id	sid	tid	token	lemma	pos
cana-4524	1	1	communications	communication	NOUN
cana-4524	1	2	on	on	ADP
cana-4524	1	3	applied	apply	VERB
cana-4524	1	4	nonlinear	nonlinear	ADJ
cana-4524	1	5	analysis	analysis	NOUN
cana-4524	1	6	issn	issn	NOUN
cana-4524	1	7	:	:	PUNCT
cana-4524	1	8	1074	1074	NUM
cana-4524	1	9	-	-	PUNCT
cana-4524	1	10	133x	133x	NUM
cana-4524	1	11	vol	vol	NOUN
cana-4524	1	12	32	32	NUM
cana-4524	1	13	no	no	NOUN
cana-4524	1	14	.	.	PUNCT
cana-4524	2	1	9s	9s	NUM
cana-4524	2	2	(	(	PUNCT
cana-4524	2	3	2025	2025	NUM
cana-4524	2	4	)	)	PUNCT
cana-4524	2	5	2370	2370	NUM
cana-4524	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	2	7	equitable	equitable	VERB
cana-4524	2	8	total	total	ADJ
cana-4524	2	9	coloring	coloring	NOUN
cana-4524	2	10	of	of	ADP
cana-4524	2	11	line	line	NOUN
cana-4524	2	12	graph	graph	NOUN
cana-4524	2	13	of	of	ADP
cana-4524	2	14	certain	certain	ADJ
cana-4524	2	15	graphs	graph	NOUN
cana-4524	2	16	r.	r.	PROPN
cana-4524	2	17	sudhakar1	sudhakar1	PROPN
cana-4524	2	18	,	,	PUNCT
cana-4524	2	19	g.	g.	PROPN
cana-4524	2	20	jayaraman2	jayaraman2	PROPN
cana-4524	3	1	*	*	PUNCT
cana-4524	3	2	,	,	PUNCT
cana-4524	4	1	a.	a.	NOUN
cana-4524	4	2	punitha3	punitha3	NOUN
cana-4524	4	3	and	and	CCONJ
cana-4524	4	4	r.	r.	PROPN
cana-4524	4	5	arasu4	arasu4	PROPN
cana-4524	5	1	123department	123department	PROPN
cana-4524	5	2	of	of	ADP
cana-4524	5	3	mathematics	mathematic	NOUN
cana-4524	5	4	,	,	PUNCT
cana-4524	5	5	vels	vels	PROPN
cana-4524	5	6	institute	institute	PROPN
cana-4524	5	7	of	of	ADP
cana-4524	5	8	science	science	NOUN
cana-4524	5	9	,	,	PUNCT
cana-4524	5	10	technology	technology	NOUN
cana-4524	5	11	and	and	CCONJ
cana-4524	5	12	advanced	advanced	ADJ
cana-4524	5	13	studies	study	NOUN
cana-4524	5	14	,	,	PUNCT
cana-4524	5	15	pallavaram	pallavaram	PROPN
cana-4524	5	16	,	,	PUNCT
cana-4524	5	17	chennai-117	chennai-117	NOUN
cana-4524	5	18	,	,	PUNCT
cana-4524	5	19	india	india	PROPN
cana-4524	5	20	4department	4department	NUM
cana-4524	5	21	of	of	ADP
cana-4524	5	22	mathematics	mathematic	NOUN
cana-4524	5	23	,	,	PUNCT
cana-4524	5	24	vel	vel	ADJ
cana-4524	5	25	tech	tech	ADJ
cana-4524	5	26	multi	multi	ADJ
cana-4524	5	27	-	-	ADJ
cana-4524	5	28	tech	tech	ADJ
cana-4524	5	29	dr	dr	PROPN
cana-4524	5	30	.	.	PROPN
cana-4524	5	31	rangarajan	rangarajan	PROPN
cana-4524	5	32	dr	dr	PROPN
cana-4524	5	33	.	.	PROPN
cana-4524	5	34	sakunthala	sakunthala	PROPN
cana-4524	5	35	engineering	engineering	PROPN
cana-4524	5	36	college	college	PROPN
cana-4524	5	37	,	,	PUNCT
cana-4524	5	38	chennai	chennai	VERB
cana-4524	5	39	600	600	NUM
cana-4524	5	40	062	062	NUM
cana-4524	5	41	,	,	PUNCT
cana-4524	5	42	india	india	PROPN
cana-4524	5	43	*	*	PUNCT
cana-4524	5	44	corresponding	correspond	VERB
cana-4524	5	45	author	author	NOUN
cana-4524	5	46	email	email	NOUN
cana-4524	5	47	:	:	PUNCT
cana-4524	5	48	jayaram07maths@gmail.com	jayaram07maths@gmail.com	X
cana-4524	5	49	article	article	NOUN
cana-4524	5	50	history	history	NOUN
cana-4524	5	51	:	:	PUNCT
cana-4524	5	52	received	receive	VERB
cana-4524	5	53	:	:	PUNCT
cana-4524	5	54	12	12	NUM
cana-4524	5	55	-	-	SYM
cana-4524	5	56	01	01	NUM
cana-4524	5	57	-	-	PUNCT
cana-4524	5	58	2025	2025	NUM
cana-4524	5	59	revised	revise	VERB
cana-4524	5	60	:	:	PUNCT
cana-4524	5	61	15	15	NUM
cana-4524	5	62	-	-	NUM
cana-4524	5	63	02	02	NUM
cana-4524	5	64	-	-	PUNCT
cana-4524	5	65	2025	2025	NUM
cana-4524	5	66	accepted	accept	VERB
cana-4524	5	67	:	:	PUNCT
cana-4524	5	68	01	01	NUM
cana-4524	5	69	-	-	SYM
cana-4524	5	70	03	03	NUM
cana-4524	5	71	-	-	PUNCT
cana-4524	5	72	2025	2025	NUM
cana-4524	5	73	abstract	abstract	NOUN
cana-4524	5	74	:	:	PUNCT
cana-4524	5	75	an	an	DET
cana-4524	5	76	equitable	equitable	ADJ
cana-4524	5	77	total	total	NOUN
cana-4524	5	78	-	-	PUNCT
cana-4524	5	79	coloring	coloring	NOUN
cana-4524	5	80	of	of	ADP
cana-4524	5	81	a	a	DET
cana-4524	5	82	graph	graph	NOUN
cana-4524	5	83	g	g	NOUN
cana-4524	5	84	is	be	AUX
cana-4524	5	85	a	a	DET
cana-4524	5	86	proper	proper	ADJ
cana-4524	5	87	total	total	NOUN
cana-4524	5	88	-	-	PUNCT
cana-4524	5	89	coloring	coloring	NOUN
cana-4524	5	90	such	such	ADJ
cana-4524	5	91	that	that	SCONJ
cana-4524	5	92	the	the	DET
cana-4524	5	93	number	number	NOUN
cana-4524	5	94	of	of	ADP
cana-4524	5	95	vertices	vertex	NOUN
cana-4524	5	96	and	and	CCONJ
cana-4524	5	97	edges	edge	NOUN
cana-4524	5	98	in	in	ADP
cana-4524	5	99	any	any	DET
cana-4524	5	100	two	two	NUM
cana-4524	5	101	color	color	NOUN
cana-4524	5	102	classes	class	NOUN
cana-4524	5	103	differ	differ	VERB
cana-4524	5	104	by	by	ADP
cana-4524	5	105	at	at	ADP
cana-4524	5	106	most	most	ADJ
cana-4524	5	107	one	one	NUM
cana-4524	5	108	.	.	PUNCT
cana-4524	6	1	in	in	ADP
cana-4524	6	2	this	this	DET
cana-4524	6	3	paper	paper	NOUN
cana-4524	6	4	,	,	PUNCT
cana-4524	6	5	we	we	PRON
cana-4524	6	6	determined	determine	VERB
cana-4524	6	7	the	the	DET
cana-4524	6	8	equitable	equitable	ADJ
cana-4524	6	9	total	total	ADJ
cana-4524	6	10	chromatic	chromatic	ADJ
cana-4524	6	11	number	number	NOUN
cana-4524	6	12	for	for	ADP
cana-4524	6	13	line	line	NOUN
cana-4524	6	14	graph	graph	NOUN
cana-4524	6	15	of	of	ADP
cana-4524	6	16	ladder	ladder	NOUN
cana-4524	6	17	,	,	PUNCT
cana-4524	6	18	slanting	slanting	NOUN
cana-4524	6	19	ladder	ladder	NOUN
cana-4524	6	20	,	,	PUNCT
cana-4524	6	21	triangular	triangular	NOUN
cana-4524	6	22	snake	snake	NOUN
cana-4524	6	23	,	,	PUNCT
cana-4524	6	24	alternate	alternate	ADJ
cana-4524	6	25	triangular	triangular	NOUN
cana-4524	6	26	snake	snake	NOUN
cana-4524	6	27	,	,	PUNCT
cana-4524	6	28	quadrilateral	quadrilateral	ADJ
cana-4524	6	29	snake	snake	NOUN
cana-4524	6	30	and	and	CCONJ
cana-4524	6	31	alternate	alternate	ADJ
cana-4524	6	32	quadrilateral	quadrilateral	ADJ
cana-4524	6	33	snake	snake	NOUN
cana-4524	6	34	introduction	introduction	NOUN
cana-4524	6	35	:	:	PUNCT
cana-4524	6	36	graph	graph	NOUN
cana-4524	6	37	coloring	coloring	NOUN
cana-4524	6	38	is	be	AUX
cana-4524	6	39	a	a	DET
cana-4524	6	40	fundamental	fundamental	ADJ
cana-4524	6	41	problem	problem	NOUN
cana-4524	6	42	in	in	ADP
cana-4524	6	43	graph	graph	NOUN
cana-4524	6	44	theory	theory	NOUN
cana-4524	6	45	with	with	ADP
cana-4524	6	46	applications	application	NOUN
cana-4524	6	47	in	in	ADP
cana-4524	6	48	scheduling	scheduling	NOUN
cana-4524	6	49	,	,	PUNCT
cana-4524	6	50	networking	networking	NOUN
cana-4524	6	51	,	,	PUNCT
cana-4524	6	52	and	and	CCONJ
cana-4524	6	53	resource	resource	NOUN
cana-4524	6	54	allocation	allocation	NOUN
cana-4524	6	55	.	.	PUNCT
cana-4524	7	1	a	a	DET
cana-4524	7	2	total	total	NOUN
cana-4524	7	3	-	-	PUNCT
cana-4524	7	4	coloring	coloring	NOUN
cana-4524	7	5	of	of	ADP
cana-4524	7	6	a	a	DET
cana-4524	7	7	graph	graph	NOUN
cana-4524	7	8	g	g	NOUN
cana-4524	7	9	is	be	AUX
cana-4524	7	10	an	an	DET
cana-4524	7	11	assignment	assignment	NOUN
cana-4524	7	12	of	of	ADP
cana-4524	7	13	colors	color	NOUN
cana-4524	7	14	to	to	ADP
cana-4524	7	15	both	both	DET
cana-4524	7	16	vertices	vertex	NOUN
cana-4524	7	17	and	and	CCONJ
cana-4524	7	18	edges	edge	VERB
cana-4524	7	19	such	such	ADJ
cana-4524	7	20	that	that	SCONJ
cana-4524	7	21	adjacent	adjacent	ADJ
cana-4524	7	22	vertices	vertex	NOUN
cana-4524	7	23	,	,	PUNCT
cana-4524	7	24	adjacent	adjacent	ADJ
cana-4524	7	25	edges	edge	NOUN
cana-4524	7	26	,	,	PUNCT
cana-4524	7	27	and	and	CCONJ
cana-4524	7	28	incident	incident	NOUN
cana-4524	7	29	vertex	vertex	NOUN
cana-4524	7	30	-	-	PUNCT
cana-4524	7	31	edge	edge	NOUN
cana-4524	7	32	pairs	pair	NOUN
cana-4524	7	33	receive	receive	VERB
cana-4524	7	34	distinct	distinct	ADJ
cana-4524	7	35	colors	color	NOUN
cana-4524	7	36	.	.	PUNCT
cana-4524	8	1	an	an	DET
cana-4524	8	2	equitable	equitable	ADJ
cana-4524	8	3	total	total	NOUN
cana-4524	8	4	-	-	PUNCT
cana-4524	8	5	coloring	coloring	NOUN
cana-4524	8	6	is	be	AUX
cana-4524	8	7	a	a	DET
cana-4524	8	8	special	special	ADJ
cana-4524	8	9	type	type	NOUN
cana-4524	8	10	of	of	ADP
cana-4524	8	11	total	total	NOUN
cana-4524	8	12	-	-	PUNCT
cana-4524	8	13	coloring	coloring	NOUN
cana-4524	8	14	where	where	SCONJ
cana-4524	8	15	the	the	DET
cana-4524	8	16	sizes	size	NOUN
cana-4524	8	17	of	of	ADP
cana-4524	8	18	any	any	DET
cana-4524	8	19	two	two	NUM
cana-4524	8	20	color	color	NOUN
cana-4524	8	21	classes	class	NOUN
cana-4524	8	22	differ	differ	VERB
cana-4524	8	23	by	by	ADP
cana-4524	8	24	at	at	ADP
cana-4524	8	25	most	most	ADJ
cana-4524	8	26	one	one	NUM
cana-4524	8	27	.	.	PUNCT
cana-4524	9	1	the	the	DET
cana-4524	9	2	equitable	equitable	ADJ
cana-4524	9	3	total	total	ADJ
cana-4524	9	4	chromatic	chromatic	ADJ
cana-4524	9	5	number	number	NOUN
cana-4524	9	6	,	,	PUNCT
cana-4524	9	7	denoted	denote	VERB
cana-4524	9	8	as	as	ADP
cana-4524	9	9	(	(	PUNCT
cana-4524	9	10	)	)	PUNCT
cana-4524	9	11	''	''	PUNCT
cana-4524	10	1	e	e	PROPN
cana-4524	10	2	g	g	NOUN
cana-4524	10	3	is	be	AUX
cana-4524	10	4	the	the	DET
cana-4524	10	5	minimum	minimum	ADJ
cana-4524	10	6	number	number	NOUN
cana-4524	10	7	of	of	ADP
cana-4524	10	8	colors	color	NOUN
cana-4524	10	9	required	require	VERB
cana-4524	10	10	for	for	ADP
cana-4524	10	11	such	such	DET
cana-4524	10	12	a	a	DET
cana-4524	10	13	coloring	coloring	NOUN
cana-4524	10	14	.	.	PUNCT
cana-4524	11	1	objectives	objective	NOUN
cana-4524	11	2	:	:	PUNCT
cana-4524	11	3	to	to	PART
cana-4524	11	4	establish	establish	VERB
cana-4524	11	5	the	the	DET
cana-4524	11	6	equitable	equitable	ADJ
cana-4524	11	7	total	total	ADJ
cana-4524	11	8	chromatic	chromatic	ADJ
cana-4524	11	9	number	number	NOUN
cana-4524	11	10	for	for	ADP
cana-4524	11	11	the	the	DET
cana-4524	11	12	line	line	NOUN
cana-4524	11	13	graph	graph	NOUN
cana-4524	11	14	of	of	ADP
cana-4524	11	15	specific	specific	ADJ
cana-4524	11	16	families	family	NOUN
cana-4524	11	17	of	of	ADP
cana-4524	11	18	structured	structured	ADJ
cana-4524	11	19	graphs	graph	NOUN
cana-4524	11	20	.	.	PUNCT
cana-4524	12	1	to	to	PART
cana-4524	12	2	develop	develop	VERB
cana-4524	12	3	systematic	systematic	ADJ
cana-4524	12	4	coloring	coloring	NOUN
cana-4524	12	5	techniques	technique	NOUN
cana-4524	12	6	for	for	ADP
cana-4524	12	7	achieving	achieve	VERB
cana-4524	12	8	an	an	DET
cana-4524	12	9	equitable	equitable	ADJ
cana-4524	12	10	total	total	ADJ
cana-4524	12	11	coloring	coloring	NOUN
cana-4524	12	12	of	of	ADP
cana-4524	12	13	these	these	DET
cana-4524	12	14	graphs	graph	NOUN
cana-4524	12	15	.	.	PUNCT
cana-4524	13	1	to	to	PART
cana-4524	13	2	contribute	contribute	VERB
cana-4524	13	3	to	to	ADP
cana-4524	13	4	the	the	DET
cana-4524	13	5	broader	broad	ADJ
cana-4524	13	6	study	study	NOUN
cana-4524	13	7	of	of	ADP
cana-4524	13	8	equitable	equitable	ADJ
cana-4524	13	9	colorings	coloring	NOUN
cana-4524	13	10	in	in	ADP
cana-4524	13	11	graph	graph	NOUN
cana-4524	13	12	theory	theory	NOUN
cana-4524	13	13	and	and	CCONJ
cana-4524	13	14	expand	expand	VERB
cana-4524	13	15	the	the	DET
cana-4524	13	16	known	know	VERB
cana-4524	13	17	results	result	NOUN
cana-4524	13	18	in	in	ADP
cana-4524	13	19	this	this	DET
cana-4524	13	20	domain	domain	NOUN
cana-4524	13	21	.	.	PUNCT
cana-4524	14	1	methods	method	NOUN
cana-4524	14	2	:	:	PUNCT
cana-4524	14	3	to	to	PART
cana-4524	14	4	determine	determine	VERB
cana-4524	14	5	the	the	DET
cana-4524	14	6	equitable	equitable	ADJ
cana-4524	14	7	total	total	ADJ
cana-4524	14	8	chromatic	chromatic	ADJ
cana-4524	14	9	number	number	NOUN
cana-4524	14	10	for	for	ADP
cana-4524	14	11	the	the	DET
cana-4524	14	12	line	line	NOUN
cana-4524	14	13	graphs	graph	NOUN
cana-4524	14	14	of	of	ADP
cana-4524	14	15	the	the	DET
cana-4524	14	16	given	give	VERB
cana-4524	14	17	graph	graph	NOUN
cana-4524	14	18	families	family	NOUN
cana-4524	14	19	,	,	PUNCT
cana-4524	14	20	we	we	PRON
cana-4524	14	21	employ	employ	VERB
cana-4524	14	22	the	the	DET
cana-4524	14	23	following	follow	VERB
cana-4524	14	24	methodology	methodology	NOUN
cana-4524	14	25	:	:	PUNCT
cana-4524	14	26	graph	graph	NOUN
cana-4524	14	27	construction	construction	NOUN
cana-4524	14	28	:	:	PUNCT
cana-4524	14	29	we	we	PRON
cana-4524	14	30	formally	formally	ADV
cana-4524	14	31	define	define	VERB
cana-4524	14	32	the	the	DET
cana-4524	14	33	structure	structure	NOUN
cana-4524	14	34	of	of	ADP
cana-4524	14	35	the	the	DET
cana-4524	14	36	ladder	ladder	NOUN
cana-4524	14	37	,	,	PUNCT
cana-4524	14	38	slanting	slanting	NOUN
cana-4524	14	39	ladder	ladder	NOUN
cana-4524	14	40	,	,	PUNCT
cana-4524	14	41	triangular	triangular	NOUN
cana-4524	14	42	snake	snake	NOUN
cana-4524	14	43	,	,	PUNCT
cana-4524	14	44	alternate	alternate	ADJ
cana-4524	14	45	triangular	triangular	NOUN
cana-4524	14	46	snake	snake	NOUN
cana-4524	14	47	,	,	PUNCT
cana-4524	14	48	quadrilateral	quadrilateral	ADJ
cana-4524	14	49	snake	snake	NOUN
cana-4524	14	50	,	,	PUNCT
cana-4524	14	51	and	and	CCONJ
cana-4524	14	52	alternate	alternate	ADJ
cana-4524	14	53	quadrilateral	quadrilateral	ADJ
cana-4524	14	54	snake	snake	NOUN
cana-4524	14	55	,	,	PUNCT
cana-4524	14	56	along	along	ADP
cana-4524	14	57	with	with	ADP
cana-4524	14	58	their	their	PRON
cana-4524	14	59	corresponding	correspond	VERB
cana-4524	14	60	line	line	NOUN
cana-4524	14	61	graphs	graph	NOUN
cana-4524	14	62	.	.	PUNCT
cana-4524	15	1	coloring	color	VERB
cana-4524	15	2	strategy	strategy	NOUN
cana-4524	15	3	:	:	PUNCT
cana-4524	15	4	we	we	PRON
cana-4524	15	5	apply	apply	VERB
cana-4524	15	6	systematic	systematic	ADJ
cana-4524	15	7	coloring	coloring	NOUN
cana-4524	15	8	techniques	technique	NOUN
cana-4524	15	9	ensuring	ensure	VERB
cana-4524	15	10	that	that	SCONJ
cana-4524	15	11	adjacent	adjacent	ADJ
cana-4524	15	12	vertices	vertex	NOUN
cana-4524	15	13	,	,	PUNCT
cana-4524	15	14	adjacent	adjacent	ADJ
cana-4524	15	15	edges	edge	NOUN
cana-4524	15	16	,	,	PUNCT
cana-4524	15	17	and	and	CCONJ
cana-4524	15	18	incident	incident	NOUN
cana-4524	15	19	vertex	vertex	NOUN
cana-4524	15	20	-	-	PUNCT
cana-4524	15	21	edge	edge	NOUN
cana-4524	15	22	pairs	pair	NOUN
cana-4524	15	23	receive	receive	VERB
cana-4524	15	24	different	different	ADJ
cana-4524	15	25	colors	color	NOUN
cana-4524	15	26	while	while	SCONJ
cana-4524	15	27	maintaining	maintain	VERB
cana-4524	15	28	equitable	equitable	ADJ
cana-4524	15	29	distribution	distribution	NOUN
cana-4524	15	30	of	of	ADP
cana-4524	15	31	color	color	NOUN
cana-4524	15	32	classes	class	NOUN
cana-4524	15	33	.	.	PUNCT
cana-4524	16	1	mathematical	mathematical	ADJ
cana-4524	16	2	analysis	analysis	NOUN
cana-4524	16	3	:	:	PUNCT
cana-4524	16	4	we	we	PRON
cana-4524	16	5	derive	derive	VERB
cana-4524	16	6	lower	low	ADJ
cana-4524	16	7	bounds	bound	NOUN
cana-4524	16	8	for	for	ADP
cana-4524	16	9	(	(	PUNCT
cana-4524	16	10	)	)	PUNCT
cana-4524	16	11	''	''	PUNCT
cana-4524	17	1	e	e	NOUN
cana-4524	17	2	g	g	VERB
cana-4524	17	3	and	and	CCONJ
cana-4524	17	4	establish	establish	VERB
cana-4524	17	5	its	its	PRON
cana-4524	17	6	exact	exact	ADJ
cana-4524	17	7	value	value	NOUN
cana-4524	17	8	using	use	VERB
cana-4524	17	9	combinatorial	combinatorial	ADJ
cana-4524	17	10	and	and	CCONJ
cana-4524	17	11	structural	structural	ADJ
cana-4524	17	12	properties	property	NOUN
cana-4524	17	13	of	of	ADP
cana-4524	17	14	the	the	DET
cana-4524	17	15	graphs	graph	NOUN
cana-4524	17	16	.	.	PUNCT
cana-4524	18	1	verification	verification	NOUN
cana-4524	18	2	and	and	CCONJ
cana-4524	18	3	proof	proof	NOUN
cana-4524	18	4	:	:	PUNCT
cana-4524	18	5	we	we	PRON
cana-4524	18	6	validate	validate	VERB
cana-4524	18	7	the	the	DET
cana-4524	18	8	obtained	obtain	VERB
cana-4524	18	9	chromatic	chromatic	ADJ
cana-4524	18	10	numbers	number	NOUN
cana-4524	18	11	through	through	ADP
cana-4524	18	12	case	case	NOUN
cana-4524	18	13	-	-	PUNCT
cana-4524	18	14	based	base	VERB
cana-4524	18	15	analysis	analysis	NOUN
cana-4524	18	16	and	and	CCONJ
cana-4524	18	17	,	,	PUNCT
cana-4524	18	18	where	where	SCONJ
cana-4524	18	19	applicable	applicable	ADJ
cana-4524	18	20	,	,	PUNCT
cana-4524	18	21	provide	provide	VERB
cana-4524	18	22	rigorous	rigorous	ADJ
cana-4524	18	23	proofs	proof	NOUN
cana-4524	18	24	for	for	ADP
cana-4524	18	25	correctness	correctness	NOUN
cana-4524	18	26	.	.	PUNCT
cana-4524	19	1	results	result	NOUN
cana-4524	19	2	:	:	PUNCT
cana-4524	19	3	the	the	DET
cana-4524	19	4	study	study	NOUN
cana-4524	19	5	successfully	successfully	ADV
cana-4524	19	6	determines	determine	VERB
cana-4524	19	7	the	the	DET
cana-4524	19	8	exact	exact	ADJ
cana-4524	19	9	value	value	NOUN
cana-4524	19	10	of	of	ADP
cana-4524	19	11	the	the	DET
cana-4524	19	12	equitable	equitable	ADJ
cana-4524	19	13	total	total	ADJ
cana-4524	19	14	chromatic	chromatic	ADJ
cana-4524	19	15	number	number	NOUN
cana-4524	19	16	for	for	ADP
cana-4524	19	17	the	the	DET
cana-4524	19	18	line	line	NOUN
cana-4524	19	19	graphs	graph	NOUN
cana-4524	19	20	of	of	ADP
cana-4524	19	21	the	the	DET
cana-4524	19	22	considered	consider	VERB
cana-4524	19	23	structured	structured	ADJ
cana-4524	19	24	graphs	graph	NOUN
cana-4524	19	25	.	.	PUNCT
cana-4524	20	1	the	the	DET
cana-4524	20	2	results	result	NOUN
cana-4524	20	3	provide	provide	VERB
cana-4524	20	4	new	new	ADJ
cana-4524	20	5	insights	insight	NOUN
cana-4524	20	6	into	into	ADP
cana-4524	20	7	the	the	DET
cana-4524	20	8	equitable	equitable	ADJ
cana-4524	20	9	total	total	NOUN
cana-4524	20	10	-	-	PUNCT
cana-4524	20	11	coloring	coloring	NOUN
cana-4524	20	12	of	of	ADP
cana-4524	20	13	line	line	NOUN
cana-4524	20	14	graphs	graph	NOUN
cana-4524	20	15	of	of	ADP
cana-4524	20	16	ladder	ladder	NOUN
cana-4524	20	17	-	-	PUNCT
cana-4524	20	18	based	base	VERB
cana-4524	20	19	and	and	CCONJ
cana-4524	20	20	snake	snake	NOUN
cana-4524	20	21	-	-	PUNCT
cana-4524	20	22	like	like	ADJ
cana-4524	20	23	structures	structure	NOUN
cana-4524	20	24	,	,	PUNCT
cana-4524	20	25	which	which	PRON
cana-4524	20	26	are	be	AUX
cana-4524	20	27	commonly	commonly	ADV
cana-4524	20	28	encountered	encounter	VERB
cana-4524	20	29	in	in	ADP
cana-4524	20	30	chemical	chemical	NOUN
cana-4524	20	31	graph	graph	NOUN
cana-4524	20	32	theory	theory	NOUN
cana-4524	20	33	and	and	CCONJ
cana-4524	20	34	network	network	NOUN
cana-4524	20	35	design	design	NOUN
cana-4524	20	36	problems	problem	NOUN
cana-4524	20	37	.	.	PUNCT
cana-4524	21	1	conclusions	conclusion	NOUN
cana-4524	21	2	:	:	PUNCT
cana-4524	21	3	this	this	DET
cana-4524	21	4	paper	paper	NOUN
cana-4524	21	5	establishes	establish	VERB
cana-4524	21	6	the	the	DET
cana-4524	21	7	equitable	equitable	ADJ
cana-4524	21	8	total	total	ADJ
cana-4524	21	9	chromatic	chromatic	ADJ
cana-4524	21	10	number	number	NOUN
cana-4524	21	11	for	for	ADP
cana-4524	21	12	the	the	DET
cana-4524	21	13	line	line	NOUN
cana-4524	21	14	mailto:jayaram07maths@gmail.com	mailto:jayaram07maths@gmail.com	X
cana-4524	22	1	communications	communication	NOUN
cana-4524	22	2	on	on	ADP
cana-4524	22	3	applied	apply	VERB
cana-4524	22	4	nonlinear	nonlinear	ADJ
cana-4524	22	5	analysis	analysis	NOUN
cana-4524	22	6	issn	issn	NOUN
cana-4524	22	7	:	:	PUNCT
cana-4524	22	8	1074	1074	NUM
cana-4524	22	9	-	-	PUNCT
cana-4524	22	10	133x	133x	NUM
cana-4524	22	11	vol	vol	NOUN
cana-4524	22	12	32	32	NUM
cana-4524	22	13	no	no	NOUN
cana-4524	22	14	.	.	PUNCT
cana-4524	23	1	9s	9s	NUM
cana-4524	23	2	(	(	PUNCT
cana-4524	23	3	2025	2025	NUM
cana-4524	23	4	)	)	PUNCT
cana-4524	23	5	2371	2371	NUM
cana-4524	24	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	24	2	graphs	graph	NOUN
cana-4524	24	3	of	of	ADP
cana-4524	24	4	several	several	ADJ
cana-4524	24	5	structured	structured	ADJ
cana-4524	24	6	graphs	graph	NOUN
cana-4524	24	7	,	,	PUNCT
cana-4524	24	8	contributing	contribute	VERB
cana-4524	24	9	to	to	ADP
cana-4524	24	10	the	the	DET
cana-4524	24	11	ongoing	ongoing	ADJ
cana-4524	24	12	research	research	NOUN
cana-4524	24	13	in	in	ADP
cana-4524	24	14	equitable	equitable	ADJ
cana-4524	24	15	colorings	coloring	NOUN
cana-4524	24	16	.	.	PUNCT
cana-4524	25	1	the	the	DET
cana-4524	25	2	findings	finding	NOUN
cana-4524	25	3	demonstrate	demonstrate	VERB
cana-4524	25	4	that	that	SCONJ
cana-4524	25	5	the	the	DET
cana-4524	25	6	structural	structural	ADJ
cana-4524	25	7	properties	property	NOUN
cana-4524	25	8	of	of	ADP
cana-4524	25	9	the	the	DET
cana-4524	25	10	base	base	NOUN
cana-4524	25	11	graphs	graph	NOUN
cana-4524	25	12	significantly	significantly	ADV
cana-4524	25	13	influence	influence	VERB
cana-4524	25	14	their	their	PRON
cana-4524	25	15	equitable	equitable	ADJ
cana-4524	25	16	total	total	ADJ
cana-4524	25	17	chromatic	chromatic	ADJ
cana-4524	25	18	numbers	number	NOUN
cana-4524	25	19	.	.	PUNCT
cana-4524	26	1	these	these	DET
cana-4524	26	2	results	result	NOUN
cana-4524	26	3	can	can	AUX
cana-4524	26	4	be	be	AUX
cana-4524	26	5	extended	extend	VERB
cana-4524	26	6	to	to	ADP
cana-4524	26	7	other	other	ADJ
cana-4524	26	8	classes	class	NOUN
cana-4524	26	9	of	of	ADP
cana-4524	26	10	graphs	graph	NOUN
cana-4524	26	11	,	,	PUNCT
cana-4524	26	12	and	and	CCONJ
cana-4524	26	13	future	future	ADJ
cana-4524	26	14	research	research	NOUN
cana-4524	26	15	may	may	AUX
cana-4524	26	16	explore	explore	VERB
cana-4524	26	17	algorithmic	algorithmic	ADJ
cana-4524	26	18	approaches	approach	NOUN
cana-4524	26	19	for	for	ADP
cana-4524	26	20	efficient	efficient	ADJ
cana-4524	26	21	equitable	equitable	ADJ
cana-4524	26	22	total	total	NOUN
cana-4524	26	23	-	-	PUNCT
cana-4524	26	24	coloring	coloring	NOUN
cana-4524	26	25	in	in	ADP
cana-4524	26	26	larger	large	ADJ
cana-4524	26	27	and	and	CCONJ
cana-4524	26	28	more	more	ADV
cana-4524	26	29	complex	complex	ADJ
cana-4524	26	30	graph	graph	NOUN
cana-4524	26	31	families	family	NOUN
cana-4524	26	32	keywords	keyword	NOUN
cana-4524	26	33	:	:	PUNCT
cana-4524	26	34	total	total	ADJ
cana-4524	26	35	coloring	coloring	NOUN
cana-4524	26	36	,	,	PUNCT
cana-4524	26	37	equitable	equitable	ADJ
cana-4524	26	38	total	total	ADJ
cana-4524	26	39	coloring	coloring	NOUN
cana-4524	26	40	,	,	PUNCT
cana-4524	26	41	line	line	NOUN
cana-4524	26	42	graph	graph	NOUN
cana-4524	26	43	,	,	PUNCT
cana-4524	26	44	ladder	ladder	NOUN
cana-4524	26	45	graphs	graph	NOUN
cana-4524	26	46	,	,	PUNCT
cana-4524	26	47	snake	snake	NOUN
cana-4524	26	48	graphs	graph	NOUN
cana-4524	26	49	.	.	PUNCT
cana-4524	27	1	1	1	X
cana-4524	27	2	.	.	X
cana-4524	27	3	introduction	introduction	NOUN
cana-4524	27	4	in	in	ADP
cana-4524	27	5	this	this	DET
cana-4524	27	6	paper	paper	NOUN
cana-4524	27	7	,	,	PUNCT
cana-4524	27	8	we	we	PRON
cana-4524	27	9	consider	consider	VERB
cana-4524	27	10	only	only	ADV
cana-4524	27	11	finite	finite	VERB
cana-4524	27	12	undirected	undirected	ADJ
cana-4524	27	13	graphs	graph	NOUN
cana-4524	27	14	without	without	ADP
cana-4524	27	15	loops	loop	NOUN
cana-4524	27	16	or	or	CCONJ
cana-4524	27	17	multiple	multiple	ADJ
cana-4524	27	18	edges	edge	NOUN
cana-4524	27	19	.	.	PUNCT
cana-4524	28	1	let	let	VERB
cana-4524	28	2	g	g	PROPN
cana-4524	28	3	=	=	SYM
cana-4524	28	4	(	(	PUNCT
cana-4524	28	5	v(g	v(g	PROPN
cana-4524	28	6	)	)	PUNCT
cana-4524	28	7	,	,	PUNCT
cana-4524	28	8	e(g	e(g	PROPN
cana-4524	28	9	)	)	PUNCT
cana-4524	28	10	)	)	PUNCT
cana-4524	29	1	be	be	AUX
cana-4524	29	2	a	a	DET
cana-4524	29	3	graph	graph	NOUN
cana-4524	29	4	with	with	ADP
cana-4524	29	5	vertex	vertex	NOUN
cana-4524	29	6	set	set	VERB
cana-4524	29	7	v	v	NOUN
cana-4524	29	8	(	(	PUNCT
cana-4524	29	9	g	g	NOUN
cana-4524	29	10	)	)	PUNCT
cana-4524	29	11	and	and	CCONJ
cana-4524	29	12	edge	edge	VERB
cana-4524	29	13	set	set	VERB
cana-4524	29	14	e(g	e(g	PROPN
cana-4524	29	15	)	)	PUNCT
cana-4524	29	16	.	.	PUNCT
cana-4524	30	1	the	the	DET
cana-4524	30	2	total	total	ADJ
cana-4524	30	3	coloring	coloring	NOUN
cana-4524	30	4	of	of	ADP
cana-4524	30	5	a	a	DET
cana-4524	30	6	graph	graph	NOUN
cana-4524	30	7	g	g	NOUN
cana-4524	30	8	is	be	AUX
cana-4524	30	9	an	an	DET
cana-4524	30	10	assignment	assignment	NOUN
cana-4524	30	11	of	of	ADP
cana-4524	30	12	colors	color	NOUN
cana-4524	30	13	to	to	ADP
cana-4524	30	14	both	both	CCONJ
cana-4524	30	15	the	the	DET
cana-4524	30	16	vertices	vertex	NOUN
cana-4524	30	17	and	and	CCONJ
cana-4524	30	18	edges	edge	NOUN
cana-4524	30	19	of	of	ADP
cana-4524	30	20	g	g	NOUN
cana-4524	30	21	,	,	PUNCT
cana-4524	30	22	such	such	ADJ
cana-4524	30	23	that	that	SCONJ
cana-4524	30	24	no	no	DET
cana-4524	30	25	two	two	NUM
cana-4524	30	26	adjacent	adjacent	ADJ
cana-4524	30	27	or	or	CCONJ
cana-4524	30	28	incident	incident	NOUN
cana-4524	30	29	vertices	vertex	NOUN
cana-4524	30	30	and	and	CCONJ
cana-4524	30	31	edges	edge	NOUN
cana-4524	30	32	of	of	ADP
cana-4524	30	33	g	g	NOUN
cana-4524	30	34	are	be	AUX
cana-4524	30	35	received	receive	VERB
cana-4524	30	36	the	the	DET
cana-4524	30	37	same	same	ADJ
cana-4524	30	38	colors	color	NOUN
cana-4524	30	39	.	.	PUNCT
cana-4524	31	1	they	they	PRON
cana-4524	31	2	both	both	PRON
cana-4524	31	3	conjectured	conjecture	VERB
cana-4524	31	4	that	that	SCONJ
cana-4524	31	5	for	for	ADP
cana-4524	31	6	any	any	DET
cana-4524	31	7	graph	graph	NOUN
cana-4524	31	8	g	g	ADP
cana-4524	31	9	the	the	DET
cana-4524	31	10	following	follow	VERB
cana-4524	31	11	inequality	inequality	NOUN
cana-4524	31	12	holds	hold	VERB
cana-4524	31	13	:	:	PUNCT
cana-4524	31	14	''	''	PUNCT
cana-4524	31	15	(	(	PUNCT
cana-4524	31	16	)	)	PUNCT
cana-4524	31	17	1	1	NUM
cana-4524	31	18	(	(	PUNCT
cana-4524	31	19	)	)	PUNCT
cana-4524	31	20	(	(	PUNCT
cana-4524	31	21	)	)	PUNCT
cana-4524	31	22	2	2	NUM
cana-4524	31	23	g	g	NOUN
cana-4524	31	24	g	g	PROPN
cana-4524	31	25	g	g	PROPN
cana-4524	31	26	+	+	CCONJ
cana-4524	31	27			NOUN
cana-4524	31	28			NOUN
cana-4524	31	29			PUNCT
cana-4524	32	1	+	+	CCONJ
cana-4524	32	2	,	,	PUNCT
cana-4524	32	3	where	where	SCONJ
cana-4524	32	4	(	(	PUNCT
cana-4524	32	5	)	)	PUNCT
cana-4524	32	6	g	g	PROPN
cana-4524	32	7	is	be	AUX
cana-4524	32	8	the	the	DET
cana-4524	32	9	maximum	maximum	ADJ
cana-4524	32	10	degree	degree	NOUN
cana-4524	32	11	of	of	ADP
cana-4524	32	12	g.	g.	PROPN
cana-4524	32	13	it	it	PRON
cana-4524	32	14	is	be	AUX
cana-4524	32	15	clear	clear	ADJ
cana-4524	33	1	that	that	SCONJ
cana-4524	33	2	(	(	PUNCT
cana-4524	33	3	)	)	PUNCT
cana-4524	33	4	1g	1g	NUM
cana-4524	33	5	+	+	CCONJ
cana-4524	33	6	is	be	AUX
cana-4524	33	7	the	the	DET
cana-4524	33	8	possible	possible	ADJ
cana-4524	33	9	lower	lower	ADV
cana-4524	33	10	bound	bind	VERB
cana-4524	33	11	.	.	PUNCT
cana-4524	34	1	in	in	ADP
cana-4524	34	2	1994	1994	NUM
cana-4524	34	3	,	,	PUNCT
cana-4524	34	4	fu	fu	NOUN
cana-4524	35	1	[	[	X
cana-4524	35	2	4	4	NUM
cana-4524	35	3	]	]	PUNCT
cana-4524	35	4	first	first	ADV
cana-4524	35	5	introduced	introduce	VERB
cana-4524	35	6	the	the	DET
cana-4524	35	7	concept	concept	NOUN
cana-4524	35	8	of	of	ADP
cana-4524	35	9	equitable	equitable	ADJ
cana-4524	35	10	total	total	ADJ
cana-4524	35	11	coloring	coloring	NOUN
cana-4524	35	12	and	and	CCONJ
cana-4524	35	13	the	the	DET
cana-4524	35	14	equitable	equitable	ADJ
cana-4524	35	15	total	total	ADJ
cana-4524	35	16	chromatic	chromatic	ADJ
cana-4524	35	17	number	number	NOUN
