam-5734	372	39	cn	cn	PROPN
ejpam-5734	372	40	,	,	PUNCT
ejpam-5734	372	41	an+3	an+3	PROPN
ejpam-5734	372	42	=	=	PRON
ejpam-5734	372	43	{	{	PUNCT
ejpam-5734	372	44	cn	cn	X
ejpam-5734	372	45	}	}	PUNCT
ejpam-5734	372	46	.	.	PUNCT
ejpam-5734	373	1	so	so	ADV
ejpam-5734	373	2	we	we	PRON
ejpam-5734	373	3	now	now	ADV
ejpam-5734	373	4	have	have	VERB
ejpam-5734	373	5	the	the	DET
ejpam-5734	373	6	set	set	NOUN
ejpam-5734	373	7	of	of	ADP
ejpam-5734	373	8	color	color	NOUN
ejpam-5734	373	9	classes	class	NOUN
ejpam-5734	373	10	:	:	PUNCT
ejpam-5734	373	11	{	{	PUNCT
ejpam-5734	373	12	a1,a2	a1,a2	PROPN
ejpam-5734	373	13	,	,	PUNCT
ejpam-5734	373	14	.	.	PUNCT
ejpam-5734	373	15	.	.	PUNCT
ejpam-5734	374	1	.	.	PUNCT
ejpam-5734	375	1	,	,	PUNCT
ejpam-5734	375	2	an	an	DET
ejpam-5734	375	3	,	,	PUNCT
ejpam-5734	375	4	an+1,an+2,an+3	an+1,an+2,an+3	NOUN
ejpam-5734	375	5	}	}	PUNCT
ejpam-5734	375	6	.	.	PUNCT
ejpam-5734	376	1	m.	m.	PROPN
ejpam-5734	376	2	f.	f.	PROPN
ejpam-5734	376	3	libao	libao	PROPN
ejpam-5734	376	4	,	,	PUNCT
ejpam-5734	376	5	k.	k.	PROPN
ejpam-5734	376	6	b.	b.	PROPN
ejpam-5734	376	7	abarca	abarca	PROPN
ejpam-5734	376	8	/	/	SYM
ejpam-5734	376	9	eur	eur	PROPN
ejpam-5734	376	10	.	.	PUNCT
ejpam-5734	377	1	j.	j.	PROPN
ejpam-5734	377	2	pure	pure	PROPN
ejpam-5734	377	3	appl	appl	PROPN
ejpam-5734	377	4	.	.	PROPN
ejpam-5734	377	5	math	math	PROPN
ejpam-5734	377	6	,	,	PUNCT
ejpam-5734	377	7	18	18	NUM
ejpam-5734	377	8	(	(	PUNCT
ejpam-5734	377	9	2	2	NUM
ejpam-5734	377	10	)	)	PUNCT
ejpam-5734	377	11	(	(	PUNCT
ejpam-5734	377	12	2025	2025	NUM
ejpam-5734	377	13	)	)	PUNCT
ejpam-5734	377	14	,	,	PUNCT
ejpam-5734	377	15	5734	5734	NUM
ejpam-5734	377	16	19	19	NUM
ejpam-5734	377	17	of	of	ADP
ejpam-5734	377	18	25	25	NUM
ejpam-5734	377	19	i.	i.	NOUN
ejpam-5734	377	20	to	to	PART
ejpam-5734	377	21	ensure	ensure	VERB
ejpam-5734	377	22	that	that	SCONJ
ejpam-5734	377	23	every	every	DET
ejpam-5734	377	24	vertex	vertex	NOUN
ejpam-5734	377	25	in	in	ADP
ejpam-5734	377	26	the	the	DET
ejpam-5734	377	27	graph	graph	NOUN
ejpam-5734	377	28	belongs	belong	VERB
ejpam-5734	377	29	to	to	ADP
ejpam-5734	377	30	exactly	exactly	ADV
ejpam-5734	377	31	one	one	NUM
ejpam-5734	377	32	color	color	NOUN
ejpam-5734	377	33	class:⋃	class:⋃	PUNCT
ejpam-5734	377	34	a∈c	a∈c	VERB
ejpam-5734	377	35	a	a	PRON
ejpam-5734	377	36	=	=	X
ejpam-5734	377	37	{	{	PUNCT
ejpam-5734	377	38	a1,a2	a1,a2	PROPN
ejpam-5734	377	39	,	,	PUNCT
ejpam-5734	377	40	.	.	PUNCT
ejpam-5734	377	41	.	.	PUNCT
ejpam-5734	378	1	.	.	PUNCT
ejpam-5734	379	1	,	,	PUNCT
ejpam-5734	379	2	an	an	DET
ejpam-5734	379	3	,	,	PUNCT
ejpam-5734	379	4	an+1,an+2,an+3	an+1,an+2,an+3	NOUN
ejpam-5734	379	5	}	}	PUNCT
ejpam-5734	379	6	=	=	SYM
ejpam-5734	379	7	{	{	PUNCT
ejpam-5734	379	8	a1,a2	a1,a2	PROPN
ejpam-5734	379	9	,	,	PUNCT
ejpam-5734	379	10	.	.	PUNCT
ejpam-5734	379	11	.	.	PUNCT
ejpam-5734	380	1	.	.	PUNCT
ejpam-5734	381	1	,	,	PUNCT
ejpam-5734	381	2	an	an	DET
ejpam-5734	381	3	}	}	PUNCT
ejpam-5734	381	4	∪	∪	ADJ
ejpam-5734	381	5	{	{	PUNCT
ejpam-5734	381	6	an+1	an+1	NOUN
ejpam-5734	381	7	}	}	PUNCT
ejpam-5734	381	8	∪	∪	X
ejpam-5734	381	9	{	{	PUNCT
ejpam-5734	381	10	an+2	an+2	NOUN
ejpam-5734	381	11	}	}	PUNCT
ejpam-5734	381	12	∪	∪	ADJ
ejpam-5734	381	13	{	{	PUNCT
ejpam-5734	381	14	an+3	an+3	NOUN
ejpam-5734	381	15	}	}	PUNCT
ejpam-5734	381	16	=	=	SYM
ejpam-5734	381	17	{	{	PUNCT
ejpam-5734	381	18	v1	v1	NOUN
ejpam-5734	381	19	,	,	PUNCT
ejpam-5734	381	20	v2	v2	PROPN
ejpam-5734	381	21	,	,	PUNCT
ejpam-5734	381	22	.	.	PUNCT
ejpam-5734	381	23	.	.	PUNCT
ejpam-5734	382	1	.	.	PUNCT
ejpam-5734	383	1	,	,	PUNCT
ejpam-5734	383	2	vn	vn	VERB
ejpam-5734	383	3	}	}	PUNCT
ejpam-5734	383	4	∪	∪	ADJ
ejpam-5734	383	5	{	{	PUNCT
ejpam-5734	383	6	c1	c1	NOUN
ejpam-5734	383	7	,	,	PUNCT
ejpam-5734	383	8	c3	c3	PROPN
ejpam-5734	383	9	,	,	PUNCT
ejpam-5734	383	10	.	.	PUNCT
ejpam-5734	383	11	.	.	PUNCT
ejpam-5734	384	1	.	.	PUNCT
ejpam-5734	385	1	,	,	PUNCT
ejpam-5734	385	2	cn−2	cn−2	PROPN
ejpam-5734	385	3	}	}	PUNCT
ejpam-5734	385	4	∪	∪	X
ejpam-5734	385	5	{	{	PUNCT
ejpam-5734	385	6	c2	c2	PROPN
ejpam-5734	385	7	,	,	PUNCT
ejpam-5734	385	8	c4	c4	NOUN
ejpam-5734	385	9	,	,	PUNCT
ejpam-5734	385	10	.	.	PUNCT
ejpam-5734	385	11	.	.	PUNCT
ejpam-5734	386	1	.	.	PUNCT
ejpam-5734	387	1	,	,	PUNCT
ejpam-5734	387	2	cn−1	cn−1	ADV
ejpam-5734	387	3	}	}	PUNCT
ejpam-5734	387	4	∪	∪	X
ejpam-5734	387	5	{	{	PUNCT
ejpam-5734	387	6	cn	cn	NOUN
ejpam-5734	387	7	}	}	PUNCT
ejpam-5734	387	8	=	=	SYM
ejpam-5734	387	9	{	{	PUNCT
ejpam-5734	387	10	v1	v1	NOUN
ejpam-5734	387	11	,	,	PUNCT
ejpam-5734	387	12	v2	v2	PROPN
ejpam-5734	387	13	,	,	PUNCT
ejpam-5734	387	14	.	.	PUNCT
ejpam-5734	387	15	.	.	PUNCT
ejpam-5734	388	1	.	.	PUNCT
ejpam-5734	389	1	,	,	PUNCT
ejpam-5734	389	2	vn	vn	VERB
ejpam-5734	389	3	}	}	PUNCT
ejpam-5734	389	4	∪	∪	ADJ
ejpam-5734	389	5	{	{	PUNCT
ejpam-5734	389	6	c1	c1	NOUN
ejpam-5734	389	7	,	,	PUNCT
ejpam-5734	389	8	c2	c2	PROPN
ejpam-5734	389	9	,	,	PUNCT
ejpam-5734	389	10	.	.	PUNCT
ejpam-5734	389	11	.	.	PUNCT
ejpam-5734	390	1	.	.	PUNCT
ejpam-5734	391	1	,	,	PUNCT
ejpam-5734	391	2	cn	cn	PROPN
ejpam-5734	391	3	}	}	PUNCT
ejpam-5734	391	4	=	=	SYM
ejpam-5734	391	5	{	{	PUNCT
ejpam-5734	391	6	vi	vi	NOUN
ejpam-5734	391	7	}	}	PUNCT
ejpam-5734	391	8	∪	∪	ADJ
ejpam-5734	391	9	{	{	PUNCT
ejpam-5734	391	10	ci	ci	NOUN
ejpam-5734	391	11	}	}	PUNCT
ejpam-5734	391	12	,	,	PUNCT
ejpam-5734	392	1	1	1	NUM
ejpam-5734	392	2	≤	≤	NUM
ejpam-5734	392	3	i	i	PRON
ejpam-5734	392	4	≤	≤	ADJ
ejpam-5734	392	5	n	n	CCONJ
ejpam-5734	392	6	=	=	SYM
ejpam-5734	392	7	v	v	NOUN
ejpam-5734	392	8	[	[	X
ejpam-5734	392	9	c(cn	c(cn	NOUN
ejpam-5734	392	10	)	)	PUNCT
ejpam-5734	392	11	]	]	PUNCT
ejpam-5734	392	12	ii	ii	X
ejpam-5734	392	13	.	.	PUNCT
ejpam-5734	392	14	to	to	PART
ejpam-5734	392	15	show	show	VERB
ejpam-5734	392	16	that	that	SCONJ
ejpam-5734	392	17	the	the	DET
ejpam-5734	392	18	color	color	NOUN
ejpam-5734	392	19	classes	class	NOUN
ejpam-5734	392	20	are	be	AUX
ejpam-5734	392	21	disjoint	disjoint	ADJ
ejpam-5734	392	22	,	,	PUNCT
ejpam-5734	392	23	we	we	PRON
ejpam-5734	392	24	also	also	ADV
ejpam-5734	392	25	have	have	VERB
ejpam-5734	392	26	to	to	PART
ejpam-5734	392	27	show	show	VERB
ejpam-5734	392	28	that	that	SCONJ
ejpam-5734	392	29	∑	∑	PROPN
ejpam-5734	392	30	a∈c	a∈c	PROPN
ejpam-5734	392	31	|a|	|a|	PROPN
ejpam-5734	392	32	=	=	PROPN
ejpam-5734	392	33	|v	|v	PROPN
ejpam-5734	393	1	[	[	X
ejpam-5734	393	2	c(cn)]|	c(cn)]|	VERB
ejpam-5734	393	3	in	in	ADP
ejpam-5734	393	4	addition	addition	NOUN
ejpam-5734	393	5	to	to	ADP
ejpam-5734	393	6	the	the	DET
ejpam-5734	393	7	above	above	ADJ
ejpam-5734	393	8	condition	condition	NOUN
ejpam-5734	393	9	.	.	PUNCT
ejpam-5734	394	1	∑	∑	PROPN
ejpam-5734	394	2	a∈c	a∈c	PROPN
ejpam-5734	394	3	|a|	|a|	PROPN
ejpam-5734	394	4	=	=	PUNCT
ejpam-5734	394	5	|a1|+	|a1|+	X
ejpam-5734	394	6	|a2|+	|a2|+	X
ejpam-5734	394	7	·	·	PUNCT
ejpam-5734	394	8	·	·	PUNCT
ejpam-5734	394	9	·	·	PUNCT
ejpam-5734	395	1	+	+	PUNCT
ejpam-5734	395	2	|an|+	|an|+	NUM
ejpam-5734	395	3	|an+1|+	|an+1|+	NOUN
ejpam-5734	395	4	|an+2|+	|an+2|+	ADJ
ejpam-5734	395	5	|an+3|	|an+3|	NOUN
ejpam-5734	395	6	=	=	SYM
ejpam-5734	395	7	1	1	NUM
ejpam-5734	395	8	+	+	NUM
ejpam-5734	395	9	1	1	NUM
ejpam-5734	395	10	+	+	CCONJ
ejpam-5734	395	11	·	·	PUNCT
ejpam-5734	395	12	·	·	PUNCT
ejpam-5734	395	13	·	·	PUNCT
ejpam-5734	396	1	+	+	SYM
ejpam-5734	396	2	1	1	NUM
ejpam-5734	396	3	+	+	NUM
ejpam-5734	396	4	n−	n−	NOUN
ejpam-5734	396	5	1	1	NUM
ejpam-5734	396	6	2	2	NUM
ejpam-5734	396	7	+	+	NUM
ejpam-5734	396	8	n−	n−	NOUN
ejpam-5734	396	9	1	1	NUM
ejpam-5734	396	10	2	2	NUM
ejpam-5734	396	11	+	+	NUM
ejpam-5734	396	12	1	1	NUM
ejpam-5734	396	13	=	=	SYM
ejpam-5734	396	14	n+	n+	NUM
ejpam-5734	396	15	n−	n−	NOUN
ejpam-5734	396	16	1	1	NUM
ejpam-5734	396	17	+	+	CCONJ
ejpam-5734	396	18	1	1	NUM
ejpam-5734	396	19	=	=	SYM
ejpam-5734	396	20	2n	2n	NUM
ejpam-5734	396	21	=	=	SYM
ejpam-5734	396	22	|v	|v	PROPN
ejpam-5734	396	23	[	[	X
ejpam-5734	396	24	c(cn)]|	c(cn)]|	VERB
ejpam-5734	396	25	.	.	PUNCT
ejpam-5734	396	26	by	by	ADP
ejpam-5734	396	27	lemma	lemma	PROPN
ejpam-5734	396	28	1	1	NUM
ejpam-5734	396	29	,	,	PUNCT
ejpam-5734	396	30	color	color	NOUN
ejpam-5734	396	31	classes	class	NOUN
ejpam-5734	396	32	are	be	AUX
ejpam-5734	396	33	mutually	mutually	ADV
ejpam-5734	396	34	exclusive	exclusive	ADJ
ejpam-5734	396	35	,	,	PUNCT
ejpam-5734	396	36	that	that	ADV
ejpam-5734	396	37	is	is	ADV
ejpam-5734	396	38	,	,	PUNCT
ejpam-5734	396	39	ak	ak	PROPN
ejpam-5734	396	40	∩	∩	PROPN
ejpam-5734	396	41	aj	aj	PROPN
ejpam-5734	396	42	=	=	PROPN
ejpam-5734	396	43	∅	∅	NOUN
ejpam-5734	396	44	for	for	ADP
ejpam-5734	396	45	k	k	PROPN
ejpam-5734	396	46	̸=	̸=	PROPN
ejpam-5734	396	47	j.	j.	PROPN
ejpam-5734	396	48	thus	thus	ADV
ejpam-5734	396	49	,	,	PUNCT
ejpam-5734	396	50	c	c	X
ejpam-5734	396	51	=	=	SYM
ejpam-5734	396	52	{	{	PUNCT
ejpam-5734	396	53	a1,a2	a1,a2	PROPN
ejpam-5734	396	54	,	,	PUNCT
ejpam-5734	396	55	.	.	PUNCT
ejpam-5734	396	56	.	.	PUNCT
ejpam-5734	397	1	.	.	PUNCT
ejpam-5734	398	1	,	,	PUNCT
ejpam-5734	398	2	an	an	PRON
ejpam-5734	398	3	,	,	PUNCT
ejpam-5734	398	4	an+1,an+2,an+3	an+1,an+2,an+3	PROPN
ejpam-5734	398	5	}	}	PUNCT
ejpam-5734	398	6	is	be	AUX
ejpam-5734	398	7	a	a	DET
ejpam-5734	398	8	distance-2	distance-2	CCONJ
ejpam-5734	398	9	chromatic	chromatic	ADJ
ejpam-5734	398	10	set	set	NOUN
ejpam-5734	398	11	and	and	CCONJ
ejpam-5734	398	12	|c	|c	ADJ
ejpam-5734	398	13	|	|	NOUN
ejpam-5734	398	14	=	=	SYM
ejpam-5734	398	15	n+3	n+3	PROPN
ejpam-5734	398	16	.	.	PUNCT
ejpam-5734	399	1	we	we	PRON
ejpam-5734	399	2	can	can	AUX
ejpam-5734	399	3	now	now	ADV
ejpam-5734	399	4	say	say	VERB
ejpam-5734	399	5	that	that	SCONJ
ejpam-5734	399	6	χ2[c(cn	χ2[c(cn	PROPN
ejpam-5734	399	7	)	)	PUNCT
ejpam-5734	399	8	]	]	PUNCT
ejpam-5734	399	9	≤	≤	NUM
ejpam-5734	399	10	n+3	n+3	NUM
ejpam-5734	399	11	.	.	PUNCT
ejpam-5734	400	1	now	now	ADV
ejpam-5734	400	2	,	,	PUNCT
ejpam-5734	400	3	χ2[c(cn	χ2[c(cn	PROPN
ejpam-5734	400	4	)	)	PUNCT
ejpam-5734	400	5	]	]	PUNCT
ejpam-5734	400	6	̸	̸	NUM
ejpam-5734	400	7	<	<	X
ejpam-5734	400	8	n+3	n+3	PROPN
ejpam-5734	400	9	since	since	SCONJ
ejpam-5734	400	10	taking	take	VERB
ejpam-5734	400	11	out	out	ADP
ejpam-5734	400	12	any	any	DET
ejpam-5734	400	13	ak	ak	PROPN
ejpam-5734	400	14	∈	∈	PROPN
ejpam-5734	400	15	c	c	NOUN
ejpam-5734	400	16	will	will	AUX
ejpam-5734	400	17	violate	violate	VERB
ejpam-5734	400	18	the	the	DET