cana-4524	35	18	of	of	ADP
cana-4524	35	19	a	a	DET
cana-4524	35	20	graph	graph	NOUN
cana-4524	35	21	.	.	PUNCT
cana-4524	36	1	gong	gong	PROPN
cana-4524	36	2	kun	kun	PROPN
cana-4524	36	3	et.al	et.al	PROPN
cana-4524	37	1	[	[	X
cana-4524	37	2	3	3	NUM
cana-4524	37	3	]	]	PUNCT
cana-4524	37	4	proved	prove	VERB
cana-4524	37	5	some	some	DET
cana-4524	37	6	results	result	NOUN
cana-4524	37	7	on	on	ADP
cana-4524	37	8	the	the	DET
cana-4524	37	9	equitable	equitable	ADJ
cana-4524	37	10	total	total	ADJ
cana-4524	37	11	chromatic	chromatic	ADJ
cana-4524	37	12	number	number	NOUN
cana-4524	37	13	of	of	ADP
cana-4524	37	14	,	,	PUNCT
cana-4524	37	15	n	n	CCONJ
cana-4524	37	16	n	n	ADV
cana-4524	37	17	m	m	VERB
cana-4524	38	1	nw	nw	NOUN
cana-4524	38	2	k	k	PROPN
cana-4524	38	3	f	f	PROPN
cana-4524	38	4	k	k	PROPN
cana-4524	38	5			NOUN
cana-4524	38	6	and	and	CCONJ
cana-4524	38	7	m	m	VERB
cana-4524	38	8	ns	ns	ADJ
cana-4524	38	9	k	k	PROPN
cana-4524	38	10	.	.	PUNCT
cana-4524	39	1	jayaraman	jayaraman	PROPN
cana-4524	39	2	et	et	PROPN
cana-4524	39	3	al.[5	al.[5	PROPN
cana-4524	39	4	,	,	PUNCT
cana-4524	39	5	6	6	NUM
cana-4524	39	6	]	]	PUNCT
cana-4524	39	7	determined	determine	VERB
cana-4524	39	8	the	the	DET
cana-4524	39	9	equitable	equitable	ADJ
cana-4524	39	10	total	total	ADJ
cana-4524	39	11	chromatic	chromatic	ADJ
cana-4524	39	12	number	number	NOUN
cana-4524	39	13	for	for	ADP
cana-4524	39	14	the	the	DET
cana-4524	39	15	splitting	splitting	NOUN
cana-4524	39	16	midde	midde	NOUN
cana-4524	39	17	,	,	PUNCT
cana-4524	39	18	total	total	ADJ
cana-4524	39	19	graph	graph	NOUN
cana-4524	39	20	of	of	ADP
cana-4524	39	21	paths	path	NOUN
cana-4524	39	22	,	,	PUNCT
cana-4524	39	23	cycles	cycle	NOUN
cana-4524	39	24	and	and	CCONJ
cana-4524	39	25	splitting	splitting	NOUN
cana-4524	39	26	graph	graph	NOUN
cana-4524	39	27	of	of	ADP
cana-4524	39	28	star	star	NOUN
cana-4524	39	29	graphs	graph	NOUN
cana-4524	39	30	.	.	PUNCT
cana-4524	40	1	veninstine	veninstine	VERB
cana-4524	40	2	vivik	vivik	NOUN
cana-4524	40	3	et.al	et.al	ADJ
cana-4524	41	1	[	[	X
cana-4524	41	2	8	8	NUM
cana-4524	41	3	]	]	PUNCT
cana-4524	41	4	determining	determine	VERB
cana-4524	41	5	the	the	DET
cana-4524	41	6	equitable	equitable	ADJ
cana-4524	41	7	total	total	ADJ
cana-4524	41	8	chromatic	chromatic	ADJ
cana-4524	41	9	number	number	NOUN
cana-4524	41	10	for	for	ADP
cana-4524	41	11	wheel	wheel	NOUN
cana-4524	41	12	,	,	PUNCT
cana-4524	41	13	gear	gear	NOUN
cana-4524	41	14	,	,	PUNCT
cana-4524	41	15	helm	helm	NOUN
cana-4524	41	16	,	,	PUNCT
cana-4524	41	17	and	and	CCONJ
cana-4524	41	18	sunlet	sunlet	NOUN
cana-4524	41	19	graphs	graph	NOUN
cana-4524	41	20	.	.	PUNCT
cana-4524	42	1	gong	gong	PROPN
cana-4524	42	2	kun	kun	PROPN
cana-4524	42	3	et.al	et.al	PROPN
cana-4524	43	1	[	[	X
cana-4524	43	2	2	2	X
cana-4524	43	3	]	]	PUNCT
cana-4524	43	4	derived	derive	VERB
cana-4524	43	5	several	several	ADJ
cana-4524	43	6	findings	finding	NOUN
cana-4524	43	7	regarding	regard	VERB
cana-4524	43	8	the	the	DET
cana-4524	43	9	equitable	equitable	ADJ
cana-4524	43	10	total	total	ADJ
cana-4524	43	11	chromatic	chromatic	ADJ
cana-4524	43	12	number	number	NOUN
cana-4524	43	13	for	for	ADP
cana-4524	43	14	the	the	DET
cana-4524	43	15	graphs	graph	NOUN
cana-4524	43	16	,	,	PUNCT
cana-4524	43	17	n	n	CCONJ
cana-4524	43	18	n	n	CCONJ
cana-4524	43	19	n	n	ADV
cana-4524	43	20	nw	nw	NOUN
cana-4524	44	1	k	k	PROPN
cana-4524	44	2	f	f	PROPN
cana-4524	44	3	k	k	PROPN
cana-4524	44	4			NOUN
cana-4524	44	5	and	and	CCONJ
cana-4524	44	6	m	m	VERB
cana-4524	44	7	ns	ns	ADJ
cana-4524	44	8	k	k	PROPN
cana-4524	44	9	.	.	PUNCT
cana-4524	45	1	wang	wang	PROPN
cana-4524	45	2	et.al	et.al	PROPN
cana-4524	46	1	[	[	X
cana-4524	46	2	9	9	NUM
cana-4524	46	3	]	]	PUNCT
cana-4524	46	4	addressed	address	VERB
cana-4524	46	5	the	the	DET
cana-4524	46	6	equitable	equitable	ADJ
cana-4524	46	7	total	total	ADJ
cana-4524	46	8	coloring	coloring	NOUN
cana-4524	46	9	for	for	ADP
cana-4524	46	10	the	the	DET
cana-4524	46	11	graphs	graph	NOUN
cana-4524	46	12	with	with	ADP
cana-4524	46	13	a	a	DET
cana-4524	46	14	maximum	maximum	ADJ
cana-4524	46	15	degree	degree	NOUN
cana-4524	46	16	of	of	ADP
cana-4524	46	17	3	3	NUM
cana-4524	46	18	,	,	PUNCT
cana-4524	46	19	while	while	SCONJ
cana-4524	46	20	zhang	zhang	PROPN
cana-4524	46	21	zhongfu	zhongfu	PROPN
cana-4524	47	1	[	[	X
cana-4524	47	2	10	10	NUM
cana-4524	47	3	]	]	PUNCT
cana-4524	47	4	investigated	investigate	VERB
cana-4524	47	5	the	the	DET
cana-4524	47	6	equitable	equitable	ADJ
cana-4524	47	7	total	total	ADJ
cana-4524	47	8	coloring	coloring	NOUN
cana-4524	47	9	of	of	ADP
cana-4524	47	10	certain	certain	ADJ
cana-4524	47	11	join	join	NOUN
cana-4524	47	12	graphs	graph	NOUN
cana-4524	47	13	.	.	PUNCT
cana-4524	48	1	2	2	X
cana-4524	48	2	.	.	X
cana-4524	48	3	preliminaries	preliminary	NOUN
cana-4524	48	4	definition	definition	NOUN
cana-4524	48	5	2.1	2.1	NUM
cana-4524	48	6	.	.	PUNCT
cana-4524	49	1	the	the	DET
cana-4524	49	2	line	line	NOUN
cana-4524	49	3	graph	graph	NOUN
cana-4524	49	4	l(g	l(g	PROPN
cana-4524	49	5	)	)	PUNCT
cana-4524	49	6	is	be	AUX
cana-4524	49	7	defined	define	VERB
cana-4524	49	8	such	such	ADJ
cana-4524	49	9	that	that	SCONJ
cana-4524	49	10	its	its	PRON
cana-4524	49	11	vertices	vertex	NOUN
cana-4524	49	12	correspond	correspond	VERB
cana-4524	49	13	to	to	ADP
cana-4524	49	14	the	the	DET
cana-4524	49	15	edges	edge	NOUN
cana-4524	49	16	of	of	ADP
cana-4524	49	17	g	g	NOUN
cana-4524	49	18	,	,	PUNCT
cana-4524	49	19	and	and	CCONJ
cana-4524	49	20	two	two	NUM
cana-4524	49	21	vertices	vertex	NOUN
cana-4524	49	22	in	in	ADP
cana-4524	49	23	l(g	l(g	NOUN
cana-4524	49	24	)	)	PUNCT
cana-4524	49	25	are	be	AUX
cana-4524	49	26	adjacent	adjacent	ADJ
cana-4524	49	27	if	if	SCONJ
cana-4524	49	28	their	their	PRON
cana-4524	49	29	corresponding	corresponding	ADJ
cana-4524	49	30	edges	edge	NOUN
cana-4524	49	31	in	in	ADP
cana-4524	49	32	g	g	PROPN
cana-4524	49	33	share	share	NOUN
cana-4524	49	34	a	a	DET
cana-4524	49	35	common	common	ADJ
cana-4524	49	36	vertex	vertex	NOUN
cana-4524	49	37	.	.	PUNCT
cana-4524	50	1	definition	definition	NOUN
cana-4524	50	2	2.2	2.2	NUM
cana-4524	50	3	.	.	PUNCT
cana-4524	51	1	the	the	DET
cana-4524	51	2	ladder	ladder	NOUN
cana-4524	51	3	graph	graph	NOUN
cana-4524	51	4	formed	form	VERB
cana-4524	51	5	by	by	ADP
cana-4524	51	6	taking	take	VERB
cana-4524	51	7	two	two	NUM
cana-4524	51	8	parallel	parallel	ADJ
cana-4524	51	9	paths	path	NOUN
cana-4524	51	10	of	of	ADP
cana-4524	51	11	length	length	NOUN
cana-4524	51	12	and	and	CCONJ
cana-4524	51	13	connecting	connect	VERB
cana-4524	51	14	corresponding	corresponding	ADJ
cana-4524	51	15	vertices	vertex	NOUN
cana-4524	51	16	with	with	ADP
cana-4524	51	17	additional	additional	ADJ
cana-4524	51	18	edges	edge	NOUN
cana-4524	51	19	.	.	PUNCT
cana-4524	52	1	definition	definition	NOUN
cana-4524	52	2	2.3	2.3	NUM
cana-4524	52	3	.	.	PUNCT
cana-4524	53	1	the	the	DET
cana-4524	53	2	slanting	slanting	NOUN
cana-4524	53	3	ladder	ladder	NOUN
cana-4524	53	4	is	be	AUX
cana-4524	53	5	a	a	DET
cana-4524	53	6	graph	graph	NOUN
cana-4524	53	7	that	that	PRON
cana-4524	53	8	consists	consist	VERB
cana-4524	53	9	of	of	ADP
cana-4524	53	10	two	two	NUM
cana-4524	53	11	copies	copy	NOUN
cana-4524	53	12	of	of	ADP
cana-4524	53	13	having	have	VERB
cana-4524	53	14	vertex	vertex	NOUN
cana-4524	53	15	set	set	NOUN
cana-4524	53	16	and	and	CCONJ
cana-4524	53	17	the	the	DET
cana-4524	53	18	edge	edge	NOUN
cana-4524	53	19	set	set	NOUN
cana-4524	53	20	is	be	AUX
cana-4524	53	21	formed	form	VERB
cana-4524	53	22	by	by	ADP
cana-4524	53	23	adjoining	adjoining	NOUN
cana-4524	53	24	and	and	CCONJ
cana-4524	53	25	for	for	ADP
cana-4524	53	26	all	all	PRON
cana-4524	53	27	.	.	PUNCT
cana-4524	54	1	definition	definition	NOUN
cana-4524	54	2	2.4	2.4	NUM
cana-4524	54	3	.	.	PUNCT
cana-4524	55	1	a	a	DET
cana-4524	55	2	triangular	triangular	NOUN
cana-4524	55	3	snake	snake	NOUN
cana-4524	55	4	nt	not	PART
cana-4524	56	1	[	[	X
cana-4524	56	2	1	1	NUM
cana-4524	56	3	]	]	PUNCT
cana-4524	56	4	is	be	AUX
cana-4524	56	5	obtained	obtain	VERB
cana-4524	56	6	from	from	ADP
cana-4524	56	7	th	th	NUM
cana-4524	56	8	1	1	NUM
cana-4524	56	9	2	2	NUM
cana-4524	56	10	,	,	PUNCT
cana-4524	56	11	,	,	PUNCT
cana-4524	56	12	...	...	PUNCT
cana-4524	56	13	,	,	PUNCT
cana-4524	56	14	nv	nv	PROPN
cana-4524	56	15	v	v	NUM
cana-4524	56	16	v	v	NOUN
cana-4524	56	17	by	by	ADP
cana-4524	56	18	joining	join	VERB
cana-4524	56	19	iv	iv	PRON
cana-4524	56	20	and	and	CCONJ
cana-4524	56	21	1iv	1iv	ADJ
cana-4524	57	1	+	+	CCONJ
cana-4524	57	2	to	to	ADP
cana-4524	57	3	a	a	DET
cana-4524	57	4	new	new	ADJ
cana-4524	57	5	vertex	vertex	NOUN
cana-4524	57	6	iu	iu	ADP
cana-4524	57	7	for	for	ADP
cana-4524	57	8	1,2,3	1,2,3	NUM
cana-4524	57	9	,	,	PUNCT
cana-4524	57	10	....	....	PUNCT
cana-4524	57	11	,	,	PUNCT
cana-4524	57	12	1i	1i	NOUN
cana-4524	57	13	n=	n=	ADJ
cana-4524	57	14	−	−	PROPN
cana-4524	57	15	.	.	PUNCT
cana-4524	58	1	definition	definition	NOUN
cana-4524	58	2	2.5	2.5	NUM
cana-4524	58	3	.	.	PUNCT
cana-4524	59	1	an	an	DET
cana-4524	59	2	alternate	alternate	ADJ
cana-4524	59	3	triangular	triangular	NOUN
cana-4524	59	4	snake	snake	NOUN
cana-4524	59	5	nat	nat	NOUN
cana-4524	60	1	[	[	X
cana-4524	60	2	1	1	NUM
cana-4524	60	3	]	]	PUNCT
cana-4524	60	4	is	be	AUX
cana-4524	60	5	a	a	DET
cana-4524	60	6	graph	graph	NOUN
cana-4524	60	7	having	have	VERB
cana-4524	60	8	vertex	vertex	NOUN
cana-4524	60	9	and	and	CCONJ
cana-4524	60	10	edge	edge	NOUN
cana-4524	60	11	set	set	NOUN
cana-4524	60	12	(	(	PUNCT
cana-4524	60	13	)	)	PUNCT
cana-4524	60	14	{	{	PUNCT
cana-4524	60	15	:1	:1	PUNCT
cana-4524	60	16	}	}	PUNCT
cana-4524	60	17	:1	:1	PUNCT
cana-4524	60	18	2	2	NUM
cana-4524	60	19	m	m	NOUN
cana-4524	60	20	l	l	NOUN
cana-4524	60	21	l	l	NOUN
cana-4524	60	22	m	m	NOUN
cana-4524	60	23	v	v	NOUN
cana-4524	60	24	at	at	ADP
cana-4524	60	25	v	v	NUM
cana-4524	60	26	l	l	NOUN
cana-4524	60	27	m	m	VERB
cana-4524	60	28	u	u	NOUN
cana-4524	60	29	l	l	NOUN
cana-4524	60	30			NOUN
cana-4524	60	31			ADJ
cana-4524	60	32			NOUN
cana-4524	60	33	=	=	PUNCT
cana-4524	60	34			NOUN
cana-4524	60	35			NOUN
cana-4524	60	36			NOUN
cana-4524	60	37			VERB
cana-4524	60	38			ADJ
cana-4524	60	39			NOUN
cana-4524	60	40			VERB
cana-4524	60	41			NOUN
cana-4524	60	42			PROPN
cana-4524	60	43	and	and	CCONJ
cana-4524	60	44	nl	nl	PROPN
cana-4524	60	45	'	'	PUNCT
cana-4524	60	46	'	'	VERB
cana-4524	60	47	n	n	VERB
cana-4524	60	48	nsl	nsl	NOUN
cana-4524	61	1	np	np	INTJ
cana-4524	61	2	{	{	PUNCT
cana-4524	61	3	:1	:1	PUNCT
cana-4524	61	4	}	}	PUNCT
cana-4524	61	5	{	{	PUNCT
cana-4524	61	6	:1	:1	PUNCT
cana-4524	61	7	}	}	PUNCT
cana-4524	61	8	i	i	PRON
cana-4524	61	9	iu	iu	VERB
cana-4524	61	10	i	i	PROPN
cana-4524	61	11	n	n	PROPN
cana-4524	61	12	v	v	VERB
cana-4524	62	1	i	i	PRON
cana-4524	62	2	n	n	VERB
cana-4524	62	3			PROPN
cana-4524	62	4			NOUN
cana-4524	62	5			NOUN
cana-4524	62	6			NOUN
cana-4524	62	7	iu	iu	SCONJ
cana-4524	62	8	1iv	1iv	ADJ
cana-4524	62	9	+	+	CCONJ
cana-4524	62	10	1	1	NUM
cana-4524	62	11	1i	1i	NOUN
cana-4524	62	12	n	n	X
cana-4524	62	13			NOUN
cana-4524	62	14	−	−	PROPN
cana-4524	62	15	communications	communication	NOUN
cana-4524	62	16	on	on	ADP
cana-4524	62	17	applied	apply	VERB
cana-4524	62	18	nonlinear	nonlinear	ADJ
cana-4524	62	19	analysis	analysis	NOUN
cana-4524	62	20	issn	issn	NOUN
cana-4524	62	21	:	:	PUNCT
cana-4524	62	22	1074	1074	NUM
cana-4524	62	23	-	-	PUNCT
cana-4524	62	24	133x	133x	NUM
cana-4524	62	25	vol	vol	NOUN
cana-4524	62	26	32	32	NUM
cana-4524	62	27	no	no	NOUN
cana-4524	62	28	.	.	PUNCT
cana-4524	63	1	9s	9s	NUM
cana-4524	63	2	(	(	PUNCT
cana-4524	63	3	2025	2025	NUM
cana-4524	63	4	)	)	PUNCT
cana-4524	63	5	2372	2372	NUM
cana-4524	63	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	63	7	1	1	NUM
cana-4524	63	8	(	(	PUNCT
cana-4524	63	9	)	)	PUNCT
cana-4524	63	10	{	{	PUNCT
cana-4524	64	1	:1	:1	PUNCT
cana-4524	64	2	1}m	1}m	NUM
cana-4524	64	3	l	l	X
cana-4524	64	4	le	le	X
cana-4524	64	5	at	at	ADP
cana-4524	64	6	v	v	NUM
cana-4524	64	7	v	v	NOUN
cana-4524	64	8	l	l	NOUN
cana-4524	64	9	m+=	m+=	NOUN
cana-4524	64	10			NOUN
cana-4524	64	11			NOUN
cana-4524	64	12	−	−	NOUN
cana-4524	64	13	2	2	NUM
cana-4524	64	14	1	1	NUM
cana-4524	64	15	2:1	2:1	NUM
cana-4524	64	16	:1	:1	SYM
cana-4524	64	17	2	2	NUM
cana-4524	64	18	2	2	NUM
cana-4524	64	19	l	l	NOUN
cana-4524	64	20	l	l	NOUN
cana-4524	64	21	l	l	X
cana-4524	64	22	l	l	X
cana-4524	64	23	m	m	VERB
cana-4524	64	24	m	m	VERB
cana-4524	64	25	v	v	ADP
cana-4524	64	26	u	u	PROPN
cana-4524	64	27	l	l	NOUN
cana-4524	64	28	v	v	NOUN
cana-4524	64	29	u	u	NOUN
cana-4524	64	30	l−	l−	NOUN
cana-4524	64	31			ADV
cana-4524	65	1			NOUN
cana-4524	65	2			ADV
cana-4524	65	3			ADJ
cana-4524	65	4			PROPN
cana-4524	65	5			NOUN
cana-4524	65	6			NOUN
cana-4524	65	7			NOUN
cana-4524	65	8			NOUN
cana-4524	65	9			NOUN
cana-4524	65	10			VERB
cana-4524	65	11			ADP
cana-4524	65	12			PROPN
cana-4524	65	13			VERB
cana-4524	65	14			NOUN
cana-4524	65	15			NOUN
cana-4524	65	16			NOUN
cana-4524	65	17			NOUN
cana-4524	65	18			PROPN
cana-4524	65	19			VERB
cana-4524	65	20			NOUN
cana-4524	66	1			PROPN
cana-4524	66	2			PROPN
cana-4524	66	3			PROPN
cana-4524	66	4	definition	definition	NOUN
cana-4524	66	5	2.6	2.6	NUM
cana-4524	66	6	.	.	PUNCT
cana-4524	67	1	a	a	DET
cana-4524	67	2	quadrilateral	quadrilateral	ADJ
cana-4524	67	3	snake	snake	NOUN
cana-4524	67	4	q	q	PUNCT
cana-4524	68	1	[	[	X
cana-4524	68	2	7	7	NUM
cana-4524	68	3	]	]	PUNCT
cana-4524	68	4	is	be	AUX
cana-4524	68	5	obtained	obtain	VERB
cana-4524	68	6	from	from	ADP
cana-4524	68	7	a	a	DET
cana-4524	68	8	path	path	NOUN
cana-4524	68	9	by	by	ADP
cana-4524	68	10	replacing	replace	VERB
cana-4524	68	11	every	every	DET
cana-4524	68	12	edge	edge	NOUN
cana-4524	68	13	by	by	ADP
cana-4524	68	14	a	a	DET
cana-4524	68	15	cycle	cycle	NOUN
cana-4524	68	16	4.c	4.c	NUM
cana-4524	68	17	definition	definition	NOUN
cana-4524	68	18	2.7	2.7	NUM
cana-4524	68	19	.	.	PUNCT
cana-4524	69	1	an	an	DET
cana-4524	69	2	alternate	alternate	ADJ
cana-4524	69	3	quadrilateral	quadrilateral	ADJ
cana-4524	69	4	snake	snake	NOUN
cana-4524	69	5	aq	aq	NOUN
cana-4524	69	6	[	[	X
cana-4524	69	7	7	7	NUM
cana-4524	69	8	]	]	PUNCT
cana-4524	69	9	is	be	AUX
cana-4524	69	10	a	a	DET
cana-4524	69	11	graph	graph	NOUN
cana-4524	69	12	constructed	construct	VERB
cana-4524	69	13	from	from	ADP
cana-4524	69	14	a	a	DET
cana-4524	69	15	path	path	NOUN
cana-4524	69	16	p	p	NOUN
cana-4524	70	1	by	by	ADP
cana-4524	70	2	replacing	replace	VERB
cana-4524	70	3	every	every	DET
cana-4524	70	4	alternate	alternate	ADJ
cana-4524	70	5	edges	edge	NOUN
cana-4524	70	6	with	with	ADP
cana-4524	70	7	a	a	DET
cana-4524	70	8	quadrilateral	quadrilateral	ADJ
cana-4524	70	9	cycle	cycle	NOUN
cana-4524	70	10	4c	4c	NOUN
cana-4524	70	11	,	,	PUNCT
cana-4524	70	12	forming	form	VERB
cana-4524	70	13	a	a	DET
cana-4524	70	14	sequence	sequence	NOUN
cana-4524	70	15	of	of	ADP
cana-4524	70	16	interspersed	intersperse	VERB
cana-4524	70	17	4c	4c	NUM
cana-4524	70	18	cycles	cycle	NOUN
cana-4524	70	19	along	along	ADP
cana-4524	70	20	the	the	DET
cana-4524	70	21	path	path	NOUN
cana-4524	70	22	.	.	PUNCT
cana-4524	71	1	conjecture	conjecture	VERB
cana-4524	71	2	2.8([4	2.8([4	NOUN
cana-4524	71	3	]	]	PUNCT
cana-4524	71	4	)	)	PUNCT
cana-4524	71	5	.	.	PUNCT
cana-4524	72	1	for	for	ADP
cana-4524	72	2	any	any	DET
cana-4524	72	3	simple	simple	ADJ
cana-4524	72	4	graph	graph	NOUN
cana-4524	72	5	,	,	PUNCT
cana-4524	72	6	g	g	NOUN
cana-4524	72	7	''	''	PUNCT
cana-4524	72	8	(	(	PUNCT
cana-4524	72	9	)	)	PUNCT
cana-4524	72	10	(	(	PUNCT
cana-4524	72	11	)	)	PUNCT
cana-4524	72	12	2.e	2.e	PROPN
cana-4524	72	13	g	g	PROPN
cana-4524	72	14	g	g	NOUN
cana-4524	72	15			NOUN
cana-4524	72	16			PUNCT
cana-4524	73	1	+	+	NUM
cana-4524	73	2	conjecture	conjecture	NOUN
cana-4524	73	3	2.9([9	2.9([9	NOUN
cana-4524	73	4	]	]	X
cana-4524	73	5	)	)	PUNCT
cana-4524	73	6	.	.	PUNCT
cana-4524	74	1	for	for	ADP
cana-4524	74	2	every	every	DET
cana-4524	74	3	graph	graph	NOUN
cana-4524	74	4	g	g	NOUN
cana-4524	74	5	,	,	PUNCT
cana-4524	74	6	g	g	PROPN
cana-4524	74	7	has	have	VERB
cana-4524	74	8	an	an	DET
cana-4524	74	9	equitable	equitable	ADJ
cana-4524	74	10	total	total	ADJ
cana-4524	74	11	k	k	NOUN
cana-4524	74	12	-	-	NOUN
cana-4524	74	13	coloring	coloring	NOUN
cana-4524	74	14	for	for	ADP
cana-4524	74	15	each	each	DET
cana-4524	74	16	''	''	PUNCT
cana-4524	74	17	max	max	PROPN
cana-4524	74	18	{	{	PUNCT
cana-4524	74	19	(	(	PUNCT
cana-4524	74	20	)	)	PUNCT
cana-4524	74	21	,	,	PUNCT
cana-4524	74	22	(	(	PUNCT
cana-4524	74	23	)	)	PUNCT
cana-4524	74	24	2}k	2}k	NUM
cana-4524	74	25	g	g	PROPN
cana-4524	74	26	g	g	PROPN
cana-4524	74	27			X
cana-4524	75	1	+	+	NUM
cana-4524	75	2	.	.	X
cana-4524	76	1	3	3	X
cana-4524	76	2	.	.	NOUN
cana-4524	76	3	results	result	NOUN
cana-4524	76	4	and	and	CCONJ
cana-4524	76	5	discussion	discussion	NOUN
cana-4524	76	6	theorem	theorem	VERB
cana-4524	76	7	3.1	3.1	NUM
cana-4524	76	8	:	:	PUNCT
cana-4524	76	9	let	let	VERB
cana-4524	76	10	(	(	PUNCT
cana-4524	76	11	)	)	PUNCT
cana-4524	76	12	nl	nl	PROPN
cana-4524	76	13	l	l	PROPN
cana-4524	76	14	represent	represent	VERB
cana-4524	76	15	the	the	DET
cana-4524	76	16	line	line	NOUN
cana-4524	76	17	graph	graph	NOUN
cana-4524	76	18	of	of	ADP
cana-4524	76	19	a	a	DET
cana-4524	76	20	ladder	ladder	NOUN
cana-4524	76	21	graph	graph	NOUN
cana-4524	76	22	,	,	PUNCT
cana-4524	76	23	then	then	ADV
cana-4524	76	24	(	(	PUNCT
cana-4524	76	25	)	)	PUNCT
cana-4524	76	26	''	''	PUNCT
cana-4524	77	1	(	(	PUNCT
cana-4524	77	2	)	)	PUNCT
cana-4524	77	3	5.e	5.e	NUM
cana-4524	77	4	nl	nl	NOUN
cana-4524	77	5	l	l	NOUN
cana-4524	77	6	=	=	SYM
cana-4524	77	7	proof	proof	NOUN
cana-4524	77	8	:	:	PUNCT
cana-4524	77	9	let	let	VERB
cana-4524	77	10			PRON
cana-4524	77	11			VERB
cana-4524	77	12			PROPN
cana-4524	77	13			PROPN
cana-4524	77	14	'	'	PUNCT
cana-4524	77	15	(	(	PUNCT
cana-4524	77	16	(	(	PUNCT
cana-4524	77	17	)	)	PUNCT
cana-4524	77	18	)	)	PUNCT
cana-4524	77	19	,	,	PUNCT
cana-4524	77	20	:1	:1	PUNCT
cana-4524	77	21	1	1	NUM
cana-4524	77	22	:	:	PUNCT
cana-4524	77	23	1nv	1nv	ADJ
cana-4524	77	24	l	l	NOUN
cana-4524	77	25	l	l	X
cana-4524	77	26	u	u	NOUN
cana-4524	77	27	v	v	ADP
cana-4524	77	28	n	n	CCONJ
cana-4524	77	29	u	u	PROPN
cana-4524	77	30	n	n	NOUN
cana-4524	77	31			NOUN
cana-4524	77	32			NOUN
cana-4524	77	33	=	=	NOUN
cana-4524	77	34			NUM
cana-4524	77	35			NOUN
cana-4524	77	36	−	−	ADP
cana-4524	77	37			NOUN
cana-4524	77	38			NOUN
cana-4524	77	39	and	and	CCONJ
cana-4524	77	40			PROPN
cana-4524	77	41			PROPN
cana-4524	77	42			PROPN
cana-4524	77	43			PROPN
cana-4524	77	44	'	'	PUNCT
cana-4524	77	45	''	''	PUNCT
cana-4524	77	46	'	'	PUNCT
cana-4524	77	47	''	''	PUNCT
cana-4524	77	48	(	(	PUNCT
cana-4524	77	49	(	(	PUNCT
cana-4524	77	50	)	)	PUNCT
cana-4524	77	51	)	)	PUNCT
cana-4524	77	52	,	,	PUNCT
cana-4524	77	53	:1	:1	NUM
cana-4524	77	54	2	2	NUM
cana-4524	77	55	,	,	PUNCT
cana-4524	77	56	,	,	PUNCT
cana-4524	77	57	,	,	PUNCT
cana-4524	77	58	:1	:1	PUNCT
cana-4524	77	59	1ne	1ne	X
cana-4524	77	60	l	l	PUNCT
cana-4524	77	61	l	l	NOUN
cana-4524	77	62	e	e	X
cana-4524	77	63	f	f	PROPN
cana-4524	77	64	n	n	X
cana-4524	77	65	e	e	X
cana-4524	77	66	e	e	X
cana-4524	77	67	f	f	PROPN
cana-4524	77	68	f	f	PROPN
cana-4524	77	69	n	n	NOUN
cana-4524	77	70			NOUN
cana-4524	77	71			NOUN
cana-4524	77	72			NOUN
cana-4524	77	73			ADV
cana-4524	77	74			NOUN
cana-4524	77	75	=	=	NOUN
cana-4524	77	76			NUM
cana-4524	77	77			NOUN
cana-4524	77	78	−	−	ADP
cana-4524	77	79			NOUN
cana-4524	77	80			NOUN
cana-4524	77	81	−	−	NOUN
cana-4524	77	82	,	,	PUNCT
cana-4524	77	83	where	where	SCONJ
cana-4524	77	84	1,e	1,e	NUM
cana-4524	77	85	u	u	NOUN
cana-4524	77	86	u	u	NOUN
cana-4524	77	87			NOUN
cana-4524	77	88			NOUN
cana-4524	77	89	+	+	NOUN
cana-4524	77	90	=	=	X
cana-4524	77	91	'	'	PUNCT
cana-4524	77	92	'	'	PUNCT
cana-4524	77	93	,	,	PUNCT
cana-4524	77	94	e	e	X
cana-4524	77	95	u	u	X
cana-4524	77	96	u	u	PROPN
cana-4524	77	97			NOUN
cana-4524	77	98	=	=	NOUN
cana-4524	77	99	''	''	PUNCT
cana-4524	77	100	'	'	PUNCT
cana-4524	77	101	1,e	1,e	NUM
cana-4524	77	102	u	u	NOUN
cana-4524	77	103	u	u	NOUN
cana-4524	77	104			NOUN
cana-4524	77	105			NOUN
cana-4524	78	1	+	+	PROPN
cana-4524	78	2	=	=	X
cana-4524	78	3	1,f	1,f	NUM
cana-4524	78	4	v	v	ADP
cana-4524	78	5	v	v	PRON
cana-4524	78	6			NOUN
cana-4524	78	7			NOUN
cana-4524	78	8	+	+	NOUN
cana-4524	78	9	=	=	X
cana-4524	78	10	'	'	PUNCT
cana-4524	78	11	'	'	PUNCT
cana-4524	78	12	,	,	PUNCT
cana-4524	78	13	f	f	PROPN
cana-4524	78	14	u	u	NOUN
cana-4524	78	15	v	v	PROPN
cana-4524	78	16			NOUN
cana-4524	78	17	=	=	NOUN
cana-4524	78	18	''	''	PUNCT
cana-4524	78	19	'	'	PUNCT
cana-4524	78	20	1.f	1.f	NUM
cana-4524	78	21	v	v	X
cana-4524	78	22	u	u	PROPN
cana-4524	78	23			NOUN
cana-4524	78	24	+=	+=	NOUN
cana-4524	78	25	we	we	PRON
cana-4524	78	26	divide	divide	VERB
cana-4524	78	27	the	the	DET
cana-4524	78	28	vertex	vertex	NOUN
cana-4524	78	29	and	and	CCONJ
cana-4524	78	30	edge	edge	NOUN
cana-4524	78	31	set	set	NOUN
cana-4524	78	32	of	of	ADP
cana-4524	78	33	(	(	PUNCT
cana-4524	78	34	)	)	PUNCT
cana-4524	78	35	nl	nl	NOUN
cana-4524	78	36	l	l	NOUN
cana-4524	78	37	into	into	ADP
cana-4524	78	38	distinct	distinct	ADJ
cana-4524	78	39	partition	partition	NOUN
cana-4524	78	40	as	as	SCONJ
cana-4524	78	41	described	describe	VERB
cana-4524	78	42	below	below	ADV
cana-4524	78	43	.	.	PUNCT
cana-4524	79	1	for1	for1	VERB
cana-4524	79	2	1n	1n	NUM
cana-4524	79	3			NOUN
cana-4524	79	4	−	−	NOUN
cana-4524	79	5	.	.	PUNCT
cana-4524	79	6	'	'	PUNCT
cana-4524	79	7	'	'	PUNCT
cana-4524	79	8	'	'	PUNCT
cana-4524	79	9	'	'	PUNCT
cana-4524	79	10	'	'	PUNCT
cana-4524	79	11	'	'	PUNCT
cana-4524	79	12	4	4	NUM
cana-4524	79	13	9	9	NUM
cana-4524	79	14	5	5	NUM
cana-4524	79	15	1	1	NUM
cana-4524	79	16	2	2	NUM
cana-4524	79	17	7	7	NUM
cana-4524	79	18	5	5	NUM
cana-4524	79	19	3	3	NUM
cana-4524	79	20	1	1	NUM
cana-4524	79	21	6	6	NUM
cana-4524	79	22	5	5	NUM
cana-4524	79	23	4	4	NUM
cana-4524	79	24	5	5	NUM
cana-4524	79	25	10	10	NUM
cana-4524	79	26	5	5	NUM
cana-4524	79	27	2	2	NUM
cana-4524	79	28	7	7	NUM
cana-4524	79	29	5	5	NUM
cana-4524	79	30	3	3	NUM
cana-4524	79	31	1	1	NUM
cana-4524	79	32	''	''	PUNCT
cana-4524	79	33	''	''	PUNCT
cana-4524	79	34	''	''	PUNCT
cana-4524	79	35	'	'	PUNCT
cana-4524	79	36	'	'	PUNCT
cana-4524	79	37	'	'	PUNCT
cana-4524	79	38	''	''	PUNCT
cana-4524	79	39	''	''	PUNCT
cana-4524	79	40	''	''	PUNCT
cana-4524	79	41	3	3	NUM
cana-4524	79	42	8	8	NUM
cana-4524	79	43	5	5	NUM
cana-4524	79	44	2	2	NUM
cana-4524	79	45	5	5	NUM
cana-4524	79	46	10	10	NUM
cana-4524	79	47	5	5	NUM
cana-4524	79	48	3	3	NUM
cana-4524	79	49	8	8	NUM
cana-4524	79	50	5	5	NUM
cana-4524	79	51	2	2	NUM
cana-4524	79	52	4	4	NUM
cana-4524	79	53	9	9	NUM
cana-4524	79	54	5	5	NUM
cana-4524	79	55	1	1	NUM
cana-4524	79	56	{	{	PUNCT
cana-4524	79	57	,	,	PUNCT
cana-4524	79	58	,	,	PUNCT
cana-4524	79	59	...	...	PUNCT
cana-4524	79	60	,	,	PUNCT
cana-4524	79	61	}	}	PUNCT
cana-4524	79	62	{	{	PUNCT
cana-4524	79	63	,	,	PUNCT
cana-4524	79	64	,	,	PUNCT
cana-4524	79	65	...	...	PUNCT
cana-4524	79	66	,	,	PUNCT
cana-4524	79	67	}	}	PUNCT
cana-4524	79	68	{	{	PUNCT
cana-4524	79	69	,	,	PUNCT
cana-4524	79	70	,	,	PUNCT
cana-4524	79	71	...	...	PUNCT
cana-4524	79	72	,	,	PUNCT
cana-4524	79	73	}	}	PUNCT
cana-4524	79	74	{	{	PUNCT
cana-4524	79	75	,	,	PUNCT
cana-4524	79	76	,	,	PUNCT
cana-4524	79	77	...	...	PUNCT
cana-4524	79	78	,	,	PUNCT
cana-4524	79	79	}	}	PUNCT
cana-4524	79	80	{	{	PUNCT
cana-4524	79	81	,	,	PUNCT
cana-4524	79	82	,	,	PUNCT
cana-4524	79	83	...	...	PUNCT
cana-4524	79	84	,	,	PUNCT
cana-4524	79	85	}	}	PUNCT
cana-4524	79	86	{	{	PUNCT
cana-4524	79	87	,	,	PUNCT
cana-4524	79	88	,	,	PUNCT
cana-4524	79	89	...	...	PUNCT
cana-4524	79	90	,	,	PUNCT
cana-4524	79	91	}	}	PUNCT
cana-4524	79	92	{	{	PUNCT
cana-4524	79	93	,	,	PUNCT
cana-4524	79	94	,	,	PUNCT
cana-4524	79	95	...	...	PUNCT
cana-4524	79	96	,	,	PUNCT
cana-4524	79	97	}	}	PUNCT
cana-4524	79	98	{	{	PUNCT
cana-4524	79	99	,	,	PUNCT
cana-4524	79	100	,	,	PUNCT
cana-4524	79	101	...	...	PUNCT
cana-4524	79	102	,	,	PUNCT
cana-4524	79	103	}	}	PUNCT
cana-4524	79	104	{	{	PUNCT
cana-4524	79	105	,	,	PUNCT
cana-4524	79	106	,	,	PUNCT
cana-4524	79	107	...	...	PUNCT
cana-4524	79	108	,	,	PUNCT
cana-4524	79	109	}	}	PUNCT
cana-4524	79	110	u	u	NOUN
cana-4524	79	111	u	u	NOUN
cana-4524	79	112	u	u	NOUN
cana-4524	79	113	v	v	ADP
cana-4524	79	114	v	v	NUM
cana-4524	79	115	v	v	NOUN
cana-4524	79	116	u	u	NOUN
cana-4524	79	117	u	u	X
cana-4524	79	118	u	u	NOUN
cana-4524	79	119	e	e	X
cana-4524	79	120	e	e	X
cana-4524	79	121	e	e	X
cana-4524	79	122	e	e	X
cana-4524	79	123	e	e	X
cana-4524	79	124	e	e	X
cana-4524	79	125	t	t	NOUN
cana-4524	79	126	e	e	X
cana-4524	79	127	e	e	X
cana-4524	79	128	e	e	X
cana-4524	79	129	f	f	PROPN
cana-4524	80	1	f	f	PROPN
cana-4524	80	2	f	f	PROPN
cana-4524	81	1	f	f	PROPN
cana-4524	81	2	f	f	X
cana-4524	82	1	f	f	PROPN
cana-4524	82	2	f	f	PROPN
cana-4524	82	3	f	f	PROPN
cana-4524	82	4	f	f	PROPN
cana-4524	82	5			NOUN
cana-4524	82	6			NOUN
cana-4524	82	7			NOUN
cana-4524	82	8			NOUN
cana-4524	82	9			NOUN
cana-4524	82	10			NOUN
cana-4524	82	11			NOUN
cana-4524	82	12			NOUN
cana-4524	82	13			NOUN
cana-4524	82	14	−	−	PROPN
cana-4524	82	15	−	−	PROPN
cana-4524	82	16	−	−	PROPN
cana-4524	82	17	−	−	PROPN
cana-4524	82	18	−	−	PROPN
cana-4524	82	19	−	−	NOUN
cana-4524	82	20	−	−	NOUN
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cana-4524	82	22			ADP
cana-4524	82	23			NOUN
cana-4524	82	24			NUM
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cana-4524	82	27	'	'	PUNCT
cana-4524	82	28	'	'	PUNCT
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cana-4524	82	31	5	5	NUM
cana-4524	82	32	10	10	NUM
cana-4524	82	33	5	5	NUM
cana-4524	82	34	3	3	NUM
cana-4524	82	35	8	8	NUM
cana-4524	82	36	5	5	NUM
cana-4524	82	37	2	2	NUM
cana-4524	82	38	2	2	NUM
cana-4524	82	39	7	7	NUM
cana-4524	82	40	5	5	NUM
cana-4524	82	41	3	3	NUM
cana-4524	82	42	6	6	NUM
cana-4524	82	43	11	11	NUM
cana-4524	82	44	5	5	NUM
cana-4524	82	45	1	1	NUM
cana-4524	82	46	3	3	NUM
cana-4524	82	47	8	8	NUM
cana-4524	82	48	5	5	NUM
cana-4524	82	49	2	2	NUM
cana-4524	82	50	2	2	NUM
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cana-4524	82	52	''	''	PUNCT
cana-4524	82	53	''	''	PUNCT
cana-4524	82	54	'	'	PUNCT
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cana-4524	82	57	''	''	PUNCT
cana-4524	82	58	''	''	PUNCT
cana-4524	82	59	''	''	PUNCT
cana-4524	82	60	4	4	NUM
cana-4524	82	61	9	9	NUM
cana-4524	82	62	5	5	NUM
cana-4524	82	63	1	1	NUM
cana-4524	82	64	1	1	NUM
cana-4524	82	65	6	6	NUM
cana-4524	82	66	5	5	NUM
cana-4524	82	67	4	4	NUM
cana-4524	82	68	4	4	NUM
cana-4524	82	69	9	9	NUM
cana-4524	82	70	5	5	NUM
cana-4524	82	71	1	1	NUM
cana-4524	82	72	5	5	NUM
cana-4524	82	73	10	10	NUM
cana-4524	82	74	5	5	NUM
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cana-4524	82	79	,	,	PUNCT
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cana-4524	82	85	,	,	PUNCT
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cana-4524	82	129	u	u	NOUN
cana-4524	82	130	u	u	NOUN
cana-4524	82	131	u	u	NOUN
cana-4524	82	132	v	v	ADP
cana-4524	82	133	v	v	NUM
cana-4524	82	134	v	v	NOUN
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cana-4524	82	136	u	u	X
cana-4524	82	137	u	u	NOUN
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cana-4524	82	139	e	e	X
cana-4524	82	140	e	e	X
cana-4524	82	141	e	e	X
cana-4524	82	142	e	e	X
cana-4524	82	143	e	e	X
cana-4524	82	144	t	t	NOUN
cana-4524	82	145	e	e	X
cana-4524	82	146	e	e	X
cana-4524	82	147	e	e	X
cana-4524	82	148	f	f	PROPN
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cana-4524	84	2	f	f	PROPN
cana-4524	84	3	f	f	PROPN
cana-4524	84	4	f	f	PROPN
cana-4524	84	5	f	f	PROPN
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cana-4524	84	7			NOUN
cana-4524	84	8			NOUN
cana-4524	84	9			NOUN
cana-4524	84	10			NOUN
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cana-4524	84	12			NOUN
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cana-4524	84	14			NOUN
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cana-4524	84	16	−	−	PROPN
cana-4524	85	1	+	+	CCONJ
cana-4524	85	2	−	−	PROPN
cana-4524	85	3	−	−	NUM
cana-4524	85	4	−	−	NOUN
cana-4524	86	1	−	−	NOUN
cana-4524	86	2	=	=	SYM
cana-4524	86	3			ADP
cana-4524	86	4			NOUN
cana-4524	86	5			NUM
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cana-4524	86	7	'	'	PUNCT
cana-4524	86	8	'	'	PUNCT
cana-4524	86	9	'	'	PUNCT
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cana-4524	86	12	1	1	NUM
cana-4524	86	13	6	6	NUM
cana-4524	86	14	5	5	NUM
cana-4524	86	15	4	4	NUM
cana-4524	86	16	4	4	NUM
cana-4524	86	17	9	9	NUM
cana-4524	86	18	5	5	NUM
cana-4524	86	19	1	1	NUM
cana-4524	86	20	3	3	NUM
cana-4524	86	21	8	8	NUM
cana-4524	86	22	5	5	NUM
cana-4524	86	23	2	2	NUM
cana-4524	86	24	2	2	NUM
cana-4524	86	25	7	7	NUM
cana-4524	86	26	5	5	NUM
cana-4524	86	27	3	3	NUM
cana-4524	86	28	4	4	NUM
cana-4524	86	29	9	9	NUM
cana-4524	86	30	5	5	NUM
cana-4524	86	31	1	1	NUM
cana-4524	86	32	3	3	NUM
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cana-4524	86	34	''	''	PUNCT
cana-4524	86	35	''	''	PUNCT
cana-4524	86	36	'	'	PUNCT
cana-4524	86	37	'	'	PUNCT
cana-4524	86	38	'	'	PUNCT
cana-4524	86	39	''	''	PUNCT
cana-4524	86	40	''	''	PUNCT
cana-4524	86	41	''	''	PUNCT
cana-4524	86	42	5	5	NUM
cana-4524	86	43	10	10	NUM
cana-4524	86	44	5	5	NUM
cana-4524	86	45	2	2	NUM
cana-4524	86	46	7	7	NUM
cana-4524	86	47	5	5	NUM
cana-4524	86	48	3	3	NUM
cana-4524	86	49	5	5	NUM
cana-4524	86	50	10	10	NUM
cana-4524	86	51	5	5	NUM
cana-4524	86	52	1	1	NUM
cana-4524	86	53	6	6	NUM
cana-4524	86	54	5	5	NUM
cana-4524	86	55	4	4	NUM
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cana-4524	86	58	,	,	PUNCT
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cana-4524	86	60	,	,	PUNCT
cana-4524	86	61	}	}	PUNCT
cana-4524	86	62	{	{	PUNCT
cana-4524	86	63	,	,	PUNCT
cana-4524	86	64	,	,	PUNCT
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cana-4524	86	66	,	,	PUNCT
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cana-4524	86	70	,	,	PUNCT
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cana-4524	86	72	,	,	PUNCT
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cana-4524	86	78	,	,	PUNCT
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cana-4524	86	84	,	,	PUNCT
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cana-4524	86	90	,	,	PUNCT
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cana-4524	86	110	u	u	NOUN
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cana-4524	86	112	u	u	NOUN
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cana-4524	86	114	v	v	NUM
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cana-4524	86	117	u	u	X
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cana-4524	86	119	e	e	X
cana-4524	86	120	e	e	X
cana-4524	86	121	e	e	X
cana-4524	86	122	e	e	X
cana-4524	86	123	e	e	X
cana-4524	86	124	e	e	X
cana-4524	86	125	t	t	NOUN
cana-4524	86	126	e	e	X
cana-4524	86	127	e	e	X
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cana-4524	86	129	f	f	PROPN
cana-4524	86	130	f	f	PROPN
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cana-4524	88	2	f	f	PROPN
cana-4524	88	3	f	f	PROPN
cana-4524	88	4	f	f	PROPN
cana-4524	88	5	f	f	PROPN
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cana-4524	88	7			NOUN
cana-4524	88	8			NOUN
cana-4524	88	9			NOUN
cana-4524	88	10			NOUN
cana-4524	88	11			NOUN
cana-4524	88	12			NOUN
cana-4524	88	13			NOUN
cana-4524	88	14			NOUN
cana-4524	88	15	−	−	PROPN
cana-4524	88	16	−	−	PROPN
cana-4524	88	17	−	−	PROPN
cana-4524	88	18	−	−	PROPN
cana-4524	88	19	−	−	PROPN
cana-4524	88	20	−	−	NOUN
cana-4524	88	21	−	−	NOUN
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cana-4524	88	23			ADP
cana-4524	88	24			NOUN
cana-4524	88	25			NUM
cana-4524	88	26	'	'	PUNCT
cana-4524	88	27	'	'	PUNCT
cana-4524	88	28	'	'	PUNCT
cana-4524	88	29	'	'	PUNCT
cana-4524	88	30	'	'	PUNCT
cana-4524	88	31	'	'	NUM
cana-4524	88	32	2	2	NUM
cana-4524	88	33	7	7	NUM
cana-4524	88	34	5	5	NUM
cana-4524	88	35	3	3	NUM
cana-4524	88	36	5	5	NUM
cana-4524	88	37	10	10	NUM
cana-4524	88	38	5	5	NUM
cana-4524	88	39	4	4	NUM
cana-4524	88	40	9	9	NUM
cana-4524	88	41	5	5	NUM
cana-4524	88	42	1	1	NUM
cana-4524	88	43	3	3	NUM
cana-4524	88	44	8	8	NUM
cana-4524	88	45	5	5	NUM
cana-4524	88	46	2	2	NUM
cana-4524	88	47	5	5	NUM
cana-4524	88	48	10	10	NUM
cana-4524	88	49	5	5	NUM
cana-4524	88	50	4	4	NUM
cana-4524	88	51	''	''	PUNCT
cana-4524	88	52	''	''	PUNCT
cana-4524	88	53	''	''	PUNCT
cana-4524	88	54	'	'	PUNCT
cana-4524	88	55	'	'	PUNCT
cana-4524	88	56	'	'	PUNCT
cana-4524	88	57	''	''	PUNCT
cana-4524	88	58	''	''	PUNCT
cana-4524	88	59	''	''	PUNCT
cana-4524	88	60	1	1	NUM
cana-4524	88	61	6	6	NUM
cana-4524	88	62	5	5	NUM
cana-4524	88	63	4	4	NUM
cana-4524	88	64	3	3	NUM
cana-4524	88	65	8	8	NUM
cana-4524	88	66	5	5	NUM
cana-4524	88	67	2	2	NUM
cana-4524	88	68	1	1	NUM
cana-4524	88	69	6	6	NUM
cana-4524	88	70	5	5	NUM
cana-4524	88	71	4	4	NUM
cana-4524	88	72	2	2	NUM
cana-4524	88	73	7	7	NUM
cana-4524	88	74	5	5	NUM
cana-4524	88	75	3	3	NUM
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cana-4524	88	77	,	,	PUNCT
cana-4524	88	78	,	,	PUNCT
cana-4524	88	79	...	...	PUNCT
cana-4524	88	80	,	,	PUNCT
cana-4524	88	81	}	}	PUNCT
cana-4524	88	82	{	{	PUNCT
cana-4524	88	83	,	,	PUNCT
cana-4524	88	84	,	,	PUNCT
cana-4524	88	85	...	...	PUNCT
cana-4524	88	86	,	,	PUNCT
cana-4524	88	87	}	}	PUNCT
cana-4524	88	88	{	{	PUNCT
cana-4524	88	89	,	,	PUNCT
cana-4524	88	90	,	,	PUNCT
cana-4524	88	91	...	...	PUNCT
cana-4524	88	92	,	,	PUNCT
cana-4524	88	93	}	}	PUNCT
cana-4524	88	94	{	{	PUNCT
cana-4524	88	95	,	,	PUNCT
cana-4524	88	96	,	,	PUNCT
cana-4524	88	97	...	...	PUNCT
cana-4524	88	98	,	,	PUNCT
cana-4524	88	99	}	}	PUNCT
cana-4524	88	100	{	{	PUNCT
cana-4524	88	101	,	,	PUNCT
cana-4524	88	102	,	,	PUNCT
cana-4524	88	103	...	...	PUNCT
cana-4524	88	104	,	,	PUNCT
cana-4524	88	105	}	}	PUNCT
cana-4524	88	106	{	{	PUNCT
cana-4524	88	107	,	,	PUNCT
cana-4524	88	108	,	,	PUNCT
cana-4524	88	109	...	...	PUNCT
cana-4524	88	110	,	,	PUNCT
cana-4524	88	111	}	}	PUNCT
cana-4524	88	112	{	{	PUNCT
cana-4524	88	113	,	,	PUNCT
cana-4524	88	114	,	,	PUNCT
cana-4524	88	115	...	...	PUNCT
cana-4524	88	116	,	,	PUNCT
cana-4524	88	117	}	}	PUNCT
cana-4524	88	118	{	{	PUNCT
cana-4524	88	119	,	,	PUNCT
cana-4524	88	120	,	,	PUNCT
cana-4524	88	121	...	...	PUNCT
cana-4524	88	122	,	,	PUNCT
cana-4524	88	123	}	}	PUNCT
cana-4524	88	124	{	{	PUNCT
cana-4524	88	125	,	,	PUNCT
cana-4524	88	126	,	,	PUNCT
cana-4524	88	127	...	...	PUNCT
cana-4524	88	128	,	,	PUNCT
cana-4524	88	129	}	}	PUNCT
cana-4524	88	130	u	u	NOUN
cana-4524	88	131	u	u	NOUN
cana-4524	88	132	u	u	NOUN
cana-4524	88	133	v	v	ADP
cana-4524	88	134	v	v	NUM
cana-4524	88	135	v	v	NOUN
cana-4524	88	136	u	u	NOUN
cana-4524	88	137	u	u	X
cana-4524	88	138	u	u	NOUN
cana-4524	88	139	e	e	X
cana-4524	88	140	e	e	X
cana-4524	88	141	e	e	X
cana-4524	88	142	e	e	X
cana-4524	88	143	e	e	X
cana-4524	88	144	e	e	X
cana-4524	88	145	t	t	NOUN
cana-4524	88	146	e	e	X
cana-4524	88	147	e	e	X
cana-4524	88	148	e	e	X
cana-4524	88	149	f	f	PROPN
cana-4524	88	150	f	f	PROPN
cana-4524	89	1	f	f	PROPN
cana-4524	89	2	f	f	PROPN
cana-4524	90	1	f	f	X
cana-4524	90	2	f	f	PROPN
cana-4524	90	3	f	f	PROPN
cana-4524	90	4	f	f	PROPN
cana-4524	90	5	f	f	PROPN
cana-4524	90	6			NOUN
cana-4524	90	7			NOUN
cana-4524	90	8			NOUN
cana-4524	90	9			NOUN
cana-4524	90	10			NOUN
cana-4524	90	11			NOUN
cana-4524	90	12			NOUN
cana-4524	90	13			NOUN
cana-4524	90	14			NOUN
cana-4524	90	15	−	−	PROPN
cana-4524	90	16	−	−	PROPN
cana-4524	90	17	−	−	PROPN
cana-4524	90	18	−	−	PROPN
cana-4524	90	19	−	−	PROPN
cana-4524	90	20	−	−	NOUN
cana-4524	90	21	−	−	NOUN
cana-4524	90	22	=	=	SYM
cana-4524	90	23			ADP
cana-4524	90	24			NOUN
cana-4524	90	25			NUM
cana-4524	90	26	'	'	PUNCT
cana-4524	90	27	'	'	PUNCT
cana-4524	90	28	'	'	PUNCT
cana-4524	90	29	'	'	PUNCT
cana-4524	90	30	'	'	PUNCT
cana-4524	90	31	'	'	PUNCT
cana-4524	90	32	3	3	NUM
cana-4524	90	33	8	8	NUM
cana-4524	90	34	5	5	NUM
cana-4524	90	35	2	2	NUM
cana-4524	90	36	1	1	NUM
cana-4524	90	37	6	6	NUM
cana-4524	90	38	5	5	NUM
cana-4524	90	39	4	4	NUM
cana-4524	90	40	5	5	NUM
cana-4524	90	41	10	10	NUM
cana-4524	90	42	5	5	NUM
cana-4524	90	43	4	4	NUM
cana-4524	90	44	9	9	NUM
cana-4524	90	45	5	5	NUM
cana-4524	90	46	1	1	NUM
cana-4524	90	47	1	1	NUM
cana-4524	90	48	6	6	NUM
cana-4524	90	49	5	5	NUM
cana-4524	90	50	4	4	NUM
cana-4524	90	51	5	5	NUM
cana-4524	90	52	''	''	PUNCT
cana-4524	90	53	''	''	PUNCT
cana-4524	90	54	''	''	PUNCT
cana-4524	90	55	'	'	PUNCT
cana-4524	90	56	'	'	PUNCT
cana-4524	90	57	'	'	PUNCT
cana-4524	90	58	''	''	PUNCT
cana-4524	90	59	''	''	PUNCT
cana-4524	90	60	''	''	PUNCT
cana-4524	90	61	2	2	NUM
cana-4524	90	62	7	7	NUM
cana-4524	90	63	5	5	NUM
cana-4524	90	64	3	3	NUM
cana-4524	90	65	4	4	NUM
cana-4524	90	66	9	9	NUM
cana-4524	90	67	5	5	NUM
cana-4524	90	68	1	1	NUM
cana-4524	90	69	2	2	NUM
cana-4524	90	70	7	7	NUM
cana-4524	90	71	5	5	NUM
cana-4524	90	72	3	3	NUM
cana-4524	90	73	3	3	NUM
cana-4524	90	74	8	8	NUM
cana-4524	90	75	5	5	NUM
cana-4524	90	76	2	2	NUM
cana-4524	90	77	{	{	PUNCT
cana-4524	90	78	,	,	PUNCT
cana-4524	90	79	,	,	PUNCT
cana-4524	90	80	...	...	PUNCT
cana-4524	90	81	,	,	PUNCT
cana-4524	90	82	}	}	PUNCT
cana-4524	90	83	{	{	PUNCT
cana-4524	90	84	,	,	PUNCT
cana-4524	90	85	,	,	PUNCT
cana-4524	90	86	...	...	PUNCT
cana-4524	90	87	,	,	PUNCT
cana-4524	90	88	}	}	PUNCT
cana-4524	90	89	{	{	PUNCT
cana-4524	90	90	,	,	PUNCT
cana-4524	90	91	,	,	PUNCT
cana-4524	90	92	...	...	PUNCT
cana-4524	90	93	,	,	PUNCT
cana-4524	90	94	}	}	PUNCT
cana-4524	90	95	{	{	PUNCT
cana-4524	90	96	,	,	PUNCT
cana-4524	90	97	,	,	PUNCT
cana-4524	90	98	...	...	PUNCT
cana-4524	90	99	,	,	PUNCT
cana-4524	90	100	}	}	PUNCT
cana-4524	90	101	{	{	PUNCT
cana-4524	90	102	,	,	PUNCT
cana-4524	90	103	,	,	PUNCT
cana-4524	90	104	...	...	PUNCT
cana-4524	90	105	,	,	PUNCT
cana-4524	90	106	}	}	PUNCT
cana-4524	90	107	{	{	PUNCT
cana-4524	90	108	,	,	PUNCT
cana-4524	90	109	,	,	PUNCT
cana-4524	90	110	...	...	PUNCT
cana-4524	90	111	,	,	PUNCT
cana-4524	90	112	}	}	PUNCT
cana-4524	90	113	{	{	PUNCT
cana-4524	90	114	,	,	PUNCT
cana-4524	90	115	,	,	PUNCT
cana-4524	90	116	...	...	PUNCT
cana-4524	90	117	,	,	PUNCT
cana-4524	90	118	}	}	PUNCT
cana-4524	90	119	{	{	PUNCT
cana-4524	90	120	,	,	PUNCT
cana-4524	90	121	,	,	PUNCT
cana-4524	90	122	...	...	PUNCT
cana-4524	90	123	,	,	PUNCT
cana-4524	90	124	}	}	PUNCT
cana-4524	90	125	{	{	PUNCT
cana-4524	90	126	,	,	PUNCT
cana-4524	90	127	,	,	PUNCT
cana-4524	90	128	...	...	PUNCT
cana-4524	90	129	,	,	PUNCT
cana-4524	90	130	}	}	PUNCT
cana-4524	90	131	u	u	NOUN
cana-4524	90	132	u	u	NOUN
cana-4524	90	133	u	u	NOUN
cana-4524	90	134	v	v	ADP
cana-4524	90	135	v	v	NUM
cana-4524	90	136	v	v	NOUN
cana-4524	90	137	u	u	NOUN
cana-4524	90	138	u	u	X
cana-4524	90	139	u	u	NOUN
cana-4524	90	140	e	e	X
cana-4524	90	141	e	e	X
cana-4524	90	142	e	e	X
cana-4524	90	143	e	e	X
cana-4524	90	144	e	e	X
cana-4524	90	145	e	e	X
cana-4524	90	146	t	t	NOUN
cana-4524	90	147	e	e	X
cana-4524	90	148	e	e	X
cana-4524	90	149	e	e	X
cana-4524	90	150	f	f	PROPN
cana-4524	90	151	f	f	PROPN
cana-4524	91	1	f	f	PROPN
cana-4524	91	2	f	f	PROPN
cana-4524	92	1	f	f	X
cana-4524	92	2	f	f	PROPN
cana-4524	92	3	f	f	PROPN
cana-4524	92	4	f	f	PROPN
cana-4524	92	5	f	f	PROPN
cana-4524	92	6			NOUN
cana-4524	92	7			NOUN
cana-4524	92	8			NOUN
cana-4524	92	9			NOUN
cana-4524	92	10			NOUN
cana-4524	92	11			NOUN
cana-4524	92	12			NOUN
cana-4524	92	13			NOUN
cana-4524	92	14			NOUN
cana-4524	92	15	−	−	PROPN
cana-4524	92	16	−	−	PROPN
cana-4524	92	17	−	−	PROPN
cana-4524	92	18	−	−	PROPN
cana-4524	92	19	−	−	PROPN
cana-4524	92	20	−	−	PROPN
cana-4524	92	21	−	−	NOUN
cana-4524	92	22	−	−	NOUN
cana-4524	92	23	=	=	SYM
cana-4524	92	24			X
cana-4524	92	25			NOUN
cana-4524	92	26			NUM
cana-4524	92	27	based	base	VERB
cana-4524	92	28	on	on	ADP
cana-4524	92	29	the	the	DET
cana-4524	92	30	above	above	ADJ
cana-4524	92	31	procedure	procedure	NOUN
cana-4524	92	32	of	of	ADP
cana-4524	92	33	coloring	coloring	NOUN
cana-4524	92	34	,	,	PUNCT
cana-4524	92	35	it	it	PRON
cana-4524	92	36	is	be	AUX
cana-4524	92	37	evident	evident	ADJ
cana-4524	92	38	that	that	SCONJ
cana-4524	92	39	the	the	DET
cana-4524	92	40	color	color	NOUN
cana-4524	92	41	classes	class	NOUN
cana-4524	92	42	1	1	NUM
cana-4524	92	43	2	2	NUM
cana-4524	92	44	3	3	NUM
cana-4524	92	45	4	4	NUM
cana-4524	92	46	,	,	PUNCT
cana-4524	92	47	,	,	PUNCT
cana-4524	92	48	,	,	PUNCT
cana-4524	92	49	t	t	PROPN
cana-4524	92	50	t	t	PROPN
cana-4524	92	51	t	t	PROPN
cana-4524	92	52	t	t	PROPN
cana-4524	92	53	and	and	CCONJ
cana-4524	92	54	5	5	NUM
cana-4524	92	55	t	t	NOUN
cana-4524	92	56	are	be	AUX
cana-4524	92	57	independent	independent	ADJ
cana-4524	92	58	sets	set	NOUN
cana-4524	92	59	of	of	ADP
cana-4524	92	60	(	(	PUNCT
cana-4524	92	61	)	)	PUNCT
cana-4524	92	62	nl	nl	NOUN
cana-4524	92	63	l	l	NOUN
cana-4524	92	64	and	and	CCONJ
cana-4524	92	65	it	it	PRON
cana-4524	92	66	holds	hold	VERB
cana-4524	92	67	inequality	inequality	NOUN
cana-4524	93	1	|	|	ADV
cana-4524	94	1	|	|	ADV
cana-4524	94	2	|	|	ADV
cana-4524	94	3	|	|	ADV
cana-4524	94	4	1a	1a	VERB
cana-4524	94	5	bt	bt	VERB
cana-4524	94	6	t−	t−	PROPN
cana-4524	94	7			NOUN
cana-4524	94	8	for	for	ADP
cana-4524	94	9	a	a	DET
cana-4524	94	10	b	b	PROPN
cana-4524	94	11	.	.	PUNCT
cana-4524	95	1	this	this	PRON
cana-4524	95	2	implies	imply	VERB
cana-4524	95	3	that	that	SCONJ
cana-4524	95	4	communications	communication	NOUN
cana-4524	95	5	on	on	ADP
cana-4524	95	6	applied	apply	VERB
cana-4524	95	7	nonlinear	nonlinear	ADJ
cana-4524	95	8	analysis	analysis	NOUN
cana-4524	95	9	issn	issn	NOUN
cana-4524	95	10	:	:	PUNCT
cana-4524	95	11	1074	1074	NUM
cana-4524	95	12	-	-	PUNCT
cana-4524	95	13	133x	133x	NUM
cana-4524	95	14	vol	vol	NOUN
cana-4524	95	15	32	32	NUM
cana-4524	95	16	no	no	NOUN
cana-4524	95	17	.	.	PUNCT
cana-4524	96	1	9s	9s	NUM
cana-4524	96	2	(	(	PUNCT
cana-4524	96	3	2025	2025	NUM
cana-4524	96	4	)	)	PUNCT
cana-4524	96	5	2373	2373	NUM
cana-4524	96	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	96	7	(	(	PUNCT
cana-4524	96	8	)	)	PUNCT
cana-4524	96	9	''	''	PUNCT
cana-4524	97	1	(	(	PUNCT
cana-4524	97	2	)	)	PUNCT
cana-4524	97	3	5e	5e	NOUN
cana-4524	97	4	nl	nl	NOUN
cana-4524	97	5	l	l	VERB
cana-4524	97	6			NOUN
cana-4524	97	7	.	.	PUNCT
cana-4524	98	1	further	far	ADV
cana-4524	98	2	,	,	PUNCT
cana-4524	98	3	since	since	SCONJ
cana-4524	98	4	4	4	NUM
cana-4524	98	5	=	=	PRON
cana-4524	98	6	,	,	PUNCT
cana-4524	98	7	we	we	PRON
cana-4524	98	8	have	have	AUX
cana-4524	98	9	(	(	PUNCT
cana-4524	98	10	)	)	PUNCT
cana-4524	98	11	(	(	PUNCT
cana-4524	98	12	)	)	PUNCT
cana-4524	98	13	''	''	PUNCT
cana-4524	98	14	"	"	PUNCT
cana-4524	98	15	(	(	PUNCT
cana-4524	98	16	)	)	PUNCT
cana-4524	98	17	(	(	PUNCT
cana-4524	98	18	)	)	PUNCT
cana-4524	98	19	1	1	NUM
cana-4524	98	20	4	4	NUM
cana-4524	98	21	1	1	NUM
cana-4524	98	22	5e	5e	NOUN
cana-4524	98	23	n	n	PRON
cana-4524	98	24	nl	nl	NOUN
cana-4524	98	25	l	l	NOUN
cana-4524	98	26	l	l	NOUN
cana-4524	98	27	l	l	X
cana-4524	98	28	=	=	PROPN
cana-4524	98	29			NUM
cana-4524	98	30	+	+	X
cana-4524	98	31			X
cana-4524	98	32	+	+	SYM
cana-4524	98	33			NUM
cana-4524	98	34	.	.	PUNCT
cana-4524	99	1	hence	hence	ADV
cana-4524	99	2	(	(	PUNCT
cana-4524	99	3	)	)	PUNCT
cana-4524	99	4	''	''	PUNCT
cana-4524	99	5	(	(	PUNCT
cana-4524	99	6	)	)	PUNCT
cana-4524	99	7	5.e	5.e	NUM
cana-4524	99	8	nl	nl	NOUN
cana-4524	99	9	l	l	NOUN
cana-4524	99	10	=	=	SYM
cana-4524	99	11	example	example	NOUN
cana-4524	99	12	3.1	3.1	NUM
cana-4524	99	13	:	:	PUNCT
cana-4524	99	14	the	the	DET
cana-4524	99	15	graph	graph	NOUN
cana-4524	99	16	7	7	NUM
cana-4524	99	17	(	(	PUNCT
cana-4524	99	18	)	)	PUNCT
cana-4524	99	19	l	l	NOUN
cana-4524	99	20	l	l	NOUN
cana-4524	99	21	and	and	CCONJ
cana-4524	99	22	its	its	PRON
cana-4524	99	23	equitable	equitable	ADJ
cana-4524	99	24	total	total	ADJ
cana-4524	99	25	coloring	coloring	NOUN
cana-4524	99	26	is	be	AUX
cana-4524	99	27	shown	show	VERB
cana-4524	99	28	in	in	ADP
cana-4524	99	29	figure	figure	NOUN
cana-4524	99	30	1	1	NUM
cana-4524	99	31	.	.	PUNCT
cana-4524	99	32	figure	figure	NOUN
cana-4524	99	33	1	1	NUM
cana-4524	99	34	:	:	SYM
cana-4524	99	35	7	7	NUM
cana-4524	99	36	(	(	PUNCT
cana-4524	99	37	)	)	PUNCT
cana-4524	99	38	l	l	NOUN
cana-4524	99	39	l	l	NOUN
cana-4524	99	40	and	and	CCONJ
cana-4524	99	41	its	its	PRON
cana-4524	99	42	equitable	equitable	ADJ
cana-4524	99	43	total	total	ADJ
cana-4524	99	44	coloring	coloring	NOUN
cana-4524	99	45	it	it	PRON
cana-4524	99	46	is	be	AUX
cana-4524	99	47	clear	clear	ADJ
cana-4524	99	48	that	that	SCONJ
cana-4524	99	49	the	the	DET
cana-4524	99	50	color	color	NOUN
cana-4524	99	51	classes	class	NOUN
cana-4524	99	52	1	1	NUM
cana-4524	99	53	2	2	NUM
cana-4524	99	54	3	3	NUM
cana-4524	99	55	4	4	NUM
cana-4524	99	56	,	,	PUNCT
cana-4524	99	57	,	,	PUNCT
cana-4524	99	58	,	,	PUNCT
cana-4524	99	59	t	t	PROPN
cana-4524	99	60	t	t	PROPN
cana-4524	99	61	t	t	PROPN
cana-4524	99	62	t	t	PROPN
cana-4524	99	63	and	and	CCONJ
cana-4524	99	64	5	5	NUM
cana-4524	99	65	t	t	NOUN
cana-4524	99	66	are	be	AUX
cana-4524	99	67	independent	independent	ADJ
cana-4524	99	68	sets	set	NOUN
cana-4524	99	69	of	of	ADP
cana-4524	99	70	7	7	NUM
cana-4524	99	71	(	(	PUNCT
cana-4524	99	72	)	)	PUNCT
cana-4524	99	73	l	l	NOUN
cana-4524	99	74	l	l	NOUN
cana-4524	99	75	.	.	PUNCT
cana-4524	100	1	for	for	ADP
cana-4524	100	2	which	which	PRON
cana-4524	100	3	the	the	DET
cana-4524	100	4	color	color	NOUN
cana-4524	100	5	classes	class	NOUN
cana-4524	100	6	are	be	AUX
cana-4524	100	7	partition	partition	NOUN
cana-4524	100	8	into	into	ADP
cana-4524	100	9	1	1	NUM
cana-4524	100	10	2	2	NUM
cana-4524	100	11	4	4	NUM
cana-4524	100	12	10	10	NUM
cana-4524	100	13	t	t	NOUN
cana-4524	100	14	t	t	NOUN
cana-4524	100	15	t=	t=	ADJ
cana-4524	101	1	=	=	PUNCT
cana-4524	102	1	=	=	PUNCT
cana-4524	102	2	and	and	CCONJ
cana-4524	102	3	3	3	NUM
cana-4524	102	4	5	5	NUM
cana-4524	102	5	11	11	NUM
cana-4524	102	6	t	t	NOUN
cana-4524	102	7	t=	t=	NOUN
cana-4524	102	8	=	=	PUNCT
cana-4524	102	9	(	(	PUNCT
cana-4524	102	10	see	see	VERB
cana-4524	102	11	figure	figure	NOUN
cana-4524	102	12	1	1	NUM
cana-4524	102	13	)	)	PUNCT
cana-4524	102	14	and	and	CCONJ
cana-4524	102	15	it	it	PRON
cana-4524	102	16	holds	hold	VERB
cana-4524	102	17	the	the	DET
cana-4524	102	18	inequality	inequality	NOUN
cana-4524	103	1	|	|	ADV
cana-4524	104	1	|	|	ADV
cana-4524	105	1	|	|	ADV
cana-4524	106	1	|	|	INTJ
cana-4524	106	2	1,i	1,i	PROPN
cana-4524	106	3	jt	jt	PROPN
cana-4524	106	4	t−	t−	PROPN
cana-4524	106	5			PROPN
cana-4524	106	6	for	for	ADP
cana-4524	106	7	every	every	DET
cana-4524	106	8	pair	pair	NOUN
cana-4524	106	9	of	of	ADP
cana-4524	106	10	(	(	PUNCT
cana-4524	106	11	,	,	PUNCT
cana-4524	106	12	)	)	PUNCT
cana-4524	106	13	i	i	PRON
cana-4524	106	14	j	j	PROPN
cana-4524	106	15	.	.	PUNCT
cana-4524	107	1	this	this	PRON
cana-4524	107	2	implies	imply	VERB
cana-4524	107	3	that	that	SCONJ
cana-4524	107	4	(	(	PUNCT
cana-4524	107	5	)	)	PUNCT
cana-4524	107	6	''	''	PUNCT
cana-4524	107	7	7	7	NUM
cana-4524	107	8	(	(	PUNCT
cana-4524	107	9	)	)	PUNCT
cana-4524	107	10	5e	5e	NOUN
cana-4524	107	11	l	l	NOUN
cana-4524	107	12	l	l	VERB
cana-4524	107	13			NOUN
cana-4524	107	14	.	.	PUNCT
cana-4524	108	1	moreover	moreover	ADV
cana-4524	108	2	,	,	PUNCT
cana-4524	108	3	4	4	NOUN
cana-4524	108	4	=	=	PUNCT
cana-4524	108	5	.	.	PUNCT
cana-4524	109	1	we	we	PRON
cana-4524	109	2	have	have	VERB
cana-4524	109	3	(	(	PUNCT
cana-4524	109	4	)	)	PUNCT
cana-4524	109	5	''	''	PUNCT
cana-4524	109	6	7	7	NUM
cana-4524	109	7	(	(	PUNCT
cana-4524	109	8	)	)	PUNCT
cana-4524	109	9	e	e	NOUN
cana-4524	109	10	l	l	NOUN
cana-4524	109	11	l	l	NOUN
cana-4524	109	12			NUM
cana-4524	109	13	1	1	NUM
cana-4524	109	14	4	4	NUM
cana-4524	109	15	1	1	NUM
cana-4524	109	16	5+	5+	NUM
cana-4524	109	17			NUM
cana-4524	109	18	+	+	CCONJ
cana-4524	109	19			NUM
cana-4524	109	20	.	.	PUNCT
cana-4524	110	1	hence	hence	ADV
cana-4524	110	2	(	(	PUNCT
cana-4524	110	3	)	)	PUNCT
cana-4524	110	4	''	''	PUNCT
cana-4524	110	5	7	7	NUM
cana-4524	110	6	(	(	PUNCT
cana-4524	110	7	)	)	PUNCT
cana-4524	110	8	5e	5e	NOUN
cana-4524	110	9	l	l	NOUN
cana-4524	110	10	l	l	NOUN
cana-4524	110	11	=	=	SYM
cana-4524	110	12	.	.	PUNCT
cana-4524	111	1	theorem	theorem	ADJ
cana-4524	111	2	3.2	3.2	NUM
cana-4524	111	3	:	:	PUNCT
cana-4524	111	4	let	let	VERB
cana-4524	111	5	(	(	PUNCT
cana-4524	111	6	)	)	PUNCT
cana-4524	111	7	nl	nl	PROPN
cana-4524	111	8	sl	sl	PROPN
cana-4524	111	9	represent	represent	VERB
cana-4524	111	10	the	the	DET
cana-4524	111	11	line	line	NOUN
cana-4524	111	12	graph	graph	NOUN
cana-4524	111	13	of	of	ADP
cana-4524	111	14	a	a	DET
cana-4524	111	15	slanting	slanting	NOUN
cana-4524	111	16	ladder	ladder	NOUN
cana-4524	111	17	,	,	PUNCT
cana-4524	111	18	then	then	ADV
cana-4524	111	19	(	(	PUNCT
cana-4524	111	20	)	)	PUNCT
cana-4524	111	21	''	''	PUNCT
cana-4524	112	1	(	(	PUNCT
cana-4524	112	2	)	)	PUNCT
cana-4524	112	3	5.e	5.e	NUM
cana-4524	112	4	nl	nl	NOUN
cana-4524	112	5	sl	sl	NOUN
cana-4524	112	6	=	=	NOUN
cana-4524	112	7	proof	proof	NOUN
cana-4524	112	8	:	:	PUNCT
cana-4524	112	9	'	'	PUNCT
cana-4524	112	10	(	(	PUNCT
cana-4524	112	11	(	(	PUNCT
cana-4524	112	12	)	)	PUNCT
cana-4524	112	13	)	)	PUNCT
cana-4524	112	14	{	{	PUNCT
cana-4524	112	15	,	,	PUNCT
cana-4524	112	16	,	,	PUNCT
cana-4524	112	17	:1	:1	PUNCT
cana-4524	112	18	}	}	PUNCT
cana-4524	112	19	nv	nv	PROPN
cana-4524	112	20	l	l	NOUN
cana-4524	112	21	sl	sl	INTJ
cana-4524	112	22	u	u	NOUN
cana-4524	112	23	v	v	NOUN
cana-4524	112	24	u	u	NOUN
cana-4524	112	25	n	n	NOUN
cana-4524	112	26			NOUN
cana-4524	112	27			NOUN
cana-4524	112	28	=	=	NOUN
cana-4524	112	29			NOUN
cana-4524	112	30			NOUN
cana-4524	112	31			PRON
cana-4524	112	32			PROPN
cana-4524	112	33			PROPN
cana-4524	112	34			PROPN
cana-4524	112	35	'	'	PUNCT
cana-4524	112	36	''	''	PUNCT
cana-4524	112	37	'	'	PUNCT
cana-4524	112	38	''	''	PUNCT
cana-4524	112	39	(	(	PUNCT
cana-4524	112	40	(	(	PUNCT
cana-4524	112	41	)	)	PUNCT
cana-4524	112	42	)	)	PUNCT
cana-4524	112	43	,	,	PUNCT
cana-4524	112	44	:1	:1	NUM
cana-4524	112	45	2	2	NUM
cana-4524	112	46	,	,	PUNCT
cana-4524	112	47	,	,	PUNCT
cana-4524	112	48	,	,	PUNCT
cana-4524	112	49	:1	:1	PUNCT
cana-4524	112	50	1ne	1ne	X
cana-4524	112	51	l	l	NOUN
cana-4524	112	52	sl	sl	X
cana-4524	112	53	e	e	X
cana-4524	112	54	f	f	PROPN
cana-4524	112	55	n	n	X
cana-4524	112	56	e	e	X
cana-4524	112	57	e	e	X
cana-4524	112	58	f	f	PROPN
cana-4524	112	59	f	f	PROPN
cana-4524	112	60	n	n	NOUN
cana-4524	112	61			NOUN
cana-4524	112	62			NOUN
cana-4524	112	63			NOUN
cana-4524	112	64			ADV
cana-4524	112	65			NOUN
cana-4524	112	66	=	=	NOUN
cana-4524	112	67			NUM
cana-4524	112	68			NOUN
cana-4524	112	69	−	−	ADP
cana-4524	112	70			NOUN
cana-4524	112	71			NOUN
cana-4524	112	72	−	−	NOUN
cana-4524	112	73	,	,	PUNCT
cana-4524	112	74	where	where	SCONJ
cana-4524	112	75	1,e	1,e	NUM
cana-4524	112	76	u	u	NOUN
cana-4524	112	77	u	u	NOUN
cana-4524	112	78			NOUN
cana-4524	112	79			NOUN
cana-4524	112	80	+	+	NOUN
cana-4524	112	81	=	=	X
cana-4524	112	82	'	'	PUNCT
cana-4524	112	83	'	'	PUNCT
cana-4524	112	84	,	,	PUNCT
cana-4524	112	85	e	e	X
cana-4524	112	86	u	u	X
cana-4524	112	87	u	u	PROPN
cana-4524	112	88			NOUN
cana-4524	112	89	=	=	NOUN
cana-4524	112	90	'	'	PUNCT
cana-4524	112	91	'	'	PUNCT
cana-4524	112	92	,	,	PUNCT
cana-4524	112	93	e	e	X
cana-4524	112	94	u	u	X
cana-4524	112	95	u	u	PROPN
cana-4524	112	96			NOUN
cana-4524	112	97	=	=	NOUN
cana-4524	112	98	''	''	PUNCT
cana-4524	112	99	'	'	PUNCT
cana-4524	112	100	1,e	1,e	NUM
cana-4524	112	101	u	u	NOUN
cana-4524	112	102	u	u	NOUN
cana-4524	112	103			NOUN
cana-4524	112	104			NOUN
cana-4524	112	105	+	+	PROPN
cana-4524	112	106	=	=	X
cana-4524	112	107	1,f	1,f	NUM
cana-4524	112	108	v	v	ADP
cana-4524	112	109	v	v	PRON
cana-4524	112	110			NOUN
cana-4524	112	111			NOUN
cana-4524	112	112	+	+	NOUN
cana-4524	112	113	=	=	X
cana-4524	112	114	'	'	PUNCT
cana-4524	112	115	'	'	PUNCT
cana-4524	112	116	,	,	PUNCT
cana-4524	112	117	f	f	PROPN
cana-4524	112	118	u	u	NOUN
cana-4524	112	119	v	v	PROPN
cana-4524	112	120			NOUN
cana-4524	112	121	=	=	NOUN
cana-4524	112	122	''	''	PUNCT
cana-4524	112	123	'	'	PUNCT
cana-4524	112	124	1.f	1.f	NUM
cana-4524	112	125	v	v	X
cana-4524	112	126	u	u	PROPN
cana-4524	112	127			NOUN
cana-4524	112	128	+=	+=	NOUN
cana-4524	112	129	we	we	PRON
cana-4524	112	130	divide	divide	VERB
cana-4524	112	131	the	the	DET
cana-4524	112	132	vertex	vertex	NOUN
cana-4524	112	133	and	and	CCONJ
cana-4524	112	134	edge	edge	NOUN
cana-4524	112	135	set	set	NOUN
cana-4524	112	136	of	of	ADP
cana-4524	112	137	(	(	PUNCT
cana-4524	112	138	)	)	PUNCT
cana-4524	112	139	nl	nl	PROPN
cana-4524	112	140	sl	sl	VERB
cana-4524	112	141	into	into	ADP
cana-4524	112	142	distinct	distinct	ADJ
cana-4524	112	143	partition	partition	NOUN
cana-4524	112	144	as	as	SCONJ
cana-4524	112	145	described	describe	VERB
cana-4524	112	146	below	below	ADV
cana-4524	112	147	.	.	PUNCT
cana-4524	112	148	'	'	PUNCT
cana-4524	112	149	'	'	PUNCT
cana-4524	112	150	'	'	PUNCT
cana-4524	112	151	'	'	PUNCT
cana-4524	112	152	'	'	PUNCT
cana-4524	112	153	'	'	PUNCT
cana-4524	112	154	4	4	NUM
cana-4524	112	155	9	9	NUM
cana-4524	112	156	5	5	NUM
cana-4524	112	157	1	1	NUM
cana-4524	112	158	2	2	NUM
cana-4524	112	159	7	7	NUM
cana-4524	112	160	5	5	NUM
cana-4524	112	161	3	3	NUM
cana-4524	112	162	5	5	NUM
cana-4524	112	163	10	10	NUM
cana-4524	112	164	5	5	NUM
cana-4524	112	165	1	1	NUM
cana-4524	112	166	6	6	NUM
cana-4524	112	167	5	5	NUM
cana-4524	112	168	4	4	NUM
cana-4524	112	169	3	3	NUM
cana-4524	112	170	8	8	NUM