ejpam-5734	400	19	distance-2	distance-2	NUM
ejpam-5734	400	20	coloring	coloring	NOUN
ejpam-5734	400	21	.	.	PUNCT
ejpam-5734	401	1	for	for	ADP
ejpam-5734	401	2	instance	instance	NOUN
ejpam-5734	401	3	,	,	PUNCT
ejpam-5734	401	4	if	if	SCONJ
ejpam-5734	401	5	we	we	PRON
ejpam-5734	401	6	assign	assign	VERB
ejpam-5734	401	7	any	any	PRON
ejpam-5734	401	8	of	of	ADP
ejpam-5734	401	9	the	the	DET
ejpam-5734	401	10	color	color	NOUN
ejpam-5734	401	11	classes	class	NOUN
ejpam-5734	401	12	a2,a3	a2,a3	PROPN
ejpam-5734	401	13	,	,	PUNCT
ejpam-5734	401	14	.	.	PUNCT
ejpam-5734	401	15	.	.	PUNCT
ejpam-5734	402	1	.	.	PUNCT
ejpam-5734	403	1	,	,	PUNCT
ejpam-5734	403	2	an	an	DET
ejpam-5734	403	3	to	to	PART
ejpam-5734	403	4	v1	v1	VERB
ejpam-5734	403	5	,	,	PUNCT
ejpam-5734	403	6	the	the	DET
ejpam-5734	403	7	distance	distance	NOUN
ejpam-5734	403	8	d(v1	d(v1	NOUN
ejpam-5734	403	9	,	,	PUNCT
ejpam-5734	403	10	vi	vi	NOUN
ejpam-5734	403	11	)	)	PUNCT
ejpam-5734	403	12	=	=	SYM
ejpam-5734	403	13	1	1	NUM
ejpam-5734	403	14	for	for	ADP
ejpam-5734	403	15	i	i	PRON
ejpam-5734	403	16	=	=	SYM
ejpam-5734	403	17	2	2	NUM
ejpam-5734	403	18	,	,	PUNCT
ejpam-5734	403	19	3	3	NUM
ejpam-5734	403	20	,	,	PUNCT
ejpam-5734	403	21	.	.	PUNCT
ejpam-5734	403	22	.	.	PUNCT
ejpam-5734	404	1	.	.	PUNCT
ejpam-5734	405	1	,	,	PUNCT
ejpam-5734	405	2	n.	n.	PROPN
ejpam-5734	405	3	also	also	ADV
ejpam-5734	405	4	,	,	PUNCT
ejpam-5734	405	5	for	for	ADP
ejpam-5734	405	6	the	the	DET
ejpam-5734	405	7	remaining	remain	VERB
ejpam-5734	405	8	colors	color	NOUN
ejpam-5734	405	9	,	,	PUNCT
ejpam-5734	405	10	an+1	an+1	NOUN
ejpam-5734	405	11	,	,	PUNCT
ejpam-5734	405	12	an+2	an+2	ADV
ejpam-5734	405	13	,	,	PUNCT
ejpam-5734	405	14	and	and	CCONJ
ejpam-5734	405	15	an+3	an+3	NOUN
ejpam-5734	405	16	,	,	PUNCT
ejpam-5734	405	17	d(v1	d(v1	NOUN
ejpam-5734	405	18	,	,	PUNCT
ejpam-5734	405	19	cs	cs	ADJ
ejpam-5734	405	20	)	)	PUNCT
ejpam-5734	405	21	=	=	SYM
ejpam-5734	405	22	1	1	NUM
ejpam-5734	405	23	when	when	SCONJ
ejpam-5734	405	24	s	s	VERB
ejpam-5734	405	25	=	=	SYM
ejpam-5734	405	26	1	1	NUM
ejpam-5734	405	27	,	,	PUNCT
ejpam-5734	405	28	d(v1	d(v1	NOUN
ejpam-5734	405	29	,	,	PUNCT
ejpam-5734	405	30	ct	ct	PROPN
ejpam-5734	405	31	)	)	PUNCT
ejpam-5734	405	32	=	=	SYM
ejpam-5734	405	33	2	2	NUM
ejpam-5734	405	34	,	,	PUNCT
ejpam-5734	405	35	and	and	CCONJ
ejpam-5734	405	36	d(v1	d(v1	PROPN
ejpam-5734	405	37	,	,	PUNCT
ejpam-5734	405	38	cn	cn	PROPN
ejpam-5734	405	39	)	)	PUNCT
ejpam-5734	405	40	=	=	SYM
ejpam-5734	406	1	1	1	X
ejpam-5734	406	2	.	.	PUNCT
ejpam-5734	406	3	therefore	therefore	ADV
ejpam-5734	406	4	,	,	PUNCT
ejpam-5734	406	5	χ2[c(cn	χ2[c(cn	PROPN
ejpam-5734	406	6	)	)	PUNCT
ejpam-5734	406	7	]	]	PUNCT
ejpam-5734	407	1	=	=	SYM
ejpam-5734	407	2	n+	n+	PUNCT
ejpam-5734	407	3	3	3	X
ejpam-5734	407	4	.	.	X
ejpam-5734	407	5	below	below	ADV
ejpam-5734	407	6	is	be	AUX
ejpam-5734	407	7	an	an	DET
ejpam-5734	407	8	example	example	NOUN
ejpam-5734	407	9	of	of	ADP
ejpam-5734	407	10	a	a	DET
ejpam-5734	407	11	central	central	ADJ
ejpam-5734	407	12	graph	graph	NOUN
ejpam-5734	407	13	of	of	ADP
ejpam-5734	407	14	c7	c7	PROPN
ejpam-5734	407	15	,	,	PUNCT
ejpam-5734	407	16	c(c7	c(c7	NOUN
ejpam-5734	407	17	)	)	PUNCT
ejpam-5734	407	18	with	with	ADP
ejpam-5734	407	19	χ2[c(c7	χ2[c(c7	NUM
ejpam-5734	407	20	)	)	PUNCT
ejpam-5734	407	21	]	]	PUNCT
ejpam-5734	408	1	=	=	PUNCT
ejpam-5734	408	2	10	10	NUM
ejpam-5734	408	3	.	.	PUNCT
ejpam-5734	409	1	here	here	ADV
ejpam-5734	409	2	,	,	PUNCT
ejpam-5734	409	3	c	c	X
ejpam-5734	409	4	=	=	PRON
ejpam-5734	409	5	{	{	PUNCT
ejpam-5734	409	6	red	red	NOUN
ejpam-5734	409	7	(	(	PUNCT
ejpam-5734	409	8	v1),blue	v1),blue	NOUN
ejpam-5734	409	9	(	(	PUNCT
ejpam-5734	409	10	v2),violet	v2),violet	NOUN
ejpam-5734	409	11	(	(	PUNCT
ejpam-5734	409	12	v3),green	v3),green	X
ejpam-5734	409	13	(	(	PUNCT
ejpam-5734	409	14	v4),pink	v4),pink	NOUN
ejpam-5734	409	15	(	(	PUNCT
ejpam-5734	409	16	v5),yellow	v5),yellow	X
ejpam-5734	409	17	(	(	PUNCT
ejpam-5734	409	18	v6),gray	v6),gray	X
ejpam-5734	409	19	(	(	PUNCT
ejpam-5734	409	20	v7),orange	v7),orange	NOUN
ejpam-5734	409	21	(	(	PUNCT
ejpam-5734	409	22	c1	c1	PROPN
ejpam-5734	409	23	,	,	PUNCT
ejpam-5734	409	24	c3	c3	PROPN
ejpam-5734	409	25	,	,	PUNCT
ejpam-5734	409	26	c5),black	c5),black	X
ejpam-5734	409	27	(	(	PUNCT
ejpam-5734	409	28	c2	c2	PROPN
ejpam-5734	409	29	,	,	PUNCT
ejpam-5734	409	30	c4	c4	NOUN
ejpam-5734	409	31	,	,	PUNCT
ejpam-5734	409	32	c6),magenta	c6),magenta	X
ejpam-5734	409	33	(	(	PUNCT
ejpam-5734	409	34	c7	c7	PROPN
ejpam-5734	409	35	)	)	PUNCT
ejpam-5734	409	36	}	}	PUNCT
ejpam-5734	409	37	m.	m.	NOUN
ejpam-5734	409	38	f.	f.	PROPN
ejpam-5734	409	39	libao	libao	PROPN
ejpam-5734	409	40	,	,	PUNCT
ejpam-5734	409	41	k.	k.	PROPN
ejpam-5734	409	42	b.	b.	PROPN
ejpam-5734	409	43	abarca	abarca	PROPN
ejpam-5734	409	44	/	/	SYM
ejpam-5734	409	45	eur	eur	PROPN
ejpam-5734	409	46	.	.	PUNCT
ejpam-5734	410	1	j.	j.	PROPN
ejpam-5734	410	2	pure	pure	PROPN
ejpam-5734	410	3	appl	appl	PROPN
ejpam-5734	410	4	.	.	PROPN
ejpam-5734	410	5	math	math	PROPN
ejpam-5734	410	6	,	,	PUNCT
ejpam-5734	410	7	18	18	NUM
ejpam-5734	410	8	(	(	PUNCT
ejpam-5734	410	9	2	2	NUM
ejpam-5734	410	10	)	)	PUNCT
ejpam-5734	410	11	(	(	PUNCT
ejpam-5734	410	12	2025	2025	NUM
ejpam-5734	410	13	)	)	PUNCT
ejpam-5734	410	14	,	,	PUNCT
ejpam-5734	410	15	5734	5734	NUM
ejpam-5734	410	16	20	20	NUM
ejpam-5734	410	17	of	of	ADP
ejpam-5734	410	18	25	25	NUM
ejpam-5734	410	19	c(c7	c(c7	NOUN
ejpam-5734	410	20	)	)	PUNCT
ejpam-5734	410	21	:	:	PUNCT
ejpam-5734	411	1	v1	v1	VERB
ejpam-5734	411	2	v2	v2	PROPN
ejpam-5734	411	3	v3	v3	PROPN
ejpam-5734	411	4	v4	v4	PROPN
ejpam-5734	411	5	v5v6v7	v5v6v7	PROPN
ejpam-5734	411	6	c1	c1	PROPN
ejpam-5734	411	7	c7	c7	PROPN
ejpam-5734	411	8	c6	c6	PROPN
ejpam-5734	411	9	c2	c2	PROPN
ejpam-5734	411	10	c3	c3	PROPN
ejpam-5734	411	11	c4	c4	PROPN
ejpam-5734	411	12	c5	c5	PROPN
ejpam-5734	411	13	figure	figure	VERB
ejpam-5734	411	14	11	11	NUM
ejpam-5734	411	15	:	:	PUNCT
ejpam-5734	411	16	a	a	DET
ejpam-5734	411	17	central	central	ADJ
ejpam-5734	411	18	graph	graph	NOUN
ejpam-5734	411	19	of	of	ADP
ejpam-5734	411	20	cycle	cycle	NOUN
ejpam-5734	411	21	graph	graph	NOUN
ejpam-5734	411	22	with	with	ADP
ejpam-5734	411	23	c7	c7	PROPN
ejpam-5734	411	24	with	with	ADP
ejpam-5734	411	25	χ2[c(c7	χ2[c(c7	NUM
ejpam-5734	411	26	)	)	PUNCT
ejpam-5734	411	27	]	]	PUNCT
ejpam-5734	412	1	=	=	PUNCT
ejpam-5734	412	2	10	10	NUM
ejpam-5734	412	3	5	5	NUM
ejpam-5734	412	4	.	.	PUNCT
ejpam-5734	412	5	applications	application	NOUN
ejpam-5734	412	6	to	to	PART
ejpam-5734	412	7	understand	understand	VERB
ejpam-5734	412	8	the	the	DET
ejpam-5734	412	9	practical	practical	ADJ
ejpam-5734	412	10	importance	importance	NOUN
ejpam-5734	412	11	of	of	ADP
ejpam-5734	412	12	the	the	DET
ejpam-5734	412	13	distance-2	distance-2	NUM
ejpam-5734	412	14	chromatic	chromatic	ADJ
ejpam-5734	412	15	number	number	NOUN
ejpam-5734	412	16	(	(	PUNCT
ejpam-5734	412	17	x2(g	x2(g	PROPN
ejpam-5734	412	18	)	)	PUNCT
ejpam-5734	412	19	)	)	PUNCT
ejpam-5734	412	20	,	,	PUNCT
ejpam-5734	412	21	consider	consider	VERB
ejpam-5734	412	22	two	two	NUM
ejpam-5734	412	23	useful	useful	ADJ
ejpam-5734	412	24	analogies	analogy	NOUN
ejpam-5734	412	25	:	:	PUNCT
ejpam-5734	412	26	the	the	DET
ejpam-5734	412	27	twin	twin	ADJ
ejpam-5734	412	28	building	building	NOUN
ejpam-5734	412	29	analogy	analogy	NOUN
ejpam-5734	412	30	and	and	CCONJ
ejpam-5734	412	31	the	the	DET
ejpam-5734	412	32	office	office	NOUN
ejpam-5734	412	33	building	building	NOUN
ejpam-5734	412	34	analogy	analogy	NOUN
ejpam-5734	412	35	.	.	PUNCT
ejpam-5734	413	1	both	both	PRON
ejpam-5734	413	2	illustrate	illustrate	VERB
ejpam-5734	413	3	how	how	SCONJ
ejpam-5734	413	4	efficient	efficient	ADJ
ejpam-5734	413	5	resource	resource	NOUN
ejpam-5734	413	6	allocation	allocation	NOUN
ejpam-5734	413	7	and	and	CCONJ
ejpam-5734	413	8	conflict	conflict	NOUN
ejpam-5734	413	9	-	-	PUNCT
ejpam-5734	413	10	free	free	ADJ
ejpam-5734	413	11	communication	communication	NOUN
ejpam-5734	413	12	can	can	AUX
ejpam-5734	413	13	be	be	AUX
ejpam-5734	413	14	achieved	achieve	VERB
ejpam-5734	413	15	by	by	ADP
ejpam-5734	413	16	minimizing	minimize	VERB
ejpam-5734	413	17	the	the	DET
ejpam-5734	413	18	number	number	NOUN
ejpam-5734	413	19	of	of	ADP
ejpam-5734	413	20	resources	resource	NOUN
ejpam-5734	413	21	or	or	CCONJ
ejpam-5734	413	22	channels	channel	NOUN
ejpam-5734	413	23	needed	need	VERB
ejpam-5734	413	24	.	.	PUNCT
ejpam-5734	414	1	5.1	5.1	NUM
ejpam-5734	414	2	.	.	PUNCT
ejpam-5734	415	1	twin	twin	PROPN
ejpam-5734	415	2	building	building	NOUN
ejpam-5734	415	3	analogy	analogy	NOUN
ejpam-5734	415	4	recent	recent	ADJ
ejpam-5734	415	5	studies	study	NOUN
ejpam-5734	415	6	support	support	VERB
ejpam-5734	415	7	the	the	DET
ejpam-5734	415	8	use	use	NOUN
ejpam-5734	415	9	of	of	ADP
ejpam-5734	415	10	graph	graph	NOUN
ejpam-5734	415	11	-	-	PUNCT
ejpam-5734	415	12	based	base	VERB
ejpam-5734	415	13	models	model	NOUN
ejpam-5734	415	14	for	for	ADP
ejpam-5734	415	15	optimizing	optimize	VERB
ejpam-5734	415	16	network	network	NOUN
ejpam-5734	415	17	topologies	topology	NOUN
ejpam-5734	415	18	and	and	CCONJ
ejpam-5734	415	19	managing	manage	VERB
ejpam-5734	415	20	interference	interference	NOUN
ejpam-5734	415	21	in	in	ADP
ejpam-5734	415	22	communication	communication	NOUN
ejpam-5734	415	23	systems	system	NOUN
ejpam-5734	415	24	.	.	PUNCT
ejpam-5734	416	1	jain	jain	PROPN
ejpam-5734	416	2	and	and	CCONJ
ejpam-5734	416	3	jain	jain	PROPN
ejpam-5734	416	4	(	(	PUNCT
ejpam-5734	416	5	2023	2023	NUM
ejpam-5734	416	6	)	)	PUNCT
ejpam-5734	417	1	[	[	X
ejpam-5734	417	2	14	14	NUM
ejpam-5734	417	3	]	]	PUNCT
ejpam-5734	417	4	emphasized	emphasize	VERB
ejpam-5734	417	5	how	how	SCONJ
ejpam-5734	417	6	such	such	ADJ
ejpam-5734	417	7	models	model	NOUN
ejpam-5734	417	8	improve	improve	VERB
ejpam-5734	417	9	communication	communication	NOUN
ejpam-5734	417	10	efficiency	efficiency	NOUN
ejpam-5734	417	11	by	by	ADP
ejpam-5734	417	12	minimizing	minimize	VERB
ejpam-5734	417	13	interference	interference	NOUN
ejpam-5734	417	14	,	,	PUNCT
ejpam-5734	417	15	particularly	particularly	ADV
ejpam-5734	417	16	in	in	ADP
ejpam-5734	417	17	multi	multi	ADJ
ejpam-5734	417	18	-	-	ADJ
ejpam-5734	417	19	hop	hop	ADJ
ejpam-5734	417	20	networks	network	NOUN
ejpam-5734	417	21	.	.	PUNCT
ejpam-5734	418	1	the	the	DET
ejpam-5734	418	2	shadow	shadow	NOUN