cana-4524	112	171	5	5	NUM
cana-4524	112	172	2	2	NUM
cana-4524	112	173	1	1	NUM
cana-4524	112	174	''	''	PUNCT
cana-4524	112	175	''	''	PUNCT
cana-4524	112	176	''	''	PUNCT
cana-4524	112	177	'	'	PUNCT
cana-4524	112	178	'	'	PUNCT
cana-4524	112	179	'	'	PUNCT
cana-4524	112	180	''	''	PUNCT
cana-4524	112	181	''	''	PUNCT
cana-4524	112	182	''	''	PUNCT
cana-4524	113	1	5	5	NUM
cana-4524	113	2	10	10	NUM
cana-4524	113	3	5	5	NUM
cana-4524	113	4	5	5	NUM
cana-4524	113	5	10	10	NUM
cana-4524	113	6	5	5	NUM
cana-4524	113	7	4	4	NUM
cana-4524	113	8	9	9	NUM
cana-4524	113	9	5	5	NUM
cana-4524	113	10	1	1	NUM
cana-4524	113	11	2	2	NUM
cana-4524	113	12	7	7	NUM
cana-4524	113	13	5	5	NUM
cana-4524	113	14	3	3	NUM
cana-4524	113	15	{	{	PUNCT
cana-4524	113	16	,	,	PUNCT
cana-4524	113	17	,	,	PUNCT
cana-4524	113	18	...	...	PUNCT
cana-4524	113	19	,	,	PUNCT
cana-4524	113	20	}	}	PUNCT
cana-4524	113	21	{	{	PUNCT
cana-4524	113	22	,	,	PUNCT
cana-4524	113	23	,	,	PUNCT
cana-4524	113	24	...	...	PUNCT
cana-4524	113	25	,	,	PUNCT
cana-4524	113	26	}	}	PUNCT
cana-4524	113	27	{	{	PUNCT
cana-4524	113	28	,	,	PUNCT
cana-4524	113	29	,	,	PUNCT
cana-4524	113	30	...	...	PUNCT
cana-4524	113	31	,	,	PUNCT
cana-4524	113	32	}	}	PUNCT
cana-4524	113	33	{	{	PUNCT
cana-4524	113	34	,	,	PUNCT
cana-4524	113	35	,	,	PUNCT
cana-4524	113	36	...	...	PUNCT
cana-4524	113	37	,	,	PUNCT
cana-4524	113	38	}	}	PUNCT
cana-4524	113	39	{	{	PUNCT
cana-4524	113	40	,	,	PUNCT
cana-4524	113	41	,	,	PUNCT
cana-4524	113	42	...	...	PUNCT
cana-4524	113	43	,	,	PUNCT
cana-4524	113	44	}	}	PUNCT
cana-4524	113	45	{	{	PUNCT
cana-4524	113	46	,	,	PUNCT
cana-4524	113	47	,	,	PUNCT
cana-4524	113	48	...	...	PUNCT
cana-4524	113	49	,	,	PUNCT
cana-4524	113	50	}	}	PUNCT
cana-4524	113	51	{	{	PUNCT
cana-4524	113	52	,	,	PUNCT
cana-4524	113	53	,	,	PUNCT
cana-4524	113	54	...	...	PUNCT
cana-4524	113	55	,	,	PUNCT
cana-4524	113	56	}	}	PUNCT
cana-4524	113	57	{	{	PUNCT
cana-4524	113	58	,	,	PUNCT
cana-4524	113	59	,	,	PUNCT
cana-4524	113	60	...	...	PUNCT
cana-4524	113	61	,	,	PUNCT
cana-4524	113	62	}	}	PUNCT
cana-4524	113	63	{	{	PUNCT
cana-4524	113	64	,	,	PUNCT
cana-4524	113	65	,	,	PUNCT
cana-4524	113	66	...	...	PUNCT
cana-4524	113	67	,	,	PUNCT
cana-4524	113	68	}	}	PUNCT
cana-4524	113	69	u	u	NOUN
cana-4524	113	70	u	u	NOUN
cana-4524	113	71	u	u	NOUN
cana-4524	113	72	v	v	ADP
cana-4524	113	73	v	v	NUM
cana-4524	113	74	v	v	NOUN
cana-4524	113	75	u	u	NOUN
cana-4524	113	76	u	u	X
cana-4524	113	77	u	u	NOUN
cana-4524	113	78	e	e	X
cana-4524	113	79	e	e	X
cana-4524	113	80	e	e	X
cana-4524	113	81	e	e	X
cana-4524	113	82	e	e	X
cana-4524	113	83	e	e	X
cana-4524	113	84	t	t	NOUN
cana-4524	113	85	e	e	X
cana-4524	113	86	e	e	X
cana-4524	113	87	e	e	X
cana-4524	113	88	f	f	PROPN
cana-4524	113	89	f	f	PROPN
cana-4524	114	1	f	f	PROPN
cana-4524	114	2	f	f	PROPN
cana-4524	115	1	f	f	X
cana-4524	115	2	f	f	PROPN
cana-4524	115	3	f	f	PROPN
cana-4524	115	4	f	f	PROPN
cana-4524	115	5	f	f	PROPN
cana-4524	115	6			NOUN
cana-4524	115	7			NOUN
cana-4524	115	8			NOUN
cana-4524	115	9			NOUN
cana-4524	115	10			NOUN
cana-4524	115	11			NOUN
cana-4524	115	12			NOUN
cana-4524	115	13			NOUN
cana-4524	115	14			NOUN
cana-4524	115	15	−	−	PROPN
cana-4524	115	16	−	−	PROPN
cana-4524	115	17	−	−	PROPN
cana-4524	115	18	−	−	PROPN
cana-4524	115	19	−	−	NOUN
cana-4524	115	20	−	−	NOUN
cana-4524	115	21	=	=	SYM
cana-4524	115	22			ADP
cana-4524	115	23			NOUN
cana-4524	115	24			NUM
cana-4524	115	25	'	'	PUNCT
cana-4524	115	26	'	'	PUNCT
cana-4524	115	27	'	'	PUNCT
cana-4524	115	28	'	'	PUNCT
cana-4524	115	29	'	'	PUNCT
cana-4524	115	30	'	'	NUM
cana-4524	115	31	5	5	NUM
cana-4524	115	32	10	10	NUM
cana-4524	115	33	5	5	NUM
cana-4524	115	34	3	3	NUM
cana-4524	115	35	8	8	NUM
cana-4524	115	36	5	5	NUM
cana-4524	115	37	2	2	NUM
cana-4524	115	38	1	1	NUM
cana-4524	115	39	6	6	NUM
cana-4524	115	40	5	5	NUM
cana-4524	115	41	4	4	NUM
cana-4524	115	42	2	2	NUM
cana-4524	115	43	7	7	NUM
cana-4524	115	44	5	5	NUM
cana-4524	115	45	2	2	NUM
cana-4524	115	46	4	4	NUM
cana-4524	115	47	9	9	NUM
cana-4524	115	48	5	5	NUM
cana-4524	115	49	1	1	NUM
cana-4524	115	50	2	2	NUM
cana-4524	115	51	''	''	PUNCT
cana-4524	115	52	''	''	PUNCT
cana-4524	115	53	''	''	PUNCT
cana-4524	115	54	'	'	PUNCT
cana-4524	115	55	'	'	PUNCT
cana-4524	115	56	'	'	PUNCT
cana-4524	115	57	''	''	PUNCT
cana-4524	115	58	''	''	PUNCT
cana-4524	115	59	''	''	PUNCT
cana-4524	115	60	1	1	NUM
cana-4524	115	61	6	6	NUM
cana-4524	115	62	5	5	NUM
cana-4524	115	63	4	4	NUM
cana-4524	115	64	1	1	NUM
cana-4524	115	65	6	6	NUM
cana-4524	115	66	5	5	NUM
cana-4524	115	67	4	4	NUM
cana-4524	115	68	5	5	NUM
cana-4524	115	69	10	10	NUM
cana-4524	115	70	5	5	NUM
cana-4524	115	71	3	3	NUM
cana-4524	115	72	8	8	NUM
cana-4524	115	73	5	5	NUM
cana-4524	115	74	2	2	NUM
cana-4524	115	75	{	{	PUNCT
cana-4524	115	76	,	,	PUNCT
cana-4524	115	77	,	,	PUNCT
cana-4524	115	78	...	...	PUNCT
cana-4524	115	79	,	,	PUNCT
cana-4524	115	80	}	}	PUNCT
cana-4524	115	81	{	{	PUNCT
cana-4524	115	82	,	,	PUNCT
cana-4524	115	83	,	,	PUNCT
cana-4524	115	84	...	...	PUNCT
cana-4524	115	85	,	,	PUNCT
cana-4524	115	86	}	}	PUNCT
cana-4524	115	87	{	{	PUNCT
cana-4524	115	88	,	,	PUNCT
cana-4524	115	89	,	,	PUNCT
cana-4524	115	90	...	...	PUNCT
cana-4524	115	91	,	,	PUNCT
cana-4524	115	92	}	}	PUNCT
cana-4524	115	93	{	{	PUNCT
cana-4524	115	94	,	,	PUNCT
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cana-4524	115	103	,	,	PUNCT
cana-4524	115	104	}	}	PUNCT
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cana-4524	115	107	,	,	PUNCT
cana-4524	115	108	...	...	PUNCT
cana-4524	115	109	,	,	PUNCT
cana-4524	115	110	}	}	PUNCT
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cana-4524	115	112	,	,	PUNCT
cana-4524	115	113	,	,	PUNCT
cana-4524	115	114	...	...	PUNCT
cana-4524	115	115	,	,	PUNCT
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cana-4524	115	118	,	,	PUNCT
cana-4524	115	119	,	,	PUNCT
cana-4524	115	120	...	...	PUNCT
cana-4524	115	121	,	,	PUNCT
cana-4524	115	122	}	}	PUNCT
cana-4524	115	123	{	{	PUNCT
cana-4524	115	124	,	,	PUNCT
cana-4524	115	125	,	,	PUNCT
cana-4524	115	126	...	...	PUNCT
cana-4524	115	127	,	,	PUNCT
cana-4524	115	128	}	}	PUNCT
cana-4524	115	129	u	u	NOUN
cana-4524	115	130	u	u	NOUN
cana-4524	115	131	u	u	NOUN
cana-4524	115	132	v	v	ADP
cana-4524	115	133	v	v	NUM
cana-4524	115	134	v	v	NOUN
cana-4524	115	135	u	u	NOUN
cana-4524	115	136	u	u	X
cana-4524	115	137	u	u	NOUN
cana-4524	115	138	e	e	X
cana-4524	115	139	e	e	X
cana-4524	115	140	e	e	X
cana-4524	115	141	e	e	X
cana-4524	115	142	e	e	X
cana-4524	115	143	e	e	X
cana-4524	115	144	t	t	NOUN
cana-4524	115	145	e	e	X
cana-4524	115	146	e	e	X
cana-4524	115	147	e	e	X
cana-4524	115	148	f	f	PROPN
cana-4524	115	149	f	f	PROPN
cana-4524	116	1	f	f	PROPN
cana-4524	116	2	f	f	PROPN
cana-4524	117	1	f	f	X
cana-4524	117	2	f	f	PROPN
cana-4524	117	3	f	f	PROPN
cana-4524	117	4	f	f	PROPN
cana-4524	117	5	f	f	PROPN
cana-4524	117	6			NOUN
cana-4524	117	7			NOUN
cana-4524	117	8			NOUN
cana-4524	117	9			NOUN
cana-4524	117	10			NOUN
cana-4524	117	11			NOUN
cana-4524	117	12			NOUN
cana-4524	117	13			NOUN
cana-4524	117	14			NOUN
cana-4524	117	15	−	−	PROPN
cana-4524	117	16	−	−	PROPN
cana-4524	117	17	−	−	PROPN
cana-4524	117	18	−	−	PROPN
cana-4524	117	19	−	−	PROPN
cana-4524	117	20	−	−	NOUN
cana-4524	117	21	−	−	NOUN
cana-4524	117	22	=	=	SYM
cana-4524	117	23			ADP
cana-4524	117	24			NOUN
cana-4524	117	25			NUM
cana-4524	117	26	'	'	PUNCT
cana-4524	117	27	'	'	PUNCT
cana-4524	117	28	'	'	PUNCT
cana-4524	117	29	'	'	PUNCT
cana-4524	117	30	'	'	PUNCT
cana-4524	117	31	'	'	NUM
cana-4524	117	32	1	1	NUM
cana-4524	117	33	6	6	NUM
cana-4524	117	34	5	5	NUM
cana-4524	117	35	4	4	NUM
cana-4524	117	36	4	4	NUM
cana-4524	117	37	9	9	NUM
cana-4524	117	38	5	5	NUM
cana-4524	117	39	1	1	NUM
cana-4524	117	40	2	2	NUM
cana-4524	117	41	7	7	NUM
cana-4524	117	42	5	5	NUM
cana-4524	117	43	3	3	NUM
cana-4524	117	44	3	3	NUM
cana-4524	117	45	8	8	NUM
cana-4524	117	46	5	5	NUM
cana-4524	117	47	2	2	NUM
cana-4524	117	48	5	5	NUM
cana-4524	117	49	10	10	NUM
cana-4524	117	50	5	5	NUM
cana-4524	117	51	3	3	NUM
cana-4524	117	52	''	''	PUNCT
cana-4524	117	53	''	''	PUNCT
cana-4524	117	54	''	''	PUNCT
cana-4524	117	55	'	'	PUNCT
cana-4524	117	56	'	'	PUNCT
cana-4524	117	57	'	'	PUNCT
cana-4524	117	58	''	''	PUNCT
cana-4524	117	59	''	''	PUNCT
cana-4524	117	60	''	''	PUNCT
cana-4524	117	61	2	2	NUM
cana-4524	117	62	7	7	NUM
cana-4524	117	63	5	5	NUM
cana-4524	117	64	3	3	NUM
cana-4524	117	65	2	2	NUM
cana-4524	117	66	7	7	NUM
cana-4524	117	67	5	5	NUM
cana-4524	117	68	3	3	NUM
cana-4524	117	69	1	1	NUM
cana-4524	117	70	6	6	NUM
cana-4524	117	71	5	5	NUM
cana-4524	117	72	4	4	NUM
cana-4524	117	73	4	4	NUM
cana-4524	117	74	9	9	NUM
cana-4524	117	75	5	5	NUM
cana-4524	117	76	1	1	NUM
cana-4524	117	77	{	{	PUNCT
cana-4524	117	78	,	,	PUNCT
cana-4524	117	79	,	,	PUNCT
cana-4524	117	80	...	...	PUNCT
cana-4524	117	81	,	,	PUNCT
cana-4524	117	82	}	}	PUNCT
cana-4524	117	83	{	{	PUNCT
cana-4524	117	84	,	,	PUNCT
cana-4524	117	85	,	,	PUNCT
cana-4524	117	86	...	...	PUNCT
cana-4524	117	87	,	,	PUNCT
cana-4524	117	88	}	}	PUNCT
cana-4524	117	89	{	{	PUNCT
cana-4524	117	90	,	,	PUNCT
cana-4524	117	91	,	,	PUNCT
cana-4524	117	92	...	...	PUNCT
cana-4524	117	93	,	,	PUNCT
cana-4524	117	94	}	}	PUNCT
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cana-4524	117	99	,	,	PUNCT
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cana-4524	117	102	,	,	PUNCT
cana-4524	117	103	,	,	PUNCT
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cana-4524	117	105	,	,	PUNCT
cana-4524	117	106	}	}	PUNCT
cana-4524	117	107	{	{	PUNCT
cana-4524	117	108	,	,	PUNCT
cana-4524	117	109	,	,	PUNCT
cana-4524	117	110	...	...	PUNCT
cana-4524	117	111	,	,	PUNCT
cana-4524	117	112	}	}	PUNCT
cana-4524	117	113	{	{	PUNCT
cana-4524	117	114	,	,	PUNCT
cana-4524	117	115	,	,	PUNCT
cana-4524	117	116	...	...	PUNCT
cana-4524	117	117	,	,	PUNCT
cana-4524	117	118	}	}	PUNCT
cana-4524	117	119	{	{	PUNCT
cana-4524	117	120	,	,	PUNCT
cana-4524	117	121	,	,	PUNCT
cana-4524	117	122	...	...	PUNCT
cana-4524	117	123	,	,	PUNCT
cana-4524	117	124	}	}	PUNCT
cana-4524	117	125	{	{	PUNCT
cana-4524	117	126	,	,	PUNCT
cana-4524	117	127	,	,	PUNCT
cana-4524	117	128	...	...	PUNCT
cana-4524	117	129	,	,	PUNCT
cana-4524	117	130	}	}	PUNCT
cana-4524	117	131	u	u	NOUN
cana-4524	117	132	u	u	NOUN
cana-4524	117	133	u	u	NOUN
cana-4524	117	134	v	v	ADP
cana-4524	117	135	v	v	NUM
cana-4524	117	136	v	v	NOUN
cana-4524	117	137	u	u	NOUN
cana-4524	117	138	u	u	X
cana-4524	117	139	u	u	NOUN
cana-4524	117	140	e	e	X
cana-4524	117	141	e	e	X
cana-4524	117	142	e	e	X
cana-4524	117	143	e	e	X
cana-4524	117	144	e	e	X
cana-4524	117	145	e	e	X
cana-4524	117	146	t	t	NOUN
cana-4524	117	147	e	e	X
cana-4524	117	148	e	e	X
cana-4524	117	149	e	e	X
cana-4524	117	150	f	f	PROPN
cana-4524	117	151	f	f	PROPN
cana-4524	118	1	f	f	PROPN
cana-4524	118	2	f	f	PROPN
cana-4524	119	1	f	f	X
cana-4524	119	2	f	f	PROPN
cana-4524	119	3	f	f	PROPN
cana-4524	119	4	f	f	PROPN
cana-4524	119	5	f	f	PROPN
cana-4524	119	6			NOUN
cana-4524	119	7			NOUN
cana-4524	119	8			NOUN
cana-4524	119	9			NOUN
cana-4524	119	10			NOUN
cana-4524	119	11			NOUN
cana-4524	119	12			NOUN
cana-4524	119	13			NOUN
cana-4524	119	14			NOUN
cana-4524	119	15	−	−	PROPN
cana-4524	119	16	−	−	PROPN
cana-4524	119	17	−	−	PROPN
cana-4524	119	18	−	−	PROPN
cana-4524	119	19	−	−	PROPN
cana-4524	119	20	−	−	PROPN
cana-4524	119	21	−	−	NOUN
cana-4524	119	22	−	−	NOUN
cana-4524	119	23	=	=	SYM
cana-4524	119	24			ADP
cana-4524	119	25			NOUN
cana-4524	119	26			NUM
cana-4524	119	27	'	'	PUNCT
cana-4524	119	28	'	'	PUNCT
cana-4524	119	29	'	'	PUNCT
cana-4524	119	30	'	'	PUNCT
cana-4524	119	31	'	'	PUNCT
cana-4524	119	32	'	'	NUM
cana-4524	119	33	2	2	NUM
cana-4524	119	34	7	7	NUM
cana-4524	119	35	5	5	NUM
cana-4524	119	36	3	3	NUM
cana-4524	119	37	5	5	NUM
cana-4524	119	38	10	10	NUM
cana-4524	119	39	5	5	NUM
cana-4524	119	40	3	3	NUM
cana-4524	119	41	8	8	NUM
cana-4524	119	42	5	5	NUM
cana-4524	119	43	2	2	NUM
cana-4524	119	44	4	4	NUM
cana-4524	119	45	9	9	NUM
cana-4524	119	46	5	5	NUM
cana-4524	119	47	1	1	NUM
cana-4524	119	48	1	1	NUM
cana-4524	119	49	6	6	NUM
cana-4524	119	50	5	5	NUM
cana-4524	119	51	4	4	NUM
cana-4524	119	52	4	4	NUM
cana-4524	119	53	''	''	PUNCT
cana-4524	119	54	''	''	PUNCT
cana-4524	119	55	''	''	PUNCT
cana-4524	119	56	'	'	PUNCT
cana-4524	119	57	'	'	PUNCT
cana-4524	119	58	'	'	PUNCT
cana-4524	119	59	''	''	PUNCT
cana-4524	119	60	''	''	PUNCT
cana-4524	119	61	''	''	PUNCT
cana-4524	119	62	3	3	NUM
cana-4524	119	63	8	8	NUM
cana-4524	119	64	5	5	NUM
cana-4524	119	65	2	2	NUM
cana-4524	119	66	3	3	NUM
cana-4524	119	67	8	8	NUM
cana-4524	119	68	5	5	NUM
cana-4524	119	69	2	2	NUM
cana-4524	119	70	2	2	NUM
cana-4524	119	71	7	7	NUM
cana-4524	119	72	5	5	NUM
cana-4524	119	73	3	3	NUM
cana-4524	119	74	5	5	NUM
cana-4524	119	75	10	10	NUM
cana-4524	119	76	5	5	NUM
cana-4524	119	77	{	{	PUNCT
cana-4524	119	78	,	,	PUNCT
cana-4524	119	79	,	,	PUNCT
cana-4524	119	80	...	...	PUNCT
cana-4524	119	81	,	,	PUNCT
cana-4524	119	82	}	}	PUNCT
cana-4524	119	83	{	{	PUNCT
cana-4524	119	84	,	,	PUNCT
cana-4524	119	85	,	,	PUNCT
cana-4524	119	86	...	...	PUNCT
cana-4524	119	87	,	,	PUNCT
cana-4524	119	88	}	}	PUNCT
cana-4524	119	89	{	{	PUNCT
cana-4524	119	90	,	,	PUNCT
cana-4524	119	91	,	,	PUNCT
cana-4524	119	92	...	...	PUNCT
cana-4524	119	93	,	,	PUNCT
cana-4524	119	94	}	}	PUNCT
cana-4524	119	95	{	{	PUNCT
cana-4524	119	96	,	,	PUNCT
cana-4524	119	97	,	,	PUNCT
cana-4524	119	98	...	...	PUNCT
cana-4524	119	99	,	,	PUNCT
cana-4524	119	100	}	}	PUNCT
cana-4524	119	101	{	{	PUNCT
cana-4524	119	102	,	,	PUNCT
cana-4524	119	103	,	,	PUNCT
cana-4524	119	104	...	...	PUNCT
cana-4524	119	105	,	,	PUNCT
cana-4524	119	106	}	}	PUNCT
cana-4524	119	107	{	{	PUNCT
cana-4524	119	108	,	,	PUNCT
cana-4524	119	109	,	,	PUNCT
cana-4524	119	110	...	...	PUNCT
cana-4524	119	111	,	,	PUNCT
cana-4524	119	112	}	}	PUNCT
cana-4524	119	113	{	{	PUNCT
cana-4524	119	114	,	,	PUNCT
cana-4524	119	115	,	,	PUNCT
cana-4524	119	116	...	...	PUNCT
cana-4524	119	117	,	,	PUNCT
cana-4524	119	118	}	}	PUNCT
cana-4524	119	119	{	{	PUNCT
cana-4524	119	120	,	,	PUNCT
cana-4524	119	121	,	,	PUNCT
cana-4524	119	122	...	...	PUNCT
cana-4524	119	123	,	,	PUNCT
cana-4524	119	124	}	}	PUNCT
cana-4524	119	125	{	{	PUNCT
cana-4524	119	126	,	,	PUNCT
cana-4524	119	127	,	,	PUNCT
cana-4524	119	128	...	...	PUNCT
cana-4524	119	129	,	,	PUNCT
cana-4524	119	130	}	}	PUNCT
cana-4524	119	131	u	u	NOUN
cana-4524	119	132	u	u	NOUN
cana-4524	119	133	u	u	NOUN
cana-4524	119	134	v	v	ADP
cana-4524	119	135	v	v	NUM
cana-4524	119	136	v	v	NOUN
cana-4524	119	137	u	u	NOUN
cana-4524	119	138	u	u	X
cana-4524	119	139	u	u	NOUN
cana-4524	119	140	e	e	X
cana-4524	119	141	e	e	X
cana-4524	119	142	e	e	X
cana-4524	119	143	e	e	X
cana-4524	119	144	e	e	X
cana-4524	119	145	e	e	X
cana-4524	119	146	t	t	NOUN
cana-4524	119	147	e	e	X
cana-4524	119	148	e	e	X
cana-4524	119	149	e	e	X
cana-4524	119	150	f	f	PROPN
cana-4524	119	151	f	f	PROPN
cana-4524	120	1	f	f	PROPN
cana-4524	120	2	f	f	PROPN
cana-4524	121	1	f	f	X
cana-4524	121	2	f	f	PROPN
cana-4524	121	3	f	f	PROPN
cana-4524	121	4	f	f	PROPN
cana-4524	121	5	f	f	PROPN
cana-4524	121	6			NOUN
cana-4524	121	7			NOUN
cana-4524	121	8			NOUN
cana-4524	121	9			NOUN
cana-4524	121	10			NOUN
cana-4524	121	11			NOUN
cana-4524	121	12			NOUN
cana-4524	121	13			NOUN
cana-4524	121	14			NOUN
cana-4524	121	15	−	−	PROPN
cana-4524	121	16	−	−	PROPN
cana-4524	121	17	−	−	PROPN
cana-4524	121	18	−	−	PROPN
cana-4524	121	19	−	−	PROPN
cana-4524	121	20	−	−	NOUN
cana-4524	121	21	−	−	NOUN
cana-4524	121	22	=	=	SYM
cana-4524	121	23			ADP
cana-4524	121	24			NOUN
cana-4524	121	25			PROPN
cana-4524	121	26	communications	communication	NOUN
cana-4524	121	27	on	on	ADP
cana-4524	121	28	applied	apply	VERB
cana-4524	121	29	nonlinear	nonlinear	ADJ
cana-4524	121	30	analysis	analysis	NOUN
cana-4524	121	31	issn	issn	NOUN
cana-4524	121	32	:	:	PUNCT
cana-4524	121	33	1074	1074	NUM
cana-4524	121	34	-	-	PUNCT
cana-4524	121	35	133x	133x	NUM
cana-4524	121	36	vol	vol	NOUN
cana-4524	121	37	32	32	NUM
cana-4524	121	38	no	no	NOUN
cana-4524	121	39	.	.	PUNCT
cana-4524	122	1	9s	9s	NUM
cana-4524	122	2	(	(	PUNCT
cana-4524	122	3	2025	2025	NUM
cana-4524	122	4	)	)	PUNCT
cana-4524	122	5	2374	2374	NUM
cana-4524	122	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	122	7	'	'	PUNCT
cana-4524	122	8	'	'	PUNCT
cana-4524	122	9	'	'	PUNCT
cana-4524	122	10	'	'	PUNCT
cana-4524	122	11	'	'	PUNCT
cana-4524	122	12	'	'	PUNCT
cana-4524	122	13	3	3	NUM
cana-4524	122	14	8	8	NUM
cana-4524	122	15	5	5	NUM
cana-4524	122	16	2	2	NUM
cana-4524	122	17	1	1	NUM
cana-4524	122	18	6	6	NUM
cana-4524	122	19	5	5	NUM
cana-4524	122	20	4	4	NUM
cana-4524	122	21	4	4	NUM
cana-4524	122	22	9	9	NUM
cana-4524	122	23	5	5	NUM
cana-4524	122	24	1	1	NUM
cana-4524	122	25	5	5	NUM
cana-4524	122	26	10	10	NUM
cana-4524	122	27	5	5	NUM
cana-4524	122	28	2	2	NUM
cana-4524	122	29	7	7	NUM
cana-4524	122	30	5	5	NUM
cana-4524	122	31	3	3	NUM
cana-4524	122	32	5	5	NUM
cana-4524	122	33	''	''	PUNCT
cana-4524	122	34	''	''	PUNCT
cana-4524	122	35	''	''	PUNCT
cana-4524	122	36	'	'	PUNCT
cana-4524	122	37	'	'	PUNCT
cana-4524	122	38	'	'	PUNCT
cana-4524	122	39	''	''	PUNCT
cana-4524	122	40	''	''	PUNCT
cana-4524	122	41	''	''	PUNCT
cana-4524	122	42	4	4	NUM
cana-4524	122	43	9	9	NUM
cana-4524	122	44	5	5	NUM
cana-4524	122	45	1	1	NUM
cana-4524	122	46	4	4	NUM
cana-4524	122	47	9	9	NUM
cana-4524	122	48	5	5	NUM
cana-4524	122	49	1	1	NUM
cana-4524	122	50	3	3	NUM
cana-4524	122	51	8	8	NUM
cana-4524	122	52	5	5	NUM
cana-4524	122	53	2	2	NUM
cana-4524	122	54	1	1	NUM
cana-4524	122	55	6	6	NUM
cana-4524	122	56	5	5	NUM
cana-4524	122	57	4	4	NUM
cana-4524	122	58	{	{	PUNCT
cana-4524	122	59	,	,	PUNCT
cana-4524	122	60	,	,	PUNCT
cana-4524	122	61	...	...	PUNCT
cana-4524	122	62	,	,	PUNCT
cana-4524	122	63	}	}	PUNCT
cana-4524	122	64	{	{	PUNCT
cana-4524	122	65	,	,	PUNCT
cana-4524	122	66	,	,	PUNCT
cana-4524	122	67	...	...	PUNCT
cana-4524	122	68	,	,	PUNCT
cana-4524	122	69	}	}	PUNCT
cana-4524	122	70	{	{	PUNCT
cana-4524	122	71	,	,	PUNCT
cana-4524	122	72	,	,	PUNCT
cana-4524	122	73	...	...	PUNCT
cana-4524	122	74	,	,	PUNCT
cana-4524	122	75	}	}	PUNCT
cana-4524	122	76	{	{	PUNCT
cana-4524	122	77	,	,	PUNCT
cana-4524	122	78	,	,	PUNCT
cana-4524	122	79	...	...	PUNCT
cana-4524	122	80	,	,	PUNCT
cana-4524	122	81	}	}	PUNCT
cana-4524	122	82	{	{	PUNCT
cana-4524	122	83	,	,	PUNCT
cana-4524	122	84	,	,	PUNCT
cana-4524	122	85	...	...	PUNCT
cana-4524	122	86	,	,	PUNCT
cana-4524	122	87	}	}	PUNCT
cana-4524	122	88	{	{	PUNCT
cana-4524	122	89	,	,	PUNCT
cana-4524	122	90	,	,	PUNCT
cana-4524	122	91	...	...	PUNCT
cana-4524	122	92	,	,	PUNCT
cana-4524	122	93	}	}	PUNCT
cana-4524	122	94	{	{	PUNCT
cana-4524	122	95	,	,	PUNCT
cana-4524	122	96	,	,	PUNCT
cana-4524	122	97	...	...	PUNCT
cana-4524	122	98	,	,	PUNCT
cana-4524	122	99	}	}	PUNCT
cana-4524	122	100	{	{	PUNCT
cana-4524	122	101	,	,	PUNCT
cana-4524	122	102	,	,	PUNCT
cana-4524	122	103	...	...	PUNCT
cana-4524	122	104	,	,	PUNCT
cana-4524	122	105	}	}	PUNCT
cana-4524	122	106	{	{	PUNCT
cana-4524	122	107	,	,	PUNCT
cana-4524	122	108	,	,	PUNCT
cana-4524	122	109	...	...	PUNCT
cana-4524	122	110	,	,	PUNCT
cana-4524	122	111	}	}	PUNCT
cana-4524	122	112	u	u	NOUN
cana-4524	122	113	u	u	NOUN
cana-4524	122	114	u	u	NOUN
cana-4524	122	115	v	v	ADP
cana-4524	122	116	v	v	NUM
cana-4524	122	117	v	v	NOUN
cana-4524	122	118	u	u	NOUN
cana-4524	122	119	u	u	X
cana-4524	122	120	u	u	NOUN
cana-4524	122	121	e	e	X
cana-4524	122	122	e	e	X
cana-4524	122	123	e	e	X
cana-4524	122	124	e	e	X
cana-4524	122	125	e	e	X
cana-4524	122	126	e	e	X
cana-4524	122	127	t	t	NOUN
cana-4524	122	128	e	e	X
cana-4524	122	129	e	e	X
cana-4524	122	130	e	e	X
cana-4524	122	131	f	f	PROPN
cana-4524	123	1	f	f	PROPN
cana-4524	123	2	f	f	PROPN
cana-4524	124	1	f	f	PROPN
cana-4524	124	2	f	f	X
cana-4524	125	1	f	f	PROPN
cana-4524	125	2	f	f	PROPN
cana-4524	125	3	f	f	PROPN
cana-4524	125	4	f	f	PROPN
cana-4524	125	5			NOUN
cana-4524	125	6			NOUN
cana-4524	125	7			NOUN
cana-4524	125	8			NOUN
cana-4524	125	9			NOUN
cana-4524	125	10			NOUN
cana-4524	125	11			NOUN
cana-4524	125	12			NOUN
cana-4524	125	13			NOUN
cana-4524	125	14	−	−	PROPN
cana-4524	125	15	−	−	PROPN
cana-4524	125	16	−	−	PROPN
cana-4524	125	17	−	−	PROPN
cana-4524	125	18	−	−	PROPN
cana-4524	125	19	−	−	PROPN
cana-4524	125	20	−	−	NOUN
cana-4524	125	21	−	−	NOUN
cana-4524	125	22	=	=	SYM
cana-4524	125	23			X
cana-4524	125	24			NOUN
cana-4524	125	25			NUM
cana-4524	125	26	based	base	VERB
cana-4524	125	27	on	on	ADP
cana-4524	125	28	the	the	DET
cana-4524	125	29	coloring	coloring	NOUN
cana-4524	125	30	technique	technique	NOUN
cana-4524	125	31	described	describe	VERB
cana-4524	125	32	above	above	ADV
cana-4524	125	33	,	,	PUNCT
cana-4524	125	34	it	it	PRON
cana-4524	125	35	is	be	AUX
cana-4524	125	36	evident	evident	ADJ
cana-4524	125	37	that	that	SCONJ
cana-4524	125	38	the	the	DET
cana-4524	125	39	color	color	NOUN
cana-4524	125	40	classes	class	NOUN
cana-4524	125	41	1	1	NUM
cana-4524	125	42	2	2	NUM
cana-4524	125	43	3	3	NUM
cana-4524	125	44	4	4	NUM
cana-4524	125	45	,	,	PUNCT
cana-4524	125	46	,	,	PUNCT
cana-4524	125	47	,	,	PUNCT
cana-4524	125	48	t	t	PROPN
cana-4524	125	49	t	t	PROPN
cana-4524	125	50	t	t	PROPN
cana-4524	125	51	t	t	PROPN
cana-4524	125	52	and	and	CCONJ
cana-4524	125	53	5	5	NUM
cana-4524	125	54	t	t	NOUN
cana-4524	125	55	are	be	AUX
cana-4524	125	56	independent	independent	ADJ
cana-4524	125	57	sets	set	NOUN
cana-4524	125	58	of	of	ADP
cana-4524	125	59	(	(	PUNCT
cana-4524	125	60	)	)	PUNCT
cana-4524	125	61	nl	nl	PROPN
cana-4524	125	62	sl	sl	INTJ
cana-4524	126	1	and	and	CCONJ
cana-4524	126	2	it	it	PRON
cana-4524	126	3	holds	hold	VERB
cana-4524	126	4	inequality	inequality	NOUN
cana-4524	127	1	|	|	ADV
cana-4524	128	1	|	|	ADV
cana-4524	128	2	|	|	ADV
cana-4524	128	3	|	|	ADV
cana-4524	128	4	1a	1a	VERB
cana-4524	128	5	bt	bt	VERB
cana-4524	128	6	t−	t−	PROPN
cana-4524	128	7			NOUN
cana-4524	128	8	for	for	ADP
cana-4524	128	9	a	a	DET
cana-4524	128	10	b	b	PROPN
cana-4524	128	11	.	.	PUNCT
cana-4524	129	1	this	this	PRON
cana-4524	129	2	implies	imply	VERB
cana-4524	129	3	that	that	SCONJ
cana-4524	129	4	(	(	PUNCT
cana-4524	129	5	)	)	PUNCT
cana-4524	129	6	''	''	PUNCT
cana-4524	129	7	(	(	PUNCT
cana-4524	129	8	)	)	PUNCT
cana-4524	129	9	5e	5e	PROPN
cana-4524	129	10	nl	nl	NOUN
cana-4524	129	11	sl	sl	VERB
cana-4524	129	12			NOUN
cana-4524	129	13	.	.	PUNCT
cana-4524	130	1	further	far	ADV
cana-4524	130	2	,	,	PUNCT
cana-4524	130	3	since	since	SCONJ
cana-4524	130	4	4	4	NUM
cana-4524	130	5	=	=	PRON
cana-4524	130	6	,	,	PUNCT
cana-4524	130	7	we	we	PRON
cana-4524	130	8	have	have	VERB
cana-4524	130	9	(	(	PUNCT
cana-4524	130	10	)	)	PUNCT
cana-4524	130	11	''	''	PUNCT
cana-4524	131	1	(	(	PUNCT
cana-4524	131	2	)	)	PUNCT
cana-4524	131	3	e	e	NOUN
cana-4524	131	4	nl	nl	NOUN
cana-4524	131	5	sl	sl	NOUN
cana-4524	131	6	=	=	SYM
cana-4524	131	7	(	(	PUNCT
cana-4524	131	8	)	)	PUNCT
cana-4524	131	9	"	"	PUNCT
cana-4524	131	10	(	(	PUNCT
cana-4524	131	11	)	)	PUNCT
cana-4524	131	12	nl	nl	PROPN
cana-4524	131	13	sl	sl	NOUN
cana-4524	131	14			NUM
cana-4524	131	15	1	1	NUM
cana-4524	131	16	4	4	NUM
cana-4524	131	17	1	1	NUM
cana-4524	131	18	5+	5+	NUM
cana-4524	131	19			NUM
cana-4524	131	20	+	+	CCONJ
cana-4524	131	21			NUM
cana-4524	131	22	.	.	PUNCT
cana-4524	132	1	hence	hence	ADV
cana-4524	132	2	(	(	PUNCT
cana-4524	132	3	)	)	PUNCT
cana-4524	132	4	''	''	PUNCT
cana-4524	132	5	(	(	PUNCT
cana-4524	132	6	)	)	PUNCT
cana-4524	132	7	5e	5e	PROPN
cana-4524	132	8	nl	nl	NOUN
cana-4524	132	9	sl	sl	PROPN
cana-4524	133	1	=	=	PUNCT
cana-4524	133	2	.	.	PUNCT
cana-4524	134	1	example	example	NOUN
cana-4524	134	2	3.2	3.2	NUM
cana-4524	134	3	:	:	PUNCT
cana-4524	134	4	the	the	DET
cana-4524	134	5	graph	graph	NOUN
cana-4524	134	6	7	7	NUM
cana-4524	134	7	(	(	PUNCT
cana-4524	134	8	)	)	PUNCT
cana-4524	134	9	l	l	NOUN
cana-4524	134	10	sl	sl	NOUN
cana-4524	134	11	and	and	CCONJ
cana-4524	134	12	its	its	PRON
cana-4524	134	13	equitable	equitable	ADJ
cana-4524	134	14	total	total	ADJ
cana-4524	134	15	coloring	coloring	NOUN
cana-4524	134	16	is	be	AUX
cana-4524	134	17	shown	show	VERB
cana-4524	134	18	in	in	ADP
cana-4524	134	19	figure	figure	NOUN
cana-4524	134	20	2	2	NUM
cana-4524	134	21	.	.	PUNCT
cana-4524	134	22	figure	figure	NOUN
cana-4524	134	23	2	2	NUM
cana-4524	134	24	:	:	SYM
cana-4524	134	25	7	7	NUM
cana-4524	134	26	(	(	PUNCT
cana-4524	134	27	)	)	PUNCT
cana-4524	134	28	l	l	NOUN
cana-4524	134	29	sl	sl	NOUN
cana-4524	134	30	and	and	CCONJ
cana-4524	134	31	its	its	PRON
cana-4524	134	32	equitable	equitable	ADJ
cana-4524	134	33	total	total	ADJ
cana-4524	134	34	coloring	color	VERB
cana-4524	134	35	the	the	DET
cana-4524	134	36	color	color	NOUN
cana-4524	134	37	classes	class	NOUN
cana-4524	134	38	are	be	AUX
cana-4524	134	39	(	(	PUNCT
cana-4524	134	40	)	)	PUNCT
cana-4524	134	41			NOUN
cana-4524	134	42	7	7	NOUN
cana-4524	134	43	1	1	NUM
cana-4524	134	44	2	2	NUM
cana-4524	134	45	3	3	NUM
cana-4524	134	46	4	4	NUM
cana-4524	134	47	5	5	NUM
cana-4524	134	48	(	(	PUNCT
cana-4524	134	49	)	)	PUNCT
cana-4524	134	50	,	,	PUNCT
cana-4524	134	51	,	,	PUNCT
cana-4524	134	52	,	,	PUNCT
cana-4524	134	53	,	,	PUNCT
cana-4524	134	54	t	t	PROPN
cana-4524	134	55	l	l	PROPN
cana-4524	135	1	sl	sl	INTJ
cana-4524	135	2	t	t	PROPN
cana-4524	135	3	t	t	PROPN
cana-4524	135	4	t	t	PROPN
cana-4524	135	5	t	t	PROPN
cana-4524	135	6	t=	t=	PROPN
cana-4524	135	7	.	.	PUNCT
cana-4524	136	1	it	it	PRON
cana-4524	136	2	is	be	AUX
cana-4524	136	3	clear	clear	ADJ
cana-4524	136	4	that	that	SCONJ
cana-4524	136	5	the	the	DET
cana-4524	136	6	color	color	NOUN
cana-4524	136	7	classes	class	NOUN
cana-4524	136	8	1	1	NUM
cana-4524	136	9	2	2	NUM
cana-4524	136	10	3	3	NUM
cana-4524	136	11	4	4	NUM
cana-4524	136	12	,	,	PUNCT
cana-4524	136	13	,	,	PUNCT
cana-4524	136	14	,	,	PUNCT
cana-4524	136	15	t	t	PROPN
cana-4524	136	16	t	t	PROPN
cana-4524	136	17	t	t	PROPN
cana-4524	136	18	t	t	PROPN
cana-4524	136	19	and	and	CCONJ
cana-4524	136	20	5	5	NUM
cana-4524	136	21	t	t	NOUN
cana-4524	136	22	are	be	AUX
cana-4524	136	23	independent	independent	ADJ
cana-4524	136	24	sets	set	NOUN
cana-4524	136	25	of	of	ADP
cana-4524	136	26	7	7	NUM
cana-4524	136	27	(	(	PUNCT
cana-4524	136	28	)	)	PUNCT
cana-4524	137	1	l	l	NOUN
cana-4524	137	2	sl	sl	INTJ
cana-4524	137	3	.	.	PUNCT
cana-4524	138	1	for	for	ADP
cana-4524	138	2	which	which	PRON
cana-4524	138	3	the	the	DET
cana-4524	138	4	color	color	NOUN
cana-4524	138	5	classes	class	NOUN
cana-4524	138	6	are	be	AUX
cana-4524	138	7	partition	partition	NOUN
cana-4524	138	8	into	into	ADP
cana-4524	138	9	2	2	NUM
cana-4524	138	10	3	3	NUM
cana-4524	138	11	5	5	NUM
cana-4524	138	12	12	12	NUM
cana-4524	138	13	t	t	NOUN
cana-4524	138	14	t	t	NOUN
cana-4524	138	15	t=	t=	NOUN
cana-4524	139	1	=	=	PUNCT
cana-4524	140	1	=	=	PUNCT
cana-4524	140	2	and	and	CCONJ
cana-4524	140	3	1	1	NUM
cana-4524	140	4	4	4	NUM
cana-4524	140	5	11	11	NUM
cana-4524	140	6	t	t	NOUN
cana-4524	140	7	t=	t=	NOUN
cana-4524	140	8	=	=	PUNCT
cana-4524	140	9	(	(	PUNCT
cana-4524	140	10	see	see	VERB
cana-4524	140	11	figure	figure	NOUN
cana-4524	140	12	2	2	NUM
cana-4524	140	13	)	)	PUNCT
cana-4524	140	14	and	and	CCONJ
cana-4524	140	15	it	it	PRON
cana-4524	140	16	holds	hold	VERB
cana-4524	140	17	the	the	DET
cana-4524	140	18	inequality	inequality	NOUN
cana-4524	141	1	|	|	ADV
cana-4524	142	1	|	|	ADV
cana-4524	143	1	|	|	ADV
cana-4524	144	1	|	|	INTJ
cana-4524	144	2	1,i	1,i	PROPN
cana-4524	144	3	jt	jt	PROPN
cana-4524	144	4	t−	t−	PROPN
cana-4524	144	5			PROPN
cana-4524	144	6	for	for	ADP
cana-4524	144	7	every	every	DET
cana-4524	144	8	pair	pair	NOUN
cana-4524	144	9	of	of	ADP
cana-4524	144	10	(	(	PUNCT
cana-4524	144	11	,	,	PUNCT
cana-4524	144	12	)	)	PUNCT
cana-4524	144	13	i	i	PRON
cana-4524	144	14	j	j	PROPN
cana-4524	144	15	.	.	PUNCT
cana-4524	145	1	this	this	PRON
cana-4524	145	2	implies	imply	VERB
cana-4524	145	3	that	that	SCONJ
cana-4524	145	4	(	(	PUNCT
cana-4524	145	5	)	)	PUNCT
cana-4524	145	6	''	''	PUNCT
cana-4524	145	7	7	7	NUM
cana-4524	145	8	(	(	PUNCT
cana-4524	145	9	)	)	PUNCT
cana-4524	145	10	5e	5e	NOUN
cana-4524	145	11	l	l	NOUN
cana-4524	145	12	sl	sl	NOUN
cana-4524	145	13			NOUN
cana-4524	145	14	.	.	PUNCT
cana-4524	146	1	moreover	moreover	ADV
cana-4524	146	2	,	,	PUNCT
cana-4524	146	3	4	4	NOUN
cana-4524	146	4	=	=	PUNCT
cana-4524	146	5	.	.	PUNCT
cana-4524	147	1	we	we	PRON
cana-4524	147	2	have	have	VERB
cana-4524	147	3	(	(	PUNCT
cana-4524	147	4	)	)	PUNCT
cana-4524	147	5	''	''	PUNCT
cana-4524	147	6	7	7	NUM
cana-4524	147	7	(	(	PUNCT
cana-4524	147	8	)	)	PUNCT
cana-4524	147	9	e	e	X
cana-4524	147	10	l	l	NOUN
cana-4524	147	11	sl	sl	NOUN
cana-4524	147	12			NUM
cana-4524	147	13	1	1	NUM
cana-4524	147	14	4	4	NUM
cana-4524	147	15	1	1	NUM
cana-4524	147	16	5+	5+	NUM
cana-4524	147	17			NUM
cana-4524	147	18	+	+	CCONJ
cana-4524	147	19			NUM
cana-4524	147	20	.	.	PUNCT
cana-4524	148	1	hence	hence	ADV
cana-4524	148	2	(	(	PUNCT
cana-4524	148	3	)	)	PUNCT
cana-4524	148	4	''	''	PUNCT
cana-4524	148	5	7	7	NUM
cana-4524	148	6	(	(	PUNCT
cana-4524	148	7	)	)	PUNCT
cana-4524	148	8	5e	5e	NOUN
cana-4524	148	9	l	l	NOUN
cana-4524	148	10	sl	sl	NOUN
cana-4524	148	11	=	=	SYM
cana-4524	148	12	.	.	PUNCT
cana-4524	149	1	theorem	theorem	VERB
cana-4524	149	2	3.3	3.3	NUM
cana-4524	149	3	:	:	PUNCT
cana-4524	149	4	let	let	VERB
cana-4524	149	5	(	(	PUNCT
cana-4524	149	6	)	)	PUNCT
cana-4524	149	7	nl	nl	PROPN
cana-4524	149	8	t	t	PROPN
cana-4524	149	9	represent	represent	VERB
cana-4524	149	10	the	the	DET
cana-4524	149	11	line	line	NOUN
cana-4524	149	12	graph	graph	NOUN
cana-4524	149	13	of	of	ADP
cana-4524	149	14	a	a	DET
cana-4524	149	15	triangular	triangular	NOUN
cana-4524	149	16	snake	snake	NOUN
cana-4524	149	17	graph	graph	NOUN
cana-4524	149	18	,	,	PUNCT
cana-4524	149	19	then	then	ADV
cana-4524	149	20	(	(	PUNCT
cana-4524	149	21	)	)	PUNCT
cana-4524	149	22	''	''	PUNCT
cana-4524	150	1	(	(	PUNCT
cana-4524	150	2	)	)	PUNCT
cana-4524	150	3	(	(	PUNCT
cana-4524	150	4	(	(	PUNCT
cana-4524	150	5	)	)	PUNCT
cana-4524	150	6	)	)	PUNCT
cana-4524	150	7	1.e	1.e	NUM
cana-4524	150	8	n	n	NUM
cana-4524	150	9	nl	nl	NOUN
cana-4524	150	10	t	t	PROPN
cana-4524	150	11	l	l	NOUN
cana-4524	150	12	t	t	NOUN
cana-4524	150	13	=	=	PUNCT
cana-4524	150	14			X
cana-4524	151	1	+	+	NUM
cana-4524	151	2	proof	proof	NOUN
cana-4524	151	3	:	:	PUNCT
cana-4524	151	4	let	let	VERB
cana-4524	151	5	'	'	PUNCT
cana-4524	151	6	(	(	PUNCT
cana-4524	151	7	(	(	PUNCT
cana-4524	151	8	)	)	PUNCT
cana-4524	151	9	)	)	PUNCT
cana-4524	151	10	{	{	PUNCT
cana-4524	151	11	,	,	PUNCT
cana-4524	151	12	,	,	PUNCT
cana-4524	151	13	:1	:1	PUNCT
cana-4524	151	14	1}nv	1}nv	ADJ
cana-4524	151	15	l	l	NOUN
cana-4524	151	16	t	t	X
cana-4524	151	17	u	u	PRON
cana-4524	151	18	v	v	ADP
cana-4524	151	19	u	u	NOUN
cana-4524	151	20	n	n	NOUN
cana-4524	151	21			NOUN
cana-4524	151	22			NOUN
cana-4524	151	23	=	=	NOUN
cana-4524	151	24			NOUN
cana-4524	151	25			NOUN
cana-4524	151	26	−	−	ADP
cana-4524	151	27			PROPN
cana-4524	151	28			PROPN
cana-4524	151	29			PROPN
cana-4524	151	30			PROPN
cana-4524	151	31	'	'	PUNCT
cana-4524	151	32	'	'	PUNCT
cana-4524	151	33	''	''	PUNCT
cana-4524	151	34	''	''	PUNCT
cana-4524	152	1	'	'	PUNCT
cana-4524	152	2	''	''	PUNCT
cana-4524	152	3	(	(	PUNCT
cana-4524	152	4	(	(	PUNCT
cana-4524	152	5	)	)	PUNCT
cana-4524	152	6	)	)	PUNCT
cana-4524	152	7	,	,	PUNCT
cana-4524	152	8	,	,	PUNCT
cana-4524	152	9	:1	:1	PUNCT
cana-4524	152	10	1	1	NUM
cana-4524	152	11	,	,	PUNCT
cana-4524	152	12	,	,	PUNCT
cana-4524	152	13	,	,	PUNCT
cana-4524	152	14	:1	:1	PUNCT
cana-4524	152	15	2ne	2ne	NOUN
cana-4524	152	16	l	l	NOUN
cana-4524	152	17	sl	sl	X
cana-4524	152	18	e	e	NOUN
cana-4524	152	19	f	f	PROPN
cana-4524	152	20	f	f	PROPN
cana-4524	152	21	n	n	CCONJ
cana-4524	152	22	e	e	X
cana-4524	152	23	e	e	X
cana-4524	152	24	f	f	PROPN
cana-4524	152	25	f	f	PROPN
cana-4524	152	26	n	n	NOUN
cana-4524	152	27			NOUN
cana-4524	152	28			NOUN
cana-4524	152	29			NOUN
cana-4524	152	30			NOUN
cana-4524	152	31			NOUN
cana-4524	152	32			NOUN
cana-4524	152	33	=	=	NOUN
cana-4524	152	34			NUM
cana-4524	152	35			NOUN
cana-4524	152	36	−	−	ADP
cana-4524	152	37			NOUN
cana-4524	152	38			NOUN
cana-4524	152	39	−	−	NOUN
cana-4524	152	40	,	,	PUNCT
cana-4524	152	41	where	where	SCONJ
cana-4524	152	42	'	'	PUNCT
cana-4524	152	43	,	,	PUNCT
cana-4524	152	44	e	e	X
cana-4524	152	45	u	u	X
cana-4524	152	46	u	u	PROPN
cana-4524	152	47			NOUN
cana-4524	152	48	=	=	NOUN
cana-4524	152	49	'	'	PUNCT
cana-4524	152	50	'	'	PUNCT
cana-4524	152	51	1,e	1,e	NUM
cana-4524	152	52	u	u	NOUN
cana-4524	152	53	u	u	NOUN
cana-4524	152	54			NOUN
cana-4524	152	55			NOUN
cana-4524	152	56	+	+	NOUN
cana-4524	152	57	=	=	X
cana-4524	152	58	''	''	PUNCT
cana-4524	152	59	1,e	1,e	NUM
cana-4524	152	60	v	v	ADP
cana-4524	152	61	v	v	PRON
cana-4524	152	62			NOUN
cana-4524	152	63			NOUN
cana-4524	152	64	+	+	NOUN
cana-4524	152	65	=	=	X
cana-4524	152	66	,	,	PUNCT
cana-4524	152	67	f	f	PROPN
cana-4524	152	68	u	u	NOUN
cana-4524	152	69	v	v	PROPN
cana-4524	152	70			NOUN
cana-4524	152	71	=	=	NOUN
cana-4524	152	72	'	'	PUNCT
cana-4524	152	73	'	'	PUNCT
cana-4524	152	74	,	,	PUNCT
cana-4524	152	75	f	f	PROPN
cana-4524	152	76	u	u	NOUN
cana-4524	152	77	v	v	PROPN
cana-4524	152	78			NOUN
cana-4524	152	79	=	=	NOUN
cana-4524	152	80	''	''	PUNCT
cana-4524	152	81	'	'	PUNCT
cana-4524	153	1	1,f	1,f	NUM
cana-4524	153	2	u	u	NOUN
cana-4524	153	3	v	v	VERB
cana-4524	153	4			NOUN
cana-4524	153	5			NOUN
cana-4524	153	6	+	+	NOUN
cana-4524	153	7	=	=	SYM
cana-4524	153	8	''	''	PUNCT
cana-4524	153	9	1f	1f	NUM
cana-4524	153	10	v	v	X
cana-4524	153	11	u	u	NOUN
cana-4524	153	12			NOUN
cana-4524	153	13			NOUN
cana-4524	153	14	+	+	NOUN
cana-4524	153	15	=	=	ADJ
cana-4524	153	16	we	we	PRON
cana-4524	153	17	divide	divide	VERB
cana-4524	153	18	the	the	DET
cana-4524	153	19	vertex	vertex	NOUN
cana-4524	153	20	and	and	CCONJ
cana-4524	153	21	edge	edge	NOUN
cana-4524	153	22	set	set	NOUN
cana-4524	153	23	of	of	ADP
cana-4524	153	24	(	(	PUNCT
cana-4524	153	25	)	)	PUNCT
cana-4524	153	26	nl	nl	PROPN
cana-4524	153	27	t	t	PROPN
cana-4524	153	28	into	into	ADP
cana-4524	153	29	distinct	distinct	ADJ
cana-4524	153	30	partition	partition	NOUN
cana-4524	153	31	as	as	SCONJ
cana-4524	153	32	described	describe	VERB
cana-4524	153	33	below	below	ADV
cana-4524	153	34	.	.	PUNCT
cana-4524	154	1	for	for	ADP
cana-4524	154	2	1	1	NUM
cana-4524	154	3	1n	1n	NUM
cana-4524	154	4			NOUN
cana-4524	154	5	−	−	NOUN
cana-4524	154	6	.	.	PUNCT
cana-4524	154	7	'	'	PUNCT
cana-4524	154	8	'	'	PUNCT
cana-4524	154	9	'	'	PUNCT
cana-4524	154	10	''	''	PUNCT
cana-4524	154	11	''	''	PUNCT
cana-4524	154	12	''	''	PUNCT
cana-4524	154	13	'	'	PUNCT
cana-4524	154	14	1	1	NUM
cana-4524	154	15	1	1	NUM
cana-4524	154	16	4	4	NUM
cana-4524	154	17	3	3	NUM
cana-4524	154	18	2	2	NUM
cana-4524	154	19	3	3	NUM
cana-4524	154	20	6	6	NUM
cana-4524	154	21	3	3	NUM
cana-4524	154	22	1	1	NUM
cana-4524	154	23	4	4	NUM
cana-4524	154	24	3	3	NUM
cana-4524	154	25	2	2	NUM
cana-4524	154	26	2	2	NUM
cana-4524	154	27	5	5	NUM
cana-4524	154	28	3	3	NUM
cana-4524	154	29	1	1	NUM
cana-4524	154	30	1	1	NUM
cana-4524	154	31	{	{	PUNCT
cana-4524	154	32	,	,	PUNCT
cana-4524	154	33	,	,	PUNCT
cana-4524	154	34	...	...	PUNCT
cana-4524	154	35	,	,	PUNCT
cana-4524	154	36	}	}	PUNCT
cana-4524	154	37	{	{	PUNCT
cana-4524	154	38	,	,	PUNCT
cana-4524	154	39	,	,	PUNCT
cana-4524	154	40	...	...	PUNCT
cana-4524	154	41	,	,	PUNCT
cana-4524	154	42	}	}	PUNCT
cana-4524	154	43	{	{	PUNCT
cana-4524	154	44	,	,	PUNCT
cana-4524	154	45	,	,	PUNCT
cana-4524	154	46	...	...	PUNCT
cana-4524	154	47	,	,	PUNCT
cana-4524	154	48	}	}	PUNCT
cana-4524	154	49	{	{	PUNCT
cana-4524	154	50	,	,	PUNCT
cana-4524	154	51	,	,	PUNCT
cana-4524	154	52	...	...	PUNCT
cana-4524	154	53	,	,	PUNCT
cana-4524	154	54	}	}	PUNCT
cana-4524	154	55	{	{	PUNCT
cana-4524	154	56	,	,	PUNCT
cana-4524	154	57	0(mod3)}nt	0(mod3)}nt	NUM
cana-4524	154	58	v	v	NUM
cana-4524	154	59	v	v	NOUN
cana-4524	154	60	v	v	NOUN
cana-4524	154	61	e	e	X
cana-4524	154	62	e	e	X
cana-4524	154	63	e	e	X
cana-4524	154	64	e	e	X
cana-4524	154	65	e	e	X
cana-4524	154	66	e	e	X
cana-4524	154	67	e	e	X
cana-4524	154	68	e	e	X
cana-4524	154	69	e	e	X
cana-4524	154	70	f	f	PROPN
cana-4524	154	71	n	n	NOUN
cana-4524	154	72			NOUN
cana-4524	154	73			VERB
cana-4524	154	74	−	−	ADV
cana-4524	154	75	−	−	VERB
cana-4524	154	76	−	−	PROPN
cana-4524	154	77	−=	−=	NOUN
cana-4524	154	78			PROPN
cana-4524	154	79	communications	communication	NOUN
cana-4524	154	80	on	on	ADP
cana-4524	154	81	applied	apply	VERB
cana-4524	154	82	nonlinear	nonlinear	ADJ
cana-4524	154	83	analysis	analysis	NOUN
cana-4524	154	84	issn	issn	NOUN
cana-4524	154	85	:	:	PUNCT
cana-4524	154	86	1074	1074	NUM
cana-4524	154	87	-	-	PUNCT
cana-4524	154	88	133x	133x	NUM
cana-4524	154	89	vol	vol	NOUN
cana-4524	154	90	32	32	NUM
cana-4524	155	1	no	no	NOUN
cana-4524	155	2	.	.	PUNCT
cana-4524	156	1	9s	9s	NUM
cana-4524	156	2	(	(	PUNCT
cana-4524	156	3	2025	2025	NUM
cana-4524	156	4	)	)	PUNCT
cana-4524	156	5	2375	2375	NUM
cana-4524	156	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	156	7	'	'	PUNCT
cana-4524	156	8	'	'	PUNCT
cana-4524	156	9	'	'	PUNCT
cana-4524	156	10	''	''	PUNCT
cana-4524	156	11	''	''	PUNCT
cana-4524	156	12	''	''	PUNCT
cana-4524	156	13	'	'	PART
cana-4524	156	14	2	2	NUM
cana-4524	156	15	2	2	NUM
cana-4524	156	16	5	5	NUM
cana-4524	156	17	3	3	NUM
cana-4524	156	18	1	1	NUM
cana-4524	156	19	2	2	NUM
cana-4524	156	20	5	5	NUM
cana-4524	156	21	3	3	NUM
cana-4524	156	22	1	1	NUM
cana-4524	156	23	3	3	NUM
cana-4524	156	24	6	6	NUM
cana-4524	156	25	3	3	NUM
cana-4524	156	26	3	3	NUM
cana-4524	156	27	6	6	NUM
cana-4524	156	28	3	3	NUM
cana-4524	156	29	1	1	NUM
cana-4524	156	30	1	1	NUM
cana-4524	156	31	{	{	PUNCT
cana-4524	156	32	,	,	PUNCT
cana-4524	156	33	,	,	PUNCT
cana-4524	156	34	...	...	PUNCT
cana-4524	156	35	,	,	PUNCT
cana-4524	156	36	}	}	PUNCT
cana-4524	156	37	{	{	PUNCT
cana-4524	156	38	,	,	PUNCT
cana-4524	156	39	,	,	PUNCT
cana-4524	156	40	...	...	PUNCT
cana-4524	156	41	,	,	PUNCT
cana-4524	156	42	}	}	PUNCT
cana-4524	156	43	{	{	PUNCT
cana-4524	156	44	,	,	PUNCT
cana-4524	156	45	,	,	PUNCT
cana-4524	156	46	...	...	PUNCT
cana-4524	156	47	,	,	PUNCT
cana-4524	156	48	}	}	PUNCT
cana-4524	156	49	{	{	PUNCT
cana-4524	156	50	,	,	PUNCT
cana-4524	156	51	,	,	PUNCT
cana-4524	156	52	...	...	PUNCT
cana-4524	156	53	,	,	PUNCT
cana-4524	156	54	}	}	PUNCT
cana-4524	156	55	{	{	PUNCT
cana-4524	156	56	}	}	PUNCT
cana-4524	156	57	{	{	PUNCT
cana-4524	156	58	,	,	PUNCT
cana-4524	156	59	1(mod3)}nt	1(mod3)}nt	NUM
cana-4524	156	60	v	v	NOUN
cana-4524	156	61	v	v	NOUN
cana-4524	156	62	v	v	NOUN
cana-4524	156	63	e	e	X
cana-4524	156	64	e	e	X
cana-4524	156	65	e	e	X
cana-4524	156	66	e	e	X
cana-4524	156	67	e	e	X
cana-4524	156	68	e	e	X
cana-4524	156	69	e	e	X
cana-4524	156	70	e	e	X
cana-4524	156	71	e	e	PROPN
cana-4524	156	72	f	f	PROPN
cana-4524	156	73	f	f	PROPN
cana-4524	156	74	n	n	NOUN
cana-4524	156	75			NOUN
cana-4524	156	76			VERB
cana-4524	156	77	−	−	ADV
cana-4524	156	78	−	−	VERB
cana-4524	156	79	−=	−=	ADP
cana-4524	156	80			PROPN
cana-4524	156	81	'	'	PUNCT
cana-4524	156	82	'	'	PUNCT
cana-4524	156	83	'	'	PUNCT
cana-4524	156	84	''	''	PUNCT
cana-4524	156	85	''	''	PUNCT
cana-4524	156	86	''	''	PUNCT
cana-4524	157	1	3	3	NUM
cana-4524	157	2	6	6	NUM
cana-4524	157	3	3	3	NUM
cana-4524	157	4	4	4	NUM
cana-4524	157	5	7	7	NUM
cana-4524	157	6	3	3	NUM
cana-4524	157	7	1	1	NUM
cana-4524	157	8	2	2	NUM
cana-4524	157	9	5	5	NUM
cana-4524	157	10	3	3	NUM
cana-4524	157	11	1	1	NUM
cana-4524	157	12	4	4	NUM
cana-4524	157	13	7	7	NUM
cana-4524	157	14	3	3	NUM
cana-4524	157	15	1	1	NUM
cana-4524	157	16	3	3	NUM
cana-4524	157	17	'	'	NUM
cana-4524	157	18	1	1	NUM
cana-4524	157	19	2	2	NUM
cana-4524	157	20	1	1	NUM
cana-4524	157	21	{	{	PUNCT
cana-4524	157	22	,	,	PUNCT
cana-4524	157	23	,	,	PUNCT
cana-4524	157	24	...	...	PUNCT
cana-4524	157	25	,	,	PUNCT
cana-4524	157	26	}	}	PUNCT
cana-4524	157	27	{	{	PUNCT
cana-4524	157	28	,	,	PUNCT
cana-4524	157	29	,	,	PUNCT
cana-4524	157	30	...	...	PUNCT
cana-4524	157	31	,	,	PUNCT
cana-4524	157	32	}	}	PUNCT
cana-4524	157	33	{	{	PUNCT
cana-4524	157	34	,	,	PUNCT
cana-4524	157	35	,	,	PUNCT
cana-4524	157	36	...	...	PUNCT
cana-4524	157	37	,	,	PUNCT
cana-4524	157	38	}	}	PUNCT
cana-4524	157	39	{	{	PUNCT
cana-4524	157	40	,	,	PUNCT
cana-4524	157	41	,	,	PUNCT
cana-4524	157	42	...	...	PUNCT
cana-4524	157	43	,	,	PUNCT
cana-4524	157	44	}	}	PUNCT
cana-4524	157	45	{	{	PUNCT
cana-4524	157	46	}	}	PUNCT
cana-4524	157	47	{	{	PUNCT
cana-4524	157	48	}	}	PUNCT
cana-4524	157	49	{	{	PUNCT
cana-4524	157	50	,	,	PUNCT
cana-4524	157	51	0,2(mod3	0,2(mod3	NUM
cana-4524	157	52	)	)	PUNCT
cana-4524	157	53	}	}	PUNCT
cana-4524	157	54	v	v	ADP
cana-4524	157	55	v	v	NUM
cana-4524	157	56	v	v	NOUN
cana-4524	157	57	e	e	X
cana-4524	157	58	e	e	X
cana-4524	157	59	e	e	X
cana-4524	157	60	e	e	X
cana-4524	157	61	e	e	X
cana-4524	157	62	e	e	X
cana-4524	157	63	e	e	X
cana-4524	157	64	e	e	X
cana-4524	157	65	e	e	PROPN
cana-4524	157	66	t	t	PROPN
cana-4524	157	67	u	u	X
cana-4524	157	68	f	f	PROPN
cana-4524	157	69	f	f	PROPN
cana-4524	157	70	n	n	PRON
cana-4524	157	71			NOUN
cana-4524	157	72			NOUN
cana-4524	157	73			ADV
cana-4524	157	74	+	+	NOUN
cana-4524	157	75	−	−	PROPN
cana-4524	158	1	+	+	SYM
cana-4524	158	2			NOUN
cana-4524	158	3	=	=	SYM
cana-4524	158	4			NUM
cana-4524	158	5			NOUN
cana-4524	158	6	'	'	PUNCT
cana-4524	158	7	'	'	PUNCT
cana-4524	158	8	'	'	PUNCT
cana-4524	158	9	'	'	PUNCT
cana-4524	158	10	4	4	NUM
cana-4524	158	11	1	1	NUM
cana-4524	158	12	3	3	NUM
cana-4524	158	13	2	2	NUM
cana-4524	158	14	1	1	NUM
cana-4524	158	15	3	3	NUM
cana-4524	158	16	4	4	NUM
cana-4524	158	17	1	1	NUM
cana-4524	158	18	2	2	NUM
cana-4524	158	19	{	{	PUNCT
cana-4524	158	20	,	,	PUNCT
cana-4524	158	21	,	,	PUNCT
cana-4524	158	22	...	...	PUNCT
cana-4524	158	23	,	,	PUNCT
cana-4524	158	24	}	}	PUNCT
cana-4524	158	25	{	{	PUNCT
cana-4524	158	26	,	,	PUNCT
cana-4524	158	27	,	,	PUNCT
cana-4524	158	28	...	...	PUNCT
cana-4524	158	29	,	,	PUNCT
cana-4524	158	30	}	}	PUNCT
cana-4524	158	31	{	{	PUNCT
cana-4524	158	32	}	}	PUNCT
cana-4524	158	33	nt	not	PART
cana-4524	158	34	u	u	X
cana-4524	158	35	u	u	X
cana-4524	158	36	u	u	NOUN
cana-4524	158	37	f	f	PROPN
cana-4524	158	38	f	f	PROPN
cana-4524	158	39	f	f	PROPN
cana-4524	158	40	f	f	PROPN
cana-4524	158	41	−	−	ADP
cana-4524	158	42	−=	−=	NOUN
cana-4524	158	43	'	'	PUNCT
cana-4524	158	44	''	''	PUNCT
cana-4524	158	45	'	'	PUNCT
cana-4524	158	46	'	'	PUNCT
cana-4524	158	47	'	'	PUNCT
cana-4524	158	48	'	'	PUNCT
cana-4524	158	49	'	'	PUNCT
cana-4524	158	50	5	5	NUM
cana-4524	158	51	2	2	NUM
cana-4524	158	52	4	4	NUM
cana-4524	158	53	1	1	NUM
cana-4524	158	54	2	2	NUM
cana-4524	158	55	3	3	NUM
cana-4524	158	56	4	4	NUM
cana-4524	158	57	2	2	NUM
cana-4524	158	58	1	1	NUM
cana-4524	158	59	1	1	NUM
cana-4524	158	60	{	{	PUNCT
cana-4524	158	61	,	,	PUNCT
cana-4524	158	62	,	,	PUNCT
cana-4524	158	63	...	...	PUNCT
cana-4524	158	64	,	,	PUNCT
cana-4524	158	65	}	}	PUNCT
cana-4524	158	66	{	{	PUNCT
cana-4524	158	67	}	}	PUNCT
cana-4524	158	68	{	{	PUNCT
cana-4524	158	69	,	,	PUNCT
cana-4524	158	70	,	,	PUNCT
cana-4524	158	71	...	...	PUNCT
cana-4524	158	72	,	,	PUNCT
cana-4524	158	73	}	}	PUNCT
cana-4524	158	74	{	{	PUNCT
cana-4524	158	75	,	,	PUNCT
cana-4524	158	76	2(mod3	2(mod3	NUM
cana-4524	158	77	)	)	PUNCT
cana-4524	158	78	6	6	NUM
cana-4524	158	79	}	}	PUNCT
cana-4524	158	80	{	{	PUNCT
cana-4524	158	81	,	,	PUNCT
cana-4524	158	82	1(mod3)}n	1(mod3)}n	NUM
cana-4524	158	83	n	n	CCONJ
cana-4524	158	84	nt	not	PART
cana-4524	158	85	u	u	X
cana-4524	158	86	u	u	NOUN
cana-4524	158	87	u	u	NOUN
cana-4524	158	88	f	f	PROPN
cana-4524	158	89	f	f	PROPN
cana-4524	159	1	f	f	PROPN
cana-4524	159	2	f	f	PROPN
cana-4524	159	3	f	f	PROPN
cana-4524	159	4	n	n	PROPN
cana-4524	159	5	and	and	CCONJ
cana-4524	159	6	n	n	CCONJ
cana-4524	159	7	f	f	PROPN
cana-4524	159	8	n−	n−	NOUN
cana-4524	159	9	−	−	PROPN
cana-4524	159	10	−=	−=	NOUN
cana-4524	159	11			PROPN
cana-4524	159	12	=	=	SYM
cana-4524	159	13			PROPN
cana-4524	159	14	'	'	PUNCT
cana-4524	159	15	'	'	PUNCT
cana-4524	159	16	'	'	PUNCT
cana-4524	159	17	'	'	PUNCT
cana-4524	159	18	''	''	PUNCT
cana-4524	160	1	'	'	PUNCT
cana-4524	160	2	''	''	PUNCT
cana-4524	160	3	'	'	PUNCT
cana-4524	160	4	''	''	PUNCT
cana-4524	160	5	''	''	PUNCT
cana-4524	160	6	'	'	PUNCT
cana-4524	160	7	''	''	PUNCT
cana-4524	160	8	6	6	NUM
cana-4524	160	9	2	2	NUM
cana-4524	160	10	4	4	NUM
cana-4524	160	11	1	1	NUM
cana-4524	160	12	3	3	NUM
cana-4524	160	13	4	4	NUM
cana-4524	160	14	2	2	NUM
cana-4524	160	15	1	1	NUM
cana-4524	160	16	1	1	NUM
cana-4524	160	17	{	{	PUNCT
cana-4524	160	18	,	,	PUNCT
cana-4524	160	19	,	,	PUNCT
cana-4524	160	20	...	...	PUNCT
cana-4524	160	21	,	,	PUNCT
cana-4524	160	22	}	}	PUNCT
cana-4524	160	23	{	{	PUNCT
cana-4524	160	24	,	,	PUNCT
cana-4524	160	25	,	,	PUNCT
cana-4524	160	26	...	...	PUNCT
cana-4524	160	27	,	,	PUNCT
cana-4524	160	28	}	}	PUNCT
cana-4524	160	29	{	{	PUNCT
cana-4524	160	30	}	}	PUNCT
cana-4524	160	31	{	{	PUNCT
cana-4524	160	32	}	}	PUNCT
cana-4524	160	33	n	n	CCONJ
cana-4524	160	34	nt	not	PART
cana-4524	160	35	u	u	VERB
cana-4524	160	36	u	u	NOUN
cana-4524	160	37	u	u	NOUN
cana-4524	160	38	f	f	PROPN
cana-4524	160	39	f	f	PROPN
cana-4524	160	40	f	f	PROPN
cana-4524	160	41	f	f	PROPN
cana-4524	160	42	f−	f−	PROPN
cana-4524	160	43	−=	−=	PUNCT
cana-4524	160	44	''	''	PUNCT
cana-4524	160	45	''	''	PUNCT
cana-4524	160	46	''	''	PUNCT
cana-4524	160	47	''	''	PUNCT
cana-4524	160	48	7	7	NUM
cana-4524	160	49	3	3	NUM
cana-4524	160	50	7	7	NUM
cana-4524	160	51	2	2	NUM
cana-4524	160	52	2	2	NUM
cana-4524	160	53	3	3	NUM
cana-4524	160	54	2	2	NUM
cana-4524	160	55	1	1	NUM
cana-4524	160	56	1	1	NUM
cana-4524	160	57	{	{	PUNCT
cana-4524	160	58	,	,	PUNCT
cana-4524	160	59	,	,	PUNCT
cana-4524	160	60	...	...	PUNCT
cana-4524	160	61	,	,	PUNCT
cana-4524	160	62	}	}	PUNCT
cana-4524	160	63	{	{	PUNCT
cana-4524	160	64	,	,	PUNCT
cana-4524	160	65	,	,	PUNCT
cana-4524	160	66	...	...	PUNCT
cana-4524	160	67	,	,	PUNCT
cana-4524	160	68	}	}	PUNCT
cana-4524	160	69	{	{	PUNCT
cana-4524	160	70	}	}	PUNCT
cana-4524	160	71	{	{	PUNCT
cana-4524	160	72	}	}	PUNCT
cana-4524	160	73	n	n	CCONJ
cana-4524	160	74	nt	not	PART
cana-4524	160	75	u	u	VERB
cana-4524	160	76	u	u	NOUN
cana-4524	160	77	u	u	NOUN
cana-4524	160	78	f	f	PROPN
cana-4524	160	79	f	f	PROPN
cana-4524	160	80	f	f	PROPN
cana-4524	160	81	e	e	X
cana-4524	160	82	e−	e−	PROPN
cana-4524	160	83	−=	−=	ADP
cana-4524	160	84	…	…	PUNCT
cana-4524	160	85	…	…	PUNCT
cana-4524	160	86	…	…	PUNCT
cana-4524	160	87	…	…	PUNCT
cana-4524	160	88	…	…	PUNCT
cana-4524	160	89	……	……	NOUN
cana-4524	160	90	……	……	NOUN
cana-4524	160	91	……	……	NOUN
cana-4524	160	92	…	…	PUNCT
cana-4524	160	93	…	…	SYM
cana-4524	160	94	…	…	PUNCT
cana-4524	160	95	…	…	PUNCT
cana-4524	160	96	…	…	PUNCT
cana-4524	160	97	……	……	NOUN
cana-4524	160	98	……	……	NOUN
cana-4524	160	99	……	……	NOUN
cana-4524	160	100	'	'	PUNCT
cana-4524	160	101	''	''	PUNCT
cana-4524	160	102	'	'	PUNCT
cana-4524	160	103	'	'	PUNCT
cana-4524	160	104	'	'	PUNCT
cana-4524	160	105	'	'	PUNCT
cana-4524	160	106	'	'	PUNCT
cana-4524	160	107	1	1	NUM
cana-4524	160	108	2	2	NUM
cana-4524	160	109	4	4	NUM
cana-4524	160	110	1	1	NUM
cana-4524	160	111	2	2	NUM
cana-4524	160	112	3	3	NUM
cana-4524	160	113	4	4	NUM
cana-4524	160	114	2	2	NUM
cana-4524	160	115	1	1	NUM
cana-4524	160	116	1	1	NUM
cana-4524	160	117	{	{	PUNCT
cana-4524	160	118	,	,	PUNCT
cana-4524	160	119	,	,	PUNCT
cana-4524	160	120	...	...	PUNCT
cana-4524	160	121	,	,	PUNCT
cana-4524	160	122	}	}	PUNCT
cana-4524	160	123	{	{	PUNCT
cana-4524	160	124	}	}	PUNCT
cana-4524	160	125	{	{	PUNCT
cana-4524	160	126	,	,	PUNCT
cana-4524	160	127	,	,	PUNCT
cana-4524	160	128	...	...	PUNCT
cana-4524	160	129	,	,	PUNCT
cana-4524	160	130	}	}	PUNCT
cana-4524	160	131	{	{	PUNCT
cana-4524	160	132	,	,	PUNCT
cana-4524	160	133	2(mod3	2(mod3	NUM
cana-4524	160	134	)	)	PUNCT
cana-4524	160	135	6	6	NUM
cana-4524	160	136	}	}	PUNCT
cana-4524	160	137	{	{	PUNCT
cana-4524	160	138	,	,	PUNCT
cana-4524	160	139	1(mod3)}n	1(mod3)}n	NUM
cana-4524	160	140	n	n	CCONJ
cana-4524	160	141	nt	not	PART
cana-4524	160	142	u	u	X
cana-4524	160	143	u	u	NOUN
cana-4524	160	144	u	u	NOUN
cana-4524	160	145	f	f	PROPN
cana-4524	160	146	f	f	PROPN
cana-4524	161	1	f	f	PROPN
cana-4524	161	2	f	f	PROPN
cana-4524	161	3	f	f	PROPN
cana-4524	161	4	n	n	PROPN
cana-4524	161	5	and	and	CCONJ
cana-4524	161	6	n	n	PROPN
cana-4524	161	7	f	f	PROPN
cana-4524	161	8	n−	n−	PROPN
cana-4524	162	1	−	−	PROPN
cana-4524	162	2	−	−	PROPN
cana-4524	162	3	−=	−=	NOUN
cana-4524	162	4			PROPN
cana-4524	162	5	=	=	SYM
cana-4524	162	6			PROPN
cana-4524	162	7	'	'	PUNCT
cana-4524	162	8	'	'	PUNCT
cana-4524	162	9	'	'	PUNCT
cana-4524	162	10	'	'	PUNCT
cana-4524	162	11	''	''	PUNCT
cana-4524	162	12	'	'	PUNCT
cana-4524	162	13	''	''	PUNCT
cana-4524	162	14	'	'	PUNCT
cana-4524	162	15	''	''	PUNCT
cana-4524	162	16	''	''	PUNCT
cana-4524	162	17	'	'	PUNCT
cana-4524	162	18	''	''	PUNCT
cana-4524	162	19	2	2	NUM
cana-4524	162	20	4	4	NUM
cana-4524	162	21	1	1	NUM
cana-4524	162	22	3	3	NUM
cana-4524	162	23	4	4	NUM
cana-4524	162	24	2	2	NUM
cana-4524	162	25	1	1	NUM
cana-4524	162	26	1	1	NUM
cana-4524	162	27	{	{	PUNCT
cana-4524	162	28	,	,	PUNCT
cana-4524	162	29	,	,	PUNCT
cana-4524	162	30	...	...	PUNCT
cana-4524	162	31	,	,	PUNCT
cana-4524	162	32	}	}	PUNCT
cana-4524	162	33	{	{	PUNCT
cana-4524	162	34	,	,	PUNCT
cana-4524	162	35	,	,	PUNCT
cana-4524	162	36	...	...	PUNCT
cana-4524	162	37	,	,	PUNCT
cana-4524	162	38	}	}	PUNCT
cana-4524	162	39	{	{	PUNCT
cana-4524	162	40	}	}	PUNCT
cana-4524	162	41	{	{	PUNCT
cana-4524	162	42	}	}	PUNCT
cana-4524	162	43	n	n	CCONJ
cana-4524	162	44	nt	not	PART
cana-4524	162	45	u	u	VERB
cana-4524	162	46	u	u	NOUN
cana-4524	162	47	u	u	NOUN
cana-4524	162	48	f	f	PROPN
cana-4524	162	49	f	f	PROPN
cana-4524	162	50	f	f	PROPN
cana-4524	162	51	f	f	PROPN
cana-4524	162	52	f	f	PROPN
cana-4524	162	53	−	−	PROPN
cana-4524	162	54	−=	−=	NOUN
cana-4524	162	55	''	''	PUNCT
cana-4524	162	56	''	''	PUNCT
cana-4524	162	57	''	''	PUNCT
cana-4524	162	58	''	''	PUNCT
cana-4524	162	59	1	1	NUM
cana-4524	162	60	3	3	NUM
cana-4524	162	61	7	7	NUM
cana-4524	162	62	2	2	NUM
cana-4524	162	63	2	2	NUM
cana-4524	162	64	3	3	NUM
cana-4524	162	65	2	2	NUM
cana-4524	162	66	1	1	NUM
cana-4524	162	67	1	1	NUM
cana-4524	162	68	{	{	PUNCT
cana-4524	162	69	,	,	PUNCT
cana-4524	162	70	,	,	PUNCT
cana-4524	162	71	...	...	PUNCT
cana-4524	162	72	,	,	PUNCT
cana-4524	162	73	}	}	PUNCT
cana-4524	162	74	{	{	PUNCT
cana-4524	162	75	,	,	PUNCT
cana-4524	162	76	,	,	PUNCT
cana-4524	162	77	...	...	PUNCT
cana-4524	162	78	,	,	PUNCT
cana-4524	162	79	}	}	PUNCT
cana-4524	162	80	{	{	PUNCT
cana-4524	162	81	}	}	PUNCT
cana-4524	162	82	{	{	PUNCT
cana-4524	162	83	}	}	PUNCT
cana-4524	162	84	n	n	CCONJ
cana-4524	162	85	nt	not	PART
cana-4524	162	86	u	u	VERB
cana-4524	162	87	u	u	NOUN
cana-4524	162	88	u	u	NOUN
cana-4524	162	89	f	f	PROPN
cana-4524	162	90	f	f	PROPN
cana-4524	162	91	f	f	PROPN
cana-4524	162	92	e	e	PROPN
cana-4524	162	93	e+	e+	PROPN
cana-4524	162	94	−	−	PROPN
cana-4524	162	95	−=	−=	NOUN
cana-4524	162	96	based	base	VERB
cana-4524	162	97	on	on	ADP
cana-4524	162	98	the	the	DET
cana-4524	162	99	coloring	coloring	NOUN
cana-4524	162	100	technique	technique	NOUN
cana-4524	162	101	described	describe	VERB
cana-4524	162	102	above	above	ADV
cana-4524	162	103	,	,	PUNCT
cana-4524	162	104	it	it	PRON
cana-4524	162	105	is	be	AUX
cana-4524	162	106	evident	evident	ADJ
cana-4524	162	107	that	that	SCONJ
cana-4524	162	108	the	the	DET
cana-4524	162	109	color	color	NOUN
cana-4524	162	110	classes	class	NOUN
cana-4524	162	111	1	1	NUM
cana-4524	162	112	2	2	NUM
cana-4524	162	113	3	3	NUM
cana-4524	162	114	,	,	PUNCT
cana-4524	162	115	,	,	PUNCT
cana-4524	162	116	,	,	PUNCT
cana-4524	162	117	...	...	PUNCT
cana-4524	162	118	t	t	PROPN
cana-4524	162	119	t	t	PROPN
cana-4524	162	120	t	t	PROPN
cana-4524	162	121	and	and	CCONJ
cana-4524	162	122	1t+	1t+	PROPN
cana-4524	162	123	are	be	AUX
cana-4524	162	124	independent	independent	ADJ
cana-4524	162	125	sets	set	NOUN
cana-4524	162	126	of	of	ADP
cana-4524	162	127	(	(	PUNCT
cana-4524	162	128	)	)	PUNCT
cana-4524	162	129	nl	nl	PROPN
cana-4524	162	130	t	t	PROPN
cana-4524	162	131	and	and	CCONJ
cana-4524	162	132	it	it	PRON
cana-4524	162	133	holds	hold	VERB
cana-4524	162	134	inequality	inequality	NOUN
cana-4524	163	1	|	|	ADV
cana-4524	164	1	|	|	ADV
cana-4524	164	2	|	|	ADV
cana-4524	164	3	|	|	ADV
cana-4524	164	4	1a	1a	VERB
cana-4524	164	5	bt	bt	VERB
cana-4524	164	6	t−	t−	PROPN
cana-4524	164	7			NOUN
cana-4524	164	8	for	for	ADP
cana-4524	164	9	a	a	DET
cana-4524	164	10	b	b	PROPN
cana-4524	164	11	.	.	PUNCT
cana-4524	165	1	this	this	PRON
cana-4524	165	2	implies	imply	VERB
cana-4524	165	3	that	that	SCONJ
cana-4524	165	4	(	(	PUNCT
cana-4524	165	5	)	)	PUNCT
cana-4524	165	6	''	''	PUNCT
cana-4524	165	7	(	(	PUNCT
cana-4524	165	8	)	)	PUNCT
cana-4524	165	9	1e	1e	NOUN
cana-4524	165	10	nl	nl	PROPN
cana-4524	165	11	t	t	VERB
cana-4524	165	12			NUM
cana-4524	165	13	+	+	VERB
cana-4524	165	14	.	.	PUNCT
cana-4524	166	1	further	far	ADV
cana-4524	166	2	,	,	PUNCT
cana-4524	166	3	we	we	PRON
cana-4524	166	4	have	have	VERB
cana-4524	166	5	(	(	PUNCT
cana-4524	166	6	)	)	PUNCT
cana-4524	166	7	''	''	PUNCT
cana-4524	167	1	(	(	PUNCT
cana-4524	167	2	)	)	PUNCT
cana-4524	167	3	e	e	X
cana-4524	167	4	nl	nl	NOUN
cana-4524	167	5	t	t	NOUN
cana-4524	167	6	=	=	PUNCT
cana-4524	167	7	(	(	PUNCT
cana-4524	167	8	)	)	PUNCT
cana-4524	167	9	''	''	PUNCT
cana-4524	168	1	(	(	PUNCT
cana-4524	168	2	)	)	PUNCT
cana-4524	168	3	1nl	1nl	ADJ
cana-4524	168	4	t	t	NOUN
cana-4524	168	5			NUM