ejpam-5734	418	3	graph	graph	NOUN
ejpam-5734	418	4	structure	structure	NOUN
ejpam-5734	418	5	reflects	reflect	VERB
ejpam-5734	418	6	this	this	DET
ejpam-5734	418	7	principle	principle	NOUN
ejpam-5734	418	8	,	,	PUNCT
ejpam-5734	418	9	as	as	SCONJ
ejpam-5734	418	10	it	it	PRON
ejpam-5734	418	11	models	model	VERB
ejpam-5734	418	12	indirect	indirect	ADJ
ejpam-5734	418	13	connections	connection	NOUN
ejpam-5734	418	14	through	through	ADP
ejpam-5734	418	15	duplicated	duplicate	VERB
ejpam-5734	418	16	vertices	vertex	NOUN
ejpam-5734	418	17	,	,	PUNCT
ejpam-5734	418	18	allowing	allow	VERB
ejpam-5734	418	19	for	for	ADP
ejpam-5734	418	20	more	more	ADV
ejpam-5734	418	21	precise	precise	ADJ
ejpam-5734	418	22	frequency	frequency	NOUN
ejpam-5734	418	23	assignments	assignment	NOUN
ejpam-5734	418	24	.	.	PUNCT
ejpam-5734	419	1	borodin	borodin	NOUN
ejpam-5734	419	2	and	and	CCONJ
ejpam-5734	419	3	ivanova	ivanova	PROPN
ejpam-5734	419	4	(	(	PUNCT
ejpam-5734	419	5	2009	2009	NUM
ejpam-5734	419	6	)	)	PUNCT
ejpam-5734	420	1	[	[	X
ejpam-5734	420	2	9	9	NUM
ejpam-5734	420	3	]	]	PUNCT
ejpam-5734	420	4	further	far	ADV
ejpam-5734	420	5	introduced	introduce	VERB
ejpam-5734	420	6	the	the	DET
ejpam-5734	420	7	concept	concept	NOUN
ejpam-5734	420	8	of	of	ADP
ejpam-5734	420	9	distance-2	distance-2	PRON
ejpam-5734	420	10	coloring	color	VERB
ejpam-5734	420	11	to	to	PART
ejpam-5734	420	12	allocate	allocate	VERB
ejpam-5734	420	13	resources	resource	NOUN
ejpam-5734	420	14	in	in	ADP
ejpam-5734	420	15	networks	network	NOUN
ejpam-5734	420	16	without	without	ADP
ejpam-5734	420	17	conflict	conflict	NOUN
ejpam-5734	420	18	.	.	PUNCT
ejpam-5734	421	1	when	when	SCONJ
ejpam-5734	421	2	applied	apply	VERB
ejpam-5734	421	3	to	to	ADP
ejpam-5734	421	4	shadow	shadow	NOUN
ejpam-5734	421	5	graphs	graph	NOUN
ejpam-5734	421	6	,	,	PUNCT
ejpam-5734	421	7	this	this	DET
ejpam-5734	421	8	approach	approach	NOUN
ejpam-5734	421	9	ensures	ensure	VERB
ejpam-5734	421	10	that	that	SCONJ
ejpam-5734	421	11	no	no	DET
ejpam-5734	421	12	two	two	NUM
ejpam-5734	421	13	vertices	vertex	NOUN
ejpam-5734	421	14	within	within	ADP
ejpam-5734	421	15	two	two	NUM
ejpam-5734	421	16	hops	hop	NOUN
ejpam-5734	421	17	share	share	VERB
ejpam-5734	421	18	the	the	DET
ejpam-5734	421	19	same	same	ADJ
ejpam-5734	421	20	frequency	frequency	NOUN
ejpam-5734	421	21	,	,	PUNCT
ejpam-5734	421	22	thereby	thereby	ADV
ejpam-5734	421	23	reducing	reduce	VERB
ejpam-5734	421	24	cross	cross	ADJ
ejpam-5734	421	25	-	-	ADJ
ejpam-5734	421	26	channel	channel	ADJ
ejpam-5734	421	27	interference	interference	NOUN
ejpam-5734	421	28	and	and	CCONJ
ejpam-5734	421	29	enhancing	enhance	VERB
ejpam-5734	421	30	network	network	NOUN
ejpam-5734	421	31	stability	stability	NOUN
ejpam-5734	421	32	.	.	PUNCT
ejpam-5734	422	1	this	this	DET
ejpam-5734	422	2	foundation	foundation	NOUN
ejpam-5734	422	3	sets	set	VERB
ejpam-5734	422	4	the	the	DET
ejpam-5734	422	5	stage	stage	NOUN
ejpam-5734	422	6	for	for	ADP
ejpam-5734	422	7	the	the	DET
ejpam-5734	422	8	first	first	ADJ
ejpam-5734	422	9	application	application	NOUN
ejpam-5734	422	10	using	use	VERB
ejpam-5734	422	11	the	the	DET
ejpam-5734	422	12	twin	twin	ADJ
ejpam-5734	422	13	-	-	PUNCT
ejpam-5734	422	14	building	building	NOUN
ejpam-5734	422	15	analogy	analogy	NOUN
ejpam-5734	422	16	.	.	PUNCT
ejpam-5734	423	1	imagine	imagine	VERB
ejpam-5734	423	2	two	two	NUM
ejpam-5734	423	3	identical	identical	ADJ
ejpam-5734	423	4	buildings	building	NOUN
ejpam-5734	423	5	(	(	PUNCT
ejpam-5734	423	6	building	build	VERB
ejpam-5734	423	7	a	a	PRON
ejpam-5734	423	8	and	and	CCONJ
ejpam-5734	423	9	building	build	VERB
ejpam-5734	423	10	b	b	PROPN
ejpam-5734	423	11	)	)	PUNCT
ejpam-5734	423	12	,	,	PUNCT
ejpam-5734	423	13	each	each	PRON
ejpam-5734	423	14	with	with	ADP
ejpam-5734	423	15	six	six	NUM
ejpam-5734	423	16	floors	floor	NOUN
ejpam-5734	423	17	,	,	PUNCT
ejpam-5734	423	18	representing	represent	VERB
ejpam-5734	423	19	two	two	NUM
ejpam-5734	423	20	interconnected	interconnected	ADJ
ejpam-5734	423	21	wireless	wireless	ADJ
ejpam-5734	423	22	networks	network	NOUN
ejpam-5734	423	23	.	.	PUNCT
ejpam-5734	424	1	each	each	DET
ejpam-5734	424	2	color	color	NOUN
ejpam-5734	424	3	class	class	NOUN
ejpam-5734	424	4	in	in	ADP
ejpam-5734	424	5	the	the	DET
ejpam-5734	424	6	figure	figure	NOUN
ejpam-5734	424	7	represents	represent	VERB
ejpam-5734	424	8	a	a	DET
ejpam-5734	424	9	unique	unique	ADJ
ejpam-5734	424	10	communication	communication	NOUN
ejpam-5734	424	11	channel	channel	NOUN
ejpam-5734	424	12	or	or	CCONJ
ejpam-5734	424	13	frequency	frequency	NOUN
ejpam-5734	424	14	.	.	PUNCT
ejpam-5734	425	1	these	these	DET
ejpam-5734	425	2	assignments	assignment	NOUN
ejpam-5734	425	3	must	must	AUX
ejpam-5734	425	4	avoid	avoid	VERB
ejpam-5734	425	5	conflicts	conflict	NOUN
ejpam-5734	425	6	(	(	PUNCT
ejpam-5734	425	7	interference	interference	NOUN
ejpam-5734	425	8	)	)	PUNCT
ejpam-5734	425	9	to	to	PART
ejpam-5734	425	10	ensure	ensure	VERB
ejpam-5734	425	11	efficient	efficient	ADJ
ejpam-5734	425	12	signal	signal	NOUN
ejpam-5734	425	13	transmission	transmission	NOUN
ejpam-5734	425	14	.	.	PUNCT
ejpam-5734	426	1	the	the	DET
ejpam-5734	426	2	shadow	shadow	NOUN
ejpam-5734	426	3	graph	graph	NOUN
ejpam-5734	426	4	d2(c6	d2(c6	NOUN
ejpam-5734	426	5	)	)	PUNCT
ejpam-5734	426	6	models	model	NOUN
ejpam-5734	426	7	this	this	DET
ejpam-5734	426	8	configuration	configuration	NOUN
ejpam-5734	426	9	using	use	VERB
ejpam-5734	426	10	the	the	DET
ejpam-5734	426	11	twin	twin	ADJ
ejpam-5734	426	12	building	building	NOUN
ejpam-5734	426	13	structure	structure	NOUN
ejpam-5734	426	14	.	.	PUNCT
ejpam-5734	427	1	m.	m.	NOUN
ejpam-5734	427	2	f.	f.	PROPN
ejpam-5734	427	3	libao	libao	PROPN
ejpam-5734	427	4	,	,	PUNCT
ejpam-5734	427	5	k.	k.	PROPN
ejpam-5734	427	6	b.	b.	PROPN
ejpam-5734	427	7	abarca	abarca	PROPN
ejpam-5734	427	8	/	/	SYM
ejpam-5734	427	9	eur	eur	PROPN
ejpam-5734	427	10	.	.	PUNCT
ejpam-5734	428	1	j.	j.	PROPN
ejpam-5734	428	2	pure	pure	PROPN
ejpam-5734	428	3	appl	appl	PROPN
ejpam-5734	428	4	.	.	PROPN
ejpam-5734	428	5	math	math	PROPN
ejpam-5734	428	6	,	,	PUNCT
ejpam-5734	428	7	18	18	NUM
ejpam-5734	428	8	(	(	PUNCT
ejpam-5734	428	9	2	2	NUM
ejpam-5734	428	10	)	)	PUNCT
ejpam-5734	428	11	(	(	PUNCT
ejpam-5734	428	12	2025	2025	NUM
ejpam-5734	428	13	)	)	PUNCT
ejpam-5734	428	14	,	,	PUNCT
ejpam-5734	428	15	5734	5734	NUM
ejpam-5734	428	16	21	21	NUM
ejpam-5734	428	17	of	of	ADP
ejpam-5734	428	18	25	25	NUM
ejpam-5734	428	19	a	a	DET
ejpam-5734	428	20	b	b	NOUN
ejpam-5734	428	21	figure	figure	NOUN
ejpam-5734	428	22	12	12	NUM
ejpam-5734	428	23	:	:	PUNCT
ejpam-5734	428	24	the	the	DET
ejpam-5734	428	25	twin	twin	ADJ
ejpam-5734	428	26	building	building	NOUN
ejpam-5734	428	27	,	,	PUNCT
ejpam-5734	428	28	a	a	PRON
ejpam-5734	428	29	and	and	CCONJ
ejpam-5734	428	30	b.	b.	PROPN
ejpam-5734	428	31	color	color	NOUN
ejpam-5734	428	32	assignments	assignment	NOUN
ejpam-5734	428	33	and	and	CCONJ
ejpam-5734	428	34	their	their	PRON
ejpam-5734	428	35	interpretations	interpretation	NOUN
ejpam-5734	428	36	table	table	NOUN
ejpam-5734	428	37	1	1	NUM
ejpam-5734	428	38	:	:	PUNCT
ejpam-5734	428	39	d2(c6	d2(c6	NOUN
ejpam-5734	428	40	)	)	PUNCT
ejpam-5734	428	41	as	as	SCONJ
ejpam-5734	428	42	the	the	DET
ejpam-5734	428	43	twin	twin	ADJ
ejpam-5734	428	44	building	building	NOUN
ejpam-5734	428	45	blocks	block	VERB
ejpam-5734	428	46	color	color	NOUN
ejpam-5734	428	47	floors	floor	NOUN
ejpam-5734	428	48	/	/	SYM
ejpam-5734	428	49	vertices	vertice	VERB
ejpam-5734	428	50	assigned	assign	VERB
ejpam-5734	428	51	frequency	frequency	NOUN
ejpam-5734	428	52	assignment	assignment	NOUN
ejpam-5734	428	53	red	red	ADJ
ejpam-5734	428	54	floors	floor	NOUN
ejpam-5734	428	55	1	1	NUM
ejpam-5734	428	56	and	and	CCONJ
ejpam-5734	428	57	4	4	NUM
ejpam-5734	428	58	of	of	ADP
ejpam-5734	428	59	building	build	VERB
ejpam-5734	428	60	a	a	DET
ejpam-5734	428	61	channel	channel	NOUN
ejpam-5734	428	62	1	1	NUM
ejpam-5734	428	63	purple	purple	ADJ
ejpam-5734	428	64	floors	floor	NOUN
ejpam-5734	428	65	2	2	NUM
ejpam-5734	428	66	and	and	CCONJ
ejpam-5734	428	67	5	5	NUM
ejpam-5734	428	68	of	of	ADP
ejpam-5734	428	69	building	build	VERB
ejpam-5734	428	70	a	a	DET
ejpam-5734	428	71	channel	channel	NOUN
ejpam-5734	428	72	2	2	NUM
ejpam-5734	428	73	green	green	ADJ
ejpam-5734	428	74	floors	floor	NOUN
ejpam-5734	428	75	3	3	NUM
ejpam-5734	428	76	and	and	CCONJ
ejpam-5734	428	77	6	6	NUM
ejpam-5734	428	78	of	of	ADP
ejpam-5734	428	79	building	build	VERB
ejpam-5734	428	80	a	a	DET
ejpam-5734	428	81	channel	channel	NOUN
ejpam-5734	428	82	3	3	NUM
ejpam-5734	428	83	orange	orange	ADJ
ejpam-5734	428	84	floors	floor	NOUN
ejpam-5734	428	85	1	1	NUM
ejpam-5734	428	86	and	and	CCONJ
ejpam-5734	428	87	4	4	NUM
ejpam-5734	428	88	of	of	ADP
ejpam-5734	428	89	building	building	NOUN
ejpam-5734	428	90	b	b	PROPN
ejpam-5734	428	91	channel	channel	NOUN
ejpam-5734	428	92	4	4	NUM
ejpam-5734	428	93	pink	pink	ADJ
ejpam-5734	428	94	floors	floor	NOUN
ejpam-5734	428	95	2	2	NUM
ejpam-5734	428	96	and	and	CCONJ
ejpam-5734	428	97	5	5	NUM
ejpam-5734	428	98	of	of	ADP
ejpam-5734	428	99	building	building	PROPN
ejpam-5734	428	100	b	b	PROPN
ejpam-5734	428	101	channel	channel	NOUN
ejpam-5734	428	102	5	5	NUM
ejpam-5734	428	103	yellow	yellow	ADJ
ejpam-5734	428	104	floors	floor	NOUN
ejpam-5734	428	105	3	3	NUM
ejpam-5734	428	106	and	and	CCONJ
ejpam-5734	428	107	6	6	NUM
ejpam-5734	428	108	of	of	ADP
ejpam-5734	428	109	building	building	PROPN
ejpam-5734	428	110	b	b	PROPN
ejpam-5734	428	111	channel	channel	PROPN
ejpam-5734	428	112	6	6	NUM
ejpam-5734	428	113	adjacency	adjacency	NOUN
ejpam-5734	428	114	&	&	CCONJ
ejpam-5734	428	115	interference	interference	PROPN
ejpam-5734	428	116	avoidance	avoidance	NOUN
ejpam-5734	428	117	.	.	PUNCT
ejpam-5734	429	1	•	•	NUM
ejpam-5734	429	2	adjacency	adjacency	NOUN
ejpam-5734	429	3	in	in	ADP
ejpam-5734	429	4	the	the	DET
ejpam-5734	429	5	graph	graph	NOUN
ejpam-5734	429	6	means	mean	VERB
ejpam-5734	429	7	two	two	NUM
ejpam-5734	429	8	access	access	NOUN
ejpam-5734	429	9	points	point	NOUN
ejpam-5734	429	10	(	(	PUNCT
ejpam-5734	429	11	or	or	CCONJ
ejpam-5734	429	12	floors	floor	NOUN
ejpam-5734	429	13	)	)	PUNCT
ejpam-5734	429	14	are	be	AUX
ejpam-5734	429	15	close	close	ADJ
ejpam-5734	429	16	enough	enough	ADV
ejpam-5734	429	17	to	to	PART
ejpam-5734	429	18	cause	cause	VERB