cana-4524	168	6	+	+	PROPN
cana-4524	168	7	.	.	PUNCT
cana-4524	169	1	hence	hence	ADV
cana-4524	169	2	(	(	PUNCT
cana-4524	169	3	)	)	PUNCT
cana-4524	169	4	''	''	PUNCT
cana-4524	169	5	(	(	PUNCT
cana-4524	169	6	)	)	PUNCT
cana-4524	169	7	1e	1e	NOUN
cana-4524	169	8	nl	nl	PROPN
cana-4524	169	9	t	t	NOUN
cana-4524	169	10	=	=	SYM
cana-4524	169	11	+	+	PROPN
cana-4524	169	12	.	.	PUNCT
cana-4524	169	13	example	example	NOUN
cana-4524	169	14	3.3	3.3	NUM
cana-4524	169	15	:	:	PUNCT
cana-4524	169	16	the	the	DET
cana-4524	169	17	graph	graph	NOUN
cana-4524	169	18	6	6	NUM
cana-4524	169	19	(	(	PUNCT
cana-4524	169	20	)	)	PUNCT
cana-4524	169	21	l	l	NOUN
cana-4524	169	22	t	t	NOUN
cana-4524	169	23	and	and	CCONJ
cana-4524	169	24	its	its	PRON
cana-4524	169	25	equitable	equitable	ADJ
cana-4524	169	26	total	total	ADJ
cana-4524	169	27	coloring	coloring	NOUN
cana-4524	169	28	is	be	AUX
cana-4524	169	29	shown	show	VERB
cana-4524	169	30	in	in	ADP
cana-4524	169	31	figure	figure	NOUN
cana-4524	169	32	3	3	NUM
cana-4524	169	33	.	.	PUNCT
cana-4524	169	34	figure	figure	VERB
cana-4524	169	35	3	3	NUM
cana-4524	169	36	:	:	SYM
cana-4524	169	37	6	6	NUM
cana-4524	169	38	(	(	PUNCT
cana-4524	169	39	)	)	PUNCT
cana-4524	169	40	l	l	NOUN
cana-4524	169	41	t	t	NOUN
cana-4524	169	42	and	and	CCONJ
cana-4524	169	43	its	its	PRON
cana-4524	169	44	equitable	equitable	ADJ
cana-4524	169	45	total	total	ADJ
cana-4524	169	46	coloring	coloring	NOUN
cana-4524	169	47	theorem	theorem	VERB
cana-4524	169	48	3.4	3.4	NUM
cana-4524	169	49	:	:	PUNCT
cana-4524	169	50	let	let	VERB
cana-4524	169	51	(	(	PUNCT
cana-4524	169	52	)	)	PUNCT
cana-4524	169	53	nl	nl	PROPN
cana-4524	169	54	at	at	AUX
cana-4524	169	55	represent	represent	VERB
cana-4524	169	56	the	the	DET
cana-4524	169	57	line	line	NOUN
cana-4524	169	58	graph	graph	NOUN
cana-4524	169	59	of	of	ADP
cana-4524	169	60	alternate	alternate	ADJ
cana-4524	169	61	triangular	triangular	NOUN
cana-4524	169	62	snake	snake	NOUN
cana-4524	169	63	graph	graph	NOUN
cana-4524	169	64	,	,	PUNCT
cana-4524	169	65	then	then	ADV
cana-4524	169	66	(	(	PUNCT
cana-4524	169	67	)	)	PUNCT
cana-4524	169	68	''	''	PUNCT
cana-4524	170	1	(	(	PUNCT
cana-4524	170	2	)	)	PUNCT
cana-4524	170	3	5	5	NUM
cana-4524	170	4	,	,	PUNCT
cana-4524	170	5	7e	7e	PROPN
cana-4524	170	6	nl	nl	PROPN
cana-4524	170	7	t	t	PROPN
cana-4524	170	8	n	n	NOUN
cana-4524	170	9	=	=	PUNCT
cana-4524	170	10			NOUN
cana-4524	170	11	.	.	PUNCT
cana-4524	171	1	proof	proof	NOUN
cana-4524	171	2	:	:	PUNCT
cana-4524	171	3	(	(	PUNCT
cana-4524	171	4	(	(	PUNCT
cana-4524	171	5	)	)	PUNCT
cana-4524	171	6	)	)	PUNCT
cana-4524	171	7	{	{	PUNCT
cana-4524	171	8	:1	:1	PUNCT
cana-4524	171	9	}	}	PUNCT
cana-4524	171	10	{	{	PUNCT
cana-4524	171	11	:1	:1	NUM
cana-4524	171	12	1}nv	1}nv	ADJ
cana-4524	171	13	l	l	NOUN
cana-4524	171	14	at	at	ADP
cana-4524	171	15	u	u	PROPN
cana-4524	171	16	n	n	ADP
cana-4524	171	17	v	v	ADP
cana-4524	171	18	n	n	NOUN
cana-4524	171	19			NOUN
cana-4524	171	20	=	=	NOUN
cana-4524	171	21			NOUN
cana-4524	171	22			NOUN
cana-4524	171	23			NOUN
cana-4524	171	24			NOUN
cana-4524	171	25	−	−	NOUN
cana-4524	171	26	and	and	CCONJ
cana-4524	171	27			PROPN
cana-4524	171	28			PROPN
cana-4524	171	29	'	'	PUNCT
cana-4524	171	30	'	'	PUNCT
cana-4524	171	31	(	(	PUNCT
cana-4524	171	32	(	(	PUNCT
cana-4524	171	33	)	)	PUNCT
cana-4524	171	34	)	)	PUNCT
cana-4524	172	1	:1	:1	PUNCT
cana-4524	172	2	:1	:1	PUNCT
cana-4524	172	3	2	2	X
cana-4524	172	4	{	{	PUNCT
cana-4524	172	5	,	,	PUNCT
cana-4524	172	6	:1	:1	PUNCT
cana-4524	172	7	1	1	NUM
cana-4524	172	8	}	}	SYM
cana-4524	172	9	2	2	NUM
cana-4524	172	10	n	n	CCONJ
cana-4524	172	11	n	n	NOUN
cana-4524	172	12	e	e	NOUN
cana-4524	172	13	l	l	NOUN
cana-4524	172	14	at	at	ADP
cana-4524	172	15	e	e	PROPN
cana-4524	172	16	e	e	X
cana-4524	172	17	n	n	CCONJ
cana-4524	172	18	f	f	PROPN
cana-4524	172	19	f	f	PROPN
cana-4524	172	20	n	n	NOUN
cana-4524	172	21			NOUN
cana-4524	172	22			NOUN
cana-4524	172	23			NOUN
cana-4524	172	24			NOUN
cana-4524	172	25			NOUN
cana-4524	172	26			ADV
cana-4524	172	27			ADJ
cana-4524	172	28			NOUN
cana-4524	172	29	=	=	PUNCT
cana-4524	172	30			NOUN
cana-4524	172	31			NOUN
cana-4524	172	32			NOUN
cana-4524	172	33			NOUN
cana-4524	172	34	−	−	ADP
cana-4524	172	35			PROPN
cana-4524	172	36			NOUN
cana-4524	172	37	−	−	NOUN
cana-4524	172	38			VERB
cana-4524	172	39			NOUN
cana-4524	172	40			VERB
cana-4524	172	41			ADJ
cana-4524	172	42			PROPN
cana-4524	172	43	,	,	PUNCT
cana-4524	172	44	where	where	SCONJ
cana-4524	172	45	2	2	NUM
cana-4524	172	46	1	1	NUM
cana-4524	172	47	2	2	NUM
cana-4524	172	48	,	,	PUNCT
cana-4524	172	49	e	e	X
cana-4524	172	50	u	u	NOUN
cana-4524	172	51	u	u	PROPN
cana-4524	172	52			NOUN
cana-4524	172	53	−=	−=	X
cana-4524	172	54	'	'	PUNCT
cana-4524	172	55	1,e	1,e	NUM
cana-4524	172	56	v	v	ADP
cana-4524	172	57	v	v	PRON
cana-4524	172	58			NOUN
cana-4524	172	59			NOUN
cana-4524	172	60	+	+	NOUN
cana-4524	172	61	=	=	X
cana-4524	172	62	,	,	PUNCT
cana-4524	172	63	f	f	PROPN
cana-4524	172	64	u	u	NOUN
cana-4524	172	65	v	v	PROPN
cana-4524	172	66			NOUN
cana-4524	172	67	=	=	NOUN
cana-4524	172	68	'	'	PUNCT
cana-4524	172	69	1,f	1,f	NUM
cana-4524	172	70	v	v	NUM
cana-4524	172	71	u	u	PROPN
cana-4524	172	72			NOUN
cana-4524	172	73	+=	+=	NOUN
cana-4524	172	74	we	we	PRON
cana-4524	172	75	divide	divide	VERB
cana-4524	172	76	the	the	DET
cana-4524	172	77	vertex	vertex	NOUN
cana-4524	172	78	and	and	CCONJ
cana-4524	172	79	edge	edge	NOUN
cana-4524	172	80	set	set	NOUN
cana-4524	172	81	of	of	ADP
cana-4524	172	82	(	(	PUNCT
cana-4524	172	83	)	)	PUNCT
cana-4524	172	84	nl	nl	PROPN
cana-4524	172	85	sl	sl	VERB
cana-4524	172	86	into	into	ADP
cana-4524	172	87	distinct	distinct	ADJ
cana-4524	172	88	partition	partition	NOUN
cana-4524	172	89	as	as	SCONJ
cana-4524	172	90	described	describe	VERB
cana-4524	172	91	below	below	ADV
cana-4524	172	92	.	.	PUNCT
cana-4524	173	1	communications	communication	NOUN
cana-4524	173	2	on	on	ADP
cana-4524	173	3	applied	apply	VERB
cana-4524	173	4	nonlinear	nonlinear	ADJ
cana-4524	173	5	analysis	analysis	NOUN
cana-4524	173	6	issn	issn	NOUN
cana-4524	173	7	:	:	PUNCT
cana-4524	173	8	1074	1074	NUM
cana-4524	173	9	-	-	PUNCT
cana-4524	173	10	133x	133x	NUM
cana-4524	173	11	vol	vol	NOUN
cana-4524	173	12	32	32	NUM
cana-4524	173	13	no	no	NOUN
cana-4524	173	14	.	.	PUNCT
cana-4524	174	1	9s	9s	NUM
cana-4524	174	2	(	(	PUNCT
cana-4524	174	3	2025	2025	NUM
cana-4524	174	4	)	)	PUNCT
cana-4524	174	5	2376	2376	NUM
cana-4524	174	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	174	7	for1	for1	VERB
cana-4524	174	8	1n	1n	NUM
cana-4524	174	9			NOUN
cana-4524	174	10	−	−	NOUN
cana-4524	174	11	.	.	PUNCT
cana-4524	175	1	4	4	NUM
cana-4524	175	2	9	9	NUM
cana-4524	175	3	5	5	NUM
cana-4524	175	4	1	1	NUM
cana-4524	175	5	1	1	NUM
cana-4524	175	6	6	6	NUM
cana-4524	175	7	5	5	NUM
cana-4524	175	8	4	4	NUM
cana-4524	175	9	1	1	NUM
cana-4524	175	10	6	6	NUM
cana-4524	175	11	5	5	NUM
cana-4524	175	12	4	4	NUM
cana-4524	175	13	1	1	NUM
cana-4524	175	14	'	'	PUNCT
cana-4524	175	15	'	'	PUNCT
cana-4524	175	16	'	'	PUNCT
cana-4524	175	17	'	'	PUNCT
cana-4524	175	18	'	'	PUNCT
cana-4524	175	19	'	'	PUNCT
cana-4524	175	20	3	3	NUM
cana-4524	175	21	8	8	NUM
cana-4524	175	22	5	5	NUM
cana-4524	175	23	2	2	NUM
cana-4524	175	24	5	5	NUM
cana-4524	175	25	10	10	NUM
cana-4524	175	26	5	5	NUM
cana-4524	175	27	2	2	NUM
cana-4524	175	28	7	7	NUM
cana-4524	175	29	5	5	NUM
cana-4524	175	30	3	3	NUM
cana-4524	175	31	{	{	PUNCT
cana-4524	175	32	,	,	PUNCT
cana-4524	175	33	,	,	PUNCT
cana-4524	175	34	...	...	PUNCT
cana-4524	175	35	,	,	PUNCT
cana-4524	175	36	}	}	PUNCT
cana-4524	175	37	{	{	PUNCT
cana-4524	175	38	,	,	PUNCT
cana-4524	175	39	,	,	PUNCT
cana-4524	175	40	...	...	PUNCT
cana-4524	175	41	,	,	PUNCT
cana-4524	175	42	}	}	PUNCT
cana-4524	175	43	{	{	PUNCT
cana-4524	175	44	,	,	PUNCT
cana-4524	175	45	,	,	PUNCT
cana-4524	175	46	...	...	PUNCT
cana-4524	175	47	,	,	PUNCT
cana-4524	175	48	}	}	PUNCT
cana-4524	175	49	{	{	PUNCT
cana-4524	175	50	,	,	PUNCT
cana-4524	175	51	,	,	PUNCT
cana-4524	175	52	...	...	PUNCT
cana-4524	175	53	,	,	PUNCT
cana-4524	175	54	}	}	PUNCT
cana-4524	175	55	{	{	PUNCT
cana-4524	175	56	,	,	PUNCT
cana-4524	175	57	,	,	PUNCT
cana-4524	175	58	...	...	PUNCT
cana-4524	175	59	,	,	PUNCT
cana-4524	175	60	}	}	PUNCT
cana-4524	175	61	{	{	PUNCT
cana-4524	175	62	,	,	PUNCT
cana-4524	175	63	,	,	PUNCT
cana-4524	175	64	...	...	PUNCT
cana-4524	175	65	,	,	PUNCT
cana-4524	175	66	}	}	PUNCT
cana-4524	175	67	u	u	NOUN
cana-4524	175	68	u	u	NOUN
cana-4524	175	69	u	u	NOUN
cana-4524	175	70	v	v	ADP
cana-4524	175	71	v	v	ADP
cana-4524	175	72	v	v	NOUN
cana-4524	175	73	e	e	X
cana-4524	175	74	e	e	X
cana-4524	175	75	e	e	X
cana-4524	175	76	t	t	NOUN
cana-4524	175	77	e	e	X
cana-4524	175	78	e	e	X
cana-4524	175	79	e	e	X
cana-4524	175	80	f	f	PROPN
cana-4524	176	1	f	f	PROPN
cana-4524	176	2	f	f	PROPN
cana-4524	177	1	f	f	PROPN
cana-4524	177	2	f	f	PROPN
cana-4524	177	3	f	f	PROPN
cana-4524	177	4			NOUN
cana-4524	177	5			NOUN
cana-4524	177	6			NOUN
cana-4524	177	7			NOUN
cana-4524	177	8			NOUN
cana-4524	177	9			NOUN
cana-4524	177	10	−	−	PROPN
cana-4524	177	11	−	−	PROPN
cana-4524	177	12	−	−	PROPN
cana-4524	177	13	−	−	NOUN
cana-4524	177	14	−	−	NOUN
cana-4524	177	15			NOUN
cana-4524	177	16	=	=	PUNCT
cana-4524	178	1			NUM
cana-4524	178	2			PROPN
cana-4524	178	3	2	2	NUM
cana-4524	178	4	7	7	NUM
cana-4524	178	5	5	5	NUM
cana-4524	178	6	3	3	NUM
cana-4524	178	7	4	4	NUM
cana-4524	178	8	9	9	NUM
cana-4524	178	9	5	5	NUM
cana-4524	178	10	1	1	NUM
cana-4524	178	11	5	5	NUM
cana-4524	178	12	10	10	NUM
cana-4524	178	13	5	5	NUM
cana-4524	178	14	2	2	NUM
cana-4524	178	15	'	'	PUNCT
cana-4524	178	16	'	'	PUNCT
cana-4524	178	17	'	'	PUNCT
cana-4524	178	18	'	'	PUNCT
cana-4524	178	19	'	'	PUNCT
cana-4524	178	20	'	'	NUM
cana-4524	178	21	1	1	NUM
cana-4524	178	22	6	6	NUM
cana-4524	178	23	5	5	NUM
cana-4524	178	24	4	4	NUM
cana-4524	178	25	3	3	NUM
cana-4524	178	26	8	8	NUM
cana-4524	178	27	5	5	NUM
cana-4524	178	28	2	2	NUM
cana-4524	178	29	5	5	NUM
cana-4524	178	30	10	10	NUM
cana-4524	178	31	5	5	NUM
cana-4524	178	32	{	{	PUNCT
cana-4524	178	33	,	,	PUNCT
cana-4524	178	34	,	,	PUNCT
cana-4524	178	35	...	...	PUNCT
cana-4524	178	36	,	,	PUNCT
cana-4524	178	37	}	}	PUNCT
cana-4524	178	38	{	{	PUNCT
cana-4524	178	39	,	,	PUNCT
cana-4524	178	40	,	,	PUNCT
cana-4524	178	41	...	...	PUNCT
cana-4524	178	42	,	,	PUNCT
cana-4524	178	43	}	}	PUNCT
cana-4524	178	44	{	{	PUNCT
cana-4524	178	45	,	,	PUNCT
cana-4524	178	46	,	,	PUNCT
cana-4524	178	47	...	...	PUNCT
cana-4524	178	48	,	,	PUNCT
cana-4524	178	49	}	}	PUNCT
cana-4524	178	50	{	{	PUNCT
cana-4524	178	51	,	,	PUNCT
cana-4524	178	52	,	,	PUNCT
cana-4524	178	53	...	...	PUNCT
cana-4524	178	54	,	,	PUNCT
cana-4524	178	55	}	}	PUNCT
cana-4524	178	56	{	{	PUNCT
cana-4524	178	57	,	,	PUNCT
cana-4524	178	58	,	,	PUNCT
cana-4524	178	59	...	...	PUNCT
cana-4524	178	60	,	,	PUNCT
cana-4524	178	61	}	}	PUNCT
cana-4524	178	62	{	{	PUNCT
cana-4524	178	63	,	,	PUNCT
cana-4524	178	64	,	,	PUNCT
cana-4524	178	65	...	...	PUNCT
cana-4524	178	66	,	,	PUNCT
cana-4524	178	67	}	}	PUNCT
cana-4524	178	68	u	u	NOUN
cana-4524	178	69	u	u	NOUN
cana-4524	178	70	u	u	NOUN
cana-4524	178	71	v	v	ADP
cana-4524	178	72	v	v	ADP
cana-4524	178	73	v	v	NOUN
cana-4524	178	74	e	e	X
cana-4524	178	75	e	e	X
cana-4524	178	76	e	e	X
cana-4524	178	77	t	t	NOUN
cana-4524	178	78	e	e	X
cana-4524	178	79	e	e	X
cana-4524	178	80	e	e	X
cana-4524	178	81	f	f	PROPN
cana-4524	178	82	f	f	PROPN
cana-4524	179	1	f	f	PROPN
cana-4524	179	2	f	f	PROPN
cana-4524	179	3	f	f	PROPN
cana-4524	179	4	f	f	PROPN
cana-4524	179	5			NOUN
cana-4524	179	6			NOUN
cana-4524	179	7			NOUN
cana-4524	179	8			NOUN
cana-4524	179	9			NOUN
cana-4524	179	10			NOUN
cana-4524	179	11	−	−	PROPN
cana-4524	179	12	−	−	PROPN
cana-4524	180	1	−	−	NOUN
cana-4524	180	2	−	−	NOUN
cana-4524	180	3			NOUN
cana-4524	180	4	=	=	PUNCT
cana-4524	181	1			NUM
cana-4524	181	2			PROPN
cana-4524	181	3	5	5	NUM
cana-4524	181	4	10	10	NUM
cana-4524	181	5	5	5	NUM
cana-4524	181	6	2	2	NUM
cana-4524	181	7	7	7	NUM
cana-4524	181	8	5	5	NUM
cana-4524	181	9	3	3	NUM
cana-4524	181	10	4	4	NUM
cana-4524	181	11	9	9	NUM
cana-4524	181	12	5	5	NUM
cana-4524	181	13	1	1	NUM
cana-4524	181	14	3	3	NUM
cana-4524	181	15	'	'	PUNCT
cana-4524	181	16	'	'	PUNCT
cana-4524	181	17	'	'	PUNCT
cana-4524	181	18	'	'	PUNCT
cana-4524	181	19	'	'	PUNCT
cana-4524	181	20	'	'	PUNCT
cana-4524	181	21	4	4	NUM
cana-4524	181	22	9	9	NUM
cana-4524	181	23	5	5	NUM
cana-4524	181	24	1	1	NUM
cana-4524	181	25	1	1	NUM
cana-4524	181	26	6	6	NUM
cana-4524	181	27	5	5	NUM
cana-4524	181	28	4	4	NUM
cana-4524	181	29	3	3	NUM
cana-4524	181	30	8	8	NUM
cana-4524	181	31	5	5	NUM
cana-4524	181	32	2	2	NUM
cana-4524	181	33	{	{	PUNCT
cana-4524	181	34	,	,	PUNCT
cana-4524	181	35	,	,	PUNCT
cana-4524	181	36	...	...	PUNCT
cana-4524	181	37	,	,	PUNCT
cana-4524	181	38	}	}	PUNCT
cana-4524	181	39	{	{	PUNCT
cana-4524	181	40	,	,	PUNCT
cana-4524	181	41	,	,	PUNCT
cana-4524	181	42	...	...	PUNCT
cana-4524	181	43	,	,	PUNCT
cana-4524	181	44	}	}	PUNCT
cana-4524	181	45	{	{	PUNCT
cana-4524	181	46	,	,	PUNCT
cana-4524	181	47	,	,	PUNCT
cana-4524	181	48	...	...	PUNCT
cana-4524	181	49	,	,	PUNCT
cana-4524	181	50	}	}	PUNCT
cana-4524	181	51	{	{	PUNCT
cana-4524	181	52	,	,	PUNCT
cana-4524	181	53	,	,	PUNCT
cana-4524	181	54	...	...	PUNCT
cana-4524	181	55	,	,	PUNCT
cana-4524	181	56	}	}	PUNCT
cana-4524	181	57	{	{	PUNCT
cana-4524	181	58	,	,	PUNCT
cana-4524	181	59	,	,	PUNCT
cana-4524	181	60	...	...	PUNCT
cana-4524	181	61	,	,	PUNCT
cana-4524	181	62	}	}	PUNCT
cana-4524	181	63	{	{	PUNCT
cana-4524	181	64	,	,	PUNCT
cana-4524	181	65	,	,	PUNCT
cana-4524	181	66	...	...	PUNCT
cana-4524	181	67	,	,	PUNCT
cana-4524	181	68	}	}	PUNCT
cana-4524	181	69	u	u	NOUN
cana-4524	181	70	u	u	NOUN
cana-4524	181	71	u	u	NOUN
cana-4524	181	72	v	v	ADP
cana-4524	181	73	v	v	ADP
cana-4524	181	74	v	v	NOUN
cana-4524	181	75	e	e	X
cana-4524	181	76	e	e	X
cana-4524	181	77	e	e	X
cana-4524	181	78	t	t	NOUN
cana-4524	181	79	e	e	X
cana-4524	181	80	e	e	X
cana-4524	181	81	e	e	X
cana-4524	181	82	f	f	PROPN
cana-4524	182	1	f	f	PROPN
cana-4524	182	2	f	f	PROPN
cana-4524	183	1	f	f	PROPN
cana-4524	183	2	f	f	PROPN
cana-4524	183	3	f	f	PROPN
cana-4524	183	4			NOUN
cana-4524	183	5			NOUN
cana-4524	183	6			NOUN
cana-4524	183	7			NOUN
cana-4524	183	8			NOUN
cana-4524	183	9			NOUN
cana-4524	183	10	−	−	PROPN
cana-4524	183	11	−	−	PROPN
cana-4524	183	12	−	−	PROPN
cana-4524	183	13	−	−	NOUN
cana-4524	183	14	−	−	NOUN
cana-4524	183	15			NOUN
cana-4524	183	16	=	=	PUNCT
cana-4524	184	1			NUM
cana-4524	184	2			NOUN
cana-4524	184	3	3	3	NUM
cana-4524	184	4	8	8	NUM
cana-4524	184	5	5	5	NUM
cana-4524	184	6	2	2	NUM
cana-4524	184	7	5	5	NUM
cana-4524	184	8	10	10	NUM
cana-4524	184	9	5	5	NUM
cana-4524	184	10	3	3	NUM
cana-4524	184	11	8	8	NUM
cana-4524	184	12	5	5	NUM
cana-4524	184	13	2	2	NUM
cana-4524	184	14	4	4	NUM
cana-4524	184	15	'	'	PUNCT
cana-4524	184	16	'	'	PUNCT
cana-4524	184	17	'	'	PUNCT
cana-4524	184	18	'	'	PUNCT
cana-4524	184	19	'	'	PUNCT
cana-4524	184	20	'	'	NUM
cana-4524	184	21	2	2	NUM
cana-4524	184	22	7	7	NUM
cana-4524	184	23	5	5	NUM
cana-4524	184	24	3	3	NUM
cana-4524	184	25	4	4	NUM
cana-4524	184	26	9	9	NUM
cana-4524	184	27	5	5	NUM
cana-4524	184	28	1	1	NUM
cana-4524	184	29	1	1	NUM
cana-4524	184	30	6	6	NUM
cana-4524	184	31	5	5	NUM
cana-4524	184	32	4	4	NUM
cana-4524	184	33	{	{	PUNCT
cana-4524	184	34	,	,	PUNCT
cana-4524	184	35	,	,	PUNCT
cana-4524	184	36	...	...	PUNCT
cana-4524	184	37	,	,	PUNCT
cana-4524	184	38	}	}	PUNCT
cana-4524	184	39	{	{	PUNCT
cana-4524	184	40	,	,	PUNCT
cana-4524	184	41	,	,	PUNCT
cana-4524	184	42	...	...	PUNCT
cana-4524	184	43	,	,	PUNCT
cana-4524	184	44	}	}	PUNCT
cana-4524	184	45	{	{	PUNCT
cana-4524	184	46	,	,	PUNCT
cana-4524	184	47	,	,	PUNCT
cana-4524	184	48	...	...	PUNCT
cana-4524	184	49	,	,	PUNCT
cana-4524	184	50	}	}	PUNCT
cana-4524	184	51	{	{	PUNCT
cana-4524	184	52	,	,	PUNCT
cana-4524	184	53	,	,	PUNCT
cana-4524	184	54	...	...	PUNCT
cana-4524	184	55	,	,	PUNCT
cana-4524	184	56	}	}	PUNCT
cana-4524	184	57	{	{	PUNCT
cana-4524	184	58	,	,	PUNCT
cana-4524	184	59	,	,	PUNCT
cana-4524	184	60	...	...	PUNCT
cana-4524	184	61	,	,	PUNCT
cana-4524	184	62	}	}	PUNCT
cana-4524	184	63	{	{	PUNCT
cana-4524	184	64	,	,	PUNCT
cana-4524	184	65	,	,	PUNCT
cana-4524	184	66	...	...	PUNCT
cana-4524	184	67	,	,	PUNCT
cana-4524	184	68	}	}	PUNCT
cana-4524	184	69	u	u	NOUN
cana-4524	184	70	u	u	NOUN
cana-4524	184	71	u	u	NOUN
cana-4524	184	72	v	v	ADP
cana-4524	184	73	v	v	ADP
cana-4524	184	74	v	v	NOUN
cana-4524	184	75	e	e	X
cana-4524	184	76	e	e	X
cana-4524	184	77	e	e	X
cana-4524	184	78	t	t	NOUN
cana-4524	184	79	e	e	X
cana-4524	184	80	e	e	X
cana-4524	184	81	e	e	X
cana-4524	184	82	f	f	PROPN
cana-4524	185	1	f	f	PROPN
cana-4524	185	2	f	f	PROPN
cana-4524	186	1	f	f	PROPN
cana-4524	186	2	f	f	PROPN
cana-4524	186	3	f	f	PROPN
cana-4524	186	4			NOUN
cana-4524	186	5			NOUN
cana-4524	186	6			NOUN
cana-4524	186	7			NOUN
cana-4524	186	8			NOUN
cana-4524	186	9			NOUN
cana-4524	186	10	−	−	PROPN
cana-4524	186	11	−	−	PROPN
cana-4524	186	12	−	−	PROPN
cana-4524	186	13	−	−	NOUN
cana-4524	186	14	−	−	NOUN
cana-4524	186	15			NOUN
cana-4524	186	16	=	=	PUNCT
cana-4524	187	1			NUM
cana-4524	187	2			NOUN
cana-4524	187	3	1	1	NUM
cana-4524	187	4	6	6	NUM
cana-4524	187	5	5	5	NUM
cana-4524	187	6	4	4	NUM
cana-4524	187	7	3	3	NUM
cana-4524	187	8	8	8	NUM
cana-4524	187	9	5	5	NUM
cana-4524	187	10	2	2	NUM
cana-4524	187	11	2	2	NUM
cana-4524	187	12	7	7	NUM
cana-4524	187	13	5	5	NUM
cana-4524	187	14	3	3	NUM
cana-4524	187	15	5	5	NUM
cana-4524	187	16	'	'	PUNCT
cana-4524	187	17	'	'	PUNCT
cana-4524	187	18	'	'	PUNCT
cana-4524	187	19	'	'	PUNCT
cana-4524	187	20	'	'	PUNCT
cana-4524	187	21	'	'	NUM
cana-4524	187	22	5	5	NUM
cana-4524	187	23	10	10	NUM
cana-4524	187	24	5	5	NUM
cana-4524	187	25	2	2	NUM
cana-4524	187	26	7	7	NUM
cana-4524	187	27	5	5	NUM
cana-4524	187	28	3	3	NUM
cana-4524	187	29	4	4	NUM
cana-4524	187	30	9	9	NUM
cana-4524	187	31	5	5	NUM
cana-4524	187	32	1	1	NUM
cana-4524	187	33	{	{	PUNCT
cana-4524	187	34	,	,	PUNCT
cana-4524	187	35	,	,	PUNCT
cana-4524	187	36	...	...	PUNCT
cana-4524	187	37	,	,	PUNCT
cana-4524	187	38	}	}	PUNCT
cana-4524	187	39	{	{	PUNCT
cana-4524	187	40	,	,	PUNCT
cana-4524	187	41	,	,	PUNCT
cana-4524	187	42	...	...	PUNCT
cana-4524	187	43	,	,	PUNCT
cana-4524	187	44	}	}	PUNCT
cana-4524	187	45	{	{	PUNCT
cana-4524	187	46	,	,	PUNCT
cana-4524	187	47	,	,	PUNCT
cana-4524	187	48	...	...	PUNCT
cana-4524	187	49	,	,	PUNCT
cana-4524	187	50	}	}	PUNCT
cana-4524	187	51	{	{	PUNCT
cana-4524	187	52	,	,	PUNCT
cana-4524	187	53	,	,	PUNCT
cana-4524	187	54	...	...	PUNCT
cana-4524	187	55	,	,	PUNCT
cana-4524	187	56	}	}	PUNCT
cana-4524	187	57	{	{	PUNCT
cana-4524	187	58	,	,	PUNCT
cana-4524	187	59	,	,	PUNCT
cana-4524	187	60	...	...	PUNCT
cana-4524	187	61	,	,	PUNCT
cana-4524	187	62	}	}	PUNCT
cana-4524	187	63	{	{	PUNCT
cana-4524	187	64	,	,	PUNCT
cana-4524	187	65	,	,	PUNCT
cana-4524	187	66	...	...	PUNCT
cana-4524	187	67	,	,	PUNCT
cana-4524	187	68	}	}	PUNCT
cana-4524	187	69	u	u	NOUN
cana-4524	187	70	u	u	NOUN
cana-4524	187	71	u	u	NOUN
cana-4524	187	72	v	v	ADP
cana-4524	187	73	v	v	ADP
cana-4524	187	74	v	v	NOUN
cana-4524	187	75	e	e	X
cana-4524	187	76	e	e	X
cana-4524	187	77	e	e	X
cana-4524	187	78	t	t	NOUN
cana-4524	187	79	e	e	X
cana-4524	187	80	e	e	X
cana-4524	187	81	e	e	X
cana-4524	187	82	f	f	PROPN
cana-4524	188	1	f	f	PROPN
cana-4524	188	2	f	f	PROPN
cana-4524	189	1	f	f	PROPN
cana-4524	189	2	f	f	PROPN
cana-4524	189	3	f	f	PROPN
cana-4524	189	4			NOUN
cana-4524	189	5			NOUN
cana-4524	189	6			NOUN
cana-4524	189	7			NOUN
cana-4524	189	8			NOUN
cana-4524	189	9			NOUN
cana-4524	189	10	−	−	PROPN
cana-4524	189	11	−	−	PROPN
cana-4524	189	12	−	−	PROPN
cana-4524	189	13	−	−	NOUN
cana-4524	189	14	−	−	NOUN
cana-4524	189	15			NOUN
cana-4524	189	16	=	=	PUNCT
cana-4524	190	1			NUM
cana-4524	190	2			NUM
cana-4524	190	3	based	base	VERB
cana-4524	190	4	on	on	ADP
cana-4524	190	5	the	the	DET
cana-4524	190	6	coloring	coloring	NOUN
cana-4524	190	7	technique	technique	NOUN
cana-4524	190	8	described	describe	VERB
cana-4524	190	9	above	above	ADV
cana-4524	190	10	,	,	PUNCT
cana-4524	190	11	it	it	PRON
cana-4524	190	12	is	be	AUX
cana-4524	190	13	evident	evident	ADJ
cana-4524	190	14	that	that	SCONJ
cana-4524	190	15	the	the	DET
cana-4524	190	16	color	color	NOUN
cana-4524	190	17	classes	class	NOUN
cana-4524	190	18	1	1	NUM
cana-4524	190	19	2	2	NUM
cana-4524	190	20	3	3	NUM
cana-4524	190	21	4	4	NUM
cana-4524	190	22	,	,	PUNCT
cana-4524	190	23	,	,	PUNCT
cana-4524	190	24	,	,	PUNCT
cana-4524	190	25	t	t	PROPN
cana-4524	190	26	t	t	PROPN
cana-4524	190	27	t	t	PROPN
cana-4524	190	28	t	t	PROPN
cana-4524	190	29	and	and	CCONJ
cana-4524	190	30	5	5	NUM
cana-4524	190	31	t	t	NOUN
cana-4524	190	32	are	be	AUX
cana-4524	190	33	independent	independent	ADJ
cana-4524	190	34	sets	set	NOUN
cana-4524	190	35	of	of	ADP
cana-4524	190	36	(	(	PUNCT
cana-4524	190	37	)	)	PUNCT
cana-4524	190	38	nl	nl	NOUN
cana-4524	190	39	at	at	ADP
cana-4524	190	40	,	,	PUNCT
cana-4524	190	41	and	and	CCONJ
cana-4524	190	42	it	it	PRON
cana-4524	190	43	holds	hold	VERB
cana-4524	190	44	the	the	DET
cana-4524	190	45	inequality	inequality	NOUN
cana-4524	191	1	|	|	ADV
cana-4524	192	1	|	|	ADV
cana-4524	192	2	|	|	ADV
cana-4524	192	3	|	|	ADV
cana-4524	192	4	1a	1a	VERB
cana-4524	192	5	bt	bt	VERB
cana-4524	192	6	t−	t−	PROPN
cana-4524	192	7			NOUN
cana-4524	192	8	for	for	ADP
cana-4524	192	9	a	a	DET
cana-4524	192	10	b	b	PROPN
cana-4524	192	11	.	.	PUNCT
cana-4524	193	1	this	this	PRON
cana-4524	193	2	implies	imply	VERB
cana-4524	193	3	that	that	SCONJ
cana-4524	193	4	(	(	PUNCT
cana-4524	193	5	)	)	PUNCT
cana-4524	193	6	''	''	PUNCT
cana-4524	193	7	(	(	PUNCT
cana-4524	193	8	)	)	PUNCT
cana-4524	193	9	1e	1e	NOUN
cana-4524	193	10	nl	nl	PROPN
cana-4524	193	11	at	at	PROPN
cana-4524	193	12			NUM
cana-4524	193	13	+	+	VERB
cana-4524	193	14	.	.	PUNCT
cana-4524	194	1	further	far	ADV
cana-4524	194	2	,	,	PUNCT
cana-4524	194	3	we	we	PRON
cana-4524	194	4	have	have	VERB
cana-4524	194	5	(	(	PUNCT
cana-4524	194	6	)	)	PUNCT
cana-4524	194	7	''	''	PUNCT
cana-4524	195	1	(	(	PUNCT
cana-4524	195	2	)	)	PUNCT
cana-4524	195	3	e	e	NOUN
cana-4524	195	4	nl	nl	NOUN
cana-4524	195	5	at	at	NOUN
cana-4524	195	6	=	=	SYM
cana-4524	195	7	(	(	PUNCT
cana-4524	195	8	)	)	PUNCT
cana-4524	195	9	"	"	PUNCT
cana-4524	195	10	(	(	PUNCT
cana-4524	195	11	)	)	PUNCT
cana-4524	195	12	1nl	1nl	ADJ
cana-4524	195	13	at	at	NOUN
cana-4524	195	14			X
cana-4524	195	15	+	+	PROPN
cana-4524	195	16	1	1	NUM
cana-4524	195	17	4	4	NUM
cana-4524	195	18	1	1	NUM
cana-4524	195	19	5+	5+	NUM
cana-4524	195	20			NUM
cana-4524	195	21	+	+	CCONJ
cana-4524	195	22			NUM
cana-4524	195	23	.	.	PUNCT
cana-4524	196	1	hence	hence	ADV
cana-4524	196	2	(	(	PUNCT
cana-4524	196	3	)	)	PUNCT
cana-4524	196	4	''	''	PUNCT
cana-4524	196	5	(	(	PUNCT
cana-4524	196	6	)	)	PUNCT
cana-4524	196	7	5.e	5.e	NUM
cana-4524	196	8	nl	nl	NOUN
cana-4524	196	9	at	at	NOUN
cana-4524	197	1	=	=	SYM
cana-4524	197	2	example	example	NOUN
cana-4524	197	3	3.4	3.4	NUM
cana-4524	197	4	:	:	PUNCT
cana-4524	197	5	the	the	DET
cana-4524	197	6	graph	graph	NOUN
cana-4524	197	7	8	8	NUM
cana-4524	197	8	(	(	PUNCT
cana-4524	197	9	)	)	PUNCT
cana-4524	197	10	l	l	NOUN
cana-4524	197	11	at	at	ADP
cana-4524	197	12	and	and	CCONJ
cana-4524	197	13	its	its	PRON
cana-4524	197	14	equitable	equitable	ADJ
cana-4524	197	15	total	total	ADJ
cana-4524	197	16	coloring	coloring	NOUN
cana-4524	197	17	is	be	AUX
cana-4524	197	18	shown	show	VERB
cana-4524	197	19	in	in	ADP
cana-4524	197	20	figure	figure	NOUN
cana-4524	197	21	4	4	NUM
cana-4524	197	22	.	.	PUNCT
cana-4524	197	23	figure	figure	VERB
cana-4524	197	24	4	4	NUM
cana-4524	197	25	:	:	SYM
cana-4524	197	26	7	7	NUM
cana-4524	197	27	(	(	PUNCT
cana-4524	197	28	)	)	PUNCT
cana-4524	197	29	l	l	NOUN
cana-4524	197	30	at	at	ADP
cana-4524	197	31	and	and	CCONJ
cana-4524	197	32	its	its	PRON
cana-4524	197	33	equitable	equitable	ADJ
cana-4524	197	34	total	total	ADJ
cana-4524	197	35	coloring	coloring	NOUN
cana-4524	197	36	theorem	theorem	VERB
cana-4524	197	37	3.5	3.5	NUM
cana-4524	197	38	:	:	PUNCT
cana-4524	197	39	let	let	VERB
cana-4524	197	40	(	(	PUNCT
cana-4524	197	41	)	)	PUNCT
cana-4524	197	42	nl	nl	PROPN
cana-4524	197	43	q	q	PROPN
cana-4524	197	44	represent	represent	VERB
cana-4524	197	45	the	the	DET
cana-4524	197	46	line	line	NOUN
cana-4524	197	47	graph	graph	NOUN
cana-4524	197	48	of	of	ADP
cana-4524	197	49	quadrilateral	quadrilateral	ADJ
cana-4524	197	50	snake	snake	NOUN
cana-4524	197	51	graph	graph	NOUN
cana-4524	197	52	,	,	PUNCT
cana-4524	197	53	then	then	ADV
cana-4524	197	54	(	(	PUNCT
cana-4524	197	55	)	)	PUNCT
cana-4524	197	56	''	''	PUNCT
cana-4524	198	1	(	(	PUNCT
cana-4524	198	2	)	)	PUNCT
cana-4524	198	3	7.e	7.e	NUM
cana-4524	198	4	nl	nl	NOUN
cana-4524	198	5	q	q	VERB
cana-4524	198	6	=	=	SYM
cana-4524	198	7	proof	proof	NOUN
cana-4524	198	8	:	:	PUNCT
cana-4524	198	9	(	(	PUNCT
cana-4524	198	10	(	(	PUNCT
cana-4524	198	11	)	)	PUNCT
cana-4524	198	12	)	)	PUNCT
cana-4524	198	13	{	{	PUNCT
cana-4524	199	1	:1	:1	PUNCT
cana-4524	199	2	1	1	X
cana-4524	199	3	}	}	PUNCT
cana-4524	199	4	{	{	PUNCT
cana-4524	199	5	:1	:1	NUM
cana-4524	199	6	2	2	NUM
cana-4524	199	7	2	2	NUM
cana-4524	199	8	}	}	PUNCT
cana-4524	199	9	{	{	PUNCT
cana-4524	199	10	:1	:1	NUM
cana-4524	199	11	1}nv	1}nv	NOUN
cana-4524	199	12	l	l	NOUN
cana-4524	199	13	q	q	X
cana-4524	199	14	u	u	PROPN
cana-4524	199	15	n	n	ADP
cana-4524	199	16	v	v	NOUN
cana-4524	199	17	n	n	PROPN
cana-4524	199	18	z	z	PROPN
cana-4524	199	19	n	n	NOUN
cana-4524	199	20			NOUN
cana-4524	199	21			NOUN
cana-4524	199	22			NOUN
cana-4524	199	23	=	=	NOUN
cana-4524	199	24			NOUN
cana-4524	199	25			NOUN
cana-4524	199	26	−	−	ADP
cana-4524	199	27			NOUN
cana-4524	199	28			NOUN
cana-4524	199	29	−	−	ADP
cana-4524	199	30			NOUN
cana-4524	199	31			NOUN
cana-4524	199	32	−	−	NOUN
cana-4524	199	33	and	and	CCONJ
cana-4524	199	34			PROPN
cana-4524	199	35			PROPN
cana-4524	199	36			PROPN
cana-4524	199	37			PROPN
cana-4524	199	38	'	'	PUNCT
cana-4524	199	39	''	''	PUNCT
cana-4524	200	1	'	'	PUNCT
cana-4524	200	2	''	''	PUNCT
cana-4524	200	3	'	'	PUNCT
cana-4524	200	4	''	''	PUNCT
cana-4524	201	1	'	'	PUNCT
cana-4524	201	2	''	''	PUNCT
cana-4524	201	3	(	(	PUNCT
cana-4524	201	4	(	(	PUNCT
cana-4524	201	5	)	)	PUNCT
cana-4524	201	6	)	)	PUNCT
cana-4524	201	7	,	,	PUNCT
cana-4524	201	8	,	,	PUNCT
cana-4524	201	9	,	,	PUNCT
cana-4524	201	10	:1	:1	NUM
cana-4524	201	11	2	2	NUM
cana-4524	201	12	,	,	PUNCT
cana-4524	201	13	,	,	PUNCT
cana-4524	201	14	,	,	PUNCT
cana-4524	201	15	:1	:1	PUNCT
cana-4524	201	16	1ne	1ne	X
cana-4524	201	17	l	l	X
cana-4524	201	18	q	q	X
cana-4524	201	19	e	e	X
cana-4524	201	20	e	e	X
cana-4524	201	21	x	x	SYM
cana-4524	201	22	x	x	X
cana-4524	201	23	n	n	NOUN