ejpam-5734	429	19	interference	interference	NOUN
ejpam-5734	429	20	.	.	PUNCT
ejpam-5734	430	1	•	•	NUM
ejpam-5734	430	2	the	the	DET
ejpam-5734	430	3	distance-2	distance-2	NUM
ejpam-5734	430	4	coloring	coloring	NOUN
ejpam-5734	430	5	ensures	ensure	VERB
ejpam-5734	430	6	that	that	SCONJ
ejpam-5734	430	7	any	any	DET
ejpam-5734	430	8	pair	pair	NOUN
ejpam-5734	430	9	of	of	ADP
ejpam-5734	430	10	vertices	vertex	NOUN
ejpam-5734	430	11	within	within	ADP
ejpam-5734	430	12	two	two	NUM
ejpam-5734	430	13	hops	hop	NOUN
ejpam-5734	430	14	(	(	PUNCT
ejpam-5734	430	15	not	not	PART
ejpam-5734	430	16	just	just	ADV
ejpam-5734	430	17	directly	directly	ADV
ejpam-5734	430	18	connected	connect	VERB
ejpam-5734	430	19	)	)	PUNCT
ejpam-5734	430	20	are	be	AUX
ejpam-5734	430	21	assigned	assign	VERB
ejpam-5734	430	22	different	different	ADJ
ejpam-5734	430	23	colors	color	NOUN
ejpam-5734	430	24	.	.	PUNCT
ejpam-5734	431	1	for	for	ADP
ejpam-5734	431	2	example	example	NOUN
ejpam-5734	431	3	:	:	PUNCT
ejpam-5734	431	4	•	•	NUM
ejpam-5734	431	5	floor	floor	NOUN
ejpam-5734	431	6	1	1	NUM
ejpam-5734	431	7	of	of	ADP
ejpam-5734	431	8	building	build	VERB
ejpam-5734	431	9	a	a	PRON
ejpam-5734	431	10	is	be	AUX
ejpam-5734	431	11	adjacent	adjacent	ADJ
ejpam-5734	431	12	to	to	ADP
ejpam-5734	431	13	floors	floor	NOUN
ejpam-5734	431	14	2	2	NUM
ejpam-5734	431	15	and	and	CCONJ
ejpam-5734	431	16	6	6	NUM
ejpam-5734	431	17	of	of	ADP
ejpam-5734	431	18	building	build	VERB
ejpam-5734	431	19	a	a	PRON
ejpam-5734	431	20	,	,	PUNCT
ejpam-5734	431	21	as	as	ADV
ejpam-5734	431	22	well	well	ADV
ejpam-5734	431	23	as	as	ADP
ejpam-5734	431	24	floors	floor	NOUN
ejpam-5734	431	25	2	2	NUM
ejpam-5734	431	26	and	and	CCONJ
ejpam-5734	431	27	6	6	NUM
ejpam-5734	431	28	of	of	ADP
ejpam-5734	431	29	building	building	NOUN
ejpam-5734	431	30	b	b	PROPN
ejpam-5734	431	31	,	,	PUNCT
ejpam-5734	431	32	and	and	CCONJ
ejpam-5734	431	33	all	all	DET
ejpam-5734	431	34	these	these	DET
ejpam-5734	431	35	floors	floor	NOUN
ejpam-5734	431	36	are	be	AUX
ejpam-5734	431	37	colored	color	VERB
ejpam-5734	431	38	differently	differently	ADV
ejpam-5734	431	39	.	.	PUNCT
ejpam-5734	432	1	•	•	NUM
ejpam-5734	432	2	floor	floor	NOUN
ejpam-5734	432	3	1	1	NUM
ejpam-5734	432	4	of	of	ADP
ejpam-5734	432	5	building	building	NOUN
ejpam-5734	432	6	b	b	PROPN
ejpam-5734	432	7	is	be	AUX
ejpam-5734	432	8	adjacent	adjacent	ADJ
ejpam-5734	432	9	to	to	ADP
ejpam-5734	432	10	floors	floor	NOUN
ejpam-5734	432	11	2	2	NUM
ejpam-5734	432	12	and	and	CCONJ
ejpam-5734	432	13	6	6	NUM
ejpam-5734	432	14	of	of	ADP
ejpam-5734	432	15	building	build	VERB
ejpam-5734	432	16	a	a	PRON
ejpam-5734	432	17	,	,	PUNCT
ejpam-5734	432	18	as	as	ADV
ejpam-5734	432	19	well	well	ADV
ejpam-5734	432	20	as	as	ADP
ejpam-5734	432	21	floors	floor	NOUN
ejpam-5734	432	22	2	2	NUM
ejpam-5734	432	23	and	and	CCONJ
ejpam-5734	432	24	6	6	NUM
ejpam-5734	432	25	of	of	ADP
ejpam-5734	432	26	building	build	VERB
ejpam-5734	432	27	b	b	NOUN
ejpam-5734	432	28	,	,	PUNCT
ejpam-5734	432	29	again	again	ADV
ejpam-5734	432	30	ensuring	ensure	VERB
ejpam-5734	432	31	different	different	ADJ
ejpam-5734	432	32	colors	color	NOUN
ejpam-5734	432	33	.	.	PUNCT
ejpam-5734	433	1	when	when	SCONJ
ejpam-5734	433	2	two	two	NUM
ejpam-5734	433	3	floors	floor	NOUN
ejpam-5734	433	4	in	in	ADP
ejpam-5734	433	5	the	the	DET
ejpam-5734	433	6	graph	graph	NOUN
ejpam-5734	433	7	have	have	VERB
ejpam-5734	433	8	the	the	DET
ejpam-5734	433	9	same	same	ADJ
ejpam-5734	433	10	color	color	NOUN
ejpam-5734	433	11	,	,	PUNCT
ejpam-5734	433	12	it	it	PRON
ejpam-5734	433	13	implies	imply	VERB
ejpam-5734	433	14	the	the	DET
ejpam-5734	433	15	following	follow	VERB
ejpam-5734	433	16	:	:	PUNCT
ejpam-5734	433	17	m.	m.	PROPN
ejpam-5734	433	18	f.	f.	PROPN
ejpam-5734	433	19	libao	libao	PROPN
ejpam-5734	433	20	,	,	PUNCT
ejpam-5734	433	21	k.	k.	PROPN
ejpam-5734	433	22	b.	b.	PROPN
ejpam-5734	433	23	abarca	abarca	PROPN
ejpam-5734	433	24	/	/	SYM
ejpam-5734	433	25	eur	eur	PROPN
ejpam-5734	433	26	.	.	PUNCT
ejpam-5734	434	1	j.	j.	PROPN
ejpam-5734	434	2	pure	pure	PROPN
ejpam-5734	434	3	appl	appl	PROPN
ejpam-5734	434	4	.	.	PROPN
ejpam-5734	434	5	math	math	PROPN
ejpam-5734	434	6	,	,	PUNCT
ejpam-5734	434	7	18	18	NUM
ejpam-5734	434	8	(	(	PUNCT
ejpam-5734	434	9	2	2	NUM
ejpam-5734	434	10	)	)	PUNCT
ejpam-5734	434	11	(	(	PUNCT
ejpam-5734	434	12	2025	2025	NUM
ejpam-5734	434	13	)	)	PUNCT
ejpam-5734	434	14	,	,	PUNCT
ejpam-5734	434	15	5734	5734	NUM
ejpam-5734	434	16	22	22	NUM
ejpam-5734	434	17	of	of	ADP
ejpam-5734	434	18	25	25	NUM
ejpam-5734	434	19	table	table	NOUN
ejpam-5734	434	20	2	2	NUM
ejpam-5734	434	21	:	:	PUNCT
ejpam-5734	434	22	floors	floor	NOUN
ejpam-5734	434	23	with	with	ADP
ejpam-5734	434	24	the	the	DET
ejpam-5734	434	25	same	same	ADJ
ejpam-5734	434	26	color	color	NOUN
ejpam-5734	434	27	and	and	CCONJ
ejpam-5734	434	28	its	its	PRON
ejpam-5734	434	29	meaning	meaning	ADJ
ejpam-5734	434	30	floors	floor	NOUN
ejpam-5734	434	31	with	with	ADP
ejpam-5734	434	32	same	same	ADJ
ejpam-5734	434	33	color	color	NOUN
ejpam-5734	434	34	meaning	mean	VERB
ejpam-5734	434	35	far	far	ADV
ejpam-5734	434	36	enough	enough	ADV
ejpam-5734	434	37	apart	apart	ADP
ejpam-5734	434	38	✓	✓	ADJ
ejpam-5734	434	39	safe	safe	ADJ
ejpam-5734	434	40	to	to	PART
ejpam-5734	434	41	share	share	VERB
ejpam-5734	434	42	a	a	DET
ejpam-5734	434	43	channel	channel	NOUN
ejpam-5734	434	44	no	no	DET
ejpam-5734	434	45	conflict	conflict	NOUN
ejpam-5734	434	46	within	within	ADP
ejpam-5734	434	47	2	2	NUM
ejpam-5734	434	48	hops	hop	NOUN
ejpam-5734	434	49	✓	✓	ADJ
ejpam-5734	434	50	no	no	DET
ejpam-5734	434	51	interference	interference	NOUN
ejpam-5734	434	52	same	same	ADJ
ejpam-5734	434	53	resource	resource	NOUN
ejpam-5734	434	54	/	/	SYM
ejpam-5734	434	55	frequency	frequency	NOUN
ejpam-5734	434	56	✓	✓	ADJ
ejpam-5734	434	57	efficient	efficient	ADJ
ejpam-5734	434	58	allocation	allocation	NOUN
ejpam-5734	434	59	that	that	PRON
ejpam-5734	434	60	is	be	AUX
ejpam-5734	434	61	,	,	PUNCT
ejpam-5734	434	62	floors	floor	NOUN
ejpam-5734	434	63	that	that	PRON
ejpam-5734	434	64	are	be	AUX
ejpam-5734	434	65	sufficiently	sufficiently	ADV
ejpam-5734	434	66	separated	separate	VERB
ejpam-5734	434	67	(	(	PUNCT
ejpam-5734	434	68	distance	distance	NOUN
ejpam-5734	434	69	≥	≥	NOUN
ejpam-5734	434	70	3	3	NUM
ejpam-5734	434	71	in	in	ADP
ejpam-5734	434	72	the	the	DET
ejpam-5734	434	73	graph	graph	NOUN
ejpam-5734	434	74	)	)	PUNCT
ejpam-5734	434	75	can	can	AUX
ejpam-5734	434	76	operate	operate	VERB
ejpam-5734	434	77	on	on	ADP
ejpam-5734	434	78	the	the	DET
ejpam-5734	434	79	same	same	ADJ
ejpam-5734	434	80	frequency	frequency	NOUN
ejpam-5734	434	81	without	without	ADP
ejpam-5734	434	82	interference	interference	NOUN
ejpam-5734	434	83	.	.	PUNCT
ejpam-5734	435	1	the	the	DET
ejpam-5734	435	2	shadow	shadow	NOUN
ejpam-5734	435	3	graph	graph	NOUN
ejpam-5734	435	4	illustrated	illustrate	VERB
ejpam-5734	435	5	how	how	SCONJ
ejpam-5734	435	6	duplicating	duplicate	VERB
ejpam-5734	435	7	structures	structure	NOUN
ejpam-5734	435	8	helps	help	VERB
ejpam-5734	435	9	in	in	ADP
ejpam-5734	435	10	organizing	organize	VERB
ejpam-5734	435	11	resource	resource	NOUN
ejpam-5734	435	12	use	use	NOUN
ejpam-5734	435	13	across	across	ADP
ejpam-5734	435	14	separate	separate	ADJ
ejpam-5734	435	15	but	but	CCONJ
ejpam-5734	435	16	structurally	structurally	ADV
ejpam-5734	435	17	similar	similar	ADJ
ejpam-5734	435	18	units	unit	NOUN
ejpam-5734	435	19	—	—	PUNCT
ejpam-5734	435	20	ensuring	ensure	VERB
ejpam-5734	435	21	that	that	SCONJ
ejpam-5734	435	22	no	no	DET
ejpam-5734	435	23	closely	closely	ADV
ejpam-5734	435	24	related	related	ADJ
ejpam-5734	435	25	units	unit	NOUN
ejpam-5734	435	26	simultaneously	simultaneously	ADV
ejpam-5734	435	27	access	access	VERB
ejpam-5734	435	28	the	the	DET
ejpam-5734	435	29	same	same	ADJ
ejpam-5734	435	30	resource	resource	NOUN
ejpam-5734	435	31	.	.	PUNCT
ejpam-5734	436	1	5.2	5.2	NUM
ejpam-5734	436	2	.	.	PUNCT
ejpam-5734	437	1	the	the	DET
ejpam-5734	437	2	office	office	NOUN
ejpam-5734	437	3	building	building	NOUN
ejpam-5734	437	4	analogy	analogy	NOUN
ejpam-5734	437	5	recent	recent	ADJ
ejpam-5734	437	6	studies	study	NOUN
ejpam-5734	437	7	such	such	ADJ
ejpam-5734	437	8	as	as	ADP
ejpam-5734	437	9	jain	jain	NOUN
ejpam-5734	437	10	and	and	CCONJ
ejpam-5734	437	11	jain	jain	PROPN
ejpam-5734	437	12	(	(	PUNCT
ejpam-5734	437	13	2023	2023	NUM
ejpam-5734	437	14	)	)	PUNCT
ejpam-5734	437	15	and	and	CCONJ
ejpam-5734	437	16	majeed	majeed	PROPN
ejpam-5734	437	17	and	and	CCONJ
ejpam-5734	437	18	rauf	rauf	PROPN
ejpam-5734	437	19	(	(	PUNCT
ejpam-5734	437	20	2020	2020	NUM
ejpam-5734	437	21	)	)	PUNCT
ejpam-5734	438	1	[	[	X
ejpam-5734	438	2	5	5	NUM
ejpam-5734	438	3	,	,	PUNCT
ejpam-5734	438	4	14	14	NUM
ejpam-5734	438	5	]	]	PUNCT
ejpam-5734	438	6	,	,	PUNCT
ejpam-5734	438	7	emphasize	emphasize	VERB
ejpam-5734	438	8	the	the	DET
ejpam-5734	438	9	effectiveness	effectiveness	NOUN
ejpam-5734	438	10	of	of	ADP
ejpam-5734	438	11	graph	graph	NOUN
ejpam-5734	438	12	-	-	PUNCT
ejpam-5734	438	13	based	base	VERB
ejpam-5734	438	14	models	model	NOUN
ejpam-5734	438	15	and	and	CCONJ
ejpam-5734	438	16	graph	graph	NOUN
ejpam-5734	438	17	coloring	coloring	NOUN
ejpam-5734	438	18	techniques	technique	NOUN
ejpam-5734	438	19	in	in	ADP
ejpam-5734	438	20	optimizing	optimize	VERB
ejpam-5734	438	21	network	network	NOUN
ejpam-5734	438	22	topology	topology	NOUN
ejpam-5734	438	23	,	,	PUNCT
ejpam-5734	438	24	resource	resource	NOUN
ejpam-5734	438	25	allocation	allocation	NOUN
ejpam-5734	438	26	,	,	PUNCT
ejpam-5734	438	27	and	and	CCONJ
ejpam-5734	438	28	communication	communication	NOUN
ejpam-5734	438	29	efficiency	efficiency	NOUN
ejpam-5734	438	30	.	.	PUNCT
ejpam-5734	439	1	these	these	DET
ejpam-5734	439	2	works	work	NOUN
ejpam-5734	439	3	demonstrate	demonstrate	VERB
ejpam-5734	439	4	how	how	SCONJ
ejpam-5734	439	5	distance-2	distance-2	PRON
ejpam-5734	439	6	coloring	coloring	NOUN
ejpam-5734	439	7	can	can	AUX
ejpam-5734	439	8	manage	manage	VERB
ejpam-5734	439	9	interference	interference	NOUN
ejpam-5734	439	10	by	by	ADP
ejpam-5734	439	11	assigning	assign	VERB
ejpam-5734	439	12	distinct	distinct	ADJ
ejpam-5734	439	13	frequencies	frequency	NOUN
ejpam-5734	439	14	to	to	ADP
ejpam-5734	439	15	nodes	node	NOUN
ejpam-5734	439	16	within	within	ADP
ejpam-5734	439	17	two	two	NUM
ejpam-5734	439	18	-	-	PUNCT
ejpam-5734	439	19	hop	hop	NOUN
ejpam-5734	439	20	proximity	proximity	NOUN
ejpam-5734	439	21	.	.	PUNCT
ejpam-5734	440	1	in	in	ADP
ejpam-5734	440	2	line	line	NOUN
ejpam-5734	440	3	with	with	ADP
ejpam-5734	440	4	these	these	DET
ejpam-5734	440	5	findings	finding	NOUN
ejpam-5734	440	6	,	,	PUNCT
ejpam-5734	440	7	the	the	DET
ejpam-5734	440	8	central	central	ADJ
ejpam-5734	440	9	graph	graph	NOUN
ejpam-5734	440	10	of	of	ADP
ejpam-5734	440	11	a	a	DET
ejpam-5734	440	12	cycle	cycle	NOUN
ejpam-5734	440	13	offers	offer	VERB
ejpam-5734	440	14	a	a	DET
ejpam-5734	440	15	practical	practical	ADJ
ejpam-5734	440	16	and	and	CCONJ
ejpam-5734	440	17	efficient	efficient	ADJ
ejpam-5734	440	18	configuration	configuration	NOUN
ejpam-5734	440	19	by	by	ADP
ejpam-5734	440	20	introducing	introduce	VERB
ejpam-5734	440	21	central	central	ADJ
ejpam-5734	440	22	nodes	node	NOUN
ejpam-5734	440	23	that	that	PRON
ejpam-5734	440	24	transform	transform	VERB
ejpam-5734	440	25	a	a	DET
ejpam-5734	440	26	simple	simple	ADJ
ejpam-5734	440	27	circular	circular	ADJ
ejpam-5734	440	28	structure	structure	NOUN
ejpam-5734	440	29	—	—	PUNCT
ejpam-5734	440	30	where	where	SCONJ
ejpam-5734	440	31	nodes	node	NOUN
ejpam-5734	440	32	are	be	AUX
ejpam-5734	440	33	initially	initially	ADV
ejpam-5734	440	34	connected	connect	VERB
ejpam-5734	440	35	only	only	ADV
ejpam-5734	440	36	to	to	ADP
ejpam-5734	440	37	immediate	immediate	ADJ
ejpam-5734	440	38	neighbors	neighbor	NOUN
ejpam-5734	440	39	—	—	PUNCT
ejpam-5734	440	40	into	into	ADP
ejpam-5734	440	41	a	a	DET
ejpam-5734	440	42	highly	highly	ADV
ejpam-5734	440	43	interconnected	interconnected	ADJ
ejpam-5734	440	44	network	network	NOUN
ejpam-5734	440	45	.	.	PUNCT
ejpam-5734	441	1	this	this	PRON
ejpam-5734	441	2	ensures	ensure	VERB
ejpam-5734	441	3	more	more	ADJ
ejpam-5734	441	4	direct	direct	ADJ
ejpam-5734	441	5	communication	communication	NOUN
ejpam-5734	441	6	pathways	pathway	NOUN
ejpam-5734	441	7	among	among	ADP
ejpam-5734	441	8	all	all	DET
ejpam-5734	441	9	previously	previously	ADV
ejpam-5734	441	10	non	non	ADJ
ejpam-5734	441	11	-	-	ADJ
ejpam-5734	441	12	adjacent	adjacent	ADJ
ejpam-5734	441	13	nodes	node	NOUN
ejpam-5734	441	14	,	,	PUNCT
ejpam-5734	441	15	significantly	significantly	ADV
ejpam-5734	441	16	enhancing	enhance	VERB
ejpam-5734	441	17	the	the	DET
ejpam-5734	441	18	network	network	NOUN
ejpam-5734	441	19	’s	’s	PART
ejpam-5734	441	20	overall	overall	ADJ
ejpam-5734	441	21	performance	performance	NOUN
ejpam-5734	441	22	.	.	PUNCT
ejpam-5734	442	1	consider	consider	VERB
ejpam-5734	442	2	an	an	DET
ejpam-5734	442	3	office	office	NOUN
ejpam-5734	442	4	building	building	NOUN
ejpam-5734	442	5	with	with	ADP
ejpam-5734	442	6	six	six	NUM
ejpam-5734	442	7	distinct	distinct	ADJ
ejpam-5734	442	8	offices	office	NOUN
ejpam-5734	442	9	,	,	PUNCT
ejpam-5734	442	10	each	each	PRON
ejpam-5734	442	11	assigned	assign	VERB
ejpam-5734	442	12	a	a	DET
ejpam-5734	442	13	unique	unique	ADJ
ejpam-5734	442	14	color	color	NOUN
ejpam-5734	442	15	representing	represent	VERB
ejpam-5734	442	16	a	a	DET
ejpam-5734	442	17	specific	specific	ADJ
ejpam-5734	442	18	frequency	frequency	NOUN
ejpam-5734	442	19	or	or	CCONJ
ejpam-5734	442	20	communication	communication	NOUN
ejpam-5734	442	21	channel	channel	NOUN
ejpam-5734	442	22	.	.	PUNCT
ejpam-5734	443	1	in	in	ADP
ejpam-5734	443	2	the	the	DET
ejpam-5734	443	3	original	original	ADJ
ejpam-5734	443	4	layout	layout	NOUN
ejpam-5734	443	5	,	,	PUNCT
ejpam-5734	443	6	each	each	DET
ejpam-5734	443	7	office	office	NOUN
ejpam-5734	443	8	can	can	AUX
ejpam-5734	443	9	only	only	ADV
ejpam-5734	443	10	interact	interact	VERB
ejpam-5734	443	11	directly	directly	ADV
ejpam-5734	443	12	with	with	ADP
ejpam-5734	443	13	its	its	PRON
ejpam-5734	443	14	immediate	immediate	ADJ
ejpam-5734	443	15	neighbors	neighbor	NOUN
ejpam-5734	443	16	.	.	PUNCT
ejpam-5734	444	1	however	however	ADV
ejpam-5734	444	2	,	,	PUNCT
ejpam-5734	444	3	by	by	ADP
ejpam-5734	444	4	introducing	introduce	VERB
ejpam-5734	444	5	two	two	NUM
ejpam-5734	444	6	central	central	ADJ
ejpam-5734	444	7	nodes	node	NOUN
ejpam-5734	444	8	,	,	PUNCT
ejpam-5734	444	9	one	one	NUM
ejpam-5734	444	10	representing	represent	VERB
ejpam-5734	444	11	a	a	DET
ejpam-5734	444	12	shared	share	VERB
ejpam-5734	444	13	pantry	pantry	NOUN
ejpam-5734	444	14	or	or	CCONJ
ejpam-5734	444	15	lounge	lounge	NOUN
ejpam-5734	444	16	(	(	PUNCT
ejpam-5734	444	17	orange	orange	ADJ
ejpam-5734	444	18	)	)	PUNCT
ejpam-5734	444	19	and	and	CCONJ
ejpam-5734	444	20	the	the	DET
ejpam-5734	444	21	other	other	ADJ
ejpam-5734	444	22	a	a	DET
ejpam-5734	444	23	comfort	comfort	NOUN
ejpam-5734	444	24	room	room	NOUN
ejpam-5734	444	25	(	(	PUNCT
ejpam-5734	444	26	black	black	NOUN
ejpam-5734	444	27	)	)	PUNCT
ejpam-5734	444	28	,	,	PUNCT
ejpam-5734	444	29	the	the	DET
ejpam-5734	444	30	structure	structure	NOUN
ejpam-5734	444	31	transforms	transform	VERB
ejpam-5734	444	32	into	into	ADP
ejpam-5734	444	33	a	a	DET
ejpam-5734	444	34	highly	highly	ADV
ejpam-5734	444	35	connected	connected	ADJ
ejpam-5734	444	36	environment	environment	NOUN
ejpam-5734	444	37	.	.	PUNCT
ejpam-5734	445	1	these	these	DET
ejpam-5734	445	2	central	central	ADJ
ejpam-5734	445	3	hubs	hub	NOUN
ejpam-5734	445	4	provide	provide	VERB
ejpam-5734	445	5	indirect	indirect	ADJ
ejpam-5734	445	6	links	link	NOUN
ejpam-5734	445	7	between	between	ADP
ejpam-5734	445	8	all	all	DET
ejpam-5734	445	9	offices	office	NOUN
ejpam-5734	445	10	,	,	PUNCT
ejpam-5734	445	11	modeling	model	VERB
ejpam-5734	445	12	a	a	DET
ejpam-5734	445	13	real	real	ADJ
ejpam-5734	445	14	-	-	PUNCT
ejpam-5734	445	15	world	world	NOUN
ejpam-5734	445	16	setup	setup	NOUN
ejpam-5734	445	17	where	where	SCONJ
ejpam-5734	445	18	shared	share	VERB
ejpam-5734	445	19	facilities	facility	NOUN
ejpam-5734	445	20	foster	foster	VERB
ejpam-5734	445	21	broader	broad	ADJ
ejpam-5734	445	22	communication	communication	NOUN
ejpam-5734	445	23	and	and	CCONJ
ejpam-5734	445	24	interaction	interaction	NOUN
ejpam-5734	445	25	across	across	ADP
ejpam-5734	445	26	the	the	DET
ejpam-5734	445	27	network	network	NOUN
ejpam-5734	445	28	.	.	PUNCT
ejpam-5734	446	1	meaning	mean	VERB
ejpam-5734	446	2	behind	behind	ADP
ejpam-5734	446	3	the	the	DET
ejpam-5734	446	4	color	color	NOUN
ejpam-5734	446	5	assignments	assignment	NOUN
ejpam-5734	446	6	m.	m.	NOUN
ejpam-5734	446	7	f.	f.	PROPN
ejpam-5734	446	8	libao	libao	PROPN
ejpam-5734	446	9	,	,	PUNCT
ejpam-5734	446	10	k.	k.	PROPN
ejpam-5734	446	11	b.	b.	PROPN
ejpam-5734	446	12	abarca	abarca	PROPN
ejpam-5734	446	13	/	/	SYM
ejpam-5734	446	14	eur	eur	PROPN
ejpam-5734	446	15	.	.	PUNCT
ejpam-5734	447	1	j.	j.	PROPN
ejpam-5734	447	2	pure	pure	PROPN
ejpam-5734	447	3	appl	appl	PROPN
ejpam-5734	447	4	.	.	PROPN
ejpam-5734	447	5	math	math	PROPN
ejpam-5734	447	6	,	,	PUNCT
ejpam-5734	447	7	18	18	NUM
ejpam-5734	447	8	(	(	PUNCT
ejpam-5734	447	9	2	2	NUM
ejpam-5734	447	10	)	)	PUNCT
ejpam-5734	447	11	(	(	PUNCT
ejpam-5734	447	12	2025	2025	NUM
ejpam-5734	447	13	)	)	PUNCT
ejpam-5734	447	14	,	,	PUNCT
ejpam-5734	447	15	5734	5734	NUM
ejpam-5734	447	16	23	23	NUM
ejpam-5734	447	17	of	of	ADP
ejpam-5734	447	18	25	25	NUM
ejpam-5734	447	19	figure	figure	NOUN
ejpam-5734	447	20	13	13	NUM
ejpam-5734	447	21	:	:	PUNCT
ejpam-5734	447	22	the	the	DET
ejpam-5734	447	23	circular	circular	ADJ
ejpam-5734	447	24	office	office	NOUN
ejpam-5734	447	25	bulding	bulding	NOUN
ejpam-5734	447	26	table	table	NOUN
ejpam-5734	447	27	3	3	NUM
ejpam-5734	447	28	:	:	PUNCT
ejpam-5734	447	29	the	the	DET
ejpam-5734	447	30	central	central	ADJ
ejpam-5734	447	31	graph	graph	NOUN
ejpam-5734	447	32	c(c6	c(c6	NOUN
ejpam-5734	447	33	)	)	PUNCT
ejpam-5734	447	34	as	as	ADP
ejpam-5734	447	35	an	an	DET
ejpam-5734	447	36	office	office	NOUN
ejpam-5734	447	37	layout	layout	NOUN
ejpam-5734	447	38	graph	graph	NOUN
ejpam-5734	447	39	element	element	ADJ
ejpam-5734	447	40	real	real	ADJ
ejpam-5734	447	41	-	-	PUNCT
ejpam-5734	447	42	world	world	NOUN
ejpam-5734	447	43	analogy	analogy	NOUN
ejpam-5734	447	44	interpretation	interpretation	NOUN
ejpam-5734	447	45	colors	color	NOUN
ejpam-5734	447	46	red	red	ADJ
ejpam-5734	447	47	,	,	PUNCT
ejpam-5734	447	48	blue	blue	ADJ
ejpam-5734	447	49	,	,	PUNCT
ejpam-5734	447	50	yellow	yellow	ADJ
ejpam-5734	447	51	,	,	PUNCT
ejpam-5734	447	52	green	green	ADJ
ejpam-5734	447	53	,	,	PUNCT
ejpam-5734	447	54	magenta	magenta	NOUN
ejpam-5734	447	55	,	,	PUNCT
ejpam-5734	447	56	violet	violet	ADJ
ejpam-5734	447	57	office	office	NOUN
ejpam-5734	447	58	rooms	room	NOUN
ejpam-5734	447	59	(	(	PUNCT
ejpam-5734	447	60	floors	floor	NOUN
ejpam-5734	447	61	)	)	PUNCT
ejpam-5734	447	62	each	each	DET
ejpam-5734	447	63	vertex	vertex	NOUN
ejpam-5734	447	64	vi	vi	PROPN
ejpam-5734	447	65	represents	represent	VERB
ejpam-5734	447	66	an	an	DET
ejpam-5734	447	67	individual	individual	ADJ
ejpam-5734	447	68	office	office	NOUN
ejpam-5734	447	69	(	(	PUNCT
ejpam-5734	447	70	or	or	CCONJ
ejpam-5734	447	71	floor	floor	NOUN
ejpam-5734	447	72	)	)	PUNCT
ejpam-5734	447	73	in	in	ADP
ejpam-5734	447	74	a	a	DET
ejpam-5734	447	75	circular	circular	ADJ
ejpam-5734	447	76	hallway	hallway	NOUN
ejpam-5734	447	77	.	.	PUNCT
ejpam-5734	448	1	these	these	DET
ejpam-5734	448	2	offices	office	NOUN
ejpam-5734	448	3	are	be	AUX
ejpam-5734	448	4	arranged	arrange	VERB
ejpam-5734	448	5	so	so	SCONJ
ejpam-5734	448	6	that	that	SCONJ
ejpam-5734	448	7	each	each	PRON
ejpam-5734	448	8	is	be	AUX
ejpam-5734	448	9	adjacent	adjacent	ADJ
ejpam-5734	448	10	to	to	ADP
ejpam-5734	448	11	its	its	PRON
ejpam-5734	448	12	neighbors	neighbor	NOUN
ejpam-5734	448	13	(	(	PUNCT
ejpam-5734	448	14	e.g.	e.g.	ADV
ejpam-5734	448	15	,	,	PUNCT
ejpam-5734	448	16	room	room	NOUN
ejpam-5734	448	17	1	1	NUM
ejpam-5734	448	18	is	be	AUX
ejpam-5734	448	19	beside	beside	ADP
ejpam-5734	448	20	rooms	room	NOUN
ejpam-5734	448	21	2	2	NUM
ejpam-5734	448	22	and	and	CCONJ
ejpam-5734	448	23	6	6	NUM
ejpam-5734	448	24	)	)	PUNCT
ejpam-5734	448	25	.	.	PUNCT
ejpam-5734	449	1	colors	color	NOUN
ejpam-5734	449	2	orange	orange	PROPN
ejpam-5734	449	3	and	and	CCONJ
ejpam-5734	449	4	black	black	ADJ
ejpam-5734	449	5	shared	share	VERB
ejpam-5734	449	6	pantries	pantry	NOUN
ejpam-5734	449	7	or	or	CCONJ
ejpam-5734	449	8	lounges	lounge	NOUN
ejpam-5734	449	9	orange	orange	PROPN
ejpam-5734	449	10	represents	represent	VERB
ejpam-5734	449	11	a	a	DET
ejpam-5734	449	12	comfort	comfort	NOUN
ejpam-5734	449	13	room	room	NOUN