cana-4524	201	24	x	x	SYM
cana-4524	201	25	x	x	PUNCT
cana-4524	201	26	e	e	NOUN
cana-4524	201	27	e	e	X
cana-4524	201	28	n	n	NOUN
cana-4524	201	29			NOUN
cana-4524	201	30			NOUN
cana-4524	201	31			NOUN
cana-4524	201	32			NOUN
cana-4524	201	33			NOUN
cana-4524	201	34			NOUN
cana-4524	201	35			NOUN
cana-4524	201	36	=	=	NOUN
cana-4524	201	37			NUM
cana-4524	201	38			NOUN
cana-4524	201	39	−	−	ADP
cana-4524	201	40			NOUN
cana-4524	201	41			NOUN
cana-4524	201	42	−	−	NOUN
cana-4524	201	43	,	,	PUNCT
cana-4524	201	44	where	where	SCONJ
cana-4524	201	45	1,e	1,e	X
cana-4524	201	46	z	z	NOUN
cana-4524	202	1	z	z	VERB
cana-4524	202	2			NOUN
cana-4524	202	3			NOUN
cana-4524	202	4	+	+	NOUN
cana-4524	202	5	=	=	X
cana-4524	202	6	'	'	PART
cana-4524	202	7	2	2	NUM
cana-4524	202	8	2	2	NUM
cana-4524	202	9	1,e	1,e	NUM
cana-4524	202	10	v	v	ADP
cana-4524	202	11	v	v	PRON
cana-4524	202	12			NOUN
cana-4524	202	13			NOUN
cana-4524	202	14	+	+	NOUN
cana-4524	202	15	=	=	SYM
cana-4524	202	16	''	''	PUNCT
cana-4524	202	17	2	2	NUM
cana-4524	202	18	1	1	NUM
cana-4524	202	19	2	2	NUM
cana-4524	202	20	,	,	PUNCT
cana-4524	202	21	e	e	X
cana-4524	202	22	v	v	ADP
cana-4524	202	23	v	v	DET
cana-4524	202	24			NOUN
cana-4524	202	25	−=	−=	NOUN
cana-4524	202	26	'	'	PUNCT
cana-4524	202	27	''	''	PUNCT
cana-4524	202	28	2	2	NUM
cana-4524	202	29	,	,	PUNCT
cana-4524	202	30	e	e	X
cana-4524	202	31	z	z	X
cana-4524	202	32	v	v	PRON
cana-4524	202	33			NOUN
cana-4524	202	34	=	=	NOUN
cana-4524	202	35	2	2	NUM
cana-4524	202	36	1,x	1,x	NUM
cana-4524	202	37	u	u	NOUN
cana-4524	202	38	v	v	PRON
cana-4524	202	39			NOUN
cana-4524	202	40			NOUN
cana-4524	202	41	−=	−=	NOUN
cana-4524	202	42	'	'	NUM
cana-4524	202	43	2	2	NUM
cana-4524	202	44	,	,	PUNCT
cana-4524	202	45	x	x	PUNCT
cana-4524	202	46	u	u	NOUN
cana-4524	202	47	v	v	PROPN
cana-4524	202	48			NOUN
cana-4524	202	49	=	=	NOUN
cana-4524	202	50	''	''	PUNCT
cana-4524	202	51	2	2	NUM
cana-4524	202	52	1,x	1,x	NUM
cana-4524	202	53	v	v	ADP
cana-4524	202	54	z	z	VERB
cana-4524	202	55			NOUN
cana-4524	202	56			NOUN
cana-4524	202	57	+	+	NOUN
cana-4524	202	58	=	=	X
cana-4524	202	59	'	'	PUNCT
cana-4524	202	60	''	''	PUNCT
cana-4524	202	61	2	2	NUM
cana-4524	202	62	1.x	1.x	NUM
cana-4524	202	63	z	z	NOUN
cana-4524	203	1	v	v	PRON
cana-4524	203	2			NOUN
cana-4524	203	3			NOUN
cana-4524	203	4	+	+	NOUN
cana-4524	203	5	=	=	ADJ
cana-4524	203	6	we	we	PRON
cana-4524	203	7	divide	divide	VERB
cana-4524	203	8	the	the	DET
cana-4524	203	9	vertex	vertex	NOUN
cana-4524	203	10	and	and	CCONJ
cana-4524	203	11	edge	edge	NOUN
cana-4524	203	12	set	set	NOUN
cana-4524	203	13	of	of	ADP
cana-4524	203	14	(	(	PUNCT
cana-4524	203	15	)	)	PUNCT
cana-4524	203	16	nl	nl	PROPN
cana-4524	203	17	q	q	NOUN
cana-4524	203	18	into	into	ADP
cana-4524	203	19	distinct	distinct	ADJ
cana-4524	203	20	partition	partition	NOUN
cana-4524	203	21	as	as	SCONJ
cana-4524	203	22	described	describe	VERB
cana-4524	203	23	below	below	ADV
cana-4524	203	24	.	.	PUNCT
cana-4524	204	1	there	there	PRON
cana-4524	204	2	are	be	VERB
cana-4524	204	3	two	two	NUM
cana-4524	204	4	cases	case	NOUN
cana-4524	204	5	case	case	NOUN
cana-4524	204	6	(	(	PUNCT
cana-4524	204	7	i	i	NOUN
cana-4524	204	8	):	):	PUNCT
cana-4524	204	9	suppose	suppose	VERB
cana-4524	204	10	n	n	PRON
cana-4524	204	11	is	be	AUX
cana-4524	204	12	even	even	ADV
cana-4524	204	13	'	'	PUNCT
cana-4524	204	14	'	'	PUNCT
cana-4524	204	15	'	'	PUNCT
cana-4524	204	16	''	''	PUNCT
cana-4524	204	17	''	''	PUNCT
cana-4524	204	18	''	''	PUNCT
cana-4524	204	19	1	1	NUM
cana-4524	204	20	1	1	NUM
cana-4524	204	21	3	3	NUM
cana-4524	204	22	1	1	NUM
cana-4524	204	23	4	4	NUM
cana-4524	204	24	2	2	NUM
cana-4524	204	25	2	2	NUM
cana-4524	204	26	4	4	NUM
cana-4524	204	27	2	2	NUM
cana-4524	204	28	2	2	NUM
cana-4524	204	29	4	4	NUM
cana-4524	204	30	2	2	NUM
cana-4524	204	31	{	{	PUNCT
cana-4524	204	32	,	,	PUNCT
cana-4524	204	33	,	,	PUNCT
cana-4524	204	34	...	...	PUNCT
cana-4524	204	35	,	,	PUNCT
cana-4524	204	36	}	}	PUNCT
cana-4524	204	37	{	{	PUNCT
cana-4524	204	38	,	,	PUNCT
cana-4524	204	39	}	}	PUNCT
cana-4524	204	40	{	{	PUNCT
cana-4524	204	41	,	,	PUNCT
cana-4524	204	42	,	,	PUNCT
cana-4524	204	43	...	...	PUNCT
cana-4524	204	44	,	,	PUNCT
cana-4524	204	45	}	}	PUNCT
cana-4524	204	46	{	{	PUNCT
cana-4524	204	47	,	,	PUNCT
cana-4524	204	48	,	,	PUNCT
cana-4524	204	49	...	...	PUNCT
cana-4524	204	50	,	,	PUNCT
cana-4524	204	51	}	}	PUNCT
cana-4524	204	52	n	n	CCONJ
cana-4524	204	53	n	n	CCONJ
cana-4524	204	54	n	n	CCONJ
cana-4524	204	55	n	n	NOUN
cana-4524	204	56	nt	not	PART
cana-4524	204	57	z	z	NOUN
cana-4524	204	58	z	z	NOUN
cana-4524	205	1	z	z	PUNCT
cana-4524	206	1	u	u	NOUN
cana-4524	206	2	u	u	X
cana-4524	206	3	e	e	X
cana-4524	206	4	e	e	X
cana-4524	206	5	e	e	X
cana-4524	206	6	e	e	X
cana-4524	206	7	e	e	X
cana-4524	206	8	e−	e−	X
cana-4524	206	9	−	−	PROPN
cana-4524	206	10	−	−	PROPN
cana-4524	206	11	−	−	PROPN
cana-4524	206	12	−=	−=	NOUN
cana-4524	206	13	communications	communication	NOUN
cana-4524	206	14	on	on	ADP
cana-4524	206	15	applied	apply	VERB
cana-4524	206	16	nonlinear	nonlinear	ADJ
cana-4524	206	17	analysis	analysis	NOUN
cana-4524	206	18	issn	issn	NOUN
cana-4524	206	19	:	:	PUNCT
cana-4524	206	20	1074	1074	NUM
cana-4524	206	21	-	-	PUNCT
cana-4524	206	22	133x	133x	NUM
cana-4524	206	23	vol	vol	NOUN
cana-4524	206	24	32	32	NUM
cana-4524	206	25	no	no	NOUN
cana-4524	206	26	.	.	PUNCT
cana-4524	207	1	9s	9s	NUM
cana-4524	207	2	(	(	PUNCT
cana-4524	207	3	2025	2025	NUM
cana-4524	207	4	)	)	PUNCT
cana-4524	207	5	2377	2377	NUM
cana-4524	207	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	207	7	'	'	PUNCT
cana-4524	207	8	'	'	PUNCT
cana-4524	207	9	'	'	PUNCT
cana-4524	207	10	''	''	PUNCT
cana-4524	207	11	''	''	PUNCT
cana-4524	207	12	''	''	PUNCT
cana-4524	207	13	'	'	PART
cana-4524	207	14	2	2	NUM
cana-4524	207	15	2	2	NUM
cana-4524	207	16	4	4	NUM
cana-4524	207	17	2	2	NUM
cana-4524	207	18	3	3	NUM
cana-4524	207	19	1	1	NUM
cana-4524	207	20	1	1	NUM
cana-4524	207	21	3	3	NUM
cana-4524	207	22	3	3	NUM
cana-4524	207	23	1	1	NUM
cana-4524	207	24	3	3	NUM
cana-4524	207	25	1	1	NUM
cana-4524	207	26	2	2	NUM
cana-4524	207	27	{	{	PUNCT
cana-4524	207	28	,	,	PUNCT
cana-4524	207	29	,	,	PUNCT
cana-4524	207	30	...	...	PUNCT
cana-4524	207	31	,	,	PUNCT
cana-4524	207	32	}	}	PUNCT
cana-4524	207	33	{	{	PUNCT
cana-4524	207	34	,	,	PUNCT
cana-4524	207	35	}	}	PUNCT
cana-4524	207	36	{	{	PUNCT
cana-4524	207	37	,	,	PUNCT
cana-4524	207	38	,	,	PUNCT
cana-4524	207	39	...	...	PUNCT
cana-4524	207	40	,	,	PUNCT
cana-4524	207	41	}	}	PUNCT
cana-4524	207	42	{	{	PUNCT
cana-4524	207	43	,	,	PUNCT
cana-4524	207	44	,	,	PUNCT
cana-4524	207	45	...	...	PUNCT
cana-4524	207	46	,	,	PUNCT
cana-4524	207	47	}	}	PUNCT
cana-4524	207	48	{	{	PUNCT
cana-4524	207	49	}	}	PUNCT
cana-4524	207	50	n	n	CCONJ
cana-4524	207	51	n	n	CCONJ
cana-4524	207	52	n	n	CCONJ
cana-4524	207	53	n	n	CCONJ
cana-4524	207	54	n	n	NOUN
cana-4524	207	55	nt	not	PART
cana-4524	207	56	z	z	NOUN
cana-4524	207	57	z	z	NOUN
cana-4524	207	58	z	z	PUNCT
cana-4524	207	59	u	u	NOUN
cana-4524	207	60	u	u	X
cana-4524	207	61	e	e	X
cana-4524	207	62	e	e	X
cana-4524	207	63	e	e	X
cana-4524	207	64	e	e	X
cana-4524	207	65	e	e	X
cana-4524	207	66	e	e	X
cana-4524	207	67	x−	x−	PROPN
cana-4524	207	68	−	−	PROPN
cana-4524	208	1	−	−	PROPN
cana-4524	209	1	−	−	PROPN
cana-4524	209	2	−	−	PROPN
cana-4524	209	3	−=	−=	PUNCT
cana-4524	209	4	'	'	PUNCT
cana-4524	209	5	'	'	NUM
cana-4524	209	6	3	3	NUM
cana-4524	209	7	1	1	NUM
cana-4524	209	8	3	3	NUM
cana-4524	209	9	2	2	NUM
cana-4524	209	10	3	3	NUM
cana-4524	209	11	3	3	NUM
cana-4524	209	12	1	1	NUM
cana-4524	209	13	1	1	NUM
cana-4524	209	14	3	3	NUM
cana-4524	209	15	3	3	NUM
cana-4524	209	16	{	{	PUNCT
cana-4524	209	17	,	,	PUNCT
cana-4524	209	18	,	,	PUNCT
cana-4524	209	19	...	...	PUNCT
cana-4524	209	20	,	,	PUNCT
cana-4524	209	21	}	}	PUNCT
cana-4524	209	22	{	{	PUNCT
cana-4524	209	23	,	,	PUNCT
cana-4524	209	24	}	}	PUNCT
cana-4524	209	25	{	{	PUNCT
cana-4524	209	26	,	,	PUNCT
cana-4524	209	27	...	...	PUNCT
cana-4524	209	28	,	,	PUNCT
cana-4524	209	29	}	}	PUNCT
cana-4524	209	30	n	n	CCONJ
cana-4524	209	31	n	n	NOUN
cana-4524	209	32	n	n	ADV
cana-4524	209	33	nt	not	PART
cana-4524	209	34	v	v	VERB
cana-4524	209	35	v	v	PRON
cana-4524	209	36	v	v	NOUN
cana-4524	209	37	x	x	SYM
cana-4524	209	38	x	x	X
cana-4524	209	39	e	e	X
cana-4524	209	40	e	e	X
cana-4524	209	41	e−	e−	X
cana-4524	209	42	−	−	PROPN
cana-4524	209	43	−	−	PROPN
cana-4524	209	44	−=	−=	NOUN
cana-4524	209	45	4	4	NUM
cana-4524	209	46	2	2	NUM
cana-4524	209	47	4	4	NUM
cana-4524	209	48	2	2	NUM
cana-4524	209	49	2	2	NUM
cana-4524	209	50	3	3	NUM
cana-4524	209	51	2	2	NUM
cana-4524	209	52	1	1	NUM
cana-4524	209	53	2	2	NUM
cana-4524	209	54	4	4	NUM
cana-4524	209	55	2	2	NUM
cana-4524	209	56	{	{	PUNCT
cana-4524	209	57	,	,	PUNCT
cana-4524	209	58	,	,	PUNCT
cana-4524	209	59	...	...	PUNCT
cana-4524	209	60	,	,	PUNCT
cana-4524	209	61	}	}	PUNCT
cana-4524	209	62	{	{	PUNCT
cana-4524	209	63	,	,	PUNCT
cana-4524	209	64	,	,	PUNCT
cana-4524	209	65	}	}	PUNCT
cana-4524	209	66	{	{	PUNCT
cana-4524	209	67	,	,	PUNCT
cana-4524	209	68	...	...	PUNCT
cana-4524	209	69	,	,	PUNCT
cana-4524	209	70	}	}	PUNCT
cana-4524	209	71	n	n	CCONJ
cana-4524	209	72	n	n	CCONJ
cana-4524	209	73	n	n	CCONJ
cana-4524	209	74	n	n	NOUN
cana-4524	209	75	nt	not	PART
cana-4524	209	76	v	v	VERB
cana-4524	209	77	v	v	PRON
cana-4524	209	78	v	v	NOUN
cana-4524	209	79	x	x	NOUN
cana-4524	209	80	x	x	PUNCT
cana-4524	209	81	x	x	PUNCT
cana-4524	209	82	e	e	X
cana-4524	209	83	e	e	X
cana-4524	209	84	e−	e−	X
cana-4524	209	85	−	−	PROPN
cana-4524	209	86	−	−	PROPN
cana-4524	209	87	−	−	PROPN
cana-4524	209	88	−=	−=	NOUN
cana-4524	209	89	''	''	PUNCT
cana-4524	209	90	5	5	NUM
cana-4524	209	91	{	{	PUNCT
cana-4524	209	92	:1	:1	NOUN
cana-4524	209	93	4	4	X
cana-4524	209	94	}	}	PUNCT
cana-4524	209	95	{	{	PUNCT
cana-4524	209	96	:1	:1	NUM
cana-4524	209	97	2}t	2}t	NUM
cana-4524	209	98	x	x	SYM
cana-4524	209	99	n	n	PROPN
cana-4524	209	100	x	x	PROPN
cana-4524	209	101	n	n	NOUN
cana-4524	209	102			NOUN
cana-4524	209	103	=	=	NOUN
cana-4524	209	104			NUM
cana-4524	209	105			NOUN
cana-4524	209	106	−	−	ADP
cana-4524	209	107			PROPN
cana-4524	209	108			NOUN
cana-4524	209	109	−	−	NOUN
cana-4524	209	110	'	'	PUNCT
cana-4524	209	111	'	'	PUNCT
cana-4524	209	112	''	''	PUNCT
cana-4524	209	113	6	6	NUM
cana-4524	209	114	{	{	PUNCT
cana-4524	209	115	:1	:1	SYM
cana-4524	209	116	4	4	NUM
cana-4524	209	117	}	}	PUNCT
cana-4524	209	118	{	{	PUNCT
cana-4524	209	119	:1	:1	NUM
cana-4524	209	120	2}t	2}t	NUM
cana-4524	209	121	x	x	SYM
cana-4524	209	122	n	n	PROPN
cana-4524	209	123	x	x	PROPN
cana-4524	209	124	n	n	NOUN
cana-4524	209	125			NOUN
cana-4524	209	126	=	=	NOUN
cana-4524	209	127			NUM
cana-4524	209	128			NOUN
cana-4524	209	129	−	−	ADP
cana-4524	209	130			NOUN
cana-4524	209	131			NOUN
cana-4524	209	132	−	−	NOUN
cana-4524	209	133	'	'	PUNCT
cana-4524	209	134	''	''	PUNCT
cana-4524	209	135	7	7	NUM
cana-4524	209	136	{	{	PUNCT
cana-4524	209	137	:1	:1	SYM
cana-4524	209	138	5	5	NUM
cana-4524	209	139	}	}	PUNCT
cana-4524	209	140	{	{	PUNCT
cana-4524	209	141	:1	:1	PUNCT
cana-4524	209	142	1}t	1}t	NUM
cana-4524	209	143	u	u	NOUN
cana-4524	209	144	n	n	ADP
cana-4524	209	145	e	e	X
cana-4524	209	146	n	n	NOUN
cana-4524	209	147			NOUN
cana-4524	209	148	=	=	NOUN
cana-4524	209	149			NUM
cana-4524	209	150			NOUN
cana-4524	209	151	−	−	ADP
cana-4524	209	152			NOUN
cana-4524	209	153			NOUN
cana-4524	209	154	−	−	NOUN
cana-4524	209	155	case	case	NOUN
cana-4524	209	156	(	(	PUNCT
cana-4524	209	157	ii	ii	NOUN
cana-4524	209	158	):	):	PUNCT
cana-4524	209	159	suppose	suppose	VERB
cana-4524	209	160	n	n	PRON
cana-4524	209	161	is	be	AUX
cana-4524	209	162	odd	odd	ADJ
cana-4524	209	163	'	'	PUNCT
cana-4524	209	164	'	'	PUNCT
cana-4524	209	165	'	'	PUNCT
cana-4524	209	166	''	''	PUNCT
cana-4524	209	167	''	''	PUNCT
cana-4524	209	168	''	''	PUNCT
cana-4524	209	169	'	'	PUNCT
cana-4524	209	170	1	1	NUM
cana-4524	209	171	1	1	NUM
cana-4524	209	172	3	3	NUM
cana-4524	209	173	2	2	NUM
cana-4524	209	174	3	3	NUM
cana-4524	209	175	1	1	NUM
cana-4524	209	176	2	2	NUM
cana-4524	209	177	4	4	NUM
cana-4524	209	178	3	3	NUM
cana-4524	209	179	2	2	NUM
cana-4524	209	180	4	4	NUM
cana-4524	209	181	1	1	NUM
cana-4524	209	182	2	2	NUM
cana-4524	209	183	{	{	PUNCT
cana-4524	209	184	,	,	PUNCT
cana-4524	209	185	,	,	PUNCT
cana-4524	209	186	...	...	PUNCT
cana-4524	209	187	,	,	PUNCT
cana-4524	209	188	}	}	PUNCT
cana-4524	209	189	{	{	PUNCT
cana-4524	209	190	,	,	PUNCT
cana-4524	209	191	}	}	PUNCT
cana-4524	209	192	{	{	PUNCT
cana-4524	209	193	,	,	PUNCT
cana-4524	209	194	,	,	PUNCT
cana-4524	209	195	...	...	PUNCT
cana-4524	209	196	,	,	PUNCT
cana-4524	209	197	}	}	PUNCT
cana-4524	209	198	{	{	PUNCT
cana-4524	209	199	,	,	PUNCT
cana-4524	209	200	,	,	PUNCT
cana-4524	209	201	...	...	PUNCT
cana-4524	209	202	,	,	PUNCT
cana-4524	209	203	}	}	PUNCT
cana-4524	209	204	{	{	PUNCT
cana-4524	209	205	}	}	PUNCT
cana-4524	209	206	n	n	CCONJ
cana-4524	209	207	n	n	CCONJ
cana-4524	209	208	n	n	CCONJ
cana-4524	209	209	n	n	CCONJ
cana-4524	209	210	n	n	NOUN
cana-4524	209	211	nt	not	PART
cana-4524	209	212	z	z	NOUN
cana-4524	209	213	z	z	NOUN
cana-4524	209	214	z	z	PUNCT
cana-4524	209	215	u	u	NOUN
cana-4524	209	216	u	u	X
cana-4524	209	217	e	e	X
cana-4524	209	218	e	e	X
cana-4524	209	219	e	e	X
cana-4524	209	220	e	e	X
cana-4524	209	221	e	e	X
cana-4524	209	222	e	e	X
cana-4524	209	223	x−	x−	PROPN
cana-4524	209	224	−	−	PROPN
cana-4524	210	1	−	−	PROPN
cana-4524	211	1	−	−	PROPN
cana-4524	211	2	−	−	PROPN
cana-4524	211	3	−=	−=	PUNCT
cana-4524	211	4	'	'	PUNCT
cana-4524	211	5	'	'	PUNCT
cana-4524	211	6	'	'	PUNCT
cana-4524	211	7	''	''	PUNCT
cana-4524	211	8	''	''	PUNCT
cana-4524	211	9	''	''	PUNCT
cana-4524	211	10	2	2	NUM
cana-4524	211	11	2	2	NUM
cana-4524	211	12	4	4	NUM
cana-4524	211	13	1	1	NUM
cana-4524	211	14	4	4	NUM
cana-4524	211	15	2	2	NUM
cana-4524	211	16	1	1	NUM
cana-4524	211	17	3	3	NUM
cana-4524	211	18	2	2	NUM
cana-4524	211	19	1	1	NUM
cana-4524	211	20	3	3	NUM
cana-4524	211	21	2	2	NUM
cana-4524	211	22	{	{	PUNCT
cana-4524	211	23	,	,	PUNCT
cana-4524	211	24	,	,	PUNCT
cana-4524	211	25	...	...	PUNCT
cana-4524	211	26	,	,	PUNCT
cana-4524	211	27	}	}	PUNCT
cana-4524	211	28	{	{	PUNCT
cana-4524	211	29	,	,	PUNCT
cana-4524	211	30	}	}	PUNCT
cana-4524	211	31	{	{	PUNCT
cana-4524	211	32	,	,	PUNCT
cana-4524	211	33	,	,	PUNCT
cana-4524	211	34	...	...	PUNCT
cana-4524	211	35	,	,	PUNCT
cana-4524	211	36	}	}	PUNCT
cana-4524	211	37	{	{	PUNCT
cana-4524	211	38	,	,	PUNCT
cana-4524	211	39	,	,	PUNCT
cana-4524	211	40	...	...	PUNCT
cana-4524	211	41	,	,	PUNCT
cana-4524	211	42	}	}	PUNCT
cana-4524	211	43	n	n	CCONJ
cana-4524	211	44	n	n	CCONJ
cana-4524	211	45	n	n	CCONJ
cana-4524	211	46	n	n	NOUN
cana-4524	211	47	nt	not	PART
cana-4524	211	48	z	z	NOUN
cana-4524	211	49	z	z	NOUN
cana-4524	211	50	z	z	PUNCT
cana-4524	211	51	u	u	NOUN
cana-4524	211	52	u	u	X
cana-4524	211	53	e	e	X
cana-4524	211	54	e	e	X
cana-4524	211	55	e	e	X
cana-4524	211	56	e	e	X
cana-4524	211	57	e	e	X
cana-4524	211	58	e−	e−	X
cana-4524	211	59	−	−	PROPN
cana-4524	211	60	−	−	PROPN
cana-4524	211	61	−	−	PROPN
cana-4524	211	62	−=	−=	PUNCT
cana-4524	211	63	'	'	PUNCT
cana-4524	211	64	'	'	NUM
cana-4524	211	65	3	3	NUM
cana-4524	211	66	1	1	NUM
cana-4524	211	67	3	3	NUM
cana-4524	211	68	2	2	NUM
cana-4524	211	69	3	3	NUM
cana-4524	211	70	3	3	NUM
cana-4524	211	71	1	1	NUM
cana-4524	211	72	1	1	NUM
cana-4524	211	73	3	3	NUM
cana-4524	211	74	2	2	NUM
cana-4524	211	75	{	{	PUNCT
cana-4524	211	76	,	,	PUNCT
cana-4524	211	77	,	,	PUNCT
cana-4524	211	78	...	...	PUNCT
cana-4524	211	79	,	,	PUNCT
cana-4524	211	80	}	}	PUNCT
cana-4524	211	81	{	{	PUNCT
cana-4524	211	82	,	,	PUNCT
cana-4524	211	83	}	}	PUNCT
cana-4524	211	84	{	{	PUNCT
cana-4524	211	85	,	,	PUNCT
cana-4524	211	86	...	...	PUNCT
cana-4524	211	87	,	,	PUNCT
cana-4524	211	88	}	}	PUNCT
cana-4524	211	89	n	n	CCONJ
cana-4524	211	90	n	n	NOUN
cana-4524	211	91	n	n	ADV
cana-4524	211	92	nt	not	PART
cana-4524	211	93	v	v	VERB
cana-4524	211	94	v	v	PRON
cana-4524	211	95	v	v	NOUN
cana-4524	211	96	x	x	SYM
cana-4524	211	97	x	x	X
cana-4524	211	98	e	e	X
cana-4524	211	99	e	e	X
cana-4524	211	100	e−	e−	X
cana-4524	211	101	−	−	PROPN
cana-4524	211	102	−	−	PROPN
cana-4524	211	103	−=	−=	NOUN
cana-4524	211	104	4	4	NUM
cana-4524	211	105	2	2	NUM
cana-4524	211	106	4	4	NUM
cana-4524	211	107	2	2	NUM
cana-4524	211	108	2	2	NUM
cana-4524	211	109	3	3	NUM
cana-4524	211	110	2	2	NUM
cana-4524	211	111	1	1	NUM
cana-4524	211	112	2	2	NUM
cana-4524	211	113	4	4	NUM
cana-4524	211	114	3	3	NUM
cana-4524	211	115	{	{	PUNCT
cana-4524	211	116	,	,	PUNCT
cana-4524	211	117	,	,	PUNCT
cana-4524	211	118	...	...	PUNCT
cana-4524	211	119	,	,	PUNCT
cana-4524	211	120	}	}	PUNCT
cana-4524	211	121	{	{	PUNCT
cana-4524	211	122	,	,	PUNCT
cana-4524	211	123	,	,	PUNCT
cana-4524	211	124	}	}	PUNCT
cana-4524	211	125	{	{	PUNCT
cana-4524	211	126	,	,	PUNCT
cana-4524	211	127	...	...	PUNCT
cana-4524	211	128	,	,	PUNCT
cana-4524	211	129	}	}	PUNCT
cana-4524	211	130	n	n	CCONJ
cana-4524	211	131	n	n	CCONJ
cana-4524	211	132	n	n	CCONJ
cana-4524	211	133	n	n	NOUN
cana-4524	211	134	nt	not	PART
cana-4524	211	135	v	v	VERB
cana-4524	211	136	v	v	PRON
cana-4524	211	137	v	v	NOUN
cana-4524	211	138	x	x	NOUN
cana-4524	211	139	x	x	PUNCT
cana-4524	211	140	x	x	PUNCT
cana-4524	211	141	e	e	X
cana-4524	211	142	e	e	X
cana-4524	211	143	e−	e−	X
cana-4524	211	144	−	−	PROPN
cana-4524	212	1	−	−	PROPN
cana-4524	212	2	−	−	PROPN
cana-4524	212	3	−=	−=	NOUN
cana-4524	212	4	''	''	PUNCT
cana-4524	212	5	5	5	NUM
cana-4524	212	6	{	{	PUNCT
cana-4524	212	7	:1	:1	NOUN
cana-4524	212	8	4	4	X
cana-4524	212	9	}	}	PUNCT
cana-4524	212	10	{	{	PUNCT
cana-4524	212	11	:1	:1	NUM
cana-4524	212	12	2}t	2}t	NUM
cana-4524	212	13	x	x	SYM
cana-4524	212	14	n	n	PROPN
cana-4524	212	15	x	x	PROPN
cana-4524	212	16	n	n	NOUN
cana-4524	212	17			NOUN
cana-4524	212	18	=	=	NOUN
cana-4524	212	19			NUM
cana-4524	212	20			NOUN
cana-4524	212	21	−	−	ADP
cana-4524	212	22			PROPN
cana-4524	212	23			NOUN
cana-4524	212	24	−	−	NOUN
cana-4524	212	25	'	'	PUNCT
cana-4524	212	26	'	'	PUNCT
cana-4524	212	27	''	''	PUNCT
cana-4524	212	28	6	6	NUM
cana-4524	212	29	{	{	PUNCT
cana-4524	212	30	:1	:1	SYM
cana-4524	212	31	4	4	NUM
cana-4524	212	32	}	}	PUNCT
cana-4524	212	33	{	{	PUNCT
cana-4524	212	34	:1	:1	NUM
cana-4524	212	35	2}t	2}t	NUM
cana-4524	212	36	x	x	SYM
cana-4524	212	37	n	n	PROPN
cana-4524	212	38	x	x	PROPN
cana-4524	212	39	n	n	NOUN
cana-4524	212	40			NOUN
cana-4524	212	41	=	=	NOUN
cana-4524	212	42			NUM
cana-4524	212	43			NOUN
cana-4524	212	44	−	−	ADP
cana-4524	212	45			NOUN
cana-4524	212	46			NOUN
cana-4524	212	47	−	−	NOUN
cana-4524	212	48	'	'	PUNCT
cana-4524	212	49	''	''	PUNCT
cana-4524	212	50	7	7	NUM
cana-4524	212	51	{	{	PUNCT
cana-4524	212	52	:1	:1	SYM
cana-4524	212	53	5	5	NUM
cana-4524	212	54	}	}	PUNCT
cana-4524	212	55	{	{	PUNCT
cana-4524	212	56	:1	:1	PUNCT
cana-4524	212	57	1}t	1}t	NUM
cana-4524	212	58	u	u	NOUN
cana-4524	212	59	n	n	ADP
cana-4524	212	60	e	e	X
cana-4524	212	61	n	n	NOUN
cana-4524	212	62			NOUN
cana-4524	212	63	=	=	NOUN
cana-4524	212	64			NUM
cana-4524	212	65			NOUN
cana-4524	212	66	−	−	ADP
cana-4524	212	67			NOUN
cana-4524	212	68			NOUN
cana-4524	212	69	−	−	NUM
cana-4524	212	70	based	base	VERB
cana-4524	212	71	on	on	ADP
cana-4524	212	72	the	the	DET
cana-4524	212	73	coloring	coloring	NOUN
cana-4524	212	74	technique	technique	NOUN
cana-4524	212	75	described	describe	VERB
cana-4524	212	76	above	above	ADV
cana-4524	212	77	,	,	PUNCT
cana-4524	212	78	clearly	clearly	ADV
cana-4524	212	79	the	the	DET
cana-4524	212	80	color	color	NOUN
cana-4524	212	81	classes	class	NOUN
cana-4524	212	82	1	1	NUM
cana-4524	212	83	2	2	NUM
cana-4524	212	84	,	,	PUNCT
cana-4524	212	85	,	,	PUNCT
cana-4524	212	86	...	...	PUNCT
cana-4524	212	87	,	,	PUNCT
cana-4524	212	88	t	t	PROPN
cana-4524	212	89	t	t	PROPN
cana-4524	212	90	and	and	CCONJ
cana-4524	212	91	7	7	NUM
cana-4524	212	92	t	t	NOUN
cana-4524	212	93	are	be	AUX
cana-4524	212	94	independent	independent	ADJ
cana-4524	212	95	sets	set	NOUN
cana-4524	212	96	of	of	ADP
cana-4524	212	97	(	(	PUNCT
cana-4524	212	98	)	)	PUNCT
cana-4524	212	99	nl	nl	PROPN
cana-4524	212	100	q	q	NOUN
cana-4524	212	101	,	,	PUNCT
cana-4524	212	102	and	and	CCONJ
cana-4524	212	103	it	it	PRON
cana-4524	212	104	holds	hold	VERB
cana-4524	212	105	the	the	DET
cana-4524	212	106	inequality	inequality	NOUN
cana-4524	213	1	|	|	ADV
cana-4524	214	1	|	|	ADV
cana-4524	214	2	|	|	ADV
cana-4524	214	3	|	|	ADV
cana-4524	214	4	1a	1a	VERB
cana-4524	214	5	bt	bt	VERB
cana-4524	214	6	t−	t−	PROPN
cana-4524	214	7			NOUN
cana-4524	214	8	for	for	ADP
cana-4524	214	9	a	a	DET
cana-4524	214	10	b	b	PROPN
cana-4524	214	11	.	.	PUNCT
cana-4524	215	1	this	this	PRON
cana-4524	215	2	implies	imply	VERB
cana-4524	215	3	that	that	SCONJ
cana-4524	215	4	(	(	PUNCT
cana-4524	215	5	)	)	PUNCT
cana-4524	215	6	''	''	PUNCT
cana-4524	215	7	(	(	PUNCT
cana-4524	215	8	)	)	PUNCT
cana-4524	215	9	7.e	7.e	NUM
cana-4524	215	10	nl	nl	NOUN
cana-4524	215	11	q	q	VERB
cana-4524	215	12			NOUN
cana-4524	215	13	further	far	ADV
cana-4524	215	14	,	,	PUNCT
cana-4524	215	15	we	we	PRON
cana-4524	215	16	have	have	VERB
cana-4524	215	17	(	(	PUNCT
cana-4524	215	18	)	)	PUNCT
cana-4524	215	19	''	''	PUNCT
cana-4524	216	1	(	(	PUNCT
cana-4524	216	2	)	)	PUNCT
cana-4524	216	3	e	e	X
cana-4524	216	4	nl	nl	NOUN
cana-4524	216	5	q	q	VERB
cana-4524	216	6	=	=	PUNCT
cana-4524	216	7	(	(	PUNCT
cana-4524	216	8	)	)	PUNCT
cana-4524	216	9	"	"	PUNCT
cana-4524	216	10	(	(	PUNCT
cana-4524	216	11	)	)	PUNCT
cana-4524	216	12	1nl	1nl	PROPN
cana-4524	216	13	q	q	VERB
cana-4524	216	14			NUM
cana-4524	216	15	+	+	PROPN
cana-4524	216	16	6	6	NUM
cana-4524	216	17	1	1	NUM
cana-4524	216	18	7	7	NUM
cana-4524	216	19	+	+	NUM
cana-4524	216	20			NUM
cana-4524	216	21	.	.	PUNCT
cana-4524	217	1	hence	hence	ADV
cana-4524	217	2	(	(	PUNCT
cana-4524	217	3	)	)	PUNCT
cana-4524	217	4	''	''	PUNCT
cana-4524	217	5	(	(	PUNCT
cana-4524	217	6	)	)	PUNCT
cana-4524	217	7	7.e	7.e	NUM
cana-4524	217	8	nl	nl	NOUN
cana-4524	217	9	q	q	VERB
cana-4524	217	10	=	=	PUNCT
cana-4524	217	11	example	example	NOUN
cana-4524	217	12	3.5.1	3.5.1	NUM
cana-4524	217	13	:	:	PUNCT
cana-4524	217	14	the	the	DET
cana-4524	217	15	graph	graph	NOUN
cana-4524	217	16	6	6	NUM
cana-4524	217	17	(	(	PUNCT
cana-4524	217	18	)	)	PUNCT
cana-4524	217	19	l	l	NOUN
cana-4524	217	20	q	q	NOUN
cana-4524	217	21	and	and	CCONJ
cana-4524	217	22	its	its	PRON
cana-4524	217	23	equitable	equitable	ADJ
cana-4524	217	24	total	total	ADJ
cana-4524	217	25	coloring	coloring	NOUN
cana-4524	217	26	is	be	AUX
cana-4524	217	27	shown	show	VERB
cana-4524	217	28	in	in	ADP
cana-4524	217	29	figure	figure	NOUN
cana-4524	217	30	5	5	NUM
cana-4524	217	31	.	.	PUNCT
cana-4524	217	32	figure	figure	VERB
cana-4524	217	33	5	5	NUM
cana-4524	217	34	:	:	SYM
cana-4524	217	35	6	6	NUM
cana-4524	217	36	(	(	PUNCT
cana-4524	217	37	)	)	PUNCT
cana-4524	217	38	l	l	NOUN
cana-4524	217	39	q	q	NOUN
cana-4524	218	1	and	and	CCONJ
cana-4524	218	2	its	its	PRON
cana-4524	218	3	equitable	equitable	ADJ
cana-4524	218	4	total	total	ADJ
cana-4524	218	5	coloring	coloring	NOUN
cana-4524	218	6	example	example	NOUN
cana-4524	218	7	3.5.2	3.5.2	NUM
cana-4524	218	8	:	:	PUNCT
cana-4524	218	9	the	the	DET
cana-4524	218	10	graph	graph	NOUN
cana-4524	218	11	5	5	NUM
cana-4524	218	12	(	(	PUNCT
cana-4524	218	13	)	)	PUNCT
cana-4524	218	14	l	l	NOUN
cana-4524	218	15	q	q	NOUN
cana-4524	218	16	and	and	CCONJ
cana-4524	218	17	its	its	PRON
cana-4524	218	18	equitable	equitable	ADJ
cana-4524	218	19	total	total	ADJ
cana-4524	218	20	coloring	coloring	NOUN
cana-4524	218	21	is	be	AUX
cana-4524	218	22	shown	show	VERB
cana-4524	218	23	in	in	ADP
cana-4524	218	24	figure	figure	NOUN
cana-4524	218	25	6	6	NUM
cana-4524	218	26	.	.	PUNCT
cana-4524	218	27	figure	figure	VERB
cana-4524	218	28	6	6	NUM
cana-4524	218	29	:	:	SYM
cana-4524	218	30	5	5	NUM
cana-4524	218	31	(	(	PUNCT
cana-4524	218	32	)	)	PUNCT
cana-4524	218	33	l	l	NOUN
cana-4524	218	34	q	q	NOUN
cana-4524	219	1	and	and	CCONJ
cana-4524	219	2	its	its	PRON
cana-4524	219	3	equitable	equitable	ADJ
cana-4524	219	4	total	total	ADJ
cana-4524	219	5	coloring	coloring	NOUN
cana-4524	219	6	communications	communication	NOUN
cana-4524	219	7	on	on	ADP
cana-4524	219	8	applied	apply	VERB
cana-4524	219	9	nonlinear	nonlinear	ADJ
cana-4524	219	10	analysis	analysis	NOUN
cana-4524	219	11	issn	issn	NOUN
cana-4524	219	12	:	:	PUNCT
cana-4524	219	13	1074	1074	NUM
cana-4524	219	14	-	-	PUNCT
cana-4524	219	15	133x	133x	NUM
cana-4524	219	16	vol	vol	NOUN
cana-4524	219	17	32	32	NUM
cana-4524	219	18	no	no	NOUN
cana-4524	219	19	.	.	PUNCT
cana-4524	220	1	9s	9s	NUM
cana-4524	220	2	(	(	PUNCT
cana-4524	220	3	2025	2025	NUM
cana-4524	220	4	)	)	PUNCT
cana-4524	220	5	2378	2378	NUM
cana-4524	220	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	220	7	theorem	theorem	VERB
cana-4524	220	8	3.6	3.6	NUM
cana-4524	220	9	:	:	PUNCT
cana-4524	220	10	let	let	VERB
cana-4524	220	11	(	(	PUNCT
cana-4524	220	12	)	)	PUNCT
cana-4524	220	13	nl	nl	PROPN
cana-4524	220	14	aq	aq	PROPN
cana-4524	220	15	represent	represent	VERB
cana-4524	220	16	the	the	DET
cana-4524	220	17	line	line	NOUN
cana-4524	220	18	graph	graph	NOUN
cana-4524	220	19	of	of	ADP
cana-4524	220	20	alternate	alternate	ADJ
cana-4524	220	21	quadrilateral	quadrilateral	ADJ
cana-4524	220	22	snake	snake	NOUN
cana-4524	220	23	graph	graph	NOUN
cana-4524	220	24	,	,	PUNCT
cana-4524	220	25	then	then	ADV
cana-4524	220	26	(	(	PUNCT
cana-4524	220	27	)	)	PUNCT
cana-4524	220	28	''	''	PUNCT
cana-4524	221	1	(	(	PUNCT
cana-4524	221	2	)	)	PUNCT
cana-4524	221	3	5.e	5.e	NUM
cana-4524	221	4	nl	nl	NOUN
cana-4524	221	5	aq	aq	NOUN
cana-4524	222	1	=	=	PUNCT
cana-4524	222	2	proof	proof	NOUN
cana-4524	222	3	:	:	PUNCT
cana-4524	222	4	(	(	PUNCT
cana-4524	222	5	(	(	PUNCT
cana-4524	222	6	)	)	PUNCT
cana-4524	222	7	)	)	PUNCT
cana-4524	223	1	:1	:1	PUNCT
cana-4524	223	2	{	{	PUNCT
cana-4524	223	3	:1	:1	PUNCT
cana-4524	223	4	}	}	PUNCT
cana-4524	223	5	{	{	PUNCT
cana-4524	223	6	:1	:1	SYM
cana-4524	223	7	1	1	NUM
cana-4524	223	8	}	}	SYM
cana-4524	223	9	2	2	NUM
cana-4524	223	10	n	n	CCONJ
cana-4524	223	11	n	n	PRON
cana-4524	223	12	v	v	NOUN
cana-4524	223	13	l	l	NOUN
cana-4524	223	14	aq	aq	NOUN
cana-4524	223	15	u	u	PROPN
cana-4524	223	16	v	v	ADP
cana-4524	223	17	n	n	PROPN
cana-4524	223	18	z	z	PROPN
cana-4524	223	19	n	n	NOUN
cana-4524	223	20			NOUN
cana-4524	223	21			NOUN
cana-4524	223	22			NOUN
cana-4524	223	23			NOUN
cana-4524	223	24			ADV
cana-4524	223	25			ADJ
cana-4524	223	26			NOUN
cana-4524	223	27	=	=	PUNCT
cana-4524	224	1			NOUN
cana-4524	224	2			NOUN
cana-4524	224	3			NOUN
cana-4524	224	4			NOUN
cana-4524	224	5			NOUN
cana-4524	224	6			NOUN
cana-4524	224	7	−	−	NOUN
cana-4524	224	8			VERB
cana-4524	224	9			NOUN