ejpam-5734	449	14	(	(	PUNCT
ejpam-5734	449	15	cr	cr	NOUN
ejpam-5734	449	16	)	)	PUNCT
ejpam-5734	449	17	,	,	PUNCT
ejpam-5734	449	18	black	black	ADJ
ejpam-5734	449	19	for	for	ADP
ejpam-5734	449	20	lounge	lounge	NOUN
ejpam-5734	449	21	,	,	PUNCT
ejpam-5734	449	22	placed	place	VERB
ejpam-5734	449	23	between	between	ADP
ejpam-5734	449	24	two	two	NUM
ejpam-5734	449	25	adjacent	adjacent	ADJ
ejpam-5734	449	26	offices	office	NOUN
ejpam-5734	449	27	.	.	PUNCT
ejpam-5734	450	1	for	for	ADP
ejpam-5734	450	2	instance	instance	NOUN
ejpam-5734	450	3	,	,	PUNCT
ejpam-5734	450	4	one	one	NUM
ejpam-5734	450	5	lounge	lounge	NOUN
ejpam-5734	450	6	sits	sit	VERB
ejpam-5734	450	7	between	between	ADP
ejpam-5734	450	8	two	two	NUM
ejpam-5734	450	9	offices	office	NOUN
ejpam-5734	450	10	,	,	PUNCT
ejpam-5734	450	11	serving	serve	VERB
ejpam-5734	450	12	both.this	both.this	PRON
ejpam-5734	450	13	ensures	ensure	NOUN
ejpam-5734	450	14	that	that	SCONJ
ejpam-5734	450	15	nearby	nearby	ADJ
ejpam-5734	450	16	rooms	room	NOUN
ejpam-5734	450	17	do	do	AUX
ejpam-5734	450	18	not	not	PART
ejpam-5734	450	19	share	share	VERB
ejpam-5734	450	20	the	the	DET
ejpam-5734	450	21	same	same	ADJ
ejpam-5734	450	22	resource	resource	NOUN
ejpam-5734	450	23	at	at	ADP
ejpam-5734	450	24	once	once	ADV
ejpam-5734	450	25	,	,	PUNCT
ejpam-5734	450	26	preventing	prevent	VERB
ejpam-5734	450	27	overcrowding	overcrowding	NOUN
ejpam-5734	450	28	or	or	CCONJ
ejpam-5734	450	29	scheduling	scheduling	NOUN
ejpam-5734	450	30	overlap	overlap	NOUN
ejpam-5734	450	31	.	.	PUNCT
ejpam-5734	451	1	edges	edge	NOUN
ejpam-5734	451	2	from	from	ADP
ejpam-5734	451	3	one	one	NUM
ejpam-5734	451	4	office	office	NOUN
ejpam-5734	451	5	to	to	ADP
ejpam-5734	451	6	an	an	DET
ejpam-5734	451	7	originally	originally	ADV
ejpam-5734	451	8	nonadjacent	nonadjacent	ADJ
ejpam-5734	451	9	offices	office	NOUN
ejpam-5734	451	10	access	access	NOUN
ejpam-5734	451	11	to	to	PART
ejpam-5734	451	12	open	open	VERB
ejpam-5734	451	13	façade	façade	PROPN
ejpam-5734	451	14	or	or	CCONJ
ejpam-5734	451	15	mini	mini	NOUN
ejpam-5734	451	16	-	-	NOUN
ejpam-5734	451	17	park	park	NOUN
ejpam-5734	451	18	these	these	DET
ejpam-5734	451	19	edges	edge	NOUN
ejpam-5734	451	20	indicate	indicate	VERB
ejpam-5734	451	21	shared	shared	ADJ
ejpam-5734	451	22	access	access	NOUN
ejpam-5734	451	23	to	to	ADP
ejpam-5734	451	24	open	open	ADJ
ejpam-5734	451	25	spaces	space	NOUN
ejpam-5734	451	26	like	like	ADP
ejpam-5734	451	27	a	a	DET
ejpam-5734	451	28	mini	mini	NOUN
ejpam-5734	451	29	-	-	NOUN
ejpam-5734	451	30	park	park	NOUN
ejpam-5734	451	31	or	or	CCONJ
ejpam-5734	451	32	facade	facade	NOUN
ejpam-5734	451	33	between	between	ADP
ejpam-5734	451	34	adjacent	adjacent	ADJ
ejpam-5734	451	35	offices	office	NOUN
ejpam-5734	451	36	,	,	PUNCT
ejpam-5734	451	37	enhancing	enhance	VERB
ejpam-5734	451	38	connectivity	connectivity	NOUN
ejpam-5734	451	39	and	and	CCONJ
ejpam-5734	451	40	wellness	wellness	NOUN
ejpam-5734	451	41	.	.	PUNCT
ejpam-5734	452	1	m.	m.	PROPN
ejpam-5734	452	2	f.	f.	PROPN
ejpam-5734	452	3	libao	libao	PROPN
ejpam-5734	452	4	,	,	PUNCT
ejpam-5734	452	5	k.	k.	PROPN
ejpam-5734	452	6	b.	b.	PROPN
ejpam-5734	452	7	abarca	abarca	PROPN
ejpam-5734	452	8	/	/	SYM
ejpam-5734	452	9	eur	eur	PROPN
ejpam-5734	452	10	.	.	PUNCT
ejpam-5734	453	1	j.	j.	PROPN
ejpam-5734	453	2	pure	pure	PROPN
ejpam-5734	453	3	appl	appl	PROPN
ejpam-5734	453	4	.	.	PROPN
ejpam-5734	453	5	math	math	PROPN
ejpam-5734	453	6	,	,	PUNCT
ejpam-5734	453	7	18	18	NUM
ejpam-5734	453	8	(	(	PUNCT
ejpam-5734	453	9	2	2	NUM
ejpam-5734	453	10	)	)	PUNCT
ejpam-5734	453	11	(	(	PUNCT
ejpam-5734	453	12	2025	2025	NUM
ejpam-5734	453	13	)	)	PUNCT
ejpam-5734	453	14	,	,	PUNCT
ejpam-5734	453	15	5734	5734	NUM
ejpam-5734	453	16	24	24	NUM
ejpam-5734	453	17	of	of	ADP
ejpam-5734	453	18	25	25	NUM
ejpam-5734	453	19	the	the	DET
ejpam-5734	453	20	central	central	ADJ
ejpam-5734	453	21	graph	graph	NOUN
ejpam-5734	453	22	showed	show	VERB
ejpam-5734	453	23	how	how	SCONJ
ejpam-5734	453	24	introducing	introduce	VERB
ejpam-5734	453	25	shared	share	VERB
ejpam-5734	453	26	nodes	node	NOUN
ejpam-5734	453	27	such	such	ADJ
ejpam-5734	453	28	as	as	ADP
ejpam-5734	453	29	lounges	lounge	NOUN
ejpam-5734	453	30	or	or	CCONJ
ejpam-5734	453	31	comfort	comfort	NOUN
ejpam-5734	453	32	rooms	room	NOUN
ejpam-5734	453	33	enhances	enhance	VERB
ejpam-5734	453	34	accessibility	accessibility	NOUN
ejpam-5734	453	35	and	and	CCONJ
ejpam-5734	453	36	interaction	interaction	NOUN
ejpam-5734	453	37	among	among	ADP
ejpam-5734	453	38	spaces	space	NOUN
ejpam-5734	453	39	,	,	PUNCT
ejpam-5734	453	40	while	while	SCONJ
ejpam-5734	453	41	distance-2	distance-2	NUM
ejpam-5734	453	42	coloring	color	VERB
ejpam-5734	453	43	prevents	prevent	VERB
ejpam-5734	453	44	congestion	congestion	NOUN
ejpam-5734	453	45	or	or	CCONJ
ejpam-5734	453	46	overlap	overlap	NOUN
ejpam-5734	453	47	in	in	ADP
ejpam-5734	453	48	their	their	PRON
ejpam-5734	453	49	usage	usage	NOUN
ejpam-5734	453	50	.	.	PUNCT
ejpam-5734	454	1	these	these	DET
ejpam-5734	454	2	applications	application	NOUN
ejpam-5734	454	3	demonstrate	demonstrate	VERB
ejpam-5734	454	4	that	that	SCONJ
ejpam-5734	454	5	distance-2	distance-2	PRON
ejpam-5734	454	6	coloring	coloring	NOUN
ejpam-5734	454	7	is	be	AUX
ejpam-5734	454	8	not	not	PART
ejpam-5734	454	9	only	only	ADV
ejpam-5734	454	10	of	of	ADP
ejpam-5734	454	11	theoretical	theoretical	ADJ
ejpam-5734	454	12	interest	interest	NOUN
ejpam-5734	454	13	but	but	CCONJ
ejpam-5734	454	14	also	also	ADV
ejpam-5734	454	15	a	a	DET
ejpam-5734	454	16	powerful	powerful	ADJ
ejpam-5734	454	17	tool	tool	NOUN
ejpam-5734	454	18	in	in	ADP
ejpam-5734	454	19	designing	designing	NOUN
ejpam-5734	454	20	systems	system	NOUN
ejpam-5734	454	21	where	where	SCONJ
ejpam-5734	454	22	resources	resource	NOUN
ejpam-5734	454	23	must	must	AUX
ejpam-5734	454	24	be	be	AUX
ejpam-5734	454	25	distributed	distribute	VERB
ejpam-5734	454	26	efficiently	efficiently	ADV
ejpam-5734	454	27	without	without	ADP
ejpam-5734	454	28	conflict	conflict	NOUN
ejpam-5734	454	29	.	.	PUNCT
ejpam-5734	455	1	6	6	X
ejpam-5734	455	2	.	.	X
ejpam-5734	455	3	conclusion	conclusion	NOUN
ejpam-5734	455	4	and	and	CCONJ
ejpam-5734	455	5	recommendation	recommendation	NOUN
ejpam-5734	455	6	this	this	DET
ejpam-5734	455	7	study	study	NOUN
ejpam-5734	455	8	investigated	investigate	VERB
ejpam-5734	455	9	the	the	DET
ejpam-5734	455	10	distance-2	distance-2	NUM
ejpam-5734	455	11	chromatic	chromatic	ADJ
ejpam-5734	455	12	number	number	NOUN
ejpam-5734	455	13	of	of	ADP
ejpam-5734	455	14	the	the	DET
ejpam-5734	455	15	shadow	shadow	NOUN
ejpam-5734	455	16	and	and	CCONJ
ejpam-5734	455	17	central	central	ADJ
ejpam-5734	455	18	graphs	graph	NOUN
ejpam-5734	455	19	of	of	ADP
ejpam-5734	455	20	a	a	DET
ejpam-5734	455	21	cycle	cycle	NOUN
ejpam-5734	455	22	,	,	PUNCT
ejpam-5734	455	23	uncovering	uncover	VERB
ejpam-5734	455	24	their	their	PRON
ejpam-5734	455	25	distinct	distinct	ADJ
ejpam-5734	455	26	structural	structural	ADJ
ejpam-5734	455	27	properties	property	NOUN
ejpam-5734	455	28	and	and	CCONJ
ejpam-5734	455	29	coloring	coloring	NOUN
ejpam-5734	455	30	requirements	requirement	NOUN
ejpam-5734	455	31	.	.	PUNCT
ejpam-5734	456	1	for	for	ADP
ejpam-5734	456	2	the	the	DET
ejpam-5734	456	3	shadow	shadow	NOUN
ejpam-5734	456	4	graph	graph	NOUN
ejpam-5734	456	5	,	,	PUNCT
ejpam-5734	456	6	the	the	DET
ejpam-5734	456	7	duplication	duplication	NOUN
ejpam-5734	456	8	of	of	ADP
ejpam-5734	456	9	vertices	vertex	NOUN
ejpam-5734	456	10	introduces	introduce	NOUN
ejpam-5734	456	11	constraints	constraint	NOUN
ejpam-5734	456	12	that	that	PRON
ejpam-5734	456	13	demand	demand	VERB
ejpam-5734	456	14	a	a	DET
ejpam-5734	456	15	broader	broad	ADJ
ejpam-5734	456	16	spread	spread	NOUN
ejpam-5734	456	17	of	of	ADP
ejpam-5734	456	18	color	color	NOUN
ejpam-5734	456	19	assignments	assignment	NOUN
ejpam-5734	456	20	to	to	PART
ejpam-5734	456	21	avoid	avoid	VERB
ejpam-5734	456	22	conflicts	conflict	NOUN
ejpam-5734	456	23	within	within	ADP
ejpam-5734	456	24	two	two	NUM
ejpam-5734	456	25	steps	step	NOUN
ejpam-5734	456	26	,	,	PUNCT
ejpam-5734	456	27	reflecting	reflect	VERB
ejpam-5734	456	28	how	how	SCONJ
ejpam-5734	456	29	indirect	indirect	ADJ
ejpam-5734	456	30	connections	connection	NOUN
ejpam-5734	456	31	influence	influence	NOUN
ejpam-5734	456	32	partitioning	partitioning	NOUN
ejpam-5734	456	33	.	.	PUNCT
ejpam-5734	457	1	in	in	ADP
ejpam-5734	457	2	the	the	DET
ejpam-5734	457	3	central	central	ADJ
ejpam-5734	457	4	graph	graph	NOUN
ejpam-5734	457	5	,	,	PUNCT
ejpam-5734	457	6	the	the	DET
ejpam-5734	457	7	addition	addition	NOUN
ejpam-5734	457	8	of	of	ADP
ejpam-5734	457	9	central	central	ADJ
ejpam-5734	457	10	vertices	vertex	NOUN
ejpam-5734	457	11	between	between	ADP
ejpam-5734	457	12	adjacent	adjacent	ADJ
ejpam-5734	457	13	nodes	node	NOUN
ejpam-5734	457	14	increases	increase	VERB
ejpam-5734	457	15	connectivity	connectivity	NOUN
ejpam-5734	457	16	,	,	PUNCT
ejpam-5734	457	17	resulting	result	VERB
ejpam-5734	457	18	in	in	ADP
ejpam-5734	457	19	more	more	ADV
ejpam-5734	457	20	efficient	efficient	ADJ
ejpam-5734	457	21	groupings	grouping	NOUN
ejpam-5734	457	22	while	while	SCONJ
ejpam-5734	457	23	still	still	ADV
ejpam-5734	457	24	adhering	adhere	VERB
ejpam-5734	457	25	to	to	ADP
ejpam-5734	457	26	distance-2	distance-2	NUM
ejpam-5734	457	27	restrictions	restriction	NOUN
ejpam-5734	457	28	.	.	PUNCT
ejpam-5734	458	1	these	these	DET
ejpam-5734	458	2	theoretical	theoretical	ADJ
ejpam-5734	458	3	insights	insight	NOUN
ejpam-5734	458	4	were	be	AUX
ejpam-5734	458	5	further	far	ADV
ejpam-5734	458	6	illustrated	illustrate	VERB
ejpam-5734	458	7	through	through	ADP
ejpam-5734	458	8	resource	resource	NOUN
ejpam-5734	458	9	-	-	PUNCT
ejpam-5734	458	10	based	base	VERB
ejpam-5734	458	11	analogies	analogy	NOUN
ejpam-5734	458	12	:	:	PUNCT
ejpam-5734	458	13	the	the	DET
ejpam-5734	458	14	shadow	shadow	NOUN
ejpam-5734	458	15	graph	graph	VERB
ejpam-5734	458	16	modeled	model	VERB
ejpam-5734	458	17	resource	resource	NOUN
ejpam-5734	458	18	separation	separation	NOUN
ejpam-5734	458	19	across	across	ADP
ejpam-5734	458	20	twin	twin	ADJ
ejpam-5734	458	21	structures	structure	NOUN
ejpam-5734	458	22	,	,	PUNCT
ejpam-5734	458	23	while	while	SCONJ
ejpam-5734	458	24	the	the	DET
ejpam-5734	458	25	central	central	ADJ
ejpam-5734	458	26	graph	graph	NOUN
ejpam-5734	458	27	captured	capture	VERB
ejpam-5734	458	28	shared	share	VERB
ejpam-5734	458	29	access	access	NOUN
ejpam-5734	458	30	through	through	ADP
ejpam-5734	458	31	central	central	ADJ
ejpam-5734	458	32	facilities	facility	NOUN
ejpam-5734	458	33	such	such	ADJ
ejpam-5734	458	34	as	as	ADP
ejpam-5734	458	35	lounges	lounge	NOUN
ejpam-5734	458	36	or	or	CCONJ
ejpam-5734	458	37	comfort	comfort	NOUN
ejpam-5734	458	38	rooms	room	NOUN
ejpam-5734	458	39	.	.	PUNCT
ejpam-5734	459	1	overall	overall	ADV
ejpam-5734	459	2	,	,	PUNCT
ejpam-5734	459	3	the	the	DET
ejpam-5734	459	4	distance-2	distance-2	NUM
ejpam-5734	459	5	chromatic	chromatic	ADJ
ejpam-5734	459	6	number	number	NOUN
ejpam-5734	459	7	serves	serve	VERB
ejpam-5734	459	8	not	not	PART
ejpam-5734	459	9	only	only	ADV
ejpam-5734	459	10	as	as	ADP
ejpam-5734	459	11	a	a	DET
ejpam-5734	459	12	theoretical	theoretical	ADJ
ejpam-5734	459	13	measure	measure	NOUN
ejpam-5734	459	14	of	of	ADP
ejpam-5734	459	15	graph	graph	NOUN
ejpam-5734	459	16	complexity	complexity	NOUN
ejpam-5734	459	17	,	,	PUNCT
ejpam-5734	459	18	but	but	CCONJ
ejpam-5734	459	19	also	also	ADV
ejpam-5734	459	20	as	as	ADP
ejpam-5734	459	21	a	a	DET
ejpam-5734	459	22	practical	practical	ADJ
ejpam-5734	459	23	tool	tool	NOUN
ejpam-5734	459	24	for	for	ADP
ejpam-5734	459	25	designing	design	VERB
ejpam-5734	459	26	efficient	efficient	ADJ
ejpam-5734	459	27	,	,	PUNCT
ejpam-5734	459	28	conflict	conflict	NOUN
ejpam-5734	459	29	-	-	PUNCT
ejpam-5734	459	30	free	free	ADJ
ejpam-5734	459	31	resource	resource	NOUN
ejpam-5734	459	32	allocation	allocation	NOUN
ejpam-5734	459	33	systems	system	NOUN
ejpam-5734	459	34	in	in	ADP
ejpam-5734	459	35	structured	structured	ADJ
ejpam-5734	459	36	environments	environment	NOUN
ejpam-5734	459	37	.	.	PUNCT
ejpam-5734	460	1	given	give	VERB
ejpam-5734	460	2	the	the	DET
ejpam-5734	460	3	practical	practical	ADJ
ejpam-5734	460	4	importance	importance	NOUN
ejpam-5734	460	5	demonstrated	demonstrate	VERB
ejpam-5734	460	6	in	in	ADP
ejpam-5734	460	7	this	this	DET
ejpam-5734	460	8	study	study	NOUN
ejpam-5734	460	9	,	,	PUNCT
ejpam-5734	460	10	future	future	ADJ
ejpam-5734	460	11	research	research	NOUN
ejpam-5734	460	12	is	be	AUX
ejpam-5734	460	13	recommended	recommend	VERB
ejpam-5734	460	14	in	in	ADP
ejpam-5734	460	15	several	several	ADJ
ejpam-5734	460	16	directions	direction	NOUN
ejpam-5734	460	17	.	.	PUNCT
ejpam-5734	461	1	first	first	ADV
ejpam-5734	461	2	,	,	PUNCT
ejpam-5734	461	3	extending	extend	VERB
ejpam-5734	461	4	the	the	DET
ejpam-5734	461	5	analysis	analysis	NOUN
ejpam-5734	461	6	of	of	ADP
ejpam-5734	461	7	the	the	DET
ejpam-5734	461	8	distance-2	distance-2	NUM
ejpam-5734	461	9	chromatic	chromatic	ADJ
ejpam-5734	461	10	number	number	NOUN
ejpam-5734	461	11	to	to	ADP
ejpam-5734	461	12	other	other	ADJ
ejpam-5734	461	13	graph	graph	NOUN
ejpam-5734	461	14	families	family	NOUN
ejpam-5734	461	15	—	—	PUNCT
ejpam-5734	461	16	such	such	ADJ
ejpam-5734	461	17	as	as	ADP
ejpam-5734	461	18	trees	tree	NOUN
ejpam-5734	461	19	,	,	PUNCT
ejpam-5734	461	20	grid	grid	NOUN
ejpam-5734	461	21	graphs	graph	NOUN
ejpam-5734	461	22	,	,	PUNCT
ejpam-5734	461	23	and	and	CCONJ
ejpam-5734	461	24	bipartite	bipartite	ADJ
ejpam-5734	461	25	graphs	graph	NOUN
ejpam-5734	461	26	—	—	PUNCT
ejpam-5734	461	27	could	could	AUX
ejpam-5734	461	28	yield	yield	VERB
ejpam-5734	461	29	broader	broad	ADJ
ejpam-5734	461	30	insights	insight	NOUN
ejpam-5734	461	31	beneficial	beneficial	ADJ
ejpam-5734	461	32	to	to	ADP
ejpam-5734	461	33	various	various	ADJ
ejpam-5734	461	34	applications	application	NOUN
ejpam-5734	461	35	in	in	ADP
ejpam-5734	461	36	network	network	NOUN
ejpam-5734	461	37	topology	topology	NOUN
ejpam-5734	461	38	,	,	PUNCT
ejpam-5734	461	39	scheduling	scheduling	NOUN
ejpam-5734	461	40	,	,	PUNCT
ejpam-5734	461	41	and	and	CCONJ
ejpam-5734	461	42	distributed	distributed	ADJ
ejpam-5734	461	43	computing	computing	NOUN
ejpam-5734	461	44	.	.	PUNCT
ejpam-5734	462	1	second	second	ADJ
ejpam-5734	462	2	,	,	PUNCT
ejpam-5734	462	3	further	further	ADJ
ejpam-5734	462	4	exploration	exploration	NOUN
ejpam-5734	462	5	of	of	ADP
ejpam-5734	462	6	practical	practical	ADJ
ejpam-5734	462	7	constraints	constraint	NOUN
ejpam-5734	462	8	in	in	ADP
ejpam-5734	462	9	realworld	realworld	PROPN
ejpam-5734	462	10	implementations	implementation	NOUN
ejpam-5734	462	11	,	,	PUNCT
ejpam-5734	462	12	such	such	ADJ
ejpam-5734	462	13	as	as	ADP
ejpam-5734	462	14	dynamic	dynamic	ADJ
ejpam-5734	462	15	network	network	NOUN
ejpam-5734	462	16	conditions	condition	NOUN
ejpam-5734	462	17	or	or	CCONJ
ejpam-5734	462	18	varying	vary	VERB
ejpam-5734	462	19	resource	resource	NOUN
ejpam-5734	462	20	availability	availability	NOUN
ejpam-5734	462	21	,	,	PUNCT
ejpam-5734	462	22	could	could	AUX
ejpam-5734	462	23	provide	provide	VERB
ejpam-5734	462	24	deeper	deep	ADJ
ejpam-5734	462	25	insights	insight	NOUN
ejpam-5734	462	26	into	into	ADP
ejpam-5734	462	27	the	the	DET
ejpam-5734	462	28	robustness	robustness	NOUN
ejpam-5734	462	29	and	and	CCONJ
ejpam-5734	462	30	adaptability	adaptability	NOUN
ejpam-5734	462	31	of	of	ADP
ejpam-5734	462	32	distance-2	distance-2	PRON
ejpam-5734	462	33	coloring	color	VERB
ejpam-5734	462	34	.	.	PUNCT
ejpam-5734	463	1	finally	finally	ADV
ejpam-5734	463	2	,	,	PUNCT
ejpam-5734	463	3	empirical	empirical	ADJ
ejpam-5734	463	4	studies	study	NOUN
ejpam-5734	463	5	or	or	CCONJ
ejpam-5734	463	6	simulations	simulation	NOUN
ejpam-5734	463	7	in	in	ADP
ejpam-5734	463	8	collaboration	collaboration	NOUN
ejpam-5734	463	9	with	with	ADP
ejpam-5734	463	10	network	network	NOUN
ejpam-5734	463	11	engineers	engineer	NOUN
ejpam-5734	463	12	and	and	CCONJ
ejpam-5734	463	13	practitioners	practitioner	NOUN
ejpam-5734	463	14	are	be	AUX
ejpam-5734	463	15	highly	highly	ADV
ejpam-5734	463	16	recommended	recommend	VERB
ejpam-5734	463	17	to	to	PART
ejpam-5734	463	18	validate	validate	VERB
ejpam-5734	463	19	theoretical	theoretical	ADJ
ejpam-5734	463	20	predictions	prediction	NOUN
ejpam-5734	463	21	and	and	CCONJ
ejpam-5734	463	22	to	to	PART
ejpam-5734	463	23	further	far	ADV
ejpam-5734	463	24	bridge	bridge	VERB
ejpam-5734	463	25	the	the	DET
ejpam-5734	463	26	gap	gap	NOUN
ejpam-5734	463	27	between	between	ADP
ejpam-5734	463	28	graph	graph	NOUN
ejpam-5734	463	29	theory	theory	NOUN
ejpam-5734	463	30	research	research	NOUN
ejpam-5734	463	31	and	and	CCONJ
ejpam-5734	463	32	practical	practical	ADJ
ejpam-5734	463	33	network	network	NOUN
ejpam-5734	463	34	optimization	optimization	NOUN
ejpam-5734	463	35	.	.	PUNCT
ejpam-5734	464	1	acknowledgements	acknowledgement	NOUN
ejpam-5734	464	2	the	the	DET
ejpam-5734	464	3	authors	author	NOUN
ejpam-5734	464	4	would	would	AUX
ejpam-5734	464	5	like	like	VERB
ejpam-5734	464	6	to	to	PART
ejpam-5734	464	7	express	express	VERB
ejpam-5734	464	8	their	their	PRON
ejpam-5734	464	9	gratitude	gratitude	NOUN
ejpam-5734	464	10	todr	todr	ADV
ejpam-5734	464	11	.	.	PUNCT
ejpam-5734	465	1	esamel	esamel	PROPN
ejpam-5734	465	2	m.	m.	PROPN
ejpam-5734	465	3	paluga	paluga	PROPN
ejpam-5734	465	4	andms	andms	PROPN
ejpam-5734	465	5	.	.	PUNCT
ejpam-5734	466	1	airish	airish	PROPN
ejpam-5734	466	2	p.	p.	PROPN
ejpam-5734	466	3	jumonong	jumonong	NOUN
ejpam-5734	466	4	for	for	ADP
ejpam-5734	466	5	their	their	PRON
ejpam-5734	466	6	valuable	valuable	ADJ
ejpam-5734	466	7	critiques	critique	NOUN
ejpam-5734	466	8	and	and	CCONJ
ejpam-5734	466	9	recommendations	recommendation	NOUN
ejpam-5734	466	10	,	,	PUNCT
ejpam-5734	466	11	which	which	PRON
ejpam-5734	466	12	greatly	greatly	ADV
ejpam-5734	466	13	contributed	contribute	VERB
ejpam-5734	466	14	to	to	ADP
ejpam-5734	466	15	the	the	DET
ejpam-5734	466	16	refinement	refinement	NOUN
ejpam-5734	466	17	and	and	CCONJ
ejpam-5734	466	18	direction	direction	NOUN
ejpam-5734	466	19	of	of	ADP
ejpam-5734	466	20	this	this	DET
ejpam-5734	466	21	research	research	NOUN
ejpam-5734	466	22	.	.	PUNCT
ejpam-5734	467	1	references	reference	NOUN
ejpam-5734	467	2	[	[	X
ejpam-5734	467	3	1	1	NUM
ejpam-5734	467	4	]	]	PUNCT
ejpam-5734	467	5	norman	norman	PROPN
ejpam-5734	467	6	l.	l.	PROPN
ejpam-5734	467	7	biggs	biggs	PROPN
ejpam-5734	467	8	.	.	PUNCT
ejpam-5734	468	1	graph	graph	NOUN
ejpam-5734	468	2	theory	theory	NOUN
ejpam-5734	468	3	,	,	PUNCT
ejpam-5734	468	4	1736–1936	1736–1936	NUM
ejpam-5734	468	5	.	.	PUNCT
ejpam-5734	469	1	clarendon	clarendon	PROPN
ejpam-5734	469	2	press	press	PROPN
ejpam-5734	469	3	,	,	PUNCT
ejpam-5734	469	4	oxford	oxford	PROPN
ejpam-5734	469	5	,	,	PUNCT
ejpam-5734	469	6	uk	uk	PROPN
ejpam-5734	469	7	,	,	PUNCT
ejpam-5734	469	8	1976	1976	NUM
ejpam-5734	469	9	.	.	PUNCT
ejpam-5734	470	1	[	[	X
ejpam-5734	470	2	2	2	NUM
ejpam-5734	470	3	]	]	PUNCT
ejpam-5734	470	4	f.	f.	PROPN
ejpam-5734	470	5	harary	harary	PROPN
ejpam-5734	470	6	.	.	PUNCT
ejpam-5734	471	1	graph	graph	NOUN
ejpam-5734	471	2	theory	theory	NOUN
ejpam-5734	471	3	.	.	PUNCT
ejpam-5734	472	1	addison	addison	PROPN
ejpam-5734	472	2	-	-	PUNCT
ejpam-5734	472	3	wesley	wesley	PROPN
ejpam-5734	472	4	,	,	PUNCT
ejpam-5734	472	5	1969	1969	NUM
ejpam-5734	472	6	.	.	PUNCT
ejpam-5734	473	1	[	[	X
ejpam-5734	473	2	3	3	X
ejpam-5734	473	3	]	]	X
ejpam-5734	473	4	g.	g.	PROPN
ejpam-5734	473	5	chartrand	chartrand	PROPN
ejpam-5734	473	6	and	and	CCONJ
ejpam-5734	473	7	p.	p.	PROPN
ejpam-5734	473	8	zhang	zhang	PROPN
ejpam-5734	473	9	.	.	PUNCT
ejpam-5734	474	1	introduction	introduction	NOUN
ejpam-5734	474	2	to	to	AUX
ejpam-5734	474	3	graph	graph	NOUN
ejpam-5734	474	4	theory	theory	NOUN
ejpam-5734	474	5	.	.	PUNCT
ejpam-5734	475	1	mcgraw	mcgraw	PROPN
ejpam-5734	475	2	-	-	PUNCT
ejpam-5734	475	3	hill	hill	PROPN
ejpam-5734	475	4	,	,	PUNCT
ejpam-5734	475	5	5th	5th	ADJ
ejpam-5734	475	6	edition	edition	NOUN
ejpam-5734	475	7	,	,	PUNCT
ejpam-5734	475	8	2008	2008	NUM
ejpam-5734	475	9	.	.	PUNCT
ejpam-5734	476	1	m.	m.	PROPN
ejpam-5734	476	2	f.	f.	PROPN
ejpam-5734	476	3	libao	libao	PROPN
ejpam-5734	476	4	,	,	PUNCT
ejpam-5734	476	5	k.	k.	PROPN
ejpam-5734	476	6	b.	b.	PROPN
ejpam-5734	476	7	abarca	abarca	PROPN
ejpam-5734	476	8	/	/	SYM
ejpam-5734	476	9	eur	eur	PROPN
ejpam-5734	476	10	.	.	PUNCT
ejpam-5734	477	1	j.	j.	PROPN
ejpam-5734	477	2	pure	pure	PROPN
ejpam-5734	477	3	appl	appl	PROPN
ejpam-5734	477	4	.	.	PROPN
ejpam-5734	477	5	math	math	PROPN
ejpam-5734	477	6	,	,	PUNCT
ejpam-5734	477	7	18	18	NUM
ejpam-5734	477	8	(	(	PUNCT