cana-4524	224	10			VERB
cana-4524	224	11			NOUN
cana-4524	224	12			PROPN
cana-4524	224	13	and	and	CCONJ
cana-4524	224	14			PROPN
cana-4524	224	15			PROPN
cana-4524	224	16			PROPN
cana-4524	224	17			PROPN
cana-4524	224	18	'	'	PUNCT
cana-4524	224	19	''	''	PUNCT
cana-4524	225	1	'	'	PUNCT
cana-4524	225	2	(	(	PUNCT
cana-4524	225	3	(	(	PUNCT
cana-4524	225	4	)	)	PUNCT
cana-4524	225	5	)	)	PUNCT
cana-4524	226	1	:1	:1	SYM
cana-4524	226	2	2	2	X
cana-4524	226	3	,	,	PUNCT
cana-4524	226	4	:1	:1	NUM
cana-4524	226	5	1	1	NUM
cana-4524	226	6	,	,	PUNCT
cana-4524	226	7	:1	:1	NUM
cana-4524	226	8	2	2	NUM
cana-4524	226	9	n	n	CCONJ
cana-4524	226	10	n	n	NOUN
cana-4524	226	11	e	e	NOUN
cana-4524	226	12	l	l	NOUN
cana-4524	226	13	aq	aq	X
cana-4524	226	14	e	e	NOUN
cana-4524	226	15	n	n	X
cana-4524	226	16	e	e	NOUN
cana-4524	226	17	e	e	X
cana-4524	226	18	n	n	PROPN
cana-4524	226	19	x	x	PROPN
cana-4524	226	20	x	x	PROPN
cana-4524	226	21			NOUN
cana-4524	226	22			NOUN
cana-4524	226	23			NOUN
cana-4524	226	24			NOUN
cana-4524	226	25			NOUN
cana-4524	226	26			NOUN
cana-4524	226	27			ADV
cana-4524	226	28			ADJ
cana-4524	226	29			NOUN
cana-4524	226	30	=	=	PUNCT
cana-4524	227	1			NOUN
cana-4524	227	2			NOUN
cana-4524	227	3	−	−	PART
cana-4524	227	4			NOUN
cana-4524	227	5			NOUN
cana-4524	227	6	−	−	ADP
cana-4524	227	7			NOUN
cana-4524	227	8			VERB
cana-4524	227	9			ADJ
cana-4524	227	10			NOUN
cana-4524	227	11			VERB
cana-4524	227	12			ADJ
cana-4524	227	13			PROPN
cana-4524	227	14	,	,	PUNCT
cana-4524	227	15	where	where	SCONJ
cana-4524	227	16	1,e	1,e	X
cana-4524	227	17	z	z	NOUN
cana-4524	228	1	z	z	VERB
cana-4524	228	2			NOUN
cana-4524	228	3			NOUN
cana-4524	228	4	+	+	NOUN
cana-4524	228	5	=	=	X
cana-4524	228	6	'	'	PUNCT
cana-4524	228	7	,	,	PUNCT
cana-4524	228	8	e	e	NOUN
cana-4524	228	9	v	v	X
cana-4524	228	10	z	z	VERB
cana-4524	228	11			NOUN
cana-4524	228	12	=	=	NOUN
cana-4524	228	13	''	''	PUNCT
cana-4524	228	14	1,e	1,e	NUM
cana-4524	228	15	z	z	NOUN
cana-4524	229	1	v	v	PRON
cana-4524	229	2			NOUN
cana-4524	229	3			NOUN
cana-4524	229	4	+	+	NOUN
cana-4524	229	5	=	=	SYM
cana-4524	229	6	2	2	NUM
cana-4524	229	7	1,x	1,x	NUM
cana-4524	229	8	u	u	NOUN
cana-4524	229	9	v	v	PRON
cana-4524	229	10			NOUN
cana-4524	229	11			NOUN
cana-4524	229	12	−=	−=	NOUN
cana-4524	229	13	'	'	NUM
cana-4524	229	14	2	2	NUM
cana-4524	229	15	.x	.x	NOUN
cana-4524	229	16	u	u	NOUN
cana-4524	229	17	v	v	PROPN
cana-4524	229	18			NOUN
cana-4524	229	19	=	=	ADV
cana-4524	229	20	we	we	PRON
cana-4524	229	21	divide	divide	VERB
cana-4524	229	22	the	the	DET
cana-4524	229	23	vertex	vertex	NOUN
cana-4524	229	24	and	and	CCONJ
cana-4524	229	25	edge	edge	NOUN
cana-4524	229	26	set	set	NOUN
cana-4524	229	27	of	of	ADP
cana-4524	229	28	(	(	PUNCT
cana-4524	229	29	)	)	PUNCT
cana-4524	229	30	nl	nl	PROPN
cana-4524	229	31	aq	aq	VERB
cana-4524	229	32	into	into	ADP
cana-4524	229	33	distinct	distinct	ADJ
cana-4524	229	34	partition	partition	NOUN
cana-4524	229	35	as	as	SCONJ
cana-4524	229	36	described	describe	VERB
cana-4524	229	37	below	below	ADV
cana-4524	229	38	.	.	PUNCT
cana-4524	230	1			PROPN
cana-4524	230	2			PROPN
cana-4524	230	3	2	2	NUM
cana-4524	230	4	''	''	PUNCT
cana-4524	230	5	''	''	PUNCT
cana-4524	230	6	''	''	PUNCT
cana-4524	230	7	'	'	PUNCT
cana-4524	230	8	1	1	NUM
cana-4524	230	9	1	1	NUM
cana-4524	230	10	3	3	NUM
cana-4524	230	11	1	1	NUM
cana-4524	230	12	2	2	NUM
cana-4524	230	13	4	4	NUM
cana-4524	230	14	1	1	NUM
cana-4524	230	15	2	2	NUM
cana-4524	230	16	1	1	NUM
cana-4524	230	17	{	{	PUNCT
cana-4524	230	18	,	,	PUNCT
cana-4524	230	19	,	,	PUNCT
cana-4524	230	20	...	...	PUNCT
cana-4524	230	21	,	,	PUNCT
cana-4524	230	22	}	}	PUNCT
cana-4524	230	23	{	{	PUNCT
cana-4524	230	24	,	,	PUNCT
cana-4524	230	25	,	,	PUNCT
cana-4524	230	26	...	...	PUNCT
cana-4524	230	27	,	,	PUNCT
cana-4524	230	28	}	}	PUNCT
cana-4524	230	29	:1	:1	PUNCT
cana-4524	230	30	3	3	NUM
cana-4524	230	31	2	2	NUM
cana-4524	230	32	nn	nn	X
cana-4524	230	33	n	n	CCONJ
cana-4524	230	34	n	n	PROPN
cana-4524	230	35	t	t	NOUN
cana-4524	230	36	z	z	NOUN
cana-4524	230	37	z	z	NOUN
cana-4524	230	38	z	z	NOUN
cana-4524	230	39	e	e	NOUN
cana-4524	230	40	e	e	X
cana-4524	230	41	e	e	X
cana-4524	230	42	x	x	X
cana-4524	230	43	u	u	VERB
cana-4524	230	44	−	−	ADV
cana-4524	230	45	−	−	PROPN
cana-4524	231	1	−	−	NOUN
cana-4524	231	2			ADV
cana-4524	231	3			ADJ
cana-4524	231	4			NOUN
cana-4524	231	5	=	=	PUNCT
cana-4524	231	6			PROPN
cana-4524	231	7			NOUN
cana-4524	231	8	−	−	NOUN
cana-4524	231	9			VERB
cana-4524	231	10			NOUN
cana-4524	231	11			VERB
cana-4524	232	1			NOUN
cana-4524	232	2			NUM
cana-4524	232	3	2	2	NUM
cana-4524	232	4	''	''	PUNCT
cana-4524	232	5	''	''	PUNCT
cana-4524	232	6	''	''	PUNCT
cana-4524	232	7	2	2	NUM
cana-4524	232	8	2	2	NUM
cana-4524	232	9	4	4	NUM
cana-4524	232	10	2	2	NUM
cana-4524	232	11	2	2	NUM
cana-4524	232	12	1	1	NUM
cana-4524	232	13	1	1	NUM
cana-4524	232	14	3	3	NUM
cana-4524	232	15	2	2	NUM
cana-4524	232	16	{	{	PUNCT
cana-4524	232	17	,	,	PUNCT
cana-4524	232	18	,	,	PUNCT
cana-4524	232	19	...	...	PUNCT
cana-4524	232	20	,	,	PUNCT
cana-4524	232	21	}	}	PUNCT
cana-4524	232	22	:1	:1	SYM
cana-4524	232	23	1	1	X
cana-4524	232	24	{	{	PUNCT
cana-4524	232	25	,	,	PUNCT
cana-4524	232	26	,	,	PUNCT
cana-4524	232	27	...	...	PUNCT
cana-4524	232	28	,	,	PUNCT
cana-4524	232	29	}	}	PUNCT
cana-4524	232	30	{	{	PUNCT
cana-4524	232	31	}	}	SYM
cana-4524	232	32	2	2	NUM
cana-4524	232	33	nn	nn	NOUN
cana-4524	232	34	n	n	CCONJ
cana-4524	232	35	n	n	PROPN
cana-4524	232	36	t	t	NOUN
cana-4524	232	37	z	z	NOUN
cana-4524	233	1	z	z	NOUN
cana-4524	233	2	z	z	NOUN
cana-4524	233	3	x	x	PUNCT
cana-4524	233	4	e	e	NOUN
cana-4524	233	5	e	e	X
cana-4524	233	6	e	e	X
cana-4524	233	7	u	u	X
cana-4524	233	8	−	−	ADV
cana-4524	233	9	−	−	NUM
cana-4524	233	10	−	−	PROPN
cana-4524	233	11			NOUN
cana-4524	233	12			PROPN
cana-4524	233	13			PROPN
cana-4524	233	14			NOUN
cana-4524	233	15			NOUN
cana-4524	233	16			NOUN
cana-4524	233	17	=	=	PUNCT
cana-4524	233	18			PROPN
cana-4524	233	19			NOUN
cana-4524	233	20	−	−	NOUN
cana-4524	233	21			VERB
cana-4524	233	22			NOUN
cana-4524	233	23			VERB
cana-4524	234	1			NOUN
cana-4524	235	1			X
cana-4524	235	2			PROPN
cana-4524	235	3			PROPN
cana-4524	235	4			PROPN
cana-4524	235	5			PROPN
cana-4524	235	6	2	2	NUM
cana-4524	235	7	2	2	NUM
cana-4524	235	8	'	'	PUNCT
cana-4524	235	9	'	'	PUNCT
cana-4524	235	10	'	'	PUNCT
cana-4524	235	11	'	'	PUNCT
cana-4524	235	12	3	3	NUM
cana-4524	235	13	2	2	NUM
cana-4524	235	14	4	4	NUM
cana-4524	235	15	1	1	NUM
cana-4524	235	16	3	3	NUM
cana-4524	235	17	2	2	NUM
cana-4524	235	18	1	1	NUM
cana-4524	235	19	3	3	NUM
cana-4524	235	20	2	2	NUM
cana-4524	235	21	1	1	NUM
cana-4524	235	22	,	,	PUNCT
cana-4524	235	23	,	,	PUNCT
cana-4524	235	24	,	,	PUNCT
cana-4524	235	25	...	...	PUNCT
cana-4524	235	26	,	,	PUNCT
cana-4524	235	27	{	{	PUNCT
cana-4524	235	28	,	,	PUNCT
cana-4524	235	29	...	...	PUNCT
cana-4524	235	30	,	,	PUNCT
cana-4524	235	31	}	}	PUNCT
cana-4524	235	32	{	{	PUNCT
cana-4524	235	33	,	,	PUNCT
cana-4524	235	34	...	...	PUNCT
cana-4524	235	35	,	,	PUNCT
cana-4524	235	36	}	}	PUNCT
cana-4524	235	37	n	n	CCONJ
cana-4524	235	38	nn	nn	INTJ
cana-4524	235	39	nt	not	PART
cana-4524	235	40	x	x	NOUN
cana-4524	235	41	x	x	PUNCT
cana-4524	235	42	x	x	SYM
cana-4524	236	1	v	v	ADP
cana-4524	236	2	v	v	NUM
cana-4524	236	3	v	v	NOUN
cana-4524	236	4	e	e	X
cana-4524	236	5	e	e	X
cana-4524	236	6	e	e	X
cana-4524	236	7	x−	x−	PROPN
cana-4524	236	8	−	−	PUNCT
cana-4524	236	9			PROPN
cana-4524	236	10			NOUN
cana-4524	236	11	−	−	ADV
cana-4524	236	12			PROPN
cana-4524	236	13			VERB
cana-4524	236	14			PROPN
cana-4524	236	15	=	=	PUNCT
cana-4524	236	16			PROPN
cana-4524	236	17			PROPN
cana-4524	236	18	2	2	NUM
cana-4524	236	19	'	'	NUM
cana-4524	236	20	4	4	NUM
cana-4524	236	21	2	2	NUM
cana-4524	236	22	4	4	NUM
cana-4524	236	23	1	1	NUM
cana-4524	236	24	2	2	NUM
cana-4524	236	25	4	4	NUM
cana-4524	236	26	3	3	NUM
cana-4524	236	27	2	2	NUM
cana-4524	236	28	4	4	NUM
cana-4524	236	29	1	1	NUM
cana-4524	236	30	{	{	PUNCT
cana-4524	236	31	,	,	PUNCT
cana-4524	236	32	,	,	PUNCT
cana-4524	236	33	...	...	PUNCT
cana-4524	236	34	,	,	PUNCT
cana-4524	236	35	}	}	PUNCT
cana-4524	236	36	{	{	PUNCT
cana-4524	236	37	,	,	PUNCT
cana-4524	236	38	...	...	PUNCT
cana-4524	236	39	,	,	PUNCT
cana-4524	236	40	}	}	PUNCT
cana-4524	236	41	,	,	PUNCT
cana-4524	236	42	,	,	PUNCT
cana-4524	236	43	...	...	PUNCT
cana-4524	236	44	,	,	PUNCT
cana-4524	236	45	{	{	PUNCT
cana-4524	236	46	}	}	PUNCT
cana-4524	236	47	nn	nn	INTJ
cana-4524	236	48	nt	not	PART
cana-4524	236	49	v	v	NOUN
cana-4524	236	50	v	v	PRON
cana-4524	236	51	v	v	NOUN
cana-4524	236	52	e	e	X
cana-4524	236	53	e	e	X
cana-4524	236	54	e	e	X
cana-4524	236	55	x	x	X
cana-4524	236	56	x	x	SYM
cana-4524	236	57	x	x	SYM
cana-4524	236	58	e−	e−	NUM
cana-4524	236	59	−	−	PROPN
cana-4524	236	60			VERB
cana-4524	236	61			PROPN
cana-4524	236	62			PROPN
cana-4524	236	63	=	=	SYM
cana-4524	236	64	'	'	PART
cana-4524	236	65	5	5	NUM
cana-4524	236	66	2	2	NUM
cana-4524	236	67	{	{	PUNCT
cana-4524	236	68	:1	:1	NOUN
cana-4524	236	69	1	1	NUM
cana-4524	236	70	}	}	PUNCT
cana-4524	236	71	{	{	PUNCT
cana-4524	236	72	:	:	PUNCT
cana-4524	236	73	2	2	NUM
cana-4524	236	74	2}nt	2}nt	NOUN
cana-4524	236	75	u	u	NOUN
cana-4524	236	76	e	e	X
cana-4524	236	77	n	n	NOUN
cana-4524	236	78			NOUN
cana-4524	236	79	=	=	NOUN
cana-4524	236	80			NUM
cana-4524	236	81			NOUN
cana-4524	236	82	−	−	ADP
cana-4524	236	83			NOUN
cana-4524	236	84			NOUN
cana-4524	236	85	−	−	PUNCT
cana-4524	236	86			PROPN
cana-4524	236	87			PROPN
cana-4524	236	88	based	base	VERB
cana-4524	236	89	on	on	ADP
cana-4524	236	90	the	the	DET
cana-4524	236	91	coloring	coloring	NOUN
cana-4524	236	92	technique	technique	NOUN
cana-4524	236	93	described	describe	VERB
cana-4524	236	94	above	above	ADV
cana-4524	236	95	,	,	PUNCT
cana-4524	236	96	clearly	clearly	ADV
cana-4524	236	97	the	the	DET
cana-4524	236	98	color	color	NOUN
cana-4524	236	99	classes	class	NOUN
cana-4524	236	100	1	1	NUM
cana-4524	236	101	2	2	NUM
cana-4524	236	102	3	3	NUM
cana-4524	236	103	4	4	NUM
cana-4524	236	104	,	,	PUNCT
cana-4524	236	105	,	,	PUNCT
cana-4524	236	106	,	,	PUNCT
cana-4524	236	107	t	t	PROPN
cana-4524	236	108	t	t	PROPN
cana-4524	236	109	t	t	PROPN
cana-4524	236	110	t	t	PROPN
cana-4524	236	111	and	and	CCONJ
cana-4524	236	112	5	5	NUM
cana-4524	236	113	t	t	NOUN
cana-4524	236	114	are	be	AUX
cana-4524	236	115	independent	independent	ADJ
cana-4524	236	116	sets	set	NOUN
cana-4524	236	117	of	of	ADP
cana-4524	236	118	(	(	PUNCT
cana-4524	236	119	)	)	PUNCT
cana-4524	236	120	nl	nl	PROPN
cana-4524	236	121	aq	aq	PROPN
cana-4524	236	122	,	,	PUNCT
cana-4524	236	123	and	and	CCONJ
cana-4524	236	124	it	it	PRON
cana-4524	236	125	holds	hold	VERB
cana-4524	236	126	the	the	DET
cana-4524	236	127	inequality	inequality	NOUN
cana-4524	237	1	|	|	ADV
cana-4524	238	1	|	|	ADV
cana-4524	238	2	|	|	ADV
cana-4524	238	3	|	|	ADV
cana-4524	238	4	1a	1a	VERB
cana-4524	238	5	bt	bt	VERB
cana-4524	238	6	t−	t−	PROPN
cana-4524	238	7			NOUN
cana-4524	238	8	for	for	ADP
cana-4524	238	9	a	a	DET
cana-4524	238	10	b	b	PROPN
cana-4524	238	11	.	.	PUNCT
cana-4524	239	1	this	this	PRON
cana-4524	239	2	implies	imply	VERB
cana-4524	239	3	that	that	SCONJ
cana-4524	239	4	(	(	PUNCT
cana-4524	239	5	)	)	PUNCT
cana-4524	239	6	''	''	PUNCT
cana-4524	239	7	(	(	PUNCT
cana-4524	239	8	)	)	PUNCT
cana-4524	239	9	5.e	5.e	NUM
cana-4524	239	10	nl	nl	NOUN
cana-4524	239	11	aq	aq	NOUN
cana-4524	239	12			NOUN
cana-4524	239	13	further	far	ADV
cana-4524	239	14	,	,	PUNCT
cana-4524	239	15	we	we	PRON
cana-4524	239	16	have	have	VERB
cana-4524	239	17	(	(	PUNCT
cana-4524	239	18	)	)	PUNCT
cana-4524	239	19	''	''	PUNCT
cana-4524	240	1	(	(	PUNCT
cana-4524	240	2	)	)	PUNCT
cana-4524	240	3	e	e	NOUN
cana-4524	240	4	nl	nl	NOUN
cana-4524	240	5	aq	aq	NUM
cana-4524	240	6	=	=	SYM
cana-4524	240	7	(	(	PUNCT
cana-4524	240	8	)	)	PUNCT
cana-4524	240	9	"	"	PUNCT
cana-4524	240	10	(	(	PUNCT
cana-4524	240	11	)	)	PUNCT
cana-4524	240	12	1nl	1nl	ADJ
cana-4524	240	13	aq	aq	NOUN
cana-4524	240	14			X
cana-4524	240	15	+	+	PROPN
cana-4524	240	16	4	4	NUM
cana-4524	240	17	1	1	NUM
cana-4524	240	18	5	5	NUM
cana-4524	240	19	+	+	SYM
cana-4524	240	20			NUM
cana-4524	240	21	.	.	PUNCT
cana-4524	241	1	hence	hence	ADV
cana-4524	241	2	(	(	PUNCT
cana-4524	241	3	)	)	PUNCT
cana-4524	241	4	''	''	PUNCT
cana-4524	241	5	(	(	PUNCT
cana-4524	241	6	)	)	PUNCT
cana-4524	241	7	5.e	5.e	NUM
cana-4524	241	8	nl	nl	NOUN
cana-4524	241	9	aq	aq	NUM
cana-4524	241	10	=	=	NOUN
cana-4524	241	11	example	example	NOUN
cana-4524	241	12	3.6.1	3.6.1	NUM
cana-4524	241	13	:	:	PUNCT
cana-4524	241	14	the	the	DET
cana-4524	241	15	graph	graph	NOUN
cana-4524	241	16	7	7	NUM
cana-4524	241	17	(	(	PUNCT
cana-4524	241	18	)	)	PUNCT
cana-4524	241	19	l	l	NOUN
cana-4524	241	20	aq	aq	NOUN
cana-4524	241	21	and	and	CCONJ
cana-4524	241	22	its	its	PRON
cana-4524	241	23	equitable	equitable	ADJ
cana-4524	241	24	total	total	ADJ
cana-4524	241	25	coloring	coloring	NOUN
cana-4524	241	26	is	be	AUX
cana-4524	241	27	shown	show	VERB
cana-4524	241	28	in	in	ADP
cana-4524	241	29	figure	figure	NOUN
cana-4524	241	30	7	7	NUM
cana-4524	241	31	.	.	PUNCT
cana-4524	241	32	figure	figure	VERB
cana-4524	241	33	7	7	NUM
cana-4524	241	34	:	:	SYM
cana-4524	241	35	7	7	NUM
cana-4524	241	36	(	(	PUNCT
cana-4524	241	37	)	)	PUNCT
cana-4524	241	38	l	l	NOUN
cana-4524	241	39	aq	aq	NOUN
cana-4524	241	40	and	and	CCONJ
cana-4524	241	41	its	its	PRON
cana-4524	241	42	equitable	equitable	ADJ
cana-4524	241	43	total	total	ADJ
cana-4524	241	44	coloring	coloring	NOUN
cana-4524	241	45	references	reference	NOUN
cana-4524	241	46	[	[	X
cana-4524	241	47	1	1	NUM
cana-4524	241	48	]	]	X
cana-4524	241	49	barasara	barasara	NOUN
cana-4524	241	50	,	,	PUNCT
cana-4524	241	51	c.	c.	PROPN
cana-4524	241	52	,	,	PUNCT
cana-4524	241	53	prajapati	prajapati	PROPN
cana-4524	241	54	,	,	PUNCT
cana-4524	241	55	p	p	X
cana-4524	241	56	,	,	PUNCT
cana-4524	241	57	antimagic	antimagic	ADJ
cana-4524	241	58	labeling	labeling	NOUN
cana-4524	241	59	for	for	ADP
cana-4524	241	60	some	some	DET
cana-4524	241	61	snake	snake	NOUN
cana-4524	241	62	graphs	graph	NOUN
cana-4524	241	63	.	.	PUNCT
cana-4524	242	1	proyecciones	proyeccione	NOUN
cana-4524	242	2	(	(	PUNCT
cana-4524	242	3	antofagasta	antofagasta	PROPN
cana-4524	242	4	)	)	PUNCT
cana-4524	242	5	,	,	PUNCT
cana-4524	242	6	43(2	43(2	NUM
cana-4524	242	7	)	)	PUNCT
cana-4524	242	8	,	,	PUNCT
cana-4524	242	9	(	(	PUNCT
cana-4524	242	10	2024	2024	NUM
cana-4524	242	11	)	)	PUNCT
cana-4524	242	12	,	,	PUNCT
cana-4524	242	13	521–537	521–537	NUM
cana-4524	242	14	.	.	PUNCT
cana-4524	242	15	https://doi.org/10.22199/issn.0717-6279-6005	https://doi.org/10.22199/issn.0717-6279-6005	PROPN
cana-4524	242	16	.	.	PUNCT
cana-4524	243	1	[	[	X
cana-4524	243	2	2	2	NUM
cana-4524	243	3	]	]	PUNCT
cana-4524	243	4	gong	gong	NOUN
cana-4524	243	5	kun	kun	PROPN
cana-4524	243	6	,	,	PUNCT
cana-4524	243	7	zhang	zhang	PROPN
cana-4524	243	8	zhongfu	zhongfu	PROPN
cana-4524	243	9	,	,	PUNCT
cana-4524	243	10	wang	wang	PROPN
cana-4524	243	11	jian	jian	PROPN
cana-4524	243	12	fang	fang	PROPN
cana-4524	243	13	,	,	PUNCT
cana-4524	243	14	equitable	equitable	ADJ
cana-4524	243	15	total	total	ADJ
cana-4524	243	16	coloring	coloring	NOUN
cana-4524	243	17	of	of	ADP
cana-4524	243	18	some	some	DET
cana-4524	243	19	join	join	NOUN
cana-4524	243	20	graphs	graph	NOUN
cana-4524	243	21	,	,	PUNCT
cana-4524	243	22	journal	journal	NOUN
cana-4524	243	23	of	of	ADP
cana-4524	243	24	mathematical	mathematical	ADJ
cana-4524	243	25	research	research	NOUN
cana-4524	243	26	&	&	CCONJ
cana-4524	243	27	exposition	exposition	PROPN
cana-4524	243	28	,	,	PUNCT
cana-4524	243	29	28(4	28(4	NUM
cana-4524	243	30	)	)	PUNCT
cana-4524	243	31	,	,	PUNCT
cana-4524	243	32	(	(	PUNCT
cana-4524	243	33	2008	2008	NUM
cana-4524	243	34	)	)	PUNCT
cana-4524	243	35	.	.	PUNCT
cana-4524	244	1	823	823	NUM
cana-4524	244	2	-	-	SYM
cana-4524	244	3	828	828	NUM
cana-4524	244	4	.	.	PUNCT
cana-4524	244	5	doi:10.3770	doi:10.3770	NOUN
cana-4524	244	6	/	/	SYM
cana-4524	244	7	j.issn	j.issn	NOUN
cana-4524	244	8	:	:	PUNCT
cana-4524	244	9	1000341x.2008.04.010	1000341x.2008.04.010	NUM
cana-4524	244	10	.	.	PUNCT
cana-4524	245	1	https://doi.org/10.22199/issn.0717-6279-6005	https://doi.org/10.22199/issn.0717-6279-6005	PROPN
cana-4524	245	2	communications	communication	NOUN
cana-4524	245	3	on	on	ADP
cana-4524	245	4	applied	apply	VERB
cana-4524	245	5	nonlinear	nonlinear	ADJ
cana-4524	245	6	analysis	analysis	NOUN
cana-4524	245	7	issn	issn	NOUN
cana-4524	245	8	:	:	PUNCT
cana-4524	245	9	1074	1074	NUM
cana-4524	245	10	-	-	PUNCT
cana-4524	245	11	133x	133x	NUM
cana-4524	245	12	vol	vol	NOUN
cana-4524	245	13	32	32	NUM
cana-4524	245	14	no	no	NOUN
cana-4524	245	15	.	.	PUNCT
cana-4524	246	1	9s	9s	NUM
cana-4524	246	2	(	(	PUNCT
cana-4524	246	3	2025	2025	NUM
cana-4524	246	4	)	)	PUNCT
cana-4524	246	5	2379	2379	NUM
cana-4524	246	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-4524	247	1	[	[	X
cana-4524	247	2	3	3	NUM
cana-4524	247	3	]	]	X
cana-4524	247	4	gui	gui	PROPN
cana-4524	247	5	,	,	PUNCT
cana-4524	247	6	h.	h.	PROPN
cana-4524	247	7	,	,	PUNCT
cana-4524	247	8	wang	wang	PROPN
cana-4524	247	9	,	,	PUNCT
cana-4524	247	10	w.	w.	PROPN
cana-4524	247	11	,	,	PUNCT
cana-4524	247	12	wang	wang	PROPN
cana-4524	247	13	,	,	PUNCT
cana-4524	247	14	y.	y.	PROPN
cana-4524	247	15	,	,	PUNCT
cana-4524	247	16	&	&	CCONJ
cana-4524	247	17	zhang	zhang	PROPN
cana-4524	247	18	,	,	PUNCT
cana-4524	247	19	z	z	PROPN
cana-4524	247	20	,	,	PUNCT
cana-4524	247	21	equitable	equitable	ADJ
cana-4524	247	22	total	total	ADJ
cana-4524	247	23	-	-	PUNCT
cana-4524	247	24	coloring	coloring	NOUN
cana-4524	247	25	of	of	ADP
cana-4524	247	26	subcubic	subcubic	ADJ
cana-4524	247	27	graphs	graph	NOUN
cana-4524	247	28	.	.	PUNCT
cana-4524	248	1	discrete	discrete	ADJ
cana-4524	248	2	applied	applied	ADJ
cana-4524	248	3	mathematics	mathematic	NOUN
cana-4524	248	4	,	,	PUNCT
cana-4524	248	5	184	184	NUM
cana-4524	248	6	,	,	PUNCT
cana-4524	248	7	(	(	PUNCT
cana-4524	248	8	2014	2014	NUM
cana-4524	248	9	)	)	PUNCT
cana-4524	248	10	.	.	PUNCT
cana-4524	249	1	167–170	167–170	NUM
cana-4524	249	2	.	.	PUNCT
cana-4524	250	1	https://doi.org/10.1016/j.dam.2014.11.014	https://doi.org/10.1016/j.dam.2014.11.014	PROPN
cana-4524	250	2	.	.	PUNCT
cana-4524	251	1	[	[	X
cana-4524	251	2	4	4	NUM
cana-4524	251	3	]	]	X
cana-4524	251	4	hung	hung	PROPN
cana-4524	251	5	-	-	PUNCT
cana-4524	251	6	lin	lin	PROPN
cana-4524	251	7	fu	fu	PROPN
cana-4524	251	8	,	,	PUNCT
cana-4524	251	9	some	some	DET
cana-4524	251	10	results	result	NOUN
cana-4524	251	11	on	on	ADP
cana-4524	251	12	equalized	equalized	ADJ
cana-4524	251	13	total	total	ADJ
cana-4524	251	14	coloring	coloring	NOUN
cana-4524	251	15	,	,	PUNCT
cana-4524	251	16	congr	congr	NOUN
cana-4524	251	17	.	.	PUNCT
cana-4524	252	1	numer	numer	PROPN
cana-4524	252	2	,	,	PUNCT
cana-4524	252	3	102	102	NUM
cana-4524	252	4	,	,	PUNCT
cana-4524	252	5	(	(	PUNCT
cana-4524	252	6	1994	1994	NUM
cana-4524	252	7	)	)	PUNCT
cana-4524	252	8	,	,	PUNCT
cana-4524	252	9	111	111	NUM
cana-4524	252	10	-	-	SYM
cana-4524	252	11	119	119	NUM
cana-4524	252	12	.	.	PUNCT
cana-4524	253	1	[	[	X
cana-4524	253	2	5	5	X
cana-4524	253	3	]	]	X
cana-4524	253	4	g.	g.	PROPN
cana-4524	253	5	jayaraman	jayaraman	PROPN
cana-4524	253	6	and	and	CCONJ
cana-4524	253	7	d.	d.	PROPN
cana-4524	253	8	muthuramakrishnan	muthuramakrishnan	PROPN
cana-4524	253	9	,	,	PUNCT
cana-4524	253	10	equitable	equitable	ADJ
cana-4524	253	11	total	total	ADJ
cana-4524	253	12	chromatic	chromatic	ADJ
cana-4524	253	13	number	number	NOUN
cana-4524	253	14	of	of	ADP
cana-4524	253	15	splitting	splitting	NOUN
cana-4524	253	16	graph	graph	NOUN
cana-4524	253	17	,	,	PUNCT
cana-4524	253	18	proyecciones	proyeccione	NOUN
cana-4524	253	19	journal	journal	NOUN
cana-4524	253	20	of	of	ADP
cana-4524	253	21	mathematics	mathematic	NOUN
cana-4524	253	22	,	,	PUNCT
cana-4524	253	23	vol	vol	NOUN
cana-4524	253	24	38(4),(2019),699	38(4),(2019),699	NUM
cana-4524	253	25	-	-	SYM
cana-4524	253	26	705	705	NUM
cana-4524	253	27	.	.	PUNCT
cana-4524	254	1	https://doi.org/10.22199/issn.0717-6279-2019-04-0045	https://doi.org/10.22199/issn.0717-6279-2019-04-0045	PROPN
cana-4524	254	2	[	[	X
cana-4524	254	3	6	6	NUM
cana-4524	254	4	]	]	X
cana-4524	254	5	g.	g.	PROPN
cana-4524	254	6	jayaraman	jayaraman	PROPN
cana-4524	254	7	and	and	CCONJ
cana-4524	254	8	d.	d.	PROPN
cana-4524	254	9	muthuramakrishnan	muthuramakrishnan	PROPN
cana-4524	254	10	,	,	PUNCT
cana-4524	254	11	a	a	DET
cana-4524	254	12	note	note	NOUN
cana-4524	254	13	on	on	ADP
cana-4524	254	14	equitable	equitable	ADJ
cana-4524	254	15	total	total	ADJ
cana-4524	254	16	coloring	coloring	NOUN
cana-4524	254	17	of	of	ADP
cana-4524	254	18	middle	middle	ADJ
cana-4524	254	19	graph	graph	NOUN
cana-4524	254	20	and	and	CCONJ
cana-4524	254	21	total	total	ADJ
cana-4524	254	22	graph	graph	NOUN
cana-4524	254	23	of	of	ADP
cana-4524	254	24	some	some	DET
cana-4524	254	25	graph	graph	NOUN
cana-4524	254	26	,	,	PUNCT
cana-4524	254	27	journal	journal	NOUN
cana-4524	254	28	of	of	ADP
cana-4524	254	29	combinatorial	combinatorial	ADJ
cana-4524	254	30	mathematics	mathematic	NOUN
cana-4524	254	31	and	and	CCONJ
cana-4524	254	32	combinatorial	combinatorial	ADJ
cana-4524	254	33	computing	computing	NOUN
cana-4524	254	34	,	,	PUNCT
cana-4524	254	35	112	112	NUM
cana-4524	254	36	,	,	PUNCT
cana-4524	254	37	(	(	PUNCT
cana-4524	254	38	2020	2020	NUM
cana-4524	254	39	)	)	PUNCT
cana-4524	254	40	,	,	PUNCT
cana-4524	254	41	75	75	NUM
cana-4524	254	42	-	-	SYM
cana-4524	254	43	85	85	NUM
cana-4524	254	44	.	.	PUNCT
cana-4524	255	1	[	[	X
cana-4524	255	2	7	7	X
cana-4524	255	3	]	]	PUNCT
cana-4524	255	4	a.punitha	a.punitha	NOUN
cana-4524	255	5	,	,	PUNCT
cana-4524	255	6	g.	g.	PROPN
cana-4524	255	7	jayaramn	jayaramn	PROPN
cana-4524	255	8	,	,	PUNCT
cana-4524	255	9	total	total	ADJ
cana-4524	255	10	coloring	coloring	NOUN
cana-4524	255	11	of	of	ADP
cana-4524	255	12	middle	middle	ADJ
cana-4524	255	13	graph	graph	NOUN
cana-4524	255	14	of	of	ADP
cana-4524	255	15	certain	certain	ADJ
cana-4524	255	16	snake	snake	NOUN
cana-4524	255	17	graph	graph	NOUN
cana-4524	255	18	families	family	NOUN
cana-4524	255	19	,	,	PUNCT
cana-4524	255	20	j.	j.	PROPN
cana-4524	255	21	appl	appl	PROPN
cana-4524	255	22	.	.	PROPN
cana-4524	255	23	math	math	PROPN
cana-4524	255	24	.	.	PUNCT
cana-4524	256	1	&	&	CCONJ
cana-4524	256	2	informatics	informatics	PROPN
cana-4524	256	3	vol	vol	NOUN
cana-4524	256	4	.	.	PUNCT
cana-4524	257	1	42(2024	42(2024	NUM
cana-4524	257	2	)	)	PUNCT
cana-4524	257	3	,	,	PUNCT
cana-4524	258	1	no	no	INTJ
cana-4524	258	2	.	.	NOUN
cana-4524	258	3	2	2	NUM
cana-4524	258	4	,	,	PUNCT
cana-4524	258	5	pp	pp	ADJ
cana-4524	258	6	.	.	PUNCT
cana-4524	259	1	353	353	NUM
cana-4524	259	2	–	–	PUNCT
cana-4524	259	3	366	366	NUM
cana-4524	259	4	.	.	PUNCT
cana-4524	260	1	https://doi.org/10.14317/jami.2024.353	https://doi.org/10.14317/jami.2024.353	PRON
cana-4524	260	2	[	[	X
cana-4524	260	3	8	8	NUM
cana-4524	260	4	]	]	SYM
cana-4524	260	5	vivik	vivik	NOUN
cana-4524	260	6	,	,	PUNCT
cana-4524	260	7	v.	v.	ADV
cana-4524	260	8	,	,	PUNCT
cana-4524	260	9	g.	g.	PROPN
cana-4524	260	10	girija	girija	PROPN
cana-4524	260	11	,	,	PUNCT
cana-4524	260	12	an	an	DET
cana-4524	260	13	algorithmic	algorithmic	ADJ
cana-4524	260	14	approach	approach	NOUN
cana-4524	260	15	to	to	ADP
cana-4524	260	16	equitable	equitable	VERB
cana-4524	260	17	total	total	ADJ
cana-4524	260	18	chromatic	chromatic	ADJ
cana-4524	260	19	number	number	NOUN
cana-4524	260	20	of	of	ADP
cana-4524	260	21	graphs	graph	NOUN
cana-4524	260	22	,	,	PUNCT
cana-4524	260	23	proyecciones	proyeccione	NOUN
cana-4524	260	24	journal	journal	NOUN
cana-4524	260	25	of	of	ADP
cana-4524	260	26	mathematics	mathematic	NOUN
cana-4524	260	27	,	,	PUNCT
cana-4524	260	28	36(2	36(2	NUM
cana-4524	260	29	)	)	PUNCT
cana-4524	260	30	,	,	PUNCT
cana-4524	260	31	(	(	PUNCT
cana-4524	260	32	2017)307–324	2017)307–324	NUM
cana-4524	260	33	.	.	PUNCT
cana-4524	261	1	[	[	X
cana-4524	261	2	9	9	NUM
cana-4524	261	3	]	]	X
cana-4524	261	4	wang	wang	PROPN
cana-4524	261	5	,	,	PUNCT
cana-4524	261	6	wf	wf	PROPN
cana-4524	261	7	,	,	PUNCT
cana-4524	261	8	equitable	equitable	ADJ
cana-4524	261	9	total	total	ADJ
cana-4524	261	10	coloring	coloring	NOUN
cana-4524	261	11	of	of	ADP
cana-4524	261	12	graphs	graph	NOUN
cana-4524	261	13	with	with	ADP
cana-4524	261	14	maximum	maximum	ADJ
cana-4524	261	15	degree	degree	NOUN
cana-4524	261	16	3	3	NUM
cana-4524	261	17	.	.	PUNCT
cana-4524	261	18	graphs	graph	NOUN
cana-4524	261	19	comb	comb	VERB
cana-4524	261	20	18	18	NUM
cana-4524	261	21	,	,	PUNCT
cana-4524	261	22	(	(	PUNCT
cana-4524	261	23	2002	2002	NUM
cana-4524	261	24	)	)	PUNCT
cana-4524	262	1	677–685	677–685	NUM
cana-4524	262	2	.	.	PUNCT
cana-4524	263	1	https://doi.org/10.1007/s003730200051	https://doi.org/10.1007/s003730200051	NUM
cana-4524	263	2	.	.	PUNCT
cana-4524	264	1	[	[	X
cana-4524	264	2	10	10	NUM
cana-4524	264	3	]	]	X
cana-4524	264	4	zhang	zhang	PROPN
cana-4524	264	5	zhong	zhong	PROPN
cana-4524	264	6	-	-	PUNCT
cana-4524	264	7	fu	fu	PROPN
cana-4524	264	8	,	,	PUNCT
cana-4524	264	9	wang	wang	PROPN
cana-4524	264	10	wei	wei	PROPN
cana-4524	264	11	-	-	PROPN
cana-4524	264	12	fan	fan	PROPN
cana-4524	264	13	,	,	PUNCT
cana-4524	264	14	bau	bau	PROPN
cana-4524	264	15	sheng	sheng	PROPN
cana-4524	264	16	.	.	PUNCT
cana-4524	264	17	et	et	PROPN
cana-4524	264	18	al	al	PROPN
cana-4524	264	19	.	.	PROPN
cana-4524	265	1	on	on	ADP
cana-4524	265	2	the	the	DET
cana-4524	265	3	equitable	equitable	ADJ
cana-4524	265	4	total	total	ADJ
cana-4524	265	5	coloring	coloring	NOUN
cana-4524	265	6	of	of	ADP
cana-4524	265	7	some	some	DET
cana-4524	265	8	join	join	NOUN
cana-4524	265	9	graphs	graph	NOUN
cana-4524	265	10	,	,	PUNCT
cana-4524	265	11	j.info	j.info	NOUN
cana-4524	265	12	comput	comput	NOUN
cana-4524	265	13	.	.	PUNCT
cana-4524	266	1	sci	sci	PROPN
cana-4524	266	2	.	.	PROPN
cana-4524	266	3	,	,	PUNCT
cana-4524	266	4	2(4	2(4	NUM
cana-4524	266	5	)	)	PUNCT
cana-4524	266	6	,	,	PUNCT
cana-4524	266	7	(	(	PUNCT
cana-4524	266	8	2005	2005	NUM
cana-4524	266	9	)	)	PUNCT
cana-4524	266	10	,	,	PUNCT
cana-4524	266	11	829	829	NUM
cana-4524	266	12	-	-	SYM
cana-4524	266	13	834	834	NUM
cana-4524	266	14	.	.	PUNCT
cana-4524	266	15	https://doi.org/10.1016/j.dam.2014.11.014	https://doi.org/10.1016/j.dam.2014.11.014	PROPN
cana-4524	266	16	https://doi.org/10.22199/issn.0717-6279-2019-04-0045	https://doi.org/10.22199/issn.0717-6279-2019-04-0045	ADV
cana-4524	266	17	https://doi.org/10.14317/jami.2024.353	https://doi.org/10.14317/jami.2024.353	PROPN
cana-4524	266	18	https://doi.org/10.1007/s003730200051	https://doi.org/10.1007/s003730200051	NUM