ejpam-5734	477	9	2	2	NUM
ejpam-5734	477	10	)	)	PUNCT
ejpam-5734	477	11	(	(	PUNCT
ejpam-5734	477	12	2025	2025	NUM
ejpam-5734	477	13	)	)	PUNCT
ejpam-5734	477	14	,	,	PUNCT
ejpam-5734	477	15	5734	5734	NUM
ejpam-5734	477	16	25	25	NUM
ejpam-5734	477	17	of	of	ADP
ejpam-5734	477	18	25	25	NUM
ejpam-5734	477	19	[	[	SYM
ejpam-5734	477	20	4	4	NUM
ejpam-5734	477	21	]	]	PUNCT
ejpam-5734	477	22	k.	k.	PROPN
ejpam-5734	477	23	appel	appel	PROPN
ejpam-5734	477	24	and	and	CCONJ
ejpam-5734	477	25	w.	w.	PROPN
ejpam-5734	477	26	haken	haken	PROPN
ejpam-5734	477	27	.	.	PUNCT
ejpam-5734	478	1	every	every	DET
ejpam-5734	478	2	planar	planar	ADJ
ejpam-5734	478	3	map	map	NOUN
ejpam-5734	478	4	is	be	AUX
ejpam-5734	478	5	four	four	NUM
ejpam-5734	478	6	colorable	colorable	ADJ
ejpam-5734	478	7	:	:	PUNCT
ejpam-5734	478	8	part	part	PROPN
ejpam-5734	478	9	i.	i.	PROPN
ejpam-5734	478	10	discharging	discharging	PROPN
ejpam-5734	478	11	.	.	PUNCT
ejpam-5734	479	1	illinois	illinois	PROPN
ejpam-5734	479	2	journal	journal	PROPN
ejpam-5734	479	3	of	of	ADP
ejpam-5734	479	4	mathematics	mathematic	NOUN
ejpam-5734	479	5	,	,	PUNCT
ejpam-5734	479	6	21(3):429–490	21(3):429–490	NUM
ejpam-5734	479	7	,	,	PUNCT
ejpam-5734	479	8	1976	1976	NUM
ejpam-5734	479	9	.	.	PUNCT
ejpam-5734	480	1	[	[	X
ejpam-5734	480	2	5	5	NUM
ejpam-5734	480	3	]	]	PUNCT
ejpam-5734	480	4	a.	a.	NOUN
ejpam-5734	480	5	majeed	majeed	PROPN
ejpam-5734	480	6	and	and	CCONJ
ejpam-5734	480	7	i.	i.	PROPN
ejpam-5734	480	8	rauf	rauf	PROPN
ejpam-5734	480	9	.	.	PUNCT
ejpam-5734	481	1	graph	graph	NOUN
ejpam-5734	481	2	theory	theory	NOUN
ejpam-5734	481	3	:	:	PUNCT
ejpam-5734	481	4	a	a	DET
ejpam-5734	481	5	comprehensive	comprehensive	ADJ
ejpam-5734	481	6	survey	survey	NOUN
ejpam-5734	481	7	about	about	ADP
ejpam-5734	481	8	graph	graph	NOUN
ejpam-5734	481	9	theory	theory	NOUN
ejpam-5734	481	10	applications	application	NOUN
ejpam-5734	481	11	in	in	ADP
ejpam-5734	481	12	computer	computer	NOUN
ejpam-5734	481	13	science	science	NOUN
ejpam-5734	481	14	and	and	CCONJ
ejpam-5734	481	15	social	social	ADJ
ejpam-5734	481	16	networks	network	NOUN
ejpam-5734	481	17	.	.	PUNCT
ejpam-5734	482	1	inventions	invention	NOUN
ejpam-5734	482	2	,	,	PUNCT
ejpam-5734	482	3	5(1):10	5(1):10	NUM
ejpam-5734	482	4	,	,	PUNCT
ejpam-5734	482	5	2020	2020	NUM
ejpam-5734	482	6	.	.	PUNCT
ejpam-5734	483	1	[	[	X
ejpam-5734	483	2	6	6	NUM
ejpam-5734	483	3	]	]	PUNCT
ejpam-5734	483	4	a.	a.	NOUN
ejpam-5734	483	5	agrawal	agrawal	PROPN
ejpam-5734	483	6	,	,	PUNCT
ejpam-5734	483	7	s.	s.	PROPN
ejpam-5734	483	8	gupta	gupta	PROPN
ejpam-5734	483	9	,	,	PUNCT
ejpam-5734	483	10	and	and	CCONJ
ejpam-5734	483	11	p.	p.	PROPN
ejpam-5734	483	12	rao	rao	PROPN
ejpam-5734	483	13	.	.	PUNCT
ejpam-5734	484	1	square	square	ADJ
ejpam-5734	484	2	coloring	coloring	NOUN
ejpam-5734	484	3	of	of	ADP
ejpam-5734	484	4	graphs	graph	NOUN
ejpam-5734	484	5	with	with	ADP
ejpam-5734	484	6	bounded	bounded	ADJ
ejpam-5734	484	7	treewidth	treewidth	NOUN
ejpam-5734	484	8	.	.	PUNCT
ejpam-5734	485	1	journal	journal	NOUN
ejpam-5734	485	2	of	of	ADP
ejpam-5734	485	3	graph	graph	NOUN
ejpam-5734	485	4	theory	theory	NOUN
ejpam-5734	485	5	,	,	PUNCT
ejpam-5734	485	6	75(2):123–139	75(2):123–139	NOUN
ejpam-5734	485	7	,	,	PUNCT
ejpam-5734	485	8	2023	2023	NUM
ejpam-5734	485	9	.	.	PUNCT
ejpam-5734	486	1	[	[	X
ejpam-5734	486	2	7	7	X
ejpam-5734	486	3	]	]	X
ejpam-5734	486	4	v.	v.	CCONJ
ejpam-5734	486	5	ramachandran	ramachandran	PROPN
ejpam-5734	486	6	.	.	PUNCT
ejpam-5734	487	1	square	square	ADJ
ejpam-5734	487	2	coloring	coloring	NOUN
ejpam-5734	487	3	of	of	ADP
ejpam-5734	487	4	planar	planar	ADJ
ejpam-5734	487	5	graphs	graph	NOUN
ejpam-5734	487	6	.	.	PUNCT
ejpam-5734	488	1	discrete	discrete	ADJ
ejpam-5734	488	2	applied	apply	VERB
ejpam-5734	488	3	mathematics	mathematic	NOUN
ejpam-5734	488	4	,	,	PUNCT
ejpam-5734	488	5	6(4):285–294	6(4):285–294	NOUN
ejpam-5734	488	6	,	,	PUNCT
ejpam-5734	488	7	1978	1978	NUM
ejpam-5734	488	8	.	.	PUNCT
ejpam-5734	489	1	[	[	X
ejpam-5734	489	2	8	8	NUM
ejpam-5734	489	3	]	]	X
ejpam-5734	489	4	v.	v.	PROPN
ejpam-5734	489	5	i.	i.	PROPN
ejpam-5734	489	6	voloshin	voloshin	PROPN
ejpam-5734	489	7	.	.	PUNCT
ejpam-5734	490	1	graph	graph	NOUN
ejpam-5734	490	2	coloring	coloring	NOUN
ejpam-5734	490	3	and	and	CCONJ
ejpam-5734	490	4	its	its	PRON
ejpam-5734	490	5	generalizations	generalization	NOUN
ejpam-5734	490	6	,	,	PUNCT
ejpam-5734	490	7	volume	volume	NOUN
ejpam-5734	490	8	78	78	NUM
ejpam-5734	490	9	of	of	ADP
ejpam-5734	490	10	mathematical	mathematical	ADJ
ejpam-5734	490	11	surveys	survey	NOUN
ejpam-5734	490	12	and	and	CCONJ
ejpam-5734	490	13	monographs	monograph	NOUN
ejpam-5734	490	14	.	.	PUNCT
ejpam-5734	491	1	2010	2010	NUM
ejpam-5734	491	2	.	.	PUNCT
ejpam-5734	492	1	[	[	X
ejpam-5734	492	2	9	9	NUM
ejpam-5734	492	3	]	]	X
ejpam-5734	492	4	o.	o.	NOUN
ejpam-5734	492	5	v.	v.	ADP
ejpam-5734	492	6	borodin	borodin	PROPN
ejpam-5734	492	7	and	and	CCONJ
ejpam-5734	492	8	a.	a.	NOUN
ejpam-5734	492	9	o.	o.	PROPN
ejpam-5734	492	10	ivanova	ivanova	PROPN
ejpam-5734	492	11	.	.	PUNCT
ejpam-5734	493	1	distance-2	distance-2	PRON
ejpam-5734	493	2	coloring	coloring	NOUN
ejpam-5734	493	3	of	of	ADP
ejpam-5734	493	4	sparse	sparse	ADJ
ejpam-5734	493	5	graphs	graph	NOUN
ejpam-5734	493	6	:	:	PUNCT
ejpam-5734	493	7	a	a	DET
ejpam-5734	493	8	survey	survey	NOUN
ejpam-5734	493	9	.	.	PUNCT
ejpam-5734	494	1	discrete	discrete	ADJ
ejpam-5734	494	2	mathematics	mathematic	NOUN
ejpam-5734	494	3	,	,	PUNCT
ejpam-5734	494	4	309(16):3791–3796	309(16):3791–3796	NUM
ejpam-5734	494	5	,	,	PUNCT
ejpam-5734	494	6	2009	2009	NUM
ejpam-5734	494	7	.	.	PUNCT
ejpam-5734	495	1	[	[	X
ejpam-5734	495	2	10	10	NUM
ejpam-5734	495	3	]	]	PUNCT
ejpam-5734	495	4	j.	j.	PROPN
ejpam-5734	495	5	r.	r.	PROPN
ejpam-5734	495	6	griggs	griggs	PROPN
ejpam-5734	495	7	and	and	CCONJ
ejpam-5734	495	8	r.	r.	PROPN
ejpam-5734	495	9	k.	k.	PROPN
ejpam-5734	495	10	yeh	yeh	PROPN
ejpam-5734	495	11	.	.	PUNCT
ejpam-5734	496	1	labeling	labeling	NOUN
ejpam-5734	496	2	graphs	graph	NOUN
ejpam-5734	496	3	with	with	ADP
ejpam-5734	496	4	a	a	DET
ejpam-5734	496	5	condition	condition	NOUN
ejpam-5734	496	6	at	at	ADP
ejpam-5734	496	7	distance	distance	NOUN
ejpam-5734	496	8	two	two	NUM
ejpam-5734	496	9	.	.	PUNCT
ejpam-5734	497	1	siam	siam	PROPN
ejpam-5734	497	2	journal	journal	PROPN
ejpam-5734	497	3	on	on	ADP
ejpam-5734	497	4	discrete	discrete	ADJ
ejpam-5734	497	5	mathematics	mathematic	NOUN
ejpam-5734	497	6	,	,	PUNCT
ejpam-5734	497	7	5(4):586–595	5(4):586–595	NUM
ejpam-5734	497	8	,	,	PUNCT
ejpam-5734	497	9	1992	1992	NUM
ejpam-5734	497	10	.	.	PUNCT
ejpam-5734	498	1	[	[	X
ejpam-5734	498	2	11	11	NUM
ejpam-5734	498	3	]	]	X
ejpam-5734	498	4	f.	f.	PROPN
ejpam-5734	498	5	harary	harary	PROPN
ejpam-5734	498	6	and	and	CCONJ
ejpam-5734	498	7	s.	s.	PROPN
ejpam-5734	498	8	hedetniemi	hedetniemi	PROPN
ejpam-5734	498	9	.	.	PUNCT
ejpam-5734	499	1	the	the	DET
ejpam-5734	499	2	concept	concept	NOUN
ejpam-5734	499	3	of	of	ADP
ejpam-5734	499	4	shadow	shadow	NOUN
ejpam-5734	499	5	graphs	graph	NOUN
ejpam-5734	499	6	.	.	PUNCT
ejpam-5734	500	1	proceedings	proceeding	NOUN
ejpam-5734	500	2	of	of	ADP
ejpam-5734	500	3	the	the	DET
ejpam-5734	500	4	american	american	PROPN
ejpam-5734	500	5	mathematical	mathematical	PROPN
ejpam-5734	500	6	society	society	NOUN
ejpam-5734	500	7	,	,	PUNCT
ejpam-5734	500	8	26(1):31–34	26(1):31–34	NUM
ejpam-5734	500	9	,	,	PUNCT
ejpam-5734	500	10	1970	1970	NUM
ejpam-5734	500	11	.	.	PUNCT
ejpam-5734	501	1	[	[	X
ejpam-5734	501	2	12	12	NUM
ejpam-5734	501	3	]	]	X
ejpam-5734	501	4	e.	e.	PROPN
ejpam-5734	501	5	sampathkumar	sampathkumar	PROPN
ejpam-5734	501	6	and	and	CCONJ
ejpam-5734	501	7	h.	h.	PROPN
ejpam-5734	501	8	b.	b.	PROPN
ejpam-5734	501	9	walikar	walikar	PROPN
ejpam-5734	501	10	.	.	PUNCT
ejpam-5734	502	1	the	the	DET
ejpam-5734	502	2	central	central	ADJ
ejpam-5734	502	3	graph	graph	NOUN
ejpam-5734	502	4	of	of	ADP
ejpam-5734	502	5	a	a	DET
ejpam-5734	502	6	graph	graph	NOUN
ejpam-5734	502	7	.	.	PUNCT
ejpam-5734	503	1	in	in	ADP
ejpam-5734	503	2	proceedings	proceeding	NOUN
ejpam-5734	503	3	of	of	ADP
ejpam-5734	503	4	the	the	DET
ejpam-5734	503	5	indian	indian	PROPN
ejpam-5734	503	6	academy	academy	PROPN
ejpam-5734	503	7	of	of	ADP
ejpam-5734	503	8	sciences	sciences	PROPN
ejpam-5734	503	9	mathematical	mathematical	PROPN
ejpam-5734	503	10	sciences	sciences	PROPN
ejpam-5734	503	11	,	,	PUNCT
ejpam-5734	503	12	volume	volume	NOUN
ejpam-5734	503	13	80	80	NUM
ejpam-5734	503	14	,	,	PUNCT
ejpam-5734	503	15	pages	page	NOUN
ejpam-5734	503	16	1–13	1–13	NOUN
ejpam-5734	503	17	,	,	PUNCT
ejpam-5734	503	18	1974	1974	NUM
ejpam-5734	503	19	.	.	PUNCT
ejpam-5734	504	1	[	[	X
ejpam-5734	504	2	13	13	NUM
ejpam-5734	504	3	]	]	PUNCT
ejpam-5734	504	4	s.	s.	PROPN
ejpam-5734	504	5	ahmed	ahmed	PROPN
ejpam-5734	504	6	.	.	PUNCT
ejpam-5734	505	1	applications	application	NOUN
ejpam-5734	505	2	of	of	ADP
ejpam-5734	505	3	graph	graph	NOUN
ejpam-5734	505	4	coloring	color	VERB
ejpam-5734	505	5	in	in	ADP
ejpam-5734	505	6	modern	modern	ADJ
ejpam-5734	505	7	computer	computer	NOUN
ejpam-5734	505	8	science	science	NOUN
ejpam-5734	505	9	.	.	PUNCT
ejpam-5734	506	1	journal	journal	PROPN
ejpam-5734	506	2	of	of	ADP
ejpam-5734	506	3	computational	computational	ADJ
ejpam-5734	506	4	science	science	NOUN
ejpam-5734	506	5	,	,	PUNCT
ejpam-5734	506	6	36:100734	36:100734	NUM
ejpam-5734	506	7	,	,	PUNCT
ejpam-5734	506	8	2012	2012	NUM
ejpam-5734	506	9	.	.	PUNCT
ejpam-5734	507	1	[	[	X
ejpam-5734	507	2	14	14	NUM
ejpam-5734	507	3	]	]	X
ejpam-5734	507	4	r.	r.	PROPN
ejpam-5734	507	5	jain	jain	PROPN
ejpam-5734	507	6	and	and	CCONJ
ejpam-5734	507	7	a.	a.	PROPN
ejpam-5734	507	8	k.	k.	PROPN
ejpam-5734	507	9	jain	jain	PROPN
ejpam-5734	507	10	.	.	PUNCT
ejpam-5734	508	1	applications	application	NOUN
ejpam-5734	508	2	of	of	ADP
ejpam-5734	508	3	graph	graph	NOUN
ejpam-5734	508	4	theory	theory	NOUN
ejpam-5734	508	5	in	in	ADP
ejpam-5734	508	6	computer	computer	NOUN
ejpam-5734	508	7	science	science	NOUN
ejpam-5734	508	8	.	.	PUNCT
ejpam-5734	509	1	journal	journal	PROPN
ejpam-5734	509	2	of	of	ADP
ejpam-5734	509	3	open	open	ADJ
ejpam-5734	509	4	source	source	NOUN
ejpam-5734	509	5	developments	development	NOUN
ejpam-5734	509	6	,	,	PUNCT
ejpam-5734	509	7	10(3	10(3	NUM
ejpam-5734	509	8	)	)	PUNCT
ejpam-5734	509	9	,	,	PUNCT
ejpam-5734	509	10	2023	2023	NUM
ejpam-5734	509	11	.	.	PUNCT